
                  +-------------------------+
                  | THEORY NATURALLY SORTED |
                  +-------------------------+

================================================================
tm-name          tm-1
in-theory        1
times-derived    1679
----------------------------------------------------------------
theorem          (A -> (B -> A))
theorem-size     5
proof            axiom
axioms-used      (tm-1)
proof-size       5
proof-steps      1
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
================================================================
tm-name          tm-2
in-theory        2
times-derived    1682
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))
theorem-size     13
proof            axiom
axioms-used      (tm-2)
proof-size       13
proof-steps      1
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
================================================================
tm-name          tm-3
in-theory        3
times-derived    1679
----------------------------------------------------------------
theorem          ((A and B) -> A)
theorem-size     5
proof            axiom
axioms-used      (tm-3)
proof-size       5
proof-steps      1
----------------------------------------------------------------
tm-3.            ((A and B) -> A), axiom
================================================================
tm-name          tm-4
in-theory        4
times-derived    1679
----------------------------------------------------------------
theorem          ((A and B) -> B)
theorem-size     5
proof            axiom
axioms-used      (tm-4)
proof-size       5
proof-steps      1
----------------------------------------------------------------
tm-4.            ((A and B) -> B), axiom
================================================================
tm-name          tm-5
in-theory        5
times-derived    1679
----------------------------------------------------------------
theorem          (A -> (B -> (A and B)))
theorem-size     7
proof            axiom
axioms-used      (tm-5)
proof-size       7
proof-steps      1
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
================================================================
tm-name          tm-6
in-theory        6
times-derived    1678
----------------------------------------------------------------
theorem          (A -> (A or B))
theorem-size     5
proof            axiom
axioms-used      (tm-6)
proof-size       5
proof-steps      1
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
================================================================
tm-name          tm-7
in-theory        7
times-derived    1678
----------------------------------------------------------------
theorem          (A -> (B or A))
theorem-size     5
proof            axiom
axioms-used      (tm-7)
proof-size       5
proof-steps      1
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
================================================================
tm-name          tm-8
in-theory        8
times-derived    1130
----------------------------------------------------------------
theorem          ((A -> B) -> ((B -> C) -> ((A or B) -> C)))
theorem-size     13
proof            axiom
axioms-used      (tm-8)
proof-size       13
proof-steps      1
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
================================================================
tm-name          tm-9
in-theory        9
times-derived    1076
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> (not B)) -> (not A)))
theorem-size     11
proof            axiom
axioms-used      (tm-9)
proof-size       11
proof-steps      1
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
================================================================
tm-name          tm-10
in-theory        10
times-derived    1074
----------------------------------------------------------------
theorem          ((not (not A)) -> A)
theorem-size     5
proof            axiom
axioms-used      (tm-10)
proof-size       5
proof-steps      1
----------------------------------------------------------------
tm-10.           ((not (not A)) -> A), axiom
================================================================
tm-name          tm-11
in-theory        11
times-derived    1146
----------------------------------------------------------------
theorem          (A -> (B -> (C -> B)))
theorem-size     7
proof            (modus-ponens tm-1 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-1)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-12
in-theory        12
times-derived    1142
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> A))
theorem-size     7
proof            (modus-ponens tm-2 tm-1 ((A Am) (B Bm) (C Am)))
axioms-used      (tm-2 tm-1)
proof-size       25
proof-steps      3
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
================================================================
tm-name          tm-13
in-theory        13
times-derived    1143
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     19
proof            (modus-ponens tm-2 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm))))
axioms-used      (tm-2)
proof-size       45
proof-steps      3
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
================================================================
tm-name          tm-14
in-theory        14
times-derived    1146
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-1 tm-2)
proof-size       33
proof-steps      3
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-15
in-theory        15
times-derived    1142
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))
theorem-size     15
proof            (modus-ponens tm-2 tm-3 ((A (and (-> B C) Bm)) (Am (-> B C))))
axioms-used      (tm-2 tm-3)
proof-size       33
proof-steps      3
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
================================================================
tm-name          tm-16
in-theory        16
times-derived    1146
----------------------------------------------------------------
theorem          (A -> ((B and C) -> B))
theorem-size     7
proof            (modus-ponens tm-1 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-1 tm-3)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-17
in-theory        17
times-derived    1142
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))
theorem-size     15
proof            (modus-ponens tm-2 tm-4 ((A (and Am (-> B C))) (Bm (-> B C))))
axioms-used      (tm-2 tm-4)
proof-size       33
proof-steps      3
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
================================================================
tm-name          tm-18
in-theory        18
times-derived    1146
----------------------------------------------------------------
theorem          (A -> ((B and C) -> C))
theorem-size     7
proof            (modus-ponens tm-1 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-1 tm-4)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-19
in-theory        19
times-derived    1140
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and A))
theorem-size     9
proof            (modus-ponens tm-5 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-1)
proof-size       21
proof-steps      3
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-20
in-theory        20
times-derived    1140
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       37
proof-steps      3
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-21
in-theory        21
times-derived    1140
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and A))
theorem-size     9
proof            (modus-ponens tm-5 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-3)
proof-size       21
proof-steps      3
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-22
in-theory        22
times-derived    1140
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and A))
theorem-size     9
proof            (modus-ponens tm-5 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-4)
proof-size       21
proof-steps      3
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-23
in-theory        23
times-derived    1140
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5)
proof-size       25
proof-steps      3
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-24
in-theory        24
times-derived    1142
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> (A and B)))
theorem-size     9
proof            (modus-ponens tm-2 tm-5 ((A Am) (B Bm) (C (and Am Bm))))
axioms-used      (tm-2 tm-5)
proof-size       29
proof-steps      3
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
================================================================
tm-name          tm-25
in-theory        25
times-derived    1147
----------------------------------------------------------------
theorem          (A -> (B -> (C -> (B and C))))
theorem-size     9
proof            (modus-ponens tm-1 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-1 tm-5)
proof-size       21
proof-steps      3
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-26
in-theory        26
times-derived    1138
----------------------------------------------------------------
theorem          ((A -> (B -> A)) or C)
theorem-size     7
proof            (modus-ponens tm-6 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-6 tm-1)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-27
in-theory        27
times-derived    1138
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-6 tm-2)
proof-size       33
proof-steps      3
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-28
in-theory        28
times-derived    1138
----------------------------------------------------------------
theorem          (((A and B) -> A) or C)
theorem-size     7
proof            (modus-ponens tm-6 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-6 tm-3)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-29
in-theory        29
times-derived    1138
----------------------------------------------------------------
theorem          (((A and B) -> B) or C)
theorem-size     7
proof            (modus-ponens tm-6 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-6 tm-4)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-30
in-theory        30
times-derived    1138
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) or C)
theorem-size     9
proof            (modus-ponens tm-6 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-6 tm-5)
proof-size       21
proof-steps      3
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-31
in-theory        31
times-derived    1138
----------------------------------------------------------------
theorem          ((A -> (A or B)) or C)
theorem-size     7
proof            (modus-ponens tm-6 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-6)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-32
in-theory        32
times-derived    1141
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and A))
theorem-size     9
proof            (modus-ponens tm-5 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-6)
proof-size       21
proof-steps      3
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-33
in-theory        33
times-derived    1147
----------------------------------------------------------------
theorem          (A -> (B -> (B or C)))
theorem-size     7
proof            (modus-ponens tm-1 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-1 tm-6)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-34
in-theory        34
times-derived    1138
----------------------------------------------------------------
theorem          (A or (B -> (C -> B)))
theorem-size     7
proof            (modus-ponens tm-7 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-7 tm-1)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-35
in-theory        35
times-derived    1138
----------------------------------------------------------------
theorem          (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-7 tm-2)
proof-size       33
proof-steps      3
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-36
in-theory        36
times-derived    1138
----------------------------------------------------------------
theorem          (A or ((B and C) -> B))
theorem-size     7
proof            (modus-ponens tm-7 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-7 tm-3)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-37
in-theory        37
times-derived    1138
----------------------------------------------------------------
theorem          (A or ((B and C) -> C))
theorem-size     7
proof            (modus-ponens tm-7 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-7 tm-4)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-38
in-theory        38
times-derived    1138
----------------------------------------------------------------
theorem          (A or (B -> (C -> (B and C))))
theorem-size     9
proof            (modus-ponens tm-7 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-7 tm-5)
proof-size       21
proof-steps      3
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-39
in-theory        39
times-derived    1138
----------------------------------------------------------------
theorem          (A or (B -> (B or C)))
theorem-size     7
proof            (modus-ponens tm-7 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-7 tm-6)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-40
in-theory        40
times-derived    1138
----------------------------------------------------------------
theorem          (A or (B -> (C or B)))
theorem-size     7
proof            (modus-ponens tm-7 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-7)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-41
in-theory        41
times-derived    1138
----------------------------------------------------------------
theorem          ((A -> (B or A)) or C)
theorem-size     7
proof            (modus-ponens tm-6 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-6 tm-7)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-42
in-theory        42
times-derived    1141
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and A))
theorem-size     9
proof            (modus-ponens tm-5 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-7)
proof-size       21
proof-steps      3
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-43
in-theory        43
times-derived    1147
----------------------------------------------------------------
theorem          (A -> (B -> (C or B)))
theorem-size     7
proof            (modus-ponens tm-1 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-1 tm-7)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-44
in-theory        44
times-derived    1144
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> ((B or (A -> B)) -> C))
theorem-size     13
proof            (modus-ponens tm-8 tm-1 ((A Am) (B (-> Bm Am))))
axioms-used      (tm-8 tm-1)
proof-size       31
proof-steps      3
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-45
in-theory        45
times-derived    1144
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       51
proof-steps      3
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-46
in-theory        46
times-derived    1144
----------------------------------------------------------------
theorem          ((A -> B) -> (((A and C) or A) -> B))
theorem-size     11
proof            (modus-ponens tm-8 tm-3 ((A (and Am Bm)) (B Am)))
axioms-used      (tm-8 tm-3)
proof-size       29
proof-steps      3
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
================================================================
tm-name          tm-47
in-theory        47
times-derived    1144
----------------------------------------------------------------
theorem          ((A -> B) -> (((C and A) or A) -> B))
theorem-size     11
proof            (modus-ponens tm-8 tm-4 ((A (and Am Bm)) (B Bm)))
axioms-used      (tm-8 tm-4)
proof-size       29
proof-steps      3
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-48
in-theory        48
times-derived    1144
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-5 ((A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-8 tm-5)
proof-size       37
proof-steps      3
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-49
in-theory        49
times-derived    1144
----------------------------------------------------------------
theorem          (((A or B) -> C) -> ((A or (A or B)) -> C))
theorem-size     13
proof            (modus-ponens tm-8 tm-6 ((A Am) (B (or Am Bm))))
axioms-used      (tm-8 tm-6)
proof-size       31
proof-steps      3
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
================================================================
tm-name          tm-50
in-theory        50
times-derived    1144
----------------------------------------------------------------
theorem          (((A or B) -> C) -> ((B or (A or B)) -> C))
theorem-size     13
proof            (modus-ponens tm-8 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-8 tm-7)
proof-size       31
proof-steps      3
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-51
in-theory        51
times-derived    1082
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))
theorem-size     27
proof            (modus-ponens tm-8 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8)
proof-size       53
proof-steps      3
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-52
in-theory        52
times-derived    1077
----------------------------------------------------------------
theorem          (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-7 tm-8)
proof-size       33
proof-steps      3
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-53
in-theory        53
times-derived    1077
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-6 tm-8)
proof-size       33
proof-steps      3
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-54
in-theory        54
times-derived    9
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8)
proof-size       37
proof-steps      3
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-55
in-theory        55
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C)))
theorem-size     17
proof            (modus-ponens tm-2 tm-8 ((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-8)
proof-size       43
proof-steps      3
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-56
in-theory        56
times-derived    10
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-1 tm-8)
proof-size       33
proof-steps      3
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-57
in-theory        57
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (not (B -> A))) -> (not A))
theorem-size     9
proof            (modus-ponens tm-9 tm-1 ((A Am) (B (-> Bm Am))))
axioms-used      (tm-9 tm-1)
proof-size       25
proof-steps      3
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-58
in-theory        58
times-derived    16
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C))))
theorem-size     21
proof            (modus-ponens tm-9 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-9 tm-2)
proof-size       45
proof-steps      3
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59
in-theory        59
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> (not A)) -> (not (A and B)))
theorem-size     11
proof            (modus-ponens tm-9 tm-3 ((A (and Am Bm)) (B Am)))
axioms-used      (tm-9 tm-3)
proof-size       27
proof-steps      3
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
================================================================
tm-name          tm-60
in-theory        60
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> (not B)) -> (not (A and B)))
theorem-size     11
proof            (modus-ponens tm-9 tm-4 ((A (and Am Bm)) (B Bm)))
axioms-used      (tm-9 tm-4)
proof-size       27
proof-steps      3
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-61
in-theory        61
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (not (B -> (A and B)))) -> (not A))
theorem-size     11
proof            (modus-ponens tm-9 tm-5 ((A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-9 tm-5)
proof-size       29
proof-steps      3
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-62
in-theory        62
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (not (A or B))) -> (not A))
theorem-size     9
proof            (modus-ponens tm-9 tm-6 ((A Am) (B (or Am Bm))))
axioms-used      (tm-9 tm-6)
proof-size       25
proof-steps      3
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
================================================================
tm-name          tm-63
in-theory        63
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (not (B or A))) -> (not A))
theorem-size     9
proof            (modus-ponens tm-9 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-9 tm-7)
proof-size       25
proof-steps      3
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-64
in-theory        64
times-derived    8
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B)))
theorem-size     19
proof            (modus-ponens tm-9 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-9 tm-8)
proof-size       43
proof-steps      3
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-65
in-theory        65
times-derived    7
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B)))
theorem-size     17
proof            (modus-ponens tm-9 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-9)
proof-size       39
proof-steps      3
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-66
in-theory        66
times-derived    9
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))
theorem-size     23
proof            (modus-ponens tm-8 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-8 tm-9)
proof-size       47
proof-steps      3
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-67
in-theory        67
times-derived    6
----------------------------------------------------------------
theorem          (A or ((B -> C) -> ((B -> (not C)) -> (not B))))
theorem-size     13
proof            (modus-ponens tm-7 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-7 tm-9)
proof-size       29
proof-steps      3
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-68
in-theory        68
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) or C)
theorem-size     13
proof            (modus-ponens tm-6 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-6 tm-9)
proof-size       29
proof-steps      3
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-69
in-theory        69
times-derived    7
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-9)
proof-size       33
proof-steps      3
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-70
in-theory        70
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A)))
theorem-size     15
proof            (modus-ponens tm-2 tm-9 ((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am))))
axioms-used      (tm-2 tm-9)
proof-size       39
proof-steps      3
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
================================================================
tm-name          tm-71
in-theory        71
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> ((B -> (not C)) -> (not B))))
theorem-size     13
proof            (modus-ponens tm-1 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-1 tm-9)
proof-size       29
proof-steps      3
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-72
in-theory        72
times-derived    7
----------------------------------------------------------------
theorem          (((not (not A)) -> (not A)) -> (not (not (not A))))
theorem-size     11
proof            (modus-ponens tm-9 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-9 tm-10)
proof-size       27
proof-steps      3
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-73
in-theory        73
times-derived    9
----------------------------------------------------------------
theorem          ((A -> B) -> (((not (not A)) or A) -> B))
theorem-size     11
proof            (modus-ponens tm-8 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-8 tm-10)
proof-size       29
proof-steps      3
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-74
in-theory        74
times-derived    6
----------------------------------------------------------------
theorem          (A or ((not (not B)) -> B))
theorem-size     7
proof            (modus-ponens tm-7 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-7 tm-10)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-75
in-theory        75
times-derived    6
----------------------------------------------------------------
theorem          (((not (not A)) -> A) or B)
theorem-size     7
proof            (modus-ponens tm-6 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-6 tm-10)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-76
in-theory        76
times-derived    7
----------------------------------------------------------------
theorem          (A -> (((not (not B)) -> B) and A))
theorem-size     9
proof            (modus-ponens tm-5 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-10)
proof-size       21
proof-steps      3
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-77
in-theory        77
times-derived    9
----------------------------------------------------------------
theorem          (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B))
theorem-size     15
proof            (modus-ponens tm-2 tm-10 ((A (not (not (-> B C)))) (Am (-> B C))))
axioms-used      (tm-2 tm-10)
proof-size       33
proof-steps      3
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
================================================================
tm-name          tm-78
in-theory        78
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((not (not B)) -> B))
theorem-size     7
proof            (modus-ponens tm-1 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-1 tm-10)
proof-size       17
proof-steps      3
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-79
in-theory        79
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> B)))) -> (not A))
theorem-size     11
proof            (modus-ponens tm-9 tm-11 ((A Am) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-9 tm-1)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-80
in-theory        80
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-11 ((A Am) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-1)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-81
in-theory        81
times-derived    7
----------------------------------------------------------------
theorem          (A or (B -> (C -> (D -> C))))
theorem-size     9
proof            (modus-ponens tm-7 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-7 tm-1)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-82
in-theory        82
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-6 tm-1)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-83
in-theory        83
times-derived    8
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (D -> C))) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-84
in-theory        84
times-derived    10
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> (C -> B)))
theorem-size     9
proof            (modus-ponens tm-2 tm-11 ((A Am) (B Bm) (C (-> Cm Bm))))
axioms-used      (tm-2 tm-1)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
================================================================
tm-name          tm-85
in-theory        85
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B -> (C -> (D -> C))))
theorem-size     9
proof            (modus-ponens tm-1 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-1)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-86
in-theory        86
times-derived    410
----------------------------------------------------------------
theorem          (A -> A)
theorem-size     3
proof            (modus-ponens tm-12 tm-1 ((A Am) (B (-> Bm Am))))
axioms-used      (tm-2 tm-1)
proof-size       33
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-87
in-theory        87
times-derived    21
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (A -> (B -> C)))
theorem-size     11
proof            (modus-ponens tm-12 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-1)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-88
in-theory        88
times-derived    35
----------------------------------------------------------------
theorem          ((A and B) -> (A and B))
theorem-size     7
proof            (modus-ponens tm-12 tm-3 ((A (and Am Bm)) (B Am)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
================================================================
tm-name          tm-89
in-theory        89
times-derived    68
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> B))
theorem-size     7
proof            (modus-ponens tm-12 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-90
in-theory        90
times-derived    9
----------------------------------------------------------------
theorem          ((not (not A)) -> (not (not A)))
theorem-size     7
proof            (modus-ponens tm-12 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-2 tm-1 tm-10)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-91
in-theory        91
times-derived    9
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> A))) -> (not (A -> B)))
theorem-size     13
proof            (modus-ponens tm-9 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-9 tm-2 tm-1)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-92
in-theory        92
times-derived    11
----------------------------------------------------------------
theorem          (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B))
theorem-size     15
proof            (modus-ponens tm-8 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-93
in-theory        93
times-derived    8
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (B -> B)))
theorem-size     9
proof            (modus-ponens tm-7 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-7 tm-2 tm-1)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-94
in-theory        94
times-derived    8
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) or C)
theorem-size     9
proof            (modus-ponens tm-6 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-6 tm-2 tm-1)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-95
in-theory        95
times-derived    9
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> B)) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-96
in-theory        96
times-derived    16
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> ((A -> B) -> A))
theorem-size     11
proof            (modus-ponens tm-2 tm-12 ((A (-> Am Bm)) (B Am) (C Am)))
axioms-used      (tm-2 tm-1)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
================================================================
tm-name          tm-97
in-theory        97
times-derived    12
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (B -> B)))
theorem-size     9
proof            (modus-ponens tm-1 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-1 tm-2)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-98
in-theory        98
times-derived    10
----------------------------------------------------------------
theorem          ((A -> ((B -> A) -> C)) -> (A -> C))
theorem-size     11
proof            (modus-ponens tm-13 tm-11 ((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-1)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
================================================================
tm-name          tm-99
in-theory        99
times-derived    10
----------------------------------------------------------------
theorem          ((A -> (A -> B)) -> (A -> B))
theorem-size     9
proof            (modus-ponens tm-13 tm-12 ((Bm (-> Am C)) (A Am) (B Am)))
axioms-used      (tm-2 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
================================================================
tm-name          tm-100
in-theory        100
times-derived    14
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B)))
theorem-size     19
proof            (modus-ponens tm-12 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-101
in-theory        101
times-derived    9
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B))))
theorem-size     31
proof            (modus-ponens tm-9 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-9 tm-2)
proof-size       87
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-102
in-theory        102
times-derived    11
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       91
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-103
in-theory        103
times-derived    8
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     21
proof            (modus-ponens tm-7 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-7 tm-2)
proof-size       71
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-104
in-theory        104
times-derived    8
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D)
theorem-size     21
proof            (modus-ponens tm-6 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-6 tm-2)
proof-size       71
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-105
in-theory        105
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       75
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-106
in-theory        106
times-derived    11
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))
theorem-size     29
proof            (modus-ponens tm-2 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm))))
axioms-used      (tm-2)
proof-size       87
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
================================================================
tm-name          tm-107
in-theory        107
times-derived    12
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     21
proof            (modus-ponens tm-1 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-1 tm-2)
proof-size       71
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-108
in-theory        108
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D))
theorem-size     23
proof            (modus-ponens tm-13 tm-14 ((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-109
in-theory        109
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A))
theorem-size     19
proof            (modus-ponens tm-9 tm-14 ((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-110
in-theory        110
times-derived    10
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-14 ((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       79
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-111
in-theory        111
times-derived    7
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-7 tm-1 tm-2)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-112
in-theory        112
times-derived    7
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-6 tm-1 tm-2)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-113
in-theory        113
times-derived    8
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-114
in-theory        114
times-derived    10
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D))))
theorem-size     17
proof            (modus-ponens tm-2 tm-14 ((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-115
in-theory        115
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-1 tm-2)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-116
in-theory        116
times-derived    16
----------------------------------------------------------------
theorem          (((A -> B) and A) -> B)
theorem-size     7
proof            (modus-ponens tm-15 tm-4 ((Am (-> Bm B)) (C Bm) (A Bm)))
axioms-used      (tm-2 tm-3 tm-4)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
================================================================
tm-name          tm-117
in-theory        117
times-derived    7
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) and D) -> C)
theorem-size     11
proof            (modus-ponens tm-15 tm-11 ((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-118
in-theory        118
times-derived    7
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D)
theorem-size     19
proof            (modus-ponens tm-15 tm-14 ((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-119
in-theory        119
times-derived    10
----------------------------------------------------------------
theorem          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B))
theorem-size     21
proof            (modus-ponens tm-13 tm-15 ((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm)))
axioms-used      (tm-2 tm-3)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
================================================================
tm-name          tm-120
in-theory        120
times-derived    13
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A))
theorem-size     15
proof            (modus-ponens tm-12 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-121
in-theory        121
times-derived    9
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A)))
theorem-size     25
proof            (modus-ponens tm-9 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-9 tm-2 tm-3)
proof-size       69
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-122
in-theory        122
times-derived    11
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))
theorem-size     27
proof            (modus-ponens tm-8 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       73
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-123
in-theory        123
times-derived    8
----------------------------------------------------------------
theorem          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))
theorem-size     17
proof            (modus-ponens tm-7 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-7 tm-2 tm-3)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-124
in-theory        124
times-derived    8
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-6 tm-2 tm-3)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-125
in-theory        125
times-derived    9
----------------------------------------------------------------
theorem          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-126
in-theory        126
times-derived    11
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B))
theorem-size     23
proof            (modus-ponens tm-2 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm)))
axioms-used      (tm-2 tm-3)
proof-size       69
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
================================================================
tm-name          tm-127
in-theory        127
times-derived    12
----------------------------------------------------------------
theorem          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))
theorem-size     17
proof            (modus-ponens tm-1 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-1 tm-2 tm-3)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-128
in-theory        128
times-derived    7
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) and D) -> C)
theorem-size     11
proof            (modus-ponens tm-15 tm-16 ((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-129
in-theory        129
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) -> (A -> C)) -> ((A and B) -> C))
theorem-size     13
proof            (modus-ponens tm-13 tm-16 ((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
================================================================
tm-name          tm-130
in-theory        130
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (not ((B and C) -> B))) -> (not A))
theorem-size     11
proof            (modus-ponens tm-9 tm-16 ((A Am) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-9 tm-1 tm-3)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-131
in-theory        131
times-derived    10
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-16 ((A Am) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-132
in-theory        132
times-derived    7
----------------------------------------------------------------
theorem          (A or (B -> ((C and D) -> C)))
theorem-size     9
proof            (modus-ponens tm-7 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-7 tm-1 tm-3)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-133
in-theory        133
times-derived    7
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-6 tm-1 tm-3)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-134
in-theory        134
times-derived    8
----------------------------------------------------------------
theorem          (A -> ((B -> ((C and D) -> C)) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-135
in-theory        135
times-derived    10
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> (A -> B))
theorem-size     9
proof            (modus-ponens tm-2 tm-16 ((A Am) (B (and Bm Cm)) (C Bm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
================================================================
tm-name          tm-136
in-theory        136
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B -> ((C and D) -> C)))
theorem-size     9
proof            (modus-ponens tm-1 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-1 tm-3)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-137
in-theory        137
times-derived    16
----------------------------------------------------------------
theorem          ((A and (A -> B)) -> B)
theorem-size     7
proof            (modus-ponens tm-17 tm-3 ((A Am) (Bm (-> Am C)) (B Am)))
axioms-used      (tm-2 tm-4 tm-3)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
================================================================
tm-name          tm-138
in-theory        138
times-derived    7
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> D)) -> D)
theorem-size     11
proof            (modus-ponens tm-17 tm-11 ((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-139
in-theory        139
times-derived    7
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E)
theorem-size     19
proof            (modus-ponens tm-17 tm-14 ((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-140
in-theory        140
times-derived    7
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> D)) -> D)
theorem-size     11
proof            (modus-ponens tm-17 tm-16 ((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-4 tm-1 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-141
in-theory        141
times-derived    10
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C))
theorem-size     21
proof            (modus-ponens tm-13 tm-17 ((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm)))
axioms-used      (tm-2 tm-4)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
================================================================
tm-name          tm-142
in-theory        142
times-derived    13
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B))
theorem-size     15
proof            (modus-ponens tm-12 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-143
in-theory        143
times-derived    9
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B)))
theorem-size     25
proof            (modus-ponens tm-9 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-9 tm-2 tm-4)
proof-size       69
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-144
in-theory        144
times-derived    11
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))
theorem-size     27
proof            (modus-ponens tm-8 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-8 tm-2 tm-4)
proof-size       73
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-145
in-theory        145
times-derived    8
----------------------------------------------------------------
theorem          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))
theorem-size     17
proof            (modus-ponens tm-7 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-7 tm-2 tm-4)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-146
in-theory        146
times-derived    8
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-6 tm-2 tm-4)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-147
in-theory        147
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-148
in-theory        148
times-derived    11
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C))
theorem-size     23
proof            (modus-ponens tm-2 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm)))
axioms-used      (tm-2 tm-4)
proof-size       69
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
================================================================
tm-name          tm-149
in-theory        149
times-derived    12
----------------------------------------------------------------
theorem          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))
theorem-size     17
proof            (modus-ponens tm-1 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-1 tm-2 tm-4)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-150
in-theory        150
times-derived    7
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> D)) -> D)
theorem-size     11
proof            (modus-ponens tm-17 tm-18 ((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-151
in-theory        151
times-derived    7
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) and D) -> C)
theorem-size     11
proof            (modus-ponens tm-15 tm-18 ((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-3 tm-1 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-152
in-theory        152
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) -> (B -> C)) -> ((A and B) -> C))
theorem-size     13
proof            (modus-ponens tm-13 tm-18 ((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
================================================================
tm-name          tm-153
in-theory        153
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (not ((B and C) -> C))) -> (not A))
theorem-size     11
proof            (modus-ponens tm-9 tm-18 ((A Am) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-9 tm-1 tm-4)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-154
in-theory        154
times-derived    10
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-18 ((A Am) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-155
in-theory        155
times-derived    7
----------------------------------------------------------------
theorem          (A or (B -> ((C and D) -> D)))
theorem-size     9
proof            (modus-ponens tm-7 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-7 tm-1 tm-4)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-156
in-theory        156
times-derived    7
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-6 tm-1 tm-4)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-157
in-theory        157
times-derived    8
----------------------------------------------------------------
theorem          (A -> ((B -> ((C and D) -> D)) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-158
in-theory        158
times-derived    10
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> (A -> C))
theorem-size     9
proof            (modus-ponens tm-2 tm-18 ((A Am) (B (and Bm Cm)) (C Cm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
================================================================
tm-name          tm-159
in-theory        159
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B -> ((C and D) -> D)))
theorem-size     9
proof            (modus-ponens tm-1 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-1 tm-4)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-160
in-theory        160
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> C)))
theorem-size     11
proof            (modus-ponens tm-19 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-1)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-161
in-theory        161
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-162
in-theory        162
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C and D) -> C))
theorem-size     11
proof            (modus-ponens tm-19 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-163
in-theory        163
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C and D) -> D))
theorem-size     11
proof            (modus-ponens tm-19 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-164
in-theory        164
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-19 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-165
in-theory        165
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C or D)))
theorem-size     11
proof            (modus-ponens tm-19 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-166
in-theory        166
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D or C)))
theorem-size     11
proof            (modus-ponens tm-19 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-167
in-theory        167
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-168
in-theory        168
times-derived    6
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     17
proof            (modus-ponens tm-19 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-169
in-theory        169
times-derived    6
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((not (not C)) -> C))
theorem-size     11
proof            (modus-ponens tm-19 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-170
in-theory        170
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-19 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-171
in-theory        171
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (C -> C)))
theorem-size     13
proof            (modus-ponens tm-19 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-172
in-theory        172
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-19 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-173
in-theory        173
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-174
in-theory        174
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-19 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-175
in-theory        175
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-19 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-176
in-theory        176
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-19 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-177
in-theory        177
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-19 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-178
in-theory        178
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C)))
theorem-size     15
proof            (modus-ponens tm-19 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-179
in-theory        179
times-derived    9
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> B)) and A))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-9 tm-5 tm-1)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-180
in-theory        180
times-derived    11
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-181
in-theory        181
times-derived    8
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (D -> C)) and B)))
theorem-size     11
proof            (modus-ponens tm-7 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-182
in-theory        182
times-derived    8
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-183
in-theory        183
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D -> C)) and B)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-184
in-theory        184
times-derived    12
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> C)) and B)))
theorem-size     11
proof            (modus-ponens tm-1 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-1 tm-5)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-185
in-theory        185
times-derived    16
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-20 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-186
in-theory        186
times-derived    16
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       77
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-187
in-theory        187
times-derived    16
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-20 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-188
in-theory        188
times-derived    16
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-20 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-189
in-theory        189
times-derived    16
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-20 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       65
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-190
in-theory        190
times-derived    16
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-20 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-191
in-theory        191
times-derived    16
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-20 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-192
in-theory        192
times-derived    7
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       77
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-193
in-theory        193
times-derived    6
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-20 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       73
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-194
in-theory        194
times-derived    6
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D))
theorem-size     19
proof            (modus-ponens tm-20 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-195
in-theory        195
times-derived    7
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-20 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-196
in-theory        196
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-20 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-197
in-theory        197
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-20 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-198
in-theory        198
times-derived    7
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-199
in-theory        199
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-20 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-200
in-theory        200
times-derived    7
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-20 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-201
in-theory        201
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-20 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-202
in-theory        202
times-derived    7
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-20 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-203
in-theory        203
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-20 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-204
in-theory        204
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-20 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-205
in-theory        205
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-19 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-206
in-theory        206
times-derived    9
----------------------------------------------------------------
theorem          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A))
theorem-size     21
proof            (modus-ponens tm-9 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-9 tm-5 tm-2)
proof-size       69
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-207
in-theory        207
times-derived    11
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       87
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-208
in-theory        208
times-derived    8
----------------------------------------------------------------
theorem          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))
theorem-size     19
proof            (modus-ponens tm-7 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-209
in-theory        209
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-210
in-theory        210
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       65
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-211
in-theory        211
times-derived    12
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))
theorem-size     19
proof            (modus-ponens tm-1 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-212
in-theory        212
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> C)))
theorem-size     11
proof            (modus-ponens tm-21 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-213
in-theory        213
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-214
in-theory        214
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C and D) -> C))
theorem-size     11
proof            (modus-ponens tm-21 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-3)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-215
in-theory        215
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C and D) -> D))
theorem-size     11
proof            (modus-ponens tm-21 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-216
in-theory        216
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-21 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-3)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-217
in-theory        217
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C or D)))
theorem-size     11
proof            (modus-ponens tm-21 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-218
in-theory        218
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D or C)))
theorem-size     11
proof            (modus-ponens tm-21 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-219
in-theory        219
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-220
in-theory        220
times-derived    6
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     17
proof            (modus-ponens tm-21 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-221
in-theory        221
times-derived    6
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((not (not C)) -> C))
theorem-size     11
proof            (modus-ponens tm-21 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-3 tm-10)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-222
in-theory        222
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-21 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-223
in-theory        223
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (C -> C)))
theorem-size     13
proof            (modus-ponens tm-21 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-224
in-theory        224
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-21 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-225
in-theory        225
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-226
in-theory        226
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-21 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-227
in-theory        227
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-21 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-228
in-theory        228
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-21 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-229
in-theory        229
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-21 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-230
in-theory        230
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C)))
theorem-size     15
proof            (modus-ponens tm-21 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-231
in-theory        231
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-21 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-232
in-theory        232
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D and E) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-21 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-233
in-theory        233
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-20 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-234
in-theory        234
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-19 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-235
in-theory        235
times-derived    9
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> B) and A))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-9 tm-5 tm-3)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-236
in-theory        236
times-derived    11
----------------------------------------------------------------
theorem          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-237
in-theory        237
times-derived    8
----------------------------------------------------------------
theorem          (A or (B -> (((C and D) -> C) and B)))
theorem-size     11
proof            (modus-ponens tm-7 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-238
in-theory        238
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-239
in-theory        239
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B -> (((C and D) -> C) and B)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-3)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-240
in-theory        240
times-derived    12
----------------------------------------------------------------
theorem          (A -> (B -> (((C and D) -> C) and B)))
theorem-size     11
proof            (modus-ponens tm-1 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-241
in-theory        241
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> C)))
theorem-size     11
proof            (modus-ponens tm-22 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-242
in-theory        242
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-243
in-theory        243
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C and D) -> C))
theorem-size     11
proof            (modus-ponens tm-22 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-244
in-theory        244
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C and D) -> D))
theorem-size     11
proof            (modus-ponens tm-22 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-4)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-245
in-theory        245
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-22 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-4)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-246
in-theory        246
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C or D)))
theorem-size     11
proof            (modus-ponens tm-22 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-247
in-theory        247
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D or C)))
theorem-size     11
proof            (modus-ponens tm-22 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-248
in-theory        248
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-249
in-theory        249
times-derived    6
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     17
proof            (modus-ponens tm-22 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-250
in-theory        250
times-derived    6
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((not (not C)) -> C))
theorem-size     11
proof            (modus-ponens tm-22 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-4 tm-10)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-251
in-theory        251
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-22 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-252
in-theory        252
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (C -> C)))
theorem-size     13
proof            (modus-ponens tm-22 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-253
in-theory        253
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-22 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-254
in-theory        254
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-255
in-theory        255
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-22 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-256
in-theory        256
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-22 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-257
in-theory        257
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-22 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-258
in-theory        258
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-22 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-259
in-theory        259
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C)))
theorem-size     15
proof            (modus-ponens tm-22 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-260
in-theory        260
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-22 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-261
in-theory        261
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D and E) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-22 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-262
in-theory        262
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D and E) -> E) and C)))
theorem-size     15
proof            (modus-ponens tm-22 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-263
in-theory        263
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D and E) -> E) and C)))
theorem-size     15
proof            (modus-ponens tm-21 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-264
in-theory        264
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-20 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-265
in-theory        265
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C)))
theorem-size     15
proof            (modus-ponens tm-19 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-266
in-theory        266
times-derived    9
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> C) and A))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-9 tm-5 tm-4)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-267
in-theory        267
times-derived    11
----------------------------------------------------------------
theorem          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-268
in-theory        268
times-derived    8
----------------------------------------------------------------
theorem          (A or (B -> (((C and D) -> D) and B)))
theorem-size     11
proof            (modus-ponens tm-7 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-269
in-theory        269
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-270
in-theory        270
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B -> (((C and D) -> D) and B)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-4)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-271
in-theory        271
times-derived    12
----------------------------------------------------------------
theorem          (A -> (B -> (((C and D) -> D) and B)))
theorem-size     11
proof            (modus-ponens tm-1 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-272
in-theory        272
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-23 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-1)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-273
in-theory        273
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-274
in-theory        274
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-23 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-3)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-275
in-theory        275
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-23 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-4)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-276
in-theory        276
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-23 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-277
in-theory        277
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-23 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-6)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-278
in-theory        278
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-23 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-7)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-279
in-theory        279
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-280
in-theory        280
times-derived    6
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     19
proof            (modus-ponens tm-23 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-9)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-281
in-theory        281
times-derived    6
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((not (not C)) -> C))
theorem-size     13
proof            (modus-ponens tm-23 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-10)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-282
in-theory        282
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-23 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-283
in-theory        283
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C)))
theorem-size     15
proof            (modus-ponens tm-23 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-284
in-theory        284
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-23 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-285
in-theory        285
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-286
in-theory        286
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-23 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-287
in-theory        287
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D)))
theorem-size     15
proof            (modus-ponens tm-23 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-288
in-theory        288
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-23 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-289
in-theory        289
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E)))
theorem-size     15
proof            (modus-ponens tm-23 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-290
in-theory        290
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C)))
theorem-size     17
proof            (modus-ponens tm-23 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-291
in-theory        291
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     25
proof            (modus-ponens tm-23 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-292
in-theory        292
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C)))
theorem-size     17
proof            (modus-ponens tm-23 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-293
in-theory        293
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C)))
theorem-size     17
proof            (modus-ponens tm-23 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-294
in-theory        294
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-295
in-theory        295
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-296
in-theory        296
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-297
in-theory        297
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-298
in-theory        298
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-299
in-theory        299
times-derived    9
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-9 tm-5)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-300
in-theory        300
times-derived    11
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-8 tm-5)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-301
in-theory        301
times-derived    8
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (D -> (C and D))) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-7 tm-5)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-302
in-theory        302
times-derived    8
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-6 tm-5)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-303
in-theory        303
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-304
in-theory        304
times-derived    12
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> (C and D))) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-1 tm-5)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-305
in-theory        305
times-derived    16
----------------------------------------------------------------
theorem          (A -> (A and (B -> A)))
theorem-size     7
proof            (modus-ponens tm-24 tm-1 ((A Am) (B (-> Bm Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-306
in-theory        306
times-derived    17
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))
theorem-size     19
proof            (modus-ponens tm-24 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-307
in-theory        307
times-derived    16
----------------------------------------------------------------
theorem          ((A and B) -> ((A and B) and A))
theorem-size     9
proof            (modus-ponens tm-24 tm-3 ((A (and Am Bm)) (B Am)))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
================================================================
tm-name          tm-308
in-theory        308
times-derived    16
----------------------------------------------------------------
theorem          ((A and B) -> ((A and B) and B))
theorem-size     9
proof            (modus-ponens tm-24 tm-4 ((A (and Am Bm)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-309
in-theory        309
times-derived    16
----------------------------------------------------------------
theorem          (A -> (A and (B -> (A and B))))
theorem-size     9
proof            (modus-ponens tm-24 tm-5 ((A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-2 tm-5)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-310
in-theory        310
times-derived    16
----------------------------------------------------------------
theorem          (A -> (A and (A or B)))
theorem-size     7
proof            (modus-ponens tm-24 tm-6 ((A Am) (B (or Am Bm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
================================================================
tm-name          tm-311
in-theory        311
times-derived    16
----------------------------------------------------------------
theorem          (A -> (A and (B or A)))
theorem-size     7
proof            (modus-ponens tm-24 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-312
in-theory        312
times-derived    8
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))
theorem-size     17
proof            (modus-ponens tm-24 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-313
in-theory        313
times-derived    7
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A))))
theorem-size     15
proof            (modus-ponens tm-24 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-314
in-theory        314
times-derived    6
----------------------------------------------------------------
theorem          ((not (not A)) -> ((not (not A)) and A))
theorem-size     9
proof            (modus-ponens tm-24 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-315
in-theory        315
times-derived    7
----------------------------------------------------------------
theorem          (A -> (A and (B -> (C -> B))))
theorem-size     9
proof            (modus-ponens tm-24 tm-11 ((A Am) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-316
in-theory        316
times-derived    9
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (A -> A)))
theorem-size     11
proof            (modus-ponens tm-24 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-317
in-theory        317
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-24 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-318
in-theory        318
times-derived    7
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     17
proof            (modus-ponens tm-24 tm-14 ((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-319
in-theory        319
times-derived    9
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))
theorem-size     23
proof            (modus-ponens tm-24 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-320
in-theory        320
times-derived    7
----------------------------------------------------------------
theorem          (A -> (A and ((B and C) -> B)))
theorem-size     9
proof            (modus-ponens tm-24 tm-16 ((A Am) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-321
in-theory        321
times-derived    9
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))
theorem-size     23
proof            (modus-ponens tm-24 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-322
in-theory        322
times-derived    7
----------------------------------------------------------------
theorem          (A -> (A and ((B and C) -> C)))
theorem-size     9
proof            (modus-ponens tm-24 tm-18 ((A Am) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-323
in-theory        323
times-derived    8
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (C -> B)) and A)))
theorem-size     11
proof            (modus-ponens tm-24 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-324
in-theory        324
times-derived    8
----------------------------------------------------------------
theorem          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     19
proof            (modus-ponens tm-24 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-325
in-theory        325
times-derived    8
----------------------------------------------------------------
theorem          (A -> (A and (((B and C) -> B) and A)))
theorem-size     11
proof            (modus-ponens tm-24 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-326
in-theory        326
times-derived    8
----------------------------------------------------------------
theorem          (A -> (A and (((B and C) -> C) and A)))
theorem-size     11
proof            (modus-ponens tm-24 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-327
in-theory        327
times-derived    8
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (C -> (B and C))) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-5)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-328
in-theory        328
times-derived    9
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (A -> (A and B))))
theorem-size     13
proof            (modus-ponens tm-24 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-329
in-theory        329
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-23 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-330
in-theory        330
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (C -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-22 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-331
in-theory        331
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (C -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-21 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-332
in-theory        332
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-20 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-333
in-theory        333
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-19 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-334
in-theory        334
times-derived    9
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B)))
theorem-size     15
proof            (modus-ponens tm-9 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-9 tm-2 tm-5)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-335
in-theory        335
times-derived    11
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C))
theorem-size     19
proof            (modus-ponens tm-8 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-336
in-theory        336
times-derived    8
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (B -> (B and C))))
theorem-size     11
proof            (modus-ponens tm-7 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-7 tm-2 tm-5)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-337
in-theory        337
times-derived    8
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) or C)
theorem-size     11
proof            (modus-ponens tm-6 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-6 tm-2 tm-5)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-338
in-theory        338
times-derived    9
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> (B and C))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-339
in-theory        339
times-derived    11
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> ((A -> B) -> (A and B)))
theorem-size     13
proof            (modus-ponens tm-2 tm-24 ((A (-> Am Bm)) (B Am) (C (and Am Bm))))
axioms-used      (tm-2 tm-5)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
================================================================
tm-name          tm-340
in-theory        340
times-derived    12
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (B -> (B and C))))
theorem-size     11
proof            (modus-ponens tm-1 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-341
in-theory        341
times-derived    7
----------------------------------------------------------------
theorem          (A -> (A and (B -> (C -> (B and C)))))
theorem-size     11
proof            (modus-ponens tm-24 tm-25 ((A Am) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-342
in-theory        342
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-343
in-theory        343
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-344
in-theory        344
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-345
in-theory        345
times-derived    7
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-346
in-theory        346
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-347
in-theory        347
times-derived    7
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> D)) -> D)
theorem-size     13
proof            (modus-ponens tm-17 tm-25 ((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-348
in-theory        348
times-derived    7
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) and D) -> C)
theorem-size     13
proof            (modus-ponens tm-15 tm-25 ((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-349
in-theory        349
times-derived    10
----------------------------------------------------------------
theorem          ((A -> ((B -> (A and B)) -> C)) -> (A -> C))
theorem-size     13
proof            (modus-ponens tm-13 tm-25 ((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-350
in-theory        350
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> (B and C))))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-25 ((A Am) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-351
in-theory        351
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-25 ((A Am) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-352
in-theory        352
times-derived    7
----------------------------------------------------------------
theorem          (A or (B -> (C -> (D -> (C and D)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-7 tm-1 tm-5)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-353
in-theory        353
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-6 tm-1 tm-5)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-354
in-theory        354
times-derived    8
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (D -> (C and D)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-355
in-theory        355
times-derived    10
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> (C -> (B and C))))
theorem-size     11
proof            (modus-ponens tm-2 tm-25 ((A Am) (B Bm) (C (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-356
in-theory        356
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B -> (C -> (D -> (C and D)))))
theorem-size     11
proof            (modus-ponens tm-1 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-1 tm-5)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-357
in-theory        357
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-23 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-358
in-theory        358
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) or E))
theorem-size     13
proof            (modus-ponens tm-22 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-359
in-theory        359
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) or E))
theorem-size     13
proof            (modus-ponens tm-21 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-360
in-theory        360
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-20 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-361
in-theory        361
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) or E))
theorem-size     13
proof            (modus-ponens tm-19 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-362
in-theory        362
times-derived    8
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) or D))
theorem-size     9
proof            (modus-ponens tm-7 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-7 tm-6 tm-1)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-363
in-theory        363
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-6 tm-1)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-364
in-theory        364
times-derived    9
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) or D) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-365
in-theory        365
times-derived    11
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) or D))
theorem-size     9
proof            (modus-ponens tm-1 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-1 tm-6)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-366
in-theory        366
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     23
proof            (modus-ponens tm-23 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-367
in-theory        367
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-22 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-368
in-theory        368
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-21 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-369
in-theory        369
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-20 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-370
in-theory        370
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-19 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-371
in-theory        371
times-derived    8
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))
theorem-size     17
proof            (modus-ponens tm-7 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-7 tm-6 tm-2)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-372
in-theory        372
times-derived    8
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-6 tm-2)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-373
in-theory        373
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-374
in-theory        374
times-derived    11
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))
theorem-size     17
proof            (modus-ponens tm-1 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-1 tm-6 tm-2)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-375
in-theory        375
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) or E))
theorem-size     15
proof            (modus-ponens tm-23 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-376
in-theory        376
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) or E))
theorem-size     13
proof            (modus-ponens tm-22 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-377
in-theory        377
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) or E))
theorem-size     13
proof            (modus-ponens tm-21 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-378
in-theory        378
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F))
theorem-size     21
proof            (modus-ponens tm-20 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-379
in-theory        379
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) or E))
theorem-size     13
proof            (modus-ponens tm-19 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-380
in-theory        380
times-derived    8
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) or D))
theorem-size     9
proof            (modus-ponens tm-7 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-7 tm-6 tm-3)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-381
in-theory        381
times-derived    8
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-6 tm-3)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-382
in-theory        382
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) or D) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-383
in-theory        383
times-derived    11
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) or D))
theorem-size     9
proof            (modus-ponens tm-1 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-1 tm-6 tm-3)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-384
in-theory        384
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-23 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-385
in-theory        385
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) or E))
theorem-size     13
proof            (modus-ponens tm-22 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-386
in-theory        386
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) or E))
theorem-size     13
proof            (modus-ponens tm-21 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-387
in-theory        387
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F))
theorem-size     21
proof            (modus-ponens tm-20 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-388
in-theory        388
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) or E))
theorem-size     13
proof            (modus-ponens tm-19 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-389
in-theory        389
times-derived    8
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) or D))
theorem-size     9
proof            (modus-ponens tm-7 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-7 tm-6 tm-4)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-390
in-theory        390
times-derived    8
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-6 tm-4)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-391
in-theory        391
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) or D) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-392
in-theory        392
times-derived    11
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) or D))
theorem-size     9
proof            (modus-ponens tm-1 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-1 tm-6 tm-4)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-393
in-theory        393
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E))
theorem-size     17
proof            (modus-ponens tm-23 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-394
in-theory        394
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) or E))
theorem-size     15
proof            (modus-ponens tm-22 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-395
in-theory        395
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) or E))
theorem-size     15
proof            (modus-ponens tm-21 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-396
in-theory        396
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F))
theorem-size     23
proof            (modus-ponens tm-20 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-397
in-theory        397
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E))
theorem-size     15
proof            (modus-ponens tm-19 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-398
in-theory        398
times-derived    8
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) or D))
theorem-size     11
proof            (modus-ponens tm-7 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-7 tm-6 tm-5)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-399
in-theory        399
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-6 tm-5)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-400
in-theory        400
times-derived    9
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) or D) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-401
in-theory        401
times-derived    11
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) or D))
theorem-size     11
proof            (modus-ponens tm-1 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-1 tm-6 tm-5)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-402
in-theory        402
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E))
theorem-size     15
proof            (modus-ponens tm-23 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-403
in-theory        403
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) or E))
theorem-size     13
proof            (modus-ponens tm-22 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-404
in-theory        404
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) or E))
theorem-size     13
proof            (modus-ponens tm-21 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-405
in-theory        405
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F))
theorem-size     21
proof            (modus-ponens tm-20 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-406
in-theory        406
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) or E))
theorem-size     13
proof            (modus-ponens tm-19 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-407
in-theory        407
times-derived    8
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) or D))
theorem-size     9
proof            (modus-ponens tm-7 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-7 tm-6)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-408
in-theory        408
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-6)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-409
in-theory        409
times-derived    9
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) or D) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-6)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-410
in-theory        410
times-derived    11
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) or D))
theorem-size     9
proof            (modus-ponens tm-1 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-1 tm-6)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-411
in-theory        411
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> C)))
theorem-size     11
proof            (modus-ponens tm-32 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-412
in-theory        412
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-413
in-theory        413
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C and D) -> C))
theorem-size     11
proof            (modus-ponens tm-32 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-414
in-theory        414
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C and D) -> D))
theorem-size     11
proof            (modus-ponens tm-32 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-415
in-theory        415
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-32 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-6)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-416
in-theory        416
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C or D)))
theorem-size     11
proof            (modus-ponens tm-32 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-6)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-417
in-theory        417
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D or C)))
theorem-size     11
proof            (modus-ponens tm-32 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-418
in-theory        418
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-419
in-theory        419
times-derived    6
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     17
proof            (modus-ponens tm-32 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-420
in-theory        420
times-derived    6
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((not (not C)) -> C))
theorem-size     11
proof            (modus-ponens tm-32 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-421
in-theory        421
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-32 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-422
in-theory        422
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (C -> C)))
theorem-size     13
proof            (modus-ponens tm-32 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-423
in-theory        423
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-32 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-424
in-theory        424
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-425
in-theory        425
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-32 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-426
in-theory        426
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-32 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-427
in-theory        427
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-32 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-428
in-theory        428
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-32 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-429
in-theory        429
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C)))
theorem-size     15
proof            (modus-ponens tm-32 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-430
in-theory        430
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-32 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-431
in-theory        431
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D and E) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-32 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-432
in-theory        432
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D and E) -> E) and C)))
theorem-size     15
proof            (modus-ponens tm-32 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-433
in-theory        433
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-434
in-theory        434
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-32 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-435
in-theory        435
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-436
in-theory        436
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) or E))
theorem-size     13
proof            (modus-ponens tm-32 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-437
in-theory        437
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-32 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-438
in-theory        438
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) or E))
theorem-size     13
proof            (modus-ponens tm-32 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-439
in-theory        439
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) or E))
theorem-size     13
proof            (modus-ponens tm-32 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-440
in-theory        440
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E))
theorem-size     15
proof            (modus-ponens tm-32 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-441
in-theory        441
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) or E))
theorem-size     13
proof            (modus-ponens tm-32 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-442
in-theory        442
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C)))
theorem-size     15
proof            (modus-ponens tm-32 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-443
in-theory        443
times-derived    8
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (B or C)) and A)))
theorem-size     11
proof            (modus-ponens tm-24 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-444
in-theory        444
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C)))
theorem-size     17
proof            (modus-ponens tm-23 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-445
in-theory        445
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (D or E)) and C)))
theorem-size     15
proof            (modus-ponens tm-22 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-446
in-theory        446
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (D or E)) and C)))
theorem-size     15
proof            (modus-ponens tm-21 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-447
in-theory        447
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-20 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-448
in-theory        448
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C)))
theorem-size     15
proof            (modus-ponens tm-19 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-449
in-theory        449
times-derived    9
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (B or C)) and A))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-9 tm-5 tm-6)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-450
in-theory        450
times-derived    11
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-451
in-theory        451
times-derived    8
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (C or D)) and B)))
theorem-size     11
proof            (modus-ponens tm-7 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-452
in-theory        452
times-derived    8
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-6 tm-5)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-453
in-theory        453
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (C or D)) and B)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-454
in-theory        454
times-derived    12
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (C or D)) and B)))
theorem-size     11
proof            (modus-ponens tm-1 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-455
in-theory        455
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-32 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-456
in-theory        456
times-derived    7
----------------------------------------------------------------
theorem          (A -> (A and (B -> (B or C))))
theorem-size     9
proof            (modus-ponens tm-24 tm-33 ((A Am) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-457
in-theory        457
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-23 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-458
in-theory        458
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-22 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-459
in-theory        459
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-21 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-460
in-theory        460
times-derived    7
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-20 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-461
in-theory        461
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-19 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-462
in-theory        462
times-derived    7
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> D)) -> D)
theorem-size     11
proof            (modus-ponens tm-17 tm-33 ((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-463
in-theory        463
times-derived    7
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) and D) -> C)
theorem-size     11
proof            (modus-ponens tm-15 tm-33 ((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-464
in-theory        464
times-derived    10
----------------------------------------------------------------
theorem          ((A -> ((A or B) -> C)) -> (A -> C))
theorem-size     11
proof            (modus-ponens tm-13 tm-33 ((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
================================================================
tm-name          tm-465
in-theory        465
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (not (B -> (B or C)))) -> (not A))
theorem-size     11
proof            (modus-ponens tm-9 tm-33 ((A Am) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-9 tm-1 tm-6)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-466
in-theory        466
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-33 ((A Am) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-467
in-theory        467
times-derived    7
----------------------------------------------------------------
theorem          (A or (B -> (C -> (C or D))))
theorem-size     9
proof            (modus-ponens tm-7 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-7 tm-1 tm-6)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-468
in-theory        468
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-6 tm-1)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-469
in-theory        469
times-derived    8
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (C or D))) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-470
in-theory        470
times-derived    10
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> (B or C)))
theorem-size     9
proof            (modus-ponens tm-2 tm-33 ((A Am) (B Bm) (C (or Bm Cm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
================================================================
tm-name          tm-471
in-theory        471
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B -> (C -> (C or D))))
theorem-size     9
proof            (modus-ponens tm-1 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-1 tm-6)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-472
in-theory        472
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-32 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-473
in-theory        473
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-23 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-474
in-theory        474
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-22 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-475
in-theory        475
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-21 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-476
in-theory        476
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-20 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-477
in-theory        477
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-19 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-478
in-theory        478
times-derived    8
----------------------------------------------------------------
theorem          (A or (B or (C -> (D -> C))))
theorem-size     9
proof            (modus-ponens tm-7 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-7 tm-1)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-479
in-theory        479
times-derived    8
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-6 tm-7 tm-1)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-480
in-theory        480
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (D -> C))) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-481
in-theory        481
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B or (C -> (D -> C))))
theorem-size     9
proof            (modus-ponens tm-1 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-1 tm-7)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-482
in-theory        482
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-483
in-theory        483
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-484
in-theory        484
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-485
in-theory        485
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-486
in-theory        486
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-487
in-theory        487
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-488
in-theory        488
times-derived    8
----------------------------------------------------------------
theorem          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-7 tm-2)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-489
in-theory        489
times-derived    8
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-6 tm-7 tm-2)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-490
in-theory        490
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-491
in-theory        491
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-1 tm-7 tm-2)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-492
in-theory        492
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-32 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-493
in-theory        493
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((D and E) -> D)))
theorem-size     15
proof            (modus-ponens tm-23 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-494
in-theory        494
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-22 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-495
in-theory        495
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-21 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-496
in-theory        496
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-20 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-497
in-theory        497
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-19 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-498
in-theory        498
times-derived    8
----------------------------------------------------------------
theorem          (A or (B or ((C and D) -> C)))
theorem-size     9
proof            (modus-ponens tm-7 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-7 tm-3)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-499
in-theory        499
times-derived    8
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-6 tm-7 tm-3)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-500
in-theory        500
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B or ((C and D) -> C)) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-501
in-theory        501
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B or ((C and D) -> C)))
theorem-size     9
proof            (modus-ponens tm-1 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-1 tm-7 tm-3)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-502
in-theory        502
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-32 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-503
in-theory        503
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((D and E) -> E)))
theorem-size     15
proof            (modus-ponens tm-23 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-504
in-theory        504
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-22 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-505
in-theory        505
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-21 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-506
in-theory        506
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-20 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-507
in-theory        507
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-19 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-508
in-theory        508
times-derived    8
----------------------------------------------------------------
theorem          (A or (B or ((C and D) -> D)))
theorem-size     9
proof            (modus-ponens tm-7 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-7 tm-4)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-509
in-theory        509
times-derived    8
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-6 tm-7 tm-4)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-510
in-theory        510
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B or ((C and D) -> D)) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-511
in-theory        511
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B or ((C and D) -> D)))
theorem-size     9
proof            (modus-ponens tm-1 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-1 tm-7 tm-4)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-512
in-theory        512
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-513
in-theory        513
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-514
in-theory        514
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-515
in-theory        515
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-516
in-theory        516
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-517
in-theory        517
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-518
in-theory        518
times-derived    8
----------------------------------------------------------------
theorem          (A or (B or (C -> (D -> (C and D)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-7 tm-5)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-519
in-theory        519
times-derived    8
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-6 tm-7 tm-5)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-520
in-theory        520
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (D -> (C and D)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-521
in-theory        521
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B or (C -> (D -> (C and D)))))
theorem-size     11
proof            (modus-ponens tm-1 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-1 tm-7 tm-5)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-522
in-theory        522
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-32 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-523
in-theory        523
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-23 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-524
in-theory        524
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-22 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-525
in-theory        525
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-21 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-526
in-theory        526
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-20 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-527
in-theory        527
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-19 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-528
in-theory        528
times-derived    8
----------------------------------------------------------------
theorem          (A or (B or (C -> (C or D))))
theorem-size     9
proof            (modus-ponens tm-7 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-7 tm-6)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-529
in-theory        529
times-derived    8
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-6 tm-7)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-530
in-theory        530
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (C or D))) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-531
in-theory        531
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B or (C -> (C or D))))
theorem-size     9
proof            (modus-ponens tm-1 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-1 tm-7 tm-6)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-532
in-theory        532
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-32 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-533
in-theory        533
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-23 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-534
in-theory        534
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-22 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-535
in-theory        535
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-21 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-536
in-theory        536
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-20 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-537
in-theory        537
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-19 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-538
in-theory        538
times-derived    8
----------------------------------------------------------------
theorem          (A or (B or (C -> (D or C))))
theorem-size     9
proof            (modus-ponens tm-7 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-7)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-539
in-theory        539
times-derived    8
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-6 tm-7)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-540
in-theory        540
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (D or C))) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-541
in-theory        541
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B or (C -> (D or C))))
theorem-size     9
proof            (modus-ponens tm-1 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-1 tm-7)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-542
in-theory        542
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) or E))
theorem-size     13
proof            (modus-ponens tm-32 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-543
in-theory        543
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E))
theorem-size     15
proof            (modus-ponens tm-23 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-544
in-theory        544
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) or E))
theorem-size     13
proof            (modus-ponens tm-22 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-545
in-theory        545
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) or E))
theorem-size     13
proof            (modus-ponens tm-21 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-546
in-theory        546
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F))
theorem-size     21
proof            (modus-ponens tm-20 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-547
in-theory        547
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) or E))
theorem-size     13
proof            (modus-ponens tm-19 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-548
in-theory        548
times-derived    8
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) or D))
theorem-size     9
proof            (modus-ponens tm-7 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-7 tm-6)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-549
in-theory        549
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-6 tm-7)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-550
in-theory        550
times-derived    9
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) or D) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-551
in-theory        551
times-derived    11
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) or D))
theorem-size     9
proof            (modus-ponens tm-1 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-1 tm-6 tm-7)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-552
in-theory        552
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> C)))
theorem-size     11
proof            (modus-ponens tm-42 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-553
in-theory        553
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-554
in-theory        554
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C and D) -> C))
theorem-size     11
proof            (modus-ponens tm-42 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-555
in-theory        555
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C and D) -> D))
theorem-size     11
proof            (modus-ponens tm-42 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-556
in-theory        556
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-42 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-557
in-theory        557
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C or D)))
theorem-size     11
proof            (modus-ponens tm-42 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-558
in-theory        558
times-derived    16
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D or C)))
theorem-size     11
proof            (modus-ponens tm-42 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-7)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-559
in-theory        559
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-560
in-theory        560
times-derived    6
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     17
proof            (modus-ponens tm-42 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-561
in-theory        561
times-derived    6
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((not (not C)) -> C))
theorem-size     11
proof            (modus-ponens tm-42 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-562
in-theory        562
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-42 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-563
in-theory        563
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (C -> C)))
theorem-size     13
proof            (modus-ponens tm-42 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-564
in-theory        564
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-42 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-565
in-theory        565
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-566
in-theory        566
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-42 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-567
in-theory        567
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-42 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-568
in-theory        568
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-42 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-569
in-theory        569
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-42 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-570
in-theory        570
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C)))
theorem-size     15
proof            (modus-ponens tm-42 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-571
in-theory        571
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-42 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-572
in-theory        572
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D and E) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-42 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-573
in-theory        573
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D and E) -> E) and C)))
theorem-size     15
proof            (modus-ponens tm-42 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-574
in-theory        574
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-575
in-theory        575
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-42 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-576
in-theory        576
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-577
in-theory        577
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) or E))
theorem-size     13
proof            (modus-ponens tm-42 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-578
in-theory        578
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-42 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-579
in-theory        579
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) or E))
theorem-size     13
proof            (modus-ponens tm-42 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-580
in-theory        580
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) or E))
theorem-size     13
proof            (modus-ponens tm-42 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-581
in-theory        581
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E))
theorem-size     15
proof            (modus-ponens tm-42 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-582
in-theory        582
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) or E))
theorem-size     13
proof            (modus-ponens tm-42 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-583
in-theory        583
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C)))
theorem-size     15
proof            (modus-ponens tm-42 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-584
in-theory        584
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-42 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-585
in-theory        585
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-42 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-586
in-theory        586
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-587
in-theory        587
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-42 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-588
in-theory        588
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-42 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-589
in-theory        589
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-590
in-theory        590
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-42 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-591
in-theory        591
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-42 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-592
in-theory        592
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) or E))
theorem-size     13
proof            (modus-ponens tm-42 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-593
in-theory        593
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C)))
theorem-size     15
proof            (modus-ponens tm-42 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-594
in-theory        594
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C)))
theorem-size     15
proof            (modus-ponens tm-32 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-595
in-theory        595
times-derived    8
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (C or B)) and A)))
theorem-size     11
proof            (modus-ponens tm-24 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-596
in-theory        596
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C)))
theorem-size     17
proof            (modus-ponens tm-23 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-597
in-theory        597
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (E or D)) and C)))
theorem-size     15
proof            (modus-ponens tm-22 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-598
in-theory        598
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (E or D)) and C)))
theorem-size     15
proof            (modus-ponens tm-21 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-599
in-theory        599
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D)))
theorem-size     23
proof            (modus-ponens tm-20 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-600
in-theory        600
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C)))
theorem-size     15
proof            (modus-ponens tm-19 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-601
in-theory        601
times-derived    9
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C or B)) and A))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-9 tm-5 tm-7)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-602
in-theory        602
times-derived    11
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-603
in-theory        603
times-derived    8
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (D or C)) and B)))
theorem-size     11
proof            (modus-ponens tm-7 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-7 tm-5)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-604
in-theory        604
times-derived    8
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-605
in-theory        605
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D or C)) and B)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-606
in-theory        606
times-derived    12
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D or C)) and B)))
theorem-size     11
proof            (modus-ponens tm-1 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-607
in-theory        607
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-42 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-608
in-theory        608
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-32 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-609
in-theory        609
times-derived    7
----------------------------------------------------------------
theorem          (A -> (A and (B -> (C or B))))
theorem-size     9
proof            (modus-ponens tm-24 tm-43 ((A Am) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-610
in-theory        610
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-23 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-611
in-theory        611
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-22 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-612
in-theory        612
times-derived    7
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-21 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-613
in-theory        613
times-derived    7
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-20 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-614
in-theory        614
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-19 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-615
in-theory        615
times-derived    7
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> D)) -> D)
theorem-size     11
proof            (modus-ponens tm-17 tm-43 ((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-616
in-theory        616
times-derived    7
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) and D) -> C)
theorem-size     11
proof            (modus-ponens tm-15 tm-43 ((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-617
in-theory        617
times-derived    10
----------------------------------------------------------------
theorem          ((A -> ((B or A) -> C)) -> (A -> C))
theorem-size     11
proof            (modus-ponens tm-13 tm-43 ((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
================================================================
tm-name          tm-618
in-theory        618
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C or B)))) -> (not A))
theorem-size     11
proof            (modus-ponens tm-9 tm-43 ((A Am) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-9 tm-1 tm-7)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-619
in-theory        619
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-43 ((A Am) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-620
in-theory        620
times-derived    7
----------------------------------------------------------------
theorem          (A or (B -> (C -> (D or C))))
theorem-size     9
proof            (modus-ponens tm-7 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-7 tm-1)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-621
in-theory        621
times-derived    7
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) or D)
theorem-size     9
proof            (modus-ponens tm-6 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-6 tm-1 tm-7)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-622
in-theory        622
times-derived    8
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (D or C))) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-623
in-theory        623
times-derived    10
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> (C or B)))
theorem-size     9
proof            (modus-ponens tm-2 tm-43 ((A Am) (B Bm) (C (or Cm Bm))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
================================================================
tm-name          tm-624
in-theory        624
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B -> (C -> (D or C))))
theorem-size     9
proof            (modus-ponens tm-1 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-1 tm-7)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-625
in-theory        625
times-derived    17
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (B -> A)))
theorem-size     11
proof            (modus-ponens tm-44 tm-1 ((Am (-> A B)) (C (-> Bm (-> A B)))))
axioms-used      (tm-8 tm-1)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
================================================================
tm-name          tm-626
in-theory        626
times-derived    17
----------------------------------------------------------------
theorem          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B)))
theorem-size     17
proof            (modus-ponens tm-44 tm-2 ((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-627
in-theory        627
times-derived    17
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((B -> A) and C)))
theorem-size     13
proof            (modus-ponens tm-44 tm-5 ((Am (-> A B)) (C (-> Bm (and (-> A B) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
================================================================
tm-name          tm-628
in-theory        628
times-derived    16
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) or C))
theorem-size     11
proof            (modus-ponens tm-44 tm-6 ((Am (-> A B)) (C (or (-> A B) Bm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
================================================================
tm-name          tm-629
in-theory        629
times-derived    16
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (B -> A)))
theorem-size     11
proof            (modus-ponens tm-44 tm-7 ((Am (-> A B)) (C (or Bm (-> A B)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
================================================================
tm-name          tm-630
in-theory        630
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C)))
theorem-size     15
proof            (modus-ponens tm-44 tm-8 ((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-1)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-631
in-theory        631
times-derived    8
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> (not A)) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-44 tm-9 ((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-632
in-theory        632
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (D -> C)))
theorem-size     11
proof            (modus-ponens tm-44 tm-11 ((Am (-> A B)) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-633
in-theory        633
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (B -> B))
theorem-size     9
proof            (modus-ponens tm-44 tm-12 ((A Am) (B Bm) (C (-> Am Am))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
================================================================
tm-name          tm-634
in-theory        634
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     23
proof            (modus-ponens tm-44 tm-13 ((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-635
in-theory        635
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     19
proof            (modus-ponens tm-44 tm-14 ((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-636
in-theory        636
times-derived    10
----------------------------------------------------------------
theorem          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))
theorem-size     17
proof            (modus-ponens tm-44 tm-15 ((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-637
in-theory        637
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C and D) -> C))
theorem-size     11
proof            (modus-ponens tm-44 tm-16 ((Am (-> A B)) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-638
in-theory        638
times-derived    10
----------------------------------------------------------------
theorem          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C))
theorem-size     17
proof            (modus-ponens tm-44 tm-17 ((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-639
in-theory        639
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C and D) -> D))
theorem-size     11
proof            (modus-ponens tm-44 tm-18 ((Am (-> A B)) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-640
in-theory        640
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A)))
theorem-size     15
proof            (modus-ponens tm-44 tm-19 ((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
================================================================
tm-name          tm-641
in-theory        641
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-44 tm-20 ((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
================================================================
tm-name          tm-642
in-theory        642
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A)))
theorem-size     15
proof            (modus-ponens tm-44 tm-21 ((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
================================================================
tm-name          tm-643
in-theory        643
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A)))
theorem-size     15
proof            (modus-ponens tm-44 tm-22 ((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
================================================================
tm-name          tm-644
in-theory        644
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-23 ((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
================================================================
tm-name          tm-645
in-theory        645
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (B -> (B and A)))
theorem-size     11
proof            (modus-ponens tm-44 tm-24 ((A Am) (B Bm) (C (-> Am (and Am Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
================================================================
tm-name          tm-646
in-theory        646
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (D -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-44 tm-25 ((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-647
in-theory        647
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A)))
theorem-size     15
proof            (modus-ponens tm-44 tm-32 ((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
================================================================
tm-name          tm-648
in-theory        648
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (C or D)))
theorem-size     11
proof            (modus-ponens tm-44 tm-33 ((Am (-> A B)) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-649
in-theory        649
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A)))
theorem-size     15
proof            (modus-ponens tm-44 tm-42 ((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
================================================================
tm-name          tm-650
in-theory        650
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (D or C)))
theorem-size     11
proof            (modus-ponens tm-44 tm-43 ((Am (-> A B)) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-651
in-theory        651
times-derived    10
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A))
theorem-size     15
proof            (modus-ponens tm-44 tm-44 ((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-8 tm-1)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-652
in-theory        652
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-42 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-653
in-theory        653
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-32 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-654
in-theory        654
times-derived    9
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))
theorem-size     19
proof            (modus-ponens tm-24 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-655
in-theory        655
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     21
proof            (modus-ponens tm-23 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-656
in-theory        656
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-22 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-657
in-theory        657
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-21 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-658
in-theory        658
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-20 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-659
in-theory        659
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-19 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-660
in-theory        660
times-derived    13
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> ((A -> B) -> C))
theorem-size     11
proof            (modus-ponens tm-12 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-661
in-theory        661
times-derived    9
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C)))
theorem-size     21
proof            (modus-ponens tm-9 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-9 tm-8 tm-1)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-662
in-theory        662
times-derived    11
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-8 tm-1)
proof-size       69
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-663
in-theory        663
times-derived    8
----------------------------------------------------------------
theorem          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D)))
theorem-size     15
proof            (modus-ponens tm-7 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-7 tm-8 tm-1)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-664
in-theory        664
times-derived    8
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-6 tm-8 tm-1)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-665
in-theory        665
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-666
in-theory        666
times-derived    11
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C))
theorem-size     19
proof            (modus-ponens tm-2 tm-44 ((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
================================================================
tm-name          tm-667
in-theory        667
times-derived    11
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D)))
theorem-size     15
proof            (modus-ponens tm-1 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-1 tm-8)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-668
in-theory        668
times-derived    17
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-45 tm-1 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       79
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-669
in-theory        669
times-derived    17
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C)))
theorem-size     25
proof            (modus-ponens tm-45 tm-2 ((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       89
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
================================================================
tm-name          tm-670
in-theory        670
times-derived    17
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D)))
theorem-size     25
proof            (modus-ponens tm-45 tm-5 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       83
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
================================================================
tm-name          tm-671
in-theory        671
times-derived    16
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D))
theorem-size     23
proof            (modus-ponens tm-45 tm-6 ((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm))))
axioms-used      (tm-8 tm-2 tm-6)
proof-size       79
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
================================================================
tm-name          tm-672
in-theory        672
times-derived    16
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-45 tm-7 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-7)
proof-size       79
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-673
in-theory        673
times-derived    9
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))
theorem-size     29
proof            (modus-ponens tm-45 tm-8 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       93
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
================================================================
tm-name          tm-674
in-theory        674
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))
theorem-size     27
proof            (modus-ponens tm-45 tm-9 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B))))))
axioms-used      (tm-8 tm-2 tm-9)
proof-size       89
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
================================================================
tm-name          tm-675
in-theory        675
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-45 tm-11 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-676
in-theory        676
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B)))
theorem-size     21
proof            (modus-ponens tm-45 tm-12 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
================================================================
tm-name          tm-677
in-theory        677
times-derived    10
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     27
proof            (modus-ponens tm-45 tm-13 ((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-678
in-theory        678
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-45 tm-14 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-679
in-theory        679
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-45 tm-16 ((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-680
in-theory        680
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-45 tm-18 ((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-681
in-theory        681
times-derived    9
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-45 tm-19 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-682
in-theory        682
times-derived    9
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-45 tm-20 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-683
in-theory        683
times-derived    9
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-45 tm-21 ((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-684
in-theory        684
times-derived    9
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-45 tm-22 ((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-685
in-theory        685
times-derived    9
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-23 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-686
in-theory        686
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C))))
theorem-size     25
proof            (modus-ponens tm-45 tm-24 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
================================================================
tm-name          tm-687
in-theory        687
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-45 tm-25 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-688
in-theory        688
times-derived    9
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-45 tm-32 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-689
in-theory        689
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-45 tm-33 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-690
in-theory        690
times-derived    9
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-45 tm-42 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-691
in-theory        691
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-45 tm-43 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-692
in-theory        692
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C)))
theorem-size     23
proof            (modus-ponens tm-45 tm-44 ((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
================================================================
tm-name          tm-693
in-theory        693
times-derived    10
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))
theorem-size     43
proof            (modus-ponens tm-45 tm-45 ((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C)))))
axioms-used      (tm-8 tm-2)
proof-size       145
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
================================================================
tm-name          tm-694
in-theory        694
times-derived    10
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))
theorem-size     27
proof            (modus-ponens tm-44 tm-45 ((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-695
in-theory        695
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-42 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-696
in-theory        696
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-32 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-697
in-theory        697
times-derived    9
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     35
proof            (modus-ponens tm-24 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-698
in-theory        698
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     33
proof            (modus-ponens tm-23 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-699
in-theory        699
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-22 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-700
in-theory        700
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-21 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-701
in-theory        701
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     39
proof            (modus-ponens tm-20 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-702
in-theory        702
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-19 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-703
in-theory        703
times-derived    13
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D))
theorem-size     19
proof            (modus-ponens tm-12 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-704
in-theory        704
times-derived    9
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D)))
theorem-size     37
proof            (modus-ponens tm-9 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-9 tm-8 tm-2)
proof-size       99
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-705
in-theory        705
times-derived    11
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))
theorem-size     45
proof            (modus-ponens tm-8 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-2)
proof-size       109
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-706
in-theory        706
times-derived    8
----------------------------------------------------------------
theorem          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     27
proof            (modus-ponens tm-7 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-7 tm-8 tm-2)
proof-size       83
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-707
in-theory        707
times-derived    8
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E)
theorem-size     27
proof            (modus-ponens tm-6 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-6 tm-8 tm-2)
proof-size       83
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-708
in-theory        708
times-derived    9
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       87
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-709
in-theory        709
times-derived    11
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D))
theorem-size     35
proof            (modus-ponens tm-2 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm)))
axioms-used      (tm-2 tm-8)
proof-size       99
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
================================================================
tm-name          tm-710
in-theory        710
times-derived    11
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     27
proof            (modus-ponens tm-1 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       83
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-711
in-theory        711
times-derived    17
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> A))
theorem-size     9
proof            (modus-ponens tm-46 tm-1 ((A Am) (B (-> Bm Am))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-712
in-theory        712
times-derived    17
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))
theorem-size     21
proof            (modus-ponens tm-46 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-713
in-theory        713
times-derived    16
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> A)
theorem-size     11
proof            (modus-ponens tm-46 tm-3 ((A (and Am Bm)) (B Am)))
axioms-used      (tm-8 tm-3)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
================================================================
tm-name          tm-714
in-theory        714
times-derived    16
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> B)
theorem-size     11
proof            (modus-ponens tm-46 tm-4 ((A (and Am Bm)) (B Bm)))
axioms-used      (tm-8 tm-3 tm-4)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-715
in-theory        715
times-derived    17
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (A and C)))
theorem-size     11
proof            (modus-ponens tm-46 tm-5 ((A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-716
in-theory        716
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A or C))
theorem-size     9
proof            (modus-ponens tm-46 tm-6 ((A Am) (B (or Am Bm))))
axioms-used      (tm-8 tm-3 tm-6)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
================================================================
tm-name          tm-717
in-theory        717
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or A))
theorem-size     9
proof            (modus-ponens tm-46 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-8 tm-3 tm-7)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-718
in-theory        718
times-derived    9
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D)))
theorem-size     19
proof            (modus-ponens tm-46 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-3)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-719
in-theory        719
times-derived    8
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A)))
theorem-size     17
proof            (modus-ponens tm-46 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-8 tm-3 tm-9)
proof-size       57
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-720
in-theory        720
times-derived    7
----------------------------------------------------------------
theorem          ((((not (not A)) and B) or (not (not A))) -> A)
theorem-size     11
proof            (modus-ponens tm-46 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-8 tm-3 tm-10)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-721
in-theory        721
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (D -> C)))
theorem-size     11
proof            (modus-ponens tm-46 tm-11 ((A Am) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-722
in-theory        722
times-derived    10
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (A -> A))
theorem-size     13
proof            (modus-ponens tm-46 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-723
in-theory        723
times-derived    10
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     31
proof            (modus-ponens tm-46 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-724
in-theory        724
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     19
proof            (modus-ponens tm-46 tm-14 ((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-725
in-theory        725
times-derived    10
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))
theorem-size     25
proof            (modus-ponens tm-46 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-726
in-theory        726
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C and D) -> C))
theorem-size     11
proof            (modus-ponens tm-46 tm-16 ((A Am) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-727
in-theory        727
times-derived    10
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))
theorem-size     25
proof            (modus-ponens tm-46 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-4)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-728
in-theory        728
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C and D) -> D))
theorem-size     11
proof            (modus-ponens tm-46 tm-18 ((A Am) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-3 tm-1 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-729
in-theory        729
times-derived    9
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (D -> C)) and A))
theorem-size     13
proof            (modus-ponens tm-46 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-730
in-theory        730
times-derived    9
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))
theorem-size     21
proof            (modus-ponens tm-46 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-731
in-theory        731
times-derived    9
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C and D) -> C) and A))
theorem-size     13
proof            (modus-ponens tm-46 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-732
in-theory        732
times-derived    9
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C and D) -> D) and A))
theorem-size     13
proof            (modus-ponens tm-46 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-733
in-theory        733
times-derived    9
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (D -> (C and D))) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-734
in-theory        734
times-derived    10
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B)))
theorem-size     15
proof            (modus-ponens tm-46 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-735
in-theory        735
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (D -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-46 tm-25 ((A Am) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-736
in-theory        736
times-derived    9
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (C or D)) and A))
theorem-size     13
proof            (modus-ponens tm-46 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-737
in-theory        737
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (C or D)))
theorem-size     11
proof            (modus-ponens tm-46 tm-33 ((A Am) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-738
in-theory        738
times-derived    9
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (D or C)) and A))
theorem-size     13
proof            (modus-ponens tm-46 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-739
in-theory        739
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (D or C)))
theorem-size     11
proof            (modus-ponens tm-46 tm-43 ((A Am) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-740
in-theory        740
times-derived    10
----------------------------------------------------------------
theorem          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C))
theorem-size     21
proof            (modus-ponens tm-46 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-741
in-theory        741
times-derived    10
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     37
proof            (modus-ponens tm-46 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-742
in-theory        742
times-derived    10
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-46 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-8 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-743
in-theory        743
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))
theorem-size     27
proof            (modus-ponens tm-45 tm-46 ((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C)))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
================================================================
tm-name          tm-744
in-theory        744
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((B and C) or B) -> A))
theorem-size     13
proof            (modus-ponens tm-44 tm-46 ((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-745
in-theory        745
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-42 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-746
in-theory        746
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-32 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-747
in-theory        747
times-derived    9
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B)))
theorem-size     15
proof            (modus-ponens tm-24 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-748
in-theory        748
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-23 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-749
in-theory        749
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-22 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-750
in-theory        750
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-21 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-751
in-theory        751
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-20 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-752
in-theory        752
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-19 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-753
in-theory        753
times-derived    9
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B)))
theorem-size     17
proof            (modus-ponens tm-9 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-9 tm-8 tm-3)
proof-size       57
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-754
in-theory        754
times-derived    11
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D))
theorem-size     23
proof            (modus-ponens tm-8 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-8 tm-3)
proof-size       65
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-755
in-theory        755
times-derived    8
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (((B and D) or B) -> C)))
theorem-size     13
proof            (modus-ponens tm-7 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-7 tm-8 tm-3)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-756
in-theory        756
times-derived    8
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-6 tm-8 tm-3)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-757
in-theory        757
times-derived    9
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-758
in-theory        758
times-derived    11
----------------------------------------------------------------
theorem          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B))
theorem-size     15
proof            (modus-ponens tm-2 tm-46 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm)))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       57
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
================================================================
tm-name          tm-759
in-theory        759
times-derived    11
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (((B and D) or B) -> C)))
theorem-size     13
proof            (modus-ponens tm-1 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-760
in-theory        760
times-derived    17
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> B))
theorem-size     9
proof            (modus-ponens tm-47 tm-1 ((A Am) (B (-> Bm Am))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-761
in-theory        761
times-derived    17
----------------------------------------------------------------
theorem          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))
theorem-size     21
proof            (modus-ponens tm-47 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-762
in-theory        762
times-derived    16
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> B)
theorem-size     11
proof            (modus-ponens tm-47 tm-3 ((A (and Am Bm)) (B Am)))
axioms-used      (tm-8 tm-4 tm-3)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
================================================================
tm-name          tm-763
in-theory        763
times-derived    16
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> C)
theorem-size     11
proof            (modus-ponens tm-47 tm-4 ((A (and Am Bm)) (B Bm)))
axioms-used      (tm-8 tm-4)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-764
in-theory        764
times-derived    17
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (B and C)))
theorem-size     11
proof            (modus-ponens tm-47 tm-5 ((A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-765
in-theory        765
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B or C))
theorem-size     9
proof            (modus-ponens tm-47 tm-6 ((A Am) (B (or Am Bm))))
axioms-used      (tm-8 tm-4 tm-6)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
================================================================
tm-name          tm-766
in-theory        766
times-derived    16
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or B))
theorem-size     9
proof            (modus-ponens tm-47 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-8 tm-4 tm-7)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-767
in-theory        767
times-derived    9
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-47 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-4)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-768
in-theory        768
times-derived    8
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B)))
theorem-size     17
proof            (modus-ponens tm-47 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-8 tm-4 tm-9)
proof-size       57
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-769
in-theory        769
times-derived    7
----------------------------------------------------------------
theorem          (((A and (not (not B))) or (not (not B))) -> B)
theorem-size     11
proof            (modus-ponens tm-47 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-8 tm-4 tm-10)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-770
in-theory        770
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (D -> C)))
theorem-size     11
proof            (modus-ponens tm-47 tm-11 ((A Am) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-771
in-theory        771
times-derived    10
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (B -> B))
theorem-size     13
proof            (modus-ponens tm-47 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-772
in-theory        772
times-derived    10
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))
theorem-size     31
proof            (modus-ponens tm-47 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-773
in-theory        773
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     19
proof            (modus-ponens tm-47 tm-14 ((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-774
in-theory        774
times-derived    10
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))
theorem-size     25
proof            (modus-ponens tm-47 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-3)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-775
in-theory        775
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C and D) -> C))
theorem-size     11
proof            (modus-ponens tm-47 tm-16 ((A Am) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-4 tm-1 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-776
in-theory        776
times-derived    10
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))
theorem-size     25
proof            (modus-ponens tm-47 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-777
in-theory        777
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C and D) -> D))
theorem-size     11
proof            (modus-ponens tm-47 tm-18 ((A Am) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-778
in-theory        778
times-derived    9
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (D -> C)) and B))
theorem-size     13
proof            (modus-ponens tm-47 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-1)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-779
in-theory        779
times-derived    9
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))
theorem-size     21
proof            (modus-ponens tm-47 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-780
in-theory        780
times-derived    9
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C and D) -> C) and B))
theorem-size     13
proof            (modus-ponens tm-47 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-781
in-theory        781
times-derived    9
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C and D) -> D) and B))
theorem-size     13
proof            (modus-ponens tm-47 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-782
in-theory        782
times-derived    9
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (D -> (C and D))) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-783
in-theory        783
times-derived    10
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C)))
theorem-size     15
proof            (modus-ponens tm-47 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-784
in-theory        784
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (D -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-47 tm-25 ((A Am) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-784.          (((A and B) or B) -> (C -> (D -> (C and D)))), M:tm-47, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-785
in-theory        785
times-derived    9
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (C or D)) and B))
theorem-size     13
proof            (modus-ponens tm-47 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-785.          (((A and B) or B) -> ((C -> (C or D)) and B)), M:tm-47, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-786
in-theory        786
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (C or D)))
theorem-size     11
proof            (modus-ponens tm-47 tm-33 ((A Am) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-786.          (((A and B) or B) -> (C -> (C or D))), M:tm-47, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-787
in-theory        787
times-derived    9
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (D or C)) and B))
theorem-size     13
proof            (modus-ponens tm-47 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-787.          (((A and B) or B) -> ((C -> (D or C)) and B)), M:tm-47, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-788
in-theory        788
times-derived    10
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (D or C)))
theorem-size     11
proof            (modus-ponens tm-47 tm-43 ((A Am) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-788.          (((A and B) or B) -> (C -> (D or C))), M:tm-47, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-789
in-theory        789
times-derived    10
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D))
theorem-size     21
proof            (modus-ponens tm-47 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-789.          (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)), M:tm-47, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-790
in-theory        790
times-derived    10
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))
theorem-size     37
proof            (modus-ponens tm-47 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-790.          (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)), M:tm-47, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-791
in-theory        791
times-derived    10
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C))
theorem-size     17
proof            (modus-ponens tm-47 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-8 tm-4 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-791.          (((A and (B -> C)) or (B -> C)) -> (((B and D) or B) -> C)), M:tm-47, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-792
in-theory        792
times-derived    10
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C))
theorem-size     17
proof            (modus-ponens tm-47 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-8 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-792.          (((A and (B -> C)) or (B -> C)) -> (((D and B) or B) -> C)), M:tm-47, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-793
in-theory        793
times-derived    10
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-46 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-8 tm-3 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-793.          ((((A -> B) and C) or (A -> B)) -> (((D and A) or A) -> B)), M:tm-46, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-794
in-theory        794
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))
theorem-size     27
proof            (modus-ponens tm-45 tm-47 ((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and Cm (-> A B)) (-> A B)) (-> A C)))))
axioms-used      (tm-8 tm-2 tm-4)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-794.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-47, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and Cm (-> A B)) (-> A B)) (-> A C))))
================================================================
tm-name          tm-795
in-theory        795
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C and B) or B) -> A))
theorem-size     13
proof            (modus-ponens tm-44 tm-47 ((A Am) (B Bm) (C (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-795.          ((A or (B -> A)) -> (((C and B) or B) -> A)), M:tm-44, m:tm-47, u:((A Am) (B Bm) (C (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-796
in-theory        796
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-42 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-796.          ((A -> (B or A)) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-42, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-797
in-theory        797
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-32 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-797.          ((A -> (A or B)) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-32, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-798
in-theory        798
times-derived    9
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (((C and A) or A) -> B)))
theorem-size     15
proof            (modus-ponens tm-24 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-798.          ((A -> B) -> ((A -> B) and (((C and A) or A) -> B))), M:tm-24, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-799
in-theory        799
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-23 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-799.          ((A -> (B -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-23, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-800
in-theory        800
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-22 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-800.          (((A and B) -> B) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-22, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-801
in-theory        801
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-21 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-801.          (((A and B) -> A) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-21, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-802
in-theory        802
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-20 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-802.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-20, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-803
in-theory        803
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-19 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-803.          ((A -> (B -> A)) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-19, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-804
in-theory        804
times-derived    9
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B)))
theorem-size     17
proof            (modus-ponens tm-9 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-9 tm-8 tm-4)
proof-size       57
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-804.          (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-805
in-theory        805
times-derived    11
----------------------------------------------------------------
theorem          (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D))
theorem-size     23
proof            (modus-ponens tm-8 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-8 tm-4)
proof-size       65
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-805.          (((((A and B) or B) -> C) -> D) -> (((B -> C) or (((A and B) or B) -> C)) -> D)), M:tm-8, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-806
in-theory        806
times-derived    8
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (((D and B) or B) -> C)))
theorem-size     13
proof            (modus-ponens tm-7 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-7 tm-8 tm-4)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-806.          (A or ((B -> C) -> (((D and B) or B) -> C))), M:tm-7, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-807
in-theory        807
times-derived    8
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-6 tm-8 tm-4)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-807.          (((A -> B) -> (((C and A) or A) -> B)) or D), M:tm-6, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-808
in-theory        808
times-derived    9
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (((D and B) or B) -> C)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-808.          (A -> (((B -> C) -> (((D and B) or B) -> C)) and A)), M:tm-5, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-809
in-theory        809
times-derived    11
----------------------------------------------------------------
theorem          (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B))
theorem-size     15
proof            (modus-ponens tm-2 tm-47 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm)))
axioms-used      (tm-2 tm-8 tm-4)
proof-size       57
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-809.          (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-47, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm))
================================================================
tm-name          tm-810
in-theory        810
times-derived    11
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (((D and B) or B) -> C)))
theorem-size     13
proof            (modus-ponens tm-1 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-1 tm-8 tm-4)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-810.          (A -> ((B -> C) -> (((D and B) or B) -> C))), M:tm-1, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-811
in-theory        811
times-derived    17
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (B -> (A and B))))
theorem-size     15
proof            (modus-ponens tm-48 tm-1 ((Am (-> A (and B A))) (C (-> Bm (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       57
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-811.          ((A or (B -> (A and B))) -> (C -> (B -> (A and B)))), M:tm-48, m:tm-1, u:((Am (-> A (and B A))) (C (-> Bm (-> A (and B A)))))
================================================================
tm-name          tm-812
in-theory        812
times-derived    17
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C)))
theorem-size     17
proof            (modus-ponens tm-48 tm-5 ((Am (-> A (and B A))) (C (-> Bm (and (-> A (and B A)) Bm)))))
axioms-used      (tm-8 tm-5)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-812.          ((A or (B -> (A and B))) -> (C -> ((B -> (A and B)) and C))), M:tm-48, m:tm-5, u:((Am (-> A (and B A))) (C (-> Bm (and (-> A (and B A)) Bm))))
================================================================
tm-name          tm-813
in-theory        813
times-derived    16
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) or C))
theorem-size     15
proof            (modus-ponens tm-48 tm-6 ((Am (-> A (and B A))) (C (or (-> A (and B A)) Bm))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       57
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-813.          ((A or (B -> (A and B))) -> ((B -> (A and B)) or C)), M:tm-48, m:tm-6, u:((Am (-> A (and B A))) (C (or (-> A (and B A)) Bm)))
================================================================
tm-name          tm-814
in-theory        814
times-derived    16
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (B -> (A and B))))
theorem-size     15
proof            (modus-ponens tm-48 tm-7 ((Am (-> A (and B A))) (C (or Bm (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       57
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-814.          ((A or (B -> (A and B))) -> (C or (B -> (A and B)))), M:tm-48, m:tm-7, u:((Am (-> A (and B A))) (C (or Bm (-> A (and B A)))))
================================================================
tm-name          tm-815
in-theory        815
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C)))
theorem-size     21
proof            (modus-ponens tm-48 tm-8 ((A Am) (Bm (and B Am)) (C (-> (-> (and B Am) Cm) (-> (or Am (and B Am)) Cm)))))
axioms-used      (tm-8 tm-5)
proof-size       71
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-815.          ((A or (B -> (A and B))) -> (((A and B) -> C) -> ((B or (A and B)) -> C))), M:tm-48, m:tm-8, u:((A Am) (Bm (and B Am)) (C (-> (-> (and B Am) Cm) (-> (or Am (and B Am)) Cm))))
================================================================
tm-name          tm-816
in-theory        816
times-derived    8
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B)))
theorem-size     17
proof            (modus-ponens tm-48 tm-9 ((A Am) (Bm (and B Am)) (C (-> (-> Am (not (and B Am))) (not Am)))))
axioms-used      (tm-8 tm-5 tm-9)
proof-size       65
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-816.          ((A or (B -> (A and B))) -> ((B -> (not (A and B))) -> (not B))), M:tm-48, m:tm-9, u:((A Am) (Bm (and B Am)) (C (-> (-> Am (not (and B Am))) (not Am))))
================================================================
tm-name          tm-817
in-theory        817
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-48 tm-11 ((Am (-> A (and B A))) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-817.          ((A or (B -> (A and B))) -> (C -> (D -> C))), M:tm-48, m:tm-11, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-818
in-theory        818
times-derived    12
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (B -> B))
theorem-size     11
proof            (modus-ponens tm-48 tm-12 ((A Am) (Bm (and B Am)) (C (-> Am Am))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-818.          ((A or (B -> (A and B))) -> (B -> B)), M:tm-48, m:tm-12, u:((A Am) (Bm (and B Am)) (C (-> Am Am)))
================================================================
tm-name          tm-819
in-theory        819
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-48 tm-14 ((Am (-> A (and B A))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-819.          ((A or (B -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-48, m:tm-14, u:((Am (-> A (and B A))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-820
in-theory        820
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-48 tm-16 ((Am (-> A (and B A))) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-820.          ((A or (B -> (A and B))) -> ((C and D) -> C)), M:tm-48, m:tm-16, u:((Am (-> A (and B A))) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-821
in-theory        821
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-48 tm-18 ((Am (-> A (and B A))) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-821.          ((A or (B -> (A and B))) -> ((C and D) -> D)), M:tm-48, m:tm-18, u:((Am (-> A (and B A))) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-822
in-theory        822
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-48 tm-19 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm Bm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-822.          ((A or (B -> (A and B))) -> ((C -> (D -> C)) and (B -> (A and B)))), M:tm-48, m:tm-19, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-823
in-theory        823
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))
theorem-size     27
proof            (modus-ponens tm-48 tm-20 ((Am (-> A (and B A))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-823.          ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))), M:tm-48, m:tm-20, u:((Am (-> A (and B A))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (and B A)))))
================================================================
tm-name          tm-824
in-theory        824
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-48 tm-21 ((Am (-> A (and B A))) (C (and (-> (and Bm Cm) Bm) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-824.          ((A or (B -> (A and B))) -> (((C and D) -> C) and (B -> (A and B)))), M:tm-48, m:tm-21, u:((Am (-> A (and B A))) (C (and (-> (and Bm Cm) Bm) (-> A (and B A)))))
================================================================
tm-name          tm-825
in-theory        825
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-48 tm-22 ((Am (-> A (and B A))) (C (and (-> (and Bm Cm) Cm) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-825.          ((A or (B -> (A and B))) -> (((C and D) -> D) and (B -> (A and B)))), M:tm-48, m:tm-22, u:((Am (-> A (and B A))) (C (and (-> (and Bm Cm) Cm) (-> A (and B A)))))
================================================================
tm-name          tm-826
in-theory        826
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-23 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-826.          ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) and (B -> (A and B)))), M:tm-48, m:tm-23, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-827
in-theory        827
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (B -> (B and (A and B))))
theorem-size     15
proof            (modus-ponens tm-48 tm-24 ((A Am) (Bm (and B Am)) (C (-> Am (and Am (and B Am))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-827.          ((A or (B -> (A and B))) -> (B -> (B and (A and B)))), M:tm-48, m:tm-24, u:((A Am) (Bm (and B Am)) (C (-> Am (and Am (and B Am)))))
================================================================
tm-name          tm-828
in-theory        828
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-48 tm-25 ((Am (-> A (and B A))) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-828.          ((A or (B -> (A and B))) -> (C -> (D -> (C and D)))), M:tm-48, m:tm-25, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-829
in-theory        829
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-48 tm-32 ((Am (-> A (and B A))) (C (and (-> Bm (or Bm Cm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-829.          ((A or (B -> (A and B))) -> ((C -> (C or D)) and (B -> (A and B)))), M:tm-48, m:tm-32, u:((Am (-> A (and B A))) (C (and (-> Bm (or Bm Cm)) (-> A (and B A)))))
================================================================
tm-name          tm-830
in-theory        830
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-48 tm-33 ((Am (-> A (and B A))) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-830.          ((A or (B -> (A and B))) -> (C -> (C or D))), M:tm-48, m:tm-33, u:((Am (-> A (and B A))) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-831
in-theory        831
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-48 tm-42 ((Am (-> A (and B A))) (C (and (-> Bm (or Cm Bm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-831.          ((A or (B -> (A and B))) -> ((C -> (D or C)) and (B -> (A and B)))), M:tm-48, m:tm-42, u:((Am (-> A (and B A))) (C (and (-> Bm (or Cm Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-832
in-theory        832
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-48 tm-43 ((Am (-> A (and B A))) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-832.          ((A or (B -> (A and B))) -> (C -> (D or C))), M:tm-48, m:tm-43, u:((Am (-> A (and B A))) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-833
in-theory        833
times-derived    10
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C))))
theorem-size     23
proof            (modus-ponens tm-48 tm-44 ((A (-> Am Bm)) (Cm (and B (-> Am Bm))) (C (-> (or Bm (-> Am Bm)) (and B (-> Am Bm))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-833.          ((A or ((B -> C) -> (A and (B -> C)))) -> ((C or (B -> C)) -> (A and (B -> C)))), M:tm-48, m:tm-44, u:((A (-> Am Bm)) (Cm (and B (-> Am Bm))) (C (-> (or Bm (-> Am Bm)) (and B (-> Am Bm)))))
================================================================
tm-name          tm-834
in-theory        834
times-derived    10
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D)))))
theorem-size     43
proof            (modus-ponens tm-48 tm-45 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (and B (-> (-> Am Bm) (-> Am Cm)))) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and B (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       131
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-834.          ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D))))), M:tm-48, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (and B (-> (-> Am Bm) (-> Am Cm)))) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and B (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-835
in-theory        835
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B)))
theorem-size     17
proof            (modus-ponens tm-48 tm-46 ((A Am) (Bm (and B Am)) (C (-> (or (and Am Cm) Am) (and B Am)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-835.          ((A or (B -> (A and B))) -> (((B and C) or B) -> (A and B))), M:tm-48, m:tm-46, u:((A Am) (Bm (and B Am)) (C (-> (or (and Am Cm) Am) (and B Am))))
================================================================
tm-name          tm-836
in-theory        836
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B)))
theorem-size     17
proof            (modus-ponens tm-48 tm-47 ((A Am) (Bm (and B Am)) (C (-> (or (and Cm Am) Am) (and B Am)))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-836.          ((A or (B -> (A and B))) -> (((C and B) or B) -> (A and B))), M:tm-48, m:tm-47, u:((A Am) (Bm (and B Am)) (C (-> (or (and Cm Am) Am) (and B Am))))
================================================================
tm-name          tm-837
in-theory        837
times-derived    10
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B)))))
theorem-size     31
proof            (modus-ponens tm-48 tm-48 ((A (-> Am (and Bm Am))) (Cm (and B (-> Am (and Bm Am)))) (C (-> (or Bm (-> Am (and Bm Am))) (and B (-> Am (and Bm Am)))))))
axioms-used      (tm-8 tm-5)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-837.          ((A or ((B -> (C and B)) -> (A and (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (A and (B -> (C and B))))), M:tm-48, m:tm-48, u:((A (-> Am (and Bm Am))) (Cm (and B (-> Am (and Bm Am)))) (C (-> (or Bm (-> Am (and Bm Am))) (and B (-> Am (and Bm Am))))))
================================================================
tm-name          tm-838
in-theory        838
times-derived    10
----------------------------------------------------------------
theorem          (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D))
theorem-size     27
proof            (modus-ponens tm-47 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-838.          (((A and ((B -> (C and B)) -> D)) or ((B -> (C and B)) -> D)) -> ((C or (B -> (C and B))) -> D)), M:tm-47, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-839
in-theory        839
times-derived    10
----------------------------------------------------------------
theorem          (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C))
theorem-size     27
proof            (modus-ponens tm-46 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-839.          (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)), M:tm-46, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-840
in-theory        840
times-derived    10
----------------------------------------------------------------
theorem          (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C)))
theorem-size     29
proof            (modus-ponens tm-45 tm-48 ((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (-> (or Bm (-> Am (and Bm Am))) (-> Am C)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-840.          (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))), M:tm-45, m:tm-48, u:((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (-> (or Bm (-> Am (and Bm Am))) (-> Am C))))
================================================================
tm-name          tm-841
in-theory        841
times-derived    10
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A))
theorem-size     19
proof            (modus-ponens tm-44 tm-48 ((A (-> Am (and Bm Am))) (B Cm) (C (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-841.          ((A or ((B -> (C and B)) -> A)) -> ((C or (B -> (C and B))) -> A)), M:tm-44, m:tm-48, u:((A (-> Am (and Bm Am))) (B Cm) (C (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-842
in-theory        842
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-42 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-842.          ((A -> (B or A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-42, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-843
in-theory        843
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-32 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-843.          ((A -> (A or B)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-32, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-844
in-theory        844
times-derived    9
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))
theorem-size     25
proof            (modus-ponens tm-24 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-844.          (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))), M:tm-24, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-845
in-theory        845
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     25
proof            (modus-ponens tm-23 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-845.          ((A -> (B -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-23, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-846
in-theory        846
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-22 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-846.          (((A and B) -> B) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-22, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-847
in-theory        847
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-21 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-847.          (((A and B) -> A) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-21, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-848
in-theory        848
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-20 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-848.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-20, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-849
in-theory        849
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-19 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-849.          ((A -> (B -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-19, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-850
in-theory        850
times-derived    13
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C))
theorem-size     15
proof            (modus-ponens tm-12 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-850.          (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)), M:tm-12, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-851
in-theory        851
times-derived    9
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C)))
theorem-size     27
proof            (modus-ponens tm-9 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-9 tm-8 tm-5)
proof-size       75
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-851.          ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))), M:tm-9, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-852
in-theory        852
times-derived    11
----------------------------------------------------------------
theorem          ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D))
theorem-size     31
proof            (modus-ponens tm-8 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-8 tm-5)
proof-size       81
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-852.          ((((A or (B -> (A and B))) -> C) -> D) -> ((((B -> (A and B)) -> C) or ((A or (B -> (A and B))) -> C)) -> D)), M:tm-8, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-853
in-theory        853
times-derived    8
----------------------------------------------------------------
theorem          (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))
theorem-size     19
proof            (modus-ponens tm-7 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-7 tm-8 tm-5)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-853.          (A or (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))), M:tm-7, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-854
in-theory        854
times-derived    8
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D)
theorem-size     19
proof            (modus-ponens tm-6 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-6 tm-8 tm-5)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-854.          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D), M:tm-6, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-855
in-theory        855
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8)
proof-size       65
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-855.          (A -> ((((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)) and A)), M:tm-5, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-856
in-theory        856
times-derived    11
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C))
theorem-size     25
proof            (modus-ponens tm-2 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       75
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-856.          ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)), M:tm-2, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm))
================================================================
tm-name          tm-857
in-theory        857
times-derived    11
----------------------------------------------------------------
theorem          (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))
theorem-size     19
proof            (modus-ponens tm-1 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-857.          (A -> (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))), M:tm-1, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-858
in-theory        858
times-derived    17
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (A or B)))
theorem-size     11
proof            (modus-ponens tm-49 tm-1 ((Am (or A B)) (C (-> Bm (or A B)))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-858.          ((A or (A or B)) -> (C -> (A or B))), M:tm-49, m:tm-1, u:((Am (or A B)) (C (-> Bm (or A B))))
================================================================
tm-name          tm-859
in-theory        859
times-derived    17
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((A or B) and C)))
theorem-size     13
proof            (modus-ponens tm-49 tm-5 ((Am (or A B)) (C (-> Bm (and (or A B) Bm)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-859.          ((A or (A or B)) -> (C -> ((A or B) and C))), M:tm-49, m:tm-5, u:((Am (or A B)) (C (-> Bm (and (or A B) Bm))))
================================================================
tm-name          tm-860
in-theory        860
times-derived    16
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) or C))
theorem-size     11
proof            (modus-ponens tm-49 tm-6 ((Am (or A B)) (C (or (or A B) Bm))))
axioms-used      (tm-8 tm-6)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-860.          ((A or (A or B)) -> ((A or B) or C)), M:tm-49, m:tm-6, u:((Am (or A B)) (C (or (or A B) Bm)))
================================================================
tm-name          tm-861
in-theory        861
times-derived    16
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (A or B)))
theorem-size     11
proof            (modus-ponens tm-49 tm-7 ((Am (or A B)) (C (or Bm (or A B)))))
axioms-used      (tm-8 tm-6 tm-7)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-861.          ((A or (A or B)) -> (C or (A or B))), M:tm-49, m:tm-7, u:((Am (or A B)) (C (or Bm (or A B))))
================================================================
tm-name          tm-862
in-theory        862
times-derived    10
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (D -> C)))
theorem-size     11
proof            (modus-ponens tm-49 tm-11 ((Am (or A B)) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-862.          ((A or (A or B)) -> (C -> (D -> C))), M:tm-49, m:tm-11, u:((Am (or A B)) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-863
in-theory        863
times-derived    10
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     19
proof            (modus-ponens tm-49 tm-14 ((Am (or A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-863.          ((A or (A or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-49, m:tm-14, u:((Am (or A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-864
in-theory        864
times-derived    10
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C and D) -> C))
theorem-size     11
proof            (modus-ponens tm-49 tm-16 ((Am (or A B)) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-6 tm-1 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-864.          ((A or (A or B)) -> ((C and D) -> C)), M:tm-49, m:tm-16, u:((Am (or A B)) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-865
in-theory        865
times-derived    10
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C and D) -> D))
theorem-size     11
proof            (modus-ponens tm-49 tm-18 ((Am (or A B)) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-6 tm-1 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-865.          ((A or (A or B)) -> ((C and D) -> D)), M:tm-49, m:tm-18, u:((Am (or A B)) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-866
in-theory        866
times-derived    9
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (D -> C)) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-49 tm-19 ((Am (or A B)) (C (and (-> Bm (-> Cm Bm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-866.          ((A or (A or B)) -> ((C -> (D -> C)) and (A or B))), M:tm-49, m:tm-19, u:((Am (or A B)) (C (and (-> Bm (-> Cm Bm)) (or A B))))
================================================================
tm-name          tm-867
in-theory        867
times-derived    9
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-49 tm-20 ((Am (or A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-867.          ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))), M:tm-49, m:tm-20, u:((Am (or A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A B))))
================================================================
tm-name          tm-868
in-theory        868
times-derived    9
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C and D) -> C) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-49 tm-21 ((Am (or A B)) (C (and (-> (and Bm Cm) Bm) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-868.          ((A or (A or B)) -> (((C and D) -> C) and (A or B))), M:tm-49, m:tm-21, u:((Am (or A B)) (C (and (-> (and Bm Cm) Bm) (or A B))))
================================================================
tm-name          tm-869
in-theory        869
times-derived    9
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C and D) -> D) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-49 tm-22 ((Am (or A B)) (C (and (-> (and Bm Cm) Cm) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-869.          ((A or (A or B)) -> (((C and D) -> D) and (A or B))), M:tm-49, m:tm-22, u:((Am (or A B)) (C (and (-> (and Bm Cm) Cm) (or A B))))
================================================================
tm-name          tm-870
in-theory        870
times-derived    9
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-23 ((Am (or A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-870.          ((A or (A or B)) -> ((C -> (D -> (C and D))) and (A or B))), M:tm-49, m:tm-23, u:((Am (or A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (or A B))))
================================================================
tm-name          tm-871
in-theory        871
times-derived    10
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (D -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-49 tm-25 ((Am (or A B)) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-871.          ((A or (A or B)) -> (C -> (D -> (C and D)))), M:tm-49, m:tm-25, u:((Am (or A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-872
in-theory        872
times-derived    9
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (C or D)) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-49 tm-32 ((Am (or A B)) (C (and (-> Bm (or Bm Cm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-872.          ((A or (A or B)) -> ((C -> (C or D)) and (A or B))), M:tm-49, m:tm-32, u:((Am (or A B)) (C (and (-> Bm (or Bm Cm)) (or A B))))
================================================================
tm-name          tm-873
in-theory        873
times-derived    10
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (C or D)))
theorem-size     11
proof            (modus-ponens tm-49 tm-33 ((Am (or A B)) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-873.          ((A or (A or B)) -> (C -> (C or D))), M:tm-49, m:tm-33, u:((Am (or A B)) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-874
in-theory        874
times-derived    9
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (D or C)) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-49 tm-42 ((Am (or A B)) (C (and (-> Bm (or Cm Bm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-874.          ((A or (A or B)) -> ((C -> (D or C)) and (A or B))), M:tm-49, m:tm-42, u:((Am (or A B)) (C (and (-> Bm (or Cm Bm)) (or A B))))
================================================================
tm-name          tm-875
in-theory        875
times-derived    10
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (D or C)))
theorem-size     11
proof            (modus-ponens tm-49 tm-43 ((Am (or A B)) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-875.          ((A or (A or B)) -> (C -> (D or C))), M:tm-49, m:tm-43, u:((Am (or A B)) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-876
in-theory        876
times-derived    10
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C))))
theorem-size     23
proof            (modus-ponens tm-48 tm-49 ((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (-> (or Am (or Am Bm)) (and B (or Am Bm))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-876.          ((A or ((B or C) -> (A and (B or C)))) -> ((B or (B or C)) -> (A and (B or C)))), M:tm-48, m:tm-49, u:((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (-> (or Am (or Am Bm)) (and B (or Am Bm)))))
================================================================
tm-name          tm-877
in-theory        877
times-derived    10
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D))
theorem-size     21
proof            (modus-ponens tm-47 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-4 tm-6)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-877.          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((B or (B or C)) -> D)), M:tm-47, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-878
in-theory        878
times-derived    10
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C))
theorem-size     21
proof            (modus-ponens tm-46 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-3 tm-6)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-878.          (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)), M:tm-46, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-879
in-theory        879
times-derived    10
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A))
theorem-size     15
proof            (modus-ponens tm-44 tm-49 ((A (or Am Bm)) (B Cm) (C (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-879.          ((A or ((B or C) -> A)) -> ((B or (B or C)) -> A)), M:tm-44, m:tm-49, u:((A (or Am Bm)) (B Cm) (C (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-880
in-theory        880
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-42 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-880.          ((A -> (B or A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-42, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-881
in-theory        881
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-32 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-881.          ((A -> (A or B)) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-32, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-882
in-theory        882
times-derived    9
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C)))
theorem-size     19
proof            (modus-ponens tm-24 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-882.          (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))), M:tm-24, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-883
in-theory        883
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     21
proof            (modus-ponens tm-23 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-883.          ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-23, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-884
in-theory        884
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-22 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-884.          (((A and B) -> B) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-22, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-885
in-theory        885
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-21 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-885.          (((A and B) -> A) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-21, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-886
in-theory        886
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-20 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-886.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-20, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-887
in-theory        887
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-19 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-887.          ((A -> (B -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-19, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-888
in-theory        888
times-derived    21
----------------------------------------------------------------
theorem          (((A or B) -> C) -> ((A or B) -> C))
theorem-size     11
proof            (modus-ponens tm-12 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-888.          (((A or B) -> C) -> ((A or B) -> C)), M:tm-12, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-889
in-theory        889
times-derived    9
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C)))
theorem-size     21
proof            (modus-ponens tm-9 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-9 tm-8 tm-6)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-889.          ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))), M:tm-9, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-890
in-theory        890
times-derived    11
----------------------------------------------------------------
theorem          ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-6)
proof-size       69
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-890.          ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)), M:tm-8, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-891
in-theory        891
times-derived    8
----------------------------------------------------------------
theorem          (A or (((B or C) -> D) -> ((B or (B or C)) -> D)))
theorem-size     15
proof            (modus-ponens tm-7 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-7 tm-8 tm-6)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-891.          (A or (((B or C) -> D) -> ((B or (B or C)) -> D))), M:tm-7, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-892
in-theory        892
times-derived    8
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-6 tm-8)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-892.          ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D), M:tm-6, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-893
in-theory        893
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-893.          (A -> ((((B or C) -> D) -> ((B or (B or C)) -> D)) and A)), M:tm-5, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-894
in-theory        894
times-derived    11
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C))
theorem-size     19
proof            (modus-ponens tm-2 tm-49 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-6)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-894.          ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)), M:tm-2, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm))
================================================================
tm-name          tm-895
in-theory        895
times-derived    11
----------------------------------------------------------------
theorem          (A -> (((B or C) -> D) -> ((B or (B or C)) -> D)))
theorem-size     15
proof            (modus-ponens tm-1 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-1 tm-8 tm-6)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-895.          (A -> (((B or C) -> D) -> ((B or (B or C)) -> D))), M:tm-1, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-896
in-theory        896
times-derived    17
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (B or A)))
theorem-size     11
proof            (modus-ponens tm-50 tm-1 ((Am (or A B)) (C (-> Bm (or A B)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-896.          ((A or (B or A)) -> (C -> (B or A))), M:tm-50, m:tm-1, u:((Am (or A B)) (C (-> Bm (or A B))))
================================================================
tm-name          tm-897
in-theory        897
times-derived    17
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((B or A) and C)))
theorem-size     13
proof            (modus-ponens tm-50 tm-5 ((Am (or A B)) (C (-> Bm (and (or A B) Bm)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-897.          ((A or (B or A)) -> (C -> ((B or A) and C))), M:tm-50, m:tm-5, u:((Am (or A B)) (C (-> Bm (and (or A B) Bm))))
================================================================
tm-name          tm-898
in-theory        898
times-derived    16
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) or C))
theorem-size     11
proof            (modus-ponens tm-50 tm-6 ((Am (or A B)) (C (or (or A B) Bm))))
axioms-used      (tm-8 tm-7 tm-6)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-898.          ((A or (B or A)) -> ((B or A) or C)), M:tm-50, m:tm-6, u:((Am (or A B)) (C (or (or A B) Bm)))
================================================================
tm-name          tm-899
in-theory        899
times-derived    16
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (B or A)))
theorem-size     11
proof            (modus-ponens tm-50 tm-7 ((Am (or A B)) (C (or Bm (or A B)))))
axioms-used      (tm-8 tm-7)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-899.          ((A or (B or A)) -> (C or (B or A))), M:tm-50, m:tm-7, u:((Am (or A B)) (C (or Bm (or A B))))
================================================================
tm-name          tm-900
in-theory        900
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (D -> C)))
theorem-size     11
proof            (modus-ponens tm-50 tm-11 ((Am (or A B)) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-900.          ((A or (B or A)) -> (C -> (D -> C))), M:tm-50, m:tm-11, u:((Am (or A B)) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-901
in-theory        901
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     19
proof            (modus-ponens tm-50 tm-14 ((Am (or A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-901.          ((A or (B or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-50, m:tm-14, u:((Am (or A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-902
in-theory        902
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C and D) -> C))
theorem-size     11
proof            (modus-ponens tm-50 tm-16 ((Am (or A B)) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-7 tm-1 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-902.          ((A or (B or A)) -> ((C and D) -> C)), M:tm-50, m:tm-16, u:((Am (or A B)) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-903
in-theory        903
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C and D) -> D))
theorem-size     11
proof            (modus-ponens tm-50 tm-18 ((Am (or A B)) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-7 tm-1 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-903.          ((A or (B or A)) -> ((C and D) -> D)), M:tm-50, m:tm-18, u:((Am (or A B)) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-904
in-theory        904
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (D -> C)) and (B or A)))
theorem-size     15
proof            (modus-ponens tm-50 tm-19 ((Am (or A B)) (C (and (-> Bm (-> Cm Bm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-904.          ((A or (B or A)) -> ((C -> (D -> C)) and (B or A))), M:tm-50, m:tm-19, u:((Am (or A B)) (C (and (-> Bm (-> Cm Bm)) (or A B))))
================================================================
tm-name          tm-905
in-theory        905
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-50 tm-20 ((Am (or A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-905.          ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))), M:tm-50, m:tm-20, u:((Am (or A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A B))))
================================================================
tm-name          tm-906
in-theory        906
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C and D) -> C) and (B or A)))
theorem-size     15
proof            (modus-ponens tm-50 tm-21 ((Am (or A B)) (C (and (-> (and Bm Cm) Bm) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-906.          ((A or (B or A)) -> (((C and D) -> C) and (B or A))), M:tm-50, m:tm-21, u:((Am (or A B)) (C (and (-> (and Bm Cm) Bm) (or A B))))
================================================================
tm-name          tm-907
in-theory        907
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C and D) -> D) and (B or A)))
theorem-size     15
proof            (modus-ponens tm-50 tm-22 ((Am (or A B)) (C (and (-> (and Bm Cm) Cm) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-907.          ((A or (B or A)) -> (((C and D) -> D) and (B or A))), M:tm-50, m:tm-22, u:((Am (or A B)) (C (and (-> (and Bm Cm) Cm) (or A B))))
================================================================
tm-name          tm-908
in-theory        908
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-23 ((Am (or A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-908.          ((A or (B or A)) -> ((C -> (D -> (C and D))) and (B or A))), M:tm-50, m:tm-23, u:((Am (or A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (or A B))))
================================================================
tm-name          tm-909
in-theory        909
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (D -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-50 tm-25 ((Am (or A B)) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-909.          ((A or (B or A)) -> (C -> (D -> (C and D)))), M:tm-50, m:tm-25, u:((Am (or A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-910
in-theory        910
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (C or D)) and (B or A)))
theorem-size     15
proof            (modus-ponens tm-50 tm-32 ((Am (or A B)) (C (and (-> Bm (or Bm Cm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-910.          ((A or (B or A)) -> ((C -> (C or D)) and (B or A))), M:tm-50, m:tm-32, u:((Am (or A B)) (C (and (-> Bm (or Bm Cm)) (or A B))))
================================================================
tm-name          tm-911
in-theory        911
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (C or D)))
theorem-size     11
proof            (modus-ponens tm-50 tm-33 ((Am (or A B)) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-911.          ((A or (B or A)) -> (C -> (C or D))), M:tm-50, m:tm-33, u:((Am (or A B)) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-912
in-theory        912
times-derived    9
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (D or C)) and (B or A)))
theorem-size     15
proof            (modus-ponens tm-50 tm-42 ((Am (or A B)) (C (and (-> Bm (or Cm Bm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-912.          ((A or (B or A)) -> ((C -> (D or C)) and (B or A))), M:tm-50, m:tm-42, u:((Am (or A B)) (C (and (-> Bm (or Cm Bm)) (or A B))))
================================================================
tm-name          tm-913
in-theory        913
times-derived    10
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (D or C)))
theorem-size     11
proof            (modus-ponens tm-50 tm-43 ((Am (or A B)) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-913.          ((A or (B or A)) -> (C -> (D or C))), M:tm-50, m:tm-43, u:((Am (or A B)) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-914
in-theory        914
times-derived    10
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C))))
theorem-size     23
proof            (modus-ponens tm-48 tm-50 ((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (-> (or Bm (or Am Bm)) (and B (or Am Bm))))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-914.          ((A or ((B or C) -> (A and (B or C)))) -> ((C or (B or C)) -> (A and (B or C)))), M:tm-48, m:tm-50, u:((A (or Am Bm)) (Cm (and B (or Am Bm))) (C (-> (or Bm (or Am Bm)) (and B (or Am Bm)))))
================================================================
tm-name          tm-915
in-theory        915
times-derived    10
----------------------------------------------------------------
theorem          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D))
theorem-size     21
proof            (modus-ponens tm-47 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-4 tm-7)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-915.          (((A and ((B or C) -> D)) or ((B or C) -> D)) -> ((C or (B or C)) -> D)), M:tm-47, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-916
in-theory        916
times-derived    10
----------------------------------------------------------------
theorem          (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C))
theorem-size     21
proof            (modus-ponens tm-46 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-3 tm-7)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-916.          (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)), M:tm-46, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-917
in-theory        917
times-derived    10
----------------------------------------------------------------
theorem          ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A))
theorem-size     15
proof            (modus-ponens tm-44 tm-50 ((A (or Am Bm)) (B Cm) (C (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-917.          ((A or ((B or C) -> A)) -> ((C or (B or C)) -> A)), M:tm-44, m:tm-50, u:((A (or Am Bm)) (B Cm) (C (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-918
in-theory        918
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-42 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-918.          ((A -> (B or A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-42, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-919
in-theory        919
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-32 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-919.          ((A -> (A or B)) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-32, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-920
in-theory        920
times-derived    9
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C)))
theorem-size     19
proof            (modus-ponens tm-24 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-920.          (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))), M:tm-24, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-921
in-theory        921
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     21
proof            (modus-ponens tm-23 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-921.          ((A -> (B -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-23, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-922
in-theory        922
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-22 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-922.          (((A and B) -> B) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-22, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-923
in-theory        923
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-21 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-923.          (((A and B) -> A) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-21, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-924
in-theory        924
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-20 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-924.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-20, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-925
in-theory        925
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-19 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-925.          ((A -> (B -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-19, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-926
in-theory        926
times-derived    9
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C)))
theorem-size     21
proof            (modus-ponens tm-9 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-9 tm-8 tm-7)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-926.          ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))), M:tm-9, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-927
in-theory        927
times-derived    11
----------------------------------------------------------------
theorem          ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-7)
proof-size       69
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-927.          ((((A or (B or A)) -> C) -> D) -> ((((B or A) -> C) or ((A or (B or A)) -> C)) -> D)), M:tm-8, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-928
in-theory        928
times-derived    8
----------------------------------------------------------------
theorem          (A or (((B or C) -> D) -> ((C or (B or C)) -> D)))
theorem-size     15
proof            (modus-ponens tm-7 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-7 tm-8)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-928.          (A or (((B or C) -> D) -> ((C or (B or C)) -> D))), M:tm-7, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-929
in-theory        929
times-derived    8
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-6 tm-8 tm-7)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-929.          ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D), M:tm-6, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-930
in-theory        930
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-930.          (A -> ((((B or C) -> D) -> ((C or (B or C)) -> D)) and A)), M:tm-5, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-931
in-theory        931
times-derived    11
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C))
theorem-size     19
proof            (modus-ponens tm-2 tm-50 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-7)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-931.          ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)), M:tm-2, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm))
================================================================
tm-name          tm-932
in-theory        932
times-derived    11
----------------------------------------------------------------
theorem          (A -> (((B or C) -> D) -> ((C or (B or C)) -> D)))
theorem-size     15
proof            (modus-ponens tm-1 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-1 tm-8 tm-7)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-932.          (A -> (((B or C) -> D) -> ((C or (B or C)) -> D))), M:tm-1, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-933
in-theory        933
times-derived    17
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C))))
theorem-size     25
proof            (modus-ponens tm-51 tm-1 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-1)
proof-size       83
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-933.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-1, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-934
in-theory        934
times-derived    17
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))
theorem-size     27
proof            (modus-ponens tm-51 tm-2 ((Am (-> A Cm)) (Bm (or C A)) (B Cm) (D (-> (-> (-> A Cm) (or C A)) (-> (-> A Cm) Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       93
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-934.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))), M:tm-51, m:tm-2, u:((Am (-> A Cm)) (Bm (or C A)) (B Cm) (D (-> (-> (-> A Cm) (or C A)) (-> (-> A Cm) Cm))))
================================================================
tm-name          tm-935
in-theory        935
times-derived    17
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-51 tm-5 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (-> A B) (-> (or C A) B)) Bm)))))
axioms-used      (tm-8 tm-5)
proof-size       87
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-935.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((B -> C) -> ((A or B) -> C)) and D))), M:tm-51, m:tm-5, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (-> A B) (-> (or C A) B)) Bm))))
================================================================
tm-name          tm-936
in-theory        936
times-derived    16
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D))
theorem-size     25
proof            (modus-ponens tm-51 tm-6 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> A B) (-> (or C A) B)) Bm))))
axioms-used      (tm-8 tm-6)
proof-size       83
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-936.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) or D)), M:tm-51, m:tm-6, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> A B) (-> (or C A) B)) Bm)))
================================================================
tm-name          tm-937
in-theory        937
times-derived    16
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C))))
theorem-size     25
proof            (modus-ponens tm-51 tm-7 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-7)
proof-size       83
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-937.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-7, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-938
in-theory        938
times-derived    9
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))
theorem-size     33
proof            (modus-ponens tm-51 tm-8 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> (-> (or C A) B) Cm) (-> (or (-> A B) (-> (or C A) B)) Cm)))))
axioms-used      (tm-8)
proof-size       99
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-938.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))), M:tm-51, m:tm-8, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> (-> (or C A) B) Cm) (-> (or (-> A B) (-> (or C A) B)) Cm))))
================================================================
tm-name          tm-939
in-theory        939
times-derived    8
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))
theorem-size     29
proof            (modus-ponens tm-51 tm-9 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> (-> A B) (not (-> (or C A) B))) (not (-> A B))))))
axioms-used      (tm-8 tm-9)
proof-size       93
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-939.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))), M:tm-51, m:tm-9, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> (-> A B) (not (-> (or C A) B))) (not (-> A B)))))
================================================================
tm-name          tm-940
in-theory        940
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-51 tm-11 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-1)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-940.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> D))), M:tm-51, m:tm-11, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-941
in-theory        941
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C)))
theorem-size     21
proof            (modus-ponens tm-51 tm-12 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> A B)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-941.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (B -> C))), M:tm-51, m:tm-12, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> A B))))
================================================================
tm-name          tm-942
in-theory        942
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-51 tm-14 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-942.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-51, m:tm-14, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-943
in-theory        943
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-51 tm-16 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-943.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> D)), M:tm-51, m:tm-16, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-944
in-theory        944
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-51 tm-18 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-944.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D and E) -> E)), M:tm-51, m:tm-18, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-945
in-theory        945
times-derived    9
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-51 tm-19 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-945.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-19, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-946
in-theory        946
times-derived    9
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-51 tm-20 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-946.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-20, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-947
in-theory        947
times-derived    9
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-51 tm-21 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-947.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-21, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-948
in-theory        948
times-derived    9
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-51 tm-22 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-948.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-22, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-949
in-theory        949
times-derived    9
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-23 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-949.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-23, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-950
in-theory        950
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C))))
theorem-size     27
proof            (modus-ponens tm-51 tm-24 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (and (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-950.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((B -> C) and ((A or B) -> C)))), M:tm-51, m:tm-24, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (and (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-951
in-theory        951
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-51 tm-25 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-951.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (D and E)))), M:tm-51, m:tm-25, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-952
in-theory        952
times-derived    9
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-51 tm-32 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-952.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-32, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-953
in-theory        953
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-51 tm-33 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-953.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (D or E))), M:tm-51, m:tm-33, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-954
in-theory        954
times-derived    9
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-51 tm-42 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-954.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-42, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-955
in-theory        955
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-51 tm-43 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-955.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E or D))), M:tm-51, m:tm-43, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-956
in-theory        956
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C)))
theorem-size     25
proof            (modus-ponens tm-51 tm-44 ((A Am) (B Bm) (Cm (-> (or C Am) Bm)) (D (-> (or Bm (-> Am Bm)) (-> (or C Am) Bm)))))
axioms-used      (tm-8 tm-1)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-956.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((C or (B -> C)) -> ((A or B) -> C))), M:tm-51, m:tm-44, u:((A Am) (B Bm) (Cm (-> (or C Am) Bm)) (D (-> (or Bm (-> Am Bm)) (-> (or C Am) Bm))))
================================================================
tm-name          tm-957
in-theory        957
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D))))
theorem-size     47
proof            (modus-ponens tm-51 tm-45 ((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (or C (-> Am Bm)) (-> Am Cm))) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or C (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-8 tm-2)
proof-size       151
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-957.          (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D)))), M:tm-51, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (or C (-> Am Bm)) (-> Am Cm))) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or C (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-958
in-theory        958
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))
theorem-size     29
proof            (modus-ponens tm-51 tm-46 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> (or C A) B)))))
axioms-used      (tm-8 tm-3)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-958.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))), M:tm-51, m:tm-46, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> (or C A) B))))
================================================================
tm-name          tm-959
in-theory        959
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C)))
theorem-size     29
proof            (modus-ponens tm-51 tm-47 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (or (and Cm (-> A B)) (-> A B)) (-> (or C A) B)))))
axioms-used      (tm-8 tm-4)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-959.          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (B -> C)) or (B -> C)) -> ((A or B) -> C))), M:tm-51, m:tm-47, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (or (and Cm (-> A B)) (-> A B)) (-> (or C A) B))))
================================================================
tm-name          tm-960
in-theory        960
times-derived    10
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> ((C or (B -> (C and B))) -> ((A or B) -> (C and B))))
theorem-size     33
proof            (modus-ponens tm-51 tm-48 ((A Am) (B (and Bm Am)) (Cm (-> (or C Am) (and Bm Am))) (D (-> (or Bm (-> Am (and Bm Am))) (-> (or C Am) (and Bm Am))))))
axioms-used      (tm-8 tm-5)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-960.          (((A -> B) or ((B -> (C and B)) -> ((A or B) -> (C and B)))) -> ((C or (B -> (C and B))) -> ((A or B) -> (C and B)))), M:tm-51, m:tm-48, u:((A Am) (B (and Bm Am)) (Cm (-> (or C Am) (and Bm Am))) (D (-> (or Bm (-> Am (and Bm Am))) (-> (or C Am) (and Bm Am)))))
================================================================
tm-name          tm-961
in-theory        961
times-derived    10
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C))))
theorem-size     53
proof            (modus-ponens tm-51 tm-51 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (D (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))))))
axioms-used      (tm-8)
proof-size       159
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-961.          (((A -> (B -> C)) or (((B -> C) -> ((D or B) -> C)) -> ((A or (B -> C)) -> ((D or B) -> C)))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> ((A or (B -> C)) -> ((D or B) -> C)))), M:tm-51, m:tm-51, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm))) (D (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (or C (-> Am Bm)) (-> (or Cm Am) Bm)))))
================================================================
tm-name          tm-962
in-theory        962
times-derived    10
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-48 tm-51 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))))))
axioms-used      (tm-8 tm-5)
proof-size       139
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-962.          ((A or (((B -> C) -> ((D or B) -> C)) -> (A and ((B -> C) -> ((D or B) -> C))))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (A and ((B -> C) -> ((D or B) -> C))))), M:tm-48, m:tm-51, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (and B (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
================================================================
tm-name          tm-963
in-theory        963
times-derived    10
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))
theorem-size     41
proof            (modus-ponens tm-47 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-8 tm-4)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-963.          (((A and (((B -> C) -> ((D or B) -> C)) -> E)) or (((B -> C) -> ((D or B) -> C)) -> E)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)), M:tm-47, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-964
in-theory        964
times-derived    10
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))
theorem-size     41
proof            (modus-ponens tm-46 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-8 tm-3)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-964.          ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-46, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-965
in-theory        965
times-derived    10
----------------------------------------------------------------
theorem          ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))
theorem-size     47
proof            (modus-ponens tm-45 tm-51 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) C)))))
axioms-used      (tm-8 tm-2)
proof-size       151
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-965.          ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))), M:tm-45, m:tm-51, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) C))))
================================================================
tm-name          tm-966
in-theory        966
times-derived    10
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A))
theorem-size     29
proof            (modus-ponens tm-44 tm-51 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B Dm) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-8 tm-1)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-966.          ((A or (((B -> C) -> ((D or B) -> C)) -> A)) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> A)), M:tm-44, m:tm-51, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B Dm) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-967
in-theory        967
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-42 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-967.          ((A -> (B or A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-42, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-968
in-theory        968
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-32 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-968.          ((A -> (A or B)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-32, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-969
in-theory        969
times-derived    9
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     39
proof            (modus-ponens tm-24 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       121
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-969.          ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-24, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-970
in-theory        970
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-23 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-8)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-970.          ((A -> (B -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-23, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-971
in-theory        971
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-22 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-971.          (((A and B) -> B) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-22, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-972
in-theory        972
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-21 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-972.          (((A and B) -> A) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-21, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-973
in-theory        973
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     41
proof            (modus-ponens tm-20 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       131
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-973.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-20, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-974
in-theory        974
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-19 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-974.          ((A -> (B -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-19, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-975
in-theory        975
times-derived    13
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D))
theorem-size     23
proof            (modus-ponens tm-12 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-975.          ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)), M:tm-12, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-976
in-theory        976
times-derived    9
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (not (((A -> B) -> ((C or A) -> B)) -> D)))
theorem-size     41
proof            (modus-ponens tm-9 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-9 tm-8)
proof-size       105
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-976.          (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (not (((A -> B) -> ((C or A) -> B)) -> D))), M:tm-9, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-977
in-theory        977
times-derived    11
----------------------------------------------------------------
theorem          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E))
theorem-size     47
proof            (modus-ponens tm-8 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-8)
proof-size       113
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-977.          (((((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D) -> E) -> (((((B -> C) -> ((A or B) -> C)) -> D) or (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)) -> E)), M:tm-8, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-978
in-theory        978
times-derived    8
----------------------------------------------------------------
theorem          (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))
theorem-size     29
proof            (modus-ponens tm-7 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-7 tm-8)
proof-size       87
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-978.          (A or ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))), M:tm-7, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-979
in-theory        979
times-derived    8
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E)
theorem-size     29
proof            (modus-ponens tm-6 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-6 tm-8)
proof-size       87
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-979.          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E), M:tm-6, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-980
in-theory        980
times-derived    9
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-8)
proof-size       91
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-980.          (A -> (((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)) and A)), M:tm-5, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-981
in-theory        981
times-derived    11
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D))
theorem-size     39
proof            (modus-ponens tm-2 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm)))
axioms-used      (tm-2 tm-8)
proof-size       105
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-981.          (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)), M:tm-2, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm))
================================================================
tm-name          tm-982
in-theory        982
times-derived    11
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))
theorem-size     29
proof            (modus-ponens tm-1 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-1 tm-8)
proof-size       87
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-982.          (A -> ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))), M:tm-1, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-983
in-theory        983
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-983.          ((A -> (B or A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-42, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-984
in-theory        984
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-984.          ((A -> (A or B)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-32, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-985
in-theory        985
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-985.          ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-23, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-986
in-theory        986
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-986.          (((A and B) -> B) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-22, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-987
in-theory        987
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-987.          (((A and B) -> A) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-21, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-988
in-theory        988
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-988.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-20, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-989
in-theory        989
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-989.          ((A -> (B -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-19, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-990
in-theory        990
times-derived    8
----------------------------------------------------------------
theorem          (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-7 tm-8)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-990.          (A or (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))), M:tm-7, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-991
in-theory        991
times-derived    8
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-6 tm-7 tm-8)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-991.          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E), M:tm-6, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-992
in-theory        992
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-992.          (A -> ((B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)), M:tm-5, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-993
in-theory        993
times-derived    11
----------------------------------------------------------------
theorem          (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-1 tm-7 tm-8)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-993.          (A -> (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))), M:tm-1, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-994
in-theory        994
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-42 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-994.          ((A -> (B or A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-42, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-995
in-theory        995
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-32 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-995.          ((A -> (A or B)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-32, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-996
in-theory        996
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     23
proof            (modus-ponens tm-23 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-996.          ((A -> (B -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-23, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-997
in-theory        997
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-22 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-997.          (((A and B) -> B) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-22, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-998
in-theory        998
times-derived    8
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-21 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-998.          (((A and B) -> A) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-21, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-999
in-theory        999
times-derived    8
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-20 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-999.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-20, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-1000
in-theory        1000
times-derived    8
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-19 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1000.         ((A -> (B -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-19, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-1001
in-theory        1001
times-derived    8
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))
theorem-size     17
proof            (modus-ponens tm-7 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-7 tm-6 tm-8)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1001.         (A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)), M:tm-7, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-1002
in-theory        1002
times-derived    8
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-6 tm-8)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1002.         ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E), M:tm-6, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-1003
in-theory        1003
times-derived    9
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1003.         (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E) and A)), M:tm-5, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-1004
in-theory        1004
times-derived    11
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))
theorem-size     17
proof            (modus-ponens tm-1 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-1 tm-6 tm-8)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1004.         (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)), M:tm-1, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-1005
in-theory        1005
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-54 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-1005.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> D))), M:tm-54, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-1006
in-theory        1006
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       77
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1006.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-54, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-1007
in-theory        1007
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-54 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-1007.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> D)), M:tm-54, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-1008
in-theory        1008
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-54 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-1008.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> E)), M:tm-54, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-1009
in-theory        1009
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-54 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-8)
proof-size       65
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1009.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (D and E)))), M:tm-54, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-1010
in-theory        1010
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-54 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1010.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D or E))), M:tm-54, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-1011
in-theory        1011
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-54 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1011.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or D))), M:tm-54, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-1012
in-theory        1012
times-derived    4
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8)
proof-size       77
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1012.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-54, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1013
in-theory        1013
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-54 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       73
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1013.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-54, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-1014
in-theory        1014
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D))
theorem-size     19
proof            (modus-ponens tm-54 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-8 tm-10)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-1014.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> D)), M:tm-54, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-1015
in-theory        1015
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-54 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1015.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> E)))), M:tm-54, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-1016
in-theory        1016
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-54 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-1016.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> D))), M:tm-54, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-1017
in-theory        1017
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-54 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1017.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-54, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-1018
in-theory        1018
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1018.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-54, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-1019
in-theory        1019
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-54 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1019.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-54, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-1020
in-theory        1020
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-54 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1020.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> E))), M:tm-54, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-1021
in-theory        1021
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-54 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1021.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-54, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-1022
in-theory        1022
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-54 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1022.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E and F) -> F))), M:tm-54, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-1023
in-theory        1023
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-54 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1023.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-54, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-1024
in-theory        1024
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-54 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1024.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-54, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-1025
in-theory        1025
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-54 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1025.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) and D))), M:tm-54, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-1026
in-theory        1026
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-54 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1026.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) and D))), M:tm-54, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-1027
in-theory        1027
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-8)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1027.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-54, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-1028
in-theory        1028
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-54 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1028.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-54, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-1029
in-theory        1029
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1029.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-54, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-1030
in-theory        1030
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-54 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1030.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) or F)), M:tm-54, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-1031
in-theory        1031
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-54 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1031.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-54, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-1032
in-theory        1032
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F))
theorem-size     21
proof            (modus-ponens tm-54 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-8 tm-6 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1032.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) or F)), M:tm-54, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-1033
in-theory        1033
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F))
theorem-size     21
proof            (modus-ponens tm-54 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-8 tm-6 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1033.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) or F)), M:tm-54, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-1034
in-theory        1034
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F))
theorem-size     23
proof            (modus-ponens tm-54 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1034.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-54, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-1035
in-theory        1035
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F))
theorem-size     21
proof            (modus-ponens tm-54 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1035.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) or F)), M:tm-54, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-1036
in-theory        1036
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-54 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1036.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-54, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-1037
in-theory        1037
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-54 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1037.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (E or F)))), M:tm-54, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-1038
in-theory        1038
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-54 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1038.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> E)))), M:tm-54, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-1039
in-theory        1039
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1039.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-54, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-1040
in-theory        1040
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-54 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1040.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> E))), M:tm-54, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-1041
in-theory        1041
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-54 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1041.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E and F) -> F))), M:tm-54, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-1042
in-theory        1042
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1042.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (E and F))))), M:tm-54, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-1043
in-theory        1043
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-54 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1043.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (E or F)))), M:tm-54, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-1044
in-theory        1044
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-54 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1044.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F or E)))), M:tm-54, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-1045
in-theory        1045
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F))
theorem-size     21
proof            (modus-ponens tm-54 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1045.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) or F)), M:tm-54, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-1046
in-theory        1046
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D)))
theorem-size     23
proof            (modus-ponens tm-54 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1046.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-54, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-1047
in-theory        1047
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-54 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1047.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F or E)))), M:tm-54, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-1048
in-theory        1048
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-54 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1048.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-54, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-1049
in-theory        1049
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     39
proof            (modus-ponens tm-54 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1049.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-54, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-1050
in-theory        1050
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-54 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1050.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-54, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-1051
in-theory        1051
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-54 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1051.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-54, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-1052
in-theory        1052
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-54 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1052.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-54, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-1053
in-theory        1053
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-54 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1053.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-54, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-1054
in-theory        1054
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-54 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1054.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-54, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-1055
in-theory        1055
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     41
proof            (modus-ponens tm-54 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-8)
proof-size       131
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1055.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-54, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-1056
in-theory        1056
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1056.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-54, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1057
in-theory        1057
times-derived    6
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-54 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1057.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-54, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-1058
in-theory        1058
times-derived    4
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-54 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-8)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1058.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-54, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-1059
in-theory        1059
times-derived    5
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-51 tm-54 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1059.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-54, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-1060
in-theory        1060
times-derived    5
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-50 tm-54 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1060.         ((A or (B or A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B or A))), M:tm-50, m:tm-54, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (or A B))))
================================================================
tm-name          tm-1061
in-theory        1061
times-derived    5
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-49 tm-54 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1061.         ((A or (A or B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A or B))), M:tm-49, m:tm-54, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (or A B))))
================================================================
tm-name          tm-1062
in-theory        1062
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B))))
theorem-size     27
proof            (modus-ponens tm-48 tm-54 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1062.         ((A or (B -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> (A and B)))), M:tm-48, m:tm-54, u:((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A (and B A)))))
================================================================
tm-name          tm-1063
in-theory        1063
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and B))
theorem-size     21
proof            (modus-ponens tm-47 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1063.         (((A and B) or B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and B)), M:tm-47, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-1064
in-theory        1064
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and A))
theorem-size     21
proof            (modus-ponens tm-46 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1064.         (((A and B) or A) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and A)), M:tm-46, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-1065
in-theory        1065
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-45 tm-54 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1065.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-54, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-1066
in-theory        1066
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-44 tm-54 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1066.         ((A or (B -> A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (B -> A))), M:tm-44, m:tm-54, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A B))))
================================================================
tm-name          tm-1067
in-theory        1067
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-42 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1067.         ((A -> (B or A)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C))), M:tm-42, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-1068
in-theory        1068
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-32 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1068.         ((A -> (A or B)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C))), M:tm-32, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-1069
in-theory        1069
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)))
theorem-size     19
proof            (modus-ponens tm-24 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1069.         (A -> (A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))), M:tm-24, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-1070
in-theory        1070
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C)))
theorem-size     25
proof            (modus-ponens tm-23 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-8)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1070.         ((A -> (B -> (A and B))) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C))), M:tm-23, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-1071
in-theory        1071
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-22 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1071.         (((A and B) -> B) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C))), M:tm-22, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-1072
in-theory        1072
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-21 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1072.         (((A and B) -> A) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C))), M:tm-21, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-1073
in-theory        1073
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-20 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1073.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-20, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-1074
in-theory        1074
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-19 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1074.         ((A -> (B -> A)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C))), M:tm-19, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-1075
in-theory        1075
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))) -> (not A))
theorem-size     21
proof            (modus-ponens tm-9 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-9 tm-5 tm-8)
proof-size       69
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1075.         ((A -> (not (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))) -> (not A)), M:tm-9, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-1076
in-theory        1076
times-derived    3
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and D) -> E) -> ((D or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and D)) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-8 tm-5)
proof-size       87
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1076.         (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) and D) -> E) -> ((D or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and D)) -> E)), M:tm-8, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-1077
in-theory        1077
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and B)))
theorem-size     19
proof            (modus-ponens tm-7 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1077.         (A or (B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and B))), M:tm-7, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-1078
in-theory        1078
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1078.         ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) or E), M:tm-6, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-1079
in-theory        1079
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and B)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-8)
proof-size       65
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1079.         (A -> ((B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and B)) and A)), M:tm-5, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-1080
in-theory        1080
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and B)))
theorem-size     19
proof            (modus-ponens tm-1 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1080.         (A -> (B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and B))), M:tm-1, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-1081
in-theory        1081
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> (A -> B)))
theorem-size     11
proof            (modus-ponens tm-55 tm-1 ((Am (-> A Bm)) (B Bm) (C (-> A Bm))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-1081.         ((A -> B) -> ((A or B) -> (A -> B))), M:tm-55, m:tm-1, u:((Am (-> A Bm)) (B Bm) (C (-> A Bm)))
================================================================
tm-name          tm-1082
in-theory        1082
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A -> A)) -> ((A or (A -> A)) -> (A -> A)))
theorem-size     15
proof            (modus-ponens tm-55 tm-2 ((A Cm) (Am Cm) (Bm Cm) (B (-> Cm Cm)) (C (-> Cm Cm))))
axioms-used      (tm-2 tm-8)
proof-size       71
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1082.         ((A -> (A -> A)) -> ((A or (A -> A)) -> (A -> A))), M:tm-55, m:tm-2, u:((A Cm) (Am Cm) (Bm Cm) (B (-> Cm Cm)) (C (-> Cm Cm)))
================================================================
tm-name          tm-1083
in-theory        1083
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> ((A -> B) and B)))
theorem-size     13
proof            (modus-ponens tm-55 tm-5 ((Am (-> A Bm)) (B Bm) (C (and (-> A Bm) Bm))))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1083.         ((A -> B) -> ((A or B) -> ((A -> B) and B))), M:tm-55, m:tm-5, u:((Am (-> A Bm)) (B Bm) (C (and (-> A Bm) Bm)))
================================================================
tm-name          tm-1084
in-theory        1084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> (C -> B)))
theorem-size     11
proof            (modus-ponens tm-55 tm-11 ((Am (-> A Bm)) (B Bm) (C (-> Cm Bm))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1084.         ((A -> B) -> ((A or B) -> (C -> B))), M:tm-55, m:tm-11, u:((Am (-> A Bm)) (B Bm) (C (-> Cm Bm)))
================================================================
tm-name          tm-1085
in-theory        1085
times-derived    4
----------------------------------------------------------------
theorem          ((A -> A) -> ((A or A) -> A))
theorem-size     9
proof            (modus-ponens tm-55 tm-12 ((A Bm) (Am Bm) (B Bm) (C Bm)))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-1085.         ((A -> A) -> ((A or A) -> A)), M:tm-55, m:tm-12, u:((A Bm) (Am Bm) (B Bm) (C Bm))
================================================================
tm-name          tm-1086
in-theory        1086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> D))) -> ((A or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))
theorem-size     23
proof            (modus-ponens tm-55 tm-14 ((Am (-> A (-> Bm (-> Cm Dm)))) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1086.         ((A -> (B -> (C -> D))) -> ((A or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))), M:tm-55, m:tm-14, u:((Am (-> A (-> Bm (-> Cm Dm)))) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-1087
in-theory        1087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> ((A or (B and C)) -> B))
theorem-size     13
proof            (modus-ponens tm-55 tm-16 ((Am (-> A (and Bm Cm))) (B (and Bm Cm)) (C Bm)))
axioms-used      (tm-2 tm-8 tm-1 tm-3)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1087.         ((A -> (B and C)) -> ((A or (B and C)) -> B)), M:tm-55, m:tm-16, u:((Am (-> A (and Bm Cm))) (B (and Bm Cm)) (C Bm))
================================================================
tm-name          tm-1088
in-theory        1088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> ((A or (B and C)) -> C))
theorem-size     13
proof            (modus-ponens tm-55 tm-18 ((Am (-> A (and Bm Cm))) (B (and Bm Cm)) (C Cm)))
axioms-used      (tm-2 tm-8 tm-1 tm-4)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1088.         ((A -> (B and C)) -> ((A or (B and C)) -> C)), M:tm-55, m:tm-18, u:((Am (-> A (and Bm Cm))) (B (and Bm Cm)) (C Cm))
================================================================
tm-name          tm-1089
in-theory        1089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) -> ((A or A) -> (A and A)))
theorem-size     11
proof            (modus-ponens tm-55 tm-24 ((A Bm) (Am Bm) (B Bm) (C (and Bm Bm))))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1089.         ((A -> A) -> ((A or A) -> (A and A))), M:tm-55, m:tm-24, u:((A Bm) (Am Bm) (B Bm) (C (and Bm Bm)))
================================================================
tm-name          tm-1090
in-theory        1090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> (C -> (B and C))))
theorem-size     13
proof            (modus-ponens tm-55 tm-25 ((Am (-> A Bm)) (B Bm) (C (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1090.         ((A -> B) -> ((A or B) -> (C -> (B and C)))), M:tm-55, m:tm-25, u:((Am (-> A Bm)) (B Bm) (C (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-1091
in-theory        1091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> (B or C)))
theorem-size     11
proof            (modus-ponens tm-55 tm-33 ((Am (-> A Bm)) (B Bm) (C (or Bm Cm))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1091.         ((A -> B) -> ((A or B) -> (B or C))), M:tm-55, m:tm-33, u:((Am (-> A Bm)) (B Bm) (C (or Bm Cm)))
================================================================
tm-name          tm-1092
in-theory        1092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> (C or B)))
theorem-size     11
proof            (modus-ponens tm-55 tm-43 ((Am (-> A Bm)) (B Bm) (C (or Cm Bm))))
axioms-used      (tm-2 tm-8 tm-1 tm-7)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1092.         ((A -> B) -> ((A or B) -> (C or B))), M:tm-55, m:tm-43, u:((Am (-> A Bm)) (B Bm) (C (or Cm Bm)))
================================================================
tm-name          tm-1093
in-theory        1093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (B or (A -> B))) -> (((A -> B) or (B or (A -> B))) -> (B or (A -> B))))
theorem-size     25
proof            (modus-ponens tm-55 tm-44 ((A (-> Am Bm)) (Cm (or Bm (-> Am Bm))) (B (or Bm (-> Am Bm))) (C (or Bm (-> Am Bm)))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1093.         (((A -> B) -> (B or (A -> B))) -> (((A -> B) or (B or (A -> B))) -> (B or (A -> B)))), M:tm-55, m:tm-44, u:((A (-> Am Bm)) (Cm (or Bm (-> Am Bm))) (B (or Bm (-> Am Bm))) (C (or Bm (-> Am Bm))))
================================================================
tm-name          tm-1094
in-theory        1094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-55 tm-45 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-8)
proof-size       151
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1094.         ((((A -> B) -> (A -> C)) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-55, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-1095
in-theory        1095
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((A and B) or A)) -> ((A or ((A and B) or A)) -> ((A and B) or A)))
theorem-size     21
proof            (modus-ponens tm-55 tm-46 ((A Am) (Bm (or (and Am Cm) Am)) (B (or (and Am Cm) Am)) (C (or (and Am Cm) Am))))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1095.         ((A -> ((A and B) or A)) -> ((A or ((A and B) or A)) -> ((A and B) or A))), M:tm-55, m:tm-46, u:((A Am) (Bm (or (and Am Cm) Am)) (B (or (and Am Cm) Am)) (C (or (and Am Cm) Am)))
================================================================
tm-name          tm-1096
in-theory        1096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and A) or A)) -> ((A or ((B and A) or A)) -> ((B and A) or A)))
theorem-size     21
proof            (modus-ponens tm-55 tm-47 ((A Am) (Bm (or (and Cm Am) Am)) (B (or (and Cm Am) Am)) (C (or (and Cm Am) Am))))
axioms-used      (tm-2 tm-8 tm-4)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1096.         ((A -> ((B and A) or A)) -> ((A or ((B and A) or A)) -> ((B and A) or A))), M:tm-55, m:tm-47, u:((A Am) (Bm (or (and Cm Am) Am)) (B (or (and Cm Am) Am)) (C (or (and Cm Am) Am)))
================================================================
tm-name          tm-1097
in-theory        1097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) or (B or (A -> (B and A)))) -> (B or (A -> (B and A)))))
theorem-size     35
proof            (modus-ponens tm-55 tm-48 ((A (-> Am (and Bm Am))) (Cm (or Bm (-> Am (and Bm Am)))) (B (or Bm (-> Am (and Bm Am)))) (C (or Bm (-> Am (and Bm Am))))))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1097.         (((A -> (B and A)) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) or (B or (A -> (B and A)))) -> (B or (A -> (B and A))))), M:tm-55, m:tm-48, u:((A (-> Am (and Bm Am))) (Cm (or Bm (-> Am (and Bm Am)))) (B (or Bm (-> Am (and Bm Am)))) (C (or Bm (-> Am (and Bm Am)))))
================================================================
tm-name          tm-1098
in-theory        1098
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (A or (A or B))) -> (((A or B) or (A or (A or B))) -> (A or (A or B))))
theorem-size     25
proof            (modus-ponens tm-55 tm-49 ((A (or Am Bm)) (Cm (or Am (or Am Bm))) (B (or Am (or Am Bm))) (C (or Am (or Am Bm)))))
axioms-used      (tm-2 tm-8 tm-6)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1098.         (((A or B) -> (A or (A or B))) -> (((A or B) or (A or (A or B))) -> (A or (A or B)))), M:tm-55, m:tm-49, u:((A (or Am Bm)) (Cm (or Am (or Am Bm))) (B (or Am (or Am Bm))) (C (or Am (or Am Bm))))
================================================================
tm-name          tm-1099
in-theory        1099
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (B or (A or B))) -> (((A or B) or (B or (A or B))) -> (B or (A or B))))
theorem-size     25
proof            (modus-ponens tm-55 tm-50 ((A (or Am Bm)) (Cm (or Bm (or Am Bm))) (B (or Bm (or Am Bm))) (C (or Bm (or Am Bm)))))
axioms-used      (tm-2 tm-8 tm-7)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1099.         (((A or B) -> (B or (A or B))) -> (((A or B) or (B or (A or B))) -> (B or (A or B)))), M:tm-55, m:tm-50, u:((A (or Am Bm)) (Cm (or Bm (or Am Bm))) (B (or Bm (or Am Bm))) (C (or Bm (or Am Bm))))
================================================================
tm-name          tm-1100
in-theory        1100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))))
theorem-size     61
proof            (modus-ponens tm-55 tm-51 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
axioms-used      (tm-2 tm-8)
proof-size       157
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1100.         ((((A -> B) -> ((C or A) -> B)) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) or ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((C -> A) or ((A -> B) -> ((C or A) -> B))))), M:tm-55, m:tm-51, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))))
================================================================
tm-name          tm-1101
in-theory        1101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> (A -> A)) -> (((A -> A) or (A -> A)) -> ((A or A) -> A)))
theorem-size     21
proof            (modus-ponens tm-55 tm-55 ((A (-> Cm Cm)) (Am Cm) (Bm Cm) (B (-> Cm Cm)) (C (-> (or Cm Cm) Cm))))
axioms-used      (tm-2 tm-8)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1101.         (((A -> A) -> (A -> A)) -> (((A -> A) or (A -> A)) -> ((A or A) -> A))), M:tm-55, m:tm-55, u:((A (-> Cm Cm)) (Am Cm) (Bm Cm) (B (-> Cm Cm)) (C (-> (or Cm Cm) Cm)))
================================================================
tm-name          tm-1102
in-theory        1102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-54 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1102.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-54, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1103
in-theory        1103
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (A or B)) -> ((A or B) -> (A or B)))) -> ((B -> (A or B)) -> ((B or (A or B)) -> (A or B))))
theorem-size     33
proof            (modus-ponens tm-51 tm-55 ((A Am) (Cm (or C Am)) (Bm (or C Am)) (B (or C Am)) (D (-> (-> Am (or C Am)) (-> (or Am (or C Am)) (or C Am))))))
axioms-used      (tm-8 tm-2)
proof-size       129
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1103.         (((A -> B) or ((B -> (A or B)) -> ((A or B) -> (A or B)))) -> ((B -> (A or B)) -> ((B or (A or B)) -> (A or B)))), M:tm-51, m:tm-55, u:((A Am) (Cm (or C Am)) (Bm (or C Am)) (B (or C Am)) (D (-> (-> Am (or C Am)) (-> (or Am (or C Am)) (or C Am)))))
================================================================
tm-name          tm-1104
in-theory        1104
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> (C -> D))) or ((B -> C) -> (C -> D))) -> ((B -> C) -> ((B or C) -> D)))
theorem-size     27
proof            (modus-ponens tm-47 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1104.         (((A and ((B -> C) -> (C -> D))) or ((B -> C) -> (C -> D))) -> ((B -> C) -> ((B or C) -> D))), M:tm-47, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-1105
in-theory        1105
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (B -> C)) and D) or ((A -> B) -> (B -> C))) -> ((A -> B) -> ((A or B) -> C)))
theorem-size     27
proof            (modus-ponens tm-46 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1105.         (((((A -> B) -> (B -> C)) and D) or ((A -> B) -> (B -> C))) -> ((A -> B) -> ((A or B) -> C))), M:tm-46, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-1106
in-theory        1106
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (A -> B)) or ((A -> A) -> (A -> B))) -> ((A -> A) -> ((A or A) -> B)))
theorem-size     23
proof            (modus-ponens tm-45 tm-55 ((Bm Am) (B Am) (A Am) (C Cm) (D (-> (-> Am Am) (-> (or Am Am) Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1106.         (((A -> (A -> B)) or ((A -> A) -> (A -> B))) -> ((A -> A) -> ((A or A) -> B))), M:tm-45, m:tm-55, u:((Bm Am) (B Am) (A Am) (C Cm) (D (-> (-> Am Am) (-> (or Am Am) Cm))))
================================================================
tm-name          tm-1107
in-theory        1107
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((C -> A) -> (A -> B))) -> ((C -> A) -> ((C or A) -> B)))
theorem-size     21
proof            (modus-ponens tm-44 tm-55 ((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1107.         (((A -> B) or ((C -> A) -> (A -> B))) -> ((C -> A) -> ((C or A) -> B))), M:tm-44, m:tm-55, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-1108
in-theory        1108
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-42 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1108.         ((A -> (B or A)) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E)))), M:tm-42, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1109
in-theory        1109
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-32 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1109.         ((A -> (A or B)) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E)))), M:tm-32, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1110
in-theory        1110
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (B -> C)) -> (((A -> B) -> (B -> C)) and ((A -> B) -> ((A or B) -> C))))
theorem-size     25
proof            (modus-ponens tm-24 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1110.         (((A -> B) -> (B -> C)) -> (((A -> B) -> (B -> C)) and ((A -> B) -> ((A or B) -> C)))), M:tm-24, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-1111
in-theory        1111
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-23 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1111.         ((A -> (B -> (A and B))) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E)))), M:tm-23, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1112
in-theory        1112
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-22 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1112.         (((A and B) -> B) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E)))), M:tm-22, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1113
in-theory        1113
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-21 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1113.         (((A and B) -> A) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E)))), M:tm-21, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1114
in-theory        1114
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-20 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1114.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-20, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1115
in-theory        1115
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-19 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1115.         ((A -> (B -> A)) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E)))), M:tm-19, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1116
in-theory        1116
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (B -> C)) -> ((A -> B) -> (B -> C)))
theorem-size     15
proof            (modus-ponens tm-12 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1116.         (((A -> B) -> (B -> C)) -> ((A -> B) -> (B -> C))), M:tm-12, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-1117
in-theory        1117
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> (not ((A -> B) -> ((A or B) -> C)))) -> (not ((A -> B) -> (B -> C))))
theorem-size     27
proof            (modus-ponens tm-9 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-9 tm-2 tm-8)
proof-size       81
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1117.         ((((A -> B) -> (B -> C)) -> (not ((A -> B) -> ((A or B) -> C)))) -> (not ((A -> B) -> (B -> C)))), M:tm-9, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-1118
in-theory        1118
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A or B) -> C)) -> D) -> ((((A -> B) -> (B -> C)) or ((A -> B) -> ((A or B) -> C))) -> D))
theorem-size     31
proof            (modus-ponens tm-8 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       87
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1118.         ((((A -> B) -> ((A or B) -> C)) -> D) -> ((((A -> B) -> (B -> C)) or ((A -> B) -> ((A or B) -> C))) -> D)), M:tm-8, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-1119
in-theory        1119
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> C) -> (C -> D)) -> ((B -> C) -> ((B or C) -> D))))
theorem-size     19
proof            (modus-ponens tm-7 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-7 tm-2 tm-8)
proof-size       67
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1119.         (A or (((B -> C) -> (C -> D)) -> ((B -> C) -> ((B or C) -> D)))), M:tm-7, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1120
in-theory        1120
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) or D)
theorem-size     19
proof            (modus-ponens tm-6 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-6 tm-2 tm-8)
proof-size       67
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1120.         ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) or D), M:tm-6, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1121
in-theory        1121
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (C -> D)) -> ((B -> C) -> ((B or C) -> D))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       71
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1121.         (A -> ((((B -> C) -> (C -> D)) -> ((B -> C) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1122
in-theory        1122
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> (A -> B)) -> (((A -> B) -> (B -> C)) -> ((A or B) -> C)))
theorem-size     25
proof            (modus-ponens tm-2 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> Am Bm)) (C (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-8)
proof-size       81
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1122.         ((((A -> B) -> (B -> C)) -> (A -> B)) -> (((A -> B) -> (B -> C)) -> ((A or B) -> C))), M:tm-2, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> Am Bm)) (C (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-1123
in-theory        1123
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (C -> D)) -> ((B -> C) -> ((B or C) -> D))))
theorem-size     19
proof            (modus-ponens tm-1 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-1 tm-2 tm-8)
proof-size       67
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1123.         (A -> (((B -> C) -> (C -> D)) -> ((B -> C) -> ((B or C) -> D)))), M:tm-1, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1124
in-theory        1124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((A or (B -> C)) -> ((C -> D) -> ((B or C) -> D))))
theorem-size     21
proof            (modus-ponens tm-55 tm-56 ((Am (-> A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1124.         ((A -> (B -> C)) -> ((A or (B -> C)) -> ((C -> D) -> ((B or C) -> D)))), M:tm-55, m:tm-56, u:((Am (-> A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-1125
in-theory        1125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1125.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-54, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1126
in-theory        1126
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-51 tm-56 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-1)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1126.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-51, m:tm-56, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1127
in-theory        1127
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-50 tm-56 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1127.         ((A or (B or A)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-50, m:tm-56, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1128
in-theory        1128
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-49 tm-56 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1128.         ((A or (A or B)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-49, m:tm-56, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1129
in-theory        1129
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-48 tm-56 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1129.         ((A or (B -> (A and B))) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-48, m:tm-56, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1130
in-theory        1130
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-47 tm-56 ((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1130.         (((A and B) or B) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-47, m:tm-56, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1131
in-theory        1131
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-46 tm-56 ((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1131.         (((A and B) or A) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-46, m:tm-56, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1132
in-theory        1132
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-45 tm-56 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1132.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-45, m:tm-56, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1133
in-theory        1133
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-44 tm-56 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1133.         ((A or (B -> A)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-44, m:tm-56, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1134
in-theory        1134
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1134.         ((A -> (B or A)) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-42, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1135
in-theory        1135
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1135.         ((A -> (A or B)) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-32, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1136
in-theory        1136
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     17
proof            (modus-ponens tm-24 tm-56 ((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1136.         (A -> (A and ((B -> C) -> ((C -> D) -> ((B or C) -> D))))), M:tm-24, m:tm-56, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1137
in-theory        1137
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1137.         ((A -> (B -> (A and B))) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-23, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1138
in-theory        1138
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1138.         (((A and B) -> B) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-22, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1139
in-theory        1139
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1139.         (((A and B) -> A) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-21, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1140
in-theory        1140
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1140.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-20, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1141
in-theory        1141
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1141.         ((A -> (B -> A)) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-19, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1142
in-theory        1142
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) -> E)) -> E)
theorem-size     19
proof            (modus-ponens tm-17 tm-56 ((Am (and A (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) C))) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-4 tm-1 tm-8)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1142.         ((A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) -> E)) -> E), M:tm-17, m:tm-56, u:((Am (and A (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) C))) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1143
in-theory        1143
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) and E) -> D)
theorem-size     19
proof            (modus-ponens tm-15 tm-56 ((Am (and (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B) C)) (A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-3 tm-1 tm-8)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1143.         (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) and E) -> D), M:tm-15, m:tm-56, u:((Am (and (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B) C)) (A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1144
in-theory        1144
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((B -> C) -> ((A or B) -> C)) -> D)) -> ((A -> B) -> D))
theorem-size     21
proof            (modus-ponens tm-13 tm-56 ((Am (-> (-> Bm Cm) (-> (-> (-> Cm Dm) (-> (or Bm Cm) Dm)) C))) (A (-> Bm Cm)) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1144.         (((A -> B) -> (((B -> C) -> ((A or B) -> C)) -> D)) -> ((A -> B) -> D)), M:tm-13, m:tm-56, u:((Am (-> (-> Bm Cm) (-> (-> (-> Cm Dm) (-> (or Bm Cm) Dm)) C))) (A (-> Bm Cm)) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-1145
in-theory        1145
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> C) -> ((C -> D) -> ((B or C) -> D))))) -> (not A))
theorem-size     19
proof            (modus-ponens tm-9 tm-56 ((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-9 tm-1 tm-8)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1145.         ((A -> (not ((B -> C) -> ((C -> D) -> ((B or C) -> D))))) -> (not A)), M:tm-9, m:tm-56, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1146
in-theory        1146
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) -> ((E or ((A -> B) -> ((B -> C) -> ((A or B) -> C)))) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-56 ((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-1)
proof-size       79
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1146.         ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) -> ((E or ((A -> B) -> ((B -> C) -> ((A or B) -> C)))) -> D)), M:tm-8, m:tm-56, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1147
in-theory        1147
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-7 tm-1 tm-8)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1147.         (A or (B -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))), M:tm-7, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1148
in-theory        1148
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-6 tm-1 tm-8)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1148.         ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E), M:tm-6, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1149
in-theory        1149
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1149.         (A -> ((B -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and A)), M:tm-5, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1150
in-theory        1150
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (A -> ((C -> D) -> ((B or C) -> D))))
theorem-size     17
proof            (modus-ponens tm-2 tm-56 ((A Am) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1150.         ((A -> (B -> C)) -> (A -> ((C -> D) -> ((B or C) -> D)))), M:tm-2, m:tm-56, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-1151
in-theory        1151
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-1 tm-8)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1151.         (A -> (B -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))), M:tm-1, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1152
in-theory        1152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-54 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-1)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1152.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (E -> D))) -> (not D))), M:tm-54, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-1153
in-theory        1153
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not (C -> B)))) or (B -> (not (C -> B)))) -> (not B))
theorem-size     18
proof            (modus-ponens tm-47 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-1)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1153.         (((A and (B -> (not (C -> B)))) or (B -> (not (C -> B)))) -> (not B)), M:tm-47, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-1154
in-theory        1154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not (B -> A))) and C) or (A -> (not (B -> A)))) -> (not A))
theorem-size     18
proof            (modus-ponens tm-46 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-1)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1154.         ((((A -> (not (B -> A))) and C) or (A -> (not (B -> A)))) -> (not A)), M:tm-46, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-1155
in-theory        1155
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> B)) or (B -> (not (A -> B)))) -> (not B))
theorem-size     14
proof            (modus-ponens tm-44 tm-57 ((A Am) (B (not (-> Bm Am))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       70
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1155.         (((not (A -> B)) or (B -> (not (A -> B)))) -> (not B)), M:tm-44, m:tm-57, u:((A Am) (B (not (-> Bm Am))) (C (not Am)))
================================================================
tm-name          tm-1156
in-theory        1156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not (D -> C))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-42 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1156.         ((A -> (B or A)) and ((C -> (not (D -> C))) -> (not C))), M:tm-42, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-1157
in-theory        1157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not (D -> C))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-32 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1157.         ((A -> (A or B)) and ((C -> (not (D -> C))) -> (not C))), M:tm-32, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-1158
in-theory        1158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> A))) -> ((A -> (not (B -> A))) and (not A)))
theorem-size     16
proof            (modus-ponens tm-24 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       70
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1158.         ((A -> (not (B -> A))) -> ((A -> (not (B -> A))) and (not A))), M:tm-24, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-1159
in-theory        1159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not (D -> C))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-23 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1159.         ((A -> (B -> (A and B))) and ((C -> (not (D -> C))) -> (not C))), M:tm-23, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-1160
in-theory        1160
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not (D -> C))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-22 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1160.         (((A and B) -> B) and ((C -> (not (D -> C))) -> (not C))), M:tm-22, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-1161
in-theory        1161
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not (D -> C))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-21 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1161.         (((A and B) -> A) and ((C -> (not (D -> C))) -> (not C))), M:tm-21, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-1162
in-theory        1162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-20 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1162.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (E -> D))) -> (not D))), M:tm-20, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-1163
in-theory        1163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not (D -> C))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-19 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1163.         ((A -> (B -> A)) and ((C -> (not (D -> C))) -> (not C))), M:tm-19, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-1164
in-theory        1164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> A))) -> (A -> (not (B -> A))))
theorem-size     13
proof            (modus-ponens tm-12 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1164.         ((A -> (not (B -> A))) -> (A -> (not (B -> A)))), M:tm-12, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-1165
in-theory        1165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not (not A))) -> (not (A -> (not (B -> A)))))
theorem-size     18
proof            (modus-ponens tm-9 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-9 tm-1)
proof-size       54
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1165.         (((A -> (not (B -> A))) -> (not (not A))) -> (not (A -> (not (B -> A))))), M:tm-9, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-1166
in-theory        1166
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not (C -> A))) or (not A)) -> B))
theorem-size     16
proof            (modus-ponens tm-8 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-1)
proof-size       54
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1166.         (((not A) -> B) -> (((A -> (not (C -> A))) or (not A)) -> B)), M:tm-8, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-1167
in-theory        1167
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not (C -> B))) -> (not B)))
theorem-size     11
proof            (modus-ponens tm-7 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-1)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1167.         (A or ((B -> (not (C -> B))) -> (not B))), M:tm-7, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-1168
in-theory        1168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) or C)
theorem-size     11
proof            (modus-ponens tm-6 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-1)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1168.         (((A -> (not (B -> A))) -> (not A)) or C), M:tm-6, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-1169
in-theory        1169
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not (C -> B))) -> (not B)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1169.         (A -> (((B -> (not (C -> B))) -> (not B)) and A)), M:tm-5, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-1170
in-theory        1170
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not (C -> B))) -> (not B)))
theorem-size     11
proof            (modus-ponens tm-1 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-1 tm-9)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1170.         (A -> ((B -> (not (C -> B))) -> (not B))), M:tm-1, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-1171
in-theory        1171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-9 tm-2)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1171.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-54, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-1172
in-theory        1172
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> (not ((B -> C) -> (B -> D))))) or ((B -> (C -> D)) -> (not ((B -> C) -> (B -> D))))) -> (not (B -> (C -> D))))
theorem-size     38
proof            (modus-ponens tm-47 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-8 tm-4 tm-9 tm-2)
proof-size       112
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1172.         (((A and ((B -> (C -> D)) -> (not ((B -> C) -> (B -> D))))) or ((B -> (C -> D)) -> (not ((B -> C) -> (B -> D))))) -> (not (B -> (C -> D)))), M:tm-47, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-1173
in-theory        1173
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) and D) or ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C))))
theorem-size     38
proof            (modus-ponens tm-46 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-8 tm-3 tm-9 tm-2)
proof-size       112
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1173.         (((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) and D) or ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C)))), M:tm-46, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-1174
in-theory        1174
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A -> B) -> (A -> C))) or ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C))))
theorem-size     30
proof            (modus-ponens tm-44 tm-58 ((A (-> Am (-> Bm Cm))) (B (not (-> (-> Am Bm) (-> Am Cm)))) (C (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-9 tm-2)
proof-size       106
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1174.         (((not ((A -> B) -> (A -> C))) or ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C)))), M:tm-44, m:tm-58, u:((A (-> Am (-> Bm Cm))) (B (not (-> (-> Am Bm) (-> Am Cm)))) (C (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-1175
in-theory        1175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1175.         ((A -> (B or A)) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E))))), M:tm-42, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-1176
in-theory        1176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1176.         ((A -> (A or B)) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E))))), M:tm-32, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-1177
in-theory        1177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) and (not (A -> (B -> C)))))
theorem-size     36
proof            (modus-ponens tm-24 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       110
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1177.         (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) and (not (A -> (B -> C))))), M:tm-24, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-1178
in-theory        1178
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1178.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E))))), M:tm-23, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-1179
in-theory        1179
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-9 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1179.         (((A and B) -> B) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E))))), M:tm-22, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-1180
in-theory        1180
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-9 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1180.         (((A and B) -> A) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E))))), M:tm-21, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-1181
in-theory        1181
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1181.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-20, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-1182
in-theory        1182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1182.         ((A -> (B -> A)) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E))))), M:tm-19, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-1183
in-theory        1183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-12 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1183.         (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))), M:tm-12, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-1184
in-theory        1184
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (not (A -> (B -> C))))) -> (not ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))))
theorem-size     38
proof            (modus-ponens tm-9 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-9 tm-2)
proof-size       94
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1184.         ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (not (A -> (B -> C))))) -> (not ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))))), M:tm-9, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-1185
in-theory        1185
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> (B -> C))) -> D) -> ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) or (not (A -> (B -> C)))) -> D))
theorem-size     32
proof            (modus-ponens tm-8 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-8 tm-9 tm-2)
proof-size       90
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1185.         (((not (A -> (B -> C))) -> D) -> ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) or (not (A -> (B -> C)))) -> D)), M:tm-8, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-1186
in-theory        1186
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> (not ((B -> C) -> (B -> D)))) -> (not (B -> (C -> D)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-7 tm-9 tm-2)
proof-size       73
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1186.         (A or (((B -> (C -> D)) -> (not ((B -> C) -> (B -> D)))) -> (not (B -> (C -> D))))), M:tm-7, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-1187
in-theory        1187
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) or D)
theorem-size     23
proof            (modus-ponens tm-6 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-6 tm-9 tm-2)
proof-size       73
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1187.         ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) or D), M:tm-6, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-1188
in-theory        1188
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> (not ((B -> C) -> (B -> D)))) -> (not (B -> (C -> D)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       77
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1188.         (A -> ((((B -> (C -> D)) -> (not ((B -> C) -> (B -> D)))) -> (not (B -> (C -> D)))) and A)), M:tm-5, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-1189
in-theory        1189
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> (not ((B -> C) -> (B -> D)))) -> (not (B -> (C -> D)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-1 tm-9 tm-2)
proof-size       73
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1189.         (A -> (((B -> (C -> D)) -> (not ((B -> C) -> (B -> D)))) -> (not (B -> (C -> D))))), M:tm-1, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-1190
in-theory        1190
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (not A)))
theorem-size     5
proof            (modus-ponens tm-59 tm-4 ((A Am) (B (not Am)) (Bm (not Am))))
axioms-used      (tm-9 tm-3 tm-4)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-1190.         (not (A and (not A))), M:tm-59, m:tm-4, u:((A Am) (B (not Am)) (Bm (not Am)))
================================================================
tm-name          tm-1191
in-theory        1191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     25
proof            (modus-ponens tm-54 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-3)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1191.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-54, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-1192
in-theory        1192
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) -> (not B))) or ((B and C) -> (not B))) -> (not (B and C)))
theorem-size     20
proof            (modus-ponens tm-47 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-8 tm-4 tm-9 tm-3)
proof-size       76
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1192.         (((A and ((B and C) -> (not B))) or ((B and C) -> (not B))) -> (not (B and C))), M:tm-47, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-1193
in-theory        1193
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> (not A)) and C) or ((A and B) -> (not A))) -> (not (A and B)))
theorem-size     20
proof            (modus-ponens tm-46 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-8 tm-3 tm-9)
proof-size       76
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1193.         (((((A and B) -> (not A)) and C) or ((A and B) -> (not A))) -> (not (A and B))), M:tm-46, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-1194
in-theory        1194
times-derived    1
----------------------------------------------------------------
theorem          (((not A) or ((A and B) -> (not A))) -> (not (A and B)))
theorem-size     14
proof            (modus-ponens tm-44 tm-59 ((A (and Am Bm)) (B (not Am)) (C (not (and Am Bm)))))
axioms-used      (tm-8 tm-1 tm-9 tm-3)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1194.         (((not A) or ((A and B) -> (not A))) -> (not (A and B))), M:tm-44, m:tm-59, u:((A (and Am Bm)) (B (not Am)) (C (not (and Am Bm))))
================================================================
tm-name          tm-1195
in-theory        1195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> (not C)) -> (not (C and D))))
theorem-size     17
proof            (modus-ponens tm-42 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1195.         ((A -> (B or A)) and (((C and D) -> (not C)) -> (not (C and D)))), M:tm-42, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-1196
in-theory        1196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> (not C)) -> (not (C and D))))
theorem-size     17
proof            (modus-ponens tm-32 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1196.         ((A -> (A or B)) and (((C and D) -> (not C)) -> (not (C and D)))), M:tm-32, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-1197
in-theory        1197
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not A)) -> (((A and B) -> (not A)) and (not (A and B))))
theorem-size     18
proof            (modus-ponens tm-24 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       74
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1197.         (((A and B) -> (not A)) -> (((A and B) -> (not A)) and (not (A and B)))), M:tm-24, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-1198
in-theory        1198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> (not C)) -> (not (C and D))))
theorem-size     19
proof            (modus-ponens tm-23 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1198.         ((A -> (B -> (A and B))) and (((C and D) -> (not C)) -> (not (C and D)))), M:tm-23, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-1199
in-theory        1199
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> (not C)) -> (not (C and D))))
theorem-size     17
proof            (modus-ponens tm-22 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1199.         (((A and B) -> B) and (((C and D) -> (not C)) -> (not (C and D)))), M:tm-22, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-1200
in-theory        1200
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> (not C)) -> (not (C and D))))
theorem-size     17
proof            (modus-ponens tm-21 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1200.         (((A and B) -> A) and (((C and D) -> (not C)) -> (not (C and D)))), M:tm-21, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-1201
in-theory        1201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     25
proof            (modus-ponens tm-20 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-3)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1201.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-20, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-1202
in-theory        1202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> (not C)) -> (not (C and D))))
theorem-size     17
proof            (modus-ponens tm-19 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1202.         ((A -> (B -> A)) and (((C and D) -> (not C)) -> (not (C and D)))), M:tm-19, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-1203
in-theory        1203
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not A)) -> ((A and B) -> (not A)))
theorem-size     13
proof            (modus-ponens tm-12 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1203.         (((A and B) -> (not A)) -> ((A and B) -> (not A))), M:tm-12, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-1204
in-theory        1204
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (not (A and B)))) -> (not ((A and B) -> (not A))))
theorem-size     20
proof            (modus-ponens tm-9 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-9 tm-3)
proof-size       58
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1204.         ((((A and B) -> (not A)) -> (not (not (A and B)))) -> (not ((A and B) -> (not A)))), M:tm-9, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-1205
in-theory        1205
times-derived    1
----------------------------------------------------------------
theorem          (((not (A and B)) -> C) -> ((((A and B) -> (not A)) or (not (A and B))) -> C))
theorem-size     20
proof            (modus-ponens tm-8 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-8 tm-9 tm-3)
proof-size       60
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1205.         (((not (A and B)) -> C) -> ((((A and B) -> (not A)) or (not (A and B))) -> C)), M:tm-8, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-1206
in-theory        1206
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> (not B)) -> (not (B and C))))
theorem-size     13
proof            (modus-ponens tm-7 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-7 tm-9 tm-3)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1206.         (A or (((B and C) -> (not B)) -> (not (B and C)))), M:tm-7, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-1207
in-theory        1207
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) or C)
theorem-size     13
proof            (modus-ponens tm-6 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-6 tm-9 tm-3)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1207.         ((((A and B) -> (not A)) -> (not (A and B))) or C), M:tm-6, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-1208
in-theory        1208
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> (not B)) -> (not (B and C))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1208.         (A -> ((((B and C) -> (not B)) -> (not (B and C))) and A)), M:tm-5, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-1209
in-theory        1209
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> (not B)) -> (not (B and C))))
theorem-size     13
proof            (modus-ponens tm-1 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-1 tm-9 tm-3)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1209.         (A -> (((B and C) -> (not B)) -> (not (B and C)))), M:tm-1, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-1210
in-theory        1210
times-derived    1
----------------------------------------------------------------
theorem          (not ((not A) and A))
theorem-size     5
proof            (modus-ponens tm-60 tm-3 ((A (not Bm)) (B Bm) (Am (not Bm))))
axioms-used      (tm-9 tm-4 tm-3)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-1210.         (not ((not A) and A)), M:tm-60, m:tm-3, u:((A (not Bm)) (B Bm) (Am (not Bm)))
================================================================
tm-name          tm-1211
in-theory        1211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     25
proof            (modus-ponens tm-54 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-4)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1211.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-54, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-1212
in-theory        1212
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) -> (not C))) or ((B and C) -> (not C))) -> (not (B and C)))
theorem-size     20
proof            (modus-ponens tm-47 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-8 tm-4 tm-9)
proof-size       76
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1212.         (((A and ((B and C) -> (not C))) or ((B and C) -> (not C))) -> (not (B and C))), M:tm-47, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-1213
in-theory        1213
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> (not B)) and C) or ((A and B) -> (not B))) -> (not (A and B)))
theorem-size     20
proof            (modus-ponens tm-46 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-8 tm-3 tm-9 tm-4)
proof-size       76
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1213.         (((((A and B) -> (not B)) and C) or ((A and B) -> (not B))) -> (not (A and B))), M:tm-46, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-1214
in-theory        1214
times-derived    1
----------------------------------------------------------------
theorem          (((not A) or ((B and A) -> (not A))) -> (not (B and A)))
theorem-size     14
proof            (modus-ponens tm-44 tm-60 ((A (and Am Bm)) (B (not Bm)) (C (not (and Am Bm)))))
axioms-used      (tm-8 tm-1 tm-9 tm-4)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1214.         (((not A) or ((B and A) -> (not A))) -> (not (B and A))), M:tm-44, m:tm-60, u:((A (and Am Bm)) (B (not Bm)) (C (not (and Am Bm))))
================================================================
tm-name          tm-1215
in-theory        1215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> (not D)) -> (not (C and D))))
theorem-size     17
proof            (modus-ponens tm-42 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1215.         ((A -> (B or A)) and (((C and D) -> (not D)) -> (not (C and D)))), M:tm-42, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-1216
in-theory        1216
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> (not D)) -> (not (C and D))))
theorem-size     17
proof            (modus-ponens tm-32 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1216.         ((A -> (A or B)) and (((C and D) -> (not D)) -> (not (C and D)))), M:tm-32, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-1217
in-theory        1217
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not B)) -> (((A and B) -> (not B)) and (not (A and B))))
theorem-size     18
proof            (modus-ponens tm-24 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       74
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1217.         (((A and B) -> (not B)) -> (((A and B) -> (not B)) and (not (A and B)))), M:tm-24, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-1218
in-theory        1218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> (not D)) -> (not (C and D))))
theorem-size     19
proof            (modus-ponens tm-23 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1218.         ((A -> (B -> (A and B))) and (((C and D) -> (not D)) -> (not (C and D)))), M:tm-23, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-1219
in-theory        1219
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> (not D)) -> (not (C and D))))
theorem-size     17
proof            (modus-ponens tm-22 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1219.         (((A and B) -> B) and (((C and D) -> (not D)) -> (not (C and D)))), M:tm-22, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-1220
in-theory        1220
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> (not D)) -> (not (C and D))))
theorem-size     17
proof            (modus-ponens tm-21 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1220.         (((A and B) -> A) and (((C and D) -> (not D)) -> (not (C and D)))), M:tm-21, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-1221
in-theory        1221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     25
proof            (modus-ponens tm-20 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-4)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1221.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-20, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-1222
in-theory        1222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> (not D)) -> (not (C and D))))
theorem-size     17
proof            (modus-ponens tm-19 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1222.         ((A -> (B -> A)) and (((C and D) -> (not D)) -> (not (C and D)))), M:tm-19, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-1223
in-theory        1223
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not B)) -> ((A and B) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-12 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1223.         (((A and B) -> (not B)) -> ((A and B) -> (not B))), M:tm-12, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-1224
in-theory        1224
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (not (A and B)))) -> (not ((A and B) -> (not B))))
theorem-size     20
proof            (modus-ponens tm-9 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-9 tm-4)
proof-size       58
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1224.         ((((A and B) -> (not B)) -> (not (not (A and B)))) -> (not ((A and B) -> (not B)))), M:tm-9, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-1225
in-theory        1225
times-derived    1
----------------------------------------------------------------
theorem          (((not (A and B)) -> C) -> ((((A and B) -> (not B)) or (not (A and B))) -> C))
theorem-size     20
proof            (modus-ponens tm-8 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-8 tm-9 tm-4)
proof-size       60
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1225.         (((not (A and B)) -> C) -> ((((A and B) -> (not B)) or (not (A and B))) -> C)), M:tm-8, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-1226
in-theory        1226
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> (not C)) -> (not (B and C))))
theorem-size     13
proof            (modus-ponens tm-7 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-7 tm-9 tm-4)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1226.         (A or (((B and C) -> (not C)) -> (not (B and C)))), M:tm-7, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-1227
in-theory        1227
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) or C)
theorem-size     13
proof            (modus-ponens tm-6 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-6 tm-9 tm-4)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1227.         ((((A and B) -> (not B)) -> (not (A and B))) or C), M:tm-6, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-1228
in-theory        1228
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> (not C)) -> (not (B and C))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1228.         (A -> ((((B and C) -> (not C)) -> (not (B and C))) and A)), M:tm-5, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-1229
in-theory        1229
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> (not C)) -> (not (B and C))))
theorem-size     13
proof            (modus-ponens tm-1 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-1 tm-9 tm-4)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1229.         (A -> (((B and C) -> (not C)) -> (not (B and C)))), M:tm-1, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-1230
in-theory        1230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1230.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-54, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-1231
in-theory        1231
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not (C -> (B and C))))) or (B -> (not (C -> (B and C))))) -> (not B))
theorem-size     22
proof            (modus-ponens tm-47 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-5)
proof-size       80
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1231.         (((A and (B -> (not (C -> (B and C))))) or (B -> (not (C -> (B and C))))) -> (not B)), M:tm-47, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-1232
in-theory        1232
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not (B -> (A and B)))) and C) or (A -> (not (B -> (A and B))))) -> (not A))
theorem-size     22
proof            (modus-ponens tm-46 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-5)
proof-size       80
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1232.         ((((A -> (not (B -> (A and B)))) and C) or (A -> (not (B -> (A and B))))) -> (not A)), M:tm-46, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-1233
in-theory        1233
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> (B and A))) or (B -> (not (A -> (B and A))))) -> (not B))
theorem-size     18
proof            (modus-ponens tm-44 tm-61 ((A Am) (B (not (-> Bm (and Am Bm)))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-5)
proof-size       78
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1233.         (((not (A -> (B and A))) or (B -> (not (A -> (B and A))))) -> (not B)), M:tm-44, m:tm-61, u:((A Am) (B (not (-> Bm (and Am Bm)))) (C (not Am)))
================================================================
tm-name          tm-1234
in-theory        1234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not (D -> (C and D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1234.         ((A -> (B or A)) and ((C -> (not (D -> (C and D)))) -> (not C))), M:tm-42, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-1235
in-theory        1235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not (D -> (C and D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1235.         ((A -> (A or B)) and ((C -> (not (D -> (C and D)))) -> (not C))), M:tm-32, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-1236
in-theory        1236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (A and B)))) -> ((A -> (not (B -> (A and B)))) and (not A)))
theorem-size     20
proof            (modus-ponens tm-24 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       78
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1236.         ((A -> (not (B -> (A and B)))) -> ((A -> (not (B -> (A and B)))) and (not A))), M:tm-24, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-1237
in-theory        1237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not (D -> (C and D)))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1237.         ((A -> (B -> (A and B))) and ((C -> (not (D -> (C and D)))) -> (not C))), M:tm-23, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-1238
in-theory        1238
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not (D -> (C and D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1238.         (((A and B) -> B) and ((C -> (not (D -> (C and D)))) -> (not C))), M:tm-22, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-1239
in-theory        1239
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not (D -> (C and D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1239.         (((A and B) -> A) and ((C -> (not (D -> (C and D)))) -> (not C))), M:tm-21, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-1240
in-theory        1240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1240.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-20, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-1241
in-theory        1241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not (D -> (C and D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1241.         ((A -> (B -> A)) and ((C -> (not (D -> (C and D)))) -> (not C))), M:tm-19, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-1242
in-theory        1242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (A and B)))) -> (A -> (not (B -> (A and B)))))
theorem-size     17
proof            (modus-ponens tm-12 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1242.         ((A -> (not (B -> (A and B)))) -> (A -> (not (B -> (A and B))))), M:tm-12, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-1243
in-theory        1243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not (not A))) -> (not (A -> (not (B -> (A and B))))))
theorem-size     22
proof            (modus-ponens tm-9 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-9 tm-5)
proof-size       62
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1243.         (((A -> (not (B -> (A and B)))) -> (not (not A))) -> (not (A -> (not (B -> (A and B)))))), M:tm-9, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-1244
in-theory        1244
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not (C -> (A and C)))) or (not A)) -> B))
theorem-size     18
proof            (modus-ponens tm-8 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-5)
proof-size       60
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1244.         (((not A) -> B) -> (((A -> (not (C -> (A and C)))) or (not A)) -> B)), M:tm-8, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-1245
in-theory        1245
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not (C -> (B and C)))) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-5)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1245.         (A or ((B -> (not (C -> (B and C)))) -> (not B))), M:tm-7, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-1246
in-theory        1246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) or C)
theorem-size     13
proof            (modus-ponens tm-6 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-5)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1246.         (((A -> (not (B -> (A and B)))) -> (not A)) or C), M:tm-6, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-1247
in-theory        1247
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not (C -> (B and C)))) -> (not B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-9)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1247.         (A -> (((B -> (not (C -> (B and C)))) -> (not B)) and A)), M:tm-5, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-1248
in-theory        1248
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not (C -> (B and C)))) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-5)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1248.         (A -> ((B -> (not (C -> (B and C)))) -> (not B))), M:tm-1, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-1249
in-theory        1249
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (D or E))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-54 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-6)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1249.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (D or E))) -> (not D))), M:tm-54, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-1250
in-theory        1250
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not (B or C)))) or (B -> (not (B or C)))) -> (not B))
theorem-size     18
proof            (modus-ponens tm-47 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-6)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1250.         (((A and (B -> (not (B or C)))) or (B -> (not (B or C)))) -> (not B)), M:tm-47, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-1251
in-theory        1251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not (A or B))) and C) or (A -> (not (A or B)))) -> (not A))
theorem-size     18
proof            (modus-ponens tm-46 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-6)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1251.         ((((A -> (not (A or B))) and C) or (A -> (not (A or B)))) -> (not A)), M:tm-46, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-1252
in-theory        1252
times-derived    1
----------------------------------------------------------------
theorem          (((not (A or B)) or (A -> (not (A or B)))) -> (not A))
theorem-size     14
proof            (modus-ponens tm-44 tm-62 ((A Am) (B (not (or Am Bm))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-6)
proof-size       70
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1252.         (((not (A or B)) or (A -> (not (A or B)))) -> (not A)), M:tm-44, m:tm-62, u:((A Am) (B (not (or Am Bm))) (C (not Am)))
================================================================
tm-name          tm-1253
in-theory        1253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not (C or D))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-42 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1253.         ((A -> (B or A)) and ((C -> (not (C or D))) -> (not C))), M:tm-42, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-1254
in-theory        1254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not (C or D))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-32 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1254.         ((A -> (A or B)) and ((C -> (not (C or D))) -> (not C))), M:tm-32, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-1255
in-theory        1255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A or B))) -> ((A -> (not (A or B))) and (not A)))
theorem-size     16
proof            (modus-ponens tm-24 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       70
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1255.         ((A -> (not (A or B))) -> ((A -> (not (A or B))) and (not A))), M:tm-24, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-1256
in-theory        1256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not (C or D))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-23 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1256.         ((A -> (B -> (A and B))) and ((C -> (not (C or D))) -> (not C))), M:tm-23, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-1257
in-theory        1257
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not (C or D))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-22 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1257.         (((A and B) -> B) and ((C -> (not (C or D))) -> (not C))), M:tm-22, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-1258
in-theory        1258
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not (C or D))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-21 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1258.         (((A and B) -> A) and ((C -> (not (C or D))) -> (not C))), M:tm-21, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-1259
in-theory        1259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (D or E))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-20 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-6)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1259.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (D or E))) -> (not D))), M:tm-20, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-1260
in-theory        1260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not (C or D))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-19 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1260.         ((A -> (B -> A)) and ((C -> (not (C or D))) -> (not C))), M:tm-19, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-1261
in-theory        1261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A or B))) -> (A -> (not (A or B))))
theorem-size     13
proof            (modus-ponens tm-12 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-6)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1261.         ((A -> (not (A or B))) -> (A -> (not (A or B)))), M:tm-12, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-1262
in-theory        1262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not (not A))) -> (not (A -> (not (A or B)))))
theorem-size     18
proof            (modus-ponens tm-9 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-9 tm-6)
proof-size       54
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1262.         (((A -> (not (A or B))) -> (not (not A))) -> (not (A -> (not (A or B))))), M:tm-9, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-1263
in-theory        1263
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not (A or C))) or (not A)) -> B))
theorem-size     16
proof            (modus-ponens tm-8 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-6)
proof-size       54
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1263.         (((not A) -> B) -> (((A -> (not (A or C))) or (not A)) -> B)), M:tm-8, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-1264
in-theory        1264
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not (B or C))) -> (not B)))
theorem-size     11
proof            (modus-ponens tm-7 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-6)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1264.         (A or ((B -> (not (B or C))) -> (not B))), M:tm-7, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-1265
in-theory        1265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) or C)
theorem-size     11
proof            (modus-ponens tm-6 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-6 tm-9)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1265.         (((A -> (not (A or B))) -> (not A)) or C), M:tm-6, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-1266
in-theory        1266
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not (B or C))) -> (not B)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1266.         (A -> (((B -> (not (B or C))) -> (not B)) and A)), M:tm-5, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-1267
in-theory        1267
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not (B or C))) -> (not B)))
theorem-size     11
proof            (modus-ponens tm-1 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-6)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1267.         (A -> ((B -> (not (B or C))) -> (not B))), M:tm-1, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-1268
in-theory        1268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (E or D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-54 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-7)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1268.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (E or D))) -> (not D))), M:tm-54, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-1269
in-theory        1269
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not (C or B)))) or (B -> (not (C or B)))) -> (not B))
theorem-size     18
proof            (modus-ponens tm-47 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-7)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1269.         (((A and (B -> (not (C or B)))) or (B -> (not (C or B)))) -> (not B)), M:tm-47, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-1270
in-theory        1270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not (B or A))) and C) or (A -> (not (B or A)))) -> (not A))
theorem-size     18
proof            (modus-ponens tm-46 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-7)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1270.         ((((A -> (not (B or A))) and C) or (A -> (not (B or A)))) -> (not A)), M:tm-46, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-1271
in-theory        1271
times-derived    1
----------------------------------------------------------------
theorem          (((not (A or B)) or (B -> (not (A or B)))) -> (not B))
theorem-size     14
proof            (modus-ponens tm-44 tm-63 ((A Am) (B (not (or Bm Am))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-7)
proof-size       70
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1271.         (((not (A or B)) or (B -> (not (A or B)))) -> (not B)), M:tm-44, m:tm-63, u:((A Am) (B (not (or Bm Am))) (C (not Am)))
================================================================
tm-name          tm-1272
in-theory        1272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not (D or C))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-42 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1272.         ((A -> (B or A)) and ((C -> (not (D or C))) -> (not C))), M:tm-42, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-1273
in-theory        1273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not (D or C))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-32 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1273.         ((A -> (A or B)) and ((C -> (not (D or C))) -> (not C))), M:tm-32, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-1274
in-theory        1274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B or A))) -> ((A -> (not (B or A))) and (not A)))
theorem-size     16
proof            (modus-ponens tm-24 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       70
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1274.         ((A -> (not (B or A))) -> ((A -> (not (B or A))) and (not A))), M:tm-24, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-1275
in-theory        1275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not (D or C))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-23 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1275.         ((A -> (B -> (A and B))) and ((C -> (not (D or C))) -> (not C))), M:tm-23, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-1276
in-theory        1276
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not (D or C))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-22 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1276.         (((A and B) -> B) and ((C -> (not (D or C))) -> (not C))), M:tm-22, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-1277
in-theory        1277
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not (D or C))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-21 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1277.         (((A and B) -> A) and ((C -> (not (D or C))) -> (not C))), M:tm-21, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-1278
in-theory        1278
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (E or D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-20 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-7)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1278.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (E or D))) -> (not D))), M:tm-20, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-1279
in-theory        1279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not (D or C))) -> (not C)))
theorem-size     15
proof            (modus-ponens tm-19 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1279.         ((A -> (B -> A)) and ((C -> (not (D or C))) -> (not C))), M:tm-19, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-1280
in-theory        1280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B or A))) -> (A -> (not (B or A))))
theorem-size     13
proof            (modus-ponens tm-12 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-7)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1280.         ((A -> (not (B or A))) -> (A -> (not (B or A)))), M:tm-12, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-1281
in-theory        1281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not (not A))) -> (not (A -> (not (B or A)))))
theorem-size     18
proof            (modus-ponens tm-9 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-9 tm-7)
proof-size       54
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1281.         (((A -> (not (B or A))) -> (not (not A))) -> (not (A -> (not (B or A))))), M:tm-9, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-1282
in-theory        1282
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not (C or A))) or (not A)) -> B))
theorem-size     16
proof            (modus-ponens tm-8 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-7)
proof-size       54
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1282.         (((not A) -> B) -> (((A -> (not (C or A))) or (not A)) -> B)), M:tm-8, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-1283
in-theory        1283
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not (C or B))) -> (not B)))
theorem-size     11
proof            (modus-ponens tm-7 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-7 tm-9)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1283.         (A or ((B -> (not (C or B))) -> (not B))), M:tm-7, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-1284
in-theory        1284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) or C)
theorem-size     11
proof            (modus-ponens tm-6 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-7)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1284.         (((A -> (not (B or A))) -> (not A)) or C), M:tm-6, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-1285
in-theory        1285
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not (C or B))) -> (not B)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1285.         (A -> (((B -> (not (C or B))) -> (not B)) and A)), M:tm-5, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-1286
in-theory        1286
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not (C or B))) -> (not B)))
theorem-size     11
proof            (modus-ponens tm-1 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-7)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1286.         (A -> ((B -> (not (C or B))) -> (not B))), M:tm-1, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-1287
in-theory        1287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     33
proof            (modus-ponens tm-54 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1287.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-54, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1288
in-theory        1288
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> (not ((C -> D) -> ((B or C) -> D))))) or ((B -> C) -> (not ((C -> D) -> ((B or C) -> D))))) -> (not (B -> C)))
theorem-size     36
proof            (modus-ponens tm-47 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-4 tm-9)
proof-size       108
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1288.         (((A and ((B -> C) -> (not ((C -> D) -> ((B or C) -> D))))) or ((B -> C) -> (not ((C -> D) -> ((B or C) -> D))))) -> (not (B -> C))), M:tm-47, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-1289
in-theory        1289
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) and D) or ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))) -> (not (A -> B)))
theorem-size     36
proof            (modus-ponens tm-46 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-3 tm-9)
proof-size       108
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1289.         (((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) and D) or ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))) -> (not (A -> B))), M:tm-46, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-1290
in-theory        1290
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A -> B) -> ((C or A) -> B))) or ((C -> A) -> (not ((A -> B) -> ((C or A) -> B))))) -> (not (C -> A)))
theorem-size     30
proof            (modus-ponens tm-44 tm-64 ((A (-> Am Bm)) (B (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (C (not (-> Am Bm)))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       104
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1290.         (((not ((A -> B) -> ((C or A) -> B))) or ((C -> A) -> (not ((A -> B) -> ((C or A) -> B))))) -> (not (C -> A))), M:tm-44, m:tm-64, u:((A (-> Am Bm)) (B (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (C (not (-> Am Bm))))
================================================================
tm-name          tm-1291
in-theory        1291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D))))
theorem-size     25
proof            (modus-ponens tm-42 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1291.         ((A -> (B or A)) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D)))), M:tm-42, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1292
in-theory        1292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D))))
theorem-size     25
proof            (modus-ponens tm-32 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1292.         ((A -> (A or B)) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D)))), M:tm-32, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1293
in-theory        1293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) and (not (A -> B))))
theorem-size     34
proof            (modus-ponens tm-24 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       106
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1293.         (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) and (not (A -> B)))), M:tm-24, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-1294
in-theory        1294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D))))
theorem-size     27
proof            (modus-ponens tm-23 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1294.         ((A -> (B -> (A and B))) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D)))), M:tm-23, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1295
in-theory        1295
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D))))
theorem-size     25
proof            (modus-ponens tm-22 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1295.         (((A and B) -> B) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D)))), M:tm-22, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1296
in-theory        1296
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D))))
theorem-size     25
proof            (modus-ponens tm-21 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1296.         (((A and B) -> A) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D)))), M:tm-21, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1297
in-theory        1297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     33
proof            (modus-ponens tm-20 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1297.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-20, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1298
in-theory        1298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D))))
theorem-size     25
proof            (modus-ponens tm-19 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1298.         ((A -> (B -> A)) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D)))), M:tm-19, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1299
in-theory        1299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> ((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-12 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-8)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1299.         (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))), M:tm-12, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-1300
in-theory        1300
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))))
theorem-size     36
proof            (modus-ponens tm-9 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-9 tm-8)
proof-size       90
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1300.         ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))))), M:tm-9, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-1301
in-theory        1301
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> B)) -> C) -> ((((A -> B) -> (not ((B -> D) -> ((A or B) -> D)))) or (not (A -> B))) -> C))
theorem-size     28
proof            (modus-ponens tm-8 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-9)
proof-size       84
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1301.         (((not (A -> B)) -> C) -> ((((A -> B) -> (not ((B -> D) -> ((A or B) -> D)))) or (not (A -> B))) -> C)), M:tm-8, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-1302
in-theory        1302
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> (not ((C -> D) -> ((B or C) -> D)))) -> (not (B -> C))))
theorem-size     21
proof            (modus-ponens tm-7 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-7 tm-9 tm-8)
proof-size       69
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1302.         (A or (((B -> C) -> (not ((C -> D) -> ((B or C) -> D)))) -> (not (B -> C)))), M:tm-7, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1303
in-theory        1303
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) or D)
theorem-size     21
proof            (modus-ponens tm-6 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-6 tm-9 tm-8)
proof-size       69
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1303.         ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) or D), M:tm-6, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1304
in-theory        1304
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (not ((C -> D) -> ((B or C) -> D)))) -> (not (B -> C))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       73
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1304.         (A -> ((((B -> C) -> (not ((C -> D) -> ((B or C) -> D)))) -> (not (B -> C))) and A)), M:tm-5, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1305
in-theory        1305
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (not ((C -> D) -> ((B or C) -> D)))) -> (not (B -> C))))
theorem-size     21
proof            (modus-ponens tm-1 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-1 tm-9 tm-8)
proof-size       69
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1305.         (A -> (((B -> C) -> (not ((C -> D) -> ((B or C) -> D)))) -> (not (B -> C)))), M:tm-1, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1306
in-theory        1306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-54 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1306.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-54, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1307
in-theory        1307
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> (not ((B -> (not C)) -> (not B))))) or ((B -> C) -> (not ((B -> (not C)) -> (not B))))) -> (not (B -> C)))
theorem-size     32
proof            (modus-ponens tm-47 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-4 tm-9)
proof-size       100
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1307.         (((A and ((B -> C) -> (not ((B -> (not C)) -> (not B))))) or ((B -> C) -> (not ((B -> (not C)) -> (not B))))) -> (not (B -> C))), M:tm-47, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-1308
in-theory        1308
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (not ((A -> (not B)) -> (not A)))) and C) or ((A -> B) -> (not ((A -> (not B)) -> (not A))))) -> (not (A -> B)))
theorem-size     32
proof            (modus-ponens tm-46 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-3 tm-9)
proof-size       100
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1308.         (((((A -> B) -> (not ((A -> (not B)) -> (not A)))) and C) or ((A -> B) -> (not ((A -> (not B)) -> (not A))))) -> (not (A -> B))), M:tm-46, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-1309
in-theory        1309
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A -> (not B)) -> (not A))) or ((A -> B) -> (not ((A -> (not B)) -> (not A))))) -> (not (A -> B)))
theorem-size     26
proof            (modus-ponens tm-44 tm-65 ((A (-> Am Bm)) (B (not (-> (-> Am (not Bm)) (not Am)))) (C (not (-> Am Bm)))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       96
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1309.         (((not ((A -> (not B)) -> (not A))) or ((A -> B) -> (not ((A -> (not B)) -> (not A))))) -> (not (A -> B))), M:tm-44, m:tm-65, u:((A (-> Am Bm)) (B (not (-> (-> Am (not Bm)) (not Am)))) (C (not (-> Am Bm))))
================================================================
tm-name          tm-1310
in-theory        1310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-42 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1310.         ((A -> (B or A)) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D)))), M:tm-42, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1311
in-theory        1311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-32 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1311.         ((A -> (A or B)) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D)))), M:tm-32, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1312
in-theory        1312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (((A -> B) -> (not ((A -> (not B)) -> (not A)))) and (not (A -> B))))
theorem-size     30
proof            (modus-ponens tm-24 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       98
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1312.         (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (((A -> B) -> (not ((A -> (not B)) -> (not A)))) and (not (A -> B)))), M:tm-24, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-1313
in-theory        1313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D))))
theorem-size     25
proof            (modus-ponens tm-23 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1313.         ((A -> (B -> (A and B))) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D)))), M:tm-23, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1314
in-theory        1314
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-22 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1314.         (((A and B) -> B) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D)))), M:tm-22, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1315
in-theory        1315
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-21 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1315.         (((A and B) -> A) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D)))), M:tm-21, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1316
in-theory        1316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-20 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1316.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-20, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1317
in-theory        1317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-19 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1317.         ((A -> (B -> A)) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D)))), M:tm-19, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1318
in-theory        1318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> ((A -> B) -> (not ((A -> (not B)) -> (not A)))))
theorem-size     25
proof            (modus-ponens tm-12 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1318.         (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> ((A -> B) -> (not ((A -> (not B)) -> (not A))))), M:tm-12, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-1319
in-theory        1319
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not ((A -> (not B)) -> (not A))))))
theorem-size     32
proof            (modus-ponens tm-9 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-9)
proof-size       82
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1319.         ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not ((A -> (not B)) -> (not A)))))), M:tm-9, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-1320
in-theory        1320
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> B)) -> C) -> ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) or (not (A -> B))) -> C))
theorem-size     26
proof            (modus-ponens tm-8 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-9)
proof-size       78
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1320.         (((not (A -> B)) -> C) -> ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) or (not (A -> B))) -> C)), M:tm-8, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-1321
in-theory        1321
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> (not ((B -> (not C)) -> (not B)))) -> (not (B -> C))))
theorem-size     19
proof            (modus-ponens tm-7 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-7 tm-9)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1321.         (A or (((B -> C) -> (not ((B -> (not C)) -> (not B)))) -> (not (B -> C)))), M:tm-7, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1322
in-theory        1322
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) or C)
theorem-size     19
proof            (modus-ponens tm-6 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-6 tm-9)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1322.         ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) or C), M:tm-6, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1323
in-theory        1323
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (not ((B -> (not C)) -> (not B)))) -> (not (B -> C))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9)
proof-size       67
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1323.         (A -> ((((B -> C) -> (not ((B -> (not C)) -> (not B)))) -> (not (B -> C))) and A)), M:tm-5, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1324
in-theory        1324
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (not ((B -> (not C)) -> (not B)))) -> (not (B -> C))))
theorem-size     19
proof            (modus-ponens tm-1 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-1 tm-9)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1324.         (A -> (((B -> C) -> (not ((B -> (not C)) -> (not B)))) -> (not (B -> C)))), M:tm-1, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1325
in-theory        1325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((A -> (not B)) -> (not A))))
theorem-size     21
proof            (modus-ponens tm-66 tm-1 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-1)
proof-size       73
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-1325.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-1, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-1326
in-theory        1326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (((A -> (not B)) -> (not A)) and C)))
theorem-size     23
proof            (modus-ponens tm-66 tm-5 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> (-> A (not B)) (not A)) Bm)))))
axioms-used      (tm-8 tm-9 tm-5)
proof-size       77
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1326.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (((A -> (not B)) -> (not A)) and C))), M:tm-66, m:tm-5, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> (-> A (not B)) (not A)) Bm))))
================================================================
tm-name          tm-1327
in-theory        1327
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) or C))
theorem-size     21
proof            (modus-ponens tm-66 tm-6 ((Am (-> (-> A (not B)) (not A))) (C (or (-> (-> A (not B)) (not A)) Bm))))
axioms-used      (tm-8 tm-9 tm-6)
proof-size       73
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-1327.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) or C)), M:tm-66, m:tm-6, u:((Am (-> (-> A (not B)) (not A))) (C (or (-> (-> A (not B)) (not A)) Bm)))
================================================================
tm-name          tm-1328
in-theory        1328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or ((A -> (not B)) -> (not A))))
theorem-size     21
proof            (modus-ponens tm-66 tm-7 ((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-7)
proof-size       73
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-1328.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-7, u:((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-1329
in-theory        1329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((not A) -> C) -> (((A -> (not B)) or (not A)) -> C)))
theorem-size     26
proof            (modus-ponens tm-66 tm-8 ((Am (-> A (not B))) (Bm (not A)) (C (-> (-> (not A) Cm) (-> (or (-> A (not B)) (not A)) Cm)))))
axioms-used      (tm-8 tm-9)
proof-size       86
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1329.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((not A) -> C) -> (((A -> (not B)) or (not A)) -> C))), M:tm-66, m:tm-8, u:((Am (-> A (not B))) (Bm (not A)) (C (-> (-> (not A) Cm) (-> (or (-> A (not B)) (not A)) Cm))))
================================================================
tm-name          tm-1330
in-theory        1330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not (not A))) -> (not (A -> (not B)))))
theorem-size     26
proof            (modus-ponens tm-66 tm-9 ((Am (-> A (not B))) (Bm (not A)) (C (-> (-> (-> A (not B)) (not (not A))) (not (-> A (not B)))))))
axioms-used      (tm-8 tm-9)
proof-size       84
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1330.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not (not A))) -> (not (A -> (not B))))), M:tm-66, m:tm-9, u:((Am (-> A (not B))) (Bm (not A)) (C (-> (-> (-> A (not B)) (not (not A))) (not (-> A (not B))))))
================================================================
tm-name          tm-1331
in-theory        1331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-66 tm-11 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-9 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1331.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (D -> C))), M:tm-66, m:tm-11, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-1332
in-theory        1332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> (A -> (not B))))
theorem-size     21
proof            (modus-ponens tm-66 tm-12 ((Am (-> A (not B))) (Bm (not A)) (C (-> (-> A (not B)) (-> A (not B))))))
axioms-used      (tm-8 tm-9 tm-2 tm-1)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-1332.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> (A -> (not B)))), M:tm-66, m:tm-12, u:((Am (-> A (not B))) (Bm (not A)) (C (-> (-> A (not B)) (-> A (not B)))))
================================================================
tm-name          tm-1333
in-theory        1333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-66 tm-14 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-9 tm-1 tm-2)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1333.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-66, m:tm-14, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-1334
in-theory        1334
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-66 tm-16 ((Am (-> (-> A (not B)) (not A))) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-9 tm-1 tm-3)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1334.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C and D) -> C)), M:tm-66, m:tm-16, u:((Am (-> (-> A (not B)) (not A))) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-1335
in-theory        1335
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-66 tm-18 ((Am (-> (-> A (not B)) (not A))) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-9 tm-1 tm-4)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1335.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C and D) -> D)), M:tm-66, m:tm-18, u:((Am (-> (-> A (not B)) (not A))) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-1336
in-theory        1336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> C)) and ((A -> (not B)) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-66 tm-19 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> Cm Bm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-1)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1336.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> C)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-19, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> Cm Bm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-1337
in-theory        1337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> (not B)) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-66 tm-20 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-2)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1337.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-20, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-1338
in-theory        1338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C and D) -> C) and ((A -> (not B)) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-66 tm-21 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (and Bm Cm) Bm) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-3)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1338.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C and D) -> C) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-21, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (and Bm Cm) Bm) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-1339
in-theory        1339
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C and D) -> D) and ((A -> (not B)) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-66 tm-22 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (and Bm Cm) Cm) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-4)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1339.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C and D) -> D) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-22, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (and Bm Cm) Cm) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-1340
in-theory        1340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> (C and D))) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-23 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1340.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> (C and D))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-23, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-1341
in-theory        1341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> ((A -> (not B)) and (not A))))
theorem-size     24
proof            (modus-ponens tm-66 tm-24 ((Am (-> A (not B))) (Bm (not A)) (C (-> (-> A (not B)) (and (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5)
proof-size       100
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1341.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> ((A -> (not B)) and (not A)))), M:tm-66, m:tm-24, u:((Am (-> A (not B))) (Bm (not A)) (C (-> (-> A (not B)) (and (-> A (not B)) (not A)))))
================================================================
tm-name          tm-1342
in-theory        1342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-66 tm-25 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-9 tm-1 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1342.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (D -> (C and D)))), M:tm-66, m:tm-25, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-1343
in-theory        1343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (C or D)) and ((A -> (not B)) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-66 tm-32 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (or Bm Cm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-6)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1343.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (C or D)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-32, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (or Bm Cm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-1344
in-theory        1344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-66 tm-33 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-6)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1344.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (C or D))), M:tm-66, m:tm-33, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-1345
in-theory        1345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D or C)) and ((A -> (not B)) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-66 tm-42 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (or Cm Bm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-7)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1345.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D or C)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-42, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (or Cm Bm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-1346
in-theory        1346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-66 tm-43 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-7)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1346.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (D or C))), M:tm-66, m:tm-43, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-1347
in-theory        1347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((not B) or (A -> (not B))) -> (not A)))
theorem-size     22
proof            (modus-ponens tm-66 tm-44 ((A Am) (Bm (not B)) (Cm (not Am)) (C (-> (or (not B) (-> Am (not B))) (not Am)))))
axioms-used      (tm-8 tm-9 tm-1)
proof-size       100
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1347.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((not B) or (A -> (not B))) -> (not A))), M:tm-66, m:tm-44, u:((A Am) (Bm (not B)) (Cm (not Am)) (C (-> (or (not B) (-> Am (not B))) (not Am))))
================================================================
tm-name          tm-1348
in-theory        1348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((A -> (not B)) and C) or (A -> (not B))) -> (not A)))
theorem-size     26
proof            (modus-ponens tm-66 tm-46 ((Am (-> A (not B))) (Bm (not A)) (C (-> (or (and (-> A (not B)) Cm) (-> A (not B))) (not A)))))
axioms-used      (tm-8 tm-9 tm-3)
proof-size       102
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1348.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((A -> (not B)) and C) or (A -> (not B))) -> (not A))), M:tm-66, m:tm-46, u:((Am (-> A (not B))) (Bm (not A)) (C (-> (or (and (-> A (not B)) Cm) (-> A (not B))) (not A))))
================================================================
tm-name          tm-1349
in-theory        1349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C and (A -> (not B))) or (A -> (not B))) -> (not A)))
theorem-size     26
proof            (modus-ponens tm-66 tm-47 ((Am (-> A (not B))) (Bm (not A)) (C (-> (or (and Cm (-> A (not B))) (-> A (not B))) (not A)))))
axioms-used      (tm-8 tm-9 tm-4)
proof-size       102
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1349.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C and (A -> (not B))) or (A -> (not B))) -> (not A))), M:tm-66, m:tm-47, u:((Am (-> A (not B))) (Bm (not A)) (C (-> (or (and Cm (-> A (not B))) (-> A (not B))) (not A))))
================================================================
tm-name          tm-1350
in-theory        1350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((A -> (not B)) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-66 tm-54 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1350.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-54, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-1351
in-theory        1351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-66 tm-56 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-9 tm-1)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1351.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-66, m:tm-56, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1352
in-theory        1352
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> A) or (((A -> (not B)) -> (not A)) -> (not (A -> (not B))))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> (not (A -> (not B)))))
theorem-size     38
proof            (modus-ponens tm-66 tm-66 ((A (-> Am (not Bm))) (B Am) (Cm (not (-> Am (not Bm)))) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (not (-> Am (not Bm)))))))
axioms-used      (tm-8 tm-9)
proof-size       132
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1352.         ((((A -> (not B)) -> A) or (((A -> (not B)) -> (not A)) -> (not (A -> (not B))))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> (not (A -> (not B))))), M:tm-66, m:tm-66, u:((A (-> Am (not Bm))) (B Am) (Cm (not (-> Am (not Bm)))) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (not (-> Am (not Bm))))))
================================================================
tm-name          tm-1353
in-theory        1353
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> ((A -> B) or ((A -> (not B)) -> (not A)))) -> ((((A -> (not B)) -> (not A)) or ((A -> B) or ((A -> (not B)) -> (not A)))) -> ((A -> B) or ((A -> (not B)) -> (not A)))))
theorem-size     51
proof            (modus-ponens tm-55 tm-66 ((A (-> (-> Am (not Bm)) (not Am))) (Cm (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))) (B (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))) (C (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-8 tm-9)
proof-size       141
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1353.         ((((A -> (not B)) -> (not A)) -> ((A -> B) or ((A -> (not B)) -> (not A)))) -> ((((A -> (not B)) -> (not A)) or ((A -> B) or ((A -> (not B)) -> (not A)))) -> ((A -> B) or ((A -> (not B)) -> (not A))))), M:tm-55, m:tm-66, u:((A (-> (-> Am (not Bm)) (not Am))) (Cm (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))) (B (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))) (C (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-1354
in-theory        1354
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-54 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       121
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1354.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-54, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-1355
in-theory        1355
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (not C))) or (((B -> (not C)) -> (not B)) -> ((A or (B -> (not C))) -> (not B)))) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> ((A or (B -> (not C))) -> (not B))))
theorem-size     46
proof            (modus-ponens tm-51 tm-66 ((A (-> Am (not Bm))) (B (not Am)) (Cm (-> (or C (-> Am (not Bm))) (not Am))) (D (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (-> (or C (-> Am (not Bm))) (not Am))))))
axioms-used      (tm-8 tm-9)
proof-size       146
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1355.         (((A -> (B -> (not C))) or (((B -> (not C)) -> (not B)) -> ((A or (B -> (not C))) -> (not B)))) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> ((A or (B -> (not C))) -> (not B)))), M:tm-51, m:tm-66, u:((A (-> Am (not Bm))) (B (not Am)) (Cm (-> (or C (-> Am (not Bm))) (not Am))) (D (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (-> (or C (-> Am (not Bm))) (not Am)))))
================================================================
tm-name          tm-1356
in-theory        1356
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (not C)) -> (not B)) -> (A and ((B -> (not C)) -> (not B))))) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> (A and ((B -> (not C)) -> (not B)))))
theorem-size     41
proof            (modus-ponens tm-48 tm-66 ((A (-> (-> Am (not Bm)) (not Am))) (Cm (and B (-> (-> Am (not Bm)) (not Am)))) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (and B (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-8 tm-5 tm-9)
proof-size       125
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1356.         ((A or (((B -> (not C)) -> (not B)) -> (A and ((B -> (not C)) -> (not B))))) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> (A and ((B -> (not C)) -> (not B))))), M:tm-48, m:tm-66, u:((A (-> (-> Am (not Bm)) (not Am))) (Cm (and B (-> (-> Am (not Bm)) (not Am)))) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (and B (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-1357
in-theory        1357
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B -> (not C)) -> (not B)) -> D)) or (((B -> (not C)) -> (not B)) -> D)) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> D))
theorem-size     35
proof            (modus-ponens tm-47 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-8 tm-4 tm-9)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1357.         (((A and (((B -> (not C)) -> (not B)) -> D)) or (((B -> (not C)) -> (not B)) -> D)) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> D)), M:tm-47, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1358
in-theory        1358
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (not B)) -> (not A)) -> C) and D) or (((A -> (not B)) -> (not A)) -> C)) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))
theorem-size     35
proof            (modus-ponens tm-46 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-8 tm-3 tm-9)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1358.         ((((((A -> (not B)) -> (not A)) -> C) and D) or (((A -> (not B)) -> (not A)) -> C)) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-46, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1359
in-theory        1359
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> ((not A) -> C)) or (((A -> (not B)) -> (not A)) -> ((A -> (not B)) -> C))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> C)))
theorem-size     43
proof            (modus-ponens tm-45 tm-66 ((A (-> Am (not Bm))) (B (not Am)) (Cm (-> (-> Am (not Bm)) C)) (D (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (-> (-> Am (not Bm)) C)))))
axioms-used      (tm-8 tm-2 tm-9)
proof-size       141
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1359.         ((((A -> (not B)) -> ((not A) -> C)) or (((A -> (not B)) -> (not A)) -> ((A -> (not B)) -> C))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> C))), M:tm-45, m:tm-66, u:((A (-> Am (not Bm))) (B (not Am)) (Cm (-> (-> Am (not Bm)) C)) (D (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (-> (-> Am (not Bm)) C))))
================================================================
tm-name          tm-1360
in-theory        1360
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (not C)) -> (not B)) -> A)) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> A))
theorem-size     25
proof            (modus-ponens tm-44 tm-66 ((A (-> (-> Am (not Bm)) (not Am))) (B Cm) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1360.         ((A or (((B -> (not C)) -> (not B)) -> A)) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> A)), M:tm-44, m:tm-66, u:((A (-> (-> Am (not Bm)) (not Am))) (B Cm) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1361
in-theory        1361
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E)))
theorem-size     29
proof            (modus-ponens tm-42 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1361.         ((A -> (B or A)) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E))), M:tm-42, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-1362
in-theory        1362
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E)))
theorem-size     29
proof            (modus-ponens tm-32 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1362.         ((A -> (A or B)) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E))), M:tm-32, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-1363
in-theory        1363
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> C) -> ((((A -> (not B)) -> (not A)) -> C) and (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))
theorem-size     33
proof            (modus-ponens tm-24 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1363.         ((((A -> (not B)) -> (not A)) -> C) -> ((((A -> (not B)) -> (not A)) -> C) and (((A -> B) or ((A -> (not B)) -> (not A))) -> C))), M:tm-24, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1364
in-theory        1364
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E)))
theorem-size     31
proof            (modus-ponens tm-23 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1364.         ((A -> (B -> (A and B))) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E))), M:tm-23, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-1365
in-theory        1365
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E)))
theorem-size     29
proof            (modus-ponens tm-22 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-9)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1365.         (((A and B) -> B) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E))), M:tm-22, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-1366
in-theory        1366
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E)))
theorem-size     29
proof            (modus-ponens tm-21 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-9)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1366.         (((A and B) -> A) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E))), M:tm-21, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-1367
in-theory        1367
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-20 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-9)
proof-size       121
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1367.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-20, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-1368
in-theory        1368
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E)))
theorem-size     29
proof            (modus-ponens tm-19 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1368.         ((A -> (B -> A)) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E))), M:tm-19, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-1369
in-theory        1369
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> C) -> (((A -> (not B)) -> (not A)) -> C))
theorem-size     19
proof            (modus-ponens tm-12 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-9)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1369.         ((((A -> (not B)) -> (not A)) -> C) -> (((A -> (not B)) -> (not A)) -> C)), M:tm-12, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1370
in-theory        1370
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (not (((A -> B) or ((A -> (not B)) -> (not A))) -> C))) -> (not (((A -> (not B)) -> (not A)) -> C)))
theorem-size     35
proof            (modus-ponens tm-9 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-9 tm-8)
proof-size       93
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1370.         (((((A -> (not B)) -> (not A)) -> C) -> (not (((A -> B) or ((A -> (not B)) -> (not A))) -> C))) -> (not (((A -> (not B)) -> (not A)) -> C))), M:tm-9, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1371
in-theory        1371
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) or ((A -> (not B)) -> (not A))) -> C) -> D) -> (((((A -> (not B)) -> (not A)) -> C) or (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) -> D))
theorem-size     41
proof            (modus-ponens tm-8 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-8 tm-9)
proof-size       101
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1371.         (((((A -> B) or ((A -> (not B)) -> (not A))) -> C) -> D) -> (((((A -> (not B)) -> (not A)) -> C) or (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) -> D)), M:tm-8, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1372
in-theory        1372
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> (not C)) -> (not B)) -> D) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> D)))
theorem-size     25
proof            (modus-ponens tm-7 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-7 tm-8 tm-9)
proof-size       77
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1372.         (A or ((((B -> (not C)) -> (not B)) -> D) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> D))), M:tm-7, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-1373
in-theory        1373
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) or D)
theorem-size     25
proof            (modus-ponens tm-6 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-6 tm-8 tm-9)
proof-size       77
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1373.         (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) or D), M:tm-6, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-1374
in-theory        1374
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> (not C)) -> (not B)) -> D) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> D)) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       81
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1374.         (A -> (((((B -> (not C)) -> (not B)) -> D) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> D)) and A)), M:tm-5, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-1375
in-theory        1375
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> ((A -> B) or ((A -> (not B)) -> (not A)))) -> ((((A -> (not B)) -> (not A)) -> C) -> C))
theorem-size     33
proof            (modus-ponens tm-2 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-9)
proof-size       93
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1375.         (((((A -> (not B)) -> (not A)) -> C) -> ((A -> B) or ((A -> (not B)) -> (not A)))) -> ((((A -> (not B)) -> (not A)) -> C) -> C)), M:tm-2, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))) (C Cm))
================================================================
tm-name          tm-1376
in-theory        1376
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (not C)) -> (not B)) -> D) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> D)))
theorem-size     25
proof            (modus-ponens tm-1 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-1 tm-8 tm-9)
proof-size       77
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1376.         (A -> ((((B -> (not C)) -> (not B)) -> D) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> D))), M:tm-1, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-1377
in-theory        1377
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-9)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1377.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-54, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1378
in-theory        1378
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1378.         ((A -> (B or A)) and (C or ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-42, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1379
in-theory        1379
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1379.         ((A -> (A or B)) and (C or ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-32, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1380
in-theory        1380
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1380.         ((A -> (B -> (A and B))) and (C or ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-23, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1381
in-theory        1381
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1381.         (((A and B) -> B) and (C or ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-22, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1382
in-theory        1382
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1382.         (((A and B) -> A) and (C or ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-21, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1383
in-theory        1383
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-9)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1383.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-20, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1384
in-theory        1384
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1384.         ((A -> (B -> A)) and (C or ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-19, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1385
in-theory        1385
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or ((C -> D) -> ((C -> (not D)) -> (not C)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-7 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1385.         (A or (B or ((C -> D) -> ((C -> (not D)) -> (not C))))), M:tm-7, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1386
in-theory        1386
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-6 tm-7 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1386.         ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) or D), M:tm-6, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1387
in-theory        1387
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> D) -> ((C -> (not D)) -> (not C)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1387.         (A -> ((B or ((C -> D) -> ((C -> (not D)) -> (not C)))) and A)), M:tm-5, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1388
in-theory        1388
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or ((C -> D) -> ((C -> (not D)) -> (not C)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-1 tm-7 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1388.         (A -> (B or ((C -> D) -> ((C -> (not D)) -> (not C))))), M:tm-1, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1389
in-theory        1389
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     27
proof            (modus-ponens tm-54 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-8 tm-6 tm-9)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1389.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-54, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1390
in-theory        1390
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E))
theorem-size     19
proof            (modus-ponens tm-42 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1390.         ((A -> (B or A)) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E)), M:tm-42, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1391
in-theory        1391
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E))
theorem-size     19
proof            (modus-ponens tm-32 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1391.         ((A -> (A or B)) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E)), M:tm-32, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1392
in-theory        1392
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E))
theorem-size     21
proof            (modus-ponens tm-23 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1392.         ((A -> (B -> (A and B))) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E)), M:tm-23, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1393
in-theory        1393
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E))
theorem-size     19
proof            (modus-ponens tm-22 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-4 tm-6 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1393.         (((A and B) -> B) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E)), M:tm-22, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1394
in-theory        1394
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E))
theorem-size     19
proof            (modus-ponens tm-21 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-3 tm-6 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1394.         (((A and B) -> A) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E)), M:tm-21, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1395
in-theory        1395
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     27
proof            (modus-ponens tm-20 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-9)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1395.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-20, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1396
in-theory        1396
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E))
theorem-size     19
proof            (modus-ponens tm-19 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1396.         ((A -> (B -> A)) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E)), M:tm-19, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1397
in-theory        1397
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((B -> (not C)) -> (not B))) or D))
theorem-size     15
proof            (modus-ponens tm-7 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-7 tm-6 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1397.         (A or (((B -> C) -> ((B -> (not C)) -> (not B))) or D)), M:tm-7, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1398
in-theory        1398
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-6 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1398.         ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) or D), M:tm-6, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1399
in-theory        1399
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((B -> (not C)) -> (not B))) or D) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1399.         (A -> ((((B -> C) -> ((B -> (not C)) -> (not B))) or D) and A)), M:tm-5, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1400
in-theory        1400
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) or D))
theorem-size     15
proof            (modus-ponens tm-1 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-1 tm-6 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1400.         (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) or D)), M:tm-1, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1401
in-theory        1401
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-69 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-1401.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> C))), M:tm-69, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-1402
in-theory        1402
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       71
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1402.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-69, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-1403
in-theory        1403
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-69 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-1403.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and D) -> C)), M:tm-69, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-1404
in-theory        1404
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-69 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-1404.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and D) -> D)), M:tm-69, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-1405
in-theory        1405
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-69 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-9)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1405.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (C and D)))), M:tm-69, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-1406
in-theory        1406
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-69 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-1406.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C or D))), M:tm-69, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-1407
in-theory        1407
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-69 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-1407.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or C))), M:tm-69, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-1408
in-theory        1408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       71
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1408.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-69, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1409
in-theory        1409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     23
proof            (modus-ponens tm-69 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-9)
proof-size       67
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1409.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-69, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-1410
in-theory        1410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((not (not C)) -> C))
theorem-size     17
proof            (modus-ponens tm-69 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-9 tm-10)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10.           ((not (not A)) -> A), axiom
tm-1410.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((not (not C)) -> C)), M:tm-69, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-1411
in-theory        1411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-69 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1411.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (E -> D)))), M:tm-69, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-1412
in-theory        1412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (C -> C)))
theorem-size     19
proof            (modus-ponens tm-69 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-1412.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (C -> C))), M:tm-69, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-1413
in-theory        1413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     31
proof            (modus-ponens tm-69 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1413.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-69, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-1414
in-theory        1414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1414.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-69, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-1415
in-theory        1415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-69 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1415.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-69, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-1416
in-theory        1416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D and E) -> D)))
theorem-size     19
proof            (modus-ponens tm-69 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-9 tm-1 tm-3)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1416.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D and E) -> D))), M:tm-69, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-1417
in-theory        1417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     27
proof            (modus-ponens tm-69 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1417.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-69, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-1418
in-theory        1418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D and E) -> E)))
theorem-size     19
proof            (modus-ponens tm-69 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-9 tm-1 tm-4)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1418.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D and E) -> E))), M:tm-69, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-1419
in-theory        1419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> D)) and C)))
theorem-size     21
proof            (modus-ponens tm-69 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1419.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> D)) and C))), M:tm-69, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-1420
in-theory        1420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     29
proof            (modus-ponens tm-69 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1420.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-69, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-1421
in-theory        1421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D and E) -> D) and C)))
theorem-size     21
proof            (modus-ponens tm-69 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1421.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D and E) -> D) and C))), M:tm-69, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-1422
in-theory        1422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D and E) -> E) and C)))
theorem-size     21
proof            (modus-ponens tm-69 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1422.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D and E) -> E) and C))), M:tm-69, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-1423
in-theory        1423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1423.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-69, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-1424
in-theory        1424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (C -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-69 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1424.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (C -> (C and D)))), M:tm-69, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-1425
in-theory        1425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1425.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (E -> (D and E))))), M:tm-69, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-1426
in-theory        1426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) or E))
theorem-size     19
proof            (modus-ponens tm-69 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-9 tm-6 tm-1)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1426.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) or E)), M:tm-69, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-1427
in-theory        1427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     27
proof            (modus-ponens tm-69 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1427.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-69, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-1428
in-theory        1428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) or E))
theorem-size     19
proof            (modus-ponens tm-69 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-9 tm-6 tm-3)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1428.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) or E)), M:tm-69, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-1429
in-theory        1429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) or E))
theorem-size     19
proof            (modus-ponens tm-69 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-9 tm-6 tm-4)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1429.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) or E)), M:tm-69, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-1430
in-theory        1430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) or E))
theorem-size     21
proof            (modus-ponens tm-69 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1430.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) or E)), M:tm-69, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-1431
in-theory        1431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) or E))
theorem-size     19
proof            (modus-ponens tm-69 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1431.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) or E)), M:tm-69, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-1432
in-theory        1432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (D or E)) and C)))
theorem-size     21
proof            (modus-ponens tm-69 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1432.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (D or E)) and C))), M:tm-69, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-1433
in-theory        1433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-69 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1433.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (D or E)))), M:tm-69, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-1434
in-theory        1434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-69 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1434.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (E -> D)))), M:tm-69, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-1435
in-theory        1435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1435.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-69, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-1436
in-theory        1436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D and E) -> D)))
theorem-size     19
proof            (modus-ponens tm-69 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-9 tm-7 tm-3)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1436.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D and E) -> D))), M:tm-69, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-1437
in-theory        1437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D and E) -> E)))
theorem-size     19
proof            (modus-ponens tm-69 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-9 tm-7 tm-4)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1437.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D and E) -> E))), M:tm-69, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-1438
in-theory        1438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1438.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (E -> (D and E))))), M:tm-69, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-1439
in-theory        1439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-69 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-6)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1439.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (D or E)))), M:tm-69, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-1440
in-theory        1440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-69 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1440.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (E or D)))), M:tm-69, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-1441
in-theory        1441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) or E))
theorem-size     19
proof            (modus-ponens tm-69 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-9 tm-6 tm-7)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1441.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) or E)), M:tm-69, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-1442
in-theory        1442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E or D)) and C)))
theorem-size     21
proof            (modus-ponens tm-69 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1442.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E or D)) and C))), M:tm-69, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-1443
in-theory        1443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-69 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1443.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (E or D)))), M:tm-69, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-1444
in-theory        1444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-69 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1444.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-69, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-1445
in-theory        1445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     37
proof            (modus-ponens tm-69 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       121
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1445.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-69, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-1446
in-theory        1446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-69 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1446.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-69, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-1447
in-theory        1447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-69 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1447.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-69, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-1448
in-theory        1448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     29
proof            (modus-ponens tm-69 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1448.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-69, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-1449
in-theory        1449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-69 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1449.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-69, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-1450
in-theory        1450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-69 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1450.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-69, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-1451
in-theory        1451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     39
proof            (modus-ponens tm-69 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       125
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1451.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-69, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-1452
in-theory        1452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1452.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-69, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1453
in-theory        1453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     27
proof            (modus-ponens tm-69 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-8)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1453.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-69, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-1454
in-theory        1454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C)))
theorem-size     29
proof            (modus-ponens tm-69 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1454.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C))), M:tm-69, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-1455
in-theory        1455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-69 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1455.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E)))), M:tm-69, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1456
in-theory        1456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1456.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-69, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1457
in-theory        1457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (D -> C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-69 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1457.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (D -> C))) -> (not C))), M:tm-69, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-1458
in-theory        1458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1458.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E))))), M:tm-69, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-1459
in-theory        1459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> (not C)) -> (not (C and D))))
theorem-size     23
proof            (modus-ponens tm-69 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1459.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> (not C)) -> (not (C and D)))), M:tm-69, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-1460
in-theory        1460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> (not D)) -> (not (C and D))))
theorem-size     23
proof            (modus-ponens tm-69 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1460.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> (not D)) -> (not (C and D)))), M:tm-69, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-1461
in-theory        1461
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (D -> (C and D)))) -> (not C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-9)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1461.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (D -> (C and D)))) -> (not C))), M:tm-69, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-1462
in-theory        1462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (C or D))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-69 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1462.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (C or D))) -> (not C))), M:tm-69, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-1463
in-theory        1463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (D or C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-69 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1463.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (D or C))) -> (not C))), M:tm-69, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-1464
in-theory        1464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D))))
theorem-size     31
proof            (modus-ponens tm-69 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1464.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D)))), M:tm-69, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1465
in-theory        1465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D))))
theorem-size     29
proof            (modus-ponens tm-69 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1465.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D)))), M:tm-69, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1466
in-theory        1466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E)))
theorem-size     35
proof            (modus-ponens tm-69 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1466.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E))), M:tm-69, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-1467
in-theory        1467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1467.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-69, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1468
in-theory        1468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E))
theorem-size     25
proof            (modus-ponens tm-69 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1468.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E)), M:tm-69, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1469
in-theory        1469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C)))
theorem-size     27
proof            (modus-ponens tm-69 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-9)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1469.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C))), M:tm-69, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-1470
in-theory        1470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and ((A -> (not B)) -> (not A))))
theorem-size     31
proof            (modus-ponens tm-66 tm-69 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1470.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-69, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-1471
in-theory        1471
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     29
proof            (modus-ponens tm-54 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1471.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-54, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-1472
in-theory        1472
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-51 tm-69 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-9)
proof-size       121
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1472.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-69, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-1473
in-theory        1473
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (B or A)))
theorem-size     21
proof            (modus-ponens tm-50 tm-69 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-9)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1473.         ((A or (B or A)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (B or A))), M:tm-50, m:tm-69, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (or A B))))
================================================================
tm-name          tm-1474
in-theory        1474
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A or B)))
theorem-size     21
proof            (modus-ponens tm-49 tm-69 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-9)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1474.         ((A or (A or B)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A or B))), M:tm-49, m:tm-69, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (or A B))))
================================================================
tm-name          tm-1475
in-theory        1475
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-48 tm-69 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-9)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1475.         ((A or (B -> (A and B))) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (B -> (A and B)))), M:tm-48, m:tm-69, u:((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A (and B A)))))
================================================================
tm-name          tm-1476
in-theory        1476
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and B))
theorem-size     19
proof            (modus-ponens tm-47 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1476.         (((A and B) or B) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and B)), M:tm-47, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-1477
in-theory        1477
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and A))
theorem-size     19
proof            (modus-ponens tm-46 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1477.         (((A and B) or A) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and A)), M:tm-46, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-1478
in-theory        1478
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-45 tm-69 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-9)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1478.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-69, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-1479
in-theory        1479
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (B -> A)))
theorem-size     21
proof            (modus-ponens tm-44 tm-69 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-9)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1479.         ((A or (B -> A)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (B -> A))), M:tm-44, m:tm-69, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A B))))
================================================================
tm-name          tm-1480
in-theory        1480
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C)))
theorem-size     21
proof            (modus-ponens tm-42 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1480.         ((A -> (B or A)) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C))), M:tm-42, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-1481
in-theory        1481
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C)))
theorem-size     21
proof            (modus-ponens tm-32 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1481.         ((A -> (A or B)) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C))), M:tm-32, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-1482
in-theory        1482
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> C) -> ((B -> (not C)) -> (not B))) and A)))
theorem-size     17
proof            (modus-ponens tm-24 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1482.         (A -> (A and (((B -> C) -> ((B -> (not C)) -> (not B))) and A))), M:tm-24, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-1483
in-theory        1483
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C)))
theorem-size     23
proof            (modus-ponens tm-23 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1483.         ((A -> (B -> (A and B))) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C))), M:tm-23, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-1484
in-theory        1484
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C)))
theorem-size     21
proof            (modus-ponens tm-22 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1484.         (((A and B) -> B) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C))), M:tm-22, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-1485
in-theory        1485
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C)))
theorem-size     21
proof            (modus-ponens tm-21 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1485.         (((A and B) -> A) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C))), M:tm-21, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-1486
in-theory        1486
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     29
proof            (modus-ponens tm-20 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1486.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-20, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-1487
in-theory        1487
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C)))
theorem-size     21
proof            (modus-ponens tm-19 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1487.         ((A -> (B -> A)) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C))), M:tm-19, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-1488
in-theory        1488
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> C) -> ((B -> (not C)) -> (not B))) and A))) -> (not A))
theorem-size     19
proof            (modus-ponens tm-9 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-9 tm-5)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1488.         ((A -> (not (((B -> C) -> ((B -> (not C)) -> (not B))) and A))) -> (not A)), M:tm-9, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-1489
in-theory        1489
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> (not B)) -> (not A))) and C) -> D) -> ((C or (((A -> B) -> ((A -> (not B)) -> (not A))) and C)) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-8 tm-5 tm-9)
proof-size       79
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1489.         (((((A -> B) -> ((A -> (not B)) -> (not A))) and C) -> D) -> ((C or (((A -> B) -> ((A -> (not B)) -> (not A))) and C)) -> D)), M:tm-8, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-1490
in-theory        1490
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> D) -> ((C -> (not D)) -> (not C))) and B)))
theorem-size     17
proof            (modus-ponens tm-7 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-7 tm-5 tm-9)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1490.         (A or (B -> (((C -> D) -> ((C -> (not D)) -> (not C))) and B))), M:tm-7, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-1491
in-theory        1491
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-6 tm-5 tm-9)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1491.         ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) or D), M:tm-6, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-1492
in-theory        1492
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> D) -> ((C -> (not D)) -> (not C))) and B)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-9)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1492.         (A -> ((B -> (((C -> D) -> ((C -> (not D)) -> (not C))) and B)) and A)), M:tm-5, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-1493
in-theory        1493
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> D) -> ((C -> (not D)) -> (not C))) and B)))
theorem-size     17
proof            (modus-ponens tm-1 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-1 tm-5 tm-9)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1493.         (A -> (B -> (((C -> D) -> ((C -> (not D)) -> (not C))) and B))), M:tm-1, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-1494
in-theory        1494
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> A) -> (not (not A)))
theorem-size     8
proof            (modus-ponens tm-70 tm-12 ((B Bm) (A (not Bm)) (Am (not Bm))))
axioms-used      (tm-2 tm-9 tm-1)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-1494.         (((not A) -> A) -> (not (not A))), M:tm-70, m:tm-12, u:((B Bm) (A (not Bm)) (Am (not Bm)))
================================================================
tm-name          tm-1495
in-theory        1495
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not A)) and B) -> A) -> (not ((A -> (not A)) and B)))
theorem-size     16
proof            (modus-ponens tm-70 tm-15 ((B Am) (A (and (-> Am (not Am)) Cm)) (Bm (not Am))))
axioms-used      (tm-2 tm-9 tm-3)
proof-size       88
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1495.         ((((A -> (not A)) and B) -> A) -> (not ((A -> (not A)) and B))), M:tm-70, m:tm-15, u:((B Am) (A (and (-> Am (not Am)) Cm)) (Bm (not Am)))
================================================================
tm-name          tm-1496
in-theory        1496
times-derived    1
----------------------------------------------------------------
theorem          ((((not A) and B) -> A) -> (not ((not A) and B)))
theorem-size     12
proof            (modus-ponens tm-70 tm-16 ((Am (-> (and (not B) Cm) B)) (A (and (not B) Cm)) (Bm (not B))))
axioms-used      (tm-2 tm-9 tm-1 tm-3)
proof-size       68
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1496.         ((((not A) and B) -> A) -> (not ((not A) and B))), M:tm-70, m:tm-16, u:((Am (-> (and (not B) Cm) B)) (A (and (not B) Cm)) (Bm (not B)))
================================================================
tm-name          tm-1497
in-theory        1497
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not B))) -> B) -> (not (A and (B -> (not B)))))
theorem-size     16
proof            (modus-ponens tm-70 tm-17 ((B Bm) (A (and Am (-> Bm (not Bm)))) (Cm (not Bm))))
axioms-used      (tm-2 tm-9 tm-4)
proof-size       88
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1497.         (((A and (B -> (not B))) -> B) -> (not (A and (B -> (not B))))), M:tm-70, m:tm-17, u:((B Bm) (A (and Am (-> Bm (not Bm)))) (Cm (not Bm)))
================================================================
tm-name          tm-1498
in-theory        1498
times-derived    1
----------------------------------------------------------------
theorem          (((A and (not B)) -> B) -> (not (A and (not B))))
theorem-size     12
proof            (modus-ponens tm-70 tm-18 ((Am (-> (and Bm (not B)) B)) (A (and Bm (not B))) (Cm (not B))))
axioms-used      (tm-2 tm-9 tm-1 tm-4)
proof-size       68
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1498.         (((A and (not B)) -> B) -> (not (A and (not B)))), M:tm-70, m:tm-18, u:((Am (-> (and Bm (not B)) B)) (A (and Bm (not B))) (Cm (not B)))
================================================================
tm-name          tm-1499
in-theory        1499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C))))
theorem-size     27
proof            (modus-ponens tm-69 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1499.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C)))), M:tm-69, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-1500
in-theory        1500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     29
proof            (modus-ponens tm-54 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1500.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-54, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-1501
in-theory        1501
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> (B -> (not C)))) or ((B -> C) -> (B -> (not C)))) -> ((B -> C) -> (not B)))
theorem-size     26
proof            (modus-ponens tm-47 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-8 tm-4 tm-2 tm-9)
proof-size       94
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1501.         (((A and ((B -> C) -> (B -> (not C)))) or ((B -> C) -> (B -> (not C)))) -> ((B -> C) -> (not B))), M:tm-47, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-1502
in-theory        1502
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> (not B))) and C) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A)))
theorem-size     26
proof            (modus-ponens tm-46 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-8 tm-3 tm-2 tm-9)
proof-size       94
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1502.         (((((A -> B) -> (A -> (not B))) and C) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A))), M:tm-46, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-1503
in-theory        1503
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (not B))) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A)))
theorem-size     22
proof            (modus-ponens tm-45 tm-70 ((B Bm) (A Am) (C (not Bm)) (D (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-8 tm-2 tm-9)
proof-size       112
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1503.         (((A -> (B -> (not B))) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A))), M:tm-45, m:tm-70, u:((B Bm) (A Am) (C (not Bm)) (D (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-1504
in-theory        1504
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (not B)) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A)))
theorem-size     20
proof            (modus-ponens tm-44 tm-70 ((A (-> Am Bm)) (B (-> Am (not Bm))) (C (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-8 tm-1 tm-2 tm-9)
proof-size       90
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1504.         (((A -> (not B)) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A))), M:tm-44, m:tm-70, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-1505
in-theory        1505
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C))))
theorem-size     21
proof            (modus-ponens tm-42 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1505.         ((A -> (B or A)) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C)))), M:tm-42, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-1506
in-theory        1506
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C))))
theorem-size     21
proof            (modus-ponens tm-32 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1506.         ((A -> (A or B)) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C)))), M:tm-32, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-1507
in-theory        1507
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (not B))) -> (((A -> B) -> (A -> (not B))) and ((A -> B) -> (not A))))
theorem-size     24
proof            (modus-ponens tm-24 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       92
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1507.         (((A -> B) -> (A -> (not B))) -> (((A -> B) -> (A -> (not B))) and ((A -> B) -> (not A)))), M:tm-24, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-1508
in-theory        1508
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C))))
theorem-size     23
proof            (modus-ponens tm-23 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1508.         ((A -> (B -> (A and B))) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C)))), M:tm-23, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-1509
in-theory        1509
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C))))
theorem-size     21
proof            (modus-ponens tm-22 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1509.         (((A and B) -> B) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C)))), M:tm-22, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-1510
in-theory        1510
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C))))
theorem-size     21
proof            (modus-ponens tm-21 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1510.         (((A and B) -> A) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C)))), M:tm-21, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-1511
in-theory        1511
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     29
proof            (modus-ponens tm-20 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1511.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-20, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-1512
in-theory        1512
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C))))
theorem-size     21
proof            (modus-ponens tm-19 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1512.         ((A -> (B -> A)) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C)))), M:tm-19, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-1513
in-theory        1513
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (A -> (not B))))
theorem-size     17
proof            (modus-ponens tm-12 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1513.         (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (A -> (not B)))), M:tm-12, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-1514
in-theory        1514
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> (not ((A -> B) -> (not A)))) -> (not ((A -> B) -> (A -> (not B)))))
theorem-size     26
proof            (modus-ponens tm-9 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-9 tm-2)
proof-size       76
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1514.         ((((A -> B) -> (A -> (not B))) -> (not ((A -> B) -> (not A)))) -> (not ((A -> B) -> (A -> (not B))))), M:tm-9, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-1515
in-theory        1515
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (not A)) -> C) -> ((((A -> B) -> (A -> (not B))) or ((A -> B) -> (not A))) -> C))
theorem-size     26
proof            (modus-ponens tm-8 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-8 tm-2 tm-9)
proof-size       78
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1515.         ((((A -> B) -> (not A)) -> C) -> ((((A -> B) -> (A -> (not B))) or ((A -> B) -> (not A))) -> C)), M:tm-8, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-1516
in-theory        1516
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> C) -> (B -> (not C))) -> ((B -> C) -> (not B))))
theorem-size     17
proof            (modus-ponens tm-7 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-7 tm-2 tm-9)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1516.         (A or (((B -> C) -> (B -> (not C))) -> ((B -> C) -> (not B)))), M:tm-7, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-1517
in-theory        1517
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) or C)
theorem-size     17
proof            (modus-ponens tm-6 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-6 tm-2 tm-9)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1517.         ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) or C), M:tm-6, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-1518
in-theory        1518
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (B -> (not C))) -> ((B -> C) -> (not B))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       65
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1518.         (A -> ((((B -> C) -> (B -> (not C))) -> ((B -> C) -> (not B))) and A)), M:tm-5, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-1519
in-theory        1519
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> (A -> B)) -> (((A -> B) -> (A -> (not B))) -> (not A)))
theorem-size     24
proof            (modus-ponens tm-2 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> Am Bm)) (C (not Am))))
axioms-used      (tm-2 tm-9)
proof-size       76
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1519.         ((((A -> B) -> (A -> (not B))) -> (A -> B)) -> (((A -> B) -> (A -> (not B))) -> (not A))), M:tm-2, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> Am Bm)) (C (not Am)))
================================================================
tm-name          tm-1520
in-theory        1520
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> (not C))) -> ((B -> C) -> (not B))))
theorem-size     17
proof            (modus-ponens tm-1 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-1 tm-2 tm-9)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1520.         (A -> (((B -> C) -> (B -> (not C))) -> ((B -> C) -> (not B)))), M:tm-1, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-1521
in-theory        1521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1521.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-69, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1522
in-theory        1522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     23
proof            (modus-ponens tm-66 tm-71 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-9 tm-1)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1522.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-66, m:tm-71, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1523
in-theory        1523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((A or (B -> C)) -> ((B -> (not C)) -> (not B))))
theorem-size     19
proof            (modus-ponens tm-55 tm-71 ((Am (-> A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-8 tm-1 tm-9)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1523.         ((A -> (B -> C)) -> ((A or (B -> C)) -> ((B -> (not C)) -> (not B)))), M:tm-55, m:tm-71, u:((Am (-> A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-1524
in-theory        1524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1524.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-54, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1525
in-theory        1525
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-51 tm-71 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1525.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-51, m:tm-71, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1526
in-theory        1526
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     17
proof            (modus-ponens tm-50 tm-71 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1526.         ((A or (B or A)) -> ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-50, m:tm-71, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1527
in-theory        1527
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     17
proof            (modus-ponens tm-49 tm-71 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1527.         ((A or (A or B)) -> ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-49, m:tm-71, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1528
in-theory        1528
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     19
proof            (modus-ponens tm-48 tm-71 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-9)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1528.         ((A or (B -> (A and B))) -> ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-48, m:tm-71, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1529
in-theory        1529
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     17
proof            (modus-ponens tm-47 tm-71 ((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1529.         (((A and B) or B) -> ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-47, m:tm-71, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1530
in-theory        1530
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     17
proof            (modus-ponens tm-46 tm-71 ((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1530.         (((A and B) or A) -> ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-46, m:tm-71, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1531
in-theory        1531
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-45 tm-71 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-9)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1531.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-45, m:tm-71, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1532
in-theory        1532
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     17
proof            (modus-ponens tm-44 tm-71 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1532.         ((A or (B -> A)) -> ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-44, m:tm-71, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1533
in-theory        1533
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1533.         ((A -> (B or A)) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-42, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1534
in-theory        1534
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1534.         ((A -> (A or B)) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-32, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1535
in-theory        1535
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> C) -> ((B -> (not C)) -> (not B)))))
theorem-size     15
proof            (modus-ponens tm-24 tm-71 ((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1535.         (A -> (A and ((B -> C) -> ((B -> (not C)) -> (not B))))), M:tm-24, m:tm-71, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1536
in-theory        1536
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1536.         ((A -> (B -> (A and B))) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-23, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1537
in-theory        1537
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1537.         (((A and B) -> B) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-22, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1538
in-theory        1538
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1538.         (((A and B) -> A) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-21, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1539
in-theory        1539
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1539.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-20, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1540
in-theory        1540
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1540.         ((A -> (B -> A)) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-19, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1541
in-theory        1541
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> ((B -> (not C)) -> (not B))) -> D)) -> D)
theorem-size     17
proof            (modus-ponens tm-17 tm-71 ((Am (and A (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) C))) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-4 tm-1 tm-9)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1541.         ((A and (((B -> C) -> ((B -> (not C)) -> (not B))) -> D)) -> D), M:tm-17, m:tm-71, u:((Am (and A (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) C))) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1542
in-theory        1542
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> (not B)) -> (not A))) -> C) and D) -> C)
theorem-size     17
proof            (modus-ponens tm-15 tm-71 ((Am (and (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) B) C)) (A (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-3 tm-1 tm-9)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1542.         (((((A -> B) -> ((A -> (not B)) -> (not A))) -> C) and D) -> C), M:tm-15, m:tm-71, u:((Am (and (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) B) C)) (A (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1543
in-theory        1543
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((A -> (not B)) -> (not A)) -> C)) -> ((A -> B) -> C))
theorem-size     19
proof            (modus-ponens tm-13 tm-71 ((Am (-> (-> Bm Cm) (-> (-> (-> Bm (not Cm)) (not Bm)) C))) (A (-> Bm Cm)) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1543.         (((A -> B) -> (((A -> (not B)) -> (not A)) -> C)) -> ((A -> B) -> C)), M:tm-13, m:tm-71, u:((Am (-> (-> Bm Cm) (-> (-> (-> Bm (not Cm)) (not Bm)) C))) (A (-> Bm Cm)) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-1544
in-theory        1544
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> C) -> ((B -> (not C)) -> (not B))))) -> (not A))
theorem-size     17
proof            (modus-ponens tm-9 tm-71 ((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-9 tm-1)
proof-size       57
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1544.         ((A -> (not ((B -> C) -> ((B -> (not C)) -> (not B))))) -> (not A)), M:tm-9, m:tm-71, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1545
in-theory        1545
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) -> C) -> ((D or ((A -> B) -> ((A -> (not B)) -> (not A)))) -> C))
theorem-size     29
proof            (modus-ponens tm-8 tm-71 ((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       71
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1545.         ((((A -> B) -> ((A -> (not B)) -> (not A))) -> C) -> ((D or ((A -> B) -> ((A -> (not B)) -> (not A)))) -> C)), M:tm-8, m:tm-71, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1546
in-theory        1546
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> D) -> ((C -> (not D)) -> (not C)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-7 tm-1 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1546.         (A or (B -> ((C -> D) -> ((C -> (not D)) -> (not C))))), M:tm-7, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1547
in-theory        1547
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-6 tm-1 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1547.         ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) or D), M:tm-6, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1548
in-theory        1548
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> D) -> ((C -> (not D)) -> (not C)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1548.         (A -> ((B -> ((C -> D) -> ((C -> (not D)) -> (not C)))) and A)), M:tm-5, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1549
in-theory        1549
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (A -> ((B -> (not C)) -> (not B))))
theorem-size     15
proof            (modus-ponens tm-2 tm-71 ((A Am) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       57
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1549.         ((A -> (B -> C)) -> (A -> ((B -> (not C)) -> (not B)))), M:tm-2, m:tm-71, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-1550
in-theory        1550
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> D) -> ((C -> (not D)) -> (not C)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-1 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1550.         (A -> (B -> ((C -> D) -> ((C -> (not D)) -> (not C))))), M:tm-1, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1551
in-theory        1551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((not (not C)) -> (not C)) -> (not (not (not C)))))
theorem-size     23
proof            (modus-ponens tm-69 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-9 tm-10)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1551.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((not (not C)) -> (not C)) -> (not (not (not C))))), M:tm-69, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-1552
in-theory        1552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     25
proof            (modus-ponens tm-54 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-8 tm-9 tm-10)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1552.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-54, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-1553
in-theory        1553
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((not (not B)) -> (not B))) or ((not (not B)) -> (not B))) -> (not (not (not B))))
theorem-size     20
proof            (modus-ponens tm-47 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-8 tm-4 tm-9 tm-10)
proof-size       76
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1553.         (((A and ((not (not B)) -> (not B))) or ((not (not B)) -> (not B))) -> (not (not (not B)))), M:tm-47, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-1554
in-theory        1554
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) -> (not A)) and B) or ((not (not A)) -> (not A))) -> (not (not (not A))))
theorem-size     20
proof            (modus-ponens tm-46 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-8 tm-3 tm-9 tm-10)
proof-size       76
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1554.         (((((not (not A)) -> (not A)) and B) or ((not (not A)) -> (not A))) -> (not (not (not A)))), M:tm-46, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-1555
in-theory        1555
times-derived    1
----------------------------------------------------------------
theorem          (((not A) or ((not (not A)) -> (not A))) -> (not (not (not A))))
theorem-size     14
proof            (modus-ponens tm-44 tm-72 ((A (not (not Am))) (B (not Am)) (C (not (not (not Am))))))
axioms-used      (tm-8 tm-1 tm-9 tm-10)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1555.         (((not A) or ((not (not A)) -> (not A))) -> (not (not (not A)))), M:tm-44, m:tm-72, u:((A (not (not Am))) (B (not Am)) (C (not (not (not Am)))))
================================================================
tm-name          tm-1556
in-theory        1556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((not (not C)) -> (not C)) -> (not (not (not C)))))
theorem-size     17
proof            (modus-ponens tm-42 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-7 tm-9 tm-10)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1556.         ((A -> (B or A)) and (((not (not C)) -> (not C)) -> (not (not (not C))))), M:tm-42, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-1557
in-theory        1557
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((not (not C)) -> (not C)) -> (not (not (not C)))))
theorem-size     17
proof            (modus-ponens tm-32 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-6 tm-9 tm-10)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1557.         ((A -> (A or B)) and (((not (not C)) -> (not C)) -> (not (not (not C))))), M:tm-32, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-1558
in-theory        1558
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not A)) -> (((not (not A)) -> (not A)) and (not (not (not A)))))
theorem-size     18
proof            (modus-ponens tm-24 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-9 tm-10)
proof-size       74
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1558.         (((not (not A)) -> (not A)) -> (((not (not A)) -> (not A)) and (not (not (not A))))), M:tm-24, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-1559
in-theory        1559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((not (not C)) -> (not C)) -> (not (not (not C)))))
theorem-size     19
proof            (modus-ponens tm-23 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-9 tm-10)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1559.         ((A -> (B -> (A and B))) and (((not (not C)) -> (not C)) -> (not (not (not C))))), M:tm-23, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-1560
in-theory        1560
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((not (not C)) -> (not C)) -> (not (not (not C)))))
theorem-size     17
proof            (modus-ponens tm-22 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-4 tm-9 tm-10)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1560.         (((A and B) -> B) and (((not (not C)) -> (not C)) -> (not (not (not C))))), M:tm-22, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-1561
in-theory        1561
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((not (not C)) -> (not C)) -> (not (not (not C)))))
theorem-size     17
proof            (modus-ponens tm-21 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-3 tm-9 tm-10)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1561.         (((A and B) -> A) and (((not (not C)) -> (not C)) -> (not (not (not C))))), M:tm-21, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-1562
in-theory        1562
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     25
proof            (modus-ponens tm-20 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-2 tm-9 tm-10)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1562.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-20, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-1563
in-theory        1563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((not (not C)) -> (not C)) -> (not (not (not C)))))
theorem-size     17
proof            (modus-ponens tm-19 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-1 tm-9 tm-10)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1563.         ((A -> (B -> A)) and (((not (not C)) -> (not C)) -> (not (not (not C))))), M:tm-19, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-1564
in-theory        1564
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not A)) -> ((not (not A)) -> (not A)))
theorem-size     13
proof            (modus-ponens tm-12 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-2 tm-1 tm-9 tm-10)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1564.         (((not (not A)) -> (not A)) -> ((not (not A)) -> (not A))), M:tm-12, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-1565
in-theory        1565
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not (not A))))) -> (not ((not (not A)) -> (not A))))
theorem-size     20
proof            (modus-ponens tm-9 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-9 tm-10)
proof-size       58
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1565.         ((((not (not A)) -> (not A)) -> (not (not (not (not A))))) -> (not ((not (not A)) -> (not A)))), M:tm-9, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-1566
in-theory        1566
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (not A))) -> B) -> ((((not (not A)) -> (not A)) or (not (not (not A)))) -> B))
theorem-size     20
proof            (modus-ponens tm-8 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-8 tm-9 tm-10)
proof-size       60
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1566.         (((not (not (not A))) -> B) -> ((((not (not A)) -> (not A)) or (not (not (not A)))) -> B)), M:tm-8, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-1567
in-theory        1567
times-derived    1
----------------------------------------------------------------
theorem          (A or (((not (not B)) -> (not B)) -> (not (not (not B)))))
theorem-size     13
proof            (modus-ponens tm-7 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-7 tm-9 tm-10)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1567.         (A or (((not (not B)) -> (not B)) -> (not (not (not B))))), M:tm-7, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-1568
in-theory        1568
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) or B)
theorem-size     13
proof            (modus-ponens tm-6 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-6 tm-9 tm-10)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1568.         ((((not (not A)) -> (not A)) -> (not (not (not A)))) or B), M:tm-6, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-1569
in-theory        1569
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((not (not B)) -> (not B)) -> (not (not (not B)))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-9 tm-10)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1569.         (A -> ((((not (not B)) -> (not B)) -> (not (not (not B)))) and A)), M:tm-5, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-1570
in-theory        1570
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((not (not B)) -> (not B)) -> (not (not (not B)))))
theorem-size     13
proof            (modus-ponens tm-1 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-1 tm-9 tm-10)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1570.         (A -> (((not (not B)) -> (not B)) -> (not (not (not B))))), M:tm-1, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-1571
in-theory        1571
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> A))
theorem-size     9
proof            (modus-ponens tm-73 tm-1 ((A Am) (B (-> Bm Am))))
axioms-used      (tm-8 tm-10 tm-1)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-1571.         (((not (not A)) or A) -> (B -> A)), M:tm-73, m:tm-1, u:((A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-1572
in-theory        1572
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (B -> C)))) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))
theorem-size     21
proof            (modus-ponens tm-73 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       63
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1572.         (((not (not (A -> (B -> C)))) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-73, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-1573
in-theory        1573
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A and B))) or (A and B)) -> A)
theorem-size     11
proof            (modus-ponens tm-73 tm-3 ((A (and Am Bm)) (B Am)))
axioms-used      (tm-8 tm-10 tm-3)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-1573.         (((not (not (A and B))) or (A and B)) -> A), M:tm-73, m:tm-3, u:((A (and Am Bm)) (B Am))
================================================================
tm-name          tm-1574
in-theory        1574
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A and B))) or (A and B)) -> B)
theorem-size     11
proof            (modus-ponens tm-73 tm-4 ((A (and Am Bm)) (B Bm)))
axioms-used      (tm-8 tm-10 tm-4)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-1574.         (((not (not (A and B))) or (A and B)) -> B), M:tm-73, m:tm-4, u:((A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-1575
in-theory        1575
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> (A and B)))
theorem-size     11
proof            (modus-ponens tm-73 tm-5 ((A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-8 tm-10 tm-5)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1575.         (((not (not A)) or A) -> (B -> (A and B))), M:tm-73, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-1576
in-theory        1576
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A or B))
theorem-size     9
proof            (modus-ponens tm-73 tm-6 ((A Am) (B (or Am Bm))))
axioms-used      (tm-8 tm-10 tm-6)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-1576.         (((not (not A)) or A) -> (A or B)), M:tm-73, m:tm-6, u:((A Am) (B (or Am Bm)))
================================================================
tm-name          tm-1577
in-theory        1577
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B or A))
theorem-size     9
proof            (modus-ponens tm-73 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-8 tm-10 tm-7)
proof-size       43
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-1577.         (((not (not A)) or A) -> (B or A)), M:tm-73, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-1578
in-theory        1578
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> ((B -> C) -> ((A or B) -> C)))
theorem-size     19
proof            (modus-ponens tm-73 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-10)
proof-size       61
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1578.         (((not (not (A -> B))) or (A -> B)) -> ((B -> C) -> ((A or B) -> C))), M:tm-73, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-1579
in-theory        1579
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> ((A -> (not B)) -> (not A)))
theorem-size     17
proof            (modus-ponens tm-73 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-8 tm-10 tm-9)
proof-size       57
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1579.         (((not (not (A -> B))) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-73, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-1580
in-theory        1580
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (not (not A)))) or (not (not A))) -> A)
theorem-size     11
proof            (modus-ponens tm-73 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-8 tm-10)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1580.         (((not (not (not (not A)))) or (not (not A))) -> A), M:tm-73, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-1581
in-theory        1581
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> (C -> B)))
theorem-size     11
proof            (modus-ponens tm-73 tm-11 ((A Am) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-10 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1581.         (((not (not A)) or A) -> (B -> (C -> B))), M:tm-73, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-1582
in-theory        1582
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> (A -> A))
theorem-size     13
proof            (modus-ponens tm-73 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-1582.         (((not (not (A -> B))) or (A -> B)) -> (A -> A)), M:tm-73, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-1583
in-theory        1583
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) -> (A -> B)))) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     31
proof            (modus-ponens tm-73 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1583.         (((not (not ((A -> (B -> C)) -> (A -> B)))) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-73, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-1584
in-theory        1584
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     19
proof            (modus-ponens tm-73 tm-14 ((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-10 tm-1 tm-2)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1584.         (((not (not A)) or A) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-73, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-1585
in-theory        1585
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) and C) -> A))) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))
theorem-size     25
proof            (modus-ponens tm-73 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-10 tm-2 tm-3)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1585.         (((not (not (((A -> B) and C) -> A))) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-73, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-1586
in-theory        1586
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B and C) -> B))
theorem-size     11
proof            (modus-ponens tm-73 tm-16 ((A Am) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-10 tm-1 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1586.         (((not (not A)) or A) -> ((B and C) -> B)), M:tm-73, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-1587
in-theory        1587
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (B -> C)) -> B))) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))
theorem-size     25
proof            (modus-ponens tm-73 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-4)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1587.         (((not (not ((A and (B -> C)) -> B))) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-73, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-1588
in-theory        1588
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B and C) -> C))
theorem-size     11
proof            (modus-ponens tm-73 tm-18 ((A Am) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-10 tm-1 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1588.         (((not (not A)) or A) -> ((B and C) -> C)), M:tm-73, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-1589
in-theory        1589
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (C -> B)) and A))
theorem-size     13
proof            (modus-ponens tm-73 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-1)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1589.         (((not (not A)) or A) -> ((B -> (C -> B)) and A)), M:tm-73, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-1590
in-theory        1590
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))
theorem-size     21
proof            (modus-ponens tm-73 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1590.         (((not (not A)) or A) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-73, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-1591
in-theory        1591
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B and C) -> B) and A))
theorem-size     13
proof            (modus-ponens tm-73 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1591.         (((not (not A)) or A) -> (((B and C) -> B) and A)), M:tm-73, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-1592
in-theory        1592
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B and C) -> C) and A))
theorem-size     13
proof            (modus-ponens tm-73 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1592.         (((not (not A)) or A) -> (((B and C) -> C) and A)), M:tm-73, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-1593
in-theory        1593
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (C -> (B and C))) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-8 tm-10 tm-5)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1593.         (((not (not A)) or A) -> ((B -> (C -> (B and C))) and A)), M:tm-73, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-1594
in-theory        1594
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> (A -> (A and B)))
theorem-size     15
proof            (modus-ponens tm-73 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1594.         (((not (not (A -> B))) or (A -> B)) -> (A -> (A and B))), M:tm-73, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-1595
in-theory        1595
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> (C -> (B and C))))
theorem-size     13
proof            (modus-ponens tm-73 tm-25 ((A Am) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-10 tm-1 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1595.         (((not (not A)) or A) -> (B -> (C -> (B and C)))), M:tm-73, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-1596
in-theory        1596
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (B or C)) and A))
theorem-size     13
proof            (modus-ponens tm-73 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-6)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1596.         (((not (not A)) or A) -> ((B -> (B or C)) and A)), M:tm-73, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-1597
in-theory        1597
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> (B or C)))
theorem-size     11
proof            (modus-ponens tm-73 tm-33 ((A Am) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1597.         (((not (not A)) or A) -> (B -> (B or C))), M:tm-73, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-1598
in-theory        1598
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (C or B)) and A))
theorem-size     13
proof            (modus-ponens tm-73 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-7)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1598.         (((not (not A)) or A) -> ((B -> (C or B)) and A)), M:tm-73, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-1599
in-theory        1599
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> (C or B)))
theorem-size     11
proof            (modus-ponens tm-73 tm-43 ((A Am) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1599.         (((not (not A)) or A) -> (B -> (C or B))), M:tm-73, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-1600
in-theory        1600
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> C))) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C))
theorem-size     21
proof            (modus-ponens tm-73 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-8 tm-10 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1600.         (((not (not ((A -> B) -> C))) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-73, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-1601
in-theory        1601
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) -> (A -> C)) -> D))) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     37
proof            (modus-ponens tm-73 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1601.         (((not (not (((A -> B) -> (A -> C)) -> D))) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-73, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-1602
in-theory        1602
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> (((A and C) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-73 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-8 tm-10 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1602.         (((not (not (A -> B))) or (A -> B)) -> (((A and C) or A) -> B)), M:tm-73, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-1603
in-theory        1603
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> (((C and A) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-73 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-8 tm-10 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1603.         (((not (not (A -> B))) or (A -> B)) -> (((C and A) or A) -> B)), M:tm-73, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-1604
in-theory        1604
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B and A)) -> C))) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C))
theorem-size     27
proof            (modus-ponens tm-73 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-8 tm-10 tm-5)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1604.         (((not (not ((A -> (B and A)) -> C))) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)), M:tm-73, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-1605
in-theory        1605
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A or B) -> C))) or ((A or B) -> C)) -> ((A or (A or B)) -> C))
theorem-size     21
proof            (modus-ponens tm-73 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-10 tm-6)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1605.         (((not (not ((A or B) -> C))) or ((A or B) -> C)) -> ((A or (A or B)) -> C)), M:tm-73, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-1606
in-theory        1606
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A or B) -> C))) or ((A or B) -> C)) -> ((B or (A or B)) -> C))
theorem-size     21
proof            (modus-ponens tm-73 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-8 tm-10 tm-7)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1606.         (((not (not ((A or B) -> C))) or ((A or B) -> C)) -> ((B or (A or B)) -> C)), M:tm-73, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-1607
in-theory        1607
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) -> ((C or A) -> B)) -> D))) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))
theorem-size     41
proof            (modus-ponens tm-73 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-8 tm-10)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1607.         (((not (not (((A -> B) -> ((C or A) -> B)) -> D))) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-73, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-1608
in-theory        1608
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))
theorem-size     21
proof            (modus-ponens tm-73 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-8 tm-10 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1608.         (((not (not A)) or A) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-73, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-1609
in-theory        1609
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> (B -> C)))) or ((A -> B) -> (B -> C))) -> ((A -> B) -> ((A or B) -> C)))
theorem-size     27
proof            (modus-ponens tm-73 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1609.         (((not (not ((A -> B) -> (B -> C)))) or ((A -> B) -> (B -> C))) -> ((A -> B) -> ((A or B) -> C))), M:tm-73, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-1610
in-theory        1610
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> C) -> ((C -> D) -> ((B or C) -> D))))
theorem-size     19
proof            (modus-ponens tm-73 tm-56 ((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-10 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1610.         (((not (not A)) or A) -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-73, m:tm-56, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1611
in-theory        1611
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not (B -> A))))) or (A -> (not (B -> A)))) -> (not A))
theorem-size     18
proof            (modus-ponens tm-73 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-1)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1611.         (((not (not (A -> (not (B -> A))))) or (A -> (not (B -> A)))) -> (not A)), M:tm-73, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-1612
in-theory        1612
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))))) or ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C))))
theorem-size     38
proof            (modus-ponens tm-73 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-8 tm-10 tm-9 tm-2)
proof-size       112
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1612.         (((not (not ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))))) or ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C)))), M:tm-73, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-1613
in-theory        1613
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) -> (not A)))) or ((A and B) -> (not A))) -> (not (A and B)))
theorem-size     20
proof            (modus-ponens tm-73 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-8 tm-10 tm-9 tm-3)
proof-size       76
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1613.         (((not (not ((A and B) -> (not A)))) or ((A and B) -> (not A))) -> (not (A and B))), M:tm-73, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-1614
in-theory        1614
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) -> (not B)))) or ((A and B) -> (not B))) -> (not (A and B)))
theorem-size     20
proof            (modus-ponens tm-73 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-8 tm-10 tm-9 tm-4)
proof-size       76
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1614.         (((not (not ((A and B) -> (not B)))) or ((A and B) -> (not B))) -> (not (A and B))), M:tm-73, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-1615
in-theory        1615
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not (B -> (A and B)))))) or (A -> (not (B -> (A and B))))) -> (not A))
theorem-size     22
proof            (modus-ponens tm-73 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-5)
proof-size       80
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1615.         (((not (not (A -> (not (B -> (A and B)))))) or (A -> (not (B -> (A and B))))) -> (not A)), M:tm-73, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-1616
in-theory        1616
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not (A or B))))) or (A -> (not (A or B)))) -> (not A))
theorem-size     18
proof            (modus-ponens tm-73 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-6)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1616.         (((not (not (A -> (not (A or B))))) or (A -> (not (A or B)))) -> (not A)), M:tm-73, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-1617
in-theory        1617
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not (B or A))))) or (A -> (not (B or A)))) -> (not A))
theorem-size     18
proof            (modus-ponens tm-73 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-7)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1617.         (((not (not (A -> (not (B or A))))) or (A -> (not (B or A)))) -> (not A)), M:tm-73, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-1618
in-theory        1618
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))))) or ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))) -> (not (A -> B)))
theorem-size     36
proof            (modus-ponens tm-73 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-10 tm-9)
proof-size       108
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1618.         (((not (not ((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))))) or ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))) -> (not (A -> B))), M:tm-73, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-1619
in-theory        1619
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> (not ((A -> (not B)) -> (not A)))))) or ((A -> B) -> (not ((A -> (not B)) -> (not A))))) -> (not (A -> B)))
theorem-size     32
proof            (modus-ponens tm-73 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-10 tm-9)
proof-size       100
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1619.         (((not (not ((A -> B) -> (not ((A -> (not B)) -> (not A)))))) or ((A -> B) -> (not ((A -> (not B)) -> (not A))))) -> (not (A -> B))), M:tm-73, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-1620
in-theory        1620
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (not B)) -> (not A)) -> C))) or (((A -> (not B)) -> (not A)) -> C)) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))
theorem-size     35
proof            (modus-ponens tm-73 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-8 tm-10 tm-9)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1620.         (((not (not (((A -> (not B)) -> (not A)) -> C))) or (((A -> (not B)) -> (not A)) -> C)) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-73, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1621
in-theory        1621
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A))
theorem-size     19
proof            (modus-ponens tm-73 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1621.         (((not (not A)) or A) -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-73, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-1622
in-theory        1622
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> (A -> (not B))))) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A)))
theorem-size     26
proof            (modus-ponens tm-73 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-8 tm-10 tm-2 tm-9)
proof-size       94
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1622.         (((not (not ((A -> B) -> (A -> (not B))))) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A))), M:tm-73, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-1623
in-theory        1623
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> C) -> ((B -> (not C)) -> (not B))))
theorem-size     17
proof            (modus-ponens tm-73 tm-71 ((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-10 tm-1 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1623.         (((not (not A)) or A) -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-73, m:tm-71, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1624
in-theory        1624
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((not (not A)) -> (not A)))) or ((not (not A)) -> (not A))) -> (not (not (not A))))
theorem-size     20
proof            (modus-ponens tm-73 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-8 tm-10 tm-9)
proof-size       76
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1624.         (((not (not ((not (not A)) -> (not A)))) or ((not (not A)) -> (not A))) -> (not (not (not A)))), M:tm-73, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-1625
in-theory        1625
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> (((not (not A)) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-73 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-8 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1625.         (((not (not (A -> B))) or (A -> B)) -> (((not (not A)) or A) -> B)), M:tm-73, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1626
in-theory        1626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (((not (not C)) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-69 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-10)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1626.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (((not (not C)) or C) -> D))), M:tm-69, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-1627
in-theory        1627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((not (not (A -> (not B)))) or (A -> (not B))) -> (not A)))
theorem-size     26
proof            (modus-ponens tm-66 tm-73 ((Am (-> A (not B))) (Bm (not A)) (C (-> (or (not (not (-> A (not B)))) (-> A (not B))) (not A)))))
axioms-used      (tm-8 tm-9 tm-10)
proof-size       102
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1627.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((not (not (A -> (not B)))) or (A -> (not B))) -> (not A))), M:tm-66, m:tm-73, u:((Am (-> A (not B))) (Bm (not A)) (C (-> (or (not (not (-> A (not B)))) (-> A (not B))) (not A))))
================================================================
tm-name          tm-1628
in-theory        1628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not A)) or A)) -> ((A or ((not (not A)) or A)) -> ((not (not A)) or A)))
theorem-size     21
proof            (modus-ponens tm-55 tm-73 ((A Am) (Bm (or (not (not Am)) Am)) (B (or (not (not Am)) Am)) (C (or (not (not Am)) Am))))
axioms-used      (tm-2 tm-8 tm-10)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1628.         ((A -> ((not (not A)) or A)) -> ((A or ((not (not A)) or A)) -> ((not (not A)) or A))), M:tm-55, m:tm-73, u:((A Am) (Bm (or (not (not Am)) Am)) (B (or (not (not Am)) Am)) (C (or (not (not Am)) Am)))
================================================================
tm-name          tm-1629
in-theory        1629
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-54 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-10)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1629.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-54, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-1630
in-theory        1630
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((not (not (B -> C))) or (B -> C)) -> ((A or B) -> C)))
theorem-size     29
proof            (modus-ponens tm-51 tm-73 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (or (not (not (-> A B))) (-> A B)) (-> (or C A) B)))))
axioms-used      (tm-8 tm-10)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1630.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((not (not (B -> C))) or (B -> C)) -> ((A or B) -> C))), M:tm-51, m:tm-73, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (or (not (not (-> A B))) (-> A B)) (-> (or C A) B))))
================================================================
tm-name          tm-1631
in-theory        1631
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((not (not B)) or B) -> (A and B)))
theorem-size     17
proof            (modus-ponens tm-48 tm-73 ((A Am) (Bm (and B Am)) (C (-> (or (not (not Am)) Am) (and B Am)))))
axioms-used      (tm-8 tm-5 tm-10)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1631.         ((A or (B -> (A and B))) -> (((not (not B)) or B) -> (A and B))), M:tm-48, m:tm-73, u:((A Am) (Bm (and B Am)) (C (-> (or (not (not Am)) Am) (and B Am))))
================================================================
tm-name          tm-1632
in-theory        1632
times-derived    2
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (((not (not B)) or B) -> C))
theorem-size     17
proof            (modus-ponens tm-47 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-8 tm-4 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1632.         (((A and (B -> C)) or (B -> C)) -> (((not (not B)) or B) -> C)), M:tm-47, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1633
in-theory        1633
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (((not (not A)) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-46 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-8 tm-3 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1633.         ((((A -> B) and C) or (A -> B)) -> (((not (not A)) or A) -> B)), M:tm-46, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1634
in-theory        1634
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((not (not (A -> B))) or (A -> B)) -> (A -> C)))
theorem-size     27
proof            (modus-ponens tm-45 tm-73 ((Am (-> A B)) (Bm (-> A C)) (D (-> (or (not (not (-> A B))) (-> A B)) (-> A C)))))
axioms-used      (tm-8 tm-2 tm-10)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1634.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((not (not (A -> B))) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-73, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (not (not (-> A B))) (-> A B)) (-> A C))))
================================================================
tm-name          tm-1635
in-theory        1635
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((not (not B)) or B) -> A))
theorem-size     13
proof            (modus-ponens tm-44 tm-73 ((A Am) (B Bm) (C (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-8 tm-1 tm-10)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1635.         ((A or (B -> A)) -> (((not (not B)) or B) -> A)), M:tm-44, m:tm-73, u:((A Am) (B Bm) (C (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1636
in-theory        1636
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (((not (not C)) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-42 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-10)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1636.         ((A -> (B or A)) and ((C -> D) -> (((not (not C)) or C) -> D))), M:tm-42, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-1637
in-theory        1637
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (((not (not C)) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-32 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-10)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1637.         ((A -> (A or B)) and ((C -> D) -> (((not (not C)) or C) -> D))), M:tm-32, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-1638
in-theory        1638
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (((not (not A)) or A) -> B)))
theorem-size     15
proof            (modus-ponens tm-24 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1638.         ((A -> B) -> ((A -> B) and (((not (not A)) or A) -> B))), M:tm-24, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1639
in-theory        1639
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (((not (not C)) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-23 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-10)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1639.         ((A -> (B -> (A and B))) and ((C -> D) -> (((not (not C)) or C) -> D))), M:tm-23, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-1640
in-theory        1640
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (((not (not C)) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-22 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-10)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1640.         (((A and B) -> B) and ((C -> D) -> (((not (not C)) or C) -> D))), M:tm-22, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-1641
in-theory        1641
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (((not (not C)) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-21 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-10)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1641.         (((A and B) -> A) and ((C -> D) -> (((not (not C)) or C) -> D))), M:tm-21, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-1642
in-theory        1642
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-20 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-10)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1642.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-20, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-1643
in-theory        1643
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (((not (not C)) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-19 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-10)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1643.         ((A -> (B -> A)) and ((C -> D) -> (((not (not C)) or C) -> D))), M:tm-19, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-1644
in-theory        1644
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((not (not A)) or A) -> B))) -> (not (A -> B)))
theorem-size     17
proof            (modus-ponens tm-9 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-9 tm-8 tm-10)
proof-size       57
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1644.         (((A -> B) -> (not (((not (not A)) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1645
in-theory        1645
times-derived    2
----------------------------------------------------------------
theorem          (((((not (not A)) or A) -> B) -> C) -> (((A -> B) or (((not (not A)) or A) -> B)) -> C))
theorem-size     23
proof            (modus-ponens tm-8 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-8 tm-10)
proof-size       65
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1645.         (((((not (not A)) or A) -> B) -> C) -> (((A -> B) or (((not (not A)) or A) -> B)) -> C)), M:tm-8, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1646
in-theory        1646
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (((not (not B)) or B) -> C)))
theorem-size     13
proof            (modus-ponens tm-7 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-7 tm-8 tm-10)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1646.         (A or ((B -> C) -> (((not (not B)) or B) -> C))), M:tm-7, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-1647
in-theory        1647
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) or C)
theorem-size     13
proof            (modus-ponens tm-6 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-6 tm-8 tm-10)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1647.         (((A -> B) -> (((not (not A)) or A) -> B)) or C), M:tm-6, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-1648
in-theory        1648
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (((not (not B)) or B) -> C)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-10)
proof-size       51
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1648.         (A -> (((B -> C) -> (((not (not B)) or B) -> C)) and A)), M:tm-5, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-1649
in-theory        1649
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((not (not A)) or A)) -> ((A -> B) -> B))
theorem-size     15
proof            (modus-ponens tm-2 tm-73 ((A (-> Am Bm)) (B (or (not (not Am)) Am)) (C Bm)))
axioms-used      (tm-2 tm-8 tm-10)
proof-size       57
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1649.         (((A -> B) -> ((not (not A)) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-73, u:((A (-> Am Bm)) (B (or (not (not Am)) Am)) (C Bm))
================================================================
tm-name          tm-1650
in-theory        1650
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (((not (not B)) or B) -> C)))
theorem-size     13
proof            (modus-ponens tm-1 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-1 tm-8 tm-10)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1650.         (A -> ((B -> C) -> (((not (not B)) or B) -> C))), M:tm-1, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-1651
in-theory        1651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((not (not D)) -> D)))
theorem-size     19
proof            (modus-ponens tm-69 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-9 tm-7 tm-10)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1651.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((not (not D)) -> D))), M:tm-69, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1652
in-theory        1652
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-54 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1652.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((not (not E)) -> E))), M:tm-54, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1653
in-theory        1653
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-42 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1653.         ((A -> (B or A)) and (C or ((not (not D)) -> D))), M:tm-42, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1654
in-theory        1654
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-32 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1654.         ((A -> (A or B)) and (C or ((not (not D)) -> D))), M:tm-32, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1655
in-theory        1655
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((not (not D)) -> D)))
theorem-size     15
proof            (modus-ponens tm-23 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1655.         ((A -> (B -> (A and B))) and (C or ((not (not D)) -> D))), M:tm-23, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1656
in-theory        1656
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-22 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1656.         (((A and B) -> B) and (C or ((not (not D)) -> D))), M:tm-22, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1657
in-theory        1657
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-21 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1657.         (((A and B) -> A) and (C or ((not (not D)) -> D))), M:tm-21, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1658
in-theory        1658
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-20 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1658.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((not (not E)) -> E))), M:tm-20, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1659
in-theory        1659
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-19 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1659.         ((A -> (B -> A)) and (C or ((not (not D)) -> D))), M:tm-19, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1660
in-theory        1660
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or ((not (not C)) -> C)))
theorem-size     9
proof            (modus-ponens tm-7 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-7 tm-10)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1660.         (A or (B or ((not (not C)) -> C))), M:tm-7, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1661
in-theory        1661
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) or C)
theorem-size     9
proof            (modus-ponens tm-6 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-6 tm-7 tm-10)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1661.         ((A or ((not (not B)) -> B)) or C), M:tm-6, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1662
in-theory        1662
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or ((not (not C)) -> C)) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1662.         (A -> ((B or ((not (not C)) -> C)) and A)), M:tm-5, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1663
in-theory        1663
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or ((not (not C)) -> C)))
theorem-size     9
proof            (modus-ponens tm-1 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-1 tm-7 tm-10)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1663.         (A -> (B or ((not (not C)) -> C))), M:tm-1, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1664
in-theory        1664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((not (not C)) -> C) or D))
theorem-size     19
proof            (modus-ponens tm-69 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-9 tm-6 tm-10)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1664.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((not (not C)) -> C) or D)), M:tm-69, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1665
in-theory        1665
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((not (not D)) -> D) or E))
theorem-size     21
proof            (modus-ponens tm-54 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-6 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1665.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((not (not D)) -> D) or E)), M:tm-54, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1666
in-theory        1666
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((not (not C)) -> C) or D))
theorem-size     13
proof            (modus-ponens tm-42 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1666.         ((A -> (B or A)) and (((not (not C)) -> C) or D)), M:tm-42, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1667
in-theory        1667
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((not (not C)) -> C) or D))
theorem-size     13
proof            (modus-ponens tm-32 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1667.         ((A -> (A or B)) and (((not (not C)) -> C) or D)), M:tm-32, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1668
in-theory        1668
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((not (not C)) -> C) or D))
theorem-size     15
proof            (modus-ponens tm-23 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1668.         ((A -> (B -> (A and B))) and (((not (not C)) -> C) or D)), M:tm-23, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1669
in-theory        1669
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((not (not C)) -> C) or D))
theorem-size     13
proof            (modus-ponens tm-22 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-4 tm-6 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1669.         (((A and B) -> B) and (((not (not C)) -> C) or D)), M:tm-22, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1670
in-theory        1670
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((not (not C)) -> C) or D))
theorem-size     13
proof            (modus-ponens tm-21 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-3 tm-6 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1670.         (((A and B) -> A) and (((not (not C)) -> C) or D)), M:tm-21, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1671
in-theory        1671
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((not (not D)) -> D) or E))
theorem-size     21
proof            (modus-ponens tm-20 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-6 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1671.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((not (not D)) -> D) or E)), M:tm-20, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1672
in-theory        1672
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((not (not C)) -> C) or D))
theorem-size     13
proof            (modus-ponens tm-19 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1672.         ((A -> (B -> A)) and (((not (not C)) -> C) or D)), M:tm-19, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1673
in-theory        1673
times-derived    2
----------------------------------------------------------------
theorem          (A or (((not (not B)) -> B) or C))
theorem-size     9
proof            (modus-ponens tm-7 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-7 tm-6 tm-10)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1673.         (A or (((not (not B)) -> B) or C)), M:tm-7, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1674
in-theory        1674
times-derived    2
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) or C)
theorem-size     9
proof            (modus-ponens tm-6 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-6 tm-10)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1674.         ((((not (not A)) -> A) or B) or C), M:tm-6, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1675
in-theory        1675
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((not (not B)) -> B) or C) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1675.         (A -> ((((not (not B)) -> B) or C) and A)), M:tm-5, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1676
in-theory        1676
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((not (not B)) -> B) or C))
theorem-size     9
proof            (modus-ponens tm-1 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-1 tm-6 tm-10)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1676.         (A -> (((not (not B)) -> B) or C)), M:tm-1, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1677
in-theory        1677
times-derived    2
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> B)))
theorem-size     11
proof            (modus-ponens tm-76 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-1677.         (((not (not A)) -> A) and (B -> (C -> B))), M:tm-76, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-1678
in-theory        1678
times-derived    2
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1678.         (((not (not A)) -> A) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-76, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-1679
in-theory        1679
times-derived    2
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B and C) -> B))
theorem-size     11
proof            (modus-ponens tm-76 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-10 tm-3)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-1679.         (((not (not A)) -> A) and ((B and C) -> B)), M:tm-76, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-1680
in-theory        1680
times-derived    2
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B and C) -> C))
theorem-size     11
proof            (modus-ponens tm-76 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-10 tm-4)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-1680.         (((not (not A)) -> A) and ((B and C) -> C)), M:tm-76, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-1681
in-theory        1681
times-derived    2
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> (B and C))))
theorem-size     13
proof            (modus-ponens tm-76 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-10)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1681.         (((not (not A)) -> A) and (B -> (C -> (B and C)))), M:tm-76, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-1682
in-theory        1682
times-derived    2
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B or C)))
theorem-size     11
proof            (modus-ponens tm-76 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1682.         (((not (not A)) -> A) and (B -> (B or C))), M:tm-76, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-1683
in-theory        1683
times-derived    2
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C or B)))
theorem-size     11
proof            (modus-ponens tm-76 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1683.         (((not (not A)) -> A) and (B -> (C or B))), M:tm-76, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-1684
in-theory        1684
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> ((C -> D) -> ((B or C) -> D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-10 tm-8)
proof-size       53
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1684.         (((not (not A)) -> A) and ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-76, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1685
in-theory        1685
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> ((B -> (not C)) -> (not B))))
theorem-size     17
proof            (modus-ponens tm-76 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-10 tm-9)
proof-size       49
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1685.         (((not (not A)) -> A) and ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-76, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-1686
in-theory        1686
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((not (not B)) -> B))
theorem-size     11
proof            (modus-ponens tm-76 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-10)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1686.         (((not (not A)) -> A) and ((not (not B)) -> B)), M:tm-76, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-1687
in-theory        1687
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> (D -> C))))
theorem-size     13
proof            (modus-ponens tm-76 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1687.         (((not (not A)) -> A) and (B -> (C -> (D -> C)))), M:tm-76, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-1688
in-theory        1688
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> (B -> B)))
theorem-size     13
proof            (modus-ponens tm-76 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-1688.         (((not (not A)) -> A) and ((B -> C) -> (B -> B))), M:tm-76, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-1689
in-theory        1689
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     25
proof            (modus-ponens tm-76 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1689.         (((not (not A)) -> A) and (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-76, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-1690
in-theory        1690
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1690.         (((not (not A)) -> A) and (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-76, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-1691
in-theory        1691
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))
theorem-size     21
proof            (modus-ponens tm-76 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1691.         (((not (not A)) -> A) and ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-76, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-1692
in-theory        1692
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C and D) -> C)))
theorem-size     13
proof            (modus-ponens tm-76 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-10 tm-1 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1692.         (((not (not A)) -> A) and (B -> ((C and D) -> C))), M:tm-76, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-1693
in-theory        1693
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))
theorem-size     21
proof            (modus-ponens tm-76 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1693.         (((not (not A)) -> A) and (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-76, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-1694
in-theory        1694
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C and D) -> D)))
theorem-size     13
proof            (modus-ponens tm-76 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-10 tm-1 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1694.         (((not (not A)) -> A) and (B -> ((C and D) -> D))), M:tm-76, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-1695
in-theory        1695
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (D -> C)) and B)))
theorem-size     15
proof            (modus-ponens tm-76 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1695.         (((not (not A)) -> A) and (B -> ((C -> (D -> C)) and B))), M:tm-76, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-1696
in-theory        1696
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))
theorem-size     23
proof            (modus-ponens tm-76 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1696.         (((not (not A)) -> A) and (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-76, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-1697
in-theory        1697
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C and D) -> C) and B)))
theorem-size     15
proof            (modus-ponens tm-76 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-10 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1697.         (((not (not A)) -> A) and (B -> (((C and D) -> C) and B))), M:tm-76, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-1698
in-theory        1698
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C and D) -> D) and B)))
theorem-size     15
proof            (modus-ponens tm-76 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-10 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1698.         (((not (not A)) -> A) and (B -> (((C and D) -> D) and B))), M:tm-76, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-1699
in-theory        1699
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (D -> (C and D))) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1699.         (((not (not A)) -> A) and (B -> ((C -> (D -> (C and D))) and B))), M:tm-76, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-1700
in-theory        1700
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> (B -> (B and C))))
theorem-size     15
proof            (modus-ponens tm-76 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1700.         (((not (not A)) -> A) and ((B -> C) -> (B -> (B and C)))), M:tm-76, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-1701
in-theory        1701
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> (D -> (C and D)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1701.         (((not (not A)) -> A) and (B -> (C -> (D -> (C and D))))), M:tm-76, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-1702
in-theory        1702
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) or D))
theorem-size     13
proof            (modus-ponens tm-76 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-10 tm-6 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1702.         (((not (not A)) -> A) and ((B -> (C -> B)) or D)), M:tm-76, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-1703
in-theory        1703
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))
theorem-size     21
proof            (modus-ponens tm-76 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1703.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-76, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-1704
in-theory        1704
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) or D))
theorem-size     13
proof            (modus-ponens tm-76 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-10 tm-6 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1704.         (((not (not A)) -> A) and (((B and C) -> B) or D)), M:tm-76, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-1705
in-theory        1705
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) or D))
theorem-size     13
proof            (modus-ponens tm-76 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-10 tm-6 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1705.         (((not (not A)) -> A) and (((B and C) -> C) or D)), M:tm-76, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-1706
in-theory        1706
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) or D))
theorem-size     15
proof            (modus-ponens tm-76 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1706.         (((not (not A)) -> A) and ((B -> (C -> (B and C))) or D)), M:tm-76, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-1707
in-theory        1707
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) or D))
theorem-size     13
proof            (modus-ponens tm-76 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1707.         (((not (not A)) -> A) and ((B -> (B or C)) or D)), M:tm-76, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-1708
in-theory        1708
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (C or D)) and B)))
theorem-size     15
proof            (modus-ponens tm-76 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1708.         (((not (not A)) -> A) and (B -> ((C -> (C or D)) and B))), M:tm-76, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-1709
in-theory        1709
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> (C or D))))
theorem-size     13
proof            (modus-ponens tm-76 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1709.         (((not (not A)) -> A) and (B -> (C -> (C or D)))), M:tm-76, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-1710
in-theory        1710
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> (D -> C))))
theorem-size     13
proof            (modus-ponens tm-76 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1710.         (((not (not A)) -> A) and (B or (C -> (D -> C)))), M:tm-76, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-1711
in-theory        1711
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1711.         (((not (not A)) -> A) and (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-76, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-1712
in-theory        1712
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((C and D) -> C)))
theorem-size     13
proof            (modus-ponens tm-76 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-10 tm-7 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1712.         (((not (not A)) -> A) and (B or ((C and D) -> C))), M:tm-76, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-1713
in-theory        1713
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((C and D) -> D)))
theorem-size     13
proof            (modus-ponens tm-76 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-10 tm-7 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1713.         (((not (not A)) -> A) and (B or ((C and D) -> D))), M:tm-76, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-1714
in-theory        1714
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> (D -> (C and D)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1714.         (((not (not A)) -> A) and (B or (C -> (D -> (C and D))))), M:tm-76, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-1715
in-theory        1715
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> (C or D))))
theorem-size     13
proof            (modus-ponens tm-76 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1715.         (((not (not A)) -> A) and (B or (C -> (C or D)))), M:tm-76, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-1716
in-theory        1716
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> (D or C))))
theorem-size     13
proof            (modus-ponens tm-76 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1716.         (((not (not A)) -> A) and (B or (C -> (D or C)))), M:tm-76, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-1717
in-theory        1717
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) or D))
theorem-size     13
proof            (modus-ponens tm-76 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-10 tm-6 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1717.         (((not (not A)) -> A) and ((B -> (C or B)) or D)), M:tm-76, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-1718
in-theory        1718
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (D or C)) and B)))
theorem-size     15
proof            (modus-ponens tm-76 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1718.         (((not (not A)) -> A) and (B -> ((C -> (D or C)) and B))), M:tm-76, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-1719
in-theory        1719
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> (D or C))))
theorem-size     13
proof            (modus-ponens tm-76 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1719.         (((not (not A)) -> A) and (B -> (C -> (D or C)))), M:tm-76, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-1720
in-theory        1720
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> D) -> ((C or (B -> C)) -> D)))
theorem-size     19
proof            (modus-ponens tm-76 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1720.         (((not (not A)) -> A) and (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-76, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-1721
in-theory        1721
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     31
proof            (modus-ponens tm-76 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1721.         (((not (not A)) -> A) and ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-76, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-1722
in-theory        1722
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> (((B and D) or B) -> C)))
theorem-size     17
proof            (modus-ponens tm-76 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1722.         (((not (not A)) -> A) and ((B -> C) -> (((B and D) or B) -> C))), M:tm-76, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-1723
in-theory        1723
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> (((D and B) or B) -> C)))
theorem-size     17
proof            (modus-ponens tm-76 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1723.         (((not (not A)) -> A) and ((B -> C) -> (((D and B) or B) -> C))), M:tm-76, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-1724
in-theory        1724
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D)))
theorem-size     23
proof            (modus-ponens tm-76 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-10 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1724.         (((not (not A)) -> A) and (((B -> (C and B)) -> D) -> ((C or (B -> (C and B))) -> D))), M:tm-76, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-1725
in-theory        1725
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B or C) -> D) -> ((B or (B or C)) -> D)))
theorem-size     19
proof            (modus-ponens tm-76 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-6)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1725.         (((not (not A)) -> A) and (((B or C) -> D) -> ((B or (B or C)) -> D))), M:tm-76, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-1726
in-theory        1726
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B or C) -> D) -> ((C or (B or C)) -> D)))
theorem-size     19
proof            (modus-ponens tm-76 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-7)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1726.         (((not (not A)) -> A) and (((B or C) -> D) -> ((C or (B or C)) -> D))), M:tm-76, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-1727
in-theory        1727
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-76 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-10 tm-8)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1727.         (((not (not A)) -> A) and ((((B -> C) -> ((D or B) -> C)) -> E) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> E))), M:tm-76, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-1728
in-theory        1728
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1728.         (((not (not A)) -> A) and (B or ((C -> D) -> ((D -> E) -> ((C or D) -> E))))), M:tm-76, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1729
in-theory        1729
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E))
theorem-size     21
proof            (modus-ponens tm-76 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1729.         (((not (not A)) -> A) and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) or E)), M:tm-76, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-1730
in-theory        1730
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and B)))
theorem-size     23
proof            (modus-ponens tm-76 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-10 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1730.         (((not (not A)) -> A) and (B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and B))), M:tm-76, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-1731
in-theory        1731
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> (C -> D)) -> ((B -> C) -> ((B or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-76 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1731.         (((not (not A)) -> A) and (((B -> C) -> (C -> D)) -> ((B -> C) -> ((B or C) -> D)))), M:tm-76, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1732
in-theory        1732
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1732.         (((not (not A)) -> A) and (B -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))), M:tm-76, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-1733
in-theory        1733
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not (C -> B))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-76 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1733.         (((not (not A)) -> A) and ((B -> (not (C -> B))) -> (not B))), M:tm-76, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-1734
in-theory        1734
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> (not ((B -> C) -> (B -> D)))) -> (not (B -> (C -> D)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-10 tm-9 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1734.         (((not (not A)) -> A) and (((B -> (C -> D)) -> (not ((B -> C) -> (B -> D)))) -> (not (B -> (C -> D))))), M:tm-76, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-1735
in-theory        1735
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> (not B)) -> (not (B and C))))
theorem-size     17
proof            (modus-ponens tm-76 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-10 tm-9 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1735.         (((not (not A)) -> A) and (((B and C) -> (not B)) -> (not (B and C)))), M:tm-76, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-1736
in-theory        1736
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> (not C)) -> (not (B and C))))
theorem-size     17
proof            (modus-ponens tm-76 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-10 tm-9 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1736.         (((not (not A)) -> A) and (((B and C) -> (not C)) -> (not (B and C)))), M:tm-76, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-1737
in-theory        1737
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not (C -> (B and C)))) -> (not B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1737.         (((not (not A)) -> A) and ((B -> (not (C -> (B and C)))) -> (not B))), M:tm-76, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-1738
in-theory        1738
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not (B or C))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-76 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1738.         (((not (not A)) -> A) and ((B -> (not (B or C))) -> (not B))), M:tm-76, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-1739
in-theory        1739
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not (C or B))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-76 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1739.         (((not (not A)) -> A) and ((B -> (not (C or B))) -> (not B))), M:tm-76, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-1740
in-theory        1740
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> (not ((C -> D) -> ((B or C) -> D)))) -> (not (B -> C))))
theorem-size     25
proof            (modus-ponens tm-76 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-10 tm-9 tm-8)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1740.         (((not (not A)) -> A) and (((B -> C) -> (not ((C -> D) -> ((B or C) -> D)))) -> (not (B -> C)))), M:tm-76, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1741
in-theory        1741
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> (not ((B -> (not C)) -> (not B)))) -> (not (B -> C))))
theorem-size     23
proof            (modus-ponens tm-76 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-10 tm-9)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1741.         (((not (not A)) -> A) and (((B -> C) -> (not ((B -> (not C)) -> (not B)))) -> (not (B -> C)))), M:tm-76, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-1742
in-theory        1742
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (not C)) -> (not B)) -> D) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> D)))
theorem-size     29
proof            (modus-ponens tm-76 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-9)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1742.         (((not (not A)) -> A) and ((((B -> (not C)) -> (not B)) -> D) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> D))), M:tm-76, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-1743
in-theory        1743
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((C -> D) -> ((C -> (not D)) -> (not C)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1743.         (((not (not A)) -> A) and (B or ((C -> D) -> ((C -> (not D)) -> (not C))))), M:tm-76, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1744
in-theory        1744
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((B -> (not C)) -> (not B))) or D))
theorem-size     19
proof            (modus-ponens tm-76 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-10 tm-6 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1744.         (((not (not A)) -> A) and (((B -> C) -> ((B -> (not C)) -> (not B))) or D)), M:tm-76, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-1745
in-theory        1745
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> D) -> ((C -> (not D)) -> (not C))) and B)))
theorem-size     21
proof            (modus-ponens tm-76 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-10 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1745.         (((not (not A)) -> A) and (B -> (((C -> D) -> ((C -> (not D)) -> (not C))) and B))), M:tm-76, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-1746
in-theory        1746
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> (B -> (not C))) -> ((B -> C) -> (not B))))
theorem-size     21
proof            (modus-ponens tm-76 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-10 tm-2 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1746.         (((not (not A)) -> A) and (((B -> C) -> (B -> (not C))) -> ((B -> C) -> (not B)))), M:tm-76, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-1747
in-theory        1747
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> D) -> ((C -> (not D)) -> (not C)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-9)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1747.         (((not (not A)) -> A) and (B -> ((C -> D) -> ((C -> (not D)) -> (not C))))), M:tm-76, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-1748
in-theory        1748
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((not (not B)) -> (not B)) -> (not (not (not B)))))
theorem-size     17
proof            (modus-ponens tm-76 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-10 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1748.         (((not (not A)) -> A) and (((not (not B)) -> (not B)) -> (not (not (not B))))), M:tm-76, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-1749
in-theory        1749
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> (((not (not B)) or B) -> C)))
theorem-size     17
proof            (modus-ponens tm-76 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-10 tm-8)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1749.         (((not (not A)) -> A) and ((B -> C) -> (((not (not B)) or B) -> C))), M:tm-76, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-1750
in-theory        1750
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((not (not C)) -> C)))
theorem-size     13
proof            (modus-ponens tm-76 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1750.         (((not (not A)) -> A) and (B or ((not (not C)) -> C))), M:tm-76, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1751
in-theory        1751
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((not (not B)) -> B) or C))
theorem-size     13
proof            (modus-ponens tm-76 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1751.         (((not (not A)) -> A) and (((not (not B)) -> B) or C)), M:tm-76, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-1752
in-theory        1752
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((not (not C)) -> C) and B)))
theorem-size     15
proof            (modus-ponens tm-76 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-10)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1752.         (((not (not A)) -> A) and (B -> (((not (not C)) -> C) and B))), M:tm-76, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-1753
in-theory        1753
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((not (not B)) -> B) and A))
theorem-size     13
proof            (modus-ponens tm-73 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-8 tm-10 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1753.         (((not (not A)) or A) -> (((not (not B)) -> B) and A)), M:tm-73, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-1754
in-theory        1754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((not (not D)) -> D) and C)))
theorem-size     21
proof            (modus-ponens tm-69 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-9 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1754.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((not (not D)) -> D) and C))), M:tm-69, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-1755
in-theory        1755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((not (not C)) -> C) and ((A -> (not B)) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-66 tm-76 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (not (not Bm)) Bm) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-10)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1755.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((not (not C)) -> C) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-76, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (not (not Bm)) Bm) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-1756
in-theory        1756
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((not (not E)) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-54 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-10)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1756.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((not (not E)) -> E) and D))), M:tm-54, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-1757
in-theory        1757
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((not (not D)) -> D) and ((B -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-51 tm-76 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (not (not Bm)) Bm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-10)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1757.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((not (not D)) -> D) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-76, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (not (not Bm)) Bm) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-1758
in-theory        1758
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((not (not C)) -> C) and (B or A)))
theorem-size     15
proof            (modus-ponens tm-50 tm-76 ((Am (or A B)) (C (and (-> (not (not Bm)) Bm) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-10)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1758.         ((A or (B or A)) -> (((not (not C)) -> C) and (B or A))), M:tm-50, m:tm-76, u:((Am (or A B)) (C (and (-> (not (not Bm)) Bm) (or A B))))
================================================================
tm-name          tm-1759
in-theory        1759
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((not (not C)) -> C) and (A or B)))
theorem-size     15
proof            (modus-ponens tm-49 tm-76 ((Am (or A B)) (C (and (-> (not (not Bm)) Bm) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-10)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1759.         ((A or (A or B)) -> (((not (not C)) -> C) and (A or B))), M:tm-49, m:tm-76, u:((Am (or A B)) (C (and (-> (not (not Bm)) Bm) (or A B))))
================================================================
tm-name          tm-1760
in-theory        1760
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((not (not C)) -> C) and (B -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-48 tm-76 ((Am (-> A (and B A))) (C (and (-> (not (not Bm)) Bm) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-10)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1760.         ((A or (B -> (A and B))) -> (((not (not C)) -> C) and (B -> (A and B)))), M:tm-48, m:tm-76, u:((Am (-> A (and B A))) (C (and (-> (not (not Bm)) Bm) (-> A (and B A)))))
================================================================
tm-name          tm-1761
in-theory        1761
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((not (not C)) -> C) and B))
theorem-size     13
proof            (modus-ponens tm-47 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1761.         (((A and B) or B) -> (((not (not C)) -> C) and B)), M:tm-47, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-1762
in-theory        1762
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((not (not C)) -> C) and A))
theorem-size     13
proof            (modus-ponens tm-46 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1762.         (((A and B) or A) -> (((not (not C)) -> C) and A)), M:tm-46, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-1763
in-theory        1763
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((not (not D)) -> D) and ((A -> B) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-45 tm-76 ((Am (-> (-> A B) (-> A C))) (D (and (-> (not (not Bm)) Bm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-10)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1763.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((not (not D)) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-76, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (not (not Bm)) Bm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-1764
in-theory        1764
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((not (not C)) -> C) and (B -> A)))
theorem-size     15
proof            (modus-ponens tm-44 tm-76 ((Am (-> A B)) (C (and (-> (not (not Bm)) Bm) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-10)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1764.         ((A or (B -> A)) -> (((not (not C)) -> C) and (B -> A))), M:tm-44, m:tm-76, u:((Am (-> A B)) (C (and (-> (not (not Bm)) Bm) (-> A B))))
================================================================
tm-name          tm-1765
in-theory        1765
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((not (not D)) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-42 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1765.         ((A -> (B or A)) and (C -> (((not (not D)) -> D) and C))), M:tm-42, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-1766
in-theory        1766
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((not (not D)) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-32 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1766.         ((A -> (A or B)) and (C -> (((not (not D)) -> D) and C))), M:tm-32, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-1767
in-theory        1767
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((not (not B)) -> B) and A)))
theorem-size     11
proof            (modus-ponens tm-24 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1767.         (A -> (A and (((not (not B)) -> B) and A))), M:tm-24, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-1768
in-theory        1768
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((not (not D)) -> D) and C)))
theorem-size     17
proof            (modus-ponens tm-23 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1768.         ((A -> (B -> (A and B))) and (C -> (((not (not D)) -> D) and C))), M:tm-23, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-1769
in-theory        1769
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((not (not D)) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-22 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-4 tm-10)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1769.         (((A and B) -> B) and (C -> (((not (not D)) -> D) and C))), M:tm-22, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-1770
in-theory        1770
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((not (not D)) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-21 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-3 tm-10)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1770.         (((A and B) -> A) and (C -> (((not (not D)) -> D) and C))), M:tm-21, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-1771
in-theory        1771
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((not (not E)) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-20 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1771.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((not (not E)) -> E) and D))), M:tm-20, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-1772
in-theory        1772
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((not (not D)) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-19 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1772.         ((A -> (B -> A)) and (C -> (((not (not D)) -> D) and C))), M:tm-19, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-1773
in-theory        1773
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((not (not B)) -> B) and A))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-9 tm-5 tm-10)
proof-size       45
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1773.         ((A -> (not (((not (not B)) -> B) and A))) -> (not A)), M:tm-9, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-1774
in-theory        1774
times-derived    2
----------------------------------------------------------------
theorem          (((((not (not A)) -> A) and B) -> C) -> ((B or (((not (not A)) -> A) and B)) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-8 tm-5 tm-10)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1774.         (((((not (not A)) -> A) and B) -> C) -> ((B or (((not (not A)) -> A) and B)) -> C)), M:tm-8, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-1775
in-theory        1775
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((not (not C)) -> C) and B)))
theorem-size     11
proof            (modus-ponens tm-7 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-7 tm-5 tm-10)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1775.         (A or (B -> (((not (not C)) -> C) and B))), M:tm-7, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-1776
in-theory        1776
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) or C)
theorem-size     11
proof            (modus-ponens tm-6 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-6 tm-5 tm-10)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1776.         ((A -> (((not (not B)) -> B) and A)) or C), M:tm-6, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-1777
in-theory        1777
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((not (not C)) -> C) and B)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-10)
proof-size       41
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1777.         (A -> ((B -> (((not (not C)) -> C) and B)) and A)), M:tm-5, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-1778
in-theory        1778
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((not (not C)) -> C) and B)))
theorem-size     11
proof            (modus-ponens tm-1 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-1 tm-5 tm-10)
proof-size       37
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1778.         (A -> (B -> (((not (not C)) -> C) and B))), M:tm-1, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-1779
in-theory        1779
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> (B -> A)) -> C))) -> C)
theorem-size     11
proof            (modus-ponens tm-77 tm-11 ((Am (not (not (-> (-> Bm (-> Cm Bm)) B)))) (A (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-10 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1779.         ((not (not ((A -> (B -> A)) -> C))) -> C), M:tm-77, m:tm-11, u:((Am (not (not (-> (-> Bm (-> Cm Bm)) B)))) (A (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-1780
in-theory        1780
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D)
theorem-size     19
proof            (modus-ponens tm-77 tm-14 ((Am (not (not (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B)))) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-10 tm-1)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1780.         ((not (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D), M:tm-77, m:tm-14, u:((Am (not (not (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B)))) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-1781
in-theory        1781
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((A and B) -> A) -> C))) -> C)
theorem-size     11
proof            (modus-ponens tm-77 tm-16 ((Am (not (not (-> (-> (and Bm Cm) Bm) B)))) (A (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-10 tm-1 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1781.         ((not (not (((A and B) -> A) -> C))) -> C), M:tm-77, m:tm-16, u:((Am (not (not (-> (-> (and Bm Cm) Bm) B)))) (A (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-1782
in-theory        1782
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((A and B) -> B) -> C))) -> C)
theorem-size     11
proof            (modus-ponens tm-77 tm-18 ((Am (not (not (-> (-> (and Bm Cm) Cm) B)))) (A (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-10 tm-1 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1782.         ((not (not (((A and B) -> B) -> C))) -> C), M:tm-77, m:tm-18, u:((Am (not (not (-> (-> (and Bm Cm) Cm) B)))) (A (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-1783
in-theory        1783
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> (B -> (A and B))) -> C))) -> C)
theorem-size     13
proof            (modus-ponens tm-77 tm-25 ((Am (not (not (-> (-> Bm (-> Cm (and Bm Cm))) B)))) (A (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-10 tm-1 tm-5)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1783.         ((not (not ((A -> (B -> (A and B))) -> C))) -> C), M:tm-77, m:tm-25, u:((Am (not (not (-> (-> Bm (-> Cm (and Bm Cm))) B)))) (A (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-1784
in-theory        1784
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> (A or B)) -> C))) -> C)
theorem-size     11
proof            (modus-ponens tm-77 tm-33 ((Am (not (not (-> (-> Bm (or Bm Cm)) B)))) (A (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1784.         ((not (not ((A -> (A or B)) -> C))) -> C), M:tm-77, m:tm-33, u:((Am (not (not (-> (-> Bm (or Bm Cm)) B)))) (A (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-1785
in-theory        1785
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> (B or A)) -> C))) -> C)
theorem-size     11
proof            (modus-ponens tm-77 tm-43 ((Am (not (not (-> (-> Bm (or Cm Bm)) B)))) (A (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1785.         ((not (not ((A -> (B or A)) -> C))) -> C), M:tm-77, m:tm-43, u:((Am (not (not (-> (-> Bm (or Cm Bm)) B)))) (A (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-1786
in-theory        1786
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D))) -> D)
theorem-size     19
proof            (modus-ponens tm-77 tm-56 ((Am (not (not (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B)))) (A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-10 tm-1 tm-8)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1786.         ((not (not (((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D))) -> D), M:tm-77, m:tm-56, u:((Am (not (not (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B)))) (A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1787
in-theory        1787
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((A -> B) -> ((A -> (not B)) -> (not A))) -> C))) -> C)
theorem-size     17
proof            (modus-ponens tm-77 tm-71 ((Am (not (not (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) B)))) (A (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-10 tm-1 tm-9)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1787.         ((not (not (((A -> B) -> ((A -> (not B)) -> (not A))) -> C))) -> C), M:tm-77, m:tm-71, u:((Am (not (not (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) B)))) (A (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1788
in-theory        1788
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((not (not (B -> C))) -> B) -> ((not (not (B -> C))) -> C)))
theorem-size     21
proof            (modus-ponens tm-76 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1788.         (((not (not A)) -> A) and (((not (not (B -> C))) -> B) -> ((not (not (B -> C))) -> C))), M:tm-76, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-1789
in-theory        1789
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((not (not (A -> B))) -> A))) or ((not (not (A -> B))) -> A)) -> ((not (not (A -> B))) -> B))
theorem-size     25
proof            (modus-ponens tm-73 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1789.         (((not (not ((not (not (A -> B))) -> A))) or ((not (not (A -> B))) -> A)) -> ((not (not (A -> B))) -> B)), M:tm-73, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-1790
in-theory        1790
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not A)))) -> A) -> (not (not (not (A -> (not A))))))
theorem-size     16
proof            (modus-ponens tm-70 tm-77 ((B Am) (A (not (not (-> Am (not Am))))) (Bm (not Am))))
axioms-used      (tm-2 tm-9 tm-10)
proof-size       88
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1790.         (((not (not (A -> (not A)))) -> A) -> (not (not (not (A -> (not A)))))), M:tm-70, m:tm-77, u:((B Am) (A (not (not (-> Am (not Am))))) (Bm (not Am)))
================================================================
tm-name          tm-1791
in-theory        1791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D)))
theorem-size     27
proof            (modus-ponens tm-69 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-10)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1791.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D))), M:tm-69, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-1792
in-theory        1792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     29
proof            (modus-ponens tm-54 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-10)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1792.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-54, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-1793
in-theory        1793
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((not (not (B -> C))) -> B)) or ((not (not (B -> C))) -> B)) -> ((not (not (B -> C))) -> C))
theorem-size     25
proof            (modus-ponens tm-47 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-10)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1793.         (((A and ((not (not (B -> C))) -> B)) or ((not (not (B -> C))) -> B)) -> ((not (not (B -> C))) -> C)), M:tm-47, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-1794
in-theory        1794
times-derived    2
----------------------------------------------------------------
theorem          (((((not (not (A -> B))) -> A) and C) or ((not (not (A -> B))) -> A)) -> ((not (not (A -> B))) -> B))
theorem-size     25
proof            (modus-ponens tm-46 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-8 tm-3 tm-2 tm-10)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1794.         (((((not (not (A -> B))) -> A) and C) or ((not (not (A -> B))) -> A)) -> ((not (not (A -> B))) -> B)), M:tm-46, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-1795
in-theory        1795
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((not (not (A -> B))) -> A)) -> ((not (not (A -> B))) -> B))
theorem-size     17
proof            (modus-ponens tm-44 tm-77 ((A (not (not (-> Am Bm)))) (B Am) (C (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-8 tm-1 tm-2 tm-10)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1795.         ((A or ((not (not (A -> B))) -> A)) -> ((not (not (A -> B))) -> B)), M:tm-44, m:tm-77, u:((A (not (not (-> Am Bm)))) (B Am) (C (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-1796
in-theory        1796
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D)))
theorem-size     21
proof            (modus-ponens tm-42 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1796.         ((A -> (B or A)) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D))), M:tm-42, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-1797
in-theory        1797
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D)))
theorem-size     21
proof            (modus-ponens tm-32 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1797.         ((A -> (A or B)) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D))), M:tm-32, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-1798
in-theory        1798
times-derived    2
----------------------------------------------------------------
theorem          (((not (not (A -> B))) -> A) -> (((not (not (A -> B))) -> A) and ((not (not (A -> B))) -> B)))
theorem-size     23
proof            (modus-ponens tm-24 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1798.         (((not (not (A -> B))) -> A) -> (((not (not (A -> B))) -> A) and ((not (not (A -> B))) -> B))), M:tm-24, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-1799
in-theory        1799
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D)))
theorem-size     23
proof            (modus-ponens tm-23 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1799.         ((A -> (B -> (A and B))) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D))), M:tm-23, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-1800
in-theory        1800
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D)))
theorem-size     21
proof            (modus-ponens tm-22 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1800.         (((A and B) -> B) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D))), M:tm-22, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-1801
in-theory        1801
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D)))
theorem-size     21
proof            (modus-ponens tm-21 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1801.         (((A and B) -> A) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D))), M:tm-21, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-1802
in-theory        1802
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     29
proof            (modus-ponens tm-20 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1802.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-20, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-1803
in-theory        1803
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D)))
theorem-size     21
proof            (modus-ponens tm-19 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1803.         ((A -> (B -> A)) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D))), M:tm-19, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-1804
in-theory        1804
times-derived    2
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> A))) -> (A -> B)) -> ((not (not ((A -> B) -> A))) -> B))
theorem-size     21
proof            (modus-ponens tm-13 tm-77 ((Am (-> Bm C)) (A (not (not (-> (-> Bm C) Bm)))) (B Bm)))
axioms-used      (tm-2 tm-10)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1804.         (((not (not ((A -> B) -> A))) -> (A -> B)) -> ((not (not ((A -> B) -> A))) -> B)), M:tm-13, m:tm-77, u:((Am (-> Bm C)) (A (not (not (-> (-> Bm C) Bm)))) (B Bm))
================================================================
tm-name          tm-1805
in-theory        1805
times-derived    2
----------------------------------------------------------------
theorem          (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> A))
theorem-size     15
proof            (modus-ponens tm-12 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-2 tm-1 tm-10)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1805.         (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> A)), M:tm-12, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-1806
in-theory        1806
times-derived    2
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> (not ((not (not (A -> B))) -> B))) -> (not ((not (not (A -> B))) -> A)))
theorem-size     25
proof            (modus-ponens tm-9 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-9 tm-2 tm-10)
proof-size       69
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1806.         ((((not (not (A -> B))) -> A) -> (not ((not (not (A -> B))) -> B))) -> (not ((not (not (A -> B))) -> A))), M:tm-9, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-1807
in-theory        1807
times-derived    2
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> B) -> C) -> ((((not (not (A -> B))) -> A) or ((not (not (A -> B))) -> B)) -> C))
theorem-size     27
proof            (modus-ponens tm-8 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-8 tm-2 tm-10)
proof-size       73
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1807.         ((((not (not (A -> B))) -> B) -> C) -> ((((not (not (A -> B))) -> A) or ((not (not (A -> B))) -> B)) -> C)), M:tm-8, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-1808
in-theory        1808
times-derived    2
----------------------------------------------------------------
theorem          (A or (((not (not (B -> C))) -> B) -> ((not (not (B -> C))) -> C)))
theorem-size     17
proof            (modus-ponens tm-7 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-7 tm-2 tm-10)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1808.         (A or (((not (not (B -> C))) -> B) -> ((not (not (B -> C))) -> C))), M:tm-7, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-1809
in-theory        1809
times-derived    2
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) or C)
theorem-size     17
proof            (modus-ponens tm-6 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-6 tm-2 tm-10)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1809.         ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) or C), M:tm-6, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-1810
in-theory        1810
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((not (not (B -> C))) -> B) -> ((not (not (B -> C))) -> C)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       59
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1810.         (A -> ((((not (not (B -> C))) -> B) -> ((not (not (B -> C))) -> C)) and A)), M:tm-5, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-1811
in-theory        1811
times-derived    2
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> (not (not (A -> B)))) -> (((not (not (A -> B))) -> A) -> B))
theorem-size     23
proof            (modus-ponens tm-2 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (not (not (-> Am Bm)))) (C Bm)))
axioms-used      (tm-2 tm-10)
proof-size       69
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1811.         ((((not (not (A -> B))) -> A) -> (not (not (A -> B)))) -> (((not (not (A -> B))) -> A) -> B)), M:tm-2, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (not (not (-> Am Bm)))) (C Bm))
================================================================
tm-name          tm-1812
in-theory        1812
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((not (not (B -> C))) -> B) -> ((not (not (B -> C))) -> C)))
theorem-size     17
proof            (modus-ponens tm-1 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-1 tm-2 tm-10)
proof-size       55
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1812.         (A -> (((not (not (B -> C))) -> B) -> ((not (not (B -> C))) -> C))), M:tm-1, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-1813
in-theory        1813
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((not (not A)) -> A) -> B))) -> B)
theorem-size     11
proof            (modus-ponens tm-77 tm-78 ((Am (not (not (-> (-> (not (not Bm)) Bm) B)))) (A (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-10 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1813.         ((not (not (((not (not A)) -> A) -> B))) -> B), M:tm-77, m:tm-78, u:((Am (not (not (-> (-> (not (not Bm)) Bm) B)))) (A (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1814
in-theory        1814
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((not (not C)) -> C)))
theorem-size     13
proof            (modus-ponens tm-76 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1814.         (((not (not A)) -> A) and (B -> ((not (not C)) -> C))), M:tm-76, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1815
in-theory        1815
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((not (not B)) -> B))
theorem-size     11
proof            (modus-ponens tm-73 tm-78 ((A Am) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-10 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1815.         (((not (not A)) or A) -> ((not (not B)) -> B)), M:tm-73, m:tm-78, u:((A Am) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1816
in-theory        1816
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (not A))) -> A) -> (not (not (not (not A)))))
theorem-size     12
proof            (modus-ponens tm-70 tm-78 ((Am (-> (not (not (not B))) B)) (A (not (not (not B)))) (Bm (not B))))
axioms-used      (tm-2 tm-9 tm-1 tm-10)
proof-size       68
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1816.         (((not (not (not A))) -> A) -> (not (not (not (not A))))), M:tm-70, m:tm-78, u:((Am (-> (not (not (not B))) B)) (A (not (not (not B)))) (Bm (not B)))
================================================================
tm-name          tm-1817
in-theory        1817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((not (not D)) -> D)))
theorem-size     19
proof            (modus-ponens tm-69 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-9 tm-1 tm-10)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1817.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((not (not D)) -> D))), M:tm-69, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1818
in-theory        1818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((not (not C)) -> C))
theorem-size     17
proof            (modus-ponens tm-66 tm-78 ((Am (-> (-> A (not B)) (not A))) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-9 tm-1 tm-10)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1818.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((not (not C)) -> C)), M:tm-66, m:tm-78, u:((Am (-> (-> A (not B)) (not A))) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1819
in-theory        1819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (not B))) -> ((A or (not (not B))) -> B))
theorem-size     13
proof            (modus-ponens tm-55 tm-78 ((Am (-> A (not (not Bm)))) (B (not (not Bm))) (C Bm)))
axioms-used      (tm-2 tm-8 tm-1 tm-10)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1819.         ((A -> (not (not B))) -> ((A or (not (not B))) -> B)), M:tm-55, m:tm-78, u:((Am (-> A (not (not Bm)))) (B (not (not Bm))) (C Bm))
================================================================
tm-name          tm-1820
in-theory        1820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-54 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1820.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((not (not E)) -> E))), M:tm-54, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1821
in-theory        1821
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((not (not D)) -> D))
theorem-size     19
proof            (modus-ponens tm-51 tm-78 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-10)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1821.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((not (not D)) -> D)), M:tm-51, m:tm-78, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1822
in-theory        1822
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((not (not C)) -> C))
theorem-size     11
proof            (modus-ponens tm-50 tm-78 ((Am (or A B)) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-7 tm-1 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1822.         ((A or (B or A)) -> ((not (not C)) -> C)), M:tm-50, m:tm-78, u:((Am (or A B)) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1823
in-theory        1823
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((not (not C)) -> C))
theorem-size     11
proof            (modus-ponens tm-49 tm-78 ((Am (or A B)) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-6 tm-1 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1823.         ((A or (A or B)) -> ((not (not C)) -> C)), M:tm-49, m:tm-78, u:((Am (or A B)) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1824
in-theory        1824
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((not (not C)) -> C))
theorem-size     13
proof            (modus-ponens tm-48 tm-78 ((Am (-> A (and B A))) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-5 tm-1 tm-10)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1824.         ((A or (B -> (A and B))) -> ((not (not C)) -> C)), M:tm-48, m:tm-78, u:((Am (-> A (and B A))) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1825
in-theory        1825
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((not (not C)) -> C))
theorem-size     11
proof            (modus-ponens tm-47 tm-78 ((A Am) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-4 tm-1 tm-10)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1825.         (((A and B) or B) -> ((not (not C)) -> C)), M:tm-47, m:tm-78, u:((A Am) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1826
in-theory        1826
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((not (not C)) -> C))
theorem-size     11
proof            (modus-ponens tm-46 tm-78 ((A Am) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-3 tm-1 tm-10)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1826.         (((A and B) or A) -> ((not (not C)) -> C)), M:tm-46, m:tm-78, u:((A Am) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1827
in-theory        1827
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((not (not D)) -> D))
theorem-size     19
proof            (modus-ponens tm-45 tm-78 ((Am (-> (-> A B) (-> A C))) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-10)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1827.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((not (not D)) -> D)), M:tm-45, m:tm-78, u:((Am (-> (-> A B) (-> A C))) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1828
in-theory        1828
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((not (not C)) -> C))
theorem-size     11
proof            (modus-ponens tm-44 tm-78 ((Am (-> A B)) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1828.         ((A or (B -> A)) -> ((not (not C)) -> C)), M:tm-44, m:tm-78, u:((Am (-> A B)) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1829
in-theory        1829
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-42 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1829.         ((A -> (B or A)) and (C -> ((not (not D)) -> D))), M:tm-42, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1830
in-theory        1830
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-32 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1830.         ((A -> (A or B)) and (C -> ((not (not D)) -> D))), M:tm-32, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1831
in-theory        1831
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((not (not B)) -> B)))
theorem-size     9
proof            (modus-ponens tm-24 tm-78 ((A Am) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1831.         (A -> (A and ((not (not B)) -> B))), M:tm-24, m:tm-78, u:((A Am) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1832
in-theory        1832
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((not (not D)) -> D)))
theorem-size     15
proof            (modus-ponens tm-23 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1832.         ((A -> (B -> (A and B))) and (C -> ((not (not D)) -> D))), M:tm-23, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1833
in-theory        1833
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-22 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1833.         (((A and B) -> B) and (C -> ((not (not D)) -> D))), M:tm-22, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1834
in-theory        1834
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-21 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1834.         (((A and B) -> A) and (C -> ((not (not D)) -> D))), M:tm-21, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1835
in-theory        1835
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-20 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1835.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((not (not E)) -> E))), M:tm-20, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1836
in-theory        1836
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-19 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1836.         ((A -> (B -> A)) and (C -> ((not (not D)) -> D))), M:tm-19, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1837
in-theory        1837
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((not (not B)) -> B) -> C)) -> C)
theorem-size     11
proof            (modus-ponens tm-17 tm-78 ((Am (and A (-> (-> (not (not Bm)) Bm) C))) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-4 tm-1 tm-10)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1837.         ((A and (((not (not B)) -> B) -> C)) -> C), M:tm-17, m:tm-78, u:((Am (and A (-> (-> (not (not Bm)) Bm) C))) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1838
in-theory        1838
times-derived    2
----------------------------------------------------------------
theorem          (((((not (not A)) -> A) -> B) and C) -> B)
theorem-size     11
proof            (modus-ponens tm-15 tm-78 ((Am (and (-> (-> (not (not Bm)) Bm) B) C)) (A (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-3 tm-1 tm-10)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1838.         (((((not (not A)) -> A) -> B) and C) -> B), M:tm-15, m:tm-78, u:((Am (and (-> (-> (not (not Bm)) Bm) B) C)) (A (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1839
in-theory        1839
times-derived    2
----------------------------------------------------------------
theorem          (((not (not A)) -> (A -> B)) -> ((not (not A)) -> B))
theorem-size     13
proof            (modus-ponens tm-13 tm-78 ((Am (-> (not (not Bm)) (-> Bm C))) (A (not (not Bm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1839.         (((not (not A)) -> (A -> B)) -> ((not (not A)) -> B)), M:tm-13, m:tm-78, u:((Am (-> (not (not Bm)) (-> Bm C))) (A (not (not Bm))) (B Bm))
================================================================
tm-name          tm-1840
in-theory        1840
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((not (not B)) -> B))) -> (not A))
theorem-size     11
proof            (modus-ponens tm-9 tm-78 ((A Am) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-9 tm-1 tm-10)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1840.         ((A -> (not ((not (not B)) -> B))) -> (not A)), M:tm-9, m:tm-78, u:((A Am) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1841
in-theory        1841
times-derived    2
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) -> B) -> ((C or ((not (not A)) -> A)) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-78 ((A Am) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-10)
proof-size       47
proof-steps      5
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1841.         ((((not (not A)) -> A) -> B) -> ((C or ((not (not A)) -> A)) -> B)), M:tm-8, m:tm-78, u:((A Am) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1842
in-theory        1842
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((not (not C)) -> C)))
theorem-size     9
proof            (modus-ponens tm-7 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-7 tm-1 tm-10)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1842.         (A or (B -> ((not (not C)) -> C))), M:tm-7, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1843
in-theory        1843
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) or C)
theorem-size     9
proof            (modus-ponens tm-6 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-6 tm-1 tm-10)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1843.         ((A -> ((not (not B)) -> B)) or C), M:tm-6, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1844
in-theory        1844
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((not (not C)) -> C)) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       35
proof-steps      5
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1844.         (A -> ((B -> ((not (not C)) -> C)) and A)), M:tm-5, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1845
in-theory        1845
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (not B))) -> (A -> B))
theorem-size     9
proof            (modus-ponens tm-2 tm-78 ((A Am) (B (not (not Bm))) (C Bm)))
axioms-used      (tm-2 tm-1 tm-10)
proof-size       39
proof-steps      5
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1845.         ((A -> (not (not B))) -> (A -> B)), M:tm-2, m:tm-78, u:((A Am) (B (not (not Bm))) (C Bm))
================================================================
tm-name          tm-1846
in-theory        1846
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((not (not C)) -> C)))
theorem-size     9
proof            (modus-ponens tm-1 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-1 tm-10)
proof-size       31
proof-steps      5
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1846.         (A -> (B -> ((not (not C)) -> C))), M:tm-1, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-1847
in-theory        1847
times-derived    1
----------------------------------------------------------------
theorem          (not ((not (A -> (B -> A))) and C))
theorem-size     9
proof            (modus-ponens tm-79 tm-3 ((A (and (not (-> B (-> C B))) Bm)) (Am (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-1847.         (not ((not (A -> (B -> A))) and C)), M:tm-79, m:tm-3, u:((A (and (not (-> B (-> C B))) Bm)) (Am (not (-> B (-> C B)))))
================================================================
tm-name          tm-1848
in-theory        1848
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (not (B -> (C -> B)))))
theorem-size     9
proof            (modus-ponens tm-79 tm-4 ((A (and Am (not (-> B (-> C B))))) (Bm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-1848.         (not (A and (not (B -> (C -> B))))), M:tm-79, m:tm-4, u:((A (and Am (not (-> B (-> C B))))) (Bm (not (-> B (-> C B)))))
================================================================
tm-name          tm-1849
in-theory        1849
times-derived    1
----------------------------------------------------------------
theorem          (not (not (not (not (A -> (B -> A))))))
theorem-size     9
proof            (modus-ponens tm-79 tm-10 ((A (not (not (not (-> B (-> C B)))))) (Am (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-1849.         (not (not (not (not (A -> (B -> A)))))), M:tm-79, m:tm-10, u:((A (not (not (not (-> B (-> C B)))))) (Am (not (-> B (-> C B)))))
================================================================
tm-name          tm-1850
in-theory        1850
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (C -> (A -> (B -> A))))))
theorem-size     15
proof            (modus-ponens tm-79 tm-57 ((A (-> (-> B (-> C B)) (not (-> Bm (-> B (-> C B)))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1850.         (not ((A -> (B -> A)) -> (not (C -> (A -> (B -> A)))))), M:tm-79, m:tm-57, u:((A (-> (-> B (-> C B)) (not (-> Bm (-> B (-> C B)))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-1851
in-theory        1851
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not ((A -> B) -> (A -> A)))))
theorem-size     15
proof            (modus-ponens tm-79 tm-58 ((A (-> (-> Am (-> Bm Am)) (not (-> (-> Am Bm) (-> Am Am))))) (Cm Am) (C Bm) (B Am)))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1851.         (not ((A -> (B -> A)) -> (not ((A -> B) -> (A -> A))))), M:tm-79, m:tm-58, u:((A (-> (-> Am (-> Bm Am)) (not (-> (-> Am Bm) (-> Am Am))))) (Cm Am) (C Bm) (B Am))
================================================================
tm-name          tm-1852
in-theory        1852
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (C -> ((A -> (B -> A)) and C)))))
theorem-size     17
proof            (modus-ponens tm-79 tm-61 ((A (-> (-> B (-> C B)) (not (-> Bm (and (-> B (-> C B)) Bm))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1852.         (not ((A -> (B -> A)) -> (not (C -> ((A -> (B -> A)) and C))))), M:tm-79, m:tm-61, u:((A (-> (-> B (-> C B)) (not (-> Bm (and (-> B (-> C B)) Bm))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-1853
in-theory        1853
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not ((A -> (B -> A)) or C))))
theorem-size     15
proof            (modus-ponens tm-79 tm-62 ((A (-> (-> B (-> C B)) (not (or (-> B (-> C B)) Bm)))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1853.         (not ((A -> (B -> A)) -> (not ((A -> (B -> A)) or C)))), M:tm-79, m:tm-62, u:((A (-> (-> B (-> C B)) (not (or (-> B (-> C B)) Bm)))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-1854
in-theory        1854
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (C or (A -> (B -> A))))))
theorem-size     15
proof            (modus-ponens tm-79 tm-63 ((A (-> (-> B (-> C B)) (not (or Bm (-> B (-> C B)))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1854.         (not ((A -> (B -> A)) -> (not (C or (A -> (B -> A)))))), M:tm-79, m:tm-63, u:((A (-> (-> B (-> C B)) (not (or Bm (-> B (-> C B)))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-1855
in-theory        1855
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (((B -> A) -> C) -> ((A or (B -> A)) -> C)))))
theorem-size     21
proof            (modus-ponens tm-79 tm-64 ((A (-> (-> Am (-> C Am)) (not (-> (-> (-> C Am) Cm) (-> (or Am (-> C Am)) Cm))))) (B Am) (Bm (-> C Am))))
axioms-used      (tm-9 tm-1 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1855.         (not ((A -> (B -> A)) -> (not (((B -> A) -> C) -> ((A or (B -> A)) -> C))))), M:tm-79, m:tm-64, u:((A (-> (-> Am (-> C Am)) (not (-> (-> (-> C Am) Cm) (-> (or Am (-> C Am)) Cm))))) (B Am) (Bm (-> C Am)))
================================================================
tm-name          tm-1856
in-theory        1856
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not ((A -> (not (B -> A))) -> (not A)))))
theorem-size     17
proof            (modus-ponens tm-79 tm-65 ((A (-> (-> Am (-> C Am)) (not (-> (-> Am (not (-> C Am))) (not Am))))) (B Am) (Bm (-> C Am))))
axioms-used      (tm-9 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1856.         (not ((A -> (B -> A)) -> (not ((A -> (not (B -> A))) -> (not A))))), M:tm-79, m:tm-65, u:((A (-> (-> Am (-> C Am)) (not (-> (-> Am (not (-> C Am))) (not Am))))) (B Am) (Bm (-> C Am)))
================================================================
tm-name          tm-1857
in-theory        1857
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (C -> (D -> C)))))
theorem-size     13
proof            (modus-ponens tm-79 tm-79 ((A (-> (-> B (-> C B)) (not (-> Bm (-> Cm Bm))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1857.         (not ((A -> (B -> A)) -> (not (C -> (D -> C))))), M:tm-79, m:tm-79, u:((A (-> (-> B (-> C B)) (not (-> Bm (-> Cm Bm))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-1858
in-theory        1858
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not (C -> (D -> C)))) -> (not B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1858.         (((not (not A)) -> A) and ((B -> (not (C -> (D -> C)))) -> (not B))), M:tm-76, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-1859
in-theory        1859
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not (B -> (C -> B)))))) or (A -> (not (B -> (C -> B))))) -> (not A))
theorem-size     22
proof            (modus-ponens tm-73 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-1)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1859.         (((not (not (A -> (not (B -> (C -> B)))))) or (A -> (not (B -> (C -> B))))) -> (not A)), M:tm-73, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-1860
in-theory        1860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (D -> (E -> D)))) -> (not C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1860.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (D -> (E -> D)))) -> (not C))), M:tm-69, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-1861
in-theory        1861
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) or (((A -> (B -> A)) -> (not C)) -> (not (A -> (B -> A))))) -> (not ((A -> (B -> A)) -> (not C))))
theorem-size     33
proof            (modus-ponens tm-66 tm-79 ((Am (-> (-> Bm (-> Cm Bm)) (not B))) (A (-> Bm (-> Cm Bm))) (C (not (-> (-> Bm (-> Cm Bm)) (not B))))))
axioms-used      (tm-8 tm-9 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1861.         ((((A -> (B -> A)) -> C) or (((A -> (B -> A)) -> (not C)) -> (not (A -> (B -> A))))) -> (not ((A -> (B -> A)) -> (not C)))), M:tm-66, m:tm-79, u:((Am (-> (-> Bm (-> Cm Bm)) (not B))) (A (-> Bm (-> Cm Bm))) (C (not (-> (-> Bm (-> Cm Bm)) (not B)))))
================================================================
tm-name          tm-1862
in-theory        1862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1862.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-54, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-1863
in-theory        1863
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not (C -> (D -> C))))) or (B -> (not (C -> (D -> C))))) -> (not B))
theorem-size     22
proof            (modus-ponens tm-47 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-1)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1863.         (((A and (B -> (not (C -> (D -> C))))) or (B -> (not (C -> (D -> C))))) -> (not B)), M:tm-47, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-1864
in-theory        1864
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not (B -> (C -> B)))) and D) or (A -> (not (B -> (C -> B))))) -> (not A))
theorem-size     22
proof            (modus-ponens tm-46 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-1)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1864.         ((((A -> (not (B -> (C -> B)))) and D) or (A -> (not (B -> (C -> B))))) -> (not A)), M:tm-46, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-1865
in-theory        1865
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> (B -> A))) or (C -> (not (A -> (B -> A))))) -> (not C))
theorem-size     18
proof            (modus-ponens tm-44 tm-79 ((A Am) (B (not (-> Bm (-> Cm Bm)))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       88
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1865.         (((not (A -> (B -> A))) or (C -> (not (A -> (B -> A))))) -> (not C)), M:tm-44, m:tm-79, u:((A Am) (B (not (-> Bm (-> Cm Bm)))) (C (not Am)))
================================================================
tm-name          tm-1866
in-theory        1866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not (D -> (E -> D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1866.         ((A -> (B or A)) and ((C -> (not (D -> (E -> D)))) -> (not C))), M:tm-42, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-1867
in-theory        1867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not (D -> (E -> D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1867.         ((A -> (A or B)) and ((C -> (not (D -> (E -> D)))) -> (not C))), M:tm-32, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-1868
in-theory        1868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> B)))) -> ((A -> (not (B -> (C -> B)))) and (not A)))
theorem-size     20
proof            (modus-ponens tm-24 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       88
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1868.         ((A -> (not (B -> (C -> B)))) -> ((A -> (not (B -> (C -> B)))) and (not A))), M:tm-24, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-1869
in-theory        1869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not (D -> (E -> D)))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1869.         ((A -> (B -> (A and B))) and ((C -> (not (D -> (E -> D)))) -> (not C))), M:tm-23, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-1870
in-theory        1870
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not (D -> (E -> D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1870.         (((A and B) -> B) and ((C -> (not (D -> (E -> D)))) -> (not C))), M:tm-22, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-1871
in-theory        1871
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not (D -> (E -> D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1871.         (((A and B) -> A) and ((C -> (not (D -> (E -> D)))) -> (not C))), M:tm-21, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-1872
in-theory        1872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1872.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-20, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-1873
in-theory        1873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not (D -> (E -> D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1873.         ((A -> (B -> A)) and ((C -> (not (D -> (E -> D)))) -> (not C))), M:tm-19, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-1874
in-theory        1874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> B)))) -> (A -> (not (B -> (C -> B)))))
theorem-size     17
proof            (modus-ponens tm-12 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1874.         ((A -> (not (B -> (C -> B)))) -> (A -> (not (B -> (C -> B))))), M:tm-12, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-1875
in-theory        1875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not (not A))) -> (not (A -> (not (B -> (C -> B))))))
theorem-size     22
proof            (modus-ponens tm-9 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-9 tm-1)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1875.         (((A -> (not (B -> (C -> B)))) -> (not (not A))) -> (not (A -> (not (B -> (C -> B)))))), M:tm-9, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-1876
in-theory        1876
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not (C -> (D -> C)))) or (not A)) -> B))
theorem-size     18
proof            (modus-ponens tm-8 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-1)
proof-size       70
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1876.         (((not A) -> B) -> (((A -> (not (C -> (D -> C)))) or (not A)) -> B)), M:tm-8, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-1877
in-theory        1877
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not (C -> (D -> C)))) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1877.         (A or ((B -> (not (C -> (D -> C)))) -> (not B))), M:tm-7, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-1878
in-theory        1878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1878.         (((A -> (not (B -> (C -> B)))) -> (not A)) or D), M:tm-6, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-1879
in-theory        1879
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not (C -> (D -> C)))) -> (not B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1879.         (A -> (((B -> (not (C -> (D -> C)))) -> (not B)) and A)), M:tm-5, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-1880
in-theory        1880
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not (C -> (D -> C)))) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-1 tm-9)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1880.         (A -> ((B -> (not (C -> (D -> C)))) -> (not B))), M:tm-1, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-1881
in-theory        1881
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> (B -> (C -> B))))
theorem-size     15
proof            (modus-ponens tm-80 tm-1 ((Am (-> A (-> B A))) (C (-> Bm (-> A (-> B A))))))
axioms-used      (tm-8 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1881.         ((A or (B -> (C -> B))) -> (D -> (B -> (C -> B)))), M:tm-80, m:tm-1, u:((Am (-> A (-> B A))) (C (-> Bm (-> A (-> B A)))))
================================================================
tm-name          tm-1882
in-theory        1882
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> C) -> (B -> B)))
theorem-size     15
proof            (modus-ponens tm-80 tm-2 ((Cm Am) (B Bm) (A Am) (C (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1882.         ((A or (B -> (C -> B))) -> ((B -> C) -> (B -> B))), M:tm-80, m:tm-2, u:((Cm Am) (B Bm) (A Am) (C (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-1883
in-theory        1883
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> ((B -> (C -> B)) and D)))
theorem-size     17
proof            (modus-ponens tm-80 tm-5 ((Am (-> A (-> B A))) (C (-> Bm (and (-> A (-> B A)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1883.         ((A or (B -> (C -> B))) -> (D -> ((B -> (C -> B)) and D))), M:tm-80, m:tm-5, u:((Am (-> A (-> B A))) (C (-> Bm (and (-> A (-> B A)) Bm))))
================================================================
tm-name          tm-1884
in-theory        1884
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) or D))
theorem-size     15
proof            (modus-ponens tm-80 tm-6 ((Am (-> A (-> B A))) (C (or (-> A (-> B A)) Bm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1884.         ((A or (B -> (C -> B))) -> ((B -> (C -> B)) or D)), M:tm-80, m:tm-6, u:((Am (-> A (-> B A))) (C (or (-> A (-> B A)) Bm)))
================================================================
tm-name          tm-1885
in-theory        1885
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D or (B -> (C -> B))))
theorem-size     15
proof            (modus-ponens tm-80 tm-7 ((Am (-> A (-> B A))) (C (or Bm (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1885.         ((A or (B -> (C -> B))) -> (D or (B -> (C -> B)))), M:tm-80, m:tm-7, u:((Am (-> A (-> B A))) (C (or Bm (-> A (-> B A)))))
================================================================
tm-name          tm-1886
in-theory        1886
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((C -> B) -> D) -> ((B or (C -> B)) -> D)))
theorem-size     21
proof            (modus-ponens tm-80 tm-8 ((A Am) (Bm (-> B Am)) (C (-> (-> (-> B Am) Cm) (-> (or Am (-> B Am)) Cm)))))
axioms-used      (tm-8 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1886.         ((A or (B -> (C -> B))) -> (((C -> B) -> D) -> ((B or (C -> B)) -> D))), M:tm-80, m:tm-8, u:((A Am) (Bm (-> B Am)) (C (-> (-> (-> B Am) Cm) (-> (or Am (-> B Am)) Cm))))
================================================================
tm-name          tm-1887
in-theory        1887
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (not (C -> B))) -> (not B)))
theorem-size     17
proof            (modus-ponens tm-80 tm-9 ((A Am) (Bm (-> B Am)) (C (-> (-> Am (not (-> B Am))) (not Am)))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1887.         ((A or (B -> (C -> B))) -> ((B -> (not (C -> B))) -> (not B))), M:tm-80, m:tm-9, u:((A Am) (Bm (-> B Am)) (C (-> (-> Am (not (-> B Am))) (not Am))))
================================================================
tm-name          tm-1888
in-theory        1888
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-80 tm-11 ((Am (-> A (-> B A))) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1888.         ((A or (B -> (C -> B))) -> (D -> (E -> D))), M:tm-80, m:tm-11, u:((Am (-> A (-> B A))) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-1889
in-theory        1889
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (B -> B))
theorem-size     11
proof            (modus-ponens tm-80 tm-12 ((A Am) (Bm (-> B Am)) (C (-> Am Am))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-1889.         ((A or (B -> (C -> B))) -> (B -> B)), M:tm-80, m:tm-12, u:((A Am) (Bm (-> B Am)) (C (-> Am Am)))
================================================================
tm-name          tm-1890
in-theory        1890
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-80 tm-14 ((Am (-> A (-> B A))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1890.         ((A or (B -> (C -> B))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-80, m:tm-14, u:((Am (-> A (-> B A))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-1891
in-theory        1891
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-80 tm-16 ((Am (-> A (-> B A))) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1891.         ((A or (B -> (C -> B))) -> ((D and E) -> D)), M:tm-80, m:tm-16, u:((Am (-> A (-> B A))) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-1892
in-theory        1892
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-80 tm-18 ((Am (-> A (-> B A))) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1892.         ((A or (B -> (C -> B))) -> ((D and E) -> E)), M:tm-80, m:tm-18, u:((Am (-> A (-> B A))) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-1893
in-theory        1893
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (E -> D)) and (B -> (C -> B))))
theorem-size     19
proof            (modus-ponens tm-80 tm-19 ((Am (-> A (-> B A))) (C (and (-> Bm (-> Cm Bm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1893.         ((A or (B -> (C -> B))) -> ((D -> (E -> D)) and (B -> (C -> B)))), M:tm-80, m:tm-19, u:((Am (-> A (-> B A))) (C (and (-> Bm (-> Cm Bm)) (-> A (-> B A)))))
================================================================
tm-name          tm-1894
in-theory        1894
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (C -> B))))
theorem-size     27
proof            (modus-ponens tm-80 tm-20 ((Am (-> A (-> B A))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1894.         ((A or (B -> (C -> B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (C -> B)))), M:tm-80, m:tm-20, u:((Am (-> A (-> B A))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (-> B A)))))
================================================================
tm-name          tm-1895
in-theory        1895
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D and E) -> D) and (B -> (C -> B))))
theorem-size     19
proof            (modus-ponens tm-80 tm-21 ((Am (-> A (-> B A))) (C (and (-> (and Bm Cm) Bm) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1895.         ((A or (B -> (C -> B))) -> (((D and E) -> D) and (B -> (C -> B)))), M:tm-80, m:tm-21, u:((Am (-> A (-> B A))) (C (and (-> (and Bm Cm) Bm) (-> A (-> B A)))))
================================================================
tm-name          tm-1896
in-theory        1896
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D and E) -> E) and (B -> (C -> B))))
theorem-size     19
proof            (modus-ponens tm-80 tm-22 ((Am (-> A (-> B A))) (C (and (-> (and Bm Cm) Cm) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1896.         ((A or (B -> (C -> B))) -> (((D and E) -> E) and (B -> (C -> B)))), M:tm-80, m:tm-22, u:((Am (-> A (-> B A))) (C (and (-> (and Bm Cm) Cm) (-> A (-> B A)))))
================================================================
tm-name          tm-1897
in-theory        1897
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (E -> (D and E))) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-23 ((Am (-> A (-> B A))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1897.         ((A or (B -> (C -> B))) -> ((D -> (E -> (D and E))) and (B -> (C -> B)))), M:tm-80, m:tm-23, u:((Am (-> A (-> B A))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (-> B A)))))
================================================================
tm-name          tm-1898
in-theory        1898
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (B -> (B and (C -> B))))
theorem-size     15
proof            (modus-ponens tm-80 tm-24 ((A Am) (Bm (-> B Am)) (C (-> Am (and Am (-> B Am))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1898.         ((A or (B -> (C -> B))) -> (B -> (B and (C -> B)))), M:tm-80, m:tm-24, u:((A Am) (Bm (-> B Am)) (C (-> Am (and Am (-> B Am)))))
================================================================
tm-name          tm-1899
in-theory        1899
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-80 tm-25 ((Am (-> A (-> B A))) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1899.         ((A or (B -> (C -> B))) -> (D -> (E -> (D and E)))), M:tm-80, m:tm-25, u:((Am (-> A (-> B A))) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-1900
in-theory        1900
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (D or E)) and (B -> (C -> B))))
theorem-size     19
proof            (modus-ponens tm-80 tm-32 ((Am (-> A (-> B A))) (C (and (-> Bm (or Bm Cm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1900.         ((A or (B -> (C -> B))) -> ((D -> (D or E)) and (B -> (C -> B)))), M:tm-80, m:tm-32, u:((Am (-> A (-> B A))) (C (and (-> Bm (or Bm Cm)) (-> A (-> B A)))))
================================================================
tm-name          tm-1901
in-theory        1901
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-80 tm-33 ((Am (-> A (-> B A))) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1901.         ((A or (B -> (C -> B))) -> (D -> (D or E))), M:tm-80, m:tm-33, u:((Am (-> A (-> B A))) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-1902
in-theory        1902
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (E or D)) and (B -> (C -> B))))
theorem-size     19
proof            (modus-ponens tm-80 tm-42 ((Am (-> A (-> B A))) (C (and (-> Bm (or Cm Bm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1902.         ((A or (B -> (C -> B))) -> ((D -> (E or D)) and (B -> (C -> B)))), M:tm-80, m:tm-42, u:((Am (-> A (-> B A))) (C (and (-> Bm (or Cm Bm)) (-> A (-> B A)))))
================================================================
tm-name          tm-1903
in-theory        1903
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-80 tm-43 ((Am (-> A (-> B A))) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1903.         ((A or (B -> (C -> B))) -> (D -> (E or D))), M:tm-80, m:tm-43, u:((Am (-> A (-> B A))) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-1904
in-theory        1904
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (D -> (B -> C)))) -> ((C or (B -> C)) -> (D -> (B -> C))))
theorem-size     23
proof            (modus-ponens tm-80 tm-44 ((A (-> Am Bm)) (Cm (-> B (-> Am Bm))) (C (-> (or Bm (-> Am Bm)) (-> B (-> Am Bm))))))
axioms-used      (tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-1904.         ((A or ((B -> C) -> (D -> (B -> C)))) -> ((C or (B -> C)) -> (D -> (B -> C)))), M:tm-80, m:tm-44, u:((A (-> Am Bm)) (Cm (-> B (-> Am Bm))) (C (-> (or Bm (-> Am Bm)) (-> B (-> Am Bm)))))
================================================================
tm-name          tm-1905
in-theory        1905
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (E -> ((B -> C) -> (B -> D))))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> ((B -> C) -> (B -> D)))))
theorem-size     43
proof            (modus-ponens tm-80 tm-45 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (-> B (-> (-> Am Bm) (-> Am Cm)))) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1905.         ((A or (((B -> C) -> (B -> D)) -> (E -> ((B -> C) -> (B -> D))))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> ((B -> C) -> (B -> D))))), M:tm-80, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (-> B (-> (-> Am Bm) (-> Am Cm)))) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-1906
in-theory        1906
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((B and D) or B) -> (C -> B)))
theorem-size     17
proof            (modus-ponens tm-80 tm-46 ((A Am) (Bm (-> B Am)) (C (-> (or (and Am Cm) Am) (-> B Am)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1906.         ((A or (B -> (C -> B))) -> (((B and D) or B) -> (C -> B))), M:tm-80, m:tm-46, u:((A Am) (Bm (-> B Am)) (C (-> (or (and Am Cm) Am) (-> B Am))))
================================================================
tm-name          tm-1907
in-theory        1907
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D and B) or B) -> (C -> B)))
theorem-size     17
proof            (modus-ponens tm-80 tm-47 ((A Am) (Bm (-> B Am)) (C (-> (or (and Cm Am) Am) (-> B Am)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1907.         ((A or (B -> (C -> B))) -> (((D and B) or B) -> (C -> B))), M:tm-80, m:tm-47, u:((A Am) (Bm (-> B Am)) (C (-> (or (and Cm Am) Am) (-> B Am))))
================================================================
tm-name          tm-1908
in-theory        1908
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (D -> (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (D -> (B -> (C and B)))))
theorem-size     31
proof            (modus-ponens tm-80 tm-48 ((A (-> Am (and Bm Am))) (Cm (-> B (-> Am (and Bm Am)))) (C (-> (or Bm (-> Am (and Bm Am))) (-> B (-> Am (and Bm Am)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1908.         ((A or ((B -> (C and B)) -> (D -> (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (D -> (B -> (C and B))))), M:tm-80, m:tm-48, u:((A (-> Am (and Bm Am))) (Cm (-> B (-> Am (and Bm Am)))) (C (-> (or Bm (-> Am (and Bm Am))) (-> B (-> Am (and Bm Am))))))
================================================================
tm-name          tm-1909
in-theory        1909
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D -> (B or C)))) -> ((B or (B or C)) -> (D -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-80 tm-49 ((A (or Am Bm)) (Cm (-> B (or Am Bm))) (C (-> (or Am (or Am Bm)) (-> B (or Am Bm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1909.         ((A or ((B or C) -> (D -> (B or C)))) -> ((B or (B or C)) -> (D -> (B or C)))), M:tm-80, m:tm-49, u:((A (or Am Bm)) (Cm (-> B (or Am Bm))) (C (-> (or Am (or Am Bm)) (-> B (or Am Bm)))))
================================================================
tm-name          tm-1910
in-theory        1910
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D -> (B or C)))) -> ((C or (B or C)) -> (D -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-80 tm-50 ((A (or Am Bm)) (Cm (-> B (or Am Bm))) (C (-> (or Bm (or Am Bm)) (-> B (or Am Bm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1910.         ((A or ((B or C) -> (D -> (B or C)))) -> ((C or (B or C)) -> (D -> (B or C)))), M:tm-80, m:tm-50, u:((A (or Am Bm)) (Cm (-> B (or Am Bm))) (C (-> (or Bm (or Am Bm)) (-> B (or Am Bm)))))
================================================================
tm-name          tm-1911
in-theory        1911
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (E -> ((B -> C) -> ((D or B) -> C))))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (E -> ((B -> C) -> ((D or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-80 tm-51 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> B (-> (-> Am Bm) (-> (or Cm Am) Bm)))))))
axioms-used      (tm-8 tm-1)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1911.         ((A or (((B -> C) -> ((D or B) -> C)) -> (E -> ((B -> C) -> ((D or B) -> C))))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (E -> ((B -> C) -> ((D or B) -> C))))), M:tm-80, m:tm-51, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> B (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
================================================================
tm-name          tm-1912
in-theory        1912
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B -> (C -> B))))
theorem-size     27
proof            (modus-ponens tm-80 tm-54 ((Am (-> A (-> B A))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1912.         ((A or (B -> (C -> B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B -> (C -> B)))), M:tm-80, m:tm-54, u:((Am (-> A (-> B A))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A (-> B A)))))
================================================================
tm-name          tm-1913
in-theory        1913
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (C -> (B -> C)))) -> ((B -> C) -> ((B or C) -> (B -> C))))
theorem-size     23
proof            (modus-ponens tm-80 tm-55 ((Cm (-> Am Bm)) (B Bm) (A (-> Am Bm)) (C (-> (-> Am Bm) (-> (or Am Bm) (-> Am Bm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1913.         ((A or ((B -> C) -> (C -> (B -> C)))) -> ((B -> C) -> ((B or C) -> (B -> C)))), M:tm-80, m:tm-55, u:((Cm (-> Am Bm)) (B Bm) (A (-> Am Bm)) (C (-> (-> Am Bm) (-> (or Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-1914
in-theory        1914
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-80 tm-56 ((Am (-> A (-> B A))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1914.         ((A or (B -> (C -> B))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-80, m:tm-56, u:((Am (-> A (-> B A))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-1915
in-theory        1915
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (not C)) -> (not B)) -> (D -> ((B -> (not C)) -> (not B))))) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> (D -> ((B -> (not C)) -> (not B)))))
theorem-size     41
proof            (modus-ponens tm-80 tm-66 ((A (-> (-> Am (not Bm)) (not Am))) (Cm (-> B (-> (-> Am (not Bm)) (not Am)))) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (-> B (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1915.         ((A or (((B -> (not C)) -> (not B)) -> (D -> ((B -> (not C)) -> (not B))))) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> (D -> ((B -> (not C)) -> (not B))))), M:tm-80, m:tm-66, u:((A (-> (-> Am (not Bm)) (not Am))) (Cm (-> B (-> (-> Am (not Bm)) (not Am)))) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (-> B (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-1916
in-theory        1916
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (B -> (C -> B))))
theorem-size     25
proof            (modus-ponens tm-80 tm-69 ((Am (-> A (-> B A))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1916.         ((A or (B -> (C -> B))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (B -> (C -> B)))), M:tm-80, m:tm-69, u:((Am (-> A (-> B A))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A (-> B A)))))
================================================================
tm-name          tm-1917
in-theory        1917
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-80 tm-71 ((Am (-> A (-> B A))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1917.         ((A or (B -> (C -> B))) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-80, m:tm-71, u:((Am (-> A (-> B A))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-1918
in-theory        1918
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((not (not B)) or B) -> (C -> B)))
theorem-size     17
proof            (modus-ponens tm-80 tm-73 ((A Am) (Bm (-> B Am)) (C (-> (or (not (not Am)) Am) (-> B Am)))))
axioms-used      (tm-8 tm-1 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1918.         ((A or (B -> (C -> B))) -> (((not (not B)) or B) -> (C -> B))), M:tm-80, m:tm-73, u:((A Am) (Bm (-> B Am)) (C (-> (or (not (not Am)) Am) (-> B Am))))
================================================================
tm-name          tm-1919
in-theory        1919
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((not (not D)) -> D) and (B -> (C -> B))))
theorem-size     19
proof            (modus-ponens tm-80 tm-76 ((Am (-> A (-> B A))) (C (and (-> (not (not Bm)) Bm) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1919.         ((A or (B -> (C -> B))) -> (((not (not D)) -> D) and (B -> (C -> B)))), M:tm-80, m:tm-76, u:((Am (-> A (-> B A))) (C (and (-> (not (not Bm)) Bm) (-> A (-> B A)))))
================================================================
tm-name          tm-1920
in-theory        1920
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-80 tm-78 ((Am (-> A (-> B A))) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-10)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1920.         ((A or (B -> (C -> B))) -> ((not (not D)) -> D)), M:tm-80, m:tm-78, u:((Am (-> A (-> B A))) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-1921
in-theory        1921
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) -> (D -> (B -> (C -> B))))) -> ((E or (B -> (C -> B))) -> (D -> (B -> (C -> B)))))
theorem-size     31
proof            (modus-ponens tm-80 tm-80 ((A (-> Am (-> Bm Am))) (Cm (-> B (-> Am (-> Bm Am)))) (C (-> (or Dm (-> Am (-> Bm Am))) (-> B (-> Am (-> Bm Am)))))))
axioms-used      (tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1921.         ((A or ((B -> (C -> B)) -> (D -> (B -> (C -> B))))) -> ((E or (B -> (C -> B))) -> (D -> (B -> (C -> B))))), M:tm-80, m:tm-80, u:((A (-> Am (-> Bm Am))) (Cm (-> B (-> Am (-> Bm Am)))) (C (-> (or Dm (-> Am (-> Bm Am))) (-> B (-> Am (-> Bm Am))))))
================================================================
tm-name          tm-1922
in-theory        1922
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> B)) -> D) -> ((E or (B -> (C -> B))) -> D)))
theorem-size     23
proof            (modus-ponens tm-76 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1922.         (((not (not A)) -> A) and (((B -> (C -> B)) -> D) -> ((E or (B -> (C -> B))) -> D))), M:tm-76, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-1923
in-theory        1923
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> A)) -> C))) or ((A -> (B -> A)) -> C)) -> ((D or (A -> (B -> A))) -> C))
theorem-size     27
proof            (modus-ponens tm-73 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-8 tm-10 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1923.         (((not (not ((A -> (B -> A)) -> C))) or ((A -> (B -> A)) -> C)) -> ((D or (A -> (B -> A))) -> C)), M:tm-73, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-1924
in-theory        1924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E)))
theorem-size     29
proof            (modus-ponens tm-69 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1924.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E))), M:tm-69, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-1925
in-theory        1925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> (C or (A -> (B -> A)))) -> (((A -> (B -> A)) or (C or (A -> (B -> A)))) -> (C or (A -> (B -> A)))))
theorem-size     35
proof            (modus-ponens tm-55 tm-80 ((A (-> Am (-> Bm Am))) (Cm (or Dm (-> Am (-> Bm Am)))) (B (or Dm (-> Am (-> Bm Am)))) (C (or Dm (-> Am (-> Bm Am))))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1925.         (((A -> (B -> A)) -> (C or (A -> (B -> A)))) -> (((A -> (B -> A)) or (C or (A -> (B -> A)))) -> (C or (A -> (B -> A))))), M:tm-55, m:tm-80, u:((A (-> Am (-> Bm Am))) (Cm (or Dm (-> Am (-> Bm Am)))) (B (or Dm (-> Am (-> Bm Am)))) (C (or Dm (-> Am (-> Bm Am)))))
================================================================
tm-name          tm-1926
in-theory        1926
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-54 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1926.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-54, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-1927
in-theory        1927
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (C -> B)) -> ((A or B) -> (C -> B)))) -> ((D or (B -> (C -> B))) -> ((A or B) -> (C -> B))))
theorem-size     33
proof            (modus-ponens tm-51 tm-80 ((A Am) (B (-> Bm Am)) (Cm (-> (or C Am) (-> Bm Am))) (D (-> (or Dm (-> Am (-> Bm Am))) (-> (or C Am) (-> Bm Am))))))
axioms-used      (tm-8 tm-1)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1927.         (((A -> B) or ((B -> (C -> B)) -> ((A or B) -> (C -> B)))) -> ((D or (B -> (C -> B))) -> ((A or B) -> (C -> B)))), M:tm-51, m:tm-80, u:((A Am) (B (-> Bm Am)) (Cm (-> (or C Am) (-> Bm Am))) (D (-> (or Dm (-> Am (-> Bm Am))) (-> (or C Am) (-> Bm Am)))))
================================================================
tm-name          tm-1928
in-theory        1928
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) -> (A and (B -> (C -> B))))) -> ((D or (B -> (C -> B))) -> (A and (B -> (C -> B)))))
theorem-size     31
proof            (modus-ponens tm-48 tm-80 ((A (-> Am (-> Bm Am))) (Cm (and B (-> Am (-> Bm Am)))) (C (-> (or Dm (-> Am (-> Bm Am))) (and B (-> Am (-> Bm Am)))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1928.         ((A or ((B -> (C -> B)) -> (A and (B -> (C -> B))))) -> ((D or (B -> (C -> B))) -> (A and (B -> (C -> B))))), M:tm-48, m:tm-80, u:((A (-> Am (-> Bm Am))) (Cm (and B (-> Am (-> Bm Am)))) (C (-> (or Dm (-> Am (-> Bm Am))) (and B (-> Am (-> Bm Am))))))
================================================================
tm-name          tm-1929
in-theory        1929
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) or ((B -> (C -> B)) -> D)) -> ((E or (B -> (C -> B))) -> D))
theorem-size     27
proof            (modus-ponens tm-47 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1929.         (((A and ((B -> (C -> B)) -> D)) or ((B -> (C -> B)) -> D)) -> ((E or (B -> (C -> B))) -> D)), M:tm-47, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-1930
in-theory        1930
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) or ((A -> (B -> A)) -> C)) -> ((E or (A -> (B -> A))) -> C))
theorem-size     27
proof            (modus-ponens tm-46 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1930.         (((((A -> (B -> A)) -> C) and D) or ((A -> (B -> A)) -> C)) -> ((E or (A -> (B -> A))) -> C)), M:tm-46, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-1931
in-theory        1931
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) or ((A -> (B -> A)) -> (A -> C))) -> ((D or (A -> (B -> A))) -> (A -> C)))
theorem-size     29
proof            (modus-ponens tm-45 tm-80 ((A Am) (B (-> Bm Am)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (-> Bm Am))) (-> Am C)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1931.         (((A -> ((B -> A) -> C)) or ((A -> (B -> A)) -> (A -> C))) -> ((D or (A -> (B -> A))) -> (A -> C))), M:tm-45, m:tm-80, u:((A Am) (B (-> Bm Am)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (-> Bm Am))) (-> Am C))))
================================================================
tm-name          tm-1932
in-theory        1932
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) -> A)) -> ((D or (B -> (C -> B))) -> A))
theorem-size     19
proof            (modus-ponens tm-44 tm-80 ((A (-> Am (-> Bm Am))) (B Cm) (C (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-8 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1932.         ((A or ((B -> (C -> B)) -> A)) -> ((D or (B -> (C -> B))) -> A)), M:tm-44, m:tm-80, u:((A (-> Am (-> Bm Am))) (B Cm) (C (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-1933
in-theory        1933
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-42 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1933.         ((A -> (B or A)) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E))), M:tm-42, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-1934
in-theory        1934
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-32 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1934.         ((A -> (A or B)) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E))), M:tm-32, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-1935
in-theory        1935
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> (((A -> (B -> A)) -> C) and ((D or (A -> (B -> A))) -> C)))
theorem-size     25
proof            (modus-ponens tm-24 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1935.         (((A -> (B -> A)) -> C) -> (((A -> (B -> A)) -> C) and ((D or (A -> (B -> A))) -> C))), M:tm-24, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-1936
in-theory        1936
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E)))
theorem-size     25
proof            (modus-ponens tm-23 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1936.         ((A -> (B -> (A and B))) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E))), M:tm-23, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-1937
in-theory        1937
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-22 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1937.         (((A and B) -> B) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E))), M:tm-22, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-1938
in-theory        1938
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-21 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1938.         (((A and B) -> A) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E))), M:tm-21, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-1939
in-theory        1939
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-20 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1939.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-20, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-1940
in-theory        1940
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-19 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1940.         ((A -> (B -> A)) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E))), M:tm-19, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-1941
in-theory        1941
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> ((A -> (B -> A)) -> C))
theorem-size     15
proof            (modus-ponens tm-12 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1941.         (((A -> (B -> A)) -> C) -> ((A -> (B -> A)) -> C)), M:tm-12, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-1942
in-theory        1942
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> (not ((D or (A -> (B -> A))) -> C))) -> (not ((A -> (B -> A)) -> C)))
theorem-size     27
proof            (modus-ponens tm-9 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-9 tm-8 tm-1)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1942.         ((((A -> (B -> A)) -> C) -> (not ((D or (A -> (B -> A))) -> C))) -> (not ((A -> (B -> A)) -> C))), M:tm-9, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-1943
in-theory        1943
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (C -> B))) -> D) -> E) -> ((((B -> (C -> B)) -> D) or ((A or (B -> (C -> B))) -> D)) -> E))
theorem-size     31
proof            (modus-ponens tm-8 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-8 tm-1)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1943.         ((((A or (B -> (C -> B))) -> D) -> E) -> ((((B -> (C -> B)) -> D) or ((A or (B -> (C -> B))) -> D)) -> E)), M:tm-8, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-1944
in-theory        1944
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> (C -> B)) -> D) -> ((E or (B -> (C -> B))) -> D)))
theorem-size     19
proof            (modus-ponens tm-7 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-7 tm-8 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1944.         (A or (((B -> (C -> B)) -> D) -> ((E or (B -> (C -> B))) -> D))), M:tm-7, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-1945
in-theory        1945
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-6 tm-8 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1945.         ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) or E), M:tm-6, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-1946
in-theory        1946
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> B)) -> D) -> ((E or (B -> (C -> B))) -> D)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1946.         (A -> ((((B -> (C -> B)) -> D) -> ((E or (B -> (C -> B))) -> D)) and A)), M:tm-5, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-1947
in-theory        1947
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> (D or (A -> (B -> A)))) -> (((A -> (B -> A)) -> C) -> C))
theorem-size     25
proof            (modus-ponens tm-2 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (or Dm (-> Am (-> Bm Am)))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1947.         ((((A -> (B -> A)) -> C) -> (D or (A -> (B -> A)))) -> (((A -> (B -> A)) -> C) -> C)), M:tm-2, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (or Dm (-> Am (-> Bm Am)))) (C Cm))
================================================================
tm-name          tm-1948
in-theory        1948
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) -> D) -> ((E or (B -> (C -> B))) -> D)))
theorem-size     19
proof            (modus-ponens tm-1 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-1 tm-8)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-1948.         (A -> (((B -> (C -> B)) -> D) -> ((E or (B -> (C -> B))) -> D))), M:tm-1, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-1949
in-theory        1949
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> (D -> (E -> D)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1949.         (((not (not A)) -> A) and (B or (C -> (D -> (E -> D))))), M:tm-76, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-1950
in-theory        1950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (E -> (F -> E)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1950.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (E -> (F -> E))))), M:tm-69, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-1951
in-theory        1951
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1951.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (G -> F))))), M:tm-54, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-1952
in-theory        1952
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1952.         ((A -> (B or A)) and (C or (D -> (E -> (F -> E))))), M:tm-42, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-1953
in-theory        1953
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1953.         ((A -> (A or B)) and (C or (D -> (E -> (F -> E))))), M:tm-32, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-1954
in-theory        1954
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1954.         ((A -> (B -> (A and B))) and (C or (D -> (E -> (F -> E))))), M:tm-23, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-1955
in-theory        1955
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1955.         (((A and B) -> B) and (C or (D -> (E -> (F -> E))))), M:tm-22, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-1956
in-theory        1956
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1956.         (((A and B) -> A) and (C or (D -> (E -> (F -> E))))), M:tm-21, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-1957
in-theory        1957
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1957.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (G -> F))))), M:tm-20, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-1958
in-theory        1958
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1958.         ((A -> (B -> A)) and (C or (D -> (E -> (F -> E))))), M:tm-19, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-1959
in-theory        1959
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C -> (D -> (E -> D)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-7 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1959.         (A or (B or (C -> (D -> (E -> D))))), M:tm-7, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-1960
in-theory        1960
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-6 tm-7 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1960.         ((A or (B -> (C -> (D -> C)))) or E), M:tm-6, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-1961
in-theory        1961
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (D -> (E -> D)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1961.         (A -> ((B or (C -> (D -> (E -> D)))) and A)), M:tm-5, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-1962
in-theory        1962
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C -> (D -> (E -> D)))))
theorem-size     11
proof            (modus-ponens tm-1 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-1 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1962.         (A -> (B or (C -> (D -> (E -> D))))), M:tm-1, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-1963
in-theory        1963
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (D -> C))) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1963.         (((not (not A)) -> A) and ((B -> (C -> (D -> C))) or E)), M:tm-76, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-1964
in-theory        1964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (E -> D))) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1964.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (E -> D))) or F)), M:tm-69, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-1965
in-theory        1965
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (F -> E))) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1965.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (F -> E))) or G)), M:tm-54, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-1966
in-theory        1966
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (E -> D))) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1966.         ((A -> (B or A)) and ((C -> (D -> (E -> D))) or F)), M:tm-42, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-1967
in-theory        1967
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (E -> D))) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1967.         ((A -> (A or B)) and ((C -> (D -> (E -> D))) or F)), M:tm-32, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-1968
in-theory        1968
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (E -> D))) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1968.         ((A -> (B -> (A and B))) and ((C -> (D -> (E -> D))) or F)), M:tm-23, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-1969
in-theory        1969
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (E -> D))) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1969.         (((A and B) -> B) and ((C -> (D -> (E -> D))) or F)), M:tm-22, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-1970
in-theory        1970
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (E -> D))) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1970.         (((A and B) -> A) and ((C -> (D -> (E -> D))) or F)), M:tm-21, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-1971
in-theory        1971
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (F -> E))) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1971.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (F -> E))) or G)), M:tm-20, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-1972
in-theory        1972
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (E -> D))) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1972.         ((A -> (B -> A)) and ((C -> (D -> (E -> D))) or F)), M:tm-19, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-1973
in-theory        1973
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (D -> C))) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-7 tm-6 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1973.         (A or ((B -> (C -> (D -> C))) or E)), M:tm-7, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-1974
in-theory        1974
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-6 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1974.         (((A -> (B -> (C -> B))) or D) or E), M:tm-6, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-1975
in-theory        1975
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (D -> C))) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1975.         (A -> (((B -> (C -> (D -> C))) or E) and A)), M:tm-5, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-1976
in-theory        1976
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (D -> C))) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-1 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1976.         (A -> ((B -> (C -> (D -> C))) or E)), M:tm-1, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-1977
in-theory        1977
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-83 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-1)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1977.         ((A -> (B -> (C -> B))) and (D -> (E -> D))), M:tm-83, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-1978
in-theory        1978
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1978.         ((A -> (B -> (C -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-83, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-1979
in-theory        1979
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-83 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-1979.         ((A -> (B -> (C -> B))) and ((D and E) -> D)), M:tm-83, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-1980
in-theory        1980
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-83 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-1980.         ((A -> (B -> (C -> B))) and ((D and E) -> E)), M:tm-83, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-1981
in-theory        1981
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-83 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1981.         ((A -> (B -> (C -> B))) and (D -> (E -> (D and E)))), M:tm-83, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-1982
in-theory        1982
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-83 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1982.         ((A -> (B -> (C -> B))) and (D -> (D or E))), M:tm-83, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-1983
in-theory        1983
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-83 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1983.         ((A -> (B -> (C -> B))) and (D -> (E or D))), M:tm-83, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-1984
in-theory        1984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1984.         ((A -> (B -> (C -> B))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-83, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-1985
in-theory        1985
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-83 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1985.         ((A -> (B -> (C -> B))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-83, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-1986
in-theory        1986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-83 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-1986.         ((A -> (B -> (C -> B))) and ((not (not D)) -> D)), M:tm-83, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-1987
in-theory        1987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-83 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-1987.         ((A -> (B -> (C -> B))) and (D -> (E -> (F -> E)))), M:tm-83, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-1988
in-theory        1988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-83 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-1988.         ((A -> (B -> (C -> B))) and ((D -> E) -> (D -> D))), M:tm-83, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-1989
in-theory        1989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-83 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1989.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-83, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-1990
in-theory        1990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1990.         ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-83, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-1991
in-theory        1991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-83 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1991.         ((A -> (B -> (C -> B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-83, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-1992
in-theory        1992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-83 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1992.         ((A -> (B -> (C -> B))) and (D -> ((E and F) -> E))), M:tm-83, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-1993
in-theory        1993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-83 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1993.         ((A -> (B -> (C -> B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-83, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-1994
in-theory        1994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-83 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1994.         ((A -> (B -> (C -> B))) and (D -> ((E and F) -> F))), M:tm-83, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-1995
in-theory        1995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-83 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-1995.         ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> E)) and D))), M:tm-83, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-1996
in-theory        1996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-83 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1996.         ((A -> (B -> (C -> B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-83, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-1997
in-theory        1997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-83 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1997.         ((A -> (B -> (C -> B))) and (D -> (((E and F) -> E) and D))), M:tm-83, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-1998
in-theory        1998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-83 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1998.         ((A -> (B -> (C -> B))) and (D -> (((E and F) -> F) and D))), M:tm-83, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-1999
in-theory        1999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1999.         ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-83, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-2000
in-theory        2000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-83 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-2000.         ((A -> (B -> (C -> B))) and ((D -> E) -> (D -> (D and E)))), M:tm-83, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-2001
in-theory        2001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2001.         ((A -> (B -> (C -> B))) and (D -> (E -> (F -> (E and F))))), M:tm-83, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-2002
in-theory        2002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-83 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2002.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) or F)), M:tm-83, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-2003
in-theory        2003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-83 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2003.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-83, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2004
in-theory        2004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-83 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2004.         ((A -> (B -> (C -> B))) and (((D and E) -> D) or F)), M:tm-83, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-2005
in-theory        2005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-83 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2005.         ((A -> (B -> (C -> B))) and (((D and E) -> E) or F)), M:tm-83, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-2006
in-theory        2006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-83 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2006.         ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) or F)), M:tm-83, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-2007
in-theory        2007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-83 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2007.         ((A -> (B -> (C -> B))) and ((D -> (D or E)) or F)), M:tm-83, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-2008
in-theory        2008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-83 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2008.         ((A -> (B -> (C -> B))) and (D -> ((E -> (E or F)) and D))), M:tm-83, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-2009
in-theory        2009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-83 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2009.         ((A -> (B -> (C -> B))) and (D -> (E -> (E or F)))), M:tm-83, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-2010
in-theory        2010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-83 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2010.         ((A -> (B -> (C -> B))) and (D or (E -> (F -> E)))), M:tm-83, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-2011
in-theory        2011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2011.         ((A -> (B -> (C -> B))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-83, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-2012
in-theory        2012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-83 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2012.         ((A -> (B -> (C -> B))) and (D or ((E and F) -> E))), M:tm-83, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-2013
in-theory        2013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-83 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2013.         ((A -> (B -> (C -> B))) and (D or ((E and F) -> F))), M:tm-83, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-2014
in-theory        2014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2014.         ((A -> (B -> (C -> B))) and (D or (E -> (F -> (E and F))))), M:tm-83, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-2015
in-theory        2015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-83 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2015.         ((A -> (B -> (C -> B))) and (D or (E -> (E or F)))), M:tm-83, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-2016
in-theory        2016
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-83 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2016.         ((A -> (B -> (C -> B))) and (D or (E -> (F or E)))), M:tm-83, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-2017
in-theory        2017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-83 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2017.         ((A -> (B -> (C -> B))) and ((D -> (E or D)) or F)), M:tm-83, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-2018
in-theory        2018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-83 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2018.         ((A -> (B -> (C -> B))) and (D -> ((E -> (F or E)) and D))), M:tm-83, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-2019
in-theory        2019
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-83 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2019.         ((A -> (B -> (C -> B))) and (D -> (E -> (F or E)))), M:tm-83, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-2020
in-theory        2020
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-83 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2020.         ((A -> (B -> (C -> B))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-83, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-2021
in-theory        2021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-83 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2021.         ((A -> (B -> (C -> B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-83, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2022
in-theory        2022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-83 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2022.         ((A -> (B -> (C -> B))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-83, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-2023
in-theory        2023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-83 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2023.         ((A -> (B -> (C -> B))) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-83, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-2024
in-theory        2024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-83 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2024.         ((A -> (B -> (C -> B))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-83, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-2025
in-theory        2025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-83 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2025.         ((A -> (B -> (C -> B))) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-83, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-2026
in-theory        2026
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-83 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2026.         ((A -> (B -> (C -> B))) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-83, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-2027
in-theory        2027
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-83 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2027.         ((A -> (B -> (C -> B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-83, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-2028
in-theory        2028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2028.         ((A -> (B -> (C -> B))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-83, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-2029
in-theory        2029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-83 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2029.         ((A -> (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-83, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-2030
in-theory        2030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-83 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2030.         ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-83, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-2031
in-theory        2031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-83 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-2031.         ((A -> (B -> (C -> B))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-83, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-2032
in-theory        2032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2032.         ((A -> (B -> (C -> B))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-83, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-2033
in-theory        2033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-83 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2033.         ((A -> (B -> (C -> B))) and ((D -> (not (E -> D))) -> (not D))), M:tm-83, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-2034
in-theory        2034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2034.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-83, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-2035
in-theory        2035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-83 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2035.         ((A -> (B -> (C -> B))) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-83, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-2036
in-theory        2036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-83 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2036.         ((A -> (B -> (C -> B))) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-83, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-2037
in-theory        2037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2037.         ((A -> (B -> (C -> B))) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-83, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-2038
in-theory        2038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-83 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2038.         ((A -> (B -> (C -> B))) and ((D -> (not (D or E))) -> (not D))), M:tm-83, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-2039
in-theory        2039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-83 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2039.         ((A -> (B -> (C -> B))) and ((D -> (not (E or D))) -> (not D))), M:tm-83, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-2040
in-theory        2040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-83 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2040.         ((A -> (B -> (C -> B))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-83, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2041
in-theory        2041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-83 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2041.         ((A -> (B -> (C -> B))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-83, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2042
in-theory        2042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-83 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2042.         ((A -> (B -> (C -> B))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-83, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-2043
in-theory        2043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2043.         ((A -> (B -> (C -> B))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-83, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-2044
in-theory        2044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-83 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2044.         ((A -> (B -> (C -> B))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-83, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-2045
in-theory        2045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-83 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2045.         ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-83, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-2046
in-theory        2046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-83 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-2046.         ((A -> (B -> (C -> B))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-83, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-2047
in-theory        2047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2047.         ((A -> (B -> (C -> B))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-83, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-2048
in-theory        2048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-83 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-1 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2048.         ((A -> (B -> (C -> B))) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-83, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-2049
in-theory        2049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-83 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2049.         ((A -> (B -> (C -> B))) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-83, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-2050
in-theory        2050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-83 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2050.         ((A -> (B -> (C -> B))) and (D or ((not (not E)) -> E))), M:tm-83, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-2051
in-theory        2051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-83 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2051.         ((A -> (B -> (C -> B))) and (((not (not D)) -> D) or E)), M:tm-83, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-2052
in-theory        2052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-83 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2052.         ((A -> (B -> (C -> B))) and (D -> (((not (not E)) -> E) and D))), M:tm-83, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-2053
in-theory        2053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-83 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-2053.         ((A -> (B -> (C -> B))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-83, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-2054
in-theory        2054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-83 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2054.         ((A -> (B -> (C -> B))) and (D -> ((not (not E)) -> E))), M:tm-83, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-2055
in-theory        2055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2055.         ((A -> (B -> (C -> B))) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-83, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-2056
in-theory        2056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-83 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2056.         ((A -> (B -> (C -> B))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-83, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-2057
in-theory        2057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2057.         ((A -> (B -> (C -> B))) and (D or (E -> (F -> (G -> F))))), M:tm-83, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2058
in-theory        2058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2058.         ((A -> (B -> (C -> B))) and ((D -> (E -> (F -> E))) or G)), M:tm-83, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-2059
in-theory        2059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2059.         ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-83, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2060
in-theory        2060
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (E -> (F -> E))) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-83 ((Am (-> A (-> B A))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2060.         ((A or (B -> (C -> B))) -> ((D -> (E -> (F -> E))) and (B -> (C -> B)))), M:tm-80, m:tm-83, u:((Am (-> A (-> B A))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (-> B A)))))
================================================================
tm-name          tm-2061
in-theory        2061
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (D -> (E -> D))) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2061.         (((not (not A)) -> A) and (B -> ((C -> (D -> (E -> D))) and B))), M:tm-76, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2062
in-theory        2062
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (C -> (D -> C))) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2062.         (((not (not A)) or A) -> ((B -> (C -> (D -> C))) and A)), M:tm-73, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-2063
in-theory        2063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> (F -> E))) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2063.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> (F -> E))) and C))), M:tm-69, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2064
in-theory        2064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> (E -> D))) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-83 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2064.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> (E -> D))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-83, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-2065
in-theory        2065
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2065.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-54, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2066
in-theory        2066
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (F -> E))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-83 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2066.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (F -> E))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-83, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-2067
in-theory        2067
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (D -> (E -> D))) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-83 ((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2067.         ((A or (B or A)) -> ((C -> (D -> (E -> D))) and (B or A))), M:tm-50, m:tm-83, u:((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (or A B))))
================================================================
tm-name          tm-2068
in-theory        2068
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (D -> (E -> D))) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-83 ((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2068.         ((A or (A or B)) -> ((C -> (D -> (E -> D))) and (A or B))), M:tm-49, m:tm-83, u:((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (or A B))))
================================================================
tm-name          tm-2069
in-theory        2069
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (D -> (E -> D))) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-83 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2069.         ((A or (B -> (A and B))) -> ((C -> (D -> (E -> D))) and (B -> (A and B)))), M:tm-48, m:tm-83, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-2070
in-theory        2070
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (D -> (E -> D))) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2070.         (((A and B) or B) -> ((C -> (D -> (E -> D))) and B)), M:tm-47, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-2071
in-theory        2071
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (D -> (E -> D))) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2071.         (((A and B) or A) -> ((C -> (D -> (E -> D))) and A)), M:tm-46, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-2072
in-theory        2072
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (F -> E))) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-83 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2072.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (F -> E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-83, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-2073
in-theory        2073
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (D -> (E -> D))) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-83 ((Am (-> A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2073.         ((A or (B -> A)) -> ((C -> (D -> (E -> D))) and (B -> A))), M:tm-44, m:tm-83, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A B))))
================================================================
tm-name          tm-2074
in-theory        2074
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (E -> (F -> E))) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2074.         ((A -> (B or A)) and (C -> ((D -> (E -> (F -> E))) and C))), M:tm-42, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2075
in-theory        2075
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (E -> (F -> E))) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2075.         ((A -> (A or B)) and (C -> ((D -> (E -> (F -> E))) and C))), M:tm-32, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2076
in-theory        2076
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (C -> (D -> C))) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2076.         (A -> (A and ((B -> (C -> (D -> C))) and A))), M:tm-24, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-2077
in-theory        2077
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (F -> E))) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2077.         ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (F -> E))) and C))), M:tm-23, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2078
in-theory        2078
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (E -> (F -> E))) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2078.         (((A and B) -> B) and (C -> ((D -> (E -> (F -> E))) and C))), M:tm-22, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2079
in-theory        2079
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (E -> (F -> E))) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2079.         (((A and B) -> A) and (C -> ((D -> (E -> (F -> E))) and C))), M:tm-21, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2080
in-theory        2080
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2080.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-20, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2081
in-theory        2081
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (E -> (F -> E))) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2081.         ((A -> (B -> A)) and (C -> ((D -> (E -> (F -> E))) and C))), M:tm-19, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2082
in-theory        2082
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> (D -> C))) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-9 tm-5 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2082.         ((A -> (not ((B -> (C -> (D -> C))) and A))) -> (not A)), M:tm-9, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-2083
in-theory        2083
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (C -> B))) and D) -> E) -> ((D or ((A -> (B -> (C -> B))) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2083.         ((((A -> (B -> (C -> B))) and D) -> E) -> ((D or ((A -> (B -> (C -> B))) and D)) -> E)), M:tm-8, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-2084
in-theory        2084
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (D -> (E -> D))) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2084.         (A or (B -> ((C -> (D -> (E -> D))) and B))), M:tm-7, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2085
in-theory        2085
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2085.         ((A -> ((B -> (C -> (D -> C))) and A)) or E), M:tm-6, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2086
in-theory        2086
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D -> (E -> D))) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2086.         (A -> ((B -> ((C -> (D -> (E -> D))) and B)) and A)), M:tm-5, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2087
in-theory        2087
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> (E -> D))) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-1 tm-5)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2087.         (A -> (B -> ((C -> (D -> (E -> D))) and B))), M:tm-1, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2088
in-theory        2088
times-derived    2
----------------------------------------------------------------
theorem          (A -> (B -> (C -> A)))
theorem-size     7
proof            (modus-ponens tm-84 tm-1 ((A Am) (B (-> Bm Am))))
axioms-used      (tm-2 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2088.         (A -> (B -> (C -> A))), M:tm-84, m:tm-1, u:((A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-2089
in-theory        2089
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (D -> ((A -> B) -> (A -> C))))
theorem-size     15
proof            (modus-ponens tm-84 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2089.         ((A -> (B -> C)) -> (D -> ((A -> B) -> (A -> C)))), M:tm-84, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-2090
in-theory        2090
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> (C -> A))
theorem-size     7
proof            (modus-ponens tm-84 tm-3 ((A (and Am Bm)) (B Am)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-2090.         ((A and B) -> (C -> A)), M:tm-84, m:tm-3, u:((A (and Am Bm)) (B Am))
================================================================
tm-name          tm-2091
in-theory        2091
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> (C -> B))
theorem-size     7
proof            (modus-ponens tm-84 tm-4 ((A (and Am Bm)) (B Bm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-2091.         ((A and B) -> (C -> B)), M:tm-84, m:tm-4, u:((A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-2092
in-theory        2092
times-derived    2
----------------------------------------------------------------
theorem          (A -> (B -> (C -> (A and C))))
theorem-size     9
proof            (modus-ponens tm-84 tm-5 ((A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2092.         (A -> (B -> (C -> (A and C)))), M:tm-84, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-2093
in-theory        2093
times-derived    2
----------------------------------------------------------------
theorem          (A -> (B -> (A or C)))
theorem-size     7
proof            (modus-ponens tm-84 tm-6 ((A Am) (B (or Am Bm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2093.         (A -> (B -> (A or C))), M:tm-84, m:tm-6, u:((A Am) (B (or Am Bm)))
================================================================
tm-name          tm-2094
in-theory        2094
times-derived    2
----------------------------------------------------------------
theorem          (A -> (B -> (C or A)))
theorem-size     7
proof            (modus-ponens tm-84 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2094.         (A -> (B -> (C or A))), M:tm-84, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-2095
in-theory        2095
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((B -> D) -> ((A or B) -> D))))
theorem-size     15
proof            (modus-ponens tm-84 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2095.         ((A -> B) -> (C -> ((B -> D) -> ((A or B) -> D)))), M:tm-84, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-2096
in-theory        2096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((A -> (not B)) -> (not A))))
theorem-size     13
proof            (modus-ponens tm-84 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2096.         ((A -> B) -> (C -> ((A -> (not B)) -> (not A)))), M:tm-84, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-2097
in-theory        2097
times-derived    1
----------------------------------------------------------------
theorem          ((not (not A)) -> (B -> A))
theorem-size     7
proof            (modus-ponens tm-84 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-2 tm-1 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-2097.         ((not (not A)) -> (B -> A)), M:tm-84, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-2098
in-theory        2098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (A -> A)))
theorem-size     9
proof            (modus-ponens tm-84 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-2 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-2098.         ((A -> B) -> (C -> (A -> A))), M:tm-84, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-2099
in-theory        2099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (D -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     21
proof            (modus-ponens tm-84 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-2099.         (((A -> (B -> C)) -> (A -> B)) -> (D -> ((A -> (B -> C)) -> (A -> C)))), M:tm-84, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2100
in-theory        2100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> (D -> (((A -> B) and C) -> B)))
theorem-size     17
proof            (modus-ponens tm-84 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-2100.         ((((A -> B) and C) -> A) -> (D -> (((A -> B) and C) -> B))), M:tm-84, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-2101
in-theory        2101
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> (D -> ((A and (B -> C)) -> C)))
theorem-size     17
proof            (modus-ponens tm-84 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-2101.         (((A and (B -> C)) -> B) -> (D -> ((A and (B -> C)) -> C))), M:tm-84, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-2102
in-theory        2102
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> C)) and A)))
theorem-size     11
proof            (modus-ponens tm-84 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2102.         (A -> (B -> ((C -> (D -> C)) and A))), M:tm-84, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-2103
in-theory        2103
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))
theorem-size     19
proof            (modus-ponens tm-84 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2103.         (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))), M:tm-84, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-2104
in-theory        2104
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C and D) -> C) and A)))
theorem-size     11
proof            (modus-ponens tm-84 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2104.         (A -> (B -> (((C and D) -> C) and A))), M:tm-84, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-2105
in-theory        2105
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C and D) -> D) and A)))
theorem-size     11
proof            (modus-ponens tm-84 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2105.         (A -> (B -> (((C and D) -> D) and A))), M:tm-84, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-2106
in-theory        2106
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> (C and D))) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2106.         (A -> (B -> ((C -> (D -> (C and D))) and A))), M:tm-84, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-2107
in-theory        2107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (A -> (A and B))))
theorem-size     11
proof            (modus-ponens tm-84 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-2107.         ((A -> B) -> (C -> (A -> (A and B)))), M:tm-84, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-2108
in-theory        2108
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (C or D)) and A)))
theorem-size     11
proof            (modus-ponens tm-84 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2108.         (A -> (B -> ((C -> (C or D)) and A))), M:tm-84, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-2109
in-theory        2109
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D or C)) and A)))
theorem-size     11
proof            (modus-ponens tm-84 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2109.         (A -> (B -> ((C -> (D or C)) and A))), M:tm-84, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-2110
in-theory        2110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (D -> ((B or (A -> B)) -> C)))
theorem-size     15
proof            (modus-ponens tm-84 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2110.         (((A -> B) -> C) -> (D -> ((B or (A -> B)) -> C))), M:tm-84, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-2111
in-theory        2111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     27
proof            (modus-ponens tm-84 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2111.         ((((A -> B) -> (A -> C)) -> D) -> (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-84, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2112
in-theory        2112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (((A and D) or A) -> B)))
theorem-size     13
proof            (modus-ponens tm-84 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2112.         ((A -> B) -> (C -> (((A and D) or A) -> B))), M:tm-84, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-2113
in-theory        2113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (((D and A) or A) -> B)))
theorem-size     13
proof            (modus-ponens tm-84 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2113.         ((A -> B) -> (C -> (((D and A) or A) -> B))), M:tm-84, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-2114
in-theory        2114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> (D -> ((B or (A -> (B and A))) -> C)))
theorem-size     19
proof            (modus-ponens tm-84 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2114.         (((A -> (B and A)) -> C) -> (D -> ((B or (A -> (B and A))) -> C))), M:tm-84, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-2115
in-theory        2115
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D -> ((A or (A or B)) -> C)))
theorem-size     15
proof            (modus-ponens tm-84 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2115.         (((A or B) -> C) -> (D -> ((A or (A or B)) -> C))), M:tm-84, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-2116
in-theory        2116
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D -> ((B or (A or B)) -> C)))
theorem-size     15
proof            (modus-ponens tm-84 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2116.         (((A or B) -> C) -> (D -> ((B or (A or B)) -> C))), M:tm-84, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-2117
in-theory        2117
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> (E -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     29
proof            (modus-ponens tm-84 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2117.         ((((A -> B) -> ((C or A) -> B)) -> D) -> (E -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-84, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-2118
in-theory        2118
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and A)))
theorem-size     19
proof            (modus-ponens tm-84 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2118.         (A -> (B -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and A))), M:tm-84, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-2119
in-theory        2119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (B -> C)) -> (D -> ((A -> B) -> ((A or B) -> C))))
theorem-size     19
proof            (modus-ponens tm-84 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-2119.         (((A -> B) -> (B -> C)) -> (D -> ((A -> B) -> ((A or B) -> C)))), M:tm-84, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-2120
in-theory        2120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> A))) -> (C -> (not A)))
theorem-size     11
proof            (modus-ponens tm-84 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2120.         ((A -> (not (B -> A))) -> (C -> (not A))), M:tm-84, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-2121
in-theory        2121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (D -> (not (A -> (B -> C)))))
theorem-size     23
proof            (modus-ponens tm-84 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2121.         (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (D -> (not (A -> (B -> C))))), M:tm-84, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2122
in-theory        2122
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not A)) -> (C -> (not (A and B))))
theorem-size     13
proof            (modus-ponens tm-84 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2122.         (((A and B) -> (not A)) -> (C -> (not (A and B)))), M:tm-84, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-2123
in-theory        2123
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not B)) -> (C -> (not (A and B))))
theorem-size     13
proof            (modus-ponens tm-84 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2123.         (((A and B) -> (not B)) -> (C -> (not (A and B)))), M:tm-84, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-2124
in-theory        2124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (A and B)))) -> (C -> (not A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2124.         ((A -> (not (B -> (A and B)))) -> (C -> (not A))), M:tm-84, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-2125
in-theory        2125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A or B))) -> (C -> (not A)))
theorem-size     11
proof            (modus-ponens tm-84 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2125.         ((A -> (not (A or B))) -> (C -> (not A))), M:tm-84, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-2126
in-theory        2126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B or A))) -> (C -> (not A)))
theorem-size     11
proof            (modus-ponens tm-84 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2126.         ((A -> (not (B or A))) -> (C -> (not A))), M:tm-84, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-2127
in-theory        2127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (D -> (not (A -> B))))
theorem-size     21
proof            (modus-ponens tm-84 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2127.         (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (D -> (not (A -> B)))), M:tm-84, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-2128
in-theory        2128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (C -> (not (A -> B))))
theorem-size     19
proof            (modus-ponens tm-84 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2128.         (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (C -> (not (A -> B)))), M:tm-84, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-2129
in-theory        2129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> C) -> (D -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))
theorem-size     25
proof            (modus-ponens tm-84 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-9)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2129.         ((((A -> (not B)) -> (not A)) -> C) -> (D -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))), M:tm-84, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-2130
in-theory        2130
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> D) -> ((C -> (not D)) -> (not C))) and A)))
theorem-size     17
proof            (modus-ponens tm-84 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2130.         (A -> (B -> (((C -> D) -> ((C -> (not D)) -> (not C))) and A))), M:tm-84, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-2131
in-theory        2131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (not B))) -> (C -> ((A -> B) -> (not A))))
theorem-size     17
proof            (modus-ponens tm-84 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-2131.         (((A -> B) -> (A -> (not B))) -> (C -> ((A -> B) -> (not A)))), M:tm-84, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-2132
in-theory        2132
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not A)) -> (B -> (not (not (not A)))))
theorem-size     13
proof            (modus-ponens tm-84 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-2 tm-1 tm-9 tm-10)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2132.         (((not (not A)) -> (not A)) -> (B -> (not (not (not A))))), M:tm-84, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-2133
in-theory        2133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (((not (not A)) or A) -> B)))
theorem-size     13
proof            (modus-ponens tm-84 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2133.         ((A -> B) -> (C -> (((not (not A)) or A) -> B))), M:tm-84, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-2134
in-theory        2134
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((not (not C)) -> C) and A)))
theorem-size     11
proof            (modus-ponens tm-84 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-10)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2134.         (A -> (B -> (((not (not C)) -> C) and A))), M:tm-84, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-2135
in-theory        2135
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) -> A) -> (C -> ((not (not (A -> B))) -> B)))
theorem-size     17
proof            (modus-ponens tm-84 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-2 tm-1 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-2135.         (((not (not (A -> B))) -> A) -> (C -> ((not (not (A -> B))) -> B))), M:tm-84, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-2136
in-theory        2136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> B)))) -> (D -> (not A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2136.         ((A -> (not (B -> (C -> B)))) -> (D -> (not A))), M:tm-84, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-2137
in-theory        2137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> (D -> ((E or (A -> (B -> A))) -> C)))
theorem-size     19
proof            (modus-ponens tm-84 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2137.         (((A -> (B -> A)) -> C) -> (D -> ((E or (A -> (B -> A))) -> C))), M:tm-84, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-2138
in-theory        2138
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> (E -> D))) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2138.         (A -> (B -> ((C -> (D -> (E -> D))) and A))), M:tm-84, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-2139
in-theory        2139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (A -> (D -> B))))
theorem-size     11
proof            (modus-ponens tm-84 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-2 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2139.         ((A -> B) -> (C -> (A -> (D -> B)))), M:tm-84, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-2140
in-theory        2140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-83 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2140.         ((A -> (B -> (C -> B))) and ((D -> E) -> (D -> (F -> E)))), M:tm-83, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2141
in-theory        2141
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (B -> (D -> (C -> B))))
theorem-size     15
proof            (modus-ponens tm-80 tm-84 ((A Am) (Bm (-> B Am)) (C (-> Am (-> Cm (-> B Am))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2141.         ((A or (B -> (C -> B))) -> (B -> (D -> (C -> B)))), M:tm-80, m:tm-84, u:((A Am) (Bm (-> B Am)) (C (-> Am (-> Cm (-> B Am)))))
================================================================
tm-name          tm-2142
in-theory        2142
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> (B -> (D -> C))))
theorem-size     15
proof            (modus-ponens tm-76 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2142.         (((not (not A)) -> A) and ((B -> C) -> (B -> (D -> C)))), M:tm-76, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2143
in-theory        2143
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> (A -> (C -> B)))
theorem-size     15
proof            (modus-ponens tm-73 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2143.         (((not (not (A -> B))) or (A -> B)) -> (A -> (C -> B))), M:tm-73, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-2144
in-theory        2144
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (C -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-69 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2144.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (C -> (E -> D)))), M:tm-69, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2145
in-theory        2145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> (C -> (not A))))
theorem-size     21
proof            (modus-ponens tm-66 tm-84 ((Am (-> A (not B))) (Bm (not A)) (C (-> (-> A (not B)) (-> Cm (not A))))))
axioms-used      (tm-8 tm-9 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2145.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> (C -> (not A)))), M:tm-66, m:tm-84, u:((Am (-> A (not B))) (Bm (not A)) (C (-> (-> A (not B)) (-> Cm (not A)))))
================================================================
tm-name          tm-2146
in-theory        2146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) -> ((A or A) -> (B -> A)))
theorem-size     11
proof            (modus-ponens tm-55 tm-84 ((A Bm) (Am Bm) (B Bm) (C (-> Cm Bm))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2146.         ((A -> A) -> ((A or A) -> (B -> A))), M:tm-55, m:tm-84, u:((A Bm) (Am Bm) (B Bm) (C (-> Cm Bm)))
================================================================
tm-name          tm-2147
in-theory        2147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-54 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2147.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (F -> E)))), M:tm-54, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2148
in-theory        2148
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (D -> ((A or B) -> C))))
theorem-size     25
proof            (modus-ponens tm-51 tm-84 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> Cm (-> (or C A) B))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2148.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (D -> ((A or B) -> C)))), M:tm-51, m:tm-84, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> Cm (-> (or C A) B)))))
================================================================
tm-name          tm-2149
in-theory        2149
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (B -> (C -> (A and B))))
theorem-size     15
proof            (modus-ponens tm-48 tm-84 ((A Am) (Bm (and B Am)) (C (-> Am (-> Cm (and B Am))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2149.         ((A or (B -> (A and B))) -> (B -> (C -> (A and B)))), M:tm-48, m:tm-84, u:((A Am) (Bm (and B Am)) (C (-> Am (-> Cm (and B Am)))))
================================================================
tm-name          tm-2150
in-theory        2150
times-derived    2
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (B -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-47 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2150.         (((A and (B -> C)) or (B -> C)) -> (B -> (D -> C))), M:tm-47, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-2151
in-theory        2151
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (A -> (D -> B)))
theorem-size     15
proof            (modus-ponens tm-46 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2151.         ((((A -> B) and C) or (A -> B)) -> (A -> (D -> B))), M:tm-46, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-2152
in-theory        2152
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-45 tm-84 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> Cm (-> A C))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2152.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D -> (A -> C)))), M:tm-45, m:tm-84, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> Cm (-> A C)))))
================================================================
tm-name          tm-2153
in-theory        2153
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (B -> (C -> A)))
theorem-size     11
proof            (modus-ponens tm-44 tm-84 ((A Am) (B Bm) (C (-> Am (-> Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2153.         ((A or (B -> A)) -> (B -> (C -> A))), M:tm-44, m:tm-84, u:((A Am) (B Bm) (C (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-2154
in-theory        2154
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (C -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-42 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2154.         ((A -> (B or A)) and ((C -> D) -> (C -> (E -> D)))), M:tm-42, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2155
in-theory        2155
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (C -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-32 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2155.         ((A -> (A or B)) and ((C -> D) -> (C -> (E -> D)))), M:tm-32, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2156
in-theory        2156
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (A -> (C -> B))))
theorem-size     13
proof            (modus-ponens tm-24 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2156.         ((A -> B) -> ((A -> B) and (A -> (C -> B)))), M:tm-24, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-2157
in-theory        2157
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-23 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2157.         ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (E -> D)))), M:tm-23, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2158
in-theory        2158
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (C -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-22 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2158.         (((A and B) -> B) and ((C -> D) -> (C -> (E -> D)))), M:tm-22, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2159
in-theory        2159
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (C -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-21 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2159.         (((A and B) -> A) and ((C -> D) -> (C -> (E -> D)))), M:tm-21, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2160
in-theory        2160
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-20 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2160.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (F -> E)))), M:tm-20, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2161
in-theory        2161
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (C -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-19 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2161.         ((A -> (B -> A)) and ((C -> D) -> (C -> (E -> D)))), M:tm-19, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2162
in-theory        2162
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (C -> B)))) -> (not (A -> B)))
theorem-size     15
proof            (modus-ponens tm-9 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-9 tm-2 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2162.         (((A -> B) -> (not (A -> (C -> B)))) -> (not (A -> B))), M:tm-9, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-2163
in-theory        2163
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> D) -> (((A -> C) or (A -> (B -> C))) -> D))
theorem-size     19
proof            (modus-ponens tm-8 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2163.         (((A -> (B -> C)) -> D) -> (((A -> C) or (A -> (B -> C))) -> D)), M:tm-8, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-2164
in-theory        2164
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (B -> (D -> C))))
theorem-size     11
proof            (modus-ponens tm-7 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-7 tm-2 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2164.         (A or ((B -> C) -> (B -> (D -> C)))), M:tm-7, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2165
in-theory        2165
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-6 tm-2 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2165.         (((A -> B) -> (A -> (C -> B))) or D), M:tm-6, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2166
in-theory        2166
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> (D -> C))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2166.         (A -> (((B -> C) -> (B -> (D -> C))) and A)), M:tm-5, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2167
in-theory        2167
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> ((A -> B) -> (C -> B)))
theorem-size     13
proof            (modus-ponens tm-2 tm-84 ((A (-> Am Bm)) (B Am) (C (-> Cm Bm))))
axioms-used      (tm-2 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2167.         (((A -> B) -> A) -> ((A -> B) -> (C -> B))), M:tm-2, m:tm-84, u:((A (-> Am Bm)) (B Am) (C (-> Cm Bm)))
================================================================
tm-name          tm-2168
in-theory        2168
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (B -> (D -> C))))
theorem-size     11
proof            (modus-ponens tm-1 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-1 tm-2)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2168.         (A -> ((B -> C) -> (B -> (D -> C)))), M:tm-1, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2169
in-theory        2169
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C -> (D -> (E -> D)))))
theorem-size     11
proof            (modus-ponens tm-84 tm-85 ((A Am) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-1)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2169.         (A -> (B -> (C -> (D -> (E -> D))))), M:tm-84, m:tm-85, u:((A Am) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2170
in-theory        2170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2170.         ((A -> (B -> (C -> B))) and (D -> (E -> (F -> (G -> F))))), M:tm-83, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2171
in-theory        2171
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-80 tm-85 ((Am (-> A (-> B A))) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2171.         ((A or (B -> (C -> B))) -> (D -> (E -> (F -> E)))), M:tm-80, m:tm-85, u:((Am (-> A (-> B A))) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2172
in-theory        2172
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> (B -> (C -> B))) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-85 ((Am (not (not (-> (-> Bm (-> Cm (-> Dm Cm))) B)))) (A (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-10 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2172.         ((not (not ((A -> (B -> (C -> B))) -> D))) -> D), M:tm-77, m:tm-85, u:((Am (not (not (-> (-> Bm (-> Cm (-> Dm Cm))) B)))) (A (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2173
in-theory        2173
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> (D -> (E -> D)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2173.         (((not (not A)) -> A) and (B -> (C -> (D -> (E -> D))))), M:tm-76, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2174
in-theory        2174
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> (C -> (D -> C))))
theorem-size     13
proof            (modus-ponens tm-73 tm-85 ((A Am) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-10 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2174.         (((not (not A)) or A) -> (B -> (C -> (D -> C)))), M:tm-73, m:tm-85, u:((A Am) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2175
in-theory        2175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (E -> (F -> E)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2175.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (E -> (F -> E))))), M:tm-69, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2176
in-theory        2176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (D -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-66 tm-85 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-9 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2176.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (D -> (E -> D)))), M:tm-66, m:tm-85, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2177
in-theory        2177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> (C -> (D -> C))))
theorem-size     13
proof            (modus-ponens tm-55 tm-85 ((Am (-> A Bm)) (B Bm) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2177.         ((A -> B) -> ((A or B) -> (C -> (D -> C)))), M:tm-55, m:tm-85, u:((Am (-> A Bm)) (B Bm) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-2178
in-theory        2178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2178.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (G -> F))))), M:tm-54, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2179
in-theory        2179
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-51 tm-85 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2179.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (F -> E)))), M:tm-51, m:tm-85, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2180
in-theory        2180
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-50 tm-85 ((Am (or A B)) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2180.         ((A or (B or A)) -> (C -> (D -> (E -> D)))), M:tm-50, m:tm-85, u:((Am (or A B)) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2181
in-theory        2181
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-49 tm-85 ((Am (or A B)) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2181.         ((A or (A or B)) -> (C -> (D -> (E -> D)))), M:tm-49, m:tm-85, u:((Am (or A B)) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2182
in-theory        2182
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (D -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-48 tm-85 ((Am (-> A (and B A))) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2182.         ((A or (B -> (A and B))) -> (C -> (D -> (E -> D)))), M:tm-48, m:tm-85, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2183
in-theory        2183
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-47 tm-85 ((A Am) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2183.         (((A and B) or B) -> (C -> (D -> (E -> D)))), M:tm-47, m:tm-85, u:((A Am) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2184
in-theory        2184
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-46 tm-85 ((A Am) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2184.         (((A and B) or A) -> (C -> (D -> (E -> D)))), M:tm-46, m:tm-85, u:((A Am) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2185
in-theory        2185
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-45 tm-85 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2185.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (F -> E)))), M:tm-45, m:tm-85, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2186
in-theory        2186
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-44 tm-85 ((Am (-> A B)) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2186.         ((A or (B -> A)) -> (C -> (D -> (E -> D)))), M:tm-44, m:tm-85, u:((Am (-> A B)) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2187
in-theory        2187
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2187.         ((A -> (B or A)) and (C -> (D -> (E -> (F -> E))))), M:tm-42, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2188
in-theory        2188
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2188.         ((A -> (A or B)) and (C -> (D -> (E -> (F -> E))))), M:tm-32, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2189
in-theory        2189
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B -> (C -> (D -> C)))))
theorem-size     11
proof            (modus-ponens tm-24 tm-85 ((A Am) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2189.         (A -> (A and (B -> (C -> (D -> C))))), M:tm-24, m:tm-85, u:((A Am) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2190
in-theory        2190
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2190.         ((A -> (B -> (A and B))) and (C -> (D -> (E -> (F -> E))))), M:tm-23, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2191
in-theory        2191
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2191.         (((A and B) -> B) and (C -> (D -> (E -> (F -> E))))), M:tm-22, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2192
in-theory        2192
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2192.         (((A and B) -> A) and (C -> (D -> (E -> (F -> E))))), M:tm-21, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2193
in-theory        2193
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2193.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (G -> F))))), M:tm-20, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2194
in-theory        2194
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2194.         ((A -> (B -> A)) and (C -> (D -> (E -> (F -> E))))), M:tm-19, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2195
in-theory        2195
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (D -> C))) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-85 ((Am (and A (-> (-> Bm (-> Cm (-> Dm Cm))) C))) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2195.         ((A and ((B -> (C -> (D -> C))) -> E)) -> E), M:tm-17, m:tm-85, u:((Am (and A (-> (-> Bm (-> Cm (-> Dm Cm))) C))) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2196
in-theory        2196
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (C -> B))) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-85 ((Am (and (-> (-> Bm (-> Cm (-> Dm Cm))) B) C)) (A (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2196.         ((((A -> (B -> (C -> B))) -> D) and E) -> D), M:tm-15, m:tm-85, u:((Am (and (-> (-> Bm (-> Cm (-> Dm Cm))) B) C)) (A (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2197
in-theory        2197
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) -> D)) -> (A -> D))
theorem-size     13
proof            (modus-ponens tm-13 tm-85 ((Am (-> Bm (-> (-> Cm (-> Dm Cm)) C))) (A Bm) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2197.         ((A -> ((B -> (C -> B)) -> D)) -> (A -> D)), M:tm-13, m:tm-85, u:((Am (-> Bm (-> (-> Cm (-> Dm Cm)) C))) (A Bm) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-2198
in-theory        2198
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> (D -> C))))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-85 ((A Am) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-9 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2198.         ((A -> (not (B -> (C -> (D -> C))))) -> (not A)), M:tm-9, m:tm-85, u:((A Am) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2199
in-theory        2199
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) -> D) -> ((E or (A -> (B -> (C -> B)))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-85 ((A Am) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2199.         (((A -> (B -> (C -> B))) -> D) -> ((E or (A -> (B -> (C -> B)))) -> D)), M:tm-8, m:tm-85, u:((A Am) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2200
in-theory        2200
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C -> (D -> (E -> D)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-7 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2200.         (A or (B -> (C -> (D -> (E -> D))))), M:tm-7, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2201
in-theory        2201
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-6 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2201.         ((A -> (B -> (C -> (D -> C)))) or E), M:tm-6, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2202
in-theory        2202
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (D -> (E -> D)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2202.         (A -> ((B -> (C -> (D -> (E -> D)))) and A)), M:tm-5, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2203
in-theory        2203
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> (C -> (D -> C))))
theorem-size     11
proof            (modus-ponens tm-2 tm-85 ((A Am) (B Bm) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2203.         ((A -> B) -> (A -> (C -> (D -> C)))), M:tm-2, m:tm-85, u:((A Am) (B Bm) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-2204
in-theory        2204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-83 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2204.         ((A -> (B -> (C -> B))) and (D -> D)), M:tm-83, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2205
in-theory        2205
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (B -> (C -> B)))
theorem-size     13
proof            (modus-ponens tm-80 tm-86 ((Am (-> A (-> B A))) (C (-> A (-> B A)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2205.         ((A or (B -> (C -> B))) -> (B -> (C -> B))), M:tm-80, m:tm-86, u:((Am (-> A (-> B A))) (C (-> A (-> B A))))
================================================================
tm-name          tm-2206
in-theory        2206
times-derived    1
----------------------------------------------------------------
theorem          (not (not (A -> (B -> A))))
theorem-size     7
proof            (modus-ponens tm-79 tm-86 ((A (not (-> B (-> C B)))) (Am (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2206.         (not (not (A -> (B -> A)))), M:tm-79, m:tm-86, u:((A (not (-> B (-> C B)))) (Am (not (-> B (-> C B)))))
================================================================
tm-name          tm-2207
in-theory        2207
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> B))
theorem-size     9
proof            (modus-ponens tm-76 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       63
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2207.         (((not (not A)) -> A) and (B -> B)), M:tm-76, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2208
in-theory        2208
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> A)
theorem-size     7
proof            (modus-ponens tm-73 tm-86 ((A Am) (B Am)))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       69
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2208.         (((not (not A)) or A) -> A), M:tm-73, m:tm-86, u:((A Am) (B Am))
================================================================
tm-name          tm-2209
in-theory        2209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> C))
theorem-size     15
proof            (modus-ponens tm-69 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2209.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> C)), M:tm-69, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2210
in-theory        2210
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> (not A)))
theorem-size     19
proof            (modus-ponens tm-66 tm-86 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> A (not B)) (not A)))))
axioms-used      (tm-8 tm-9 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2210.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> (not A))), M:tm-66, m:tm-86, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> A (not B)) (not A))))
================================================================
tm-name          tm-2211
in-theory        2211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> D))
theorem-size     17
proof            (modus-ponens tm-54 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2211.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> D)), M:tm-54, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2212
in-theory        2212
times-derived    17
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((A or B) -> C)))
theorem-size     23
proof            (modus-ponens tm-51 tm-86 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> A B) (-> (or C A) B)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2212.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> ((A or B) -> C))), M:tm-51, m:tm-86, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> A B) (-> (or C A) B))))
================================================================
tm-name          tm-2213
in-theory        2213
times-derived    14
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (B or A))
theorem-size     9
proof            (modus-ponens tm-50 tm-86 ((Am (or A B)) (C (or A B))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2213.         ((A or (B or A)) -> (B or A)), M:tm-50, m:tm-86, u:((Am (or A B)) (C (or A B)))
================================================================
tm-name          tm-2214
in-theory        2214
times-derived    14
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (A or B))
theorem-size     9
proof            (modus-ponens tm-49 tm-86 ((Am (or A B)) (C (or A B))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2214.         ((A or (A or B)) -> (A or B)), M:tm-49, m:tm-86, u:((Am (or A B)) (C (or A B)))
================================================================
tm-name          tm-2215
in-theory        2215
times-derived    14
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (B -> (A and B)))
theorem-size     13
proof            (modus-ponens tm-48 tm-86 ((Am (-> A (and B A))) (C (-> A (and B A)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2215.         ((A or (B -> (A and B))) -> (B -> (A and B))), M:tm-48, m:tm-86, u:((Am (-> A (and B A))) (C (-> A (and B A))))
================================================================
tm-name          tm-2216
in-theory        2216
times-derived    13
----------------------------------------------------------------
theorem          (((A and B) or B) -> B)
theorem-size     7
proof            (modus-ponens tm-47 tm-86 ((A Am) (B Am)))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       69
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2216.         (((A and B) or B) -> B), M:tm-47, m:tm-86, u:((A Am) (B Am))
================================================================
tm-name          tm-2217
in-theory        2217
times-derived    13
----------------------------------------------------------------
theorem          (((A and B) or A) -> A)
theorem-size     7
proof            (modus-ponens tm-46 tm-86 ((A Am) (B Am)))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       69
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2217.         (((A and B) or A) -> A), M:tm-46, m:tm-86, u:((A Am) (B Am))
================================================================
tm-name          tm-2218
in-theory        2218
times-derived    16
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> C)))
theorem-size     21
proof            (modus-ponens tm-45 tm-86 ((Am (-> (-> A B) (-> A C))) (D (-> (-> A B) (-> A C)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2218.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> C))), M:tm-45, m:tm-86, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> A B) (-> A C))))
================================================================
tm-name          tm-2219
in-theory        2219
times-derived    14
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (B -> A))
theorem-size     9
proof            (modus-ponens tm-44 tm-86 ((Am (-> A B)) (C (-> A B))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2219.         ((A or (B -> A)) -> (B -> A)), M:tm-44, m:tm-86, u:((Am (-> A B)) (C (-> A B)))
================================================================
tm-name          tm-2220
in-theory        2220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> C))
theorem-size     9
proof            (modus-ponens tm-42 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       63
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2220.         ((A -> (B or A)) and (C -> C)), M:tm-42, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2221
in-theory        2221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> C))
theorem-size     9
proof            (modus-ponens tm-32 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       63
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2221.         ((A -> (A or B)) and (C -> C)), M:tm-32, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2222
in-theory        2222
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and A))
theorem-size     5
proof            (modus-ponens tm-24 tm-86 ((A Am) (B Am)))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2222.         (A -> (A and A)), M:tm-24, m:tm-86, u:((A Am) (B Am))
================================================================
tm-name          tm-2223
in-theory        2223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> C))
theorem-size     11
proof            (modus-ponens tm-23 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       69
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2223.         ((A -> (B -> (A and B))) and (C -> C)), M:tm-23, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2224
in-theory        2224
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> C))
theorem-size     9
proof            (modus-ponens tm-22 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       63
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2224.         (((A and B) -> B) and (C -> C)), M:tm-22, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2225
in-theory        2225
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> C))
theorem-size     9
proof            (modus-ponens tm-21 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       63
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2225.         (((A and B) -> A) and (C -> C)), M:tm-21, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2226
in-theory        2226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> D))
theorem-size     17
proof            (modus-ponens tm-20 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2226.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> D)), M:tm-20, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2227
in-theory        2227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> C))
theorem-size     9
proof            (modus-ponens tm-19 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       63
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2227.         ((A -> (B -> A)) and (C -> C)), M:tm-19, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2228
in-theory        2228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not A)) -> (not A))
theorem-size     7
proof            (modus-ponens tm-9 tm-86 ((A Am) (B Am)))
axioms-used      (tm-9 tm-2 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2228.         ((A -> (not A)) -> (not A)), M:tm-9, m:tm-86, u:((A Am) (B Am))
================================================================
tm-name          tm-2229
in-theory        2229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or A) -> B))
theorem-size     9
proof            (modus-ponens tm-8 tm-86 ((A Am) (B Am)))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2229.         ((A -> B) -> ((A or A) -> B)), M:tm-8, m:tm-86, u:((A Am) (B Am))
================================================================
tm-name          tm-2230
in-theory        2230
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> B))
theorem-size     5
proof            (modus-ponens tm-7 tm-86 ((A (-> Am Am))))
axioms-used      (tm-7 tm-2 tm-1)
proof-size       43
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2230.         (A or (B -> B)), M:tm-7, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2231
in-theory        2231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) or B)
theorem-size     5
proof            (modus-ponens tm-6 tm-86 ((A (-> Am Am))))
axioms-used      (tm-6 tm-2 tm-1)
proof-size       43
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2231.         ((A -> A) or B), M:tm-6, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2232
in-theory        2232
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> B) and A))
theorem-size     7
proof            (modus-ponens tm-5 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2232.         (A -> ((B -> B) and A)), M:tm-5, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2233
in-theory        2233
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> ((A -> B) -> B))
theorem-size     11
proof            (modus-ponens tm-2 tm-86 ((A (-> B C)) (Am (-> B C))))
axioms-used      (tm-2 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2233.         (((A -> B) -> A) -> ((A -> B) -> B)), M:tm-2, m:tm-86, u:((A (-> B C)) (Am (-> B C)))
================================================================
tm-name          tm-2234
in-theory        2234
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> B))
theorem-size     5
proof            (modus-ponens tm-1 tm-86 ((A (-> Am Am))))
axioms-used      (tm-1 tm-2)
proof-size       43
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2234.         (A -> (B -> B)), M:tm-1, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2235
in-theory        2235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and C) -> (A -> B))
theorem-size     9
proof            (modus-ponens tm-87 tm-3 ((A (and (-> B C) Bm)) (Am (-> B C))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-2235.         (((A -> B) and C) -> (A -> B)), M:tm-87, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
================================================================
tm-name          tm-2236
in-theory        2236
times-derived    1
----------------------------------------------------------------
theorem          ((A and (B -> C)) -> (B -> C))
theorem-size     9
proof            (modus-ponens tm-87 tm-4 ((A (and Am (-> B C))) (Bm (-> B C))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-2236.         ((A and (B -> C)) -> (B -> C)), M:tm-87, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
================================================================
tm-name          tm-2237
in-theory        2237
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (A -> B))) -> (A -> B))
theorem-size     9
proof            (modus-ponens tm-87 tm-10 ((A (not (not (-> B C)))) (Am (-> B C))))
axioms-used      (tm-2 tm-1 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-2237.         ((not (not (A -> B))) -> (A -> B)), M:tm-87, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
================================================================
tm-name          tm-2238
in-theory        2238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (D -> (A -> (B -> C))))
theorem-size     13
proof            (modus-ponens tm-84 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-2 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2238.         ((A -> (B -> C)) -> (D -> (A -> (B -> C)))), M:tm-84, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-2239
in-theory        2239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2239.         ((A -> (B -> (C -> B))) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-83, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2240
in-theory        2240
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> D)) -> (B -> (C -> D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2240.         (((not (not A)) -> A) and ((B -> (C -> D)) -> (B -> (C -> D)))), M:tm-76, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2241
in-theory        2241
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (B -> C)))) or (A -> (B -> C))) -> (A -> (B -> C)))
theorem-size     19
proof            (modus-ponens tm-73 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2241.         (((not (not (A -> (B -> C)))) or (A -> (B -> C))) -> (A -> (B -> C))), M:tm-73, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-2242
in-theory        2242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> E)) -> (C -> (D -> E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2242.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> E)) -> (C -> (D -> E)))), M:tm-69, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2243
in-theory        2243
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) -> (((A -> B) or (A -> B)) -> (A -> B)))
theorem-size     19
proof            (modus-ponens tm-55 tm-87 ((A (-> Bm Cm)) (Am (-> Bm Cm)) (B (-> Bm Cm)) (C (-> Bm Cm))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2243.         (((A -> B) -> (A -> B)) -> (((A -> B) or (A -> B)) -> (A -> B))), M:tm-55, m:tm-87, u:((A (-> Bm Cm)) (Am (-> Bm Cm)) (B (-> Bm Cm)) (C (-> Bm Cm)))
================================================================
tm-name          tm-2244
in-theory        2244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2244.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-54, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2245
in-theory        2245
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (B -> (C -> D)))
theorem-size     19
proof            (modus-ponens tm-47 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2245.         (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (B -> (C -> D))), M:tm-47, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-2246
in-theory        2246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> (B -> C)))
theorem-size     19
proof            (modus-ponens tm-46 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2246.         ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> (B -> C))), M:tm-46, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-2247
in-theory        2247
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (C -> (A -> B))) -> (C -> (A -> B)))
theorem-size     15
proof            (modus-ponens tm-44 tm-87 ((A Am) (B (-> Bm Cm)) (C (-> Am (-> Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2247.         (((A -> B) or (C -> (A -> B))) -> (C -> (A -> B))), M:tm-44, m:tm-87, u:((A Am) (B (-> Bm Cm)) (C (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-2248
in-theory        2248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> E)) -> (C -> (D -> E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2248.         ((A -> (B or A)) and ((C -> (D -> E)) -> (C -> (D -> E)))), M:tm-42, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2249
in-theory        2249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> E)) -> (C -> (D -> E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2249.         ((A -> (A or B)) and ((C -> (D -> E)) -> (C -> (D -> E)))), M:tm-32, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2250
in-theory        2250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((A -> (B -> C)) and (A -> (B -> C))))
theorem-size     17
proof            (modus-ponens tm-24 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2250.         ((A -> (B -> C)) -> ((A -> (B -> C)) and (A -> (B -> C)))), M:tm-24, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-2251
in-theory        2251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> (C -> (D -> E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2251.         ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> (C -> (D -> E)))), M:tm-23, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2252
in-theory        2252
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> E)) -> (C -> (D -> E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2252.         (((A and B) -> B) and ((C -> (D -> E)) -> (C -> (D -> E)))), M:tm-22, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2253
in-theory        2253
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> E)) -> (C -> (D -> E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2253.         (((A and B) -> A) and ((C -> (D -> E)) -> (C -> (D -> E)))), M:tm-21, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2254
in-theory        2254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2254.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-20, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2255
in-theory        2255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> E)) -> (C -> (D -> E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2255.         ((A -> (B -> A)) and ((C -> (D -> E)) -> (C -> (D -> E)))), M:tm-19, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2256
in-theory        2256
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (not (A -> (B -> C)))) -> (not (A -> (B -> C))))
theorem-size     19
proof            (modus-ponens tm-9 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-9 tm-2 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2256.         (((A -> (B -> C)) -> (not (A -> (B -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-2257
in-theory        2257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> D) -> (((A -> (B -> C)) or (A -> (B -> C))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2257.         (((A -> (B -> C)) -> D) -> (((A -> (B -> C)) or (A -> (B -> C))) -> D)), M:tm-8, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-2258
in-theory        2258
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> D)) -> (B -> (C -> D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-7 tm-2 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2258.         (A or ((B -> (C -> D)) -> (B -> (C -> D)))), M:tm-7, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2259
in-theory        2259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-6 tm-2 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2259.         (((A -> (B -> C)) -> (A -> (B -> C))) or D), M:tm-6, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2260
in-theory        2260
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> (B -> (C -> D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2260.         (A -> (((B -> (C -> D)) -> (B -> (C -> D))) and A)), M:tm-5, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2261
in-theory        2261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> (B -> C)))
theorem-size     17
proof            (modus-ponens tm-2 tm-87 ((A (-> Am (-> Bm Cm))) (B Am) (C (-> Bm Cm))))
axioms-used      (tm-2 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2261.         (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> (B -> C))), M:tm-2, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B Am) (C (-> Bm Cm)))
================================================================
tm-name          tm-2262
in-theory        2262
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> D)) -> (B -> (C -> D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-1 tm-2)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2262.         (A -> ((B -> (C -> D)) -> (B -> (C -> D)))), M:tm-1, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2263
in-theory        2263
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (C -> (A and B)))
theorem-size     9
proof            (modus-ponens tm-84 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2263.         ((A and B) -> (C -> (A and B))), M:tm-84, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-2264
in-theory        2264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-83 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2264.         ((A -> (B -> (C -> B))) and ((D and E) -> (D and E))), M:tm-83, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2265
in-theory        2265
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B and C) -> (B and C)))
theorem-size     13
proof            (modus-ponens tm-76 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2265.         (((not (not A)) -> A) and ((B and C) -> (B and C))), M:tm-76, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2266
in-theory        2266
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A and B))) or (A and B)) -> (A and B))
theorem-size     13
proof            (modus-ponens tm-73 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2266.         (((not (not (A and B))) or (A and B)) -> (A and B)), M:tm-73, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-2267
in-theory        2267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and D) -> (C and D)))
theorem-size     19
proof            (modus-ponens tm-69 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2267.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and D) -> (C and D))), M:tm-69, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2268
in-theory        2268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> (D and E)))
theorem-size     21
proof            (modus-ponens tm-54 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2268.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> (D and E))), M:tm-54, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2269
in-theory        2269
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> (B and C))
theorem-size     13
proof            (modus-ponens tm-47 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2269.         (((A and (B and C)) or (B and C)) -> (B and C)), M:tm-47, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-2270
in-theory        2270
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> (A and B))
theorem-size     13
proof            (modus-ponens tm-46 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2270.         ((((A and B) and C) or (A and B)) -> (A and B)), M:tm-46, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-2271
in-theory        2271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C and D) -> (C and D)))
theorem-size     13
proof            (modus-ponens tm-42 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2271.         ((A -> (B or A)) and ((C and D) -> (C and D))), M:tm-42, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2272
in-theory        2272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C and D) -> (C and D)))
theorem-size     13
proof            (modus-ponens tm-32 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2272.         ((A -> (A or B)) and ((C and D) -> (C and D))), M:tm-32, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2273
in-theory        2273
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> ((A and B) and (A and B)))
theorem-size     11
proof            (modus-ponens tm-24 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2273.         ((A and B) -> ((A and B) and (A and B))), M:tm-24, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-2274
in-theory        2274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C and D) -> (C and D)))
theorem-size     15
proof            (modus-ponens tm-23 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2274.         ((A -> (B -> (A and B))) and ((C and D) -> (C and D))), M:tm-23, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2275
in-theory        2275
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C and D) -> (C and D)))
theorem-size     13
proof            (modus-ponens tm-22 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2275.         (((A and B) -> B) and ((C and D) -> (C and D))), M:tm-22, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2276
in-theory        2276
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C and D) -> (C and D)))
theorem-size     13
proof            (modus-ponens tm-21 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2276.         (((A and B) -> A) and ((C and D) -> (C and D))), M:tm-21, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2277
in-theory        2277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> (D and E)))
theorem-size     21
proof            (modus-ponens tm-20 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2277.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> (D and E))), M:tm-20, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2278
in-theory        2278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C and D) -> (C and D)))
theorem-size     13
proof            (modus-ponens tm-19 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2278.         ((A -> (B -> A)) and ((C and D) -> (C and D))), M:tm-19, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2279
in-theory        2279
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not (A and B))) -> (not (A and B)))
theorem-size     13
proof            (modus-ponens tm-9 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-9 tm-2 tm-1 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2279.         (((A and B) -> (not (A and B))) -> (not (A and B))), M:tm-9, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-2280
in-theory        2280
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> C) -> (((A and B) or (A and B)) -> C))
theorem-size     15
proof            (modus-ponens tm-8 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2280.         (((A and B) -> C) -> (((A and B) or (A and B)) -> C)), M:tm-8, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-2281
in-theory        2281
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B and C) -> (B and C)))
theorem-size     9
proof            (modus-ponens tm-7 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-7 tm-2 tm-1 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2281.         (A or ((B and C) -> (B and C))), M:tm-7, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2282
in-theory        2282
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) or C)
theorem-size     9
proof            (modus-ponens tm-6 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-6 tm-2 tm-1 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2282.         (((A and B) -> (A and B)) or C), M:tm-6, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2283
in-theory        2283
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> (B and C)) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2283.         (A -> (((B and C) -> (B and C)) and A)), M:tm-5, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2284
in-theory        2284
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B and C) -> (B and C)))
theorem-size     9
proof            (modus-ponens tm-1 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-1 tm-2 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2284.         (A -> ((B and C) -> (B and C))), M:tm-1, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2285
in-theory        2285
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (A -> B)))
theorem-size     9
proof            (modus-ponens tm-84 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2285.         ((A -> B) -> (C -> (A -> B))), M:tm-84, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-2286
in-theory        2286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-83 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2286.         ((A -> (B -> (C -> B))) and ((D -> E) -> (D -> E))), M:tm-83, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2287
in-theory        2287
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> (B -> C)))
theorem-size     13
proof            (modus-ponens tm-76 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-8)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2287.         (((not (not A)) -> A) and ((B -> C) -> (B -> C))), M:tm-76, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2288
in-theory        2288
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> (A -> B))
theorem-size     13
proof            (modus-ponens tm-73 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2288.         (((not (not (A -> B))) or (A -> B)) -> (A -> B)), M:tm-73, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-2289
in-theory        2289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (C -> D)))
theorem-size     19
proof            (modus-ponens tm-69 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2289.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (C -> D))), M:tm-69, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2290
in-theory        2290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> E)))
theorem-size     21
proof            (modus-ponens tm-54 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2290.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> E))), M:tm-54, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2291
in-theory        2291
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (B -> C))
theorem-size     13
proof            (modus-ponens tm-47 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2291.         (((A and (B -> C)) or (B -> C)) -> (B -> C)), M:tm-47, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-2292
in-theory        2292
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (A -> B))
theorem-size     13
proof            (modus-ponens tm-46 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2292.         ((((A -> B) and C) or (A -> B)) -> (A -> B)), M:tm-46, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-2293
in-theory        2293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (C -> D)))
theorem-size     13
proof            (modus-ponens tm-42 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2293.         ((A -> (B or A)) and ((C -> D) -> (C -> D))), M:tm-42, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2294
in-theory        2294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (C -> D)))
theorem-size     13
proof            (modus-ponens tm-32 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2294.         ((A -> (A or B)) and ((C -> D) -> (C -> D))), M:tm-32, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2295
in-theory        2295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (A -> B)))
theorem-size     11
proof            (modus-ponens tm-24 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2295.         ((A -> B) -> ((A -> B) and (A -> B))), M:tm-24, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-2296
in-theory        2296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> D)))
theorem-size     15
proof            (modus-ponens tm-23 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2296.         ((A -> (B -> (A and B))) and ((C -> D) -> (C -> D))), M:tm-23, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2297
in-theory        2297
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (C -> D)))
theorem-size     13
proof            (modus-ponens tm-22 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-8)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2297.         (((A and B) -> B) and ((C -> D) -> (C -> D))), M:tm-22, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2298
in-theory        2298
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (C -> D)))
theorem-size     13
proof            (modus-ponens tm-21 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-8)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2298.         (((A and B) -> A) and ((C -> D) -> (C -> D))), M:tm-21, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2299
in-theory        2299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> E)))
theorem-size     21
proof            (modus-ponens tm-20 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2299.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> E))), M:tm-20, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2300
in-theory        2300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (C -> D)))
theorem-size     13
proof            (modus-ponens tm-19 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2300.         ((A -> (B -> A)) and ((C -> D) -> (C -> D))), M:tm-19, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2301
in-theory        2301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> B))) -> (not (A -> B)))
theorem-size     13
proof            (modus-ponens tm-9 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-9 tm-2 tm-1 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2301.         (((A -> B) -> (not (A -> B))) -> (not (A -> B))), M:tm-9, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-2302
in-theory        2302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (((A -> B) or (A -> B)) -> C))
theorem-size     15
proof            (modus-ponens tm-8 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2302.         (((A -> B) -> C) -> (((A -> B) or (A -> B)) -> C)), M:tm-8, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-2303
in-theory        2303
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (B -> C)))
theorem-size     9
proof            (modus-ponens tm-7 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-7 tm-2 tm-1 tm-8)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2303.         (A or ((B -> C) -> (B -> C))), M:tm-7, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2304
in-theory        2304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) or C)
theorem-size     9
proof            (modus-ponens tm-6 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-6 tm-2 tm-1 tm-8)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2304.         (((A -> B) -> (A -> B)) or C), M:tm-6, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2305
in-theory        2305
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> C)) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2305.         (A -> (((B -> C) -> (B -> C)) and A)), M:tm-5, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2306
in-theory        2306
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (B -> C)))
theorem-size     9
proof            (modus-ponens tm-1 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-1 tm-2 tm-8)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2306.         (A -> ((B -> C) -> (B -> C))), M:tm-1, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2307
in-theory        2307
times-derived    1
----------------------------------------------------------------
theorem          ((not (not A)) -> (B -> (not (not A))))
theorem-size     9
proof            (modus-ponens tm-84 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-2 tm-1 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2307.         ((not (not A)) -> (B -> (not (not A)))), M:tm-84, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-2308
in-theory        2308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-83 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2308.         ((A -> (B -> (C -> B))) and ((not (not D)) -> (not (not D)))), M:tm-83, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2309
in-theory        2309
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((not (not B)) -> (not (not B))))
theorem-size     13
proof            (modus-ponens tm-76 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2309.         (((not (not A)) -> A) and ((not (not B)) -> (not (not B)))), M:tm-76, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2310
in-theory        2310
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (not (not A)))) or (not (not A))) -> (not (not A)))
theorem-size     13
proof            (modus-ponens tm-73 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2310.         (((not (not (not (not A)))) or (not (not A))) -> (not (not A))), M:tm-73, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-2311
in-theory        2311
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((not (not C)) -> (not (not C))))
theorem-size     19
proof            (modus-ponens tm-69 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2311.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((not (not C)) -> (not (not C)))), M:tm-69, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2312
in-theory        2312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> (not (not D))))
theorem-size     21
proof            (modus-ponens tm-54 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-10)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2312.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> (not (not D)))), M:tm-54, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2313
in-theory        2313
times-derived    1
----------------------------------------------------------------
theorem          (((A and (not (not B))) or (not (not B))) -> (not (not B)))
theorem-size     13
proof            (modus-ponens tm-47 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-10)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2313.         (((A and (not (not B))) or (not (not B))) -> (not (not B))), M:tm-47, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-2314
in-theory        2314
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) and B) or (not (not A))) -> (not (not A)))
theorem-size     13
proof            (modus-ponens tm-46 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-10)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2314.         ((((not (not A)) and B) or (not (not A))) -> (not (not A))), M:tm-46, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-2315
in-theory        2315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((not (not C)) -> (not (not C))))
theorem-size     13
proof            (modus-ponens tm-42 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-10)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2315.         ((A -> (B or A)) and ((not (not C)) -> (not (not C)))), M:tm-42, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2316
in-theory        2316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((not (not C)) -> (not (not C))))
theorem-size     13
proof            (modus-ponens tm-32 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-10)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2316.         ((A -> (A or B)) and ((not (not C)) -> (not (not C)))), M:tm-32, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2317
in-theory        2317
times-derived    1
----------------------------------------------------------------
theorem          ((not (not A)) -> ((not (not A)) and (not (not A))))
theorem-size     11
proof            (modus-ponens tm-24 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2317.         ((not (not A)) -> ((not (not A)) and (not (not A)))), M:tm-24, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-2318
in-theory        2318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((not (not C)) -> (not (not C))))
theorem-size     15
proof            (modus-ponens tm-23 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2318.         ((A -> (B -> (A and B))) and ((not (not C)) -> (not (not C)))), M:tm-23, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2319
in-theory        2319
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((not (not C)) -> (not (not C))))
theorem-size     13
proof            (modus-ponens tm-22 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-10)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2319.         (((A and B) -> B) and ((not (not C)) -> (not (not C)))), M:tm-22, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2320
in-theory        2320
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((not (not C)) -> (not (not C))))
theorem-size     13
proof            (modus-ponens tm-21 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-10)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2320.         (((A and B) -> A) and ((not (not C)) -> (not (not C)))), M:tm-21, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2321
in-theory        2321
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> (not (not D))))
theorem-size     21
proof            (modus-ponens tm-20 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2321.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> (not (not D)))), M:tm-20, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2322
in-theory        2322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((not (not C)) -> (not (not C))))
theorem-size     13
proof            (modus-ponens tm-19 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2322.         ((A -> (B -> A)) and ((not (not C)) -> (not (not C)))), M:tm-19, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2323
in-theory        2323
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not (not A)))) -> (not (not (not A))))
theorem-size     13
proof            (modus-ponens tm-9 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-9 tm-2 tm-1 tm-10)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2323.         (((not (not A)) -> (not (not (not A)))) -> (not (not (not A)))), M:tm-9, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-2324
in-theory        2324
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> B) -> (((not (not A)) or (not (not A))) -> B))
theorem-size     15
proof            (modus-ponens tm-8 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-8 tm-2 tm-1 tm-10)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2324.         (((not (not A)) -> B) -> (((not (not A)) or (not (not A))) -> B)), M:tm-8, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-2325
in-theory        2325
times-derived    1
----------------------------------------------------------------
theorem          (A or ((not (not B)) -> (not (not B))))
theorem-size     9
proof            (modus-ponens tm-7 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-7 tm-2 tm-1 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2325.         (A or ((not (not B)) -> (not (not B)))), M:tm-7, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2326
in-theory        2326
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) or B)
theorem-size     9
proof            (modus-ponens tm-6 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-6 tm-2 tm-1 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2326.         (((not (not A)) -> (not (not A))) or B), M:tm-6, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2327
in-theory        2327
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((not (not B)) -> (not (not B))) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2327.         (A -> (((not (not B)) -> (not (not B))) and A)), M:tm-5, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2328
in-theory        2328
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((not (not B)) -> (not (not B))))
theorem-size     9
proof            (modus-ponens tm-1 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-1 tm-2 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2328.         (A -> ((not (not B)) -> (not (not B)))), M:tm-1, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2329
in-theory        2329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> A))) -> (C -> (not (A -> B))))
theorem-size     15
proof            (modus-ponens tm-84 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2329.         (((A -> B) -> (not (A -> A))) -> (C -> (not (A -> B)))), M:tm-84, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-2330
in-theory        2330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-83 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2330.         ((A -> (B -> (C -> B))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-83, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2331
in-theory        2331
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (A -> A))))
theorem-size     11
proof            (modus-ponens tm-79 tm-91 ((A (-> (-> Am (-> C Am)) (not (-> Am Am)))) (B Am) (Bm (-> C Am))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2331.         (not ((A -> (B -> A)) -> (not (A -> A)))), M:tm-79, m:tm-91, u:((A (-> (-> Am (-> C Am)) (not (-> Am Am)))) (B Am) (Bm (-> C Am)))
================================================================
tm-name          tm-2332
in-theory        2332
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> (not (B -> B))) -> (not (B -> C))))
theorem-size     19
proof            (modus-ponens tm-76 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-10 tm-9 tm-2 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2332.         (((not (not A)) -> A) and (((B -> C) -> (not (B -> B))) -> (not (B -> C)))), M:tm-76, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2333
in-theory        2333
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> (not (A -> A))))) or ((A -> B) -> (not (A -> A)))) -> (not (A -> B)))
theorem-size     24
proof            (modus-ponens tm-73 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-10 tm-9 tm-2 tm-1)
proof-size       102
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2333.         (((not (not ((A -> B) -> (not (A -> A))))) or ((A -> B) -> (not (A -> A)))) -> (not (A -> B))), M:tm-73, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-2334
in-theory        2334
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (not (C -> C))) -> (not (C -> D))))
theorem-size     25
proof            (modus-ponens tm-69 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2334.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (not (C -> C))) -> (not (C -> D)))), M:tm-69, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2335
in-theory        2335
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-54 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-2 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2335.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-54, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2336
in-theory        2336
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> (not (B -> B)))) or ((B -> C) -> (not (B -> B)))) -> (not (B -> C)))
theorem-size     24
proof            (modus-ponens tm-47 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-4 tm-9 tm-2 tm-1)
proof-size       102
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2336.         (((A and ((B -> C) -> (not (B -> B)))) or ((B -> C) -> (not (B -> B)))) -> (not (B -> C))), M:tm-47, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-2337
in-theory        2337
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (not (A -> A))) and C) or ((A -> B) -> (not (A -> A)))) -> (not (A -> B)))
theorem-size     24
proof            (modus-ponens tm-46 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-3 tm-9 tm-2 tm-1)
proof-size       102
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2337.         (((((A -> B) -> (not (A -> A))) and C) or ((A -> B) -> (not (A -> A)))) -> (not (A -> B))), M:tm-46, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-2338
in-theory        2338
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> A)) or ((A -> B) -> (not (A -> A)))) -> (not (A -> B)))
theorem-size     18
proof            (modus-ponens tm-44 tm-91 ((A (-> Am Bm)) (B (not (-> Am Am))) (C (not (-> Am Bm)))))
axioms-used      (tm-8 tm-1 tm-9 tm-2)
proof-size       98
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2338.         (((not (A -> A)) or ((A -> B) -> (not (A -> A)))) -> (not (A -> B))), M:tm-44, m:tm-91, u:((A (-> Am Bm)) (B (not (-> Am Am))) (C (not (-> Am Bm))))
================================================================
tm-name          tm-2339
in-theory        2339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> (not (C -> C))) -> (not (C -> D))))
theorem-size     19
proof            (modus-ponens tm-42 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2339.         ((A -> (B or A)) and (((C -> D) -> (not (C -> C))) -> (not (C -> D)))), M:tm-42, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2340
in-theory        2340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> (not (C -> C))) -> (not (C -> D))))
theorem-size     19
proof            (modus-ponens tm-32 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2340.         ((A -> (A or B)) and (((C -> D) -> (not (C -> C))) -> (not (C -> D)))), M:tm-32, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2341
in-theory        2341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> A))) -> (((A -> B) -> (not (A -> A))) and (not (A -> B))))
theorem-size     22
proof            (modus-ponens tm-24 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2341.         (((A -> B) -> (not (A -> A))) -> (((A -> B) -> (not (A -> A))) and (not (A -> B)))), M:tm-24, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-2342
in-theory        2342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> (not (C -> C))) -> (not (C -> D))))
theorem-size     21
proof            (modus-ponens tm-23 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2342.         ((A -> (B -> (A and B))) and (((C -> D) -> (not (C -> C))) -> (not (C -> D)))), M:tm-23, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2343
in-theory        2343
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> (not (C -> C))) -> (not (C -> D))))
theorem-size     19
proof            (modus-ponens tm-22 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-2 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2343.         (((A and B) -> B) and (((C -> D) -> (not (C -> C))) -> (not (C -> D)))), M:tm-22, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2344
in-theory        2344
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> (not (C -> C))) -> (not (C -> D))))
theorem-size     19
proof            (modus-ponens tm-21 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-2 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2344.         (((A and B) -> A) and (((C -> D) -> (not (C -> C))) -> (not (C -> D)))), M:tm-21, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2345
in-theory        2345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-20 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2345.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-20, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2346
in-theory        2346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> (not (C -> C))) -> (not (C -> D))))
theorem-size     19
proof            (modus-ponens tm-19 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2346.         ((A -> (B -> A)) and (((C -> D) -> (not (C -> C))) -> (not (C -> D)))), M:tm-19, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2347
in-theory        2347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> A))) -> ((A -> B) -> (not (A -> A))))
theorem-size     17
proof            (modus-ponens tm-12 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2347.         (((A -> B) -> (not (A -> A))) -> ((A -> B) -> (not (A -> A)))), M:tm-12, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-2348
in-theory        2348
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (A -> A)))))
theorem-size     24
proof            (modus-ponens tm-9 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-9 tm-2 tm-1)
proof-size       84
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2348.         ((((A -> B) -> (not (A -> A))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (A -> A))))), M:tm-9, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-2349
in-theory        2349
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> B)) -> C) -> ((((A -> B) -> (not (A -> A))) or (not (A -> B))) -> C))
theorem-size     22
proof            (modus-ponens tm-8 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-9 tm-2 tm-1)
proof-size       84
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2349.         (((not (A -> B)) -> C) -> ((((A -> B) -> (not (A -> A))) or (not (A -> B))) -> C)), M:tm-8, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-2350
in-theory        2350
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> (not (B -> B))) -> (not (B -> C))))
theorem-size     15
proof            (modus-ponens tm-7 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-7 tm-9 tm-2 tm-1)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2350.         (A or (((B -> C) -> (not (B -> B))) -> (not (B -> C)))), M:tm-7, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2351
in-theory        2351
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) or C)
theorem-size     15
proof            (modus-ponens tm-6 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-6 tm-9 tm-2 tm-1)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2351.         ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) or C), M:tm-6, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2352
in-theory        2352
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (not (B -> B))) -> (not (B -> C))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2352.         (A -> ((((B -> C) -> (not (B -> B))) -> (not (B -> C))) and A)), M:tm-5, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2353
in-theory        2353
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (not (B -> B))) -> (not (B -> C))))
theorem-size     15
proof            (modus-ponens tm-1 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-1 tm-9 tm-2)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2353.         (A -> (((B -> C) -> (not (B -> B))) -> (not (B -> C)))), M:tm-1, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2354
in-theory        2354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> (A -> A)))
theorem-size     13
proof            (modus-ponens tm-92 tm-1 ((Am (-> A A)) (B (-> Bm (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2354.         (((A -> B) or (A -> A)) -> (C -> (A -> A))), M:tm-92, m:tm-1, u:((Am (-> A A)) (B (-> Bm (-> A A))))
================================================================
tm-name          tm-2355
in-theory        2355
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((A -> B) -> (A -> B))) -> (((A -> B) -> A) -> ((A -> B) -> B)))
theorem-size     25
proof            (modus-ponens tm-92 tm-2 ((Am (-> Bm Cm)) (A (-> Bm Cm)) (B (-> (-> (-> Bm Cm) Bm) (-> (-> Bm Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2355.         ((((A -> B) -> C) or ((A -> B) -> (A -> B))) -> (((A -> B) -> A) -> ((A -> B) -> B))), M:tm-92, m:tm-2, u:((Am (-> Bm Cm)) (A (-> Bm Cm)) (B (-> (-> (-> Bm Cm) Bm) (-> (-> Bm Cm) Cm))))
================================================================
tm-name          tm-2356
in-theory        2356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> ((A -> A) and C)))
theorem-size     15
proof            (modus-ponens tm-92 tm-5 ((Am (-> A A)) (B (-> Bm (and (-> A A) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2356.         (((A -> B) or (A -> A)) -> (C -> ((A -> A) and C))), M:tm-92, m:tm-5, u:((Am (-> A A)) (B (-> Bm (and (-> A A) Bm))))
================================================================
tm-name          tm-2357
in-theory        2357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) or C))
theorem-size     13
proof            (modus-ponens tm-92 tm-6 ((Am (-> A A)) (B (or (-> A A) Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-2357.         (((A -> B) or (A -> A)) -> ((A -> A) or C)), M:tm-92, m:tm-6, u:((Am (-> A A)) (B (or (-> A A) Bm)))
================================================================
tm-name          tm-2358
in-theory        2358
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C or (A -> A)))
theorem-size     13
proof            (modus-ponens tm-92 tm-7 ((Am (-> A A)) (B (or Bm (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-2358.         (((A -> B) or (A -> A)) -> (C or (A -> A))), M:tm-92, m:tm-7, u:((Am (-> A A)) (B (or Bm (-> A A))))
================================================================
tm-name          tm-2359
in-theory        2359
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> C) -> ((A or A) -> C)))
theorem-size     17
proof            (modus-ponens tm-92 tm-8 ((Bm Am) (A Am) (B (-> (-> Am Cm) (-> (or Am Am) Cm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2359.         (((A -> B) or (A -> A)) -> ((A -> C) -> ((A or A) -> C))), M:tm-92, m:tm-8, u:((Bm Am) (A Am) (B (-> (-> Am Cm) (-> (or Am Am) Cm))))
================================================================
tm-name          tm-2360
in-theory        2360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> (not A)) -> (not A)))
theorem-size     15
proof            (modus-ponens tm-92 tm-9 ((Bm Am) (A Am) (B (-> (-> Am (not Am)) (not Am)))))
axioms-used      (tm-8 tm-2 tm-1 tm-9)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2360.         (((A -> B) or (A -> A)) -> ((A -> (not A)) -> (not A))), M:tm-92, m:tm-9, u:((Bm Am) (A Am) (B (-> (-> Am (not Am)) (not Am))))
================================================================
tm-name          tm-2361
in-theory        2361
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-92 tm-11 ((Am (-> A A)) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2361.         (((A -> B) or (A -> A)) -> (C -> (D -> C))), M:tm-92, m:tm-11, u:((Am (-> A A)) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-2362
in-theory        2362
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (A -> A))
theorem-size     11
proof            (modus-ponens tm-92 tm-12 ((Bm Am) (A Am) (B (-> Am Am))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2362.         (((A -> B) or (A -> A)) -> (A -> A)), M:tm-92, m:tm-12, u:((Bm Am) (A Am) (B (-> Am Am)))
================================================================
tm-name          tm-2363
in-theory        2363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-92 tm-14 ((Am (-> A A)) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2363.         (((A -> B) or (A -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-92, m:tm-14, u:((Am (-> A A)) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-2364
in-theory        2364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-92 tm-16 ((Am (-> A A)) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2364.         (((A -> B) or (A -> A)) -> ((C and D) -> C)), M:tm-92, m:tm-16, u:((Am (-> A A)) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-2365
in-theory        2365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-92 tm-18 ((Am (-> A A)) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2365.         (((A -> B) or (A -> A)) -> ((C and D) -> D)), M:tm-92, m:tm-18, u:((Am (-> A A)) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-2366
in-theory        2366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (D -> C)) and (A -> A)))
theorem-size     17
proof            (modus-ponens tm-92 tm-19 ((Am (-> A A)) (B (and (-> Bm (-> Cm Bm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2366.         (((A -> B) or (A -> A)) -> ((C -> (D -> C)) and (A -> A))), M:tm-92, m:tm-19, u:((Am (-> A A)) (B (and (-> Bm (-> Cm Bm)) (-> A A))))
================================================================
tm-name          tm-2367
in-theory        2367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> A)))
theorem-size     25
proof            (modus-ponens tm-92 tm-20 ((Am (-> A A)) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2367.         (((A -> B) or (A -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> A))), M:tm-92, m:tm-20, u:((Am (-> A A)) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A A))))
================================================================
tm-name          tm-2368
in-theory        2368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C and D) -> C) and (A -> A)))
theorem-size     17
proof            (modus-ponens tm-92 tm-21 ((Am (-> A A)) (B (and (-> (and Bm Cm) Bm) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2368.         (((A -> B) or (A -> A)) -> (((C and D) -> C) and (A -> A))), M:tm-92, m:tm-21, u:((Am (-> A A)) (B (and (-> (and Bm Cm) Bm) (-> A A))))
================================================================
tm-name          tm-2369
in-theory        2369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C and D) -> D) and (A -> A)))
theorem-size     17
proof            (modus-ponens tm-92 tm-22 ((Am (-> A A)) (B (and (-> (and Bm Cm) Cm) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2369.         (((A -> B) or (A -> A)) -> (((C and D) -> D) and (A -> A))), M:tm-92, m:tm-22, u:((Am (-> A A)) (B (and (-> (and Bm Cm) Cm) (-> A A))))
================================================================
tm-name          tm-2370
in-theory        2370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (D -> (C and D))) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-23 ((Am (-> A A)) (B (and (-> Bm (-> Cm (and Bm Cm))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2370.         (((A -> B) or (A -> A)) -> ((C -> (D -> (C and D))) and (A -> A))), M:tm-92, m:tm-23, u:((Am (-> A A)) (B (and (-> Bm (-> Cm (and Bm Cm))) (-> A A))))
================================================================
tm-name          tm-2371
in-theory        2371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (A -> (A and A)))
theorem-size     13
proof            (modus-ponens tm-92 tm-24 ((Bm Am) (A Am) (B (-> Am (and Am Am)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-2371.         (((A -> B) or (A -> A)) -> (A -> (A and A))), M:tm-92, m:tm-24, u:((Bm Am) (A Am) (B (-> Am (and Am Am))))
================================================================
tm-name          tm-2372
in-theory        2372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-92 tm-25 ((Am (-> A A)) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2372.         (((A -> B) or (A -> A)) -> (C -> (D -> (C and D)))), M:tm-92, m:tm-25, u:((Am (-> A A)) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-2373
in-theory        2373
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (C or D)) and (A -> A)))
theorem-size     17
proof            (modus-ponens tm-92 tm-32 ((Am (-> A A)) (B (and (-> Bm (or Bm Cm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2373.         (((A -> B) or (A -> A)) -> ((C -> (C or D)) and (A -> A))), M:tm-92, m:tm-32, u:((Am (-> A A)) (B (and (-> Bm (or Bm Cm)) (-> A A))))
================================================================
tm-name          tm-2374
in-theory        2374
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-92 tm-33 ((Am (-> A A)) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2374.         (((A -> B) or (A -> A)) -> (C -> (C or D))), M:tm-92, m:tm-33, u:((Am (-> A A)) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-2375
in-theory        2375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (D or C)) and (A -> A)))
theorem-size     17
proof            (modus-ponens tm-92 tm-42 ((Am (-> A A)) (B (and (-> Bm (or Cm Bm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2375.         (((A -> B) or (A -> A)) -> ((C -> (D or C)) and (A -> A))), M:tm-92, m:tm-42, u:((Am (-> A A)) (B (and (-> Bm (or Cm Bm)) (-> A A))))
================================================================
tm-name          tm-2376
in-theory        2376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-92 tm-43 ((Am (-> A A)) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2376.         (((A -> B) or (A -> A)) -> (C -> (D or C))), M:tm-92, m:tm-43, u:((Am (-> A A)) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-2377
in-theory        2377
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((A -> B) -> (A -> B))) -> ((B or (A -> B)) -> (A -> B)))
theorem-size     23
proof            (modus-ponens tm-92 tm-44 ((Cm (-> Am Bm)) (A (-> Am Bm)) (B (-> (or Bm (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2377.         ((((A -> B) -> C) or ((A -> B) -> (A -> B))) -> ((B or (A -> B)) -> (A -> B))), M:tm-92, m:tm-44, u:((Cm (-> Am Bm)) (A (-> Am Bm)) (B (-> (or Bm (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2378
in-theory        2378
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> C))))
theorem-size     47
proof            (modus-ponens tm-92 tm-45 ((Dm (-> (-> Am Bm) (-> Am Cm))) (A (-> (-> Am Bm) (-> Am Cm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2378.         (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> C)))), M:tm-92, m:tm-45, u:((Dm (-> (-> Am Bm) (-> Am Cm))) (A (-> (-> Am Bm) (-> Am Cm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-2379
in-theory        2379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((A and C) or A) -> A))
theorem-size     15
proof            (modus-ponens tm-92 tm-46 ((Bm Am) (A Am) (B (-> (or (and Am Cm) Am) Am))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2379.         (((A -> B) or (A -> A)) -> (((A and C) or A) -> A)), M:tm-92, m:tm-46, u:((Bm Am) (A Am) (B (-> (or (and Am Cm) Am) Am)))
================================================================
tm-name          tm-2380
in-theory        2380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C and A) or A) -> A))
theorem-size     15
proof            (modus-ponens tm-92 tm-47 ((Bm Am) (A Am) (B (-> (or (and Cm Am) Am) Am))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2380.         (((A -> B) or (A -> A)) -> (((C and A) or A) -> A)), M:tm-92, m:tm-47, u:((Bm Am) (A Am) (B (-> (or (and Cm Am) Am) Am)))
================================================================
tm-name          tm-2381
in-theory        2381
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> (A -> (B and A)))) -> ((B or (A -> (B and A))) -> (A -> (B and A))))
theorem-size     33
proof            (modus-ponens tm-92 tm-48 ((Cm (-> Am (and Bm Am))) (A (-> Am (and Bm Am))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am (and Bm Am))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2381.         ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> (A -> (B and A)))) -> ((B or (A -> (B and A))) -> (A -> (B and A)))), M:tm-92, m:tm-48, u:((Cm (-> Am (and Bm Am))) (A (-> Am (and Bm Am))) (B (-> (or Bm (-> Am (and Bm Am))) (-> Am (and Bm Am)))))
================================================================
tm-name          tm-2382
in-theory        2382
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or B) -> (A or B))) -> ((A or (A or B)) -> (A or B)))
theorem-size     23
proof            (modus-ponens tm-92 tm-49 ((Cm (or Am Bm)) (A (or Am Bm)) (B (-> (or Am (or Am Bm)) (or Am Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2382.         ((((A or B) -> C) or ((A or B) -> (A or B))) -> ((A or (A or B)) -> (A or B))), M:tm-92, m:tm-49, u:((Cm (or Am Bm)) (A (or Am Bm)) (B (-> (or Am (or Am Bm)) (or Am Bm))))
================================================================
tm-name          tm-2383
in-theory        2383
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or B) -> (A or B))) -> ((B or (A or B)) -> (A or B)))
theorem-size     23
proof            (modus-ponens tm-92 tm-50 ((Cm (or Am Bm)) (A (or Am Bm)) (B (-> (or Bm (or Am Bm)) (or Am Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2383.         ((((A or B) -> C) or ((A or B) -> (A or B))) -> ((B or (A or B)) -> (A or B))), M:tm-92, m:tm-50, u:((Cm (or Am Bm)) (A (or Am Bm)) (B (-> (or Bm (or Am Bm)) (or Am Bm))))
================================================================
tm-name          tm-2384
in-theory        2384
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B)))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> ((C or A) -> B))))
theorem-size     55
proof            (modus-ponens tm-92 tm-51 ((Dm (-> (-> Am Bm) (-> (or Cm Am) Bm))) (A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2384.         (((((A -> B) -> ((C or A) -> B)) -> D) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> ((C or A) -> B)))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> ((C or A) -> B)))), M:tm-92, m:tm-51, u:((Dm (-> (-> Am Bm) (-> (or Cm Am) Bm))) (A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) (-> (or Cm Am) Bm)))))
================================================================
tm-name          tm-2385
in-theory        2385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> A)))
theorem-size     25
proof            (modus-ponens tm-92 tm-54 ((Am (-> A A)) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2385.         (((A -> B) or (A -> A)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> A))), M:tm-92, m:tm-54, u:((Am (-> A A)) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A A))))
================================================================
tm-name          tm-2386
in-theory        2386
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) or ((A -> A) -> (A -> A))) -> ((A -> A) -> ((A or A) -> A)))
theorem-size     23
proof            (modus-ponens tm-92 tm-55 ((Bm Am) (Cm Am) (A (-> Am Am)) (B (-> (-> Am Am) (-> (or Am Am) Am)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-2386.         ((((A -> A) -> B) or ((A -> A) -> (A -> A))) -> ((A -> A) -> ((A or A) -> A))), M:tm-92, m:tm-55, u:((Bm Am) (Cm Am) (A (-> Am Am)) (B (-> (-> Am Am) (-> (or Am Am) Am))))
================================================================
tm-name          tm-2387
in-theory        2387
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-92 tm-56 ((Am (-> A A)) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2387.         (((A -> B) or (A -> A)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-92, m:tm-56, u:((Am (-> A A)) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-2388
in-theory        2388
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) or (((A -> (not B)) -> (not A)) -> ((A -> (not B)) -> (not A)))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> (not A))))
theorem-size     45
proof            (modus-ponens tm-92 tm-66 ((Cm (-> (-> Am (not Bm)) (not Am))) (A (-> (-> Am (not Bm)) (not Am))) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-8 tm-2 tm-1 tm-9)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2388.         (((((A -> (not B)) -> (not A)) -> C) or (((A -> (not B)) -> (not A)) -> ((A -> (not B)) -> (not A)))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> (not A)))), M:tm-92, m:tm-66, u:((Cm (-> (-> Am (not Bm)) (not Am))) (A (-> (-> Am (not Bm)) (not Am))) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-2389
in-theory        2389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> A)))
theorem-size     23
proof            (modus-ponens tm-92 tm-69 ((Am (-> A A)) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-9)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2389.         (((A -> B) or (A -> A)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> A))), M:tm-92, m:tm-69, u:((Am (-> A A)) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A A))))
================================================================
tm-name          tm-2390
in-theory        2390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     19
proof            (modus-ponens tm-92 tm-71 ((Am (-> A A)) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2390.         (((A -> B) or (A -> A)) -> ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-92, m:tm-71, u:((Am (-> A A)) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-2391
in-theory        2391
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((not (not A)) or A) -> A))
theorem-size     15
proof            (modus-ponens tm-92 tm-73 ((Bm Am) (A Am) (B (-> (or (not (not Am)) Am) Am))))
axioms-used      (tm-8 tm-2 tm-1 tm-10)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2391.         (((A -> B) or (A -> A)) -> (((not (not A)) or A) -> A)), M:tm-92, m:tm-73, u:((Bm Am) (A Am) (B (-> (or (not (not Am)) Am) Am)))
================================================================
tm-name          tm-2392
in-theory        2392
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((not (not C)) -> C) and (A -> A)))
theorem-size     17
proof            (modus-ponens tm-92 tm-76 ((Am (-> A A)) (B (and (-> (not (not Bm)) Bm) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2392.         (((A -> B) or (A -> A)) -> (((not (not C)) -> C) and (A -> A))), M:tm-92, m:tm-76, u:((Am (-> A A)) (B (and (-> (not (not Bm)) Bm) (-> A A))))
================================================================
tm-name          tm-2393
in-theory        2393
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((not (not C)) -> C))
theorem-size     13
proof            (modus-ponens tm-92 tm-78 ((Am (-> A A)) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2393.         (((A -> B) or (A -> A)) -> ((not (not C)) -> C)), M:tm-92, m:tm-78, u:((Am (-> A A)) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-2394
in-theory        2394
times-derived    1
----------------------------------------------------------------
theorem          ((((not (A -> (B -> A))) -> C) or ((not (A -> (B -> A))) -> (not (A -> (B -> A))))) -> (not (not (A -> (B -> A)))))
theorem-size     30
proof            (modus-ponens tm-92 tm-79 ((Am (not (-> Bm (-> Cm Bm)))) (A (not (-> Bm (-> Cm Bm)))) (B (not (not (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-9)
proof-size       122
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2394.         ((((not (A -> (B -> A))) -> C) or ((not (A -> (B -> A))) -> (not (A -> (B -> A))))) -> (not (not (A -> (B -> A))))), M:tm-92, m:tm-79, u:((Am (not (-> Bm (-> Cm Bm)))) (A (not (-> Bm (-> Cm Bm)))) (B (not (not (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-2395
in-theory        2395
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) or ((A -> (B -> A)) -> (A -> (B -> A)))) -> ((D or (A -> (B -> A))) -> (A -> (B -> A))))
theorem-size     33
proof            (modus-ponens tm-92 tm-80 ((Cm (-> Am (-> Bm Am))) (A (-> Am (-> Bm Am))) (B (-> (or Dm (-> Am (-> Bm Am))) (-> Am (-> Bm Am))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2395.         ((((A -> (B -> A)) -> C) or ((A -> (B -> A)) -> (A -> (B -> A)))) -> ((D or (A -> (B -> A))) -> (A -> (B -> A)))), M:tm-92, m:tm-80, u:((Cm (-> Am (-> Bm Am))) (A (-> Am (-> Bm Am))) (B (-> (or Dm (-> Am (-> Bm Am))) (-> Am (-> Bm Am)))))
================================================================
tm-name          tm-2396
in-theory        2396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (D -> (E -> D))) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-83 ((Am (-> A A)) (B (and (-> Bm (-> Cm (-> Dm Cm))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2396.         (((A -> B) or (A -> A)) -> ((C -> (D -> (E -> D))) and (A -> A))), M:tm-92, m:tm-83, u:((Am (-> A A)) (B (and (-> Bm (-> Cm (-> Dm Cm))) (-> A A))))
================================================================
tm-name          tm-2397
in-theory        2397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (A -> (C -> A)))
theorem-size     13
proof            (modus-ponens tm-92 tm-84 ((Bm Am) (A Am) (B (-> Am (-> Cm Am)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2397.         (((A -> B) or (A -> A)) -> (A -> (C -> A))), M:tm-92, m:tm-84, u:((Bm Am) (A Am) (B (-> Am (-> Cm Am))))
================================================================
tm-name          tm-2398
in-theory        2398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> (D -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-92 tm-85 ((Am (-> A A)) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2398.         (((A -> B) or (A -> A)) -> (C -> (D -> (E -> D)))), M:tm-92, m:tm-85, u:((Am (-> A A)) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2399
in-theory        2399
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((A -> B) -> (A -> B))) -> ((A -> B) -> (A -> B)))
theorem-size     21
proof            (modus-ponens tm-92 tm-87 ((Am (-> Bm Cm)) (A (-> Bm Cm)) (B (-> (-> Bm Cm) (-> Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2399.         ((((A -> B) -> C) or ((A -> B) -> (A -> B))) -> ((A -> B) -> (A -> B))), M:tm-92, m:tm-87, u:((Am (-> Bm Cm)) (A (-> Bm Cm)) (B (-> (-> Bm Cm) (-> Bm Cm))))
================================================================
tm-name          tm-2400
in-theory        2400
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) or ((A -> A) -> (A -> A))) -> (((A -> C) or (A -> A)) -> (A -> A)))
theorem-size     25
proof            (modus-ponens tm-92 tm-92 ((Bm (-> Am Am)) (A (-> Am Am)) (B (-> (or (-> Am Cm) (-> Am Am)) (-> Am Am)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2400.         ((((A -> A) -> B) or ((A -> A) -> (A -> A))) -> (((A -> C) or (A -> A)) -> (A -> A))), M:tm-92, m:tm-92, u:((Bm (-> Am Am)) (A (-> Am Am)) (B (-> (or (-> Am Cm) (-> Am Am)) (-> Am Am))))
================================================================
tm-name          tm-2401
in-theory        2401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> B) -> (C -> (((A -> D) or (A -> A)) -> B)))
theorem-size     17
proof            (modus-ponens tm-84 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2401.         (((A -> A) -> B) -> (C -> (((A -> D) or (A -> A)) -> B))), M:tm-84, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-2402
in-theory        2402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-83 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2402.         ((A -> (B -> (C -> B))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-83, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2403
in-theory        2403
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> B) -> (C -> (B -> B)))) -> (((B -> D) or (B -> B)) -> (C -> (B -> B))))
theorem-size     25
proof            (modus-ponens tm-80 tm-92 ((A (-> Am Am)) (Bm (-> B (-> Am Am))) (C (-> (or (-> Am Cm) (-> Am Am)) (-> B (-> Am Am))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2403.         ((A or ((B -> B) -> (C -> (B -> B)))) -> (((B -> D) or (B -> B)) -> (C -> (B -> B)))), M:tm-80, m:tm-92, u:((A (-> Am Am)) (Bm (-> B (-> Am Am))) (C (-> (or (-> Am Cm) (-> Am Am)) (-> B (-> Am Am)))))
================================================================
tm-name          tm-2404
in-theory        2404
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> B) -> C) -> (((B -> D) or (B -> B)) -> C)))
theorem-size     21
proof            (modus-ponens tm-76 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2404.         (((not (not A)) -> A) and (((B -> B) -> C) -> (((B -> D) or (B -> B)) -> C))), M:tm-76, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2405
in-theory        2405
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> A) -> B))) or ((A -> A) -> B)) -> (((A -> C) or (A -> A)) -> B))
theorem-size     23
proof            (modus-ponens tm-73 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2405.         (((not (not ((A -> A) -> B))) or ((A -> A) -> B)) -> (((A -> C) or (A -> A)) -> B)), M:tm-73, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-2406
in-theory        2406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-69 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2406.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D))), M:tm-69, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2407
in-theory        2407
times-derived    1
----------------------------------------------------------------
theorem          ((((not A) -> A) or (((not A) -> (not A)) -> (not (not A)))) -> ((((not A) -> B) or ((not A) -> (not A))) -> (not (not A))))
theorem-size     29
proof            (modus-ponens tm-66 tm-92 ((A (not B)) (Am (not B)) (Bm (not (not B))) (C (-> (or (-> (not B) Cm) (-> (not B) (not B))) (not (not B))))))
axioms-used      (tm-8 tm-9 tm-2 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2407.         ((((not A) -> A) or (((not A) -> (not A)) -> (not (not A)))) -> ((((not A) -> B) or ((not A) -> (not A))) -> (not (not A)))), M:tm-66, m:tm-92, u:((A (not B)) (Am (not B)) (Bm (not (not B))) (C (-> (or (-> (not B) Cm) (-> (not B) (not B))) (not (not B)))))
================================================================
tm-name          tm-2408
in-theory        2408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> ((A -> B) or (A -> A))) -> (((A -> A) or ((A -> B) or (A -> A))) -> ((A -> B) or (A -> A))))
theorem-size     31
proof            (modus-ponens tm-55 tm-92 ((A (-> Am Am)) (Bm (or (-> Am Cm) (-> Am Am))) (B (or (-> Am Cm) (-> Am Am))) (C (or (-> Am Cm) (-> Am Am)))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2408.         (((A -> A) -> ((A -> B) or (A -> A))) -> (((A -> A) or ((A -> B) or (A -> A))) -> ((A -> B) or (A -> A)))), M:tm-55, m:tm-92, u:((A (-> Am Am)) (Bm (or (-> Am Cm) (-> Am Am))) (B (or (-> Am Cm) (-> Am Am))) (C (or (-> Am Cm) (-> Am Am))))
================================================================
tm-name          tm-2409
in-theory        2409
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-54 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2409.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-54, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2410
in-theory        2410
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> B) -> ((A or B) -> B))) -> (((B -> C) or (B -> B)) -> ((A or B) -> B)))
theorem-size     27
proof            (modus-ponens tm-51 tm-92 ((A Am) (B Am) (Bm (-> (or C Am) Am)) (D (-> (or (-> Am Cm) (-> Am Am)) (-> (or C Am) Am)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2410.         (((A -> B) or ((B -> B) -> ((A or B) -> B))) -> (((B -> C) or (B -> B)) -> ((A or B) -> B))), M:tm-51, m:tm-92, u:((A Am) (B Am) (Bm (-> (or C Am) Am)) (D (-> (or (-> Am Cm) (-> Am Am)) (-> (or C Am) Am))))
================================================================
tm-name          tm-2411
in-theory        2411
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> B) -> (A and (B -> B)))) -> (((B -> C) or (B -> B)) -> (A and (B -> B))))
theorem-size     25
proof            (modus-ponens tm-48 tm-92 ((A (-> Am Am)) (Bm (and B (-> Am Am))) (C (-> (or (-> Am Cm) (-> Am Am)) (and B (-> Am Am))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2411.         ((A or ((B -> B) -> (A and (B -> B)))) -> (((B -> C) or (B -> B)) -> (A and (B -> B)))), M:tm-48, m:tm-92, u:((A (-> Am Am)) (Bm (and B (-> Am Am))) (C (-> (or (-> Am Cm) (-> Am Am)) (and B (-> Am Am)))))
================================================================
tm-name          tm-2412
in-theory        2412
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((B -> B) -> C)) or ((B -> B) -> C)) -> (((B -> D) or (B -> B)) -> C))
theorem-size     23
proof            (modus-ponens tm-47 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2412.         (((A and ((B -> B) -> C)) or ((B -> B) -> C)) -> (((B -> D) or (B -> B)) -> C)), M:tm-47, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-2413
in-theory        2413
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> A) -> B) and C) or ((A -> A) -> B)) -> (((A -> D) or (A -> A)) -> B))
theorem-size     23
proof            (modus-ponens tm-46 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2413.         (((((A -> A) -> B) and C) or ((A -> A) -> B)) -> (((A -> D) or (A -> A)) -> B)), M:tm-46, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-2414
in-theory        2414
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (A -> B)) or ((A -> A) -> (A -> B))) -> (((A -> C) or (A -> A)) -> (A -> B)))
theorem-size     25
proof            (modus-ponens tm-45 tm-92 ((A Am) (B Am) (Bm (-> Am C)) (D (-> (or (-> Am Cm) (-> Am Am)) (-> Am C)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2414.         (((A -> (A -> B)) or ((A -> A) -> (A -> B))) -> (((A -> C) or (A -> A)) -> (A -> B))), M:tm-45, m:tm-92, u:((A Am) (B Am) (Bm (-> Am C)) (D (-> (or (-> Am Cm) (-> Am Am)) (-> Am C))))
================================================================
tm-name          tm-2415
in-theory        2415
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> B) -> A)) -> (((B -> C) or (B -> B)) -> A))
theorem-size     17
proof            (modus-ponens tm-44 tm-92 ((A (-> Am Am)) (B Bm) (C (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2415.         ((A or ((B -> B) -> A)) -> (((B -> C) or (B -> B)) -> A)), M:tm-44, m:tm-92, u:((A (-> Am Am)) (B Bm) (C (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-2416
in-theory        2416
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D)))
theorem-size     21
proof            (modus-ponens tm-42 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2416.         ((A -> (B or A)) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D))), M:tm-42, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2417
in-theory        2417
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D)))
theorem-size     21
proof            (modus-ponens tm-32 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2417.         ((A -> (A or B)) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D))), M:tm-32, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2418
in-theory        2418
times-derived    2
----------------------------------------------------------------
theorem          (((A -> A) -> B) -> (((A -> A) -> B) and (((A -> C) or (A -> A)) -> B)))
theorem-size     21
proof            (modus-ponens tm-24 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2418.         (((A -> A) -> B) -> (((A -> A) -> B) and (((A -> C) or (A -> A)) -> B))), M:tm-24, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-2419
in-theory        2419
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-23 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2419.         ((A -> (B -> (A and B))) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D))), M:tm-23, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2420
in-theory        2420
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D)))
theorem-size     21
proof            (modus-ponens tm-22 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2420.         (((A and B) -> B) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D))), M:tm-22, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2421
in-theory        2421
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D)))
theorem-size     21
proof            (modus-ponens tm-21 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2421.         (((A and B) -> A) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D))), M:tm-21, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2422
in-theory        2422
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-20 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2422.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-20, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2423
in-theory        2423
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D)))
theorem-size     21
proof            (modus-ponens tm-19 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2423.         ((A -> (B -> A)) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D))), M:tm-19, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2424
in-theory        2424
times-derived    2
----------------------------------------------------------------
theorem          (((A -> A) -> B) -> ((A -> A) -> B))
theorem-size     11
proof            (modus-ponens tm-12 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2424.         (((A -> A) -> B) -> ((A -> A) -> B)), M:tm-12, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-2425
in-theory        2425
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (not (((A -> C) or (A -> A)) -> B))) -> (not ((A -> A) -> B)))
theorem-size     23
proof            (modus-ponens tm-9 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-9 tm-8 tm-2 tm-1)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2425.         ((((A -> A) -> B) -> (not (((A -> C) or (A -> A)) -> B))) -> (not ((A -> A) -> B))), M:tm-9, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-2426
in-theory        2426
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) or (A -> A)) -> C) -> D) -> ((((A -> A) -> C) or (((A -> B) or (A -> A)) -> C)) -> D))
theorem-size     29
proof            (modus-ponens tm-8 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2426.         (((((A -> B) or (A -> A)) -> C) -> D) -> ((((A -> A) -> C) or (((A -> B) or (A -> A)) -> C)) -> D)), M:tm-8, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-2427
in-theory        2427
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> B) -> C) -> (((B -> D) or (B -> B)) -> C)))
theorem-size     17
proof            (modus-ponens tm-7 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-7 tm-8 tm-2 tm-1)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2427.         (A or (((B -> B) -> C) -> (((B -> D) or (B -> B)) -> C))), M:tm-7, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2428
in-theory        2428
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-6 tm-8 tm-2 tm-1)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2428.         ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) or D), M:tm-6, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2429
in-theory        2429
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> B) -> C) -> (((B -> D) or (B -> B)) -> C)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2429.         (A -> ((((B -> B) -> C) -> (((B -> D) or (B -> B)) -> C)) and A)), M:tm-5, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2430
in-theory        2430
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> ((A -> C) or (A -> A))) -> (((A -> A) -> B) -> B))
theorem-size     21
proof            (modus-ponens tm-2 tm-92 ((A (-> (-> Am Am) Bm)) (B (or (-> Am Cm) (-> Am Am))) (C Bm)))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2430.         ((((A -> A) -> B) -> ((A -> C) or (A -> A))) -> (((A -> A) -> B) -> B)), M:tm-2, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (or (-> Am Cm) (-> Am Am))) (C Bm))
================================================================
tm-name          tm-2431
in-theory        2431
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> B) -> C) -> (((B -> D) or (B -> B)) -> C)))
theorem-size     17
proof            (modus-ponens tm-1 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2431.         (A -> (((B -> B) -> C) -> (((B -> D) or (B -> B)) -> C))), M:tm-1, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2432
in-theory        2432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-83 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2432.         ((A -> (B -> (C -> B))) and (D or ((E -> F) -> (E -> E)))), M:tm-83, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2433
in-theory        2433
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((C -> D) -> (C -> C))))
theorem-size     15
proof            (modus-ponens tm-76 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2433.         (((not (not A)) -> A) and (B or ((C -> D) -> (C -> C)))), M:tm-76, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2434
in-theory        2434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> E) -> (D -> D))))
theorem-size     21
proof            (modus-ponens tm-69 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2434.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> E) -> (D -> D)))), M:tm-69, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2435
in-theory        2435
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-54 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2435.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> (E -> E)))), M:tm-54, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2436
in-theory        2436
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-42 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2436.         ((A -> (B or A)) and (C or ((D -> E) -> (D -> D)))), M:tm-42, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2437
in-theory        2437
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-32 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2437.         ((A -> (A or B)) and (C or ((D -> E) -> (D -> D)))), M:tm-32, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2438
in-theory        2438
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((D -> E) -> (D -> D))))
theorem-size     17
proof            (modus-ponens tm-23 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2438.         ((A -> (B -> (A and B))) and (C or ((D -> E) -> (D -> D)))), M:tm-23, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2439
in-theory        2439
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-22 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2439.         (((A and B) -> B) and (C or ((D -> E) -> (D -> D)))), M:tm-22, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2440
in-theory        2440
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-21 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2440.         (((A and B) -> A) and (C or ((D -> E) -> (D -> D)))), M:tm-21, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2441
in-theory        2441
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-20 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2441.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> (E -> E)))), M:tm-20, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2442
in-theory        2442
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-19 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2442.         ((A -> (B -> A)) and (C or ((D -> E) -> (D -> D)))), M:tm-19, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2443
in-theory        2443
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or ((C -> D) -> (C -> C))))
theorem-size     11
proof            (modus-ponens tm-7 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-7 tm-2 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2443.         (A or (B or ((C -> D) -> (C -> C)))), M:tm-7, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2444
in-theory        2444
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-6 tm-7 tm-2 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2444.         ((A or ((B -> C) -> (B -> B))) or D), M:tm-6, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2445
in-theory        2445
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> D) -> (C -> C))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2445.         (A -> ((B or ((C -> D) -> (C -> C))) and A)), M:tm-5, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2446
in-theory        2446
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or ((C -> D) -> (C -> C))))
theorem-size     11
proof            (modus-ponens tm-1 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-1 tm-7 tm-2)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2446.         (A -> (B or ((C -> D) -> (C -> C)))), M:tm-1, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2447
in-theory        2447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-83 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2447.         ((A -> (B -> (C -> B))) and (((D -> E) -> (D -> D)) or F)), M:tm-83, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2448
in-theory        2448
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> (B -> B)) or D))
theorem-size     15
proof            (modus-ponens tm-76 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-10 tm-6 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2448.         (((not (not A)) -> A) and (((B -> C) -> (B -> B)) or D)), M:tm-76, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2449
in-theory        2449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (C -> C)) or E))
theorem-size     21
proof            (modus-ponens tm-69 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-9 tm-6 tm-2 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2449.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (C -> C)) or E)), M:tm-69, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2450
in-theory        2450
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (D -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-54 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2450.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (D -> D)) or F)), M:tm-54, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2451
in-theory        2451
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> (C -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-42 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2451.         ((A -> (B or A)) and (((C -> D) -> (C -> C)) or E)), M:tm-42, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2452
in-theory        2452
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> (C -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-32 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2452.         ((A -> (A or B)) and (((C -> D) -> (C -> C)) or E)), M:tm-32, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2453
in-theory        2453
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> (C -> C)) or E))
theorem-size     17
proof            (modus-ponens tm-23 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2453.         ((A -> (B -> (A and B))) and (((C -> D) -> (C -> C)) or E)), M:tm-23, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2454
in-theory        2454
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> (C -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-22 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-4 tm-6 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2454.         (((A and B) -> B) and (((C -> D) -> (C -> C)) or E)), M:tm-22, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2455
in-theory        2455
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> (C -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-21 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-3 tm-6 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2455.         (((A and B) -> A) and (((C -> D) -> (C -> C)) or E)), M:tm-21, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2456
in-theory        2456
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (D -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-20 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2456.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (D -> D)) or F)), M:tm-20, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2457
in-theory        2457
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> (C -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-19 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2457.         ((A -> (B -> A)) and (((C -> D) -> (C -> C)) or E)), M:tm-19, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2458
in-theory        2458
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> C) -> (B -> B)) or D))
theorem-size     11
proof            (modus-ponens tm-7 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-7 tm-6 tm-2 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2458.         (A or (((B -> C) -> (B -> B)) or D)), M:tm-7, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2459
in-theory        2459
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-6 tm-2 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2459.         ((((A -> B) -> (A -> A)) or C) or D), M:tm-6, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2460
in-theory        2460
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (B -> B)) or D) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2460.         (A -> ((((B -> C) -> (B -> B)) or D) and A)), M:tm-5, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2461
in-theory        2461
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> B)) or D))
theorem-size     11
proof            (modus-ponens tm-1 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-1 tm-6 tm-2)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2461.         (A -> (((B -> C) -> (B -> B)) or D)), M:tm-1, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2462
in-theory        2462
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-95 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2462.         (((A -> B) -> (A -> A)) and (C -> (D -> C))), M:tm-95, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-2463
in-theory        2463
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2463.         (((A -> B) -> (A -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-95, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-2464
in-theory        2464
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-95 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-2464.         (((A -> B) -> (A -> A)) and ((C and D) -> C)), M:tm-95, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-2465
in-theory        2465
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-95 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-2465.         (((A -> B) -> (A -> A)) and ((C and D) -> D)), M:tm-95, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-2466
in-theory        2466
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-95 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2466.         (((A -> B) -> (A -> A)) and (C -> (D -> (C and D)))), M:tm-95, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-2467
in-theory        2467
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-95 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-2467.         (((A -> B) -> (A -> A)) and (C -> (C or D))), M:tm-95, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-2468
in-theory        2468
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-95 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-2468.         (((A -> B) -> (A -> A)) and (C -> (D or C))), M:tm-95, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-2469
in-theory        2469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2469.         (((A -> B) -> (A -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-95, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-2470
in-theory        2470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     19
proof            (modus-ponens tm-95 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2470.         (((A -> B) -> (A -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-95, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-2471
in-theory        2471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((not (not C)) -> C))
theorem-size     13
proof            (modus-ponens tm-95 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-2471.         (((A -> B) -> (A -> A)) and ((not (not C)) -> C)), M:tm-95, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-2472
in-theory        2472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-95 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2472.         (((A -> B) -> (A -> A)) and (C -> (D -> (E -> D)))), M:tm-95, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-2473
in-theory        2473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> (C -> C)))
theorem-size     15
proof            (modus-ponens tm-95 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2473.         (((A -> B) -> (A -> A)) and ((C -> D) -> (C -> C))), M:tm-95, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-2474
in-theory        2474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-95 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-2474.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-95, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-2475
in-theory        2475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2475.         (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-95, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-2476
in-theory        2476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-95 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-2476.         (((A -> B) -> (A -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-95, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-2477
in-theory        2477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D and E) -> D)))
theorem-size     15
proof            (modus-ponens tm-95 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2477.         (((A -> B) -> (A -> A)) and (C -> ((D and E) -> D))), M:tm-95, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-2478
in-theory        2478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-95 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-2478.         (((A -> B) -> (A -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-95, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-2479
in-theory        2479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D and E) -> E)))
theorem-size     15
proof            (modus-ponens tm-95 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2479.         (((A -> B) -> (A -> A)) and (C -> ((D and E) -> E))), M:tm-95, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-2480
in-theory        2480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> D)) and C)))
theorem-size     17
proof            (modus-ponens tm-95 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2480.         (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-95, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-2481
in-theory        2481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     25
proof            (modus-ponens tm-95 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2481.         (((A -> B) -> (A -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-95, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-2482
in-theory        2482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D and E) -> D) and C)))
theorem-size     17
proof            (modus-ponens tm-95 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2482.         (((A -> B) -> (A -> A)) and (C -> (((D and E) -> D) and C))), M:tm-95, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-2483
in-theory        2483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D and E) -> E) and C)))
theorem-size     17
proof            (modus-ponens tm-95 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2483.         (((A -> B) -> (A -> A)) and (C -> (((D and E) -> E) and C))), M:tm-95, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-2484
in-theory        2484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2484.         (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-95, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-2485
in-theory        2485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> (C -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-95 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-2485.         (((A -> B) -> (A -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-95, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-2486
in-theory        2486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2486.         (((A -> B) -> (A -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-95, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-2487
in-theory        2487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-95 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2487.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) or E)), M:tm-95, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-2488
in-theory        2488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     23
proof            (modus-ponens tm-95 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2488.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-95, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2489
in-theory        2489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) or E))
theorem-size     15
proof            (modus-ponens tm-95 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2489.         (((A -> B) -> (A -> A)) and (((C and D) -> C) or E)), M:tm-95, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-2490
in-theory        2490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-95 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2490.         (((A -> B) -> (A -> A)) and (((C and D) -> D) or E)), M:tm-95, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-2491
in-theory        2491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) or E))
theorem-size     17
proof            (modus-ponens tm-95 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2491.         (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-95, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-2492
in-theory        2492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) or E))
theorem-size     15
proof            (modus-ponens tm-95 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2492.         (((A -> B) -> (A -> A)) and ((C -> (C or D)) or E)), M:tm-95, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-2493
in-theory        2493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (D or E)) and C)))
theorem-size     17
proof            (modus-ponens tm-95 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2493.         (((A -> B) -> (A -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-95, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-2494
in-theory        2494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-95 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2494.         (((A -> B) -> (A -> A)) and (C -> (D -> (D or E)))), M:tm-95, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-2495
in-theory        2495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-95 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2495.         (((A -> B) -> (A -> A)) and (C or (D -> (E -> D)))), M:tm-95, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-2496
in-theory        2496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2496.         (((A -> B) -> (A -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-95, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-2497
in-theory        2497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((D and E) -> D)))
theorem-size     15
proof            (modus-ponens tm-95 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2497.         (((A -> B) -> (A -> A)) and (C or ((D and E) -> D))), M:tm-95, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-2498
in-theory        2498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((D and E) -> E)))
theorem-size     15
proof            (modus-ponens tm-95 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2498.         (((A -> B) -> (A -> A)) and (C or ((D and E) -> E))), M:tm-95, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-2499
in-theory        2499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2499.         (((A -> B) -> (A -> A)) and (C or (D -> (E -> (D and E))))), M:tm-95, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-2500
in-theory        2500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-95 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2500.         (((A -> B) -> (A -> A)) and (C or (D -> (D or E)))), M:tm-95, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-2501
in-theory        2501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-95 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2501.         (((A -> B) -> (A -> A)) and (C or (D -> (E or D)))), M:tm-95, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-2502
in-theory        2502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) or E))
theorem-size     15
proof            (modus-ponens tm-95 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2502.         (((A -> B) -> (A -> A)) and ((C -> (D or C)) or E)), M:tm-95, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-2503
in-theory        2503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (E or D)) and C)))
theorem-size     17
proof            (modus-ponens tm-95 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2503.         (((A -> B) -> (A -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-95, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-2504
in-theory        2504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-95 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2504.         (((A -> B) -> (A -> A)) and (C -> (D -> (E or D)))), M:tm-95, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-2505
in-theory        2505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     21
proof            (modus-ponens tm-95 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2505.         (((A -> B) -> (A -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-95, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-2506
in-theory        2506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     33
proof            (modus-ponens tm-95 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2506.         (((A -> B) -> (A -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-95, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2507
in-theory        2507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-95 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2507.         (((A -> B) -> (A -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-95, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-2508
in-theory        2508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-95 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2508.         (((A -> B) -> (A -> A)) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-95, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-2509
in-theory        2509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     25
proof            (modus-ponens tm-95 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2509.         (((A -> B) -> (A -> A)) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-95, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-2510
in-theory        2510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     21
proof            (modus-ponens tm-95 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2510.         (((A -> B) -> (A -> A)) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-95, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-2511
in-theory        2511
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     21
proof            (modus-ponens tm-95 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2511.         (((A -> B) -> (A -> A)) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-95, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-2512
in-theory        2512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-95 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2512.         (((A -> B) -> (A -> A)) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-95, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-2513
in-theory        2513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2513.         (((A -> B) -> (A -> A)) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-95, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-2514
in-theory        2514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     23
proof            (modus-ponens tm-95 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2514.         (((A -> B) -> (A -> A)) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-95, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-2515
in-theory        2515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C)))
theorem-size     25
proof            (modus-ponens tm-95 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2515.         (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C))), M:tm-95, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-2516
in-theory        2516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-95 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-2516.         (((A -> B) -> (A -> A)) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E)))), M:tm-95, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-2517
in-theory        2517
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2517.         (((A -> B) -> (A -> A)) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-95, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-2518
in-theory        2518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not (D -> C))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-95 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2518.         (((A -> B) -> (A -> A)) and ((C -> (not (D -> C))) -> (not C))), M:tm-95, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-2519
in-theory        2519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2519.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E))))), M:tm-95, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-2520
in-theory        2520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> (not C)) -> (not (C and D))))
theorem-size     19
proof            (modus-ponens tm-95 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2520.         (((A -> B) -> (A -> A)) and (((C and D) -> (not C)) -> (not (C and D)))), M:tm-95, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-2521
in-theory        2521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> (not D)) -> (not (C and D))))
theorem-size     19
proof            (modus-ponens tm-95 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2521.         (((A -> B) -> (A -> A)) and (((C and D) -> (not D)) -> (not (C and D)))), M:tm-95, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-2522
in-theory        2522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not (D -> (C and D)))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2522.         (((A -> B) -> (A -> A)) and ((C -> (not (D -> (C and D)))) -> (not C))), M:tm-95, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-2523
in-theory        2523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not (C or D))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-95 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2523.         (((A -> B) -> (A -> A)) and ((C -> (not (C or D))) -> (not C))), M:tm-95, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-2524
in-theory        2524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not (D or C))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-95 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2524.         (((A -> B) -> (A -> A)) and ((C -> (not (D or C))) -> (not C))), M:tm-95, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-2525
in-theory        2525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D))))
theorem-size     27
proof            (modus-ponens tm-95 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2525.         (((A -> B) -> (A -> A)) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D)))), M:tm-95, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2526
in-theory        2526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D))))
theorem-size     25
proof            (modus-ponens tm-95 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2526.         (((A -> B) -> (A -> A)) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D)))), M:tm-95, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2527
in-theory        2527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E)))
theorem-size     31
proof            (modus-ponens tm-95 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-9)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2527.         (((A -> B) -> (A -> A)) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E))), M:tm-95, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-2528
in-theory        2528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2528.         (((A -> B) -> (A -> A)) and (C or ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-95, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-2529
in-theory        2529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E))
theorem-size     21
proof            (modus-ponens tm-95 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2529.         (((A -> B) -> (A -> A)) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E)), M:tm-95, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-2530
in-theory        2530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C)))
theorem-size     23
proof            (modus-ponens tm-95 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2530.         (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C))), M:tm-95, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-2531
in-theory        2531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C))))
theorem-size     23
proof            (modus-ponens tm-95 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-2531.         (((A -> B) -> (A -> A)) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C)))), M:tm-95, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-2532
in-theory        2532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2532.         (((A -> B) -> (A -> A)) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-95, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-2533
in-theory        2533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((not (not C)) -> (not C)) -> (not (not (not C)))))
theorem-size     19
proof            (modus-ponens tm-95 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2533.         (((A -> B) -> (A -> A)) and (((not (not C)) -> (not C)) -> (not (not (not C))))), M:tm-95, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-2534
in-theory        2534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> (((not (not C)) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-95 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2534.         (((A -> B) -> (A -> A)) and ((C -> D) -> (((not (not C)) or C) -> D))), M:tm-95, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-2535
in-theory        2535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((not (not D)) -> D)))
theorem-size     15
proof            (modus-ponens tm-95 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2535.         (((A -> B) -> (A -> A)) and (C or ((not (not D)) -> D))), M:tm-95, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-2536
in-theory        2536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((not (not C)) -> C) or D))
theorem-size     15
proof            (modus-ponens tm-95 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2536.         (((A -> B) -> (A -> A)) and (((not (not C)) -> C) or D)), M:tm-95, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-2537
in-theory        2537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((not (not D)) -> D) and C)))
theorem-size     17
proof            (modus-ponens tm-95 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2537.         (((A -> B) -> (A -> A)) and (C -> (((not (not D)) -> D) and C))), M:tm-95, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-2538
in-theory        2538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D)))
theorem-size     23
proof            (modus-ponens tm-95 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-2538.         (((A -> B) -> (A -> A)) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D))), M:tm-95, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-2539
in-theory        2539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((not (not D)) -> D)))
theorem-size     15
proof            (modus-ponens tm-95 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2539.         (((A -> B) -> (A -> A)) and (C -> ((not (not D)) -> D))), M:tm-95, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-2540
in-theory        2540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not (D -> (E -> D)))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2540.         (((A -> B) -> (A -> A)) and ((C -> (not (D -> (E -> D)))) -> (not C))), M:tm-95, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-2541
in-theory        2541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E)))
theorem-size     25
proof            (modus-ponens tm-95 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2541.         (((A -> B) -> (A -> A)) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E))), M:tm-95, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-2542
in-theory        2542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2542.         (((A -> B) -> (A -> A)) and (C or (D -> (E -> (F -> E))))), M:tm-95, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2543
in-theory        2543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (E -> D))) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2543.         (((A -> B) -> (A -> A)) and ((C -> (D -> (E -> D))) or F)), M:tm-95, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-2544
in-theory        2544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> (F -> E))) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2544.         (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> (F -> E))) and C))), M:tm-95, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2545
in-theory        2545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> (C -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-95 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2545.         (((A -> B) -> (A -> A)) and ((C -> D) -> (C -> (E -> D)))), M:tm-95, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2546
in-theory        2546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2546.         (((A -> B) -> (A -> A)) and (C -> (D -> (E -> (F -> E))))), M:tm-95, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2547
in-theory        2547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> C))
theorem-size     11
proof            (modus-ponens tm-95 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2547.         (((A -> B) -> (A -> A)) and (C -> C)), M:tm-95, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2548
in-theory        2548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> E)) -> (C -> (D -> E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2548.         (((A -> B) -> (A -> A)) and ((C -> (D -> E)) -> (C -> (D -> E)))), M:tm-95, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2549
in-theory        2549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C and D) -> (C and D)))
theorem-size     15
proof            (modus-ponens tm-95 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2549.         (((A -> B) -> (A -> A)) and ((C and D) -> (C and D))), M:tm-95, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2550
in-theory        2550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> (C -> D)))
theorem-size     15
proof            (modus-ponens tm-95 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2550.         (((A -> B) -> (A -> A)) and ((C -> D) -> (C -> D))), M:tm-95, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2551
in-theory        2551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((not (not C)) -> (not (not C))))
theorem-size     15
proof            (modus-ponens tm-95 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2551.         (((A -> B) -> (A -> A)) and ((not (not C)) -> (not (not C)))), M:tm-95, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2552
in-theory        2552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> (not (C -> C))) -> (not (C -> D))))
theorem-size     21
proof            (modus-ponens tm-95 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2552.         (((A -> B) -> (A -> A)) and (((C -> D) -> (not (C -> C))) -> (not (C -> D)))), M:tm-95, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2553
in-theory        2553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-95 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2553.         (((A -> B) -> (A -> A)) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D))), M:tm-95, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2554
in-theory        2554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((D -> E) -> (D -> D))))
theorem-size     17
proof            (modus-ponens tm-95 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2554.         (((A -> B) -> (A -> A)) and (C or ((D -> E) -> (D -> D)))), M:tm-95, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2555
in-theory        2555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> (C -> C)) or E))
theorem-size     17
proof            (modus-ponens tm-95 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2555.         (((A -> B) -> (A -> A)) and (((C -> D) -> (C -> C)) or E)), M:tm-95, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2556
in-theory        2556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> (D -> D)) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2556.         (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> (D -> D)) and C))), M:tm-95, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2557
in-theory        2557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> D) -> (C -> C)) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-95 ((Am (-> A A)) (B (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2557.         (((A -> B) or (A -> A)) -> (((C -> D) -> (C -> C)) and (A -> A))), M:tm-92, m:tm-95, u:((Am (-> A A)) (B (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A A))))
================================================================
tm-name          tm-2558
in-theory        2558
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> D) -> (C -> C)) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2558.         (A -> (B -> (((C -> D) -> (C -> C)) and A))), M:tm-84, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-2559
in-theory        2559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2559.         ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-83, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2560
in-theory        2560
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> E) -> (D -> D)) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-95 ((Am (-> A (-> B A))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2560.         ((A or (B -> (C -> B))) -> (((D -> E) -> (D -> D)) and (B -> (C -> B)))), M:tm-80, m:tm-95, u:((Am (-> A (-> B A))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (-> B A)))))
================================================================
tm-name          tm-2561
in-theory        2561
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> D) -> (C -> C)) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2561.         (((not (not A)) -> A) and (B -> (((C -> D) -> (C -> C)) and B))), M:tm-76, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2562
in-theory        2562
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> C) -> (B -> B)) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2562.         (((not (not A)) or A) -> (((B -> C) -> (B -> B)) and A)), M:tm-73, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-2563
in-theory        2563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> (D -> D)) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2563.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> (D -> D)) and C))), M:tm-69, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2564
in-theory        2564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> (C -> C)) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-95 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-2 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2564.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> (C -> C)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-95, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-2565
in-theory        2565
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2565.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-54, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2566
in-theory        2566
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> (D -> D)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-95 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2566.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> (D -> D)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-95, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-2567
in-theory        2567
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> D) -> (C -> C)) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-95 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2567.         ((A or (B or A)) -> (((C -> D) -> (C -> C)) and (B or A))), M:tm-50, m:tm-95, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (or A B))))
================================================================
tm-name          tm-2568
in-theory        2568
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> D) -> (C -> C)) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-95 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2568.         ((A or (A or B)) -> (((C -> D) -> (C -> C)) and (A or B))), M:tm-49, m:tm-95, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (or A B))))
================================================================
tm-name          tm-2569
in-theory        2569
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> D) -> (C -> C)) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-95 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2569.         ((A or (B -> (A and B))) -> (((C -> D) -> (C -> C)) and (B -> (A and B)))), M:tm-48, m:tm-95, u:((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-2570
in-theory        2570
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> D) -> (C -> C)) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2570.         (((A and B) or B) -> (((C -> D) -> (C -> C)) and B)), M:tm-47, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-2571
in-theory        2571
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> D) -> (C -> C)) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2571.         (((A and B) or A) -> (((C -> D) -> (C -> C)) and A)), M:tm-46, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-2572
in-theory        2572
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (D -> D)) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-95 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2572.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (D -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-95, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-2573
in-theory        2573
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> D) -> (C -> C)) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-95 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2573.         ((A or (B -> A)) -> (((C -> D) -> (C -> C)) and (B -> A))), M:tm-44, m:tm-95, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A B))))
================================================================
tm-name          tm-2574
in-theory        2574
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> E) -> (D -> D)) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2574.         ((A -> (B or A)) and (C -> (((D -> E) -> (D -> D)) and C))), M:tm-42, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2575
in-theory        2575
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> E) -> (D -> D)) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2575.         ((A -> (A or B)) and (C -> (((D -> E) -> (D -> D)) and C))), M:tm-32, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2576
in-theory        2576
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> C) -> (B -> B)) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2576.         (A -> (A and (((B -> C) -> (B -> B)) and A))), M:tm-24, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-2577
in-theory        2577
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> E) -> (D -> D)) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2577.         ((A -> (B -> (A and B))) and (C -> (((D -> E) -> (D -> D)) and C))), M:tm-23, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2578
in-theory        2578
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> E) -> (D -> D)) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2578.         (((A and B) -> B) and (C -> (((D -> E) -> (D -> D)) and C))), M:tm-22, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2579
in-theory        2579
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> E) -> (D -> D)) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2579.         (((A and B) -> A) and (C -> (((D -> E) -> (D -> D)) and C))), M:tm-21, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2580
in-theory        2580
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2580.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-20, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2581
in-theory        2581
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> E) -> (D -> D)) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2581.         ((A -> (B -> A)) and (C -> (((D -> E) -> (D -> D)) and C))), M:tm-19, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2582
in-theory        2582
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> C) -> (B -> B)) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-9 tm-5 tm-2 tm-1)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2582.         ((A -> (not (((B -> C) -> (B -> B)) and A))) -> (not A)), M:tm-9, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-2583
in-theory        2583
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> A)) and C) -> D) -> ((C or (((A -> B) -> (A -> A)) and C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2583.         (((((A -> B) -> (A -> A)) and C) -> D) -> ((C or (((A -> B) -> (A -> A)) and C)) -> D)), M:tm-8, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-2584
in-theory        2584
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> D) -> (C -> C)) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-7 tm-5 tm-2 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2584.         (A or (B -> (((C -> D) -> (C -> C)) and B))), M:tm-7, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2585
in-theory        2585
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-6 tm-5 tm-2 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2585.         ((A -> (((B -> C) -> (B -> B)) and A)) or D), M:tm-6, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2586
in-theory        2586
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> D) -> (C -> C)) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2586.         (A -> ((B -> (((C -> D) -> (C -> C)) and B)) and A)), M:tm-5, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2587
in-theory        2587
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> D) -> (C -> C)) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2587.         (A -> (B -> (((C -> D) -> (C -> C)) and B))), M:tm-1, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2588
in-theory        2588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> (A -> (B -> A)))
theorem-size     13
proof            (modus-ponens tm-96 tm-11 ((Am (-> (-> Bm (-> Cm Bm)) B)) (A (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2588.         (((A -> (B -> A)) -> C) -> (A -> (B -> A))), M:tm-96, m:tm-11, u:((Am (-> (-> Bm (-> Cm Bm)) B)) (A (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-2589
in-theory        2589
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-96 tm-14 ((Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2589.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-96, m:tm-14, u:((Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-2590
in-theory        2590
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> ((A and B) -> A))
theorem-size     13
proof            (modus-ponens tm-96 tm-16 ((Am (-> (-> (and Bm Cm) Bm) B)) (A (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2590.         ((((A and B) -> A) -> C) -> ((A and B) -> A)), M:tm-96, m:tm-16, u:((Am (-> (-> (and Bm Cm) Bm) B)) (A (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-2591
in-theory        2591
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> ((A and B) -> B))
theorem-size     13
proof            (modus-ponens tm-96 tm-18 ((Am (-> (-> (and Bm Cm) Cm) B)) (A (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2591.         ((((A and B) -> B) -> C) -> ((A and B) -> B)), M:tm-96, m:tm-18, u:((Am (-> (-> (and Bm Cm) Cm) B)) (A (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-2592
in-theory        2592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> (A -> (B -> (A and B))))
theorem-size     17
proof            (modus-ponens tm-96 tm-25 ((Am (-> (-> Bm (-> Cm (and Bm Cm))) B)) (A (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2592.         (((A -> (B -> (A and B))) -> C) -> (A -> (B -> (A and B)))), M:tm-96, m:tm-25, u:((Am (-> (-> Bm (-> Cm (and Bm Cm))) B)) (A (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-2593
in-theory        2593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> (A -> (A or B)))
theorem-size     13
proof            (modus-ponens tm-96 tm-33 ((Am (-> (-> Bm (or Bm Cm)) B)) (A (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2593.         (((A -> (A or B)) -> C) -> (A -> (A or B))), M:tm-96, m:tm-33, u:((Am (-> (-> Bm (or Bm Cm)) B)) (A (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-2594
in-theory        2594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> (A -> (B or A)))
theorem-size     13
proof            (modus-ponens tm-96 tm-43 ((Am (-> (-> Bm (or Cm Bm)) B)) (A (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2594.         (((A -> (B or A)) -> C) -> (A -> (B or A))), M:tm-96, m:tm-43, u:((Am (-> (-> Bm (or Cm Bm)) B)) (A (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-2595
in-theory        2595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) -> ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-96 tm-56 ((Am (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B)) (A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2595.         ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) -> ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-96, m:tm-56, u:((Am (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B)) (A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-2596
in-theory        2596
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) -> C) -> ((A -> B) -> ((A -> (not B)) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-96 tm-71 ((Am (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) B)) (A (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2596.         ((((A -> B) -> ((A -> (not B)) -> (not A))) -> C) -> ((A -> B) -> ((A -> (not B)) -> (not A)))), M:tm-96, m:tm-71, u:((Am (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) B)) (A (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-2597
in-theory        2597
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) -> B) -> ((not (not A)) -> A))
theorem-size     13
proof            (modus-ponens tm-96 tm-78 ((Am (-> (-> (not (not Bm)) Bm) B)) (A (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-1 tm-10)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2597.         ((((not (not A)) -> A) -> B) -> ((not (not A)) -> A)), M:tm-96, m:tm-78, u:((Am (-> (-> (not (not Bm)) Bm) B)) (A (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-2598
in-theory        2598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) -> D) -> (A -> (B -> (C -> B))))
theorem-size     17
proof            (modus-ponens tm-96 tm-85 ((Am (-> (-> Bm (-> Cm (-> Dm Cm))) B)) (A (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2598.         (((A -> (B -> (C -> B))) -> D) -> (A -> (B -> (C -> B)))), M:tm-96, m:tm-85, u:((Am (-> (-> Bm (-> Cm (-> Dm Cm))) B)) (A (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2599
in-theory        2599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> C) -> ((C -> D) -> C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2599.         (((A -> B) -> (A -> A)) and (((C -> D) -> C) -> ((C -> D) -> C))), M:tm-95, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2600
in-theory        2600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> (C -> ((A -> B) -> A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-2 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2600.         (((A -> B) -> A) -> (C -> ((A -> B) -> A))), M:tm-84, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-2601
in-theory        2601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2601.         ((A -> (B -> (C -> B))) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-83, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2602
in-theory        2602
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> B) -> ((B -> C) -> B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2602.         (((not (not A)) -> A) and (((B -> C) -> B) -> ((B -> C) -> B))), M:tm-76, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2603
in-theory        2603
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> A))) or ((A -> B) -> A)) -> ((A -> B) -> A))
theorem-size     19
proof            (modus-ponens tm-73 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2603.         (((not (not ((A -> B) -> A))) or ((A -> B) -> A)) -> ((A -> B) -> A)), M:tm-73, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-2604
in-theory        2604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> C) -> ((C -> D) -> C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2604.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> C) -> ((C -> D) -> C))), M:tm-69, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2605
in-theory        2605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2605.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-54, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2606
in-theory        2606
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> B)) or ((B -> C) -> B)) -> ((B -> C) -> B))
theorem-size     19
proof            (modus-ponens tm-47 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2606.         (((A and ((B -> C) -> B)) or ((B -> C) -> B)) -> ((B -> C) -> B)), M:tm-47, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-2607
in-theory        2607
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> A) and C) or ((A -> B) -> A)) -> ((A -> B) -> A))
theorem-size     19
proof            (modus-ponens tm-46 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2607.         (((((A -> B) -> A) and C) or ((A -> B) -> A)) -> ((A -> B) -> A)), M:tm-46, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-2608
in-theory        2608
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((A -> B) -> A)) -> ((A -> B) -> A))
theorem-size     13
proof            (modus-ponens tm-44 tm-96 ((A (-> Am Bm)) (B Am) (C (-> (-> Am Bm) Am))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2608.         ((A or ((A -> B) -> A)) -> ((A -> B) -> A)), M:tm-44, m:tm-96, u:((A (-> Am Bm)) (B Am) (C (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-2609
in-theory        2609
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> C) -> ((C -> D) -> C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2609.         ((A -> (B or A)) and (((C -> D) -> C) -> ((C -> D) -> C))), M:tm-42, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2610
in-theory        2610
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> C) -> ((C -> D) -> C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2610.         ((A -> (A or B)) and (((C -> D) -> C) -> ((C -> D) -> C))), M:tm-32, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2611
in-theory        2611
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> (((A -> B) -> A) and ((A -> B) -> A)))
theorem-size     17
proof            (modus-ponens tm-24 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2611.         (((A -> B) -> A) -> (((A -> B) -> A) and ((A -> B) -> A))), M:tm-24, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-2612
in-theory        2612
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> C) -> ((C -> D) -> C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2612.         ((A -> (B -> (A and B))) and (((C -> D) -> C) -> ((C -> D) -> C))), M:tm-23, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2613
in-theory        2613
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> C) -> ((C -> D) -> C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2613.         (((A and B) -> B) and (((C -> D) -> C) -> ((C -> D) -> C))), M:tm-22, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2614
in-theory        2614
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> C) -> ((C -> D) -> C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2614.         (((A and B) -> A) and (((C -> D) -> C) -> ((C -> D) -> C))), M:tm-21, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2615
in-theory        2615
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2615.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-20, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2616
in-theory        2616
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> C) -> ((C -> D) -> C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2616.         ((A -> (B -> A)) and (((C -> D) -> C) -> ((C -> D) -> C))), M:tm-19, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2617
in-theory        2617
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> (not ((A -> B) -> A))) -> (not ((A -> B) -> A)))
theorem-size     19
proof            (modus-ponens tm-9 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-9 tm-2 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2617.         ((((A -> B) -> A) -> (not ((A -> B) -> A))) -> (not ((A -> B) -> A))), M:tm-9, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-2618
in-theory        2618
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> C) -> ((((A -> B) -> A) or ((A -> B) -> A)) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2618.         ((((A -> B) -> A) -> C) -> ((((A -> B) -> A) or ((A -> B) -> A)) -> C)), M:tm-8, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-2619
in-theory        2619
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> C) -> B) -> ((B -> C) -> B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-7 tm-2 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2619.         (A or (((B -> C) -> B) -> ((B -> C) -> B))), M:tm-7, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2620
in-theory        2620
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) or C)
theorem-size     13
proof            (modus-ponens tm-6 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-6 tm-2 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2620.         ((((A -> B) -> A) -> ((A -> B) -> A)) or C), M:tm-6, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2621
in-theory        2621
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> B) -> ((B -> C) -> B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2621.         (A -> ((((B -> C) -> B) -> ((B -> C) -> B)) and A)), M:tm-5, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2622
in-theory        2622
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> (A -> B)) -> (((A -> B) -> A) -> A))
theorem-size     17
proof            (modus-ponens tm-2 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> Am Bm)) (C Am)))
axioms-used      (tm-2 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2622.         ((((A -> B) -> A) -> (A -> B)) -> (((A -> B) -> A) -> A)), M:tm-2, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> Am Bm)) (C Am))
================================================================
tm-name          tm-2623
in-theory        2623
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> B) -> ((B -> C) -> B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-1 tm-2)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2623.         (A -> (((B -> C) -> B) -> ((B -> C) -> B))), M:tm-1, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2624
in-theory        2624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) -> C) -> ((A -> B) -> (A -> A)))
theorem-size     17
proof            (modus-ponens tm-96 tm-97 ((Am (-> (-> (-> Bm Cm) (-> Bm Bm)) B)) (A (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2624.         ((((A -> B) -> (A -> A)) -> C) -> ((A -> B) -> (A -> A))), M:tm-96, m:tm-97, u:((Am (-> (-> (-> Bm Cm) (-> Bm Bm)) B)) (A (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2625
in-theory        2625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> E) -> (D -> D))))
theorem-size     17
proof            (modus-ponens tm-95 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2625.         (((A -> B) -> (A -> A)) and (C -> ((D -> E) -> (D -> D)))), M:tm-95, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2626
in-theory        2626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> D) -> (C -> C)))
theorem-size     15
proof            (modus-ponens tm-92 tm-97 ((Am (-> A A)) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2626.         (((A -> B) or (A -> A)) -> ((C -> D) -> (C -> C))), M:tm-92, m:tm-97, u:((Am (-> A A)) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2627
in-theory        2627
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> D) -> (C -> C))))
theorem-size     11
proof            (modus-ponens tm-84 tm-97 ((A Am) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2627.         (A -> (B -> ((C -> D) -> (C -> C)))), M:tm-84, m:tm-97, u:((A Am) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2628
in-theory        2628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-83 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2628.         ((A -> (B -> (C -> B))) and (D -> ((E -> F) -> (E -> E)))), M:tm-83, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2629
in-theory        2629
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-80 tm-97 ((Am (-> A (-> B A))) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2629.         ((A or (B -> (C -> B))) -> ((D -> E) -> (D -> D))), M:tm-80, m:tm-97, u:((Am (-> A (-> B A))) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2630
in-theory        2630
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((A -> B) -> (A -> A)) -> C))) -> C)
theorem-size     13
proof            (modus-ponens tm-77 tm-97 ((Am (not (not (-> (-> (-> Bm Cm) (-> Bm Bm)) B)))) (A (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-10 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2630.         ((not (not (((A -> B) -> (A -> A)) -> C))) -> C), M:tm-77, m:tm-97, u:((Am (not (not (-> (-> (-> Bm Cm) (-> Bm Bm)) B)))) (A (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2631
in-theory        2631
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> D) -> (C -> C))))
theorem-size     15
proof            (modus-ponens tm-76 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2631.         (((not (not A)) -> A) and (B -> ((C -> D) -> (C -> C)))), M:tm-76, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2632
in-theory        2632
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> C) -> (B -> B)))
theorem-size     13
proof            (modus-ponens tm-73 tm-97 ((A Am) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2632.         (((not (not A)) or A) -> ((B -> C) -> (B -> B))), M:tm-73, m:tm-97, u:((A Am) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2633
in-theory        2633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> E) -> (D -> D))))
theorem-size     21
proof            (modus-ponens tm-69 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2633.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> E) -> (D -> D)))), M:tm-69, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2634
in-theory        2634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> D) -> (C -> C)))
theorem-size     19
proof            (modus-ponens tm-66 tm-97 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2634.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> D) -> (C -> C))), M:tm-66, m:tm-97, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2635
in-theory        2635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((A or (B -> C)) -> (B -> B)))
theorem-size     15
proof            (modus-ponens tm-55 tm-97 ((Am (-> A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm Bm))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2635.         ((A -> (B -> C)) -> ((A or (B -> C)) -> (B -> B))), M:tm-55, m:tm-97, u:((Am (-> A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm Bm)))
================================================================
tm-name          tm-2636
in-theory        2636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-54 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2636.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> F) -> (E -> E)))), M:tm-54, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2637
in-theory        2637
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-51 tm-97 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2637.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> (D -> D))), M:tm-51, m:tm-97, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2638
in-theory        2638
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> D) -> (C -> C)))
theorem-size     13
proof            (modus-ponens tm-50 tm-97 ((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2638.         ((A or (B or A)) -> ((C -> D) -> (C -> C))), M:tm-50, m:tm-97, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2639
in-theory        2639
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> D) -> (C -> C)))
theorem-size     13
proof            (modus-ponens tm-49 tm-97 ((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2639.         ((A or (A or B)) -> ((C -> D) -> (C -> C))), M:tm-49, m:tm-97, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2640
in-theory        2640
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> D) -> (C -> C)))
theorem-size     15
proof            (modus-ponens tm-48 tm-97 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2640.         ((A or (B -> (A and B))) -> ((C -> D) -> (C -> C))), M:tm-48, m:tm-97, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2641
in-theory        2641
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> D) -> (C -> C)))
theorem-size     13
proof            (modus-ponens tm-47 tm-97 ((A Am) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2641.         (((A and B) or B) -> ((C -> D) -> (C -> C))), M:tm-47, m:tm-97, u:((A Am) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2642
in-theory        2642
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> D) -> (C -> C)))
theorem-size     13
proof            (modus-ponens tm-46 tm-97 ((A Am) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2642.         (((A and B) or A) -> ((C -> D) -> (C -> C))), M:tm-46, m:tm-97, u:((A Am) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2643
in-theory        2643
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-45 tm-97 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2643.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (D -> D))), M:tm-45, m:tm-97, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2644
in-theory        2644
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> D) -> (C -> C)))
theorem-size     13
proof            (modus-ponens tm-44 tm-97 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2644.         ((A or (B -> A)) -> ((C -> D) -> (C -> C))), M:tm-44, m:tm-97, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2645
in-theory        2645
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-42 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2645.         ((A -> (B or A)) and (C -> ((D -> E) -> (D -> D)))), M:tm-42, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2646
in-theory        2646
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-32 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2646.         ((A -> (A or B)) and (C -> ((D -> E) -> (D -> D)))), M:tm-32, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2647
in-theory        2647
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> C) -> (B -> B))))
theorem-size     11
proof            (modus-ponens tm-24 tm-97 ((A Am) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2647.         (A -> (A and ((B -> C) -> (B -> B)))), M:tm-24, m:tm-97, u:((A Am) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2648
in-theory        2648
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> E) -> (D -> D))))
theorem-size     17
proof            (modus-ponens tm-23 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2648.         ((A -> (B -> (A and B))) and (C -> ((D -> E) -> (D -> D)))), M:tm-23, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2649
in-theory        2649
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-22 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2649.         (((A and B) -> B) and (C -> ((D -> E) -> (D -> D)))), M:tm-22, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2650
in-theory        2650
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-21 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2650.         (((A and B) -> A) and (C -> ((D -> E) -> (D -> D)))), M:tm-21, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2651
in-theory        2651
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-20 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2651.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> F) -> (E -> E)))), M:tm-20, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2652
in-theory        2652
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-19 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2652.         ((A -> (B -> A)) and (C -> ((D -> E) -> (D -> D)))), M:tm-19, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2653
in-theory        2653
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> (B -> B)) -> D)) -> D)
theorem-size     13
proof            (modus-ponens tm-17 tm-97 ((Am (and A (-> (-> (-> Bm Cm) (-> Bm Bm)) C))) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2653.         ((A and (((B -> C) -> (B -> B)) -> D)) -> D), M:tm-17, m:tm-97, u:((Am (and A (-> (-> (-> Bm Cm) (-> Bm Bm)) C))) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2654
in-theory        2654
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> A)) -> C) and D) -> C)
theorem-size     13
proof            (modus-ponens tm-15 tm-97 ((Am (and (-> (-> (-> Bm Cm) (-> Bm Bm)) B) C)) (A (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2654.         (((((A -> B) -> (A -> A)) -> C) and D) -> C), M:tm-15, m:tm-97, u:((Am (and (-> (-> (-> Bm Cm) (-> Bm Bm)) B) C)) (A (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2655
in-theory        2655
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> A) -> C)) -> ((A -> B) -> C))
theorem-size     15
proof            (modus-ponens tm-13 tm-97 ((Am (-> (-> Bm Cm) (-> (-> Bm Bm) C))) (A (-> Bm Cm)) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2655.         (((A -> B) -> ((A -> A) -> C)) -> ((A -> B) -> C)), M:tm-13, m:tm-97, u:((Am (-> (-> Bm Cm) (-> (-> Bm Bm) C))) (A (-> Bm Cm)) (B (-> Bm Bm)))
================================================================
tm-name          tm-2656
in-theory        2656
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> C) -> (B -> B)))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-97 ((A Am) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2656.         ((A -> (not ((B -> C) -> (B -> B)))) -> (not A)), M:tm-9, m:tm-97, u:((A Am) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2657
in-theory        2657
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) -> C) -> ((D or ((A -> B) -> (A -> A))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-97 ((A Am) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2657.         ((((A -> B) -> (A -> A)) -> C) -> ((D or ((A -> B) -> (A -> A))) -> C)), M:tm-8, m:tm-97, u:((A Am) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2658
in-theory        2658
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> D) -> (C -> C))))
theorem-size     11
proof            (modus-ponens tm-7 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-7 tm-1 tm-2)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2658.         (A or (B -> ((C -> D) -> (C -> C)))), M:tm-7, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2659
in-theory        2659
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-6 tm-1 tm-2)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2659.         ((A -> ((B -> C) -> (B -> B))) or D), M:tm-6, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2660
in-theory        2660
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> D) -> (C -> C))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2660.         (A -> ((B -> ((C -> D) -> (C -> C))) and A)), M:tm-5, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2661
in-theory        2661
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (A -> (B -> B)))
theorem-size     11
proof            (modus-ponens tm-2 tm-97 ((A Am) (B (-> Bm Cm)) (C (-> Bm Bm))))
axioms-used      (tm-2 tm-1)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2661.         ((A -> (B -> C)) -> (A -> (B -> B))), M:tm-2, m:tm-97, u:((A Am) (B (-> Bm Cm)) (C (-> Bm Bm)))
================================================================
tm-name          tm-2662
in-theory        2662
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> A) -> (C -> B)))
theorem-size     11
proof            (modus-ponens tm-98 tm-14 ((Am (-> Cm Dm)) (B Bm) (A (-> Cm Dm)) (C (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2662.         ((A -> B) -> ((C -> A) -> (C -> B))), M:tm-98, m:tm-14, u:((Am (-> Cm Dm)) (B Bm) (A (-> Cm Dm)) (C (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-2663
in-theory        2663
times-derived    2
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> A) and B)))
theorem-size     9
proof            (modus-ponens tm-98 tm-25 ((A Am) (Bm (-> B Am)) (C (-> Cm (and (-> B Am) Cm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2663.         (A -> (B -> ((C -> A) and B))), M:tm-98, m:tm-25, u:((A Am) (Bm (-> B Am)) (C (-> Cm (and (-> B Am) Cm))))
================================================================
tm-name          tm-2664
in-theory        2664
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> A) or C))
theorem-size     7
proof            (modus-ponens tm-98 tm-33 ((A Am) (Bm (-> B Am)) (C (or (-> B Am) Cm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2664.         (A -> ((B -> A) or C)), M:tm-98, m:tm-33, u:((A Am) (Bm (-> B Am)) (C (or (-> B Am) Cm)))
================================================================
tm-name          tm-2665
in-theory        2665
times-derived    2
----------------------------------------------------------------
theorem          (A -> (B or (C -> A)))
theorem-size     7
proof            (modus-ponens tm-98 tm-43 ((A Am) (Bm (-> B Am)) (C (or Cm (-> B Am)))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2665.         (A -> (B or (C -> A))), M:tm-98, m:tm-43, u:((A Am) (Bm (-> B Am)) (C (or Cm (-> B Am))))
================================================================
tm-name          tm-2666
in-theory        2666
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A -> B) -> ((C or A) -> B)))
theorem-size     11
proof            (modus-ponens tm-98 tm-56 ((Cm Am) (B Bm) (A Am) (C (-> (-> Am Dm) (-> (or Bm Am) Dm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2666.         (A -> ((A -> B) -> ((C or A) -> B))), M:tm-98, m:tm-56, u:((Cm Am) (B Bm) (A Am) (C (-> (-> Am Dm) (-> (or Bm Am) Dm))))
================================================================
tm-name          tm-2667
in-theory        2667
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not A)) -> (not B)))
theorem-size     9
proof            (modus-ponens tm-98 tm-71 ((Cm Am) (B Bm) (A Am) (C (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2667.         (A -> ((B -> (not A)) -> (not B))), M:tm-98, m:tm-71, u:((Cm Am) (B Bm) (A Am) (C (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-2668
in-theory        2668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> ((D -> C) -> E)) -> (C -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2668.         (((A -> B) -> (A -> A)) and ((C -> ((D -> C) -> E)) -> (C -> E))), M:tm-95, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2669
in-theory        2669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> A) -> C)) -> (D -> (A -> C)))
theorem-size     13
proof            (modus-ponens tm-84 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2669.         ((A -> ((B -> A) -> C)) -> (D -> (A -> C))), M:tm-84, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-2670
in-theory        2670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2670.         ((A -> (B -> (C -> B))) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-83, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2671
in-theory        2671
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> B) -> B))) -> (B -> B))
theorem-size     13
proof            (modus-ponens tm-80 tm-98 ((Cm Am) (B (-> Bm Am)) (A Am) (C (-> Am Am))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2671.         ((A or (B -> ((C -> B) -> B))) -> (B -> B)), M:tm-80, m:tm-98, u:((Cm Am) (B (-> Bm Am)) (A Am) (C (-> Am Am)))
================================================================
tm-name          tm-2672
in-theory        2672
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> ((C -> B) -> D)) -> (B -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2672.         (((not (not A)) -> A) and ((B -> ((C -> B) -> D)) -> (B -> D))), M:tm-76, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2673
in-theory        2673
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> ((B -> A) -> C)))) or (A -> ((B -> A) -> C))) -> (A -> C))
theorem-size     21
proof            (modus-ponens tm-73 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2673.         (((not (not (A -> ((B -> A) -> C)))) or (A -> ((B -> A) -> C))) -> (A -> C)), M:tm-73, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-2674
in-theory        2674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D -> C) -> E)) -> (C -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2674.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D -> C) -> E)) -> (C -> E))), M:tm-69, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2675
in-theory        2675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2675.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-54, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2676
in-theory        2676
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> ((C -> B) -> D))) or (B -> ((C -> B) -> D))) -> (B -> D))
theorem-size     21
proof            (modus-ponens tm-47 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2676.         (((A and (B -> ((C -> B) -> D))) or (B -> ((C -> B) -> D))) -> (B -> D)), M:tm-47, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-2677
in-theory        2677
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> A) -> C)) and D) or (A -> ((B -> A) -> C))) -> (A -> C))
theorem-size     21
proof            (modus-ponens tm-46 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2677.         ((((A -> ((B -> A) -> C)) and D) or (A -> ((B -> A) -> C))) -> (A -> C)), M:tm-46, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-2678
in-theory        2678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or (B -> ((A -> B) -> C))) -> (B -> C))
theorem-size     17
proof            (modus-ponens tm-44 tm-98 ((A Am) (B (-> (-> Bm Am) Cm)) (C (-> Am Cm))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2678.         ((((A -> B) -> C) or (B -> ((A -> B) -> C))) -> (B -> C)), M:tm-44, m:tm-98, u:((A Am) (B (-> (-> Bm Am) Cm)) (C (-> Am Cm)))
================================================================
tm-name          tm-2679
in-theory        2679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> ((D -> C) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2679.         ((A -> (B or A)) and ((C -> ((D -> C) -> E)) -> (C -> E))), M:tm-42, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2680
in-theory        2680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> ((D -> C) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2680.         ((A -> (A or B)) and ((C -> ((D -> C) -> E)) -> (C -> E))), M:tm-32, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2681
in-theory        2681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> A) -> C)) -> ((A -> ((B -> A) -> C)) and (A -> C)))
theorem-size     19
proof            (modus-ponens tm-24 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2681.         ((A -> ((B -> A) -> C)) -> ((A -> ((B -> A) -> C)) and (A -> C))), M:tm-24, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-2682
in-theory        2682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> ((D -> C) -> E)) -> (C -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2682.         ((A -> (B -> (A and B))) and ((C -> ((D -> C) -> E)) -> (C -> E))), M:tm-23, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2683
in-theory        2683
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> ((D -> C) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2683.         (((A and B) -> B) and ((C -> ((D -> C) -> E)) -> (C -> E))), M:tm-22, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2684
in-theory        2684
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> ((D -> C) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2684.         (((A and B) -> A) and ((C -> ((D -> C) -> E)) -> (C -> E))), M:tm-21, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2685
in-theory        2685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2685.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-20, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2686
in-theory        2686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> ((D -> C) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2686.         ((A -> (B -> A)) and ((C -> ((D -> C) -> E)) -> (C -> E))), M:tm-19, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2687
in-theory        2687
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> A) -> (B -> A))) -> (A -> (B -> A)))
theorem-size     15
proof            (modus-ponens tm-13 tm-98 ((Cm (-> Bm Am)) (C (-> Bm Am)) (A Am) (B (-> Bm Am))))
axioms-used      (tm-2 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2687.         ((A -> ((B -> A) -> (B -> A))) -> (A -> (B -> A))), M:tm-13, m:tm-98, u:((Cm (-> Bm Am)) (C (-> Bm Am)) (A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-2688
in-theory        2688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> A) -> C)) -> (A -> ((B -> A) -> C)))
theorem-size     15
proof            (modus-ponens tm-12 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2688.         ((A -> ((B -> A) -> C)) -> (A -> ((B -> A) -> C))), M:tm-12, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-2689
in-theory        2689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (not (A -> C))) -> (not (A -> ((B -> A) -> C))))
theorem-size     21
proof            (modus-ponens tm-9 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-9 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2689.         (((A -> ((B -> A) -> C)) -> (not (A -> C))) -> (not (A -> ((B -> A) -> C)))), M:tm-9, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-2690
in-theory        2690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (((A -> ((D -> A) -> B)) or (A -> B)) -> C))
theorem-size     19
proof            (modus-ponens tm-8 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2690.         (((A -> B) -> C) -> (((A -> ((D -> A) -> B)) or (A -> B)) -> C)), M:tm-8, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-2691
in-theory        2691
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> ((C -> B) -> D)) -> (B -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-7 tm-2 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2691.         (A or ((B -> ((C -> B) -> D)) -> (B -> D))), M:tm-7, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2692
in-theory        2692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-6 tm-2 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2692.         (((A -> ((B -> A) -> C)) -> (A -> C)) or D), M:tm-6, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2693
in-theory        2693
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> ((C -> B) -> D)) -> (B -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2693.         (A -> (((B -> ((C -> B) -> D)) -> (B -> D)) and A)), M:tm-5, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2694
in-theory        2694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> A) -> ((A -> ((B -> A) -> C)) -> C))
theorem-size     19
proof            (modus-ponens tm-2 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B Am) (C Cm)))
axioms-used      (tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2694.         (((A -> ((B -> A) -> C)) -> A) -> ((A -> ((B -> A) -> C)) -> C)), M:tm-2, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B Am) (C Cm))
================================================================
tm-name          tm-2695
in-theory        2695
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> B) -> D)) -> (B -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2695.         (A -> ((B -> ((C -> B) -> D)) -> (B -> D))), M:tm-1, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2696
in-theory        2696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C -> D)) -> (C -> D)))
theorem-size     17
proof            (modus-ponens tm-95 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2696.         (((A -> B) -> (A -> A)) and ((C -> (C -> D)) -> (C -> D))), M:tm-95, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2697
in-theory        2697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A -> B)) -> (C -> (A -> B)))
theorem-size     11
proof            (modus-ponens tm-84 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2697.         ((A -> (A -> B)) -> (C -> (A -> B))), M:tm-84, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-2698
in-theory        2698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-83 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2698.         ((A -> (B -> (C -> B))) and ((D -> (D -> E)) -> (D -> E))), M:tm-83, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2699
in-theory        2699
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B -> B))) -> (B -> B))
theorem-size     11
proof            (modus-ponens tm-80 tm-99 ((Bm Am) (B Am) (A Am) (C (-> Am Am))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2699.         ((A or (B -> (B -> B))) -> (B -> B)), M:tm-80, m:tm-99, u:((Bm Am) (B Am) (A Am) (C (-> Am Am)))
================================================================
tm-name          tm-2700
in-theory        2700
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B -> C)) -> (B -> C)))
theorem-size     15
proof            (modus-ponens tm-76 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2700.         (((not (not A)) -> A) and ((B -> (B -> C)) -> (B -> C))), M:tm-76, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2701
in-theory        2701
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (A -> B)))) or (A -> (A -> B))) -> (A -> B))
theorem-size     17
proof            (modus-ponens tm-73 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2701.         (((not (not (A -> (A -> B)))) or (A -> (A -> B))) -> (A -> B)), M:tm-73, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-2702
in-theory        2702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C -> D)) -> (C -> D)))
theorem-size     21
proof            (modus-ponens tm-69 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2702.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C -> D)) -> (C -> D))), M:tm-69, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2703
in-theory        2703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     23
proof            (modus-ponens tm-54 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2703.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D -> E)) -> (D -> E))), M:tm-54, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2704
in-theory        2704
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (B -> C))) or (B -> (B -> C))) -> (B -> C))
theorem-size     17
proof            (modus-ponens tm-47 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2704.         (((A and (B -> (B -> C))) or (B -> (B -> C))) -> (B -> C)), M:tm-47, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-2705
in-theory        2705
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A -> B)) and C) or (A -> (A -> B))) -> (A -> B))
theorem-size     17
proof            (modus-ponens tm-46 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2705.         ((((A -> (A -> B)) and C) or (A -> (A -> B))) -> (A -> B)), M:tm-46, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-2706
in-theory        2706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A -> B))) -> (A -> B))
theorem-size     13
proof            (modus-ponens tm-44 tm-99 ((A Am) (B (-> Am Bm)) (C (-> Am Bm))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2706.         (((A -> B) or (A -> (A -> B))) -> (A -> B)), M:tm-44, m:tm-99, u:((A Am) (B (-> Am Bm)) (C (-> Am Bm)))
================================================================
tm-name          tm-2707
in-theory        2707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C -> D)) -> (C -> D)))
theorem-size     15
proof            (modus-ponens tm-42 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2707.         ((A -> (B or A)) and ((C -> (C -> D)) -> (C -> D))), M:tm-42, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2708
in-theory        2708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C -> D)) -> (C -> D)))
theorem-size     15
proof            (modus-ponens tm-32 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2708.         ((A -> (A or B)) and ((C -> (C -> D)) -> (C -> D))), M:tm-32, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2709
in-theory        2709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A -> B)) -> ((A -> (A -> B)) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-24 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2709.         ((A -> (A -> B)) -> ((A -> (A -> B)) and (A -> B))), M:tm-24, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-2710
in-theory        2710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C -> D)) -> (C -> D)))
theorem-size     17
proof            (modus-ponens tm-23 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2710.         ((A -> (B -> (A and B))) and ((C -> (C -> D)) -> (C -> D))), M:tm-23, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2711
in-theory        2711
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C -> D)) -> (C -> D)))
theorem-size     15
proof            (modus-ponens tm-22 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2711.         (((A and B) -> B) and ((C -> (C -> D)) -> (C -> D))), M:tm-22, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2712
in-theory        2712
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C -> D)) -> (C -> D)))
theorem-size     15
proof            (modus-ponens tm-21 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2712.         (((A and B) -> A) and ((C -> (C -> D)) -> (C -> D))), M:tm-21, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2713
in-theory        2713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     23
proof            (modus-ponens tm-20 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2713.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D -> E)) -> (D -> E))), M:tm-20, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2714
in-theory        2714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C -> D)) -> (C -> D)))
theorem-size     15
proof            (modus-ponens tm-19 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2714.         ((A -> (B -> A)) and ((C -> (C -> D)) -> (C -> D))), M:tm-19, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2715
in-theory        2715
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A -> A)) -> (A -> A))
theorem-size     9
proof            (modus-ponens tm-13 tm-99 ((Bm Am) (C Am) (A Am) (B Am)))
axioms-used      (tm-2 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2715.         ((A -> (A -> A)) -> (A -> A)), M:tm-13, m:tm-99, u:((Bm Am) (C Am) (A Am) (B Am))
================================================================
tm-name          tm-2716
in-theory        2716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A -> B)) -> (A -> (A -> B)))
theorem-size     11
proof            (modus-ponens tm-12 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2716.         ((A -> (A -> B)) -> (A -> (A -> B))), M:tm-12, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-2717
in-theory        2717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (not (A -> B))) -> (not (A -> (A -> B))))
theorem-size     17
proof            (modus-ponens tm-9 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-9 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2717.         (((A -> (A -> B)) -> (not (A -> B))) -> (not (A -> (A -> B)))), M:tm-9, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-2718
in-theory        2718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (((A -> (A -> B)) or (A -> B)) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2718.         (((A -> B) -> C) -> (((A -> (A -> B)) or (A -> B)) -> C)), M:tm-8, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-2719
in-theory        2719
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B -> C)) -> (B -> C)))
theorem-size     11
proof            (modus-ponens tm-7 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-7 tm-2 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2719.         (A or ((B -> (B -> C)) -> (B -> C))), M:tm-7, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2720
in-theory        2720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) or C)
theorem-size     11
proof            (modus-ponens tm-6 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-6 tm-2 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2720.         (((A -> (A -> B)) -> (A -> B)) or C), M:tm-6, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2721
in-theory        2721
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B -> C)) -> (B -> C)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2721.         (A -> (((B -> (B -> C)) -> (B -> C)) and A)), M:tm-5, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2722
in-theory        2722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> A) -> ((A -> (A -> B)) -> B))
theorem-size     15
proof            (modus-ponens tm-2 tm-99 ((A (-> Am (-> Am Bm))) (B Am) (C Bm)))
axioms-used      (tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2722.         (((A -> (A -> B)) -> A) -> ((A -> (A -> B)) -> B)), M:tm-2, m:tm-99, u:((A (-> Am (-> Am Bm))) (B Am) (C Bm))
================================================================
tm-name          tm-2723
in-theory        2723
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B -> C)) -> (B -> C)))
theorem-size     11
proof            (modus-ponens tm-1 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-1 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2723.         (A -> ((B -> (B -> C)) -> (B -> C))), M:tm-1, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-2724
in-theory        2724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> A) -> C)) -> (A -> (B -> A)))
theorem-size     13
proof            (modus-ponens tm-100 tm-11 ((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2724.         ((A -> ((B -> A) -> C)) -> (A -> (B -> A))), M:tm-100, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
================================================================
tm-name          tm-2725
in-theory        2725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A -> B)) -> (A -> A))
theorem-size     9
proof            (modus-ponens tm-100 tm-12 ((Bm (-> Am C)) (A Am) (B Am)))
axioms-used      (tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2725.         ((A -> (A -> B)) -> (A -> A)), M:tm-100, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
================================================================
tm-name          tm-2726
in-theory        2726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-100 tm-14 ((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2726.         (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-100, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-2727
in-theory        2727
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> A))
theorem-size     21
proof            (modus-ponens tm-100 tm-15 ((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-2727.         (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> A)), M:tm-100, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
================================================================
tm-name          tm-2728
in-theory        2728
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A -> C)) -> ((A and B) -> A))
theorem-size     13
proof            (modus-ponens tm-100 tm-16 ((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2728.         (((A and B) -> (A -> C)) -> ((A and B) -> A)), M:tm-100, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
================================================================
tm-name          tm-2729
in-theory        2729
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> B))
theorem-size     21
proof            (modus-ponens tm-100 tm-17 ((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-2729.         (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> B)), M:tm-100, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
================================================================
tm-name          tm-2730
in-theory        2730
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (B -> C)) -> ((A and B) -> B))
theorem-size     13
proof            (modus-ponens tm-100 tm-18 ((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2730.         (((A and B) -> (B -> C)) -> ((A and B) -> B)), M:tm-100, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
================================================================
tm-name          tm-2731
in-theory        2731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (A and B)) -> C)) -> (A -> (B -> (A and B))))
theorem-size     17
proof            (modus-ponens tm-100 tm-25 ((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2731.         ((A -> ((B -> (A and B)) -> C)) -> (A -> (B -> (A and B)))), M:tm-100, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-2732
in-theory        2732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((A or B) -> C)) -> (A -> (A or B)))
theorem-size     13
proof            (modus-ponens tm-100 tm-33 ((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2732.         ((A -> ((A or B) -> C)) -> (A -> (A or B))), M:tm-100, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
================================================================
tm-name          tm-2733
in-theory        2733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or A) -> C)) -> (A -> (B or A)))
theorem-size     13
proof            (modus-ponens tm-100 tm-43 ((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2733.         ((A -> ((B or A) -> C)) -> (A -> (B or A))), M:tm-100, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
================================================================
tm-name          tm-2734
in-theory        2734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((B -> C) -> ((A or B) -> C)) -> D)) -> ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-100 tm-56 ((Am (-> (-> Bm Cm) (-> (-> (-> Cm Dm) (-> (or Bm Cm) Dm)) C))) (A (-> Bm Cm)) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2734.         (((A -> B) -> (((B -> C) -> ((A or B) -> C)) -> D)) -> ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-100, m:tm-56, u:((Am (-> (-> Bm Cm) (-> (-> (-> Cm Dm) (-> (or Bm Cm) Dm)) C))) (A (-> Bm Cm)) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-2735
in-theory        2735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A -> (not B)) -> (not A)) -> C)) -> ((A -> B) -> ((A -> (not B)) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-100 tm-71 ((Am (-> (-> Bm Cm) (-> (-> (-> Bm (not Cm)) (not Bm)) C))) (A (-> Bm Cm)) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2735.         (((A -> B) -> (((A -> (not B)) -> (not A)) -> C)) -> ((A -> B) -> ((A -> (not B)) -> (not A)))), M:tm-100, m:tm-71, u:((Am (-> (-> Bm Cm) (-> (-> (-> Bm (not Cm)) (not Bm)) C))) (A (-> Bm Cm)) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-2736
in-theory        2736
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> A))) -> (A -> B)) -> ((not (not ((A -> B) -> A))) -> A))
theorem-size     21
proof            (modus-ponens tm-100 tm-77 ((Am (-> Bm C)) (A (not (not (-> (-> Bm C) Bm)))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-10)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-2736.         (((not (not ((A -> B) -> A))) -> (A -> B)) -> ((not (not ((A -> B) -> A))) -> A)), M:tm-100, m:tm-77, u:((Am (-> Bm C)) (A (not (not (-> (-> Bm C) Bm)))) (B Bm))
================================================================
tm-name          tm-2737
in-theory        2737
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (A -> B)) -> ((not (not A)) -> A))
theorem-size     13
proof            (modus-ponens tm-100 tm-78 ((Am (-> (not (not Bm)) (-> Bm C))) (A (not (not Bm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2737.         (((not (not A)) -> (A -> B)) -> ((not (not A)) -> A)), M:tm-100, m:tm-78, u:((Am (-> (not (not Bm)) (-> Bm C))) (A (not (not Bm))) (B Bm))
================================================================
tm-name          tm-2738
in-theory        2738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) -> D)) -> (A -> (B -> (C -> B))))
theorem-size     17
proof            (modus-ponens tm-100 tm-85 ((Am (-> Bm (-> (-> Cm (-> Dm Cm)) C))) (A Bm) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2738.         ((A -> ((B -> (C -> B)) -> D)) -> (A -> (B -> (C -> B)))), M:tm-100, m:tm-85, u:((Am (-> Bm (-> (-> Cm (-> Dm Cm)) C))) (A Bm) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-2739
in-theory        2739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> A) -> C)) -> ((A -> B) -> (A -> A)))
theorem-size     17
proof            (modus-ponens tm-100 tm-97 ((Am (-> (-> Bm Cm) (-> (-> Bm Bm) C))) (A (-> Bm Cm)) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2739.         (((A -> B) -> ((A -> A) -> C)) -> ((A -> B) -> (A -> A))), M:tm-100, m:tm-97, u:((Am (-> (-> Bm Cm) (-> (-> Bm Bm) C))) (A (-> Bm Cm)) (B (-> Bm Bm)))
================================================================
tm-name          tm-2740
in-theory        2740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D))))
theorem-size     27
proof            (modus-ponens tm-95 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2740.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D)))), M:tm-95, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2741
in-theory        2741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (D -> ((A -> (B -> C)) -> (A -> B))))
theorem-size     21
proof            (modus-ponens tm-84 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2741.         (((A -> (B -> C)) -> (A -> B)) -> (D -> ((A -> (B -> C)) -> (A -> B)))), M:tm-84, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-2742
in-theory        2742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-83 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2742.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-83, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2743
in-theory        2743
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> C))))
theorem-size     25
proof            (modus-ponens tm-76 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2743.         (((not (not A)) -> A) and (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> C)))), M:tm-76, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2744
in-theory        2744
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) -> (A -> B)))) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B)))
theorem-size     31
proof            (modus-ponens tm-73 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2744.         (((not (not ((A -> (B -> C)) -> (A -> B)))) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B))), M:tm-73, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-2745
in-theory        2745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D))))
theorem-size     31
proof            (modus-ponens tm-69 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2745.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D)))), M:tm-69, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2746
in-theory        2746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     33
proof            (modus-ponens tm-54 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2746.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-54, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2747
in-theory        2747
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> C)))
theorem-size     31
proof            (modus-ponens tm-47 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2747.         (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> C))), M:tm-47, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-2748
in-theory        2748
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B)))
theorem-size     31
proof            (modus-ponens tm-46 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2748.         (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B))), M:tm-46, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-2749
in-theory        2749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B)))
theorem-size     27
proof            (modus-ponens tm-45 tm-100 ((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2749.         (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B))), M:tm-45, m:tm-100, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-2750
in-theory        2750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B)))
theorem-size     23
proof            (modus-ponens tm-44 tm-100 ((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2750.         (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B))), M:tm-44, m:tm-100, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-2751
in-theory        2751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D))))
theorem-size     25
proof            (modus-ponens tm-42 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2751.         ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D)))), M:tm-42, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2752
in-theory        2752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D))))
theorem-size     25
proof            (modus-ponens tm-32 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2752.         ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D)))), M:tm-32, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2753
in-theory        2753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> B))))
theorem-size     29
proof            (modus-ponens tm-24 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2753.         (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> B)))), M:tm-24, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-2754
in-theory        2754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D))))
theorem-size     27
proof            (modus-ponens tm-23 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2754.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D)))), M:tm-23, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2755
in-theory        2755
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D))))
theorem-size     25
proof            (modus-ponens tm-22 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2755.         (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D)))), M:tm-22, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2756
in-theory        2756
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D))))
theorem-size     25
proof            (modus-ponens tm-21 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2756.         (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D)))), M:tm-21, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2757
in-theory        2757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     33
proof            (modus-ponens tm-20 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2757.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-20, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2758
in-theory        2758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D))))
theorem-size     25
proof            (modus-ponens tm-19 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2758.         ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D)))), M:tm-19, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2759
in-theory        2759
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> B)))) -> (not ((A -> (B -> C)) -> (A -> B))))
theorem-size     31
proof            (modus-ponens tm-9 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-9 tm-2 tm-1)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2759.         ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> B)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-2760
in-theory        2760
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> B))) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2760.         ((((A -> (B -> C)) -> (A -> B)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> B))) -> D)), M:tm-8, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-2761
in-theory        2761
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> C))))
theorem-size     21
proof            (modus-ponens tm-7 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-7 tm-2 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2761.         (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> C)))), M:tm-7, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2762
in-theory        2762
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) or D)
theorem-size     21
proof            (modus-ponens tm-6 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-6 tm-2 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2762.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) or D), M:tm-6, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2763
in-theory        2763
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> C))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2763.         (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> C))) and A)), M:tm-5, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2764
in-theory        2764
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> B)))
theorem-size     29
proof            (modus-ponens tm-2 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Bm))))
axioms-used      (tm-2 tm-1)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2764.         ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> B))), M:tm-2, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Bm)))
================================================================
tm-name          tm-2765
in-theory        2765
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> C))))
theorem-size     21
proof            (modus-ponens tm-1 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-1 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2765.         (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> C)))), M:tm-1, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2766
in-theory        2766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D)))))
theorem-size     39
proof            (modus-ponens tm-95 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2766.         (((A -> B) -> (A -> A)) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D))))), M:tm-95, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2767
in-theory        2767
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (D -> (not ((A -> (B -> C)) -> (A -> B)))))
theorem-size     33
proof            (modus-ponens tm-84 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2767.         ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (D -> (not ((A -> (B -> C)) -> (A -> B))))), M:tm-84, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2768
in-theory        2768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-83 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2768.         ((A -> (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-83, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2769
in-theory        2769
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C -> D)) -> (B -> C)) -> (not ((B -> (C -> D)) -> (B -> D)))) -> (not ((B -> (C -> D)) -> (B -> C)))))
theorem-size     37
proof            (modus-ponens tm-76 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-10 tm-9 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2769.         (((not (not A)) -> A) and ((((B -> (C -> D)) -> (B -> C)) -> (not ((B -> (C -> D)) -> (B -> D)))) -> (not ((B -> (C -> D)) -> (B -> C))))), M:tm-76, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2770
in-theory        2770
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))))) or (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C))))) -> (not ((A -> (B -> C)) -> (A -> B))))
theorem-size     54
proof            (modus-ponens tm-73 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-8 tm-10 tm-9 tm-2)
proof-size       170
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2770.         (((not (not (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))))) or (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C))))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-73, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2771
in-theory        2771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D)))))
theorem-size     43
proof            (modus-ponens tm-69 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2771.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D))))), M:tm-69, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2772
in-theory        2772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     45
proof            (modus-ponens tm-54 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-9 tm-2)
proof-size       169
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2772.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-54, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2773
in-theory        2773
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> (B -> C)) -> (not ((B -> (C -> D)) -> (B -> D))))) or (((B -> (C -> D)) -> (B -> C)) -> (not ((B -> (C -> D)) -> (B -> D))))) -> (not ((B -> (C -> D)) -> (B -> C))))
theorem-size     54
proof            (modus-ponens tm-47 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-8 tm-4 tm-9 tm-2)
proof-size       170
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2773.         (((A and (((B -> (C -> D)) -> (B -> C)) -> (not ((B -> (C -> D)) -> (B -> D))))) or (((B -> (C -> D)) -> (B -> C)) -> (not ((B -> (C -> D)) -> (B -> D))))) -> (not ((B -> (C -> D)) -> (B -> C)))), M:tm-47, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2774
in-theory        2774
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) and D) or (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C))))) -> (not ((A -> (B -> C)) -> (A -> B))))
theorem-size     54
proof            (modus-ponens tm-46 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-8 tm-3 tm-9 tm-2)
proof-size       170
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2774.         ((((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) and D) or (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C))))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-46, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2775
in-theory        2775
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A -> (B -> C)) -> (A -> C))) or (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C))))) -> (not ((A -> (B -> C)) -> (A -> B))))
theorem-size     42
proof            (modus-ponens tm-44 tm-101 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-8 tm-1 tm-9 tm-2)
proof-size       160
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2775.         (((not ((A -> (B -> C)) -> (A -> C))) or (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C))))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-44, m:tm-101, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2776
in-theory        2776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D)))))
theorem-size     37
proof            (modus-ponens tm-42 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2776.         ((A -> (B or A)) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D))))), M:tm-42, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2777
in-theory        2777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D)))))
theorem-size     37
proof            (modus-ponens tm-32 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2777.         ((A -> (A or B)) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D))))), M:tm-32, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2778
in-theory        2778
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) and (not ((A -> (B -> C)) -> (A -> B)))))
theorem-size     52
proof            (modus-ponens tm-24 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       168
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2778.         ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) and (not ((A -> (B -> C)) -> (A -> B))))), M:tm-24, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2779
in-theory        2779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D)))))
theorem-size     39
proof            (modus-ponens tm-23 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2779.         ((A -> (B -> (A and B))) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D))))), M:tm-23, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2780
in-theory        2780
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D)))))
theorem-size     37
proof            (modus-ponens tm-22 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-9 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2780.         (((A and B) -> B) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D))))), M:tm-22, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2781
in-theory        2781
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D)))))
theorem-size     37
proof            (modus-ponens tm-21 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-9 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2781.         (((A and B) -> A) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D))))), M:tm-21, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2782
in-theory        2782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     45
proof            (modus-ponens tm-20 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       169
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2782.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-20, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2783
in-theory        2783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D)))))
theorem-size     37
proof            (modus-ponens tm-19 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2783.         ((A -> (B -> A)) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D))))), M:tm-19, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2784
in-theory        2784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-12 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2784.         ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C))))), M:tm-12, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2785
in-theory        2785
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not (not ((A -> (B -> C)) -> (A -> B))))) -> (not (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C))))))
theorem-size     54
proof            (modus-ponens tm-9 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-9 tm-2)
proof-size       152
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2785.         (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not (not ((A -> (B -> C)) -> (A -> B))))) -> (not (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))))), M:tm-9, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2786
in-theory        2786
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A -> (B -> C)) -> (A -> B))) -> D) -> (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) or (not ((A -> (B -> C)) -> (A -> B)))) -> D))
theorem-size     46
proof            (modus-ponens tm-8 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-8 tm-9 tm-2)
proof-size       146
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2786.         (((not ((A -> (B -> C)) -> (A -> B))) -> D) -> (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) or (not ((A -> (B -> C)) -> (A -> B)))) -> D)), M:tm-8, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-2787
in-theory        2787
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> (C -> D)) -> (B -> C)) -> (not ((B -> (C -> D)) -> (B -> D)))) -> (not ((B -> (C -> D)) -> (B -> C)))))
theorem-size     33
proof            (modus-ponens tm-7 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-7 tm-9 tm-2)
proof-size       125
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2787.         (A or ((((B -> (C -> D)) -> (B -> C)) -> (not ((B -> (C -> D)) -> (B -> D)))) -> (not ((B -> (C -> D)) -> (B -> C))))), M:tm-7, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2788
in-theory        2788
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) or D)
theorem-size     33
proof            (modus-ponens tm-6 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-6 tm-9 tm-2)
proof-size       125
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2788.         (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) or D), M:tm-6, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2789
in-theory        2789
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> D)) -> (B -> C)) -> (not ((B -> (C -> D)) -> (B -> D)))) -> (not ((B -> (C -> D)) -> (B -> C)))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       129
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2789.         (A -> (((((B -> (C -> D)) -> (B -> C)) -> (not ((B -> (C -> D)) -> (B -> D)))) -> (not ((B -> (C -> D)) -> (B -> C)))) and A)), M:tm-5, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2790
in-theory        2790
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> (B -> C)) -> (not ((B -> (C -> D)) -> (B -> D)))) -> (not ((B -> (C -> D)) -> (B -> C)))))
theorem-size     33
proof            (modus-ponens tm-1 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-1 tm-9 tm-2)
proof-size       125
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2790.         (A -> ((((B -> (C -> D)) -> (B -> C)) -> (not ((B -> (C -> D)) -> (B -> D)))) -> (not ((B -> (C -> D)) -> (B -> C))))), M:tm-1, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-2791
in-theory        2791
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-102 tm-1 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2791.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-1, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2792
in-theory        2792
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> C)))
theorem-size     35
proof            (modus-ponens tm-102 tm-2 ((Am (-> Bm (-> B Cm))) (A Bm) (C Cm) (D (-> (-> (-> Bm (-> B Cm)) Bm) (-> (-> Bm (-> B Cm)) Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       139
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2792.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> C))), M:tm-102, m:tm-2, u:((Am (-> Bm (-> B Cm))) (A Bm) (C Cm) (D (-> (-> (-> Bm (-> B Cm)) Bm) (-> (-> Bm (-> B Cm)) Cm))))
================================================================
tm-name          tm-2793
in-theory        2793
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (((A -> (B -> C)) -> (A -> C)) and D)))
theorem-size     33
proof            (modus-ponens tm-102 tm-5 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> (-> A (-> B C)) (-> A C)) Bm)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       131
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2793.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (((A -> (B -> C)) -> (A -> C)) and D))), M:tm-102, m:tm-5, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> (-> A (-> B C)) (-> A C)) Bm))))
================================================================
tm-name          tm-2794
in-theory        2794
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) or D))
theorem-size     31
proof            (modus-ponens tm-102 tm-6 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> (-> A (-> B C)) (-> A C)) Bm))))
axioms-used      (tm-8 tm-2 tm-6)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2794.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) or D)), M:tm-102, m:tm-6, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> (-> A (-> B C)) (-> A C)) Bm)))
================================================================
tm-name          tm-2795
in-theory        2795
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or ((A -> (B -> C)) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-102 tm-7 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-7)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2795.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-7, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2796
in-theory        2796
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> (B -> C)) or (A -> C)) -> D)))
theorem-size     37
proof            (modus-ponens tm-102 tm-8 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A (-> B C)) (-> A C)) Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       141
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2796.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> (B -> C)) or (A -> C)) -> D))), M:tm-102, m:tm-8, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A (-> B C)) (-> A C)) Cm))))
================================================================
tm-name          tm-2797
in-theory        2797
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (not (A -> C))) -> (not (A -> (B -> C)))))
theorem-size     37
proof            (modus-ponens tm-102 tm-9 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> (-> A (-> B C)) (not (-> A C))) (not (-> A (-> B C)))))))
axioms-used      (tm-8 tm-2 tm-9)
proof-size       139
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2797.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (not (A -> C))) -> (not (A -> (B -> C))))), M:tm-102, m:tm-9, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> (-> A (-> B C)) (not (-> A C))) (not (-> A (-> B C))))))
================================================================
tm-name          tm-2798
in-theory        2798
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-102 tm-11 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2798.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (E -> D))), M:tm-102, m:tm-11, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-2799
in-theory        2799
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> (A -> (B -> C))))
theorem-size     31
proof            (modus-ponens tm-102 tm-12 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> A (-> B C)) (-> A (-> B C))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-2799.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> (A -> (B -> C)))), M:tm-102, m:tm-12, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> A (-> B C)) (-> A (-> B C)))))
================================================================
tm-name          tm-2800
in-theory        2800
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> B)) -> (A -> B)) or ((A -> (B -> B)) -> (A -> B))) -> ((A -> (B -> B)) -> (A -> B)))
theorem-size     29
proof            (modus-ponens tm-102 tm-13 ((B Cm) (Bm Cm) (A Am) (C Cm) (D (-> (-> Am (-> Cm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2800.         ((((A -> (B -> B)) -> (A -> B)) or ((A -> (B -> B)) -> (A -> B))) -> ((A -> (B -> B)) -> (A -> B))), M:tm-102, m:tm-13, u:((B Cm) (Bm Cm) (A Am) (C Cm) (D (-> (-> Am (-> Cm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2801
in-theory        2801
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-102 tm-14 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2801.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-102, m:tm-14, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-2802
in-theory        2802
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-102 tm-16 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2802.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D and E) -> D)), M:tm-102, m:tm-16, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-2803
in-theory        2803
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-102 tm-18 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2803.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D and E) -> E)), M:tm-102, m:tm-18, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-2804
in-theory        2804
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-102 tm-19 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2804.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-19, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2805
in-theory        2805
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-102 tm-20 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2805.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-20, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2806
in-theory        2806
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D and E) -> D) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-102 tm-21 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2806.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D and E) -> D) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-21, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2807
in-theory        2807
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D and E) -> E) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-102 tm-22 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2807.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D and E) -> E) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-22, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2808
in-theory        2808
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-23 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2808.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-23, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2809
in-theory        2809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> ((A -> (B -> C)) and (A -> C))))
theorem-size     35
proof            (modus-ponens tm-102 tm-24 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> A (-> B C)) (and (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-2809.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> ((A -> (B -> C)) and (A -> C)))), M:tm-102, m:tm-24, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> A (-> B C)) (and (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2810
in-theory        2810
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (E -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-102 tm-25 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2810.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-102, m:tm-25, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-2811
in-theory        2811
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (D or E)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-102 tm-32 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2811.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (D or E)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-32, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2812
in-theory        2812
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-102 tm-33 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2812.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (D or E))), M:tm-102, m:tm-33, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-2813
in-theory        2813
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E or D)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-102 tm-42 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2813.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E or D)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-42, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2814
in-theory        2814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-102 tm-43 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2814.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (E or D))), M:tm-102, m:tm-43, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-2815
in-theory        2815
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((B -> C) or (A -> (B -> C))) -> (A -> C)))
theorem-size     33
proof            (modus-ponens tm-102 tm-44 ((A Am) (Bm (-> B C)) (Cm (-> Am C)) (D (-> (or (-> B C) (-> Am (-> B C))) (-> Am C)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2815.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((B -> C) or (A -> (B -> C))) -> (A -> C))), M:tm-102, m:tm-44, u:((A Am) (Bm (-> B C)) (Cm (-> Am C)) (D (-> (or (-> B C) (-> Am (-> B C))) (-> Am C))))
================================================================
tm-name          tm-2816
in-theory        2816
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((A -> B) -> A)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> C)))
theorem-size     47
proof            (modus-ponens tm-102 tm-45 ((A (-> Am Bm)) (B Am) (C Cm) (Dm (-> (-> Am Bm) Cm)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       189
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2816.         (((((A -> B) -> (A -> C)) -> ((A -> B) -> A)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> C))), M:tm-102, m:tm-45, u:((A (-> Am Bm)) (B Am) (C Cm) (Dm (-> (-> Am Bm) Cm)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-2817
in-theory        2817
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> C)))
theorem-size     37
proof            (modus-ponens tm-102 tm-46 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (or (and (-> A (-> B C)) Cm) (-> A (-> B C))) (-> A C)))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2817.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> C))), M:tm-102, m:tm-46, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (or (and (-> A (-> B C)) Cm) (-> A (-> B C))) (-> A C))))
================================================================
tm-name          tm-2818
in-theory        2818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D and (A -> (B -> C))) or (A -> (B -> C))) -> (A -> C)))
theorem-size     37
proof            (modus-ponens tm-102 tm-47 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (or (and Cm (-> A (-> B C))) (-> A (-> B C))) (-> A C)))))
axioms-used      (tm-8 tm-2 tm-4)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2818.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D and (A -> (B -> C))) or (A -> (B -> C))) -> (A -> C))), M:tm-102, m:tm-47, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (or (and Cm (-> A (-> B C))) (-> A (-> B C))) (-> A C))))
================================================================
tm-name          tm-2819
in-theory        2819
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (C or A))) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> B))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> B)))
theorem-size     53
proof            (modus-ponens tm-102 tm-51 ((A (-> Am Bm)) (B (or Cm Am)) (C Bm) (Dm (-> (-> Am Bm) Bm)) (D (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2)
proof-size       197
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2819.         (((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> (C or A))) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> B))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> B))), M:tm-102, m:tm-51, u:((A (-> Am Bm)) (B (or Cm Am)) (C Bm) (Dm (-> (-> Am Bm) Bm)) (D (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-2820
in-theory        2820
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-102 tm-54 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2820.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-54, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2821
in-theory        2821
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> B)) -> ((A -> B) -> A)) or (((A -> B) -> (A -> B)) -> ((A -> B) -> B))) -> (((A -> B) -> (A -> B)) -> (((A -> B) or (A -> B)) -> B)))
theorem-size     45
proof            (modus-ponens tm-102 tm-55 ((Am (-> B Cm)) (Bm (-> B Cm)) (A (-> B Cm)) (C Cm) (D (-> (-> (-> B Cm) (-> B Cm)) (-> (or (-> B Cm) (-> B Cm)) Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       179
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-2821.         (((((A -> B) -> (A -> B)) -> ((A -> B) -> A)) or (((A -> B) -> (A -> B)) -> ((A -> B) -> B))) -> (((A -> B) -> (A -> B)) -> (((A -> B) or (A -> B)) -> B))), M:tm-102, m:tm-55, u:((Am (-> B Cm)) (Bm (-> B Cm)) (A (-> B Cm)) (C Cm) (D (-> (-> (-> B Cm) (-> B Cm)) (-> (or (-> B Cm) (-> B Cm)) Cm))))
================================================================
tm-name          tm-2822
in-theory        2822
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-102 tm-56 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2822.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-102, m:tm-56, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-2823
in-theory        2823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-102 tm-69 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-9)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2823.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-69, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2824
in-theory        2824
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     31
proof            (modus-ponens tm-102 tm-71 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-9)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2824.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-102, m:tm-71, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-2825
in-theory        2825
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((not (not (A -> (B -> C)))) or (A -> (B -> C))) -> (A -> C)))
theorem-size     37
proof            (modus-ponens tm-102 tm-73 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (or (not (not (-> A (-> B C)))) (-> A (-> B C))) (-> A C)))))
axioms-used      (tm-8 tm-2 tm-10)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2825.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((not (not (A -> (B -> C)))) or (A -> (B -> C))) -> (A -> C))), M:tm-102, m:tm-73, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (or (not (not (-> A (-> B C)))) (-> A (-> B C))) (-> A C))))
================================================================
tm-name          tm-2826
in-theory        2826
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((not (not D)) -> D) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-102 tm-76 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (not (not Bm)) Bm) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-10)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2826.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((not (not D)) -> D) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-76, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (not (not Bm)) Bm) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2827
in-theory        2827
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((not (not D)) -> D))
theorem-size     25
proof            (modus-ponens tm-102 tm-78 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-10)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2827.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((not (not D)) -> D)), M:tm-102, m:tm-78, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-2828
in-theory        2828
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> (A -> B)) or ((A -> (B -> A)) -> (A -> A))) -> ((C or (A -> (B -> A))) -> (A -> A)))
theorem-size     31
proof            (modus-ponens tm-102 tm-80 ((A Am) (B Bm) (C Am) (Cm (-> Am Am)) (D (-> (or Dm (-> Am (-> Bm Am))) (-> Am Am)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2828.         ((((A -> (B -> A)) -> (A -> B)) or ((A -> (B -> A)) -> (A -> A))) -> ((C or (A -> (B -> A))) -> (A -> A))), M:tm-102, m:tm-80, u:((A Am) (B Bm) (C Am) (Cm (-> Am Am)) (D (-> (or Dm (-> Am (-> Bm Am))) (-> Am Am))))
================================================================
tm-name          tm-2829
in-theory        2829
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> (F -> E))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-83 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2829.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> (F -> E))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-83, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2830
in-theory        2830
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> (D -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-102 tm-84 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> A (-> B C)) (-> Cm (-> A C))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2830.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> (D -> (A -> C)))), M:tm-102, m:tm-84, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> A (-> B C)) (-> Cm (-> A C)))))
================================================================
tm-name          tm-2831
in-theory        2831
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (E -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-102 tm-85 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2831.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (E -> (F -> E)))), M:tm-102, m:tm-85, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-2832
in-theory        2832
times-derived    4
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     29
proof            (modus-ponens tm-102 tm-86 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> A (-> B C)) (-> A C)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2832.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-102, m:tm-86, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> A (-> B C)) (-> A C))))
================================================================
tm-name          tm-2833
in-theory        2833
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> B)) -> ((A -> B) -> A)) or (((A -> B) -> (A -> B)) -> ((A -> B) -> B))) -> ((((A -> B) -> C) or ((A -> B) -> (A -> B))) -> ((A -> B) -> B)))
theorem-size     47
proof            (modus-ponens tm-102 tm-92 ((A (-> B C)) (Am (-> B C)) (Bm (-> (-> B C) C)) (D (-> (or (-> (-> B C) Cm) (-> (-> B C) (-> B C))) (-> (-> B C) C)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2833.         (((((A -> B) -> (A -> B)) -> ((A -> B) -> A)) or (((A -> B) -> (A -> B)) -> ((A -> B) -> B))) -> ((((A -> B) -> C) or ((A -> B) -> (A -> B))) -> ((A -> B) -> B))), M:tm-102, m:tm-92, u:((A (-> B C)) (Am (-> B C)) (Bm (-> (-> B C) C)) (D (-> (or (-> (-> B C) Cm) (-> (-> B C) (-> B C))) (-> (-> B C) C))))
================================================================
tm-name          tm-2834
in-theory        2834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> (D -> D)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-95 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2834.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> (D -> D)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-95, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-2835
in-theory        2835
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> E) -> (D -> D)))
theorem-size     27
proof            (modus-ponens tm-102 tm-97 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2835.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> E) -> (D -> D))), M:tm-102, m:tm-97, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-2836
in-theory        2836
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> ((A -> (B -> C)) -> A)) or (((A -> (B -> C)) -> (A -> C)) -> ((A -> (B -> C)) -> C))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> C)))
theorem-size     63
proof            (modus-ponens tm-102 tm-102 ((A (-> Am (-> Bm Cm))) (B Am) (C Cm) (Dm (-> (-> Am (-> Bm Cm)) Cm)) (D (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> (-> Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       245
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2836.         (((((A -> (B -> C)) -> (A -> C)) -> ((A -> (B -> C)) -> A)) or (((A -> (B -> C)) -> (A -> C)) -> ((A -> (B -> C)) -> C))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> C))), M:tm-102, m:tm-102, u:((A (-> Am (-> Bm Cm))) (B Am) (C Cm) (Dm (-> (-> Am (-> Bm Cm)) Cm)) (D (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> (-> Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-2837
in-theory        2837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F)))
theorem-size     41
proof            (modus-ponens tm-95 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2837.         (((A -> B) -> (A -> A)) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F))), M:tm-95, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2838
in-theory        2838
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) or (((A -> (B -> C)) -> (A -> C)) -> ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     61
proof            (modus-ponens tm-92 tm-102 ((Dm (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2838.         (((((A -> (B -> C)) -> (A -> C)) -> D) or (((A -> (B -> C)) -> (A -> C)) -> ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-92, m:tm-102, u:((Dm (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-2839
in-theory        2839
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> D) -> (E -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))
theorem-size     35
proof            (modus-ponens tm-84 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2839.         ((((A -> (B -> C)) -> (A -> C)) -> D) -> (E -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))), M:tm-84, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2840
in-theory        2840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-83 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2840.         ((A -> (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-83, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2841
in-theory        2841
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> D)) -> (E -> ((B -> (C -> D)) -> (B -> D))))) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> (E -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     55
proof            (modus-ponens tm-80 tm-102 ((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (Dm (-> B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2841.         ((A or (((B -> (C -> D)) -> (B -> D)) -> (E -> ((B -> (C -> D)) -> (B -> D))))) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> (E -> ((B -> (C -> D)) -> (B -> D))))), M:tm-80, m:tm-102, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (Dm (-> B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-2842
in-theory        2842
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C -> D)) -> (B -> D)) -> E) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> E)))
theorem-size     39
proof            (modus-ponens tm-76 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2842.         (((not (not A)) -> A) and ((((B -> (C -> D)) -> (B -> D)) -> E) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> E))), M:tm-76, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2843
in-theory        2843
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (B -> C)) -> (A -> C)) -> D))) or (((A -> (B -> C)) -> (A -> C)) -> D)) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))
theorem-size     47
proof            (modus-ponens tm-73 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2843.         (((not (not (((A -> (B -> C)) -> (A -> C)) -> D))) or (((A -> (B -> C)) -> (A -> C)) -> D)) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-73, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2844
in-theory        2844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F)))
theorem-size     45
proof            (modus-ponens tm-69 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       169
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2844.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F))), M:tm-69, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2845
in-theory        2845
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> (((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> C)) or (((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C)))) -> (((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C)))))
theorem-size     79
proof            (modus-ponens tm-55 tm-102 ((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (Dm (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (B (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-8)
proof-size       213
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2845.         ((((A -> (B -> C)) -> (A -> C)) -> (((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> C)) or (((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C)))) -> (((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))))), M:tm-55, m:tm-102, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (Dm (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (B (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-2846
in-theory        2846
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     47
proof            (modus-ponens tm-54 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       175
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2846.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-54, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2847
in-theory        2847
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) or (((B -> (C -> D)) -> (B -> D)) -> ((A or (B -> (C -> D))) -> (B -> D)))) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> ((A or (B -> (C -> D))) -> (B -> D))))
theorem-size     61
proof            (modus-ponens tm-51 tm-102 ((A (-> Am (-> Bm Cm))) (B (-> Am Cm)) (Dm (-> (or C (-> Am (-> Bm Cm))) (-> Am Cm))) (D (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> (or C (-> Am (-> Bm Cm))) (-> Am Cm))))))
axioms-used      (tm-8 tm-2)
proof-size       205
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2847.         (((A -> (B -> (C -> D))) or (((B -> (C -> D)) -> (B -> D)) -> ((A or (B -> (C -> D))) -> (B -> D)))) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> ((A or (B -> (C -> D))) -> (B -> D)))), M:tm-51, m:tm-102, u:((A (-> Am (-> Bm Cm))) (B (-> Am Cm)) (Dm (-> (or C (-> Am (-> Bm Cm))) (-> Am Cm))) (D (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> (or C (-> Am (-> Bm Cm))) (-> Am Cm)))))
================================================================
tm-name          tm-2848
in-theory        2848
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> D)) -> (A and ((B -> (C -> D)) -> (B -> D))))) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> (A and ((B -> (C -> D)) -> (B -> D)))))
theorem-size     55
proof            (modus-ponens tm-48 tm-102 ((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (Dm (and B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (and B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       183
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2848.         ((A or (((B -> (C -> D)) -> (B -> D)) -> (A and ((B -> (C -> D)) -> (B -> D))))) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> (A and ((B -> (C -> D)) -> (B -> D))))), M:tm-48, m:tm-102, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (Dm (and B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (and B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-2849
in-theory        2849
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> (B -> D)) -> E)) or (((B -> (C -> D)) -> (B -> D)) -> E)) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> E))
theorem-size     47
proof            (modus-ponens tm-47 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2849.         (((A and (((B -> (C -> D)) -> (B -> D)) -> E)) or (((B -> (C -> D)) -> (B -> D)) -> E)) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> E)), M:tm-47, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2850
in-theory        2850
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> C)) -> D) and E) or (((A -> (B -> C)) -> (A -> C)) -> D)) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))
theorem-size     47
proof            (modus-ponens tm-46 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2850.         ((((((A -> (B -> C)) -> (A -> C)) -> D) and E) or (((A -> (B -> C)) -> (A -> C)) -> D)) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-46, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2851
in-theory        2851
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> C) -> D)) or (((A -> (B -> C)) -> (A -> C)) -> ((A -> (B -> C)) -> D))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> D)))
theorem-size     57
proof            (modus-ponens tm-45 tm-102 ((A (-> Am (-> Bm Cm))) (B (-> Am Cm)) (Dm (-> (-> Am (-> Bm Cm)) C)) (D (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> (-> Am (-> Bm Cm)) C)))))
axioms-used      (tm-8 tm-2)
proof-size       199
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2851.         ((((A -> (B -> C)) -> ((A -> C) -> D)) or (((A -> (B -> C)) -> (A -> C)) -> ((A -> (B -> C)) -> D))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> D))), M:tm-45, m:tm-102, u:((A (-> Am (-> Bm Cm))) (B (-> Am Cm)) (Dm (-> (-> Am (-> Bm Cm)) C)) (D (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> (-> Am (-> Bm Cm)) C))))
================================================================
tm-name          tm-2852
in-theory        2852
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> D)) -> A)) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> A))
theorem-size     35
proof            (modus-ponens tm-44 tm-102 ((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (B Dm) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2852.         ((A or (((B -> (C -> D)) -> (B -> D)) -> A)) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> A)), M:tm-44, m:tm-102, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (B Dm) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2853
in-theory        2853
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F)))
theorem-size     39
proof            (modus-ponens tm-42 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2853.         ((A -> (B or A)) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F))), M:tm-42, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2854
in-theory        2854
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F)))
theorem-size     39
proof            (modus-ponens tm-32 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2854.         ((A -> (A or B)) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F))), M:tm-32, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2855
in-theory        2855
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> C)) -> D) and ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))
theorem-size     45
proof            (modus-ponens tm-24 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2855.         ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> C)) -> D) and ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))), M:tm-24, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2856
in-theory        2856
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F)))
theorem-size     41
proof            (modus-ponens tm-23 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2856.         ((A -> (B -> (A and B))) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F))), M:tm-23, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2857
in-theory        2857
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F)))
theorem-size     39
proof            (modus-ponens tm-22 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2857.         (((A and B) -> B) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F))), M:tm-22, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2858
in-theory        2858
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F)))
theorem-size     39
proof            (modus-ponens tm-21 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2858.         (((A and B) -> A) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F))), M:tm-21, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2859
in-theory        2859
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     47
proof            (modus-ponens tm-20 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       175
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2859.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-20, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2860
in-theory        2860
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F)))
theorem-size     39
proof            (modus-ponens tm-19 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2860.         ((A -> (B -> A)) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F))), M:tm-19, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2861
in-theory        2861
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> D) -> (((A -> (B -> C)) -> (A -> C)) -> D))
theorem-size     23
proof            (modus-ponens tm-12 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2861.         ((((A -> (B -> C)) -> (A -> C)) -> D) -> (((A -> (B -> C)) -> (A -> C)) -> D)), M:tm-12, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2862
in-theory        2862
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> (not ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))) -> (not (((A -> (B -> C)) -> (A -> C)) -> D)))
theorem-size     47
proof            (modus-ponens tm-9 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-9 tm-8 tm-2)
proof-size       149
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2862.         (((((A -> (B -> C)) -> (A -> C)) -> D) -> (not ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))) -> (not (((A -> (B -> C)) -> (A -> C)) -> D))), M:tm-9, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2863
in-theory        2863
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D) -> E) -> (((((A -> (B -> C)) -> (A -> C)) -> D) or ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) -> E))
theorem-size     59
proof            (modus-ponens tm-8 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-2)
proof-size       163
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2863.         ((((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D) -> E) -> (((((A -> (B -> C)) -> (A -> C)) -> D) or ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2864
in-theory        2864
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> (C -> D)) -> (B -> D)) -> E) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> E)))
theorem-size     35
proof            (modus-ponens tm-7 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-7 tm-8 tm-2)
proof-size       131
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2864.         (A or ((((B -> (C -> D)) -> (B -> D)) -> E) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> E))), M:tm-7, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2865
in-theory        2865
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) or E)
theorem-size     35
proof            (modus-ponens tm-6 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-6 tm-8 tm-2)
proof-size       131
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2865.         (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2866
in-theory        2866
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> D)) -> (B -> D)) -> E) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> E)) and A))
theorem-size     37
proof            (modus-ponens tm-5 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       135
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2866.         (A -> (((((B -> (C -> D)) -> (B -> D)) -> E) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2867
in-theory        2867
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> (((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> C)) -> D) -> D))
theorem-size     45
proof            (modus-ponens tm-2 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C Dm)))
axioms-used      (tm-2 tm-8)
proof-size       149
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2867.         (((((A -> (B -> C)) -> (A -> C)) -> D) -> (((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C Dm))
================================================================
tm-name          tm-2868
in-theory        2868
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> (B -> D)) -> E) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> E)))
theorem-size     35
proof            (modus-ponens tm-1 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       131
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-2868.         (A -> ((((B -> (C -> D)) -> (B -> D)) -> E) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> E))), M:tm-1, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2869
in-theory        2869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2869.         (((A -> B) -> (A -> A)) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-95, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2870
in-theory        2870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2870.         ((A -> (B -> (C -> B))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-83, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2871
in-theory        2871
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2871.         (((not (not A)) -> A) and (B or (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))), M:tm-76, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2872
in-theory        2872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2872.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-69, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2873
in-theory        2873
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2873.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-54, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2874
in-theory        2874
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2874.         ((A -> (B or A)) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-42, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2875
in-theory        2875
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2875.         ((A -> (A or B)) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-32, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2876
in-theory        2876
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2876.         ((A -> (B -> (A and B))) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-23, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2877
in-theory        2877
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2877.         (((A and B) -> B) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-22, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2878
in-theory        2878
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2878.         (((A and B) -> A) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-21, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2879
in-theory        2879
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2879.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-20, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2880
in-theory        2880
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2880.         ((A -> (B -> A)) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-19, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2881
in-theory        2881
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-7 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2881.         (A or (B or (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))), M:tm-7, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2882
in-theory        2882
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-6 tm-7 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2882.         ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) or E), M:tm-6, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2883
in-theory        2883
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2883.         (A -> ((B or (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and A)), M:tm-5, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2884
in-theory        2884
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-1 tm-7 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2884.         (A -> (B or (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))), M:tm-1, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-2885
in-theory        2885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F))
theorem-size     29
proof            (modus-ponens tm-95 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2885.         (((A -> B) -> (A -> A)) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F)), M:tm-95, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2886
in-theory        2886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-83 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2886.         ((A -> (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-83, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2887
in-theory        2887
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) or E))
theorem-size     27
proof            (modus-ponens tm-76 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2887.         (((not (not A)) -> A) and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) or E)), M:tm-76, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2888
in-theory        2888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F))
theorem-size     33
proof            (modus-ponens tm-69 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2888.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F)), M:tm-69, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2889
in-theory        2889
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     35
proof            (modus-ponens tm-54 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2889.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-54, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2890
in-theory        2890
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F))
theorem-size     27
proof            (modus-ponens tm-42 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2890.         ((A -> (B or A)) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F)), M:tm-42, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2891
in-theory        2891
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F))
theorem-size     27
proof            (modus-ponens tm-32 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2891.         ((A -> (A or B)) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F)), M:tm-32, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2892
in-theory        2892
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F))
theorem-size     29
proof            (modus-ponens tm-23 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2892.         ((A -> (B -> (A and B))) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F)), M:tm-23, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2893
in-theory        2893
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F))
theorem-size     27
proof            (modus-ponens tm-22 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2893.         (((A and B) -> B) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F)), M:tm-22, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2894
in-theory        2894
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F))
theorem-size     27
proof            (modus-ponens tm-21 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2894.         (((A and B) -> A) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F)), M:tm-21, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2895
in-theory        2895
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     35
proof            (modus-ponens tm-20 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2895.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-20, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2896
in-theory        2896
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F))
theorem-size     27
proof            (modus-ponens tm-19 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2896.         ((A -> (B -> A)) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F)), M:tm-19, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2897
in-theory        2897
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) or E))
theorem-size     23
proof            (modus-ponens tm-7 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-7 tm-6 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2897.         (A or ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) or E)), M:tm-7, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2898
in-theory        2898
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-6 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2898.         (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) or E), M:tm-6, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2899
in-theory        2899
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) or E) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2899.         (A -> (((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) or E) and A)), M:tm-5, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2900
in-theory        2900
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) or E))
theorem-size     23
proof            (modus-ponens tm-1 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-1 tm-6 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2900.         (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) or E)), M:tm-1, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2901
in-theory        2901
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-105 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2901.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> D))), M:tm-105, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-2902
in-theory        2902
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       121
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2902.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-105, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-2903
in-theory        2903
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-105 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-2903.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> D)), M:tm-105, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-2904
in-theory        2904
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-105 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-2904.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> E)), M:tm-105, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-2905
in-theory        2905
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-105 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2905.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-105, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-2906
in-theory        2906
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-105 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-2906.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D or E))), M:tm-105, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-2907
in-theory        2907
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-105 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2907.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or D))), M:tm-105, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-2908
in-theory        2908
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       121
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2908.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-105, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-2909
in-theory        2909
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     31
proof            (modus-ponens tm-105 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2909.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-105, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-2910
in-theory        2910
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((not (not D)) -> D))
theorem-size     25
proof            (modus-ponens tm-105 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-2910.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((not (not D)) -> D)), M:tm-105, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-2911
in-theory        2911
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-105 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2911.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-105, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-2912
in-theory        2912
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (D -> D)))
theorem-size     27
proof            (modus-ponens tm-105 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-2912.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-105, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-2913
in-theory        2913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-105 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-2913.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-105, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-2914
in-theory        2914
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2914.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-105, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-2915
in-theory        2915
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-105 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-2915.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-105, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-2916
in-theory        2916
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-105 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2916.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-105, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-2917
in-theory        2917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     35
proof            (modus-ponens tm-105 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-2917.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-105, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-2918
in-theory        2918
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E and F) -> F)))
theorem-size     27
proof            (modus-ponens tm-105 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2918.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-105, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-2919
in-theory        2919
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> E)) and D)))
theorem-size     29
proof            (modus-ponens tm-105 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2919.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-105, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-2920
in-theory        2920
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     37
proof            (modus-ponens tm-105 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2920.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-105, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-2921
in-theory        2921
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E and F) -> E) and D)))
theorem-size     29
proof            (modus-ponens tm-105 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2921.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-105, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-2922
in-theory        2922
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E and F) -> F) and D)))
theorem-size     29
proof            (modus-ponens tm-105 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2922.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-105, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-2923
in-theory        2923
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2923.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-105, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-2924
in-theory        2924
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (D -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-105 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-2924.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-105, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-2925
in-theory        2925
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (F -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2925.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-105, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-2926
in-theory        2926
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) or F))
theorem-size     27
proof            (modus-ponens tm-105 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2926.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-105, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-2927
in-theory        2927
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     35
proof            (modus-ponens tm-105 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2927.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-105, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-2928
in-theory        2928
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) or F))
theorem-size     27
proof            (modus-ponens tm-105 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2928.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-105, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-2929
in-theory        2929
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) or F))
theorem-size     27
proof            (modus-ponens tm-105 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2929.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-105, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-2930
in-theory        2930
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) or F))
theorem-size     29
proof            (modus-ponens tm-105 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2930.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-105, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-2931
in-theory        2931
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) or F))
theorem-size     27
proof            (modus-ponens tm-105 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2931.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-105, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-2932
in-theory        2932
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (E or F)) and D)))
theorem-size     29
proof            (modus-ponens tm-105 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2932.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-105, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-2933
in-theory        2933
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (E or F))))
theorem-size     27
proof            (modus-ponens tm-105 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2933.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-105, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-2934
in-theory        2934
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-105 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2934.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-105, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-2935
in-theory        2935
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-2935.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-105, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-2936
in-theory        2936
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-105 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2936.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-105, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-2937
in-theory        2937
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E and F) -> F)))
theorem-size     27
proof            (modus-ponens tm-105 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2937.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-105, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-2938
in-theory        2938
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (F -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2938.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-105, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-2939
in-theory        2939
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (E or F))))
theorem-size     27
proof            (modus-ponens tm-105 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2939.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-105, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-2940
in-theory        2940
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (F or E))))
theorem-size     27
proof            (modus-ponens tm-105 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2940.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-105, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-2941
in-theory        2941
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) or F))
theorem-size     27
proof            (modus-ponens tm-105 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2941.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-105, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-2942
in-theory        2942
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F or E)) and D)))
theorem-size     29
proof            (modus-ponens tm-105 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2942.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-105, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-2943
in-theory        2943
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (F or E))))
theorem-size     27
proof            (modus-ponens tm-105 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2943.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-105, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-2944
in-theory        2944
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-105 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2944.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-105, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-2945
in-theory        2945
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-105 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2945.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-105, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-2946
in-theory        2946
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     31
proof            (modus-ponens tm-105 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2946.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-105, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-2947
in-theory        2947
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     31
proof            (modus-ponens tm-105 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2947.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-105, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-2948
in-theory        2948
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-105 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2948.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-105, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-2949
in-theory        2949
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-105 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2949.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-105, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-2950
in-theory        2950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-105 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2950.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-105, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-2951
in-theory        2951
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     47
proof            (modus-ponens tm-105 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       175
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2951.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-105, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-2952
in-theory        2952
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2952.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-105, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-2953
in-theory        2953
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     35
proof            (modus-ponens tm-105 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2953.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-105, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-2954
in-theory        2954
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     37
proof            (modus-ponens tm-105 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2954.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-105, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-2955
in-theory        2955
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     37
proof            (modus-ponens tm-105 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-2955.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-105, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-2956
in-theory        2956
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2956.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-105, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-2957
in-theory        2957
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-105 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2957.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (E -> D))) -> (not D))), M:tm-105, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-2958
in-theory        2958
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2958.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-105, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-2959
in-theory        2959
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     31
proof            (modus-ponens tm-105 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-3)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2959.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-105, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-2960
in-theory        2960
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     31
proof            (modus-ponens tm-105 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-4)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2960.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-105, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-2961
in-theory        2961
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2961.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-105, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-2962
in-theory        2962
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (D or E))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-105 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-6)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2962.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (D or E))) -> (not D))), M:tm-105, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-2963
in-theory        2963
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (E or D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-105 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-7)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2963.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (E or D))) -> (not D))), M:tm-105, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-2964
in-theory        2964
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     39
proof            (modus-ponens tm-105 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2964.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-105, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2965
in-theory        2965
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     37
proof            (modus-ponens tm-105 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2965.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-105, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2966
in-theory        2966
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     43
proof            (modus-ponens tm-105 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-9)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2966.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-105, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-2967
in-theory        2967
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-9)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2967.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-105, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-2968
in-theory        2968
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     33
proof            (modus-ponens tm-105 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-9)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2968.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-105, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-2969
in-theory        2969
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     35
proof            (modus-ponens tm-105 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2969.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-105, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-2970
in-theory        2970
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     35
proof            (modus-ponens tm-105 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-2970.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-105, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-2971
in-theory        2971
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2971.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-105, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-2972
in-theory        2972
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     31
proof            (modus-ponens tm-105 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-2 tm-9 tm-10)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2972.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-105, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-2973
in-theory        2973
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     31
proof            (modus-ponens tm-105 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-10)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2973.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-105, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-2974
in-theory        2974
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((not (not E)) -> E)))
theorem-size     27
proof            (modus-ponens tm-105 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-10)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2974.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((not (not E)) -> E))), M:tm-105, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-2975
in-theory        2975
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((not (not D)) -> D) or E))
theorem-size     27
proof            (modus-ponens tm-105 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-6 tm-10)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2975.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((not (not D)) -> D) or E)), M:tm-105, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-2976
in-theory        2976
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((not (not E)) -> E) and D)))
theorem-size     29
proof            (modus-ponens tm-105 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2976.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((not (not E)) -> E) and D))), M:tm-105, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-2977
in-theory        2977
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     35
proof            (modus-ponens tm-105 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-2977.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-105, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-2978
in-theory        2978
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((not (not E)) -> E)))
theorem-size     27
proof            (modus-ponens tm-105 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2978.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((not (not E)) -> E))), M:tm-105, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-2979
in-theory        2979
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2979.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-105, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-2980
in-theory        2980
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-105 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2980.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-105, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-2981
in-theory        2981
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (F -> (G -> F)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2981.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (F -> (G -> F))))), M:tm-105, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2982
in-theory        2982
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (F -> E))) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2982.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (F -> E))) or G)), M:tm-105, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-2983
in-theory        2983
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2983.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-105, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-2984
in-theory        2984
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (D -> (F -> E))))
theorem-size     29
proof            (modus-ponens tm-105 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-2984.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (D -> (F -> E)))), M:tm-105, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-2985
in-theory        2985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (F -> (G -> F)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2985.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (F -> (G -> F))))), M:tm-105, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-2986
in-theory        2986
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> D))
theorem-size     23
proof            (modus-ponens tm-105 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2986.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> D)), M:tm-105, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-2987
in-theory        2987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-2987.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-105, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-2988
in-theory        2988
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> (D and E)))
theorem-size     27
proof            (modus-ponens tm-105 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2988.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> (D and E))), M:tm-105, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-2989
in-theory        2989
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (D -> E)))
theorem-size     27
proof            (modus-ponens tm-105 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2989.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (D -> E))), M:tm-105, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-2990
in-theory        2990
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((not (not D)) -> (not (not D))))
theorem-size     27
proof            (modus-ponens tm-105 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2990.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((not (not D)) -> (not (not D)))), M:tm-105, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-2991
in-theory        2991
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     33
proof            (modus-ponens tm-105 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2991.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-105, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-2992
in-theory        2992
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     35
proof            (modus-ponens tm-105 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-2992.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-105, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-2993
in-theory        2993
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> F) -> (E -> E))))
theorem-size     29
proof            (modus-ponens tm-105 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2993.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> F) -> (E -> E)))), M:tm-105, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2994
in-theory        2994
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (D -> D)) or F))
theorem-size     29
proof            (modus-ponens tm-105 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2994.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (D -> D)) or F)), M:tm-105, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-2995
in-theory        2995
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2995.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-105, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-2996
in-theory        2996
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-2996.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-105, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-2997
in-theory        2997
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> F) -> (E -> E))))
theorem-size     29
proof            (modus-ponens tm-105 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-2997.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> F) -> (E -> E)))), M:tm-105, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-2998
in-theory        2998
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-2998.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-105, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-2999
in-theory        2999
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     29
proof            (modus-ponens tm-105 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-2999.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D -> E)) -> (D -> E))), M:tm-105, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-3000
in-theory        3000
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     39
proof            (modus-ponens tm-105 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3000.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-105, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-3001
in-theory        3001
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     51
proof            (modus-ponens tm-105 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       213
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3001.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-105, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-3002
in-theory        3002
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     53
proof            (modus-ponens tm-105 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       219
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3002.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-105, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-3003
in-theory        3003
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3003.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-105, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3004
in-theory        3004
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     41
proof            (modus-ponens tm-105 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3004.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-105, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-3005
in-theory        3005
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     43
proof            (modus-ponens tm-105 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3005.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-105, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3006
in-theory        3006
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     49
proof            (modus-ponens tm-102 tm-105 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3006.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-105, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-3007
in-theory        3007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C)))
theorem-size     31
proof            (modus-ponens tm-95 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3007.         (((A -> B) -> (A -> A)) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C))), M:tm-95, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3008
in-theory        3008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> A)))
theorem-size     31
proof            (modus-ponens tm-92 tm-105 ((Am (-> A A)) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3008.         (((A -> B) or (A -> A)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> A))), M:tm-92, m:tm-105, u:((Am (-> A A)) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A A))))
================================================================
tm-name          tm-3009
in-theory        3009
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and A)))
theorem-size     25
proof            (modus-ponens tm-84 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3009.         (A -> (B -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and A))), M:tm-84, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-3010
in-theory        3010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-83 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3010.         ((A -> (B -> (C -> B))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-83, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3011
in-theory        3011
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (B -> (C -> B))))
theorem-size     33
proof            (modus-ponens tm-80 tm-105 ((Am (-> A (-> B A))) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3011.         ((A or (B -> (C -> B))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (B -> (C -> B)))), M:tm-80, m:tm-105, u:((Am (-> A (-> B A))) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A (-> B A)))))
================================================================
tm-name          tm-3012
in-theory        3012
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and B)))
theorem-size     29
proof            (modus-ponens tm-76 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3012.         (((not (not A)) -> A) and (B -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and B))), M:tm-76, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3013
in-theory        3013
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))
theorem-size     27
proof            (modus-ponens tm-73 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3013.         (((not (not A)) or A) -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-73, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-3014
in-theory        3014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C)))
theorem-size     35
proof            (modus-ponens tm-69 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3014.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C))), M:tm-69, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3015
in-theory        3015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and ((A -> (not B)) -> (not A))))
theorem-size     39
proof            (modus-ponens tm-66 tm-105 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-2)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3015.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-105, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-3016
in-theory        3016
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     37
proof            (modus-ponens tm-54 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3016.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-54, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3017
in-theory        3017
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-51 tm-105 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3017.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-105, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-3018
in-theory        3018
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (B or A)))
theorem-size     29
proof            (modus-ponens tm-50 tm-105 ((Am (or A B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3018.         ((A or (B or A)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (B or A))), M:tm-50, m:tm-105, u:((Am (or A B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (or A B))))
================================================================
tm-name          tm-3019
in-theory        3019
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A or B)))
theorem-size     29
proof            (modus-ponens tm-49 tm-105 ((Am (or A B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3019.         ((A or (A or B)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A or B))), M:tm-49, m:tm-105, u:((Am (or A B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (or A B))))
================================================================
tm-name          tm-3020
in-theory        3020
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (B -> (A and B))))
theorem-size     33
proof            (modus-ponens tm-48 tm-105 ((Am (-> A (and B A))) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3020.         ((A or (B -> (A and B))) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (B -> (A and B)))), M:tm-48, m:tm-105, u:((Am (-> A (and B A))) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A (and B A)))))
================================================================
tm-name          tm-3021
in-theory        3021
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and B))
theorem-size     27
proof            (modus-ponens tm-47 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3021.         (((A and B) or B) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and B)), M:tm-47, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-3022
in-theory        3022
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and A))
theorem-size     27
proof            (modus-ponens tm-46 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3022.         (((A and B) or A) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and A)), M:tm-46, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-3023
in-theory        3023
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> B) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-45 tm-105 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3023.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-105, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-3024
in-theory        3024
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (B -> A)))
theorem-size     29
proof            (modus-ponens tm-44 tm-105 ((Am (-> A B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3024.         ((A or (B -> A)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-105, u:((Am (-> A B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A B))))
================================================================
tm-name          tm-3025
in-theory        3025
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C)))
theorem-size     29
proof            (modus-ponens tm-42 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3025.         ((A -> (B or A)) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C))), M:tm-42, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3026
in-theory        3026
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C)))
theorem-size     29
proof            (modus-ponens tm-32 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3026.         ((A -> (A or B)) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C))), M:tm-32, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3027
in-theory        3027
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)))
theorem-size     25
proof            (modus-ponens tm-24 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3027.         (A -> (A and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))), M:tm-24, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-3028
in-theory        3028
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C)))
theorem-size     31
proof            (modus-ponens tm-23 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3028.         ((A -> (B -> (A and B))) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C))), M:tm-23, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3029
in-theory        3029
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C)))
theorem-size     29
proof            (modus-ponens tm-22 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3029.         (((A and B) -> B) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C))), M:tm-22, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3030
in-theory        3030
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C)))
theorem-size     29
proof            (modus-ponens tm-21 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3030.         (((A and B) -> A) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C))), M:tm-21, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3031
in-theory        3031
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     37
proof            (modus-ponens tm-20 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3031.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-20, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3032
in-theory        3032
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C)))
theorem-size     29
proof            (modus-ponens tm-19 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3032.         ((A -> (B -> A)) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C))), M:tm-19, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3033
in-theory        3033
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))) -> (not A))
theorem-size     27
proof            (modus-ponens tm-9 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-9 tm-5 tm-2)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3033.         ((A -> (not ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-3034
in-theory        3034
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and D) -> E) -> ((D or ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and D)) -> E))
theorem-size     49
proof            (modus-ponens tm-8 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       137
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3034.         ((((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and D) -> E) -> ((D or ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-3035
in-theory        3035
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and B)))
theorem-size     25
proof            (modus-ponens tm-7 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3035.         (A or (B -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and B))), M:tm-7, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3036
in-theory        3036
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) or E)
theorem-size     25
proof            (modus-ponens tm-6 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3036.         ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) or E), M:tm-6, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3037
in-theory        3037
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and B)) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3037.         (A -> ((B -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3038
in-theory        3038
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and B)))
theorem-size     25
proof            (modus-ponens tm-1 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3038.         (A -> (B -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and B))), M:tm-1, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3039
in-theory        3039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> (A -> B)) -> (A -> A))
theorem-size     13
proof            (modus-ponens tm-106 tm-11 ((Am (-> (-> Bm (-> Cm Bm)) (-> Bm Cm))) (A Bm) (B Cm) (C Bm)))
axioms-used      (tm-2 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3039.         (((A -> (B -> A)) -> (A -> B)) -> (A -> A)), M:tm-106, m:tm-11, u:((Am (-> (-> Bm (-> Cm Bm)) (-> Bm Cm))) (A Bm) (B Cm) (C Bm))
================================================================
tm-name          tm-3040
in-theory        3040
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     33
proof            (modus-ponens tm-106 tm-14 ((Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (A (-> Bm (-> Cm Dm))) (B (-> Bm Cm)) (C (-> Bm Dm))))
axioms-used      (tm-2 tm-1)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3040.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-106, m:tm-14, u:((Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (A (-> Bm (-> Cm Dm))) (B (-> Bm Cm)) (C (-> Bm Dm)))
================================================================
tm-name          tm-3041
in-theory        3041
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> (A -> B)) -> (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))
theorem-size     25
proof            (modus-ponens tm-106 tm-16 ((Am (-> (-> (and (-> B C) Cm) (-> B C)) (-> (and (-> B C) Cm) B))) (A (and (-> B C) Cm)) (Bm (-> B C))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3041.         (((((A -> B) and C) -> (A -> B)) -> (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-106, m:tm-16, u:((Am (-> (-> (and (-> B C) Cm) (-> B C)) (-> (and (-> B C) Cm) B))) (A (and (-> B C) Cm)) (Bm (-> B C)))
================================================================
tm-name          tm-3042
in-theory        3042
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> (B -> C)) -> ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))
theorem-size     25
proof            (modus-ponens tm-106 tm-18 ((Am (-> (-> (and Bm (-> B C)) (-> B C)) (-> (and Bm (-> B C)) B))) (A (and Bm (-> B C))) (Cm (-> B C))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3042.         ((((A and (B -> C)) -> (B -> C)) -> ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-106, m:tm-18, u:((Am (-> (-> (and Bm (-> B C)) (-> B C)) (-> (and Bm (-> B C)) B))) (A (and Bm (-> B C))) (Cm (-> B C)))
================================================================
tm-name          tm-3043
in-theory        3043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> (A -> B)) -> (A -> (A and B)))
theorem-size     17
proof            (modus-ponens tm-106 tm-25 ((Am (-> (-> Bm (-> Cm (and Bm Cm))) (-> Bm Cm))) (A Bm) (B Cm) (C (and Bm Cm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3043.         (((A -> (B -> (A and B))) -> (A -> B)) -> (A -> (A and B))), M:tm-106, m:tm-25, u:((Am (-> (-> Bm (-> Cm (and Bm Cm))) (-> Bm Cm))) (A Bm) (B Cm) (C (and Bm Cm)))
================================================================
tm-name          tm-3044
in-theory        3044
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> ((A -> B) -> (B -> C))) -> ((A -> B) -> ((A or B) -> C)))
theorem-size     31
proof            (modus-ponens tm-106 tm-56 ((Am (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> Bm Cm) (-> Cm Dm)))) (A (-> Bm Cm)) (B (-> Cm Dm)) (C (-> (or Bm Cm) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3044.         ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> ((A -> B) -> (B -> C))) -> ((A -> B) -> ((A or B) -> C))), M:tm-106, m:tm-56, u:((Am (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> Bm Cm) (-> Cm Dm)))) (A (-> Bm Cm)) (B (-> Cm Dm)) (C (-> (or Bm Cm) Dm)))
================================================================
tm-name          tm-3045
in-theory        3045
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) -> ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-106 tm-71 ((Am (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> Bm Cm) (-> Bm (not Cm))))) (A (-> Bm Cm)) (B (-> Bm (not Cm))) (C (not Bm))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3045.         ((((A -> B) -> ((A -> (not B)) -> (not A))) -> ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A))), M:tm-106, m:tm-71, u:((Am (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> Bm Cm) (-> Bm (not Cm))))) (A (-> Bm Cm)) (B (-> Bm (not Cm))) (C (not Bm)))
================================================================
tm-name          tm-3046
in-theory        3046
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> (A -> B)) -> ((not (not (A -> B))) -> A)) -> ((not (not (A -> B))) -> B))
theorem-size     25
proof            (modus-ponens tm-106 tm-78 ((Am (-> (-> (not (not (-> B C))) (-> B C)) (-> (not (not (-> B C))) B))) (A (not (not (-> B C)))) (Bm (-> B C))))
axioms-used      (tm-2 tm-1 tm-10)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3046.         ((((not (not (A -> B))) -> (A -> B)) -> ((not (not (A -> B))) -> A)) -> ((not (not (A -> B))) -> B)), M:tm-106, m:tm-78, u:((Am (-> (-> (not (not (-> B C))) (-> B C)) (-> (not (not (-> B C))) B))) (A (not (not (-> B C)))) (Bm (-> B C)))
================================================================
tm-name          tm-3047
in-theory        3047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) -> (A -> B)) -> (A -> (C -> B)))
theorem-size     17
proof            (modus-ponens tm-106 tm-85 ((Am (-> (-> Bm (-> Cm (-> Dm Cm))) (-> Bm Cm))) (A Bm) (B Cm) (C (-> Dm Cm))))
axioms-used      (tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3047.         (((A -> (B -> (C -> B))) -> (A -> B)) -> (A -> (C -> B))), M:tm-106, m:tm-85, u:((Am (-> (-> Bm (-> Cm (-> Dm Cm))) (-> Bm Cm))) (A Bm) (B Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-3048
in-theory        3048
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) -> ((A -> B) -> A)) -> ((A -> B) -> A))
theorem-size     19
proof            (modus-ponens tm-106 tm-97 ((Am (-> (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> Bm Cm) Bm))) (A (-> Bm Cm)) (B Bm) (C Bm)))
axioms-used      (tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3048.         ((((A -> B) -> (A -> A)) -> ((A -> B) -> A)) -> ((A -> B) -> A)), M:tm-106, m:tm-97, u:((Am (-> (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> Bm Cm) Bm))) (A (-> Bm Cm)) (B Bm) (C Bm))
================================================================
tm-name          tm-3049
in-theory        3049
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     49
proof            (modus-ponens tm-105 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3049.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-105, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3050
in-theory        3050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E))))
theorem-size     37
proof            (modus-ponens tm-95 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3050.         (((A -> B) -> (A -> A)) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E)))), M:tm-95, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3051
in-theory        3051
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (D -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-84 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3051.         ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (D -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))), M:tm-84, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-3052
in-theory        3052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-83 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3052.         ((A -> (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-83, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3053
in-theory        3053
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C -> D)) -> (B -> C)) -> (B -> (C -> D))) -> (((B -> (C -> D)) -> (B -> C)) -> (B -> D))))
theorem-size     35
proof            (modus-ponens tm-76 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3053.         (((not (not A)) -> A) and ((((B -> (C -> D)) -> (B -> C)) -> (B -> (C -> D))) -> (((B -> (C -> D)) -> (B -> C)) -> (B -> D)))), M:tm-76, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3054
in-theory        3054
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))))) or (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))
theorem-size     47
proof            (modus-ponens tm-73 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3054.         (((not (not (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))))) or (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-73, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-3055
in-theory        3055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E))))
theorem-size     41
proof            (modus-ponens tm-69 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3055.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E)))), M:tm-69, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3056
in-theory        3056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-54 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3056.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-54, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3057
in-theory        3057
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> (B -> C)) -> (B -> (C -> D)))) or (((B -> (C -> D)) -> (B -> C)) -> (B -> (C -> D)))) -> (((B -> (C -> D)) -> (B -> C)) -> (B -> D)))
theorem-size     47
proof            (modus-ponens tm-47 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3057.         (((A and (((B -> (C -> D)) -> (B -> C)) -> (B -> (C -> D)))) or (((B -> (C -> D)) -> (B -> C)) -> (B -> (C -> D)))) -> (((B -> (C -> D)) -> (B -> C)) -> (B -> D))), M:tm-47, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-3058
in-theory        3058
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) and D) or (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))
theorem-size     47
proof            (modus-ponens tm-46 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3058.         ((((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) and D) or (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-46, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-3059
in-theory        3059
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))
theorem-size     35
proof            (modus-ponens tm-44 tm-106 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3059.         (((A -> (B -> C)) or (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-44, m:tm-106, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-3060
in-theory        3060
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-42 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3060.         ((A -> (B or A)) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E)))), M:tm-42, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3061
in-theory        3061
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-32 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3061.         ((A -> (A or B)) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E)))), M:tm-32, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3062
in-theory        3062
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) and (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))
theorem-size     45
proof            (modus-ponens tm-24 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3062.         ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) and (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))), M:tm-24, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-3063
in-theory        3063
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E))))
theorem-size     37
proof            (modus-ponens tm-23 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3063.         ((A -> (B -> (A and B))) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E)))), M:tm-23, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3064
in-theory        3064
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-22 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3064.         (((A and B) -> B) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E)))), M:tm-22, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3065
in-theory        3065
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-21 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3065.         (((A and B) -> A) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E)))), M:tm-21, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3066
in-theory        3066
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-20 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3066.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-20, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3067
in-theory        3067
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-19 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3067.         ((A -> (B -> A)) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E)))), M:tm-19, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3068
in-theory        3068
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))))
theorem-size     31
proof            (modus-ponens tm-12 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3068.         ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))), M:tm-12, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-3069
in-theory        3069
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (not (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))) -> (not (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))))
theorem-size     47
proof            (modus-ponens tm-9 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-9 tm-2)
proof-size       145
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3069.         (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (not (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))) -> (not (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))))), M:tm-9, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-3070
in-theory        3070
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> C)) -> D) -> (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) or (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) -> D))
theorem-size     47
proof            (modus-ponens tm-8 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       147
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3070.         (((((A -> (B -> C)) -> (A -> B)) -> (A -> C)) -> D) -> (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) or (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) -> D)), M:tm-8, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-3071
in-theory        3071
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> (C -> D)) -> (B -> C)) -> (B -> (C -> D))) -> (((B -> (C -> D)) -> (B -> C)) -> (B -> D))))
theorem-size     31
proof            (modus-ponens tm-7 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-7 tm-2)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3071.         (A or ((((B -> (C -> D)) -> (B -> C)) -> (B -> (C -> D))) -> (((B -> (C -> D)) -> (B -> C)) -> (B -> D)))), M:tm-7, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3072
in-theory        3072
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) or D)
theorem-size     31
proof            (modus-ponens tm-6 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-6 tm-2)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3072.         (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) or D), M:tm-6, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3073
in-theory        3073
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> D)) -> (B -> C)) -> (B -> (C -> D))) -> (((B -> (C -> D)) -> (B -> C)) -> (B -> D))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3073.         (A -> (((((B -> (C -> D)) -> (B -> C)) -> (B -> (C -> D))) -> (((B -> (C -> D)) -> (B -> C)) -> (B -> D))) and A)), M:tm-5, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3074
in-theory        3074
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> ((A -> (B -> C)) -> (A -> B))) -> ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (A -> C)))
theorem-size     45
proof            (modus-ponens tm-2 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> Am Cm))))
axioms-used      (tm-2)
proof-size       145
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3074.         (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> ((A -> (B -> C)) -> (A -> B))) -> ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (A -> C))), M:tm-2, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> Am Cm)))
================================================================
tm-name          tm-3075
in-theory        3075
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> (B -> C)) -> (B -> (C -> D))) -> (((B -> (C -> D)) -> (B -> C)) -> (B -> D))))
theorem-size     31
proof            (modus-ponens tm-1 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-1 tm-2)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3075.         (A -> ((((B -> (C -> D)) -> (B -> C)) -> (B -> (C -> D))) -> (((B -> (C -> D)) -> (B -> C)) -> (B -> D)))), M:tm-1, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3076
in-theory        3076
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))
theorem-size     49
proof            (modus-ponens tm-106 tm-107 ((Am (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> Bm (-> Cm Dm))))) (A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (B (-> Bm (-> Cm Dm))) (C (-> Bm Dm))))
axioms-used      (tm-2 tm-1)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3076.         (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-106, m:tm-107, u:((Am (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> Bm (-> Cm Dm))))) (A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (B (-> Bm (-> Cm Dm))) (C (-> Bm Dm)))
================================================================
tm-name          tm-3077
in-theory        3077
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3077.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-105, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3078
in-theory        3078
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-102 tm-107 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3078.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-102, m:tm-107, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3079
in-theory        3079
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> C)) -> D)) -> (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-100 tm-107 ((Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)) C))) (A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3079.         ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> C)) -> D)) -> (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-100, m:tm-107, u:((Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)) C))) (A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-3080
in-theory        3080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     13
proof            (modus-ponens tm-98 tm-107 ((Am (-> Bm Cm)) (B (-> Bm (-> Cm Dm))) (A (-> Bm Cm)) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3080.         ((A -> B) -> ((A -> (B -> C)) -> (A -> C))), M:tm-98, m:tm-107, u:((Am (-> Bm Cm)) (B (-> Bm (-> Cm Dm))) (A (-> Bm Cm)) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-3081
in-theory        3081
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) -> (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-96 tm-107 ((Am (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) B)) (A (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3081.         (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) -> (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-96, m:tm-107, u:((Am (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) B)) (A (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3082
in-theory        3082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3082.         (((A -> B) -> (A -> A)) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-95, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3083
in-theory        3083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-92 tm-107 ((Am (-> A A)) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3083.         (((A -> B) or (A -> A)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-92, m:tm-107, u:((Am (-> A A)) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3084
in-theory        3084
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))
theorem-size     23
proof            (modus-ponens tm-84 tm-107 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3084.         (A -> (B -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))), M:tm-84, m:tm-107, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3085
in-theory        3085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3085.         ((A -> (B -> (C -> B))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-83, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3086
in-theory        3086
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-80 tm-107 ((Am (-> A (-> B A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3086.         ((A or (B -> (C -> B))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-80, m:tm-107, u:((Am (-> A (-> B A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3087
in-theory        3087
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D))) -> D)
theorem-size     25
proof            (modus-ponens tm-77 tm-107 ((Am (not (not (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) B)))) (A (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-10 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3087.         ((not (not ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D))) -> D), M:tm-77, m:tm-107, u:((Am (not (not (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) B)))) (A (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3088
in-theory        3088
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3088.         (((not (not A)) -> A) and (B -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))), M:tm-76, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3089
in-theory        3089
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     25
proof            (modus-ponens tm-73 tm-107 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-10 tm-1 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3089.         (((not (not A)) or A) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-73, m:tm-107, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3090
in-theory        3090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3090.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-69, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3091
in-theory        3091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     31
proof            (modus-ponens tm-66 tm-107 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-9 tm-1 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3091.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-66, m:tm-107, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3092
in-theory        3092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> (B -> C))) -> ((A or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     33
proof            (modus-ponens tm-55 tm-107 ((Am (-> A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3092.         ((A -> ((B -> (C -> D)) -> (B -> C))) -> ((A or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-55, m:tm-107, u:((Am (-> A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-3093
in-theory        3093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3093.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-54, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3094
in-theory        3094
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-51 tm-107 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3094.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-51, m:tm-107, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3095
in-theory        3095
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-50 tm-107 ((Am (or A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3095.         ((A or (B or A)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-50, m:tm-107, u:((Am (or A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3096
in-theory        3096
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-49 tm-107 ((Am (or A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3096.         ((A or (A or B)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-49, m:tm-107, u:((Am (or A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3097
in-theory        3097
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-48 tm-107 ((Am (-> A (and B A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3097.         ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-48, m:tm-107, u:((Am (-> A (and B A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3098
in-theory        3098
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-47 tm-107 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3098.         (((A and B) or B) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-47, m:tm-107, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3099
in-theory        3099
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-46 tm-107 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3099.         (((A and B) or A) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-46, m:tm-107, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3100
in-theory        3100
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-45 tm-107 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3100.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-45, m:tm-107, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3101
in-theory        3101
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-44 tm-107 ((Am (-> A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3101.         ((A or (B -> A)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-44, m:tm-107, u:((Am (-> A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3102
in-theory        3102
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3102.         ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-42, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3103
in-theory        3103
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3103.         ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-32, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3104
in-theory        3104
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     23
proof            (modus-ponens tm-24 tm-107 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3104.         (A -> (A and (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))), M:tm-24, m:tm-107, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3105
in-theory        3105
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3105.         ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-23, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3106
in-theory        3106
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3106.         (((A and B) -> B) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-22, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3107
in-theory        3107
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3107.         (((A and B) -> A) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-21, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3108
in-theory        3108
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3108.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-20, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3109
in-theory        3109
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3109.         ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-19, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3110
in-theory        3110
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) -> E)) -> E)
theorem-size     25
proof            (modus-ponens tm-17 tm-107 ((Am (and A (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) C))) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3110.         ((A and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-107, u:((Am (and A (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) C))) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3111
in-theory        3111
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) and E) -> D)
theorem-size     25
proof            (modus-ponens tm-15 tm-107 ((Am (and (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) B) C)) (A (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3111.         ((((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-107, u:((Am (and (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) B) C)) (A (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3112
in-theory        3112
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> C)) -> D)) -> (((A -> (B -> C)) -> (A -> B)) -> D))
theorem-size     33
proof            (modus-ponens tm-13 tm-107 ((Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)) C))) (A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3112.         ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> C)) -> D)) -> (((A -> (B -> C)) -> (A -> B)) -> D)), M:tm-13, m:tm-107, u:((Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)) C))) (A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-3113
in-theory        3113
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))) -> (not A))
theorem-size     25
proof            (modus-ponens tm-9 tm-107 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3113.         ((A -> (not (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-107, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3114
in-theory        3114
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) -> ((E or (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))) -> D))
theorem-size     45
proof            (modus-ponens tm-8 tm-107 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       129
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3114.         (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) -> ((E or (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))) -> D)), M:tm-8, m:tm-107, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3115
in-theory        3115
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-7 tm-1 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3115.         (A or (B -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))), M:tm-7, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3116
in-theory        3116
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-6 tm-1 tm-2)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3116.         ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) or E), M:tm-6, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3117
in-theory        3117
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3117.         (A -> ((B -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and A)), M:tm-5, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3118
in-theory        3118
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> (B -> C))) -> (A -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     23
proof            (modus-ponens tm-2 tm-107 ((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3118.         ((A -> ((B -> (C -> D)) -> (B -> C))) -> (A -> ((B -> (C -> D)) -> (B -> D)))), M:tm-2, m:tm-107, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-3119
in-theory        3119
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (((A -> B) -> A) -> ((A -> B) -> C)))
theorem-size     17
proof            (modus-ponens tm-108 tm-14 ((Am (-> Cm (-> B Dm))) (Bm (-> Cm B)) (A Cm) (C Dm) (D (-> (-> (-> Cm B) Cm) (-> (-> Cm B) Dm)))))
axioms-used      (tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3119.         ((A -> (B -> C)) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-108, m:tm-14, u:((Am (-> Cm (-> B Dm))) (Bm (-> Cm B)) (A Cm) (C Dm) (D (-> (-> (-> Cm B) Cm) (-> (-> Cm B) Dm))))
================================================================
tm-name          tm-3120
in-theory        3120
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (D -> (((A -> B) -> (A -> C)) and D)))
theorem-size     17
proof            (modus-ponens tm-108 tm-25 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> Cm (and (-> (-> A B) (-> A C)) Cm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3120.         ((A -> (B -> C)) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-108, m:tm-25, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> Cm (and (-> (-> A B) (-> A C)) Cm))))
================================================================
tm-name          tm-3121
in-theory        3121
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) or D))
theorem-size     15
proof            (modus-ponens tm-108 tm-33 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Cm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3121.         ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) or D)), M:tm-108, m:tm-33, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Cm)))
================================================================
tm-name          tm-3122
in-theory        3122
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (D or ((A -> B) -> (A -> C))))
theorem-size     15
proof            (modus-ponens tm-108 tm-43 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (or Cm (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3122.         ((A -> (B -> C)) -> (D or ((A -> B) -> (A -> C)))), M:tm-108, m:tm-43, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (or Cm (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-3123
in-theory        3123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))
theorem-size     21
proof            (modus-ponens tm-108 tm-56 ((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (-> (-> (-> A C) Dm) (-> (or (-> A B) (-> A C)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3123.         ((A -> (B -> C)) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-108, m:tm-56, u:((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (-> (-> (-> A C) Dm) (-> (or (-> A B) (-> A C)) Dm))))
================================================================
tm-name          tm-3124
in-theory        3124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))
theorem-size     19
proof            (modus-ponens tm-108 tm-71 ((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B))))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3124.         ((A -> (B -> C)) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-108, m:tm-71, u:((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
================================================================
tm-name          tm-3125
in-theory        3125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (D -> (E -> D)))
theorem-size     11
proof            (modus-ponens tm-108 tm-85 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3125.         ((A -> (B -> C)) -> (D -> (E -> D))), M:tm-108, m:tm-85, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-3126
in-theory        3126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((A -> B) -> (A -> B)))
theorem-size     13
proof            (modus-ponens tm-108 tm-97 ((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (-> (-> A B) (-> A B)))))
axioms-used      (tm-2 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3126.         ((A -> (B -> C)) -> ((A -> B) -> (A -> B))), M:tm-108, m:tm-97, u:((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (-> (-> A B) (-> A B))))
================================================================
tm-name          tm-3127
in-theory        3127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> B)) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     17
proof            (modus-ponens tm-108 tm-107 ((Am (-> Bm (-> (-> Cm Dm) Cm))) (B (-> Cm Dm)) (A Bm) (C Cm) (D (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3127.         ((A -> ((B -> C) -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-108, m:tm-107, u:((Am (-> Bm (-> (-> Cm Dm) Cm))) (B (-> Cm Dm)) (A Bm) (C Cm) (D (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-3128
in-theory        3128
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-105 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3128.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-105, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3129
in-theory        3129
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-100 tm-108 ((Dm (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (-> Am Cm))) (A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-1)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3129.         (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-100, m:tm-108, u:((Dm (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (-> Am Cm))) (A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-3130
in-theory        3130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-95 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3130.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F))), M:tm-95, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3131
in-theory        3131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (E -> ((A -> (B -> C)) -> D)))
theorem-size     25
proof            (modus-ponens tm-84 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3131.         (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (E -> ((A -> (B -> C)) -> D))), M:tm-84, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-3132
in-theory        3132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-83 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3132.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-83, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3133
in-theory        3133
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> (B -> (C -> D))))) -> ((B -> (C -> D)) -> (B -> (C -> D))))
theorem-size     33
proof            (modus-ponens tm-80 tm-108 ((Dm (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (A (-> Am (-> Bm Cm))) (C (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3133.         ((A or ((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> (B -> (C -> D))))) -> ((B -> (C -> D)) -> (B -> (C -> D)))), M:tm-80, m:tm-108, u:((Dm (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (A (-> Am (-> Bm Cm))) (C (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-3134
in-theory        3134
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> E)) -> ((B -> (C -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-76 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3134.         (((not (not A)) -> A) and (((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> E)) -> ((B -> (C -> D)) -> E))), M:tm-76, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3135
in-theory        3135
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)))) or ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))) -> ((A -> (B -> C)) -> D))
theorem-size     41
proof            (modus-ponens tm-73 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3135.         (((not (not ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)))) or ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))) -> ((A -> (B -> C)) -> D)), M:tm-73, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-3136
in-theory        3136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-69 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3136.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F))), M:tm-69, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3137
in-theory        3137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-54 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3137.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-54, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3138
in-theory        3138
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> E))) or ((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> E))) -> ((B -> (C -> D)) -> E))
theorem-size     41
proof            (modus-ponens tm-47 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3138.         (((A and ((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> E))) or ((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> E))) -> ((B -> (C -> D)) -> E)), M:tm-47, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-3139
in-theory        3139
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) and E) or ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))) -> ((A -> (B -> C)) -> D))
theorem-size     41
proof            (modus-ponens tm-46 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3139.         (((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) and E) or ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))) -> ((A -> (B -> C)) -> D)), M:tm-46, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-3140
in-theory        3140
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))) -> ((A -> (B -> C)) -> D))
theorem-size     33
proof            (modus-ponens tm-44 tm-108 ((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (C (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3140.         (((((A -> B) -> (A -> C)) -> D) or ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))) -> ((A -> (B -> C)) -> D)), M:tm-44, m:tm-108, u:((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (C (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-3141
in-theory        3141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-42 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3141.         ((A -> (B or A)) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F))), M:tm-42, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3142
in-theory        3142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-32 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3142.         ((A -> (A or B)) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F))), M:tm-32, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3143
in-theory        3143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) and ((A -> (B -> C)) -> D)))
theorem-size     39
proof            (modus-ponens tm-24 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3143.         (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) and ((A -> (B -> C)) -> D))), M:tm-24, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-3144
in-theory        3144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-23 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3144.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F))), M:tm-23, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3145
in-theory        3145
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-22 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3145.         (((A and B) -> B) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F))), M:tm-22, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3146
in-theory        3146
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-21 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3146.         (((A and B) -> A) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F))), M:tm-21, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3147
in-theory        3147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-20 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3147.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-20, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3148
in-theory        3148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-19 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3148.         ((A -> (B -> A)) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F))), M:tm-19, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3149
in-theory        3149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-12 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3149.         (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))), M:tm-12, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-3150
in-theory        3150
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (not ((A -> (B -> C)) -> D))) -> (not ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))))
theorem-size     41
proof            (modus-ponens tm-9 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-9 tm-2 tm-1)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3150.         ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (not ((A -> (B -> C)) -> D))) -> (not ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)))), M:tm-9, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-3151
in-theory        3151
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> D) -> E) -> ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) or ((A -> (B -> C)) -> D)) -> E))
theorem-size     35
proof            (modus-ponens tm-8 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3151.         ((((A -> (B -> C)) -> D) -> E) -> ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) or ((A -> (B -> C)) -> D)) -> E)), M:tm-8, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-3152
in-theory        3152
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> E)) -> ((B -> (C -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-7 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-7 tm-2 tm-1)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3152.         (A or (((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> E)) -> ((B -> (C -> D)) -> E))), M:tm-7, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3153
in-theory        3153
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) or E)
theorem-size     25
proof            (modus-ponens tm-6 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-6 tm-2 tm-1)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3153.         ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) or E), M:tm-6, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3154
in-theory        3154
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> E)) -> ((B -> (C -> D)) -> E)) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3154.         (A -> ((((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> E)) -> ((B -> (C -> D)) -> E)) and A)), M:tm-5, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3155
in-theory        3155
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> D))
theorem-size     39
proof            (modus-ponens tm-2 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> Am (-> Bm Cm))) (C Dm)))
axioms-used      (tm-2 tm-1)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3155.         ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> D)), M:tm-2, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> Am (-> Bm Cm))) (C Dm))
================================================================
tm-name          tm-3156
in-theory        3156
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> E)) -> ((B -> (C -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-1 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-1 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3156.         (A -> (((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> E)) -> ((B -> (C -> D)) -> E))), M:tm-1, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3157
in-theory        3157
times-derived    1
----------------------------------------------------------------
theorem          (not ((not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and D))
theorem-size     17
proof            (modus-ponens tm-109 tm-3 ((A (and (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))) Bm)) (Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-3157.         (not ((not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and D)), M:tm-109, m:tm-3, u:((A (and (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))) Bm)) (Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-3158
in-theory        3158
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     17
proof            (modus-ponens tm-109 tm-4 ((A (and Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))) (Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-3158.         (not (A and (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-109, m:tm-4, u:((A (and Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))) (Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-3159
in-theory        3159
times-derived    1
----------------------------------------------------------------
theorem          (not (not (not (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))))
theorem-size     17
proof            (modus-ponens tm-109 tm-10 ((A (not (not (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-10)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-3159.         (not (not (not (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))), M:tm-109, m:tm-10, u:((A (not (not (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-3160
in-theory        3160
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))))
theorem-size     31
proof            (modus-ponens tm-109 tm-57 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> Bm (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3160.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))), M:tm-109, m:tm-57, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> Bm (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-3161
in-theory        3161
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))))))
theorem-size     35
proof            (modus-ponens tm-109 tm-58 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (-> (-> B (-> C D)) (-> B C)) (-> (-> B (-> C D)) (-> B D)))))) (Am (-> B (-> C D))) (Bm (-> B C)) (Cm (-> B D))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3161.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))))), M:tm-109, m:tm-58, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (-> (-> B (-> C D)) (-> B C)) (-> (-> B (-> C D)) (-> B D)))))) (Am (-> B (-> C D))) (Bm (-> B C)) (Cm (-> B D)))
================================================================
tm-name          tm-3162
in-theory        3162
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)))))
theorem-size     33
proof            (modus-ponens tm-109 tm-61 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> Bm (and (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) Bm))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-5)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3162.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))))), M:tm-109, m:tm-61, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> Bm (and (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) Bm))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-3163
in-theory        3163
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D))))
theorem-size     31
proof            (modus-ponens tm-109 tm-62 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (or (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) Bm)))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-6)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3163.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)))), M:tm-109, m:tm-62, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (or (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) Bm)))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-3164
in-theory        3164
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))))
theorem-size     31
proof            (modus-ponens tm-109 tm-63 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (or Bm (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-7)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3164.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D or ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))), M:tm-109, m:tm-63, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (or Bm (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-3165
in-theory        3165
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))))
theorem-size     41
proof            (modus-ponens tm-109 tm-64 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (-> (-> (-> B C) (-> B D)) Cm) (-> (or (-> B (-> C D)) (-> (-> B C) (-> B D))) Cm))))) (Am (-> B (-> C D))) (Bm (-> (-> B C) (-> B D)))))
axioms-used      (tm-9 tm-1 tm-2 tm-8)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3165.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))), M:tm-109, m:tm-64, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (-> (-> (-> B C) (-> B D)) Cm) (-> (or (-> B (-> C D)) (-> (-> B C) (-> B D))) Cm))))) (Am (-> B (-> C D))) (Bm (-> (-> B C) (-> B D))))
================================================================
tm-name          tm-3166
in-theory        3166
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))))))
theorem-size     37
proof            (modus-ponens tm-109 tm-65 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (-> (-> B (-> C D)) (not (-> (-> B C) (-> B D)))) (not (-> B (-> C D))))))) (Am (-> B (-> C D))) (Bm (-> (-> B C) (-> B D)))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3166.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C))))))), M:tm-109, m:tm-65, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (-> (-> B (-> C D)) (not (-> (-> B C) (-> B D)))) (not (-> B (-> C D))))))) (Am (-> B (-> C D))) (Bm (-> (-> B C) (-> B D))))
================================================================
tm-name          tm-3167
in-theory        3167
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (E -> D)))))
theorem-size     21
proof            (modus-ponens tm-109 tm-79 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> Bm (-> Cm Bm))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3167.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (E -> D))))), M:tm-109, m:tm-79, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> Bm (-> Cm Bm))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-3168
in-theory        3168
times-derived    1
----------------------------------------------------------------
theorem          (not (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))
theorem-size     15
proof            (modus-ponens tm-109 tm-86 ((A (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) (Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3168.         (not (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))), M:tm-109, m:tm-86, u:((A (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) (Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-3169
in-theory        3169
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((A -> (B -> C)) -> (A -> (B -> C))))))
theorem-size     27
proof            (modus-ponens tm-109 tm-91 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (-> B (-> C D)) (-> B (-> C D)))))) (Am (-> B (-> C D))) (Bm (-> (-> B C) (-> B D)))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3169.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((A -> (B -> C)) -> (A -> (B -> C)))))), M:tm-109, m:tm-91, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (-> B (-> C D)) (-> B (-> C D)))))) (Am (-> B (-> C D))) (Bm (-> (-> B C) (-> B D))))
================================================================
tm-name          tm-3170
in-theory        3170
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     29
proof            (modus-ponens tm-109 tm-109 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3170.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-109, m:tm-109, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-3171
in-theory        3171
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     39
proof            (modus-ponens tm-105 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3171.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-105, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3172
in-theory        3172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C)))
theorem-size     27
proof            (modus-ponens tm-95 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3172.         (((A -> B) -> (A -> A)) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C))), M:tm-95, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3173
in-theory        3173
times-derived    1
----------------------------------------------------------------
theorem          ((((not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D) or ((not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))) -> (not (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))
theorem-size     62
proof            (modus-ponens tm-92 tm-109 ((Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (A (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (B (not (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-8 tm-2 tm-1 tm-9)
proof-size       178
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3173.         ((((not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D) or ((not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))) -> (not (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))), M:tm-92, m:tm-109, u:((Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (A (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (B (not (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-3174
in-theory        3174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (E -> (not A)))
theorem-size     21
proof            (modus-ponens tm-84 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3174.         ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (E -> (not A))), M:tm-84, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-3175
in-theory        3175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-83 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3175.         ((A -> (B -> (C -> B))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-83, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3176
in-theory        3176
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     21
proof            (modus-ponens tm-79 tm-109 ((A (-> (-> B (-> C B)) (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3176.         (not ((A -> (B -> A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-79, m:tm-109, u:((A (-> (-> B (-> C B)) (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-3177
in-theory        3177
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not B)))
theorem-size     25
proof            (modus-ponens tm-76 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-1 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3177.         (((not (not A)) -> A) and ((B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not B))), M:tm-76, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3178
in-theory        3178
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))) or (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not A))
theorem-size     38
proof            (modus-ponens tm-73 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-1 tm-2)
proof-size       130
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3178.         (((not (not (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))) or (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not A)), M:tm-73, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-3179
in-theory        3179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C)))
theorem-size     31
proof            (modus-ponens tm-69 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3179.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C))), M:tm-69, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3180
in-theory        3180
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not D)) -> (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))) -> (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not D))))
theorem-size     65
proof            (modus-ponens tm-66 tm-109 ((Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not B))) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (not (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not B))))))
axioms-used      (tm-8 tm-9 tm-1 tm-2)
proof-size       175
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3180.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not D)) -> (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))) -> (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not D)))), M:tm-66, m:tm-109, u:((Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not B))) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (not (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not B)))))
================================================================
tm-name          tm-3181
in-theory        3181
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-54 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-1 tm-2)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3181.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-54, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3182
in-theory        3182
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) or (B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not B))
theorem-size     38
proof            (modus-ponens tm-47 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-1 tm-2)
proof-size       130
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3182.         (((A and (B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) or (B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not B)), M:tm-47, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-3183
in-theory        3183
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and E) or (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not A))
theorem-size     38
proof            (modus-ponens tm-46 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-1 tm-2)
proof-size       130
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3183.         ((((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and E) or (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not A)), M:tm-46, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-3184
in-theory        3184
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) or (D -> (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))) -> (not D))
theorem-size     34
proof            (modus-ponens tm-44 tm-109 ((A Am) (B (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-2)
proof-size       128
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3184.         (((not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) or (D -> (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))) -> (not D)), M:tm-44, m:tm-109, u:((A Am) (B (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (C (not Am)))
================================================================
tm-name          tm-3185
in-theory        3185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C)))
theorem-size     25
proof            (modus-ponens tm-42 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3185.         ((A -> (B or A)) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C))), M:tm-42, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3186
in-theory        3186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C)))
theorem-size     25
proof            (modus-ponens tm-32 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3186.         ((A -> (A or B)) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C))), M:tm-32, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3187
in-theory        3187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (not A)))
theorem-size     36
proof            (modus-ponens tm-24 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       128
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3187.         ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (not A))), M:tm-24, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-3188
in-theory        3188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C)))
theorem-size     27
proof            (modus-ponens tm-23 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3188.         ((A -> (B -> (A and B))) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C))), M:tm-23, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3189
in-theory        3189
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C)))
theorem-size     25
proof            (modus-ponens tm-22 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3189.         (((A and B) -> B) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C))), M:tm-22, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3190
in-theory        3190
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C)))
theorem-size     25
proof            (modus-ponens tm-21 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3190.         (((A and B) -> A) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C))), M:tm-21, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3191
in-theory        3191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-20 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3191.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-20, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3192
in-theory        3192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C)))
theorem-size     25
proof            (modus-ponens tm-19 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3192.         ((A -> (B -> A)) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C))), M:tm-19, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3193
in-theory        3193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     33
proof            (modus-ponens tm-12 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3193.         ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-12, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-3194
in-theory        3194
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not (not A))) -> (not (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))
theorem-size     38
proof            (modus-ponens tm-9 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       112
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3194.         (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not (not A))) -> (not (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))), M:tm-9, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-3195
in-theory        3195
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or (not A)) -> B))
theorem-size     26
proof            (modus-ponens tm-8 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-1 tm-2)
proof-size       102
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3195.         (((not A) -> B) -> (((A -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or (not A)) -> B)), M:tm-8, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-3196
in-theory        3196
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not B)))
theorem-size     21
proof            (modus-ponens tm-7 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-1 tm-2)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3196.         (A or ((B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not B))), M:tm-7, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3197
in-theory        3197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-1 tm-2)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3197.         (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) or E), M:tm-6, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3198
in-theory        3198
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not B)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3198.         (A -> (((B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not B)) and A)), M:tm-5, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3199
in-theory        3199
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not B)))
theorem-size     21
proof            (modus-ponens tm-1 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-2)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3199.         (A -> ((B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not B))), M:tm-1, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3200
in-theory        3200
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     31
proof            (modus-ponens tm-110 tm-1 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3200.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-1, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3201
in-theory        3201
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     35
proof            (modus-ponens tm-110 tm-2 ((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (-> (-> (-> A (-> B C)) (-> A B)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3201.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-110, m:tm-2, u:((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (-> (-> (-> A (-> B C)) (-> A B)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-3202
in-theory        3202
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))
theorem-size     33
proof            (modus-ponens tm-110 tm-5 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       119
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3202.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E))), M:tm-110, m:tm-5, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm))))
================================================================
tm-name          tm-3203
in-theory        3203
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))
theorem-size     31
proof            (modus-ponens tm-110 tm-6 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-3203.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-110, m:tm-6, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)))
================================================================
tm-name          tm-3204
in-theory        3204
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     31
proof            (modus-ponens tm-110 tm-7 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-7)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-3204.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-7, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3205
in-theory        3205
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     41
proof            (modus-ponens tm-110 tm-8 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> (-> (-> A B) (-> A C)) Cm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       133
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3205.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-110, m:tm-8, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> (-> (-> A B) (-> A C)) Cm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm))))
================================================================
tm-name          tm-3206
in-theory        3206
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> (not ((B -> C) -> (B -> D)))) -> (not (B -> (C -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-9 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> (-> A (-> B C)) (not (-> (-> A B) (-> A C)))) (not (-> A (-> B C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-9)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3206.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> (not ((B -> C) -> (B -> D)))) -> (not (B -> (C -> D))))), M:tm-110, m:tm-9, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> (-> A (-> B C)) (not (-> (-> A B) (-> A C)))) (not (-> A (-> B C))))))
================================================================
tm-name          tm-3207
in-theory        3207
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-110 tm-11 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3207.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (F -> E))), M:tm-110, m:tm-11, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-3208
in-theory        3208
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> (B -> (C -> D))))
theorem-size     27
proof            (modus-ponens tm-110 tm-12 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> A (-> B C)) (-> A (-> B C))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3208.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> (B -> (C -> D)))), M:tm-110, m:tm-12, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> A (-> B C)) (-> A (-> B C)))))
================================================================
tm-name          tm-3209
in-theory        3209
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-110 tm-14 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3209.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-110, m:tm-14, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3210
in-theory        3210
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-110 tm-16 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3210.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E and F) -> E)), M:tm-110, m:tm-16, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-3211
in-theory        3211
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-110 tm-18 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3211.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E and F) -> F)), M:tm-110, m:tm-18, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-3212
in-theory        3212
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     35
proof            (modus-ponens tm-110 tm-19 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3212.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-19, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3213
in-theory        3213
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     43
proof            (modus-ponens tm-110 tm-20 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3213.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-20, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3214
in-theory        3214
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E and F) -> E) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     35
proof            (modus-ponens tm-110 tm-21 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (and Bm Cm) Bm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3214.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E and F) -> E) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-21, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (and Bm Cm) Bm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3215
in-theory        3215
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E and F) -> F) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     35
proof            (modus-ponens tm-110 tm-22 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (and Bm Cm) Cm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3215.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E and F) -> F) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-22, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (and Bm Cm) Cm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3216
in-theory        3216
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> (E and F))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-23 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3216.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> (E and F))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-23, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3217
in-theory        3217
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D)))))
theorem-size     35
proof            (modus-ponens tm-110 tm-24 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> A (-> B C)) (and (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3217.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D))))), M:tm-110, m:tm-24, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> A (-> B C)) (and (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3218
in-theory        3218
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-110 tm-25 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3218.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (F -> (E and F)))), M:tm-110, m:tm-25, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-3219
in-theory        3219
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (E or F)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     35
proof            (modus-ponens tm-110 tm-32 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (or Bm Cm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3219.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (E or F)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-32, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (or Bm Cm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3220
in-theory        3220
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-110 tm-33 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3220.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (E or F))), M:tm-110, m:tm-33, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-3221
in-theory        3221
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F or E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     35
proof            (modus-ponens tm-110 tm-42 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (or Cm Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3221.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F or E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-42, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (or Cm Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3222
in-theory        3222
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-110 tm-43 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3222.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (F or E))), M:tm-110, m:tm-43, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-3223
in-theory        3223
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((C -> D) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))
theorem-size     33
proof            (modus-ponens tm-110 tm-44 ((A Am) (Bm (-> B C)) (Cm (-> (-> Am B) (-> Am C))) (D (-> (or (-> B C) (-> Am (-> B C))) (-> (-> Am B) (-> Am C))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3223.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((C -> D) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))), M:tm-110, m:tm-44, u:((A Am) (Bm (-> B C)) (Cm (-> (-> Am B) (-> Am C))) (D (-> (or (-> B C) (-> Am (-> B C))) (-> (-> Am B) (-> Am C)))))
================================================================
tm-name          tm-3224
in-theory        3224
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (((B -> C) -> B) -> ((B -> C) -> D)))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> B) -> ((B -> C) -> D))))
theorem-size     47
proof            (modus-ponens tm-110 tm-45 ((A (-> Am Bm)) (B Am) (C Cm) (Dm (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3224.         ((A or (((B -> C) -> (B -> D)) -> (((B -> C) -> B) -> ((B -> C) -> D)))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> B) -> ((B -> C) -> D)))), M:tm-110, m:tm-45, u:((A (-> Am Bm)) (B Am) (C Cm) (Dm (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-3225
in-theory        3225
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((B -> (C -> D)) and E) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))
theorem-size     37
proof            (modus-ponens tm-110 tm-46 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (or (and (-> A (-> B C)) Cm) (-> A (-> B C))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-3225.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((B -> (C -> D)) and E) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))), M:tm-110, m:tm-46, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (or (and (-> A (-> B C)) Cm) (-> A (-> B C))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-3226
in-theory        3226
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))
theorem-size     37
proof            (modus-ponens tm-110 tm-47 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (or (and Cm (-> A (-> B C))) (-> A (-> B C))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3226.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))), M:tm-110, m:tm-47, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (or (and Cm (-> A (-> B C))) (-> A (-> B C))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-3227
in-theory        3227
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> (D or B)) -> ((B -> C) -> C)))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (((B -> C) -> (D or B)) -> ((B -> C) -> C))))
theorem-size     53
proof            (modus-ponens tm-110 tm-51 ((A (-> Am Bm)) (B (or Cm Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm))) (D (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       185
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3227.         ((A or (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> (D or B)) -> ((B -> C) -> C)))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (((B -> C) -> (D or B)) -> ((B -> C) -> C)))), M:tm-110, m:tm-51, u:((A (-> Am Bm)) (B (or Cm Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm))) (D (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> (-> Am Bm) (or Cm Am)) (-> (-> Am Bm) Bm)))))
================================================================
tm-name          tm-3228
in-theory        3228
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     43
proof            (modus-ponens tm-110 tm-54 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3228.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-54, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3229
in-theory        3229
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B -> B)) -> ((B -> B) -> (B -> B)))) -> ((B -> (B -> B)) -> ((B or (B -> B)) -> (B -> B))))
theorem-size     31
proof            (modus-ponens tm-110 tm-55 ((A Am) (B Am) (C Am) (Bm (-> Am Am)) (Cm (-> Am Am)) (D (-> (-> Am (-> Am Am)) (-> (or Am (-> Am Am)) (-> Am Am))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-3229.         ((A or ((B -> (B -> B)) -> ((B -> B) -> (B -> B)))) -> ((B -> (B -> B)) -> ((B or (B -> B)) -> (B -> B)))), M:tm-110, m:tm-55, u:((A Am) (B Am) (C Am) (Bm (-> Am Am)) (Cm (-> Am Am)) (D (-> (-> Am (-> Am Am)) (-> (or Am (-> Am Am)) (-> Am Am)))))
================================================================
tm-name          tm-3230
in-theory        3230
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-110 tm-56 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3230.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))), M:tm-110, m:tm-56, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-3231
in-theory        3231
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> ((E -> (not F)) -> (not E))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     41
proof            (modus-ponens tm-110 tm-69 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-9)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3231.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> ((E -> (not F)) -> (not E))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-69, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3232
in-theory        3232
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> F) -> ((E -> (not F)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-110 tm-71 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-9)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3232.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> F) -> ((E -> (not F)) -> (not E)))), M:tm-110, m:tm-71, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-3233
in-theory        3233
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((not (not (B -> (C -> D)))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))
theorem-size     37
proof            (modus-ponens tm-110 tm-73 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (or (not (not (-> A (-> B C)))) (-> A (-> B C))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-10)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3233.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((not (not (B -> (C -> D)))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))), M:tm-110, m:tm-73, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (or (not (not (-> A (-> B C)))) (-> A (-> B C))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-3234
in-theory        3234
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((not (not E)) -> E) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     35
proof            (modus-ponens tm-110 tm-76 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (not (not Bm)) Bm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-10)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3234.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((not (not E)) -> E) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-76, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (not (not Bm)) Bm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3235
in-theory        3235
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((not (not E)) -> E))
theorem-size     21
proof            (modus-ponens tm-110 tm-78 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-2 tm-10)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3235.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((not (not E)) -> E)), M:tm-110, m:tm-78, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-3236
in-theory        3236
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) -> ((B -> C) -> (B -> B)))) -> ((D or (B -> (C -> B))) -> ((B -> C) -> (B -> B))))
theorem-size     31
proof            (modus-ponens tm-110 tm-80 ((A Am) (B Bm) (C Am) (Cm (-> (-> Am Bm) (-> Am Am))) (D (-> (or Dm (-> Am (-> Bm Am))) (-> (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3236.         ((A or ((B -> (C -> B)) -> ((B -> C) -> (B -> B)))) -> ((D or (B -> (C -> B))) -> ((B -> C) -> (B -> B)))), M:tm-110, m:tm-80, u:((A Am) (B Bm) (C Am) (Cm (-> (-> Am Bm) (-> Am Am))) (D (-> (or Dm (-> Am (-> Bm Am))) (-> (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-3237
in-theory        3237
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> (G -> F))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-83 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3237.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> (G -> F))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-83, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3238
in-theory        3238
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> (E -> ((B -> C) -> (B -> D)))))
theorem-size     31
proof            (modus-ponens tm-110 tm-84 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> A (-> B C)) (-> Cm (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3238.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> (E -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-84, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> A (-> B C)) (-> Cm (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3239
in-theory        3239
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-110 tm-85 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3239.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (F -> (G -> F)))), M:tm-110, m:tm-85, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-3240
in-theory        3240
times-derived    4
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     29
proof            (modus-ponens tm-110 tm-86 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3240.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-110, m:tm-86, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-3241
in-theory        3241
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> C)) -> (((B -> C) -> B) -> ((B -> C) -> C)))) -> ((((B -> C) -> D) or ((B -> C) -> (B -> C))) -> (((B -> C) -> B) -> ((B -> C) -> C))))
theorem-size     47
proof            (modus-ponens tm-110 tm-92 ((A (-> B C)) (Am (-> B C)) (Bm (-> (-> (-> B C) B) (-> (-> B C) C))) (D (-> (or (-> (-> B C) Cm) (-> (-> B C) (-> B C))) (-> (-> (-> B C) B) (-> (-> B C) C))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3241.         ((A or (((B -> C) -> (B -> C)) -> (((B -> C) -> B) -> ((B -> C) -> C)))) -> ((((B -> C) -> D) or ((B -> C) -> (B -> C))) -> (((B -> C) -> B) -> ((B -> C) -> C)))), M:tm-110, m:tm-92, u:((A (-> B C)) (Am (-> B C)) (Bm (-> (-> (-> B C) B) (-> (-> B C) C))) (D (-> (or (-> (-> B C) Cm) (-> (-> B C) (-> B C))) (-> (-> (-> B C) B) (-> (-> B C) C)))))
================================================================
tm-name          tm-3242
in-theory        3242
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> (E -> E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-95 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3242.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> (E -> E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-95, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3243
in-theory        3243
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> F) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-110 tm-97 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3243.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> F) -> (E -> E))), M:tm-110, m:tm-97, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-3244
in-theory        3244
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> D)) -> (((B -> (C -> D)) -> B) -> ((B -> (C -> D)) -> D)))) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> (((B -> (C -> D)) -> B) -> ((B -> (C -> D)) -> D))))
theorem-size     63
proof            (modus-ponens tm-110 tm-102 ((A (-> Am (-> Bm Cm))) (B Am) (C Cm) (Dm (-> (-> (-> Am (-> Bm Cm)) Am) (-> (-> Am (-> Bm Cm)) Cm))) (D (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> (-> (-> Am (-> Bm Cm)) Am) (-> (-> Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       233
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3244.         ((A or (((B -> (C -> D)) -> (B -> D)) -> (((B -> (C -> D)) -> B) -> ((B -> (C -> D)) -> D)))) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> (((B -> (C -> D)) -> B) -> ((B -> (C -> D)) -> D)))), M:tm-110, m:tm-102, u:((A (-> Am (-> Bm Cm))) (B Am) (C Cm) (Dm (-> (-> (-> Am (-> Bm Cm)) Am) (-> (-> Am (-> Bm Cm)) Cm))) (D (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> (-> (-> Am (-> Bm Cm)) Am) (-> (-> Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-3245
in-theory        3245
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     49
proof            (modus-ponens tm-110 tm-105 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3245.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-105, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3246
in-theory        3246
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-110 tm-107 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3246.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-110, m:tm-107, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3247
in-theory        3247
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))) -> ((E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     71
proof            (modus-ponens tm-110 tm-110 ((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)) (Dm (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (D (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       229
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3247.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))) -> ((E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))), M:tm-110, m:tm-110, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)) (Dm (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (D (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-3248
in-theory        3248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     53
proof            (modus-ponens tm-105 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3248.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-105, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3249
in-theory        3249
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> (A -> B))) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> (A -> C)))) -> ((D or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     73
proof            (modus-ponens tm-102 tm-110 ((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)) (Dm (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (D (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       243
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3249.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> (A -> B))) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> (A -> C)))) -> ((D or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-110, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)) (Dm (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (D (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-3250
in-theory        3250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     41
proof            (modus-ponens tm-95 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3250.         (((A -> B) -> (A -> A)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-95, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3251
in-theory        3251
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))
theorem-size     73
proof            (modus-ponens tm-92 tm-110 ((Dm (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3251.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))), M:tm-92, m:tm-110, u:((Dm (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-3252
in-theory        3252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (E -> ((F or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))
theorem-size     35
proof            (modus-ponens tm-84 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3252.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (E -> ((F or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))), M:tm-84, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-3253
in-theory        3253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-83 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3253.         ((A -> (B -> (C -> B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-83, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3254
in-theory        3254
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     63
proof            (modus-ponens tm-80 tm-110 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3254.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-80, m:tm-110, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
================================================================
tm-name          tm-3255
in-theory        3255
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E)))
theorem-size     39
proof            (modus-ponens tm-76 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-2)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3255.         (((not (not A)) -> A) and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E))), M:tm-76, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3256
in-theory        3256
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D)) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))
theorem-size     51
proof            (modus-ponens tm-73 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-8 tm-10 tm-1 tm-2)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3256.         (((not (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D)) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-73, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-3257
in-theory        3257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     45
proof            (modus-ponens tm-69 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-2)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3257.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-69, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3258
in-theory        3258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D or ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or (D or ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> (D or ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))
theorem-size     75
proof            (modus-ponens tm-55 tm-110 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       197
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3258.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D or ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or (D or ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> (D or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))), M:tm-55, m:tm-110, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-3259
in-theory        3259
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     47
proof            (modus-ponens tm-54 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3259.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-54, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3260
in-theory        3260
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> ((A or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))) -> ((E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((A or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))))
theorem-size     69
proof            (modus-ponens tm-51 tm-110 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (-> (or C (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))) (D (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (or C (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       201
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3260.         (((A -> (B -> (C -> D))) or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> ((A or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))) -> ((E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((A or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))), M:tm-51, m:tm-110, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (-> (or C (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))) (D (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (or C (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-3261
in-theory        3261
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> ((E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     63
proof            (modus-ponens tm-48 tm-110 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (and B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (and B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       179
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3261.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> ((E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-48, m:tm-110, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (and B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (and B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
================================================================
tm-name          tm-3262
in-theory        3262
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E))
theorem-size     51
proof            (modus-ponens tm-47 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3262.         (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E)), M:tm-47, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-3263
in-theory        3263
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D)) -> ((F or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))
theorem-size     51
proof            (modus-ponens tm-46 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3263.         ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D)) -> ((F or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-46, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-3264
in-theory        3264
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> D))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> D)))
theorem-size     61
proof            (modus-ponens tm-45 tm-110 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (-> (-> Am (-> Bm Cm)) C)) (D (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> Am (-> Bm Cm)) C)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       191
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3264.         ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> D))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> D))), M:tm-45, m:tm-110, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (-> (-> Am (-> Bm Cm)) C)) (D (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> Am (-> Bm Cm)) C))))
================================================================
tm-name          tm-3265
in-theory        3265
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> A)) -> ((E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> A))
theorem-size     35
proof            (modus-ponens tm-44 tm-110 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3265.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> A)) -> ((E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> A)), M:tm-44, m:tm-110, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-3266
in-theory        3266
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     39
proof            (modus-ponens tm-42 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3266.         ((A -> (B or A)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-42, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3267
in-theory        3267
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     39
proof            (modus-ponens tm-32 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3267.         ((A -> (A or B)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-32, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3268
in-theory        3268
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))
theorem-size     49
proof            (modus-ponens tm-24 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3268.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))), M:tm-24, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-3269
in-theory        3269
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     41
proof            (modus-ponens tm-23 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3269.         ((A -> (B -> (A and B))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-23, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3270
in-theory        3270
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     39
proof            (modus-ponens tm-22 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3270.         (((A and B) -> B) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-22, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3271
in-theory        3271
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     39
proof            (modus-ponens tm-21 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3271.         (((A and B) -> A) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-21, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3272
in-theory        3272
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     47
proof            (modus-ponens tm-20 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3272.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-20, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3273
in-theory        3273
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     39
proof            (modus-ponens tm-19 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3273.         ((A -> (B -> A)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-19, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3274
in-theory        3274
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))
theorem-size     31
proof            (modus-ponens tm-12 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3274.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D)), M:tm-12, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-3275
in-theory        3275
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (not ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))) -> (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D)))
theorem-size     51
proof            (modus-ponens tm-9 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-9 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3275.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (not ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))) -> (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))), M:tm-9, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-3276
in-theory        3276
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> F) -> (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) or ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E)) -> F))
theorem-size     55
proof            (modus-ponens tm-8 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       147
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3276.         ((((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> F) -> (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) or ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E)) -> F)), M:tm-8, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-3277
in-theory        3277
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E)))
theorem-size     35
proof            (modus-ponens tm-7 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-7 tm-8 tm-1 tm-2)
proof-size       119
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3277.         (A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E))), M:tm-7, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3278
in-theory        3278
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) or F)
theorem-size     35
proof            (modus-ponens tm-6 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-6 tm-8 tm-1 tm-2)
proof-size       119
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3278.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) or F), M:tm-6, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3279
in-theory        3279
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E)) and A))
theorem-size     37
proof            (modus-ponens tm-5 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3279.         (A -> (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E)) and A)), M:tm-5, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3280
in-theory        3280
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> D))
theorem-size     49
proof            (modus-ponens tm-2 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       141
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3280.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> D)), M:tm-2, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C Dm))
================================================================
tm-name          tm-3281
in-theory        3281
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E)))
theorem-size     35
proof            (modus-ponens tm-1 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       119
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3281.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E))), M:tm-1, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3282
in-theory        3282
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     37
proof            (modus-ponens tm-105 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3282.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-105, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3283
in-theory        3283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-95 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3283.         (((A -> B) -> (A -> A)) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-95, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3284
in-theory        3284
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-83 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3284.         ((A -> (B -> (C -> B))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-83, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3285
in-theory        3285
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     23
proof            (modus-ponens tm-76 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3285.         (((not (not A)) -> A) and (B or (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-76, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3286
in-theory        3286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     29
proof            (modus-ponens tm-69 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3286.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-69, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3287
in-theory        3287
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-54 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3287.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-54, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3288
in-theory        3288
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-42 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3288.         ((A -> (B or A)) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-42, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3289
in-theory        3289
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-32 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3289.         ((A -> (A or B)) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-32, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3290
in-theory        3290
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-23 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3290.         ((A -> (B -> (A and B))) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-23, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3291
in-theory        3291
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-22 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3291.         (((A and B) -> B) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-22, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3292
in-theory        3292
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-21 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3292.         (((A and B) -> A) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-21, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3293
in-theory        3293
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-20 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3293.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-20, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3294
in-theory        3294
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-19 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3294.         ((A -> (B -> A)) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-19, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3295
in-theory        3295
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     19
proof            (modus-ponens tm-7 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-7 tm-1 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3295.         (A or (B or (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-7, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3296
in-theory        3296
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-6 tm-7 tm-1 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3296.         ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F), M:tm-6, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3297
in-theory        3297
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3297.         (A -> ((B or (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and A)), M:tm-5, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3298
in-theory        3298
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     19
proof            (modus-ponens tm-1 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-1 tm-7 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3298.         (A -> (B or (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-1, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3299
in-theory        3299
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     37
proof            (modus-ponens tm-105 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3299.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-105, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3300
in-theory        3300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     25
proof            (modus-ponens tm-95 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3300.         (((A -> B) -> (A -> A)) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-95, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3301
in-theory        3301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-83 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3301.         ((A -> (B -> (C -> B))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-83, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3302
in-theory        3302
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     23
proof            (modus-ponens tm-76 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-10 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3302.         (((not (not A)) -> A) and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-76, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3303
in-theory        3303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     29
proof            (modus-ponens tm-69 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-9 tm-6 tm-1 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3303.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-69, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3304
in-theory        3304
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-54 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3304.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-54, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3305
in-theory        3305
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-42 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3305.         ((A -> (B or A)) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-42, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3306
in-theory        3306
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-32 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3306.         ((A -> (A or B)) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-32, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3307
in-theory        3307
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     25
proof            (modus-ponens tm-23 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3307.         ((A -> (B -> (A and B))) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-23, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3308
in-theory        3308
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-22 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-4 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3308.         (((A and B) -> B) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-22, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3309
in-theory        3309
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-21 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-3 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3309.         (((A and B) -> A) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-21, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3310
in-theory        3310
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-20 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3310.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-20, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3311
in-theory        3311
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-19 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3311.         ((A -> (B -> A)) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-19, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3312
in-theory        3312
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     19
proof            (modus-ponens tm-7 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-7 tm-6 tm-1 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3312.         (A or ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-7, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3313
in-theory        3313
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-6 tm-1 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3313.         (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) or F), M:tm-6, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3314
in-theory        3314
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3314.         (A -> (((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F) and A)), M:tm-5, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3315
in-theory        3315
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     19
proof            (modus-ponens tm-1 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-1 tm-6 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3315.         (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-1, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3316
in-theory        3316
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-113 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3316.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> E))), M:tm-113, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-3317
in-theory        3317
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3317.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-113, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-3318
in-theory        3318
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-113 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-3318.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> E)), M:tm-113, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-3319
in-theory        3319
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-113 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-3319.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> F)), M:tm-113, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-3320
in-theory        3320
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-113 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3320.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (E and F)))), M:tm-113, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-3321
in-theory        3321
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-113 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3321.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E or F))), M:tm-113, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-3322
in-theory        3322
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-113 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-3322.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or E))), M:tm-113, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-3323
in-theory        3323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3323.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))), M:tm-113, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-3324
in-theory        3324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> (not F)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-113 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3324.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> (not F)) -> (not E)))), M:tm-113, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-3325
in-theory        3325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((not (not E)) -> E))
theorem-size     21
proof            (modus-ponens tm-113 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10.           ((not (not A)) -> A), axiom
tm-3325.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((not (not E)) -> E)), M:tm-113, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-3326
in-theory        3326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-113 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3326.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> F)))), M:tm-113, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-3327
in-theory        3327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-113 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3327.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> E))), M:tm-113, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-3328
in-theory        3328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-113 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3328.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-113, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-3329
in-theory        3329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3329.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-113, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3330
in-theory        3330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-113 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-3330.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))), M:tm-113, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-3331
in-theory        3331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-113 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3331.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F and G) -> F))), M:tm-113, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-3332
in-theory        3332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))
theorem-size     31
proof            (modus-ponens tm-113 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3332.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))), M:tm-113, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-3333
in-theory        3333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-113 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3333.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F and G) -> G))), M:tm-113, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-3334
in-theory        3334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> F)) and E)))
theorem-size     25
proof            (modus-ponens tm-113 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3334.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> F)) and E))), M:tm-113, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-3335
in-theory        3335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     33
proof            (modus-ponens tm-113 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3335.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-113, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3336
in-theory        3336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> F) and E)))
theorem-size     25
proof            (modus-ponens tm-113 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3336.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> F) and E))), M:tm-113, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-3337
in-theory        3337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> G) and E)))
theorem-size     25
proof            (modus-ponens tm-113 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3337.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> G) and E))), M:tm-113, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-3338
in-theory        3338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (F and G))) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3338.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (F and G))) and E))), M:tm-113, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-3339
in-theory        3339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-113 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3339.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (E and F)))), M:tm-113, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-3340
in-theory        3340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3340.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (F and G))))), M:tm-113, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-3341
in-theory        3341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-113 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3341.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) or G)), M:tm-113, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-3342
in-theory        3342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))
theorem-size     31
proof            (modus-ponens tm-113 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3342.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)), M:tm-113, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-3343
in-theory        3343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) or G))
theorem-size     23
proof            (modus-ponens tm-113 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3343.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) or G)), M:tm-113, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-3344
in-theory        3344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) or G))
theorem-size     23
proof            (modus-ponens tm-113 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3344.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) or G)), M:tm-113, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-3345
in-theory        3345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) or G))
theorem-size     25
proof            (modus-ponens tm-113 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3345.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) or G)), M:tm-113, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-3346
in-theory        3346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) or G))
theorem-size     23
proof            (modus-ponens tm-113 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3346.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) or G)), M:tm-113, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-3347
in-theory        3347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (F or G)) and E)))
theorem-size     25
proof            (modus-ponens tm-113 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3347.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (F or G)) and E))), M:tm-113, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-3348
in-theory        3348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-113 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3348.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (F or G)))), M:tm-113, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-3349
in-theory        3349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-113 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3349.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> F)))), M:tm-113, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-3350
in-theory        3350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3350.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-113, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3351
in-theory        3351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-113 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3351.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F and G) -> F))), M:tm-113, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-3352
in-theory        3352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-113 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3352.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F and G) -> G))), M:tm-113, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-3353
in-theory        3353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3353.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (F and G))))), M:tm-113, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-3354
in-theory        3354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-113 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3354.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (F or G)))), M:tm-113, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-3355
in-theory        3355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-113 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3355.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G or F)))), M:tm-113, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-3356
in-theory        3356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) or G))
theorem-size     23
proof            (modus-ponens tm-113 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3356.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) or G)), M:tm-113, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-3357
in-theory        3357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G or F)) and E)))
theorem-size     25
proof            (modus-ponens tm-113 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3357.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G or F)) and E))), M:tm-113, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-3358
in-theory        3358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-113 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3358.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G or F)))), M:tm-113, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-3359
in-theory        3359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-113 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3359.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))), M:tm-113, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-3360
in-theory        3360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     41
proof            (modus-ponens tm-113 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3360.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-113, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-3361
in-theory        3361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (((E and G) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-113 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-3361.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (((E and G) or E) -> F))), M:tm-113, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-3362
in-theory        3362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (((G and E) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-113 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3362.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (((G and E) or E) -> F))), M:tm-113, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-3363
in-theory        3363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-113 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3363.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))), M:tm-113, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-3364
in-theory        3364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-113 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3364.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> ((E or (E or F)) -> G))), M:tm-113, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-3365
in-theory        3365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-113 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3365.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> ((F or (E or F)) -> G))), M:tm-113, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-3366
in-theory        3366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     43
proof            (modus-ponens tm-113 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3366.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-113, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-3367
in-theory        3367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3367.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-113, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-3368
in-theory        3368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))
theorem-size     31
proof            (modus-ponens tm-113 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3368.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)), M:tm-113, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-3369
in-theory        3369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E)))
theorem-size     33
proof            (modus-ponens tm-113 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3369.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E))), M:tm-113, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-3370
in-theory        3370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-113 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-3370.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G)))), M:tm-113, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-3371
in-theory        3371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3371.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-113, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-3372
in-theory        3372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> E))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-113 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3372.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> E))) -> (not E))), M:tm-113, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-3373
in-theory        3373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3373.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G))))), M:tm-113, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-3374
in-theory        3374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (not E)) -> (not (E and F))))
theorem-size     27
proof            (modus-ponens tm-113 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-3374.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (not E)) -> (not (E and F)))), M:tm-113, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-3375
in-theory        3375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (not F)) -> (not (E and F))))
theorem-size     27
proof            (modus-ponens tm-113 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3375.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (not F)) -> (not (E and F)))), M:tm-113, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-3376
in-theory        3376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (E and F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3376.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (E and F)))) -> (not E))), M:tm-113, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-3377
in-theory        3377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (E or F))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-113 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3377.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (E or F))) -> (not E))), M:tm-113, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-3378
in-theory        3378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F or E))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-113 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3378.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F or E))) -> (not E))), M:tm-113, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-3379
in-theory        3379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F))))
theorem-size     35
proof            (modus-ponens tm-113 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-8)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3379.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F)))), M:tm-113, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-3380
in-theory        3380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-113 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3380.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F)))), M:tm-113, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-3381
in-theory        3381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G)))
theorem-size     39
proof            (modus-ponens tm-113 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-9)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3381.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G))), M:tm-113, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-3382
in-theory        3382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3382.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-113, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-3383
in-theory        3383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G))
theorem-size     29
proof            (modus-ponens tm-113 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3383.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G)), M:tm-113, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-3384
in-theory        3384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E)))
theorem-size     31
proof            (modus-ponens tm-113 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3384.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E))), M:tm-113, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-3385
in-theory        3385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-113 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-3385.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E)))), M:tm-113, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-3386
in-theory        3386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3386.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-113, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-3387
in-theory        3387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((not (not E)) -> (not E)) -> (not (not (not E)))))
theorem-size     27
proof            (modus-ponens tm-113 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-10)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3387.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((not (not E)) -> (not E)) -> (not (not (not E))))), M:tm-113, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-3388
in-theory        3388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (((not (not E)) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-113 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-10)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3388.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (((not (not E)) or E) -> F))), M:tm-113, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-3389
in-theory        3389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-113 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3389.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((not (not F)) -> F))), M:tm-113, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-3390
in-theory        3390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((not (not E)) -> E) or F))
theorem-size     23
proof            (modus-ponens tm-113 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3390.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((not (not E)) -> E) or F)), M:tm-113, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-3391
in-theory        3391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((not (not F)) -> F) and E)))
theorem-size     25
proof            (modus-ponens tm-113 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3391.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((not (not F)) -> F) and E))), M:tm-113, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-3392
in-theory        3392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F)))
theorem-size     31
proof            (modus-ponens tm-113 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-3392.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F))), M:tm-113, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-3393
in-theory        3393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-113 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3393.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((not (not F)) -> F))), M:tm-113, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-3394
in-theory        3394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (G -> F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3394.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (G -> F)))) -> (not E))), M:tm-113, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-3395
in-theory        3395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-113 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3395.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G))), M:tm-113, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-3396
in-theory        3396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3396.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (H -> G))))), M:tm-113, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-3397
in-theory        3397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G -> F))) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3397.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G -> F))) or H)), M:tm-113, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-3398
in-theory        3398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (H -> G))) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3398.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (H -> G))) and E))), M:tm-113, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-3399
in-theory        3399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-113 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3399.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (G -> F)))), M:tm-113, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-3400
in-theory        3400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3400.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (H -> G))))), M:tm-113, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-3401
in-theory        3401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> E))
theorem-size     19
proof            (modus-ponens tm-113 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3401.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> E)), M:tm-113, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-3402
in-theory        3402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> G)) -> (E -> (F -> G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3402.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> G)) -> (E -> (F -> G)))), M:tm-113, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-3403
in-theory        3403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> (E and F)))
theorem-size     23
proof            (modus-ponens tm-113 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-3403.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> (E and F))), M:tm-113, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-3404
in-theory        3404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> F)))
theorem-size     23
proof            (modus-ponens tm-113 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3404.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> F))), M:tm-113, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-3405
in-theory        3405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((not (not E)) -> (not (not E))))
theorem-size     23
proof            (modus-ponens tm-113 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3405.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((not (not E)) -> (not (not E)))), M:tm-113, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-3406
in-theory        3406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (E -> E))) -> (not (E -> F))))
theorem-size     29
proof            (modus-ponens tm-113 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3406.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (E -> E))) -> (not (E -> F)))), M:tm-113, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-3407
in-theory        3407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-113 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3407.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F))), M:tm-113, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-3408
in-theory        3408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-113 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3408.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (F -> F)))), M:tm-113, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-3409
in-theory        3409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (E -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-113 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3409.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (E -> E)) or G)), M:tm-113, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-3410
in-theory        3410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (F -> F)) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3410.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (F -> F)) and E))), M:tm-113, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-3411
in-theory        3411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> E) -> ((E -> F) -> E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-3411.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> E) -> ((E -> F) -> E))), M:tm-113, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-3412
in-theory        3412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-113 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3412.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (F -> F)))), M:tm-113, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-3413
in-theory        3413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> E) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-3413.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> E) -> G)) -> (E -> G))), M:tm-113, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-3414
in-theory        3414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E -> F)) -> (E -> F)))
theorem-size     25
proof            (modus-ponens tm-113 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-3414.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E -> F)) -> (E -> F))), M:tm-113, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-3415
in-theory        3415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F))))
theorem-size     35
proof            (modus-ponens tm-113 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3415.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F)))), M:tm-113, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-3416
in-theory        3416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> (not ((E -> (F -> G)) -> (E -> G)))) -> (not ((E -> (F -> G)) -> (E -> F)))))
theorem-size     47
proof            (modus-ponens tm-113 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3416.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> (not ((E -> (F -> G)) -> (E -> G)))) -> (not ((E -> (F -> G)) -> (E -> F))))), M:tm-113, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-3417
in-theory        3417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> G)) -> H) -> ((((E -> (F -> G)) -> (E -> F)) or ((E -> (F -> G)) -> (E -> G))) -> H)))
theorem-size     49
proof            (modus-ponens tm-113 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3417.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> G)) -> H) -> ((((E -> (F -> G)) -> (E -> F)) or ((E -> (F -> G)) -> (E -> G))) -> H))), M:tm-113, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-3418
in-theory        3418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3418.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-113, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3419
in-theory        3419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H))
theorem-size     37
proof            (modus-ponens tm-113 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3419.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H)), M:tm-113, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-3420
in-theory        3420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E)))
theorem-size     39
proof            (modus-ponens tm-113 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3420.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E))), M:tm-113, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3421
in-theory        3421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> (E -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-113 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3421.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> (E -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G)))), M:tm-113, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-3422
in-theory        3422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3422.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-113, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-3423
in-theory        3423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (((E -> F) -> (E -> G)) -> H)) -> ((E -> (F -> G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-113 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3423.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (((E -> F) -> (E -> G)) -> H)) -> ((E -> (F -> G)) -> H))), M:tm-113, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-3424
in-theory        3424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E)))
theorem-size     35
proof            (modus-ponens tm-113 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3424.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E))), M:tm-113, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-3425
in-theory        3425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) -> ((I or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) -> H)))
theorem-size     49
proof            (modus-ponens tm-113 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3425.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) -> ((I or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) -> H))), M:tm-113, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-3426
in-theory        3426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-113 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3426.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-113, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3427
in-theory        3427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-113 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3427.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-113, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-3428
in-theory        3428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-113 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3428.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-113, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3429
in-theory        3429
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     45
proof            (modus-ponens tm-110 tm-113 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3429.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-113, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-3430
in-theory        3430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     39
proof            (modus-ponens tm-105 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3430.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-105, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3431
in-theory        3431
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     45
proof            (modus-ponens tm-102 tm-113 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3431.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-113, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-3432
in-theory        3432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     27
proof            (modus-ponens tm-95 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3432.         (((A -> B) -> (A -> A)) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-95, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3433
in-theory        3433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> A)))
theorem-size     27
proof            (modus-ponens tm-92 tm-113 ((Am (-> A A)) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3433.         (((A -> B) or (A -> A)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> A))), M:tm-92, m:tm-113, u:((Am (-> A A)) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A A))))
================================================================
tm-name          tm-3434
in-theory        3434
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)))
theorem-size     21
proof            (modus-ponens tm-84 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3434.         (A -> (B -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))), M:tm-84, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-3435
in-theory        3435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-83 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3435.         ((A -> (B -> (C -> B))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-83, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3436
in-theory        3436
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (C -> B))))
theorem-size     29
proof            (modus-ponens tm-80 tm-113 ((Am (-> A (-> B A))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3436.         ((A or (B -> (C -> B))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (C -> B)))), M:tm-80, m:tm-113, u:((Am (-> A (-> B A))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (-> B A)))))
================================================================
tm-name          tm-3437
in-theory        3437
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B)))
theorem-size     25
proof            (modus-ponens tm-76 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-10 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3437.         (((not (not A)) -> A) and (B -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B))), M:tm-76, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3438
in-theory        3438
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))
theorem-size     23
proof            (modus-ponens tm-73 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3438.         (((not (not A)) or A) -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-73, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-3439
in-theory        3439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     31
proof            (modus-ponens tm-69 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3439.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-69, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3440
in-theory        3440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((A -> (not B)) -> (not A))))
theorem-size     35
proof            (modus-ponens tm-66 tm-113 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-1 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3440.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-113, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-3441
in-theory        3441
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-54 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3441.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-54, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3442
in-theory        3442
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-51 tm-113 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3442.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-113, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-3443
in-theory        3443
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (B or A)))
theorem-size     25
proof            (modus-ponens tm-50 tm-113 ((Am (or A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3443.         ((A or (B or A)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (B or A))), M:tm-50, m:tm-113, u:((Am (or A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B))))
================================================================
tm-name          tm-3444
in-theory        3444
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B)))
theorem-size     25
proof            (modus-ponens tm-49 tm-113 ((Am (or A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3444.         ((A or (A or B)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))), M:tm-49, m:tm-113, u:((Am (or A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B))))
================================================================
tm-name          tm-3445
in-theory        3445
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-48 tm-113 ((Am (-> A (and B A))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3445.         ((A or (B -> (A and B))) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (B -> (A and B)))), M:tm-48, m:tm-113, u:((Am (-> A (and B A))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (and B A)))))
================================================================
tm-name          tm-3446
in-theory        3446
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B))
theorem-size     23
proof            (modus-ponens tm-47 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3446.         (((A and B) or B) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B)), M:tm-47, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-3447
in-theory        3447
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-46 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3447.         (((A and B) or A) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)), M:tm-46, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-3448
in-theory        3448
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-45 tm-113 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3448.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-113, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-3449
in-theory        3449
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (B -> A)))
theorem-size     25
proof            (modus-ponens tm-44 tm-113 ((Am (-> A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3449.         ((A or (B -> A)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (B -> A))), M:tm-44, m:tm-113, u:((Am (-> A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A B))))
================================================================
tm-name          tm-3450
in-theory        3450
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-42 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3450.         ((A -> (B or A)) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-42, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3451
in-theory        3451
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-32 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3451.         ((A -> (A or B)) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-32, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3452
in-theory        3452
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))
theorem-size     21
proof            (modus-ponens tm-24 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3452.         (A -> (A and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))), M:tm-24, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-3453
in-theory        3453
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     27
proof            (modus-ponens tm-23 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3453.         ((A -> (B -> (A and B))) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-23, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3454
in-theory        3454
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-22 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3454.         (((A and B) -> B) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-22, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3455
in-theory        3455
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-21 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3455.         (((A and B) -> A) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-21, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3456
in-theory        3456
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-20 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3456.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-20, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3457
in-theory        3457
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-19 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3457.         ((A -> (B -> A)) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-19, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3458
in-theory        3458
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))) -> (not A))
theorem-size     23
proof            (modus-ponens tm-9 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-9 tm-5 tm-1 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3458.         ((A -> (not ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))) -> (not A)), M:tm-9, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-3459
in-theory        3459
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E) -> F) -> ((E or ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E)) -> F))
theorem-size     41
proof            (modus-ponens tm-8 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3459.         ((((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E) -> F) -> ((E or ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E)) -> F)), M:tm-8, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-3460
in-theory        3460
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B)))
theorem-size     21
proof            (modus-ponens tm-7 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-7 tm-5 tm-1 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3460.         (A or (B -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B))), M:tm-7, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3461
in-theory        3461
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-6 tm-5 tm-1 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3461.         ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) or F), M:tm-6, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3462
in-theory        3462
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3462.         (A -> ((B -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B)) and A)), M:tm-5, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3463
in-theory        3463
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B)))
theorem-size     21
proof            (modus-ponens tm-1 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3463.         (A -> (B -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B))), M:tm-1, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-3464
in-theory        3464
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) and D) -> ((A -> B) -> (A -> C)))
theorem-size     15
proof            (modus-ponens tm-114 tm-3 ((A (and (-> B (-> C D)) Bm)) (Am (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3.            ((A and B) -> A), axiom
tm-3464.         (((A -> (B -> C)) and D) -> ((A -> B) -> (A -> C))), M:tm-114, m:tm-3, u:((A (and (-> B (-> C D)) Bm)) (Am (-> B (-> C D))))
================================================================
tm-name          tm-3465
in-theory        3465
times-derived    2
----------------------------------------------------------------
theorem          ((A and (B -> (C -> D))) -> ((B -> C) -> (B -> D)))
theorem-size     15
proof            (modus-ponens tm-114 tm-4 ((A (and Am (-> B (-> C D)))) (Bm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4.            ((A and B) -> B), axiom
tm-3465.         ((A and (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-114, m:tm-4, u:((A (and Am (-> B (-> C D)))) (Bm (-> B (-> C D))))
================================================================
tm-name          tm-3466
in-theory        3466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C)))
theorem-size     17
proof            (modus-ponens tm-114 tm-8 ((A (-> Am Bm)) (B (-> Bm Cm)) (C (or Am Bm)) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3466.         ((A -> B) -> (((B -> C) -> (A or B)) -> ((B -> C) -> C))), M:tm-114, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (or Am Bm)) (D Cm))
================================================================
tm-name          tm-3467
in-theory        3467
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (A -> (B -> C)))) -> ((A -> B) -> (A -> C)))
theorem-size     15
proof            (modus-ponens tm-114 tm-10 ((A (not (not (-> B (-> C D))))) (Am (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-10)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-10.           ((not (not A)) -> A), axiom
tm-3467.         ((not (not (A -> (B -> C)))) -> ((A -> B) -> (A -> C))), M:tm-114, m:tm-10, u:((A (not (not (-> B (-> C D))))) (Am (-> B (-> C D))))
================================================================
tm-name          tm-3468
in-theory        3468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (((A -> B) -> A) -> ((A -> B) -> B)))
theorem-size     17
proof            (modus-ponens tm-114 tm-12 ((A (-> (-> C D) Bm)) (B (-> C D)) (Am (-> C D))))
axioms-used      (tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3468.         (((A -> B) -> C) -> (((A -> B) -> A) -> ((A -> B) -> B))), M:tm-114, m:tm-12, u:((A (-> (-> C D) Bm)) (B (-> C D)) (Am (-> C D)))
================================================================
tm-name          tm-3469
in-theory        3469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> C)))
theorem-size     25
proof            (modus-ponens tm-114 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C Am) (D Cm)))
axioms-used      (tm-2 tm-1)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3469.         (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> C))), M:tm-114, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C Am) (D Cm))
================================================================
tm-name          tm-3470
in-theory        3470
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and D) -> A) -> ((((A -> (B -> C)) and D) -> B) -> (((A -> (B -> C)) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-114 tm-15 ((A (-> (and (-> Am (-> C D)) Cm) Am)) (B (and (-> Am (-> C D)) Cm)) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-3470.         ((((A -> (B -> C)) and D) -> A) -> ((((A -> (B -> C)) and D) -> B) -> (((A -> (B -> C)) and D) -> C))), M:tm-114, m:tm-15, u:((A (-> (and (-> Am (-> C D)) Cm) Am)) (B (and (-> Am (-> C D)) Cm)) (Bm (-> C D)))
================================================================
tm-name          tm-3471
in-theory        3471
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> D))) -> B) -> (((A and (B -> (C -> D))) -> C) -> ((A and (B -> (C -> D))) -> D)))
theorem-size     29
proof            (modus-ponens tm-114 tm-17 ((A (-> (and Am (-> Bm (-> C D))) Bm)) (B (and Am (-> Bm (-> C D)))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3471.         (((A and (B -> (C -> D))) -> B) -> (((A and (B -> (C -> D))) -> C) -> ((A and (B -> (C -> D))) -> D))), M:tm-114, m:tm-17, u:((A (-> (and Am (-> Bm (-> C D))) Bm)) (B (and Am (-> Bm (-> C D)))) (Cm (-> C D)))
================================================================
tm-name          tm-3472
in-theory        3472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> D)) -> (((B or (A -> B)) -> C) -> ((B or (A -> B)) -> D)))
theorem-size     23
proof            (modus-ponens tm-114 tm-44 ((A (-> (-> Am Bm) (-> C D))) (B (or Bm (-> Am Bm))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3472.         (((A -> B) -> (C -> D)) -> (((B or (A -> B)) -> C) -> ((B or (A -> B)) -> D))), M:tm-114, m:tm-44, u:((A (-> (-> Am Bm) (-> C D))) (B (or Bm (-> Am Bm))) (Cm (-> C D)))
================================================================
tm-name          tm-3473
in-theory        3473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> E)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)))
theorem-size     43
proof            (modus-ponens tm-114 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) (-> C D))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3473.         ((((A -> B) -> (A -> C)) -> (D -> E)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))), M:tm-114, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) (-> C D))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> C D)))
================================================================
tm-name          tm-3474
in-theory        3474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((((A and D) or A) -> B) -> (((A and D) or A) -> C)))
theorem-size     21
proof            (modus-ponens tm-114 tm-46 ((A (-> Am (-> C D))) (B (or (and Am Cm) Am)) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-3474.         ((A -> (B -> C)) -> ((((A and D) or A) -> B) -> (((A and D) or A) -> C))), M:tm-114, m:tm-46, u:((A (-> Am (-> C D))) (B (or (and Am Cm) Am)) (Bm (-> C D)))
================================================================
tm-name          tm-3475
in-theory        3475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((((D and A) or A) -> B) -> (((D and A) or A) -> C)))
theorem-size     21
proof            (modus-ponens tm-114 tm-47 ((A (-> Am (-> C D))) (B (or (and Cm Am) Am)) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3475.         ((A -> (B -> C)) -> ((((D and A) or A) -> B) -> (((D and A) or A) -> C))), M:tm-114, m:tm-47, u:((A (-> Am (-> C D))) (B (or (and Cm Am) Am)) (Bm (-> C D)))
================================================================
tm-name          tm-3476
in-theory        3476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (C -> D)) -> (((B or (A -> (B and A))) -> C) -> ((B or (A -> (B and A))) -> D)))
theorem-size     29
proof            (modus-ponens tm-114 tm-48 ((A (-> (-> Am (and Bm Am)) (-> C D))) (B (or Bm (-> Am (and Bm Am)))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3476.         (((A -> (B and A)) -> (C -> D)) -> (((B or (A -> (B and A))) -> C) -> ((B or (A -> (B and A))) -> D))), M:tm-114, m:tm-48, u:((A (-> (-> Am (and Bm Am)) (-> C D))) (B (or Bm (-> Am (and Bm Am)))) (Cm (-> C D)))
================================================================
tm-name          tm-3477
in-theory        3477
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> D)) -> (((A or (A or B)) -> C) -> ((A or (A or B)) -> D)))
theorem-size     23
proof            (modus-ponens tm-114 tm-49 ((A (-> (or Am Bm) (-> C D))) (B (or Am (or Am Bm))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3477.         (((A or B) -> (C -> D)) -> (((A or (A or B)) -> C) -> ((A or (A or B)) -> D))), M:tm-114, m:tm-49, u:((A (-> (or Am Bm) (-> C D))) (B (or Am (or Am Bm))) (Cm (-> C D)))
================================================================
tm-name          tm-3478
in-theory        3478
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> (C -> D)) -> (((B or (A or B)) -> C) -> ((B or (A or B)) -> D)))
theorem-size     23
proof            (modus-ponens tm-114 tm-50 ((A (-> (or Am Bm) (-> C D))) (B (or Bm (or Am Bm))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3478.         (((A or B) -> (C -> D)) -> (((B or (A or B)) -> C) -> ((B or (A or B)) -> D))), M:tm-114, m:tm-50, u:((A (-> (or Am Bm) (-> C D))) (B (or Bm (or Am Bm))) (Cm (-> C D)))
================================================================
tm-name          tm-3479
in-theory        3479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> (D -> E)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> E)))
theorem-size     45
proof            (modus-ponens tm-114 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C D))) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3479.         ((((A -> B) -> ((C or A) -> B)) -> (D -> E)) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> E))), M:tm-114, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) (-> C D))) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (Dm (-> C D)))
================================================================
tm-name          tm-3480
in-theory        3480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (B -> C)) -> (((A -> B) -> (A or B)) -> ((A -> B) -> C)))
theorem-size     21
proof            (modus-ponens tm-114 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> Am Bm)) (C (or Am Bm)) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-3480.         (((A -> B) -> (B -> C)) -> (((A -> B) -> (A or B)) -> ((A -> B) -> C))), M:tm-114, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> Am Bm)) (C (or Am Bm)) (D Cm))
================================================================
tm-name          tm-3481
in-theory        3481
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> (C -> D)) -> ((((A -> B) or ((A -> (not B)) -> (not A))) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> D)))
theorem-size     39
proof            (modus-ponens tm-114 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) (-> C D))) (B (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-9)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3481.         ((((A -> (not B)) -> (not A)) -> (C -> D)) -> ((((A -> B) or ((A -> (not B)) -> (not A))) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> D))), M:tm-114, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) (-> C D))) (B (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))) (Cm (-> C D)))
================================================================
tm-name          tm-3482
in-theory        3482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((((not (not A)) or A) -> B) -> (((not (not A)) or A) -> C)))
theorem-size     21
proof            (modus-ponens tm-114 tm-73 ((A (-> Am (-> C D))) (B (or (not (not Am)) Am)) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-10)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3482.         ((A -> (B -> C)) -> ((((not (not A)) or A) -> B) -> (((not (not A)) or A) -> C))), M:tm-114, m:tm-73, u:((A (-> Am (-> C D))) (B (or (not (not Am)) Am)) (Bm (-> C D)))
================================================================
tm-name          tm-3483
in-theory        3483
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (B -> C)))) -> A) -> (((not (not (A -> (B -> C)))) -> B) -> ((not (not (A -> (B -> C)))) -> C)))
theorem-size     29
proof            (modus-ponens tm-114 tm-77 ((A (-> (not (not (-> Am (-> C D)))) Am)) (B (not (not (-> Am (-> C D))))) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-10)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-3483.         (((not (not (A -> (B -> C)))) -> A) -> (((not (not (A -> (B -> C)))) -> B) -> ((not (not (A -> (B -> C)))) -> C))), M:tm-114, m:tm-77, u:((A (-> (not (not (-> Am (-> C D)))) Am)) (B (not (not (-> Am (-> C D))))) (Bm (-> C D)))
================================================================
tm-name          tm-3484
in-theory        3484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> (C -> D)) -> (((E or (A -> (B -> A))) -> C) -> ((E or (A -> (B -> A))) -> D)))
theorem-size     29
proof            (modus-ponens tm-114 tm-80 ((A (-> (-> Am (-> Bm Am)) (-> C D))) (B (or Dm (-> Am (-> Bm Am)))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3484.         (((A -> (B -> A)) -> (C -> D)) -> (((E or (A -> (B -> A))) -> C) -> ((E or (A -> (B -> A))) -> D))), M:tm-114, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) (-> C D))) (B (or Dm (-> Am (-> Bm Am)))) (Cm (-> C D)))
================================================================
tm-name          tm-3485
in-theory        3485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> C) -> (A -> B)))
theorem-size     11
proof            (modus-ponens tm-114 tm-84 ((A (-> Am Bm)) (B Am) (C Cm) (D Bm)))
axioms-used      (tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3485.         ((A -> B) -> ((A -> C) -> (A -> B))), M:tm-114, m:tm-84, u:((A (-> Am Bm)) (B Am) (C Cm) (D Bm))
================================================================
tm-name          tm-3486
in-theory        3486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> (B -> C)) -> ((((A -> D) or (A -> A)) -> B) -> (((A -> D) or (A -> A)) -> C)))
theorem-size     27
proof            (modus-ponens tm-114 tm-92 ((A (-> (-> Am Am) (-> C D))) (B (or (-> Am Cm) (-> Am Am))) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3486.         (((A -> A) -> (B -> C)) -> ((((A -> D) or (A -> A)) -> B) -> (((A -> D) or (A -> A)) -> C))), M:tm-114, m:tm-92, u:((A (-> (-> Am Am) (-> C D))) (B (or (-> Am Cm) (-> Am Am))) (Bm (-> C D)))
================================================================
tm-name          tm-3487
in-theory        3487
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (A -> B)) -> ((((A -> B) -> C) -> A) -> (((A -> B) -> C) -> B)))
theorem-size     25
proof            (modus-ponens tm-114 tm-96 ((A (-> (-> (-> C D) Bm) (-> C D))) (B (-> (-> C D) Bm)) (Am (-> C D))))
axioms-used      (tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-3487.         ((((A -> B) -> C) -> (A -> B)) -> ((((A -> B) -> C) -> A) -> (((A -> B) -> C) -> B))), M:tm-114, m:tm-96, u:((A (-> (-> (-> C D) Bm) (-> C D))) (B (-> (-> C D) Bm)) (Am (-> C D)))
================================================================
tm-name          tm-3488
in-theory        3488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> A) -> (C -> D))) -> ((A -> C) -> (A -> D)))
theorem-size     17
proof            (modus-ponens tm-114 tm-98 ((A (-> Am (-> (-> Bm Am) (-> C D)))) (B Am) (Cm (-> C D))))
axioms-used      (tm-2 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-3488.         ((A -> ((B -> A) -> (C -> D))) -> ((A -> C) -> (A -> D))), M:tm-114, m:tm-98, u:((A (-> Am (-> (-> Bm Am) (-> C D)))) (B Am) (Cm (-> C D)))
================================================================
tm-name          tm-3489
in-theory        3489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A -> (B -> C))) -> ((A -> B) -> (A -> C)))
theorem-size     15
proof            (modus-ponens tm-114 tm-99 ((A (-> Am (-> Am (-> C D)))) (B Am) (Bm (-> C D))))
axioms-used      (tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-3489.         ((A -> (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-114, m:tm-99, u:((A (-> Am (-> Am (-> C D)))) (B Am) (Bm (-> C D)))
================================================================
tm-name          tm-3490
in-theory        3490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> B)))
theorem-size     25
proof            (modus-ponens tm-114 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C Am) (D Bm)))
axioms-used      (tm-2 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3490.         (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> B))), M:tm-114, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C Am) (D Bm))
================================================================
tm-name          tm-3491
in-theory        3491
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> (D -> E)) -> (((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> E)))
theorem-size     57
proof            (modus-ponens tm-114 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) (-> C D))) (B (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3491.         ((((A -> (B -> C)) -> (A -> C)) -> (D -> E)) -> (((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> E))), M:tm-114, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) (-> C D))) (B (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (Dm (-> C D)))
================================================================
tm-name          tm-3492
in-theory        3492
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> ((((A -> (B -> C)) -> (A -> B)) -> A) -> (((A -> (B -> C)) -> (A -> B)) -> C)))
theorem-size     39
proof            (modus-ponens tm-114 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C Am) (D Cm)))
axioms-used      (tm-2 tm-1)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-3492.         ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> ((((A -> (B -> C)) -> (A -> B)) -> A) -> (((A -> (B -> C)) -> (A -> B)) -> C))), M:tm-114, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C Am) (D Cm))
================================================================
tm-name          tm-3493
in-theory        3493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> (D -> E))) -> (((A -> (B -> C)) -> D) -> ((A -> (B -> C)) -> E)))
theorem-size     33
proof            (modus-ponens tm-114 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> C D)))) (B (-> Am (-> Bm Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3493.         (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> (D -> E))) -> (((A -> (B -> C)) -> D) -> ((A -> (B -> C)) -> E))), M:tm-114, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> C D)))) (B (-> Am (-> Bm Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-3494
in-theory        3494
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) -> (((F or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D) -> ((F or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> E)))
theorem-size     53
proof            (modus-ponens tm-114 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> C D))) (B (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3494.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) -> (((F or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D) -> ((F or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> E))), M:tm-114, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> C D))) (B (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (Dm (-> C D)))
================================================================
tm-name          tm-3495
in-theory        3495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> D))) -> ((A -> (B -> C)) -> (A -> (B -> D))))
theorem-size     19
proof            (modus-ponens tm-114 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B Am) (C (-> Bm Cm)) (D (-> Bm Dm))))
axioms-used      (tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3495.         ((A -> (B -> (C -> D))) -> ((A -> (B -> C)) -> (A -> (B -> D)))), M:tm-114, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B Am) (C (-> Bm Cm)) (D (-> Bm Dm)))
================================================================
tm-name          tm-3496
in-theory        3496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-113 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3496.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H))))), M:tm-113, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3497
in-theory        3497
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> (((B -> C) -> B) -> ((B -> C) -> D))))
theorem-size     33
proof            (modus-ponens tm-110 tm-114 ((Am (-> Cm (-> B Dm))) (Bm (-> Cm B)) (A Cm) (C Dm) (D (-> (-> Cm (-> B Dm)) (-> (-> (-> Cm B) Cm) (-> (-> Cm B) Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3497.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> (((B -> C) -> B) -> ((B -> C) -> D)))), M:tm-110, m:tm-114, u:((Am (-> Cm (-> B Dm))) (Bm (-> Cm B)) (A Cm) (C Dm) (D (-> (-> Cm (-> B Dm)) (-> (-> (-> Cm B) Cm) (-> (-> Cm B) Dm)))))
================================================================
tm-name          tm-3498
in-theory        3498
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     37
proof            (modus-ponens tm-105 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3498.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-105, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3499
in-theory        3499
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (C -> D))) -> (A -> B)) or ((A -> (B -> (C -> D))) -> (A -> (C -> D)))) -> ((A -> (B -> (C -> D))) -> ((A -> C) -> (A -> D))))
theorem-size     41
proof            (modus-ponens tm-102 tm-114 ((Am (-> Bm (-> B (-> Cm Dm)))) (A Bm) (C (-> Cm Dm)) (D (-> (-> Bm (-> B (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3499.         ((((A -> (B -> (C -> D))) -> (A -> B)) or ((A -> (B -> (C -> D))) -> (A -> (C -> D)))) -> ((A -> (B -> (C -> D))) -> ((A -> C) -> (A -> D)))), M:tm-102, m:tm-114, u:((Am (-> Bm (-> B (-> Cm Dm)))) (A Bm) (C (-> Cm Dm)) (D (-> (-> Bm (-> B (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3500
in-theory        3500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-95 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3500.         (((A -> B) -> (A -> A)) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F))))), M:tm-95, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3501
in-theory        3501
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> D) or ((A -> (B -> C)) -> (A -> (B -> C)))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-92 tm-114 ((Am (-> Bm (-> Cm Dm))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3501.         ((((A -> (B -> C)) -> D) or ((A -> (B -> C)) -> (A -> (B -> C)))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-92, m:tm-114, u:((Am (-> Bm (-> Cm Dm))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3502
in-theory        3502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> D))) -> (E -> (A -> ((B -> C) -> (B -> D)))))
theorem-size     19
proof            (modus-ponens tm-84 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3502.         ((A -> (B -> (C -> D))) -> (E -> (A -> ((B -> C) -> (B -> D))))), M:tm-84, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3503
in-theory        3503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-83 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3503.         ((A -> (B -> (C -> B))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-83, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3504
in-theory        3504
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (D -> (B -> C)))) -> ((B -> C) -> ((D -> B) -> (D -> C))))
theorem-size     23
proof            (modus-ponens tm-80 tm-114 ((Am (-> Cm Dm)) (B Bm) (A (-> Cm Dm)) (C (-> (-> Cm Dm) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3504.         ((A or ((B -> C) -> (D -> (B -> C)))) -> ((B -> C) -> ((D -> B) -> (D -> C)))), M:tm-80, m:tm-114, u:((Am (-> Cm Dm)) (B Bm) (A (-> Cm Dm)) (C (-> (-> Cm Dm) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3505
in-theory        3505
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (D -> E))) -> (B -> ((C -> D) -> (C -> E)))))
theorem-size     23
proof            (modus-ponens tm-76 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3505.         (((not (not A)) -> A) and ((B -> (C -> (D -> E))) -> (B -> ((C -> D) -> (C -> E))))), M:tm-76, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3506
in-theory        3506
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (B -> (C -> D))))) or (A -> (B -> (C -> D)))) -> (A -> ((B -> C) -> (B -> D))))
theorem-size     27
proof            (modus-ponens tm-73 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3506.         (((not (not (A -> (B -> (C -> D))))) or (A -> (B -> (C -> D)))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-73, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3507
in-theory        3507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-69 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3507.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F))))), M:tm-69, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3508
in-theory        3508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) -> (((A -> (B -> C)) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-55 tm-114 ((A (-> Bm (-> Cm Dm))) (Am (-> Bm (-> Cm Dm))) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3508.         (((A -> (B -> C)) -> (A -> (B -> C))) -> (((A -> (B -> C)) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))), M:tm-55, m:tm-114, u:((A (-> Bm (-> Cm Dm))) (Am (-> Bm (-> Cm Dm))) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-3509
in-theory        3509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-54 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3509.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-54, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3510
in-theory        3510
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (C -> D)) -> ((A or B) -> (C -> D)))) -> ((B -> (C -> D)) -> (((A or B) -> C) -> ((A or B) -> D))))
theorem-size     35
proof            (modus-ponens tm-51 tm-114 ((Am (-> A (-> Cm Dm))) (Bm (or C A)) (B (-> Cm Dm)) (D (-> (-> A (-> Cm Dm)) (-> (-> (or C A) Cm) (-> (or C A) Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3510.         (((A -> B) or ((B -> (C -> D)) -> ((A or B) -> (C -> D)))) -> ((B -> (C -> D)) -> (((A or B) -> C) -> ((A or B) -> D)))), M:tm-51, m:tm-114, u:((Am (-> A (-> Cm Dm))) (Bm (or C A)) (B (-> Cm Dm)) (D (-> (-> A (-> Cm Dm)) (-> (-> (or C A) Cm) (-> (or C A) Dm)))))
================================================================
tm-name          tm-3511
in-theory        3511
times-derived    2
----------------------------------------------------------------
theorem          (((A and (B -> (C -> (D -> E)))) or (B -> (C -> (D -> E)))) -> (B -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-47 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3511.         (((A and (B -> (C -> (D -> E)))) or (B -> (C -> (D -> E)))) -> (B -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3512
in-theory        3512
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (C -> D))) and E) or (A -> (B -> (C -> D)))) -> (A -> ((B -> C) -> (B -> D))))
theorem-size     27
proof            (modus-ponens tm-46 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3512.         ((((A -> (B -> (C -> D))) and E) or (A -> (B -> (C -> D)))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-46, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3513
in-theory        3513
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) or ((A -> B) -> (A -> (C -> D)))) -> ((A -> B) -> ((A -> C) -> (A -> D))))
theorem-size     29
proof            (modus-ponens tm-45 tm-114 ((Am (-> Bm B)) (A Bm) (C (-> Cm Dm)) (D (-> (-> Bm B) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3513.         (((A -> (B -> (C -> D))) or ((A -> B) -> (A -> (C -> D)))) -> ((A -> B) -> ((A -> C) -> (A -> D)))), M:tm-45, m:tm-114, u:((Am (-> Bm B)) (A Bm) (C (-> Cm Dm)) (D (-> (-> Bm B) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3514
in-theory        3514
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (D -> (A -> (B -> C)))) -> (D -> ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-44 tm-114 ((A Am) (B (-> Bm (-> Cm Dm))) (C (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3514.         (((A -> (B -> C)) or (D -> (A -> (B -> C)))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-44, m:tm-114, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3515
in-theory        3515
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-42 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3515.         ((A -> (B or A)) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3516
in-theory        3516
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-32 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3516.         ((A -> (A or B)) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3517
in-theory        3517
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> D))) -> ((A -> (B -> (C -> D))) and (A -> ((B -> C) -> (B -> D)))))
theorem-size     25
proof            (modus-ponens tm-24 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3517.         ((A -> (B -> (C -> D))) -> ((A -> (B -> (C -> D))) and (A -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3518
in-theory        3518
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-23 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3518.         ((A -> (B -> (A and B))) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3519
in-theory        3519
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-22 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3519.         (((A and B) -> B) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3520
in-theory        3520
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-21 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3520.         (((A and B) -> A) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3521
in-theory        3521
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-20 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3521.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3522
in-theory        3522
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-19 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3522.         ((A -> (B -> A)) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3523
in-theory        3523
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> D))) -> (A -> (B -> (C -> D))))
theorem-size     15
proof            (modus-ponens tm-12 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3523.         ((A -> (B -> (C -> D))) -> (A -> (B -> (C -> D)))), M:tm-12, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3524
in-theory        3524
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (not (A -> ((B -> C) -> (B -> D))))) -> (not (A -> (B -> (C -> D)))))
theorem-size     27
proof            (modus-ponens tm-9 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-9 tm-2 tm-1)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3524.         (((A -> (B -> (C -> D))) -> (not (A -> ((B -> C) -> (B -> D))))) -> (not (A -> (B -> (C -> D))))), M:tm-9, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3525
in-theory        3525
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> (B -> D))) -> E) -> (((A -> (B -> (C -> D))) or (A -> ((B -> C) -> (B -> D)))) -> E))
theorem-size     31
proof            (modus-ponens tm-8 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3525.         (((A -> ((B -> C) -> (B -> D))) -> E) -> (((A -> (B -> (C -> D))) or (A -> ((B -> C) -> (B -> D)))) -> E)), M:tm-8, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3526
in-theory        3526
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (D -> E))) -> (B -> ((C -> D) -> (C -> E)))))
theorem-size     19
proof            (modus-ponens tm-7 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-7 tm-2 tm-1)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3526.         (A or ((B -> (C -> (D -> E))) -> (B -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3527
in-theory        3527
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-6 tm-2 tm-1)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3527.         (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3528
in-theory        3528
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (D -> E))) -> (B -> ((C -> D) -> (C -> E)))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3528.         (A -> (((B -> (C -> (D -> E))) -> (B -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3529
in-theory        3529
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> A) -> ((A -> (B -> (C -> D))) -> ((B -> C) -> (B -> D))))
theorem-size     25
proof            (modus-ponens tm-2 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B Am) (C (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3529.         (((A -> (B -> (C -> D))) -> A) -> ((A -> (B -> (C -> D))) -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B Am) (C (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-3530
in-theory        3530
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (D -> E))) -> (B -> ((C -> D) -> (C -> E)))))
theorem-size     19
proof            (modus-ponens tm-1 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-1 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3530.         (A -> ((B -> (C -> (D -> E))) -> (B -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3531
in-theory        3531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-113 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3531.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-113, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3532
in-theory        3532
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-110 tm-115 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3532.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-110, m:tm-115, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3533
in-theory        3533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     19
proof            (modus-ponens tm-108 tm-115 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3533.         ((A -> (B -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-108, m:tm-115, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-3534
in-theory        3534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (A -> (B -> (C -> D)))) -> (A -> ((B -> C) -> (B -> D))))
theorem-size     33
proof            (modus-ponens tm-106 tm-115 ((Am (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> Bm (-> Cm (-> Dm Em))))) (A Bm) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-2 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3534.         (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (A -> (B -> (C -> D)))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-106, m:tm-115, u:((Am (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> Bm (-> Cm (-> Dm Em))))) (A Bm) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-3535
in-theory        3535
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     37
proof            (modus-ponens tm-105 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3535.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-105, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3536
in-theory        3536
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-102 tm-115 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3536.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-102, m:tm-115, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3537
in-theory        3537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     33
proof            (modus-ponens tm-100 tm-115 ((Am (-> Bm (-> (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) C))) (A Bm) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3537.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-100, m:tm-115, u:((Am (-> Bm (-> (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) C))) (A Bm) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-3538
in-theory        3538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     33
proof            (modus-ponens tm-96 tm-115 ((Am (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B)) (A (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3538.         (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-96, m:tm-115, u:((Am (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B)) (A (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3539
in-theory        3539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-95 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3539.         (((A -> B) -> (A -> A)) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-95, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3540
in-theory        3540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-92 tm-115 ((Am (-> A A)) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3540.         (((A -> B) or (A -> A)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-92, m:tm-115, u:((Am (-> A A)) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3541
in-theory        3541
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     19
proof            (modus-ponens tm-84 tm-115 ((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3541.         (A -> (B -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-84, m:tm-115, u:((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3542
in-theory        3542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-83 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3542.         ((A -> (B -> (C -> B))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-83, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3543
in-theory        3543
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-80 tm-115 ((Am (-> A (-> B A))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3543.         ((A or (B -> (C -> B))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-80, m:tm-115, u:((Am (-> A (-> B A))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3544
in-theory        3544
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E))) -> E)
theorem-size     21
proof            (modus-ponens tm-77 tm-115 ((Am (not (not (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B)))) (A (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-10 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3544.         ((not (not ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E))) -> E), M:tm-77, m:tm-115, u:((Am (not (not (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B)))) (A (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3545
in-theory        3545
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     23
proof            (modus-ponens tm-76 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3545.         (((not (not A)) -> A) and (B -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-76, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3546
in-theory        3546
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     21
proof            (modus-ponens tm-73 tm-115 ((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-10 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3546.         (((not (not A)) or A) -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-73, m:tm-115, u:((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3547
in-theory        3547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     29
proof            (modus-ponens tm-69 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3547.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-69, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3548
in-theory        3548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-66 tm-115 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-9 tm-1 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3548.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-66, m:tm-115, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3549
in-theory        3549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     21
proof            (modus-ponens tm-55 tm-115 ((Am (-> A Bm)) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3549.         ((A -> B) -> ((A or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-55, m:tm-115, u:((Am (-> A Bm)) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-3550
in-theory        3550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-54 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3550.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-54, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3551
in-theory        3551
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-51 tm-115 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3551.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-51, m:tm-115, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3552
in-theory        3552
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-50 tm-115 ((Am (or A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3552.         ((A or (B or A)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-50, m:tm-115, u:((Am (or A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3553
in-theory        3553
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-49 tm-115 ((Am (or A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3553.         ((A or (A or B)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-49, m:tm-115, u:((Am (or A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3554
in-theory        3554
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-48 tm-115 ((Am (-> A (and B A))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3554.         ((A or (B -> (A and B))) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-48, m:tm-115, u:((Am (-> A (and B A))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3555
in-theory        3555
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-47 tm-115 ((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3555.         (((A and B) or B) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-47, m:tm-115, u:((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3556
in-theory        3556
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-46 tm-115 ((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3556.         (((A and B) or A) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-46, m:tm-115, u:((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3557
in-theory        3557
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-45 tm-115 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3557.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-45, m:tm-115, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3558
in-theory        3558
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-44 tm-115 ((Am (-> A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3558.         ((A or (B -> A)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-44, m:tm-115, u:((Am (-> A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3559
in-theory        3559
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-42 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3559.         ((A -> (B or A)) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-42, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3560
in-theory        3560
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-32 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3560.         ((A -> (A or B)) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-32, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3561
in-theory        3561
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     19
proof            (modus-ponens tm-24 tm-115 ((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3561.         (A -> (A and (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-24, m:tm-115, u:((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3562
in-theory        3562
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-23 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3562.         ((A -> (B -> (A and B))) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-23, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3563
in-theory        3563
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-22 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3563.         (((A and B) -> B) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-22, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3564
in-theory        3564
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-21 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3564.         (((A and B) -> A) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-21, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3565
in-theory        3565
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-20 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3565.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-20, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3566
in-theory        3566
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-19 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3566.         ((A -> (B -> A)) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-19, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3567
in-theory        3567
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> F)
theorem-size     21
proof            (modus-ponens tm-17 tm-115 ((Am (and A (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) C))) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3567.         ((A and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> F), M:tm-17, m:tm-115, u:((Am (and A (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) C))) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3568
in-theory        3568
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> E)
theorem-size     21
proof            (modus-ponens tm-15 tm-115 ((Am (and (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B) C)) (A (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3568.         ((((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> E), M:tm-15, m:tm-115, u:((Am (and (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B) C)) (A (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3569
in-theory        3569
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (A -> E))
theorem-size     21
proof            (modus-ponens tm-13 tm-115 ((Am (-> Bm (-> (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) C))) (A Bm) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-1)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3569.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (A -> E)), M:tm-13, m:tm-115, u:((Am (-> Bm (-> (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) C))) (A Bm) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-3570
in-theory        3570
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not A))
theorem-size     21
proof            (modus-ponens tm-9 tm-115 ((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-9 tm-1 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3570.         ((A -> (not (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not A)), M:tm-9, m:tm-115, u:((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3571
in-theory        3571
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> ((F or (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-115 ((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3571.         (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> ((F or (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> E)), M:tm-8, m:tm-115, u:((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3572
in-theory        3572
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     19
proof            (modus-ponens tm-7 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-7 tm-1 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3572.         (A or (B -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-7, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3573
in-theory        3573
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-6 tm-1 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3573.         ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F), M:tm-6, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3574
in-theory        3574
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3574.         (A -> ((B -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and A)), M:tm-5, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-3575
in-theory        3575
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     19
proof            (modus-ponens tm-2 tm-115 ((A Am) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-1)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3575.         ((A -> B) -> (A -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-2, m:tm-115, u:((A Am) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-3576
in-theory        3576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) and A) -> ((B -> C) -> (B -> D)))
theorem-size     17
proof            (modus-ponens tm-114 tm-116 ((A (and (-> Am (-> B (-> C D))) Am)) (Bm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3576.         (((A -> (B -> (C -> D))) and A) -> ((B -> C) -> (B -> D))), M:tm-114, m:tm-116, u:((A (and (-> Am (-> B (-> C D))) Am)) (Bm (-> B (-> C D))))
================================================================
tm-name          tm-3577
in-theory        3577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) and E) -> F))
theorem-size     23
proof            (modus-ponens tm-113 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3577.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) and E) -> F)), M:tm-113, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3578
in-theory        3578
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and A))
theorem-size     19
proof            (modus-ponens tm-109 tm-116 ((A (and (-> Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Am)) (Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3578.         (not ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and A)), M:tm-109, m:tm-116, u:((A (and (-> Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Am)) (Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-3579
in-theory        3579
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) and D) -> E))
theorem-size     27
proof            (modus-ponens tm-105 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3579.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) and D) -> E)), M:tm-105, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3580
in-theory        3580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) and C) -> D))
theorem-size     15
proof            (modus-ponens tm-95 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3580.         (((A -> B) -> (A -> A)) and (((C -> D) and C) -> D)), M:tm-95, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3581
in-theory        3581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) and A) -> (B -> C))
theorem-size     11
proof            (modus-ponens tm-87 tm-116 ((A (and (-> Am (-> B C)) Am)) (Bm (-> B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3581.         (((A -> (B -> C)) and A) -> (B -> C)), M:tm-87, m:tm-116, u:((A (and (-> Am (-> B C)) Am)) (Bm (-> B C)))
================================================================
tm-name          tm-3582
in-theory        3582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and A) -> (C -> B))
theorem-size     9
proof            (modus-ponens tm-84 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3582.         (((A -> B) and A) -> (C -> B)), M:tm-84, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-3583
in-theory        3583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-83 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3583.         ((A -> (B -> (C -> B))) and (((D -> E) and D) -> E)), M:tm-83, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3584
in-theory        3584
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (not (B -> (C -> B)))) and A))
theorem-size     11
proof            (modus-ponens tm-79 tm-116 ((A (and (-> Am (not (-> B (-> C B)))) Am)) (Bm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3584.         (not ((A -> (not (B -> (C -> B)))) and A)), M:tm-79, m:tm-116, u:((A (and (-> Am (not (-> B (-> C B)))) Am)) (Bm (not (-> B (-> C B)))))
================================================================
tm-name          tm-3585
in-theory        3585
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) and B) -> C))
theorem-size     13
proof            (modus-ponens tm-76 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-10 tm-2 tm-3 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3585.         (((not (not A)) -> A) and (((B -> C) and B) -> C)), M:tm-76, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3586
in-theory        3586
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) and A))) or ((A -> B) and A)) -> B)
theorem-size     15
proof            (modus-ponens tm-73 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-8 tm-10 tm-2 tm-3 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3586.         (((not (not ((A -> B) and A))) or ((A -> B) and A)) -> B), M:tm-73, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-3587
in-theory        3587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) and C) -> D))
theorem-size     19
proof            (modus-ponens tm-69 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-9 tm-2 tm-3 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3587.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) and C) -> D)), M:tm-69, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3588
in-theory        3588
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (not A)) and A))
theorem-size     7
proof            (modus-ponens tm-60 tm-116 ((A (-> Am (not Am))) (B Am) (Bm (not Am))))
axioms-used      (tm-9 tm-4 tm-2 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3588.         (not ((A -> (not A)) and A)), M:tm-60, m:tm-116, u:((A (-> Am (not Am))) (B Am) (Bm (not Am)))
================================================================
tm-name          tm-3589
in-theory        3589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) and D) -> E))
theorem-size     21
proof            (modus-ponens tm-54 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3589.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) and D) -> E)), M:tm-54, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3590
in-theory        3590
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) and B)) or ((B -> C) and B)) -> C)
theorem-size     15
proof            (modus-ponens tm-47 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-8 tm-4 tm-2 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3590.         (((A and ((B -> C) and B)) or ((B -> C) and B)) -> C), M:tm-47, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-3591
in-theory        3591
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and A) and C) or ((A -> B) and A)) -> B)
theorem-size     15
proof            (modus-ponens tm-46 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-8 tm-3 tm-2 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3591.         (((((A -> B) and A) and C) or ((A -> B) and A)) -> B), M:tm-46, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-3592
in-theory        3592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) and C) -> D))
theorem-size     13
proof            (modus-ponens tm-42 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3592.         ((A -> (B or A)) and (((C -> D) and C) -> D)), M:tm-42, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3593
in-theory        3593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) and C) -> D))
theorem-size     13
proof            (modus-ponens tm-32 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3593.         ((A -> (A or B)) and (((C -> D) and C) -> D)), M:tm-32, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3594
in-theory        3594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and A) -> (((A -> B) and A) and B))
theorem-size     13
proof            (modus-ponens tm-24 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3594.         (((A -> B) and A) -> (((A -> B) and A) and B)), M:tm-24, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-3595
in-theory        3595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) and C) -> D))
theorem-size     15
proof            (modus-ponens tm-23 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3595.         ((A -> (B -> (A and B))) and (((C -> D) and C) -> D)), M:tm-23, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3596
in-theory        3596
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) and C) -> D))
theorem-size     13
proof            (modus-ponens tm-22 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3596.         (((A and B) -> B) and (((C -> D) and C) -> D)), M:tm-22, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3597
in-theory        3597
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) and C) -> D))
theorem-size     13
proof            (modus-ponens tm-21 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3597.         (((A and B) -> A) and (((C -> D) and C) -> D)), M:tm-21, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3598
in-theory        3598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) and D) -> E))
theorem-size     21
proof            (modus-ponens tm-20 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3598.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) and D) -> E)), M:tm-20, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3599
in-theory        3599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) and C) -> D))
theorem-size     13
proof            (modus-ponens tm-19 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3599.         ((A -> (B -> A)) and (((C -> D) and C) -> D)), M:tm-19, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3600
in-theory        3600
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> A) and (A -> B)) -> B)
theorem-size     11
proof            (modus-ponens tm-17 tm-116 ((A (-> (-> Bm C) Bm)) (Am (-> Bm C)) (B Bm)))
axioms-used      (tm-2 tm-4 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3600.         ((((A -> B) -> A) and (A -> B)) -> B), M:tm-17, m:tm-116, u:((A (-> (-> Bm C) Bm)) (Am (-> Bm C)) (B Bm))
================================================================
tm-name          tm-3601
in-theory        3601
times-derived    2
----------------------------------------------------------------
theorem          (((A -> A) and A) -> A)
theorem-size     7
proof            (modus-ponens tm-15 tm-116 ((Bm Am) (B Am) (C Am) (A Am)))
axioms-used      (tm-2 tm-3 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3601.         (((A -> A) and A) -> A), M:tm-15, m:tm-116, u:((Bm Am) (B Am) (C Am) (A Am))
================================================================
tm-name          tm-3602
in-theory        3602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and A) -> ((A -> B) and A))
theorem-size     11
proof            (modus-ponens tm-12 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3602.         (((A -> B) and A) -> ((A -> B) and A)), M:tm-12, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-3603
in-theory        3603
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> (not B)) -> (not ((A -> B) and A)))
theorem-size     15
proof            (modus-ponens tm-9 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-9 tm-2 tm-3 tm-4)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3603.         ((((A -> B) and A) -> (not B)) -> (not ((A -> B) and A))), M:tm-9, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-3604
in-theory        3604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C -> A) and C) or A) -> B))
theorem-size     13
proof            (modus-ponens tm-8 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-8 tm-2 tm-3 tm-4)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3604.         ((A -> B) -> ((((C -> A) and C) or A) -> B)), M:tm-8, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-3605
in-theory        3605
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) and B) -> C))
theorem-size     9
proof            (modus-ponens tm-7 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-7 tm-2 tm-3 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3605.         (A or (((B -> C) and B) -> C)), M:tm-7, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3606
in-theory        3606
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) or C)
theorem-size     9
proof            (modus-ponens tm-6 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-6 tm-2 tm-3 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3606.         ((((A -> B) and A) -> B) or C), M:tm-6, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3607
in-theory        3607
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) and B) -> C) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3607.         (A -> ((((B -> C) and B) -> C) and A)), M:tm-5, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3608
in-theory        3608
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and A) -> B) -> (((A -> (B -> C)) and A) -> C))
theorem-size     19
proof            (modus-ponens tm-2 tm-116 ((A (and (-> Am (-> B C)) Am)) (Bm (-> B C))))
axioms-used      (tm-2 tm-3 tm-4)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3608.         ((((A -> (B -> C)) and A) -> B) -> (((A -> (B -> C)) and A) -> C)), M:tm-2, m:tm-116, u:((A (and (-> Am (-> B C)) Am)) (Bm (-> B C)))
================================================================
tm-name          tm-3609
in-theory        3609
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) and B) -> C))
theorem-size     9
proof            (modus-ponens tm-1 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-1 tm-2 tm-3 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-3609.         (A -> (((B -> C) and B) -> C)), M:tm-1, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-3610
in-theory        3610
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> (C -> (D -> E))) and F) -> ((C -> D) -> (C -> E)))
theorem-size     21
proof            (modus-ponens tm-114 tm-117 ((A (and (-> (-> Am (-> Bm Am)) (-> B (-> C D))) Dm)) (Cm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3610.         ((((A -> (B -> A)) -> (C -> (D -> E))) and F) -> ((C -> D) -> (C -> E))), M:tm-114, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) (-> B (-> C D))) Dm)) (Cm (-> B (-> C D))))
================================================================
tm-name          tm-3611
in-theory        3611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> E)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-113 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3611.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> E)) -> G) and H) -> G)), M:tm-113, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3612
in-theory        3612
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F))
theorem-size     23
proof            (modus-ponens tm-109 tm-117 ((A (and (-> (-> Am (-> Bm Am)) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Dm)) (Cm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3612.         (not (((A -> (B -> A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F)), M:tm-109, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Dm)) (Cm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-3613
in-theory        3613
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     31
proof            (modus-ponens tm-105 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3613.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-105, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3614
in-theory        3614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D -> C)) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-95 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3614.         (((A -> B) -> (A -> A)) and ((((C -> (D -> C)) -> E) and F) -> E)), M:tm-95, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3615
in-theory        3615
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> (C -> D)) and E) -> (C -> D))
theorem-size     15
proof            (modus-ponens tm-87 tm-117 ((A (and (-> (-> Am (-> Bm Am)) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3615.         ((((A -> (B -> A)) -> (C -> D)) and E) -> (C -> D)), M:tm-87, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-3616
in-theory        3616
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) and D) -> (E -> C))
theorem-size     13
proof            (modus-ponens tm-84 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3616.         ((((A -> (B -> A)) -> C) and D) -> (E -> C)), M:tm-84, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-3617
in-theory        3617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-83 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3617.         ((A -> (B -> (C -> B))) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-83, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3618
in-theory        3618
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> A)) -> (not (C -> (D -> C)))) and E))
theorem-size     15
proof            (modus-ponens tm-79 tm-117 ((A (and (-> (-> Am (-> Bm Am)) (not (-> B (-> C B)))) Dm)) (Cm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3618.         (not (((A -> (B -> A)) -> (not (C -> (D -> C)))) and E)), M:tm-79, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) (not (-> B (-> C B)))) Dm)) (Cm (not (-> B (-> C B)))))
================================================================
tm-name          tm-3619
in-theory        3619
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C -> B)) -> D) and E) -> D))
theorem-size     17
proof            (modus-ponens tm-76 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-10 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3619.         (((not (not A)) -> A) and ((((B -> (C -> B)) -> D) and E) -> D)), M:tm-76, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3620
in-theory        3620
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (B -> A)) -> C) and D))) or (((A -> (B -> A)) -> C) and D)) -> C)
theorem-size     23
proof            (modus-ponens tm-73 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-10 tm-2 tm-3 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3620.         (((not (not (((A -> (B -> A)) -> C) and D))) or (((A -> (B -> A)) -> C) and D)) -> C), M:tm-73, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-3621
in-theory        3621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> C)) -> E) and F) -> E))
theorem-size     23
proof            (modus-ponens tm-69 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-9 tm-2 tm-3 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3621.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> C)) -> E) and F) -> E)), M:tm-69, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3622
in-theory        3622
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> A)) -> (not C)) and C))
theorem-size     11
proof            (modus-ponens tm-60 tm-117 ((A (-> (-> Am (-> Bm Am)) (not Dm))) (B Dm) (Cm (not Dm))))
axioms-used      (tm-9 tm-4 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3622.         (not (((A -> (B -> A)) -> (not C)) and C)), M:tm-60, m:tm-117, u:((A (-> (-> Am (-> Bm Am)) (not Dm))) (B Dm) (Cm (not Dm)))
================================================================
tm-name          tm-3623
in-theory        3623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-54 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3623.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-54, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3624
in-theory        3624
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> B)) -> D) and E)) or (((B -> (C -> B)) -> D) and E)) -> D)
theorem-size     23
proof            (modus-ponens tm-47 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-4 tm-2 tm-3 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3624.         (((A and (((B -> (C -> B)) -> D) and E)) or (((B -> (C -> B)) -> D) and E)) -> D), M:tm-47, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-3625
in-theory        3625
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> A)) -> C) and D) and E) or (((A -> (B -> A)) -> C) and D)) -> C)
theorem-size     23
proof            (modus-ponens tm-46 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3625.         ((((((A -> (B -> A)) -> C) and D) and E) or (((A -> (B -> A)) -> C) and D)) -> C), M:tm-46, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-3626
in-theory        3626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D -> C)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-42 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3626.         ((A -> (B or A)) and ((((C -> (D -> C)) -> E) and F) -> E)), M:tm-42, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3627
in-theory        3627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D -> C)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-32 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3627.         ((A -> (A or B)) and ((((C -> (D -> C)) -> E) and F) -> E)), M:tm-32, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3628
in-theory        3628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) and D) -> ((((A -> (B -> A)) -> C) and D) and C))
theorem-size     21
proof            (modus-ponens tm-24 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3628.         ((((A -> (B -> A)) -> C) and D) -> ((((A -> (B -> A)) -> C) and D) and C)), M:tm-24, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-3629
in-theory        3629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D -> C)) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-23 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3629.         ((A -> (B -> (A and B))) and ((((C -> (D -> C)) -> E) and F) -> E)), M:tm-23, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3630
in-theory        3630
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D -> C)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-22 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3630.         (((A and B) -> B) and ((((C -> (D -> C)) -> E) and F) -> E)), M:tm-22, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3631
in-theory        3631
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D -> C)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-21 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3631.         (((A and B) -> A) and ((((C -> (D -> C)) -> E) and F) -> E)), M:tm-21, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3632
in-theory        3632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-20 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3632.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-20, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3633
in-theory        3633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D -> C)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-19 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3633.         ((A -> (B -> A)) and ((((C -> (D -> C)) -> E) and F) -> E)), M:tm-19, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3634
in-theory        3634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) and (C -> D)) -> D)
theorem-size     13
proof            (modus-ponens tm-17 tm-117 ((A (-> (-> Am (-> Bm Am)) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-4 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3634.         ((((A -> (B -> A)) -> C) and (C -> D)) -> D), M:tm-17, m:tm-117, u:((A (-> (-> Am (-> Bm Am)) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-3635
in-theory        3635
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> (A -> (B -> A))) and C) -> (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-15 tm-117 ((Cm (-> Am (-> Bm Am))) (B (-> Am (-> Bm Am))) (C Dm) (A (-> Am (-> Bm Am)))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3635.         ((((A -> (B -> A)) -> (A -> (B -> A))) and C) -> (A -> (B -> A))), M:tm-15, m:tm-117, u:((Cm (-> Am (-> Bm Am))) (B (-> Am (-> Bm Am))) (C Dm) (A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-3636
in-theory        3636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) and D) -> (((A -> (B -> A)) -> C) and D))
theorem-size     19
proof            (modus-ponens tm-12 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3636.         ((((A -> (B -> A)) -> C) and D) -> (((A -> (B -> A)) -> C) and D)), M:tm-12, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-3637
in-theory        3637
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> (not C)) -> (not (((A -> (B -> A)) -> C) and D)))
theorem-size     23
proof            (modus-ponens tm-9 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-9 tm-2 tm-3 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3637.         (((((A -> (B -> A)) -> C) and D) -> (not C)) -> (not (((A -> (B -> A)) -> C) and D))), M:tm-9, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-3638
in-theory        3638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((((C -> (D -> C)) -> A) and E) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3638.         ((A -> B) -> (((((C -> (D -> C)) -> A) and E) or A) -> B)), M:tm-8, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-3639
in-theory        3639
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> (C -> B)) -> D) and E) -> D))
theorem-size     13
proof            (modus-ponens tm-7 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-7 tm-2 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3639.         (A or ((((B -> (C -> B)) -> D) and E) -> D)), M:tm-7, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3640
in-theory        3640
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-6 tm-2 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3640.         (((((A -> (B -> A)) -> C) and D) -> C) or E), M:tm-6, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3641
in-theory        3641
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> B)) -> D) and E) -> D) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3641.         (A -> (((((B -> (C -> B)) -> D) and E) -> D) and A)), M:tm-5, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3642
in-theory        3642
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> (C -> D)) and E) -> C) -> ((((A -> (B -> A)) -> (C -> D)) and E) -> D))
theorem-size     27
proof            (modus-ponens tm-2 tm-117 ((A (and (-> (-> Am (-> Bm Am)) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3642.         (((((A -> (B -> A)) -> (C -> D)) and E) -> C) -> ((((A -> (B -> A)) -> (C -> D)) and E) -> D)), M:tm-2, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-3643
in-theory        3643
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> B)) -> D) and E) -> D))
theorem-size     13
proof            (modus-ponens tm-1 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-1 tm-2 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-3643.         (A -> ((((B -> (C -> B)) -> D) and E) -> D)), M:tm-1, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-3644
in-theory        3644
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> (E -> F))) and G) -> ((D -> E) -> (D -> F)))
theorem-size     29
proof            (modus-ponens tm-114 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B (-> C D))) Em)) (Dm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3644.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> (E -> F))) and G) -> ((D -> E) -> (D -> F))), M:tm-114, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B (-> C D))) Em)) (Dm (-> B (-> C D))))
================================================================
tm-name          tm-3645
in-theory        3645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) and I) -> H))
theorem-size     35
proof            (modus-ponens tm-113 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3645.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) and I) -> H)), M:tm-113, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3646
in-theory        3646
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G))
theorem-size     31
proof            (modus-ponens tm-109 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Em)) (Dm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3646.         (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G)), M:tm-109, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Em)) (Dm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-3647
in-theory        3647
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     39
proof            (modus-ponens tm-105 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3647.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-105, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3648
in-theory        3648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-95 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3648.         (((A -> B) -> (A -> A)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F)), M:tm-95, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3649
in-theory        3649
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and F) -> (D -> E))
theorem-size     23
proof            (modus-ponens tm-87 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B C)) Em)) (Dm (-> B C))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3649.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and F) -> (D -> E)), M:tm-87, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B C)) Em)) (Dm (-> B C)))
================================================================
tm-name          tm-3650
in-theory        3650
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (F -> D))
theorem-size     21
proof            (modus-ponens tm-84 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3650.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (F -> D)), M:tm-84, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-3651
in-theory        3651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-83 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3651.         ((A -> (B -> (C -> B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-83, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3652
in-theory        3652
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (E -> D)))) and F))
theorem-size     23
proof            (modus-ponens tm-79 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not (-> B (-> C B)))) Em)) (Dm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3652.         (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (E -> D)))) and F)), M:tm-79, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not (-> B (-> C B)))) Em)) (Dm (not (-> B (-> C B)))))
================================================================
tm-name          tm-3653
in-theory        3653
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) and F) -> E))
theorem-size     25
proof            (modus-ponens tm-76 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-10 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3653.         (((not (not A)) -> A) and (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) and F) -> E)), M:tm-76, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3654
in-theory        3654
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E))) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E)) -> D)
theorem-size     39
proof            (modus-ponens tm-73 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-8 tm-10 tm-2 tm-3 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3654.         (((not (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E))) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E)) -> D), M:tm-73, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-3655
in-theory        3655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F))
theorem-size     31
proof            (modus-ponens tm-69 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-9 tm-2 tm-3 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3655.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F)), M:tm-69, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3656
in-theory        3656
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not D)) and D))
theorem-size     19
proof            (modus-ponens tm-60 tm-118 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not Em))) (B Em) (Dm (not Em))))
axioms-used      (tm-9 tm-4 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3656.         (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not D)) and D)), M:tm-60, m:tm-118, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not Em))) (B Em) (Dm (not Em)))
================================================================
tm-name          tm-3657
in-theory        3657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     33
proof            (modus-ponens tm-54 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3657.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-54, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3658
in-theory        3658
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) and F)) or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) and F)) -> E)
theorem-size     39
proof            (modus-ponens tm-47 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-8 tm-4 tm-2 tm-3 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3658.         (((A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) and F)) or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) and F)) -> E), M:tm-47, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-3659
in-theory        3659
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) and F) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E)) -> D)
theorem-size     39
proof            (modus-ponens tm-46 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3659.         (((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) and F) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E)) -> D), M:tm-46, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-3660
in-theory        3660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-42 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3660.         ((A -> (B or A)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F)), M:tm-42, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3661
in-theory        3661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-32 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3661.         ((A -> (A or B)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F)), M:tm-32, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3662
in-theory        3662
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) and D))
theorem-size     37
proof            (modus-ponens tm-24 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3662.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) and D)), M:tm-24, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-3663
in-theory        3663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-23 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3663.         ((A -> (B -> (A and B))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F)), M:tm-23, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3664
in-theory        3664
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-22 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3664.         (((A and B) -> B) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F)), M:tm-22, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3665
in-theory        3665
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-21 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3665.         (((A and B) -> A) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F)), M:tm-21, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3666
in-theory        3666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     33
proof            (modus-ponens tm-20 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3666.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-20, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3667
in-theory        3667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-19 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3667.         ((A -> (B -> A)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F)), M:tm-19, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3668
in-theory        3668
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and (D -> E)) -> E)
theorem-size     21
proof            (modus-ponens tm-17 tm-118 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> Dm C)) (B Dm)))
axioms-used      (tm-2 tm-4 tm-3 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3668.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and (D -> E)) -> E), M:tm-17, m:tm-118, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> Dm C)) (B Dm))
================================================================
tm-name          tm-3669
in-theory        3669
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and D) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-15 tm-118 ((Dm (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Em) (A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3669.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and D) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-15, m:tm-118, u:((Dm (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Em) (A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-3670
in-theory        3670
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E))
theorem-size     35
proof            (modus-ponens tm-12 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3670.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E)), M:tm-12, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-3671
in-theory        3671
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (not D)) -> (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E)))
theorem-size     39
proof            (modus-ponens tm-9 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-9 tm-2 tm-3 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3671.         ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (not D)) -> (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E))), M:tm-9, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-3672
in-theory        3672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> A) and F) or A) -> B))
theorem-size     25
proof            (modus-ponens tm-8 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3672.         ((A -> B) -> ((((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> A) and F) or A) -> B)), M:tm-8, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-3673
in-theory        3673
times-derived    1
----------------------------------------------------------------
theorem          (A or (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) and F) -> E))
theorem-size     21
proof            (modus-ponens tm-7 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-7 tm-2 tm-3 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3673.         (A or (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) and F) -> E)), M:tm-7, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3674
in-theory        3674
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-6 tm-2 tm-3 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3674.         ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) or F), M:tm-6, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3675
in-theory        3675
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) and F) -> E) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3675.         (A -> ((((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) and F) -> E) and A)), M:tm-5, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3676
in-theory        3676
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and F) -> D) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and F) -> E))
theorem-size     43
proof            (modus-ponens tm-2 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B C)) Em)) (Dm (-> B C))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3676.         ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and F) -> D) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and F) -> E)), M:tm-2, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B C)) Em)) (Dm (-> B C)))
================================================================
tm-name          tm-3677
in-theory        3677
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) and F) -> E))
theorem-size     21
proof            (modus-ponens tm-1 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-1 tm-2 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3677.         (A -> (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) and F) -> E)), M:tm-1, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-3678
in-theory        3678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> A) and C) -> (B -> A))
theorem-size     13
proof            (modus-ponens tm-119 tm-11 ((Am (and (-> (-> Bm (-> Cm Bm)) Bm) C)) (A Bm) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3678.         ((((A -> (B -> A)) -> A) and C) -> (B -> A)), M:tm-119, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) Bm) C)) (A Bm) (B (-> Cm Bm)))
================================================================
tm-name          tm-3679
in-theory        3679
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (A -> (B -> C))) and D) -> ((A -> B) -> (A -> C)))
theorem-size     29
proof            (modus-ponens tm-119 tm-14 ((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> Bm (-> Cm Dm))) C)) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3679.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (A -> (B -> C))) and D) -> ((A -> B) -> (A -> C))), M:tm-119, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> Bm (-> Cm Dm))) C)) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-3680
in-theory        3680
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> (A and B)) and C) -> A)
theorem-size     13
proof            (modus-ponens tm-119 tm-16 ((Am (and (-> (-> (and Bm Cm) Bm) (and Bm Cm)) C)) (A (and Bm Cm)) (B Bm)))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3680.         (((((A and B) -> A) -> (A and B)) and C) -> A), M:tm-119, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) (and Bm Cm)) C)) (A (and Bm Cm)) (B Bm))
================================================================
tm-name          tm-3681
in-theory        3681
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> (A and B)) and C) -> B)
theorem-size     13
proof            (modus-ponens tm-119 tm-18 ((Am (and (-> (-> (and Bm Cm) Cm) (and Bm Cm)) C)) (A (and Bm Cm)) (B Cm)))
axioms-used      (tm-2 tm-3 tm-1 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3681.         (((((A and B) -> B) -> (A and B)) and C) -> B), M:tm-119, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) (and Bm Cm)) C)) (A (and Bm Cm)) (B Cm))
================================================================
tm-name          tm-3682
in-theory        3682
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> A) and C) -> (B -> (A and B)))
theorem-size     17
proof            (modus-ponens tm-119 tm-25 ((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) Bm) C)) (A Bm) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3682.         ((((A -> (B -> (A and B))) -> A) and C) -> (B -> (A and B))), M:tm-119, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) Bm) C)) (A Bm) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-3683
in-theory        3683
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> A) and C) -> (A or B))
theorem-size     13
proof            (modus-ponens tm-119 tm-33 ((Am (and (-> (-> Bm (or Bm Cm)) Bm) C)) (A Bm) (B (or Bm Cm))))
axioms-used      (tm-2 tm-3 tm-1 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3683.         ((((A -> (A or B)) -> A) and C) -> (A or B)), M:tm-119, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) Bm) C)) (A Bm) (B (or Bm Cm)))
================================================================
tm-name          tm-3684
in-theory        3684
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> A) and C) -> (B or A))
theorem-size     13
proof            (modus-ponens tm-119 tm-43 ((Am (and (-> (-> Bm (or Cm Bm)) Bm) C)) (A Bm) (B (or Cm Bm))))
axioms-used      (tm-2 tm-3 tm-1 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3684.         ((((A -> (B or A)) -> A) and C) -> (B or A)), M:tm-119, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) Bm) C)) (A Bm) (B (or Cm Bm)))
================================================================
tm-name          tm-3685
in-theory        3685
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> (A -> B)) and D) -> ((B -> C) -> ((A or B) -> C)))
theorem-size     29
proof            (modus-ponens tm-119 tm-56 ((Am (and (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> Bm Cm)) C)) (A (-> Bm Cm)) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-8)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3685.         (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> (A -> B)) and D) -> ((B -> C) -> ((A or B) -> C))), M:tm-119, m:tm-56, u:((Am (and (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> Bm Cm)) C)) (A (-> Bm Cm)) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-3686
in-theory        3686
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> (not B)) -> (not A))) -> (A -> B)) and C) -> ((A -> (not B)) -> (not A)))
theorem-size     25
proof            (modus-ponens tm-119 tm-71 ((Am (and (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> Bm Cm)) C)) (A (-> Bm Cm)) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-9)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3686.         (((((A -> B) -> ((A -> (not B)) -> (not A))) -> (A -> B)) and C) -> ((A -> (not B)) -> (not A))), M:tm-119, m:tm-71, u:((Am (and (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> Bm Cm)) C)) (A (-> Bm Cm)) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-3687
in-theory        3687
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) -> A) -> (not (not A))) and B) -> A)
theorem-size     13
proof            (modus-ponens tm-119 tm-78 ((Am (and (-> (-> (not (not Bm)) Bm) (not (not Bm))) C)) (A (not (not Bm))) (B Bm)))
axioms-used      (tm-2 tm-3 tm-1 tm-10)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3687.         (((((not (not A)) -> A) -> (not (not A))) and B) -> A), M:tm-119, m:tm-78, u:((Am (and (-> (-> (not (not Bm)) Bm) (not (not Bm))) C)) (A (not (not Bm))) (B Bm))
================================================================
tm-name          tm-3688
in-theory        3688
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (C -> B))) -> A) and D) -> (B -> (C -> B)))
theorem-size     17
proof            (modus-ponens tm-119 tm-85 ((Am (and (-> (-> Bm (-> Cm (-> Dm Cm))) Bm) C)) (A Bm) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3688.         ((((A -> (B -> (C -> B))) -> A) and D) -> (B -> (C -> B))), M:tm-119, m:tm-85, u:((Am (and (-> (-> Bm (-> Cm (-> Dm Cm))) Bm) C)) (A Bm) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-3689
in-theory        3689
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> A)) -> (A -> B)) and C) -> (A -> A))
theorem-size     17
proof            (modus-ponens tm-119 tm-97 ((Am (and (-> (-> (-> Bm Cm) (-> Bm Bm)) (-> Bm Cm)) C)) (A (-> Bm Cm)) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3689.         (((((A -> B) -> (A -> A)) -> (A -> B)) and C) -> (A -> A)), M:tm-119, m:tm-97, u:((Am (and (-> (-> (-> Bm Cm) (-> Bm Bm)) (-> Bm Cm)) C)) (A (-> Bm Cm)) (B (-> Bm Bm)))
================================================================
tm-name          tm-3690
in-theory        3690
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> (A -> B))) and D) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     41
proof            (modus-ponens tm-119 tm-107 ((Am (and (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) C)) (A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3690.         ((((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> (A -> B))) and D) -> ((A -> (B -> C)) -> (A -> C))), M:tm-119, m:tm-107, u:((Am (and (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) C)) (A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-3691
in-theory        3691
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> A) and E) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     33
proof            (modus-ponens tm-119 tm-115 ((Am (and (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Bm) C)) (A Bm) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3691.         ((((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> A) and E) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-119, m:tm-115, u:((Am (and (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Bm) C)) (A Bm) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-3692
in-theory        3692
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> A) and D) -> (A -> (B -> C))) -> (((((A -> (B -> C)) -> A) and D) -> B) -> ((((A -> (B -> C)) -> A) and D) -> C)))
theorem-size     39
proof            (modus-ponens tm-114 tm-119 ((A (-> (and (-> (-> Am (-> C D)) Am) Cm) (-> Am (-> C D)))) (B (and (-> (-> Am (-> C D)) Am) Cm)) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3692.         (((((A -> (B -> C)) -> A) and D) -> (A -> (B -> C))) -> (((((A -> (B -> C)) -> A) and D) -> B) -> ((((A -> (B -> C)) -> A) and D) -> C))), M:tm-114, m:tm-119, u:((A (-> (and (-> (-> Am (-> C D)) Am) Cm) (-> Am (-> C D)))) (B (and (-> (-> Am (-> C D)) Am) Cm)) (Bm (-> C D)))
================================================================
tm-name          tm-3693
in-theory        3693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F)))
theorem-size     37
proof            (modus-ponens tm-113 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3693.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F))), M:tm-113, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3694
in-theory        3694
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     41
proof            (modus-ponens tm-105 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3694.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-105, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3695
in-theory        3695
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> A) -> A) and B) -> (A -> A)) -> ((((A -> A) -> A) and B) -> A))
theorem-size     21
proof            (modus-ponens tm-100 tm-119 ((Bm Am) (C Am) (A (and (-> (-> Am Am) Am) Cm)) (B Am)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3695.         (((((A -> A) -> A) and B) -> (A -> A)) -> ((((A -> A) -> A) and B) -> A)), M:tm-100, m:tm-119, u:((Bm Am) (C Am) (A (and (-> (-> Am Am) Am) Cm)) (B Am))
================================================================
tm-name          tm-3696
in-theory        3696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D)))
theorem-size     29
proof            (modus-ponens tm-95 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3696.         (((A -> B) -> (A -> A)) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D))), M:tm-95, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3697
in-theory        3697
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> A) and C) -> (A -> B)) -> (D -> ((((A -> B) -> A) and C) -> B)))
theorem-size     23
proof            (modus-ponens tm-84 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3697.         (((((A -> B) -> A) and C) -> (A -> B)) -> (D -> ((((A -> B) -> A) and C) -> B))), M:tm-84, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-3698
in-theory        3698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-83 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3698.         ((A -> (B -> (C -> B))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-83, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3699
in-theory        3699
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> C) -> B) and D) -> (B -> C)) -> ((((B -> C) -> B) and D) -> C)))
theorem-size     27
proof            (modus-ponens tm-76 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3699.         (((not (not A)) -> A) and (((((B -> C) -> B) and D) -> (B -> C)) -> ((((B -> C) -> B) and D) -> C))), M:tm-76, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3700
in-theory        3700
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> B) -> A) and C) -> (A -> B)))) or ((((A -> B) -> A) and C) -> (A -> B))) -> ((((A -> B) -> A) and C) -> B))
theorem-size     35
proof            (modus-ponens tm-73 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-8 tm-10 tm-2 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3700.         (((not (not ((((A -> B) -> A) and C) -> (A -> B)))) or ((((A -> B) -> A) and C) -> (A -> B))) -> ((((A -> B) -> A) and C) -> B)), M:tm-73, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-3701
in-theory        3701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D)))
theorem-size     33
proof            (modus-ponens tm-69 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3701.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D))), M:tm-69, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3702
in-theory        3702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-54 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3702.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-54, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3703
in-theory        3703
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B -> C) -> B) and D) -> (B -> C))) or ((((B -> C) -> B) and D) -> (B -> C))) -> ((((B -> C) -> B) and D) -> C))
theorem-size     35
proof            (modus-ponens tm-47 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3703.         (((A and ((((B -> C) -> B) and D) -> (B -> C))) or ((((B -> C) -> B) and D) -> (B -> C))) -> ((((B -> C) -> B) and D) -> C)), M:tm-47, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-3704
in-theory        3704
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> A) and C) -> (A -> B)) and D) or ((((A -> B) -> A) and C) -> (A -> B))) -> ((((A -> B) -> A) and C) -> B))
theorem-size     35
proof            (modus-ponens tm-46 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3704.         (((((((A -> B) -> A) and C) -> (A -> B)) and D) or ((((A -> B) -> A) and C) -> (A -> B))) -> ((((A -> B) -> A) and C) -> B)), M:tm-46, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-3705
in-theory        3705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((((A -> B) -> A) and C) -> (A -> B))) -> ((((A -> B) -> A) and C) -> B))
theorem-size     25
proof            (modus-ponens tm-44 tm-119 ((A (and (-> (-> Am Bm) Am) Cm)) (B (-> Am Bm)) (C (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3705.         (((A -> B) or ((((A -> B) -> A) and C) -> (A -> B))) -> ((((A -> B) -> A) and C) -> B)), M:tm-44, m:tm-119, u:((A (and (-> (-> Am Bm) Am) Cm)) (B (-> Am Bm)) (C (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-3706
in-theory        3706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-42 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3706.         ((A -> (B or A)) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D))), M:tm-42, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3707
in-theory        3707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-32 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3707.         ((A -> (A or B)) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D))), M:tm-32, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3708
in-theory        3708
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> A) and C) -> (A -> B)) -> (((((A -> B) -> A) and C) -> (A -> B)) and ((((A -> B) -> A) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-24 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3708.         (((((A -> B) -> A) and C) -> (A -> B)) -> (((((A -> B) -> A) and C) -> (A -> B)) and ((((A -> B) -> A) and C) -> B))), M:tm-24, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-3709
in-theory        3709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D)))
theorem-size     29
proof            (modus-ponens tm-23 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3709.         ((A -> (B -> (A and B))) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D))), M:tm-23, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3710
in-theory        3710
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-22 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3710.         (((A and B) -> B) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D))), M:tm-22, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3711
in-theory        3711
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-21 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3711.         (((A and B) -> A) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D))), M:tm-21, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3712
in-theory        3712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-20 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3712.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-20, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3713
in-theory        3713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-19 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3713.         ((A -> (B -> A)) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D))), M:tm-19, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3714
in-theory        3714
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> (A -> B)))
theorem-size     23
proof            (modus-ponens tm-12 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3714.         (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> (A -> B))), M:tm-12, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-3715
in-theory        3715
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> (not ((((A -> B) -> A) and C) -> B))) -> (not ((((A -> B) -> A) and C) -> (A -> B))))
theorem-size     35
proof            (modus-ponens tm-9 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-9 tm-2 tm-3)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3715.         ((((((A -> B) -> A) and C) -> (A -> B)) -> (not ((((A -> B) -> A) and C) -> B))) -> (not ((((A -> B) -> A) and C) -> (A -> B)))), M:tm-9, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-3716
in-theory        3716
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> B) -> D) -> ((((((A -> B) -> A) and C) -> (A -> B)) or ((((A -> B) -> A) and C) -> B)) -> D))
theorem-size     35
proof            (modus-ponens tm-8 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3716.         ((((((A -> B) -> A) and C) -> B) -> D) -> ((((((A -> B) -> A) and C) -> (A -> B)) or ((((A -> B) -> A) and C) -> B)) -> D)), M:tm-8, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-3717
in-theory        3717
times-derived    1
----------------------------------------------------------------
theorem          (A or (((((B -> C) -> B) and D) -> (B -> C)) -> ((((B -> C) -> B) and D) -> C)))
theorem-size     23
proof            (modus-ponens tm-7 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-7 tm-2 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3717.         (A or (((((B -> C) -> B) and D) -> (B -> C)) -> ((((B -> C) -> B) and D) -> C))), M:tm-7, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3718
in-theory        3718
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) or D)
theorem-size     23
proof            (modus-ponens tm-6 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-6 tm-2 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3718.         ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) or D), M:tm-6, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3719
in-theory        3719
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) -> B) and D) -> (B -> C)) -> ((((B -> C) -> B) and D) -> C)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3719.         (A -> ((((((B -> C) -> B) and D) -> (B -> C)) -> ((((B -> C) -> B) and D) -> C)) and A)), M:tm-5, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3720
in-theory        3720
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> (((A -> B) -> A) and C)) -> (((((A -> B) -> A) and C) -> (A -> B)) -> B))
theorem-size     33
proof            (modus-ponens tm-2 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (and (-> (-> Am Bm) Am) Cm)) (C Bm)))
axioms-used      (tm-2 tm-3)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3720.         ((((((A -> B) -> A) and C) -> (A -> B)) -> (((A -> B) -> A) and C)) -> (((((A -> B) -> A) and C) -> (A -> B)) -> B)), M:tm-2, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (and (-> (-> Am Bm) Am) Cm)) (C Bm))
================================================================
tm-name          tm-3721
in-theory        3721
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> B) and D) -> (B -> C)) -> ((((B -> C) -> B) and D) -> C)))
theorem-size     23
proof            (modus-ponens tm-1 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-1 tm-2 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-3721.         (A -> (((((B -> C) -> B) and D) -> (B -> C)) -> ((((B -> C) -> B) and D) -> C))), M:tm-1, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-3722
in-theory        3722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and A) -> A)
theorem-size     7
proof            (modus-ponens tm-120 tm-4 ((Am (-> Bm B)) (C Bm) (A Bm)))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-3722.         (((A -> B) and A) -> A), M:tm-120, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
================================================================
tm-name          tm-3723
in-theory        3723
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) and D) -> (A -> (B -> A)))
theorem-size     15
proof            (modus-ponens tm-120 tm-11 ((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3723.         ((((A -> (B -> A)) -> C) and D) -> (A -> (B -> A))), M:tm-120, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-3724
in-theory        3724
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-120 tm-14 ((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3724.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-120, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3725
in-theory        3725
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) and D) -> ((A and B) -> A))
theorem-size     15
proof            (modus-ponens tm-120 tm-16 ((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3725.         (((((A and B) -> A) -> C) and D) -> ((A and B) -> A)), M:tm-120, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-3726
in-theory        3726
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) and D) -> ((A and B) -> B))
theorem-size     15
proof            (modus-ponens tm-120 tm-18 ((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3726.         (((((A and B) -> B) -> C) and D) -> ((A and B) -> B)), M:tm-120, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-3727
in-theory        3727
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) and D) -> (A -> (B -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-120 tm-25 ((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3727.         ((((A -> (B -> (A and B))) -> C) and D) -> (A -> (B -> (A and B)))), M:tm-120, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-3728
in-theory        3728
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) and D) -> (A -> (A or B)))
theorem-size     15
proof            (modus-ponens tm-120 tm-33 ((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3728.         ((((A -> (A or B)) -> C) and D) -> (A -> (A or B))), M:tm-120, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-3729
in-theory        3729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) and D) -> (A -> (B or A)))
theorem-size     15
proof            (modus-ponens tm-120 tm-43 ((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3729.         ((((A -> (B or A)) -> C) and D) -> (A -> (B or A))), M:tm-120, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-3730
in-theory        3730
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) and E) -> ((A -> B) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-120 tm-56 ((Am (and (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B) C)) (A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-1 tm-3 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3730.         (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) and E) -> ((A -> B) -> ((B -> C) -> ((A or B) -> C)))), M:tm-120, m:tm-56, u:((Am (and (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B) C)) (A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-3731
in-theory        3731
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> (not B)) -> (not A))) -> C) and D) -> ((A -> B) -> ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-120 tm-71 ((Am (and (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) B) C)) (A (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-1 tm-3 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3731.         (((((A -> B) -> ((A -> (not B)) -> (not A))) -> C) and D) -> ((A -> B) -> ((A -> (not B)) -> (not A)))), M:tm-120, m:tm-71, u:((Am (and (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) B) C)) (A (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-3732
in-theory        3732
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) -> A) -> B) and C) -> ((not (not A)) -> A))
theorem-size     15
proof            (modus-ponens tm-120 tm-78 ((Am (and (-> (-> (not (not Bm)) Bm) B) C)) (A (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-1 tm-3 tm-10)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3732.         (((((not (not A)) -> A) -> B) and C) -> ((not (not A)) -> A)), M:tm-120, m:tm-78, u:((Am (and (-> (-> (not (not Bm)) Bm) B) C)) (A (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-3733
in-theory        3733
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (C -> B))) -> D) and E) -> (A -> (B -> (C -> B))))
theorem-size     19
proof            (modus-ponens tm-120 tm-85 ((Am (and (-> (-> Bm (-> Cm (-> Dm Cm))) B) C)) (A (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3733.         ((((A -> (B -> (C -> B))) -> D) and E) -> (A -> (B -> (C -> B)))), M:tm-120, m:tm-85, u:((Am (and (-> (-> Bm (-> Cm (-> Dm Cm))) B) C)) (A (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-3734
in-theory        3734
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> A)) -> C) and D) -> ((A -> B) -> (A -> A)))
theorem-size     19
proof            (modus-ponens tm-120 tm-97 ((Am (and (-> (-> (-> Bm Cm) (-> Bm Bm)) B) C)) (A (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3734.         (((((A -> B) -> (A -> A)) -> C) and D) -> ((A -> B) -> (A -> A))), M:tm-120, m:tm-97, u:((Am (and (-> (-> (-> Bm Cm) (-> Bm Bm)) B) C)) (A (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-3735
in-theory        3735
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) and E) -> (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-120 tm-107 ((Am (and (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) B) C)) (A (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3735.         ((((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) and E) -> (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-120, m:tm-107, u:((Am (and (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) B) C)) (A (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3736
in-theory        3736
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     35
proof            (modus-ponens tm-120 tm-115 ((Am (and (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B) C)) (A (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3736.         ((((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-120, m:tm-115, u:((Am (and (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B) C)) (A (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3737
in-theory        3737
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) and D) -> (A -> B)) -> (((((A -> B) -> C) and D) -> A) -> ((((A -> B) -> C) and D) -> B)))
theorem-size     31
proof            (modus-ponens tm-114 tm-120 ((A (-> (and (-> (-> C D) Bm) Cm) (-> C D))) (B (and (-> (-> C D) Bm) Cm)) (Am (-> C D))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3737.         (((((A -> B) -> C) and D) -> (A -> B)) -> (((((A -> B) -> C) and D) -> A) -> ((((A -> B) -> C) and D) -> B))), M:tm-114, m:tm-120, u:((A (-> (and (-> (-> C D) Bm) Cm) (-> C D))) (B (and (-> (-> C D) Bm) Cm)) (Am (-> C D)))
================================================================
tm-name          tm-3738
in-theory        3738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E)))
theorem-size     31
proof            (modus-ponens tm-113 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3738.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E))), M:tm-113, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3739
in-theory        3739
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     35
proof            (modus-ponens tm-105 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3739.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-105, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3740
in-theory        3740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C)))
theorem-size     23
proof            (modus-ponens tm-95 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3740.         (((A -> B) -> (A -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C))), M:tm-95, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3741
in-theory        3741
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> (D -> (((A -> B) and C) -> A)))
theorem-size     17
proof            (modus-ponens tm-84 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3741.         ((((A -> B) and C) -> A) -> (D -> (((A -> B) and C) -> A))), M:tm-84, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-3742
in-theory        3742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-83 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3742.         ((A -> (B -> (C -> B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-83, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3743
in-theory        3743
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) and D) -> B) -> (((B -> C) and D) -> B)))
theorem-size     21
proof            (modus-ponens tm-76 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3743.         (((not (not A)) -> A) and ((((B -> C) and D) -> B) -> (((B -> C) and D) -> B))), M:tm-76, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3744
in-theory        3744
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) and C) -> A))) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> A))
theorem-size     25
proof            (modus-ponens tm-73 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3744.         (((not (not (((A -> B) and C) -> A))) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> A)), M:tm-73, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-3745
in-theory        3745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C)))
theorem-size     27
proof            (modus-ponens tm-69 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3745.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C))), M:tm-69, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3746
in-theory        3746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     29
proof            (modus-ponens tm-54 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3746.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-54, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3747
in-theory        3747
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> B))
theorem-size     25
proof            (modus-ponens tm-47 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3747.         (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> B)), M:tm-47, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-3748
in-theory        3748
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> A))
theorem-size     25
proof            (modus-ponens tm-46 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3748.         ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> A)), M:tm-46, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-3749
in-theory        3749
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> A))
theorem-size     17
proof            (modus-ponens tm-44 tm-120 ((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3749.         ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> A)), M:tm-44, m:tm-120, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-3750
in-theory        3750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C)))
theorem-size     21
proof            (modus-ponens tm-42 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3750.         ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C))), M:tm-42, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3751
in-theory        3751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C)))
theorem-size     21
proof            (modus-ponens tm-32 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3751.         ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C))), M:tm-32, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3752
in-theory        3752
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> A)))
theorem-size     23
proof            (modus-ponens tm-24 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3752.         ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> A))), M:tm-24, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-3753
in-theory        3753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C)))
theorem-size     23
proof            (modus-ponens tm-23 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3753.         ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C))), M:tm-23, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3754
in-theory        3754
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C)))
theorem-size     21
proof            (modus-ponens tm-22 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3754.         (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C))), M:tm-22, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3755
in-theory        3755
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C)))
theorem-size     21
proof            (modus-ponens tm-21 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3755.         (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C))), M:tm-21, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3756
in-theory        3756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     29
proof            (modus-ponens tm-20 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3756.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-20, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3757
in-theory        3757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C)))
theorem-size     21
proof            (modus-ponens tm-19 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3757.         ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C))), M:tm-19, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3758
in-theory        3758
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> A))) -> (not (((A -> B) and C) -> A)))
theorem-size     25
proof            (modus-ponens tm-9 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-9 tm-2 tm-1 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3758.         (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> A))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-3759
in-theory        3759
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> A)) -> D))
theorem-size     27
proof            (modus-ponens tm-8 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3759.         (((((A -> B) and C) -> A) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> A)) -> D)), M:tm-8, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-3760
in-theory        3760
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> B)))
theorem-size     17
proof            (modus-ponens tm-7 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-7 tm-2 tm-1 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3760.         (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> B))), M:tm-7, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3761
in-theory        3761
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-6 tm-2 tm-1 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3761.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) or D), M:tm-6, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3762
in-theory        3762
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> B)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3762.         (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> B)) and A)), M:tm-5, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3763
in-theory        3763
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> A))
theorem-size     23
proof            (modus-ponens tm-2 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Am)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3763.         (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> A)), M:tm-2, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Am))
================================================================
tm-name          tm-3764
in-theory        3764
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> B)))
theorem-size     17
proof            (modus-ponens tm-1 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-1 tm-2 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3764.         (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> B))), M:tm-1, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3765
in-theory        3765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> E) -> (not (((E -> F) and G) -> F))) -> (not (((E -> F) and G) -> E))))
theorem-size     41
proof            (modus-ponens tm-113 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3765.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> E) -> (not (((E -> F) and G) -> F))) -> (not (((E -> F) and G) -> E)))), M:tm-113, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3766
in-theory        3766
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     45
proof            (modus-ponens tm-105 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-9 tm-3)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3766.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-105, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3767
in-theory        3767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C))))
theorem-size     33
proof            (modus-ponens tm-95 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3767.         (((A -> B) -> (A -> A)) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C)))), M:tm-95, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3768
in-theory        3768
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (D -> (not (((A -> B) and C) -> A))))
theorem-size     27
proof            (modus-ponens tm-84 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-1 tm-9 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3768.         (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (D -> (not (((A -> B) and C) -> A)))), M:tm-84, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3769
in-theory        3769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-83 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3769.         ((A -> (B -> (C -> B))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-83, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3770
in-theory        3770
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> C) and D) -> B) -> (not (((B -> C) and D) -> C))) -> (not (((B -> C) and D) -> B))))
theorem-size     31
proof            (modus-ponens tm-76 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-10 tm-9 tm-2 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3770.         (((not (not A)) -> A) and (((((B -> C) and D) -> B) -> (not (((B -> C) and D) -> C))) -> (not (((B -> C) and D) -> B)))), M:tm-76, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3771
in-theory        3771
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))))) or ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B)))) -> (not (((A -> B) and C) -> A)))
theorem-size     44
proof            (modus-ponens tm-73 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-8 tm-10 tm-9 tm-2 tm-3)
proof-size       142
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3771.         (((not (not ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))))) or ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B)))) -> (not (((A -> B) and C) -> A))), M:tm-73, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3772
in-theory        3772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C))))
theorem-size     37
proof            (modus-ponens tm-69 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3772.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C)))), M:tm-69, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3773
in-theory        3773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     39
proof            (modus-ponens tm-54 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-8 tm-9 tm-2 tm-3)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3773.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-54, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3774
in-theory        3774
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B -> C) and D) -> B) -> (not (((B -> C) and D) -> C)))) or ((((B -> C) and D) -> B) -> (not (((B -> C) and D) -> C)))) -> (not (((B -> C) and D) -> B)))
theorem-size     44
proof            (modus-ponens tm-47 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-8 tm-4 tm-9 tm-2 tm-3)
proof-size       142
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3774.         (((A and ((((B -> C) and D) -> B) -> (not (((B -> C) and D) -> C)))) or ((((B -> C) and D) -> B) -> (not (((B -> C) and D) -> C)))) -> (not (((B -> C) and D) -> B))), M:tm-47, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3775
in-theory        3775
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) and D) or ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B)))) -> (not (((A -> B) and C) -> A)))
theorem-size     44
proof            (modus-ponens tm-46 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-8 tm-3 tm-9 tm-2)
proof-size       142
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3775.         (((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) and D) or ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B)))) -> (not (((A -> B) and C) -> A))), M:tm-46, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3776
in-theory        3776
times-derived    1
----------------------------------------------------------------
theorem          (((not (((A -> B) and C) -> B)) or ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B)))) -> (not (((A -> B) and C) -> A)))
theorem-size     34
proof            (modus-ponens tm-44 tm-121 ((A (-> (and (-> Am Bm) Cm) Am)) (B (not (-> (and (-> Am Bm) Cm) Bm))) (C (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-8 tm-1 tm-9 tm-2 tm-3)
proof-size       134
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3776.         (((not (((A -> B) and C) -> B)) or ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B)))) -> (not (((A -> B) and C) -> A))), M:tm-44, m:tm-121, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (not (-> (and (-> Am Bm) Cm) Bm))) (C (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3777
in-theory        3777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C))))
theorem-size     31
proof            (modus-ponens tm-42 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3777.         ((A -> (B or A)) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C)))), M:tm-42, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3778
in-theory        3778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C))))
theorem-size     31
proof            (modus-ponens tm-32 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3778.         ((A -> (A or B)) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C)))), M:tm-32, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3779
in-theory        3779
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) and (not (((A -> B) and C) -> A))))
theorem-size     42
proof            (modus-ponens tm-24 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       140
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3779.         (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) and (not (((A -> B) and C) -> A)))), M:tm-24, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3780
in-theory        3780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C))))
theorem-size     33
proof            (modus-ponens tm-23 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3780.         ((A -> (B -> (A and B))) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C)))), M:tm-23, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3781
in-theory        3781
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C))))
theorem-size     31
proof            (modus-ponens tm-22 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-4 tm-9 tm-2 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3781.         (((A and B) -> B) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C)))), M:tm-22, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3782
in-theory        3782
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C))))
theorem-size     31
proof            (modus-ponens tm-21 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-3 tm-9 tm-2)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3782.         (((A and B) -> A) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C)))), M:tm-21, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3783
in-theory        3783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     39
proof            (modus-ponens tm-20 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-9 tm-3)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3783.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-20, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3784
in-theory        3784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C))))
theorem-size     31
proof            (modus-ponens tm-19 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3784.         ((A -> (B -> A)) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C)))), M:tm-19, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3785
in-theory        3785
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))))
theorem-size     33
proof            (modus-ponens tm-12 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-1 tm-9 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3785.         (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B)))), M:tm-12, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3786
in-theory        3786
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (not (((A -> B) and C) -> A)))) -> (not ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B)))))
theorem-size     44
proof            (modus-ponens tm-9 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-9 tm-2 tm-3)
proof-size       124
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3786.         ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (not (((A -> B) and C) -> A)))) -> (not ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))))), M:tm-9, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3787
in-theory        3787
times-derived    1
----------------------------------------------------------------
theorem          (((not (((A -> B) and C) -> A)) -> D) -> ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) or (not (((A -> B) and C) -> A))) -> D))
theorem-size     38
proof            (modus-ponens tm-8 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-8 tm-9 tm-2 tm-3)
proof-size       120
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3787.         (((not (((A -> B) and C) -> A)) -> D) -> ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) or (not (((A -> B) and C) -> A))) -> D)), M:tm-8, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-3788
in-theory        3788
times-derived    1
----------------------------------------------------------------
theorem          (A or (((((B -> C) and D) -> B) -> (not (((B -> C) and D) -> C))) -> (not (((B -> C) and D) -> B))))
theorem-size     27
proof            (modus-ponens tm-7 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-7 tm-9 tm-2 tm-3)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3788.         (A or (((((B -> C) and D) -> B) -> (not (((B -> C) and D) -> C))) -> (not (((B -> C) and D) -> B)))), M:tm-7, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3789
in-theory        3789
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) or D)
theorem-size     27
proof            (modus-ponens tm-6 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-6 tm-9 tm-2 tm-3)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3789.         ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) or D), M:tm-6, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3790
in-theory        3790
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) and D) -> B) -> (not (((B -> C) and D) -> C))) -> (not (((B -> C) and D) -> B))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3790.         (A -> ((((((B -> C) and D) -> B) -> (not (((B -> C) and D) -> C))) -> (not (((B -> C) and D) -> B))) and A)), M:tm-5, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3791
in-theory        3791
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) and D) -> B) -> (not (((B -> C) and D) -> C))) -> (not (((B -> C) and D) -> B))))
theorem-size     27
proof            (modus-ponens tm-1 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-1 tm-9 tm-2 tm-3)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3791.         (A -> (((((B -> C) and D) -> B) -> (not (((B -> C) and D) -> C))) -> (not (((B -> C) and D) -> B)))), M:tm-1, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-3792
in-theory        3792
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (((A -> B) and C) -> B)))
theorem-size     25
proof            (modus-ponens tm-122 tm-1 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3792.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (((A -> B) and C) -> B))), M:tm-122, m:tm-1, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3793
in-theory        3793
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) -> A) or (((A -> (B -> C)) and D) -> (B -> C))) -> ((((A -> (B -> C)) and D) -> B) -> (((A -> (B -> C)) and D) -> C)))
theorem-size     41
proof            (modus-ponens tm-122 tm-2 ((Am (and (-> A (-> Bm Cm)) C)) (B (-> Bm Cm)) (D (-> (-> (and (-> A (-> Bm Cm)) C) Bm) (-> (and (-> A (-> Bm Cm)) C) Cm)))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3793.         (((((A -> (B -> C)) and D) -> A) or (((A -> (B -> C)) and D) -> (B -> C))) -> ((((A -> (B -> C)) and D) -> B) -> (((A -> (B -> C)) and D) -> C))), M:tm-122, m:tm-2, u:((Am (and (-> A (-> Bm Cm)) C)) (B (-> Bm Cm)) (D (-> (-> (and (-> A (-> Bm Cm)) C) Bm) (-> (and (-> A (-> Bm Cm)) C) Cm))))
================================================================
tm-name          tm-3794
in-theory        3794
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((((A -> B) and C) -> B) and D)))
theorem-size     27
proof            (modus-ponens tm-122 tm-5 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> (and (-> A B) C) B) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3794.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((((A -> B) and C) -> B) and D))), M:tm-122, m:tm-5, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> (and (-> A B) C) B) Bm))))
================================================================
tm-name          tm-3795
in-theory        3795
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) or D))
theorem-size     25
proof            (modus-ponens tm-122 tm-6 ((Am (-> (and (-> A B) C) B)) (D (or (-> (and (-> A B) C) B) Bm))))
axioms-used      (tm-8 tm-2 tm-3 tm-6)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3795.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) or D)), M:tm-122, m:tm-6, u:((Am (-> (and (-> A B) C) B)) (D (or (-> (and (-> A B) C) B) Bm)))
================================================================
tm-name          tm-3796
in-theory        3796
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or (((A -> B) and C) -> B)))
theorem-size     25
proof            (modus-ponens tm-122 tm-7 ((Am (-> (and (-> A B) C) B)) (D (or Bm (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-7)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3796.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or (((A -> B) and C) -> B))), M:tm-122, m:tm-7, u:((Am (-> (and (-> A B) C) B)) (D (or Bm (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3797
in-theory        3797
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((B -> D) -> ((((A -> B) and C) or B) -> D)))
theorem-size     29
proof            (modus-ponens tm-122 tm-8 ((Am (and (-> A Bm) C)) (B Bm) (D (-> (-> Bm Cm) (-> (or (and (-> A Bm) C) Bm) Cm)))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3797.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((B -> D) -> ((((A -> B) and C) or B) -> D))), M:tm-122, m:tm-8, u:((Am (and (-> A Bm) C)) (B Bm) (D (-> (-> Bm Cm) (-> (or (and (-> A Bm) C) Bm) Cm))))
================================================================
tm-name          tm-3798
in-theory        3798
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> (not B)) -> (not ((A -> B) and C))))
theorem-size     31
proof            (modus-ponens tm-122 tm-9 ((Am (and (-> A Bm) C)) (B Bm) (D (-> (-> (and (-> A Bm) C) (not Bm)) (not (and (-> A Bm) C))))))
axioms-used      (tm-8 tm-2 tm-3 tm-9)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3798.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> (not B)) -> (not ((A -> B) and C)))), M:tm-122, m:tm-9, u:((Am (and (-> A Bm) C)) (B Bm) (D (-> (-> (and (-> A Bm) C) (not Bm)) (not (and (-> A Bm) C)))))
================================================================
tm-name          tm-3799
in-theory        3799
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-122 tm-11 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3799.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (E -> D))), M:tm-122, m:tm-11, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-3800
in-theory        3800
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> ((A -> B) and C)))
theorem-size     27
proof            (modus-ponens tm-122 tm-12 ((Am (and (-> A Bm) C)) (B Bm) (D (-> (and (-> A Bm) C) (and (-> A Bm) C)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3800.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> ((A -> B) and C))), M:tm-122, m:tm-12, u:((Am (and (-> A Bm) C)) (B Bm) (D (-> (and (-> A Bm) C) (and (-> A Bm) C))))
================================================================
tm-name          tm-3801
in-theory        3801
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-122 tm-14 ((Am (-> (and (-> A B) C) B)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3801.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-122, m:tm-14, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3802
in-theory        3802
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> A) and B) -> A) or (((A -> A) and B) -> A)) -> (((A -> A) and B) -> A))
theorem-size     23
proof            (modus-ponens tm-122 tm-15 ((A Bm) (Am Bm) (C Cm) (B Bm) (D (-> (and (-> Bm Bm) Cm) Bm))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3802.         (((((A -> A) and B) -> A) or (((A -> A) and B) -> A)) -> (((A -> A) and B) -> A)), M:tm-122, m:tm-15, u:((A Bm) (Am Bm) (C Cm) (B Bm) (D (-> (and (-> Bm Bm) Cm) Bm)))
================================================================
tm-name          tm-3803
in-theory        3803
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-122 tm-16 ((Am (-> (and (-> A B) C) B)) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3803.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D and E) -> D)), M:tm-122, m:tm-16, u:((Am (-> (and (-> A B) C) B)) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-3804
in-theory        3804
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and (B -> C)) -> A) or (((A -> B) and (B -> C)) -> B)) -> (((A -> B) and (B -> C)) -> C))
theorem-size     29
proof            (modus-ponens tm-122 tm-17 ((Am (-> A Bm)) (C (-> Bm Cm)) (B Bm) (D (-> (and (-> A Bm) (-> Bm Cm)) Cm))))
axioms-used      (tm-8 tm-2 tm-3 tm-4)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3804.         (((((A -> B) and (B -> C)) -> A) or (((A -> B) and (B -> C)) -> B)) -> (((A -> B) and (B -> C)) -> C)), M:tm-122, m:tm-17, u:((Am (-> A Bm)) (C (-> Bm Cm)) (B Bm) (D (-> (and (-> A Bm) (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-3805
in-theory        3805
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-122 tm-18 ((Am (-> (and (-> A B) C) B)) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3805.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D and E) -> E)), M:tm-122, m:tm-18, u:((Am (-> (and (-> A B) C) B)) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-3806
in-theory        3806
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> D)) and (((A -> B) and C) -> B)))
theorem-size     29
proof            (modus-ponens tm-122 tm-19 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> Cm Bm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3806.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> D)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-19, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> Cm Bm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3807
in-theory        3807
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) and C) -> B)))
theorem-size     37
proof            (modus-ponens tm-122 tm-20 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3807.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-20, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3808
in-theory        3808
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D and E) -> D) and (((A -> B) and C) -> B)))
theorem-size     29
proof            (modus-ponens tm-122 tm-21 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and Bm Cm) Bm) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3808.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D and E) -> D) and (((A -> B) and C) -> B))), M:tm-122, m:tm-21, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and Bm Cm) Bm) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3809
in-theory        3809
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D and E) -> E) and (((A -> B) and C) -> B)))
theorem-size     29
proof            (modus-ponens tm-122 tm-22 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and Bm Cm) Cm) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3809.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D and E) -> E) and (((A -> B) and C) -> B))), M:tm-122, m:tm-22, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and Bm Cm) Cm) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3810
in-theory        3810
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> (D and E))) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-23 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3810.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> (D and E))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-23, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3811
in-theory        3811
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> (((A -> B) and C) and B)))
theorem-size     29
proof            (modus-ponens tm-122 tm-24 ((Am (and (-> A Bm) C)) (B Bm) (D (-> (and (-> A Bm) C) (and (and (-> A Bm) C) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3811.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> (((A -> B) and C) and B))), M:tm-122, m:tm-24, u:((Am (and (-> A Bm) C)) (B Bm) (D (-> (and (-> A Bm) C) (and (and (-> A Bm) C) Bm))))
================================================================
tm-name          tm-3812
in-theory        3812
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-122 tm-25 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3812.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (E -> (D and E)))), M:tm-122, m:tm-25, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-3813
in-theory        3813
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (D or E)) and (((A -> B) and C) -> B)))
theorem-size     29
proof            (modus-ponens tm-122 tm-32 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (or Bm Cm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3813.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (D or E)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-32, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (or Bm Cm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3814
in-theory        3814
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-122 tm-33 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3814.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (D or E))), M:tm-122, m:tm-33, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-3815
in-theory        3815
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E or D)) and (((A -> B) and C) -> B)))
theorem-size     29
proof            (modus-ponens tm-122 tm-42 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (or Cm Bm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3815.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E or D)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-42, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (or Cm Bm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3816
in-theory        3816
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-122 tm-43 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3816.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (E or D))), M:tm-122, m:tm-43, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-3817
in-theory        3817
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((((A -> B) and C) and D) or ((A -> B) and C)) -> B))
theorem-size     31
proof            (modus-ponens tm-122 tm-46 ((Am (and (-> A Bm) C)) (B Bm) (D (-> (or (and (and (-> A Bm) C) Cm) (and (-> A Bm) C)) Bm))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-3817.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((((A -> B) and C) and D) or ((A -> B) and C)) -> B)), M:tm-122, m:tm-46, u:((Am (and (-> A Bm) C)) (B Bm) (D (-> (or (and (and (-> A Bm) C) Cm) (and (-> A Bm) C)) Bm)))
================================================================
tm-name          tm-3818
in-theory        3818
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D and ((A -> B) and C)) or ((A -> B) and C)) -> B))
theorem-size     31
proof            (modus-ponens tm-122 tm-47 ((Am (and (-> A Bm) C)) (B Bm) (D (-> (or (and Cm (and (-> A Bm) C)) (and (-> A Bm) C)) Bm))))
axioms-used      (tm-8 tm-2 tm-3 tm-4)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3818.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D and ((A -> B) and C)) or ((A -> B) and C)) -> B)), M:tm-122, m:tm-47, u:((Am (and (-> A Bm) C)) (B Bm) (D (-> (or (and Cm (and (-> A Bm) C)) (and (-> A Bm) C)) Bm)))
================================================================
tm-name          tm-3819
in-theory        3819
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((A -> B) and C) -> B)))
theorem-size     37
proof            (modus-ponens tm-122 tm-54 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3819.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-54, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3820
in-theory        3820
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-122 tm-56 ((Am (-> (and (-> A B) C) B)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3820.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-122, m:tm-56, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-3821
in-theory        3821
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) and B) -> A) or (((A -> (not B)) and B) -> (not B))) -> (not ((A -> (not B)) and B)))
theorem-size     26
proof            (modus-ponens tm-122 tm-60 ((Am (-> A (not Bm))) (C Bm) (B (not Bm)) (D (not (and (-> A (not Bm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-9 tm-4)
proof-size       126
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3821.         (((((A -> (not B)) and B) -> A) or (((A -> (not B)) and B) -> (not B))) -> (not ((A -> (not B)) and B))), M:tm-122, m:tm-60, u:((Am (-> A (not Bm))) (C Bm) (B (not Bm)) (D (not (and (-> A (not Bm)) Bm))))
================================================================
tm-name          tm-3822
in-theory        3822
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (((A -> B) and C) -> B)))
theorem-size     35
proof            (modus-ponens tm-122 tm-69 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-9)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3822.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-69, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3823
in-theory        3823
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-122 tm-71 ((Am (-> (and (-> A B) C) B)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-9)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3823.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-122, m:tm-71, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-3824
in-theory        3824
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((not (not ((A -> B) and C))) or ((A -> B) and C)) -> B))
theorem-size     31
proof            (modus-ponens tm-122 tm-73 ((Am (and (-> A Bm) C)) (B Bm) (D (-> (or (not (not (and (-> A Bm) C))) (and (-> A Bm) C)) Bm))))
axioms-used      (tm-8 tm-2 tm-3 tm-10)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3824.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((not (not ((A -> B) and C))) or ((A -> B) and C)) -> B)), M:tm-122, m:tm-73, u:((Am (and (-> A Bm) C)) (B Bm) (D (-> (or (not (not (and (-> A Bm) C))) (and (-> A Bm) C)) Bm)))
================================================================
tm-name          tm-3825
in-theory        3825
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((not (not D)) -> D) and (((A -> B) and C) -> B)))
theorem-size     29
proof            (modus-ponens tm-122 tm-76 ((Am (-> (and (-> A B) C) B)) (D (and (-> (not (not Bm)) Bm) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-10)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3825.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((not (not D)) -> D) and (((A -> B) and C) -> B))), M:tm-122, m:tm-76, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (not (not Bm)) Bm) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3826
in-theory        3826
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((not (not D)) -> D))
theorem-size     21
proof            (modus-ponens tm-122 tm-78 ((Am (-> (and (-> A B) C) B)) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-10)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3826.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((not (not D)) -> D)), M:tm-122, m:tm-78, u:((Am (-> (and (-> A B) C) B)) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-3827
in-theory        3827
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not (B -> (C -> B)))) and D) -> A) or (((A -> (not (B -> (C -> B)))) and D) -> (not (B -> (C -> B))))) -> (not ((A -> (not (B -> (C -> B)))) and D)))
theorem-size     42
proof            (modus-ponens tm-122 tm-79 ((Am (and (-> A (not (-> Bm (-> Cm Bm)))) C)) (B (not (-> Bm (-> Cm Bm)))) (D (not (and (-> A (not (-> Bm (-> Cm Bm)))) C)))))
axioms-used      (tm-8 tm-2 tm-3 tm-9 tm-1)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3827.         (((((A -> (not (B -> (C -> B)))) and D) -> A) or (((A -> (not (B -> (C -> B)))) and D) -> (not (B -> (C -> B))))) -> (not ((A -> (not (B -> (C -> B)))) and D))), M:tm-122, m:tm-79, u:((Am (and (-> A (not (-> Bm (-> Cm Bm)))) C)) (B (not (-> Bm (-> Cm Bm)))) (D (not (and (-> A (not (-> Bm (-> Cm Bm)))) C))))
================================================================
tm-name          tm-3828
in-theory        3828
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> (F -> E))) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-83 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3828.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> (F -> E))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-83, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3829
in-theory        3829
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> (D -> B)))
theorem-size     25
proof            (modus-ponens tm-122 tm-84 ((Am (and (-> A Bm) C)) (B Bm) (D (-> (and (-> A Bm) C) (-> Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3829.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> (D -> B))), M:tm-122, m:tm-84, u:((Am (and (-> A Bm) C)) (B Bm) (D (-> (and (-> A Bm) C) (-> Cm Bm))))
================================================================
tm-name          tm-3830
in-theory        3830
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-122 tm-85 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3830.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (E -> (F -> E)))), M:tm-122, m:tm-85, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-3831
in-theory        3831
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> B))
theorem-size     23
proof            (modus-ponens tm-122 tm-86 ((Am (-> (and (-> A B) C) B)) (D (-> (and (-> A B) C) B))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3831.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> B)), M:tm-122, m:tm-86, u:((Am (-> (and (-> A B) C) B)) (D (-> (and (-> A B) C) B)))
================================================================
tm-name          tm-3832
in-theory        3832
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) -> A) or (((A -> (B -> C)) and D) -> (B -> C))) -> (((A -> (B -> C)) and D) -> (B -> C)))
theorem-size     33
proof            (modus-ponens tm-122 tm-87 ((Am (and (-> A (-> Bm Cm)) C)) (B (-> Bm Cm)) (D (-> (and (-> A (-> Bm Cm)) C) (-> Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3832.         (((((A -> (B -> C)) and D) -> A) or (((A -> (B -> C)) and D) -> (B -> C))) -> (((A -> (B -> C)) and D) -> (B -> C))), M:tm-122, m:tm-87, u:((Am (and (-> A (-> Bm Cm)) C)) (B (-> Bm Cm)) (D (-> (and (-> A (-> Bm Cm)) C) (-> Bm Cm))))
================================================================
tm-name          tm-3833
in-theory        3833
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> (D -> D)) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-95 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3833.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> (D -> D)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-95, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3834
in-theory        3834
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> E) -> (D -> D)))
theorem-size     23
proof            (modus-ponens tm-122 tm-97 ((Am (-> (and (-> A B) C) B)) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3834.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> E) -> (D -> D))), M:tm-122, m:tm-97, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-3835
in-theory        3835
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (((A -> B) and C) -> B)))
theorem-size     43
proof            (modus-ponens tm-122 tm-105 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3835.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-105, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3836
in-theory        3836
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-122 tm-107 ((Am (-> (and (-> A B) C) B)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3836.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-122, m:tm-107, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-3837
in-theory        3837
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and E) -> A) or (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and E) -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and E)))
theorem-size     74
proof            (modus-ponens tm-122 tm-109 ((Am (and (-> A (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) C)) (B (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (and (-> A (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) C)))))
axioms-used      (tm-8 tm-2 tm-3 tm-9 tm-1)
proof-size       210
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3837.         (((((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and E) -> A) or (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and E) -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and E))), M:tm-122, m:tm-109, u:((Am (and (-> A (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) C)) (B (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (and (-> A (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) C))))
================================================================
tm-name          tm-3838
in-theory        3838
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((A -> B) and C) -> B)))
theorem-size     39
proof            (modus-ponens tm-122 tm-113 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3838.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-113, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-3839
in-theory        3839
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (C -> D))) and E) -> A) or (((A -> (B -> (C -> D))) and E) -> (B -> (C -> D)))) -> (((A -> (B -> (C -> D))) and E) -> ((B -> C) -> (B -> D))))
theorem-size     45
proof            (modus-ponens tm-122 tm-114 ((Am (and (-> A (-> Bm (-> Cm Dm))) C)) (B (-> Bm (-> Cm Dm))) (D (-> (and (-> A (-> Bm (-> Cm Dm))) C) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3839.         (((((A -> (B -> (C -> D))) and E) -> A) or (((A -> (B -> (C -> D))) and E) -> (B -> (C -> D)))) -> (((A -> (B -> (C -> D))) and E) -> ((B -> C) -> (B -> D)))), M:tm-122, m:tm-114, u:((Am (and (-> A (-> Bm (-> Cm Dm))) C)) (B (-> Bm (-> Cm Dm))) (D (-> (and (-> A (-> Bm (-> Cm Dm))) C) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-3840
in-theory        3840
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-122 tm-115 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3840.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-122, m:tm-115, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-3841
in-theory        3841
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> (D -> E)) -> ((((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> E)))
theorem-size     47
proof            (modus-ponens tm-114 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) (-> C D))) (B (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3841.         (((((A -> B) and C) -> B) -> (D -> E)) -> ((((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> E))), M:tm-114, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) (-> C D))) (B (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))) (Dm (-> C D)))
================================================================
tm-name          tm-3842
in-theory        3842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> F) -> H) -> (((((E -> F) and G) -> E) or (((E -> F) and G) -> F)) -> H)))
theorem-size     43
proof            (modus-ponens tm-113 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3842.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> F) -> H) -> (((((E -> F) and G) -> E) or (((E -> F) and G) -> F)) -> H))), M:tm-113, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3843
in-theory        3843
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) and E) -> (C -> D)) -> ((((B -> (C -> D)) and E) -> C) -> (((B -> (C -> D)) and E) -> D)))) -> (((((B -> (C -> D)) and E) -> B) or (((B -> (C -> D)) and E) -> (C -> D))) -> ((((B -> (C -> D)) and E) -> C) -> (((B -> (C -> D)) and E) -> D))))
theorem-size     75
proof            (modus-ponens tm-110 tm-122 ((A (and (-> Am (-> B C)) Cm)) (Bm (-> B C)) (Dm (-> (-> (and (-> Am (-> B C)) Cm) B) (-> (and (-> Am (-> B C)) Cm) C))) (D (-> (or (-> (and (-> Am (-> B C)) Cm) Am) (-> (and (-> Am (-> B C)) Cm) (-> B C))) (-> (-> (and (-> Am (-> B C)) Cm) B) (-> (and (-> Am (-> B C)) Cm) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       227
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3843.         ((A or ((((B -> (C -> D)) and E) -> (C -> D)) -> ((((B -> (C -> D)) and E) -> C) -> (((B -> (C -> D)) and E) -> D)))) -> (((((B -> (C -> D)) and E) -> B) or (((B -> (C -> D)) and E) -> (C -> D))) -> ((((B -> (C -> D)) and E) -> C) -> (((B -> (C -> D)) and E) -> D)))), M:tm-110, m:tm-122, u:((A (and (-> Am (-> B C)) Cm)) (Bm (-> B C)) (Dm (-> (-> (and (-> Am (-> B C)) Cm) B) (-> (and (-> Am (-> B C)) Cm) C))) (D (-> (or (-> (and (-> Am (-> B C)) Cm) Am) (-> (and (-> Am (-> B C)) Cm) (-> B C))) (-> (-> (and (-> Am (-> B C)) Cm) B) (-> (and (-> Am (-> B C)) Cm) C)))))
================================================================
tm-name          tm-3844
in-theory        3844
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     47
proof            (modus-ponens tm-105 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3844.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-105, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3845
in-theory        3845
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) and D) -> (B -> C)) -> (((A -> (B -> C)) and D) -> B)) or ((((A -> (B -> C)) and D) -> (B -> C)) -> (((A -> (B -> C)) and D) -> C))) -> (((((A -> (B -> C)) and D) -> A) or (((A -> (B -> C)) and D) -> (B -> C))) -> (((A -> (B -> C)) and D) -> C)))
theorem-size     75
proof            (modus-ponens tm-102 tm-122 ((A (and (-> Am (-> B C)) Cm)) (Bm (-> B C)) (Dm (-> (and (-> Am (-> B C)) Cm) C)) (D (-> (or (-> (and (-> Am (-> B C)) Cm) Am) (-> (and (-> Am (-> B C)) Cm) (-> B C))) (-> (and (-> Am (-> B C)) Cm) C)))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       239
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3845.         ((((((A -> (B -> C)) and D) -> (B -> C)) -> (((A -> (B -> C)) and D) -> B)) or ((((A -> (B -> C)) and D) -> (B -> C)) -> (((A -> (B -> C)) and D) -> C))) -> (((((A -> (B -> C)) and D) -> A) or (((A -> (B -> C)) and D) -> (B -> C))) -> (((A -> (B -> C)) and D) -> C))), M:tm-102, m:tm-122, u:((A (and (-> Am (-> B C)) Cm)) (Bm (-> B C)) (Dm (-> (and (-> Am (-> B C)) Cm) C)) (D (-> (or (-> (and (-> Am (-> B C)) Cm) Am) (-> (and (-> Am (-> B C)) Cm) (-> B C))) (-> (and (-> Am (-> B C)) Cm) C))))
================================================================
tm-name          tm-3846
in-theory        3846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F)))
theorem-size     35
proof            (modus-ponens tm-95 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3846.         (((A -> B) -> (A -> A)) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F))), M:tm-95, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3847
in-theory        3847
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) or ((((A -> B) and C) -> B) -> (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> B)))
theorem-size     49
proof            (modus-ponens tm-92 tm-122 ((Dm (-> (and (-> Am Bm) Cm) Bm)) (A (-> (and (-> Am Bm) Cm) Bm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3847.         ((((((A -> B) and C) -> B) -> D) or ((((A -> B) and C) -> B) -> (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> B))), M:tm-92, m:tm-122, u:((Dm (-> (and (-> Am Bm) Cm) Bm)) (A (-> (and (-> Am Bm) Cm) Bm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-3848
in-theory        3848
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> D) -> (E -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))
theorem-size     29
proof            (modus-ponens tm-84 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3848.         (((((A -> B) and C) -> B) -> D) -> (E -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))), M:tm-84, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3849
in-theory        3849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-83 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3849.         ((A -> (B -> (C -> B))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-83, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3850
in-theory        3850
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> C) -> (E -> (((B -> C) and D) -> C)))) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> (E -> (((B -> C) and D) -> C))))
theorem-size     45
proof            (modus-ponens tm-80 tm-122 ((A (-> (and (-> Am Bm) Cm) Bm)) (Dm (-> B (-> (and (-> Am Bm) Cm) Bm))) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (-> B (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3850.         ((A or ((((B -> C) and D) -> C) -> (E -> (((B -> C) and D) -> C)))) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> (E -> (((B -> C) and D) -> C)))), M:tm-80, m:tm-122, u:((A (-> (and (-> Am Bm) Cm) Bm)) (Dm (-> B (-> (and (-> Am Bm) Cm) Bm))) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (-> B (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-3851
in-theory        3851
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> C) and D) -> C) -> E) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> E)))
theorem-size     33
proof            (modus-ponens tm-76 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3851.         (((not (not A)) -> A) and (((((B -> C) and D) -> C) -> E) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> E))), M:tm-76, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3852
in-theory        3852
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> B) and C) -> B) -> D))) or ((((A -> B) and C) -> B) -> D)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))
theorem-size     39
proof            (modus-ponens tm-73 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-8 tm-10 tm-2 tm-3)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3852.         (((not (not ((((A -> B) and C) -> B) -> D))) or ((((A -> B) and C) -> B) -> D)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-73, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3853
in-theory        3853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F)))
theorem-size     39
proof            (modus-ponens tm-69 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-3)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3853.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F))), M:tm-69, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3854
in-theory        3854
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) and C) -> B) or ((((A -> (not B)) and C) -> (not B)) -> (not ((A -> (not B)) and C)))) -> (((((A -> (not B)) and C) -> A) or (((A -> (not B)) and C) -> (not B))) -> (not ((A -> (not B)) and C))))
theorem-size     53
proof            (modus-ponens tm-66 tm-122 ((A (and (-> Am (not B)) Cm)) (Bm (not B)) (Dm (not (and (-> Am (not B)) Cm))) (C (-> (or (-> (and (-> Am (not B)) Cm) Am) (-> (and (-> Am (not B)) Cm) (not B))) (not (and (-> Am (not B)) Cm))))))
axioms-used      (tm-8 tm-9 tm-2 tm-3)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3854.         (((((A -> (not B)) and C) -> B) or ((((A -> (not B)) and C) -> (not B)) -> (not ((A -> (not B)) and C)))) -> (((((A -> (not B)) and C) -> A) or (((A -> (not B)) and C) -> (not B))) -> (not ((A -> (not B)) and C)))), M:tm-66, m:tm-122, u:((A (and (-> Am (not B)) Cm)) (Bm (not B)) (Dm (not (and (-> Am (not B)) Cm))) (C (-> (or (-> (and (-> Am (not B)) Cm) Am) (-> (and (-> Am (not B)) Cm) (not B))) (not (and (-> Am (not B)) Cm)))))
================================================================
tm-name          tm-3855
in-theory        3855
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> ((((A -> B) and C) -> A) or (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> B) or ((((A -> B) and C) -> A) or (((A -> B) and C) -> B))) -> ((((A -> B) and C) -> A) or (((A -> B) and C) -> B))))
theorem-size     63
proof            (modus-ponens tm-55 tm-122 ((A (-> (and (-> Am Bm) Cm) Bm)) (Dm (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))) (B (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))) (C (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       179
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3855.         (((((A -> B) and C) -> B) -> ((((A -> B) and C) -> A) or (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> B) or ((((A -> B) and C) -> A) or (((A -> B) and C) -> B))) -> ((((A -> B) and C) -> A) or (((A -> B) and C) -> B)))), M:tm-55, m:tm-122, u:((A (-> (and (-> Am Bm) Cm) Bm)) (Dm (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))) (B (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))) (C (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-3856
in-theory        3856
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     41
proof            (modus-ponens tm-54 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3856.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-54, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3857
in-theory        3857
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> C) and D)) or ((((B -> C) and D) -> C) -> ((A or ((B -> C) and D)) -> C))) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> ((A or ((B -> C) and D)) -> C)))
theorem-size     51
proof            (modus-ponens tm-51 tm-122 ((A (and (-> Am Bm) Cm)) (B Bm) (Dm (-> (or C (and (-> Am Bm) Cm)) Bm)) (D (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (-> (or C (and (-> Am Bm) Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3857.         (((A -> ((B -> C) and D)) or ((((B -> C) and D) -> C) -> ((A or ((B -> C) and D)) -> C))) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> ((A or ((B -> C) and D)) -> C))), M:tm-51, m:tm-122, u:((A (and (-> Am Bm) Cm)) (B Bm) (Dm (-> (or C (and (-> Am Bm) Cm)) Bm)) (D (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (-> (or C (and (-> Am Bm) Cm)) Bm))))
================================================================
tm-name          tm-3858
in-theory        3858
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> C) -> (A and (((B -> C) and D) -> C)))) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> (A and (((B -> C) and D) -> C))))
theorem-size     45
proof            (modus-ponens tm-48 tm-122 ((A (-> (and (-> Am Bm) Cm) Bm)) (Dm (and B (-> (and (-> Am Bm) Cm) Bm))) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (and B (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3858.         ((A or ((((B -> C) and D) -> C) -> (A and (((B -> C) and D) -> C)))) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> (A and (((B -> C) and D) -> C)))), M:tm-48, m:tm-122, u:((A (-> (and (-> Am Bm) Cm) Bm)) (Dm (and B (-> (and (-> Am Bm) Cm) Bm))) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (and B (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-3859
in-theory        3859
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((((B -> C) and D) -> C) -> E)) or ((((B -> C) and D) -> C) -> E)) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> E))
theorem-size     39
proof            (modus-ponens tm-47 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-8 tm-4 tm-2 tm-3)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3859.         (((A and ((((B -> C) and D) -> C) -> E)) or ((((B -> C) and D) -> C) -> E)) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> E)), M:tm-47, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3860
in-theory        3860
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> B) -> D) and E) or ((((A -> B) and C) -> B) -> D)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))
theorem-size     39
proof            (modus-ponens tm-46 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3860.         (((((((A -> B) and C) -> B) -> D) and E) or ((((A -> B) and C) -> B) -> D)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-46, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3861
in-theory        3861
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> (B -> D)) or ((((A -> B) and C) -> B) -> (((A -> B) and C) -> D))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> D)))
theorem-size     49
proof            (modus-ponens tm-45 tm-122 ((A (and (-> Am Bm) Cm)) (B Bm) (Dm (-> (and (-> Am Bm) Cm) C)) (D (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (-> (and (-> Am Bm) Cm) C)))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3861.         (((((A -> B) and C) -> (B -> D)) or ((((A -> B) and C) -> B) -> (((A -> B) and C) -> D))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> D))), M:tm-45, m:tm-122, u:((A (and (-> Am Bm) Cm)) (B Bm) (Dm (-> (and (-> Am Bm) Cm) C)) (D (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (-> (and (-> Am Bm) Cm) C))))
================================================================
tm-name          tm-3862
in-theory        3862
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> C) -> A)) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> A))
theorem-size     29
proof            (modus-ponens tm-44 tm-122 ((A (-> (and (-> Am Bm) Cm) Bm)) (B Dm) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3862.         ((A or ((((B -> C) and D) -> C) -> A)) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> A)), M:tm-44, m:tm-122, u:((A (-> (and (-> Am Bm) Cm) Bm)) (B Dm) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3863
in-theory        3863
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F)))
theorem-size     33
proof            (modus-ponens tm-42 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3863.         ((A -> (B or A)) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F))), M:tm-42, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3864
in-theory        3864
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F)))
theorem-size     33
proof            (modus-ponens tm-32 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3864.         ((A -> (A or B)) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F))), M:tm-32, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3865
in-theory        3865
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> B) -> D) and (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))
theorem-size     37
proof            (modus-ponens tm-24 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3865.         (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> B) -> D) and (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))), M:tm-24, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3866
in-theory        3866
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F)))
theorem-size     35
proof            (modus-ponens tm-23 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3866.         ((A -> (B -> (A and B))) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F))), M:tm-23, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3867
in-theory        3867
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F)))
theorem-size     33
proof            (modus-ponens tm-22 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3867.         (((A and B) -> B) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F))), M:tm-22, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3868
in-theory        3868
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F)))
theorem-size     33
proof            (modus-ponens tm-21 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3868.         (((A and B) -> A) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F))), M:tm-21, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3869
in-theory        3869
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     41
proof            (modus-ponens tm-20 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3869.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-20, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3870
in-theory        3870
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F)))
theorem-size     33
proof            (modus-ponens tm-19 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3870.         ((A -> (B -> A)) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F))), M:tm-19, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3871
in-theory        3871
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> D) -> ((((A -> B) and C) -> B) -> D))
theorem-size     19
proof            (modus-ponens tm-12 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3871.         (((((A -> B) and C) -> B) -> D) -> ((((A -> B) and C) -> B) -> D)), M:tm-12, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3872
in-theory        3872
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (not (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))) -> (not ((((A -> B) and C) -> B) -> D)))
theorem-size     39
proof            (modus-ponens tm-9 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-9 tm-8 tm-2 tm-3)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3872.         ((((((A -> B) and C) -> B) -> D) -> (not (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))) -> (not ((((A -> B) and C) -> B) -> D))), M:tm-9, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3873
in-theory        3873
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D) -> E) -> ((((((A -> B) and C) -> B) -> D) or (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) -> E))
theorem-size     49
proof            (modus-ponens tm-8 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       135
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3873.         (((((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D) -> E) -> ((((((A -> B) and C) -> B) -> D) or (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) -> E)), M:tm-8, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3874
in-theory        3874
times-derived    2
----------------------------------------------------------------
theorem          (A or (((((B -> C) and D) -> C) -> E) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> E)))
theorem-size     29
proof            (modus-ponens tm-7 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-2 tm-3)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3874.         (A or (((((B -> C) and D) -> C) -> E) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> E))), M:tm-7, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3875
in-theory        3875
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) or E)
theorem-size     29
proof            (modus-ponens tm-6 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-2 tm-3)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3875.         ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) or E), M:tm-6, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3876
in-theory        3876
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) and D) -> C) -> E) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> E)) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3876.         (A -> ((((((B -> C) and D) -> C) -> E) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> E)) and A)), M:tm-5, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3877
in-theory        3877
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> ((((A -> B) and C) -> A) or (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> B) -> D) -> D))
theorem-size     37
proof            (modus-ponens tm-2 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3877.         ((((((A -> B) and C) -> B) -> D) -> ((((A -> B) and C) -> A) or (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> B) -> D) -> D)), M:tm-2, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))) (C Dm))
================================================================
tm-name          tm-3878
in-theory        3878
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> C) and D) -> C) -> E) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> E)))
theorem-size     29
proof            (modus-ponens tm-1 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-2 tm-3)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-3878.         (A -> (((((B -> C) and D) -> C) -> E) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> E))), M:tm-1, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-3879
in-theory        3879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-113 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3879.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-113, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3880
in-theory        3880
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     37
proof            (modus-ponens tm-105 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3880.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-105, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3881
in-theory        3881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     25
proof            (modus-ponens tm-95 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3881.         (((A -> B) -> (A -> A)) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-95, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3882
in-theory        3882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-83 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3882.         ((A -> (B -> (C -> B))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-83, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3883
in-theory        3883
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))
theorem-size     23
proof            (modus-ponens tm-76 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3883.         (((not (not A)) -> A) and (B or ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))), M:tm-76, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3884
in-theory        3884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     29
proof            (modus-ponens tm-69 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3884.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-69, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3885
in-theory        3885
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-54 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3885.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-54, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3886
in-theory        3886
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-42 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3886.         ((A -> (B or A)) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-42, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3887
in-theory        3887
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-32 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3887.         ((A -> (A or B)) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-32, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3888
in-theory        3888
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     25
proof            (modus-ponens tm-23 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3888.         ((A -> (B -> (A and B))) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-23, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3889
in-theory        3889
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-22 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3889.         (((A and B) -> B) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-22, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3890
in-theory        3890
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-21 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3890.         (((A and B) -> A) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-21, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3891
in-theory        3891
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-20 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3891.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-20, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3892
in-theory        3892
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-19 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3892.         ((A -> (B -> A)) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-19, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3893
in-theory        3893
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))
theorem-size     19
proof            (modus-ponens tm-7 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-7 tm-2 tm-3)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3893.         (A or (B or ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))), M:tm-7, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3894
in-theory        3894
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-6 tm-7 tm-2 tm-3)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3894.         ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) or E), M:tm-6, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3895
in-theory        3895
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3895.         (A -> ((B or ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and A)), M:tm-5, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3896
in-theory        3896
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))
theorem-size     19
proof            (modus-ponens tm-1 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-1 tm-7 tm-2 tm-3)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3896.         (A -> (B or ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))), M:tm-1, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-3897
in-theory        3897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H))
theorem-size     33
proof            (modus-ponens tm-113 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3897.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H)), M:tm-113, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3898
in-theory        3898
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     37
proof            (modus-ponens tm-105 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3898.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-105, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3899
in-theory        3899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F))
theorem-size     25
proof            (modus-ponens tm-95 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3899.         (((A -> B) -> (A -> A)) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F)), M:tm-95, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3900
in-theory        3900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-83 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3900.         ((A -> (B -> (C -> B))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-83, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3901
in-theory        3901
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) or E))
theorem-size     23
proof            (modus-ponens tm-76 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3901.         (((not (not A)) -> A) and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) or E)), M:tm-76, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3902
in-theory        3902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F))
theorem-size     29
proof            (modus-ponens tm-69 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-2 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3902.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F)), M:tm-69, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3903
in-theory        3903
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     31
proof            (modus-ponens tm-54 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3903.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-54, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3904
in-theory        3904
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-42 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3904.         ((A -> (B or A)) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F)), M:tm-42, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3905
in-theory        3905
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-32 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3905.         ((A -> (A or B)) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F)), M:tm-32, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3906
in-theory        3906
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F))
theorem-size     25
proof            (modus-ponens tm-23 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3906.         ((A -> (B -> (A and B))) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F)), M:tm-23, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3907
in-theory        3907
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-22 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3907.         (((A and B) -> B) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F)), M:tm-22, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3908
in-theory        3908
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-21 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3908.         (((A and B) -> A) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F)), M:tm-21, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3909
in-theory        3909
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     31
proof            (modus-ponens tm-20 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3909.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-20, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3910
in-theory        3910
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-19 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3910.         ((A -> (B -> A)) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F)), M:tm-19, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3911
in-theory        3911
times-derived    2
----------------------------------------------------------------
theorem          (A or (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) or E))
theorem-size     19
proof            (modus-ponens tm-7 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-7 tm-6 tm-2 tm-3)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3911.         (A or (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) or E)), M:tm-7, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3912
in-theory        3912
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-6 tm-2 tm-3)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3912.         ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) or E), M:tm-6, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3913
in-theory        3913
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) or E) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3913.         (A -> ((((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) or E) and A)), M:tm-5, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3914
in-theory        3914
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) or E))
theorem-size     19
proof            (modus-ponens tm-1 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-1 tm-6 tm-2 tm-3)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3914.         (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) or E)), M:tm-1, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-3915
in-theory        3915
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-125 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3915.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> D))), M:tm-125, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-3916
in-theory        3916
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3916.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-125, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-3917
in-theory        3917
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-125 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3917.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and E) -> D)), M:tm-125, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-3918
in-theory        3918
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-125 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-3918.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and E) -> E)), M:tm-125, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-3919
in-theory        3919
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-125 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3919.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (D and E)))), M:tm-125, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-3920
in-theory        3920
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-125 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3920.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D or E))), M:tm-125, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-3921
in-theory        3921
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-125 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3921.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or D))), M:tm-125, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-3922
in-theory        3922
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3922.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-125, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-3923
in-theory        3923
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-125 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3923.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-125, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-3924
in-theory        3924
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((not (not D)) -> D))
theorem-size     21
proof            (modus-ponens tm-125 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-2 tm-3 tm-10)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-3924.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((not (not D)) -> D)), M:tm-125, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-3925
in-theory        3925
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-125 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3925.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (F -> E)))), M:tm-125, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-3926
in-theory        3926
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (D -> D)))
theorem-size     23
proof            (modus-ponens tm-125 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3926.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (D -> D))), M:tm-125, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-3927
in-theory        3927
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-125 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3927.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-125, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-3928
in-theory        3928
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3928.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-125, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3929
in-theory        3929
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-125 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-3929.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-125, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-3930
in-theory        3930
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-125 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3930.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E and F) -> E))), M:tm-125, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-3931
in-theory        3931
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-125 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3931.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-125, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-3932
in-theory        3932
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-125 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3932.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E and F) -> F))), M:tm-125, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-3933
in-theory        3933
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     25
proof            (modus-ponens tm-125 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3933.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> E)) and D))), M:tm-125, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-3934
in-theory        3934
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-125 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3934.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-125, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-3935
in-theory        3935
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E and F) -> E) and D)))
theorem-size     25
proof            (modus-ponens tm-125 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3935.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E and F) -> E) and D))), M:tm-125, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-3936
in-theory        3936
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E and F) -> F) and D)))
theorem-size     25
proof            (modus-ponens tm-125 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3936.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E and F) -> F) and D))), M:tm-125, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-3937
in-theory        3937
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3937.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-125, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-3938
in-theory        3938
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (D -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-125 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3938.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (D -> (D and E)))), M:tm-125, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-3939
in-theory        3939
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3939.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (F -> (E and F))))), M:tm-125, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-3940
in-theory        3940
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-125 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3940.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) or F)), M:tm-125, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-3941
in-theory        3941
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-125 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3941.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-125, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-3942
in-theory        3942
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) or F))
theorem-size     23
proof            (modus-ponens tm-125 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3942.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) or F)), M:tm-125, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-3943
in-theory        3943
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) or F))
theorem-size     23
proof            (modus-ponens tm-125 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3943.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) or F)), M:tm-125, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-3944
in-theory        3944
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) or F))
theorem-size     25
proof            (modus-ponens tm-125 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3944.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) or F)), M:tm-125, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-3945
in-theory        3945
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) or F))
theorem-size     23
proof            (modus-ponens tm-125 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3945.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) or F)), M:tm-125, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-3946
in-theory        3946
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (E or F)) and D)))
theorem-size     25
proof            (modus-ponens tm-125 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3946.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (E or F)) and D))), M:tm-125, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-3947
in-theory        3947
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-125 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3947.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (E or F)))), M:tm-125, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-3948
in-theory        3948
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-125 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3948.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (F -> E)))), M:tm-125, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-3949
in-theory        3949
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3949.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-125, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-3950
in-theory        3950
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-125 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-3950.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E and F) -> E))), M:tm-125, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-3951
in-theory        3951
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-125 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3951.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E and F) -> F))), M:tm-125, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-3952
in-theory        3952
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3952.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (F -> (E and F))))), M:tm-125, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-3953
in-theory        3953
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-125 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3953.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (E or F)))), M:tm-125, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-3954
in-theory        3954
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-125 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3954.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (F or E)))), M:tm-125, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-3955
in-theory        3955
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) or F))
theorem-size     23
proof            (modus-ponens tm-125 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3955.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) or F)), M:tm-125, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-3956
in-theory        3956
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F or E)) and D)))
theorem-size     25
proof            (modus-ponens tm-125 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3956.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F or E)) and D))), M:tm-125, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-3957
in-theory        3957
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-125 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3957.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (F or E)))), M:tm-125, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-3958
in-theory        3958
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-125 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3958.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-125, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-3959
in-theory        3959
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-125 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3959.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-125, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-3960
in-theory        3960
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-125 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-3960.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-125, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-3961
in-theory        3961
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-125 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3961.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-125, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-3962
in-theory        3962
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-125 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3962.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-125, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-3963
in-theory        3963
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-125 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3963.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-125, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-3964
in-theory        3964
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-125 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3964.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-125, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-3965
in-theory        3965
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-125 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3965.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-125, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-3966
in-theory        3966
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3966.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-125, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-3967
in-theory        3967
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-125 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3967.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-125, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-3968
in-theory        3968
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-125 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3968.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-125, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-3969
in-theory        3969
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-125 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-3969.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-125, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-3970
in-theory        3970
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3970.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-125, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-3971
in-theory        3971
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-125 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3971.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (E -> D))) -> (not D))), M:tm-125, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-3972
in-theory        3972
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3972.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-125, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-3973
in-theory        3973
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     27
proof            (modus-ponens tm-125 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-3973.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-125, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-3974
in-theory        3974
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     27
proof            (modus-ponens tm-125 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3974.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-125, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-3975
in-theory        3975
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3975.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-125, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-3976
in-theory        3976
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-125 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3976.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (D or E))) -> (not D))), M:tm-125, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-3977
in-theory        3977
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-125 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3977.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (E or D))) -> (not D))), M:tm-125, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-3978
in-theory        3978
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     35
proof            (modus-ponens tm-125 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-8)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3978.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-125, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-3979
in-theory        3979
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     33
proof            (modus-ponens tm-125 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3979.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-125, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-3980
in-theory        3980
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     39
proof            (modus-ponens tm-125 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-9)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3980.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-125, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-3981
in-theory        3981
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3981.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-125, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-3982
in-theory        3982
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     29
proof            (modus-ponens tm-125 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3982.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-125, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-3983
in-theory        3983
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     31
proof            (modus-ponens tm-125 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3983.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-125, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-3984
in-theory        3984
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     31
proof            (modus-ponens tm-125 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-3984.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-125, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-3985
in-theory        3985
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3985.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-125, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-3986
in-theory        3986
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     27
proof            (modus-ponens tm-125 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-10)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3986.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-125, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-3987
in-theory        3987
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-125 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-10)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3987.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-125, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-3988
in-theory        3988
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((not (not E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-125 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3988.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((not (not E)) -> E))), M:tm-125, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-3989
in-theory        3989
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((not (not D)) -> D) or E))
theorem-size     23
proof            (modus-ponens tm-125 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3989.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((not (not D)) -> D) or E)), M:tm-125, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-3990
in-theory        3990
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     25
proof            (modus-ponens tm-125 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-10)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3990.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((not (not E)) -> E) and D))), M:tm-125, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-3991
in-theory        3991
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     31
proof            (modus-ponens tm-125 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-10)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-3991.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-125, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-3992
in-theory        3992
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((not (not E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-125 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3992.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((not (not E)) -> E))), M:tm-125, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-3993
in-theory        3993
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3993.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-125, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-3994
in-theory        3994
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-125 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3994.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-125, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-3995
in-theory        3995
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3995.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (F -> (G -> F))))), M:tm-125, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-3996
in-theory        3996
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (F -> E))) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3996.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (F -> E))) or G)), M:tm-125, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-3997
in-theory        3997
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3997.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-125, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-3998
in-theory        3998
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-125 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3998.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (D -> (F -> E)))), M:tm-125, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-3999
in-theory        3999
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3999.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (F -> (G -> F))))), M:tm-125, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-4000
in-theory        4000
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> D))
theorem-size     19
proof            (modus-ponens tm-125 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4000.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> D)), M:tm-125, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-4001
in-theory        4001
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4001.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-125, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-4002
in-theory        4002
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and E) -> (D and E)))
theorem-size     23
proof            (modus-ponens tm-125 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4002.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and E) -> (D and E))), M:tm-125, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-4003
in-theory        4003
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (D -> E)))
theorem-size     23
proof            (modus-ponens tm-125 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4003.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (D -> E))), M:tm-125, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-4004
in-theory        4004
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((not (not D)) -> (not (not D))))
theorem-size     23
proof            (modus-ponens tm-125 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4004.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((not (not D)) -> (not (not D)))), M:tm-125, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-4005
in-theory        4005
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-125 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4005.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-125, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-4006
in-theory        4006
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-125 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4006.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-125, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-4007
in-theory        4007
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> F) -> (E -> E))))
theorem-size     25
proof            (modus-ponens tm-125 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4007.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> F) -> (E -> E)))), M:tm-125, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-4008
in-theory        4008
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (D -> D)) or F))
theorem-size     25
proof            (modus-ponens tm-125 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4008.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (D -> D)) or F)), M:tm-125, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-4009
in-theory        4009
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4009.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-125, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-4010
in-theory        4010
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-4010.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-125, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-4011
in-theory        4011
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     25
proof            (modus-ponens tm-125 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4011.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> F) -> (E -> E)))), M:tm-125, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-4012
in-theory        4012
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-4012.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-125, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-4013
in-theory        4013
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     25
proof            (modus-ponens tm-125 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-4013.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D -> E)) -> (D -> E))), M:tm-125, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-4014
in-theory        4014
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     35
proof            (modus-ponens tm-125 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4014.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-125, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-4015
in-theory        4015
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     47
proof            (modus-ponens tm-125 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4015.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-125, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-4016
in-theory        4016
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     49
proof            (modus-ponens tm-125 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4016.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-125, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-4017
in-theory        4017
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4017.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-125, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-4018
in-theory        4018
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     37
proof            (modus-ponens tm-125 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4018.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-125, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-4019
in-theory        4019
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     39
proof            (modus-ponens tm-125 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4019.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-125, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-4020
in-theory        4020
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     45
proof            (modus-ponens tm-125 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-4020.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-125, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-4021
in-theory        4021
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4021.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-125, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-4022
in-theory        4022
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-125 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-4022.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-125, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-4023
in-theory        4023
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     35
proof            (modus-ponens tm-125 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4023.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-125, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-4024
in-theory        4024
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     49
proof            (modus-ponens tm-125 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4024.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-125, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-4025
in-theory        4025
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-125 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4025.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-125, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-4026
in-theory        4026
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     33
proof            (modus-ponens tm-125 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4026.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-125, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-4027
in-theory        4027
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     35
proof            (modus-ponens tm-125 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4027.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-125, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-4028
in-theory        4028
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-125 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4028.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-125, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-4029
in-theory        4029
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-125 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4029.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-125, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-4030
in-theory        4030
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) and D) -> E))
theorem-size     23
proof            (modus-ponens tm-125 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-4030.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) and D) -> E)), M:tm-125, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-4031
in-theory        4031
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-125 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-4031.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-125, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-4032
in-theory        4032
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     35
proof            (modus-ponens tm-125 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4032.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-125, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-4033
in-theory        4033
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     37
proof            (modus-ponens tm-125 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-4033.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-125, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-4034
in-theory        4034
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     31
proof            (modus-ponens tm-125 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4034.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-125, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-4035
in-theory        4035
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     41
proof            (modus-ponens tm-125 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4035.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-125, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-4036
in-theory        4036
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     43
proof            (modus-ponens tm-125 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4036.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-125, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-4037
in-theory        4037
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     33
proof            (modus-ponens tm-125 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4037.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-125, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4038
in-theory        4038
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     33
proof            (modus-ponens tm-125 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4038.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-125, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-4039
in-theory        4039
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     35
proof            (modus-ponens tm-125 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4039.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-125, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4040
in-theory        4040
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (((A -> B) and C) -> B)))
theorem-size     39
proof            (modus-ponens tm-122 tm-125 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4040.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-125, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-4041
in-theory        4041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E)))
theorem-size     35
proof            (modus-ponens tm-113 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4041.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E))), M:tm-113, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4042
in-theory        4042
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     45
proof            (modus-ponens tm-110 tm-125 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4042.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-125, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-4043
in-theory        4043
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     39
proof            (modus-ponens tm-105 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4043.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-105, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4044
in-theory        4044
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     45
proof            (modus-ponens tm-102 tm-125 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4044.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-125, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-4045
in-theory        4045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C)))
theorem-size     27
proof            (modus-ponens tm-95 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4045.         (((A -> B) -> (A -> A)) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C))), M:tm-95, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4046
in-theory        4046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> A)))
theorem-size     27
proof            (modus-ponens tm-92 tm-125 ((Am (-> A A)) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4046.         (((A -> B) or (A -> A)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> A))), M:tm-92, m:tm-125, u:((Am (-> A A)) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A A))))
================================================================
tm-name          tm-4047
in-theory        4047
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and A)))
theorem-size     21
proof            (modus-ponens tm-84 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4047.         (A -> (B -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and A))), M:tm-84, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-4048
in-theory        4048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-83 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4048.         ((A -> (B -> (C -> B))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-83, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4049
in-theory        4049
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (B -> (C -> B))))
theorem-size     29
proof            (modus-ponens tm-80 tm-125 ((Am (-> A (-> B A))) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4049.         ((A or (B -> (C -> B))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (B -> (C -> B)))), M:tm-80, m:tm-125, u:((Am (-> A (-> B A))) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A (-> B A)))))
================================================================
tm-name          tm-4050
in-theory        4050
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and B)))
theorem-size     25
proof            (modus-ponens tm-76 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-10 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4050.         (((not (not A)) -> A) and (B -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and B))), M:tm-76, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4051
in-theory        4051
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))
theorem-size     23
proof            (modus-ponens tm-73 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-2 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4051.         (((not (not A)) or A) -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-73, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-4052
in-theory        4052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C)))
theorem-size     31
proof            (modus-ponens tm-69 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4052.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C))), M:tm-69, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4053
in-theory        4053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and ((A -> (not B)) -> (not A))))
theorem-size     35
proof            (modus-ponens tm-66 tm-125 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-2 tm-3)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4053.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-125, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-4054
in-theory        4054
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     33
proof            (modus-ponens tm-54 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4054.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-54, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4055
in-theory        4055
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-51 tm-125 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4055.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-125, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-4056
in-theory        4056
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (B or A)))
theorem-size     25
proof            (modus-ponens tm-50 tm-125 ((Am (or A B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4056.         ((A or (B or A)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (B or A))), M:tm-50, m:tm-125, u:((Am (or A B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (or A B))))
================================================================
tm-name          tm-4057
in-theory        4057
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A or B)))
theorem-size     25
proof            (modus-ponens tm-49 tm-125 ((Am (or A B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4057.         ((A or (A or B)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A or B))), M:tm-49, m:tm-125, u:((Am (or A B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (or A B))))
================================================================
tm-name          tm-4058
in-theory        4058
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-48 tm-125 ((Am (-> A (and B A))) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4058.         ((A or (B -> (A and B))) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (B -> (A and B)))), M:tm-48, m:tm-125, u:((Am (-> A (and B A))) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A (and B A)))))
================================================================
tm-name          tm-4059
in-theory        4059
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and B))
theorem-size     23
proof            (modus-ponens tm-47 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-2 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4059.         (((A and B) or B) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and B)), M:tm-47, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-4060
in-theory        4060
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and A))
theorem-size     23
proof            (modus-ponens tm-46 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4060.         (((A and B) or A) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and A)), M:tm-46, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-4061
in-theory        4061
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-45 tm-125 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4061.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-125, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-4062
in-theory        4062
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (B -> A)))
theorem-size     25
proof            (modus-ponens tm-44 tm-125 ((Am (-> A B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4062.         ((A or (B -> A)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (B -> A))), M:tm-44, m:tm-125, u:((Am (-> A B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A B))))
================================================================
tm-name          tm-4063
in-theory        4063
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C)))
theorem-size     25
proof            (modus-ponens tm-42 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4063.         ((A -> (B or A)) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C))), M:tm-42, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4064
in-theory        4064
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C)))
theorem-size     25
proof            (modus-ponens tm-32 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4064.         ((A -> (A or B)) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C))), M:tm-32, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4065
in-theory        4065
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)))
theorem-size     21
proof            (modus-ponens tm-24 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4065.         (A -> (A and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))), M:tm-24, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-4066
in-theory        4066
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C)))
theorem-size     27
proof            (modus-ponens tm-23 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4066.         ((A -> (B -> (A and B))) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C))), M:tm-23, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4067
in-theory        4067
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C)))
theorem-size     25
proof            (modus-ponens tm-22 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4067.         (((A and B) -> B) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C))), M:tm-22, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4068
in-theory        4068
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C)))
theorem-size     25
proof            (modus-ponens tm-21 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4068.         (((A and B) -> A) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C))), M:tm-21, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4069
in-theory        4069
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     33
proof            (modus-ponens tm-20 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4069.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-20, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4070
in-theory        4070
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C)))
theorem-size     25
proof            (modus-ponens tm-19 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4070.         ((A -> (B -> A)) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C))), M:tm-19, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4071
in-theory        4071
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))) -> (not A))
theorem-size     23
proof            (modus-ponens tm-9 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-9 tm-5 tm-2 tm-3)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4071.         ((A -> (not (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))) -> (not A)), M:tm-9, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-4072
in-theory        4072
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and D) -> E) -> ((D or (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and D)) -> E))
theorem-size     41
proof            (modus-ponens tm-8 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4072.         (((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and D) -> E) -> ((D or (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and D)) -> E)), M:tm-8, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-4073
in-theory        4073
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and B)))
theorem-size     21
proof            (modus-ponens tm-7 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-7 tm-5 tm-2 tm-3)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4073.         (A or (B -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and B))), M:tm-7, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4074
in-theory        4074
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-6 tm-5 tm-2 tm-3)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4074.         ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) or E), M:tm-6, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4075
in-theory        4075
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and B)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4075.         (A -> ((B -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and B)) and A)), M:tm-5, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4076
in-theory        4076
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and B)))
theorem-size     21
proof            (modus-ponens tm-1 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-1 tm-5 tm-2 tm-3)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4076.         (A -> (B -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and B))), M:tm-1, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4077
in-theory        4077
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     39
proof            (modus-ponens tm-125 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4077.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-125, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4078
in-theory        4078
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) -> A) -> ((A -> (B -> C)) and D)) -> (((((A -> (B -> C)) and D) -> A) -> B) -> ((((A -> (B -> C)) and D) -> A) -> C)))
theorem-size     41
proof            (modus-ponens tm-114 tm-126 ((A (-> (-> (and (-> Am (-> C D)) Cm) Am) (and (-> Am (-> C D)) Cm))) (B (-> (and (-> Am (-> C D)) Cm) Am)) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4078.         (((((A -> (B -> C)) and D) -> A) -> ((A -> (B -> C)) and D)) -> (((((A -> (B -> C)) and D) -> A) -> B) -> ((((A -> (B -> C)) and D) -> A) -> C))), M:tm-114, m:tm-126, u:((A (-> (-> (and (-> Am (-> C D)) Cm) Am) (and (-> Am (-> C D)) Cm))) (B (-> (and (-> Am (-> C D)) Cm) Am)) (Bm (-> C D)))
================================================================
tm-name          tm-4079
in-theory        4079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F)))
theorem-size     39
proof            (modus-ponens tm-113 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4079.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F))), M:tm-113, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4080
in-theory        4080
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     43
proof            (modus-ponens tm-105 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4080.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-105, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4081
in-theory        4081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D)))
theorem-size     31
proof            (modus-ponens tm-95 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4081.         (((A -> B) -> (A -> A)) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D))), M:tm-95, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4082
in-theory        4082
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (D -> ((((A -> B) and C) -> A) -> B)))
theorem-size     25
proof            (modus-ponens tm-84 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4082.         (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (D -> ((((A -> B) and C) -> A) -> B))), M:tm-84, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-4083
in-theory        4083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-83 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4083.         ((A -> (B -> (C -> B))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-83, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4084
in-theory        4084
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> C) and D) -> B) -> ((B -> C) and D)) -> ((((B -> C) and D) -> B) -> C)))
theorem-size     29
proof            (modus-ponens tm-76 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4084.         (((not (not A)) -> A) and (((((B -> C) and D) -> B) -> ((B -> C) and D)) -> ((((B -> C) and D) -> B) -> C))), M:tm-76, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4085
in-theory        4085
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> B) and C) -> A) -> ((A -> B) and C)))) or ((((A -> B) and C) -> A) -> ((A -> B) and C))) -> ((((A -> B) and C) -> A) -> B))
theorem-size     39
proof            (modus-ponens tm-73 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-8 tm-10 tm-2 tm-3)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4085.         (((not (not ((((A -> B) and C) -> A) -> ((A -> B) and C)))) or ((((A -> B) and C) -> A) -> ((A -> B) and C))) -> ((((A -> B) and C) -> A) -> B)), M:tm-73, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-4086
in-theory        4086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D)))
theorem-size     35
proof            (modus-ponens tm-69 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4086.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D))), M:tm-69, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4087
in-theory        4087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     37
proof            (modus-ponens tm-54 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4087.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-54, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4088
in-theory        4088
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((((B -> C) and D) -> B) -> ((B -> C) and D))) or ((((B -> C) and D) -> B) -> ((B -> C) and D))) -> ((((B -> C) and D) -> B) -> C))
theorem-size     39
proof            (modus-ponens tm-47 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-3)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4088.         (((A and ((((B -> C) and D) -> B) -> ((B -> C) and D))) or ((((B -> C) and D) -> B) -> ((B -> C) and D))) -> ((((B -> C) and D) -> B) -> C)), M:tm-47, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-4089
in-theory        4089
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) -> ((A -> B) and C)) and D) or ((((A -> B) and C) -> A) -> ((A -> B) and C))) -> ((((A -> B) and C) -> A) -> B))
theorem-size     39
proof            (modus-ponens tm-46 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4089.         (((((((A -> B) and C) -> A) -> ((A -> B) and C)) and D) or ((((A -> B) and C) -> A) -> ((A -> B) and C))) -> ((((A -> B) and C) -> A) -> B)), M:tm-46, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-4090
in-theory        4090
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) and C) or ((((A -> B) and C) -> A) -> ((A -> B) and C))) -> ((((A -> B) and C) -> A) -> B))
theorem-size     29
proof            (modus-ponens tm-44 tm-126 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4090.         ((((A -> B) and C) or ((((A -> B) and C) -> A) -> ((A -> B) and C))) -> ((((A -> B) and C) -> A) -> B)), M:tm-44, m:tm-126, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-4091
in-theory        4091
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D)))
theorem-size     29
proof            (modus-ponens tm-42 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4091.         ((A -> (B or A)) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D))), M:tm-42, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4092
in-theory        4092
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D)))
theorem-size     29
proof            (modus-ponens tm-32 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4092.         ((A -> (A or B)) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D))), M:tm-32, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4093
in-theory        4093
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (((((A -> B) and C) -> A) -> ((A -> B) and C)) and ((((A -> B) and C) -> A) -> B)))
theorem-size     37
proof            (modus-ponens tm-24 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4093.         (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (((((A -> B) and C) -> A) -> ((A -> B) and C)) and ((((A -> B) and C) -> A) -> B))), M:tm-24, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-4094
in-theory        4094
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D)))
theorem-size     31
proof            (modus-ponens tm-23 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4094.         ((A -> (B -> (A and B))) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D))), M:tm-23, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4095
in-theory        4095
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D)))
theorem-size     29
proof            (modus-ponens tm-22 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4095.         (((A and B) -> B) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D))), M:tm-22, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4096
in-theory        4096
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D)))
theorem-size     29
proof            (modus-ponens tm-21 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4096.         (((A and B) -> A) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D))), M:tm-21, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4097
in-theory        4097
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     37
proof            (modus-ponens tm-20 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4097.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-20, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4098
in-theory        4098
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D)))
theorem-size     29
proof            (modus-ponens tm-19 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4098.         ((A -> (B -> A)) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D))), M:tm-19, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4099
in-theory        4099
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> ((A -> B) and C)))
theorem-size     27
proof            (modus-ponens tm-12 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4099.         (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> ((A -> B) and C))), M:tm-12, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-4100
in-theory        4100
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (not ((((A -> B) and C) -> A) -> B))) -> (not ((((A -> B) and C) -> A) -> ((A -> B) and C))))
theorem-size     39
proof            (modus-ponens tm-9 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-9 tm-2 tm-3)
proof-size       119
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4100.         ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (not ((((A -> B) and C) -> A) -> B))) -> (not ((((A -> B) and C) -> A) -> ((A -> B) and C)))), M:tm-9, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-4101
in-theory        4101
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> B) -> D) -> ((((((A -> B) and C) -> A) -> ((A -> B) and C)) or ((((A -> B) and C) -> A) -> B)) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       119
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4101.         ((((((A -> B) and C) -> A) -> B) -> D) -> ((((((A -> B) and C) -> A) -> ((A -> B) and C)) or ((((A -> B) and C) -> A) -> B)) -> D)), M:tm-8, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-4102
in-theory        4102
times-derived    2
----------------------------------------------------------------
theorem          (A or (((((B -> C) and D) -> B) -> ((B -> C) and D)) -> ((((B -> C) and D) -> B) -> C)))
theorem-size     25
proof            (modus-ponens tm-7 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-7 tm-2 tm-3)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4102.         (A or (((((B -> C) and D) -> B) -> ((B -> C) and D)) -> ((((B -> C) and D) -> B) -> C))), M:tm-7, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4103
in-theory        4103
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) or D)
theorem-size     25
proof            (modus-ponens tm-6 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-6 tm-2 tm-3)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4103.         ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) or D), M:tm-6, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4104
in-theory        4104
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) and D) -> B) -> ((B -> C) and D)) -> ((((B -> C) and D) -> B) -> C)) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4104.         (A -> ((((((B -> C) and D) -> B) -> ((B -> C) and D)) -> ((((B -> C) and D) -> B) -> C)) and A)), M:tm-5, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4105
in-theory        4105
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (((A -> B) and C) -> A)) -> (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> B))
theorem-size     37
proof            (modus-ponens tm-2 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (and (-> Am Bm) Cm) Am)) (C Bm)))
axioms-used      (tm-2 tm-3)
proof-size       119
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4105.         ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (((A -> B) and C) -> A)) -> (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> B)), M:tm-2, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (and (-> Am Bm) Cm) Am)) (C Bm))
================================================================
tm-name          tm-4106
in-theory        4106
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((((B -> C) and D) -> B) -> ((B -> C) and D)) -> ((((B -> C) and D) -> B) -> C)))
theorem-size     25
proof            (modus-ponens tm-1 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-1 tm-2 tm-3)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4106.         (A -> (((((B -> C) and D) -> B) -> ((B -> C) and D)) -> ((((B -> C) and D) -> B) -> C))), M:tm-1, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4107
in-theory        4107
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     33
proof            (modus-ponens tm-125 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4107.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-125, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4108
in-theory        4108
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-122 tm-127 ((Am (-> (and (-> A B) C) B)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4108.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-122, m:tm-127, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4109
in-theory        4109
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) and E) -> ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)))
theorem-size     35
proof            (modus-ponens tm-120 tm-127 ((Am (and (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) B) C)) (A (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4109.         (((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) and E) -> ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))), M:tm-120, m:tm-127, u:((Am (and (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) B) C)) (A (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4110
in-theory        4110
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> (((A -> B) and C) -> A)) and D) -> (((A -> B) and C) -> B))
theorem-size     33
proof            (modus-ponens tm-119 tm-127 ((Am (and (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (and (-> Bm Cm) Dm) Bm)) C)) (A (-> (and (-> Bm Cm) Dm) Bm)) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4110.         (((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> (((A -> B) and C) -> A)) and D) -> (((A -> B) and C) -> B)), M:tm-119, m:tm-127, u:((Am (and (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (and (-> Bm Cm) Dm) Bm)) C)) (A (-> (and (-> Bm Cm) Dm) Bm)) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-4111
in-theory        4111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-113 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4111.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-113, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4112
in-theory        4112
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-110 tm-127 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4112.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))), M:tm-110, m:tm-127, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4113
in-theory        4113
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> A) -> ((A -> B) and C))) -> ((((A -> B) and C) -> A) -> B))
theorem-size     39
proof            (modus-ponens tm-106 tm-127 ((Am (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> (and (-> Bm Cm) Dm) Bm) (and (-> Bm Cm) Dm)))) (A (-> (and (-> Bm Cm) Dm) Bm)) (B (and (-> Bm Cm) Dm)) (C Cm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4113.         ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> A) -> ((A -> B) and C))) -> ((((A -> B) and C) -> A) -> B)), M:tm-106, m:tm-127, u:((Am (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> (and (-> Bm Cm) Dm) Bm) (and (-> Bm Cm) Dm)))) (A (-> (and (-> Bm Cm) Dm) Bm)) (B (and (-> Bm Cm) Dm)) (C Cm))
================================================================
tm-name          tm-4114
in-theory        4114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     37
proof            (modus-ponens tm-105 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4114.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-105, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4115
in-theory        4115
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-102 tm-127 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4115.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-102, m:tm-127, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4116
in-theory        4116
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> B) -> D)) -> ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-100 tm-127 ((Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (-> (and (-> Bm Cm) Dm) Cm) C))) (A (-> (and (-> Bm Cm) Dm) Bm)) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4116.         (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> B) -> D)) -> ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))), M:tm-100, m:tm-127, u:((Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (-> (and (-> Bm Cm) Dm) Cm) C))) (A (-> (and (-> Bm Cm) Dm) Bm)) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-4117
in-theory        4117
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((A -> B) and C) -> B))
theorem-size     9
proof            (modus-ponens tm-98 tm-127 ((Bm Am) (B (and (-> Am Cm) Dm)) (A Am) (C (-> (and (-> Am Cm) Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4117.         (A -> (((A -> B) and C) -> B)), M:tm-98, m:tm-127, u:((Bm Am) (B (and (-> Am Cm) Dm)) (A Am) (C (-> (and (-> Am Cm) Dm) Cm)))
================================================================
tm-name          tm-4118
in-theory        4118
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) -> ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-96 tm-127 ((Am (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) B)) (A (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4118.         ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) -> ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))), M:tm-96, m:tm-127, u:((Am (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) B)) (A (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4119
in-theory        4119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     25
proof            (modus-ponens tm-95 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4119.         (((A -> B) -> (A -> A)) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-95, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4120
in-theory        4120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-92 tm-127 ((Am (-> A A)) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4120.         (((A -> B) or (A -> A)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-92, m:tm-127, u:((Am (-> A A)) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4121
in-theory        4121
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))
theorem-size     19
proof            (modus-ponens tm-84 tm-127 ((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4121.         (A -> (B -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))), M:tm-84, m:tm-127, u:((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4122
in-theory        4122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-83 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4122.         ((A -> (B -> (C -> B))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-83, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4123
in-theory        4123
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-80 tm-127 ((Am (-> A (-> B A))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4123.         ((A or (B -> (C -> B))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-80, m:tm-127, u:((Am (-> A (-> B A))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4124
in-theory        4124
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D))) -> D)
theorem-size     21
proof            (modus-ponens tm-77 tm-127 ((Am (not (not (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) B)))) (A (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4124.         ((not (not (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D))) -> D), M:tm-77, m:tm-127, u:((Am (not (not (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) B)))) (A (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4125
in-theory        4125
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))
theorem-size     23
proof            (modus-ponens tm-76 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4125.         (((not (not A)) -> A) and (B -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))), M:tm-76, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4126
in-theory        4126
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))
theorem-size     21
proof            (modus-ponens tm-73 tm-127 ((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4126.         (((not (not A)) or A) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-73, m:tm-127, u:((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4127
in-theory        4127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     29
proof            (modus-ponens tm-69 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4127.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-69, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4128
in-theory        4128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-66 tm-127 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-2 tm-3)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4128.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-66, m:tm-127, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4129
in-theory        4129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) and D) -> B)) -> ((A or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))
theorem-size     27
proof            (modus-ponens tm-55 tm-127 ((Am (-> A (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4129.         ((A -> (((B -> C) and D) -> B)) -> ((A or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))), M:tm-55, m:tm-127, u:((Am (-> A (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-4130
in-theory        4130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-54 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4130.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-54, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4131
in-theory        4131
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-51 tm-127 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4131.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-51, m:tm-127, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4132
in-theory        4132
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-50 tm-127 ((Am (or A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4132.         ((A or (B or A)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-50, m:tm-127, u:((Am (or A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4133
in-theory        4133
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-49 tm-127 ((Am (or A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4133.         ((A or (A or B)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-49, m:tm-127, u:((Am (or A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4134
in-theory        4134
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-48 tm-127 ((Am (-> A (and B A))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4134.         ((A or (B -> (A and B))) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-48, m:tm-127, u:((Am (-> A (and B A))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4135
in-theory        4135
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-47 tm-127 ((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4135.         (((A and B) or B) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-47, m:tm-127, u:((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4136
in-theory        4136
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-46 tm-127 ((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4136.         (((A and B) or A) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-46, m:tm-127, u:((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4137
in-theory        4137
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-45 tm-127 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4137.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-45, m:tm-127, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4138
in-theory        4138
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-44 tm-127 ((Am (-> A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4138.         ((A or (B -> A)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-44, m:tm-127, u:((Am (-> A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4139
in-theory        4139
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-42 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4139.         ((A -> (B or A)) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-42, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4140
in-theory        4140
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-32 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4140.         ((A -> (A or B)) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-32, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4141
in-theory        4141
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))
theorem-size     19
proof            (modus-ponens tm-24 tm-127 ((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4141.         (A -> (A and ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))), M:tm-24, m:tm-127, u:((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4142
in-theory        4142
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     25
proof            (modus-ponens tm-23 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4142.         ((A -> (B -> (A and B))) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-23, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4143
in-theory        4143
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-22 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4143.         (((A and B) -> B) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-22, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4144
in-theory        4144
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-21 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4144.         (((A and B) -> A) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-21, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4145
in-theory        4145
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-20 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4145.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-20, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4146
in-theory        4146
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-19 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4146.         ((A -> (B -> A)) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-19, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4147
in-theory        4147
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) -> E)) -> E)
theorem-size     21
proof            (modus-ponens tm-17 tm-127 ((Am (and A (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) C))) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4147.         ((A and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) -> E)) -> E), M:tm-17, m:tm-127, u:((Am (and A (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) C))) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4148
in-theory        4148
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) and E) -> D)
theorem-size     21
proof            (modus-ponens tm-15 tm-127 ((Am (and (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) B) C)) (A (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4148.         (((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) and E) -> D), M:tm-15, m:tm-127, u:((Am (and (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) B) C)) (A (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4149
in-theory        4149
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> B) -> D)) -> ((((A -> B) and C) -> A) -> D))
theorem-size     27
proof            (modus-ponens tm-13 tm-127 ((Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (-> (and (-> Bm Cm) Dm) Cm) C))) (A (-> (and (-> Bm Cm) Dm) Bm)) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4149.         (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> B) -> D)) -> ((((A -> B) and C) -> A) -> D)), M:tm-13, m:tm-127, u:((Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (-> (and (-> Bm Cm) Dm) Cm) C))) (A (-> (and (-> Bm Cm) Dm) Bm)) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-4150
in-theory        4150
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))) -> (not A))
theorem-size     21
proof            (modus-ponens tm-9 tm-127 ((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-9 tm-1 tm-2 tm-3)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4150.         ((A -> (not ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))) -> (not A)), M:tm-9, m:tm-127, u:((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4151
in-theory        4151
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) -> ((E or ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-127 ((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4151.         ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) -> ((E or ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))) -> D)), M:tm-8, m:tm-127, u:((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4152
in-theory        4152
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))
theorem-size     19
proof            (modus-ponens tm-7 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-7 tm-1 tm-2 tm-3)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4152.         (A or (B -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))), M:tm-7, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4153
in-theory        4153
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-6 tm-1 tm-2 tm-3)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4153.         ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) or E), M:tm-6, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4154
in-theory        4154
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4154.         (A -> ((B -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and A)), M:tm-5, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4155
in-theory        4155
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> C) and D) -> B)) -> (A -> (((B -> C) and D) -> C)))
theorem-size     19
proof            (modus-ponens tm-2 tm-127 ((A Am) (B (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4155.         ((A -> (((B -> C) and D) -> B)) -> (A -> (((B -> C) and D) -> C))), M:tm-2, m:tm-127, u:((A Am) (B (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-4156
in-theory        4156
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-125 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4156.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-125, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4157
in-theory        4157
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> ((A and B) -> A)) and C) -> ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-120 tm-128 ((Cm (-> (and Am Bm) Am)) (B (-> (and Am Bm) Am)) (C Dm) (A (-> (and Am Bm) Am))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4157.         (((((A and B) -> A) -> ((A and B) -> A)) and C) -> ((A and B) -> A)), M:tm-120, m:tm-128, u:((Cm (-> (and Am Bm) Am)) (B (-> (and Am Bm) Am)) (C Dm) (A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-4158
in-theory        4158
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> (C -> (D -> E))) and F) -> ((C -> D) -> (C -> E)))
theorem-size     21
proof            (modus-ponens tm-114 tm-128 ((A (and (-> (-> (and Am Bm) Am) (-> B (-> C D))) Dm)) (Cm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4158.         (((((A and B) -> A) -> (C -> (D -> E))) and F) -> ((C -> D) -> (C -> E))), M:tm-114, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) (-> B (-> C D))) Dm)) (Cm (-> B (-> C D))))
================================================================
tm-name          tm-4159
in-theory        4159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> E) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-113 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4159.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> E) -> G) and H) -> G)), M:tm-113, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4160
in-theory        4160
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> A) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F))
theorem-size     23
proof            (modus-ponens tm-109 tm-128 ((A (and (-> (-> (and Am Bm) Am) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Dm)) (Cm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4160.         (not ((((A and B) -> A) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F)), M:tm-109, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Dm)) (Cm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-4161
in-theory        4161
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     31
proof            (modus-ponens tm-105 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4161.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-105, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4162
in-theory        4162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C and D) -> C) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-95 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4162.         (((A -> B) -> (A -> A)) and (((((C and D) -> C) -> E) and F) -> E)), M:tm-95, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4163
in-theory        4163
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> (C -> D)) and E) -> (C -> D))
theorem-size     15
proof            (modus-ponens tm-87 tm-128 ((A (and (-> (-> (and Am Bm) Am) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4163.         (((((A and B) -> A) -> (C -> D)) and E) -> (C -> D)), M:tm-87, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-4164
in-theory        4164
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) and D) -> (E -> C))
theorem-size     13
proof            (modus-ponens tm-84 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4164.         (((((A and B) -> A) -> C) and D) -> (E -> C)), M:tm-84, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-4165
in-theory        4165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-83 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4165.         ((A -> (B -> (C -> B))) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-83, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4166
in-theory        4166
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> A) -> (not (C -> (D -> C)))) and E))
theorem-size     15
proof            (modus-ponens tm-79 tm-128 ((A (and (-> (-> (and Am Bm) Am) (not (-> B (-> C B)))) Dm)) (Cm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4166.         (not ((((A and B) -> A) -> (not (C -> (D -> C)))) and E)), M:tm-79, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) (not (-> B (-> C B)))) Dm)) (Cm (not (-> B (-> C B)))))
================================================================
tm-name          tm-4167
in-theory        4167
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B and C) -> B) -> D) and E) -> D))
theorem-size     17
proof            (modus-ponens tm-76 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-10 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4167.         (((not (not A)) -> A) and (((((B and C) -> B) -> D) and E) -> D)), M:tm-76, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4168
in-theory        4168
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A and B) -> A) -> C) and D))) or ((((A and B) -> A) -> C) and D)) -> C)
theorem-size     23
proof            (modus-ponens tm-73 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-10 tm-2 tm-3 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4168.         (((not (not ((((A and B) -> A) -> C) and D))) or ((((A and B) -> A) -> C) and D)) -> C), M:tm-73, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-4169
in-theory        4169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C and D) -> C) -> E) and F) -> E))
theorem-size     23
proof            (modus-ponens tm-69 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-9 tm-2 tm-3 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4169.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C and D) -> C) -> E) and F) -> E)), M:tm-69, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4170
in-theory        4170
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> A) -> (not C)) and C))
theorem-size     11
proof            (modus-ponens tm-60 tm-128 ((A (-> (-> (and Am Bm) Am) (not Dm))) (B Dm) (Cm (not Dm))))
axioms-used      (tm-9 tm-4 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4170.         (not ((((A and B) -> A) -> (not C)) and C)), M:tm-60, m:tm-128, u:((A (-> (-> (and Am Bm) Am) (not Dm))) (B Dm) (Cm (not Dm)))
================================================================
tm-name          tm-4171
in-theory        4171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-54 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4171.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-54, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4172
in-theory        4172
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B and C) -> B) -> D) and E)) or ((((B and C) -> B) -> D) and E)) -> D)
theorem-size     23
proof            (modus-ponens tm-47 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-4 tm-2 tm-3 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4172.         (((A and ((((B and C) -> B) -> D) and E)) or ((((B and C) -> B) -> D) and E)) -> D), M:tm-47, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-4173
in-theory        4173
times-derived    1
----------------------------------------------------------------
theorem          (((((((A and B) -> A) -> C) and D) and E) or ((((A and B) -> A) -> C) and D)) -> C)
theorem-size     23
proof            (modus-ponens tm-46 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4173.         (((((((A and B) -> A) -> C) and D) and E) or ((((A and B) -> A) -> C) and D)) -> C), M:tm-46, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-4174
in-theory        4174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C and D) -> C) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-42 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4174.         ((A -> (B or A)) and (((((C and D) -> C) -> E) and F) -> E)), M:tm-42, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4175
in-theory        4175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C and D) -> C) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-32 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4175.         ((A -> (A or B)) and (((((C and D) -> C) -> E) and F) -> E)), M:tm-32, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4176
in-theory        4176
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) and D) -> (((((A and B) -> A) -> C) and D) and C))
theorem-size     21
proof            (modus-ponens tm-24 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4176.         (((((A and B) -> A) -> C) and D) -> (((((A and B) -> A) -> C) and D) and C)), M:tm-24, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-4177
in-theory        4177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C and D) -> C) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-23 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4177.         ((A -> (B -> (A and B))) and (((((C and D) -> C) -> E) and F) -> E)), M:tm-23, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4178
in-theory        4178
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C and D) -> C) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-22 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4178.         (((A and B) -> B) and (((((C and D) -> C) -> E) and F) -> E)), M:tm-22, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4179
in-theory        4179
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C and D) -> C) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-21 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4179.         (((A and B) -> A) and (((((C and D) -> C) -> E) and F) -> E)), M:tm-21, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4180
in-theory        4180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-20 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4180.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-20, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4181
in-theory        4181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C and D) -> C) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-19 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4181.         ((A -> (B -> A)) and (((((C and D) -> C) -> E) and F) -> E)), M:tm-19, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4182
in-theory        4182
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) and (C -> D)) -> D)
theorem-size     13
proof            (modus-ponens tm-17 tm-128 ((A (-> (-> (and Am Bm) Am) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-4 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4182.         (((((A and B) -> A) -> C) and (C -> D)) -> D), M:tm-17, m:tm-128, u:((A (-> (-> (and Am Bm) Am) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-4183
in-theory        4183
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) and D) -> ((((A and B) -> A) -> C) and D))
theorem-size     19
proof            (modus-ponens tm-12 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4183.         (((((A and B) -> A) -> C) and D) -> ((((A and B) -> A) -> C) and D)), M:tm-12, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-4184
in-theory        4184
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> (not C)) -> (not ((((A and B) -> A) -> C) and D)))
theorem-size     23
proof            (modus-ponens tm-9 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-9 tm-2 tm-3 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4184.         ((((((A and B) -> A) -> C) and D) -> (not C)) -> (not ((((A and B) -> A) -> C) and D))), M:tm-9, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-4185
in-theory        4185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((((C and D) -> C) -> A) and E) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4185.         ((A -> B) -> ((((((C and D) -> C) -> A) and E) or A) -> B)), M:tm-8, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-4186
in-theory        4186
times-derived    1
----------------------------------------------------------------
theorem          (A or (((((B and C) -> B) -> D) and E) -> D))
theorem-size     13
proof            (modus-ponens tm-7 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-7 tm-2 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4186.         (A or (((((B and C) -> B) -> D) and E) -> D)), M:tm-7, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4187
in-theory        4187
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-6 tm-2 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4187.         ((((((A and B) -> A) -> C) and D) -> C) or E), M:tm-6, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4188
in-theory        4188
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B and C) -> B) -> D) and E) -> D) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4188.         (A -> ((((((B and C) -> B) -> D) and E) -> D) and A)), M:tm-5, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4189
in-theory        4189
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> (C -> D)) and E) -> C) -> (((((A and B) -> A) -> (C -> D)) and E) -> D))
theorem-size     27
proof            (modus-ponens tm-2 tm-128 ((A (and (-> (-> (and Am Bm) Am) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4189.         ((((((A and B) -> A) -> (C -> D)) and E) -> C) -> (((((A and B) -> A) -> (C -> D)) and E) -> D)), M:tm-2, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-4190
in-theory        4190
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B and C) -> B) -> D) and E) -> D))
theorem-size     13
proof            (modus-ponens tm-1 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-1 tm-2 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4190.         (A -> (((((B and C) -> B) -> D) and E) -> D)), M:tm-1, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4191
in-theory        4191
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) and C) -> A)
theorem-size     7
proof            (modus-ponens tm-129 tm-16 ((Am (and (and Bm Cm) B)) (A (and Bm Cm)) (C Bm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4191.         (((A and B) and C) -> A), M:tm-129, m:tm-16, u:((Am (and (and Bm Cm) B)) (A (and Bm Cm)) (C Bm))
================================================================
tm-name          tm-4192
in-theory        4192
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) and C) -> B)
theorem-size     7
proof            (modus-ponens tm-129 tm-18 ((Am (and (and Bm Cm) B)) (A (and Bm Cm)) (C Cm)))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-4192.         (((A and B) and C) -> B), M:tm-129, m:tm-18, u:((Am (and (and Bm Cm) B)) (A (and Bm Cm)) (C Cm))
================================================================
tm-name          tm-4193
in-theory        4193
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> (C -> (A and C)))
theorem-size     9
proof            (modus-ponens tm-129 tm-25 ((Am (and Bm B)) (A Bm) (C (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4193.         ((A and B) -> (C -> (A and C))), M:tm-129, m:tm-25, u:((Am (and Bm B)) (A Bm) (C (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-4194
in-theory        4194
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> (A or C))
theorem-size     7
proof            (modus-ponens tm-129 tm-33 ((Am (and Bm B)) (A Bm) (C (or Bm Cm))))
axioms-used      (tm-2 tm-1 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4194.         ((A and B) -> (A or C)), M:tm-129, m:tm-33, u:((Am (and Bm B)) (A Bm) (C (or Bm Cm)))
================================================================
tm-name          tm-4195
in-theory        4195
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> (C or A))
theorem-size     7
proof            (modus-ponens tm-129 tm-43 ((Am (and Bm B)) (A Bm) (C (or Cm Bm))))
axioms-used      (tm-2 tm-1 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4195.         ((A and B) -> (C or A)), M:tm-129, m:tm-43, u:((Am (and Bm B)) (A Bm) (C (or Cm Bm)))
================================================================
tm-name          tm-4196
in-theory        4196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and C) -> ((B -> D) -> ((A or B) -> D)))
theorem-size     15
proof            (modus-ponens tm-129 tm-56 ((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4196.         (((A -> B) and C) -> ((B -> D) -> ((A or B) -> D))), M:tm-129, m:tm-56, u:((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-4197
in-theory        4197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and C) -> ((A -> (not B)) -> (not A)))
theorem-size     13
proof            (modus-ponens tm-129 tm-71 ((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4197.         (((A -> B) and C) -> ((A -> (not B)) -> (not A))), M:tm-129, m:tm-71, u:((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-4198
in-theory        4198
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) and B) -> A)
theorem-size     7
proof            (modus-ponens tm-129 tm-78 ((Am (and (not (not Bm)) B)) (A (not (not Bm))) (C Bm)))
axioms-used      (tm-2 tm-1 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4198.         (((not (not A)) and B) -> A), M:tm-129, m:tm-78, u:((Am (and (not (not Bm)) B)) (A (not (not Bm))) (C Bm))
================================================================
tm-name          tm-4199
in-theory        4199
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> (C -> (D -> C)))
theorem-size     9
proof            (modus-ponens tm-129 tm-85 ((Am (and Bm B)) (A Bm) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4199.         ((A and B) -> (C -> (D -> C))), M:tm-129, m:tm-85, u:((Am (and Bm B)) (A Bm) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-4200
in-theory        4200
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and C) -> (A -> A))
theorem-size     9
proof            (modus-ponens tm-129 tm-97 ((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> Bm Bm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4200.         (((A -> B) and C) -> (A -> A)), M:tm-129, m:tm-97, u:((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> Bm Bm)))
================================================================
tm-name          tm-4201
in-theory        4201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) and D) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     21
proof            (modus-ponens tm-129 tm-107 ((Am (and (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) B)) (A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4201.         ((((A -> (B -> C)) -> (A -> B)) and D) -> ((A -> (B -> C)) -> (A -> C))), M:tm-129, m:tm-107, u:((Am (and (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) B)) (A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-4202
in-theory        4202
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     17
proof            (modus-ponens tm-129 tm-115 ((Am (and Bm B)) (A Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4202.         ((A and B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-129, m:tm-115, u:((Am (and Bm B)) (A Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-4203
in-theory        4203
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) and D) -> (((A -> B) and C) -> B))
theorem-size     17
proof            (modus-ponens tm-129 tm-127 ((Am (and (-> (and (-> Bm Cm) Dm) Bm) B)) (A (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4203.         (((((A -> B) and C) -> A) and D) -> (((A -> B) and C) -> B)), M:tm-129, m:tm-127, u:((Am (and (-> (and (-> Bm Cm) Dm) Bm) B)) (A (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-4204
in-theory        4204
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     29
proof            (modus-ponens tm-125 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4204.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-125, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4205
in-theory        4205
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A -> (C -> D))) -> (((A and B) -> C) -> ((A and B) -> D)))
theorem-size     21
proof            (modus-ponens tm-114 tm-129 ((A (-> (and Am Bm) (-> Am (-> C D)))) (B (and Am Bm)) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4205.         (((A and B) -> (A -> (C -> D))) -> (((A and B) -> C) -> ((A and B) -> D))), M:tm-114, m:tm-129, u:((A (-> (and Am Bm) (-> Am (-> C D)))) (B (and Am Bm)) (Cm (-> C D)))
================================================================
tm-name          tm-4206
in-theory        4206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (E -> G)) -> ((E and F) -> G)))
theorem-size     29
proof            (modus-ponens tm-113 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4206.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (E -> G)) -> ((E and F) -> G))), M:tm-113, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4207
in-theory        4207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     33
proof            (modus-ponens tm-105 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4207.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-105, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4208
in-theory        4208
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> (A -> A)) -> ((A and B) -> A))
theorem-size     13
proof            (modus-ponens tm-100 tm-129 ((Cm Am) (C Am) (A (and Am Bm)) (B Am)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4208.         (((A and B) -> (A -> A)) -> ((A and B) -> A)), M:tm-100, m:tm-129, u:((Cm Am) (C Am) (A (and Am Bm)) (B Am))
================================================================
tm-name          tm-4209
in-theory        4209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> (C -> E)) -> ((C and D) -> E)))
theorem-size     21
proof            (modus-ponens tm-95 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4209.         (((A -> B) -> (A -> A)) and (((C and D) -> (C -> E)) -> ((C and D) -> E))), M:tm-95, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4210
in-theory        4210
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A -> C)) -> (D -> ((A and B) -> C)))
theorem-size     15
proof            (modus-ponens tm-84 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4210.         (((A and B) -> (A -> C)) -> (D -> ((A and B) -> C))), M:tm-84, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-4211
in-theory        4211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-83 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4211.         ((A -> (B -> (C -> B))) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-83, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4212
in-theory        4212
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> (B -> (B and C)))) -> ((B and C) -> (B and C)))
theorem-size     19
proof            (modus-ponens tm-80 tm-129 ((Cm (and Am Bm)) (B Am) (A (and Am Bm)) (C (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4212.         ((A or ((B and C) -> (B -> (B and C)))) -> ((B and C) -> (B and C))), M:tm-80, m:tm-129, u:((Cm (and Am Bm)) (B Am) (A (and Am Bm)) (C (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-4213
in-theory        4213
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> (B -> D)) -> ((B and C) -> D)))
theorem-size     19
proof            (modus-ponens tm-76 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4213.         (((not (not A)) -> A) and (((B and C) -> (B -> D)) -> ((B and C) -> D))), M:tm-76, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4214
in-theory        4214
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) -> (A -> C)))) or ((A and B) -> (A -> C))) -> ((A and B) -> C))
theorem-size     23
proof            (modus-ponens tm-73 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4214.         (((not (not ((A and B) -> (A -> C)))) or ((A and B) -> (A -> C))) -> ((A and B) -> C)), M:tm-73, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-4215
in-theory        4215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> (C -> E)) -> ((C and D) -> E)))
theorem-size     25
proof            (modus-ponens tm-69 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4215.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> (C -> E)) -> ((C and D) -> E))), M:tm-69, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4216
in-theory        4216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     27
proof            (modus-ponens tm-54 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4216.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-54, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4217
in-theory        4217
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) -> (B -> D))) or ((B and C) -> (B -> D))) -> ((B and C) -> D))
theorem-size     23
proof            (modus-ponens tm-47 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4217.         (((A and ((B and C) -> (B -> D))) or ((B and C) -> (B -> D))) -> ((B and C) -> D)), M:tm-47, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-4218
in-theory        4218
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> (A -> C)) and D) or ((A and B) -> (A -> C))) -> ((A and B) -> C))
theorem-size     23
proof            (modus-ponens tm-46 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4218.         (((((A and B) -> (A -> C)) and D) or ((A and B) -> (A -> C))) -> ((A and B) -> C)), M:tm-46, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-4219
in-theory        4219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A and C) -> (A -> B))) -> ((A and C) -> B))
theorem-size     17
proof            (modus-ponens tm-44 tm-129 ((A (and Am Bm)) (B (-> Am Cm)) (C (-> (and Am Bm) Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4219.         (((A -> B) or ((A and C) -> (A -> B))) -> ((A and C) -> B)), M:tm-44, m:tm-129, u:((A (and Am Bm)) (B (-> Am Cm)) (C (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-4220
in-theory        4220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> (C -> E)) -> ((C and D) -> E)))
theorem-size     19
proof            (modus-ponens tm-42 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4220.         ((A -> (B or A)) and (((C and D) -> (C -> E)) -> ((C and D) -> E))), M:tm-42, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4221
in-theory        4221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> (C -> E)) -> ((C and D) -> E)))
theorem-size     19
proof            (modus-ponens tm-32 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4221.         ((A -> (A or B)) and (((C and D) -> (C -> E)) -> ((C and D) -> E))), M:tm-32, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4222
in-theory        4222
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A -> C)) -> (((A and B) -> (A -> C)) and ((A and B) -> C)))
theorem-size     21
proof            (modus-ponens tm-24 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4222.         (((A and B) -> (A -> C)) -> (((A and B) -> (A -> C)) and ((A and B) -> C))), M:tm-24, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-4223
in-theory        4223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> (C -> E)) -> ((C and D) -> E)))
theorem-size     21
proof            (modus-ponens tm-23 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4223.         ((A -> (B -> (A and B))) and (((C and D) -> (C -> E)) -> ((C and D) -> E))), M:tm-23, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4224
in-theory        4224
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> (C -> E)) -> ((C and D) -> E)))
theorem-size     19
proof            (modus-ponens tm-22 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4224.         (((A and B) -> B) and (((C and D) -> (C -> E)) -> ((C and D) -> E))), M:tm-22, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4225
in-theory        4225
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> (C -> E)) -> ((C and D) -> E)))
theorem-size     19
proof            (modus-ponens tm-21 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4225.         (((A and B) -> A) and (((C and D) -> (C -> E)) -> ((C and D) -> E))), M:tm-21, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4226
in-theory        4226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     27
proof            (modus-ponens tm-20 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4226.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-20, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4227
in-theory        4227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> (C -> E)) -> ((C and D) -> E)))
theorem-size     19
proof            (modus-ponens tm-19 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4227.         ((A -> (B -> A)) and (((C and D) -> (C -> E)) -> ((C and D) -> E))), M:tm-19, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4228
in-theory        4228
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A -> C)) -> ((A and B) -> (A -> C)))
theorem-size     15
proof            (modus-ponens tm-12 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4228.         (((A and B) -> (A -> C)) -> ((A and B) -> (A -> C))), M:tm-12, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-4229
in-theory        4229
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> (not ((A and B) -> C))) -> (not ((A and B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-9 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-9 tm-2 tm-1 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4229.         ((((A and B) -> (A -> C)) -> (not ((A and B) -> C))) -> (not ((A and B) -> (A -> C)))), M:tm-9, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-4230
in-theory        4230
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> C) -> D) -> ((((A and B) -> (A -> C)) or ((A and B) -> C)) -> D))
theorem-size     23
proof            (modus-ponens tm-8 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4230.         ((((A and B) -> C) -> D) -> ((((A and B) -> (A -> C)) or ((A and B) -> C)) -> D)), M:tm-8, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-4231
in-theory        4231
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> (B -> D)) -> ((B and C) -> D)))
theorem-size     15
proof            (modus-ponens tm-7 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-7 tm-2 tm-1 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4231.         (A or (((B and C) -> (B -> D)) -> ((B and C) -> D))), M:tm-7, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4232
in-theory        4232
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-6 tm-2 tm-1 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4232.         ((((A and B) -> (A -> C)) -> ((A and B) -> C)) or D), M:tm-6, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4233
in-theory        4233
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> (B -> D)) -> ((B and C) -> D)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4233.         (A -> ((((B and C) -> (B -> D)) -> ((B and C) -> D)) and A)), M:tm-5, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4234
in-theory        4234
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> (A and B)) -> (((A and B) -> (A -> C)) -> C))
theorem-size     21
proof            (modus-ponens tm-2 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (and Am Bm)) (C Cm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4234.         ((((A and B) -> (A -> C)) -> (A and B)) -> (((A and B) -> (A -> C)) -> C)), M:tm-2, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (and Am Bm)) (C Cm))
================================================================
tm-name          tm-4235
in-theory        4235
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> (B -> D)) -> ((B and C) -> D)))
theorem-size     15
proof            (modus-ponens tm-1 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-1 tm-2 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4235.         (A -> (((B and C) -> (B -> D)) -> ((B and C) -> D))), M:tm-1, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4236
in-theory        4236
times-derived    1
----------------------------------------------------------------
theorem          (not ((not ((A and B) -> A)) and C))
theorem-size     9
proof            (modus-ponens tm-130 tm-3 ((A (and (not (-> (and B C) B)) Bm)) (Am (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4236.         (not ((not ((A and B) -> A)) and C)), M:tm-130, m:tm-3, u:((A (and (not (-> (and B C) B)) Bm)) (Am (not (-> (and B C) B))))
================================================================
tm-name          tm-4237
in-theory        4237
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (not ((B and C) -> B))))
theorem-size     9
proof            (modus-ponens tm-130 tm-4 ((A (and Am (not (-> (and B C) B)))) (Bm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-4237.         (not (A and (not ((B and C) -> B)))), M:tm-130, m:tm-4, u:((A (and Am (not (-> (and B C) B)))) (Bm (not (-> (and B C) B))))
================================================================
tm-name          tm-4238
in-theory        4238
times-derived    1
----------------------------------------------------------------
theorem          (not (not (not (not ((A and B) -> A)))))
theorem-size     9
proof            (modus-ponens tm-130 tm-10 ((A (not (not (not (-> (and B C) B))))) (Am (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-4238.         (not (not (not (not ((A and B) -> A))))), M:tm-130, m:tm-10, u:((A (not (not (not (-> (and B C) B))))) (Am (not (-> (and B C) B))))
================================================================
tm-name          tm-4239
in-theory        4239
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not (C -> ((A and B) -> A)))))
theorem-size     15
proof            (modus-ponens tm-130 tm-57 ((A (-> (-> (and B C) B) (not (-> Bm (-> (and B C) B))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4239.         (not (((A and B) -> A) -> (not (C -> ((A and B) -> A))))), M:tm-130, m:tm-57, u:((A (-> (-> (and B C) B) (not (-> Bm (-> (and B C) B))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-4240
in-theory        4240
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> B) and C) -> (A -> B)) -> (not ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)))))
theorem-size     27
proof            (modus-ponens tm-130 tm-58 ((A (-> (-> (and (-> Bm Cm) C) (-> Bm Cm)) (not (-> (-> (and (-> Bm Cm) C) Bm) (-> (and (-> Bm Cm) C) Cm))))) (Am (and (-> Bm Cm) C)) (B (-> Bm Cm))))
axioms-used      (tm-9 tm-1 tm-3 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4240.         (not ((((A -> B) and C) -> (A -> B)) -> (not ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))))), M:tm-130, m:tm-58, u:((A (-> (-> (and (-> Bm Cm) C) (-> Bm Cm)) (not (-> (-> (and (-> Bm Cm) C) Bm) (-> (and (-> Bm Cm) C) Cm))))) (Am (and (-> Bm Cm) C)) (B (-> Bm Cm)))
================================================================
tm-name          tm-4241
in-theory        4241
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not (C -> (((A and B) -> A) and C)))))
theorem-size     17
proof            (modus-ponens tm-130 tm-61 ((A (-> (-> (and B C) B) (not (-> Bm (and (-> (and B C) B) Bm))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4241.         (not (((A and B) -> A) -> (not (C -> (((A and B) -> A) and C))))), M:tm-130, m:tm-61, u:((A (-> (-> (and B C) B) (not (-> Bm (and (-> (and B C) B) Bm))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-4242
in-theory        4242
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not (((A and B) -> A) or C))))
theorem-size     15
proof            (modus-ponens tm-130 tm-62 ((A (-> (-> (and B C) B) (not (or (-> (and B C) B) Bm)))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4242.         (not (((A and B) -> A) -> (not (((A and B) -> A) or C)))), M:tm-130, m:tm-62, u:((A (-> (-> (and B C) B) (not (or (-> (and B C) B) Bm)))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-4243
in-theory        4243
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not (C or ((A and B) -> A)))))
theorem-size     15
proof            (modus-ponens tm-130 tm-63 ((A (-> (-> (and B C) B) (not (or Bm (-> (and B C) B))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4243.         (not (((A and B) -> A) -> (not (C or ((A and B) -> A))))), M:tm-130, m:tm-63, u:((A (-> (-> (and B C) B) (not (or Bm (-> (and B C) B))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-4244
in-theory        4244
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not ((A -> C) -> (((A and B) or A) -> C)))))
theorem-size     19
proof            (modus-ponens tm-130 tm-64 ((A (-> (-> (and Bm C) Bm) (not (-> (-> Bm Cm) (-> (or (and Bm C) Bm) Cm))))) (Am (and Bm C)) (B Bm)))
axioms-used      (tm-9 tm-1 tm-3 tm-8)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4244.         (not (((A and B) -> A) -> (not ((A -> C) -> (((A and B) or A) -> C))))), M:tm-130, m:tm-64, u:((A (-> (-> (and Bm C) Bm) (not (-> (-> Bm Cm) (-> (or (and Bm C) Bm) Cm))))) (Am (and Bm C)) (B Bm))
================================================================
tm-name          tm-4245
in-theory        4245
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not (((A and B) -> (not A)) -> (not (A and B))))))
theorem-size     19
proof            (modus-ponens tm-130 tm-65 ((A (-> (-> (and Bm C) Bm) (not (-> (-> (and Bm C) (not Bm)) (not (and Bm C)))))) (Am (and Bm C)) (B Bm)))
axioms-used      (tm-9 tm-1 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4245.         (not (((A and B) -> A) -> (not (((A and B) -> (not A)) -> (not (A and B)))))), M:tm-130, m:tm-65, u:((A (-> (-> (and Bm C) Bm) (not (-> (-> (and Bm C) (not Bm)) (not (and Bm C)))))) (Am (and Bm C)) (B Bm))
================================================================
tm-name          tm-4246
in-theory        4246
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not (C -> (D -> C)))))
theorem-size     13
proof            (modus-ponens tm-130 tm-79 ((A (-> (-> (and B C) B) (not (-> Bm (-> Cm Bm))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4246.         (not (((A and B) -> A) -> (not (C -> (D -> C))))), M:tm-130, m:tm-79, u:((A (-> (-> (and B C) B) (not (-> Bm (-> Cm Bm))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-4247
in-theory        4247
times-derived    1
----------------------------------------------------------------
theorem          (not (not ((A and B) -> A)))
theorem-size     7
proof            (modus-ponens tm-130 tm-86 ((A (not (-> (and B C) B))) (Am (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4247.         (not (not ((A and B) -> A))), M:tm-130, m:tm-86, u:((A (not (-> (and B C) B))) (Am (not (-> (and B C) B))))
================================================================
tm-name          tm-4248
in-theory        4248
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not ((A and B) -> (A and B)))))
theorem-size     15
proof            (modus-ponens tm-130 tm-91 ((A (-> (-> (and Bm C) Bm) (not (-> (and Bm C) (and Bm C))))) (Am (and Bm C)) (B Bm)))
axioms-used      (tm-9 tm-1 tm-3 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4248.         (not (((A and B) -> A) -> (not ((A and B) -> (A and B))))), M:tm-130, m:tm-91, u:((A (-> (-> (and Bm C) Bm) (not (-> (and Bm C) (and Bm C))))) (Am (and Bm C)) (B Bm))
================================================================
tm-name          tm-4249
in-theory        4249
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     21
proof            (modus-ponens tm-130 tm-109 ((A (-> (-> (and B C) B) (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4249.         (not (((A and B) -> A) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-130, m:tm-109, u:((A (-> (-> (and B C) B) (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-4250
in-theory        4250
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (not ((B and C) -> B))) and A))
theorem-size     11
proof            (modus-ponens tm-130 tm-116 ((A (and (-> Am (not (-> (and B C) B))) Am)) (Bm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-4250.         (not ((A -> (not ((B and C) -> B))) and A)), M:tm-130, m:tm-116, u:((A (and (-> Am (not (-> (and B C) B))) Am)) (Bm (not (-> (and B C) B))))
================================================================
tm-name          tm-4251
in-theory        4251
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> A)) -> (not ((C and D) -> C))) and E))
theorem-size     15
proof            (modus-ponens tm-130 tm-117 ((A (and (-> (-> Am (-> Bm Am)) (not (-> (and B C) B))) Dm)) (Cm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-4251.         (not (((A -> (B -> A)) -> (not ((C and D) -> C))) and E)), M:tm-130, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) (not (-> (and B C) B))) Dm)) (Cm (not (-> (and B C) B))))
================================================================
tm-name          tm-4252
in-theory        4252
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D and E) -> D))) and F))
theorem-size     23
proof            (modus-ponens tm-130 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not (-> (and B C) B))) Em)) (Dm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4252.         (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D and E) -> D))) and F)), M:tm-130, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not (-> (and B C) B))) Em)) (Dm (not (-> (and B C) B))))
================================================================
tm-name          tm-4253
in-theory        4253
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> A) -> (not ((C and D) -> C))) and E))
theorem-size     15
proof            (modus-ponens tm-130 tm-128 ((A (and (-> (-> (and Am Bm) Am) (not (-> (and B C) B))) Dm)) (Cm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4253.         (not ((((A and B) -> A) -> (not ((C and D) -> C))) and E)), M:tm-130, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) (not (-> (and B C) B))) Dm)) (Cm (not (-> (and B C) B))))
================================================================
tm-name          tm-4254
in-theory        4254
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not ((C and D) -> C))))
theorem-size     13
proof            (modus-ponens tm-130 tm-130 ((A (-> (-> (and B C) B) (not (-> (and Bm Cm) Bm)))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4254.         (not (((A and B) -> A) -> (not ((C and D) -> C)))), M:tm-130, m:tm-130, u:((A (-> (-> (and B C) B) (not (-> (and Bm Cm) Bm)))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-4255
in-theory        4255
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4255.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-125, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4256
in-theory        4256
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not ((B and C) -> B))) and D) -> A) or (((A -> (not ((B and C) -> B))) and D) -> (not ((B and C) -> B)))) -> (not ((A -> (not ((B and C) -> B))) and D)))
theorem-size     42
proof            (modus-ponens tm-122 tm-130 ((Am (and (-> A (not (-> (and Bm Cm) Bm))) C)) (B (not (-> (and Bm Cm) Bm))) (D (not (and (-> A (not (-> (and Bm Cm) Bm))) C)))))
axioms-used      (tm-8 tm-2 tm-3 tm-9 tm-1)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4256.         (((((A -> (not ((B and C) -> B))) and D) -> A) or (((A -> (not ((B and C) -> B))) and D) -> (not ((B and C) -> B)))) -> (not ((A -> (not ((B and C) -> B))) and D))), M:tm-122, m:tm-130, u:((Am (and (-> A (not (-> (and Bm Cm) Bm))) C)) (B (not (-> (and Bm Cm) Bm))) (D (not (and (-> A (not (-> (and Bm Cm) Bm))) C))))
================================================================
tm-name          tm-4257
in-theory        4257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F and G) -> F))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4257.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F and G) -> F))) -> (not E))), M:tm-113, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4258
in-theory        4258
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D and E) -> D))))
theorem-size     21
proof            (modus-ponens tm-109 tm-130 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (and Bm Cm) Bm)))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4258.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D and E) -> D)))), M:tm-109, m:tm-130, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (and Bm Cm) Bm)))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-4259
in-theory        4259
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4259.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-105, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4260
in-theory        4260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not ((D and E) -> D))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4260.         (((A -> B) -> (A -> A)) and ((C -> (not ((D and E) -> D))) -> (not C))), M:tm-95, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4261
in-theory        4261
times-derived    1
----------------------------------------------------------------
theorem          ((((not ((A and B) -> A)) -> C) or ((not ((A and B) -> A)) -> (not ((A and B) -> A)))) -> (not (not ((A and B) -> A))))
theorem-size     30
proof            (modus-ponens tm-92 tm-130 ((Am (not (-> (and Bm Cm) Bm))) (A (not (-> (and Bm Cm) Bm))) (B (not (not (-> (and Bm Cm) Bm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-9 tm-3)
proof-size       122
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4261.         ((((not ((A and B) -> A)) -> C) or ((not ((A and B) -> A)) -> (not ((A and B) -> A)))) -> (not (not ((A and B) -> A)))), M:tm-92, m:tm-130, u:((Am (not (-> (and Bm Cm) Bm))) (A (not (-> (and Bm Cm) Bm))) (B (not (not (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-4262
in-theory        4262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B and C) -> B))) -> (D -> (not A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4262.         ((A -> (not ((B and C) -> B))) -> (D -> (not A))), M:tm-84, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-4263
in-theory        4263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4263.         ((A -> (B -> (C -> B))) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-83, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4264
in-theory        4264
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not ((C and D) -> C))))
theorem-size     13
proof            (modus-ponens tm-79 tm-130 ((A (-> (-> B (-> C B)) (not (-> (and Bm Cm) Bm)))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4264.         (not ((A -> (B -> A)) -> (not ((C and D) -> C)))), M:tm-79, m:tm-130, u:((A (-> (-> B (-> C B)) (not (-> (and Bm Cm) Bm)))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-4265
in-theory        4265
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not ((C and D) -> C))) -> (not B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-1 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4265.         (((not (not A)) -> A) and ((B -> (not ((C and D) -> C))) -> (not B))), M:tm-76, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4266
in-theory        4266
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not ((B and C) -> B))))) or (A -> (not ((B and C) -> B)))) -> (not A))
theorem-size     22
proof            (modus-ponens tm-73 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-1 tm-3)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4266.         (((not (not (A -> (not ((B and C) -> B))))) or (A -> (not ((B and C) -> B)))) -> (not A)), M:tm-73, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-4267
in-theory        4267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not ((D and E) -> D))) -> (not C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4267.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not ((D and E) -> D))) -> (not C))), M:tm-69, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4268
in-theory        4268
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) or ((((A and B) -> A) -> (not C)) -> (not ((A and B) -> A)))) -> (not (((A and B) -> A) -> (not C))))
theorem-size     33
proof            (modus-ponens tm-66 tm-130 ((Am (-> (-> (and Bm Cm) Bm) (not B))) (A (-> (and Bm Cm) Bm)) (C (not (-> (-> (and Bm Cm) Bm) (not B))))))
axioms-used      (tm-8 tm-9 tm-1 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4268.         (((((A and B) -> A) -> C) or ((((A and B) -> A) -> (not C)) -> (not ((A and B) -> A)))) -> (not (((A and B) -> A) -> (not C)))), M:tm-66, m:tm-130, u:((Am (-> (-> (and Bm Cm) Bm) (not B))) (A (-> (and Bm Cm) Bm)) (C (not (-> (-> (and Bm Cm) Bm) (not B)))))
================================================================
tm-name          tm-4269
in-theory        4269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-1 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4269.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-54, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4270
in-theory        4270
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not ((C and D) -> C)))) or (B -> (not ((C and D) -> C)))) -> (not B))
theorem-size     22
proof            (modus-ponens tm-47 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-1 tm-3)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4270.         (((A and (B -> (not ((C and D) -> C)))) or (B -> (not ((C and D) -> C)))) -> (not B)), M:tm-47, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-4271
in-theory        4271
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not ((B and C) -> B))) and D) or (A -> (not ((B and C) -> B)))) -> (not A))
theorem-size     22
proof            (modus-ponens tm-46 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-1)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4271.         ((((A -> (not ((B and C) -> B))) and D) or (A -> (not ((B and C) -> B)))) -> (not A)), M:tm-46, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-4272
in-theory        4272
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A and B) -> A)) or (C -> (not ((A and B) -> A)))) -> (not C))
theorem-size     18
proof            (modus-ponens tm-44 tm-130 ((A Am) (B (not (-> (and Bm Cm) Bm))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-3)
proof-size       88
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4272.         (((not ((A and B) -> A)) or (C -> (not ((A and B) -> A)))) -> (not C)), M:tm-44, m:tm-130, u:((A Am) (B (not (-> (and Bm Cm) Bm))) (C (not Am)))
================================================================
tm-name          tm-4273
in-theory        4273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not ((D and E) -> D))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4273.         ((A -> (B or A)) and ((C -> (not ((D and E) -> D))) -> (not C))), M:tm-42, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4274
in-theory        4274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not ((D and E) -> D))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4274.         ((A -> (A or B)) and ((C -> (not ((D and E) -> D))) -> (not C))), M:tm-32, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4275
in-theory        4275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B and C) -> B))) -> ((A -> (not ((B and C) -> B))) and (not A)))
theorem-size     20
proof            (modus-ponens tm-24 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       88
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4275.         ((A -> (not ((B and C) -> B))) -> ((A -> (not ((B and C) -> B))) and (not A))), M:tm-24, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-4276
in-theory        4276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not ((D and E) -> D))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4276.         ((A -> (B -> (A and B))) and ((C -> (not ((D and E) -> D))) -> (not C))), M:tm-23, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4277
in-theory        4277
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not ((D and E) -> D))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4277.         (((A and B) -> B) and ((C -> (not ((D and E) -> D))) -> (not C))), M:tm-22, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4278
in-theory        4278
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not ((D and E) -> D))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4278.         (((A and B) -> A) and ((C -> (not ((D and E) -> D))) -> (not C))), M:tm-21, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4279
in-theory        4279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4279.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-20, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4280
in-theory        4280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not ((D and E) -> D))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4280.         ((A -> (B -> A)) and ((C -> (not ((D and E) -> D))) -> (not C))), M:tm-19, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4281
in-theory        4281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B and C) -> B))) -> (A -> (not ((B and C) -> B))))
theorem-size     17
proof            (modus-ponens tm-12 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4281.         ((A -> (not ((B and C) -> B))) -> (A -> (not ((B and C) -> B)))), M:tm-12, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-4282
in-theory        4282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not (not A))) -> (not (A -> (not ((B and C) -> B)))))
theorem-size     22
proof            (modus-ponens tm-9 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-9 tm-1 tm-3)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4282.         (((A -> (not ((B and C) -> B))) -> (not (not A))) -> (not (A -> (not ((B and C) -> B))))), M:tm-9, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-4283
in-theory        4283
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not ((C and D) -> C))) or (not A)) -> B))
theorem-size     18
proof            (modus-ponens tm-8 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-1 tm-3)
proof-size       70
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4283.         (((not A) -> B) -> (((A -> (not ((C and D) -> C))) or (not A)) -> B)), M:tm-8, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-4284
in-theory        4284
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not ((C and D) -> C))) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-1 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4284.         (A or ((B -> (not ((C and D) -> C))) -> (not B))), M:tm-7, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4285
in-theory        4285
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-1 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4285.         (((A -> (not ((B and C) -> B))) -> (not A)) or D), M:tm-6, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4286
in-theory        4286
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not ((C and D) -> C))) -> (not B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4286.         (A -> (((B -> (not ((C and D) -> C))) -> (not B)) and A)), M:tm-5, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4287
in-theory        4287
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not ((C and D) -> C))) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4287.         (A -> ((B -> (not ((C and D) -> C))) -> (not B))), M:tm-1, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4288
in-theory        4288
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> ((B and C) -> B)))
theorem-size     15
proof            (modus-ponens tm-131 tm-1 ((Am (-> (and A B) A)) (C (-> Bm (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4288.         ((A or ((B and C) -> B)) -> (D -> ((B and C) -> B))), M:tm-131, m:tm-1, u:((Am (-> (and A B) A)) (C (-> Bm (-> (and A B) A))))
================================================================
tm-name          tm-4289
in-theory        4289
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) and D) -> (B -> C))) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))
theorem-size     27
proof            (modus-ponens tm-131 tm-2 ((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> (-> (and (-> Bm Cm) B) Bm) (-> (and (-> Bm Cm) B) Cm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4289.         ((A or (((B -> C) and D) -> (B -> C))) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-131, m:tm-2, u:((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> (-> (and (-> Bm Cm) B) Bm) (-> (and (-> Bm Cm) B) Cm))))
================================================================
tm-name          tm-4290
in-theory        4290
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> (((B and C) -> B) and D)))
theorem-size     17
proof            (modus-ponens tm-131 tm-5 ((Am (-> (and A B) A)) (C (-> Bm (and (-> (and A B) A) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4290.         ((A or ((B and C) -> B)) -> (D -> (((B and C) -> B) and D))), M:tm-131, m:tm-5, u:((Am (-> (and A B) A)) (C (-> Bm (and (-> (and A B) A) Bm))))
================================================================
tm-name          tm-4291
in-theory        4291
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) or D))
theorem-size     15
proof            (modus-ponens tm-131 tm-6 ((Am (-> (and A B) A)) (C (or (-> (and A B) A) Bm))))
axioms-used      (tm-8 tm-1 tm-3 tm-6)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-4291.         ((A or ((B and C) -> B)) -> (((B and C) -> B) or D)), M:tm-131, m:tm-6, u:((Am (-> (and A B) A)) (C (or (-> (and A B) A) Bm)))
================================================================
tm-name          tm-4292
in-theory        4292
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D or ((B and C) -> B)))
theorem-size     15
proof            (modus-ponens tm-131 tm-7 ((Am (-> (and A B) A)) (C (or Bm (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-7)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4292.         ((A or ((B and C) -> B)) -> (D or ((B and C) -> B))), M:tm-131, m:tm-7, u:((Am (-> (and A B) A)) (C (or Bm (-> (and A B) A))))
================================================================
tm-name          tm-4293
in-theory        4293
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((B -> D) -> (((B and C) or B) -> D)))
theorem-size     19
proof            (modus-ponens tm-131 tm-8 ((Am (and Bm B)) (A Bm) (C (-> (-> Bm Cm) (-> (or (and Bm B) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4293.         ((A or ((B and C) -> B)) -> ((B -> D) -> (((B and C) or B) -> D))), M:tm-131, m:tm-8, u:((Am (and Bm B)) (A Bm) (C (-> (-> Bm Cm) (-> (or (and Bm B) Bm) Cm))))
================================================================
tm-name          tm-4294
in-theory        4294
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> (not B)) -> (not (B and C))))
theorem-size     19
proof            (modus-ponens tm-131 tm-9 ((Am (and Bm B)) (A Bm) (C (-> (-> (and Bm B) (not Bm)) (not (and Bm B))))))
axioms-used      (tm-8 tm-1 tm-3 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4294.         ((A or ((B and C) -> B)) -> (((B and C) -> (not B)) -> (not (B and C)))), M:tm-131, m:tm-9, u:((Am (and Bm B)) (A Bm) (C (-> (-> (and Bm B) (not Bm)) (not (and Bm B)))))
================================================================
tm-name          tm-4295
in-theory        4295
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-131 tm-11 ((Am (-> (and A B) A)) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4295.         ((A or ((B and C) -> B)) -> (D -> (E -> D))), M:tm-131, m:tm-11, u:((Am (-> (and A B) A)) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-4296
in-theory        4296
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((B and C) -> (B and C)))
theorem-size     15
proof            (modus-ponens tm-131 tm-12 ((Am (and Bm B)) (A Bm) (C (-> (and Bm B) (and Bm B)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4296.         ((A or ((B and C) -> B)) -> ((B and C) -> (B and C))), M:tm-131, m:tm-12, u:((Am (and Bm B)) (A Bm) (C (-> (and Bm B) (and Bm B))))
================================================================
tm-name          tm-4297
in-theory        4297
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-131 tm-14 ((Am (-> (and A B) A)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4297.         ((A or ((B and C) -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-131, m:tm-14, u:((Am (-> (and A B) A)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-4298
in-theory        4298
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-131 tm-16 ((Am (-> (and A B) A)) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4298.         ((A or ((B and C) -> B)) -> ((D and E) -> D)), M:tm-131, m:tm-16, u:((Am (-> (and A B) A)) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-4299
in-theory        4299
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (B -> C)) -> B)) -> ((B and (B -> C)) -> C))
theorem-size     17
proof            (modus-ponens tm-131 tm-17 ((Bm Am) (B (-> Am Cm)) (A Am) (C (-> (and Am (-> Am Cm)) Cm))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-4299.         ((A or ((B and (B -> C)) -> B)) -> ((B and (B -> C)) -> C)), M:tm-131, m:tm-17, u:((Bm Am) (B (-> Am Cm)) (A Am) (C (-> (and Am (-> Am Cm)) Cm)))
================================================================
tm-name          tm-4300
in-theory        4300
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-131 tm-18 ((Am (-> (and A B) A)) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-1 tm-3 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-4300.         ((A or ((B and C) -> B)) -> ((D and E) -> E)), M:tm-131, m:tm-18, u:((Am (-> (and A B) A)) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-4301
in-theory        4301
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (E -> D)) and ((B and C) -> B)))
theorem-size     19
proof            (modus-ponens tm-131 tm-19 ((Am (-> (and A B) A)) (C (and (-> Bm (-> Cm Bm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4301.         ((A or ((B and C) -> B)) -> ((D -> (E -> D)) and ((B and C) -> B))), M:tm-131, m:tm-19, u:((Am (-> (and A B) A)) (C (and (-> Bm (-> Cm Bm)) (-> (and A B) A))))
================================================================
tm-name          tm-4302
in-theory        4302
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B and C) -> B)))
theorem-size     27
proof            (modus-ponens tm-131 tm-20 ((Am (-> (and A B) A)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4302.         ((A or ((B and C) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B and C) -> B))), M:tm-131, m:tm-20, u:((Am (-> (and A B) A)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and A B) A))))
================================================================
tm-name          tm-4303
in-theory        4303
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D and E) -> D) and ((B and C) -> B)))
theorem-size     19
proof            (modus-ponens tm-131 tm-21 ((Am (-> (and A B) A)) (C (and (-> (and Bm Cm) Bm) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4303.         ((A or ((B and C) -> B)) -> (((D and E) -> D) and ((B and C) -> B))), M:tm-131, m:tm-21, u:((Am (-> (and A B) A)) (C (and (-> (and Bm Cm) Bm) (-> (and A B) A))))
================================================================
tm-name          tm-4304
in-theory        4304
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D and E) -> E) and ((B and C) -> B)))
theorem-size     19
proof            (modus-ponens tm-131 tm-22 ((Am (-> (and A B) A)) (C (and (-> (and Bm Cm) Cm) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-4304.         ((A or ((B and C) -> B)) -> (((D and E) -> E) and ((B and C) -> B))), M:tm-131, m:tm-22, u:((Am (-> (and A B) A)) (C (and (-> (and Bm Cm) Cm) (-> (and A B) A))))
================================================================
tm-name          tm-4305
in-theory        4305
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (E -> (D and E))) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-23 ((Am (-> (and A B) A)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4305.         ((A or ((B and C) -> B)) -> ((D -> (E -> (D and E))) and ((B and C) -> B))), M:tm-131, m:tm-23, u:((Am (-> (and A B) A)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> (and A B) A))))
================================================================
tm-name          tm-4306
in-theory        4306
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((B and C) -> ((B and C) and B)))
theorem-size     17
proof            (modus-ponens tm-131 tm-24 ((Am (and Bm B)) (A Bm) (C (-> (and Bm B) (and (and Bm B) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4306.         ((A or ((B and C) -> B)) -> ((B and C) -> ((B and C) and B))), M:tm-131, m:tm-24, u:((Am (and Bm B)) (A Bm) (C (-> (and Bm B) (and (and Bm B) Bm))))
================================================================
tm-name          tm-4307
in-theory        4307
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-131 tm-25 ((Am (-> (and A B) A)) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4307.         ((A or ((B and C) -> B)) -> (D -> (E -> (D and E)))), M:tm-131, m:tm-25, u:((Am (-> (and A B) A)) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-4308
in-theory        4308
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (D or E)) and ((B and C) -> B)))
theorem-size     19
proof            (modus-ponens tm-131 tm-32 ((Am (-> (and A B) A)) (C (and (-> Bm (or Bm Cm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4308.         ((A or ((B and C) -> B)) -> ((D -> (D or E)) and ((B and C) -> B))), M:tm-131, m:tm-32, u:((Am (-> (and A B) A)) (C (and (-> Bm (or Bm Cm)) (-> (and A B) A))))
================================================================
tm-name          tm-4309
in-theory        4309
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-131 tm-33 ((Am (-> (and A B) A)) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4309.         ((A or ((B and C) -> B)) -> (D -> (D or E))), M:tm-131, m:tm-33, u:((Am (-> (and A B) A)) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-4310
in-theory        4310
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (E or D)) and ((B and C) -> B)))
theorem-size     19
proof            (modus-ponens tm-131 tm-42 ((Am (-> (and A B) A)) (C (and (-> Bm (or Cm Bm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4310.         ((A or ((B and C) -> B)) -> ((D -> (E or D)) and ((B and C) -> B))), M:tm-131, m:tm-42, u:((Am (-> (and A B) A)) (C (and (-> Bm (or Cm Bm)) (-> (and A B) A))))
================================================================
tm-name          tm-4311
in-theory        4311
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-131 tm-43 ((Am (-> (and A B) A)) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4311.         ((A or ((B and C) -> B)) -> (D -> (E or D))), M:tm-131, m:tm-43, u:((Am (-> (and A B) A)) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-4312
in-theory        4312
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((((B and C) and D) or (B and C)) -> B))
theorem-size     19
proof            (modus-ponens tm-131 tm-46 ((Am (and Bm B)) (A Bm) (C (-> (or (and (and Bm B) Cm) (and Bm B)) Bm))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4312.         ((A or ((B and C) -> B)) -> ((((B and C) and D) or (B and C)) -> B)), M:tm-131, m:tm-46, u:((Am (and Bm B)) (A Bm) (C (-> (or (and (and Bm B) Cm) (and Bm B)) Bm)))
================================================================
tm-name          tm-4313
in-theory        4313
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D and (B and C)) or (B and C)) -> B))
theorem-size     19
proof            (modus-ponens tm-131 tm-47 ((Am (and Bm B)) (A Bm) (C (-> (or (and Cm (and Bm B)) (and Bm B)) Bm))))
axioms-used      (tm-8 tm-1 tm-3 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-4313.         ((A or ((B and C) -> B)) -> (((D and (B and C)) or (B and C)) -> B)), M:tm-131, m:tm-47, u:((Am (and Bm B)) (A Bm) (C (-> (or (and Cm (and Bm B)) (and Bm B)) Bm)))
================================================================
tm-name          tm-4314
in-theory        4314
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B and C) -> B)))
theorem-size     27
proof            (modus-ponens tm-131 tm-54 ((Am (-> (and A B) A)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4314.         ((A or ((B and C) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B and C) -> B))), M:tm-131, m:tm-54, u:((Am (-> (and A B) A)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (and A B) A))))
================================================================
tm-name          tm-4315
in-theory        4315
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-131 tm-56 ((Am (-> (and A B) A)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4315.         ((A or ((B and C) -> B)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-131, m:tm-56, u:((Am (-> (and A B) A)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-4316
in-theory        4316
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((not B) and B) -> (not B))) -> (not ((not B) and B)))
theorem-size     15
proof            (modus-ponens tm-131 tm-60 ((Am (not Bm)) (B Bm) (A (not Bm)) (C (not (and (not Bm) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-9 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-4316.         ((A or (((not B) and B) -> (not B))) -> (not ((not B) and B))), M:tm-131, m:tm-60, u:((Am (not Bm)) (B Bm) (A (not Bm)) (C (not (and (not Bm) Bm))))
================================================================
tm-name          tm-4317
in-theory        4317
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B and C) -> B)))
theorem-size     25
proof            (modus-ponens tm-131 tm-69 ((Am (-> (and A B) A)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4317.         ((A or ((B and C) -> B)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B and C) -> B))), M:tm-131, m:tm-69, u:((Am (-> (and A B) A)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (and A B) A))))
================================================================
tm-name          tm-4318
in-theory        4318
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-131 tm-71 ((Am (-> (and A B) A)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4318.         ((A or ((B and C) -> B)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-131, m:tm-71, u:((Am (-> (and A B) A)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-4319
in-theory        4319
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((not (not (B and C))) or (B and C)) -> B))
theorem-size     19
proof            (modus-ponens tm-131 tm-73 ((Am (and Bm B)) (A Bm) (C (-> (or (not (not (and Bm B))) (and Bm B)) Bm))))
axioms-used      (tm-8 tm-1 tm-3 tm-10)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4319.         ((A or ((B and C) -> B)) -> (((not (not (B and C))) or (B and C)) -> B)), M:tm-131, m:tm-73, u:((Am (and Bm B)) (A Bm) (C (-> (or (not (not (and Bm B))) (and Bm B)) Bm)))
================================================================
tm-name          tm-4320
in-theory        4320
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((not (not D)) -> D) and ((B and C) -> B)))
theorem-size     19
proof            (modus-ponens tm-131 tm-76 ((Am (-> (and A B) A)) (C (and (-> (not (not Bm)) Bm) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4320.         ((A or ((B and C) -> B)) -> (((not (not D)) -> D) and ((B and C) -> B))), M:tm-131, m:tm-76, u:((Am (-> (and A B) A)) (C (and (-> (not (not Bm)) Bm) (-> (and A B) A))))
================================================================
tm-name          tm-4321
in-theory        4321
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-131 tm-78 ((Am (-> (and A B) A)) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-3 tm-10)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4321.         ((A or ((B and C) -> B)) -> ((not (not D)) -> D)), M:tm-131, m:tm-78, u:((Am (-> (and A B) A)) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-4322
in-theory        4322
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((not (B -> (C -> B))) and D) -> (not (B -> (C -> B))))) -> (not ((not (B -> (C -> B))) and D)))
theorem-size     27
proof            (modus-ponens tm-131 tm-79 ((Am (and (not (-> Bm (-> Cm Bm))) B)) (A (not (-> Bm (-> Cm Bm)))) (C (not (and (not (-> Bm (-> Cm Bm))) B)))))
axioms-used      (tm-8 tm-1 tm-3 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4322.         ((A or (((not (B -> (C -> B))) and D) -> (not (B -> (C -> B))))) -> (not ((not (B -> (C -> B))) and D))), M:tm-131, m:tm-79, u:((Am (and (not (-> Bm (-> Cm Bm))) B)) (A (not (-> Bm (-> Cm Bm)))) (C (not (and (not (-> Bm (-> Cm Bm))) B))))
================================================================
tm-name          tm-4323
in-theory        4323
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (E -> (F -> E))) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-83 ((Am (-> (and A B) A)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4323.         ((A or ((B and C) -> B)) -> ((D -> (E -> (F -> E))) and ((B and C) -> B))), M:tm-131, m:tm-83, u:((Am (-> (and A B) A)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> (and A B) A))))
================================================================
tm-name          tm-4324
in-theory        4324
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((B and C) -> (D -> B)))
theorem-size     15
proof            (modus-ponens tm-131 tm-84 ((Am (and Bm B)) (A Bm) (C (-> (and Bm B) (-> Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4324.         ((A or ((B and C) -> B)) -> ((B and C) -> (D -> B))), M:tm-131, m:tm-84, u:((Am (and Bm B)) (A Bm) (C (-> (and Bm B) (-> Cm Bm))))
================================================================
tm-name          tm-4325
in-theory        4325
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-131 tm-85 ((Am (-> (and A B) A)) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4325.         ((A or ((B and C) -> B)) -> (D -> (E -> (F -> E)))), M:tm-131, m:tm-85, u:((Am (-> (and A B) A)) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-4326
in-theory        4326
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((B and C) -> B))
theorem-size     13
proof            (modus-ponens tm-131 tm-86 ((Am (-> (and A B) A)) (C (-> (and A B) A))))
axioms-used      (tm-8 tm-1 tm-3 tm-2)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4326.         ((A or ((B and C) -> B)) -> ((B and C) -> B)), M:tm-131, m:tm-86, u:((Am (-> (and A B) A)) (C (-> (and A B) A)))
================================================================
tm-name          tm-4327
in-theory        4327
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) and D) -> (B -> C))) -> (((B -> C) and D) -> (B -> C)))
theorem-size     21
proof            (modus-ponens tm-131 tm-87 ((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> (and (-> Bm Cm) B) (-> Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4327.         ((A or (((B -> C) and D) -> (B -> C))) -> (((B -> C) and D) -> (B -> C))), M:tm-131, m:tm-87, u:((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> (and (-> Bm Cm) B) (-> Bm Cm))))
================================================================
tm-name          tm-4328
in-theory        4328
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> E) -> (D -> D)) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-95 ((Am (-> (and A B) A)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4328.         ((A or ((B and C) -> B)) -> (((D -> E) -> (D -> D)) and ((B and C) -> B))), M:tm-131, m:tm-95, u:((Am (-> (and A B) A)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (and A B) A))))
================================================================
tm-name          tm-4329
in-theory        4329
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-131 tm-97 ((Am (-> (and A B) A)) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4329.         ((A or ((B and C) -> B)) -> ((D -> E) -> (D -> D))), M:tm-131, m:tm-97, u:((Am (-> (and A B) A)) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-4330
in-theory        4330
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-131 tm-105 ((Am (-> (and A B) A)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4330.         ((A or ((B and C) -> B)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B and C) -> B))), M:tm-131, m:tm-105, u:((Am (-> (and A B) A)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (and A B) A))))
================================================================
tm-name          tm-4331
in-theory        4331
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-131 tm-107 ((Am (-> (and A B) A)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4331.         ((A or ((B and C) -> B)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-131, m:tm-107, u:((Am (-> (and A B) A)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-4332
in-theory        4332
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E) -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not ((not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E)))
theorem-size     51
proof            (modus-ponens tm-131 tm-109 ((Am (and (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) B)) (A (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (C (not (and (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) B)))))
axioms-used      (tm-8 tm-1 tm-3 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4332.         ((A or (((not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E) -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not ((not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E))), M:tm-131, m:tm-109, u:((Am (and (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) B)) (A (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (C (not (and (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) B))))
================================================================
tm-name          tm-4333
in-theory        4333
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B and C) -> B)))
theorem-size     29
proof            (modus-ponens tm-131 tm-113 ((Am (-> (and A B) A)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4333.         ((A or ((B and C) -> B)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B and C) -> B))), M:tm-131, m:tm-113, u:((Am (-> (and A B) A)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and A B) A))))
================================================================
tm-name          tm-4334
in-theory        4334
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) and E) -> (B -> (C -> D)))) -> (((B -> (C -> D)) and E) -> ((B -> C) -> (B -> D))))
theorem-size     31
proof            (modus-ponens tm-131 tm-114 ((Am (and (-> Bm (-> Cm Dm)) B)) (A (-> Bm (-> Cm Dm))) (C (-> (and (-> Bm (-> Cm Dm)) B) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4334.         ((A or (((B -> (C -> D)) and E) -> (B -> (C -> D)))) -> (((B -> (C -> D)) and E) -> ((B -> C) -> (B -> D)))), M:tm-131, m:tm-114, u:((Am (and (-> Bm (-> Cm Dm)) B)) (A (-> Bm (-> Cm Dm))) (C (-> (and (-> Bm (-> Cm Dm)) B) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-4335
in-theory        4335
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-131 tm-115 ((Am (-> (and A B) A)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4335.         ((A or ((B and C) -> B)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-131, m:tm-115, u:((Am (-> (and A B) A)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-4336
in-theory        4336
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B and C) -> B)))
theorem-size     29
proof            (modus-ponens tm-131 tm-125 ((Am (-> (and A B) A)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4336.         ((A or ((B and C) -> B)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B and C) -> B))), M:tm-131, m:tm-125, u:((Am (-> (and A B) A)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (and A B) A))))
================================================================
tm-name          tm-4337
in-theory        4337
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-131 tm-127 ((Am (-> (and A B) A)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4337.         ((A or ((B and C) -> B)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-131, m:tm-127, u:((Am (-> (and A B) A)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4338
in-theory        4338
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((not ((B and C) -> B)) and D) -> (not ((B and C) -> B)))) -> (not ((not ((B and C) -> B)) and D)))
theorem-size     27
proof            (modus-ponens tm-131 tm-130 ((Am (and (not (-> (and Bm Cm) Bm)) B)) (A (not (-> (and Bm Cm) Bm))) (C (not (and (not (-> (and Bm Cm) Bm)) B)))))
axioms-used      (tm-8 tm-1 tm-3 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4338.         ((A or (((not ((B and C) -> B)) and D) -> (not ((B and C) -> B)))) -> (not ((not ((B and C) -> B)) and D))), M:tm-131, m:tm-130, u:((Am (and (not (-> (and Bm Cm) Bm)) B)) (A (not (-> (and Bm Cm) Bm))) (C (not (and (not (-> (and Bm Cm) Bm)) B))))
================================================================
tm-name          tm-4339
in-theory        4339
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     33
proof            (modus-ponens tm-125 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4339.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-125, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4340
in-theory        4340
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> (C -> D)) -> (((E or ((A and B) -> A)) -> C) -> ((E or ((A and B) -> A)) -> D)))
theorem-size     29
proof            (modus-ponens tm-114 tm-131 ((A (-> (-> (and Am Bm) Am) (-> C D))) (B (or Dm (-> (and Am Bm) Am))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4340.         ((((A and B) -> A) -> (C -> D)) -> (((E or ((A and B) -> A)) -> C) -> ((E or ((A and B) -> A)) -> D))), M:tm-114, m:tm-131, u:((A (-> (-> (and Am Bm) Am) (-> C D))) (B (or Dm (-> (and Am Bm) Am))) (Cm (-> C D)))
================================================================
tm-name          tm-4341
in-theory        4341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G)))
theorem-size     33
proof            (modus-ponens tm-113 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4341.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G))), M:tm-113, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4342
in-theory        4342
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> (B -> C)) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))) -> ((E or (((B -> C) and D) -> (B -> C))) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))
theorem-size     55
proof            (modus-ponens tm-110 tm-131 ((A (and (-> B C) Bm)) (Am (-> B C)) (Cm (-> (-> (and (-> B C) Bm) B) (-> (and (-> B C) Bm) C))) (D (-> (or Dm (-> (and (-> B C) Bm) (-> B C))) (-> (-> (and (-> B C) Bm) B) (-> (and (-> B C) Bm) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4342.         ((A or ((((B -> C) and D) -> (B -> C)) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))) -> ((E or (((B -> C) and D) -> (B -> C))) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))), M:tm-110, m:tm-131, u:((A (and (-> B C) Bm)) (Am (-> B C)) (Cm (-> (-> (and (-> B C) Bm) B) (-> (and (-> B C) Bm) C))) (D (-> (or Dm (-> (and (-> B C) Bm) (-> B C))) (-> (-> (and (-> B C) Bm) B) (-> (and (-> B C) Bm) C)))))
================================================================
tm-name          tm-4343
in-theory        4343
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     37
proof            (modus-ponens tm-105 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4343.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-105, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4344
in-theory        4344
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> (A -> B)) -> (((A -> B) and C) -> A)) or ((((A -> B) and C) -> (A -> B)) -> (((A -> B) and C) -> B))) -> ((D or (((A -> B) and C) -> (A -> B))) -> (((A -> B) and C) -> B)))
theorem-size     55
proof            (modus-ponens tm-102 tm-131 ((A (and (-> B C) Bm)) (Am (-> B C)) (Cm (-> (and (-> B C) Bm) C)) (D (-> (or Dm (-> (and (-> B C) Bm) (-> B C))) (-> (and (-> B C) Bm) C)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4344.         ((((((A -> B) and C) -> (A -> B)) -> (((A -> B) and C) -> A)) or ((((A -> B) and C) -> (A -> B)) -> (((A -> B) and C) -> B))) -> ((D or (((A -> B) and C) -> (A -> B))) -> (((A -> B) and C) -> B))), M:tm-102, m:tm-131, u:((A (and (-> B C) Bm)) (Am (-> B C)) (Cm (-> (and (-> B C) Bm) C)) (D (-> (or Dm (-> (and (-> B C) Bm) (-> B C))) (-> (and (-> B C) Bm) C))))
================================================================
tm-name          tm-4345
in-theory        4345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E)))
theorem-size     25
proof            (modus-ponens tm-95 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4345.         (((A -> B) -> (A -> A)) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E))), M:tm-95, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4346
in-theory        4346
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) or (((A and B) -> A) -> ((A and B) -> A))) -> ((D or ((A and B) -> A)) -> ((A and B) -> A)))
theorem-size     33
proof            (modus-ponens tm-92 tm-131 ((Cm (-> (and Am Bm) Am)) (A (-> (and Am Bm) Am)) (B (-> (or Dm (-> (and Am Bm) Am)) (-> (and Am Bm) Am)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4346.         (((((A and B) -> A) -> C) or (((A and B) -> A) -> ((A and B) -> A))) -> ((D or ((A and B) -> A)) -> ((A and B) -> A))), M:tm-92, m:tm-131, u:((Cm (-> (and Am Bm) Am)) (A (-> (and Am Bm) Am)) (B (-> (or Dm (-> (and Am Bm) Am)) (-> (and Am Bm) Am))))
================================================================
tm-name          tm-4347
in-theory        4347
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> (D -> ((E or ((A and B) -> A)) -> C)))
theorem-size     19
proof            (modus-ponens tm-84 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4347.         ((((A and B) -> A) -> C) -> (D -> ((E or ((A and B) -> A)) -> C))), M:tm-84, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-4348
in-theory        4348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-83 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4348.         ((A -> (B -> (C -> B))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-83, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4349
in-theory        4349
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) -> (D -> ((B and C) -> B)))) -> ((E or ((B and C) -> B)) -> (D -> ((B and C) -> B))))
theorem-size     31
proof            (modus-ponens tm-80 tm-131 ((A (-> (and Am Bm) Am)) (Cm (-> B (-> (and Am Bm) Am))) (C (-> (or Dm (-> (and Am Bm) Am)) (-> B (-> (and Am Bm) Am))))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4349.         ((A or (((B and C) -> B) -> (D -> ((B and C) -> B)))) -> ((E or ((B and C) -> B)) -> (D -> ((B and C) -> B)))), M:tm-80, m:tm-131, u:((A (-> (and Am Bm) Am)) (Cm (-> B (-> (and Am Bm) Am))) (C (-> (or Dm (-> (and Am Bm) Am)) (-> B (-> (and Am Bm) Am)))))
================================================================
tm-name          tm-4350
in-theory        4350
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B and C) -> B) -> D) -> ((E or ((B and C) -> B)) -> D)))
theorem-size     23
proof            (modus-ponens tm-76 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4350.         (((not (not A)) -> A) and ((((B and C) -> B) -> D) -> ((E or ((B and C) -> B)) -> D))), M:tm-76, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4351
in-theory        4351
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A and B) -> A) -> C))) or (((A and B) -> A) -> C)) -> ((D or ((A and B) -> A)) -> C))
theorem-size     27
proof            (modus-ponens tm-73 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-8 tm-10 tm-1 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4351.         (((not (not (((A and B) -> A) -> C))) or (((A and B) -> A) -> C)) -> ((D or ((A and B) -> A)) -> C)), M:tm-73, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-4352
in-theory        4352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E)))
theorem-size     29
proof            (modus-ponens tm-69 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4352.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E))), M:tm-69, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4353
in-theory        4353
times-derived    1
----------------------------------------------------------------
theorem          (((((not A) and B) -> A) or ((((not A) and B) -> (not A)) -> (not ((not A) and B)))) -> ((C or (((not A) and B) -> (not A))) -> (not ((not A) and B))))
theorem-size     36
proof            (modus-ponens tm-66 tm-131 ((A (and (not B) Bm)) (Am (not B)) (Cm (not (and (not B) Bm))) (C (-> (or Dm (-> (and (not B) Bm) (not B))) (not (and (not B) Bm))))))
axioms-used      (tm-8 tm-9 tm-1 tm-3)
proof-size       130
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4353.         (((((not A) and B) -> A) or ((((not A) and B) -> (not A)) -> (not ((not A) and B)))) -> ((C or (((not A) and B) -> (not A))) -> (not ((not A) and B)))), M:tm-66, m:tm-131, u:((A (and (not B) Bm)) (Am (not B)) (Cm (not (and (not B) Bm))) (C (-> (or Dm (-> (and (not B) Bm) (not B))) (not (and (not B) Bm)))))
================================================================
tm-name          tm-4354
in-theory        4354
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> (C or ((A and B) -> A))) -> ((((A and B) -> A) or (C or ((A and B) -> A))) -> (C or ((A and B) -> A))))
theorem-size     35
proof            (modus-ponens tm-55 tm-131 ((A (-> (and Am Bm) Am)) (Cm (or Dm (-> (and Am Bm) Am))) (B (or Dm (-> (and Am Bm) Am))) (C (or Dm (-> (and Am Bm) Am)))))
axioms-used      (tm-2 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4354.         ((((A and B) -> A) -> (C or ((A and B) -> A))) -> ((((A and B) -> A) or (C or ((A and B) -> A))) -> (C or ((A and B) -> A)))), M:tm-55, m:tm-131, u:((A (-> (and Am Bm) Am)) (Cm (or Dm (-> (and Am Bm) Am))) (B (or Dm (-> (and Am Bm) Am))) (C (or Dm (-> (and Am Bm) Am))))
================================================================
tm-name          tm-4355
in-theory        4355
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     31
proof            (modus-ponens tm-54 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4355.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-54, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4356
in-theory        4356
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B and C)) or (((B and C) -> B) -> ((A or (B and C)) -> B))) -> ((D or ((B and C) -> B)) -> ((A or (B and C)) -> B)))
theorem-size     35
proof            (modus-ponens tm-51 tm-131 ((A (and Am Bm)) (B Am) (Cm (-> (or C (and Am Bm)) Am)) (D (-> (or Dm (-> (and Am Bm) Am)) (-> (or C (and Am Bm)) Am)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4356.         (((A -> (B and C)) or (((B and C) -> B) -> ((A or (B and C)) -> B))) -> ((D or ((B and C) -> B)) -> ((A or (B and C)) -> B))), M:tm-51, m:tm-131, u:((A (and Am Bm)) (B Am) (Cm (-> (or C (and Am Bm)) Am)) (D (-> (or Dm (-> (and Am Bm) Am)) (-> (or C (and Am Bm)) Am))))
================================================================
tm-name          tm-4357
in-theory        4357
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) -> (A and ((B and C) -> B)))) -> ((D or ((B and C) -> B)) -> (A and ((B and C) -> B))))
theorem-size     31
proof            (modus-ponens tm-48 tm-131 ((A (-> (and Am Bm) Am)) (Cm (and B (-> (and Am Bm) Am))) (C (-> (or Dm (-> (and Am Bm) Am)) (and B (-> (and Am Bm) Am))))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4357.         ((A or (((B and C) -> B) -> (A and ((B and C) -> B)))) -> ((D or ((B and C) -> B)) -> (A and ((B and C) -> B)))), M:tm-48, m:tm-131, u:((A (-> (and Am Bm) Am)) (Cm (and B (-> (and Am Bm) Am))) (C (-> (or Dm (-> (and Am Bm) Am)) (and B (-> (and Am Bm) Am)))))
================================================================
tm-name          tm-4358
in-theory        4358
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) or (((B and C) -> B) -> D)) -> ((E or ((B and C) -> B)) -> D))
theorem-size     27
proof            (modus-ponens tm-47 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-8 tm-4 tm-1 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4358.         (((A and (((B and C) -> B) -> D)) or (((B and C) -> B) -> D)) -> ((E or ((B and C) -> B)) -> D)), M:tm-47, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-4359
in-theory        4359
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) or (((A and B) -> A) -> C)) -> ((E or ((A and B) -> A)) -> C))
theorem-size     27
proof            (modus-ponens tm-46 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4359.         ((((((A and B) -> A) -> C) and D) or (((A and B) -> A) -> C)) -> ((E or ((A and B) -> A)) -> C)), M:tm-46, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-4360
in-theory        4360
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) or (((A and B) -> A) -> ((A and B) -> C))) -> ((D or ((A and B) -> A)) -> ((A and B) -> C)))
theorem-size     33
proof            (modus-ponens tm-45 tm-131 ((A (and Am Bm)) (B Am) (Cm (-> (and Am Bm) C)) (D (-> (or Dm (-> (and Am Bm) Am)) (-> (and Am Bm) C)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4360.         ((((A and B) -> (A -> C)) or (((A and B) -> A) -> ((A and B) -> C))) -> ((D or ((A and B) -> A)) -> ((A and B) -> C))), M:tm-45, m:tm-131, u:((A (and Am Bm)) (B Am) (Cm (-> (and Am Bm) C)) (D (-> (or Dm (-> (and Am Bm) Am)) (-> (and Am Bm) C))))
================================================================
tm-name          tm-4361
in-theory        4361
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) -> A)) -> ((D or ((B and C) -> B)) -> A))
theorem-size     19
proof            (modus-ponens tm-44 tm-131 ((A (-> (and Am Bm) Am)) (B Cm) (C (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4361.         ((A or (((B and C) -> B) -> A)) -> ((D or ((B and C) -> B)) -> A)), M:tm-44, m:tm-131, u:((A (-> (and Am Bm) Am)) (B Cm) (C (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-4362
in-theory        4362
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E)))
theorem-size     23
proof            (modus-ponens tm-42 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4362.         ((A -> (B or A)) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E))), M:tm-42, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4363
in-theory        4363
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E)))
theorem-size     23
proof            (modus-ponens tm-32 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4363.         ((A -> (A or B)) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E))), M:tm-32, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4364
in-theory        4364
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> ((((A and B) -> A) -> C) and ((D or ((A and B) -> A)) -> C)))
theorem-size     25
proof            (modus-ponens tm-24 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4364.         ((((A and B) -> A) -> C) -> ((((A and B) -> A) -> C) and ((D or ((A and B) -> A)) -> C))), M:tm-24, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-4365
in-theory        4365
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E)))
theorem-size     25
proof            (modus-ponens tm-23 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4365.         ((A -> (B -> (A and B))) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E))), M:tm-23, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4366
in-theory        4366
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E)))
theorem-size     23
proof            (modus-ponens tm-22 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4366.         (((A and B) -> B) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E))), M:tm-22, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4367
in-theory        4367
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E)))
theorem-size     23
proof            (modus-ponens tm-21 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4367.         (((A and B) -> A) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E))), M:tm-21, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4368
in-theory        4368
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     31
proof            (modus-ponens tm-20 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4368.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-20, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4369
in-theory        4369
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E)))
theorem-size     23
proof            (modus-ponens tm-19 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4369.         ((A -> (B -> A)) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E))), M:tm-19, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4370
in-theory        4370
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> (((A and B) -> A) -> C))
theorem-size     15
proof            (modus-ponens tm-12 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4370.         ((((A and B) -> A) -> C) -> (((A and B) -> A) -> C)), M:tm-12, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-4371
in-theory        4371
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> (not ((D or ((A and B) -> A)) -> C))) -> (not (((A and B) -> A) -> C)))
theorem-size     27
proof            (modus-ponens tm-9 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-9 tm-8 tm-1 tm-3)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4371.         (((((A and B) -> A) -> C) -> (not ((D or ((A and B) -> A)) -> C))) -> (not (((A and B) -> A) -> C))), M:tm-9, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-4372
in-theory        4372
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B and C) -> B)) -> D) -> E) -> (((((B and C) -> B) -> D) or ((A or ((B and C) -> B)) -> D)) -> E))
theorem-size     31
proof            (modus-ponens tm-8 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4372.         ((((A or ((B and C) -> B)) -> D) -> E) -> (((((B and C) -> B) -> D) or ((A or ((B and C) -> B)) -> D)) -> E)), M:tm-8, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-4373
in-theory        4373
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B and C) -> B) -> D) -> ((E or ((B and C) -> B)) -> D)))
theorem-size     19
proof            (modus-ponens tm-7 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-7 tm-8 tm-1 tm-3)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4373.         (A or ((((B and C) -> B) -> D) -> ((E or ((B and C) -> B)) -> D))), M:tm-7, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4374
in-theory        4374
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-6 tm-8 tm-1 tm-3)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4374.         (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) or E), M:tm-6, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4375
in-theory        4375
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B and C) -> B) -> D) -> ((E or ((B and C) -> B)) -> D)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4375.         (A -> (((((B and C) -> B) -> D) -> ((E or ((B and C) -> B)) -> D)) and A)), M:tm-5, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4376
in-theory        4376
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> (D or ((A and B) -> A))) -> ((((A and B) -> A) -> C) -> C))
theorem-size     25
proof            (modus-ponens tm-2 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (or Dm (-> (and Am Bm) Am))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-1 tm-3)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4376.         (((((A and B) -> A) -> C) -> (D or ((A and B) -> A))) -> ((((A and B) -> A) -> C) -> C)), M:tm-2, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (or Dm (-> (and Am Bm) Am))) (C Cm))
================================================================
tm-name          tm-4377
in-theory        4377
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) -> D) -> ((E or ((B and C) -> B)) -> D)))
theorem-size     19
proof            (modus-ponens tm-1 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4377.         (A -> ((((B and C) -> B) -> D) -> ((E or ((B and C) -> B)) -> D))), M:tm-1, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4378
in-theory        4378
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-125 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4378.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> ((F and G) -> F)))), M:tm-125, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4379
in-theory        4379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-113 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4379.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G and H) -> G)))), M:tm-113, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4380
in-theory        4380
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> ((F and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-105 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4380.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> ((F and G) -> F)))), M:tm-105, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4381
in-theory        4381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-95 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4381.         (((A -> B) -> (A -> A)) and (C or (D -> ((E and F) -> E)))), M:tm-95, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4382
in-theory        4382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-83 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4382.         ((A -> (B -> (C -> B))) and (D or (E -> ((F and G) -> F)))), M:tm-83, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4383
in-theory        4383
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> ((D and E) -> D))))
theorem-size     15
proof            (modus-ponens tm-76 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4383.         (((not (not A)) -> A) and (B or (C -> ((D and E) -> D)))), M:tm-76, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4384
in-theory        4384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> ((E and F) -> E))))
theorem-size     21
proof            (modus-ponens tm-69 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4384.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> ((E and F) -> E)))), M:tm-69, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4385
in-theory        4385
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-54 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4385.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> ((F and G) -> F)))), M:tm-54, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4386
in-theory        4386
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-42 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4386.         ((A -> (B or A)) and (C or (D -> ((E and F) -> E)))), M:tm-42, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4387
in-theory        4387
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-32 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4387.         ((A -> (A or B)) and (C or (D -> ((E and F) -> E)))), M:tm-32, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4388
in-theory        4388
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-23 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4388.         ((A -> (B -> (A and B))) and (C or (D -> ((E and F) -> E)))), M:tm-23, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4389
in-theory        4389
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-22 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4389.         (((A and B) -> B) and (C or (D -> ((E and F) -> E)))), M:tm-22, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4390
in-theory        4390
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-21 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4390.         (((A and B) -> A) and (C or (D -> ((E and F) -> E)))), M:tm-21, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4391
in-theory        4391
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-20 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4391.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> ((F and G) -> F)))), M:tm-20, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4392
in-theory        4392
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-19 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4392.         ((A -> (B -> A)) and (C or (D -> ((E and F) -> E)))), M:tm-19, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4393
in-theory        4393
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C -> ((D and E) -> D))))
theorem-size     11
proof            (modus-ponens tm-7 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-7 tm-1 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4393.         (A or (B or (C -> ((D and E) -> D)))), M:tm-7, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4394
in-theory        4394
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-6 tm-7 tm-1 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4394.         ((A or (B -> ((C and D) -> C))) or E), M:tm-6, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4395
in-theory        4395
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C -> ((D and E) -> D))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4395.         (A -> ((B or (C -> ((D and E) -> D))) and A)), M:tm-5, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4396
in-theory        4396
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C -> ((D and E) -> D))))
theorem-size     11
proof            (modus-ponens tm-1 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-1 tm-7 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4396.         (A -> (B or (C -> ((D and E) -> D)))), M:tm-1, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4397
in-theory        4397
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4397.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E and F) -> E)) or G)), M:tm-125, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4398
in-theory        4398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F and G) -> F)) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4398.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F and G) -> F)) or H)), M:tm-113, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4399
in-theory        4399
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E and F) -> E)) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4399.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E and F) -> E)) or G)), M:tm-105, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4400
in-theory        4400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> ((D and E) -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4400.         (((A -> B) -> (A -> A)) and ((C -> ((D and E) -> D)) or F)), M:tm-95, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4401
in-theory        4401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4401.         ((A -> (B -> (C -> B))) and ((D -> ((E and F) -> E)) or G)), M:tm-83, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4402
in-theory        4402
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> ((C and D) -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4402.         (((not (not A)) -> A) and ((B -> ((C and D) -> C)) or E)), M:tm-76, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4403
in-theory        4403
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D and E) -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-1 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4403.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D and E) -> D)) or F)), M:tm-69, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4404
in-theory        4404
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E and F) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4404.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E and F) -> E)) or G)), M:tm-54, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4405
in-theory        4405
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> ((D and E) -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4405.         ((A -> (B or A)) and ((C -> ((D and E) -> D)) or F)), M:tm-42, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4406
in-theory        4406
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> ((D and E) -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4406.         ((A -> (A or B)) and ((C -> ((D and E) -> D)) or F)), M:tm-32, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4407
in-theory        4407
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> ((D and E) -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4407.         ((A -> (B -> (A and B))) and ((C -> ((D and E) -> D)) or F)), M:tm-23, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4408
in-theory        4408
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> ((D and E) -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4408.         (((A and B) -> B) and ((C -> ((D and E) -> D)) or F)), M:tm-22, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4409
in-theory        4409
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> ((D and E) -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4409.         (((A and B) -> A) and ((C -> ((D and E) -> D)) or F)), M:tm-21, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4410
in-theory        4410
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E and F) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4410.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E and F) -> E)) or G)), M:tm-20, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4411
in-theory        4411
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> ((D and E) -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4411.         ((A -> (B -> A)) and ((C -> ((D and E) -> D)) or F)), M:tm-19, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4412
in-theory        4412
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> ((C and D) -> C)) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-7 tm-6 tm-1 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4412.         (A or ((B -> ((C and D) -> C)) or E)), M:tm-7, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4413
in-theory        4413
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-6 tm-1 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4413.         (((A -> ((B and C) -> B)) or D) or E), M:tm-6, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4414
in-theory        4414
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> ((C and D) -> C)) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4414.         (A -> (((B -> ((C and D) -> C)) or E) and A)), M:tm-5, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4415
in-theory        4415
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> ((C and D) -> C)) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-1 tm-6 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4415.         (A -> ((B -> ((C and D) -> C)) or E)), M:tm-1, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4416
in-theory        4416
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-134 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4416.         ((A -> ((B and C) -> B)) and (D -> (E -> D))), M:tm-134, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-4417
in-theory        4417
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4417.         ((A -> ((B and C) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-134, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-4418
in-theory        4418
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-134 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4418.         ((A -> ((B and C) -> B)) and ((D and E) -> D)), M:tm-134, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-4419
in-theory        4419
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-134 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-4419.         ((A -> ((B and C) -> B)) and ((D and E) -> E)), M:tm-134, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-4420
in-theory        4420
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-134 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4420.         ((A -> ((B and C) -> B)) and (D -> (E -> (D and E)))), M:tm-134, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-4421
in-theory        4421
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-134 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4421.         ((A -> ((B and C) -> B)) and (D -> (D or E))), M:tm-134, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-4422
in-theory        4422
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-134 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4422.         ((A -> ((B and C) -> B)) and (D -> (E or D))), M:tm-134, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-4423
in-theory        4423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4423.         ((A -> ((B and C) -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-134, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-4424
in-theory        4424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-134 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4424.         ((A -> ((B and C) -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-134, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-4425
in-theory        4425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-134 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-1 tm-3 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-4425.         ((A -> ((B and C) -> B)) and ((not (not D)) -> D)), M:tm-134, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-4426
in-theory        4426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-134 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4426.         ((A -> ((B and C) -> B)) and (D -> (E -> (F -> E)))), M:tm-134, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-4427
in-theory        4427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-134 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4427.         ((A -> ((B and C) -> B)) and ((D -> E) -> (D -> D))), M:tm-134, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-4428
in-theory        4428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-134 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4428.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-134, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-4429
in-theory        4429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4429.         ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-134, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-4430
in-theory        4430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-134 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4430.         ((A -> ((B and C) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-134, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-4431
in-theory        4431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-134 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4431.         ((A -> ((B and C) -> B)) and (D -> ((E and F) -> E))), M:tm-134, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-4432
in-theory        4432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-134 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-4432.         ((A -> ((B and C) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-134, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-4433
in-theory        4433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-134 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-4433.         ((A -> ((B and C) -> B)) and (D -> ((E and F) -> F))), M:tm-134, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-4434
in-theory        4434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-134 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4434.         ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> E)) and D))), M:tm-134, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-4435
in-theory        4435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-134 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4435.         ((A -> ((B and C) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-134, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-4436
in-theory        4436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-134 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4436.         ((A -> ((B and C) -> B)) and (D -> (((E and F) -> E) and D))), M:tm-134, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-4437
in-theory        4437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-134 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-4437.         ((A -> ((B and C) -> B)) and (D -> (((E and F) -> F) and D))), M:tm-134, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-4438
in-theory        4438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4438.         ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-134, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-4439
in-theory        4439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-134 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4439.         ((A -> ((B and C) -> B)) and ((D -> E) -> (D -> (D and E)))), M:tm-134, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-4440
in-theory        4440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4440.         ((A -> ((B and C) -> B)) and (D -> (E -> (F -> (E and F))))), M:tm-134, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-4441
in-theory        4441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-134 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4441.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) or F)), M:tm-134, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-4442
in-theory        4442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-134 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4442.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-134, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-4443
in-theory        4443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-134 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4443.         ((A -> ((B and C) -> B)) and (((D and E) -> D) or F)), M:tm-134, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-4444
in-theory        4444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-134 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-4444.         ((A -> ((B and C) -> B)) and (((D and E) -> E) or F)), M:tm-134, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-4445
in-theory        4445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-134 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4445.         ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) or F)), M:tm-134, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-4446
in-theory        4446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-134 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4446.         ((A -> ((B and C) -> B)) and ((D -> (D or E)) or F)), M:tm-134, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-4447
in-theory        4447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-134 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4447.         ((A -> ((B and C) -> B)) and (D -> ((E -> (E or F)) and D))), M:tm-134, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-4448
in-theory        4448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-134 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4448.         ((A -> ((B and C) -> B)) and (D -> (E -> (E or F)))), M:tm-134, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-4449
in-theory        4449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-134 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4449.         ((A -> ((B and C) -> B)) and (D or (E -> (F -> E)))), M:tm-134, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-4450
in-theory        4450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4450.         ((A -> ((B and C) -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-134, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-4451
in-theory        4451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-134 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4451.         ((A -> ((B and C) -> B)) and (D or ((E and F) -> E))), M:tm-134, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-4452
in-theory        4452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-134 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-4452.         ((A -> ((B and C) -> B)) and (D or ((E and F) -> F))), M:tm-134, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-4453
in-theory        4453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4453.         ((A -> ((B and C) -> B)) and (D or (E -> (F -> (E and F))))), M:tm-134, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-4454
in-theory        4454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-134 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4454.         ((A -> ((B and C) -> B)) and (D or (E -> (E or F)))), M:tm-134, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-4455
in-theory        4455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-134 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4455.         ((A -> ((B and C) -> B)) and (D or (E -> (F or E)))), M:tm-134, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-4456
in-theory        4456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-134 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4456.         ((A -> ((B and C) -> B)) and ((D -> (E or D)) or F)), M:tm-134, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-4457
in-theory        4457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-134 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4457.         ((A -> ((B and C) -> B)) and (D -> ((E -> (F or E)) and D))), M:tm-134, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-4458
in-theory        4458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-134 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4458.         ((A -> ((B and C) -> B)) and (D -> (E -> (F or E)))), M:tm-134, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-4459
in-theory        4459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-134 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4459.         ((A -> ((B and C) -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-134, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-4460
in-theory        4460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-134 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4460.         ((A -> ((B and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-134, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-4461
in-theory        4461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-134 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4461.         ((A -> ((B and C) -> B)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-134, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-4462
in-theory        4462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-134 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-4462.         ((A -> ((B and C) -> B)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-134, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-4463
in-theory        4463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-134 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4463.         ((A -> ((B and C) -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-134, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-4464
in-theory        4464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-134 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4464.         ((A -> ((B and C) -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-134, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-4465
in-theory        4465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-134 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4465.         ((A -> ((B and C) -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-134, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-4466
in-theory        4466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-134 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4466.         ((A -> ((B and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-134, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-4467
in-theory        4467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4467.         ((A -> ((B and C) -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-134, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-4468
in-theory        4468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-134 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4468.         ((A -> ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-134, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-4469
in-theory        4469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-134 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4469.         ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-134, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-4470
in-theory        4470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-134 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-4470.         ((A -> ((B and C) -> B)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-134, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-4471
in-theory        4471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4471.         ((A -> ((B and C) -> B)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-134, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-4472
in-theory        4472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-134 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4472.         ((A -> ((B and C) -> B)) and ((D -> (not (E -> D))) -> (not D))), M:tm-134, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-4473
in-theory        4473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4473.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-134, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-4474
in-theory        4474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-134 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4474.         ((A -> ((B and C) -> B)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-134, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-4475
in-theory        4475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-134 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-4475.         ((A -> ((B and C) -> B)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-134, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-4476
in-theory        4476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4476.         ((A -> ((B and C) -> B)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-134, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-4477
in-theory        4477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-134 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4477.         ((A -> ((B and C) -> B)) and ((D -> (not (D or E))) -> (not D))), M:tm-134, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-4478
in-theory        4478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-134 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4478.         ((A -> ((B and C) -> B)) and ((D -> (not (E or D))) -> (not D))), M:tm-134, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-4479
in-theory        4479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-134 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4479.         ((A -> ((B and C) -> B)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-134, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-4480
in-theory        4480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-134 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4480.         ((A -> ((B and C) -> B)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-134, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-4481
in-theory        4481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-134 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4481.         ((A -> ((B and C) -> B)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-134, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-4482
in-theory        4482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4482.         ((A -> ((B and C) -> B)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-134, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-4483
in-theory        4483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-134 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4483.         ((A -> ((B and C) -> B)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-134, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-4484
in-theory        4484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-134 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4484.         ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-134, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-4485
in-theory        4485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-134 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-4485.         ((A -> ((B and C) -> B)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-134, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-4486
in-theory        4486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4486.         ((A -> ((B and C) -> B)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-134, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-4487
in-theory        4487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-134 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4487.         ((A -> ((B and C) -> B)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-134, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-4488
in-theory        4488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-134 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4488.         ((A -> ((B and C) -> B)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-134, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-4489
in-theory        4489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-134 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4489.         ((A -> ((B and C) -> B)) and (D or ((not (not E)) -> E))), M:tm-134, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-4490
in-theory        4490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-134 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4490.         ((A -> ((B and C) -> B)) and (((not (not D)) -> D) or E)), M:tm-134, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-4491
in-theory        4491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-134 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4491.         ((A -> ((B and C) -> B)) and (D -> (((not (not E)) -> E) and D))), M:tm-134, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-4492
in-theory        4492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-134 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-4492.         ((A -> ((B and C) -> B)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-134, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-4493
in-theory        4493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-134 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4493.         ((A -> ((B and C) -> B)) and (D -> ((not (not E)) -> E))), M:tm-134, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-4494
in-theory        4494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4494.         ((A -> ((B and C) -> B)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-134, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-4495
in-theory        4495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-134 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4495.         ((A -> ((B and C) -> B)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-134, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-4496
in-theory        4496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4496.         ((A -> ((B and C) -> B)) and (D or (E -> (F -> (G -> F))))), M:tm-134, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-4497
in-theory        4497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4497.         ((A -> ((B and C) -> B)) and ((D -> (E -> (F -> E))) or G)), M:tm-134, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-4498
in-theory        4498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4498.         ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-134, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-4499
in-theory        4499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-134 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4499.         ((A -> ((B and C) -> B)) and ((D -> E) -> (D -> (F -> E)))), M:tm-134, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-4500
in-theory        4500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4500.         ((A -> ((B and C) -> B)) and (D -> (E -> (F -> (G -> F))))), M:tm-134, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-4501
in-theory        4501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-134 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4501.         ((A -> ((B and C) -> B)) and (D -> D)), M:tm-134, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-4502
in-theory        4502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4502.         ((A -> ((B and C) -> B)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-134, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-4503
in-theory        4503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-134 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4503.         ((A -> ((B and C) -> B)) and ((D and E) -> (D and E))), M:tm-134, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-4504
in-theory        4504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-134 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4504.         ((A -> ((B and C) -> B)) and ((D -> E) -> (D -> E))), M:tm-134, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-4505
in-theory        4505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-134 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4505.         ((A -> ((B and C) -> B)) and ((not (not D)) -> (not (not D)))), M:tm-134, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-4506
in-theory        4506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-134 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4506.         ((A -> ((B and C) -> B)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-134, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-4507
in-theory        4507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-134 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4507.         ((A -> ((B and C) -> B)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-134, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-4508
in-theory        4508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-134 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4508.         ((A -> ((B and C) -> B)) and (D or ((E -> F) -> (E -> E)))), M:tm-134, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-4509
in-theory        4509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-134 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4509.         ((A -> ((B and C) -> B)) and (((D -> E) -> (D -> D)) or F)), M:tm-134, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-4510
in-theory        4510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4510.         ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-134, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-4511
in-theory        4511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-4511.         ((A -> ((B and C) -> B)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-134, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-4512
in-theory        4512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-134 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4512.         ((A -> ((B and C) -> B)) and (D -> ((E -> F) -> (E -> E)))), M:tm-134, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-4513
in-theory        4513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-4513.         ((A -> ((B and C) -> B)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-134, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-4514
in-theory        4514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-134 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-4514.         ((A -> ((B and C) -> B)) and ((D -> (D -> E)) -> (D -> E))), M:tm-134, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-4515
in-theory        4515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-134 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4515.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-134, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-4516
in-theory        4516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-134 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4516.         ((A -> ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-134, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-4517
in-theory        4517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-134 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4517.         ((A -> ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-134, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-4518
in-theory        4518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4518.         ((A -> ((B and C) -> B)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-134, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-4519
in-theory        4519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-134 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4519.         ((A -> ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-134, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-4520
in-theory        4520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-134 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4520.         ((A -> ((B and C) -> B)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-134, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-4521
in-theory        4521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-134 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-4521.         ((A -> ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-134, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-4522
in-theory        4522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4522.         ((A -> ((B and C) -> B)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-134, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-4523
in-theory        4523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-134 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-4523.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-134, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-4524
in-theory        4524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-134 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4524.         ((A -> ((B and C) -> B)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-134, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-4525
in-theory        4525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-134 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4525.         ((A -> ((B and C) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-134, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-4526
in-theory        4526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-134 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4526.         ((A -> ((B and C) -> B)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-134, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-4527
in-theory        4527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-134 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4527.         ((A -> ((B and C) -> B)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-134, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-4528
in-theory        4528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-134 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4528.         ((A -> ((B and C) -> B)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-134, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-4529
in-theory        4529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-134 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4529.         ((A -> ((B and C) -> B)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-134, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-4530
in-theory        4530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-134 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4530.         ((A -> ((B and C) -> B)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-134, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-4531
in-theory        4531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-134 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-4531.         ((A -> ((B and C) -> B)) and (((D -> E) and D) -> E)), M:tm-134, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-4532
in-theory        4532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-134 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-4532.         ((A -> ((B and C) -> B)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-134, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-4533
in-theory        4533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-134 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4533.         ((A -> ((B and C) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-134, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-4534
in-theory        4534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-134 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-4534.         ((A -> ((B and C) -> B)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-134, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-4535
in-theory        4535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-134 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4535.         ((A -> ((B and C) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-134, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-4536
in-theory        4536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-134 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4536.         ((A -> ((B and C) -> B)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-134, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-4537
in-theory        4537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-134 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4537.         ((A -> ((B and C) -> B)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-134, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-4538
in-theory        4538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-134 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4538.         ((A -> ((B and C) -> B)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-134, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4539
in-theory        4539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-134 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4539.         ((A -> ((B and C) -> B)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-134, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-4540
in-theory        4540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-134 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4540.         ((A -> ((B and C) -> B)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-134, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-4541
in-theory        4541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-134 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-4541.         ((A -> ((B and C) -> B)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-134, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-4542
in-theory        4542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-134 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4542.         ((A -> ((B and C) -> B)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-134, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-4543
in-theory        4543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-134 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4543.         ((A -> ((B and C) -> B)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-134, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-4544
in-theory        4544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-134 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4544.         ((A -> ((B and C) -> B)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-134, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-4545
in-theory        4545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4545.         ((A -> ((B and C) -> B)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-134, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-4546
in-theory        4546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-134 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4546.         ((A -> ((B and C) -> B)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-134, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-4547
in-theory        4547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-134 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4547.         ((A -> ((B and C) -> B)) and (D or (E -> ((F and G) -> F)))), M:tm-134, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4548
in-theory        4548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4548.         ((A -> ((B and C) -> B)) and ((D -> ((E and F) -> E)) or G)), M:tm-134, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-4549
in-theory        4549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4549.         ((A -> ((B and C) -> B)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-134, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4550
in-theory        4550
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> ((E and F) -> E)) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-134 ((Am (-> (and A B) A)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4550.         ((A or ((B and C) -> B)) -> ((D -> ((E and F) -> E)) and ((B and C) -> B))), M:tm-131, m:tm-134, u:((Am (-> (and A B) A)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> (and A B) A))))
================================================================
tm-name          tm-4551
in-theory        4551
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4551.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-125, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4552
in-theory        4552
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> ((E and F) -> E)) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-134 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4552.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> ((E and F) -> E)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-134, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-4553
in-theory        4553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G and H) -> G)) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4553.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G and H) -> G)) and E))), M:tm-113, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4554
in-theory        4554
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> ((F and G) -> F)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-134 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4554.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> ((F and G) -> F)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-134, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-4555
in-theory        4555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4555.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-105, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4556
in-theory        4556
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> ((E and F) -> E)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-134 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4556.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> ((E and F) -> E)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-134, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-4557
in-theory        4557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> ((E and F) -> E)) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4557.         (((A -> B) -> (A -> A)) and (C -> ((D -> ((E and F) -> E)) and C))), M:tm-95, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4558
in-theory        4558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> ((D and E) -> D)) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-134 ((Am (-> A A)) (B (and (-> Bm (-> (and Cm Dm) Cm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4558.         (((A -> B) or (A -> A)) -> ((C -> ((D and E) -> D)) and (A -> A))), M:tm-92, m:tm-134, u:((Am (-> A A)) (B (and (-> Bm (-> (and Cm Dm) Cm)) (-> A A))))
================================================================
tm-name          tm-4559
in-theory        4559
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> ((D and E) -> D)) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4559.         (A -> (B -> ((C -> ((D and E) -> D)) and A))), M:tm-84, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-4560
in-theory        4560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4560.         ((A -> (B -> (C -> B))) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-83, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4561
in-theory        4561
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> ((E and F) -> E)) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-134 ((Am (-> A (-> B A))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4561.         ((A or (B -> (C -> B))) -> ((D -> ((E and F) -> E)) and (B -> (C -> B)))), M:tm-80, m:tm-134, u:((Am (-> A (-> B A))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (-> B A)))))
================================================================
tm-name          tm-4562
in-theory        4562
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> ((D and E) -> D)) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-10 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4562.         (((not (not A)) -> A) and (B -> ((C -> ((D and E) -> D)) and B))), M:tm-76, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4563
in-theory        4563
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> ((C and D) -> C)) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4563.         (((not (not A)) or A) -> ((B -> ((C and D) -> C)) and A)), M:tm-73, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-4564
in-theory        4564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> ((E and F) -> E)) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4564.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> ((E and F) -> E)) and C))), M:tm-69, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4565
in-theory        4565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> ((D and E) -> D)) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-134 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4565.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> ((D and E) -> D)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-134, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-4566
in-theory        4566
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4566.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-54, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4567
in-theory        4567
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((E and F) -> E)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-134 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4567.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((E and F) -> E)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-134, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-4568
in-theory        4568
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> ((D and E) -> D)) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-134 ((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4568.         ((A or (B or A)) -> ((C -> ((D and E) -> D)) and (B or A))), M:tm-50, m:tm-134, u:((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (or A B))))
================================================================
tm-name          tm-4569
in-theory        4569
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> ((D and E) -> D)) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-134 ((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4569.         ((A or (A or B)) -> ((C -> ((D and E) -> D)) and (A or B))), M:tm-49, m:tm-134, u:((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (or A B))))
================================================================
tm-name          tm-4570
in-theory        4570
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> ((D and E) -> D)) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-134 ((Am (-> A (and B A))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4570.         ((A or (B -> (A and B))) -> ((C -> ((D and E) -> D)) and (B -> (A and B)))), M:tm-48, m:tm-134, u:((Am (-> A (and B A))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (and B A)))))
================================================================
tm-name          tm-4571
in-theory        4571
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> ((D and E) -> D)) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4571.         (((A and B) or B) -> ((C -> ((D and E) -> D)) and B)), M:tm-47, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-4572
in-theory        4572
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> ((D and E) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4572.         (((A and B) or A) -> ((C -> ((D and E) -> D)) and A)), M:tm-46, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-4573
in-theory        4573
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E and F) -> E)) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-134 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4573.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E and F) -> E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-134, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-4574
in-theory        4574
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> ((D and E) -> D)) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-134 ((Am (-> A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4574.         ((A or (B -> A)) -> ((C -> ((D and E) -> D)) and (B -> A))), M:tm-44, m:tm-134, u:((Am (-> A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A B))))
================================================================
tm-name          tm-4575
in-theory        4575
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> ((E and F) -> E)) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4575.         ((A -> (B or A)) and (C -> ((D -> ((E and F) -> E)) and C))), M:tm-42, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4576
in-theory        4576
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> ((E and F) -> E)) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4576.         ((A -> (A or B)) and (C -> ((D -> ((E and F) -> E)) and C))), M:tm-32, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4577
in-theory        4577
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> ((C and D) -> C)) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4577.         (A -> (A and ((B -> ((C and D) -> C)) and A))), M:tm-24, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-4578
in-theory        4578
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> ((E and F) -> E)) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4578.         ((A -> (B -> (A and B))) and (C -> ((D -> ((E and F) -> E)) and C))), M:tm-23, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4579
in-theory        4579
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> ((E and F) -> E)) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4579.         (((A and B) -> B) and (C -> ((D -> ((E and F) -> E)) and C))), M:tm-22, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4580
in-theory        4580
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> ((E and F) -> E)) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4580.         (((A and B) -> A) and (C -> ((D -> ((E and F) -> E)) and C))), M:tm-21, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4581
in-theory        4581
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4581.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-20, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4582
in-theory        4582
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> ((E and F) -> E)) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4582.         ((A -> (B -> A)) and (C -> ((D -> ((E and F) -> E)) and C))), M:tm-19, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4583
in-theory        4583
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> ((C and D) -> C)) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-9 tm-5 tm-1 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4583.         ((A -> (not ((B -> ((C and D) -> C)) and A))) -> (not A)), M:tm-9, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-4584
in-theory        4584
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> ((B and C) -> B)) and D) -> E) -> ((D or ((A -> ((B and C) -> B)) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4584.         ((((A -> ((B and C) -> B)) and D) -> E) -> ((D or ((A -> ((B and C) -> B)) and D)) -> E)), M:tm-8, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-4585
in-theory        4585
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> ((D and E) -> D)) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-7 tm-5 tm-1 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4585.         (A or (B -> ((C -> ((D and E) -> D)) and B))), M:tm-7, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4586
in-theory        4586
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-6 tm-5 tm-1 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4586.         ((A -> ((B -> ((C and D) -> C)) and A)) or E), M:tm-6, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4587
in-theory        4587
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> ((D and E) -> D)) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4587.         (A -> ((B -> ((C -> ((D and E) -> D)) and B)) and A)), M:tm-5, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4588
in-theory        4588
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> ((D and E) -> D)) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4588.         (A -> (B -> ((C -> ((D and E) -> D)) and B))), M:tm-1, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-4589
in-theory        4589
times-derived    2
----------------------------------------------------------------
theorem          ((A and (B and C)) -> B)
theorem-size     7
proof            (modus-ponens tm-135 tm-4 ((A (and Am (and B C))) (Bm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4.            ((A and B) -> B), axiom
tm-4589.         ((A and (B and C)) -> B), M:tm-135, m:tm-4, u:((A (and Am (and B C))) (Bm (and B C)))
================================================================
tm-name          tm-4590
in-theory        4590
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (A and B))) -> A)
theorem-size     7
proof            (modus-ponens tm-135 tm-10 ((A (not (not (and B C)))) (Am (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-4590.         ((not (not (A and B))) -> A), M:tm-135, m:tm-10, u:((A (not (not (and B C)))) (Am (and B C)))
================================================================
tm-name          tm-4591
in-theory        4591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) and A) -> B)
theorem-size     9
proof            (modus-ponens tm-135 tm-116 ((A (and (-> Am (and B C)) Am)) (Bm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-4591.         (((A -> (B and C)) and A) -> B), M:tm-135, m:tm-116, u:((A (and (-> Am (and B C)) Am)) (Bm (and B C)))
================================================================
tm-name          tm-4592
in-theory        4592
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> (C and D)) and E) -> C)
theorem-size     13
proof            (modus-ponens tm-135 tm-117 ((A (and (-> (-> Am (-> Bm Am)) (and B C)) Dm)) (Cm (and B C))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-4592.         ((((A -> (B -> A)) -> (C and D)) and E) -> C), M:tm-135, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) (and B C)) Dm)) (Cm (and B C)))
================================================================
tm-name          tm-4593
in-theory        4593
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D and E)) and F) -> D)
theorem-size     21
proof            (modus-ponens tm-135 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and B C)) Em)) (Dm (and B C))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4593.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D and E)) and F) -> D), M:tm-135, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and B C)) Em)) (Dm (and B C)))
================================================================
tm-name          tm-4594
in-theory        4594
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> (C and D)) and E) -> C)
theorem-size     13
proof            (modus-ponens tm-135 tm-128 ((A (and (-> (-> (and Am Bm) Am) (and B C)) Dm)) (Cm (and B C))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4594.         (((((A and B) -> A) -> (C and D)) and E) -> C), M:tm-135, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) (and B C)) Dm)) (Cm (and B C)))
================================================================
tm-name          tm-4595
in-theory        4595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-134 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4595.         ((A -> ((B and C) -> B)) and ((D -> (E and F)) -> (D -> E))), M:tm-134, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4596
in-theory        4596
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) and D) -> (B and C))) -> (((B and C) and D) -> B))
theorem-size     19
proof            (modus-ponens tm-131 tm-135 ((Am (and (and Bm Cm) B)) (A (and Bm Cm)) (C (-> (and (and Bm Cm) B) Bm))))
axioms-used      (tm-8 tm-1 tm-3 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4596.         ((A or (((B and C) and D) -> (B and C))) -> (((B and C) and D) -> B)), M:tm-131, m:tm-135, u:((Am (and (and Bm Cm) B)) (A (and Bm Cm)) (C (-> (and (and Bm Cm) B) Bm)))
================================================================
tm-name          tm-4597
in-theory        4597
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     25
proof            (modus-ponens tm-125 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4597.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E and F)) -> (D -> E))), M:tm-125, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4598
in-theory        4598
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and C)) and D) -> A) or (((A -> (B and C)) and D) -> (B and C))) -> (((A -> (B and C)) and D) -> B))
theorem-size     31
proof            (modus-ponens tm-122 tm-135 ((Am (and (-> A (and Bm Cm)) C)) (B (and Bm Cm)) (D (-> (and (-> A (and Bm Cm)) C) Bm))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4598.         (((((A -> (B and C)) and D) -> A) or (((A -> (B and C)) and D) -> (B and C))) -> (((A -> (B and C)) and D) -> B)), M:tm-122, m:tm-135, u:((Am (and (-> A (and Bm Cm)) C)) (B (and Bm Cm)) (D (-> (and (-> A (and Bm Cm)) C) Bm)))
================================================================
tm-name          tm-4599
in-theory        4599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) and D)) -> ((A -> B) -> (A -> C)))
theorem-size     15
proof            (modus-ponens tm-114 tm-135 ((A (-> Am (and (-> C D) Cm))) (B Am) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4599.         ((A -> ((B -> C) and D)) -> ((A -> B) -> (A -> C))), M:tm-114, m:tm-135, u:((A (-> Am (and (-> C D) Cm))) (B Am) (Bm (-> C D)))
================================================================
tm-name          tm-4600
in-theory        4600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F and G)) -> (E -> F)))
theorem-size     25
proof            (modus-ponens tm-113 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4600.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F and G)) -> (E -> F))), M:tm-113, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4601
in-theory        4601
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E and F)) -> (D -> E)))
theorem-size     29
proof            (modus-ponens tm-105 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4601.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E and F)) -> (D -> E))), M:tm-105, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4602
in-theory        4602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D and E)) -> (C -> D)))
theorem-size     17
proof            (modus-ponens tm-95 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4602.         (((A -> B) -> (A -> A)) and ((C -> (D and E)) -> (C -> D))), M:tm-95, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4603
in-theory        4603
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> C) or ((A and B) -> (A and B))) -> ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-92 tm-135 ((Am (and Bm Cm)) (A (and Bm Cm)) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4603.         ((((A and B) -> C) or ((A and B) -> (A and B))) -> ((A and B) -> A)), M:tm-92, m:tm-135, u:((Am (and Bm Cm)) (A (and Bm Cm)) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-4604
in-theory        4604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> (D -> (A -> B)))
theorem-size     11
proof            (modus-ponens tm-84 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4604.         ((A -> (B and C)) -> (D -> (A -> B))), M:tm-84, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-4605
in-theory        4605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-83 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4605.         ((A -> (B -> (C -> B))) and ((D -> (E and F)) -> (D -> E))), M:tm-83, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4606
in-theory        4606
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C and D)) -> (B -> C)))
theorem-size     15
proof            (modus-ponens tm-76 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4606.         (((not (not A)) -> A) and ((B -> (C and D)) -> (B -> C))), M:tm-76, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4607
in-theory        4607
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (B and C)))) or (A -> (B and C))) -> (A -> B))
theorem-size     17
proof            (modus-ponens tm-73 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4607.         (((not (not (A -> (B and C)))) or (A -> (B and C))) -> (A -> B)), M:tm-73, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-4608
in-theory        4608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D and E)) -> (C -> D)))
theorem-size     21
proof            (modus-ponens tm-69 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4608.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D and E)) -> (C -> D))), M:tm-69, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4609
in-theory        4609
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) -> (((A and B) or (A and B)) -> A))
theorem-size     17
proof            (modus-ponens tm-55 tm-135 ((A (and Bm Cm)) (Am (and Bm Cm)) (B (and Bm Cm)) (C Bm)))
axioms-used      (tm-2 tm-8 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4609.         (((A and B) -> (A and B)) -> (((A and B) or (A and B)) -> A)), M:tm-55, m:tm-135, u:((A (and Bm Cm)) (Am (and Bm Cm)) (B (and Bm Cm)) (C Bm))
================================================================
tm-name          tm-4610
in-theory        4610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E and F)) -> (D -> E)))
theorem-size     23
proof            (modus-ponens tm-54 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4610.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E and F)) -> (D -> E))), M:tm-54, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4611
in-theory        4611
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (B -> A))
theorem-size     11
proof            (modus-ponens tm-48 tm-135 ((Cm Am) (B Bm) (A Am) (C (-> Am Bm))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4611.         ((A or (B -> (A and B))) -> (B -> A)), M:tm-48, m:tm-135, u:((Cm Am) (B Bm) (A Am) (C (-> Am Bm)))
================================================================
tm-name          tm-4612
in-theory        4612
times-derived    2
----------------------------------------------------------------
theorem          (((A and (B -> (C and D))) or (B -> (C and D))) -> (B -> C))
theorem-size     17
proof            (modus-ponens tm-47 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4612.         (((A and (B -> (C and D))) or (B -> (C and D))) -> (B -> C)), M:tm-47, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-4613
in-theory        4613
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B and C)) and D) or (A -> (B and C))) -> (A -> B))
theorem-size     17
proof            (modus-ponens tm-46 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4613.         ((((A -> (B and C)) and D) or (A -> (B and C))) -> (A -> B)), M:tm-46, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-4614
in-theory        4614
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or (C -> (A and B))) -> (C -> A))
theorem-size     13
proof            (modus-ponens tm-44 tm-135 ((A Am) (B (and Bm Cm)) (C (-> Am Bm))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4614.         (((A and B) or (C -> (A and B))) -> (C -> A)), M:tm-44, m:tm-135, u:((A Am) (B (and Bm Cm)) (C (-> Am Bm)))
================================================================
tm-name          tm-4615
in-theory        4615
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D and E)) -> (C -> D)))
theorem-size     15
proof            (modus-ponens tm-42 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4615.         ((A -> (B or A)) and ((C -> (D and E)) -> (C -> D))), M:tm-42, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4616
in-theory        4616
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D and E)) -> (C -> D)))
theorem-size     15
proof            (modus-ponens tm-32 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4616.         ((A -> (A or B)) and ((C -> (D and E)) -> (C -> D))), M:tm-32, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4617
in-theory        4617
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> ((A -> (B and C)) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-24 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4617.         ((A -> (B and C)) -> ((A -> (B and C)) and (A -> B))), M:tm-24, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-4618
in-theory        4618
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D and E)) -> (C -> D)))
theorem-size     17
proof            (modus-ponens tm-23 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4618.         ((A -> (B -> (A and B))) and ((C -> (D and E)) -> (C -> D))), M:tm-23, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4619
in-theory        4619
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D and E)) -> (C -> D)))
theorem-size     15
proof            (modus-ponens tm-22 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4619.         (((A and B) -> B) and ((C -> (D and E)) -> (C -> D))), M:tm-22, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4620
in-theory        4620
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D and E)) -> (C -> D)))
theorem-size     15
proof            (modus-ponens tm-21 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4620.         (((A and B) -> A) and ((C -> (D and E)) -> (C -> D))), M:tm-21, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4621
in-theory        4621
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E and F)) -> (D -> E)))
theorem-size     23
proof            (modus-ponens tm-20 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4621.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E and F)) -> (D -> E))), M:tm-20, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4622
in-theory        4622
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D and E)) -> (C -> D)))
theorem-size     15
proof            (modus-ponens tm-19 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4622.         ((A -> (B -> A)) and ((C -> (D and E)) -> (C -> D))), M:tm-19, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4623
in-theory        4623
times-derived    4
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> (A -> (B and C)))
theorem-size     11
proof            (modus-ponens tm-12 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4623.         ((A -> (B and C)) -> (A -> (B and C))), M:tm-12, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-4624
in-theory        4624
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (not (A -> B))) -> (not (A -> (B and C))))
theorem-size     17
proof            (modus-ponens tm-9 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-9 tm-2 tm-1 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4624.         (((A -> (B and C)) -> (not (A -> B))) -> (not (A -> (B and C)))), M:tm-9, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-4625
in-theory        4625
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (((A -> (B and D)) or (A -> B)) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4625.         (((A -> B) -> C) -> (((A -> (B and D)) or (A -> B)) -> C)), M:tm-8, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-4626
in-theory        4626
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> (C and D)) -> (B -> C)))
theorem-size     11
proof            (modus-ponens tm-7 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-7 tm-2 tm-1 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4626.         (A or ((B -> (C and D)) -> (B -> C))), M:tm-7, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4627
in-theory        4627
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-6 tm-2 tm-1 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4627.         (((A -> (B and C)) -> (A -> B)) or D), M:tm-6, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4628
in-theory        4628
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (C and D)) -> (B -> C)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4628.         (A -> (((B -> (C and D)) -> (B -> C)) and A)), M:tm-5, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4629
in-theory        4629
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> A) -> ((A -> (B and C)) -> B))
theorem-size     15
proof            (modus-ponens tm-2 tm-135 ((A (-> Am (and Bm Cm))) (B Am) (C Bm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4629.         (((A -> (B and C)) -> A) -> ((A -> (B and C)) -> B)), M:tm-2, m:tm-135, u:((A (-> Am (and Bm Cm))) (B Am) (C Bm))
================================================================
tm-name          tm-4630
in-theory        4630
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> (C and D)) -> (B -> C)))
theorem-size     11
proof            (modus-ponens tm-1 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-1 tm-2 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4630.         (A -> ((B -> (C and D)) -> (B -> C))), M:tm-1, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-4631
in-theory        4631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-134 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4631.         ((A -> ((B and C) -> B)) and (D -> (E -> ((F and G) -> F)))), M:tm-134, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4632
in-theory        4632
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-131 tm-136 ((Am (-> (and A B) A)) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4632.         ((A or ((B and C) -> B)) -> (D -> ((E and F) -> E))), M:tm-131, m:tm-136, u:((Am (-> (and A B) A)) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4633
in-theory        4633
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> ((C and D) -> C))
theorem-size     9
proof            (modus-ponens tm-129 tm-136 ((Am (and Bm B)) (A Bm) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4633.         ((A and B) -> ((C and D) -> C)), M:tm-129, m:tm-136, u:((Am (and Bm B)) (A Bm) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-4634
in-theory        4634
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-125 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4634.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> ((F and G) -> F)))), M:tm-125, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4635
in-theory        4635
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-122 tm-136 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4635.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((E and F) -> E))), M:tm-122, m:tm-136, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4636
in-theory        4636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and C) -> B)) -> D) and E) -> (A -> ((B and C) -> B)))
theorem-size     19
proof            (modus-ponens tm-120 tm-136 ((Am (and (-> (-> Bm (-> (and Cm Dm) Cm)) B) C)) (A (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4636.         ((((A -> ((B and C) -> B)) -> D) and E) -> (A -> ((B and C) -> B))), M:tm-120, m:tm-136, u:((Am (and (-> (-> Bm (-> (and Cm Dm) Cm)) B) C)) (A (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4637
in-theory        4637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and C) -> B)) -> A) and D) -> ((B and C) -> B))
theorem-size     17
proof            (modus-ponens tm-119 tm-136 ((Am (and (-> (-> Bm (-> (and Cm Dm) Cm)) Bm) C)) (A Bm) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4637.         ((((A -> ((B and C) -> B)) -> A) and D) -> ((B and C) -> B)), M:tm-119, m:tm-136, u:((Am (and (-> (-> Bm (-> (and Cm Dm) Cm)) Bm) C)) (A Bm) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-4638
in-theory        4638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-113 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4638.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G and H) -> G)))), M:tm-113, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4639
in-theory        4639
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-110 tm-136 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4639.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((F and G) -> F))), M:tm-110, m:tm-136, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4640
in-theory        4640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((D and E) -> D))
theorem-size     11
proof            (modus-ponens tm-108 tm-136 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4640.         ((A -> (B -> C)) -> ((D and E) -> D)), M:tm-108, m:tm-136, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-4641
in-theory        4641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) -> (A -> (B and C))) -> (A -> B))
theorem-size     17
proof            (modus-ponens tm-106 tm-136 ((Am (-> (-> Bm (-> (and Cm Dm) Cm)) (-> Bm (and Cm Dm)))) (A Bm) (B (and Cm Dm)) (C Cm)))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4641.         (((A -> ((B and C) -> B)) -> (A -> (B and C))) -> (A -> B)), M:tm-106, m:tm-136, u:((Am (-> (-> Bm (-> (and Cm Dm) Cm)) (-> Bm (and Cm Dm)))) (A Bm) (B (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-4642
in-theory        4642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> ((F and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-105 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4642.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> ((F and G) -> F)))), M:tm-105, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4643
in-theory        4643
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((E and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-102 tm-136 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4643.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((E and F) -> E))), M:tm-102, m:tm-136, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4644
in-theory        4644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) -> D)) -> (A -> ((B and C) -> B)))
theorem-size     17
proof            (modus-ponens tm-100 tm-136 ((Am (-> Bm (-> (-> (and Cm Dm) Cm) C))) (A Bm) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4644.         ((A -> (((B and C) -> B) -> D)) -> (A -> ((B and C) -> B))), M:tm-100, m:tm-136, u:((Am (-> Bm (-> (-> (and Cm Dm) Cm) C))) (A Bm) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-4645
in-theory        4645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) -> D) -> (A -> ((B and C) -> B)))
theorem-size     17
proof            (modus-ponens tm-96 tm-136 ((Am (-> (-> Bm (-> (and Cm Dm) Cm)) B)) (A (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4645.         (((A -> ((B and C) -> B)) -> D) -> (A -> ((B and C) -> B))), M:tm-96, m:tm-136, u:((Am (-> (-> Bm (-> (and Cm Dm) Cm)) B)) (A (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4646
in-theory        4646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-95 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4646.         (((A -> B) -> (A -> A)) and (C -> (D -> ((E and F) -> E)))), M:tm-95, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4647
in-theory        4647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> ((D and E) -> D)))
theorem-size     15
proof            (modus-ponens tm-92 tm-136 ((Am (-> A A)) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4647.         (((A -> B) or (A -> A)) -> (C -> ((D and E) -> D))), M:tm-92, m:tm-136, u:((Am (-> A A)) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4648
in-theory        4648
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C -> ((D and E) -> D))))
theorem-size     11
proof            (modus-ponens tm-84 tm-136 ((A Am) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4648.         (A -> (B -> (C -> ((D and E) -> D)))), M:tm-84, m:tm-136, u:((A Am) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4649
in-theory        4649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-83 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4649.         ((A -> (B -> (C -> B))) and (D -> (E -> ((F and G) -> F)))), M:tm-83, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4650
in-theory        4650
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-80 tm-136 ((Am (-> A (-> B A))) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4650.         ((A or (B -> (C -> B))) -> (D -> ((E and F) -> E))), M:tm-80, m:tm-136, u:((Am (-> A (-> B A))) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4651
in-theory        4651
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> ((B and C) -> B)) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-136 ((Am (not (not (-> (-> Bm (-> (and Cm Dm) Cm)) B)))) (A (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4651.         ((not (not ((A -> ((B and C) -> B)) -> D))) -> D), M:tm-77, m:tm-136, u:((Am (not (not (-> (-> Bm (-> (and Cm Dm) Cm)) B)))) (A (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4652
in-theory        4652
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> ((D and E) -> D))))
theorem-size     15
proof            (modus-ponens tm-76 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4652.         (((not (not A)) -> A) and (B -> (C -> ((D and E) -> D)))), M:tm-76, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4653
in-theory        4653
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> ((C and D) -> C)))
theorem-size     13
proof            (modus-ponens tm-73 tm-136 ((A Am) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4653.         (((not (not A)) or A) -> (B -> ((C and D) -> C))), M:tm-73, m:tm-136, u:((A Am) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4654
in-theory        4654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> ((E and F) -> E))))
theorem-size     21
proof            (modus-ponens tm-69 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4654.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> ((E and F) -> E)))), M:tm-69, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4655
in-theory        4655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((D and E) -> D)))
theorem-size     19
proof            (modus-ponens tm-66 tm-136 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4655.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((D and E) -> D))), M:tm-66, m:tm-136, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4656
in-theory        4656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> ((C and D) -> C)))
theorem-size     13
proof            (modus-ponens tm-55 tm-136 ((Am (-> A Bm)) (B Bm) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-8 tm-1 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4656.         ((A -> B) -> ((A or B) -> ((C and D) -> C))), M:tm-55, m:tm-136, u:((Am (-> A Bm)) (B Bm) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-4657
in-theory        4657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-54 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4657.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> ((F and G) -> F)))), M:tm-54, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4658
in-theory        4658
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-51 tm-136 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4658.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E and F) -> E))), M:tm-51, m:tm-136, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4659
in-theory        4659
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-50 tm-136 ((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4659.         ((A or (B or A)) -> (C -> ((D and E) -> D))), M:tm-50, m:tm-136, u:((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4660
in-theory        4660
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-49 tm-136 ((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4660.         ((A or (A or B)) -> (C -> ((D and E) -> D))), M:tm-49, m:tm-136, u:((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4661
in-theory        4661
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D and E) -> D)))
theorem-size     15
proof            (modus-ponens tm-48 tm-136 ((Am (-> A (and B A))) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4661.         ((A or (B -> (A and B))) -> (C -> ((D and E) -> D))), M:tm-48, m:tm-136, u:((Am (-> A (and B A))) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4662
in-theory        4662
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-47 tm-136 ((A Am) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4662.         (((A and B) or B) -> (C -> ((D and E) -> D))), M:tm-47, m:tm-136, u:((A Am) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4663
in-theory        4663
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-46 tm-136 ((A Am) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4663.         (((A and B) or A) -> (C -> ((D and E) -> D))), M:tm-46, m:tm-136, u:((A Am) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4664
in-theory        4664
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-45 tm-136 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4664.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E and F) -> E))), M:tm-45, m:tm-136, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4665
in-theory        4665
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-44 tm-136 ((Am (-> A B)) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4665.         ((A or (B -> A)) -> (C -> ((D and E) -> D))), M:tm-44, m:tm-136, u:((Am (-> A B)) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4666
in-theory        4666
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-42 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4666.         ((A -> (B or A)) and (C -> (D -> ((E and F) -> E)))), M:tm-42, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4667
in-theory        4667
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-32 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4667.         ((A -> (A or B)) and (C -> (D -> ((E and F) -> E)))), M:tm-32, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4668
in-theory        4668
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B -> ((C and D) -> C))))
theorem-size     11
proof            (modus-ponens tm-24 tm-136 ((A Am) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4668.         (A -> (A and (B -> ((C and D) -> C)))), M:tm-24, m:tm-136, u:((A Am) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4669
in-theory        4669
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-23 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4669.         ((A -> (B -> (A and B))) and (C -> (D -> ((E and F) -> E)))), M:tm-23, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4670
in-theory        4670
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-22 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4670.         (((A and B) -> B) and (C -> (D -> ((E and F) -> E)))), M:tm-22, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4671
in-theory        4671
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-21 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4671.         (((A and B) -> A) and (C -> (D -> ((E and F) -> E)))), M:tm-21, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4672
in-theory        4672
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-20 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4672.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> ((F and G) -> F)))), M:tm-20, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4673
in-theory        4673
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-19 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4673.         ((A -> (B -> A)) and (C -> (D -> ((E and F) -> E)))), M:tm-19, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4674
in-theory        4674
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> ((C and D) -> C)) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-136 ((Am (and A (-> (-> Bm (-> (and Cm Dm) Cm)) C))) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4674.         ((A and ((B -> ((C and D) -> C)) -> E)) -> E), M:tm-17, m:tm-136, u:((Am (and A (-> (-> Bm (-> (and Cm Dm) Cm)) C))) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4675
in-theory        4675
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> ((B and C) -> B)) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-136 ((Am (and (-> (-> Bm (-> (and Cm Dm) Cm)) B) C)) (A (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-3 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4675.         ((((A -> ((B and C) -> B)) -> D) and E) -> D), M:tm-15, m:tm-136, u:((Am (and (-> (-> Bm (-> (and Cm Dm) Cm)) B) C)) (A (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4676
in-theory        4676
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) -> D)) -> (A -> D))
theorem-size     13
proof            (modus-ponens tm-13 tm-136 ((Am (-> Bm (-> (-> (and Cm Dm) Cm) C))) (A Bm) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4676.         ((A -> (((B and C) -> B) -> D)) -> (A -> D)), M:tm-13, m:tm-136, u:((Am (-> Bm (-> (-> (and Cm Dm) Cm) C))) (A Bm) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-4677
in-theory        4677
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B -> ((C and D) -> C)))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-136 ((A Am) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-9 tm-1 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4677.         ((A -> (not (B -> ((C and D) -> C)))) -> (not A)), M:tm-9, m:tm-136, u:((A Am) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4678
in-theory        4678
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) -> D) -> ((E or (A -> ((B and C) -> B))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-136 ((A Am) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4678.         (((A -> ((B and C) -> B)) -> D) -> ((E or (A -> ((B and C) -> B))) -> D)), M:tm-8, m:tm-136, u:((A Am) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4679
in-theory        4679
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C -> ((D and E) -> D))))
theorem-size     11
proof            (modus-ponens tm-7 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-7 tm-1 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4679.         (A or (B -> (C -> ((D and E) -> D)))), M:tm-7, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4680
in-theory        4680
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-6 tm-1 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4680.         ((A -> (B -> ((C and D) -> C))) or E), M:tm-6, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4681
in-theory        4681
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> ((D and E) -> D))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4681.         (A -> ((B -> (C -> ((D and E) -> D))) and A)), M:tm-5, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-4682
in-theory        4682
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> ((C and D) -> C)))
theorem-size     11
proof            (modus-ponens tm-2 tm-136 ((A Am) (B Bm) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4682.         ((A -> B) -> (A -> ((C and D) -> C))), M:tm-2, m:tm-136, u:((A Am) (B Bm) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-4683
in-theory        4683
times-derived    1
----------------------------------------------------------------
theorem          ((A and (A -> (B and C))) -> B)
theorem-size     9
proof            (modus-ponens tm-135 tm-137 ((A (and Am (-> Am (and B C)))) (Bm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4683.         ((A and (A -> (B and C))) -> B), M:tm-135, m:tm-137, u:((A (and Am (-> Am (and B C)))) (Bm (and B C)))
================================================================
tm-name          tm-4684
in-theory        4684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-134 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4684.         ((A -> ((B and C) -> B)) and ((D and (D -> E)) -> E)), M:tm-134, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4685
in-theory        4685
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (A -> (not ((B and C) -> B)))))
theorem-size     11
proof            (modus-ponens tm-130 tm-137 ((A (and Am (-> Am (not (-> (and B C) B))))) (Bm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4685.         (not (A and (A -> (not ((B and C) -> B))))), M:tm-130, m:tm-137, u:((A (and Am (-> Am (not (-> (and B C) B))))) (Bm (not (-> (and B C) B))))
================================================================
tm-name          tm-4686
in-theory        4686
times-derived    1
----------------------------------------------------------------
theorem          ((A and (A -> (A -> B))) -> B)
theorem-size     9
proof            (modus-ponens tm-129 tm-137 ((A Am) (B (-> Am (-> Am C))) (Bm (-> Am C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4686.         ((A and (A -> (A -> B))) -> B), M:tm-129, m:tm-137, u:((A Am) (B (-> Am (-> Am C))) (Bm (-> Am C)))
================================================================
tm-name          tm-4687
in-theory        4687
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and (D -> E)) -> E))
theorem-size     23
proof            (modus-ponens tm-125 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4687.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and (D -> E)) -> E)), M:tm-125, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4688
in-theory        4688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and ((A -> B) -> A)) -> A)
theorem-size     11
proof            (modus-ponens tm-120 tm-137 ((Am (-> Bm B)) (C (-> (-> Bm B) Bm)) (A Bm)))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4688.         (((A -> B) and ((A -> B) -> A)) -> A), M:tm-120, m:tm-137, u:((Am (-> Bm B)) (C (-> (-> Bm B) Bm)) (A Bm))
================================================================
tm-name          tm-4689
in-theory        4689
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) and (((A -> B) -> A) -> (A -> B))) -> B)
theorem-size     17
proof            (modus-ponens tm-119 tm-137 ((Am (-> (-> A B) A)) (C (-> (-> (-> A B) A) (-> A B))) (Bm (-> A B))))
axioms-used      (tm-2 tm-3 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4689.         ((((A -> B) -> A) and (((A -> B) -> A) -> (A -> B))) -> B), M:tm-119, m:tm-137, u:((Am (-> (-> A B) A)) (C (-> (-> (-> A B) A) (-> A B))) (Bm (-> A B)))
================================================================
tm-name          tm-4690
in-theory        4690
times-derived    1
----------------------------------------------------------------
theorem          ((A and (A -> (B -> (C -> D)))) -> ((B -> C) -> (B -> D)))
theorem-size     17
proof            (modus-ponens tm-114 tm-137 ((A (and Am (-> Am (-> B (-> C D))))) (Bm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4690.         ((A and (A -> (B -> (C -> D)))) -> ((B -> C) -> (B -> D))), M:tm-114, m:tm-137, u:((A (and Am (-> Am (-> B (-> C D))))) (Bm (-> B (-> C D))))
================================================================
tm-name          tm-4691
in-theory        4691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (E -> F)) -> F))
theorem-size     23
proof            (modus-ponens tm-113 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4691.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (E -> F)) -> F)), M:tm-113, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4692
in-theory        4692
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))
theorem-size     19
proof            (modus-ponens tm-109 tm-137 ((A (and Am (-> Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4692.         (not (A and (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))), M:tm-109, m:tm-137, u:((A (and Am (-> Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-4693
in-theory        4693
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and (D -> E)) -> E))
theorem-size     27
proof            (modus-ponens tm-105 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4693.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and (D -> E)) -> E)), M:tm-105, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4694
in-theory        4694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C and (C -> D)) -> D))
theorem-size     15
proof            (modus-ponens tm-95 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4694.         (((A -> B) -> (A -> A)) and ((C and (C -> D)) -> D)), M:tm-95, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4695
in-theory        4695
times-derived    1
----------------------------------------------------------------
theorem          ((A and (A -> (B -> C))) -> (B -> C))
theorem-size     11
proof            (modus-ponens tm-87 tm-137 ((A (and Am (-> Am (-> B C)))) (Bm (-> B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4695.         ((A and (A -> (B -> C))) -> (B -> C)), M:tm-87, m:tm-137, u:((A (and Am (-> Am (-> B C)))) (Bm (-> B C)))
================================================================
tm-name          tm-4696
in-theory        4696
times-derived    1
----------------------------------------------------------------
theorem          ((A and (A -> B)) -> (C -> B))
theorem-size     9
proof            (modus-ponens tm-84 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4696.         ((A and (A -> B)) -> (C -> B)), M:tm-84, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-4697
in-theory        4697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-83 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4697.         ((A -> (B -> (C -> B))) and ((D and (D -> E)) -> E)), M:tm-83, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4698
in-theory        4698
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (A -> (not (B -> (C -> B))))))
theorem-size     11
proof            (modus-ponens tm-79 tm-137 ((A (and Am (-> Am (not (-> B (-> C B)))))) (Bm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4698.         (not (A and (A -> (not (B -> (C -> B)))))), M:tm-79, m:tm-137, u:((A (and Am (-> Am (not (-> B (-> C B)))))) (Bm (not (-> B (-> C B)))))
================================================================
tm-name          tm-4699
in-theory        4699
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B and (B -> C)) -> C))
theorem-size     13
proof            (modus-ponens tm-76 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-10 tm-2 tm-4 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4699.         (((not (not A)) -> A) and ((B and (B -> C)) -> C)), M:tm-76, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4700
in-theory        4700
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A and (A -> B)))) or (A and (A -> B))) -> B)
theorem-size     15
proof            (modus-ponens tm-73 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-8 tm-10 tm-2 tm-4 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4700.         (((not (not (A and (A -> B)))) or (A and (A -> B))) -> B), M:tm-73, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-4701
in-theory        4701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and (C -> D)) -> D))
theorem-size     19
proof            (modus-ponens tm-69 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-9 tm-2 tm-4 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4701.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and (C -> D)) -> D)), M:tm-69, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4702
in-theory        4702
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (A -> (not A))))
theorem-size     7
proof            (modus-ponens tm-59 tm-137 ((A Am) (B (-> Am (not Am))) (Bm (not Am))))
axioms-used      (tm-9 tm-3 tm-2 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4702.         (not (A and (A -> (not A)))), M:tm-59, m:tm-137, u:((A Am) (B (-> Am (not Am))) (Bm (not Am)))
================================================================
tm-name          tm-4703
in-theory        4703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and (D -> E)) -> E))
theorem-size     21
proof            (modus-ponens tm-54 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4703.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and (D -> E)) -> E)), M:tm-54, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4704
in-theory        4704
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and (B -> C))) or (B and (B -> C))) -> C)
theorem-size     15
proof            (modus-ponens tm-47 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-8 tm-4 tm-2 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4704.         (((A and (B and (B -> C))) or (B and (B -> C))) -> C), M:tm-47, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-4705
in-theory        4705
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (A -> B)) and C) or (A and (A -> B))) -> B)
theorem-size     15
proof            (modus-ponens tm-46 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-8 tm-3 tm-2 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4705.         ((((A and (A -> B)) and C) or (A and (A -> B))) -> B), M:tm-46, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-4706
in-theory        4706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C and (C -> D)) -> D))
theorem-size     13
proof            (modus-ponens tm-42 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4706.         ((A -> (B or A)) and ((C and (C -> D)) -> D)), M:tm-42, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4707
in-theory        4707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C and (C -> D)) -> D))
theorem-size     13
proof            (modus-ponens tm-32 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4707.         ((A -> (A or B)) and ((C and (C -> D)) -> D)), M:tm-32, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4708
in-theory        4708
times-derived    1
----------------------------------------------------------------
theorem          ((A and (A -> B)) -> ((A and (A -> B)) and B))
theorem-size     13
proof            (modus-ponens tm-24 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4708.         ((A and (A -> B)) -> ((A and (A -> B)) and B)), M:tm-24, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-4709
in-theory        4709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C and (C -> D)) -> D))
theorem-size     15
proof            (modus-ponens tm-23 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4709.         ((A -> (B -> (A and B))) and ((C and (C -> D)) -> D)), M:tm-23, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4710
in-theory        4710
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C and (C -> D)) -> D))
theorem-size     13
proof            (modus-ponens tm-22 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4710.         (((A and B) -> B) and ((C and (C -> D)) -> D)), M:tm-22, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4711
in-theory        4711
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C and (C -> D)) -> D))
theorem-size     13
proof            (modus-ponens tm-21 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4711.         (((A and B) -> A) and ((C and (C -> D)) -> D)), M:tm-21, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4712
in-theory        4712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and (D -> E)) -> E))
theorem-size     21
proof            (modus-ponens tm-20 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4712.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and (D -> E)) -> E)), M:tm-20, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4713
in-theory        4713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C and (C -> D)) -> D))
theorem-size     13
proof            (modus-ponens tm-19 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4713.         ((A -> (B -> A)) and ((C and (C -> D)) -> D)), M:tm-19, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4714
in-theory        4714
times-derived    2
----------------------------------------------------------------
theorem          ((A and (A -> A)) -> A)
theorem-size     7
proof            (modus-ponens tm-17 tm-137 ((A Am) (Bm Am) (C Am) (B Am)))
axioms-used      (tm-2 tm-4 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4714.         ((A and (A -> A)) -> A), M:tm-17, m:tm-137, u:((A Am) (Bm Am) (C Am) (B Am))
================================================================
tm-name          tm-4715
in-theory        4715
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) and ((A -> B) -> A)) -> B)
theorem-size     11
proof            (modus-ponens tm-15 tm-137 ((Am (-> Bm B)) (C (-> (-> Bm B) Bm)) (A Bm)))
axioms-used      (tm-2 tm-3 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4715.         (((A -> B) and ((A -> B) -> A)) -> B), M:tm-15, m:tm-137, u:((Am (-> Bm B)) (C (-> (-> Bm B) Bm)) (A Bm))
================================================================
tm-name          tm-4716
in-theory        4716
times-derived    1
----------------------------------------------------------------
theorem          ((A and (A -> B)) -> (A and (A -> B)))
theorem-size     11
proof            (modus-ponens tm-12 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4716.         ((A and (A -> B)) -> (A and (A -> B))), M:tm-12, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-4717
in-theory        4717
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> (not B)) -> (not (A and (A -> B))))
theorem-size     15
proof            (modus-ponens tm-9 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-9 tm-2 tm-4 tm-3)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4717.         (((A and (A -> B)) -> (not B)) -> (not (A and (A -> B)))), M:tm-9, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-4718
in-theory        4718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C and (C -> A)) or A) -> B))
theorem-size     13
proof            (modus-ponens tm-8 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-8 tm-2 tm-4 tm-3)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4718.         ((A -> B) -> (((C and (C -> A)) or A) -> B)), M:tm-8, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-4719
in-theory        4719
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B and (B -> C)) -> C))
theorem-size     9
proof            (modus-ponens tm-7 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-7 tm-2 tm-4 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4719.         (A or ((B and (B -> C)) -> C)), M:tm-7, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4720
in-theory        4720
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) or C)
theorem-size     9
proof            (modus-ponens tm-6 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-6 tm-2 tm-4 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4720.         (((A and (A -> B)) -> B) or C), M:tm-6, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4721
in-theory        4721
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (B -> C)) -> C) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4721.         (A -> (((B and (B -> C)) -> C) and A)), M:tm-5, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4722
in-theory        4722
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> (B -> C))) -> B) -> ((A and (A -> (B -> C))) -> C))
theorem-size     19
proof            (modus-ponens tm-2 tm-137 ((A (and Am (-> Am (-> B C)))) (Bm (-> B C))))
axioms-used      (tm-2 tm-4 tm-3)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4722.         (((A and (A -> (B -> C))) -> B) -> ((A and (A -> (B -> C))) -> C)), M:tm-2, m:tm-137, u:((A (and Am (-> Am (-> B C)))) (Bm (-> B C)))
================================================================
tm-name          tm-4723
in-theory        4723
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B and (B -> C)) -> C))
theorem-size     9
proof            (modus-ponens tm-1 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-1 tm-2 tm-4 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-4723.         (A -> ((B and (B -> C)) -> C)), M:tm-1, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-4724
in-theory        4724
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> (D and E))) -> D)
theorem-size     13
proof            (modus-ponens tm-135 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) (and B C)))) (Dm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4724.         ((A and ((B -> (C -> B)) -> (D and E))) -> D), M:tm-135, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) (and B C)))) (Dm (and B C)))
================================================================
tm-name          tm-4725
in-theory        4725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-134 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4725.         ((A -> ((B and C) -> B)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-134, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4726
in-theory        4726
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> B)) -> (not ((D and E) -> D)))))
theorem-size     15
proof            (modus-ponens tm-130 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) (not (-> (and B C) B))))) (Dm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4726.         (not (A and ((B -> (C -> B)) -> (not ((D and E) -> D))))), M:tm-130, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) (not (-> (and B C) B))))) (Dm (not (-> (and B C) B))))
================================================================
tm-name          tm-4727
in-theory        4727
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> (A -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-129 tm-138 ((A Am) (B (-> (-> Bm (-> Cm Bm)) (-> Am C))) (Dm (-> Am C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4727.         ((A and ((B -> (C -> B)) -> (A -> D))) -> D), M:tm-129, m:tm-138, u:((A Am) (B (-> (-> Bm (-> Cm Bm)) (-> Am C))) (Dm (-> Am C)))
================================================================
tm-name          tm-4728
in-theory        4728
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-125 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4728.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-125, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4729
in-theory        4729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and ((C -> (D -> C)) -> A)) -> A)
theorem-size     13
proof            (modus-ponens tm-120 tm-138 ((Am (-> Dm B)) (C (-> (-> Bm (-> Cm Bm)) Dm)) (A Dm)))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4729.         (((A -> B) and ((C -> (D -> C)) -> A)) -> A), M:tm-120, m:tm-138, u:((Am (-> Dm B)) (C (-> (-> Bm (-> Cm Bm)) Dm)) (A Dm))
================================================================
tm-name          tm-4730
in-theory        4730
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) and ((C -> (D -> C)) -> (A -> B))) -> B)
theorem-size     17
proof            (modus-ponens tm-119 tm-138 ((Am (-> (-> A B) A)) (C (-> (-> Bm (-> Cm Bm)) (-> A B))) (Dm (-> A B))))
axioms-used      (tm-2 tm-3 tm-4 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4730.         ((((A -> B) -> A) and ((C -> (D -> C)) -> (A -> B))) -> B), M:tm-119, m:tm-138, u:((Am (-> (-> A B) A)) (C (-> (-> Bm (-> Cm Bm)) (-> A B))) (Dm (-> A B)))
================================================================
tm-name          tm-4731
in-theory        4731
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> (D -> (E -> F)))) -> ((D -> E) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-114 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) (-> B (-> C D))))) (Dm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4731.         ((A and ((B -> (C -> B)) -> (D -> (E -> F)))) -> ((D -> E) -> (D -> F))), M:tm-114, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) (-> B (-> C D))))) (Dm (-> B (-> C D))))
================================================================
tm-name          tm-4732
in-theory        4732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (G -> F)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-113 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4732.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (G -> F)) -> H)) -> H)), M:tm-113, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4733
in-theory        4733
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> B)) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     23
proof            (modus-ponens tm-109 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Dm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4733.         (not (A and ((B -> (C -> B)) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-109, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Dm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-4734
in-theory        4734
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     31
proof            (modus-ponens tm-105 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4734.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-105, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4735
in-theory        4735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C and ((D -> (E -> D)) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-95 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4735.         (((A -> B) -> (A -> A)) and ((C and ((D -> (E -> D)) -> F)) -> F)), M:tm-95, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4736
in-theory        4736
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> (D -> E))) -> (D -> E))
theorem-size     15
proof            (modus-ponens tm-87 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4736.         ((A and ((B -> (C -> B)) -> (D -> E))) -> (D -> E)), M:tm-87, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-4737
in-theory        4737
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> D)) -> (E -> D))
theorem-size     13
proof            (modus-ponens tm-84 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4737.         ((A and ((B -> (C -> B)) -> D)) -> (E -> D)), M:tm-84, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-4738
in-theory        4738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-83 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4738.         ((A -> (B -> (C -> B))) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-83, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4739
in-theory        4739
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> B)) -> (not (D -> (E -> D))))))
theorem-size     15
proof            (modus-ponens tm-79 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) (not (-> B (-> C B)))))) (Dm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4739.         (not (A and ((B -> (C -> B)) -> (not (D -> (E -> D)))))), M:tm-79, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) (not (-> B (-> C B)))))) (Dm (not (-> B (-> C B)))))
================================================================
tm-name          tm-4740
in-theory        4740
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B and ((C -> (D -> C)) -> E)) -> E))
theorem-size     17
proof            (modus-ponens tm-76 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-10 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4740.         (((not (not A)) -> A) and ((B and ((C -> (D -> C)) -> E)) -> E)), M:tm-76, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4741
in-theory        4741
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A and ((B -> (C -> B)) -> D)))) or (A and ((B -> (C -> B)) -> D))) -> D)
theorem-size     23
proof            (modus-ponens tm-73 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-8 tm-10 tm-2 tm-4 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4741.         (((not (not (A and ((B -> (C -> B)) -> D)))) or (A and ((B -> (C -> B)) -> D))) -> D), M:tm-73, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-4742
in-theory        4742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and ((D -> (E -> D)) -> F)) -> F))
theorem-size     23
proof            (modus-ponens tm-69 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-9 tm-2 tm-4 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4742.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and ((D -> (E -> D)) -> F)) -> F)), M:tm-69, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4743
in-theory        4743
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> B)) -> (not A))))
theorem-size     11
proof            (modus-ponens tm-59 tm-138 ((A Am) (B (-> (-> Bm (-> Cm Bm)) (not Am))) (Dm (not Am))))
axioms-used      (tm-9 tm-3 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4743.         (not (A and ((B -> (C -> B)) -> (not A)))), M:tm-59, m:tm-138, u:((A Am) (B (-> (-> Bm (-> Cm Bm)) (not Am))) (Dm (not Am)))
================================================================
tm-name          tm-4744
in-theory        4744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-54 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4744.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-54, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4745
in-theory        4745
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and ((C -> (D -> C)) -> E))) or (B and ((C -> (D -> C)) -> E))) -> E)
theorem-size     23
proof            (modus-ponens tm-47 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4745.         (((A and (B and ((C -> (D -> C)) -> E))) or (B and ((C -> (D -> C)) -> E))) -> E), M:tm-47, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-4746
in-theory        4746
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> B)) -> D)) and E) or (A and ((B -> (C -> B)) -> D))) -> D)
theorem-size     23
proof            (modus-ponens tm-46 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-8 tm-3 tm-2 tm-4 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4746.         ((((A and ((B -> (C -> B)) -> D)) and E) or (A and ((B -> (C -> B)) -> D))) -> D), M:tm-46, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-4747
in-theory        4747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C and ((D -> (E -> D)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-42 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4747.         ((A -> (B or A)) and ((C and ((D -> (E -> D)) -> F)) -> F)), M:tm-42, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4748
in-theory        4748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C and ((D -> (E -> D)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-32 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4748.         ((A -> (A or B)) and ((C and ((D -> (E -> D)) -> F)) -> F)), M:tm-32, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4749
in-theory        4749
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> D)) -> ((A and ((B -> (C -> B)) -> D)) and D))
theorem-size     21
proof            (modus-ponens tm-24 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4749.         ((A and ((B -> (C -> B)) -> D)) -> ((A and ((B -> (C -> B)) -> D)) and D)), M:tm-24, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-4750
in-theory        4750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C and ((D -> (E -> D)) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-23 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4750.         ((A -> (B -> (A and B))) and ((C and ((D -> (E -> D)) -> F)) -> F)), M:tm-23, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4751
in-theory        4751
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C and ((D -> (E -> D)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-22 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4751.         (((A and B) -> B) and ((C and ((D -> (E -> D)) -> F)) -> F)), M:tm-22, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4752
in-theory        4752
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C and ((D -> (E -> D)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-21 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4752.         (((A and B) -> A) and ((C and ((D -> (E -> D)) -> F)) -> F)), M:tm-21, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4753
in-theory        4753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-20 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4753.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-20, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4754
in-theory        4754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C and ((D -> (E -> D)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-19 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4754.         ((A -> (B -> A)) and ((C and ((D -> (E -> D)) -> F)) -> F)), M:tm-19, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4755
in-theory        4755
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> (B -> (C -> B)))) -> (B -> (C -> B)))
theorem-size     19
proof            (modus-ponens tm-17 tm-138 ((A Am) (Dm (-> Bm (-> Cm Bm))) (C (-> Bm (-> Cm Bm))) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4755.         ((A and ((B -> (C -> B)) -> (B -> (C -> B)))) -> (B -> (C -> B))), M:tm-17, m:tm-138, u:((A Am) (Dm (-> Bm (-> Cm Bm))) (C (-> Bm (-> Cm Bm))) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-4756
in-theory        4756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and ((C -> (D -> C)) -> A)) -> B)
theorem-size     13
proof            (modus-ponens tm-15 tm-138 ((Am (-> Dm B)) (C (-> (-> Bm (-> Cm Bm)) Dm)) (A Dm)))
axioms-used      (tm-2 tm-3 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4756.         (((A -> B) and ((C -> (D -> C)) -> A)) -> B), M:tm-15, m:tm-138, u:((Am (-> Dm B)) (C (-> (-> Bm (-> Cm Bm)) Dm)) (A Dm))
================================================================
tm-name          tm-4757
in-theory        4757
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> D)) -> (A and ((B -> (C -> B)) -> D)))
theorem-size     19
proof            (modus-ponens tm-12 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4757.         ((A and ((B -> (C -> B)) -> D)) -> (A and ((B -> (C -> B)) -> D))), M:tm-12, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-4758
in-theory        4758
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> (not D)) -> (not (A and ((B -> (C -> B)) -> D))))
theorem-size     23
proof            (modus-ponens tm-9 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-9 tm-2 tm-4 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4758.         (((A and ((B -> (C -> B)) -> D)) -> (not D)) -> (not (A and ((B -> (C -> B)) -> D)))), M:tm-9, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-4759
in-theory        4759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C and ((D -> (E -> D)) -> A)) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4759.         ((A -> B) -> (((C and ((D -> (E -> D)) -> A)) or A) -> B)), M:tm-8, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-4760
in-theory        4760
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B and ((C -> (D -> C)) -> E)) -> E))
theorem-size     13
proof            (modus-ponens tm-7 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-7 tm-2 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4760.         (A or ((B and ((C -> (D -> C)) -> E)) -> E)), M:tm-7, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4761
in-theory        4761
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-6 tm-2 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4761.         (((A and ((B -> (C -> B)) -> D)) -> D) or E), M:tm-6, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4762
in-theory        4762
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and ((C -> (D -> C)) -> E)) -> E) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4762.         (A -> (((B and ((C -> (D -> C)) -> E)) -> E) and A)), M:tm-5, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4763
in-theory        4763
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> (D -> E))) -> D) -> ((A and ((B -> (C -> B)) -> (D -> E))) -> E))
theorem-size     27
proof            (modus-ponens tm-2 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4763.         (((A and ((B -> (C -> B)) -> (D -> E))) -> D) -> ((A and ((B -> (C -> B)) -> (D -> E))) -> E)), M:tm-2, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-4764
in-theory        4764
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B and ((C -> (D -> C)) -> E)) -> E))
theorem-size     13
proof            (modus-ponens tm-1 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-1 tm-2 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-4764.         (A -> ((B and ((C -> (D -> C)) -> E)) -> E)), M:tm-1, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-4765
in-theory        4765
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E and F))) -> E)
theorem-size     21
proof            (modus-ponens tm-135 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and B C)))) (Em (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4765.         ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E and F))) -> E), M:tm-135, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and B C)))) (Em (and B C)))
================================================================
tm-name          tm-4766
in-theory        4766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-134 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4766.         ((A -> ((B and C) -> B)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-134, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4767
in-theory        4767
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not ((E and F) -> E)))))
theorem-size     23
proof            (modus-ponens tm-130 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not (-> (and B C) B))))) (Em (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4767.         (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not ((E and F) -> E))))), M:tm-130, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not (-> (and B C) B))))) (Em (not (-> (and B C) B))))
================================================================
tm-name          tm-4768
in-theory        4768
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (A -> E))) -> E)
theorem-size     21
proof            (modus-ponens tm-129 tm-139 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> Am C))) (Em (-> Am C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4768.         ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (A -> E))) -> E), M:tm-129, m:tm-139, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> Am C))) (Em (-> Am C)))
================================================================
tm-name          tm-4769
in-theory        4769
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     35
proof            (modus-ponens tm-125 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4769.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-125, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4770
in-theory        4770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> A)) -> A)
theorem-size     21
proof            (modus-ponens tm-120 tm-139 ((Am (-> Em B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (A Em)))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4770.         (((A -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> A)) -> A), M:tm-120, m:tm-139, u:((Am (-> Em B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (A Em))
================================================================
tm-name          tm-4771
in-theory        4771
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> (A -> B))) -> B)
theorem-size     25
proof            (modus-ponens tm-119 tm-139 ((Am (-> (-> A B) A)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))) (Em (-> A B))))
axioms-used      (tm-2 tm-3 tm-4 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4771.         ((((A -> B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> (A -> B))) -> B), M:tm-119, m:tm-139, u:((Am (-> (-> A B) A)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))) (Em (-> A B)))
================================================================
tm-name          tm-4772
in-theory        4772
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> (F -> G)))) -> ((E -> F) -> (E -> G)))
theorem-size     29
proof            (modus-ponens tm-114 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B (-> C D))))) (Em (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4772.         ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> (F -> G)))) -> ((E -> F) -> (E -> G))), M:tm-114, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B (-> C D))))) (Em (-> B (-> C D))))
================================================================
tm-name          tm-4773
in-theory        4773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I))
theorem-size     35
proof            (modus-ponens tm-113 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4773.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I)), M:tm-113, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4774
in-theory        4774
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     31
proof            (modus-ponens tm-109 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Em (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4774.         (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-109, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Em (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-4775
in-theory        4775
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     39
proof            (modus-ponens tm-105 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4775.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-105, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4776
in-theory        4776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-95 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4776.         (((A -> B) -> (A -> A)) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G)), M:tm-95, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4777
in-theory        4777
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> F))) -> (E -> F))
theorem-size     23
proof            (modus-ponens tm-87 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B C)))) (Em (-> B C))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4777.         ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> F))) -> (E -> F)), M:tm-87, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B C)))) (Em (-> B C)))
================================================================
tm-name          tm-4778
in-theory        4778
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (F -> E))
theorem-size     21
proof            (modus-ponens tm-84 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4778.         ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (F -> E)), M:tm-84, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-4779
in-theory        4779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-83 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4779.         ((A -> (B -> (C -> B))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-83, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4780
in-theory        4780
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not (E -> (F -> E))))))
theorem-size     23
proof            (modus-ponens tm-79 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not (-> B (-> C B)))))) (Em (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4780.         (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not (E -> (F -> E)))))), M:tm-79, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not (-> B (-> C B)))))) (Em (not (-> B (-> C B)))))
================================================================
tm-name          tm-4781
in-theory        4781
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F)) -> F))
theorem-size     25
proof            (modus-ponens tm-76 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-10 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4781.         (((not (not A)) -> A) and ((B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F)) -> F)), M:tm-76, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4782
in-theory        4782
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)))) or (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E))) -> E)
theorem-size     39
proof            (modus-ponens tm-73 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-8 tm-10 tm-2 tm-4 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4782.         (((not (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)))) or (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E))) -> E), M:tm-73, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-4783
in-theory        4783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G))
theorem-size     31
proof            (modus-ponens tm-69 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-9 tm-2 tm-4 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4783.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G)), M:tm-69, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4784
in-theory        4784
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not A))))
theorem-size     19
proof            (modus-ponens tm-59 tm-139 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not Am))) (Em (not Am))))
axioms-used      (tm-9 tm-3 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4784.         (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not A)))), M:tm-59, m:tm-139, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not Am))) (Em (not Am)))
================================================================
tm-name          tm-4785
in-theory        4785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     33
proof            (modus-ponens tm-54 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4785.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-54, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4786
in-theory        4786
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F))) or (B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F))) -> F)
theorem-size     39
proof            (modus-ponens tm-47 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4786.         (((A and (B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F))) or (B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F))) -> F), M:tm-47, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-4787
in-theory        4787
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) and F) or (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E))) -> E)
theorem-size     39
proof            (modus-ponens tm-46 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-8 tm-3 tm-2 tm-4 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4787.         ((((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) and F) or (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E))) -> E), M:tm-46, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-4788
in-theory        4788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-42 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4788.         ((A -> (B or A)) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G)), M:tm-42, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4789
in-theory        4789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-32 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4789.         ((A -> (A or B)) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G)), M:tm-32, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4790
in-theory        4790
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) and E))
theorem-size     37
proof            (modus-ponens tm-24 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4790.         ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) and E)), M:tm-24, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-4791
in-theory        4791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-23 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4791.         ((A -> (B -> (A and B))) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G)), M:tm-23, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4792
in-theory        4792
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-22 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4792.         (((A and B) -> B) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G)), M:tm-22, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4793
in-theory        4793
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-21 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4793.         (((A and B) -> A) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G)), M:tm-21, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4794
in-theory        4794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     33
proof            (modus-ponens tm-20 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4794.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-20, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4795
in-theory        4795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-19 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4795.         ((A -> (B -> A)) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G)), M:tm-19, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4796
in-theory        4796
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     43
proof            (modus-ponens tm-17 tm-139 ((A Am) (Em (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4796.         ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-17, m:tm-139, u:((A Am) (Em (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-4797
in-theory        4797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> A)) -> B)
theorem-size     21
proof            (modus-ponens tm-15 tm-139 ((Am (-> Em B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (A Em)))
axioms-used      (tm-2 tm-3 tm-4 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4797.         (((A -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> A)) -> B), M:tm-15, m:tm-139, u:((Am (-> Em B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (A Em))
================================================================
tm-name          tm-4798
in-theory        4798
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)))
theorem-size     35
proof            (modus-ponens tm-12 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4798.         ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E))), M:tm-12, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-4799
in-theory        4799
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (not E)) -> (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E))))
theorem-size     39
proof            (modus-ponens tm-9 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-9 tm-2 tm-4 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4799.         (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (not E)) -> (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)))), M:tm-9, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-4800
in-theory        4800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> A)) or A) -> B))
theorem-size     25
proof            (modus-ponens tm-8 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4800.         ((A -> B) -> (((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> A)) or A) -> B)), M:tm-8, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-4801
in-theory        4801
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F)) -> F))
theorem-size     21
proof            (modus-ponens tm-7 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-7 tm-2 tm-4 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4801.         (A or ((B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F)) -> F)), M:tm-7, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4802
in-theory        4802
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-6 tm-2 tm-4 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4802.         (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) or F), M:tm-6, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4803
in-theory        4803
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F)) -> F) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4803.         (A -> (((B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F)) -> F) and A)), M:tm-5, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4804
in-theory        4804
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> F))) -> E) -> ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> F))) -> F))
theorem-size     43
proof            (modus-ponens tm-2 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B C)))) (Em (-> B C))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4804.         (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> F))) -> E) -> ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> F))) -> F)), M:tm-2, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B C)))) (Em (-> B C)))
================================================================
tm-name          tm-4805
in-theory        4805
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F)) -> F))
theorem-size     21
proof            (modus-ponens tm-1 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-1 tm-2 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4805.         (A -> ((B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F)) -> F)), M:tm-1, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-4806
in-theory        4806
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> (D and E))) -> D)
theorem-size     13
proof            (modus-ponens tm-135 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) (and B C)))) (Dm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4806.         ((A and (((B and C) -> B) -> (D and E))) -> D), M:tm-135, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) (and B C)))) (Dm (and B C)))
================================================================
tm-name          tm-4807
in-theory        4807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-134 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4807.         ((A -> ((B and C) -> B)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-134, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4808
in-theory        4808
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> B) -> (not ((D and E) -> D)))))
theorem-size     15
proof            (modus-ponens tm-130 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) (not (-> (and B C) B))))) (Dm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4808.         (not (A and (((B and C) -> B) -> (not ((D and E) -> D))))), M:tm-130, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) (not (-> (and B C) B))))) (Dm (not (-> (and B C) B))))
================================================================
tm-name          tm-4809
in-theory        4809
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> (A -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-129 tm-140 ((A Am) (B (-> (-> (and Bm Cm) Bm) (-> Am C))) (Dm (-> Am C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4809.         ((A and (((B and C) -> B) -> (A -> D))) -> D), M:tm-129, m:tm-140, u:((A Am) (B (-> (-> (and Bm Cm) Bm) (-> Am C))) (Dm (-> Am C)))
================================================================
tm-name          tm-4810
in-theory        4810
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-125 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4810.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-125, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4811
in-theory        4811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and (((C and D) -> C) -> A)) -> A)
theorem-size     13
proof            (modus-ponens tm-120 tm-140 ((Am (-> Dm B)) (C (-> (-> (and Bm Cm) Bm) Dm)) (A Dm)))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4811.         (((A -> B) and (((C and D) -> C) -> A)) -> A), M:tm-120, m:tm-140, u:((Am (-> Dm B)) (C (-> (-> (and Bm Cm) Bm) Dm)) (A Dm))
================================================================
tm-name          tm-4812
in-theory        4812
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) and (((C and D) -> C) -> (A -> B))) -> B)
theorem-size     17
proof            (modus-ponens tm-119 tm-140 ((Am (-> (-> A B) A)) (C (-> (-> (and Bm Cm) Bm) (-> A B))) (Dm (-> A B))))
axioms-used      (tm-2 tm-3 tm-4 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4812.         ((((A -> B) -> A) and (((C and D) -> C) -> (A -> B))) -> B), M:tm-119, m:tm-140, u:((Am (-> (-> A B) A)) (C (-> (-> (and Bm Cm) Bm) (-> A B))) (Dm (-> A B)))
================================================================
tm-name          tm-4813
in-theory        4813
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> (D -> (E -> F)))) -> ((D -> E) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-114 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) (-> B (-> C D))))) (Dm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4813.         ((A and (((B and C) -> B) -> (D -> (E -> F)))) -> ((D -> E) -> (D -> F))), M:tm-114, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) (-> B (-> C D))))) (Dm (-> B (-> C D))))
================================================================
tm-name          tm-4814
in-theory        4814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (((F and G) -> F) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-113 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4814.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (((F and G) -> F) -> H)) -> H)), M:tm-113, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4815
in-theory        4815
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> B) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     23
proof            (modus-ponens tm-109 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Dm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4815.         (not (A and (((B and C) -> B) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-109, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Dm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-4816
in-theory        4816
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     31
proof            (modus-ponens tm-105 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4816.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-105, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4817
in-theory        4817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C and (((D and E) -> D) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-95 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4817.         (((A -> B) -> (A -> A)) and ((C and (((D and E) -> D) -> F)) -> F)), M:tm-95, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4818
in-theory        4818
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> (D -> E))) -> (D -> E))
theorem-size     15
proof            (modus-ponens tm-87 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4818.         ((A and (((B and C) -> B) -> (D -> E))) -> (D -> E)), M:tm-87, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-4819
in-theory        4819
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> D)) -> (E -> D))
theorem-size     13
proof            (modus-ponens tm-84 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4819.         ((A and (((B and C) -> B) -> D)) -> (E -> D)), M:tm-84, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-4820
in-theory        4820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-83 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4820.         ((A -> (B -> (C -> B))) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-83, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4821
in-theory        4821
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> B) -> (not (D -> (E -> D))))))
theorem-size     15
proof            (modus-ponens tm-79 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) (not (-> B (-> C B)))))) (Dm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4821.         (not (A and (((B and C) -> B) -> (not (D -> (E -> D)))))), M:tm-79, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) (not (-> B (-> C B)))))) (Dm (not (-> B (-> C B)))))
================================================================
tm-name          tm-4822
in-theory        4822
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B and (((C and D) -> C) -> E)) -> E))
theorem-size     17
proof            (modus-ponens tm-76 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-10 tm-2 tm-4 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4822.         (((not (not A)) -> A) and ((B and (((C and D) -> C) -> E)) -> E)), M:tm-76, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4823
in-theory        4823
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A and (((B and C) -> B) -> D)))) or (A and (((B and C) -> B) -> D))) -> D)
theorem-size     23
proof            (modus-ponens tm-73 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-8 tm-10 tm-2 tm-4 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4823.         (((not (not (A and (((B and C) -> B) -> D)))) or (A and (((B and C) -> B) -> D))) -> D), M:tm-73, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-4824
in-theory        4824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and (((D and E) -> D) -> F)) -> F))
theorem-size     23
proof            (modus-ponens tm-69 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-9 tm-2 tm-4 tm-1 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4824.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and (((D and E) -> D) -> F)) -> F)), M:tm-69, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4825
in-theory        4825
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> B) -> (not A))))
theorem-size     11
proof            (modus-ponens tm-59 tm-140 ((A Am) (B (-> (-> (and Bm Cm) Bm) (not Am))) (Dm (not Am))))
axioms-used      (tm-9 tm-3 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4825.         (not (A and (((B and C) -> B) -> (not A)))), M:tm-59, m:tm-140, u:((A Am) (B (-> (-> (and Bm Cm) Bm) (not Am))) (Dm (not Am)))
================================================================
tm-name          tm-4826
in-theory        4826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-54 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4826.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-54, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4827
in-theory        4827
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and (((C and D) -> C) -> E))) or (B and (((C and D) -> C) -> E))) -> E)
theorem-size     23
proof            (modus-ponens tm-47 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4827.         (((A and (B and (((C and D) -> C) -> E))) or (B and (((C and D) -> C) -> E))) -> E), M:tm-47, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-4828
in-theory        4828
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B and C) -> B) -> D)) and E) or (A and (((B and C) -> B) -> D))) -> D)
theorem-size     23
proof            (modus-ponens tm-46 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-8 tm-3 tm-2 tm-4 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4828.         ((((A and (((B and C) -> B) -> D)) and E) or (A and (((B and C) -> B) -> D))) -> D), M:tm-46, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-4829
in-theory        4829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C and (((D and E) -> D) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-42 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4829.         ((A -> (B or A)) and ((C and (((D and E) -> D) -> F)) -> F)), M:tm-42, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4830
in-theory        4830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C and (((D and E) -> D) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-32 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4830.         ((A -> (A or B)) and ((C and (((D and E) -> D) -> F)) -> F)), M:tm-32, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4831
in-theory        4831
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> D)) -> ((A and (((B and C) -> B) -> D)) and D))
theorem-size     21
proof            (modus-ponens tm-24 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4831.         ((A and (((B and C) -> B) -> D)) -> ((A and (((B and C) -> B) -> D)) and D)), M:tm-24, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-4832
in-theory        4832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C and (((D and E) -> D) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-23 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4832.         ((A -> (B -> (A and B))) and ((C and (((D and E) -> D) -> F)) -> F)), M:tm-23, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4833
in-theory        4833
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C and (((D and E) -> D) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-22 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4833.         (((A and B) -> B) and ((C and (((D and E) -> D) -> F)) -> F)), M:tm-22, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4834
in-theory        4834
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C and (((D and E) -> D) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-21 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4834.         (((A and B) -> A) and ((C and (((D and E) -> D) -> F)) -> F)), M:tm-21, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4835
in-theory        4835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-20 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4835.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-20, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4836
in-theory        4836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C and (((D and E) -> D) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-19 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4836.         ((A -> (B -> A)) and ((C and (((D and E) -> D) -> F)) -> F)), M:tm-19, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4837
in-theory        4837
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> ((B and C) -> B))) -> ((B and C) -> B))
theorem-size     19
proof            (modus-ponens tm-17 tm-140 ((A Am) (Dm (-> (and Bm Cm) Bm)) (C (-> (and Bm Cm) Bm)) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-4 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4837.         ((A and (((B and C) -> B) -> ((B and C) -> B))) -> ((B and C) -> B)), M:tm-17, m:tm-140, u:((A Am) (Dm (-> (and Bm Cm) Bm)) (C (-> (and Bm Cm) Bm)) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-4838
in-theory        4838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and (((C and D) -> C) -> A)) -> B)
theorem-size     13
proof            (modus-ponens tm-15 tm-140 ((Am (-> Dm B)) (C (-> (-> (and Bm Cm) Bm) Dm)) (A Dm)))
axioms-used      (tm-2 tm-3 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4838.         (((A -> B) and (((C and D) -> C) -> A)) -> B), M:tm-15, m:tm-140, u:((Am (-> Dm B)) (C (-> (-> (and Bm Cm) Bm) Dm)) (A Dm))
================================================================
tm-name          tm-4839
in-theory        4839
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> D)) -> (A and (((B and C) -> B) -> D)))
theorem-size     19
proof            (modus-ponens tm-12 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4839.         ((A and (((B and C) -> B) -> D)) -> (A and (((B and C) -> B) -> D))), M:tm-12, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-4840
in-theory        4840
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> (not D)) -> (not (A and (((B and C) -> B) -> D))))
theorem-size     23
proof            (modus-ponens tm-9 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-9 tm-2 tm-4 tm-1 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4840.         (((A and (((B and C) -> B) -> D)) -> (not D)) -> (not (A and (((B and C) -> B) -> D)))), M:tm-9, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-4841
in-theory        4841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C and (((D and E) -> D) -> A)) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4841.         ((A -> B) -> (((C and (((D and E) -> D) -> A)) or A) -> B)), M:tm-8, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-4842
in-theory        4842
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B and (((C and D) -> C) -> E)) -> E))
theorem-size     13
proof            (modus-ponens tm-7 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-7 tm-2 tm-4 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4842.         (A or ((B and (((C and D) -> C) -> E)) -> E)), M:tm-7, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4843
in-theory        4843
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-6 tm-2 tm-4 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4843.         (((A and (((B and C) -> B) -> D)) -> D) or E), M:tm-6, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4844
in-theory        4844
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (((C and D) -> C) -> E)) -> E) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4844.         (A -> (((B and (((C and D) -> C) -> E)) -> E) and A)), M:tm-5, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4845
in-theory        4845
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> (D -> E))) -> D) -> ((A and (((B and C) -> B) -> (D -> E))) -> E))
theorem-size     27
proof            (modus-ponens tm-2 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-4 tm-1 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4845.         (((A and (((B and C) -> B) -> (D -> E))) -> D) -> ((A and (((B and C) -> B) -> (D -> E))) -> E)), M:tm-2, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-4846
in-theory        4846
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B and (((C and D) -> C) -> E)) -> E))
theorem-size     13
proof            (modus-ponens tm-1 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-1 tm-2 tm-4 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-4846.         (A -> ((B and (((C and D) -> C) -> E)) -> E)), M:tm-1, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-4847
in-theory        4847
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> B)) -> (C -> B))
theorem-size     13
proof            (modus-ponens tm-141 tm-11 ((Am (and A (-> (-> Bm (-> Cm Bm)) Bm))) (B Bm) (C (-> Cm Bm))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4847.         ((A and ((B -> (C -> B)) -> B)) -> (C -> B)), M:tm-141, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) Bm))) (B Bm) (C (-> Cm Bm)))
================================================================
tm-name          tm-4848
in-theory        4848
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (B -> (C -> D)))) -> ((B -> C) -> (B -> D)))
theorem-size     29
proof            (modus-ponens tm-141 tm-14 ((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> Bm (-> Cm Dm))))) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4848.         ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (B -> (C -> D)))) -> ((B -> C) -> (B -> D))), M:tm-141, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> Bm (-> Cm Dm))))) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-4849
in-theory        4849
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> (B and C))) -> B)
theorem-size     13
proof            (modus-ponens tm-141 tm-16 ((Am (and A (-> (-> (and Bm Cm) Bm) (and Bm Cm)))) (B (and Bm Cm)) (C Bm)))
axioms-used      (tm-2 tm-4 tm-1 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4849.         ((A and (((B and C) -> B) -> (B and C))) -> B), M:tm-141, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) (and Bm Cm)))) (B (and Bm Cm)) (C Bm))
================================================================
tm-name          tm-4850
in-theory        4850
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> (B and C))) -> C)
theorem-size     13
proof            (modus-ponens tm-141 tm-18 ((Am (and A (-> (-> (and Bm Cm) Cm) (and Bm Cm)))) (B (and Bm Cm)) (C Cm)))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-4850.         ((A and (((B and C) -> C) -> (B and C))) -> C), M:tm-141, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) (and Bm Cm)))) (B (and Bm Cm)) (C Cm))
================================================================
tm-name          tm-4851
in-theory        4851
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> B)) -> (C -> (B and C)))
theorem-size     17
proof            (modus-ponens tm-141 tm-25 ((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) Bm))) (B Bm) (C (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4851.         ((A and ((B -> (C -> (B and C))) -> B)) -> (C -> (B and C))), M:tm-141, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) Bm))) (B Bm) (C (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-4852
in-theory        4852
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> B)) -> (B or C))
theorem-size     13
proof            (modus-ponens tm-141 tm-33 ((Am (and A (-> (-> Bm (or Bm Cm)) Bm))) (B Bm) (C (or Bm Cm))))
axioms-used      (tm-2 tm-4 tm-1 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4852.         ((A and ((B -> (B or C)) -> B)) -> (B or C)), M:tm-141, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) Bm))) (B Bm) (C (or Bm Cm)))
================================================================
tm-name          tm-4853
in-theory        4853
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> B)) -> (C or B))
theorem-size     13
proof            (modus-ponens tm-141 tm-43 ((Am (and A (-> (-> Bm (or Cm Bm)) Bm))) (B Bm) (C (or Cm Bm))))
axioms-used      (tm-2 tm-4 tm-1 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4853.         ((A and ((B -> (C or B)) -> B)) -> (C or B)), M:tm-141, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) Bm))) (B Bm) (C (or Cm Bm)))
================================================================
tm-name          tm-4854
in-theory        4854
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) -> (B -> C))) -> ((C -> D) -> ((B or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-141 tm-56 ((Am (and A (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> Bm Cm)))) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-8)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4854.         ((A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) -> (B -> C))) -> ((C -> D) -> ((B or C) -> D))), M:tm-141, m:tm-56, u:((Am (and A (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> Bm Cm)))) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-4855
in-theory        4855
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> ((B -> (not C)) -> (not B))) -> (B -> C))) -> ((B -> (not C)) -> (not B)))
theorem-size     25
proof            (modus-ponens tm-141 tm-71 ((Am (and A (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> Bm Cm)))) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-9)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4855.         ((A and (((B -> C) -> ((B -> (not C)) -> (not B))) -> (B -> C))) -> ((B -> (not C)) -> (not B))), M:tm-141, m:tm-71, u:((Am (and A (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> Bm Cm)))) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-4856
in-theory        4856
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((not (not B)) -> B) -> (not (not B)))) -> B)
theorem-size     13
proof            (modus-ponens tm-141 tm-78 ((Am (and A (-> (-> (not (not Bm)) Bm) (not (not Bm))))) (B (not (not Bm))) (C Bm)))
axioms-used      (tm-2 tm-4 tm-1 tm-10)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4856.         ((A and (((not (not B)) -> B) -> (not (not B)))) -> B), M:tm-141, m:tm-78, u:((Am (and A (-> (-> (not (not Bm)) Bm) (not (not Bm))))) (B (not (not Bm))) (C Bm))
================================================================
tm-name          tm-4857
in-theory        4857
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (D -> C))) -> B)) -> (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-141 tm-85 ((Am (and A (-> (-> Bm (-> Cm (-> Dm Cm))) Bm))) (B Bm) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4857.         ((A and ((B -> (C -> (D -> C))) -> B)) -> (C -> (D -> C))), M:tm-141, m:tm-85, u:((Am (and A (-> (-> Bm (-> Cm (-> Dm Cm))) Bm))) (B Bm) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-4858
in-theory        4858
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> (B -> B)) -> (B -> C))) -> (B -> B))
theorem-size     17
proof            (modus-ponens tm-141 tm-97 ((Am (and A (-> (-> (-> Bm Cm) (-> Bm Bm)) (-> Bm Cm)))) (B (-> Bm Cm)) (C (-> Bm Bm))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4858.         ((A and (((B -> C) -> (B -> B)) -> (B -> C))) -> (B -> B)), M:tm-141, m:tm-97, u:((Am (and A (-> (-> (-> Bm Cm) (-> Bm Bm)) (-> Bm Cm)))) (B (-> Bm Cm)) (C (-> Bm Bm)))
================================================================
tm-name          tm-4859
in-theory        4859
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) -> ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D)))
theorem-size     41
proof            (modus-ponens tm-141 tm-107 ((Am (and A (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4859.         ((A and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) -> ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-141, m:tm-107, u:((Am (and A (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-4860
in-theory        4860
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-141 tm-115 ((Am (and A (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Bm))) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4860.         ((A and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-141, m:tm-115, u:((Am (and A (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Bm))) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-4861
in-theory        4861
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> A) -> (A -> B)) and ((A -> B) -> A)) -> B)
theorem-size     17
proof            (modus-ponens tm-141 tm-116 ((A (-> (-> (-> B C) B) (-> B C))) (Am (-> (-> B C) B)) (Bm (-> B C))))
axioms-used      (tm-2 tm-4 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-4861.         (((((A -> B) -> A) -> (A -> B)) and ((A -> B) -> A)) -> B), M:tm-141, m:tm-116, u:((A (-> (-> (-> B C) B) (-> B C))) (Am (-> (-> B C) B)) (Bm (-> B C)))
================================================================
tm-name          tm-4862
in-theory        4862
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> (C -> D)) and ((C -> D) -> C)) -> D)
theorem-size     17
proof            (modus-ponens tm-141 tm-117 ((A (-> (-> Am (-> Bm Am)) (-> B C))) (Dm (-> (-> B C) B)) (Cm (-> B C))))
axioms-used      (tm-2 tm-4 tm-3 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-4862.         ((((A -> (B -> A)) -> (C -> D)) and ((C -> D) -> C)) -> D), M:tm-141, m:tm-117, u:((A (-> (-> Am (-> Bm Am)) (-> B C))) (Dm (-> (-> B C) B)) (Cm (-> B C)))
================================================================
tm-name          tm-4863
in-theory        4863
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and ((D -> E) -> D)) -> E)
theorem-size     25
proof            (modus-ponens tm-141 tm-118 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B C))) (Em (-> (-> B C) B)) (Dm (-> B C))))
axioms-used      (tm-2 tm-4 tm-3 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4863.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and ((D -> E) -> D)) -> E), M:tm-141, m:tm-118, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B C))) (Em (-> (-> B C) B)) (Dm (-> B C)))
================================================================
tm-name          tm-4864
in-theory        4864
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) -> (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C))
theorem-size     33
proof            (modus-ponens tm-141 tm-127 ((Am (and A (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (and (-> Bm Cm) Dm) Bm)))) (B (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-4 tm-1 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4864.         ((A and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) -> (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C)), M:tm-141, m:tm-127, u:((Am (and A (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (and (-> Bm Cm) Dm) Bm)))) (B (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-4865
in-theory        4865
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> (C -> D)) and ((C -> D) -> C)) -> D)
theorem-size     17
proof            (modus-ponens tm-141 tm-128 ((A (-> (-> (and Am Bm) Am) (-> B C))) (Dm (-> (-> B C) B)) (Cm (-> B C))))
axioms-used      (tm-2 tm-4 tm-3 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4865.         (((((A and B) -> A) -> (C -> D)) and ((C -> D) -> C)) -> D), M:tm-141, m:tm-128, u:((A (-> (-> (and Am Bm) Am) (-> B C))) (Dm (-> (-> B C) B)) (Cm (-> B C)))
================================================================
tm-name          tm-4866
in-theory        4866
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> ((C and D) -> C)) -> B)) -> ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-141 tm-136 ((Am (and A (-> (-> Bm (-> (and Cm Dm) Cm)) Bm))) (B Bm) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-4 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4866.         ((A and ((B -> ((C and D) -> C)) -> B)) -> ((C and D) -> C)), M:tm-141, m:tm-136, u:((Am (and A (-> (-> Bm (-> (and Cm Dm) Cm)) Bm))) (B Bm) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-4867
in-theory        4867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-134 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4867.         ((A -> ((B and C) -> B)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-134, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4868
in-theory        4868
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) and ((B -> C) -> B)) -> (B -> C))) -> (((B -> C) and ((B -> C) -> B)) -> C))
theorem-size     27
proof            (modus-ponens tm-131 tm-141 ((Am (-> Bm Cm)) (B (-> (-> Bm Cm) Bm)) (A (-> Bm Cm)) (C (-> (and (-> Bm Cm) (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4868.         ((A or (((B -> C) and ((B -> C) -> B)) -> (B -> C))) -> (((B -> C) and ((B -> C) -> B)) -> C)), M:tm-131, m:tm-141, u:((Am (-> Bm Cm)) (B (-> (-> Bm Cm) Bm)) (A (-> Bm Cm)) (C (-> (and (-> Bm Cm) (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-4869
in-theory        4869
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-125 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4869.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-125, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4870
in-theory        4870
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and ((B -> C) -> B)) -> A) or (((A -> (B -> C)) and ((B -> C) -> B)) -> (B -> C))) -> (((A -> (B -> C)) and ((B -> C) -> B)) -> C))
theorem-size     43
proof            (modus-ponens tm-122 tm-141 ((Am (-> A (-> Bm Cm))) (C (-> (-> Bm Cm) Bm)) (B (-> Bm Cm)) (D (-> (and (-> A (-> Bm Cm)) (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-8 tm-2 tm-3 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4870.         (((((A -> (B -> C)) and ((B -> C) -> B)) -> A) or (((A -> (B -> C)) and ((B -> C) -> B)) -> (B -> C))) -> (((A -> (B -> C)) and ((B -> C) -> B)) -> C)), M:tm-122, m:tm-141, u:((Am (-> A (-> Bm Cm))) (C (-> (-> Bm Cm) Bm)) (B (-> Bm Cm)) (D (-> (and (-> A (-> Bm Cm)) (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-4871
in-theory        4871
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> B)) -> (B -> (C -> D))) -> (((A and ((B -> (C -> D)) -> B)) -> C) -> ((A and ((B -> (C -> D)) -> B)) -> D)))
theorem-size     39
proof            (modus-ponens tm-114 tm-141 ((A (-> (and Am (-> (-> Bm (-> C D)) Bm)) (-> Bm (-> C D)))) (B (and Am (-> (-> Bm (-> C D)) Bm))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4871.         (((A and ((B -> (C -> D)) -> B)) -> (B -> (C -> D))) -> (((A and ((B -> (C -> D)) -> B)) -> C) -> ((A and ((B -> (C -> D)) -> B)) -> D))), M:tm-114, m:tm-141, u:((A (-> (and Am (-> (-> Bm (-> C D)) Bm)) (-> Bm (-> C D)))) (B (and Am (-> (-> Bm (-> C D)) Bm))) (Cm (-> C D)))
================================================================
tm-name          tm-4872
in-theory        4872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-113 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4872.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G))), M:tm-113, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4873
in-theory        4873
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     41
proof            (modus-ponens tm-105 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4873.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-105, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4874
in-theory        4874
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((B -> B) -> B)) -> (B -> B)) -> ((A and ((B -> B) -> B)) -> B))
theorem-size     21
proof            (modus-ponens tm-100 tm-141 ((Cm Bm) (C Bm) (A (and Am (-> (-> Bm Bm) Bm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4874.         (((A and ((B -> B) -> B)) -> (B -> B)) -> ((A and ((B -> B) -> B)) -> B)), M:tm-100, m:tm-141, u:((Cm Bm) (C Bm) (A (and Am (-> (-> Bm Bm) Bm))) (B Bm))
================================================================
tm-name          tm-4875
in-theory        4875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-95 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4875.         (((A -> B) -> (A -> A)) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E))), M:tm-95, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4876
in-theory        4876
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> B)) -> (B -> C)) -> (D -> ((A and ((B -> C) -> B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-84 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4876.         (((A and ((B -> C) -> B)) -> (B -> C)) -> (D -> ((A and ((B -> C) -> B)) -> C))), M:tm-84, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-4877
in-theory        4877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-83 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4877.         ((A -> (B -> (C -> B))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-83, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4878
in-theory        4878
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and ((C -> D) -> C)) -> (C -> D)) -> ((B and ((C -> D) -> C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-76 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4878.         (((not (not A)) -> A) and (((B and ((C -> D) -> C)) -> (C -> D)) -> ((B and ((C -> D) -> C)) -> D))), M:tm-76, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4879
in-theory        4879
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and ((B -> C) -> B)) -> (B -> C)))) or ((A and ((B -> C) -> B)) -> (B -> C))) -> ((A and ((B -> C) -> B)) -> C))
theorem-size     35
proof            (modus-ponens tm-73 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4879.         (((not (not ((A and ((B -> C) -> B)) -> (B -> C)))) or ((A and ((B -> C) -> B)) -> (B -> C))) -> ((A and ((B -> C) -> B)) -> C)), M:tm-73, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-4880
in-theory        4880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-69 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4880.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E))), M:tm-69, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4881
in-theory        4881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-54 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4881.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-54, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4882
in-theory        4882
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and ((C -> D) -> C)) -> (C -> D))) or ((B and ((C -> D) -> C)) -> (C -> D))) -> ((B and ((C -> D) -> C)) -> D))
theorem-size     35
proof            (modus-ponens tm-47 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4882.         (((A and ((B and ((C -> D) -> C)) -> (C -> D))) or ((B and ((C -> D) -> C)) -> (C -> D))) -> ((B and ((C -> D) -> C)) -> D)), M:tm-47, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-4883
in-theory        4883
times-derived    1
----------------------------------------------------------------
theorem          (((((A and ((B -> C) -> B)) -> (B -> C)) and D) or ((A and ((B -> C) -> B)) -> (B -> C))) -> ((A and ((B -> C) -> B)) -> C))
theorem-size     35
proof            (modus-ponens tm-46 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4883.         (((((A and ((B -> C) -> B)) -> (B -> C)) and D) or ((A and ((B -> C) -> B)) -> (B -> C))) -> ((A and ((B -> C) -> B)) -> C)), M:tm-46, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-4884
in-theory        4884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((C and ((A -> B) -> A)) -> (A -> B))) -> ((C and ((A -> B) -> A)) -> B))
theorem-size     25
proof            (modus-ponens tm-44 tm-141 ((A (and Am (-> (-> Bm Cm) Bm))) (B (-> Bm Cm)) (C (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4884.         (((A -> B) or ((C and ((A -> B) -> A)) -> (A -> B))) -> ((C and ((A -> B) -> A)) -> B)), M:tm-44, m:tm-141, u:((A (and Am (-> (-> Bm Cm) Bm))) (B (-> Bm Cm)) (C (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-4885
in-theory        4885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-42 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4885.         ((A -> (B or A)) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E))), M:tm-42, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4886
in-theory        4886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-32 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4886.         ((A -> (A or B)) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E))), M:tm-32, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4887
in-theory        4887
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> B)) -> (B -> C)) -> (((A and ((B -> C) -> B)) -> (B -> C)) and ((A and ((B -> C) -> B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-24 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4887.         (((A and ((B -> C) -> B)) -> (B -> C)) -> (((A and ((B -> C) -> B)) -> (B -> C)) and ((A and ((B -> C) -> B)) -> C))), M:tm-24, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-4888
in-theory        4888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-23 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4888.         ((A -> (B -> (A and B))) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E))), M:tm-23, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4889
in-theory        4889
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-22 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4889.         (((A and B) -> B) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E))), M:tm-22, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4890
in-theory        4890
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-21 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4890.         (((A and B) -> A) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E))), M:tm-21, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4891
in-theory        4891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-20 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4891.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-20, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4892
in-theory        4892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-19 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4892.         ((A -> (B -> A)) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E))), M:tm-19, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4893
in-theory        4893
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> (B -> C)))
theorem-size     23
proof            (modus-ponens tm-12 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4893.         (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> (B -> C))), M:tm-12, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-4894
in-theory        4894
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> (not ((A and ((B -> C) -> B)) -> C))) -> (not ((A and ((B -> C) -> B)) -> (B -> C))))
theorem-size     35
proof            (modus-ponens tm-9 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-9 tm-2 tm-4)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4894.         ((((A and ((B -> C) -> B)) -> (B -> C)) -> (not ((A and ((B -> C) -> B)) -> C))) -> (not ((A and ((B -> C) -> B)) -> (B -> C)))), M:tm-9, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-4895
in-theory        4895
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> C) -> D) -> ((((A and ((B -> C) -> B)) -> (B -> C)) or ((A and ((B -> C) -> B)) -> C)) -> D))
theorem-size     35
proof            (modus-ponens tm-8 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-8 tm-2 tm-4)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4895.         ((((A and ((B -> C) -> B)) -> C) -> D) -> ((((A and ((B -> C) -> B)) -> (B -> C)) or ((A and ((B -> C) -> B)) -> C)) -> D)), M:tm-8, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-4896
in-theory        4896
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and ((C -> D) -> C)) -> (C -> D)) -> ((B and ((C -> D) -> C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-7 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-7 tm-2 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4896.         (A or (((B and ((C -> D) -> C)) -> (C -> D)) -> ((B and ((C -> D) -> C)) -> D))), M:tm-7, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4897
in-theory        4897
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) or D)
theorem-size     23
proof            (modus-ponens tm-6 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-6 tm-2 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4897.         ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) or D), M:tm-6, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4898
in-theory        4898
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and ((C -> D) -> C)) -> (C -> D)) -> ((B and ((C -> D) -> C)) -> D)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4898.         (A -> ((((B and ((C -> D) -> C)) -> (C -> D)) -> ((B and ((C -> D) -> C)) -> D)) and A)), M:tm-5, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4899
in-theory        4899
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> (A and ((B -> C) -> B))) -> (((A and ((B -> C) -> B)) -> (B -> C)) -> C))
theorem-size     33
proof            (modus-ponens tm-2 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (and Am (-> (-> Bm Cm) Bm))) (C Cm)))
axioms-used      (tm-2 tm-4)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4899.         ((((A and ((B -> C) -> B)) -> (B -> C)) -> (A and ((B -> C) -> B))) -> (((A and ((B -> C) -> B)) -> (B -> C)) -> C)), M:tm-2, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (and Am (-> (-> Bm Cm) Bm))) (C Cm))
================================================================
tm-name          tm-4900
in-theory        4900
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and ((C -> D) -> C)) -> (C -> D)) -> ((B and ((C -> D) -> C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-1 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-1 tm-2 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-4900.         (A -> (((B and ((C -> D) -> C)) -> (C -> D)) -> ((B and ((C -> D) -> C)) -> D))), M:tm-1, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-4901
in-theory        4901
times-derived    1
----------------------------------------------------------------
theorem          ((A and (A -> B)) -> A)
theorem-size     7
proof            (modus-ponens tm-142 tm-3 ((A Am) (Bm (-> Am C)) (B Am)))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-4901.         ((A and (A -> B)) -> A), M:tm-142, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
================================================================
tm-name          tm-4902
in-theory        4902
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> D)) -> (B -> (C -> B)))
theorem-size     15
proof            (modus-ponens tm-142 tm-11 ((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4902.         ((A and ((B -> (C -> B)) -> D)) -> (B -> (C -> B))), M:tm-142, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-4903
in-theory        4903
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     31
proof            (modus-ponens tm-142 tm-14 ((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4903.         ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-142, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-4904
in-theory        4904
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> D)) -> ((B and C) -> B))
theorem-size     15
proof            (modus-ponens tm-142 tm-16 ((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4904.         ((A and (((B and C) -> B) -> D)) -> ((B and C) -> B)), M:tm-142, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-4905
in-theory        4905
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> D)) -> ((B and C) -> C))
theorem-size     15
proof            (modus-ponens tm-142 tm-18 ((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-4905.         ((A and (((B and C) -> C) -> D)) -> ((B and C) -> C)), M:tm-142, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-4906
in-theory        4906
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> D)) -> (B -> (C -> (B and C))))
theorem-size     19
proof            (modus-ponens tm-142 tm-25 ((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4906.         ((A and ((B -> (C -> (B and C))) -> D)) -> (B -> (C -> (B and C)))), M:tm-142, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-4907
in-theory        4907
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> D)) -> (B -> (B or C)))
theorem-size     15
proof            (modus-ponens tm-142 tm-33 ((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4907.         ((A and ((B -> (B or C)) -> D)) -> (B -> (B or C))), M:tm-142, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-4908
in-theory        4908
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> D)) -> (B -> (C or B)))
theorem-size     15
proof            (modus-ponens tm-142 tm-43 ((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4908.         ((A and ((B -> (C or B)) -> D)) -> (B -> (C or B))), M:tm-142, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-4909
in-theory        4909
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) -> E)) -> ((B -> C) -> ((C -> D) -> ((B or C) -> D))))
theorem-size     31
proof            (modus-ponens tm-142 tm-56 ((Am (and A (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) C))) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-1 tm-4 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4909.         ((A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) -> E)) -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-142, m:tm-56, u:((Am (and A (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) C))) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-4910
in-theory        4910
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> ((B -> (not C)) -> (not B))) -> D)) -> ((B -> C) -> ((B -> (not C)) -> (not B))))
theorem-size     27
proof            (modus-ponens tm-142 tm-71 ((Am (and A (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) C))) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-1 tm-4 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4910.         ((A and (((B -> C) -> ((B -> (not C)) -> (not B))) -> D)) -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-142, m:tm-71, u:((Am (and A (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) C))) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-4911
in-theory        4911
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((not (not B)) -> B) -> C)) -> ((not (not B)) -> B))
theorem-size     15
proof            (modus-ponens tm-142 tm-78 ((Am (and A (-> (-> (not (not Bm)) Bm) C))) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-1 tm-4 tm-10)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4911.         ((A and (((not (not B)) -> B) -> C)) -> ((not (not B)) -> B)), M:tm-142, m:tm-78, u:((Am (and A (-> (-> (not (not Bm)) Bm) C))) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-4912
in-theory        4912
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (D -> C))) -> E)) -> (B -> (C -> (D -> C))))
theorem-size     19
proof            (modus-ponens tm-142 tm-85 ((Am (and A (-> (-> Bm (-> Cm (-> Dm Cm))) C))) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4912.         ((A and ((B -> (C -> (D -> C))) -> E)) -> (B -> (C -> (D -> C)))), M:tm-142, m:tm-85, u:((Am (and A (-> (-> Bm (-> Cm (-> Dm Cm))) C))) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-4913
in-theory        4913
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> (B -> B)) -> D)) -> ((B -> C) -> (B -> B)))
theorem-size     19
proof            (modus-ponens tm-142 tm-97 ((Am (and A (-> (-> (-> Bm Cm) (-> Bm Bm)) C))) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4913.         ((A and (((B -> C) -> (B -> B)) -> D)) -> ((B -> C) -> (B -> B))), M:tm-142, m:tm-97, u:((Am (and A (-> (-> (-> Bm Cm) (-> Bm Bm)) C))) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-4914
in-theory        4914
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) -> E)) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     43
proof            (modus-ponens tm-142 tm-107 ((Am (and A (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) C))) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4914.         ((A and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) -> E)) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-142, m:tm-107, u:((Am (and A (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) C))) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-4915
in-theory        4915
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-142 tm-115 ((Am (and A (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) C))) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4915.         ((A and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-142, m:tm-115, u:((Am (and A (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) C))) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-4916
in-theory        4916
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) and (A -> B)) -> A)
theorem-size     11
proof            (modus-ponens tm-142 tm-116 ((A (-> (-> Bm C) Bm)) (Am (-> Bm C)) (B Bm)))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-4916.         ((((A -> B) -> A) and (A -> B)) -> A), M:tm-142, m:tm-116, u:((A (-> (-> Bm C) Bm)) (Am (-> Bm C)) (B Bm))
================================================================
tm-name          tm-4917
in-theory        4917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) and (C -> D)) -> C)
theorem-size     13
proof            (modus-ponens tm-142 tm-117 ((A (-> (-> Am (-> Bm Am)) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-4917.         ((((A -> (B -> A)) -> C) and (C -> D)) -> C), M:tm-142, m:tm-117, u:((A (-> (-> Am (-> Bm Am)) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-4918
in-theory        4918
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and (D -> E)) -> D)
theorem-size     21
proof            (modus-ponens tm-142 tm-118 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> Dm C)) (B Dm)))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4918.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and (D -> E)) -> D), M:tm-142, m:tm-118, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> Dm C)) (B Dm))
================================================================
tm-name          tm-4919
in-theory        4919
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) -> E)) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))
theorem-size     35
proof            (modus-ponens tm-142 tm-127 ((Am (and A (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) C))) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4919.         ((A and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) -> E)) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-142, m:tm-127, u:((Am (and A (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) C))) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-4920
in-theory        4920
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) and (C -> D)) -> C)
theorem-size     13
proof            (modus-ponens tm-142 tm-128 ((A (-> (-> (and Am Bm) Am) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-4920.         (((((A and B) -> A) -> C) and (C -> D)) -> C), M:tm-142, m:tm-128, u:((A (-> (-> (and Am Bm) Am) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-4921
in-theory        4921
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> ((C and D) -> C)) -> E)) -> (B -> ((C and D) -> C)))
theorem-size     19
proof            (modus-ponens tm-142 tm-136 ((Am (and A (-> (-> Bm (-> (and Cm Dm) Cm)) C))) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4921.         ((A and ((B -> ((C and D) -> C)) -> E)) -> (B -> ((C and D) -> C))), M:tm-142, m:tm-136, u:((Am (and A (-> (-> Bm (-> (and Cm Dm) Cm)) C))) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-4922
in-theory        4922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-134 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4922.         ((A -> ((B and C) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-134, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4923
in-theory        4923
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (B -> C)) -> B)) -> ((B and (B -> C)) -> B))
theorem-size     17
proof            (modus-ponens tm-131 tm-142 ((Bm Am) (B (-> Am Cm)) (A Am) (C (-> (and Am (-> Am Cm)) Am))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4923.         ((A or ((B and (B -> C)) -> B)) -> ((B and (B -> C)) -> B)), M:tm-131, m:tm-142, u:((Bm Am) (B (-> Am Cm)) (A Am) (C (-> (and Am (-> Am Cm)) Am)))
================================================================
tm-name          tm-4924
in-theory        4924
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     31
proof            (modus-ponens tm-125 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4924.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-125, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4925
in-theory        4925
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and (B -> C)) -> A) or (((A -> B) and (B -> C)) -> B)) -> (((A -> B) and (B -> C)) -> B))
theorem-size     29
proof            (modus-ponens tm-122 tm-142 ((Am (-> A Bm)) (C (-> Bm Cm)) (B Bm) (D (-> (and (-> A Bm) (-> Bm Cm)) Bm))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4925.         (((((A -> B) and (B -> C)) -> A) or (((A -> B) and (B -> C)) -> B)) -> (((A -> B) and (B -> C)) -> B)), M:tm-122, m:tm-142, u:((Am (-> A Bm)) (C (-> Bm Cm)) (B Bm) (D (-> (and (-> A Bm) (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-4926
in-theory        4926
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> D)) -> (B -> C)) -> (((A and ((B -> C) -> D)) -> B) -> ((A and ((B -> C) -> D)) -> C)))
theorem-size     31
proof            (modus-ponens tm-114 tm-142 ((A (-> (and Am (-> (-> C D) Cm)) (-> C D))) (B (and Am (-> (-> C D) Cm))) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4926.         (((A and ((B -> C) -> D)) -> (B -> C)) -> (((A and ((B -> C) -> D)) -> B) -> ((A and ((B -> C) -> D)) -> C))), M:tm-114, m:tm-142, u:((A (-> (and Am (-> (-> C D) Cm)) (-> C D))) (B (and Am (-> (-> C D) Cm))) (Bm (-> C D)))
================================================================
tm-name          tm-4927
in-theory        4927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F)))
theorem-size     31
proof            (modus-ponens tm-113 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4927.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F))), M:tm-113, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4928
in-theory        4928
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     35
proof            (modus-ponens tm-105 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4928.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-105, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4929
in-theory        4929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D)))
theorem-size     23
proof            (modus-ponens tm-95 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4929.         (((A -> B) -> (A -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D))), M:tm-95, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4930
in-theory        4930
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> (D -> ((A and (B -> C)) -> B)))
theorem-size     17
proof            (modus-ponens tm-84 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4930.         (((A and (B -> C)) -> B) -> (D -> ((A and (B -> C)) -> B))), M:tm-84, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-4931
in-theory        4931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-83 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4931.         ((A -> (B -> (C -> B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-83, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4932
in-theory        4932
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> C)))
theorem-size     21
proof            (modus-ponens tm-76 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4932.         (((not (not A)) -> A) and (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> C))), M:tm-76, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4933
in-theory        4933
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (B -> C)) -> B))) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> B))
theorem-size     25
proof            (modus-ponens tm-73 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4933.         (((not (not ((A and (B -> C)) -> B))) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> B)), M:tm-73, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-4934
in-theory        4934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D)))
theorem-size     27
proof            (modus-ponens tm-69 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4934.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D))), M:tm-69, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4935
in-theory        4935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     29
proof            (modus-ponens tm-54 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4935.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-54, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4936
in-theory        4936
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> C))
theorem-size     25
proof            (modus-ponens tm-47 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4936.         (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> C)), M:tm-47, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-4937
in-theory        4937
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> B))
theorem-size     25
proof            (modus-ponens tm-46 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4937.         (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> B)), M:tm-46, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-4938
in-theory        4938
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> A))
theorem-size     17
proof            (modus-ponens tm-44 tm-142 ((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4938.         ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> A)), M:tm-44, m:tm-142, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-4939
in-theory        4939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D)))
theorem-size     21
proof            (modus-ponens tm-42 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4939.         ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D))), M:tm-42, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4940
in-theory        4940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D)))
theorem-size     21
proof            (modus-ponens tm-32 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4940.         ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D))), M:tm-32, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4941
in-theory        4941
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> B)))
theorem-size     23
proof            (modus-ponens tm-24 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4941.         (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> B))), M:tm-24, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-4942
in-theory        4942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D)))
theorem-size     23
proof            (modus-ponens tm-23 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4942.         ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D))), M:tm-23, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4943
in-theory        4943
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D)))
theorem-size     21
proof            (modus-ponens tm-22 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4943.         (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D))), M:tm-22, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4944
in-theory        4944
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D)))
theorem-size     21
proof            (modus-ponens tm-21 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4944.         (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D))), M:tm-21, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4945
in-theory        4945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     29
proof            (modus-ponens tm-20 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4945.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-20, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4946
in-theory        4946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D)))
theorem-size     21
proof            (modus-ponens tm-19 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4946.         ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D))), M:tm-19, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4947
in-theory        4947
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> B))) -> (not ((A and (B -> C)) -> B)))
theorem-size     25
proof            (modus-ponens tm-9 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-9 tm-2 tm-1 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4947.         ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> B))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-4948
in-theory        4948
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> B)) -> D))
theorem-size     27
proof            (modus-ponens tm-8 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4948.         ((((A and (B -> C)) -> B) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> B)) -> D)), M:tm-8, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-4949
in-theory        4949
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> C)))
theorem-size     17
proof            (modus-ponens tm-7 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-7 tm-2 tm-1 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4949.         (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> C))), M:tm-7, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4950
in-theory        4950
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-6 tm-2 tm-1 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4950.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) or D), M:tm-6, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4951
in-theory        4951
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> C)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4951.         (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> C)) and A)), M:tm-5, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4952
in-theory        4952
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> B))
theorem-size     23
proof            (modus-ponens tm-2 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Bm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4952.         ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> B)), M:tm-2, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Bm))
================================================================
tm-name          tm-4953
in-theory        4953
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> C)))
theorem-size     17
proof            (modus-ponens tm-1 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-1 tm-2 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4953.         (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> C))), M:tm-1, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4954
in-theory        4954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-134 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4954.         ((A -> ((B and C) -> B)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-134, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4955
in-theory        4955
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and (A -> B)) -> A) -> (not ((A and (A -> B)) -> B))))
theorem-size     17
proof            (modus-ponens tm-130 tm-143 ((A (-> (-> (and Am (-> Am Cm)) Am) (not (-> (and Am (-> Am Cm)) Cm)))) (Bm Am) (C (-> Am Cm)) (B Am)))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4955.         (not (((A and (A -> B)) -> A) -> (not ((A and (A -> B)) -> B)))), M:tm-130, m:tm-143, u:((A (-> (-> (and Am (-> Am Cm)) Am) (not (-> (and Am (-> Am Cm)) Cm)))) (Bm Am) (C (-> Am Cm)) (B Am))
================================================================
tm-name          tm-4956
in-theory        4956
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     41
proof            (modus-ponens tm-125 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-4)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4956.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-125, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4957
in-theory        4957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> F) -> (not ((E and (F -> G)) -> G))) -> (not ((E and (F -> G)) -> F))))
theorem-size     41
proof            (modus-ponens tm-113 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-4)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4957.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> F) -> (not ((E and (F -> G)) -> G))) -> (not ((E and (F -> G)) -> F)))), M:tm-113, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4958
in-theory        4958
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     45
proof            (modus-ponens tm-105 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-4)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4958.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-105, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4959
in-theory        4959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D))))
theorem-size     33
proof            (modus-ponens tm-95 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4959.         (((A -> B) -> (A -> A)) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D)))), M:tm-95, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4960
in-theory        4960
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (D -> (not ((A and (B -> C)) -> B))))
theorem-size     27
proof            (modus-ponens tm-84 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4960.         ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (D -> (not ((A and (B -> C)) -> B)))), M:tm-84, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4961
in-theory        4961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-83 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4961.         ((A -> (B -> (C -> B))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-83, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4962
in-theory        4962
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B and (C -> D)) -> C) -> (not ((B and (C -> D)) -> D))) -> (not ((B and (C -> D)) -> C))))
theorem-size     31
proof            (modus-ponens tm-76 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-10 tm-9 tm-2 tm-4)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4962.         (((not (not A)) -> A) and ((((B and (C -> D)) -> C) -> (not ((B and (C -> D)) -> D))) -> (not ((B and (C -> D)) -> C)))), M:tm-76, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4963
in-theory        4963
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))))) or (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C)))) -> (not ((A and (B -> C)) -> B)))
theorem-size     44
proof            (modus-ponens tm-73 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-8 tm-10 tm-9 tm-2 tm-4)
proof-size       142
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4963.         (((not (not (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))))) or (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C)))) -> (not ((A and (B -> C)) -> B))), M:tm-73, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4964
in-theory        4964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D))))
theorem-size     37
proof            (modus-ponens tm-69 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4964.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D)))), M:tm-69, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4965
in-theory        4965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     39
proof            (modus-ponens tm-54 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-2 tm-4)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4965.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-54, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4966
in-theory        4966
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and (C -> D)) -> C) -> (not ((B and (C -> D)) -> D)))) or (((B and (C -> D)) -> C) -> (not ((B and (C -> D)) -> D)))) -> (not ((B and (C -> D)) -> C)))
theorem-size     44
proof            (modus-ponens tm-47 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-8 tm-4 tm-9 tm-2)
proof-size       142
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4966.         (((A and (((B and (C -> D)) -> C) -> (not ((B and (C -> D)) -> D)))) or (((B and (C -> D)) -> C) -> (not ((B and (C -> D)) -> D)))) -> (not ((B and (C -> D)) -> C))), M:tm-47, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4967
in-theory        4967
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) and D) or (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C)))) -> (not ((A and (B -> C)) -> B)))
theorem-size     44
proof            (modus-ponens tm-46 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-8 tm-3 tm-9 tm-2 tm-4)
proof-size       142
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4967.         ((((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) and D) or (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C)))) -> (not ((A and (B -> C)) -> B))), M:tm-46, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4968
in-theory        4968
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A and (B -> C)) -> C)) or (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C)))) -> (not ((A and (B -> C)) -> B)))
theorem-size     34
proof            (modus-ponens tm-44 tm-143 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (not (-> (and Am (-> Bm Cm)) Cm))) (C (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-9 tm-2 tm-4)
proof-size       134
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4968.         (((not ((A and (B -> C)) -> C)) or (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C)))) -> (not ((A and (B -> C)) -> B))), M:tm-44, m:tm-143, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (not (-> (and Am (-> Bm Cm)) Cm))) (C (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4969
in-theory        4969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D))))
theorem-size     31
proof            (modus-ponens tm-42 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2 tm-4)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4969.         ((A -> (B or A)) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D)))), M:tm-42, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4970
in-theory        4970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D))))
theorem-size     31
proof            (modus-ponens tm-32 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2 tm-4)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4970.         ((A -> (A or B)) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D)))), M:tm-32, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4971
in-theory        4971
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) and (not ((A and (B -> C)) -> B))))
theorem-size     42
proof            (modus-ponens tm-24 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       140
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4971.         ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) and (not ((A and (B -> C)) -> B)))), M:tm-24, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4972
in-theory        4972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D))))
theorem-size     33
proof            (modus-ponens tm-23 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4972.         ((A -> (B -> (A and B))) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D)))), M:tm-23, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4973
in-theory        4973
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D))))
theorem-size     31
proof            (modus-ponens tm-22 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-2)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4973.         (((A and B) -> B) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D)))), M:tm-22, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4974
in-theory        4974
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D))))
theorem-size     31
proof            (modus-ponens tm-21 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-2 tm-4)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4974.         (((A and B) -> A) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D)))), M:tm-21, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4975
in-theory        4975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     39
proof            (modus-ponens tm-20 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-4)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4975.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-20, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4976
in-theory        4976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D))))
theorem-size     31
proof            (modus-ponens tm-19 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2 tm-4)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4976.         ((A -> (B -> A)) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D)))), M:tm-19, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4977
in-theory        4977
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))))
theorem-size     33
proof            (modus-ponens tm-12 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4977.         ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C)))), M:tm-12, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4978
in-theory        4978
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not (not ((A and (B -> C)) -> B)))) -> (not (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C)))))
theorem-size     44
proof            (modus-ponens tm-9 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-9 tm-2 tm-4)
proof-size       124
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4978.         (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not (not ((A and (B -> C)) -> B)))) -> (not (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))))), M:tm-9, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4979
in-theory        4979
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A and (B -> C)) -> B)) -> D) -> (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) or (not ((A and (B -> C)) -> B))) -> D))
theorem-size     38
proof            (modus-ponens tm-8 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-8 tm-9 tm-2 tm-4)
proof-size       120
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4979.         (((not ((A and (B -> C)) -> B)) -> D) -> (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) or (not ((A and (B -> C)) -> B))) -> D)), M:tm-8, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-4980
in-theory        4980
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B and (C -> D)) -> C) -> (not ((B and (C -> D)) -> D))) -> (not ((B and (C -> D)) -> C))))
theorem-size     27
proof            (modus-ponens tm-7 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-7 tm-9 tm-2 tm-4)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4980.         (A or ((((B and (C -> D)) -> C) -> (not ((B and (C -> D)) -> D))) -> (not ((B and (C -> D)) -> C)))), M:tm-7, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4981
in-theory        4981
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) or D)
theorem-size     27
proof            (modus-ponens tm-6 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-6 tm-9 tm-2 tm-4)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4981.         (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) or D), M:tm-6, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4982
in-theory        4982
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B and (C -> D)) -> C) -> (not ((B and (C -> D)) -> D))) -> (not ((B and (C -> D)) -> C))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4982.         (A -> (((((B and (C -> D)) -> C) -> (not ((B and (C -> D)) -> D))) -> (not ((B and (C -> D)) -> C))) and A)), M:tm-5, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4983
in-theory        4983
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (C -> D)) -> C) -> (not ((B and (C -> D)) -> D))) -> (not ((B and (C -> D)) -> C))))
theorem-size     27
proof            (modus-ponens tm-1 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-1 tm-9 tm-2 tm-4)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4983.         (A -> ((((B and (C -> D)) -> C) -> (not ((B and (C -> D)) -> D))) -> (not ((B and (C -> D)) -> C)))), M:tm-1, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-4984
in-theory        4984
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((A and (B -> C)) -> C)))
theorem-size     25
proof            (modus-ponens tm-144 tm-1 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4984.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((A and (B -> C)) -> C))), M:tm-144, m:tm-1, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-4985
in-theory        4985
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) -> B) or ((A and (B -> (C -> D))) -> (C -> D))) -> (((A and (B -> (C -> D))) -> C) -> ((A and (B -> (C -> D))) -> D)))
theorem-size     41
proof            (modus-ponens tm-144 tm-2 ((Am (and A (-> B (-> Bm Cm)))) (C (-> Bm Cm)) (D (-> (-> (and A (-> B (-> Bm Cm))) Bm) (-> (and A (-> B (-> Bm Cm))) Cm)))))
axioms-used      (tm-8 tm-2 tm-4)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4985.         ((((A and (B -> (C -> D))) -> B) or ((A and (B -> (C -> D))) -> (C -> D))) -> (((A and (B -> (C -> D))) -> C) -> ((A and (B -> (C -> D))) -> D))), M:tm-144, m:tm-2, u:((Am (and A (-> B (-> Bm Cm)))) (C (-> Bm Cm)) (D (-> (-> (and A (-> B (-> Bm Cm))) Bm) (-> (and A (-> B (-> Bm Cm))) Cm))))
================================================================
tm-name          tm-4986
in-theory        4986
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (((A and (B -> C)) -> C) and D)))
theorem-size     27
proof            (modus-ponens tm-144 tm-5 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> (and A (-> B C)) C) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4986.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (((A and (B -> C)) -> C) and D))), M:tm-144, m:tm-5, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> (and A (-> B C)) C) Bm))))
================================================================
tm-name          tm-4987
in-theory        4987
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) or D))
theorem-size     25
proof            (modus-ponens tm-144 tm-6 ((Am (-> (and A (-> B C)) C)) (D (or (-> (and A (-> B C)) C) Bm))))
axioms-used      (tm-8 tm-2 tm-4 tm-6)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-4987.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) or D)), M:tm-144, m:tm-6, u:((Am (-> (and A (-> B C)) C)) (D (or (-> (and A (-> B C)) C) Bm)))
================================================================
tm-name          tm-4988
in-theory        4988
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or ((A and (B -> C)) -> C)))
theorem-size     25
proof            (modus-ponens tm-144 tm-7 ((Am (-> (and A (-> B C)) C)) (D (or Bm (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-7)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4988.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or ((A and (B -> C)) -> C))), M:tm-144, m:tm-7, u:((Am (-> (and A (-> B C)) C)) (D (or Bm (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-4989
in-theory        4989
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((C -> D) -> (((A and (B -> C)) or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-144 tm-8 ((Am (and A (-> B Bm))) (C Bm) (D (-> (-> Bm Cm) (-> (or (and A (-> B Bm)) Bm) Cm)))))
axioms-used      (tm-8 tm-2 tm-4)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4989.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((C -> D) -> (((A and (B -> C)) or C) -> D))), M:tm-144, m:tm-8, u:((Am (and A (-> B Bm))) (C Bm) (D (-> (-> Bm Cm) (-> (or (and A (-> B Bm)) Bm) Cm))))
================================================================
tm-name          tm-4990
in-theory        4990
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> (not C)) -> (not (A and (B -> C)))))
theorem-size     31
proof            (modus-ponens tm-144 tm-9 ((Am (and A (-> B Bm))) (C Bm) (D (-> (-> (and A (-> B Bm)) (not Bm)) (not (and A (-> B Bm)))))))
axioms-used      (tm-8 tm-2 tm-4 tm-9)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4990.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> (not C)) -> (not (A and (B -> C))))), M:tm-144, m:tm-9, u:((Am (and A (-> B Bm))) (C Bm) (D (-> (-> (and A (-> B Bm)) (not Bm)) (not (and A (-> B Bm))))))
================================================================
tm-name          tm-4991
in-theory        4991
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-144 tm-11 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4991.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (E -> D))), M:tm-144, m:tm-11, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-4992
in-theory        4992
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> (A and (B -> C))))
theorem-size     27
proof            (modus-ponens tm-144 tm-12 ((Am (and A (-> B Bm))) (C Bm) (D (-> (and A (-> B Bm)) (and A (-> B Bm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4992.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> (A and (B -> C)))), M:tm-144, m:tm-12, u:((Am (and A (-> B Bm))) (C Bm) (D (-> (and A (-> B Bm)) (and A (-> B Bm)))))
================================================================
tm-name          tm-4993
in-theory        4993
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-144 tm-14 ((Am (-> (and A (-> B C)) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4993.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-144, m:tm-14, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-4994
in-theory        4994
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and (C -> A)) -> C) or (((A -> B) and (C -> A)) -> A)) -> (((A -> B) and (C -> A)) -> B))
theorem-size     29
proof            (modus-ponens tm-144 tm-15 ((A (-> Am Bm)) (Cm (-> B Am)) (C Am) (D (-> (and (-> Am Bm) (-> B Am)) Bm))))
axioms-used      (tm-8 tm-2 tm-4 tm-3)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4994.         (((((A -> B) and (C -> A)) -> C) or (((A -> B) and (C -> A)) -> A)) -> (((A -> B) and (C -> A)) -> B)), M:tm-144, m:tm-15, u:((A (-> Am Bm)) (Cm (-> B Am)) (C Am) (D (-> (and (-> Am Bm) (-> B Am)) Bm)))
================================================================
tm-name          tm-4995
in-theory        4995
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-144 tm-16 ((Am (-> (and A (-> B C)) C)) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4995.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D and E) -> D)), M:tm-144, m:tm-16, u:((Am (-> (and A (-> B C)) C)) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-4996
in-theory        4996
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> B)) -> B) or ((A and (B -> B)) -> B)) -> ((A and (B -> B)) -> B))
theorem-size     23
proof            (modus-ponens tm-144 tm-17 ((A Am) (B Cm) (Bm Cm) (C Cm) (D (-> (and Am (-> Cm Cm)) Cm))))
axioms-used      (tm-8 tm-2 tm-4)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-4996.         ((((A and (B -> B)) -> B) or ((A and (B -> B)) -> B)) -> ((A and (B -> B)) -> B)), M:tm-144, m:tm-17, u:((A Am) (B Cm) (Bm Cm) (C Cm) (D (-> (and Am (-> Cm Cm)) Cm)))
================================================================
tm-name          tm-4997
in-theory        4997
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-144 tm-18 ((Am (-> (and A (-> B C)) C)) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-4997.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D and E) -> E)), M:tm-144, m:tm-18, u:((Am (-> (and A (-> B C)) C)) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-4998
in-theory        4998
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> D)) and ((A and (B -> C)) -> C)))
theorem-size     29
proof            (modus-ponens tm-144 tm-19 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> Cm Bm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4998.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> D)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-19, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> Cm Bm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-4999
in-theory        4999
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A and (B -> C)) -> C)))
theorem-size     37
proof            (modus-ponens tm-144 tm-20 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4999.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-20, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5000
in-theory        5000
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D and E) -> D) and ((A and (B -> C)) -> C)))
theorem-size     29
proof            (modus-ponens tm-144 tm-21 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and Bm Cm) Bm) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-5000.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D and E) -> D) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-21, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and Bm Cm) Bm) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5001
in-theory        5001
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D and E) -> E) and ((A and (B -> C)) -> C)))
theorem-size     29
proof            (modus-ponens tm-144 tm-22 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and Bm Cm) Cm) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-5001.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D and E) -> E) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-22, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and Bm Cm) Cm) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5002
in-theory        5002
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> (D and E))) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-23 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-5002.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> (D and E))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-23, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5003
in-theory        5003
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> ((A and (B -> C)) and C)))
theorem-size     29
proof            (modus-ponens tm-144 tm-24 ((Am (and A (-> B Bm))) (C Bm) (D (-> (and A (-> B Bm)) (and (and A (-> B Bm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-5003.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> ((A and (B -> C)) and C))), M:tm-144, m:tm-24, u:((Am (and A (-> B Bm))) (C Bm) (D (-> (and A (-> B Bm)) (and (and A (-> B Bm)) Bm))))
================================================================
tm-name          tm-5004
in-theory        5004
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-144 tm-25 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-5004.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (E -> (D and E)))), M:tm-144, m:tm-25, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-5005
in-theory        5005
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (D or E)) and ((A and (B -> C)) -> C)))
theorem-size     29
proof            (modus-ponens tm-144 tm-32 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (or Bm Cm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-5005.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (D or E)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-32, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (or Bm Cm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5006
in-theory        5006
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-144 tm-33 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-5006.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (D or E))), M:tm-144, m:tm-33, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-5007
in-theory        5007
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E or D)) and ((A and (B -> C)) -> C)))
theorem-size     29
proof            (modus-ponens tm-144 tm-42 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (or Cm Bm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-5007.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E or D)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-42, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (or Cm Bm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5008
in-theory        5008
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-144 tm-43 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-5008.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (E or D))), M:tm-144, m:tm-43, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-5009
in-theory        5009
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((A and (B -> C)) and D) or (A and (B -> C))) -> C))
theorem-size     31
proof            (modus-ponens tm-144 tm-46 ((Am (and A (-> B Bm))) (C Bm) (D (-> (or (and (and A (-> B Bm)) Cm) (and A (-> B Bm))) Bm))))
axioms-used      (tm-8 tm-2 tm-4 tm-3)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5009.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((A and (B -> C)) and D) or (A and (B -> C))) -> C)), M:tm-144, m:tm-46, u:((Am (and A (-> B Bm))) (C Bm) (D (-> (or (and (and A (-> B Bm)) Cm) (and A (-> B Bm))) Bm)))
================================================================
tm-name          tm-5010
in-theory        5010
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D and (A and (B -> C))) or (A and (B -> C))) -> C))
theorem-size     31
proof            (modus-ponens tm-144 tm-47 ((Am (and A (-> B Bm))) (C Bm) (D (-> (or (and Cm (and A (-> B Bm))) (and A (-> B Bm))) Bm))))
axioms-used      (tm-8 tm-2 tm-4)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5010.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D and (A and (B -> C))) or (A and (B -> C))) -> C)), M:tm-144, m:tm-47, u:((Am (and A (-> B Bm))) (C Bm) (D (-> (or (and Cm (and A (-> B Bm))) (and A (-> B Bm))) Bm)))
================================================================
tm-name          tm-5011
in-theory        5011
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A and (B -> C)) -> C)))
theorem-size     37
proof            (modus-ponens tm-144 tm-54 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-5011.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-54, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5012
in-theory        5012
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-144 tm-56 ((Am (-> (and A (-> B C)) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-5012.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-144, m:tm-56, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-5013
in-theory        5013
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (not A))) -> B) or ((A and (B -> (not A))) -> (not A))) -> (not (A and (B -> (not A)))))
theorem-size     26
proof            (modus-ponens tm-144 tm-59 ((A Am) (Bm (-> B (not Am))) (C (not Am)) (D (not (and Am (-> B (not Am)))))))
axioms-used      (tm-8 tm-2 tm-4 tm-9 tm-3)
proof-size       126
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5013.         ((((A and (B -> (not A))) -> B) or ((A and (B -> (not A))) -> (not A))) -> (not (A and (B -> (not A))))), M:tm-144, m:tm-59, u:((A Am) (Bm (-> B (not Am))) (C (not Am)) (D (not (and Am (-> B (not Am))))))
================================================================
tm-name          tm-5014
in-theory        5014
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A and (B -> C)) -> C)))
theorem-size     35
proof            (modus-ponens tm-144 tm-69 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-9)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-5014.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-69, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5015
in-theory        5015
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-144 tm-71 ((Am (-> (and A (-> B C)) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-9)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-5015.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-144, m:tm-71, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-5016
in-theory        5016
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((not (not (A and (B -> C)))) or (A and (B -> C))) -> C))
theorem-size     31
proof            (modus-ponens tm-144 tm-73 ((Am (and A (-> B Bm))) (C Bm) (D (-> (or (not (not (and A (-> B Bm)))) (and A (-> B Bm))) Bm))))
axioms-used      (tm-8 tm-2 tm-4 tm-10)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5016.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((not (not (A and (B -> C)))) or (A and (B -> C))) -> C)), M:tm-144, m:tm-73, u:((Am (and A (-> B Bm))) (C Bm) (D (-> (or (not (not (and A (-> B Bm)))) (and A (-> B Bm))) Bm)))
================================================================
tm-name          tm-5017
in-theory        5017
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((not (not D)) -> D) and ((A and (B -> C)) -> C)))
theorem-size     29
proof            (modus-ponens tm-144 tm-76 ((Am (-> (and A (-> B C)) C)) (D (and (-> (not (not Bm)) Bm) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-10)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-5017.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((not (not D)) -> D) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-76, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (not (not Bm)) Bm) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5018
in-theory        5018
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((not (not D)) -> D))
theorem-size     21
proof            (modus-ponens tm-144 tm-78 ((Am (-> (and A (-> B C)) C)) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-10)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-5018.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((not (not D)) -> D)), M:tm-144, m:tm-78, u:((Am (-> (and A (-> B C)) C)) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-5019
in-theory        5019
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (not (C -> (D -> C))))) -> B) or ((A and (B -> (not (C -> (D -> C))))) -> (not (C -> (D -> C))))) -> (not (A and (B -> (not (C -> (D -> C)))))))
theorem-size     42
proof            (modus-ponens tm-144 tm-79 ((Am (and A (-> B (not (-> Bm (-> Cm Bm)))))) (C (not (-> Bm (-> Cm Bm)))) (D (not (and A (-> B (not (-> Bm (-> Cm Bm)))))))))
axioms-used      (tm-8 tm-2 tm-4 tm-9 tm-1)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5019.         ((((A and (B -> (not (C -> (D -> C))))) -> B) or ((A and (B -> (not (C -> (D -> C))))) -> (not (C -> (D -> C))))) -> (not (A and (B -> (not (C -> (D -> C))))))), M:tm-144, m:tm-79, u:((Am (and A (-> B (not (-> Bm (-> Cm Bm)))))) (C (not (-> Bm (-> Cm Bm)))) (D (not (and A (-> B (not (-> Bm (-> Cm Bm))))))))
================================================================
tm-name          tm-5020
in-theory        5020
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> (F -> E))) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-83 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-5020.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> (F -> E))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-83, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5021
in-theory        5021
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> (D -> C)))
theorem-size     25
proof            (modus-ponens tm-144 tm-84 ((Am (and A (-> B Bm))) (C Bm) (D (-> (and A (-> B Bm)) (-> Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5021.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> (D -> C))), M:tm-144, m:tm-84, u:((Am (and A (-> B Bm))) (C Bm) (D (-> (and A (-> B Bm)) (-> Cm Bm))))
================================================================
tm-name          tm-5022
in-theory        5022
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-144 tm-85 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-5022.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (E -> (F -> E)))), M:tm-144, m:tm-85, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-5023
in-theory        5023
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> C))
theorem-size     23
proof            (modus-ponens tm-144 tm-86 ((Am (-> (and A (-> B C)) C)) (D (-> (and A (-> B C)) C))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5023.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> C)), M:tm-144, m:tm-86, u:((Am (-> (and A (-> B C)) C)) (D (-> (and A (-> B C)) C)))
================================================================
tm-name          tm-5024
in-theory        5024
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) -> B) or ((A and (B -> (C -> D))) -> (C -> D))) -> ((A and (B -> (C -> D))) -> (C -> D)))
theorem-size     33
proof            (modus-ponens tm-144 tm-87 ((Am (and A (-> B (-> Bm Cm)))) (C (-> Bm Cm)) (D (-> (and A (-> B (-> Bm Cm))) (-> Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5024.         ((((A and (B -> (C -> D))) -> B) or ((A and (B -> (C -> D))) -> (C -> D))) -> ((A and (B -> (C -> D))) -> (C -> D))), M:tm-144, m:tm-87, u:((Am (and A (-> B (-> Bm Cm)))) (C (-> Bm Cm)) (D (-> (and A (-> B (-> Bm Cm))) (-> Bm Cm))))
================================================================
tm-name          tm-5025
in-theory        5025
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> (D -> D)) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-95 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-5025.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> (D -> D)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-95, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5026
in-theory        5026
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> E) -> (D -> D)))
theorem-size     23
proof            (modus-ponens tm-144 tm-97 ((Am (-> (and A (-> B C)) C)) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-5026.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> E) -> (D -> D))), M:tm-144, m:tm-97, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-5027
in-theory        5027
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A and (B -> C)) -> C)))
theorem-size     43
proof            (modus-ponens tm-144 tm-105 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-5027.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-105, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5028
in-theory        5028
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-144 tm-107 ((Am (-> (and A (-> B C)) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-5028.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-144, m:tm-107, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-5029
in-theory        5029
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> B) or ((A and (B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not (A and (B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))))
theorem-size     74
proof            (modus-ponens tm-144 tm-109 ((Am (and A (-> B (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))) (C (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (and A (-> B (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))))
axioms-used      (tm-8 tm-2 tm-4 tm-9 tm-1)
proof-size       210
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5029.         ((((A and (B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> B) or ((A and (B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not (A and (B -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))), M:tm-144, m:tm-109, u:((Am (and A (-> B (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))) (C (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (and A (-> B (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))))
================================================================
tm-name          tm-5030
in-theory        5030
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A and (B -> C)) -> C)))
theorem-size     39
proof            (modus-ponens tm-144 tm-113 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-5030.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-113, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5031
in-theory        5031
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> (D -> E)))) -> B) or ((A and (B -> (C -> (D -> E)))) -> (C -> (D -> E)))) -> ((A and (B -> (C -> (D -> E)))) -> ((C -> D) -> (C -> E))))
theorem-size     45
proof            (modus-ponens tm-144 tm-114 ((Am (and A (-> B (-> Bm (-> Cm Dm))))) (C (-> Bm (-> Cm Dm))) (D (-> (and A (-> B (-> Bm (-> Cm Dm)))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-5031.         ((((A and (B -> (C -> (D -> E)))) -> B) or ((A and (B -> (C -> (D -> E)))) -> (C -> (D -> E)))) -> ((A and (B -> (C -> (D -> E)))) -> ((C -> D) -> (C -> E)))), M:tm-144, m:tm-114, u:((Am (and A (-> B (-> Bm (-> Cm Dm))))) (C (-> Bm (-> Cm Dm))) (D (-> (and A (-> B (-> Bm (-> Cm Dm)))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-5032
in-theory        5032
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-144 tm-115 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-5032.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-144, m:tm-115, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-5033
in-theory        5033
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and (C -> (A -> B))) -> C) or ((((A -> B) -> A) and (C -> (A -> B))) -> (A -> B))) -> ((((A -> B) -> A) and (C -> (A -> B))) -> B))
theorem-size     43
proof            (modus-ponens tm-144 tm-119 ((A (-> (-> Am Bm) Am)) (Cm (-> B (-> Am Bm))) (C (-> Am Bm)) (D (-> (and (-> (-> Am Bm) Am) (-> B (-> Am Bm))) Bm))))
axioms-used      (tm-8 tm-2 tm-4 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-5033.         ((((((A -> B) -> A) and (C -> (A -> B))) -> C) or ((((A -> B) -> A) and (C -> (A -> B))) -> (A -> B))) -> ((((A -> B) -> A) and (C -> (A -> B))) -> B)), M:tm-144, m:tm-119, u:((A (-> (-> Am Bm) Am)) (Cm (-> B (-> Am Bm))) (C (-> Am Bm)) (D (-> (and (-> (-> Am Bm) Am) (-> B (-> Am Bm))) Bm)))
================================================================
tm-name          tm-5034
in-theory        5034
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and (C -> A)) -> C) or (((A -> B) and (C -> A)) -> A)) -> (((A -> B) and (C -> A)) -> A))
theorem-size     29
proof            (modus-ponens tm-144 tm-120 ((A (-> Am Bm)) (Cm (-> B Am)) (C Am) (D (-> (and (-> Am Bm) (-> B Am)) Am))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5034.         (((((A -> B) and (C -> A)) -> C) or (((A -> B) and (C -> A)) -> A)) -> (((A -> B) and (C -> A)) -> A)), M:tm-144, m:tm-120, u:((A (-> Am Bm)) (Cm (-> B Am)) (C Am) (D (-> (and (-> Am Bm) (-> B Am)) Am)))
================================================================
tm-name          tm-5035
in-theory        5035
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A and (B -> C)) -> C)))
theorem-size     39
proof            (modus-ponens tm-144 tm-125 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-5035.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-125, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5036
in-theory        5036
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-144 tm-127 ((Am (-> (and A (-> B C)) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-5036.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-144, m:tm-127, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-5037
in-theory        5037
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (A -> C))) -> B) or ((A and (B -> (A -> C))) -> (A -> C))) -> ((A and (B -> (A -> C))) -> C))
theorem-size     31
proof            (modus-ponens tm-144 tm-129 ((A Am) (Bm (-> B (-> Am Cm))) (C (-> Am Cm)) (D (-> (and Am (-> B (-> Am Cm))) Cm))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-5037.         ((((A and (B -> (A -> C))) -> B) or ((A and (B -> (A -> C))) -> (A -> C))) -> ((A and (B -> (A -> C))) -> C)), M:tm-144, m:tm-129, u:((A Am) (Bm (-> B (-> Am Cm))) (C (-> Am Cm)) (D (-> (and Am (-> B (-> Am Cm))) Cm)))
================================================================
tm-name          tm-5038
in-theory        5038
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (not ((C and D) -> C)))) -> B) or ((A and (B -> (not ((C and D) -> C)))) -> (not ((C and D) -> C)))) -> (not (A and (B -> (not ((C and D) -> C))))))
theorem-size     42
proof            (modus-ponens tm-144 tm-130 ((Am (and A (-> B (not (-> (and Bm Cm) Bm))))) (C (not (-> (and Bm Cm) Bm))) (D (not (and A (-> B (not (-> (and Bm Cm) Bm))))))))
axioms-used      (tm-8 tm-2 tm-4 tm-9 tm-1 tm-3)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5038.         ((((A and (B -> (not ((C and D) -> C)))) -> B) or ((A and (B -> (not ((C and D) -> C)))) -> (not ((C and D) -> C)))) -> (not (A and (B -> (not ((C and D) -> C)))))), M:tm-144, m:tm-130, u:((Am (and A (-> B (not (-> (and Bm Cm) Bm))))) (C (not (-> (and Bm Cm) Bm))) (D (not (and A (-> B (not (-> (and Bm Cm) Bm)))))))
================================================================
tm-name          tm-5039
in-theory        5039
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> ((E and F) -> E)) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-134 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-5039.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> ((E and F) -> E)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-134, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5040
in-theory        5040
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C and D))) -> B) or ((A and (B -> (C and D))) -> (C and D))) -> ((A and (B -> (C and D))) -> C))
theorem-size     31
proof            (modus-ponens tm-144 tm-135 ((Am (and A (-> B (and Bm Cm)))) (C (and Bm Cm)) (D (-> (and A (-> B (and Bm Cm))) Bm))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-5040.         ((((A and (B -> (C and D))) -> B) or ((A and (B -> (C and D))) -> (C and D))) -> ((A and (B -> (C and D))) -> C)), M:tm-144, m:tm-135, u:((Am (and A (-> B (and Bm Cm)))) (C (and Bm Cm)) (D (-> (and A (-> B (and Bm Cm))) Bm)))
================================================================
tm-name          tm-5041
in-theory        5041
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-144 tm-136 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-5041.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((E and F) -> E))), M:tm-144, m:tm-136, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-5042
in-theory        5042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-134 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5042.         ((A -> ((B and C) -> B)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-134, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5043
in-theory        5043
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-125 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5043.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-125, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5044
in-theory        5044
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> (D -> E)) -> (((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> E)))
theorem-size     47
proof            (modus-ponens tm-114 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) (-> C D))) (B (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5044.         ((((A and (B -> C)) -> C) -> (D -> E)) -> (((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> E))), M:tm-114, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) (-> C D))) (B (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-5045
in-theory        5045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> G) -> H) -> ((((E and (F -> G)) -> F) or ((E and (F -> G)) -> G)) -> H)))
theorem-size     43
proof            (modus-ponens tm-113 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5045.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> G) -> H) -> ((((E and (F -> G)) -> F) or ((E and (F -> G)) -> G)) -> H))), M:tm-113, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5046
in-theory        5046
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> (D -> E))) -> (D -> E)) -> (((B and (C -> (D -> E))) -> D) -> ((B and (C -> (D -> E))) -> E)))) -> ((((B and (C -> (D -> E))) -> C) or ((B and (C -> (D -> E))) -> (D -> E))) -> (((B and (C -> (D -> E))) -> D) -> ((B and (C -> (D -> E))) -> E))))
theorem-size     75
proof            (modus-ponens tm-110 tm-144 ((A (and Am (-> Bm (-> B C)))) (Cm (-> B C)) (Dm (-> (-> (and Am (-> Bm (-> B C))) B) (-> (and Am (-> Bm (-> B C))) C))) (D (-> (or (-> (and Am (-> Bm (-> B C))) Bm) (-> (and Am (-> Bm (-> B C))) (-> B C))) (-> (-> (and Am (-> Bm (-> B C))) B) (-> (and Am (-> Bm (-> B C))) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       227
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5046.         ((A or (((B and (C -> (D -> E))) -> (D -> E)) -> (((B and (C -> (D -> E))) -> D) -> ((B and (C -> (D -> E))) -> E)))) -> ((((B and (C -> (D -> E))) -> C) or ((B and (C -> (D -> E))) -> (D -> E))) -> (((B and (C -> (D -> E))) -> D) -> ((B and (C -> (D -> E))) -> E)))), M:tm-110, m:tm-144, u:((A (and Am (-> Bm (-> B C)))) (Cm (-> B C)) (Dm (-> (-> (and Am (-> Bm (-> B C))) B) (-> (and Am (-> Bm (-> B C))) C))) (D (-> (or (-> (and Am (-> Bm (-> B C))) Bm) (-> (and Am (-> Bm (-> B C))) (-> B C))) (-> (-> (and Am (-> Bm (-> B C))) B) (-> (and Am (-> Bm (-> B C))) C)))))
================================================================
tm-name          tm-5047
in-theory        5047
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     47
proof            (modus-ponens tm-105 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5047.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-105, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5048
in-theory        5048
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> (C -> D))) -> (C -> D)) -> ((A and (B -> (C -> D))) -> C)) or (((A and (B -> (C -> D))) -> (C -> D)) -> ((A and (B -> (C -> D))) -> D))) -> ((((A and (B -> (C -> D))) -> B) or ((A and (B -> (C -> D))) -> (C -> D))) -> ((A and (B -> (C -> D))) -> D)))
theorem-size     75
proof            (modus-ponens tm-102 tm-144 ((A (and Am (-> Bm (-> B C)))) (Cm (-> B C)) (Dm (-> (and Am (-> Bm (-> B C))) C)) (D (-> (or (-> (and Am (-> Bm (-> B C))) Bm) (-> (and Am (-> Bm (-> B C))) (-> B C))) (-> (and Am (-> Bm (-> B C))) C)))))
axioms-used      (tm-8 tm-2 tm-4)
proof-size       239
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5048.         (((((A and (B -> (C -> D))) -> (C -> D)) -> ((A and (B -> (C -> D))) -> C)) or (((A and (B -> (C -> D))) -> (C -> D)) -> ((A and (B -> (C -> D))) -> D))) -> ((((A and (B -> (C -> D))) -> B) or ((A and (B -> (C -> D))) -> (C -> D))) -> ((A and (B -> (C -> D))) -> D))), M:tm-102, m:tm-144, u:((A (and Am (-> Bm (-> B C)))) (Cm (-> B C)) (Dm (-> (and Am (-> Bm (-> B C))) C)) (D (-> (or (-> (and Am (-> Bm (-> B C))) Bm) (-> (and Am (-> Bm (-> B C))) (-> B C))) (-> (and Am (-> Bm (-> B C))) C))))
================================================================
tm-name          tm-5049
in-theory        5049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-95 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5049.         (((A -> B) -> (A -> A)) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F))), M:tm-95, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5050
in-theory        5050
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) or (((A and (B -> C)) -> C) -> ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> C)))
theorem-size     49
proof            (modus-ponens tm-92 tm-144 ((Dm (-> (and Am (-> Bm Cm)) Cm)) (A (-> (and Am (-> Bm Cm)) Cm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5050.         (((((A and (B -> C)) -> C) -> D) or (((A and (B -> C)) -> C) -> ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> C))), M:tm-92, m:tm-144, u:((Dm (-> (and Am (-> Bm Cm)) Cm)) (A (-> (and Am (-> Bm Cm)) Cm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-5051
in-theory        5051
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> D) -> (E -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))
theorem-size     29
proof            (modus-ponens tm-84 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5051.         ((((A and (B -> C)) -> C) -> D) -> (E -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))), M:tm-84, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5052
in-theory        5052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-83 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5052.         ((A -> (B -> (C -> B))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-83, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5053
in-theory        5053
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> D) -> (E -> ((B and (C -> D)) -> D)))) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> (E -> ((B and (C -> D)) -> D))))
theorem-size     45
proof            (modus-ponens tm-80 tm-144 ((A (-> (and Am (-> Bm Cm)) Cm)) (Dm (-> B (-> (and Am (-> Bm Cm)) Cm))) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (-> B (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5053.         ((A or (((B and (C -> D)) -> D) -> (E -> ((B and (C -> D)) -> D)))) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> (E -> ((B and (C -> D)) -> D)))), M:tm-80, m:tm-144, u:((A (-> (and Am (-> Bm Cm)) Cm)) (Dm (-> B (-> (and Am (-> Bm Cm)) Cm))) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (-> B (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-5054
in-theory        5054
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B and (C -> D)) -> D) -> E) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-76 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5054.         (((not (not A)) -> A) and ((((B and (C -> D)) -> D) -> E) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> E))), M:tm-76, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5055
in-theory        5055
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A and (B -> C)) -> C) -> D))) or (((A and (B -> C)) -> C) -> D)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))
theorem-size     39
proof            (modus-ponens tm-73 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-2 tm-4)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5055.         (((not (not (((A and (B -> C)) -> C) -> D))) or (((A and (B -> C)) -> C) -> D)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-73, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5056
in-theory        5056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F)))
theorem-size     39
proof            (modus-ponens tm-69 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-4)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5056.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F))), M:tm-69, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5057
in-theory        5057
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (not C))) -> C) or (((A and (B -> (not C))) -> (not C)) -> (not (A and (B -> (not C)))))) -> ((((A and (B -> (not C))) -> B) or ((A and (B -> (not C))) -> (not C))) -> (not (A and (B -> (not C))))))
theorem-size     53
proof            (modus-ponens tm-66 tm-144 ((A (and Am (-> Bm (not B)))) (Cm (not B)) (Dm (not (and Am (-> Bm (not B))))) (C (-> (or (-> (and Am (-> Bm (not B))) Bm) (-> (and Am (-> Bm (not B))) (not B))) (not (and Am (-> Bm (not B))))))))
axioms-used      (tm-8 tm-9 tm-2 tm-4)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5057.         ((((A and (B -> (not C))) -> C) or (((A and (B -> (not C))) -> (not C)) -> (not (A and (B -> (not C)))))) -> ((((A and (B -> (not C))) -> B) or ((A and (B -> (not C))) -> (not C))) -> (not (A and (B -> (not C)))))), M:tm-66, m:tm-144, u:((A (and Am (-> Bm (not B)))) (Cm (not B)) (Dm (not (and Am (-> Bm (not B))))) (C (-> (or (-> (and Am (-> Bm (not B))) Bm) (-> (and Am (-> Bm (not B))) (not B))) (not (and Am (-> Bm (not B)))))))
================================================================
tm-name          tm-5058
in-theory        5058
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> (((A and (B -> C)) -> B) or ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> C) or (((A and (B -> C)) -> B) or ((A and (B -> C)) -> C))) -> (((A and (B -> C)) -> B) or ((A and (B -> C)) -> C))))
theorem-size     63
proof            (modus-ponens tm-55 tm-144 ((A (-> (and Am (-> Bm Cm)) Cm)) (Dm (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))) (B (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))) (C (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-8 tm-4)
proof-size       179
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5058.         ((((A and (B -> C)) -> C) -> (((A and (B -> C)) -> B) or ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> C) or (((A and (B -> C)) -> B) or ((A and (B -> C)) -> C))) -> (((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)))), M:tm-55, m:tm-144, u:((A (-> (and Am (-> Bm Cm)) Cm)) (Dm (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))) (B (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))) (C (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-5059
in-theory        5059
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-54 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5059.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-54, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5060
in-theory        5060
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B and (C -> D))) or (((B and (C -> D)) -> D) -> ((A or (B and (C -> D))) -> D))) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> ((A or (B and (C -> D))) -> D)))
theorem-size     51
proof            (modus-ponens tm-51 tm-144 ((A (and Am (-> Bm Cm))) (B Cm) (Dm (-> (or C (and Am (-> Bm Cm))) Cm)) (D (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (-> (or C (and Am (-> Bm Cm))) Cm)))))
axioms-used      (tm-8 tm-2 tm-4)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5060.         (((A -> (B and (C -> D))) or (((B and (C -> D)) -> D) -> ((A or (B and (C -> D))) -> D))) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> ((A or (B and (C -> D))) -> D))), M:tm-51, m:tm-144, u:((A (and Am (-> Bm Cm))) (B Cm) (Dm (-> (or C (and Am (-> Bm Cm))) Cm)) (D (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (-> (or C (and Am (-> Bm Cm))) Cm))))
================================================================
tm-name          tm-5061
in-theory        5061
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> D) -> (A and ((B and (C -> D)) -> D)))) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> (A and ((B and (C -> D)) -> D))))
theorem-size     45
proof            (modus-ponens tm-48 tm-144 ((A (-> (and Am (-> Bm Cm)) Cm)) (Dm (and B (-> (and Am (-> Bm Cm)) Cm))) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (and B (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5061.         ((A or (((B and (C -> D)) -> D) -> (A and ((B and (C -> D)) -> D)))) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> (A and ((B and (C -> D)) -> D)))), M:tm-48, m:tm-144, u:((A (-> (and Am (-> Bm Cm)) Cm)) (Dm (and B (-> (and Am (-> Bm Cm)) Cm))) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (and B (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-5062
in-theory        5062
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B and (C -> D)) -> D) -> E)) or (((B and (C -> D)) -> D) -> E)) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> E))
theorem-size     39
proof            (modus-ponens tm-47 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5062.         (((A and (((B and (C -> D)) -> D) -> E)) or (((B and (C -> D)) -> D) -> E)) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> E)), M:tm-47, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5063
in-theory        5063
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> C) -> D) and E) or (((A and (B -> C)) -> C) -> D)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))
theorem-size     39
proof            (modus-ponens tm-46 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-2 tm-4)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5063.         ((((((A and (B -> C)) -> C) -> D) and E) or (((A and (B -> C)) -> C) -> D)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-46, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5064
in-theory        5064
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> (C -> D)) or (((A and (B -> C)) -> C) -> ((A and (B -> C)) -> D))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> D)))
theorem-size     49
proof            (modus-ponens tm-45 tm-144 ((A (and Am (-> Bm Cm))) (B Cm) (Dm (-> (and Am (-> Bm Cm)) C)) (D (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (-> (and Am (-> Bm Cm)) C)))))
axioms-used      (tm-8 tm-2 tm-4)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5064.         ((((A and (B -> C)) -> (C -> D)) or (((A and (B -> C)) -> C) -> ((A and (B -> C)) -> D))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> D))), M:tm-45, m:tm-144, u:((A (and Am (-> Bm Cm))) (B Cm) (Dm (-> (and Am (-> Bm Cm)) C)) (D (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (-> (and Am (-> Bm Cm)) C))))
================================================================
tm-name          tm-5065
in-theory        5065
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> D) -> A)) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> A))
theorem-size     29
proof            (modus-ponens tm-44 tm-144 ((A (-> (and Am (-> Bm Cm)) Cm)) (B Dm) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5065.         ((A or (((B and (C -> D)) -> D) -> A)) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> A)), M:tm-44, m:tm-144, u:((A (-> (and Am (-> Bm Cm)) Cm)) (B Dm) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5066
in-theory        5066
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-42 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5066.         ((A -> (B or A)) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F))), M:tm-42, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5067
in-theory        5067
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-32 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5067.         ((A -> (A or B)) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F))), M:tm-32, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5068
in-theory        5068
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> C) -> D) and ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))
theorem-size     37
proof            (modus-ponens tm-24 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5068.         ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> C) -> D) and ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))), M:tm-24, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5069
in-theory        5069
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-23 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5069.         ((A -> (B -> (A and B))) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F))), M:tm-23, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5070
in-theory        5070
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-22 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5070.         (((A and B) -> B) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F))), M:tm-22, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5071
in-theory        5071
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-21 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5071.         (((A and B) -> A) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F))), M:tm-21, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5072
in-theory        5072
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-20 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5072.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-20, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5073
in-theory        5073
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-19 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5073.         ((A -> (B -> A)) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F))), M:tm-19, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5074
in-theory        5074
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> D) -> (((A and (B -> C)) -> C) -> D))
theorem-size     19
proof            (modus-ponens tm-12 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5074.         ((((A and (B -> C)) -> C) -> D) -> (((A and (B -> C)) -> C) -> D)), M:tm-12, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5075
in-theory        5075
times-derived    2
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> (not ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))) -> (not (((A and (B -> C)) -> C) -> D)))
theorem-size     39
proof            (modus-ponens tm-9 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-2 tm-4)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5075.         (((((A and (B -> C)) -> C) -> D) -> (not ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))) -> (not (((A and (B -> C)) -> C) -> D))), M:tm-9, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5076
in-theory        5076
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D) -> E) -> (((((A and (B -> C)) -> C) -> D) or ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) -> E))
theorem-size     49
proof            (modus-ponens tm-8 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-8 tm-2 tm-4)
proof-size       135
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5076.         ((((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D) -> E) -> (((((A and (B -> C)) -> C) -> D) or ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) -> E)), M:tm-8, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5077
in-theory        5077
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B and (C -> D)) -> D) -> E) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-7 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-2 tm-4)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5077.         (A or ((((B and (C -> D)) -> D) -> E) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> E))), M:tm-7, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5078
in-theory        5078
times-derived    2
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) or E)
theorem-size     29
proof            (modus-ponens tm-6 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-2 tm-4)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5078.         (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) or E), M:tm-6, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5079
in-theory        5079
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B and (C -> D)) -> D) -> E) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> E)) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5079.         (A -> (((((B and (C -> D)) -> D) -> E) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> E)) and A)), M:tm-5, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5080
in-theory        5080
times-derived    2
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> (((A and (B -> C)) -> B) or ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> C) -> D) -> D))
theorem-size     37
proof            (modus-ponens tm-2 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-4)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5080.         (((((A and (B -> C)) -> C) -> D) -> (((A and (B -> C)) -> B) or ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> C) -> D) -> D)), M:tm-2, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))) (C Dm))
================================================================
tm-name          tm-5081
in-theory        5081
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B and (C -> D)) -> D) -> E) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-1 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-2 tm-4)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5081.         (A -> ((((B and (C -> D)) -> D) -> E) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> E))), M:tm-1, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5082
in-theory        5082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-134 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5082.         ((A -> ((B and C) -> B)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-134, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5083
in-theory        5083
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     33
proof            (modus-ponens tm-125 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5083.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-125, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5084
in-theory        5084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-113 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5084.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-113, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5085
in-theory        5085
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     37
proof            (modus-ponens tm-105 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5085.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-105, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5086
in-theory        5086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     25
proof            (modus-ponens tm-95 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5086.         (((A -> B) -> (A -> A)) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-95, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5087
in-theory        5087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-83 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5087.         ((A -> (B -> (C -> B))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-83, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5088
in-theory        5088
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))
theorem-size     23
proof            (modus-ponens tm-76 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5088.         (((not (not A)) -> A) and (B or (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))), M:tm-76, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5089
in-theory        5089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     29
proof            (modus-ponens tm-69 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2 tm-4)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5089.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-69, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5090
in-theory        5090
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-54 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5090.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-54, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5091
in-theory        5091
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-42 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5091.         ((A -> (B or A)) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-42, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5092
in-theory        5092
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-32 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5092.         ((A -> (A or B)) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-32, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5093
in-theory        5093
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     25
proof            (modus-ponens tm-23 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5093.         ((A -> (B -> (A and B))) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-23, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5094
in-theory        5094
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-22 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5094.         (((A and B) -> B) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-22, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5095
in-theory        5095
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-21 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5095.         (((A and B) -> A) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-21, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5096
in-theory        5096
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-20 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5096.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-20, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5097
in-theory        5097
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-19 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5097.         ((A -> (B -> A)) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-19, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5098
in-theory        5098
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))
theorem-size     19
proof            (modus-ponens tm-7 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-7 tm-2 tm-4)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5098.         (A or (B or (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))), M:tm-7, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5099
in-theory        5099
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-6 tm-7 tm-2 tm-4)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5099.         ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) or E), M:tm-6, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5100
in-theory        5100
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5100.         (A -> ((B or (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and A)), M:tm-5, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5101
in-theory        5101
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))
theorem-size     19
proof            (modus-ponens tm-1 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-1 tm-7 tm-2 tm-4)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5101.         (A -> (B or (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))), M:tm-1, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5102
in-theory        5102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-134 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5102.         ((A -> ((B and C) -> B)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-134, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5103
in-theory        5103
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     33
proof            (modus-ponens tm-125 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5103.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-125, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5104
in-theory        5104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H))
theorem-size     33
proof            (modus-ponens tm-113 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5104.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H)), M:tm-113, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5105
in-theory        5105
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     37
proof            (modus-ponens tm-105 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5105.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-105, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5106
in-theory        5106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F))
theorem-size     25
proof            (modus-ponens tm-95 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5106.         (((A -> B) -> (A -> A)) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F)), M:tm-95, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5107
in-theory        5107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-83 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5107.         ((A -> (B -> (C -> B))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-83, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5108
in-theory        5108
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) or E))
theorem-size     23
proof            (modus-ponens tm-76 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5108.         (((not (not A)) -> A) and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) or E)), M:tm-76, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5109
in-theory        5109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F))
theorem-size     29
proof            (modus-ponens tm-69 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-2 tm-4)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5109.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F)), M:tm-69, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5110
in-theory        5110
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     31
proof            (modus-ponens tm-54 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5110.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-54, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5111
in-theory        5111
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F))
theorem-size     23
proof            (modus-ponens tm-42 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5111.         ((A -> (B or A)) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F)), M:tm-42, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5112
in-theory        5112
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F))
theorem-size     23
proof            (modus-ponens tm-32 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5112.         ((A -> (A or B)) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F)), M:tm-32, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5113
in-theory        5113
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F))
theorem-size     25
proof            (modus-ponens tm-23 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5113.         ((A -> (B -> (A and B))) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F)), M:tm-23, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5114
in-theory        5114
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F))
theorem-size     23
proof            (modus-ponens tm-22 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5114.         (((A and B) -> B) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F)), M:tm-22, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5115
in-theory        5115
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F))
theorem-size     23
proof            (modus-ponens tm-21 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5115.         (((A and B) -> A) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F)), M:tm-21, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5116
in-theory        5116
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     31
proof            (modus-ponens tm-20 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5116.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-20, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5117
in-theory        5117
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F))
theorem-size     23
proof            (modus-ponens tm-19 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5117.         ((A -> (B -> A)) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F)), M:tm-19, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5118
in-theory        5118
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) or E))
theorem-size     19
proof            (modus-ponens tm-7 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-7 tm-6 tm-2 tm-4)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5118.         (A or ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) or E)), M:tm-7, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5119
in-theory        5119
times-derived    2
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-6 tm-2 tm-4)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5119.         (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) or E), M:tm-6, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5120
in-theory        5120
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) or E) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5120.         (A -> (((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) or E) and A)), M:tm-5, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5121
in-theory        5121
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) or E))
theorem-size     19
proof            (modus-ponens tm-1 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-1 tm-6 tm-2 tm-4)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5121.         (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) or E)), M:tm-1, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5122
in-theory        5122
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-147 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5122.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> D))), M:tm-147, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-5123
in-theory        5123
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5123.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-147, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-5124
in-theory        5124
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-147 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-5124.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and E) -> D)), M:tm-147, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-5125
in-theory        5125
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-147 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5125.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and E) -> E)), M:tm-147, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-5126
in-theory        5126
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-147 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5126.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (D and E)))), M:tm-147, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-5127
in-theory        5127
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-147 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-5127.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D or E))), M:tm-147, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-5128
in-theory        5128
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-147 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-5128.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or D))), M:tm-147, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-5129
in-theory        5129
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5129.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-147, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-5130
in-theory        5130
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-147 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5130.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-147, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-5131
in-theory        5131
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((not (not D)) -> D))
theorem-size     21
proof            (modus-ponens tm-147 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-2 tm-4 tm-10)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-5131.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((not (not D)) -> D)), M:tm-147, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-5132
in-theory        5132
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-147 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-5132.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (F -> E)))), M:tm-147, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-5133
in-theory        5133
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (D -> D)))
theorem-size     23
proof            (modus-ponens tm-147 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-5133.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (D -> D))), M:tm-147, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-5134
in-theory        5134
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-147 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-5134.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-147, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-5135
in-theory        5135
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-5135.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-147, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-5136
in-theory        5136
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-147 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5136.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-147, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-5137
in-theory        5137
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-147 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-5137.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E and F) -> E))), M:tm-147, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-5138
in-theory        5138
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-147 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5138.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-147, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-5139
in-theory        5139
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-147 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-5139.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E and F) -> F))), M:tm-147, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-5140
in-theory        5140
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     25
proof            (modus-ponens tm-147 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-5140.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> E)) and D))), M:tm-147, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-5141
in-theory        5141
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-147 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-5141.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-147, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-5142
in-theory        5142
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E and F) -> E) and D)))
theorem-size     25
proof            (modus-ponens tm-147 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-5142.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E and F) -> E) and D))), M:tm-147, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-5143
in-theory        5143
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E and F) -> F) and D)))
theorem-size     25
proof            (modus-ponens tm-147 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-5143.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E and F) -> F) and D))), M:tm-147, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-5144
in-theory        5144
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-5144.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-147, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-5145
in-theory        5145
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (D -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-147 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-5145.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (D -> (D and E)))), M:tm-147, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-5146
in-theory        5146
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-5146.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (F -> (E and F))))), M:tm-147, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-5147
in-theory        5147
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-147 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-5147.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) or F)), M:tm-147, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-5148
in-theory        5148
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-147 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-5148.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-147, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-5149
in-theory        5149
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) or F))
theorem-size     23
proof            (modus-ponens tm-147 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-5149.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) or F)), M:tm-147, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-5150
in-theory        5150
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) or F))
theorem-size     23
proof            (modus-ponens tm-147 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-5150.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) or F)), M:tm-147, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-5151
in-theory        5151
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) or F))
theorem-size     25
proof            (modus-ponens tm-147 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-5151.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) or F)), M:tm-147, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-5152
in-theory        5152
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) or F))
theorem-size     23
proof            (modus-ponens tm-147 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-5152.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) or F)), M:tm-147, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-5153
in-theory        5153
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (E or F)) and D)))
theorem-size     25
proof            (modus-ponens tm-147 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-5153.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (E or F)) and D))), M:tm-147, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-5154
in-theory        5154
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-147 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-5154.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (E or F)))), M:tm-147, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-5155
in-theory        5155
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-147 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-5155.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (F -> E)))), M:tm-147, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-5156
in-theory        5156
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-5156.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-147, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-5157
in-theory        5157
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-147 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-5157.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E and F) -> E))), M:tm-147, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-5158
in-theory        5158
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-147 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-5158.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E and F) -> F))), M:tm-147, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-5159
in-theory        5159
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-5159.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (F -> (E and F))))), M:tm-147, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-5160
in-theory        5160
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-147 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-5160.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (E or F)))), M:tm-147, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-5161
in-theory        5161
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-147 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-5161.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (F or E)))), M:tm-147, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-5162
in-theory        5162
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) or F))
theorem-size     23
proof            (modus-ponens tm-147 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-5162.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) or F)), M:tm-147, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-5163
in-theory        5163
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F or E)) and D)))
theorem-size     25
proof            (modus-ponens tm-147 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-5163.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F or E)) and D))), M:tm-147, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-5164
in-theory        5164
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-147 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-5164.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (F or E)))), M:tm-147, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-5165
in-theory        5165
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-147 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5165.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-147, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-5166
in-theory        5166
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-147 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5166.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-147, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-5167
in-theory        5167
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-147 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5167.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-147, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-5168
in-theory        5168
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-147 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5168.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-147, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-5169
in-theory        5169
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-147 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-5169.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-147, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-5170
in-theory        5170
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-147 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5170.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-147, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-5171
in-theory        5171
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-147 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5171.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-147, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-5172
in-theory        5172
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-147 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5172.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-147, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-5173
in-theory        5173
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-5173.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-147, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-5174
in-theory        5174
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-147 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-5174.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-147, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-5175
in-theory        5175
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-147 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-5175.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-147, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-5176
in-theory        5176
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-147 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-5176.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-147, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-5177
in-theory        5177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-5177.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-147, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-5178
in-theory        5178
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-147 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5178.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (E -> D))) -> (not D))), M:tm-147, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-5179
in-theory        5179
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5179.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-147, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-5180
in-theory        5180
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     27
proof            (modus-ponens tm-147 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5180.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-147, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-5181
in-theory        5181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     27
proof            (modus-ponens tm-147 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5181.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-147, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-5182
in-theory        5182
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-5182.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-147, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-5183
in-theory        5183
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-147 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5183.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (D or E))) -> (not D))), M:tm-147, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-5184
in-theory        5184
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-147 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5184.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (E or D))) -> (not D))), M:tm-147, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-5185
in-theory        5185
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     35
proof            (modus-ponens tm-147 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-8)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5185.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-147, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-5186
in-theory        5186
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     33
proof            (modus-ponens tm-147 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5186.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-147, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-5187
in-theory        5187
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     39
proof            (modus-ponens tm-147 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-9)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5187.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-147, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-5188
in-theory        5188
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-5188.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-147, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-5189
in-theory        5189
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     29
proof            (modus-ponens tm-147 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-5189.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-147, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-5190
in-theory        5190
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     31
proof            (modus-ponens tm-147 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-5190.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-147, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-5191
in-theory        5191
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     31
proof            (modus-ponens tm-147 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-5191.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-147, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-5192
in-theory        5192
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-5192.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-147, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-5193
in-theory        5193
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     27
proof            (modus-ponens tm-147 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-10)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5193.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-147, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-5194
in-theory        5194
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-147 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-10)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5194.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-147, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-5195
in-theory        5195
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((not (not E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-147 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-5195.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((not (not E)) -> E))), M:tm-147, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-5196
in-theory        5196
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((not (not D)) -> D) or E))
theorem-size     23
proof            (modus-ponens tm-147 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-5196.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((not (not D)) -> D) or E)), M:tm-147, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-5197
in-theory        5197
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     25
proof            (modus-ponens tm-147 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-10)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-5197.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((not (not E)) -> E) and D))), M:tm-147, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-5198
in-theory        5198
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     31
proof            (modus-ponens tm-147 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-10)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-5198.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-147, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-5199
in-theory        5199
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((not (not E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-147 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-5199.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((not (not E)) -> E))), M:tm-147, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-5200
in-theory        5200
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5200.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-147, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-5201
in-theory        5201
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-147 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5201.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-147, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-5202
in-theory        5202
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-5202.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (F -> (G -> F))))), M:tm-147, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-5203
in-theory        5203
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (F -> E))) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-5203.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (F -> E))) or G)), M:tm-147, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-5204
in-theory        5204
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-5204.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-147, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-5205
in-theory        5205
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-147 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5205.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (D -> (F -> E)))), M:tm-147, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-5206
in-theory        5206
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-5206.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (F -> (G -> F))))), M:tm-147, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-5207
in-theory        5207
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> D))
theorem-size     19
proof            (modus-ponens tm-147 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5207.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> D)), M:tm-147, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-5208
in-theory        5208
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5208.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-147, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-5209
in-theory        5209
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and E) -> (D and E)))
theorem-size     23
proof            (modus-ponens tm-147 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5209.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and E) -> (D and E))), M:tm-147, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-5210
in-theory        5210
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (D -> E)))
theorem-size     23
proof            (modus-ponens tm-147 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5210.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (D -> E))), M:tm-147, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-5211
in-theory        5211
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((not (not D)) -> (not (not D))))
theorem-size     23
proof            (modus-ponens tm-147 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5211.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((not (not D)) -> (not (not D)))), M:tm-147, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-5212
in-theory        5212
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-147 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5212.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-147, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-5213
in-theory        5213
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-147 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5213.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-147, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-5214
in-theory        5214
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> F) -> (E -> E))))
theorem-size     25
proof            (modus-ponens tm-147 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-5214.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> F) -> (E -> E)))), M:tm-147, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-5215
in-theory        5215
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (D -> D)) or F))
theorem-size     25
proof            (modus-ponens tm-147 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-5215.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (D -> D)) or F)), M:tm-147, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-5216
in-theory        5216
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-5216.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-147, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-5217
in-theory        5217
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-5217.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-147, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-5218
in-theory        5218
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     25
proof            (modus-ponens tm-147 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-5218.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> F) -> (E -> E)))), M:tm-147, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-5219
in-theory        5219
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-5219.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-147, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5220
in-theory        5220
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     25
proof            (modus-ponens tm-147 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-5220.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D -> E)) -> (D -> E))), M:tm-147, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-5221
in-theory        5221
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     35
proof            (modus-ponens tm-147 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5221.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-147, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-5222
in-theory        5222
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     47
proof            (modus-ponens tm-147 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5222.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-147, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-5223
in-theory        5223
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     49
proof            (modus-ponens tm-147 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5223.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-147, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-5224
in-theory        5224
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-5224.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-147, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-5225
in-theory        5225
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     37
proof            (modus-ponens tm-147 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-5225.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-147, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-5226
in-theory        5226
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     39
proof            (modus-ponens tm-147 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-5226.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-147, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-5227
in-theory        5227
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     45
proof            (modus-ponens tm-147 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-5227.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-147, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-5228
in-theory        5228
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-5228.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-147, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-5229
in-theory        5229
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-147 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-5229.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-147, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-5230
in-theory        5230
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     35
proof            (modus-ponens tm-147 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5230.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-147, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-5231
in-theory        5231
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     49
proof            (modus-ponens tm-147 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5231.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-147, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-5232
in-theory        5232
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-147 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-5232.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-147, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-5233
in-theory        5233
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     33
proof            (modus-ponens tm-147 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-5233.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-147, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-5234
in-theory        5234
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     35
proof            (modus-ponens tm-147 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-5234.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-147, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-5235
in-theory        5235
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-147 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-5235.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-147, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-5236
in-theory        5236
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-147 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-5236.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-147, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-5237
in-theory        5237
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) and D) -> E))
theorem-size     23
proof            (modus-ponens tm-147 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-5237.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) and D) -> E)), M:tm-147, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-5238
in-theory        5238
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-147 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-5238.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-147, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-5239
in-theory        5239
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     35
proof            (modus-ponens tm-147 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5239.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-147, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-5240
in-theory        5240
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     37
proof            (modus-ponens tm-147 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-5240.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-147, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-5241
in-theory        5241
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     31
proof            (modus-ponens tm-147 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5241.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-147, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-5242
in-theory        5242
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     41
proof            (modus-ponens tm-147 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5242.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-147, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-5243
in-theory        5243
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     43
proof            (modus-ponens tm-147 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5243.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-147, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-5244
in-theory        5244
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     33
proof            (modus-ponens tm-147 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-5244.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-147, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-5245
in-theory        5245
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     33
proof            (modus-ponens tm-147 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-5245.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-147, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-5246
in-theory        5246
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     35
proof            (modus-ponens tm-147 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-5246.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-147, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-5247
in-theory        5247
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     39
proof            (modus-ponens tm-147 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-5247.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-147, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-5248
in-theory        5248
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     33
proof            (modus-ponens tm-147 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-5248.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-147, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-5249
in-theory        5249
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-147 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-5249.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-147, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-5250
in-theory        5250
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     29
proof            (modus-ponens tm-147 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-5250.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-147, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5251
in-theory        5251
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-1 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5251.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-147, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-5252
in-theory        5252
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     33
proof            (modus-ponens tm-147 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5252.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-147, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-5253
in-theory        5253
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-147 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-5253.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> ((F and G) -> F)))), M:tm-147, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-5254
in-theory        5254
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-5254.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E and F) -> E)) or G)), M:tm-147, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-5255
in-theory        5255
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-5255.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-147, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-5256
in-theory        5256
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     25
proof            (modus-ponens tm-147 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-5256.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E and F)) -> (D -> E))), M:tm-147, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-5257
in-theory        5257
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-147 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-5257.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> ((F and G) -> F)))), M:tm-147, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-5258
in-theory        5258
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and (D -> E)) -> E))
theorem-size     23
proof            (modus-ponens tm-147 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-5258.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and (D -> E)) -> E)), M:tm-147, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-5259
in-theory        5259
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-147 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-5259.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-147, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-5260
in-theory        5260
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     35
proof            (modus-ponens tm-147 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5260.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-147, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-5261
in-theory        5261
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-147 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-5261.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-147, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-5262
in-theory        5262
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-147 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-5262.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-147, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-5263
in-theory        5263
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     31
proof            (modus-ponens tm-147 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5263.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-147, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-5264
in-theory        5264
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     41
proof            (modus-ponens tm-147 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5264.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-147, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-5265
in-theory        5265
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-147 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5265.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-147, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5266
in-theory        5266
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     33
proof            (modus-ponens tm-147 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5266.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-147, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5267
in-theory        5267
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     33
proof            (modus-ponens tm-147 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5267.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-147, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5268
in-theory        5268
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     35
proof            (modus-ponens tm-147 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5268.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-147, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5269
in-theory        5269
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A and (B -> C)) -> C)))
theorem-size     39
proof            (modus-ponens tm-144 tm-147 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5269.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-147, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5270
in-theory        5270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-134 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5270.         ((A -> ((B and C) -> B)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-134, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5271
in-theory        5271
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B and C) -> B)))
theorem-size     29
proof            (modus-ponens tm-131 tm-147 ((Am (-> (and A B) A)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5271.         ((A or ((B and C) -> B)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B and C) -> B))), M:tm-131, m:tm-147, u:((Am (-> (and A B) A)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (and A B) A))))
================================================================
tm-name          tm-5272
in-theory        5272
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     35
proof            (modus-ponens tm-125 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5272.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-125, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5273
in-theory        5273
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (((A -> B) and C) -> B)))
theorem-size     39
proof            (modus-ponens tm-122 tm-147 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5273.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-147, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-5274
in-theory        5274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E)))
theorem-size     35
proof            (modus-ponens tm-113 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5274.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E))), M:tm-113, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5275
in-theory        5275
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     45
proof            (modus-ponens tm-110 tm-147 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5275.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-147, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-5276
in-theory        5276
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     39
proof            (modus-ponens tm-105 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5276.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-105, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5277
in-theory        5277
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     45
proof            (modus-ponens tm-102 tm-147 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5277.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-147, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-5278
in-theory        5278
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C)))
theorem-size     27
proof            (modus-ponens tm-95 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5278.         (((A -> B) -> (A -> A)) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C))), M:tm-95, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5279
in-theory        5279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> A)))
theorem-size     27
proof            (modus-ponens tm-92 tm-147 ((Am (-> A A)) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5279.         (((A -> B) or (A -> A)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> A))), M:tm-92, m:tm-147, u:((Am (-> A A)) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A A))))
================================================================
tm-name          tm-5280
in-theory        5280
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and A)))
theorem-size     21
proof            (modus-ponens tm-84 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5280.         (A -> (B -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and A))), M:tm-84, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-5281
in-theory        5281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-83 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5281.         ((A -> (B -> (C -> B))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-83, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5282
in-theory        5282
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (B -> (C -> B))))
theorem-size     29
proof            (modus-ponens tm-80 tm-147 ((Am (-> A (-> B A))) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5282.         ((A or (B -> (C -> B))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (B -> (C -> B)))), M:tm-80, m:tm-147, u:((Am (-> A (-> B A))) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A (-> B A)))))
================================================================
tm-name          tm-5283
in-theory        5283
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and B)))
theorem-size     25
proof            (modus-ponens tm-76 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-10 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5283.         (((not (not A)) -> A) and (B -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and B))), M:tm-76, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5284
in-theory        5284
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))
theorem-size     23
proof            (modus-ponens tm-73 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-2 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5284.         (((not (not A)) or A) -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-73, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-5285
in-theory        5285
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C)))
theorem-size     31
proof            (modus-ponens tm-69 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5285.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C))), M:tm-69, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5286
in-theory        5286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and ((A -> (not B)) -> (not A))))
theorem-size     35
proof            (modus-ponens tm-66 tm-147 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-2 tm-4)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5286.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-147, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-5287
in-theory        5287
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     33
proof            (modus-ponens tm-54 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5287.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-54, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5288
in-theory        5288
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-51 tm-147 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5288.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-147, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-5289
in-theory        5289
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (B or A)))
theorem-size     25
proof            (modus-ponens tm-50 tm-147 ((Am (or A B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5289.         ((A or (B or A)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (B or A))), M:tm-50, m:tm-147, u:((Am (or A B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (or A B))))
================================================================
tm-name          tm-5290
in-theory        5290
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A or B)))
theorem-size     25
proof            (modus-ponens tm-49 tm-147 ((Am (or A B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5290.         ((A or (A or B)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A or B))), M:tm-49, m:tm-147, u:((Am (or A B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (or A B))))
================================================================
tm-name          tm-5291
in-theory        5291
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-48 tm-147 ((Am (-> A (and B A))) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5291.         ((A or (B -> (A and B))) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (B -> (A and B)))), M:tm-48, m:tm-147, u:((Am (-> A (and B A))) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A (and B A)))))
================================================================
tm-name          tm-5292
in-theory        5292
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and B))
theorem-size     23
proof            (modus-ponens tm-47 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5292.         (((A and B) or B) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and B)), M:tm-47, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-5293
in-theory        5293
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and A))
theorem-size     23
proof            (modus-ponens tm-46 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-2 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5293.         (((A and B) or A) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and A)), M:tm-46, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-5294
in-theory        5294
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-45 tm-147 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5294.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-147, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-5295
in-theory        5295
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (B -> A)))
theorem-size     25
proof            (modus-ponens tm-44 tm-147 ((Am (-> A B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5295.         ((A or (B -> A)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (B -> A))), M:tm-44, m:tm-147, u:((Am (-> A B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A B))))
================================================================
tm-name          tm-5296
in-theory        5296
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C)))
theorem-size     25
proof            (modus-ponens tm-42 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5296.         ((A -> (B or A)) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C))), M:tm-42, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5297
in-theory        5297
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C)))
theorem-size     25
proof            (modus-ponens tm-32 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5297.         ((A -> (A or B)) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C))), M:tm-32, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5298
in-theory        5298
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)))
theorem-size     21
proof            (modus-ponens tm-24 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5298.         (A -> (A and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))), M:tm-24, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-5299
in-theory        5299
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C)))
theorem-size     27
proof            (modus-ponens tm-23 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5299.         ((A -> (B -> (A and B))) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C))), M:tm-23, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5300
in-theory        5300
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C)))
theorem-size     25
proof            (modus-ponens tm-22 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5300.         (((A and B) -> B) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C))), M:tm-22, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5301
in-theory        5301
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C)))
theorem-size     25
proof            (modus-ponens tm-21 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5301.         (((A and B) -> A) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C))), M:tm-21, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5302
in-theory        5302
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     33
proof            (modus-ponens tm-20 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5302.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-20, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5303
in-theory        5303
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C)))
theorem-size     25
proof            (modus-ponens tm-19 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5303.         ((A -> (B -> A)) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C))), M:tm-19, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5304
in-theory        5304
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))) -> (not A))
theorem-size     23
proof            (modus-ponens tm-9 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-9 tm-5 tm-2 tm-4)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5304.         ((A -> (not ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))) -> (not A)), M:tm-9, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-5305
in-theory        5305
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and D) -> E) -> ((D or ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and D)) -> E))
theorem-size     41
proof            (modus-ponens tm-8 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5305.         ((((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and D) -> E) -> ((D or ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and D)) -> E)), M:tm-8, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-5306
in-theory        5306
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and B)))
theorem-size     21
proof            (modus-ponens tm-7 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-7 tm-5 tm-2 tm-4)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5306.         (A or (B -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and B))), M:tm-7, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5307
in-theory        5307
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-6 tm-5 tm-2 tm-4)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5307.         ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) or E), M:tm-6, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5308
in-theory        5308
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and B)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5308.         (A -> ((B -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and B)) and A)), M:tm-5, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5309
in-theory        5309
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and B)))
theorem-size     21
proof            (modus-ponens tm-1 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-1 tm-5 tm-2 tm-4)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5309.         (A -> (B -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and B))), M:tm-1, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5310
in-theory        5310
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     39
proof            (modus-ponens tm-147 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5310.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-147, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5311
in-theory        5311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-134 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5311.         ((A -> ((B and C) -> B)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-134, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5312
in-theory        5312
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     39
proof            (modus-ponens tm-125 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5312.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-125, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5313
in-theory        5313
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) -> B) -> (A and (B -> (C -> D)))) -> ((((A and (B -> (C -> D))) -> B) -> C) -> (((A and (B -> (C -> D))) -> B) -> D)))
theorem-size     41
proof            (modus-ponens tm-114 tm-148 ((A (-> (-> (and Am (-> Bm (-> C D))) Bm) (and Am (-> Bm (-> C D))))) (B (-> (and Am (-> Bm (-> C D))) Bm)) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5313.         ((((A and (B -> (C -> D))) -> B) -> (A and (B -> (C -> D)))) -> ((((A and (B -> (C -> D))) -> B) -> C) -> (((A and (B -> (C -> D))) -> B) -> D))), M:tm-114, m:tm-148, u:((A (-> (-> (and Am (-> Bm (-> C D))) Bm) (and Am (-> Bm (-> C D))))) (B (-> (and Am (-> Bm (-> C D))) Bm)) (Cm (-> C D)))
================================================================
tm-name          tm-5314
in-theory        5314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G)))
theorem-size     39
proof            (modus-ponens tm-113 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5314.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G))), M:tm-113, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5315
in-theory        5315
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     43
proof            (modus-ponens tm-105 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5315.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-105, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5316
in-theory        5316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-95 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5316.         (((A -> B) -> (A -> A)) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E))), M:tm-95, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5317
in-theory        5317
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (D -> (((A and (B -> C)) -> B) -> C)))
theorem-size     25
proof            (modus-ponens tm-84 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5317.         ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (D -> (((A and (B -> C)) -> B) -> C))), M:tm-84, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-5318
in-theory        5318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-83 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5318.         ((A -> (B -> (C -> B))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-83, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5319
in-theory        5319
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B and (C -> D)) -> C) -> (B and (C -> D))) -> (((B and (C -> D)) -> C) -> D)))
theorem-size     29
proof            (modus-ponens tm-76 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5319.         (((not (not A)) -> A) and ((((B and (C -> D)) -> C) -> (B and (C -> D))) -> (((B and (C -> D)) -> C) -> D))), M:tm-76, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5320
in-theory        5320
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A and (B -> C)) -> B) -> (A and (B -> C))))) or (((A and (B -> C)) -> B) -> (A and (B -> C)))) -> (((A and (B -> C)) -> B) -> C))
theorem-size     39
proof            (modus-ponens tm-73 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-4)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5320.         (((not (not (((A and (B -> C)) -> B) -> (A and (B -> C))))) or (((A and (B -> C)) -> B) -> (A and (B -> C)))) -> (((A and (B -> C)) -> B) -> C)), M:tm-73, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-5321
in-theory        5321
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E)))
theorem-size     35
proof            (modus-ponens tm-69 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5321.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E))), M:tm-69, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5322
in-theory        5322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     37
proof            (modus-ponens tm-54 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5322.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-54, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5323
in-theory        5323
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B and (C -> D)) -> C) -> (B and (C -> D)))) or (((B and (C -> D)) -> C) -> (B and (C -> D)))) -> (((B and (C -> D)) -> C) -> D))
theorem-size     39
proof            (modus-ponens tm-47 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5323.         (((A and (((B and (C -> D)) -> C) -> (B and (C -> D)))) or (((B and (C -> D)) -> C) -> (B and (C -> D)))) -> (((B and (C -> D)) -> C) -> D)), M:tm-47, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-5324
in-theory        5324
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) -> (A and (B -> C))) and D) or (((A and (B -> C)) -> B) -> (A and (B -> C)))) -> (((A and (B -> C)) -> B) -> C))
theorem-size     39
proof            (modus-ponens tm-46 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-4)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5324.         ((((((A and (B -> C)) -> B) -> (A and (B -> C))) and D) or (((A and (B -> C)) -> B) -> (A and (B -> C)))) -> (((A and (B -> C)) -> B) -> C)), M:tm-46, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-5325
in-theory        5325
times-derived    2
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (((A and (B -> C)) -> B) -> (A and (B -> C)))) -> (((A and (B -> C)) -> B) -> C))
theorem-size     29
proof            (modus-ponens tm-44 tm-148 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5325.         (((A and (B -> C)) or (((A and (B -> C)) -> B) -> (A and (B -> C)))) -> (((A and (B -> C)) -> B) -> C)), M:tm-44, m:tm-148, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-5326
in-theory        5326
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E)))
theorem-size     29
proof            (modus-ponens tm-42 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5326.         ((A -> (B or A)) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E))), M:tm-42, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5327
in-theory        5327
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E)))
theorem-size     29
proof            (modus-ponens tm-32 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5327.         ((A -> (A or B)) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E))), M:tm-32, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5328
in-theory        5328
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> ((((A and (B -> C)) -> B) -> (A and (B -> C))) and (((A and (B -> C)) -> B) -> C)))
theorem-size     37
proof            (modus-ponens tm-24 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5328.         ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> ((((A and (B -> C)) -> B) -> (A and (B -> C))) and (((A and (B -> C)) -> B) -> C))), M:tm-24, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-5329
in-theory        5329
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-23 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5329.         ((A -> (B -> (A and B))) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E))), M:tm-23, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5330
in-theory        5330
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E)))
theorem-size     29
proof            (modus-ponens tm-22 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5330.         (((A and B) -> B) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E))), M:tm-22, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5331
in-theory        5331
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E)))
theorem-size     29
proof            (modus-ponens tm-21 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5331.         (((A and B) -> A) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E))), M:tm-21, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5332
in-theory        5332
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     37
proof            (modus-ponens tm-20 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5332.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-20, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5333
in-theory        5333
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E)))
theorem-size     29
proof            (modus-ponens tm-19 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5333.         ((A -> (B -> A)) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E))), M:tm-19, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5334
in-theory        5334
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> (A and (B -> C))))
theorem-size     27
proof            (modus-ponens tm-12 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5334.         ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> (A and (B -> C)))), M:tm-12, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-5335
in-theory        5335
times-derived    2
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (not (((A and (B -> C)) -> B) -> C))) -> (not (((A and (B -> C)) -> B) -> (A and (B -> C)))))
theorem-size     39
proof            (modus-ponens tm-9 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-9 tm-2 tm-4)
proof-size       119
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5335.         (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (not (((A and (B -> C)) -> B) -> C))) -> (not (((A and (B -> C)) -> B) -> (A and (B -> C))))), M:tm-9, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-5336
in-theory        5336
times-derived    2
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> C) -> D) -> (((((A and (B -> C)) -> B) -> (A and (B -> C))) or (((A and (B -> C)) -> B) -> C)) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-8 tm-2 tm-4)
proof-size       119
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5336.         (((((A and (B -> C)) -> B) -> C) -> D) -> (((((A and (B -> C)) -> B) -> (A and (B -> C))) or (((A and (B -> C)) -> B) -> C)) -> D)), M:tm-8, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-5337
in-theory        5337
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B and (C -> D)) -> C) -> (B and (C -> D))) -> (((B and (C -> D)) -> C) -> D)))
theorem-size     25
proof            (modus-ponens tm-7 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-7 tm-2 tm-4)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5337.         (A or ((((B and (C -> D)) -> C) -> (B and (C -> D))) -> (((B and (C -> D)) -> C) -> D))), M:tm-7, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5338
in-theory        5338
times-derived    2
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) or D)
theorem-size     25
proof            (modus-ponens tm-6 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-6 tm-2 tm-4)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5338.         (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) or D), M:tm-6, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5339
in-theory        5339
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B and (C -> D)) -> C) -> (B and (C -> D))) -> (((B and (C -> D)) -> C) -> D)) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5339.         (A -> (((((B and (C -> D)) -> C) -> (B and (C -> D))) -> (((B and (C -> D)) -> C) -> D)) and A)), M:tm-5, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5340
in-theory        5340
times-derived    2
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> ((A and (B -> C)) -> B)) -> ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> C))
theorem-size     37
proof            (modus-ponens tm-2 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (and Am (-> Bm Cm)) Bm)) (C Cm)))
axioms-used      (tm-2 tm-4)
proof-size       119
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5340.         (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> ((A and (B -> C)) -> B)) -> ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> C)), M:tm-2, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (and Am (-> Bm Cm)) Bm)) (C Cm))
================================================================
tm-name          tm-5341
in-theory        5341
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B and (C -> D)) -> C) -> (B and (C -> D))) -> (((B and (C -> D)) -> C) -> D)))
theorem-size     25
proof            (modus-ponens tm-1 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-1 tm-2 tm-4)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5341.         (A -> ((((B and (C -> D)) -> C) -> (B and (C -> D))) -> (((B and (C -> D)) -> C) -> D))), M:tm-1, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5342
in-theory        5342
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     33
proof            (modus-ponens tm-147 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5342.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-147, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5343
in-theory        5343
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-144 tm-149 ((Am (-> (and A (-> B C)) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5343.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-144, m:tm-149, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5344
in-theory        5344
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) -> E)) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))
theorem-size     35
proof            (modus-ponens tm-142 tm-149 ((Am (and A (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) C))) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5344.         ((A and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) -> E)) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-142, m:tm-149, u:((Am (and A (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) C))) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5345
in-theory        5345
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) -> ((B and (C -> D)) -> C))) -> ((B and (C -> D)) -> D))
theorem-size     33
proof            (modus-ponens tm-141 tm-149 ((Am (and A (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (and Bm (-> Cm Dm)) Cm)))) (B (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5345.         ((A and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) -> ((B and (C -> D)) -> C))) -> ((B and (C -> D)) -> D)), M:tm-141, m:tm-149, u:((Am (and A (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (and Bm (-> Cm Dm)) Cm)))) (B (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-5346
in-theory        5346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-134 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5346.         ((A -> ((B and C) -> B)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-134, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5347
in-theory        5347
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-131 tm-149 ((Am (-> (and A B) A)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5347.         ((A or ((B and C) -> B)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-131, m:tm-149, u:((Am (-> (and A B) A)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5348
in-theory        5348
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) and D) -> ((A and (B -> C)) -> C))
theorem-size     17
proof            (modus-ponens tm-129 tm-149 ((Am (and (-> (and Bm (-> Cm Dm)) Cm) B)) (A (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5348.         ((((A and (B -> C)) -> B) and D) -> ((A and (B -> C)) -> C)), M:tm-129, m:tm-149, u:((Am (and (-> (and Bm (-> Cm Dm)) Cm) B)) (A (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-5349
in-theory        5349
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     33
proof            (modus-ponens tm-125 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5349.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-125, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5350
in-theory        5350
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-122 tm-149 ((Am (-> (and (-> A B) C) B)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5350.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-122, m:tm-149, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5351
in-theory        5351
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) and E) -> (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)))
theorem-size     35
proof            (modus-ponens tm-120 tm-149 ((Am (and (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) B) C)) (A (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5351.         ((((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) and E) -> (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))), M:tm-120, m:tm-149, u:((Am (and (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) B) C)) (A (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5352
in-theory        5352
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> B)) and D) -> ((A and (B -> C)) -> C))
theorem-size     33
proof            (modus-ponens tm-119 tm-149 ((Am (and (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (and Bm (-> Cm Dm)) Cm)) C)) (A (-> (and Bm (-> Cm Dm)) Cm)) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-3 tm-1 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5352.         ((((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> B)) and D) -> ((A and (B -> C)) -> C)), M:tm-119, m:tm-149, u:((Am (and (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (and Bm (-> Cm Dm)) Cm)) C)) (A (-> (and Bm (-> Cm Dm)) Cm)) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-5353
in-theory        5353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-113 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5353.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-113, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5354
in-theory        5354
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))
theorem-size     31
proof            (modus-ponens tm-110 tm-149 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5354.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))), M:tm-110, m:tm-149, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5355
in-theory        5355
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> B) -> (A and (B -> C)))) -> (((A and (B -> C)) -> B) -> C))
theorem-size     39
proof            (modus-ponens tm-106 tm-149 ((Am (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> (and Bm (-> Cm Dm)) Cm) (and Bm (-> Cm Dm))))) (A (-> (and Bm (-> Cm Dm)) Cm)) (B (and Bm (-> Cm Dm))) (C Dm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5355.         (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> B) -> (A and (B -> C)))) -> (((A and (B -> C)) -> B) -> C)), M:tm-106, m:tm-149, u:((Am (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> (and Bm (-> Cm Dm)) Cm) (and Bm (-> Cm Dm))))) (A (-> (and Bm (-> Cm Dm)) Cm)) (B (and Bm (-> Cm Dm))) (C Dm))
================================================================
tm-name          tm-5356
in-theory        5356
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     37
proof            (modus-ponens tm-105 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5356.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-105, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5357
in-theory        5357
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     35
proof            (modus-ponens tm-102 tm-149 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5357.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-102, m:tm-149, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5358
in-theory        5358
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> C) -> D)) -> (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-100 tm-149 ((Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (-> (and Bm (-> Cm Dm)) Dm) C))) (A (-> (and Bm (-> Cm Dm)) Cm)) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5358.         ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> C) -> D)) -> (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))), M:tm-100, m:tm-149, u:((Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (-> (and Bm (-> Cm Dm)) Dm) C))) (A (-> (and Bm (-> Cm Dm)) Cm)) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-5359
in-theory        5359
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B and (A -> C)) -> C))
theorem-size     9
proof            (modus-ponens tm-98 tm-149 ((Cm Am) (B (and Bm (-> Am Dm))) (A Am) (C (-> (and Bm (-> Am Dm)) Dm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5359.         (A -> ((B and (A -> C)) -> C)), M:tm-98, m:tm-149, u:((Cm Am) (B (and Bm (-> Am Dm))) (A Am) (C (-> (and Bm (-> Am Dm)) Dm)))
================================================================
tm-name          tm-5360
in-theory        5360
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) -> (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-96 tm-149 ((Am (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) B)) (A (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5360.         (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) -> (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))), M:tm-96, m:tm-149, u:((Am (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) B)) (A (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5361
in-theory        5361
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     25
proof            (modus-ponens tm-95 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5361.         (((A -> B) -> (A -> A)) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-95, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5362
in-theory        5362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-92 tm-149 ((Am (-> A A)) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5362.         (((A -> B) or (A -> A)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-92, m:tm-149, u:((Am (-> A A)) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5363
in-theory        5363
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))
theorem-size     19
proof            (modus-ponens tm-84 tm-149 ((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5363.         (A -> (B -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))), M:tm-84, m:tm-149, u:((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5364
in-theory        5364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-83 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5364.         ((A -> (B -> (C -> B))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-83, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5365
in-theory        5365
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-80 tm-149 ((Am (-> A (-> B A))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5365.         ((A or (B -> (C -> B))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-80, m:tm-149, u:((Am (-> A (-> B A))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5366
in-theory        5366
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D))) -> D)
theorem-size     21
proof            (modus-ponens tm-77 tm-149 ((Am (not (not (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) B)))) (A (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5366.         ((not (not ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D))) -> D), M:tm-77, m:tm-149, u:((Am (not (not (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) B)))) (A (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5367
in-theory        5367
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))
theorem-size     23
proof            (modus-ponens tm-76 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5367.         (((not (not A)) -> A) and (B -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))), M:tm-76, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5368
in-theory        5368
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))
theorem-size     21
proof            (modus-ponens tm-73 tm-149 ((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5368.         (((not (not A)) or A) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-73, m:tm-149, u:((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5369
in-theory        5369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     29
proof            (modus-ponens tm-69 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2 tm-4)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5369.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-69, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5370
in-theory        5370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     27
proof            (modus-ponens tm-66 tm-149 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-2 tm-4)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5370.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-66, m:tm-149, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5371
in-theory        5371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and (C -> D)) -> C)) -> ((A or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)))
theorem-size     27
proof            (modus-ponens tm-55 tm-149 ((Am (-> A (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5371.         ((A -> ((B and (C -> D)) -> C)) -> ((A or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))), M:tm-55, m:tm-149, u:((Am (-> A (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-5372
in-theory        5372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-54 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5372.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-54, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5373
in-theory        5373
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-51 tm-149 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5373.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-51, m:tm-149, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5374
in-theory        5374
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-50 tm-149 ((Am (or A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5374.         ((A or (B or A)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-50, m:tm-149, u:((Am (or A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5375
in-theory        5375
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-49 tm-149 ((Am (or A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5375.         ((A or (A or B)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-49, m:tm-149, u:((Am (or A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5376
in-theory        5376
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-48 tm-149 ((Am (-> A (and B A))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5376.         ((A or (B -> (A and B))) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-48, m:tm-149, u:((Am (-> A (and B A))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5377
in-theory        5377
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-47 tm-149 ((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5377.         (((A and B) or B) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-47, m:tm-149, u:((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5378
in-theory        5378
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-46 tm-149 ((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5378.         (((A and B) or A) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-46, m:tm-149, u:((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5379
in-theory        5379
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-45 tm-149 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5379.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-45, m:tm-149, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5380
in-theory        5380
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-44 tm-149 ((Am (-> A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5380.         ((A or (B -> A)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-44, m:tm-149, u:((Am (-> A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5381
in-theory        5381
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-42 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5381.         ((A -> (B or A)) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-42, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5382
in-theory        5382
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-32 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5382.         ((A -> (A or B)) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-32, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5383
in-theory        5383
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))
theorem-size     19
proof            (modus-ponens tm-24 tm-149 ((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5383.         (A -> (A and (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))), M:tm-24, m:tm-149, u:((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5384
in-theory        5384
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     25
proof            (modus-ponens tm-23 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5384.         ((A -> (B -> (A and B))) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-23, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5385
in-theory        5385
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-22 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5385.         (((A and B) -> B) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-22, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5386
in-theory        5386
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-21 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5386.         (((A and B) -> A) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-21, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5387
in-theory        5387
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-20 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5387.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-20, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5388
in-theory        5388
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-19 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5388.         ((A -> (B -> A)) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-19, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5389
in-theory        5389
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) -> E)) -> E)
theorem-size     21
proof            (modus-ponens tm-17 tm-149 ((Am (and A (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) C))) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5389.         ((A and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) -> E)) -> E), M:tm-17, m:tm-149, u:((Am (and A (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) C))) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5390
in-theory        5390
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) and E) -> D)
theorem-size     21
proof            (modus-ponens tm-15 tm-149 ((Am (and (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) B) C)) (A (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5390.         ((((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) and E) -> D), M:tm-15, m:tm-149, u:((Am (and (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) B) C)) (A (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5391
in-theory        5391
times-derived    2
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> C) -> D)) -> (((A and (B -> C)) -> B) -> D))
theorem-size     27
proof            (modus-ponens tm-13 tm-149 ((Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (-> (and Bm (-> Cm Dm)) Dm) C))) (A (-> (and Bm (-> Cm Dm)) Cm)) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5391.         ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> C) -> D)) -> (((A and (B -> C)) -> B) -> D)), M:tm-13, m:tm-149, u:((Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (-> (and Bm (-> Cm Dm)) Dm) C))) (A (-> (and Bm (-> Cm Dm)) Cm)) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-5392
in-theory        5392
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))) -> (not A))
theorem-size     21
proof            (modus-ponens tm-9 tm-149 ((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-9 tm-1 tm-2 tm-4)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5392.         ((A -> (not (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))) -> (not A)), M:tm-9, m:tm-149, u:((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5393
in-theory        5393
times-derived    2
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) -> ((E or (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-149 ((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5393.         (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) -> ((E or (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))) -> D)), M:tm-8, m:tm-149, u:((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5394
in-theory        5394
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))
theorem-size     19
proof            (modus-ponens tm-7 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-7 tm-1 tm-2 tm-4)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5394.         (A or (B -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))), M:tm-7, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5395
in-theory        5395
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-6 tm-1 tm-2 tm-4)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5395.         ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) or E), M:tm-6, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5396
in-theory        5396
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5396.         (A -> ((B -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and A)), M:tm-5, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5397
in-theory        5397
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and (C -> D)) -> C)) -> (A -> ((B and (C -> D)) -> D)))
theorem-size     19
proof            (modus-ponens tm-2 tm-149 ((A Am) (B (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5397.         ((A -> ((B and (C -> D)) -> C)) -> (A -> ((B and (C -> D)) -> D))), M:tm-2, m:tm-149, u:((A Am) (B (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-5398
in-theory        5398
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-147 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5398.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-147, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5399
in-theory        5399
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> ((B and C) -> C))) -> ((B and C) -> C))
theorem-size     19
proof            (modus-ponens tm-142 tm-150 ((A Am) (Dm (-> (and Bm Cm) Cm)) (C (-> (and Bm Cm) Cm)) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5399.         ((A and (((B and C) -> C) -> ((B and C) -> C))) -> ((B and C) -> C)), M:tm-142, m:tm-150, u:((A Am) (Dm (-> (and Bm Cm) Cm)) (C (-> (and Bm Cm) Cm)) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-5400
in-theory        5400
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> (D and E))) -> D)
theorem-size     13
proof            (modus-ponens tm-135 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) (and B C)))) (Dm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5400.         ((A and (((B and C) -> C) -> (D and E))) -> D), M:tm-135, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) (and B C)))) (Dm (and B C)))
================================================================
tm-name          tm-5401
in-theory        5401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-134 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5401.         ((A -> ((B and C) -> B)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-134, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5402
in-theory        5402
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> C) -> (not ((D and E) -> D)))))
theorem-size     15
proof            (modus-ponens tm-130 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) (not (-> (and B C) B))))) (Dm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5402.         (not (A and (((B and C) -> C) -> (not ((D and E) -> D))))), M:tm-130, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) (not (-> (and B C) B))))) (Dm (not (-> (and B C) B))))
================================================================
tm-name          tm-5403
in-theory        5403
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> (A -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-129 tm-150 ((A Am) (B (-> (-> (and Bm Cm) Cm) (-> Am C))) (Dm (-> Am C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5403.         ((A and (((B and C) -> C) -> (A -> D))) -> D), M:tm-129, m:tm-150, u:((A Am) (B (-> (-> (and Bm Cm) Cm) (-> Am C))) (Dm (-> Am C)))
================================================================
tm-name          tm-5404
in-theory        5404
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-125 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5404.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-125, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5405
in-theory        5405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and (((C and D) -> D) -> A)) -> A)
theorem-size     13
proof            (modus-ponens tm-120 tm-150 ((Am (-> Dm B)) (C (-> (-> (and Bm Cm) Cm) Dm)) (A Dm)))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5405.         (((A -> B) and (((C and D) -> D) -> A)) -> A), M:tm-120, m:tm-150, u:((Am (-> Dm B)) (C (-> (-> (and Bm Cm) Cm) Dm)) (A Dm))
================================================================
tm-name          tm-5406
in-theory        5406
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) and (((C and D) -> D) -> (A -> B))) -> B)
theorem-size     17
proof            (modus-ponens tm-119 tm-150 ((Am (-> (-> A B) A)) (C (-> (-> (and Bm Cm) Cm) (-> A B))) (Dm (-> A B))))
axioms-used      (tm-2 tm-3 tm-4 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5406.         ((((A -> B) -> A) and (((C and D) -> D) -> (A -> B))) -> B), M:tm-119, m:tm-150, u:((Am (-> (-> A B) A)) (C (-> (-> (and Bm Cm) Cm) (-> A B))) (Dm (-> A B)))
================================================================
tm-name          tm-5407
in-theory        5407
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> (D -> (E -> F)))) -> ((D -> E) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-114 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) (-> B (-> C D))))) (Dm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5407.         ((A and (((B and C) -> C) -> (D -> (E -> F)))) -> ((D -> E) -> (D -> F))), M:tm-114, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) (-> B (-> C D))))) (Dm (-> B (-> C D))))
================================================================
tm-name          tm-5408
in-theory        5408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (((F and G) -> G) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-113 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5408.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (((F and G) -> G) -> H)) -> H)), M:tm-113, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5409
in-theory        5409
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> C) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     23
proof            (modus-ponens tm-109 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Dm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5409.         (not (A and (((B and C) -> C) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-109, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Dm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-5410
in-theory        5410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     31
proof            (modus-ponens tm-105 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5410.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-105, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5411
in-theory        5411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C and (((D and E) -> E) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-95 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5411.         (((A -> B) -> (A -> A)) and ((C and (((D and E) -> E) -> F)) -> F)), M:tm-95, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5412
in-theory        5412
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> (D -> E))) -> (D -> E))
theorem-size     15
proof            (modus-ponens tm-87 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5412.         ((A and (((B and C) -> C) -> (D -> E))) -> (D -> E)), M:tm-87, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-5413
in-theory        5413
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> D)) -> (E -> D))
theorem-size     13
proof            (modus-ponens tm-84 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5413.         ((A and (((B and C) -> C) -> D)) -> (E -> D)), M:tm-84, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-5414
in-theory        5414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-83 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5414.         ((A -> (B -> (C -> B))) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-83, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5415
in-theory        5415
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> C) -> (not (D -> (E -> D))))))
theorem-size     15
proof            (modus-ponens tm-79 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) (not (-> B (-> C B)))))) (Dm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5415.         (not (A and (((B and C) -> C) -> (not (D -> (E -> D)))))), M:tm-79, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) (not (-> B (-> C B)))))) (Dm (not (-> B (-> C B)))))
================================================================
tm-name          tm-5416
in-theory        5416
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B and (((C and D) -> D) -> E)) -> E))
theorem-size     17
proof            (modus-ponens tm-76 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-10 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5416.         (((not (not A)) -> A) and ((B and (((C and D) -> D) -> E)) -> E)), M:tm-76, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5417
in-theory        5417
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A and (((B and C) -> C) -> D)))) or (A and (((B and C) -> C) -> D))) -> D)
theorem-size     23
proof            (modus-ponens tm-73 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-8 tm-10 tm-2 tm-4 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5417.         (((not (not (A and (((B and C) -> C) -> D)))) or (A and (((B and C) -> C) -> D))) -> D), M:tm-73, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-5418
in-theory        5418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and (((D and E) -> E) -> F)) -> F))
theorem-size     23
proof            (modus-ponens tm-69 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-9 tm-2 tm-4 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5418.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and (((D and E) -> E) -> F)) -> F)), M:tm-69, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5419
in-theory        5419
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> C) -> (not A))))
theorem-size     11
proof            (modus-ponens tm-59 tm-150 ((A Am) (B (-> (-> (and Bm Cm) Cm) (not Am))) (Dm (not Am))))
axioms-used      (tm-9 tm-3 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5419.         (not (A and (((B and C) -> C) -> (not A)))), M:tm-59, m:tm-150, u:((A Am) (B (-> (-> (and Bm Cm) Cm) (not Am))) (Dm (not Am)))
================================================================
tm-name          tm-5420
in-theory        5420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-54 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5420.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-54, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5421
in-theory        5421
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and (((C and D) -> D) -> E))) or (B and (((C and D) -> D) -> E))) -> E)
theorem-size     23
proof            (modus-ponens tm-47 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5421.         (((A and (B and (((C and D) -> D) -> E))) or (B and (((C and D) -> D) -> E))) -> E), M:tm-47, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-5422
in-theory        5422
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B and C) -> C) -> D)) and E) or (A and (((B and C) -> C) -> D))) -> D)
theorem-size     23
proof            (modus-ponens tm-46 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-8 tm-3 tm-2 tm-4 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5422.         ((((A and (((B and C) -> C) -> D)) and E) or (A and (((B and C) -> C) -> D))) -> D), M:tm-46, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-5423
in-theory        5423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C and (((D and E) -> E) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-42 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5423.         ((A -> (B or A)) and ((C and (((D and E) -> E) -> F)) -> F)), M:tm-42, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5424
in-theory        5424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C and (((D and E) -> E) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-32 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5424.         ((A -> (A or B)) and ((C and (((D and E) -> E) -> F)) -> F)), M:tm-32, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5425
in-theory        5425
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> D)) -> ((A and (((B and C) -> C) -> D)) and D))
theorem-size     21
proof            (modus-ponens tm-24 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5425.         ((A and (((B and C) -> C) -> D)) -> ((A and (((B and C) -> C) -> D)) and D)), M:tm-24, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-5426
in-theory        5426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C and (((D and E) -> E) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-23 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5426.         ((A -> (B -> (A and B))) and ((C and (((D and E) -> E) -> F)) -> F)), M:tm-23, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5427
in-theory        5427
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C and (((D and E) -> E) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-22 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5427.         (((A and B) -> B) and ((C and (((D and E) -> E) -> F)) -> F)), M:tm-22, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5428
in-theory        5428
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C and (((D and E) -> E) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-21 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5428.         (((A and B) -> A) and ((C and (((D and E) -> E) -> F)) -> F)), M:tm-21, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5429
in-theory        5429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-20 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5429.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-20, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5430
in-theory        5430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C and (((D and E) -> E) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-19 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5430.         ((A -> (B -> A)) and ((C and (((D and E) -> E) -> F)) -> F)), M:tm-19, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5431
in-theory        5431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and (((C and D) -> D) -> A)) -> B)
theorem-size     13
proof            (modus-ponens tm-15 tm-150 ((Am (-> Dm B)) (C (-> (-> (and Bm Cm) Cm) Dm)) (A Dm)))
axioms-used      (tm-2 tm-3 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5431.         (((A -> B) and (((C and D) -> D) -> A)) -> B), M:tm-15, m:tm-150, u:((Am (-> Dm B)) (C (-> (-> (and Bm Cm) Cm) Dm)) (A Dm))
================================================================
tm-name          tm-5432
in-theory        5432
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> D)) -> (A and (((B and C) -> C) -> D)))
theorem-size     19
proof            (modus-ponens tm-12 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5432.         ((A and (((B and C) -> C) -> D)) -> (A and (((B and C) -> C) -> D))), M:tm-12, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-5433
in-theory        5433
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> (not D)) -> (not (A and (((B and C) -> C) -> D))))
theorem-size     23
proof            (modus-ponens tm-9 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-9 tm-2 tm-4 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5433.         (((A and (((B and C) -> C) -> D)) -> (not D)) -> (not (A and (((B and C) -> C) -> D)))), M:tm-9, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-5434
in-theory        5434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C and (((D and E) -> E) -> A)) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5434.         ((A -> B) -> (((C and (((D and E) -> E) -> A)) or A) -> B)), M:tm-8, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-5435
in-theory        5435
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B and (((C and D) -> D) -> E)) -> E))
theorem-size     13
proof            (modus-ponens tm-7 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-7 tm-2 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5435.         (A or ((B and (((C and D) -> D) -> E)) -> E)), M:tm-7, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5436
in-theory        5436
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-6 tm-2 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5436.         (((A and (((B and C) -> C) -> D)) -> D) or E), M:tm-6, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5437
in-theory        5437
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (((C and D) -> D) -> E)) -> E) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5437.         (A -> (((B and (((C and D) -> D) -> E)) -> E) and A)), M:tm-5, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5438
in-theory        5438
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> (D -> E))) -> D) -> ((A and (((B and C) -> C) -> (D -> E))) -> E))
theorem-size     27
proof            (modus-ponens tm-2 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5438.         (((A and (((B and C) -> C) -> (D -> E))) -> D) -> ((A and (((B and C) -> C) -> (D -> E))) -> E)), M:tm-2, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-5439
in-theory        5439
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B and (((C and D) -> D) -> E)) -> E))
theorem-size     13
proof            (modus-ponens tm-1 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-1 tm-2 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5439.         (A -> ((B and (((C and D) -> D) -> E)) -> E)), M:tm-1, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5440
in-theory        5440
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-147 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5440.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-147, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5441
in-theory        5441
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) and (C -> D)) -> C)
theorem-size     13
proof            (modus-ponens tm-142 tm-151 ((A (-> (-> (and Am Bm) Bm) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5441.         (((((A and B) -> B) -> C) and (C -> D)) -> C), M:tm-142, m:tm-151, u:((A (-> (-> (and Am Bm) Bm) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-5442
in-theory        5442
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> (C -> D)) and ((C -> D) -> C)) -> D)
theorem-size     17
proof            (modus-ponens tm-141 tm-151 ((A (-> (-> (and Am Bm) Bm) (-> B C))) (Dm (-> (-> B C) B)) (Cm (-> B C))))
axioms-used      (tm-2 tm-4 tm-3 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5442.         (((((A and B) -> B) -> (C -> D)) and ((C -> D) -> C)) -> D), M:tm-141, m:tm-151, u:((A (-> (-> (and Am Bm) Bm) (-> B C))) (Dm (-> (-> B C) B)) (Cm (-> B C)))
================================================================
tm-name          tm-5443
in-theory        5443
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> (C and D)) and E) -> C)
theorem-size     13
proof            (modus-ponens tm-135 tm-151 ((A (and (-> (-> (and Am Bm) Bm) (and B C)) Dm)) (Cm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5443.         (((((A and B) -> B) -> (C and D)) and E) -> C), M:tm-135, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) (and B C)) Dm)) (Cm (and B C)))
================================================================
tm-name          tm-5444
in-theory        5444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-134 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5444.         ((A -> ((B and C) -> B)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-134, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5445
in-theory        5445
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> B) -> (not ((C and D) -> C))) and E))
theorem-size     15
proof            (modus-ponens tm-130 tm-151 ((A (and (-> (-> (and Am Bm) Bm) (not (-> (and B C) B))) Dm)) (Cm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5445.         (not ((((A and B) -> B) -> (not ((C and D) -> C))) and E)), M:tm-130, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) (not (-> (and B C) B))) Dm)) (Cm (not (-> (and B C) B))))
================================================================
tm-name          tm-5446
in-theory        5446
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-125 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5446.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-125, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5447
in-theory        5447
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> ((A and B) -> B)) and C) -> ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-120 tm-151 ((Cm (-> (and Am Bm) Bm)) (B (-> (and Am Bm) Bm)) (C Dm) (A (-> (and Am Bm) Bm))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5447.         (((((A and B) -> B) -> ((A and B) -> B)) and C) -> ((A and B) -> B)), M:tm-120, m:tm-151, u:((Cm (-> (and Am Bm) Bm)) (B (-> (and Am Bm) Bm)) (C Dm) (A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-5448
in-theory        5448
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> (C -> (D -> E))) and F) -> ((C -> D) -> (C -> E)))
theorem-size     21
proof            (modus-ponens tm-114 tm-151 ((A (and (-> (-> (and Am Bm) Bm) (-> B (-> C D))) Dm)) (Cm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5448.         (((((A and B) -> B) -> (C -> (D -> E))) and F) -> ((C -> D) -> (C -> E))), M:tm-114, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) (-> B (-> C D))) Dm)) (Cm (-> B (-> C D))))
================================================================
tm-name          tm-5449
in-theory        5449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> F) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-113 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5449.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> F) -> G) and H) -> G)), M:tm-113, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5450
in-theory        5450
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> B) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F))
theorem-size     23
proof            (modus-ponens tm-109 tm-151 ((A (and (-> (-> (and Am Bm) Bm) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Dm)) (Cm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5450.         (not ((((A and B) -> B) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F)), M:tm-109, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Dm)) (Cm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-5451
in-theory        5451
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     31
proof            (modus-ponens tm-105 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5451.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-105, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5452
in-theory        5452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C and D) -> D) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-95 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5452.         (((A -> B) -> (A -> A)) and (((((C and D) -> D) -> E) and F) -> E)), M:tm-95, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5453
in-theory        5453
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> (C -> D)) and E) -> (C -> D))
theorem-size     15
proof            (modus-ponens tm-87 tm-151 ((A (and (-> (-> (and Am Bm) Bm) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5453.         (((((A and B) -> B) -> (C -> D)) and E) -> (C -> D)), M:tm-87, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-5454
in-theory        5454
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) and D) -> (E -> C))
theorem-size     13
proof            (modus-ponens tm-84 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5454.         (((((A and B) -> B) -> C) and D) -> (E -> C)), M:tm-84, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-5455
in-theory        5455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-83 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5455.         ((A -> (B -> (C -> B))) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-83, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5456
in-theory        5456
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> B) -> (not (C -> (D -> C)))) and E))
theorem-size     15
proof            (modus-ponens tm-79 tm-151 ((A (and (-> (-> (and Am Bm) Bm) (not (-> B (-> C B)))) Dm)) (Cm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5456.         (not ((((A and B) -> B) -> (not (C -> (D -> C)))) and E)), M:tm-79, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) (not (-> B (-> C B)))) Dm)) (Cm (not (-> B (-> C B)))))
================================================================
tm-name          tm-5457
in-theory        5457
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B and C) -> C) -> D) and E) -> D))
theorem-size     17
proof            (modus-ponens tm-76 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-10 tm-2 tm-3 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5457.         (((not (not A)) -> A) and (((((B and C) -> C) -> D) and E) -> D)), M:tm-76, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5458
in-theory        5458
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A and B) -> B) -> C) and D))) or ((((A and B) -> B) -> C) and D)) -> C)
theorem-size     23
proof            (modus-ponens tm-73 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-10 tm-2 tm-3 tm-1 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5458.         (((not (not ((((A and B) -> B) -> C) and D))) or ((((A and B) -> B) -> C) and D)) -> C), M:tm-73, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-5459
in-theory        5459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C and D) -> D) -> E) and F) -> E))
theorem-size     23
proof            (modus-ponens tm-69 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-9 tm-2 tm-3 tm-1 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5459.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C and D) -> D) -> E) and F) -> E)), M:tm-69, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5460
in-theory        5460
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> B) -> (not C)) and C))
theorem-size     11
proof            (modus-ponens tm-60 tm-151 ((A (-> (-> (and Am Bm) Bm) (not Dm))) (B Dm) (Cm (not Dm))))
axioms-used      (tm-9 tm-4 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5460.         (not ((((A and B) -> B) -> (not C)) and C)), M:tm-60, m:tm-151, u:((A (-> (-> (and Am Bm) Bm) (not Dm))) (B Dm) (Cm (not Dm)))
================================================================
tm-name          tm-5461
in-theory        5461
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-54 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5461.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-54, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5462
in-theory        5462
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B and C) -> C) -> D) and E)) or ((((B and C) -> C) -> D) and E)) -> D)
theorem-size     23
proof            (modus-ponens tm-47 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-4 tm-2 tm-3 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5462.         (((A and ((((B and C) -> C) -> D) and E)) or ((((B and C) -> C) -> D) and E)) -> D), M:tm-47, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-5463
in-theory        5463
times-derived    1
----------------------------------------------------------------
theorem          (((((((A and B) -> B) -> C) and D) and E) or ((((A and B) -> B) -> C) and D)) -> C)
theorem-size     23
proof            (modus-ponens tm-46 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5463.         (((((((A and B) -> B) -> C) and D) and E) or ((((A and B) -> B) -> C) and D)) -> C), M:tm-46, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-5464
in-theory        5464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C and D) -> D) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-42 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5464.         ((A -> (B or A)) and (((((C and D) -> D) -> E) and F) -> E)), M:tm-42, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5465
in-theory        5465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C and D) -> D) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-32 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5465.         ((A -> (A or B)) and (((((C and D) -> D) -> E) and F) -> E)), M:tm-32, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5466
in-theory        5466
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) and D) -> (((((A and B) -> B) -> C) and D) and C))
theorem-size     21
proof            (modus-ponens tm-24 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5466.         (((((A and B) -> B) -> C) and D) -> (((((A and B) -> B) -> C) and D) and C)), M:tm-24, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-5467
in-theory        5467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C and D) -> D) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-23 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5467.         ((A -> (B -> (A and B))) and (((((C and D) -> D) -> E) and F) -> E)), M:tm-23, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5468
in-theory        5468
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C and D) -> D) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-22 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5468.         (((A and B) -> B) and (((((C and D) -> D) -> E) and F) -> E)), M:tm-22, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5469
in-theory        5469
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C and D) -> D) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-21 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5469.         (((A and B) -> A) and (((((C and D) -> D) -> E) and F) -> E)), M:tm-21, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5470
in-theory        5470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-20 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5470.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-20, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5471
in-theory        5471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C and D) -> D) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-19 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5471.         ((A -> (B -> A)) and (((((C and D) -> D) -> E) and F) -> E)), M:tm-19, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5472
in-theory        5472
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) and (C -> D)) -> D)
theorem-size     13
proof            (modus-ponens tm-17 tm-151 ((A (-> (-> (and Am Bm) Bm) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-4 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5472.         (((((A and B) -> B) -> C) and (C -> D)) -> D), M:tm-17, m:tm-151, u:((A (-> (-> (and Am Bm) Bm) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-5473
in-theory        5473
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) and D) -> ((((A and B) -> B) -> C) and D))
theorem-size     19
proof            (modus-ponens tm-12 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5473.         (((((A and B) -> B) -> C) and D) -> ((((A and B) -> B) -> C) and D)), M:tm-12, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-5474
in-theory        5474
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> (not C)) -> (not ((((A and B) -> B) -> C) and D)))
theorem-size     23
proof            (modus-ponens tm-9 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-9 tm-2 tm-3 tm-1 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5474.         ((((((A and B) -> B) -> C) and D) -> (not C)) -> (not ((((A and B) -> B) -> C) and D))), M:tm-9, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-5475
in-theory        5475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((((C and D) -> D) -> A) and E) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5475.         ((A -> B) -> ((((((C and D) -> D) -> A) and E) or A) -> B)), M:tm-8, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-5476
in-theory        5476
times-derived    1
----------------------------------------------------------------
theorem          (A or (((((B and C) -> C) -> D) and E) -> D))
theorem-size     13
proof            (modus-ponens tm-7 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-7 tm-2 tm-3 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5476.         (A or (((((B and C) -> C) -> D) and E) -> D)), M:tm-7, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5477
in-theory        5477
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-6 tm-2 tm-3 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5477.         ((((((A and B) -> B) -> C) and D) -> C) or E), M:tm-6, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5478
in-theory        5478
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B and C) -> C) -> D) and E) -> D) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5478.         (A -> ((((((B and C) -> C) -> D) and E) -> D) and A)), M:tm-5, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5479
in-theory        5479
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> (C -> D)) and E) -> C) -> (((((A and B) -> B) -> (C -> D)) and E) -> D))
theorem-size     27
proof            (modus-ponens tm-2 tm-151 ((A (and (-> (-> (and Am Bm) Bm) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-3 tm-1 tm-4)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5479.         ((((((A and B) -> B) -> (C -> D)) and E) -> C) -> (((((A and B) -> B) -> (C -> D)) and E) -> D)), M:tm-2, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-5480
in-theory        5480
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B and C) -> C) -> D) and E) -> D))
theorem-size     13
proof            (modus-ponens tm-1 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-1 tm-2 tm-3 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5480.         (A -> (((((B and C) -> C) -> D) and E) -> D)), M:tm-1, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5481
in-theory        5481
times-derived    2
----------------------------------------------------------------
theorem          ((A and (B and C)) -> C)
theorem-size     7
proof            (modus-ponens tm-152 tm-18 ((Am (and A (and Bm Cm))) (B (and Bm Cm)) (C Cm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5481.         ((A and (B and C)) -> C), M:tm-152, m:tm-18, u:((Am (and A (and Bm Cm))) (B (and Bm Cm)) (C Cm))
================================================================
tm-name          tm-5482
in-theory        5482
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> (C -> (B and C)))
theorem-size     9
proof            (modus-ponens tm-152 tm-25 ((Am (and A Bm)) (B Bm) (C (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-5482.         ((A and B) -> (C -> (B and C))), M:tm-152, m:tm-25, u:((Am (and A Bm)) (B Bm) (C (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-5483
in-theory        5483
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> (B or C))
theorem-size     7
proof            (modus-ponens tm-152 tm-33 ((Am (and A Bm)) (B Bm) (C (or Bm Cm))))
axioms-used      (tm-2 tm-1 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-5483.         ((A and B) -> (B or C)), M:tm-152, m:tm-33, u:((Am (and A Bm)) (B Bm) (C (or Bm Cm)))
================================================================
tm-name          tm-5484
in-theory        5484
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> (C or B))
theorem-size     7
proof            (modus-ponens tm-152 tm-43 ((Am (and A Bm)) (B Bm) (C (or Cm Bm))))
axioms-used      (tm-2 tm-1 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-5484.         ((A and B) -> (C or B)), M:tm-152, m:tm-43, u:((Am (and A Bm)) (B Bm) (C (or Cm Bm)))
================================================================
tm-name          tm-5485
in-theory        5485
times-derived    1
----------------------------------------------------------------
theorem          ((A and (B -> C)) -> ((C -> D) -> ((B or C) -> D)))
theorem-size     15
proof            (modus-ponens tm-152 tm-56 ((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-5485.         ((A and (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-152, m:tm-56, u:((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-5486
in-theory        5486
times-derived    1
----------------------------------------------------------------
theorem          ((A and (B -> C)) -> ((B -> (not C)) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-152 tm-71 ((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-5486.         ((A and (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-152, m:tm-71, u:((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-5487
in-theory        5487
times-derived    1
----------------------------------------------------------------
theorem          ((A and (not (not B))) -> B)
theorem-size     7
proof            (modus-ponens tm-152 tm-78 ((Am (and A (not (not Bm)))) (B (not (not Bm))) (C Bm)))
axioms-used      (tm-2 tm-1 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-5487.         ((A and (not (not B))) -> B), M:tm-152, m:tm-78, u:((Am (and A (not (not Bm)))) (B (not (not Bm))) (C Bm))
================================================================
tm-name          tm-5488
in-theory        5488
times-derived    1
----------------------------------------------------------------
theorem          ((A and (B -> C)) -> (B -> B))
theorem-size     9
proof            (modus-ponens tm-152 tm-97 ((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm Bm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-5488.         ((A and (B -> C)) -> (B -> B)), M:tm-152, m:tm-97, u:((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm Bm)))
================================================================
tm-name          tm-5489
in-theory        5489
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))
theorem-size     21
proof            (modus-ponens tm-152 tm-107 ((Am (and A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-5489.         ((A and ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-152, m:tm-107, u:((Am (and A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-5490
in-theory        5490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) and A) -> B)
theorem-size     9
proof            (modus-ponens tm-152 tm-116 ((A (-> Am (-> Am C))) (B Am) (Bm (-> Am C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-5490.         (((A -> (A -> B)) and A) -> B), M:tm-152, m:tm-116, u:((A (-> Am (-> Am C))) (B Am) (Bm (-> Am C)))
================================================================
tm-name          tm-5491
in-theory        5491
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> (C -> D)) and C) -> D)
theorem-size     13
proof            (modus-ponens tm-152 tm-117 ((A (-> (-> Am (-> Bm Am)) (-> Dm C))) (B Dm) (Cm (-> Dm C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-5491.         ((((A -> (B -> A)) -> (C -> D)) and C) -> D), M:tm-152, m:tm-117, u:((A (-> (-> Am (-> Bm Am)) (-> Dm C))) (B Dm) (Cm (-> Dm C)))
================================================================
tm-name          tm-5492
in-theory        5492
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and D) -> E)
theorem-size     21
proof            (modus-ponens tm-152 tm-118 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Em C))) (B Em) (Dm (-> Em C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5492.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and D) -> E), M:tm-152, m:tm-118, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Em C))) (B Em) (Dm (-> Em C)))
================================================================
tm-name          tm-5493
in-theory        5493
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))
theorem-size     17
proof            (modus-ponens tm-152 tm-127 ((Am (and A (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-5493.         ((A and (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-152, m:tm-127, u:((Am (and A (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-5494
in-theory        5494
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> (C -> D)) and C) -> D)
theorem-size     13
proof            (modus-ponens tm-152 tm-128 ((A (-> (-> (and Am Bm) Am) (-> Dm C))) (B Dm) (Cm (-> Dm C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-5494.         (((((A and B) -> A) -> (C -> D)) and C) -> D), M:tm-152, m:tm-128, u:((A (-> (-> (and Am Bm) Am) (-> Dm C))) (B Dm) (Cm (-> Dm C)))
================================================================
tm-name          tm-5495
in-theory        5495
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))
theorem-size     17
proof            (modus-ponens tm-152 tm-149 ((Am (and A (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5495.         ((A and ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-152, m:tm-149, u:((Am (and A (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-5496
in-theory        5496
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> (C -> D)) and C) -> D)
theorem-size     13
proof            (modus-ponens tm-152 tm-151 ((A (-> (-> (and Am Bm) Bm) (-> Dm C))) (B Dm) (Cm (-> Dm C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5496.         (((((A and B) -> B) -> (C -> D)) and C) -> D), M:tm-152, m:tm-151, u:((A (-> (-> (and Am Bm) Bm) (-> Dm C))) (B Dm) (Cm (-> Dm C)))
================================================================
tm-name          tm-5497
in-theory        5497
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     29
proof            (modus-ponens tm-147 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5497.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-147, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5498
in-theory        5498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-134 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5498.         ((A -> ((B and C) -> B)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-134, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5499
in-theory        5499
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) and B) -> (B -> C))) -> (((B -> C) and B) -> C))
theorem-size     19
proof            (modus-ponens tm-131 tm-152 ((Am (-> Bm Cm)) (B Bm) (A (-> Bm Cm)) (C (-> (and (-> Bm Cm) Bm) Cm))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5499.         ((A or (((B -> C) and B) -> (B -> C))) -> (((B -> C) and B) -> C)), M:tm-131, m:tm-152, u:((Am (-> Bm Cm)) (B Bm) (A (-> Bm Cm)) (C (-> (and (-> Bm Cm) Bm) Cm)))
================================================================
tm-name          tm-5500
in-theory        5500
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     29
proof            (modus-ponens tm-125 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5500.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-125, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5501
in-theory        5501
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and B) -> A) or (((A -> (B -> C)) and B) -> (B -> C))) -> (((A -> (B -> C)) and B) -> C))
theorem-size     31
proof            (modus-ponens tm-122 tm-152 ((Am (-> A (-> Bm Cm))) (C Bm) (B (-> Bm Cm)) (D (-> (and (-> A (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5501.         (((((A -> (B -> C)) and B) -> A) or (((A -> (B -> C)) and B) -> (B -> C))) -> (((A -> (B -> C)) and B) -> C)), M:tm-122, m:tm-152, u:((Am (-> A (-> Bm Cm))) (C Bm) (B (-> Bm Cm)) (D (-> (and (-> A (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-5502
in-theory        5502
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (B -> (C -> D))) -> (((A and B) -> C) -> ((A and B) -> D)))
theorem-size     21
proof            (modus-ponens tm-114 tm-152 ((A (-> (and Am Bm) (-> Bm (-> C D)))) (B (and Am Bm)) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5502.         (((A and B) -> (B -> (C -> D))) -> (((A and B) -> C) -> ((A and B) -> D))), M:tm-114, m:tm-152, u:((A (-> (and Am Bm) (-> Bm (-> C D)))) (B (and Am Bm)) (Cm (-> C D)))
================================================================
tm-name          tm-5503
in-theory        5503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (F -> G)) -> ((E and F) -> G)))
theorem-size     29
proof            (modus-ponens tm-113 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5503.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (F -> G)) -> ((E and F) -> G))), M:tm-113, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5504
in-theory        5504
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     33
proof            (modus-ponens tm-105 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5504.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-105, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5505
in-theory        5505
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> (B -> B)) -> ((A and B) -> B))
theorem-size     13
proof            (modus-ponens tm-100 tm-152 ((Cm Bm) (C Bm) (A (and Am Bm)) (B Bm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5505.         (((A and B) -> (B -> B)) -> ((A and B) -> B)), M:tm-100, m:tm-152, u:((Cm Bm) (C Bm) (A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-5506
in-theory        5506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> (D -> E)) -> ((C and D) -> E)))
theorem-size     21
proof            (modus-ponens tm-95 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5506.         (((A -> B) -> (A -> A)) and (((C and D) -> (D -> E)) -> ((C and D) -> E))), M:tm-95, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5507
in-theory        5507
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (B -> C)) -> (D -> ((A and B) -> C)))
theorem-size     15
proof            (modus-ponens tm-84 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5507.         (((A and B) -> (B -> C)) -> (D -> ((A and B) -> C))), M:tm-84, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-5508
in-theory        5508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-83 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5508.         ((A -> (B -> (C -> B))) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-83, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5509
in-theory        5509
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> (C -> (B and C)))) -> ((B and C) -> (B and C)))
theorem-size     19
proof            (modus-ponens tm-80 tm-152 ((Cm (and Am Bm)) (B Bm) (A (and Am Bm)) (C (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5509.         ((A or ((B and C) -> (C -> (B and C)))) -> ((B and C) -> (B and C))), M:tm-80, m:tm-152, u:((Cm (and Am Bm)) (B Bm) (A (and Am Bm)) (C (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-5510
in-theory        5510
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> (C -> D)) -> ((B and C) -> D)))
theorem-size     19
proof            (modus-ponens tm-76 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5510.         (((not (not A)) -> A) and (((B and C) -> (C -> D)) -> ((B and C) -> D))), M:tm-76, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5511
in-theory        5511
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) -> (B -> C)))) or ((A and B) -> (B -> C))) -> ((A and B) -> C))
theorem-size     23
proof            (modus-ponens tm-73 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5511.         (((not (not ((A and B) -> (B -> C)))) or ((A and B) -> (B -> C))) -> ((A and B) -> C)), M:tm-73, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-5512
in-theory        5512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> (D -> E)) -> ((C and D) -> E)))
theorem-size     25
proof            (modus-ponens tm-69 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5512.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> (D -> E)) -> ((C and D) -> E))), M:tm-69, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5513
in-theory        5513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     27
proof            (modus-ponens tm-54 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5513.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-54, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5514
in-theory        5514
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) -> (C -> D))) or ((B and C) -> (C -> D))) -> ((B and C) -> D))
theorem-size     23
proof            (modus-ponens tm-47 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5514.         (((A and ((B and C) -> (C -> D))) or ((B and C) -> (C -> D))) -> ((B and C) -> D)), M:tm-47, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-5515
in-theory        5515
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> (B -> C)) and D) or ((A and B) -> (B -> C))) -> ((A and B) -> C))
theorem-size     23
proof            (modus-ponens tm-46 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5515.         (((((A and B) -> (B -> C)) and D) or ((A and B) -> (B -> C))) -> ((A and B) -> C)), M:tm-46, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-5516
in-theory        5516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((C and A) -> (A -> B))) -> ((C and A) -> B))
theorem-size     17
proof            (modus-ponens tm-44 tm-152 ((A (and Am Bm)) (B (-> Bm Cm)) (C (-> (and Am Bm) Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5516.         (((A -> B) or ((C and A) -> (A -> B))) -> ((C and A) -> B)), M:tm-44, m:tm-152, u:((A (and Am Bm)) (B (-> Bm Cm)) (C (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-5517
in-theory        5517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> (D -> E)) -> ((C and D) -> E)))
theorem-size     19
proof            (modus-ponens tm-42 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5517.         ((A -> (B or A)) and (((C and D) -> (D -> E)) -> ((C and D) -> E))), M:tm-42, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5518
in-theory        5518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> (D -> E)) -> ((C and D) -> E)))
theorem-size     19
proof            (modus-ponens tm-32 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5518.         ((A -> (A or B)) and (((C and D) -> (D -> E)) -> ((C and D) -> E))), M:tm-32, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5519
in-theory        5519
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (B -> C)) -> (((A and B) -> (B -> C)) and ((A and B) -> C)))
theorem-size     21
proof            (modus-ponens tm-24 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5519.         (((A and B) -> (B -> C)) -> (((A and B) -> (B -> C)) and ((A and B) -> C))), M:tm-24, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-5520
in-theory        5520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> (D -> E)) -> ((C and D) -> E)))
theorem-size     21
proof            (modus-ponens tm-23 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5520.         ((A -> (B -> (A and B))) and (((C and D) -> (D -> E)) -> ((C and D) -> E))), M:tm-23, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5521
in-theory        5521
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> (D -> E)) -> ((C and D) -> E)))
theorem-size     19
proof            (modus-ponens tm-22 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5521.         (((A and B) -> B) and (((C and D) -> (D -> E)) -> ((C and D) -> E))), M:tm-22, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5522
in-theory        5522
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> (D -> E)) -> ((C and D) -> E)))
theorem-size     19
proof            (modus-ponens tm-21 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5522.         (((A and B) -> A) and (((C and D) -> (D -> E)) -> ((C and D) -> E))), M:tm-21, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5523
in-theory        5523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     27
proof            (modus-ponens tm-20 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5523.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-20, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5524
in-theory        5524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> (D -> E)) -> ((C and D) -> E)))
theorem-size     19
proof            (modus-ponens tm-19 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5524.         ((A -> (B -> A)) and (((C and D) -> (D -> E)) -> ((C and D) -> E))), M:tm-19, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5525
in-theory        5525
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (B -> C)) -> ((A and B) -> (B -> C)))
theorem-size     15
proof            (modus-ponens tm-12 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5525.         (((A and B) -> (B -> C)) -> ((A and B) -> (B -> C))), M:tm-12, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-5526
in-theory        5526
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> (not ((A and B) -> C))) -> (not ((A and B) -> (B -> C))))
theorem-size     23
proof            (modus-ponens tm-9 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-9 tm-2 tm-1 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5526.         ((((A and B) -> (B -> C)) -> (not ((A and B) -> C))) -> (not ((A and B) -> (B -> C)))), M:tm-9, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-5527
in-theory        5527
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> C) -> D) -> ((((A and B) -> (B -> C)) or ((A and B) -> C)) -> D))
theorem-size     23
proof            (modus-ponens tm-8 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5527.         ((((A and B) -> C) -> D) -> ((((A and B) -> (B -> C)) or ((A and B) -> C)) -> D)), M:tm-8, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-5528
in-theory        5528
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> (C -> D)) -> ((B and C) -> D)))
theorem-size     15
proof            (modus-ponens tm-7 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-7 tm-2 tm-1 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5528.         (A or (((B and C) -> (C -> D)) -> ((B and C) -> D))), M:tm-7, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5529
in-theory        5529
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-6 tm-2 tm-1 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5529.         ((((A and B) -> (B -> C)) -> ((A and B) -> C)) or D), M:tm-6, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5530
in-theory        5530
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> (C -> D)) -> ((B and C) -> D)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5530.         (A -> ((((B and C) -> (C -> D)) -> ((B and C) -> D)) and A)), M:tm-5, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5531
in-theory        5531
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> (A and B)) -> (((A and B) -> (B -> C)) -> C))
theorem-size     21
proof            (modus-ponens tm-2 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (and Am Bm)) (C Cm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5531.         ((((A and B) -> (B -> C)) -> (A and B)) -> (((A and B) -> (B -> C)) -> C)), M:tm-2, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (and Am Bm)) (C Cm))
================================================================
tm-name          tm-5532
in-theory        5532
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> (C -> D)) -> ((B and C) -> D)))
theorem-size     15
proof            (modus-ponens tm-1 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-1 tm-2 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5532.         (A -> (((B and C) -> (C -> D)) -> ((B and C) -> D))), M:tm-1, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5533
in-theory        5533
times-derived    1
----------------------------------------------------------------
theorem          (not ((not ((A and B) -> B)) and C))
theorem-size     9
proof            (modus-ponens tm-153 tm-3 ((A (and (not (-> (and B C) C)) Bm)) (Am (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-5533.         (not ((not ((A and B) -> B)) and C)), M:tm-153, m:tm-3, u:((A (and (not (-> (and B C) C)) Bm)) (Am (not (-> (and B C) C))))
================================================================
tm-name          tm-5534
in-theory        5534
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (not ((B and C) -> C))))
theorem-size     9
proof            (modus-ponens tm-153 tm-4 ((A (and Am (not (-> (and B C) C)))) (Bm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5534.         (not (A and (not ((B and C) -> C)))), M:tm-153, m:tm-4, u:((A (and Am (not (-> (and B C) C)))) (Bm (not (-> (and B C) C))))
================================================================
tm-name          tm-5535
in-theory        5535
times-derived    1
----------------------------------------------------------------
theorem          (not (not (not (not ((A and B) -> B)))))
theorem-size     9
proof            (modus-ponens tm-153 tm-10 ((A (not (not (not (-> (and B C) C))))) (Am (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-5535.         (not (not (not (not ((A and B) -> B))))), M:tm-153, m:tm-10, u:((A (not (not (not (-> (and B C) C))))) (Am (not (-> (and B C) C))))
================================================================
tm-name          tm-5536
in-theory        5536
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not (C -> ((A and B) -> B)))))
theorem-size     15
proof            (modus-ponens tm-153 tm-57 ((A (-> (-> (and B C) C) (not (-> Bm (-> (and B C) C))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5536.         (not (((A and B) -> B) -> (not (C -> ((A and B) -> B))))), M:tm-153, m:tm-57, u:((A (-> (-> (and B C) C) (not (-> Bm (-> (and B C) C))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-5537
in-theory        5537
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and (B -> C)) -> (B -> C)) -> (not (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)))))
theorem-size     27
proof            (modus-ponens tm-153 tm-58 ((A (-> (-> (and B (-> Bm Cm)) (-> Bm Cm)) (not (-> (-> (and B (-> Bm Cm)) Bm) (-> (and B (-> Bm Cm)) Cm))))) (Am (and B (-> Bm Cm))) (C (-> Bm Cm))))
axioms-used      (tm-9 tm-1 tm-4 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5537.         (not (((A and (B -> C)) -> (B -> C)) -> (not (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))))), M:tm-153, m:tm-58, u:((A (-> (-> (and B (-> Bm Cm)) (-> Bm Cm)) (not (-> (-> (and B (-> Bm Cm)) Bm) (-> (and B (-> Bm Cm)) Cm))))) (Am (and B (-> Bm Cm))) (C (-> Bm Cm)))
================================================================
tm-name          tm-5538
in-theory        5538
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not (C -> (((A and B) -> B) and C)))))
theorem-size     17
proof            (modus-ponens tm-153 tm-61 ((A (-> (-> (and B C) C) (not (-> Bm (and (-> (and B C) C) Bm))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-5538.         (not (((A and B) -> B) -> (not (C -> (((A and B) -> B) and C))))), M:tm-153, m:tm-61, u:((A (-> (-> (and B C) C) (not (-> Bm (and (-> (and B C) C) Bm))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-5539
in-theory        5539
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not (((A and B) -> B) or C))))
theorem-size     15
proof            (modus-ponens tm-153 tm-62 ((A (-> (-> (and B C) C) (not (or (-> (and B C) C) Bm)))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5539.         (not (((A and B) -> B) -> (not (((A and B) -> B) or C)))), M:tm-153, m:tm-62, u:((A (-> (-> (and B C) C) (not (or (-> (and B C) C) Bm)))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-5540
in-theory        5540
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not (C or ((A and B) -> B)))))
theorem-size     15
proof            (modus-ponens tm-153 tm-63 ((A (-> (-> (and B C) C) (not (or Bm (-> (and B C) C))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5540.         (not (((A and B) -> B) -> (not (C or ((A and B) -> B))))), M:tm-153, m:tm-63, u:((A (-> (-> (and B C) C) (not (or Bm (-> (and B C) C))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-5541
in-theory        5541
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not ((B -> C) -> (((A and B) or B) -> C)))))
theorem-size     19
proof            (modus-ponens tm-153 tm-64 ((A (-> (-> (and B Bm) Bm) (not (-> (-> Bm Cm) (-> (or (and B Bm) Bm) Cm))))) (Am (and B Bm)) (C Bm)))
axioms-used      (tm-9 tm-1 tm-4 tm-8)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5541.         (not (((A and B) -> B) -> (not ((B -> C) -> (((A and B) or B) -> C))))), M:tm-153, m:tm-64, u:((A (-> (-> (and B Bm) Bm) (not (-> (-> Bm Cm) (-> (or (and B Bm) Bm) Cm))))) (Am (and B Bm)) (C Bm))
================================================================
tm-name          tm-5542
in-theory        5542
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not (((A and B) -> (not B)) -> (not (A and B))))))
theorem-size     19
proof            (modus-ponens tm-153 tm-65 ((A (-> (-> (and B Bm) Bm) (not (-> (-> (and B Bm) (not Bm)) (not (and B Bm)))))) (Am (and B Bm)) (C Bm)))
axioms-used      (tm-9 tm-1 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5542.         (not (((A and B) -> B) -> (not (((A and B) -> (not B)) -> (not (A and B)))))), M:tm-153, m:tm-65, u:((A (-> (-> (and B Bm) Bm) (not (-> (-> (and B Bm) (not Bm)) (not (and B Bm)))))) (Am (and B Bm)) (C Bm))
================================================================
tm-name          tm-5543
in-theory        5543
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not (C -> (D -> C)))))
theorem-size     13
proof            (modus-ponens tm-153 tm-79 ((A (-> (-> (and B C) C) (not (-> Bm (-> Cm Bm))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5543.         (not (((A and B) -> B) -> (not (C -> (D -> C))))), M:tm-153, m:tm-79, u:((A (-> (-> (and B C) C) (not (-> Bm (-> Cm Bm))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-5544
in-theory        5544
times-derived    1
----------------------------------------------------------------
theorem          (not (not ((A and B) -> B)))
theorem-size     7
proof            (modus-ponens tm-153 tm-86 ((A (not (-> (and B C) C))) (Am (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5544.         (not (not ((A and B) -> B))), M:tm-153, m:tm-86, u:((A (not (-> (and B C) C))) (Am (not (-> (and B C) C))))
================================================================
tm-name          tm-5545
in-theory        5545
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not ((A and B) -> (A and B)))))
theorem-size     15
proof            (modus-ponens tm-153 tm-91 ((A (-> (-> (and B Bm) Bm) (not (-> (and B Bm) (and B Bm))))) (Am (and B Bm)) (C Bm)))
axioms-used      (tm-9 tm-1 tm-4 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5545.         (not (((A and B) -> B) -> (not ((A and B) -> (A and B))))), M:tm-153, m:tm-91, u:((A (-> (-> (and B Bm) Bm) (not (-> (and B Bm) (and B Bm))))) (Am (and B Bm)) (C Bm))
================================================================
tm-name          tm-5546
in-theory        5546
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     21
proof            (modus-ponens tm-153 tm-109 ((A (-> (-> (and B C) C) (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5546.         (not (((A and B) -> B) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-153, m:tm-109, u:((A (-> (-> (and B C) C) (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-5547
in-theory        5547
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (not ((B and C) -> C))) and A))
theorem-size     11
proof            (modus-ponens tm-153 tm-116 ((A (and (-> Am (not (-> (and B C) C))) Am)) (Bm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-5547.         (not ((A -> (not ((B and C) -> C))) and A)), M:tm-153, m:tm-116, u:((A (and (-> Am (not (-> (and B C) C))) Am)) (Bm (not (-> (and B C) C))))
================================================================
tm-name          tm-5548
in-theory        5548
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> A)) -> (not ((C and D) -> D))) and E))
theorem-size     15
proof            (modus-ponens tm-153 tm-117 ((A (and (-> (-> Am (-> Bm Am)) (not (-> (and B C) C))) Dm)) (Cm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-5548.         (not (((A -> (B -> A)) -> (not ((C and D) -> D))) and E)), M:tm-153, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) (not (-> (and B C) C))) Dm)) (Cm (not (-> (and B C) C))))
================================================================
tm-name          tm-5549
in-theory        5549
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D and E) -> E))) and F))
theorem-size     23
proof            (modus-ponens tm-153 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not (-> (and B C) C))) Em)) (Dm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5549.         (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D and E) -> E))) and F)), M:tm-153, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not (-> (and B C) C))) Em)) (Dm (not (-> (and B C) C))))
================================================================
tm-name          tm-5550
in-theory        5550
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> B) and A) -> A) -> (not (((A -> B) and A) -> B))))
theorem-size     17
proof            (modus-ponens tm-153 tm-121 ((A (-> (-> (and (-> Cm Bm) Cm) Cm) (not (-> (and (-> Cm Bm) Cm) Bm)))) (B (-> Cm Bm)) (Am Cm) (C Cm)))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5550.         (not ((((A -> B) and A) -> A) -> (not (((A -> B) and A) -> B)))), M:tm-153, m:tm-121, u:((A (-> (-> (and (-> Cm Bm) Cm) Cm) (not (-> (and (-> Cm Bm) Cm) Bm)))) (B (-> Cm Bm)) (Am Cm) (C Cm))
================================================================
tm-name          tm-5551
in-theory        5551
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> A) -> (not ((C and D) -> D))) and E))
theorem-size     15
proof            (modus-ponens tm-153 tm-128 ((A (and (-> (-> (and Am Bm) Am) (not (-> (and B C) C))) Dm)) (Cm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-5551.         (not ((((A and B) -> A) -> (not ((C and D) -> D))) and E)), M:tm-153, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) (not (-> (and B C) C))) Dm)) (Cm (not (-> (and B C) C))))
================================================================
tm-name          tm-5552
in-theory        5552
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not ((C and D) -> C))))
theorem-size     13
proof            (modus-ponens tm-153 tm-130 ((A (-> (-> (and B C) C) (not (-> (and Bm Cm) Bm)))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5552.         (not (((A and B) -> B) -> (not ((C and D) -> C)))), M:tm-153, m:tm-130, u:((A (-> (-> (and B C) C) (not (-> (and Bm Cm) Bm)))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-5553
in-theory        5553
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (A -> (not ((B and C) -> C)))))
theorem-size     11
proof            (modus-ponens tm-153 tm-137 ((A (and Am (-> Am (not (-> (and B C) C))))) (Bm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-5553.         (not (A and (A -> (not ((B and C) -> C))))), M:tm-153, m:tm-137, u:((A (and Am (-> Am (not (-> (and B C) C))))) (Bm (not (-> (and B C) C))))
================================================================
tm-name          tm-5554
in-theory        5554
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> B)) -> (not ((D and E) -> E)))))
theorem-size     15
proof            (modus-ponens tm-153 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) (not (-> (and B C) C))))) (Dm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-5554.         (not (A and ((B -> (C -> B)) -> (not ((D and E) -> E))))), M:tm-153, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) (not (-> (and B C) C))))) (Dm (not (-> (and B C) C))))
================================================================
tm-name          tm-5555
in-theory        5555
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not ((E and F) -> F)))))
theorem-size     23
proof            (modus-ponens tm-153 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not (-> (and B C) C))))) (Em (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5555.         (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not ((E and F) -> F))))), M:tm-153, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not (-> (and B C) C))))) (Em (not (-> (and B C) C))))
================================================================
tm-name          tm-5556
in-theory        5556
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> B) -> (not ((D and E) -> E)))))
theorem-size     15
proof            (modus-ponens tm-153 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) (not (-> (and B C) C))))) (Dm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-5556.         (not (A and (((B and C) -> B) -> (not ((D and E) -> E))))), M:tm-153, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) (not (-> (and B C) C))))) (Dm (not (-> (and B C) C))))
================================================================
tm-name          tm-5557
in-theory        5557
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> C) -> (not ((D and E) -> E)))))
theorem-size     15
proof            (modus-ponens tm-153 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) (not (-> (and B C) C))))) (Dm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5557.         (not (A and (((B and C) -> C) -> (not ((D and E) -> E))))), M:tm-153, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) (not (-> (and B C) C))))) (Dm (not (-> (and B C) C))))
================================================================
tm-name          tm-5558
in-theory        5558
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> B) -> (not ((C and D) -> D))) and E))
theorem-size     15
proof            (modus-ponens tm-153 tm-151 ((A (and (-> (-> (and Am Bm) Bm) (not (-> (and B C) C))) Dm)) (Cm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5558.         (not ((((A and B) -> B) -> (not ((C and D) -> D))) and E)), M:tm-153, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) (not (-> (and B C) C))) Dm)) (Cm (not (-> (and B C) C))))
================================================================
tm-name          tm-5559
in-theory        5559
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not ((C and D) -> D))))
theorem-size     13
proof            (modus-ponens tm-153 tm-153 ((A (-> (-> (and B C) C) (not (-> (and Bm Cm) Cm)))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5559.         (not (((A and B) -> B) -> (not ((C and D) -> D)))), M:tm-153, m:tm-153, u:((A (-> (-> (and B C) C) (not (-> (and Bm Cm) Cm)))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-5560
in-theory        5560
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5560.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-147, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5561
in-theory        5561
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (not ((C and D) -> D)))) -> B) or ((A and (B -> (not ((C and D) -> D)))) -> (not ((C and D) -> D)))) -> (not (A and (B -> (not ((C and D) -> D))))))
theorem-size     42
proof            (modus-ponens tm-144 tm-153 ((Am (and A (-> B (not (-> (and Bm Cm) Cm))))) (C (not (-> (and Bm Cm) Cm))) (D (not (and A (-> B (not (-> (and Bm Cm) Cm))))))))
axioms-used      (tm-8 tm-2 tm-4 tm-9 tm-1)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5561.         ((((A and (B -> (not ((C and D) -> D)))) -> B) or ((A and (B -> (not ((C and D) -> D)))) -> (not ((C and D) -> D)))) -> (not (A and (B -> (not ((C and D) -> D)))))), M:tm-144, m:tm-153, u:((Am (and A (-> B (not (-> (and Bm Cm) Cm))))) (C (not (-> (and Bm Cm) Cm))) (D (not (and A (-> B (not (-> (and Bm Cm) Cm)))))))
================================================================
tm-name          tm-5562
in-theory        5562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5562.         ((A -> ((B and C) -> B)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-134, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5563
in-theory        5563
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((not ((B and C) -> C)) and D) -> (not ((B and C) -> C)))) -> (not ((not ((B and C) -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-131 tm-153 ((Am (and (not (-> (and Bm Cm) Cm)) B)) (A (not (-> (and Bm Cm) Cm))) (C (not (and (not (-> (and Bm Cm) Cm)) B)))))
axioms-used      (tm-8 tm-1 tm-3 tm-9 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5563.         ((A or (((not ((B and C) -> C)) and D) -> (not ((B and C) -> C)))) -> (not ((not ((B and C) -> C)) and D))), M:tm-131, m:tm-153, u:((Am (and (not (-> (and Bm Cm) Cm)) B)) (A (not (-> (and Bm Cm) Cm))) (C (not (and (not (-> (and Bm Cm) Cm)) B))))
================================================================
tm-name          tm-5564
in-theory        5564
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not ((C and D) -> D))))
theorem-size     13
proof            (modus-ponens tm-130 tm-153 ((A (-> (-> (and B C) B) (not (-> (and Bm Cm) Cm)))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5564.         (not (((A and B) -> A) -> (not ((C and D) -> D)))), M:tm-130, m:tm-153, u:((A (-> (-> (and B C) B) (not (-> (and Bm Cm) Cm)))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-5565
in-theory        5565
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-1 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5565.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-125, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5566
in-theory        5566
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not ((B and C) -> C))) and D) -> A) or (((A -> (not ((B and C) -> C))) and D) -> (not ((B and C) -> C)))) -> (not ((A -> (not ((B and C) -> C))) and D)))
theorem-size     42
proof            (modus-ponens tm-122 tm-153 ((Am (and (-> A (not (-> (and Bm Cm) Cm))) C)) (B (not (-> (and Bm Cm) Cm))) (D (not (and (-> A (not (-> (and Bm Cm) Cm))) C)))))
axioms-used      (tm-8 tm-2 tm-3 tm-9 tm-1 tm-4)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5566.         (((((A -> (not ((B and C) -> C))) and D) -> A) or (((A -> (not ((B and C) -> C))) and D) -> (not ((B and C) -> C)))) -> (not ((A -> (not ((B and C) -> C))) and D))), M:tm-122, m:tm-153, u:((Am (and (-> A (not (-> (and Bm Cm) Cm))) C)) (B (not (-> (and Bm Cm) Cm))) (D (not (and (-> A (not (-> (and Bm Cm) Cm))) C))))
================================================================
tm-name          tm-5567
in-theory        5567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F and G) -> G))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5567.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F and G) -> G))) -> (not E))), M:tm-113, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5568
in-theory        5568
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D and E) -> E))))
theorem-size     21
proof            (modus-ponens tm-109 tm-153 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (and Bm Cm) Cm)))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5568.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D and E) -> E)))), M:tm-109, m:tm-153, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (and Bm Cm) Cm)))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-5569
in-theory        5569
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5569.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-105, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5570
in-theory        5570
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not ((D and E) -> E))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5570.         (((A -> B) -> (A -> A)) and ((C -> (not ((D and E) -> E))) -> (not C))), M:tm-95, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5571
in-theory        5571
times-derived    1
----------------------------------------------------------------
theorem          ((((not ((A and B) -> B)) -> C) or ((not ((A and B) -> B)) -> (not ((A and B) -> B)))) -> (not (not ((A and B) -> B))))
theorem-size     30
proof            (modus-ponens tm-92 tm-153 ((Am (not (-> (and Bm Cm) Cm))) (A (not (-> (and Bm Cm) Cm))) (B (not (not (-> (and Bm Cm) Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-9 tm-4)
proof-size       122
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5571.         ((((not ((A and B) -> B)) -> C) or ((not ((A and B) -> B)) -> (not ((A and B) -> B)))) -> (not (not ((A and B) -> B)))), M:tm-92, m:tm-153, u:((Am (not (-> (and Bm Cm) Cm))) (A (not (-> (and Bm Cm) Cm))) (B (not (not (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-5572
in-theory        5572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B and C) -> C))) -> (D -> (not A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5572.         ((A -> (not ((B and C) -> C))) -> (D -> (not A))), M:tm-84, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-5573
in-theory        5573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5573.         ((A -> (B -> (C -> B))) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-83, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5574
in-theory        5574
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not ((C and D) -> D))))
theorem-size     13
proof            (modus-ponens tm-79 tm-153 ((A (-> (-> B (-> C B)) (not (-> (and Bm Cm) Cm)))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5574.         (not ((A -> (B -> A)) -> (not ((C and D) -> D)))), M:tm-79, m:tm-153, u:((A (-> (-> B (-> C B)) (not (-> (and Bm Cm) Cm)))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-5575
in-theory        5575
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not ((C and D) -> D))) -> (not B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-1 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5575.         (((not (not A)) -> A) and ((B -> (not ((C and D) -> D))) -> (not B))), M:tm-76, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5576
in-theory        5576
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not ((B and C) -> C))))) or (A -> (not ((B and C) -> C)))) -> (not A))
theorem-size     22
proof            (modus-ponens tm-73 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-1 tm-4)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5576.         (((not (not (A -> (not ((B and C) -> C))))) or (A -> (not ((B and C) -> C)))) -> (not A)), M:tm-73, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-5577
in-theory        5577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not ((D and E) -> E))) -> (not C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5577.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not ((D and E) -> E))) -> (not C))), M:tm-69, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5578
in-theory        5578
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) or ((((A and B) -> B) -> (not C)) -> (not ((A and B) -> B)))) -> (not (((A and B) -> B) -> (not C))))
theorem-size     33
proof            (modus-ponens tm-66 tm-153 ((Am (-> (-> (and Bm Cm) Cm) (not B))) (A (-> (and Bm Cm) Cm)) (C (not (-> (-> (and Bm Cm) Cm) (not B))))))
axioms-used      (tm-8 tm-9 tm-1 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5578.         (((((A and B) -> B) -> C) or ((((A and B) -> B) -> (not C)) -> (not ((A and B) -> B)))) -> (not (((A and B) -> B) -> (not C)))), M:tm-66, m:tm-153, u:((Am (-> (-> (and Bm Cm) Cm) (not B))) (A (-> (and Bm Cm) Cm)) (C (not (-> (-> (and Bm Cm) Cm) (not B)))))
================================================================
tm-name          tm-5579
in-theory        5579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-1 tm-4)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5579.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-54, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5580
in-theory        5580
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not ((C and D) -> D)))) or (B -> (not ((C and D) -> D)))) -> (not B))
theorem-size     22
proof            (modus-ponens tm-47 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-1)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5580.         (((A and (B -> (not ((C and D) -> D)))) or (B -> (not ((C and D) -> D)))) -> (not B)), M:tm-47, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-5581
in-theory        5581
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not ((B and C) -> C))) and D) or (A -> (not ((B and C) -> C)))) -> (not A))
theorem-size     22
proof            (modus-ponens tm-46 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-1 tm-4)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5581.         ((((A -> (not ((B and C) -> C))) and D) or (A -> (not ((B and C) -> C)))) -> (not A)), M:tm-46, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-5582
in-theory        5582
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A and B) -> B)) or (C -> (not ((A and B) -> B)))) -> (not C))
theorem-size     18
proof            (modus-ponens tm-44 tm-153 ((A Am) (B (not (-> (and Bm Cm) Cm))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-4)
proof-size       88
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5582.         (((not ((A and B) -> B)) or (C -> (not ((A and B) -> B)))) -> (not C)), M:tm-44, m:tm-153, u:((A Am) (B (not (-> (and Bm Cm) Cm))) (C (not Am)))
================================================================
tm-name          tm-5583
in-theory        5583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not ((D and E) -> E))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5583.         ((A -> (B or A)) and ((C -> (not ((D and E) -> E))) -> (not C))), M:tm-42, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5584
in-theory        5584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not ((D and E) -> E))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5584.         ((A -> (A or B)) and ((C -> (not ((D and E) -> E))) -> (not C))), M:tm-32, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5585
in-theory        5585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B and C) -> C))) -> ((A -> (not ((B and C) -> C))) and (not A)))
theorem-size     20
proof            (modus-ponens tm-24 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       88
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5585.         ((A -> (not ((B and C) -> C))) -> ((A -> (not ((B and C) -> C))) and (not A))), M:tm-24, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-5586
in-theory        5586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not ((D and E) -> E))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5586.         ((A -> (B -> (A and B))) and ((C -> (not ((D and E) -> E))) -> (not C))), M:tm-23, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5587
in-theory        5587
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not ((D and E) -> E))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5587.         (((A and B) -> B) and ((C -> (not ((D and E) -> E))) -> (not C))), M:tm-22, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5588
in-theory        5588
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not ((D and E) -> E))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5588.         (((A and B) -> A) and ((C -> (not ((D and E) -> E))) -> (not C))), M:tm-21, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5589
in-theory        5589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-4)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5589.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-20, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5590
in-theory        5590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not ((D and E) -> E))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5590.         ((A -> (B -> A)) and ((C -> (not ((D and E) -> E))) -> (not C))), M:tm-19, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5591
in-theory        5591
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B and C) -> C))) -> (A -> (not ((B and C) -> C))))
theorem-size     17
proof            (modus-ponens tm-12 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5591.         ((A -> (not ((B and C) -> C))) -> (A -> (not ((B and C) -> C)))), M:tm-12, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-5592
in-theory        5592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not (not A))) -> (not (A -> (not ((B and C) -> C)))))
theorem-size     22
proof            (modus-ponens tm-9 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-9 tm-1 tm-4)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5592.         (((A -> (not ((B and C) -> C))) -> (not (not A))) -> (not (A -> (not ((B and C) -> C))))), M:tm-9, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-5593
in-theory        5593
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not ((C and D) -> D))) or (not A)) -> B))
theorem-size     18
proof            (modus-ponens tm-8 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-1 tm-4)
proof-size       70
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5593.         (((not A) -> B) -> (((A -> (not ((C and D) -> D))) or (not A)) -> B)), M:tm-8, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-5594
in-theory        5594
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not ((C and D) -> D))) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-1 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5594.         (A or ((B -> (not ((C and D) -> D))) -> (not B))), M:tm-7, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5595
in-theory        5595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-1 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5595.         (((A -> (not ((B and C) -> C))) -> (not A)) or D), M:tm-6, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5596
in-theory        5596
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not ((C and D) -> D))) -> (not B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5596.         (A -> (((B -> (not ((C and D) -> D))) -> (not B)) and A)), M:tm-5, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5597
in-theory        5597
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not ((C and D) -> D))) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5597.         (A -> ((B -> (not ((C and D) -> D))) -> (not B))), M:tm-1, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5598
in-theory        5598
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> ((B and C) -> C)))
theorem-size     15
proof            (modus-ponens tm-154 tm-1 ((Am (-> (and A B) B)) (C (-> Bm (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5598.         ((A or ((B and C) -> C)) -> (D -> ((B and C) -> C))), M:tm-154, m:tm-1, u:((Am (-> (and A B) B)) (C (-> Bm (-> (and A B) B))))
================================================================
tm-name          tm-5599
in-theory        5599
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (C -> D)) -> (C -> D))) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))
theorem-size     27
proof            (modus-ponens tm-154 tm-2 ((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> (and A (-> Bm Cm)) Bm) (-> (and A (-> Bm Cm)) Cm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5599.         ((A or ((B and (C -> D)) -> (C -> D))) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-154, m:tm-2, u:((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> (and A (-> Bm Cm)) Bm) (-> (and A (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-5600
in-theory        5600
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> (((B and C) -> C) and D)))
theorem-size     17
proof            (modus-ponens tm-154 tm-5 ((Am (-> (and A B) B)) (C (-> Bm (and (-> (and A B) B) Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-5600.         ((A or ((B and C) -> C)) -> (D -> (((B and C) -> C) and D))), M:tm-154, m:tm-5, u:((Am (-> (and A B) B)) (C (-> Bm (and (-> (and A B) B) Bm))))
================================================================
tm-name          tm-5601
in-theory        5601
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) or D))
theorem-size     15
proof            (modus-ponens tm-154 tm-6 ((Am (-> (and A B) B)) (C (or (-> (and A B) B) Bm))))
axioms-used      (tm-8 tm-1 tm-4 tm-6)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-5601.         ((A or ((B and C) -> C)) -> (((B and C) -> C) or D)), M:tm-154, m:tm-6, u:((Am (-> (and A B) B)) (C (or (-> (and A B) B) Bm)))
================================================================
tm-name          tm-5602
in-theory        5602
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D or ((B and C) -> C)))
theorem-size     15
proof            (modus-ponens tm-154 tm-7 ((Am (-> (and A B) B)) (C (or Bm (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-7)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-5602.         ((A or ((B and C) -> C)) -> (D or ((B and C) -> C))), M:tm-154, m:tm-7, u:((Am (-> (and A B) B)) (C (or Bm (-> (and A B) B))))
================================================================
tm-name          tm-5603
in-theory        5603
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((C -> D) -> (((B and C) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-154 tm-8 ((Am (and A Bm)) (B Bm) (C (-> (-> Bm Cm) (-> (or (and A Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5603.         ((A or ((B and C) -> C)) -> ((C -> D) -> (((B and C) or C) -> D))), M:tm-154, m:tm-8, u:((Am (and A Bm)) (B Bm) (C (-> (-> Bm Cm) (-> (or (and A Bm) Bm) Cm))))
================================================================
tm-name          tm-5604
in-theory        5604
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> (not C)) -> (not (B and C))))
theorem-size     19
proof            (modus-ponens tm-154 tm-9 ((Am (and A Bm)) (B Bm) (C (-> (-> (and A Bm) (not Bm)) (not (and A Bm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5604.         ((A or ((B and C) -> C)) -> (((B and C) -> (not C)) -> (not (B and C)))), M:tm-154, m:tm-9, u:((Am (and A Bm)) (B Bm) (C (-> (-> (and A Bm) (not Bm)) (not (and A Bm)))))
================================================================
tm-name          tm-5605
in-theory        5605
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-154 tm-11 ((Am (-> (and A B) B)) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-5605.         ((A or ((B and C) -> C)) -> (D -> (E -> D))), M:tm-154, m:tm-11, u:((Am (-> (and A B) B)) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-5606
in-theory        5606
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((B and C) -> (B and C)))
theorem-size     15
proof            (modus-ponens tm-154 tm-12 ((Am (and A Bm)) (B Bm) (C (-> (and A Bm) (and A Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-5606.         ((A or ((B and C) -> C)) -> ((B and C) -> (B and C))), M:tm-154, m:tm-12, u:((Am (and A Bm)) (B Bm) (C (-> (and A Bm) (and A Bm))))
================================================================
tm-name          tm-5607
in-theory        5607
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-154 tm-14 ((Am (-> (and A B) B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-5607.         ((A or ((B and C) -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-154, m:tm-14, u:((Am (-> (and A B) B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-5608
in-theory        5608
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) and B) -> B)) -> (((B -> C) and B) -> C))
theorem-size     17
proof            (modus-ponens tm-154 tm-15 ((A (-> Cm Bm)) (Am Cm) (B Cm) (C (-> (and (-> Cm Bm) Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5608.         ((A or (((B -> C) and B) -> B)) -> (((B -> C) and B) -> C)), M:tm-154, m:tm-15, u:((A (-> Cm Bm)) (Am Cm) (B Cm) (C (-> (and (-> Cm Bm) Cm) Bm)))
================================================================
tm-name          tm-5609
in-theory        5609
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-154 tm-16 ((Am (-> (and A B) B)) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-4 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-5609.         ((A or ((B and C) -> C)) -> ((D and E) -> D)), M:tm-154, m:tm-16, u:((Am (-> (and A B) B)) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-5610
in-theory        5610
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-154 tm-18 ((Am (-> (and A B) B)) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5610.         ((A or ((B and C) -> C)) -> ((D and E) -> E)), M:tm-154, m:tm-18, u:((Am (-> (and A B) B)) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-5611
in-theory        5611
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (E -> D)) and ((B and C) -> C)))
theorem-size     19
proof            (modus-ponens tm-154 tm-19 ((Am (-> (and A B) B)) (C (and (-> Bm (-> Cm Bm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-5611.         ((A or ((B and C) -> C)) -> ((D -> (E -> D)) and ((B and C) -> C))), M:tm-154, m:tm-19, u:((Am (-> (and A B) B)) (C (and (-> Bm (-> Cm Bm)) (-> (and A B) B))))
================================================================
tm-name          tm-5612
in-theory        5612
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B and C) -> C)))
theorem-size     27
proof            (modus-ponens tm-154 tm-20 ((Am (-> (and A B) B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-5612.         ((A or ((B and C) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B and C) -> C))), M:tm-154, m:tm-20, u:((Am (-> (and A B) B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and A B) B))))
================================================================
tm-name          tm-5613
in-theory        5613
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D and E) -> D) and ((B and C) -> C)))
theorem-size     19
proof            (modus-ponens tm-154 tm-21 ((Am (-> (and A B) B)) (C (and (-> (and Bm Cm) Bm) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-5613.         ((A or ((B and C) -> C)) -> (((D and E) -> D) and ((B and C) -> C))), M:tm-154, m:tm-21, u:((Am (-> (and A B) B)) (C (and (-> (and Bm Cm) Bm) (-> (and A B) B))))
================================================================
tm-name          tm-5614
in-theory        5614
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D and E) -> E) and ((B and C) -> C)))
theorem-size     19
proof            (modus-ponens tm-154 tm-22 ((Am (-> (and A B) B)) (C (and (-> (and Bm Cm) Cm) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-5614.         ((A or ((B and C) -> C)) -> (((D and E) -> E) and ((B and C) -> C))), M:tm-154, m:tm-22, u:((Am (-> (and A B) B)) (C (and (-> (and Bm Cm) Cm) (-> (and A B) B))))
================================================================
tm-name          tm-5615
in-theory        5615
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (E -> (D and E))) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-23 ((Am (-> (and A B) B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-5615.         ((A or ((B and C) -> C)) -> ((D -> (E -> (D and E))) and ((B and C) -> C))), M:tm-154, m:tm-23, u:((Am (-> (and A B) B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> (and A B) B))))
================================================================
tm-name          tm-5616
in-theory        5616
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((B and C) -> ((B and C) and C)))
theorem-size     17
proof            (modus-ponens tm-154 tm-24 ((Am (and A Bm)) (B Bm) (C (-> (and A Bm) (and (and A Bm) Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-5616.         ((A or ((B and C) -> C)) -> ((B and C) -> ((B and C) and C))), M:tm-154, m:tm-24, u:((Am (and A Bm)) (B Bm) (C (-> (and A Bm) (and (and A Bm) Bm))))
================================================================
tm-name          tm-5617
in-theory        5617
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-154 tm-25 ((Am (-> (and A B) B)) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-5617.         ((A or ((B and C) -> C)) -> (D -> (E -> (D and E)))), M:tm-154, m:tm-25, u:((Am (-> (and A B) B)) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-5618
in-theory        5618
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (D or E)) and ((B and C) -> C)))
theorem-size     19
proof            (modus-ponens tm-154 tm-32 ((Am (-> (and A B) B)) (C (and (-> Bm (or Bm Cm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-5618.         ((A or ((B and C) -> C)) -> ((D -> (D or E)) and ((B and C) -> C))), M:tm-154, m:tm-32, u:((Am (-> (and A B) B)) (C (and (-> Bm (or Bm Cm)) (-> (and A B) B))))
================================================================
tm-name          tm-5619
in-theory        5619
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-154 tm-33 ((Am (-> (and A B) B)) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-5619.         ((A or ((B and C) -> C)) -> (D -> (D or E))), M:tm-154, m:tm-33, u:((Am (-> (and A B) B)) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-5620
in-theory        5620
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (E or D)) and ((B and C) -> C)))
theorem-size     19
proof            (modus-ponens tm-154 tm-42 ((Am (-> (and A B) B)) (C (and (-> Bm (or Cm Bm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-5620.         ((A or ((B and C) -> C)) -> ((D -> (E or D)) and ((B and C) -> C))), M:tm-154, m:tm-42, u:((Am (-> (and A B) B)) (C (and (-> Bm (or Cm Bm)) (-> (and A B) B))))
================================================================
tm-name          tm-5621
in-theory        5621
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-154 tm-43 ((Am (-> (and A B) B)) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-5621.         ((A or ((B and C) -> C)) -> (D -> (E or D))), M:tm-154, m:tm-43, u:((Am (-> (and A B) B)) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-5622
in-theory        5622
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((((B and C) and D) or (B and C)) -> C))
theorem-size     19
proof            (modus-ponens tm-154 tm-46 ((Am (and A Bm)) (B Bm) (C (-> (or (and (and A Bm) Cm) (and A Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-4 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5622.         ((A or ((B and C) -> C)) -> ((((B and C) and D) or (B and C)) -> C)), M:tm-154, m:tm-46, u:((Am (and A Bm)) (B Bm) (C (-> (or (and (and A Bm) Cm) (and A Bm)) Bm)))
================================================================
tm-name          tm-5623
in-theory        5623
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D and (B and C)) or (B and C)) -> C))
theorem-size     19
proof            (modus-ponens tm-154 tm-47 ((Am (and A Bm)) (B Bm) (C (-> (or (and Cm (and A Bm)) (and A Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5623.         ((A or ((B and C) -> C)) -> (((D and (B and C)) or (B and C)) -> C)), M:tm-154, m:tm-47, u:((Am (and A Bm)) (B Bm) (C (-> (or (and Cm (and A Bm)) (and A Bm)) Bm)))
================================================================
tm-name          tm-5624
in-theory        5624
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B and C) -> C)))
theorem-size     27
proof            (modus-ponens tm-154 tm-54 ((Am (-> (and A B) B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-5624.         ((A or ((B and C) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B and C) -> C))), M:tm-154, m:tm-54, u:((Am (-> (and A B) B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (and A B) B))))
================================================================
tm-name          tm-5625
in-theory        5625
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-154 tm-56 ((Am (-> (and A B) B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-5625.         ((A or ((B and C) -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-154, m:tm-56, u:((Am (-> (and A B) B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-5626
in-theory        5626
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (not B)) -> (not B))) -> (not (B and (not B))))
theorem-size     15
proof            (modus-ponens tm-154 tm-59 ((A Am) (Bm (not Am)) (B (not Am)) (C (not (and Am (not Am))))))
axioms-used      (tm-8 tm-1 tm-4 tm-9 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5626.         ((A or ((B and (not B)) -> (not B))) -> (not (B and (not B)))), M:tm-154, m:tm-59, u:((A Am) (Bm (not Am)) (B (not Am)) (C (not (and Am (not Am)))))
================================================================
tm-name          tm-5627
in-theory        5627
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B and C) -> C)))
theorem-size     25
proof            (modus-ponens tm-154 tm-69 ((Am (-> (and A B) B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-5627.         ((A or ((B and C) -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B and C) -> C))), M:tm-154, m:tm-69, u:((Am (-> (and A B) B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (and A B) B))))
================================================================
tm-name          tm-5628
in-theory        5628
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-154 tm-71 ((Am (-> (and A B) B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-5628.         ((A or ((B and C) -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-154, m:tm-71, u:((Am (-> (and A B) B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-5629
in-theory        5629
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((not (not (B and C))) or (B and C)) -> C))
theorem-size     19
proof            (modus-ponens tm-154 tm-73 ((Am (and A Bm)) (B Bm) (C (-> (or (not (not (and A Bm))) (and A Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-4 tm-10)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5629.         ((A or ((B and C) -> C)) -> (((not (not (B and C))) or (B and C)) -> C)), M:tm-154, m:tm-73, u:((Am (and A Bm)) (B Bm) (C (-> (or (not (not (and A Bm))) (and A Bm)) Bm)))
================================================================
tm-name          tm-5630
in-theory        5630
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((not (not D)) -> D) and ((B and C) -> C)))
theorem-size     19
proof            (modus-ponens tm-154 tm-76 ((Am (-> (and A B) B)) (C (and (-> (not (not Bm)) Bm) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-5630.         ((A or ((B and C) -> C)) -> (((not (not D)) -> D) and ((B and C) -> C))), M:tm-154, m:tm-76, u:((Am (-> (and A B) B)) (C (and (-> (not (not Bm)) Bm) (-> (and A B) B))))
================================================================
tm-name          tm-5631
in-theory        5631
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-154 tm-78 ((Am (-> (and A B) B)) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-4 tm-10)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-5631.         ((A or ((B and C) -> C)) -> ((not (not D)) -> D)), M:tm-154, m:tm-78, u:((Am (-> (and A B) B)) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-5632
in-theory        5632
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (not (C -> (D -> C)))) -> (not (C -> (D -> C))))) -> (not (B and (not (C -> (D -> C))))))
theorem-size     27
proof            (modus-ponens tm-154 tm-79 ((Am (and A (not (-> Bm (-> Cm Bm))))) (B (not (-> Bm (-> Cm Bm)))) (C (not (and A (not (-> Bm (-> Cm Bm))))))))
axioms-used      (tm-8 tm-1 tm-4 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5632.         ((A or ((B and (not (C -> (D -> C)))) -> (not (C -> (D -> C))))) -> (not (B and (not (C -> (D -> C)))))), M:tm-154, m:tm-79, u:((Am (and A (not (-> Bm (-> Cm Bm))))) (B (not (-> Bm (-> Cm Bm)))) (C (not (and A (not (-> Bm (-> Cm Bm)))))))
================================================================
tm-name          tm-5633
in-theory        5633
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (E -> (F -> E))) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-83 ((Am (-> (and A B) B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-5633.         ((A or ((B and C) -> C)) -> ((D -> (E -> (F -> E))) and ((B and C) -> C))), M:tm-154, m:tm-83, u:((Am (-> (and A B) B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> (and A B) B))))
================================================================
tm-name          tm-5634
in-theory        5634
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((B and C) -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-154 tm-84 ((Am (and A Bm)) (B Bm) (C (-> (and A Bm) (-> Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5634.         ((A or ((B and C) -> C)) -> ((B and C) -> (D -> C))), M:tm-154, m:tm-84, u:((Am (and A Bm)) (B Bm) (C (-> (and A Bm) (-> Cm Bm))))
================================================================
tm-name          tm-5635
in-theory        5635
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-154 tm-85 ((Am (-> (and A B) B)) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-5635.         ((A or ((B and C) -> C)) -> (D -> (E -> (F -> E)))), M:tm-154, m:tm-85, u:((Am (-> (and A B) B)) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-5636
in-theory        5636
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((B and C) -> C))
theorem-size     13
proof            (modus-ponens tm-154 tm-86 ((Am (-> (and A B) B)) (C (-> (and A B) B))))
axioms-used      (tm-8 tm-1 tm-4 tm-2)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5636.         ((A or ((B and C) -> C)) -> ((B and C) -> C)), M:tm-154, m:tm-86, u:((Am (-> (and A B) B)) (C (-> (and A B) B)))
================================================================
tm-name          tm-5637
in-theory        5637
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (C -> D)) -> (C -> D))) -> ((B and (C -> D)) -> (C -> D)))
theorem-size     21
proof            (modus-ponens tm-154 tm-87 ((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (and A (-> Bm Cm)) (-> Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5637.         ((A or ((B and (C -> D)) -> (C -> D))) -> ((B and (C -> D)) -> (C -> D))), M:tm-154, m:tm-87, u:((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (and A (-> Bm Cm)) (-> Bm Cm))))
================================================================
tm-name          tm-5638
in-theory        5638
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> E) -> (D -> D)) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-95 ((Am (-> (and A B) B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-5638.         ((A or ((B and C) -> C)) -> (((D -> E) -> (D -> D)) and ((B and C) -> C))), M:tm-154, m:tm-95, u:((Am (-> (and A B) B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (and A B) B))))
================================================================
tm-name          tm-5639
in-theory        5639
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-154 tm-97 ((Am (-> (and A B) B)) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-5639.         ((A or ((B and C) -> C)) -> ((D -> E) -> (D -> D))), M:tm-154, m:tm-97, u:((Am (-> (and A B) B)) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-5640
in-theory        5640
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B and C) -> C)))
theorem-size     33
proof            (modus-ponens tm-154 tm-105 ((Am (-> (and A B) B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-5640.         ((A or ((B and C) -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B and C) -> C))), M:tm-154, m:tm-105, u:((Am (-> (and A B) B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (and A B) B))))
================================================================
tm-name          tm-5641
in-theory        5641
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-154 tm-107 ((Am (-> (and A B) B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-5641.         ((A or ((B and C) -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-154, m:tm-107, u:((Am (-> (and A B) B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-5642
in-theory        5642
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not (B and (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     51
proof            (modus-ponens tm-154 tm-109 ((Am (and A (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (C (not (and A (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))))
axioms-used      (tm-8 tm-1 tm-4 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5642.         ((A or ((B and (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not (B and (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-154, m:tm-109, u:((Am (and A (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (C (not (and A (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
================================================================
tm-name          tm-5643
in-theory        5643
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B and C) -> C)))
theorem-size     29
proof            (modus-ponens tm-154 tm-113 ((Am (-> (and A B) B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-5643.         ((A or ((B and C) -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B and C) -> C))), M:tm-154, m:tm-113, u:((Am (-> (and A B) B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and A B) B))))
================================================================
tm-name          tm-5644
in-theory        5644
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (C -> (D -> E))) -> (C -> (D -> E)))) -> ((B and (C -> (D -> E))) -> ((C -> D) -> (C -> E))))
theorem-size     31
proof            (modus-ponens tm-154 tm-114 ((Am (and A (-> Bm (-> Cm Dm)))) (B (-> Bm (-> Cm Dm))) (C (-> (and A (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-5644.         ((A or ((B and (C -> (D -> E))) -> (C -> (D -> E)))) -> ((B and (C -> (D -> E))) -> ((C -> D) -> (C -> E)))), M:tm-154, m:tm-114, u:((Am (and A (-> Bm (-> Cm Dm)))) (B (-> Bm (-> Cm Dm))) (C (-> (and A (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-5645
in-theory        5645
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-154 tm-115 ((Am (-> (and A B) B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-5645.         ((A or ((B and C) -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-154, m:tm-115, u:((Am (-> (and A B) B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-5646
in-theory        5646
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> B) and (B -> C)) -> (B -> C))) -> ((((B -> C) -> B) and (B -> C)) -> C))
theorem-size     27
proof            (modus-ponens tm-154 tm-119 ((A (-> (-> Am Bm) Am)) (Cm (-> Am Bm)) (B (-> Am Bm)) (C (-> (and (-> (-> Am Bm) Am) (-> Am Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-5646.         ((A or ((((B -> C) -> B) and (B -> C)) -> (B -> C))) -> ((((B -> C) -> B) and (B -> C)) -> C)), M:tm-154, m:tm-119, u:((A (-> (-> Am Bm) Am)) (Cm (-> Am Bm)) (B (-> Am Bm)) (C (-> (and (-> (-> Am Bm) Am) (-> Am Bm)) Bm)))
================================================================
tm-name          tm-5647
in-theory        5647
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) and B) -> B)) -> (((B -> C) and B) -> B))
theorem-size     17
proof            (modus-ponens tm-154 tm-120 ((A (-> Cm Bm)) (Am Cm) (B Cm) (C (-> (and (-> Cm Bm) Cm) Cm))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5647.         ((A or (((B -> C) and B) -> B)) -> (((B -> C) and B) -> B)), M:tm-154, m:tm-120, u:((A (-> Cm Bm)) (Am Cm) (B Cm) (C (-> (and (-> Cm Bm) Cm) Cm)))
================================================================
tm-name          tm-5648
in-theory        5648
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B and C) -> C)))
theorem-size     29
proof            (modus-ponens tm-154 tm-125 ((Am (-> (and A B) B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-5648.         ((A or ((B and C) -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B and C) -> C))), M:tm-154, m:tm-125, u:((Am (-> (and A B) B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (and A B) B))))
================================================================
tm-name          tm-5649
in-theory        5649
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-154 tm-127 ((Am (-> (and A B) B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-5649.         ((A or ((B and C) -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-154, m:tm-127, u:((Am (-> (and A B) B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-5650
in-theory        5650
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (B -> C)) -> (B -> C))) -> ((B and (B -> C)) -> C))
theorem-size     19
proof            (modus-ponens tm-154 tm-129 ((A Am) (Bm (-> Am Cm)) (B (-> Am Cm)) (C (-> (and Am (-> Am Cm)) Cm))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-5650.         ((A or ((B and (B -> C)) -> (B -> C))) -> ((B and (B -> C)) -> C)), M:tm-154, m:tm-129, u:((A Am) (Bm (-> Am Cm)) (B (-> Am Cm)) (C (-> (and Am (-> Am Cm)) Cm)))
================================================================
tm-name          tm-5651
in-theory        5651
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (not ((C and D) -> C))) -> (not ((C and D) -> C)))) -> (not (B and (not ((C and D) -> C)))))
theorem-size     27
proof            (modus-ponens tm-154 tm-130 ((Am (and A (not (-> (and Bm Cm) Bm)))) (B (not (-> (and Bm Cm) Bm))) (C (not (and A (not (-> (and Bm Cm) Bm)))))))
axioms-used      (tm-8 tm-1 tm-4 tm-9 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5651.         ((A or ((B and (not ((C and D) -> C))) -> (not ((C and D) -> C)))) -> (not (B and (not ((C and D) -> C))))), M:tm-154, m:tm-130, u:((Am (and A (not (-> (and Bm Cm) Bm)))) (B (not (-> (and Bm Cm) Bm))) (C (not (and A (not (-> (and Bm Cm) Bm))))))
================================================================
tm-name          tm-5652
in-theory        5652
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> ((E and F) -> E)) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-134 ((Am (-> (and A B) B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-5652.         ((A or ((B and C) -> C)) -> ((D -> ((E and F) -> E)) and ((B and C) -> C))), M:tm-154, m:tm-134, u:((Am (-> (and A B) B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> (and A B) B))))
================================================================
tm-name          tm-5653
in-theory        5653
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (C and D)) -> (C and D))) -> ((B and (C and D)) -> C))
theorem-size     19
proof            (modus-ponens tm-154 tm-135 ((Am (and A (and Bm Cm))) (B (and Bm Cm)) (C (-> (and A (and Bm Cm)) Bm))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-5653.         ((A or ((B and (C and D)) -> (C and D))) -> ((B and (C and D)) -> C)), M:tm-154, m:tm-135, u:((Am (and A (and Bm Cm))) (B (and Bm Cm)) (C (-> (and A (and Bm Cm)) Bm)))
================================================================
tm-name          tm-5654
in-theory        5654
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-154 tm-136 ((Am (-> (and A B) B)) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-5654.         ((A or ((B and C) -> C)) -> (D -> ((E and F) -> E))), M:tm-154, m:tm-136, u:((Am (-> (and A B) B)) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-5655
in-theory        5655
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B and C) -> C)))
theorem-size     29
proof            (modus-ponens tm-154 tm-147 ((Am (-> (and A B) B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5655.         ((A or ((B and C) -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B and C) -> C))), M:tm-154, m:tm-147, u:((Am (-> (and A B) B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (and A B) B))))
================================================================
tm-name          tm-5656
in-theory        5656
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-154 tm-149 ((Am (-> (and A B) B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5656.         ((A or ((B and C) -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-154, m:tm-149, u:((Am (-> (and A B) B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-5657
in-theory        5657
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (not ((C and D) -> D))) -> (not ((C and D) -> D)))) -> (not (B and (not ((C and D) -> D)))))
theorem-size     27
proof            (modus-ponens tm-154 tm-153 ((Am (and A (not (-> (and Bm Cm) Cm)))) (B (not (-> (and Bm Cm) Cm))) (C (not (and A (not (-> (and Bm Cm) Cm)))))))
axioms-used      (tm-8 tm-1 tm-4 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5657.         ((A or ((B and (not ((C and D) -> D))) -> (not ((C and D) -> D)))) -> (not (B and (not ((C and D) -> D))))), M:tm-154, m:tm-153, u:((Am (and A (not (-> (and Bm Cm) Cm)))) (B (not (-> (and Bm Cm) Cm))) (C (not (and A (not (-> (and Bm Cm) Cm))))))
================================================================
tm-name          tm-5658
in-theory        5658
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-147 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5658.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-147, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5659
in-theory        5659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-134 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5659.         ((A -> ((B and C) -> B)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-134, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5660
in-theory        5660
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-125 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5660.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-125, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5661
in-theory        5661
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> (C -> D)) -> (((E or ((A and B) -> B)) -> C) -> ((E or ((A and B) -> B)) -> D)))
theorem-size     29
proof            (modus-ponens tm-114 tm-154 ((A (-> (-> (and Am Bm) Bm) (-> C D))) (B (or Dm (-> (and Am Bm) Bm))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5661.         ((((A and B) -> B) -> (C -> D)) -> (((E or ((A and B) -> B)) -> C) -> ((E or ((A and B) -> B)) -> D))), M:tm-114, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) (-> C D))) (B (or Dm (-> (and Am Bm) Bm))) (Cm (-> C D)))
================================================================
tm-name          tm-5662
in-theory        5662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-113 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5662.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G))), M:tm-113, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5663
in-theory        5663
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> (C -> D)) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))) -> ((E or ((B and (C -> D)) -> (C -> D))) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))
theorem-size     55
proof            (modus-ponens tm-110 tm-154 ((A (and Am (-> B C))) (Bm (-> B C)) (Cm (-> (-> (and Am (-> B C)) B) (-> (and Am (-> B C)) C))) (D (-> (or Dm (-> (and Am (-> B C)) (-> B C))) (-> (-> (and Am (-> B C)) B) (-> (and Am (-> B C)) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5663.         ((A or (((B and (C -> D)) -> (C -> D)) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))) -> ((E or ((B and (C -> D)) -> (C -> D))) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))), M:tm-110, m:tm-154, u:((A (and Am (-> B C))) (Bm (-> B C)) (Cm (-> (-> (and Am (-> B C)) B) (-> (and Am (-> B C)) C))) (D (-> (or Dm (-> (and Am (-> B C)) (-> B C))) (-> (-> (and Am (-> B C)) B) (-> (and Am (-> B C)) C)))))
================================================================
tm-name          tm-5664
in-theory        5664
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-105 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5664.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-105, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5665
in-theory        5665
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> (B -> C)) -> ((A and (B -> C)) -> B)) or (((A and (B -> C)) -> (B -> C)) -> ((A and (B -> C)) -> C))) -> ((D or ((A and (B -> C)) -> (B -> C))) -> ((A and (B -> C)) -> C)))
theorem-size     55
proof            (modus-ponens tm-102 tm-154 ((A (and Am (-> B C))) (Bm (-> B C)) (Cm (-> (and Am (-> B C)) C)) (D (-> (or Dm (-> (and Am (-> B C)) (-> B C))) (-> (and Am (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5665.         (((((A and (B -> C)) -> (B -> C)) -> ((A and (B -> C)) -> B)) or (((A and (B -> C)) -> (B -> C)) -> ((A and (B -> C)) -> C))) -> ((D or ((A and (B -> C)) -> (B -> C))) -> ((A and (B -> C)) -> C))), M:tm-102, m:tm-154, u:((A (and Am (-> B C))) (Bm (-> B C)) (Cm (-> (and Am (-> B C)) C)) (D (-> (or Dm (-> (and Am (-> B C)) (-> B C))) (-> (and Am (-> B C)) C))))
================================================================
tm-name          tm-5666
in-theory        5666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-95 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5666.         (((A -> B) -> (A -> A)) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E))), M:tm-95, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5667
in-theory        5667
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) or (((A and B) -> B) -> ((A and B) -> B))) -> ((D or ((A and B) -> B)) -> ((A and B) -> B)))
theorem-size     33
proof            (modus-ponens tm-92 tm-154 ((Cm (-> (and Am Bm) Bm)) (A (-> (and Am Bm) Bm)) (B (-> (or Dm (-> (and Am Bm) Bm)) (-> (and Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5667.         (((((A and B) -> B) -> C) or (((A and B) -> B) -> ((A and B) -> B))) -> ((D or ((A and B) -> B)) -> ((A and B) -> B))), M:tm-92, m:tm-154, u:((Cm (-> (and Am Bm) Bm)) (A (-> (and Am Bm) Bm)) (B (-> (or Dm (-> (and Am Bm) Bm)) (-> (and Am Bm) Bm))))
================================================================
tm-name          tm-5668
in-theory        5668
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> (D -> ((E or ((A and B) -> B)) -> C)))
theorem-size     19
proof            (modus-ponens tm-84 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5668.         ((((A and B) -> B) -> C) -> (D -> ((E or ((A and B) -> B)) -> C))), M:tm-84, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-5669
in-theory        5669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-83 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5669.         ((A -> (B -> (C -> B))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-83, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5670
in-theory        5670
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) -> (D -> ((B and C) -> C)))) -> ((E or ((B and C) -> C)) -> (D -> ((B and C) -> C))))
theorem-size     31
proof            (modus-ponens tm-80 tm-154 ((A (-> (and Am Bm) Bm)) (Cm (-> B (-> (and Am Bm) Bm))) (C (-> (or Dm (-> (and Am Bm) Bm)) (-> B (-> (and Am Bm) Bm))))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5670.         ((A or (((B and C) -> C) -> (D -> ((B and C) -> C)))) -> ((E or ((B and C) -> C)) -> (D -> ((B and C) -> C)))), M:tm-80, m:tm-154, u:((A (-> (and Am Bm) Bm)) (Cm (-> B (-> (and Am Bm) Bm))) (C (-> (or Dm (-> (and Am Bm) Bm)) (-> B (-> (and Am Bm) Bm)))))
================================================================
tm-name          tm-5671
in-theory        5671
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B and C) -> C) -> D) -> ((E or ((B and C) -> C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-76 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5671.         (((not (not A)) -> A) and ((((B and C) -> C) -> D) -> ((E or ((B and C) -> C)) -> D))), M:tm-76, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5672
in-theory        5672
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A and B) -> B) -> C))) or (((A and B) -> B) -> C)) -> ((D or ((A and B) -> B)) -> C))
theorem-size     27
proof            (modus-ponens tm-73 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-8 tm-10 tm-1 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5672.         (((not (not (((A and B) -> B) -> C))) or (((A and B) -> B) -> C)) -> ((D or ((A and B) -> B)) -> C)), M:tm-73, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-5673
in-theory        5673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-69 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5673.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E))), M:tm-69, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5674
in-theory        5674
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not B)) -> B) or (((A and (not B)) -> (not B)) -> (not (A and (not B))))) -> ((C or ((A and (not B)) -> (not B))) -> (not (A and (not B)))))
theorem-size     36
proof            (modus-ponens tm-66 tm-154 ((A (and Am (not B))) (Bm (not B)) (Cm (not (and Am (not B)))) (C (-> (or Dm (-> (and Am (not B)) (not B))) (not (and Am (not B)))))))
axioms-used      (tm-8 tm-9 tm-1 tm-4)
proof-size       130
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5674.         ((((A and (not B)) -> B) or (((A and (not B)) -> (not B)) -> (not (A and (not B))))) -> ((C or ((A and (not B)) -> (not B))) -> (not (A and (not B))))), M:tm-66, m:tm-154, u:((A (and Am (not B))) (Bm (not B)) (Cm (not (and Am (not B)))) (C (-> (or Dm (-> (and Am (not B)) (not B))) (not (and Am (not B))))))
================================================================
tm-name          tm-5675
in-theory        5675
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> (C or ((A and B) -> B))) -> ((((A and B) -> B) or (C or ((A and B) -> B))) -> (C or ((A and B) -> B))))
theorem-size     35
proof            (modus-ponens tm-55 tm-154 ((A (-> (and Am Bm) Bm)) (Cm (or Dm (-> (and Am Bm) Bm))) (B (or Dm (-> (and Am Bm) Bm))) (C (or Dm (-> (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5675.         ((((A and B) -> B) -> (C or ((A and B) -> B))) -> ((((A and B) -> B) or (C or ((A and B) -> B))) -> (C or ((A and B) -> B)))), M:tm-55, m:tm-154, u:((A (-> (and Am Bm) Bm)) (Cm (or Dm (-> (and Am Bm) Bm))) (B (or Dm (-> (and Am Bm) Bm))) (C (or Dm (-> (and Am Bm) Bm))))
================================================================
tm-name          tm-5676
in-theory        5676
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-54 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5676.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-54, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5677
in-theory        5677
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B and C)) or (((B and C) -> C) -> ((A or (B and C)) -> C))) -> ((D or ((B and C) -> C)) -> ((A or (B and C)) -> C)))
theorem-size     35
proof            (modus-ponens tm-51 tm-154 ((A (and Am Bm)) (B Bm) (Cm (-> (or C (and Am Bm)) Bm)) (D (-> (or Dm (-> (and Am Bm) Bm)) (-> (or C (and Am Bm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5677.         (((A -> (B and C)) or (((B and C) -> C) -> ((A or (B and C)) -> C))) -> ((D or ((B and C) -> C)) -> ((A or (B and C)) -> C))), M:tm-51, m:tm-154, u:((A (and Am Bm)) (B Bm) (Cm (-> (or C (and Am Bm)) Bm)) (D (-> (or Dm (-> (and Am Bm) Bm)) (-> (or C (and Am Bm)) Bm))))
================================================================
tm-name          tm-5678
in-theory        5678
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) -> (A and ((B and C) -> C)))) -> ((D or ((B and C) -> C)) -> (A and ((B and C) -> C))))
theorem-size     31
proof            (modus-ponens tm-48 tm-154 ((A (-> (and Am Bm) Bm)) (Cm (and B (-> (and Am Bm) Bm))) (C (-> (or Dm (-> (and Am Bm) Bm)) (and B (-> (and Am Bm) Bm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5678.         ((A or (((B and C) -> C) -> (A and ((B and C) -> C)))) -> ((D or ((B and C) -> C)) -> (A and ((B and C) -> C)))), M:tm-48, m:tm-154, u:((A (-> (and Am Bm) Bm)) (Cm (and B (-> (and Am Bm) Bm))) (C (-> (or Dm (-> (and Am Bm) Bm)) (and B (-> (and Am Bm) Bm)))))
================================================================
tm-name          tm-5679
in-theory        5679
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) or (((B and C) -> C) -> D)) -> ((E or ((B and C) -> C)) -> D))
theorem-size     27
proof            (modus-ponens tm-47 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5679.         (((A and (((B and C) -> C) -> D)) or (((B and C) -> C) -> D)) -> ((E or ((B and C) -> C)) -> D)), M:tm-47, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-5680
in-theory        5680
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) or (((A and B) -> B) -> C)) -> ((E or ((A and B) -> B)) -> C))
theorem-size     27
proof            (modus-ponens tm-46 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-8 tm-3 tm-1 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5680.         ((((((A and B) -> B) -> C) and D) or (((A and B) -> B) -> C)) -> ((E or ((A and B) -> B)) -> C)), M:tm-46, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-5681
in-theory        5681
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) or (((A and B) -> B) -> ((A and B) -> C))) -> ((D or ((A and B) -> B)) -> ((A and B) -> C)))
theorem-size     33
proof            (modus-ponens tm-45 tm-154 ((A (and Am Bm)) (B Bm) (Cm (-> (and Am Bm) C)) (D (-> (or Dm (-> (and Am Bm) Bm)) (-> (and Am Bm) C)))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5681.         ((((A and B) -> (B -> C)) or (((A and B) -> B) -> ((A and B) -> C))) -> ((D or ((A and B) -> B)) -> ((A and B) -> C))), M:tm-45, m:tm-154, u:((A (and Am Bm)) (B Bm) (Cm (-> (and Am Bm) C)) (D (-> (or Dm (-> (and Am Bm) Bm)) (-> (and Am Bm) C))))
================================================================
tm-name          tm-5682
in-theory        5682
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) -> A)) -> ((D or ((B and C) -> C)) -> A))
theorem-size     19
proof            (modus-ponens tm-44 tm-154 ((A (-> (and Am Bm) Bm)) (B Cm) (C (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5682.         ((A or (((B and C) -> C) -> A)) -> ((D or ((B and C) -> C)) -> A)), M:tm-44, m:tm-154, u:((A (-> (and Am Bm) Bm)) (B Cm) (C (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-5683
in-theory        5683
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-42 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5683.         ((A -> (B or A)) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E))), M:tm-42, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5684
in-theory        5684
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-32 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5684.         ((A -> (A or B)) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E))), M:tm-32, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5685
in-theory        5685
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> ((((A and B) -> B) -> C) and ((D or ((A and B) -> B)) -> C)))
theorem-size     25
proof            (modus-ponens tm-24 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5685.         ((((A and B) -> B) -> C) -> ((((A and B) -> B) -> C) and ((D or ((A and B) -> B)) -> C))), M:tm-24, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-5686
in-theory        5686
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-23 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5686.         ((A -> (B -> (A and B))) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E))), M:tm-23, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5687
in-theory        5687
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-22 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5687.         (((A and B) -> B) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E))), M:tm-22, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5688
in-theory        5688
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-21 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5688.         (((A and B) -> A) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E))), M:tm-21, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5689
in-theory        5689
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-20 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5689.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-20, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5690
in-theory        5690
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-19 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5690.         ((A -> (B -> A)) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E))), M:tm-19, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5691
in-theory        5691
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> (((A and B) -> B) -> C))
theorem-size     15
proof            (modus-ponens tm-12 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5691.         ((((A and B) -> B) -> C) -> (((A and B) -> B) -> C)), M:tm-12, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-5692
in-theory        5692
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> (not ((D or ((A and B) -> B)) -> C))) -> (not (((A and B) -> B) -> C)))
theorem-size     27
proof            (modus-ponens tm-9 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-9 tm-8 tm-1 tm-4)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5692.         (((((A and B) -> B) -> C) -> (not ((D or ((A and B) -> B)) -> C))) -> (not (((A and B) -> B) -> C))), M:tm-9, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-5693
in-theory        5693
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B and C) -> C)) -> D) -> E) -> (((((B and C) -> C) -> D) or ((A or ((B and C) -> C)) -> D)) -> E))
theorem-size     31
proof            (modus-ponens tm-8 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5693.         ((((A or ((B and C) -> C)) -> D) -> E) -> (((((B and C) -> C) -> D) or ((A or ((B and C) -> C)) -> D)) -> E)), M:tm-8, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-5694
in-theory        5694
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B and C) -> C) -> D) -> ((E or ((B and C) -> C)) -> D)))
theorem-size     19
proof            (modus-ponens tm-7 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-7 tm-8 tm-1 tm-4)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5694.         (A or ((((B and C) -> C) -> D) -> ((E or ((B and C) -> C)) -> D))), M:tm-7, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5695
in-theory        5695
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-6 tm-8 tm-1 tm-4)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5695.         (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) or E), M:tm-6, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5696
in-theory        5696
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B and C) -> C) -> D) -> ((E or ((B and C) -> C)) -> D)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5696.         (A -> (((((B and C) -> C) -> D) -> ((E or ((B and C) -> C)) -> D)) and A)), M:tm-5, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5697
in-theory        5697
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> (D or ((A and B) -> B))) -> ((((A and B) -> B) -> C) -> C))
theorem-size     25
proof            (modus-ponens tm-2 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (or Dm (-> (and Am Bm) Bm))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-1 tm-4)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5697.         (((((A and B) -> B) -> C) -> (D or ((A and B) -> B))) -> ((((A and B) -> B) -> C) -> C)), M:tm-2, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (or Dm (-> (and Am Bm) Bm))) (C Cm))
================================================================
tm-name          tm-5698
in-theory        5698
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) -> D) -> ((E or ((B and C) -> C)) -> D)))
theorem-size     19
proof            (modus-ponens tm-1 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-1 tm-8 tm-4)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5698.         (A -> ((((B and C) -> C) -> D) -> ((E or ((B and C) -> C)) -> D))), M:tm-1, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5699
in-theory        5699
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-147 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5699.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> ((F and G) -> G)))), M:tm-147, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5700
in-theory        5700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-134 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5700.         ((A -> ((B and C) -> B)) and (D or (E -> ((F and G) -> G)))), M:tm-134, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5701
in-theory        5701
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-125 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5701.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> ((F and G) -> G)))), M:tm-125, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5702
in-theory        5702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-113 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5702.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G and H) -> H)))), M:tm-113, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5703
in-theory        5703
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> ((F and G) -> G))))
theorem-size     29
proof            (modus-ponens tm-105 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5703.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> ((F and G) -> G)))), M:tm-105, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5704
in-theory        5704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-95 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5704.         (((A -> B) -> (A -> A)) and (C or (D -> ((E and F) -> F)))), M:tm-95, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5705
in-theory        5705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-83 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5705.         ((A -> (B -> (C -> B))) and (D or (E -> ((F and G) -> G)))), M:tm-83, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5706
in-theory        5706
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> ((D and E) -> E))))
theorem-size     15
proof            (modus-ponens tm-76 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5706.         (((not (not A)) -> A) and (B or (C -> ((D and E) -> E)))), M:tm-76, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5707
in-theory        5707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> ((E and F) -> F))))
theorem-size     21
proof            (modus-ponens tm-69 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5707.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> ((E and F) -> F)))), M:tm-69, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5708
in-theory        5708
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-54 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5708.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> ((F and G) -> G)))), M:tm-54, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5709
in-theory        5709
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-42 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5709.         ((A -> (B or A)) and (C or (D -> ((E and F) -> F)))), M:tm-42, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5710
in-theory        5710
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-32 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5710.         ((A -> (A or B)) and (C or (D -> ((E and F) -> F)))), M:tm-32, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5711
in-theory        5711
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-23 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5711.         ((A -> (B -> (A and B))) and (C or (D -> ((E and F) -> F)))), M:tm-23, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5712
in-theory        5712
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-22 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5712.         (((A and B) -> B) and (C or (D -> ((E and F) -> F)))), M:tm-22, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5713
in-theory        5713
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-21 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5713.         (((A and B) -> A) and (C or (D -> ((E and F) -> F)))), M:tm-21, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5714
in-theory        5714
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-20 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5714.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> ((F and G) -> G)))), M:tm-20, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5715
in-theory        5715
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-19 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5715.         ((A -> (B -> A)) and (C or (D -> ((E and F) -> F)))), M:tm-19, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5716
in-theory        5716
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C -> ((D and E) -> E))))
theorem-size     11
proof            (modus-ponens tm-7 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-7 tm-1 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5716.         (A or (B or (C -> ((D and E) -> E)))), M:tm-7, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5717
in-theory        5717
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-6 tm-7 tm-1 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5717.         ((A or (B -> ((C and D) -> D))) or E), M:tm-6, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5718
in-theory        5718
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C -> ((D and E) -> E))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5718.         (A -> ((B or (C -> ((D and E) -> E))) and A)), M:tm-5, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5719
in-theory        5719
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C -> ((D and E) -> E))))
theorem-size     11
proof            (modus-ponens tm-1 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-1 tm-7 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5719.         (A -> (B or (C -> ((D and E) -> E)))), M:tm-1, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5720
in-theory        5720
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E and F) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5720.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E and F) -> F)) or G)), M:tm-147, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5721
in-theory        5721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5721.         ((A -> ((B and C) -> B)) and ((D -> ((E and F) -> F)) or G)), M:tm-134, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5722
in-theory        5722
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E and F) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5722.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E and F) -> F)) or G)), M:tm-125, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5723
in-theory        5723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F and G) -> G)) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5723.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F and G) -> G)) or H)), M:tm-113, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5724
in-theory        5724
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E and F) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5724.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E and F) -> F)) or G)), M:tm-105, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5725
in-theory        5725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> ((D and E) -> E)) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5725.         (((A -> B) -> (A -> A)) and ((C -> ((D and E) -> E)) or F)), M:tm-95, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5726
in-theory        5726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5726.         ((A -> (B -> (C -> B))) and ((D -> ((E and F) -> F)) or G)), M:tm-83, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5727
in-theory        5727
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> ((C and D) -> D)) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5727.         (((not (not A)) -> A) and ((B -> ((C and D) -> D)) or E)), M:tm-76, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5728
in-theory        5728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D and E) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-1 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5728.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D and E) -> E)) or F)), M:tm-69, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5729
in-theory        5729
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E and F) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5729.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E and F) -> F)) or G)), M:tm-54, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5730
in-theory        5730
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> ((D and E) -> E)) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5730.         ((A -> (B or A)) and ((C -> ((D and E) -> E)) or F)), M:tm-42, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5731
in-theory        5731
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> ((D and E) -> E)) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5731.         ((A -> (A or B)) and ((C -> ((D and E) -> E)) or F)), M:tm-32, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5732
in-theory        5732
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> ((D and E) -> E)) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5732.         ((A -> (B -> (A and B))) and ((C -> ((D and E) -> E)) or F)), M:tm-23, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5733
in-theory        5733
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> ((D and E) -> E)) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5733.         (((A and B) -> B) and ((C -> ((D and E) -> E)) or F)), M:tm-22, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5734
in-theory        5734
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> ((D and E) -> E)) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5734.         (((A and B) -> A) and ((C -> ((D and E) -> E)) or F)), M:tm-21, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5735
in-theory        5735
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E and F) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5735.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E and F) -> F)) or G)), M:tm-20, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5736
in-theory        5736
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> ((D and E) -> E)) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5736.         ((A -> (B -> A)) and ((C -> ((D and E) -> E)) or F)), M:tm-19, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5737
in-theory        5737
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> ((C and D) -> D)) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-7 tm-6 tm-1 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5737.         (A or ((B -> ((C and D) -> D)) or E)), M:tm-7, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5738
in-theory        5738
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-6 tm-1 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5738.         (((A -> ((B and C) -> C)) or D) or E), M:tm-6, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5739
in-theory        5739
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> ((C and D) -> D)) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5739.         (A -> (((B -> ((C and D) -> D)) or E) and A)), M:tm-5, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5740
in-theory        5740
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> ((C and D) -> D)) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-1 tm-6 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5740.         (A -> ((B -> ((C and D) -> D)) or E)), M:tm-1, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5741
in-theory        5741
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-157 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5741.         ((A -> ((B and C) -> C)) and (D -> (E -> D))), M:tm-157, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-5742
in-theory        5742
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5742.         ((A -> ((B and C) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-157, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-5743
in-theory        5743
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-157 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-5743.         ((A -> ((B and C) -> C)) and ((D and E) -> D)), M:tm-157, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-5744
in-theory        5744
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-157 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5744.         ((A -> ((B and C) -> C)) and ((D and E) -> E)), M:tm-157, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-5745
in-theory        5745
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-157 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5745.         ((A -> ((B and C) -> C)) and (D -> (E -> (D and E)))), M:tm-157, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-5746
in-theory        5746
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-157 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-5746.         ((A -> ((B and C) -> C)) and (D -> (D or E))), M:tm-157, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-5747
in-theory        5747
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-157 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-5747.         ((A -> ((B and C) -> C)) and (D -> (E or D))), M:tm-157, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-5748
in-theory        5748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5748.         ((A -> ((B and C) -> C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-157, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-5749
in-theory        5749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-157 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5749.         ((A -> ((B and C) -> C)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-157, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-5750
in-theory        5750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-157 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-1 tm-4 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-5750.         ((A -> ((B and C) -> C)) and ((not (not D)) -> D)), M:tm-157, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-5751
in-theory        5751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-157 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-5751.         ((A -> ((B and C) -> C)) and (D -> (E -> (F -> E)))), M:tm-157, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-5752
in-theory        5752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-157 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-5752.         ((A -> ((B and C) -> C)) and ((D -> E) -> (D -> D))), M:tm-157, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-5753
in-theory        5753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-157 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-5753.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-157, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-5754
in-theory        5754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-5754.         ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-157, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-5755
in-theory        5755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-157 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5755.         ((A -> ((B and C) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-157, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-5756
in-theory        5756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-157 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-5756.         ((A -> ((B and C) -> C)) and (D -> ((E and F) -> E))), M:tm-157, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-5757
in-theory        5757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-157 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5757.         ((A -> ((B and C) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-157, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-5758
in-theory        5758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-157 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5758.         ((A -> ((B and C) -> C)) and (D -> ((E and F) -> F))), M:tm-157, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-5759
in-theory        5759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-157 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-5759.         ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> E)) and D))), M:tm-157, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-5760
in-theory        5760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-157 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-5760.         ((A -> ((B and C) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-157, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-5761
in-theory        5761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-157 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-5761.         ((A -> ((B and C) -> C)) and (D -> (((E and F) -> E) and D))), M:tm-157, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-5762
in-theory        5762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-157 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-5762.         ((A -> ((B and C) -> C)) and (D -> (((E and F) -> F) and D))), M:tm-157, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-5763
in-theory        5763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-5763.         ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-157, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-5764
in-theory        5764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-157 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-5764.         ((A -> ((B and C) -> C)) and ((D -> E) -> (D -> (D and E)))), M:tm-157, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-5765
in-theory        5765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-5765.         ((A -> ((B and C) -> C)) and (D -> (E -> (F -> (E and F))))), M:tm-157, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-5766
in-theory        5766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-157 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-5766.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) or F)), M:tm-157, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-5767
in-theory        5767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-157 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-5767.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-157, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-5768
in-theory        5768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-157 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-5768.         ((A -> ((B and C) -> C)) and (((D and E) -> D) or F)), M:tm-157, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-5769
in-theory        5769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-157 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-5769.         ((A -> ((B and C) -> C)) and (((D and E) -> E) or F)), M:tm-157, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-5770
in-theory        5770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-157 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-5770.         ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) or F)), M:tm-157, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-5771
in-theory        5771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-157 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-5771.         ((A -> ((B and C) -> C)) and ((D -> (D or E)) or F)), M:tm-157, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-5772
in-theory        5772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-157 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-5772.         ((A -> ((B and C) -> C)) and (D -> ((E -> (E or F)) and D))), M:tm-157, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-5773
in-theory        5773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-157 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-5773.         ((A -> ((B and C) -> C)) and (D -> (E -> (E or F)))), M:tm-157, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-5774
in-theory        5774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-157 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-5774.         ((A -> ((B and C) -> C)) and (D or (E -> (F -> E)))), M:tm-157, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-5775
in-theory        5775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-5775.         ((A -> ((B and C) -> C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-157, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-5776
in-theory        5776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-157 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-5776.         ((A -> ((B and C) -> C)) and (D or ((E and F) -> E))), M:tm-157, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-5777
in-theory        5777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-157 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-5777.         ((A -> ((B and C) -> C)) and (D or ((E and F) -> F))), M:tm-157, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-5778
in-theory        5778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-5778.         ((A -> ((B and C) -> C)) and (D or (E -> (F -> (E and F))))), M:tm-157, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-5779
in-theory        5779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-157 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-5779.         ((A -> ((B and C) -> C)) and (D or (E -> (E or F)))), M:tm-157, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-5780
in-theory        5780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-157 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-5780.         ((A -> ((B and C) -> C)) and (D or (E -> (F or E)))), M:tm-157, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-5781
in-theory        5781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-157 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-5781.         ((A -> ((B and C) -> C)) and ((D -> (E or D)) or F)), M:tm-157, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-5782
in-theory        5782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-157 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-5782.         ((A -> ((B and C) -> C)) and (D -> ((E -> (F or E)) and D))), M:tm-157, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-5783
in-theory        5783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-157 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-5783.         ((A -> ((B and C) -> C)) and (D -> (E -> (F or E)))), M:tm-157, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-5784
in-theory        5784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-157 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5784.         ((A -> ((B and C) -> C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-157, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-5785
in-theory        5785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-157 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5785.         ((A -> ((B and C) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-157, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-5786
in-theory        5786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-157 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5786.         ((A -> ((B and C) -> C)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-157, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-5787
in-theory        5787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-157 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5787.         ((A -> ((B and C) -> C)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-157, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-5788
in-theory        5788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-157 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-5788.         ((A -> ((B and C) -> C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-157, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-5789
in-theory        5789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-157 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5789.         ((A -> ((B and C) -> C)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-157, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-5790
in-theory        5790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-157 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5790.         ((A -> ((B and C) -> C)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-157, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-5791
in-theory        5791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-157 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5791.         ((A -> ((B and C) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-157, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-5792
in-theory        5792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-5792.         ((A -> ((B and C) -> C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-157, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-5793
in-theory        5793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-157 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-5793.         ((A -> ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-157, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-5794
in-theory        5794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-157 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-5794.         ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-157, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-5795
in-theory        5795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-157 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-5795.         ((A -> ((B and C) -> C)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-157, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-5796
in-theory        5796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-5796.         ((A -> ((B and C) -> C)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-157, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-5797
in-theory        5797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-157 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5797.         ((A -> ((B and C) -> C)) and ((D -> (not (E -> D))) -> (not D))), M:tm-157, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-5798
in-theory        5798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5798.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-157, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-5799
in-theory        5799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-157 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5799.         ((A -> ((B and C) -> C)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-157, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-5800
in-theory        5800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-157 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5800.         ((A -> ((B and C) -> C)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-157, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-5801
in-theory        5801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-5801.         ((A -> ((B and C) -> C)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-157, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-5802
in-theory        5802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-157 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5802.         ((A -> ((B and C) -> C)) and ((D -> (not (D or E))) -> (not D))), M:tm-157, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-5803
in-theory        5803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-157 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5803.         ((A -> ((B and C) -> C)) and ((D -> (not (E or D))) -> (not D))), M:tm-157, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-5804
in-theory        5804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-157 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5804.         ((A -> ((B and C) -> C)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-157, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-5805
in-theory        5805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-157 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5805.         ((A -> ((B and C) -> C)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-157, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-5806
in-theory        5806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-157 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5806.         ((A -> ((B and C) -> C)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-157, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-5807
in-theory        5807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-5807.         ((A -> ((B and C) -> C)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-157, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-5808
in-theory        5808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-157 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-5808.         ((A -> ((B and C) -> C)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-157, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-5809
in-theory        5809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-157 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-5809.         ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-157, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-5810
in-theory        5810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-157 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-5810.         ((A -> ((B and C) -> C)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-157, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-5811
in-theory        5811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-5811.         ((A -> ((B and C) -> C)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-157, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-5812
in-theory        5812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-157 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5812.         ((A -> ((B and C) -> C)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-157, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-5813
in-theory        5813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-157 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5813.         ((A -> ((B and C) -> C)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-157, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-5814
in-theory        5814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-157 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-5814.         ((A -> ((B and C) -> C)) and (D or ((not (not E)) -> E))), M:tm-157, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-5815
in-theory        5815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-157 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-5815.         ((A -> ((B and C) -> C)) and (((not (not D)) -> D) or E)), M:tm-157, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-5816
in-theory        5816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-157 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-5816.         ((A -> ((B and C) -> C)) and (D -> (((not (not E)) -> E) and D))), M:tm-157, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-5817
in-theory        5817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-157 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-5817.         ((A -> ((B and C) -> C)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-157, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-5818
in-theory        5818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-157 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-5818.         ((A -> ((B and C) -> C)) and (D -> ((not (not E)) -> E))), M:tm-157, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-5819
in-theory        5819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5819.         ((A -> ((B and C) -> C)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-157, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-5820
in-theory        5820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-157 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5820.         ((A -> ((B and C) -> C)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-157, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-5821
in-theory        5821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-5821.         ((A -> ((B and C) -> C)) and (D or (E -> (F -> (G -> F))))), M:tm-157, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-5822
in-theory        5822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-5822.         ((A -> ((B and C) -> C)) and ((D -> (E -> (F -> E))) or G)), M:tm-157, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-5823
in-theory        5823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-5823.         ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-157, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-5824
in-theory        5824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-157 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5824.         ((A -> ((B and C) -> C)) and ((D -> E) -> (D -> (F -> E)))), M:tm-157, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-5825
in-theory        5825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-5825.         ((A -> ((B and C) -> C)) and (D -> (E -> (F -> (G -> F))))), M:tm-157, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-5826
in-theory        5826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-157 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5826.         ((A -> ((B and C) -> C)) and (D -> D)), M:tm-157, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-5827
in-theory        5827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5827.         ((A -> ((B and C) -> C)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-157, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-5828
in-theory        5828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-157 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5828.         ((A -> ((B and C) -> C)) and ((D and E) -> (D and E))), M:tm-157, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-5829
in-theory        5829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-157 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5829.         ((A -> ((B and C) -> C)) and ((D -> E) -> (D -> E))), M:tm-157, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-5830
in-theory        5830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-157 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5830.         ((A -> ((B and C) -> C)) and ((not (not D)) -> (not (not D)))), M:tm-157, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-5831
in-theory        5831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-157 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5831.         ((A -> ((B and C) -> C)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-157, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-5832
in-theory        5832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-157 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5832.         ((A -> ((B and C) -> C)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-157, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-5833
in-theory        5833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-157 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-5833.         ((A -> ((B and C) -> C)) and (D or ((E -> F) -> (E -> E)))), M:tm-157, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-5834
in-theory        5834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-157 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-5834.         ((A -> ((B and C) -> C)) and (((D -> E) -> (D -> D)) or F)), M:tm-157, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-5835
in-theory        5835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-5835.         ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-157, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-5836
in-theory        5836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-5836.         ((A -> ((B and C) -> C)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-157, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-5837
in-theory        5837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-157 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-5837.         ((A -> ((B and C) -> C)) and (D -> ((E -> F) -> (E -> E)))), M:tm-157, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-5838
in-theory        5838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-5838.         ((A -> ((B and C) -> C)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-157, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5839
in-theory        5839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-157 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-5839.         ((A -> ((B and C) -> C)) and ((D -> (D -> E)) -> (D -> E))), M:tm-157, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-5840
in-theory        5840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-157 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5840.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-157, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-5841
in-theory        5841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-157 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5841.         ((A -> ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-157, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-5842
in-theory        5842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-157 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5842.         ((A -> ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-157, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-5843
in-theory        5843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-5843.         ((A -> ((B and C) -> C)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-157, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-5844
in-theory        5844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-157 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-5844.         ((A -> ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-157, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-5845
in-theory        5845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-157 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-5845.         ((A -> ((B and C) -> C)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-157, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-5846
in-theory        5846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-157 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-5846.         ((A -> ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-157, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-5847
in-theory        5847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-5847.         ((A -> ((B and C) -> C)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-157, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-5848
in-theory        5848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-157 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-5848.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-157, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-5849
in-theory        5849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-157 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5849.         ((A -> ((B and C) -> C)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-157, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-5850
in-theory        5850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-157 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5850.         ((A -> ((B and C) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-157, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-5851
in-theory        5851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-157 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-5851.         ((A -> ((B and C) -> C)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-157, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-5852
in-theory        5852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-157 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-5852.         ((A -> ((B and C) -> C)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-157, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-5853
in-theory        5853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-157 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-5853.         ((A -> ((B and C) -> C)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-157, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-5854
in-theory        5854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-157 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-5854.         ((A -> ((B and C) -> C)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-157, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-5855
in-theory        5855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-157 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-5855.         ((A -> ((B and C) -> C)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-157, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-5856
in-theory        5856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-157 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-5856.         ((A -> ((B and C) -> C)) and (((D -> E) and D) -> E)), M:tm-157, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-5857
in-theory        5857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-157 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-5857.         ((A -> ((B and C) -> C)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-157, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-5858
in-theory        5858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-157 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5858.         ((A -> ((B and C) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-157, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-5859
in-theory        5859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-157 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-5859.         ((A -> ((B and C) -> C)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-157, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-5860
in-theory        5860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-157 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5860.         ((A -> ((B and C) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-157, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-5861
in-theory        5861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-157 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5861.         ((A -> ((B and C) -> C)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-157, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-5862
in-theory        5862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-157 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5862.         ((A -> ((B and C) -> C)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-157, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-5863
in-theory        5863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-157 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-5863.         ((A -> ((B and C) -> C)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-157, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-5864
in-theory        5864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-157 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-5864.         ((A -> ((B and C) -> C)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-157, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-5865
in-theory        5865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-157 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-5865.         ((A -> ((B and C) -> C)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-157, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-5866
in-theory        5866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-157 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-5866.         ((A -> ((B and C) -> C)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-157, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-5867
in-theory        5867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-157 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-5867.         ((A -> ((B and C) -> C)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-157, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-5868
in-theory        5868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-157 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-5868.         ((A -> ((B and C) -> C)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-157, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-5869
in-theory        5869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-157 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-5869.         ((A -> ((B and C) -> C)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-157, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5870
in-theory        5870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5870.         ((A -> ((B and C) -> C)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-157, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-5871
in-theory        5871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-157 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5871.         ((A -> ((B and C) -> C)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-157, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-5872
in-theory        5872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-157 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-5872.         ((A -> ((B and C) -> C)) and (D or (E -> ((F and G) -> F)))), M:tm-157, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-5873
in-theory        5873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-5873.         ((A -> ((B and C) -> C)) and ((D -> ((E and F) -> E)) or G)), M:tm-157, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-5874
in-theory        5874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-5874.         ((A -> ((B and C) -> C)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-157, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-5875
in-theory        5875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-157 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-5875.         ((A -> ((B and C) -> C)) and ((D -> (E and F)) -> (D -> E))), M:tm-157, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-5876
in-theory        5876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-157 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-5876.         ((A -> ((B and C) -> C)) and (D -> (E -> ((F and G) -> F)))), M:tm-157, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-5877
in-theory        5877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-157 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-5877.         ((A -> ((B and C) -> C)) and ((D and (D -> E)) -> E)), M:tm-157, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-5878
in-theory        5878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-157 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-5878.         ((A -> ((B and C) -> C)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-157, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-5879
in-theory        5879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-157 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5879.         ((A -> ((B and C) -> C)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-157, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-5880
in-theory        5880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-157 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-5880.         ((A -> ((B and C) -> C)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-157, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-5881
in-theory        5881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-157 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-5881.         ((A -> ((B and C) -> C)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-157, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-5882
in-theory        5882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-157 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5882.         ((A -> ((B and C) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-157, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-5883
in-theory        5883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-157 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5883.         ((A -> ((B and C) -> C)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-157, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-5884
in-theory        5884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-157 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5884.         ((A -> ((B and C) -> C)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-157, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-5885
in-theory        5885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-157 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5885.         ((A -> ((B and C) -> C)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-157, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5886
in-theory        5886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-157 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5886.         ((A -> ((B and C) -> C)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-157, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-5887
in-theory        5887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-157 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5887.         ((A -> ((B and C) -> C)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-157, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-5888
in-theory        5888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-157 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-5888.         ((A -> ((B and C) -> C)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-157, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-5889
in-theory        5889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-157 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-5889.         ((A -> ((B and C) -> C)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-157, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-5890
in-theory        5890
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-157 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5890.         ((A -> ((B and C) -> C)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-157, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-5891
in-theory        5891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-157 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5891.         ((A -> ((B and C) -> C)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-157, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-5892
in-theory        5892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-157 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5892.         ((A -> ((B and C) -> C)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-157, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-5893
in-theory        5893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5893.         ((A -> ((B and C) -> C)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-157, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-5894
in-theory        5894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-157 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5894.         ((A -> ((B and C) -> C)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-157, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-5895
in-theory        5895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-157 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5895.         ((A -> ((B and C) -> C)) and (D or (E -> ((F and G) -> G)))), M:tm-157, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5896
in-theory        5896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5896.         ((A -> ((B and C) -> C)) and ((D -> ((E and F) -> F)) or G)), M:tm-157, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-5897
in-theory        5897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5897.         ((A -> ((B and C) -> C)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-157, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5898
in-theory        5898
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> ((E and F) -> F)) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-157 ((Am (-> (and A B) B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5898.         ((A or ((B and C) -> C)) -> ((D -> ((E and F) -> F)) and ((B and C) -> C))), M:tm-154, m:tm-157, u:((Am (-> (and A B) B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> (and A B) B))))
================================================================
tm-name          tm-5899
in-theory        5899
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5899.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-147, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5900
in-theory        5900
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> ((E and F) -> F)) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-157 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5900.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> ((E and F) -> F)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-157, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-5901
in-theory        5901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5901.         ((A -> ((B and C) -> B)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-134, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5902
in-theory        5902
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> ((E and F) -> F)) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-157 ((Am (-> (and A B) A)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5902.         ((A or ((B and C) -> B)) -> ((D -> ((E and F) -> F)) and ((B and C) -> B))), M:tm-131, m:tm-157, u:((Am (-> (and A B) A)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> (and A B) A))))
================================================================
tm-name          tm-5903
in-theory        5903
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5903.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-125, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5904
in-theory        5904
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> ((E and F) -> F)) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-157 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5904.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> ((E and F) -> F)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-157, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-5905
in-theory        5905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G and H) -> H)) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5905.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G and H) -> H)) and E))), M:tm-113, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5906
in-theory        5906
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> ((F and G) -> G)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-157 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5906.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> ((F and G) -> G)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-157, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-5907
in-theory        5907
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5907.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-105, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5908
in-theory        5908
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> ((E and F) -> F)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-157 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5908.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> ((E and F) -> F)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-157, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-5909
in-theory        5909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> ((E and F) -> F)) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5909.         (((A -> B) -> (A -> A)) and (C -> ((D -> ((E and F) -> F)) and C))), M:tm-95, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5910
in-theory        5910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> ((D and E) -> E)) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-157 ((Am (-> A A)) (B (and (-> Bm (-> (and Cm Dm) Dm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5910.         (((A -> B) or (A -> A)) -> ((C -> ((D and E) -> E)) and (A -> A))), M:tm-92, m:tm-157, u:((Am (-> A A)) (B (and (-> Bm (-> (and Cm Dm) Dm)) (-> A A))))
================================================================
tm-name          tm-5911
in-theory        5911
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> ((D and E) -> E)) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5911.         (A -> (B -> ((C -> ((D and E) -> E)) and A))), M:tm-84, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-5912
in-theory        5912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5912.         ((A -> (B -> (C -> B))) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-83, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5913
in-theory        5913
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> ((E and F) -> F)) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-157 ((Am (-> A (-> B A))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5913.         ((A or (B -> (C -> B))) -> ((D -> ((E and F) -> F)) and (B -> (C -> B)))), M:tm-80, m:tm-157, u:((Am (-> A (-> B A))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (-> B A)))))
================================================================
tm-name          tm-5914
in-theory        5914
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> ((D and E) -> E)) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-10 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5914.         (((not (not A)) -> A) and (B -> ((C -> ((D and E) -> E)) and B))), M:tm-76, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5915
in-theory        5915
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> ((C and D) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5915.         (((not (not A)) or A) -> ((B -> ((C and D) -> D)) and A)), M:tm-73, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-5916
in-theory        5916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> ((E and F) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5916.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> ((E and F) -> F)) and C))), M:tm-69, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5917
in-theory        5917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> ((D and E) -> E)) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-157 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5917.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> ((D and E) -> E)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-157, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-5918
in-theory        5918
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5918.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-54, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5919
in-theory        5919
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((E and F) -> F)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-157 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5919.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((E and F) -> F)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-157, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-5920
in-theory        5920
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> ((D and E) -> E)) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-157 ((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5920.         ((A or (B or A)) -> ((C -> ((D and E) -> E)) and (B or A))), M:tm-50, m:tm-157, u:((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (or A B))))
================================================================
tm-name          tm-5921
in-theory        5921
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> ((D and E) -> E)) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-157 ((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5921.         ((A or (A or B)) -> ((C -> ((D and E) -> E)) and (A or B))), M:tm-49, m:tm-157, u:((Am (or A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (or A B))))
================================================================
tm-name          tm-5922
in-theory        5922
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> ((D and E) -> E)) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-157 ((Am (-> A (and B A))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5922.         ((A or (B -> (A and B))) -> ((C -> ((D and E) -> E)) and (B -> (A and B)))), M:tm-48, m:tm-157, u:((Am (-> A (and B A))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (and B A)))))
================================================================
tm-name          tm-5923
in-theory        5923
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> ((D and E) -> E)) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5923.         (((A and B) or B) -> ((C -> ((D and E) -> E)) and B)), M:tm-47, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-5924
in-theory        5924
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> ((D and E) -> E)) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5924.         (((A and B) or A) -> ((C -> ((D and E) -> E)) and A)), M:tm-46, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-5925
in-theory        5925
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E and F) -> F)) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-157 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5925.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E and F) -> F)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-157, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-5926
in-theory        5926
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> ((D and E) -> E)) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-157 ((Am (-> A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5926.         ((A or (B -> A)) -> ((C -> ((D and E) -> E)) and (B -> A))), M:tm-44, m:tm-157, u:((Am (-> A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A B))))
================================================================
tm-name          tm-5927
in-theory        5927
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> ((E and F) -> F)) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5927.         ((A -> (B or A)) and (C -> ((D -> ((E and F) -> F)) and C))), M:tm-42, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5928
in-theory        5928
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> ((E and F) -> F)) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5928.         ((A -> (A or B)) and (C -> ((D -> ((E and F) -> F)) and C))), M:tm-32, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5929
in-theory        5929
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> ((C and D) -> D)) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5929.         (A -> (A and ((B -> ((C and D) -> D)) and A))), M:tm-24, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-5930
in-theory        5930
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> ((E and F) -> F)) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5930.         ((A -> (B -> (A and B))) and (C -> ((D -> ((E and F) -> F)) and C))), M:tm-23, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5931
in-theory        5931
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> ((E and F) -> F)) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5931.         (((A and B) -> B) and (C -> ((D -> ((E and F) -> F)) and C))), M:tm-22, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5932
in-theory        5932
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> ((E and F) -> F)) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5932.         (((A and B) -> A) and (C -> ((D -> ((E and F) -> F)) and C))), M:tm-21, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5933
in-theory        5933
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5933.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-20, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5934
in-theory        5934
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> ((E and F) -> F)) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5934.         ((A -> (B -> A)) and (C -> ((D -> ((E and F) -> F)) and C))), M:tm-19, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5935
in-theory        5935
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> ((C and D) -> D)) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-9 tm-5 tm-1 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5935.         ((A -> (not ((B -> ((C and D) -> D)) and A))) -> (not A)), M:tm-9, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-5936
in-theory        5936
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> ((B and C) -> C)) and D) -> E) -> ((D or ((A -> ((B and C) -> C)) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5936.         ((((A -> ((B and C) -> C)) and D) -> E) -> ((D or ((A -> ((B and C) -> C)) and D)) -> E)), M:tm-8, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-5937
in-theory        5937
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> ((D and E) -> E)) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-7 tm-5 tm-1 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5937.         (A or (B -> ((C -> ((D and E) -> E)) and B))), M:tm-7, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5938
in-theory        5938
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-6 tm-5 tm-1 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5938.         ((A -> ((B -> ((C and D) -> D)) and A)) or E), M:tm-6, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5939
in-theory        5939
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> ((D and E) -> E)) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5939.         (A -> ((B -> ((C -> ((D and E) -> E)) and B)) and A)), M:tm-5, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5940
in-theory        5940
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> ((D and E) -> E)) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5940.         (A -> (B -> ((C -> ((D and E) -> E)) and B))), M:tm-1, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-5941
in-theory        5941
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (A and B))) -> B)
theorem-size     7
proof            (modus-ponens tm-158 tm-10 ((A (not (not (and B C)))) (Am (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-10.           ((not (not A)) -> A), axiom
tm-5941.         ((not (not (A and B))) -> B), M:tm-158, m:tm-10, u:((A (not (not (and B C)))) (Am (and B C)))
================================================================
tm-name          tm-5942
in-theory        5942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) and A) -> C)
theorem-size     9
proof            (modus-ponens tm-158 tm-116 ((A (and (-> Am (and B C)) Am)) (Bm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-5942.         (((A -> (B and C)) and A) -> C), M:tm-158, m:tm-116, u:((A (and (-> Am (and B C)) Am)) (Bm (and B C)))
================================================================
tm-name          tm-5943
in-theory        5943
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> (C and D)) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-158 tm-117 ((A (and (-> (-> Am (-> Bm Am)) (and B C)) Dm)) (Cm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-5943.         ((((A -> (B -> A)) -> (C and D)) and E) -> D), M:tm-158, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) (and B C)) Dm)) (Cm (and B C)))
================================================================
tm-name          tm-5944
in-theory        5944
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D and E)) and F) -> E)
theorem-size     21
proof            (modus-ponens tm-158 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and B C)) Em)) (Dm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5944.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D and E)) and F) -> E), M:tm-158, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and B C)) Em)) (Dm (and B C)))
================================================================
tm-name          tm-5945
in-theory        5945
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> (C and D)) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-158 tm-128 ((A (and (-> (-> (and Am Bm) Am) (and B C)) Dm)) (Cm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-5945.         (((((A and B) -> A) -> (C and D)) and E) -> D), M:tm-158, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) (and B C)) Dm)) (Cm (and B C)))
================================================================
tm-name          tm-5946
in-theory        5946
times-derived    1
----------------------------------------------------------------
theorem          ((A and (A -> (B and C))) -> C)
theorem-size     9
proof            (modus-ponens tm-158 tm-137 ((A (and Am (-> Am (and B C)))) (Bm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-5946.         ((A and (A -> (B and C))) -> C), M:tm-158, m:tm-137, u:((A (and Am (-> Am (and B C)))) (Bm (and B C)))
================================================================
tm-name          tm-5947
in-theory        5947
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> (D and E))) -> E)
theorem-size     13
proof            (modus-ponens tm-158 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) (and B C)))) (Dm (and B C))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-5947.         ((A and ((B -> (C -> B)) -> (D and E))) -> E), M:tm-158, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) (and B C)))) (Dm (and B C)))
================================================================
tm-name          tm-5948
in-theory        5948
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E and F))) -> F)
theorem-size     21
proof            (modus-ponens tm-158 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and B C)))) (Em (and B C))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5948.         ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E and F))) -> F), M:tm-158, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and B C)))) (Em (and B C)))
================================================================
tm-name          tm-5949
in-theory        5949
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> (D and E))) -> E)
theorem-size     13
proof            (modus-ponens tm-158 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) (and B C)))) (Dm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-5949.         ((A and (((B and C) -> B) -> (D and E))) -> E), M:tm-158, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) (and B C)))) (Dm (and B C)))
================================================================
tm-name          tm-5950
in-theory        5950
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> (D and E))) -> E)
theorem-size     13
proof            (modus-ponens tm-158 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) (and B C)))) (Dm (and B C))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-5950.         ((A and (((B and C) -> C) -> (D and E))) -> E), M:tm-158, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) (and B C)))) (Dm (and B C)))
================================================================
tm-name          tm-5951
in-theory        5951
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> (C and D)) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-158 tm-151 ((A (and (-> (-> (and Am Bm) Bm) (and B C)) Dm)) (Cm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-5951.         (((((A and B) -> B) -> (C and D)) and E) -> D), M:tm-158, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) (and B C)) Dm)) (Cm (and B C)))
================================================================
tm-name          tm-5952
in-theory        5952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-157 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5952.         ((A -> ((B and C) -> C)) and ((D -> (E and F)) -> (D -> F))), M:tm-157, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5953
in-theory        5953
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (C and D)) -> (C and D))) -> ((B and (C and D)) -> D))
theorem-size     19
proof            (modus-ponens tm-154 tm-158 ((Am (and A (and Bm Cm))) (B (and Bm Cm)) (C (-> (and A (and Bm Cm)) Cm))))
axioms-used      (tm-8 tm-1 tm-4 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5953.         ((A or ((B and (C and D)) -> (C and D))) -> ((B and (C and D)) -> D)), M:tm-154, m:tm-158, u:((Am (and A (and Bm Cm))) (B (and Bm Cm)) (C (-> (and A (and Bm Cm)) Cm)))
================================================================
tm-name          tm-5954
in-theory        5954
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-147 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5954.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E and F)) -> (D -> F))), M:tm-147, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5955
in-theory        5955
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C and D))) -> B) or ((A and (B -> (C and D))) -> (C and D))) -> ((A and (B -> (C and D))) -> D))
theorem-size     31
proof            (modus-ponens tm-144 tm-158 ((Am (and A (-> B (and Bm Cm)))) (C (and Bm Cm)) (D (-> (and A (-> B (and Bm Cm))) Cm))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5955.         ((((A and (B -> (C and D))) -> B) or ((A and (B -> (C and D))) -> (C and D))) -> ((A and (B -> (C and D))) -> D)), M:tm-144, m:tm-158, u:((Am (and A (-> B (and Bm Cm)))) (C (and Bm Cm)) (D (-> (and A (-> B (and Bm Cm))) Cm)))
================================================================
tm-name          tm-5956
in-theory        5956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-134 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5956.         ((A -> ((B and C) -> B)) and ((D -> (E and F)) -> (D -> F))), M:tm-134, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5957
in-theory        5957
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) and D) -> (B and C))) -> (((B and C) and D) -> C))
theorem-size     19
proof            (modus-ponens tm-131 tm-158 ((Am (and (and Bm Cm) B)) (A (and Bm Cm)) (C (-> (and (and Bm Cm) B) Cm))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5957.         ((A or (((B and C) and D) -> (B and C))) -> (((B and C) and D) -> C)), M:tm-131, m:tm-158, u:((Am (and (and Bm Cm) B)) (A (and Bm Cm)) (C (-> (and (and Bm Cm) B) Cm)))
================================================================
tm-name          tm-5958
in-theory        5958
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-125 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5958.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E and F)) -> (D -> F))), M:tm-125, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5959
in-theory        5959
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B and C)) and D) -> A) or (((A -> (B and C)) and D) -> (B and C))) -> (((A -> (B and C)) and D) -> C))
theorem-size     31
proof            (modus-ponens tm-122 tm-158 ((Am (and (-> A (and Bm Cm)) C)) (B (and Bm Cm)) (D (-> (and (-> A (and Bm Cm)) C) Cm))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5959.         (((((A -> (B and C)) and D) -> A) or (((A -> (B and C)) and D) -> (B and C))) -> (((A -> (B and C)) and D) -> C)), M:tm-122, m:tm-158, u:((Am (and (-> A (and Bm Cm)) C)) (B (and Bm Cm)) (D (-> (and (-> A (and Bm Cm)) C) Cm)))
================================================================
tm-name          tm-5960
in-theory        5960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and (C -> D))) -> ((A -> C) -> (A -> D)))
theorem-size     15
proof            (modus-ponens tm-114 tm-158 ((A (-> Am (and Bm (-> C D)))) (B Am) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5960.         ((A -> (B and (C -> D))) -> ((A -> C) -> (A -> D))), M:tm-114, m:tm-158, u:((A (-> Am (and Bm (-> C D)))) (B Am) (Cm (-> C D)))
================================================================
tm-name          tm-5961
in-theory        5961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F and G)) -> (E -> G)))
theorem-size     25
proof            (modus-ponens tm-113 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5961.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F and G)) -> (E -> G))), M:tm-113, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5962
in-theory        5962
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E and F)) -> (D -> F)))
theorem-size     29
proof            (modus-ponens tm-105 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5962.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E and F)) -> (D -> F))), M:tm-105, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5963
in-theory        5963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D and E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-95 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5963.         (((A -> B) -> (A -> A)) and ((C -> (D and E)) -> (C -> E))), M:tm-95, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5964
in-theory        5964
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> C) or ((A and B) -> (A and B))) -> ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-92 tm-158 ((Am (and Bm Cm)) (A (and Bm Cm)) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5964.         ((((A and B) -> C) or ((A and B) -> (A and B))) -> ((A and B) -> B)), M:tm-92, m:tm-158, u:((Am (and Bm Cm)) (A (and Bm Cm)) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-5965
in-theory        5965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> (D -> (A -> C)))
theorem-size     11
proof            (modus-ponens tm-84 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5965.         ((A -> (B and C)) -> (D -> (A -> C))), M:tm-84, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-5966
in-theory        5966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-83 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5966.         ((A -> (B -> (C -> B))) and ((D -> (E and F)) -> (D -> F))), M:tm-83, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5967
in-theory        5967
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C and D)) -> (B -> D)))
theorem-size     15
proof            (modus-ponens tm-76 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5967.         (((not (not A)) -> A) and ((B -> (C and D)) -> (B -> D))), M:tm-76, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5968
in-theory        5968
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (B and C)))) or (A -> (B and C))) -> (A -> C))
theorem-size     17
proof            (modus-ponens tm-73 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5968.         (((not (not (A -> (B and C)))) or (A -> (B and C))) -> (A -> C)), M:tm-73, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-5969
in-theory        5969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D and E)) -> (C -> E)))
theorem-size     21
proof            (modus-ponens tm-69 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5969.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D and E)) -> (C -> E))), M:tm-69, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5970
in-theory        5970
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) -> (((A and B) or (A and B)) -> B))
theorem-size     17
proof            (modus-ponens tm-55 tm-158 ((A (and Bm Cm)) (Am (and Bm Cm)) (B (and Bm Cm)) (C Cm)))
axioms-used      (tm-2 tm-8 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5970.         (((A and B) -> (A and B)) -> (((A and B) or (A and B)) -> B)), M:tm-55, m:tm-158, u:((A (and Bm Cm)) (Am (and Bm Cm)) (B (and Bm Cm)) (C Cm))
================================================================
tm-name          tm-5971
in-theory        5971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E and F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-54 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5971.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E and F)) -> (D -> F))), M:tm-54, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5972
in-theory        5972
times-derived    2
----------------------------------------------------------------
theorem          (((A and (B -> (C and D))) or (B -> (C and D))) -> (B -> D))
theorem-size     17
proof            (modus-ponens tm-47 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5972.         (((A and (B -> (C and D))) or (B -> (C and D))) -> (B -> D)), M:tm-47, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-5973
in-theory        5973
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B and C)) and D) or (A -> (B and C))) -> (A -> C))
theorem-size     17
proof            (modus-ponens tm-46 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5973.         ((((A -> (B and C)) and D) or (A -> (B and C))) -> (A -> C)), M:tm-46, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-5974
in-theory        5974
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or (C -> (A and B))) -> (C -> B))
theorem-size     13
proof            (modus-ponens tm-44 tm-158 ((A Am) (B (and Bm Cm)) (C (-> Am Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5974.         (((A and B) or (C -> (A and B))) -> (C -> B)), M:tm-44, m:tm-158, u:((A Am) (B (and Bm Cm)) (C (-> Am Cm)))
================================================================
tm-name          tm-5975
in-theory        5975
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D and E)) -> (C -> E)))
theorem-size     15
proof            (modus-ponens tm-42 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5975.         ((A -> (B or A)) and ((C -> (D and E)) -> (C -> E))), M:tm-42, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5976
in-theory        5976
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D and E)) -> (C -> E)))
theorem-size     15
proof            (modus-ponens tm-32 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5976.         ((A -> (A or B)) and ((C -> (D and E)) -> (C -> E))), M:tm-32, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5977
in-theory        5977
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> ((A -> (B and C)) and (A -> C)))
theorem-size     15
proof            (modus-ponens tm-24 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5977.         ((A -> (B and C)) -> ((A -> (B and C)) and (A -> C))), M:tm-24, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-5978
in-theory        5978
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D and E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-23 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5978.         ((A -> (B -> (A and B))) and ((C -> (D and E)) -> (C -> E))), M:tm-23, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5979
in-theory        5979
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D and E)) -> (C -> E)))
theorem-size     15
proof            (modus-ponens tm-22 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5979.         (((A and B) -> B) and ((C -> (D and E)) -> (C -> E))), M:tm-22, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5980
in-theory        5980
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D and E)) -> (C -> E)))
theorem-size     15
proof            (modus-ponens tm-21 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5980.         (((A and B) -> A) and ((C -> (D and E)) -> (C -> E))), M:tm-21, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5981
in-theory        5981
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E and F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-20 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5981.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E and F)) -> (D -> F))), M:tm-20, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5982
in-theory        5982
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D and E)) -> (C -> E)))
theorem-size     15
proof            (modus-ponens tm-19 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5982.         ((A -> (B -> A)) and ((C -> (D and E)) -> (C -> E))), M:tm-19, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5983
in-theory        5983
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (not (A -> C))) -> (not (A -> (B and C))))
theorem-size     17
proof            (modus-ponens tm-9 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-9 tm-2 tm-1 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5983.         (((A -> (B and C)) -> (not (A -> C))) -> (not (A -> (B and C)))), M:tm-9, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-5984
in-theory        5984
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (((A -> (D and B)) or (A -> B)) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5984.         (((A -> B) -> C) -> (((A -> (D and B)) or (A -> B)) -> C)), M:tm-8, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-5985
in-theory        5985
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> (C and D)) -> (B -> D)))
theorem-size     11
proof            (modus-ponens tm-7 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-7 tm-2 tm-1 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5985.         (A or ((B -> (C and D)) -> (B -> D))), M:tm-7, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5986
in-theory        5986
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-6 tm-2 tm-1 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5986.         (((A -> (B and C)) -> (A -> C)) or D), M:tm-6, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5987
in-theory        5987
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (C and D)) -> (B -> D)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5987.         (A -> (((B -> (C and D)) -> (B -> D)) and A)), M:tm-5, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5988
in-theory        5988
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> A) -> ((A -> (B and C)) -> C))
theorem-size     15
proof            (modus-ponens tm-2 tm-158 ((A (-> Am (and Bm Cm))) (B Am) (C Cm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5988.         (((A -> (B and C)) -> A) -> ((A -> (B and C)) -> C)), M:tm-2, m:tm-158, u:((A (-> Am (and Bm Cm))) (B Am) (C Cm))
================================================================
tm-name          tm-5989
in-theory        5989
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> (C and D)) -> (B -> D)))
theorem-size     11
proof            (modus-ponens tm-1 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-1 tm-2 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-5989.         (A -> ((B -> (C and D)) -> (B -> D))), M:tm-1, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-5990
in-theory        5990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-157 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5990.         ((A -> ((B and C) -> C)) and (D -> (E -> ((F and G) -> G)))), M:tm-157, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5991
in-theory        5991
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-154 tm-159 ((Am (-> (and A B) B)) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5991.         ((A or ((B and C) -> C)) -> (D -> ((E and F) -> F))), M:tm-154, m:tm-159, u:((Am (-> (and A B) B)) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-5992
in-theory        5992
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> ((C and D) -> D))
theorem-size     9
proof            (modus-ponens tm-152 tm-159 ((Am (and A Bm)) (B Bm) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5992.         ((A and B) -> ((C and D) -> D)), M:tm-152, m:tm-159, u:((Am (and A Bm)) (B Bm) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-5993
in-theory        5993
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-147 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5993.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> ((F and G) -> G)))), M:tm-147, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5994
in-theory        5994
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-144 tm-159 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5994.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((E and F) -> F))), M:tm-144, m:tm-159, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-5995
in-theory        5995
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> ((C and D) -> D)) -> E)) -> (B -> ((C and D) -> D)))
theorem-size     19
proof            (modus-ponens tm-142 tm-159 ((Am (and A (-> (-> Bm (-> (and Cm Dm) Dm)) C))) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5995.         ((A and ((B -> ((C and D) -> D)) -> E)) -> (B -> ((C and D) -> D))), M:tm-142, m:tm-159, u:((Am (and A (-> (-> Bm (-> (and Cm Dm) Dm)) C))) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-5996
in-theory        5996
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> ((C and D) -> D)) -> B)) -> ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-141 tm-159 ((Am (and A (-> (-> Bm (-> (and Cm Dm) Dm)) Bm))) (B Bm) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5996.         ((A and ((B -> ((C and D) -> D)) -> B)) -> ((C and D) -> D)), M:tm-141, m:tm-159, u:((Am (and A (-> (-> Bm (-> (and Cm Dm) Dm)) Bm))) (B Bm) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-5997
in-theory        5997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-134 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5997.         ((A -> ((B and C) -> B)) and (D -> (E -> ((F and G) -> G)))), M:tm-134, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-5998
in-theory        5998
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-131 tm-159 ((Am (-> (and A B) A)) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5998.         ((A or ((B and C) -> B)) -> (D -> ((E and F) -> F))), M:tm-131, m:tm-159, u:((Am (-> (and A B) A)) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-5999
in-theory        5999
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-125 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-5999.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> ((F and G) -> G)))), M:tm-125, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6000
in-theory        6000
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-122 tm-159 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6000.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((E and F) -> F))), M:tm-122, m:tm-159, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6001
in-theory        6001
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and C) -> C)) -> D) and E) -> (A -> ((B and C) -> C)))
theorem-size     19
proof            (modus-ponens tm-120 tm-159 ((Am (and (-> (-> Bm (-> (and Cm Dm) Dm)) B) C)) (A (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6001.         ((((A -> ((B and C) -> C)) -> D) and E) -> (A -> ((B and C) -> C))), M:tm-120, m:tm-159, u:((Am (and (-> (-> Bm (-> (and Cm Dm) Dm)) B) C)) (A (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6002
in-theory        6002
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B and C) -> C)) -> A) and D) -> ((B and C) -> C))
theorem-size     17
proof            (modus-ponens tm-119 tm-159 ((Am (and (-> (-> Bm (-> (and Cm Dm) Dm)) Bm) C)) (A Bm) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-3 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6002.         ((((A -> ((B and C) -> C)) -> A) and D) -> ((B and C) -> C)), M:tm-119, m:tm-159, u:((Am (and (-> (-> Bm (-> (and Cm Dm) Dm)) Bm) C)) (A Bm) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-6003
in-theory        6003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-113 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6003.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G and H) -> H)))), M:tm-113, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6004
in-theory        6004
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-110 tm-159 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6004.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((F and G) -> G))), M:tm-110, m:tm-159, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6005
in-theory        6005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((D and E) -> E))
theorem-size     11
proof            (modus-ponens tm-108 tm-159 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6005.         ((A -> (B -> C)) -> ((D and E) -> E)), M:tm-108, m:tm-159, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-6006
in-theory        6006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) -> (A -> (B and C))) -> (A -> C))
theorem-size     17
proof            (modus-ponens tm-106 tm-159 ((Am (-> (-> Bm (-> (and Cm Dm) Dm)) (-> Bm (and Cm Dm)))) (A Bm) (B (and Cm Dm)) (C Dm)))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6006.         (((A -> ((B and C) -> C)) -> (A -> (B and C))) -> (A -> C)), M:tm-106, m:tm-159, u:((Am (-> (-> Bm (-> (and Cm Dm) Dm)) (-> Bm (and Cm Dm)))) (A Bm) (B (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-6007
in-theory        6007
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> ((F and G) -> G))))
theorem-size     29
proof            (modus-ponens tm-105 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6007.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> ((F and G) -> G)))), M:tm-105, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6008
in-theory        6008
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((E and F) -> F)))
theorem-size     27
proof            (modus-ponens tm-102 tm-159 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6008.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((E and F) -> F))), M:tm-102, m:tm-159, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6009
in-theory        6009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) -> D)) -> (A -> ((B and C) -> C)))
theorem-size     17
proof            (modus-ponens tm-100 tm-159 ((Am (-> Bm (-> (-> (and Cm Dm) Dm) C))) (A Bm) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6009.         ((A -> (((B and C) -> C) -> D)) -> (A -> ((B and C) -> C))), M:tm-100, m:tm-159, u:((Am (-> Bm (-> (-> (and Cm Dm) Dm) C))) (A Bm) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-6010
in-theory        6010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) -> D) -> (A -> ((B and C) -> C)))
theorem-size     17
proof            (modus-ponens tm-96 tm-159 ((Am (-> (-> Bm (-> (and Cm Dm) Dm)) B)) (A (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6010.         (((A -> ((B and C) -> C)) -> D) -> (A -> ((B and C) -> C))), M:tm-96, m:tm-159, u:((Am (-> (-> Bm (-> (and Cm Dm) Dm)) B)) (A (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6011
in-theory        6011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-95 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6011.         (((A -> B) -> (A -> A)) and (C -> (D -> ((E and F) -> F)))), M:tm-95, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6012
in-theory        6012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> ((D and E) -> E)))
theorem-size     15
proof            (modus-ponens tm-92 tm-159 ((Am (-> A A)) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6012.         (((A -> B) or (A -> A)) -> (C -> ((D and E) -> E))), M:tm-92, m:tm-159, u:((Am (-> A A)) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6013
in-theory        6013
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C -> ((D and E) -> E))))
theorem-size     11
proof            (modus-ponens tm-84 tm-159 ((A Am) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6013.         (A -> (B -> (C -> ((D and E) -> E)))), M:tm-84, m:tm-159, u:((A Am) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6014
in-theory        6014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-83 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6014.         ((A -> (B -> (C -> B))) and (D -> (E -> ((F and G) -> G)))), M:tm-83, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6015
in-theory        6015
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-80 tm-159 ((Am (-> A (-> B A))) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6015.         ((A or (B -> (C -> B))) -> (D -> ((E and F) -> F))), M:tm-80, m:tm-159, u:((Am (-> A (-> B A))) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6016
in-theory        6016
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> ((B and C) -> C)) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-159 ((Am (not (not (-> (-> Bm (-> (and Cm Dm) Dm)) B)))) (A (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6016.         ((not (not ((A -> ((B and C) -> C)) -> D))) -> D), M:tm-77, m:tm-159, u:((Am (not (not (-> (-> Bm (-> (and Cm Dm) Dm)) B)))) (A (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6017
in-theory        6017
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> ((D and E) -> E))))
theorem-size     15
proof            (modus-ponens tm-76 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6017.         (((not (not A)) -> A) and (B -> (C -> ((D and E) -> E)))), M:tm-76, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6018
in-theory        6018
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> ((C and D) -> D)))
theorem-size     13
proof            (modus-ponens tm-73 tm-159 ((A Am) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6018.         (((not (not A)) or A) -> (B -> ((C and D) -> D))), M:tm-73, m:tm-159, u:((A Am) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6019
in-theory        6019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> ((E and F) -> F))))
theorem-size     21
proof            (modus-ponens tm-69 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6019.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> ((E and F) -> F)))), M:tm-69, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6020
in-theory        6020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((D and E) -> E)))
theorem-size     19
proof            (modus-ponens tm-66 tm-159 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6020.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((D and E) -> E))), M:tm-66, m:tm-159, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6021
in-theory        6021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> ((C and D) -> D)))
theorem-size     13
proof            (modus-ponens tm-55 tm-159 ((Am (-> A Bm)) (B Bm) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-8 tm-1 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6021.         ((A -> B) -> ((A or B) -> ((C and D) -> D))), M:tm-55, m:tm-159, u:((Am (-> A Bm)) (B Bm) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-6022
in-theory        6022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-54 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6022.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> ((F and G) -> G)))), M:tm-54, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6023
in-theory        6023
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-51 tm-159 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6023.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E and F) -> F))), M:tm-51, m:tm-159, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6024
in-theory        6024
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-50 tm-159 ((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6024.         ((A or (B or A)) -> (C -> ((D and E) -> E))), M:tm-50, m:tm-159, u:((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6025
in-theory        6025
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-49 tm-159 ((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6025.         ((A or (A or B)) -> (C -> ((D and E) -> E))), M:tm-49, m:tm-159, u:((Am (or A B)) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6026
in-theory        6026
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D and E) -> E)))
theorem-size     15
proof            (modus-ponens tm-48 tm-159 ((Am (-> A (and B A))) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6026.         ((A or (B -> (A and B))) -> (C -> ((D and E) -> E))), M:tm-48, m:tm-159, u:((Am (-> A (and B A))) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6027
in-theory        6027
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-47 tm-159 ((A Am) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6027.         (((A and B) or B) -> (C -> ((D and E) -> E))), M:tm-47, m:tm-159, u:((A Am) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6028
in-theory        6028
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-46 tm-159 ((A Am) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6028.         (((A and B) or A) -> (C -> ((D and E) -> E))), M:tm-46, m:tm-159, u:((A Am) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6029
in-theory        6029
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-45 tm-159 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6029.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E and F) -> F))), M:tm-45, m:tm-159, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6030
in-theory        6030
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-44 tm-159 ((Am (-> A B)) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6030.         ((A or (B -> A)) -> (C -> ((D and E) -> E))), M:tm-44, m:tm-159, u:((Am (-> A B)) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6031
in-theory        6031
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-42 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6031.         ((A -> (B or A)) and (C -> (D -> ((E and F) -> F)))), M:tm-42, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6032
in-theory        6032
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-32 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6032.         ((A -> (A or B)) and (C -> (D -> ((E and F) -> F)))), M:tm-32, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6033
in-theory        6033
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B -> ((C and D) -> D))))
theorem-size     11
proof            (modus-ponens tm-24 tm-159 ((A Am) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6033.         (A -> (A and (B -> ((C and D) -> D)))), M:tm-24, m:tm-159, u:((A Am) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6034
in-theory        6034
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-23 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6034.         ((A -> (B -> (A and B))) and (C -> (D -> ((E and F) -> F)))), M:tm-23, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6035
in-theory        6035
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-22 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6035.         (((A and B) -> B) and (C -> (D -> ((E and F) -> F)))), M:tm-22, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6036
in-theory        6036
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-21 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6036.         (((A and B) -> A) and (C -> (D -> ((E and F) -> F)))), M:tm-21, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6037
in-theory        6037
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-20 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6037.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> ((F and G) -> G)))), M:tm-20, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6038
in-theory        6038
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-19 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6038.         ((A -> (B -> A)) and (C -> (D -> ((E and F) -> F)))), M:tm-19, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6039
in-theory        6039
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> ((C and D) -> D)) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-159 ((Am (and A (-> (-> Bm (-> (and Cm Dm) Dm)) C))) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-4 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6039.         ((A and ((B -> ((C and D) -> D)) -> E)) -> E), M:tm-17, m:tm-159, u:((Am (and A (-> (-> Bm (-> (and Cm Dm) Dm)) C))) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6040
in-theory        6040
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> ((B and C) -> C)) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-159 ((Am (and (-> (-> Bm (-> (and Cm Dm) Dm)) B) C)) (A (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6040.         ((((A -> ((B and C) -> C)) -> D) and E) -> D), M:tm-15, m:tm-159, u:((Am (and (-> (-> Bm (-> (and Cm Dm) Dm)) B) C)) (A (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6041
in-theory        6041
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) -> D)) -> (A -> D))
theorem-size     13
proof            (modus-ponens tm-13 tm-159 ((Am (-> Bm (-> (-> (and Cm Dm) Dm) C))) (A Bm) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6041.         ((A -> (((B and C) -> C) -> D)) -> (A -> D)), M:tm-13, m:tm-159, u:((Am (-> Bm (-> (-> (and Cm Dm) Dm) C))) (A Bm) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-6042
in-theory        6042
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B -> ((C and D) -> D)))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-159 ((A Am) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-9 tm-1 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6042.         ((A -> (not (B -> ((C and D) -> D)))) -> (not A)), M:tm-9, m:tm-159, u:((A Am) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6043
in-theory        6043
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) -> D) -> ((E or (A -> ((B and C) -> C))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-159 ((A Am) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6043.         (((A -> ((B and C) -> C)) -> D) -> ((E or (A -> ((B and C) -> C))) -> D)), M:tm-8, m:tm-159, u:((A Am) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6044
in-theory        6044
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C -> ((D and E) -> E))))
theorem-size     11
proof            (modus-ponens tm-7 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-7 tm-1 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6044.         (A or (B -> (C -> ((D and E) -> E)))), M:tm-7, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6045
in-theory        6045
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-6 tm-1 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6045.         ((A -> (B -> ((C and D) -> D))) or E), M:tm-6, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6046
in-theory        6046
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> ((D and E) -> E))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6046.         (A -> ((B -> (C -> ((D and E) -> E))) and A)), M:tm-5, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6047
in-theory        6047
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> ((C and D) -> D)))
theorem-size     11
proof            (modus-ponens tm-2 tm-159 ((A Am) (B Bm) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-1 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6047.         ((A -> B) -> (A -> ((C and D) -> D))), M:tm-2, m:tm-159, u:((A Am) (B Bm) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-6048
in-theory        6048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6048.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-157, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6049
in-theory        6049
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6049.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-147, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6050
in-theory        6050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6050.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-134, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6051
in-theory        6051
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6051.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-125, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6052
in-theory        6052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6052.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> G)))), M:tm-113, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6053
in-theory        6053
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6053.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-105, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6054
in-theory        6054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6054.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (F -> E)))), M:tm-95, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6055
in-theory        6055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6055.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-83, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6056
in-theory        6056
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6056.         (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (E -> D)))), M:tm-76, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6057
in-theory        6057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6057.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (F -> E)))), M:tm-69, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6058
in-theory        6058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6058.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-54, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6059
in-theory        6059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6059.         ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (F -> E)))), M:tm-42, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6060
in-theory        6060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6060.         ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (F -> E)))), M:tm-32, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6061
in-theory        6061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6061.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> E)))), M:tm-23, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6062
in-theory        6062
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6062.         (((A and B) -> B) and ((C -> (D -> C)) and (E -> (F -> E)))), M:tm-22, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6063
in-theory        6063
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6063.         (((A and B) -> A) and ((C -> (D -> C)) and (E -> (F -> E)))), M:tm-21, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6064
in-theory        6064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6064.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-20, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6065
in-theory        6065
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6065.         ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (F -> E)))), M:tm-19, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6066
in-theory        6066
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6066.         (A or ((B -> (C -> B)) and (D -> (E -> D)))), M:tm-7, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6067
in-theory        6067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6067.         (((A -> (B -> A)) and (C -> (D -> C))) or E), M:tm-6, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6068
in-theory        6068
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> (E -> D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6068.         (A -> (((B -> (C -> B)) and (D -> (E -> D))) and A)), M:tm-5, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6069
in-theory        6069
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-1 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6069.         (A -> ((B -> (C -> B)) and (D -> (E -> D)))), M:tm-1, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6070
in-theory        6070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6070.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-157, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6071
in-theory        6071
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6071.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-147, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6072
in-theory        6072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6072.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-134, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6073
in-theory        6073
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6073.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-125, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6074
in-theory        6074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6074.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-113, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6075
in-theory        6075
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6075.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-105, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6076
in-theory        6076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6076.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-95, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6077
in-theory        6077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6077.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-83, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6078
in-theory        6078
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6078.         (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-76, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6079
in-theory        6079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6079.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-69, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6080
in-theory        6080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6080.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-54, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6081
in-theory        6081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6081.         ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-42, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6082
in-theory        6082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6082.         ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-32, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6083
in-theory        6083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6083.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-23, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6084
in-theory        6084
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6084.         (((A and B) -> B) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-22, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6085
in-theory        6085
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6085.         (((A and B) -> A) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-21, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6086
in-theory        6086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6086.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-20, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6087
in-theory        6087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6087.         ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-19, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6088
in-theory        6088
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-7 tm-5 tm-1 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6088.         (A or ((B -> (C -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-7, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6089
in-theory        6089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-6 tm-5 tm-1 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6089.         (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F), M:tm-6, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6090
in-theory        6090
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6090.         (A -> (((B -> (C -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)), M:tm-5, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6091
in-theory        6091
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6091.         (A -> ((B -> (C -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-1, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6092
in-theory        6092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6092.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-157, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6093
in-theory        6093
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6093.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-147, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6094
in-theory        6094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6094.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-134, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6095
in-theory        6095
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6095.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-125, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6096
in-theory        6096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6096.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G and H) -> G))), M:tm-113, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6097
in-theory        6097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6097.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-105, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6098
in-theory        6098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6098.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E and F) -> E))), M:tm-95, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6099
in-theory        6099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6099.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-83, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6100
in-theory        6100
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((D and E) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-10 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6100.         (((not (not A)) -> A) and ((B -> (C -> B)) and ((D and E) -> D))), M:tm-76, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6101
in-theory        6101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-9 tm-1 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6101.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E and F) -> E))), M:tm-69, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6102
in-theory        6102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6102.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-54, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6103
in-theory        6103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6103.         ((A -> (B or A)) and ((C -> (D -> C)) and ((E and F) -> E))), M:tm-42, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6104
in-theory        6104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6104.         ((A -> (A or B)) and ((C -> (D -> C)) and ((E and F) -> E))), M:tm-32, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6105
in-theory        6105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6105.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E and F) -> E))), M:tm-23, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6106
in-theory        6106
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6106.         (((A and B) -> B) and ((C -> (D -> C)) and ((E and F) -> E))), M:tm-22, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6107
in-theory        6107
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6107.         (((A and B) -> A) and ((C -> (D -> C)) and ((E and F) -> E))), M:tm-21, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6108
in-theory        6108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6108.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-20, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6109
in-theory        6109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6109.         ((A -> (B -> A)) and ((C -> (D -> C)) and ((E and F) -> E))), M:tm-19, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6110
in-theory        6110
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-7 tm-5 tm-1 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6110.         (A or ((B -> (C -> B)) and ((D and E) -> D))), M:tm-7, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6111
in-theory        6111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-6 tm-5 tm-1 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6111.         (((A -> (B -> A)) and ((C and D) -> C)) or E), M:tm-6, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6112
in-theory        6112
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((D and E) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6112.         (A -> (((B -> (C -> B)) and ((D and E) -> D)) and A)), M:tm-5, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6113
in-theory        6113
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6113.         (A -> ((B -> (C -> B)) and ((D and E) -> D))), M:tm-1, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6114
in-theory        6114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-157 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6114.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-157, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6115
in-theory        6115
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-147 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6115.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-147, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6116
in-theory        6116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-134 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6116.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-134, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6117
in-theory        6117
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-125 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6117.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-125, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6118
in-theory        6118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-113 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6118.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G and H) -> H))), M:tm-113, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6119
in-theory        6119
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-105 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6119.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-105, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6120
in-theory        6120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-95 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6120.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E and F) -> F))), M:tm-95, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6121
in-theory        6121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-83 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6121.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-83, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6122
in-theory        6122
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((D and E) -> E)))
theorem-size     17
proof            (modus-ponens tm-76 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-10 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6122.         (((not (not A)) -> A) and ((B -> (C -> B)) and ((D and E) -> E))), M:tm-76, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6123
in-theory        6123
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-69 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-9 tm-1 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6123.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E and F) -> F))), M:tm-69, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6124
in-theory        6124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-54 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6124.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-54, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6125
in-theory        6125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-42 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6125.         ((A -> (B or A)) and ((C -> (D -> C)) and ((E and F) -> F))), M:tm-42, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6126
in-theory        6126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-32 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6126.         ((A -> (A or B)) and ((C -> (D -> C)) and ((E and F) -> F))), M:tm-32, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6127
in-theory        6127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-23 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6127.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E and F) -> F))), M:tm-23, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6128
in-theory        6128
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-22 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6128.         (((A and B) -> B) and ((C -> (D -> C)) and ((E and F) -> F))), M:tm-22, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6129
in-theory        6129
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-21 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6129.         (((A and B) -> A) and ((C -> (D -> C)) and ((E and F) -> F))), M:tm-21, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6130
in-theory        6130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-20 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6130.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-20, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6131
in-theory        6131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-19 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6131.         ((A -> (B -> A)) and ((C -> (D -> C)) and ((E and F) -> F))), M:tm-19, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6132
in-theory        6132
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-7 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-7 tm-5 tm-1 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6132.         (A or ((B -> (C -> B)) and ((D and E) -> E))), M:tm-7, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6133
in-theory        6133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-6 tm-5 tm-1 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6133.         (((A -> (B -> A)) and ((C and D) -> D)) or E), M:tm-6, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6134
in-theory        6134
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((D and E) -> E)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6134.         (A -> (((B -> (C -> B)) and ((D and E) -> E)) and A)), M:tm-5, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6135
in-theory        6135
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-1 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6135.         (A -> ((B -> (C -> B)) and ((D and E) -> E))), M:tm-1, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6136
in-theory        6136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6136.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-157, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6137
in-theory        6137
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6137.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-147, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6138
in-theory        6138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6138.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-134, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6139
in-theory        6139
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6139.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-125, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6140
in-theory        6140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6140.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (G and H))))), M:tm-113, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6141
in-theory        6141
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6141.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-105, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6142
in-theory        6142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6142.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (F -> (E and F))))), M:tm-95, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6143
in-theory        6143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6143.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-83, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6144
in-theory        6144
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6144.         (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (E -> (D and E))))), M:tm-76, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6145
in-theory        6145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6145.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (F -> (E and F))))), M:tm-69, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6146
in-theory        6146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6146.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-54, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6147
in-theory        6147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6147.         ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (F -> (E and F))))), M:tm-42, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6148
in-theory        6148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6148.         ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (F -> (E and F))))), M:tm-32, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6149
in-theory        6149
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6149.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (E and F))))), M:tm-23, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6150
in-theory        6150
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6150.         (((A and B) -> B) and ((C -> (D -> C)) and (E -> (F -> (E and F))))), M:tm-22, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6151
in-theory        6151
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6151.         (((A and B) -> A) and ((C -> (D -> C)) and (E -> (F -> (E and F))))), M:tm-21, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6152
in-theory        6152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6152.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-20, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6153
in-theory        6153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6153.         ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (F -> (E and F))))), M:tm-19, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6154
in-theory        6154
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6154.         (A or ((B -> (C -> B)) and (D -> (E -> (D and E))))), M:tm-7, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6155
in-theory        6155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6155.         (((A -> (B -> A)) and (C -> (D -> (C and D)))) or E), M:tm-6, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6156
in-theory        6156
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> (E -> (D and E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6156.         (A -> (((B -> (C -> B)) and (D -> (E -> (D and E)))) and A)), M:tm-5, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6157
in-theory        6157
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-1 tm-5)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6157.         (A -> ((B -> (C -> B)) and (D -> (E -> (D and E))))), M:tm-1, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6158
in-theory        6158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-157 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6158.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-157, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6159
in-theory        6159
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-147 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6159.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-147, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6160
in-theory        6160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-134 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6160.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-134, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6161
in-theory        6161
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-125 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6161.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-125, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6162
in-theory        6162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-113 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6162.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (G or H)))), M:tm-113, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6163
in-theory        6163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-105 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6163.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-105, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6164
in-theory        6164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-95 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6164.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (E or F)))), M:tm-95, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6165
in-theory        6165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-83 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6165.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-83, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6166
in-theory        6166
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-76 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6166.         (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (D or E)))), M:tm-76, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6167
in-theory        6167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-69 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6167.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (E or F)))), M:tm-69, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6168
in-theory        6168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-54 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6168.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-54, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6169
in-theory        6169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-42 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6169.         ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (E or F)))), M:tm-42, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6170
in-theory        6170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-32 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6170.         ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (E or F)))), M:tm-32, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6171
in-theory        6171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-23 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6171.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (E or F)))), M:tm-23, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6172
in-theory        6172
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-22 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6172.         (((A and B) -> B) and ((C -> (D -> C)) and (E -> (E or F)))), M:tm-22, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6173
in-theory        6173
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-21 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6173.         (((A and B) -> A) and ((C -> (D -> C)) and (E -> (E or F)))), M:tm-21, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6174
in-theory        6174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-20 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6174.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-20, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6175
in-theory        6175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-19 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6175.         ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (E or F)))), M:tm-19, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6176
in-theory        6176
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-7 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6176.         (A or ((B -> (C -> B)) and (D -> (D or E)))), M:tm-7, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6177
in-theory        6177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6177.         (((A -> (B -> A)) and (C -> (C or D))) or E), M:tm-6, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6178
in-theory        6178
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> (D or E))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6178.         (A -> (((B -> (C -> B)) and (D -> (D or E))) and A)), M:tm-5, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6179
in-theory        6179
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-1 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6179.         (A -> ((B -> (C -> B)) and (D -> (D or E)))), M:tm-1, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6180
in-theory        6180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6180.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-157, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6181
in-theory        6181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6181.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-147, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6182
in-theory        6182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6182.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-134, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6183
in-theory        6183
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6183.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-125, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6184
in-theory        6184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6184.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H or G)))), M:tm-113, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6185
in-theory        6185
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6185.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-105, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6186
in-theory        6186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6186.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (F or E)))), M:tm-95, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6187
in-theory        6187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6187.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-83, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6188
in-theory        6188
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6188.         (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (E or D)))), M:tm-76, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6189
in-theory        6189
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6189.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (F or E)))), M:tm-69, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6190
in-theory        6190
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6190.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-54, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6191
in-theory        6191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6191.         ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (F or E)))), M:tm-42, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6192
in-theory        6192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6192.         ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (F or E)))), M:tm-32, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6193
in-theory        6193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6193.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (F or E)))), M:tm-23, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6194
in-theory        6194
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6194.         (((A and B) -> B) and ((C -> (D -> C)) and (E -> (F or E)))), M:tm-22, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6195
in-theory        6195
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6195.         (((A and B) -> A) and ((C -> (D -> C)) and (E -> (F or E)))), M:tm-21, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6196
in-theory        6196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6196.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-20, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6197
in-theory        6197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6197.         ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (F or E)))), M:tm-19, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6198
in-theory        6198
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6198.         (A or ((B -> (C -> B)) and (D -> (E or D)))), M:tm-7, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6199
in-theory        6199
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6199.         (((A -> (B -> A)) and (C -> (D or C))) or E), M:tm-6, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6200
in-theory        6200
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> (E or D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6200.         (A -> (((B -> (C -> B)) and (D -> (E or D))) and A)), M:tm-5, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6201
in-theory        6201
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6201.         (A -> ((B -> (C -> B)) and (D -> (E or D)))), M:tm-1, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6202
in-theory        6202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6202.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-157, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6203
in-theory        6203
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6203.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-147, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6204
in-theory        6204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6204.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-134, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6205
in-theory        6205
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6205.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-125, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6206
in-theory        6206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6206.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-113, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6207
in-theory        6207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6207.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-105, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6208
in-theory        6208
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6208.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-95, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6209
in-theory        6209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6209.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-83, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6210
in-theory        6210
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6210.         (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-76, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6211
in-theory        6211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6211.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-69, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6212
in-theory        6212
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6212.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-54, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6213
in-theory        6213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6213.         ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-42, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6214
in-theory        6214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6214.         ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-32, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6215
in-theory        6215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6215.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-23, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6216
in-theory        6216
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6216.         (((A and B) -> B) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-22, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6217
in-theory        6217
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6217.         (((A and B) -> A) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-21, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6218
in-theory        6218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6218.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-20, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6219
in-theory        6219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6219.         ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-19, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6220
in-theory        6220
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-7 tm-5 tm-1 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6220.         (A or ((B -> (C -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-7, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6221
in-theory        6221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-6 tm-5 tm-1 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6221.         (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F), M:tm-6, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6222
in-theory        6222
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6222.         (A -> (((B -> (C -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A)), M:tm-5, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6223
in-theory        6223
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6223.         (A -> ((B -> (C -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-1, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6224
in-theory        6224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-157 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6224.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-157, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6225
in-theory        6225
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-147 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6225.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-147, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6226
in-theory        6226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-134 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6226.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-134, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6227
in-theory        6227
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-125 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6227.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-125, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6228
in-theory        6228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-113 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6228.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-113, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6229
in-theory        6229
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     37
proof            (modus-ponens tm-105 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6229.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-105, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6230
in-theory        6230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-95 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6230.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-95, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6231
in-theory        6231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-83 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6231.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-83, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6232
in-theory        6232
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-76 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6232.         (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-76, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6233
in-theory        6233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     29
proof            (modus-ponens tm-69 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6233.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-69, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6234
in-theory        6234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-54 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6234.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-54, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6235
in-theory        6235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-42 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6235.         ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-42, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6236
in-theory        6236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-32 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6236.         ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-32, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6237
in-theory        6237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-23 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6237.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-23, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6238
in-theory        6238
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-22 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6238.         (((A and B) -> B) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-22, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6239
in-theory        6239
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-21 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6239.         (((A and B) -> A) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-21, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6240
in-theory        6240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-20 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6240.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-20, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6241
in-theory        6241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-19 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6241.         ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-19, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6242
in-theory        6242
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-7 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-7 tm-5 tm-1 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6242.         (A or ((B -> (C -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-7, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6243
in-theory        6243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-6 tm-5 tm-1 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6243.         (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E), M:tm-6, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6244
in-theory        6244
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6244.         (A -> (((B -> (C -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and A)), M:tm-5, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6245
in-theory        6245
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-1 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-1 tm-5 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6245.         (A -> ((B -> (C -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-1, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6246
in-theory        6246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6246.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-157, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6247
in-theory        6247
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6247.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-147, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6248
in-theory        6248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6248.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-134, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6249
in-theory        6249
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6249.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-125, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6250
in-theory        6250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6250.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((not (not G)) -> G))), M:tm-113, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6251
in-theory        6251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6251.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-105, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6252
in-theory        6252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6252.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((not (not E)) -> E))), M:tm-95, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6253
in-theory        6253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6253.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-83, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6254
in-theory        6254
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((not (not D)) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6254.         (((not (not A)) -> A) and ((B -> (C -> B)) and ((not (not D)) -> D))), M:tm-76, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6255
in-theory        6255
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((not (not E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-1 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6255.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((not (not E)) -> E))), M:tm-69, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6256
in-theory        6256
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6256.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-54, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6257
in-theory        6257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6257.         ((A -> (B or A)) and ((C -> (D -> C)) and ((not (not E)) -> E))), M:tm-42, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6258
in-theory        6258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6258.         ((A -> (A or B)) and ((C -> (D -> C)) and ((not (not E)) -> E))), M:tm-32, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6259
in-theory        6259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6259.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((not (not E)) -> E))), M:tm-23, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6260
in-theory        6260
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6260.         (((A and B) -> B) and ((C -> (D -> C)) and ((not (not E)) -> E))), M:tm-22, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6261
in-theory        6261
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6261.         (((A and B) -> A) and ((C -> (D -> C)) and ((not (not E)) -> E))), M:tm-21, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6262
in-theory        6262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6262.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-20, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6263
in-theory        6263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6263.         ((A -> (B -> A)) and ((C -> (D -> C)) and ((not (not E)) -> E))), M:tm-19, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6264
in-theory        6264
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-7 tm-5 tm-1 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6264.         (A or ((B -> (C -> B)) and ((not (not D)) -> D))), M:tm-7, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6265
in-theory        6265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-6 tm-5 tm-1 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6265.         (((A -> (B -> A)) and ((not (not C)) -> C)) or D), M:tm-6, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6266
in-theory        6266
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((not (not D)) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6266.         (A -> (((B -> (C -> B)) and ((not (not D)) -> D)) and A)), M:tm-5, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6267
in-theory        6267
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-1 tm-5 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6267.         (A -> ((B -> (C -> B)) and ((not (not D)) -> D))), M:tm-1, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6268
in-theory        6268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6268.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-157, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6269
in-theory        6269
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6269.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-147, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6270
in-theory        6270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6270.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-134, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6271
in-theory        6271
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6271.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-125, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6272
in-theory        6272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6272.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I -> H))))), M:tm-113, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6273
in-theory        6273
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6273.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-105, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6274
in-theory        6274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6274.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (F -> (G -> F))))), M:tm-95, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6275
in-theory        6275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6275.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-83, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6276
in-theory        6276
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6276.         (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (E -> (F -> E))))), M:tm-76, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6277
in-theory        6277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6277.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (F -> (G -> F))))), M:tm-69, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6278
in-theory        6278
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6278.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-54, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6279
in-theory        6279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6279.         ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (F -> (G -> F))))), M:tm-42, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6280
in-theory        6280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6280.         ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (F -> (G -> F))))), M:tm-32, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6281
in-theory        6281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6281.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (G -> F))))), M:tm-23, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6282
in-theory        6282
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6282.         (((A and B) -> B) and ((C -> (D -> C)) and (E -> (F -> (G -> F))))), M:tm-22, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6283
in-theory        6283
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6283.         (((A and B) -> A) and ((C -> (D -> C)) and (E -> (F -> (G -> F))))), M:tm-21, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6284
in-theory        6284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6284.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-20, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6285
in-theory        6285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6285.         ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (F -> (G -> F))))), M:tm-19, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6286
in-theory        6286
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6286.         (A or ((B -> (C -> B)) and (D -> (E -> (F -> E))))), M:tm-7, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6287
in-theory        6287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6287.         (((A -> (B -> A)) and (C -> (D -> (E -> D)))) or F), M:tm-6, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6288
in-theory        6288
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> (E -> (F -> E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6288.         (A -> (((B -> (C -> B)) and (D -> (E -> (F -> E)))) and A)), M:tm-5, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6289
in-theory        6289
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-1 tm-5)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6289.         (A -> ((B -> (C -> B)) and (D -> (E -> (F -> E))))), M:tm-1, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6290
in-theory        6290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6290.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-157, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6291
in-theory        6291
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6291.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-147, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6292
in-theory        6292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6292.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-134, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6293
in-theory        6293
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6293.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-125, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6294
in-theory        6294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6294.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (G -> G)))), M:tm-113, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6295
in-theory        6295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6295.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-105, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6296
in-theory        6296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6296.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> F) -> (E -> E)))), M:tm-95, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6297
in-theory        6297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6297.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-83, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6298
in-theory        6298
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> E) -> (D -> D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6298.         (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> E) -> (D -> D)))), M:tm-76, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6299
in-theory        6299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> F) -> (E -> E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6299.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> F) -> (E -> E)))), M:tm-69, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6300
in-theory        6300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6300.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-54, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6301
in-theory        6301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6301.         ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> F) -> (E -> E)))), M:tm-42, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6302
in-theory        6302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6302.         ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> F) -> (E -> E)))), M:tm-32, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6303
in-theory        6303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6303.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (E -> E)))), M:tm-23, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6304
in-theory        6304
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6304.         (((A and B) -> B) and ((C -> (D -> C)) and ((E -> F) -> (E -> E)))), M:tm-22, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6305
in-theory        6305
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6305.         (((A and B) -> A) and ((C -> (D -> C)) and ((E -> F) -> (E -> E)))), M:tm-21, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6306
in-theory        6306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6306.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-20, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6307
in-theory        6307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6307.         ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> F) -> (E -> E)))), M:tm-19, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6308
in-theory        6308
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-2)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6308.         (A or ((B -> (C -> B)) and ((D -> E) -> (D -> D)))), M:tm-7, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6309
in-theory        6309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-2)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6309.         (((A -> (B -> A)) and ((C -> D) -> (C -> C))) or E), M:tm-6, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6310
in-theory        6310
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((D -> E) -> (D -> D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6310.         (A -> (((B -> (C -> B)) and ((D -> E) -> (D -> D))) and A)), M:tm-5, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6311
in-theory        6311
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6311.         (A -> ((B -> (C -> B)) and ((D -> E) -> (D -> D)))), M:tm-1, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6312
in-theory        6312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-157 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6312.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-157, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6313
in-theory        6313
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-147 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6313.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-147, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6314
in-theory        6314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-134 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6314.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-134, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6315
in-theory        6315
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-125 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6315.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-125, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6316
in-theory        6316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-113 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6316.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-113, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6317
in-theory        6317
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     45
proof            (modus-ponens tm-105 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6317.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-105, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6318
in-theory        6318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-95 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6318.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-95, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6319
in-theory        6319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-83 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6319.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-83, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6320
in-theory        6320
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-76 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6320.         (((not (not A)) -> A) and ((B -> (C -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-76, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6321
in-theory        6321
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     37
proof            (modus-ponens tm-69 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6321.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-69, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6322
in-theory        6322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-54 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6322.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-54, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6323
in-theory        6323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-42 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6323.         ((A -> (B or A)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-42, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6324
in-theory        6324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-32 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6324.         ((A -> (A or B)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-32, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6325
in-theory        6325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-23 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6325.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-23, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6326
in-theory        6326
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-22 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6326.         (((A and B) -> B) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-22, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6327
in-theory        6327
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-21 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6327.         (((A and B) -> A) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-21, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6328
in-theory        6328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-20 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6328.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-20, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6329
in-theory        6329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-19 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6329.         ((A -> (B -> A)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-19, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6330
in-theory        6330
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-7 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-7 tm-5 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6330.         (A or ((B -> (C -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-7, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6331
in-theory        6331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F)
theorem-size     27
proof            (modus-ponens tm-6 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-6 tm-5 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6331.         (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F), M:tm-6, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6332
in-theory        6332
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6332.         (A -> (((B -> (C -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and A)), M:tm-5, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6333
in-theory        6333
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-1 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6333.         (A -> ((B -> (C -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-1, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6334
in-theory        6334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6334.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-157, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6335
in-theory        6335
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6335.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-147, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6336
in-theory        6336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6336.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-134, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6337
in-theory        6337
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6337.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-125, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6338
in-theory        6338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6338.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-113, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6339
in-theory        6339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6339.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-105, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6340
in-theory        6340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6340.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-95, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6341
in-theory        6341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6341.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-83, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6342
in-theory        6342
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6342.         (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-76, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6343
in-theory        6343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6343.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-69, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6344
in-theory        6344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6344.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-54, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6345
in-theory        6345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6345.         ((A -> (B or A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-42, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6346
in-theory        6346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6346.         ((A -> (A or B)) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-32, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6347
in-theory        6347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6347.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-23, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6348
in-theory        6348
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6348.         (((A and B) -> B) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-22, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6349
in-theory        6349
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6349.         (((A and B) -> A) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-21, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6350
in-theory        6350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6350.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-20, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6351
in-theory        6351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6351.         ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-19, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6352
in-theory        6352
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-7 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-7 tm-5 tm-1 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6352.         (A or ((B -> (C -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-7, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6353
in-theory        6353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-6 tm-5 tm-1 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6353.         (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G), M:tm-6, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6354
in-theory        6354
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6354.         (A -> (((B -> (C -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A)), M:tm-5, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6355
in-theory        6355
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-1 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6355.         (A -> ((B -> (C -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-1, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6356
in-theory        6356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-157 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6356.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-157, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6357
in-theory        6357
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-147 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6357.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-147, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6358
in-theory        6358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-134 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6358.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-134, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6359
in-theory        6359
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-125 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6359.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-125, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6360
in-theory        6360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-113 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6360.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-113, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6361
in-theory        6361
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     41
proof            (modus-ponens tm-105 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6361.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-105, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6362
in-theory        6362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-95 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6362.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-95, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6363
in-theory        6363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-83 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6363.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-83, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6364
in-theory        6364
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     27
proof            (modus-ponens tm-76 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6364.         (((not (not A)) -> A) and ((B -> (C -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-76, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6365
in-theory        6365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     33
proof            (modus-ponens tm-69 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6365.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-69, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6366
in-theory        6366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-54 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6366.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-54, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6367
in-theory        6367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-42 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6367.         ((A -> (B or A)) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-42, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6368
in-theory        6368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-32 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6368.         ((A -> (A or B)) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-32, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6369
in-theory        6369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-23 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6369.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-23, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6370
in-theory        6370
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-22 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6370.         (((A and B) -> B) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-22, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6371
in-theory        6371
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-21 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6371.         (((A and B) -> A) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-21, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6372
in-theory        6372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-20 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6372.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-20, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6373
in-theory        6373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-19 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6373.         ((A -> (B -> A)) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-19, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6374
in-theory        6374
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-7 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6374.         (A or ((B -> (C -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-7, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6375
in-theory        6375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6375.         (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F), M:tm-6, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6376
in-theory        6376
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6376.         (A -> (((B -> (C -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and A)), M:tm-5, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6377
in-theory        6377
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-1 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6377.         (A -> ((B -> (C -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-1, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6378
in-theory        6378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-157 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6378.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-157, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6379
in-theory        6379
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-147 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6379.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-147, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6380
in-theory        6380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-134 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6380.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-134, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6381
in-theory        6381
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-125 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6381.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-125, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6382
in-theory        6382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-113 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6382.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H and I) -> H)))), M:tm-113, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6383
in-theory        6383
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-105 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6383.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-105, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6384
in-theory        6384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-95 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6384.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> ((F and G) -> F)))), M:tm-95, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6385
in-theory        6385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-83 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6385.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-83, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6386
in-theory        6386
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-76 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6386.         (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> ((E and F) -> E)))), M:tm-76, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6387
in-theory        6387
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-69 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6387.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> ((F and G) -> F)))), M:tm-69, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6388
in-theory        6388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-54 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6388.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-54, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6389
in-theory        6389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-42 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6389.         ((A -> (B or A)) and ((C -> (D -> C)) and (E -> ((F and G) -> F)))), M:tm-42, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6390
in-theory        6390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-32 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6390.         ((A -> (A or B)) and ((C -> (D -> C)) and (E -> ((F and G) -> F)))), M:tm-32, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6391
in-theory        6391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-23 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6391.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> ((F and G) -> F)))), M:tm-23, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6392
in-theory        6392
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-22 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6392.         (((A and B) -> B) and ((C -> (D -> C)) and (E -> ((F and G) -> F)))), M:tm-22, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6393
in-theory        6393
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-21 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6393.         (((A and B) -> A) and ((C -> (D -> C)) and (E -> ((F and G) -> F)))), M:tm-21, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6394
in-theory        6394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-20 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6394.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-20, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6395
in-theory        6395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-19 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6395.         ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> ((F and G) -> F)))), M:tm-19, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6396
in-theory        6396
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-7 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6396.         (A or ((B -> (C -> B)) and (D -> ((E and F) -> E)))), M:tm-7, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6397
in-theory        6397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6397.         (((A -> (B -> A)) and (C -> ((D and E) -> D))) or F), M:tm-6, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6398
in-theory        6398
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> ((E and F) -> E))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6398.         (A -> (((B -> (C -> B)) and (D -> ((E and F) -> E))) and A)), M:tm-5, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6399
in-theory        6399
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-1 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6399.         (A -> ((B -> (C -> B)) and (D -> ((E and F) -> E)))), M:tm-1, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6400
in-theory        6400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-157 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6400.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-157, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6401
in-theory        6401
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-147 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6401.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-147, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6402
in-theory        6402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-134 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6402.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-134, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6403
in-theory        6403
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-125 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6403.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-125, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6404
in-theory        6404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-113 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6404.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-113, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6405
in-theory        6405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     41
proof            (modus-ponens tm-105 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6405.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-105, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6406
in-theory        6406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-95 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6406.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-95, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6407
in-theory        6407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-83 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6407.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-83, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6408
in-theory        6408
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     27
proof            (modus-ponens tm-76 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6408.         (((not (not A)) -> A) and ((B -> (C -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-76, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6409
in-theory        6409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     33
proof            (modus-ponens tm-69 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6409.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-69, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6410
in-theory        6410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-54 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6410.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-54, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6411
in-theory        6411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-42 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6411.         ((A -> (B or A)) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-42, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6412
in-theory        6412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-32 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6412.         ((A -> (A or B)) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-32, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6413
in-theory        6413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-23 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6413.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-23, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6414
in-theory        6414
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-22 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6414.         (((A and B) -> B) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-22, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6415
in-theory        6415
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-21 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6415.         (((A and B) -> A) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-21, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6416
in-theory        6416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-20 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6416.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-20, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6417
in-theory        6417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-19 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6417.         ((A -> (B -> A)) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-19, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6418
in-theory        6418
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-7 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-7 tm-5 tm-1 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6418.         (A or ((B -> (C -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-7, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6419
in-theory        6419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-6 tm-5 tm-1 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6419.         (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F), M:tm-6, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6420
in-theory        6420
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6420.         (A -> (((B -> (C -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and A)), M:tm-5, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6421
in-theory        6421
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-1 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-1 tm-5 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6421.         (A -> ((B -> (C -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-1, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6422
in-theory        6422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-157 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6422.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-157, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6423
in-theory        6423
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-147 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6423.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-147, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6424
in-theory        6424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-134 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6424.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-134, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6425
in-theory        6425
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-125 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6425.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-125, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6426
in-theory        6426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-113 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6426.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H and I) -> I)))), M:tm-113, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6427
in-theory        6427
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-105 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6427.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-105, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6428
in-theory        6428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-95 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6428.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> ((F and G) -> G)))), M:tm-95, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6429
in-theory        6429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-83 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6429.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-83, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6430
in-theory        6430
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-76 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-10 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6430.         (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> ((E and F) -> F)))), M:tm-76, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6431
in-theory        6431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-69 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-9 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6431.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> ((F and G) -> G)))), M:tm-69, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6432
in-theory        6432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-54 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6432.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-54, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6433
in-theory        6433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-42 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6433.         ((A -> (B or A)) and ((C -> (D -> C)) and (E -> ((F and G) -> G)))), M:tm-42, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6434
in-theory        6434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-32 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6434.         ((A -> (A or B)) and ((C -> (D -> C)) and (E -> ((F and G) -> G)))), M:tm-32, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6435
in-theory        6435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-23 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6435.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> ((F and G) -> G)))), M:tm-23, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6436
in-theory        6436
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-22 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6436.         (((A and B) -> B) and ((C -> (D -> C)) and (E -> ((F and G) -> G)))), M:tm-22, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6437
in-theory        6437
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-21 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6437.         (((A and B) -> A) and ((C -> (D -> C)) and (E -> ((F and G) -> G)))), M:tm-21, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6438
in-theory        6438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-20 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6438.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-20, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6439
in-theory        6439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-19 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6439.         ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> ((F and G) -> G)))), M:tm-19, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6440
in-theory        6440
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-7 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-7 tm-5 tm-1 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6440.         (A or ((B -> (C -> B)) and (D -> ((E and F) -> F)))), M:tm-7, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6441
in-theory        6441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-6 tm-5 tm-1 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6441.         (((A -> (B -> A)) and (C -> ((D and E) -> E))) or F), M:tm-6, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6442
in-theory        6442
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> ((E and F) -> F))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6442.         (A -> (((B -> (C -> B)) and (D -> ((E and F) -> F))) and A)), M:tm-5, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6443
in-theory        6443
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-1 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6443.         (A -> ((B -> (C -> B)) and (D -> ((E and F) -> F)))), M:tm-1, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6444
in-theory        6444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6444.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-157, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6445
in-theory        6445
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6445.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-147, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6446
in-theory        6446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6446.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-134, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6447
in-theory        6447
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6447.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-125, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6448
in-theory        6448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6448.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-113, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6449
in-theory        6449
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6449.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-105, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6450
in-theory        6450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6450.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-95, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6451
in-theory        6451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6451.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-83, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6452
in-theory        6452
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6452.         (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> ((E -> (F -> E)) and D)))), M:tm-76, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6453
in-theory        6453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6453.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-69, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6454
in-theory        6454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6454.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-54, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6455
in-theory        6455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6455.         ((A -> (B or A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-42, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6456
in-theory        6456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6456.         ((A -> (A or B)) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-32, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6457
in-theory        6457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6457.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-23, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6458
in-theory        6458
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6458.         (((A and B) -> B) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-22, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6459
in-theory        6459
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6459.         (((A and B) -> A) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-21, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6460
in-theory        6460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6460.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-20, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6461
in-theory        6461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6461.         ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-19, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6462
in-theory        6462
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6462.         (A or ((B -> (C -> B)) and (D -> ((E -> (F -> E)) and D)))), M:tm-7, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6463
in-theory        6463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6463.         (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) or F), M:tm-6, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6464
in-theory        6464
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> ((E -> (F -> E)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6464.         (A -> (((B -> (C -> B)) and (D -> ((E -> (F -> E)) and D))) and A)), M:tm-5, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6465
in-theory        6465
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-1 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6465.         (A -> ((B -> (C -> B)) and (D -> ((E -> (F -> E)) and D)))), M:tm-1, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6466
in-theory        6466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6466.         ((A -> ((B and C) -> C)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-157, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6467
in-theory        6467
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not ((C -> (D -> C)) and ((A and B) -> B)))))
theorem-size     19
proof            (modus-ponens tm-153 tm-179 ((A (-> (-> (and B C) C) (not (and (-> Bm (-> Cm Bm)) (-> (and B C) C))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6467.         (not (((A and B) -> B) -> (not ((C -> (D -> C)) and ((A and B) -> B))))), M:tm-153, m:tm-179, u:((A (-> (-> (and B C) C) (not (and (-> Bm (-> Cm Bm)) (-> (and B C) C))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-6468
in-theory        6468
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6468.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-147, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6469
in-theory        6469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6469.         ((A -> ((B and C) -> B)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-134, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6470
in-theory        6470
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not ((C -> (D -> C)) and ((A and B) -> A)))))
theorem-size     19
proof            (modus-ponens tm-130 tm-179 ((A (-> (-> (and B C) B) (not (and (-> Bm (-> Cm Bm)) (-> (and B C) B))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6470.         (not (((A and B) -> A) -> (not ((C -> (D -> C)) and ((A and B) -> A))))), M:tm-130, m:tm-179, u:((A (-> (-> (and B C) B) (not (and (-> Bm (-> Cm Bm)) (-> (and B C) B))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-6471
in-theory        6471
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6471.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-125, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6472
in-theory        6472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6472.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E))), M:tm-113, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6473
in-theory        6473
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D -> (E -> D)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))))
theorem-size     35
proof            (modus-ponens tm-109 tm-179 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (and (-> Bm (-> Cm Bm)) (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-5)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6473.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D -> (E -> D)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))), M:tm-109, m:tm-179, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (and (-> Bm (-> Cm Bm)) (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-6474
in-theory        6474
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6474.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-105, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6475
in-theory        6475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6475.         (((A -> B) -> (A -> A)) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C))), M:tm-95, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6476
in-theory        6476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> B)) and A))) -> (D -> (not A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6476.         ((A -> (not ((B -> (C -> B)) and A))) -> (D -> (not A))), M:tm-84, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-6477
in-theory        6477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6477.         ((A -> (B -> (C -> B))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-83, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6478
in-theory        6478
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not ((C -> (D -> C)) and (A -> (B -> A))))))
theorem-size     19
proof            (modus-ponens tm-79 tm-179 ((A (-> (-> B (-> C B)) (not (and (-> Bm (-> Cm Bm)) (-> B (-> C B)))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6478.         (not ((A -> (B -> A)) -> (not ((C -> (D -> C)) and (A -> (B -> A)))))), M:tm-79, m:tm-179, u:((A (-> (-> B (-> C B)) (not (and (-> Bm (-> Cm Bm)) (-> B (-> C B)))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-6479
in-theory        6479
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not ((C -> (D -> C)) and B))) -> (not B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6479.         (((not (not A)) -> A) and ((B -> (not ((C -> (D -> C)) and B))) -> (not B))), M:tm-76, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6480
in-theory        6480
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not ((B -> (C -> B)) and A))))) or (A -> (not ((B -> (C -> B)) and A)))) -> (not A))
theorem-size     26
proof            (modus-ponens tm-73 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-5 tm-1)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6480.         (((not (not (A -> (not ((B -> (C -> B)) and A))))) or (A -> (not ((B -> (C -> B)) and A)))) -> (not A)), M:tm-73, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-6481
in-theory        6481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6481.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C))), M:tm-69, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6482
in-theory        6482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6482.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-54, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6483
in-theory        6483
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not ((C -> (D -> C)) and B)))) or (B -> (not ((C -> (D -> C)) and B)))) -> (not B))
theorem-size     26
proof            (modus-ponens tm-47 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-5 tm-1)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6483.         (((A and (B -> (not ((C -> (D -> C)) and B)))) or (B -> (not ((C -> (D -> C)) and B)))) -> (not B)), M:tm-47, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-6484
in-theory        6484
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not ((B -> (C -> B)) and A))) and D) or (A -> (not ((B -> (C -> B)) and A)))) -> (not A))
theorem-size     26
proof            (modus-ponens tm-46 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-5 tm-1)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6484.         ((((A -> (not ((B -> (C -> B)) and A))) and D) or (A -> (not ((B -> (C -> B)) and A)))) -> (not A)), M:tm-46, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-6485
in-theory        6485
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A -> (B -> A)) and C)) or (C -> (not ((A -> (B -> A)) and C)))) -> (not C))
theorem-size     22
proof            (modus-ponens tm-44 tm-179 ((A Am) (B (not (and (-> Bm (-> Cm Bm)) Am))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-5)
proof-size       98
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6485.         (((not ((A -> (B -> A)) and C)) or (C -> (not ((A -> (B -> A)) and C)))) -> (not C)), M:tm-44, m:tm-179, u:((A Am) (B (not (and (-> Bm (-> Cm Bm)) Am))) (C (not Am)))
================================================================
tm-name          tm-6486
in-theory        6486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6486.         ((A -> (B or A)) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C))), M:tm-42, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6487
in-theory        6487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6487.         ((A -> (A or B)) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C))), M:tm-32, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6488
in-theory        6488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> B)) and A))) -> ((A -> (not ((B -> (C -> B)) and A))) and (not A)))
theorem-size     24
proof            (modus-ponens tm-24 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       98
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6488.         ((A -> (not ((B -> (C -> B)) and A))) -> ((A -> (not ((B -> (C -> B)) and A))) and (not A))), M:tm-24, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-6489
in-theory        6489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6489.         ((A -> (B -> (A and B))) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C))), M:tm-23, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6490
in-theory        6490
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6490.         (((A and B) -> B) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C))), M:tm-22, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6491
in-theory        6491
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6491.         (((A and B) -> A) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C))), M:tm-21, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6492
in-theory        6492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6492.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-20, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6493
in-theory        6493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6493.         ((A -> (B -> A)) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C))), M:tm-19, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6494
in-theory        6494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> B)) and A))) -> (A -> (not ((B -> (C -> B)) and A))))
theorem-size     21
proof            (modus-ponens tm-12 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6494.         ((A -> (not ((B -> (C -> B)) and A))) -> (A -> (not ((B -> (C -> B)) and A)))), M:tm-12, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-6495
in-theory        6495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (C -> B)) and A)))))
theorem-size     26
proof            (modus-ponens tm-9 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-9 tm-5 tm-1)
proof-size       82
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6495.         (((A -> (not ((B -> (C -> B)) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (C -> B)) and A))))), M:tm-9, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-6496
in-theory        6496
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not ((C -> (D -> C)) and A))) or (not A)) -> B))
theorem-size     20
proof            (modus-ponens tm-8 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-5 tm-1)
proof-size       78
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6496.         (((not A) -> B) -> (((A -> (not ((C -> (D -> C)) and A))) or (not A)) -> B)), M:tm-8, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-6497
in-theory        6497
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not ((C -> (D -> C)) and B))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-5 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6497.         (A or ((B -> (not ((C -> (D -> C)) and B))) -> (not B))), M:tm-7, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6498
in-theory        6498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-5 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6498.         (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) or D), M:tm-6, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6499
in-theory        6499
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not ((C -> (D -> C)) and B))) -> (not B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6499.         (A -> (((B -> (not ((C -> (D -> C)) and B))) -> (not B)) and A)), M:tm-5, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6500
in-theory        6500
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not ((C -> (D -> C)) and B))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6500.         (A -> ((B -> (not ((C -> (D -> C)) and B))) -> (not B))), M:tm-1, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6501
in-theory        6501
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> ((B -> (C -> B)) and A)))
theorem-size     19
proof            (modus-ponens tm-180 tm-1 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6501.         ((A or ((B -> (C -> B)) and A)) -> (D -> ((B -> (C -> B)) and A))), M:tm-180, m:tm-1, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6502
in-theory        6502
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (B -> (C -> B)))
theorem-size     15
proof            (modus-ponens tm-180 tm-3 ((Am (-> A (-> B A))) (C Bm) (D (-> A (-> B A)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-6502.         ((A or ((B -> (C -> B)) and A)) -> (B -> (C -> B))), M:tm-180, m:tm-3, u:((Am (-> A (-> B A))) (C Bm) (D (-> A (-> B A))))
================================================================
tm-name          tm-6503
in-theory        6503
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> A)
theorem-size     11
proof            (modus-ponens tm-180 tm-4 ((Am (-> A (-> B A))) (C Bm) (D Bm)))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-6503.         ((A or ((B -> (C -> B)) and A)) -> A), M:tm-180, m:tm-4, u:((Am (-> A (-> B A))) (C Bm) (D Bm))
================================================================
tm-name          tm-6504
in-theory        6504
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> (((B -> (C -> B)) and A) and D)))
theorem-size     21
proof            (modus-ponens tm-180 tm-5 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (and (-> A (-> B A)) C) Bm)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6504.         ((A or ((B -> (C -> B)) and A)) -> (D -> (((B -> (C -> B)) and A) and D))), M:tm-180, m:tm-5, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (and (-> A (-> B A)) C) Bm))))
================================================================
tm-name          tm-6505
in-theory        6505
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) or D))
theorem-size     19
proof            (modus-ponens tm-180 tm-6 ((Am (and (-> A (-> B A)) C)) (D (or (and (-> A (-> B A)) C) Bm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-6505.         ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) or D)), M:tm-180, m:tm-6, u:((Am (and (-> A (-> B A)) C)) (D (or (and (-> A (-> B A)) C) Bm)))
================================================================
tm-name          tm-6506
in-theory        6506
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D or ((B -> (C -> B)) and A)))
theorem-size     19
proof            (modus-ponens tm-180 tm-7 ((Am (and (-> A (-> B A)) C)) (D (or Bm (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6506.         ((A or ((B -> (C -> B)) and A)) -> (D or ((B -> (C -> B)) and A))), M:tm-180, m:tm-7, u:((Am (and (-> A (-> B A)) C)) (D (or Bm (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6507
in-theory        6507
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-180 tm-11 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6507.         ((A or ((B -> (C -> B)) and A)) -> (D -> (E -> D))), M:tm-180, m:tm-11, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-6508
in-theory        6508
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-180 tm-14 ((Am (and (-> A (-> B A)) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6508.         ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-180, m:tm-14, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-6509
in-theory        6509
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-180 tm-16 ((Am (and (-> A (-> B A)) C)) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6509.         ((A or ((B -> (C -> B)) and A)) -> ((D and E) -> D)), M:tm-180, m:tm-16, u:((Am (and (-> A (-> B A)) C)) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-6510
in-theory        6510
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-180 tm-18 ((Am (and (-> A (-> B A)) C)) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6510.         ((A or ((B -> (C -> B)) and A)) -> ((D and E) -> E)), M:tm-180, m:tm-18, u:((Am (and (-> A (-> B A)) C)) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-6511
in-theory        6511
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> D)) and ((B -> (C -> B)) and A)))
theorem-size     23
proof            (modus-ponens tm-180 tm-19 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> Cm Bm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6511.         ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> D)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-19, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> Cm Bm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6512
in-theory        6512
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (C -> B)) and A)))
theorem-size     31
proof            (modus-ponens tm-180 tm-20 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6512.         ((A or ((B -> (C -> B)) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-20, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6513
in-theory        6513
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D and E) -> D) and ((B -> (C -> B)) and A)))
theorem-size     23
proof            (modus-ponens tm-180 tm-21 ((Am (and (-> A (-> B A)) C)) (D (and (-> (and Bm Cm) Bm) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6513.         ((A or ((B -> (C -> B)) and A)) -> (((D and E) -> D) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-21, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (and Bm Cm) Bm) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6514
in-theory        6514
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D and E) -> E) and ((B -> (C -> B)) and A)))
theorem-size     23
proof            (modus-ponens tm-180 tm-22 ((Am (and (-> A (-> B A)) C)) (D (and (-> (and Bm Cm) Cm) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6514.         ((A or ((B -> (C -> B)) and A)) -> (((D and E) -> E) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-22, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (and Bm Cm) Cm) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6515
in-theory        6515
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> (D and E))) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-23 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6515.         ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> (D and E))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-23, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6516
in-theory        6516
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-180 tm-25 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6516.         ((A or ((B -> (C -> B)) and A)) -> (D -> (E -> (D and E)))), M:tm-180, m:tm-25, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-6517
in-theory        6517
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (D or E)) and ((B -> (C -> B)) and A)))
theorem-size     23
proof            (modus-ponens tm-180 tm-32 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (or Bm Cm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6517.         ((A or ((B -> (C -> B)) and A)) -> ((D -> (D or E)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-32, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (or Bm Cm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6518
in-theory        6518
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-180 tm-33 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6518.         ((A or ((B -> (C -> B)) and A)) -> (D -> (D or E))), M:tm-180, m:tm-33, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-6519
in-theory        6519
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (E or D)) and ((B -> (C -> B)) and A)))
theorem-size     23
proof            (modus-ponens tm-180 tm-42 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (or Cm Bm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6519.         ((A or ((B -> (C -> B)) and A)) -> ((D -> (E or D)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-42, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (or Cm Bm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6520
in-theory        6520
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-180 tm-43 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6520.         ((A or ((B -> (C -> B)) and A)) -> (D -> (E or D))), M:tm-180, m:tm-43, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-6521
in-theory        6521
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> (C -> B)) and A)))
theorem-size     31
proof            (modus-ponens tm-180 tm-54 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6521.         ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-54, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6522
in-theory        6522
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-180 tm-56 ((Am (and (-> A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6522.         ((A or ((B -> (C -> B)) and A)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-180, m:tm-56, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-6523
in-theory        6523
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B -> (C -> B)) and A)))
theorem-size     29
proof            (modus-ponens tm-180 tm-69 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6523.         ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-69, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6524
in-theory        6524
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-180 tm-71 ((Am (and (-> A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6524.         ((A or ((B -> (C -> B)) and A)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-180, m:tm-71, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-6525
in-theory        6525
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((not (not D)) -> D) and ((B -> (C -> B)) and A)))
theorem-size     23
proof            (modus-ponens tm-180 tm-76 ((Am (and (-> A (-> B A)) C)) (D (and (-> (not (not Bm)) Bm) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6525.         ((A or ((B -> (C -> B)) and A)) -> (((not (not D)) -> D) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-76, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (not (not Bm)) Bm) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6526
in-theory        6526
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-180 tm-78 ((Am (and (-> A (-> B A)) C)) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-5 tm-1 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6526.         ((A or ((B -> (C -> B)) and A)) -> ((not (not D)) -> D)), M:tm-180, m:tm-78, u:((Am (and (-> A (-> B A)) C)) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-6527
in-theory        6527
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> (F -> E))) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-83 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6527.         ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> (F -> E))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-83, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6528
in-theory        6528
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-180 tm-85 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6528.         ((A or ((B -> (C -> B)) and A)) -> (D -> (E -> (F -> E)))), M:tm-180, m:tm-85, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6529
in-theory        6529
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((B -> (C -> B)) and A))
theorem-size     17
proof            (modus-ponens tm-180 tm-86 ((Am (and (-> A (-> B A)) C)) (D (and (-> A (-> B A)) C))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6529.         ((A or ((B -> (C -> B)) and A)) -> ((B -> (C -> B)) and A)), M:tm-180, m:tm-86, u:((Am (and (-> A (-> B A)) C)) (D (and (-> A (-> B A)) C)))
================================================================
tm-name          tm-6530
in-theory        6530
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> (D -> D)) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-95 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6530.         ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> (D -> D)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-95, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6531
in-theory        6531
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-180 tm-97 ((Am (and (-> A (-> B A)) C)) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6531.         ((A or ((B -> (C -> B)) and A)) -> ((D -> E) -> (D -> D))), M:tm-180, m:tm-97, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-6532
in-theory        6532
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B -> (C -> B)) and A)))
theorem-size     37
proof            (modus-ponens tm-180 tm-105 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6532.         ((A or ((B -> (C -> B)) and A)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-105, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6533
in-theory        6533
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-180 tm-107 ((Am (and (-> A (-> B A)) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6533.         ((A or ((B -> (C -> B)) and A)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-180, m:tm-107, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-6534
in-theory        6534
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (C -> B)) and A)))
theorem-size     33
proof            (modus-ponens tm-180 tm-113 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6534.         ((A or ((B -> (C -> B)) and A)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-113, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6535
in-theory        6535
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-180 tm-115 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6535.         ((A or ((B -> (C -> B)) and A)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-180, m:tm-115, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6536
in-theory        6536
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A -> (B -> A)) and A)) -> (B -> A))
theorem-size     13
proof            (modus-ponens tm-180 tm-116 ((A Am) (Bm (-> B Am)) (C Am) (D (-> B Am))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-6536.         ((A or ((A -> (B -> A)) and A)) -> (B -> A)), M:tm-180, m:tm-116, u:((A Am) (Bm (-> B Am)) (C Am) (D (-> B Am)))
================================================================
tm-name          tm-6537
in-theory        6537
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> B)) -> (D -> (B -> (C -> B)))) and A)) -> (D -> (B -> (C -> B))))
theorem-size     25
proof            (modus-ponens tm-180 tm-117 ((A (-> Am (-> Bm Am))) (Cm (-> B (-> Am (-> Bm Am)))) (C Dm) (D (-> B (-> Am (-> Bm Am))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-6537.         ((A or (((B -> (C -> B)) -> (D -> (B -> (C -> B)))) and A)) -> (D -> (B -> (C -> B)))), M:tm-180, m:tm-117, u:((A (-> Am (-> Bm Am))) (Cm (-> B (-> Am (-> Bm Am)))) (C Dm) (D (-> B (-> Am (-> Bm Am)))))
================================================================
tm-name          tm-6538
in-theory        6538
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and A)) -> (E -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     49
proof            (modus-ponens tm-180 tm-118 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C Em) (D (-> B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6538.         ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and A)) -> (E -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-180, m:tm-118, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C Em) (D (-> B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-6539
in-theory        6539
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B -> (C -> B)) and A)))
theorem-size     33
proof            (modus-ponens tm-180 tm-125 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6539.         ((A or ((B -> (C -> B)) and A)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-125, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6540
in-theory        6540
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-180 tm-127 ((Am (and (-> A (-> B A)) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6540.         ((A or ((B -> (C -> B)) and A)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-180, m:tm-127, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-6541
in-theory        6541
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> B) -> (D -> ((B and C) -> B))) and A)) -> (D -> ((B and C) -> B)))
theorem-size     25
proof            (modus-ponens tm-180 tm-128 ((A (-> (and Am Bm) Am)) (Cm (-> B (-> (and Am Bm) Am))) (C Dm) (D (-> B (-> (and Am Bm) Am)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-6541.         ((A or ((((B and C) -> B) -> (D -> ((B and C) -> B))) and A)) -> (D -> ((B and C) -> B))), M:tm-180, m:tm-128, u:((A (-> (and Am Bm) Am)) (Cm (-> B (-> (and Am Bm) Am))) (C Dm) (D (-> B (-> (and Am Bm) Am))))
================================================================
tm-name          tm-6542
in-theory        6542
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> ((E and F) -> E)) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-134 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6542.         ((A or ((B -> (C -> B)) and A)) -> ((D -> ((E and F) -> E)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-134, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6543
in-theory        6543
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-180 tm-136 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6543.         ((A or ((B -> (C -> B)) and A)) -> (D -> ((E and F) -> E))), M:tm-180, m:tm-136, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6544
in-theory        6544
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) or ((A -> (B -> A)) and ((A -> (B -> A)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-180 tm-137 ((Am (-> A (-> B A))) (C (-> (-> A (-> B A)) Bm)) (D Bm)))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-6544.         ((((A -> (B -> A)) -> C) or ((A -> (B -> A)) and ((A -> (B -> A)) -> C))) -> C), M:tm-180, m:tm-137, u:((Am (-> A (-> B A))) (C (-> (-> A (-> B A)) Bm)) (D Bm))
================================================================
tm-name          tm-6545
in-theory        6545
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) or ((D -> (E -> D)) and ((A -> (B -> A)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-180 tm-138 ((Am (-> A (-> B A))) (C (-> (-> Bm (-> Cm Bm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-6545.         ((((A -> (B -> A)) -> C) or ((D -> (E -> D)) and ((A -> (B -> A)) -> C))) -> C), M:tm-180, m:tm-138, u:((Am (-> A (-> B A))) (C (-> (-> Bm (-> Cm Bm)) Dm)) (D Dm))
================================================================
tm-name          tm-6546
in-theory        6546
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or ((E -> (F -> E)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D)
theorem-size     39
proof            (modus-ponens tm-180 tm-139 ((Am (-> A (-> B A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (D Em)))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6546.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or ((E -> (F -> E)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D), M:tm-180, m:tm-139, u:((Am (-> A (-> B A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (D Em))
================================================================
tm-name          tm-6547
in-theory        6547
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) or ((D -> (E -> D)) and (((A and B) -> A) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-180 tm-140 ((Am (-> A (-> B A))) (C (-> (-> (and Bm Cm) Bm) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-6547.         (((((A and B) -> A) -> C) or ((D -> (E -> D)) and (((A and B) -> A) -> C))) -> C), M:tm-180, m:tm-140, u:((Am (-> A (-> B A))) (C (-> (-> (and Bm Cm) Bm) Dm)) (D Dm))
================================================================
tm-name          tm-6548
in-theory        6548
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B -> (C -> B)) and A)))
theorem-size     33
proof            (modus-ponens tm-180 tm-147 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6548.         ((A or ((B -> (C -> B)) and A)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-147, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6549
in-theory        6549
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-180 tm-149 ((Am (and (-> A (-> B A)) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6549.         ((A or ((B -> (C -> B)) and A)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-180, m:tm-149, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-6550
in-theory        6550
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) or ((D -> (E -> D)) and (((A and B) -> B) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-180 tm-150 ((Am (-> A (-> B A))) (C (-> (-> (and Bm Cm) Cm) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-6550.         (((((A and B) -> B) -> C) or ((D -> (E -> D)) and (((A and B) -> B) -> C))) -> C), M:tm-180, m:tm-150, u:((Am (-> A (-> B A))) (C (-> (-> (and Bm Cm) Cm) Dm)) (D Dm))
================================================================
tm-name          tm-6551
in-theory        6551
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> C) -> (D -> ((B and C) -> C))) and A)) -> (D -> ((B and C) -> C)))
theorem-size     25
proof            (modus-ponens tm-180 tm-151 ((A (-> (and Am Bm) Bm)) (Cm (-> B (-> (and Am Bm) Bm))) (C Dm) (D (-> B (-> (and Am Bm) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-6551.         ((A or ((((B and C) -> C) -> (D -> ((B and C) -> C))) and A)) -> (D -> ((B and C) -> C))), M:tm-180, m:tm-151, u:((A (-> (and Am Bm) Bm)) (Cm (-> B (-> (and Am Bm) Bm))) (C Dm) (D (-> B (-> (and Am Bm) Bm))))
================================================================
tm-name          tm-6552
in-theory        6552
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> ((E and F) -> F)) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-157 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6552.         ((A or ((B -> (C -> B)) and A)) -> ((D -> ((E and F) -> F)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-157, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6553
in-theory        6553
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-180 tm-159 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6553.         ((A or ((B -> (C -> B)) and A)) -> (D -> ((E and F) -> F))), M:tm-180, m:tm-159, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6554
in-theory        6554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-157 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6554.         ((A -> ((B and C) -> C)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-157, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6555
in-theory        6555
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> B)) and D) -> D)) -> ((D or ((B -> (C -> B)) and D)) -> D))
theorem-size     23
proof            (modus-ponens tm-154 tm-180 ((A (-> Am (-> Bm Am))) (Dm Cm) (B Cm) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Cm))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6555.         ((A or (((B -> (C -> B)) and D) -> D)) -> ((D or ((B -> (C -> B)) and D)) -> D)), M:tm-154, m:tm-180, u:((A (-> Am (-> Bm Am))) (Dm Cm) (B Cm) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Cm)))
================================================================
tm-name          tm-6556
in-theory        6556
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-147 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6556.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-147, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6557
in-theory        6557
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and (C -> D)) -> C) or (((A -> (B -> A)) and (C -> D)) -> D)) -> (((C -> D) or ((A -> (B -> A)) and (C -> D))) -> D))
theorem-size     39
proof            (modus-ponens tm-144 tm-180 ((A (-> Am (-> Bm Am))) (Cm (-> B Dm)) (C Dm) (D (-> (or (-> B Dm) (and (-> Am (-> Bm Am)) (-> B Dm))) Dm))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6557.         (((((A -> (B -> A)) and (C -> D)) -> C) or (((A -> (B -> A)) and (C -> D)) -> D)) -> (((C -> D) or ((A -> (B -> A)) and (C -> D))) -> D)), M:tm-144, m:tm-180, u:((A (-> Am (-> Bm Am))) (Cm (-> B Dm)) (C Dm) (D (-> (or (-> B Dm) (and (-> Am (-> Bm Am)) (-> B Dm))) Dm)))
================================================================
tm-name          tm-6558
in-theory        6558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-134 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6558.         ((A -> ((B and C) -> B)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-134, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6559
in-theory        6559
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> B)) and D) -> (B -> (C -> B)))) -> ((D or ((B -> (C -> B)) and D)) -> (B -> (C -> B))))
theorem-size     31
proof            (modus-ponens tm-131 tm-180 ((Dm (-> Am (-> Bm Am))) (B Cm) (A (-> Am (-> Bm Am))) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (-> Am (-> Bm Am))))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6559.         ((A or (((B -> (C -> B)) and D) -> (B -> (C -> B)))) -> ((D or ((B -> (C -> B)) and D)) -> (B -> (C -> B)))), M:tm-131, m:tm-180, u:((Dm (-> Am (-> Bm Am))) (B Cm) (A (-> Am (-> Bm Am))) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (-> Am (-> Bm Am)))))
================================================================
tm-name          tm-6560
in-theory        6560
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-125 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6560.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-125, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6561
in-theory        6561
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> A) or (((A -> (B -> A)) and C) -> (B -> A))) -> ((C or ((A -> (B -> A)) and C)) -> (B -> A)))
theorem-size     35
proof            (modus-ponens tm-122 tm-180 ((A Am) (Dm (-> Bm Am)) (C Cm) (B (-> Bm Am)) (D (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6561.         (((((A -> (B -> A)) and C) -> A) or (((A -> (B -> A)) and C) -> (B -> A))) -> ((C or ((A -> (B -> A)) and C)) -> (B -> A))), M:tm-122, m:tm-180, u:((A Am) (Dm (-> Bm Am)) (C Cm) (B (-> Bm Am)) (D (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (-> Bm Am))))
================================================================
tm-name          tm-6562
in-theory        6562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and C) -> (D -> E)) -> (((C or ((A -> (B -> A)) and C)) -> D) -> ((C or ((A -> (B -> A)) and C)) -> E)))
theorem-size     35
proof            (modus-ponens tm-114 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) (-> C D))) (B (or Cm (and (-> Am (-> Bm Am)) Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6562.         ((((A -> (B -> A)) and C) -> (D -> E)) -> (((C or ((A -> (B -> A)) and C)) -> D) -> ((C or ((A -> (B -> A)) and C)) -> E))), M:tm-114, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) (-> C D))) (B (or Cm (and (-> Am (-> Bm Am)) Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-6563
in-theory        6563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> E)) and G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-113 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6563.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> E)) and G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H))), M:tm-113, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6564
in-theory        6564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-105 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6564.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-105, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6565
in-theory        6565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-95 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6565.         (((A -> B) -> (A -> A)) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F))), M:tm-95, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6566
in-theory        6566
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) or (((A -> (B -> A)) and C) -> ((A -> (B -> A)) and C))) -> ((C or ((A -> (B -> A)) and C)) -> ((A -> (B -> A)) and C)))
theorem-size     43
proof            (modus-ponens tm-92 tm-180 ((Dm (and (-> Am (-> Bm Am)) Cm)) (A (and (-> Am (-> Bm Am)) Cm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (and (-> Am (-> Bm Am)) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6566.         (((((A -> (B -> A)) and C) -> D) or (((A -> (B -> A)) and C) -> ((A -> (B -> A)) and C))) -> ((C or ((A -> (B -> A)) and C)) -> ((A -> (B -> A)) and C))), M:tm-92, m:tm-180, u:((Dm (and (-> Am (-> Bm Am)) Cm)) (A (and (-> Am (-> Bm Am)) Cm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (and (-> Am (-> Bm Am)) Cm))))
================================================================
tm-name          tm-6567
in-theory        6567
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and C) -> D) -> (E -> ((C or ((A -> (B -> A)) and C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-84 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6567.         ((((A -> (B -> A)) and C) -> D) -> (E -> ((C or ((A -> (B -> A)) and C)) -> D))), M:tm-84, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-6568
in-theory        6568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-83 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6568.         ((A -> (B -> (C -> B))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-83, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6569
in-theory        6569
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> B)) and D) -> (E -> ((B -> (C -> B)) and D)))) -> ((D or ((B -> (C -> B)) and D)) -> (E -> ((B -> (C -> B)) and D))))
theorem-size     39
proof            (modus-ponens tm-80 tm-180 ((A (and (-> Am (-> Bm Am)) Cm)) (Dm (-> B (and (-> Am (-> Bm Am)) Cm))) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (-> B (and (-> Am (-> Bm Am)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6569.         ((A or (((B -> (C -> B)) and D) -> (E -> ((B -> (C -> B)) and D)))) -> ((D or ((B -> (C -> B)) and D)) -> (E -> ((B -> (C -> B)) and D)))), M:tm-80, m:tm-180, u:((A (and (-> Am (-> Bm Am)) Cm)) (Dm (-> B (and (-> Am (-> Bm Am)) Cm))) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (-> B (and (-> Am (-> Bm Am)) Cm)))))
================================================================
tm-name          tm-6570
in-theory        6570
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C -> B)) and D) -> E) -> ((D or ((B -> (C -> B)) and D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-76 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6570.         (((not (not A)) -> A) and ((((B -> (C -> B)) and D) -> E) -> ((D or ((B -> (C -> B)) and D)) -> E))), M:tm-76, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6571
in-theory        6571
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (B -> A)) and C) -> D))) or (((A -> (B -> A)) and C) -> D)) -> ((C or ((A -> (B -> A)) and C)) -> D))
theorem-size     33
proof            (modus-ponens tm-73 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-5 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6571.         (((not (not (((A -> (B -> A)) and C) -> D))) or (((A -> (B -> A)) and C) -> D)) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-73, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-6572
in-theory        6572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-69 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6572.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F))), M:tm-69, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6573
in-theory        6573
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and C) -> (C or ((A -> (B -> A)) and C))) -> ((((A -> (B -> A)) and C) or (C or ((A -> (B -> A)) and C))) -> (C or ((A -> (B -> A)) and C))))
theorem-size     45
proof            (modus-ponens tm-55 tm-180 ((A (and (-> Am (-> Bm Am)) Cm)) (Dm (or Cm (and (-> Am (-> Bm Am)) Cm))) (B (or Cm (and (-> Am (-> Bm Am)) Cm))) (C (or Cm (and (-> Am (-> Bm Am)) Cm)))))
axioms-used      (tm-2 tm-8 tm-5 tm-1)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6573.         ((((A -> (B -> A)) and C) -> (C or ((A -> (B -> A)) and C))) -> ((((A -> (B -> A)) and C) or (C or ((A -> (B -> A)) and C))) -> (C or ((A -> (B -> A)) and C)))), M:tm-55, m:tm-180, u:((A (and (-> Am (-> Bm Am)) Cm)) (Dm (or Cm (and (-> Am (-> Bm Am)) Cm))) (B (or Cm (and (-> Am (-> Bm Am)) Cm))) (C (or Cm (and (-> Am (-> Bm Am)) Cm))))
================================================================
tm-name          tm-6574
in-theory        6574
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-54 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6574.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-54, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6575
in-theory        6575
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> B)) and D) -> (A and ((B -> (C -> B)) and D)))) -> ((D or ((B -> (C -> B)) and D)) -> (A and ((B -> (C -> B)) and D))))
theorem-size     39
proof            (modus-ponens tm-48 tm-180 ((A (and (-> Am (-> Bm Am)) Cm)) (Dm (and B (and (-> Am (-> Bm Am)) Cm))) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (and B (and (-> Am (-> Bm Am)) Cm))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6575.         ((A or (((B -> (C -> B)) and D) -> (A and ((B -> (C -> B)) and D)))) -> ((D or ((B -> (C -> B)) and D)) -> (A and ((B -> (C -> B)) and D)))), M:tm-48, m:tm-180, u:((A (and (-> Am (-> Bm Am)) Cm)) (Dm (and B (and (-> Am (-> Bm Am)) Cm))) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (and B (and (-> Am (-> Bm Am)) Cm)))))
================================================================
tm-name          tm-6576
in-theory        6576
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> B)) and D) -> E)) or (((B -> (C -> B)) and D) -> E)) -> ((D or ((B -> (C -> B)) and D)) -> E))
theorem-size     33
proof            (modus-ponens tm-47 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-5 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6576.         (((A and (((B -> (C -> B)) and D) -> E)) or (((B -> (C -> B)) and D) -> E)) -> ((D or ((B -> (C -> B)) and D)) -> E)), M:tm-47, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-6577
in-theory        6577
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> A)) and C) -> D) and E) or (((A -> (B -> A)) and C) -> D)) -> ((C or ((A -> (B -> A)) and C)) -> D))
theorem-size     33
proof            (modus-ponens tm-46 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6577.         ((((((A -> (B -> A)) and C) -> D) and E) or (((A -> (B -> A)) and C) -> D)) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-46, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-6578
in-theory        6578
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> B)) and D) -> A)) -> ((D or ((B -> (C -> B)) and D)) -> A))
theorem-size     23
proof            (modus-ponens tm-44 tm-180 ((A (and (-> Am (-> Bm Am)) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6578.         ((A or (((B -> (C -> B)) and D) -> A)) -> ((D or ((B -> (C -> B)) and D)) -> A)), M:tm-44, m:tm-180, u:((A (and (-> Am (-> Bm Am)) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-6579
in-theory        6579
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-42 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6579.         ((A -> (B or A)) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F))), M:tm-42, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6580
in-theory        6580
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-32 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6580.         ((A -> (A or B)) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F))), M:tm-32, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6581
in-theory        6581
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and C) -> D) -> ((((A -> (B -> A)) and C) -> D) and ((C or ((A -> (B -> A)) and C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-24 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6581.         ((((A -> (B -> A)) and C) -> D) -> ((((A -> (B -> A)) and C) -> D) and ((C or ((A -> (B -> A)) and C)) -> D))), M:tm-24, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-6582
in-theory        6582
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-23 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6582.         ((A -> (B -> (A and B))) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F))), M:tm-23, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6583
in-theory        6583
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-22 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6583.         (((A and B) -> B) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F))), M:tm-22, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6584
in-theory        6584
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-21 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6584.         (((A and B) -> A) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F))), M:tm-21, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6585
in-theory        6585
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-20 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6585.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-20, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6586
in-theory        6586
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-19 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6586.         ((A -> (B -> A)) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F))), M:tm-19, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6587
in-theory        6587
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and C) -> D) -> (((A -> (B -> A)) and C) -> D))
theorem-size     19
proof            (modus-ponens tm-12 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6587.         ((((A -> (B -> A)) and C) -> D) -> (((A -> (B -> A)) and C) -> D)), M:tm-12, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-6588
in-theory        6588
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> (not ((C or ((A -> (B -> A)) and C)) -> D))) -> (not (((A -> (B -> A)) and C) -> D)))
theorem-size     33
proof            (modus-ponens tm-9 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-5 tm-1)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6588.         (((((A -> (B -> A)) and C) -> D) -> (not ((C or ((A -> (B -> A)) and C)) -> D))) -> (not (((A -> (B -> A)) and C) -> D))), M:tm-9, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-6589
in-theory        6589
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B -> (C -> B)) and A)) -> D) -> E) -> (((((B -> (C -> B)) and A) -> D) or ((A or ((B -> (C -> B)) and A)) -> D)) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6589.         ((((A or ((B -> (C -> B)) and A)) -> D) -> E) -> (((((B -> (C -> B)) and A) -> D) or ((A or ((B -> (C -> B)) and A)) -> D)) -> E)), M:tm-8, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-6590
in-theory        6590
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> (C -> B)) and D) -> E) -> ((D or ((B -> (C -> B)) and D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-7 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-5 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6590.         (A or ((((B -> (C -> B)) and D) -> E) -> ((D or ((B -> (C -> B)) and D)) -> E))), M:tm-7, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6591
in-theory        6591
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-5 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6591.         (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) or E), M:tm-6, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6592
in-theory        6592
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> B)) and D) -> E) -> ((D or ((B -> (C -> B)) and D)) -> E)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6592.         (A -> (((((B -> (C -> B)) and D) -> E) -> ((D or ((B -> (C -> B)) and D)) -> E)) and A)), M:tm-5, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6593
in-theory        6593
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> (C or ((A -> (B -> A)) and C))) -> ((((A -> (B -> A)) and C) -> D) -> D))
theorem-size     31
proof            (modus-ponens tm-2 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (or Cm (and (-> Am (-> Bm Am)) Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-5 tm-1)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6593.         (((((A -> (B -> A)) and C) -> D) -> (C or ((A -> (B -> A)) and C))) -> ((((A -> (B -> A)) and C) -> D) -> D)), M:tm-2, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (or Cm (and (-> Am (-> Bm Am)) Cm))) (C Dm))
================================================================
tm-name          tm-6594
in-theory        6594
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> B)) and D) -> E) -> ((D or ((B -> (C -> B)) and D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-1 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6594.         (A -> ((((B -> (C -> B)) and D) -> E) -> ((D or ((B -> (C -> B)) and D)) -> E))), M:tm-1, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6595
in-theory        6595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-157 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6595.         ((A -> ((B and C) -> C)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-157, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6596
in-theory        6596
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-147 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6596.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-147, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6597
in-theory        6597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-134 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6597.         ((A -> ((B and C) -> B)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-134, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6598
in-theory        6598
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-125 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6598.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-125, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6599
in-theory        6599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-113 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6599.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H -> G)) and F)))), M:tm-113, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6600
in-theory        6600
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     31
proof            (modus-ponens tm-105 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6600.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-105, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6601
in-theory        6601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-95 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6601.         (((A -> B) -> (A -> A)) and (C or (D -> ((E -> (F -> E)) and D)))), M:tm-95, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6602
in-theory        6602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-83 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6602.         ((A -> (B -> (C -> B))) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-83, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6603
in-theory        6603
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> ((D -> (E -> D)) and C))))
theorem-size     17
proof            (modus-ponens tm-76 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6603.         (((not (not A)) -> A) and (B or (C -> ((D -> (E -> D)) and C)))), M:tm-76, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6604
in-theory        6604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> ((E -> (F -> E)) and D))))
theorem-size     23
proof            (modus-ponens tm-69 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6604.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> ((E -> (F -> E)) and D)))), M:tm-69, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6605
in-theory        6605
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-54 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6605.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-54, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6606
in-theory        6606
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-42 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6606.         ((A -> (B or A)) and (C or (D -> ((E -> (F -> E)) and D)))), M:tm-42, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6607
in-theory        6607
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-32 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6607.         ((A -> (A or B)) and (C or (D -> ((E -> (F -> E)) and D)))), M:tm-32, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6608
in-theory        6608
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-23 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6608.         ((A -> (B -> (A and B))) and (C or (D -> ((E -> (F -> E)) and D)))), M:tm-23, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6609
in-theory        6609
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-22 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6609.         (((A and B) -> B) and (C or (D -> ((E -> (F -> E)) and D)))), M:tm-22, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6610
in-theory        6610
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-21 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6610.         (((A and B) -> A) and (C or (D -> ((E -> (F -> E)) and D)))), M:tm-21, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6611
in-theory        6611
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-20 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6611.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-20, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6612
in-theory        6612
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-19 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6612.         ((A -> (B -> A)) and (C or (D -> ((E -> (F -> E)) and D)))), M:tm-19, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6613
in-theory        6613
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C -> ((D -> (E -> D)) and C))))
theorem-size     13
proof            (modus-ponens tm-7 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6613.         (A or (B or (C -> ((D -> (E -> D)) and C)))), M:tm-7, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6614
in-theory        6614
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-6 tm-7 tm-5 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6614.         ((A or (B -> ((C -> (D -> C)) and B))) or E), M:tm-6, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6615
in-theory        6615
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C -> ((D -> (E -> D)) and C))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6615.         (A -> ((B or (C -> ((D -> (E -> D)) and C))) and A)), M:tm-5, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6616
in-theory        6616
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C -> ((D -> (E -> D)) and C))))
theorem-size     13
proof            (modus-ponens tm-1 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-1 tm-7 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6616.         (A -> (B or (C -> ((D -> (E -> D)) and C)))), M:tm-1, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6617
in-theory        6617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-157 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6617.         ((A -> ((B and C) -> C)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-157, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6618
in-theory        6618
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-147 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6618.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-147, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6619
in-theory        6619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-134 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6619.         ((A -> ((B and C) -> B)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-134, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6620
in-theory        6620
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-125 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6620.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-125, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6621
in-theory        6621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G -> F)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-113 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6621.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G -> F)) and E)) or H)), M:tm-113, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6622
in-theory        6622
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     31
proof            (modus-ponens tm-105 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6622.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-105, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6623
in-theory        6623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> ((D -> (E -> D)) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-95 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6623.         (((A -> B) -> (A -> A)) and ((C -> ((D -> (E -> D)) and C)) or F)), M:tm-95, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6624
in-theory        6624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-83 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6624.         ((A -> (B -> (C -> B))) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-83, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6625
in-theory        6625
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> ((C -> (D -> C)) and B)) or E))
theorem-size     17
proof            (modus-ponens tm-76 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6625.         (((not (not A)) -> A) and ((B -> ((C -> (D -> C)) and B)) or E)), M:tm-76, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6626
in-theory        6626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D -> (E -> D)) and C)) or F))
theorem-size     23
proof            (modus-ponens tm-69 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6626.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D -> (E -> D)) and C)) or F)), M:tm-69, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6627
in-theory        6627
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-54 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6627.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-54, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6628
in-theory        6628
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> ((D -> (E -> D)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-42 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6628.         ((A -> (B or A)) and ((C -> ((D -> (E -> D)) and C)) or F)), M:tm-42, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6629
in-theory        6629
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> ((D -> (E -> D)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-32 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6629.         ((A -> (A or B)) and ((C -> ((D -> (E -> D)) and C)) or F)), M:tm-32, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6630
in-theory        6630
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> ((D -> (E -> D)) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-23 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6630.         ((A -> (B -> (A and B))) and ((C -> ((D -> (E -> D)) and C)) or F)), M:tm-23, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6631
in-theory        6631
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> ((D -> (E -> D)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-22 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6631.         (((A and B) -> B) and ((C -> ((D -> (E -> D)) and C)) or F)), M:tm-22, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6632
in-theory        6632
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> ((D -> (E -> D)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-21 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6632.         (((A and B) -> A) and ((C -> ((D -> (E -> D)) and C)) or F)), M:tm-21, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6633
in-theory        6633
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-20 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6633.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-20, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6634
in-theory        6634
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> ((D -> (E -> D)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-19 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6634.         ((A -> (B -> A)) and ((C -> ((D -> (E -> D)) and C)) or F)), M:tm-19, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6635
in-theory        6635
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> ((C -> (D -> C)) and B)) or E))
theorem-size     13
proof            (modus-ponens tm-7 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-7 tm-6 tm-5 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6635.         (A or ((B -> ((C -> (D -> C)) and B)) or E)), M:tm-7, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6636
in-theory        6636
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6636.         (((A -> ((B -> (C -> B)) and A)) or D) or E), M:tm-6, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6637
in-theory        6637
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> ((C -> (D -> C)) and B)) or E) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6637.         (A -> (((B -> ((C -> (D -> C)) and B)) or E) and A)), M:tm-5, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6638
in-theory        6638
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D -> C)) and B)) or E))
theorem-size     13
proof            (modus-ponens tm-1 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-1 tm-6 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6638.         (A -> ((B -> ((C -> (D -> C)) and B)) or E)), M:tm-1, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6639
in-theory        6639
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-183 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6639.         ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> D))), M:tm-183, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-6640
in-theory        6640
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6640.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-183, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-6641
in-theory        6641
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-183 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-6641.         ((A -> ((B -> (C -> B)) and A)) and ((D and E) -> D)), M:tm-183, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-6642
in-theory        6642
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-183 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-6642.         ((A -> ((B -> (C -> B)) and A)) and ((D and E) -> E)), M:tm-183, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-6643
in-theory        6643
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-183 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6643.         ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (D and E)))), M:tm-183, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-6644
in-theory        6644
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-183 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-6644.         ((A -> ((B -> (C -> B)) and A)) and (D -> (D or E))), M:tm-183, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-6645
in-theory        6645
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-183 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6645.         ((A -> ((B -> (C -> B)) and A)) and (D -> (E or D))), M:tm-183, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-6646
in-theory        6646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6646.         ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-183, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-6647
in-theory        6647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-183 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6647.         ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-183, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-6648
in-theory        6648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-183 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-6648.         ((A -> ((B -> (C -> B)) and A)) and ((not (not D)) -> D)), M:tm-183, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-6649
in-theory        6649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-183 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6649.         ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (F -> E)))), M:tm-183, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-6650
in-theory        6650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-183 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-6650.         ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (D -> D))), M:tm-183, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-6651
in-theory        6651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-183 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6651.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-183, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-6652
in-theory        6652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6652.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-183, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-6653
in-theory        6653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-183 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6653.         ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-183, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-6654
in-theory        6654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-183 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6654.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E and F) -> E))), M:tm-183, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-6655
in-theory        6655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-183 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6655.         ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-183, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-6656
in-theory        6656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-183 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6656.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E and F) -> F))), M:tm-183, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-6657
in-theory        6657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-183 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6657.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> E)) and D))), M:tm-183, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-6658
in-theory        6658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-183 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6658.         ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-183, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-6659
in-theory        6659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-183 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6659.         ((A -> ((B -> (C -> B)) and A)) and (D -> (((E and F) -> E) and D))), M:tm-183, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-6660
in-theory        6660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-183 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6660.         ((A -> ((B -> (C -> B)) and A)) and (D -> (((E and F) -> F) and D))), M:tm-183, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-6661
in-theory        6661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6661.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-183, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-6662
in-theory        6662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-183 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6662.         ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (D -> (D and E)))), M:tm-183, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-6663
in-theory        6663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6663.         ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (F -> (E and F))))), M:tm-183, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-6664
in-theory        6664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-183 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6664.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) or F)), M:tm-183, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-6665
in-theory        6665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-183 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6665.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-183, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-6666
in-theory        6666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-183 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6666.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) or F)), M:tm-183, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-6667
in-theory        6667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-183 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6667.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) or F)), M:tm-183, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-6668
in-theory        6668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-183 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6668.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) or F)), M:tm-183, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-6669
in-theory        6669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-183 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6669.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) or F)), M:tm-183, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-6670
in-theory        6670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-183 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6670.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (E or F)) and D))), M:tm-183, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-6671
in-theory        6671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-183 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6671.         ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (E or F)))), M:tm-183, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-6672
in-theory        6672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-183 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6672.         ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (F -> E)))), M:tm-183, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-6673
in-theory        6673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6673.         ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-183, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-6674
in-theory        6674
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-183 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6674.         ((A -> ((B -> (C -> B)) and A)) and (D or ((E and F) -> E))), M:tm-183, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-6675
in-theory        6675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-183 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6675.         ((A -> ((B -> (C -> B)) and A)) and (D or ((E and F) -> F))), M:tm-183, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-6676
in-theory        6676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6676.         ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (F -> (E and F))))), M:tm-183, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-6677
in-theory        6677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-183 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6677.         ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (E or F)))), M:tm-183, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-6678
in-theory        6678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-183 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6678.         ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (F or E)))), M:tm-183, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-6679
in-theory        6679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-183 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6679.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) or F)), M:tm-183, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-6680
in-theory        6680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-183 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6680.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F or E)) and D))), M:tm-183, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-6681
in-theory        6681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-183 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6681.         ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (F or E)))), M:tm-183, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-6682
in-theory        6682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-183 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6682.         ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-183, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-6683
in-theory        6683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-183 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6683.         ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-183, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-6684
in-theory        6684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-183 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6684.         ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-183, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-6685
in-theory        6685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-183 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6685.         ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-183, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-6686
in-theory        6686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-183 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6686.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-183, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-6687
in-theory        6687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-183 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-6687.         ((A -> ((B -> (C -> B)) and A)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-183, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-6688
in-theory        6688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-183 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6688.         ((A -> ((B -> (C -> B)) and A)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-183, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-6689
in-theory        6689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-183 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6689.         ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-183, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-6690
in-theory        6690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6690.         ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-183, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-6691
in-theory        6691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-183 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6691.         ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-183, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-6692
in-theory        6692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-183 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6692.         ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-183, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-6693
in-theory        6693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-183 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-6693.         ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-183, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-6694
in-theory        6694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6694.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-183, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-6695
in-theory        6695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-183 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6695.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (E -> D))) -> (not D))), M:tm-183, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-6696
in-theory        6696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6696.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-183, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-6697
in-theory        6697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-183 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6697.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-183, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-6698
in-theory        6698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-183 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6698.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-183, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-6699
in-theory        6699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6699.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-183, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-6700
in-theory        6700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-183 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-6700.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (D or E))) -> (not D))), M:tm-183, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-6701
in-theory        6701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-183 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6701.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (E or D))) -> (not D))), M:tm-183, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-6702
in-theory        6702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-183 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6702.         ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-183, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-6703
in-theory        6703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-183 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6703.         ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-183, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-6704
in-theory        6704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-183 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6704.         ((A -> ((B -> (C -> B)) and A)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-183, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-6705
in-theory        6705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6705.         ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-183, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-6706
in-theory        6706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     23
proof            (modus-ponens tm-183 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6706.         ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-183, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-6707
in-theory        6707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     25
proof            (modus-ponens tm-183 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6707.         ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-183, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-6708
in-theory        6708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-183 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-6708.         ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-183, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-6709
in-theory        6709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6709.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-183, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-6710
in-theory        6710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     21
proof            (modus-ponens tm-183 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-1 tm-9 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-6710.         ((A -> ((B -> (C -> B)) and A)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-183, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-6711
in-theory        6711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-183 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-6711.         ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-183, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-6712
in-theory        6712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-183 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6712.         ((A -> ((B -> (C -> B)) and A)) and (D or ((not (not E)) -> E))), M:tm-183, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-6713
in-theory        6713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((not (not D)) -> D) or E))
theorem-size     17
proof            (modus-ponens tm-183 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6713.         ((A -> ((B -> (C -> B)) and A)) and (((not (not D)) -> D) or E)), M:tm-183, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-6714
in-theory        6714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-183 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6714.         ((A -> ((B -> (C -> B)) and A)) and (D -> (((not (not E)) -> E) and D))), M:tm-183, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-6715
in-theory        6715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     25
proof            (modus-ponens tm-183 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-6715.         ((A -> ((B -> (C -> B)) and A)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-183, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-6716
in-theory        6716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-183 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6716.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((not (not E)) -> E))), M:tm-183, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-6717
in-theory        6717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6717.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-183, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-6718
in-theory        6718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-183 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6718.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-183, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-6719
in-theory        6719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6719.         ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (F -> (G -> F))))), M:tm-183, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-6720
in-theory        6720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6720.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (F -> E))) or G)), M:tm-183, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-6721
in-theory        6721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6721.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-183, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-6722
in-theory        6722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-183 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-6722.         ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (D -> (F -> E)))), M:tm-183, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-6723
in-theory        6723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6723.         ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (F -> (G -> F))))), M:tm-183, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-6724
in-theory        6724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> D))
theorem-size     13
proof            (modus-ponens tm-183 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6724.         ((A -> ((B -> (C -> B)) and A)) and (D -> D)), M:tm-183, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-6725
in-theory        6725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6725.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-183, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-6726
in-theory        6726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D and E) -> (D and E)))
theorem-size     17
proof            (modus-ponens tm-183 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6726.         ((A -> ((B -> (C -> B)) and A)) and ((D and E) -> (D and E))), M:tm-183, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-6727
in-theory        6727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-183 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6727.         ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (D -> E))), M:tm-183, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-6728
in-theory        6728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((not (not D)) -> (not (not D))))
theorem-size     17
proof            (modus-ponens tm-183 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-6728.         ((A -> ((B -> (C -> B)) and A)) and ((not (not D)) -> (not (not D)))), M:tm-183, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-6729
in-theory        6729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-183 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6729.         ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-183, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-6730
in-theory        6730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-183 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6730.         ((A -> ((B -> (C -> B)) and A)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-183, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-6731
in-theory        6731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-183 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6731.         ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> F) -> (E -> E)))), M:tm-183, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-6732
in-theory        6732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (D -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-183 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6732.         ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (D -> D)) or F)), M:tm-183, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-6733
in-theory        6733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6733.         ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-183, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-6734
in-theory        6734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-6734.         ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-183, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-6735
in-theory        6735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-183 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6735.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> F) -> (E -> E)))), M:tm-183, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-6736
in-theory        6736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-6736.         ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-183, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-6737
in-theory        6737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-183 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-6737.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (D -> E)) -> (D -> E))), M:tm-183, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-6738
in-theory        6738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-183 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-6738.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-183, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-6739
in-theory        6739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     41
proof            (modus-ponens tm-183 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-6739.         ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-183, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-6740
in-theory        6740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-183 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-6740.         ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-183, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-6741
in-theory        6741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6741.         ((A -> ((B -> (C -> B)) and A)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-183, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-6742
in-theory        6742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-183 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6742.         ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-183, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-6743
in-theory        6743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-183 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6743.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-183, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-6744
in-theory        6744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-183 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-6744.         ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-183, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-6745
in-theory        6745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6745.         ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-183, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-6746
in-theory        6746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-183 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-6746.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-183, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-6747
in-theory        6747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-183 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6747.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-183, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-6748
in-theory        6748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     43
proof            (modus-ponens tm-183 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6748.         ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-183, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-6749
in-theory        6749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-183 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6749.         ((A -> ((B -> (C -> B)) and A)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-183, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-6750
in-theory        6750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-183 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6750.         ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-183, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-6751
in-theory        6751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-183 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6751.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-183, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-6752
in-theory        6752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-183 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-6752.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-183, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-6753
in-theory        6753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-183 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6753.         ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-183, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-6754
in-theory        6754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) and D) -> E))
theorem-size     17
proof            (modus-ponens tm-183 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-6754.         ((A -> ((B -> (C -> B)) and A)) and (((D -> E) and D) -> E)), M:tm-183, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-6755
in-theory        6755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-183 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-6755.         ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-183, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-6756
in-theory        6756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-183 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6756.         ((A -> ((B -> (C -> B)) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-183, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-6757
in-theory        6757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-183 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-6757.         ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-183, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-6758
in-theory        6758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     25
proof            (modus-ponens tm-183 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-6758.         ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-183, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-6759
in-theory        6759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     35
proof            (modus-ponens tm-183 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-6759.         ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-183, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-6760
in-theory        6760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     37
proof            (modus-ponens tm-183 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-6760.         ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-183, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-6761
in-theory        6761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-183 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6761.         ((A -> ((B -> (C -> B)) and A)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-183, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-6762
in-theory        6762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-183 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6762.         ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-183, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-6763
in-theory        6763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-183 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6763.         ((A -> ((B -> (C -> B)) and A)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-183, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-6764
in-theory        6764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     33
proof            (modus-ponens tm-183 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-6764.         ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-183, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-6765
in-theory        6765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-183 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6765.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-183, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-6766
in-theory        6766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-183 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-6766.         ((A -> ((B -> (C -> B)) and A)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-183, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-6767
in-theory        6767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-183 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-6767.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-183, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-6768
in-theory        6768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6768.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-183, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-6769
in-theory        6769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     27
proof            (modus-ponens tm-183 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6769.         ((A -> ((B -> (C -> B)) and A)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-183, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-6770
in-theory        6770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-183 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6770.         ((A -> ((B -> (C -> B)) and A)) and (D or (E -> ((F and G) -> F)))), M:tm-183, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-6771
in-theory        6771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6771.         ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E and F) -> E)) or G)), M:tm-183, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-6772
in-theory        6772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6772.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-183, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-6773
in-theory        6773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-183 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-6773.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E and F)) -> (D -> E))), M:tm-183, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-6774
in-theory        6774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-183 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6774.         ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> ((F and G) -> F)))), M:tm-183, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-6775
in-theory        6775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D and (D -> E)) -> E))
theorem-size     17
proof            (modus-ponens tm-183 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-6775.         ((A -> ((B -> (C -> B)) and A)) and ((D and (D -> E)) -> E)), M:tm-183, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-6776
in-theory        6776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-183 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-6776.         ((A -> ((B -> (C -> B)) and A)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-183, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-6777
in-theory        6777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-183 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6777.         ((A -> ((B -> (C -> B)) and A)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-183, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-6778
in-theory        6778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-183 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-6778.         ((A -> ((B -> (C -> B)) and A)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-183, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-6779
in-theory        6779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-183 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-6779.         ((A -> ((B -> (C -> B)) and A)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-183, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-6780
in-theory        6780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     25
proof            (modus-ponens tm-183 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-6780.         ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-183, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-6781
in-theory        6781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     35
proof            (modus-ponens tm-183 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-6781.         ((A -> ((B -> (C -> B)) and A)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-183, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-6782
in-theory        6782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-183 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-6782.         ((A -> ((B -> (C -> B)) and A)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-183, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-6783
in-theory        6783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-183 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6783.         ((A -> ((B -> (C -> B)) and A)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-183, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-6784
in-theory        6784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-183 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6784.         ((A -> ((B -> (C -> B)) and A)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-183, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-6785
in-theory        6785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-183 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6785.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-183, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-6786
in-theory        6786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     33
proof            (modus-ponens tm-183 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-6786.         ((A -> ((B -> (C -> B)) and A)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-183, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-6787
in-theory        6787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-183 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6787.         ((A -> ((B -> (C -> B)) and A)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-183, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-6788
in-theory        6788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-183 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-6788.         ((A -> ((B -> (C -> B)) and A)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-183, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-6789
in-theory        6789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-183 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-6789.         ((A -> ((B -> (C -> B)) and A)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-183, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-6790
in-theory        6790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-183 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-6790.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-183, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-6791
in-theory        6791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6791.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-183, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-6792
in-theory        6792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-183 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6792.         ((A -> ((B -> (C -> B)) and A)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-183, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-6793
in-theory        6793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-183 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6793.         ((A -> ((B -> (C -> B)) and A)) and (D or (E -> ((F and G) -> G)))), M:tm-183, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6794
in-theory        6794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6794.         ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E and F) -> F)) or G)), M:tm-183, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-6795
in-theory        6795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6795.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-183, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-6796
in-theory        6796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-183 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-6796.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E and F)) -> (D -> F))), M:tm-183, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-6797
in-theory        6797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-183 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6797.         ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> ((F and G) -> G)))), M:tm-183, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-6798
in-theory        6798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6798.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-183, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-6799
in-theory        6799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6799.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-183, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-6800
in-theory        6800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6800.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-183, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-6801
in-theory        6801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-183 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6801.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-183, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-6802
in-theory        6802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6802.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-183, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-6803
in-theory        6803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-183 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-6803.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-183, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-6804
in-theory        6804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6804.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-183, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-6805
in-theory        6805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6805.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-183, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-6806
in-theory        6806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-183 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6806.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-183, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-6807
in-theory        6807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6807.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-183, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-6808
in-theory        6808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6808.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-183, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-6809
in-theory        6809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6809.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-183, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-6810
in-theory        6810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-183 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6810.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-183, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-6811
in-theory        6811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6811.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-183, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-6812
in-theory        6812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-183 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6812.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-183, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-6813
in-theory        6813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-183 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6813.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-183, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-6814
in-theory        6814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-183 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6814.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-183, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-6815
in-theory        6815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-183 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6815.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-183, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-6816
in-theory        6816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6816.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-183, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-6817
in-theory        6817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6817.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-183, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-6818
in-theory        6818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-183 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6818.         ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-183, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-6819
in-theory        6819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-183 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6819.         ((A -> ((B -> (C -> B)) and A)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-183, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6820
in-theory        6820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-183 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6820.         ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-183, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-6821
in-theory        6821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6821.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-183, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6822
in-theory        6822
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> ((E -> (F -> E)) and D)) and ((B -> (C -> B)) and A)))
theorem-size     27
proof            (modus-ponens tm-180 tm-183 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6822.         ((A or ((B -> (C -> B)) and A)) -> ((D -> ((E -> (F -> E)) and D)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-183, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-6823
in-theory        6823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6823.         ((A -> ((B and C) -> C)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-157, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6824
in-theory        6824
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((B and C) -> C)))
theorem-size     23
proof            (modus-ponens tm-154 tm-183 ((Am (-> (and A B) B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6824.         ((A or ((B and C) -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((B and C) -> C))), M:tm-154, m:tm-183, u:((Am (-> (and A B) B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (and A B) B))))
================================================================
tm-name          tm-6825
in-theory        6825
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6825.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-147, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6826
in-theory        6826
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((A and (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-144 tm-183 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6826.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-183, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-6827
in-theory        6827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6827.         ((A -> ((B and C) -> B)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-134, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6828
in-theory        6828
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> ((E -> (F -> E)) and D)) and ((B and C) -> B)))
theorem-size     23
proof            (modus-ponens tm-131 tm-183 ((Am (-> (and A B) A)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6828.         ((A or ((B and C) -> B)) -> ((D -> ((E -> (F -> E)) and D)) and ((B and C) -> B))), M:tm-131, m:tm-183, u:((Am (-> (and A B) A)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (and A B) A))))
================================================================
tm-name          tm-6829
in-theory        6829
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6829.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-125, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6830
in-theory        6830
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> ((E -> (F -> E)) and D)) and (((A -> B) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-122 tm-183 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6830.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> ((E -> (F -> E)) and D)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-183, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-6831
in-theory        6831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H -> G)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6831.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H -> G)) and F)) and E))), M:tm-113, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6832
in-theory        6832
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> ((F -> (G -> F)) and E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     39
proof            (modus-ponens tm-110 tm-183 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6832.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> ((F -> (G -> F)) and E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-183, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-6833
in-theory        6833
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6833.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-105, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6834
in-theory        6834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-102 tm-183 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6834.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-183, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-6835
in-theory        6835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> ((E -> (F -> E)) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6835.         (((A -> B) -> (A -> A)) and (C -> ((D -> ((E -> (F -> E)) and D)) and C))), M:tm-95, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6836
in-theory        6836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> ((D -> (E -> D)) and C)) and (A -> A)))
theorem-size     21
proof            (modus-ponens tm-92 tm-183 ((Am (-> A A)) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6836.         (((A -> B) or (A -> A)) -> ((C -> ((D -> (E -> D)) and C)) and (A -> A))), M:tm-92, m:tm-183, u:((Am (-> A A)) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A A))))
================================================================
tm-name          tm-6837
in-theory        6837
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> ((D -> (E -> D)) and C)) and A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6837.         (A -> (B -> ((C -> ((D -> (E -> D)) and C)) and A))), M:tm-84, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-6838
in-theory        6838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6838.         ((A -> (B -> (C -> B))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-83, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6839
in-theory        6839
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> ((E -> (F -> E)) and D)) and (B -> (C -> B))))
theorem-size     23
proof            (modus-ponens tm-80 tm-183 ((Am (-> A (-> B A))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6839.         ((A or (B -> (C -> B))) -> ((D -> ((E -> (F -> E)) and D)) and (B -> (C -> B)))), M:tm-80, m:tm-183, u:((Am (-> A (-> B A))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (-> B A)))))
================================================================
tm-name          tm-6840
in-theory        6840
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> ((D -> (E -> D)) and C)) and B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6840.         (((not (not A)) -> A) and (B -> ((C -> ((D -> (E -> D)) and C)) and B))), M:tm-76, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6841
in-theory        6841
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> ((C -> (D -> C)) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-73 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6841.         (((not (not A)) or A) -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-73, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-6842
in-theory        6842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> ((E -> (F -> E)) and D)) and C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6842.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> ((E -> (F -> E)) and D)) and C))), M:tm-69, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6843
in-theory        6843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> ((D -> (E -> D)) and C)) and ((A -> (not B)) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-66 tm-183 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6843.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> ((D -> (E -> D)) and C)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-183, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-6844
in-theory        6844
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6844.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-54, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6845
in-theory        6845
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((E -> (F -> E)) and D)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-51 tm-183 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6845.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((E -> (F -> E)) and D)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-183, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-6846
in-theory        6846
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> ((D -> (E -> D)) and C)) and (B or A)))
theorem-size     19
proof            (modus-ponens tm-50 tm-183 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6846.         ((A or (B or A)) -> ((C -> ((D -> (E -> D)) and C)) and (B or A))), M:tm-50, m:tm-183, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (or A B))))
================================================================
tm-name          tm-6847
in-theory        6847
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> ((D -> (E -> D)) and C)) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-49 tm-183 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6847.         ((A or (A or B)) -> ((C -> ((D -> (E -> D)) and C)) and (A or B))), M:tm-49, m:tm-183, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (or A B))))
================================================================
tm-name          tm-6848
in-theory        6848
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> ((D -> (E -> D)) and C)) and (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-48 tm-183 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6848.         ((A or (B -> (A and B))) -> ((C -> ((D -> (E -> D)) and C)) and (B -> (A and B)))), M:tm-48, m:tm-183, u:((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-6849
in-theory        6849
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> ((D -> (E -> D)) and C)) and B))
theorem-size     17
proof            (modus-ponens tm-47 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6849.         (((A and B) or B) -> ((C -> ((D -> (E -> D)) and C)) and B)), M:tm-47, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-6850
in-theory        6850
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> ((D -> (E -> D)) and C)) and A))
theorem-size     17
proof            (modus-ponens tm-46 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6850.         (((A and B) or A) -> ((C -> ((D -> (E -> D)) and C)) and A)), M:tm-46, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-6851
in-theory        6851
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-45 tm-183 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6851.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-183, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-6852
in-theory        6852
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> ((D -> (E -> D)) and C)) and (B -> A)))
theorem-size     19
proof            (modus-ponens tm-44 tm-183 ((Am (-> A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6852.         ((A or (B -> A)) -> ((C -> ((D -> (E -> D)) and C)) and (B -> A))), M:tm-44, m:tm-183, u:((Am (-> A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A B))))
================================================================
tm-name          tm-6853
in-theory        6853
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> ((E -> (F -> E)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6853.         ((A -> (B or A)) and (C -> ((D -> ((E -> (F -> E)) and D)) and C))), M:tm-42, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6854
in-theory        6854
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> ((E -> (F -> E)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6854.         ((A -> (A or B)) and (C -> ((D -> ((E -> (F -> E)) and D)) and C))), M:tm-32, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6855
in-theory        6855
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> ((C -> (D -> C)) and B)) and A)))
theorem-size     15
proof            (modus-ponens tm-24 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6855.         (A -> (A and ((B -> ((C -> (D -> C)) and B)) and A))), M:tm-24, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-6856
in-theory        6856
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> ((E -> (F -> E)) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6856.         ((A -> (B -> (A and B))) and (C -> ((D -> ((E -> (F -> E)) and D)) and C))), M:tm-23, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6857
in-theory        6857
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> ((E -> (F -> E)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6857.         (((A and B) -> B) and (C -> ((D -> ((E -> (F -> E)) and D)) and C))), M:tm-22, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6858
in-theory        6858
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> ((E -> (F -> E)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6858.         (((A and B) -> A) and (C -> ((D -> ((E -> (F -> E)) and D)) and C))), M:tm-21, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6859
in-theory        6859
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6859.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-20, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6860
in-theory        6860
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> ((E -> (F -> E)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6860.         ((A -> (B -> A)) and (C -> ((D -> ((E -> (F -> E)) and D)) and C))), M:tm-19, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6861
in-theory        6861
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> ((C -> (D -> C)) and B)) and A))) -> (not A))
theorem-size     17
proof            (modus-ponens tm-9 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-9 tm-5 tm-1)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6861.         ((A -> (not ((B -> ((C -> (D -> C)) and B)) and A))) -> (not A)), M:tm-9, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-6862
in-theory        6862
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C -> B)) and A)) and D) -> E) -> ((D or ((A -> ((B -> (C -> B)) and A)) and D)) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6862.         ((((A -> ((B -> (C -> B)) and A)) and D) -> E) -> ((D or ((A -> ((B -> (C -> B)) and A)) and D)) -> E)), M:tm-8, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-6863
in-theory        6863
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> ((D -> (E -> D)) and C)) and B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6863.         (A or (B -> ((C -> ((D -> (E -> D)) and C)) and B))), M:tm-7, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6864
in-theory        6864
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6864.         ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) or E), M:tm-6, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6865
in-theory        6865
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> ((D -> (E -> D)) and C)) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6865.         (A -> ((B -> ((C -> ((D -> (E -> D)) and C)) and B)) and A)), M:tm-5, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6866
in-theory        6866
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> ((D -> (E -> D)) and C)) and B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-1 tm-5)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6866.         (A -> (B -> ((C -> ((D -> (E -> D)) and C)) and B))), M:tm-1, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-6867
in-theory        6867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-183 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6867.         ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-183, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6868
in-theory        6868
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-180 tm-184 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6868.         ((A or ((B -> (C -> B)) and A)) -> (D -> ((E -> (F -> E)) and D))), M:tm-180, m:tm-184, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6869
in-theory        6869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-157 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6869.         ((A -> ((B and C) -> C)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-157, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6870
in-theory        6870
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-154 tm-184 ((Am (-> (and A B) B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6870.         ((A or ((B and C) -> C)) -> (D -> ((E -> (F -> E)) and D))), M:tm-154, m:tm-184, u:((Am (-> (and A B) B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6871
in-theory        6871
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> ((C -> (D -> C)) and B))
theorem-size     11
proof            (modus-ponens tm-152 tm-184 ((Am (and A Bm)) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6871.         ((A and B) -> ((C -> (D -> C)) and B)), M:tm-152, m:tm-184, u:((Am (and A Bm)) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-6872
in-theory        6872
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-147 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6872.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-147, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6873
in-theory        6873
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     25
proof            (modus-ponens tm-144 tm-184 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6873.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((E -> (F -> E)) and D))), M:tm-144, m:tm-184, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6874
in-theory        6874
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (D -> C)) and B)) -> E)) -> (B -> ((C -> (D -> C)) and B)))
theorem-size     23
proof            (modus-ponens tm-142 tm-184 ((Am (and A (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) C))) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6874.         ((A and ((B -> ((C -> (D -> C)) and B)) -> E)) -> (B -> ((C -> (D -> C)) and B))), M:tm-142, m:tm-184, u:((Am (and A (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) C))) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6875
in-theory        6875
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (D -> C)) and B)) -> B)) -> ((C -> (D -> C)) and B))
theorem-size     21
proof            (modus-ponens tm-141 tm-184 ((Am (and A (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Bm))) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6875.         ((A and ((B -> ((C -> (D -> C)) and B)) -> B)) -> ((C -> (D -> C)) and B)), M:tm-141, m:tm-184, u:((Am (and A (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Bm))) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-6876
in-theory        6876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-134 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6876.         ((A -> ((B and C) -> B)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-134, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6877
in-theory        6877
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-131 tm-184 ((Am (-> (and A B) A)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6877.         ((A or ((B and C) -> B)) -> (D -> ((E -> (F -> E)) and D))), M:tm-131, m:tm-184, u:((Am (-> (and A B) A)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6878
in-theory        6878
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> ((C -> (D -> C)) and A))
theorem-size     11
proof            (modus-ponens tm-129 tm-184 ((Am (and Bm B)) (A Bm) (C (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6878.         ((A and B) -> ((C -> (D -> C)) and A)), M:tm-129, m:tm-184, u:((Am (and Bm B)) (A Bm) (C (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-6879
in-theory        6879
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-125 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6879.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-125, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6880
in-theory        6880
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     25
proof            (modus-ponens tm-122 tm-184 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6880.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((E -> (F -> E)) and D))), M:tm-122, m:tm-184, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6881
in-theory        6881
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C -> B)) and A)) -> D) and E) -> (A -> ((B -> (C -> B)) and A)))
theorem-size     23
proof            (modus-ponens tm-120 tm-184 ((Am (and (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6881.         ((((A -> ((B -> (C -> B)) and A)) -> D) and E) -> (A -> ((B -> (C -> B)) and A))), M:tm-120, m:tm-184, u:((Am (and (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6882
in-theory        6882
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C -> B)) and A)) -> A) and D) -> ((B -> (C -> B)) and A))
theorem-size     21
proof            (modus-ponens tm-119 tm-184 ((Am (and (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Bm) C)) (A Bm) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6882.         ((((A -> ((B -> (C -> B)) and A)) -> A) and D) -> ((B -> (C -> B)) and A)), M:tm-119, m:tm-184, u:((Am (and (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Bm) C)) (A Bm) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-6883
in-theory        6883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-113 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6883.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H -> G)) and F)))), M:tm-113, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6884
in-theory        6884
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((F -> (G -> F)) and E)))
theorem-size     25
proof            (modus-ponens tm-110 tm-184 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6884.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((F -> (G -> F)) and E))), M:tm-110, m:tm-184, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6885
in-theory        6885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))
theorem-size     19
proof            (modus-ponens tm-108 tm-184 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> Cm (-> Dm Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6885.         ((A -> (B -> C)) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-108, m:tm-184, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> Cm (-> Dm Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-6886
in-theory        6886
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     31
proof            (modus-ponens tm-105 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6886.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-105, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6887
in-theory        6887
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     29
proof            (modus-ponens tm-102 tm-184 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6887.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((E -> (F -> E)) and D))), M:tm-102, m:tm-184, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6888
in-theory        6888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) and A) -> D)) -> (A -> ((B -> (C -> B)) and A)))
theorem-size     21
proof            (modus-ponens tm-100 tm-184 ((Am (-> Bm (-> (and (-> Cm (-> Dm Cm)) Bm) C))) (A Bm) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6888.         ((A -> (((B -> (C -> B)) and A) -> D)) -> (A -> ((B -> (C -> B)) and A))), M:tm-100, m:tm-184, u:((Am (-> Bm (-> (and (-> Cm (-> Dm Cm)) Bm) C))) (A Bm) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-6889
in-theory        6889
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> A)))
theorem-size     11
proof            (modus-ponens tm-98 tm-184 ((A Am) (Bm (-> B Am)) (C (and (-> Cm (-> Dm Cm)) (-> B Am)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6889.         (A -> ((B -> (C -> B)) and (D -> A))), M:tm-98, m:tm-184, u:((A Am) (Bm (-> B Am)) (C (and (-> Cm (-> Dm Cm)) (-> B Am))))
================================================================
tm-name          tm-6890
in-theory        6890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) -> D) -> (A -> ((B -> (C -> B)) and A)))
theorem-size     21
proof            (modus-ponens tm-96 tm-184 ((Am (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) B)) (A (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6890.         (((A -> ((B -> (C -> B)) and A)) -> D) -> (A -> ((B -> (C -> B)) and A))), M:tm-96, m:tm-184, u:((Am (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) B)) (A (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6891
in-theory        6891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-95 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6891.         (((A -> B) -> (A -> A)) and (C -> (D -> ((E -> (F -> E)) and D)))), M:tm-95, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6892
in-theory        6892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> ((D -> (E -> D)) and C)))
theorem-size     17
proof            (modus-ponens tm-92 tm-184 ((Am (-> A A)) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6892.         (((A -> B) or (A -> A)) -> (C -> ((D -> (E -> D)) and C))), M:tm-92, m:tm-184, u:((Am (-> A A)) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6893
in-theory        6893
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C -> ((D -> (E -> D)) and C))))
theorem-size     13
proof            (modus-ponens tm-84 tm-184 ((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6893.         (A -> (B -> (C -> ((D -> (E -> D)) and C)))), M:tm-84, m:tm-184, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6894
in-theory        6894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-83 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6894.         ((A -> (B -> (C -> B))) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-83, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6895
in-theory        6895
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-80 tm-184 ((Am (-> A (-> B A))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6895.         ((A or (B -> (C -> B))) -> (D -> ((E -> (F -> E)) and D))), M:tm-80, m:tm-184, u:((Am (-> A (-> B A))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6896
in-theory        6896
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> ((B -> (C -> B)) and A)) -> D))) -> D)
theorem-size     15
proof            (modus-ponens tm-77 tm-184 ((Am (not (not (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) B)))) (A (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6896.         ((not (not ((A -> ((B -> (C -> B)) and A)) -> D))) -> D), M:tm-77, m:tm-184, u:((Am (not (not (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) B)))) (A (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6897
in-theory        6897
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> ((D -> (E -> D)) and C))))
theorem-size     17
proof            (modus-ponens tm-76 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6897.         (((not (not A)) -> A) and (B -> (C -> ((D -> (E -> D)) and C)))), M:tm-76, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6898
in-theory        6898
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> ((C -> (D -> C)) and B)))
theorem-size     15
proof            (modus-ponens tm-73 tm-184 ((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6898.         (((not (not A)) or A) -> (B -> ((C -> (D -> C)) and B))), M:tm-73, m:tm-184, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6899
in-theory        6899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> ((E -> (F -> E)) and D))))
theorem-size     23
proof            (modus-ponens tm-69 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6899.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> ((E -> (F -> E)) and D)))), M:tm-69, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6900
in-theory        6900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((D -> (E -> D)) and C)))
theorem-size     21
proof            (modus-ponens tm-66 tm-184 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6900.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((D -> (E -> D)) and C))), M:tm-66, m:tm-184, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6901
in-theory        6901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> ((C -> (D -> C)) and B)))
theorem-size     15
proof            (modus-ponens tm-55 tm-184 ((Am (-> A Bm)) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6901.         ((A -> B) -> ((A or B) -> ((C -> (D -> C)) and B))), M:tm-55, m:tm-184, u:((Am (-> A Bm)) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-6902
in-theory        6902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-54 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6902.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-54, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6903
in-theory        6903
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-51 tm-184 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6903.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (F -> E)) and D))), M:tm-51, m:tm-184, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6904
in-theory        6904
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D -> (E -> D)) and C)))
theorem-size     15
proof            (modus-ponens tm-50 tm-184 ((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6904.         ((A or (B or A)) -> (C -> ((D -> (E -> D)) and C))), M:tm-50, m:tm-184, u:((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6905
in-theory        6905
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D -> (E -> D)) and C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-184 ((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6905.         ((A or (A or B)) -> (C -> ((D -> (E -> D)) and C))), M:tm-49, m:tm-184, u:((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6906
in-theory        6906
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D -> (E -> D)) and C)))
theorem-size     17
proof            (modus-ponens tm-48 tm-184 ((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6906.         ((A or (B -> (A and B))) -> (C -> ((D -> (E -> D)) and C))), M:tm-48, m:tm-184, u:((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6907
in-theory        6907
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D -> (E -> D)) and C)))
theorem-size     15
proof            (modus-ponens tm-47 tm-184 ((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6907.         (((A and B) or B) -> (C -> ((D -> (E -> D)) and C))), M:tm-47, m:tm-184, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6908
in-theory        6908
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D -> (E -> D)) and C)))
theorem-size     15
proof            (modus-ponens tm-46 tm-184 ((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6908.         (((A and B) or A) -> (C -> ((D -> (E -> D)) and C))), M:tm-46, m:tm-184, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6909
in-theory        6909
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-45 tm-184 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6909.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> E)) and D))), M:tm-45, m:tm-184, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6910
in-theory        6910
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D -> (E -> D)) and C)))
theorem-size     15
proof            (modus-ponens tm-44 tm-184 ((Am (-> A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6910.         ((A or (B -> A)) -> (C -> ((D -> (E -> D)) and C))), M:tm-44, m:tm-184, u:((Am (-> A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6911
in-theory        6911
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-42 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6911.         ((A -> (B or A)) and (C -> (D -> ((E -> (F -> E)) and D)))), M:tm-42, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6912
in-theory        6912
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-32 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6912.         ((A -> (A or B)) and (C -> (D -> ((E -> (F -> E)) and D)))), M:tm-32, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6913
in-theory        6913
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B -> ((C -> (D -> C)) and B))))
theorem-size     13
proof            (modus-ponens tm-24 tm-184 ((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6913.         (A -> (A and (B -> ((C -> (D -> C)) and B)))), M:tm-24, m:tm-184, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6914
in-theory        6914
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-23 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6914.         ((A -> (B -> (A and B))) and (C -> (D -> ((E -> (F -> E)) and D)))), M:tm-23, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6915
in-theory        6915
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-22 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6915.         (((A and B) -> B) and (C -> (D -> ((E -> (F -> E)) and D)))), M:tm-22, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6916
in-theory        6916
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-21 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6916.         (((A and B) -> A) and (C -> (D -> ((E -> (F -> E)) and D)))), M:tm-21, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6917
in-theory        6917
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-20 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6917.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-20, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6918
in-theory        6918
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-19 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6918.         ((A -> (B -> A)) and (C -> (D -> ((E -> (F -> E)) and D)))), M:tm-19, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6919
in-theory        6919
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (D -> C)) and B)) -> E)) -> E)
theorem-size     15
proof            (modus-ponens tm-17 tm-184 ((Am (and A (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) C))) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6919.         ((A and ((B -> ((C -> (D -> C)) and B)) -> E)) -> E), M:tm-17, m:tm-184, u:((Am (and A (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) C))) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6920
in-theory        6920
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C -> B)) and A)) -> D) and E) -> D)
theorem-size     15
proof            (modus-ponens tm-15 tm-184 ((Am (and (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6920.         ((((A -> ((B -> (C -> B)) and A)) -> D) and E) -> D), M:tm-15, m:tm-184, u:((Am (and (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6921
in-theory        6921
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) and A) -> D)) -> (A -> D))
theorem-size     15
proof            (modus-ponens tm-13 tm-184 ((Am (-> Bm (-> (and (-> Cm (-> Dm Cm)) Bm) C))) (A Bm) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6921.         ((A -> (((B -> (C -> B)) and A) -> D)) -> (A -> D)), M:tm-13, m:tm-184, u:((Am (-> Bm (-> (and (-> Cm (-> Dm Cm)) Bm) C))) (A Bm) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-6922
in-theory        6922
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B -> ((C -> (D -> C)) and B)))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-184 ((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6922.         ((A -> (not (B -> ((C -> (D -> C)) and B)))) -> (not A)), M:tm-9, m:tm-184, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6923
in-theory        6923
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) -> D) -> ((E or (A -> ((B -> (C -> B)) and A))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-184 ((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6923.         (((A -> ((B -> (C -> B)) and A)) -> D) -> ((E or (A -> ((B -> (C -> B)) and A))) -> D)), M:tm-8, m:tm-184, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-6924
in-theory        6924
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C -> ((D -> (E -> D)) and C))))
theorem-size     13
proof            (modus-ponens tm-7 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-7 tm-1 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6924.         (A or (B -> (C -> ((D -> (E -> D)) and C)))), M:tm-7, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6925
in-theory        6925
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-6 tm-1 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6925.         ((A -> (B -> ((C -> (D -> C)) and B))) or E), M:tm-6, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6926
in-theory        6926
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> ((D -> (E -> D)) and C))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6926.         (A -> ((B -> (C -> ((D -> (E -> D)) and C))) and A)), M:tm-5, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-6927
in-theory        6927
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> ((C -> (D -> C)) and B)))
theorem-size     13
proof            (modus-ponens tm-2 tm-184 ((A Am) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6927.         ((A -> B) -> (A -> ((C -> (D -> C)) and B))), M:tm-2, m:tm-184, u:((A Am) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-6928
in-theory        6928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-183 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6928.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-183, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6929
in-theory        6929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-157 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6929.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-157, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6930
in-theory        6930
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     35
proof            (modus-ponens tm-147 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6930.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-147, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6931
in-theory        6931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-134 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6931.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-134, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6932
in-theory        6932
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     35
proof            (modus-ponens tm-125 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6932.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-125, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6933
in-theory        6933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-113 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6933.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> H)))), M:tm-113, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6934
in-theory        6934
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-105 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6934.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-105, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6935
in-theory        6935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-95 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6935.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F)))), M:tm-95, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6936
in-theory        6936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-83 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6936.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-83, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6937
in-theory        6937
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-76 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6937.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> E)))), M:tm-76, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6938
in-theory        6938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-69 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6938.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F)))), M:tm-69, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6939
in-theory        6939
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-54 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6939.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-54, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6940
in-theory        6940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-42 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6940.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F)))), M:tm-42, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6941
in-theory        6941
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-32 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6941.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F)))), M:tm-32, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6942
in-theory        6942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-23 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6942.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F)))), M:tm-23, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6943
in-theory        6943
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-22 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6943.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F)))), M:tm-22, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6944
in-theory        6944
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-21 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6944.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F)))), M:tm-21, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6945
in-theory        6945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-20 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6945.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-20, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6946
in-theory        6946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-19 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6946.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F)))), M:tm-19, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6947
in-theory        6947
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-7 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-1)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6947.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> E)))), M:tm-7, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6948
in-theory        6948
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-1)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6948.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) or F), M:tm-6, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6949
in-theory        6949
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> E))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6949.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> E))) and A)), M:tm-5, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6950
in-theory        6950
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-1 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6950.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> E)))), M:tm-1, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-6951
in-theory        6951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6951.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-183, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6952
in-theory        6952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6952.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-157, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6953
in-theory        6953
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6953.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-147, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6954
in-theory        6954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6954.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-134, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6955
in-theory        6955
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6955.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-125, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6956
in-theory        6956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6956.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-113, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6957
in-theory        6957
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6957.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-105, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6958
in-theory        6958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6958.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-95, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6959
in-theory        6959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6959.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-83, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6960
in-theory        6960
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6960.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-76, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6961
in-theory        6961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6961.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-69, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6962
in-theory        6962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-54 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6962.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-54, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6963
in-theory        6963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-42 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6963.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-42, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6964
in-theory        6964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-32 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6964.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-32, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6965
in-theory        6965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-23 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6965.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-23, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6966
in-theory        6966
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-22 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6966.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-22, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6967
in-theory        6967
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-21 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6967.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-21, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6968
in-theory        6968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-20 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6968.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-20, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6969
in-theory        6969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-19 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6969.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-19, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6970
in-theory        6970
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-7 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6970.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-7, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6971
in-theory        6971
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)
theorem-size     29
proof            (modus-ponens tm-6 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6971.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G), M:tm-6, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6972
in-theory        6972
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6972.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and A)), M:tm-5, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6973
in-theory        6973
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-1 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6973.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-1, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-6974
in-theory        6974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-183 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6974.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-183, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6975
in-theory        6975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-157 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6975.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-157, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6976
in-theory        6976
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     35
proof            (modus-ponens tm-147 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6976.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-147, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6977
in-theory        6977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-134 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6977.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-134, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6978
in-theory        6978
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     35
proof            (modus-ponens tm-125 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6978.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-125, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6979
in-theory        6979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-113 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6979.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> H))), M:tm-113, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6980
in-theory        6980
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-105 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6980.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-105, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6981
in-theory        6981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-95 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6981.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F))), M:tm-95, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6982
in-theory        6982
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-83 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6982.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-83, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6983
in-theory        6983
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-76 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6983.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> E))), M:tm-76, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6984
in-theory        6984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-69 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6984.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F))), M:tm-69, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6985
in-theory        6985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-54 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6985.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-54, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6986
in-theory        6986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-42 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6986.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F))), M:tm-42, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6987
in-theory        6987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-32 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6987.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F))), M:tm-32, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6988
in-theory        6988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-23 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6988.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F))), M:tm-23, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6989
in-theory        6989
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-22 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6989.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F))), M:tm-22, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6990
in-theory        6990
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-21 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6990.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F))), M:tm-21, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6991
in-theory        6991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-20 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6991.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-20, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6992
in-theory        6992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-19 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6992.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F))), M:tm-19, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6993
in-theory        6993
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-7 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-7 tm-5 tm-2 tm-3)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6993.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> E))), M:tm-7, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6994
in-theory        6994
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-6 tm-5 tm-2 tm-3)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6994.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) or F), M:tm-6, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6995
in-theory        6995
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> E)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6995.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> E)) and A)), M:tm-5, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6996
in-theory        6996
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-1 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-1 tm-5 tm-2 tm-3)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6996.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> E))), M:tm-1, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-6997
in-theory        6997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-183 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6997.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-183, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-6998
in-theory        6998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-157 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6998.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-157, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-6999
in-theory        6999
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     35
proof            (modus-ponens tm-147 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6999.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-147, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7000
in-theory        7000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-134 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7000.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-134, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7001
in-theory        7001
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     35
proof            (modus-ponens tm-125 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7001.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-125, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7002
in-theory        7002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-113 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7002.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> I))), M:tm-113, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7003
in-theory        7003
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-105 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7003.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-105, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7004
in-theory        7004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-95 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7004.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G))), M:tm-95, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7005
in-theory        7005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-83 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7005.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-83, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7006
in-theory        7006
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> F)))
theorem-size     25
proof            (modus-ponens tm-76 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-10 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7006.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> F))), M:tm-76, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7007
in-theory        7007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-69 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7007.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G))), M:tm-69, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7008
in-theory        7008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-54 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7008.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-54, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7009
in-theory        7009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-42 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7009.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G))), M:tm-42, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7010
in-theory        7010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-32 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7010.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G))), M:tm-32, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7011
in-theory        7011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-23 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7011.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G))), M:tm-23, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7012
in-theory        7012
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-22 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7012.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G))), M:tm-22, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7013
in-theory        7013
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-21 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7013.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G))), M:tm-21, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7014
in-theory        7014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-20 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7014.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-20, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7015
in-theory        7015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-19 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7015.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G))), M:tm-19, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7016
in-theory        7016
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-7 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-7 tm-5 tm-2 tm-4)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7016.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> F))), M:tm-7, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7017
in-theory        7017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-6 tm-5 tm-2 tm-4)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7017.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) or F), M:tm-6, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7018
in-theory        7018
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> F)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7018.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> F)) and A)), M:tm-5, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7019
in-theory        7019
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-1 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-1 tm-5 tm-2 tm-4)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7019.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> F))), M:tm-1, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7020
in-theory        7020
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7020.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-183, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7021
in-theory        7021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7021.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-157, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7022
in-theory        7022
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7022.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-147, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7023
in-theory        7023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7023.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-134, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7024
in-theory        7024
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7024.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-125, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7025
in-theory        7025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7025.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (H and I))))), M:tm-113, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7026
in-theory        7026
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7026.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-105, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7027
in-theory        7027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7027.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G))))), M:tm-95, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7028
in-theory        7028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7028.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-83, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7029
in-theory        7029
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7029.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (E and F))))), M:tm-76, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7030
in-theory        7030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7030.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G))))), M:tm-69, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7031
in-theory        7031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7031.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-54, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7032
in-theory        7032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7032.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G))))), M:tm-42, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7033
in-theory        7033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7033.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G))))), M:tm-32, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7034
in-theory        7034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7034.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G))))), M:tm-23, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7035
in-theory        7035
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7035.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G))))), M:tm-22, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7036
in-theory        7036
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7036.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G))))), M:tm-21, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7037
in-theory        7037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7037.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-20, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7038
in-theory        7038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7038.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G))))), M:tm-19, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7039
in-theory        7039
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7039.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (E and F))))), M:tm-7, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7040
in-theory        7040
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7040.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) or F), M:tm-6, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7041
in-theory        7041
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (E and F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7041.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (E and F)))) and A)), M:tm-5, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7042
in-theory        7042
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7042.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (E and F))))), M:tm-1, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7043
in-theory        7043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7043.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-183, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7044
in-theory        7044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7044.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-157, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7045
in-theory        7045
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7045.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-147, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7046
in-theory        7046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7046.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-134, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7047
in-theory        7047
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7047.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-125, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7048
in-theory        7048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7048.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (H or I)))), M:tm-113, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7049
in-theory        7049
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7049.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-105, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7050
in-theory        7050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7050.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G)))), M:tm-95, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7051
in-theory        7051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7051.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-83, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7052
in-theory        7052
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (E or F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-10 tm-2 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7052.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (E or F)))), M:tm-76, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7053
in-theory        7053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-9 tm-2 tm-6)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7053.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G)))), M:tm-69, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7054
in-theory        7054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7054.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-54, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7055
in-theory        7055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7055.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G)))), M:tm-42, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7056
in-theory        7056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7056.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G)))), M:tm-32, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7057
in-theory        7057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7057.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G)))), M:tm-23, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7058
in-theory        7058
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7058.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G)))), M:tm-22, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7059
in-theory        7059
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7059.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G)))), M:tm-21, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7060
in-theory        7060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7060.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-20, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7061
in-theory        7061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7061.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G)))), M:tm-19, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7062
in-theory        7062
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-7 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-7 tm-5 tm-2 tm-6)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7062.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (E or F)))), M:tm-7, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7063
in-theory        7063
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7063.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) or F), M:tm-6, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7064
in-theory        7064
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (E or F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7064.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (E or F))) and A)), M:tm-5, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7065
in-theory        7065
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-1 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-1 tm-5 tm-2 tm-6)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7065.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (E or F)))), M:tm-1, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7066
in-theory        7066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-183 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7066.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-183, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7067
in-theory        7067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-157 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7067.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-157, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7068
in-theory        7068
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     35
proof            (modus-ponens tm-147 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7068.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-147, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7069
in-theory        7069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-134 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7069.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-134, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7070
in-theory        7070
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     35
proof            (modus-ponens tm-125 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7070.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-125, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7071
in-theory        7071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-113 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7071.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I or H)))), M:tm-113, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7072
in-theory        7072
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-105 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7072.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-105, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7073
in-theory        7073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-95 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7073.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F)))), M:tm-95, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7074
in-theory        7074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-83 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7074.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-83, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7075
in-theory        7075
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F or E))))
theorem-size     25
proof            (modus-ponens tm-76 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7075.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F or E)))), M:tm-76, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7076
in-theory        7076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-69 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-7)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7076.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F)))), M:tm-69, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7077
in-theory        7077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-54 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7077.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-54, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7078
in-theory        7078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-42 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7078.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F)))), M:tm-42, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7079
in-theory        7079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-32 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7079.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F)))), M:tm-32, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7080
in-theory        7080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-23 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7080.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F)))), M:tm-23, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7081
in-theory        7081
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-22 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7081.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F)))), M:tm-22, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7082
in-theory        7082
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-21 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7082.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F)))), M:tm-21, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7083
in-theory        7083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-20 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7083.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-20, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7084
in-theory        7084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-19 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7084.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F)))), M:tm-19, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7085
in-theory        7085
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-7 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7085.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F or E)))), M:tm-7, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7086
in-theory        7086
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-7)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7086.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) or F), M:tm-6, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7087
in-theory        7087
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F or E))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7087.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F or E))) and A)), M:tm-5, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7088
in-theory        7088
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-1 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-7)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7088.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F or E)))), M:tm-1, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7089
in-theory        7089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7089.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-183, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7090
in-theory        7090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7090.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-157, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7091
in-theory        7091
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7091.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-147, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7092
in-theory        7092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7092.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-134, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7093
in-theory        7093
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7093.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-125, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7094
in-theory        7094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7094.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-113, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7095
in-theory        7095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7095.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-105, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7096
in-theory        7096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7096.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-95, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7097
in-theory        7097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7097.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-83, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7098
in-theory        7098
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7098.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-76, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7099
in-theory        7099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7099.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-69, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7100
in-theory        7100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     41
proof            (modus-ponens tm-54 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7100.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-54, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7101
in-theory        7101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-42 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7101.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-42, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7102
in-theory        7102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-32 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7102.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-32, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7103
in-theory        7103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-23 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7103.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-23, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7104
in-theory        7104
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-22 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7104.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-22, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7105
in-theory        7105
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-21 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7105.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-21, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7106
in-theory        7106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     41
proof            (modus-ponens tm-20 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7106.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-20, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7107
in-theory        7107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-19 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7107.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-19, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7108
in-theory        7108
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-7 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-7 tm-5 tm-2 tm-8)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7108.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-7, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7109
in-theory        7109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G)
theorem-size     29
proof            (modus-ponens tm-6 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-6 tm-5 tm-2 tm-8)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7109.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G), M:tm-6, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7110
in-theory        7110
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7110.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))) and A)), M:tm-5, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7111
in-theory        7111
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-1 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-1 tm-5 tm-2 tm-8)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7111.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-1, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7112
in-theory        7112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-183 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7112.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-183, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7113
in-theory        7113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-157 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7113.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-157, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7114
in-theory        7114
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     41
proof            (modus-ponens tm-147 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7114.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-147, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7115
in-theory        7115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-134 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7115.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-134, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7116
in-theory        7116
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     41
proof            (modus-ponens tm-125 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7116.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-125, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7117
in-theory        7117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     41
proof            (modus-ponens tm-113 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7117.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-113, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7118
in-theory        7118
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     45
proof            (modus-ponens tm-105 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7118.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-105, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7119
in-theory        7119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-95 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7119.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-95, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7120
in-theory        7120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-83 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7120.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-83, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7121
in-theory        7121
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     31
proof            (modus-ponens tm-76 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7121.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-76, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7122
in-theory        7122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     37
proof            (modus-ponens tm-69 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7122.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-69, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7123
in-theory        7123
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     39
proof            (modus-ponens tm-54 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7123.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-54, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7124
in-theory        7124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-42 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7124.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-42, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7125
in-theory        7125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-32 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7125.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-32, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7126
in-theory        7126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-23 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7126.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-23, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7127
in-theory        7127
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-22 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7127.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-22, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7128
in-theory        7128
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-21 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7128.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-21, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7129
in-theory        7129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     39
proof            (modus-ponens tm-20 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7129.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-20, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7130
in-theory        7130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-19 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7130.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-19, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7131
in-theory        7131
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-7 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-7 tm-5 tm-2 tm-9)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7131.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-7, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7132
in-theory        7132
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) or F)
theorem-size     27
proof            (modus-ponens tm-6 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-6 tm-5 tm-2 tm-9)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7132.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) or F), M:tm-6, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7133
in-theory        7133
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7133.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))) and A)), M:tm-5, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7134
in-theory        7134
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-1 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-1 tm-5 tm-2 tm-9)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7134.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-1, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7135
in-theory        7135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-183 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7135.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-183, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7136
in-theory        7136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-157 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7136.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-157, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7137
in-theory        7137
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     35
proof            (modus-ponens tm-147 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-10)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7137.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-147, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7138
in-theory        7138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-134 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7138.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-134, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7139
in-theory        7139
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     35
proof            (modus-ponens tm-125 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-10)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7139.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-125, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7140
in-theory        7140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((not (not H)) -> H)))
theorem-size     35
proof            (modus-ponens tm-113 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7140.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((not (not H)) -> H))), M:tm-113, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7141
in-theory        7141
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     39
proof            (modus-ponens tm-105 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7141.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-105, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7142
in-theory        7142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-95 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7142.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F))), M:tm-95, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7143
in-theory        7143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-83 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7143.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-83, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7144
in-theory        7144
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((not (not E)) -> E)))
theorem-size     25
proof            (modus-ponens tm-76 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7144.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((not (not E)) -> E))), M:tm-76, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7145
in-theory        7145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-69 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-10)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7145.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F))), M:tm-69, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7146
in-theory        7146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-54 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-10)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7146.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-54, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7147
in-theory        7147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-42 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7147.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F))), M:tm-42, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7148
in-theory        7148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-32 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7148.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F))), M:tm-32, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7149
in-theory        7149
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-23 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7149.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F))), M:tm-23, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7150
in-theory        7150
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-22 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7150.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F))), M:tm-22, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7151
in-theory        7151
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-21 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7151.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F))), M:tm-21, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7152
in-theory        7152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-20 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7152.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-20, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7153
in-theory        7153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-19 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7153.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F))), M:tm-19, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7154
in-theory        7154
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-7 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-7 tm-5 tm-2 tm-10)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7154.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((not (not E)) -> E))), M:tm-7, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7155
in-theory        7155
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-6 tm-5 tm-2 tm-10)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7155.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) or E), M:tm-6, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7156
in-theory        7156
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((not (not E)) -> E)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7156.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((not (not E)) -> E)) and A)), M:tm-5, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7157
in-theory        7157
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-1 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-1 tm-5 tm-2 tm-10)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7157.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((not (not E)) -> E))), M:tm-1, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7158
in-theory        7158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7158.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-183, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7159
in-theory        7159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7159.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-157, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7160
in-theory        7160
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7160.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-147, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7161
in-theory        7161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7161.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-134, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7162
in-theory        7162
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7162.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-125, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7163
in-theory        7163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7163.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> I))))), M:tm-113, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7164
in-theory        7164
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7164.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-105, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7165
in-theory        7165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7165.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G))))), M:tm-95, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7166
in-theory        7166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7166.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-83, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7167
in-theory        7167
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7167.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> F))))), M:tm-76, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7168
in-theory        7168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7168.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G))))), M:tm-69, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7169
in-theory        7169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7169.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-54, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7170
in-theory        7170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7170.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G))))), M:tm-42, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7171
in-theory        7171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7171.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G))))), M:tm-32, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7172
in-theory        7172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7172.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G))))), M:tm-23, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7173
in-theory        7173
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7173.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G))))), M:tm-22, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7174
in-theory        7174
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7174.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G))))), M:tm-21, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7175
in-theory        7175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7175.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-20, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7176
in-theory        7176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7176.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G))))), M:tm-19, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7177
in-theory        7177
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-7 tm-5 tm-2 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7177.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> F))))), M:tm-7, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7178
in-theory        7178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-6 tm-5 tm-2 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7178.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) or G), M:tm-6, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7179
in-theory        7179
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7179.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> F)))) and A)), M:tm-5, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7180
in-theory        7180
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7180.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> F))))), M:tm-1, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7181
in-theory        7181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-183 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7181.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-183, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7182
in-theory        7182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-157 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7182.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-157, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7183
in-theory        7183
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     37
proof            (modus-ponens tm-147 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7183.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-147, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7184
in-theory        7184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-134 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7184.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-134, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7185
in-theory        7185
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     37
proof            (modus-ponens tm-125 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7185.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-125, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7186
in-theory        7186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> H))))
theorem-size     37
proof            (modus-ponens tm-113 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7186.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> H)))), M:tm-113, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7187
in-theory        7187
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     41
proof            (modus-ponens tm-105 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7187.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-105, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7188
in-theory        7188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-95 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7188.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F)))), M:tm-95, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7189
in-theory        7189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-83 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7189.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-83, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7190
in-theory        7190
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> E))))
theorem-size     27
proof            (modus-ponens tm-76 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7190.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> E)))), M:tm-76, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7191
in-theory        7191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F))))
theorem-size     33
proof            (modus-ponens tm-69 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7191.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F)))), M:tm-69, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7192
in-theory        7192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     35
proof            (modus-ponens tm-54 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7192.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-54, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7193
in-theory        7193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-42 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7193.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F)))), M:tm-42, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7194
in-theory        7194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-32 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7194.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F)))), M:tm-32, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7195
in-theory        7195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-23 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7195.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F)))), M:tm-23, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7196
in-theory        7196
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-22 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7196.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F)))), M:tm-22, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7197
in-theory        7197
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-21 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7197.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F)))), M:tm-21, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7198
in-theory        7198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     35
proof            (modus-ponens tm-20 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7198.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-20, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7199
in-theory        7199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-19 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7199.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F)))), M:tm-19, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7200
in-theory        7200
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-7 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7200.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> E)))), M:tm-7, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7201
in-theory        7201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7201.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) or F), M:tm-6, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7202
in-theory        7202
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> E))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7202.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> E))) and A)), M:tm-5, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7203
in-theory        7203
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-1 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7203.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> E)))), M:tm-1, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7204
in-theory        7204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-183 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7204.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-183, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7205
in-theory        7205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-157 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7205.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-157, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7206
in-theory        7206
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     49
proof            (modus-ponens tm-147 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7206.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-147, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7207
in-theory        7207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-134 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7207.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-134, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7208
in-theory        7208
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     49
proof            (modus-ponens tm-125 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7208.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-125, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7209
in-theory        7209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J)))))
theorem-size     49
proof            (modus-ponens tm-113 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7209.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-113, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7210
in-theory        7210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     53
proof            (modus-ponens tm-105 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7210.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-105, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7211
in-theory        7211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-95 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7211.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-95, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7212
in-theory        7212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-83 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7212.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-83, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7213
in-theory        7213
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     39
proof            (modus-ponens tm-76 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7213.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-76, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7214
in-theory        7214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     45
proof            (modus-ponens tm-69 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7214.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-69, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7215
in-theory        7215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-54 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7215.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-54, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7216
in-theory        7216
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-42 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7216.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-42, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7217
in-theory        7217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-32 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7217.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-32, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7218
in-theory        7218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-23 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7218.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-23, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7219
in-theory        7219
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-22 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7219.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-22, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7220
in-theory        7220
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-21 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7220.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-21, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7221
in-theory        7221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-20 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7221.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-20, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7222
in-theory        7222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-19 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7222.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-19, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7223
in-theory        7223
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-7 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7223.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-7, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7224
in-theory        7224
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) or G)
theorem-size     35
proof            (modus-ponens tm-6 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7224.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) or G), M:tm-6, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7225
in-theory        7225
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))) and A))
theorem-size     37
proof            (modus-ponens tm-5 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7225.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))) and A)), M:tm-5, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7226
in-theory        7226
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-1 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7226.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-1, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7227
in-theory        7227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-183 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7227.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-183, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7228
in-theory        7228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-157 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7228.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-157, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7229
in-theory        7229
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     45
proof            (modus-ponens tm-147 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7229.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-147, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7230
in-theory        7230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-134 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7230.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-134, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7231
in-theory        7231
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     45
proof            (modus-ponens tm-125 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7231.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-125, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7232
in-theory        7232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-113 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7232.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-113, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7233
in-theory        7233
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-105 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7233.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-105, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7234
in-theory        7234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-95 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7234.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-95, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7235
in-theory        7235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-83 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7235.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-83, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7236
in-theory        7236
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     35
proof            (modus-ponens tm-76 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7236.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-76, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7237
in-theory        7237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-69 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7237.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-69, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7238
in-theory        7238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-54 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7238.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-54, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7239
in-theory        7239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-42 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7239.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-42, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7240
in-theory        7240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-32 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7240.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-32, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7241
in-theory        7241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-23 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7241.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-23, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7242
in-theory        7242
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-22 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7242.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-22, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7243
in-theory        7243
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-21 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7243.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-21, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7244
in-theory        7244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-20 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7244.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-20, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7245
in-theory        7245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-19 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7245.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-19, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7246
in-theory        7246
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-7 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-7 tm-5 tm-2 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7246.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-7, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7247
in-theory        7247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) or H)
theorem-size     31
proof            (modus-ponens tm-6 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-6 tm-5 tm-2 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7247.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) or H), M:tm-6, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7248
in-theory        7248
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7248.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) and A)), M:tm-5, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7249
in-theory        7249
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-1 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7249.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-1, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7250
in-theory        7250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-183 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7250.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-183, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7251
in-theory        7251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-157 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7251.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-157, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7252
in-theory        7252
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     45
proof            (modus-ponens tm-147 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7252.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-147, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7253
in-theory        7253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-134 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7253.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-134, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7254
in-theory        7254
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     45
proof            (modus-ponens tm-125 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7254.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-125, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7255
in-theory        7255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I))))
theorem-size     45
proof            (modus-ponens tm-113 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7255.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-113, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7256
in-theory        7256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     49
proof            (modus-ponens tm-105 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7256.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-105, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7257
in-theory        7257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-95 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7257.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-95, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7258
in-theory        7258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-83 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7258.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-83, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7259
in-theory        7259
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     35
proof            (modus-ponens tm-76 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-10 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7259.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-76, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7260
in-theory        7260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     41
proof            (modus-ponens tm-69 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7260.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-69, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7261
in-theory        7261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     43
proof            (modus-ponens tm-54 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7261.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-54, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7262
in-theory        7262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-42 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7262.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-42, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7263
in-theory        7263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-32 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7263.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-32, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7264
in-theory        7264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-23 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7264.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-23, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7265
in-theory        7265
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-22 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7265.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-22, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7266
in-theory        7266
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-21 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7266.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-21, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7267
in-theory        7267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     43
proof            (modus-ponens tm-20 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7267.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-20, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7268
in-theory        7268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-19 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7268.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-19, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7269
in-theory        7269
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-7 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-7 tm-5 tm-2 tm-3)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7269.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-7, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7270
in-theory        7270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) or G)
theorem-size     31
proof            (modus-ponens tm-6 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-6 tm-5 tm-2 tm-3)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7270.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) or G), M:tm-6, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7271
in-theory        7271
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7271.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))) and A)), M:tm-5, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7272
in-theory        7272
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-1 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-1 tm-5 tm-2 tm-3)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7272.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-1, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7273
in-theory        7273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-183 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7273.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-183, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7274
in-theory        7274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-157 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7274.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-157, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7275
in-theory        7275
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-147 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7275.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-147, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7276
in-theory        7276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-134 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7276.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-134, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7277
in-theory        7277
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-125 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7277.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-125, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7278
in-theory        7278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-113 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7278.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> I)))), M:tm-113, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7279
in-theory        7279
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-105 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7279.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-105, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7280
in-theory        7280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-95 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7280.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G)))), M:tm-95, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7281
in-theory        7281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-83 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7281.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-83, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7282
in-theory        7282
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-76 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7282.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> F)))), M:tm-76, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7283
in-theory        7283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-69 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7283.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G)))), M:tm-69, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7284
in-theory        7284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-54 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7284.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-54, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7285
in-theory        7285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-42 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7285.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G)))), M:tm-42, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7286
in-theory        7286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-32 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7286.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G)))), M:tm-32, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7287
in-theory        7287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-23 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7287.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G)))), M:tm-23, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7288
in-theory        7288
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-22 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7288.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G)))), M:tm-22, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7289
in-theory        7289
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-21 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7289.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G)))), M:tm-21, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7290
in-theory        7290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-20 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7290.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-20, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7291
in-theory        7291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-19 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7291.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G)))), M:tm-19, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7292
in-theory        7292
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-7 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-7 tm-5 tm-2 tm-1 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7292.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> F)))), M:tm-7, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7293
in-theory        7293
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-6 tm-5 tm-2 tm-1 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7293.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) or G), M:tm-6, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7294
in-theory        7294
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> F))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7294.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> F))) and A)), M:tm-5, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7295
in-theory        7295
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-1 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-1 tm-5 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7295.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> F)))), M:tm-1, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7296
in-theory        7296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-183 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7296.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-183, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7297
in-theory        7297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-157 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7297.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-157, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7298
in-theory        7298
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     45
proof            (modus-ponens tm-147 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7298.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-147, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7299
in-theory        7299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-134 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7299.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-134, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7300
in-theory        7300
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     45
proof            (modus-ponens tm-125 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7300.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-125, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7301
in-theory        7301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J))))
theorem-size     45
proof            (modus-ponens tm-113 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7301.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-113, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7302
in-theory        7302
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     49
proof            (modus-ponens tm-105 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7302.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-105, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7303
in-theory        7303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-95 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7303.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-95, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7304
in-theory        7304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-83 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7304.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-83, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7305
in-theory        7305
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     35
proof            (modus-ponens tm-76 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7305.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-76, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7306
in-theory        7306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     41
proof            (modus-ponens tm-69 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7306.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-69, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7307
in-theory        7307
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     43
proof            (modus-ponens tm-54 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7307.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-54, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7308
in-theory        7308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-42 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7308.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-42, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7309
in-theory        7309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-32 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7309.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-32, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7310
in-theory        7310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-23 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7310.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-23, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7311
in-theory        7311
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-22 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7311.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-22, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7312
in-theory        7312
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-21 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7312.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-21, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7313
in-theory        7313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     43
proof            (modus-ponens tm-20 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7313.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-20, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7314
in-theory        7314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-19 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7314.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-19, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7315
in-theory        7315
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-7 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-4)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7315.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-7, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7316
in-theory        7316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) or G)
theorem-size     31
proof            (modus-ponens tm-6 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-4)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7316.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) or G), M:tm-6, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7317
in-theory        7317
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7317.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))) and A)), M:tm-5, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7318
in-theory        7318
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-1 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-4)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7318.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-1, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7319
in-theory        7319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-183 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7319.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-183, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7320
in-theory        7320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-157 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7320.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-157, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7321
in-theory        7321
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     37
proof            (modus-ponens tm-147 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7321.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-147, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7322
in-theory        7322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-134 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7322.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-134, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7323
in-theory        7323
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     37
proof            (modus-ponens tm-125 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7323.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-125, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7324
in-theory        7324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-113 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7324.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> J)))), M:tm-113, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7325
in-theory        7325
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-105 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7325.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-105, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7326
in-theory        7326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-95 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7326.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H)))), M:tm-95, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7327
in-theory        7327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-83 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7327.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-83, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7328
in-theory        7328
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> G))))
theorem-size     27
proof            (modus-ponens tm-76 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7328.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> G)))), M:tm-76, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7329
in-theory        7329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-69 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7329.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H)))), M:tm-69, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7330
in-theory        7330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-54 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7330.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-54, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7331
in-theory        7331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-42 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7331.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H)))), M:tm-42, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7332
in-theory        7332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-32 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7332.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H)))), M:tm-32, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7333
in-theory        7333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-23 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7333.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H)))), M:tm-23, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7334
in-theory        7334
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-22 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7334.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H)))), M:tm-22, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7335
in-theory        7335
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-21 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7335.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H)))), M:tm-21, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7336
in-theory        7336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-20 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7336.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-20, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7337
in-theory        7337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-19 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7337.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H)))), M:tm-19, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7338
in-theory        7338
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-7 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-1 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7338.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> G)))), M:tm-7, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7339
in-theory        7339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-1 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7339.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) or G), M:tm-6, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7340
in-theory        7340
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> G))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7340.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> G))) and A)), M:tm-5, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7341
in-theory        7341
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-1 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7341.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F and G) -> G)))), M:tm-1, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7342
in-theory        7342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-183 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7342.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-183, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7343
in-theory        7343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-157 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7343.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-157, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7344
in-theory        7344
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     39
proof            (modus-ponens tm-147 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7344.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-147, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7345
in-theory        7345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-134 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7345.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-134, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7346
in-theory        7346
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     39
proof            (modus-ponens tm-125 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7346.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-125, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7347
in-theory        7347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> I)) and H))))
theorem-size     39
proof            (modus-ponens tm-113 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7347.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-113, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7348
in-theory        7348
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     43
proof            (modus-ponens tm-105 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7348.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-105, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7349
in-theory        7349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-95 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7349.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-95, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7350
in-theory        7350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-83 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7350.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-83, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7351
in-theory        7351
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     29
proof            (modus-ponens tm-76 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7351.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-76, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7352
in-theory        7352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     35
proof            (modus-ponens tm-69 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7352.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-69, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7353
in-theory        7353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     37
proof            (modus-ponens tm-54 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7353.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-54, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7354
in-theory        7354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-42 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7354.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-42, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7355
in-theory        7355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-32 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7355.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-32, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7356
in-theory        7356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-23 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7356.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-23, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7357
in-theory        7357
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-22 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7357.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-22, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7358
in-theory        7358
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-21 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7358.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-21, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7359
in-theory        7359
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     37
proof            (modus-ponens tm-20 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7359.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-20, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7360
in-theory        7360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-19 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7360.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-19, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7361
in-theory        7361
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-7 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7361.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-7, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7362
in-theory        7362
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7362.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) or G), M:tm-6, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7363
in-theory        7363
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> F)) and E))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7363.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> F)) and E))) and A)), M:tm-5, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7364
in-theory        7364
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-1 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7364.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-1, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7365
in-theory        7365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-183 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7365.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-183, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7366
in-theory        7366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-157 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7366.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-157, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7367
in-theory        7367
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     47
proof            (modus-ponens tm-147 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7367.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-147, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7368
in-theory        7368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-134 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7368.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-134, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7369
in-theory        7369
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     47
proof            (modus-ponens tm-125 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7369.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-125, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7370
in-theory        7370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H))))
theorem-size     47
proof            (modus-ponens tm-113 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7370.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-113, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7371
in-theory        7371
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     51
proof            (modus-ponens tm-105 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7371.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-105, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7372
in-theory        7372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-95 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7372.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-95, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7373
in-theory        7373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-83 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7373.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-83, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7374
in-theory        7374
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     37
proof            (modus-ponens tm-76 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7374.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-76, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7375
in-theory        7375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     43
proof            (modus-ponens tm-69 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7375.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-69, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7376
in-theory        7376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     45
proof            (modus-ponens tm-54 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7376.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-54, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7377
in-theory        7377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-42 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7377.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-42, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7378
in-theory        7378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-32 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7378.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-32, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7379
in-theory        7379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-23 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7379.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-23, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7380
in-theory        7380
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-22 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7380.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-22, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7381
in-theory        7381
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-21 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7381.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-21, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7382
in-theory        7382
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     45
proof            (modus-ponens tm-20 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7382.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-20, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7383
in-theory        7383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-19 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7383.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-19, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7384
in-theory        7384
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-7 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7384.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-7, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7385
in-theory        7385
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) or H)
theorem-size     33
proof            (modus-ponens tm-6 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7385.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) or H), M:tm-6, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7386
in-theory        7386
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7386.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) and A)), M:tm-5, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7387
in-theory        7387
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-1 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7387.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-1, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7388
in-theory        7388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-183 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7388.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-183, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7389
in-theory        7389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-157 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7389.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-157, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7390
in-theory        7390
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-147 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7390.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-147, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7391
in-theory        7391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-134 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7391.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-134, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7392
in-theory        7392
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-125 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7392.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-125, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7393
in-theory        7393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-113 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7393.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-113, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7394
in-theory        7394
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     43
proof            (modus-ponens tm-105 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7394.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-105, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7395
in-theory        7395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-95 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7395.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-95, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7396
in-theory        7396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-83 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7396.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-83, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7397
in-theory        7397
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-76 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7397.         (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-76, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7398
in-theory        7398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-69 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7398.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-69, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7399
in-theory        7399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-54 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7399.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-54, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7400
in-theory        7400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-42 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7400.         ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-42, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7401
in-theory        7401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-32 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7401.         ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-32, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7402
in-theory        7402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-23 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7402.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-23, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7403
in-theory        7403
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-22 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7403.         (((A and B) -> B) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-22, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7404
in-theory        7404
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-21 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7404.         (((A and B) -> A) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-21, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7405
in-theory        7405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-20 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7405.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-20, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7406
in-theory        7406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-19 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7406.         ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-19, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7407
in-theory        7407
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-7 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7407.         (A or ((B -> (C -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-7, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7408
in-theory        7408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7408.         (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G), M:tm-6, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7409
in-theory        7409
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7409.         (A -> (((B -> (C -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and A)), M:tm-5, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7410
in-theory        7410
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-1 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7410.         (A -> ((B -> (C -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-1, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7411
in-theory        7411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-183 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7411.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-183, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7412
in-theory        7412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-157 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7412.         ((A -> ((B and C) -> C)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-157, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7413
in-theory        7413
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and B) -> B)))))
theorem-size     27
proof            (modus-ponens tm-153 tm-206 ((A (-> (-> (and B C) C) (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and B C) C))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7413.         (not (((A and B) -> B) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and B) -> B))))), M:tm-153, m:tm-206, u:((A (-> (-> (and B C) C) (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and B C) C))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-7414
in-theory        7414
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     37
proof            (modus-ponens tm-147 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7414.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-147, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7415
in-theory        7415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-134 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7415.         ((A -> ((B and C) -> B)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-134, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7416
in-theory        7416
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and B) -> A)))))
theorem-size     27
proof            (modus-ponens tm-130 tm-206 ((A (-> (-> (and B C) B) (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and B C) B))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7416.         (not (((A and B) -> A) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and B) -> A))))), M:tm-130, m:tm-206, u:((A (-> (-> (and B C) B) (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and B C) B))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-7417
in-theory        7417
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     37
proof            (modus-ponens tm-125 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7417.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-125, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7418
in-theory        7418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-113 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7418.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E))), M:tm-113, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7419
in-theory        7419
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))))
theorem-size     43
proof            (modus-ponens tm-109 tm-206 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-5)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7419.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))), M:tm-109, m:tm-206, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-7420
in-theory        7420
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     41
proof            (modus-ponens tm-105 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7420.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-105, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7421
in-theory        7421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C)))
theorem-size     29
proof            (modus-ponens tm-95 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7421.         (((A -> B) -> (A -> A)) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C))), M:tm-95, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7422
in-theory        7422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (E -> (not A)))
theorem-size     23
proof            (modus-ponens tm-84 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7422.         ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (E -> (not A))), M:tm-84, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-7423
in-theory        7423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-83 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7423.         ((A -> (B -> (C -> B))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-83, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7424
in-theory        7424
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B -> A))))))
theorem-size     27
proof            (modus-ponens tm-79 tm-206 ((A (-> (-> B (-> C B)) (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B (-> C B)))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7424.         (not ((A -> (B -> A)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B -> A)))))), M:tm-79, m:tm-206, u:((A (-> (-> B (-> C B)) (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B (-> C B)))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-7425
in-theory        7425
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) -> (not B)))
theorem-size     27
proof            (modus-ponens tm-76 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7425.         (((not (not A)) -> A) and ((B -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) -> (not B))), M:tm-76, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7426
in-theory        7426
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))) or (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))) -> (not A))
theorem-size     42
proof            (modus-ponens tm-73 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-5 tm-2)
proof-size       140
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7426.         (((not (not (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))) or (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))) -> (not A)), M:tm-73, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-7427
in-theory        7427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C)))
theorem-size     33
proof            (modus-ponens tm-69 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7427.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C))), M:tm-69, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7428
in-theory        7428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     35
proof            (modus-ponens tm-54 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7428.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-54, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7429
in-theory        7429
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))) or (B -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))) -> (not B))
theorem-size     42
proof            (modus-ponens tm-47 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-5 tm-2)
proof-size       140
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7429.         (((A and (B -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))) or (B -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))) -> (not B)), M:tm-47, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-7430
in-theory        7430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and E) or (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))) -> (not A))
theorem-size     42
proof            (modus-ponens tm-46 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-5 tm-2)
proof-size       140
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7430.         ((((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and E) or (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))) -> (not A)), M:tm-46, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-7431
in-theory        7431
times-derived    1
----------------------------------------------------------------
theorem          (((not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) or (D -> (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)))) -> (not D))
theorem-size     38
proof            (modus-ponens tm-44 tm-206 ((A Am) (B (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-5 tm-2)
proof-size       138
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7431.         (((not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) or (D -> (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)))) -> (not D)), M:tm-44, m:tm-206, u:((A Am) (B (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (C (not Am)))
================================================================
tm-name          tm-7432
in-theory        7432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C)))
theorem-size     27
proof            (modus-ponens tm-42 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7432.         ((A -> (B or A)) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C))), M:tm-42, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7433
in-theory        7433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C)))
theorem-size     27
proof            (modus-ponens tm-32 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7433.         ((A -> (A or B)) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C))), M:tm-32, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7434
in-theory        7434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (not A)))
theorem-size     40
proof            (modus-ponens tm-24 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       138
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7434.         ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (not A))), M:tm-24, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-7435
in-theory        7435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C)))
theorem-size     29
proof            (modus-ponens tm-23 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7435.         ((A -> (B -> (A and B))) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C))), M:tm-23, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7436
in-theory        7436
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C)))
theorem-size     27
proof            (modus-ponens tm-22 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7436.         (((A and B) -> B) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C))), M:tm-22, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7437
in-theory        7437
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C)))
theorem-size     27
proof            (modus-ponens tm-21 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7437.         (((A and B) -> A) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C))), M:tm-21, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7438
in-theory        7438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     35
proof            (modus-ponens tm-20 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7438.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-20, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7439
in-theory        7439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C)))
theorem-size     27
proof            (modus-ponens tm-19 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7439.         ((A -> (B -> A)) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C))), M:tm-19, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7440
in-theory        7440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     37
proof            (modus-ponens tm-12 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7440.         ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-12, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-7441
in-theory        7441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not (not A))) -> (not (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))))
theorem-size     42
proof            (modus-ponens tm-9 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-9 tm-5 tm-2)
proof-size       122
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7441.         (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not (not A))) -> (not (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))), M:tm-9, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-7442
in-theory        7442
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))) or (not A)) -> B))
theorem-size     28
proof            (modus-ponens tm-8 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-5 tm-2)
proof-size       110
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7442.         (((not A) -> B) -> (((A -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))) or (not A)) -> B)), M:tm-8, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-7443
in-theory        7443
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) -> (not B)))
theorem-size     23
proof            (modus-ponens tm-7 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-5 tm-2)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7443.         (A or ((B -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) -> (not B))), M:tm-7, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7444
in-theory        7444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-5 tm-2)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7444.         (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) or E), M:tm-6, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7445
in-theory        7445
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) -> (not B)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7445.         (A -> (((B -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) -> (not B)) and A)), M:tm-5, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7446
in-theory        7446
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) -> (not B)))
theorem-size     23
proof            (modus-ponens tm-1 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-5 tm-2)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7446.         (A -> ((B -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) -> (not B))), M:tm-1, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7447
in-theory        7447
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     35
proof            (modus-ponens tm-207 tm-1 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7447.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-1, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7448
in-theory        7448
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     31
proof            (modus-ponens tm-207 tm-3 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-7448.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-207, m:tm-3, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-7449
in-theory        7449
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> A)
theorem-size     19
proof            (modus-ponens tm-207 tm-4 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E Bm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-7449.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> A), M:tm-207, m:tm-4, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E Bm))
================================================================
tm-name          tm-7450
in-theory        7450
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and E)))
theorem-size     37
proof            (modus-ponens tm-207 tm-5 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       131
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7450.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and E))), M:tm-207, m:tm-5, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm))))
================================================================
tm-name          tm-7451
in-theory        7451
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) or E))
theorem-size     35
proof            (modus-ponens tm-207 tm-6 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7451.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) or E)), M:tm-207, m:tm-6, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm)))
================================================================
tm-name          tm-7452
in-theory        7452
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     35
proof            (modus-ponens tm-207 tm-7 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-7452.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-7, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7453
in-theory        7453
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-207 tm-11 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7453.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (F -> E))), M:tm-207, m:tm-11, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-7454
in-theory        7454
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-207 tm-14 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7454.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-207, m:tm-14, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-7455
in-theory        7455
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-207 tm-16 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7455.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E and F) -> E)), M:tm-207, m:tm-16, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-7456
in-theory        7456
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-207 tm-18 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7456.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E and F) -> F)), M:tm-207, m:tm-18, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-7457
in-theory        7457
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     39
proof            (modus-ponens tm-207 tm-19 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7457.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-19, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7458
in-theory        7458
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     47
proof            (modus-ponens tm-207 tm-20 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7458.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-20, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7459
in-theory        7459
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E and F) -> E) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     39
proof            (modus-ponens tm-207 tm-21 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (and Bm Cm) Bm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7459.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E and F) -> E) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-21, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (and Bm Cm) Bm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7460
in-theory        7460
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E and F) -> F) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     39
proof            (modus-ponens tm-207 tm-22 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (and Bm Cm) Cm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7460.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E and F) -> F) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-22, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (and Bm Cm) Cm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7461
in-theory        7461
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> (E and F))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-23 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (and Bm Cm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7461.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> (E and F))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-23, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (and Bm Cm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7462
in-theory        7462
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-207 tm-25 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7462.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (F -> (E and F)))), M:tm-207, m:tm-25, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-7463
in-theory        7463
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (E or F)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     39
proof            (modus-ponens tm-207 tm-32 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (or Bm Cm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7463.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (E or F)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-32, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (or Bm Cm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7464
in-theory        7464
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-207 tm-33 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7464.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (E or F))), M:tm-207, m:tm-33, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-7465
in-theory        7465
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F or E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     39
proof            (modus-ponens tm-207 tm-42 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (or Cm Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7465.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F or E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-42, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (or Cm Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7466
in-theory        7466
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-207 tm-43 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7466.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (F or E))), M:tm-207, m:tm-43, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-7467
in-theory        7467
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     47
proof            (modus-ponens tm-207 tm-54 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7467.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-54, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7468
in-theory        7468
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-207 tm-56 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7468.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))), M:tm-207, m:tm-56, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-7469
in-theory        7469
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> ((E -> (not F)) -> (not E))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     45
proof            (modus-ponens tm-207 tm-69 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-9)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7469.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> ((E -> (not F)) -> (not E))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-69, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7470
in-theory        7470
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> F) -> ((E -> (not F)) -> (not E))))
theorem-size     29
proof            (modus-ponens tm-207 tm-71 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-9)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7470.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> F) -> ((E -> (not F)) -> (not E)))), M:tm-207, m:tm-71, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-7471
in-theory        7471
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((not (not E)) -> E) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     39
proof            (modus-ponens tm-207 tm-76 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (not (not Bm)) Bm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-10)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7471.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((not (not E)) -> E) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-76, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (not (not Bm)) Bm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7472
in-theory        7472
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((not (not E)) -> E))
theorem-size     23
proof            (modus-ponens tm-207 tm-78 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-10)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7472.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((not (not E)) -> E)), M:tm-207, m:tm-78, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-7473
in-theory        7473
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> (G -> F))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-83 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (-> Dm Cm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7473.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> (G -> F))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-83, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (-> Dm Cm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7474
in-theory        7474
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-207 tm-85 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7474.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (F -> (G -> F)))), M:tm-207, m:tm-85, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7475
in-theory        7475
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))
theorem-size     33
proof            (modus-ponens tm-207 tm-86 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7475.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-207, m:tm-86, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))
================================================================
tm-name          tm-7476
in-theory        7476
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> (E -> E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-95 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> Bm Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7476.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> (E -> E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-95, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> Bm Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7477
in-theory        7477
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> F) -> (E -> E)))
theorem-size     25
proof            (modus-ponens tm-207 tm-97 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7477.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> F) -> (E -> E))), M:tm-207, m:tm-97, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-7478
in-theory        7478
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     53
proof            (modus-ponens tm-207 tm-105 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7478.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-105, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7479
in-theory        7479
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-207 tm-107 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7479.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-207, m:tm-107, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-7480
in-theory        7480
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     49
proof            (modus-ponens tm-207 tm-113 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7480.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-113, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7481
in-theory        7481
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-207 tm-115 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7481.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-207, m:tm-115, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7482
in-theory        7482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (A -> (B -> C)))) -> ((A -> B) -> (A -> C)))
theorem-size     33
proof            (modus-ponens tm-207 tm-116 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> A (-> B C))) (E (-> (-> A B) (-> A C)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3 tm-4)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-7482.         (((A -> (B -> C)) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (A -> (B -> C)))) -> ((A -> B) -> (A -> C))), M:tm-207, m:tm-116, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> A (-> B C))) (E (-> (-> A B) (-> A C))))
================================================================
tm-name          tm-7483
in-theory        7483
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> B)) -> ((B -> C) -> (B -> B))) and A)) -> ((B -> C) -> (B -> B)))
theorem-size     25
proof            (modus-ponens tm-207 tm-117 ((A Am) (B Bm) (C Am) (Cm (-> (-> Am Bm) (-> Am Am))) (D Dm) (E (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-7483.         ((A or (((B -> (C -> B)) -> ((B -> C) -> (B -> B))) and A)) -> ((B -> C) -> (B -> B))), M:tm-207, m:tm-117, u:((A Am) (B Bm) (C Am) (Cm (-> (-> Am Bm) (-> Am Am))) (D Dm) (E (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-7484
in-theory        7484
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and A)) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     57
proof            (modus-ponens tm-207 tm-118 ((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)) (Dm (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (D Em) (E (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-3 tm-1)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7484.         ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and A)) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-207, m:tm-118, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)) (Dm (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (D Em) (E (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-7485
in-theory        7485
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     49
proof            (modus-ponens tm-207 tm-125 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7485.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-125, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7486
in-theory        7486
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-207 tm-127 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-3)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7486.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))), M:tm-207, m:tm-127, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-7487
in-theory        7487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((((B -> C) and D) -> (B -> C)) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and A)) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))
theorem-size     45
proof            (modus-ponens tm-207 tm-128 ((A (and (-> B C) Bm)) (Am (-> B C)) (Cm (-> (-> (and (-> B C) Bm) B) (-> (and (-> B C) Bm) C))) (D Dm) (E (-> (-> (and (-> B C) Bm) B) (-> (and (-> B C) Bm) C)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-7487.         ((A or (((((B -> C) and D) -> (B -> C)) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and A)) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-207, m:tm-128, u:((A (and (-> B C) Bm)) (Am (-> B C)) (Cm (-> (-> (and (-> B C) Bm) B) (-> (and (-> B C) Bm) C))) (D Dm) (E (-> (-> (and (-> B C) Bm) B) (-> (and (-> B C) Bm) C))))
================================================================
tm-name          tm-7488
in-theory        7488
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> ((F and G) -> F)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-134 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> (and Cm Dm) Cm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7488.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> ((F and G) -> F)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-134, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> (and Cm Dm) Cm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7489
in-theory        7489
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-207 tm-136 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7489.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((F and G) -> F))), M:tm-207, m:tm-136, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7490
in-theory        7490
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D)
theorem-size     47
proof            (modus-ponens tm-207 tm-137 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)) (E Bm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-3)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-7490.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D), M:tm-207, m:tm-137, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)) (E Bm))
================================================================
tm-name          tm-7491
in-theory        7491
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> A)) -> C))) -> C)
theorem-size     31
proof            (modus-ponens tm-207 tm-138 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm (-> Cm Bm)) Dm)) (E Dm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-7491.         ((((A -> (B -> A)) -> C) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> A)) -> C))) -> C), M:tm-207, m:tm-138, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm (-> Cm Bm)) Dm)) (E Dm))
================================================================
tm-name          tm-7492
in-theory        7492
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D)
theorem-size     47
proof            (modus-ponens tm-207 tm-139 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (E Em)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-1)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7492.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D), M:tm-207, m:tm-139, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (E Em))
================================================================
tm-name          tm-7493
in-theory        7493
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> A) -> C))) -> C)
theorem-size     31
proof            (modus-ponens tm-207 tm-140 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (and Bm Cm) Bm) Dm)) (E Dm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-7493.         (((((A and B) -> A) -> C) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> A) -> C))) -> C), M:tm-207, m:tm-140, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (and Bm Cm) Bm) Dm)) (E Dm))
================================================================
tm-name          tm-7494
in-theory        7494
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     49
proof            (modus-ponens tm-207 tm-147 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7494.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-147, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7495
in-theory        7495
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-207 tm-149 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-4)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7495.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))), M:tm-207, m:tm-149, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-7496
in-theory        7496
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> B) -> C))) -> C)
theorem-size     31
proof            (modus-ponens tm-207 tm-150 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (and Bm Cm) Cm) Dm)) (E Dm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-7496.         (((((A and B) -> B) -> C) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> B) -> C))) -> C), M:tm-207, m:tm-150, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (and Bm Cm) Cm) Dm)) (E Dm))
================================================================
tm-name          tm-7497
in-theory        7497
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and (C -> D)) -> (C -> D)) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and A)) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))
theorem-size     45
proof            (modus-ponens tm-207 tm-151 ((A (and Am (-> B C))) (Bm (-> B C)) (Cm (-> (-> (and Am (-> B C)) B) (-> (and Am (-> B C)) C))) (D Dm) (E (-> (-> (and Am (-> B C)) B) (-> (and Am (-> B C)) C)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-7497.         ((A or ((((B and (C -> D)) -> (C -> D)) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and A)) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-207, m:tm-151, u:((A (and Am (-> B C))) (Bm (-> B C)) (Cm (-> (-> (and Am (-> B C)) B) (-> (and Am (-> B C)) C))) (D Dm) (E (-> (-> (and Am (-> B C)) B) (-> (and Am (-> B C)) C))))
================================================================
tm-name          tm-7498
in-theory        7498
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> ((F and G) -> G)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-157 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> (and Cm Dm) Dm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7498.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> ((F and G) -> G)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-157, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> (and Cm Dm) Dm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7499
in-theory        7499
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-207 tm-159 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7499.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((F and G) -> G))), M:tm-207, m:tm-159, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7500
in-theory        7500
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> ((F -> (G -> F)) and E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     43
proof            (modus-ponens tm-207 tm-183 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7500.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> ((F -> (G -> F)) and E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-183, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7501
in-theory        7501
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((F -> (G -> F)) and E)))
theorem-size     27
proof            (modus-ponens tm-207 tm-184 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7501.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((F -> (G -> F)) and E))), M:tm-207, m:tm-184, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-7502
in-theory        7502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-183 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7502.         ((A -> ((B -> (C -> B)) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-183, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7503
in-theory        7503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-157 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7503.         ((A -> ((B and C) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-157, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7504
in-theory        7504
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> E)) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> E))
theorem-size     39
proof            (modus-ponens tm-154 tm-207 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Em Dm) (B Dm) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Dm))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7504.         ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> E)) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> E)), M:tm-154, m:tm-207, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Em Dm) (B Dm) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Dm)))
================================================================
tm-name          tm-7505
in-theory        7505
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-147 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7505.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-147, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7506
in-theory        7506
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> E)) -> D) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> E)) -> E)) -> (((D -> E) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> E))) -> E))
theorem-size     63
proof            (modus-ponens tm-144 tm-207 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B Em)) (C Em) (D (-> (or (-> B Em) (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B Em))) Em))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       223
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7506.         ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> E)) -> D) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> E)) -> E)) -> (((D -> E) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> E))) -> E)), M:tm-144, m:tm-207, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B Em)) (C Em) (D (-> (or (-> B Em) (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B Em))) Em)))
================================================================
tm-name          tm-7507
in-theory        7507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-134 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7507.         ((A -> ((B and C) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-134, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7508
in-theory        7508
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     63
proof            (modus-ponens tm-131 tm-207 ((Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7508.         ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-131, m:tm-207, u:((Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-7509
in-theory        7509
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-125 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7509.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-125, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7510
in-theory        7510
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> (A -> (B -> C))) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> ((A -> B) -> (A -> C)))) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> ((A -> B) -> (A -> C))))
theorem-size     71
proof            (modus-ponens tm-122 tm-207 ((A (-> Am (-> Bm Cm))) (Em (-> (-> Am Bm) (-> Am Cm))) (C Dm) (B (-> (-> Am Bm) (-> Am Cm))) (D (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       231
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7510.         ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> (A -> (B -> C))) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> ((A -> B) -> (A -> C)))) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> ((A -> B) -> (A -> C)))), M:tm-122, m:tm-207, u:((A (-> Am (-> Bm Cm))) (Em (-> (-> Am Bm) (-> Am Cm))) (C Dm) (B (-> (-> Am Bm) (-> Am Cm))) (D (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-7511
in-theory        7511
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> (E -> F)) -> (((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> F)))
theorem-size     59
proof            (modus-ponens tm-114 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> C D))) (B (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7511.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> (E -> F)) -> (((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> F))), M:tm-114, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> C D))) (B (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> C D)))
================================================================
tm-name          tm-7512
in-theory        7512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H) -> I) -> ((H or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H)) -> I)))
theorem-size     53
proof            (modus-ponens tm-113 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7512.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H) -> I) -> ((H or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H)) -> I))), M:tm-113, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7513
in-theory        7513
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     57
proof            (modus-ponens tm-105 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       219
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7513.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-105, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7514
in-theory        7514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G)))
theorem-size     45
proof            (modus-ponens tm-95 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7514.         (((A -> B) -> (A -> A)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G))), M:tm-95, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7515
in-theory        7515
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)))
theorem-size     83
proof            (modus-ponens tm-92 tm-207 ((Em (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       223
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7515.         ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))), M:tm-92, m:tm-207, u:((Em (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-7516
in-theory        7516
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (F -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))
theorem-size     39
proof            (modus-ponens tm-84 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7516.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (F -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))), M:tm-84, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-7517
in-theory        7517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-83 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7517.         ((A -> (B -> (C -> B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-83, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7518
in-theory        7518
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> (F -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> (F -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E))))
theorem-size     71
proof            (modus-ponens tm-80 tm-207 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7518.         ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> (F -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> (F -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))), M:tm-80, m:tm-207, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-7519
in-theory        7519
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> F) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> F)))
theorem-size     43
proof            (modus-ponens tm-76 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7519.         (((not (not A)) -> A) and (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> F) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> F))), M:tm-76, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7520
in-theory        7520
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E))) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E)) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))
theorem-size     57
proof            (modus-ponens tm-73 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-8 tm-10 tm-5 tm-2)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7520.         (((not (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E))) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E)) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-73, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-7521
in-theory        7521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G)))
theorem-size     49
proof            (modus-ponens tm-69 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       169
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7521.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G))), M:tm-69, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7522
in-theory        7522
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> (D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) or (D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> (D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))))
theorem-size     85
proof            (modus-ponens tm-55 tm-207 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (B (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       215
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7522.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> (D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) or (D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> (D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)))), M:tm-55, m:tm-207, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (B (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-7523
in-theory        7523
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     51
proof            (modus-ponens tm-54 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       175
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7523.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-54, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7524
in-theory        7524
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E))))
theorem-size     71
proof            (modus-ponens tm-48 tm-207 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (and B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (and B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       195
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7524.         ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))), M:tm-48, m:tm-207, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (and B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (and B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-7525
in-theory        7525
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> F)) or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> F)) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> F))
theorem-size     57
proof            (modus-ponens tm-47 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7525.         (((A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> F)) or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> F)) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> F)), M:tm-47, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-7526
in-theory        7526
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) and F) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E)) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))
theorem-size     57
proof            (modus-ponens tm-46 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7526.         (((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) and F) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E)) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-46, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-7527
in-theory        7527
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> A)) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> A))
theorem-size     39
proof            (modus-ponens tm-44 tm-207 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B Em) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7527.         ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> A)) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> A)), M:tm-44, m:tm-207, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B Em) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-7528
in-theory        7528
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-42 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7528.         ((A -> (B or A)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G))), M:tm-42, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7529
in-theory        7529
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-32 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7529.         ((A -> (A or B)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G))), M:tm-32, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7530
in-theory        7530
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) and ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))
theorem-size     55
proof            (modus-ponens tm-24 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7530.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) and ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))), M:tm-24, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-7531
in-theory        7531
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G)))
theorem-size     45
proof            (modus-ponens tm-23 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7531.         ((A -> (B -> (A and B))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G))), M:tm-23, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7532
in-theory        7532
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-22 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7532.         (((A and B) -> B) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G))), M:tm-22, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7533
in-theory        7533
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-21 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7533.         (((A and B) -> A) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G))), M:tm-21, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7534
in-theory        7534
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     51
proof            (modus-ponens tm-20 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       175
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7534.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-20, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7535
in-theory        7535
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-19 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7535.         ((A -> (B -> A)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G))), M:tm-19, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7536
in-theory        7536
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E))
theorem-size     35
proof            (modus-ponens tm-12 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7536.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E)), M:tm-12, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-7537
in-theory        7537
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (not ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))) -> (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E)))
theorem-size     57
proof            (modus-ponens tm-9 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-9 tm-8 tm-5 tm-2)
proof-size       155
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7537.         ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (not ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))) -> (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E))), M:tm-9, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-7538
in-theory        7538
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) -> F) -> ((((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) -> E) or ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E)) -> F))
theorem-size     61
proof            (modus-ponens tm-8 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       161
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7538.         ((((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) -> F) -> ((((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) -> E) or ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E)) -> F)), M:tm-8, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-7539
in-theory        7539
times-derived    2
----------------------------------------------------------------
theorem          (A or (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> F) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> F)))
theorem-size     39
proof            (modus-ponens tm-7 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-7 tm-8 tm-5 tm-2)
proof-size       131
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7539.         (A or (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> F) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> F))), M:tm-7, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7540
in-theory        7540
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) or F)
theorem-size     39
proof            (modus-ponens tm-6 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-6 tm-8 tm-5 tm-2)
proof-size       131
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7540.         ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) or F), M:tm-6, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7541
in-theory        7541
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> F) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> F)) and A))
theorem-size     41
proof            (modus-ponens tm-5 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       135
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7541.         (A -> ((((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> F) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> F)) and A)), M:tm-5, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7542
in-theory        7542
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> E))
theorem-size     55
proof            (modus-ponens tm-2 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C Em)))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       155
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7542.         ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> E)), M:tm-2, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C Em))
================================================================
tm-name          tm-7543
in-theory        7543
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> F) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> F)))
theorem-size     39
proof            (modus-ponens tm-1 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-1 tm-8 tm-5 tm-2)
proof-size       131
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7543.         (A -> (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> F) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> F))), M:tm-1, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7544
in-theory        7544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-183 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7544.         ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-183, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7545
in-theory        7545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-157 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7545.         ((A -> ((B and C) -> C)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-157, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7546
in-theory        7546
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-147 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7546.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-147, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7547
in-theory        7547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-134 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7547.         ((A -> ((B and C) -> B)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-134, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7548
in-theory        7548
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-125 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7548.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-125, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7549
in-theory        7549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-113 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7549.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-113, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7550
in-theory        7550
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     39
proof            (modus-ponens tm-105 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7550.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-105, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7551
in-theory        7551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-95 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7551.         (((A -> B) -> (A -> A)) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-95, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7552
in-theory        7552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-83 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7552.         ((A -> (B -> (C -> B))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-83, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7553
in-theory        7553
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     25
proof            (modus-ponens tm-76 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7553.         (((not (not A)) -> A) and (B or (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-76, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7554
in-theory        7554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     31
proof            (modus-ponens tm-69 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7554.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-69, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7555
in-theory        7555
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-54 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7555.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-54, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7556
in-theory        7556
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-42 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7556.         ((A -> (B or A)) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-42, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7557
in-theory        7557
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-32 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7557.         ((A -> (A or B)) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-32, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7558
in-theory        7558
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-23 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7558.         ((A -> (B -> (A and B))) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-23, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7559
in-theory        7559
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-22 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7559.         (((A and B) -> B) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-22, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7560
in-theory        7560
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-21 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7560.         (((A and B) -> A) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-21, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7561
in-theory        7561
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-20 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7561.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-20, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7562
in-theory        7562
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-19 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7562.         ((A -> (B -> A)) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-19, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7563
in-theory        7563
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     21
proof            (modus-ponens tm-7 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7563.         (A or (B or (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-7, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7564
in-theory        7564
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-6 tm-7 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7564.         ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) or F), M:tm-6, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7565
in-theory        7565
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7565.         (A -> ((B or (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and A)), M:tm-5, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7566
in-theory        7566
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     21
proof            (modus-ponens tm-1 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-1 tm-7 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7566.         (A -> (B or (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-1, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7567
in-theory        7567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     29
proof            (modus-ponens tm-183 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7567.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-183, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7568
in-theory        7568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-157 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7568.         ((A -> ((B and C) -> C)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-157, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7569
in-theory        7569
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     35
proof            (modus-ponens tm-147 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7569.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-147, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7570
in-theory        7570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-134 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7570.         ((A -> ((B and C) -> B)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-134, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7571
in-theory        7571
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     35
proof            (modus-ponens tm-125 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7571.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-125, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7572
in-theory        7572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I))
theorem-size     35
proof            (modus-ponens tm-113 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7572.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I)), M:tm-113, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7573
in-theory        7573
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     39
proof            (modus-ponens tm-105 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7573.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-105, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7574
in-theory        7574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G))
theorem-size     27
proof            (modus-ponens tm-95 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7574.         (((A -> B) -> (A -> A)) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G)), M:tm-95, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7575
in-theory        7575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-83 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7575.         ((A -> (B -> (C -> B))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-83, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7576
in-theory        7576
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) or F))
theorem-size     25
proof            (modus-ponens tm-76 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-10 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7576.         (((not (not A)) -> A) and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) or F)), M:tm-76, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7577
in-theory        7577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G))
theorem-size     31
proof            (modus-ponens tm-69 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-9 tm-6 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7577.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G)), M:tm-69, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7578
in-theory        7578
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     33
proof            (modus-ponens tm-54 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7578.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-54, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7579
in-theory        7579
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G))
theorem-size     25
proof            (modus-ponens tm-42 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7579.         ((A -> (B or A)) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G)), M:tm-42, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7580
in-theory        7580
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G))
theorem-size     25
proof            (modus-ponens tm-32 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7580.         ((A -> (A or B)) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G)), M:tm-32, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7581
in-theory        7581
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G))
theorem-size     27
proof            (modus-ponens tm-23 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7581.         ((A -> (B -> (A and B))) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G)), M:tm-23, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7582
in-theory        7582
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G))
theorem-size     25
proof            (modus-ponens tm-22 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7582.         (((A and B) -> B) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G)), M:tm-22, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7583
in-theory        7583
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G))
theorem-size     25
proof            (modus-ponens tm-21 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7583.         (((A and B) -> A) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G)), M:tm-21, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7584
in-theory        7584
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     33
proof            (modus-ponens tm-20 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7584.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-20, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7585
in-theory        7585
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G))
theorem-size     25
proof            (modus-ponens tm-19 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7585.         ((A -> (B -> A)) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G)), M:tm-19, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7586
in-theory        7586
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) or F))
theorem-size     21
proof            (modus-ponens tm-7 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-7 tm-6 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7586.         (A or ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) or F)), M:tm-7, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7587
in-theory        7587
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7587.         (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) or F), M:tm-6, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7588
in-theory        7588
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) or F) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7588.         (A -> (((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) or F) and A)), M:tm-5, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7589
in-theory        7589
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) or F))
theorem-size     21
proof            (modus-ponens tm-1 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-1 tm-6 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7589.         (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) or F)), M:tm-1, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7590
in-theory        7590
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-210 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7590.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> E))), M:tm-210, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-7591
in-theory        7591
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7591.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-210, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-7592
in-theory        7592
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-210 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-7592.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and F) -> E)), M:tm-210, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-7593
in-theory        7593
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-210 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-7593.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and F) -> F)), M:tm-210, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-7594
in-theory        7594
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-210 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7594.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (E and F)))), M:tm-210, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-7595
in-theory        7595
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-210 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7595.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E or F))), M:tm-210, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-7596
in-theory        7596
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-210 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-7596.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or E))), M:tm-210, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-7597
in-theory        7597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7597.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))), M:tm-210, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-7598
in-theory        7598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((E -> (not F)) -> (not E))))
theorem-size     29
proof            (modus-ponens tm-210 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7598.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((E -> (not F)) -> (not E)))), M:tm-210, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-7599
in-theory        7599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((not (not E)) -> E))
theorem-size     23
proof            (modus-ponens tm-210 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-7599.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((not (not E)) -> E)), M:tm-210, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-7600
in-theory        7600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-210 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7600.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (G -> F)))), M:tm-210, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-7601
in-theory        7601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (E -> E)))
theorem-size     25
proof            (modus-ponens tm-210 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-7601.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (E -> E))), M:tm-210, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-7602
in-theory        7602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-210 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7602.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-210, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-7603
in-theory        7603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7603.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-210, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-7604
in-theory        7604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-210 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7604.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))), M:tm-210, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-7605
in-theory        7605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-210 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7605.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F and G) -> F))), M:tm-210, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-7606
in-theory        7606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-210 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7606.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))), M:tm-210, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-7607
in-theory        7607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-210 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7607.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F and G) -> G))), M:tm-210, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-7608
in-theory        7608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> F)) and E)))
theorem-size     27
proof            (modus-ponens tm-210 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7608.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> F)) and E))), M:tm-210, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-7609
in-theory        7609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     35
proof            (modus-ponens tm-210 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7609.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-210, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-7610
in-theory        7610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F and G) -> F) and E)))
theorem-size     27
proof            (modus-ponens tm-210 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7610.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F and G) -> F) and E))), M:tm-210, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-7611
in-theory        7611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F and G) -> G) and E)))
theorem-size     27
proof            (modus-ponens tm-210 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7611.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F and G) -> G) and E))), M:tm-210, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-7612
in-theory        7612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> (F and G))) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7612.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> (F and G))) and E))), M:tm-210, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-7613
in-theory        7613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (E -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-210 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7613.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (E -> (E and F)))), M:tm-210, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-7614
in-theory        7614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7614.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (G -> (F and G))))), M:tm-210, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-7615
in-theory        7615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-210 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7615.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) or G)), M:tm-210, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-7616
in-theory        7616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))
theorem-size     33
proof            (modus-ponens tm-210 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7616.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)), M:tm-210, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-7617
in-theory        7617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) or G))
theorem-size     25
proof            (modus-ponens tm-210 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7617.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) or G)), M:tm-210, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-7618
in-theory        7618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) or G))
theorem-size     25
proof            (modus-ponens tm-210 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7618.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) or G)), M:tm-210, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-7619
in-theory        7619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) or G))
theorem-size     27
proof            (modus-ponens tm-210 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7619.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) or G)), M:tm-210, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-7620
in-theory        7620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) or G))
theorem-size     25
proof            (modus-ponens tm-210 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7620.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) or G)), M:tm-210, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-7621
in-theory        7621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (F or G)) and E)))
theorem-size     27
proof            (modus-ponens tm-210 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7621.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (F or G)) and E))), M:tm-210, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-7622
in-theory        7622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-210 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7622.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (F or G)))), M:tm-210, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-7623
in-theory        7623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-210 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7623.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (G -> F)))), M:tm-210, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-7624
in-theory        7624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7624.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-210, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-7625
in-theory        7625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-210 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7625.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F and G) -> F))), M:tm-210, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-7626
in-theory        7626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-210 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7626.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F and G) -> G))), M:tm-210, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-7627
in-theory        7627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7627.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (G -> (F and G))))), M:tm-210, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-7628
in-theory        7628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-210 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7628.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (F or G)))), M:tm-210, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-7629
in-theory        7629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-210 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7629.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (G or F)))), M:tm-210, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-7630
in-theory        7630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) or G))
theorem-size     25
proof            (modus-ponens tm-210 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7630.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) or G)), M:tm-210, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-7631
in-theory        7631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G or F)) and E)))
theorem-size     27
proof            (modus-ponens tm-210 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7631.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G or F)) and E))), M:tm-210, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-7632
in-theory        7632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-210 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7632.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (G or F)))), M:tm-210, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-7633
in-theory        7633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-210 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7633.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))), M:tm-210, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-7634
in-theory        7634
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     43
proof            (modus-ponens tm-210 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7634.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-210, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-7635
in-theory        7635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (((E and G) or E) -> F)))
theorem-size     29
proof            (modus-ponens tm-210 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7635.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (((E and G) or E) -> F))), M:tm-210, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-7636
in-theory        7636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (((G and E) or E) -> F)))
theorem-size     29
proof            (modus-ponens tm-210 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7636.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (((G and E) or E) -> F))), M:tm-210, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-7637
in-theory        7637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-210 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7637.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))), M:tm-210, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-7638
in-theory        7638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-210 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7638.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E or F) -> G) -> ((E or (E or F)) -> G))), M:tm-210, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-7639
in-theory        7639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-210 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-7639.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E or F) -> G) -> ((F or (E or F)) -> G))), M:tm-210, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-7640
in-theory        7640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     45
proof            (modus-ponens tm-210 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7640.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-210, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-7641
in-theory        7641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7641.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-210, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-7642
in-theory        7642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))
theorem-size     33
proof            (modus-ponens tm-210 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7642.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)), M:tm-210, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-7643
in-theory        7643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E)))
theorem-size     35
proof            (modus-ponens tm-210 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7643.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E))), M:tm-210, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-7644
in-theory        7644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-210 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-7644.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G)))), M:tm-210, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-7645
in-theory        7645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7645.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-210, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-7646
in-theory        7646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (F -> E))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-210 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7646.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (F -> E))) -> (not E))), M:tm-210, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-7647
in-theory        7647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7647.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G))))), M:tm-210, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-7648
in-theory        7648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> (not E)) -> (not (E and F))))
theorem-size     29
proof            (modus-ponens tm-210 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7648.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> (not E)) -> (not (E and F)))), M:tm-210, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-7649
in-theory        7649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> (not F)) -> (not (E and F))))
theorem-size     29
proof            (modus-ponens tm-210 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-4)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7649.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> (not F)) -> (not (E and F)))), M:tm-210, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-7650
in-theory        7650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (F -> (E and F)))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7650.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (F -> (E and F)))) -> (not E))), M:tm-210, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-7651
in-theory        7651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (E or F))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-210 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-6)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7651.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (E or F))) -> (not E))), M:tm-210, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-7652
in-theory        7652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (F or E))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-210 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-7652.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (F or E))) -> (not E))), M:tm-210, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-7653
in-theory        7653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F))))
theorem-size     37
proof            (modus-ponens tm-210 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7653.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F)))), M:tm-210, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-7654
in-theory        7654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F))))
theorem-size     35
proof            (modus-ponens tm-210 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7654.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F)))), M:tm-210, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-7655
in-theory        7655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G)))
theorem-size     41
proof            (modus-ponens tm-210 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-9)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7655.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G))), M:tm-210, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-7656
in-theory        7656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7656.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-210, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-7657
in-theory        7657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G))
theorem-size     31
proof            (modus-ponens tm-210 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7657.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G)), M:tm-210, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-7658
in-theory        7658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E)))
theorem-size     33
proof            (modus-ponens tm-210 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7658.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E))), M:tm-210, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-7659
in-theory        7659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E))))
theorem-size     33
proof            (modus-ponens tm-210 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-7659.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E)))), M:tm-210, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-7660
in-theory        7660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7660.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-210, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-7661
in-theory        7661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((not (not E)) -> (not E)) -> (not (not (not E)))))
theorem-size     29
proof            (modus-ponens tm-210 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-2 tm-9 tm-10)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-7661.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((not (not E)) -> (not E)) -> (not (not (not E))))), M:tm-210, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-7662
in-theory        7662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (((not (not E)) or E) -> F)))
theorem-size     29
proof            (modus-ponens tm-210 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-10)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-7662.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (((not (not E)) or E) -> F))), M:tm-210, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-7663
in-theory        7663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-210 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7663.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((not (not F)) -> F))), M:tm-210, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-7664
in-theory        7664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((not (not E)) -> E) or F))
theorem-size     25
proof            (modus-ponens tm-210 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-6 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7664.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((not (not E)) -> E) or F)), M:tm-210, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-7665
in-theory        7665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((not (not F)) -> F) and E)))
theorem-size     27
proof            (modus-ponens tm-210 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7665.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((not (not F)) -> F) and E))), M:tm-210, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-7666
in-theory        7666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F)))
theorem-size     33
proof            (modus-ponens tm-210 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-7666.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F))), M:tm-210, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-7667
in-theory        7667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-210 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7667.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((not (not F)) -> F))), M:tm-210, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-7668
in-theory        7668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (F -> (G -> F)))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7668.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (F -> (G -> F)))) -> (not E))), M:tm-210, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-7669
in-theory        7669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-210 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7669.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G))), M:tm-210, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-7670
in-theory        7670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7670.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (G -> (H -> G))))), M:tm-210, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-7671
in-theory        7671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (G -> F))) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7671.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (G -> F))) or H)), M:tm-210, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-7672
in-theory        7672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> (H -> G))) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7672.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> (H -> G))) and E))), M:tm-210, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-7673
in-theory        7673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (E -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-210 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-7673.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (E -> (G -> F)))), M:tm-210, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-7674
in-theory        7674
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7674.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (G -> (H -> G))))), M:tm-210, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-7675
in-theory        7675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> E))
theorem-size     21
proof            (modus-ponens tm-210 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7675.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> E)), M:tm-210, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-7676
in-theory        7676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> G)) -> (E -> (F -> G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7676.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> G)) -> (E -> (F -> G)))), M:tm-210, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-7677
in-theory        7677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and F) -> (E and F)))
theorem-size     25
proof            (modus-ponens tm-210 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7677.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and F) -> (E and F))), M:tm-210, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-7678
in-theory        7678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (E -> F)))
theorem-size     25
proof            (modus-ponens tm-210 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7678.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (E -> F))), M:tm-210, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-7679
in-theory        7679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((not (not E)) -> (not (not E))))
theorem-size     25
proof            (modus-ponens tm-210 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-7679.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((not (not E)) -> (not (not E)))), M:tm-210, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-7680
in-theory        7680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (not (E -> E))) -> (not (E -> F))))
theorem-size     31
proof            (modus-ponens tm-210 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7680.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (not (E -> E))) -> (not (E -> F)))), M:tm-210, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-7681
in-theory        7681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-210 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7681.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F))), M:tm-210, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-7682
in-theory        7682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-210 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7682.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> G) -> (F -> F)))), M:tm-210, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-7683
in-theory        7683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (E -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-210 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7683.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (E -> E)) or G)), M:tm-210, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-7684
in-theory        7684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> (F -> F)) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7684.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> (F -> F)) and E))), M:tm-210, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-7685
in-theory        7685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> E) -> ((E -> F) -> E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-7685.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> E) -> ((E -> F) -> E))), M:tm-210, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-7686
in-theory        7686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-210 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7686.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> G) -> (F -> F)))), M:tm-210, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-7687
in-theory        7687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F -> E) -> G)) -> (E -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-7687.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F -> E) -> G)) -> (E -> G))), M:tm-210, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-7688
in-theory        7688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E -> F)) -> (E -> F)))
theorem-size     27
proof            (modus-ponens tm-210 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-7688.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E -> F)) -> (E -> F))), M:tm-210, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-7689
in-theory        7689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F))))
theorem-size     37
proof            (modus-ponens tm-210 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-7689.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F)))), M:tm-210, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-7690
in-theory        7690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> G)) -> (E -> F)) -> (not ((E -> (F -> G)) -> (E -> G)))) -> (not ((E -> (F -> G)) -> (E -> F)))))
theorem-size     49
proof            (modus-ponens tm-210 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-7690.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> G)) -> (E -> F)) -> (not ((E -> (F -> G)) -> (E -> G)))) -> (not ((E -> (F -> G)) -> (E -> F))))), M:tm-210, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-7691
in-theory        7691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> G)) -> (E -> G)) -> H) -> ((((E -> (F -> G)) -> (E -> F)) or ((E -> (F -> G)) -> (E -> G))) -> H)))
theorem-size     51
proof            (modus-ponens tm-210 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-7691.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> G)) -> (E -> G)) -> H) -> ((((E -> (F -> G)) -> (E -> F)) or ((E -> (F -> G)) -> (E -> G))) -> H))), M:tm-210, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-7692
in-theory        7692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7692.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-210, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-7693
in-theory        7693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H))
theorem-size     39
proof            (modus-ponens tm-210 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7693.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H)), M:tm-210, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-7694
in-theory        7694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E)))
theorem-size     41
proof            (modus-ponens tm-210 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7694.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E))), M:tm-210, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-7695
in-theory        7695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> G)) -> (E -> F)) -> (E -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G))))
theorem-size     47
proof            (modus-ponens tm-210 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-7695.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> G)) -> (E -> F)) -> (E -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G)))), M:tm-210, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-7696
in-theory        7696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7696.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-210, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-7697
in-theory        7697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> (((E -> F) -> (E -> G)) -> H)) -> ((E -> (F -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-210 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-7697.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> (((E -> F) -> (E -> G)) -> H)) -> ((E -> (F -> G)) -> H))), M:tm-210, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-7698
in-theory        7698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-210 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7698.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E))), M:tm-210, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-7699
in-theory        7699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) -> ((I or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) -> H)))
theorem-size     51
proof            (modus-ponens tm-210 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7699.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) -> ((I or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) -> H))), M:tm-210, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-7700
in-theory        7700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-210 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7700.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-210, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-7701
in-theory        7701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     35
proof            (modus-ponens tm-210 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7701.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-210, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-7702
in-theory        7702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     37
proof            (modus-ponens tm-210 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7702.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-210, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-7703
in-theory        7703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-210 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-7703.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H))))), M:tm-210, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-7704
in-theory        7704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-210 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7704.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-210, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-7705
in-theory        7705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) and E) -> F))
theorem-size     25
proof            (modus-ponens tm-210 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-7705.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) and E) -> F)), M:tm-210, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-7706
in-theory        7706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> E)) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-210 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-7706.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> E)) -> G) and H) -> G)), M:tm-210, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-7707
in-theory        7707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) and I) -> H))
theorem-size     37
proof            (modus-ponens tm-210 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7707.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) and I) -> H)), M:tm-210, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-7708
in-theory        7708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F)))
theorem-size     39
proof            (modus-ponens tm-210 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-7708.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F))), M:tm-210, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-7709
in-theory        7709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E)))
theorem-size     33
proof            (modus-ponens tm-210 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-7709.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E))), M:tm-210, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-7710
in-theory        7710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) and G) -> E) -> (not (((E -> F) and G) -> F))) -> (not (((E -> F) and G) -> E))))
theorem-size     43
proof            (modus-ponens tm-210 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-9 tm-3)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-7710.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) and G) -> E) -> (not (((E -> F) and G) -> F))) -> (not (((E -> F) and G) -> E)))), M:tm-210, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-7711
in-theory        7711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) and G) -> F) -> H) -> (((((E -> F) and G) -> E) or (((E -> F) and G) -> F)) -> H)))
theorem-size     45
proof            (modus-ponens tm-210 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-7711.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) and G) -> F) -> H) -> (((((E -> F) and G) -> E) or (((E -> F) and G) -> F)) -> H))), M:tm-210, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-7712
in-theory        7712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-210 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7712.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-210, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-7713
in-theory        7713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H))
theorem-size     35
proof            (modus-ponens tm-210 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7713.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H)), M:tm-210, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-7714
in-theory        7714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E)))
theorem-size     37
proof            (modus-ponens tm-210 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7714.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E))), M:tm-210, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-7715
in-theory        7715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F)))
theorem-size     41
proof            (modus-ponens tm-210 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-7715.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F))), M:tm-210, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-7716
in-theory        7716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-210 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7716.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-210, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-7717
in-theory        7717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E and F) -> E) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-210 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-7717.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E and F) -> E) -> G) and H) -> G)), M:tm-210, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-7718
in-theory        7718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> (E -> G)) -> ((E and F) -> G)))
theorem-size     31
proof            (modus-ponens tm-210 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-7718.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> (E -> G)) -> ((E and F) -> G))), M:tm-210, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-7719
in-theory        7719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not ((F and G) -> F))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7719.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not ((F and G) -> F))) -> (not E))), M:tm-210, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-7720
in-theory        7720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-210 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7720.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G))), M:tm-210, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-7721
in-theory        7721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-210 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7721.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> ((G and H) -> G)))), M:tm-210, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-7722
in-theory        7722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F and G) -> F)) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7722.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F and G) -> F)) or H)), M:tm-210, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-7723
in-theory        7723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> ((G and H) -> G)) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7723.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> ((G and H) -> G)) and E))), M:tm-210, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-7724
in-theory        7724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F and G)) -> (E -> F)))
theorem-size     27
proof            (modus-ponens tm-210 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-7724.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F and G)) -> (E -> F))), M:tm-210, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-7725
in-theory        7725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-210 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7725.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> ((G and H) -> G)))), M:tm-210, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-7726
in-theory        7726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and (E -> F)) -> F))
theorem-size     25
proof            (modus-ponens tm-210 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-7726.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and (E -> F)) -> F)), M:tm-210, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-7727
in-theory        7727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and ((F -> (G -> F)) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-210 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-7727.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and ((F -> (G -> F)) -> H)) -> H)), M:tm-210, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-7728
in-theory        7728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I))
theorem-size     37
proof            (modus-ponens tm-210 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7728.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I)), M:tm-210, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-7729
in-theory        7729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and (((F and G) -> F) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-210 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-7729.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and (((F and G) -> F) -> H)) -> H)), M:tm-210, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-7730
in-theory        7730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-210 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-7730.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G))), M:tm-210, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-7731
in-theory        7731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F)))
theorem-size     33
proof            (modus-ponens tm-210 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-7731.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F))), M:tm-210, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-7732
in-theory        7732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and (F -> G)) -> F) -> (not ((E and (F -> G)) -> G))) -> (not ((E and (F -> G)) -> F))))
theorem-size     43
proof            (modus-ponens tm-210 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-4)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-7732.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and (F -> G)) -> F) -> (not ((E and (F -> G)) -> G))) -> (not ((E and (F -> G)) -> F)))), M:tm-210, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-7733
in-theory        7733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and (F -> G)) -> G) -> H) -> ((((E and (F -> G)) -> F) or ((E and (F -> G)) -> G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-210 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-7733.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and (F -> G)) -> G) -> H) -> ((((E and (F -> G)) -> F) or ((E and (F -> G)) -> G)) -> H))), M:tm-210, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-7734
in-theory        7734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-210 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7734.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-210, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-7735
in-theory        7735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-210 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7735.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H)), M:tm-210, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-7736
in-theory        7736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E)))
theorem-size     37
proof            (modus-ponens tm-210 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7736.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E))), M:tm-210, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-7737
in-theory        7737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and (F -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G)))
theorem-size     41
proof            (modus-ponens tm-210 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-7737.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and (F -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G))), M:tm-210, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-7738
in-theory        7738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-210 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7738.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-210, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-7739
in-theory        7739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and (((F and G) -> G) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-210 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-7739.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and (((F and G) -> G) -> H)) -> H)), M:tm-210, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-7740
in-theory        7740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E and F) -> F) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-210 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-7740.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E and F) -> F) -> G) and H) -> G)), M:tm-210, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-7741
in-theory        7741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> (F -> G)) -> ((E and F) -> G)))
theorem-size     31
proof            (modus-ponens tm-210 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-7741.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> (F -> G)) -> ((E and F) -> G))), M:tm-210, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-7742
in-theory        7742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not ((F and G) -> G))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7742.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not ((F and G) -> G))) -> (not E))), M:tm-210, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-7743
in-theory        7743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-210 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7743.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G))), M:tm-210, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-7744
in-theory        7744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-210 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7744.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> ((G and H) -> H)))), M:tm-210, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-7745
in-theory        7745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F and G) -> G)) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7745.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F and G) -> G)) or H)), M:tm-210, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-7746
in-theory        7746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> ((G and H) -> H)) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7746.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> ((G and H) -> H)) and E))), M:tm-210, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-7747
in-theory        7747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F and G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-210 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-7747.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F and G)) -> (E -> G))), M:tm-210, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-7748
in-theory        7748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-210 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7748.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> ((G and H) -> H)))), M:tm-210, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-7749
in-theory        7749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7749.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (H -> G)))), M:tm-210, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7750
in-theory        7750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7750.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-210, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7751
in-theory        7751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7751.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G and H) -> G))), M:tm-210, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7752
in-theory        7752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-210 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7752.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G and H) -> H))), M:tm-210, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7753
in-theory        7753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7753.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (H -> (G and H))))), M:tm-210, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-7754
in-theory        7754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-210 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7754.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (G or H)))), M:tm-210, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-7755
in-theory        7755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7755.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (H or G)))), M:tm-210, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-7756
in-theory        7756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7756.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-210, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-7757
in-theory        7757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-210 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7757.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-210, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-7758
in-theory        7758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7758.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((not (not G)) -> G))), M:tm-210, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-7759
in-theory        7759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7759.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (H -> (I -> H))))), M:tm-210, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-7760
in-theory        7760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7760.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> H) -> (G -> G)))), M:tm-210, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-7761
in-theory        7761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-210 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7761.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-210, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-7762
in-theory        7762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7762.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-210, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-7763
in-theory        7763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-210 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7763.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-210, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-7764
in-theory        7764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-210 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7764.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> ((H and I) -> H)))), M:tm-210, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-7765
in-theory        7765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-210 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7765.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-210, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-7766
in-theory        7766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-210 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7766.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> ((H and I) -> I)))), M:tm-210, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-7767
in-theory        7767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7767.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-210, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-7768
in-theory        7768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7768.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E))), M:tm-210, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-7769
in-theory        7769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> E)) and G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-210 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7769.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> E)) and G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H))), M:tm-210, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-7770
in-theory        7770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-210 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7770.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> ((G -> (H -> G)) and F)))), M:tm-210, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-7771
in-theory        7771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F -> (G -> F)) and E)) or H))
theorem-size     29
proof            (modus-ponens tm-210 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7771.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F -> (G -> F)) and E)) or H)), M:tm-210, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-7772
in-theory        7772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> ((G -> (H -> G)) and F)) and E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7772.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> ((G -> (H -> G)) and F)) and E))), M:tm-210, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-7773
in-theory        7773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-210 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7773.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> ((G -> (H -> G)) and F)))), M:tm-210, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-7774
in-theory        7774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> H))))
theorem-size     37
proof            (modus-ponens tm-210 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7774.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> H)))), M:tm-210, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-7775
in-theory        7775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7775.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-210, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-7776
in-theory        7776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> H)))
theorem-size     37
proof            (modus-ponens tm-210 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7776.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> H))), M:tm-210, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-7777
in-theory        7777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> I)))
theorem-size     37
proof            (modus-ponens tm-210 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7777.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> I))), M:tm-210, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-7778
in-theory        7778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (H and I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7778.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (H and I))))), M:tm-210, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-7779
in-theory        7779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (H or I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7779.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (H or I)))), M:tm-210, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-7780
in-theory        7780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I or H))))
theorem-size     37
proof            (modus-ponens tm-210 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-7780.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I or H)))), M:tm-210, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-7781
in-theory        7781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7781.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-210, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-7782
in-theory        7782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     43
proof            (modus-ponens tm-210 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7782.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-210, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-7783
in-theory        7783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((not (not H)) -> H)))
theorem-size     37
proof            (modus-ponens tm-210 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7783.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((not (not H)) -> H))), M:tm-210, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-7784
in-theory        7784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7784.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> I))))), M:tm-210, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-7785
in-theory        7785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> H))))
theorem-size     39
proof            (modus-ponens tm-210 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7785.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> H)))), M:tm-210, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-7786
in-theory        7786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J)))))
theorem-size     51
proof            (modus-ponens tm-210 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7786.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-210, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-7787
in-theory        7787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     47
proof            (modus-ponens tm-210 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7787.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-210, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-7788
in-theory        7788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I))))
theorem-size     47
proof            (modus-ponens tm-210 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7788.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-210, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-7789
in-theory        7789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> I))))
theorem-size     39
proof            (modus-ponens tm-210 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7789.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> I)))), M:tm-210, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-7790
in-theory        7790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J))))
theorem-size     47
proof            (modus-ponens tm-210 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7790.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-210, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-7791
in-theory        7791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> J))))
theorem-size     39
proof            (modus-ponens tm-210 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7791.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> J)))), M:tm-210, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-7792
in-theory        7792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> I)) and H))))
theorem-size     41
proof            (modus-ponens tm-210 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7792.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-210, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-7793
in-theory        7793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H))))
theorem-size     49
proof            (modus-ponens tm-210 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-2)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7793.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-210, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-7794
in-theory        7794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-210 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7794.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-210, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-7795
in-theory        7795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E)))
theorem-size     39
proof            (modus-ponens tm-210 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7795.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E))), M:tm-210, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-7796
in-theory        7796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H) -> I) -> ((H or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H)) -> I)))
theorem-size     55
proof            (modus-ponens tm-210 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7796.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H) -> I) -> ((H or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H)) -> I))), M:tm-210, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-7797
in-theory        7797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-210 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7797.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-210, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7798
in-theory        7798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I))
theorem-size     37
proof            (modus-ponens tm-210 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7798.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I)), M:tm-210, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-7799
in-theory        7799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E)))
theorem-size     39
proof            (modus-ponens tm-210 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7799.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E))), M:tm-210, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7800
in-theory        7800
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     51
proof            (modus-ponens tm-207 tm-210 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7800.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-210, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-7801
in-theory        7801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-183 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7801.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-183, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7802
in-theory        7802
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B -> (C -> B)) and A)))
theorem-size     35
proof            (modus-ponens tm-180 tm-210 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7802.         ((A or ((B -> (C -> B)) and A)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-210, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-7803
in-theory        7803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-157 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7803.         ((A -> ((B and C) -> C)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-157, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7804
in-theory        7804
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B and C) -> C)))
theorem-size     31
proof            (modus-ponens tm-154 tm-210 ((Am (-> (and A B) B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7804.         ((A or ((B and C) -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B and C) -> C))), M:tm-154, m:tm-210, u:((Am (-> (and A B) B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (and A B) B))))
================================================================
tm-name          tm-7805
in-theory        7805
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     37
proof            (modus-ponens tm-147 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7805.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-147, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7806
in-theory        7806
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A and (B -> C)) -> C)))
theorem-size     41
proof            (modus-ponens tm-144 tm-210 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7806.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-210, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-7807
in-theory        7807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-134 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7807.         ((A -> ((B and C) -> B)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-134, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7808
in-theory        7808
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-131 tm-210 ((Am (-> (and A B) A)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7808.         ((A or ((B and C) -> B)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B and C) -> B))), M:tm-131, m:tm-210, u:((Am (-> (and A B) A)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (and A B) A))))
================================================================
tm-name          tm-7809
in-theory        7809
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     37
proof            (modus-ponens tm-125 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7809.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-125, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7810
in-theory        7810
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (((A -> B) and C) -> B)))
theorem-size     41
proof            (modus-ponens tm-122 tm-210 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7810.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-210, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-7811
in-theory        7811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E)))
theorem-size     37
proof            (modus-ponens tm-113 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7811.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E))), M:tm-113, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7812
in-theory        7812
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     47
proof            (modus-ponens tm-110 tm-210 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7812.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-210, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-7813
in-theory        7813
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     41
proof            (modus-ponens tm-105 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7813.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-105, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7814
in-theory        7814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     47
proof            (modus-ponens tm-102 tm-210 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7814.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-210, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-7815
in-theory        7815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C)))
theorem-size     29
proof            (modus-ponens tm-95 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7815.         (((A -> B) -> (A -> A)) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C))), M:tm-95, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7816
in-theory        7816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> A)))
theorem-size     29
proof            (modus-ponens tm-92 tm-210 ((Am (-> A A)) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7816.         (((A -> B) or (A -> A)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> A))), M:tm-92, m:tm-210, u:((Am (-> A A)) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A A))))
================================================================
tm-name          tm-7817
in-theory        7817
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and A)))
theorem-size     23
proof            (modus-ponens tm-84 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7817.         (A -> (B -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and A))), M:tm-84, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-7818
in-theory        7818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-83 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7818.         ((A -> (B -> (C -> B))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-83, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7819
in-theory        7819
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (B -> (C -> B))))
theorem-size     31
proof            (modus-ponens tm-80 tm-210 ((Am (-> A (-> B A))) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7819.         ((A or (B -> (C -> B))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (B -> (C -> B)))), M:tm-80, m:tm-210, u:((Am (-> A (-> B A))) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A (-> B A)))))
================================================================
tm-name          tm-7820
in-theory        7820
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and B)))
theorem-size     27
proof            (modus-ponens tm-76 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7820.         (((not (not A)) -> A) and (B -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and B))), M:tm-76, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7821
in-theory        7821
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))
theorem-size     25
proof            (modus-ponens tm-73 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7821.         (((not (not A)) or A) -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-73, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-7822
in-theory        7822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C)))
theorem-size     33
proof            (modus-ponens tm-69 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7822.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C))), M:tm-69, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7823
in-theory        7823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and ((A -> (not B)) -> (not A))))
theorem-size     37
proof            (modus-ponens tm-66 tm-210 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7823.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-210, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-7824
in-theory        7824
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     35
proof            (modus-ponens tm-54 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7824.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-54, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7825
in-theory        7825
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     41
proof            (modus-ponens tm-51 tm-210 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7825.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-210, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-7826
in-theory        7826
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (B or A)))
theorem-size     27
proof            (modus-ponens tm-50 tm-210 ((Am (or A B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7826.         ((A or (B or A)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (B or A))), M:tm-50, m:tm-210, u:((Am (or A B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (or A B))))
================================================================
tm-name          tm-7827
in-theory        7827
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A or B)))
theorem-size     27
proof            (modus-ponens tm-49 tm-210 ((Am (or A B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7827.         ((A or (A or B)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A or B))), M:tm-49, m:tm-210, u:((Am (or A B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (or A B))))
================================================================
tm-name          tm-7828
in-theory        7828
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (B -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-48 tm-210 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7828.         ((A or (B -> (A and B))) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (B -> (A and B)))), M:tm-48, m:tm-210, u:((Am (-> A (and B A))) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-7829
in-theory        7829
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and B))
theorem-size     25
proof            (modus-ponens tm-47 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7829.         (((A and B) or B) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and B)), M:tm-47, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-7830
in-theory        7830
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and A))
theorem-size     25
proof            (modus-ponens tm-46 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7830.         (((A and B) or A) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and A)), M:tm-46, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-7831
in-theory        7831
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> B) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-45 tm-210 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7831.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-210, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-7832
in-theory        7832
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (B -> A)))
theorem-size     27
proof            (modus-ponens tm-44 tm-210 ((Am (-> A B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7832.         ((A or (B -> A)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (B -> A))), M:tm-44, m:tm-210, u:((Am (-> A B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A B))))
================================================================
tm-name          tm-7833
in-theory        7833
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C)))
theorem-size     27
proof            (modus-ponens tm-42 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7833.         ((A -> (B or A)) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C))), M:tm-42, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7834
in-theory        7834
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C)))
theorem-size     27
proof            (modus-ponens tm-32 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7834.         ((A -> (A or B)) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C))), M:tm-32, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7835
in-theory        7835
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)))
theorem-size     23
proof            (modus-ponens tm-24 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-2 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7835.         (A -> (A and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))), M:tm-24, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-7836
in-theory        7836
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C)))
theorem-size     29
proof            (modus-ponens tm-23 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7836.         ((A -> (B -> (A and B))) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C))), M:tm-23, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7837
in-theory        7837
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C)))
theorem-size     27
proof            (modus-ponens tm-22 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7837.         (((A and B) -> B) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C))), M:tm-22, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7838
in-theory        7838
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C)))
theorem-size     27
proof            (modus-ponens tm-21 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7838.         (((A and B) -> A) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C))), M:tm-21, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7839
in-theory        7839
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     35
proof            (modus-ponens tm-20 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7839.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-20, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7840
in-theory        7840
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C)))
theorem-size     27
proof            (modus-ponens tm-19 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7840.         ((A -> (B -> A)) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C))), M:tm-19, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7841
in-theory        7841
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))) -> (not A))
theorem-size     25
proof            (modus-ponens tm-9 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-9 tm-5 tm-2)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7841.         ((A -> (not ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))) -> (not A)), M:tm-9, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-7842
in-theory        7842
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and E) -> F) -> ((E or ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and E)) -> F))
theorem-size     45
proof            (modus-ponens tm-8 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7842.         ((((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and E) -> F) -> ((E or ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and E)) -> F)), M:tm-8, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-7843
in-theory        7843
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and B)))
theorem-size     23
proof            (modus-ponens tm-7 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7843.         (A or (B -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and B))), M:tm-7, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7844
in-theory        7844
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7844.         ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) or F), M:tm-6, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7845
in-theory        7845
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and B)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7845.         (A -> ((B -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and B)) and A)), M:tm-5, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7846
in-theory        7846
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and B)))
theorem-size     23
proof            (modus-ponens tm-1 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7846.         (A -> (B -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and B))), M:tm-1, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-7847
in-theory        7847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-210 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7847.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-210, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7848
in-theory        7848
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     35
proof            (modus-ponens tm-207 tm-211 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7848.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-207, m:tm-211, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7849
in-theory        7849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-183 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7849.         ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-183, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7850
in-theory        7850
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-180 tm-211 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7850.         ((A or ((B -> (C -> B)) and A)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-180, m:tm-211, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7851
in-theory        7851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-157 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7851.         ((A -> ((B and C) -> C)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-157, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7852
in-theory        7852
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-154 tm-211 ((Am (-> (and A B) B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7852.         ((A or ((B and C) -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-154, m:tm-211, u:((Am (-> (and A B) B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7853
in-theory        7853
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))
theorem-size     19
proof            (modus-ponens tm-152 tm-211 ((Am (and A Bm)) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7853.         ((A and B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-152, m:tm-211, u:((Am (and A Bm)) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-7854
in-theory        7854
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-147 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7854.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-147, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7855
in-theory        7855
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-144 tm-211 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-5)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7855.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-144, m:tm-211, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7856
in-theory        7856
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) -> F)) -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))
theorem-size     39
proof            (modus-ponens tm-142 tm-211 ((Am (and A (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) C))) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7856.         ((A and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) -> F)) -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-142, m:tm-211, u:((Am (and A (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) C))) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7857
in-theory        7857
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) -> B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))
theorem-size     37
proof            (modus-ponens tm-141 tm-211 ((Am (and A (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Bm))) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7857.         ((A and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) -> B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-141, m:tm-211, u:((Am (and A (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Bm))) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-7858
in-theory        7858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-134 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7858.         ((A -> ((B and C) -> B)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-134, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7859
in-theory        7859
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-131 tm-211 ((Am (-> (and A B) A)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7859.         ((A or ((B and C) -> B)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-131, m:tm-211, u:((Am (-> (and A B) A)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7860
in-theory        7860
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))
theorem-size     19
proof            (modus-ponens tm-129 tm-211 ((Am (and Bm B)) (A Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7860.         ((A and B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-129, m:tm-211, u:((Am (and Bm B)) (A Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-7861
in-theory        7861
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-125 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7861.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-125, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7862
in-theory        7862
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-122 tm-211 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-5)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7862.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-122, m:tm-211, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7863
in-theory        7863
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) and F) -> (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     39
proof            (modus-ponens tm-120 tm-211 ((Am (and (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) B) C)) (A (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7863.         ((((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) and F) -> (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-120, m:tm-211, u:((Am (and (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) B) C)) (A (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7864
in-theory        7864
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> A) and E) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))
theorem-size     37
proof            (modus-ponens tm-119 tm-211 ((Am (and (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Bm) C)) (A Bm) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7864.         ((((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> A) and E) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-119, m:tm-211, u:((Am (and (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Bm) C)) (A Bm) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-7865
in-theory        7865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-113 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7865.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-113, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7866
in-theory        7866
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     33
proof            (modus-ponens tm-110 tm-211 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7866.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-110, m:tm-211, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7867
in-theory        7867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-108 tm-211 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7867.         ((A -> (B -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-108, m:tm-211, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-7868
in-theory        7868
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     39
proof            (modus-ponens tm-105 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7868.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-105, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7869
in-theory        7869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     37
proof            (modus-ponens tm-102 tm-211 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7869.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-102, m:tm-211, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7870
in-theory        7870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) -> E)) -> (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     37
proof            (modus-ponens tm-100 tm-211 ((Am (-> Bm (-> (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm) C))) (A Bm) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7870.         ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) -> E)) -> (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-100, m:tm-211, u:((Am (-> Bm (-> (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm) C))) (A Bm) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-7871
in-theory        7871
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> A)))
theorem-size     19
proof            (modus-ponens tm-98 tm-211 ((A Am) (Bm (-> B Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> B Am)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7871.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> A))), M:tm-98, m:tm-211, u:((A Am) (Bm (-> B Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> B Am))))
================================================================
tm-name          tm-7872
in-theory        7872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) -> (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     37
proof            (modus-ponens tm-96 tm-211 ((Am (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) B)) (A (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7872.         (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) -> (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-96, m:tm-211, u:((Am (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) B)) (A (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7873
in-theory        7873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-95 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7873.         (((A -> B) -> (A -> A)) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-95, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7874
in-theory        7874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     25
proof            (modus-ponens tm-92 tm-211 ((Am (-> A A)) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7874.         (((A -> B) or (A -> A)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-92, m:tm-211, u:((Am (-> A A)) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7875
in-theory        7875
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     21
proof            (modus-ponens tm-84 tm-211 ((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7875.         (A -> (B -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-84, m:tm-211, u:((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7876
in-theory        7876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-83 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7876.         ((A -> (B -> (C -> B))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-83, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7877
in-theory        7877
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-80 tm-211 ((Am (-> A (-> B A))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7877.         ((A or (B -> (C -> B))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-80, m:tm-211, u:((Am (-> A (-> B A))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7878
in-theory        7878
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E))) -> E)
theorem-size     23
proof            (modus-ponens tm-77 tm-211 ((Am (not (not (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) B)))) (A (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7878.         ((not (not ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E))) -> E), M:tm-77, m:tm-211, u:((Am (not (not (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) B)))) (A (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7879
in-theory        7879
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     25
proof            (modus-ponens tm-76 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7879.         (((not (not A)) -> A) and (B -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-76, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7880
in-theory        7880
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))
theorem-size     23
proof            (modus-ponens tm-73 tm-211 ((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7880.         (((not (not A)) or A) -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-73, m:tm-211, u:((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7881
in-theory        7881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     31
proof            (modus-ponens tm-69 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7881.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-69, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7882
in-theory        7882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     29
proof            (modus-ponens tm-66 tm-211 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-5 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7882.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-66, m:tm-211, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7883
in-theory        7883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))
theorem-size     23
proof            (modus-ponens tm-55 tm-211 ((Am (-> A Bm)) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7883.         ((A -> B) -> ((A or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-55, m:tm-211, u:((Am (-> A Bm)) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-7884
in-theory        7884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-54 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7884.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-54, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7885
in-theory        7885
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-51 tm-211 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7885.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-51, m:tm-211, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7886
in-theory        7886
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-50 tm-211 ((Am (or A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7886.         ((A or (B or A)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-50, m:tm-211, u:((Am (or A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7887
in-theory        7887
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-49 tm-211 ((Am (or A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7887.         ((A or (A or B)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-49, m:tm-211, u:((Am (or A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7888
in-theory        7888
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     25
proof            (modus-ponens tm-48 tm-211 ((Am (-> A (and B A))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7888.         ((A or (B -> (A and B))) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-48, m:tm-211, u:((Am (-> A (and B A))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7889
in-theory        7889
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-47 tm-211 ((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7889.         (((A and B) or B) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-47, m:tm-211, u:((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7890
in-theory        7890
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-46 tm-211 ((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7890.         (((A and B) or A) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-46, m:tm-211, u:((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7891
in-theory        7891
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-45 tm-211 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7891.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-45, m:tm-211, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7892
in-theory        7892
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-44 tm-211 ((Am (-> A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7892.         ((A or (B -> A)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-44, m:tm-211, u:((Am (-> A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7893
in-theory        7893
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-42 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7893.         ((A -> (B or A)) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-42, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7894
in-theory        7894
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-32 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7894.         ((A -> (A or B)) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-32, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7895
in-theory        7895
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     21
proof            (modus-ponens tm-24 tm-211 ((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7895.         (A -> (A and (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-24, m:tm-211, u:((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7896
in-theory        7896
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-23 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7896.         ((A -> (B -> (A and B))) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-23, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7897
in-theory        7897
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-22 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7897.         (((A and B) -> B) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-22, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7898
in-theory        7898
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-21 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7898.         (((A and B) -> A) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-21, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7899
in-theory        7899
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-20 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7899.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-20, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7900
in-theory        7900
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-19 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7900.         ((A -> (B -> A)) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-19, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7901
in-theory        7901
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) -> F)) -> F)
theorem-size     23
proof            (modus-ponens tm-17 tm-211 ((Am (and A (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) C))) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7901.         ((A and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) -> F)) -> F), M:tm-17, m:tm-211, u:((Am (and A (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) C))) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7902
in-theory        7902
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) and F) -> E)
theorem-size     23
proof            (modus-ponens tm-15 tm-211 ((Am (and (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) B) C)) (A (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7902.         ((((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) and F) -> E), M:tm-15, m:tm-211, u:((Am (and (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) B) C)) (A (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7903
in-theory        7903
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) -> E)) -> (A -> E))
theorem-size     23
proof            (modus-ponens tm-13 tm-211 ((Am (-> Bm (-> (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm) C))) (A Bm) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7903.         ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) -> E)) -> (A -> E)), M:tm-13, m:tm-211, u:((Am (-> Bm (-> (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm) C))) (A Bm) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-7904
in-theory        7904
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))) -> (not A))
theorem-size     23
proof            (modus-ponens tm-9 tm-211 ((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-9 tm-1 tm-5 tm-2)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7904.         ((A -> (not (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))) -> (not A)), M:tm-9, m:tm-211, u:((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7905
in-theory        7905
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) -> ((F or (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> E))
theorem-size     41
proof            (modus-ponens tm-8 tm-211 ((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7905.         (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) -> ((F or (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> E)), M:tm-8, m:tm-211, u:((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-7906
in-theory        7906
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     21
proof            (modus-ponens tm-7 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-7 tm-1 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7906.         (A or (B -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-7, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7907
in-theory        7907
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-6 tm-1 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7907.         ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) or F), M:tm-6, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7908
in-theory        7908
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7908.         (A -> ((B -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and A)), M:tm-5, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-7909
in-theory        7909
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))
theorem-size     21
proof            (modus-ponens tm-2 tm-211 ((A Am) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7909.         ((A -> B) -> (A -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-2, m:tm-211, u:((A Am) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-7910
in-theory        7910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7910.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (H -> G)))), M:tm-210, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7911
in-theory        7911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7911.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-183, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7912
in-theory        7912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7912.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-157, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7913
in-theory        7913
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7913.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-147, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7914
in-theory        7914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7914.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-134, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7915
in-theory        7915
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7915.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-125, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7916
in-theory        7916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7916.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> G)))), M:tm-113, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7917
in-theory        7917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7917.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-105, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7918
in-theory        7918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7918.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (F -> E)))), M:tm-95, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7919
in-theory        7919
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7919.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-83, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7920
in-theory        7920
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7920.         (((not (not A)) -> A) and (((B and C) -> B) and (D -> (E -> D)))), M:tm-76, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7921
in-theory        7921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7921.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (F -> E)))), M:tm-69, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7922
in-theory        7922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7922.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-54, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7923
in-theory        7923
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7923.         ((A -> (B or A)) and (((C and D) -> C) and (E -> (F -> E)))), M:tm-42, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7924
in-theory        7924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7924.         ((A -> (A or B)) and (((C and D) -> C) and (E -> (F -> E)))), M:tm-32, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7925
in-theory        7925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7925.         ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (F -> E)))), M:tm-23, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7926
in-theory        7926
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7926.         (((A and B) -> B) and (((C and D) -> C) and (E -> (F -> E)))), M:tm-22, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7927
in-theory        7927
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7927.         (((A and B) -> A) and (((C and D) -> C) and (E -> (F -> E)))), M:tm-21, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7928
in-theory        7928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7928.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-20, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7929
in-theory        7929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7929.         ((A -> (B -> A)) and (((C and D) -> C) and (E -> (F -> E)))), M:tm-19, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7930
in-theory        7930
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-7 tm-5 tm-3 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7930.         (A or (((B and C) -> B) and (D -> (E -> D)))), M:tm-7, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7931
in-theory        7931
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-6 tm-5 tm-3 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7931.         ((((A and B) -> A) and (C -> (D -> C))) or E), M:tm-6, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7932
in-theory        7932
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> (E -> D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7932.         (A -> ((((B and C) -> B) and (D -> (E -> D))) and A)), M:tm-5, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7933
in-theory        7933
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7933.         (A -> (((B and C) -> B) and (D -> (E -> D)))), M:tm-1, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-7934
in-theory        7934
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7934.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-210, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7935
in-theory        7935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7935.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-183, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7936
in-theory        7936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7936.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-157, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7937
in-theory        7937
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7937.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-147, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7938
in-theory        7938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7938.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-134, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7939
in-theory        7939
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7939.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-125, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7940
in-theory        7940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7940.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-113, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7941
in-theory        7941
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7941.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-105, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7942
in-theory        7942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7942.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-95, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7943
in-theory        7943
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7943.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-83, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7944
in-theory        7944
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-3 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7944.         (((not (not A)) -> A) and (((B and C) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-76, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7945
in-theory        7945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-3 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7945.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-69, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7946
in-theory        7946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7946.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-54, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7947
in-theory        7947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7947.         ((A -> (B or A)) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-42, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7948
in-theory        7948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7948.         ((A -> (A or B)) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-32, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7949
in-theory        7949
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7949.         ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-23, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7950
in-theory        7950
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7950.         (((A and B) -> B) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-22, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7951
in-theory        7951
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7951.         (((A and B) -> A) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-21, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7952
in-theory        7952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7952.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-20, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7953
in-theory        7953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7953.         ((A -> (B -> A)) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-19, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7954
in-theory        7954
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-7 tm-5 tm-3 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7954.         (A or (((B and C) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-7, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7955
in-theory        7955
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-6 tm-5 tm-3 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7955.         ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F), M:tm-6, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7956
in-theory        7956
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7956.         (A -> ((((B and C) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)), M:tm-5, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7957
in-theory        7957
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-1 tm-5 tm-3 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7957.         (A -> (((B and C) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-1, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-7958
in-theory        7958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7958.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G and H) -> G))), M:tm-210, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7959
in-theory        7959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7959.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-183, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7960
in-theory        7960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7960.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-157, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7961
in-theory        7961
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7961.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-147, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7962
in-theory        7962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7962.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-134, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7963
in-theory        7963
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7963.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-125, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7964
in-theory        7964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7964.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G and H) -> G))), M:tm-113, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7965
in-theory        7965
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7965.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F and G) -> F))), M:tm-105, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7966
in-theory        7966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7966.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E and F) -> E))), M:tm-95, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7967
in-theory        7967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7967.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F and G) -> F))), M:tm-83, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7968
in-theory        7968
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((D and E) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-10 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7968.         (((not (not A)) -> A) and (((B and C) -> B) and ((D and E) -> D))), M:tm-76, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7969
in-theory        7969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7969.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E and F) -> E))), M:tm-69, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7970
in-theory        7970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7970.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F and G) -> F))), M:tm-54, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7971
in-theory        7971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7971.         ((A -> (B or A)) and (((C and D) -> C) and ((E and F) -> E))), M:tm-42, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7972
in-theory        7972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7972.         ((A -> (A or B)) and (((C and D) -> C) and ((E and F) -> E))), M:tm-32, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7973
in-theory        7973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7973.         ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E and F) -> E))), M:tm-23, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7974
in-theory        7974
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7974.         (((A and B) -> B) and (((C and D) -> C) and ((E and F) -> E))), M:tm-22, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7975
in-theory        7975
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7975.         (((A and B) -> A) and (((C and D) -> C) and ((E and F) -> E))), M:tm-21, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7976
in-theory        7976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7976.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F and G) -> F))), M:tm-20, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7977
in-theory        7977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7977.         ((A -> (B -> A)) and (((C and D) -> C) and ((E and F) -> E))), M:tm-19, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7978
in-theory        7978
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7978.         (A or (((B and C) -> B) and ((D and E) -> D))), M:tm-7, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7979
in-theory        7979
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7979.         ((((A and B) -> A) and ((C and D) -> C)) or E), M:tm-6, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7980
in-theory        7980
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((D and E) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7980.         (A -> ((((B and C) -> B) and ((D and E) -> D)) and A)), M:tm-5, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7981
in-theory        7981
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7981.         (A -> (((B and C) -> B) and ((D and E) -> D))), M:tm-1, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-7982
in-theory        7982
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-210 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7982.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G and H) -> H))), M:tm-210, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7983
in-theory        7983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-183 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7983.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-183, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7984
in-theory        7984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-157 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7984.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-157, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7985
in-theory        7985
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-147 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7985.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-147, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7986
in-theory        7986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-134 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7986.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-134, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7987
in-theory        7987
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-125 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7987.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-125, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7988
in-theory        7988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-113 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7988.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G and H) -> H))), M:tm-113, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7989
in-theory        7989
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-105 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7989.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F and G) -> G))), M:tm-105, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7990
in-theory        7990
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-95 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7990.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E and F) -> F))), M:tm-95, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7991
in-theory        7991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-83 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7991.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F and G) -> G))), M:tm-83, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7992
in-theory        7992
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((D and E) -> E)))
theorem-size     17
proof            (modus-ponens tm-76 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-10 tm-3 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7992.         (((not (not A)) -> A) and (((B and C) -> B) and ((D and E) -> E))), M:tm-76, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7993
in-theory        7993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-69 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-9 tm-3 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7993.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E and F) -> F))), M:tm-69, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7994
in-theory        7994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-54 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7994.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F and G) -> G))), M:tm-54, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7995
in-theory        7995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-42 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7995.         ((A -> (B or A)) and (((C and D) -> C) and ((E and F) -> F))), M:tm-42, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7996
in-theory        7996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-32 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7996.         ((A -> (A or B)) and (((C and D) -> C) and ((E and F) -> F))), M:tm-32, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7997
in-theory        7997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-23 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7997.         ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E and F) -> F))), M:tm-23, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7998
in-theory        7998
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-22 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7998.         (((A and B) -> B) and (((C and D) -> C) and ((E and F) -> F))), M:tm-22, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-7999
in-theory        7999
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-21 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7999.         (((A and B) -> A) and (((C and D) -> C) and ((E and F) -> F))), M:tm-21, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-8000
in-theory        8000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-20 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8000.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F and G) -> G))), M:tm-20, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-8001
in-theory        8001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-19 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8001.         ((A -> (B -> A)) and (((C and D) -> C) and ((E and F) -> F))), M:tm-19, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-8002
in-theory        8002
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-7 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-7 tm-5 tm-3 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8002.         (A or (((B and C) -> B) and ((D and E) -> E))), M:tm-7, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-8003
in-theory        8003
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-6 tm-5 tm-3 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8003.         ((((A and B) -> A) and ((C and D) -> D)) or E), M:tm-6, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-8004
in-theory        8004
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((D and E) -> E)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8004.         (A -> ((((B and C) -> B) and ((D and E) -> E)) and A)), M:tm-5, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-8005
in-theory        8005
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-1 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-1 tm-5 tm-3 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8005.         (A -> (((B and C) -> B) and ((D and E) -> E))), M:tm-1, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-8006
in-theory        8006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8006.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (H -> (G and H))))), M:tm-210, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8007
in-theory        8007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8007.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-183, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8008
in-theory        8008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8008.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-157, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8009
in-theory        8009
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8009.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-147, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8010
in-theory        8010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8010.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-134, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8011
in-theory        8011
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8011.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-125, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8012
in-theory        8012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8012.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (G and H))))), M:tm-113, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8013
in-theory        8013
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8013.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-105, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8014
in-theory        8014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8014.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (F -> (E and F))))), M:tm-95, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8015
in-theory        8015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8015.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-83, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8016
in-theory        8016
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8016.         (((not (not A)) -> A) and (((B and C) -> B) and (D -> (E -> (D and E))))), M:tm-76, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8017
in-theory        8017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8017.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (F -> (E and F))))), M:tm-69, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8018
in-theory        8018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8018.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-54, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8019
in-theory        8019
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8019.         ((A -> (B or A)) and (((C and D) -> C) and (E -> (F -> (E and F))))), M:tm-42, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8020
in-theory        8020
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8020.         ((A -> (A or B)) and (((C and D) -> C) and (E -> (F -> (E and F))))), M:tm-32, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8021
in-theory        8021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8021.         ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (F -> (E and F))))), M:tm-23, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8022
in-theory        8022
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8022.         (((A and B) -> B) and (((C and D) -> C) and (E -> (F -> (E and F))))), M:tm-22, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8023
in-theory        8023
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8023.         (((A and B) -> A) and (((C and D) -> C) and (E -> (F -> (E and F))))), M:tm-21, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8024
in-theory        8024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8024.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-20, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8025
in-theory        8025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8025.         ((A -> (B -> A)) and (((C and D) -> C) and (E -> (F -> (E and F))))), M:tm-19, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8026
in-theory        8026
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8026.         (A or (((B and C) -> B) and (D -> (E -> (D and E))))), M:tm-7, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8027
in-theory        8027
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8027.         ((((A and B) -> A) and (C -> (D -> (C and D)))) or E), M:tm-6, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8028
in-theory        8028
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> (E -> (D and E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8028.         (A -> ((((B and C) -> B) and (D -> (E -> (D and E)))) and A)), M:tm-5, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8029
in-theory        8029
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8029.         (A -> (((B and C) -> B) and (D -> (E -> (D and E))))), M:tm-1, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8030
in-theory        8030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-210 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8030.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (G or H)))), M:tm-210, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8031
in-theory        8031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-183 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8031.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-183, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8032
in-theory        8032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-157 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8032.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-157, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8033
in-theory        8033
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-147 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8033.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-147, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8034
in-theory        8034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-134 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8034.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-134, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8035
in-theory        8035
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-125 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8035.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-125, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8036
in-theory        8036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-113 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8036.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (G or H)))), M:tm-113, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8037
in-theory        8037
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-105 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8037.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (F or G)))), M:tm-105, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8038
in-theory        8038
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-95 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8038.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (E or F)))), M:tm-95, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8039
in-theory        8039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-83 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8039.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (F or G)))), M:tm-83, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8040
in-theory        8040
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-76 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8040.         (((not (not A)) -> A) and (((B and C) -> B) and (D -> (D or E)))), M:tm-76, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8041
in-theory        8041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-69 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8041.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (E or F)))), M:tm-69, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8042
in-theory        8042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-54 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8042.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (F or G)))), M:tm-54, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8043
in-theory        8043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-42 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8043.         ((A -> (B or A)) and (((C and D) -> C) and (E -> (E or F)))), M:tm-42, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8044
in-theory        8044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-32 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8044.         ((A -> (A or B)) and (((C and D) -> C) and (E -> (E or F)))), M:tm-32, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8045
in-theory        8045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-23 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8045.         ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (E or F)))), M:tm-23, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8046
in-theory        8046
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-22 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8046.         (((A and B) -> B) and (((C and D) -> C) and (E -> (E or F)))), M:tm-22, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8047
in-theory        8047
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-21 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8047.         (((A and B) -> A) and (((C and D) -> C) and (E -> (E or F)))), M:tm-21, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8048
in-theory        8048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-20 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8048.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (F or G)))), M:tm-20, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8049
in-theory        8049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-19 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8049.         ((A -> (B -> A)) and (((C and D) -> C) and (E -> (E or F)))), M:tm-19, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8050
in-theory        8050
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-7 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-7 tm-5 tm-3 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8050.         (A or (((B and C) -> B) and (D -> (D or E)))), M:tm-7, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8051
in-theory        8051
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8051.         ((((A and B) -> A) and (C -> (C or D))) or E), M:tm-6, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8052
in-theory        8052
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> (D or E))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8052.         (A -> ((((B and C) -> B) and (D -> (D or E))) and A)), M:tm-5, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8053
in-theory        8053
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-1 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-1 tm-5 tm-3 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8053.         (A -> (((B and C) -> B) and (D -> (D or E)))), M:tm-1, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8054
in-theory        8054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8054.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (H or G)))), M:tm-210, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8055
in-theory        8055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8055.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-183, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8056
in-theory        8056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8056.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-157, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8057
in-theory        8057
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8057.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-147, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8058
in-theory        8058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8058.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-134, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8059
in-theory        8059
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8059.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-125, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8060
in-theory        8060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8060.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H or G)))), M:tm-113, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8061
in-theory        8061
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8061.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (G or F)))), M:tm-105, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8062
in-theory        8062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8062.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (F or E)))), M:tm-95, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8063
in-theory        8063
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8063.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (G or F)))), M:tm-83, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8064
in-theory        8064
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8064.         (((not (not A)) -> A) and (((B and C) -> B) and (D -> (E or D)))), M:tm-76, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8065
in-theory        8065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8065.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (F or E)))), M:tm-69, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8066
in-theory        8066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8066.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (G or F)))), M:tm-54, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8067
in-theory        8067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8067.         ((A -> (B or A)) and (((C and D) -> C) and (E -> (F or E)))), M:tm-42, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8068
in-theory        8068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8068.         ((A -> (A or B)) and (((C and D) -> C) and (E -> (F or E)))), M:tm-32, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8069
in-theory        8069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8069.         ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (F or E)))), M:tm-23, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8070
in-theory        8070
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8070.         (((A and B) -> B) and (((C and D) -> C) and (E -> (F or E)))), M:tm-22, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8071
in-theory        8071
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8071.         (((A and B) -> A) and (((C and D) -> C) and (E -> (F or E)))), M:tm-21, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8072
in-theory        8072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8072.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (G or F)))), M:tm-20, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8073
in-theory        8073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8073.         ((A -> (B -> A)) and (((C and D) -> C) and (E -> (F or E)))), M:tm-19, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8074
in-theory        8074
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8074.         (A or (((B and C) -> B) and (D -> (E or D)))), M:tm-7, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8075
in-theory        8075
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-6 tm-5 tm-3 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8075.         ((((A and B) -> A) and (C -> (D or C))) or E), M:tm-6, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8076
in-theory        8076
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> (E or D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8076.         (A -> ((((B and C) -> B) and (D -> (E or D))) and A)), M:tm-5, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8077
in-theory        8077
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-1 tm-5 tm-3 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8077.         (A -> (((B and C) -> B) and (D -> (E or D)))), M:tm-1, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8078
in-theory        8078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8078.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-210, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8079
in-theory        8079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8079.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-183, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8080
in-theory        8080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8080.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-157, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8081
in-theory        8081
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8081.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-147, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8082
in-theory        8082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8082.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-134, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8083
in-theory        8083
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8083.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-125, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8084
in-theory        8084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8084.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-113, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8085
in-theory        8085
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8085.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-105, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8086
in-theory        8086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8086.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-95, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8087
in-theory        8087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8087.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-83, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8088
in-theory        8088
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-10 tm-3 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8088.         (((not (not A)) -> A) and (((B and C) -> B) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-76, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8089
in-theory        8089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-9 tm-3 tm-8)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8089.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-69, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8090
in-theory        8090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8090.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-54, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8091
in-theory        8091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8091.         ((A -> (B or A)) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-42, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8092
in-theory        8092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8092.         ((A -> (A or B)) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-32, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8093
in-theory        8093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8093.         ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-23, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8094
in-theory        8094
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8094.         (((A and B) -> B) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-22, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8095
in-theory        8095
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8095.         (((A and B) -> A) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-21, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8096
in-theory        8096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8096.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-20, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8097
in-theory        8097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8097.         ((A -> (B -> A)) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-19, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8098
in-theory        8098
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-7 tm-5 tm-3 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8098.         (A or (((B and C) -> B) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-7, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8099
in-theory        8099
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-6 tm-5 tm-3 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8099.         ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F), M:tm-6, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8100
in-theory        8100
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8100.         (A -> ((((B and C) -> B) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A)), M:tm-5, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8101
in-theory        8101
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-1 tm-5 tm-3 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8101.         (A -> (((B and C) -> B) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-1, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8102
in-theory        8102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-210 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8102.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-210, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8103
in-theory        8103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-183 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8103.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-183, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8104
in-theory        8104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-157 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8104.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-157, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8105
in-theory        8105
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-147 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8105.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-147, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8106
in-theory        8106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-134 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8106.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-134, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8107
in-theory        8107
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-125 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8107.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-125, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8108
in-theory        8108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-113 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8108.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-113, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8109
in-theory        8109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     37
proof            (modus-ponens tm-105 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8109.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-105, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8110
in-theory        8110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-95 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8110.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-95, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8111
in-theory        8111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-83 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8111.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-83, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8112
in-theory        8112
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-76 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-10 tm-3 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8112.         (((not (not A)) -> A) and (((B and C) -> B) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-76, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8113
in-theory        8113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     29
proof            (modus-ponens tm-69 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8113.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-69, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8114
in-theory        8114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-54 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8114.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-54, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8115
in-theory        8115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-42 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8115.         ((A -> (B or A)) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-42, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8116
in-theory        8116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-32 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8116.         ((A -> (A or B)) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-32, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8117
in-theory        8117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-23 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8117.         ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-23, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8118
in-theory        8118
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-22 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8118.         (((A and B) -> B) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-22, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8119
in-theory        8119
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-21 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8119.         (((A and B) -> A) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-21, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8120
in-theory        8120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-20 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8120.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-20, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8121
in-theory        8121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-19 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8121.         ((A -> (B -> A)) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-19, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8122
in-theory        8122
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-7 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-7 tm-5 tm-3 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8122.         (A or (((B and C) -> B) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-7, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8123
in-theory        8123
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-6 tm-5 tm-3 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8123.         ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E), M:tm-6, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8124
in-theory        8124
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8124.         (A -> ((((B and C) -> B) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and A)), M:tm-5, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8125
in-theory        8125
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-1 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-1 tm-5 tm-3 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8125.         (A -> (((B and C) -> B) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-1, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8126
in-theory        8126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8126.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((not (not G)) -> G))), M:tm-210, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8127
in-theory        8127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8127.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-183, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8128
in-theory        8128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8128.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-157, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8129
in-theory        8129
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8129.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-147, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8130
in-theory        8130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8130.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-134, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8131
in-theory        8131
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8131.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-125, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8132
in-theory        8132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8132.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((not (not G)) -> G))), M:tm-113, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8133
in-theory        8133
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-10)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8133.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-105, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8134
in-theory        8134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8134.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((not (not E)) -> E))), M:tm-95, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8135
in-theory        8135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8135.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-83, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8136
in-theory        8136
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((not (not D)) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8136.         (((not (not A)) -> A) and (((B and C) -> B) and ((not (not D)) -> D))), M:tm-76, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8137
in-theory        8137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((not (not E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-3 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8137.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((not (not E)) -> E))), M:tm-69, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8138
in-theory        8138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8138.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-54, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8139
in-theory        8139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8139.         ((A -> (B or A)) and (((C and D) -> C) and ((not (not E)) -> E))), M:tm-42, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8140
in-theory        8140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8140.         ((A -> (A or B)) and (((C and D) -> C) and ((not (not E)) -> E))), M:tm-32, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8141
in-theory        8141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8141.         ((A -> (B -> (A and B))) and (((C and D) -> C) and ((not (not E)) -> E))), M:tm-23, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8142
in-theory        8142
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-3 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8142.         (((A and B) -> B) and (((C and D) -> C) and ((not (not E)) -> E))), M:tm-22, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8143
in-theory        8143
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8143.         (((A and B) -> A) and (((C and D) -> C) and ((not (not E)) -> E))), M:tm-21, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8144
in-theory        8144
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8144.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-20, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8145
in-theory        8145
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8145.         ((A -> (B -> A)) and (((C and D) -> C) and ((not (not E)) -> E))), M:tm-19, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8146
in-theory        8146
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-7 tm-5 tm-3 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8146.         (A or (((B and C) -> B) and ((not (not D)) -> D))), M:tm-7, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8147
in-theory        8147
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-6 tm-5 tm-3 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8147.         ((((A and B) -> A) and ((not (not C)) -> C)) or D), M:tm-6, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8148
in-theory        8148
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((not (not D)) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8148.         (A -> ((((B and C) -> B) and ((not (not D)) -> D)) and A)), M:tm-5, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8149
in-theory        8149
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-1 tm-5 tm-3 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8149.         (A -> (((B and C) -> B) and ((not (not D)) -> D))), M:tm-1, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8150
in-theory        8150
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8150.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (H -> (I -> H))))), M:tm-210, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8151
in-theory        8151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8151.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-183, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8152
in-theory        8152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8152.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-157, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8153
in-theory        8153
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8153.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-147, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8154
in-theory        8154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8154.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-134, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8155
in-theory        8155
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8155.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-125, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8156
in-theory        8156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8156.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (I -> H))))), M:tm-113, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8157
in-theory        8157
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8157.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-105, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8158
in-theory        8158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8158.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (F -> (G -> F))))), M:tm-95, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8159
in-theory        8159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8159.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-83, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8160
in-theory        8160
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8160.         (((not (not A)) -> A) and (((B and C) -> B) and (D -> (E -> (F -> E))))), M:tm-76, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8161
in-theory        8161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-3 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8161.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (F -> (G -> F))))), M:tm-69, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8162
in-theory        8162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8162.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-54, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8163
in-theory        8163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8163.         ((A -> (B or A)) and (((C and D) -> C) and (E -> (F -> (G -> F))))), M:tm-42, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8164
in-theory        8164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8164.         ((A -> (A or B)) and (((C and D) -> C) and (E -> (F -> (G -> F))))), M:tm-32, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8165
in-theory        8165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8165.         ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (F -> (G -> F))))), M:tm-23, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8166
in-theory        8166
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8166.         (((A and B) -> B) and (((C and D) -> C) and (E -> (F -> (G -> F))))), M:tm-22, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8167
in-theory        8167
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8167.         (((A and B) -> A) and (((C and D) -> C) and (E -> (F -> (G -> F))))), M:tm-21, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8168
in-theory        8168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8168.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-20, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8169
in-theory        8169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8169.         ((A -> (B -> A)) and (((C and D) -> C) and (E -> (F -> (G -> F))))), M:tm-19, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8170
in-theory        8170
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-3 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8170.         (A or (((B and C) -> B) and (D -> (E -> (F -> E))))), M:tm-7, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8171
in-theory        8171
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-3 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8171.         ((((A and B) -> A) and (C -> (D -> (E -> D)))) or F), M:tm-6, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8172
in-theory        8172
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> (E -> (F -> E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8172.         (A -> ((((B and C) -> B) and (D -> (E -> (F -> E)))) and A)), M:tm-5, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8173
in-theory        8173
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8173.         (A -> (((B and C) -> B) and (D -> (E -> (F -> E))))), M:tm-1, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8174
in-theory        8174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8174.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> H) -> (G -> G)))), M:tm-210, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8175
in-theory        8175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8175.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-183, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8176
in-theory        8176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8176.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-157, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8177
in-theory        8177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8177.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-147, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8178
in-theory        8178
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8178.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-134, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8179
in-theory        8179
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8179.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-125, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8180
in-theory        8180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8180.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (G -> G)))), M:tm-113, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8181
in-theory        8181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8181.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-105, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8182
in-theory        8182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8182.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> F) -> (E -> E)))), M:tm-95, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8183
in-theory        8183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8183.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-83, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8184
in-theory        8184
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((D -> E) -> (D -> D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8184.         (((not (not A)) -> A) and (((B and C) -> B) and ((D -> E) -> (D -> D)))), M:tm-76, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8185
in-theory        8185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> F) -> (E -> E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-2 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8185.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> F) -> (E -> E)))), M:tm-69, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8186
in-theory        8186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8186.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-54, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8187
in-theory        8187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8187.         ((A -> (B or A)) and (((C and D) -> C) and ((E -> F) -> (E -> E)))), M:tm-42, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8188
in-theory        8188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8188.         ((A -> (A or B)) and (((C and D) -> C) and ((E -> F) -> (E -> E)))), M:tm-32, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8189
in-theory        8189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8189.         ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (E -> E)))), M:tm-23, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8190
in-theory        8190
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8190.         (((A and B) -> B) and (((C and D) -> C) and ((E -> F) -> (E -> E)))), M:tm-22, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8191
in-theory        8191
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8191.         (((A and B) -> A) and (((C and D) -> C) and ((E -> F) -> (E -> E)))), M:tm-21, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8192
in-theory        8192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8192.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-20, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8193
in-theory        8193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8193.         ((A -> (B -> A)) and (((C and D) -> C) and ((E -> F) -> (E -> E)))), M:tm-19, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8194
in-theory        8194
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-7 tm-5 tm-3 tm-2 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8194.         (A or (((B and C) -> B) and ((D -> E) -> (D -> D)))), M:tm-7, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8195
in-theory        8195
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-6 tm-5 tm-3 tm-2 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8195.         ((((A and B) -> A) and ((C -> D) -> (C -> C))) or E), M:tm-6, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8196
in-theory        8196
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((D -> E) -> (D -> D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8196.         (A -> ((((B and C) -> B) and ((D -> E) -> (D -> D))) and A)), M:tm-5, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8197
in-theory        8197
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-1 tm-5 tm-3 tm-2)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8197.         (A -> (((B and C) -> B) and ((D -> E) -> (D -> D)))), M:tm-1, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8198
in-theory        8198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-210 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8198.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-210, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8199
in-theory        8199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-183 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8199.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-183, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8200
in-theory        8200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-157 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8200.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-157, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8201
in-theory        8201
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-147 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8201.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-147, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8202
in-theory        8202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-134 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8202.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-134, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8203
in-theory        8203
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-125 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8203.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-125, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8204
in-theory        8204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-113 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8204.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-113, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8205
in-theory        8205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     45
proof            (modus-ponens tm-105 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8205.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-105, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8206
in-theory        8206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-95 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8206.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-95, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8207
in-theory        8207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-83 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8207.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-83, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8208
in-theory        8208
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-76 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-3 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8208.         (((not (not A)) -> A) and (((B and C) -> B) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-76, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8209
in-theory        8209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     37
proof            (modus-ponens tm-69 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-3 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8209.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-69, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8210
in-theory        8210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-54 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8210.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-54, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8211
in-theory        8211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-42 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8211.         ((A -> (B or A)) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-42, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8212
in-theory        8212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-32 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8212.         ((A -> (A or B)) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-32, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8213
in-theory        8213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-23 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8213.         ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-23, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8214
in-theory        8214
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-22 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8214.         (((A and B) -> B) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-22, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8215
in-theory        8215
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-21 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8215.         (((A and B) -> A) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-21, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8216
in-theory        8216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-20 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8216.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-20, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8217
in-theory        8217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-19 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8217.         ((A -> (B -> A)) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-19, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8218
in-theory        8218
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-7 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-7 tm-5 tm-3 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8218.         (A or (((B and C) -> B) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-7, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8219
in-theory        8219
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F)
theorem-size     27
proof            (modus-ponens tm-6 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-6 tm-5 tm-3 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8219.         ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F), M:tm-6, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8220
in-theory        8220
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8220.         (A -> ((((B and C) -> B) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and A)), M:tm-5, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8221
in-theory        8221
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-1 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-1 tm-5 tm-3 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8221.         (A -> (((B and C) -> B) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-1, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8222
in-theory        8222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8222.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-210, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8223
in-theory        8223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8223.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-183, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8224
in-theory        8224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8224.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-157, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8225
in-theory        8225
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8225.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-147, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8226
in-theory        8226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8226.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-134, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8227
in-theory        8227
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8227.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-125, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8228
in-theory        8228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8228.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-113, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8229
in-theory        8229
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8229.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-105, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8230
in-theory        8230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8230.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-95, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8231
in-theory        8231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8231.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-83, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8232
in-theory        8232
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-10 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8232.         (((not (not A)) -> A) and (((B and C) -> B) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-76, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8233
in-theory        8233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-9 tm-3 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8233.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-69, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8234
in-theory        8234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8234.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-54, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8235
in-theory        8235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8235.         ((A -> (B or A)) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-42, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8236
in-theory        8236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8236.         ((A -> (A or B)) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-32, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8237
in-theory        8237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8237.         ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-23, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8238
in-theory        8238
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8238.         (((A and B) -> B) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-22, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8239
in-theory        8239
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8239.         (((A and B) -> A) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-21, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8240
in-theory        8240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8240.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-20, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8241
in-theory        8241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8241.         ((A -> (B -> A)) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-19, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8242
in-theory        8242
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-7 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-7 tm-5 tm-3 tm-1 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8242.         (A or (((B and C) -> B) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-7, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8243
in-theory        8243
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-6 tm-5 tm-3 tm-1 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8243.         ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G), M:tm-6, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8244
in-theory        8244
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8244.         (A -> ((((B and C) -> B) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A)), M:tm-5, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8245
in-theory        8245
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-1 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-1 tm-5 tm-3 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8245.         (A -> (((B and C) -> B) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-1, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8246
in-theory        8246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-210 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8246.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-210, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8247
in-theory        8247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-183 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8247.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-183, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8248
in-theory        8248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-157 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8248.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-157, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8249
in-theory        8249
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-147 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8249.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-147, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8250
in-theory        8250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-134 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8250.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-134, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8251
in-theory        8251
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-125 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8251.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-125, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8252
in-theory        8252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-113 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8252.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-113, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8253
in-theory        8253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     41
proof            (modus-ponens tm-105 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8253.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-105, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8254
in-theory        8254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-95 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8254.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-95, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8255
in-theory        8255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-83 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8255.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-83, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8256
in-theory        8256
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     27
proof            (modus-ponens tm-76 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8256.         (((not (not A)) -> A) and (((B and C) -> B) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-76, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8257
in-theory        8257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     33
proof            (modus-ponens tm-69 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8257.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-69, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8258
in-theory        8258
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-54 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8258.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-54, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8259
in-theory        8259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-42 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8259.         ((A -> (B or A)) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-42, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8260
in-theory        8260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-32 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8260.         ((A -> (A or B)) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-32, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8261
in-theory        8261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-23 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8261.         ((A -> (B -> (A and B))) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-23, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8262
in-theory        8262
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-22 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8262.         (((A and B) -> B) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-22, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8263
in-theory        8263
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-21 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8263.         (((A and B) -> A) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-21, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8264
in-theory        8264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-20 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8264.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-20, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8265
in-theory        8265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-19 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8265.         ((A -> (B -> A)) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-19, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8266
in-theory        8266
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-7 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-3 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8266.         (A or (((B and C) -> B) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-7, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8267
in-theory        8267
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-3 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8267.         ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F), M:tm-6, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8268
in-theory        8268
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8268.         (A -> ((((B and C) -> B) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and A)), M:tm-5, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8269
in-theory        8269
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-1 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-3 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8269.         (A -> (((B and C) -> B) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-1, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8270
in-theory        8270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-210 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8270.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> ((H and I) -> H)))), M:tm-210, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8271
in-theory        8271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-183 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8271.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-183, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8272
in-theory        8272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-157 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8272.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-157, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8273
in-theory        8273
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-147 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8273.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-147, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8274
in-theory        8274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-134 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8274.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-134, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8275
in-theory        8275
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-125 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8275.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-125, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8276
in-theory        8276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-113 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8276.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H and I) -> H)))), M:tm-113, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8277
in-theory        8277
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-105 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8277.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-105, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8278
in-theory        8278
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-95 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8278.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> ((F and G) -> F)))), M:tm-95, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8279
in-theory        8279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-83 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8279.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-83, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8280
in-theory        8280
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-76 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8280.         (((not (not A)) -> A) and (((B and C) -> B) and (D -> ((E and F) -> E)))), M:tm-76, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8281
in-theory        8281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-69 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8281.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> ((F and G) -> F)))), M:tm-69, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8282
in-theory        8282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-54 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8282.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-54, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8283
in-theory        8283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-42 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8283.         ((A -> (B or A)) and (((C and D) -> C) and (E -> ((F and G) -> F)))), M:tm-42, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8284
in-theory        8284
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-32 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8284.         ((A -> (A or B)) and (((C and D) -> C) and (E -> ((F and G) -> F)))), M:tm-32, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8285
in-theory        8285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-23 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8285.         ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> ((F and G) -> F)))), M:tm-23, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8286
in-theory        8286
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-22 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8286.         (((A and B) -> B) and (((C and D) -> C) and (E -> ((F and G) -> F)))), M:tm-22, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8287
in-theory        8287
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-21 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8287.         (((A and B) -> A) and (((C and D) -> C) and (E -> ((F and G) -> F)))), M:tm-21, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8288
in-theory        8288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-20 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8288.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-20, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8289
in-theory        8289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-19 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8289.         ((A -> (B -> A)) and (((C and D) -> C) and (E -> ((F and G) -> F)))), M:tm-19, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8290
in-theory        8290
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-7 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-3 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8290.         (A or (((B and C) -> B) and (D -> ((E and F) -> E)))), M:tm-7, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8291
in-theory        8291
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-3 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8291.         ((((A and B) -> A) and (C -> ((D and E) -> D))) or F), M:tm-6, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8292
in-theory        8292
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> ((E and F) -> E))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8292.         (A -> ((((B and C) -> B) and (D -> ((E and F) -> E))) and A)), M:tm-5, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8293
in-theory        8293
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-1 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8293.         (A -> (((B and C) -> B) and (D -> ((E and F) -> E)))), M:tm-1, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8294
in-theory        8294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-210 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8294.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-210, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8295
in-theory        8295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-183 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8295.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-183, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8296
in-theory        8296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-157 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8296.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-157, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8297
in-theory        8297
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-147 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8297.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-147, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8298
in-theory        8298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-134 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8298.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-134, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8299
in-theory        8299
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-125 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8299.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-125, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8300
in-theory        8300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-113 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8300.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-113, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8301
in-theory        8301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     41
proof            (modus-ponens tm-105 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8301.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-105, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8302
in-theory        8302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-95 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8302.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-95, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8303
in-theory        8303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-83 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8303.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-83, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8304
in-theory        8304
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     27
proof            (modus-ponens tm-76 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-10 tm-3 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8304.         (((not (not A)) -> A) and (((B and C) -> B) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-76, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8305
in-theory        8305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     33
proof            (modus-ponens tm-69 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-9 tm-3 tm-2 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8305.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-69, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8306
in-theory        8306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-54 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8306.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-54, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8307
in-theory        8307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-42 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8307.         ((A -> (B or A)) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-42, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8308
in-theory        8308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-32 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8308.         ((A -> (A or B)) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-32, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8309
in-theory        8309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-23 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8309.         ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-23, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8310
in-theory        8310
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-22 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8310.         (((A and B) -> B) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-22, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8311
in-theory        8311
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-21 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8311.         (((A and B) -> A) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-21, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8312
in-theory        8312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-20 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8312.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-20, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8313
in-theory        8313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-19 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8313.         ((A -> (B -> A)) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-19, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8314
in-theory        8314
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-7 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-7 tm-5 tm-3 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8314.         (A or (((B and C) -> B) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-7, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8315
in-theory        8315
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-6 tm-5 tm-3 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8315.         ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F), M:tm-6, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8316
in-theory        8316
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8316.         (A -> ((((B and C) -> B) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and A)), M:tm-5, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8317
in-theory        8317
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-1 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-1 tm-5 tm-3 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8317.         (A -> (((B and C) -> B) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-1, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8318
in-theory        8318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-210 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8318.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> ((H and I) -> I)))), M:tm-210, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8319
in-theory        8319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-183 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8319.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-183, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8320
in-theory        8320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-157 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8320.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-157, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8321
in-theory        8321
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-147 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8321.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-147, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8322
in-theory        8322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-134 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8322.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-134, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8323
in-theory        8323
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-125 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8323.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-125, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8324
in-theory        8324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-113 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8324.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H and I) -> I)))), M:tm-113, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8325
in-theory        8325
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-105 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8325.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-105, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8326
in-theory        8326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-95 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8326.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> ((F and G) -> G)))), M:tm-95, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8327
in-theory        8327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-83 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8327.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-83, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8328
in-theory        8328
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-76 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-10 tm-3 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8328.         (((not (not A)) -> A) and (((B and C) -> B) and (D -> ((E and F) -> F)))), M:tm-76, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8329
in-theory        8329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-69 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-9 tm-3 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8329.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> ((F and G) -> G)))), M:tm-69, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8330
in-theory        8330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-54 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8330.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-54, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8331
in-theory        8331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-42 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8331.         ((A -> (B or A)) and (((C and D) -> C) and (E -> ((F and G) -> G)))), M:tm-42, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8332
in-theory        8332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-32 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8332.         ((A -> (A or B)) and (((C and D) -> C) and (E -> ((F and G) -> G)))), M:tm-32, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8333
in-theory        8333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-23 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8333.         ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> ((F and G) -> G)))), M:tm-23, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8334
in-theory        8334
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-22 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8334.         (((A and B) -> B) and (((C and D) -> C) and (E -> ((F and G) -> G)))), M:tm-22, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8335
in-theory        8335
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-21 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8335.         (((A and B) -> A) and (((C and D) -> C) and (E -> ((F and G) -> G)))), M:tm-21, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8336
in-theory        8336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-20 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8336.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-20, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8337
in-theory        8337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-19 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8337.         ((A -> (B -> A)) and (((C and D) -> C) and (E -> ((F and G) -> G)))), M:tm-19, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8338
in-theory        8338
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-7 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-7 tm-5 tm-3 tm-1 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8338.         (A or (((B and C) -> B) and (D -> ((E and F) -> F)))), M:tm-7, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8339
in-theory        8339
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-6 tm-5 tm-3 tm-1 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8339.         ((((A and B) -> A) and (C -> ((D and E) -> E))) or F), M:tm-6, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8340
in-theory        8340
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> ((E and F) -> F))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8340.         (A -> ((((B and C) -> B) and (D -> ((E and F) -> F))) and A)), M:tm-5, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8341
in-theory        8341
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-1 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-1 tm-5 tm-3 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8341.         (A -> (((B and C) -> B) and (D -> ((E and F) -> F)))), M:tm-1, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8342
in-theory        8342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8342.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G)))), M:tm-210, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8343
in-theory        8343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8343.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-183, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8344
in-theory        8344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8344.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-157, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8345
in-theory        8345
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8345.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-147, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8346
in-theory        8346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8346.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-134, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8347
in-theory        8347
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8347.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-125, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8348
in-theory        8348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8348.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G)))), M:tm-113, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8349
in-theory        8349
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8349.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-105, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8350
in-theory        8350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8350.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E)))), M:tm-95, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8351
in-theory        8351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8351.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-83, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8352
in-theory        8352
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8352.         (((not (not A)) -> A) and (((B and C) -> B) and (D -> ((E -> (F -> E)) and D)))), M:tm-76, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8353
in-theory        8353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8353.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E)))), M:tm-69, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8354
in-theory        8354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8354.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-54, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8355
in-theory        8355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8355.         ((A -> (B or A)) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E)))), M:tm-42, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8356
in-theory        8356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8356.         ((A -> (A or B)) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E)))), M:tm-32, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8357
in-theory        8357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8357.         ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E)))), M:tm-23, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8358
in-theory        8358
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8358.         (((A and B) -> B) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E)))), M:tm-22, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8359
in-theory        8359
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8359.         (((A and B) -> A) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E)))), M:tm-21, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8360
in-theory        8360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8360.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-20, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8361
in-theory        8361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8361.         ((A -> (B -> A)) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E)))), M:tm-19, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8362
in-theory        8362
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-7 tm-5 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8362.         (A or (((B and C) -> B) and (D -> ((E -> (F -> E)) and D)))), M:tm-7, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8363
in-theory        8363
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-6 tm-5 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8363.         ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) or F), M:tm-6, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8364
in-theory        8364
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> ((E -> (F -> E)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8364.         (A -> ((((B and C) -> B) and (D -> ((E -> (F -> E)) and D))) and A)), M:tm-5, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8365
in-theory        8365
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8365.         (A -> (((B and C) -> B) and (D -> ((E -> (F -> E)) and D)))), M:tm-1, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8366
in-theory        8366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-210 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8366.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-210, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8367
in-theory        8367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-183 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8367.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-183, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8368
in-theory        8368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-157 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8368.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-157, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8369
in-theory        8369
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-147 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8369.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-147, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8370
in-theory        8370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-134 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8370.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-134, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8371
in-theory        8371
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-125 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8371.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-125, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8372
in-theory        8372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-113 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8372.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-113, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8373
in-theory        8373
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     43
proof            (modus-ponens tm-105 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8373.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-105, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8374
in-theory        8374
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-95 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8374.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-95, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8375
in-theory        8375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-83 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8375.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-83, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8376
in-theory        8376
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-76 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8376.         (((not (not A)) -> A) and (((B and C) -> B) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-76, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8377
in-theory        8377
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-69 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8377.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-69, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8378
in-theory        8378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-54 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8378.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-54, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8379
in-theory        8379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-42 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8379.         ((A -> (B or A)) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-42, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8380
in-theory        8380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-32 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8380.         ((A -> (A or B)) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-32, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8381
in-theory        8381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-23 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8381.         ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-23, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8382
in-theory        8382
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-22 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8382.         (((A and B) -> B) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-22, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8383
in-theory        8383
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-21 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8383.         (((A and B) -> A) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-21, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8384
in-theory        8384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-20 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8384.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-20, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8385
in-theory        8385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-19 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8385.         ((A -> (B -> A)) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-19, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8386
in-theory        8386
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-7 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-7 tm-5 tm-3 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8386.         (A or (((B and C) -> B) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-7, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8387
in-theory        8387
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-6 tm-5 tm-3 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8387.         ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G), M:tm-6, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8388
in-theory        8388
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8388.         (A -> ((((B and C) -> B) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and A)), M:tm-5, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8389
in-theory        8389
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-1 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-1 tm-5 tm-3 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8389.         (A -> (((B and C) -> B) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-1, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8390
in-theory        8390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8390.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (((H and I) -> H) and G)))), M:tm-210, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8391
in-theory        8391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8391.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-183, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8392
in-theory        8392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8392.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-157, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8393
in-theory        8393
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8393.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-147, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8394
in-theory        8394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8394.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-134, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8395
in-theory        8395
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8395.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-125, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8396
in-theory        8396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8396.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (((H and I) -> H) and G)))), M:tm-113, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8397
in-theory        8397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8397.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-105, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8398
in-theory        8398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8398.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (((F and G) -> F) and E)))), M:tm-95, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8399
in-theory        8399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8399.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-83, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8400
in-theory        8400
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-10 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8400.         (((not (not A)) -> A) and (((B and C) -> B) and (D -> (((E and F) -> E) and D)))), M:tm-76, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8401
in-theory        8401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8401.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (((F and G) -> F) and E)))), M:tm-69, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8402
in-theory        8402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8402.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-54, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8403
in-theory        8403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8403.         ((A -> (B or A)) and (((C and D) -> C) and (E -> (((F and G) -> F) and E)))), M:tm-42, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8404
in-theory        8404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8404.         ((A -> (A or B)) and (((C and D) -> C) and (E -> (((F and G) -> F) and E)))), M:tm-32, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8405
in-theory        8405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8405.         ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (((F and G) -> F) and E)))), M:tm-23, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8406
in-theory        8406
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8406.         (((A and B) -> B) and (((C and D) -> C) and (E -> (((F and G) -> F) and E)))), M:tm-22, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8407
in-theory        8407
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8407.         (((A and B) -> A) and (((C and D) -> C) and (E -> (((F and G) -> F) and E)))), M:tm-21, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8408
in-theory        8408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8408.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-20, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8409
in-theory        8409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8409.         ((A -> (B -> A)) and (((C and D) -> C) and (E -> (((F and G) -> F) and E)))), M:tm-19, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8410
in-theory        8410
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8410.         (A or (((B and C) -> B) and (D -> (((E and F) -> E) and D)))), M:tm-7, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8411
in-theory        8411
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8411.         ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) or F), M:tm-6, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8412
in-theory        8412
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> (((E and F) -> E) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8412.         (A -> ((((B and C) -> B) and (D -> (((E and F) -> E) and D))) and A)), M:tm-5, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8413
in-theory        8413
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8413.         (A -> (((B and C) -> B) and (D -> (((E and F) -> E) and D)))), M:tm-1, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8414
in-theory        8414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> I) and H))))
theorem-size     41
proof            (modus-ponens tm-210 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8414.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-210, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8415
in-theory        8415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-183 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8415.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-183, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8416
in-theory        8416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-157 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8416.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-157, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8417
in-theory        8417
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     39
proof            (modus-ponens tm-147 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8417.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-147, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8418
in-theory        8418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-134 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8418.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-134, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8419
in-theory        8419
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     39
proof            (modus-ponens tm-125 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8419.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-125, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8420
in-theory        8420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> I) and H))))
theorem-size     39
proof            (modus-ponens tm-113 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8420.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-113, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8421
in-theory        8421
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     43
proof            (modus-ponens tm-105 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8421.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-105, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8422
in-theory        8422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-95 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8422.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-95, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8423
in-theory        8423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-83 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8423.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-83, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8424
in-theory        8424
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> F) and E))))
theorem-size     29
proof            (modus-ponens tm-76 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8424.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> F) and E)))), M:tm-76, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8425
in-theory        8425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     35
proof            (modus-ponens tm-69 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8425.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-69, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8426
in-theory        8426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     37
proof            (modus-ponens tm-54 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8426.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-54, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8427
in-theory        8427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-42 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8427.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-42, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8428
in-theory        8428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-32 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8428.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-32, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8429
in-theory        8429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-23 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8429.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-23, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8430
in-theory        8430
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-22 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8430.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-22, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8431
in-theory        8431
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-21 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8431.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-21, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8432
in-theory        8432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     37
proof            (modus-ponens tm-20 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8432.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-20, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8433
in-theory        8433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-19 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8433.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-19, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8434
in-theory        8434
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-7 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8434.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> F) and E)))), M:tm-7, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8435
in-theory        8435
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8435.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) or G), M:tm-6, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8436
in-theory        8436
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> F) and E))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8436.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> F) and E))) and A)), M:tm-5, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8437
in-theory        8437
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-1 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8437.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> F) and E)))), M:tm-1, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8438
in-theory        8438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8438.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G)))), M:tm-210, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8439
in-theory        8439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8439.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-183, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8440
in-theory        8440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8440.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-157, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8441
in-theory        8441
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8441.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-147, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8442
in-theory        8442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8442.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-134, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8443
in-theory        8443
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8443.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-125, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8444
in-theory        8444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8444.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G)))), M:tm-113, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8445
in-theory        8445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8445.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-105, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8446
in-theory        8446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8446.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E)))), M:tm-95, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8447
in-theory        8447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8447.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-83, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8448
in-theory        8448
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8448.         (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (((E and F) -> E) and D)))), M:tm-76, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8449
in-theory        8449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8449.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E)))), M:tm-69, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8450
in-theory        8450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8450.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-54, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8451
in-theory        8451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8451.         ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E)))), M:tm-42, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8452
in-theory        8452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8452.         ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E)))), M:tm-32, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8453
in-theory        8453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8453.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E)))), M:tm-23, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8454
in-theory        8454
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8454.         (((A and B) -> B) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E)))), M:tm-22, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8455
in-theory        8455
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8455.         (((A and B) -> A) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E)))), M:tm-21, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8456
in-theory        8456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8456.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-20, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8457
in-theory        8457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8457.         ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E)))), M:tm-19, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8458
in-theory        8458
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8458.         (A or ((B -> (C -> B)) and (D -> (((E and F) -> E) and D)))), M:tm-7, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8459
in-theory        8459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8459.         (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) or F), M:tm-6, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8460
in-theory        8460
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> (((E and F) -> E) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8460.         (A -> (((B -> (C -> B)) and (D -> (((E and F) -> E) and D))) and A)), M:tm-5, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8461
in-theory        8461
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8461.         (A -> ((B -> (C -> B)) and (D -> (((E and F) -> E) and D)))), M:tm-1, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8462
in-theory        8462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (((F and G) -> F) and E))) -> (not E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8462.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (((F and G) -> F) and E))) -> (not E))), M:tm-210, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8463
in-theory        8463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8463.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-183, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8464
in-theory        8464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8464.         ((A -> ((B and C) -> C)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-157, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8465
in-theory        8465
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not (((C and D) -> C) and ((A and B) -> B)))))
theorem-size     19
proof            (modus-ponens tm-153 tm-235 ((A (-> (-> (and B C) C) (not (and (-> (and Bm Cm) Bm) (-> (and B C) C))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-5 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8465.         (not (((A and B) -> B) -> (not (((C and D) -> C) and ((A and B) -> B))))), M:tm-153, m:tm-235, u:((A (-> (-> (and B C) C) (not (and (-> (and Bm Cm) Bm) (-> (and B C) C))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-8466
in-theory        8466
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8466.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-147, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8467
in-theory        8467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8467.         ((A -> ((B and C) -> B)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-134, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8468
in-theory        8468
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not (((C and D) -> C) and ((A and B) -> A)))))
theorem-size     19
proof            (modus-ponens tm-130 tm-235 ((A (-> (-> (and B C) B) (not (and (-> (and Bm Cm) Bm) (-> (and B C) B))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8468.         (not (((A and B) -> A) -> (not (((C and D) -> C) and ((A and B) -> A))))), M:tm-130, m:tm-235, u:((A (-> (-> (and B C) B) (not (and (-> (and Bm Cm) Bm) (-> (and B C) B))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-8469
in-theory        8469
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8469.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-125, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8470
in-theory        8470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (((F and G) -> F) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8470.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (((F and G) -> F) and E))) -> (not E))), M:tm-113, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8471
in-theory        8471
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((D and E) -> D) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))))
theorem-size     35
proof            (modus-ponens tm-109 tm-235 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (and (-> (and Bm Cm) Bm) (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-5 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8471.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((D and E) -> D) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))), M:tm-109, m:tm-235, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (and (-> (and Bm Cm) Bm) (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-8472
in-theory        8472
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8472.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-105, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8473
in-theory        8473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not (((D and E) -> D) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8473.         (((A -> B) -> (A -> A)) and ((C -> (not (((D and E) -> D) and C))) -> (not C))), M:tm-95, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8474
in-theory        8474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> B) and A))) -> (D -> (not A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8474.         ((A -> (not (((B and C) -> B) and A))) -> (D -> (not A))), M:tm-84, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-8475
in-theory        8475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8475.         ((A -> (B -> (C -> B))) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-83, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8476
in-theory        8476
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (((C and D) -> C) and (A -> (B -> A))))))
theorem-size     19
proof            (modus-ponens tm-79 tm-235 ((A (-> (-> B (-> C B)) (not (and (-> (and Bm Cm) Bm) (-> B (-> C B)))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-5 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8476.         (not ((A -> (B -> A)) -> (not (((C and D) -> C) and (A -> (B -> A)))))), M:tm-79, m:tm-235, u:((A (-> (-> B (-> C B)) (not (and (-> (and Bm Cm) Bm) (-> B (-> C B)))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-8477
in-theory        8477
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not (((C and D) -> C) and B))) -> (not B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8477.         (((not (not A)) -> A) and ((B -> (not (((C and D) -> C) and B))) -> (not B))), M:tm-76, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8478
in-theory        8478
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not (((B and C) -> B) and A))))) or (A -> (not (((B and C) -> B) and A)))) -> (not A))
theorem-size     26
proof            (modus-ponens tm-73 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-5 tm-3)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8478.         (((not (not (A -> (not (((B and C) -> B) and A))))) or (A -> (not (((B and C) -> B) and A)))) -> (not A)), M:tm-73, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-8479
in-theory        8479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (((D and E) -> D) and C))) -> (not C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8479.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (((D and E) -> D) and C))) -> (not C))), M:tm-69, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8480
in-theory        8480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8480.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-54, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8481
in-theory        8481
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not (((C and D) -> C) and B)))) or (B -> (not (((C and D) -> C) and B)))) -> (not B))
theorem-size     26
proof            (modus-ponens tm-47 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-5 tm-3)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8481.         (((A and (B -> (not (((C and D) -> C) and B)))) or (B -> (not (((C and D) -> C) and B)))) -> (not B)), M:tm-47, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-8482
in-theory        8482
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not (((B and C) -> B) and A))) and D) or (A -> (not (((B and C) -> B) and A)))) -> (not A))
theorem-size     26
proof            (modus-ponens tm-46 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-5)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8482.         ((((A -> (not (((B and C) -> B) and A))) and D) or (A -> (not (((B and C) -> B) and A)))) -> (not A)), M:tm-46, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-8483
in-theory        8483
times-derived    1
----------------------------------------------------------------
theorem          (((not (((A and B) -> A) and C)) or (C -> (not (((A and B) -> A) and C)))) -> (not C))
theorem-size     22
proof            (modus-ponens tm-44 tm-235 ((A Am) (B (not (and (-> (and Bm Cm) Bm) Am))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-5 tm-3)
proof-size       98
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8483.         (((not (((A and B) -> A) and C)) or (C -> (not (((A and B) -> A) and C)))) -> (not C)), M:tm-44, m:tm-235, u:((A Am) (B (not (and (-> (and Bm Cm) Bm) Am))) (C (not Am)))
================================================================
tm-name          tm-8484
in-theory        8484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not (((D and E) -> D) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8484.         ((A -> (B or A)) and ((C -> (not (((D and E) -> D) and C))) -> (not C))), M:tm-42, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8485
in-theory        8485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not (((D and E) -> D) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8485.         ((A -> (A or B)) and ((C -> (not (((D and E) -> D) and C))) -> (not C))), M:tm-32, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8486
in-theory        8486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> B) and A))) -> ((A -> (not (((B and C) -> B) and A))) and (not A)))
theorem-size     24
proof            (modus-ponens tm-24 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       98
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8486.         ((A -> (not (((B and C) -> B) and A))) -> ((A -> (not (((B and C) -> B) and A))) and (not A))), M:tm-24, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-8487
in-theory        8487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not (((D and E) -> D) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8487.         ((A -> (B -> (A and B))) and ((C -> (not (((D and E) -> D) and C))) -> (not C))), M:tm-23, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8488
in-theory        8488
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not (((D and E) -> D) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8488.         (((A and B) -> B) and ((C -> (not (((D and E) -> D) and C))) -> (not C))), M:tm-22, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8489
in-theory        8489
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not (((D and E) -> D) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8489.         (((A and B) -> A) and ((C -> (not (((D and E) -> D) and C))) -> (not C))), M:tm-21, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8490
in-theory        8490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8490.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-20, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8491
in-theory        8491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not (((D and E) -> D) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8491.         ((A -> (B -> A)) and ((C -> (not (((D and E) -> D) and C))) -> (not C))), M:tm-19, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8492
in-theory        8492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> B) and A))) -> (A -> (not (((B and C) -> B) and A))))
theorem-size     21
proof            (modus-ponens tm-12 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8492.         ((A -> (not (((B and C) -> B) and A))) -> (A -> (not (((B and C) -> B) and A)))), M:tm-12, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-8493
in-theory        8493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not (not A))) -> (not (A -> (not (((B and C) -> B) and A)))))
theorem-size     26
proof            (modus-ponens tm-9 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-9 tm-5 tm-3)
proof-size       82
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8493.         (((A -> (not (((B and C) -> B) and A))) -> (not (not A))) -> (not (A -> (not (((B and C) -> B) and A))))), M:tm-9, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-8494
in-theory        8494
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not (((C and D) -> C) and A))) or (not A)) -> B))
theorem-size     20
proof            (modus-ponens tm-8 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-5 tm-3)
proof-size       78
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8494.         (((not A) -> B) -> (((A -> (not (((C and D) -> C) and A))) or (not A)) -> B)), M:tm-8, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-8495
in-theory        8495
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not (((C and D) -> C) and B))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-5 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8495.         (A or ((B -> (not (((C and D) -> C) and B))) -> (not B))), M:tm-7, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8496
in-theory        8496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-5 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8496.         (((A -> (not (((B and C) -> B) and A))) -> (not A)) or D), M:tm-6, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8497
in-theory        8497
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not (((C and D) -> C) and B))) -> (not B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8497.         (A -> (((B -> (not (((C and D) -> C) and B))) -> (not B)) and A)), M:tm-5, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8498
in-theory        8498
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not (((C and D) -> C) and B))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-5 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8498.         (A -> ((B -> (not (((C and D) -> C) and B))) -> (not B))), M:tm-1, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8499
in-theory        8499
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> (((B and C) -> B) and A)))
theorem-size     19
proof            (modus-ponens tm-236 tm-1 ((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8499.         ((A or (((B and C) -> B) and A)) -> (D -> (((B and C) -> B) and A))), M:tm-236, m:tm-1, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8500
in-theory        8500
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((B and C) -> B))
theorem-size     15
proof            (modus-ponens tm-236 tm-3 ((Am (-> (and A B) A)) (C Bm) (D (-> (and A B) A))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8500.         ((A or (((B and C) -> B) and A)) -> ((B and C) -> B)), M:tm-236, m:tm-3, u:((Am (-> (and A B) A)) (C Bm) (D (-> (and A B) A)))
================================================================
tm-name          tm-8501
in-theory        8501
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> A)
theorem-size     11
proof            (modus-ponens tm-236 tm-4 ((Am (-> (and A B) A)) (C Bm) (D Bm)))
axioms-used      (tm-8 tm-5 tm-3 tm-4)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-8501.         ((A or (((B and C) -> B) and A)) -> A), M:tm-236, m:tm-4, u:((Am (-> (and A B) A)) (C Bm) (D Bm))
================================================================
tm-name          tm-8502
in-theory        8502
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> ((((B and C) -> B) and A) and D)))
theorem-size     21
proof            (modus-ponens tm-236 tm-5 ((Am (and (-> (and A B) A) C)) (D (-> Bm (and (and (-> (and A B) A) C) Bm)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8502.         ((A or (((B and C) -> B) and A)) -> (D -> ((((B and C) -> B) and A) and D))), M:tm-236, m:tm-5, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (and (and (-> (and A B) A) C) Bm))))
================================================================
tm-name          tm-8503
in-theory        8503
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) or D))
theorem-size     19
proof            (modus-ponens tm-236 tm-6 ((Am (and (-> (and A B) A) C)) (D (or (and (-> (and A B) A) C) Bm))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8503.         ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) or D)), M:tm-236, m:tm-6, u:((Am (and (-> (and A B) A) C)) (D (or (and (-> (and A B) A) C) Bm)))
================================================================
tm-name          tm-8504
in-theory        8504
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D or (((B and C) -> B) and A)))
theorem-size     19
proof            (modus-ponens tm-236 tm-7 ((Am (and (-> (and A B) A) C)) (D (or Bm (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8504.         ((A or (((B and C) -> B) and A)) -> (D or (((B and C) -> B) and A))), M:tm-236, m:tm-7, u:((Am (and (-> (and A B) A) C)) (D (or Bm (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8505
in-theory        8505
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-236 tm-11 ((Am (and (-> (and A B) A) C)) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8505.         ((A or (((B and C) -> B) and A)) -> (D -> (E -> D))), M:tm-236, m:tm-11, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-8506
in-theory        8506
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-236 tm-14 ((Am (and (-> (and A B) A) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8506.         ((A or (((B and C) -> B) and A)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-236, m:tm-14, u:((Am (and (-> (and A B) A) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-8507
in-theory        8507
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-236 tm-16 ((Am (and (-> (and A B) A) C)) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8507.         ((A or (((B and C) -> B) and A)) -> ((D and E) -> D)), M:tm-236, m:tm-16, u:((Am (and (-> (and A B) A) C)) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-8508
in-theory        8508
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-236 tm-18 ((Am (and (-> (and A B) A) C)) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8508.         ((A or (((B and C) -> B) and A)) -> ((D and E) -> E)), M:tm-236, m:tm-18, u:((Am (and (-> (and A B) A) C)) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-8509
in-theory        8509
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (E -> D)) and (((B and C) -> B) and A)))
theorem-size     23
proof            (modus-ponens tm-236 tm-19 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> Cm Bm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8509.         ((A or (((B and C) -> B) and A)) -> ((D -> (E -> D)) and (((B and C) -> B) and A))), M:tm-236, m:tm-19, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> Cm Bm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8510
in-theory        8510
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((B and C) -> B) and A)))
theorem-size     31
proof            (modus-ponens tm-236 tm-20 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8510.         ((A or (((B and C) -> B) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((B and C) -> B) and A))), M:tm-236, m:tm-20, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8511
in-theory        8511
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D and E) -> D) and (((B and C) -> B) and A)))
theorem-size     23
proof            (modus-ponens tm-236 tm-21 ((Am (and (-> (and A B) A) C)) (D (and (-> (and Bm Cm) Bm) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8511.         ((A or (((B and C) -> B) and A)) -> (((D and E) -> D) and (((B and C) -> B) and A))), M:tm-236, m:tm-21, u:((Am (and (-> (and A B) A) C)) (D (and (-> (and Bm Cm) Bm) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8512
in-theory        8512
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D and E) -> E) and (((B and C) -> B) and A)))
theorem-size     23
proof            (modus-ponens tm-236 tm-22 ((Am (and (-> (and A B) A) C)) (D (and (-> (and Bm Cm) Cm) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8512.         ((A or (((B and C) -> B) and A)) -> (((D and E) -> E) and (((B and C) -> B) and A))), M:tm-236, m:tm-22, u:((Am (and (-> (and A B) A) C)) (D (and (-> (and Bm Cm) Cm) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8513
in-theory        8513
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (E -> (D and E))) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-23 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8513.         ((A or (((B and C) -> B) and A)) -> ((D -> (E -> (D and E))) and (((B and C) -> B) and A))), M:tm-236, m:tm-23, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8514
in-theory        8514
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-236 tm-25 ((Am (and (-> (and A B) A) C)) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8514.         ((A or (((B and C) -> B) and A)) -> (D -> (E -> (D and E)))), M:tm-236, m:tm-25, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-8515
in-theory        8515
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (D or E)) and (((B and C) -> B) and A)))
theorem-size     23
proof            (modus-ponens tm-236 tm-32 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (or Bm Cm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8515.         ((A or (((B and C) -> B) and A)) -> ((D -> (D or E)) and (((B and C) -> B) and A))), M:tm-236, m:tm-32, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (or Bm Cm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8516
in-theory        8516
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-236 tm-33 ((Am (and (-> (and A B) A) C)) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8516.         ((A or (((B and C) -> B) and A)) -> (D -> (D or E))), M:tm-236, m:tm-33, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-8517
in-theory        8517
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (E or D)) and (((B and C) -> B) and A)))
theorem-size     23
proof            (modus-ponens tm-236 tm-42 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (or Cm Bm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8517.         ((A or (((B and C) -> B) and A)) -> ((D -> (E or D)) and (((B and C) -> B) and A))), M:tm-236, m:tm-42, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (or Cm Bm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8518
in-theory        8518
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-236 tm-43 ((Am (and (-> (and A B) A) C)) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8518.         ((A or (((B and C) -> B) and A)) -> (D -> (E or D))), M:tm-236, m:tm-43, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-8519
in-theory        8519
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((B and C) -> B) and A)))
theorem-size     31
proof            (modus-ponens tm-236 tm-54 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8519.         ((A or (((B and C) -> B) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((B and C) -> B) and A))), M:tm-236, m:tm-54, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8520
in-theory        8520
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-236 tm-56 ((Am (and (-> (and A B) A) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8520.         ((A or (((B and C) -> B) and A)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-236, m:tm-56, u:((Am (and (-> (and A B) A) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-8521
in-theory        8521
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (((B and C) -> B) and A)))
theorem-size     29
proof            (modus-ponens tm-236 tm-69 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8521.         ((A or (((B and C) -> B) and A)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (((B and C) -> B) and A))), M:tm-236, m:tm-69, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8522
in-theory        8522
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-236 tm-71 ((Am (and (-> (and A B) A) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8522.         ((A or (((B and C) -> B) and A)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-236, m:tm-71, u:((Am (and (-> (and A B) A) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-8523
in-theory        8523
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((not (not D)) -> D) and (((B and C) -> B) and A)))
theorem-size     23
proof            (modus-ponens tm-236 tm-76 ((Am (and (-> (and A B) A) C)) (D (and (-> (not (not Bm)) Bm) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8523.         ((A or (((B and C) -> B) and A)) -> (((not (not D)) -> D) and (((B and C) -> B) and A))), M:tm-236, m:tm-76, u:((Am (and (-> (and A B) A) C)) (D (and (-> (not (not Bm)) Bm) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8524
in-theory        8524
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-236 tm-78 ((Am (and (-> (and A B) A) C)) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8524.         ((A or (((B and C) -> B) and A)) -> ((not (not D)) -> D)), M:tm-236, m:tm-78, u:((Am (and (-> (and A B) A) C)) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-8525
in-theory        8525
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (E -> (F -> E))) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-83 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8525.         ((A or (((B and C) -> B) and A)) -> ((D -> (E -> (F -> E))) and (((B and C) -> B) and A))), M:tm-236, m:tm-83, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8526
in-theory        8526
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-236 tm-85 ((Am (and (-> (and A B) A) C)) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8526.         ((A or (((B and C) -> B) and A)) -> (D -> (E -> (F -> E)))), M:tm-236, m:tm-85, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-8527
in-theory        8527
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((B and C) -> B) and A))
theorem-size     17
proof            (modus-ponens tm-236 tm-86 ((Am (and (-> (and A B) A) C)) (D (and (-> (and A B) A) C))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8527.         ((A or (((B and C) -> B) and A)) -> (((B and C) -> B) and A)), M:tm-236, m:tm-86, u:((Am (and (-> (and A B) A) C)) (D (and (-> (and A B) A) C)))
================================================================
tm-name          tm-8528
in-theory        8528
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> E) -> (D -> D)) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-95 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8528.         ((A or (((B and C) -> B) and A)) -> (((D -> E) -> (D -> D)) and (((B and C) -> B) and A))), M:tm-236, m:tm-95, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8529
in-theory        8529
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-236 tm-97 ((Am (and (-> (and A B) A) C)) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8529.         ((A or (((B and C) -> B) and A)) -> ((D -> E) -> (D -> D))), M:tm-236, m:tm-97, u:((Am (and (-> (and A B) A) C)) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-8530
in-theory        8530
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (((B and C) -> B) and A)))
theorem-size     37
proof            (modus-ponens tm-236 tm-105 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8530.         ((A or (((B and C) -> B) and A)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (((B and C) -> B) and A))), M:tm-236, m:tm-105, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8531
in-theory        8531
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-236 tm-107 ((Am (and (-> (and A B) A) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8531.         ((A or (((B and C) -> B) and A)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-236, m:tm-107, u:((Am (and (-> (and A B) A) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-8532
in-theory        8532
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((B and C) -> B) and A)))
theorem-size     33
proof            (modus-ponens tm-236 tm-113 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8532.         ((A or (((B and C) -> B) and A)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((B and C) -> B) and A))), M:tm-236, m:tm-113, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8533
in-theory        8533
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-236 tm-115 ((Am (and (-> (and A B) A) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8533.         ((A or (((B and C) -> B) and A)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-236, m:tm-115, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-8534
in-theory        8534
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or (((A and B) -> A) and (A and B))) -> A)
theorem-size     15
proof            (modus-ponens tm-236 tm-116 ((Am (and Bm B)) (A Bm) (C (and Bm B)) (D Bm)))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-8534.         (((A and B) or (((A and B) -> A) and (A and B))) -> A), M:tm-236, m:tm-116, u:((Am (and Bm B)) (A Bm) (C (and Bm B)) (D Bm))
================================================================
tm-name          tm-8535
in-theory        8535
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (((B and C) -> B) and A)))
theorem-size     33
proof            (modus-ponens tm-236 tm-125 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8535.         ((A or (((B and C) -> B) and A)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (((B and C) -> B) and A))), M:tm-236, m:tm-125, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8536
in-theory        8536
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-236 tm-127 ((Am (and (-> (and A B) A) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8536.         ((A or (((B and C) -> B) and A)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-236, m:tm-127, u:((Am (and (-> (and A B) A) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-8537
in-theory        8537
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> ((E and F) -> E)) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-134 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8537.         ((A or (((B and C) -> B) and A)) -> ((D -> ((E and F) -> E)) and (((B and C) -> B) and A))), M:tm-236, m:tm-134, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8538
in-theory        8538
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-236 tm-136 ((Am (and (-> (and A B) A) C)) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8538.         ((A or (((B and C) -> B) and A)) -> (D -> ((E and F) -> E))), M:tm-236, m:tm-136, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-8539
in-theory        8539
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) or (((A and B) -> A) and (((A and B) -> A) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-236 tm-137 ((Am (-> (and A B) A)) (C (-> (-> (and A B) A) Bm)) (D Bm)))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-8539.         (((((A and B) -> A) -> C) or (((A and B) -> A) and (((A and B) -> A) -> C))) -> C), M:tm-236, m:tm-137, u:((Am (-> (and A B) A)) (C (-> (-> (and A B) A) Bm)) (D Bm))
================================================================
tm-name          tm-8540
in-theory        8540
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) or (((D and E) -> D) and ((A -> (B -> A)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-236 tm-138 ((Am (-> (and A B) A)) (C (-> (-> Bm (-> Cm Bm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-8540.         ((((A -> (B -> A)) -> C) or (((D and E) -> D) and ((A -> (B -> A)) -> C))) -> C), M:tm-236, m:tm-138, u:((Am (-> (and A B) A)) (C (-> (-> Bm (-> Cm Bm)) Dm)) (D Dm))
================================================================
tm-name          tm-8541
in-theory        8541
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or (((E and F) -> E) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D)
theorem-size     39
proof            (modus-ponens tm-236 tm-139 ((Am (-> (and A B) A)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (D Em)))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8541.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or (((E and F) -> E) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D), M:tm-236, m:tm-139, u:((Am (-> (and A B) A)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (D Em))
================================================================
tm-name          tm-8542
in-theory        8542
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) or (((D and E) -> D) and (((A and B) -> A) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-236 tm-140 ((Am (-> (and A B) A)) (C (-> (-> (and Bm Cm) Bm) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-8542.         (((((A and B) -> A) -> C) or (((D and E) -> D) and (((A and B) -> A) -> C))) -> C), M:tm-236, m:tm-140, u:((Am (-> (and A B) A)) (C (-> (-> (and Bm Cm) Bm) Dm)) (D Dm))
================================================================
tm-name          tm-8543
in-theory        8543
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (((B and C) -> B) and A)))
theorem-size     33
proof            (modus-ponens tm-236 tm-147 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8543.         ((A or (((B and C) -> B) and A)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (((B and C) -> B) and A))), M:tm-236, m:tm-147, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8544
in-theory        8544
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-236 tm-149 ((Am (and (-> (and A B) A) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8544.         ((A or (((B and C) -> B) and A)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-236, m:tm-149, u:((Am (and (-> (and A B) A) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-8545
in-theory        8545
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) or (((D and E) -> D) and (((A and B) -> B) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-236 tm-150 ((Am (-> (and A B) A)) (C (-> (-> (and Bm Cm) Cm) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-8545.         (((((A and B) -> B) -> C) or (((D and E) -> D) and (((A and B) -> B) -> C))) -> C), M:tm-236, m:tm-150, u:((Am (-> (and A B) A)) (C (-> (-> (and Bm Cm) Cm) Dm)) (D Dm))
================================================================
tm-name          tm-8546
in-theory        8546
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> ((E and F) -> F)) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-157 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8546.         ((A or (((B and C) -> B) and A)) -> ((D -> ((E and F) -> F)) and (((B and C) -> B) and A))), M:tm-236, m:tm-157, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8547
in-theory        8547
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-236 tm-159 ((Am (and (-> (and A B) A) C)) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8547.         ((A or (((B and C) -> B) and A)) -> (D -> ((E and F) -> F))), M:tm-236, m:tm-159, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-8548
in-theory        8548
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> ((E -> (F -> E)) and D)) and (((B and C) -> B) and A)))
theorem-size     27
proof            (modus-ponens tm-236 tm-183 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8548.         ((A or (((B and C) -> B) and A)) -> ((D -> ((E -> (F -> E)) and D)) and (((B and C) -> B) and A))), M:tm-236, m:tm-183, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8549
in-theory        8549
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-236 tm-184 ((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8549.         ((A or (((B and C) -> B) and A)) -> (D -> ((E -> (F -> E)) and D))), M:tm-236, m:tm-184, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-8550
in-theory        8550
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (((B and C) -> B) and A)))
theorem-size     35
proof            (modus-ponens tm-236 tm-210 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8550.         ((A or (((B and C) -> B) and A)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (((B and C) -> B) and A))), M:tm-236, m:tm-210, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8551
in-theory        8551
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-236 tm-211 ((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8551.         ((A or (((B and C) -> B) and A)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-236, m:tm-211, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-8552
in-theory        8552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E and F) -> E) and G) -> H) -> ((G or (((E and F) -> E) and G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-210 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8552.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E and F) -> E) and G) -> H) -> ((G or (((E and F) -> E) and G)) -> H))), M:tm-210, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8553
in-theory        8553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-183 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8553.         ((A -> ((B -> (C -> B)) and A)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-183, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8554
in-theory        8554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-157 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8554.         ((A -> ((B and C) -> C)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-157, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8555
in-theory        8555
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> B) and D) -> D)) -> ((D or (((B and C) -> B) and D)) -> D))
theorem-size     23
proof            (modus-ponens tm-154 tm-236 ((A (-> (and Am Bm) Am)) (Dm Cm) (B Cm) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Cm))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8555.         ((A or ((((B and C) -> B) and D) -> D)) -> ((D or (((B and C) -> B) and D)) -> D)), M:tm-154, m:tm-236, u:((A (-> (and Am Bm) Am)) (Dm Cm) (B Cm) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Cm)))
================================================================
tm-name          tm-8556
in-theory        8556
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-147 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8556.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-147, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8557
in-theory        8557
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and (C -> D)) -> C) or ((((A and B) -> A) and (C -> D)) -> D)) -> (((C -> D) or (((A and B) -> A) and (C -> D))) -> D))
theorem-size     39
proof            (modus-ponens tm-144 tm-236 ((A (-> (and Am Bm) Am)) (Cm (-> B Dm)) (C Dm) (D (-> (or (-> B Dm) (and (-> (and Am Bm) Am) (-> B Dm))) Dm))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8557.         ((((((A and B) -> A) and (C -> D)) -> C) or ((((A and B) -> A) and (C -> D)) -> D)) -> (((C -> D) or (((A and B) -> A) and (C -> D))) -> D)), M:tm-144, m:tm-236, u:((A (-> (and Am Bm) Am)) (Cm (-> B Dm)) (C Dm) (D (-> (or (-> B Dm) (and (-> (and Am Bm) Am) (-> B Dm))) Dm)))
================================================================
tm-name          tm-8558
in-theory        8558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-134 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8558.         ((A -> ((B and C) -> B)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-134, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8559
in-theory        8559
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> B) and D) -> ((B and C) -> B))) -> ((D or (((B and C) -> B) and D)) -> ((B and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-131 tm-236 ((Dm (-> (and Am Bm) Am)) (B Cm) (A (-> (and Am Bm) Am)) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (-> (and Am Bm) Am)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8559.         ((A or ((((B and C) -> B) and D) -> ((B and C) -> B))) -> ((D or (((B and C) -> B) and D)) -> ((B and C) -> B))), M:tm-131, m:tm-236, u:((Dm (-> (and Am Bm) Am)) (B Cm) (A (-> (and Am Bm) Am)) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (-> (and Am Bm) Am))))
================================================================
tm-name          tm-8560
in-theory        8560
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-125 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8560.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-125, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8561
in-theory        8561
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> (A and B)) or ((((A and B) -> A) and C) -> A)) -> ((C or (((A and B) -> A) and C)) -> A))
theorem-size     33
proof            (modus-ponens tm-122 tm-236 ((A (and Am Bm)) (Dm Am) (C Cm) (B Am) (D (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Am))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8561.         ((((((A and B) -> A) and C) -> (A and B)) or ((((A and B) -> A) and C) -> A)) -> ((C or (((A and B) -> A) and C)) -> A)), M:tm-122, m:tm-236, u:((A (and Am Bm)) (Dm Am) (C Cm) (B Am) (D (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Am)))
================================================================
tm-name          tm-8562
in-theory        8562
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and C) -> (D -> E)) -> (((C or (((A and B) -> A) and C)) -> D) -> ((C or (((A and B) -> A) and C)) -> E)))
theorem-size     35
proof            (modus-ponens tm-114 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) (-> C D))) (B (or Cm (and (-> (and Am Bm) Am) Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8562.         (((((A and B) -> A) and C) -> (D -> E)) -> (((C or (((A and B) -> A) and C)) -> D) -> ((C or (((A and B) -> A) and C)) -> E))), M:tm-114, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) (-> C D))) (B (or Cm (and (-> (and Am Bm) Am) Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-8563
in-theory        8563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> E) and G) -> H) -> ((G or (((E and F) -> E) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-113 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8563.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> E) and G) -> H) -> ((G or (((E and F) -> E) and G)) -> H))), M:tm-113, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8564
in-theory        8564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-105 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8564.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-105, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8565
in-theory        8565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-95 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8565.         (((A -> B) -> (A -> A)) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F))), M:tm-95, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8566
in-theory        8566
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) or ((((A and B) -> A) and C) -> (((A and B) -> A) and C))) -> ((C or (((A and B) -> A) and C)) -> (((A and B) -> A) and C)))
theorem-size     43
proof            (modus-ponens tm-92 tm-236 ((Dm (and (-> (and Am Bm) Am) Cm)) (A (and (-> (and Am Bm) Am) Cm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (and (-> (and Am Bm) Am) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8566.         ((((((A and B) -> A) and C) -> D) or ((((A and B) -> A) and C) -> (((A and B) -> A) and C))) -> ((C or (((A and B) -> A) and C)) -> (((A and B) -> A) and C))), M:tm-92, m:tm-236, u:((Dm (and (-> (and Am Bm) Am) Cm)) (A (and (-> (and Am Bm) Am) Cm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (and (-> (and Am Bm) Am) Cm))))
================================================================
tm-name          tm-8567
in-theory        8567
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and C) -> D) -> (E -> ((C or (((A and B) -> A) and C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-84 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8567.         (((((A and B) -> A) and C) -> D) -> (E -> ((C or (((A and B) -> A) and C)) -> D))), M:tm-84, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-8568
in-theory        8568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-83 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8568.         ((A -> (B -> (C -> B))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-83, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8569
in-theory        8569
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> B) and D) -> (E -> (((B and C) -> B) and D)))) -> ((D or (((B and C) -> B) and D)) -> (E -> (((B and C) -> B) and D))))
theorem-size     39
proof            (modus-ponens tm-80 tm-236 ((A (and (-> (and Am Bm) Am) Cm)) (Dm (-> B (and (-> (and Am Bm) Am) Cm))) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (-> B (and (-> (and Am Bm) Am) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8569.         ((A or ((((B and C) -> B) and D) -> (E -> (((B and C) -> B) and D)))) -> ((D or (((B and C) -> B) and D)) -> (E -> (((B and C) -> B) and D)))), M:tm-80, m:tm-236, u:((A (and (-> (and Am Bm) Am) Cm)) (Dm (-> B (and (-> (and Am Bm) Am) Cm))) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (-> B (and (-> (and Am Bm) Am) Cm)))))
================================================================
tm-name          tm-8570
in-theory        8570
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B and C) -> B) and D) -> E) -> ((D or (((B and C) -> B) and D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-76 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8570.         (((not (not A)) -> A) and (((((B and C) -> B) and D) -> E) -> ((D or (((B and C) -> B) and D)) -> E))), M:tm-76, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8571
in-theory        8571
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A and B) -> A) and C) -> D))) or ((((A and B) -> A) and C) -> D)) -> ((C or (((A and B) -> A) and C)) -> D))
theorem-size     33
proof            (modus-ponens tm-73 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-5 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8571.         (((not (not ((((A and B) -> A) and C) -> D))) or ((((A and B) -> A) and C) -> D)) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-73, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-8572
in-theory        8572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-69 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8572.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F))), M:tm-69, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8573
in-theory        8573
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and C) -> (C or (((A and B) -> A) and C))) -> (((((A and B) -> A) and C) or (C or (((A and B) -> A) and C))) -> (C or (((A and B) -> A) and C))))
theorem-size     45
proof            (modus-ponens tm-55 tm-236 ((A (and (-> (and Am Bm) Am) Cm)) (Dm (or Cm (and (-> (and Am Bm) Am) Cm))) (B (or Cm (and (-> (and Am Bm) Am) Cm))) (C (or Cm (and (-> (and Am Bm) Am) Cm)))))
axioms-used      (tm-2 tm-8 tm-5 tm-3)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8573.         (((((A and B) -> A) and C) -> (C or (((A and B) -> A) and C))) -> (((((A and B) -> A) and C) or (C or (((A and B) -> A) and C))) -> (C or (((A and B) -> A) and C)))), M:tm-55, m:tm-236, u:((A (and (-> (and Am Bm) Am) Cm)) (Dm (or Cm (and (-> (and Am Bm) Am) Cm))) (B (or Cm (and (-> (and Am Bm) Am) Cm))) (C (or Cm (and (-> (and Am Bm) Am) Cm))))
================================================================
tm-name          tm-8574
in-theory        8574
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-54 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8574.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-54, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8575
in-theory        8575
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> B) and D) -> (A and (((B and C) -> B) and D)))) -> ((D or (((B and C) -> B) and D)) -> (A and (((B and C) -> B) and D))))
theorem-size     39
proof            (modus-ponens tm-48 tm-236 ((A (and (-> (and Am Bm) Am) Cm)) (Dm (and B (and (-> (and Am Bm) Am) Cm))) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (and B (and (-> (and Am Bm) Am) Cm))))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8575.         ((A or ((((B and C) -> B) and D) -> (A and (((B and C) -> B) and D)))) -> ((D or (((B and C) -> B) and D)) -> (A and (((B and C) -> B) and D)))), M:tm-48, m:tm-236, u:((A (and (-> (and Am Bm) Am) Cm)) (Dm (and B (and (-> (and Am Bm) Am) Cm))) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (and B (and (-> (and Am Bm) Am) Cm)))))
================================================================
tm-name          tm-8576
in-theory        8576
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((((B and C) -> B) and D) -> E)) or ((((B and C) -> B) and D) -> E)) -> ((D or (((B and C) -> B) and D)) -> E))
theorem-size     33
proof            (modus-ponens tm-47 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-5 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8576.         (((A and ((((B and C) -> B) and D) -> E)) or ((((B and C) -> B) and D) -> E)) -> ((D or (((B and C) -> B) and D)) -> E)), M:tm-47, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-8577
in-theory        8577
times-derived    2
----------------------------------------------------------------
theorem          (((((((A and B) -> A) and C) -> D) and E) or ((((A and B) -> A) and C) -> D)) -> ((C or (((A and B) -> A) and C)) -> D))
theorem-size     33
proof            (modus-ponens tm-46 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8577.         (((((((A and B) -> A) and C) -> D) and E) or ((((A and B) -> A) and C) -> D)) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-46, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-8578
in-theory        8578
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> B) and D) -> A)) -> ((D or (((B and C) -> B) and D)) -> A))
theorem-size     23
proof            (modus-ponens tm-44 tm-236 ((A (and (-> (and Am Bm) Am) Cm)) (B Dm) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8578.         ((A or ((((B and C) -> B) and D) -> A)) -> ((D or (((B and C) -> B) and D)) -> A)), M:tm-44, m:tm-236, u:((A (and (-> (and Am Bm) Am) Cm)) (B Dm) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-8579
in-theory        8579
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-42 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8579.         ((A -> (B or A)) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F))), M:tm-42, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8580
in-theory        8580
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-32 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8580.         ((A -> (A or B)) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F))), M:tm-32, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8581
in-theory        8581
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> A) and C) -> D) -> (((((A and B) -> A) and C) -> D) and ((C or (((A and B) -> A) and C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-24 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8581.         (((((A and B) -> A) and C) -> D) -> (((((A and B) -> A) and C) -> D) and ((C or (((A and B) -> A) and C)) -> D))), M:tm-24, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-8582
in-theory        8582
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-23 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8582.         ((A -> (B -> (A and B))) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F))), M:tm-23, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8583
in-theory        8583
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-22 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8583.         (((A and B) -> B) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F))), M:tm-22, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8584
in-theory        8584
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-21 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8584.         (((A and B) -> A) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F))), M:tm-21, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8585
in-theory        8585
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-20 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8585.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-20, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8586
in-theory        8586
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-19 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8586.         ((A -> (B -> A)) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F))), M:tm-19, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8587
in-theory        8587
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> A) and C) -> D) -> ((((A and B) -> A) and C) -> D))
theorem-size     19
proof            (modus-ponens tm-12 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8587.         (((((A and B) -> A) and C) -> D) -> ((((A and B) -> A) and C) -> D)), M:tm-12, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-8588
in-theory        8588
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> (not ((C or (((A and B) -> A) and C)) -> D))) -> (not ((((A and B) -> A) and C) -> D)))
theorem-size     33
proof            (modus-ponens tm-9 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-5 tm-3)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8588.         ((((((A and B) -> A) and C) -> D) -> (not ((C or (((A and B) -> A) and C)) -> D))) -> (not ((((A and B) -> A) and C) -> D))), M:tm-9, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-8589
in-theory        8589
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (((B and C) -> B) and A)) -> D) -> E) -> ((((((B and C) -> B) and A) -> D) or ((A or (((B and C) -> B) and A)) -> D)) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8589.         ((((A or (((B and C) -> B) and A)) -> D) -> E) -> ((((((B and C) -> B) and A) -> D) or ((A or (((B and C) -> B) and A)) -> D)) -> E)), M:tm-8, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-8590
in-theory        8590
times-derived    2
----------------------------------------------------------------
theorem          (A or (((((B and C) -> B) and D) -> E) -> ((D or (((B and C) -> B) and D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-7 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-5 tm-3)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8590.         (A or (((((B and C) -> B) and D) -> E) -> ((D or (((B and C) -> B) and D)) -> E))), M:tm-7, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8591
in-theory        8591
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-5 tm-3)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8591.         ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) or E), M:tm-6, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8592
in-theory        8592
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((((B and C) -> B) and D) -> E) -> ((D or (((B and C) -> B) and D)) -> E)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8592.         (A -> ((((((B and C) -> B) and D) -> E) -> ((D or (((B and C) -> B) and D)) -> E)) and A)), M:tm-5, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8593
in-theory        8593
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> (C or (((A and B) -> A) and C))) -> (((((A and B) -> A) and C) -> D) -> D))
theorem-size     31
proof            (modus-ponens tm-2 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (or Cm (and (-> (and Am Bm) Am) Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-5 tm-3)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8593.         ((((((A and B) -> A) and C) -> D) -> (C or (((A and B) -> A) and C))) -> (((((A and B) -> A) and C) -> D) -> D)), M:tm-2, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (or Cm (and (-> (and Am Bm) Am) Cm))) (C Dm))
================================================================
tm-name          tm-8594
in-theory        8594
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B and C) -> B) and D) -> E) -> ((D or (((B and C) -> B) and D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-1 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-5 tm-3)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8594.         (A -> (((((B and C) -> B) and D) -> E) -> ((D or (((B and C) -> B) and D)) -> E))), M:tm-1, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8595
in-theory        8595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-210 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8595.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (((G and H) -> G) and F)))), M:tm-210, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8596
in-theory        8596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-183 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8596.         ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-183, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8597
in-theory        8597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-157 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8597.         ((A -> ((B and C) -> C)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-157, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8598
in-theory        8598
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-147 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8598.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-147, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8599
in-theory        8599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-134 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8599.         ((A -> ((B and C) -> B)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-134, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8600
in-theory        8600
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-125 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8600.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-125, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8601
in-theory        8601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-113 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8601.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (((G and H) -> G) and F)))), M:tm-113, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8602
in-theory        8602
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     31
proof            (modus-ponens tm-105 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8602.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (((F and G) -> F) and E)))), M:tm-105, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8603
in-theory        8603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-95 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8603.         (((A -> B) -> (A -> A)) and (C or (D -> (((E and F) -> E) and D)))), M:tm-95, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8604
in-theory        8604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-83 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8604.         ((A -> (B -> (C -> B))) and (D or (E -> (((F and G) -> F) and E)))), M:tm-83, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8605
in-theory        8605
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> (((D and E) -> D) and C))))
theorem-size     17
proof            (modus-ponens tm-76 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8605.         (((not (not A)) -> A) and (B or (C -> (((D and E) -> D) and C)))), M:tm-76, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8606
in-theory        8606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (((E and F) -> E) and D))))
theorem-size     23
proof            (modus-ponens tm-69 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8606.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (((E and F) -> E) and D)))), M:tm-69, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8607
in-theory        8607
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-54 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8607.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (((F and G) -> F) and E)))), M:tm-54, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8608
in-theory        8608
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-42 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8608.         ((A -> (B or A)) and (C or (D -> (((E and F) -> E) and D)))), M:tm-42, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8609
in-theory        8609
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-32 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8609.         ((A -> (A or B)) and (C or (D -> (((E and F) -> E) and D)))), M:tm-32, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8610
in-theory        8610
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-23 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8610.         ((A -> (B -> (A and B))) and (C or (D -> (((E and F) -> E) and D)))), M:tm-23, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8611
in-theory        8611
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-22 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8611.         (((A and B) -> B) and (C or (D -> (((E and F) -> E) and D)))), M:tm-22, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8612
in-theory        8612
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-21 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8612.         (((A and B) -> A) and (C or (D -> (((E and F) -> E) and D)))), M:tm-21, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8613
in-theory        8613
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-20 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8613.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (((F and G) -> F) and E)))), M:tm-20, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8614
in-theory        8614
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-19 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8614.         ((A -> (B -> A)) and (C or (D -> (((E and F) -> E) and D)))), M:tm-19, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8615
in-theory        8615
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C -> (((D and E) -> D) and C))))
theorem-size     13
proof            (modus-ponens tm-7 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8615.         (A or (B or (C -> (((D and E) -> D) and C)))), M:tm-7, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8616
in-theory        8616
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-6 tm-7 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8616.         ((A or (B -> (((C and D) -> C) and B))) or E), M:tm-6, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8617
in-theory        8617
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (((D and E) -> D) and C))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8617.         (A -> ((B or (C -> (((D and E) -> D) and C))) and A)), M:tm-5, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8618
in-theory        8618
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C -> (((D and E) -> D) and C))))
theorem-size     13
proof            (modus-ponens tm-1 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-1 tm-7 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8618.         (A -> (B or (C -> (((D and E) -> D) and C)))), M:tm-1, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8619
in-theory        8619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (((F and G) -> F) and E)) or H))
theorem-size     29
proof            (modus-ponens tm-210 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8619.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (((F and G) -> F) and E)) or H)), M:tm-210, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8620
in-theory        8620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-183 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8620.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-183, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8621
in-theory        8621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-157 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8621.         ((A -> ((B and C) -> C)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-157, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8622
in-theory        8622
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-147 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8622.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-147, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8623
in-theory        8623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-134 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8623.         ((A -> ((B and C) -> B)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-134, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8624
in-theory        8624
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-125 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8624.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-125, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8625
in-theory        8625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (((F and G) -> F) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-113 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8625.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (((F and G) -> F) and E)) or H)), M:tm-113, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8626
in-theory        8626
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     31
proof            (modus-ponens tm-105 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8626.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-105, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8627
in-theory        8627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (((D and E) -> D) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-95 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8627.         (((A -> B) -> (A -> A)) and ((C -> (((D and E) -> D) and C)) or F)), M:tm-95, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8628
in-theory        8628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-83 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8628.         ((A -> (B -> (C -> B))) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-83, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8629
in-theory        8629
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (((C and D) -> C) and B)) or E))
theorem-size     17
proof            (modus-ponens tm-76 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8629.         (((not (not A)) -> A) and ((B -> (((C and D) -> C) and B)) or E)), M:tm-76, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8630
in-theory        8630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (((D and E) -> D) and C)) or F))
theorem-size     23
proof            (modus-ponens tm-69 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8630.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (((D and E) -> D) and C)) or F)), M:tm-69, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8631
in-theory        8631
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-54 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8631.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-54, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8632
in-theory        8632
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (((D and E) -> D) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-42 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8632.         ((A -> (B or A)) and ((C -> (((D and E) -> D) and C)) or F)), M:tm-42, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8633
in-theory        8633
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (((D and E) -> D) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-32 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8633.         ((A -> (A or B)) and ((C -> (((D and E) -> D) and C)) or F)), M:tm-32, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8634
in-theory        8634
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (((D and E) -> D) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-23 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8634.         ((A -> (B -> (A and B))) and ((C -> (((D and E) -> D) and C)) or F)), M:tm-23, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8635
in-theory        8635
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (((D and E) -> D) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-22 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8635.         (((A and B) -> B) and ((C -> (((D and E) -> D) and C)) or F)), M:tm-22, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8636
in-theory        8636
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (((D and E) -> D) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-21 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8636.         (((A and B) -> A) and ((C -> (((D and E) -> D) and C)) or F)), M:tm-21, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8637
in-theory        8637
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-20 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8637.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-20, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8638
in-theory        8638
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (((D and E) -> D) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-19 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8638.         ((A -> (B -> A)) and ((C -> (((D and E) -> D) and C)) or F)), M:tm-19, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8639
in-theory        8639
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> (((C and D) -> C) and B)) or E))
theorem-size     13
proof            (modus-ponens tm-7 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-7 tm-6 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8639.         (A or ((B -> (((C and D) -> C) and B)) or E)), M:tm-7, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8640
in-theory        8640
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8640.         (((A -> (((B and C) -> B) and A)) or D) or E), M:tm-6, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8641
in-theory        8641
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (((C and D) -> C) and B)) or E) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8641.         (A -> (((B -> (((C and D) -> C) and B)) or E) and A)), M:tm-5, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8642
in-theory        8642
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> (((C and D) -> C) and B)) or E))
theorem-size     13
proof            (modus-ponens tm-1 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-1 tm-6 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8642.         (A -> ((B -> (((C and D) -> C) and B)) or E)), M:tm-1, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8643
in-theory        8643
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-239 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8643.         ((A -> (((B and C) -> B) and A)) and (D -> (E -> D))), M:tm-239, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-8644
in-theory        8644
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8644.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-239, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-8645
in-theory        8645
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-239 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8645.         ((A -> (((B and C) -> B) and A)) and ((D and E) -> D)), M:tm-239, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-8646
in-theory        8646
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-239 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-8646.         ((A -> (((B and C) -> B) and A)) and ((D and E) -> E)), M:tm-239, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-8647
in-theory        8647
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-239 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8647.         ((A -> (((B and C) -> B) and A)) and (D -> (E -> (D and E)))), M:tm-239, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-8648
in-theory        8648
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-239 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8648.         ((A -> (((B and C) -> B) and A)) and (D -> (D or E))), M:tm-239, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-8649
in-theory        8649
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-239 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8649.         ((A -> (((B and C) -> B) and A)) and (D -> (E or D))), M:tm-239, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-8650
in-theory        8650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-8650.         ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-239, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-8651
in-theory        8651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-239 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8651.         ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-239, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-8652
in-theory        8652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-239 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-3 tm-10)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-8652.         ((A -> (((B and C) -> B) and A)) and ((not (not D)) -> D)), M:tm-239, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-8653
in-theory        8653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-239 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8653.         ((A -> (((B and C) -> B) and A)) and (D -> (E -> (F -> E)))), M:tm-239, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-8654
in-theory        8654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-239 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8654.         ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (D -> D))), M:tm-239, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-8655
in-theory        8655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-239 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-8655.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-239, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-8656
in-theory        8656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8656.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-239, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-8657
in-theory        8657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-239 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-8657.         ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-239, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-8658
in-theory        8658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-239 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8658.         ((A -> (((B and C) -> B) and A)) and (D -> ((E and F) -> E))), M:tm-239, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-8659
in-theory        8659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-239 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-8659.         ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-239, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-8660
in-theory        8660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-239 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8660.         ((A -> (((B and C) -> B) and A)) and (D -> ((E and F) -> F))), M:tm-239, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-8661
in-theory        8661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-239 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8661.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> E)) and D))), M:tm-239, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-8662
in-theory        8662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-239 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8662.         ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-239, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-8663
in-theory        8663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-239 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8663.         ((A -> (((B and C) -> B) and A)) and (D -> (((E and F) -> E) and D))), M:tm-239, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-8664
in-theory        8664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-239 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8664.         ((A -> (((B and C) -> B) and A)) and (D -> (((E and F) -> F) and D))), M:tm-239, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-8665
in-theory        8665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8665.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-239, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-8666
in-theory        8666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-239 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8666.         ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (D -> (D and E)))), M:tm-239, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-8667
in-theory        8667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8667.         ((A -> (((B and C) -> B) and A)) and (D -> (E -> (F -> (E and F))))), M:tm-239, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-8668
in-theory        8668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-239 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8668.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) or F)), M:tm-239, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-8669
in-theory        8669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-239 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8669.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-239, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-8670
in-theory        8670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-239 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8670.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) or F)), M:tm-239, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-8671
in-theory        8671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-239 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8671.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) or F)), M:tm-239, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-8672
in-theory        8672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-239 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8672.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) or F)), M:tm-239, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-8673
in-theory        8673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-239 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8673.         ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) or F)), M:tm-239, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-8674
in-theory        8674
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-239 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8674.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (E or F)) and D))), M:tm-239, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-8675
in-theory        8675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-239 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8675.         ((A -> (((B and C) -> B) and A)) and (D -> (E -> (E or F)))), M:tm-239, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-8676
in-theory        8676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-239 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8676.         ((A -> (((B and C) -> B) and A)) and (D or (E -> (F -> E)))), M:tm-239, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-8677
in-theory        8677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8677.         ((A -> (((B and C) -> B) and A)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-239, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-8678
in-theory        8678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-239 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8678.         ((A -> (((B and C) -> B) and A)) and (D or ((E and F) -> E))), M:tm-239, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-8679
in-theory        8679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-239 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8679.         ((A -> (((B and C) -> B) and A)) and (D or ((E and F) -> F))), M:tm-239, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-8680
in-theory        8680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8680.         ((A -> (((B and C) -> B) and A)) and (D or (E -> (F -> (E and F))))), M:tm-239, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-8681
in-theory        8681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-239 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8681.         ((A -> (((B and C) -> B) and A)) and (D or (E -> (E or F)))), M:tm-239, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-8682
in-theory        8682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-239 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8682.         ((A -> (((B and C) -> B) and A)) and (D or (E -> (F or E)))), M:tm-239, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-8683
in-theory        8683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-239 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8683.         ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) or F)), M:tm-239, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-8684
in-theory        8684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-239 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8684.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F or E)) and D))), M:tm-239, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-8685
in-theory        8685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-239 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8685.         ((A -> (((B and C) -> B) and A)) and (D -> (E -> (F or E)))), M:tm-239, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-8686
in-theory        8686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-239 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8686.         ((A -> (((B and C) -> B) and A)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-239, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-8687
in-theory        8687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-239 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8687.         ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-239, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-8688
in-theory        8688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-239 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-8688.         ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-239, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-8689
in-theory        8689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-239 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-8689.         ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-239, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-8690
in-theory        8690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-239 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8690.         ((A -> (((B and C) -> B) and A)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-239, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-8691
in-theory        8691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-239 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8691.         ((A -> (((B and C) -> B) and A)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-239, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-8692
in-theory        8692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-239 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8692.         ((A -> (((B and C) -> B) and A)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-239, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-8693
in-theory        8693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-239 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-8693.         ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-239, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-8694
in-theory        8694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8694.         ((A -> (((B and C) -> B) and A)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-239, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-8695
in-theory        8695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-239 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8695.         ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-239, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-8696
in-theory        8696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-239 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8696.         ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-239, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-8697
in-theory        8697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-239 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-8697.         ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-239, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-8698
in-theory        8698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8698.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-239, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-8699
in-theory        8699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-239 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8699.         ((A -> (((B and C) -> B) and A)) and ((D -> (not (E -> D))) -> (not D))), M:tm-239, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-8700
in-theory        8700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-9 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8700.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-239, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-8701
in-theory        8701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-239 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-8701.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-239, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-8702
in-theory        8702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-239 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-8702.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-239, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-8703
in-theory        8703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8703.         ((A -> (((B and C) -> B) and A)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-239, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-8704
in-theory        8704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-239 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8704.         ((A -> (((B and C) -> B) and A)) and ((D -> (not (D or E))) -> (not D))), M:tm-239, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-8705
in-theory        8705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-239 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8705.         ((A -> (((B and C) -> B) and A)) and ((D -> (not (E or D))) -> (not D))), M:tm-239, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-8706
in-theory        8706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-239 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-8706.         ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-239, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-8707
in-theory        8707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-239 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8707.         ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-239, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-8708
in-theory        8708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-239 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-9)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8708.         ((A -> (((B and C) -> B) and A)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-239, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-8709
in-theory        8709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8709.         ((A -> (((B and C) -> B) and A)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-239, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-8710
in-theory        8710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     23
proof            (modus-ponens tm-239 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-3 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8710.         ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-239, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-8711
in-theory        8711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     25
proof            (modus-ponens tm-239 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8711.         ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-239, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-8712
in-theory        8712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-239 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-8712.         ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-239, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-8713
in-theory        8713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8713.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-239, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-8714
in-theory        8714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     21
proof            (modus-ponens tm-239 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-3 tm-9 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-8714.         ((A -> (((B and C) -> B) and A)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-239, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-8715
in-theory        8715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-239 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-8715.         ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-239, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-8716
in-theory        8716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-239 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8716.         ((A -> (((B and C) -> B) and A)) and (D or ((not (not E)) -> E))), M:tm-239, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-8717
in-theory        8717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((not (not D)) -> D) or E))
theorem-size     17
proof            (modus-ponens tm-239 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-3 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8717.         ((A -> (((B and C) -> B) and A)) and (((not (not D)) -> D) or E)), M:tm-239, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-8718
in-theory        8718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-239 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-3 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8718.         ((A -> (((B and C) -> B) and A)) and (D -> (((not (not E)) -> E) and D))), M:tm-239, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-8719
in-theory        8719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     25
proof            (modus-ponens tm-239 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-8719.         ((A -> (((B and C) -> B) and A)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-239, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-8720
in-theory        8720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-239 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8720.         ((A -> (((B and C) -> B) and A)) and (D -> ((not (not E)) -> E))), M:tm-239, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-8721
in-theory        8721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8721.         ((A -> (((B and C) -> B) and A)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-239, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-8722
in-theory        8722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-239 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8722.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-239, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-8723
in-theory        8723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8723.         ((A -> (((B and C) -> B) and A)) and (D or (E -> (F -> (G -> F))))), M:tm-239, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-8724
in-theory        8724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8724.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (F -> E))) or G)), M:tm-239, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-8725
in-theory        8725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8725.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-239, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-8726
in-theory        8726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-239 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8726.         ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (D -> (F -> E)))), M:tm-239, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-8727
in-theory        8727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8727.         ((A -> (((B and C) -> B) and A)) and (D -> (E -> (F -> (G -> F))))), M:tm-239, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-8728
in-theory        8728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> D))
theorem-size     13
proof            (modus-ponens tm-239 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8728.         ((A -> (((B and C) -> B) and A)) and (D -> D)), M:tm-239, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-8729
in-theory        8729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8729.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-239, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-8730
in-theory        8730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D and E) -> (D and E)))
theorem-size     17
proof            (modus-ponens tm-239 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-8730.         ((A -> (((B and C) -> B) and A)) and ((D and E) -> (D and E))), M:tm-239, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-8731
in-theory        8731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-239 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-8731.         ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (D -> E))), M:tm-239, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-8732
in-theory        8732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((not (not D)) -> (not (not D))))
theorem-size     17
proof            (modus-ponens tm-239 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-8732.         ((A -> (((B and C) -> B) and A)) and ((not (not D)) -> (not (not D)))), M:tm-239, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-8733
in-theory        8733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-239 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8733.         ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-239, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-8734
in-theory        8734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-239 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8734.         ((A -> (((B and C) -> B) and A)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-239, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-8735
in-theory        8735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-239 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8735.         ((A -> (((B and C) -> B) and A)) and (D or ((E -> F) -> (E -> E)))), M:tm-239, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-8736
in-theory        8736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (D -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-239 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-3 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8736.         ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (D -> D)) or F)), M:tm-239, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-8737
in-theory        8737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8737.         ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-239, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-8738
in-theory        8738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-8738.         ((A -> (((B and C) -> B) and A)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-239, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-8739
in-theory        8739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-239 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8739.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> F) -> (E -> E)))), M:tm-239, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-8740
in-theory        8740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8740.         ((A -> (((B and C) -> B) and A)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-239, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-8741
in-theory        8741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-239 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8741.         ((A -> (((B and C) -> B) and A)) and ((D -> (D -> E)) -> (D -> E))), M:tm-239, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-8742
in-theory        8742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-239 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-8742.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-239, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-8743
in-theory        8743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     41
proof            (modus-ponens tm-239 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-9 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-8743.         ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-239, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-8744
in-theory        8744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-239 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-8744.         ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-239, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-8745
in-theory        8745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8745.         ((A -> (((B and C) -> B) and A)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-239, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-8746
in-theory        8746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-239 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8746.         ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-239, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-8747
in-theory        8747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-239 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8747.         ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-239, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-8748
in-theory        8748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-239 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-8748.         ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-239, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-8749
in-theory        8749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8749.         ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-239, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-8750
in-theory        8750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-239 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-8750.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-239, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-8751
in-theory        8751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-239 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8751.         ((A -> (((B and C) -> B) and A)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-239, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-8752
in-theory        8752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     43
proof            (modus-ponens tm-239 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8752.         ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-239, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-8753
in-theory        8753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-239 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8753.         ((A -> (((B and C) -> B) and A)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-239, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-8754
in-theory        8754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-239 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-3 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8754.         ((A -> (((B and C) -> B) and A)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-239, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-8755
in-theory        8755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-239 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8755.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-239, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-8756
in-theory        8756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-239 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8756.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-239, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-8757
in-theory        8757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-239 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8757.         ((A -> (((B and C) -> B) and A)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-239, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-8758
in-theory        8758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) and D) -> E))
theorem-size     17
proof            (modus-ponens tm-239 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-8758.         ((A -> (((B and C) -> B) and A)) and (((D -> E) and D) -> E)), M:tm-239, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-8759
in-theory        8759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-239 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-8759.         ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-239, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-8760
in-theory        8760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-239 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8760.         ((A -> (((B and C) -> B) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-239, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-8761
in-theory        8761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-239 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-8761.         ((A -> (((B and C) -> B) and A)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-239, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-8762
in-theory        8762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     25
proof            (modus-ponens tm-239 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-8762.         ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-239, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-8763
in-theory        8763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     35
proof            (modus-ponens tm-239 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-3 tm-9 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-8763.         ((A -> (((B and C) -> B) and A)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-239, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-8764
in-theory        8764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     37
proof            (modus-ponens tm-239 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-8764.         ((A -> (((B and C) -> B) and A)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-239, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-8765
in-theory        8765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-239 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8765.         ((A -> (((B and C) -> B) and A)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-239, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-8766
in-theory        8766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-239 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8766.         ((A -> (((B and C) -> B) and A)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-239, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-8767
in-theory        8767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-239 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8767.         ((A -> (((B and C) -> B) and A)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-239, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-8768
in-theory        8768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     33
proof            (modus-ponens tm-239 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-8768.         ((A -> (((B and C) -> B) and A)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-239, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-8769
in-theory        8769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-239 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8769.         ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-239, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-8770
in-theory        8770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-239 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-8770.         ((A -> (((B and C) -> B) and A)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-239, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-8771
in-theory        8771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-239 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-8771.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-239, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-8772
in-theory        8772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8772.         ((A -> (((B and C) -> B) and A)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-239, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-8773
in-theory        8773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     27
proof            (modus-ponens tm-239 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8773.         ((A -> (((B and C) -> B) and A)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-239, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-8774
in-theory        8774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-239 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8774.         ((A -> (((B and C) -> B) and A)) and (D or (E -> ((F and G) -> F)))), M:tm-239, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-8775
in-theory        8775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8775.         ((A -> (((B and C) -> B) and A)) and ((D -> ((E and F) -> E)) or G)), M:tm-239, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-8776
in-theory        8776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8776.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-239, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-8777
in-theory        8777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-239 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-8777.         ((A -> (((B and C) -> B) and A)) and ((D -> (E and F)) -> (D -> E))), M:tm-239, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-8778
in-theory        8778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-239 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8778.         ((A -> (((B and C) -> B) and A)) and (D -> (E -> ((F and G) -> F)))), M:tm-239, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-8779
in-theory        8779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D and (D -> E)) -> E))
theorem-size     17
proof            (modus-ponens tm-239 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-8779.         ((A -> (((B and C) -> B) and A)) and ((D and (D -> E)) -> E)), M:tm-239, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-8780
in-theory        8780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-239 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-8780.         ((A -> (((B and C) -> B) and A)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-239, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-8781
in-theory        8781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-239 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8781.         ((A -> (((B and C) -> B) and A)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-239, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-8782
in-theory        8782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-239 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-8782.         ((A -> (((B and C) -> B) and A)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-239, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-8783
in-theory        8783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-239 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-8783.         ((A -> (((B and C) -> B) and A)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-239, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-8784
in-theory        8784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     25
proof            (modus-ponens tm-239 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-8784.         ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-239, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-8785
in-theory        8785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     35
proof            (modus-ponens tm-239 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-2 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-8785.         ((A -> (((B and C) -> B) and A)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-239, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-8786
in-theory        8786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-239 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-8786.         ((A -> (((B and C) -> B) and A)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-239, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-8787
in-theory        8787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-239 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8787.         ((A -> (((B and C) -> B) and A)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-239, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-8788
in-theory        8788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-239 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8788.         ((A -> (((B and C) -> B) and A)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-239, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-8789
in-theory        8789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-239 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8789.         ((A -> (((B and C) -> B) and A)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-239, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-8790
in-theory        8790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     33
proof            (modus-ponens tm-239 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-8790.         ((A -> (((B and C) -> B) and A)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-239, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-8791
in-theory        8791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-239 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8791.         ((A -> (((B and C) -> B) and A)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-239, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-8792
in-theory        8792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-239 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-8792.         ((A -> (((B and C) -> B) and A)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-239, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-8793
in-theory        8793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-239 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-8793.         ((A -> (((B and C) -> B) and A)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-239, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-8794
in-theory        8794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-239 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-8794.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-239, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-8795
in-theory        8795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8795.         ((A -> (((B and C) -> B) and A)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-239, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-8796
in-theory        8796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-239 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8796.         ((A -> (((B and C) -> B) and A)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-239, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-8797
in-theory        8797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-239 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8797.         ((A -> (((B and C) -> B) and A)) and (D or (E -> ((F and G) -> G)))), M:tm-239, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-8798
in-theory        8798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8798.         ((A -> (((B and C) -> B) and A)) and ((D -> ((E and F) -> F)) or G)), M:tm-239, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-8799
in-theory        8799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8799.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-239, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-8800
in-theory        8800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-239 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-8800.         ((A -> (((B and C) -> B) and A)) and ((D -> (E and F)) -> (D -> F))), M:tm-239, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-8801
in-theory        8801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-239 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8801.         ((A -> (((B and C) -> B) and A)) and (D -> (E -> ((F and G) -> G)))), M:tm-239, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-8802
in-theory        8802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8802.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-239, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-8803
in-theory        8803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8803.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-239, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-8804
in-theory        8804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8804.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-239, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-8805
in-theory        8805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-239 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8805.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-239, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-8806
in-theory        8806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8806.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-239, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8807
in-theory        8807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-239 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8807.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-239, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8808
in-theory        8808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8808.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-239, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8809
in-theory        8809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8809.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-239, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8810
in-theory        8810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-239 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8810.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-239, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8811
in-theory        8811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8811.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-239, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8812
in-theory        8812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8812.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-239, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8813
in-theory        8813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8813.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-239, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8814
in-theory        8814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-239 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8814.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-239, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8815
in-theory        8815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8815.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-239, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8816
in-theory        8816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-239 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8816.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-239, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8817
in-theory        8817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-239 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8817.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-239, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8818
in-theory        8818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-239 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8818.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-239, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8819
in-theory        8819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-239 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8819.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-239, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8820
in-theory        8820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8820.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-239, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8821
in-theory        8821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8821.         ((A -> (((B and C) -> B) and A)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-239, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-8822
in-theory        8822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-239 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8822.         ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-239, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-8823
in-theory        8823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-239 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8823.         ((A -> (((B and C) -> B) and A)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-239, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-8824
in-theory        8824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-239 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8824.         ((A -> (((B and C) -> B) and A)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-239, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-8825
in-theory        8825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8825.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-239, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-8826
in-theory        8826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-239 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8826.         ((A -> (((B and C) -> B) and A)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-239, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-8827
in-theory        8827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-239 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8827.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-239, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-8828
in-theory        8828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8828.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-239, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-8829
in-theory        8829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-239 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8829.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-239, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-8830
in-theory        8830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-239 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8830.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-239, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-8831
in-theory        8831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8831.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-239, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-8832
in-theory        8832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8832.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-239, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-8833
in-theory        8833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-239 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8833.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-239, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-8834
in-theory        8834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8834.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-239, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-8835
in-theory        8835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-239 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8835.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-239, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-8836
in-theory        8836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-239 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8836.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-239, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-8837
in-theory        8837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8837.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-239, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-8838
in-theory        8838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-239 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8838.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-239, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-8839
in-theory        8839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-239 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8839.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-239, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-8840
in-theory        8840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-239 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8840.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-239, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-8841
in-theory        8841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-239 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8841.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-239, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-8842
in-theory        8842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-239 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8842.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-239, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-8843
in-theory        8843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-239 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8843.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-239, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-8844
in-theory        8844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-239 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8844.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-239, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-8845
in-theory        8845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-239 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8845.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-239, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-8846
in-theory        8846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-239 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8846.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-239, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-8847
in-theory        8847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-239 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8847.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-239, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8848
in-theory        8848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-239 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8848.         ((A -> (((B and C) -> B) and A)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-239, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-8849
in-theory        8849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-239 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8849.         ((A -> (((B and C) -> B) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-239, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-8850
in-theory        8850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-239 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8850.         ((A -> (((B and C) -> B) and A)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-239, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-8851
in-theory        8851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     29
proof            (modus-ponens tm-239 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8851.         ((A -> (((B and C) -> B) and A)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-239, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-8852
in-theory        8852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-239 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8852.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-239, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-8853
in-theory        8853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-239 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8853.         ((A -> (((B and C) -> B) and A)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-239, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-8854
in-theory        8854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8854.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-239, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-8855
in-theory        8855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8855.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-239, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-8856
in-theory        8856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8856.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-239, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-8857
in-theory        8857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-239 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8857.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-239, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-8858
in-theory        8858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8858.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-239, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-8859
in-theory        8859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-239 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8859.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-239, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-8860
in-theory        8860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8860.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-239, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-8861
in-theory        8861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-8861.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-239, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-8862
in-theory        8862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-239 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8862.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-239, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-8863
in-theory        8863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8863.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-239, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-8864
in-theory        8864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8864.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-239, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-8865
in-theory        8865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8865.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-239, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-8866
in-theory        8866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-239 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8866.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-239, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-8867
in-theory        8867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8867.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-239, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-8868
in-theory        8868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-239 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8868.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-239, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-8869
in-theory        8869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-239 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8869.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-239, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-8870
in-theory        8870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-239 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8870.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-239, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-8871
in-theory        8871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-239 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8871.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-239, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-8872
in-theory        8872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8872.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-239, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-8873
in-theory        8873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-239 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8873.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-239, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-8874
in-theory        8874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8874.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-239, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8875
in-theory        8875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-239 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8875.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-239, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-8876
in-theory        8876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8876.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-239, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-8877
in-theory        8877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8877.         ((A -> (((B and C) -> B) and A)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-239, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-8878
in-theory        8878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-239 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8878.         ((A -> (((B and C) -> B) and A)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-239, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-8879
in-theory        8879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-239 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8879.         ((A -> (((B and C) -> B) and A)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-239, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8880
in-theory        8880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-239 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8880.         ((A -> (((B and C) -> B) and A)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-239, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-8881
in-theory        8881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8881.         ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-239, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8882
in-theory        8882
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (((E and F) -> E) and D)) and (((B and C) -> B) and A)))
theorem-size     27
proof            (modus-ponens tm-236 tm-239 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8882.         ((A or (((B and C) -> B) and A)) -> ((D -> (((E and F) -> E) and D)) and (((B and C) -> B) and A))), M:tm-236, m:tm-239, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-8883
in-theory        8883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (((G and H) -> G) and F)) and E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8883.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (((G and H) -> G) and F)) and E))), M:tm-210, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8884
in-theory        8884
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (((F and G) -> F) and E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     43
proof            (modus-ponens tm-207 tm-239 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8884.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (((F and G) -> F) and E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-239, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-8885
in-theory        8885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8885.         ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-183, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8886
in-theory        8886
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (((E and F) -> E) and D)) and ((B -> (C -> B)) and A)))
theorem-size     27
proof            (modus-ponens tm-180 tm-239 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8886.         ((A or ((B -> (C -> B)) and A)) -> ((D -> (((E and F) -> E) and D)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-239, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-8887
in-theory        8887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8887.         ((A -> ((B and C) -> C)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-157, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8888
in-theory        8888
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (((E and F) -> E) and D)) and ((B and C) -> C)))
theorem-size     23
proof            (modus-ponens tm-154 tm-239 ((Am (-> (and A B) B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8888.         ((A or ((B and C) -> C)) -> ((D -> (((E and F) -> E) and D)) and ((B and C) -> C))), M:tm-154, m:tm-239, u:((Am (-> (and A B) B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (and A B) B))))
================================================================
tm-name          tm-8889
in-theory        8889
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8889.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-147, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8890
in-theory        8890
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (((E and F) -> E) and D)) and ((A and (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-144 tm-239 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8890.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (((E and F) -> E) and D)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-239, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-8891
in-theory        8891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8891.         ((A -> ((B and C) -> B)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-134, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8892
in-theory        8892
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (((E and F) -> E) and D)) and ((B and C) -> B)))
theorem-size     23
proof            (modus-ponens tm-131 tm-239 ((Am (-> (and A B) A)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8892.         ((A or ((B and C) -> B)) -> ((D -> (((E and F) -> E) and D)) and ((B and C) -> B))), M:tm-131, m:tm-239, u:((Am (-> (and A B) A)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (and A B) A))))
================================================================
tm-name          tm-8893
in-theory        8893
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8893.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-125, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8894
in-theory        8894
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (((E and F) -> E) and D)) and (((A -> B) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-122 tm-239 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8894.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (((E and F) -> E) and D)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-239, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-8895
in-theory        8895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (((G and H) -> G) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8895.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (((G and H) -> G) and F)) and E))), M:tm-113, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8896
in-theory        8896
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (((F and G) -> F) and E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     39
proof            (modus-ponens tm-110 tm-239 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8896.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (((F and G) -> F) and E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-239, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-8897
in-theory        8897
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8897.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-105, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8898
in-theory        8898
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (((E and F) -> E) and D)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-102 tm-239 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8898.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (((E and F) -> E) and D)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-239, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-8899
in-theory        8899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (((E and F) -> E) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8899.         (((A -> B) -> (A -> A)) and (C -> ((D -> (((E and F) -> E) and D)) and C))), M:tm-95, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8900
in-theory        8900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (((D and E) -> D) and C)) and (A -> A)))
theorem-size     21
proof            (modus-ponens tm-92 tm-239 ((Am (-> A A)) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8900.         (((A -> B) or (A -> A)) -> ((C -> (((D and E) -> D) and C)) and (A -> A))), M:tm-92, m:tm-239, u:((Am (-> A A)) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A A))))
================================================================
tm-name          tm-8901
in-theory        8901
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (((D and E) -> D) and C)) and A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8901.         (A -> (B -> ((C -> (((D and E) -> D) and C)) and A))), M:tm-84, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-8902
in-theory        8902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8902.         ((A -> (B -> (C -> B))) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-83, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8903
in-theory        8903
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (((E and F) -> E) and D)) and (B -> (C -> B))))
theorem-size     23
proof            (modus-ponens tm-80 tm-239 ((Am (-> A (-> B A))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8903.         ((A or (B -> (C -> B))) -> ((D -> (((E and F) -> E) and D)) and (B -> (C -> B)))), M:tm-80, m:tm-239, u:((Am (-> A (-> B A))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A (-> B A)))))
================================================================
tm-name          tm-8904
in-theory        8904
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (((D and E) -> D) and C)) and B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-10 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8904.         (((not (not A)) -> A) and (B -> ((C -> (((D and E) -> D) and C)) and B))), M:tm-76, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8905
in-theory        8905
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (((C and D) -> C) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-73 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8905.         (((not (not A)) or A) -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-73, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-8906
in-theory        8906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (((E and F) -> E) and D)) and C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8906.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (((E and F) -> E) and D)) and C))), M:tm-69, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8907
in-theory        8907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (((D and E) -> D) and C)) and ((A -> (not B)) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-66 tm-239 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8907.         (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (((D and E) -> D) and C)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-239, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-8908
in-theory        8908
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8908.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-54, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8909
in-theory        8909
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (((E and F) -> E) and D)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-51 tm-239 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8909.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (((E and F) -> E) and D)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-239, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-8910
in-theory        8910
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (((D and E) -> D) and C)) and (B or A)))
theorem-size     19
proof            (modus-ponens tm-50 tm-239 ((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8910.         ((A or (B or A)) -> ((C -> (((D and E) -> D) and C)) and (B or A))), M:tm-50, m:tm-239, u:((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (or A B))))
================================================================
tm-name          tm-8911
in-theory        8911
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (((D and E) -> D) and C)) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-49 tm-239 ((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8911.         ((A or (A or B)) -> ((C -> (((D and E) -> D) and C)) and (A or B))), M:tm-49, m:tm-239, u:((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (or A B))))
================================================================
tm-name          tm-8912
in-theory        8912
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (((D and E) -> D) and C)) and (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-48 tm-239 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8912.         ((A or (B -> (A and B))) -> ((C -> (((D and E) -> D) and C)) and (B -> (A and B)))), M:tm-48, m:tm-239, u:((Am (-> A (and B A))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-8913
in-theory        8913
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (((D and E) -> D) and C)) and B))
theorem-size     17
proof            (modus-ponens tm-47 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8913.         (((A and B) or B) -> ((C -> (((D and E) -> D) and C)) and B)), M:tm-47, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-8914
in-theory        8914
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (((D and E) -> D) and C)) and A))
theorem-size     17
proof            (modus-ponens tm-46 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8914.         (((A and B) or A) -> ((C -> (((D and E) -> D) and C)) and A)), M:tm-46, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-8915
in-theory        8915
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((E and F) -> E) and D)) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-45 tm-239 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8915.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((E and F) -> E) and D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-239, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-8916
in-theory        8916
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (((D and E) -> D) and C)) and (B -> A)))
theorem-size     19
proof            (modus-ponens tm-44 tm-239 ((Am (-> A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8916.         ((A or (B -> A)) -> ((C -> (((D and E) -> D) and C)) and (B -> A))), M:tm-44, m:tm-239, u:((Am (-> A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A B))))
================================================================
tm-name          tm-8917
in-theory        8917
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (((E and F) -> E) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8917.         ((A -> (B or A)) and (C -> ((D -> (((E and F) -> E) and D)) and C))), M:tm-42, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8918
in-theory        8918
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (((E and F) -> E) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8918.         ((A -> (A or B)) and (C -> ((D -> (((E and F) -> E) and D)) and C))), M:tm-32, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8919
in-theory        8919
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (((C and D) -> C) and B)) and A)))
theorem-size     15
proof            (modus-ponens tm-24 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8919.         (A -> (A and ((B -> (((C and D) -> C) and B)) and A))), M:tm-24, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-8920
in-theory        8920
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (((E and F) -> E) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8920.         ((A -> (B -> (A and B))) and (C -> ((D -> (((E and F) -> E) and D)) and C))), M:tm-23, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8921
in-theory        8921
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (((E and F) -> E) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8921.         (((A and B) -> B) and (C -> ((D -> (((E and F) -> E) and D)) and C))), M:tm-22, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8922
in-theory        8922
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (((E and F) -> E) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8922.         (((A and B) -> A) and (C -> ((D -> (((E and F) -> E) and D)) and C))), M:tm-21, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8923
in-theory        8923
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8923.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-20, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8924
in-theory        8924
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (((E and F) -> E) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8924.         ((A -> (B -> A)) and (C -> ((D -> (((E and F) -> E) and D)) and C))), M:tm-19, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8925
in-theory        8925
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (((C and D) -> C) and B)) and A))) -> (not A))
theorem-size     17
proof            (modus-ponens tm-9 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-9 tm-5 tm-3)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8925.         ((A -> (not ((B -> (((C and D) -> C) and B)) and A))) -> (not A)), M:tm-9, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-8926
in-theory        8926
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (((B and C) -> B) and A)) and D) -> E) -> ((D or ((A -> (((B and C) -> B) and A)) and D)) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8926.         ((((A -> (((B and C) -> B) and A)) and D) -> E) -> ((D or ((A -> (((B and C) -> B) and A)) and D)) -> E)), M:tm-8, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-8927
in-theory        8927
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (((D and E) -> D) and C)) and B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8927.         (A or (B -> ((C -> (((D and E) -> D) and C)) and B))), M:tm-7, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8928
in-theory        8928
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8928.         ((A -> ((B -> (((C and D) -> C) and B)) and A)) or E), M:tm-6, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8929
in-theory        8929
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (((D and E) -> D) and C)) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8929.         (A -> ((B -> ((C -> (((D and E) -> D) and C)) and B)) and A)), M:tm-5, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8930
in-theory        8930
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (((D and E) -> D) and C)) and B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8930.         (A -> (B -> ((C -> (((D and E) -> D) and C)) and B))), M:tm-1, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-8931
in-theory        8931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-239 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8931.         ((A -> (((B and C) -> B) and A)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-239, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8932
in-theory        8932
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-236 tm-240 ((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8932.         ((A or (((B and C) -> B) and A)) -> (D -> (((E and F) -> E) and D))), M:tm-236, m:tm-240, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8933
in-theory        8933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-210 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8933.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (((G and H) -> G) and F)))), M:tm-210, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8934
in-theory        8934
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (((F and G) -> F) and E)))
theorem-size     27
proof            (modus-ponens tm-207 tm-240 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8934.         ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (((F and G) -> F) and E))), M:tm-207, m:tm-240, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8935
in-theory        8935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-183 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8935.         ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-183, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8936
in-theory        8936
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-180 tm-240 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8936.         ((A or ((B -> (C -> B)) and A)) -> (D -> (((E and F) -> E) and D))), M:tm-180, m:tm-240, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8937
in-theory        8937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-157 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8937.         ((A -> ((B and C) -> C)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-157, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8938
in-theory        8938
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-154 tm-240 ((Am (-> (and A B) B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8938.         ((A or ((B and C) -> C)) -> (D -> (((E and F) -> E) and D))), M:tm-154, m:tm-240, u:((Am (-> (and A B) B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8939
in-theory        8939
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (((C and D) -> C) and B))
theorem-size     11
proof            (modus-ponens tm-152 tm-240 ((Am (and A Bm)) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-4 tm-5 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8939.         ((A and B) -> (((C and D) -> C) and B)), M:tm-152, m:tm-240, u:((Am (and A Bm)) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-8940
in-theory        8940
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-147 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8940.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-147, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8941
in-theory        8941
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (((E and F) -> E) and D)))
theorem-size     25
proof            (modus-ponens tm-144 tm-240 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-5 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8941.         ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (((E and F) -> E) and D))), M:tm-144, m:tm-240, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8942
in-theory        8942
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (((C and D) -> C) and B)) -> E)) -> (B -> (((C and D) -> C) and B)))
theorem-size     23
proof            (modus-ponens tm-142 tm-240 ((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) C))) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-5 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8942.         ((A and ((B -> (((C and D) -> C) and B)) -> E)) -> (B -> (((C and D) -> C) and B))), M:tm-142, m:tm-240, u:((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) C))) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8943
in-theory        8943
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (((C and D) -> C) and B)) -> B)) -> (((C and D) -> C) and B))
theorem-size     21
proof            (modus-ponens tm-141 tm-240 ((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Bm))) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-4 tm-1 tm-5 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8943.         ((A and ((B -> (((C and D) -> C) and B)) -> B)) -> (((C and D) -> C) and B)), M:tm-141, m:tm-240, u:((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Bm))) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-8944
in-theory        8944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-134 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8944.         ((A -> ((B and C) -> B)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-134, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8945
in-theory        8945
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-131 tm-240 ((Am (-> (and A B) A)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8945.         ((A or ((B and C) -> B)) -> (D -> (((E and F) -> E) and D))), M:tm-131, m:tm-240, u:((Am (-> (and A B) A)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8946
in-theory        8946
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (((C and D) -> C) and A))
theorem-size     11
proof            (modus-ponens tm-129 tm-240 ((Am (and Bm B)) (A Bm) (C (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8946.         ((A and B) -> (((C and D) -> C) and A)), M:tm-129, m:tm-240, u:((Am (and Bm B)) (A Bm) (C (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-8947
in-theory        8947
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-125 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8947.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-125, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8948
in-theory        8948
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (((E and F) -> E) and D)))
theorem-size     25
proof            (modus-ponens tm-122 tm-240 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8948.         (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (((E and F) -> E) and D))), M:tm-122, m:tm-240, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8949
in-theory        8949
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (((B and C) -> B) and A)) -> D) and E) -> (A -> (((B and C) -> B) and A)))
theorem-size     23
proof            (modus-ponens tm-120 tm-240 ((Am (and (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) B) C)) (A (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8949.         ((((A -> (((B and C) -> B) and A)) -> D) and E) -> (A -> (((B and C) -> B) and A))), M:tm-120, m:tm-240, u:((Am (and (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) B) C)) (A (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8950
in-theory        8950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (((B and C) -> B) and A)) -> A) and D) -> (((B and C) -> B) and A))
theorem-size     21
proof            (modus-ponens tm-119 tm-240 ((Am (and (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Bm) C)) (A Bm) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8950.         ((((A -> (((B and C) -> B) and A)) -> A) and D) -> (((B and C) -> B) and A)), M:tm-119, m:tm-240, u:((Am (and (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Bm) C)) (A Bm) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-8951
in-theory        8951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-113 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8951.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (((G and H) -> G) and F)))), M:tm-113, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8952
in-theory        8952
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (((F and G) -> F) and E)))
theorem-size     25
proof            (modus-ponens tm-110 tm-240 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8952.         ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (((F and G) -> F) and E))), M:tm-110, m:tm-240, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8953
in-theory        8953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))
theorem-size     19
proof            (modus-ponens tm-108 tm-240 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (and Cm Dm) Cm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8953.         ((A -> (B -> C)) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-108, m:tm-240, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (and Cm Dm) Cm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-8954
in-theory        8954
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     31
proof            (modus-ponens tm-105 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8954.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-105, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8955
in-theory        8955
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (((E and F) -> E) and D)))
theorem-size     29
proof            (modus-ponens tm-102 tm-240 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-3)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8955.         ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (((E and F) -> E) and D))), M:tm-102, m:tm-240, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8956
in-theory        8956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) and A) -> D)) -> (A -> (((B and C) -> B) and A)))
theorem-size     21
proof            (modus-ponens tm-100 tm-240 ((Am (-> Bm (-> (and (-> (and Cm Dm) Cm) Bm) C))) (A Bm) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8956.         ((A -> ((((B and C) -> B) and A) -> D)) -> (A -> (((B and C) -> B) and A))), M:tm-100, m:tm-240, u:((Am (-> Bm (-> (and (-> (and Cm Dm) Cm) Bm) C))) (A Bm) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-8957
in-theory        8957
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> A)))
theorem-size     11
proof            (modus-ponens tm-98 tm-240 ((A Am) (Bm (-> B Am)) (C (and (-> (and Cm Dm) Cm) (-> B Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8957.         (A -> (((B and C) -> B) and (D -> A))), M:tm-98, m:tm-240, u:((A Am) (Bm (-> B Am)) (C (and (-> (and Cm Dm) Cm) (-> B Am))))
================================================================
tm-name          tm-8958
in-theory        8958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) -> D) -> (A -> (((B and C) -> B) and A)))
theorem-size     21
proof            (modus-ponens tm-96 tm-240 ((Am (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) B)) (A (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8958.         (((A -> (((B and C) -> B) and A)) -> D) -> (A -> (((B and C) -> B) and A))), M:tm-96, m:tm-240, u:((Am (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) B)) (A (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8959
in-theory        8959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-95 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8959.         (((A -> B) -> (A -> A)) and (C -> (D -> (((E and F) -> E) and D)))), M:tm-95, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8960
in-theory        8960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> (((D and E) -> D) and C)))
theorem-size     17
proof            (modus-ponens tm-92 tm-240 ((Am (-> A A)) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8960.         (((A -> B) or (A -> A)) -> (C -> (((D and E) -> D) and C))), M:tm-92, m:tm-240, u:((Am (-> A A)) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8961
in-theory        8961
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C -> (((D and E) -> D) and C))))
theorem-size     13
proof            (modus-ponens tm-84 tm-240 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8961.         (A -> (B -> (C -> (((D and E) -> D) and C)))), M:tm-84, m:tm-240, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8962
in-theory        8962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-83 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8962.         ((A -> (B -> (C -> B))) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-83, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8963
in-theory        8963
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-80 tm-240 ((Am (-> A (-> B A))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8963.         ((A or (B -> (C -> B))) -> (D -> (((E and F) -> E) and D))), M:tm-80, m:tm-240, u:((Am (-> A (-> B A))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8964
in-theory        8964
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> (((B and C) -> B) and A)) -> D))) -> D)
theorem-size     15
proof            (modus-ponens tm-77 tm-240 ((Am (not (not (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) B)))) (A (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-5 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8964.         ((not (not ((A -> (((B and C) -> B) and A)) -> D))) -> D), M:tm-77, m:tm-240, u:((Am (not (not (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) B)))) (A (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8965
in-theory        8965
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> (((D and E) -> D) and C))))
theorem-size     17
proof            (modus-ponens tm-76 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8965.         (((not (not A)) -> A) and (B -> (C -> (((D and E) -> D) and C)))), M:tm-76, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8966
in-theory        8966
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> (((C and D) -> C) and B)))
theorem-size     15
proof            (modus-ponens tm-73 tm-240 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8966.         (((not (not A)) or A) -> (B -> (((C and D) -> C) and B))), M:tm-73, m:tm-240, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8967
in-theory        8967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (((E and F) -> E) and D))))
theorem-size     23
proof            (modus-ponens tm-69 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8967.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (((E and F) -> E) and D)))), M:tm-69, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8968
in-theory        8968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (((D and E) -> D) and C)))
theorem-size     21
proof            (modus-ponens tm-66 tm-240 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-5 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8968.         (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (((D and E) -> D) and C))), M:tm-66, m:tm-240, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8969
in-theory        8969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> (((C and D) -> C) and B)))
theorem-size     15
proof            (modus-ponens tm-55 tm-240 ((Am (-> A Bm)) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-8 tm-1 tm-5 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8969.         ((A -> B) -> ((A or B) -> (((C and D) -> C) and B))), M:tm-55, m:tm-240, u:((Am (-> A Bm)) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-8970
in-theory        8970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-54 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8970.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-54, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8971
in-theory        8971
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E and F) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-51 tm-240 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8971.         (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E and F) -> E) and D))), M:tm-51, m:tm-240, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8972
in-theory        8972
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (((D and E) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-50 tm-240 ((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8972.         ((A or (B or A)) -> (C -> (((D and E) -> D) and C))), M:tm-50, m:tm-240, u:((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8973
in-theory        8973
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (((D and E) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-240 ((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8973.         ((A or (A or B)) -> (C -> (((D and E) -> D) and C))), M:tm-49, m:tm-240, u:((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8974
in-theory        8974
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((D and E) -> D) and C)))
theorem-size     17
proof            (modus-ponens tm-48 tm-240 ((Am (-> A (and B A))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8974.         ((A or (B -> (A and B))) -> (C -> (((D and E) -> D) and C))), M:tm-48, m:tm-240, u:((Am (-> A (and B A))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8975
in-theory        8975
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (((D and E) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-47 tm-240 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8975.         (((A and B) or B) -> (C -> (((D and E) -> D) and C))), M:tm-47, m:tm-240, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8976
in-theory        8976
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (((D and E) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-46 tm-240 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8976.         (((A and B) or A) -> (C -> (((D and E) -> D) and C))), M:tm-46, m:tm-240, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8977
in-theory        8977
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E and F) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-45 tm-240 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8977.         (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E and F) -> E) and D))), M:tm-45, m:tm-240, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8978
in-theory        8978
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((D and E) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-44 tm-240 ((Am (-> A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8978.         ((A or (B -> A)) -> (C -> (((D and E) -> D) and C))), M:tm-44, m:tm-240, u:((Am (-> A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8979
in-theory        8979
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-42 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8979.         ((A -> (B or A)) and (C -> (D -> (((E and F) -> E) and D)))), M:tm-42, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8980
in-theory        8980
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-32 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8980.         ((A -> (A or B)) and (C -> (D -> (((E and F) -> E) and D)))), M:tm-32, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8981
in-theory        8981
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B -> (((C and D) -> C) and B))))
theorem-size     13
proof            (modus-ponens tm-24 tm-240 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8981.         (A -> (A and (B -> (((C and D) -> C) and B)))), M:tm-24, m:tm-240, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8982
in-theory        8982
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-23 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8982.         ((A -> (B -> (A and B))) and (C -> (D -> (((E and F) -> E) and D)))), M:tm-23, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8983
in-theory        8983
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-22 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8983.         (((A and B) -> B) and (C -> (D -> (((E and F) -> E) and D)))), M:tm-22, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8984
in-theory        8984
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-21 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8984.         (((A and B) -> A) and (C -> (D -> (((E and F) -> E) and D)))), M:tm-21, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8985
in-theory        8985
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-20 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8985.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-20, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8986
in-theory        8986
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-19 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8986.         ((A -> (B -> A)) and (C -> (D -> (((E and F) -> E) and D)))), M:tm-19, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8987
in-theory        8987
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> (((C and D) -> C) and B)) -> E)) -> E)
theorem-size     15
proof            (modus-ponens tm-17 tm-240 ((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) C))) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-5 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8987.         ((A and ((B -> (((C and D) -> C) and B)) -> E)) -> E), M:tm-17, m:tm-240, u:((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) C))) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8988
in-theory        8988
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (((B and C) -> B) and A)) -> D) and E) -> D)
theorem-size     15
proof            (modus-ponens tm-15 tm-240 ((Am (and (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) B) C)) (A (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8988.         ((((A -> (((B and C) -> B) and A)) -> D) and E) -> D), M:tm-15, m:tm-240, u:((Am (and (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) B) C)) (A (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8989
in-theory        8989
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) and A) -> D)) -> (A -> D))
theorem-size     15
proof            (modus-ponens tm-13 tm-240 ((Am (-> Bm (-> (and (-> (and Cm Dm) Cm) Bm) C))) (A Bm) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8989.         ((A -> ((((B and C) -> B) and A) -> D)) -> (A -> D)), M:tm-13, m:tm-240, u:((Am (-> Bm (-> (and (-> (and Cm Dm) Cm) Bm) C))) (A Bm) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-8990
in-theory        8990
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B -> (((C and D) -> C) and B)))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-240 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-9 tm-1 tm-5 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8990.         ((A -> (not (B -> (((C and D) -> C) and B)))) -> (not A)), M:tm-9, m:tm-240, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8991
in-theory        8991
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) -> D) -> ((E or (A -> (((B and C) -> B) and A))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-240 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8991.         (((A -> (((B and C) -> B) and A)) -> D) -> ((E or (A -> (((B and C) -> B) and A))) -> D)), M:tm-8, m:tm-240, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-8992
in-theory        8992
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C -> (((D and E) -> D) and C))))
theorem-size     13
proof            (modus-ponens tm-7 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-7 tm-1 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8992.         (A or (B -> (C -> (((D and E) -> D) and C)))), M:tm-7, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8993
in-theory        8993
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-6 tm-1 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8993.         ((A -> (B -> (((C and D) -> C) and B))) or E), M:tm-6, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8994
in-theory        8994
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (((D and E) -> D) and C))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8994.         (A -> ((B -> (C -> (((D and E) -> D) and C))) and A)), M:tm-5, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-8995
in-theory        8995
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> (((C and D) -> C) and B)))
theorem-size     13
proof            (modus-ponens tm-2 tm-240 ((A Am) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8995.         ((A -> B) -> (A -> (((C and D) -> C) and B))), M:tm-2, m:tm-240, u:((A Am) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-8996
in-theory        8996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8996.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-239, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-8997
in-theory        8997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8997.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (H -> G)))), M:tm-210, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-8998
in-theory        8998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8998.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-183, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-8999
in-theory        8999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8999.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-157, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9000
in-theory        9000
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9000.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-147, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9001
in-theory        9001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9001.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-134, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9002
in-theory        9002
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9002.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-125, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9003
in-theory        9003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9003.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> G)))), M:tm-113, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9004
in-theory        9004
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9004.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-105, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9005
in-theory        9005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9005.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (F -> E)))), M:tm-95, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9006
in-theory        9006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9006.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-83, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9007
in-theory        9007
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9007.         (((not (not A)) -> A) and (((B and C) -> C) and (D -> (E -> D)))), M:tm-76, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9008
in-theory        9008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9008.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (F -> E)))), M:tm-69, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9009
in-theory        9009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9009.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-54, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9010
in-theory        9010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9010.         ((A -> (B or A)) and (((C and D) -> D) and (E -> (F -> E)))), M:tm-42, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9011
in-theory        9011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9011.         ((A -> (A or B)) and (((C and D) -> D) and (E -> (F -> E)))), M:tm-32, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9012
in-theory        9012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9012.         ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (F -> E)))), M:tm-23, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9013
in-theory        9013
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9013.         (((A and B) -> B) and (((C and D) -> D) and (E -> (F -> E)))), M:tm-22, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9014
in-theory        9014
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9014.         (((A and B) -> A) and (((C and D) -> D) and (E -> (F -> E)))), M:tm-21, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9015
in-theory        9015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9015.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-20, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9016
in-theory        9016
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9016.         ((A -> (B -> A)) and (((C and D) -> D) and (E -> (F -> E)))), M:tm-19, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9017
in-theory        9017
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-7 tm-5 tm-4 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9017.         (A or (((B and C) -> C) and (D -> (E -> D)))), M:tm-7, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9018
in-theory        9018
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-6 tm-5 tm-4 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9018.         ((((A and B) -> B) and (C -> (D -> C))) or E), M:tm-6, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9019
in-theory        9019
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> (E -> D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9019.         (A -> ((((B and C) -> C) and (D -> (E -> D))) and A)), M:tm-5, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9020
in-theory        9020
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9020.         (A -> (((B and C) -> C) and (D -> (E -> D)))), M:tm-1, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9021
in-theory        9021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9021.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-239, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9022
in-theory        9022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9022.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-210, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9023
in-theory        9023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9023.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-183, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9024
in-theory        9024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9024.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-157, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9025
in-theory        9025
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9025.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-147, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9026
in-theory        9026
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9026.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-134, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9027
in-theory        9027
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9027.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-125, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9028
in-theory        9028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9028.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-113, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9029
in-theory        9029
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9029.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-105, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9030
in-theory        9030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9030.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-95, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9031
in-theory        9031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9031.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-83, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9032
in-theory        9032
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-4 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9032.         (((not (not A)) -> A) and (((B and C) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-76, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9033
in-theory        9033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-4 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9033.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-69, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9034
in-theory        9034
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9034.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-54, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9035
in-theory        9035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9035.         ((A -> (B or A)) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-42, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9036
in-theory        9036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9036.         ((A -> (A or B)) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-32, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9037
in-theory        9037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9037.         ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-23, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9038
in-theory        9038
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9038.         (((A and B) -> B) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-22, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9039
in-theory        9039
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9039.         (((A and B) -> A) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-21, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9040
in-theory        9040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9040.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-20, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9041
in-theory        9041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9041.         ((A -> (B -> A)) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-19, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9042
in-theory        9042
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-7 tm-5 tm-4 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9042.         (A or (((B and C) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-7, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9043
in-theory        9043
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-6 tm-5 tm-4 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9043.         ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F), M:tm-6, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9044
in-theory        9044
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9044.         (A -> ((((B and C) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)), M:tm-5, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9045
in-theory        9045
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-1 tm-5 tm-4 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9045.         (A -> (((B and C) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-1, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9046
in-theory        9046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9046.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-239, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9047
in-theory        9047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9047.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G and H) -> G))), M:tm-210, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9048
in-theory        9048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9048.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-183, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9049
in-theory        9049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9049.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-157, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9050
in-theory        9050
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9050.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-147, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9051
in-theory        9051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9051.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-134, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9052
in-theory        9052
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9052.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-125, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9053
in-theory        9053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9053.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G and H) -> G))), M:tm-113, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9054
in-theory        9054
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9054.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F and G) -> F))), M:tm-105, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9055
in-theory        9055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9055.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E and F) -> E))), M:tm-95, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9056
in-theory        9056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9056.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F and G) -> F))), M:tm-83, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9057
in-theory        9057
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((D and E) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-10 tm-4 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9057.         (((not (not A)) -> A) and (((B and C) -> C) and ((D and E) -> D))), M:tm-76, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9058
in-theory        9058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-9 tm-4 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9058.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E and F) -> E))), M:tm-69, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9059
in-theory        9059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9059.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F and G) -> F))), M:tm-54, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9060
in-theory        9060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9060.         ((A -> (B or A)) and (((C and D) -> D) and ((E and F) -> E))), M:tm-42, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9061
in-theory        9061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9061.         ((A -> (A or B)) and (((C and D) -> D) and ((E and F) -> E))), M:tm-32, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9062
in-theory        9062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9062.         ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E and F) -> E))), M:tm-23, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9063
in-theory        9063
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9063.         (((A and B) -> B) and (((C and D) -> D) and ((E and F) -> E))), M:tm-22, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9064
in-theory        9064
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9064.         (((A and B) -> A) and (((C and D) -> D) and ((E and F) -> E))), M:tm-21, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9065
in-theory        9065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9065.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F and G) -> F))), M:tm-20, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9066
in-theory        9066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9066.         ((A -> (B -> A)) and (((C and D) -> D) and ((E and F) -> E))), M:tm-19, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9067
in-theory        9067
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-7 tm-5 tm-4 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9067.         (A or (((B and C) -> C) and ((D and E) -> D))), M:tm-7, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9068
in-theory        9068
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-6 tm-5 tm-4 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9068.         ((((A and B) -> B) and ((C and D) -> C)) or E), M:tm-6, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9069
in-theory        9069
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((D and E) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9069.         (A -> ((((B and C) -> C) and ((D and E) -> D)) and A)), M:tm-5, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9070
in-theory        9070
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-1 tm-5 tm-4 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9070.         (A -> (((B and C) -> C) and ((D and E) -> D))), M:tm-1, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9071
in-theory        9071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-239 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9071.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-239, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9072
in-theory        9072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-210 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9072.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G and H) -> H))), M:tm-210, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9073
in-theory        9073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-183 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9073.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-183, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9074
in-theory        9074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-157 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9074.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-157, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9075
in-theory        9075
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-147 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9075.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-147, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9076
in-theory        9076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-134 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9076.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-134, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9077
in-theory        9077
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-125 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9077.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-125, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9078
in-theory        9078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-113 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9078.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G and H) -> H))), M:tm-113, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9079
in-theory        9079
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-105 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9079.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F and G) -> G))), M:tm-105, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9080
in-theory        9080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-95 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9080.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E and F) -> F))), M:tm-95, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9081
in-theory        9081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-83 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9081.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F and G) -> G))), M:tm-83, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9082
in-theory        9082
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((D and E) -> E)))
theorem-size     17
proof            (modus-ponens tm-76 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-10 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9082.         (((not (not A)) -> A) and (((B and C) -> C) and ((D and E) -> E))), M:tm-76, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9083
in-theory        9083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-69 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9083.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E and F) -> F))), M:tm-69, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9084
in-theory        9084
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-54 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9084.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F and G) -> G))), M:tm-54, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9085
in-theory        9085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-42 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9085.         ((A -> (B or A)) and (((C and D) -> D) and ((E and F) -> F))), M:tm-42, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9086
in-theory        9086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-32 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9086.         ((A -> (A or B)) and (((C and D) -> D) and ((E and F) -> F))), M:tm-32, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9087
in-theory        9087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-23 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9087.         ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E and F) -> F))), M:tm-23, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9088
in-theory        9088
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-22 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9088.         (((A and B) -> B) and (((C and D) -> D) and ((E and F) -> F))), M:tm-22, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9089
in-theory        9089
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-21 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9089.         (((A and B) -> A) and (((C and D) -> D) and ((E and F) -> F))), M:tm-21, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9090
in-theory        9090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-20 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9090.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F and G) -> G))), M:tm-20, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9091
in-theory        9091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-19 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9091.         ((A -> (B -> A)) and (((C and D) -> D) and ((E and F) -> F))), M:tm-19, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9092
in-theory        9092
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-7 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9092.         (A or (((B and C) -> C) and ((D and E) -> E))), M:tm-7, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9093
in-theory        9093
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9093.         ((((A and B) -> B) and ((C and D) -> D)) or E), M:tm-6, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9094
in-theory        9094
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((D and E) -> E)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9094.         (A -> ((((B and C) -> C) and ((D and E) -> E)) and A)), M:tm-5, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9095
in-theory        9095
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-1 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9095.         (A -> (((B and C) -> C) and ((D and E) -> E))), M:tm-1, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9096
in-theory        9096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9096.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-239, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9097
in-theory        9097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9097.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (H -> (G and H))))), M:tm-210, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9098
in-theory        9098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9098.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-183, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9099
in-theory        9099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9099.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-157, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9100
in-theory        9100
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9100.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-147, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9101
in-theory        9101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9101.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-134, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9102
in-theory        9102
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9102.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-125, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9103
in-theory        9103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9103.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (G and H))))), M:tm-113, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9104
in-theory        9104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9104.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-105, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9105
in-theory        9105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9105.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (F -> (E and F))))), M:tm-95, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9106
in-theory        9106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9106.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-83, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9107
in-theory        9107
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9107.         (((not (not A)) -> A) and (((B and C) -> C) and (D -> (E -> (D and E))))), M:tm-76, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9108
in-theory        9108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9108.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (F -> (E and F))))), M:tm-69, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9109
in-theory        9109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9109.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-54, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9110
in-theory        9110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9110.         ((A -> (B or A)) and (((C and D) -> D) and (E -> (F -> (E and F))))), M:tm-42, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9111
in-theory        9111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9111.         ((A -> (A or B)) and (((C and D) -> D) and (E -> (F -> (E and F))))), M:tm-32, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9112
in-theory        9112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9112.         ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (F -> (E and F))))), M:tm-23, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9113
in-theory        9113
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9113.         (((A and B) -> B) and (((C and D) -> D) and (E -> (F -> (E and F))))), M:tm-22, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9114
in-theory        9114
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9114.         (((A and B) -> A) and (((C and D) -> D) and (E -> (F -> (E and F))))), M:tm-21, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9115
in-theory        9115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9115.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-20, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9116
in-theory        9116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9116.         ((A -> (B -> A)) and (((C and D) -> D) and (E -> (F -> (E and F))))), M:tm-19, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9117
in-theory        9117
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9117.         (A or (((B and C) -> C) and (D -> (E -> (D and E))))), M:tm-7, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9118
in-theory        9118
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9118.         ((((A and B) -> B) and (C -> (D -> (C and D)))) or E), M:tm-6, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9119
in-theory        9119
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> (E -> (D and E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9119.         (A -> ((((B and C) -> C) and (D -> (E -> (D and E)))) and A)), M:tm-5, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9120
in-theory        9120
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9120.         (A -> (((B and C) -> C) and (D -> (E -> (D and E))))), M:tm-1, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9121
in-theory        9121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-239 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9121.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-239, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9122
in-theory        9122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-210 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9122.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (G or H)))), M:tm-210, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9123
in-theory        9123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-183 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9123.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-183, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9124
in-theory        9124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-157 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9124.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-157, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9125
in-theory        9125
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-147 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9125.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-147, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9126
in-theory        9126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-134 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9126.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-134, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9127
in-theory        9127
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-125 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9127.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-125, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9128
in-theory        9128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-113 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9128.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (G or H)))), M:tm-113, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9129
in-theory        9129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-105 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9129.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (F or G)))), M:tm-105, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9130
in-theory        9130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-95 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9130.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (E or F)))), M:tm-95, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9131
in-theory        9131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-83 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9131.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (F or G)))), M:tm-83, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9132
in-theory        9132
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-76 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9132.         (((not (not A)) -> A) and (((B and C) -> C) and (D -> (D or E)))), M:tm-76, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9133
in-theory        9133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-69 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9133.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (E or F)))), M:tm-69, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9134
in-theory        9134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-54 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9134.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (F or G)))), M:tm-54, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9135
in-theory        9135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-42 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9135.         ((A -> (B or A)) and (((C and D) -> D) and (E -> (E or F)))), M:tm-42, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9136
in-theory        9136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-32 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9136.         ((A -> (A or B)) and (((C and D) -> D) and (E -> (E or F)))), M:tm-32, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9137
in-theory        9137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-23 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9137.         ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (E or F)))), M:tm-23, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9138
in-theory        9138
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-22 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9138.         (((A and B) -> B) and (((C and D) -> D) and (E -> (E or F)))), M:tm-22, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9139
in-theory        9139
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-21 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9139.         (((A and B) -> A) and (((C and D) -> D) and (E -> (E or F)))), M:tm-21, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9140
in-theory        9140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-20 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9140.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (F or G)))), M:tm-20, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9141
in-theory        9141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-19 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9141.         ((A -> (B -> A)) and (((C and D) -> D) and (E -> (E or F)))), M:tm-19, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9142
in-theory        9142
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-7 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-7 tm-5 tm-4 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9142.         (A or (((B and C) -> C) and (D -> (D or E)))), M:tm-7, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9143
in-theory        9143
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9143.         ((((A and B) -> B) and (C -> (C or D))) or E), M:tm-6, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9144
in-theory        9144
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> (D or E))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9144.         (A -> ((((B and C) -> C) and (D -> (D or E))) and A)), M:tm-5, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9145
in-theory        9145
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-1 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-1 tm-5 tm-4 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9145.         (A -> (((B and C) -> C) and (D -> (D or E)))), M:tm-1, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9146
in-theory        9146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9146.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-239, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9147
in-theory        9147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9147.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (H or G)))), M:tm-210, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9148
in-theory        9148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9148.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-183, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9149
in-theory        9149
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9149.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-157, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9150
in-theory        9150
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9150.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-147, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9151
in-theory        9151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9151.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-134, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9152
in-theory        9152
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9152.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-125, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9153
in-theory        9153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9153.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H or G)))), M:tm-113, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9154
in-theory        9154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9154.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (G or F)))), M:tm-105, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9155
in-theory        9155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9155.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (F or E)))), M:tm-95, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9156
in-theory        9156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9156.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (G or F)))), M:tm-83, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9157
in-theory        9157
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9157.         (((not (not A)) -> A) and (((B and C) -> C) and (D -> (E or D)))), M:tm-76, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9158
in-theory        9158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9158.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (F or E)))), M:tm-69, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9159
in-theory        9159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9159.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (G or F)))), M:tm-54, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9160
in-theory        9160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9160.         ((A -> (B or A)) and (((C and D) -> D) and (E -> (F or E)))), M:tm-42, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9161
in-theory        9161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9161.         ((A -> (A or B)) and (((C and D) -> D) and (E -> (F or E)))), M:tm-32, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9162
in-theory        9162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9162.         ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (F or E)))), M:tm-23, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9163
in-theory        9163
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9163.         (((A and B) -> B) and (((C and D) -> D) and (E -> (F or E)))), M:tm-22, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9164
in-theory        9164
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9164.         (((A and B) -> A) and (((C and D) -> D) and (E -> (F or E)))), M:tm-21, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9165
in-theory        9165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9165.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (G or F)))), M:tm-20, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9166
in-theory        9166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9166.         ((A -> (B -> A)) and (((C and D) -> D) and (E -> (F or E)))), M:tm-19, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9167
in-theory        9167
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9167.         (A or (((B and C) -> C) and (D -> (E or D)))), M:tm-7, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9168
in-theory        9168
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-6 tm-5 tm-4 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9168.         ((((A and B) -> B) and (C -> (D or C))) or E), M:tm-6, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9169
in-theory        9169
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> (E or D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9169.         (A -> ((((B and C) -> C) and (D -> (E or D))) and A)), M:tm-5, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9170
in-theory        9170
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-1 tm-5 tm-4 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9170.         (A -> (((B and C) -> C) and (D -> (E or D)))), M:tm-1, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9171
in-theory        9171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9171.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-239, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9172
in-theory        9172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9172.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-210, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9173
in-theory        9173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9173.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-183, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9174
in-theory        9174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9174.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-157, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9175
in-theory        9175
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9175.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-147, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9176
in-theory        9176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9176.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-134, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9177
in-theory        9177
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9177.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-125, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9178
in-theory        9178
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9178.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-113, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9179
in-theory        9179
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9179.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-105, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9180
in-theory        9180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9180.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-95, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9181
in-theory        9181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9181.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-83, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9182
in-theory        9182
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-10 tm-4 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9182.         (((not (not A)) -> A) and (((B and C) -> C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-76, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9183
in-theory        9183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-9 tm-4 tm-8)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9183.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-69, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9184
in-theory        9184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9184.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-54, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9185
in-theory        9185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9185.         ((A -> (B or A)) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-42, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9186
in-theory        9186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9186.         ((A -> (A or B)) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-32, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9187
in-theory        9187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9187.         ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-23, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9188
in-theory        9188
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9188.         (((A and B) -> B) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-22, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9189
in-theory        9189
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9189.         (((A and B) -> A) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-21, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9190
in-theory        9190
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9190.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-20, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9191
in-theory        9191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9191.         ((A -> (B -> A)) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-19, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9192
in-theory        9192
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-7 tm-5 tm-4 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9192.         (A or (((B and C) -> C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-7, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9193
in-theory        9193
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-6 tm-5 tm-4 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9193.         ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F), M:tm-6, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9194
in-theory        9194
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9194.         (A -> ((((B and C) -> C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A)), M:tm-5, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9195
in-theory        9195
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-1 tm-5 tm-4 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9195.         (A -> (((B and C) -> C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-1, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9196
in-theory        9196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-239 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9196.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-239, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9197
in-theory        9197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-210 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9197.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-210, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9198
in-theory        9198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-183 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9198.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-183, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9199
in-theory        9199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-157 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9199.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-157, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9200
in-theory        9200
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-147 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9200.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-147, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9201
in-theory        9201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-134 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9201.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-134, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9202
in-theory        9202
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-125 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9202.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-125, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9203
in-theory        9203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-113 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9203.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-113, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9204
in-theory        9204
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     37
proof            (modus-ponens tm-105 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9204.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-105, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9205
in-theory        9205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-95 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9205.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-95, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9206
in-theory        9206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-83 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9206.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-83, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9207
in-theory        9207
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-76 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-10 tm-4 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9207.         (((not (not A)) -> A) and (((B and C) -> C) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-76, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9208
in-theory        9208
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     29
proof            (modus-ponens tm-69 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9208.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-69, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9209
in-theory        9209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-54 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9209.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-54, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9210
in-theory        9210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-42 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9210.         ((A -> (B or A)) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-42, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9211
in-theory        9211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-32 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9211.         ((A -> (A or B)) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-32, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9212
in-theory        9212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-23 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9212.         ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-23, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9213
in-theory        9213
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-22 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9213.         (((A and B) -> B) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-22, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9214
in-theory        9214
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-21 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9214.         (((A and B) -> A) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-21, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9215
in-theory        9215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-20 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9215.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-20, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9216
in-theory        9216
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-19 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9216.         ((A -> (B -> A)) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-19, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9217
in-theory        9217
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-7 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-7 tm-5 tm-4 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9217.         (A or (((B and C) -> C) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-7, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9218
in-theory        9218
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-6 tm-5 tm-4 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9218.         ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E), M:tm-6, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9219
in-theory        9219
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9219.         (A -> ((((B and C) -> C) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and A)), M:tm-5, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9220
in-theory        9220
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-1 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-1 tm-5 tm-4 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9220.         (A -> (((B and C) -> C) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-1, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9221
in-theory        9221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9221.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-239, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9222
in-theory        9222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9222.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((not (not G)) -> G))), M:tm-210, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9223
in-theory        9223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9223.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-183, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9224
in-theory        9224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9224.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-157, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9225
in-theory        9225
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9225.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-147, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9226
in-theory        9226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9226.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-134, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9227
in-theory        9227
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9227.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-125, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9228
in-theory        9228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9228.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((not (not G)) -> G))), M:tm-113, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9229
in-theory        9229
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-10)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9229.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-105, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9230
in-theory        9230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9230.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((not (not E)) -> E))), M:tm-95, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9231
in-theory        9231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9231.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-83, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9232
in-theory        9232
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((not (not D)) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9232.         (((not (not A)) -> A) and (((B and C) -> C) and ((not (not D)) -> D))), M:tm-76, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9233
in-theory        9233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((not (not E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-4 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9233.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((not (not E)) -> E))), M:tm-69, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9234
in-theory        9234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9234.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-54, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9235
in-theory        9235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9235.         ((A -> (B or A)) and (((C and D) -> D) and ((not (not E)) -> E))), M:tm-42, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9236
in-theory        9236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9236.         ((A -> (A or B)) and (((C and D) -> D) and ((not (not E)) -> E))), M:tm-32, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9237
in-theory        9237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9237.         ((A -> (B -> (A and B))) and (((C and D) -> D) and ((not (not E)) -> E))), M:tm-23, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9238
in-theory        9238
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9238.         (((A and B) -> B) and (((C and D) -> D) and ((not (not E)) -> E))), M:tm-22, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9239
in-theory        9239
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-4 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9239.         (((A and B) -> A) and (((C and D) -> D) and ((not (not E)) -> E))), M:tm-21, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9240
in-theory        9240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9240.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-20, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9241
in-theory        9241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9241.         ((A -> (B -> A)) and (((C and D) -> D) and ((not (not E)) -> E))), M:tm-19, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9242
in-theory        9242
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-7 tm-5 tm-4 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9242.         (A or (((B and C) -> C) and ((not (not D)) -> D))), M:tm-7, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9243
in-theory        9243
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-6 tm-5 tm-4 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9243.         ((((A and B) -> B) and ((not (not C)) -> C)) or D), M:tm-6, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9244
in-theory        9244
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((not (not D)) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9244.         (A -> ((((B and C) -> C) and ((not (not D)) -> D)) and A)), M:tm-5, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9245
in-theory        9245
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-1 tm-5 tm-4 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9245.         (A -> (((B and C) -> C) and ((not (not D)) -> D))), M:tm-1, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9246
in-theory        9246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9246.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-239, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9247
in-theory        9247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9247.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (H -> (I -> H))))), M:tm-210, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9248
in-theory        9248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9248.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-183, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9249
in-theory        9249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9249.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-157, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9250
in-theory        9250
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9250.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-147, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9251
in-theory        9251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9251.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-134, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9252
in-theory        9252
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9252.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-125, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9253
in-theory        9253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9253.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (I -> H))))), M:tm-113, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9254
in-theory        9254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9254.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-105, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9255
in-theory        9255
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9255.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (F -> (G -> F))))), M:tm-95, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9256
in-theory        9256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9256.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-83, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9257
in-theory        9257
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9257.         (((not (not A)) -> A) and (((B and C) -> C) and (D -> (E -> (F -> E))))), M:tm-76, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9258
in-theory        9258
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-4 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9258.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (F -> (G -> F))))), M:tm-69, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9259
in-theory        9259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9259.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-54, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9260
in-theory        9260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9260.         ((A -> (B or A)) and (((C and D) -> D) and (E -> (F -> (G -> F))))), M:tm-42, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9261
in-theory        9261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9261.         ((A -> (A or B)) and (((C and D) -> D) and (E -> (F -> (G -> F))))), M:tm-32, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9262
in-theory        9262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9262.         ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (F -> (G -> F))))), M:tm-23, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9263
in-theory        9263
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9263.         (((A and B) -> B) and (((C and D) -> D) and (E -> (F -> (G -> F))))), M:tm-22, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9264
in-theory        9264
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9264.         (((A and B) -> A) and (((C and D) -> D) and (E -> (F -> (G -> F))))), M:tm-21, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9265
in-theory        9265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9265.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-20, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9266
in-theory        9266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9266.         ((A -> (B -> A)) and (((C and D) -> D) and (E -> (F -> (G -> F))))), M:tm-19, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9267
in-theory        9267
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-4 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9267.         (A or (((B and C) -> C) and (D -> (E -> (F -> E))))), M:tm-7, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9268
in-theory        9268
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-4 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9268.         ((((A and B) -> B) and (C -> (D -> (E -> D)))) or F), M:tm-6, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9269
in-theory        9269
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> (E -> (F -> E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9269.         (A -> ((((B and C) -> C) and (D -> (E -> (F -> E)))) and A)), M:tm-5, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9270
in-theory        9270
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9270.         (A -> (((B and C) -> C) and (D -> (E -> (F -> E))))), M:tm-1, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9271
in-theory        9271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9271.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-239, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9272
in-theory        9272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9272.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> H) -> (G -> G)))), M:tm-210, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9273
in-theory        9273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9273.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-183, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9274
in-theory        9274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9274.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-157, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9275
in-theory        9275
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9275.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-147, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9276
in-theory        9276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9276.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-134, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9277
in-theory        9277
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9277.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-125, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9278
in-theory        9278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9278.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (G -> G)))), M:tm-113, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9279
in-theory        9279
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9279.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-105, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9280
in-theory        9280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9280.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> F) -> (E -> E)))), M:tm-95, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9281
in-theory        9281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9281.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-83, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9282
in-theory        9282
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((D -> E) -> (D -> D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9282.         (((not (not A)) -> A) and (((B and C) -> C) and ((D -> E) -> (D -> D)))), M:tm-76, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9283
in-theory        9283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> F) -> (E -> E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-2 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9283.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> F) -> (E -> E)))), M:tm-69, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9284
in-theory        9284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9284.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-54, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9285
in-theory        9285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9285.         ((A -> (B or A)) and (((C and D) -> D) and ((E -> F) -> (E -> E)))), M:tm-42, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9286
in-theory        9286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9286.         ((A -> (A or B)) and (((C and D) -> D) and ((E -> F) -> (E -> E)))), M:tm-32, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9287
in-theory        9287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9287.         ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (E -> E)))), M:tm-23, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9288
in-theory        9288
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9288.         (((A and B) -> B) and (((C and D) -> D) and ((E -> F) -> (E -> E)))), M:tm-22, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9289
in-theory        9289
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9289.         (((A and B) -> A) and (((C and D) -> D) and ((E -> F) -> (E -> E)))), M:tm-21, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9290
in-theory        9290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9290.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-20, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9291
in-theory        9291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9291.         ((A -> (B -> A)) and (((C and D) -> D) and ((E -> F) -> (E -> E)))), M:tm-19, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9292
in-theory        9292
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-7 tm-5 tm-4 tm-2 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9292.         (A or (((B and C) -> C) and ((D -> E) -> (D -> D)))), M:tm-7, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9293
in-theory        9293
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-6 tm-5 tm-4 tm-2 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9293.         ((((A and B) -> B) and ((C -> D) -> (C -> C))) or E), M:tm-6, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9294
in-theory        9294
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((D -> E) -> (D -> D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9294.         (A -> ((((B and C) -> C) and ((D -> E) -> (D -> D))) and A)), M:tm-5, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9295
in-theory        9295
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-1 tm-5 tm-4 tm-2)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9295.         (A -> (((B and C) -> C) and ((D -> E) -> (D -> D)))), M:tm-1, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9296
in-theory        9296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-239 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9296.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-239, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9297
in-theory        9297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-210 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9297.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-210, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9298
in-theory        9298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-183 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9298.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-183, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9299
in-theory        9299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-157 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9299.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-157, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9300
in-theory        9300
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-147 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9300.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-147, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9301
in-theory        9301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-134 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9301.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-134, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9302
in-theory        9302
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-125 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9302.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-125, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9303
in-theory        9303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-113 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9303.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-113, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9304
in-theory        9304
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     45
proof            (modus-ponens tm-105 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9304.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-105, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9305
in-theory        9305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-95 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9305.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-95, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9306
in-theory        9306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-83 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9306.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-83, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9307
in-theory        9307
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-76 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-4 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9307.         (((not (not A)) -> A) and (((B and C) -> C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-76, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9308
in-theory        9308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     37
proof            (modus-ponens tm-69 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-4 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9308.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-69, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9309
in-theory        9309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-54 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9309.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-54, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9310
in-theory        9310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-42 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9310.         ((A -> (B or A)) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-42, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9311
in-theory        9311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-32 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9311.         ((A -> (A or B)) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-32, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9312
in-theory        9312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-23 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9312.         ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-23, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9313
in-theory        9313
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-22 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9313.         (((A and B) -> B) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-22, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9314
in-theory        9314
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-21 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9314.         (((A and B) -> A) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-21, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9315
in-theory        9315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-20 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9315.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-20, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9316
in-theory        9316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-19 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9316.         ((A -> (B -> A)) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-19, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9317
in-theory        9317
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-7 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-7 tm-5 tm-4 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9317.         (A or (((B and C) -> C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-7, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9318
in-theory        9318
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F)
theorem-size     27
proof            (modus-ponens tm-6 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-6 tm-5 tm-4 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9318.         ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F), M:tm-6, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9319
in-theory        9319
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9319.         (A -> ((((B and C) -> C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and A)), M:tm-5, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9320
in-theory        9320
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-1 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-1 tm-5 tm-4 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9320.         (A -> (((B and C) -> C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-1, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9321
in-theory        9321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9321.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-239, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9322
in-theory        9322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9322.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-210, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9323
in-theory        9323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9323.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-183, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9324
in-theory        9324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9324.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-157, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9325
in-theory        9325
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9325.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-147, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9326
in-theory        9326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9326.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-134, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9327
in-theory        9327
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9327.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-125, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9328
in-theory        9328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9328.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-113, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9329
in-theory        9329
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9329.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-105, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9330
in-theory        9330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9330.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-95, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9331
in-theory        9331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9331.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-83, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9332
in-theory        9332
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-10 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9332.         (((not (not A)) -> A) and (((B and C) -> C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-76, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9333
in-theory        9333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-9 tm-4 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9333.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-69, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9334
in-theory        9334
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9334.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-54, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9335
in-theory        9335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9335.         ((A -> (B or A)) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-42, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9336
in-theory        9336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9336.         ((A -> (A or B)) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-32, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9337
in-theory        9337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9337.         ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-23, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9338
in-theory        9338
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9338.         (((A and B) -> B) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-22, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9339
in-theory        9339
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9339.         (((A and B) -> A) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-21, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9340
in-theory        9340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9340.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-20, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9341
in-theory        9341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9341.         ((A -> (B -> A)) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-19, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9342
in-theory        9342
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-7 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-7 tm-5 tm-4 tm-1 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9342.         (A or (((B and C) -> C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-7, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9343
in-theory        9343
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-6 tm-5 tm-4 tm-1 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9343.         ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G), M:tm-6, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9344
in-theory        9344
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9344.         (A -> ((((B and C) -> C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A)), M:tm-5, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9345
in-theory        9345
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-1 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-1 tm-5 tm-4 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9345.         (A -> (((B and C) -> C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-1, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9346
in-theory        9346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-239 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9346.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-239, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9347
in-theory        9347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-210 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9347.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-210, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9348
in-theory        9348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-183 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9348.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-183, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9349
in-theory        9349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-157 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9349.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-157, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9350
in-theory        9350
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-147 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9350.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-147, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9351
in-theory        9351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-134 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9351.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-134, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9352
in-theory        9352
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-125 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9352.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-125, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9353
in-theory        9353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-113 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9353.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-113, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9354
in-theory        9354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     41
proof            (modus-ponens tm-105 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9354.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-105, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9355
in-theory        9355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-95 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9355.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-95, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9356
in-theory        9356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-83 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9356.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-83, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9357
in-theory        9357
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     27
proof            (modus-ponens tm-76 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9357.         (((not (not A)) -> A) and (((B and C) -> C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-76, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9358
in-theory        9358
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     33
proof            (modus-ponens tm-69 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-2 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9358.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-69, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9359
in-theory        9359
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-54 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9359.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-54, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9360
in-theory        9360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-42 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9360.         ((A -> (B or A)) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-42, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9361
in-theory        9361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-32 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9361.         ((A -> (A or B)) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-32, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9362
in-theory        9362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-23 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9362.         ((A -> (B -> (A and B))) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-23, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9363
in-theory        9363
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-22 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9363.         (((A and B) -> B) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-22, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9364
in-theory        9364
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-21 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9364.         (((A and B) -> A) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-21, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9365
in-theory        9365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-20 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9365.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-20, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9366
in-theory        9366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-19 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9366.         ((A -> (B -> A)) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-19, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9367
in-theory        9367
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-7 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-4 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9367.         (A or (((B and C) -> C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-7, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9368
in-theory        9368
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-4 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9368.         ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F), M:tm-6, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9369
in-theory        9369
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9369.         (A -> ((((B and C) -> C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and A)), M:tm-5, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9370
in-theory        9370
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-1 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-4 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9370.         (A -> (((B and C) -> C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-1, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9371
in-theory        9371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-239 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9371.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-239, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9372
in-theory        9372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-210 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9372.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> ((H and I) -> H)))), M:tm-210, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9373
in-theory        9373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-183 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9373.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-183, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9374
in-theory        9374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-157 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9374.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-157, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9375
in-theory        9375
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-147 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9375.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-147, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9376
in-theory        9376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-134 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9376.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-134, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9377
in-theory        9377
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-125 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9377.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-125, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9378
in-theory        9378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-113 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9378.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H and I) -> H)))), M:tm-113, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9379
in-theory        9379
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-105 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9379.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-105, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9380
in-theory        9380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-95 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9380.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> ((F and G) -> F)))), M:tm-95, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9381
in-theory        9381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-83 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9381.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-83, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9382
in-theory        9382
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-76 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9382.         (((not (not A)) -> A) and (((B and C) -> C) and (D -> ((E and F) -> E)))), M:tm-76, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9383
in-theory        9383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-69 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9383.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> ((F and G) -> F)))), M:tm-69, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9384
in-theory        9384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-54 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9384.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-54, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9385
in-theory        9385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-42 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9385.         ((A -> (B or A)) and (((C and D) -> D) and (E -> ((F and G) -> F)))), M:tm-42, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9386
in-theory        9386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-32 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9386.         ((A -> (A or B)) and (((C and D) -> D) and (E -> ((F and G) -> F)))), M:tm-32, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9387
in-theory        9387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-23 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9387.         ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> ((F and G) -> F)))), M:tm-23, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9388
in-theory        9388
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-22 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9388.         (((A and B) -> B) and (((C and D) -> D) and (E -> ((F and G) -> F)))), M:tm-22, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9389
in-theory        9389
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-21 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9389.         (((A and B) -> A) and (((C and D) -> D) and (E -> ((F and G) -> F)))), M:tm-21, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9390
in-theory        9390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-20 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9390.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-20, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9391
in-theory        9391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-19 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9391.         ((A -> (B -> A)) and (((C and D) -> D) and (E -> ((F and G) -> F)))), M:tm-19, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9392
in-theory        9392
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-7 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-4 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9392.         (A or (((B and C) -> C) and (D -> ((E and F) -> E)))), M:tm-7, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9393
in-theory        9393
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-4 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9393.         ((((A and B) -> B) and (C -> ((D and E) -> D))) or F), M:tm-6, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9394
in-theory        9394
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> ((E and F) -> E))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9394.         (A -> ((((B and C) -> C) and (D -> ((E and F) -> E))) and A)), M:tm-5, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9395
in-theory        9395
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-1 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-4 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9395.         (A -> (((B and C) -> C) and (D -> ((E and F) -> E)))), M:tm-1, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9396
in-theory        9396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-239 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9396.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-239, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9397
in-theory        9397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-210 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9397.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-210, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9398
in-theory        9398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-183 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9398.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-183, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9399
in-theory        9399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-157 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9399.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-157, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9400
in-theory        9400
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-147 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9400.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-147, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9401
in-theory        9401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-134 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9401.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-134, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9402
in-theory        9402
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-125 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9402.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-125, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9403
in-theory        9403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-113 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9403.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-113, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9404
in-theory        9404
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     41
proof            (modus-ponens tm-105 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9404.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-105, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9405
in-theory        9405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-95 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9405.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-95, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9406
in-theory        9406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-83 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9406.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-83, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9407
in-theory        9407
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     27
proof            (modus-ponens tm-76 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-10 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9407.         (((not (not A)) -> A) and (((B and C) -> C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-76, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9408
in-theory        9408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     33
proof            (modus-ponens tm-69 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-9 tm-4 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9408.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-69, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9409
in-theory        9409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-54 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9409.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-54, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9410
in-theory        9410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-42 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9410.         ((A -> (B or A)) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-42, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9411
in-theory        9411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-32 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9411.         ((A -> (A or B)) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-32, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9412
in-theory        9412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-23 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9412.         ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-23, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9413
in-theory        9413
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-22 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9413.         (((A and B) -> B) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-22, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9414
in-theory        9414
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-21 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9414.         (((A and B) -> A) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-21, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9415
in-theory        9415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-20 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9415.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-20, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9416
in-theory        9416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-19 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9416.         ((A -> (B -> A)) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-19, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9417
in-theory        9417
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-7 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-7 tm-5 tm-4 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9417.         (A or (((B and C) -> C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-7, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9418
in-theory        9418
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-6 tm-5 tm-4 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9418.         ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F), M:tm-6, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9419
in-theory        9419
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9419.         (A -> ((((B and C) -> C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and A)), M:tm-5, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9420
in-theory        9420
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-1 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-1 tm-5 tm-4 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9420.         (A -> (((B and C) -> C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-1, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9421
in-theory        9421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-239 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9421.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-239, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9422
in-theory        9422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-210 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9422.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> ((H and I) -> I)))), M:tm-210, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9423
in-theory        9423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-183 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9423.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-183, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9424
in-theory        9424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-157 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9424.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-157, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9425
in-theory        9425
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-147 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9425.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-147, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9426
in-theory        9426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-134 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9426.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-134, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9427
in-theory        9427
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-125 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9427.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-125, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9428
in-theory        9428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-113 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9428.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H and I) -> I)))), M:tm-113, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9429
in-theory        9429
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-105 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9429.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-105, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9430
in-theory        9430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-95 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9430.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> ((F and G) -> G)))), M:tm-95, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9431
in-theory        9431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-83 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9431.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-83, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9432
in-theory        9432
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-76 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-10 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9432.         (((not (not A)) -> A) and (((B and C) -> C) and (D -> ((E and F) -> F)))), M:tm-76, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9433
in-theory        9433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-69 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-9 tm-4 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9433.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> ((F and G) -> G)))), M:tm-69, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9434
in-theory        9434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-54 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9434.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-54, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9435
in-theory        9435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-42 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9435.         ((A -> (B or A)) and (((C and D) -> D) and (E -> ((F and G) -> G)))), M:tm-42, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9436
in-theory        9436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-32 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9436.         ((A -> (A or B)) and (((C and D) -> D) and (E -> ((F and G) -> G)))), M:tm-32, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9437
in-theory        9437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-23 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9437.         ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> ((F and G) -> G)))), M:tm-23, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9438
in-theory        9438
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-22 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9438.         (((A and B) -> B) and (((C and D) -> D) and (E -> ((F and G) -> G)))), M:tm-22, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9439
in-theory        9439
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-21 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9439.         (((A and B) -> A) and (((C and D) -> D) and (E -> ((F and G) -> G)))), M:tm-21, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9440
in-theory        9440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-20 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9440.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-20, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9441
in-theory        9441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-19 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9441.         ((A -> (B -> A)) and (((C and D) -> D) and (E -> ((F and G) -> G)))), M:tm-19, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9442
in-theory        9442
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-7 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-7 tm-5 tm-4 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9442.         (A or (((B and C) -> C) and (D -> ((E and F) -> F)))), M:tm-7, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9443
in-theory        9443
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-6 tm-5 tm-4 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9443.         ((((A and B) -> B) and (C -> ((D and E) -> E))) or F), M:tm-6, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9444
in-theory        9444
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> ((E and F) -> F))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9444.         (A -> ((((B and C) -> C) and (D -> ((E and F) -> F))) and A)), M:tm-5, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9445
in-theory        9445
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-1 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9445.         (A -> (((B and C) -> C) and (D -> ((E and F) -> F)))), M:tm-1, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9446
in-theory        9446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9446.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-239, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9447
in-theory        9447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9447.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G)))), M:tm-210, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9448
in-theory        9448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9448.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-183, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9449
in-theory        9449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9449.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-157, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9450
in-theory        9450
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9450.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-147, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9451
in-theory        9451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9451.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-134, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9452
in-theory        9452
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9452.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-125, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9453
in-theory        9453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9453.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G)))), M:tm-113, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9454
in-theory        9454
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9454.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-105, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9455
in-theory        9455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9455.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E)))), M:tm-95, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9456
in-theory        9456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9456.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-83, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9457
in-theory        9457
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9457.         (((not (not A)) -> A) and (((B and C) -> C) and (D -> ((E -> (F -> E)) and D)))), M:tm-76, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9458
in-theory        9458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9458.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E)))), M:tm-69, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9459
in-theory        9459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9459.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-54, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9460
in-theory        9460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9460.         ((A -> (B or A)) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E)))), M:tm-42, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9461
in-theory        9461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9461.         ((A -> (A or B)) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E)))), M:tm-32, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9462
in-theory        9462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9462.         ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E)))), M:tm-23, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9463
in-theory        9463
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9463.         (((A and B) -> B) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E)))), M:tm-22, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9464
in-theory        9464
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9464.         (((A and B) -> A) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E)))), M:tm-21, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9465
in-theory        9465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9465.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-20, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9466
in-theory        9466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9466.         ((A -> (B -> A)) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E)))), M:tm-19, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9467
in-theory        9467
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-7 tm-5 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9467.         (A or (((B and C) -> C) and (D -> ((E -> (F -> E)) and D)))), M:tm-7, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9468
in-theory        9468
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-6 tm-5 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9468.         ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) or F), M:tm-6, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9469
in-theory        9469
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> ((E -> (F -> E)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9469.         (A -> ((((B and C) -> C) and (D -> ((E -> (F -> E)) and D))) and A)), M:tm-5, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9470
in-theory        9470
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9470.         (A -> (((B and C) -> C) and (D -> ((E -> (F -> E)) and D)))), M:tm-1, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9471
in-theory        9471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-239 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9471.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-239, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9472
in-theory        9472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-210 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9472.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-210, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9473
in-theory        9473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-183 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9473.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-183, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9474
in-theory        9474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-157 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9474.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-157, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9475
in-theory        9475
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-147 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9475.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-147, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9476
in-theory        9476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-134 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9476.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-134, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9477
in-theory        9477
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-125 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9477.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-125, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9478
in-theory        9478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-113 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9478.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-113, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9479
in-theory        9479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     43
proof            (modus-ponens tm-105 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9479.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-105, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9480
in-theory        9480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-95 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9480.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-95, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9481
in-theory        9481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-83 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9481.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-83, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9482
in-theory        9482
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-76 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9482.         (((not (not A)) -> A) and (((B and C) -> C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-76, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9483
in-theory        9483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-69 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9483.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-69, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9484
in-theory        9484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-54 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9484.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-54, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9485
in-theory        9485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-42 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9485.         ((A -> (B or A)) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-42, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9486
in-theory        9486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-32 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9486.         ((A -> (A or B)) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-32, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9487
in-theory        9487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-23 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9487.         ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-23, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9488
in-theory        9488
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-22 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9488.         (((A and B) -> B) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-22, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9489
in-theory        9489
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-21 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9489.         (((A and B) -> A) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-21, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9490
in-theory        9490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-20 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9490.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-20, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9491
in-theory        9491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-19 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9491.         ((A -> (B -> A)) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-19, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9492
in-theory        9492
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-7 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-7 tm-5 tm-4 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9492.         (A or (((B and C) -> C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-7, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9493
in-theory        9493
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-6 tm-5 tm-4 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9493.         ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G), M:tm-6, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9494
in-theory        9494
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9494.         (A -> ((((B and C) -> C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and A)), M:tm-5, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9495
in-theory        9495
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-1 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-1 tm-5 tm-4 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9495.         (A -> (((B and C) -> C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-1, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-9496
in-theory        9496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9496.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-239, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9497
in-theory        9497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9497.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (((H and I) -> H) and G)))), M:tm-210, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9498
in-theory        9498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9498.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-183, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9499
in-theory        9499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9499.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-157, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9500
in-theory        9500
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9500.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-147, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9501
in-theory        9501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9501.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-134, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9502
in-theory        9502
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9502.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-125, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9503
in-theory        9503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9503.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (((H and I) -> H) and G)))), M:tm-113, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9504
in-theory        9504
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9504.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-105, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9505
in-theory        9505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9505.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (((F and G) -> F) and E)))), M:tm-95, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9506
in-theory        9506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9506.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-83, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9507
in-theory        9507
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9507.         (((not (not A)) -> A) and (((B and C) -> C) and (D -> (((E and F) -> E) and D)))), M:tm-76, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9508
in-theory        9508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9508.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (((F and G) -> F) and E)))), M:tm-69, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9509
in-theory        9509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9509.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-54, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9510
in-theory        9510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9510.         ((A -> (B or A)) and (((C and D) -> D) and (E -> (((F and G) -> F) and E)))), M:tm-42, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9511
in-theory        9511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9511.         ((A -> (A or B)) and (((C and D) -> D) and (E -> (((F and G) -> F) and E)))), M:tm-32, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9512
in-theory        9512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9512.         ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (((F and G) -> F) and E)))), M:tm-23, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9513
in-theory        9513
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9513.         (((A and B) -> B) and (((C and D) -> D) and (E -> (((F and G) -> F) and E)))), M:tm-22, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9514
in-theory        9514
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9514.         (((A and B) -> A) and (((C and D) -> D) and (E -> (((F and G) -> F) and E)))), M:tm-21, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9515
in-theory        9515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9515.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-20, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9516
in-theory        9516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9516.         ((A -> (B -> A)) and (((C and D) -> D) and (E -> (((F and G) -> F) and E)))), M:tm-19, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9517
in-theory        9517
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-7 tm-5 tm-4 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9517.         (A or (((B and C) -> C) and (D -> (((E and F) -> E) and D)))), M:tm-7, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9518
in-theory        9518
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-6 tm-5 tm-4 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9518.         ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) or F), M:tm-6, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9519
in-theory        9519
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> (((E and F) -> E) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9519.         (A -> ((((B and C) -> C) and (D -> (((E and F) -> E) and D))) and A)), M:tm-5, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9520
in-theory        9520
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-1 tm-5 tm-4 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9520.         (A -> (((B and C) -> C) and (D -> (((E and F) -> E) and D)))), M:tm-1, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-9521
in-theory        9521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9521.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-239, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9522
in-theory        9522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9522.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (((H and I) -> I) and G)))), M:tm-210, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9523
in-theory        9523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9523.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-183, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9524
in-theory        9524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9524.         ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-157, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9525
in-theory        9525
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9525.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-147, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9526
in-theory        9526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9526.         ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-134, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9527
in-theory        9527
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9527.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-125, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9528
in-theory        9528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9528.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (((H and I) -> I) and G)))), M:tm-113, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9529
in-theory        9529
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9529.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-105, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9530
in-theory        9530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9530.         (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (((F and G) -> G) and E)))), M:tm-95, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9531
in-theory        9531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9531.         ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-83, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9532
in-theory        9532
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-10 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9532.         (((not (not A)) -> A) and (((B and C) -> C) and (D -> (((E and F) -> F) and D)))), M:tm-76, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9533
in-theory        9533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9533.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (((F and G) -> G) and E)))), M:tm-69, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9534
in-theory        9534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9534.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-54, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9535
in-theory        9535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9535.         ((A -> (B or A)) and (((C and D) -> D) and (E -> (((F and G) -> G) and E)))), M:tm-42, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9536
in-theory        9536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9536.         ((A -> (A or B)) and (((C and D) -> D) and (E -> (((F and G) -> G) and E)))), M:tm-32, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9537
in-theory        9537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9537.         ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (((F and G) -> G) and E)))), M:tm-23, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9538
in-theory        9538
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9538.         (((A and B) -> B) and (((C and D) -> D) and (E -> (((F and G) -> G) and E)))), M:tm-22, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9539
in-theory        9539
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9539.         (((A and B) -> A) and (((C and D) -> D) and (E -> (((F and G) -> G) and E)))), M:tm-21, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9540
in-theory        9540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9540.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-20, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9541
in-theory        9541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9541.         ((A -> (B -> A)) and (((C and D) -> D) and (E -> (((F and G) -> G) and E)))), M:tm-19, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9542
in-theory        9542
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9542.         (A or (((B and C) -> C) and (D -> (((E and F) -> F) and D)))), M:tm-7, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9543
in-theory        9543
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9543.         ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) or F), M:tm-6, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9544
in-theory        9544
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> (((E and F) -> F) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9544.         (A -> ((((B and C) -> C) and (D -> (((E and F) -> F) and D))) and A)), M:tm-5, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9545
in-theory        9545
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9545.         (A -> (((B and C) -> C) and (D -> (((E and F) -> F) and D)))), M:tm-1, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9546
in-theory        9546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9546.         ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-239, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9547
in-theory        9547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9547.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (((H and I) -> I) and G)))), M:tm-210, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9548
in-theory        9548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9548.         ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-183, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9549
in-theory        9549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9549.         ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-157, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9550
in-theory        9550
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9550.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-147, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9551
in-theory        9551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9551.         ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-134, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9552
in-theory        9552
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9552.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-125, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9553
in-theory        9553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9553.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (((H and I) -> I) and G)))), M:tm-113, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9554
in-theory        9554
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9554.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-105, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9555
in-theory        9555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9555.         (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (((F and G) -> G) and E)))), M:tm-95, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9556
in-theory        9556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9556.         ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-83, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9557
in-theory        9557
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9557.         (((not (not A)) -> A) and (((B and C) -> B) and (D -> (((E and F) -> F) and D)))), M:tm-76, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9558
in-theory        9558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9558.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (((F and G) -> G) and E)))), M:tm-69, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9559
in-theory        9559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9559.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-54, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9560
in-theory        9560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9560.         ((A -> (B or A)) and (((C and D) -> C) and (E -> (((F and G) -> G) and E)))), M:tm-42, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9561
in-theory        9561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9561.         ((A -> (A or B)) and (((C and D) -> C) and (E -> (((F and G) -> G) and E)))), M:tm-32, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9562
in-theory        9562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9562.         ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (((F and G) -> G) and E)))), M:tm-23, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9563
in-theory        9563
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9563.         (((A and B) -> B) and (((C and D) -> C) and (E -> (((F and G) -> G) and E)))), M:tm-22, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9564
in-theory        9564
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9564.         (((A and B) -> A) and (((C and D) -> C) and (E -> (((F and G) -> G) and E)))), M:tm-21, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9565
in-theory        9565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9565.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-20, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9566
in-theory        9566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9566.         ((A -> (B -> A)) and (((C and D) -> C) and (E -> (((F and G) -> G) and E)))), M:tm-19, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9567
in-theory        9567
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-7 tm-5 tm-3 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9567.         (A or (((B and C) -> B) and (D -> (((E and F) -> F) and D)))), M:tm-7, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9568
in-theory        9568
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-6 tm-5 tm-3 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9568.         ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) or F), M:tm-6, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9569
in-theory        9569
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> (((E and F) -> F) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9569.         (A -> ((((B and C) -> B) and (D -> (((E and F) -> F) and D))) and A)), M:tm-5, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9570
in-theory        9570
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-1 tm-5 tm-3 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9570.         (A -> (((B and C) -> B) and (D -> (((E and F) -> F) and D)))), M:tm-1, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9571
in-theory        9571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-239 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9571.         ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-239, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9572
in-theory        9572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> J) and H))))
theorem-size     41
proof            (modus-ponens tm-210 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9572.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-210, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9573
in-theory        9573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-183 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9573.         ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-183, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9574
in-theory        9574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-157 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9574.         ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-157, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9575
in-theory        9575
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     39
proof            (modus-ponens tm-147 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9575.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-147, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9576
in-theory        9576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-134 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9576.         ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-134, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9577
in-theory        9577
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     39
proof            (modus-ponens tm-125 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9577.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-125, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9578
in-theory        9578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> J) and H))))
theorem-size     39
proof            (modus-ponens tm-113 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9578.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-113, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9579
in-theory        9579
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     43
proof            (modus-ponens tm-105 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9579.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-105, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9580
in-theory        9580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-95 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9580.         (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-95, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9581
in-theory        9581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-83 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9581.         ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-83, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9582
in-theory        9582
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> G) and E))))
theorem-size     29
proof            (modus-ponens tm-76 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9582.         (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> G) and E)))), M:tm-76, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9583
in-theory        9583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     35
proof            (modus-ponens tm-69 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9583.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-69, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9584
in-theory        9584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     37
proof            (modus-ponens tm-54 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9584.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-54, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9585
in-theory        9585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-42 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9585.         ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-42, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9586
in-theory        9586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-32 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9586.         ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-32, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9587
in-theory        9587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-23 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9587.         ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-23, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9588
in-theory        9588
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-22 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9588.         (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-22, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9589
in-theory        9589
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-21 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9589.         (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-21, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9590
in-theory        9590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     37
proof            (modus-ponens tm-20 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9590.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-20, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9591
in-theory        9591
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-19 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9591.         ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-19, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9592
in-theory        9592
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-7 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9592.         (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> G) and E)))), M:tm-7, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9593
in-theory        9593
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9593.         ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) or G), M:tm-6, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9594
in-theory        9594
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> G) and E))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9594.         (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> G) and E))) and A)), M:tm-5, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9595
in-theory        9595
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-1 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9595.         (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((F and G) -> G) and E)))), M:tm-1, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-9596
in-theory        9596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9596.         ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-239, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9597
in-theory        9597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9597.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G)))), M:tm-210, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9598
in-theory        9598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9598.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-183, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9599
in-theory        9599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9599.         ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-157, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9600
in-theory        9600
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9600.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-147, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9601
in-theory        9601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9601.         ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-134, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9602
in-theory        9602
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9602.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-125, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9603
in-theory        9603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9603.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G)))), M:tm-113, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9604
in-theory        9604
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9604.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-105, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9605
in-theory        9605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9605.         (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E)))), M:tm-95, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9606
in-theory        9606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9606.         ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-83, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9607
in-theory        9607
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9607.         (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (((E and F) -> F) and D)))), M:tm-76, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9608
in-theory        9608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9608.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E)))), M:tm-69, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9609
in-theory        9609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9609.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-54, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9610
in-theory        9610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9610.         ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E)))), M:tm-42, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9611
in-theory        9611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9611.         ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E)))), M:tm-32, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9612
in-theory        9612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9612.         ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E)))), M:tm-23, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9613
in-theory        9613
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9613.         (((A and B) -> B) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E)))), M:tm-22, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9614
in-theory        9614
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9614.         (((A and B) -> A) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E)))), M:tm-21, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9615
in-theory        9615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9615.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-20, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9616
in-theory        9616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9616.         ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E)))), M:tm-19, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9617
in-theory        9617
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9617.         (A or ((B -> (C -> B)) and (D -> (((E and F) -> F) and D)))), M:tm-7, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9618
in-theory        9618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9618.         (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) or F), M:tm-6, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9619
in-theory        9619
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> (((E and F) -> F) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9619.         (A -> (((B -> (C -> B)) and (D -> (((E and F) -> F) and D))) and A)), M:tm-5, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9620
in-theory        9620
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9620.         (A -> ((B -> (C -> B)) and (D -> (((E and F) -> F) and D)))), M:tm-1, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-9621
in-theory        9621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9621.         ((A -> (((B and C) -> B) and A)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-239, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9622
in-theory        9622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (((F and G) -> G) and E))) -> (not E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9622.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (((F and G) -> G) and E))) -> (not E))), M:tm-210, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9623
in-theory        9623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9623.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-183, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9624
in-theory        9624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9624.         ((A -> ((B and C) -> C)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-157, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9625
in-theory        9625
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not (((C and D) -> D) and ((A and B) -> B)))))
theorem-size     19
proof            (modus-ponens tm-153 tm-266 ((A (-> (-> (and B C) C) (not (and (-> (and Bm Cm) Cm) (-> (and B C) C))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9625.         (not (((A and B) -> B) -> (not (((C and D) -> D) and ((A and B) -> B))))), M:tm-153, m:tm-266, u:((A (-> (-> (and B C) C) (not (and (-> (and Bm Cm) Cm) (-> (and B C) C))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-9626
in-theory        9626
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9626.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-147, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9627
in-theory        9627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9627.         ((A -> ((B and C) -> B)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-134, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9628
in-theory        9628
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not (((C and D) -> D) and ((A and B) -> A)))))
theorem-size     19
proof            (modus-ponens tm-130 tm-266 ((A (-> (-> (and B C) B) (not (and (-> (and Bm Cm) Cm) (-> (and B C) B))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-5 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9628.         (not (((A and B) -> A) -> (not (((C and D) -> D) and ((A and B) -> A))))), M:tm-130, m:tm-266, u:((A (-> (-> (and B C) B) (not (and (-> (and Bm Cm) Cm) (-> (and B C) B))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-9629
in-theory        9629
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9629.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-125, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9630
in-theory        9630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (((F and G) -> G) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9630.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (((F and G) -> G) and E))) -> (not E))), M:tm-113, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9631
in-theory        9631
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((D and E) -> E) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))))
theorem-size     35
proof            (modus-ponens tm-109 tm-266 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (and (-> (and Bm Cm) Cm) (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-5 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9631.         (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((D and E) -> E) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))), M:tm-109, m:tm-266, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (and (-> (and Bm Cm) Cm) (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-9632
in-theory        9632
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9632.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-105, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9633
in-theory        9633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not (((D and E) -> E) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9633.         (((A -> B) -> (A -> A)) and ((C -> (not (((D and E) -> E) and C))) -> (not C))), M:tm-95, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9634
in-theory        9634
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> C) and A))) -> (D -> (not A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9634.         ((A -> (not (((B and C) -> C) and A))) -> (D -> (not A))), M:tm-84, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-9635
in-theory        9635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9635.         ((A -> (B -> (C -> B))) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-83, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9636
in-theory        9636
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (((C and D) -> D) and (A -> (B -> A))))))
theorem-size     19
proof            (modus-ponens tm-79 tm-266 ((A (-> (-> B (-> C B)) (not (and (-> (and Bm Cm) Cm) (-> B (-> C B)))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-5 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9636.         (not ((A -> (B -> A)) -> (not (((C and D) -> D) and (A -> (B -> A)))))), M:tm-79, m:tm-266, u:((A (-> (-> B (-> C B)) (not (and (-> (and Bm Cm) Cm) (-> B (-> C B)))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-9637
in-theory        9637
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not (((C and D) -> D) and B))) -> (not B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9637.         (((not (not A)) -> A) and ((B -> (not (((C and D) -> D) and B))) -> (not B))), M:tm-76, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9638
in-theory        9638
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not (((B and C) -> C) and A))))) or (A -> (not (((B and C) -> C) and A)))) -> (not A))
theorem-size     26
proof            (modus-ponens tm-73 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-5 tm-4)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9638.         (((not (not (A -> (not (((B and C) -> C) and A))))) or (A -> (not (((B and C) -> C) and A)))) -> (not A)), M:tm-73, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-9639
in-theory        9639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (((D and E) -> E) and C))) -> (not C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9639.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (((D and E) -> E) and C))) -> (not C))), M:tm-69, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9640
in-theory        9640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9640.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-54, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9641
in-theory        9641
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not (((C and D) -> D) and B)))) or (B -> (not (((C and D) -> D) and B)))) -> (not B))
theorem-size     26
proof            (modus-ponens tm-47 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-5)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9641.         (((A and (B -> (not (((C and D) -> D) and B)))) or (B -> (not (((C and D) -> D) and B)))) -> (not B)), M:tm-47, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-9642
in-theory        9642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not (((B and C) -> C) and A))) and D) or (A -> (not (((B and C) -> C) and A)))) -> (not A))
theorem-size     26
proof            (modus-ponens tm-46 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-5 tm-4)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9642.         ((((A -> (not (((B and C) -> C) and A))) and D) or (A -> (not (((B and C) -> C) and A)))) -> (not A)), M:tm-46, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-9643
in-theory        9643
times-derived    1
----------------------------------------------------------------
theorem          (((not (((A and B) -> B) and C)) or (C -> (not (((A and B) -> B) and C)))) -> (not C))
theorem-size     22
proof            (modus-ponens tm-44 tm-266 ((A Am) (B (not (and (-> (and Bm Cm) Cm) Am))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-5 tm-4)
proof-size       98
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9643.         (((not (((A and B) -> B) and C)) or (C -> (not (((A and B) -> B) and C)))) -> (not C)), M:tm-44, m:tm-266, u:((A Am) (B (not (and (-> (and Bm Cm) Cm) Am))) (C (not Am)))
================================================================
tm-name          tm-9644
in-theory        9644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not (((D and E) -> E) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9644.         ((A -> (B or A)) and ((C -> (not (((D and E) -> E) and C))) -> (not C))), M:tm-42, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9645
in-theory        9645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not (((D and E) -> E) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9645.         ((A -> (A or B)) and ((C -> (not (((D and E) -> E) and C))) -> (not C))), M:tm-32, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9646
in-theory        9646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> C) and A))) -> ((A -> (not (((B and C) -> C) and A))) and (not A)))
theorem-size     24
proof            (modus-ponens tm-24 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       98
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9646.         ((A -> (not (((B and C) -> C) and A))) -> ((A -> (not (((B and C) -> C) and A))) and (not A))), M:tm-24, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-9647
in-theory        9647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not (((D and E) -> E) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9647.         ((A -> (B -> (A and B))) and ((C -> (not (((D and E) -> E) and C))) -> (not C))), M:tm-23, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9648
in-theory        9648
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not (((D and E) -> E) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9648.         (((A and B) -> B) and ((C -> (not (((D and E) -> E) and C))) -> (not C))), M:tm-22, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9649
in-theory        9649
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not (((D and E) -> E) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9649.         (((A and B) -> A) and ((C -> (not (((D and E) -> E) and C))) -> (not C))), M:tm-21, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9650
in-theory        9650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9650.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-20, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9651
in-theory        9651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not (((D and E) -> E) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9651.         ((A -> (B -> A)) and ((C -> (not (((D and E) -> E) and C))) -> (not C))), M:tm-19, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9652
in-theory        9652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> C) and A))) -> (A -> (not (((B and C) -> C) and A))))
theorem-size     21
proof            (modus-ponens tm-12 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9652.         ((A -> (not (((B and C) -> C) and A))) -> (A -> (not (((B and C) -> C) and A)))), M:tm-12, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-9653
in-theory        9653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not (not A))) -> (not (A -> (not (((B and C) -> C) and A)))))
theorem-size     26
proof            (modus-ponens tm-9 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-9 tm-5 tm-4)
proof-size       82
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9653.         (((A -> (not (((B and C) -> C) and A))) -> (not (not A))) -> (not (A -> (not (((B and C) -> C) and A))))), M:tm-9, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-9654
in-theory        9654
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not (((C and D) -> D) and A))) or (not A)) -> B))
theorem-size     20
proof            (modus-ponens tm-8 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-5 tm-4)
proof-size       78
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9654.         (((not A) -> B) -> (((A -> (not (((C and D) -> D) and A))) or (not A)) -> B)), M:tm-8, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-9655
in-theory        9655
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not (((C and D) -> D) and B))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-5 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9655.         (A or ((B -> (not (((C and D) -> D) and B))) -> (not B))), M:tm-7, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9656
in-theory        9656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-5 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9656.         (((A -> (not (((B and C) -> C) and A))) -> (not A)) or D), M:tm-6, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9657
in-theory        9657
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not (((C and D) -> D) and B))) -> (not B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9657.         (A -> (((B -> (not (((C and D) -> D) and B))) -> (not B)) and A)), M:tm-5, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9658
in-theory        9658
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not (((C and D) -> D) and B))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-5 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9658.         (A -> ((B -> (not (((C and D) -> D) and B))) -> (not B))), M:tm-1, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-9659
in-theory        9659
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> (((B and C) -> C) and A)))
theorem-size     19
proof            (modus-ponens tm-267 tm-1 ((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9659.         ((A or (((B and C) -> C) and A)) -> (D -> (((B and C) -> C) and A))), M:tm-267, m:tm-1, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9660
in-theory        9660
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((B and C) -> C))
theorem-size     15
proof            (modus-ponens tm-267 tm-3 ((Am (-> (and A B) B)) (C Bm) (D (-> (and A B) B))))
axioms-used      (tm-8 tm-5 tm-4 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-9660.         ((A or (((B and C) -> C) and A)) -> ((B and C) -> C)), M:tm-267, m:tm-3, u:((Am (-> (and A B) B)) (C Bm) (D (-> (and A B) B)))
================================================================
tm-name          tm-9661
in-theory        9661
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> A)
theorem-size     11
proof            (modus-ponens tm-267 tm-4 ((Am (-> (and A B) B)) (C Bm) (D Bm)))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9661.         ((A or (((B and C) -> C) and A)) -> A), M:tm-267, m:tm-4, u:((Am (-> (and A B) B)) (C Bm) (D Bm))
================================================================
tm-name          tm-9662
in-theory        9662
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> ((((B and C) -> C) and A) and D)))
theorem-size     21
proof            (modus-ponens tm-267 tm-5 ((Am (and (-> (and A B) B) C)) (D (-> Bm (and (and (-> (and A B) B) C) Bm)))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9662.         ((A or (((B and C) -> C) and A)) -> (D -> ((((B and C) -> C) and A) and D))), M:tm-267, m:tm-5, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (and (and (-> (and A B) B) C) Bm))))
================================================================
tm-name          tm-9663
in-theory        9663
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) or D))
theorem-size     19
proof            (modus-ponens tm-267 tm-6 ((Am (and (-> (and A B) B) C)) (D (or (and (-> (and A B) B) C) Bm))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-9663.         ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) or D)), M:tm-267, m:tm-6, u:((Am (and (-> (and A B) B) C)) (D (or (and (-> (and A B) B) C) Bm)))
================================================================
tm-name          tm-9664
in-theory        9664
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D or (((B and C) -> C) and A)))
theorem-size     19
proof            (modus-ponens tm-267 tm-7 ((Am (and (-> (and A B) B) C)) (D (or Bm (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-9664.         ((A or (((B and C) -> C) and A)) -> (D or (((B and C) -> C) and A))), M:tm-267, m:tm-7, u:((Am (and (-> (and A B) B) C)) (D (or Bm (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9665
in-theory        9665
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-267 tm-11 ((Am (and (-> (and A B) B) C)) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9665.         ((A or (((B and C) -> C) and A)) -> (D -> (E -> D))), M:tm-267, m:tm-11, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-9666
in-theory        9666
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-267 tm-14 ((Am (and (-> (and A B) B) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9666.         ((A or (((B and C) -> C) and A)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-267, m:tm-14, u:((Am (and (-> (and A B) B) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-9667
in-theory        9667
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-267 tm-16 ((Am (and (-> (and A B) B) C)) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9667.         ((A or (((B and C) -> C) and A)) -> ((D and E) -> D)), M:tm-267, m:tm-16, u:((Am (and (-> (and A B) B) C)) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-9668
in-theory        9668
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-267 tm-18 ((Am (and (-> (and A B) B) C)) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9668.         ((A or (((B and C) -> C) and A)) -> ((D and E) -> E)), M:tm-267, m:tm-18, u:((Am (and (-> (and A B) B) C)) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-9669
in-theory        9669
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (E -> D)) and (((B and C) -> C) and A)))
theorem-size     23
proof            (modus-ponens tm-267 tm-19 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> Cm Bm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9669.         ((A or (((B and C) -> C) and A)) -> ((D -> (E -> D)) and (((B and C) -> C) and A))), M:tm-267, m:tm-19, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> Cm Bm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9670
in-theory        9670
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((B and C) -> C) and A)))
theorem-size     31
proof            (modus-ponens tm-267 tm-20 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9670.         ((A or (((B and C) -> C) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((B and C) -> C) and A))), M:tm-267, m:tm-20, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9671
in-theory        9671
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D and E) -> D) and (((B and C) -> C) and A)))
theorem-size     23
proof            (modus-ponens tm-267 tm-21 ((Am (and (-> (and A B) B) C)) (D (and (-> (and Bm Cm) Bm) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9671.         ((A or (((B and C) -> C) and A)) -> (((D and E) -> D) and (((B and C) -> C) and A))), M:tm-267, m:tm-21, u:((Am (and (-> (and A B) B) C)) (D (and (-> (and Bm Cm) Bm) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9672
in-theory        9672
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D and E) -> E) and (((B and C) -> C) and A)))
theorem-size     23
proof            (modus-ponens tm-267 tm-22 ((Am (and (-> (and A B) B) C)) (D (and (-> (and Bm Cm) Cm) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9672.         ((A or (((B and C) -> C) and A)) -> (((D and E) -> E) and (((B and C) -> C) and A))), M:tm-267, m:tm-22, u:((Am (and (-> (and A B) B) C)) (D (and (-> (and Bm Cm) Cm) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9673
in-theory        9673
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (E -> (D and E))) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-23 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9673.         ((A or (((B and C) -> C) and A)) -> ((D -> (E -> (D and E))) and (((B and C) -> C) and A))), M:tm-267, m:tm-23, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9674
in-theory        9674
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-267 tm-25 ((Am (and (-> (and A B) B) C)) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9674.         ((A or (((B and C) -> C) and A)) -> (D -> (E -> (D and E)))), M:tm-267, m:tm-25, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-9675
in-theory        9675
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (D or E)) and (((B and C) -> C) and A)))
theorem-size     23
proof            (modus-ponens tm-267 tm-32 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (or Bm Cm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9675.         ((A or (((B and C) -> C) and A)) -> ((D -> (D or E)) and (((B and C) -> C) and A))), M:tm-267, m:tm-32, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (or Bm Cm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9676
in-theory        9676
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-267 tm-33 ((Am (and (-> (and A B) B) C)) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9676.         ((A or (((B and C) -> C) and A)) -> (D -> (D or E))), M:tm-267, m:tm-33, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-9677
in-theory        9677
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (E or D)) and (((B and C) -> C) and A)))
theorem-size     23
proof            (modus-ponens tm-267 tm-42 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (or Cm Bm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9677.         ((A or (((B and C) -> C) and A)) -> ((D -> (E or D)) and (((B and C) -> C) and A))), M:tm-267, m:tm-42, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (or Cm Bm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9678
in-theory        9678
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-267 tm-43 ((Am (and (-> (and A B) B) C)) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9678.         ((A or (((B and C) -> C) and A)) -> (D -> (E or D))), M:tm-267, m:tm-43, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-9679
in-theory        9679
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((B and C) -> C) and A)))
theorem-size     31
proof            (modus-ponens tm-267 tm-54 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9679.         ((A or (((B and C) -> C) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((B and C) -> C) and A))), M:tm-267, m:tm-54, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9680
in-theory        9680
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-267 tm-56 ((Am (and (-> (and A B) B) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9680.         ((A or (((B and C) -> C) and A)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-267, m:tm-56, u:((Am (and (-> (and A B) B) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-9681
in-theory        9681
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (((B and C) -> C) and A)))
theorem-size     29
proof            (modus-ponens tm-267 tm-69 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9681.         ((A or (((B and C) -> C) and A)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (((B and C) -> C) and A))), M:tm-267, m:tm-69, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9682
in-theory        9682
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-267 tm-71 ((Am (and (-> (and A B) B) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9682.         ((A or (((B and C) -> C) and A)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-267, m:tm-71, u:((Am (and (-> (and A B) B) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-9683
in-theory        9683
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((not (not D)) -> D) and (((B and C) -> C) and A)))
theorem-size     23
proof            (modus-ponens tm-267 tm-76 ((Am (and (-> (and A B) B) C)) (D (and (-> (not (not Bm)) Bm) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9683.         ((A or (((B and C) -> C) and A)) -> (((not (not D)) -> D) and (((B and C) -> C) and A))), M:tm-267, m:tm-76, u:((Am (and (-> (and A B) B) C)) (D (and (-> (not (not Bm)) Bm) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9684
in-theory        9684
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-267 tm-78 ((Am (and (-> (and A B) B) C)) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9684.         ((A or (((B and C) -> C) and A)) -> ((not (not D)) -> D)), M:tm-267, m:tm-78, u:((Am (and (-> (and A B) B) C)) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-9685
in-theory        9685
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (E -> (F -> E))) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-83 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9685.         ((A or (((B and C) -> C) and A)) -> ((D -> (E -> (F -> E))) and (((B and C) -> C) and A))), M:tm-267, m:tm-83, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9686
in-theory        9686
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-267 tm-85 ((Am (and (-> (and A B) B) C)) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9686.         ((A or (((B and C) -> C) and A)) -> (D -> (E -> (F -> E)))), M:tm-267, m:tm-85, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9687
in-theory        9687
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((B and C) -> C) and A))
theorem-size     17
proof            (modus-ponens tm-267 tm-86 ((Am (and (-> (and A B) B) C)) (D (and (-> (and A B) B) C))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9687.         ((A or (((B and C) -> C) and A)) -> (((B and C) -> C) and A)), M:tm-267, m:tm-86, u:((Am (and (-> (and A B) B) C)) (D (and (-> (and A B) B) C)))
================================================================
tm-name          tm-9688
in-theory        9688
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> E) -> (D -> D)) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-95 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9688.         ((A or (((B and C) -> C) and A)) -> (((D -> E) -> (D -> D)) and (((B and C) -> C) and A))), M:tm-267, m:tm-95, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9689
in-theory        9689
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-267 tm-97 ((Am (and (-> (and A B) B) C)) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9689.         ((A or (((B and C) -> C) and A)) -> ((D -> E) -> (D -> D))), M:tm-267, m:tm-97, u:((Am (and (-> (and A B) B) C)) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-9690
in-theory        9690
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (((B and C) -> C) and A)))
theorem-size     37
proof            (modus-ponens tm-267 tm-105 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9690.         ((A or (((B and C) -> C) and A)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (((B and C) -> C) and A))), M:tm-267, m:tm-105, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9691
in-theory        9691
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-267 tm-107 ((Am (and (-> (and A B) B) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9691.         ((A or (((B and C) -> C) and A)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-267, m:tm-107, u:((Am (and (-> (and A B) B) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-9692
in-theory        9692
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((B and C) -> C) and A)))
theorem-size     33
proof            (modus-ponens tm-267 tm-113 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9692.         ((A or (((B and C) -> C) and A)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((B and C) -> C) and A))), M:tm-267, m:tm-113, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9693
in-theory        9693
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-267 tm-115 ((Am (and (-> (and A B) B) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9693.         ((A or (((B and C) -> C) and A)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-267, m:tm-115, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9694
in-theory        9694
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or (((A and B) -> B) and (A and B))) -> B)
theorem-size     15
proof            (modus-ponens tm-267 tm-116 ((Am (and A Bm)) (B Bm) (C (and A Bm)) (D Bm)))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-9694.         (((A and B) or (((A and B) -> B) and (A and B))) -> B), M:tm-267, m:tm-116, u:((Am (and A Bm)) (B Bm) (C (and A Bm)) (D Bm))
================================================================
tm-name          tm-9695
in-theory        9695
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (((B and C) -> C) and A)))
theorem-size     33
proof            (modus-ponens tm-267 tm-125 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9695.         ((A or (((B and C) -> C) and A)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (((B and C) -> C) and A))), M:tm-267, m:tm-125, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9696
in-theory        9696
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-267 tm-127 ((Am (and (-> (and A B) B) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9696.         ((A or (((B and C) -> C) and A)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-267, m:tm-127, u:((Am (and (-> (and A B) B) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-9697
in-theory        9697
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> ((E and F) -> E)) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-134 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9697.         ((A or (((B and C) -> C) and A)) -> ((D -> ((E and F) -> E)) and (((B and C) -> C) and A))), M:tm-267, m:tm-134, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9698
in-theory        9698
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-267 tm-136 ((Am (and (-> (and A B) B) C)) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9698.         ((A or (((B and C) -> C) and A)) -> (D -> ((E and F) -> E))), M:tm-267, m:tm-136, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9699
in-theory        9699
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) or (((A and B) -> B) and (((A and B) -> B) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-267 tm-137 ((Am (-> (and A B) B)) (C (-> (-> (and A B) B) Bm)) (D Bm)))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-9699.         (((((A and B) -> B) -> C) or (((A and B) -> B) and (((A and B) -> B) -> C))) -> C), M:tm-267, m:tm-137, u:((Am (-> (and A B) B)) (C (-> (-> (and A B) B) Bm)) (D Bm))
================================================================
tm-name          tm-9700
in-theory        9700
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) or (((D and E) -> E) and ((A -> (B -> A)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-267 tm-138 ((Am (-> (and A B) B)) (C (-> (-> Bm (-> Cm Bm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-9700.         ((((A -> (B -> A)) -> C) or (((D and E) -> E) and ((A -> (B -> A)) -> C))) -> C), M:tm-267, m:tm-138, u:((Am (-> (and A B) B)) (C (-> (-> Bm (-> Cm Bm)) Dm)) (D Dm))
================================================================
tm-name          tm-9701
in-theory        9701
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or (((E and F) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D)
theorem-size     39
proof            (modus-ponens tm-267 tm-139 ((Am (-> (and A B) B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (D Em)))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9701.         (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or (((E and F) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D), M:tm-267, m:tm-139, u:((Am (-> (and A B) B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (D Em))
================================================================
tm-name          tm-9702
in-theory        9702
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) or (((D and E) -> E) and (((A and B) -> A) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-267 tm-140 ((Am (-> (and A B) B)) (C (-> (-> (and Bm Cm) Bm) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-9702.         (((((A and B) -> A) -> C) or (((D and E) -> E) and (((A and B) -> A) -> C))) -> C), M:tm-267, m:tm-140, u:((Am (-> (and A B) B)) (C (-> (-> (and Bm Cm) Bm) Dm)) (D Dm))
================================================================
tm-name          tm-9703
in-theory        9703
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (((B and C) -> C) and A)))
theorem-size     33
proof            (modus-ponens tm-267 tm-147 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9703.         ((A or (((B and C) -> C) and A)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (((B and C) -> C) and A))), M:tm-267, m:tm-147, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9704
in-theory        9704
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-267 tm-149 ((Am (and (-> (and A B) B) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9704.         ((A or (((B and C) -> C) and A)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-267, m:tm-149, u:((Am (and (-> (and A B) B) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-9705
in-theory        9705
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) or (((D and E) -> E) and (((A and B) -> B) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-267 tm-150 ((Am (-> (and A B) B)) (C (-> (-> (and Bm Cm) Cm) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-9705.         (((((A and B) -> B) -> C) or (((D and E) -> E) and (((A and B) -> B) -> C))) -> C), M:tm-267, m:tm-150, u:((Am (-> (and A B) B)) (C (-> (-> (and Bm Cm) Cm) Dm)) (D Dm))
================================================================
tm-name          tm-9706
in-theory        9706
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> ((E and F) -> F)) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-157 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9706.         ((A or (((B and C) -> C) and A)) -> ((D -> ((E and F) -> F)) and (((B and C) -> C) and A))), M:tm-267, m:tm-157, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9707
in-theory        9707
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-267 tm-159 ((Am (and (-> (and A B) B) C)) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9707.         ((A or (((B and C) -> C) and A)) -> (D -> ((E and F) -> F))), M:tm-267, m:tm-159, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9708
in-theory        9708
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> ((E -> (F -> E)) and D)) and (((B and C) -> C) and A)))
theorem-size     27
proof            (modus-ponens tm-267 tm-183 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9708.         ((A or (((B and C) -> C) and A)) -> ((D -> ((E -> (F -> E)) and D)) and (((B and C) -> C) and A))), M:tm-267, m:tm-183, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9709
in-theory        9709
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-267 tm-184 ((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9709.         ((A or (((B and C) -> C) and A)) -> (D -> ((E -> (F -> E)) and D))), M:tm-267, m:tm-184, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-9710
in-theory        9710
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (((B and C) -> C) and A)))
theorem-size     35
proof            (modus-ponens tm-267 tm-210 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9710.         ((A or (((B and C) -> C) and A)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (((B and C) -> C) and A))), M:tm-267, m:tm-210, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9711
in-theory        9711
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-267 tm-211 ((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9711.         ((A or (((B and C) -> C) and A)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-267, m:tm-211, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-9712
in-theory        9712
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (((E and F) -> E) and D)) and (((B and C) -> C) and A)))
theorem-size     27
proof            (modus-ponens tm-267 tm-239 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9712.         ((A or (((B and C) -> C) and A)) -> ((D -> (((E and F) -> E) and D)) and (((B and C) -> C) and A))), M:tm-267, m:tm-239, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-9713
in-theory        9713
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-267 tm-240 ((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9713.         ((A or (((B and C) -> C) and A)) -> (D -> (((E and F) -> E) and D))), M:tm-267, m:tm-240, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-9714
in-theory        9714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-239 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9714.         ((A -> (((B and C) -> B) and A)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-239, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9715
in-theory        9715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E and F) -> F) and G) -> H) -> ((G or (((E and F) -> F) and G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-210 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9715.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E and F) -> F) and G) -> H) -> ((G or (((E and F) -> F) and G)) -> H))), M:tm-210, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9716
in-theory        9716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-183 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9716.         ((A -> ((B -> (C -> B)) and A)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-183, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9717
in-theory        9717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-157 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9717.         ((A -> ((B and C) -> C)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-157, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9718
in-theory        9718
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> C) and D) -> D)) -> ((D or (((B and C) -> C) and D)) -> D))
theorem-size     23
proof            (modus-ponens tm-154 tm-267 ((A (-> (and Am Bm) Bm)) (Dm Cm) (B Cm) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Cm))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9718.         ((A or ((((B and C) -> C) and D) -> D)) -> ((D or (((B and C) -> C) and D)) -> D)), M:tm-154, m:tm-267, u:((A (-> (and Am Bm) Bm)) (Dm Cm) (B Cm) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Cm)))
================================================================
tm-name          tm-9719
in-theory        9719
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-147 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9719.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-147, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9720
in-theory        9720
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and (C -> D)) -> C) or ((((A and B) -> B) and (C -> D)) -> D)) -> (((C -> D) or (((A and B) -> B) and (C -> D))) -> D))
theorem-size     39
proof            (modus-ponens tm-144 tm-267 ((A (-> (and Am Bm) Bm)) (Cm (-> B Dm)) (C Dm) (D (-> (or (-> B Dm) (and (-> (and Am Bm) Bm) (-> B Dm))) Dm))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9720.         ((((((A and B) -> B) and (C -> D)) -> C) or ((((A and B) -> B) and (C -> D)) -> D)) -> (((C -> D) or (((A and B) -> B) and (C -> D))) -> D)), M:tm-144, m:tm-267, u:((A (-> (and Am Bm) Bm)) (Cm (-> B Dm)) (C Dm) (D (-> (or (-> B Dm) (and (-> (and Am Bm) Bm) (-> B Dm))) Dm)))
================================================================
tm-name          tm-9721
in-theory        9721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-134 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9721.         ((A -> ((B and C) -> B)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-134, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9722
in-theory        9722
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> C) and D) -> ((B and C) -> C))) -> ((D or (((B and C) -> C) and D)) -> ((B and C) -> C)))
theorem-size     31
proof            (modus-ponens tm-131 tm-267 ((Dm (-> (and Am Bm) Bm)) (B Cm) (A (-> (and Am Bm) Bm)) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (-> (and Am Bm) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9722.         ((A or ((((B and C) -> C) and D) -> ((B and C) -> C))) -> ((D or (((B and C) -> C) and D)) -> ((B and C) -> C))), M:tm-131, m:tm-267, u:((Dm (-> (and Am Bm) Bm)) (B Cm) (A (-> (and Am Bm) Bm)) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (-> (and Am Bm) Bm))))
================================================================
tm-name          tm-9723
in-theory        9723
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-125 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9723.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-125, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9724
in-theory        9724
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> (A and B)) or ((((A and B) -> B) and C) -> B)) -> ((C or (((A and B) -> B) and C)) -> B))
theorem-size     33
proof            (modus-ponens tm-122 tm-267 ((A (and Am Bm)) (Dm Bm) (C Cm) (B Bm) (D (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Bm))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9724.         ((((((A and B) -> B) and C) -> (A and B)) or ((((A and B) -> B) and C) -> B)) -> ((C or (((A and B) -> B) and C)) -> B)), M:tm-122, m:tm-267, u:((A (and Am Bm)) (Dm Bm) (C Cm) (B Bm) (D (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Bm)))
================================================================
tm-name          tm-9725
in-theory        9725
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and C) -> (D -> E)) -> (((C or (((A and B) -> B) and C)) -> D) -> ((C or (((A and B) -> B) and C)) -> E)))
theorem-size     35
proof            (modus-ponens tm-114 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) (-> C D))) (B (or Cm (and (-> (and Am Bm) Bm) Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9725.         (((((A and B) -> B) and C) -> (D -> E)) -> (((C or (((A and B) -> B) and C)) -> D) -> ((C or (((A and B) -> B) and C)) -> E))), M:tm-114, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) (-> C D))) (B (or Cm (and (-> (and Am Bm) Bm) Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-9726
in-theory        9726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> F) and G) -> H) -> ((G or (((E and F) -> F) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-113 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9726.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> F) and G) -> H) -> ((G or (((E and F) -> F) and G)) -> H))), M:tm-113, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9727
in-theory        9727
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-105 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9727.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-105, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9728
in-theory        9728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-95 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9728.         (((A -> B) -> (A -> A)) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F))), M:tm-95, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9729
in-theory        9729
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) or ((((A and B) -> B) and C) -> (((A and B) -> B) and C))) -> ((C or (((A and B) -> B) and C)) -> (((A and B) -> B) and C)))
theorem-size     43
proof            (modus-ponens tm-92 tm-267 ((Dm (and (-> (and Am Bm) Bm) Cm)) (A (and (-> (and Am Bm) Bm) Cm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (and (-> (and Am Bm) Bm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9729.         ((((((A and B) -> B) and C) -> D) or ((((A and B) -> B) and C) -> (((A and B) -> B) and C))) -> ((C or (((A and B) -> B) and C)) -> (((A and B) -> B) and C))), M:tm-92, m:tm-267, u:((Dm (and (-> (and Am Bm) Bm) Cm)) (A (and (-> (and Am Bm) Bm) Cm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (and (-> (and Am Bm) Bm) Cm))))
================================================================
tm-name          tm-9730
in-theory        9730
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and C) -> D) -> (E -> ((C or (((A and B) -> B) and C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-84 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9730.         (((((A and B) -> B) and C) -> D) -> (E -> ((C or (((A and B) -> B) and C)) -> D))), M:tm-84, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-9731
in-theory        9731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-83 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9731.         ((A -> (B -> (C -> B))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-83, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9732
in-theory        9732
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> C) and D) -> (E -> (((B and C) -> C) and D)))) -> ((D or (((B and C) -> C) and D)) -> (E -> (((B and C) -> C) and D))))
theorem-size     39
proof            (modus-ponens tm-80 tm-267 ((A (and (-> (and Am Bm) Bm) Cm)) (Dm (-> B (and (-> (and Am Bm) Bm) Cm))) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (-> B (and (-> (and Am Bm) Bm) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9732.         ((A or ((((B and C) -> C) and D) -> (E -> (((B and C) -> C) and D)))) -> ((D or (((B and C) -> C) and D)) -> (E -> (((B and C) -> C) and D)))), M:tm-80, m:tm-267, u:((A (and (-> (and Am Bm) Bm) Cm)) (Dm (-> B (and (-> (and Am Bm) Bm) Cm))) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (-> B (and (-> (and Am Bm) Bm) Cm)))))
================================================================
tm-name          tm-9733
in-theory        9733
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B and C) -> C) and D) -> E) -> ((D or (((B and C) -> C) and D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-76 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9733.         (((not (not A)) -> A) and (((((B and C) -> C) and D) -> E) -> ((D or (((B and C) -> C) and D)) -> E))), M:tm-76, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9734
in-theory        9734
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A and B) -> B) and C) -> D))) or ((((A and B) -> B) and C) -> D)) -> ((C or (((A and B) -> B) and C)) -> D))
theorem-size     33
proof            (modus-ponens tm-73 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-5 tm-4)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9734.         (((not (not ((((A and B) -> B) and C) -> D))) or ((((A and B) -> B) and C) -> D)) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-73, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-9735
in-theory        9735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-69 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9735.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F))), M:tm-69, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9736
in-theory        9736
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and C) -> (C or (((A and B) -> B) and C))) -> (((((A and B) -> B) and C) or (C or (((A and B) -> B) and C))) -> (C or (((A and B) -> B) and C))))
theorem-size     45
proof            (modus-ponens tm-55 tm-267 ((A (and (-> (and Am Bm) Bm) Cm)) (Dm (or Cm (and (-> (and Am Bm) Bm) Cm))) (B (or Cm (and (-> (and Am Bm) Bm) Cm))) (C (or Cm (and (-> (and Am Bm) Bm) Cm)))))
axioms-used      (tm-2 tm-8 tm-5 tm-4)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9736.         (((((A and B) -> B) and C) -> (C or (((A and B) -> B) and C))) -> (((((A and B) -> B) and C) or (C or (((A and B) -> B) and C))) -> (C or (((A and B) -> B) and C)))), M:tm-55, m:tm-267, u:((A (and (-> (and Am Bm) Bm) Cm)) (Dm (or Cm (and (-> (and Am Bm) Bm) Cm))) (B (or Cm (and (-> (and Am Bm) Bm) Cm))) (C (or Cm (and (-> (and Am Bm) Bm) Cm))))
================================================================
tm-name          tm-9737
in-theory        9737
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-54 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9737.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-54, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9738
in-theory        9738
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> C) and D) -> (A and (((B and C) -> C) and D)))) -> ((D or (((B and C) -> C) and D)) -> (A and (((B and C) -> C) and D))))
theorem-size     39
proof            (modus-ponens tm-48 tm-267 ((A (and (-> (and Am Bm) Bm) Cm)) (Dm (and B (and (-> (and Am Bm) Bm) Cm))) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (and B (and (-> (and Am Bm) Bm) Cm))))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9738.         ((A or ((((B and C) -> C) and D) -> (A and (((B and C) -> C) and D)))) -> ((D or (((B and C) -> C) and D)) -> (A and (((B and C) -> C) and D)))), M:tm-48, m:tm-267, u:((A (and (-> (and Am Bm) Bm) Cm)) (Dm (and B (and (-> (and Am Bm) Bm) Cm))) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (and B (and (-> (and Am Bm) Bm) Cm)))))
================================================================
tm-name          tm-9739
in-theory        9739
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((((B and C) -> C) and D) -> E)) or ((((B and C) -> C) and D) -> E)) -> ((D or (((B and C) -> C) and D)) -> E))
theorem-size     33
proof            (modus-ponens tm-47 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9739.         (((A and ((((B and C) -> C) and D) -> E)) or ((((B and C) -> C) and D) -> E)) -> ((D or (((B and C) -> C) and D)) -> E)), M:tm-47, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-9740
in-theory        9740
times-derived    2
----------------------------------------------------------------
theorem          (((((((A and B) -> B) and C) -> D) and E) or ((((A and B) -> B) and C) -> D)) -> ((C or (((A and B) -> B) and C)) -> D))
theorem-size     33
proof            (modus-ponens tm-46 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-5 tm-4)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9740.         (((((((A and B) -> B) and C) -> D) and E) or ((((A and B) -> B) and C) -> D)) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-46, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-9741
in-theory        9741
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> C) and D) -> A)) -> ((D or (((B and C) -> C) and D)) -> A))
theorem-size     23
proof            (modus-ponens tm-44 tm-267 ((A (and (-> (and Am Bm) Bm) Cm)) (B Dm) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9741.         ((A or ((((B and C) -> C) and D) -> A)) -> ((D or (((B and C) -> C) and D)) -> A)), M:tm-44, m:tm-267, u:((A (and (-> (and Am Bm) Bm) Cm)) (B Dm) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-9742
in-theory        9742
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-42 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9742.         ((A -> (B or A)) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F))), M:tm-42, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9743
in-theory        9743
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-32 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9743.         ((A -> (A or B)) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F))), M:tm-32, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9744
in-theory        9744
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> B) and C) -> D) -> (((((A and B) -> B) and C) -> D) and ((C or (((A and B) -> B) and C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-24 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9744.         (((((A and B) -> B) and C) -> D) -> (((((A and B) -> B) and C) -> D) and ((C or (((A and B) -> B) and C)) -> D))), M:tm-24, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-9745
in-theory        9745
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-23 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9745.         ((A -> (B -> (A and B))) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F))), M:tm-23, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9746
in-theory        9746
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-22 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9746.         (((A and B) -> B) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F))), M:tm-22, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9747
in-theory        9747
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-21 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9747.         (((A and B) -> A) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F))), M:tm-21, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9748
in-theory        9748
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-20 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9748.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-20, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9749
in-theory        9749
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-19 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9749.         ((A -> (B -> A)) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F))), M:tm-19, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9750
in-theory        9750
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> B) and C) -> D) -> ((((A and B) -> B) and C) -> D))
theorem-size     19
proof            (modus-ponens tm-12 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9750.         (((((A and B) -> B) and C) -> D) -> ((((A and B) -> B) and C) -> D)), M:tm-12, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-9751
in-theory        9751
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> (not ((C or (((A and B) -> B) and C)) -> D))) -> (not ((((A and B) -> B) and C) -> D)))
theorem-size     33
proof            (modus-ponens tm-9 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-5 tm-4)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9751.         ((((((A and B) -> B) and C) -> D) -> (not ((C or (((A and B) -> B) and C)) -> D))) -> (not ((((A and B) -> B) and C) -> D))), M:tm-9, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-9752
in-theory        9752
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (((B and C) -> C) and A)) -> D) -> E) -> ((((((B and C) -> C) and A) -> D) or ((A or (((B and C) -> C) and A)) -> D)) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9752.         ((((A or (((B and C) -> C) and A)) -> D) -> E) -> ((((((B and C) -> C) and A) -> D) or ((A or (((B and C) -> C) and A)) -> D)) -> E)), M:tm-8, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-9753
in-theory        9753
times-derived    2
----------------------------------------------------------------
theorem          (A or (((((B and C) -> C) and D) -> E) -> ((D or (((B and C) -> C) and D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-7 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-5 tm-4)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9753.         (A or (((((B and C) -> C) and D) -> E) -> ((D or (((B and C) -> C) and D)) -> E))), M:tm-7, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9754
in-theory        9754
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-5 tm-4)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9754.         ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) or E), M:tm-6, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9755
in-theory        9755
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((((B and C) -> C) and D) -> E) -> ((D or (((B and C) -> C) and D)) -> E)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9755.         (A -> ((((((B and C) -> C) and D) -> E) -> ((D or (((B and C) -> C) and D)) -> E)) and A)), M:tm-5, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9756
in-theory        9756
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> (C or (((A and B) -> B) and C))) -> (((((A and B) -> B) and C) -> D) -> D))
theorem-size     31
proof            (modus-ponens tm-2 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (or Cm (and (-> (and Am Bm) Bm) Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-5 tm-4)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9756.         ((((((A and B) -> B) and C) -> D) -> (C or (((A and B) -> B) and C))) -> (((((A and B) -> B) and C) -> D) -> D)), M:tm-2, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (or Cm (and (-> (and Am Bm) Bm) Cm))) (C Dm))
================================================================
tm-name          tm-9757
in-theory        9757
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B and C) -> C) and D) -> E) -> ((D or (((B and C) -> C) and D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-1 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-5 tm-4)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9757.         (A -> (((((B and C) -> C) and D) -> E) -> ((D or (((B and C) -> C) and D)) -> E))), M:tm-1, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-9758
in-theory        9758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-239 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9758.         ((A -> (((B and C) -> B) and A)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-239, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9759
in-theory        9759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-210 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9759.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (((G and H) -> H) and F)))), M:tm-210, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9760
in-theory        9760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-183 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9760.         ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-183, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9761
in-theory        9761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-157 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9761.         ((A -> ((B and C) -> C)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-157, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9762
in-theory        9762
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-147 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9762.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-147, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9763
in-theory        9763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-134 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9763.         ((A -> ((B and C) -> B)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-134, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9764
in-theory        9764
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-125 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9764.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-125, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9765
in-theory        9765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-113 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9765.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (((G and H) -> H) and F)))), M:tm-113, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9766
in-theory        9766
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     31
proof            (modus-ponens tm-105 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9766.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (((F and G) -> G) and E)))), M:tm-105, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9767
in-theory        9767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-95 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9767.         (((A -> B) -> (A -> A)) and (C or (D -> (((E and F) -> F) and D)))), M:tm-95, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9768
in-theory        9768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-83 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9768.         ((A -> (B -> (C -> B))) and (D or (E -> (((F and G) -> G) and E)))), M:tm-83, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9769
in-theory        9769
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> (((D and E) -> E) and C))))
theorem-size     17
proof            (modus-ponens tm-76 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9769.         (((not (not A)) -> A) and (B or (C -> (((D and E) -> E) and C)))), M:tm-76, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9770
in-theory        9770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (((E and F) -> F) and D))))
theorem-size     23
proof            (modus-ponens tm-69 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9770.         (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (((E and F) -> F) and D)))), M:tm-69, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9771
in-theory        9771
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-54 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9771.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (((F and G) -> G) and E)))), M:tm-54, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9772
in-theory        9772
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-42 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9772.         ((A -> (B or A)) and (C or (D -> (((E and F) -> F) and D)))), M:tm-42, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9773
in-theory        9773
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-32 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9773.         ((A -> (A or B)) and (C or (D -> (((E and F) -> F) and D)))), M:tm-32, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9774
in-theory        9774
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-23 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9774.         ((A -> (B -> (A and B))) and (C or (D -> (((E and F) -> F) and D)))), M:tm-23, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9775
in-theory        9775
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-22 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9775.         (((A and B) -> B) and (C or (D -> (((E and F) -> F) and D)))), M:tm-22, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9776
in-theory        9776
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-21 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9776.         (((A and B) -> A) and (C or (D -> (((E and F) -> F) and D)))), M:tm-21, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9777
in-theory        9777
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-20 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9777.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (((F and G) -> G) and E)))), M:tm-20, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9778
in-theory        9778
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-19 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9778.         ((A -> (B -> A)) and (C or (D -> (((E and F) -> F) and D)))), M:tm-19, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9779
in-theory        9779
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C -> (((D and E) -> E) and C))))
theorem-size     13
proof            (modus-ponens tm-7 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9779.         (A or (B or (C -> (((D and E) -> E) and C)))), M:tm-7, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9780
in-theory        9780
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-6 tm-7 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9780.         ((A or (B -> (((C and D) -> D) and B))) or E), M:tm-6, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9781
in-theory        9781
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (((D and E) -> E) and C))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9781.         (A -> ((B or (C -> (((D and E) -> E) and C))) and A)), M:tm-5, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9782
in-theory        9782
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C -> (((D and E) -> E) and C))))
theorem-size     13
proof            (modus-ponens tm-1 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-1 tm-7 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9782.         (A -> (B or (C -> (((D and E) -> E) and C)))), M:tm-1, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-9783
in-theory        9783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-239 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9783.         ((A -> (((B and C) -> B) and A)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-239, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9784
in-theory        9784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (((F and G) -> G) and E)) or H))
theorem-size     29
proof            (modus-ponens tm-210 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9784.         ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (((F and G) -> G) and E)) or H)), M:tm-210, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9785
in-theory        9785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-183 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9785.         ((A -> ((B -> (C -> B)) and A)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-183, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9786
in-theory        9786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-157 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9786.         ((A -> ((B and C) -> C)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-157, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9787
in-theory        9787
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-147 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9787.         ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-147, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9788
in-theory        9788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-134 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9788.         ((A -> ((B and C) -> B)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-134, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9789
in-theory        9789
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-125 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9789.         (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-125, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9790
in-theory        9790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (((F and G) -> G) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-113 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9790.         ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (((F and G) -> G) and E)) or H)), M:tm-113, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9791
in-theory        9791
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     31
proof            (modus-ponens tm-105 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9791.         ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-105, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9792
in-theory        9792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (((D and E) -> E) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-95 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9792.         (((A -> B) -> (A -> A)) and ((C -> (((D and E) -> E) and C)) or F)), M:tm-95, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9793
in-theory        9793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-83 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9793.         ((A -> (B -> (C -> B))) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-83, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9794
in-theory        9794
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (((C and D) -> D) and B)) or E))
theorem-size     17
proof            (modus-ponens tm-76 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9794.         (((not (not A)) -> A) and ((B -> (((C and D) -> D) and B)) or E)), M:tm-76, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9795
in-theory        9795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (((D and E) -> E) and C)) or F))
theorem-size     23
proof            (modus-ponens tm-69 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9795.         (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (((D and E) -> E) and C)) or F)), M:tm-69, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9796
in-theory        9796
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-54 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9796.         (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-54, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9797
in-theory        9797
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (((D and E) -> E) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-42 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9797.         ((A -> (B or A)) and ((C -> (((D and E) -> E) and C)) or F)), M:tm-42, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9798
in-theory        9798
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (((D and E) -> E) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-32 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9798.         ((A -> (A or B)) and ((C -> (((D and E) -> E) and C)) or F)), M:tm-32, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9799
in-theory        9799
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (((D and E) -> E) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-23 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9799.         ((A -> (B -> (A and B))) and ((C -> (((D and E) -> E) and C)) or F)), M:tm-23, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9800
in-theory        9800
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (((D and E) -> E) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-22 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9800.         (((A and B) -> B) and ((C -> (((D and E) -> E) and C)) or F)), M:tm-22, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9801
in-theory        9801
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (((D and E) -> E) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-21 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9801.         (((A and B) -> A) and ((C -> (((D and E) -> E) and C)) or F)), M:tm-21, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9802
in-theory        9802
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-20 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9802.         (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-20, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9803
in-theory        9803
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (((D and E) -> E) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-19 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9803.         ((A -> (B -> A)) and ((C -> (((D and E) -> E) and C)) or F)), M:tm-19, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9804
in-theory        9804
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> (((C and D) -> D) and B)) or E))
theorem-size     13
proof            (modus-ponens tm-7 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-7 tm-6 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9804.         (A or ((B -> (((C and D) -> D) and B)) or E)), M:tm-7, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9805
in-theory        9805
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9805.         (((A -> (((B and C) -> C) and A)) or D) or E), M:tm-6, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9806
in-theory        9806
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (((C and D) -> D) and B)) or E) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9806.         (A -> (((B -> (((C and D) -> D) and B)) or E) and A)), M:tm-5, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9807
in-theory        9807
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> (((C and D) -> D) and B)) or E))
theorem-size     13
proof            (modus-ponens tm-1 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-1 tm-6 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9807.         (A -> ((B -> (((C and D) -> D) and B)) or E)), M:tm-1, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-9808
in-theory        9808
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-270 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-9808.         ((A -> (((B and C) -> C) and A)) and (D -> (E -> D))), M:tm-270, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-9809
in-theory        9809
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9809.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-270, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-9810
in-theory        9810
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-270 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-9810.         ((A -> (((B and C) -> C) and A)) and ((D and E) -> D)), M:tm-270, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-9811
in-theory        9811
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-270 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9811.         ((A -> (((B and C) -> C) and A)) and ((D and E) -> E)), M:tm-270, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-9812
in-theory        9812
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-270 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9812.         ((A -> (((B and C) -> C) and A)) and (D -> (E -> (D and E)))), M:tm-270, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-9813
in-theory        9813
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-270 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-9813.         ((A -> (((B and C) -> C) and A)) and (D -> (D or E))), M:tm-270, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-9814
in-theory        9814
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-270 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-9814.         ((A -> (((B and C) -> C) and A)) and (D -> (E or D))), M:tm-270, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-9815
in-theory        9815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9815.         ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-270, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-9816
in-theory        9816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-270 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-9816.         ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-270, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-9817
in-theory        9817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-270 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-4 tm-10)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-9817.         ((A -> (((B and C) -> C) and A)) and ((not (not D)) -> D)), M:tm-270, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-9818
in-theory        9818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-270 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9818.         ((A -> (((B and C) -> C) and A)) and (D -> (E -> (F -> E)))), M:tm-270, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-9819
in-theory        9819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-270 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9819.         ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (D -> D))), M:tm-270, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-9820
in-theory        9820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-270 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-9820.         ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-270, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-9821
in-theory        9821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9821.         ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-270, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-9822
in-theory        9822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-270 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-9822.         ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-270, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-9823
in-theory        9823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-270 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9823.         ((A -> (((B and C) -> C) and A)) and (D -> ((E and F) -> E))), M:tm-270, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-9824
in-theory        9824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-270 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-9824.         ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-270, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-9825
in-theory        9825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-270 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9825.         ((A -> (((B and C) -> C) and A)) and (D -> ((E and F) -> F))), M:tm-270, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-9826
in-theory        9826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-270 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9826.         ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> E)) and D))), M:tm-270, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-9827
in-theory        9827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-270 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9827.         ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-270, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-9828
in-theory        9828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-270 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9828.         ((A -> (((B and C) -> C) and A)) and (D -> (((E and F) -> E) and D))), M:tm-270, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-9829
in-theory        9829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-270 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9829.         ((A -> (((B and C) -> C) and A)) and (D -> (((E and F) -> F) and D))), M:tm-270, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-9830
in-theory        9830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9830.         ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-270, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-9831
in-theory        9831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-270 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9831.         ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (D -> (D and E)))), M:tm-270, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-9832
in-theory        9832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9832.         ((A -> (((B and C) -> C) and A)) and (D -> (E -> (F -> (E and F))))), M:tm-270, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-9833
in-theory        9833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-270 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9833.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) or F)), M:tm-270, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-9834
in-theory        9834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-270 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9834.         ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-270, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-9835
in-theory        9835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-270 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9835.         ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) or F)), M:tm-270, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-9836
in-theory        9836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-270 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9836.         ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) or F)), M:tm-270, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-9837
in-theory        9837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-270 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9837.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) or F)), M:tm-270, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-9838
in-theory        9838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-270 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9838.         ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) or F)), M:tm-270, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-9839
in-theory        9839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-270 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9839.         ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (E or F)) and D))), M:tm-270, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-9840
in-theory        9840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-270 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9840.         ((A -> (((B and C) -> C) and A)) and (D -> (E -> (E or F)))), M:tm-270, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-9841
in-theory        9841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-270 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9841.         ((A -> (((B and C) -> C) and A)) and (D or (E -> (F -> E)))), M:tm-270, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-9842
in-theory        9842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9842.         ((A -> (((B and C) -> C) and A)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-270, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-9843
in-theory        9843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-270 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9843.         ((A -> (((B and C) -> C) and A)) and (D or ((E and F) -> E))), M:tm-270, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-9844
in-theory        9844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-270 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9844.         ((A -> (((B and C) -> C) and A)) and (D or ((E and F) -> F))), M:tm-270, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-9845
in-theory        9845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9845.         ((A -> (((B and C) -> C) and A)) and (D or (E -> (F -> (E and F))))), M:tm-270, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-9846
in-theory        9846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-270 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9846.         ((A -> (((B and C) -> C) and A)) and (D or (E -> (E or F)))), M:tm-270, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-9847
in-theory        9847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-270 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9847.         ((A -> (((B and C) -> C) and A)) and (D or (E -> (F or E)))), M:tm-270, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-9848
in-theory        9848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-270 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9848.         ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) or F)), M:tm-270, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-9849
in-theory        9849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-270 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9849.         ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F or E)) and D))), M:tm-270, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-9850
in-theory        9850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-270 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9850.         ((A -> (((B and C) -> C) and A)) and (D -> (E -> (F or E)))), M:tm-270, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-9851
in-theory        9851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-270 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9851.         ((A -> (((B and C) -> C) and A)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-270, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-9852
in-theory        9852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-270 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9852.         ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-270, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-9853
in-theory        9853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-270 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9853.         ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-270, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-9854
in-theory        9854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-270 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9854.         ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-270, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-9855
in-theory        9855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-270 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9855.         ((A -> (((B and C) -> C) and A)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-270, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-9856
in-theory        9856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-270 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9856.         ((A -> (((B and C) -> C) and A)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-270, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-9857
in-theory        9857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-270 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9857.         ((A -> (((B and C) -> C) and A)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-270, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-9858
in-theory        9858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-270 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9858.         ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-270, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-9859
in-theory        9859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9859.         ((A -> (((B and C) -> C) and A)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-270, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-9860
in-theory        9860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-270 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9860.         ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-270, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-9861
in-theory        9861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-270 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9861.         ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-270, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-9862
in-theory        9862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-270 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-9862.         ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-270, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-9863
in-theory        9863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9863.         ((A -> (((B and C) -> C) and A)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-270, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-9864
in-theory        9864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-270 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9864.         ((A -> (((B and C) -> C) and A)) and ((D -> (not (E -> D))) -> (not D))), M:tm-270, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-9865
in-theory        9865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-9 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9865.         ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-270, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-9866
in-theory        9866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-270 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9866.         ((A -> (((B and C) -> C) and A)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-270, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-9867
in-theory        9867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-270 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9867.         ((A -> (((B and C) -> C) and A)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-270, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-9868
in-theory        9868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9868.         ((A -> (((B and C) -> C) and A)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-270, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-9869
in-theory        9869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-270 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9869.         ((A -> (((B and C) -> C) and A)) and ((D -> (not (D or E))) -> (not D))), M:tm-270, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-9870
in-theory        9870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-270 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9870.         ((A -> (((B and C) -> C) and A)) and ((D -> (not (E or D))) -> (not D))), M:tm-270, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-9871
in-theory        9871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-270 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9871.         ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-270, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-9872
in-theory        9872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-270 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-9872.         ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-270, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-9873
in-theory        9873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-270 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-9)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-9873.         ((A -> (((B and C) -> C) and A)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-270, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-9874
in-theory        9874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9874.         ((A -> (((B and C) -> C) and A)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-270, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-9875
in-theory        9875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     23
proof            (modus-ponens tm-270 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-4 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9875.         ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-270, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-9876
in-theory        9876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     25
proof            (modus-ponens tm-270 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9876.         ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-270, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-9877
in-theory        9877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-270 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-9877.         ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-270, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-9878
in-theory        9878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9878.         ((A -> (((B and C) -> C) and A)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-270, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-9879
in-theory        9879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     21
proof            (modus-ponens tm-270 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-4 tm-9 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9879.         ((A -> (((B and C) -> C) and A)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-270, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-9880
in-theory        9880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-270 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9880.         ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-270, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-9881
in-theory        9881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-270 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9881.         ((A -> (((B and C) -> C) and A)) and (D or ((not (not E)) -> E))), M:tm-270, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-9882
in-theory        9882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((not (not D)) -> D) or E))
theorem-size     17
proof            (modus-ponens tm-270 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-4 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9882.         ((A -> (((B and C) -> C) and A)) and (((not (not D)) -> D) or E)), M:tm-270, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-9883
in-theory        9883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-270 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-4 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9883.         ((A -> (((B and C) -> C) and A)) and (D -> (((not (not E)) -> E) and D))), M:tm-270, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-9884
in-theory        9884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     25
proof            (modus-ponens tm-270 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-9884.         ((A -> (((B and C) -> C) and A)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-270, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-9885
in-theory        9885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-270 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9885.         ((A -> (((B and C) -> C) and A)) and (D -> ((not (not E)) -> E))), M:tm-270, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-9886
in-theory        9886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9886.         ((A -> (((B and C) -> C) and A)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-270, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-9887
in-theory        9887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-270 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9887.         ((A -> (((B and C) -> C) and A)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-270, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-9888
in-theory        9888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9888.         ((A -> (((B and C) -> C) and A)) and (D or (E -> (F -> (G -> F))))), M:tm-270, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-9889
in-theory        9889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9889.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (F -> E))) or G)), M:tm-270, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-9890
in-theory        9890
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9890.         ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-270, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-9891
in-theory        9891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-270 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9891.         ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (D -> (F -> E)))), M:tm-270, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-9892
in-theory        9892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9892.         ((A -> (((B and C) -> C) and A)) and (D -> (E -> (F -> (G -> F))))), M:tm-270, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-9893
in-theory        9893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> D))
theorem-size     13
proof            (modus-ponens tm-270 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9893.         ((A -> (((B and C) -> C) and A)) and (D -> D)), M:tm-270, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-9894
in-theory        9894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9894.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-270, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-9895
in-theory        9895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D and E) -> (D and E)))
theorem-size     17
proof            (modus-ponens tm-270 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9895.         ((A -> (((B and C) -> C) and A)) and ((D and E) -> (D and E))), M:tm-270, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-9896
in-theory        9896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-270 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9896.         ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (D -> E))), M:tm-270, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-9897
in-theory        9897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((not (not D)) -> (not (not D))))
theorem-size     17
proof            (modus-ponens tm-270 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9897.         ((A -> (((B and C) -> C) and A)) and ((not (not D)) -> (not (not D)))), M:tm-270, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-9898
in-theory        9898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-270 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9898.         ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-270, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-9899
in-theory        9899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-270 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9899.         ((A -> (((B and C) -> C) and A)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-270, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-9900
in-theory        9900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-270 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9900.         ((A -> (((B and C) -> C) and A)) and (D or ((E -> F) -> (E -> E)))), M:tm-270, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-9901
in-theory        9901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (D -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-270 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-4 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9901.         ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (D -> D)) or F)), M:tm-270, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-9902
in-theory        9902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9902.         ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-270, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-9903
in-theory        9903
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-9903.         ((A -> (((B and C) -> C) and A)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-270, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-9904
in-theory        9904
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-270 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9904.         ((A -> (((B and C) -> C) and A)) and (D -> ((E -> F) -> (E -> E)))), M:tm-270, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-9905
in-theory        9905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-9905.         ((A -> (((B and C) -> C) and A)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-270, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-9906
in-theory        9906
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-270 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-9906.         ((A -> (((B and C) -> C) and A)) and ((D -> (D -> E)) -> (D -> E))), M:tm-270, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-9907
in-theory        9907
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-270 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-9907.         ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-270, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-9908
in-theory        9908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     41
proof            (modus-ponens tm-270 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-9 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-9908.         ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-270, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-9909
in-theory        9909
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-270 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-9909.         ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-270, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-9910
in-theory        9910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9910.         ((A -> (((B and C) -> C) and A)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-270, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-9911
in-theory        9911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-270 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9911.         ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-270, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-9912
in-theory        9912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-270 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9912.         ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-270, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-9913
in-theory        9913
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-270 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-9913.         ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-270, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-9914
in-theory        9914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9914.         ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-270, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-9915
in-theory        9915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-270 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-9915.         ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-270, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-9916
in-theory        9916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-270 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9916.         ((A -> (((B and C) -> C) and A)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-270, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-9917
in-theory        9917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     43
proof            (modus-ponens tm-270 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9917.         ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-270, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-9918
in-theory        9918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-270 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9918.         ((A -> (((B and C) -> C) and A)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-270, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-9919
in-theory        9919
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-270 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-4 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9919.         ((A -> (((B and C) -> C) and A)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-270, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-9920
in-theory        9920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-270 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9920.         ((A -> (((B and C) -> C) and A)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-270, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-9921
in-theory        9921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-270 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-9921.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-270, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-9922
in-theory        9922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-270 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9922.         ((A -> (((B and C) -> C) and A)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-270, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-9923
in-theory        9923
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) and D) -> E))
theorem-size     17
proof            (modus-ponens tm-270 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-9923.         ((A -> (((B and C) -> C) and A)) and (((D -> E) and D) -> E)), M:tm-270, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-9924
in-theory        9924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-270 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-9924.         ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-270, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-9925
in-theory        9925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-270 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9925.         ((A -> (((B and C) -> C) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-270, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-9926
in-theory        9926
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-270 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-9926.         ((A -> (((B and C) -> C) and A)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-270, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-9927
in-theory        9927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     25
proof            (modus-ponens tm-270 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-9927.         ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-270, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-9928
in-theory        9928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     35
proof            (modus-ponens tm-270 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-4 tm-9 tm-2 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-9928.         ((A -> (((B and C) -> C) and A)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-270, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-9929
in-theory        9929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     37
proof            (modus-ponens tm-270 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-9929.         ((A -> (((B and C) -> C) and A)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-270, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-9930
in-theory        9930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-270 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9930.         ((A -> (((B and C) -> C) and A)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-270, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-9931
in-theory        9931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-270 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9931.         ((A -> (((B and C) -> C) and A)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-270, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-9932
in-theory        9932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-270 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9932.         ((A -> (((B and C) -> C) and A)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-270, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-9933
in-theory        9933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     33
proof            (modus-ponens tm-270 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-9933.         ((A -> (((B and C) -> C) and A)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-270, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-9934
in-theory        9934
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-270 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9934.         ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-270, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-9935
in-theory        9935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-270 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-9935.         ((A -> (((B and C) -> C) and A)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-270, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-9936
in-theory        9936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-270 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-9936.         ((A -> (((B and C) -> C) and A)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-270, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-9937
in-theory        9937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9937.         ((A -> (((B and C) -> C) and A)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-270, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-9938
in-theory        9938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     27
proof            (modus-ponens tm-270 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9938.         ((A -> (((B and C) -> C) and A)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-270, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-9939
in-theory        9939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-270 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9939.         ((A -> (((B and C) -> C) and A)) and (D or (E -> ((F and G) -> F)))), M:tm-270, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-9940
in-theory        9940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9940.         ((A -> (((B and C) -> C) and A)) and ((D -> ((E and F) -> E)) or G)), M:tm-270, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-9941
in-theory        9941
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9941.         ((A -> (((B and C) -> C) and A)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-270, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-9942
in-theory        9942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-270 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-9942.         ((A -> (((B and C) -> C) and A)) and ((D -> (E and F)) -> (D -> E))), M:tm-270, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-9943
in-theory        9943
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-270 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9943.         ((A -> (((B and C) -> C) and A)) and (D -> (E -> ((F and G) -> F)))), M:tm-270, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-9944
in-theory        9944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D and (D -> E)) -> E))
theorem-size     17
proof            (modus-ponens tm-270 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-9944.         ((A -> (((B and C) -> C) and A)) and ((D and (D -> E)) -> E)), M:tm-270, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-9945
in-theory        9945
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-270 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-9945.         ((A -> (((B and C) -> C) and A)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-270, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-9946
in-theory        9946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-270 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9946.         ((A -> (((B and C) -> C) and A)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-270, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-9947
in-theory        9947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-270 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-9947.         ((A -> (((B and C) -> C) and A)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-270, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-9948
in-theory        9948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-270 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-9948.         ((A -> (((B and C) -> C) and A)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-270, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-9949
in-theory        9949
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     25
proof            (modus-ponens tm-270 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-9949.         ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-270, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-9950
in-theory        9950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     35
proof            (modus-ponens tm-270 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-9950.         ((A -> (((B and C) -> C) and A)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-270, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-9951
in-theory        9951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-270 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-9951.         ((A -> (((B and C) -> C) and A)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-270, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-9952
in-theory        9952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-270 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9952.         ((A -> (((B and C) -> C) and A)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-270, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-9953
in-theory        9953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-270 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9953.         ((A -> (((B and C) -> C) and A)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-270, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-9954
in-theory        9954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-270 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9954.         ((A -> (((B and C) -> C) and A)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-270, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-9955
in-theory        9955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     33
proof            (modus-ponens tm-270 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-9955.         ((A -> (((B and C) -> C) and A)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-270, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-9956
in-theory        9956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-270 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9956.         ((A -> (((B and C) -> C) and A)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-270, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-9957
in-theory        9957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-270 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-9957.         ((A -> (((B and C) -> C) and A)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-270, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-9958
in-theory        9958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-270 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-9958.         ((A -> (((B and C) -> C) and A)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-270, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-9959
in-theory        9959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-270 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-9959.         ((A -> (((B and C) -> C) and A)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-270, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-9960
in-theory        9960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9960.         ((A -> (((B and C) -> C) and A)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-270, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-9961
in-theory        9961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-270 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9961.         ((A -> (((B and C) -> C) and A)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-270, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-9962
in-theory        9962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-270 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9962.         ((A -> (((B and C) -> C) and A)) and (D or (E -> ((F and G) -> G)))), M:tm-270, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-9963
in-theory        9963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9963.         ((A -> (((B and C) -> C) and A)) and ((D -> ((E and F) -> F)) or G)), M:tm-270, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-9964
in-theory        9964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9964.         ((A -> (((B and C) -> C) and A)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-270, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-9965
in-theory        9965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-270 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-9965.         ((A -> (((B and C) -> C) and A)) and ((D -> (E and F)) -> (D -> F))), M:tm-270, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-9966
in-theory        9966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-270 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9966.         ((A -> (((B and C) -> C) and A)) and (D -> (E -> ((F and G) -> G)))), M:tm-270, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-9967
in-theory        9967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9967.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-270, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-9968
in-theory        9968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9968.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-270, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-9969
in-theory        9969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9969.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-270, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-9970
in-theory        9970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-270 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9970.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-270, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-9971
in-theory        9971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9971.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-270, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-9972
in-theory        9972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-270 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9972.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-270, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-9973
in-theory        9973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9973.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-270, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-9974
in-theory        9974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9974.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-270, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-9975
in-theory        9975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-270 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-9975.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-270, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-9976
in-theory        9976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9976.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-270, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-9977
in-theory        9977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9977.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-270, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-9978
in-theory        9978
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9978.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-270, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-9979
in-theory        9979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-270 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9979.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-270, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-9980
in-theory        9980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9980.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-270, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-9981
in-theory        9981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-270 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9981.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-270, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-9982
in-theory        9982
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-270 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9982.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-270, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-9983
in-theory        9983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-270 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9983.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-270, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-9984
in-theory        9984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-270 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9984.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-270, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-9985
in-theory        9985
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9985.         ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-270, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-9986
in-theory        9986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9986.         ((A -> (((B and C) -> C) and A)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-270, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-9987
in-theory        9987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-270 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9987.         ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-270, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-9988
in-theory        9988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-270 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9988.         ((A -> (((B and C) -> C) and A)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-270, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-9989
in-theory        9989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-270 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9989.         ((A -> (((B and C) -> C) and A)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-270, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-9990
in-theory        9990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9990.         ((A -> (((B and C) -> C) and A)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-270, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-9991
in-theory        9991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-270 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9991.         ((A -> (((B and C) -> C) and A)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-270, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-9992
in-theory        9992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-270 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9992.         ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-270, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-9993
in-theory        9993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9993.         ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-270, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-9994
in-theory        9994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-270 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9994.         ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-270, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-9995
in-theory        9995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-270 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9995.         ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-270, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-9996
in-theory        9996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9996.         ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-270, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-9997
in-theory        9997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9997.         ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-270, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-9998
in-theory        9998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-270 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9998.         ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-270, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-9999
in-theory        9999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9999.         ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-270, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-10000
in-theory        10000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-270 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10000.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-270, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-10001
in-theory        10001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-270 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10001.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-270, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-10002
in-theory        10002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10002.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-270, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-10003
in-theory        10003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-270 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10003.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-270, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-10004
in-theory        10004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-270 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10004.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-270, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-10005
in-theory        10005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-270 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10005.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-270, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-10006
in-theory        10006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-270 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10006.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-270, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-10007
in-theory        10007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-270 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10007.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-270, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-10008
in-theory        10008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-270 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10008.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-270, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-10009
in-theory        10009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-270 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10009.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-270, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-10010
in-theory        10010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-270 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10010.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-270, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-10011
in-theory        10011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-270 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10011.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-270, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-10012
in-theory        10012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-270 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10012.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-270, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10013
in-theory        10013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-270 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-10013.        ((A -> (((B and C) -> C) and A)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-270, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-10014
in-theory        10014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-270 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-10014.        ((A -> (((B and C) -> C) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-270, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-10015
in-theory        10015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-270 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10015.        ((A -> (((B and C) -> C) and A)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-270, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-10016
in-theory        10016
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     29
proof            (modus-ponens tm-270 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10016.        ((A -> (((B and C) -> C) and A)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-270, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-10017
in-theory        10017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-270 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10017.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-270, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-10018
in-theory        10018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-270 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10018.        ((A -> (((B and C) -> C) and A)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-270, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-10019
in-theory        10019
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10019.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-270, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10020
in-theory        10020
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10020.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-270, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10021
in-theory        10021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10021.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-270, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10022
in-theory        10022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-270 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10022.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-270, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10023
in-theory        10023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10023.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-270, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10024
in-theory        10024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-270 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10024.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-270, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10025
in-theory        10025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10025.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-270, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10026
in-theory        10026
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10026.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-270, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10027
in-theory        10027
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-270 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10027.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-270, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10028
in-theory        10028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10028.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-270, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10029
in-theory        10029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10029.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-270, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10030
in-theory        10030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10030.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-270, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10031
in-theory        10031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-270 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10031.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-270, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10032
in-theory        10032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10032.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-270, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10033
in-theory        10033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-270 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10033.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-270, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10034
in-theory        10034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-270 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10034.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-270, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10035
in-theory        10035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-270 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10035.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-270, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10036
in-theory        10036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-270 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10036.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-270, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10037
in-theory        10037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10037.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-270, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10038
in-theory        10038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-270 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10038.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-270, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10039
in-theory        10039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10039.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-270, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10040
in-theory        10040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-270 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10040.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-270, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-10041
in-theory        10041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10041.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-270, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10042
in-theory        10042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-10042.        ((A -> (((B and C) -> C) and A)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-270, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-10043
in-theory        10043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-270 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-10043.        ((A -> (((B and C) -> C) and A)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-270, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-10044
in-theory        10044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-270 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10044.        ((A -> (((B and C) -> C) and A)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-270, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-10045
in-theory        10045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-270 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10045.        ((A -> (((B and C) -> C) and A)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-270, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-10046
in-theory        10046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10046.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-270, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-10047
in-theory        10047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-270 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10047.        ((A -> (((B and C) -> C) and A)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-270, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-10048
in-theory        10048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10048.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-270, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10049
in-theory        10049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10049.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-270, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10050
in-theory        10050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10050.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-270, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10051
in-theory        10051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-270 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10051.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-270, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10052
in-theory        10052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10052.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-270, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10053
in-theory        10053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-270 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10053.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-270, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10054
in-theory        10054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10054.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-270, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10055
in-theory        10055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10055.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-270, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10056
in-theory        10056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-270 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10056.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-270, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10057
in-theory        10057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10057.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-270, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10058
in-theory        10058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10058.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-270, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10059
in-theory        10059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10059.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-270, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10060
in-theory        10060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-270 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10060.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-270, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10061
in-theory        10061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10061.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-270, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10062
in-theory        10062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-270 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10062.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-270, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10063
in-theory        10063
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-270 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10063.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-270, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10064
in-theory        10064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-270 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10064.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-270, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10065
in-theory        10065
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-270 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10065.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-270, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10066
in-theory        10066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10066.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-270, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10067
in-theory        10067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-270 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10067.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-270, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10068
in-theory        10068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10068.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-270, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10069
in-theory        10069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10069.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-270, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10070
in-theory        10070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10070.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-270, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10071
in-theory        10071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-270 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10071.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-270, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-10072
in-theory        10072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10072.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-270, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10073
in-theory        10073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-10073.        ((A -> (((B and C) -> C) and A)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-270, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-10074
in-theory        10074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-270 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-10074.        ((A -> (((B and C) -> C) and A)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-270, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-10075
in-theory        10075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-270 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10075.        ((A -> (((B and C) -> C) and A)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-270, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10076
in-theory        10076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-270 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10076.        ((A -> (((B and C) -> C) and A)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-270, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-10077
in-theory        10077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10077.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-270, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10078
in-theory        10078
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (((E and F) -> F) and D)) and (((B and C) -> C) and A)))
theorem-size     27
proof            (modus-ponens tm-267 tm-270 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10078.        ((A or (((B and C) -> C) and A)) -> ((D -> (((E and F) -> F) and D)) and (((B and C) -> C) and A))), M:tm-267, m:tm-270, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-10079
in-theory        10079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10079.        ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-239, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10080
in-theory        10080
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (((E and F) -> F) and D)) and (((B and C) -> B) and A)))
theorem-size     27
proof            (modus-ponens tm-236 tm-270 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10080.        ((A or (((B and C) -> B) and A)) -> ((D -> (((E and F) -> F) and D)) and (((B and C) -> B) and A))), M:tm-236, m:tm-270, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-10081
in-theory        10081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (((G and H) -> H) and F)) and E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10081.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (((G and H) -> H) and F)) and E))), M:tm-210, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10082
in-theory        10082
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (((F and G) -> G) and E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     43
proof            (modus-ponens tm-207 tm-270 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10082.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (((F and G) -> G) and E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-270, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-10083
in-theory        10083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10083.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-183, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10084
in-theory        10084
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (((E and F) -> F) and D)) and ((B -> (C -> B)) and A)))
theorem-size     27
proof            (modus-ponens tm-180 tm-270 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10084.        ((A or ((B -> (C -> B)) and A)) -> ((D -> (((E and F) -> F) and D)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-270, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-10085
in-theory        10085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10085.        ((A -> ((B and C) -> C)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-157, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10086
in-theory        10086
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (((E and F) -> F) and D)) and ((B and C) -> C)))
theorem-size     23
proof            (modus-ponens tm-154 tm-270 ((Am (-> (and A B) B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10086.        ((A or ((B and C) -> C)) -> ((D -> (((E and F) -> F) and D)) and ((B and C) -> C))), M:tm-154, m:tm-270, u:((Am (-> (and A B) B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (and A B) B))))
================================================================
tm-name          tm-10087
in-theory        10087
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10087.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-147, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10088
in-theory        10088
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (((E and F) -> F) and D)) and ((A and (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-144 tm-270 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10088.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (((E and F) -> F) and D)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-270, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-10089
in-theory        10089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10089.        ((A -> ((B and C) -> B)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-134, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10090
in-theory        10090
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (((E and F) -> F) and D)) and ((B and C) -> B)))
theorem-size     23
proof            (modus-ponens tm-131 tm-270 ((Am (-> (and A B) A)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10090.        ((A or ((B and C) -> B)) -> ((D -> (((E and F) -> F) and D)) and ((B and C) -> B))), M:tm-131, m:tm-270, u:((Am (-> (and A B) A)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (and A B) A))))
================================================================
tm-name          tm-10091
in-theory        10091
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10091.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-125, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10092
in-theory        10092
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (((E and F) -> F) and D)) and (((A -> B) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-122 tm-270 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10092.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (((E and F) -> F) and D)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-270, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-10093
in-theory        10093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (((G and H) -> H) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10093.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (((G and H) -> H) and F)) and E))), M:tm-113, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10094
in-theory        10094
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (((F and G) -> G) and E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     39
proof            (modus-ponens tm-110 tm-270 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10094.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (((F and G) -> G) and E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-270, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-10095
in-theory        10095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10095.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-105, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10096
in-theory        10096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (((E and F) -> F) and D)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-102 tm-270 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10096.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (((E and F) -> F) and D)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-270, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-10097
in-theory        10097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (((E and F) -> F) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10097.        (((A -> B) -> (A -> A)) and (C -> ((D -> (((E and F) -> F) and D)) and C))), M:tm-95, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10098
in-theory        10098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (((D and E) -> E) and C)) and (A -> A)))
theorem-size     21
proof            (modus-ponens tm-92 tm-270 ((Am (-> A A)) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10098.        (((A -> B) or (A -> A)) -> ((C -> (((D and E) -> E) and C)) and (A -> A))), M:tm-92, m:tm-270, u:((Am (-> A A)) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A A))))
================================================================
tm-name          tm-10099
in-theory        10099
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (((D and E) -> E) and C)) and A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10099.        (A -> (B -> ((C -> (((D and E) -> E) and C)) and A))), M:tm-84, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-10100
in-theory        10100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10100.        ((A -> (B -> (C -> B))) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-83, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10101
in-theory        10101
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (((E and F) -> F) and D)) and (B -> (C -> B))))
theorem-size     23
proof            (modus-ponens tm-80 tm-270 ((Am (-> A (-> B A))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10101.        ((A or (B -> (C -> B))) -> ((D -> (((E and F) -> F) and D)) and (B -> (C -> B)))), M:tm-80, m:tm-270, u:((Am (-> A (-> B A))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A (-> B A)))))
================================================================
tm-name          tm-10102
in-theory        10102
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (((D and E) -> E) and C)) and B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-10 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10102.        (((not (not A)) -> A) and (B -> ((C -> (((D and E) -> E) and C)) and B))), M:tm-76, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10103
in-theory        10103
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (((C and D) -> D) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-73 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10103.        (((not (not A)) or A) -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-73, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-10104
in-theory        10104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (((E and F) -> F) and D)) and C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10104.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (((E and F) -> F) and D)) and C))), M:tm-69, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10105
in-theory        10105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (((D and E) -> E) and C)) and ((A -> (not B)) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-66 tm-270 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-4)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10105.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (((D and E) -> E) and C)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-270, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-10106
in-theory        10106
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10106.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-54, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10107
in-theory        10107
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (((E and F) -> F) and D)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-51 tm-270 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10107.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (((E and F) -> F) and D)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-270, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-10108
in-theory        10108
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (((D and E) -> E) and C)) and (B or A)))
theorem-size     19
proof            (modus-ponens tm-50 tm-270 ((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10108.        ((A or (B or A)) -> ((C -> (((D and E) -> E) and C)) and (B or A))), M:tm-50, m:tm-270, u:((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (or A B))))
================================================================
tm-name          tm-10109
in-theory        10109
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (((D and E) -> E) and C)) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-49 tm-270 ((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10109.        ((A or (A or B)) -> ((C -> (((D and E) -> E) and C)) and (A or B))), M:tm-49, m:tm-270, u:((Am (or A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (or A B))))
================================================================
tm-name          tm-10110
in-theory        10110
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (((D and E) -> E) and C)) and (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-48 tm-270 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10110.        ((A or (B -> (A and B))) -> ((C -> (((D and E) -> E) and C)) and (B -> (A and B)))), M:tm-48, m:tm-270, u:((Am (-> A (and B A))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-10111
in-theory        10111
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (((D and E) -> E) and C)) and B))
theorem-size     17
proof            (modus-ponens tm-47 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10111.        (((A and B) or B) -> ((C -> (((D and E) -> E) and C)) and B)), M:tm-47, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-10112
in-theory        10112
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (((D and E) -> E) and C)) and A))
theorem-size     17
proof            (modus-ponens tm-46 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10112.        (((A and B) or A) -> ((C -> (((D and E) -> E) and C)) and A)), M:tm-46, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-10113
in-theory        10113
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((E and F) -> F) and D)) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-45 tm-270 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10113.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((E and F) -> F) and D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-270, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-10114
in-theory        10114
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (((D and E) -> E) and C)) and (B -> A)))
theorem-size     19
proof            (modus-ponens tm-44 tm-270 ((Am (-> A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10114.        ((A or (B -> A)) -> ((C -> (((D and E) -> E) and C)) and (B -> A))), M:tm-44, m:tm-270, u:((Am (-> A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A B))))
================================================================
tm-name          tm-10115
in-theory        10115
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (((E and F) -> F) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10115.        ((A -> (B or A)) and (C -> ((D -> (((E and F) -> F) and D)) and C))), M:tm-42, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10116
in-theory        10116
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (((E and F) -> F) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10116.        ((A -> (A or B)) and (C -> ((D -> (((E and F) -> F) and D)) and C))), M:tm-32, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10117
in-theory        10117
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (((C and D) -> D) and B)) and A)))
theorem-size     15
proof            (modus-ponens tm-24 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10117.        (A -> (A and ((B -> (((C and D) -> D) and B)) and A))), M:tm-24, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-10118
in-theory        10118
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (((E and F) -> F) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10118.        ((A -> (B -> (A and B))) and (C -> ((D -> (((E and F) -> F) and D)) and C))), M:tm-23, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10119
in-theory        10119
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (((E and F) -> F) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10119.        (((A and B) -> B) and (C -> ((D -> (((E and F) -> F) and D)) and C))), M:tm-22, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10120
in-theory        10120
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (((E and F) -> F) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10120.        (((A and B) -> A) and (C -> ((D -> (((E and F) -> F) and D)) and C))), M:tm-21, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10121
in-theory        10121
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10121.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-20, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10122
in-theory        10122
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (((E and F) -> F) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10122.        ((A -> (B -> A)) and (C -> ((D -> (((E and F) -> F) and D)) and C))), M:tm-19, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10123
in-theory        10123
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (((C and D) -> D) and B)) and A))) -> (not A))
theorem-size     17
proof            (modus-ponens tm-9 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-9 tm-5 tm-4)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10123.        ((A -> (not ((B -> (((C and D) -> D) and B)) and A))) -> (not A)), M:tm-9, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-10124
in-theory        10124
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (((B and C) -> C) and A)) and D) -> E) -> ((D or ((A -> (((B and C) -> C) and A)) and D)) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10124.        ((((A -> (((B and C) -> C) and A)) and D) -> E) -> ((D or ((A -> (((B and C) -> C) and A)) and D)) -> E)), M:tm-8, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-10125
in-theory        10125
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (((D and E) -> E) and C)) and B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10125.        (A or (B -> ((C -> (((D and E) -> E) and C)) and B))), M:tm-7, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10126
in-theory        10126
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10126.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) or E), M:tm-6, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10127
in-theory        10127
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (((D and E) -> E) and C)) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10127.        (A -> ((B -> ((C -> (((D and E) -> E) and C)) and B)) and A)), M:tm-5, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10128
in-theory        10128
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (((D and E) -> E) and C)) and B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10128.        (A -> (B -> ((C -> (((D and E) -> E) and C)) and B))), M:tm-1, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-10129
in-theory        10129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-270 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10129.        ((A -> (((B and C) -> C) and A)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-270, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10130
in-theory        10130
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-267 tm-271 ((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10130.        ((A or (((B and C) -> C) and A)) -> (D -> (((E and F) -> F) and D))), M:tm-267, m:tm-271, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10131
in-theory        10131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-239 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10131.        ((A -> (((B and C) -> B) and A)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-239, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10132
in-theory        10132
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-236 tm-271 ((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10132.        ((A or (((B and C) -> B) and A)) -> (D -> (((E and F) -> F) and D))), M:tm-236, m:tm-271, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10133
in-theory        10133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-210 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10133.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (((G and H) -> H) and F)))), M:tm-210, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10134
in-theory        10134
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (((F and G) -> G) and E)))
theorem-size     27
proof            (modus-ponens tm-207 tm-271 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10134.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (((F and G) -> G) and E))), M:tm-207, m:tm-271, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10135
in-theory        10135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-183 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10135.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-183, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10136
in-theory        10136
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-180 tm-271 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10136.        ((A or ((B -> (C -> B)) and A)) -> (D -> (((E and F) -> F) and D))), M:tm-180, m:tm-271, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10137
in-theory        10137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-157 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10137.        ((A -> ((B and C) -> C)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-157, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10138
in-theory        10138
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-154 tm-271 ((Am (-> (and A B) B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10138.        ((A or ((B and C) -> C)) -> (D -> (((E and F) -> F) and D))), M:tm-154, m:tm-271, u:((Am (-> (and A B) B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10139
in-theory        10139
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (((C and D) -> D) and B))
theorem-size     11
proof            (modus-ponens tm-152 tm-271 ((Am (and A Bm)) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10139.        ((A and B) -> (((C and D) -> D) and B)), M:tm-152, m:tm-271, u:((Am (and A Bm)) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-10140
in-theory        10140
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-147 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10140.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-147, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10141
in-theory        10141
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (((E and F) -> F) and D)))
theorem-size     25
proof            (modus-ponens tm-144 tm-271 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10141.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (((E and F) -> F) and D))), M:tm-144, m:tm-271, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10142
in-theory        10142
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (((C and D) -> D) and B)) -> E)) -> (B -> (((C and D) -> D) and B)))
theorem-size     23
proof            (modus-ponens tm-142 tm-271 ((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) C))) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10142.        ((A and ((B -> (((C and D) -> D) and B)) -> E)) -> (B -> (((C and D) -> D) and B))), M:tm-142, m:tm-271, u:((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) C))) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10143
in-theory        10143
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (((C and D) -> D) and B)) -> B)) -> (((C and D) -> D) and B))
theorem-size     21
proof            (modus-ponens tm-141 tm-271 ((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Bm))) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10143.        ((A and ((B -> (((C and D) -> D) and B)) -> B)) -> (((C and D) -> D) and B)), M:tm-141, m:tm-271, u:((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Bm))) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-10144
in-theory        10144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-134 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10144.        ((A -> ((B and C) -> B)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-134, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10145
in-theory        10145
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-131 tm-271 ((Am (-> (and A B) A)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10145.        ((A or ((B and C) -> B)) -> (D -> (((E and F) -> F) and D))), M:tm-131, m:tm-271, u:((Am (-> (and A B) A)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10146
in-theory        10146
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (((C and D) -> D) and A))
theorem-size     11
proof            (modus-ponens tm-129 tm-271 ((Am (and Bm B)) (A Bm) (C (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-1 tm-3 tm-5 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10146.        ((A and B) -> (((C and D) -> D) and A)), M:tm-129, m:tm-271, u:((Am (and Bm B)) (A Bm) (C (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-10147
in-theory        10147
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-125 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10147.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-125, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10148
in-theory        10148
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (((E and F) -> F) and D)))
theorem-size     25
proof            (modus-ponens tm-122 tm-271 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-5 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10148.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (((E and F) -> F) and D))), M:tm-122, m:tm-271, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10149
in-theory        10149
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (((B and C) -> C) and A)) -> D) and E) -> (A -> (((B and C) -> C) and A)))
theorem-size     23
proof            (modus-ponens tm-120 tm-271 ((Am (and (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) B) C)) (A (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-5 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10149.        ((((A -> (((B and C) -> C) and A)) -> D) and E) -> (A -> (((B and C) -> C) and A))), M:tm-120, m:tm-271, u:((Am (and (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) B) C)) (A (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10150
in-theory        10150
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (((B and C) -> C) and A)) -> A) and D) -> (((B and C) -> C) and A))
theorem-size     21
proof            (modus-ponens tm-119 tm-271 ((Am (and (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Bm) C)) (A Bm) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-3 tm-1 tm-5 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10150.        ((((A -> (((B and C) -> C) and A)) -> A) and D) -> (((B and C) -> C) and A)), M:tm-119, m:tm-271, u:((Am (and (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Bm) C)) (A Bm) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-10151
in-theory        10151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-113 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10151.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (((G and H) -> H) and F)))), M:tm-113, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10152
in-theory        10152
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (((F and G) -> G) and E)))
theorem-size     25
proof            (modus-ponens tm-110 tm-271 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10152.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (((F and G) -> G) and E))), M:tm-110, m:tm-271, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10153
in-theory        10153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))
theorem-size     19
proof            (modus-ponens tm-108 tm-271 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (and Cm Dm) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10153.        ((A -> (B -> C)) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-108, m:tm-271, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (and Cm Dm) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-10154
in-theory        10154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     31
proof            (modus-ponens tm-105 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10154.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-105, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10155
in-theory        10155
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (((E and F) -> F) and D)))
theorem-size     29
proof            (modus-ponens tm-102 tm-271 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-4)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10155.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (((E and F) -> F) and D))), M:tm-102, m:tm-271, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10156
in-theory        10156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) and A) -> D)) -> (A -> (((B and C) -> C) and A)))
theorem-size     21
proof            (modus-ponens tm-100 tm-271 ((Am (-> Bm (-> (and (-> (and Cm Dm) Dm) Bm) C))) (A Bm) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10156.        ((A -> ((((B and C) -> C) and A) -> D)) -> (A -> (((B and C) -> C) and A))), M:tm-100, m:tm-271, u:((Am (-> Bm (-> (and (-> (and Cm Dm) Dm) Bm) C))) (A Bm) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-10157
in-theory        10157
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> A)))
theorem-size     11
proof            (modus-ponens tm-98 tm-271 ((A Am) (Bm (-> B Am)) (C (and (-> (and Cm Dm) Dm) (-> B Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10157.        (A -> (((B and C) -> C) and (D -> A))), M:tm-98, m:tm-271, u:((A Am) (Bm (-> B Am)) (C (and (-> (and Cm Dm) Dm) (-> B Am))))
================================================================
tm-name          tm-10158
in-theory        10158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) -> D) -> (A -> (((B and C) -> C) and A)))
theorem-size     21
proof            (modus-ponens tm-96 tm-271 ((Am (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) B)) (A (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10158.        (((A -> (((B and C) -> C) and A)) -> D) -> (A -> (((B and C) -> C) and A))), M:tm-96, m:tm-271, u:((Am (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) B)) (A (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10159
in-theory        10159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-95 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10159.        (((A -> B) -> (A -> A)) and (C -> (D -> (((E and F) -> F) and D)))), M:tm-95, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10160
in-theory        10160
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> (((D and E) -> E) and C)))
theorem-size     17
proof            (modus-ponens tm-92 tm-271 ((Am (-> A A)) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10160.        (((A -> B) or (A -> A)) -> (C -> (((D and E) -> E) and C))), M:tm-92, m:tm-271, u:((Am (-> A A)) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10161
in-theory        10161
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C -> (((D and E) -> E) and C))))
theorem-size     13
proof            (modus-ponens tm-84 tm-271 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10161.        (A -> (B -> (C -> (((D and E) -> E) and C)))), M:tm-84, m:tm-271, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10162
in-theory        10162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-83 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10162.        ((A -> (B -> (C -> B))) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-83, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10163
in-theory        10163
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-80 tm-271 ((Am (-> A (-> B A))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10163.        ((A or (B -> (C -> B))) -> (D -> (((E and F) -> F) and D))), M:tm-80, m:tm-271, u:((Am (-> A (-> B A))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10164
in-theory        10164
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> (((B and C) -> C) and A)) -> D))) -> D)
theorem-size     15
proof            (modus-ponens tm-77 tm-271 ((Am (not (not (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) B)))) (A (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-5 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10164.        ((not (not ((A -> (((B and C) -> C) and A)) -> D))) -> D), M:tm-77, m:tm-271, u:((Am (not (not (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) B)))) (A (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10165
in-theory        10165
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> (((D and E) -> E) and C))))
theorem-size     17
proof            (modus-ponens tm-76 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10165.        (((not (not A)) -> A) and (B -> (C -> (((D and E) -> E) and C)))), M:tm-76, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10166
in-theory        10166
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> (((C and D) -> D) and B)))
theorem-size     15
proof            (modus-ponens tm-73 tm-271 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10166.        (((not (not A)) or A) -> (B -> (((C and D) -> D) and B))), M:tm-73, m:tm-271, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10167
in-theory        10167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (((E and F) -> F) and D))))
theorem-size     23
proof            (modus-ponens tm-69 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10167.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (((E and F) -> F) and D)))), M:tm-69, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10168
in-theory        10168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (((D and E) -> E) and C)))
theorem-size     21
proof            (modus-ponens tm-66 tm-271 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-5 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10168.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (((D and E) -> E) and C))), M:tm-66, m:tm-271, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10169
in-theory        10169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> (((C and D) -> D) and B)))
theorem-size     15
proof            (modus-ponens tm-55 tm-271 ((Am (-> A Bm)) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-8 tm-1 tm-5 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10169.        ((A -> B) -> ((A or B) -> (((C and D) -> D) and B))), M:tm-55, m:tm-271, u:((Am (-> A Bm)) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-10170
in-theory        10170
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-54 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10170.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-54, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10171
in-theory        10171
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E and F) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-51 tm-271 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10171.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (((E and F) -> F) and D))), M:tm-51, m:tm-271, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10172
in-theory        10172
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (((D and E) -> E) and C)))
theorem-size     15
proof            (modus-ponens tm-50 tm-271 ((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10172.        ((A or (B or A)) -> (C -> (((D and E) -> E) and C))), M:tm-50, m:tm-271, u:((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10173
in-theory        10173
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (((D and E) -> E) and C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-271 ((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10173.        ((A or (A or B)) -> (C -> (((D and E) -> E) and C))), M:tm-49, m:tm-271, u:((Am (or A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10174
in-theory        10174
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (((D and E) -> E) and C)))
theorem-size     17
proof            (modus-ponens tm-48 tm-271 ((Am (-> A (and B A))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10174.        ((A or (B -> (A and B))) -> (C -> (((D and E) -> E) and C))), M:tm-48, m:tm-271, u:((Am (-> A (and B A))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10175
in-theory        10175
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (((D and E) -> E) and C)))
theorem-size     15
proof            (modus-ponens tm-47 tm-271 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10175.        (((A and B) or B) -> (C -> (((D and E) -> E) and C))), M:tm-47, m:tm-271, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10176
in-theory        10176
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (((D and E) -> E) and C)))
theorem-size     15
proof            (modus-ponens tm-46 tm-271 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10176.        (((A and B) or A) -> (C -> (((D and E) -> E) and C))), M:tm-46, m:tm-271, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10177
in-theory        10177
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E and F) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-45 tm-271 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10177.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E and F) -> F) and D))), M:tm-45, m:tm-271, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10178
in-theory        10178
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((D and E) -> E) and C)))
theorem-size     15
proof            (modus-ponens tm-44 tm-271 ((Am (-> A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10178.        ((A or (B -> A)) -> (C -> (((D and E) -> E) and C))), M:tm-44, m:tm-271, u:((Am (-> A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10179
in-theory        10179
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-42 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10179.        ((A -> (B or A)) and (C -> (D -> (((E and F) -> F) and D)))), M:tm-42, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10180
in-theory        10180
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-32 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10180.        ((A -> (A or B)) and (C -> (D -> (((E and F) -> F) and D)))), M:tm-32, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10181
in-theory        10181
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B -> (((C and D) -> D) and B))))
theorem-size     13
proof            (modus-ponens tm-24 tm-271 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10181.        (A -> (A and (B -> (((C and D) -> D) and B)))), M:tm-24, m:tm-271, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10182
in-theory        10182
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-23 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10182.        ((A -> (B -> (A and B))) and (C -> (D -> (((E and F) -> F) and D)))), M:tm-23, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10183
in-theory        10183
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-22 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10183.        (((A and B) -> B) and (C -> (D -> (((E and F) -> F) and D)))), M:tm-22, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10184
in-theory        10184
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-21 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10184.        (((A and B) -> A) and (C -> (D -> (((E and F) -> F) and D)))), M:tm-21, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10185
in-theory        10185
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-20 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10185.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-20, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10186
in-theory        10186
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-19 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10186.        ((A -> (B -> A)) and (C -> (D -> (((E and F) -> F) and D)))), M:tm-19, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10187
in-theory        10187
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> (((C and D) -> D) and B)) -> E)) -> E)
theorem-size     15
proof            (modus-ponens tm-17 tm-271 ((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) C))) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10187.        ((A and ((B -> (((C and D) -> D) and B)) -> E)) -> E), M:tm-17, m:tm-271, u:((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) C))) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10188
in-theory        10188
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (((B and C) -> C) and A)) -> D) and E) -> D)
theorem-size     15
proof            (modus-ponens tm-15 tm-271 ((Am (and (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) B) C)) (A (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-5 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10188.        ((((A -> (((B and C) -> C) and A)) -> D) and E) -> D), M:tm-15, m:tm-271, u:((Am (and (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) B) C)) (A (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10189
in-theory        10189
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) and A) -> D)) -> (A -> D))
theorem-size     15
proof            (modus-ponens tm-13 tm-271 ((Am (-> Bm (-> (and (-> (and Cm Dm) Dm) Bm) C))) (A Bm) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10189.        ((A -> ((((B and C) -> C) and A) -> D)) -> (A -> D)), M:tm-13, m:tm-271, u:((Am (-> Bm (-> (and (-> (and Cm Dm) Dm) Bm) C))) (A Bm) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-10190
in-theory        10190
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B -> (((C and D) -> D) and B)))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-271 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-9 tm-1 tm-5 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10190.        ((A -> (not (B -> (((C and D) -> D) and B)))) -> (not A)), M:tm-9, m:tm-271, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10191
in-theory        10191
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) -> D) -> ((E or (A -> (((B and C) -> C) and A))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-271 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10191.        (((A -> (((B and C) -> C) and A)) -> D) -> ((E or (A -> (((B and C) -> C) and A))) -> D)), M:tm-8, m:tm-271, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10192
in-theory        10192
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C -> (((D and E) -> E) and C))))
theorem-size     13
proof            (modus-ponens tm-7 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-7 tm-1 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10192.        (A or (B -> (C -> (((D and E) -> E) and C)))), M:tm-7, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10193
in-theory        10193
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-6 tm-1 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10193.        ((A -> (B -> (((C and D) -> D) and B))) or E), M:tm-6, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10194
in-theory        10194
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (((D and E) -> E) and C))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10194.        (A -> ((B -> (C -> (((D and E) -> E) and C))) and A)), M:tm-5, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-10195
in-theory        10195
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> (((C and D) -> D) and B)))
theorem-size     13
proof            (modus-ponens tm-2 tm-271 ((A Am) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10195.        ((A -> B) -> (A -> (((C and D) -> D) and B))), M:tm-2, m:tm-271, u:((A Am) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-10196
in-theory        10196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10196.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-270, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10197
in-theory        10197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10197.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-239, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10198
in-theory        10198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (H -> G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10198.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (H -> G)))), M:tm-210, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10199
in-theory        10199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10199.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-183, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10200
in-theory        10200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10200.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-157, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10201
in-theory        10201
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10201.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-147, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10202
in-theory        10202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10202.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-134, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10203
in-theory        10203
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10203.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-125, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10204
in-theory        10204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10204.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> G)))), M:tm-113, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10205
in-theory        10205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10205.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-105, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10206
in-theory        10206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10206.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> E)))), M:tm-95, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10207
in-theory        10207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10207.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-83, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10208
in-theory        10208
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10208.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (E -> D)))), M:tm-76, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10209
in-theory        10209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10209.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (F -> E)))), M:tm-69, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10210
in-theory        10210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10210.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-54, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10211
in-theory        10211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10211.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (F -> E)))), M:tm-42, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10212
in-theory        10212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10212.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (F -> E)))), M:tm-32, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10213
in-theory        10213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10213.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> E)))), M:tm-23, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10214
in-theory        10214
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10214.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (F -> E)))), M:tm-22, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10215
in-theory        10215
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10215.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (F -> E)))), M:tm-21, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10216
in-theory        10216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10216.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-20, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10217
in-theory        10217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10217.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> E)))), M:tm-19, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10218
in-theory        10218
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10218.        (A or ((B -> (C -> (B and C))) and (D -> (E -> D)))), M:tm-7, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10219
in-theory        10219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10219.        (((A -> (B -> (A and B))) and (C -> (D -> C))) or E), M:tm-6, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10220
in-theory        10220
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> (E -> D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10220.        (A -> (((B -> (C -> (B and C))) and (D -> (E -> D))) and A)), M:tm-5, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10221
in-theory        10221
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-1 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10221.        (A -> ((B -> (C -> (B and C))) and (D -> (E -> D)))), M:tm-1, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10222
in-theory        10222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10222.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-270, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10223
in-theory        10223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10223.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-239, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10224
in-theory        10224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10224.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-210, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10225
in-theory        10225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10225.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-183, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10226
in-theory        10226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10226.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-157, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10227
in-theory        10227
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10227.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-147, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10228
in-theory        10228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10228.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-134, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10229
in-theory        10229
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10229.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-125, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10230
in-theory        10230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10230.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-113, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10231
in-theory        10231
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10231.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-105, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10232
in-theory        10232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10232.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-95, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10233
in-theory        10233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10233.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-83, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10234
in-theory        10234
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10234.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-76, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10235
in-theory        10235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10235.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-69, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10236
in-theory        10236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10236.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-54, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10237
in-theory        10237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10237.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-42, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10238
in-theory        10238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10238.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-32, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10239
in-theory        10239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10239.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-23, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10240
in-theory        10240
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10240.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-22, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10241
in-theory        10241
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10241.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-21, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10242
in-theory        10242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10242.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-20, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10243
in-theory        10243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10243.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-19, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10244
in-theory        10244
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10244.        (A or ((B -> (C -> (B and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-7, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10245
in-theory        10245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10245.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F), M:tm-6, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10246
in-theory        10246
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10246.        (A -> (((B -> (C -> (B and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)), M:tm-5, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10247
in-theory        10247
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10247.        (A -> ((B -> (C -> (B and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-1, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10248
in-theory        10248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-270 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10248.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-270, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10249
in-theory        10249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-239 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10249.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-239, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10250
in-theory        10250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G and H) -> G)))
theorem-size     31
proof            (modus-ponens tm-210 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10250.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G and H) -> G))), M:tm-210, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10251
in-theory        10251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-183 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10251.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-183, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10252
in-theory        10252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-157 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10252.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-157, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10253
in-theory        10253
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-147 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10253.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-147, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10254
in-theory        10254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-134 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10254.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-134, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10255
in-theory        10255
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-125 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10255.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-125, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10256
in-theory        10256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-113 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10256.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G and H) -> G))), M:tm-113, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10257
in-theory        10257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-105 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10257.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-105, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10258
in-theory        10258
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-95 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10258.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E and F) -> E))), M:tm-95, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10259
in-theory        10259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-83 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10259.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-83, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10260
in-theory        10260
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D and E) -> D)))
theorem-size     19
proof            (modus-ponens tm-76 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-10 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10260.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D and E) -> D))), M:tm-76, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10261
in-theory        10261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-69 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10261.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E and F) -> E))), M:tm-69, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10262
in-theory        10262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-54 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10262.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-54, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10263
in-theory        10263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-42 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10263.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E and F) -> E))), M:tm-42, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10264
in-theory        10264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-32 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10264.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E and F) -> E))), M:tm-32, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10265
in-theory        10265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-23 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10265.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E and F) -> E))), M:tm-23, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10266
in-theory        10266
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-22 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10266.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E and F) -> E))), M:tm-22, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10267
in-theory        10267
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-21 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10267.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E and F) -> E))), M:tm-21, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10268
in-theory        10268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-20 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10268.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-20, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10269
in-theory        10269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-19 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10269.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E and F) -> E))), M:tm-19, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10270
in-theory        10270
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((D and E) -> D)))
theorem-size     15
proof            (modus-ponens tm-7 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10270.        (A or ((B -> (C -> (B and C))) and ((D and E) -> D))), M:tm-7, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10271
in-theory        10271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10271.        (((A -> (B -> (A and B))) and ((C and D) -> C)) or E), M:tm-6, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10272
in-theory        10272
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((D and E) -> D)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10272.        (A -> (((B -> (C -> (B and C))) and ((D and E) -> D)) and A)), M:tm-5, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10273
in-theory        10273
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((D and E) -> D)))
theorem-size     15
proof            (modus-ponens tm-1 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10273.        (A -> ((B -> (C -> (B and C))) and ((D and E) -> D))), M:tm-1, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10274
in-theory        10274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-270 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10274.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-270, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10275
in-theory        10275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-239 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10275.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-239, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10276
in-theory        10276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G and H) -> H)))
theorem-size     31
proof            (modus-ponens tm-210 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10276.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G and H) -> H))), M:tm-210, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10277
in-theory        10277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-183 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10277.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-183, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10278
in-theory        10278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-157 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10278.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-157, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10279
in-theory        10279
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-147 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10279.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-147, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10280
in-theory        10280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-134 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10280.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-134, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10281
in-theory        10281
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-125 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10281.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-125, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10282
in-theory        10282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-113 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10282.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G and H) -> H))), M:tm-113, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10283
in-theory        10283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     33
proof            (modus-ponens tm-105 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10283.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-105, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10284
in-theory        10284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-95 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10284.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E and F) -> F))), M:tm-95, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10285
in-theory        10285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-83 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10285.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-83, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10286
in-theory        10286
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D and E) -> E)))
theorem-size     19
proof            (modus-ponens tm-76 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-10 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10286.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D and E) -> E))), M:tm-76, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10287
in-theory        10287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E and F) -> F)))
theorem-size     25
proof            (modus-ponens tm-69 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10287.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E and F) -> F))), M:tm-69, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10288
in-theory        10288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-54 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10288.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-54, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10289
in-theory        10289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-42 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10289.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E and F) -> F))), M:tm-42, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10290
in-theory        10290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-32 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10290.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E and F) -> F))), M:tm-32, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10291
in-theory        10291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-23 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10291.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E and F) -> F))), M:tm-23, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10292
in-theory        10292
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-22 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10292.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E and F) -> F))), M:tm-22, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10293
in-theory        10293
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-21 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10293.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E and F) -> F))), M:tm-21, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10294
in-theory        10294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-20 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10294.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-20, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10295
in-theory        10295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-19 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10295.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E and F) -> F))), M:tm-19, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10296
in-theory        10296
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((D and E) -> E)))
theorem-size     15
proof            (modus-ponens tm-7 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10296.        (A or ((B -> (C -> (B and C))) and ((D and E) -> E))), M:tm-7, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10297
in-theory        10297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10297.        (((A -> (B -> (A and B))) and ((C and D) -> D)) or E), M:tm-6, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10298
in-theory        10298
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((D and E) -> E)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10298.        (A -> (((B -> (C -> (B and C))) and ((D and E) -> E)) and A)), M:tm-5, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10299
in-theory        10299
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((D and E) -> E)))
theorem-size     15
proof            (modus-ponens tm-1 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10299.        (A -> ((B -> (C -> (B and C))) and ((D and E) -> E))), M:tm-1, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10300
in-theory        10300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10300.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-270, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10301
in-theory        10301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10301.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-239, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10302
in-theory        10302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10302.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H))))), M:tm-210, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10303
in-theory        10303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10303.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-183, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10304
in-theory        10304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10304.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-157, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10305
in-theory        10305
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10305.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-147, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10306
in-theory        10306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10306.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-134, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10307
in-theory        10307
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10307.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-125, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10308
in-theory        10308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10308.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H))))), M:tm-113, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10309
in-theory        10309
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10309.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-105, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10310
in-theory        10310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10310.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F))))), M:tm-95, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10311
in-theory        10311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10311.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-83, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10312
in-theory        10312
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10312.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (E -> (D and E))))), M:tm-76, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10313
in-theory        10313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10313.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F))))), M:tm-69, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10314
in-theory        10314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10314.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-54, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10315
in-theory        10315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10315.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F))))), M:tm-42, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10316
in-theory        10316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10316.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F))))), M:tm-32, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10317
in-theory        10317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10317.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F))))), M:tm-23, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10318
in-theory        10318
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10318.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F))))), M:tm-22, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10319
in-theory        10319
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10319.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F))))), M:tm-21, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10320
in-theory        10320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10320.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-20, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10321
in-theory        10321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10321.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F))))), M:tm-19, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10322
in-theory        10322
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-7 tm-5)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10322.        (A or ((B -> (C -> (B and C))) and (D -> (E -> (D and E))))), M:tm-7, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10323
in-theory        10323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-6 tm-5)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10323.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) or E), M:tm-6, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10324
in-theory        10324
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> (E -> (D and E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10324.        (A -> (((B -> (C -> (B and C))) and (D -> (E -> (D and E)))) and A)), M:tm-5, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10325
in-theory        10325
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-1 tm-5)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10325.        (A -> ((B -> (C -> (B and C))) and (D -> (E -> (D and E))))), M:tm-1, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-10326
in-theory        10326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-270 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10326.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-270, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10327
in-theory        10327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-239 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10327.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-239, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10328
in-theory        10328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (G or H))))
theorem-size     31
proof            (modus-ponens tm-210 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10328.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (G or H)))), M:tm-210, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10329
in-theory        10329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-183 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10329.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-183, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10330
in-theory        10330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-157 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10330.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-157, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10331
in-theory        10331
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-147 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10331.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-147, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10332
in-theory        10332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-134 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10332.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-134, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10333
in-theory        10333
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-125 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10333.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-125, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10334
in-theory        10334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-113 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10334.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (G or H)))), M:tm-113, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10335
in-theory        10335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     33
proof            (modus-ponens tm-105 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10335.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-105, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10336
in-theory        10336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-95 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10336.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (E or F)))), M:tm-95, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10337
in-theory        10337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-83 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10337.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-83, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10338
in-theory        10338
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-76 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10338.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (D or E)))), M:tm-76, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10339
in-theory        10339
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (E or F))))
theorem-size     25
proof            (modus-ponens tm-69 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10339.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (E or F)))), M:tm-69, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10340
in-theory        10340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-54 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10340.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-54, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10341
in-theory        10341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-42 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10341.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (E or F)))), M:tm-42, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10342
in-theory        10342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-32 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10342.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (E or F)))), M:tm-32, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10343
in-theory        10343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-23 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10343.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (E or F)))), M:tm-23, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10344
in-theory        10344
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-22 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10344.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (E or F)))), M:tm-22, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10345
in-theory        10345
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-21 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10345.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (E or F)))), M:tm-21, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10346
in-theory        10346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-20 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10346.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-20, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10347
in-theory        10347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-19 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10347.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (E or F)))), M:tm-19, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10348
in-theory        10348
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-7 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10348.        (A or ((B -> (C -> (B and C))) and (D -> (D or E)))), M:tm-7, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10349
in-theory        10349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-6 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10349.        (((A -> (B -> (A and B))) and (C -> (C or D))) or E), M:tm-6, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10350
in-theory        10350
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> (D or E))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10350.        (A -> (((B -> (C -> (B and C))) and (D -> (D or E))) and A)), M:tm-5, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10351
in-theory        10351
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-1 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10351.        (A -> ((B -> (C -> (B and C))) and (D -> (D or E)))), M:tm-1, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-10352
in-theory        10352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10352.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-270, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10353
in-theory        10353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10353.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-239, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10354
in-theory        10354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (H or G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10354.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (H or G)))), M:tm-210, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10355
in-theory        10355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10355.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-183, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10356
in-theory        10356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10356.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-157, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10357
in-theory        10357
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10357.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-147, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10358
in-theory        10358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10358.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-134, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10359
in-theory        10359
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10359.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-125, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10360
in-theory        10360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10360.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H or G)))), M:tm-113, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10361
in-theory        10361
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10361.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-105, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10362
in-theory        10362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10362.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (F or E)))), M:tm-95, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10363
in-theory        10363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10363.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-83, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10364
in-theory        10364
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10364.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (E or D)))), M:tm-76, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10365
in-theory        10365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (F or E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10365.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (F or E)))), M:tm-69, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10366
in-theory        10366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10366.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-54, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10367
in-theory        10367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10367.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (F or E)))), M:tm-42, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10368
in-theory        10368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10368.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (F or E)))), M:tm-32, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10369
in-theory        10369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10369.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F or E)))), M:tm-23, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10370
in-theory        10370
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10370.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (F or E)))), M:tm-22, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10371
in-theory        10371
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10371.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (F or E)))), M:tm-21, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10372
in-theory        10372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10372.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-20, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10373
in-theory        10373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10373.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (F or E)))), M:tm-19, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10374
in-theory        10374
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-7 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10374.        (A or ((B -> (C -> (B and C))) and (D -> (E or D)))), M:tm-7, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10375
in-theory        10375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10375.        (((A -> (B -> (A and B))) and (C -> (D or C))) or E), M:tm-6, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10376
in-theory        10376
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> (E or D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10376.        (A -> (((B -> (C -> (B and C))) and (D -> (E or D))) and A)), M:tm-5, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10377
in-theory        10377
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10377.        (A -> ((B -> (C -> (B and C))) and (D -> (E or D)))), M:tm-1, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-10378
in-theory        10378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10378.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-270, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10379
in-theory        10379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10379.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-239, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10380
in-theory        10380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10380.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-210, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10381
in-theory        10381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10381.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-183, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10382
in-theory        10382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10382.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-157, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10383
in-theory        10383
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10383.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-147, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10384
in-theory        10384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10384.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-134, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10385
in-theory        10385
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10385.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-125, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10386
in-theory        10386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10386.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-113, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10387
in-theory        10387
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10387.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-105, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10388
in-theory        10388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10388.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-95, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10389
in-theory        10389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10389.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-83, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10390
in-theory        10390
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-10 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10390.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-76, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10391
in-theory        10391
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10391.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-69, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10392
in-theory        10392
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10392.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-54, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10393
in-theory        10393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10393.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-42, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10394
in-theory        10394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10394.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-32, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10395
in-theory        10395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10395.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-23, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10396
in-theory        10396
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10396.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-22, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10397
in-theory        10397
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10397.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-21, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10398
in-theory        10398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10398.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-20, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10399
in-theory        10399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10399.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-19, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10400
in-theory        10400
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10400.        (A or ((B -> (C -> (B and C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-7, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10401
in-theory        10401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10401.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F), M:tm-6, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10402
in-theory        10402
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10402.        (A -> (((B -> (C -> (B and C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A)), M:tm-5, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10403
in-theory        10403
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10403.        (A -> ((B -> (C -> (B and C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-1, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-10404
in-theory        10404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10404.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-270, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10405
in-theory        10405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10405.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-239, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10406
in-theory        10406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10406.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-210, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10407
in-theory        10407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10407.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-183, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10408
in-theory        10408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10408.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-157, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10409
in-theory        10409
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10409.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-147, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10410
in-theory        10410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10410.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-134, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10411
in-theory        10411
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10411.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-125, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10412
in-theory        10412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10412.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-113, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10413
in-theory        10413
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10413.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-105, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10414
in-theory        10414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10414.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-95, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10415
in-theory        10415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10415.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-83, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10416
in-theory        10416
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-10 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10416.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-76, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10417
in-theory        10417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-9)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10417.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-69, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10418
in-theory        10418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10418.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-54, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10419
in-theory        10419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10419.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-42, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10420
in-theory        10420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10420.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-32, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10421
in-theory        10421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10421.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-23, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10422
in-theory        10422
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10422.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-22, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10423
in-theory        10423
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10423.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-21, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10424
in-theory        10424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10424.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-20, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10425
in-theory        10425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10425.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-19, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10426
in-theory        10426
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-7 tm-5 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10426.        (A or ((B -> (C -> (B and C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-7, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10427
in-theory        10427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-6 tm-5 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10427.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E), M:tm-6, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10428
in-theory        10428
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-9)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10428.        (A -> (((B -> (C -> (B and C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and A)), M:tm-5, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10429
in-theory        10429
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-1 tm-5 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10429.        (A -> ((B -> (C -> (B and C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-1, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-10430
in-theory        10430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-270 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10430.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-270, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10431
in-theory        10431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-239 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10431.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-239, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10432
in-theory        10432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((not (not G)) -> G)))
theorem-size     31
proof            (modus-ponens tm-210 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10432.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((not (not G)) -> G))), M:tm-210, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10433
in-theory        10433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-183 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10433.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-183, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10434
in-theory        10434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-157 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10434.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-157, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10435
in-theory        10435
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-147 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10435.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-147, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10436
in-theory        10436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-134 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10436.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-134, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10437
in-theory        10437
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-125 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10437.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-125, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10438
in-theory        10438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-113 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10438.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((not (not G)) -> G))), M:tm-113, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10439
in-theory        10439
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-105 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10439.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-105, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10440
in-theory        10440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-95 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10440.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((not (not E)) -> E))), M:tm-95, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10441
in-theory        10441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-83 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10441.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-83, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10442
in-theory        10442
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((not (not D)) -> D)))
theorem-size     19
proof            (modus-ponens tm-76 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10442.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((not (not D)) -> D))), M:tm-76, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10443
in-theory        10443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((not (not E)) -> E)))
theorem-size     25
proof            (modus-ponens tm-69 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-10)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10443.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((not (not E)) -> E))), M:tm-69, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10444
in-theory        10444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-54 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10444.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-54, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10445
in-theory        10445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-42 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10445.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((not (not E)) -> E))), M:tm-42, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10446
in-theory        10446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-32 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10446.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((not (not E)) -> E))), M:tm-32, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10447
in-theory        10447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-23 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10447.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((not (not E)) -> E))), M:tm-23, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10448
in-theory        10448
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-22 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10448.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((not (not E)) -> E))), M:tm-22, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10449
in-theory        10449
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-21 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10449.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((not (not E)) -> E))), M:tm-21, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10450
in-theory        10450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-20 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10450.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-20, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10451
in-theory        10451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-19 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10451.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((not (not E)) -> E))), M:tm-19, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10452
in-theory        10452
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((not (not D)) -> D)))
theorem-size     15
proof            (modus-ponens tm-7 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-7 tm-5 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10452.        (A or ((B -> (C -> (B and C))) and ((not (not D)) -> D))), M:tm-7, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10453
in-theory        10453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-6 tm-5 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10453.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) or D), M:tm-6, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10454
in-theory        10454
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((not (not D)) -> D)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-10)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10454.        (A -> (((B -> (C -> (B and C))) and ((not (not D)) -> D)) and A)), M:tm-5, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10455
in-theory        10455
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((not (not D)) -> D)))
theorem-size     15
proof            (modus-ponens tm-1 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-1 tm-5 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10455.        (A -> ((B -> (C -> (B and C))) and ((not (not D)) -> D))), M:tm-1, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-10456
in-theory        10456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10456.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-270, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10457
in-theory        10457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10457.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-239, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10458
in-theory        10458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10458.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H))))), M:tm-210, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10459
in-theory        10459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10459.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-183, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10460
in-theory        10460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10460.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-157, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10461
in-theory        10461
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10461.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-147, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10462
in-theory        10462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10462.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-134, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10463
in-theory        10463
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10463.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-125, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10464
in-theory        10464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10464.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H))))), M:tm-113, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10465
in-theory        10465
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10465.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-105, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10466
in-theory        10466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10466.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F))))), M:tm-95, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10467
in-theory        10467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10467.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-83, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10468
in-theory        10468
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (E -> (F -> E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10468.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (E -> (F -> E))))), M:tm-76, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10469
in-theory        10469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10469.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F))))), M:tm-69, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10470
in-theory        10470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10470.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-54, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10471
in-theory        10471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10471.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F))))), M:tm-42, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10472
in-theory        10472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10472.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F))))), M:tm-32, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10473
in-theory        10473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10473.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F))))), M:tm-23, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10474
in-theory        10474
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10474.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F))))), M:tm-22, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10475
in-theory        10475
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10475.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F))))), M:tm-21, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10476
in-theory        10476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10476.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-20, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10477
in-theory        10477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10477.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F))))), M:tm-19, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10478
in-theory        10478
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10478.        (A or ((B -> (C -> (B and C))) and (D -> (E -> (F -> E))))), M:tm-7, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10479
in-theory        10479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10479.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) or F), M:tm-6, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10480
in-theory        10480
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> (E -> (F -> E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10480.        (A -> (((B -> (C -> (B and C))) and (D -> (E -> (F -> E)))) and A)), M:tm-5, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10481
in-theory        10481
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-1 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10481.        (A -> ((B -> (C -> (B and C))) and (D -> (E -> (F -> E))))), M:tm-1, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-10482
in-theory        10482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10482.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-270, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10483
in-theory        10483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10483.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-239, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10484
in-theory        10484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10484.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G)))), M:tm-210, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10485
in-theory        10485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10485.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-183, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10486
in-theory        10486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10486.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-157, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10487
in-theory        10487
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10487.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-147, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10488
in-theory        10488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10488.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-134, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10489
in-theory        10489
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10489.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-125, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10490
in-theory        10490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10490.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G)))), M:tm-113, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10491
in-theory        10491
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10491.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-105, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10492
in-theory        10492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10492.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E)))), M:tm-95, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10493
in-theory        10493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10493.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-83, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10494
in-theory        10494
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> E) -> (D -> D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10494.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> E) -> (D -> D)))), M:tm-76, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10495
in-theory        10495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10495.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E)))), M:tm-69, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10496
in-theory        10496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10496.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-54, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10497
in-theory        10497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10497.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E)))), M:tm-42, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10498
in-theory        10498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10498.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E)))), M:tm-32, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10499
in-theory        10499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10499.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E)))), M:tm-23, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10500
in-theory        10500
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10500.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E)))), M:tm-22, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10501
in-theory        10501
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10501.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E)))), M:tm-21, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10502
in-theory        10502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10502.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-20, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10503
in-theory        10503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10503.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E)))), M:tm-19, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10504
in-theory        10504
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((D -> E) -> (D -> D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10504.        (A or ((B -> (C -> (B and C))) and ((D -> E) -> (D -> D)))), M:tm-7, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10505
in-theory        10505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10505.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) or E), M:tm-6, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10506
in-theory        10506
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((D -> E) -> (D -> D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10506.        (A -> (((B -> (C -> (B and C))) and ((D -> E) -> (D -> D))) and A)), M:tm-5, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10507
in-theory        10507
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((D -> E) -> (D -> D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10507.        (A -> ((B -> (C -> (B and C))) and ((D -> E) -> (D -> D)))), M:tm-1, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-10508
in-theory        10508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10508.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-270, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10509
in-theory        10509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10509.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-239, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10510
in-theory        10510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10510.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-210, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10511
in-theory        10511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10511.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-183, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10512
in-theory        10512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10512.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-157, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10513
in-theory        10513
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10513.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-147, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10514
in-theory        10514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10514.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-134, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10515
in-theory        10515
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10515.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-125, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10516
in-theory        10516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10516.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-113, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10517
in-theory        10517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10517.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-105, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10518
in-theory        10518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10518.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-95, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10519
in-theory        10519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10519.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-83, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10520
in-theory        10520
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10520.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-76, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10521
in-theory        10521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10521.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-69, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10522
in-theory        10522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-54 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10522.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-54, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10523
in-theory        10523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-42 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10523.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-42, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10524
in-theory        10524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-32 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10524.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-32, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10525
in-theory        10525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-23 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10525.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-23, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10526
in-theory        10526
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-22 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10526.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-22, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10527
in-theory        10527
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-21 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10527.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-21, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10528
in-theory        10528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-20 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10528.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-20, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10529
in-theory        10529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-19 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10529.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-19, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10530
in-theory        10530
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-7 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10530.        (A or ((B -> (C -> (B and C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-7, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10531
in-theory        10531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F)
theorem-size     29
proof            (modus-ponens tm-6 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10531.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F), M:tm-6, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10532
in-theory        10532
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10532.        (A -> (((B -> (C -> (B and C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and A)), M:tm-5, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10533
in-theory        10533
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-1 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10533.        (A -> ((B -> (C -> (B and C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-1, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-10534
in-theory        10534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-270 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10534.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-270, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10535
in-theory        10535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-239 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10535.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-239, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10536
in-theory        10536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     41
proof            (modus-ponens tm-210 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10536.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-210, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10537
in-theory        10537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-183 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10537.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-183, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10538
in-theory        10538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-157 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10538.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-157, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10539
in-theory        10539
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-147 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10539.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-147, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10540
in-theory        10540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-134 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10540.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-134, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10541
in-theory        10541
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-125 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10541.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-125, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10542
in-theory        10542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-113 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10542.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-113, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10543
in-theory        10543
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     43
proof            (modus-ponens tm-105 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10543.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-105, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10544
in-theory        10544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-95 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10544.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-95, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10545
in-theory        10545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-83 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10545.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-83, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10546
in-theory        10546
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     29
proof            (modus-ponens tm-76 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10546.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-76, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10547
in-theory        10547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     35
proof            (modus-ponens tm-69 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10547.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-69, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10548
in-theory        10548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-54 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10548.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-54, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10549
in-theory        10549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-42 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10549.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-42, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10550
in-theory        10550
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-32 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10550.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-32, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10551
in-theory        10551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-23 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10551.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-23, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10552
in-theory        10552
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-22 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10552.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-22, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10553
in-theory        10553
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-21 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10553.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-21, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10554
in-theory        10554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-20 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10554.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-20, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10555
in-theory        10555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-19 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10555.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-19, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10556
in-theory        10556
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-7 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-7 tm-5 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10556.        (A or ((B -> (C -> (B and C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-7, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10557
in-theory        10557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-6 tm-5 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10557.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G), M:tm-6, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10558
in-theory        10558
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10558.        (A -> (((B -> (C -> (B and C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A)), M:tm-5, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10559
in-theory        10559
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-1 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10559.        (A -> ((B -> (C -> (B and C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-1, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-10560
in-theory        10560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-270 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10560.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-270, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10561
in-theory        10561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-239 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10561.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-239, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10562
in-theory        10562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-210 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10562.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-210, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10563
in-theory        10563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-183 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10563.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-183, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10564
in-theory        10564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-157 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10564.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-157, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10565
in-theory        10565
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     39
proof            (modus-ponens tm-147 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10565.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-147, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10566
in-theory        10566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-134 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10566.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-134, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10567
in-theory        10567
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     39
proof            (modus-ponens tm-125 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10567.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-125, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10568
in-theory        10568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-113 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10568.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-113, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10569
in-theory        10569
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     43
proof            (modus-ponens tm-105 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10569.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-105, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10570
in-theory        10570
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-95 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10570.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-95, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10571
in-theory        10571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-83 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10571.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-83, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10572
in-theory        10572
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     29
proof            (modus-ponens tm-76 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10572.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-76, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10573
in-theory        10573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     35
proof            (modus-ponens tm-69 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10573.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-69, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10574
in-theory        10574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-54 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10574.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-54, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10575
in-theory        10575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-42 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10575.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-42, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10576
in-theory        10576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-32 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10576.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-32, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10577
in-theory        10577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-23 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10577.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-23, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10578
in-theory        10578
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-22 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10578.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-22, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10579
in-theory        10579
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-21 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10579.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-21, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10580
in-theory        10580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-20 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10580.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-20, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10581
in-theory        10581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-19 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10581.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-19, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10582
in-theory        10582
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     25
proof            (modus-ponens tm-7 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10582.        (A or ((B -> (C -> (B and C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-7, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10583
in-theory        10583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F)
theorem-size     25
proof            (modus-ponens tm-6 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10583.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F), M:tm-6, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10584
in-theory        10584
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10584.        (A -> (((B -> (C -> (B and C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and A)), M:tm-5, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10585
in-theory        10585
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     25
proof            (modus-ponens tm-1 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10585.        (A -> ((B -> (C -> (B and C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-1, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-10586
in-theory        10586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-270 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10586.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-270, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10587
in-theory        10587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-239 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10587.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-239, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10588
in-theory        10588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H))))
theorem-size     33
proof            (modus-ponens tm-210 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10588.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H)))), M:tm-210, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10589
in-theory        10589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-183 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10589.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-183, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10590
in-theory        10590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-157 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10590.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-157, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10591
in-theory        10591
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-147 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10591.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-147, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10592
in-theory        10592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-134 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10592.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-134, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10593
in-theory        10593
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-125 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10593.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-125, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10594
in-theory        10594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-113 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10594.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H)))), M:tm-113, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10595
in-theory        10595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-105 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10595.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-105, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10596
in-theory        10596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-95 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10596.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F)))), M:tm-95, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10597
in-theory        10597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-83 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10597.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-83, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10598
in-theory        10598
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> ((E and F) -> E))))
theorem-size     21
proof            (modus-ponens tm-76 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10598.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> ((E and F) -> E)))), M:tm-76, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10599
in-theory        10599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-69 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10599.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F)))), M:tm-69, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10600
in-theory        10600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-54 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10600.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-54, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10601
in-theory        10601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-42 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10601.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F)))), M:tm-42, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10602
in-theory        10602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-32 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10602.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F)))), M:tm-32, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10603
in-theory        10603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-23 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10603.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F)))), M:tm-23, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10604
in-theory        10604
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-22 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10604.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F)))), M:tm-22, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10605
in-theory        10605
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-21 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10605.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F)))), M:tm-21, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10606
in-theory        10606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-20 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10606.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-20, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10607
in-theory        10607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-19 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10607.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F)))), M:tm-19, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10608
in-theory        10608
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-7 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10608.        (A or ((B -> (C -> (B and C))) and (D -> ((E and F) -> E)))), M:tm-7, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10609
in-theory        10609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10609.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) or F), M:tm-6, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10610
in-theory        10610
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> ((E and F) -> E))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10610.        (A -> (((B -> (C -> (B and C))) and (D -> ((E and F) -> E))) and A)), M:tm-5, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10611
in-theory        10611
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-1 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10611.        (A -> ((B -> (C -> (B and C))) and (D -> ((E and F) -> E)))), M:tm-1, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-10612
in-theory        10612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-270 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10612.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-270, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10613
in-theory        10613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-239 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10613.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-239, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10614
in-theory        10614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     41
proof            (modus-ponens tm-210 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10614.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-210, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10615
in-theory        10615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-183 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10615.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-183, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10616
in-theory        10616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-157 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10616.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-157, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10617
in-theory        10617
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     39
proof            (modus-ponens tm-147 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10617.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-147, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10618
in-theory        10618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-134 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10618.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-134, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10619
in-theory        10619
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     39
proof            (modus-ponens tm-125 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10619.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-125, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10620
in-theory        10620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-113 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10620.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-113, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10621
in-theory        10621
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     43
proof            (modus-ponens tm-105 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10621.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-105, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10622
in-theory        10622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-95 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10622.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-95, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10623
in-theory        10623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-83 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10623.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-83, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10624
in-theory        10624
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     29
proof            (modus-ponens tm-76 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-10 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10624.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-76, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10625
in-theory        10625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     35
proof            (modus-ponens tm-69 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10625.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-69, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10626
in-theory        10626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-54 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10626.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-54, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10627
in-theory        10627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-42 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10627.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-42, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10628
in-theory        10628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-32 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10628.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-32, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10629
in-theory        10629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-23 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10629.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-23, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10630
in-theory        10630
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-22 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10630.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-22, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10631
in-theory        10631
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-21 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10631.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-21, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10632
in-theory        10632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-20 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10632.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-20, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10633
in-theory        10633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-19 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10633.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-19, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10634
in-theory        10634
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     25
proof            (modus-ponens tm-7 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-7 tm-5 tm-2 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10634.        (A or ((B -> (C -> (B and C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-7, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10635
in-theory        10635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F)
theorem-size     25
proof            (modus-ponens tm-6 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-6 tm-5 tm-2 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10635.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F), M:tm-6, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10636
in-theory        10636
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10636.        (A -> (((B -> (C -> (B and C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and A)), M:tm-5, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10637
in-theory        10637
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     25
proof            (modus-ponens tm-1 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-1 tm-5 tm-2 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10637.        (A -> ((B -> (C -> (B and C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-1, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-10638
in-theory        10638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-270 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10638.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-270, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10639
in-theory        10639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-239 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10639.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-239, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10640
in-theory        10640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I))))
theorem-size     33
proof            (modus-ponens tm-210 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10640.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I)))), M:tm-210, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10641
in-theory        10641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-183 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10641.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-183, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10642
in-theory        10642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-157 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10642.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-157, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10643
in-theory        10643
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-147 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10643.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-147, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10644
in-theory        10644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-134 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10644.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-134, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10645
in-theory        10645
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-125 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10645.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-125, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10646
in-theory        10646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-113 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10646.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I)))), M:tm-113, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10647
in-theory        10647
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     35
proof            (modus-ponens tm-105 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10647.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-105, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10648
in-theory        10648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-95 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10648.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G)))), M:tm-95, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10649
in-theory        10649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-83 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10649.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-83, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10650
in-theory        10650
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> ((E and F) -> F))))
theorem-size     21
proof            (modus-ponens tm-76 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-10 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10650.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> ((E and F) -> F)))), M:tm-76, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10651
in-theory        10651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G))))
theorem-size     27
proof            (modus-ponens tm-69 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-9 tm-1 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10651.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G)))), M:tm-69, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10652
in-theory        10652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-54 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10652.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-54, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10653
in-theory        10653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-42 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10653.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G)))), M:tm-42, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10654
in-theory        10654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-32 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10654.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G)))), M:tm-32, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10655
in-theory        10655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-23 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10655.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G)))), M:tm-23, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10656
in-theory        10656
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-22 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10656.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G)))), M:tm-22, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10657
in-theory        10657
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-21 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10657.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G)))), M:tm-21, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10658
in-theory        10658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-20 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10658.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-20, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10659
in-theory        10659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-19 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10659.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G)))), M:tm-19, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10660
in-theory        10660
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-7 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-7 tm-5 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10660.        (A or ((B -> (C -> (B and C))) and (D -> ((E and F) -> F)))), M:tm-7, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10661
in-theory        10661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-6 tm-5 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10661.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) or F), M:tm-6, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10662
in-theory        10662
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> ((E and F) -> F))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10662.        (A -> (((B -> (C -> (B and C))) and (D -> ((E and F) -> F))) and A)), M:tm-5, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10663
in-theory        10663
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-1 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10663.        (A -> ((B -> (C -> (B and C))) and (D -> ((E and F) -> F)))), M:tm-1, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-10664
in-theory        10664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-270 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10664.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-270, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10665
in-theory        10665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-239 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10665.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-239, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10666
in-theory        10666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     35
proof            (modus-ponens tm-210 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10666.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-210, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10667
in-theory        10667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-183 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10667.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-183, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10668
in-theory        10668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-157 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10668.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-157, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10669
in-theory        10669
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     33
proof            (modus-ponens tm-147 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10669.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-147, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10670
in-theory        10670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-134 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10670.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-134, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10671
in-theory        10671
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     33
proof            (modus-ponens tm-125 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10671.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-125, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10672
in-theory        10672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-113 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10672.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-113, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10673
in-theory        10673
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     37
proof            (modus-ponens tm-105 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10673.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-105, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10674
in-theory        10674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-95 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10674.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-95, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10675
in-theory        10675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-83 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10675.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-83, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10676
in-theory        10676
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> ((E -> (F -> E)) and D))))
theorem-size     23
proof            (modus-ponens tm-76 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10676.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> ((E -> (F -> E)) and D)))), M:tm-76, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10677
in-theory        10677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     29
proof            (modus-ponens tm-69 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10677.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-69, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10678
in-theory        10678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-54 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10678.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-54, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10679
in-theory        10679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-42 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10679.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-42, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10680
in-theory        10680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-32 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10680.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-32, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10681
in-theory        10681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-23 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10681.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-23, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10682
in-theory        10682
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-22 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10682.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-22, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10683
in-theory        10683
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-21 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10683.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-21, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10684
in-theory        10684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-20 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10684.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-20, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10685
in-theory        10685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-19 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10685.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-19, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10686
in-theory        10686
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-7 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10686.        (A or ((B -> (C -> (B and C))) and (D -> ((E -> (F -> E)) and D)))), M:tm-7, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10687
in-theory        10687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10687.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) or F), M:tm-6, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10688
in-theory        10688
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> ((E -> (F -> E)) and D))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10688.        (A -> (((B -> (C -> (B and C))) and (D -> ((E -> (F -> E)) and D))) and A)), M:tm-5, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10689
in-theory        10689
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-1 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-1 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10689.        (A -> ((B -> (C -> (B and C))) and (D -> ((E -> (F -> E)) and D)))), M:tm-1, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-10690
in-theory        10690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-270 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10690.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-270, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10691
in-theory        10691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-239 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10691.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-239, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10692
in-theory        10692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     43
proof            (modus-ponens tm-210 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10692.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-210, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10693
in-theory        10693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-183 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10693.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-183, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10694
in-theory        10694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-157 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10694.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-157, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10695
in-theory        10695
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     41
proof            (modus-ponens tm-147 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10695.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-147, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10696
in-theory        10696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-134 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10696.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-134, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10697
in-theory        10697
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     41
proof            (modus-ponens tm-125 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10697.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-125, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10698
in-theory        10698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-113 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10698.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-113, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10699
in-theory        10699
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     45
proof            (modus-ponens tm-105 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10699.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-105, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10700
in-theory        10700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-95 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10700.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-95, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10701
in-theory        10701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-83 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10701.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-83, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10702
in-theory        10702
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     31
proof            (modus-ponens tm-76 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10702.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-76, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10703
in-theory        10703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     37
proof            (modus-ponens tm-69 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10703.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-69, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10704
in-theory        10704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-54 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10704.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-54, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10705
in-theory        10705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-42 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10705.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-42, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10706
in-theory        10706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-32 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10706.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-32, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10707
in-theory        10707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-23 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10707.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-23, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10708
in-theory        10708
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-22 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10708.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-22, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10709
in-theory        10709
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-21 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10709.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-21, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10710
in-theory        10710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-20 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10710.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-20, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10711
in-theory        10711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-19 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10711.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-19, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10712
in-theory        10712
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-7 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10712.        (A or ((B -> (C -> (B and C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-7, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10713
in-theory        10713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G)
theorem-size     27
proof            (modus-ponens tm-6 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10713.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G), M:tm-6, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10714
in-theory        10714
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10714.        (A -> (((B -> (C -> (B and C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and A)), M:tm-5, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10715
in-theory        10715
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-1 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10715.        (A -> ((B -> (C -> (B and C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-1, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-10716
in-theory        10716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-270 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10716.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-270, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10717
in-theory        10717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-239 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10717.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-239, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10718
in-theory        10718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G))))
theorem-size     35
proof            (modus-ponens tm-210 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10718.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G)))), M:tm-210, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10719
in-theory        10719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-183 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10719.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-183, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10720
in-theory        10720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-157 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10720.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-157, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10721
in-theory        10721
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     33
proof            (modus-ponens tm-147 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10721.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-147, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10722
in-theory        10722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-134 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10722.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-134, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10723
in-theory        10723
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     33
proof            (modus-ponens tm-125 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10723.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-125, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10724
in-theory        10724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-113 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10724.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G)))), M:tm-113, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10725
in-theory        10725
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     37
proof            (modus-ponens tm-105 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10725.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-105, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10726
in-theory        10726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-95 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10726.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E)))), M:tm-95, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10727
in-theory        10727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-83 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10727.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-83, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10728
in-theory        10728
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (((E and F) -> E) and D))))
theorem-size     23
proof            (modus-ponens tm-76 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-10 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10728.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (((E and F) -> E) and D)))), M:tm-76, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10729
in-theory        10729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E))))
theorem-size     29
proof            (modus-ponens tm-69 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10729.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E)))), M:tm-69, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10730
in-theory        10730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-54 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10730.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-54, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10731
in-theory        10731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-42 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10731.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E)))), M:tm-42, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10732
in-theory        10732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-32 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10732.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E)))), M:tm-32, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10733
in-theory        10733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-23 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10733.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E)))), M:tm-23, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10734
in-theory        10734
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-22 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10734.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E)))), M:tm-22, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10735
in-theory        10735
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-21 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10735.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E)))), M:tm-21, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10736
in-theory        10736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-20 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10736.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-20, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10737
in-theory        10737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-19 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10737.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E)))), M:tm-19, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10738
in-theory        10738
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-7 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10738.        (A or ((B -> (C -> (B and C))) and (D -> (((E and F) -> E) and D)))), M:tm-7, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10739
in-theory        10739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10739.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) or F), M:tm-6, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10740
in-theory        10740
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> (((E and F) -> E) and D))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10740.        (A -> (((B -> (C -> (B and C))) and (D -> (((E and F) -> E) and D))) and A)), M:tm-5, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10741
in-theory        10741
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-1 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10741.        (A -> ((B -> (C -> (B and C))) and (D -> (((E and F) -> E) and D)))), M:tm-1, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-10742
in-theory        10742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-270 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10742.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-270, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10743
in-theory        10743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-239 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10743.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-239, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10744
in-theory        10744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G))))
theorem-size     35
proof            (modus-ponens tm-210 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10744.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G)))), M:tm-210, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10745
in-theory        10745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-183 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10745.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-183, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10746
in-theory        10746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-157 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10746.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-157, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10747
in-theory        10747
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     33
proof            (modus-ponens tm-147 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10747.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-147, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10748
in-theory        10748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-134 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10748.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-134, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10749
in-theory        10749
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     33
proof            (modus-ponens tm-125 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10749.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-125, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10750
in-theory        10750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-113 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10750.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G)))), M:tm-113, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10751
in-theory        10751
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     37
proof            (modus-ponens tm-105 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10751.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-105, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10752
in-theory        10752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-95 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10752.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E)))), M:tm-95, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10753
in-theory        10753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-83 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10753.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-83, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10754
in-theory        10754
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (((E and F) -> F) and D))))
theorem-size     23
proof            (modus-ponens tm-76 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-10 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10754.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (((E and F) -> F) and D)))), M:tm-76, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10755
in-theory        10755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E))))
theorem-size     29
proof            (modus-ponens tm-69 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10755.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E)))), M:tm-69, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10756
in-theory        10756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-54 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10756.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-54, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10757
in-theory        10757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-42 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10757.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E)))), M:tm-42, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10758
in-theory        10758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-32 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10758.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E)))), M:tm-32, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10759
in-theory        10759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-23 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10759.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E)))), M:tm-23, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10760
in-theory        10760
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-22 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10760.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E)))), M:tm-22, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10761
in-theory        10761
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-21 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10761.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E)))), M:tm-21, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10762
in-theory        10762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-20 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10762.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-20, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10763
in-theory        10763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-19 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10763.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E)))), M:tm-19, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10764
in-theory        10764
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-7 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10764.        (A or ((B -> (C -> (B and C))) and (D -> (((E and F) -> F) and D)))), M:tm-7, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10765
in-theory        10765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10765.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) or F), M:tm-6, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10766
in-theory        10766
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> (((E and F) -> F) and D))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10766.        (A -> (((B -> (C -> (B and C))) and (D -> (((E and F) -> F) and D))) and A)), M:tm-5, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10767
in-theory        10767
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-1 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10767.        (A -> ((B -> (C -> (B and C))) and (D -> (((E and F) -> F) and D)))), M:tm-1, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-10768
in-theory        10768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-270 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10768.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-270, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10769
in-theory        10769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-239 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10769.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-239, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10770
in-theory        10770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     37
proof            (modus-ponens tm-210 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10770.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-210, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10771
in-theory        10771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-183 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10771.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-183, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10772
in-theory        10772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-157 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10772.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-157, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10773
in-theory        10773
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     35
proof            (modus-ponens tm-147 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10773.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-147, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10774
in-theory        10774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-134 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10774.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-134, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10775
in-theory        10775
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     35
proof            (modus-ponens tm-125 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10775.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-125, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10776
in-theory        10776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-113 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10776.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-113, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10777
in-theory        10777
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     39
proof            (modus-ponens tm-105 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10777.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-105, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10778
in-theory        10778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-95 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10778.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-95, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10779
in-theory        10779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-83 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10779.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-83, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10780
in-theory        10780
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     25
proof            (modus-ponens tm-76 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-10)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10780.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-76, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10781
in-theory        10781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     31
proof            (modus-ponens tm-69 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10781.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-69, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10782
in-theory        10782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-54 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10782.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-54, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10783
in-theory        10783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-42 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10783.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-42, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10784
in-theory        10784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-32 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10784.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-32, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10785
in-theory        10785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-23 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10785.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-23, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10786
in-theory        10786
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-22 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10786.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-22, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10787
in-theory        10787
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-21 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10787.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-21, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10788
in-theory        10788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-20 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10788.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-20, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10789
in-theory        10789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-19 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10789.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-19, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10790
in-theory        10790
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-7 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-7 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10790.        (A or ((B -> (C -> (B and C))) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-7, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10791
in-theory        10791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-6 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10791.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) or F), M:tm-6, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10792
in-theory        10792
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> ((E -> (F -> (E and F))) and D))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10792.        (A -> (((B -> (C -> (B and C))) and (D -> ((E -> (F -> (E and F))) and D))) and A)), M:tm-5, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10793
in-theory        10793
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-1 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-1 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10793.        (A -> ((B -> (C -> (B and C))) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-1, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10794
in-theory        10794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-270 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10794.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-270, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10795
in-theory        10795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-239 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10795.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-239, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10796
in-theory        10796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-210 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10796.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-210, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10797
in-theory        10797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-183 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10797.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-183, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10798
in-theory        10798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-157 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10798.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-157, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10799
in-theory        10799
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-147 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10799.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-147, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10800
in-theory        10800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-134 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10800.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-134, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10801
in-theory        10801
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-125 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10801.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-125, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10802
in-theory        10802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-113 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10802.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-113, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10803
in-theory        10803
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     37
proof            (modus-ponens tm-105 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10803.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-105, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10804
in-theory        10804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-95 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10804.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-95, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10805
in-theory        10805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-83 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10805.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-83, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10806
in-theory        10806
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-76 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-10 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10806.        (((not (not A)) -> A) and (((B and C) -> C) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-76, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10807
in-theory        10807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-69 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10807.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-69, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10808
in-theory        10808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-54 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10808.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-54, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10809
in-theory        10809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-42 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10809.        ((A -> (B or A)) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-42, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10810
in-theory        10810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-32 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10810.        ((A -> (A or B)) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-32, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10811
in-theory        10811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-23 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10811.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-23, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10812
in-theory        10812
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-22 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10812.        (((A and B) -> B) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-22, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10813
in-theory        10813
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-21 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10813.        (((A and B) -> A) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-21, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10814
in-theory        10814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-20 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10814.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-20, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10815
in-theory        10815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-19 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10815.        ((A -> (B -> A)) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-19, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10816
in-theory        10816
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-7 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10816.        (A or (((B and C) -> C) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-7, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10817
in-theory        10817
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10817.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) or F), M:tm-6, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10818
in-theory        10818
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> ((E -> (F -> (E and F))) and D))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10818.        (A -> ((((B and C) -> C) and (D -> ((E -> (F -> (E and F))) and D))) and A)), M:tm-5, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10819
in-theory        10819
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-1 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10819.        (A -> (((B and C) -> C) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-1, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10820
in-theory        10820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-270 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10820.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-270, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10821
in-theory        10821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-239 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10821.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-239, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10822
in-theory        10822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-210 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10822.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-210, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10823
in-theory        10823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-183 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10823.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-183, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10824
in-theory        10824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-157 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10824.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-157, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10825
in-theory        10825
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-147 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10825.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-147, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10826
in-theory        10826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-134 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10826.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-134, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10827
in-theory        10827
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-125 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10827.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-125, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10828
in-theory        10828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-113 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10828.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-113, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10829
in-theory        10829
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     37
proof            (modus-ponens tm-105 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10829.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-105, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10830
in-theory        10830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-95 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10830.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-95, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10831
in-theory        10831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-83 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10831.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-83, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10832
in-theory        10832
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-76 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-10 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10832.        (((not (not A)) -> A) and (((B and C) -> B) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-76, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10833
in-theory        10833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-69 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10833.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-69, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10834
in-theory        10834
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-54 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10834.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-54, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10835
in-theory        10835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-42 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10835.        ((A -> (B or A)) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-42, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10836
in-theory        10836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-32 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10836.        ((A -> (A or B)) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-32, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10837
in-theory        10837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-23 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10837.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-23, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10838
in-theory        10838
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-22 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10838.        (((A and B) -> B) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-22, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10839
in-theory        10839
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-21 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10839.        (((A and B) -> A) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-21, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10840
in-theory        10840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-20 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10840.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-20, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10841
in-theory        10841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-19 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10841.        ((A -> (B -> A)) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-19, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10842
in-theory        10842
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-7 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10842.        (A or (((B and C) -> B) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-7, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10843
in-theory        10843
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10843.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) or F), M:tm-6, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10844
in-theory        10844
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> ((E -> (F -> (E and F))) and D))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10844.        (A -> ((((B and C) -> B) and (D -> ((E -> (F -> (E and F))) and D))) and A)), M:tm-5, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10845
in-theory        10845
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-1 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10845.        (A -> (((B and C) -> B) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-1, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10846
in-theory        10846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-270 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10846.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-270, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10847
in-theory        10847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-239 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10847.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-239, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10848
in-theory        10848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> (I and J))) and H))))
theorem-size     43
proof            (modus-ponens tm-210 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-2)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10848.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-210, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10849
in-theory        10849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-183 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10849.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-183, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10850
in-theory        10850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-157 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10850.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-157, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10851
in-theory        10851
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     41
proof            (modus-ponens tm-147 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10851.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-147, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10852
in-theory        10852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-134 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10852.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-134, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10853
in-theory        10853
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     41
proof            (modus-ponens tm-125 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10853.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-125, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10854
in-theory        10854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> (I and J))) and H))))
theorem-size     41
proof            (modus-ponens tm-113 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10854.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-113, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10855
in-theory        10855
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     45
proof            (modus-ponens tm-105 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10855.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-105, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10856
in-theory        10856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-95 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10856.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-95, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10857
in-theory        10857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-83 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10857.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-83, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10858
in-theory        10858
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     31
proof            (modus-ponens tm-76 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10858.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-76, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10859
in-theory        10859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     37
proof            (modus-ponens tm-69 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10859.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-69, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10860
in-theory        10860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     39
proof            (modus-ponens tm-54 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10860.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-54, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10861
in-theory        10861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-42 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10861.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-42, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10862
in-theory        10862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-32 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10862.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-32, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10863
in-theory        10863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-23 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10863.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-23, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10864
in-theory        10864
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-22 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10864.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-22, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10865
in-theory        10865
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-21 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10865.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-21, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10866
in-theory        10866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     39
proof            (modus-ponens tm-20 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10866.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-20, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10867
in-theory        10867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-19 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10867.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-19, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10868
in-theory        10868
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-7 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10868.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-7, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10869
in-theory        10869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) or G)
theorem-size     27
proof            (modus-ponens tm-6 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10869.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) or G), M:tm-6, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10870
in-theory        10870
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> (F and G))) and E))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10870.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> (F and G))) and E))) and A)), M:tm-5, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10871
in-theory        10871
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-1 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10871.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-1, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-10872
in-theory        10872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-270 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10872.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-270, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10873
in-theory        10873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-239 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10873.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-239, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10874
in-theory        10874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-210 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10874.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-210, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10875
in-theory        10875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-183 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10875.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-183, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10876
in-theory        10876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-157 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10876.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-157, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10877
in-theory        10877
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-147 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10877.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-147, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10878
in-theory        10878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-134 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10878.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-134, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10879
in-theory        10879
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-125 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10879.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-125, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10880
in-theory        10880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-113 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10880.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-113, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10881
in-theory        10881
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     37
proof            (modus-ponens tm-105 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10881.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-105, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10882
in-theory        10882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-95 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10882.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-95, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10883
in-theory        10883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-83 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10883.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-83, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10884
in-theory        10884
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-76 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10884.        (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-76, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10885
in-theory        10885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-69 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10885.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-69, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10886
in-theory        10886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-54 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10886.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-54, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10887
in-theory        10887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-42 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10887.        ((A -> (B or A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-42, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10888
in-theory        10888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-32 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10888.        ((A -> (A or B)) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-32, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10889
in-theory        10889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-23 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10889.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-23, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10890
in-theory        10890
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-22 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10890.        (((A and B) -> B) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-22, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10891
in-theory        10891
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-21 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10891.        (((A and B) -> A) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-21, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10892
in-theory        10892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-20 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10892.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-20, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10893
in-theory        10893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-19 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10893.        ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-19, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10894
in-theory        10894
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-7 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10894.        (A or ((B -> (C -> B)) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-7, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10895
in-theory        10895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10895.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) or F), M:tm-6, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10896
in-theory        10896
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> ((E -> (F -> (E and F))) and D))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10896.        (A -> (((B -> (C -> B)) and (D -> ((E -> (F -> (E and F))) and D))) and A)), M:tm-5, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10897
in-theory        10897
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-1 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-1 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10897.        (A -> ((B -> (C -> B)) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-1, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-10898
in-theory        10898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-270 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10898.        ((A -> (((B and C) -> C) and A)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-270, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10899
in-theory        10899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-239 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10899.        ((A -> (((B and C) -> B) and A)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-239, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10900
in-theory        10900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E)))
theorem-size     33
proof            (modus-ponens tm-210 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10900.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E))), M:tm-210, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10901
in-theory        10901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-183 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10901.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-183, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10902
in-theory        10902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-157 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10902.        ((A -> ((B and C) -> C)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-157, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10903
in-theory        10903
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not ((C -> (D -> (C and D))) and ((A and B) -> B)))))
theorem-size     21
proof            (modus-ponens tm-153 tm-299 ((A (-> (-> (and B C) C) (not (and (-> Bm (-> Cm (and Bm Cm))) (-> (and B C) C))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10903.        (not (((A and B) -> B) -> (not ((C -> (D -> (C and D))) and ((A and B) -> B))))), M:tm-153, m:tm-299, u:((A (-> (-> (and B C) C) (not (and (-> Bm (-> Cm (and Bm Cm))) (-> (and B C) C))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-10904
in-theory        10904
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-147 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10904.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-147, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10905
in-theory        10905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-134 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10905.        ((A -> ((B and C) -> B)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-134, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10906
in-theory        10906
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not ((C -> (D -> (C and D))) and ((A and B) -> A)))))
theorem-size     21
proof            (modus-ponens tm-130 tm-299 ((A (-> (-> (and B C) B) (not (and (-> Bm (-> Cm (and Bm Cm))) (-> (and B C) B))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10906.        (not (((A and B) -> A) -> (not ((C -> (D -> (C and D))) and ((A and B) -> A))))), M:tm-130, m:tm-299, u:((A (-> (-> (and B C) B) (not (and (-> Bm (-> Cm (and Bm Cm))) (-> (and B C) B))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-10907
in-theory        10907
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-125 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10907.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-125, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10908
in-theory        10908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E)))
theorem-size     31
proof            (modus-ponens tm-113 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10908.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E))), M:tm-113, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10909
in-theory        10909
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D -> (E -> (D and E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))))
theorem-size     37
proof            (modus-ponens tm-109 tm-299 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-5)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10909.        (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D -> (E -> (D and E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))), M:tm-109, m:tm-299, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-10910
in-theory        10910
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     35
proof            (modus-ponens tm-105 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10910.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-105, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10911
in-theory        10911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C)))
theorem-size     23
proof            (modus-ponens tm-95 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10911.        (((A -> B) -> (A -> A)) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C))), M:tm-95, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10912
in-theory        10912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (D -> (not A)))
theorem-size     17
proof            (modus-ponens tm-84 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10912.        ((A -> (not ((B -> (C -> (B and C))) and A))) -> (D -> (not A))), M:tm-84, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-10913
in-theory        10913
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-83 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10913.        ((A -> (B -> (C -> B))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-83, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10914
in-theory        10914
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not ((C -> (D -> (C and D))) and (A -> (B -> A))))))
theorem-size     21
proof            (modus-ponens tm-79 tm-299 ((A (-> (-> B (-> C B)) (not (and (-> Bm (-> Cm (and Bm Cm))) (-> B (-> C B)))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10914.        (not ((A -> (B -> A)) -> (not ((C -> (D -> (C and D))) and (A -> (B -> A)))))), M:tm-79, m:tm-299, u:((A (-> (-> B (-> C B)) (not (and (-> Bm (-> Cm (and Bm Cm))) (-> B (-> C B)))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-10915
in-theory        10915
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not ((C -> (D -> (C and D))) and B))) -> (not B)))
theorem-size     21
proof            (modus-ponens tm-76 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10915.        (((not (not A)) -> A) and ((B -> (not ((C -> (D -> (C and D))) and B))) -> (not B))), M:tm-76, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10916
in-theory        10916
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not ((B -> (C -> (B and C))) and A))))) or (A -> (not ((B -> (C -> (B and C))) and A)))) -> (not A))
theorem-size     30
proof            (modus-ponens tm-73 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-5)
proof-size       110
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10916.        (((not (not (A -> (not ((B -> (C -> (B and C))) and A))))) or (A -> (not ((B -> (C -> (B and C))) and A)))) -> (not A)), M:tm-73, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-10917
in-theory        10917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C)))
theorem-size     27
proof            (modus-ponens tm-69 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-9)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10917.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C))), M:tm-69, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10918
in-theory        10918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-54 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10918.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-54, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10919
in-theory        10919
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not ((C -> (D -> (C and D))) and B)))) or (B -> (not ((C -> (D -> (C and D))) and B)))) -> (not B))
theorem-size     30
proof            (modus-ponens tm-47 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-5)
proof-size       110
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10919.        (((A and (B -> (not ((C -> (D -> (C and D))) and B)))) or (B -> (not ((C -> (D -> (C and D))) and B)))) -> (not B)), M:tm-47, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-10920
in-theory        10920
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not ((B -> (C -> (B and C))) and A))) and D) or (A -> (not ((B -> (C -> (B and C))) and A)))) -> (not A))
theorem-size     30
proof            (modus-ponens tm-46 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-5)
proof-size       110
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10920.        ((((A -> (not ((B -> (C -> (B and C))) and A))) and D) or (A -> (not ((B -> (C -> (B and C))) and A)))) -> (not A)), M:tm-46, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-10921
in-theory        10921
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A -> (B -> (A and B))) and C)) or (C -> (not ((A -> (B -> (A and B))) and C)))) -> (not C))
theorem-size     26
proof            (modus-ponens tm-44 tm-299 ((A Am) (B (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-5)
proof-size       108
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10921.        (((not ((A -> (B -> (A and B))) and C)) or (C -> (not ((A -> (B -> (A and B))) and C)))) -> (not C)), M:tm-44, m:tm-299, u:((A Am) (B (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (C (not Am)))
================================================================
tm-name          tm-10922
in-theory        10922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-42 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10922.        ((A -> (B or A)) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C))), M:tm-42, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10923
in-theory        10923
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-32 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10923.        ((A -> (A or B)) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C))), M:tm-32, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10924
in-theory        10924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> (B and C))) and A))) -> ((A -> (not ((B -> (C -> (B and C))) and A))) and (not A)))
theorem-size     28
proof            (modus-ponens tm-24 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       108
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10924.        ((A -> (not ((B -> (C -> (B and C))) and A))) -> ((A -> (not ((B -> (C -> (B and C))) and A))) and (not A))), M:tm-24, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-10925
in-theory        10925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C)))
theorem-size     23
proof            (modus-ponens tm-23 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10925.        ((A -> (B -> (A and B))) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C))), M:tm-23, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10926
in-theory        10926
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-22 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10926.        (((A and B) -> B) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C))), M:tm-22, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10927
in-theory        10927
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-21 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10927.        (((A and B) -> A) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C))), M:tm-21, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10928
in-theory        10928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-20 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10928.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-20, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10929
in-theory        10929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-19 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10929.        ((A -> (B -> A)) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C))), M:tm-19, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10930
in-theory        10930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (A -> (not ((B -> (C -> (B and C))) and A))))
theorem-size     25
proof            (modus-ponens tm-12 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10930.        ((A -> (not ((B -> (C -> (B and C))) and A))) -> (A -> (not ((B -> (C -> (B and C))) and A)))), M:tm-12, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-10931
in-theory        10931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (C -> (B and C))) and A)))))
theorem-size     30
proof            (modus-ponens tm-9 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-9 tm-5)
proof-size       92
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10931.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (C -> (B and C))) and A))))), M:tm-9, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-10932
in-theory        10932
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not ((C -> (D -> (C and D))) and A))) or (not A)) -> B))
theorem-size     22
proof            (modus-ponens tm-8 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-5)
proof-size       86
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10932.        (((not A) -> B) -> (((A -> (not ((C -> (D -> (C and D))) and A))) or (not A)) -> B)), M:tm-8, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-10933
in-theory        10933
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not ((C -> (D -> (C and D))) and B))) -> (not B)))
theorem-size     17
proof            (modus-ponens tm-7 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-5)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10933.        (A or ((B -> (not ((C -> (D -> (C and D))) and B))) -> (not B))), M:tm-7, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10934
in-theory        10934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-5)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10934.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) or D), M:tm-6, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10935
in-theory        10935
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not ((C -> (D -> (C and D))) and B))) -> (not B)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10935.        (A -> (((B -> (not ((C -> (D -> (C and D))) and B))) -> (not B)) and A)), M:tm-5, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10936
in-theory        10936
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not ((C -> (D -> (C and D))) and B))) -> (not B)))
theorem-size     17
proof            (modus-ponens tm-1 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-5)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10936.        (A -> ((B -> (not ((C -> (D -> (C and D))) and B))) -> (not B))), M:tm-1, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-10937
in-theory        10937
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((B -> (C -> (B and C))) and A)))
theorem-size     23
proof            (modus-ponens tm-300 tm-1 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10937.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-1, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10938
in-theory        10938
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (B -> (C -> (B and C))))
theorem-size     19
proof            (modus-ponens tm-300 tm-3 ((Am (-> A (-> B (and A B)))) (C Bm) (D (-> A (-> B (and A B))))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-10938.        ((A or ((B -> (C -> (B and C))) and A)) -> (B -> (C -> (B and C)))), M:tm-300, m:tm-3, u:((Am (-> A (-> B (and A B)))) (C Bm) (D (-> A (-> B (and A B)))))
================================================================
tm-name          tm-10939
in-theory        10939
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> A)
theorem-size     13
proof            (modus-ponens tm-300 tm-4 ((Am (-> A (-> B (and A B)))) (C Bm) (D Bm)))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-10939.        ((A or ((B -> (C -> (B and C))) and A)) -> A), M:tm-300, m:tm-4, u:((Am (-> A (-> B (and A B)))) (C Bm) (D Bm))
================================================================
tm-name          tm-10940
in-theory        10940
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (((B -> (C -> (B and C))) and A) and D)))
theorem-size     25
proof            (modus-ponens tm-300 tm-5 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (and (-> A (-> B (and A B))) C) Bm)))))
axioms-used      (tm-8 tm-5)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10940.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (((B -> (C -> (B and C))) and A) and D))), M:tm-300, m:tm-5, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (and (-> A (-> B (and A B))) C) Bm))))
================================================================
tm-name          tm-10941
in-theory        10941
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) or D))
theorem-size     23
proof            (modus-ponens tm-300 tm-6 ((Am (and (-> A (-> B (and A B))) C)) (D (or (and (-> A (-> B (and A B))) C) Bm))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-10941.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) or D)), M:tm-300, m:tm-6, u:((Am (and (-> A (-> B (and A B))) C)) (D (or (and (-> A (-> B (and A B))) C) Bm)))
================================================================
tm-name          tm-10942
in-theory        10942
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D or ((B -> (C -> (B and C))) and A)))
theorem-size     23
proof            (modus-ponens tm-300 tm-7 ((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-10942.        ((A or ((B -> (C -> (B and C))) and A)) -> (D or ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-7, u:((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10943
in-theory        10943
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-300 tm-11 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10943.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (E -> D))), M:tm-300, m:tm-11, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-10944
in-theory        10944
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-300 tm-14 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10944.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-300, m:tm-14, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-10945
in-theory        10945
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-300 tm-16 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10945.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D and E) -> D)), M:tm-300, m:tm-16, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-10946
in-theory        10946
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-300 tm-18 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10946.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D and E) -> E)), M:tm-300, m:tm-18, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-10947
in-theory        10947
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> D)) and ((B -> (C -> (B and C))) and A)))
theorem-size     27
proof            (modus-ponens tm-300 tm-19 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm Bm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10947.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> D)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-19, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm Bm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10948
in-theory        10948
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (C -> (B and C))) and A)))
theorem-size     35
proof            (modus-ponens tm-300 tm-20 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10948.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-20, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10949
in-theory        10949
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D and E) -> D) and ((B -> (C -> (B and C))) and A)))
theorem-size     27
proof            (modus-ponens tm-300 tm-21 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (and Bm Cm) Bm) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10949.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D and E) -> D) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-21, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (and Bm Cm) Bm) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10950
in-theory        10950
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D and E) -> E) and ((B -> (C -> (B and C))) and A)))
theorem-size     27
proof            (modus-ponens tm-300 tm-22 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (and Bm Cm) Cm) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10950.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D and E) -> E) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-22, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (and Bm Cm) Cm) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10951
in-theory        10951
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> (D and E))) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-23 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10951.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> (D and E))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-23, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10952
in-theory        10952
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-300 tm-25 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10952.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (E -> (D and E)))), M:tm-300, m:tm-25, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-10953
in-theory        10953
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (D or E)) and ((B -> (C -> (B and C))) and A)))
theorem-size     27
proof            (modus-ponens tm-300 tm-32 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (or Bm Cm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10953.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (D or E)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-32, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (or Bm Cm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10954
in-theory        10954
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-300 tm-33 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10954.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (D or E))), M:tm-300, m:tm-33, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-10955
in-theory        10955
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E or D)) and ((B -> (C -> (B and C))) and A)))
theorem-size     27
proof            (modus-ponens tm-300 tm-42 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (or Cm Bm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10955.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E or D)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-42, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (or Cm Bm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10956
in-theory        10956
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-300 tm-43 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10956.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (E or D))), M:tm-300, m:tm-43, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-10957
in-theory        10957
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> (C -> (B and C))) and A)))
theorem-size     35
proof            (modus-ponens tm-300 tm-54 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10957.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-54, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10958
in-theory        10958
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-300 tm-56 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-10958.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-300, m:tm-56, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-10959
in-theory        10959
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B -> (C -> (B and C))) and A)))
theorem-size     33
proof            (modus-ponens tm-300 tm-69 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-9)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10959.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-69, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10960
in-theory        10960
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-300 tm-71 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-10960.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-300, m:tm-71, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-10961
in-theory        10961
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((not (not D)) -> D) and ((B -> (C -> (B and C))) and A)))
theorem-size     27
proof            (modus-ponens tm-300 tm-76 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (not (not Bm)) Bm) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-10)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10961.        ((A or ((B -> (C -> (B and C))) and A)) -> (((not (not D)) -> D) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-76, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (not (not Bm)) Bm) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10962
in-theory        10962
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((not (not D)) -> D))
theorem-size     17
proof            (modus-ponens tm-300 tm-78 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-5 tm-1 tm-10)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-10962.        ((A or ((B -> (C -> (B and C))) and A)) -> ((not (not D)) -> D)), M:tm-300, m:tm-78, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-10963
in-theory        10963
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> (F -> E))) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-83 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10963.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> (F -> E))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-83, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10964
in-theory        10964
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-300 tm-85 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-10964.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (E -> (F -> E)))), M:tm-300, m:tm-85, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-10965
in-theory        10965
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((B -> (C -> (B and C))) and A))
theorem-size     21
proof            (modus-ponens tm-300 tm-86 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> A (-> B (and A B))) C))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-10965.        ((A or ((B -> (C -> (B and C))) and A)) -> ((B -> (C -> (B and C))) and A)), M:tm-300, m:tm-86, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> A (-> B (and A B))) C)))
================================================================
tm-name          tm-10966
in-theory        10966
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> (D -> D)) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-95 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10966.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> (D -> D)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-95, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10967
in-theory        10967
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> E) -> (D -> D)))
theorem-size     19
proof            (modus-ponens tm-300 tm-97 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-10967.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> E) -> (D -> D))), M:tm-300, m:tm-97, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-10968
in-theory        10968
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B -> (C -> (B and C))) and A)))
theorem-size     41
proof            (modus-ponens tm-300 tm-105 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10968.        ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-105, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10969
in-theory        10969
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-300 tm-107 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-10969.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-300, m:tm-107, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-10970
in-theory        10970
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (C -> (B and C))) and A)))
theorem-size     37
proof            (modus-ponens tm-300 tm-113 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10970.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-113, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10971
in-theory        10971
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-300 tm-115 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10971.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-300, m:tm-115, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-10972
in-theory        10972
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A -> (B -> (A and B))) and A)) -> (B -> (A and B)))
theorem-size     17
proof            (modus-ponens tm-300 tm-116 ((A Am) (Bm (-> B (and Am B))) (C Am) (D (-> B (and Am B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-10972.        ((A or ((A -> (B -> (A and B))) and A)) -> (B -> (A and B))), M:tm-300, m:tm-116, u:((A Am) (Bm (-> B (and Am B))) (C Am) (D (-> B (and Am B))))
================================================================
tm-name          tm-10973
in-theory        10973
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> B)) -> (D -> ((B -> (C -> B)) and D))) and A)) -> (D -> ((B -> (C -> B)) and D)))
theorem-size     29
proof            (modus-ponens tm-300 tm-117 ((A (-> Am (-> Bm Am))) (Cm (-> B (and (-> Am (-> Bm Am)) B))) (C Dm) (D (-> B (and (-> Am (-> Bm Am)) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-10973.        ((A or (((B -> (C -> B)) -> (D -> ((B -> (C -> B)) and D))) and A)) -> (D -> ((B -> (C -> B)) and D))), M:tm-300, m:tm-117, u:((A (-> Am (-> Bm Am))) (Cm (-> B (and (-> Am (-> Bm Am)) B))) (C Dm) (D (-> B (and (-> Am (-> Bm Am)) B))))
================================================================
tm-name          tm-10974
in-theory        10974
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E))) and A)) -> (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))
theorem-size     53
proof            (modus-ponens tm-300 tm-118 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))) (C Em) (D (-> B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-10974.        ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E))) and A)) -> (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E))), M:tm-300, m:tm-118, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))) (C Em) (D (-> B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))))
================================================================
tm-name          tm-10975
in-theory        10975
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B -> (C -> (B and C))) and A)))
theorem-size     37
proof            (modus-ponens tm-300 tm-125 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10975.        ((A or ((B -> (C -> (B and C))) and A)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-125, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10976
in-theory        10976
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-300 tm-127 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-10976.        ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-300, m:tm-127, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-10977
in-theory        10977
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> B) -> (D -> (((B and C) -> B) and D))) and A)) -> (D -> (((B and C) -> B) and D)))
theorem-size     29
proof            (modus-ponens tm-300 tm-128 ((A (-> (and Am Bm) Am)) (Cm (-> B (and (-> (and Am Bm) Am) B))) (C Dm) (D (-> B (and (-> (and Am Bm) Am) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-10977.        ((A or ((((B and C) -> B) -> (D -> (((B and C) -> B) and D))) and A)) -> (D -> (((B and C) -> B) and D))), M:tm-300, m:tm-128, u:((A (-> (and Am Bm) Am)) (Cm (-> B (and (-> (and Am Bm) Am) B))) (C Dm) (D (-> B (and (-> (and Am Bm) Am) B))))
================================================================
tm-name          tm-10978
in-theory        10978
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> ((E and F) -> E)) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-134 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10978.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> ((E and F) -> E)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-134, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10979
in-theory        10979
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-300 tm-136 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-10979.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((E and F) -> E))), M:tm-300, m:tm-136, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-10980
in-theory        10980
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) or ((A -> (B -> (A and B))) and ((A -> (B -> (A and B))) -> C))) -> C)
theorem-size     29
proof            (modus-ponens tm-300 tm-137 ((Am (-> A (-> B (and A B)))) (C (-> (-> A (-> B (and A B))) Bm)) (D Bm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-10980.        ((((A -> (B -> (A and B))) -> C) or ((A -> (B -> (A and B))) and ((A -> (B -> (A and B))) -> C))) -> C), M:tm-300, m:tm-137, u:((Am (-> A (-> B (and A B)))) (C (-> (-> A (-> B (and A B))) Bm)) (D Bm))
================================================================
tm-name          tm-10981
in-theory        10981
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) or ((D -> (E -> (D and E))) and ((A -> (B -> A)) -> C))) -> C)
theorem-size     25
proof            (modus-ponens tm-300 tm-138 ((Am (-> A (-> B (and A B)))) (C (-> (-> Bm (-> Cm Bm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-10981.        ((((A -> (B -> A)) -> C) or ((D -> (E -> (D and E))) and ((A -> (B -> A)) -> C))) -> C), M:tm-300, m:tm-138, u:((Am (-> A (-> B (and A B)))) (C (-> (-> Bm (-> Cm Bm)) Dm)) (D Dm))
================================================================
tm-name          tm-10982
in-theory        10982
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or ((E -> (F -> (E and F))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D)
theorem-size     41
proof            (modus-ponens tm-300 tm-139 ((Am (-> A (-> B (and A B)))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (D Em)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-10982.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or ((E -> (F -> (E and F))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D), M:tm-300, m:tm-139, u:((Am (-> A (-> B (and A B)))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (D Em))
================================================================
tm-name          tm-10983
in-theory        10983
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) or ((D -> (E -> (D and E))) and (((A and B) -> A) -> C))) -> C)
theorem-size     25
proof            (modus-ponens tm-300 tm-140 ((Am (-> A (-> B (and A B)))) (C (-> (-> (and Bm Cm) Bm) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-10983.        (((((A and B) -> A) -> C) or ((D -> (E -> (D and E))) and (((A and B) -> A) -> C))) -> C), M:tm-300, m:tm-140, u:((Am (-> A (-> B (and A B)))) (C (-> (-> (and Bm Cm) Bm) Dm)) (D Dm))
================================================================
tm-name          tm-10984
in-theory        10984
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B -> (C -> (B and C))) and A)))
theorem-size     37
proof            (modus-ponens tm-300 tm-147 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10984.        ((A or ((B -> (C -> (B and C))) and A)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-147, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10985
in-theory        10985
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-300 tm-149 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-10985.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-300, m:tm-149, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-10986
in-theory        10986
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) or ((D -> (E -> (D and E))) and (((A and B) -> B) -> C))) -> C)
theorem-size     25
proof            (modus-ponens tm-300 tm-150 ((Am (-> A (-> B (and A B)))) (C (-> (-> (and Bm Cm) Cm) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-10986.        (((((A and B) -> B) -> C) or ((D -> (E -> (D and E))) and (((A and B) -> B) -> C))) -> C), M:tm-300, m:tm-150, u:((Am (-> A (-> B (and A B)))) (C (-> (-> (and Bm Cm) Cm) Dm)) (D Dm))
================================================================
tm-name          tm-10987
in-theory        10987
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> C) -> (D -> (((B and C) -> C) and D))) and A)) -> (D -> (((B and C) -> C) and D)))
theorem-size     29
proof            (modus-ponens tm-300 tm-151 ((A (-> (and Am Bm) Bm)) (Cm (-> B (and (-> (and Am Bm) Bm) B))) (C Dm) (D (-> B (and (-> (and Am Bm) Bm) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-10987.        ((A or ((((B and C) -> C) -> (D -> (((B and C) -> C) and D))) and A)) -> (D -> (((B and C) -> C) and D))), M:tm-300, m:tm-151, u:((A (-> (and Am Bm) Bm)) (Cm (-> B (and (-> (and Am Bm) Bm) B))) (C Dm) (D (-> B (and (-> (and Am Bm) Bm) B))))
================================================================
tm-name          tm-10988
in-theory        10988
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> ((E and F) -> F)) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-157 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10988.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> ((E and F) -> F)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-157, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10989
in-theory        10989
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-300 tm-159 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-10989.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((E and F) -> F))), M:tm-300, m:tm-159, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-10990
in-theory        10990
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> ((E -> (F -> E)) and D)) and ((B -> (C -> (B and C))) and A)))
theorem-size     31
proof            (modus-ponens tm-300 tm-183 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10990.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> ((E -> (F -> E)) and D)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-183, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10991
in-theory        10991
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-300 tm-184 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-10991.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((E -> (F -> E)) and D))), M:tm-300, m:tm-184, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-10992
in-theory        10992
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B -> (C -> (B and C))) and A)))
theorem-size     39
proof            (modus-ponens tm-300 tm-210 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10992.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-210, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10993
in-theory        10993
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     29
proof            (modus-ponens tm-300 tm-211 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-10993.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-300, m:tm-211, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-10994
in-theory        10994
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (((E and F) -> E) and D)) and ((B -> (C -> (B and C))) and A)))
theorem-size     31
proof            (modus-ponens tm-300 tm-239 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10994.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (((E and F) -> E) and D)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-239, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10995
in-theory        10995
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (((E and F) -> E) and D)))
theorem-size     21
proof            (modus-ponens tm-300 tm-240 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-10995.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (((E and F) -> E) and D))), M:tm-300, m:tm-240, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-10996
in-theory        10996
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (((E and F) -> F) and D)) and ((B -> (C -> (B and C))) and A)))
theorem-size     31
proof            (modus-ponens tm-300 tm-270 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10996.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (((E and F) -> F) and D)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-270, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-10997
in-theory        10997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (((E and F) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-300 tm-271 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-10997.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (((E and F) -> F) and D))), M:tm-300, m:tm-271, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-10998
in-theory        10998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-270 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10998.        ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-270, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-10999
in-theory        10999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-239 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10999.        ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-239, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11000
in-theory        11000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> (E and F))) and G) -> H) -> ((G or ((E -> (F -> (E and F))) and G)) -> H)))
theorem-size     43
proof            (modus-ponens tm-210 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11000.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> (E and F))) and G) -> H) -> ((G or ((E -> (F -> (E and F))) and G)) -> H))), M:tm-210, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11001
in-theory        11001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-183 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11001.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-183, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11002
in-theory        11002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-157 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11002.        ((A -> ((B and C) -> C)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-157, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11003
in-theory        11003
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> (B and C))) and D) -> D)) -> ((D or ((B -> (C -> (B and C))) and D)) -> D))
theorem-size     27
proof            (modus-ponens tm-154 tm-300 ((A (-> Am (-> Bm (and Am Bm)))) (Dm Cm) (B Cm) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Cm))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11003.        ((A or (((B -> (C -> (B and C))) and D) -> D)) -> ((D or ((B -> (C -> (B and C))) and D)) -> D)), M:tm-154, m:tm-300, u:((A (-> Am (-> Bm (and Am Bm)))) (Dm Cm) (B Cm) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Cm)))
================================================================
tm-name          tm-11004
in-theory        11004
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-147 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11004.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-147, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11005
in-theory        11005
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and (C -> D)) -> C) or (((A -> (B -> (A and B))) and (C -> D)) -> D)) -> (((C -> D) or ((A -> (B -> (A and B))) and (C -> D))) -> D))
theorem-size     45
proof            (modus-ponens tm-144 tm-300 ((A (-> Am (-> Bm (and Am Bm)))) (Cm (-> B Dm)) (C Dm) (D (-> (or (-> B Dm) (and (-> Am (-> Bm (and Am Bm))) (-> B Dm))) Dm))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11005.        (((((A -> (B -> (A and B))) and (C -> D)) -> C) or (((A -> (B -> (A and B))) and (C -> D)) -> D)) -> (((C -> D) or ((A -> (B -> (A and B))) and (C -> D))) -> D)), M:tm-144, m:tm-300, u:((A (-> Am (-> Bm (and Am Bm)))) (Cm (-> B Dm)) (C Dm) (D (-> (or (-> B Dm) (and (-> Am (-> Bm (and Am Bm))) (-> B Dm))) Dm)))
================================================================
tm-name          tm-11006
in-theory        11006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-134 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11006.        ((A -> ((B and C) -> B)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-134, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11007
in-theory        11007
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> (B and C))) and D) -> (B -> (C -> (B and C))))) -> ((D or ((B -> (C -> (B and C))) and D)) -> (B -> (C -> (B and C)))))
theorem-size     39
proof            (modus-ponens tm-131 tm-300 ((Dm (-> Am (-> Bm (and Am Bm)))) (B Cm) (A (-> Am (-> Bm (and Am Bm)))) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (-> Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11007.        ((A or (((B -> (C -> (B and C))) and D) -> (B -> (C -> (B and C))))) -> ((D or ((B -> (C -> (B and C))) and D)) -> (B -> (C -> (B and C))))), M:tm-131, m:tm-300, u:((Dm (-> Am (-> Bm (and Am Bm)))) (B Cm) (A (-> Am (-> Bm (and Am Bm)))) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (-> Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-11008
in-theory        11008
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-125 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11008.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-125, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11009
in-theory        11009
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> A) or (((A -> (B -> (A and B))) and C) -> (B -> (A and B)))) -> ((C or ((A -> (B -> (A and B))) and C)) -> (B -> (A and B))))
theorem-size     45
proof            (modus-ponens tm-122 tm-300 ((A Am) (Dm (-> Bm (and Am Bm))) (C Cm) (B (-> Bm (and Am Bm))) (D (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11009.        (((((A -> (B -> (A and B))) and C) -> A) or (((A -> (B -> (A and B))) and C) -> (B -> (A and B)))) -> ((C or ((A -> (B -> (A and B))) and C)) -> (B -> (A and B)))), M:tm-122, m:tm-300, u:((A Am) (Dm (-> Bm (and Am Bm))) (C Cm) (B (-> Bm (and Am Bm))) (D (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-11010
in-theory        11010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and C) -> (D -> E)) -> (((C or ((A -> (B -> (A and B))) and C)) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> E)))
theorem-size     41
proof            (modus-ponens tm-114 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) (-> C D))) (B (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11010.        ((((A -> (B -> (A and B))) and C) -> (D -> E)) -> (((C or ((A -> (B -> (A and B))) and C)) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> E))), M:tm-114, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) (-> C D))) (B (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-11011
in-theory        11011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> (E and F))) and G) -> H) -> ((G or ((E -> (F -> (E and F))) and G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-113 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11011.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> (E and F))) and G) -> H) -> ((G or ((E -> (F -> (E and F))) and G)) -> H))), M:tm-113, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11012
in-theory        11012
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     45
proof            (modus-ponens tm-105 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11012.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-105, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11013
in-theory        11013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-95 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11013.        (((A -> B) -> (A -> A)) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F))), M:tm-95, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11014
in-theory        11014
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) or (((A -> (B -> (A and B))) and C) -> ((A -> (B -> (A and B))) and C))) -> ((C or ((A -> (B -> (A and B))) and C)) -> ((A -> (B -> (A and B))) and C)))
theorem-size     53
proof            (modus-ponens tm-92 tm-300 ((Dm (and (-> Am (-> Bm (and Am Bm))) Cm)) (A (and (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (and (-> Am (-> Bm (and Am Bm))) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11014.        (((((A -> (B -> (A and B))) and C) -> D) or (((A -> (B -> (A and B))) and C) -> ((A -> (B -> (A and B))) and C))) -> ((C or ((A -> (B -> (A and B))) and C)) -> ((A -> (B -> (A and B))) and C))), M:tm-92, m:tm-300, u:((Dm (and (-> Am (-> Bm (and Am Bm))) Cm)) (A (and (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (and (-> Am (-> Bm (and Am Bm))) Cm))))
================================================================
tm-name          tm-11015
in-theory        11015
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and C) -> D) -> (E -> ((C or ((A -> (B -> (A and B))) and C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-84 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11015.        ((((A -> (B -> (A and B))) and C) -> D) -> (E -> ((C or ((A -> (B -> (A and B))) and C)) -> D))), M:tm-84, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-11016
in-theory        11016
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-83 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11016.        ((A -> (B -> (C -> B))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-83, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11017
in-theory        11017
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> (B and C))) and D) -> (E -> ((B -> (C -> (B and C))) and D)))) -> ((D or ((B -> (C -> (B and C))) and D)) -> (E -> ((B -> (C -> (B and C))) and D))))
theorem-size     47
proof            (modus-ponens tm-80 tm-300 ((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (-> B (and (-> Am (-> Bm (and Am Bm))) Cm))) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (-> B (and (-> Am (-> Bm (and Am Bm))) Cm))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11017.        ((A or (((B -> (C -> (B and C))) and D) -> (E -> ((B -> (C -> (B and C))) and D)))) -> ((D or ((B -> (C -> (B and C))) and D)) -> (E -> ((B -> (C -> (B and C))) and D)))), M:tm-80, m:tm-300, u:((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (-> B (and (-> Am (-> Bm (and Am Bm))) Cm))) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (-> B (and (-> Am (-> Bm (and Am Bm))) Cm)))))
================================================================
tm-name          tm-11018
in-theory        11018
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C -> (B and C))) and D) -> E) -> ((D or ((B -> (C -> (B and C))) and D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-76 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11018.        (((not (not A)) -> A) and ((((B -> (C -> (B and C))) and D) -> E) -> ((D or ((B -> (C -> (B and C))) and D)) -> E))), M:tm-76, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11019
in-theory        11019
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (B -> (A and B))) and C) -> D))) or (((A -> (B -> (A and B))) and C) -> D)) -> ((C or ((A -> (B -> (A and B))) and C)) -> D))
theorem-size     39
proof            (modus-ponens tm-73 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-5)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11019.        (((not (not (((A -> (B -> (A and B))) and C) -> D))) or (((A -> (B -> (A and B))) and C) -> D)) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-73, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-11020
in-theory        11020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-69 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11020.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F))), M:tm-69, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11021
in-theory        11021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and C) -> (C or ((A -> (B -> (A and B))) and C))) -> ((((A -> (B -> (A and B))) and C) or (C or ((A -> (B -> (A and B))) and C))) -> (C or ((A -> (B -> (A and B))) and C))))
theorem-size     55
proof            (modus-ponens tm-55 tm-300 ((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm))) (B (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm))) (C (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11021.        ((((A -> (B -> (A and B))) and C) -> (C or ((A -> (B -> (A and B))) and C))) -> ((((A -> (B -> (A and B))) and C) or (C or ((A -> (B -> (A and B))) and C))) -> (C or ((A -> (B -> (A and B))) and C)))), M:tm-55, m:tm-300, u:((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm))) (B (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm))) (C (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm))))
================================================================
tm-name          tm-11022
in-theory        11022
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-54 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11022.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-54, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11023
in-theory        11023
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> (B and C))) and D) -> (A and ((B -> (C -> (B and C))) and D)))) -> ((D or ((B -> (C -> (B and C))) and D)) -> (A and ((B -> (C -> (B and C))) and D))))
theorem-size     47
proof            (modus-ponens tm-48 tm-300 ((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (and B (and (-> Am (-> Bm (and Am Bm))) Cm))) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (and B (and (-> Am (-> Bm (and Am Bm))) Cm))))))
axioms-used      (tm-8 tm-5)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11023.        ((A or (((B -> (C -> (B and C))) and D) -> (A and ((B -> (C -> (B and C))) and D)))) -> ((D or ((B -> (C -> (B and C))) and D)) -> (A and ((B -> (C -> (B and C))) and D)))), M:tm-48, m:tm-300, u:((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (and B (and (-> Am (-> Bm (and Am Bm))) Cm))) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (and B (and (-> Am (-> Bm (and Am Bm))) Cm)))))
================================================================
tm-name          tm-11024
in-theory        11024
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> (B and C))) and D) -> E)) or (((B -> (C -> (B and C))) and D) -> E)) -> ((D or ((B -> (C -> (B and C))) and D)) -> E))
theorem-size     39
proof            (modus-ponens tm-47 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11024.        (((A and (((B -> (C -> (B and C))) and D) -> E)) or (((B -> (C -> (B and C))) and D) -> E)) -> ((D or ((B -> (C -> (B and C))) and D)) -> E)), M:tm-47, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-11025
in-theory        11025
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> (A and B))) and C) -> D) and E) or (((A -> (B -> (A and B))) and C) -> D)) -> ((C or ((A -> (B -> (A and B))) and C)) -> D))
theorem-size     39
proof            (modus-ponens tm-46 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11025.        ((((((A -> (B -> (A and B))) and C) -> D) and E) or (((A -> (B -> (A and B))) and C) -> D)) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-46, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-11026
in-theory        11026
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> (B and C))) and D) -> A)) -> ((D or ((B -> (C -> (B and C))) and D)) -> A))
theorem-size     27
proof            (modus-ponens tm-44 tm-300 ((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11026.        ((A or (((B -> (C -> (B and C))) and D) -> A)) -> ((D or ((B -> (C -> (B and C))) and D)) -> A)), M:tm-44, m:tm-300, u:((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-11027
in-theory        11027
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-42 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11027.        ((A -> (B or A)) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F))), M:tm-42, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11028
in-theory        11028
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-32 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11028.        ((A -> (A or B)) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F))), M:tm-32, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11029
in-theory        11029
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and C) -> D) -> ((((A -> (B -> (A and B))) and C) -> D) and ((C or ((A -> (B -> (A and B))) and C)) -> D)))
theorem-size     37
proof            (modus-ponens tm-24 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11029.        ((((A -> (B -> (A and B))) and C) -> D) -> ((((A -> (B -> (A and B))) and C) -> D) and ((C or ((A -> (B -> (A and B))) and C)) -> D))), M:tm-24, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-11030
in-theory        11030
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-23 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11030.        ((A -> (B -> (A and B))) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F))), M:tm-23, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11031
in-theory        11031
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-22 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11031.        (((A and B) -> B) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F))), M:tm-22, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11032
in-theory        11032
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-21 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11032.        (((A and B) -> A) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F))), M:tm-21, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11033
in-theory        11033
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-20 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11033.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-20, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11034
in-theory        11034
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-19 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11034.        ((A -> (B -> A)) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F))), M:tm-19, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11035
in-theory        11035
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and C) -> D) -> (((A -> (B -> (A and B))) and C) -> D))
theorem-size     23
proof            (modus-ponens tm-12 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11035.        ((((A -> (B -> (A and B))) and C) -> D) -> (((A -> (B -> (A and B))) and C) -> D)), M:tm-12, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-11036
in-theory        11036
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> (not ((C or ((A -> (B -> (A and B))) and C)) -> D))) -> (not (((A -> (B -> (A and B))) and C) -> D)))
theorem-size     39
proof            (modus-ponens tm-9 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-5)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11036.        (((((A -> (B -> (A and B))) and C) -> D) -> (not ((C or ((A -> (B -> (A and B))) and C)) -> D))) -> (not (((A -> (B -> (A and B))) and C) -> D))), M:tm-9, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-11037
in-theory        11037
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B -> (C -> (B and C))) and A)) -> D) -> E) -> (((((B -> (C -> (B and C))) and A) -> D) or ((A or ((B -> (C -> (B and C))) and A)) -> D)) -> E))
theorem-size     43
proof            (modus-ponens tm-8 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-8 tm-5)
proof-size       119
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11037.        ((((A or ((B -> (C -> (B and C))) and A)) -> D) -> E) -> (((((B -> (C -> (B and C))) and A) -> D) or ((A or ((B -> (C -> (B and C))) and A)) -> D)) -> E)), M:tm-8, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-11038
in-theory        11038
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> (C -> (B and C))) and D) -> E) -> ((D or ((B -> (C -> (B and C))) and D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-7 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-5)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11038.        (A or ((((B -> (C -> (B and C))) and D) -> E) -> ((D or ((B -> (C -> (B and C))) and D)) -> E))), M:tm-7, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11039
in-theory        11039
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) or E)
theorem-size     27
proof            (modus-ponens tm-6 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-5)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11039.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) or E), M:tm-6, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11040
in-theory        11040
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> (B and C))) and D) -> E) -> ((D or ((B -> (C -> (B and C))) and D)) -> E)) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11040.        (A -> (((((B -> (C -> (B and C))) and D) -> E) -> ((D or ((B -> (C -> (B and C))) and D)) -> E)) and A)), M:tm-5, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11041
in-theory        11041
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> (C or ((A -> (B -> (A and B))) and C))) -> ((((A -> (B -> (A and B))) and C) -> D) -> D))
theorem-size     37
proof            (modus-ponens tm-2 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11041.        (((((A -> (B -> (A and B))) and C) -> D) -> (C or ((A -> (B -> (A and B))) and C))) -> ((((A -> (B -> (A and B))) and C) -> D) -> D)), M:tm-2, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm))) (C Dm))
================================================================
tm-name          tm-11042
in-theory        11042
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> (B and C))) and D) -> E) -> ((D or ((B -> (C -> (B and C))) and D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-1 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11042.        (A -> ((((B -> (C -> (B and C))) and D) -> E) -> ((D or ((B -> (C -> (B and C))) and D)) -> E))), M:tm-1, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11043
in-theory        11043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-270 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11043.        ((A -> (((B and C) -> C) and A)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-270, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11044
in-theory        11044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-239 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11044.        ((A -> (((B and C) -> B) and A)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-239, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11045
in-theory        11045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-210 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11045.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> ((G -> (H -> (G and H))) and F)))), M:tm-210, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11046
in-theory        11046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-183 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11046.        ((A -> ((B -> (C -> B)) and A)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-183, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11047
in-theory        11047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-157 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11047.        ((A -> ((B and C) -> C)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-157, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11048
in-theory        11048
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-147 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11048.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-147, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11049
in-theory        11049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-134 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11049.        ((A -> ((B and C) -> B)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-134, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11050
in-theory        11050
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-125 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11050.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-125, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11051
in-theory        11051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-113 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11051.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H -> (G and H))) and F)))), M:tm-113, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11052
in-theory        11052
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     33
proof            (modus-ponens tm-105 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11052.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-105, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11053
in-theory        11053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-95 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11053.        (((A -> B) -> (A -> A)) and (C or (D -> ((E -> (F -> (E and F))) and D)))), M:tm-95, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11054
in-theory        11054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-83 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11054.        ((A -> (B -> (C -> B))) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-83, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11055
in-theory        11055
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> ((D -> (E -> (D and E))) and C))))
theorem-size     19
proof            (modus-ponens tm-76 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11055.        (((not (not A)) -> A) and (B or (C -> ((D -> (E -> (D and E))) and C)))), M:tm-76, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11056
in-theory        11056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     25
proof            (modus-ponens tm-69 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11056.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> ((E -> (F -> (E and F))) and D)))), M:tm-69, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11057
in-theory        11057
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-54 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11057.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-54, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11058
in-theory        11058
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-42 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11058.        ((A -> (B or A)) and (C or (D -> ((E -> (F -> (E and F))) and D)))), M:tm-42, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11059
in-theory        11059
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-32 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11059.        ((A -> (A or B)) and (C or (D -> ((E -> (F -> (E and F))) and D)))), M:tm-32, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11060
in-theory        11060
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-23 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11060.        ((A -> (B -> (A and B))) and (C or (D -> ((E -> (F -> (E and F))) and D)))), M:tm-23, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11061
in-theory        11061
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-22 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11061.        (((A and B) -> B) and (C or (D -> ((E -> (F -> (E and F))) and D)))), M:tm-22, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11062
in-theory        11062
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-21 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11062.        (((A and B) -> A) and (C or (D -> ((E -> (F -> (E and F))) and D)))), M:tm-21, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11063
in-theory        11063
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-20 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11063.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-20, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11064
in-theory        11064
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-19 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11064.        ((A -> (B -> A)) and (C or (D -> ((E -> (F -> (E and F))) and D)))), M:tm-19, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11065
in-theory        11065
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C -> ((D -> (E -> (D and E))) and C))))
theorem-size     15
proof            (modus-ponens tm-7 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-7 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11065.        (A or (B or (C -> ((D -> (E -> (D and E))) and C)))), M:tm-7, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11066
in-theory        11066
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-6 tm-7 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11066.        ((A or (B -> ((C -> (D -> (C and D))) and B))) or E), M:tm-6, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11067
in-theory        11067
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C -> ((D -> (E -> (D and E))) and C))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11067.        (A -> ((B or (C -> ((D -> (E -> (D and E))) and C))) and A)), M:tm-5, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11068
in-theory        11068
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C -> ((D -> (E -> (D and E))) and C))))
theorem-size     15
proof            (modus-ponens tm-1 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-1 tm-7 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11068.        (A -> (B or (C -> ((D -> (E -> (D and E))) and C)))), M:tm-1, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11069
in-theory        11069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-270 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11069.        ((A -> (((B and C) -> C) and A)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-270, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11070
in-theory        11070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-239 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11070.        ((A -> (((B and C) -> B) and A)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-239, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11071
in-theory        11071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F -> (G -> (F and G))) and E)) or H))
theorem-size     31
proof            (modus-ponens tm-210 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11071.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F -> (G -> (F and G))) and E)) or H)), M:tm-210, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11072
in-theory        11072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-183 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11072.        ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-183, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11073
in-theory        11073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-157 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11073.        ((A -> ((B and C) -> C)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-157, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11074
in-theory        11074
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     29
proof            (modus-ponens tm-147 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11074.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-147, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11075
in-theory        11075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-134 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11075.        ((A -> ((B and C) -> B)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-134, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11076
in-theory        11076
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     29
proof            (modus-ponens tm-125 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11076.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-125, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11077
in-theory        11077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G -> (F and G))) and E)) or H))
theorem-size     29
proof            (modus-ponens tm-113 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11077.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G -> (F and G))) and E)) or H)), M:tm-113, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11078
in-theory        11078
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     33
proof            (modus-ponens tm-105 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11078.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-105, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11079
in-theory        11079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> ((D -> (E -> (D and E))) and C)) or F))
theorem-size     21
proof            (modus-ponens tm-95 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11079.        (((A -> B) -> (A -> A)) and ((C -> ((D -> (E -> (D and E))) and C)) or F)), M:tm-95, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11080
in-theory        11080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-83 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11080.        ((A -> (B -> (C -> B))) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-83, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11081
in-theory        11081
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> ((C -> (D -> (C and D))) and B)) or E))
theorem-size     19
proof            (modus-ponens tm-76 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11081.        (((not (not A)) -> A) and ((B -> ((C -> (D -> (C and D))) and B)) or E)), M:tm-76, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11082
in-theory        11082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D -> (E -> (D and E))) and C)) or F))
theorem-size     25
proof            (modus-ponens tm-69 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11082.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D -> (E -> (D and E))) and C)) or F)), M:tm-69, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11083
in-theory        11083
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-54 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11083.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-54, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11084
in-theory        11084
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> ((D -> (E -> (D and E))) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-42 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11084.        ((A -> (B or A)) and ((C -> ((D -> (E -> (D and E))) and C)) or F)), M:tm-42, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11085
in-theory        11085
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> ((D -> (E -> (D and E))) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-32 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11085.        ((A -> (A or B)) and ((C -> ((D -> (E -> (D and E))) and C)) or F)), M:tm-32, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11086
in-theory        11086
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> ((D -> (E -> (D and E))) and C)) or F))
theorem-size     21
proof            (modus-ponens tm-23 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11086.        ((A -> (B -> (A and B))) and ((C -> ((D -> (E -> (D and E))) and C)) or F)), M:tm-23, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11087
in-theory        11087
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> ((D -> (E -> (D and E))) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-22 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11087.        (((A and B) -> B) and ((C -> ((D -> (E -> (D and E))) and C)) or F)), M:tm-22, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11088
in-theory        11088
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> ((D -> (E -> (D and E))) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-21 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11088.        (((A and B) -> A) and ((C -> ((D -> (E -> (D and E))) and C)) or F)), M:tm-21, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11089
in-theory        11089
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-20 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11089.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-20, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11090
in-theory        11090
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> ((D -> (E -> (D and E))) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-19 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11090.        ((A -> (B -> A)) and ((C -> ((D -> (E -> (D and E))) and C)) or F)), M:tm-19, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11091
in-theory        11091
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> ((C -> (D -> (C and D))) and B)) or E))
theorem-size     15
proof            (modus-ponens tm-7 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-7 tm-6 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11091.        (A or ((B -> ((C -> (D -> (C and D))) and B)) or E)), M:tm-7, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11092
in-theory        11092
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-6 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11092.        (((A -> ((B -> (C -> (B and C))) and A)) or D) or E), M:tm-6, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11093
in-theory        11093
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> ((C -> (D -> (C and D))) and B)) or E) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11093.        (A -> (((B -> ((C -> (D -> (C and D))) and B)) or E) and A)), M:tm-5, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11094
in-theory        11094
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D -> (C and D))) and B)) or E))
theorem-size     15
proof            (modus-ponens tm-1 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-1 tm-6 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11094.        (A -> ((B -> ((C -> (D -> (C and D))) and B)) or E)), M:tm-1, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11095
in-theory        11095
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-303 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-5 tm-1)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11095.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> D))), M:tm-303, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-11096
in-theory        11096
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11096.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-303, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-11097
in-theory        11097
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-303 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-5 tm-3)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-11097.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D and E) -> D)), M:tm-303, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-11098
in-theory        11098
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-303 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-5 tm-4)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-11098.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D and E) -> E)), M:tm-303, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-11099
in-theory        11099
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-303 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11099.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (D and E)))), M:tm-303, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-11100
in-theory        11100
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-303 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-6)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-11100.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D or E))), M:tm-303, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-11101
in-theory        11101
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-303 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-7)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-11101.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or D))), M:tm-303, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-11102
in-theory        11102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11102.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-303, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-11103
in-theory        11103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-303 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11103.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-303, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-11104
in-theory        11104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((not (not D)) -> D))
theorem-size     17
proof            (modus-ponens tm-303 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-10)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-11104.        ((A -> ((B -> (C -> (B and C))) and A)) and ((not (not D)) -> D)), M:tm-303, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-11105
in-theory        11105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-303 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11105.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (F -> E)))), M:tm-303, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-11106
in-theory        11106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (D -> D)))
theorem-size     19
proof            (modus-ponens tm-303 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-11106.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (D -> D))), M:tm-303, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-11107
in-theory        11107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-303 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11107.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-303, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-11108
in-theory        11108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11108.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-303, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-11109
in-theory        11109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-303 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11109.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-303, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-11110
in-theory        11110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-303 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11110.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E and F) -> E))), M:tm-303, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-11111
in-theory        11111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-303 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11111.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-303, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-11112
in-theory        11112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-303 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11112.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E and F) -> F))), M:tm-303, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-11113
in-theory        11113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-303 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11113.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> E)) and D))), M:tm-303, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-11114
in-theory        11114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     29
proof            (modus-ponens tm-303 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11114.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-303, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-11115
in-theory        11115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E and F) -> E) and D)))
theorem-size     21
proof            (modus-ponens tm-303 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11115.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E and F) -> E) and D))), M:tm-303, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-11116
in-theory        11116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E and F) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-303 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11116.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E and F) -> F) and D))), M:tm-303, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-11117
in-theory        11117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11117.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-303, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-11118
in-theory        11118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (D -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-303 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11118.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (D -> (D and E)))), M:tm-303, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-11119
in-theory        11119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11119.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (F -> (E and F))))), M:tm-303, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-11120
in-theory        11120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-303 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11120.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) or F)), M:tm-303, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-11121
in-theory        11121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     27
proof            (modus-ponens tm-303 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11121.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-303, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-11122
in-theory        11122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) or F))
theorem-size     19
proof            (modus-ponens tm-303 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11122.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) or F)), M:tm-303, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-11123
in-theory        11123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) or F))
theorem-size     19
proof            (modus-ponens tm-303 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11123.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) or F)), M:tm-303, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-11124
in-theory        11124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) or F))
theorem-size     21
proof            (modus-ponens tm-303 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11124.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) or F)), M:tm-303, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-11125
in-theory        11125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) or F))
theorem-size     19
proof            (modus-ponens tm-303 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11125.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) or F)), M:tm-303, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-11126
in-theory        11126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (E or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-303 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11126.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (E or F)) and D))), M:tm-303, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-11127
in-theory        11127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-303 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11127.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (E or F)))), M:tm-303, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-11128
in-theory        11128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-303 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11128.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (F -> E)))), M:tm-303, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-11129
in-theory        11129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11129.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-303, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-11130
in-theory        11130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-303 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11130.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E and F) -> E))), M:tm-303, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-11131
in-theory        11131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-303 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11131.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E and F) -> F))), M:tm-303, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-11132
in-theory        11132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11132.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (F -> (E and F))))), M:tm-303, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-11133
in-theory        11133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-303 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11133.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (E or F)))), M:tm-303, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-11134
in-theory        11134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-303 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11134.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (F or E)))), M:tm-303, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-11135
in-theory        11135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) or F))
theorem-size     19
proof            (modus-ponens tm-303 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11135.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) or F)), M:tm-303, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-11136
in-theory        11136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F or E)) and D)))
theorem-size     21
proof            (modus-ponens tm-303 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11136.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F or E)) and D))), M:tm-303, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-11137
in-theory        11137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-303 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11137.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (F or E)))), M:tm-303, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-11138
in-theory        11138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-303 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11138.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-303, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-11139
in-theory        11139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     37
proof            (modus-ponens tm-303 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11139.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-303, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-11140
in-theory        11140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-303 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11140.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-303, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-11141
in-theory        11141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-303 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11141.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-303, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-11142
in-theory        11142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     29
proof            (modus-ponens tm-303 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-11142.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-303, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-11143
in-theory        11143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-303 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-11143.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-303, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-11144
in-theory        11144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-303 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-11144.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-303, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-11145
in-theory        11145
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     39
proof            (modus-ponens tm-303 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-8)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-11145.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-303, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-11146
in-theory        11146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11146.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-303, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-11147
in-theory        11147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     27
proof            (modus-ponens tm-303 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11147.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-303, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-11148
in-theory        11148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     29
proof            (modus-ponens tm-303 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11148.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-303, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-11149
in-theory        11149
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-303 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-11149.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-303, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-11150
in-theory        11150
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11150.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-303, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-11151
in-theory        11151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-303 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11151.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (E -> D))) -> (not D))), M:tm-303, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-11152
in-theory        11152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11152.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-303, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-11153
in-theory        11153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     23
proof            (modus-ponens tm-303 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11153.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-303, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-11154
in-theory        11154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     23
proof            (modus-ponens tm-303 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11154.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-303, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-11155
in-theory        11155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-11155.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-303, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-11156
in-theory        11156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-303 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-11156.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (D or E))) -> (not D))), M:tm-303, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-11157
in-theory        11157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-303 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-11157.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (E or D))) -> (not D))), M:tm-303, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-11158
in-theory        11158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-303 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-11158.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-303, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-11159
in-theory        11159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-303 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-11159.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-303, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-11160
in-theory        11160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-303 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-9)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-11160.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-303, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-11161
in-theory        11161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11161.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-303, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-11162
in-theory        11162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     25
proof            (modus-ponens tm-303 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11162.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-303, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-11163
in-theory        11163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     27
proof            (modus-ponens tm-303 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11163.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-303, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-11164
in-theory        11164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-303 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-11164.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-303, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-11165
in-theory        11165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11165.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-303, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-11166
in-theory        11166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     23
proof            (modus-ponens tm-303 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-9 tm-10)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-11166.        ((A -> ((B -> (C -> (B and C))) and A)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-303, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-11167
in-theory        11167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-303 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-11167.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-303, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-11168
in-theory        11168
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-303 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11168.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((not (not E)) -> E))), M:tm-303, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-11169
in-theory        11169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((not (not D)) -> D) or E))
theorem-size     19
proof            (modus-ponens tm-303 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11169.        ((A -> ((B -> (C -> (B and C))) and A)) and (((not (not D)) -> D) or E)), M:tm-303, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-11170
in-theory        11170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     21
proof            (modus-ponens tm-303 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11170.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((not (not E)) -> E) and D))), M:tm-303, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-11171
in-theory        11171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     27
proof            (modus-ponens tm-303 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-11171.        ((A -> ((B -> (C -> (B and C))) and A)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-303, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-11172
in-theory        11172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-303 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11172.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((not (not E)) -> E))), M:tm-303, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-11173
in-theory        11173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-11173.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-303, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-11174
in-theory        11174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     29
proof            (modus-ponens tm-303 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-11174.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-303, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-11175
in-theory        11175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11175.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (F -> (G -> F))))), M:tm-303, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-11176
in-theory        11176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (F -> E))) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11176.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (F -> E))) or G)), M:tm-303, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-11177
in-theory        11177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11177.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-303, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-11178
in-theory        11178
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-303 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-11178.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (D -> (F -> E)))), M:tm-303, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-11179
in-theory        11179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11179.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (F -> (G -> F))))), M:tm-303, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-11180
in-theory        11180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> D))
theorem-size     15
proof            (modus-ponens tm-303 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11180.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> D)), M:tm-303, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-11181
in-theory        11181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11181.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-303, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-11182
in-theory        11182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D and E) -> (D and E)))
theorem-size     19
proof            (modus-ponens tm-303 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11182.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D and E) -> (D and E))), M:tm-303, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-11183
in-theory        11183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-303 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-11183.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (D -> E))), M:tm-303, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-11184
in-theory        11184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((not (not D)) -> (not (not D))))
theorem-size     19
proof            (modus-ponens tm-303 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-11184.        ((A -> ((B -> (C -> (B and C))) and A)) and ((not (not D)) -> (not (not D)))), M:tm-303, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-11185
in-theory        11185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-303 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-11185.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-303, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-11186
in-theory        11186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-303 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-11186.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-303, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-11187
in-theory        11187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-303 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11187.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> F) -> (E -> E)))), M:tm-303, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-11188
in-theory        11188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (D -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-303 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11188.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (D -> D)) or F)), M:tm-303, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-11189
in-theory        11189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11189.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-303, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-11190
in-theory        11190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-11190.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-303, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-11191
in-theory        11191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-303 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11191.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> F) -> (E -> E)))), M:tm-303, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-11192
in-theory        11192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-11192.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-303, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-11193
in-theory        11193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     21
proof            (modus-ponens tm-303 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-11193.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D -> E)) -> (D -> E))), M:tm-303, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-11194
in-theory        11194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     31
proof            (modus-ponens tm-303 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-11194.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-303, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-11195
in-theory        11195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     43
proof            (modus-ponens tm-303 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-11195.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-303, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-11196
in-theory        11196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-303 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-11196.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-303, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-11197
in-theory        11197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11197.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-303, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-11198
in-theory        11198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     33
proof            (modus-ponens tm-303 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11198.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-303, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-11199
in-theory        11199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     35
proof            (modus-ponens tm-303 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11199.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-303, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-11200
in-theory        11200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-303 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-11200.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-303, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-11201
in-theory        11201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11201.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-303, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-11202
in-theory        11202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-303 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-11202.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-303, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-11203
in-theory        11203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-303 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11203.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-303, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-11204
in-theory        11204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     45
proof            (modus-ponens tm-303 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11204.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-303, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-11205
in-theory        11205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-303 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11205.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-303, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-11206
in-theory        11206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     29
proof            (modus-ponens tm-303 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11206.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-303, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-11207
in-theory        11207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     31
proof            (modus-ponens tm-303 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11207.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-303, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-11208
in-theory        11208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-303 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-11208.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-303, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-11209
in-theory        11209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-303 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11209.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-303, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-11210
in-theory        11210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) and D) -> E))
theorem-size     19
proof            (modus-ponens tm-303 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-11210.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) and D) -> E)), M:tm-303, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-11211
in-theory        11211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-303 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-11211.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-303, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-11212
in-theory        11212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     31
proof            (modus-ponens tm-303 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11212.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-303, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-11213
in-theory        11213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-303 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-11213.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-303, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-11214
in-theory        11214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     27
proof            (modus-ponens tm-303 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-11214.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-303, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-11215
in-theory        11215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     37
proof            (modus-ponens tm-303 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-11215.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-303, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-11216
in-theory        11216
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     39
proof            (modus-ponens tm-303 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-11216.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-303, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-11217
in-theory        11217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-303 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11217.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-303, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-11218
in-theory        11218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     29
proof            (modus-ponens tm-303 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11218.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-303, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-11219
in-theory        11219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     31
proof            (modus-ponens tm-303 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11219.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-303, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-11220
in-theory        11220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     35
proof            (modus-ponens tm-303 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-11220.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-303, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-11221
in-theory        11221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-303 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11221.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-303, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-11222
in-theory        11222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-303 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-11222.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-303, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-11223
in-theory        11223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     25
proof            (modus-ponens tm-303 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-11223.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-303, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-11224
in-theory        11224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-11224.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-303, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-11225
in-theory        11225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     29
proof            (modus-ponens tm-303 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-11225.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-303, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-11226
in-theory        11226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-303 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11226.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> ((F and G) -> F)))), M:tm-303, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-11227
in-theory        11227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E and F) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11227.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E and F) -> E)) or G)), M:tm-303, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-11228
in-theory        11228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11228.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-303, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-11229
in-theory        11229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     21
proof            (modus-ponens tm-303 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-11229.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E and F)) -> (D -> E))), M:tm-303, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-11230
in-theory        11230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-303 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11230.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> ((F and G) -> F)))), M:tm-303, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-11231
in-theory        11231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D and (D -> E)) -> E))
theorem-size     19
proof            (modus-ponens tm-303 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-11231.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D and (D -> E)) -> E)), M:tm-303, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-11232
in-theory        11232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-303 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-11232.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-303, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-11233
in-theory        11233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     31
proof            (modus-ponens tm-303 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11233.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-303, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-11234
in-theory        11234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-303 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-11234.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-303, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-11235
in-theory        11235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-303 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-11235.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-303, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-11236
in-theory        11236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     27
proof            (modus-ponens tm-303 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-11236.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-303, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-11237
in-theory        11237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     37
proof            (modus-ponens tm-303 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-11237.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-303, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-11238
in-theory        11238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-303 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-11238.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-303, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-11239
in-theory        11239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-303 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11239.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-303, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-11240
in-theory        11240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-303 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11240.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-303, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-11241
in-theory        11241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-303 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11241.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-303, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-11242
in-theory        11242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     35
proof            (modus-ponens tm-303 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-11242.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-303, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-11243
in-theory        11243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-303 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11243.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-303, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-11244
in-theory        11244
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-303 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-11244.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-303, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-11245
in-theory        11245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-303 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-11245.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-303, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-11246
in-theory        11246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     25
proof            (modus-ponens tm-303 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-11246.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-303, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-11247
in-theory        11247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-11247.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-303, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-11248
in-theory        11248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-303 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-11248.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-303, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-11249
in-theory        11249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-303 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11249.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> ((F and G) -> G)))), M:tm-303, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-11250
in-theory        11250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E and F) -> F)) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11250.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E and F) -> F)) or G)), M:tm-303, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-11251
in-theory        11251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11251.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-303, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-11252
in-theory        11252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-303 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-11252.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E and F)) -> (D -> F))), M:tm-303, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-11253
in-theory        11253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-303 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11253.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> ((F and G) -> G)))), M:tm-303, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-11254
in-theory        11254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11254.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-303, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-11255
in-theory        11255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11255.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-303, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-11256
in-theory        11256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11256.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-303, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-11257
in-theory        11257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-303 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11257.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-303, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-11258
in-theory        11258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11258.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-303, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-11259
in-theory        11259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-303 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11259.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-303, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-11260
in-theory        11260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11260.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-303, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-11261
in-theory        11261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11261.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-303, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-11262
in-theory        11262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-303 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11262.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-303, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-11263
in-theory        11263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11263.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-303, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-11264
in-theory        11264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11264.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-303, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-11265
in-theory        11265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11265.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-303, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-11266
in-theory        11266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-303 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11266.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-303, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-11267
in-theory        11267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11267.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-303, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-11268
in-theory        11268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-303 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11268.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-303, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-11269
in-theory        11269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-303 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11269.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-303, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-11270
in-theory        11270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-303 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11270.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-303, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-11271
in-theory        11271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-303 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11271.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-303, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-11272
in-theory        11272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11272.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-303, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-11273
in-theory        11273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-11273.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-303, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-11274
in-theory        11274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-303 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-11274.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-303, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-11275
in-theory        11275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-303 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11275.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-303, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-11276
in-theory        11276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-303 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11276.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-303, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-11277
in-theory        11277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11277.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-303, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-11278
in-theory        11278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-303 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11278.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-303, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-11279
in-theory        11279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     31
proof            (modus-ponens tm-303 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11279.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-303, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-11280
in-theory        11280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11280.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-303, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-11281
in-theory        11281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     31
proof            (modus-ponens tm-303 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11281.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-303, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-11282
in-theory        11282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     31
proof            (modus-ponens tm-303 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11282.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-303, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-11283
in-theory        11283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11283.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-303, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-11284
in-theory        11284
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11284.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-303, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-11285
in-theory        11285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     31
proof            (modus-ponens tm-303 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11285.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-303, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-11286
in-theory        11286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11286.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-303, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-11287
in-theory        11287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     37
proof            (modus-ponens tm-303 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11287.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-303, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-11288
in-theory        11288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     31
proof            (modus-ponens tm-303 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11288.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-303, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-11289
in-theory        11289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11289.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-303, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-11290
in-theory        11290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     33
proof            (modus-ponens tm-303 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11290.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-303, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-11291
in-theory        11291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-303 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11291.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-303, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-11292
in-theory        11292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     41
proof            (modus-ponens tm-303 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11292.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-303, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-11293
in-theory        11293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-303 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11293.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-303, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-11294
in-theory        11294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     33
proof            (modus-ponens tm-303 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11294.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-303, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-11295
in-theory        11295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     41
proof            (modus-ponens tm-303 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11295.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-303, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-11296
in-theory        11296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     33
proof            (modus-ponens tm-303 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11296.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-303, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-11297
in-theory        11297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     35
proof            (modus-ponens tm-303 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11297.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-303, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-11298
in-theory        11298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     43
proof            (modus-ponens tm-303 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-2)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11298.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-303, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-11299
in-theory        11299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-303 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11299.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-303, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-11300
in-theory        11300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-303 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-11300.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-303, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-11301
in-theory        11301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     49
proof            (modus-ponens tm-303 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-11301.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-303, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-11302
in-theory        11302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-303 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11302.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-303, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-11303
in-theory        11303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     31
proof            (modus-ponens tm-303 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11303.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-303, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-11304
in-theory        11304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     33
proof            (modus-ponens tm-303 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11304.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-303, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-11305
in-theory        11305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-303 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11305.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-303, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-11306
in-theory        11306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11306.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-303, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-11307
in-theory        11307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11307.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-303, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-11308
in-theory        11308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11308.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-303, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-11309
in-theory        11309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-303 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11309.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-303, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-11310
in-theory        11310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11310.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-303, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-11311
in-theory        11311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-303 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11311.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-303, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-11312
in-theory        11312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11312.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-303, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-11313
in-theory        11313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11313.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-303, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-11314
in-theory        11314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-303 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11314.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-303, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-11315
in-theory        11315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11315.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-303, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-11316
in-theory        11316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11316.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-303, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-11317
in-theory        11317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11317.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-303, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-11318
in-theory        11318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-303 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11318.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-303, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-11319
in-theory        11319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11319.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-303, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-11320
in-theory        11320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-303 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11320.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-303, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-11321
in-theory        11321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-303 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11321.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-303, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-11322
in-theory        11322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-303 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11322.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-303, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-11323
in-theory        11323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-303 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11323.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-303, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-11324
in-theory        11324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11324.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-303, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-11325
in-theory        11325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-303 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11325.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-303, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-11326
in-theory        11326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11326.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-303, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-11327
in-theory        11327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     35
proof            (modus-ponens tm-303 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11327.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-303, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-11328
in-theory        11328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11328.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-303, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-11329
in-theory        11329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-11329.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-303, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-11330
in-theory        11330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-303 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-11330.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-303, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-11331
in-theory        11331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-303 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11331.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-303, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-11332
in-theory        11332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-303 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11332.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-303, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-11333
in-theory        11333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11333.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-303, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-11334
in-theory        11334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-303 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11334.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-303, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-11335
in-theory        11335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11335.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-303, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-11336
in-theory        11336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11336.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-303, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-11337
in-theory        11337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11337.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-303, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-11338
in-theory        11338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-303 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11338.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-303, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-11339
in-theory        11339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11339.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-303, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-11340
in-theory        11340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-303 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11340.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-303, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-11341
in-theory        11341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11341.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-303, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-11342
in-theory        11342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11342.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-303, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-11343
in-theory        11343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-303 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11343.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-303, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-11344
in-theory        11344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11344.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-303, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-11345
in-theory        11345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11345.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-303, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-11346
in-theory        11346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11346.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-303, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-11347
in-theory        11347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-303 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11347.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-303, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-11348
in-theory        11348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11348.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-303, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-11349
in-theory        11349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-303 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11349.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-303, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-11350
in-theory        11350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-303 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11350.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-303, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-11351
in-theory        11351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-303 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11351.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-303, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-11352
in-theory        11352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-303 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11352.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-303, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-11353
in-theory        11353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11353.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-303, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-11354
in-theory        11354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-303 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11354.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-303, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-11355
in-theory        11355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11355.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-303, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-11356
in-theory        11356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11356.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-303, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-11357
in-theory        11357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11357.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-303, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-11358
in-theory        11358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     35
proof            (modus-ponens tm-303 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11358.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-303, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-11359
in-theory        11359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11359.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-303, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-11360
in-theory        11360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-11360.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-303, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-11361
in-theory        11361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-303 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-11361.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-303, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-11362
in-theory        11362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-303 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11362.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-303, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-11363
in-theory        11363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-303 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11363.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-303, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-11364
in-theory        11364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11364.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-303, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-11365
in-theory        11365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-303 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11365.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-303, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-11366
in-theory        11366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11366.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-303, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-11367
in-theory        11367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11367.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-303, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-11368
in-theory        11368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-303 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11368.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-303, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-11369
in-theory        11369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-303 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11369.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-303, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-11370
in-theory        11370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11370.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-303, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-11371
in-theory        11371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-303 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11371.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-303, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-11372
in-theory        11372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11372.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-303, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-11373
in-theory        11373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11373.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-303, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-11374
in-theory        11374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11374.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-303, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-11375
in-theory        11375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-303 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-10)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11375.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-303, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-11376
in-theory        11376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11376.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-303, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-11377
in-theory        11377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11377.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-303, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-11378
in-theory        11378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11378.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-303, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-11379
in-theory        11379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-303 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11379.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-303, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-11380
in-theory        11380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-303 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11380.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-303, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-11381
in-theory        11381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-303 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11381.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-303, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-11382
in-theory        11382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-303 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11382.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-303, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-11383
in-theory        11383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-303 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11383.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-303, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-11384
in-theory        11384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-303 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11384.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-303, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-11385
in-theory        11385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-303 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11385.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-303, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-11386
in-theory        11386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-303 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11386.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-303, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-11387
in-theory        11387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-303 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11387.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-303, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-11388
in-theory        11388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-303 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11388.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-303, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-11389
in-theory        11389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-303 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11389.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-303, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-11390
in-theory        11390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-303 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11390.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-303, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-11391
in-theory        11391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     37
proof            (modus-ponens tm-303 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11391.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-303, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-11392
in-theory        11392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-303 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11392.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-303, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-11393
in-theory        11393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-303 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11393.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-303, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-11394
in-theory        11394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-303 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11394.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-303, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11395
in-theory        11395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-303 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11395.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-303, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11396
in-theory        11396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-303 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11396.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-303, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11397
in-theory        11397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-303 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11397.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-303, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11398
in-theory        11398
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B -> (C -> (B and C))) and A)))
theorem-size     33
proof            (modus-ponens tm-300 tm-303 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11398.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-303, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-11399
in-theory        11399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-270 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11399.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-270, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11400
in-theory        11400
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> ((E -> (F -> (E and F))) and D)) and (((B and C) -> C) and A)))
theorem-size     29
proof            (modus-ponens tm-267 tm-303 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11400.        ((A or (((B and C) -> C) and A)) -> ((D -> ((E -> (F -> (E and F))) and D)) and (((B and C) -> C) and A))), M:tm-267, m:tm-303, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-11401
in-theory        11401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-239 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11401.        ((A -> (((B and C) -> B) and A)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-239, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11402
in-theory        11402
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> ((E -> (F -> (E and F))) and D)) and (((B and C) -> B) and A)))
theorem-size     29
proof            (modus-ponens tm-236 tm-303 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11402.        ((A or (((B and C) -> B) and A)) -> ((D -> ((E -> (F -> (E and F))) and D)) and (((B and C) -> B) and A))), M:tm-236, m:tm-303, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-11403
in-theory        11403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E)))
theorem-size     33
proof            (modus-ponens tm-210 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11403.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E))), M:tm-210, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11404
in-theory        11404
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> ((F -> (G -> (F and G))) and E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     45
proof            (modus-ponens tm-207 tm-303 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11404.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> ((F -> (G -> (F and G))) and E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-303, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-11405
in-theory        11405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-183 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11405.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-183, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11406
in-theory        11406
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B -> (C -> B)) and A)))
theorem-size     29
proof            (modus-ponens tm-180 tm-303 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11406.        ((A or ((B -> (C -> B)) and A)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-303, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-11407
in-theory        11407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-157 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11407.        ((A -> ((B and C) -> C)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-157, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11408
in-theory        11408
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B and C) -> C)))
theorem-size     25
proof            (modus-ponens tm-154 tm-303 ((Am (-> (and A B) B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11408.        ((A or ((B and C) -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B and C) -> C))), M:tm-154, m:tm-303, u:((Am (-> (and A B) B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (and A B) B))))
================================================================
tm-name          tm-11409
in-theory        11409
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-147 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11409.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-147, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11410
in-theory        11410
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A and (B -> C)) -> C)))
theorem-size     35
proof            (modus-ponens tm-144 tm-303 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11410.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-303, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-11411
in-theory        11411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-134 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11411.        ((A -> ((B and C) -> B)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-134, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11412
in-theory        11412
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B and C) -> B)))
theorem-size     25
proof            (modus-ponens tm-131 tm-303 ((Am (-> (and A B) A)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11412.        ((A or ((B and C) -> B)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B and C) -> B))), M:tm-131, m:tm-303, u:((Am (-> (and A B) A)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (and A B) A))))
================================================================
tm-name          tm-11413
in-theory        11413
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-125 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11413.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-125, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11414
in-theory        11414
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> ((E -> (F -> (E and F))) and D)) and (((A -> B) and C) -> B)))
theorem-size     35
proof            (modus-ponens tm-122 tm-303 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11414.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> ((E -> (F -> (E and F))) and D)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-303, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-11415
in-theory        11415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E)))
theorem-size     31
proof            (modus-ponens tm-113 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11415.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E))), M:tm-113, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11416
in-theory        11416
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> ((F -> (G -> (F and G))) and E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     41
proof            (modus-ponens tm-110 tm-303 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11416.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> ((F -> (G -> (F and G))) and E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-303, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-11417
in-theory        11417
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     35
proof            (modus-ponens tm-105 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11417.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-105, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11418
in-theory        11418
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-102 tm-303 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11418.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-303, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-11419
in-theory        11419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C)))
theorem-size     23
proof            (modus-ponens tm-95 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11419.        (((A -> B) -> (A -> A)) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C))), M:tm-95, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11420
in-theory        11420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> A)))
theorem-size     23
proof            (modus-ponens tm-92 tm-303 ((Am (-> A A)) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11420.        (((A -> B) or (A -> A)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> A))), M:tm-92, m:tm-303, u:((Am (-> A A)) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A A))))
================================================================
tm-name          tm-11421
in-theory        11421
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> ((D -> (E -> (D and E))) and C)) and A)))
theorem-size     17
proof            (modus-ponens tm-84 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11421.        (A -> (B -> ((C -> ((D -> (E -> (D and E))) and C)) and A))), M:tm-84, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-11422
in-theory        11422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-83 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11422.        ((A -> (B -> (C -> B))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-83, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11423
in-theory        11423
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> ((E -> (F -> (E and F))) and D)) and (B -> (C -> B))))
theorem-size     25
proof            (modus-ponens tm-80 tm-303 ((Am (-> A (-> B A))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11423.        ((A or (B -> (C -> B))) -> ((D -> ((E -> (F -> (E and F))) and D)) and (B -> (C -> B)))), M:tm-80, m:tm-303, u:((Am (-> A (-> B A))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A (-> B A)))))
================================================================
tm-name          tm-11424
in-theory        11424
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> ((D -> (E -> (D and E))) and C)) and B)))
theorem-size     21
proof            (modus-ponens tm-76 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11424.        (((not (not A)) -> A) and (B -> ((C -> ((D -> (E -> (D and E))) and C)) and B))), M:tm-76, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11425
in-theory        11425
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> ((C -> (D -> (C and D))) and B)) and A))
theorem-size     19
proof            (modus-ponens tm-73 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-8 tm-10 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11425.        (((not (not A)) or A) -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-73, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-11426
in-theory        11426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C)))
theorem-size     27
proof            (modus-ponens tm-69 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11426.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C))), M:tm-69, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11427
in-theory        11427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> ((D -> (E -> (D and E))) and C)) and ((A -> (not B)) -> (not A))))
theorem-size     31
proof            (modus-ponens tm-66 tm-303 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11427.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> ((D -> (E -> (D and E))) and C)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-303, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-11428
in-theory        11428
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-54 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11428.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-54, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11429
in-theory        11429
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-51 tm-303 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11429.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-303, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-11430
in-theory        11430
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (B or A)))
theorem-size     21
proof            (modus-ponens tm-50 tm-303 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11430.        ((A or (B or A)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (B or A))), M:tm-50, m:tm-303, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (or A B))))
================================================================
tm-name          tm-11431
in-theory        11431
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A or B)))
theorem-size     21
proof            (modus-ponens tm-49 tm-303 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11431.        ((A or (A or B)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A or B))), M:tm-49, m:tm-303, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (or A B))))
================================================================
tm-name          tm-11432
in-theory        11432
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> ((D -> (E -> (D and E))) and C)) and (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-48 tm-303 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11432.        ((A or (B -> (A and B))) -> ((C -> ((D -> (E -> (D and E))) and C)) and (B -> (A and B)))), M:tm-48, m:tm-303, u:((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-11433
in-theory        11433
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> ((D -> (E -> (D and E))) and C)) and B))
theorem-size     19
proof            (modus-ponens tm-47 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11433.        (((A and B) or B) -> ((C -> ((D -> (E -> (D and E))) and C)) and B)), M:tm-47, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-11434
in-theory        11434
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> ((D -> (E -> (D and E))) and C)) and A))
theorem-size     19
proof            (modus-ponens tm-46 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11434.        (((A and B) or A) -> ((C -> ((D -> (E -> (D and E))) and C)) and A)), M:tm-46, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-11435
in-theory        11435
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-45 tm-303 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11435.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-303, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-11436
in-theory        11436
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (B -> A)))
theorem-size     21
proof            (modus-ponens tm-44 tm-303 ((Am (-> A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11436.        ((A or (B -> A)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (B -> A))), M:tm-44, m:tm-303, u:((Am (-> A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A B))))
================================================================
tm-name          tm-11437
in-theory        11437
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-42 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11437.        ((A -> (B or A)) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C))), M:tm-42, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11438
in-theory        11438
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-32 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11438.        ((A -> (A or B)) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C))), M:tm-32, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11439
in-theory        11439
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> ((C -> (D -> (C and D))) and B)) and A)))
theorem-size     17
proof            (modus-ponens tm-24 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-2 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11439.        (A -> (A and ((B -> ((C -> (D -> (C and D))) and B)) and A))), M:tm-24, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-11440
in-theory        11440
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C)))
theorem-size     23
proof            (modus-ponens tm-23 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11440.        ((A -> (B -> (A and B))) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C))), M:tm-23, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11441
in-theory        11441
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-22 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11441.        (((A and B) -> B) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C))), M:tm-22, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11442
in-theory        11442
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-21 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11442.        (((A and B) -> A) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C))), M:tm-21, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11443
in-theory        11443
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-20 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11443.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-20, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11444
in-theory        11444
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-19 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11444.        ((A -> (B -> A)) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C))), M:tm-19, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11445
in-theory        11445
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> ((C -> (D -> (C and D))) and B)) and A))) -> (not A))
theorem-size     19
proof            (modus-ponens tm-9 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-9 tm-5)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11445.        ((A -> (not ((B -> ((C -> (D -> (C and D))) and B)) and A))) -> (not A)), M:tm-9, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-11446
in-theory        11446
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C -> (B and C))) and A)) and D) -> E) -> ((D or ((A -> ((B -> (C -> (B and C))) and A)) and D)) -> E))
theorem-size     33
proof            (modus-ponens tm-8 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-8 tm-5)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11446.        ((((A -> ((B -> (C -> (B and C))) and A)) and D) -> E) -> ((D or ((A -> ((B -> (C -> (B and C))) and A)) and D)) -> E)), M:tm-8, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-11447
in-theory        11447
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> ((D -> (E -> (D and E))) and C)) and B)))
theorem-size     17
proof            (modus-ponens tm-7 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-7 tm-5)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11447.        (A or (B -> ((C -> ((D -> (E -> (D and E))) and C)) and B))), M:tm-7, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11448
in-theory        11448
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-6 tm-5)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11448.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) or E), M:tm-6, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11449
in-theory        11449
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> ((D -> (E -> (D and E))) and C)) and B)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11449.        (A -> ((B -> ((C -> ((D -> (E -> (D and E))) and C)) and B)) and A)), M:tm-5, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11450
in-theory        11450
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> ((D -> (E -> (D and E))) and C)) and B)))
theorem-size     17
proof            (modus-ponens tm-1 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-1 tm-5)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11450.        (A -> (B -> ((C -> ((D -> (E -> (D and E))) and C)) and B))), M:tm-1, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11451
in-theory        11451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-303 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11451.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-303, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11452
in-theory        11452
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-300 tm-304 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11452.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-300, m:tm-304, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11453
in-theory        11453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-270 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11453.        ((A -> (((B and C) -> C) and A)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-270, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11454
in-theory        11454
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-267 tm-304 ((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11454.        ((A or (((B and C) -> C) and A)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-267, m:tm-304, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11455
in-theory        11455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-239 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11455.        ((A -> (((B and C) -> B) and A)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-239, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11456
in-theory        11456
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-236 tm-304 ((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11456.        ((A or (((B and C) -> B) and A)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-236, m:tm-304, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11457
in-theory        11457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-210 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11457.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> ((G -> (H -> (G and H))) and F)))), M:tm-210, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11458
in-theory        11458
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((F -> (G -> (F and G))) and E)))
theorem-size     29
proof            (modus-ponens tm-207 tm-304 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11458.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((F -> (G -> (F and G))) and E))), M:tm-207, m:tm-304, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11459
in-theory        11459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-183 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11459.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-183, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11460
in-theory        11460
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-180 tm-304 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11460.        ((A or ((B -> (C -> B)) and A)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-180, m:tm-304, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11461
in-theory        11461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-157 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11461.        ((A -> ((B and C) -> C)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-157, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11462
in-theory        11462
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-154 tm-304 ((Am (-> (and A B) B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11462.        ((A or ((B and C) -> C)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-154, m:tm-304, u:((Am (-> (and A B) B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11463
in-theory        11463
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> ((C -> (D -> (C and D))) and B))
theorem-size     13
proof            (modus-ponens tm-152 tm-304 ((Am (and A Bm)) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11463.        ((A and B) -> ((C -> (D -> (C and D))) and B)), M:tm-152, m:tm-304, u:((Am (and A Bm)) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-11464
in-theory        11464
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-147 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11464.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-147, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11465
in-theory        11465
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     27
proof            (modus-ponens tm-144 tm-304 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-5)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11465.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-144, m:tm-304, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11466
in-theory        11466
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (D -> (C and D))) and B)) -> E)) -> (B -> ((C -> (D -> (C and D))) and B)))
theorem-size     27
proof            (modus-ponens tm-142 tm-304 ((Am (and A (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) C))) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11466.        ((A and ((B -> ((C -> (D -> (C and D))) and B)) -> E)) -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-142, m:tm-304, u:((Am (and A (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) C))) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11467
in-theory        11467
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (D -> (C and D))) and B)) -> B)) -> ((C -> (D -> (C and D))) and B))
theorem-size     25
proof            (modus-ponens tm-141 tm-304 ((Am (and A (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Bm))) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11467.        ((A and ((B -> ((C -> (D -> (C and D))) and B)) -> B)) -> ((C -> (D -> (C and D))) and B)), M:tm-141, m:tm-304, u:((Am (and A (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Bm))) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-11468
in-theory        11468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-134 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11468.        ((A -> ((B and C) -> B)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-134, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11469
in-theory        11469
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-131 tm-304 ((Am (-> (and A B) A)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11469.        ((A or ((B and C) -> B)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-131, m:tm-304, u:((Am (-> (and A B) A)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11470
in-theory        11470
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> ((C -> (D -> (C and D))) and A))
theorem-size     13
proof            (modus-ponens tm-129 tm-304 ((Am (and Bm B)) (A Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11470.        ((A and B) -> ((C -> (D -> (C and D))) and A)), M:tm-129, m:tm-304, u:((Am (and Bm B)) (A Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-11471
in-theory        11471
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-125 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11471.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-125, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11472
in-theory        11472
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     27
proof            (modus-ponens tm-122 tm-304 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-5)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11472.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-122, m:tm-304, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11473
in-theory        11473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C -> (B and C))) and A)) -> D) and E) -> (A -> ((B -> (C -> (B and C))) and A)))
theorem-size     27
proof            (modus-ponens tm-120 tm-304 ((Am (and (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) B) C)) (A (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11473.        ((((A -> ((B -> (C -> (B and C))) and A)) -> D) and E) -> (A -> ((B -> (C -> (B and C))) and A))), M:tm-120, m:tm-304, u:((Am (and (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) B) C)) (A (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11474
in-theory        11474
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C -> (B and C))) and A)) -> A) and D) -> ((B -> (C -> (B and C))) and A))
theorem-size     25
proof            (modus-ponens tm-119 tm-304 ((Am (and (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Bm) C)) (A Bm) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11474.        ((((A -> ((B -> (C -> (B and C))) and A)) -> A) and D) -> ((B -> (C -> (B and C))) and A)), M:tm-119, m:tm-304, u:((Am (and (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Bm) C)) (A Bm) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-11475
in-theory        11475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-113 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11475.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H -> (G and H))) and F)))), M:tm-113, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11476
in-theory        11476
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((F -> (G -> (F and G))) and E)))
theorem-size     27
proof            (modus-ponens tm-110 tm-304 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11476.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((F -> (G -> (F and G))) and E))), M:tm-110, m:tm-304, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11477
in-theory        11477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))
theorem-size     21
proof            (modus-ponens tm-108 tm-304 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> Cm (-> Dm (and Cm Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11477.        ((A -> (B -> C)) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-108, m:tm-304, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> Cm (-> Dm (and Cm Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-11478
in-theory        11478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     33
proof            (modus-ponens tm-105 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11478.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-105, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11479
in-theory        11479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     31
proof            (modus-ponens tm-102 tm-304 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11479.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-102, m:tm-304, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11480
in-theory        11480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) and A) -> D)) -> (A -> ((B -> (C -> (B and C))) and A)))
theorem-size     25
proof            (modus-ponens tm-100 tm-304 ((Am (-> Bm (-> (and (-> Cm (-> Dm (and Cm Dm))) Bm) C))) (A Bm) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11480.        ((A -> (((B -> (C -> (B and C))) and A) -> D)) -> (A -> ((B -> (C -> (B and C))) and A))), M:tm-100, m:tm-304, u:((Am (-> Bm (-> (and (-> Cm (-> Dm (and Cm Dm))) Bm) C))) (A Bm) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-11481
in-theory        11481
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> A)))
theorem-size     13
proof            (modus-ponens tm-98 tm-304 ((A Am) (Bm (-> B Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> B Am)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11481.        (A -> ((B -> (C -> (B and C))) and (D -> A))), M:tm-98, m:tm-304, u:((A Am) (Bm (-> B Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> B Am))))
================================================================
tm-name          tm-11482
in-theory        11482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) -> D) -> (A -> ((B -> (C -> (B and C))) and A)))
theorem-size     25
proof            (modus-ponens tm-96 tm-304 ((Am (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) B)) (A (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11482.        (((A -> ((B -> (C -> (B and C))) and A)) -> D) -> (A -> ((B -> (C -> (B and C))) and A))), M:tm-96, m:tm-304, u:((Am (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) B)) (A (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11483
in-theory        11483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-95 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11483.        (((A -> B) -> (A -> A)) and (C -> (D -> ((E -> (F -> (E and F))) and D)))), M:tm-95, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11484
in-theory        11484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     19
proof            (modus-ponens tm-92 tm-304 ((Am (-> A A)) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11484.        (((A -> B) or (A -> A)) -> (C -> ((D -> (E -> (D and E))) and C))), M:tm-92, m:tm-304, u:((Am (-> A A)) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11485
in-theory        11485
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C -> ((D -> (E -> (D and E))) and C))))
theorem-size     15
proof            (modus-ponens tm-84 tm-304 ((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11485.        (A -> (B -> (C -> ((D -> (E -> (D and E))) and C)))), M:tm-84, m:tm-304, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11486
in-theory        11486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-83 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11486.        ((A -> (B -> (C -> B))) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-83, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11487
in-theory        11487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-80 tm-304 ((Am (-> A (-> B A))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11487.        ((A or (B -> (C -> B))) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-80, m:tm-304, u:((Am (-> A (-> B A))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11488
in-theory        11488
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> ((B -> (C -> (B and C))) and A)) -> D))) -> D)
theorem-size     17
proof            (modus-ponens tm-77 tm-304 ((Am (not (not (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) B)))) (A (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11488.        ((not (not ((A -> ((B -> (C -> (B and C))) and A)) -> D))) -> D), M:tm-77, m:tm-304, u:((Am (not (not (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) B)))) (A (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11489
in-theory        11489
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> ((D -> (E -> (D and E))) and C))))
theorem-size     19
proof            (modus-ponens tm-76 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11489.        (((not (not A)) -> A) and (B -> (C -> ((D -> (E -> (D and E))) and C)))), M:tm-76, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11490
in-theory        11490
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> ((C -> (D -> (C and D))) and B)))
theorem-size     17
proof            (modus-ponens tm-73 tm-304 ((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11490.        (((not (not A)) or A) -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-73, m:tm-304, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11491
in-theory        11491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     25
proof            (modus-ponens tm-69 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11491.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> ((E -> (F -> (E and F))) and D)))), M:tm-69, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11492
in-theory        11492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     23
proof            (modus-ponens tm-66 tm-304 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-5)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11492.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((D -> (E -> (D and E))) and C))), M:tm-66, m:tm-304, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11493
in-theory        11493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> ((C -> (D -> (C and D))) and B)))
theorem-size     17
proof            (modus-ponens tm-55 tm-304 ((Am (-> A Bm)) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11493.        ((A -> B) -> ((A or B) -> ((C -> (D -> (C and D))) and B))), M:tm-55, m:tm-304, u:((Am (-> A Bm)) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-11494
in-theory        11494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-54 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11494.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-54, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11495
in-theory        11495
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     25
proof            (modus-ponens tm-51 tm-304 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11495.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-51, m:tm-304, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11496
in-theory        11496
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     17
proof            (modus-ponens tm-50 tm-304 ((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11496.        ((A or (B or A)) -> (C -> ((D -> (E -> (D and E))) and C))), M:tm-50, m:tm-304, u:((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11497
in-theory        11497
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     17
proof            (modus-ponens tm-49 tm-304 ((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11497.        ((A or (A or B)) -> (C -> ((D -> (E -> (D and E))) and C))), M:tm-49, m:tm-304, u:((Am (or A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11498
in-theory        11498
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     19
proof            (modus-ponens tm-48 tm-304 ((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11498.        ((A or (B -> (A and B))) -> (C -> ((D -> (E -> (D and E))) and C))), M:tm-48, m:tm-304, u:((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11499
in-theory        11499
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     17
proof            (modus-ponens tm-47 tm-304 ((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11499.        (((A and B) or B) -> (C -> ((D -> (E -> (D and E))) and C))), M:tm-47, m:tm-304, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11500
in-theory        11500
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     17
proof            (modus-ponens tm-46 tm-304 ((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11500.        (((A and B) or A) -> (C -> ((D -> (E -> (D and E))) and C))), M:tm-46, m:tm-304, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11501
in-theory        11501
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     25
proof            (modus-ponens tm-45 tm-304 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11501.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-45, m:tm-304, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11502
in-theory        11502
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     17
proof            (modus-ponens tm-44 tm-304 ((Am (-> A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11502.        ((A or (B -> A)) -> (C -> ((D -> (E -> (D and E))) and C))), M:tm-44, m:tm-304, u:((Am (-> A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11503
in-theory        11503
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-42 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11503.        ((A -> (B or A)) and (C -> (D -> ((E -> (F -> (E and F))) and D)))), M:tm-42, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11504
in-theory        11504
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-32 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11504.        ((A -> (A or B)) and (C -> (D -> ((E -> (F -> (E and F))) and D)))), M:tm-32, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11505
in-theory        11505
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B -> ((C -> (D -> (C and D))) and B))))
theorem-size     15
proof            (modus-ponens tm-24 tm-304 ((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11505.        (A -> (A and (B -> ((C -> (D -> (C and D))) and B)))), M:tm-24, m:tm-304, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11506
in-theory        11506
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-23 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11506.        ((A -> (B -> (A and B))) and (C -> (D -> ((E -> (F -> (E and F))) and D)))), M:tm-23, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11507
in-theory        11507
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-22 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11507.        (((A and B) -> B) and (C -> (D -> ((E -> (F -> (E and F))) and D)))), M:tm-22, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11508
in-theory        11508
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-21 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11508.        (((A and B) -> A) and (C -> (D -> ((E -> (F -> (E and F))) and D)))), M:tm-21, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11509
in-theory        11509
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-20 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11509.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-20, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11510
in-theory        11510
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-19 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11510.        ((A -> (B -> A)) and (C -> (D -> ((E -> (F -> (E and F))) and D)))), M:tm-19, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11511
in-theory        11511
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (D -> (C and D))) and B)) -> E)) -> E)
theorem-size     17
proof            (modus-ponens tm-17 tm-304 ((Am (and A (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) C))) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11511.        ((A and ((B -> ((C -> (D -> (C and D))) and B)) -> E)) -> E), M:tm-17, m:tm-304, u:((Am (and A (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) C))) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11512
in-theory        11512
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C -> (B and C))) and A)) -> D) and E) -> D)
theorem-size     17
proof            (modus-ponens tm-15 tm-304 ((Am (and (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) B) C)) (A (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11512.        ((((A -> ((B -> (C -> (B and C))) and A)) -> D) and E) -> D), M:tm-15, m:tm-304, u:((Am (and (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) B) C)) (A (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11513
in-theory        11513
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) and A) -> D)) -> (A -> D))
theorem-size     17
proof            (modus-ponens tm-13 tm-304 ((Am (-> Bm (-> (and (-> Cm (-> Dm (and Cm Dm))) Bm) C))) (A Bm) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11513.        ((A -> (((B -> (C -> (B and C))) and A) -> D)) -> (A -> D)), M:tm-13, m:tm-304, u:((Am (-> Bm (-> (and (-> Cm (-> Dm (and Cm Dm))) Bm) C))) (A Bm) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-11514
in-theory        11514
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B -> ((C -> (D -> (C and D))) and B)))) -> (not A))
theorem-size     17
proof            (modus-ponens tm-9 tm-304 ((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11514.        ((A -> (not (B -> ((C -> (D -> (C and D))) and B)))) -> (not A)), M:tm-9, m:tm-304, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11515
in-theory        11515
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) -> D) -> ((E or (A -> ((B -> (C -> (B and C))) and A))) -> D))
theorem-size     29
proof            (modus-ponens tm-8 tm-304 ((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11515.        (((A -> ((B -> (C -> (B and C))) and A)) -> D) -> ((E or (A -> ((B -> (C -> (B and C))) and A))) -> D)), M:tm-8, m:tm-304, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-11516
in-theory        11516
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C -> ((D -> (E -> (D and E))) and C))))
theorem-size     15
proof            (modus-ponens tm-7 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-7 tm-1 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11516.        (A or (B -> (C -> ((D -> (E -> (D and E))) and C)))), M:tm-7, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11517
in-theory        11517
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-6 tm-1 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11517.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) or E), M:tm-6, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11518
in-theory        11518
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> ((D -> (E -> (D and E))) and C))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11518.        (A -> ((B -> (C -> ((D -> (E -> (D and E))) and C))) and A)), M:tm-5, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11519
in-theory        11519
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> ((C -> (D -> (C and D))) and B)))
theorem-size     15
proof            (modus-ponens tm-2 tm-304 ((A Am) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11519.        ((A -> B) -> (A -> ((C -> (D -> (C and D))) and B))), M:tm-2, m:tm-304, u:((A Am) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-11520
in-theory        11520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (A -> (B -> A))))
theorem-size     13
proof            (modus-ponens tm-305 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11520.        ((A -> (B -> A)) and (C -> (A -> (B -> A)))), M:tm-305, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-11521
in-theory        11521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11521.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))), M:tm-305, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-11522
in-theory        11522
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((A and B) -> A)))
theorem-size     13
proof            (modus-ponens tm-305 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-11522.        (((A and B) -> A) and (C -> ((A and B) -> A))), M:tm-305, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-11523
in-theory        11523
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((A and B) -> B)))
theorem-size     13
proof            (modus-ponens tm-305 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-11523.        (((A and B) -> B) and (C -> ((A and B) -> B))), M:tm-305, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-11524
in-theory        11524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (A -> (B -> (A and B)))))
theorem-size     17
proof            (modus-ponens tm-305 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11524.        ((A -> (B -> (A and B))) and (C -> (A -> (B -> (A and B))))), M:tm-305, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-11525
in-theory        11525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (A -> (A or B))))
theorem-size     13
proof            (modus-ponens tm-305 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-11525.        ((A -> (A or B)) and (C -> (A -> (A or B)))), M:tm-305, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-11526
in-theory        11526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (A -> (B or A))))
theorem-size     13
proof            (modus-ponens tm-305 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-11526.        ((A -> (B or A)) and (C -> (A -> (B or A)))), M:tm-305, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-11527
in-theory        11527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((A -> B) -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11527.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((A -> B) -> ((B -> C) -> ((A or B) -> C))))), M:tm-305, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-11528
in-theory        11528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((A -> B) -> ((A -> (not B)) -> (not A)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11528.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((A -> B) -> ((A -> (not B)) -> (not A))))), M:tm-305, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-11529
in-theory        11529
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((not (not A)) -> A)))
theorem-size     13
proof            (modus-ponens tm-305 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-11529.        (((not (not A)) -> A) and (B -> ((not (not A)) -> A))), M:tm-305, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-11530
in-theory        11530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (A -> (B -> (C -> B)))))
theorem-size     17
proof            (modus-ponens tm-305 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11530.        ((A -> (B -> (C -> B))) and (D -> (A -> (B -> (C -> B))))), M:tm-305, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-11531
in-theory        11531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((A -> B) -> (A -> A))))
theorem-size     17
proof            (modus-ponens tm-305 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-11531.        (((A -> B) -> (A -> A)) and (C -> ((A -> B) -> (A -> A)))), M:tm-305, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-11532
in-theory        11532
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11532.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-305, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-11533
in-theory        11533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11533.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-305, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-11534
in-theory        11534
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))))
theorem-size     33
proof            (modus-ponens tm-305 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11534.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)))), M:tm-305, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-11535
in-theory        11535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (A -> ((B and C) -> B))))
theorem-size     17
proof            (modus-ponens tm-305 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11535.        ((A -> ((B and C) -> B)) and (D -> (A -> ((B and C) -> B)))), M:tm-305, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-11536
in-theory        11536
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))))
theorem-size     33
proof            (modus-ponens tm-305 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11536.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)))), M:tm-305, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-11537
in-theory        11537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (A -> ((B and C) -> C))))
theorem-size     17
proof            (modus-ponens tm-305 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11537.        ((A -> ((B and C) -> C)) and (D -> (A -> ((B and C) -> C)))), M:tm-305, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-11538
in-theory        11538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (A -> ((B -> (C -> B)) and A))))
theorem-size     21
proof            (modus-ponens tm-305 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11538.        ((A -> ((B -> (C -> B)) and A)) and (D -> (A -> ((B -> (C -> B)) and A)))), M:tm-305, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-11539
in-theory        11539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     37
proof            (modus-ponens tm-305 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11539.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-305, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-11540
in-theory        11540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (A -> (((B and C) -> B) and A))))
theorem-size     21
proof            (modus-ponens tm-305 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11540.        ((A -> (((B and C) -> B) and A)) and (D -> (A -> (((B and C) -> B) and A)))), M:tm-305, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-11541
in-theory        11541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (A -> (((B and C) -> C) and A))))
theorem-size     21
proof            (modus-ponens tm-305 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11541.        ((A -> (((B and C) -> C) and A)) and (D -> (A -> (((B and C) -> C) and A)))), M:tm-305, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-11542
in-theory        11542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (A -> ((B -> (C -> (B and C))) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11542.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (A -> ((B -> (C -> (B and C))) and A)))), M:tm-305, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-11543
in-theory        11543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((A -> B) -> (A -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11543.        (((A -> B) -> (A -> (A and B))) and (C -> ((A -> B) -> (A -> (A and B))))), M:tm-305, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-11544
in-theory        11544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (A -> (B -> (C -> (B and C))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11544.        ((A -> (B -> (C -> (B and C)))) and (D -> (A -> (B -> (C -> (B and C)))))), M:tm-305, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-11545
in-theory        11545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((A -> (B -> A)) or C)))
theorem-size     17
proof            (modus-ponens tm-305 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11545.        (((A -> (B -> A)) or C) and (D -> ((A -> (B -> A)) or C))), M:tm-305, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-11546
in-theory        11546
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)))
theorem-size     33
proof            (modus-ponens tm-305 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11546.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D))), M:tm-305, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-11547
in-theory        11547
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((A and B) -> A) or C)))
theorem-size     17
proof            (modus-ponens tm-305 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11547.        ((((A and B) -> A) or C) and (D -> (((A and B) -> A) or C))), M:tm-305, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-11548
in-theory        11548
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((A and B) -> B) or C)))
theorem-size     17
proof            (modus-ponens tm-305 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11548.        ((((A and B) -> B) or C) and (D -> (((A and B) -> B) or C))), M:tm-305, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-11549
in-theory        11549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((A -> (B -> (A and B))) or C)))
theorem-size     21
proof            (modus-ponens tm-305 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11549.        (((A -> (B -> (A and B))) or C) and (D -> ((A -> (B -> (A and B))) or C))), M:tm-305, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-11550
in-theory        11550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((A -> (A or B)) or C)))
theorem-size     17
proof            (modus-ponens tm-305 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11550.        (((A -> (A or B)) or C) and (D -> ((A -> (A or B)) or C))), M:tm-305, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-11551
in-theory        11551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (A -> ((B -> (B or C)) and A))))
theorem-size     21
proof            (modus-ponens tm-305 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11551.        ((A -> ((B -> (B or C)) and A)) and (D -> (A -> ((B -> (B or C)) and A)))), M:tm-305, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-11552
in-theory        11552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (A -> (B -> (B or C)))))
theorem-size     17
proof            (modus-ponens tm-305 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11552.        ((A -> (B -> (B or C))) and (D -> (A -> (B -> (B or C))))), M:tm-305, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-11553
in-theory        11553
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (A or (B -> (C -> B)))))
theorem-size     17
proof            (modus-ponens tm-305 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11553.        ((A or (B -> (C -> B))) and (D -> (A or (B -> (C -> B))))), M:tm-305, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-11554
in-theory        11554
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11554.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-305, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-11555
in-theory        11555
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (A or ((B and C) -> B))))
theorem-size     17
proof            (modus-ponens tm-305 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11555.        ((A or ((B and C) -> B)) and (D -> (A or ((B and C) -> B)))), M:tm-305, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-11556
in-theory        11556
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (A or ((B and C) -> C))))
theorem-size     17
proof            (modus-ponens tm-305 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11556.        ((A or ((B and C) -> C)) and (D -> (A or ((B and C) -> C)))), M:tm-305, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-11557
in-theory        11557
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (A or (B -> (C -> (B and C))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11557.        ((A or (B -> (C -> (B and C)))) and (D -> (A or (B -> (C -> (B and C)))))), M:tm-305, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-11558
in-theory        11558
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (A or (B -> (B or C)))))
theorem-size     17
proof            (modus-ponens tm-305 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11558.        ((A or (B -> (B or C))) and (D -> (A or (B -> (B or C))))), M:tm-305, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-11559
in-theory        11559
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (A or (B -> (C or B)))))
theorem-size     17
proof            (modus-ponens tm-305 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11559.        ((A or (B -> (C or B))) and (D -> (A or (B -> (C or B))))), M:tm-305, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-11560
in-theory        11560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((A -> (B or A)) or C)))
theorem-size     17
proof            (modus-ponens tm-305 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11560.        (((A -> (B or A)) or C) and (D -> ((A -> (B or A)) or C))), M:tm-305, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-11561
in-theory        11561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (A -> ((B -> (C or B)) and A))))
theorem-size     21
proof            (modus-ponens tm-305 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11561.        ((A -> ((B -> (C or B)) and A)) and (D -> (A -> ((B -> (C or B)) and A)))), M:tm-305, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-11562
in-theory        11562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (A -> (B -> (C or B)))))
theorem-size     17
proof            (modus-ponens tm-305 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11562.        ((A -> (B -> (C or B))) and (D -> (A -> (B -> (C or B))))), M:tm-305, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-11563
in-theory        11563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((A -> B) -> C) -> ((B or (A -> B)) -> C))))
theorem-size     29
proof            (modus-ponens tm-305 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11563.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((A -> B) -> C) -> ((B or (A -> B)) -> C)))), M:tm-305, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-11564
in-theory        11564
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     53
proof            (modus-ponens tm-305 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11564.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-305, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-11565
in-theory        11565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((A -> B) -> (((A and C) or A) -> B))))
theorem-size     25
proof            (modus-ponens tm-305 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11565.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((A -> B) -> (((A and C) or A) -> B)))), M:tm-305, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-11566
in-theory        11566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((A -> B) -> (((C and A) or A) -> B))))
theorem-size     25
proof            (modus-ponens tm-305 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11566.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> ((A -> B) -> (((C and A) or A) -> B)))), M:tm-305, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-11567
in-theory        11567
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))))
theorem-size     37
proof            (modus-ponens tm-305 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-11567.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)))), M:tm-305, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-11568
in-theory        11568
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((A or B) -> C) -> ((A or (A or B)) -> C))))
theorem-size     29
proof            (modus-ponens tm-305 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-11568.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (((A or B) -> C) -> ((A or (A or B)) -> C)))), M:tm-305, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-11569
in-theory        11569
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((A or B) -> C) -> ((B or (A or B)) -> C))))
theorem-size     29
proof            (modus-ponens tm-305 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-11569.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (((A or B) -> C) -> ((B or (A or B)) -> C)))), M:tm-305, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-11570
in-theory        11570
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     57
proof            (modus-ponens tm-305 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-11570.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-305, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-11571
in-theory        11571
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11571.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-305, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-11572
in-theory        11572
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)))
theorem-size     33
proof            (modus-ponens tm-305 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11572.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D))), M:tm-305, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-11573
in-theory        11573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (E -> (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))))
theorem-size     37
proof            (modus-ponens tm-305 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11573.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (E -> (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)))), M:tm-305, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-11574
in-theory        11574
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (D -> (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-11574.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (D -> (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))))), M:tm-305, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-11575
in-theory        11575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11575.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-305, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-11576
in-theory        11576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (C -> ((A -> (not (B -> A))) -> (not A))))
theorem-size     21
proof            (modus-ponens tm-305 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11576.        (((A -> (not (B -> A))) -> (not A)) and (C -> ((A -> (not (B -> A))) -> (not A)))), M:tm-305, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-11577
in-theory        11577
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (D -> (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11577.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (D -> (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))))), M:tm-305, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-11578
in-theory        11578
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (C -> (((A and B) -> (not A)) -> (not (A and B)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11578.        ((((A and B) -> (not A)) -> (not (A and B))) and (C -> (((A and B) -> (not A)) -> (not (A and B))))), M:tm-305, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-11579
in-theory        11579
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (C -> (((A and B) -> (not B)) -> (not (A and B)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11579.        ((((A and B) -> (not B)) -> (not (A and B))) and (C -> (((A and B) -> (not B)) -> (not (A and B))))), M:tm-305, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-11580
in-theory        11580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (C -> ((A -> (not (B -> (A and B)))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-11580.        (((A -> (not (B -> (A and B)))) -> (not A)) and (C -> ((A -> (not (B -> (A and B)))) -> (not A)))), M:tm-305, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-11581
in-theory        11581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (C -> ((A -> (not (A or B))) -> (not A))))
theorem-size     21
proof            (modus-ponens tm-305 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-11581.        (((A -> (not (A or B))) -> (not A)) and (C -> ((A -> (not (A or B))) -> (not A)))), M:tm-305, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-11582
in-theory        11582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (C -> ((A -> (not (B or A))) -> (not A))))
theorem-size     21
proof            (modus-ponens tm-305 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-11582.        (((A -> (not (B or A))) -> (not A)) and (C -> ((A -> (not (B or A))) -> (not A)))), M:tm-305, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-11583
in-theory        11583
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (D -> (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-11583.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (D -> (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))))), M:tm-305, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-11584
in-theory        11584
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (C -> (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-11584.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (C -> (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))))), M:tm-305, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-11585
in-theory        11585
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (D -> ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))))
theorem-size     49
proof            (modus-ponens tm-305 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-11585.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (D -> ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))), M:tm-305, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-11586
in-theory        11586
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (A or ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11586.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (A or ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-305, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-11587
in-theory        11587
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (D -> (((A -> B) -> ((A -> (not B)) -> (not A))) or C)))
theorem-size     29
proof            (modus-ponens tm-305 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11587.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (D -> (((A -> B) -> ((A -> (not B)) -> (not A))) or C))), M:tm-305, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-11588
in-theory        11588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (D -> (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A))))
theorem-size     33
proof            (modus-ponens tm-305 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11588.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (D -> (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)))), M:tm-305, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-11589
in-theory        11589
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (C -> (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-11589.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (C -> (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))))), M:tm-305, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-11590
in-theory        11590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (A -> ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11590.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-305, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-11591
in-theory        11591
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (B -> (((not (not A)) -> (not A)) -> (not (not (not A))))))
theorem-size     25
proof            (modus-ponens tm-305 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-11591.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (B -> (((not (not A)) -> (not A)) -> (not (not (not A)))))), M:tm-305, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-11592
in-theory        11592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (C -> ((A -> B) -> (((not (not A)) or A) -> B))))
theorem-size     25
proof            (modus-ponens tm-305 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-10)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-11592.        (((A -> B) -> (((not (not A)) or A) -> B)) and (C -> ((A -> B) -> (((not (not A)) or A) -> B)))), M:tm-305, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-11593
in-theory        11593
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and (C -> (A or ((not (not B)) -> B))))
theorem-size     17
proof            (modus-ponens tm-305 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11593.        ((A or ((not (not B)) -> B)) and (C -> (A or ((not (not B)) -> B)))), M:tm-305, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-11594
in-theory        11594
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and (C -> (((not (not A)) -> A) or B)))
theorem-size     17
proof            (modus-ponens tm-305 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11594.        ((((not (not A)) -> A) or B) and (C -> (((not (not A)) -> A) or B))), M:tm-305, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-11595
in-theory        11595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (C -> (A -> (((not (not B)) -> B) and A))))
theorem-size     21
proof            (modus-ponens tm-305 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11595.        ((A -> (((not (not B)) -> B) and A)) and (C -> (A -> (((not (not B)) -> B) and A)))), M:tm-305, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-11596
in-theory        11596
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (C -> (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B))))
theorem-size     33
proof            (modus-ponens tm-305 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-11596.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (C -> (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)))), M:tm-305, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-11597
in-theory        11597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and (C -> (A -> ((not (not B)) -> B))))
theorem-size     17
proof            (modus-ponens tm-305 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11597.        ((A -> ((not (not B)) -> B)) and (C -> (A -> ((not (not B)) -> B)))), M:tm-305, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-11598
in-theory        11598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (D -> ((A -> (not (B -> (C -> B)))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-11598.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (D -> ((A -> (not (B -> (C -> B)))) -> (not A)))), M:tm-305, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-11599
in-theory        11599
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (E -> (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C))))
theorem-size     37
proof            (modus-ponens tm-305 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-11599.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (E -> (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)))), M:tm-305, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-11600
in-theory        11600
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and (E -> (A or (B -> (C -> (D -> C))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11600.        ((A or (B -> (C -> (D -> C)))) and (E -> (A or (B -> (C -> (D -> C)))))), M:tm-305, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-11601
in-theory        11601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and (E -> ((A -> (B -> (C -> B))) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11601.        (((A -> (B -> (C -> B))) or D) and (E -> ((A -> (B -> (C -> B))) or D))), M:tm-305, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-11602
in-theory        11602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and (E -> (A -> ((B -> (C -> (D -> C))) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11602.        ((A -> ((B -> (C -> (D -> C))) and A)) and (E -> (A -> ((B -> (C -> (D -> C))) and A)))), M:tm-305, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-11603
in-theory        11603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (D -> ((A -> B) -> (A -> (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-11603.        (((A -> B) -> (A -> (C -> B))) and (D -> ((A -> B) -> (A -> (C -> B))))), M:tm-305, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-11604
in-theory        11604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (E -> (A -> (B -> (C -> (D -> C))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11604.        ((A -> (B -> (C -> (D -> C)))) and (E -> (A -> (B -> (C -> (D -> C)))))), M:tm-305, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-11605
in-theory        11605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and (B -> (A -> A)))
theorem-size     9
proof            (modus-ponens tm-305 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11605.        ((A -> A) and (B -> (A -> A))), M:tm-305, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-11606
in-theory        11606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (D -> ((A -> (B -> C)) -> (A -> (B -> C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11606.        (((A -> (B -> C)) -> (A -> (B -> C))) and (D -> ((A -> (B -> C)) -> (A -> (B -> C))))), M:tm-305, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-11607
in-theory        11607
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and (C -> ((A and B) -> (A and B))))
theorem-size     17
proof            (modus-ponens tm-305 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11607.        (((A and B) -> (A and B)) and (C -> ((A and B) -> (A and B)))), M:tm-305, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-11608
in-theory        11608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (C -> ((A -> B) -> (A -> B))))
theorem-size     17
proof            (modus-ponens tm-305 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-11608.        (((A -> B) -> (A -> B)) and (C -> ((A -> B) -> (A -> B)))), M:tm-305, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-11609
in-theory        11609
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and (B -> ((not (not A)) -> (not (not A)))))
theorem-size     17
proof            (modus-ponens tm-305 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-11609.        (((not (not A)) -> (not (not A))) and (B -> ((not (not A)) -> (not (not A))))), M:tm-305, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-11610
in-theory        11610
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (C -> (((A -> B) -> (not (A -> A))) -> (not (A -> B)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-11610.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (C -> (((A -> B) -> (not (A -> A))) -> (not (A -> B))))), M:tm-305, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-11611
in-theory        11611
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (D -> (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B))))
theorem-size     33
proof            (modus-ponens tm-305 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-11611.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (D -> (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)))), M:tm-305, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-11612
in-theory        11612
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and (D -> (A or ((B -> C) -> (B -> B)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11612.        ((A or ((B -> C) -> (B -> B))) and (D -> (A or ((B -> C) -> (B -> B))))), M:tm-305, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-11613
in-theory        11613
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and (D -> (((A -> B) -> (A -> A)) or C)))
theorem-size     21
proof            (modus-ponens tm-305 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11613.        ((((A -> B) -> (A -> A)) or C) and (D -> (((A -> B) -> (A -> A)) or C))), M:tm-305, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-11614
in-theory        11614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (D -> (A -> (((B -> C) -> (B -> B)) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11614.        ((A -> (((B -> C) -> (B -> B)) and A)) and (D -> (A -> (((B -> C) -> (B -> B)) and A)))), M:tm-305, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-11615
in-theory        11615
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and (C -> (((A -> B) -> A) -> ((A -> B) -> A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-11615.        ((((A -> B) -> A) -> ((A -> B) -> A)) and (C -> (((A -> B) -> A) -> ((A -> B) -> A)))), M:tm-305, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-11616
in-theory        11616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and (D -> (A -> ((B -> C) -> (B -> B)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11616.        ((A -> ((B -> C) -> (B -> B))) and (D -> (A -> ((B -> C) -> (B -> B))))), M:tm-305, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-11617
in-theory        11617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (D -> ((A -> ((B -> A) -> C)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-11617.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (D -> ((A -> ((B -> A) -> C)) -> (A -> C)))), M:tm-305, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-11618
in-theory        11618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (C -> ((A -> (A -> B)) -> (A -> B))))
theorem-size     21
proof            (modus-ponens tm-305 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-11618.        (((A -> (A -> B)) -> (A -> B)) and (C -> ((A -> (A -> B)) -> (A -> B)))), M:tm-305, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-11619
in-theory        11619
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (D -> (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-11619.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (D -> (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))))), M:tm-305, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-11620
in-theory        11620
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (D -> ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B))))))
theorem-size     65
proof            (modus-ponens tm-305 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-11620.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (D -> ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))))), M:tm-305, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-11621
in-theory        11621
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (E -> ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))))
theorem-size     69
proof            (modus-ponens tm-305 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-11621.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (E -> ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))), M:tm-305, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-11622
in-theory        11622
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11622.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-305, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-11623
in-theory        11623
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (E -> ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D)))
theorem-size     45
proof            (modus-ponens tm-305 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11623.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (E -> ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D))), M:tm-305, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-11624
in-theory        11624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (E -> (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))))
theorem-size     49
proof            (modus-ponens tm-305 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11624.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (E -> (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)))), M:tm-305, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-11625
in-theory        11625
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (D -> ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-305 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-11625.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (D -> ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))), M:tm-305, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-11626
in-theory        11626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11626.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-305, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-11627
in-theory        11627
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (E -> (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-305 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-11627.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (E -> (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)))), M:tm-305, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-11628
in-theory        11628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (E -> ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A))))
theorem-size     41
proof            (modus-ponens tm-305 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11628.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (E -> ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)))), M:tm-305, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-11629
in-theory        11629
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))))
theorem-size     69
proof            (modus-ponens tm-305 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11629.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))), M:tm-305, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-11630
in-theory        11630
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11630.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-305, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-11631
in-theory        11631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     37
proof            (modus-ponens tm-305 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11631.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-305, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-11632
in-theory        11632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     41
proof            (modus-ponens tm-305 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11632.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-305, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-11633
in-theory        11633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (E -> ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-11633.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (E -> ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))))), M:tm-305, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-11634
in-theory        11634
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11634.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-305, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-11635
in-theory        11635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and (C -> (((A -> B) and A) -> B)))
theorem-size     17
proof            (modus-ponens tm-305 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-11635.        ((((A -> B) and A) -> B) and (C -> (((A -> B) and A) -> B))), M:tm-305, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-11636
in-theory        11636
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and (E -> ((((A -> (B -> A)) -> C) and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-305 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-11636.        (((((A -> (B -> A)) -> C) and D) -> C) and (E -> ((((A -> (B -> A)) -> C) and D) -> C))), M:tm-305, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-11637
in-theory        11637
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (F -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D)))
theorem-size     41
proof            (modus-ponens tm-305 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11637.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (F -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D))), M:tm-305, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-11638
in-theory        11638
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (D -> (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B))))
theorem-size     45
proof            (modus-ponens tm-305 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-11638.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (D -> (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)))), M:tm-305, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-11639
in-theory        11639
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (D -> ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A))))
theorem-size     33
proof            (modus-ponens tm-305 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-11639.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (D -> ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)))), M:tm-305, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-11640
in-theory        11640
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (D -> (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A)))))
theorem-size     53
proof            (modus-ponens tm-305 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-11640.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (D -> (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))))), M:tm-305, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-11641
in-theory        11641
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (E -> (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))))
theorem-size     57
proof            (modus-ponens tm-305 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-11641.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (E -> (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))), M:tm-305, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-11642
in-theory        11642
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11642.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-305, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-11643
in-theory        11643
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (E -> (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D)))
theorem-size     37
proof            (modus-ponens tm-305 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11643.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (E -> (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D))), M:tm-305, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-11644
in-theory        11644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (E -> (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))))
theorem-size     41
proof            (modus-ponens tm-305 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11644.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (E -> (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)))), M:tm-305, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-11645
in-theory        11645
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (D -> (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B))))
theorem-size     49
proof            (modus-ponens tm-305 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-11645.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (D -> (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)))), M:tm-305, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-11646
in-theory        11646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11646.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-305, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-11647
in-theory        11647
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and (E -> (((((A and B) -> A) -> C) and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-305 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-11647.        ((((((A and B) -> A) -> C) and D) -> C) and (E -> (((((A and B) -> A) -> C) and D) -> C))), M:tm-305, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-11648
in-theory        11648
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (D -> (((A and B) -> (A -> C)) -> ((A and B) -> C))))
theorem-size     29
proof            (modus-ponens tm-305 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-11648.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (D -> (((A and B) -> (A -> C)) -> ((A and B) -> C)))), M:tm-305, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-11649
in-theory        11649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (D -> ((A -> (not ((B and C) -> B))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-11649.        (((A -> (not ((B and C) -> B))) -> (not A)) and (D -> ((A -> (not ((B and C) -> B))) -> (not A)))), M:tm-305, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-11650
in-theory        11650
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (E -> ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C))))
theorem-size     37
proof            (modus-ponens tm-305 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-11650.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (E -> ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)))), M:tm-305, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-11651
in-theory        11651
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and (E -> (A or (B -> ((C and D) -> C)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11651.        ((A or (B -> ((C and D) -> C))) and (E -> (A or (B -> ((C and D) -> C))))), M:tm-305, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-11652
in-theory        11652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and (E -> ((A -> ((B and C) -> B)) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11652.        (((A -> ((B and C) -> B)) or D) and (E -> ((A -> ((B and C) -> B)) or D))), M:tm-305, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-11653
in-theory        11653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and (E -> (A -> ((B -> ((C and D) -> C)) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11653.        ((A -> ((B -> ((C and D) -> C)) and A)) and (E -> (A -> ((B -> ((C and D) -> C)) and A)))), M:tm-305, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-11654
in-theory        11654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (D -> ((A -> (B and C)) -> (A -> B))))
theorem-size     21
proof            (modus-ponens tm-305 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-11654.        (((A -> (B and C)) -> (A -> B)) and (D -> ((A -> (B and C)) -> (A -> B)))), M:tm-305, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-11655
in-theory        11655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (E -> (A -> (B -> ((C and D) -> C)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11655.        ((A -> (B -> ((C and D) -> C))) and (E -> (A -> (B -> ((C and D) -> C))))), M:tm-305, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-11656
in-theory        11656
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and (C -> ((A and (A -> B)) -> B)))
theorem-size     17
proof            (modus-ponens tm-305 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-11656.        (((A and (A -> B)) -> B) and (C -> ((A and (A -> B)) -> B))), M:tm-305, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-11657
in-theory        11657
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and (E -> ((A and ((B -> (C -> B)) -> D)) -> D)))
theorem-size     25
proof            (modus-ponens tm-305 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-11657.        (((A and ((B -> (C -> B)) -> D)) -> D) and (E -> ((A and ((B -> (C -> B)) -> D)) -> D))), M:tm-305, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-11658
in-theory        11658
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (F -> ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E)))
theorem-size     41
proof            (modus-ponens tm-305 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11658.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (F -> ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E))), M:tm-305, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-11659
in-theory        11659
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and (E -> ((A and (((B and C) -> B) -> D)) -> D)))
theorem-size     25
proof            (modus-ponens tm-305 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-11659.        (((A and (((B and C) -> B) -> D)) -> D) and (E -> ((A and (((B and C) -> B) -> D)) -> D))), M:tm-305, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-11660
in-theory        11660
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (D -> (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C))))
theorem-size     45
proof            (modus-ponens tm-305 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-11660.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (D -> (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)))), M:tm-305, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-11661
in-theory        11661
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (D -> (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B))))
theorem-size     33
proof            (modus-ponens tm-305 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-11661.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (D -> (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)))), M:tm-305, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-11662
in-theory        11662
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (D -> ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B)))))
theorem-size     53
proof            (modus-ponens tm-305 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-11662.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (D -> ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))))), M:tm-305, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-11663
in-theory        11663
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (E -> ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-305 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-11663.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (E -> ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))), M:tm-305, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-11664
in-theory        11664
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11664.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-305, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-11665
in-theory        11665
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (E -> ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-305 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11665.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (E -> ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D))), M:tm-305, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-11666
in-theory        11666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (E -> (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-305 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11666.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (E -> (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)))), M:tm-305, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-11667
in-theory        11667
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (D -> ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C))))
theorem-size     49
proof            (modus-ponens tm-305 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-11667.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (D -> ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)))), M:tm-305, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-11668
in-theory        11668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11668.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-305, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-11669
in-theory        11669
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and (E -> ((A and (((B and C) -> C) -> D)) -> D)))
theorem-size     25
proof            (modus-ponens tm-305 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-11669.        (((A and (((B and C) -> C) -> D)) -> D) and (E -> ((A and (((B and C) -> C) -> D)) -> D))), M:tm-305, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-11670
in-theory        11670
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and (E -> (((((A and B) -> B) -> C) and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-305 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-11670.        ((((((A and B) -> B) -> C) and D) -> C) and (E -> (((((A and B) -> B) -> C) and D) -> C))), M:tm-305, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-11671
in-theory        11671
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (D -> (((A and B) -> (B -> C)) -> ((A and B) -> C))))
theorem-size     29
proof            (modus-ponens tm-305 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-11671.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (D -> (((A and B) -> (B -> C)) -> ((A and B) -> C)))), M:tm-305, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-11672
in-theory        11672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (D -> ((A -> (not ((B and C) -> C))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-11672.        (((A -> (not ((B and C) -> C))) -> (not A)) and (D -> ((A -> (not ((B and C) -> C))) -> (not A)))), M:tm-305, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-11673
in-theory        11673
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (E -> ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C))))
theorem-size     37
proof            (modus-ponens tm-305 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-11673.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (E -> ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)))), M:tm-305, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-11674
in-theory        11674
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and (E -> (A or (B -> ((C and D) -> D)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11674.        ((A or (B -> ((C and D) -> D))) and (E -> (A or (B -> ((C and D) -> D))))), M:tm-305, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-11675
in-theory        11675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and (E -> ((A -> ((B and C) -> C)) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11675.        (((A -> ((B and C) -> C)) or D) and (E -> ((A -> ((B and C) -> C)) or D))), M:tm-305, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-11676
in-theory        11676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and (E -> (A -> ((B -> ((C and D) -> D)) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11676.        ((A -> ((B -> ((C and D) -> D)) and A)) and (E -> (A -> ((B -> ((C and D) -> D)) and A)))), M:tm-305, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-11677
in-theory        11677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (D -> ((A -> (B and C)) -> (A -> C))))
theorem-size     21
proof            (modus-ponens tm-305 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-11677.        (((A -> (B and C)) -> (A -> C)) and (D -> ((A -> (B and C)) -> (A -> C)))), M:tm-305, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-11678
in-theory        11678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (E -> (A -> (B -> ((C and D) -> D)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11678.        ((A -> (B -> ((C and D) -> D))) and (E -> (A -> (B -> ((C and D) -> D))))), M:tm-305, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-11679
in-theory        11679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and (E -> ((A -> (B -> A)) and (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11679.        (((A -> (B -> A)) and (C -> (D -> C))) and (E -> ((A -> (B -> A)) and (C -> (D -> C))))), M:tm-305, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-11680
in-theory        11680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11680.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-305, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-11681
in-theory        11681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and (E -> ((A -> (B -> A)) and ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11681.        (((A -> (B -> A)) and ((C and D) -> C)) and (E -> ((A -> (B -> A)) and ((C and D) -> C)))), M:tm-305, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-11682
in-theory        11682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and (E -> ((A -> (B -> A)) and ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-305 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11682.        (((A -> (B -> A)) and ((C and D) -> D)) and (E -> ((A -> (B -> A)) and ((C and D) -> D)))), M:tm-305, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-11683
in-theory        11683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (E -> ((A -> (B -> A)) and (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11683.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (E -> ((A -> (B -> A)) and (C -> (D -> (C and D)))))), M:tm-305, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-11684
in-theory        11684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and (E -> ((A -> (B -> A)) and (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11684.        (((A -> (B -> A)) and (C -> (C or D))) and (E -> ((A -> (B -> A)) and (C -> (C or D))))), M:tm-305, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-11685
in-theory        11685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and (E -> ((A -> (B -> A)) and (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11685.        (((A -> (B -> A)) and (C -> (D or C))) and (E -> ((A -> (B -> A)) and (C -> (D or C))))), M:tm-305, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-11686
in-theory        11686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11686.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-305, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-11687
in-theory        11687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11687.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-305, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-11688
in-theory        11688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and (D -> ((A -> (B -> A)) and ((not (not C)) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11688.        (((A -> (B -> A)) and ((not (not C)) -> C)) and (D -> ((A -> (B -> A)) and ((not (not C)) -> C)))), M:tm-305, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-11689
in-theory        11689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (F -> ((A -> (B -> A)) and (C -> (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11689.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (F -> ((A -> (B -> A)) and (C -> (D -> (E -> D)))))), M:tm-305, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-11690
in-theory        11690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (E -> ((A -> (B -> A)) and ((C -> D) -> (C -> C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11690.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (E -> ((A -> (B -> A)) and ((C -> D) -> (C -> C))))), M:tm-305, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-11691
in-theory        11691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-305 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11691.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-305, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-11692
in-theory        11692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11692.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-305, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-11693
in-theory        11693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11693.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-305, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-11694
in-theory        11694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (F -> ((A -> (B -> A)) and (C -> ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11694.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (F -> ((A -> (B -> A)) and (C -> ((D and E) -> D))))), M:tm-305, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-11695
in-theory        11695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11695.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-305, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-11696
in-theory        11696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (F -> ((A -> (B -> A)) and (C -> ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11696.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (F -> ((A -> (B -> A)) and (C -> ((D and E) -> E))))), M:tm-305, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-11697
in-theory        11697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (F -> ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11697.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (F -> ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-305, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-11698
in-theory        11698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (D -> ((A -> (not ((B -> (C -> B)) and A))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-11698.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (D -> ((A -> (not ((B -> (C -> B)) and A))) -> (not A)))), M:tm-305, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-11699
in-theory        11699
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (E -> ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-305 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-11699.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (E -> ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)))), M:tm-305, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-11700
in-theory        11700
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and (E -> (A or (B -> ((C -> (D -> C)) and B)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11700.        ((A or (B -> ((C -> (D -> C)) and B))) and (E -> (A or (B -> ((C -> (D -> C)) and B))))), M:tm-305, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-11701
in-theory        11701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and (E -> ((A -> ((B -> (C -> B)) and A)) or D)))
theorem-size     25
proof            (modus-ponens tm-305 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11701.        (((A -> ((B -> (C -> B)) and A)) or D) and (E -> ((A -> ((B -> (C -> B)) and A)) or D))), M:tm-305, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-11702
in-theory        11702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (E -> (A -> ((B -> ((C -> (D -> C)) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11702.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (E -> (A -> ((B -> ((C -> (D -> C)) and B)) and A)))), M:tm-305, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-11703
in-theory        11703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (E -> (A -> (B -> ((C -> (D -> C)) and B)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11703.        ((A -> (B -> ((C -> (D -> C)) and B))) and (E -> (A -> (B -> ((C -> (D -> C)) and B))))), M:tm-305, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-11704
in-theory        11704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11704.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))))), M:tm-305, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-11705
in-theory        11705
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11705.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-305, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-11706
in-theory        11706
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D))))
theorem-size     41
proof            (modus-ponens tm-305 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11706.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)))), M:tm-305, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-11707
in-theory        11707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E))))
theorem-size     41
proof            (modus-ponens tm-305 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11707.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)))), M:tm-305, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-11708
in-theory        11708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11708.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))))), M:tm-305, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-11709
in-theory        11709
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11709.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))))), M:tm-305, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-11710
in-theory        11710
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11710.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))))), M:tm-305, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-11711
in-theory        11711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11711.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-305, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-11712
in-theory        11712
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     53
proof            (modus-ponens tm-305 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11712.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-305, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-11713
in-theory        11713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (E -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D))))
theorem-size     41
proof            (modus-ponens tm-305 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11713.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (E -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)))), M:tm-305, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-11714
in-theory        11714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11714.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))))), M:tm-305, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-11715
in-theory        11715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11715.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))))), M:tm-305, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-11716
in-theory        11716
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     69
proof            (modus-ponens tm-305 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11716.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-305, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-11717
in-theory        11717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     61
proof            (modus-ponens tm-305 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11717.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-305, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-11718
in-theory        11718
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     61
proof            (modus-ponens tm-305 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11718.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-305, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-11719
in-theory        11719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11719.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))))), M:tm-305, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-11720
in-theory        11720
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-305 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11720.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-305, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-11721
in-theory        11721
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11721.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))))), M:tm-305, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-11722
in-theory        11722
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11722.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-305, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-11723
in-theory        11723
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     65
proof            (modus-ponens tm-305 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11723.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-305, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-11724
in-theory        11724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11724.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-305, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-11725
in-theory        11725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (E -> ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A))))
theorem-size     45
proof            (modus-ponens tm-305 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-11725.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (E -> ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)))), M:tm-305, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-11726
in-theory        11726
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (F -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))))
theorem-size     77
proof            (modus-ponens tm-305 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-11726.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (F -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))), M:tm-305, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-11727
in-theory        11727
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11727.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-305, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-11728
in-theory        11728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (F -> ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E)))
theorem-size     41
proof            (modus-ponens tm-305 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11728.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (F -> ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E))), M:tm-305, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-11729
in-theory        11729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (F -> (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))))
theorem-size     45
proof            (modus-ponens tm-305 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11729.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (F -> (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)))), M:tm-305, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-11730
in-theory        11730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11730.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-305, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-11731
in-theory        11731
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and (E -> (((A and B) -> A) and (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11731.        ((((A and B) -> A) and (C -> (D -> C))) and (E -> (((A and B) -> A) and (C -> (D -> C))))), M:tm-305, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-11732
in-theory        11732
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11732.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-305, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-11733
in-theory        11733
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and (E -> (((A and B) -> A) and ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11733.        ((((A and B) -> A) and ((C and D) -> C)) and (E -> (((A and B) -> A) and ((C and D) -> C)))), M:tm-305, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-11734
in-theory        11734
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and (E -> (((A and B) -> A) and ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-305 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11734.        ((((A and B) -> A) and ((C and D) -> D)) and (E -> (((A and B) -> A) and ((C and D) -> D)))), M:tm-305, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-11735
in-theory        11735
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and (E -> (((A and B) -> A) and (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11735.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and (E -> (((A and B) -> A) and (C -> (D -> (C and D)))))), M:tm-305, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-11736
in-theory        11736
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and (E -> (((A and B) -> A) and (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11736.        ((((A and B) -> A) and (C -> (C or D))) and (E -> (((A and B) -> A) and (C -> (C or D))))), M:tm-305, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-11737
in-theory        11737
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and (E -> (((A and B) -> A) and (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11737.        ((((A and B) -> A) and (C -> (D or C))) and (E -> (((A and B) -> A) and (C -> (D or C))))), M:tm-305, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-11738
in-theory        11738
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11738.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-305, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-11739
in-theory        11739
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11739.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-305, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-11740
in-theory        11740
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and (D -> (((A and B) -> A) and ((not (not C)) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11740.        ((((A and B) -> A) and ((not (not C)) -> C)) and (D -> (((A and B) -> A) and ((not (not C)) -> C)))), M:tm-305, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-11741
in-theory        11741
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (F -> (((A and B) -> A) and (C -> (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11741.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (F -> (((A and B) -> A) and (C -> (D -> (E -> D)))))), M:tm-305, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-11742
in-theory        11742
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (E -> (((A and B) -> A) and ((C -> D) -> (C -> C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11742.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (E -> (((A and B) -> A) and ((C -> D) -> (C -> C))))), M:tm-305, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-11743
in-theory        11743
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-305 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11743.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-305, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-11744
in-theory        11744
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11744.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-305, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-11745
in-theory        11745
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11745.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-305, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-11746
in-theory        11746
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and (F -> (((A and B) -> A) and (C -> ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11746.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and (F -> (((A and B) -> A) and (C -> ((D and E) -> D))))), M:tm-305, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-11747
in-theory        11747
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11747.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-305, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-11748
in-theory        11748
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and (F -> (((A and B) -> A) and (C -> ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11748.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and (F -> (((A and B) -> A) and (C -> ((D and E) -> E))))), M:tm-305, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-11749
in-theory        11749
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (F -> (((A and B) -> A) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11749.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (F -> (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))))), M:tm-305, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-11750
in-theory        11750
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11750.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-305, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-11751
in-theory        11751
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (F -> (((A and B) -> A) and (C -> (((D and E) -> D) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11751.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (F -> (((A and B) -> A) and (C -> (((D and E) -> D) and C))))), M:tm-305, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-11752
in-theory        11752
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11752.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-305, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-11753
in-theory        11753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (F -> ((A -> (B -> A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11753.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (F -> ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))))), M:tm-305, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-11754
in-theory        11754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (D -> ((A -> (not (((B and C) -> B) and A))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-11754.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (D -> ((A -> (not (((B and C) -> B) and A))) -> (not A)))), M:tm-305, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-11755
in-theory        11755
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (E -> (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-305 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-11755.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (E -> (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)))), M:tm-305, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-11756
in-theory        11756
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and (E -> (A or (B -> (((C and D) -> C) and B)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11756.        ((A or (B -> (((C and D) -> C) and B))) and (E -> (A or (B -> (((C and D) -> C) and B))))), M:tm-305, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-11757
in-theory        11757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and (E -> ((A -> (((B and C) -> B) and A)) or D)))
theorem-size     25
proof            (modus-ponens tm-305 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11757.        (((A -> (((B and C) -> B) and A)) or D) and (E -> ((A -> (((B and C) -> B) and A)) or D))), M:tm-305, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-11758
in-theory        11758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (E -> (A -> ((B -> (((C and D) -> C) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11758.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (E -> (A -> ((B -> (((C and D) -> C) and B)) and A)))), M:tm-305, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-11759
in-theory        11759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (E -> (A -> (B -> (((C and D) -> C) and B)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11759.        ((A -> (B -> (((C and D) -> C) and B))) and (E -> (A -> (B -> (((C and D) -> C) and B))))), M:tm-305, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-11760
in-theory        11760
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and (E -> (((A and B) -> B) and (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11760.        ((((A and B) -> B) and (C -> (D -> C))) and (E -> (((A and B) -> B) and (C -> (D -> C))))), M:tm-305, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-11761
in-theory        11761
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11761.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-305, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-11762
in-theory        11762
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and (E -> (((A and B) -> B) and ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11762.        ((((A and B) -> B) and ((C and D) -> C)) and (E -> (((A and B) -> B) and ((C and D) -> C)))), M:tm-305, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-11763
in-theory        11763
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and (E -> (((A and B) -> B) and ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-305 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11763.        ((((A and B) -> B) and ((C and D) -> D)) and (E -> (((A and B) -> B) and ((C and D) -> D)))), M:tm-305, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-11764
in-theory        11764
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and (E -> (((A and B) -> B) and (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11764.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and (E -> (((A and B) -> B) and (C -> (D -> (C and D)))))), M:tm-305, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-11765
in-theory        11765
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and (E -> (((A and B) -> B) and (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11765.        ((((A and B) -> B) and (C -> (C or D))) and (E -> (((A and B) -> B) and (C -> (C or D))))), M:tm-305, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-11766
in-theory        11766
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and (E -> (((A and B) -> B) and (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11766.        ((((A and B) -> B) and (C -> (D or C))) and (E -> (((A and B) -> B) and (C -> (D or C))))), M:tm-305, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-11767
in-theory        11767
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11767.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-305, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-11768
in-theory        11768
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11768.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-305, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-11769
in-theory        11769
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and (D -> (((A and B) -> B) and ((not (not C)) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11769.        ((((A and B) -> B) and ((not (not C)) -> C)) and (D -> (((A and B) -> B) and ((not (not C)) -> C)))), M:tm-305, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-11770
in-theory        11770
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (F -> (((A and B) -> B) and (C -> (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11770.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (F -> (((A and B) -> B) and (C -> (D -> (E -> D)))))), M:tm-305, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-11771
in-theory        11771
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (E -> (((A and B) -> B) and ((C -> D) -> (C -> C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11771.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (E -> (((A and B) -> B) and ((C -> D) -> (C -> C))))), M:tm-305, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-11772
in-theory        11772
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-305 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11772.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-305, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-11773
in-theory        11773
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11773.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-305, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-11774
in-theory        11774
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11774.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-305, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-11775
in-theory        11775
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and (F -> (((A and B) -> B) and (C -> ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11775.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and (F -> (((A and B) -> B) and (C -> ((D and E) -> D))))), M:tm-305, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-11776
in-theory        11776
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11776.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-305, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-11777
in-theory        11777
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and (F -> (((A and B) -> B) and (C -> ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11777.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and (F -> (((A and B) -> B) and (C -> ((D and E) -> E))))), M:tm-305, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-11778
in-theory        11778
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (F -> (((A and B) -> B) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11778.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (F -> (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))))), M:tm-305, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-11779
in-theory        11779
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11779.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-305, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-11780
in-theory        11780
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (F -> (((A and B) -> B) and (C -> (((D and E) -> D) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11780.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (F -> (((A and B) -> B) and (C -> (((D and E) -> D) and C))))), M:tm-305, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-11781
in-theory        11781
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (F -> (((A and B) -> B) and (C -> (((D and E) -> E) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11781.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (F -> (((A and B) -> B) and (C -> (((D and E) -> E) and C))))), M:tm-305, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-11782
in-theory        11782
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (F -> (((A and B) -> A) and (C -> (((D and E) -> E) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11782.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (F -> (((A and B) -> A) and (C -> (((D and E) -> E) and C))))), M:tm-305, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-11783
in-theory        11783
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11783.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-305, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-11784
in-theory        11784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (F -> ((A -> (B -> A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11784.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (F -> ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))))), M:tm-305, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-11785
in-theory        11785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (D -> ((A -> (not (((B and C) -> C) and A))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-11785.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (D -> ((A -> (not (((B and C) -> C) and A))) -> (not A)))), M:tm-305, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-11786
in-theory        11786
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (E -> (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-305 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-11786.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (E -> (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)))), M:tm-305, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-11787
in-theory        11787
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and (E -> (A or (B -> (((C and D) -> D) and B)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11787.        ((A or (B -> (((C and D) -> D) and B))) and (E -> (A or (B -> (((C and D) -> D) and B))))), M:tm-305, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-11788
in-theory        11788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and (E -> ((A -> (((B and C) -> C) and A)) or D)))
theorem-size     25
proof            (modus-ponens tm-305 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11788.        (((A -> (((B and C) -> C) and A)) or D) and (E -> ((A -> (((B and C) -> C) and A)) or D))), M:tm-305, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-11789
in-theory        11789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (E -> (A -> ((B -> (((C and D) -> D) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11789.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (E -> (A -> ((B -> (((C and D) -> D) and B)) and A)))), M:tm-305, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-11790
in-theory        11790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (E -> (A -> (B -> (((C and D) -> D) and B)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11790.        ((A -> (B -> (((C and D) -> D) and B))) and (E -> (A -> (B -> (((C and D) -> D) and B))))), M:tm-305, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-11791
in-theory        11791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and (E -> ((A -> (B -> (A and B))) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11791.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and (E -> ((A -> (B -> (A and B))) and (C -> (D -> C))))), M:tm-305, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-11792
in-theory        11792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11792.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-305, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-11793
in-theory        11793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and (E -> ((A -> (B -> (A and B))) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-305 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11793.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and (E -> ((A -> (B -> (A and B))) and ((C and D) -> C)))), M:tm-305, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-11794
in-theory        11794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and (E -> ((A -> (B -> (A and B))) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-305 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11794.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and (E -> ((A -> (B -> (A and B))) and ((C and D) -> D)))), M:tm-305, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-11795
in-theory        11795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (E -> ((A -> (B -> (A and B))) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11795.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (E -> ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))))), M:tm-305, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-11796
in-theory        11796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and (E -> ((A -> (B -> (A and B))) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11796.        (((A -> (B -> (A and B))) and (C -> (C or D))) and (E -> ((A -> (B -> (A and B))) and (C -> (C or D))))), M:tm-305, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-11797
in-theory        11797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and (E -> ((A -> (B -> (A and B))) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11797.        (((A -> (B -> (A and B))) and (C -> (D or C))) and (E -> ((A -> (B -> (A and B))) and (C -> (D or C))))), M:tm-305, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-11798
in-theory        11798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11798.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-305, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-11799
in-theory        11799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11799.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-305, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-11800
in-theory        11800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (D -> ((A -> (B -> (A and B))) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-305 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11800.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (D -> ((A -> (B -> (A and B))) and ((not (not C)) -> C)))), M:tm-305, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-11801
in-theory        11801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (F -> ((A -> (B -> (A and B))) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11801.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (F -> ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))))), M:tm-305, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-11802
in-theory        11802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (E -> ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11802.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (E -> ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))))), M:tm-305, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-11803
in-theory        11803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11803.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-305, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-11804
in-theory        11804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-305 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11804.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-305, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-11805
in-theory        11805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11805.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-305, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-11806
in-theory        11806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (F -> ((A -> (B -> (A and B))) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11806.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (F -> ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))))), M:tm-305, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-11807
in-theory        11807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11807.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-305, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-11808
in-theory        11808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (F -> ((A -> (B -> (A and B))) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11808.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (F -> ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))))), M:tm-305, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-11809
in-theory        11809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (F -> ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11809.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (F -> ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))))), M:tm-305, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-11810
in-theory        11810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-305 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11810.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-305, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-11811
in-theory        11811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (F -> ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11811.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (F -> ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))))), M:tm-305, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-11812
in-theory        11812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (F -> ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11812.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (F -> ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))))), M:tm-305, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-11813
in-theory        11813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11813.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-305, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-11814
in-theory        11814
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11814.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-305, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-11815
in-theory        11815
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11815.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-305, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-11816
in-theory        11816
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     53
proof            (modus-ponens tm-305 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11816.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-305, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-11817
in-theory        11817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11817.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-305, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-11818
in-theory        11818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (D -> ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-305 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11818.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (D -> ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)))), M:tm-305, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-11819
in-theory        11819
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (E -> ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-305 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11819.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (E -> ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)))), M:tm-305, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-11820
in-theory        11820
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and (E -> (A or (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11820.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and (E -> (A or (B -> ((C -> (D -> (C and D))) and B))))), M:tm-305, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11821
in-theory        11821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and (E -> ((A -> ((B -> (C -> (B and C))) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-305 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11821.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and (E -> ((A -> ((B -> (C -> (B and C))) and A)) or D))), M:tm-305, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-11822
in-theory        11822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (E -> (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-305 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11822.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (E -> (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)))), M:tm-305, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-11823
in-theory        11823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (E -> (A -> (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11823.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (E -> (A -> (B -> ((C -> (D -> (C and D))) and B))))), M:tm-305, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-11824
in-theory        11824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (C -> (A -> (A and (B -> A)))))
theorem-size     17
proof            (modus-ponens tm-305 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11824.        ((A -> (A and (B -> A))) and (C -> (A -> (A and (B -> A))))), M:tm-305, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11825
in-theory        11825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (E -> D))))
theorem-size     19
proof            (modus-ponens tm-303 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11825.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (E -> D)))), M:tm-303, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11826
in-theory        11826
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (D -> ((B -> (C -> (B and C))) and A))))
theorem-size     33
proof            (modus-ponens tm-300 tm-305 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> Bm (and (-> A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11826.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (D -> ((B -> (C -> (B and C))) and A)))), M:tm-300, m:tm-305, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> Bm (and (-> A (-> B (and A B))) C)))))
================================================================
tm-name          tm-11827
in-theory        11827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and (E -> D))))
theorem-size     17
proof            (modus-ponens tm-270 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11827.        ((A -> (((B and C) -> C) and A)) and (D -> (D and (E -> D)))), M:tm-270, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11828
in-theory        11828
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (D -> (((B and C) -> C) and A))))
theorem-size     27
proof            (modus-ponens tm-267 tm-305 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> Bm (and (-> (and A B) B) C))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11828.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (D -> (((B and C) -> C) and A)))), M:tm-267, m:tm-305, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> Bm (and (-> (and A B) B) C)))))
================================================================
tm-name          tm-11829
in-theory        11829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and (E -> D))))
theorem-size     17
proof            (modus-ponens tm-239 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11829.        ((A -> (((B and C) -> B) and A)) and (D -> (D and (E -> D)))), M:tm-239, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11830
in-theory        11830
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (D -> (((B and C) -> B) and A))))
theorem-size     27
proof            (modus-ponens tm-236 tm-305 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> Bm (and (-> (and A B) A) C))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11830.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (D -> (((B and C) -> B) and A)))), M:tm-236, m:tm-305, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> Bm (and (-> (and A B) A) C)))))
================================================================
tm-name          tm-11831
in-theory        11831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (F -> E))))
theorem-size     25
proof            (modus-ponens tm-210 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11831.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (F -> E)))), M:tm-210, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11832
in-theory        11832
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     51
proof            (modus-ponens tm-207 tm-305 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11832.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-207, m:tm-305, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-11833
in-theory        11833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (E -> D))))
theorem-size     17
proof            (modus-ponens tm-183 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11833.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (E -> D)))), M:tm-183, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11834
in-theory        11834
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (D -> ((B -> (C -> B)) and A))))
theorem-size     27
proof            (modus-ponens tm-180 tm-305 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> Bm (and (-> A (-> B A)) C))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11834.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (D -> ((B -> (C -> B)) and A)))), M:tm-180, m:tm-305, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> Bm (and (-> A (-> B A)) C)))))
================================================================
tm-name          tm-11835
in-theory        11835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-157 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11835.        ((A -> ((B and C) -> C)) and (D -> (D and (E -> D)))), M:tm-157, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11836
in-theory        11836
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and (D -> ((B and C) -> C))))
theorem-size     21
proof            (modus-ponens tm-154 tm-305 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> Bm (-> (and A B) B))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11836.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and (D -> ((B and C) -> C)))), M:tm-154, m:tm-305, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> Bm (-> (and A B) B)))))
================================================================
tm-name          tm-11837
in-theory        11837
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-147 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11837.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (E -> D)))), M:tm-147, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11838
in-theory        11838
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (D -> ((A and (B -> C)) -> C))))
theorem-size     33
proof            (modus-ponens tm-144 tm-305 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> Bm (-> (and A (-> B C)) C))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11838.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (D -> ((A and (B -> C)) -> C)))), M:tm-144, m:tm-305, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> Bm (-> (and A (-> B C)) C)))))
================================================================
tm-name          tm-11839
in-theory        11839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-134 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11839.        ((A -> ((B and C) -> B)) and (D -> (D and (E -> D)))), M:tm-134, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11840
in-theory        11840
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and (D -> ((B and C) -> B))))
theorem-size     21
proof            (modus-ponens tm-131 tm-305 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> Bm (-> (and A B) A))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11840.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and (D -> ((B and C) -> B)))), M:tm-131, m:tm-305, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> Bm (-> (and A B) A)))))
================================================================
tm-name          tm-11841
in-theory        11841
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-125 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11841.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (E -> D)))), M:tm-125, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11842
in-theory        11842
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (D -> (((A -> B) and C) -> B))))
theorem-size     33
proof            (modus-ponens tm-122 tm-305 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> Bm (-> (and (-> A B) C) B))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11842.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (D -> (((A -> B) and C) -> B)))), M:tm-122, m:tm-305, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> Bm (-> (and (-> A B) C) B)))))
================================================================
tm-name          tm-11843
in-theory        11843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> E))))
theorem-size     23
proof            (modus-ponens tm-113 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11843.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> E)))), M:tm-113, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11844
in-theory        11844
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     45
proof            (modus-ponens tm-110 tm-305 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11844.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-110, m:tm-305, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
================================================================
tm-name          tm-11845
in-theory        11845
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-105 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11845.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (E -> D)))), M:tm-105, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11846
in-theory        11846
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (D -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-102 tm-305 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> Bm (-> (-> A (-> B C)) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11846.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (D -> ((A -> (B -> C)) -> (A -> C))))), M:tm-102, m:tm-305, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> Bm (-> (-> A (-> B C)) (-> A C))))))
================================================================
tm-name          tm-11847
in-theory        11847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and (D -> C))))
theorem-size     15
proof            (modus-ponens tm-95 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11847.        (((A -> B) -> (A -> A)) and (C -> (C and (D -> C)))), M:tm-95, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11848
in-theory        11848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and (C -> (A -> A))))
theorem-size     17
proof            (modus-ponens tm-92 tm-305 ((Am (-> A A)) (B (and (-> A A) (-> Bm (-> A A))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11848.        (((A -> B) or (A -> A)) -> ((A -> A) and (C -> (A -> A)))), M:tm-92, m:tm-305, u:((Am (-> A A)) (B (and (-> A A) (-> Bm (-> A A)))))
================================================================
tm-name          tm-11849
in-theory        11849
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and (C -> A))))
theorem-size     9
proof            (modus-ponens tm-84 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11849.        (A -> (B -> (A and (C -> A)))), M:tm-84, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-11850
in-theory        11850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-83 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11850.        ((A -> (B -> (C -> B))) and (D -> (D and (E -> D)))), M:tm-83, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11851
in-theory        11851
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (D -> (B -> (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-80 tm-305 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> Bm (-> A (-> B A)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11851.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (D -> (B -> (C -> B))))), M:tm-80, m:tm-305, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> Bm (-> A (-> B A))))))
================================================================
tm-name          tm-11852
in-theory        11852
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and (C -> B))))
theorem-size     13
proof            (modus-ponens tm-76 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11852.        (((not (not A)) -> A) and (B -> (B and (C -> B)))), M:tm-76, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11853
in-theory        11853
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and (B -> A)))
theorem-size     11
proof            (modus-ponens tm-73 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11853.        (((not (not A)) or A) -> (A and (B -> A))), M:tm-73, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-11854
in-theory        11854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (D -> C))))
theorem-size     19
proof            (modus-ponens tm-69 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11854.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (D -> C)))), M:tm-69, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11855
in-theory        11855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (C -> ((A -> (not B)) -> (not A)))))
theorem-size     29
proof            (modus-ponens tm-66 tm-305 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> Bm (-> (-> A (not B)) (not A)))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11855.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (C -> ((A -> (not B)) -> (not A))))), M:tm-66, m:tm-305, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> Bm (-> (-> A (not B)) (not A))))))
================================================================
tm-name          tm-11856
in-theory        11856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (E -> D))))
theorem-size     21
proof            (modus-ponens tm-54 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11856.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (E -> D)))), M:tm-54, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11857
in-theory        11857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     35
proof            (modus-ponens tm-51 tm-305 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (-> (-> A B) (-> (or C A) B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11857.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> ((B -> C) -> ((A or B) -> C))))), M:tm-51, m:tm-305, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (-> (-> A B) (-> (or C A) B))))))
================================================================
tm-name          tm-11858
in-theory        11858
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and (C -> (B or A))))
theorem-size     15
proof            (modus-ponens tm-50 tm-305 ((Am (or A B)) (C (and (or A B) (-> Bm (or A B))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11858.        ((A or (B or A)) -> ((B or A) and (C -> (B or A)))), M:tm-50, m:tm-305, u:((Am (or A B)) (C (and (or A B) (-> Bm (or A B)))))
================================================================
tm-name          tm-11859
in-theory        11859
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and (C -> (A or B))))
theorem-size     15
proof            (modus-ponens tm-49 tm-305 ((Am (or A B)) (C (and (or A B) (-> Bm (or A B))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11859.        ((A or (A or B)) -> ((A or B) and (C -> (A or B)))), M:tm-49, m:tm-305, u:((Am (or A B)) (C (and (or A B) (-> Bm (or A B)))))
================================================================
tm-name          tm-11860
in-theory        11860
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-48 tm-305 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> A (and B A)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11860.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> (B -> (A and B))))), M:tm-48, m:tm-305, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> A (and B A))))))
================================================================
tm-name          tm-11861
in-theory        11861
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (C -> B)))
theorem-size     11
proof            (modus-ponens tm-47 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11861.        (((A and B) or B) -> (B and (C -> B))), M:tm-47, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-11862
in-theory        11862
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (C -> A)))
theorem-size     11
proof            (modus-ponens tm-46 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11862.        (((A and B) or A) -> (A and (C -> A))), M:tm-46, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-11863
in-theory        11863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> ((A -> B) -> (A -> C)))))
theorem-size     31
proof            (modus-ponens tm-45 tm-305 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11863.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> ((A -> B) -> (A -> C))))), M:tm-45, m:tm-305, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-11864
in-theory        11864
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (C -> (B -> A))))
theorem-size     15
proof            (modus-ponens tm-44 tm-305 ((Am (-> A B)) (C (and (-> A B) (-> Bm (-> A B))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11864.        ((A or (B -> A)) -> ((B -> A) and (C -> (B -> A)))), M:tm-44, m:tm-305, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (-> A B)))))
================================================================
tm-name          tm-11865
in-theory        11865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and (D -> C))))
theorem-size     13
proof            (modus-ponens tm-42 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11865.        ((A -> (B or A)) and (C -> (C and (D -> C)))), M:tm-42, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11866
in-theory        11866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and (D -> C))))
theorem-size     13
proof            (modus-ponens tm-32 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11866.        ((A -> (A or B)) and (C -> (C and (D -> C)))), M:tm-32, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11867
in-theory        11867
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and (B -> A))))
theorem-size     9
proof            (modus-ponens tm-24 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11867.        (A -> (A and (A and (B -> A)))), M:tm-24, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-11868
in-theory        11868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and (D -> C))))
theorem-size     15
proof            (modus-ponens tm-23 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11868.        ((A -> (B -> (A and B))) and (C -> (C and (D -> C)))), M:tm-23, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11869
in-theory        11869
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and (D -> C))))
theorem-size     13
proof            (modus-ponens tm-22 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11869.        (((A and B) -> B) and (C -> (C and (D -> C)))), M:tm-22, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11870
in-theory        11870
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and (D -> C))))
theorem-size     13
proof            (modus-ponens tm-21 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11870.        (((A and B) -> A) and (C -> (C and (D -> C)))), M:tm-21, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11871
in-theory        11871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (E -> D))))
theorem-size     21
proof            (modus-ponens tm-20 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11871.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (E -> D)))), M:tm-20, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11872
in-theory        11872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and (D -> C))))
theorem-size     13
proof            (modus-ponens tm-19 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11872.        ((A -> (B -> A)) and (C -> (C and (D -> C)))), M:tm-19, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11873
in-theory        11873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and (B -> A)))) -> (not A))
theorem-size     11
proof            (modus-ponens tm-9 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-9 tm-2 tm-5 tm-1)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11873.        ((A -> (not (A and (B -> A)))) -> (not A)), M:tm-9, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-11874
in-theory        11874
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> A)) -> C) -> ((A or (A and (B -> A))) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11874.        (((A and (B -> A)) -> C) -> ((A or (A and (B -> A))) -> C)), M:tm-8, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-11875
in-theory        11875
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and (C -> B))))
theorem-size     9
proof            (modus-ponens tm-7 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-7 tm-2 tm-5 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11875.        (A or (B -> (B and (C -> B)))), M:tm-7, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11876
in-theory        11876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) or C)
theorem-size     9
proof            (modus-ponens tm-6 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-6 tm-2 tm-5 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11876.        ((A -> (A and (B -> A))) or C), M:tm-6, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11877
in-theory        11877
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and (C -> B))) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11877.        (A -> ((B -> (B and (C -> B))) and A)), M:tm-5, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11878
in-theory        11878
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and (C -> B))))
theorem-size     9
proof            (modus-ponens tm-1 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11878.        (A -> (B -> (B and (C -> B)))), M:tm-1, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-11879
in-theory        11879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((A -> B) -> (A -> A)))
theorem-size     13
proof            (modus-ponens tm-306 tm-1 ((A Am) (B Bm) (C Am)))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11879.        ((A -> (B -> A)) and ((A -> B) -> (A -> A))), M:tm-306, m:tm-1, u:((A Am) (B Bm) (C Am))
================================================================
tm-name          tm-11880
in-theory        11880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-306 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11880.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-306, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
================================================================
tm-name          tm-11881
in-theory        11881
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> (A -> B)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)))
theorem-size     25
proof            (modus-ponens tm-306 tm-3 ((A (and (-> B C) Bm)) (Am (-> B C))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-11881.        ((((A -> B) and C) -> (A -> B)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))), M:tm-306, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
================================================================
tm-name          tm-11882
in-theory        11882
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> (B -> C)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)))
theorem-size     25
proof            (modus-ponens tm-306 tm-4 ((A (and Am (-> B C))) (Bm (-> B C))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-11882.        (((A and (B -> C)) -> (B -> C)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))), M:tm-306, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
================================================================
tm-name          tm-11883
in-theory        11883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((A -> B) -> (A -> (A and B))))
theorem-size     17
proof            (modus-ponens tm-306 tm-5 ((A Am) (B Bm) (C (and Am Bm))))
axioms-used      (tm-2 tm-5)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11883.        ((A -> (B -> (A and B))) and ((A -> B) -> (A -> (A and B)))), M:tm-306, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
================================================================
tm-name          tm-11884
in-theory        11884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-306 tm-8 ((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11884.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C)))), M:tm-306, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-11885
in-theory        11885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-306 tm-9 ((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11885.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A)))), M:tm-306, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
================================================================
tm-name          tm-11886
in-theory        11886
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) -> (A -> B)) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)))
theorem-size     25
proof            (modus-ponens tm-306 tm-10 ((A (not (not (-> B C)))) (Am (-> B C))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-11886.        (((not (not (A -> B))) -> (A -> B)) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B))), M:tm-306, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
================================================================
tm-name          tm-11887
in-theory        11887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((A -> B) -> (A -> (C -> B))))
theorem-size     17
proof            (modus-ponens tm-306 tm-11 ((A Am) (B Bm) (C (-> Cm Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11887.        ((A -> (B -> (C -> B))) and ((A -> B) -> (A -> (C -> B)))), M:tm-306, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
================================================================
tm-name          tm-11888
in-theory        11888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((A -> B) -> A) -> ((A -> B) -> A)))
theorem-size     19
proof            (modus-ponens tm-306 tm-12 ((A (-> Am Bm)) (B Am) (C Am)))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-11888.        (((A -> B) -> (A -> A)) and (((A -> B) -> A) -> ((A -> B) -> A))), M:tm-306, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
================================================================
tm-name          tm-11889
in-theory        11889
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))
theorem-size     49
proof            (modus-ponens tm-306 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11889.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))), M:tm-306, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
================================================================
tm-name          tm-11890
in-theory        11890
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))))
theorem-size     33
proof            (modus-ponens tm-306 tm-14 ((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11890.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D))))), M:tm-306, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-11891
in-theory        11891
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)))
theorem-size     39
proof            (modus-ponens tm-306 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11891.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B))), M:tm-306, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
================================================================
tm-name          tm-11892
in-theory        11892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((A -> (B and C)) -> (A -> B)))
theorem-size     17
proof            (modus-ponens tm-306 tm-16 ((A Am) (B (and Bm Cm)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11892.        ((A -> ((B and C) -> B)) and ((A -> (B and C)) -> (A -> B))), M:tm-306, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
================================================================
tm-name          tm-11893
in-theory        11893
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)))
theorem-size     39
proof            (modus-ponens tm-306 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11893.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C))), M:tm-306, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
================================================================
tm-name          tm-11894
in-theory        11894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((A -> (B and C)) -> (A -> C)))
theorem-size     17
proof            (modus-ponens tm-306 tm-18 ((A Am) (B (and Bm Cm)) (C Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11894.        ((A -> ((B and C) -> C)) and ((A -> (B and C)) -> (A -> C))), M:tm-306, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
================================================================
tm-name          tm-11895
in-theory        11895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((A -> B) -> A) -> ((A -> B) -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-306 tm-24 ((A (-> Am Bm)) (B Am) (C (and Am Bm))))
axioms-used      (tm-2 tm-5)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11895.        (((A -> B) -> (A -> (A and B))) and (((A -> B) -> A) -> ((A -> B) -> (A and B)))), M:tm-306, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
================================================================
tm-name          tm-11896
in-theory        11896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((A -> B) -> (A -> (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-306 tm-25 ((A Am) (B Bm) (C (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11896.        ((A -> (B -> (C -> (B and C)))) and ((A -> B) -> (A -> (C -> (B and C))))), M:tm-306, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-11897
in-theory        11897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((A -> B) -> (A -> (B or C))))
theorem-size     17
proof            (modus-ponens tm-306 tm-33 ((A Am) (B Bm) (C (or Bm Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11897.        ((A -> (B -> (B or C))) and ((A -> B) -> (A -> (B or C)))), M:tm-306, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
================================================================
tm-name          tm-11898
in-theory        11898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((A -> B) -> (A -> (C or B))))
theorem-size     17
proof            (modus-ponens tm-306 tm-43 ((A Am) (B Bm) (C (or Cm Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11898.        ((A -> (B -> (C or B))) and ((A -> B) -> (A -> (C or B)))), M:tm-306, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
================================================================
tm-name          tm-11899
in-theory        11899
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)))
theorem-size     33
proof            (modus-ponens tm-306 tm-44 ((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11899.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C))), M:tm-306, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
================================================================
tm-name          tm-11900
in-theory        11900
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)))
theorem-size     61
proof            (modus-ponens tm-306 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11900.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D))), M:tm-306, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
================================================================
tm-name          tm-11901
in-theory        11901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)))
theorem-size     27
proof            (modus-ponens tm-306 tm-46 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11901.        (((A -> B) -> (((A and C) or A) -> B)) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B))), M:tm-306, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
================================================================
tm-name          tm-11902
in-theory        11902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B)))
theorem-size     27
proof            (modus-ponens tm-306 tm-47 ((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11902.        (((A -> B) -> (((C and A) or A) -> B)) and (((A -> B) -> ((C and A) or A)) -> ((A -> B) -> B))), M:tm-306, m:tm-47, u:((A (-> Am Bm)) (B (or (and Cm Am) Am)) (C Bm))
================================================================
tm-name          tm-11903
in-theory        11903
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C)))
theorem-size     43
proof            (modus-ponens tm-306 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-11903.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((A -> (B and A)) -> C) -> (B or (A -> (B and A)))) -> (((A -> (B and A)) -> C) -> C))), M:tm-306, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (or Bm (-> Am (and Bm Am)))) (C Cm))
================================================================
tm-name          tm-11904
in-theory        11904
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C)))
theorem-size     33
proof            (modus-ponens tm-306 tm-49 ((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-11904.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((A or B) -> C) -> (A or (A or B))) -> (((A or B) -> C) -> C))), M:tm-306, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (or Am (or Am Bm))) (C Cm))
================================================================
tm-name          tm-11905
in-theory        11905
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C)))
theorem-size     33
proof            (modus-ponens tm-306 tm-50 ((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-11905.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((A or B) -> C) -> (B or (A or B))) -> (((A or B) -> C) -> C))), M:tm-306, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (or Bm (or Am Bm))) (C Cm))
================================================================
tm-name          tm-11906
in-theory        11906
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D)))
theorem-size     67
proof            (modus-ponens tm-306 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       181
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-11906.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> ((C -> A) or ((A -> B) -> ((C or A) -> B)))) -> ((((A -> B) -> ((C or A) -> B)) -> D) -> D))), M:tm-306, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C Dm))
================================================================
tm-name          tm-11907
in-theory        11907
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((((A -> B) -> (B -> C)) -> (A -> B)) -> (((A -> B) -> (B -> C)) -> ((A or B) -> C))))
theorem-size     43
proof            (modus-ponens tm-306 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> Am Bm)) (C (-> (or Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-11907.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((((A -> B) -> (B -> C)) -> (A -> B)) -> (((A -> B) -> (B -> C)) -> ((A or B) -> C)))), M:tm-306, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> Am Bm)) (C (-> (or Am Bm) Cm)))
================================================================
tm-name          tm-11908
in-theory        11908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((A -> (B -> C)) -> (A -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     33
proof            (modus-ponens tm-306 tm-56 ((A Am) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-11908.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((A -> (B -> C)) -> (A -> ((C -> D) -> ((B or C) -> D))))), M:tm-306, m:tm-56, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-11909
in-theory        11909
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((((A -> (not B)) -> (not A)) -> C) -> ((A -> B) or ((A -> (not B)) -> (not A)))) -> ((((A -> (not B)) -> (not A)) -> C) -> C)))
theorem-size     57
proof            (modus-ponens tm-306 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-11909.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((((A -> (not B)) -> (not A)) -> C) -> ((A -> B) or ((A -> (not B)) -> (not A)))) -> ((((A -> (not B)) -> (not A)) -> C) -> C))), M:tm-306, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))) (C Cm))
================================================================
tm-name          tm-11910
in-theory        11910
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((((A -> B) -> (A -> (not B))) -> (A -> B)) -> (((A -> B) -> (A -> (not B))) -> (not A))))
theorem-size     40
proof            (modus-ponens tm-306 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> Am Bm)) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       140
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-11910.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((((A -> B) -> (A -> (not B))) -> (A -> B)) -> (((A -> B) -> (A -> (not B))) -> (not A)))), M:tm-306, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> Am Bm)) (C (not Am)))
================================================================
tm-name          tm-11911
in-theory        11911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((A -> (B -> C)) -> (A -> ((B -> (not C)) -> (not B)))))
theorem-size     29
proof            (modus-ponens tm-306 tm-71 ((A Am) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-11911.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((A -> (B -> C)) -> (A -> ((B -> (not C)) -> (not B))))), M:tm-306, m:tm-71, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-11912
in-theory        11912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (((A -> B) -> ((not (not A)) or A)) -> ((A -> B) -> B)))
theorem-size     27
proof            (modus-ponens tm-306 tm-73 ((A (-> Am Bm)) (B (or (not (not Am)) Am)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-11912.        (((A -> B) -> (((not (not A)) or A) -> B)) and (((A -> B) -> ((not (not A)) or A)) -> ((A -> B) -> B))), M:tm-306, m:tm-73, u:((A (-> Am Bm)) (B (or (not (not Am)) Am)) (C Bm))
================================================================
tm-name          tm-11913
in-theory        11913
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((((not (not (A -> B))) -> A) -> (not (not (A -> B)))) -> (((not (not (A -> B))) -> A) -> B)))
theorem-size     39
proof            (modus-ponens tm-306 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (not (not (-> Am Bm)))) (C Bm)))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-11913.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((((not (not (A -> B))) -> A) -> (not (not (A -> B)))) -> (((not (not (A -> B))) -> A) -> B))), M:tm-306, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (not (not (-> Am Bm)))) (C Bm))
================================================================
tm-name          tm-11914
in-theory        11914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and ((A -> (not (not B))) -> (A -> B)))
theorem-size     17
proof            (modus-ponens tm-306 tm-78 ((A Am) (B (not (not Bm))) (C Bm)))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-11914.        ((A -> ((not (not B)) -> B)) and ((A -> (not (not B))) -> (A -> B))), M:tm-306, m:tm-78, u:((A Am) (B (not (not Bm))) (C Bm))
================================================================
tm-name          tm-11915
in-theory        11915
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((((A -> (B -> A)) -> C) -> (D or (A -> (B -> A)))) -> (((A -> (B -> A)) -> C) -> C)))
theorem-size     43
proof            (modus-ponens tm-306 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (or Dm (-> Am (-> Bm Am)))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-11915.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((((A -> (B -> A)) -> C) -> (D or (A -> (B -> A)))) -> (((A -> (B -> A)) -> C) -> C))), M:tm-306, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (or Dm (-> Am (-> Bm Am)))) (C Cm))
================================================================
tm-name          tm-11916
in-theory        11916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (((A -> B) -> A) -> ((A -> B) -> (C -> B))))
theorem-size     23
proof            (modus-ponens tm-306 tm-84 ((A (-> Am Bm)) (B Am) (C (-> Cm Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-11916.        (((A -> B) -> (A -> (C -> B))) and (((A -> B) -> A) -> ((A -> B) -> (C -> B)))), M:tm-306, m:tm-84, u:((A (-> Am Bm)) (B Am) (C (-> Cm Bm)))
================================================================
tm-name          tm-11917
in-theory        11917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and ((A -> B) -> (A -> (C -> (D -> C)))))
theorem-size     21
proof            (modus-ponens tm-306 tm-85 ((A Am) (B Bm) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-11917.        ((A -> (B -> (C -> (D -> C)))) and ((A -> B) -> (A -> (C -> (D -> C))))), M:tm-306, m:tm-85, u:((A Am) (B Bm) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-11918
in-theory        11918
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (((A -> B) -> A) -> ((A -> B) -> B)))
theorem-size     19
proof            (modus-ponens tm-306 tm-86 ((A (-> B C)) (Am (-> B C))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11918.        (((A -> B) -> (A -> B)) and (((A -> B) -> A) -> ((A -> B) -> B))), M:tm-306, m:tm-86, u:((A (-> B C)) (Am (-> B C)))
================================================================
tm-name          tm-11919
in-theory        11919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> (B -> C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-87 ((A (-> Am (-> Bm Cm))) (B Am) (C (-> Bm Cm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11919.        (((A -> (B -> C)) -> (A -> (B -> C))) and (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> (B -> C)))), M:tm-306, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B Am) (C (-> Bm Cm)))
================================================================
tm-name          tm-11920
in-theory        11920
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((((A -> A) -> B) -> ((A -> C) or (A -> A))) -> (((A -> A) -> B) -> B)))
theorem-size     37
proof            (modus-ponens tm-306 tm-92 ((A (-> (-> Am Am) Bm)) (B (or (-> Am Cm) (-> Am Am))) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-11920.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((((A -> A) -> B) -> ((A -> C) or (A -> A))) -> (((A -> A) -> B) -> B))), M:tm-306, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (or (-> Am Cm) (-> Am Am))) (C Bm))
================================================================
tm-name          tm-11921
in-theory        11921
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and ((((A -> B) -> A) -> (A -> B)) -> (((A -> B) -> A) -> A)))
theorem-size     29
proof            (modus-ponens tm-306 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> Am Bm)) (C Am)))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-11921.        ((((A -> B) -> A) -> ((A -> B) -> A)) and ((((A -> B) -> A) -> (A -> B)) -> (((A -> B) -> A) -> A))), M:tm-306, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> Am Bm)) (C Am))
================================================================
tm-name          tm-11922
in-theory        11922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and ((A -> (B -> C)) -> (A -> (B -> B))))
theorem-size     21
proof            (modus-ponens tm-306 tm-97 ((A Am) (B (-> Bm Cm)) (C (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-11922.        ((A -> ((B -> C) -> (B -> B))) and ((A -> (B -> C)) -> (A -> (B -> B)))), M:tm-306, m:tm-97, u:((A Am) (B (-> Bm Cm)) (C (-> Bm Bm)))
================================================================
tm-name          tm-11923
in-theory        11923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (((A -> ((B -> A) -> C)) -> A) -> ((A -> ((B -> A) -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-306 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B Am) (C Cm)))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-11923.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (((A -> ((B -> A) -> C)) -> A) -> ((A -> ((B -> A) -> C)) -> C))), M:tm-306, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B Am) (C Cm))
================================================================
tm-name          tm-11924
in-theory        11924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (((A -> (A -> B)) -> A) -> ((A -> (A -> B)) -> B)))
theorem-size     25
proof            (modus-ponens tm-306 tm-99 ((A (-> Am (-> Am Bm))) (B Am) (C Bm)))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-11924.        (((A -> (A -> B)) -> (A -> B)) and (((A -> (A -> B)) -> A) -> ((A -> (A -> B)) -> B))), M:tm-306, m:tm-99, u:((A (-> Am (-> Am Bm))) (B Am) (C Bm))
================================================================
tm-name          tm-11925
in-theory        11925
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> B))))
theorem-size     49
proof            (modus-ponens tm-306 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-11925.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> B)))), M:tm-306, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Bm)))
================================================================
tm-name          tm-11926
in-theory        11926
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (((((A -> (B -> C)) -> (A -> C)) -> D) -> (((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> C)) -> D) -> D)))
theorem-size     79
proof            (modus-ponens tm-306 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       231
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-11926.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (((((A -> (B -> C)) -> (A -> C)) -> D) -> (((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> C)) -> D) -> D))), M:tm-306, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C Dm))
================================================================
tm-name          tm-11927
in-theory        11927
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> ((A -> (B -> C)) -> (A -> B))) -> ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (A -> C))))
theorem-size     75
proof            (modus-ponens tm-306 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5)
proof-size       223
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-11927.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> ((A -> (B -> C)) -> (A -> B))) -> ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (A -> C)))), M:tm-306, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> Am Cm)))
================================================================
tm-name          tm-11928
in-theory        11928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((A -> ((B -> (C -> D)) -> (B -> C))) -> (A -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     45
proof            (modus-ponens tm-306 tm-107 ((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-11928.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((A -> ((B -> (C -> D)) -> (B -> C))) -> (A -> ((B -> (C -> D)) -> (B -> D))))), M:tm-306, m:tm-107, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-11929
in-theory        11929
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> D)))
theorem-size     63
proof            (modus-ponens tm-306 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> Am (-> Bm Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-11929.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> D))), M:tm-306, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> Am (-> Bm Cm))) (C Dm))
================================================================
tm-name          tm-11930
in-theory        11930
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> D)))
theorem-size     83
proof            (modus-ponens tm-306 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       223
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11930.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> D))), M:tm-306, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C Dm))
================================================================
tm-name          tm-11931
in-theory        11931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((A -> (B -> (C -> D))) -> A) -> ((A -> (B -> (C -> D))) -> ((B -> C) -> (B -> D)))))
theorem-size     43
proof            (modus-ponens tm-306 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B Am) (C (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-11931.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((A -> (B -> (C -> D))) -> A) -> ((A -> (B -> (C -> D))) -> ((B -> C) -> (B -> D))))), M:tm-306, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B Am) (C (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-11932
in-theory        11932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A -> B) -> (A -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     37
proof            (modus-ponens tm-306 tm-115 ((A Am) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-11932.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A -> B) -> (A -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-306, m:tm-115, u:((A Am) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-11933
in-theory        11933
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and A) -> (B -> C)) and ((((A -> (B -> C)) and A) -> B) -> (((A -> (B -> C)) and A) -> C)))
theorem-size     31
proof            (modus-ponens tm-306 tm-116 ((A (and (-> Am (-> B C)) Am)) (Bm (-> B C))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-11933.        ((((A -> (B -> C)) and A) -> (B -> C)) and ((((A -> (B -> C)) and A) -> B) -> (((A -> (B -> C)) and A) -> C))), M:tm-306, m:tm-116, u:((A (and (-> Am (-> B C)) Am)) (Bm (-> B C)))
================================================================
tm-name          tm-11934
in-theory        11934
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> (C -> D)) and E) -> (C -> D)) and (((((A -> (B -> A)) -> (C -> D)) and E) -> C) -> ((((A -> (B -> A)) -> (C -> D)) and E) -> D)))
theorem-size     43
proof            (modus-ponens tm-306 tm-117 ((A (and (-> (-> Am (-> Bm Am)) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-11934.        (((((A -> (B -> A)) -> (C -> D)) and E) -> (C -> D)) and (((((A -> (B -> A)) -> (C -> D)) and E) -> C) -> ((((A -> (B -> A)) -> (C -> D)) and E) -> D))), M:tm-306, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-11935
in-theory        11935
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and F) -> (D -> E)) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and F) -> D) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and F) -> E)))
theorem-size     67
proof            (modus-ponens tm-306 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B C)) Em)) (Dm (-> B C))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11935.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and F) -> (D -> E)) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and F) -> D) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (D -> E)) and F) -> E))), M:tm-306, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B C)) Em)) (Dm (-> B C)))
================================================================
tm-name          tm-11936
in-theory        11936
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((((((A -> B) -> A) and C) -> (A -> B)) -> (((A -> B) -> A) and C)) -> (((((A -> B) -> A) and C) -> (A -> B)) -> B)))
theorem-size     55
proof            (modus-ponens tm-306 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (and (-> (-> Am Bm) Am) Cm)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-11936.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((((((A -> B) -> A) and C) -> (A -> B)) -> (((A -> B) -> A) and C)) -> (((((A -> B) -> A) and C) -> (A -> B)) -> B))), M:tm-306, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (and (-> (-> Am Bm) Am) Cm)) (C Bm))
================================================================
tm-name          tm-11937
in-theory        11937
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> A)))
theorem-size     39
proof            (modus-ponens tm-306 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Am)))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-11937.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> A))), M:tm-306, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Am))
================================================================
tm-name          tm-11938
in-theory        11938
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((((((A -> B) and C) -> B) -> D) -> ((((A -> B) and C) -> A) or (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> B) -> D) -> D)))
theorem-size     65
proof            (modus-ponens tm-306 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-11938.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((((((A -> B) and C) -> B) -> D) -> ((((A -> B) and C) -> A) or (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> B) -> D) -> D))), M:tm-306, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))) (C Dm))
================================================================
tm-name          tm-11939
in-theory        11939
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (((A -> B) and C) -> A)) -> (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> B)))
theorem-size     61
proof            (modus-ponens tm-306 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (and (-> Am Bm) Cm) Am)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-11939.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (((A -> B) and C) -> A)) -> (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> B))), M:tm-306, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (and (-> Am Bm) Cm) Am)) (C Bm))
================================================================
tm-name          tm-11940
in-theory        11940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((A -> (((B -> C) and D) -> B)) -> (A -> (((B -> C) and D) -> C))))
theorem-size     37
proof            (modus-ponens tm-306 tm-127 ((A Am) (B (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-11940.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((A -> (((B -> C) and D) -> B)) -> (A -> (((B -> C) and D) -> C)))), M:tm-306, m:tm-127, u:((A Am) (B (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-11941
in-theory        11941
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> (C -> D)) and E) -> (C -> D)) and ((((((A and B) -> A) -> (C -> D)) and E) -> C) -> (((((A and B) -> A) -> (C -> D)) and E) -> D)))
theorem-size     43
proof            (modus-ponens tm-306 tm-128 ((A (and (-> (-> (and Am Bm) Am) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-11941.        ((((((A and B) -> A) -> (C -> D)) and E) -> (C -> D)) and ((((((A and B) -> A) -> (C -> D)) and E) -> C) -> (((((A and B) -> A) -> (C -> D)) and E) -> D))), M:tm-306, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-11942
in-theory        11942
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((((A and B) -> (A -> C)) -> (A and B)) -> (((A and B) -> (A -> C)) -> C)))
theorem-size     35
proof            (modus-ponens tm-306 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (and Am Bm)) (C Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-11942.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((((A and B) -> (A -> C)) -> (A and B)) -> (((A and B) -> (A -> C)) -> C))), M:tm-306, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (and Am Bm)) (C Cm))
================================================================
tm-name          tm-11943
in-theory        11943
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (((((A and B) -> A) -> C) -> (D or ((A and B) -> A))) -> ((((A and B) -> A) -> C) -> C)))
theorem-size     43
proof            (modus-ponens tm-306 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (or Dm (-> (and Am Bm) Am))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-11943.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (((((A and B) -> A) -> C) -> (D or ((A and B) -> A))) -> ((((A and B) -> A) -> C) -> C))), M:tm-306, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (or Dm (-> (and Am Bm) Am))) (C Cm))
================================================================
tm-name          tm-11944
in-theory        11944
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (((A -> (B and C)) -> A) -> ((A -> (B and C)) -> B)))
theorem-size     25
proof            (modus-ponens tm-306 tm-135 ((A (-> Am (and Bm Cm))) (B Am) (C Bm)))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-11944.        (((A -> (B and C)) -> (A -> B)) and (((A -> (B and C)) -> A) -> ((A -> (B and C)) -> B))), M:tm-306, m:tm-135, u:((A (-> Am (and Bm Cm))) (B Am) (C Bm))
================================================================
tm-name          tm-11945
in-theory        11945
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and ((A -> B) -> (A -> ((C and D) -> C))))
theorem-size     21
proof            (modus-ponens tm-306 tm-136 ((A Am) (B Bm) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-11945.        ((A -> (B -> ((C and D) -> C))) and ((A -> B) -> (A -> ((C and D) -> C)))), M:tm-306, m:tm-136, u:((A Am) (B Bm) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-11946
in-theory        11946
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> (B -> C))) -> (B -> C)) and (((A and (A -> (B -> C))) -> B) -> ((A and (A -> (B -> C))) -> C)))
theorem-size     31
proof            (modus-ponens tm-306 tm-137 ((A (and Am (-> Am (-> B C)))) (Bm (-> B C))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-11946.        (((A and (A -> (B -> C))) -> (B -> C)) and (((A and (A -> (B -> C))) -> B) -> ((A and (A -> (B -> C))) -> C))), M:tm-306, m:tm-137, u:((A (and Am (-> Am (-> B C)))) (Bm (-> B C)))
================================================================
tm-name          tm-11947
in-theory        11947
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> (D -> E))) -> (D -> E)) and (((A and ((B -> (C -> B)) -> (D -> E))) -> D) -> ((A and ((B -> (C -> B)) -> (D -> E))) -> E)))
theorem-size     43
proof            (modus-ponens tm-306 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-11947.        (((A and ((B -> (C -> B)) -> (D -> E))) -> (D -> E)) and (((A and ((B -> (C -> B)) -> (D -> E))) -> D) -> ((A and ((B -> (C -> B)) -> (D -> E))) -> E))), M:tm-306, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-11948
in-theory        11948
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> F))) -> (E -> F)) and (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> F))) -> E) -> ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> F))) -> F)))
theorem-size     67
proof            (modus-ponens tm-306 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B C)))) (Em (-> B C))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11948.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> F))) -> (E -> F)) and (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> F))) -> E) -> ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> F))) -> F))), M:tm-306, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B C)))) (Em (-> B C)))
================================================================
tm-name          tm-11949
in-theory        11949
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> (D -> E))) -> (D -> E)) and (((A and (((B and C) -> B) -> (D -> E))) -> D) -> ((A and (((B and C) -> B) -> (D -> E))) -> E)))
theorem-size     43
proof            (modus-ponens tm-306 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-11949.        (((A and (((B and C) -> B) -> (D -> E))) -> (D -> E)) and (((A and (((B and C) -> B) -> (D -> E))) -> D) -> ((A and (((B and C) -> B) -> (D -> E))) -> E))), M:tm-306, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-11950
in-theory        11950
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((((A and ((B -> C) -> B)) -> (B -> C)) -> (A and ((B -> C) -> B))) -> (((A and ((B -> C) -> B)) -> (B -> C)) -> C)))
theorem-size     55
proof            (modus-ponens tm-306 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (and Am (-> (-> Bm Cm) Bm))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-11950.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((((A and ((B -> C) -> B)) -> (B -> C)) -> (A and ((B -> C) -> B))) -> (((A and ((B -> C) -> B)) -> (B -> C)) -> C))), M:tm-306, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (and Am (-> (-> Bm Cm) Bm))) (C Cm))
================================================================
tm-name          tm-11951
in-theory        11951
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> B)))
theorem-size     39
proof            (modus-ponens tm-306 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Bm)))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-11951.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> B))), M:tm-306, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Bm))
================================================================
tm-name          tm-11952
in-theory        11952
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (((((A and (B -> C)) -> C) -> D) -> (((A and (B -> C)) -> B) or ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> C) -> D) -> D)))
theorem-size     65
proof            (modus-ponens tm-306 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-11952.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (((((A and (B -> C)) -> C) -> D) -> (((A and (B -> C)) -> B) or ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> C) -> D) -> D))), M:tm-306, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))) (C Dm))
================================================================
tm-name          tm-11953
in-theory        11953
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> ((A and (B -> C)) -> B)) -> ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> C)))
theorem-size     61
proof            (modus-ponens tm-306 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (and Am (-> Bm Cm)) Bm)) (C Cm)))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-11953.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> ((A and (B -> C)) -> B)) -> ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> C))), M:tm-306, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (and Am (-> Bm Cm)) Bm)) (C Cm))
================================================================
tm-name          tm-11954
in-theory        11954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((A -> ((B and (C -> D)) -> C)) -> (A -> ((B and (C -> D)) -> D))))
theorem-size     37
proof            (modus-ponens tm-306 tm-149 ((A Am) (B (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-11954.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((A -> ((B and (C -> D)) -> C)) -> (A -> ((B and (C -> D)) -> D)))), M:tm-306, m:tm-149, u:((A Am) (B (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-11955
in-theory        11955
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> (D -> E))) -> (D -> E)) and (((A and (((B and C) -> C) -> (D -> E))) -> D) -> ((A and (((B and C) -> C) -> (D -> E))) -> E)))
theorem-size     43
proof            (modus-ponens tm-306 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-11955.        (((A and (((B and C) -> C) -> (D -> E))) -> (D -> E)) and (((A and (((B and C) -> C) -> (D -> E))) -> D) -> ((A and (((B and C) -> C) -> (D -> E))) -> E))), M:tm-306, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-11956
in-theory        11956
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> (C -> D)) and E) -> (C -> D)) and ((((((A and B) -> B) -> (C -> D)) and E) -> C) -> (((((A and B) -> B) -> (C -> D)) and E) -> D)))
theorem-size     43
proof            (modus-ponens tm-306 tm-151 ((A (and (-> (-> (and Am Bm) Bm) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-11956.        ((((((A and B) -> B) -> (C -> D)) and E) -> (C -> D)) and ((((((A and B) -> B) -> (C -> D)) and E) -> C) -> (((((A and B) -> B) -> (C -> D)) and E) -> D))), M:tm-306, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-11957
in-theory        11957
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((((A and B) -> (B -> C)) -> (A and B)) -> (((A and B) -> (B -> C)) -> C)))
theorem-size     35
proof            (modus-ponens tm-306 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (and Am Bm)) (C Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-11957.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((((A and B) -> (B -> C)) -> (A and B)) -> (((A and B) -> (B -> C)) -> C))), M:tm-306, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (and Am Bm)) (C Cm))
================================================================
tm-name          tm-11958
in-theory        11958
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (((((A and B) -> B) -> C) -> (D or ((A and B) -> B))) -> ((((A and B) -> B) -> C) -> C)))
theorem-size     43
proof            (modus-ponens tm-306 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (or Dm (-> (and Am Bm) Bm))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-11958.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (((((A and B) -> B) -> C) -> (D or ((A and B) -> B))) -> ((((A and B) -> B) -> C) -> C))), M:tm-306, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (or Dm (-> (and Am Bm) Bm))) (C Cm))
================================================================
tm-name          tm-11959
in-theory        11959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (((A -> (B and C)) -> A) -> ((A -> (B and C)) -> C)))
theorem-size     25
proof            (modus-ponens tm-306 tm-158 ((A (-> Am (and Bm Cm))) (B Am) (C Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-11959.        (((A -> (B and C)) -> (A -> C)) and (((A -> (B and C)) -> A) -> ((A -> (B and C)) -> C))), M:tm-306, m:tm-158, u:((A (-> Am (and Bm Cm))) (B Am) (C Cm))
================================================================
tm-name          tm-11960
in-theory        11960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and ((A -> B) -> (A -> ((C and D) -> D))))
theorem-size     21
proof            (modus-ponens tm-306 tm-159 ((A Am) (B Bm) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-11960.        ((A -> (B -> ((C and D) -> D))) and ((A -> B) -> (A -> ((C and D) -> D)))), M:tm-306, m:tm-159, u:((A Am) (B Bm) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-11961
in-theory        11961
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (((((A -> (B -> A)) and C) -> D) -> (C or ((A -> (B -> A)) and C))) -> ((((A -> (B -> A)) and C) -> D) -> D)))
theorem-size     53
proof            (modus-ponens tm-306 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (or Cm (and (-> Am (-> Bm Am)) Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-11961.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (((((A -> (B -> A)) and C) -> D) -> (C or ((A -> (B -> A)) and C))) -> ((((A -> (B -> A)) and C) -> D) -> D))), M:tm-306, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (or Cm (and (-> Am (-> Bm Am)) Cm))) (C Dm))
================================================================
tm-name          tm-11962
in-theory        11962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and ((A -> B) -> (A -> ((C -> (D -> C)) and B))))
theorem-size     25
proof            (modus-ponens tm-306 tm-184 ((A Am) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-11962.        ((A -> (B -> ((C -> (D -> C)) and B))) and ((A -> B) -> (A -> ((C -> (D -> C)) and B)))), M:tm-306, m:tm-184, u:((A Am) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-11963
in-theory        11963
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> E)))
theorem-size     93
proof            (modus-ponens tm-306 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C Em)))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       241
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-11963.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> E))), M:tm-306, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C Em))
================================================================
tm-name          tm-11964
in-theory        11964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((A -> B) -> (A -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     41
proof            (modus-ponens tm-306 tm-211 ((A Am) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-11964.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((A -> B) -> (A -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-306, m:tm-211, u:((A Am) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-11965
in-theory        11965
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((((((A and B) -> A) and C) -> D) -> (C or (((A and B) -> A) and C))) -> (((((A and B) -> A) and C) -> D) -> D)))
theorem-size     53
proof            (modus-ponens tm-306 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (or Cm (and (-> (and Am Bm) Am) Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-11965.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((((((A and B) -> A) and C) -> D) -> (C or (((A and B) -> A) and C))) -> (((((A and B) -> A) and C) -> D) -> D))), M:tm-306, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (or Cm (and (-> (and Am Bm) Am) Cm))) (C Dm))
================================================================
tm-name          tm-11966
in-theory        11966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and ((A -> B) -> (A -> (((C and D) -> C) and B))))
theorem-size     25
proof            (modus-ponens tm-306 tm-240 ((A Am) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-11966.        ((A -> (B -> (((C and D) -> C) and B))) and ((A -> B) -> (A -> (((C and D) -> C) and B)))), M:tm-306, m:tm-240, u:((A Am) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-11967
in-theory        11967
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((((((A and B) -> B) and C) -> D) -> (C or (((A and B) -> B) and C))) -> (((((A and B) -> B) and C) -> D) -> D)))
theorem-size     53
proof            (modus-ponens tm-306 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (or Cm (and (-> (and Am Bm) Bm) Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-11967.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((((((A and B) -> B) and C) -> D) -> (C or (((A and B) -> B) and C))) -> (((((A and B) -> B) and C) -> D) -> D))), M:tm-306, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (or Cm (and (-> (and Am Bm) Bm) Cm))) (C Dm))
================================================================
tm-name          tm-11968
in-theory        11968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and ((A -> B) -> (A -> (((C and D) -> D) and B))))
theorem-size     25
proof            (modus-ponens tm-306 tm-271 ((A Am) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-11968.        ((A -> (B -> (((C and D) -> D) and B))) and ((A -> B) -> (A -> (((C and D) -> D) and B)))), M:tm-306, m:tm-271, u:((A Am) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-11969
in-theory        11969
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (((((A -> (B -> (A and B))) and C) -> D) -> (C or ((A -> (B -> (A and B))) and C))) -> ((((A -> (B -> (A and B))) and C) -> D) -> D)))
theorem-size     63
proof            (modus-ponens tm-306 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-11969.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (((((A -> (B -> (A and B))) and C) -> D) -> (C or ((A -> (B -> (A and B))) and C))) -> ((((A -> (B -> (A and B))) and C) -> D) -> D))), M:tm-306, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm))) (C Dm))
================================================================
tm-name          tm-11970
in-theory        11970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((A -> B) -> (A -> ((C -> (D -> (C and D))) and B))))
theorem-size     29
proof            (modus-ponens tm-306 tm-304 ((A Am) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-11970.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((A -> B) -> (A -> ((C -> (D -> (C and D))) and B)))), M:tm-306, m:tm-304, u:((A Am) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-11971
in-theory        11971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (D -> ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11971.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (D -> ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))), M:tm-305, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11972
in-theory        11972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11972.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-303, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11973
in-theory        11973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11973.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-270, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11974
in-theory        11974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11974.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-239, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11975
in-theory        11975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11975.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G))))), M:tm-210, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11976
in-theory        11976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11976.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-183, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11977
in-theory        11977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11977.        ((A -> ((B and C) -> C)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-157, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11978
in-theory        11978
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (C -> D)) -> (C -> D))) -> (((B and (C -> D)) -> (C -> D)) and (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))
theorem-size     37
proof            (modus-ponens tm-154 tm-306 ((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (and (-> (and A (-> Bm Cm)) (-> Bm Cm)) (-> (-> (and A (-> Bm Cm)) Bm) (-> (and A (-> Bm Cm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11978.        ((A or ((B and (C -> D)) -> (C -> D))) -> (((B and (C -> D)) -> (C -> D)) and (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))), M:tm-154, m:tm-306, u:((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (and (-> (and A (-> Bm Cm)) (-> Bm Cm)) (-> (-> (and A (-> Bm Cm)) Bm) (-> (and A (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-11979
in-theory        11979
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11979.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-147, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11980
in-theory        11980
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) -> B) or ((A and (B -> (C -> D))) -> (C -> D))) -> (((A and (B -> (C -> D))) -> (C -> D)) and (((A and (B -> (C -> D))) -> C) -> ((A and (B -> (C -> D))) -> D))))
theorem-size     53
proof            (modus-ponens tm-144 tm-306 ((Am (and A (-> B (-> Bm Cm)))) (C (-> Bm Cm)) (D (and (-> (and A (-> B (-> Bm Cm))) (-> Bm Cm)) (-> (-> (and A (-> B (-> Bm Cm))) Bm) (-> (and A (-> B (-> Bm Cm))) Cm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11980.        ((((A and (B -> (C -> D))) -> B) or ((A and (B -> (C -> D))) -> (C -> D))) -> (((A and (B -> (C -> D))) -> (C -> D)) and (((A and (B -> (C -> D))) -> C) -> ((A and (B -> (C -> D))) -> D)))), M:tm-144, m:tm-306, u:((Am (and A (-> B (-> Bm Cm)))) (C (-> Bm Cm)) (D (and (-> (and A (-> B (-> Bm Cm))) (-> Bm Cm)) (-> (-> (and A (-> B (-> Bm Cm))) Bm) (-> (and A (-> B (-> Bm Cm))) Cm)))))
================================================================
tm-name          tm-11981
in-theory        11981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11981.        ((A -> ((B and C) -> B)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-134, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11982
in-theory        11982
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) and D) -> (B -> C))) -> ((((B -> C) and D) -> (B -> C)) and ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))
theorem-size     37
proof            (modus-ponens tm-131 tm-306 ((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (and (-> (and (-> Bm Cm) B) (-> Bm Cm)) (-> (-> (and (-> Bm Cm) B) Bm) (-> (and (-> Bm Cm) B) Cm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11982.        ((A or (((B -> C) and D) -> (B -> C))) -> ((((B -> C) and D) -> (B -> C)) and ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))), M:tm-131, m:tm-306, u:((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (and (-> (and (-> Bm Cm) B) (-> Bm Cm)) (-> (-> (and (-> Bm Cm) B) Bm) (-> (and (-> Bm Cm) B) Cm)))))
================================================================
tm-name          tm-11983
in-theory        11983
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11983.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-125, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11984
in-theory        11984
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) -> A) or (((A -> (B -> C)) and D) -> (B -> C))) -> ((((A -> (B -> C)) and D) -> (B -> C)) and ((((A -> (B -> C)) and D) -> B) -> (((A -> (B -> C)) and D) -> C))))
theorem-size     53
proof            (modus-ponens tm-122 tm-306 ((Am (and (-> A (-> Bm Cm)) C)) (B (-> Bm Cm)) (D (and (-> (and (-> A (-> Bm Cm)) C) (-> Bm Cm)) (-> (-> (and (-> A (-> Bm Cm)) C) Bm) (-> (and (-> A (-> Bm Cm)) C) Cm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11984.        (((((A -> (B -> C)) and D) -> A) or (((A -> (B -> C)) and D) -> (B -> C))) -> ((((A -> (B -> C)) and D) -> (B -> C)) and ((((A -> (B -> C)) and D) -> B) -> (((A -> (B -> C)) and D) -> C)))), M:tm-122, m:tm-306, u:((Am (and (-> A (-> Bm Cm)) C)) (B (-> Bm Cm)) (D (and (-> (and (-> A (-> Bm Cm)) C) (-> Bm Cm)) (-> (-> (and (-> A (-> Bm Cm)) C) Bm) (-> (and (-> A (-> Bm Cm)) C) Cm)))))
================================================================
tm-name          tm-11985
in-theory        11985
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11985.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G))))), M:tm-113, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11986
in-theory        11986
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     49
proof            (modus-ponens tm-110 tm-306 ((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (-> (-> A (-> B C)) (-> A B)) (-> (-> A (-> B C)) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11986.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))), M:tm-110, m:tm-306, u:((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (-> (-> A (-> B C)) (-> A B)) (-> (-> A (-> B C)) (-> A C))))))
================================================================
tm-name          tm-11987
in-theory        11987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11987.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-105, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11988
in-theory        11988
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> C))))
theorem-size     45
proof            (modus-ponens tm-102 tm-306 ((Am (-> Bm (-> B Cm))) (A Bm) (C Cm) (D (and (-> (-> Bm (-> B Cm)) (-> Bm Cm)) (-> (-> (-> Bm (-> B Cm)) Bm) (-> (-> Bm (-> B Cm)) Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11988.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> C)))), M:tm-102, m:tm-306, u:((Am (-> Bm (-> B Cm))) (A Bm) (C Cm) (D (and (-> (-> Bm (-> B Cm)) (-> Bm Cm)) (-> (-> (-> Bm (-> B Cm)) Bm) (-> (-> Bm (-> B Cm)) Cm)))))
================================================================
tm-name          tm-11989
in-theory        11989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11989.        (((A -> B) -> (A -> A)) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E))))), M:tm-95, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11990
in-theory        11990
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((A -> B) -> (A -> B))) -> (((A -> B) -> (A -> B)) and (((A -> B) -> A) -> ((A -> B) -> B))))
theorem-size     33
proof            (modus-ponens tm-92 tm-306 ((Am (-> Bm Cm)) (A (-> Bm Cm)) (B (and (-> (-> Bm Cm) (-> Bm Cm)) (-> (-> (-> Bm Cm) Bm) (-> (-> Bm Cm) Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11990.        ((((A -> B) -> C) or ((A -> B) -> (A -> B))) -> (((A -> B) -> (A -> B)) and (((A -> B) -> A) -> ((A -> B) -> B)))), M:tm-92, m:tm-306, u:((Am (-> Bm Cm)) (A (-> Bm Cm)) (B (and (-> (-> Bm Cm) (-> Bm Cm)) (-> (-> (-> Bm Cm) Bm) (-> (-> Bm Cm) Cm)))))
================================================================
tm-name          tm-11991
in-theory        11991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (D -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))
theorem-size     21
proof            (modus-ponens tm-84 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11991.        ((A -> (B -> C)) -> (D -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))), M:tm-84, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-11992
in-theory        11992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11992.        ((A -> (B -> (C -> B))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-83, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11993
in-theory        11993
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((B -> C) -> (B -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-306 ((Cm Am) (B Bm) (A Am) (C (and (-> Am (-> Bm Am)) (-> (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11993.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((B -> C) -> (B -> B)))), M:tm-80, m:tm-306, u:((Cm Am) (B Bm) (A Am) (C (and (-> Am (-> Bm Am)) (-> (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-11994
in-theory        11994
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11994.        (((not (not A)) -> A) and ((B -> (C -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D))))), M:tm-76, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11995
in-theory        11995
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (B -> C)))) or (A -> (B -> C))) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-73 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11995.        (((not (not (A -> (B -> C)))) or (A -> (B -> C))) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-73, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-11996
in-theory        11996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11996.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E))))), M:tm-69, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11997
in-theory        11997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11997.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-54, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-11998
in-theory        11998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((B -> C) -> (A or B)) -> ((B -> C) -> C))))
theorem-size     37
proof            (modus-ponens tm-51 tm-306 ((Am (-> A Cm)) (Bm (or C A)) (B Cm) (D (and (-> (-> A Cm) (-> (or C A) Cm)) (-> (-> (-> A Cm) (or C A)) (-> (-> A Cm) Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11998.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((B -> C) -> (A or B)) -> ((B -> C) -> C)))), M:tm-51, m:tm-306, u:((Am (-> A Cm)) (Bm (or C A)) (B Cm) (D (and (-> (-> A Cm) (-> (or C A) Cm)) (-> (-> (-> A Cm) (or C A)) (-> (-> A Cm) Cm)))))
================================================================
tm-name          tm-11999
in-theory        11999
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D))))
theorem-size     27
proof            (modus-ponens tm-47 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11999.        (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D)))), M:tm-47, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-12000
in-theory        12000
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-46 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12000.        ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-46, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-12001
in-theory        12001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> B) -> A) -> ((A -> B) -> C))))
theorem-size     33
proof            (modus-ponens tm-45 tm-306 ((Am (-> Bm B)) (A Bm) (C Cm) (D (and (-> (-> Bm B) (-> Bm Cm)) (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12001.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> B) -> A) -> ((A -> B) -> C)))), M:tm-45, m:tm-306, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (and (-> (-> Bm B) (-> Bm Cm)) (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm)))))
================================================================
tm-name          tm-12002
in-theory        12002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (C -> (A -> B))) -> ((C -> (A -> B)) and ((C -> A) -> (C -> B))))
theorem-size     23
proof            (modus-ponens tm-44 tm-306 ((A Am) (B (-> Bm Cm)) (C (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12002.        (((A -> B) or (C -> (A -> B))) -> ((C -> (A -> B)) and ((C -> A) -> (C -> B)))), M:tm-44, m:tm-306, u:((A Am) (B (-> Bm Cm)) (C (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-12003
in-theory        12003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12003.        ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E))))), M:tm-42, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-12004
in-theory        12004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12004.        ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E))))), M:tm-32, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-12005
in-theory        12005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))
theorem-size     25
proof            (modus-ponens tm-24 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12005.        ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> (B -> C)) and ((A -> B) -> (A -> C))))), M:tm-24, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-12006
in-theory        12006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12006.        ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E))))), M:tm-23, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-12007
in-theory        12007
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12007.        (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E))))), M:tm-22, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-12008
in-theory        12008
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12008.        (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E))))), M:tm-21, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-12009
in-theory        12009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12009.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-20, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-12010
in-theory        12010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12010.        ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E))))), M:tm-19, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-12011
in-theory        12011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (not ((A -> (B -> C)) and ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C))))
theorem-size     27
proof            (modus-ponens tm-9 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-9 tm-2 tm-5)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12011.        (((A -> (B -> C)) -> (not ((A -> (B -> C)) and ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-12012
in-theory        12012
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12012.        ((((A -> (B -> C)) and ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-12013
in-theory        12013
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-7 tm-2 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12013.        (A or ((B -> (C -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D))))), M:tm-7, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-12014
in-theory        12014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) or D)
theorem-size     21
proof            (modus-ponens tm-6 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-6 tm-2 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12014.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) or D), M:tm-6, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-12015
in-theory        12015
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12015.        (A -> (((B -> (C -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D)))) and A)), M:tm-5, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-12016
in-theory        12016
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12016.        (A -> ((B -> (C -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D))))), M:tm-1, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-12017
in-theory        12017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and (A -> (B -> A)))
theorem-size     17
proof            (modus-ponens tm-307 tm-160 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12017.        (((A -> (B -> A)) and (C -> (D -> C))) and (A -> (B -> A))), M:tm-307, m:tm-160, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-12018
in-theory        12018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (A -> (B -> A)))
theorem-size     25
proof            (modus-ponens tm-307 tm-161 ((A (-> Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12018.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (A -> (B -> A))), M:tm-307, m:tm-161, u:((A (-> Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-12019
in-theory        12019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and (A -> (B -> A)))
theorem-size     17
proof            (modus-ponens tm-307 tm-162 ((A (-> Am (-> Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12019.        (((A -> (B -> A)) and ((C and D) -> C)) and (A -> (B -> A))), M:tm-307, m:tm-162, u:((A (-> Am (-> Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-12020
in-theory        12020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and (A -> (B -> A)))
theorem-size     17
proof            (modus-ponens tm-307 tm-163 ((A (-> Am (-> Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12020.        (((A -> (B -> A)) and ((C and D) -> D)) and (A -> (B -> A))), M:tm-307, m:tm-163, u:((A (-> Am (-> Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-12021
in-theory        12021
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-164 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12021.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (A -> (B -> A))), M:tm-307, m:tm-164, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-12022
in-theory        12022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and (A -> (B -> A)))
theorem-size     17
proof            (modus-ponens tm-307 tm-165 ((A (-> Am (-> Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12022.        (((A -> (B -> A)) and (C -> (C or D))) and (A -> (B -> A))), M:tm-307, m:tm-165, u:((A (-> Am (-> Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-12023
in-theory        12023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and (A -> (B -> A)))
theorem-size     17
proof            (modus-ponens tm-307 tm-166 ((A (-> Am (-> Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12023.        (((A -> (B -> A)) and (C -> (D or C))) and (A -> (B -> A))), M:tm-307, m:tm-166, u:((A (-> Am (-> Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-12024
in-theory        12024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (A -> (B -> A)))
theorem-size     25
proof            (modus-ponens tm-307 tm-167 ((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12024.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (A -> (B -> A))), M:tm-307, m:tm-167, u:((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))
================================================================
tm-name          tm-12025
in-theory        12025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (A -> (B -> A)))
theorem-size     23
proof            (modus-ponens tm-307 tm-168 ((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12025.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (A -> (B -> A))), M:tm-307, m:tm-168, u:((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))
================================================================
tm-name          tm-12026
in-theory        12026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and (A -> (B -> A)))
theorem-size     17
proof            (modus-ponens tm-307 tm-169 ((A (-> Am (-> Bm Am))) (B (-> (not (not Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12026.        (((A -> (B -> A)) and ((not (not C)) -> C)) and (A -> (B -> A))), M:tm-307, m:tm-169, u:((A (-> Am (-> Bm Am))) (B (-> (not (not Cm)) Cm)))
================================================================
tm-name          tm-12027
in-theory        12027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-170 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12027.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (A -> (B -> A))), M:tm-307, m:tm-170, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-12028
in-theory        12028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-171 ((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> Cm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12028.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (A -> (B -> A))), M:tm-307, m:tm-171, u:((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> Cm Cm))))
================================================================
tm-name          tm-12029
in-theory        12029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (A -> (B -> A)))
theorem-size     31
proof            (modus-ponens tm-307 tm-172 ((A (-> Am (-> Bm Am))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12029.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (A -> (B -> A))), M:tm-307, m:tm-172, u:((A (-> Am (-> Bm Am))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))
================================================================
tm-name          tm-12030
in-theory        12030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (B -> A)))
theorem-size     27
proof            (modus-ponens tm-307 tm-173 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12030.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (B -> A))), M:tm-307, m:tm-173, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-12031
in-theory        12031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (A -> (B -> A)))
theorem-size     27
proof            (modus-ponens tm-307 tm-174 ((A (-> Am (-> Bm Am))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12031.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (A -> (B -> A))), M:tm-307, m:tm-174, u:((A (-> Am (-> Bm Am))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))
================================================================
tm-name          tm-12032
in-theory        12032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-175 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12032.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (A -> (B -> A))), M:tm-307, m:tm-175, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-12033
in-theory        12033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (A -> (B -> A)))
theorem-size     27
proof            (modus-ponens tm-307 tm-176 ((A (-> Am (-> Bm Am))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12033.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (A -> (B -> A))), M:tm-307, m:tm-176, u:((A (-> Am (-> Bm Am))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))
================================================================
tm-name          tm-12034
in-theory        12034
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-177 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12034.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (A -> (B -> A))), M:tm-307, m:tm-177, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-12035
in-theory        12035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (A -> (B -> A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-178 ((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12035.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (A -> (B -> A))), M:tm-307, m:tm-178, u:((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm))))
================================================================
tm-name          tm-12036
in-theory        12036
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-307 tm-185 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12036.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-185, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-12037
in-theory        12037
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-307 tm-186 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12037.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-186, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-12038
in-theory        12038
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-307 tm-187 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12038.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-187, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-12039
in-theory        12039
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-307 tm-188 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12039.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-188, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-12040
in-theory        12040
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-189 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12040.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-189, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-12041
in-theory        12041
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-307 tm-190 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12041.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-190, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-12042
in-theory        12042
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-307 tm-191 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12042.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-191, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-12043
in-theory        12043
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-307 tm-192 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12043.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-192, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))
================================================================
tm-name          tm-12044
in-theory        12044
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-307 tm-193 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12044.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-193, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))
================================================================
tm-name          tm-12045
in-theory        12045
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-307 tm-194 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (not (not Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-10)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12045.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-194, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (not (not Dm)) Dm)))
================================================================
tm-name          tm-12046
in-theory        12046
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-195 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (-> Fm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12046.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-195, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (-> Fm Em)))))
================================================================
tm-name          tm-12047
in-theory        12047
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-196 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> Dm Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12047.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-196, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> Dm Dm))))
================================================================
tm-name          tm-12048
in-theory        12048
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     47
proof            (modus-ponens tm-307 tm-197 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12048.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-197, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))
================================================================
tm-name          tm-12049
in-theory        12049
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-307 tm-198 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12049.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-198, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))
================================================================
tm-name          tm-12050
in-theory        12050
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-307 tm-199 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12050.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-199, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))
================================================================
tm-name          tm-12051
in-theory        12051
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-200 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (and Em Fm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12051.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-200, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (and Em Fm) Em))))
================================================================
tm-name          tm-12052
in-theory        12052
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-307 tm-201 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12052.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-201, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))
================================================================
tm-name          tm-12053
in-theory        12053
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-202 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (and Em Fm) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12053.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-202, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (and Em Fm) Fm))))
================================================================
tm-name          tm-12054
in-theory        12054
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-203 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12054.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-203, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (-> Fm Em)) Dm))))
================================================================
tm-name          tm-12055
in-theory        12055
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     45
proof            (modus-ponens tm-307 tm-204 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12055.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-204, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))
================================================================
tm-name          tm-12056
in-theory        12056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (A -> (B -> A)))
theorem-size     29
proof            (modus-ponens tm-307 tm-205 ((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12056.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (A -> (B -> A))), M:tm-307, m:tm-205, u:((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))
================================================================
tm-name          tm-12057
in-theory        12057
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and ((A and B) -> A))
theorem-size     17
proof            (modus-ponens tm-307 tm-212 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12057.        ((((A and B) -> A) and (C -> (D -> C))) and ((A and B) -> A)), M:tm-307, m:tm-212, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-12058
in-theory        12058
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A and B) -> A))
theorem-size     25
proof            (modus-ponens tm-307 tm-213 ((A (-> (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12058.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A and B) -> A)), M:tm-307, m:tm-213, u:((A (-> (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-12059
in-theory        12059
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and ((A and B) -> A))
theorem-size     17
proof            (modus-ponens tm-307 tm-214 ((A (-> (and Am Bm) Am)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12059.        ((((A and B) -> A) and ((C and D) -> C)) and ((A and B) -> A)), M:tm-307, m:tm-214, u:((A (-> (and Am Bm) Am)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-12060
in-theory        12060
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and ((A and B) -> A))
theorem-size     17
proof            (modus-ponens tm-307 tm-215 ((A (-> (and Am Bm) Am)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12060.        ((((A and B) -> A) and ((C and D) -> D)) and ((A and B) -> A)), M:tm-307, m:tm-215, u:((A (-> (and Am Bm) Am)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-12061
in-theory        12061
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-216 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12061.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((A and B) -> A)), M:tm-307, m:tm-216, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-12062
in-theory        12062
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and ((A and B) -> A))
theorem-size     17
proof            (modus-ponens tm-307 tm-217 ((A (-> (and Am Bm) Am)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12062.        ((((A and B) -> A) and (C -> (C or D))) and ((A and B) -> A)), M:tm-307, m:tm-217, u:((A (-> (and Am Bm) Am)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-12063
in-theory        12063
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and ((A and B) -> A))
theorem-size     17
proof            (modus-ponens tm-307 tm-218 ((A (-> (and Am Bm) Am)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12063.        ((((A and B) -> A) and (C -> (D or C))) and ((A and B) -> A)), M:tm-307, m:tm-218, u:((A (-> (and Am Bm) Am)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-12064
in-theory        12064
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((A and B) -> A))
theorem-size     25
proof            (modus-ponens tm-307 tm-219 ((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12064.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((A and B) -> A)), M:tm-307, m:tm-219, u:((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))
================================================================
tm-name          tm-12065
in-theory        12065
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((A and B) -> A))
theorem-size     23
proof            (modus-ponens tm-307 tm-220 ((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12065.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((A and B) -> A)), M:tm-307, m:tm-220, u:((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))
================================================================
tm-name          tm-12066
in-theory        12066
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and ((A and B) -> A))
theorem-size     17
proof            (modus-ponens tm-307 tm-221 ((A (-> (and Am Bm) Am)) (B (-> (not (not Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12066.        ((((A and B) -> A) and ((not (not C)) -> C)) and ((A and B) -> A)), M:tm-307, m:tm-221, u:((A (-> (and Am Bm) Am)) (B (-> (not (not Cm)) Cm)))
================================================================
tm-name          tm-12067
in-theory        12067
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-222 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12067.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((A and B) -> A)), M:tm-307, m:tm-222, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-12068
in-theory        12068
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-223 ((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> Cm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12068.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((A and B) -> A)), M:tm-307, m:tm-223, u:((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> Cm Cm))))
================================================================
tm-name          tm-12069
in-theory        12069
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((A and B) -> A))
theorem-size     31
proof            (modus-ponens tm-307 tm-224 ((A (-> (and Am Bm) Am)) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12069.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((A and B) -> A)), M:tm-307, m:tm-224, u:((A (-> (and Am Bm) Am)) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))
================================================================
tm-name          tm-12070
in-theory        12070
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((A and B) -> A))
theorem-size     27
proof            (modus-ponens tm-307 tm-225 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12070.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((A and B) -> A)), M:tm-307, m:tm-225, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-12071
in-theory        12071
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((A and B) -> A))
theorem-size     27
proof            (modus-ponens tm-307 tm-226 ((A (-> (and Am Bm) Am)) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12071.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((A and B) -> A)), M:tm-307, m:tm-226, u:((A (-> (and Am Bm) Am)) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))
================================================================
tm-name          tm-12072
in-theory        12072
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-227 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12072.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((A and B) -> A)), M:tm-307, m:tm-227, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-12073
in-theory        12073
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((A and B) -> A))
theorem-size     27
proof            (modus-ponens tm-307 tm-228 ((A (-> (and Am Bm) Am)) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12073.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((A and B) -> A)), M:tm-307, m:tm-228, u:((A (-> (and Am Bm) Am)) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))
================================================================
tm-name          tm-12074
in-theory        12074
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-229 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12074.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((A and B) -> A)), M:tm-307, m:tm-229, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-12075
in-theory        12075
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((A and B) -> A))
theorem-size     21
proof            (modus-ponens tm-307 tm-230 ((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12075.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((A and B) -> A)), M:tm-307, m:tm-230, u:((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm))))
================================================================
tm-name          tm-12076
in-theory        12076
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((A and B) -> A))
theorem-size     29
proof            (modus-ponens tm-307 tm-231 ((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12076.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((A and B) -> A)), M:tm-307, m:tm-231, u:((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))
================================================================
tm-name          tm-12077
in-theory        12077
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((A and B) -> A))
theorem-size     21
proof            (modus-ponens tm-307 tm-232 ((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12077.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((A and B) -> A)), M:tm-307, m:tm-232, u:((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> (and Dm Em) Dm) Cm))))
================================================================
tm-name          tm-12078
in-theory        12078
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-233 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (and Em Fm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12078.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-233, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (and Em Fm) Em) Dm))))
================================================================
tm-name          tm-12079
in-theory        12079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (A -> (B -> A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-234 ((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12079.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (A -> (B -> A))), M:tm-307, m:tm-234, u:((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm))))
================================================================
tm-name          tm-12080
in-theory        12080
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and ((A and B) -> B))
theorem-size     17
proof            (modus-ponens tm-307 tm-241 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12080.        ((((A and B) -> B) and (C -> (D -> C))) and ((A and B) -> B)), M:tm-307, m:tm-241, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-12081
in-theory        12081
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A and B) -> B))
theorem-size     25
proof            (modus-ponens tm-307 tm-242 ((A (-> (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12081.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A and B) -> B)), M:tm-307, m:tm-242, u:((A (-> (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-12082
in-theory        12082
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and ((A and B) -> B))
theorem-size     17
proof            (modus-ponens tm-307 tm-243 ((A (-> (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12082.        ((((A and B) -> B) and ((C and D) -> C)) and ((A and B) -> B)), M:tm-307, m:tm-243, u:((A (-> (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-12083
in-theory        12083
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and ((A and B) -> B))
theorem-size     17
proof            (modus-ponens tm-307 tm-244 ((A (-> (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12083.        ((((A and B) -> B) and ((C and D) -> D)) and ((A and B) -> B)), M:tm-307, m:tm-244, u:((A (-> (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-12084
in-theory        12084
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-245 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12084.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((A and B) -> B)), M:tm-307, m:tm-245, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-12085
in-theory        12085
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and ((A and B) -> B))
theorem-size     17
proof            (modus-ponens tm-307 tm-246 ((A (-> (and Am Bm) Bm)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12085.        ((((A and B) -> B) and (C -> (C or D))) and ((A and B) -> B)), M:tm-307, m:tm-246, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-12086
in-theory        12086
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and ((A and B) -> B))
theorem-size     17
proof            (modus-ponens tm-307 tm-247 ((A (-> (and Am Bm) Bm)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12086.        ((((A and B) -> B) and (C -> (D or C))) and ((A and B) -> B)), M:tm-307, m:tm-247, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-12087
in-theory        12087
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((A and B) -> B))
theorem-size     25
proof            (modus-ponens tm-307 tm-248 ((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12087.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((A and B) -> B)), M:tm-307, m:tm-248, u:((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))
================================================================
tm-name          tm-12088
in-theory        12088
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((A and B) -> B))
theorem-size     23
proof            (modus-ponens tm-307 tm-249 ((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12088.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((A and B) -> B)), M:tm-307, m:tm-249, u:((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))
================================================================
tm-name          tm-12089
in-theory        12089
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and ((A and B) -> B))
theorem-size     17
proof            (modus-ponens tm-307 tm-250 ((A (-> (and Am Bm) Bm)) (B (-> (not (not Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12089.        ((((A and B) -> B) and ((not (not C)) -> C)) and ((A and B) -> B)), M:tm-307, m:tm-250, u:((A (-> (and Am Bm) Bm)) (B (-> (not (not Cm)) Cm)))
================================================================
tm-name          tm-12090
in-theory        12090
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-251 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12090.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((A and B) -> B)), M:tm-307, m:tm-251, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-12091
in-theory        12091
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-252 ((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> Cm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12091.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((A and B) -> B)), M:tm-307, m:tm-252, u:((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> Cm Cm))))
================================================================
tm-name          tm-12092
in-theory        12092
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((A and B) -> B))
theorem-size     31
proof            (modus-ponens tm-307 tm-253 ((A (-> (and Am Bm) Bm)) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12092.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((A and B) -> B)), M:tm-307, m:tm-253, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))
================================================================
tm-name          tm-12093
in-theory        12093
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((A and B) -> B))
theorem-size     27
proof            (modus-ponens tm-307 tm-254 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12093.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((A and B) -> B)), M:tm-307, m:tm-254, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-12094
in-theory        12094
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((A and B) -> B))
theorem-size     27
proof            (modus-ponens tm-307 tm-255 ((A (-> (and Am Bm) Bm)) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12094.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((A and B) -> B)), M:tm-307, m:tm-255, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))
================================================================
tm-name          tm-12095
in-theory        12095
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-256 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12095.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((A and B) -> B)), M:tm-307, m:tm-256, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-12096
in-theory        12096
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((A and B) -> B))
theorem-size     27
proof            (modus-ponens tm-307 tm-257 ((A (-> (and Am Bm) Bm)) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12096.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((A and B) -> B)), M:tm-307, m:tm-257, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))
================================================================
tm-name          tm-12097
in-theory        12097
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-258 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12097.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((A and B) -> B)), M:tm-307, m:tm-258, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-12098
in-theory        12098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((A and B) -> B))
theorem-size     21
proof            (modus-ponens tm-307 tm-259 ((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12098.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((A and B) -> B)), M:tm-307, m:tm-259, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm))))
================================================================
tm-name          tm-12099
in-theory        12099
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((A and B) -> B))
theorem-size     29
proof            (modus-ponens tm-307 tm-260 ((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12099.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((A and B) -> B)), M:tm-307, m:tm-260, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))
================================================================
tm-name          tm-12100
in-theory        12100
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((A and B) -> B))
theorem-size     21
proof            (modus-ponens tm-307 tm-261 ((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12100.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((A and B) -> B)), M:tm-307, m:tm-261, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> (and Dm Em) Dm) Cm))))
================================================================
tm-name          tm-12101
in-theory        12101
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((A and B) -> B))
theorem-size     21
proof            (modus-ponens tm-307 tm-262 ((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> (and Dm Em) Em) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12101.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((A and B) -> B)), M:tm-307, m:tm-262, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> (and Dm Em) Em) Cm))))
================================================================
tm-name          tm-12102
in-theory        12102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((A and B) -> A))
theorem-size     21
proof            (modus-ponens tm-307 tm-263 ((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> (and Dm Em) Em) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12102.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((A and B) -> A)), M:tm-307, m:tm-263, u:((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> (and Dm Em) Em) Cm))))
================================================================
tm-name          tm-12103
in-theory        12103
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-264 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12103.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-264, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (and Em Fm) Fm) Dm))))
================================================================
tm-name          tm-12104
in-theory        12104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (A -> (B -> A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-265 ((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> (and Dm Em) Em) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12104.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (A -> (B -> A))), M:tm-307, m:tm-265, u:((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> (and Dm Em) Em) Cm))))
================================================================
tm-name          tm-12105
in-theory        12105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and (A -> (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-307 tm-272 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12105.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-272, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-12106
in-theory        12106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (A -> (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-307 tm-273 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12106.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-273, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-12107
in-theory        12107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and (A -> (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-307 tm-274 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12107.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and (A -> (B -> (A and B)))), M:tm-307, m:tm-274, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-12108
in-theory        12108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and (A -> (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-307 tm-275 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12108.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and (A -> (B -> (A and B)))), M:tm-307, m:tm-275, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-12109
in-theory        12109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-276 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12109.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-276, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-12110
in-theory        12110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and (A -> (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-307 tm-277 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12110.        (((A -> (B -> (A and B))) and (C -> (C or D))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-277, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-12111
in-theory        12111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and (A -> (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-307 tm-278 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12111.        (((A -> (B -> (A and B))) and (C -> (D or C))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-278, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-12112
in-theory        12112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (A -> (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-307 tm-279 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12112.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-279, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))
================================================================
tm-name          tm-12113
in-theory        12113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (A -> (B -> (A and B))))
theorem-size     27
proof            (modus-ponens tm-307 tm-280 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12113.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-280, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))
================================================================
tm-name          tm-12114
in-theory        12114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (A -> (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-307 tm-281 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (not (not Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12114.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (A -> (B -> (A and B)))), M:tm-307, m:tm-281, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (not (not Cm)) Cm)))
================================================================
tm-name          tm-12115
in-theory        12115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-282 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12115.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-282, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-12116
in-theory        12116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-283 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> Cm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12116.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-283, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> Cm Cm))))
================================================================
tm-name          tm-12117
in-theory        12117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (A -> (B -> (A and B))))
theorem-size     35
proof            (modus-ponens tm-307 tm-284 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12117.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-284, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))
================================================================
tm-name          tm-12118
in-theory        12118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (B -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-307 tm-285 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12118.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-285, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-12119
in-theory        12119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (A -> (B -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-307 tm-286 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12119.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-286, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))
================================================================
tm-name          tm-12120
in-theory        12120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-287 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12120.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-287, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-12121
in-theory        12121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (A -> (B -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-307 tm-288 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12121.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-288, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))
================================================================
tm-name          tm-12122
in-theory        12122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-289 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12122.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-289, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-12123
in-theory        12123
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (A -> (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-307 tm-290 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12123.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-290, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm))))
================================================================
tm-name          tm-12124
in-theory        12124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (A -> (B -> (A and B))))
theorem-size     33
proof            (modus-ponens tm-307 tm-291 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12124.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-291, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))
================================================================
tm-name          tm-12125
in-theory        12125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (A -> (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-307 tm-292 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12125.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-292, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm))))
================================================================
tm-name          tm-12126
in-theory        12126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (A -> (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-307 tm-293 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> (and Dm Em) Em) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12126.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-293, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> (and Dm Em) Em) Cm))))
================================================================
tm-name          tm-12127
in-theory        12127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (A -> (B -> (A and B))))
theorem-size     27
proof            (modus-ponens tm-307 tm-294 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12127.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-294, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))
================================================================
tm-name          tm-12128
in-theory        12128
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((A and B) -> B))
theorem-size     23
proof            (modus-ponens tm-307 tm-295 ((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12128.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((A and B) -> B)), M:tm-307, m:tm-295, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))
================================================================
tm-name          tm-12129
in-theory        12129
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((A and B) -> A))
theorem-size     23
proof            (modus-ponens tm-307 tm-296 ((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12129.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((A and B) -> A)), M:tm-307, m:tm-296, u:((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))
================================================================
tm-name          tm-12130
in-theory        12130
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-307 tm-297 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12130.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-297, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))
================================================================
tm-name          tm-12131
in-theory        12131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (A -> (B -> A)))
theorem-size     23
proof            (modus-ponens tm-307 tm-298 ((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12131.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (A -> (B -> A))), M:tm-307, m:tm-298, u:((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))
================================================================
tm-name          tm-12132
in-theory        12132
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and (C -> ((A and B) -> ((A and B) and A))))
theorem-size     21
proof            (modus-ponens tm-305 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12132.        (((A and B) -> ((A and B) and A)) and (C -> ((A and B) -> ((A and B) and A)))), M:tm-305, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12133
in-theory        12133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D and E) -> ((D and E) and D)))
theorem-size     21
proof            (modus-ponens tm-303 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12133.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D and E) -> ((D and E) and D))), M:tm-303, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12134
in-theory        12134
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (B -> (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-300 tm-307 ((Am (-> A (-> B (and A B)))) (C Bm) (D (and (and (-> A (-> B (and A B))) Bm) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12134.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (B -> (C -> (B and C))))), M:tm-300, m:tm-307, u:((Am (-> A (-> B (and A B)))) (C Bm) (D (and (and (-> A (-> B (and A B))) Bm) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-12135
in-theory        12135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D and E) -> ((D and E) and D)))
theorem-size     19
proof            (modus-ponens tm-270 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12135.        ((A -> (((B and C) -> C) and A)) and ((D and E) -> ((D and E) and D))), M:tm-270, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12136
in-theory        12136
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((B and C) -> C)))
theorem-size     23
proof            (modus-ponens tm-267 tm-307 ((Am (-> (and A B) B)) (C Bm) (D (and (and (-> (and A B) B) Bm) (-> (and A B) B)))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12136.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((B and C) -> C))), M:tm-267, m:tm-307, u:((Am (-> (and A B) B)) (C Bm) (D (and (and (-> (and A B) B) Bm) (-> (and A B) B))))
================================================================
tm-name          tm-12137
in-theory        12137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D and E) -> ((D and E) and D)))
theorem-size     19
proof            (modus-ponens tm-239 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12137.        ((A -> (((B and C) -> B) and A)) and ((D and E) -> ((D and E) and D))), M:tm-239, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12138
in-theory        12138
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((B and C) -> B)))
theorem-size     23
proof            (modus-ponens tm-236 tm-307 ((Am (-> (and A B) A)) (C Bm) (D (and (and (-> (and A B) A) Bm) (-> (and A B) A)))))
axioms-used      (tm-8 tm-5 tm-3 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12138.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((B and C) -> B))), M:tm-236, m:tm-307, u:((Am (-> (and A B) A)) (C Bm) (D (and (and (-> (and A B) A) Bm) (-> (and A B) A))))
================================================================
tm-name          tm-12139
in-theory        12139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and F) -> ((E and F) and E)))
theorem-size     27
proof            (modus-ponens tm-210 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12139.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and F) -> ((E and F) and E))), M:tm-210, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12140
in-theory        12140
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     47
proof            (modus-ponens tm-207 tm-307 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12140.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-207, m:tm-307, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-12141
in-theory        12141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D and E) -> ((D and E) and D)))
theorem-size     19
proof            (modus-ponens tm-183 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12141.        ((A -> ((B -> (C -> B)) and A)) and ((D and E) -> ((D and E) and D))), M:tm-183, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12142
in-theory        12142
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (B -> (C -> B))))
theorem-size     23
proof            (modus-ponens tm-180 tm-307 ((Am (-> A (-> B A))) (C Bm) (D (and (and (-> A (-> B A)) Bm) (-> A (-> B A))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12142.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (B -> (C -> B)))), M:tm-180, m:tm-307, u:((Am (-> A (-> B A))) (C Bm) (D (and (and (-> A (-> B A)) Bm) (-> A (-> B A)))))
================================================================
tm-name          tm-12143
in-theory        12143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-157 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12143.        ((A -> ((B and C) -> C)) and ((D and E) -> ((D and E) and D))), M:tm-157, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12144
in-theory        12144
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and E) -> ((D and E) and D)))
theorem-size     25
proof            (modus-ponens tm-147 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12144.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and E) -> ((D and E) and D))), M:tm-147, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12145
in-theory        12145
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-134 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12145.        ((A -> ((B and C) -> B)) and ((D and E) -> ((D and E) and D))), M:tm-134, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12146
in-theory        12146
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and E) -> ((D and E) and D)))
theorem-size     25
proof            (modus-ponens tm-125 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12146.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and E) -> ((D and E) and D))), M:tm-125, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12147
in-theory        12147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> ((E and F) and E)))
theorem-size     25
proof            (modus-ponens tm-113 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12147.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> ((E and F) and E))), M:tm-113, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12148
in-theory        12148
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> ((D and E) and D)))
theorem-size     29
proof            (modus-ponens tm-105 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12148.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> ((D and E) and D))), M:tm-105, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12149
in-theory        12149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C and D) -> ((C and D) and C)))
theorem-size     17
proof            (modus-ponens tm-95 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12149.        (((A -> B) -> (A -> A)) and ((C and D) -> ((C and D) and C))), M:tm-95, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12150
in-theory        12150
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (C -> ((A and B) and A)))
theorem-size     11
proof            (modus-ponens tm-84 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12150.        ((A and B) -> (C -> ((A and B) and A))), M:tm-84, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-12151
in-theory        12151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-83 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12151.        ((A -> (B -> (C -> B))) and ((D and E) -> ((D and E) and D))), M:tm-83, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12152
in-theory        12152
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B and C) -> ((B and C) and B)))
theorem-size     15
proof            (modus-ponens tm-76 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-10 tm-2 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12152.        (((not (not A)) -> A) and ((B and C) -> ((B and C) and B))), M:tm-76, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12153
in-theory        12153
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A and B))) or (A and B)) -> ((A and B) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12153.        (((not (not (A and B))) or (A and B)) -> ((A and B) and A)), M:tm-73, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-12154
in-theory        12154
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and D) -> ((C and D) and C)))
theorem-size     21
proof            (modus-ponens tm-69 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12154.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and D) -> ((C and D) and C))), M:tm-69, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12155
in-theory        12155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> ((D and E) and D)))
theorem-size     23
proof            (modus-ponens tm-54 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12155.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> ((D and E) and D))), M:tm-54, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12156
in-theory        12156
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> ((B and C) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12156.        (((A and (B and C)) or (B and C)) -> ((B and C) and B)), M:tm-47, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-12157
in-theory        12157
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> ((A and B) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12157.        ((((A and B) and C) or (A and B)) -> ((A and B) and A)), M:tm-46, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-12158
in-theory        12158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C and D) -> ((C and D) and C)))
theorem-size     15
proof            (modus-ponens tm-42 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12158.        ((A -> (B or A)) and ((C and D) -> ((C and D) and C))), M:tm-42, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12159
in-theory        12159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C and D) -> ((C and D) and C)))
theorem-size     15
proof            (modus-ponens tm-32 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12159.        ((A -> (A or B)) and ((C and D) -> ((C and D) and C))), M:tm-32, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12160
in-theory        12160
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> ((A and B) and ((A and B) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12160.        ((A and B) -> ((A and B) and ((A and B) and A))), M:tm-24, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-12161
in-theory        12161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C and D) -> ((C and D) and C)))
theorem-size     17
proof            (modus-ponens tm-23 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12161.        ((A -> (B -> (A and B))) and ((C and D) -> ((C and D) and C))), M:tm-23, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12162
in-theory        12162
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C and D) -> ((C and D) and C)))
theorem-size     15
proof            (modus-ponens tm-22 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12162.        (((A and B) -> B) and ((C and D) -> ((C and D) and C))), M:tm-22, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12163
in-theory        12163
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C and D) -> ((C and D) and C)))
theorem-size     15
proof            (modus-ponens tm-21 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12163.        (((A and B) -> A) and ((C and D) -> ((C and D) and C))), M:tm-21, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12164
in-theory        12164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> ((D and E) and D)))
theorem-size     23
proof            (modus-ponens tm-20 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12164.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> ((D and E) and D))), M:tm-20, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12165
in-theory        12165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C and D) -> ((C and D) and C)))
theorem-size     15
proof            (modus-ponens tm-19 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12165.        ((A -> (B -> A)) and ((C and D) -> ((C and D) and C))), M:tm-19, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12166
in-theory        12166
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not ((A and B) and A))) -> (not (A and B)))
theorem-size     15
proof            (modus-ponens tm-9 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-9 tm-2 tm-5 tm-3)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12166.        (((A and B) -> (not ((A and B) and A))) -> (not (A and B))), M:tm-9, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-12167
in-theory        12167
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and A) -> C) -> (((A and B) or ((A and B) and A)) -> C))
theorem-size     19
proof            (modus-ponens tm-8 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12167.        ((((A and B) and A) -> C) -> (((A and B) or ((A and B) and A)) -> C)), M:tm-8, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-12168
in-theory        12168
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B and C) -> ((B and C) and B)))
theorem-size     11
proof            (modus-ponens tm-7 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-7 tm-2 tm-5 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12168.        (A or ((B and C) -> ((B and C) and B))), M:tm-7, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12169
in-theory        12169
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) or C)
theorem-size     11
proof            (modus-ponens tm-6 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-6 tm-2 tm-5 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12169.        (((A and B) -> ((A and B) and A)) or C), M:tm-6, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12170
in-theory        12170
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> ((B and C) and B)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12170.        (A -> (((B and C) -> ((B and C) and B)) and A)), M:tm-5, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12171
in-theory        12171
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B and C) -> ((B and C) and B)))
theorem-size     11
proof            (modus-ponens tm-1 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-1 tm-2 tm-5 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12171.        (A -> ((B and C) -> ((B and C) and B))), M:tm-1, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12172
in-theory        12172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-308 tm-160 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12172.        (((A -> (B -> A)) and (C -> (D -> C))) and (C -> (D -> C))), M:tm-308, m:tm-160, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-12173
in-theory        12173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-308 tm-161 ((A (-> Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12173.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-308, m:tm-161, u:((A (-> Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-12174
in-theory        12174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-308 tm-162 ((A (-> Am (-> Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12174.        (((A -> (B -> A)) and ((C and D) -> C)) and ((C and D) -> C)), M:tm-308, m:tm-162, u:((A (-> Am (-> Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-12175
in-theory        12175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-308 tm-163 ((A (-> Am (-> Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12175.        (((A -> (B -> A)) and ((C and D) -> D)) and ((C and D) -> D)), M:tm-308, m:tm-163, u:((A (-> Am (-> Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-12176
in-theory        12176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-164 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12176.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (C -> (D -> (C and D)))), M:tm-308, m:tm-164, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-12177
in-theory        12177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-308 tm-165 ((A (-> Am (-> Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12177.        (((A -> (B -> A)) and (C -> (C or D))) and (C -> (C or D))), M:tm-308, m:tm-165, u:((A (-> Am (-> Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-12178
in-theory        12178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-308 tm-166 ((A (-> Am (-> Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12178.        (((A -> (B -> A)) and (C -> (D or C))) and (C -> (D or C))), M:tm-308, m:tm-166, u:((A (-> Am (-> Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-12179
in-theory        12179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     33
proof            (modus-ponens tm-308 tm-167 ((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12179.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-308, m:tm-167, u:((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))
================================================================
tm-name          tm-12180
in-theory        12180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     29
proof            (modus-ponens tm-308 tm-168 ((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12180.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-308, m:tm-168, u:((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))
================================================================
tm-name          tm-12181
in-theory        12181
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and ((not (not C)) -> C))
theorem-size     17
proof            (modus-ponens tm-308 tm-169 ((A (-> Am (-> Bm Am))) (B (-> (not (not Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12181.        (((A -> (B -> A)) and ((not (not C)) -> C)) and ((not (not C)) -> C)), M:tm-308, m:tm-169, u:((A (-> Am (-> Bm Am))) (B (-> (not (not Cm)) Cm)))
================================================================
tm-name          tm-12182
in-theory        12182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (C -> (D -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-170 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12182.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (C -> (D -> (E -> D)))), M:tm-308, m:tm-170, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-12183
in-theory        12183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((C -> D) -> (C -> C)))
theorem-size     21
proof            (modus-ponens tm-308 tm-171 ((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> Cm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12183.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((C -> D) -> (C -> C))), M:tm-308, m:tm-171, u:((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> Cm Cm))))
================================================================
tm-name          tm-12184
in-theory        12184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     45
proof            (modus-ponens tm-308 tm-172 ((A (-> Am (-> Bm Am))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12184.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-308, m:tm-172, u:((A (-> Am (-> Bm Am))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))
================================================================
tm-name          tm-12185
in-theory        12185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-173 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12185.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-308, m:tm-173, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-12186
in-theory        12186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     37
proof            (modus-ponens tm-308 tm-174 ((A (-> Am (-> Bm Am))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12186.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-308, m:tm-174, u:((A (-> Am (-> Bm Am))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))
================================================================
tm-name          tm-12187
in-theory        12187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (C -> ((D and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-308 tm-175 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12187.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (C -> ((D and E) -> D))), M:tm-308, m:tm-175, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-12188
in-theory        12188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     37
proof            (modus-ponens tm-308 tm-176 ((A (-> Am (-> Bm Am))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12188.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-308, m:tm-176, u:((A (-> Am (-> Bm Am))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))
================================================================
tm-name          tm-12189
in-theory        12189
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (C -> ((D and E) -> E)))
theorem-size     21
proof            (modus-ponens tm-308 tm-177 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12189.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (C -> ((D and E) -> E))), M:tm-308, m:tm-177, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-12190
in-theory        12190
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (C -> ((D -> (E -> D)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-178 ((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12190.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (C -> ((D -> (E -> D)) and C))), M:tm-308, m:tm-178, u:((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm))))
================================================================
tm-name          tm-12191
in-theory        12191
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-308 tm-185 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12191.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (D -> (E -> D))), M:tm-308, m:tm-185, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-12192
in-theory        12192
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-308 tm-186 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12192.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-308, m:tm-186, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-12193
in-theory        12193
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-308 tm-187 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12193.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((D and E) -> D)), M:tm-308, m:tm-187, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-12194
in-theory        12194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-308 tm-188 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12194.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((D and E) -> E)), M:tm-308, m:tm-188, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-12195
in-theory        12195
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (D -> (E -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-308 tm-189 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12195.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (D -> (E -> (D and E)))), M:tm-308, m:tm-189, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-12196
in-theory        12196
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-308 tm-190 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12196.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (D -> (D or E))), M:tm-308, m:tm-190, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-12197
in-theory        12197
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-308 tm-191 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12197.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (D -> (E or D))), M:tm-308, m:tm-191, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-12198
in-theory        12198
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     41
proof            (modus-ponens tm-308 tm-192 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12198.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-308, m:tm-192, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))
================================================================
tm-name          tm-12199
in-theory        12199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     37
proof            (modus-ponens tm-308 tm-193 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12199.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-308, m:tm-193, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))
================================================================
tm-name          tm-12200
in-theory        12200
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((not (not D)) -> D))
theorem-size     25
proof            (modus-ponens tm-308 tm-194 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (not (not Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-10)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12200.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((not (not D)) -> D)), M:tm-308, m:tm-194, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (not (not Dm)) Dm)))
================================================================
tm-name          tm-12201
in-theory        12201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (D -> (E -> (F -> E))))
theorem-size     29
proof            (modus-ponens tm-308 tm-195 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (-> Fm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12201.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (D -> (E -> (F -> E)))), M:tm-308, m:tm-195, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (-> Fm Em)))))
================================================================
tm-name          tm-12202
in-theory        12202
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((D -> E) -> (D -> D)))
theorem-size     29
proof            (modus-ponens tm-308 tm-196 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> Dm Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12202.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((D -> E) -> (D -> D))), M:tm-308, m:tm-196, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> Dm Dm))))
================================================================
tm-name          tm-12203
in-theory        12203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     53
proof            (modus-ponens tm-308 tm-197 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12203.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-308, m:tm-197, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))
================================================================
tm-name          tm-12204
in-theory        12204
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     45
proof            (modus-ponens tm-308 tm-198 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12204.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-308, m:tm-198, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))
================================================================
tm-name          tm-12205
in-theory        12205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     45
proof            (modus-ponens tm-308 tm-199 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12205.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-308, m:tm-199, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))
================================================================
tm-name          tm-12206
in-theory        12206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (D -> ((E and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-308 tm-200 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (and Em Fm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12206.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (D -> ((E and F) -> E))), M:tm-308, m:tm-200, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (and Em Fm) Em))))
================================================================
tm-name          tm-12207
in-theory        12207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     45
proof            (modus-ponens tm-308 tm-201 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12207.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-308, m:tm-201, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))
================================================================
tm-name          tm-12208
in-theory        12208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (D -> ((E and F) -> F)))
theorem-size     29
proof            (modus-ponens tm-308 tm-202 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (and Em Fm) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12208.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (D -> ((E and F) -> F))), M:tm-308, m:tm-202, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (and Em Fm) Fm))))
================================================================
tm-name          tm-12209
in-theory        12209
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (D -> ((E -> (F -> E)) and D)))
theorem-size     33
proof            (modus-ponens tm-308 tm-203 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12209.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (D -> ((E -> (F -> E)) and D))), M:tm-308, m:tm-203, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (-> Fm Em)) Dm))))
================================================================
tm-name          tm-12210
in-theory        12210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     49
proof            (modus-ponens tm-308 tm-204 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12210.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-308, m:tm-204, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))
================================================================
tm-name          tm-12211
in-theory        12211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     41
proof            (modus-ponens tm-308 tm-205 ((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12211.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-308, m:tm-205, u:((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))
================================================================
tm-name          tm-12212
in-theory        12212
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-308 tm-212 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12212.        ((((A and B) -> A) and (C -> (D -> C))) and (C -> (D -> C))), M:tm-308, m:tm-212, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-12213
in-theory        12213
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-308 tm-213 ((A (-> (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12213.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-308, m:tm-213, u:((A (-> (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-12214
in-theory        12214
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-308 tm-214 ((A (-> (and Am Bm) Am)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12214.        ((((A and B) -> A) and ((C and D) -> C)) and ((C and D) -> C)), M:tm-308, m:tm-214, u:((A (-> (and Am Bm) Am)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-12215
in-theory        12215
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-308 tm-215 ((A (-> (and Am Bm) Am)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12215.        ((((A and B) -> A) and ((C and D) -> D)) and ((C and D) -> D)), M:tm-308, m:tm-215, u:((A (-> (and Am Bm) Am)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-12216
in-theory        12216
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-216 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12216.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and (C -> (D -> (C and D)))), M:tm-308, m:tm-216, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-12217
in-theory        12217
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-308 tm-217 ((A (-> (and Am Bm) Am)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12217.        ((((A and B) -> A) and (C -> (C or D))) and (C -> (C or D))), M:tm-308, m:tm-217, u:((A (-> (and Am Bm) Am)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-12218
in-theory        12218
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-308 tm-218 ((A (-> (and Am Bm) Am)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12218.        ((((A and B) -> A) and (C -> (D or C))) and (C -> (D or C))), M:tm-308, m:tm-218, u:((A (-> (and Am Bm) Am)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-12219
in-theory        12219
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     33
proof            (modus-ponens tm-308 tm-219 ((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12219.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-308, m:tm-219, u:((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))
================================================================
tm-name          tm-12220
in-theory        12220
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     29
proof            (modus-ponens tm-308 tm-220 ((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12220.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-308, m:tm-220, u:((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))
================================================================
tm-name          tm-12221
in-theory        12221
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and ((not (not C)) -> C))
theorem-size     17
proof            (modus-ponens tm-308 tm-221 ((A (-> (and Am Bm) Am)) (B (-> (not (not Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12221.        ((((A and B) -> A) and ((not (not C)) -> C)) and ((not (not C)) -> C)), M:tm-308, m:tm-221, u:((A (-> (and Am Bm) Am)) (B (-> (not (not Cm)) Cm)))
================================================================
tm-name          tm-12222
in-theory        12222
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (C -> (D -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-222 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12222.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (C -> (D -> (E -> D)))), M:tm-308, m:tm-222, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-12223
in-theory        12223
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((C -> D) -> (C -> C)))
theorem-size     21
proof            (modus-ponens tm-308 tm-223 ((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> Cm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12223.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((C -> D) -> (C -> C))), M:tm-308, m:tm-223, u:((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> Cm Cm))))
================================================================
tm-name          tm-12224
in-theory        12224
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     45
proof            (modus-ponens tm-308 tm-224 ((A (-> (and Am Bm) Am)) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12224.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-308, m:tm-224, u:((A (-> (and Am Bm) Am)) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))
================================================================
tm-name          tm-12225
in-theory        12225
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-225 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12225.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-308, m:tm-225, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-12226
in-theory        12226
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     37
proof            (modus-ponens tm-308 tm-226 ((A (-> (and Am Bm) Am)) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12226.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-308, m:tm-226, u:((A (-> (and Am Bm) Am)) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))
================================================================
tm-name          tm-12227
in-theory        12227
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and (C -> ((D and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-308 tm-227 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12227.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and (C -> ((D and E) -> D))), M:tm-308, m:tm-227, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-12228
in-theory        12228
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     37
proof            (modus-ponens tm-308 tm-228 ((A (-> (and Am Bm) Am)) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12228.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-308, m:tm-228, u:((A (-> (and Am Bm) Am)) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))
================================================================
tm-name          tm-12229
in-theory        12229
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and (C -> ((D and E) -> E)))
theorem-size     21
proof            (modus-ponens tm-308 tm-229 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12229.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and (C -> ((D and E) -> E))), M:tm-308, m:tm-229, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-12230
in-theory        12230
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (C -> ((D -> (E -> D)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-230 ((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12230.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (C -> ((D -> (E -> D)) and C))), M:tm-308, m:tm-230, u:((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm))))
================================================================
tm-name          tm-12231
in-theory        12231
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     41
proof            (modus-ponens tm-308 tm-231 ((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12231.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-308, m:tm-231, u:((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))
================================================================
tm-name          tm-12232
in-theory        12232
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (C -> (((D and E) -> D) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-232 ((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12232.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (C -> (((D and E) -> D) and C))), M:tm-308, m:tm-232, u:((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> (and Dm Em) Dm) Cm))))
================================================================
tm-name          tm-12233
in-theory        12233
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (D -> (((E and F) -> E) and D)))
theorem-size     33
proof            (modus-ponens tm-308 tm-233 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (and Em Fm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12233.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (D -> (((E and F) -> E) and D))), M:tm-308, m:tm-233, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (and Em Fm) Em) Dm))))
================================================================
tm-name          tm-12234
in-theory        12234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (C -> (((D and E) -> D) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-234 ((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12234.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (C -> (((D and E) -> D) and C))), M:tm-308, m:tm-234, u:((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm))))
================================================================
tm-name          tm-12235
in-theory        12235
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-308 tm-241 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12235.        ((((A and B) -> B) and (C -> (D -> C))) and (C -> (D -> C))), M:tm-308, m:tm-241, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-12236
in-theory        12236
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-308 tm-242 ((A (-> (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12236.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-308, m:tm-242, u:((A (-> (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-12237
in-theory        12237
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-308 tm-243 ((A (-> (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12237.        ((((A and B) -> B) and ((C and D) -> C)) and ((C and D) -> C)), M:tm-308, m:tm-243, u:((A (-> (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-12238
in-theory        12238
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-308 tm-244 ((A (-> (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12238.        ((((A and B) -> B) and ((C and D) -> D)) and ((C and D) -> D)), M:tm-308, m:tm-244, u:((A (-> (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-12239
in-theory        12239
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-245 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12239.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and (C -> (D -> (C and D)))), M:tm-308, m:tm-245, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-12240
in-theory        12240
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-308 tm-246 ((A (-> (and Am Bm) Bm)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12240.        ((((A and B) -> B) and (C -> (C or D))) and (C -> (C or D))), M:tm-308, m:tm-246, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-12241
in-theory        12241
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-308 tm-247 ((A (-> (and Am Bm) Bm)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12241.        ((((A and B) -> B) and (C -> (D or C))) and (C -> (D or C))), M:tm-308, m:tm-247, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-12242
in-theory        12242
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     33
proof            (modus-ponens tm-308 tm-248 ((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12242.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-308, m:tm-248, u:((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))
================================================================
tm-name          tm-12243
in-theory        12243
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     29
proof            (modus-ponens tm-308 tm-249 ((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12243.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-308, m:tm-249, u:((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))
================================================================
tm-name          tm-12244
in-theory        12244
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and ((not (not C)) -> C))
theorem-size     17
proof            (modus-ponens tm-308 tm-250 ((A (-> (and Am Bm) Bm)) (B (-> (not (not Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12244.        ((((A and B) -> B) and ((not (not C)) -> C)) and ((not (not C)) -> C)), M:tm-308, m:tm-250, u:((A (-> (and Am Bm) Bm)) (B (-> (not (not Cm)) Cm)))
================================================================
tm-name          tm-12245
in-theory        12245
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (C -> (D -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-251 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12245.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (C -> (D -> (E -> D)))), M:tm-308, m:tm-251, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-12246
in-theory        12246
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((C -> D) -> (C -> C)))
theorem-size     21
proof            (modus-ponens tm-308 tm-252 ((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> Cm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12246.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((C -> D) -> (C -> C))), M:tm-308, m:tm-252, u:((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> Cm Cm))))
================================================================
tm-name          tm-12247
in-theory        12247
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     45
proof            (modus-ponens tm-308 tm-253 ((A (-> (and Am Bm) Bm)) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12247.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-308, m:tm-253, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))
================================================================
tm-name          tm-12248
in-theory        12248
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-254 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12248.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-308, m:tm-254, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-12249
in-theory        12249
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     37
proof            (modus-ponens tm-308 tm-255 ((A (-> (and Am Bm) Bm)) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12249.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-308, m:tm-255, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))
================================================================
tm-name          tm-12250
in-theory        12250
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and (C -> ((D and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-308 tm-256 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12250.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and (C -> ((D and E) -> D))), M:tm-308, m:tm-256, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-12251
in-theory        12251
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     37
proof            (modus-ponens tm-308 tm-257 ((A (-> (and Am Bm) Bm)) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12251.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-308, m:tm-257, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))
================================================================
tm-name          tm-12252
in-theory        12252
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and (C -> ((D and E) -> E)))
theorem-size     21
proof            (modus-ponens tm-308 tm-258 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12252.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and (C -> ((D and E) -> E))), M:tm-308, m:tm-258, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-12253
in-theory        12253
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (C -> ((D -> (E -> D)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-259 ((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12253.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (C -> ((D -> (E -> D)) and C))), M:tm-308, m:tm-259, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm))))
================================================================
tm-name          tm-12254
in-theory        12254
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     41
proof            (modus-ponens tm-308 tm-260 ((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12254.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-308, m:tm-260, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))
================================================================
tm-name          tm-12255
in-theory        12255
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (C -> (((D and E) -> D) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-261 ((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12255.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (C -> (((D and E) -> D) and C))), M:tm-308, m:tm-261, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> (and Dm Em) Dm) Cm))))
================================================================
tm-name          tm-12256
in-theory        12256
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (C -> (((D and E) -> E) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-262 ((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> (and Dm Em) Em) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12256.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (C -> (((D and E) -> E) and C))), M:tm-308, m:tm-262, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> (and Dm Em) Em) Cm))))
================================================================
tm-name          tm-12257
in-theory        12257
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (C -> (((D and E) -> E) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-263 ((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> (and Dm Em) Em) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12257.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (C -> (((D and E) -> E) and C))), M:tm-308, m:tm-263, u:((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> (and Dm Em) Em) Cm))))
================================================================
tm-name          tm-12258
in-theory        12258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (D -> (((E and F) -> F) and D)))
theorem-size     33
proof            (modus-ponens tm-308 tm-264 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12258.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (D -> (((E and F) -> F) and D))), M:tm-308, m:tm-264, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (and Em Fm) Fm) Dm))))
================================================================
tm-name          tm-12259
in-theory        12259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (C -> (((D and E) -> E) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-265 ((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> (and Dm Em) Em) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12259.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (C -> (((D and E) -> E) and C))), M:tm-308, m:tm-265, u:((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> (and Dm Em) Em) Cm))))
================================================================
tm-name          tm-12260
in-theory        12260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and (C -> (D -> C)))
theorem-size     19
proof            (modus-ponens tm-308 tm-272 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12260.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and (C -> (D -> C))), M:tm-308, m:tm-272, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-12261
in-theory        12261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-308 tm-273 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12261.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-308, m:tm-273, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-12262
in-theory        12262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((C and D) -> C))
theorem-size     19
proof            (modus-ponens tm-308 tm-274 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12262.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((C and D) -> C)), M:tm-308, m:tm-274, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-12263
in-theory        12263
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((C and D) -> D))
theorem-size     19
proof            (modus-ponens tm-308 tm-275 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12263.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((C and D) -> D)), M:tm-308, m:tm-275, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-12264
in-theory        12264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (C -> (D -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-308 tm-276 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12264.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (C -> (D -> (C and D)))), M:tm-308, m:tm-276, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-12265
in-theory        12265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and (C -> (C or D)))
theorem-size     19
proof            (modus-ponens tm-308 tm-277 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12265.        (((A -> (B -> (A and B))) and (C -> (C or D))) and (C -> (C or D))), M:tm-308, m:tm-277, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-12266
in-theory        12266
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and (C -> (D or C)))
theorem-size     19
proof            (modus-ponens tm-308 tm-278 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12266.        (((A -> (B -> (A and B))) and (C -> (D or C))) and (C -> (D or C))), M:tm-308, m:tm-278, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-12267
in-theory        12267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     35
proof            (modus-ponens tm-308 tm-279 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12267.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-308, m:tm-279, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))
================================================================
tm-name          tm-12268
in-theory        12268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     31
proof            (modus-ponens tm-308 tm-280 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12268.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-308, m:tm-280, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))
================================================================
tm-name          tm-12269
in-theory        12269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((not (not C)) -> C))
theorem-size     19
proof            (modus-ponens tm-308 tm-281 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (not (not Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-10)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12269.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((not (not C)) -> C)), M:tm-308, m:tm-281, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (not (not Cm)) Cm)))
================================================================
tm-name          tm-12270
in-theory        12270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (C -> (D -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-308 tm-282 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12270.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (C -> (D -> (E -> D)))), M:tm-308, m:tm-282, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-12271
in-theory        12271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((C -> D) -> (C -> C)))
theorem-size     23
proof            (modus-ponens tm-308 tm-283 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> Cm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12271.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((C -> D) -> (C -> C))), M:tm-308, m:tm-283, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> Cm Cm))))
================================================================
tm-name          tm-12272
in-theory        12272
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     47
proof            (modus-ponens tm-308 tm-284 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12272.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-308, m:tm-284, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))
================================================================
tm-name          tm-12273
in-theory        12273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-308 tm-285 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12273.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-308, m:tm-285, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-12274
in-theory        12274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     39
proof            (modus-ponens tm-308 tm-286 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12274.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-308, m:tm-286, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))
================================================================
tm-name          tm-12275
in-theory        12275
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (C -> ((D and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-308 tm-287 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12275.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (C -> ((D and E) -> D))), M:tm-308, m:tm-287, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-12276
in-theory        12276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     39
proof            (modus-ponens tm-308 tm-288 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12276.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-308, m:tm-288, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))
================================================================
tm-name          tm-12277
in-theory        12277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (C -> ((D and E) -> E)))
theorem-size     23
proof            (modus-ponens tm-308 tm-289 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12277.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (C -> ((D and E) -> E))), M:tm-308, m:tm-289, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-12278
in-theory        12278
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (C -> ((D -> (E -> D)) and C)))
theorem-size     27
proof            (modus-ponens tm-308 tm-290 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12278.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (C -> ((D -> (E -> D)) and C))), M:tm-308, m:tm-290, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm))))
================================================================
tm-name          tm-12279
in-theory        12279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     43
proof            (modus-ponens tm-308 tm-291 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12279.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-308, m:tm-291, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))
================================================================
tm-name          tm-12280
in-theory        12280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (C -> (((D and E) -> D) and C)))
theorem-size     27
proof            (modus-ponens tm-308 tm-292 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12280.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (C -> (((D and E) -> D) and C))), M:tm-308, m:tm-292, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm))))
================================================================
tm-name          tm-12281
in-theory        12281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (C -> (((D and E) -> E) and C)))
theorem-size     27
proof            (modus-ponens tm-308 tm-293 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> (and Dm Em) Em) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12281.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (C -> (((D and E) -> E) and C))), M:tm-308, m:tm-293, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> (and Dm Em) Em) Cm))))
================================================================
tm-name          tm-12282
in-theory        12282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     31
proof            (modus-ponens tm-308 tm-294 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12282.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-308, m:tm-294, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))
================================================================
tm-name          tm-12283
in-theory        12283
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     29
proof            (modus-ponens tm-308 tm-295 ((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12283.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-308, m:tm-295, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))
================================================================
tm-name          tm-12284
in-theory        12284
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     29
proof            (modus-ponens tm-308 tm-296 ((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12284.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-308, m:tm-296, u:((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))
================================================================
tm-name          tm-12285
in-theory        12285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     37
proof            (modus-ponens tm-308 tm-297 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12285.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-308, m:tm-297, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))
================================================================
tm-name          tm-12286
in-theory        12286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     29
proof            (modus-ponens tm-308 tm-298 ((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12286.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-308, m:tm-298, u:((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))
================================================================
tm-name          tm-12287
in-theory        12287
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and (C -> ((A and B) -> ((A and B) and B))))
theorem-size     21
proof            (modus-ponens tm-305 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12287.        (((A and B) -> ((A and B) and B)) and (C -> ((A and B) -> ((A and B) and B)))), M:tm-305, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12288
in-theory        12288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D and E) -> ((D and E) and E)))
theorem-size     21
proof            (modus-ponens tm-303 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12288.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D and E) -> ((D and E) and E))), M:tm-303, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12289
in-theory        12289
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and A))
theorem-size     23
proof            (modus-ponens tm-300 tm-308 ((Am (-> A (-> B (and A B)))) (C Bm) (D (and (and (-> A (-> B (and A B))) Bm) Bm))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12289.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and A)), M:tm-300, m:tm-308, u:((Am (-> A (-> B (and A B)))) (C Bm) (D (and (and (-> A (-> B (and A B))) Bm) Bm)))
================================================================
tm-name          tm-12290
in-theory        12290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D and E) -> ((D and E) and E)))
theorem-size     19
proof            (modus-ponens tm-270 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12290.        ((A -> (((B and C) -> C) and A)) and ((D and E) -> ((D and E) and E))), M:tm-270, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12291
in-theory        12291
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and A))
theorem-size     19
proof            (modus-ponens tm-267 tm-308 ((Am (-> (and A B) B)) (C Bm) (D (and (and (-> (and A B) B) Bm) Bm))))
axioms-used      (tm-8 tm-5 tm-4 tm-2)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12291.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and A)), M:tm-267, m:tm-308, u:((Am (-> (and A B) B)) (C Bm) (D (and (and (-> (and A B) B) Bm) Bm)))
================================================================
tm-name          tm-12292
in-theory        12292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D and E) -> ((D and E) and E)))
theorem-size     19
proof            (modus-ponens tm-239 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12292.        ((A -> (((B and C) -> B) and A)) and ((D and E) -> ((D and E) and E))), M:tm-239, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12293
in-theory        12293
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and A))
theorem-size     19
proof            (modus-ponens tm-236 tm-308 ((Am (-> (and A B) A)) (C Bm) (D (and (and (-> (and A B) A) Bm) Bm))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12293.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and A)), M:tm-236, m:tm-308, u:((Am (-> (and A B) A)) (C Bm) (D (and (and (-> (and A B) A) Bm) Bm)))
================================================================
tm-name          tm-12294
in-theory        12294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and F) -> ((E and F) and F)))
theorem-size     27
proof            (modus-ponens tm-210 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12294.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and F) -> ((E and F) and F))), M:tm-210, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12295
in-theory        12295
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and A))
theorem-size     35
proof            (modus-ponens tm-207 tm-308 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) Bm))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12295.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and A)), M:tm-207, m:tm-308, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) Bm)))
================================================================
tm-name          tm-12296
in-theory        12296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D and E) -> ((D and E) and E)))
theorem-size     19
proof            (modus-ponens tm-183 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12296.        ((A -> ((B -> (C -> B)) and A)) and ((D and E) -> ((D and E) and E))), M:tm-183, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12297
in-theory        12297
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and A))
theorem-size     19
proof            (modus-ponens tm-180 tm-308 ((Am (-> A (-> B A))) (C Bm) (D (and (and (-> A (-> B A)) Bm) Bm))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12297.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and A)), M:tm-180, m:tm-308, u:((Am (-> A (-> B A))) (C Bm) (D (and (and (-> A (-> B A)) Bm) Bm)))
================================================================
tm-name          tm-12298
in-theory        12298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-157 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12298.        ((A -> ((B and C) -> C)) and ((D and E) -> ((D and E) and E))), M:tm-157, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12299
in-theory        12299
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and E) -> ((D and E) and E)))
theorem-size     25
proof            (modus-ponens tm-147 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12299.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and E) -> ((D and E) and E))), M:tm-147, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12300
in-theory        12300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-134 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12300.        ((A -> ((B and C) -> B)) and ((D and E) -> ((D and E) and E))), M:tm-134, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12301
in-theory        12301
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and E) -> ((D and E) and E)))
theorem-size     25
proof            (modus-ponens tm-125 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12301.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and E) -> ((D and E) and E))), M:tm-125, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12302
in-theory        12302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> ((E and F) and F)))
theorem-size     25
proof            (modus-ponens tm-113 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12302.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> ((E and F) and F))), M:tm-113, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12303
in-theory        12303
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> ((D and E) and E)))
theorem-size     29
proof            (modus-ponens tm-105 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12303.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> ((D and E) and E))), M:tm-105, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12304
in-theory        12304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C and D) -> ((C and D) and D)))
theorem-size     17
proof            (modus-ponens tm-95 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12304.        (((A -> B) -> (A -> A)) and ((C and D) -> ((C and D) and D))), M:tm-95, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12305
in-theory        12305
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (C -> ((A and B) and B)))
theorem-size     11
proof            (modus-ponens tm-84 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12305.        ((A and B) -> (C -> ((A and B) and B))), M:tm-84, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-12306
in-theory        12306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-83 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12306.        ((A -> (B -> (C -> B))) and ((D and E) -> ((D and E) and E))), M:tm-83, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12307
in-theory        12307
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B and C) -> ((B and C) and C)))
theorem-size     15
proof            (modus-ponens tm-76 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12307.        (((not (not A)) -> A) and ((B and C) -> ((B and C) and C))), M:tm-76, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12308
in-theory        12308
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A and B))) or (A and B)) -> ((A and B) and B))
theorem-size     15
proof            (modus-ponens tm-73 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12308.        (((not (not (A and B))) or (A and B)) -> ((A and B) and B)), M:tm-73, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-12309
in-theory        12309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and D) -> ((C and D) and D)))
theorem-size     21
proof            (modus-ponens tm-69 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12309.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and D) -> ((C and D) and D))), M:tm-69, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12310
in-theory        12310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> ((D and E) and E)))
theorem-size     23
proof            (modus-ponens tm-54 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12310.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and E) -> ((D and E) and E))), M:tm-54, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12311
in-theory        12311
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> ((B and C) and C))
theorem-size     15
proof            (modus-ponens tm-47 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12311.        (((A and (B and C)) or (B and C)) -> ((B and C) and C)), M:tm-47, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-12312
in-theory        12312
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> ((A and B) and B))
theorem-size     15
proof            (modus-ponens tm-46 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12312.        ((((A and B) and C) or (A and B)) -> ((A and B) and B)), M:tm-46, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-12313
in-theory        12313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C and D) -> ((C and D) and D)))
theorem-size     15
proof            (modus-ponens tm-42 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12313.        ((A -> (B or A)) and ((C and D) -> ((C and D) and D))), M:tm-42, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12314
in-theory        12314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C and D) -> ((C and D) and D)))
theorem-size     15
proof            (modus-ponens tm-32 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12314.        ((A -> (A or B)) and ((C and D) -> ((C and D) and D))), M:tm-32, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12315
in-theory        12315
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> ((A and B) and ((A and B) and B)))
theorem-size     13
proof            (modus-ponens tm-24 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12315.        ((A and B) -> ((A and B) and ((A and B) and B))), M:tm-24, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-12316
in-theory        12316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C and D) -> ((C and D) and D)))
theorem-size     17
proof            (modus-ponens tm-23 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12316.        ((A -> (B -> (A and B))) and ((C and D) -> ((C and D) and D))), M:tm-23, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12317
in-theory        12317
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C and D) -> ((C and D) and D)))
theorem-size     15
proof            (modus-ponens tm-22 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12317.        (((A and B) -> B) and ((C and D) -> ((C and D) and D))), M:tm-22, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12318
in-theory        12318
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C and D) -> ((C and D) and D)))
theorem-size     15
proof            (modus-ponens tm-21 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12318.        (((A and B) -> A) and ((C and D) -> ((C and D) and D))), M:tm-21, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12319
in-theory        12319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> ((D and E) and E)))
theorem-size     23
proof            (modus-ponens tm-20 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12319.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> ((D and E) and E))), M:tm-20, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12320
in-theory        12320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C and D) -> ((C and D) and D)))
theorem-size     15
proof            (modus-ponens tm-19 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12320.        ((A -> (B -> A)) and ((C and D) -> ((C and D) and D))), M:tm-19, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12321
in-theory        12321
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not ((A and B) and B))) -> (not (A and B)))
theorem-size     15
proof            (modus-ponens tm-9 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-9 tm-2 tm-5 tm-4)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12321.        (((A and B) -> (not ((A and B) and B))) -> (not (A and B))), M:tm-9, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-12322
in-theory        12322
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and B) -> C) -> (((A and B) or ((A and B) and B)) -> C))
theorem-size     19
proof            (modus-ponens tm-8 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12322.        ((((A and B) and B) -> C) -> (((A and B) or ((A and B) and B)) -> C)), M:tm-8, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-12323
in-theory        12323
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B and C) -> ((B and C) and C)))
theorem-size     11
proof            (modus-ponens tm-7 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-7 tm-2 tm-5 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12323.        (A or ((B and C) -> ((B and C) and C))), M:tm-7, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12324
in-theory        12324
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) or C)
theorem-size     11
proof            (modus-ponens tm-6 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-6 tm-2 tm-5 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12324.        (((A and B) -> ((A and B) and B)) or C), M:tm-6, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12325
in-theory        12325
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> ((B and C) and C)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12325.        (A -> (((B and C) -> ((B and C) and C)) and A)), M:tm-5, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12326
in-theory        12326
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B and C) -> ((B and C) and C)))
theorem-size     11
proof            (modus-ponens tm-1 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-1 tm-2 tm-5 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12326.        (A -> ((B and C) -> ((B and C) and C))), M:tm-1, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12327
in-theory        12327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((A -> (B -> A)) and C)))
theorem-size     15
proof            (modus-ponens tm-309 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12327.        ((A -> (B -> A)) and (C -> ((A -> (B -> A)) and C))), M:tm-309, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-12328
in-theory        12328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12328.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))), M:tm-309, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-12329
in-theory        12329
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((A and B) -> A) and C)))
theorem-size     15
proof            (modus-ponens tm-309 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-12329.        (((A and B) -> A) and (C -> (((A and B) -> A) and C))), M:tm-309, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-12330
in-theory        12330
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((A and B) -> B) and C)))
theorem-size     15
proof            (modus-ponens tm-309 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-12330.        (((A and B) -> B) and (C -> (((A and B) -> B) and C))), M:tm-309, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-12331
in-theory        12331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((A -> (B -> (A and B))) and C)))
theorem-size     19
proof            (modus-ponens tm-309 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12331.        ((A -> (B -> (A and B))) and (C -> ((A -> (B -> (A and B))) and C))), M:tm-309, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-12332
in-theory        12332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((A -> (A or B)) and C)))
theorem-size     15
proof            (modus-ponens tm-309 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-12332.        ((A -> (A or B)) and (C -> ((A -> (A or B)) and C))), M:tm-309, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-12333
in-theory        12333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((A -> (B or A)) and C)))
theorem-size     15
proof            (modus-ponens tm-309 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-12333.        ((A -> (B or A)) and (C -> ((A -> (B or A)) and C))), M:tm-309, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-12334
in-theory        12334
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12334.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and D))), M:tm-309, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-12335
in-theory        12335
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((A -> B) -> ((A -> (not B)) -> (not A))) and C)))
theorem-size     27
proof            (modus-ponens tm-309 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12335.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((A -> B) -> ((A -> (not B)) -> (not A))) and C))), M:tm-309, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-12336
in-theory        12336
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((not (not A)) -> A) and B)))
theorem-size     15
proof            (modus-ponens tm-309 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-12336.        (((not (not A)) -> A) and (B -> (((not (not A)) -> A) and B))), M:tm-309, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-12337
in-theory        12337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((A -> (B -> (C -> B))) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12337.        ((A -> (B -> (C -> B))) and (D -> ((A -> (B -> (C -> B))) and D))), M:tm-309, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-12338
in-theory        12338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((A -> B) -> (A -> A)) and C)))
theorem-size     19
proof            (modus-ponens tm-309 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-12338.        (((A -> B) -> (A -> A)) and (C -> (((A -> B) -> (A -> A)) and C))), M:tm-309, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-12339
in-theory        12339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and D)))
theorem-size     43
proof            (modus-ponens tm-309 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12339.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and D))), M:tm-309, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-12340
in-theory        12340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12340.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E))), M:tm-309, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-12341
in-theory        12341
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-12341.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and D))), M:tm-309, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-12342
in-theory        12342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((A -> ((B and C) -> B)) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12342.        ((A -> ((B and C) -> B)) and (D -> ((A -> ((B and C) -> B)) and D))), M:tm-309, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-12343
in-theory        12343
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-12343.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and D))), M:tm-309, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-12344
in-theory        12344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((A -> ((B and C) -> C)) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12344.        ((A -> ((B and C) -> C)) and (D -> ((A -> ((B and C) -> C)) and D))), M:tm-309, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-12345
in-theory        12345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((A -> ((B -> (C -> B)) and A)) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12345.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((A -> ((B -> (C -> B)) and A)) and D))), M:tm-309, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-12346
in-theory        12346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12346.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and E))), M:tm-309, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-12347
in-theory        12347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((A -> (((B and C) -> B) and A)) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12347.        ((A -> (((B and C) -> B) and A)) and (D -> ((A -> (((B and C) -> B) and A)) and D))), M:tm-309, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-12348
in-theory        12348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((A -> (((B and C) -> C) and A)) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12348.        ((A -> (((B and C) -> C) and A)) and (D -> ((A -> (((B and C) -> C) and A)) and D))), M:tm-309, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-12349
in-theory        12349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((A -> ((B -> (C -> (B and C))) and A)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12349.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((A -> ((B -> (C -> (B and C))) and A)) and D))), M:tm-309, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-12350
in-theory        12350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((A -> B) -> (A -> (A and B))) and C)))
theorem-size     23
proof            (modus-ponens tm-309 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12350.        (((A -> B) -> (A -> (A and B))) and (C -> (((A -> B) -> (A -> (A and B))) and C))), M:tm-309, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-12351
in-theory        12351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((A -> (B -> (C -> (B and C)))) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12351.        ((A -> (B -> (C -> (B and C)))) and (D -> ((A -> (B -> (C -> (B and C)))) and D))), M:tm-309, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-12352
in-theory        12352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((A -> (B -> A)) or C) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12352.        (((A -> (B -> A)) or C) and (D -> (((A -> (B -> A)) or C) and D))), M:tm-309, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-12353
in-theory        12353
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12353.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and E))), M:tm-309, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-12354
in-theory        12354
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((((A and B) -> A) or C) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12354.        ((((A and B) -> A) or C) and (D -> ((((A and B) -> A) or C) and D))), M:tm-309, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-12355
in-theory        12355
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((((A and B) -> B) or C) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12355.        ((((A and B) -> B) or C) and (D -> ((((A and B) -> B) or C) and D))), M:tm-309, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-12356
in-theory        12356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((A -> (B -> (A and B))) or C) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12356.        (((A -> (B -> (A and B))) or C) and (D -> (((A -> (B -> (A and B))) or C) and D))), M:tm-309, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-12357
in-theory        12357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((A -> (A or B)) or C) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12357.        (((A -> (A or B)) or C) and (D -> (((A -> (A or B)) or C) and D))), M:tm-309, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-12358
in-theory        12358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((A -> ((B -> (B or C)) and A)) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12358.        ((A -> ((B -> (B or C)) and A)) and (D -> ((A -> ((B -> (B or C)) and A)) and D))), M:tm-309, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-12359
in-theory        12359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((A -> (B -> (B or C))) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12359.        ((A -> (B -> (B or C))) and (D -> ((A -> (B -> (B or C))) and D))), M:tm-309, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-12360
in-theory        12360
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((A or (B -> (C -> B))) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12360.        ((A or (B -> (C -> B))) and (D -> ((A or (B -> (C -> B))) and D))), M:tm-309, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-12361
in-theory        12361
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12361.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E))), M:tm-309, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-12362
in-theory        12362
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((A or ((B and C) -> B)) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12362.        ((A or ((B and C) -> B)) and (D -> ((A or ((B and C) -> B)) and D))), M:tm-309, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-12363
in-theory        12363
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((A or ((B and C) -> C)) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12363.        ((A or ((B and C) -> C)) and (D -> ((A or ((B and C) -> C)) and D))), M:tm-309, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-12364
in-theory        12364
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((A or (B -> (C -> (B and C)))) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12364.        ((A or (B -> (C -> (B and C)))) and (D -> ((A or (B -> (C -> (B and C)))) and D))), M:tm-309, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-12365
in-theory        12365
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((A or (B -> (B or C))) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12365.        ((A or (B -> (B or C))) and (D -> ((A or (B -> (B or C))) and D))), M:tm-309, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-12366
in-theory        12366
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((A or (B -> (C or B))) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12366.        ((A or (B -> (C or B))) and (D -> ((A or (B -> (C or B))) and D))), M:tm-309, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-12367
in-theory        12367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((A -> (B or A)) or C) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12367.        (((A -> (B or A)) or C) and (D -> (((A -> (B or A)) or C) and D))), M:tm-309, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-12368
in-theory        12368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((A -> ((B -> (C or B)) and A)) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12368.        ((A -> ((B -> (C or B)) and A)) and (D -> ((A -> ((B -> (C or B)) and A)) and D))), M:tm-309, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-12369
in-theory        12369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((A -> (B -> (C or B))) and D)))
theorem-size     19
proof            (modus-ponens tm-309 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12369.        ((A -> (B -> (C or B))) and (D -> ((A -> (B -> (C or B))) and D))), M:tm-309, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-12370
in-theory        12370
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12370.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and D))), M:tm-309, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-12371
in-theory        12371
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and E)))
theorem-size     55
proof            (modus-ponens tm-309 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12371.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and E))), M:tm-309, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-12372
in-theory        12372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((A -> B) -> (((A and C) or A) -> B)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12372.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((A -> B) -> (((A and C) or A) -> B)) and D))), M:tm-309, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-12373
in-theory        12373
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((A -> B) -> (((C and A) or A) -> B)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12373.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (((A -> B) -> (((C and A) or A) -> B)) and D))), M:tm-309, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-12374
in-theory        12374
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and D)))
theorem-size     39
proof            (modus-ponens tm-309 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12374.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and D))), M:tm-309, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-12375
in-theory        12375
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((A or B) -> C) -> ((A or (A or B)) -> C)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-12375.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> ((((A or B) -> C) -> ((A or (A or B)) -> C)) and D))), M:tm-309, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-12376
in-theory        12376
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((A or B) -> C) -> ((B or (A or B)) -> C)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-12376.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> ((((A or B) -> C) -> ((B or (A or B)) -> C)) and D))), M:tm-309, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-12377
in-theory        12377
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and E)))
theorem-size     59
proof            (modus-ponens tm-309 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-12377.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and E))), M:tm-309, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-12378
in-theory        12378
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12378.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and E))), M:tm-309, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-12379
in-theory        12379
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12379.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and E))), M:tm-309, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-12380
in-theory        12380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (E -> ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12380.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (E -> ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and E))), M:tm-309, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-12381
in-theory        12381
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (D -> ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and D)))
theorem-size     39
proof            (modus-ponens tm-309 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-12381.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (D -> ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and D))), M:tm-309, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-12382
in-theory        12382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12382.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and E))), M:tm-309, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-12383
in-theory        12383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (C -> (((A -> (not (B -> A))) -> (not A)) and C)))
theorem-size     23
proof            (modus-ponens tm-309 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12383.        (((A -> (not (B -> A))) -> (not A)) and (C -> (((A -> (not (B -> A))) -> (not A)) and C))), M:tm-309, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-12384
in-theory        12384
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (D -> ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and D)))
theorem-size     47
proof            (modus-ponens tm-309 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12384.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (D -> ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and D))), M:tm-309, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-12385
in-theory        12385
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (C -> ((((A and B) -> (not A)) -> (not (A and B))) and C)))
theorem-size     27
proof            (modus-ponens tm-309 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12385.        ((((A and B) -> (not A)) -> (not (A and B))) and (C -> ((((A and B) -> (not A)) -> (not (A and B))) and C))), M:tm-309, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-12386
in-theory        12386
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (C -> ((((A and B) -> (not B)) -> (not (A and B))) and C)))
theorem-size     27
proof            (modus-ponens tm-309 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12386.        ((((A and B) -> (not B)) -> (not (A and B))) and (C -> ((((A and B) -> (not B)) -> (not (A and B))) and C))), M:tm-309, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-12387
in-theory        12387
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (C -> (((A -> (not (B -> (A and B)))) -> (not A)) and C)))
theorem-size     27
proof            (modus-ponens tm-309 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12387.        (((A -> (not (B -> (A and B)))) -> (not A)) and (C -> (((A -> (not (B -> (A and B)))) -> (not A)) and C))), M:tm-309, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-12388
in-theory        12388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (C -> (((A -> (not (A or B))) -> (not A)) and C)))
theorem-size     23
proof            (modus-ponens tm-309 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-12388.        (((A -> (not (A or B))) -> (not A)) and (C -> (((A -> (not (A or B))) -> (not A)) and C))), M:tm-309, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-12389
in-theory        12389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (C -> (((A -> (not (B or A))) -> (not A)) and C)))
theorem-size     23
proof            (modus-ponens tm-309 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-12389.        (((A -> (not (B or A))) -> (not A)) and (C -> (((A -> (not (B or A))) -> (not A)) and C))), M:tm-309, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-12390
in-theory        12390
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (D -> ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and D)))
theorem-size     43
proof            (modus-ponens tm-309 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-12390.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (D -> ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and D))), M:tm-309, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-12391
in-theory        12391
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (C -> ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and C)))
theorem-size     39
proof            (modus-ponens tm-309 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-12391.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (C -> ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and C))), M:tm-309, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-12392
in-theory        12392
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (D -> (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and D)))
theorem-size     51
proof            (modus-ponens tm-309 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-12392.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (D -> (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and D))), M:tm-309, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-12393
in-theory        12393
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12393.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and D))), M:tm-309, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-12394
in-theory        12394
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (D -> ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12394.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (D -> ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and D))), M:tm-309, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-12395
in-theory        12395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (D -> ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12395.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (D -> ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and D))), M:tm-309, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-12396
in-theory        12396
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (C -> ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and C)))
theorem-size     35
proof            (modus-ponens tm-309 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-12396.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (C -> ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and C))), M:tm-309, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-12397
in-theory        12397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12397.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and D))), M:tm-309, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-12398
in-theory        12398
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (B -> ((((not (not A)) -> (not A)) -> (not (not (not A)))) and B)))
theorem-size     27
proof            (modus-ponens tm-309 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-9 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-12398.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (B -> ((((not (not A)) -> (not A)) -> (not (not (not A)))) and B))), M:tm-309, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-12399
in-theory        12399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (C -> (((A -> B) -> (((not (not A)) or A) -> B)) and C)))
theorem-size     27
proof            (modus-ponens tm-309 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-12399.        (((A -> B) -> (((not (not A)) or A) -> B)) and (C -> (((A -> B) -> (((not (not A)) or A) -> B)) and C))), M:tm-309, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-12400
in-theory        12400
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and (C -> ((A or ((not (not B)) -> B)) and C)))
theorem-size     19
proof            (modus-ponens tm-309 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12400.        ((A or ((not (not B)) -> B)) and (C -> ((A or ((not (not B)) -> B)) and C))), M:tm-309, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-12401
in-theory        12401
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and (C -> ((((not (not A)) -> A) or B) and C)))
theorem-size     19
proof            (modus-ponens tm-309 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12401.        ((((not (not A)) -> A) or B) and (C -> ((((not (not A)) -> A) or B) and C))), M:tm-309, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-12402
in-theory        12402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (C -> ((A -> (((not (not B)) -> B) and A)) and C)))
theorem-size     23
proof            (modus-ponens tm-309 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12402.        ((A -> (((not (not B)) -> B) and A)) and (C -> ((A -> (((not (not B)) -> B) and A)) and C))), M:tm-309, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-12403
in-theory        12403
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (C -> ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and C)))
theorem-size     35
proof            (modus-ponens tm-309 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-12403.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (C -> ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and C))), M:tm-309, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-12404
in-theory        12404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and (C -> ((A -> ((not (not B)) -> B)) and C)))
theorem-size     19
proof            (modus-ponens tm-309 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12404.        ((A -> ((not (not B)) -> B)) and (C -> ((A -> ((not (not B)) -> B)) and C))), M:tm-309, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-12405
in-theory        12405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (D -> (((A -> (not (B -> (C -> B)))) -> (not A)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12405.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (D -> (((A -> (not (B -> (C -> B)))) -> (not A)) and D))), M:tm-309, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-12406
in-theory        12406
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (E -> ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12406.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (E -> ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and E))), M:tm-309, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-12407
in-theory        12407
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and (E -> ((A or (B -> (C -> (D -> C)))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12407.        ((A or (B -> (C -> (D -> C)))) and (E -> ((A or (B -> (C -> (D -> C)))) and E))), M:tm-309, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-12408
in-theory        12408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and (E -> (((A -> (B -> (C -> B))) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12408.        (((A -> (B -> (C -> B))) or D) and (E -> (((A -> (B -> (C -> B))) or D) and E))), M:tm-309, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-12409
in-theory        12409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and (E -> ((A -> ((B -> (C -> (D -> C))) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12409.        ((A -> ((B -> (C -> (D -> C))) and A)) and (E -> ((A -> ((B -> (C -> (D -> C))) and A)) and E))), M:tm-309, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-12410
in-theory        12410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (D -> (((A -> B) -> (A -> (C -> B))) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-12410.        (((A -> B) -> (A -> (C -> B))) and (D -> (((A -> B) -> (A -> (C -> B))) and D))), M:tm-309, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-12411
in-theory        12411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (E -> ((A -> (B -> (C -> (D -> C)))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12411.        ((A -> (B -> (C -> (D -> C)))) and (E -> ((A -> (B -> (C -> (D -> C)))) and E))), M:tm-309, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-12412
in-theory        12412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and (B -> ((A -> A) and B)))
theorem-size     11
proof            (modus-ponens tm-309 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12412.        ((A -> A) and (B -> ((A -> A) and B))), M:tm-309, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-12413
in-theory        12413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (D -> (((A -> (B -> C)) -> (A -> (B -> C))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12413.        (((A -> (B -> C)) -> (A -> (B -> C))) and (D -> (((A -> (B -> C)) -> (A -> (B -> C))) and D))), M:tm-309, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-12414
in-theory        12414
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and (C -> (((A and B) -> (A and B)) and C)))
theorem-size     19
proof            (modus-ponens tm-309 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12414.        (((A and B) -> (A and B)) and (C -> (((A and B) -> (A and B)) and C))), M:tm-309, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-12415
in-theory        12415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (C -> (((A -> B) -> (A -> B)) and C)))
theorem-size     19
proof            (modus-ponens tm-309 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-12415.        (((A -> B) -> (A -> B)) and (C -> (((A -> B) -> (A -> B)) and C))), M:tm-309, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-12416
in-theory        12416
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and (B -> (((not (not A)) -> (not (not A))) and B)))
theorem-size     19
proof            (modus-ponens tm-309 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-12416.        (((not (not A)) -> (not (not A))) and (B -> (((not (not A)) -> (not (not A))) and B))), M:tm-309, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-12417
in-theory        12417
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (C -> ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and C)))
theorem-size     31
proof            (modus-ponens tm-309 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-12417.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (C -> ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and C))), M:tm-309, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-12418
in-theory        12418
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (D -> ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-12418.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (D -> ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and D))), M:tm-309, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-12419
in-theory        12419
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and (D -> ((A or ((B -> C) -> (B -> B))) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12419.        ((A or ((B -> C) -> (B -> B))) and (D -> ((A or ((B -> C) -> (B -> B))) and D))), M:tm-309, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-12420
in-theory        12420
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and (D -> ((((A -> B) -> (A -> A)) or C) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12420.        ((((A -> B) -> (A -> A)) or C) and (D -> ((((A -> B) -> (A -> A)) or C) and D))), M:tm-309, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-12421
in-theory        12421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (D -> ((A -> (((B -> C) -> (B -> B)) and A)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12421.        ((A -> (((B -> C) -> (B -> B)) and A)) and (D -> ((A -> (((B -> C) -> (B -> B)) and A)) and D))), M:tm-309, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-12422
in-theory        12422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and (C -> ((((A -> B) -> A) -> ((A -> B) -> A)) and C)))
theorem-size     27
proof            (modus-ponens tm-309 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-12422.        ((((A -> B) -> A) -> ((A -> B) -> A)) and (C -> ((((A -> B) -> A) -> ((A -> B) -> A)) and C))), M:tm-309, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-12423
in-theory        12423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and (D -> ((A -> ((B -> C) -> (B -> B))) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12423.        ((A -> ((B -> C) -> (B -> B))) and (D -> ((A -> ((B -> C) -> (B -> B))) and D))), M:tm-309, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-12424
in-theory        12424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (D -> (((A -> ((B -> A) -> C)) -> (A -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-12424.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (D -> (((A -> ((B -> A) -> C)) -> (A -> C)) and D))), M:tm-309, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-12425
in-theory        12425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (C -> (((A -> (A -> B)) -> (A -> B)) and C)))
theorem-size     23
proof            (modus-ponens tm-309 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-12425.        (((A -> (A -> B)) -> (A -> B)) and (C -> (((A -> (A -> B)) -> (A -> B)) and C))), M:tm-309, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-12426
in-theory        12426
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (D -> ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and D)))
theorem-size     43
proof            (modus-ponens tm-309 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-12426.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (D -> ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and D))), M:tm-309, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-12427
in-theory        12427
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (D -> (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and D)))
theorem-size     67
proof            (modus-ponens tm-309 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-12427.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (D -> (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and D))), M:tm-309, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-12428
in-theory        12428
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (E -> (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and E)))
theorem-size     71
proof            (modus-ponens tm-309 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-12428.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (E -> (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and E))), M:tm-309, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-12429
in-theory        12429
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12429.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and E))), M:tm-309, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-12430
in-theory        12430
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (E -> (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12430.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (E -> (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and E))), M:tm-309, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-12431
in-theory        12431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (E -> ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and E)))
theorem-size     51
proof            (modus-ponens tm-309 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12431.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (E -> ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and E))), M:tm-309, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-12432
in-theory        12432
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (D -> (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and D)))
theorem-size     63
proof            (modus-ponens tm-309 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-12432.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (D -> (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and D))), M:tm-309, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-12433
in-theory        12433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12433.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and E))), M:tm-309, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-12434
in-theory        12434
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (E -> ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and E)))
theorem-size     51
proof            (modus-ponens tm-309 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-12434.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (E -> ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and E))), M:tm-309, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-12435
in-theory        12435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (E -> (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12435.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (E -> (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and E))), M:tm-309, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-12436
in-theory        12436
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (F -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and F)))
theorem-size     71
proof            (modus-ponens tm-309 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12436.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (F -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and F))), M:tm-309, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-12437
in-theory        12437
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12437.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F))), M:tm-309, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-12438
in-theory        12438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12438.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and F))), M:tm-309, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-12439
in-theory        12439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12439.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and F))), M:tm-309, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-12440
in-theory        12440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (E -> (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-12440.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (E -> (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and E))), M:tm-309, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-12441
in-theory        12441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12441.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F))), M:tm-309, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-12442
in-theory        12442
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and (C -> ((((A -> B) and A) -> B) and C)))
theorem-size     19
proof            (modus-ponens tm-309 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-12442.        ((((A -> B) and A) -> B) and (C -> ((((A -> B) and A) -> B) and C))), M:tm-309, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-12443
in-theory        12443
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and (E -> (((((A -> (B -> A)) -> C) and D) -> C) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-12443.        (((((A -> (B -> A)) -> C) and D) -> C) and (E -> (((((A -> (B -> A)) -> C) and D) -> C) and E))), M:tm-309, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-12444
in-theory        12444
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (F -> ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12444.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (F -> ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and F))), M:tm-309, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-12445
in-theory        12445
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (D -> ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and D)))
theorem-size     47
proof            (modus-ponens tm-309 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-12445.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (D -> ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and D))), M:tm-309, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-12446
in-theory        12446
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (D -> (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-12446.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (D -> (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and D))), M:tm-309, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-12447
in-theory        12447
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (D -> ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and D)))
theorem-size     55
proof            (modus-ponens tm-309 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-12447.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (D -> ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and D))), M:tm-309, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-12448
in-theory        12448
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (E -> ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and E)))
theorem-size     59
proof            (modus-ponens tm-309 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-12448.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (E -> ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and E))), M:tm-309, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-12449
in-theory        12449
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12449.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and E))), M:tm-309, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-12450
in-theory        12450
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (E -> ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12450.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (E -> ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and E))), M:tm-309, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-12451
in-theory        12451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (E -> ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12451.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (E -> ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and E))), M:tm-309, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-12452
in-theory        12452
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (D -> ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and D)))
theorem-size     51
proof            (modus-ponens tm-309 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-12452.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (D -> ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and D))), M:tm-309, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-12453
in-theory        12453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12453.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and E))), M:tm-309, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-12454
in-theory        12454
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and (E -> ((((((A and B) -> A) -> C) and D) -> C) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-12454.        ((((((A and B) -> A) -> C) and D) -> C) and (E -> ((((((A and B) -> A) -> C) and D) -> C) and E))), M:tm-309, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-12455
in-theory        12455
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (D -> ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-12455.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (D -> ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and D))), M:tm-309, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-12456
in-theory        12456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (D -> (((A -> (not ((B and C) -> B))) -> (not A)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12456.        (((A -> (not ((B and C) -> B))) -> (not A)) and (D -> (((A -> (not ((B and C) -> B))) -> (not A)) and D))), M:tm-309, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-12457
in-theory        12457
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (E -> (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12457.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (E -> (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and E))), M:tm-309, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-12458
in-theory        12458
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and (E -> ((A or (B -> ((C and D) -> C))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12458.        ((A or (B -> ((C and D) -> C))) and (E -> ((A or (B -> ((C and D) -> C))) and E))), M:tm-309, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-12459
in-theory        12459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and (E -> (((A -> ((B and C) -> B)) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12459.        (((A -> ((B and C) -> B)) or D) and (E -> (((A -> ((B and C) -> B)) or D) and E))), M:tm-309, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-12460
in-theory        12460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and (E -> ((A -> ((B -> ((C and D) -> C)) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12460.        ((A -> ((B -> ((C and D) -> C)) and A)) and (E -> ((A -> ((B -> ((C and D) -> C)) and A)) and E))), M:tm-309, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-12461
in-theory        12461
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (D -> (((A -> (B and C)) -> (A -> B)) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-12461.        (((A -> (B and C)) -> (A -> B)) and (D -> (((A -> (B and C)) -> (A -> B)) and D))), M:tm-309, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-12462
in-theory        12462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (E -> ((A -> (B -> ((C and D) -> C))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12462.        ((A -> (B -> ((C and D) -> C))) and (E -> ((A -> (B -> ((C and D) -> C))) and E))), M:tm-309, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-12463
in-theory        12463
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and (C -> (((A and (A -> B)) -> B) and C)))
theorem-size     19
proof            (modus-ponens tm-309 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-12463.        (((A and (A -> B)) -> B) and (C -> (((A and (A -> B)) -> B) and C))), M:tm-309, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-12464
in-theory        12464
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and (E -> (((A and ((B -> (C -> B)) -> D)) -> D) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-12464.        (((A and ((B -> (C -> B)) -> D)) -> D) and (E -> (((A and ((B -> (C -> B)) -> D)) -> D) and E))), M:tm-309, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-12465
in-theory        12465
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (F -> (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12465.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (F -> (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and F))), M:tm-309, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-12466
in-theory        12466
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and (E -> (((A and (((B and C) -> B) -> D)) -> D) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-12466.        (((A and (((B and C) -> B) -> D)) -> D) and (E -> (((A and (((B and C) -> B) -> D)) -> D) and E))), M:tm-309, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-12467
in-theory        12467
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (D -> ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and D)))
theorem-size     47
proof            (modus-ponens tm-309 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-12467.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (D -> ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and D))), M:tm-309, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-12468
in-theory        12468
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (D -> ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-12468.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (D -> ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and D))), M:tm-309, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-12469
in-theory        12469
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (D -> (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and D)))
theorem-size     55
proof            (modus-ponens tm-309 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-12469.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (D -> (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and D))), M:tm-309, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-12470
in-theory        12470
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (E -> (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and E)))
theorem-size     59
proof            (modus-ponens tm-309 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-12470.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (E -> (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and E))), M:tm-309, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-12471
in-theory        12471
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12471.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and E))), M:tm-309, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-12472
in-theory        12472
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (E -> (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12472.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (E -> (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and E))), M:tm-309, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-12473
in-theory        12473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (E -> ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12473.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (E -> ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and E))), M:tm-309, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-12474
in-theory        12474
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (D -> (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and D)))
theorem-size     51
proof            (modus-ponens tm-309 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-12474.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (D -> (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and D))), M:tm-309, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-12475
in-theory        12475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12475.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and E))), M:tm-309, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-12476
in-theory        12476
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and (E -> (((A and (((B and C) -> C) -> D)) -> D) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-12476.        (((A and (((B and C) -> C) -> D)) -> D) and (E -> (((A and (((B and C) -> C) -> D)) -> D) and E))), M:tm-309, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-12477
in-theory        12477
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and (E -> ((((((A and B) -> B) -> C) and D) -> C) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-12477.        ((((((A and B) -> B) -> C) and D) -> C) and (E -> ((((((A and B) -> B) -> C) and D) -> C) and E))), M:tm-309, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-12478
in-theory        12478
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (D -> ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-12478.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (D -> ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and D))), M:tm-309, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-12479
in-theory        12479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (D -> (((A -> (not ((B and C) -> C))) -> (not A)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12479.        (((A -> (not ((B and C) -> C))) -> (not A)) and (D -> (((A -> (not ((B and C) -> C))) -> (not A)) and D))), M:tm-309, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-12480
in-theory        12480
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (E -> (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12480.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (E -> (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and E))), M:tm-309, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-12481
in-theory        12481
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and (E -> ((A or (B -> ((C and D) -> D))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12481.        ((A or (B -> ((C and D) -> D))) and (E -> ((A or (B -> ((C and D) -> D))) and E))), M:tm-309, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-12482
in-theory        12482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and (E -> (((A -> ((B and C) -> C)) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12482.        (((A -> ((B and C) -> C)) or D) and (E -> (((A -> ((B and C) -> C)) or D) and E))), M:tm-309, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-12483
in-theory        12483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and (E -> ((A -> ((B -> ((C and D) -> D)) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12483.        ((A -> ((B -> ((C and D) -> D)) and A)) and (E -> ((A -> ((B -> ((C and D) -> D)) and A)) and E))), M:tm-309, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-12484
in-theory        12484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (D -> (((A -> (B and C)) -> (A -> C)) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-12484.        (((A -> (B and C)) -> (A -> C)) and (D -> (((A -> (B and C)) -> (A -> C)) and D))), M:tm-309, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-12485
in-theory        12485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (E -> ((A -> (B -> ((C and D) -> D))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12485.        ((A -> (B -> ((C and D) -> D))) and (E -> ((A -> (B -> ((C and D) -> D))) and E))), M:tm-309, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-12486
in-theory        12486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and (E -> (((A -> (B -> A)) and (C -> (D -> C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12486.        (((A -> (B -> A)) and (C -> (D -> C))) and (E -> (((A -> (B -> A)) and (C -> (D -> C))) and E))), M:tm-309, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-12487
in-theory        12487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12487.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F))), M:tm-309, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-12488
in-theory        12488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and (E -> (((A -> (B -> A)) and ((C and D) -> C)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12488.        (((A -> (B -> A)) and ((C and D) -> C)) and (E -> (((A -> (B -> A)) and ((C and D) -> C)) and E))), M:tm-309, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-12489
in-theory        12489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and (E -> (((A -> (B -> A)) and ((C and D) -> D)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12489.        (((A -> (B -> A)) and ((C and D) -> D)) and (E -> (((A -> (B -> A)) and ((C and D) -> D)) and E))), M:tm-309, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-12490
in-theory        12490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (E -> (((A -> (B -> A)) and (C -> (D -> (C and D)))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12490.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (E -> (((A -> (B -> A)) and (C -> (D -> (C and D)))) and E))), M:tm-309, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-12491
in-theory        12491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and (E -> (((A -> (B -> A)) and (C -> (C or D))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12491.        (((A -> (B -> A)) and (C -> (C or D))) and (E -> (((A -> (B -> A)) and (C -> (C or D))) and E))), M:tm-309, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-12492
in-theory        12492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and (E -> (((A -> (B -> A)) and (C -> (D or C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12492.        (((A -> (B -> A)) and (C -> (D or C))) and (E -> (((A -> (B -> A)) and (C -> (D or C))) and E))), M:tm-309, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-12493
in-theory        12493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12493.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and F))), M:tm-309, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-12494
in-theory        12494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12494.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and E))), M:tm-309, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-12495
in-theory        12495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and (D -> (((A -> (B -> A)) and ((not (not C)) -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12495.        (((A -> (B -> A)) and ((not (not C)) -> C)) and (D -> (((A -> (B -> A)) and ((not (not C)) -> C)) and D))), M:tm-309, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-12496
in-theory        12496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (F -> (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12496.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (F -> (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and F))), M:tm-309, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-12497
in-theory        12497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (E -> (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12497.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (E -> (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and E))), M:tm-309, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-12498
in-theory        12498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and F)))
theorem-size     55
proof            (modus-ponens tm-309 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12498.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and F))), M:tm-309, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-12499
in-theory        12499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12499.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G))), M:tm-309, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-12500
in-theory        12500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12500.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and F))), M:tm-309, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-12501
in-theory        12501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (F -> (((A -> (B -> A)) and (C -> ((D and E) -> D))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12501.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (F -> (((A -> (B -> A)) and (C -> ((D and E) -> D))) and F))), M:tm-309, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-12502
in-theory        12502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12502.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and F))), M:tm-309, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-12503
in-theory        12503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (F -> (((A -> (B -> A)) and (C -> ((D and E) -> E))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12503.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (F -> (((A -> (B -> A)) and (C -> ((D and E) -> E))) and F))), M:tm-309, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-12504
in-theory        12504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12504.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and F))), M:tm-309, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-12505
in-theory        12505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (D -> (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12505.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (D -> (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and D))), M:tm-309, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-12506
in-theory        12506
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (E -> (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12506.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (E -> (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and E))), M:tm-309, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-12507
in-theory        12507
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and (E -> ((A or (B -> ((C -> (D -> C)) and B))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12507.        ((A or (B -> ((C -> (D -> C)) and B))) and (E -> ((A or (B -> ((C -> (D -> C)) and B))) and E))), M:tm-309, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-12508
in-theory        12508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and (E -> (((A -> ((B -> (C -> B)) and A)) or D) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12508.        (((A -> ((B -> (C -> B)) and A)) or D) and (E -> (((A -> ((B -> (C -> B)) and A)) or D) and E))), M:tm-309, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-12509
in-theory        12509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (E -> ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12509.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (E -> ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and E))), M:tm-309, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-12510
in-theory        12510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (E -> ((A -> (B -> ((C -> (D -> C)) and B))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12510.        ((A -> (B -> ((C -> (D -> C)) and B))) and (E -> ((A -> (B -> ((C -> (D -> C)) and B))) and E))), M:tm-309, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-12511
in-theory        12511
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12511.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and F))), M:tm-309, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-12512
in-theory        12512
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and G)))
theorem-size     59
proof            (modus-ponens tm-309 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12512.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and G))), M:tm-309, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-12513
in-theory        12513
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12513.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and F))), M:tm-309, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-12514
in-theory        12514
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12514.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and F))), M:tm-309, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-12515
in-theory        12515
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12515.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and F))), M:tm-309, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-12516
in-theory        12516
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12516.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and F))), M:tm-309, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-12517
in-theory        12517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12517.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and F))), M:tm-309, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-12518
in-theory        12518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and G)))
theorem-size     59
proof            (modus-ponens tm-309 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12518.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and G))), M:tm-309, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-12519
in-theory        12519
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and F)))
theorem-size     55
proof            (modus-ponens tm-309 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12519.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and F))), M:tm-309, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-12520
in-theory        12520
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (E -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12520.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (E -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and E))), M:tm-309, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-12521
in-theory        12521
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12521.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and G))), M:tm-309, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-12522
in-theory        12522
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12522.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and F))), M:tm-309, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-12523
in-theory        12523
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and G)))
theorem-size     71
proof            (modus-ponens tm-309 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12523.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and G))), M:tm-309, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-12524
in-theory        12524
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and H)))
theorem-size     63
proof            (modus-ponens tm-309 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12524.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and H))), M:tm-309, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-12525
in-theory        12525
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and G)))
theorem-size     63
proof            (modus-ponens tm-309 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12525.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and G))), M:tm-309, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-12526
in-theory        12526
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12526.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and G))), M:tm-309, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-12527
in-theory        12527
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and G)))
theorem-size     63
proof            (modus-ponens tm-309 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12527.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and G))), M:tm-309, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-12528
in-theory        12528
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12528.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and G))), M:tm-309, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-12529
in-theory        12529
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12529.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and G))), M:tm-309, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-12530
in-theory        12530
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and H)))
theorem-size     67
proof            (modus-ponens tm-309 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12530.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and H))), M:tm-309, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-12531
in-theory        12531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12531.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and G))), M:tm-309, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-12532
in-theory        12532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (E -> (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-12532.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (E -> (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and E))), M:tm-309, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-12533
in-theory        12533
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (F -> ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and F)))
theorem-size     79
proof            (modus-ponens tm-309 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-12533.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (F -> ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and F))), M:tm-309, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-12534
in-theory        12534
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12534.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and F))), M:tm-309, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-12535
in-theory        12535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (F -> (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12535.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (F -> (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and F))), M:tm-309, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-12536
in-theory        12536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (F -> ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12536.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (F -> ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and F))), M:tm-309, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-12537
in-theory        12537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12537.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and F))), M:tm-309, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-12538
in-theory        12538
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and (E -> ((((A and B) -> A) and (C -> (D -> C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12538.        ((((A and B) -> A) and (C -> (D -> C))) and (E -> ((((A and B) -> A) and (C -> (D -> C))) and E))), M:tm-309, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-12539
in-theory        12539
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12539.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F))), M:tm-309, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-12540
in-theory        12540
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and (E -> ((((A and B) -> A) and ((C and D) -> C)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12540.        ((((A and B) -> A) and ((C and D) -> C)) and (E -> ((((A and B) -> A) and ((C and D) -> C)) and E))), M:tm-309, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-12541
in-theory        12541
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and (E -> ((((A and B) -> A) and ((C and D) -> D)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12541.        ((((A and B) -> A) and ((C and D) -> D)) and (E -> ((((A and B) -> A) and ((C and D) -> D)) and E))), M:tm-309, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-12542
in-theory        12542
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and (E -> ((((A and B) -> A) and (C -> (D -> (C and D)))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12542.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and (E -> ((((A and B) -> A) and (C -> (D -> (C and D)))) and E))), M:tm-309, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-12543
in-theory        12543
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and (E -> ((((A and B) -> A) and (C -> (C or D))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12543.        ((((A and B) -> A) and (C -> (C or D))) and (E -> ((((A and B) -> A) and (C -> (C or D))) and E))), M:tm-309, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-12544
in-theory        12544
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and (E -> ((((A and B) -> A) and (C -> (D or C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12544.        ((((A and B) -> A) and (C -> (D or C))) and (E -> ((((A and B) -> A) and (C -> (D or C))) and E))), M:tm-309, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-12545
in-theory        12545
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12545.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and F))), M:tm-309, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-12546
in-theory        12546
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12546.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and E))), M:tm-309, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-12547
in-theory        12547
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and (D -> ((((A and B) -> A) and ((not (not C)) -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-10)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12547.        ((((A and B) -> A) and ((not (not C)) -> C)) and (D -> ((((A and B) -> A) and ((not (not C)) -> C)) and D))), M:tm-309, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-12548
in-theory        12548
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (F -> ((((A and B) -> A) and (C -> (D -> (E -> D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12548.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (F -> ((((A and B) -> A) and (C -> (D -> (E -> D)))) and F))), M:tm-309, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-12549
in-theory        12549
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (E -> ((((A and B) -> A) and ((C -> D) -> (C -> C))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12549.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (E -> ((((A and B) -> A) and ((C -> D) -> (C -> C))) and E))), M:tm-309, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-12550
in-theory        12550
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and F)))
theorem-size     55
proof            (modus-ponens tm-309 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12550.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and F))), M:tm-309, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-12551
in-theory        12551
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12551.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G))), M:tm-309, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-12552
in-theory        12552
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12552.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and F))), M:tm-309, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-12553
in-theory        12553
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and (F -> ((((A and B) -> A) and (C -> ((D and E) -> D))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12553.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and (F -> ((((A and B) -> A) and (C -> ((D and E) -> D))) and F))), M:tm-309, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-12554
in-theory        12554
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12554.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and F))), M:tm-309, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-12555
in-theory        12555
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and (F -> ((((A and B) -> A) and (C -> ((D and E) -> E))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12555.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and (F -> ((((A and B) -> A) and (C -> ((D and E) -> E))) and F))), M:tm-309, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-12556
in-theory        12556
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (F -> ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12556.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (F -> ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and F))), M:tm-309, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-12557
in-theory        12557
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12557.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and G))), M:tm-309, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-12558
in-theory        12558
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (F -> ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12558.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (F -> ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and F))), M:tm-309, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-12559
in-theory        12559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12559.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and G))), M:tm-309, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-12560
in-theory        12560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (F -> (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12560.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (F -> (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and F))), M:tm-309, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-12561
in-theory        12561
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (D -> (((A -> (not (((B and C) -> B) and A))) -> (not A)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-12561.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (D -> (((A -> (not (((B and C) -> B) and A))) -> (not A)) and D))), M:tm-309, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-12562
in-theory        12562
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (E -> ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-12562.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (E -> ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and E))), M:tm-309, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-12563
in-theory        12563
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and (E -> ((A or (B -> (((C and D) -> C) and B))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12563.        ((A or (B -> (((C and D) -> C) and B))) and (E -> ((A or (B -> (((C and D) -> C) and B))) and E))), M:tm-309, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-12564
in-theory        12564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and (E -> (((A -> (((B and C) -> B) and A)) or D) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12564.        (((A -> (((B and C) -> B) and A)) or D) and (E -> (((A -> (((B and C) -> B) and A)) or D) and E))), M:tm-309, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-12565
in-theory        12565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (E -> ((A -> ((B -> (((C and D) -> C) and B)) and A)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12565.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (E -> ((A -> ((B -> (((C and D) -> C) and B)) and A)) and E))), M:tm-309, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-12566
in-theory        12566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (E -> ((A -> (B -> (((C and D) -> C) and B))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12566.        ((A -> (B -> (((C and D) -> C) and B))) and (E -> ((A -> (B -> (((C and D) -> C) and B))) and E))), M:tm-309, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-12567
in-theory        12567
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and (E -> ((((A and B) -> B) and (C -> (D -> C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12567.        ((((A and B) -> B) and (C -> (D -> C))) and (E -> ((((A and B) -> B) and (C -> (D -> C))) and E))), M:tm-309, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-12568
in-theory        12568
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12568.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F))), M:tm-309, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-12569
in-theory        12569
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and (E -> ((((A and B) -> B) and ((C and D) -> C)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12569.        ((((A and B) -> B) and ((C and D) -> C)) and (E -> ((((A and B) -> B) and ((C and D) -> C)) and E))), M:tm-309, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-12570
in-theory        12570
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and (E -> ((((A and B) -> B) and ((C and D) -> D)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12570.        ((((A and B) -> B) and ((C and D) -> D)) and (E -> ((((A and B) -> B) and ((C and D) -> D)) and E))), M:tm-309, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-12571
in-theory        12571
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and (E -> ((((A and B) -> B) and (C -> (D -> (C and D)))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12571.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and (E -> ((((A and B) -> B) and (C -> (D -> (C and D)))) and E))), M:tm-309, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-12572
in-theory        12572
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and (E -> ((((A and B) -> B) and (C -> (C or D))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12572.        ((((A and B) -> B) and (C -> (C or D))) and (E -> ((((A and B) -> B) and (C -> (C or D))) and E))), M:tm-309, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-12573
in-theory        12573
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and (E -> ((((A and B) -> B) and (C -> (D or C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12573.        ((((A and B) -> B) and (C -> (D or C))) and (E -> ((((A and B) -> B) and (C -> (D or C))) and E))), M:tm-309, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-12574
in-theory        12574
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12574.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and F))), M:tm-309, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-12575
in-theory        12575
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12575.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and E))), M:tm-309, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-12576
in-theory        12576
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and (D -> ((((A and B) -> B) and ((not (not C)) -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-10)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12576.        ((((A and B) -> B) and ((not (not C)) -> C)) and (D -> ((((A and B) -> B) and ((not (not C)) -> C)) and D))), M:tm-309, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-12577
in-theory        12577
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (F -> ((((A and B) -> B) and (C -> (D -> (E -> D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12577.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (F -> ((((A and B) -> B) and (C -> (D -> (E -> D)))) and F))), M:tm-309, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-12578
in-theory        12578
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (E -> ((((A and B) -> B) and ((C -> D) -> (C -> C))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12578.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (E -> ((((A and B) -> B) and ((C -> D) -> (C -> C))) and E))), M:tm-309, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-12579
in-theory        12579
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and F)))
theorem-size     55
proof            (modus-ponens tm-309 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12579.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and F))), M:tm-309, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-12580
in-theory        12580
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12580.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G))), M:tm-309, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-12581
in-theory        12581
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12581.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and F))), M:tm-309, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-12582
in-theory        12582
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and (F -> ((((A and B) -> B) and (C -> ((D and E) -> D))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12582.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and (F -> ((((A and B) -> B) and (C -> ((D and E) -> D))) and F))), M:tm-309, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-12583
in-theory        12583
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12583.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and F))), M:tm-309, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-12584
in-theory        12584
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and (F -> ((((A and B) -> B) and (C -> ((D and E) -> E))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12584.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and (F -> ((((A and B) -> B) and (C -> ((D and E) -> E))) and F))), M:tm-309, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-12585
in-theory        12585
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (F -> ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12585.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (F -> ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and F))), M:tm-309, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-12586
in-theory        12586
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12586.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and G))), M:tm-309, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-12587
in-theory        12587
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (F -> ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12587.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (F -> ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and F))), M:tm-309, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-12588
in-theory        12588
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (F -> ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12588.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (F -> ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and F))), M:tm-309, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-12589
in-theory        12589
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (F -> ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12589.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (F -> ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and F))), M:tm-309, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-12590
in-theory        12590
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12590.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and G))), M:tm-309, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-12591
in-theory        12591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (F -> (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12591.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (F -> (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and F))), M:tm-309, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-12592
in-theory        12592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (D -> (((A -> (not (((B and C) -> C) and A))) -> (not A)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-12592.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (D -> (((A -> (not (((B and C) -> C) and A))) -> (not A)) and D))), M:tm-309, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-12593
in-theory        12593
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (E -> ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-12593.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (E -> ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and E))), M:tm-309, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-12594
in-theory        12594
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and (E -> ((A or (B -> (((C and D) -> D) and B))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12594.        ((A or (B -> (((C and D) -> D) and B))) and (E -> ((A or (B -> (((C and D) -> D) and B))) and E))), M:tm-309, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-12595
in-theory        12595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and (E -> (((A -> (((B and C) -> C) and A)) or D) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12595.        (((A -> (((B and C) -> C) and A)) or D) and (E -> (((A -> (((B and C) -> C) and A)) or D) and E))), M:tm-309, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-12596
in-theory        12596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (E -> ((A -> ((B -> (((C and D) -> D) and B)) and A)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12596.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (E -> ((A -> ((B -> (((C and D) -> D) and B)) and A)) and E))), M:tm-309, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-12597
in-theory        12597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (E -> ((A -> (B -> (((C and D) -> D) and B))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12597.        ((A -> (B -> (((C and D) -> D) and B))) and (E -> ((A -> (B -> (((C and D) -> D) and B))) and E))), M:tm-309, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-12598
in-theory        12598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and (E -> (((A -> (B -> (A and B))) and (C -> (D -> C))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12598.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and (E -> (((A -> (B -> (A and B))) and (C -> (D -> C))) and E))), M:tm-309, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-12599
in-theory        12599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12599.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F))), M:tm-309, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-12600
in-theory        12600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and (E -> (((A -> (B -> (A and B))) and ((C and D) -> C)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12600.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and (E -> (((A -> (B -> (A and B))) and ((C and D) -> C)) and E))), M:tm-309, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-12601
in-theory        12601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and (E -> (((A -> (B -> (A and B))) and ((C and D) -> D)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12601.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and (E -> (((A -> (B -> (A and B))) and ((C and D) -> D)) and E))), M:tm-309, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-12602
in-theory        12602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (E -> (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12602.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (E -> (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and E))), M:tm-309, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-12603
in-theory        12603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and (E -> (((A -> (B -> (A and B))) and (C -> (C or D))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12603.        (((A -> (B -> (A and B))) and (C -> (C or D))) and (E -> (((A -> (B -> (A and B))) and (C -> (C or D))) and E))), M:tm-309, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-12604
in-theory        12604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and (E -> (((A -> (B -> (A and B))) and (C -> (D or C))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12604.        (((A -> (B -> (A and B))) and (C -> (D or C))) and (E -> (((A -> (B -> (A and B))) and (C -> (D or C))) and E))), M:tm-309, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-12605
in-theory        12605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12605.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and F))), M:tm-309, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-12606
in-theory        12606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12606.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and E))), M:tm-309, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-12607
in-theory        12607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (D -> (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12607.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (D -> (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and D))), M:tm-309, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-12608
in-theory        12608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (F -> (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12608.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (F -> (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and F))), M:tm-309, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-12609
in-theory        12609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (E -> (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12609.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (E -> (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and E))), M:tm-309, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-12610
in-theory        12610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and F)))
theorem-size     59
proof            (modus-ponens tm-309 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12610.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and F))), M:tm-309, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-12611
in-theory        12611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12611.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G))), M:tm-309, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-12612
in-theory        12612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and F)))
theorem-size     51
proof            (modus-ponens tm-309 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12612.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and F))), M:tm-309, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-12613
in-theory        12613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (F -> (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12613.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (F -> (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and F))), M:tm-309, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-12614
in-theory        12614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and F)))
theorem-size     51
proof            (modus-ponens tm-309 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12614.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and F))), M:tm-309, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-12615
in-theory        12615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (F -> (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12615.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (F -> (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and F))), M:tm-309, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-12616
in-theory        12616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (F -> (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12616.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (F -> (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and F))), M:tm-309, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-12617
in-theory        12617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and G)))
theorem-size     55
proof            (modus-ponens tm-309 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12617.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and G))), M:tm-309, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-12618
in-theory        12618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (F -> (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12618.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (F -> (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and F))), M:tm-309, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-12619
in-theory        12619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (F -> (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12619.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (F -> (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and F))), M:tm-309, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-12620
in-theory        12620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12620.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and F))), M:tm-309, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-12621
in-theory        12621
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12621.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and F))), M:tm-309, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-12622
in-theory        12622
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12622.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and F))), M:tm-309, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-12623
in-theory        12623
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and G)))
theorem-size     55
proof            (modus-ponens tm-309 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12623.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and G))), M:tm-309, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-12624
in-theory        12624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12624.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and F))), M:tm-309, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-12625
in-theory        12625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (D -> (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-12625.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (D -> (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and D))), M:tm-309, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-12626
in-theory        12626
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (E -> (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and E)))
theorem-size     55
proof            (modus-ponens tm-309 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-12626.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (E -> (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and E))), M:tm-309, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-12627
in-theory        12627
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and (E -> ((A or (B -> ((C -> (D -> (C and D))) and B))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12627.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and (E -> ((A or (B -> ((C -> (D -> (C and D))) and B))) and E))), M:tm-309, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-12628
in-theory        12628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and (E -> (((A -> ((B -> (C -> (B and C))) and A)) or D) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12628.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and (E -> (((A -> ((B -> (C -> (B and C))) and A)) or D) and E))), M:tm-309, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-12629
in-theory        12629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (E -> ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12629.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (E -> ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and E))), M:tm-309, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-12630
in-theory        12630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (E -> ((A -> (B -> ((C -> (D -> (C and D))) and B))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12630.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (E -> ((A -> (B -> ((C -> (D -> (C and D))) and B))) and E))), M:tm-309, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-12631
in-theory        12631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (C -> ((A -> (A and (B -> A))) and C)))
theorem-size     19
proof            (modus-ponens tm-309 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12631.        ((A -> (A and (B -> A))) and (C -> ((A -> (A and (B -> A))) and C))), M:tm-309, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-12632
in-theory        12632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (D -> (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and D)))
theorem-size     43
proof            (modus-ponens tm-309 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12632.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (D -> (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and D))), M:tm-309, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-12633
in-theory        12633
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and (C -> (((A and B) -> ((A and B) and A)) and C)))
theorem-size     23
proof            (modus-ponens tm-309 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12633.        (((A and B) -> ((A and B) and A)) and (C -> (((A and B) -> ((A and B) and A)) and C))), M:tm-309, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12634
in-theory        12634
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and (C -> (((A and B) -> ((A and B) and B)) and C)))
theorem-size     23
proof            (modus-ponens tm-309 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12634.        (((A and B) -> ((A and B) and B)) and (C -> (((A and B) -> ((A and B) and B)) and C))), M:tm-309, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12635
in-theory        12635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (C -> ((A -> (A and (B -> (A and B)))) and C)))
theorem-size     23
proof            (modus-ponens tm-309 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12635.        ((A -> (A and (B -> (A and B)))) and (C -> ((A -> (A and (B -> (A and B)))) and C))), M:tm-309, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12636
in-theory        12636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (C -> (A -> (A and (B -> (A and B))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12636.        ((A -> (A and (B -> (A and B)))) and (C -> (A -> (A and (B -> (A and B)))))), M:tm-305, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12637
in-theory        12637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12637.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (E -> (D and E))))), M:tm-303, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12638
in-theory        12638
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (D -> (((B -> (C -> (B and C))) and A) and D))))
theorem-size     35
proof            (modus-ponens tm-300 tm-309 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> Bm (and (and (-> A (-> B (and A B))) C) Bm))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12638.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (D -> (((B -> (C -> (B and C))) and A) and D)))), M:tm-300, m:tm-309, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> Bm (and (and (-> A (-> B (and A B))) C) Bm)))))
================================================================
tm-name          tm-12639
in-theory        12639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12639.        ((A -> (((B and C) -> C) and A)) and (D -> (D and (E -> (D and E))))), M:tm-270, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12640
in-theory        12640
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (D -> ((((B and C) -> C) and A) and D))))
theorem-size     29
proof            (modus-ponens tm-267 tm-309 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> Bm (and (and (-> (and A B) B) C) Bm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12640.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (D -> ((((B and C) -> C) and A) and D)))), M:tm-267, m:tm-309, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> Bm (and (and (-> (and A B) B) C) Bm)))))
================================================================
tm-name          tm-12641
in-theory        12641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12641.        ((A -> (((B and C) -> B) and A)) and (D -> (D and (E -> (D and E))))), M:tm-239, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12642
in-theory        12642
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (D -> ((((B and C) -> B) and A) and D))))
theorem-size     29
proof            (modus-ponens tm-236 tm-309 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> Bm (and (and (-> (and A B) A) C) Bm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12642.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (D -> ((((B and C) -> B) and A) and D)))), M:tm-236, m:tm-309, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> Bm (and (and (-> (and A B) A) C) Bm)))))
================================================================
tm-name          tm-12643
in-theory        12643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (F -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12643.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (F -> (E and F))))), M:tm-210, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12644
in-theory        12644
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (E -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and E))))
theorem-size     53
proof            (modus-ponens tm-207 tm-309 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12644.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (E -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and E)))), M:tm-207, m:tm-309, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm)))))
================================================================
tm-name          tm-12645
in-theory        12645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12645.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (E -> (D and E))))), M:tm-183, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12646
in-theory        12646
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (D -> (((B -> (C -> B)) and A) and D))))
theorem-size     29
proof            (modus-ponens tm-180 tm-309 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> Bm (and (and (-> A (-> B A)) C) Bm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12646.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (D -> (((B -> (C -> B)) and A) and D)))), M:tm-180, m:tm-309, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> Bm (and (and (-> A (-> B A)) C) Bm)))))
================================================================
tm-name          tm-12647
in-theory        12647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12647.        ((A -> ((B and C) -> C)) and (D -> (D and (E -> (D and E))))), M:tm-157, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12648
in-theory        12648
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and (D -> (((B and C) -> C) and D))))
theorem-size     23
proof            (modus-ponens tm-154 tm-309 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> Bm (and (-> (and A B) B) Bm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12648.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and (D -> (((B and C) -> C) and D)))), M:tm-154, m:tm-309, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> Bm (and (-> (and A B) B) Bm)))))
================================================================
tm-name          tm-12649
in-theory        12649
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12649.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (E -> (D and E))))), M:tm-147, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12650
in-theory        12650
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (D -> (((A and (B -> C)) -> C) and D))))
theorem-size     35
proof            (modus-ponens tm-144 tm-309 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> Bm (and (-> (and A (-> B C)) C) Bm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12650.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (D -> (((A and (B -> C)) -> C) and D)))), M:tm-144, m:tm-309, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> Bm (and (-> (and A (-> B C)) C) Bm)))))
================================================================
tm-name          tm-12651
in-theory        12651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12651.        ((A -> ((B and C) -> B)) and (D -> (D and (E -> (D and E))))), M:tm-134, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12652
in-theory        12652
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and (D -> (((B and C) -> B) and D))))
theorem-size     23
proof            (modus-ponens tm-131 tm-309 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> Bm (and (-> (and A B) A) Bm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12652.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and (D -> (((B and C) -> B) and D)))), M:tm-131, m:tm-309, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> Bm (and (-> (and A B) A) Bm)))))
================================================================
tm-name          tm-12653
in-theory        12653
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12653.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (E -> (D and E))))), M:tm-125, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12654
in-theory        12654
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (D -> ((((A -> B) and C) -> B) and D))))
theorem-size     35
proof            (modus-ponens tm-122 tm-309 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> Bm (and (-> (and (-> A B) C) B) Bm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12654.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (D -> ((((A -> B) and C) -> B) and D)))), M:tm-122, m:tm-309, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> Bm (and (-> (and (-> A B) C) B) Bm)))))
================================================================
tm-name          tm-12655
in-theory        12655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12655.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (E and F))))), M:tm-113, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12656
in-theory        12656
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E))))
theorem-size     47
proof            (modus-ponens tm-110 tm-309 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12656.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))), M:tm-110, m:tm-309, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)))))
================================================================
tm-name          tm-12657
in-theory        12657
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12657.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (E -> (D and E))))), M:tm-105, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12658
in-theory        12658
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (D -> (((A -> (B -> C)) -> (A -> C)) and D))))
theorem-size     43
proof            (modus-ponens tm-102 tm-309 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> Bm (and (-> (-> A (-> B C)) (-> A C)) Bm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12658.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (D -> (((A -> (B -> C)) -> (A -> C)) and D)))), M:tm-102, m:tm-309, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> Bm (and (-> (-> A (-> B C)) (-> A C)) Bm)))))
================================================================
tm-name          tm-12659
in-theory        12659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and (D -> (C and D)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12659.        (((A -> B) -> (A -> A)) and (C -> (C and (D -> (C and D))))), M:tm-95, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12660
in-theory        12660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and (C -> ((A -> A) and C))))
theorem-size     19
proof            (modus-ponens tm-92 tm-309 ((Am (-> A A)) (B (and (-> A A) (-> Bm (and (-> A A) Bm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12660.        (((A -> B) or (A -> A)) -> ((A -> A) and (C -> ((A -> A) and C)))), M:tm-92, m:tm-309, u:((Am (-> A A)) (B (and (-> A A) (-> Bm (and (-> A A) Bm)))))
================================================================
tm-name          tm-12661
in-theory        12661
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and (C -> (A and C)))))
theorem-size     11
proof            (modus-ponens tm-84 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12661.        (A -> (B -> (A and (C -> (A and C))))), M:tm-84, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-12662
in-theory        12662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12662.        ((A -> (B -> (C -> B))) and (D -> (D and (E -> (D and E))))), M:tm-83, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12663
in-theory        12663
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (D -> ((B -> (C -> B)) and D))))
theorem-size     23
proof            (modus-ponens tm-80 tm-309 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> Bm (and (-> A (-> B A)) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12663.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (D -> ((B -> (C -> B)) and D)))), M:tm-80, m:tm-309, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> Bm (and (-> A (-> B A)) Bm)))))
================================================================
tm-name          tm-12664
in-theory        12664
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and (C -> (B and C)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12664.        (((not (not A)) -> A) and (B -> (B and (C -> (B and C))))), M:tm-76, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12665
in-theory        12665
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and (B -> (A and B))))
theorem-size     13
proof            (modus-ponens tm-73 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12665.        (((not (not A)) or A) -> (A and (B -> (A and B)))), M:tm-73, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-12666
in-theory        12666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (D -> (C and D)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12666.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (D -> (C and D))))), M:tm-69, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12667
in-theory        12667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (C -> (((A -> (not B)) -> (not A)) and C))))
theorem-size     31
proof            (modus-ponens tm-66 tm-309 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> Bm (and (-> (-> A (not B)) (not A)) Bm))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12667.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (C -> (((A -> (not B)) -> (not A)) and C)))), M:tm-66, m:tm-309, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> Bm (and (-> (-> A (not B)) (not A)) Bm)))))
================================================================
tm-name          tm-12668
in-theory        12668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12668.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (E -> (D and E))))), M:tm-54, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12669
in-theory        12669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> (((B -> C) -> ((A or B) -> C)) and D))))
theorem-size     37
proof            (modus-ponens tm-51 tm-309 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (and (-> (-> A B) (-> (or C A) B)) Bm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12669.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> (((B -> C) -> ((A or B) -> C)) and D)))), M:tm-51, m:tm-309, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (and (-> (-> A B) (-> (or C A) B)) Bm)))))
================================================================
tm-name          tm-12670
in-theory        12670
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and (C -> ((B or A) and C))))
theorem-size     17
proof            (modus-ponens tm-50 tm-309 ((Am (or A B)) (C (and (or A B) (-> Bm (and (or A B) Bm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12670.        ((A or (B or A)) -> ((B or A) and (C -> ((B or A) and C)))), M:tm-50, m:tm-309, u:((Am (or A B)) (C (and (or A B) (-> Bm (and (or A B) Bm)))))
================================================================
tm-name          tm-12671
in-theory        12671
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and (C -> ((A or B) and C))))
theorem-size     17
proof            (modus-ponens tm-49 tm-309 ((Am (or A B)) (C (and (or A B) (-> Bm (and (or A B) Bm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12671.        ((A or (A or B)) -> ((A or B) and (C -> ((A or B) and C)))), M:tm-49, m:tm-309, u:((Am (or A B)) (C (and (or A B) (-> Bm (and (or A B) Bm)))))
================================================================
tm-name          tm-12672
in-theory        12672
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> ((B -> (A and B)) and C))))
theorem-size     23
proof            (modus-ponens tm-48 tm-309 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (and (-> A (and B A)) Bm))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12672.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> ((B -> (A and B)) and C)))), M:tm-48, m:tm-309, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (and (-> A (and B A)) Bm)))))
================================================================
tm-name          tm-12673
in-theory        12673
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (C -> (B and C))))
theorem-size     13
proof            (modus-ponens tm-47 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12673.        (((A and B) or B) -> (B and (C -> (B and C)))), M:tm-47, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-12674
in-theory        12674
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (C -> (A and C))))
theorem-size     13
proof            (modus-ponens tm-46 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12674.        (((A and B) or A) -> (A and (C -> (A and C)))), M:tm-46, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-12675
in-theory        12675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (((A -> B) -> (A -> C)) and D))))
theorem-size     33
proof            (modus-ponens tm-45 tm-309 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (and (-> (-> A B) (-> A C)) Bm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12675.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (((A -> B) -> (A -> C)) and D)))), M:tm-45, m:tm-309, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (and (-> (-> A B) (-> A C)) Bm)))))
================================================================
tm-name          tm-12676
in-theory        12676
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (C -> ((B -> A) and C))))
theorem-size     17
proof            (modus-ponens tm-44 tm-309 ((Am (-> A B)) (C (and (-> A B) (-> Bm (and (-> A B) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12676.        ((A or (B -> A)) -> ((B -> A) and (C -> ((B -> A) and C)))), M:tm-44, m:tm-309, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (and (-> A B) Bm)))))
================================================================
tm-name          tm-12677
in-theory        12677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and (D -> (C and D)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12677.        ((A -> (B or A)) and (C -> (C and (D -> (C and D))))), M:tm-42, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12678
in-theory        12678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and (D -> (C and D)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12678.        ((A -> (A or B)) and (C -> (C and (D -> (C and D))))), M:tm-32, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12679
in-theory        12679
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and (B -> (A and B)))))
theorem-size     11
proof            (modus-ponens tm-24 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12679.        (A -> (A and (A and (B -> (A and B))))), M:tm-24, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-12680
in-theory        12680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and (D -> (C and D)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12680.        ((A -> (B -> (A and B))) and (C -> (C and (D -> (C and D))))), M:tm-23, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12681
in-theory        12681
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and (D -> (C and D)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12681.        (((A and B) -> B) and (C -> (C and (D -> (C and D))))), M:tm-22, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12682
in-theory        12682
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and (D -> (C and D)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12682.        (((A and B) -> A) and (C -> (C and (D -> (C and D))))), M:tm-21, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12683
in-theory        12683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12683.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (E -> (D and E))))), M:tm-20, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12684
in-theory        12684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and (D -> (C and D)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12684.        ((A -> (B -> A)) and (C -> (C and (D -> (C and D))))), M:tm-19, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12685
in-theory        12685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and (B -> (A and B))))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-9 tm-2 tm-5)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12685.        ((A -> (not (A and (B -> (A and B))))) -> (not A)), M:tm-9, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-12686
in-theory        12686
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (A and B))) -> C) -> ((A or (A and (B -> (A and B)))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12686.        (((A and (B -> (A and B))) -> C) -> ((A or (A and (B -> (A and B)))) -> C)), M:tm-8, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-12687
in-theory        12687
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and (C -> (B and C)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-7 tm-2 tm-5)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12687.        (A or (B -> (B and (C -> (B and C))))), M:tm-7, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12688
in-theory        12688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) or C)
theorem-size     11
proof            (modus-ponens tm-6 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-6 tm-2 tm-5)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12688.        ((A -> (A and (B -> (A and B)))) or C), M:tm-6, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12689
in-theory        12689
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and (C -> (B and C)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12689.        (A -> ((B -> (B and (C -> (B and C)))) and A)), M:tm-5, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12690
in-theory        12690
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and (C -> (B and C)))))
theorem-size     11
proof            (modus-ponens tm-1 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12690.        (A -> (B -> (B and (C -> (B and C))))), M:tm-1, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-12691
in-theory        12691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((A -> (B -> A)) or C))
theorem-size     13
proof            (modus-ponens tm-310 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12691.        ((A -> (B -> A)) and ((A -> (B -> A)) or C)), M:tm-310, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-12692
in-theory        12692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-12692.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)), M:tm-310, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-12693
in-theory        12693
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((A and B) -> A) or C))
theorem-size     13
proof            (modus-ponens tm-310 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-12693.        (((A and B) -> A) and (((A and B) -> A) or C)), M:tm-310, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-12694
in-theory        12694
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((A and B) -> B) or C))
theorem-size     13
proof            (modus-ponens tm-310 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-12694.        (((A and B) -> B) and (((A and B) -> B) or C)), M:tm-310, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-12695
in-theory        12695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((A -> (B -> (A and B))) or C))
theorem-size     17
proof            (modus-ponens tm-310 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-12695.        ((A -> (B -> (A and B))) and ((A -> (B -> (A and B))) or C)), M:tm-310, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-12696
in-theory        12696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((A -> (A or B)) or C))
theorem-size     13
proof            (modus-ponens tm-310 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-12696.        ((A -> (A or B)) and ((A -> (A or B)) or C)), M:tm-310, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-12697
in-theory        12697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((A -> (B or A)) or C))
theorem-size     13
proof            (modus-ponens tm-310 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-12697.        ((A -> (B or A)) and ((A -> (B or A)) or C)), M:tm-310, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-12698
in-theory        12698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12698.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)), M:tm-310, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-12699
in-theory        12699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C))
theorem-size     25
proof            (modus-ponens tm-310 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12699.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C)), M:tm-310, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-12700
in-theory        12700
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((not (not A)) -> A) or B))
theorem-size     13
proof            (modus-ponens tm-310 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-12700.        (((not (not A)) -> A) and (((not (not A)) -> A) or B)), M:tm-310, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-12701
in-theory        12701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((A -> (B -> (C -> B))) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12701.        ((A -> (B -> (C -> B))) and ((A -> (B -> (C -> B))) or D)), M:tm-310, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-12702
in-theory        12702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((A -> B) -> (A -> A)) or C))
theorem-size     17
proof            (modus-ponens tm-310 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-12702.        (((A -> B) -> (A -> A)) and (((A -> B) -> (A -> A)) or C)), M:tm-310, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-12703
in-theory        12703
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D))
theorem-size     41
proof            (modus-ponens tm-310 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12703.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D)), M:tm-310, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-12704
in-theory        12704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12704.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)), M:tm-310, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-12705
in-theory        12705
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-12705.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D)), M:tm-310, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-12706
in-theory        12706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((A -> ((B and C) -> B)) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12706.        ((A -> ((B and C) -> B)) and ((A -> ((B and C) -> B)) or D)), M:tm-310, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-12707
in-theory        12707
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-12707.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D)), M:tm-310, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-12708
in-theory        12708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((A -> ((B and C) -> C)) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12708.        ((A -> ((B and C) -> C)) and ((A -> ((B and C) -> C)) or D)), M:tm-310, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-12709
in-theory        12709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((A -> ((B -> (C -> B)) and A)) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12709.        ((A -> ((B -> (C -> B)) and A)) and ((A -> ((B -> (C -> B)) and A)) or D)), M:tm-310, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-12710
in-theory        12710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12710.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E)), M:tm-310, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-12711
in-theory        12711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((A -> (((B and C) -> B) and A)) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12711.        ((A -> (((B and C) -> B) and A)) and ((A -> (((B and C) -> B) and A)) or D)), M:tm-310, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-12712
in-theory        12712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((A -> (((B and C) -> C) and A)) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12712.        ((A -> (((B and C) -> C) and A)) and ((A -> (((B and C) -> C) and A)) or D)), M:tm-310, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-12713
in-theory        12713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((A -> ((B -> (C -> (B and C))) and A)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12713.        ((A -> ((B -> (C -> (B and C))) and A)) and ((A -> ((B -> (C -> (B and C))) and A)) or D)), M:tm-310, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-12714
in-theory        12714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((A -> B) -> (A -> (A and B))) or C))
theorem-size     21
proof            (modus-ponens tm-310 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-12714.        (((A -> B) -> (A -> (A and B))) and (((A -> B) -> (A -> (A and B))) or C)), M:tm-310, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-12715
in-theory        12715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((A -> (B -> (C -> (B and C)))) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12715.        ((A -> (B -> (C -> (B and C)))) and ((A -> (B -> (C -> (B and C)))) or D)), M:tm-310, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-12716
in-theory        12716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((A -> (B -> A)) or C) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12716.        (((A -> (B -> A)) or C) and (((A -> (B -> A)) or C) or D)), M:tm-310, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-12717
in-theory        12717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12717.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E)), M:tm-310, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-12718
in-theory        12718
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((A and B) -> A) or C) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12718.        ((((A and B) -> A) or C) and ((((A and B) -> A) or C) or D)), M:tm-310, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-12719
in-theory        12719
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((A and B) -> B) or C) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12719.        ((((A and B) -> B) or C) and ((((A and B) -> B) or C) or D)), M:tm-310, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-12720
in-theory        12720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((A -> (B -> (A and B))) or C) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12720.        (((A -> (B -> (A and B))) or C) and (((A -> (B -> (A and B))) or C) or D)), M:tm-310, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-12721
in-theory        12721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((A -> (A or B)) or C) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12721.        (((A -> (A or B)) or C) and (((A -> (A or B)) or C) or D)), M:tm-310, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-12722
in-theory        12722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((A -> ((B -> (B or C)) and A)) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12722.        ((A -> ((B -> (B or C)) and A)) and ((A -> ((B -> (B or C)) and A)) or D)), M:tm-310, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-12723
in-theory        12723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((A -> (B -> (B or C))) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12723.        ((A -> (B -> (B or C))) and ((A -> (B -> (B or C))) or D)), M:tm-310, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-12724
in-theory        12724
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((A or (B -> (C -> B))) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12724.        ((A or (B -> (C -> B))) and ((A or (B -> (C -> B))) or D)), M:tm-310, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-12725
in-theory        12725
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12725.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)), M:tm-310, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-12726
in-theory        12726
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((A or ((B and C) -> B)) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12726.        ((A or ((B and C) -> B)) and ((A or ((B and C) -> B)) or D)), M:tm-310, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-12727
in-theory        12727
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((A or ((B and C) -> C)) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12727.        ((A or ((B and C) -> C)) and ((A or ((B and C) -> C)) or D)), M:tm-310, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-12728
in-theory        12728
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((A or (B -> (C -> (B and C)))) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12728.        ((A or (B -> (C -> (B and C)))) and ((A or (B -> (C -> (B and C)))) or D)), M:tm-310, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-12729
in-theory        12729
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((A or (B -> (B or C))) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12729.        ((A or (B -> (B or C))) and ((A or (B -> (B or C))) or D)), M:tm-310, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-12730
in-theory        12730
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((A or (B -> (C or B))) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12730.        ((A or (B -> (C or B))) and ((A or (B -> (C or B))) or D)), M:tm-310, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-12731
in-theory        12731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((A -> (B or A)) or C) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12731.        (((A -> (B or A)) or C) and (((A -> (B or A)) or C) or D)), M:tm-310, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-12732
in-theory        12732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((A -> ((B -> (C or B)) and A)) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12732.        ((A -> ((B -> (C or B)) and A)) and ((A -> ((B -> (C or B)) and A)) or D)), M:tm-310, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-12733
in-theory        12733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((A -> (B -> (C or B))) or D))
theorem-size     17
proof            (modus-ponens tm-310 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12733.        ((A -> (B -> (C or B))) and ((A -> (B -> (C or B))) or D)), M:tm-310, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-12734
in-theory        12734
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12734.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D)), M:tm-310, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-12735
in-theory        12735
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E))
theorem-size     53
proof            (modus-ponens tm-310 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12735.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E)), M:tm-310, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-12736
in-theory        12736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((A -> B) -> (((A and C) or A) -> B)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12736.        (((A -> B) -> (((A and C) or A) -> B)) and (((A -> B) -> (((A and C) or A) -> B)) or D)), M:tm-310, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-12737
in-theory        12737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((A -> B) -> (((C and A) or A) -> B)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12737.        (((A -> B) -> (((C and A) or A) -> B)) and (((A -> B) -> (((C and A) or A) -> B)) or D)), M:tm-310, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-12738
in-theory        12738
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D))
theorem-size     37
proof            (modus-ponens tm-310 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12738.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) or D)), M:tm-310, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-12739
in-theory        12739
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-12739.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((A or B) -> C) -> ((A or (A or B)) -> C)) or D)), M:tm-310, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-12740
in-theory        12740
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-12740.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((A or B) -> C) -> ((B or (A or B)) -> C)) or D)), M:tm-310, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-12741
in-theory        12741
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E))
theorem-size     57
proof            (modus-ponens tm-310 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-12741.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) or E)), M:tm-310, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-12742
in-theory        12742
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12742.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E)), M:tm-310, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-12743
in-theory        12743
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12743.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) or E)), M:tm-310, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-12744
in-theory        12744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12744.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) or E)), M:tm-310, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-12745
in-theory        12745
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) or D))
theorem-size     37
proof            (modus-ponens tm-310 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-12745.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) or D)), M:tm-310, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-12746
in-theory        12746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12746.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) or E)), M:tm-310, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-12747
in-theory        12747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (((A -> (not (B -> A))) -> (not A)) or C))
theorem-size     21
proof            (modus-ponens tm-310 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12747.        (((A -> (not (B -> A))) -> (not A)) and (((A -> (not (B -> A))) -> (not A)) or C)), M:tm-310, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-12748
in-theory        12748
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) or D))
theorem-size     45
proof            (modus-ponens tm-310 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12748.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) or D)), M:tm-310, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-12749
in-theory        12749
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and ((((A and B) -> (not A)) -> (not (A and B))) or C))
theorem-size     25
proof            (modus-ponens tm-310 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12749.        ((((A and B) -> (not A)) -> (not (A and B))) and ((((A and B) -> (not A)) -> (not (A and B))) or C)), M:tm-310, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-12750
in-theory        12750
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and ((((A and B) -> (not B)) -> (not (A and B))) or C))
theorem-size     25
proof            (modus-ponens tm-310 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12750.        ((((A and B) -> (not B)) -> (not (A and B))) and ((((A and B) -> (not B)) -> (not (A and B))) or C)), M:tm-310, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-12751
in-theory        12751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (((A -> (not (B -> (A and B)))) -> (not A)) or C))
theorem-size     25
proof            (modus-ponens tm-310 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12751.        (((A -> (not (B -> (A and B)))) -> (not A)) and (((A -> (not (B -> (A and B)))) -> (not A)) or C)), M:tm-310, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-12752
in-theory        12752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (((A -> (not (A or B))) -> (not A)) or C))
theorem-size     21
proof            (modus-ponens tm-310 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-12752.        (((A -> (not (A or B))) -> (not A)) and (((A -> (not (A or B))) -> (not A)) or C)), M:tm-310, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-12753
in-theory        12753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (((A -> (not (B or A))) -> (not A)) or C))
theorem-size     21
proof            (modus-ponens tm-310 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-12753.        (((A -> (not (B or A))) -> (not A)) and (((A -> (not (B or A))) -> (not A)) or C)), M:tm-310, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-12754
in-theory        12754
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) or D))
theorem-size     41
proof            (modus-ponens tm-310 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-8)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-12754.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) or D)), M:tm-310, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-12755
in-theory        12755
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) or C))
theorem-size     37
proof            (modus-ponens tm-310 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-12755.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) or C)), M:tm-310, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-12756
in-theory        12756
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) or D))
theorem-size     49
proof            (modus-ponens tm-310 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-9)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-12756.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) or D)), M:tm-310, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-12757
in-theory        12757
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12757.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) or D)), M:tm-310, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-12758
in-theory        12758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12758.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) or D)), M:tm-310, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-12759
in-theory        12759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12759.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) or D)), M:tm-310, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-12760
in-theory        12760
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) or C))
theorem-size     33
proof            (modus-ponens tm-310 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-12760.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) or C)), M:tm-310, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-12761
in-theory        12761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12761.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) or D)), M:tm-310, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-12762
in-theory        12762
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((((not (not A)) -> (not A)) -> (not (not (not A)))) or B))
theorem-size     25
proof            (modus-ponens tm-310 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-12762.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((((not (not A)) -> (not A)) -> (not (not (not A)))) or B)), M:tm-310, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-12763
in-theory        12763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (((A -> B) -> (((not (not A)) or A) -> B)) or C))
theorem-size     25
proof            (modus-ponens tm-310 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-10)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-12763.        (((A -> B) -> (((not (not A)) or A) -> B)) and (((A -> B) -> (((not (not A)) or A) -> B)) or C)), M:tm-310, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-12764
in-theory        12764
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and ((A or ((not (not B)) -> B)) or C))
theorem-size     17
proof            (modus-ponens tm-310 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12764.        ((A or ((not (not B)) -> B)) and ((A or ((not (not B)) -> B)) or C)), M:tm-310, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-12765
in-theory        12765
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and ((((not (not A)) -> A) or B) or C))
theorem-size     17
proof            (modus-ponens tm-310 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12765.        ((((not (not A)) -> A) or B) and ((((not (not A)) -> A) or B) or C)), M:tm-310, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-12766
in-theory        12766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and ((A -> (((not (not B)) -> B) and A)) or C))
theorem-size     21
proof            (modus-ponens tm-310 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12766.        ((A -> (((not (not B)) -> B) and A)) and ((A -> (((not (not B)) -> B) and A)) or C)), M:tm-310, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-12767
in-theory        12767
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) or C))
theorem-size     33
proof            (modus-ponens tm-310 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-12767.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) or C)), M:tm-310, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-12768
in-theory        12768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and ((A -> ((not (not B)) -> B)) or C))
theorem-size     17
proof            (modus-ponens tm-310 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12768.        ((A -> ((not (not B)) -> B)) and ((A -> ((not (not B)) -> B)) or C)), M:tm-310, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-12769
in-theory        12769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (((A -> (not (B -> (C -> B)))) -> (not A)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12769.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (((A -> (not (B -> (C -> B)))) -> (not A)) or D)), M:tm-310, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-12770
in-theory        12770
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12770.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) or E)), M:tm-310, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-12771
in-theory        12771
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and ((A or (B -> (C -> (D -> C)))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12771.        ((A or (B -> (C -> (D -> C)))) and ((A or (B -> (C -> (D -> C)))) or E)), M:tm-310, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-12772
in-theory        12772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and (((A -> (B -> (C -> B))) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12772.        (((A -> (B -> (C -> B))) or D) and (((A -> (B -> (C -> B))) or D) or E)), M:tm-310, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-12773
in-theory        12773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and ((A -> ((B -> (C -> (D -> C))) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12773.        ((A -> ((B -> (C -> (D -> C))) and A)) and ((A -> ((B -> (C -> (D -> C))) and A)) or E)), M:tm-310, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-12774
in-theory        12774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (((A -> B) -> (A -> (C -> B))) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-12774.        (((A -> B) -> (A -> (C -> B))) and (((A -> B) -> (A -> (C -> B))) or D)), M:tm-310, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-12775
in-theory        12775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and ((A -> (B -> (C -> (D -> C)))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12775.        ((A -> (B -> (C -> (D -> C)))) and ((A -> (B -> (C -> (D -> C)))) or E)), M:tm-310, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-12776
in-theory        12776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and ((A -> A) or B))
theorem-size     9
proof            (modus-ponens tm-310 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12776.        ((A -> A) and ((A -> A) or B)), M:tm-310, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-12777
in-theory        12777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (((A -> (B -> C)) -> (A -> (B -> C))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12777.        (((A -> (B -> C)) -> (A -> (B -> C))) and (((A -> (B -> C)) -> (A -> (B -> C))) or D)), M:tm-310, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-12778
in-theory        12778
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and (((A and B) -> (A and B)) or C))
theorem-size     17
proof            (modus-ponens tm-310 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12778.        (((A and B) -> (A and B)) and (((A and B) -> (A and B)) or C)), M:tm-310, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-12779
in-theory        12779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (((A -> B) -> (A -> B)) or C))
theorem-size     17
proof            (modus-ponens tm-310 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-12779.        (((A -> B) -> (A -> B)) and (((A -> B) -> (A -> B)) or C)), M:tm-310, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-12780
in-theory        12780
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and (((not (not A)) -> (not (not A))) or B))
theorem-size     17
proof            (modus-ponens tm-310 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-12780.        (((not (not A)) -> (not (not A))) and (((not (not A)) -> (not (not A))) or B)), M:tm-310, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-12781
in-theory        12781
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) or C))
theorem-size     29
proof            (modus-ponens tm-310 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-12781.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) or C)), M:tm-310, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-12782
in-theory        12782
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-12782.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) or D)), M:tm-310, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-12783
in-theory        12783
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and ((A or ((B -> C) -> (B -> B))) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12783.        ((A or ((B -> C) -> (B -> B))) and ((A or ((B -> C) -> (B -> B))) or D)), M:tm-310, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-12784
in-theory        12784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and ((((A -> B) -> (A -> A)) or C) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12784.        ((((A -> B) -> (A -> A)) or C) and ((((A -> B) -> (A -> A)) or C) or D)), M:tm-310, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-12785
in-theory        12785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and ((A -> (((B -> C) -> (B -> B)) and A)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12785.        ((A -> (((B -> C) -> (B -> B)) and A)) and ((A -> (((B -> C) -> (B -> B)) and A)) or D)), M:tm-310, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-12786
in-theory        12786
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and ((((A -> B) -> A) -> ((A -> B) -> A)) or C))
theorem-size     25
proof            (modus-ponens tm-310 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-12786.        ((((A -> B) -> A) -> ((A -> B) -> A)) and ((((A -> B) -> A) -> ((A -> B) -> A)) or C)), M:tm-310, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-12787
in-theory        12787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and ((A -> ((B -> C) -> (B -> B))) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12787.        ((A -> ((B -> C) -> (B -> B))) and ((A -> ((B -> C) -> (B -> B))) or D)), M:tm-310, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-12788
in-theory        12788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (((A -> ((B -> A) -> C)) -> (A -> C)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-12788.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (((A -> ((B -> A) -> C)) -> (A -> C)) or D)), M:tm-310, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-12789
in-theory        12789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (((A -> (A -> B)) -> (A -> B)) or C))
theorem-size     21
proof            (modus-ponens tm-310 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-12789.        (((A -> (A -> B)) -> (A -> B)) and (((A -> (A -> B)) -> (A -> B)) or C)), M:tm-310, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-12790
in-theory        12790
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) or D))
theorem-size     41
proof            (modus-ponens tm-310 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-12790.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) or D)), M:tm-310, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-12791
in-theory        12791
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) or D))
theorem-size     65
proof            (modus-ponens tm-310 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-12791.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) or D)), M:tm-310, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-12792
in-theory        12792
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) or E))
theorem-size     69
proof            (modus-ponens tm-310 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-12792.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) or E)), M:tm-310, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-12793
in-theory        12793
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12793.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) or E)), M:tm-310, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-12794
in-theory        12794
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12794.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) or E)), M:tm-310, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-12795
in-theory        12795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) or E))
theorem-size     49
proof            (modus-ponens tm-310 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12795.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) or E)), M:tm-310, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-12796
in-theory        12796
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) or D))
theorem-size     61
proof            (modus-ponens tm-310 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-12796.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) or D)), M:tm-310, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-12797
in-theory        12797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12797.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) or E)), M:tm-310, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-12798
in-theory        12798
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) or E))
theorem-size     49
proof            (modus-ponens tm-310 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-12798.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) or E)), M:tm-310, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-12799
in-theory        12799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12799.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) or E)), M:tm-310, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-12800
in-theory        12800
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) or F))
theorem-size     69
proof            (modus-ponens tm-310 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12800.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) or F)), M:tm-310, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-12801
in-theory        12801
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12801.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F)), M:tm-310, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-12802
in-theory        12802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12802.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) or F)), M:tm-310, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-12803
in-theory        12803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12803.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) or F)), M:tm-310, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-12804
in-theory        12804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-12804.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) or E)), M:tm-310, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-12805
in-theory        12805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12805.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F)), M:tm-310, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-12806
in-theory        12806
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and ((((A -> B) and A) -> B) or C))
theorem-size     17
proof            (modus-ponens tm-310 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-12806.        ((((A -> B) and A) -> B) and ((((A -> B) and A) -> B) or C)), M:tm-310, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-12807
in-theory        12807
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and (((((A -> (B -> A)) -> C) and D) -> C) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-12807.        (((((A -> (B -> A)) -> C) and D) -> C) and (((((A -> (B -> A)) -> C) and D) -> C) or E)), M:tm-310, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-12808
in-theory        12808
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12808.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) or F)), M:tm-310, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-12809
in-theory        12809
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) or D))
theorem-size     45
proof            (modus-ponens tm-310 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-12809.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) or D)), M:tm-310, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-12810
in-theory        12810
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-12810.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) or D)), M:tm-310, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-12811
in-theory        12811
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) or D))
theorem-size     53
proof            (modus-ponens tm-310 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-12811.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) or D)), M:tm-310, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-12812
in-theory        12812
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) or E))
theorem-size     57
proof            (modus-ponens tm-310 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-12812.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) or E)), M:tm-310, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-12813
in-theory        12813
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12813.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) or E)), M:tm-310, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-12814
in-theory        12814
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12814.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) or E)), M:tm-310, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-12815
in-theory        12815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12815.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) or E)), M:tm-310, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-12816
in-theory        12816
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) or D))
theorem-size     49
proof            (modus-ponens tm-310 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-12816.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) or D)), M:tm-310, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-12817
in-theory        12817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12817.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) or E)), M:tm-310, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-12818
in-theory        12818
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and ((((((A and B) -> A) -> C) and D) -> C) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-12818.        ((((((A and B) -> A) -> C) and D) -> C) and ((((((A and B) -> A) -> C) and D) -> C) or E)), M:tm-310, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-12819
in-theory        12819
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((((A and B) -> (A -> C)) -> ((A and B) -> C)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-12819.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((((A and B) -> (A -> C)) -> ((A and B) -> C)) or D)), M:tm-310, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-12820
in-theory        12820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (((A -> (not ((B and C) -> B))) -> (not A)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12820.        (((A -> (not ((B and C) -> B))) -> (not A)) and (((A -> (not ((B and C) -> B))) -> (not A)) or D)), M:tm-310, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-12821
in-theory        12821
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12821.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) or E)), M:tm-310, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-12822
in-theory        12822
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and ((A or (B -> ((C and D) -> C))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12822.        ((A or (B -> ((C and D) -> C))) and ((A or (B -> ((C and D) -> C))) or E)), M:tm-310, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-12823
in-theory        12823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and (((A -> ((B and C) -> B)) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12823.        (((A -> ((B and C) -> B)) or D) and (((A -> ((B and C) -> B)) or D) or E)), M:tm-310, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-12824
in-theory        12824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and ((A -> ((B -> ((C and D) -> C)) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12824.        ((A -> ((B -> ((C and D) -> C)) and A)) and ((A -> ((B -> ((C and D) -> C)) and A)) or E)), M:tm-310, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-12825
in-theory        12825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (((A -> (B and C)) -> (A -> B)) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-12825.        (((A -> (B and C)) -> (A -> B)) and (((A -> (B and C)) -> (A -> B)) or D)), M:tm-310, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-12826
in-theory        12826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and ((A -> (B -> ((C and D) -> C))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12826.        ((A -> (B -> ((C and D) -> C))) and ((A -> (B -> ((C and D) -> C))) or E)), M:tm-310, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-12827
in-theory        12827
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and (((A and (A -> B)) -> B) or C))
theorem-size     17
proof            (modus-ponens tm-310 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-12827.        (((A and (A -> B)) -> B) and (((A and (A -> B)) -> B) or C)), M:tm-310, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-12828
in-theory        12828
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and (((A and ((B -> (C -> B)) -> D)) -> D) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-12828.        (((A and ((B -> (C -> B)) -> D)) -> D) and (((A and ((B -> (C -> B)) -> D)) -> D) or E)), M:tm-310, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-12829
in-theory        12829
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12829.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) or F)), M:tm-310, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-12830
in-theory        12830
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and (((A and (((B and C) -> B) -> D)) -> D) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-12830.        (((A and (((B and C) -> B) -> D)) -> D) and (((A and (((B and C) -> B) -> D)) -> D) or E)), M:tm-310, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-12831
in-theory        12831
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) or D))
theorem-size     45
proof            (modus-ponens tm-310 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-12831.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) or D)), M:tm-310, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-12832
in-theory        12832
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-12832.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) or D)), M:tm-310, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-12833
in-theory        12833
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) or D))
theorem-size     53
proof            (modus-ponens tm-310 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-12833.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) or D)), M:tm-310, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-12834
in-theory        12834
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) or E))
theorem-size     57
proof            (modus-ponens tm-310 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-12834.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) or E)), M:tm-310, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-12835
in-theory        12835
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12835.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) or E)), M:tm-310, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-12836
in-theory        12836
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12836.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) or E)), M:tm-310, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-12837
in-theory        12837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12837.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) or E)), M:tm-310, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-12838
in-theory        12838
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) or D))
theorem-size     49
proof            (modus-ponens tm-310 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-12838.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) or D)), M:tm-310, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-12839
in-theory        12839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12839.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) or E)), M:tm-310, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-12840
in-theory        12840
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and (((A and (((B and C) -> C) -> D)) -> D) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-12840.        (((A and (((B and C) -> C) -> D)) -> D) and (((A and (((B and C) -> C) -> D)) -> D) or E)), M:tm-310, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-12841
in-theory        12841
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and ((((((A and B) -> B) -> C) and D) -> C) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-12841.        ((((((A and B) -> B) -> C) and D) -> C) and ((((((A and B) -> B) -> C) and D) -> C) or E)), M:tm-310, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-12842
in-theory        12842
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((((A and B) -> (B -> C)) -> ((A and B) -> C)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-12842.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((((A and B) -> (B -> C)) -> ((A and B) -> C)) or D)), M:tm-310, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-12843
in-theory        12843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (((A -> (not ((B and C) -> C))) -> (not A)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12843.        (((A -> (not ((B and C) -> C))) -> (not A)) and (((A -> (not ((B and C) -> C))) -> (not A)) or D)), M:tm-310, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-12844
in-theory        12844
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12844.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) or E)), M:tm-310, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-12845
in-theory        12845
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and ((A or (B -> ((C and D) -> D))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12845.        ((A or (B -> ((C and D) -> D))) and ((A or (B -> ((C and D) -> D))) or E)), M:tm-310, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-12846
in-theory        12846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and (((A -> ((B and C) -> C)) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12846.        (((A -> ((B and C) -> C)) or D) and (((A -> ((B and C) -> C)) or D) or E)), M:tm-310, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-12847
in-theory        12847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and ((A -> ((B -> ((C and D) -> D)) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12847.        ((A -> ((B -> ((C and D) -> D)) and A)) and ((A -> ((B -> ((C and D) -> D)) and A)) or E)), M:tm-310, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-12848
in-theory        12848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (((A -> (B and C)) -> (A -> C)) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-12848.        (((A -> (B and C)) -> (A -> C)) and (((A -> (B and C)) -> (A -> C)) or D)), M:tm-310, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-12849
in-theory        12849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and ((A -> (B -> ((C and D) -> D))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12849.        ((A -> (B -> ((C and D) -> D))) and ((A -> (B -> ((C and D) -> D))) or E)), M:tm-310, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-12850
in-theory        12850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and (((A -> (B -> A)) and (C -> (D -> C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12850.        (((A -> (B -> A)) and (C -> (D -> C))) and (((A -> (B -> A)) and (C -> (D -> C))) or E)), M:tm-310, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-12851
in-theory        12851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12851.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-310, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-12852
in-theory        12852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and (((A -> (B -> A)) and ((C and D) -> C)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12852.        (((A -> (B -> A)) and ((C and D) -> C)) and (((A -> (B -> A)) and ((C and D) -> C)) or E)), M:tm-310, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-12853
in-theory        12853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and (((A -> (B -> A)) and ((C and D) -> D)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12853.        (((A -> (B -> A)) and ((C and D) -> D)) and (((A -> (B -> A)) and ((C and D) -> D)) or E)), M:tm-310, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-12854
in-theory        12854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (((A -> (B -> A)) and (C -> (D -> (C and D)))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12854.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (((A -> (B -> A)) and (C -> (D -> (C and D)))) or E)), M:tm-310, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-12855
in-theory        12855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and (((A -> (B -> A)) and (C -> (C or D))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12855.        (((A -> (B -> A)) and (C -> (C or D))) and (((A -> (B -> A)) and (C -> (C or D))) or E)), M:tm-310, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-12856
in-theory        12856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and (((A -> (B -> A)) and (C -> (D or C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12856.        (((A -> (B -> A)) and (C -> (D or C))) and (((A -> (B -> A)) and (C -> (D or C))) or E)), M:tm-310, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-12857
in-theory        12857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12857.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)), M:tm-310, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-12858
in-theory        12858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12858.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E)), M:tm-310, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-12859
in-theory        12859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and (((A -> (B -> A)) and ((not (not C)) -> C)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12859.        (((A -> (B -> A)) and ((not (not C)) -> C)) and (((A -> (B -> A)) and ((not (not C)) -> C)) or D)), M:tm-310, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-12860
in-theory        12860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (((A -> (B -> A)) and (C -> (D -> (E -> D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12860.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (((A -> (B -> A)) and (C -> (D -> (E -> D)))) or F)), M:tm-310, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-12861
in-theory        12861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (((A -> (B -> A)) and ((C -> D) -> (C -> C))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12861.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (((A -> (B -> A)) and ((C -> D) -> (C -> C))) or E)), M:tm-310, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-12862
in-theory        12862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F))
theorem-size     53
proof            (modus-ponens tm-310 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12862.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F)), M:tm-310, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-12863
in-theory        12863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12863.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)), M:tm-310, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-12864
in-theory        12864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12864.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F)), M:tm-310, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-12865
in-theory        12865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (((A -> (B -> A)) and (C -> ((D and E) -> D))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12865.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (((A -> (B -> A)) and (C -> ((D and E) -> D))) or F)), M:tm-310, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-12866
in-theory        12866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12866.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F)), M:tm-310, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-12867
in-theory        12867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (((A -> (B -> A)) and (C -> ((D and E) -> E))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12867.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (((A -> (B -> A)) and (C -> ((D and E) -> E))) or F)), M:tm-310, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-12868
in-theory        12868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12868.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) or F)), M:tm-310, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-12869
in-theory        12869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12869.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) or D)), M:tm-310, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-12870
in-theory        12870
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12870.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) or E)), M:tm-310, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-12871
in-theory        12871
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and ((A or (B -> ((C -> (D -> C)) and B))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12871.        ((A or (B -> ((C -> (D -> C)) and B))) and ((A or (B -> ((C -> (D -> C)) and B))) or E)), M:tm-310, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-12872
in-theory        12872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and (((A -> ((B -> (C -> B)) and A)) or D) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12872.        (((A -> ((B -> (C -> B)) and A)) or D) and (((A -> ((B -> (C -> B)) and A)) or D) or E)), M:tm-310, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-12873
in-theory        12873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12873.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) or E)), M:tm-310, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-12874
in-theory        12874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and ((A -> (B -> ((C -> (D -> C)) and B))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12874.        ((A -> (B -> ((C -> (D -> C)) and B))) and ((A -> (B -> ((C -> (D -> C)) and B))) or E)), M:tm-310, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-12875
in-theory        12875
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12875.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) or F)), M:tm-310, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-12876
in-theory        12876
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     57
proof            (modus-ponens tm-310 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12876.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-310, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-12877
in-theory        12877
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12877.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) or F)), M:tm-310, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-12878
in-theory        12878
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12878.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) or F)), M:tm-310, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-12879
in-theory        12879
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12879.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) or F)), M:tm-310, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-12880
in-theory        12880
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12880.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) or F)), M:tm-310, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-12881
in-theory        12881
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12881.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) or F)), M:tm-310, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-12882
in-theory        12882
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G))
theorem-size     57
proof            (modus-ponens tm-310 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12882.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) or G)), M:tm-310, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-12883
in-theory        12883
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) or F))
theorem-size     53
proof            (modus-ponens tm-310 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12883.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) or F)), M:tm-310, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-12884
in-theory        12884
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12884.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) or E)), M:tm-310, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-12885
in-theory        12885
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12885.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) or G)), M:tm-310, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-12886
in-theory        12886
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12886.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) or F)), M:tm-310, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-12887
in-theory        12887
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) or G))
theorem-size     69
proof            (modus-ponens tm-310 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12887.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) or G)), M:tm-310, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-12888
in-theory        12888
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) or H))
theorem-size     61
proof            (modus-ponens tm-310 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12888.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) or H)), M:tm-310, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-12889
in-theory        12889
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) or G))
theorem-size     61
proof            (modus-ponens tm-310 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12889.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) or G)), M:tm-310, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-12890
in-theory        12890
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12890.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) or G)), M:tm-310, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-12891
in-theory        12891
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) or G))
theorem-size     61
proof            (modus-ponens tm-310 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12891.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) or G)), M:tm-310, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-12892
in-theory        12892
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12892.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) or G)), M:tm-310, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-12893
in-theory        12893
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12893.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) or G)), M:tm-310, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-12894
in-theory        12894
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) or H))
theorem-size     65
proof            (modus-ponens tm-310 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12894.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) or H)), M:tm-310, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-12895
in-theory        12895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12895.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G)), M:tm-310, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-12896
in-theory        12896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-12896.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) or E)), M:tm-310, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-12897
in-theory        12897
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) or F))
theorem-size     77
proof            (modus-ponens tm-310 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-12897.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) or F)), M:tm-310, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-12898
in-theory        12898
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12898.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) or F)), M:tm-310, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-12899
in-theory        12899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12899.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) or F)), M:tm-310, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-12900
in-theory        12900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12900.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) or F)), M:tm-310, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-12901
in-theory        12901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12901.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) or F)), M:tm-310, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-12902
in-theory        12902
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and ((((A and B) -> A) and (C -> (D -> C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12902.        ((((A and B) -> A) and (C -> (D -> C))) and ((((A and B) -> A) and (C -> (D -> C))) or E)), M:tm-310, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-12903
in-theory        12903
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12903.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-310, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-12904
in-theory        12904
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and ((((A and B) -> A) and ((C and D) -> C)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12904.        ((((A and B) -> A) and ((C and D) -> C)) and ((((A and B) -> A) and ((C and D) -> C)) or E)), M:tm-310, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-12905
in-theory        12905
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and ((((A and B) -> A) and ((C and D) -> D)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12905.        ((((A and B) -> A) and ((C and D) -> D)) and ((((A and B) -> A) and ((C and D) -> D)) or E)), M:tm-310, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-12906
in-theory        12906
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((((A and B) -> A) and (C -> (D -> (C and D)))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12906.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((((A and B) -> A) and (C -> (D -> (C and D)))) or E)), M:tm-310, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-12907
in-theory        12907
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and ((((A and B) -> A) and (C -> (C or D))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12907.        ((((A and B) -> A) and (C -> (C or D))) and ((((A and B) -> A) and (C -> (C or D))) or E)), M:tm-310, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-12908
in-theory        12908
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and ((((A and B) -> A) and (C -> (D or C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12908.        ((((A and B) -> A) and (C -> (D or C))) and ((((A and B) -> A) and (C -> (D or C))) or E)), M:tm-310, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-12909
in-theory        12909
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12909.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)), M:tm-310, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-12910
in-theory        12910
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12910.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E)), M:tm-310, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-12911
in-theory        12911
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and ((((A and B) -> A) and ((not (not C)) -> C)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12911.        ((((A and B) -> A) and ((not (not C)) -> C)) and ((((A and B) -> A) and ((not (not C)) -> C)) or D)), M:tm-310, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-12912
in-theory        12912
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((((A and B) -> A) and (C -> (D -> (E -> D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12912.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((((A and B) -> A) and (C -> (D -> (E -> D)))) or F)), M:tm-310, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-12913
in-theory        12913
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((((A and B) -> A) and ((C -> D) -> (C -> C))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12913.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((((A and B) -> A) and ((C -> D) -> (C -> C))) or E)), M:tm-310, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-12914
in-theory        12914
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F))
theorem-size     53
proof            (modus-ponens tm-310 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12914.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F)), M:tm-310, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-12915
in-theory        12915
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12915.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)), M:tm-310, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-12916
in-theory        12916
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12916.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F)), M:tm-310, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-12917
in-theory        12917
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((((A and B) -> A) and (C -> ((D and E) -> D))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12917.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((((A and B) -> A) and (C -> ((D and E) -> D))) or F)), M:tm-310, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-12918
in-theory        12918
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12918.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F)), M:tm-310, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-12919
in-theory        12919
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((((A and B) -> A) and (C -> ((D and E) -> E))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12919.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((((A and B) -> A) and (C -> ((D and E) -> E))) or F)), M:tm-310, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-12920
in-theory        12920
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12920.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) or F)), M:tm-310, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-12921
in-theory        12921
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12921.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G)), M:tm-310, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-12922
in-theory        12922
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12922.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) or F)), M:tm-310, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-12923
in-theory        12923
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12923.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) or G)), M:tm-310, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-12924
in-theory        12924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12924.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) or F)), M:tm-310, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-12925
in-theory        12925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((A -> (not (((B and C) -> B) and A))) -> (not A)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-12925.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((A -> (not (((B and C) -> B) and A))) -> (not A)) or D)), M:tm-310, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-12926
in-theory        12926
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-12926.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) or E)), M:tm-310, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-12927
in-theory        12927
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and ((A or (B -> (((C and D) -> C) and B))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12927.        ((A or (B -> (((C and D) -> C) and B))) and ((A or (B -> (((C and D) -> C) and B))) or E)), M:tm-310, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-12928
in-theory        12928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and (((A -> (((B and C) -> B) and A)) or D) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12928.        (((A -> (((B and C) -> B) and A)) or D) and (((A -> (((B and C) -> B) and A)) or D) or E)), M:tm-310, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-12929
in-theory        12929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((A -> ((B -> (((C and D) -> C) and B)) and A)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12929.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((A -> ((B -> (((C and D) -> C) and B)) and A)) or E)), M:tm-310, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-12930
in-theory        12930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and ((A -> (B -> (((C and D) -> C) and B))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12930.        ((A -> (B -> (((C and D) -> C) and B))) and ((A -> (B -> (((C and D) -> C) and B))) or E)), M:tm-310, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-12931
in-theory        12931
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and ((((A and B) -> B) and (C -> (D -> C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12931.        ((((A and B) -> B) and (C -> (D -> C))) and ((((A and B) -> B) and (C -> (D -> C))) or E)), M:tm-310, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-12932
in-theory        12932
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12932.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-310, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-12933
in-theory        12933
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and ((((A and B) -> B) and ((C and D) -> C)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12933.        ((((A and B) -> B) and ((C and D) -> C)) and ((((A and B) -> B) and ((C and D) -> C)) or E)), M:tm-310, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-12934
in-theory        12934
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and ((((A and B) -> B) and ((C and D) -> D)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12934.        ((((A and B) -> B) and ((C and D) -> D)) and ((((A and B) -> B) and ((C and D) -> D)) or E)), M:tm-310, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-12935
in-theory        12935
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((((A and B) -> B) and (C -> (D -> (C and D)))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12935.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((((A and B) -> B) and (C -> (D -> (C and D)))) or E)), M:tm-310, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-12936
in-theory        12936
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and ((((A and B) -> B) and (C -> (C or D))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12936.        ((((A and B) -> B) and (C -> (C or D))) and ((((A and B) -> B) and (C -> (C or D))) or E)), M:tm-310, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-12937
in-theory        12937
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and ((((A and B) -> B) and (C -> (D or C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12937.        ((((A and B) -> B) and (C -> (D or C))) and ((((A and B) -> B) and (C -> (D or C))) or E)), M:tm-310, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-12938
in-theory        12938
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12938.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)), M:tm-310, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-12939
in-theory        12939
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12939.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E)), M:tm-310, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-12940
in-theory        12940
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and ((((A and B) -> B) and ((not (not C)) -> C)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12940.        ((((A and B) -> B) and ((not (not C)) -> C)) and ((((A and B) -> B) and ((not (not C)) -> C)) or D)), M:tm-310, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-12941
in-theory        12941
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((((A and B) -> B) and (C -> (D -> (E -> D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12941.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((((A and B) -> B) and (C -> (D -> (E -> D)))) or F)), M:tm-310, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-12942
in-theory        12942
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((((A and B) -> B) and ((C -> D) -> (C -> C))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12942.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((((A and B) -> B) and ((C -> D) -> (C -> C))) or E)), M:tm-310, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-12943
in-theory        12943
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F))
theorem-size     53
proof            (modus-ponens tm-310 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12943.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F)), M:tm-310, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-12944
in-theory        12944
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12944.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)), M:tm-310, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-12945
in-theory        12945
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12945.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F)), M:tm-310, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-12946
in-theory        12946
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((((A and B) -> B) and (C -> ((D and E) -> D))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12946.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((((A and B) -> B) and (C -> ((D and E) -> D))) or F)), M:tm-310, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-12947
in-theory        12947
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12947.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F)), M:tm-310, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-12948
in-theory        12948
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((((A and B) -> B) and (C -> ((D and E) -> E))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12948.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((((A and B) -> B) and (C -> ((D and E) -> E))) or F)), M:tm-310, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-12949
in-theory        12949
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12949.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) or F)), M:tm-310, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-12950
in-theory        12950
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12950.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G)), M:tm-310, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-12951
in-theory        12951
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12951.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) or F)), M:tm-310, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-12952
in-theory        12952
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12952.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) or F)), M:tm-310, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-12953
in-theory        12953
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12953.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) or F)), M:tm-310, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-12954
in-theory        12954
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12954.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) or G)), M:tm-310, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-12955
in-theory        12955
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12955.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) or F)), M:tm-310, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-12956
in-theory        12956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((A -> (not (((B and C) -> C) and A))) -> (not A)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-12956.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((A -> (not (((B and C) -> C) and A))) -> (not A)) or D)), M:tm-310, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-12957
in-theory        12957
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-12957.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) or E)), M:tm-310, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-12958
in-theory        12958
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and ((A or (B -> (((C and D) -> D) and B))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12958.        ((A or (B -> (((C and D) -> D) and B))) and ((A or (B -> (((C and D) -> D) and B))) or E)), M:tm-310, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-12959
in-theory        12959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and (((A -> (((B and C) -> C) and A)) or D) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12959.        (((A -> (((B and C) -> C) and A)) or D) and (((A -> (((B and C) -> C) and A)) or D) or E)), M:tm-310, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-12960
in-theory        12960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((A -> ((B -> (((C and D) -> D) and B)) and A)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12960.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((A -> ((B -> (((C and D) -> D) and B)) and A)) or E)), M:tm-310, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-12961
in-theory        12961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and ((A -> (B -> (((C and D) -> D) and B))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12961.        ((A -> (B -> (((C and D) -> D) and B))) and ((A -> (B -> (((C and D) -> D) and B))) or E)), M:tm-310, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-12962
in-theory        12962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and (((A -> (B -> (A and B))) and (C -> (D -> C))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12962.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and (((A -> (B -> (A and B))) and (C -> (D -> C))) or E)), M:tm-310, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-12963
in-theory        12963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12963.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-310, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-12964
in-theory        12964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and (((A -> (B -> (A and B))) and ((C and D) -> C)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12964.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and (((A -> (B -> (A and B))) and ((C and D) -> C)) or E)), M:tm-310, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-12965
in-theory        12965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and (((A -> (B -> (A and B))) and ((C and D) -> D)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12965.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and (((A -> (B -> (A and B))) and ((C and D) -> D)) or E)), M:tm-310, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-12966
in-theory        12966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12966.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) or E)), M:tm-310, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-12967
in-theory        12967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and (((A -> (B -> (A and B))) and (C -> (C or D))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12967.        (((A -> (B -> (A and B))) and (C -> (C or D))) and (((A -> (B -> (A and B))) and (C -> (C or D))) or E)), M:tm-310, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-12968
in-theory        12968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and (((A -> (B -> (A and B))) and (C -> (D or C))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12968.        (((A -> (B -> (A and B))) and (C -> (D or C))) and (((A -> (B -> (A and B))) and (C -> (D or C))) or E)), M:tm-310, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-12969
in-theory        12969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-12969.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)), M:tm-310, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-12970
in-theory        12970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-12970.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E)), M:tm-310, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-12971
in-theory        12971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (((A -> (B -> (A and B))) and ((not (not C)) -> C)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-12971.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (((A -> (B -> (A and B))) and ((not (not C)) -> C)) or D)), M:tm-310, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-12972
in-theory        12972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-12972.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) or F)), M:tm-310, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-12973
in-theory        12973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-12973.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) or E)), M:tm-310, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-12974
in-theory        12974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F))
theorem-size     57
proof            (modus-ponens tm-310 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-12974.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F)), M:tm-310, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-12975
in-theory        12975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12975.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)), M:tm-310, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-12976
in-theory        12976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F))
theorem-size     49
proof            (modus-ponens tm-310 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-12976.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F)), M:tm-310, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-12977
in-theory        12977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-12977.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) or F)), M:tm-310, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-12978
in-theory        12978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F))
theorem-size     49
proof            (modus-ponens tm-310 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-12978.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F)), M:tm-310, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-12979
in-theory        12979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-12979.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) or F)), M:tm-310, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-12980
in-theory        12980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-12980.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) or F)), M:tm-310, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-12981
in-theory        12981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G))
theorem-size     53
proof            (modus-ponens tm-310 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-12981.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G)), M:tm-310, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-12982
in-theory        12982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-12982.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) or F)), M:tm-310, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-12983
in-theory        12983
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-12983.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) or F)), M:tm-310, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-12984
in-theory        12984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12984.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) or F)), M:tm-310, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-12985
in-theory        12985
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12985.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) or F)), M:tm-310, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-12986
in-theory        12986
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12986.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) or F)), M:tm-310, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-12987
in-theory        12987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) or G))
theorem-size     53
proof            (modus-ponens tm-310 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12987.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) or G)), M:tm-310, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-12988
in-theory        12988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12988.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) or F)), M:tm-310, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-12989
in-theory        12989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-12989.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) or D)), M:tm-310, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-12990
in-theory        12990
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) or E))
theorem-size     53
proof            (modus-ponens tm-310 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-12990.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) or E)), M:tm-310, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-12991
in-theory        12991
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((A or (B -> ((C -> (D -> (C and D))) and B))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12991.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((A or (B -> ((C -> (D -> (C and D))) and B))) or E)), M:tm-310, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-12992
in-theory        12992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and (((A -> ((B -> (C -> (B and C))) and A)) or D) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12992.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and (((A -> ((B -> (C -> (B and C))) and A)) or D) or E)), M:tm-310, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-12993
in-theory        12993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12993.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) or E)), M:tm-310, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-12994
in-theory        12994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((A -> (B -> ((C -> (D -> (C and D))) and B))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-12994.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((A -> (B -> ((C -> (D -> (C and D))) and B))) or E)), M:tm-310, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-12995
in-theory        12995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and ((A -> (A and (B -> A))) or C))
theorem-size     17
proof            (modus-ponens tm-310 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12995.        ((A -> (A and (B -> A))) and ((A -> (A and (B -> A))) or C)), M:tm-310, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-12996
in-theory        12996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) or D))
theorem-size     41
proof            (modus-ponens tm-310 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12996.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) or D)), M:tm-310, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-12997
in-theory        12997
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and (((A and B) -> ((A and B) and A)) or C))
theorem-size     21
proof            (modus-ponens tm-310 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12997.        (((A and B) -> ((A and B) and A)) and (((A and B) -> ((A and B) and A)) or C)), M:tm-310, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-12998
in-theory        12998
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and (((A and B) -> ((A and B) and B)) or C))
theorem-size     21
proof            (modus-ponens tm-310 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12998.        (((A and B) -> ((A and B) and B)) and (((A and B) -> ((A and B) and B)) or C)), M:tm-310, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-12999
in-theory        12999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and ((A -> (A and (B -> (A and B)))) or C))
theorem-size     21
proof            (modus-ponens tm-310 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-12999.        ((A -> (A and (B -> (A and B)))) and ((A -> (A and (B -> (A and B)))) or C)), M:tm-310, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-13000
in-theory        13000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and ((A -> (A and (A or B))) or C))
theorem-size     17
proof            (modus-ponens tm-310 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13000.        ((A -> (A and (A or B))) and ((A -> (A and (A or B))) or C)), M:tm-310, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13001
in-theory        13001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (C -> ((A -> (A and (A or B))) and C)))
theorem-size     19
proof            (modus-ponens tm-309 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13001.        ((A -> (A and (A or B))) and (C -> ((A -> (A and (A or B))) and C))), M:tm-309, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13002
in-theory        13002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (C -> (A -> (A and (A or B)))))
theorem-size     17
proof            (modus-ponens tm-305 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13002.        ((A -> (A and (A or B))) and (C -> (A -> (A and (A or B))))), M:tm-305, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13003
in-theory        13003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (D or E))))
theorem-size     19
proof            (modus-ponens tm-303 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13003.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (D or E)))), M:tm-303, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13004
in-theory        13004
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (((B -> (C -> (B and C))) and A) or D)))
theorem-size     33
proof            (modus-ponens tm-300 tm-310 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (or (and (-> A (-> B (and A B))) C) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13004.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (((B -> (C -> (B and C))) and A) or D))), M:tm-300, m:tm-310, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (or (and (-> A (-> B (and A B))) C) Bm))))
================================================================
tm-name          tm-13005
in-theory        13005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and (D or E))))
theorem-size     17
proof            (modus-ponens tm-270 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13005.        ((A -> (((B and C) -> C) and A)) and (D -> (D and (D or E)))), M:tm-270, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13006
in-theory        13006
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((((B and C) -> C) and A) or D)))
theorem-size     27
proof            (modus-ponens tm-267 tm-310 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (or (and (-> (and A B) B) C) Bm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13006.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((((B and C) -> C) and A) or D))), M:tm-267, m:tm-310, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (or (and (-> (and A B) B) C) Bm))))
================================================================
tm-name          tm-13007
in-theory        13007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and (D or E))))
theorem-size     17
proof            (modus-ponens tm-239 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13007.        ((A -> (((B and C) -> B) and A)) and (D -> (D and (D or E)))), M:tm-239, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13008
in-theory        13008
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((((B and C) -> B) and A) or D)))
theorem-size     27
proof            (modus-ponens tm-236 tm-310 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (or (and (-> (and A B) A) C) Bm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13008.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((((B and C) -> B) and A) or D))), M:tm-236, m:tm-310, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (or (and (-> (and A B) A) C) Bm))))
================================================================
tm-name          tm-13009
in-theory        13009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (E or F))))
theorem-size     25
proof            (modus-ponens tm-210 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13009.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (E or F)))), M:tm-210, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13010
in-theory        13010
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) or E)))
theorem-size     51
proof            (modus-ponens tm-207 tm-310 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (or (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13010.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) or E))), M:tm-207, m:tm-310, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (or (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm))))
================================================================
tm-name          tm-13011
in-theory        13011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (D or E))))
theorem-size     17
proof            (modus-ponens tm-183 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13011.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (D or E)))), M:tm-183, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13012
in-theory        13012
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (((B -> (C -> B)) and A) or D)))
theorem-size     27
proof            (modus-ponens tm-180 tm-310 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (or (and (-> A (-> B A)) C) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13012.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (((B -> (C -> B)) and A) or D))), M:tm-180, m:tm-310, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (or (and (-> A (-> B A)) C) Bm))))
================================================================
tm-name          tm-13013
in-theory        13013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-157 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13013.        ((A -> ((B and C) -> C)) and (D -> (D and (D or E)))), M:tm-157, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13014
in-theory        13014
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and (((B and C) -> C) or D)))
theorem-size     21
proof            (modus-ponens tm-154 tm-310 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (or (-> (and A B) B) Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13014.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and (((B and C) -> C) or D))), M:tm-154, m:tm-310, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (or (-> (and A B) B) Bm))))
================================================================
tm-name          tm-13015
in-theory        13015
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (D or E))))
theorem-size     23
proof            (modus-ponens tm-147 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13015.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (D or E)))), M:tm-147, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13016
in-theory        13016
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (((A and (B -> C)) -> C) or D)))
theorem-size     33
proof            (modus-ponens tm-144 tm-310 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (or (-> (and A (-> B C)) C) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13016.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (((A and (B -> C)) -> C) or D))), M:tm-144, m:tm-310, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (or (-> (and A (-> B C)) C) Bm))))
================================================================
tm-name          tm-13017
in-theory        13017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-134 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13017.        ((A -> ((B and C) -> B)) and (D -> (D and (D or E)))), M:tm-134, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13018
in-theory        13018
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and (((B and C) -> B) or D)))
theorem-size     21
proof            (modus-ponens tm-131 tm-310 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (or (-> (and A B) A) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13018.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and (((B and C) -> B) or D))), M:tm-131, m:tm-310, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (or (-> (and A B) A) Bm))))
================================================================
tm-name          tm-13019
in-theory        13019
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (D or E))))
theorem-size     23
proof            (modus-ponens tm-125 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13019.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (D or E)))), M:tm-125, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13020
in-theory        13020
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((((A -> B) and C) -> B) or D)))
theorem-size     33
proof            (modus-ponens tm-122 tm-310 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (or (-> (and (-> A B) C) B) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13020.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((((A -> B) and C) -> B) or D))), M:tm-122, m:tm-310, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (or (-> (and (-> A B) C) B) Bm))))
================================================================
tm-name          tm-13021
in-theory        13021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (E or F))))
theorem-size     23
proof            (modus-ponens tm-113 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13021.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (E or F)))), M:tm-113, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13022
in-theory        13022
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))
theorem-size     45
proof            (modus-ponens tm-110 tm-310 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (or (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13022.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))), M:tm-110, m:tm-310, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (or (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm))))
================================================================
tm-name          tm-13023
in-theory        13023
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (D or E))))
theorem-size     27
proof            (modus-ponens tm-105 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13023.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (D or E)))), M:tm-105, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13024
in-theory        13024
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((A -> (B -> C)) -> (A -> C)) or D)))
theorem-size     41
proof            (modus-ponens tm-102 tm-310 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (or (-> (-> A (-> B C)) (-> A C)) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13024.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((A -> (B -> C)) -> (A -> C)) or D))), M:tm-102, m:tm-310, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (or (-> (-> A (-> B C)) (-> A C)) Bm))))
================================================================
tm-name          tm-13025
in-theory        13025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and (C or D))))
theorem-size     15
proof            (modus-ponens tm-95 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13025.        (((A -> B) -> (A -> A)) and (C -> (C and (C or D)))), M:tm-95, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13026
in-theory        13026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and ((A -> A) or C)))
theorem-size     17
proof            (modus-ponens tm-92 tm-310 ((Am (-> A A)) (B (and (-> A A) (or (-> A A) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13026.        (((A -> B) or (A -> A)) -> ((A -> A) and ((A -> A) or C))), M:tm-92, m:tm-310, u:((Am (-> A A)) (B (and (-> A A) (or (-> A A) Bm))))
================================================================
tm-name          tm-13027
in-theory        13027
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and (A or C))))
theorem-size     9
proof            (modus-ponens tm-84 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13027.        (A -> (B -> (A and (A or C)))), M:tm-84, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-13028
in-theory        13028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-83 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13028.        ((A -> (B -> (C -> B))) and (D -> (D and (D or E)))), M:tm-83, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13029
in-theory        13029
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((B -> (C -> B)) or D)))
theorem-size     21
proof            (modus-ponens tm-80 tm-310 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (or (-> A (-> B A)) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13029.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((B -> (C -> B)) or D))), M:tm-80, m:tm-310, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (or (-> A (-> B A)) Bm))))
================================================================
tm-name          tm-13030
in-theory        13030
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and (B or C))))
theorem-size     13
proof            (modus-ponens tm-76 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13030.        (((not (not A)) -> A) and (B -> (B and (B or C)))), M:tm-76, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13031
in-theory        13031
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and (A or B)))
theorem-size     11
proof            (modus-ponens tm-73 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13031.        (((not (not A)) or A) -> (A and (A or B))), M:tm-73, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-13032
in-theory        13032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (C or D))))
theorem-size     19
proof            (modus-ponens tm-69 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13032.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (C or D)))), M:tm-69, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13033
in-theory        13033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((A -> (not B)) -> (not A)) or C)))
theorem-size     29
proof            (modus-ponens tm-66 tm-310 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (or (-> (-> A (not B)) (not A)) Bm)))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-6)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13033.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((A -> (not B)) -> (not A)) or C))), M:tm-66, m:tm-310, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (or (-> (-> A (not B)) (not A)) Bm))))
================================================================
tm-name          tm-13034
in-theory        13034
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (D or E))))
theorem-size     21
proof            (modus-ponens tm-54 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13034.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (D or E)))), M:tm-54, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13035
in-theory        13035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((B -> C) -> ((A or B) -> C)) or D)))
theorem-size     35
proof            (modus-ponens tm-51 tm-310 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (or (-> (-> A B) (-> (or C A) B)) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13035.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((B -> C) -> ((A or B) -> C)) or D))), M:tm-51, m:tm-310, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (or (-> (-> A B) (-> (or C A) B)) Bm))))
================================================================
tm-name          tm-13036
in-theory        13036
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and ((B or A) or C)))
theorem-size     15
proof            (modus-ponens tm-50 tm-310 ((Am (or A B)) (C (and (or A B) (or (or A B) Bm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13036.        ((A or (B or A)) -> ((B or A) and ((B or A) or C))), M:tm-50, m:tm-310, u:((Am (or A B)) (C (and (or A B) (or (or A B) Bm))))
================================================================
tm-name          tm-13037
in-theory        13037
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and ((A or B) or C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-310 ((Am (or A B)) (C (and (or A B) (or (or A B) Bm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13037.        ((A or (A or B)) -> ((A or B) and ((A or B) or C))), M:tm-49, m:tm-310, u:((Am (or A B)) (C (and (or A B) (or (or A B) Bm))))
================================================================
tm-name          tm-13038
in-theory        13038
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((B -> (A and B)) or C)))
theorem-size     21
proof            (modus-ponens tm-48 tm-310 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (or (-> A (and B A)) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13038.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((B -> (A and B)) or C))), M:tm-48, m:tm-310, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (or (-> A (and B A)) Bm))))
================================================================
tm-name          tm-13039
in-theory        13039
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (B or C)))
theorem-size     11
proof            (modus-ponens tm-47 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13039.        (((A and B) or B) -> (B and (B or C))), M:tm-47, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-13040
in-theory        13040
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (A or C)))
theorem-size     11
proof            (modus-ponens tm-46 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13040.        (((A and B) or A) -> (A and (A or C))), M:tm-46, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-13041
in-theory        13041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (A -> C)) or D)))
theorem-size     31
proof            (modus-ponens tm-45 tm-310 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (or (-> (-> A B) (-> A C)) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13041.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (A -> C)) or D))), M:tm-45, m:tm-310, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (or (-> (-> A B) (-> A C)) Bm))))
================================================================
tm-name          tm-13042
in-theory        13042
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and ((B -> A) or C)))
theorem-size     15
proof            (modus-ponens tm-44 tm-310 ((Am (-> A B)) (C (and (-> A B) (or (-> A B) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13042.        ((A or (B -> A)) -> ((B -> A) and ((B -> A) or C))), M:tm-44, m:tm-310, u:((Am (-> A B)) (C (and (-> A B) (or (-> A B) Bm))))
================================================================
tm-name          tm-13043
in-theory        13043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and (C or D))))
theorem-size     13
proof            (modus-ponens tm-42 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13043.        ((A -> (B or A)) and (C -> (C and (C or D)))), M:tm-42, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13044
in-theory        13044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and (C or D))))
theorem-size     13
proof            (modus-ponens tm-32 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13044.        ((A -> (A or B)) and (C -> (C and (C or D)))), M:tm-32, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13045
in-theory        13045
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and (A or B))))
theorem-size     9
proof            (modus-ponens tm-24 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13045.        (A -> (A and (A and (A or B)))), M:tm-24, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-13046
in-theory        13046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and (C or D))))
theorem-size     15
proof            (modus-ponens tm-23 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13046.        ((A -> (B -> (A and B))) and (C -> (C and (C or D)))), M:tm-23, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13047
in-theory        13047
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and (C or D))))
theorem-size     13
proof            (modus-ponens tm-22 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13047.        (((A and B) -> B) and (C -> (C and (C or D)))), M:tm-22, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13048
in-theory        13048
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and (C or D))))
theorem-size     13
proof            (modus-ponens tm-21 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13048.        (((A and B) -> A) and (C -> (C and (C or D)))), M:tm-21, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13049
in-theory        13049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (D or E))))
theorem-size     21
proof            (modus-ponens tm-20 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13049.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (D or E)))), M:tm-20, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13050
in-theory        13050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and (C or D))))
theorem-size     13
proof            (modus-ponens tm-19 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13050.        ((A -> (B -> A)) and (C -> (C and (C or D)))), M:tm-19, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13051
in-theory        13051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and (A or B)))) -> (not A))
theorem-size     11
proof            (modus-ponens tm-9 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-9 tm-2 tm-5 tm-6)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13051.        ((A -> (not (A and (A or B)))) -> (not A)), M:tm-9, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-13052
in-theory        13052
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A or B)) -> C) -> ((A or (A and (A or B))) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13052.        (((A and (A or B)) -> C) -> ((A or (A and (A or B))) -> C)), M:tm-8, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-13053
in-theory        13053
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and (B or C))))
theorem-size     9
proof            (modus-ponens tm-7 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-7 tm-2 tm-5 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13053.        (A or (B -> (B and (B or C)))), M:tm-7, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13054
in-theory        13054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) or C)
theorem-size     9
proof            (modus-ponens tm-6 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-6 tm-2 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13054.        ((A -> (A and (A or B))) or C), M:tm-6, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13055
in-theory        13055
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and (B or C))) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13055.        (A -> ((B -> (B and (B or C))) and A)), M:tm-5, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13056
in-theory        13056
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and (B or C))))
theorem-size     9
proof            (modus-ponens tm-1 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-1 tm-2 tm-5 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13056.        (A -> (B -> (B and (B or C)))), M:tm-1, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13057
in-theory        13057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (A -> (B -> A))))
theorem-size     13
proof            (modus-ponens tm-311 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-13057.        ((A -> (B -> A)) and (C or (A -> (B -> A)))), M:tm-311, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-13058
in-theory        13058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13058.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))), M:tm-311, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-13059
in-theory        13059
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((A and B) -> A)))
theorem-size     13
proof            (modus-ponens tm-311 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-13059.        (((A and B) -> A) and (C or ((A and B) -> A))), M:tm-311, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-13060
in-theory        13060
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((A and B) -> B)))
theorem-size     13
proof            (modus-ponens tm-311 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-13060.        (((A and B) -> B) and (C or ((A and B) -> B))), M:tm-311, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-13061
in-theory        13061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (A -> (B -> (A and B)))))
theorem-size     17
proof            (modus-ponens tm-311 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13061.        ((A -> (B -> (A and B))) and (C or (A -> (B -> (A and B))))), M:tm-311, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-13062
in-theory        13062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (A -> (A or B))))
theorem-size     13
proof            (modus-ponens tm-311 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-13062.        ((A -> (A or B)) and (C or (A -> (A or B)))), M:tm-311, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-13063
in-theory        13063
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (A -> (B or A))))
theorem-size     13
proof            (modus-ponens tm-311 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13063.        ((A -> (B or A)) and (C or (A -> (B or A)))), M:tm-311, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-13064
in-theory        13064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((A -> B) -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13064.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((A -> B) -> ((B -> C) -> ((A or B) -> C))))), M:tm-311, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-13065
in-theory        13065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((A -> B) -> ((A -> (not B)) -> (not A)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13065.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((A -> B) -> ((A -> (not B)) -> (not A))))), M:tm-311, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-13066
in-theory        13066
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((not (not A)) -> A)))
theorem-size     13
proof            (modus-ponens tm-311 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-13066.        (((not (not A)) -> A) and (B or ((not (not A)) -> A))), M:tm-311, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-13067
in-theory        13067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (A -> (B -> (C -> B)))))
theorem-size     17
proof            (modus-ponens tm-311 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13067.        ((A -> (B -> (C -> B))) and (D or (A -> (B -> (C -> B))))), M:tm-311, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-13068
in-theory        13068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((A -> B) -> (A -> A))))
theorem-size     17
proof            (modus-ponens tm-311 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13068.        (((A -> B) -> (A -> A)) and (C or ((A -> B) -> (A -> A)))), M:tm-311, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-13069
in-theory        13069
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-13069.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-311, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-13070
in-theory        13070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13070.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-311, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-13071
in-theory        13071
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))))
theorem-size     33
proof            (modus-ponens tm-311 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-13071.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)))), M:tm-311, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-13072
in-theory        13072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (A -> ((B and C) -> B))))
theorem-size     17
proof            (modus-ponens tm-311 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13072.        ((A -> ((B and C) -> B)) and (D or (A -> ((B and C) -> B)))), M:tm-311, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-13073
in-theory        13073
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))))
theorem-size     33
proof            (modus-ponens tm-311 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-13073.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)))), M:tm-311, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-13074
in-theory        13074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (A -> ((B and C) -> C))))
theorem-size     17
proof            (modus-ponens tm-311 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13074.        ((A -> ((B and C) -> C)) and (D or (A -> ((B and C) -> C)))), M:tm-311, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-13075
in-theory        13075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (A -> ((B -> (C -> B)) and A))))
theorem-size     21
proof            (modus-ponens tm-311 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13075.        ((A -> ((B -> (C -> B)) and A)) and (D or (A -> ((B -> (C -> B)) and A)))), M:tm-311, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-13076
in-theory        13076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     37
proof            (modus-ponens tm-311 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13076.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-311, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-13077
in-theory        13077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (A -> (((B and C) -> B) and A))))
theorem-size     21
proof            (modus-ponens tm-311 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13077.        ((A -> (((B and C) -> B) and A)) and (D or (A -> (((B and C) -> B) and A)))), M:tm-311, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-13078
in-theory        13078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (A -> (((B and C) -> C) and A))))
theorem-size     21
proof            (modus-ponens tm-311 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13078.        ((A -> (((B and C) -> C) and A)) and (D or (A -> (((B and C) -> C) and A)))), M:tm-311, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-13079
in-theory        13079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (A -> ((B -> (C -> (B and C))) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13079.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (A -> ((B -> (C -> (B and C))) and A)))), M:tm-311, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-13080
in-theory        13080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((A -> B) -> (A -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13080.        (((A -> B) -> (A -> (A and B))) and (C or ((A -> B) -> (A -> (A and B))))), M:tm-311, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-13081
in-theory        13081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (A -> (B -> (C -> (B and C))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13081.        ((A -> (B -> (C -> (B and C)))) and (D or (A -> (B -> (C -> (B and C)))))), M:tm-311, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-13082
in-theory        13082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((A -> (B -> A)) or C)))
theorem-size     17
proof            (modus-ponens tm-311 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13082.        (((A -> (B -> A)) or C) and (D or ((A -> (B -> A)) or C))), M:tm-311, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-13083
in-theory        13083
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)))
theorem-size     33
proof            (modus-ponens tm-311 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13083.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D))), M:tm-311, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-13084
in-theory        13084
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (((A and B) -> A) or C)))
theorem-size     17
proof            (modus-ponens tm-311 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13084.        ((((A and B) -> A) or C) and (D or (((A and B) -> A) or C))), M:tm-311, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-13085
in-theory        13085
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (((A and B) -> B) or C)))
theorem-size     17
proof            (modus-ponens tm-311 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13085.        ((((A and B) -> B) or C) and (D or (((A and B) -> B) or C))), M:tm-311, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-13086
in-theory        13086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((A -> (B -> (A and B))) or C)))
theorem-size     21
proof            (modus-ponens tm-311 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13086.        (((A -> (B -> (A and B))) or C) and (D or ((A -> (B -> (A and B))) or C))), M:tm-311, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-13087
in-theory        13087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((A -> (A or B)) or C)))
theorem-size     17
proof            (modus-ponens tm-311 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13087.        (((A -> (A or B)) or C) and (D or ((A -> (A or B)) or C))), M:tm-311, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-13088
in-theory        13088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (A -> ((B -> (B or C)) and A))))
theorem-size     21
proof            (modus-ponens tm-311 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13088.        ((A -> ((B -> (B or C)) and A)) and (D or (A -> ((B -> (B or C)) and A)))), M:tm-311, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-13089
in-theory        13089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (A -> (B -> (B or C)))))
theorem-size     17
proof            (modus-ponens tm-311 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13089.        ((A -> (B -> (B or C))) and (D or (A -> (B -> (B or C))))), M:tm-311, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-13090
in-theory        13090
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (A or (B -> (C -> B)))))
theorem-size     17
proof            (modus-ponens tm-311 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13090.        ((A or (B -> (C -> B))) and (D or (A or (B -> (C -> B))))), M:tm-311, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-13091
in-theory        13091
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13091.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-311, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-13092
in-theory        13092
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (A or ((B and C) -> B))))
theorem-size     17
proof            (modus-ponens tm-311 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13092.        ((A or ((B and C) -> B)) and (D or (A or ((B and C) -> B)))), M:tm-311, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-13093
in-theory        13093
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (A or ((B and C) -> C))))
theorem-size     17
proof            (modus-ponens tm-311 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13093.        ((A or ((B and C) -> C)) and (D or (A or ((B and C) -> C)))), M:tm-311, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-13094
in-theory        13094
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (A or (B -> (C -> (B and C))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13094.        ((A or (B -> (C -> (B and C)))) and (D or (A or (B -> (C -> (B and C)))))), M:tm-311, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-13095
in-theory        13095
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (A or (B -> (B or C)))))
theorem-size     17
proof            (modus-ponens tm-311 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13095.        ((A or (B -> (B or C))) and (D or (A or (B -> (B or C))))), M:tm-311, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-13096
in-theory        13096
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (A or (B -> (C or B)))))
theorem-size     17
proof            (modus-ponens tm-311 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13096.        ((A or (B -> (C or B))) and (D or (A or (B -> (C or B))))), M:tm-311, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-13097
in-theory        13097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((A -> (B or A)) or C)))
theorem-size     17
proof            (modus-ponens tm-311 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13097.        (((A -> (B or A)) or C) and (D or ((A -> (B or A)) or C))), M:tm-311, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-13098
in-theory        13098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (A -> ((B -> (C or B)) and A))))
theorem-size     21
proof            (modus-ponens tm-311 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13098.        ((A -> ((B -> (C or B)) and A)) and (D or (A -> ((B -> (C or B)) and A)))), M:tm-311, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-13099
in-theory        13099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (A -> (B -> (C or B)))))
theorem-size     17
proof            (modus-ponens tm-311 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13099.        ((A -> (B -> (C or B))) and (D or (A -> (B -> (C or B))))), M:tm-311, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-13100
in-theory        13100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((A -> B) -> C) -> ((B or (A -> B)) -> C))))
theorem-size     29
proof            (modus-ponens tm-311 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13100.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((A -> B) -> C) -> ((B or (A -> B)) -> C)))), M:tm-311, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-13101
in-theory        13101
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     53
proof            (modus-ponens tm-311 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13101.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-311, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-13102
in-theory        13102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((A -> B) -> (((A and C) or A) -> B))))
theorem-size     25
proof            (modus-ponens tm-311 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13102.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((A -> B) -> (((A and C) or A) -> B)))), M:tm-311, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-13103
in-theory        13103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D or ((A -> B) -> (((C and A) or A) -> B))))
theorem-size     25
proof            (modus-ponens tm-311 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13103.        (((A -> B) -> (((C and A) or A) -> B)) and (D or ((A -> B) -> (((C and A) or A) -> B)))), M:tm-311, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-13104
in-theory        13104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))))
theorem-size     37
proof            (modus-ponens tm-311 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13104.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D or (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)))), M:tm-311, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-13105
in-theory        13105
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((A or B) -> C) -> ((A or (A or B)) -> C))))
theorem-size     29
proof            (modus-ponens tm-311 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13105.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D or (((A or B) -> C) -> ((A or (A or B)) -> C)))), M:tm-311, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-13106
in-theory        13106
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((A or B) -> C) -> ((B or (A or B)) -> C))))
theorem-size     29
proof            (modus-ponens tm-311 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13106.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D or (((A or B) -> C) -> ((B or (A or B)) -> C)))), M:tm-311, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-13107
in-theory        13107
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     57
proof            (modus-ponens tm-311 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13107.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E or ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-311, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-13108
in-theory        13108
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13108.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-311, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-13109
in-theory        13109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)))
theorem-size     33
proof            (modus-ponens tm-311 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13109.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E or (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D))), M:tm-311, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-13110
in-theory        13110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (E or (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))))
theorem-size     37
proof            (modus-ponens tm-311 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13110.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (E or (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)))), M:tm-311, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-13111
in-theory        13111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (D or (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-13111.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (D or (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))))), M:tm-311, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-13112
in-theory        13112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13112.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E or (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-311, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-13113
in-theory        13113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (C or ((A -> (not (B -> A))) -> (not A))))
theorem-size     21
proof            (modus-ponens tm-311 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13113.        (((A -> (not (B -> A))) -> (not A)) and (C or ((A -> (not (B -> A))) -> (not A)))), M:tm-311, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-13114
in-theory        13114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (D or (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13114.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (D or (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))))), M:tm-311, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-13115
in-theory        13115
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (C or (((A and B) -> (not A)) -> (not (A and B)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13115.        ((((A and B) -> (not A)) -> (not (A and B))) and (C or (((A and B) -> (not A)) -> (not (A and B))))), M:tm-311, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-13116
in-theory        13116
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (C or (((A and B) -> (not B)) -> (not (A and B)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13116.        ((((A and B) -> (not B)) -> (not (A and B))) and (C or (((A and B) -> (not B)) -> (not (A and B))))), M:tm-311, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-13117
in-theory        13117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (C or ((A -> (not (B -> (A and B)))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13117.        (((A -> (not (B -> (A and B)))) -> (not A)) and (C or ((A -> (not (B -> (A and B)))) -> (not A)))), M:tm-311, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-13118
in-theory        13118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (C or ((A -> (not (A or B))) -> (not A))))
theorem-size     21
proof            (modus-ponens tm-311 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13118.        (((A -> (not (A or B))) -> (not A)) and (C or ((A -> (not (A or B))) -> (not A)))), M:tm-311, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-13119
in-theory        13119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (C or ((A -> (not (B or A))) -> (not A))))
theorem-size     21
proof            (modus-ponens tm-311 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13119.        (((A -> (not (B or A))) -> (not A)) and (C or ((A -> (not (B or A))) -> (not A)))), M:tm-311, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-13120
in-theory        13120
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (D or (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-8)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13120.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (D or (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))))), M:tm-311, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-13121
in-theory        13121
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (C or (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13121.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (C or (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))))), M:tm-311, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-13122
in-theory        13122
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (D or ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))))
theorem-size     49
proof            (modus-ponens tm-311 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-9)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13122.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (D or ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))), M:tm-311, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-13123
in-theory        13123
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D or (A or ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13123.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D or (A or ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-311, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-13124
in-theory        13124
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (D or (((A -> B) -> ((A -> (not B)) -> (not A))) or C)))
theorem-size     29
proof            (modus-ponens tm-311 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13124.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (D or (((A -> B) -> ((A -> (not B)) -> (not A))) or C))), M:tm-311, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-13125
in-theory        13125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (D or (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A))))
theorem-size     33
proof            (modus-ponens tm-311 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13125.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (D or (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)))), M:tm-311, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-13126
in-theory        13126
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (C or (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-13126.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (C or (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))))), M:tm-311, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-13127
in-theory        13127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D or (A -> ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13127.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D or (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-311, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-13128
in-theory        13128
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (B or (((not (not A)) -> (not A)) -> (not (not (not A))))))
theorem-size     25
proof            (modus-ponens tm-311 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13128.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (B or (((not (not A)) -> (not A)) -> (not (not (not A)))))), M:tm-311, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-13129
in-theory        13129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (C or ((A -> B) -> (((not (not A)) or A) -> B))))
theorem-size     25
proof            (modus-ponens tm-311 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-10)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13129.        (((A -> B) -> (((not (not A)) or A) -> B)) and (C or ((A -> B) -> (((not (not A)) or A) -> B)))), M:tm-311, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-13130
in-theory        13130
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and (C or (A or ((not (not B)) -> B))))
theorem-size     17
proof            (modus-ponens tm-311 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13130.        ((A or ((not (not B)) -> B)) and (C or (A or ((not (not B)) -> B)))), M:tm-311, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-13131
in-theory        13131
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and (C or (((not (not A)) -> A) or B)))
theorem-size     17
proof            (modus-ponens tm-311 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13131.        ((((not (not A)) -> A) or B) and (C or (((not (not A)) -> A) or B))), M:tm-311, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-13132
in-theory        13132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (C or (A -> (((not (not B)) -> B) and A))))
theorem-size     21
proof            (modus-ponens tm-311 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13132.        ((A -> (((not (not B)) -> B) and A)) and (C or (A -> (((not (not B)) -> B) and A)))), M:tm-311, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-13133
in-theory        13133
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (C or (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B))))
theorem-size     33
proof            (modus-ponens tm-311 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-13133.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (C or (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)))), M:tm-311, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-13134
in-theory        13134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and (C or (A -> ((not (not B)) -> B))))
theorem-size     17
proof            (modus-ponens tm-311 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13134.        ((A -> ((not (not B)) -> B)) and (C or (A -> ((not (not B)) -> B)))), M:tm-311, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-13135
in-theory        13135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (D or ((A -> (not (B -> (C -> B)))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13135.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (D or ((A -> (not (B -> (C -> B)))) -> (not A)))), M:tm-311, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-13136
in-theory        13136
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (E or (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C))))
theorem-size     37
proof            (modus-ponens tm-311 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13136.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (E or (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)))), M:tm-311, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-13137
in-theory        13137
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and (E or (A or (B -> (C -> (D -> C))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13137.        ((A or (B -> (C -> (D -> C)))) and (E or (A or (B -> (C -> (D -> C)))))), M:tm-311, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-13138
in-theory        13138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and (E or ((A -> (B -> (C -> B))) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13138.        (((A -> (B -> (C -> B))) or D) and (E or ((A -> (B -> (C -> B))) or D))), M:tm-311, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-13139
in-theory        13139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and (E or (A -> ((B -> (C -> (D -> C))) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13139.        ((A -> ((B -> (C -> (D -> C))) and A)) and (E or (A -> ((B -> (C -> (D -> C))) and A)))), M:tm-311, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-13140
in-theory        13140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (D or ((A -> B) -> (A -> (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13140.        (((A -> B) -> (A -> (C -> B))) and (D or ((A -> B) -> (A -> (C -> B))))), M:tm-311, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-13141
in-theory        13141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (E or (A -> (B -> (C -> (D -> C))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13141.        ((A -> (B -> (C -> (D -> C)))) and (E or (A -> (B -> (C -> (D -> C)))))), M:tm-311, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-13142
in-theory        13142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and (B or (A -> A)))
theorem-size     9
proof            (modus-ponens tm-311 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13142.        ((A -> A) and (B or (A -> A))), M:tm-311, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-13143
in-theory        13143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (D or ((A -> (B -> C)) -> (A -> (B -> C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13143.        (((A -> (B -> C)) -> (A -> (B -> C))) and (D or ((A -> (B -> C)) -> (A -> (B -> C))))), M:tm-311, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-13144
in-theory        13144
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and (C or ((A and B) -> (A and B))))
theorem-size     17
proof            (modus-ponens tm-311 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13144.        (((A and B) -> (A and B)) and (C or ((A and B) -> (A and B)))), M:tm-311, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-13145
in-theory        13145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (C or ((A -> B) -> (A -> B))))
theorem-size     17
proof            (modus-ponens tm-311 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13145.        (((A -> B) -> (A -> B)) and (C or ((A -> B) -> (A -> B)))), M:tm-311, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-13146
in-theory        13146
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and (B or ((not (not A)) -> (not (not A)))))
theorem-size     17
proof            (modus-ponens tm-311 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13146.        (((not (not A)) -> (not (not A))) and (B or ((not (not A)) -> (not (not A))))), M:tm-311, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-13147
in-theory        13147
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (C or (((A -> B) -> (not (A -> A))) -> (not (A -> B)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13147.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (C or (((A -> B) -> (not (A -> A))) -> (not (A -> B))))), M:tm-311, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-13148
in-theory        13148
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (D or (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B))))
theorem-size     33
proof            (modus-ponens tm-311 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13148.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (D or (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)))), M:tm-311, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-13149
in-theory        13149
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and (D or (A or ((B -> C) -> (B -> B)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13149.        ((A or ((B -> C) -> (B -> B))) and (D or (A or ((B -> C) -> (B -> B))))), M:tm-311, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-13150
in-theory        13150
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and (D or (((A -> B) -> (A -> A)) or C)))
theorem-size     21
proof            (modus-ponens tm-311 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13150.        ((((A -> B) -> (A -> A)) or C) and (D or (((A -> B) -> (A -> A)) or C))), M:tm-311, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-13151
in-theory        13151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (D or (A -> (((B -> C) -> (B -> B)) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13151.        ((A -> (((B -> C) -> (B -> B)) and A)) and (D or (A -> (((B -> C) -> (B -> B)) and A)))), M:tm-311, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-13152
in-theory        13152
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and (C or (((A -> B) -> A) -> ((A -> B) -> A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-13152.        ((((A -> B) -> A) -> ((A -> B) -> A)) and (C or (((A -> B) -> A) -> ((A -> B) -> A)))), M:tm-311, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-13153
in-theory        13153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and (D or (A -> ((B -> C) -> (B -> B)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13153.        ((A -> ((B -> C) -> (B -> B))) and (D or (A -> ((B -> C) -> (B -> B))))), M:tm-311, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-13154
in-theory        13154
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (D or ((A -> ((B -> A) -> C)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-13154.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (D or ((A -> ((B -> A) -> C)) -> (A -> C)))), M:tm-311, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-13155
in-theory        13155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (C or ((A -> (A -> B)) -> (A -> B))))
theorem-size     21
proof            (modus-ponens tm-311 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-13155.        (((A -> (A -> B)) -> (A -> B)) and (C or ((A -> (A -> B)) -> (A -> B)))), M:tm-311, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-13156
in-theory        13156
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (D or (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-13156.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (D or (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))))), M:tm-311, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-13157
in-theory        13157
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (D or ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B))))))
theorem-size     65
proof            (modus-ponens tm-311 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-13157.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (D or ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))))), M:tm-311, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-13158
in-theory        13158
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (E or ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))))
theorem-size     69
proof            (modus-ponens tm-311 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-13158.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (E or ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))), M:tm-311, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-13159
in-theory        13159
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E or (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13159.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E or (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-311, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-13160
in-theory        13160
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (E or ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D)))
theorem-size     45
proof            (modus-ponens tm-311 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13160.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (E or ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D))), M:tm-311, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-13161
in-theory        13161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (E or (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))))
theorem-size     49
proof            (modus-ponens tm-311 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13161.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (E or (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)))), M:tm-311, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-13162
in-theory        13162
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (D or ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-311 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-13162.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (D or ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))), M:tm-311, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-13163
in-theory        13163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E or (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13163.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E or (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-311, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-13164
in-theory        13164
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (E or (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-311 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-13164.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (E or (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)))), M:tm-311, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-13165
in-theory        13165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (E or ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A))))
theorem-size     41
proof            (modus-ponens tm-311 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13165.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (E or ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)))), M:tm-311, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-13166
in-theory        13166
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (F or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))))
theorem-size     69
proof            (modus-ponens tm-311 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13166.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (F or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))), M:tm-311, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-13167
in-theory        13167
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F or (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13167.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F or (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-311, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-13168
in-theory        13168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F or ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     37
proof            (modus-ponens tm-311 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13168.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F or ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-311, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-13169
in-theory        13169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F or (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     41
proof            (modus-ponens tm-311 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13169.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F or (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-311, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-13170
in-theory        13170
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (E or ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13170.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (E or ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))))), M:tm-311, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-13171
in-theory        13171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F or (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13171.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F or (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-311, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-13172
in-theory        13172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and (C or (((A -> B) and A) -> B)))
theorem-size     17
proof            (modus-ponens tm-311 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-13172.        ((((A -> B) and A) -> B) and (C or (((A -> B) and A) -> B))), M:tm-311, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-13173
in-theory        13173
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and (E or ((((A -> (B -> A)) -> C) and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-311 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-13173.        (((((A -> (B -> A)) -> C) and D) -> C) and (E or ((((A -> (B -> A)) -> C) and D) -> C))), M:tm-311, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-13174
in-theory        13174
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (F or (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D)))
theorem-size     41
proof            (modus-ponens tm-311 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13174.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (F or (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D))), M:tm-311, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-13175
in-theory        13175
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (D or (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B))))
theorem-size     45
proof            (modus-ponens tm-311 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-13175.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (D or (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)))), M:tm-311, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-13176
in-theory        13176
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (D or ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A))))
theorem-size     33
proof            (modus-ponens tm-311 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13176.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (D or ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)))), M:tm-311, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-13177
in-theory        13177
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (D or (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A)))))
theorem-size     53
proof            (modus-ponens tm-311 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13177.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (D or (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))))), M:tm-311, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-13178
in-theory        13178
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (E or (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))))
theorem-size     57
proof            (modus-ponens tm-311 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13178.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (E or (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))), M:tm-311, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-13179
in-theory        13179
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E or (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13179.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E or (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-311, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-13180
in-theory        13180
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (E or (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D)))
theorem-size     37
proof            (modus-ponens tm-311 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13180.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (E or (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D))), M:tm-311, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-13181
in-theory        13181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (E or (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))))
theorem-size     41
proof            (modus-ponens tm-311 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13181.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (E or (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)))), M:tm-311, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-13182
in-theory        13182
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (D or (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B))))
theorem-size     49
proof            (modus-ponens tm-311 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-13182.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (D or (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)))), M:tm-311, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-13183
in-theory        13183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E or (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13183.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E or (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-311, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-13184
in-theory        13184
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and (E or (((((A and B) -> A) -> C) and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-311 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-13184.        ((((((A and B) -> A) -> C) and D) -> C) and (E or (((((A and B) -> A) -> C) and D) -> C))), M:tm-311, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-13185
in-theory        13185
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (D or (((A and B) -> (A -> C)) -> ((A and B) -> C))))
theorem-size     29
proof            (modus-ponens tm-311 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-13185.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (D or (((A and B) -> (A -> C)) -> ((A and B) -> C)))), M:tm-311, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-13186
in-theory        13186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (D or ((A -> (not ((B and C) -> B))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13186.        (((A -> (not ((B and C) -> B))) -> (not A)) and (D or ((A -> (not ((B and C) -> B))) -> (not A)))), M:tm-311, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-13187
in-theory        13187
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (E or ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C))))
theorem-size     37
proof            (modus-ponens tm-311 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13187.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (E or ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)))), M:tm-311, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-13188
in-theory        13188
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and (E or (A or (B -> ((C and D) -> C)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13188.        ((A or (B -> ((C and D) -> C))) and (E or (A or (B -> ((C and D) -> C))))), M:tm-311, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-13189
in-theory        13189
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and (E or ((A -> ((B and C) -> B)) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13189.        (((A -> ((B and C) -> B)) or D) and (E or ((A -> ((B and C) -> B)) or D))), M:tm-311, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-13190
in-theory        13190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and (E or (A -> ((B -> ((C and D) -> C)) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13190.        ((A -> ((B -> ((C and D) -> C)) and A)) and (E or (A -> ((B -> ((C and D) -> C)) and A)))), M:tm-311, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-13191
in-theory        13191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (D or ((A -> (B and C)) -> (A -> B))))
theorem-size     21
proof            (modus-ponens tm-311 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-13191.        (((A -> (B and C)) -> (A -> B)) and (D or ((A -> (B and C)) -> (A -> B)))), M:tm-311, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-13192
in-theory        13192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (E or (A -> (B -> ((C and D) -> C)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13192.        ((A -> (B -> ((C and D) -> C))) and (E or (A -> (B -> ((C and D) -> C))))), M:tm-311, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-13193
in-theory        13193
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and (C or ((A and (A -> B)) -> B)))
theorem-size     17
proof            (modus-ponens tm-311 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-13193.        (((A and (A -> B)) -> B) and (C or ((A and (A -> B)) -> B))), M:tm-311, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-13194
in-theory        13194
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and (E or ((A and ((B -> (C -> B)) -> D)) -> D)))
theorem-size     25
proof            (modus-ponens tm-311 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-13194.        (((A and ((B -> (C -> B)) -> D)) -> D) and (E or ((A and ((B -> (C -> B)) -> D)) -> D))), M:tm-311, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-13195
in-theory        13195
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (F or ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E)))
theorem-size     41
proof            (modus-ponens tm-311 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13195.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (F or ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E))), M:tm-311, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-13196
in-theory        13196
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and (E or ((A and (((B and C) -> B) -> D)) -> D)))
theorem-size     25
proof            (modus-ponens tm-311 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-13196.        (((A and (((B and C) -> B) -> D)) -> D) and (E or ((A and (((B and C) -> B) -> D)) -> D))), M:tm-311, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-13197
in-theory        13197
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (D or (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C))))
theorem-size     45
proof            (modus-ponens tm-311 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-13197.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (D or (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)))), M:tm-311, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-13198
in-theory        13198
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (D or (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B))))
theorem-size     33
proof            (modus-ponens tm-311 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13198.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (D or (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)))), M:tm-311, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-13199
in-theory        13199
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (D or ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B)))))
theorem-size     53
proof            (modus-ponens tm-311 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13199.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (D or ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))))), M:tm-311, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-13200
in-theory        13200
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (E or ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-311 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13200.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (E or ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))), M:tm-311, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-13201
in-theory        13201
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E or (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13201.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E or (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-311, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-13202
in-theory        13202
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (E or ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-311 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13202.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (E or ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D))), M:tm-311, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-13203
in-theory        13203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (E or (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-311 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13203.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (E or (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)))), M:tm-311, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-13204
in-theory        13204
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (D or ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C))))
theorem-size     49
proof            (modus-ponens tm-311 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-13204.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (D or ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)))), M:tm-311, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-13205
in-theory        13205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E or (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13205.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E or (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-311, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-13206
in-theory        13206
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and (E or ((A and (((B and C) -> C) -> D)) -> D)))
theorem-size     25
proof            (modus-ponens tm-311 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-13206.        (((A and (((B and C) -> C) -> D)) -> D) and (E or ((A and (((B and C) -> C) -> D)) -> D))), M:tm-311, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-13207
in-theory        13207
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and (E or (((((A and B) -> B) -> C) and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-311 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-13207.        ((((((A and B) -> B) -> C) and D) -> C) and (E or (((((A and B) -> B) -> C) and D) -> C))), M:tm-311, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-13208
in-theory        13208
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (D or (((A and B) -> (B -> C)) -> ((A and B) -> C))))
theorem-size     29
proof            (modus-ponens tm-311 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-13208.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (D or (((A and B) -> (B -> C)) -> ((A and B) -> C)))), M:tm-311, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-13209
in-theory        13209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (D or ((A -> (not ((B and C) -> C))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13209.        (((A -> (not ((B and C) -> C))) -> (not A)) and (D or ((A -> (not ((B and C) -> C))) -> (not A)))), M:tm-311, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-13210
in-theory        13210
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (E or ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C))))
theorem-size     37
proof            (modus-ponens tm-311 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13210.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (E or ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)))), M:tm-311, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-13211
in-theory        13211
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and (E or (A or (B -> ((C and D) -> D)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-13211.        ((A or (B -> ((C and D) -> D))) and (E or (A or (B -> ((C and D) -> D))))), M:tm-311, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-13212
in-theory        13212
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and (E or ((A -> ((B and C) -> C)) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-13212.        (((A -> ((B and C) -> C)) or D) and (E or ((A -> ((B and C) -> C)) or D))), M:tm-311, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-13213
in-theory        13213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and (E or (A -> ((B -> ((C and D) -> D)) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-13213.        ((A -> ((B -> ((C and D) -> D)) and A)) and (E or (A -> ((B -> ((C and D) -> D)) and A)))), M:tm-311, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-13214
in-theory        13214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (D or ((A -> (B and C)) -> (A -> C))))
theorem-size     21
proof            (modus-ponens tm-311 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-13214.        (((A -> (B and C)) -> (A -> C)) and (D or ((A -> (B and C)) -> (A -> C)))), M:tm-311, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-13215
in-theory        13215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (E or (A -> (B -> ((C and D) -> D)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-13215.        ((A -> (B -> ((C and D) -> D))) and (E or (A -> (B -> ((C and D) -> D))))), M:tm-311, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-13216
in-theory        13216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and (E or ((A -> (B -> A)) and (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13216.        (((A -> (B -> A)) and (C -> (D -> C))) and (E or ((A -> (B -> A)) and (C -> (D -> C))))), M:tm-311, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-13217
in-theory        13217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13217.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-311, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-13218
in-theory        13218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and (E or ((A -> (B -> A)) and ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13218.        (((A -> (B -> A)) and ((C and D) -> C)) and (E or ((A -> (B -> A)) and ((C and D) -> C)))), M:tm-311, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-13219
in-theory        13219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and (E or ((A -> (B -> A)) and ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-311 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13219.        (((A -> (B -> A)) and ((C and D) -> D)) and (E or ((A -> (B -> A)) and ((C and D) -> D)))), M:tm-311, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-13220
in-theory        13220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (E or ((A -> (B -> A)) and (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13220.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (E or ((A -> (B -> A)) and (C -> (D -> (C and D)))))), M:tm-311, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-13221
in-theory        13221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and (E or ((A -> (B -> A)) and (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13221.        (((A -> (B -> A)) and (C -> (C or D))) and (E or ((A -> (B -> A)) and (C -> (C or D))))), M:tm-311, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-13222
in-theory        13222
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and (E or ((A -> (B -> A)) and (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13222.        (((A -> (B -> A)) and (C -> (D or C))) and (E or ((A -> (B -> A)) and (C -> (D or C))))), M:tm-311, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-13223
in-theory        13223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F or ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13223.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F or ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-311, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-13224
in-theory        13224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E or ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13224.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E or ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-311, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-13225
in-theory        13225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and (D or ((A -> (B -> A)) and ((not (not C)) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13225.        (((A -> (B -> A)) and ((not (not C)) -> C)) and (D or ((A -> (B -> A)) and ((not (not C)) -> C)))), M:tm-311, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-13226
in-theory        13226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (F or ((A -> (B -> A)) and (C -> (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13226.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (F or ((A -> (B -> A)) and (C -> (D -> (E -> D)))))), M:tm-311, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-13227
in-theory        13227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (E or ((A -> (B -> A)) and ((C -> D) -> (C -> C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13227.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (E or ((A -> (B -> A)) and ((C -> D) -> (C -> C))))), M:tm-311, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-13228
in-theory        13228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F or ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-311 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13228.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F or ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-311, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-13229
in-theory        13229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13229.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-311, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-13230
in-theory        13230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F or ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13230.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F or ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-311, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-13231
in-theory        13231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (F or ((A -> (B -> A)) and (C -> ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13231.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (F or ((A -> (B -> A)) and (C -> ((D and E) -> D))))), M:tm-311, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-13232
in-theory        13232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F or ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13232.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F or ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-311, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-13233
in-theory        13233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (F or ((A -> (B -> A)) and (C -> ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-13233.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (F or ((A -> (B -> A)) and (C -> ((D and E) -> E))))), M:tm-311, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-13234
in-theory        13234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (F or ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-13234.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (F or ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-311, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-13235
in-theory        13235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (D or ((A -> (not ((B -> (C -> B)) and A))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13235.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (D or ((A -> (not ((B -> (C -> B)) and A))) -> (not A)))), M:tm-311, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-13236
in-theory        13236
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (E or ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-311 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13236.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (E or ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)))), M:tm-311, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-13237
in-theory        13237
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and (E or (A or (B -> ((C -> (D -> C)) and B)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-13237.        ((A or (B -> ((C -> (D -> C)) and B))) and (E or (A or (B -> ((C -> (D -> C)) and B))))), M:tm-311, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-13238
in-theory        13238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and (E or ((A -> ((B -> (C -> B)) and A)) or D)))
theorem-size     25
proof            (modus-ponens tm-311 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-13238.        (((A -> ((B -> (C -> B)) and A)) or D) and (E or ((A -> ((B -> (C -> B)) and A)) or D))), M:tm-311, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-13239
in-theory        13239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (E or (A -> ((B -> ((C -> (D -> C)) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-13239.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (E or (A -> ((B -> ((C -> (D -> C)) and B)) and A)))), M:tm-311, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-13240
in-theory        13240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (E or (A -> (B -> ((C -> (D -> C)) and B)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-13240.        ((A -> (B -> ((C -> (D -> C)) and B))) and (E or (A -> (B -> ((C -> (D -> C)) and B))))), M:tm-311, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-13241
in-theory        13241
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13241.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))))), M:tm-311, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-13242
in-theory        13242
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13242.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-311, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-13243
in-theory        13243
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D))))
theorem-size     41
proof            (modus-ponens tm-311 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13243.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)))), M:tm-311, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-13244
in-theory        13244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E))))
theorem-size     41
proof            (modus-ponens tm-311 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13244.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)))), M:tm-311, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-13245
in-theory        13245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13245.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))))), M:tm-311, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-13246
in-theory        13246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13246.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))))), M:tm-311, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-13247
in-theory        13247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13247.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))))), M:tm-311, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-13248
in-theory        13248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13248.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-311, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-13249
in-theory        13249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     53
proof            (modus-ponens tm-311 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13249.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-311, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-13250
in-theory        13250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (E or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D))))
theorem-size     41
proof            (modus-ponens tm-311 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13250.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (E or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)))), M:tm-311, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-13251
in-theory        13251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13251.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))))), M:tm-311, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-13252
in-theory        13252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13252.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))))), M:tm-311, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-13253
in-theory        13253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     69
proof            (modus-ponens tm-311 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13253.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-311, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-13254
in-theory        13254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     61
proof            (modus-ponens tm-311 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13254.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-311, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-13255
in-theory        13255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     61
proof            (modus-ponens tm-311 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13255.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-311, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-13256
in-theory        13256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13256.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))))), M:tm-311, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-13257
in-theory        13257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-311 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13257.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-311, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-13258
in-theory        13258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-13258.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))))), M:tm-311, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-13259
in-theory        13259
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-13259.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-311, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-13260
in-theory        13260
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     65
proof            (modus-ponens tm-311 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13260.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-311, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-13261
in-theory        13261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G or ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13261.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G or ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-311, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-13262
in-theory        13262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (E or ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A))))
theorem-size     45
proof            (modus-ponens tm-311 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13262.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (E or ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)))), M:tm-311, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-13263
in-theory        13263
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (F or (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))))
theorem-size     77
proof            (modus-ponens tm-311 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13263.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (F or (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))), M:tm-311, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-13264
in-theory        13264
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F or (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13264.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F or (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-311, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-13265
in-theory        13265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (F or ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E)))
theorem-size     41
proof            (modus-ponens tm-311 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13265.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (F or ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E))), M:tm-311, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-13266
in-theory        13266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (F or (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))))
theorem-size     45
proof            (modus-ponens tm-311 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13266.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (F or (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)))), M:tm-311, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-13267
in-theory        13267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F or (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13267.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F or (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-311, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-13268
in-theory        13268
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and (E or (((A and B) -> A) and (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13268.        ((((A and B) -> A) and (C -> (D -> C))) and (E or (((A and B) -> A) and (C -> (D -> C))))), M:tm-311, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-13269
in-theory        13269
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13269.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-311, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-13270
in-theory        13270
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and (E or (((A and B) -> A) and ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13270.        ((((A and B) -> A) and ((C and D) -> C)) and (E or (((A and B) -> A) and ((C and D) -> C)))), M:tm-311, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-13271
in-theory        13271
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and (E or (((A and B) -> A) and ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-311 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13271.        ((((A and B) -> A) and ((C and D) -> D)) and (E or (((A and B) -> A) and ((C and D) -> D)))), M:tm-311, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-13272
in-theory        13272
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and (E or (((A and B) -> A) and (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13272.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and (E or (((A and B) -> A) and (C -> (D -> (C and D)))))), M:tm-311, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-13273
in-theory        13273
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and (E or (((A and B) -> A) and (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13273.        ((((A and B) -> A) and (C -> (C or D))) and (E or (((A and B) -> A) and (C -> (C or D))))), M:tm-311, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-13274
in-theory        13274
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and (E or (((A and B) -> A) and (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13274.        ((((A and B) -> A) and (C -> (D or C))) and (E or (((A and B) -> A) and (C -> (D or C))))), M:tm-311, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-13275
in-theory        13275
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F or (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13275.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F or (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-311, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-13276
in-theory        13276
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E or (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13276.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E or (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-311, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-13277
in-theory        13277
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and (D or (((A and B) -> A) and ((not (not C)) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13277.        ((((A and B) -> A) and ((not (not C)) -> C)) and (D or (((A and B) -> A) and ((not (not C)) -> C)))), M:tm-311, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-13278
in-theory        13278
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (F or (((A and B) -> A) and (C -> (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13278.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (F or (((A and B) -> A) and (C -> (D -> (E -> D)))))), M:tm-311, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-13279
in-theory        13279
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (E or (((A and B) -> A) and ((C -> D) -> (C -> C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13279.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (E or (((A and B) -> A) and ((C -> D) -> (C -> C))))), M:tm-311, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-13280
in-theory        13280
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F or (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-311 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13280.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F or (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-311, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-13281
in-theory        13281
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13281.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-311, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-13282
in-theory        13282
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F or (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13282.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F or (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-311, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-13283
in-theory        13283
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and (F or (((A and B) -> A) and (C -> ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13283.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and (F or (((A and B) -> A) and (C -> ((D and E) -> D))))), M:tm-311, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-13284
in-theory        13284
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F or (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13284.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F or (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-311, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-13285
in-theory        13285
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and (F or (((A and B) -> A) and (C -> ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-13285.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and (F or (((A and B) -> A) and (C -> ((D and E) -> E))))), M:tm-311, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-13286
in-theory        13286
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (F or (((A and B) -> A) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-13286.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (F or (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))))), M:tm-311, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-13287
in-theory        13287
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G or (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13287.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G or (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-311, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-13288
in-theory        13288
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (F or (((A and B) -> A) and (C -> (((D and E) -> D) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-13288.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (F or (((A and B) -> A) and (C -> (((D and E) -> D) and C))))), M:tm-311, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-13289
in-theory        13289
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-13289.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-311, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-13290
in-theory        13290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (F or ((A -> (B -> A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-13290.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (F or ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))))), M:tm-311, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-13291
in-theory        13291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (D or ((A -> (not (((B and C) -> B) and A))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13291.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (D or ((A -> (not (((B and C) -> B) and A))) -> (not A)))), M:tm-311, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-13292
in-theory        13292
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (E or (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-311 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13292.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (E or (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)))), M:tm-311, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-13293
in-theory        13293
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and (E or (A or (B -> (((C and D) -> C) and B)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-13293.        ((A or (B -> (((C and D) -> C) and B))) and (E or (A or (B -> (((C and D) -> C) and B))))), M:tm-311, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-13294
in-theory        13294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and (E or ((A -> (((B and C) -> B) and A)) or D)))
theorem-size     25
proof            (modus-ponens tm-311 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-13294.        (((A -> (((B and C) -> B) and A)) or D) and (E or ((A -> (((B and C) -> B) and A)) or D))), M:tm-311, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-13295
in-theory        13295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (E or (A -> ((B -> (((C and D) -> C) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-13295.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (E or (A -> ((B -> (((C and D) -> C) and B)) and A)))), M:tm-311, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-13296
in-theory        13296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (E or (A -> (B -> (((C and D) -> C) and B)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-13296.        ((A -> (B -> (((C and D) -> C) and B))) and (E or (A -> (B -> (((C and D) -> C) and B))))), M:tm-311, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-13297
in-theory        13297
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and (E or (((A and B) -> B) and (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13297.        ((((A and B) -> B) and (C -> (D -> C))) and (E or (((A and B) -> B) and (C -> (D -> C))))), M:tm-311, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-13298
in-theory        13298
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13298.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-311, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-13299
in-theory        13299
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and (E or (((A and B) -> B) and ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13299.        ((((A and B) -> B) and ((C and D) -> C)) and (E or (((A and B) -> B) and ((C and D) -> C)))), M:tm-311, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-13300
in-theory        13300
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and (E or (((A and B) -> B) and ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-311 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13300.        ((((A and B) -> B) and ((C and D) -> D)) and (E or (((A and B) -> B) and ((C and D) -> D)))), M:tm-311, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-13301
in-theory        13301
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and (E or (((A and B) -> B) and (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13301.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and (E or (((A and B) -> B) and (C -> (D -> (C and D)))))), M:tm-311, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-13302
in-theory        13302
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and (E or (((A and B) -> B) and (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13302.        ((((A and B) -> B) and (C -> (C or D))) and (E or (((A and B) -> B) and (C -> (C or D))))), M:tm-311, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-13303
in-theory        13303
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and (E or (((A and B) -> B) and (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13303.        ((((A and B) -> B) and (C -> (D or C))) and (E or (((A and B) -> B) and (C -> (D or C))))), M:tm-311, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-13304
in-theory        13304
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F or (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13304.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F or (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-311, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-13305
in-theory        13305
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E or (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13305.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E or (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-311, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-13306
in-theory        13306
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and (D or (((A and B) -> B) and ((not (not C)) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13306.        ((((A and B) -> B) and ((not (not C)) -> C)) and (D or (((A and B) -> B) and ((not (not C)) -> C)))), M:tm-311, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-13307
in-theory        13307
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (F or (((A and B) -> B) and (C -> (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13307.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (F or (((A and B) -> B) and (C -> (D -> (E -> D)))))), M:tm-311, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-13308
in-theory        13308
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (E or (((A and B) -> B) and ((C -> D) -> (C -> C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13308.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (E or (((A and B) -> B) and ((C -> D) -> (C -> C))))), M:tm-311, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-13309
in-theory        13309
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F or (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-311 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13309.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F or (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-311, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-13310
in-theory        13310
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13310.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-311, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-13311
in-theory        13311
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F or (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13311.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F or (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-311, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-13312
in-theory        13312
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and (F or (((A and B) -> B) and (C -> ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13312.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and (F or (((A and B) -> B) and (C -> ((D and E) -> D))))), M:tm-311, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-13313
in-theory        13313
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F or (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13313.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F or (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-311, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-13314
in-theory        13314
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and (F or (((A and B) -> B) and (C -> ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-13314.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and (F or (((A and B) -> B) and (C -> ((D and E) -> E))))), M:tm-311, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-13315
in-theory        13315
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (F or (((A and B) -> B) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-13315.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (F or (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))))), M:tm-311, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-13316
in-theory        13316
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G or (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13316.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G or (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-311, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-13317
in-theory        13317
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (F or (((A and B) -> B) and (C -> (((D and E) -> D) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-13317.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (F or (((A and B) -> B) and (C -> (((D and E) -> D) and C))))), M:tm-311, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-13318
in-theory        13318
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (F or (((A and B) -> B) and (C -> (((D and E) -> E) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-13318.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (F or (((A and B) -> B) and (C -> (((D and E) -> E) and C))))), M:tm-311, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-13319
in-theory        13319
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (F or (((A and B) -> A) and (C -> (((D and E) -> E) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-13319.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (F or (((A and B) -> A) and (C -> (((D and E) -> E) and C))))), M:tm-311, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-13320
in-theory        13320
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-13320.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-311, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-13321
in-theory        13321
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (F or ((A -> (B -> A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-13321.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (F or ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))))), M:tm-311, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-13322
in-theory        13322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (D or ((A -> (not (((B and C) -> C) and A))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13322.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (D or ((A -> (not (((B and C) -> C) and A))) -> (not A)))), M:tm-311, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-13323
in-theory        13323
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (E or (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-311 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13323.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (E or (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)))), M:tm-311, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-13324
in-theory        13324
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and (E or (A or (B -> (((C and D) -> D) and B)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-13324.        ((A or (B -> (((C and D) -> D) and B))) and (E or (A or (B -> (((C and D) -> D) and B))))), M:tm-311, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-13325
in-theory        13325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and (E or ((A -> (((B and C) -> C) and A)) or D)))
theorem-size     25
proof            (modus-ponens tm-311 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-13325.        (((A -> (((B and C) -> C) and A)) or D) and (E or ((A -> (((B and C) -> C) and A)) or D))), M:tm-311, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-13326
in-theory        13326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (E or (A -> ((B -> (((C and D) -> D) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-13326.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (E or (A -> ((B -> (((C and D) -> D) and B)) and A)))), M:tm-311, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-13327
in-theory        13327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (E or (A -> (B -> (((C and D) -> D) and B)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-13327.        ((A -> (B -> (((C and D) -> D) and B))) and (E or (A -> (B -> (((C and D) -> D) and B))))), M:tm-311, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-13328
in-theory        13328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and (E or ((A -> (B -> (A and B))) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13328.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and (E or ((A -> (B -> (A and B))) and (C -> (D -> C))))), M:tm-311, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-13329
in-theory        13329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13329.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-311, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-13330
in-theory        13330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and (E or ((A -> (B -> (A and B))) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-311 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13330.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and (E or ((A -> (B -> (A and B))) and ((C and D) -> C)))), M:tm-311, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-13331
in-theory        13331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and (E or ((A -> (B -> (A and B))) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-311 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13331.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and (E or ((A -> (B -> (A and B))) and ((C and D) -> D)))), M:tm-311, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-13332
in-theory        13332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (E or ((A -> (B -> (A and B))) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13332.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (E or ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))))), M:tm-311, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-13333
in-theory        13333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and (E or ((A -> (B -> (A and B))) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13333.        (((A -> (B -> (A and B))) and (C -> (C or D))) and (E or ((A -> (B -> (A and B))) and (C -> (C or D))))), M:tm-311, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-13334
in-theory        13334
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and (E or ((A -> (B -> (A and B))) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13334.        (((A -> (B -> (A and B))) and (C -> (D or C))) and (E or ((A -> (B -> (A and B))) and (C -> (D or C))))), M:tm-311, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-13335
in-theory        13335
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F or ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13335.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F or ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-311, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-13336
in-theory        13336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E or ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13336.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E or ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-311, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-13337
in-theory        13337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (D or ((A -> (B -> (A and B))) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-311 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13337.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (D or ((A -> (B -> (A and B))) and ((not (not C)) -> C)))), M:tm-311, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-13338
in-theory        13338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (F or ((A -> (B -> (A and B))) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13338.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (F or ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))))), M:tm-311, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-13339
in-theory        13339
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (E or ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13339.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (E or ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))))), M:tm-311, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-13340
in-theory        13340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F or ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13340.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F or ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-311, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-13341
in-theory        13341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-311 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13341.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-311, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-13342
in-theory        13342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F or ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13342.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F or ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-311, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-13343
in-theory        13343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (F or ((A -> (B -> (A and B))) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13343.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (F or ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))))), M:tm-311, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-13344
in-theory        13344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F or ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13344.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F or ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-311, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-13345
in-theory        13345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (F or ((A -> (B -> (A and B))) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-13345.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (F or ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))))), M:tm-311, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-13346
in-theory        13346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (F or ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-13346.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (F or ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))))), M:tm-311, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-13347
in-theory        13347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G or ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-311 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13347.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G or ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-311, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-13348
in-theory        13348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (F or ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-13348.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (F or ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))))), M:tm-311, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-13349
in-theory        13349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (F or ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-13349.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (F or ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))))), M:tm-311, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-13350
in-theory        13350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (F or ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-13350.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (F or ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-311, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-13351
in-theory        13351
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (F or (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-13351.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (F or (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-311, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-13352
in-theory        13352
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (F or (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-13352.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (F or (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-311, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-13353
in-theory        13353
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     53
proof            (modus-ponens tm-311 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-13353.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-311, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-13354
in-theory        13354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F or ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-13354.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F or ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-311, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-13355
in-theory        13355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (D or ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-311 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13355.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (D or ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)))), M:tm-311, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-13356
in-theory        13356
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (E or ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-311 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13356.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (E or ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)))), M:tm-311, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-13357
in-theory        13357
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and (E or (A or (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-13357.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and (E or (A or (B -> ((C -> (D -> (C and D))) and B))))), M:tm-311, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-13358
in-theory        13358
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and (E or ((A -> ((B -> (C -> (B and C))) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-311 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-13358.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and (E or ((A -> ((B -> (C -> (B and C))) and A)) or D))), M:tm-311, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-13359
in-theory        13359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (E or (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-311 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-13359.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (E or (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)))), M:tm-311, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-13360
in-theory        13360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (E or (A -> (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-13360.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (E or (A -> (B -> ((C -> (D -> (C and D))) and B))))), M:tm-311, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-13361
in-theory        13361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (C or (A -> (A and (B -> A)))))
theorem-size     17
proof            (modus-ponens tm-311 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13361.        ((A -> (A and (B -> A))) and (C or (A -> (A and (B -> A))))), M:tm-311, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-13362
in-theory        13362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (D or ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13362.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (D or ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))), M:tm-311, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-13363
in-theory        13363
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and (C or ((A and B) -> ((A and B) and A))))
theorem-size     21
proof            (modus-ponens tm-311 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13363.        (((A and B) -> ((A and B) and A)) and (C or ((A and B) -> ((A and B) and A)))), M:tm-311, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-13364
in-theory        13364
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and (C or ((A and B) -> ((A and B) and B))))
theorem-size     21
proof            (modus-ponens tm-311 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13364.        (((A and B) -> ((A and B) and B)) and (C or ((A and B) -> ((A and B) and B)))), M:tm-311, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-13365
in-theory        13365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (C or (A -> (A and (B -> (A and B))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13365.        ((A -> (A and (B -> (A and B)))) and (C or (A -> (A and (B -> (A and B)))))), M:tm-311, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-13366
in-theory        13366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (C or (A -> (A and (A or B)))))
theorem-size     17
proof            (modus-ponens tm-311 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13366.        ((A -> (A and (A or B))) and (C or (A -> (A and (A or B))))), M:tm-311, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-13367
in-theory        13367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (C or (A -> (A and (B or A)))))
theorem-size     17
proof            (modus-ponens tm-311 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13367.        ((A -> (A and (B or A))) and (C or (A -> (A and (B or A))))), M:tm-311, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13368
in-theory        13368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and ((A -> (A and (B or A))) or C))
theorem-size     17
proof            (modus-ponens tm-310 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13368.        ((A -> (A and (B or A))) and ((A -> (A and (B or A))) or C)), M:tm-310, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13369
in-theory        13369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (C -> ((A -> (A and (B or A))) and C)))
theorem-size     19
proof            (modus-ponens tm-309 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13369.        ((A -> (A and (B or A))) and (C -> ((A -> (A and (B or A))) and C))), M:tm-309, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13370
in-theory        13370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (C -> (A -> (A and (B or A)))))
theorem-size     17
proof            (modus-ponens tm-305 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13370.        ((A -> (A and (B or A))) and (C -> (A -> (A and (B or A))))), M:tm-305, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13371
in-theory        13371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (E or D))))
theorem-size     19
proof            (modus-ponens tm-303 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13371.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (E or D)))), M:tm-303, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13372
in-theory        13372
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (D or ((B -> (C -> (B and C))) and A))))
theorem-size     33
proof            (modus-ponens tm-300 tm-311 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (or Bm (and (-> A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13372.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (D or ((B -> (C -> (B and C))) and A)))), M:tm-300, m:tm-311, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (or Bm (and (-> A (-> B (and A B))) C)))))
================================================================
tm-name          tm-13373
in-theory        13373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and (E or D))))
theorem-size     17
proof            (modus-ponens tm-270 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13373.        ((A -> (((B and C) -> C) and A)) and (D -> (D and (E or D)))), M:tm-270, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13374
in-theory        13374
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (D or (((B and C) -> C) and A))))
theorem-size     27
proof            (modus-ponens tm-267 tm-311 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (or Bm (and (-> (and A B) B) C))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13374.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (D or (((B and C) -> C) and A)))), M:tm-267, m:tm-311, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (or Bm (and (-> (and A B) B) C)))))
================================================================
tm-name          tm-13375
in-theory        13375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and (E or D))))
theorem-size     17
proof            (modus-ponens tm-239 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13375.        ((A -> (((B and C) -> B) and A)) and (D -> (D and (E or D)))), M:tm-239, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13376
in-theory        13376
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (D or (((B and C) -> B) and A))))
theorem-size     27
proof            (modus-ponens tm-236 tm-311 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (or Bm (and (-> (and A B) A) C))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13376.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (D or (((B and C) -> B) and A)))), M:tm-236, m:tm-311, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (or Bm (and (-> (and A B) A) C)))))
================================================================
tm-name          tm-13377
in-theory        13377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (F or E))))
theorem-size     25
proof            (modus-ponens tm-210 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13377.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (F or E)))), M:tm-210, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13378
in-theory        13378
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     51
proof            (modus-ponens tm-207 tm-311 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (or Bm (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13378.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-207, m:tm-311, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (or Bm (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-13379
in-theory        13379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (E or D))))
theorem-size     17
proof            (modus-ponens tm-183 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13379.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (E or D)))), M:tm-183, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13380
in-theory        13380
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (D or ((B -> (C -> B)) and A))))
theorem-size     27
proof            (modus-ponens tm-180 tm-311 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (or Bm (and (-> A (-> B A)) C))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13380.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (D or ((B -> (C -> B)) and A)))), M:tm-180, m:tm-311, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (or Bm (and (-> A (-> B A)) C)))))
================================================================
tm-name          tm-13381
in-theory        13381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-157 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13381.        ((A -> ((B and C) -> C)) and (D -> (D and (E or D)))), M:tm-157, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13382
in-theory        13382
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and (D or ((B and C) -> C))))
theorem-size     21
proof            (modus-ponens tm-154 tm-311 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (or Bm (-> (and A B) B))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13382.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and (D or ((B and C) -> C)))), M:tm-154, m:tm-311, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (or Bm (-> (and A B) B)))))
================================================================
tm-name          tm-13383
in-theory        13383
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (E or D))))
theorem-size     23
proof            (modus-ponens tm-147 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13383.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (E or D)))), M:tm-147, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13384
in-theory        13384
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (D or ((A and (B -> C)) -> C))))
theorem-size     33
proof            (modus-ponens tm-144 tm-311 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (or Bm (-> (and A (-> B C)) C))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13384.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (D or ((A and (B -> C)) -> C)))), M:tm-144, m:tm-311, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (or Bm (-> (and A (-> B C)) C)))))
================================================================
tm-name          tm-13385
in-theory        13385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-134 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13385.        ((A -> ((B and C) -> B)) and (D -> (D and (E or D)))), M:tm-134, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13386
in-theory        13386
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and (D or ((B and C) -> B))))
theorem-size     21
proof            (modus-ponens tm-131 tm-311 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (or Bm (-> (and A B) A))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13386.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and (D or ((B and C) -> B)))), M:tm-131, m:tm-311, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (or Bm (-> (and A B) A)))))
================================================================
tm-name          tm-13387
in-theory        13387
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (E or D))))
theorem-size     23
proof            (modus-ponens tm-125 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13387.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (E or D)))), M:tm-125, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13388
in-theory        13388
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (D or (((A -> B) and C) -> B))))
theorem-size     33
proof            (modus-ponens tm-122 tm-311 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (or Bm (-> (and (-> A B) C) B))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13388.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (D or (((A -> B) and C) -> B)))), M:tm-122, m:tm-311, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (or Bm (-> (and (-> A B) C) B)))))
================================================================
tm-name          tm-13389
in-theory        13389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F or E))))
theorem-size     23
proof            (modus-ponens tm-113 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13389.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F or E)))), M:tm-113, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13390
in-theory        13390
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     45
proof            (modus-ponens tm-110 tm-311 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (or Bm (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13390.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-110, m:tm-311, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (or Bm (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
================================================================
tm-name          tm-13391
in-theory        13391
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (E or D))))
theorem-size     27
proof            (modus-ponens tm-105 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13391.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (E or D)))), M:tm-105, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13392
in-theory        13392
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (D or ((A -> (B -> C)) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-102 tm-311 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (or Bm (-> (-> A (-> B C)) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13392.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (D or ((A -> (B -> C)) -> (A -> C))))), M:tm-102, m:tm-311, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (or Bm (-> (-> A (-> B C)) (-> A C))))))
================================================================
tm-name          tm-13393
in-theory        13393
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and (D or C))))
theorem-size     15
proof            (modus-ponens tm-95 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13393.        (((A -> B) -> (A -> A)) and (C -> (C and (D or C)))), M:tm-95, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13394
in-theory        13394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and (C or (A -> A))))
theorem-size     17
proof            (modus-ponens tm-92 tm-311 ((Am (-> A A)) (B (and (-> A A) (or Bm (-> A A))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13394.        (((A -> B) or (A -> A)) -> ((A -> A) and (C or (A -> A)))), M:tm-92, m:tm-311, u:((Am (-> A A)) (B (and (-> A A) (or Bm (-> A A)))))
================================================================
tm-name          tm-13395
in-theory        13395
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and (C or A))))
theorem-size     9
proof            (modus-ponens tm-84 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13395.        (A -> (B -> (A and (C or A)))), M:tm-84, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-13396
in-theory        13396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-83 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13396.        ((A -> (B -> (C -> B))) and (D -> (D and (E or D)))), M:tm-83, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13397
in-theory        13397
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (D or (B -> (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-80 tm-311 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (or Bm (-> A (-> B A)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13397.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (D or (B -> (C -> B))))), M:tm-80, m:tm-311, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (or Bm (-> A (-> B A))))))
================================================================
tm-name          tm-13398
in-theory        13398
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and (C or B))))
theorem-size     13
proof            (modus-ponens tm-76 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-10 tm-2 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13398.        (((not (not A)) -> A) and (B -> (B and (C or B)))), M:tm-76, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13399
in-theory        13399
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and (B or A)))
theorem-size     11
proof            (modus-ponens tm-73 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13399.        (((not (not A)) or A) -> (A and (B or A))), M:tm-73, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-13400
in-theory        13400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (D or C))))
theorem-size     19
proof            (modus-ponens tm-69 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-9 tm-2 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13400.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (D or C)))), M:tm-69, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13401
in-theory        13401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (C or ((A -> (not B)) -> (not A)))))
theorem-size     29
proof            (modus-ponens tm-66 tm-311 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (or Bm (-> (-> A (not B)) (not A)))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13401.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (C or ((A -> (not B)) -> (not A))))), M:tm-66, m:tm-311, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (or Bm (-> (-> A (not B)) (not A))))))
================================================================
tm-name          tm-13402
in-theory        13402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (E or D))))
theorem-size     21
proof            (modus-ponens tm-54 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13402.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (E or D)))), M:tm-54, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13403
in-theory        13403
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D or ((B -> C) -> ((A or B) -> C)))))
theorem-size     35
proof            (modus-ponens tm-51 tm-311 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (or Bm (-> (-> A B) (-> (or C A) B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13403.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D or ((B -> C) -> ((A or B) -> C))))), M:tm-51, m:tm-311, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (or Bm (-> (-> A B) (-> (or C A) B))))))
================================================================
tm-name          tm-13404
in-theory        13404
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and (C or (B or A))))
theorem-size     15
proof            (modus-ponens tm-50 tm-311 ((Am (or A B)) (C (and (or A B) (or Bm (or A B))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13404.        ((A or (B or A)) -> ((B or A) and (C or (B or A)))), M:tm-50, m:tm-311, u:((Am (or A B)) (C (and (or A B) (or Bm (or A B)))))
================================================================
tm-name          tm-13405
in-theory        13405
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and (C or (A or B))))
theorem-size     15
proof            (modus-ponens tm-49 tm-311 ((Am (or A B)) (C (and (or A B) (or Bm (or A B))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13405.        ((A or (A or B)) -> ((A or B) and (C or (A or B)))), M:tm-49, m:tm-311, u:((Am (or A B)) (C (and (or A B) (or Bm (or A B)))))
================================================================
tm-name          tm-13406
in-theory        13406
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C or (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-48 tm-311 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (or Bm (-> A (and B A)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13406.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C or (B -> (A and B))))), M:tm-48, m:tm-311, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (or Bm (-> A (and B A))))))
================================================================
tm-name          tm-13407
in-theory        13407
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (C or B)))
theorem-size     11
proof            (modus-ponens tm-47 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13407.        (((A and B) or B) -> (B and (C or B))), M:tm-47, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-13408
in-theory        13408
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (C or A)))
theorem-size     11
proof            (modus-ponens tm-46 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13408.        (((A and B) or A) -> (A and (C or A))), M:tm-46, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-13409
in-theory        13409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D or ((A -> B) -> (A -> C)))))
theorem-size     31
proof            (modus-ponens tm-45 tm-311 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (or Bm (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13409.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D or ((A -> B) -> (A -> C))))), M:tm-45, m:tm-311, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (or Bm (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-13410
in-theory        13410
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (C or (B -> A))))
theorem-size     15
proof            (modus-ponens tm-44 tm-311 ((Am (-> A B)) (C (and (-> A B) (or Bm (-> A B))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13410.        ((A or (B -> A)) -> ((B -> A) and (C or (B -> A)))), M:tm-44, m:tm-311, u:((Am (-> A B)) (C (and (-> A B) (or Bm (-> A B)))))
================================================================
tm-name          tm-13411
in-theory        13411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and (D or C))))
theorem-size     13
proof            (modus-ponens tm-42 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13411.        ((A -> (B or A)) and (C -> (C and (D or C)))), M:tm-42, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13412
in-theory        13412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and (D or C))))
theorem-size     13
proof            (modus-ponens tm-32 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13412.        ((A -> (A or B)) and (C -> (C and (D or C)))), M:tm-32, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13413
in-theory        13413
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and (B or A))))
theorem-size     9
proof            (modus-ponens tm-24 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13413.        (A -> (A and (A and (B or A)))), M:tm-24, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-13414
in-theory        13414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and (D or C))))
theorem-size     15
proof            (modus-ponens tm-23 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13414.        ((A -> (B -> (A and B))) and (C -> (C and (D or C)))), M:tm-23, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13415
in-theory        13415
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and (D or C))))
theorem-size     13
proof            (modus-ponens tm-22 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13415.        (((A and B) -> B) and (C -> (C and (D or C)))), M:tm-22, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13416
in-theory        13416
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and (D or C))))
theorem-size     13
proof            (modus-ponens tm-21 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13416.        (((A and B) -> A) and (C -> (C and (D or C)))), M:tm-21, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13417
in-theory        13417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (E or D))))
theorem-size     21
proof            (modus-ponens tm-20 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13417.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (E or D)))), M:tm-20, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13418
in-theory        13418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and (D or C))))
theorem-size     13
proof            (modus-ponens tm-19 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13418.        ((A -> (B -> A)) and (C -> (C and (D or C)))), M:tm-19, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13419
in-theory        13419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and (B or A)))) -> (not A))
theorem-size     11
proof            (modus-ponens tm-9 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-9 tm-2 tm-5 tm-7)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13419.        ((A -> (not (A and (B or A)))) -> (not A)), M:tm-9, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-13420
in-theory        13420
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or A)) -> C) -> ((A or (A and (B or A))) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13420.        (((A and (B or A)) -> C) -> ((A or (A and (B or A))) -> C)), M:tm-8, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-13421
in-theory        13421
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and (C or B))))
theorem-size     9
proof            (modus-ponens tm-7 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-7 tm-2 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13421.        (A or (B -> (B and (C or B)))), M:tm-7, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13422
in-theory        13422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) or C)
theorem-size     9
proof            (modus-ponens tm-6 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-6 tm-2 tm-5 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13422.        ((A -> (A and (B or A))) or C), M:tm-6, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13423
in-theory        13423
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and (C or B))) and A))
theorem-size     11
proof            (modus-ponens tm-5 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13423.        (A -> ((B -> (B and (C or B))) and A)), M:tm-5, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13424
in-theory        13424
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and (C or B))))
theorem-size     9
proof            (modus-ponens tm-1 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-1 tm-2 tm-5 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13424.        (A -> (B -> (B and (C or B)))), M:tm-1, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-13425
in-theory        13425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((B -> A) -> C) -> ((A or (B -> A)) -> C)))
theorem-size     19
proof            (modus-ponens tm-312 tm-1 ((A Am) (B (-> Bm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-13425.        ((A -> (B -> A)) and (((B -> A) -> C) -> ((A or (B -> A)) -> C))), M:tm-312, m:tm-1, u:((A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-13426
in-theory        13426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     39
proof            (modus-ponens tm-312 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13426.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-312, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-13427
in-theory        13427
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((A -> C) -> (((A and B) or A) -> C)))
theorem-size     17
proof            (modus-ponens tm-312 tm-3 ((A (and Am Bm)) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-13427.        (((A and B) -> A) and ((A -> C) -> (((A and B) or A) -> C))), M:tm-312, m:tm-3, u:((A (and Am Bm)) (B Am))
================================================================
tm-name          tm-13428
in-theory        13428
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((B -> C) -> (((A and B) or B) -> C)))
theorem-size     17
proof            (modus-ponens tm-312 tm-4 ((A (and Am Bm)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-13428.        (((A and B) -> B) and ((B -> C) -> (((A and B) or B) -> C))), M:tm-312, m:tm-4, u:((A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-13429
in-theory        13429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((B -> (A and B)) -> C) -> ((A or (B -> (A and B))) -> C)))
theorem-size     25
proof            (modus-ponens tm-312 tm-5 ((A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13429.        ((A -> (B -> (A and B))) and (((B -> (A and B)) -> C) -> ((A or (B -> (A and B))) -> C))), M:tm-312, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-13430
in-theory        13430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((A or B) -> C) -> ((A or (A or B)) -> C)))
theorem-size     19
proof            (modus-ponens tm-312 tm-6 ((A Am) (B (or Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-13430.        ((A -> (A or B)) and (((A or B) -> C) -> ((A or (A or B)) -> C))), M:tm-312, m:tm-6, u:((A Am) (B (or Am Bm)))
================================================================
tm-name          tm-13431
in-theory        13431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((B or A) -> C) -> ((A or (B or A)) -> C)))
theorem-size     19
proof            (modus-ponens tm-312 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-13431.        ((A -> (B or A)) and (((B or A) -> C) -> ((A or (B or A)) -> C))), M:tm-312, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-13432
in-theory        13432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((B -> C) -> ((A or B) -> C)) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D)))
theorem-size     41
proof            (modus-ponens tm-312 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13432.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((B -> C) -> ((A or B) -> C)) -> D) -> (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> D))), M:tm-312, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-13433
in-theory        13433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-312 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13433.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))), M:tm-312, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-13434
in-theory        13434
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((A -> B) -> (((not (not A)) or A) -> B)))
theorem-size     17
proof            (modus-ponens tm-312 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-13434.        (((not (not A)) -> A) and ((A -> B) -> (((not (not A)) or A) -> B))), M:tm-312, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-13435
in-theory        13435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((B -> (C -> B)) -> D) -> ((A or (B -> (C -> B))) -> D)))
theorem-size     25
proof            (modus-ponens tm-312 tm-11 ((A Am) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13435.        ((A -> (B -> (C -> B))) and (((B -> (C -> B)) -> D) -> ((A or (B -> (C -> B))) -> D))), M:tm-312, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-13436
in-theory        13436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((A -> A) -> C) -> (((A -> B) or (A -> A)) -> C)))
theorem-size     23
proof            (modus-ponens tm-312 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13436.        (((A -> B) -> (A -> A)) and (((A -> A) -> C) -> (((A -> B) or (A -> A)) -> C))), M:tm-312, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-13437
in-theory        13437
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))
theorem-size     53
proof            (modus-ponens tm-312 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-13437.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))), M:tm-312, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-13438
in-theory        13438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) -> ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E)))
theorem-size     49
proof            (modus-ponens tm-312 tm-14 ((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13438.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E) -> ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E))), M:tm-312, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-13439
in-theory        13439
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))
theorem-size     43
proof            (modus-ponens tm-312 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-13439.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))), M:tm-312, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-13440
in-theory        13440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((B and C) -> B) -> D) -> ((A or ((B and C) -> B)) -> D)))
theorem-size     25
proof            (modus-ponens tm-312 tm-16 ((A Am) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13440.        ((A -> ((B and C) -> B)) and ((((B and C) -> B) -> D) -> ((A or ((B and C) -> B)) -> D))), M:tm-312, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-13441
in-theory        13441
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))
theorem-size     43
proof            (modus-ponens tm-312 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-13441.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))), M:tm-312, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-13442
in-theory        13442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((B and C) -> C) -> D) -> ((A or ((B and C) -> C)) -> D)))
theorem-size     25
proof            (modus-ponens tm-312 tm-18 ((A Am) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13442.        ((A -> ((B and C) -> C)) and ((((B and C) -> C) -> D) -> ((A or ((B and C) -> C)) -> D))), M:tm-312, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-13443
in-theory        13443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((B -> (C -> B)) and A) -> D) -> ((A or ((B -> (C -> B)) and A)) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13443.        ((A -> ((B -> (C -> B)) and A)) and ((((B -> (C -> B)) and A) -> D) -> ((A or ((B -> (C -> B)) and A)) -> D))), M:tm-312, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-13444
in-theory        13444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) -> E) -> ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13444.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) -> E) -> ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E))), M:tm-312, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-13445
in-theory        13445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((B and C) -> B) and A) -> D) -> ((A or (((B and C) -> B) and A)) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13445.        ((A -> (((B and C) -> B) and A)) and (((((B and C) -> B) and A) -> D) -> ((A or (((B and C) -> B) and A)) -> D))), M:tm-312, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-13446
in-theory        13446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((B and C) -> C) and A) -> D) -> ((A or (((B and C) -> C) and A)) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13446.        ((A -> (((B and C) -> C) and A)) and (((((B and C) -> C) and A) -> D) -> ((A or (((B and C) -> C) and A)) -> D))), M:tm-312, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-13447
in-theory        13447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((B -> (C -> (B and C))) and A) -> D) -> ((A or ((B -> (C -> (B and C))) and A)) -> D)))
theorem-size     37
proof            (modus-ponens tm-312 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13447.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((B -> (C -> (B and C))) and A) -> D) -> ((A or ((B -> (C -> (B and C))) and A)) -> D))), M:tm-312, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-13448
in-theory        13448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)))
theorem-size     29
proof            (modus-ponens tm-312 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13448.        (((A -> B) -> (A -> (A and B))) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C))), M:tm-312, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-13449
in-theory        13449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((B -> (C -> (B and C))) -> D) -> ((A or (B -> (C -> (B and C)))) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-25 ((A Am) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13449.        ((A -> (B -> (C -> (B and C)))) and (((B -> (C -> (B and C))) -> D) -> ((A or (B -> (C -> (B and C)))) -> D))), M:tm-312, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-13450
in-theory        13450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((B -> (B or C)) and A) -> D) -> ((A or ((B -> (B or C)) and A)) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13450.        ((A -> ((B -> (B or C)) and A)) and ((((B -> (B or C)) and A) -> D) -> ((A or ((B -> (B or C)) and A)) -> D))), M:tm-312, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-13451
in-theory        13451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((B -> (B or C)) -> D) -> ((A or (B -> (B or C))) -> D)))
theorem-size     25
proof            (modus-ponens tm-312 tm-33 ((A Am) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13451.        ((A -> (B -> (B or C))) and (((B -> (B or C)) -> D) -> ((A or (B -> (B or C))) -> D))), M:tm-312, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-13452
in-theory        13452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((B -> (C or B)) and A) -> D) -> ((A or ((B -> (C or B)) and A)) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13452.        ((A -> ((B -> (C or B)) and A)) and ((((B -> (C or B)) and A) -> D) -> ((A or ((B -> (C or B)) and A)) -> D))), M:tm-312, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-13453
in-theory        13453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((B -> (C or B)) -> D) -> ((A or (B -> (C or B))) -> D)))
theorem-size     25
proof            (modus-ponens tm-312 tm-43 ((A Am) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13453.        ((A -> (B -> (C or B))) and (((B -> (C or B)) -> D) -> ((A or (B -> (C or B))) -> D))), M:tm-312, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-13454
in-theory        13454
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((B or (A -> B)) -> C) -> D) -> ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> D)))
theorem-size     39
proof            (modus-ponens tm-312 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13454.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((B or (A -> B)) -> C) -> D) -> ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> D))), M:tm-312, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-13455
in-theory        13455
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))
theorem-size     71
proof            (modus-ponens tm-312 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       181
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13455.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))), M:tm-312, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-13456
in-theory        13456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((A and C) or A) -> B) -> D) -> (((A -> B) or (((A and C) or A) -> B)) -> D)))
theorem-size     35
proof            (modus-ponens tm-312 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13456.        (((A -> B) -> (((A and C) or A) -> B)) and (((((A and C) or A) -> B) -> D) -> (((A -> B) or (((A and C) or A) -> B)) -> D))), M:tm-312, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-13457
in-theory        13457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((((C and A) or A) -> B) -> D) -> (((A -> B) or (((C and A) or A) -> B)) -> D)))
theorem-size     35
proof            (modus-ponens tm-312 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13457.        (((A -> B) -> (((C and A) or A) -> B)) and (((((C and A) or A) -> B) -> D) -> (((A -> B) or (((C and A) or A) -> B)) -> D))), M:tm-312, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-13458
in-theory        13458
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((B or (A -> (B and A))) -> C) -> D) -> ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> D)))
theorem-size     49
proof            (modus-ponens tm-312 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13458.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((B or (A -> (B and A))) -> C) -> D) -> ((((A -> (B and A)) -> C) or ((B or (A -> (B and A))) -> C)) -> D))), M:tm-312, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-13459
in-theory        13459
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D)))
theorem-size     39
proof            (modus-ponens tm-312 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13459.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((A or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((A or (A or B)) -> C)) -> D))), M:tm-312, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-13460
in-theory        13460
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((B or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((B or (A or B)) -> C)) -> D)))
theorem-size     39
proof            (modus-ponens tm-312 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13460.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((B or (A or B)) -> C) -> D) -> ((((A or B) -> C) or ((B or (A or B)) -> C)) -> D))), M:tm-312, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-13461
in-theory        13461
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> E) -> (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E)))
theorem-size     75
proof            (modus-ponens tm-312 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       187
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13461.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) -> E) -> (((((A -> B) -> ((C or A) -> B)) -> D) or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) -> E))), M:tm-312, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-13462
in-theory        13462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A) -> E) -> ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13462.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A) -> E) -> ((A or (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) -> E))), M:tm-312, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-13463
in-theory        13463
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((((A -> B) -> ((A or B) -> C)) -> D) -> ((((A -> B) -> (B -> C)) or ((A -> B) -> ((A or B) -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-312 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-13463.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((((A -> B) -> ((A or B) -> C)) -> D) -> ((((A -> B) -> (B -> C)) or ((A -> B) -> ((A or B) -> C))) -> D))), M:tm-312, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-13464
in-theory        13464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) -> E) -> ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E)))
theorem-size     49
proof            (modus-ponens tm-312 tm-56 ((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13464.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) -> E) -> ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) -> E))), M:tm-312, m:tm-56, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-13465
in-theory        13465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (((not A) -> C) -> (((A -> (not (B -> A))) or (not A)) -> C)))
theorem-size     26
proof            (modus-ponens tm-312 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-1)
proof-size       110
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13465.        (((A -> (not (B -> A))) -> (not A)) and (((not A) -> C) -> (((A -> (not (B -> A))) or (not A)) -> C))), M:tm-312, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-13466
in-theory        13466
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((not (A -> (B -> C))) -> D) -> ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) or (not (A -> (B -> C)))) -> D)))
theorem-size     54
proof            (modus-ponens tm-312 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       158
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13466.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((not (A -> (B -> C))) -> D) -> ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) or (not (A -> (B -> C)))) -> D))), M:tm-312, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-13467
in-theory        13467
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (((not (A and B)) -> C) -> ((((A and B) -> (not A)) or (not (A and B))) -> C)))
theorem-size     32
proof            (modus-ponens tm-312 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-3)
proof-size       118
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13467.        ((((A and B) -> (not A)) -> (not (A and B))) and (((not (A and B)) -> C) -> ((((A and B) -> (not A)) or (not (A and B))) -> C))), M:tm-312, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-13468
in-theory        13468
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (((not (A and B)) -> C) -> ((((A and B) -> (not B)) or (not (A and B))) -> C)))
theorem-size     32
proof            (modus-ponens tm-312 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-4)
proof-size       118
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13468.        ((((A and B) -> (not B)) -> (not (A and B))) and (((not (A and B)) -> C) -> ((((A and B) -> (not B)) or (not (A and B))) -> C))), M:tm-312, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-13469
in-theory        13469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (((not A) -> C) -> (((A -> (not (B -> (A and B)))) or (not A)) -> C)))
theorem-size     30
proof            (modus-ponens tm-312 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       118
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13469.        (((A -> (not (B -> (A and B)))) -> (not A)) and (((not A) -> C) -> (((A -> (not (B -> (A and B)))) or (not A)) -> C))), M:tm-312, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-13470
in-theory        13470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (((not A) -> C) -> (((A -> (not (A or B))) or (not A)) -> C)))
theorem-size     26
proof            (modus-ponens tm-312 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-6)
proof-size       110
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13470.        (((A -> (not (A or B))) -> (not A)) and (((not A) -> C) -> (((A -> (not (A or B))) or (not A)) -> C))), M:tm-312, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-13471
in-theory        13471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (((not A) -> C) -> (((A -> (not (B or A))) or (not A)) -> C)))
theorem-size     26
proof            (modus-ponens tm-312 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-7)
proof-size       110
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13471.        (((A -> (not (B or A))) -> (not A)) and (((not A) -> C) -> (((A -> (not (B or A))) or (not A)) -> C))), M:tm-312, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-13472
in-theory        13472
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((not (A -> B)) -> D) -> ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) or (not (A -> B))) -> D)))
theorem-size     48
proof            (modus-ponens tm-312 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       150
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13472.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((not (A -> B)) -> D) -> ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) or (not (A -> B))) -> D))), M:tm-312, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-13473
in-theory        13473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((not (A -> B)) -> C) -> ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) or (not (A -> B))) -> C)))
theorem-size     44
proof            (modus-ponens tm-312 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       142
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13473.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((not (A -> B)) -> C) -> ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) or (not (A -> B))) -> C))), M:tm-312, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-13474
in-theory        13474
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((((A -> B) or ((A -> (not B)) -> (not A))) -> C) -> D) -> (((((A -> (not B)) -> (not A)) -> C) or (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) -> D)))
theorem-size     65
proof            (modus-ponens tm-312 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13474.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((((A -> B) or ((A -> (not B)) -> (not A))) -> C) -> D) -> (((((A -> (not B)) -> (not A)) -> C) or (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) -> D))), M:tm-312, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-13475
in-theory        13475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (((((B -> C) -> ((B -> (not C)) -> (not B))) and A) -> D) -> ((A or (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) -> D)))
theorem-size     49
proof            (modus-ponens tm-312 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13475.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (((((B -> C) -> ((B -> (not C)) -> (not B))) and A) -> D) -> ((A or (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) -> D))), M:tm-312, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-13476
in-theory        13476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((((A -> B) -> (not A)) -> C) -> ((((A -> B) -> (A -> (not B))) or ((A -> B) -> (not A))) -> C)))
theorem-size     42
proof            (modus-ponens tm-312 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       140
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-13476.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((((A -> B) -> (not A)) -> C) -> ((((A -> B) -> (A -> (not B))) or ((A -> B) -> (not A))) -> C))), M:tm-312, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-13477
in-theory        13477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((((B -> C) -> ((B -> (not C)) -> (not B))) -> D) -> ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) -> D)))
theorem-size     43
proof            (modus-ponens tm-312 tm-71 ((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13477.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((((B -> C) -> ((B -> (not C)) -> (not B))) -> D) -> ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) -> D))), M:tm-312, m:tm-71, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-13478
in-theory        13478
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((not (not (not A))) -> B) -> ((((not (not A)) -> (not A)) or (not (not (not A)))) -> B)))
theorem-size     32
proof            (modus-ponens tm-312 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-10)
proof-size       118
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13478.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((not (not (not A))) -> B) -> ((((not (not A)) -> (not A)) or (not (not (not A)))) -> B))), M:tm-312, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-13479
in-theory        13479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (((((not (not A)) or A) -> B) -> C) -> (((A -> B) or (((not (not A)) or A) -> B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-312 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13479.        (((A -> B) -> (((not (not A)) or A) -> B)) and (((((not (not A)) or A) -> B) -> C) -> (((A -> B) or (((not (not A)) or A) -> B)) -> C))), M:tm-312, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-13480
in-theory        13480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (((((not (not B)) -> B) and A) -> C) -> ((A or (((not (not B)) -> B) and A)) -> C)))
theorem-size     31
proof            (modus-ponens tm-312 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13480.        ((A -> (((not (not B)) -> B) and A)) and (((((not (not B)) -> B) and A) -> C) -> ((A or (((not (not B)) -> B) and A)) -> C))), M:tm-312, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-13481
in-theory        13481
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((((not (not (A -> B))) -> B) -> C) -> ((((not (not (A -> B))) -> A) or ((not (not (A -> B))) -> B)) -> C)))
theorem-size     43
proof            (modus-ponens tm-312 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-13481.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((((not (not (A -> B))) -> B) -> C) -> ((((not (not (A -> B))) -> A) or ((not (not (A -> B))) -> B)) -> C))), M:tm-312, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-13482
in-theory        13482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and ((((not (not B)) -> B) -> C) -> ((A or ((not (not B)) -> B)) -> C)))
theorem-size     25
proof            (modus-ponens tm-312 tm-78 ((A Am) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-10)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13482.        ((A -> ((not (not B)) -> B)) and ((((not (not B)) -> B) -> C) -> ((A or ((not (not B)) -> B)) -> C))), M:tm-312, m:tm-78, u:((A Am) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-13483
in-theory        13483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (((not A) -> D) -> (((A -> (not (B -> (C -> B)))) or (not A)) -> D)))
theorem-size     30
proof            (modus-ponens tm-312 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-1)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13483.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (((not A) -> D) -> (((A -> (not (B -> (C -> B)))) or (not A)) -> D))), M:tm-312, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-13484
in-theory        13484
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((((D or (A -> (B -> A))) -> C) -> E) -> ((((A -> (B -> A)) -> C) or ((D or (A -> (B -> A))) -> C)) -> E)))
theorem-size     49
proof            (modus-ponens tm-312 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13484.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((((D or (A -> (B -> A))) -> C) -> E) -> ((((A -> (B -> A)) -> C) or ((D or (A -> (B -> A))) -> C)) -> E))), M:tm-312, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-13485
in-theory        13485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and ((((B -> (C -> (D -> C))) and A) -> E) -> ((A or ((B -> (C -> (D -> C))) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13485.        ((A -> ((B -> (C -> (D -> C))) and A)) and ((((B -> (C -> (D -> C))) and A) -> E) -> ((A or ((B -> (C -> (D -> C))) and A)) -> E))), M:tm-312, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-13486
in-theory        13486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (((A -> (C -> B)) -> D) -> (((A -> B) or (A -> (C -> B))) -> D)))
theorem-size     29
proof            (modus-ponens tm-312 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13486.        (((A -> B) -> (A -> (C -> B))) and (((A -> (C -> B)) -> D) -> (((A -> B) or (A -> (C -> B))) -> D))), M:tm-312, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-13487
in-theory        13487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (((B -> (C -> (D -> C))) -> E) -> ((A or (B -> (C -> (D -> C)))) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-85 ((A Am) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13487.        ((A -> (B -> (C -> (D -> C)))) and (((B -> (C -> (D -> C))) -> E) -> ((A or (B -> (C -> (D -> C)))) -> E))), M:tm-312, m:tm-85, u:((A Am) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-13488
in-theory        13488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and ((A -> B) -> ((A or A) -> B)))
theorem-size     13
proof            (modus-ponens tm-312 tm-86 ((A Am) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13488.        ((A -> A) and ((A -> B) -> ((A or A) -> B))), M:tm-312, m:tm-86, u:((A Am) (B Am))
================================================================
tm-name          tm-13489
in-theory        13489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (((A -> (B -> C)) -> D) -> (((A -> (B -> C)) or (A -> (B -> C))) -> D)))
theorem-size     33
proof            (modus-ponens tm-312 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13489.        (((A -> (B -> C)) -> (A -> (B -> C))) and (((A -> (B -> C)) -> D) -> (((A -> (B -> C)) or (A -> (B -> C))) -> D))), M:tm-312, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-13490
in-theory        13490
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and (((A and B) -> C) -> (((A and B) or (A and B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-312 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13490.        (((A and B) -> (A and B)) and (((A and B) -> C) -> (((A and B) or (A and B)) -> C))), M:tm-312, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-13491
in-theory        13491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (((A -> B) -> C) -> (((A -> B) or (A -> B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-312 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13491.        (((A -> B) -> (A -> B)) and (((A -> B) -> C) -> (((A -> B) or (A -> B)) -> C))), M:tm-312, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-13492
in-theory        13492
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and (((not (not A)) -> B) -> (((not (not A)) or (not (not A))) -> B)))
theorem-size     23
proof            (modus-ponens tm-312 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13492.        (((not (not A)) -> (not (not A))) and (((not (not A)) -> B) -> (((not (not A)) or (not (not A))) -> B))), M:tm-312, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-13493
in-theory        13493
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((not (A -> B)) -> C) -> ((((A -> B) -> (not (A -> A))) or (not (A -> B))) -> C)))
theorem-size     36
proof            (modus-ponens tm-312 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-1)
proof-size       144
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13493.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((not (A -> B)) -> C) -> ((((A -> B) -> (not (A -> A))) or (not (A -> B))) -> C))), M:tm-312, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-13494
in-theory        13494
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((((A -> C) or (A -> A)) -> B) -> D) -> ((((A -> A) -> B) or (((A -> C) or (A -> A)) -> B)) -> D)))
theorem-size     45
proof            (modus-ponens tm-312 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13494.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((((A -> C) or (A -> A)) -> B) -> D) -> ((((A -> A) -> B) or (((A -> C) or (A -> A)) -> B)) -> D))), M:tm-312, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-13495
in-theory        13495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (((((B -> C) -> (B -> B)) and A) -> D) -> ((A or (((B -> C) -> (B -> B)) and A)) -> D)))
theorem-size     37
proof            (modus-ponens tm-312 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13495.        ((A -> (((B -> C) -> (B -> B)) and A)) and (((((B -> C) -> (B -> B)) and A) -> D) -> ((A or (((B -> C) -> (B -> B)) and A)) -> D))), M:tm-312, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-13496
in-theory        13496
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and ((((A -> B) -> A) -> C) -> ((((A -> B) -> A) or ((A -> B) -> A)) -> C)))
theorem-size     33
proof            (modus-ponens tm-312 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-13496.        ((((A -> B) -> A) -> ((A -> B) -> A)) and ((((A -> B) -> A) -> C) -> ((((A -> B) -> A) or ((A -> B) -> A)) -> C))), M:tm-312, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-13497
in-theory        13497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and ((((B -> C) -> (B -> B)) -> D) -> ((A or ((B -> C) -> (B -> B))) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-97 ((A Am) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13497.        ((A -> ((B -> C) -> (B -> B))) and ((((B -> C) -> (B -> B)) -> D) -> ((A or ((B -> C) -> (B -> B))) -> D))), M:tm-312, m:tm-97, u:((A Am) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-13498
in-theory        13498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (((A -> C) -> D) -> (((A -> ((B -> A) -> C)) or (A -> C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-13498.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (((A -> C) -> D) -> (((A -> ((B -> A) -> C)) or (A -> C)) -> D))), M:tm-312, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-13499
in-theory        13499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (((A -> B) -> C) -> (((A -> (A -> B)) or (A -> B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-312 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-13499.        (((A -> (A -> B)) -> (A -> B)) and (((A -> B) -> C) -> (((A -> (A -> B)) or (A -> B)) -> C))), M:tm-312, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-13500
in-theory        13500
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((((A -> (B -> C)) -> (A -> B)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> B))) -> D)))
theorem-size     53
proof            (modus-ponens tm-312 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-13500.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((((A -> (B -> C)) -> (A -> B)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> B))) -> D))), M:tm-312, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-13501
in-theory        13501
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((not ((A -> (B -> C)) -> (A -> B))) -> D) -> (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) or (not ((A -> (B -> C)) -> (A -> B)))) -> D)))
theorem-size     78
proof            (modus-ponens tm-312 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       224
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-13501.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((not ((A -> (B -> C)) -> (A -> B))) -> D) -> (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) or (not ((A -> (B -> C)) -> (A -> B)))) -> D))), M:tm-312, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-13502
in-theory        13502
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D) -> E) -> (((((A -> (B -> C)) -> (A -> C)) -> D) or ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) -> E)))
theorem-size     93
proof            (modus-ponens tm-312 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       243
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-13502.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D) -> E) -> (((((A -> (B -> C)) -> (A -> C)) -> D) or ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) -> E))), M:tm-312, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-13503
in-theory        13503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A) -> E) -> ((A or ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) -> E)))
theorem-size     73
proof            (modus-ponens tm-312 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13503.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A) -> E) -> ((A or ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) -> E))), M:tm-312, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-13504
in-theory        13504
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((((A -> (B -> C)) -> (A -> B)) -> (A -> C)) -> D) -> (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) or (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) -> D)))
theorem-size     77
proof            (modus-ponens tm-312 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       223
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-13504.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((((A -> (B -> C)) -> (A -> B)) -> (A -> C)) -> D) -> (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) or (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) -> D))), M:tm-312, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-13505
in-theory        13505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) -> E) -> ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) -> E)))
theorem-size     67
proof            (modus-ponens tm-312 tm-107 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13505.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) -> E) -> ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) -> E))), M:tm-312, m:tm-107, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-13506
in-theory        13506
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((((A -> (B -> C)) -> D) -> E) -> ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) or ((A -> (B -> C)) -> D)) -> E)))
theorem-size     59
proof            (modus-ponens tm-312 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-13506.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((((A -> (B -> C)) -> D) -> E) -> ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) or ((A -> (B -> C)) -> D)) -> E))), M:tm-312, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-13507
in-theory        13507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((not A) -> E) -> (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) or (not A)) -> E)))
theorem-size     46
proof            (modus-ponens tm-312 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-1)
proof-size       168
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13507.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((not A) -> E) -> (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) or (not A)) -> E))), M:tm-312, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-13508
in-theory        13508
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D) -> F) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) -> F)))
theorem-size     89
proof            (modus-ponens tm-312 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       227
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13508.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D) -> F) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) -> F))), M:tm-312, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-13509
in-theory        13509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A) -> F) -> ((A or ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) -> F)))
theorem-size     61
proof            (modus-ponens tm-312 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13509.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A) -> F) -> ((A or ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) -> F))), M:tm-312, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-13510
in-theory        13510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((A -> ((B -> C) -> (B -> D))) -> E) -> (((A -> (B -> (C -> D))) or (A -> ((B -> C) -> (B -> D)))) -> E)))
theorem-size     49
proof            (modus-ponens tm-312 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13510.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((A -> ((B -> C) -> (B -> D))) -> E) -> (((A -> (B -> (C -> D))) or (A -> ((B -> C) -> (B -> D)))) -> E))), M:tm-312, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-13511
in-theory        13511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F) -> ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> F)))
theorem-size     55
proof            (modus-ponens tm-312 tm-115 ((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13511.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F) -> ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> F))), M:tm-312, m:tm-115, u:((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-13512
in-theory        13512
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and ((B -> C) -> ((((A -> B) and A) or B) -> C)))
theorem-size     21
proof            (modus-ponens tm-312 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-13512.        ((((A -> B) and A) -> B) and ((B -> C) -> ((((A -> B) and A) or B) -> C))), M:tm-312, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-13513
in-theory        13513
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and ((C -> E) -> (((((A -> (B -> A)) -> C) and D) or C) -> E)))
theorem-size     29
proof            (modus-ponens tm-312 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-13513.        (((((A -> (B -> A)) -> C) and D) -> C) and ((C -> E) -> (((((A -> (B -> A)) -> C) and D) or C) -> E))), M:tm-312, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-13514
in-theory        13514
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((D -> F) -> ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) or D) -> F)))
theorem-size     45
proof            (modus-ponens tm-312 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13514.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((D -> F) -> ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) or D) -> F))), M:tm-312, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-13515
in-theory        13515
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((((((A -> B) -> A) and C) -> B) -> D) -> ((((((A -> B) -> A) and C) -> (A -> B)) or ((((A -> B) -> A) and C) -> B)) -> D)))
theorem-size     57
proof            (modus-ponens tm-312 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-13515.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((((((A -> B) -> A) and C) -> B) -> D) -> ((((((A -> B) -> A) and C) -> (A -> B)) or ((((A -> B) -> A) and C) -> B)) -> D))), M:tm-312, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-13516
in-theory        13516
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((((A -> B) and C) -> A) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> A)) -> D)))
theorem-size     43
proof            (modus-ponens tm-312 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13516.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((((A -> B) and C) -> A) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> A)) -> D))), M:tm-312, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-13517
in-theory        13517
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((not (((A -> B) and C) -> A)) -> D) -> ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) or (not (((A -> B) and C) -> A))) -> D)))
theorem-size     64
proof            (modus-ponens tm-312 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-3)
proof-size       192
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13517.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((not (((A -> B) and C) -> A)) -> D) -> ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) or (not (((A -> B) and C) -> A))) -> D))), M:tm-312, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-13518
in-theory        13518
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D) -> E) -> ((((((A -> B) and C) -> B) -> D) or (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) -> E)))
theorem-size     77
proof            (modus-ponens tm-312 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13518.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D) -> E) -> ((((((A -> B) and C) -> B) -> D) or (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) -> E))), M:tm-312, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-13519
in-theory        13519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (((((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A) -> E) -> ((A or (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) -> E)))
theorem-size     61
proof            (modus-ponens tm-312 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13519.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (((((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A) -> E) -> ((A or (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) -> E))), M:tm-312, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-13520
in-theory        13520
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((((((A -> B) and C) -> A) -> B) -> D) -> ((((((A -> B) and C) -> A) -> ((A -> B) and C)) or ((((A -> B) and C) -> A) -> B)) -> D)))
theorem-size     61
proof            (modus-ponens tm-312 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-13520.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((((((A -> B) and C) -> A) -> B) -> D) -> ((((((A -> B) and C) -> A) -> ((A -> B) and C)) or ((((A -> B) and C) -> A) -> B)) -> D))), M:tm-312, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-13521
in-theory        13521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) -> E) -> ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-127 ((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13521.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) -> E) -> ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) -> E))), M:tm-312, m:tm-127, u:((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-13522
in-theory        13522
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and ((C -> E) -> ((((((A and B) -> A) -> C) and D) or C) -> E)))
theorem-size     29
proof            (modus-ponens tm-312 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-13522.        ((((((A and B) -> A) -> C) and D) -> C) and ((C -> E) -> ((((((A and B) -> A) -> C) and D) or C) -> E))), M:tm-312, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-13523
in-theory        13523
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((((A and B) -> C) -> D) -> ((((A and B) -> (A -> C)) or ((A and B) -> C)) -> D)))
theorem-size     37
proof            (modus-ponens tm-312 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-13523.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((((A and B) -> C) -> D) -> ((((A and B) -> (A -> C)) or ((A and B) -> C)) -> D))), M:tm-312, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-13524
in-theory        13524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (((not A) -> D) -> (((A -> (not ((B and C) -> B))) or (not A)) -> D)))
theorem-size     30
proof            (modus-ponens tm-312 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-1 tm-3)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13524.        (((A -> (not ((B and C) -> B))) -> (not A)) and (((not A) -> D) -> (((A -> (not ((B and C) -> B))) or (not A)) -> D))), M:tm-312, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-13525
in-theory        13525
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((((D or ((A and B) -> A)) -> C) -> E) -> (((((A and B) -> A) -> C) or ((D or ((A and B) -> A)) -> C)) -> E)))
theorem-size     49
proof            (modus-ponens tm-312 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13525.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((((D or ((A and B) -> A)) -> C) -> E) -> (((((A and B) -> A) -> C) or ((D or ((A and B) -> A)) -> C)) -> E))), M:tm-312, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-13526
in-theory        13526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and ((((B -> ((C and D) -> C)) and A) -> E) -> ((A or ((B -> ((C and D) -> C)) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13526.        ((A -> ((B -> ((C and D) -> C)) and A)) and ((((B -> ((C and D) -> C)) and A) -> E) -> ((A or ((B -> ((C and D) -> C)) and A)) -> E))), M:tm-312, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-13527
in-theory        13527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (((A -> B) -> D) -> (((A -> (B and C)) or (A -> B)) -> D)))
theorem-size     27
proof            (modus-ponens tm-312 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-13527.        (((A -> (B and C)) -> (A -> B)) and (((A -> B) -> D) -> (((A -> (B and C)) or (A -> B)) -> D))), M:tm-312, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-13528
in-theory        13528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (((B -> ((C and D) -> C)) -> E) -> ((A or (B -> ((C and D) -> C))) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-136 ((A Am) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13528.        ((A -> (B -> ((C and D) -> C))) and (((B -> ((C and D) -> C)) -> E) -> ((A or (B -> ((C and D) -> C))) -> E))), M:tm-312, m:tm-136, u:((A Am) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-13529
in-theory        13529
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and ((B -> C) -> (((A and (A -> B)) or B) -> C)))
theorem-size     21
proof            (modus-ponens tm-312 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-13529.        (((A and (A -> B)) -> B) and ((B -> C) -> (((A and (A -> B)) or B) -> C))), M:tm-312, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-13530
in-theory        13530
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and ((D -> E) -> (((A and ((B -> (C -> B)) -> D)) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-312 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-13530.        (((A and ((B -> (C -> B)) -> D)) -> D) and ((D -> E) -> (((A and ((B -> (C -> B)) -> D)) or D) -> E))), M:tm-312, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-13531
in-theory        13531
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((E -> F) -> (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) or E) -> F)))
theorem-size     45
proof            (modus-ponens tm-312 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13531.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((E -> F) -> (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) or E) -> F))), M:tm-312, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-13532
in-theory        13532
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and ((D -> E) -> (((A and (((B and C) -> B) -> D)) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-312 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-13532.        (((A and (((B and C) -> B) -> D)) -> D) and ((D -> E) -> (((A and (((B and C) -> B) -> D)) or D) -> E))), M:tm-312, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-13533
in-theory        13533
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((((A and ((B -> C) -> B)) -> C) -> D) -> ((((A and ((B -> C) -> B)) -> (B -> C)) or ((A and ((B -> C) -> B)) -> C)) -> D)))
theorem-size     57
proof            (modus-ponens tm-312 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-13533.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((((A and ((B -> C) -> B)) -> C) -> D) -> ((((A and ((B -> C) -> B)) -> (B -> C)) or ((A and ((B -> C) -> B)) -> C)) -> D))), M:tm-312, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-13534
in-theory        13534
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((((A and (B -> C)) -> B) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> B)) -> D)))
theorem-size     43
proof            (modus-ponens tm-312 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13534.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((((A and (B -> C)) -> B) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> B)) -> D))), M:tm-312, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-13535
in-theory        13535
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((not ((A and (B -> C)) -> B)) -> D) -> (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) or (not ((A and (B -> C)) -> B))) -> D)))
theorem-size     64
proof            (modus-ponens tm-312 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-4)
proof-size       192
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13535.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((not ((A and (B -> C)) -> B)) -> D) -> (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) or (not ((A and (B -> C)) -> B))) -> D))), M:tm-312, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-13536
in-theory        13536
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D) -> E) -> (((((A and (B -> C)) -> C) -> D) or ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) -> E)))
theorem-size     77
proof            (modus-ponens tm-312 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13536.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D) -> E) -> (((((A and (B -> C)) -> C) -> D) or ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) -> E))), M:tm-312, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-13537
in-theory        13537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A) -> E) -> ((A or ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) -> E)))
theorem-size     61
proof            (modus-ponens tm-312 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13537.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A) -> E) -> ((A or ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) -> E))), M:tm-312, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-13538
in-theory        13538
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((((A and (B -> C)) -> B) -> C) -> D) -> (((((A and (B -> C)) -> B) -> (A and (B -> C))) or (((A and (B -> C)) -> B) -> C)) -> D)))
theorem-size     61
proof            (modus-ponens tm-312 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-13538.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((((A and (B -> C)) -> B) -> C) -> D) -> (((((A and (B -> C)) -> B) -> (A and (B -> C))) or (((A and (B -> C)) -> B) -> C)) -> D))), M:tm-312, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-13539
in-theory        13539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) -> E) -> ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-149 ((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13539.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) -> E) -> ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) -> E))), M:tm-312, m:tm-149, u:((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-13540
in-theory        13540
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and ((D -> E) -> (((A and (((B and C) -> C) -> D)) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-312 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-13540.        (((A and (((B and C) -> C) -> D)) -> D) and ((D -> E) -> (((A and (((B and C) -> C) -> D)) or D) -> E))), M:tm-312, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-13541
in-theory        13541
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and ((C -> E) -> ((((((A and B) -> B) -> C) and D) or C) -> E)))
theorem-size     29
proof            (modus-ponens tm-312 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-13541.        ((((((A and B) -> B) -> C) and D) -> C) and ((C -> E) -> ((((((A and B) -> B) -> C) and D) or C) -> E))), M:tm-312, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-13542
in-theory        13542
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((((A and B) -> C) -> D) -> ((((A and B) -> (B -> C)) or ((A and B) -> C)) -> D)))
theorem-size     37
proof            (modus-ponens tm-312 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-13542.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((((A and B) -> C) -> D) -> ((((A and B) -> (B -> C)) or ((A and B) -> C)) -> D))), M:tm-312, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-13543
in-theory        13543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (((not A) -> D) -> (((A -> (not ((B and C) -> C))) or (not A)) -> D)))
theorem-size     30
proof            (modus-ponens tm-312 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-1 tm-4)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13543.        (((A -> (not ((B and C) -> C))) -> (not A)) and (((not A) -> D) -> (((A -> (not ((B and C) -> C))) or (not A)) -> D))), M:tm-312, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-13544
in-theory        13544
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((((D or ((A and B) -> B)) -> C) -> E) -> (((((A and B) -> B) -> C) or ((D or ((A and B) -> B)) -> C)) -> E)))
theorem-size     49
proof            (modus-ponens tm-312 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13544.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((((D or ((A and B) -> B)) -> C) -> E) -> (((((A and B) -> B) -> C) or ((D or ((A and B) -> B)) -> C)) -> E))), M:tm-312, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-13545
in-theory        13545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and ((((B -> ((C and D) -> D)) and A) -> E) -> ((A or ((B -> ((C and D) -> D)) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-13545.        ((A -> ((B -> ((C and D) -> D)) and A)) and ((((B -> ((C and D) -> D)) and A) -> E) -> ((A or ((B -> ((C and D) -> D)) and A)) -> E))), M:tm-312, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-13546
in-theory        13546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (((A -> C) -> D) -> (((A -> (B and C)) or (A -> C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-312 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-13546.        (((A -> (B and C)) -> (A -> C)) and (((A -> C) -> D) -> (((A -> (B and C)) or (A -> C)) -> D))), M:tm-312, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-13547
in-theory        13547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (((B -> ((C and D) -> D)) -> E) -> ((A or (B -> ((C and D) -> D))) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-159 ((A Am) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-13547.        ((A -> (B -> ((C and D) -> D))) and (((B -> ((C and D) -> D)) -> E) -> ((A or (B -> ((C and D) -> D))) -> E))), M:tm-312, m:tm-159, u:((A Am) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-13548
in-theory        13548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((not A) -> D) -> (((A -> (not ((B -> (C -> B)) and A))) or (not A)) -> D)))
theorem-size     34
proof            (modus-ponens tm-312 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-1)
proof-size       138
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13548.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((not A) -> D) -> (((A -> (not ((B -> (C -> B)) and A))) or (not A)) -> D))), M:tm-312, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-13549
in-theory        13549
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((((C or ((A -> (B -> A)) and C)) -> D) -> E) -> (((((A -> (B -> A)) and C) -> D) or ((C or ((A -> (B -> A)) and C)) -> D)) -> E)))
theorem-size     59
proof            (modus-ponens tm-312 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13549.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((((C or ((A -> (B -> A)) and C)) -> D) -> E) -> (((((A -> (B -> A)) and C) -> D) or ((C or ((A -> (B -> A)) and C)) -> D)) -> E))), M:tm-312, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-13550
in-theory        13550
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((((B -> ((C -> (D -> C)) and B)) and A) -> E) -> ((A or ((B -> ((C -> (D -> C)) and B)) and A)) -> E)))
theorem-size     43
proof            (modus-ponens tm-312 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-13550.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((((B -> ((C -> (D -> C)) and B)) and A) -> E) -> ((A or ((B -> ((C -> (D -> C)) and B)) and A)) -> E))), M:tm-312, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-13551
in-theory        13551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (((B -> ((C -> (D -> C)) and B)) -> E) -> ((A or (B -> ((C -> (D -> C)) and B))) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-184 ((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-13551.        ((A -> (B -> ((C -> (D -> C)) and B))) and (((B -> ((C -> (D -> C)) and B)) -> E) -> ((A or (B -> ((C -> (D -> C)) and B))) -> E))), M:tm-312, m:tm-184, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-13552
in-theory        13552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((not A) -> E) -> (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) or (not A)) -> E)))
theorem-size     50
proof            (modus-ponens tm-312 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       178
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13552.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((not A) -> E) -> (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) or (not A)) -> E))), M:tm-312, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-13553
in-theory        13553
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E) -> F) -> ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) or ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) -> F)))
theorem-size     99
proof            (modus-ponens tm-312 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       245
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13553.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E) -> F) -> ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) or ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) -> F))), M:tm-312, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-13554
in-theory        13554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A) -> F) -> ((A or ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) -> F)))
theorem-size     67
proof            (modus-ponens tm-312 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13554.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A) -> F) -> ((A or ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) -> F))), M:tm-312, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-13555
in-theory        13555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) -> F) -> ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) -> F)))
theorem-size     61
proof            (modus-ponens tm-312 tm-211 ((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13555.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) -> F) -> ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) -> F))), M:tm-312, m:tm-211, u:((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-13556
in-theory        13556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((not A) -> D) -> (((A -> (not (((B and C) -> B) and A))) or (not A)) -> D)))
theorem-size     34
proof            (modus-ponens tm-312 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-3)
proof-size       138
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13556.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((not A) -> D) -> (((A -> (not (((B and C) -> B) and A))) or (not A)) -> D))), M:tm-312, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-13557
in-theory        13557
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((((C or (((A and B) -> A) and C)) -> D) -> E) -> ((((((A and B) -> A) and C) -> D) or ((C or (((A and B) -> A) and C)) -> D)) -> E)))
theorem-size     59
proof            (modus-ponens tm-312 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13557.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((((C or (((A and B) -> A) and C)) -> D) -> E) -> ((((((A and B) -> A) and C) -> D) or ((C or (((A and B) -> A) and C)) -> D)) -> E))), M:tm-312, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-13558
in-theory        13558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((((B -> (((C and D) -> C) and B)) and A) -> E) -> ((A or ((B -> (((C and D) -> C) and B)) and A)) -> E)))
theorem-size     43
proof            (modus-ponens tm-312 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-13558.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((((B -> (((C and D) -> C) and B)) and A) -> E) -> ((A or ((B -> (((C and D) -> C) and B)) and A)) -> E))), M:tm-312, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-13559
in-theory        13559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (((B -> (((C and D) -> C) and B)) -> E) -> ((A or (B -> (((C and D) -> C) and B))) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-240 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-13559.        ((A -> (B -> (((C and D) -> C) and B))) and (((B -> (((C and D) -> C) and B)) -> E) -> ((A or (B -> (((C and D) -> C) and B))) -> E))), M:tm-312, m:tm-240, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-13560
in-theory        13560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((not A) -> D) -> (((A -> (not (((B and C) -> C) and A))) or (not A)) -> D)))
theorem-size     34
proof            (modus-ponens tm-312 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-4)
proof-size       138
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13560.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((not A) -> D) -> (((A -> (not (((B and C) -> C) and A))) or (not A)) -> D))), M:tm-312, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-13561
in-theory        13561
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((((C or (((A and B) -> B) and C)) -> D) -> E) -> ((((((A and B) -> B) and C) -> D) or ((C or (((A and B) -> B) and C)) -> D)) -> E)))
theorem-size     59
proof            (modus-ponens tm-312 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13561.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((((C or (((A and B) -> B) and C)) -> D) -> E) -> ((((((A and B) -> B) and C) -> D) or ((C or (((A and B) -> B) and C)) -> D)) -> E))), M:tm-312, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-13562
in-theory        13562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((((B -> (((C and D) -> D) and B)) and A) -> E) -> ((A or ((B -> (((C and D) -> D) and B)) and A)) -> E)))
theorem-size     43
proof            (modus-ponens tm-312 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-13562.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((((B -> (((C and D) -> D) and B)) and A) -> E) -> ((A or ((B -> (((C and D) -> D) and B)) and A)) -> E))), M:tm-312, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-13563
in-theory        13563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (((B -> (((C and D) -> D) and B)) -> E) -> ((A or (B -> (((C and D) -> D) and B))) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-271 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-13563.        ((A -> (B -> (((C and D) -> D) and B))) and (((B -> (((C and D) -> D) and B)) -> E) -> ((A or (B -> (((C and D) -> D) and B))) -> E))), M:tm-312, m:tm-271, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-13564
in-theory        13564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((not A) -> D) -> (((A -> (not ((B -> (C -> (B and C))) and A))) or (not A)) -> D)))
theorem-size     38
proof            (modus-ponens tm-312 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       148
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13564.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((not A) -> D) -> (((A -> (not ((B -> (C -> (B and C))) and A))) or (not A)) -> D))), M:tm-312, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-13565
in-theory        13565
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((((C or ((A -> (B -> (A and B))) and C)) -> D) -> E) -> (((((A -> (B -> (A and B))) and C) -> D) or ((C or ((A -> (B -> (A and B))) and C)) -> D)) -> E)))
theorem-size     69
proof            (modus-ponens tm-312 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13565.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((((C or ((A -> (B -> (A and B))) and C)) -> D) -> E) -> (((((A -> (B -> (A and B))) and C) -> D) or ((C or ((A -> (B -> (A and B))) and C)) -> D)) -> E))), M:tm-312, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-13566
in-theory        13566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((((B -> ((C -> (D -> (C and D))) and B)) and A) -> E) -> ((A or ((B -> ((C -> (D -> (C and D))) and B)) and A)) -> E)))
theorem-size     49
proof            (modus-ponens tm-312 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-13566.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((((B -> ((C -> (D -> (C and D))) and B)) and A) -> E) -> ((A or ((B -> ((C -> (D -> (C and D))) and B)) and A)) -> E))), M:tm-312, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-13567
in-theory        13567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (((B -> ((C -> (D -> (C and D))) and B)) -> E) -> ((A or (B -> ((C -> (D -> (C and D))) and B))) -> E)))
theorem-size     43
proof            (modus-ponens tm-312 tm-304 ((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-13567.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (((B -> ((C -> (D -> (C and D))) and B)) -> E) -> ((A or (B -> ((C -> (D -> (C and D))) and B))) -> E))), M:tm-312, m:tm-304, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-13568
in-theory        13568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (((A and (B -> A)) -> C) -> ((A or (A and (B -> A))) -> C)))
theorem-size     25
proof            (modus-ponens tm-312 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13568.        ((A -> (A and (B -> A))) and (((A and (B -> A)) -> C) -> ((A or (A and (B -> A))) -> C))), M:tm-312, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-13569
in-theory        13569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) and ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) -> D)))
theorem-size     57
proof            (modus-ponens tm-312 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13569.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) and ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) -> D))), M:tm-312, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-13570
in-theory        13570
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and ((((A and B) and A) -> C) -> (((A and B) or ((A and B) and A)) -> C)))
theorem-size     29
proof            (modus-ponens tm-312 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13570.        (((A and B) -> ((A and B) and A)) and ((((A and B) and A) -> C) -> (((A and B) or ((A and B) and A)) -> C))), M:tm-312, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-13571
in-theory        13571
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and ((((A and B) and B) -> C) -> (((A and B) or ((A and B) and B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-312 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13571.        (((A and B) -> ((A and B) and B)) and ((((A and B) and B) -> C) -> (((A and B) or ((A and B) and B)) -> C))), M:tm-312, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-13572
in-theory        13572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (((A and (B -> (A and B))) -> C) -> ((A or (A and (B -> (A and B)))) -> C)))
theorem-size     31
proof            (modus-ponens tm-312 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13572.        ((A -> (A and (B -> (A and B)))) and (((A and (B -> (A and B))) -> C) -> ((A or (A and (B -> (A and B)))) -> C))), M:tm-312, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-13573
in-theory        13573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (((A and (A or B)) -> C) -> ((A or (A and (A or B))) -> C)))
theorem-size     25
proof            (modus-ponens tm-312 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13573.        ((A -> (A and (A or B))) and (((A and (A or B)) -> C) -> ((A or (A and (A or B))) -> C))), M:tm-312, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-13574
in-theory        13574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (((A and (B or A)) -> C) -> ((A or (A and (B or A))) -> C)))
theorem-size     25
proof            (modus-ponens tm-312 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13574.        ((A -> (A and (B or A))) and (((A and (B or A)) -> C) -> ((A or (A and (B or A))) -> C))), M:tm-312, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-13575
in-theory        13575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) and ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((A -> B) and ((B -> C) -> ((A or B) -> C)))) -> D)))
theorem-size     53
proof            (modus-ponens tm-312 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13575.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) and ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((A -> B) and ((B -> C) -> ((A or B) -> C)))) -> D))), M:tm-312, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-13576
in-theory        13576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (D or ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13576.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (D or ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))))), M:tm-311, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13577
in-theory        13577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) or D))
theorem-size     37
proof            (modus-ponens tm-310 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13577.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) or D)), M:tm-310, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13578
in-theory        13578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (D -> (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and D)))
theorem-size     39
proof            (modus-ponens tm-309 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13578.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (D -> (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and D))), M:tm-309, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13579
in-theory        13579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (D -> ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13579.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (D -> ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))))), M:tm-305, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13580
in-theory        13580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     29
proof            (modus-ponens tm-303 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13580.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-303, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13581
in-theory        13581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     27
proof            (modus-ponens tm-270 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13581.        ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-270, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13582
in-theory        13582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     27
proof            (modus-ponens tm-239 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13582.        ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-239, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13583
in-theory        13583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     35
proof            (modus-ponens tm-210 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13583.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G))))), M:tm-210, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13584
in-theory        13584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     27
proof            (modus-ponens tm-183 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13584.        ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-183, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13585
in-theory        13585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-157 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13585.        ((A -> ((B and C) -> C)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-157, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13586
in-theory        13586
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((C -> D) -> (((B and C) or C) -> D))))
theorem-size     25
proof            (modus-ponens tm-154 tm-312 ((Am (and A Bm)) (B Bm) (C (and (-> (and A Bm) Bm) (-> (-> Bm Cm) (-> (or (and A Bm) Bm) Cm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13586.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((C -> D) -> (((B and C) or C) -> D)))), M:tm-154, m:tm-312, u:((Am (and A Bm)) (B Bm) (C (and (-> (and A Bm) Bm) (-> (-> Bm Cm) (-> (or (and A Bm) Bm) Cm)))))
================================================================
tm-name          tm-13587
in-theory        13587
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-147 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13587.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-147, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13588
in-theory        13588
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((C -> D) -> (((A and (B -> C)) or C) -> D))))
theorem-size     37
proof            (modus-ponens tm-144 tm-312 ((Am (and A (-> B Bm))) (C Bm) (D (and (-> (and A (-> B Bm)) Bm) (-> (-> Bm Cm) (-> (or (and A (-> B Bm)) Bm) Cm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13588.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((C -> D) -> (((A and (B -> C)) or C) -> D)))), M:tm-144, m:tm-312, u:((Am (and A (-> B Bm))) (C Bm) (D (and (-> (and A (-> B Bm)) Bm) (-> (-> Bm Cm) (-> (or (and A (-> B Bm)) Bm) Cm)))))
================================================================
tm-name          tm-13589
in-theory        13589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-134 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13589.        ((A -> ((B and C) -> B)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-134, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13590
in-theory        13590
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((B -> D) -> (((B and C) or B) -> D))))
theorem-size     25
proof            (modus-ponens tm-131 tm-312 ((Am (and Bm B)) (A Bm) (C (and (-> (and Bm B) Bm) (-> (-> Bm Cm) (-> (or (and Bm B) Bm) Cm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13590.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((B -> D) -> (((B and C) or B) -> D)))), M:tm-131, m:tm-312, u:((Am (and Bm B)) (A Bm) (C (and (-> (and Bm B) Bm) (-> (-> Bm Cm) (-> (or (and Bm B) Bm) Cm)))))
================================================================
tm-name          tm-13591
in-theory        13591
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     33
proof            (modus-ponens tm-125 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13591.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-125, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13592
in-theory        13592
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((B -> D) -> ((((A -> B) and C) or B) -> D))))
theorem-size     37
proof            (modus-ponens tm-122 tm-312 ((Am (and (-> A Bm) C)) (B Bm) (D (and (-> (and (-> A Bm) C) Bm) (-> (-> Bm Cm) (-> (or (and (-> A Bm) C) Bm) Cm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13592.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((B -> D) -> ((((A -> B) and C) or B) -> D)))), M:tm-122, m:tm-312, u:((Am (and (-> A Bm) C)) (B Bm) (D (and (-> (and (-> A Bm) C) Bm) (-> (-> Bm Cm) (-> (or (and (-> A Bm) C) Bm) Cm)))))
================================================================
tm-name          tm-13593
in-theory        13593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     33
proof            (modus-ponens tm-113 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13593.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G))))), M:tm-113, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13594
in-theory        13594
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     55
proof            (modus-ponens tm-110 tm-312 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (-> (-> (-> A B) (-> A C)) Cm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13594.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-110, m:tm-312, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (-> (-> (-> A B) (-> A C)) Cm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm)))))
================================================================
tm-name          tm-13595
in-theory        13595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     37
proof            (modus-ponens tm-105 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13595.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-105, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13596
in-theory        13596
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((A -> C) -> D) -> (((A -> (B -> C)) or (A -> C)) -> D))))
theorem-size     47
proof            (modus-ponens tm-102 tm-312 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (-> (-> A C) Cm) (-> (or (-> A (-> B C)) (-> A C)) Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13596.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((A -> C) -> D) -> (((A -> (B -> C)) or (A -> C)) -> D)))), M:tm-102, m:tm-312, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (-> (-> A C) Cm) (-> (or (-> A (-> B C)) (-> A C)) Cm)))))
================================================================
tm-name          tm-13597
in-theory        13597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     25
proof            (modus-ponens tm-95 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13597.        (((A -> B) -> (A -> A)) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E))))), M:tm-95, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13598
in-theory        13598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and ((A -> C) -> ((A or A) -> C))))
theorem-size     21
proof            (modus-ponens tm-92 tm-312 ((Bm Am) (A Am) (B (and (-> Am Am) (-> (-> Am Cm) (-> (or Am Am) Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13598.        (((A -> B) or (A -> A)) -> ((A -> A) and ((A -> C) -> ((A or A) -> C)))), M:tm-92, m:tm-312, u:((Bm Am) (A Am) (B (and (-> Am Am) (-> (-> Am Cm) (-> (or Am Am) Cm)))))
================================================================
tm-name          tm-13599
in-theory        13599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((A -> B) and ((B -> D) -> ((A or B) -> D)))))
theorem-size     19
proof            (modus-ponens tm-84 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13599.        ((A -> B) -> (C -> ((A -> B) and ((B -> D) -> ((A or B) -> D))))), M:tm-84, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-13600
in-theory        13600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-83 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13600.        ((A -> (B -> (C -> B))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-83, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13601
in-theory        13601
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (((C -> B) -> D) -> ((B or (C -> B)) -> D))))
theorem-size     27
proof            (modus-ponens tm-80 tm-312 ((A Am) (Bm (-> B Am)) (C (and (-> Am (-> B Am)) (-> (-> (-> B Am) Cm) (-> (or Am (-> B Am)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13601.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (((C -> B) -> D) -> ((B or (C -> B)) -> D)))), M:tm-80, m:tm-312, u:((A Am) (Bm (-> B Am)) (C (and (-> Am (-> B Am)) (-> (-> (-> B Am) Cm) (-> (or Am (-> B Am)) Cm)))))
================================================================
tm-name          tm-13602
in-theory        13602
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> ((B -> C) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     23
proof            (modus-ponens tm-76 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13602.        (((not (not A)) -> A) and ((B -> C) -> ((B -> C) and ((C -> D) -> ((B or C) -> D))))), M:tm-76, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13603
in-theory        13603
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))
theorem-size     23
proof            (modus-ponens tm-73 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13603.        (((not (not (A -> B))) or (A -> B)) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-73, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-13604
in-theory        13604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     29
proof            (modus-ponens tm-69 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13604.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E))))), M:tm-69, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13605
in-theory        13605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((not A) -> C) -> (((A -> (not B)) or (not A)) -> C))))
theorem-size     34
proof            (modus-ponens tm-66 tm-312 ((Am (-> A (not B))) (Bm (not A)) (C (and (-> (-> A (not B)) (not A)) (-> (-> (not A) Cm) (-> (or (-> A (not B)) (not A)) Cm))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5)
proof-size       140
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13605.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((not A) -> C) -> (((A -> (not B)) or (not A)) -> C)))), M:tm-66, m:tm-312, u:((Am (-> A (not B))) (Bm (not A)) (C (and (-> (-> A (not B)) (not A)) (-> (-> (not A) Cm) (-> (or (-> A (not B)) (not A)) Cm)))))
================================================================
tm-name          tm-13606
in-theory        13606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     31
proof            (modus-ponens tm-54 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13606.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-54, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13607
in-theory        13607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D))))
theorem-size     43
proof            (modus-ponens tm-51 tm-312 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (-> (-> (or C A) B) Cm) (-> (or (-> A B) (-> (or C A) B)) Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13607.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((((A or B) -> C) -> D) -> (((B -> C) or ((A or B) -> C)) -> D)))), M:tm-51, m:tm-312, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (-> (-> (or C A) B) Cm) (-> (or (-> A B) (-> (or C A) B)) Cm)))))
================================================================
tm-name          tm-13608
in-theory        13608
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (((A and B) -> C) -> ((B or (A and B)) -> C))))
theorem-size     27
proof            (modus-ponens tm-48 tm-312 ((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> (-> (and B Am) Cm) (-> (or Am (and B Am)) Cm))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13608.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (((A and B) -> C) -> ((B or (A and B)) -> C)))), M:tm-48, m:tm-312, u:((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> (-> (and B Am) Cm) (-> (or Am (and B Am)) Cm)))))
================================================================
tm-name          tm-13609
in-theory        13609
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((B -> C) and ((C -> D) -> ((B or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-47 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13609.        (((A and (B -> C)) or (B -> C)) -> ((B -> C) and ((C -> D) -> ((B or C) -> D)))), M:tm-47, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-13610
in-theory        13610
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((A -> B) and ((B -> D) -> ((A or B) -> D))))
theorem-size     23
proof            (modus-ponens tm-46 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13610.        ((((A -> B) and C) or (A -> B)) -> ((A -> B) and ((B -> D) -> ((A or B) -> D)))), M:tm-46, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-13611
in-theory        13611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))
theorem-size     37
proof            (modus-ponens tm-45 tm-312 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13611.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))), M:tm-45, m:tm-312, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm)))))
================================================================
tm-name          tm-13612
in-theory        13612
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and ((A -> C) -> ((B or A) -> C))))
theorem-size     19
proof            (modus-ponens tm-44 tm-312 ((A Am) (B Bm) (C (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13612.        ((A or (B -> A)) -> ((B -> A) and ((A -> C) -> ((B or A) -> C)))), M:tm-44, m:tm-312, u:((A Am) (B Bm) (C (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-13613
in-theory        13613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     23
proof            (modus-ponens tm-42 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13613.        ((A -> (B or A)) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E))))), M:tm-42, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13614
in-theory        13614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     23
proof            (modus-ponens tm-32 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13614.        ((A -> (A or B)) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E))))), M:tm-32, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13615
in-theory        13615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((A -> B) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     21
proof            (modus-ponens tm-24 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13615.        ((A -> B) -> ((A -> B) and ((A -> B) and ((B -> C) -> ((A or B) -> C))))), M:tm-24, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-13616
in-theory        13616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     25
proof            (modus-ponens tm-23 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13616.        ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E))))), M:tm-23, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13617
in-theory        13617
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     23
proof            (modus-ponens tm-22 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13617.        (((A and B) -> B) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E))))), M:tm-22, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13618
in-theory        13618
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     23
proof            (modus-ponens tm-21 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13618.        (((A and B) -> A) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E))))), M:tm-21, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13619
in-theory        13619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     31
proof            (modus-ponens tm-20 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13619.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-20, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13620
in-theory        13620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     23
proof            (modus-ponens tm-19 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13620.        ((A -> (B -> A)) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E))))), M:tm-19, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13621
in-theory        13621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((A -> B) and ((B -> C) -> ((A or B) -> C))))) -> (not (A -> B)))
theorem-size     23
proof            (modus-ponens tm-9 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-9 tm-2 tm-5 tm-8)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13621.        (((A -> B) -> (not ((A -> B) and ((B -> C) -> ((A or B) -> C))))) -> (not (A -> B))), M:tm-9, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-13622
in-theory        13622
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((A -> B) and ((B -> C) -> ((A or B) -> C)))) -> D))
theorem-size     35
proof            (modus-ponens tm-8 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13622.        ((((A -> B) and ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) or ((A -> B) and ((B -> C) -> ((A or B) -> C)))) -> D)), M:tm-8, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-13623
in-theory        13623
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> C) -> ((B -> C) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     19
proof            (modus-ponens tm-7 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-7 tm-2 tm-5 tm-8)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13623.        (A or ((B -> C) -> ((B -> C) and ((C -> D) -> ((B or C) -> D))))), M:tm-7, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13624
in-theory        13624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) or D)
theorem-size     19
proof            (modus-ponens tm-6 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-6 tm-2 tm-5 tm-8)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13624.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) or D), M:tm-6, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13625
in-theory        13625
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((B -> C) and ((C -> D) -> ((B or C) -> D)))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13625.        (A -> (((B -> C) -> ((B -> C) and ((C -> D) -> ((B or C) -> D)))) and A)), M:tm-5, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13626
in-theory        13626
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> ((B -> C) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     19
proof            (modus-ponens tm-1 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-1 tm-2 tm-5 tm-8)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13626.        (A -> ((B -> C) -> ((B -> C) and ((C -> D) -> ((B or C) -> D))))), M:tm-1, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-13627
in-theory        13627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((A -> (not (B -> A))) -> (not A)))
theorem-size     15
proof            (modus-ponens tm-313 tm-1 ((A Am) (B (-> Bm Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-13627.        ((A -> (B -> A)) and ((A -> (not (B -> A))) -> (not A))), M:tm-313, m:tm-1, u:((A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-13628
in-theory        13628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13628.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C))))), M:tm-313, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-13629
in-theory        13629
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((A and B) -> (not A)) -> (not (A and B))))
theorem-size     17
proof            (modus-ponens tm-313 tm-3 ((A (and Am Bm)) (B Am)))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-13629.        (((A and B) -> A) and (((A and B) -> (not A)) -> (not (A and B)))), M:tm-313, m:tm-3, u:((A (and Am Bm)) (B Am))
================================================================
tm-name          tm-13630
in-theory        13630
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((A and B) -> (not B)) -> (not (A and B))))
theorem-size     17
proof            (modus-ponens tm-313 tm-4 ((A (and Am Bm)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-13630.        (((A and B) -> B) and (((A and B) -> (not B)) -> (not (A and B)))), M:tm-313, m:tm-4, u:((A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-13631
in-theory        13631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((A -> (not (B -> (A and B)))) -> (not A)))
theorem-size     19
proof            (modus-ponens tm-313 tm-5 ((A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13631.        ((A -> (B -> (A and B))) and ((A -> (not (B -> (A and B)))) -> (not A))), M:tm-313, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-13632
in-theory        13632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((A -> (not (A or B))) -> (not A)))
theorem-size     15
proof            (modus-ponens tm-313 tm-6 ((A Am) (B (or Am Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-13632.        ((A -> (A or B)) and ((A -> (not (A or B))) -> (not A))), M:tm-313, m:tm-6, u:((A Am) (B (or Am Bm)))
================================================================
tm-name          tm-13633
in-theory        13633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((A -> (not (B or A))) -> (not A)))
theorem-size     15
proof            (modus-ponens tm-313 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-13633.        ((A -> (B or A)) and ((A -> (not (B or A))) -> (not A))), M:tm-313, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-13634
in-theory        13634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))))
theorem-size     33
proof            (modus-ponens tm-313 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13634.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B)))), M:tm-313, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-13635
in-theory        13635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))))
theorem-size     29
proof            (modus-ponens tm-313 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13635.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B)))), M:tm-313, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-13636
in-theory        13636
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((not (not A)) -> (not A)) -> (not (not (not A)))))
theorem-size     17
proof            (modus-ponens tm-313 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-2 tm-5 tm-9 tm-10)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-13636.        (((not (not A)) -> A) and (((not (not A)) -> (not A)) -> (not (not (not A))))), M:tm-313, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-13637
in-theory        13637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((A -> (not (B -> (C -> B)))) -> (not A)))
theorem-size     19
proof            (modus-ponens tm-313 tm-11 ((A Am) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13637.        ((A -> (B -> (C -> B))) and ((A -> (not (B -> (C -> B)))) -> (not A))), M:tm-313, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-13638
in-theory        13638
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((A -> B) -> (not (A -> A))) -> (not (A -> B))))
theorem-size     21
proof            (modus-ponens tm-313 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13638.        (((A -> B) -> (A -> A)) and (((A -> B) -> (not (A -> A))) -> (not (A -> B)))), M:tm-313, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-13639
in-theory        13639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))))
theorem-size     51
proof            (modus-ponens tm-313 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-13639.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B))))), M:tm-313, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-13640
in-theory        13640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)))
theorem-size     35
proof            (modus-ponens tm-313 tm-14 ((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13640.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A))), M:tm-313, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-13641
in-theory        13641
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))))
theorem-size     41
proof            (modus-ponens tm-313 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-13641.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A)))), M:tm-313, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-13642
in-theory        13642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((A -> (not ((B and C) -> B))) -> (not A)))
theorem-size     19
proof            (modus-ponens tm-313 tm-16 ((A Am) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13642.        ((A -> ((B and C) -> B)) and ((A -> (not ((B and C) -> B))) -> (not A))), M:tm-313, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-13643
in-theory        13643
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))))
theorem-size     41
proof            (modus-ponens tm-313 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-13643.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B)))), M:tm-313, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-13644
in-theory        13644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((A -> (not ((B and C) -> C))) -> (not A)))
theorem-size     19
proof            (modus-ponens tm-313 tm-18 ((A Am) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13644.        ((A -> ((B and C) -> C)) and ((A -> (not ((B and C) -> C))) -> (not A))), M:tm-313, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-13645
in-theory        13645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13645.        ((A -> ((B -> (C -> B)) and A)) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A))), M:tm-313, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-13646
in-theory        13646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)))
theorem-size     39
proof            (modus-ponens tm-313 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13646.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A))), M:tm-313, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-13647
in-theory        13647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((A -> (not (((B and C) -> B) and A))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13647.        ((A -> (((B and C) -> B) and A)) and ((A -> (not (((B and C) -> B) and A))) -> (not A))), M:tm-313, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-13648
in-theory        13648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((A -> (not (((B and C) -> C) and A))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13648.        ((A -> (((B and C) -> C) and A)) and ((A -> (not (((B and C) -> C) and A))) -> (not A))), M:tm-313, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-13649
in-theory        13649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13649.        ((A -> ((B -> (C -> (B and C))) and A)) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A))), M:tm-313, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-13650
in-theory        13650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))))
theorem-size     25
proof            (modus-ponens tm-313 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13650.        (((A -> B) -> (A -> (A and B))) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B)))), M:tm-313, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-13651
in-theory        13651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((A -> (not (B -> (C -> (B and C))))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-25 ((A Am) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13651.        ((A -> (B -> (C -> (B and C)))) and ((A -> (not (B -> (C -> (B and C))))) -> (not A))), M:tm-313, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-13652
in-theory        13652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((A -> (not ((B -> (B or C)) and A))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13652.        ((A -> ((B -> (B or C)) and A)) and ((A -> (not ((B -> (B or C)) and A))) -> (not A))), M:tm-313, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-13653
in-theory        13653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((A -> (not (B -> (B or C)))) -> (not A)))
theorem-size     19
proof            (modus-ponens tm-313 tm-33 ((A Am) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13653.        ((A -> (B -> (B or C))) and ((A -> (not (B -> (B or C)))) -> (not A))), M:tm-313, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-13654
in-theory        13654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((A -> (not ((B -> (C or B)) and A))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13654.        ((A -> ((B -> (C or B)) and A)) and ((A -> (not ((B -> (C or B)) and A))) -> (not A))), M:tm-313, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-13655
in-theory        13655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((A -> (not (B -> (C or B)))) -> (not A)))
theorem-size     19
proof            (modus-ponens tm-313 tm-43 ((A Am) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13655.        ((A -> (B -> (C or B))) and ((A -> (not (B -> (C or B)))) -> (not A))), M:tm-313, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-13656
in-theory        13656
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))))
theorem-size     35
proof            (modus-ponens tm-313 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13656.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C)))), M:tm-313, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-13657
in-theory        13657
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))))
theorem-size     63
proof            (modus-ponens tm-313 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       169
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13657.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D)))), M:tm-313, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-13658
in-theory        13658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))))
theorem-size     29
proof            (modus-ponens tm-313 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13658.        (((A -> B) -> (((A and C) or A) -> B)) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B)))), M:tm-313, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-13659
in-theory        13659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B))))
theorem-size     29
proof            (modus-ponens tm-313 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13659.        (((A -> B) -> (((C and A) or A) -> B)) and (((A -> B) -> (not (((C and A) or A) -> B))) -> (not (A -> B)))), M:tm-313, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-13660
in-theory        13660
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C))))
theorem-size     45
proof            (modus-ponens tm-313 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13660.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((((A -> (B and A)) -> C) -> (not ((B or (A -> (B and A))) -> C))) -> (not ((A -> (B and A)) -> C)))), M:tm-313, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-13661
in-theory        13661
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-313 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-6)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13661.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((((A or B) -> C) -> (not ((A or (A or B)) -> C))) -> (not ((A or B) -> C)))), M:tm-313, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-13662
in-theory        13662
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-313 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-7)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13662.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((((A or B) -> C) -> (not ((B or (A or B)) -> C))) -> (not ((A or B) -> C)))), M:tm-313, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-13663
in-theory        13663
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (not (((A -> B) -> ((C or A) -> B)) -> D))))
theorem-size     69
proof            (modus-ponens tm-313 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13663.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((((A -> B) -> ((C or A) -> B)) -> D) -> (not (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))) -> (not (((A -> B) -> ((C or A) -> B)) -> D)))), M:tm-313, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-13664
in-theory        13664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((A -> (not (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))) -> (not A)))
theorem-size     39
proof            (modus-ponens tm-313 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13664.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((A -> (not (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))) -> (not A))), M:tm-313, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-13665
in-theory        13665
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((((A -> B) -> (B -> C)) -> (not ((A -> B) -> ((A or B) -> C)))) -> (not ((A -> B) -> (B -> C)))))
theorem-size     45
proof            (modus-ponens tm-313 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-13665.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((((A -> B) -> (B -> C)) -> (not ((A -> B) -> ((A or B) -> C)))) -> (not ((A -> B) -> (B -> C))))), M:tm-313, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-13666
in-theory        13666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((A -> (not ((B -> C) -> ((C -> D) -> ((B or C) -> D))))) -> (not A)))
theorem-size     35
proof            (modus-ponens tm-313 tm-56 ((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13666.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((A -> (not ((B -> C) -> ((C -> D) -> ((B or C) -> D))))) -> (not A))), M:tm-313, m:tm-56, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-13667
in-theory        13667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (((A -> (not (B -> A))) -> (not (not A))) -> (not (A -> (not (B -> A))))))
theorem-size     28
proof            (modus-ponens tm-313 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       108
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13667.        (((A -> (not (B -> A))) -> (not A)) and (((A -> (not (B -> A))) -> (not (not A))) -> (not (A -> (not (B -> A)))))), M:tm-313, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-13668
in-theory        13668
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (not (A -> (B -> C))))) -> (not ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))))))
theorem-size     60
proof            (modus-ponens tm-313 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       160
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13668.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (not (A -> (B -> C))))) -> (not ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))))), M:tm-313, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-13669
in-theory        13669
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and ((((A and B) -> (not A)) -> (not (not (A and B)))) -> (not ((A and B) -> (not A)))))
theorem-size     32
proof            (modus-ponens tm-313 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       114
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13669.        ((((A and B) -> (not A)) -> (not (A and B))) and ((((A and B) -> (not A)) -> (not (not (A and B)))) -> (not ((A and B) -> (not A))))), M:tm-313, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-13670
in-theory        13670
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and ((((A and B) -> (not B)) -> (not (not (A and B)))) -> (not ((A and B) -> (not B)))))
theorem-size     32
proof            (modus-ponens tm-313 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       114
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13670.        ((((A and B) -> (not B)) -> (not (A and B))) and ((((A and B) -> (not B)) -> (not (not (A and B)))) -> (not ((A and B) -> (not B))))), M:tm-313, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-13671
in-theory        13671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (((A -> (not (B -> (A and B)))) -> (not (not A))) -> (not (A -> (not (B -> (A and B)))))))
theorem-size     34
proof            (modus-ponens tm-313 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       118
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13671.        (((A -> (not (B -> (A and B)))) -> (not A)) and (((A -> (not (B -> (A and B)))) -> (not (not A))) -> (not (A -> (not (B -> (A and B))))))), M:tm-313, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-13672
in-theory        13672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (((A -> (not (A or B))) -> (not (not A))) -> (not (A -> (not (A or B))))))
theorem-size     28
proof            (modus-ponens tm-313 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       108
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13672.        (((A -> (not (A or B))) -> (not A)) and (((A -> (not (A or B))) -> (not (not A))) -> (not (A -> (not (A or B)))))), M:tm-313, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-13673
in-theory        13673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (((A -> (not (B or A))) -> (not (not A))) -> (not (A -> (not (B or A))))))
theorem-size     28
proof            (modus-ponens tm-313 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       108
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13673.        (((A -> (not (B or A))) -> (not A)) and (((A -> (not (B or A))) -> (not (not A))) -> (not (A -> (not (B or A)))))), M:tm-313, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-13674
in-theory        13674
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))))))
theorem-size     56
proof            (modus-ponens tm-313 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       154
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13674.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))))), M:tm-313, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-13675
in-theory        13675
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not ((A -> (not B)) -> (not A)))))))
theorem-size     50
proof            (modus-ponens tm-313 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       144
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13675.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not ((A -> (not B)) -> (not A))))))), M:tm-313, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-13676
in-theory        13676
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((((A -> (not B)) -> (not A)) -> C) -> (not (((A -> B) or ((A -> (not B)) -> (not A))) -> C))) -> (not (((A -> (not B)) -> (not A)) -> C))))
theorem-size     59
proof            (modus-ponens tm-313 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13676.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((((A -> (not B)) -> (not A)) -> C) -> (not (((A -> B) or ((A -> (not B)) -> (not A))) -> C))) -> (not (((A -> (not B)) -> (not A)) -> C)))), M:tm-313, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-13677
in-theory        13677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((A -> (not (((B -> C) -> ((B -> (not C)) -> (not B))) and A))) -> (not A)))
theorem-size     35
proof            (modus-ponens tm-313 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13677.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((A -> (not (((B -> C) -> ((B -> (not C)) -> (not B))) and A))) -> (not A))), M:tm-313, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-13678
in-theory        13678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((((A -> B) -> (A -> (not B))) -> (not ((A -> B) -> (not A)))) -> (not ((A -> B) -> (A -> (not B))))))
theorem-size     42
proof            (modus-ponens tm-313 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       136
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-13678.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((((A -> B) -> (A -> (not B))) -> (not ((A -> B) -> (not A)))) -> (not ((A -> B) -> (A -> (not B)))))), M:tm-313, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-13679
in-theory        13679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((A -> (not ((B -> C) -> ((B -> (not C)) -> (not B))))) -> (not A)))
theorem-size     31
proof            (modus-ponens tm-313 tm-71 ((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13679.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((A -> (not ((B -> C) -> ((B -> (not C)) -> (not B))))) -> (not A))), M:tm-313, m:tm-71, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-13680
in-theory        13680
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((((not (not A)) -> (not A)) -> (not (not (not (not A))))) -> (not ((not (not A)) -> (not A)))))
theorem-size     32
proof            (modus-ponens tm-313 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-9 tm-10)
proof-size       114
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13680.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((((not (not A)) -> (not A)) -> (not (not (not (not A))))) -> (not ((not (not A)) -> (not A))))), M:tm-313, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-13681
in-theory        13681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (((A -> B) -> (not (((not (not A)) or A) -> B))) -> (not (A -> B))))
theorem-size     29
proof            (modus-ponens tm-313 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-10)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13681.        (((A -> B) -> (((not (not A)) or A) -> B)) and (((A -> B) -> (not (((not (not A)) or A) -> B))) -> (not (A -> B)))), M:tm-313, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-13682
in-theory        13682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and ((A -> (not (((not (not B)) -> B) and A))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13682.        ((A -> (((not (not B)) -> B) and A)) and ((A -> (not (((not (not B)) -> B) and A))) -> (not A))), M:tm-313, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-13683
in-theory        13683
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((((not (not (A -> B))) -> A) -> (not ((not (not (A -> B))) -> B))) -> (not ((not (not (A -> B))) -> A))))
theorem-size     41
proof            (modus-ponens tm-313 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-10)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-13683.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((((not (not (A -> B))) -> A) -> (not ((not (not (A -> B))) -> B))) -> (not ((not (not (A -> B))) -> A)))), M:tm-313, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-13684
in-theory        13684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and ((A -> (not ((not (not B)) -> B))) -> (not A)))
theorem-size     19
proof            (modus-ponens tm-313 tm-78 ((A Am) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13684.        ((A -> ((not (not B)) -> B)) and ((A -> (not ((not (not B)) -> B))) -> (not A))), M:tm-313, m:tm-78, u:((A Am) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-13685
in-theory        13685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (((A -> (not (B -> (C -> B)))) -> (not (not A))) -> (not (A -> (not (B -> (C -> B)))))))
theorem-size     34
proof            (modus-ponens tm-313 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13685.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (((A -> (not (B -> (C -> B)))) -> (not (not A))) -> (not (A -> (not (B -> (C -> B))))))), M:tm-313, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-13686
in-theory        13686
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((((A -> (B -> A)) -> C) -> (not ((D or (A -> (B -> A))) -> C))) -> (not ((A -> (B -> A)) -> C))))
theorem-size     45
proof            (modus-ponens tm-313 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13686.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((((A -> (B -> A)) -> C) -> (not ((D or (A -> (B -> A))) -> C))) -> (not ((A -> (B -> A)) -> C)))), M:tm-313, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-13687
in-theory        13687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and ((A -> (not ((B -> (C -> (D -> C))) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13687.        ((A -> ((B -> (C -> (D -> C))) and A)) and ((A -> (not ((B -> (C -> (D -> C))) and A))) -> (not A))), M:tm-313, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-13688
in-theory        13688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (((A -> B) -> (not (A -> (C -> B)))) -> (not (A -> B))))
theorem-size     25
proof            (modus-ponens tm-313 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13688.        (((A -> B) -> (A -> (C -> B))) and (((A -> B) -> (not (A -> (C -> B)))) -> (not (A -> B)))), M:tm-313, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-13689
in-theory        13689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and ((A -> (not (B -> (C -> (D -> C))))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-85 ((A Am) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13689.        ((A -> (B -> (C -> (D -> C)))) and ((A -> (not (B -> (C -> (D -> C))))) -> (not A))), M:tm-313, m:tm-85, u:((A Am) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-13690
in-theory        13690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and ((A -> (not A)) -> (not A)))
theorem-size     11
proof            (modus-ponens tm-313 tm-86 ((A Am) (B Am)))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13690.        ((A -> A) and ((A -> (not A)) -> (not A))), M:tm-313, m:tm-86, u:((A Am) (B Am))
================================================================
tm-name          tm-13691
in-theory        13691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (((A -> (B -> C)) -> (not (A -> (B -> C)))) -> (not (A -> (B -> C)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13691.        (((A -> (B -> C)) -> (A -> (B -> C))) and (((A -> (B -> C)) -> (not (A -> (B -> C)))) -> (not (A -> (B -> C))))), M:tm-313, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-13692
in-theory        13692
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and (((A and B) -> (not (A and B))) -> (not (A and B))))
theorem-size     21
proof            (modus-ponens tm-313 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13692.        (((A and B) -> (A and B)) and (((A and B) -> (not (A and B))) -> (not (A and B)))), M:tm-313, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-13693
in-theory        13693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (((A -> B) -> (not (A -> B))) -> (not (A -> B))))
theorem-size     21
proof            (modus-ponens tm-313 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13693.        (((A -> B) -> (A -> B)) and (((A -> B) -> (not (A -> B))) -> (not (A -> B)))), M:tm-313, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-13694
in-theory        13694
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and (((not (not A)) -> (not (not (not A)))) -> (not (not (not A)))))
theorem-size     21
proof            (modus-ponens tm-313 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-10)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13694.        (((not (not A)) -> (not (not A))) and (((not (not A)) -> (not (not (not A)))) -> (not (not (not A))))), M:tm-313, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-13695
in-theory        13695
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((((A -> B) -> (not (A -> A))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (A -> A))))))
theorem-size     38
proof            (modus-ponens tm-313 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       142
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13695.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((((A -> B) -> (not (A -> A))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (A -> A)))))), M:tm-313, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-13696
in-theory        13696
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((((A -> A) -> B) -> (not (((A -> C) or (A -> A)) -> B))) -> (not ((A -> A) -> B))))
theorem-size     39
proof            (modus-ponens tm-313 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13696.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((((A -> A) -> B) -> (not (((A -> C) or (A -> A)) -> B))) -> (not ((A -> A) -> B)))), M:tm-313, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-13697
in-theory        13697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and ((A -> (not (((B -> C) -> (B -> B)) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13697.        ((A -> (((B -> C) -> (B -> B)) and A)) and ((A -> (not (((B -> C) -> (B -> B)) and A))) -> (not A))), M:tm-313, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-13698
in-theory        13698
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and ((((A -> B) -> A) -> (not ((A -> B) -> A))) -> (not ((A -> B) -> A))))
theorem-size     31
proof            (modus-ponens tm-313 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-13698.        ((((A -> B) -> A) -> ((A -> B) -> A)) and ((((A -> B) -> A) -> (not ((A -> B) -> A))) -> (not ((A -> B) -> A)))), M:tm-313, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-13699
in-theory        13699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and ((A -> (not ((B -> C) -> (B -> B)))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-97 ((A Am) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13699.        ((A -> ((B -> C) -> (B -> B))) and ((A -> (not ((B -> C) -> (B -> B)))) -> (not A))), M:tm-313, m:tm-97, u:((A Am) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-13700
in-theory        13700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (((A -> ((B -> A) -> C)) -> (not (A -> C))) -> (not (A -> ((B -> A) -> C)))))
theorem-size     33
proof            (modus-ponens tm-313 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-13700.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (((A -> ((B -> A) -> C)) -> (not (A -> C))) -> (not (A -> ((B -> A) -> C))))), M:tm-313, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-13701
in-theory        13701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (((A -> (A -> B)) -> (not (A -> B))) -> (not (A -> (A -> B)))))
theorem-size     27
proof            (modus-ponens tm-313 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-13701.        (((A -> (A -> B)) -> (A -> B)) and (((A -> (A -> B)) -> (not (A -> B))) -> (not (A -> (A -> B))))), M:tm-313, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-13702
in-theory        13702
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> B)))) -> (not ((A -> (B -> C)) -> (A -> B)))))
theorem-size     51
proof            (modus-ponens tm-313 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-13702.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> B)))) -> (not ((A -> (B -> C)) -> (A -> B))))), M:tm-313, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-13703
in-theory        13703
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not (not ((A -> (B -> C)) -> (A -> B))))) -> (not (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))))))
theorem-size     86
proof            (modus-ponens tm-313 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       228
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-13703.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not (not ((A -> (B -> C)) -> (A -> B))))) -> (not (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C))))))), M:tm-313, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-13704
in-theory        13704
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (((((A -> (B -> C)) -> (A -> C)) -> D) -> (not ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))) -> (not (((A -> (B -> C)) -> (A -> C)) -> D))))
theorem-size     81
proof            (modus-ponens tm-313 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       227
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-13704.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (((((A -> (B -> C)) -> (A -> C)) -> D) -> (not ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))) -> (not (((A -> (B -> C)) -> (A -> C)) -> D)))), M:tm-313, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-13705
in-theory        13705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((A -> (not ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))) -> (not A)))
theorem-size     51
proof            (modus-ponens tm-313 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13705.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((A -> (not ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))) -> (not A))), M:tm-313, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-13706
in-theory        13706
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (not (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))) -> (not (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))))))
theorem-size     77
proof            (modus-ponens tm-313 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       219
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-13706.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (not (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))) -> (not (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))))), M:tm-313, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-13707
in-theory        13707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((A -> (not (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))) -> (not A)))
theorem-size     47
proof            (modus-ponens tm-313 tm-107 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13707.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((A -> (not (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))) -> (not A))), M:tm-313, m:tm-107, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-13708
in-theory        13708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (not ((A -> (B -> C)) -> D))) -> (not ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)))))
theorem-size     65
proof            (modus-ponens tm-313 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-13708.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (not ((A -> (B -> C)) -> D))) -> (not ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))))), M:tm-313, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-13709
in-theory        13709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not (not A))) -> (not (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))))
theorem-size     58
proof            (modus-ponens tm-313 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       176
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13709.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not (not A))) -> (not (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))), M:tm-313, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-13710
in-theory        13710
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (not ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))) -> (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))))
theorem-size     85
proof            (modus-ponens tm-313 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       219
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13710.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (not ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))) -> (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D)))), M:tm-313, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-13711
in-theory        13711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((A -> (not ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))) -> (not A)))
theorem-size     43
proof            (modus-ponens tm-313 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13711.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((A -> (not ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))) -> (not A))), M:tm-313, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-13712
in-theory        13712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((A -> (B -> (C -> D))) -> (not (A -> ((B -> C) -> (B -> D))))) -> (not (A -> (B -> (C -> D))))))
theorem-size     45
proof            (modus-ponens tm-313 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13712.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((A -> (B -> (C -> D))) -> (not (A -> ((B -> C) -> (B -> D))))) -> (not (A -> (B -> (C -> D)))))), M:tm-313, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-13713
in-theory        13713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A -> (not (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not A)))
theorem-size     39
proof            (modus-ponens tm-313 tm-115 ((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13713.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A -> (not (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not A))), M:tm-313, m:tm-115, u:((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-13714
in-theory        13714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and ((((A -> B) and A) -> (not B)) -> (not ((A -> B) and A))))
theorem-size     23
proof            (modus-ponens tm-313 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-9 tm-3 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-13714.        ((((A -> B) and A) -> B) and ((((A -> B) and A) -> (not B)) -> (not ((A -> B) and A)))), M:tm-313, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-13715
in-theory        13715
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and (((((A -> (B -> A)) -> C) and D) -> (not C)) -> (not (((A -> (B -> A)) -> C) and D))))
theorem-size     35
proof            (modus-ponens tm-313 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-9 tm-3 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-13715.        (((((A -> (B -> A)) -> C) and D) -> C) and (((((A -> (B -> A)) -> C) and D) -> (not C)) -> (not (((A -> (B -> A)) -> C) and D)))), M:tm-313, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-13716
in-theory        13716
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (not D)) -> (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E))))
theorem-size     59
proof            (modus-ponens tm-313 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-2 tm-5 tm-9 tm-3 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13716.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (not D)) -> (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E)))), M:tm-313, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-13717
in-theory        13717
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((((((A -> B) -> A) and C) -> (A -> B)) -> (not ((((A -> B) -> A) and C) -> B))) -> (not ((((A -> B) -> A) and C) -> (A -> B)))))
theorem-size     57
proof            (modus-ponens tm-313 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-13717.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((((((A -> B) -> A) and C) -> (A -> B)) -> (not ((((A -> B) -> A) and C) -> B))) -> (not ((((A -> B) -> A) and C) -> (A -> B))))), M:tm-313, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-13718
in-theory        13718
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> A))) -> (not (((A -> B) and C) -> A))))
theorem-size     41
proof            (modus-ponens tm-313 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13718.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> A))) -> (not (((A -> B) and C) -> A)))), M:tm-313, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-13719
in-theory        13719
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (not (((A -> B) and C) -> A)))) -> (not ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))))))
theorem-size     70
proof            (modus-ponens tm-313 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       194
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13719.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (not (((A -> B) and C) -> A)))) -> (not ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B)))))), M:tm-313, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-13720
in-theory        13720
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((((((A -> B) and C) -> B) -> D) -> (not (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))) -> (not ((((A -> B) and C) -> B) -> D))))
theorem-size     67
proof            (modus-ponens tm-313 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13720.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((((((A -> B) and C) -> B) -> D) -> (not (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))) -> (not ((((A -> B) and C) -> B) -> D)))), M:tm-313, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-13721
in-theory        13721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((A -> (not (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))) -> (not A)))
theorem-size     43
proof            (modus-ponens tm-313 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13721.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((A -> (not (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))) -> (not A))), M:tm-313, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-13722
in-theory        13722
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (not ((((A -> B) and C) -> A) -> B))) -> (not ((((A -> B) and C) -> A) -> ((A -> B) and C)))))
theorem-size     63
proof            (modus-ponens tm-313 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-13722.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (not ((((A -> B) and C) -> A) -> B))) -> (not ((((A -> B) and C) -> A) -> ((A -> B) and C))))), M:tm-313, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-13723
in-theory        13723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((A -> (not ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))) -> (not A)))
theorem-size     39
proof            (modus-ponens tm-313 tm-127 ((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13723.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((A -> (not ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))) -> (not A))), M:tm-313, m:tm-127, u:((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-13724
in-theory        13724
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and ((((((A and B) -> A) -> C) and D) -> (not C)) -> (not ((((A and B) -> A) -> C) and D))))
theorem-size     35
proof            (modus-ponens tm-313 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-9 tm-3 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-13724.        ((((((A and B) -> A) -> C) and D) -> C) and ((((((A and B) -> A) -> C) and D) -> (not C)) -> (not ((((A and B) -> A) -> C) and D)))), M:tm-313, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-13725
in-theory        13725
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((((A and B) -> (A -> C)) -> (not ((A and B) -> C))) -> (not ((A and B) -> (A -> C)))))
theorem-size     37
proof            (modus-ponens tm-313 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-13725.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((((A and B) -> (A -> C)) -> (not ((A and B) -> C))) -> (not ((A and B) -> (A -> C))))), M:tm-313, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-13726
in-theory        13726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (((A -> (not ((B and C) -> B))) -> (not (not A))) -> (not (A -> (not ((B and C) -> B))))))
theorem-size     34
proof            (modus-ponens tm-313 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13726.        (((A -> (not ((B and C) -> B))) -> (not A)) and (((A -> (not ((B and C) -> B))) -> (not (not A))) -> (not (A -> (not ((B and C) -> B)))))), M:tm-313, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-13727
in-theory        13727
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (((((A and B) -> A) -> C) -> (not ((D or ((A and B) -> A)) -> C))) -> (not (((A and B) -> A) -> C))))
theorem-size     45
proof            (modus-ponens tm-313 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13727.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (((((A and B) -> A) -> C) -> (not ((D or ((A and B) -> A)) -> C))) -> (not (((A and B) -> A) -> C)))), M:tm-313, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-13728
in-theory        13728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and ((A -> (not ((B -> ((C and D) -> C)) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13728.        ((A -> ((B -> ((C and D) -> C)) and A)) and ((A -> (not ((B -> ((C and D) -> C)) and A))) -> (not A))), M:tm-313, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-13729
in-theory        13729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (((A -> (B and C)) -> (not (A -> B))) -> (not (A -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-313 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-13729.        (((A -> (B and C)) -> (A -> B)) and (((A -> (B and C)) -> (not (A -> B))) -> (not (A -> (B and C))))), M:tm-313, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-13730
in-theory        13730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and ((A -> (not (B -> ((C and D) -> C)))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-136 ((A Am) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13730.        ((A -> (B -> ((C and D) -> C))) and ((A -> (not (B -> ((C and D) -> C)))) -> (not A))), M:tm-313, m:tm-136, u:((A Am) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-13731
in-theory        13731
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and (((A and (A -> B)) -> (not B)) -> (not (A and (A -> B)))))
theorem-size     23
proof            (modus-ponens tm-313 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-9 tm-4 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-13731.        (((A and (A -> B)) -> B) and (((A and (A -> B)) -> (not B)) -> (not (A and (A -> B))))), M:tm-313, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-13732
in-theory        13732
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and (((A and ((B -> (C -> B)) -> D)) -> (not D)) -> (not (A and ((B -> (C -> B)) -> D)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-9 tm-4 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-13732.        (((A and ((B -> (C -> B)) -> D)) -> D) and (((A and ((B -> (C -> B)) -> D)) -> (not D)) -> (not (A and ((B -> (C -> B)) -> D))))), M:tm-313, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-13733
in-theory        13733
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (not E)) -> (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)))))
theorem-size     59
proof            (modus-ponens tm-313 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-2 tm-5 tm-9 tm-4 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13733.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (not E)) -> (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E))))), M:tm-313, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-13734
in-theory        13734
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and (((A and (((B and C) -> B) -> D)) -> (not D)) -> (not (A and (((B and C) -> B) -> D)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-9 tm-4 tm-1 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-13734.        (((A and (((B and C) -> B) -> D)) -> D) and (((A and (((B and C) -> B) -> D)) -> (not D)) -> (not (A and (((B and C) -> B) -> D))))), M:tm-313, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-13735
in-theory        13735
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((((A and ((B -> C) -> B)) -> (B -> C)) -> (not ((A and ((B -> C) -> B)) -> C))) -> (not ((A and ((B -> C) -> B)) -> (B -> C)))))
theorem-size     57
proof            (modus-ponens tm-313 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-13735.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((((A and ((B -> C) -> B)) -> (B -> C)) -> (not ((A and ((B -> C) -> B)) -> C))) -> (not ((A and ((B -> C) -> B)) -> (B -> C))))), M:tm-313, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-13736
in-theory        13736
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> B))) -> (not ((A and (B -> C)) -> B))))
theorem-size     41
proof            (modus-ponens tm-313 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13736.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> B))) -> (not ((A and (B -> C)) -> B)))), M:tm-313, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-13737
in-theory        13737
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not (not ((A and (B -> C)) -> B)))) -> (not (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))))))
theorem-size     70
proof            (modus-ponens tm-313 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       194
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13737.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not (not ((A and (B -> C)) -> B)))) -> (not (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C)))))), M:tm-313, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-13738
in-theory        13738
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (((((A and (B -> C)) -> C) -> D) -> (not ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))) -> (not (((A and (B -> C)) -> C) -> D))))
theorem-size     67
proof            (modus-ponens tm-313 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13738.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (((((A and (B -> C)) -> C) -> D) -> (not ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))) -> (not (((A and (B -> C)) -> C) -> D)))), M:tm-313, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-13739
in-theory        13739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((A -> (not ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))) -> (not A)))
theorem-size     43
proof            (modus-ponens tm-313 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13739.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((A -> (not ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))) -> (not A))), M:tm-313, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-13740
in-theory        13740
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (not (((A and (B -> C)) -> B) -> C))) -> (not (((A and (B -> C)) -> B) -> (A and (B -> C))))))
theorem-size     63
proof            (modus-ponens tm-313 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-13740.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (not (((A and (B -> C)) -> B) -> C))) -> (not (((A and (B -> C)) -> B) -> (A and (B -> C)))))), M:tm-313, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-13741
in-theory        13741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((A -> (not (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))) -> (not A)))
theorem-size     39
proof            (modus-ponens tm-313 tm-149 ((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13741.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((A -> (not (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))) -> (not A))), M:tm-313, m:tm-149, u:((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-13742
in-theory        13742
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and (((A and (((B and C) -> C) -> D)) -> (not D)) -> (not (A and (((B and C) -> C) -> D)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-9 tm-4 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-13742.        (((A and (((B and C) -> C) -> D)) -> D) and (((A and (((B and C) -> C) -> D)) -> (not D)) -> (not (A and (((B and C) -> C) -> D))))), M:tm-313, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-13743
in-theory        13743
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and ((((((A and B) -> B) -> C) and D) -> (not C)) -> (not ((((A and B) -> B) -> C) and D))))
theorem-size     35
proof            (modus-ponens tm-313 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-9 tm-3 tm-1 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-13743.        ((((((A and B) -> B) -> C) and D) -> C) and ((((((A and B) -> B) -> C) and D) -> (not C)) -> (not ((((A and B) -> B) -> C) and D)))), M:tm-313, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-13744
in-theory        13744
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((((A and B) -> (B -> C)) -> (not ((A and B) -> C))) -> (not ((A and B) -> (B -> C)))))
theorem-size     37
proof            (modus-ponens tm-313 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-13744.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((((A and B) -> (B -> C)) -> (not ((A and B) -> C))) -> (not ((A and B) -> (B -> C))))), M:tm-313, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-13745
in-theory        13745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (((A -> (not ((B and C) -> C))) -> (not (not A))) -> (not (A -> (not ((B and C) -> C))))))
theorem-size     34
proof            (modus-ponens tm-313 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13745.        (((A -> (not ((B and C) -> C))) -> (not A)) and (((A -> (not ((B and C) -> C))) -> (not (not A))) -> (not (A -> (not ((B and C) -> C)))))), M:tm-313, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-13746
in-theory        13746
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (((((A and B) -> B) -> C) -> (not ((D or ((A and B) -> B)) -> C))) -> (not (((A and B) -> B) -> C))))
theorem-size     45
proof            (modus-ponens tm-313 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13746.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (((((A and B) -> B) -> C) -> (not ((D or ((A and B) -> B)) -> C))) -> (not (((A and B) -> B) -> C)))), M:tm-313, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-13747
in-theory        13747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and ((A -> (not ((B -> ((C and D) -> D)) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-13747.        ((A -> ((B -> ((C and D) -> D)) and A)) and ((A -> (not ((B -> ((C and D) -> D)) and A))) -> (not A))), M:tm-313, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-13748
in-theory        13748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (((A -> (B and C)) -> (not (A -> C))) -> (not (A -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-313 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-13748.        (((A -> (B and C)) -> (A -> C)) and (((A -> (B and C)) -> (not (A -> C))) -> (not (A -> (B and C))))), M:tm-313, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-13749
in-theory        13749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and ((A -> (not (B -> ((C and D) -> D)))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-159 ((A Am) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-13749.        ((A -> (B -> ((C and D) -> D))) and ((A -> (not (B -> ((C and D) -> D)))) -> (not A))), M:tm-313, m:tm-159, u:((A Am) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-13750
in-theory        13750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((A -> (not ((B -> (C -> B)) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (C -> B)) and A))))))
theorem-size     40
proof            (modus-ponens tm-313 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       140
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13750.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((A -> (not ((B -> (C -> B)) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (C -> B)) and A)))))), M:tm-313, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-13751
in-theory        13751
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (((((A -> (B -> A)) and C) -> D) -> (not ((C or ((A -> (B -> A)) and C)) -> D))) -> (not (((A -> (B -> A)) and C) -> D))))
theorem-size     55
proof            (modus-ponens tm-313 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13751.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (((((A -> (B -> A)) and C) -> D) -> (not ((C or ((A -> (B -> A)) and C)) -> D))) -> (not (((A -> (B -> A)) and C) -> D)))), M:tm-313, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-13752
in-theory        13752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((A -> (not ((B -> ((C -> (D -> C)) and B)) and A))) -> (not A)))
theorem-size     31
proof            (modus-ponens tm-313 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-13752.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((A -> (not ((B -> ((C -> (D -> C)) and B)) and A))) -> (not A))), M:tm-313, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-13753
in-theory        13753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and ((A -> (not (B -> ((C -> (D -> C)) and B)))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-184 ((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-13753.        ((A -> (B -> ((C -> (D -> C)) and B))) and ((A -> (not (B -> ((C -> (D -> C)) and B)))) -> (not A))), M:tm-313, m:tm-184, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-13754
in-theory        13754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not (not A))) -> (not (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))))
theorem-size     64
proof            (modus-ponens tm-313 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       188
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13754.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not (not A))) -> (not (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))))), M:tm-313, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-13755
in-theory        13755
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (not ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))) -> (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E))))
theorem-size     95
proof            (modus-ponens tm-313 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       237
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13755.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (not ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))) -> (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E)))), M:tm-313, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-13756
in-theory        13756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((A -> (not ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))) -> (not A)))
theorem-size     47
proof            (modus-ponens tm-313 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13756.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((A -> (not ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))) -> (not A))), M:tm-313, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-13757
in-theory        13757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((A -> (not (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))) -> (not A)))
theorem-size     43
proof            (modus-ponens tm-313 tm-211 ((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13757.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((A -> (not (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))) -> (not A))), M:tm-313, m:tm-211, u:((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-13758
in-theory        13758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((A -> (not (((B and C) -> B) and A))) -> (not (not A))) -> (not (A -> (not (((B and C) -> B) and A))))))
theorem-size     40
proof            (modus-ponens tm-313 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       140
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13758.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((A -> (not (((B and C) -> B) and A))) -> (not (not A))) -> (not (A -> (not (((B and C) -> B) and A)))))), M:tm-313, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-13759
in-theory        13759
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((((((A and B) -> A) and C) -> D) -> (not ((C or (((A and B) -> A) and C)) -> D))) -> (not ((((A and B) -> A) and C) -> D))))
theorem-size     55
proof            (modus-ponens tm-313 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13759.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((((((A and B) -> A) and C) -> D) -> (not ((C or (((A and B) -> A) and C)) -> D))) -> (not ((((A and B) -> A) and C) -> D)))), M:tm-313, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-13760
in-theory        13760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((A -> (not ((B -> (((C and D) -> C) and B)) and A))) -> (not A)))
theorem-size     31
proof            (modus-ponens tm-313 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-13760.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((A -> (not ((B -> (((C and D) -> C) and B)) and A))) -> (not A))), M:tm-313, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-13761
in-theory        13761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and ((A -> (not (B -> (((C and D) -> C) and B)))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-240 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-13761.        ((A -> (B -> (((C and D) -> C) and B))) and ((A -> (not (B -> (((C and D) -> C) and B)))) -> (not A))), M:tm-313, m:tm-240, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-13762
in-theory        13762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((A -> (not (((B and C) -> C) and A))) -> (not (not A))) -> (not (A -> (not (((B and C) -> C) and A))))))
theorem-size     40
proof            (modus-ponens tm-313 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       140
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13762.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((A -> (not (((B and C) -> C) and A))) -> (not (not A))) -> (not (A -> (not (((B and C) -> C) and A)))))), M:tm-313, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-13763
in-theory        13763
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((((((A and B) -> B) and C) -> D) -> (not ((C or (((A and B) -> B) and C)) -> D))) -> (not ((((A and B) -> B) and C) -> D))))
theorem-size     55
proof            (modus-ponens tm-313 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13763.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((((((A and B) -> B) and C) -> D) -> (not ((C or (((A and B) -> B) and C)) -> D))) -> (not ((((A and B) -> B) and C) -> D)))), M:tm-313, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-13764
in-theory        13764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((A -> (not ((B -> (((C and D) -> D) and B)) and A))) -> (not A)))
theorem-size     31
proof            (modus-ponens tm-313 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-13764.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((A -> (not ((B -> (((C and D) -> D) and B)) and A))) -> (not A))), M:tm-313, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-13765
in-theory        13765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and ((A -> (not (B -> (((C and D) -> D) and B)))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-271 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-13765.        ((A -> (B -> (((C and D) -> D) and B))) and ((A -> (not (B -> (((C and D) -> D) and B)))) -> (not A))), M:tm-313, m:tm-271, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-13766
in-theory        13766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (C -> (B and C))) and A))))))
theorem-size     46
proof            (modus-ponens tm-313 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       152
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13766.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (C -> (B and C))) and A)))))), M:tm-313, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-13767
in-theory        13767
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (((((A -> (B -> (A and B))) and C) -> D) -> (not ((C or ((A -> (B -> (A and B))) and C)) -> D))) -> (not (((A -> (B -> (A and B))) and C) -> D))))
theorem-size     65
proof            (modus-ponens tm-313 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13767.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (((((A -> (B -> (A and B))) and C) -> D) -> (not ((C or ((A -> (B -> (A and B))) and C)) -> D))) -> (not (((A -> (B -> (A and B))) and C) -> D)))), M:tm-313, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-13768
in-theory        13768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((A -> (not ((B -> ((C -> (D -> (C and D))) and B)) and A))) -> (not A)))
theorem-size     35
proof            (modus-ponens tm-313 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-13768.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((A -> (not ((B -> ((C -> (D -> (C and D))) and B)) and A))) -> (not A))), M:tm-313, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-13769
in-theory        13769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((A -> (not (B -> ((C -> (D -> (C and D))) and B)))) -> (not A)))
theorem-size     31
proof            (modus-ponens tm-313 tm-304 ((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-13769.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((A -> (not (B -> ((C -> (D -> (C and D))) and B)))) -> (not A))), M:tm-313, m:tm-304, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-13770
in-theory        13770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and ((A -> (not (A and (B -> A)))) -> (not A)))
theorem-size     19
proof            (modus-ponens tm-313 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13770.        ((A -> (A and (B -> A))) and ((A -> (not (A and (B -> A)))) -> (not A))), M:tm-313, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-13771
in-theory        13771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) -> (not ((A -> (B -> C)) and ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C)))))
theorem-size     47
proof            (modus-ponens tm-313 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13771.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) -> (not ((A -> (B -> C)) and ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C))))), M:tm-313, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-13772
in-theory        13772
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and (((A and B) -> (not ((A and B) and A))) -> (not (A and B))))
theorem-size     25
proof            (modus-ponens tm-313 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13772.        (((A and B) -> ((A and B) and A)) and (((A and B) -> (not ((A and B) and A))) -> (not (A and B)))), M:tm-313, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-13773
in-theory        13773
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and (((A and B) -> (not ((A and B) and B))) -> (not (A and B))))
theorem-size     25
proof            (modus-ponens tm-313 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13773.        (((A and B) -> ((A and B) and B)) and (((A and B) -> (not ((A and B) and B))) -> (not (A and B)))), M:tm-313, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-13774
in-theory        13774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and ((A -> (not (A and (B -> (A and B))))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13774.        ((A -> (A and (B -> (A and B)))) and ((A -> (not (A and (B -> (A and B))))) -> (not A))), M:tm-313, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-13775
in-theory        13775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and ((A -> (not (A and (A or B)))) -> (not A)))
theorem-size     19
proof            (modus-ponens tm-313 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13775.        ((A -> (A and (A or B))) and ((A -> (not (A and (A or B)))) -> (not A))), M:tm-313, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-13776
in-theory        13776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and ((A -> (not (A and (B or A)))) -> (not A)))
theorem-size     19
proof            (modus-ponens tm-313 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13776.        ((A -> (A and (B or A))) and ((A -> (not (A and (B or A)))) -> (not A))), M:tm-313, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-13777
in-theory        13777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) -> (not ((A -> B) and ((B -> C) -> ((A or B) -> C))))) -> (not (A -> B))))
theorem-size     41
proof            (modus-ponens tm-313 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13777.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (((A -> B) -> (not ((A -> B) and ((B -> C) -> ((A or B) -> C))))) -> (not (A -> B)))), M:tm-313, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-13778
in-theory        13778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (((A -> B) -> (not ((A -> B) and ((A -> (not B)) -> (not A))))) -> (not (A -> B))))
theorem-size     37
proof            (modus-ponens tm-313 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13778.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (((A -> B) -> (not ((A -> B) and ((A -> (not B)) -> (not A))))) -> (not (A -> B)))), M:tm-313, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-13779
in-theory        13779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((((A -> B) and ((A -> (not B)) -> (not A))) -> C) -> (((A -> B) or ((A -> B) and ((A -> (not B)) -> (not A)))) -> C)))
theorem-size     47
proof            (modus-ponens tm-312 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13779.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((((A -> B) and ((A -> (not B)) -> (not A))) -> C) -> (((A -> B) or ((A -> B) and ((A -> (not B)) -> (not A)))) -> C))), M:tm-312, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-13780
in-theory        13780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (C or ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13780.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (C or ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))))), M:tm-311, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13781
in-theory        13781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) or C))
theorem-size     33
proof            (modus-ponens tm-310 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13781.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) or C)), M:tm-310, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13782
in-theory        13782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (C -> (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and C)))
theorem-size     35
proof            (modus-ponens tm-309 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13782.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (C -> (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and C))), M:tm-309, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13783
in-theory        13783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (C -> ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13783.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (C -> ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))))), M:tm-305, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13784
in-theory        13784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13784.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-303, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13785
in-theory        13785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13785.        ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-270, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13786
in-theory        13786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13786.        ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-239, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13787
in-theory        13787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13787.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E))))), M:tm-210, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13788
in-theory        13788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13788.        ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-183, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13789
in-theory        13789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13789.        ((A -> ((B and C) -> C)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-157, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13790
in-theory        13790
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and (((B and C) -> (not C)) -> (not (B and C)))))
theorem-size     25
proof            (modus-ponens tm-154 tm-313 ((Am (and A Bm)) (B Bm) (C (and (-> (and A Bm) Bm) (-> (-> (and A Bm) (not Bm)) (not (and A Bm)))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13790.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and (((B and C) -> (not C)) -> (not (B and C))))), M:tm-154, m:tm-313, u:((Am (and A Bm)) (B Bm) (C (and (-> (and A Bm) Bm) (-> (-> (and A Bm) (not Bm)) (not (and A Bm))))))
================================================================
tm-name          tm-13791
in-theory        13791
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13791.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-147, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13792
in-theory        13792
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (((A and (B -> C)) -> (not C)) -> (not (A and (B -> C))))))
theorem-size     39
proof            (modus-ponens tm-144 tm-313 ((Am (and A (-> B Bm))) (C Bm) (D (and (-> (and A (-> B Bm)) Bm) (-> (-> (and A (-> B Bm)) (not Bm)) (not (and A (-> B Bm))))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13792.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (((A and (B -> C)) -> (not C)) -> (not (A and (B -> C)))))), M:tm-144, m:tm-313, u:((Am (and A (-> B Bm))) (C Bm) (D (and (-> (and A (-> B Bm)) Bm) (-> (-> (and A (-> B Bm)) (not Bm)) (not (and A (-> B Bm)))))))
================================================================
tm-name          tm-13793
in-theory        13793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13793.        ((A -> ((B and C) -> B)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-134, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13794
in-theory        13794
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and (((B and C) -> (not B)) -> (not (B and C)))))
theorem-size     25
proof            (modus-ponens tm-131 tm-313 ((Am (and Bm B)) (A Bm) (C (and (-> (and Bm B) Bm) (-> (-> (and Bm B) (not Bm)) (not (and Bm B)))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13794.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and (((B and C) -> (not B)) -> (not (B and C))))), M:tm-131, m:tm-313, u:((Am (and Bm B)) (A Bm) (C (and (-> (and Bm B) Bm) (-> (-> (and Bm B) (not Bm)) (not (and Bm B))))))
================================================================
tm-name          tm-13795
in-theory        13795
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13795.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-125, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13796
in-theory        13796
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((((A -> B) and C) -> (not B)) -> (not ((A -> B) and C)))))
theorem-size     39
proof            (modus-ponens tm-122 tm-313 ((Am (and (-> A Bm) C)) (B Bm) (D (and (-> (and (-> A Bm) C) Bm) (-> (-> (and (-> A Bm) C) (not Bm)) (not (and (-> A Bm) C)))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13796.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((((A -> B) and C) -> (not B)) -> (not ((A -> B) and C))))), M:tm-122, m:tm-313, u:((Am (and (-> A Bm) C)) (B Bm) (D (and (-> (and (-> A Bm) C) Bm) (-> (-> (and (-> A Bm) C) (not Bm)) (not (and (-> A Bm) C))))))
================================================================
tm-name          tm-13797
in-theory        13797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13797.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E))))), M:tm-113, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13798
in-theory        13798
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((B -> (C -> D)) -> (not ((B -> C) -> (B -> D)))) -> (not (B -> (C -> D))))))
theorem-size     51
proof            (modus-ponens tm-110 tm-313 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (-> (-> A (-> B C)) (not (-> (-> A B) (-> A C)))) (not (-> A (-> B C))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-9)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13798.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((B -> (C -> D)) -> (not ((B -> C) -> (B -> D)))) -> (not (B -> (C -> D)))))), M:tm-110, m:tm-313, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (-> (-> A (-> B C)) (not (-> (-> A B) (-> A C)))) (not (-> A (-> B C)))))))
================================================================
tm-name          tm-13799
in-theory        13799
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13799.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-105, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13800
in-theory        13800
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((A -> (B -> C)) -> (not (A -> C))) -> (not (A -> (B -> C))))))
theorem-size     47
proof            (modus-ponens tm-102 tm-313 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (-> (-> A (-> B C)) (not (-> A C))) (not (-> A (-> B C))))))))
axioms-used      (tm-8 tm-2 tm-5 tm-9)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13800.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((A -> (B -> C)) -> (not (A -> C))) -> (not (A -> (B -> C)))))), M:tm-102, m:tm-313, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (-> (-> A (-> B C)) (not (-> A C))) (not (-> A (-> B C)))))))
================================================================
tm-name          tm-13801
in-theory        13801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13801.        (((A -> B) -> (A -> A)) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C))))), M:tm-95, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13802
in-theory        13802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and ((A -> (not A)) -> (not A))))
theorem-size     19
proof            (modus-ponens tm-92 tm-313 ((Bm Am) (A Am) (B (and (-> Am Am) (-> (-> Am (not Am)) (not Am))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13802.        (((A -> B) or (A -> A)) -> ((A -> A) and ((A -> (not A)) -> (not A)))), M:tm-92, m:tm-313, u:((Bm Am) (A Am) (B (and (-> Am Am) (-> (-> Am (not Am)) (not Am)))))
================================================================
tm-name          tm-13803
in-theory        13803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((A -> B) and ((A -> (not B)) -> (not A)))))
theorem-size     17
proof            (modus-ponens tm-84 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13803.        ((A -> B) -> (C -> ((A -> B) and ((A -> (not B)) -> (not A))))), M:tm-84, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-13804
in-theory        13804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13804.        ((A -> (B -> (C -> B))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-83, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13805
in-theory        13805
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((B -> (not (C -> B))) -> (not B))))
theorem-size     23
proof            (modus-ponens tm-80 tm-313 ((A Am) (Bm (-> B Am)) (C (and (-> Am (-> B Am)) (-> (-> Am (not (-> B Am))) (not Am))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13805.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((B -> (not (C -> B))) -> (not B)))), M:tm-80, m:tm-313, u:((A Am) (Bm (-> B Am)) (C (and (-> Am (-> B Am)) (-> (-> Am (not (-> B Am))) (not Am)))))
================================================================
tm-name          tm-13806
in-theory        13806
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> ((B -> C) and ((B -> (not C)) -> (not B)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13806.        (((not (not A)) -> A) and ((B -> C) -> ((B -> C) and ((B -> (not C)) -> (not B))))), M:tm-76, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13807
in-theory        13807
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> ((A -> B) and ((A -> (not B)) -> (not A))))
theorem-size     21
proof            (modus-ponens tm-73 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13807.        (((not (not (A -> B))) or (A -> B)) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-73, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-13808
in-theory        13808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13808.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C))))), M:tm-69, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13809
in-theory        13809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((A -> (not B)) -> (not (not A))) -> (not (A -> (not B))))))
theorem-size     34
proof            (modus-ponens tm-66 tm-313 ((Am (-> A (not B))) (Bm (not A)) (C (and (-> (-> A (not B)) (not A)) (-> (-> (-> A (not B)) (not (not A))) (not (-> A (not B))))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5)
proof-size       136
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13809.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((A -> (not B)) -> (not (not A))) -> (not (A -> (not B)))))), M:tm-66, m:tm-313, u:((Am (-> A (not B))) (Bm (not A)) (C (and (-> (-> A (not B)) (not A)) (-> (-> (-> A (not B)) (not (not A))) (not (-> A (not B)))))))
================================================================
tm-name          tm-13810
in-theory        13810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13810.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-54, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13811
in-theory        13811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C)))))
theorem-size     39
proof            (modus-ponens tm-51 tm-313 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (-> (-> A B) (not (-> (or C A) B))) (not (-> A B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-9)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13811.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((B -> C) -> (not ((A or B) -> C))) -> (not (B -> C))))), M:tm-51, m:tm-313, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (-> (-> A B) (not (-> (or C A) B))) (not (-> A B))))))
================================================================
tm-name          tm-13812
in-theory        13812
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((B -> (not (A and B))) -> (not B))))
theorem-size     23
proof            (modus-ponens tm-48 tm-313 ((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> (-> Am (not (and B Am))) (not Am))))))
axioms-used      (tm-8 tm-5 tm-2 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13812.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((B -> (not (A and B))) -> (not B)))), M:tm-48, m:tm-313, u:((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> (-> Am (not (and B Am))) (not Am)))))
================================================================
tm-name          tm-13813
in-theory        13813
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((B -> C) and ((B -> (not C)) -> (not B))))
theorem-size     21
proof            (modus-ponens tm-47 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13813.        (((A and (B -> C)) or (B -> C)) -> ((B -> C) and ((B -> (not C)) -> (not B)))), M:tm-47, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-13814
in-theory        13814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((A -> B) and ((A -> (not B)) -> (not A))))
theorem-size     21
proof            (modus-ponens tm-46 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13814.        ((((A -> B) and C) or (A -> B)) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-46, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-13815
in-theory        13815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))
theorem-size     35
proof            (modus-ponens tm-45 tm-313 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-9)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13815.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (not (A -> C))) -> (not (A -> B))))), M:tm-45, m:tm-313, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> (-> A B) (not (-> A C))) (not (-> A B))))))
================================================================
tm-name          tm-13816
in-theory        13816
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and ((B -> (not A)) -> (not B))))
theorem-size     17
proof            (modus-ponens tm-44 tm-313 ((A Am) (B Bm) (C (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-9)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13816.        ((A or (B -> A)) -> ((B -> A) and ((B -> (not A)) -> (not B)))), M:tm-44, m:tm-313, u:((A Am) (B Bm) (C (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-13817
in-theory        13817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13817.        ((A -> (B or A)) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C))))), M:tm-42, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13818
in-theory        13818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13818.        ((A -> (A or B)) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C))))), M:tm-32, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13819
in-theory        13819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((A -> B) and ((A -> (not B)) -> (not A)))))
theorem-size     19
proof            (modus-ponens tm-24 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13819.        ((A -> B) -> ((A -> B) and ((A -> B) and ((A -> (not B)) -> (not A))))), M:tm-24, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-13820
in-theory        13820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13820.        ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C))))), M:tm-23, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13821
in-theory        13821
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13821.        (((A and B) -> B) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C))))), M:tm-22, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13822
in-theory        13822
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13822.        (((A and B) -> A) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C))))), M:tm-21, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13823
in-theory        13823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13823.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-20, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13824
in-theory        13824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13824.        ((A -> (B -> A)) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C))))), M:tm-19, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13825
in-theory        13825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((A -> B) and ((A -> (not B)) -> (not A))))) -> (not (A -> B)))
theorem-size     21
proof            (modus-ponens tm-9 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-9 tm-2 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13825.        (((A -> B) -> (not ((A -> B) and ((A -> (not B)) -> (not A))))) -> (not (A -> B))), M:tm-9, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-13826
in-theory        13826
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and ((A -> (not B)) -> (not A))) -> C) -> (((A -> B) or ((A -> B) and ((A -> (not B)) -> (not A)))) -> C))
theorem-size     31
proof            (modus-ponens tm-8 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-8 tm-2 tm-5 tm-9)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13826.        ((((A -> B) and ((A -> (not B)) -> (not A))) -> C) -> (((A -> B) or ((A -> B) and ((A -> (not B)) -> (not A)))) -> C)), M:tm-8, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-13827
in-theory        13827
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> C) -> ((B -> C) and ((B -> (not C)) -> (not B)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-7 tm-2 tm-5 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13827.        (A or ((B -> C) -> ((B -> C) and ((B -> (not C)) -> (not B))))), M:tm-7, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13828
in-theory        13828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) or C)
theorem-size     17
proof            (modus-ponens tm-6 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-6 tm-2 tm-5 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13828.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) or C), M:tm-6, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13829
in-theory        13829
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((B -> C) and ((B -> (not C)) -> (not B)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13829.        (A -> (((B -> C) -> ((B -> C) and ((B -> (not C)) -> (not B)))) and A)), M:tm-5, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13830
in-theory        13830
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> ((B -> C) and ((B -> (not C)) -> (not B)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-1 tm-2 tm-5 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13830.        (A -> ((B -> C) -> ((B -> C) and ((B -> (not C)) -> (not B))))), M:tm-1, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-13831
in-theory        13831
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and (((not (not A)) -> (not ((not (not A)) and A))) -> (not (not (not A)))))
theorem-size     25
proof            (modus-ponens tm-313 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13831.        (((not (not A)) -> ((not (not A)) and A)) and (((not (not A)) -> (not ((not (not A)) and A))) -> (not (not (not A))))), M:tm-313, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-13832
in-theory        13832
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and ((((not (not A)) and A) -> B) -> (((not (not A)) or ((not (not A)) and A)) -> B)))
theorem-size     29
proof            (modus-ponens tm-312 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13832.        (((not (not A)) -> ((not (not A)) and A)) and ((((not (not A)) and A) -> B) -> (((not (not A)) or ((not (not A)) and A)) -> B))), M:tm-312, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-13833
in-theory        13833
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and (B or ((not (not A)) -> ((not (not A)) and A))))
theorem-size     21
proof            (modus-ponens tm-311 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13833.        (((not (not A)) -> ((not (not A)) and A)) and (B or ((not (not A)) -> ((not (not A)) and A)))), M:tm-311, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13834
in-theory        13834
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and (((not (not A)) -> ((not (not A)) and A)) or B))
theorem-size     21
proof            (modus-ponens tm-310 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13834.        (((not (not A)) -> ((not (not A)) and A)) and (((not (not A)) -> ((not (not A)) and A)) or B)), M:tm-310, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13835
in-theory        13835
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and (B -> (((not (not A)) -> ((not (not A)) and A)) and B)))
theorem-size     23
proof            (modus-ponens tm-309 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13835.        (((not (not A)) -> ((not (not A)) and A)) and (B -> (((not (not A)) -> ((not (not A)) and A)) and B))), M:tm-309, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13836
in-theory        13836
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and (B -> ((not (not A)) -> ((not (not A)) and A))))
theorem-size     21
proof            (modus-ponens tm-305 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13836.        (((not (not A)) -> ((not (not A)) and A)) and (B -> ((not (not A)) -> ((not (not A)) and A)))), M:tm-305, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13837
in-theory        13837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     21
proof            (modus-ponens tm-303 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13837.        ((A -> ((B -> (C -> (B and C))) and A)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-303, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13838
in-theory        13838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     19
proof            (modus-ponens tm-270 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-4 tm-2 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13838.        ((A -> (((B and C) -> C) and A)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-270, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13839
in-theory        13839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     19
proof            (modus-ponens tm-239 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-3 tm-2 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13839.        ((A -> (((B and C) -> B) and A)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-239, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13840
in-theory        13840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((not (not E)) -> ((not (not E)) and E)))
theorem-size     27
proof            (modus-ponens tm-210 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13840.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((not (not E)) -> ((not (not E)) and E))), M:tm-210, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13841
in-theory        13841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     19
proof            (modus-ponens tm-183 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13841.        ((A -> ((B -> (C -> B)) and A)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-183, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13842
in-theory        13842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-157 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13842.        ((A -> ((B and C) -> C)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-157, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13843
in-theory        13843
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     25
proof            (modus-ponens tm-147 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-10)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13843.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-147, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13844
in-theory        13844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-134 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13844.        ((A -> ((B and C) -> B)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-134, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13845
in-theory        13845
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     25
proof            (modus-ponens tm-125 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-10)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13845.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-125, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13846
in-theory        13846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((not (not E)) -> ((not (not E)) and E)))
theorem-size     25
proof            (modus-ponens tm-113 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13846.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((not (not E)) -> ((not (not E)) and E))), M:tm-113, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13847
in-theory        13847
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     29
proof            (modus-ponens tm-105 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13847.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((not (not D)) -> ((not (not D)) and D))), M:tm-105, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13848
in-theory        13848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((not (not C)) -> ((not (not C)) and C)))
theorem-size     17
proof            (modus-ponens tm-95 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13848.        (((A -> B) -> (A -> A)) and ((not (not C)) -> ((not (not C)) and C))), M:tm-95, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13849
in-theory        13849
times-derived    1
----------------------------------------------------------------
theorem          ((not (not A)) -> (B -> ((not (not A)) and A)))
theorem-size     11
proof            (modus-ponens tm-84 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-10)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13849.        ((not (not A)) -> (B -> ((not (not A)) and A))), M:tm-84, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-13850
in-theory        13850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-83 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13850.        ((A -> (B -> (C -> B))) and ((not (not D)) -> ((not (not D)) and D))), M:tm-83, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13851
in-theory        13851
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((not (not B)) -> ((not (not B)) and B)))
theorem-size     15
proof            (modus-ponens tm-76 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13851.        (((not (not A)) -> A) and ((not (not B)) -> ((not (not B)) and B))), M:tm-76, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13852
in-theory        13852
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (not (not A)))) or (not (not A))) -> ((not (not A)) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13852.        (((not (not (not (not A)))) or (not (not A))) -> ((not (not A)) and A)), M:tm-73, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-13853
in-theory        13853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((not (not C)) -> ((not (not C)) and C)))
theorem-size     21
proof            (modus-ponens tm-69 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-9 tm-2 tm-10)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13853.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((not (not C)) -> ((not (not C)) and C))), M:tm-69, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13854
in-theory        13854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     23
proof            (modus-ponens tm-54 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-10)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13854.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((not (not D)) -> ((not (not D)) and D))), M:tm-54, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13855
in-theory        13855
times-derived    1
----------------------------------------------------------------
theorem          (((A and (not (not B))) or (not (not B))) -> ((not (not B)) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13855.        (((A and (not (not B))) or (not (not B))) -> ((not (not B)) and B)), M:tm-47, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-13856
in-theory        13856
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) and B) or (not (not A))) -> ((not (not A)) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13856.        ((((not (not A)) and B) or (not (not A))) -> ((not (not A)) and A)), M:tm-46, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-13857
in-theory        13857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((not (not C)) -> ((not (not C)) and C)))
theorem-size     15
proof            (modus-ponens tm-42 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13857.        ((A -> (B or A)) and ((not (not C)) -> ((not (not C)) and C))), M:tm-42, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13858
in-theory        13858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((not (not C)) -> ((not (not C)) and C)))
theorem-size     15
proof            (modus-ponens tm-32 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13858.        ((A -> (A or B)) and ((not (not C)) -> ((not (not C)) and C))), M:tm-32, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13859
in-theory        13859
times-derived    1
----------------------------------------------------------------
theorem          ((not (not A)) -> ((not (not A)) and ((not (not A)) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13859.        ((not (not A)) -> ((not (not A)) and ((not (not A)) and A))), M:tm-24, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-13860
in-theory        13860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((not (not C)) -> ((not (not C)) and C)))
theorem-size     17
proof            (modus-ponens tm-23 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13860.        ((A -> (B -> (A and B))) and ((not (not C)) -> ((not (not C)) and C))), M:tm-23, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13861
in-theory        13861
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((not (not C)) -> ((not (not C)) and C)))
theorem-size     15
proof            (modus-ponens tm-22 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-4 tm-2 tm-10)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13861.        (((A and B) -> B) and ((not (not C)) -> ((not (not C)) and C))), M:tm-22, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13862
in-theory        13862
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((not (not C)) -> ((not (not C)) and C)))
theorem-size     15
proof            (modus-ponens tm-21 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-3 tm-2 tm-10)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13862.        (((A and B) -> A) and ((not (not C)) -> ((not (not C)) and C))), M:tm-21, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13863
in-theory        13863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     23
proof            (modus-ponens tm-20 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13863.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> ((not (not D)) and D))), M:tm-20, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13864
in-theory        13864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((not (not C)) -> ((not (not C)) and C)))
theorem-size     15
proof            (modus-ponens tm-19 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13864.        ((A -> (B -> A)) and ((not (not C)) -> ((not (not C)) and C))), M:tm-19, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13865
in-theory        13865
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not ((not (not A)) and A))) -> (not (not (not A))))
theorem-size     15
proof            (modus-ponens tm-9 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-9 tm-2 tm-5 tm-10)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13865.        (((not (not A)) -> (not ((not (not A)) and A))) -> (not (not (not A)))), M:tm-9, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-13866
in-theory        13866
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) and A) -> B) -> (((not (not A)) or ((not (not A)) and A)) -> B))
theorem-size     19
proof            (modus-ponens tm-8 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-8 tm-2 tm-5 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13866.        ((((not (not A)) and A) -> B) -> (((not (not A)) or ((not (not A)) and A)) -> B)), M:tm-8, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-13867
in-theory        13867
times-derived    1
----------------------------------------------------------------
theorem          (A or ((not (not B)) -> ((not (not B)) and B)))
theorem-size     11
proof            (modus-ponens tm-7 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-7 tm-2 tm-5 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13867.        (A or ((not (not B)) -> ((not (not B)) and B))), M:tm-7, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13868
in-theory        13868
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) or B)
theorem-size     11
proof            (modus-ponens tm-6 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-6 tm-2 tm-5 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13868.        (((not (not A)) -> ((not (not A)) and A)) or B), M:tm-6, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13869
in-theory        13869
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((not (not B)) -> ((not (not B)) and B)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13869.        (A -> (((not (not B)) -> ((not (not B)) and B)) and A)), M:tm-5, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13870
in-theory        13870
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((not (not B)) -> ((not (not B)) and B)))
theorem-size     11
proof            (modus-ponens tm-1 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-1 tm-2 tm-5 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13870.        (A -> ((not (not B)) -> ((not (not B)) and B))), M:tm-1, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-13871
in-theory        13871
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-315 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13871.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> C))), M:tm-315, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-13872
in-theory        13872
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13872.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> D))), M:tm-315, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-13873
in-theory        13873
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-315 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13873.        (((A -> (B -> A)) or C) and (D -> (E -> D))), M:tm-315, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-13874
in-theory        13874
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13874.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> E))), M:tm-315, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-13875
in-theory        13875
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-315 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13875.        ((((A and B) -> A) or C) and (D -> (E -> D))), M:tm-315, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-13876
in-theory        13876
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-315 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13876.        ((((A and B) -> B) or C) and (D -> (E -> D))), M:tm-315, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-13877
in-theory        13877
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13877.        (((A -> (B -> (A and B))) or C) and (D -> (E -> D))), M:tm-315, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-13878
in-theory        13878
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-315 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13878.        (((A -> (A or B)) or C) and (D -> (E -> D))), M:tm-315, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-13879
in-theory        13879
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13879.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> D))), M:tm-315, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-13880
in-theory        13880
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-315 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13880.        ((A -> (B -> (B or C))) and (D -> (E -> D))), M:tm-315, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-13881
in-theory        13881
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-315 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13881.        ((A or (B -> (C -> B))) and (D -> (E -> D))), M:tm-315, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-13882
in-theory        13882
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13882.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> E))), M:tm-315, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-13883
in-theory        13883
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-315 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13883.        ((A or ((B and C) -> B)) and (D -> (E -> D))), M:tm-315, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-13884
in-theory        13884
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-315 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13884.        ((A or ((B and C) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-13885
in-theory        13885
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13885.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> D))), M:tm-315, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-13886
in-theory        13886
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-315 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13886.        ((A or (B -> (B or C))) and (D -> (E -> D))), M:tm-315, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-13887
in-theory        13887
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-315 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13887.        ((A or (B -> (C or B))) and (D -> (E -> D))), M:tm-315, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-13888
in-theory        13888
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-315 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13888.        (((A -> (B or A)) or C) and (D -> (E -> D))), M:tm-315, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-13889
in-theory        13889
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13889.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> D))), M:tm-315, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-13890
in-theory        13890
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-315 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13890.        ((A -> (B -> (C or B))) and (D -> (E -> D))), M:tm-315, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-13891
in-theory        13891
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13891.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-13892
in-theory        13892
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> E)))
theorem-size     31
proof            (modus-ponens tm-315 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13892.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-13893
in-theory        13893
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13893.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> D))), M:tm-315, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-13894
in-theory        13894
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13894.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> D))), M:tm-315, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-13895
in-theory        13895
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-315 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13895.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-13896
in-theory        13896
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13896.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-13897
in-theory        13897
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13897.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-13898
in-theory        13898
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> E)))
theorem-size     33
proof            (modus-ponens tm-315 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13898.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-13899
in-theory        13899
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13899.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> E))), M:tm-315, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-13900
in-theory        13900
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13900.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> E))), M:tm-315, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-13901
in-theory        13901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13901.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (E -> (F -> E))), M:tm-315, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-13902
in-theory        13902
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-315 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-13902.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-13903
in-theory        13903
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-13903.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> E))), M:tm-315, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-13904
in-theory        13904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-315 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13904.        (((A -> (not (B -> A))) -> (not A)) and (C -> (D -> C))), M:tm-315, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-13905
in-theory        13905
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (D -> (E -> D)))
theorem-size     27
proof            (modus-ponens tm-315 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13905.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (D -> (E -> D))), M:tm-315, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-13906
in-theory        13906
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-315 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13906.        ((((A and B) -> (not A)) -> (not (A and B))) and (C -> (D -> C))), M:tm-315, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-13907
in-theory        13907
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-315 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13907.        ((((A and B) -> (not B)) -> (not (A and B))) and (C -> (D -> C))), M:tm-315, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-13908
in-theory        13908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-315 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13908.        (((A -> (not (B -> (A and B)))) -> (not A)) and (C -> (D -> C))), M:tm-315, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-13909
in-theory        13909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-315 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13909.        (((A -> (not (A or B))) -> (not A)) and (C -> (D -> C))), M:tm-315, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-13910
in-theory        13910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-315 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13910.        (((A -> (not (B or A))) -> (not A)) and (C -> (D -> C))), M:tm-315, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-13911
in-theory        13911
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-315 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13911.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (D -> (E -> D))), M:tm-315, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-13912
in-theory        13912
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (C -> (D -> C)))
theorem-size     23
proof            (modus-ponens tm-315 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13912.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (C -> (D -> C))), M:tm-315, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-13913
in-theory        13913
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (D -> (E -> D)))
theorem-size     29
proof            (modus-ponens tm-315 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13913.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-13914
in-theory        13914
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13914.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (E -> D))), M:tm-315, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-13915
in-theory        13915
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13915.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (D -> (E -> D))), M:tm-315, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-13916
in-theory        13916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13916.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (D -> (E -> D))), M:tm-315, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-13917
in-theory        13917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (C -> (D -> C)))
theorem-size     21
proof            (modus-ponens tm-315 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-13917.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (C -> (D -> C))), M:tm-315, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-13918
in-theory        13918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-13918.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (E -> D))), M:tm-315, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-13919
in-theory        13919
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (B -> (C -> B)))
theorem-size     17
proof            (modus-ponens tm-315 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13919.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (B -> (C -> B))), M:tm-315, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-13920
in-theory        13920
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-315 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-10)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13920.        (((A -> B) -> (((not (not A)) or A) -> B)) and (C -> (D -> C))), M:tm-315, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-13921
in-theory        13921
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-315 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13921.        ((A or ((not (not B)) -> B)) and (C -> (D -> C))), M:tm-315, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-13922
in-theory        13922
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-315 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13922.        ((((not (not A)) -> A) or B) and (C -> (D -> C))), M:tm-315, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-13923
in-theory        13923
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-315 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13923.        ((A -> (((not (not B)) -> B) and A)) and (C -> (D -> C))), M:tm-315, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-13924
in-theory        13924
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (C -> (D -> C)))
theorem-size     21
proof            (modus-ponens tm-315 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-13924.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (C -> (D -> C))), M:tm-315, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-13925
in-theory        13925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-315 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-13925.        ((A -> ((not (not B)) -> B)) and (C -> (D -> C))), M:tm-315, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-13926
in-theory        13926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13926.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (D -> (E -> D))), M:tm-315, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-13927
in-theory        13927
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13927.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-13928
in-theory        13928
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13928.        ((A or (B -> (C -> (D -> C)))) and (E -> (F -> E))), M:tm-315, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-13929
in-theory        13929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13929.        (((A -> (B -> (C -> B))) or D) and (E -> (F -> E))), M:tm-315, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-13930
in-theory        13930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13930.        ((A -> ((B -> (C -> (D -> C))) and A)) and (E -> (F -> E))), M:tm-315, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-13931
in-theory        13931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13931.        (((A -> B) -> (A -> (C -> B))) and (D -> (E -> D))), M:tm-315, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-13932
in-theory        13932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-13932.        ((A -> (B -> (C -> (D -> C)))) and (E -> (F -> E))), M:tm-315, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-13933
in-theory        13933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and (B -> (C -> B)))
theorem-size     9
proof            (modus-ponens tm-315 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       97
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13933.        ((A -> A) and (B -> (C -> B))), M:tm-315, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-13934
in-theory        13934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13934.        (((A -> (B -> C)) -> (A -> (B -> C))) and (D -> (E -> D))), M:tm-315, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-13935
in-theory        13935
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-315 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13935.        (((A and B) -> (A and B)) and (C -> (D -> C))), M:tm-315, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-13936
in-theory        13936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-315 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13936.        (((A -> B) -> (A -> B)) and (C -> (D -> C))), M:tm-315, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-13937
in-theory        13937
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and (B -> (C -> B)))
theorem-size     13
proof            (modus-ponens tm-315 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-13937.        (((not (not A)) -> (not (not A))) and (B -> (C -> B))), M:tm-315, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-13938
in-theory        13938
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (C -> (D -> C)))
theorem-size     19
proof            (modus-ponens tm-315 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13938.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (C -> (D -> C))), M:tm-315, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-13939
in-theory        13939
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13939.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (D -> (E -> D))), M:tm-315, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-13940
in-theory        13940
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13940.        ((A or ((B -> C) -> (B -> B))) and (D -> (E -> D))), M:tm-315, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-13941
in-theory        13941
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13941.        ((((A -> B) -> (A -> A)) or C) and (D -> (E -> D))), M:tm-315, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-13942
in-theory        13942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13942.        ((A -> (((B -> C) -> (B -> B)) and A)) and (D -> (E -> D))), M:tm-315, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-13943
in-theory        13943
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-315 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-13943.        ((((A -> B) -> A) -> ((A -> B) -> A)) and (C -> (D -> C))), M:tm-315, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-13944
in-theory        13944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13944.        ((A -> ((B -> C) -> (B -> B))) and (D -> (E -> D))), M:tm-315, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-13945
in-theory        13945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-13945.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (D -> (E -> D))), M:tm-315, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-13946
in-theory        13946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-315 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-13946.        (((A -> (A -> B)) -> (A -> B)) and (C -> (D -> C))), M:tm-315, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-13947
in-theory        13947
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-315 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-13947.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (D -> (E -> D))), M:tm-315, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-13948
in-theory        13948
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (D -> (E -> D)))
theorem-size     37
proof            (modus-ponens tm-315 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-13948.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (D -> (E -> D))), M:tm-315, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-13949
in-theory        13949
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (E -> (F -> E)))
theorem-size     39
proof            (modus-ponens tm-315 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-13949.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-13950
in-theory        13950
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13950.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (F -> E))), M:tm-315, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-13951
in-theory        13951
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13951.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (E -> (F -> E))), M:tm-315, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-13952
in-theory        13952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (E -> (F -> E)))
theorem-size     29
proof            (modus-ponens tm-315 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13952.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (E -> (F -> E))), M:tm-315, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-13953
in-theory        13953
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (D -> (E -> D)))
theorem-size     35
proof            (modus-ponens tm-315 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-13953.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (D -> (E -> D))), M:tm-315, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-13954
in-theory        13954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-13954.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (F -> E))), M:tm-315, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-13955
in-theory        13955
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (E -> (F -> E)))
theorem-size     29
proof            (modus-ponens tm-315 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-13955.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-13956
in-theory        13956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13956.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (E -> (F -> E))), M:tm-315, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-13957
in-theory        13957
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (F -> (G -> F)))
theorem-size     39
proof            (modus-ponens tm-315 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13957.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (F -> (G -> F))), M:tm-315, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-13958
in-theory        13958
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13958.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> F))), M:tm-315, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-13959
in-theory        13959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13959.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (G -> F))), M:tm-315, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-13960
in-theory        13960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13960.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (G -> F))), M:tm-315, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-13961
in-theory        13961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13961.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (E -> (F -> E))), M:tm-315, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-13962
in-theory        13962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13962.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> F))), M:tm-315, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-13963
in-theory        13963
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-315 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-13963.        ((((A -> B) and A) -> B) and (C -> (D -> C))), M:tm-315, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-13964
in-theory        13964
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-13964.        (((((A -> (B -> A)) -> C) and D) -> C) and (E -> (F -> E))), M:tm-315, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-13965
in-theory        13965
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13965.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (F -> (G -> F))), M:tm-315, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-13966
in-theory        13966
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (D -> (E -> D)))
theorem-size     27
proof            (modus-ponens tm-315 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-13966.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (D -> (E -> D))), M:tm-315, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-13967
in-theory        13967
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13967.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (D -> (E -> D))), M:tm-315, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-13968
in-theory        13968
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (D -> (E -> D)))
theorem-size     31
proof            (modus-ponens tm-315 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13968.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (D -> (E -> D))), M:tm-315, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-13969
in-theory        13969
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (E -> (F -> E)))
theorem-size     33
proof            (modus-ponens tm-315 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-13969.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-13970
in-theory        13970
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13970.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (F -> E))), M:tm-315, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-13971
in-theory        13971
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13971.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (E -> (F -> E))), M:tm-315, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-13972
in-theory        13972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13972.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-13973
in-theory        13973
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (D -> (E -> D)))
theorem-size     29
proof            (modus-ponens tm-315 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-13973.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (D -> (E -> D))), M:tm-315, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-13974
in-theory        13974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13974.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (F -> E))), M:tm-315, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-13975
in-theory        13975
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-13975.        ((((((A and B) -> A) -> C) and D) -> C) and (E -> (F -> E))), M:tm-315, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-13976
in-theory        13976
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-13976.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-13977
in-theory        13977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13977.        (((A -> (not ((B and C) -> B))) -> (not A)) and (D -> (E -> D))), M:tm-315, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-13978
in-theory        13978
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13978.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-13979
in-theory        13979
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13979.        ((A or (B -> ((C and D) -> C))) and (E -> (F -> E))), M:tm-315, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-13980
in-theory        13980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13980.        (((A -> ((B and C) -> B)) or D) and (E -> (F -> E))), M:tm-315, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-13981
in-theory        13981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13981.        ((A -> ((B -> ((C and D) -> C)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-13982
in-theory        13982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-13982.        (((A -> (B and C)) -> (A -> B)) and (D -> (E -> D))), M:tm-315, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-13983
in-theory        13983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-13983.        ((A -> (B -> ((C and D) -> C))) and (E -> (F -> E))), M:tm-315, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-13984
in-theory        13984
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-315 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-13984.        (((A and (A -> B)) -> B) and (C -> (D -> C))), M:tm-315, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-13985
in-theory        13985
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-13985.        (((A and ((B -> (C -> B)) -> D)) -> D) and (E -> (F -> E))), M:tm-315, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-13986
in-theory        13986
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13986.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (F -> (G -> F))), M:tm-315, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-13987
in-theory        13987
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-13987.        (((A and (((B and C) -> B) -> D)) -> D) and (E -> (F -> E))), M:tm-315, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-13988
in-theory        13988
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (D -> (E -> D)))
theorem-size     27
proof            (modus-ponens tm-315 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-13988.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-13989
in-theory        13989
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13989.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (D -> (E -> D))), M:tm-315, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-13990
in-theory        13990
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (D -> (E -> D)))
theorem-size     31
proof            (modus-ponens tm-315 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13990.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (D -> (E -> D))), M:tm-315, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-13991
in-theory        13991
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (E -> (F -> E)))
theorem-size     33
proof            (modus-ponens tm-315 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-13991.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-13992
in-theory        13992
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13992.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-13993
in-theory        13993
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13993.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (E -> (F -> E))), M:tm-315, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-13994
in-theory        13994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13994.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-13995
in-theory        13995
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (D -> (E -> D)))
theorem-size     29
proof            (modus-ponens tm-315 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-13995.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-13996
in-theory        13996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13996.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-13997
in-theory        13997
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-13997.        (((A and (((B and C) -> C) -> D)) -> D) and (E -> (F -> E))), M:tm-315, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-13998
in-theory        13998
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-13998.        ((((((A and B) -> B) -> C) and D) -> C) and (E -> (F -> E))), M:tm-315, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-13999
in-theory        13999
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-13999.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-14000
in-theory        14000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-14000.        (((A -> (not ((B and C) -> C))) -> (not A)) and (D -> (E -> D))), M:tm-315, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-14001
in-theory        14001
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-14001.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-14002
in-theory        14002
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14002.        ((A or (B -> ((C and D) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-14003
in-theory        14003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14003.        (((A -> ((B and C) -> C)) or D) and (E -> (F -> E))), M:tm-315, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-14004
in-theory        14004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14004.        ((A -> ((B -> ((C and D) -> D)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-14005
in-theory        14005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-14005.        (((A -> (B and C)) -> (A -> C)) and (D -> (E -> D))), M:tm-315, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-14006
in-theory        14006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14006.        ((A -> (B -> ((C and D) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-14007
in-theory        14007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14007.        (((A -> (B -> A)) and (C -> (D -> C))) and (E -> (F -> E))), M:tm-315, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-14008
in-theory        14008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14008.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-14009
in-theory        14009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14009.        (((A -> (B -> A)) and ((C and D) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-14010
in-theory        14010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14010.        (((A -> (B -> A)) and ((C and D) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-14011
in-theory        14011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14011.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-14012
in-theory        14012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14012.        (((A -> (B -> A)) and (C -> (C or D))) and (E -> (F -> E))), M:tm-315, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-14013
in-theory        14013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14013.        (((A -> (B -> A)) and (C -> (D or C))) and (E -> (F -> E))), M:tm-315, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-14014
in-theory        14014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14014.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-14015
in-theory        14015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14015.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> E))), M:tm-315, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-14016
in-theory        14016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14016.        (((A -> (B -> A)) and ((not (not C)) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-14017
in-theory        14017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14017.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (F -> (G -> F))), M:tm-315, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-14018
in-theory        14018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14018.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (E -> (F -> E))), M:tm-315, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-14019
in-theory        14019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     31
proof            (modus-ponens tm-315 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14019.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-14020
in-theory        14020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14020.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-14021
in-theory        14021
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14021.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-14022
in-theory        14022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14022.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-14023
in-theory        14023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14023.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-14024
in-theory        14024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14024.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-14025
in-theory        14025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14025.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-14026
in-theory        14026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-14026.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (D -> (E -> D))), M:tm-315, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-14027
in-theory        14027
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-14027.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-14028
in-theory        14028
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14028.        ((A or (B -> ((C -> (D -> C)) and B))) and (E -> (F -> E))), M:tm-315, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-14029
in-theory        14029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14029.        (((A -> ((B -> (C -> B)) and A)) or D) and (E -> (F -> E))), M:tm-315, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-14030
in-theory        14030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14030.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-14031
in-theory        14031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14031.        ((A -> (B -> ((C -> (D -> C)) and B))) and (E -> (F -> E))), M:tm-315, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-14032
in-theory        14032
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14032.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (F -> (G -> F))), M:tm-315, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-14033
in-theory        14033
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H -> G)))
theorem-size     33
proof            (modus-ponens tm-315 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14033.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H -> G))), M:tm-315, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-14034
in-theory        14034
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14034.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (F -> (G -> F))), M:tm-315, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-14035
in-theory        14035
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14035.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (F -> (G -> F))), M:tm-315, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-14036
in-theory        14036
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14036.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (F -> (G -> F))), M:tm-315, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-14037
in-theory        14037
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14037.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (F -> (G -> F))), M:tm-315, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-14038
in-theory        14038
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14038.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (F -> (G -> F))), M:tm-315, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-14039
in-theory        14039
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (H -> G)))
theorem-size     33
proof            (modus-ponens tm-315 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14039.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (H -> G))), M:tm-315, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-14040
in-theory        14040
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (G -> F)))
theorem-size     31
proof            (modus-ponens tm-315 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14040.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (G -> F))), M:tm-315, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-14041
in-theory        14041
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14041.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-14042
in-theory        14042
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14042.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (G -> (H -> G))), M:tm-315, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-14043
in-theory        14043
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14043.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (F -> (G -> F))), M:tm-315, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-14044
in-theory        14044
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (H -> G)))
theorem-size     39
proof            (modus-ponens tm-315 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14044.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (H -> G))), M:tm-315, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-14045
in-theory        14045
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I -> H)))
theorem-size     35
proof            (modus-ponens tm-315 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14045.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I -> H))), M:tm-315, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-14046
in-theory        14046
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (H -> G)))
theorem-size     35
proof            (modus-ponens tm-315 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14046.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (H -> G))), M:tm-315, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-14047
in-theory        14047
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14047.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (G -> (H -> G))), M:tm-315, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-14048
in-theory        14048
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (H -> G)))
theorem-size     35
proof            (modus-ponens tm-315 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14048.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-14049
in-theory        14049
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14049.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-14050
in-theory        14050
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14050.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (H -> G))), M:tm-315, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-14051
in-theory        14051
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (I -> H)))
theorem-size     37
proof            (modus-ponens tm-315 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14051.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (I -> H))), M:tm-315, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-14052
in-theory        14052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14052.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> G))), M:tm-315, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-14053
in-theory        14053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-14053.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (E -> (F -> E))), M:tm-315, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-14054
in-theory        14054
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (F -> (G -> F)))
theorem-size     43
proof            (modus-ponens tm-315 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-14054.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (F -> (G -> F))), M:tm-315, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-14055
in-theory        14055
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14055.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (G -> F))), M:tm-315, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-14056
in-theory        14056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14056.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (F -> (G -> F))), M:tm-315, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-14057
in-theory        14057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14057.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (F -> (G -> F))), M:tm-315, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-14058
in-theory        14058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14058.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (G -> F))), M:tm-315, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-14059
in-theory        14059
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14059.        ((((A and B) -> A) and (C -> (D -> C))) and (E -> (F -> E))), M:tm-315, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-14060
in-theory        14060
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14060.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-14061
in-theory        14061
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14061.        ((((A and B) -> A) and ((C and D) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-14062
in-theory        14062
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14062.        ((((A and B) -> A) and ((C and D) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-14063
in-theory        14063
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14063.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-14064
in-theory        14064
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14064.        ((((A and B) -> A) and (C -> (C or D))) and (E -> (F -> E))), M:tm-315, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-14065
in-theory        14065
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14065.        ((((A and B) -> A) and (C -> (D or C))) and (E -> (F -> E))), M:tm-315, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-14066
in-theory        14066
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14066.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-14067
in-theory        14067
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14067.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> E))), M:tm-315, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-14068
in-theory        14068
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14068.        ((((A and B) -> A) and ((not (not C)) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-14069
in-theory        14069
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14069.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (F -> (G -> F))), M:tm-315, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-14070
in-theory        14070
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14070.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (E -> (F -> E))), M:tm-315, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-14071
in-theory        14071
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     31
proof            (modus-ponens tm-315 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14071.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-14072
in-theory        14072
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14072.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-14073
in-theory        14073
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14073.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-14074
in-theory        14074
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14074.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-14075
in-theory        14075
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14075.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-14076
in-theory        14076
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14076.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-14077
in-theory        14077
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14077.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-14078
in-theory        14078
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14078.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> G))), M:tm-315, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-14079
in-theory        14079
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14079.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (F -> (G -> F))), M:tm-315, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-14080
in-theory        14080
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14080.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (H -> G))), M:tm-315, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-14081
in-theory        14081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14081.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (F -> (G -> F))), M:tm-315, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-14082
in-theory        14082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-14082.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (D -> (E -> D))), M:tm-315, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-14083
in-theory        14083
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-14083.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-14084
in-theory        14084
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14084.        ((A or (B -> (((C and D) -> C) and B))) and (E -> (F -> E))), M:tm-315, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-14085
in-theory        14085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14085.        (((A -> (((B and C) -> B) and A)) or D) and (E -> (F -> E))), M:tm-315, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-14086
in-theory        14086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14086.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-14087
in-theory        14087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14087.        ((A -> (B -> (((C and D) -> C) and B))) and (E -> (F -> E))), M:tm-315, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-14088
in-theory        14088
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14088.        ((((A and B) -> B) and (C -> (D -> C))) and (E -> (F -> E))), M:tm-315, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-14089
in-theory        14089
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14089.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-14090
in-theory        14090
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14090.        ((((A and B) -> B) and ((C and D) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-14091
in-theory        14091
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14091.        ((((A and B) -> B) and ((C and D) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-14092
in-theory        14092
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14092.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-14093
in-theory        14093
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14093.        ((((A and B) -> B) and (C -> (C or D))) and (E -> (F -> E))), M:tm-315, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-14094
in-theory        14094
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14094.        ((((A and B) -> B) and (C -> (D or C))) and (E -> (F -> E))), M:tm-315, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-14095
in-theory        14095
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14095.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-14096
in-theory        14096
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14096.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> E))), M:tm-315, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-14097
in-theory        14097
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14097.        ((((A and B) -> B) and ((not (not C)) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-14098
in-theory        14098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14098.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (F -> (G -> F))), M:tm-315, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-14099
in-theory        14099
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14099.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (E -> (F -> E))), M:tm-315, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-14100
in-theory        14100
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     31
proof            (modus-ponens tm-315 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14100.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-14101
in-theory        14101
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14101.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-14102
in-theory        14102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14102.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-14103
in-theory        14103
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14103.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-14104
in-theory        14104
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14104.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-14105
in-theory        14105
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14105.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-14106
in-theory        14106
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14106.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-14107
in-theory        14107
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14107.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> G))), M:tm-315, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-14108
in-theory        14108
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14108.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (F -> (G -> F))), M:tm-315, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-14109
in-theory        14109
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14109.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (F -> (G -> F))), M:tm-315, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-14110
in-theory        14110
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14110.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (F -> (G -> F))), M:tm-315, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-14111
in-theory        14111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14111.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (H -> G))), M:tm-315, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-14112
in-theory        14112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14112.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (F -> (G -> F))), M:tm-315, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-14113
in-theory        14113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-14113.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (D -> (E -> D))), M:tm-315, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-14114
in-theory        14114
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-14114.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-14115
in-theory        14115
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14115.        ((A or (B -> (((C and D) -> D) and B))) and (E -> (F -> E))), M:tm-315, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-14116
in-theory        14116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14116.        (((A -> (((B and C) -> C) and A)) or D) and (E -> (F -> E))), M:tm-315, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-14117
in-theory        14117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14117.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-14118
in-theory        14118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14118.        ((A -> (B -> (((C and D) -> D) and B))) and (E -> (F -> E))), M:tm-315, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-14119
in-theory        14119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14119.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and (E -> (F -> E))), M:tm-315, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-14120
in-theory        14120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14120.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-14121
in-theory        14121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14121.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-14122
in-theory        14122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14122.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-14123
in-theory        14123
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14123.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-14124
in-theory        14124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14124.        (((A -> (B -> (A and B))) and (C -> (C or D))) and (E -> (F -> E))), M:tm-315, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-14125
in-theory        14125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14125.        (((A -> (B -> (A and B))) and (C -> (D or C))) and (E -> (F -> E))), M:tm-315, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-14126
in-theory        14126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14126.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-14127
in-theory        14127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14127.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> E))), M:tm-315, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-14128
in-theory        14128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14128.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-14129
in-theory        14129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14129.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (F -> (G -> F))), M:tm-315, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-14130
in-theory        14130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14130.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (E -> (F -> E))), M:tm-315, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-14131
in-theory        14131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     33
proof            (modus-ponens tm-315 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14131.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-14132
in-theory        14132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14132.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-14133
in-theory        14133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> F)))
theorem-size     29
proof            (modus-ponens tm-315 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14133.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-14134
in-theory        14134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14134.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-14135
in-theory        14135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> F)))
theorem-size     29
proof            (modus-ponens tm-315 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14135.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-14136
in-theory        14136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14136.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-14137
in-theory        14137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14137.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-14138
in-theory        14138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> G)))
theorem-size     31
proof            (modus-ponens tm-315 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14138.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> G))), M:tm-315, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-14139
in-theory        14139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14139.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (F -> (G -> F))), M:tm-315, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-14140
in-theory        14140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14140.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (F -> (G -> F))), M:tm-315, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-14141
in-theory        14141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14141.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> F))), M:tm-315, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-14142
in-theory        14142
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14142.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> F))), M:tm-315, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-14143
in-theory        14143
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14143.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> F))), M:tm-315, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-14144
in-theory        14144
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (H -> G)))
theorem-size     31
proof            (modus-ponens tm-315 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14144.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (H -> G))), M:tm-315, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-14145
in-theory        14145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14145.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> F))), M:tm-315, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-14146
in-theory        14146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-14146.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (D -> (E -> D))), M:tm-315, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-14147
in-theory        14147
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (E -> (F -> E)))
theorem-size     31
proof            (modus-ponens tm-315 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-14147.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-14148
in-theory        14148
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14148.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and (E -> (F -> E))), M:tm-315, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-14149
in-theory        14149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14149.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and (E -> (F -> E))), M:tm-315, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-14150
in-theory        14150
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14150.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-14151
in-theory        14151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14151.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (E -> (F -> E))), M:tm-315, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-14152
in-theory        14152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-315 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14152.        ((A -> (A and (B -> A))) and (C -> (D -> C))), M:tm-315, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-14153
in-theory        14153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-315 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14153.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (D -> (E -> D))), M:tm-315, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-14154
in-theory        14154
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-315 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14154.        (((A and B) -> ((A and B) and A)) and (C -> (D -> C))), M:tm-315, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-14155
in-theory        14155
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-315 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14155.        (((A and B) -> ((A and B) and B)) and (C -> (D -> C))), M:tm-315, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-14156
in-theory        14156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-315 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-14156.        ((A -> (A and (B -> (A and B)))) and (C -> (D -> C))), M:tm-315, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-14157
in-theory        14157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-315 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-14157.        ((A -> (A and (A or B))) and (C -> (D -> C))), M:tm-315, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-14158
in-theory        14158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-315 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-14158.        ((A -> (A and (B or A))) and (C -> (D -> C))), M:tm-315, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-14159
in-theory        14159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-315 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-14159.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (D -> (E -> D))), M:tm-315, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-14160
in-theory        14160
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (C -> (D -> C)))
theorem-size     21
proof            (modus-ponens tm-315 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-14160.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (C -> (D -> C))), M:tm-315, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-14161
in-theory        14161
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and (B -> (C -> B)))
theorem-size     15
proof            (modus-ponens tm-315 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-14161.        (((not (not A)) -> ((not (not A)) and A)) and (B -> (C -> B))), M:tm-315, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-14162
in-theory        14162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14162.        ((A -> (A and (B -> (C -> B)))) and (D -> (E -> D))), M:tm-315, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14163
in-theory        14163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and ((A -> (not (A and (B -> (C -> B))))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14163.        ((A -> (A and (B -> (C -> B)))) and ((A -> (not (A and (B -> (C -> B))))) -> (not A))), M:tm-313, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14164
in-theory        14164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (((A and (B -> (C -> B))) -> D) -> ((A or (A and (B -> (C -> B)))) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14164.        ((A -> (A and (B -> (C -> B)))) and (((A and (B -> (C -> B))) -> D) -> ((A or (A and (B -> (C -> B)))) -> D))), M:tm-312, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14165
in-theory        14165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (D or (A -> (A and (B -> (C -> B))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14165.        ((A -> (A and (B -> (C -> B)))) and (D or (A -> (A and (B -> (C -> B)))))), M:tm-311, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14166
in-theory        14166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and ((A -> (A and (B -> (C -> B)))) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14166.        ((A -> (A and (B -> (C -> B)))) and ((A -> (A and (B -> (C -> B)))) or D)), M:tm-310, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14167
in-theory        14167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (D -> ((A -> (A and (B -> (C -> B)))) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14167.        ((A -> (A and (B -> (C -> B)))) and (D -> ((A -> (A and (B -> (C -> B)))) and D))), M:tm-309, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14168
in-theory        14168
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (D -> (A -> (A and (B -> (C -> B))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14168.        ((A -> (A and (B -> (C -> B)))) and (D -> (A -> (A and (B -> (C -> B)))))), M:tm-305, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14169
in-theory        14169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (E -> (F -> E)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14169.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (E -> (F -> E))))), M:tm-303, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14170
in-theory        14170
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (D -> (E -> D))))
theorem-size     27
proof            (modus-ponens tm-300 tm-315 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14170.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (D -> (E -> D)))), M:tm-300, m:tm-315, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14171
in-theory        14171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14171.        ((A -> (((B and C) -> C) and A)) and (D -> (D and (E -> (F -> E))))), M:tm-270, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14172
in-theory        14172
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (D -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-267 tm-315 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14172.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (D -> (E -> D)))), M:tm-267, m:tm-315, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14173
in-theory        14173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14173.        ((A -> (((B and C) -> B) and A)) and (D -> (D and (E -> (F -> E))))), M:tm-239, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14174
in-theory        14174
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (D -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-236 tm-315 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14174.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (D -> (E -> D)))), M:tm-236, m:tm-315, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14175
in-theory        14175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (F -> (G -> F)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14175.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (F -> (G -> F))))), M:tm-210, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14176
in-theory        14176
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (E -> (F -> E))))
theorem-size     39
proof            (modus-ponens tm-207 tm-315 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14176.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (E -> (F -> E)))), M:tm-207, m:tm-315, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14177
in-theory        14177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14177.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (E -> (F -> E))))), M:tm-183, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14178
in-theory        14178
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (D -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-180 tm-315 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14178.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (D -> (E -> D)))), M:tm-180, m:tm-315, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14179
in-theory        14179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14179.        ((A -> ((B and C) -> C)) and (D -> (D and (E -> (F -> E))))), M:tm-157, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14180
in-theory        14180
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and (D -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-154 tm-315 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14180.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and (D -> (E -> D)))), M:tm-154, m:tm-315, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14181
in-theory        14181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (E -> (F -> E)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14181.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (E -> (F -> E))))), M:tm-147, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14182
in-theory        14182
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (D -> (E -> D))))
theorem-size     29
proof            (modus-ponens tm-144 tm-315 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14182.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (D -> (E -> D)))), M:tm-144, m:tm-315, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14183
in-theory        14183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14183.        ((A -> ((B and C) -> B)) and (D -> (D and (E -> (F -> E))))), M:tm-134, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14184
in-theory        14184
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and (D -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-131 tm-315 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14184.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and (D -> (E -> D)))), M:tm-131, m:tm-315, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14185
in-theory        14185
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (E -> (F -> E)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14185.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (E -> (F -> E))))), M:tm-125, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14186
in-theory        14186
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (D -> (E -> D))))
theorem-size     29
proof            (modus-ponens tm-122 tm-315 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14186.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (D -> (E -> D)))), M:tm-122, m:tm-315, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14187
in-theory        14187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14187.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (G -> F))))), M:tm-113, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14188
in-theory        14188
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> E))))
theorem-size     35
proof            (modus-ponens tm-110 tm-315 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14188.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> E)))), M:tm-110, m:tm-315, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14189
in-theory        14189
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (E -> (F -> E)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14189.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (E -> (F -> E))))), M:tm-105, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14190
in-theory        14190
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (D -> (E -> D))))
theorem-size     35
proof            (modus-ponens tm-102 tm-315 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14190.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (D -> (E -> D)))), M:tm-102, m:tm-315, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14191
in-theory        14191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and (D -> (E -> D)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14191.        (((A -> B) -> (A -> A)) and (C -> (C and (D -> (E -> D))))), M:tm-95, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14192
in-theory        14192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and (C -> (D -> C))))
theorem-size     17
proof            (modus-ponens tm-92 tm-315 ((Am (-> A A)) (B (and (-> A A) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14192.        (((A -> B) or (A -> A)) -> ((A -> A) and (C -> (D -> C)))), M:tm-92, m:tm-315, u:((Am (-> A A)) (B (and (-> A A) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14193
in-theory        14193
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and (C -> (D -> C)))))
theorem-size     11
proof            (modus-ponens tm-84 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14193.        (A -> (B -> (A and (C -> (D -> C))))), M:tm-84, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14194
in-theory        14194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14194.        ((A -> (B -> (C -> B))) and (D -> (D and (E -> (F -> E))))), M:tm-83, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14195
in-theory        14195
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (D -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-80 tm-315 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14195.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (D -> (E -> D)))), M:tm-80, m:tm-315, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14196
in-theory        14196
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and (C -> (D -> C)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14196.        (((not (not A)) -> A) and (B -> (B and (C -> (D -> C))))), M:tm-76, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14197
in-theory        14197
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and (B -> (C -> B))))
theorem-size     13
proof            (modus-ponens tm-73 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14197.        (((not (not A)) or A) -> (A and (B -> (C -> B)))), M:tm-73, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14198
in-theory        14198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (D -> (E -> D)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14198.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (D -> (E -> D))))), M:tm-69, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14199
in-theory        14199
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (C -> (D -> C))))
theorem-size     25
proof            (modus-ponens tm-66 tm-315 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14199.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (C -> (D -> C)))), M:tm-66, m:tm-315, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14200
in-theory        14200
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (E -> (F -> E)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14200.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (E -> (F -> E))))), M:tm-54, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14201
in-theory        14201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> (E -> D))))
theorem-size     29
proof            (modus-ponens tm-51 tm-315 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14201.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> (E -> D)))), M:tm-51, m:tm-315, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14202
in-theory        14202
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and (C -> (D -> C))))
theorem-size     15
proof            (modus-ponens tm-50 tm-315 ((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14202.        ((A or (B or A)) -> ((B or A) and (C -> (D -> C)))), M:tm-50, m:tm-315, u:((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14203
in-theory        14203
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and (C -> (D -> C))))
theorem-size     15
proof            (modus-ponens tm-49 tm-315 ((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14203.        ((A or (A or B)) -> ((A or B) and (C -> (D -> C)))), M:tm-49, m:tm-315, u:((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14204
in-theory        14204
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> (D -> C))))
theorem-size     19
proof            (modus-ponens tm-48 tm-315 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14204.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> (D -> C)))), M:tm-48, m:tm-315, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14205
in-theory        14205
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (C -> (D -> C))))
theorem-size     13
proof            (modus-ponens tm-47 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14205.        (((A and B) or B) -> (B and (C -> (D -> C)))), M:tm-47, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14206
in-theory        14206
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (C -> (D -> C))))
theorem-size     13
proof            (modus-ponens tm-46 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14206.        (((A and B) or A) -> (A and (C -> (D -> C)))), M:tm-46, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14207
in-theory        14207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (E -> D))))
theorem-size     27
proof            (modus-ponens tm-45 tm-315 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14207.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (E -> D)))), M:tm-45, m:tm-315, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14208
in-theory        14208
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (C -> (D -> C))))
theorem-size     15
proof            (modus-ponens tm-44 tm-315 ((Am (-> A B)) (C (and (-> A B) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14208.        ((A or (B -> A)) -> ((B -> A) and (C -> (D -> C)))), M:tm-44, m:tm-315, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14209
in-theory        14209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and (D -> (E -> D)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14209.        ((A -> (B or A)) and (C -> (C and (D -> (E -> D))))), M:tm-42, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14210
in-theory        14210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and (D -> (E -> D)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14210.        ((A -> (A or B)) and (C -> (C and (D -> (E -> D))))), M:tm-32, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14211
in-theory        14211
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and (B -> (C -> B)))))
theorem-size     11
proof            (modus-ponens tm-24 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14211.        (A -> (A and (A and (B -> (C -> B))))), M:tm-24, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14212
in-theory        14212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and (D -> (E -> D)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14212.        ((A -> (B -> (A and B))) and (C -> (C and (D -> (E -> D))))), M:tm-23, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14213
in-theory        14213
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and (D -> (E -> D)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14213.        (((A and B) -> B) and (C -> (C and (D -> (E -> D))))), M:tm-22, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14214
in-theory        14214
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and (D -> (E -> D)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14214.        (((A and B) -> A) and (C -> (C and (D -> (E -> D))))), M:tm-21, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14215
in-theory        14215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (E -> (F -> E)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14215.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (E -> (F -> E))))), M:tm-20, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14216
in-theory        14216
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and (D -> (E -> D)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14216.        ((A -> (B -> A)) and (C -> (C and (D -> (E -> D))))), M:tm-19, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14217
in-theory        14217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and (B -> (C -> B))))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-9 tm-2 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14217.        ((A -> (not (A and (B -> (C -> B))))) -> (not A)), M:tm-9, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14218
in-theory        14218
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> B))) -> D) -> ((A or (A and (B -> (C -> B)))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14218.        (((A and (B -> (C -> B))) -> D) -> ((A or (A and (B -> (C -> B)))) -> D)), M:tm-8, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14219
in-theory        14219
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and (C -> (D -> C)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-7 tm-2 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14219.        (A or (B -> (B and (C -> (D -> C))))), M:tm-7, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14220
in-theory        14220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-6 tm-2 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14220.        ((A -> (A and (B -> (C -> B)))) or D), M:tm-6, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14221
in-theory        14221
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and (C -> (D -> C)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14221.        (A -> ((B -> (B and (C -> (D -> C)))) and A)), M:tm-5, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14222
in-theory        14222
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and (C -> (D -> C)))))
theorem-size     11
proof            (modus-ponens tm-1 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14222.        (A -> (B -> (B and (C -> (D -> C))))), M:tm-1, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14223
in-theory        14223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (A -> A))
theorem-size     9
proof            (modus-ponens tm-316 tm-1 ((A Am) (B (-> Bm Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14223.        ((A -> (B -> A)) and (A -> A)), M:tm-316, m:tm-1, u:((A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-14224
in-theory        14224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((A -> (B -> C)) -> (A -> (B -> C))))
theorem-size     25
proof            (modus-ponens tm-316 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14224.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((A -> (B -> C)) -> (A -> (B -> C)))), M:tm-316, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-14225
in-theory        14225
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((A and B) -> (A and B)))
theorem-size     13
proof            (modus-ponens tm-316 tm-3 ((A (and Am Bm)) (B Am)))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-14225.        (((A and B) -> A) and ((A and B) -> (A and B))), M:tm-316, m:tm-3, u:((A (and Am Bm)) (B Am))
================================================================
tm-name          tm-14226
in-theory        14226
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((A and B) -> (A and B)))
theorem-size     13
proof            (modus-ponens tm-316 tm-4 ((A (and Am Bm)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-14226.        (((A and B) -> B) and ((A and B) -> (A and B))), M:tm-316, m:tm-4, u:((A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-14227
in-theory        14227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (A -> A))
theorem-size     11
proof            (modus-ponens tm-316 tm-5 ((A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14227.        ((A -> (B -> (A and B))) and (A -> A)), M:tm-316, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-14228
in-theory        14228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (A -> A))
theorem-size     9
proof            (modus-ponens tm-316 tm-6 ((A Am) (B (or Am Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-14228.        ((A -> (A or B)) and (A -> A)), M:tm-316, m:tm-6, u:((A Am) (B (or Am Bm)))
================================================================
tm-name          tm-14229
in-theory        14229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (A -> A))
theorem-size     9
proof            (modus-ponens tm-316 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-14229.        ((A -> (B or A)) and (A -> A)), M:tm-316, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-14230
in-theory        14230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((A -> B) -> (A -> B)))
theorem-size     21
proof            (modus-ponens tm-316 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14230.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-14231
in-theory        14231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((A -> B) -> (A -> B)))
theorem-size     19
proof            (modus-ponens tm-316 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14231.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-14232
in-theory        14232
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((not (not A)) -> (not (not A))))
theorem-size     13
proof            (modus-ponens tm-316 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-14232.        (((not (not A)) -> A) and ((not (not A)) -> (not (not A)))), M:tm-316, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-14233
in-theory        14233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (A -> A))
theorem-size     11
proof            (modus-ponens tm-316 tm-11 ((A Am) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14233.        ((A -> (B -> (C -> B))) and (A -> A)), M:tm-316, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-14234
in-theory        14234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((A -> B) -> (A -> B)))
theorem-size     15
proof            (modus-ponens tm-316 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14234.        (((A -> B) -> (A -> A)) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-14235
in-theory        14235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))))
theorem-size     39
proof            (modus-ponens tm-316 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14235.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B)))), M:tm-316, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-14236
in-theory        14236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (A -> A))
theorem-size     19
proof            (modus-ponens tm-316 tm-14 ((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14236.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (A -> A)), M:tm-316, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-14237
in-theory        14237
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)))
theorem-size     31
proof            (modus-ponens tm-316 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14237.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A))), M:tm-316, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-14238
in-theory        14238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (A -> A))
theorem-size     11
proof            (modus-ponens tm-316 tm-16 ((A Am) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14238.        ((A -> ((B and C) -> B)) and (A -> A)), M:tm-316, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-14239
in-theory        14239
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)))
theorem-size     31
proof            (modus-ponens tm-316 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14239.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B))), M:tm-316, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-14240
in-theory        14240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (A -> A))
theorem-size     11
proof            (modus-ponens tm-316 tm-18 ((A Am) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14240.        ((A -> ((B and C) -> C)) and (A -> A)), M:tm-316, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-14241
in-theory        14241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14241.        ((A -> ((B -> (C -> B)) and A)) and (A -> A)), M:tm-316, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-14242
in-theory        14242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (A -> A))
theorem-size     21
proof            (modus-ponens tm-316 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14242.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (A -> A)), M:tm-316, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-14243
in-theory        14243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14243.        ((A -> (((B and C) -> B) and A)) and (A -> A)), M:tm-316, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-14244
in-theory        14244
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14244.        ((A -> (((B and C) -> C) and A)) and (A -> A)), M:tm-316, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-14245
in-theory        14245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14245.        ((A -> ((B -> (C -> (B and C))) and A)) and (A -> A)), M:tm-316, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-14246
in-theory        14246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((A -> B) -> (A -> B)))
theorem-size     17
proof            (modus-ponens tm-316 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14246.        (((A -> B) -> (A -> (A and B))) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-14247
in-theory        14247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-25 ((A Am) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14247.        ((A -> (B -> (C -> (B and C)))) and (A -> A)), M:tm-316, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-14248
in-theory        14248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14248.        ((A -> ((B -> (B or C)) and A)) and (A -> A)), M:tm-316, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-14249
in-theory        14249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (A -> A))
theorem-size     11
proof            (modus-ponens tm-316 tm-33 ((A Am) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14249.        ((A -> (B -> (B or C))) and (A -> A)), M:tm-316, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-14250
in-theory        14250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14250.        ((A -> ((B -> (C or B)) and A)) and (A -> A)), M:tm-316, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-14251
in-theory        14251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (A -> A))
theorem-size     11
proof            (modus-ponens tm-316 tm-43 ((A Am) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14251.        ((A -> (B -> (C or B))) and (A -> A)), M:tm-316, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-14252
in-theory        14252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((A -> B) -> C) -> ((A -> B) -> C)))
theorem-size     25
proof            (modus-ponens tm-316 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14252.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((A -> B) -> C) -> ((A -> B) -> C))), M:tm-316, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-14253
in-theory        14253
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)))
theorem-size     45
proof            (modus-ponens tm-316 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14253.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D))), M:tm-316, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-14254
in-theory        14254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((A -> B) -> (A -> B)))
theorem-size     19
proof            (modus-ponens tm-316 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14254.        (((A -> B) -> (((A and C) or A) -> B)) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-14255
in-theory        14255
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((A -> B) -> (A -> B)))
theorem-size     19
proof            (modus-ponens tm-316 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14255.        (((A -> B) -> (((C and A) or A) -> B)) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-14256
in-theory        14256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C)))
theorem-size     33
proof            (modus-ponens tm-316 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-14256.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((A -> (B and A)) -> C) -> ((A -> (B and A)) -> C))), M:tm-316, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-14257
in-theory        14257
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((A or B) -> C) -> ((A or B) -> C)))
theorem-size     25
proof            (modus-ponens tm-316 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-14257.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((A or B) -> C) -> ((A or B) -> C))), M:tm-316, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-14258
in-theory        14258
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((A or B) -> C) -> ((A or B) -> C)))
theorem-size     25
proof            (modus-ponens tm-316 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-14258.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((A or B) -> C) -> ((A or B) -> C))), M:tm-316, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-14259
in-theory        14259
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D)))
theorem-size     51
proof            (modus-ponens tm-316 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-14259.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A -> B) -> ((C or A) -> B)) -> D))), M:tm-316, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-14260
in-theory        14260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (A -> A))
theorem-size     21
proof            (modus-ponens tm-316 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14260.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (A -> A)), M:tm-316, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-14261
in-theory        14261
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((A -> B) -> (B -> C)) -> ((A -> B) -> (B -> C))))
theorem-size     33
proof            (modus-ponens tm-316 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-14261.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((A -> B) -> (B -> C)) -> ((A -> B) -> (B -> C)))), M:tm-316, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-14262
in-theory        14262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (A -> A))
theorem-size     19
proof            (modus-ponens tm-316 tm-56 ((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14262.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (A -> A)), M:tm-316, m:tm-56, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-14263
in-theory        14263
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and ((A -> (not (B -> A))) -> (A -> (not (B -> A)))))
theorem-size     23
proof            (modus-ponens tm-316 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14263.        (((A -> (not (B -> A))) -> (not A)) and ((A -> (not (B -> A))) -> (A -> (not (B -> A))))), M:tm-316, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-14264
in-theory        14264
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))))
theorem-size     51
proof            (modus-ponens tm-316 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14264.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))))), M:tm-316, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-14265
in-theory        14265
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (((A and B) -> (not A)) -> ((A and B) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-316 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14265.        ((((A and B) -> (not A)) -> (not (A and B))) and (((A and B) -> (not A)) -> ((A and B) -> (not A)))), M:tm-316, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-14266
in-theory        14266
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (((A and B) -> (not B)) -> ((A and B) -> (not B))))
theorem-size     25
proof            (modus-ponens tm-316 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14266.        ((((A and B) -> (not B)) -> (not (A and B))) and (((A and B) -> (not B)) -> ((A and B) -> (not B)))), M:tm-316, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-14267
in-theory        14267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and ((A -> (not (B -> (A and B)))) -> (A -> (not (B -> (A and B))))))
theorem-size     29
proof            (modus-ponens tm-316 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-14267.        (((A -> (not (B -> (A and B)))) -> (not A)) and ((A -> (not (B -> (A and B)))) -> (A -> (not (B -> (A and B)))))), M:tm-316, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-14268
in-theory        14268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and ((A -> (not (A or B))) -> (A -> (not (A or B)))))
theorem-size     23
proof            (modus-ponens tm-316 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-14268.        (((A -> (not (A or B))) -> (not A)) and ((A -> (not (A or B))) -> (A -> (not (A or B))))), M:tm-316, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-14269
in-theory        14269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and ((A -> (not (B or A))) -> (A -> (not (B or A)))))
theorem-size     23
proof            (modus-ponens tm-316 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-14269.        (((A -> (not (B or A))) -> (not A)) and ((A -> (not (B or A))) -> (A -> (not (B or A))))), M:tm-316, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-14270
in-theory        14270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))))
theorem-size     49
proof            (modus-ponens tm-316 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-14270.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> ((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))))), M:tm-316, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-14271
in-theory        14271
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> ((A -> B) -> (not ((A -> (not B)) -> (not A))))))
theorem-size     43
proof            (modus-ponens tm-316 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-14271.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> ((A -> B) -> (not ((A -> (not B)) -> (not A)))))), M:tm-316, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-14272
in-theory        14272
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> (not B)) -> (not A)) -> C)))
theorem-size     43
proof            (modus-ponens tm-316 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-14272.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> (not B)) -> (not A)) -> C))), M:tm-316, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-14273
in-theory        14273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (A -> A))
theorem-size     19
proof            (modus-ponens tm-316 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14273.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (A -> A)), M:tm-316, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-14274
in-theory        14274
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (A -> (not B)))))
theorem-size     33
proof            (modus-ponens tm-316 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-14274.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (A -> (not B))))), M:tm-316, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-14275
in-theory        14275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (A -> A))
theorem-size     17
proof            (modus-ponens tm-316 tm-71 ((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14275.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (A -> A)), M:tm-316, m:tm-71, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-14276
in-theory        14276
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((not (not A)) -> (not A)) -> ((not (not A)) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-316 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-14276.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((not (not A)) -> (not A)) -> ((not (not A)) -> (not A)))), M:tm-316, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-14277
in-theory        14277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and ((A -> B) -> (A -> B)))
theorem-size     19
proof            (modus-ponens tm-316 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-10)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-14277.        (((A -> B) -> (((not (not A)) or A) -> B)) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-14278
in-theory        14278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14278.        ((A -> (((not (not B)) -> B) and A)) and (A -> A)), M:tm-316, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-14279
in-theory        14279
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> A)))
theorem-size     31
proof            (modus-ponens tm-316 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-14279.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> A))), M:tm-316, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-14280
in-theory        14280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and (A -> A))
theorem-size     11
proof            (modus-ponens tm-316 tm-78 ((A Am) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14280.        ((A -> ((not (not B)) -> B)) and (A -> A)), M:tm-316, m:tm-78, u:((A Am) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-14281
in-theory        14281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and ((A -> (not (B -> (C -> B)))) -> (A -> (not (B -> (C -> B))))))
theorem-size     29
proof            (modus-ponens tm-316 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14281.        (((A -> (not (B -> (C -> B)))) -> (not A)) and ((A -> (not (B -> (C -> B)))) -> (A -> (not (B -> (C -> B)))))), M:tm-316, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-14282
in-theory        14282
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (((A -> (B -> A)) -> C) -> ((A -> (B -> A)) -> C)))
theorem-size     33
proof            (modus-ponens tm-316 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14282.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (((A -> (B -> A)) -> C) -> ((A -> (B -> A)) -> C))), M:tm-316, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-14283
in-theory        14283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14283.        ((A -> ((B -> (C -> (D -> C))) and A)) and (A -> A)), M:tm-316, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-14284
in-theory        14284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and ((A -> B) -> (A -> B)))
theorem-size     17
proof            (modus-ponens tm-316 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-14284.        (((A -> B) -> (A -> (C -> B))) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-14285
in-theory        14285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-85 ((A Am) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14285.        ((A -> (B -> (C -> (D -> C)))) and (A -> A)), M:tm-316, m:tm-85, u:((A Am) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-14286
in-theory        14286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and (A -> A))
theorem-size     7
proof            (modus-ponens tm-316 tm-86 ((A Am) (B Am)))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14286.        ((A -> A) and (A -> A)), M:tm-316, m:tm-86, u:((A Am) (B Am))
================================================================
tm-name          tm-14287
in-theory        14287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and ((A -> (B -> C)) -> (A -> (B -> C))))
theorem-size     23
proof            (modus-ponens tm-316 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14287.        (((A -> (B -> C)) -> (A -> (B -> C))) and ((A -> (B -> C)) -> (A -> (B -> C)))), M:tm-316, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-14288
in-theory        14288
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and ((A and B) -> (A and B)))
theorem-size     15
proof            (modus-ponens tm-316 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14288.        (((A and B) -> (A and B)) and ((A and B) -> (A and B))), M:tm-316, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-14289
in-theory        14289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and ((A -> B) -> (A -> B)))
theorem-size     15
proof            (modus-ponens tm-316 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-14289.        (((A -> B) -> (A -> B)) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-14290
in-theory        14290
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and ((not (not A)) -> (not (not A))))
theorem-size     15
proof            (modus-ponens tm-316 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-14290.        (((not (not A)) -> (not (not A))) and ((not (not A)) -> (not (not A)))), M:tm-316, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-14291
in-theory        14291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((A -> B) -> (not (A -> A))) -> ((A -> B) -> (not (A -> A)))))
theorem-size     31
proof            (modus-ponens tm-316 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14291.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((A -> B) -> (not (A -> A))) -> ((A -> B) -> (not (A -> A))))), M:tm-316, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-14292
in-theory        14292
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((A -> A) -> B) -> ((A -> A) -> B)))
theorem-size     27
proof            (modus-ponens tm-316 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14292.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((A -> A) -> B) -> ((A -> A) -> B))), M:tm-316, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-14293
in-theory        14293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14293.        ((A -> (((B -> C) -> (B -> B)) and A)) and (A -> A)), M:tm-316, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-14294
in-theory        14294
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and (((A -> B) -> A) -> ((A -> B) -> A)))
theorem-size     23
proof            (modus-ponens tm-316 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-14294.        ((((A -> B) -> A) -> ((A -> B) -> A)) and (((A -> B) -> A) -> ((A -> B) -> A))), M:tm-316, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-14295
in-theory        14295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-97 ((A Am) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14295.        ((A -> ((B -> C) -> (B -> B))) and (A -> A)), M:tm-316, m:tm-97, u:((A Am) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-14296
in-theory        14296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and ((A -> ((B -> A) -> C)) -> (A -> ((B -> A) -> C))))
theorem-size     27
proof            (modus-ponens tm-316 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-14296.        (((A -> ((B -> A) -> C)) -> (A -> C)) and ((A -> ((B -> A) -> C)) -> (A -> ((B -> A) -> C)))), M:tm-316, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-14297
in-theory        14297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and ((A -> (A -> B)) -> (A -> (A -> B))))
theorem-size     21
proof            (modus-ponens tm-316 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-14297.        (((A -> (A -> B)) -> (A -> B)) and ((A -> (A -> B)) -> (A -> (A -> B)))), M:tm-316, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-14298
in-theory        14298
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))))
theorem-size     39
proof            (modus-ponens tm-316 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14298.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B)))), M:tm-316, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-14299
in-theory        14299
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C))))))
theorem-size     73
proof            (modus-ponens tm-316 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14299.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))))), M:tm-316, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-14300
in-theory        14300
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> (((A -> (B -> C)) -> (A -> C)) -> D)))
theorem-size     57
proof            (modus-ponens tm-316 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14300.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> (((A -> (B -> C)) -> (A -> C)) -> D))), M:tm-316, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-14301
in-theory        14301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (A -> A))
theorem-size     27
proof            (modus-ponens tm-316 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14301.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (A -> A)), M:tm-316, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-14302
in-theory        14302
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))))
theorem-size     61
proof            (modus-ponens tm-316 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-14302.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))))), M:tm-316, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-14303
in-theory        14303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (A -> A))
theorem-size     25
proof            (modus-ponens tm-316 tm-107 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14303.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (A -> A)), M:tm-316, m:tm-107, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-14304
in-theory        14304
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))))
theorem-size     55
proof            (modus-ponens tm-316 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-14304.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)))), M:tm-316, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-14305
in-theory        14305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))
theorem-size     53
proof            (modus-ponens tm-316 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14305.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))), M:tm-316, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-14306
in-theory        14306
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D)))
theorem-size     65
proof            (modus-ponens tm-316 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14306.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))), M:tm-316, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-14307
in-theory        14307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (A -> A))
theorem-size     23
proof            (modus-ponens tm-316 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14307.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (A -> A)), M:tm-316, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-14308
in-theory        14308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((A -> (B -> (C -> D))) -> (A -> (B -> (C -> D)))))
theorem-size     33
proof            (modus-ponens tm-316 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-14308.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((A -> (B -> (C -> D))) -> (A -> (B -> (C -> D))))), M:tm-316, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-14309
in-theory        14309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (A -> A))
theorem-size     21
proof            (modus-ponens tm-316 tm-115 ((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14309.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (A -> A)), M:tm-316, m:tm-115, u:((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-14310
in-theory        14310
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and (((A -> B) and A) -> ((A -> B) and A)))
theorem-size     19
proof            (modus-ponens tm-316 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-14310.        ((((A -> B) and A) -> B) and (((A -> B) and A) -> ((A -> B) and A))), M:tm-316, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-14311
in-theory        14311
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and ((((A -> (B -> A)) -> C) and D) -> (((A -> (B -> A)) -> C) and D)))
theorem-size     31
proof            (modus-ponens tm-316 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-14311.        (((((A -> (B -> A)) -> C) and D) -> C) and ((((A -> (B -> A)) -> C) and D) -> (((A -> (B -> A)) -> C) and D))), M:tm-316, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-14312
in-theory        14312
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E)))
theorem-size     55
proof            (modus-ponens tm-316 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14312.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E))), M:tm-316, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-14313
in-theory        14313
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> (A -> B))))
theorem-size     45
proof            (modus-ponens tm-316 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-14313.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> (A -> B)))), M:tm-316, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-14314
in-theory        14314
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)))
theorem-size     31
proof            (modus-ponens tm-316 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14314.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A))), M:tm-316, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-14315
in-theory        14315
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B)))))
theorem-size     59
proof            (modus-ponens tm-316 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14315.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))))), M:tm-316, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-14316
in-theory        14316
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((((A -> B) and C) -> B) -> D) -> ((((A -> B) and C) -> B) -> D)))
theorem-size     47
proof            (modus-ponens tm-316 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14316.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((((A -> B) and C) -> B) -> D) -> ((((A -> B) and C) -> B) -> D))), M:tm-316, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-14317
in-theory        14317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (A -> A))
theorem-size     23
proof            (modus-ponens tm-316 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14317.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (A -> A)), M:tm-316, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-14318
in-theory        14318
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> ((A -> B) and C))))
theorem-size     51
proof            (modus-ponens tm-316 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-14318.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> ((A -> B) and C)))), M:tm-316, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-14319
in-theory        14319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (A -> A))
theorem-size     21
proof            (modus-ponens tm-316 tm-127 ((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14319.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (A -> A)), M:tm-316, m:tm-127, u:((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-14320
in-theory        14320
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and (((((A and B) -> A) -> C) and D) -> ((((A and B) -> A) -> C) and D)))
theorem-size     31
proof            (modus-ponens tm-316 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-14320.        ((((((A and B) -> A) -> C) and D) -> C) and (((((A and B) -> A) -> C) and D) -> ((((A and B) -> A) -> C) and D))), M:tm-316, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-14321
in-theory        14321
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((A and B) -> (A -> C)) -> ((A and B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-316 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-14321.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((A and B) -> (A -> C)) -> ((A and B) -> (A -> C)))), M:tm-316, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-14322
in-theory        14322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and ((A -> (not ((B and C) -> B))) -> (A -> (not ((B and C) -> B)))))
theorem-size     29
proof            (modus-ponens tm-316 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-14322.        (((A -> (not ((B and C) -> B))) -> (not A)) and ((A -> (not ((B and C) -> B))) -> (A -> (not ((B and C) -> B))))), M:tm-316, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-14323
in-theory        14323
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((((A and B) -> A) -> C) -> (((A and B) -> A) -> C)))
theorem-size     33
proof            (modus-ponens tm-316 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-14323.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((((A and B) -> A) -> C) -> (((A and B) -> A) -> C))), M:tm-316, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-14324
in-theory        14324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14324.        ((A -> ((B -> ((C and D) -> C)) and A)) and (A -> A)), M:tm-316, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-14325
in-theory        14325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and ((A -> (B and C)) -> (A -> (B and C))))
theorem-size     21
proof            (modus-ponens tm-316 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-14325.        (((A -> (B and C)) -> (A -> B)) and ((A -> (B and C)) -> (A -> (B and C)))), M:tm-316, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-14326
in-theory        14326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-136 ((A Am) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14326.        ((A -> (B -> ((C and D) -> C))) and (A -> A)), M:tm-316, m:tm-136, u:((A Am) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-14327
in-theory        14327
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and ((A and (A -> B)) -> (A and (A -> B))))
theorem-size     19
proof            (modus-ponens tm-316 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-14327.        (((A and (A -> B)) -> B) and ((A and (A -> B)) -> (A and (A -> B)))), M:tm-316, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-14328
in-theory        14328
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and ((A and ((B -> (C -> B)) -> D)) -> (A and ((B -> (C -> B)) -> D))))
theorem-size     31
proof            (modus-ponens tm-316 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-14328.        (((A and ((B -> (C -> B)) -> D)) -> D) and ((A and ((B -> (C -> B)) -> D)) -> (A and ((B -> (C -> B)) -> D)))), M:tm-316, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-14329
in-theory        14329
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E))))
theorem-size     55
proof            (modus-ponens tm-316 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14329.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)))), M:tm-316, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-14330
in-theory        14330
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and ((A and (((B and C) -> B) -> D)) -> (A and (((B and C) -> B) -> D))))
theorem-size     31
proof            (modus-ponens tm-316 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-14330.        (((A and (((B and C) -> B) -> D)) -> D) and ((A and (((B and C) -> B) -> D)) -> (A and (((B and C) -> B) -> D)))), M:tm-316, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-14331
in-theory        14331
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> (B -> C))))
theorem-size     45
proof            (modus-ponens tm-316 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-14331.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> (B -> C)))), M:tm-316, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-14332
in-theory        14332
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)))
theorem-size     31
proof            (modus-ponens tm-316 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-14332.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B))), M:tm-316, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-14333
in-theory        14333
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C)))))
theorem-size     59
proof            (modus-ponens tm-316 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-14333.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))))), M:tm-316, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-14334
in-theory        14334
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((((A and (B -> C)) -> C) -> D) -> (((A and (B -> C)) -> C) -> D)))
theorem-size     47
proof            (modus-ponens tm-316 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-14334.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((((A and (B -> C)) -> C) -> D) -> (((A and (B -> C)) -> C) -> D))), M:tm-316, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-14335
in-theory        14335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (A -> A))
theorem-size     23
proof            (modus-ponens tm-316 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14335.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (A -> A)), M:tm-316, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-14336
in-theory        14336
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> (A and (B -> C)))))
theorem-size     51
proof            (modus-ponens tm-316 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-14336.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> (A and (B -> C))))), M:tm-316, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-14337
in-theory        14337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (A -> A))
theorem-size     21
proof            (modus-ponens tm-316 tm-149 ((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14337.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (A -> A)), M:tm-316, m:tm-149, u:((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-14338
in-theory        14338
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and ((A and (((B and C) -> C) -> D)) -> (A and (((B and C) -> C) -> D))))
theorem-size     31
proof            (modus-ponens tm-316 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-14338.        (((A and (((B and C) -> C) -> D)) -> D) and ((A and (((B and C) -> C) -> D)) -> (A and (((B and C) -> C) -> D)))), M:tm-316, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-14339
in-theory        14339
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and (((((A and B) -> B) -> C) and D) -> ((((A and B) -> B) -> C) and D)))
theorem-size     31
proof            (modus-ponens tm-316 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-14339.        ((((((A and B) -> B) -> C) and D) -> C) and (((((A and B) -> B) -> C) and D) -> ((((A and B) -> B) -> C) and D))), M:tm-316, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-14340
in-theory        14340
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((A and B) -> (B -> C)) -> ((A and B) -> (B -> C))))
theorem-size     29
proof            (modus-ponens tm-316 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-14340.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((A and B) -> (B -> C)) -> ((A and B) -> (B -> C)))), M:tm-316, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-14341
in-theory        14341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and ((A -> (not ((B and C) -> C))) -> (A -> (not ((B and C) -> C)))))
theorem-size     29
proof            (modus-ponens tm-316 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-14341.        (((A -> (not ((B and C) -> C))) -> (not A)) and ((A -> (not ((B and C) -> C))) -> (A -> (not ((B and C) -> C))))), M:tm-316, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-14342
in-theory        14342
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((((A and B) -> B) -> C) -> (((A and B) -> B) -> C)))
theorem-size     33
proof            (modus-ponens tm-316 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-14342.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((((A and B) -> B) -> C) -> (((A and B) -> B) -> C))), M:tm-316, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-14343
in-theory        14343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14343.        ((A -> ((B -> ((C and D) -> D)) and A)) and (A -> A)), M:tm-316, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-14344
in-theory        14344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and ((A -> (B and C)) -> (A -> (B and C))))
theorem-size     21
proof            (modus-ponens tm-316 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-14344.        (((A -> (B and C)) -> (A -> C)) and ((A -> (B and C)) -> (A -> (B and C)))), M:tm-316, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-14345
in-theory        14345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-159 ((A Am) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14345.        ((A -> (B -> ((C and D) -> D))) and (A -> A)), M:tm-316, m:tm-159, u:((A Am) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-14346
in-theory        14346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((A -> (not ((B -> (C -> B)) and A))) -> (A -> (not ((B -> (C -> B)) and A)))))
theorem-size     35
proof            (modus-ponens tm-316 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-14346.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((A -> (not ((B -> (C -> B)) and A))) -> (A -> (not ((B -> (C -> B)) and A))))), M:tm-316, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-14347
in-theory        14347
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((((A -> (B -> A)) and C) -> D) -> (((A -> (B -> A)) and C) -> D)))
theorem-size     41
proof            (modus-ponens tm-316 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-14347.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((((A -> (B -> A)) and C) -> D) -> (((A -> (B -> A)) and C) -> D))), M:tm-316, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-14348
in-theory        14348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (A -> A))
theorem-size     17
proof            (modus-ponens tm-316 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14348.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (A -> A)), M:tm-316, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-14349
in-theory        14349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-184 ((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14349.        ((A -> (B -> ((C -> (D -> C)) and B))) and (A -> A)), M:tm-316, m:tm-184, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-14350
in-theory        14350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))))
theorem-size     59
proof            (modus-ponens tm-316 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-14350.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))), M:tm-316, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-14351
in-theory        14351
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E)))
theorem-size     73
proof            (modus-ponens tm-316 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-14351.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E))), M:tm-316, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-14352
in-theory        14352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (A -> A))
theorem-size     25
proof            (modus-ponens tm-316 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14352.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (A -> A)), M:tm-316, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-14353
in-theory        14353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (A -> A))
theorem-size     23
proof            (modus-ponens tm-316 tm-211 ((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14353.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (A -> A)), M:tm-316, m:tm-211, u:((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-14354
in-theory        14354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((A -> (not (((B and C) -> B) and A))) -> (A -> (not (((B and C) -> B) and A)))))
theorem-size     35
proof            (modus-ponens tm-316 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-14354.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((A -> (not (((B and C) -> B) and A))) -> (A -> (not (((B and C) -> B) and A))))), M:tm-316, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-14355
in-theory        14355
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (((((A and B) -> A) and C) -> D) -> ((((A and B) -> A) and C) -> D)))
theorem-size     41
proof            (modus-ponens tm-316 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-14355.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (((((A and B) -> A) and C) -> D) -> ((((A and B) -> A) and C) -> D))), M:tm-316, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-14356
in-theory        14356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (A -> A))
theorem-size     17
proof            (modus-ponens tm-316 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14356.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (A -> A)), M:tm-316, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-14357
in-theory        14357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-240 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14357.        ((A -> (B -> (((C and D) -> C) and B))) and (A -> A)), M:tm-316, m:tm-240, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-14358
in-theory        14358
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((A -> (not (((B and C) -> C) and A))) -> (A -> (not (((B and C) -> C) and A)))))
theorem-size     35
proof            (modus-ponens tm-316 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-14358.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((A -> (not (((B and C) -> C) and A))) -> (A -> (not (((B and C) -> C) and A))))), M:tm-316, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-14359
in-theory        14359
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (((((A and B) -> B) and C) -> D) -> ((((A and B) -> B) and C) -> D)))
theorem-size     41
proof            (modus-ponens tm-316 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-14359.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (((((A and B) -> B) and C) -> D) -> ((((A and B) -> B) and C) -> D))), M:tm-316, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-14360
in-theory        14360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (A -> A))
theorem-size     17
proof            (modus-ponens tm-316 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14360.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (A -> A)), M:tm-316, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-14361
in-theory        14361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-271 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14361.        ((A -> (B -> (((C and D) -> D) and B))) and (A -> A)), M:tm-316, m:tm-271, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-14362
in-theory        14362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (A -> (not ((B -> (C -> (B and C))) and A)))))
theorem-size     41
proof            (modus-ponens tm-316 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-14362.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (A -> (not ((B -> (C -> (B and C))) and A))))), M:tm-316, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-14363
in-theory        14363
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((((A -> (B -> (A and B))) and C) -> D) -> (((A -> (B -> (A and B))) and C) -> D)))
theorem-size     49
proof            (modus-ponens tm-316 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-14363.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((((A -> (B -> (A and B))) and C) -> D) -> (((A -> (B -> (A and B))) and C) -> D))), M:tm-316, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-14364
in-theory        14364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (A -> A))
theorem-size     19
proof            (modus-ponens tm-316 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14364.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (A -> A)), M:tm-316, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-14365
in-theory        14365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (A -> A))
theorem-size     17
proof            (modus-ponens tm-316 tm-304 ((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14365.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (A -> A)), M:tm-316, m:tm-304, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-14366
in-theory        14366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (A -> A))
theorem-size     11
proof            (modus-ponens tm-316 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14366.        ((A -> (A and (B -> A))) and (A -> A)), M:tm-316, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-14367
in-theory        14367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((A -> (B -> C)) -> (A -> (B -> C))))
theorem-size     31
proof            (modus-ponens tm-316 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14367.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((A -> (B -> C)) -> (A -> (B -> C)))), M:tm-316, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-14368
in-theory        14368
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and ((A and B) -> (A and B)))
theorem-size     17
proof            (modus-ponens tm-316 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14368.        (((A and B) -> ((A and B) and A)) and ((A and B) -> (A and B))), M:tm-316, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-14369
in-theory        14369
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and ((A and B) -> (A and B)))
theorem-size     17
proof            (modus-ponens tm-316 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14369.        (((A and B) -> ((A and B) and B)) and ((A and B) -> (A and B))), M:tm-316, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-14370
in-theory        14370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-14370.        ((A -> (A and (B -> (A and B)))) and (A -> A)), M:tm-316, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-14371
in-theory        14371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (A -> A))
theorem-size     11
proof            (modus-ponens tm-316 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-14371.        ((A -> (A and (A or B))) and (A -> A)), M:tm-316, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-14372
in-theory        14372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (A -> A))
theorem-size     11
proof            (modus-ponens tm-316 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-14372.        ((A -> (A and (B or A))) and (A -> A)), M:tm-316, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-14373
in-theory        14373
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((A -> B) -> (A -> B)))
theorem-size     25
proof            (modus-ponens tm-316 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-14373.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-14374
in-theory        14374
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((A -> B) -> (A -> B)))
theorem-size     23
proof            (modus-ponens tm-316 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-14374.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-14375
in-theory        14375
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and ((not (not A)) -> (not (not A))))
theorem-size     17
proof            (modus-ponens tm-316 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-14375.        (((not (not A)) -> ((not (not A)) and A)) and ((not (not A)) -> (not (not A)))), M:tm-316, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-14376
in-theory        14376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14376.        ((A -> (A and (B -> (C -> B)))) and (A -> A)), M:tm-316, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14377
in-theory        14377
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and ((A -> B) -> (A -> B)))
theorem-size     19
proof            (modus-ponens tm-316 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14377.        (((A -> B) -> ((A -> B) and (A -> A))) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-14378
in-theory        14378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-315 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14378.        (((A -> B) -> ((A -> B) and (A -> A))) and (C -> (D -> C))), M:tm-315, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14379
in-theory        14379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and (((A -> B) -> (not ((A -> B) and (A -> A)))) -> (not (A -> B))))
theorem-size     29
proof            (modus-ponens tm-313 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14379.        (((A -> B) -> ((A -> B) and (A -> A))) and (((A -> B) -> (not ((A -> B) and (A -> A)))) -> (not (A -> B)))), M:tm-313, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-14380
in-theory        14380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and ((((A -> B) and (A -> A)) -> C) -> (((A -> B) or ((A -> B) and (A -> A))) -> C)))
theorem-size     35
proof            (modus-ponens tm-312 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14380.        (((A -> B) -> ((A -> B) and (A -> A))) and ((((A -> B) and (A -> A)) -> C) -> (((A -> B) or ((A -> B) and (A -> A))) -> C))), M:tm-312, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-14381
in-theory        14381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and (C or ((A -> B) -> ((A -> B) and (A -> A)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14381.        (((A -> B) -> ((A -> B) and (A -> A))) and (C or ((A -> B) -> ((A -> B) and (A -> A))))), M:tm-311, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14382
in-theory        14382
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and (((A -> B) -> ((A -> B) and (A -> A))) or C))
theorem-size     25
proof            (modus-ponens tm-310 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14382.        (((A -> B) -> ((A -> B) and (A -> A))) and (((A -> B) -> ((A -> B) and (A -> A))) or C)), M:tm-310, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14383
in-theory        14383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and (C -> (((A -> B) -> ((A -> B) and (A -> A))) and C)))
theorem-size     27
proof            (modus-ponens tm-309 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14383.        (((A -> B) -> ((A -> B) and (A -> A))) and (C -> (((A -> B) -> ((A -> B) and (A -> A))) and C))), M:tm-309, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14384
in-theory        14384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and (C -> ((A -> B) -> ((A -> B) and (A -> A)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14384.        (((A -> B) -> ((A -> B) and (A -> A))) and (C -> ((A -> B) -> ((A -> B) and (A -> A))))), M:tm-305, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14385
in-theory        14385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     23
proof            (modus-ponens tm-303 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14385.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-303, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14386
in-theory        14386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     21
proof            (modus-ponens tm-270 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14386.        ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-270, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14387
in-theory        14387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     21
proof            (modus-ponens tm-239 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14387.        ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-239, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14388
in-theory        14388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((E -> F) and (E -> E))))
theorem-size     29
proof            (modus-ponens tm-210 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14388.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((E -> F) and (E -> E)))), M:tm-210, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14389
in-theory        14389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     21
proof            (modus-ponens tm-183 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14389.        ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-183, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14390
in-theory        14390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-157 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14390.        ((A -> ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-157, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14391
in-theory        14391
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((B and C) -> (B and C))))
theorem-size     21
proof            (modus-ponens tm-154 tm-316 ((Am (and A Bm)) (B Bm) (C (and (-> (and A Bm) Bm) (-> (and A Bm) (and A Bm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14391.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((B and C) -> (B and C)))), M:tm-154, m:tm-316, u:((Am (and A Bm)) (B Bm) (C (and (-> (and A Bm) Bm) (-> (and A Bm) (and A Bm)))))
================================================================
tm-name          tm-14392
in-theory        14392
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     27
proof            (modus-ponens tm-147 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14392.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-147, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14393
in-theory        14393
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((A and (B -> C)) -> (A and (B -> C)))))
theorem-size     35
proof            (modus-ponens tm-144 tm-316 ((Am (and A (-> B Bm))) (C Bm) (D (and (-> (and A (-> B Bm)) Bm) (-> (and A (-> B Bm)) (and A (-> B Bm)))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14393.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((A and (B -> C)) -> (A and (B -> C))))), M:tm-144, m:tm-316, u:((Am (and A (-> B Bm))) (C Bm) (D (and (-> (and A (-> B Bm)) Bm) (-> (and A (-> B Bm)) (and A (-> B Bm))))))
================================================================
tm-name          tm-14394
in-theory        14394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-134 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14394.        ((A -> ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-134, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14395
in-theory        14395
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((B and C) -> (B and C))))
theorem-size     21
proof            (modus-ponens tm-131 tm-316 ((Am (and Bm B)) (A Bm) (C (and (-> (and Bm B) Bm) (-> (and Bm B) (and Bm B))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14395.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((B and C) -> (B and C)))), M:tm-131, m:tm-316, u:((Am (and Bm B)) (A Bm) (C (and (-> (and Bm B) Bm) (-> (and Bm B) (and Bm B)))))
================================================================
tm-name          tm-14396
in-theory        14396
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     27
proof            (modus-ponens tm-125 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14396.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-125, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14397
in-theory        14397
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (((A -> B) and C) -> ((A -> B) and C))))
theorem-size     35
proof            (modus-ponens tm-122 tm-316 ((Am (and (-> A Bm) C)) (B Bm) (D (and (-> (and (-> A Bm) C) Bm) (-> (and (-> A Bm) C) (and (-> A Bm) C))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14397.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (((A -> B) and C) -> ((A -> B) and C)))), M:tm-122, m:tm-316, u:((Am (and (-> A Bm) C)) (B Bm) (D (and (-> (and (-> A Bm) C) Bm) (-> (and (-> A Bm) C) (and (-> A Bm) C)))))
================================================================
tm-name          tm-14398
in-theory        14398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (E -> E))))
theorem-size     27
proof            (modus-ponens tm-113 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14398.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (E -> E)))), M:tm-113, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14399
in-theory        14399
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((B -> (C -> D)) -> (B -> (C -> D)))))
theorem-size     41
proof            (modus-ponens tm-110 tm-316 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (-> A (-> B C)) (-> A (-> B C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14399.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((B -> (C -> D)) -> (B -> (C -> D))))), M:tm-110, m:tm-316, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (-> A (-> B C)) (-> A (-> B C))))))
================================================================
tm-name          tm-14400
in-theory        14400
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     31
proof            (modus-ponens tm-105 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14400.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-105, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14401
in-theory        14401
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((A -> (B -> C)) -> (A -> (B -> C)))))
theorem-size     41
proof            (modus-ponens tm-102 tm-316 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (-> A (-> B C)) (-> A (-> B C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14401.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((A -> (B -> C)) -> (A -> (B -> C))))), M:tm-102, m:tm-316, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (-> A (-> B C)) (-> A (-> B C))))))
================================================================
tm-name          tm-14402
in-theory        14402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> ((C -> D) and (C -> C))))
theorem-size     19
proof            (modus-ponens tm-95 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14402.        (((A -> B) -> (A -> A)) and ((C -> D) -> ((C -> D) and (C -> C)))), M:tm-95, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14403
in-theory        14403
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and (A -> A)))
theorem-size     15
proof            (modus-ponens tm-92 tm-316 ((Bm Am) (A Am) (B (and (-> Am Am) (-> Am Am)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14403.        (((A -> B) or (A -> A)) -> ((A -> A) and (A -> A))), M:tm-92, m:tm-316, u:((Bm Am) (A Am) (B (and (-> Am Am) (-> Am Am))))
================================================================
tm-name          tm-14404
in-theory        14404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((A -> B) and (A -> A))))
theorem-size     13
proof            (modus-ponens tm-84 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14404.        ((A -> B) -> (C -> ((A -> B) and (A -> A)))), M:tm-84, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-14405
in-theory        14405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-83 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14405.        ((A -> (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-83, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14406
in-theory        14406
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (B -> B)))
theorem-size     17
proof            (modus-ponens tm-80 tm-316 ((A Am) (Bm (-> B Am)) (C (and (-> Am (-> B Am)) (-> Am Am)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14406.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (B -> B))), M:tm-80, m:tm-316, u:((A Am) (Bm (-> B Am)) (C (and (-> Am (-> B Am)) (-> Am Am))))
================================================================
tm-name          tm-14407
in-theory        14407
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> ((B -> C) and (B -> B))))
theorem-size     17
proof            (modus-ponens tm-76 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14407.        (((not (not A)) -> A) and ((B -> C) -> ((B -> C) and (B -> B)))), M:tm-76, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14408
in-theory        14408
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> ((A -> B) and (A -> A)))
theorem-size     17
proof            (modus-ponens tm-73 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14408.        (((not (not (A -> B))) or (A -> B)) -> ((A -> B) and (A -> A))), M:tm-73, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-14409
in-theory        14409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((C -> D) and (C -> C))))
theorem-size     23
proof            (modus-ponens tm-69 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14409.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((C -> D) and (C -> C)))), M:tm-69, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14410
in-theory        14410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((A -> (not B)) -> (A -> (not B)))))
theorem-size     29
proof            (modus-ponens tm-66 tm-316 ((Am (-> A (not B))) (Bm (not A)) (C (and (-> (-> A (not B)) (not A)) (-> (-> A (not B)) (-> A (not B)))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14410.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((A -> (not B)) -> (A -> (not B))))), M:tm-66, m:tm-316, u:((Am (-> A (not B))) (Bm (not A)) (C (and (-> (-> A (not B)) (not A)) (-> (-> A (not B)) (-> A (not B))))))
================================================================
tm-name          tm-14411
in-theory        14411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     25
proof            (modus-ponens tm-54 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14411.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-54, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14412
in-theory        14412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((B -> C) -> (B -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-316 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (-> A B) (-> A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14412.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((B -> C) -> (B -> C)))), M:tm-51, m:tm-316, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (-> A B) (-> A B)))))
================================================================
tm-name          tm-14413
in-theory        14413
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (B -> B)))
theorem-size     17
proof            (modus-ponens tm-48 tm-316 ((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> Am Am)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14413.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (B -> B))), M:tm-48, m:tm-316, u:((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> Am Am))))
================================================================
tm-name          tm-14414
in-theory        14414
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((B -> C) and (B -> B)))
theorem-size     17
proof            (modus-ponens tm-47 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14414.        (((A and (B -> C)) or (B -> C)) -> ((B -> C) and (B -> B))), M:tm-47, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-14415
in-theory        14415
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((A -> B) and (A -> A)))
theorem-size     17
proof            (modus-ponens tm-46 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14415.        ((((A -> B) and C) or (A -> B)) -> ((A -> B) and (A -> A))), M:tm-46, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-14416
in-theory        14416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((A -> B) -> (A -> B))))
theorem-size     29
proof            (modus-ponens tm-45 tm-316 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> A B) (-> A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14416.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((A -> B) -> (A -> B)))), M:tm-45, m:tm-316, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> A B) (-> A B)))))
================================================================
tm-name          tm-14417
in-theory        14417
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (B -> B)))
theorem-size     13
proof            (modus-ponens tm-44 tm-316 ((A Am) (B Bm) (C (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14417.        ((A or (B -> A)) -> ((B -> A) and (B -> B))), M:tm-44, m:tm-316, u:((A Am) (B Bm) (C (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-14418
in-theory        14418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> ((C -> D) and (C -> C))))
theorem-size     17
proof            (modus-ponens tm-42 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14418.        ((A -> (B or A)) and ((C -> D) -> ((C -> D) and (C -> C)))), M:tm-42, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14419
in-theory        14419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> ((C -> D) and (C -> C))))
theorem-size     17
proof            (modus-ponens tm-32 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14419.        ((A -> (A or B)) and ((C -> D) -> ((C -> D) and (C -> C)))), M:tm-32, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14420
in-theory        14420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((A -> B) and (A -> A))))
theorem-size     15
proof            (modus-ponens tm-24 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14420.        ((A -> B) -> ((A -> B) and ((A -> B) and (A -> A)))), M:tm-24, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-14421
in-theory        14421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> D) and (C -> C))))
theorem-size     19
proof            (modus-ponens tm-23 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14421.        ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> D) and (C -> C)))), M:tm-23, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14422
in-theory        14422
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> ((C -> D) and (C -> C))))
theorem-size     17
proof            (modus-ponens tm-22 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14422.        (((A and B) -> B) and ((C -> D) -> ((C -> D) and (C -> C)))), M:tm-22, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14423
in-theory        14423
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> ((C -> D) and (C -> C))))
theorem-size     17
proof            (modus-ponens tm-21 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14423.        (((A and B) -> A) and ((C -> D) -> ((C -> D) and (C -> C)))), M:tm-21, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14424
in-theory        14424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     25
proof            (modus-ponens tm-20 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14424.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-20, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14425
in-theory        14425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> ((C -> D) and (C -> C))))
theorem-size     17
proof            (modus-ponens tm-19 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14425.        ((A -> (B -> A)) and ((C -> D) -> ((C -> D) and (C -> C)))), M:tm-19, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14426
in-theory        14426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((A -> B) and (A -> A)))) -> (not (A -> B)))
theorem-size     17
proof            (modus-ponens tm-9 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-9 tm-2 tm-5 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14426.        (((A -> B) -> (not ((A -> B) and (A -> A)))) -> (not (A -> B))), M:tm-9, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-14427
in-theory        14427
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and (A -> A)) -> C) -> (((A -> B) or ((A -> B) and (A -> A))) -> C))
theorem-size     23
proof            (modus-ponens tm-8 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14427.        ((((A -> B) and (A -> A)) -> C) -> (((A -> B) or ((A -> B) and (A -> A))) -> C)), M:tm-8, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-14428
in-theory        14428
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> C) -> ((B -> C) and (B -> B))))
theorem-size     13
proof            (modus-ponens tm-7 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-7 tm-2 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14428.        (A or ((B -> C) -> ((B -> C) and (B -> B)))), M:tm-7, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14429
in-theory        14429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) or C)
theorem-size     13
proof            (modus-ponens tm-6 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-6 tm-2 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14429.        (((A -> B) -> ((A -> B) and (A -> A))) or C), M:tm-6, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14430
in-theory        14430
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((B -> C) and (B -> B))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14430.        (A -> (((B -> C) -> ((B -> C) and (B -> B))) and A)), M:tm-5, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14431
in-theory        14431
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> ((B -> C) and (B -> B))))
theorem-size     13
proof            (modus-ponens tm-1 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14431.        (A -> ((B -> C) -> ((B -> C) and (B -> B)))), M:tm-1, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14432
in-theory        14432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> (B -> A))) and ((A -> ((B -> A) -> C)) -> (A -> C)))
theorem-size     25
proof            (modus-ponens tm-317 tm-11 ((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14432.        (((A -> ((B -> A) -> C)) -> (A -> (B -> A))) and ((A -> ((B -> A) -> C)) -> (A -> C))), M:tm-317, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
================================================================
tm-name          tm-14433
in-theory        14433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> A)) and ((A -> (A -> B)) -> (A -> B)))
theorem-size     19
proof            (modus-ponens tm-317 tm-12 ((Bm (-> Am C)) (A Am) (B Am)))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-14433.        (((A -> (A -> B)) -> (A -> A)) and ((A -> (A -> B)) -> (A -> B))), M:tm-317, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
================================================================
tm-name          tm-14434
in-theory        14434
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)))
theorem-size     53
proof            (modus-ponens tm-317 tm-14 ((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14434.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D))), M:tm-317, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-14435
in-theory        14435
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> A)) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)))
theorem-size     43
proof            (modus-ponens tm-317 tm-15 ((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14435.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> A)) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B))), M:tm-317, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
================================================================
tm-name          tm-14436
in-theory        14436
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> A)) and (((A and B) -> (A -> C)) -> ((A and B) -> C)))
theorem-size     27
proof            (modus-ponens tm-317 tm-16 ((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14436.        ((((A and B) -> (A -> C)) -> ((A and B) -> A)) and (((A and B) -> (A -> C)) -> ((A and B) -> C))), M:tm-317, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
================================================================
tm-name          tm-14437
in-theory        14437
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> B)) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)))
theorem-size     43
proof            (modus-ponens tm-317 tm-17 ((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm)))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14437.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> B)) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C))), M:tm-317, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
================================================================
tm-name          tm-14438
in-theory        14438
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> B)) and (((A and B) -> (B -> C)) -> ((A and B) -> C)))
theorem-size     27
proof            (modus-ponens tm-317 tm-18 ((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14438.        ((((A and B) -> (B -> C)) -> ((A and B) -> B)) and (((A and B) -> (B -> C)) -> ((A and B) -> C))), M:tm-317, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
================================================================
tm-name          tm-14439
in-theory        14439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> (B -> (A and B)))) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C)))
theorem-size     31
proof            (modus-ponens tm-317 tm-25 ((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14439.        (((A -> ((B -> (A and B)) -> C)) -> (A -> (B -> (A and B)))) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C))), M:tm-317, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-14440
in-theory        14440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> (A or B))) and ((A -> ((A or B) -> C)) -> (A -> C)))
theorem-size     25
proof            (modus-ponens tm-317 tm-33 ((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14440.        (((A -> ((A or B) -> C)) -> (A -> (A or B))) and ((A -> ((A or B) -> C)) -> (A -> C))), M:tm-317, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
================================================================
tm-name          tm-14441
in-theory        14441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> (B or A))) and ((A -> ((B or A) -> C)) -> (A -> C)))
theorem-size     25
proof            (modus-ponens tm-317 tm-43 ((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14441.        (((A -> ((B or A) -> C)) -> (A -> (B or A))) and ((A -> ((B or A) -> C)) -> (A -> C))), M:tm-317, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
================================================================
tm-name          tm-14442
in-theory        14442
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((B -> C) -> ((A or B) -> C)) -> D)) -> ((A -> B) -> ((B -> C) -> ((A or B) -> C)))) and (((A -> B) -> (((B -> C) -> ((A or B) -> C)) -> D)) -> ((A -> B) -> D)))
theorem-size     51
proof            (modus-ponens tm-317 tm-56 ((Am (-> (-> Bm Cm) (-> (-> (-> Cm Dm) (-> (or Bm Cm) Dm)) C))) (A (-> Bm Cm)) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14442.        ((((A -> B) -> (((B -> C) -> ((A or B) -> C)) -> D)) -> ((A -> B) -> ((B -> C) -> ((A or B) -> C)))) and (((A -> B) -> (((B -> C) -> ((A or B) -> C)) -> D)) -> ((A -> B) -> D))), M:tm-317, m:tm-56, u:((Am (-> (-> Bm Cm) (-> (-> (-> Cm Dm) (-> (or Bm Cm) Dm)) C))) (A (-> Bm Cm)) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-14443
in-theory        14443
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A -> (not B)) -> (not A)) -> C)) -> ((A -> B) -> ((A -> (not B)) -> (not A)))) and (((A -> B) -> (((A -> (not B)) -> (not A)) -> C)) -> ((A -> B) -> C)))
theorem-size     45
proof            (modus-ponens tm-317 tm-71 ((Am (-> (-> Bm Cm) (-> (-> (-> Bm (not Cm)) (not Bm)) C))) (A (-> Bm Cm)) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14443.        ((((A -> B) -> (((A -> (not B)) -> (not A)) -> C)) -> ((A -> B) -> ((A -> (not B)) -> (not A)))) and (((A -> B) -> (((A -> (not B)) -> (not A)) -> C)) -> ((A -> B) -> C))), M:tm-317, m:tm-71, u:((Am (-> (-> Bm Cm) (-> (-> (-> Bm (not Cm)) (not Bm)) C))) (A (-> Bm Cm)) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-14444
in-theory        14444
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not ((A -> B) -> A))) -> (A -> B)) -> ((not (not ((A -> B) -> A))) -> A)) and (((not (not ((A -> B) -> A))) -> (A -> B)) -> ((not (not ((A -> B) -> A))) -> B)))
theorem-size     43
proof            (modus-ponens tm-317 tm-77 ((Am (-> Bm C)) (A (not (not (-> (-> Bm C) Bm)))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-14444.        ((((not (not ((A -> B) -> A))) -> (A -> B)) -> ((not (not ((A -> B) -> A))) -> A)) and (((not (not ((A -> B) -> A))) -> (A -> B)) -> ((not (not ((A -> B) -> A))) -> B))), M:tm-317, m:tm-77, u:((Am (-> Bm C)) (A (not (not (-> (-> Bm C) Bm)))) (B Bm))
================================================================
tm-name          tm-14445
in-theory        14445
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (A -> B)) -> ((not (not A)) -> A)) and (((not (not A)) -> (A -> B)) -> ((not (not A)) -> B)))
theorem-size     27
proof            (modus-ponens tm-317 tm-78 ((Am (-> (not (not Bm)) (-> Bm C))) (A (not (not Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14445.        ((((not (not A)) -> (A -> B)) -> ((not (not A)) -> A)) and (((not (not A)) -> (A -> B)) -> ((not (not A)) -> B))), M:tm-317, m:tm-78, u:((Am (-> (not (not Bm)) (-> Bm C))) (A (not (not Bm))) (B Bm))
================================================================
tm-name          tm-14446
in-theory        14446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) -> D)) -> (A -> (B -> (C -> B)))) and ((A -> ((B -> (C -> B)) -> D)) -> (A -> D)))
theorem-size     31
proof            (modus-ponens tm-317 tm-85 ((Am (-> Bm (-> (-> Cm (-> Dm Cm)) C))) (A Bm) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14446.        (((A -> ((B -> (C -> B)) -> D)) -> (A -> (B -> (C -> B)))) and ((A -> ((B -> (C -> B)) -> D)) -> (A -> D))), M:tm-317, m:tm-85, u:((Am (-> Bm (-> (-> Cm (-> Dm Cm)) C))) (A Bm) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-14447
in-theory        14447
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> A) -> C)) -> ((A -> B) -> (A -> A))) and (((A -> B) -> ((A -> A) -> C)) -> ((A -> B) -> C)))
theorem-size     33
proof            (modus-ponens tm-317 tm-97 ((Am (-> (-> Bm Cm) (-> (-> Bm Bm) C))) (A (-> Bm Cm)) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14447.        ((((A -> B) -> ((A -> A) -> C)) -> ((A -> B) -> (A -> A))) and (((A -> B) -> ((A -> A) -> C)) -> ((A -> B) -> C))), M:tm-317, m:tm-97, u:((Am (-> (-> Bm Cm) (-> (-> Bm Bm) C))) (A (-> Bm Cm)) (B (-> Bm Bm)))
================================================================
tm-name          tm-14448
in-theory        14448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> (B -> A))) -> (A -> (B -> A))) and ((A -> ((B -> A) -> (B -> A))) -> (A -> (B -> A))))
theorem-size     31
proof            (modus-ponens tm-317 tm-98 ((Cm (-> Bm Am)) (C (-> Bm Am)) (A Am) (B (-> Bm Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-14448.        (((A -> ((B -> A) -> (B -> A))) -> (A -> (B -> A))) and ((A -> ((B -> A) -> (B -> A))) -> (A -> (B -> A)))), M:tm-317, m:tm-98, u:((Cm (-> Bm Am)) (C (-> Bm Am)) (A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-14449
in-theory        14449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> A)) -> (A -> A)) and ((A -> (A -> A)) -> (A -> A)))
theorem-size     19
proof            (modus-ponens tm-317 tm-99 ((Bm Am) (C Am) (A Am) (B Am)))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-14449.        (((A -> (A -> A)) -> (A -> A)) and ((A -> (A -> A)) -> (A -> A))), M:tm-317, m:tm-99, u:((Bm Am) (C Am) (A Am) (B Am))
================================================================
tm-name          tm-14450
in-theory        14450
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> C)) -> D)) -> (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))) and ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> C)) -> D)) -> (((A -> (B -> C)) -> (A -> B)) -> D)))
theorem-size     75
proof            (modus-ponens tm-317 tm-107 ((Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)) C))) (A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14450.        (((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> C)) -> D)) -> (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))) and ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> C)) -> D)) -> (((A -> (B -> C)) -> (A -> B)) -> D))), M:tm-317, m:tm-107, u:((Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)) C))) (A (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-14451
in-theory        14451
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))
theorem-size     71
proof            (modus-ponens tm-317 tm-108 ((Dm (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (-> Am Cm))) (A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       275
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-14451.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))), M:tm-317, m:tm-108, u:((Dm (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (-> Am Cm))) (A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-14452
in-theory        14452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (A -> E)))
theorem-size     55
proof            (modus-ponens tm-317 tm-115 ((Am (-> Bm (-> (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) C))) (A Bm) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14452.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (A -> E))), M:tm-317, m:tm-115, u:((Am (-> Bm (-> (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) C))) (A Bm) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-14453
in-theory        14453
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> A) -> A) and B) -> (A -> A)) -> ((((A -> A) -> A) and B) -> A)) and (((((A -> A) -> A) and B) -> (A -> A)) -> ((((A -> A) -> A) and B) -> A)))
theorem-size     43
proof            (modus-ponens tm-317 tm-119 ((Bm Am) (C Am) (A (and (-> (-> Am Am) Am) Cm)) (B Am)))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       245
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-14453.        ((((((A -> A) -> A) and B) -> (A -> A)) -> ((((A -> A) -> A) and B) -> A)) and (((((A -> A) -> A) and B) -> (A -> A)) -> ((((A -> A) -> A) and B) -> A))), M:tm-317, m:tm-119, u:((Bm Am) (C Am) (A (and (-> (-> Am Am) Am) Cm)) (B Am))
================================================================
tm-name          tm-14454
in-theory        14454
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((((A -> B) and C) -> B) -> D)) -> ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))) and (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> B) -> D)) -> ((((A -> B) and C) -> A) -> D)))
theorem-size     61
proof            (modus-ponens tm-317 tm-127 ((Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (-> (and (-> Bm Cm) Dm) Cm) C))) (A (-> (and (-> Bm Cm) Dm) Bm)) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14454.        ((((((A -> B) and C) -> A) -> ((((A -> B) and C) -> B) -> D)) -> ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))) and (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> B) -> D)) -> ((((A -> B) and C) -> A) -> D))), M:tm-317, m:tm-127, u:((Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (-> (and (-> Bm Cm) Dm) Cm) C))) (A (-> (and (-> Bm Cm) Dm) Bm)) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-14455
in-theory        14455
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> A)) -> ((A and B) -> A)) and (((A and B) -> (A -> A)) -> ((A and B) -> A)))
theorem-size     27
proof            (modus-ponens tm-317 tm-129 ((Cm Am) (C Am) (A (and Am Bm)) (B Am)))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-14455.        ((((A and B) -> (A -> A)) -> ((A and B) -> A)) and (((A and B) -> (A -> A)) -> ((A and B) -> A))), M:tm-317, m:tm-129, u:((Cm Am) (C Am) (A (and Am Bm)) (B Am))
================================================================
tm-name          tm-14456
in-theory        14456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) -> D)) -> (A -> ((B and C) -> B))) and ((A -> (((B and C) -> B) -> D)) -> (A -> D)))
theorem-size     31
proof            (modus-ponens tm-317 tm-136 ((Am (-> Bm (-> (-> (and Cm Dm) Cm) C))) (A Bm) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14456.        (((A -> (((B and C) -> B) -> D)) -> (A -> ((B and C) -> B))) and ((A -> (((B and C) -> B) -> D)) -> (A -> D))), M:tm-317, m:tm-136, u:((Am (-> Bm (-> (-> (and Cm Dm) Cm) C))) (A Bm) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-14457
in-theory        14457
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> B) -> B)) -> (B -> B)) -> ((A and ((B -> B) -> B)) -> B)) and (((A and ((B -> B) -> B)) -> (B -> B)) -> ((A and ((B -> B) -> B)) -> B)))
theorem-size     43
proof            (modus-ponens tm-317 tm-141 ((Cm Bm) (C Bm) (A (and Am (-> (-> Bm Bm) Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       245
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-14457.        ((((A and ((B -> B) -> B)) -> (B -> B)) -> ((A and ((B -> B) -> B)) -> B)) and (((A and ((B -> B) -> B)) -> (B -> B)) -> ((A and ((B -> B) -> B)) -> B))), M:tm-317, m:tm-141, u:((Cm Bm) (C Bm) (A (and Am (-> (-> Bm Bm) Bm))) (B Bm))
================================================================
tm-name          tm-14458
in-theory        14458
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> C) -> D)) -> (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))) and ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> C) -> D)) -> (((A and (B -> C)) -> B) -> D)))
theorem-size     61
proof            (modus-ponens tm-317 tm-149 ((Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (-> (and Bm (-> Cm Dm)) Dm) C))) (A (-> (and Bm (-> Cm Dm)) Cm)) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14458.        (((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> C) -> D)) -> (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))) and ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> C) -> D)) -> (((A and (B -> C)) -> B) -> D))), M:tm-317, m:tm-149, u:((Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (-> (and Bm (-> Cm Dm)) Dm) C))) (A (-> (and Bm (-> Cm Dm)) Cm)) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-14459
in-theory        14459
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> B)) -> ((A and B) -> B)) and (((A and B) -> (B -> B)) -> ((A and B) -> B)))
theorem-size     27
proof            (modus-ponens tm-317 tm-152 ((Cm Bm) (C Bm) (A (and Am Bm)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-14459.        ((((A and B) -> (B -> B)) -> ((A and B) -> B)) and (((A and B) -> (B -> B)) -> ((A and B) -> B))), M:tm-317, m:tm-152, u:((Cm Bm) (C Bm) (A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-14460
in-theory        14460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) -> D)) -> (A -> ((B and C) -> C))) and ((A -> (((B and C) -> C) -> D)) -> (A -> D)))
theorem-size     31
proof            (modus-ponens tm-317 tm-159 ((Am (-> Bm (-> (-> (and Cm Dm) Dm) C))) (A Bm) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14460.        (((A -> (((B and C) -> C) -> D)) -> (A -> ((B and C) -> C))) and ((A -> (((B and C) -> C) -> D)) -> (A -> D))), M:tm-317, m:tm-159, u:((Am (-> Bm (-> (-> (and Cm Dm) Dm) C))) (A Bm) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-14461
in-theory        14461
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> B)) and A) -> D)) -> (A -> ((B -> (C -> B)) and A))) and ((A -> (((B -> (C -> B)) and A) -> D)) -> (A -> D)))
theorem-size     37
proof            (modus-ponens tm-317 tm-184 ((Am (-> Bm (-> (and (-> Cm (-> Dm Cm)) Bm) C))) (A Bm) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14461.        (((A -> (((B -> (C -> B)) and A) -> D)) -> (A -> ((B -> (C -> B)) and A))) and ((A -> (((B -> (C -> B)) and A) -> D)) -> (A -> D))), M:tm-317, m:tm-184, u:((Am (-> Bm (-> (and (-> Cm (-> Dm Cm)) Bm) C))) (A Bm) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-14462
in-theory        14462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) -> E)) -> (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) -> E)) -> (A -> E)))
theorem-size     61
proof            (modus-ponens tm-317 tm-211 ((Am (-> Bm (-> (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm) C))) (A Bm) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14462.        (((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) -> E)) -> (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) -> E)) -> (A -> E))), M:tm-317, m:tm-211, u:((Am (-> Bm (-> (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm) C))) (A Bm) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-14463
in-theory        14463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((((B and C) -> B) and A) -> D)) -> (A -> (((B and C) -> B) and A))) and ((A -> ((((B and C) -> B) and A) -> D)) -> (A -> D)))
theorem-size     37
proof            (modus-ponens tm-317 tm-240 ((Am (-> Bm (-> (and (-> (and Cm Dm) Cm) Bm) C))) (A Bm) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14463.        (((A -> ((((B and C) -> B) and A) -> D)) -> (A -> (((B and C) -> B) and A))) and ((A -> ((((B and C) -> B) and A) -> D)) -> (A -> D))), M:tm-317, m:tm-240, u:((Am (-> Bm (-> (and (-> (and Cm Dm) Cm) Bm) C))) (A Bm) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-14464
in-theory        14464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((((B and C) -> C) and A) -> D)) -> (A -> (((B and C) -> C) and A))) and ((A -> ((((B and C) -> C) and A) -> D)) -> (A -> D)))
theorem-size     37
proof            (modus-ponens tm-317 tm-271 ((Am (-> Bm (-> (and (-> (and Cm Dm) Dm) Bm) C))) (A Bm) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14464.        (((A -> ((((B and C) -> C) and A) -> D)) -> (A -> (((B and C) -> C) and A))) and ((A -> ((((B and C) -> C) and A) -> D)) -> (A -> D))), M:tm-317, m:tm-271, u:((Am (-> Bm (-> (and (-> (and Cm Dm) Dm) Bm) C))) (A Bm) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-14465
in-theory        14465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> (B and C))) and A) -> D)) -> (A -> ((B -> (C -> (B and C))) and A))) and ((A -> (((B -> (C -> (B and C))) and A) -> D)) -> (A -> D)))
theorem-size     43
proof            (modus-ponens tm-317 tm-304 ((Am (-> Bm (-> (and (-> Cm (-> Dm (and Cm Dm))) Bm) C))) (A Bm) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14465.        (((A -> (((B -> (C -> (B and C))) and A) -> D)) -> (A -> ((B -> (C -> (B and C))) and A))) and ((A -> (((B -> (C -> (B and C))) and A) -> D)) -> (A -> D))), M:tm-317, m:tm-304, u:((Am (-> Bm (-> (and (-> Cm (-> Dm (and Cm Dm))) Bm) C))) (A Bm) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-14466
in-theory        14466
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))))
theorem-size     49
proof            (modus-ponens tm-316 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14466.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B)))), M:tm-316, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-14467
in-theory        14467
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (D -> (E -> D)))
theorem-size     35
proof            (modus-ponens tm-315 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14467.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (D -> (E -> D))), M:tm-315, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14468
in-theory        14468
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((((A -> (B -> C)) -> (A -> B)) -> (not (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))) -> (not ((A -> (B -> C)) -> (A -> B)))))
theorem-size     71
proof            (modus-ponens tm-313 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14468.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((((A -> (B -> C)) -> (A -> B)) -> (not (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))) -> (not ((A -> (B -> C)) -> (A -> B))))), M:tm-313, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-14469
in-theory        14469
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) -> D)))
theorem-size     83
proof            (modus-ponens tm-312 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       245
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14469.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) -> D))), M:tm-312, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-14470
in-theory        14470
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (D or (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-311 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14470.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (D or (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))), M:tm-311, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14471
in-theory        14471
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) or D))
theorem-size     61
proof            (modus-ponens tm-310 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14471.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) or D)), M:tm-310, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14472
in-theory        14472
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (D -> ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and D)))
theorem-size     63
proof            (modus-ponens tm-309 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14472.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (D -> ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and D))), M:tm-309, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14473
in-theory        14473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (D -> (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-305 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14473.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (D -> (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))), M:tm-305, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14474
in-theory        14474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-303 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14474.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-303, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14475
in-theory        14475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-270 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14475.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-270, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14476
in-theory        14476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-239 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14476.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-239, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14477
in-theory        14477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> (E -> F)) -> (((E -> (F -> G)) -> (E -> F)) and ((E -> (F -> G)) -> (E -> G)))))
theorem-size     47
proof            (modus-ponens tm-210 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14477.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> (E -> F)) -> (((E -> (F -> G)) -> (E -> F)) and ((E -> (F -> G)) -> (E -> G))))), M:tm-210, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14478
in-theory        14478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-183 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14478.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-183, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14479
in-theory        14479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-157 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14479.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-157, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14480
in-theory        14480
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-147 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14480.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-147, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14481
in-theory        14481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-134 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14481.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-134, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14482
in-theory        14482
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-125 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14482.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-125, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14483
in-theory        14483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> (((E -> (F -> G)) -> (E -> F)) and ((E -> (F -> G)) -> (E -> G)))))
theorem-size     45
proof            (modus-ponens tm-113 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14483.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> (((E -> (F -> G)) -> (E -> F)) and ((E -> (F -> G)) -> (E -> G))))), M:tm-113, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14484
in-theory        14484
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     49
proof            (modus-ponens tm-105 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14484.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-105, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14485
in-theory        14485
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> B)) -> (A -> B)) or ((A -> (B -> B)) -> (A -> B))) -> (((A -> (B -> B)) -> (A -> B)) and ((A -> (B -> B)) -> (A -> B))))
theorem-size     39
proof            (modus-ponens tm-102 tm-317 ((B Cm) (Bm Cm) (A Am) (C Cm) (D (and (-> (-> Am (-> Cm Cm)) (-> Am Cm)) (-> (-> Am (-> Cm Cm)) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14485.        ((((A -> (B -> B)) -> (A -> B)) or ((A -> (B -> B)) -> (A -> B))) -> (((A -> (B -> B)) -> (A -> B)) and ((A -> (B -> B)) -> (A -> B)))), M:tm-102, m:tm-317, u:((B Cm) (Bm Cm) (A Am) (C Cm) (D (and (-> (-> Am (-> Cm Cm)) (-> Am Cm)) (-> (-> Am (-> Cm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-14486
in-theory        14486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E)))))
theorem-size     37
proof            (modus-ponens tm-95 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14486.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E))))), M:tm-95, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14487
in-theory        14487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (D -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     31
proof            (modus-ponens tm-84 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14487.        (((A -> (B -> C)) -> (A -> B)) -> (D -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))), M:tm-84, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-14488
in-theory        14488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-83 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14488.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-83, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14489
in-theory        14489
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> (B -> C)) -> (((B -> (C -> D)) -> (B -> C)) and ((B -> (C -> D)) -> (B -> D)))))
theorem-size     35
proof            (modus-ponens tm-76 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14489.        (((not (not A)) -> A) and (((B -> (C -> D)) -> (B -> C)) -> (((B -> (C -> D)) -> (B -> C)) and ((B -> (C -> D)) -> (B -> D))))), M:tm-76, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14490
in-theory        14490
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) -> (A -> B)))) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-73 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14490.        (((not (not ((A -> (B -> C)) -> (A -> B)))) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-73, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-14491
in-theory        14491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E)))))
theorem-size     41
proof            (modus-ponens tm-69 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14491.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E))))), M:tm-69, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14492
in-theory        14492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-54 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14492.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-54, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14493
in-theory        14493
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (((B -> (C -> D)) -> (B -> C)) and ((B -> (C -> D)) -> (B -> D))))
theorem-size     41
proof            (modus-ponens tm-47 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14493.        (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (((B -> (C -> D)) -> (B -> C)) and ((B -> (C -> D)) -> (B -> D)))), M:tm-47, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-14494
in-theory        14494
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-46 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14494.        (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-46, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-14495
in-theory        14495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-45 tm-317 ((B (-> Bm Cm)) (A Am) (C Bm) (D (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14495.        (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-45, m:tm-317, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-14496
in-theory        14496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-44 tm-317 ((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14496.        (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-44, m:tm-317, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-14497
in-theory        14497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-42 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14497.        ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E))))), M:tm-42, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14498
in-theory        14498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-32 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14498.        ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E))))), M:tm-32, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14499
in-theory        14499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     39
proof            (modus-ponens tm-24 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14499.        (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))), M:tm-24, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-14500
in-theory        14500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E)))))
theorem-size     37
proof            (modus-ponens tm-23 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14500.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E))))), M:tm-23, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14501
in-theory        14501
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-22 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14501.        (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E))))), M:tm-22, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14502
in-theory        14502
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-21 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14502.        (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E))))), M:tm-21, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14503
in-theory        14503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-20 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14503.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-20, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14504
in-theory        14504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-19 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14504.        ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E))))), M:tm-19, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14505
in-theory        14505
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (not (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))) -> (not ((A -> (B -> C)) -> (A -> B))))
theorem-size     41
proof            (modus-ponens tm-9 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-9 tm-2 tm-5)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14505.        ((((A -> (B -> C)) -> (A -> B)) -> (not (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-14506
in-theory        14506
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) -> D))
theorem-size     53
proof            (modus-ponens tm-8 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       169
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14506.        (((((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) -> D)), M:tm-8, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-14507
in-theory        14507
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> (B -> C)) -> (((B -> (C -> D)) -> (B -> C)) and ((B -> (C -> D)) -> (B -> D)))))
theorem-size     31
proof            (modus-ponens tm-7 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-7 tm-2 tm-5)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14507.        (A or (((B -> (C -> D)) -> (B -> C)) -> (((B -> (C -> D)) -> (B -> C)) and ((B -> (C -> D)) -> (B -> D))))), M:tm-7, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14508
in-theory        14508
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) or D)
theorem-size     31
proof            (modus-ponens tm-6 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-6 tm-2 tm-5)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14508.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) or D), M:tm-6, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14509
in-theory        14509
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> (B -> C)) -> (((B -> (C -> D)) -> (B -> C)) and ((B -> (C -> D)) -> (B -> D)))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14509.        (A -> ((((B -> (C -> D)) -> (B -> C)) -> (((B -> (C -> D)) -> (B -> C)) and ((B -> (C -> D)) -> (B -> D)))) and A)), M:tm-5, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14510
in-theory        14510
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> (B -> C)) -> (((B -> (C -> D)) -> (B -> C)) and ((B -> (C -> D)) -> (B -> D)))))
theorem-size     31
proof            (modus-ponens tm-1 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14510.        (A -> (((B -> (C -> D)) -> (B -> C)) -> (((B -> (C -> D)) -> (B -> C)) and ((B -> (C -> D)) -> (B -> D))))), M:tm-1, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14511
in-theory        14511
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-318 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14511.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-14512
in-theory        14512
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14512.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-14513
in-theory        14513
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-318 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14513.        (((A -> (B -> A)) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-14514
in-theory        14514
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14514.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-14515
in-theory        14515
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-318 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14515.        ((((A and B) -> A) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-14516
in-theory        14516
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-318 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14516.        ((((A and B) -> B) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-14517
in-theory        14517
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14517.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-14518
in-theory        14518
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-318 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14518.        (((A -> (A or B)) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-14519
in-theory        14519
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14519.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-14520
in-theory        14520
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-318 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14520.        ((A -> (B -> (B or C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-14521
in-theory        14521
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-318 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14521.        ((A or (B -> (C -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14522
in-theory        14522
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14522.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14523
in-theory        14523
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-318 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14523.        ((A or ((B and C) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-14524
in-theory        14524
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-318 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14524.        ((A or ((B and C) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-14525
in-theory        14525
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14525.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-14526
in-theory        14526
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-318 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14526.        ((A or (B -> (B or C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-14527
in-theory        14527
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-318 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14527.        ((A or (B -> (C or B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-14528
in-theory        14528
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-318 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14528.        (((A -> (B or A)) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-14529
in-theory        14529
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14529.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-14530
in-theory        14530
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-318 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14530.        ((A -> (B -> (C or B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-14531
in-theory        14531
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14531.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-14532
in-theory        14532
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-318 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14532.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-14533
in-theory        14533
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14533.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-14534
in-theory        14534
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14534.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-14535
in-theory        14535
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-318 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-14535.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-14536
in-theory        14536
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-14536.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-14537
in-theory        14537
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-14537.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-14538
in-theory        14538
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-318 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-14538.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-14539
in-theory        14539
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14539.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-14540
in-theory        14540
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14540.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-14541
in-theory        14541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14541.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-14542
in-theory        14542
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-318 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-14542.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-14543
in-theory        14543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14543.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-14544
in-theory        14544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-318 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14544.        (((A -> (not (B -> A))) -> (not A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-14545
in-theory        14545
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-318 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14545.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-14546
in-theory        14546
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-318 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14546.        ((((A and B) -> (not A)) -> (not (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-14547
in-theory        14547
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-318 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14547.        ((((A and B) -> (not B)) -> (not (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-14548
in-theory        14548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-318 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-14548.        (((A -> (not (B -> (A and B)))) -> (not A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-14549
in-theory        14549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-318 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-14549.        (((A -> (not (A or B))) -> (not A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-14550
in-theory        14550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-318 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-14550.        (((A -> (not (B or A))) -> (not A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-14551
in-theory        14551
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-318 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-14551.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-14552
in-theory        14552
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     31
proof            (modus-ponens tm-318 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-14552.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-14553
in-theory        14553
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-318 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-14553.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-14554
in-theory        14554
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14554.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-14555
in-theory        14555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14555.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-14556
in-theory        14556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14556.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-14557
in-theory        14557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-318 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-14557.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-14558
in-theory        14558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14558.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-14559
in-theory        14559
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     25
proof            (modus-ponens tm-318 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-14559.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-318, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-14560
in-theory        14560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-318 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-10)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-14560.        (((A -> B) -> (((not (not A)) or A) -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-14561
in-theory        14561
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-318 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14561.        ((A or ((not (not B)) -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-14562
in-theory        14562
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-318 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14562.        ((((not (not A)) -> A) or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-14563
in-theory        14563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-318 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14563.        ((A -> (((not (not B)) -> B) and A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-14564
in-theory        14564
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-318 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-14564.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-14565
in-theory        14565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-318 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14565.        ((A -> ((not (not B)) -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-14566
in-theory        14566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14566.        (((A -> (not (B -> (C -> B)))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-14567
in-theory        14567
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14567.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-14568
in-theory        14568
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14568.        ((A or (B -> (C -> (D -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-14569
in-theory        14569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14569.        (((A -> (B -> (C -> B))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-14570
in-theory        14570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14570.        ((A -> ((B -> (C -> (D -> C))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-14571
in-theory        14571
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-14571.        (((A -> B) -> (A -> (C -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-14572
in-theory        14572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14572.        ((A -> (B -> (C -> (D -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-14573
in-theory        14573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     17
proof            (modus-ponens tm-318 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14573.        ((A -> A) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-318, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-14574
in-theory        14574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14574.        (((A -> (B -> C)) -> (A -> (B -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-14575
in-theory        14575
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-318 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14575.        (((A and B) -> (A and B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-14576
in-theory        14576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-318 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-14576.        (((A -> B) -> (A -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-14577
in-theory        14577
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     21
proof            (modus-ponens tm-318 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-14577.        (((not (not A)) -> (not (not A))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-318, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-14578
in-theory        14578
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-318 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14578.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-14579
in-theory        14579
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14579.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-14580
in-theory        14580
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14580.        ((A or ((B -> C) -> (B -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-14581
in-theory        14581
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14581.        ((((A -> B) -> (A -> A)) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-14582
in-theory        14582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14582.        ((A -> (((B -> C) -> (B -> B)) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-14583
in-theory        14583
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-318 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-14583.        ((((A -> B) -> A) -> ((A -> B) -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-14584
in-theory        14584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14584.        ((A -> ((B -> C) -> (B -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-14585
in-theory        14585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-14585.        (((A -> ((B -> A) -> C)) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-14586
in-theory        14586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-318 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-14586.        (((A -> (A -> B)) -> (A -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-14587
in-theory        14587
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-318 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14587.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-14588
in-theory        14588
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     45
proof            (modus-ponens tm-318 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14588.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-14589
in-theory        14589
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     47
proof            (modus-ponens tm-318 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14589.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-14590
in-theory        14590
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14590.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-14591
in-theory        14591
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14591.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-14592
in-theory        14592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-318 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14592.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-14593
in-theory        14593
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-318 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-14593.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-14594
in-theory        14594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14594.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-14595
in-theory        14595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-318 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-14595.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-14596
in-theory        14596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14596.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-14597
in-theory        14597
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     47
proof            (modus-ponens tm-318 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14597.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-14598
in-theory        14598
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14598.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-14599
in-theory        14599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14599.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-14600
in-theory        14600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14600.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-14601
in-theory        14601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-14601.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14602
in-theory        14602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14602.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-14603
in-theory        14603
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-318 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-14603.        ((((A -> B) and A) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-14604
in-theory        14604
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-14604.        (((((A -> (B -> A)) -> C) and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-14605
in-theory        14605
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14605.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-14606
in-theory        14606
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-318 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-14606.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-14607
in-theory        14607
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14607.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-14608
in-theory        14608
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-318 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14608.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-14609
in-theory        14609
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-318 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14609.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-14610
in-theory        14610
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14610.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-14611
in-theory        14611
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14611.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-14612
in-theory        14612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14612.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-14613
in-theory        14613
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-318 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-14613.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-14614
in-theory        14614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14614.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-14615
in-theory        14615
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-14615.        ((((((A and B) -> A) -> C) and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-14616
in-theory        14616
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-14616.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-14617
in-theory        14617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-14617.        (((A -> (not ((B and C) -> B))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-14618
in-theory        14618
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-14618.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-14619
in-theory        14619
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14619.        ((A or (B -> ((C and D) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-14620
in-theory        14620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14620.        (((A -> ((B and C) -> B)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-14621
in-theory        14621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14621.        ((A -> ((B -> ((C and D) -> C)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-14622
in-theory        14622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-14622.        (((A -> (B and C)) -> (A -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-14623
in-theory        14623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14623.        ((A -> (B -> ((C and D) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-14624
in-theory        14624
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-318 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-14624.        (((A and (A -> B)) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-14625
in-theory        14625
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-14625.        (((A and ((B -> (C -> B)) -> D)) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-14626
in-theory        14626
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14626.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-14627
in-theory        14627
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-14627.        (((A and (((B and C) -> B) -> D)) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-14628
in-theory        14628
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-318 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-14628.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-14629
in-theory        14629
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-14629.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-14630
in-theory        14630
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-318 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-14630.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-14631
in-theory        14631
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-318 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-14631.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-14632
in-theory        14632
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14632.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-14633
in-theory        14633
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14633.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-14634
in-theory        14634
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14634.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-14635
in-theory        14635
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-318 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-14635.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-14636
in-theory        14636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14636.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-14637
in-theory        14637
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-14637.        (((A and (((B and C) -> C) -> D)) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-14638
in-theory        14638
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-14638.        ((((((A and B) -> B) -> C) and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-14639
in-theory        14639
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-14639.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-14640
in-theory        14640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-14640.        (((A -> (not ((B and C) -> C))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-14641
in-theory        14641
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-14641.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-14642
in-theory        14642
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14642.        ((A or (B -> ((C and D) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-14643
in-theory        14643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14643.        (((A -> ((B and C) -> C)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-14644
in-theory        14644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14644.        ((A -> ((B -> ((C and D) -> D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-14645
in-theory        14645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-14645.        (((A -> (B and C)) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-14646
in-theory        14646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14646.        ((A -> (B -> ((C and D) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-14647
in-theory        14647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14647.        (((A -> (B -> A)) and (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-14648
in-theory        14648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14648.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-14649
in-theory        14649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14649.        (((A -> (B -> A)) and ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-14650
in-theory        14650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14650.        (((A -> (B -> A)) and ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-14651
in-theory        14651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14651.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-14652
in-theory        14652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14652.        (((A -> (B -> A)) and (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-14653
in-theory        14653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14653.        (((A -> (B -> A)) and (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-14654
in-theory        14654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14654.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-14655
in-theory        14655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14655.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-14656
in-theory        14656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14656.        (((A -> (B -> A)) and ((not (not C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-14657
in-theory        14657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14657.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-14658
in-theory        14658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14658.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-14659
in-theory        14659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     39
proof            (modus-ponens tm-318 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14659.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-14660
in-theory        14660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14660.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-14661
in-theory        14661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14661.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-14662
in-theory        14662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14662.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-14663
in-theory        14663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14663.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-14664
in-theory        14664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14664.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-14665
in-theory        14665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14665.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-14666
in-theory        14666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-14666.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-14667
in-theory        14667
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-14667.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-14668
in-theory        14668
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14668.        ((A or (B -> ((C -> (D -> C)) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-14669
in-theory        14669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14669.        (((A -> ((B -> (C -> B)) and A)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-14670
in-theory        14670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14670.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-14671
in-theory        14671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14671.        ((A -> (B -> ((C -> (D -> C)) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-14672
in-theory        14672
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14672.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-14673
in-theory        14673
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     41
proof            (modus-ponens tm-318 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14673.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-14674
in-theory        14674
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14674.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-14675
in-theory        14675
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14675.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-14676
in-theory        14676
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14676.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-14677
in-theory        14677
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14677.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-14678
in-theory        14678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14678.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-14679
in-theory        14679
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     41
proof            (modus-ponens tm-318 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14679.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-14680
in-theory        14680
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     39
proof            (modus-ponens tm-318 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14680.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-14681
in-theory        14681
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14681.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-14682
in-theory        14682
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14682.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-14683
in-theory        14683
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14683.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-14684
in-theory        14684
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     47
proof            (modus-ponens tm-318 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14684.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-14685
in-theory        14685
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))
theorem-size     43
proof            (modus-ponens tm-318 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14685.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-14686
in-theory        14686
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     43
proof            (modus-ponens tm-318 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14686.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-14687
in-theory        14687
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14687.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-14688
in-theory        14688
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     43
proof            (modus-ponens tm-318 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14688.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-14689
in-theory        14689
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14689.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-14690
in-theory        14690
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14690.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-14691
in-theory        14691
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))
theorem-size     45
proof            (modus-ponens tm-318 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14691.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-14692
in-theory        14692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14692.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-14693
in-theory        14693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-14693.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-14694
in-theory        14694
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     51
proof            (modus-ponens tm-318 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-14694.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-14695
in-theory        14695
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14695.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-14696
in-theory        14696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14696.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-14697
in-theory        14697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14697.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-14698
in-theory        14698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14698.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-14699
in-theory        14699
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14699.        ((((A and B) -> A) and (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-14700
in-theory        14700
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14700.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-14701
in-theory        14701
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14701.        ((((A and B) -> A) and ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-14702
in-theory        14702
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14702.        ((((A and B) -> A) and ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-14703
in-theory        14703
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14703.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-14704
in-theory        14704
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14704.        ((((A and B) -> A) and (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-14705
in-theory        14705
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14705.        ((((A and B) -> A) and (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-14706
in-theory        14706
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14706.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-14707
in-theory        14707
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14707.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-14708
in-theory        14708
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-10)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14708.        ((((A and B) -> A) and ((not (not C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-14709
in-theory        14709
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14709.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-14710
in-theory        14710
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14710.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-14711
in-theory        14711
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     39
proof            (modus-ponens tm-318 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14711.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-14712
in-theory        14712
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14712.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-14713
in-theory        14713
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14713.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-14714
in-theory        14714
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14714.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-14715
in-theory        14715
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14715.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-14716
in-theory        14716
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14716.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-14717
in-theory        14717
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14717.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-14718
in-theory        14718
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14718.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-14719
in-theory        14719
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14719.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-14720
in-theory        14720
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14720.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-14721
in-theory        14721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14721.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-14722
in-theory        14722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-14722.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-14723
in-theory        14723
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-14723.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-14724
in-theory        14724
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14724.        ((A or (B -> (((C and D) -> C) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-14725
in-theory        14725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14725.        (((A -> (((B and C) -> B) and A)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-14726
in-theory        14726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14726.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-14727
in-theory        14727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14727.        ((A -> (B -> (((C and D) -> C) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-14728
in-theory        14728
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14728.        ((((A and B) -> B) and (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-14729
in-theory        14729
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14729.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-14730
in-theory        14730
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14730.        ((((A and B) -> B) and ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-14731
in-theory        14731
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14731.        ((((A and B) -> B) and ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-14732
in-theory        14732
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14732.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-14733
in-theory        14733
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14733.        ((((A and B) -> B) and (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-14734
in-theory        14734
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14734.        ((((A and B) -> B) and (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-14735
in-theory        14735
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14735.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-14736
in-theory        14736
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14736.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-14737
in-theory        14737
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-10)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14737.        ((((A and B) -> B) and ((not (not C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-14738
in-theory        14738
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14738.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-14739
in-theory        14739
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14739.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-14740
in-theory        14740
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     39
proof            (modus-ponens tm-318 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14740.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-14741
in-theory        14741
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14741.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-14742
in-theory        14742
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14742.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-14743
in-theory        14743
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14743.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-14744
in-theory        14744
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14744.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-14745
in-theory        14745
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14745.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-14746
in-theory        14746
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14746.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-14747
in-theory        14747
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14747.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-14748
in-theory        14748
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14748.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-14749
in-theory        14749
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14749.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-14750
in-theory        14750
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14750.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-14751
in-theory        14751
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14751.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-14752
in-theory        14752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14752.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-14753
in-theory        14753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-14753.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-14754
in-theory        14754
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-14754.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-14755
in-theory        14755
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14755.        ((A or (B -> (((C and D) -> D) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-14756
in-theory        14756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14756.        (((A -> (((B and C) -> C) and A)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-14757
in-theory        14757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14757.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-14758
in-theory        14758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14758.        ((A -> (B -> (((C and D) -> D) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-14759
in-theory        14759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14759.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-14760
in-theory        14760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14760.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-14761
in-theory        14761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14761.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-14762
in-theory        14762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14762.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-14763
in-theory        14763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14763.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-14764
in-theory        14764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14764.        (((A -> (B -> (A and B))) and (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-14765
in-theory        14765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14765.        (((A -> (B -> (A and B))) and (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-14766
in-theory        14766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14766.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-14767
in-theory        14767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14767.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-14768
in-theory        14768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14768.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-14769
in-theory        14769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14769.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-14770
in-theory        14770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14770.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-14771
in-theory        14771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     41
proof            (modus-ponens tm-318 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14771.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-14772
in-theory        14772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14772.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-14773
in-theory        14773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-318 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14773.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-14774
in-theory        14774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14774.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-14775
in-theory        14775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-318 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14775.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-14776
in-theory        14776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14776.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-14777
in-theory        14777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14777.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-14778
in-theory        14778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     39
proof            (modus-ponens tm-318 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14778.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-14779
in-theory        14779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14779.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-14780
in-theory        14780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14780.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-14781
in-theory        14781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14781.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-14782
in-theory        14782
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14782.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-14783
in-theory        14783
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14783.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-14784
in-theory        14784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     39
proof            (modus-ponens tm-318 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14784.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-14785
in-theory        14785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14785.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-14786
in-theory        14786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-14786.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-14787
in-theory        14787
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-318 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-14787.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-14788
in-theory        14788
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14788.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-14789
in-theory        14789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14789.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-14790
in-theory        14790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14790.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-14791
in-theory        14791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14791.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-14792
in-theory        14792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-318 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14792.        ((A -> (A and (B -> A))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-14793
in-theory        14793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-318 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14793.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-14794
in-theory        14794
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-318 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14794.        (((A and B) -> ((A and B) and A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-14795
in-theory        14795
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-318 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14795.        (((A and B) -> ((A and B) and B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-14796
in-theory        14796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-318 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-14796.        ((A -> (A and (B -> (A and B)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-14797
in-theory        14797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-318 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-14797.        ((A -> (A and (A or B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-14798
in-theory        14798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-318 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-14798.        ((A -> (A and (B or A))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-14799
in-theory        14799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-318 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-14799.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-14800
in-theory        14800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-318 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-14800.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-14801
in-theory        14801
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     23
proof            (modus-ponens tm-318 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-14801.        (((not (not A)) -> ((not (not A)) and A)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-318, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-14802
in-theory        14802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14802.        ((A -> (A and (B -> (C -> B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-14803
in-theory        14803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-318 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14803.        (((A -> B) -> ((A -> B) and (A -> A))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-14804
in-theory        14804
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-318 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-14804.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-14805
in-theory        14805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14805.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14806
in-theory        14806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (A -> A))
theorem-size     21
proof            (modus-ponens tm-316 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14806.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (A -> A)), M:tm-316, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14807
in-theory        14807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14807.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (E -> (F -> E))), M:tm-315, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14808
in-theory        14808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((A -> (not (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not A)))
theorem-size     39
proof            (modus-ponens tm-313 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14808.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((A -> (not (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not A))), M:tm-313, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14809
in-theory        14809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (((A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> ((A or (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14809.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (((A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> ((A or (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> E))), M:tm-312, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14810
in-theory        14810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (E or (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14810.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (E or (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))), M:tm-311, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14811
in-theory        14811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14811.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) or E)), M:tm-310, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14812
in-theory        14812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (E -> ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14812.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (E -> ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and E))), M:tm-309, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14813
in-theory        14813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (E -> (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14813.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (E -> (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))), M:tm-305, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14814
in-theory        14814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     29
proof            (modus-ponens tm-303 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14814.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-303, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14815
in-theory        14815
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-300 tm-318 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14815.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-300, m:tm-318, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14816
in-theory        14816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-270 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14816.        ((A -> (((B and C) -> C) and A)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-270, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14817
in-theory        14817
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-267 tm-318 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14817.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-267, m:tm-318, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14818
in-theory        14818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-239 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14818.        ((A -> (((B and C) -> B) and A)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-239, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14819
in-theory        14819
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-236 tm-318 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14819.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-236, m:tm-318, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14820
in-theory        14820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     35
proof            (modus-ponens tm-210 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14820.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-210, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14821
in-theory        14821
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     47
proof            (modus-ponens tm-207 tm-318 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14821.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-207, m:tm-318, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14822
in-theory        14822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-183 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14822.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-183, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14823
in-theory        14823
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-180 tm-318 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14823.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-180, m:tm-318, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14824
in-theory        14824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-157 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14824.        ((A -> ((B and C) -> C)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-157, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14825
in-theory        14825
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-154 tm-318 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14825.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-154, m:tm-318, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14826
in-theory        14826
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     33
proof            (modus-ponens tm-147 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14826.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-147, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14827
in-theory        14827
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-144 tm-318 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14827.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-144, m:tm-318, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14828
in-theory        14828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-134 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14828.        ((A -> ((B and C) -> B)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-134, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14829
in-theory        14829
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-131 tm-318 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14829.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-131, m:tm-318, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14830
in-theory        14830
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     33
proof            (modus-ponens tm-125 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14830.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-125, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14831
in-theory        14831
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-122 tm-318 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14831.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-122, m:tm-318, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14832
in-theory        14832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-113 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14832.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-113, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14833
in-theory        14833
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-110 tm-318 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14833.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-110, m:tm-318, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14834
in-theory        14834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     37
proof            (modus-ponens tm-105 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14834.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-105, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14835
in-theory        14835
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-102 tm-318 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14835.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-102, m:tm-318, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14836
in-theory        14836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     25
proof            (modus-ponens tm-95 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14836.        (((A -> B) -> (A -> A)) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-95, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14837
in-theory        14837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     25
proof            (modus-ponens tm-92 tm-318 ((Am (-> A A)) (B (and (-> A A) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14837.        (((A -> B) or (A -> A)) -> ((A -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-92, m:tm-318, u:((Am (-> A A)) (B (and (-> A A) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14838
in-theory        14838
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     19
proof            (modus-ponens tm-84 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14838.        (A -> (B -> (A and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-84, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14839
in-theory        14839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-83 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14839.        ((A -> (B -> (C -> B))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-83, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14840
in-theory        14840
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-80 tm-318 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14840.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-80, m:tm-318, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14841
in-theory        14841
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     23
proof            (modus-ponens tm-76 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14841.        (((not (not A)) -> A) and (B -> (B and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-76, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14842
in-theory        14842
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     21
proof            (modus-ponens tm-73 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14842.        (((not (not A)) or A) -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-73, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14843
in-theory        14843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     29
proof            (modus-ponens tm-69 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14843.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-69, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14844
in-theory        14844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-66 tm-318 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14844.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-66, m:tm-318, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14845
in-theory        14845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     31
proof            (modus-ponens tm-54 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14845.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-54, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14846
in-theory        14846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-51 tm-318 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14846.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-51, m:tm-318, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14847
in-theory        14847
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     23
proof            (modus-ponens tm-50 tm-318 ((Am (or A B)) (C (and (or A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14847.        ((A or (B or A)) -> ((B or A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-50, m:tm-318, u:((Am (or A B)) (C (and (or A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14848
in-theory        14848
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     23
proof            (modus-ponens tm-49 tm-318 ((Am (or A B)) (C (and (or A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14848.        ((A or (A or B)) -> ((A or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-49, m:tm-318, u:((Am (or A B)) (C (and (or A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14849
in-theory        14849
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     27
proof            (modus-ponens tm-48 tm-318 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14849.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-48, m:tm-318, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14850
in-theory        14850
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     21
proof            (modus-ponens tm-47 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14850.        (((A and B) or B) -> (B and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-47, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14851
in-theory        14851
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     21
proof            (modus-ponens tm-46 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14851.        (((A and B) or A) -> (A and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-46, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14852
in-theory        14852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-45 tm-318 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14852.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-45, m:tm-318, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14853
in-theory        14853
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     23
proof            (modus-ponens tm-44 tm-318 ((Am (-> A B)) (C (and (-> A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14853.        ((A or (B -> A)) -> ((B -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-44, m:tm-318, u:((Am (-> A B)) (C (and (-> A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14854
in-theory        14854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     23
proof            (modus-ponens tm-42 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14854.        ((A -> (B or A)) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-42, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14855
in-theory        14855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     23
proof            (modus-ponens tm-32 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14855.        ((A -> (A or B)) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-32, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14856
in-theory        14856
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     19
proof            (modus-ponens tm-24 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14856.        (A -> (A and (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-24, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14857
in-theory        14857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     25
proof            (modus-ponens tm-23 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14857.        ((A -> (B -> (A and B))) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-23, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14858
in-theory        14858
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     23
proof            (modus-ponens tm-22 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14858.        (((A and B) -> B) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-22, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14859
in-theory        14859
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     23
proof            (modus-ponens tm-21 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14859.        (((A and B) -> A) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-21, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14860
in-theory        14860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     31
proof            (modus-ponens tm-20 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14860.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-20, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14861
in-theory        14861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     23
proof            (modus-ponens tm-19 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14861.        ((A -> (B -> A)) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-19, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14862
in-theory        14862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not A))
theorem-size     21
proof            (modus-ponens tm-9 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-9 tm-2 tm-5 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14862.        ((A -> (not (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not A)), M:tm-9, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14863
in-theory        14863
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> ((A or (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14863.        (((A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> ((A or (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> E)), M:tm-8, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14864
in-theory        14864
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     19
proof            (modus-ponens tm-7 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-7 tm-2 tm-5 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14864.        (A or (B -> (B and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-7, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14865
in-theory        14865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-6 tm-2 tm-5 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14865.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) or E), M:tm-6, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14866
in-theory        14866
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14866.        (A -> ((B -> (B and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and A)), M:tm-5, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14867
in-theory        14867
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     19
proof            (modus-ponens tm-1 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14867.        (A -> (B -> (B and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-1, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-14868
in-theory        14868
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> A) and (((A -> B) and A) -> B))
theorem-size     15
proof            (modus-ponens tm-319 tm-4 ((Am (-> Bm B)) (C Bm) (A Bm)))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-14868.        ((((A -> B) and A) -> A) and (((A -> B) and A) -> B)), M:tm-319, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
================================================================
tm-name          tm-14869
in-theory        14869
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> (A -> (B -> A))) and ((((A -> (B -> A)) -> C) and D) -> C))
theorem-size     27
proof            (modus-ponens tm-319 tm-11 ((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14869.        (((((A -> (B -> A)) -> C) and D) -> (A -> (B -> A))) and ((((A -> (B -> A)) -> C) and D) -> C)), M:tm-319, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-14870
in-theory        14870
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D))
theorem-size     51
proof            (modus-ponens tm-319 tm-14 ((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14870.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D)), M:tm-319, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-14871
in-theory        14871
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> ((A and B) -> A)) and (((((A and B) -> A) -> C) and D) -> C))
theorem-size     27
proof            (modus-ponens tm-319 tm-16 ((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14871.        ((((((A and B) -> A) -> C) and D) -> ((A and B) -> A)) and (((((A and B) -> A) -> C) and D) -> C)), M:tm-319, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-14872
in-theory        14872
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> ((A and B) -> B)) and (((((A and B) -> B) -> C) and D) -> C))
theorem-size     27
proof            (modus-ponens tm-319 tm-18 ((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14872.        ((((((A and B) -> B) -> C) and D) -> ((A and B) -> B)) and (((((A and B) -> B) -> C) and D) -> C)), M:tm-319, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-14873
in-theory        14873
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> (A -> (B -> (A and B)))) and ((((A -> (B -> (A and B))) -> C) and D) -> C))
theorem-size     33
proof            (modus-ponens tm-319 tm-25 ((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14873.        (((((A -> (B -> (A and B))) -> C) and D) -> (A -> (B -> (A and B)))) and ((((A -> (B -> (A and B))) -> C) and D) -> C)), M:tm-319, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-14874
in-theory        14874
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> (A -> (A or B))) and ((((A -> (A or B)) -> C) and D) -> C))
theorem-size     27
proof            (modus-ponens tm-319 tm-33 ((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14874.        (((((A -> (A or B)) -> C) and D) -> (A -> (A or B))) and ((((A -> (A or B)) -> C) and D) -> C)), M:tm-319, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-14875
in-theory        14875
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> (A -> (B or A))) and ((((A -> (B or A)) -> C) and D) -> C))
theorem-size     27
proof            (modus-ponens tm-319 tm-43 ((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14875.        (((((A -> (B or A)) -> C) and D) -> (A -> (B or A))) and ((((A -> (B or A)) -> C) and D) -> C)), M:tm-319, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-14876
in-theory        14876
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) and E) -> ((A -> B) -> ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) and E) -> D))
theorem-size     51
proof            (modus-ponens tm-319 tm-56 ((Am (and (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B) C)) (A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14876.        ((((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) and E) -> ((A -> B) -> ((B -> C) -> ((A or B) -> C)))) and (((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) and E) -> D)), M:tm-319, m:tm-56, u:((Am (and (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B) C)) (A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-14877
in-theory        14877
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((A -> (not B)) -> (not A))) -> C) and D) -> ((A -> B) -> ((A -> (not B)) -> (not A)))) and (((((A -> B) -> ((A -> (not B)) -> (not A))) -> C) and D) -> C))
theorem-size     45
proof            (modus-ponens tm-319 tm-71 ((Am (and (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) B) C)) (A (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14877.        ((((((A -> B) -> ((A -> (not B)) -> (not A))) -> C) and D) -> ((A -> B) -> ((A -> (not B)) -> (not A)))) and (((((A -> B) -> ((A -> (not B)) -> (not A))) -> C) and D) -> C)), M:tm-319, m:tm-71, u:((Am (and (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) B) C)) (A (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-14878
in-theory        14878
times-derived    1
----------------------------------------------------------------
theorem          ((((((not (not A)) -> A) -> B) and C) -> ((not (not A)) -> A)) and (((((not (not A)) -> A) -> B) and C) -> B))
theorem-size     27
proof            (modus-ponens tm-319 tm-78 ((Am (and (-> (-> (not (not Bm)) Bm) B) C)) (A (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-10)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14878.        ((((((not (not A)) -> A) -> B) and C) -> ((not (not A)) -> A)) and (((((not (not A)) -> A) -> B) and C) -> B)), M:tm-319, m:tm-78, u:((Am (and (-> (-> (not (not Bm)) Bm) B) C)) (A (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-14879
in-theory        14879
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (C -> B))) -> D) and E) -> (A -> (B -> (C -> B)))) and ((((A -> (B -> (C -> B))) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-85 ((Am (and (-> (-> Bm (-> Cm (-> Dm Cm))) B) C)) (A (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-14879.        (((((A -> (B -> (C -> B))) -> D) and E) -> (A -> (B -> (C -> B)))) and ((((A -> (B -> (C -> B))) -> D) and E) -> D)), M:tm-319, m:tm-85, u:((Am (and (-> (-> Bm (-> Cm (-> Dm Cm))) B) C)) (A (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-14880
in-theory        14880
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> A)) -> C) and D) -> ((A -> B) -> (A -> A))) and (((((A -> B) -> (A -> A)) -> C) and D) -> C))
theorem-size     33
proof            (modus-ponens tm-319 tm-97 ((Am (and (-> (-> (-> Bm Cm) (-> Bm Bm)) B) C)) (A (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-14880.        ((((((A -> B) -> (A -> A)) -> C) and D) -> ((A -> B) -> (A -> A))) and (((((A -> B) -> (A -> A)) -> C) and D) -> C)), M:tm-319, m:tm-97, u:((Am (and (-> (-> (-> Bm Cm) (-> Bm Bm)) B) C)) (A (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-14881
in-theory        14881
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) and E) -> (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))) and ((((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) and E) -> D))
theorem-size     69
proof            (modus-ponens tm-319 tm-107 ((Am (and (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) B) C)) (A (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-14881.        (((((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) and E) -> (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))) and ((((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) and E) -> D)), M:tm-319, m:tm-107, u:((Am (and (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) B) C)) (A (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-14882
in-theory        14882
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> E))
theorem-size     57
proof            (modus-ponens tm-319 tm-115 ((Am (and (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B) C)) (A (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-14882.        (((((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> E)), M:tm-319, m:tm-115, u:((Am (and (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B) C)) (A (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-14883
in-theory        14883
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) and A) -> A) and (((A -> A) and A) -> A))
theorem-size     15
proof            (modus-ponens tm-319 tm-116 ((Bm Am) (B Am) (C Am) (A Am)))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-14883.        ((((A -> A) and A) -> A) and (((A -> A) and A) -> A)), M:tm-319, m:tm-116, u:((Bm Am) (B Am) (C Am) (A Am))
================================================================
tm-name          tm-14884
in-theory        14884
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> (A -> (B -> A))) and C) -> (A -> (B -> A))) and ((((A -> (B -> A)) -> (A -> (B -> A))) and C) -> (A -> (B -> A))))
theorem-size     39
proof            (modus-ponens tm-319 tm-117 ((Cm (-> Am (-> Bm Am))) (B (-> Am (-> Bm Am))) (C Dm) (A (-> Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-14884.        (((((A -> (B -> A)) -> (A -> (B -> A))) and C) -> (A -> (B -> A))) and ((((A -> (B -> A)) -> (A -> (B -> A))) and C) -> (A -> (B -> A)))), M:tm-319, m:tm-117, u:((Cm (-> Am (-> Bm Am))) (B (-> Am (-> Bm Am))) (C Dm) (A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-14885
in-theory        14885
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and D) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and D) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))
theorem-size     87
proof            (modus-ponens tm-319 tm-118 ((Dm (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Em) (A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       257
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14885.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and D) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and D) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))), M:tm-319, m:tm-118, u:((Dm (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Em) (A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-14886
in-theory        14886
times-derived    1
----------------------------------------------------------------
theorem          ((((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) and E) -> ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))) and (((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) and E) -> D))
theorem-size     57
proof            (modus-ponens tm-319 tm-127 ((Am (and (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) B) C)) (A (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-14886.        ((((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) and E) -> ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))) and (((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) and E) -> D)), M:tm-319, m:tm-127, u:((Am (and (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) B) C)) (A (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-14887
in-theory        14887
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> ((A and B) -> A)) and C) -> ((A and B) -> A)) and (((((A and B) -> A) -> ((A and B) -> A)) and C) -> ((A and B) -> A)))
theorem-size     39
proof            (modus-ponens tm-319 tm-128 ((Cm (-> (and Am Bm) Am)) (B (-> (and Am Bm) Am)) (C Dm) (A (-> (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-14887.        ((((((A and B) -> A) -> ((A and B) -> A)) and C) -> ((A and B) -> A)) and (((((A and B) -> A) -> ((A and B) -> A)) and C) -> ((A and B) -> A))), M:tm-319, m:tm-128, u:((Cm (-> (and Am Bm) Am)) (B (-> (and Am Bm) Am)) (C Dm) (A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-14888
in-theory        14888
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> ((B and C) -> B)) -> D) and E) -> (A -> ((B and C) -> B))) and ((((A -> ((B and C) -> B)) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-136 ((Am (and (-> (-> Bm (-> (and Cm Dm) Cm)) B) C)) (A (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-14888.        (((((A -> ((B and C) -> B)) -> D) and E) -> (A -> ((B and C) -> B))) and ((((A -> ((B and C) -> B)) -> D) and E) -> D)), M:tm-319, m:tm-136, u:((Am (and (-> (-> Bm (-> (and Cm Dm) Cm)) B) C)) (A (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-14889
in-theory        14889
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and ((A -> B) -> A)) -> A) and (((A -> B) and ((A -> B) -> A)) -> B))
theorem-size     23
proof            (modus-ponens tm-319 tm-137 ((Am (-> Bm B)) (C (-> (-> Bm B) Bm)) (A Bm)))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-14889.        ((((A -> B) and ((A -> B) -> A)) -> A) and (((A -> B) and ((A -> B) -> A)) -> B)), M:tm-319, m:tm-137, u:((Am (-> Bm B)) (C (-> (-> Bm B) Bm)) (A Bm))
================================================================
tm-name          tm-14890
in-theory        14890
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and ((C -> (D -> C)) -> A)) -> A) and (((A -> B) and ((C -> (D -> C)) -> A)) -> B))
theorem-size     27
proof            (modus-ponens tm-319 tm-138 ((Am (-> Dm B)) (C (-> (-> Bm (-> Cm Bm)) Dm)) (A Dm)))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-14890.        ((((A -> B) and ((C -> (D -> C)) -> A)) -> A) and (((A -> B) and ((C -> (D -> C)) -> A)) -> B)), M:tm-319, m:tm-138, u:((Am (-> Dm B)) (C (-> (-> Bm (-> Cm Bm)) Dm)) (A Dm))
================================================================
tm-name          tm-14891
in-theory        14891
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> A)) -> A) and (((A -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> A)) -> B))
theorem-size     43
proof            (modus-ponens tm-319 tm-139 ((Am (-> Em B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (A Em)))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-14891.        ((((A -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> A)) -> A) and (((A -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> A)) -> B)), M:tm-319, m:tm-139, u:((Am (-> Em B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (A Em))
================================================================
tm-name          tm-14892
in-theory        14892
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and (((C and D) -> C) -> A)) -> A) and (((A -> B) and (((C and D) -> C) -> A)) -> B))
theorem-size     27
proof            (modus-ponens tm-319 tm-140 ((Am (-> Dm B)) (C (-> (-> (and Bm Cm) Bm) Dm)) (A Dm)))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-14892.        ((((A -> B) and (((C and D) -> C) -> A)) -> A) and (((A -> B) and (((C and D) -> C) -> A)) -> B)), M:tm-319, m:tm-140, u:((Am (-> Dm B)) (C (-> (-> (and Bm Cm) Bm) Dm)) (A Dm))
================================================================
tm-name          tm-14893
in-theory        14893
times-derived    1
----------------------------------------------------------------
theorem          (((((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) and E) -> (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))) and ((((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) and E) -> D))
theorem-size     57
proof            (modus-ponens tm-319 tm-149 ((Am (and (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) B) C)) (A (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-14893.        (((((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) and E) -> (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))) and ((((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) and E) -> D)), M:tm-319, m:tm-149, u:((Am (and (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) B) C)) (A (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-14894
in-theory        14894
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and (((C and D) -> D) -> A)) -> A) and (((A -> B) and (((C and D) -> D) -> A)) -> B))
theorem-size     27
proof            (modus-ponens tm-319 tm-150 ((Am (-> Dm B)) (C (-> (-> (and Bm Cm) Cm) Dm)) (A Dm)))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-14894.        ((((A -> B) and (((C and D) -> D) -> A)) -> A) and (((A -> B) and (((C and D) -> D) -> A)) -> B)), M:tm-319, m:tm-150, u:((Am (-> Dm B)) (C (-> (-> (and Bm Cm) Cm) Dm)) (A Dm))
================================================================
tm-name          tm-14895
in-theory        14895
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> ((A and B) -> B)) and C) -> ((A and B) -> B)) and (((((A and B) -> B) -> ((A and B) -> B)) and C) -> ((A and B) -> B)))
theorem-size     39
proof            (modus-ponens tm-319 tm-151 ((Cm (-> (and Am Bm) Bm)) (B (-> (and Am Bm) Bm)) (C Dm) (A (-> (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-14895.        ((((((A and B) -> B) -> ((A and B) -> B)) and C) -> ((A and B) -> B)) and (((((A and B) -> B) -> ((A and B) -> B)) and C) -> ((A and B) -> B))), M:tm-319, m:tm-151, u:((Cm (-> (and Am Bm) Bm)) (B (-> (and Am Bm) Bm)) (C Dm) (A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-14896
in-theory        14896
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> ((B and C) -> C)) -> D) and E) -> (A -> ((B and C) -> C))) and ((((A -> ((B and C) -> C)) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-159 ((Am (and (-> (-> Bm (-> (and Cm Dm) Dm)) B) C)) (A (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-14896.        (((((A -> ((B and C) -> C)) -> D) and E) -> (A -> ((B and C) -> C))) and ((((A -> ((B and C) -> C)) -> D) and E) -> D)), M:tm-319, m:tm-159, u:((Am (and (-> (-> Bm (-> (and Cm Dm) Dm)) B) C)) (A (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-14897
in-theory        14897
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> ((B -> (C -> B)) and A)) -> D) and E) -> (A -> ((B -> (C -> B)) and A))) and ((((A -> ((B -> (C -> B)) and A)) -> D) and E) -> D))
theorem-size     39
proof            (modus-ponens tm-319 tm-184 ((Am (and (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-14897.        (((((A -> ((B -> (C -> B)) and A)) -> D) and E) -> (A -> ((B -> (C -> B)) and A))) and ((((A -> ((B -> (C -> B)) and A)) -> D) and E) -> D)), M:tm-319, m:tm-184, u:((Am (and (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-14898
in-theory        14898
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) and F) -> (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) and F) -> E))
theorem-size     63
proof            (modus-ponens tm-319 tm-211 ((Am (and (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) B) C)) (A (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-14898.        (((((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) and F) -> (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) and F) -> E)), M:tm-319, m:tm-211, u:((Am (and (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) B) C)) (A (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-14899
in-theory        14899
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (((B and C) -> B) and A)) -> D) and E) -> (A -> (((B and C) -> B) and A))) and ((((A -> (((B and C) -> B) and A)) -> D) and E) -> D))
theorem-size     39
proof            (modus-ponens tm-319 tm-240 ((Am (and (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) B) C)) (A (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-14899.        (((((A -> (((B and C) -> B) and A)) -> D) and E) -> (A -> (((B and C) -> B) and A))) and ((((A -> (((B and C) -> B) and A)) -> D) and E) -> D)), M:tm-319, m:tm-240, u:((Am (and (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) B) C)) (A (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-14900
in-theory        14900
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (((B and C) -> C) and A)) -> D) and E) -> (A -> (((B and C) -> C) and A))) and ((((A -> (((B and C) -> C) and A)) -> D) and E) -> D))
theorem-size     39
proof            (modus-ponens tm-319 tm-271 ((Am (and (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) B) C)) (A (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-14900.        (((((A -> (((B and C) -> C) and A)) -> D) and E) -> (A -> (((B and C) -> C) and A))) and ((((A -> (((B and C) -> C) and A)) -> D) and E) -> D)), M:tm-319, m:tm-271, u:((Am (and (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) B) C)) (A (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-14901
in-theory        14901
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> ((B -> (C -> (B and C))) and A)) -> D) and E) -> (A -> ((B -> (C -> (B and C))) and A))) and ((((A -> ((B -> (C -> (B and C))) and A)) -> D) and E) -> D))
theorem-size     45
proof            (modus-ponens tm-319 tm-304 ((Am (and (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) B) C)) (A (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-14901.        (((((A -> ((B -> (C -> (B and C))) and A)) -> D) and E) -> (A -> ((B -> (C -> (B and C))) and A))) and ((((A -> ((B -> (C -> (B and C))) and A)) -> D) and E) -> D)), M:tm-319, m:tm-304, u:((Am (and (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) B) C)) (A (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-14902
in-theory        14902
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-318 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14902.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14903
in-theory        14903
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)))
theorem-size     39
proof            (modus-ponens tm-316 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14903.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A))), M:tm-316, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-14904
in-theory        14904
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (D -> (E -> D)))
theorem-size     29
proof            (modus-ponens tm-315 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14904.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (D -> (E -> D))), M:tm-315, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14905
in-theory        14905
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (((((A -> B) and C) -> A) -> (not ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))) -> (not (((A -> B) and C) -> A))))
theorem-size     57
proof            (modus-ponens tm-313 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14905.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (((((A -> B) and C) -> A) -> (not ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))) -> (not (((A -> B) and C) -> A)))), M:tm-313, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-14906
in-theory        14906
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((((((A -> B) and C) -> A) and (((A -> B) and C) -> B)) -> D) -> (((((A -> B) and C) -> A) or ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) -> D)))
theorem-size     67
proof            (modus-ponens tm-312 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14906.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((((((A -> B) and C) -> A) and (((A -> B) and C) -> B)) -> D) -> (((((A -> B) and C) -> A) or ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) -> D))), M:tm-312, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-14907
in-theory        14907
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (D or ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14907.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (D or ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))), M:tm-311, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14908
in-theory        14908
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) or D))
theorem-size     49
proof            (modus-ponens tm-310 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14908.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) or D)), M:tm-310, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14909
in-theory        14909
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (D -> (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and D)))
theorem-size     51
proof            (modus-ponens tm-309 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14909.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (D -> (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and D))), M:tm-309, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14910
in-theory        14910
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (D -> ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14910.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (D -> ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))), M:tm-305, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14911
in-theory        14911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     35
proof            (modus-ponens tm-303 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14911.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-303, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14912
in-theory        14912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     33
proof            (modus-ponens tm-270 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14912.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-270, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14913
in-theory        14913
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     33
proof            (modus-ponens tm-239 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14913.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-239, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14914
in-theory        14914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) -> E) -> ((((E -> F) and G) -> E) and (((E -> F) and G) -> F))))
theorem-size     41
proof            (modus-ponens tm-210 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14914.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) -> E) -> ((((E -> F) and G) -> E) and (((E -> F) and G) -> F)))), M:tm-210, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14915
in-theory        14915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     33
proof            (modus-ponens tm-183 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14915.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-183, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14916
in-theory        14916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-157 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14916.        ((A -> ((B and C) -> C)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-157, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14917
in-theory        14917
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) and B) -> B)) -> ((((B -> C) and B) -> B) and (((B -> C) and B) -> C)))
theorem-size     25
proof            (modus-ponens tm-154 tm-319 ((A (-> Cm Bm)) (Am Cm) (B Cm) (C (and (-> (and (-> Cm Bm) Cm) Cm) (-> (and (-> Cm Bm) Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14917.        ((A or (((B -> C) and B) -> B)) -> ((((B -> C) and B) -> B) and (((B -> C) and B) -> C))), M:tm-154, m:tm-319, u:((A (-> Cm Bm)) (Am Cm) (B Cm) (C (and (-> (and (-> Cm Bm) Cm) Cm) (-> (and (-> Cm Bm) Cm) Bm))))
================================================================
tm-name          tm-14918
in-theory        14918
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     39
proof            (modus-ponens tm-147 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14918.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-147, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14919
in-theory        14919
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and (C -> A)) -> C) or (((A -> B) and (C -> A)) -> A)) -> ((((A -> B) and (C -> A)) -> A) and (((A -> B) and (C -> A)) -> B)))
theorem-size     39
proof            (modus-ponens tm-144 tm-319 ((A (-> Am Bm)) (Cm (-> B Am)) (C Am) (D (and (-> (and (-> Am Bm) (-> B Am)) Am) (-> (and (-> Am Bm) (-> B Am)) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14919.        (((((A -> B) and (C -> A)) -> C) or (((A -> B) and (C -> A)) -> A)) -> ((((A -> B) and (C -> A)) -> A) and (((A -> B) and (C -> A)) -> B))), M:tm-144, m:tm-319, u:((A (-> Am Bm)) (Cm (-> B Am)) (C Am) (D (and (-> (and (-> Am Bm) (-> B Am)) Am) (-> (and (-> Am Bm) (-> B Am)) Bm))))
================================================================
tm-name          tm-14920
in-theory        14920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-134 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14920.        ((A -> ((B and C) -> B)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-134, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14921
in-theory        14921
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     39
proof            (modus-ponens tm-125 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14921.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-125, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14922
in-theory        14922
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> A) and B) -> A) or (((A -> A) and B) -> A)) -> ((((A -> A) and B) -> A) and (((A -> A) and B) -> A)))
theorem-size     31
proof            (modus-ponens tm-122 tm-319 ((A Bm) (Am Bm) (C Cm) (B Bm) (D (and (-> (and (-> Bm Bm) Cm) Bm) (-> (and (-> Bm Bm) Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14922.        (((((A -> A) and B) -> A) or (((A -> A) and B) -> A)) -> ((((A -> A) and B) -> A) and (((A -> A) and B) -> A))), M:tm-122, m:tm-319, u:((A Bm) (Am Bm) (C Cm) (B Bm) (D (and (-> (and (-> Bm Bm) Cm) Bm) (-> (and (-> Bm Bm) Cm) Bm))))
================================================================
tm-name          tm-14923
in-theory        14923
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) -> E) -> ((((E -> F) and G) -> E) and (((E -> F) and G) -> F))))
theorem-size     39
proof            (modus-ponens tm-113 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14923.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) -> E) -> ((((E -> F) and G) -> E) and (((E -> F) and G) -> F)))), M:tm-113, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14924
in-theory        14924
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     43
proof            (modus-ponens tm-105 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14924.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-105, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14925
in-theory        14925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D))))
theorem-size     31
proof            (modus-ponens tm-95 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14925.        (((A -> B) -> (A -> A)) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D)))), M:tm-95, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14926
in-theory        14926
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> (D -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))
theorem-size     25
proof            (modus-ponens tm-84 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14926.        ((((A -> B) and C) -> A) -> (D -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))), M:tm-84, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-14927
in-theory        14927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-83 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14927.        ((A -> (B -> (C -> B))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-83, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14928
in-theory        14928
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) and D) -> B) -> ((((B -> C) and D) -> B) and (((B -> C) and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-76 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14928.        (((not (not A)) -> A) and ((((B -> C) and D) -> B) -> ((((B -> C) and D) -> B) and (((B -> C) and D) -> C)))), M:tm-76, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14929
in-theory        14929
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) and C) -> A))) or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-73 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14929.        (((not (not (((A -> B) and C) -> A))) or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-73, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-14930
in-theory        14930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D))))
theorem-size     35
proof            (modus-ponens tm-69 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14930.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D)))), M:tm-69, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14931
in-theory        14931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     37
proof            (modus-ponens tm-54 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14931.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-54, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14932
in-theory        14932
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> ((((B -> C) and D) -> B) and (((B -> C) and D) -> C)))
theorem-size     33
proof            (modus-ponens tm-47 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14932.        (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> ((((B -> C) and D) -> B) and (((B -> C) and D) -> C))), M:tm-47, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-14933
in-theory        14933
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-46 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14933.        ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-46, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-14934
in-theory        14934
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))
theorem-size     25
proof            (modus-ponens tm-44 tm-319 ((A (and (-> Am Bm) Cm)) (B Am) (C (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14934.        ((A or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-44, m:tm-319, u:((A (and (-> Am Bm) Cm)) (B Am) (C (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-14935
in-theory        14935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D))))
theorem-size     29
proof            (modus-ponens tm-42 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14935.        ((A -> (B or A)) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D)))), M:tm-42, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14936
in-theory        14936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D))))
theorem-size     29
proof            (modus-ponens tm-32 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14936.        ((A -> (A or B)) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D)))), M:tm-32, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14937
in-theory        14937
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))
theorem-size     31
proof            (modus-ponens tm-24 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14937.        ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))), M:tm-24, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-14938
in-theory        14938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D))))
theorem-size     31
proof            (modus-ponens tm-23 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14938.        ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D)))), M:tm-23, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14939
in-theory        14939
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D))))
theorem-size     29
proof            (modus-ponens tm-22 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14939.        (((A and B) -> B) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D)))), M:tm-22, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14940
in-theory        14940
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D))))
theorem-size     29
proof            (modus-ponens tm-21 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14940.        (((A and B) -> A) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D)))), M:tm-21, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14941
in-theory        14941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     37
proof            (modus-ponens tm-20 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14941.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-20, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14942
in-theory        14942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D))))
theorem-size     29
proof            (modus-ponens tm-19 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14942.        ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D)))), M:tm-19, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14943
in-theory        14943
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (not ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))) -> (not (((A -> B) and C) -> A)))
theorem-size     33
proof            (modus-ponens tm-9 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-9 tm-2 tm-5 tm-3)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14943.        (((((A -> B) and C) -> A) -> (not ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-14944
in-theory        14944
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) and (((A -> B) and C) -> B)) -> D) -> (((((A -> B) and C) -> A) or ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) -> D))
theorem-size     43
proof            (modus-ponens tm-8 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14944.        ((((((A -> B) and C) -> A) and (((A -> B) and C) -> B)) -> D) -> (((((A -> B) and C) -> A) or ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) -> D)), M:tm-8, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-14945
in-theory        14945
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) and D) -> B) -> ((((B -> C) and D) -> B) and (((B -> C) and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-7 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-7 tm-2 tm-5 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14945.        (A or ((((B -> C) and D) -> B) -> ((((B -> C) and D) -> B) and (((B -> C) and D) -> C)))), M:tm-7, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14946
in-theory        14946
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) or D)
theorem-size     25
proof            (modus-ponens tm-6 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-6 tm-2 tm-5 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14946.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) or D), M:tm-6, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14947
in-theory        14947
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) and D) -> B) -> ((((B -> C) and D) -> B) and (((B -> C) and D) -> C))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14947.        (A -> (((((B -> C) and D) -> B) -> ((((B -> C) and D) -> B) and (((B -> C) and D) -> C))) and A)), M:tm-5, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14948
in-theory        14948
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) and D) -> B) -> ((((B -> C) and D) -> B) and (((B -> C) and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-1 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-1 tm-2 tm-5 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-14948.        (A -> ((((B -> C) and D) -> B) -> ((((B -> C) and D) -> B) and (((B -> C) and D) -> C)))), M:tm-1, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-14949
in-theory        14949
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-320 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-14949.        (((A -> B) -> (A -> (A and B))) and ((C and D) -> C)), M:tm-320, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-14950
in-theory        14950
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14950.        ((A -> (B -> (C -> (B and C)))) and ((D and E) -> D)), M:tm-320, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-14951
in-theory        14951
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-320 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14951.        (((A -> (B -> A)) or C) and ((D and E) -> D)), M:tm-320, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-14952
in-theory        14952
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14952.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and F) -> E)), M:tm-320, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-14953
in-theory        14953
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-320 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14953.        ((((A and B) -> A) or C) and ((D and E) -> D)), M:tm-320, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-14954
in-theory        14954
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-320 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14954.        ((((A and B) -> B) or C) and ((D and E) -> D)), M:tm-320, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-14955
in-theory        14955
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14955.        (((A -> (B -> (A and B))) or C) and ((D and E) -> D)), M:tm-320, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-14956
in-theory        14956
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-320 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14956.        (((A -> (A or B)) or C) and ((D and E) -> D)), M:tm-320, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-14957
in-theory        14957
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14957.        ((A -> ((B -> (B or C)) and A)) and ((D and E) -> D)), M:tm-320, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-14958
in-theory        14958
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-320 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14958.        ((A -> (B -> (B or C))) and ((D and E) -> D)), M:tm-320, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-14959
in-theory        14959
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-320 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14959.        ((A or (B -> (C -> B))) and ((D and E) -> D)), M:tm-320, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-14960
in-theory        14960
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14960.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> E)), M:tm-320, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-14961
in-theory        14961
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-320 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14961.        ((A or ((B and C) -> B)) and ((D and E) -> D)), M:tm-320, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-14962
in-theory        14962
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-320 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14962.        ((A or ((B and C) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-14963
in-theory        14963
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14963.        ((A or (B -> (C -> (B and C)))) and ((D and E) -> D)), M:tm-320, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-14964
in-theory        14964
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-320 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14964.        ((A or (B -> (B or C))) and ((D and E) -> D)), M:tm-320, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-14965
in-theory        14965
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-320 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14965.        ((A or (B -> (C or B))) and ((D and E) -> D)), M:tm-320, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-14966
in-theory        14966
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-320 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14966.        (((A -> (B or A)) or C) and ((D and E) -> D)), M:tm-320, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-14967
in-theory        14967
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14967.        ((A -> ((B -> (C or B)) and A)) and ((D and E) -> D)), M:tm-320, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-14968
in-theory        14968
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-320 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14968.        ((A -> (B -> (C or B))) and ((D and E) -> D)), M:tm-320, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-14969
in-theory        14969
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14969.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-14970
in-theory        14970
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and F) -> E))
theorem-size     31
proof            (modus-ponens tm-320 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14970.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-14971
in-theory        14971
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14971.        (((A -> B) -> (((A and C) or A) -> B)) and ((D and E) -> D)), M:tm-320, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-14972
in-theory        14972
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14972.        (((A -> B) -> (((C and A) or A) -> B)) and ((D and E) -> D)), M:tm-320, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-14973
in-theory        14973
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-320 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-14973.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-14974
in-theory        14974
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-14974.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-14975
in-theory        14975
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-14975.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-14976
in-theory        14976
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and F) -> E))
theorem-size     33
proof            (modus-ponens tm-320 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-14976.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-14977
in-theory        14977
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14977.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and F) -> E)), M:tm-320, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-14978
in-theory        14978
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14978.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and F) -> E)), M:tm-320, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-14979
in-theory        14979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14979.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((E and F) -> E)), M:tm-320, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-14980
in-theory        14980
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-320 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-14980.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-14981
in-theory        14981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-14981.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and F) -> E)), M:tm-320, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-14982
in-theory        14982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-320 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14982.        (((A -> (not (B -> A))) -> (not A)) and ((C and D) -> C)), M:tm-320, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-14983
in-theory        14983
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((D and E) -> D))
theorem-size     27
proof            (modus-ponens tm-320 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14983.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((D and E) -> D)), M:tm-320, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-14984
in-theory        14984
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-320 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14984.        ((((A and B) -> (not A)) -> (not (A and B))) and ((C and D) -> C)), M:tm-320, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-14985
in-theory        14985
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-320 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14985.        ((((A and B) -> (not B)) -> (not (A and B))) and ((C and D) -> C)), M:tm-320, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-14986
in-theory        14986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-320 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-14986.        (((A -> (not (B -> (A and B)))) -> (not A)) and ((C and D) -> C)), M:tm-320, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-14987
in-theory        14987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-320 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-14987.        (((A -> (not (A or B))) -> (not A)) and ((C and D) -> C)), M:tm-320, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-14988
in-theory        14988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-320 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-14988.        (((A -> (not (B or A))) -> (not A)) and ((C and D) -> C)), M:tm-320, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-14989
in-theory        14989
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-320 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-14989.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((D and E) -> D)), M:tm-320, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-14990
in-theory        14990
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((C and D) -> C))
theorem-size     23
proof            (modus-ponens tm-320 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-14990.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((C and D) -> C)), M:tm-320, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-14991
in-theory        14991
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((D and E) -> D))
theorem-size     29
proof            (modus-ponens tm-320 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-14991.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-14992
in-theory        14992
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14992.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D and E) -> D)), M:tm-320, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-14993
in-theory        14993
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14993.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((D and E) -> D)), M:tm-320, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-14994
in-theory        14994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14994.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((D and E) -> D)), M:tm-320, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-14995
in-theory        14995
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((C and D) -> C))
theorem-size     21
proof            (modus-ponens tm-320 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-14995.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((C and D) -> C)), M:tm-320, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-14996
in-theory        14996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-14996.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D and E) -> D)), M:tm-320, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-14997
in-theory        14997
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((B and C) -> B))
theorem-size     17
proof            (modus-ponens tm-320 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-14997.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((B and C) -> B)), M:tm-320, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-14998
in-theory        14998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-320 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-10)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-14998.        (((A -> B) -> (((not (not A)) or A) -> B)) and ((C and D) -> C)), M:tm-320, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-14999
in-theory        14999
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-320 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-14999.        ((A or ((not (not B)) -> B)) and ((C and D) -> C)), M:tm-320, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-15000
in-theory        15000
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-320 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15000.        ((((not (not A)) -> A) or B) and ((C and D) -> C)), M:tm-320, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-15001
in-theory        15001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-320 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15001.        ((A -> (((not (not B)) -> B) and A)) and ((C and D) -> C)), M:tm-320, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-15002
in-theory        15002
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((C and D) -> C))
theorem-size     21
proof            (modus-ponens tm-320 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-10)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-15002.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((C and D) -> C)), M:tm-320, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-15003
in-theory        15003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-320 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15003.        ((A -> ((not (not B)) -> B)) and ((C and D) -> C)), M:tm-320, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-15004
in-theory        15004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-15004.        (((A -> (not (B -> (C -> B)))) -> (not A)) and ((D and E) -> D)), M:tm-320, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-15005
in-theory        15005
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-15005.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-15006
in-theory        15006
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15006.        ((A or (B -> (C -> (D -> C)))) and ((E and F) -> E)), M:tm-320, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-15007
in-theory        15007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15007.        (((A -> (B -> (C -> B))) or D) and ((E and F) -> E)), M:tm-320, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-15008
in-theory        15008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15008.        ((A -> ((B -> (C -> (D -> C))) and A)) and ((E and F) -> E)), M:tm-320, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-15009
in-theory        15009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-15009.        (((A -> B) -> (A -> (C -> B))) and ((D and E) -> D)), M:tm-320, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-15010
in-theory        15010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15010.        ((A -> (B -> (C -> (D -> C)))) and ((E and F) -> E)), M:tm-320, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-15011
in-theory        15011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and ((B and C) -> B))
theorem-size     9
proof            (modus-ponens tm-320 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       97
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-15011.        ((A -> A) and ((B and C) -> B)), M:tm-320, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-15012
in-theory        15012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-15012.        (((A -> (B -> C)) -> (A -> (B -> C))) and ((D and E) -> D)), M:tm-320, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-15013
in-theory        15013
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-320 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15013.        (((A and B) -> (A and B)) and ((C and D) -> C)), M:tm-320, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-15014
in-theory        15014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-320 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-15014.        (((A -> B) -> (A -> B)) and ((C and D) -> C)), M:tm-320, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-15015
in-theory        15015
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and ((B and C) -> B))
theorem-size     13
proof            (modus-ponens tm-320 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-10)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-15015.        (((not (not A)) -> (not (not A))) and ((B and C) -> B)), M:tm-320, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-15016
in-theory        15016
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((C and D) -> C))
theorem-size     19
proof            (modus-ponens tm-320 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-15016.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((C and D) -> C)), M:tm-320, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-15017
in-theory        15017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-15017.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((D and E) -> D)), M:tm-320, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-15018
in-theory        15018
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15018.        ((A or ((B -> C) -> (B -> B))) and ((D and E) -> D)), M:tm-320, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-15019
in-theory        15019
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15019.        ((((A -> B) -> (A -> A)) or C) and ((D and E) -> D)), M:tm-320, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-15020
in-theory        15020
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15020.        ((A -> (((B -> C) -> (B -> B)) and A)) and ((D and E) -> D)), M:tm-320, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-15021
in-theory        15021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-320 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-15021.        ((((A -> B) -> A) -> ((A -> B) -> A)) and ((C and D) -> C)), M:tm-320, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-15022
in-theory        15022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15022.        ((A -> ((B -> C) -> (B -> B))) and ((D and E) -> D)), M:tm-320, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-15023
in-theory        15023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-15023.        (((A -> ((B -> A) -> C)) -> (A -> C)) and ((D and E) -> D)), M:tm-320, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-15024
in-theory        15024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-320 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-15024.        (((A -> (A -> B)) -> (A -> B)) and ((C and D) -> C)), M:tm-320, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-15025
in-theory        15025
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-320 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-15025.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((D and E) -> D)), M:tm-320, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-15026
in-theory        15026
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((D and E) -> D))
theorem-size     37
proof            (modus-ponens tm-320 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-15026.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((D and E) -> D)), M:tm-320, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-15027
in-theory        15027
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((E and F) -> E))
theorem-size     39
proof            (modus-ponens tm-320 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-15027.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-15028
in-theory        15028
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15028.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E and F) -> E)), M:tm-320, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-15029
in-theory        15029
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15029.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and ((E and F) -> E)), M:tm-320, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-15030
in-theory        15030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((E and F) -> E))
theorem-size     29
proof            (modus-ponens tm-320 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15030.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((E and F) -> E)), M:tm-320, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-15031
in-theory        15031
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((D and E) -> D))
theorem-size     35
proof            (modus-ponens tm-320 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-15031.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((D and E) -> D)), M:tm-320, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-15032
in-theory        15032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15032.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E and F) -> E)), M:tm-320, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-15033
in-theory        15033
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((E and F) -> E))
theorem-size     29
proof            (modus-ponens tm-320 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-15033.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-15034
in-theory        15034
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15034.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((E and F) -> E)), M:tm-320, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-15035
in-theory        15035
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((F and G) -> F))
theorem-size     39
proof            (modus-ponens tm-320 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15035.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((F and G) -> F)), M:tm-320, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-15036
in-theory        15036
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15036.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> F)), M:tm-320, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-15037
in-theory        15037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15037.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F and G) -> F)), M:tm-320, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-15038
in-theory        15038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15038.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F and G) -> F)), M:tm-320, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-15039
in-theory        15039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-15039.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((E and F) -> E)), M:tm-320, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-15040
in-theory        15040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15040.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> F)), M:tm-320, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-15041
in-theory        15041
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-320 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-15041.        ((((A -> B) and A) -> B) and ((C and D) -> C)), M:tm-320, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-15042
in-theory        15042
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-15042.        (((((A -> (B -> A)) -> C) and D) -> C) and ((E and F) -> E)), M:tm-320, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-15043
in-theory        15043
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15043.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((F and G) -> F)), M:tm-320, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-15044
in-theory        15044
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((D and E) -> D))
theorem-size     27
proof            (modus-ponens tm-320 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-15044.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((D and E) -> D)), M:tm-320, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-15045
in-theory        15045
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-15045.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((D and E) -> D)), M:tm-320, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-15046
in-theory        15046
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((D and E) -> D))
theorem-size     31
proof            (modus-ponens tm-320 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-15046.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((D and E) -> D)), M:tm-320, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-15047
in-theory        15047
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((E and F) -> E))
theorem-size     33
proof            (modus-ponens tm-320 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-15047.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-15048
in-theory        15048
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15048.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E and F) -> E)), M:tm-320, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-15049
in-theory        15049
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15049.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((E and F) -> E)), M:tm-320, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-15050
in-theory        15050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15050.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-15051
in-theory        15051
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((D and E) -> D))
theorem-size     29
proof            (modus-ponens tm-320 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-15051.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((D and E) -> D)), M:tm-320, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-15052
in-theory        15052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15052.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E and F) -> E)), M:tm-320, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-15053
in-theory        15053
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-15053.        ((((((A and B) -> A) -> C) and D) -> C) and ((E and F) -> E)), M:tm-320, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-15054
in-theory        15054
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-15054.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-15055
in-theory        15055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15055.        (((A -> (not ((B and C) -> B))) -> (not A)) and ((D and E) -> D)), M:tm-320, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-15056
in-theory        15056
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15056.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-15057
in-theory        15057
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15057.        ((A or (B -> ((C and D) -> C))) and ((E and F) -> E)), M:tm-320, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-15058
in-theory        15058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15058.        (((A -> ((B and C) -> B)) or D) and ((E and F) -> E)), M:tm-320, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-15059
in-theory        15059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15059.        ((A -> ((B -> ((C and D) -> C)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-15060
in-theory        15060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-15060.        (((A -> (B and C)) -> (A -> B)) and ((D and E) -> D)), M:tm-320, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-15061
in-theory        15061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15061.        ((A -> (B -> ((C and D) -> C))) and ((E and F) -> E)), M:tm-320, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-15062
in-theory        15062
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-320 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-15062.        (((A and (A -> B)) -> B) and ((C and D) -> C)), M:tm-320, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-15063
in-theory        15063
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-15063.        (((A and ((B -> (C -> B)) -> D)) -> D) and ((E and F) -> E)), M:tm-320, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-15064
in-theory        15064
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15064.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((F and G) -> F)), M:tm-320, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-15065
in-theory        15065
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-15065.        (((A and (((B and C) -> B) -> D)) -> D) and ((E and F) -> E)), M:tm-320, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-15066
in-theory        15066
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((D and E) -> D))
theorem-size     27
proof            (modus-ponens tm-320 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-15066.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-15067
in-theory        15067
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15067.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((D and E) -> D)), M:tm-320, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-15068
in-theory        15068
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((D and E) -> D))
theorem-size     31
proof            (modus-ponens tm-320 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15068.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((D and E) -> D)), M:tm-320, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-15069
in-theory        15069
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((E and F) -> E))
theorem-size     33
proof            (modus-ponens tm-320 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15069.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-15070
in-theory        15070
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15070.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-15071
in-theory        15071
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15071.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and ((E and F) -> E)), M:tm-320, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-15072
in-theory        15072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15072.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-15073
in-theory        15073
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((D and E) -> D))
theorem-size     29
proof            (modus-ponens tm-320 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-15073.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-15074
in-theory        15074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15074.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-15075
in-theory        15075
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-15075.        (((A and (((B and C) -> C) -> D)) -> D) and ((E and F) -> E)), M:tm-320, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-15076
in-theory        15076
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-15076.        ((((((A and B) -> B) -> C) and D) -> C) and ((E and F) -> E)), M:tm-320, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-15077
in-theory        15077
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-15077.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-15078
in-theory        15078
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15078.        (((A -> (not ((B and C) -> C))) -> (not A)) and ((D and E) -> D)), M:tm-320, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-15079
in-theory        15079
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15079.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-15080
in-theory        15080
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15080.        ((A or (B -> ((C and D) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-15081
in-theory        15081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15081.        (((A -> ((B and C) -> C)) or D) and ((E and F) -> E)), M:tm-320, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-15082
in-theory        15082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15082.        ((A -> ((B -> ((C and D) -> D)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-15083
in-theory        15083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-15083.        (((A -> (B and C)) -> (A -> C)) and ((D and E) -> D)), M:tm-320, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-15084
in-theory        15084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15084.        ((A -> (B -> ((C and D) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-15085
in-theory        15085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15085.        (((A -> (B -> A)) and (C -> (D -> C))) and ((E and F) -> E)), M:tm-320, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-15086
in-theory        15086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15086.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-15087
in-theory        15087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15087.        (((A -> (B -> A)) and ((C and D) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-15088
in-theory        15088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15088.        (((A -> (B -> A)) and ((C and D) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-15089
in-theory        15089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15089.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-15090
in-theory        15090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15090.        (((A -> (B -> A)) and (C -> (C or D))) and ((E and F) -> E)), M:tm-320, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-15091
in-theory        15091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15091.        (((A -> (B -> A)) and (C -> (D or C))) and ((E and F) -> E)), M:tm-320, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-15092
in-theory        15092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15092.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-15093
in-theory        15093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15093.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> E)), M:tm-320, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-15094
in-theory        15094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15094.        (((A -> (B -> A)) and ((not (not C)) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-15095
in-theory        15095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15095.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and ((F and G) -> F)), M:tm-320, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-15096
in-theory        15096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15096.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((E and F) -> E)), M:tm-320, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-15097
in-theory        15097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> F))
theorem-size     31
proof            (modus-ponens tm-320 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15097.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-15098
in-theory        15098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15098.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-15099
in-theory        15099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15099.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-15100
in-theory        15100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15100.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-15101
in-theory        15101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15101.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-15102
in-theory        15102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15102.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-15103
in-theory        15103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15103.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-15104
in-theory        15104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-15104.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((D and E) -> D)), M:tm-320, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-15105
in-theory        15105
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-15105.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-15106
in-theory        15106
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15106.        ((A or (B -> ((C -> (D -> C)) and B))) and ((E and F) -> E)), M:tm-320, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-15107
in-theory        15107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15107.        (((A -> ((B -> (C -> B)) and A)) or D) and ((E and F) -> E)), M:tm-320, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-15108
in-theory        15108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15108.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-15109
in-theory        15109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15109.        ((A -> (B -> ((C -> (D -> C)) and B))) and ((E and F) -> E)), M:tm-320, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-15110
in-theory        15110
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15110.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((F and G) -> F)), M:tm-320, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-15111
in-theory        15111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G and H) -> G))
theorem-size     33
proof            (modus-ponens tm-320 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15111.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G and H) -> G)), M:tm-320, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-15112
in-theory        15112
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15112.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((F and G) -> F)), M:tm-320, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-15113
in-theory        15113
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15113.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((F and G) -> F)), M:tm-320, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-15114
in-theory        15114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15114.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((F and G) -> F)), M:tm-320, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-15115
in-theory        15115
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15115.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((F and G) -> F)), M:tm-320, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-15116
in-theory        15116
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15116.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((F and G) -> F)), M:tm-320, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-15117
in-theory        15117
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G and H) -> G))
theorem-size     33
proof            (modus-ponens tm-320 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15117.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G and H) -> G)), M:tm-320, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-15118
in-theory        15118
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F and G) -> F))
theorem-size     31
proof            (modus-ponens tm-320 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15118.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F and G) -> F)), M:tm-320, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-15119
in-theory        15119
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-10)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15119.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-15120
in-theory        15120
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15120.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((G and H) -> G)), M:tm-320, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-15121
in-theory        15121
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15121.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((F and G) -> F)), M:tm-320, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-15122
in-theory        15122
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G and H) -> G))
theorem-size     39
proof            (modus-ponens tm-320 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15122.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G and H) -> G)), M:tm-320, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-15123
in-theory        15123
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H and I) -> H))
theorem-size     35
proof            (modus-ponens tm-320 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15123.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H and I) -> H)), M:tm-320, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-15124
in-theory        15124
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G and H) -> G))
theorem-size     35
proof            (modus-ponens tm-320 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15124.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G and H) -> G)), M:tm-320, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-15125
in-theory        15125
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15125.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((G and H) -> G)), M:tm-320, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-15126
in-theory        15126
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G and H) -> G))
theorem-size     35
proof            (modus-ponens tm-320 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15126.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-15127
in-theory        15127
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15127.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-15128
in-theory        15128
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15128.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G and H) -> G)), M:tm-320, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-15129
in-theory        15129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H and I) -> H))
theorem-size     37
proof            (modus-ponens tm-320 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15129.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H and I) -> H)), M:tm-320, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-15130
in-theory        15130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15130.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> G)), M:tm-320, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-15131
in-theory        15131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-15131.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((E and F) -> E)), M:tm-320, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-15132
in-theory        15132
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((F and G) -> F))
theorem-size     43
proof            (modus-ponens tm-320 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-15132.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((F and G) -> F)), M:tm-320, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-15133
in-theory        15133
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15133.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F and G) -> F)), M:tm-320, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-15134
in-theory        15134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15134.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and ((F and G) -> F)), M:tm-320, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-15135
in-theory        15135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15135.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((F and G) -> F)), M:tm-320, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-15136
in-theory        15136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15136.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F and G) -> F)), M:tm-320, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-15137
in-theory        15137
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15137.        ((((A and B) -> A) and (C -> (D -> C))) and ((E and F) -> E)), M:tm-320, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-15138
in-theory        15138
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15138.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-15139
in-theory        15139
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15139.        ((((A and B) -> A) and ((C and D) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-15140
in-theory        15140
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15140.        ((((A and B) -> A) and ((C and D) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-15141
in-theory        15141
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15141.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-15142
in-theory        15142
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15142.        ((((A and B) -> A) and (C -> (C or D))) and ((E and F) -> E)), M:tm-320, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-15143
in-theory        15143
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15143.        ((((A and B) -> A) and (C -> (D or C))) and ((E and F) -> E)), M:tm-320, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-15144
in-theory        15144
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15144.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-15145
in-theory        15145
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15145.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> E)), M:tm-320, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-15146
in-theory        15146
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15146.        ((((A and B) -> A) and ((not (not C)) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-15147
in-theory        15147
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15147.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((F and G) -> F)), M:tm-320, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-15148
in-theory        15148
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15148.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((E and F) -> E)), M:tm-320, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-15149
in-theory        15149
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> F))
theorem-size     31
proof            (modus-ponens tm-320 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15149.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-15150
in-theory        15150
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15150.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-15151
in-theory        15151
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15151.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-15152
in-theory        15152
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15152.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-15153
in-theory        15153
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15153.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-15154
in-theory        15154
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15154.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-15155
in-theory        15155
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15155.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-15156
in-theory        15156
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15156.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> G)), M:tm-320, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-15157
in-theory        15157
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15157.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((F and G) -> F)), M:tm-320, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-15158
in-theory        15158
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15158.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((G and H) -> G)), M:tm-320, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-15159
in-theory        15159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15159.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and ((F and G) -> F)), M:tm-320, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-15160
in-theory        15160
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15160.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((D and E) -> D)), M:tm-320, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-15161
in-theory        15161
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15161.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-15162
in-theory        15162
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15162.        ((A or (B -> (((C and D) -> C) and B))) and ((E and F) -> E)), M:tm-320, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-15163
in-theory        15163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15163.        (((A -> (((B and C) -> B) and A)) or D) and ((E and F) -> E)), M:tm-320, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-15164
in-theory        15164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15164.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-15165
in-theory        15165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15165.        ((A -> (B -> (((C and D) -> C) and B))) and ((E and F) -> E)), M:tm-320, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-15166
in-theory        15166
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15166.        ((((A and B) -> B) and (C -> (D -> C))) and ((E and F) -> E)), M:tm-320, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-15167
in-theory        15167
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15167.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-15168
in-theory        15168
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15168.        ((((A and B) -> B) and ((C and D) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-15169
in-theory        15169
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15169.        ((((A and B) -> B) and ((C and D) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-15170
in-theory        15170
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15170.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-15171
in-theory        15171
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15171.        ((((A and B) -> B) and (C -> (C or D))) and ((E and F) -> E)), M:tm-320, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-15172
in-theory        15172
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15172.        ((((A and B) -> B) and (C -> (D or C))) and ((E and F) -> E)), M:tm-320, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-15173
in-theory        15173
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15173.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-15174
in-theory        15174
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15174.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> E)), M:tm-320, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-15175
in-theory        15175
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15175.        ((((A and B) -> B) and ((not (not C)) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-15176
in-theory        15176
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15176.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((F and G) -> F)), M:tm-320, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-15177
in-theory        15177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15177.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((E and F) -> E)), M:tm-320, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-15178
in-theory        15178
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> F))
theorem-size     31
proof            (modus-ponens tm-320 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15178.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-15179
in-theory        15179
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15179.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-15180
in-theory        15180
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15180.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-15181
in-theory        15181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15181.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-15182
in-theory        15182
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15182.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-15183
in-theory        15183
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15183.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-15184
in-theory        15184
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15184.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-15185
in-theory        15185
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15185.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> G)), M:tm-320, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-15186
in-theory        15186
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15186.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((F and G) -> F)), M:tm-320, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-15187
in-theory        15187
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15187.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((F and G) -> F)), M:tm-320, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-15188
in-theory        15188
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15188.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((F and G) -> F)), M:tm-320, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-15189
in-theory        15189
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15189.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((G and H) -> G)), M:tm-320, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-15190
in-theory        15190
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15190.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and ((F and G) -> F)), M:tm-320, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-15191
in-theory        15191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-15191.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((D and E) -> D)), M:tm-320, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-15192
in-theory        15192
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-15192.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-15193
in-theory        15193
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15193.        ((A or (B -> (((C and D) -> D) and B))) and ((E and F) -> E)), M:tm-320, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-15194
in-theory        15194
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15194.        (((A -> (((B and C) -> C) and A)) or D) and ((E and F) -> E)), M:tm-320, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-15195
in-theory        15195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15195.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-15196
in-theory        15196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15196.        ((A -> (B -> (((C and D) -> D) and B))) and ((E and F) -> E)), M:tm-320, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-15197
in-theory        15197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15197.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and ((E and F) -> E)), M:tm-320, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-15198
in-theory        15198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15198.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-15199
in-theory        15199
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15199.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-15200
in-theory        15200
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15200.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-15201
in-theory        15201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15201.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-15202
in-theory        15202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15202.        (((A -> (B -> (A and B))) and (C -> (C or D))) and ((E and F) -> E)), M:tm-320, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-15203
in-theory        15203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15203.        (((A -> (B -> (A and B))) and (C -> (D or C))) and ((E and F) -> E)), M:tm-320, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-15204
in-theory        15204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15204.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-15205
in-theory        15205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15205.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> E)), M:tm-320, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-15206
in-theory        15206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15206.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-15207
in-theory        15207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15207.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and ((F and G) -> F)), M:tm-320, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-15208
in-theory        15208
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15208.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((E and F) -> E)), M:tm-320, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-15209
in-theory        15209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> F))
theorem-size     33
proof            (modus-ponens tm-320 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15209.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-15210
in-theory        15210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15210.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-15211
in-theory        15211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> F))
theorem-size     29
proof            (modus-ponens tm-320 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15211.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-15212
in-theory        15212
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15212.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-15213
in-theory        15213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> F))
theorem-size     29
proof            (modus-ponens tm-320 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15213.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-15214
in-theory        15214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15214.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-15215
in-theory        15215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15215.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-15216
in-theory        15216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> G))
theorem-size     31
proof            (modus-ponens tm-320 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15216.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> G)), M:tm-320, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-15217
in-theory        15217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15217.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and ((F and G) -> F)), M:tm-320, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-15218
in-theory        15218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15218.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and ((F and G) -> F)), M:tm-320, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-15219
in-theory        15219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15219.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> F)), M:tm-320, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-15220
in-theory        15220
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15220.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> F)), M:tm-320, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-15221
in-theory        15221
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15221.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> F)), M:tm-320, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-15222
in-theory        15222
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G and H) -> G))
theorem-size     31
proof            (modus-ponens tm-320 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15222.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G and H) -> G)), M:tm-320, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-15223
in-theory        15223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15223.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> F)), M:tm-320, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-15224
in-theory        15224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-15224.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((D and E) -> D)), M:tm-320, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-15225
in-theory        15225
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((E and F) -> E))
theorem-size     31
proof            (modus-ponens tm-320 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-15225.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-15226
in-theory        15226
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15226.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((E and F) -> E)), M:tm-320, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-15227
in-theory        15227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15227.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and ((E and F) -> E)), M:tm-320, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-15228
in-theory        15228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15228.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-15229
in-theory        15229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15229.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((E and F) -> E)), M:tm-320, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-15230
in-theory        15230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-320 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-15230.        ((A -> (A and (B -> A))) and ((C and D) -> C)), M:tm-320, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-15231
in-theory        15231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-320 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-15231.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((D and E) -> D)), M:tm-320, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-15232
in-theory        15232
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-320 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15232.        (((A and B) -> ((A and B) and A)) and ((C and D) -> C)), M:tm-320, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-15233
in-theory        15233
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-320 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-15233.        (((A and B) -> ((A and B) and B)) and ((C and D) -> C)), M:tm-320, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-15234
in-theory        15234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-320 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-15234.        ((A -> (A and (B -> (A and B)))) and ((C and D) -> C)), M:tm-320, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-15235
in-theory        15235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-320 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-15235.        ((A -> (A and (A or B))) and ((C and D) -> C)), M:tm-320, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-15236
in-theory        15236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-320 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-15236.        ((A -> (A and (B or A))) and ((C and D) -> C)), M:tm-320, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-15237
in-theory        15237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-320 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-15237.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((D and E) -> D)), M:tm-320, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-15238
in-theory        15238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((C and D) -> C))
theorem-size     21
proof            (modus-ponens tm-320 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-15238.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((C and D) -> C)), M:tm-320, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-15239
in-theory        15239
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and ((B and C) -> B))
theorem-size     15
proof            (modus-ponens tm-320 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-10)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-15239.        (((not (not A)) -> ((not (not A)) and A)) and ((B and C) -> B)), M:tm-320, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-15240
in-theory        15240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-15240.        ((A -> (A and (B -> (C -> B)))) and ((D and E) -> D)), M:tm-320, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-15241
in-theory        15241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-320 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-15241.        (((A -> B) -> ((A -> B) and (A -> A))) and ((C and D) -> C)), M:tm-320, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-15242
in-theory        15242
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((D and E) -> D))
theorem-size     35
proof            (modus-ponens tm-320 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-15242.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((D and E) -> D)), M:tm-320, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-15243
in-theory        15243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15243.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((E and F) -> E)), M:tm-320, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-15244
in-theory        15244
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((D and E) -> D))
theorem-size     29
proof            (modus-ponens tm-320 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-15244.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((D and E) -> D)), M:tm-320, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-15245
in-theory        15245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15245.        ((A -> (A and ((B and C) -> B))) and ((D and E) -> D)), M:tm-320, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15246
in-theory        15246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15246.        ((A -> (A and ((B and C) -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15247
in-theory        15247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15247.        ((A -> (A and ((B and C) -> B))) and (A -> A)), M:tm-316, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15248
in-theory        15248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15248.        ((A -> (A and ((B and C) -> B))) and (D -> (E -> D))), M:tm-315, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15249
in-theory        15249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and ((A -> (not (A and ((B and C) -> B)))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15249.        ((A -> (A and ((B and C) -> B))) and ((A -> (not (A and ((B and C) -> B)))) -> (not A))), M:tm-313, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15250
in-theory        15250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (((A and ((B and C) -> B)) -> D) -> ((A or (A and ((B and C) -> B))) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15250.        ((A -> (A and ((B and C) -> B))) and (((A and ((B and C) -> B)) -> D) -> ((A or (A and ((B and C) -> B))) -> D))), M:tm-312, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15251
in-theory        15251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (D or (A -> (A and ((B and C) -> B)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15251.        ((A -> (A and ((B and C) -> B))) and (D or (A -> (A and ((B and C) -> B))))), M:tm-311, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15252
in-theory        15252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and ((A -> (A and ((B and C) -> B))) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15252.        ((A -> (A and ((B and C) -> B))) and ((A -> (A and ((B and C) -> B))) or D)), M:tm-310, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15253
in-theory        15253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (D -> ((A -> (A and ((B and C) -> B))) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15253.        ((A -> (A and ((B and C) -> B))) and (D -> ((A -> (A and ((B and C) -> B))) and D))), M:tm-309, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15254
in-theory        15254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (D -> (A -> (A and ((B and C) -> B)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15254.        ((A -> (A and ((B and C) -> B))) and (D -> (A -> (A and ((B and C) -> B))))), M:tm-305, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15255
in-theory        15255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and ((E and F) -> E))))
theorem-size     21
proof            (modus-ponens tm-303 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15255.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and ((E and F) -> E)))), M:tm-303, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15256
in-theory        15256
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and ((D and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-300 tm-320 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15256.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and ((D and E) -> D))), M:tm-300, m:tm-320, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15257
in-theory        15257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-270 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15257.        ((A -> (((B and C) -> C) and A)) and (D -> (D and ((E and F) -> E)))), M:tm-270, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15258
in-theory        15258
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((D and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-267 tm-320 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15258.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((D and E) -> D))), M:tm-267, m:tm-320, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15259
in-theory        15259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-239 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15259.        ((A -> (((B and C) -> B) and A)) and (D -> (D and ((E and F) -> E)))), M:tm-239, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15260
in-theory        15260
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((D and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-236 tm-320 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15260.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((D and E) -> D))), M:tm-236, m:tm-320, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15261
in-theory        15261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and ((F and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-210 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15261.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and ((F and G) -> F)))), M:tm-210, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15262
in-theory        15262
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((E and F) -> E)))
theorem-size     39
proof            (modus-ponens tm-207 tm-320 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15262.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((E and F) -> E))), M:tm-207, m:tm-320, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15263
in-theory        15263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-183 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15263.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and ((E and F) -> E)))), M:tm-183, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15264
in-theory        15264
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and ((D and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-180 tm-320 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15264.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and ((D and E) -> D))), M:tm-180, m:tm-320, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15265
in-theory        15265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-157 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15265.        ((A -> ((B and C) -> C)) and (D -> (D and ((E and F) -> E)))), M:tm-157, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15266
in-theory        15266
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((D and E) -> D)))
theorem-size     19
proof            (modus-ponens tm-154 tm-320 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15266.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((D and E) -> D))), M:tm-154, m:tm-320, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15267
in-theory        15267
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and ((E and F) -> E))))
theorem-size     25
proof            (modus-ponens tm-147 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15267.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and ((E and F) -> E)))), M:tm-147, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15268
in-theory        15268
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((D and E) -> D)))
theorem-size     29
proof            (modus-ponens tm-144 tm-320 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15268.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((D and E) -> D))), M:tm-144, m:tm-320, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15269
in-theory        15269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-134 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15269.        ((A -> ((B and C) -> B)) and (D -> (D and ((E and F) -> E)))), M:tm-134, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15270
in-theory        15270
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((D and E) -> D)))
theorem-size     19
proof            (modus-ponens tm-131 tm-320 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15270.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((D and E) -> D))), M:tm-131, m:tm-320, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15271
in-theory        15271
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and ((E and F) -> E))))
theorem-size     25
proof            (modus-ponens tm-125 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15271.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and ((E and F) -> E)))), M:tm-125, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15272
in-theory        15272
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((D and E) -> D)))
theorem-size     29
proof            (modus-ponens tm-122 tm-320 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15272.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((D and E) -> D))), M:tm-122, m:tm-320, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15273
in-theory        15273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-113 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15273.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F and G) -> F)))), M:tm-113, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15274
in-theory        15274
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-110 tm-320 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15274.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> E))), M:tm-110, m:tm-320, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15275
in-theory        15275
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and ((E and F) -> E))))
theorem-size     29
proof            (modus-ponens tm-105 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15275.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and ((E and F) -> E)))), M:tm-105, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15276
in-theory        15276
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((D and E) -> D)))
theorem-size     35
proof            (modus-ponens tm-102 tm-320 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15276.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((D and E) -> D))), M:tm-102, m:tm-320, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15277
in-theory        15277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and ((D and E) -> D))))
theorem-size     17
proof            (modus-ponens tm-95 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15277.        (((A -> B) -> (A -> A)) and (C -> (C and ((D and E) -> D)))), M:tm-95, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15278
in-theory        15278
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and ((C and D) -> C)))
theorem-size     17
proof            (modus-ponens tm-92 tm-320 ((Am (-> A A)) (B (and (-> A A) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15278.        (((A -> B) or (A -> A)) -> ((A -> A) and ((C and D) -> C))), M:tm-92, m:tm-320, u:((Am (-> A A)) (B (and (-> A A) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15279
in-theory        15279
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and ((C and D) -> C))))
theorem-size     11
proof            (modus-ponens tm-84 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15279.        (A -> (B -> (A and ((C and D) -> C)))), M:tm-84, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15280
in-theory        15280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-83 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15280.        ((A -> (B -> (C -> B))) and (D -> (D and ((E and F) -> E)))), M:tm-83, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15281
in-theory        15281
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((D and E) -> D)))
theorem-size     19
proof            (modus-ponens tm-80 tm-320 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15281.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((D and E) -> D))), M:tm-80, m:tm-320, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15282
in-theory        15282
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and ((C and D) -> C))))
theorem-size     15
proof            (modus-ponens tm-76 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15282.        (((not (not A)) -> A) and (B -> (B and ((C and D) -> C)))), M:tm-76, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15283
in-theory        15283
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and ((B and C) -> B)))
theorem-size     13
proof            (modus-ponens tm-73 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15283.        (((not (not A)) or A) -> (A and ((B and C) -> B))), M:tm-73, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15284
in-theory        15284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and ((D and E) -> D))))
theorem-size     21
proof            (modus-ponens tm-69 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15284.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and ((D and E) -> D)))), M:tm-69, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15285
in-theory        15285
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((C and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-66 tm-320 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-1 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15285.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((C and D) -> C))), M:tm-66, m:tm-320, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15286
in-theory        15286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and ((E and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-54 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15286.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and ((E and F) -> E)))), M:tm-54, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15287
in-theory        15287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((D and E) -> D)))
theorem-size     29
proof            (modus-ponens tm-51 tm-320 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15287.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((D and E) -> D))), M:tm-51, m:tm-320, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15288
in-theory        15288
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and ((C and D) -> C)))
theorem-size     15
proof            (modus-ponens tm-50 tm-320 ((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15288.        ((A or (B or A)) -> ((B or A) and ((C and D) -> C))), M:tm-50, m:tm-320, u:((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15289
in-theory        15289
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and ((C and D) -> C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-320 ((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15289.        ((A or (A or B)) -> ((A or B) and ((C and D) -> C))), M:tm-49, m:tm-320, u:((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15290
in-theory        15290
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((C and D) -> C)))
theorem-size     19
proof            (modus-ponens tm-48 tm-320 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15290.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((C and D) -> C))), M:tm-48, m:tm-320, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15291
in-theory        15291
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and ((C and D) -> C)))
theorem-size     13
proof            (modus-ponens tm-47 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15291.        (((A and B) or B) -> (B and ((C and D) -> C))), M:tm-47, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15292
in-theory        15292
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and ((C and D) -> C)))
theorem-size     13
proof            (modus-ponens tm-46 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15292.        (((A and B) or A) -> (A and ((C and D) -> C))), M:tm-46, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15293
in-theory        15293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-45 tm-320 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15293.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D and E) -> D))), M:tm-45, m:tm-320, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15294
in-theory        15294
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and ((C and D) -> C)))
theorem-size     15
proof            (modus-ponens tm-44 tm-320 ((Am (-> A B)) (C (and (-> A B) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15294.        ((A or (B -> A)) -> ((B -> A) and ((C and D) -> C))), M:tm-44, m:tm-320, u:((Am (-> A B)) (C (and (-> A B) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15295
in-theory        15295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and ((D and E) -> D))))
theorem-size     15
proof            (modus-ponens tm-42 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15295.        ((A -> (B or A)) and (C -> (C and ((D and E) -> D)))), M:tm-42, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15296
in-theory        15296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and ((D and E) -> D))))
theorem-size     15
proof            (modus-ponens tm-32 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15296.        ((A -> (A or B)) and (C -> (C and ((D and E) -> D)))), M:tm-32, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15297
in-theory        15297
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and ((B and C) -> B))))
theorem-size     11
proof            (modus-ponens tm-24 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15297.        (A -> (A and (A and ((B and C) -> B)))), M:tm-24, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15298
in-theory        15298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and ((D and E) -> D))))
theorem-size     17
proof            (modus-ponens tm-23 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15298.        ((A -> (B -> (A and B))) and (C -> (C and ((D and E) -> D)))), M:tm-23, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15299
in-theory        15299
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and ((D and E) -> D))))
theorem-size     15
proof            (modus-ponens tm-22 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15299.        (((A and B) -> B) and (C -> (C and ((D and E) -> D)))), M:tm-22, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15300
in-theory        15300
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and ((D and E) -> D))))
theorem-size     15
proof            (modus-ponens tm-21 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15300.        (((A and B) -> A) and (C -> (C and ((D and E) -> D)))), M:tm-21, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15301
in-theory        15301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and ((E and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-20 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15301.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and ((E and F) -> E)))), M:tm-20, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15302
in-theory        15302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and ((D and E) -> D))))
theorem-size     15
proof            (modus-ponens tm-19 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15302.        ((A -> (B -> A)) and (C -> (C and ((D and E) -> D)))), M:tm-19, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15303
in-theory        15303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and ((B and C) -> B)))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-9 tm-2 tm-5 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15303.        ((A -> (not (A and ((B and C) -> B)))) -> (not A)), M:tm-9, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15304
in-theory        15304
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) -> B)) -> D) -> ((A or (A and ((B and C) -> B))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15304.        (((A and ((B and C) -> B)) -> D) -> ((A or (A and ((B and C) -> B))) -> D)), M:tm-8, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15305
in-theory        15305
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and ((C and D) -> C))))
theorem-size     11
proof            (modus-ponens tm-7 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-7 tm-2 tm-5 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15305.        (A or (B -> (B and ((C and D) -> C)))), M:tm-7, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15306
in-theory        15306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-6 tm-2 tm-5 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15306.        ((A -> (A and ((B and C) -> B))) or D), M:tm-6, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15307
in-theory        15307
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and ((C and D) -> C))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15307.        (A -> ((B -> (B and ((C and D) -> C))) and A)), M:tm-5, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15308
in-theory        15308
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and ((C and D) -> C))))
theorem-size     11
proof            (modus-ponens tm-1 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-1 tm-2 tm-5 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15308.        (A -> (B -> (B and ((C and D) -> C)))), M:tm-1, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15309
in-theory        15309
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> A) and ((A and (A -> B)) -> B))
theorem-size     15
proof            (modus-ponens tm-321 tm-3 ((A Am) (Bm (-> Am C)) (B Am)))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15309.        (((A and (A -> B)) -> A) and ((A and (A -> B)) -> B)), M:tm-321, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
================================================================
tm-name          tm-15310
in-theory        15310
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> (B -> (C -> B))) and ((A and ((B -> (C -> B)) -> D)) -> D))
theorem-size     27
proof            (modus-ponens tm-321 tm-11 ((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15310.        (((A and ((B -> (C -> B)) -> D)) -> (B -> (C -> B))) and ((A and ((B -> (C -> B)) -> D)) -> D)), M:tm-321, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-15311
in-theory        15311
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E))
theorem-size     51
proof            (modus-ponens tm-321 tm-14 ((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15311.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E)), M:tm-321, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-15312
in-theory        15312
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> ((B and C) -> B)) and ((A and (((B and C) -> B) -> D)) -> D))
theorem-size     27
proof            (modus-ponens tm-321 tm-16 ((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15312.        (((A and (((B and C) -> B) -> D)) -> ((B and C) -> B)) and ((A and (((B and C) -> B) -> D)) -> D)), M:tm-321, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-15313
in-theory        15313
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> ((B and C) -> C)) and ((A and (((B and C) -> C) -> D)) -> D))
theorem-size     27
proof            (modus-ponens tm-321 tm-18 ((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15313.        (((A and (((B and C) -> C) -> D)) -> ((B and C) -> C)) and ((A and (((B and C) -> C) -> D)) -> D)), M:tm-321, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-15314
in-theory        15314
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> (B -> (C -> (B and C)))) and ((A and ((B -> (C -> (B and C))) -> D)) -> D))
theorem-size     33
proof            (modus-ponens tm-321 tm-25 ((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15314.        (((A and ((B -> (C -> (B and C))) -> D)) -> (B -> (C -> (B and C)))) and ((A and ((B -> (C -> (B and C))) -> D)) -> D)), M:tm-321, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-15315
in-theory        15315
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> (B -> (B or C))) and ((A and ((B -> (B or C)) -> D)) -> D))
theorem-size     27
proof            (modus-ponens tm-321 tm-33 ((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15315.        (((A and ((B -> (B or C)) -> D)) -> (B -> (B or C))) and ((A and ((B -> (B or C)) -> D)) -> D)), M:tm-321, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-15316
in-theory        15316
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> (B -> (C or B))) and ((A and ((B -> (C or B)) -> D)) -> D))
theorem-size     27
proof            (modus-ponens tm-321 tm-43 ((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15316.        (((A and ((B -> (C or B)) -> D)) -> (B -> (C or B))) and ((A and ((B -> (C or B)) -> D)) -> D)), M:tm-321, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-15317
in-theory        15317
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) -> E)) -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) -> E)) -> E))
theorem-size     51
proof            (modus-ponens tm-321 tm-56 ((Am (and A (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) C))) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15317.        (((A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) -> E)) -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) -> E)) -> E)), M:tm-321, m:tm-56, u:((Am (and A (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) C))) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-15318
in-theory        15318
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> ((B -> (not C)) -> (not B))) -> D)) -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((A and (((B -> C) -> ((B -> (not C)) -> (not B))) -> D)) -> D))
theorem-size     45
proof            (modus-ponens tm-321 tm-71 ((Am (and A (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) C))) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15318.        (((A and (((B -> C) -> ((B -> (not C)) -> (not B))) -> D)) -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((A and (((B -> C) -> ((B -> (not C)) -> (not B))) -> D)) -> D)), M:tm-321, m:tm-71, u:((Am (and A (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) C))) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-15319
in-theory        15319
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((not (not B)) -> B) -> C)) -> ((not (not B)) -> B)) and ((A and (((not (not B)) -> B) -> C)) -> C))
theorem-size     27
proof            (modus-ponens tm-321 tm-78 ((Am (and A (-> (-> (not (not Bm)) Bm) C))) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-10)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15319.        (((A and (((not (not B)) -> B) -> C)) -> ((not (not B)) -> B)) and ((A and (((not (not B)) -> B) -> C)) -> C)), M:tm-321, m:tm-78, u:((Am (and A (-> (-> (not (not Bm)) Bm) C))) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-15320
in-theory        15320
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (D -> C))) -> E)) -> (B -> (C -> (D -> C)))) and ((A and ((B -> (C -> (D -> C))) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-85 ((Am (and A (-> (-> Bm (-> Cm (-> Dm Cm))) C))) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15320.        (((A and ((B -> (C -> (D -> C))) -> E)) -> (B -> (C -> (D -> C)))) and ((A and ((B -> (C -> (D -> C))) -> E)) -> E)), M:tm-321, m:tm-85, u:((Am (and A (-> (-> Bm (-> Cm (-> Dm Cm))) C))) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-15321
in-theory        15321
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (B -> B)) -> D)) -> ((B -> C) -> (B -> B))) and ((A and (((B -> C) -> (B -> B)) -> D)) -> D))
theorem-size     33
proof            (modus-ponens tm-321 tm-97 ((Am (and A (-> (-> (-> Bm Cm) (-> Bm Bm)) C))) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15321.        (((A and (((B -> C) -> (B -> B)) -> D)) -> ((B -> C) -> (B -> B))) and ((A and (((B -> C) -> (B -> B)) -> D)) -> D)), M:tm-321, m:tm-97, u:((Am (and A (-> (-> (-> Bm Cm) (-> Bm Bm)) C))) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-15322
in-theory        15322
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) -> E)) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((A and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) -> E)) -> E))
theorem-size     69
proof            (modus-ponens tm-321 tm-107 ((Am (and A (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) C))) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15322.        (((A and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) -> E)) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((A and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) -> E)) -> E)), M:tm-321, m:tm-107, u:((Am (and A (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) C))) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-15323
in-theory        15323
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> F))
theorem-size     57
proof            (modus-ponens tm-321 tm-115 ((Am (and A (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) C))) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15323.        (((A and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> F)), M:tm-321, m:tm-115, u:((Am (and A (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) C))) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-15324
in-theory        15324
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> A) and (A -> B)) -> A) and ((((A -> B) -> A) and (A -> B)) -> B))
theorem-size     23
proof            (modus-ponens tm-321 tm-116 ((A (-> (-> Bm C) Bm)) (Am (-> Bm C)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-15324.        (((((A -> B) -> A) and (A -> B)) -> A) and ((((A -> B) -> A) and (A -> B)) -> B)), M:tm-321, m:tm-116, u:((A (-> (-> Bm C) Bm)) (Am (-> Bm C)) (B Bm))
================================================================
tm-name          tm-15325
in-theory        15325
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and (C -> D)) -> C) and ((((A -> (B -> A)) -> C) and (C -> D)) -> D))
theorem-size     27
proof            (modus-ponens tm-321 tm-117 ((A (-> (-> Am (-> Bm Am)) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-15325.        (((((A -> (B -> A)) -> C) and (C -> D)) -> C) and ((((A -> (B -> A)) -> C) and (C -> D)) -> D)), M:tm-321, m:tm-117, u:((A (-> (-> Am (-> Bm Am)) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-15326
in-theory        15326
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and (D -> E)) -> D) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and (D -> E)) -> E))
theorem-size     43
proof            (modus-ponens tm-321 tm-118 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> Dm C)) (B Dm)))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15326.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and (D -> E)) -> D) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and (D -> E)) -> E)), M:tm-321, m:tm-118, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> Dm C)) (B Dm))
================================================================
tm-name          tm-15327
in-theory        15327
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) -> E)) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((A and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) -> E)) -> E))
theorem-size     57
proof            (modus-ponens tm-321 tm-127 ((Am (and A (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) C))) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15327.        (((A and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) -> E)) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((A and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) -> E)) -> E)), M:tm-321, m:tm-127, u:((Am (and A (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) C))) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-15328
in-theory        15328
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and (C -> D)) -> C) and (((((A and B) -> A) -> C) and (C -> D)) -> D))
theorem-size     27
proof            (modus-ponens tm-321 tm-128 ((A (-> (-> (and Am Bm) Am) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-15328.        ((((((A and B) -> A) -> C) and (C -> D)) -> C) and (((((A and B) -> A) -> C) and (C -> D)) -> D)), M:tm-321, m:tm-128, u:((A (-> (-> (and Am Bm) Am) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-15329
in-theory        15329
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> ((C and D) -> C)) -> E)) -> (B -> ((C and D) -> C))) and ((A and ((B -> ((C and D) -> C)) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-136 ((Am (and A (-> (-> Bm (-> (and Cm Dm) Cm)) C))) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15329.        (((A and ((B -> ((C and D) -> C)) -> E)) -> (B -> ((C and D) -> C))) and ((A and ((B -> ((C and D) -> C)) -> E)) -> E)), M:tm-321, m:tm-136, u:((Am (and A (-> (-> Bm (-> (and Cm Dm) Cm)) C))) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-15330
in-theory        15330
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> A)) -> A) and ((A and (A -> A)) -> A))
theorem-size     15
proof            (modus-ponens tm-321 tm-137 ((A Am) (Bm Am) (C Am) (B Am)))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-15330.        (((A and (A -> A)) -> A) and ((A and (A -> A)) -> A)), M:tm-321, m:tm-137, u:((A Am) (Bm Am) (C Am) (B Am))
================================================================
tm-name          tm-15331
in-theory        15331
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> (B -> (C -> B)))) -> (B -> (C -> B))) and ((A and ((B -> (C -> B)) -> (B -> (C -> B)))) -> (B -> (C -> B))))
theorem-size     39
proof            (modus-ponens tm-321 tm-138 ((A Am) (Dm (-> Bm (-> Cm Bm))) (C (-> Bm (-> Cm Bm))) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-15331.        (((A and ((B -> (C -> B)) -> (B -> (C -> B)))) -> (B -> (C -> B))) and ((A and ((B -> (C -> B)) -> (B -> (C -> B)))) -> (B -> (C -> B)))), M:tm-321, m:tm-138, u:((A Am) (Dm (-> Bm (-> Cm Bm))) (C (-> Bm (-> Cm Bm))) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-15332
in-theory        15332
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     87
proof            (modus-ponens tm-321 tm-139 ((A Am) (Em (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       257
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15332.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-321, m:tm-139, u:((A Am) (Em (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-15333
in-theory        15333
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> ((B and C) -> B))) -> ((B and C) -> B)) and ((A and (((B and C) -> B) -> ((B and C) -> B))) -> ((B and C) -> B)))
theorem-size     39
proof            (modus-ponens tm-321 tm-140 ((A Am) (Dm (-> (and Bm Cm) Bm)) (C (-> (and Bm Cm) Bm)) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-15333.        (((A and (((B and C) -> B) -> ((B and C) -> B))) -> ((B and C) -> B)) and ((A and (((B and C) -> B) -> ((B and C) -> B))) -> ((B and C) -> B))), M:tm-321, m:tm-140, u:((A Am) (Dm (-> (and Bm Cm) Bm)) (C (-> (and Bm Cm) Bm)) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-15334
in-theory        15334
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) -> E)) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((A and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) -> E)) -> E))
theorem-size     57
proof            (modus-ponens tm-321 tm-149 ((Am (and A (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) C))) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15334.        (((A and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) -> E)) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((A and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) -> E)) -> E)), M:tm-321, m:tm-149, u:((Am (and A (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) C))) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-15335
in-theory        15335
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> ((B and C) -> C))) -> ((B and C) -> C)) and ((A and (((B and C) -> C) -> ((B and C) -> C))) -> ((B and C) -> C)))
theorem-size     39
proof            (modus-ponens tm-321 tm-150 ((A Am) (Dm (-> (and Bm Cm) Cm)) (C (-> (and Bm Cm) Cm)) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-15335.        (((A and (((B and C) -> C) -> ((B and C) -> C))) -> ((B and C) -> C)) and ((A and (((B and C) -> C) -> ((B and C) -> C))) -> ((B and C) -> C))), M:tm-321, m:tm-150, u:((A Am) (Dm (-> (and Bm Cm) Cm)) (C (-> (and Bm Cm) Cm)) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-15336
in-theory        15336
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and (C -> D)) -> C) and (((((A and B) -> B) -> C) and (C -> D)) -> D))
theorem-size     27
proof            (modus-ponens tm-321 tm-151 ((A (-> (-> (and Am Bm) Bm) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-15336.        ((((((A and B) -> B) -> C) and (C -> D)) -> C) and (((((A and B) -> B) -> C) and (C -> D)) -> D)), M:tm-321, m:tm-151, u:((A (-> (-> (and Am Bm) Bm) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-15337
in-theory        15337
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> ((C and D) -> D)) -> E)) -> (B -> ((C and D) -> D))) and ((A and ((B -> ((C and D) -> D)) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-159 ((Am (and A (-> (-> Bm (-> (and Cm Dm) Dm)) C))) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15337.        (((A and ((B -> ((C and D) -> D)) -> E)) -> (B -> ((C and D) -> D))) and ((A and ((B -> ((C and D) -> D)) -> E)) -> E)), M:tm-321, m:tm-159, u:((Am (and A (-> (-> Bm (-> (and Cm Dm) Dm)) C))) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-15338
in-theory        15338
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> ((C -> (D -> C)) and B)) -> E)) -> (B -> ((C -> (D -> C)) and B))) and ((A and ((B -> ((C -> (D -> C)) and B)) -> E)) -> E))
theorem-size     39
proof            (modus-ponens tm-321 tm-184 ((Am (and A (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) C))) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15338.        (((A and ((B -> ((C -> (D -> C)) and B)) -> E)) -> (B -> ((C -> (D -> C)) and B))) and ((A and ((B -> ((C -> (D -> C)) and B)) -> E)) -> E)), M:tm-321, m:tm-184, u:((Am (and A (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) C))) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-15339
in-theory        15339
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) -> F)) -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((A and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) -> F)) -> F))
theorem-size     63
proof            (modus-ponens tm-321 tm-211 ((Am (and A (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) C))) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15339.        (((A and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) -> F)) -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((A and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) -> F)) -> F)), M:tm-321, m:tm-211, u:((Am (and A (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) C))) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-15340
in-theory        15340
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (((C and D) -> C) and B)) -> E)) -> (B -> (((C and D) -> C) and B))) and ((A and ((B -> (((C and D) -> C) and B)) -> E)) -> E))
theorem-size     39
proof            (modus-ponens tm-321 tm-240 ((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) C))) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15340.        (((A and ((B -> (((C and D) -> C) and B)) -> E)) -> (B -> (((C and D) -> C) and B))) and ((A and ((B -> (((C and D) -> C) and B)) -> E)) -> E)), M:tm-321, m:tm-240, u:((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) C))) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-15341
in-theory        15341
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (((C and D) -> D) and B)) -> E)) -> (B -> (((C and D) -> D) and B))) and ((A and ((B -> (((C and D) -> D) and B)) -> E)) -> E))
theorem-size     39
proof            (modus-ponens tm-321 tm-271 ((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) C))) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15341.        (((A and ((B -> (((C and D) -> D) and B)) -> E)) -> (B -> (((C and D) -> D) and B))) and ((A and ((B -> (((C and D) -> D) and B)) -> E)) -> E)), M:tm-321, m:tm-271, u:((Am (and A (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) C))) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-15342
in-theory        15342
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> ((C -> (D -> (C and D))) and B)) -> E)) -> (B -> ((C -> (D -> (C and D))) and B))) and ((A and ((B -> ((C -> (D -> (C and D))) and B)) -> E)) -> E))
theorem-size     45
proof            (modus-ponens tm-321 tm-304 ((Am (and A (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) C))) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15342.        (((A and ((B -> ((C -> (D -> (C and D))) and B)) -> E)) -> (B -> ((C -> (D -> (C and D))) and B))) and ((A and ((B -> ((C -> (D -> (C and D))) and B)) -> E)) -> E)), M:tm-321, m:tm-304, u:((Am (and A (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) C))) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-15343
in-theory        15343
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((D and E) -> D))
theorem-size     29
proof            (modus-ponens tm-320 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15343.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15344
in-theory        15344
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-318 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15344.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15345
in-theory        15345
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)))
theorem-size     39
proof            (modus-ponens tm-316 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15345.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B))), M:tm-316, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-15346
in-theory        15346
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (D -> (E -> D)))
theorem-size     29
proof            (modus-ponens tm-315 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15346.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15347
in-theory        15347
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((((A and (B -> C)) -> B) -> (not (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))) -> (not ((A and (B -> C)) -> B))))
theorem-size     57
proof            (modus-ponens tm-313 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15347.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((((A and (B -> C)) -> B) -> (not (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))) -> (not ((A and (B -> C)) -> B)))), M:tm-313, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-15348
in-theory        15348
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)) -> D) -> ((((A and (B -> C)) -> B) or (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) -> D)))
theorem-size     67
proof            (modus-ponens tm-312 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15348.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)) -> D) -> ((((A and (B -> C)) -> B) or (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) -> D))), M:tm-312, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-15349
in-theory        15349
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (D or (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15349.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (D or (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))), M:tm-311, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15350
in-theory        15350
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) or D))
theorem-size     49
proof            (modus-ponens tm-310 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15350.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) or D)), M:tm-310, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15351
in-theory        15351
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (D -> ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and D)))
theorem-size     51
proof            (modus-ponens tm-309 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15351.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (D -> ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and D))), M:tm-309, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15352
in-theory        15352
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (D -> (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15352.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (D -> (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))), M:tm-305, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15353
in-theory        15353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     35
proof            (modus-ponens tm-303 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15353.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-303, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15354
in-theory        15354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     33
proof            (modus-ponens tm-270 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15354.        ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-270, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15355
in-theory        15355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     33
proof            (modus-ponens tm-239 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15355.        ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-239, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15356
in-theory        15356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) -> F) -> (((E and (F -> G)) -> F) and ((E and (F -> G)) -> G))))
theorem-size     41
proof            (modus-ponens tm-210 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15356.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) -> F) -> (((E and (F -> G)) -> F) and ((E and (F -> G)) -> G)))), M:tm-210, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15357
in-theory        15357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     33
proof            (modus-ponens tm-183 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15357.        ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-183, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15358
in-theory        15358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-157 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15358.        ((A -> ((B and C) -> C)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-157, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15359
in-theory        15359
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     39
proof            (modus-ponens tm-147 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15359.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-147, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15360
in-theory        15360
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> B)) -> B) or ((A and (B -> B)) -> B)) -> (((A and (B -> B)) -> B) and ((A and (B -> B)) -> B)))
theorem-size     31
proof            (modus-ponens tm-144 tm-321 ((A Am) (B Cm) (Bm Cm) (C Cm) (D (and (-> (and Am (-> Cm Cm)) Cm) (-> (and Am (-> Cm Cm)) Cm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15360.        ((((A and (B -> B)) -> B) or ((A and (B -> B)) -> B)) -> (((A and (B -> B)) -> B) and ((A and (B -> B)) -> B))), M:tm-144, m:tm-321, u:((A Am) (B Cm) (Bm Cm) (C Cm) (D (and (-> (and Am (-> Cm Cm)) Cm) (-> (and Am (-> Cm Cm)) Cm))))
================================================================
tm-name          tm-15361
in-theory        15361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-134 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15361.        ((A -> ((B and C) -> B)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-134, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15362
in-theory        15362
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (B -> C)) -> B)) -> (((B and (B -> C)) -> B) and ((B and (B -> C)) -> C)))
theorem-size     25
proof            (modus-ponens tm-131 tm-321 ((Bm Am) (B (-> Am Cm)) (A Am) (C (and (-> (and Am (-> Am Cm)) Am) (-> (and Am (-> Am Cm)) Cm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15362.        ((A or ((B and (B -> C)) -> B)) -> (((B and (B -> C)) -> B) and ((B and (B -> C)) -> C))), M:tm-131, m:tm-321, u:((Bm Am) (B (-> Am Cm)) (A Am) (C (and (-> (and Am (-> Am Cm)) Am) (-> (and Am (-> Am Cm)) Cm))))
================================================================
tm-name          tm-15363
in-theory        15363
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     39
proof            (modus-ponens tm-125 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15363.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-125, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15364
in-theory        15364
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and (B -> C)) -> A) or (((A -> B) and (B -> C)) -> B)) -> ((((A -> B) and (B -> C)) -> B) and (((A -> B) and (B -> C)) -> C)))
theorem-size     39
proof            (modus-ponens tm-122 tm-321 ((Am (-> A Bm)) (C (-> Bm Cm)) (B Bm) (D (and (-> (and (-> A Bm) (-> Bm Cm)) Bm) (-> (and (-> A Bm) (-> Bm Cm)) Cm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-4)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15364.        (((((A -> B) and (B -> C)) -> A) or (((A -> B) and (B -> C)) -> B)) -> ((((A -> B) and (B -> C)) -> B) and (((A -> B) and (B -> C)) -> C))), M:tm-122, m:tm-321, u:((Am (-> A Bm)) (C (-> Bm Cm)) (B Bm) (D (and (-> (and (-> A Bm) (-> Bm Cm)) Bm) (-> (and (-> A Bm) (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-15365
in-theory        15365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) -> F) -> (((E and (F -> G)) -> F) and ((E and (F -> G)) -> G))))
theorem-size     39
proof            (modus-ponens tm-113 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15365.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) -> F) -> (((E and (F -> G)) -> F) and ((E and (F -> G)) -> G)))), M:tm-113, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15366
in-theory        15366
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     43
proof            (modus-ponens tm-105 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15366.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-105, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15367
in-theory        15367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E))))
theorem-size     31
proof            (modus-ponens tm-95 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15367.        (((A -> B) -> (A -> A)) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E)))), M:tm-95, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15368
in-theory        15368
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> (D -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))
theorem-size     25
proof            (modus-ponens tm-84 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15368.        (((A and (B -> C)) -> B) -> (D -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))), M:tm-84, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-15369
in-theory        15369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-83 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15369.        ((A -> (B -> (C -> B))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-83, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15370
in-theory        15370
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (C -> D)) -> C) -> (((B and (C -> D)) -> C) and ((B and (C -> D)) -> D))))
theorem-size     29
proof            (modus-ponens tm-76 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15370.        (((not (not A)) -> A) and (((B and (C -> D)) -> C) -> (((B and (C -> D)) -> C) and ((B and (C -> D)) -> D)))), M:tm-76, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15371
in-theory        15371
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (B -> C)) -> B))) or ((A and (B -> C)) -> B)) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-73 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15371.        (((not (not ((A and (B -> C)) -> B))) or ((A and (B -> C)) -> B)) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-73, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-15372
in-theory        15372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E))))
theorem-size     35
proof            (modus-ponens tm-69 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15372.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E)))), M:tm-69, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15373
in-theory        15373
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     37
proof            (modus-ponens tm-54 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15373.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-54, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15374
in-theory        15374
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (((B and (C -> D)) -> C) and ((B and (C -> D)) -> D)))
theorem-size     33
proof            (modus-ponens tm-47 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15374.        (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (((B and (C -> D)) -> C) and ((B and (C -> D)) -> D))), M:tm-47, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-15375
in-theory        15375
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-46 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15375.        (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-46, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-15376
in-theory        15376
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (A -> C)) -> A)) -> (((B and (A -> C)) -> A) and ((B and (A -> C)) -> C)))
theorem-size     25
proof            (modus-ponens tm-44 tm-321 ((A (and Am (-> Bm Cm))) (B Bm) (C (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15376.        ((A or ((B and (A -> C)) -> A)) -> (((B and (A -> C)) -> A) and ((B and (A -> C)) -> C))), M:tm-44, m:tm-321, u:((A (and Am (-> Bm Cm))) (B Bm) (C (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-15377
in-theory        15377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E))))
theorem-size     29
proof            (modus-ponens tm-42 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15377.        ((A -> (B or A)) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E)))), M:tm-42, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15378
in-theory        15378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E))))
theorem-size     29
proof            (modus-ponens tm-32 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15378.        ((A -> (A or B)) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E)))), M:tm-32, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15379
in-theory        15379
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))
theorem-size     31
proof            (modus-ponens tm-24 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15379.        (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))), M:tm-24, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-15380
in-theory        15380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E))))
theorem-size     31
proof            (modus-ponens tm-23 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15380.        ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E)))), M:tm-23, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15381
in-theory        15381
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E))))
theorem-size     29
proof            (modus-ponens tm-22 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15381.        (((A and B) -> B) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E)))), M:tm-22, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15382
in-theory        15382
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E))))
theorem-size     29
proof            (modus-ponens tm-21 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15382.        (((A and B) -> A) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E)))), M:tm-21, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15383
in-theory        15383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     37
proof            (modus-ponens tm-20 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15383.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-20, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15384
in-theory        15384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E))))
theorem-size     29
proof            (modus-ponens tm-19 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15384.        ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E)))), M:tm-19, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15385
in-theory        15385
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (not (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))) -> (not ((A and (B -> C)) -> B)))
theorem-size     33
proof            (modus-ponens tm-9 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-9 tm-2 tm-5 tm-4)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15385.        ((((A and (B -> C)) -> B) -> (not (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-15386
in-theory        15386
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)) -> D) -> ((((A and (B -> C)) -> B) or (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) -> D))
theorem-size     43
proof            (modus-ponens tm-8 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15386.        (((((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)) -> D) -> ((((A and (B -> C)) -> B) or (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) -> D)), M:tm-8, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-15387
in-theory        15387
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (C -> D)) -> C) -> (((B and (C -> D)) -> C) and ((B and (C -> D)) -> D))))
theorem-size     25
proof            (modus-ponens tm-7 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-7 tm-2 tm-5 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15387.        (A or (((B and (C -> D)) -> C) -> (((B and (C -> D)) -> C) and ((B and (C -> D)) -> D)))), M:tm-7, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15388
in-theory        15388
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) or D)
theorem-size     25
proof            (modus-ponens tm-6 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-6 tm-2 tm-5 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15388.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) or D), M:tm-6, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15389
in-theory        15389
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (C -> D)) -> C) -> (((B and (C -> D)) -> C) and ((B and (C -> D)) -> D))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15389.        (A -> ((((B and (C -> D)) -> C) -> (((B and (C -> D)) -> C) and ((B and (C -> D)) -> D))) and A)), M:tm-5, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15390
in-theory        15390
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (C -> D)) -> C) -> (((B and (C -> D)) -> C) and ((B and (C -> D)) -> D))))
theorem-size     25
proof            (modus-ponens tm-1 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-1 tm-2 tm-5 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15390.        (A -> (((B and (C -> D)) -> C) -> (((B and (C -> D)) -> C) and ((B and (C -> D)) -> D)))), M:tm-1, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15391
in-theory        15391
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-322 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15391.        (((A -> B) -> (A -> (A and B))) and ((C and D) -> D)), M:tm-322, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-15392
in-theory        15392
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15392.        ((A -> (B -> (C -> (B and C)))) and ((D and E) -> E)), M:tm-322, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-15393
in-theory        15393
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-322 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15393.        (((A -> (B -> A)) or C) and ((D and E) -> E)), M:tm-322, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-15394
in-theory        15394
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15394.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and F) -> F)), M:tm-322, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-15395
in-theory        15395
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-322 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15395.        ((((A and B) -> A) or C) and ((D and E) -> E)), M:tm-322, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-15396
in-theory        15396
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-322 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15396.        ((((A and B) -> B) or C) and ((D and E) -> E)), M:tm-322, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-15397
in-theory        15397
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15397.        (((A -> (B -> (A and B))) or C) and ((D and E) -> E)), M:tm-322, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-15398
in-theory        15398
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-322 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15398.        (((A -> (A or B)) or C) and ((D and E) -> E)), M:tm-322, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-15399
in-theory        15399
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15399.        ((A -> ((B -> (B or C)) and A)) and ((D and E) -> E)), M:tm-322, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-15400
in-theory        15400
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-322 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15400.        ((A -> (B -> (B or C))) and ((D and E) -> E)), M:tm-322, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-15401
in-theory        15401
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-322 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15401.        ((A or (B -> (C -> B))) and ((D and E) -> E)), M:tm-322, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-15402
in-theory        15402
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15402.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> F)), M:tm-322, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-15403
in-theory        15403
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-322 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15403.        ((A or ((B and C) -> B)) and ((D and E) -> E)), M:tm-322, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15404
in-theory        15404
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-322 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15404.        ((A or ((B and C) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15405
in-theory        15405
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15405.        ((A or (B -> (C -> (B and C)))) and ((D and E) -> E)), M:tm-322, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-15406
in-theory        15406
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-322 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15406.        ((A or (B -> (B or C))) and ((D and E) -> E)), M:tm-322, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-15407
in-theory        15407
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-322 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15407.        ((A or (B -> (C or B))) and ((D and E) -> E)), M:tm-322, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-15408
in-theory        15408
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-322 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15408.        (((A -> (B or A)) or C) and ((D and E) -> E)), M:tm-322, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-15409
in-theory        15409
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15409.        ((A -> ((B -> (C or B)) and A)) and ((D and E) -> E)), M:tm-322, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-15410
in-theory        15410
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-322 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15410.        ((A -> (B -> (C or B))) and ((D and E) -> E)), M:tm-322, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-15411
in-theory        15411
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-15411.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-15412
in-theory        15412
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and F) -> F))
theorem-size     31
proof            (modus-ponens tm-322 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-15412.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-15413
in-theory        15413
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15413.        (((A -> B) -> (((A and C) or A) -> B)) and ((D and E) -> E)), M:tm-322, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-15414
in-theory        15414
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-15414.        (((A -> B) -> (((C and A) or A) -> B)) and ((D and E) -> E)), M:tm-322, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-15415
in-theory        15415
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-322 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-15415.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-15416
in-theory        15416
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-15416.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-15417
in-theory        15417
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-15417.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-15418
in-theory        15418
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and F) -> F))
theorem-size     33
proof            (modus-ponens tm-322 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-15418.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-15419
in-theory        15419
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15419.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and F) -> F)), M:tm-322, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-15420
in-theory        15420
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15420.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E and F) -> F)), M:tm-322, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-15421
in-theory        15421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15421.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((E and F) -> F)), M:tm-322, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-15422
in-theory        15422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-322 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-15422.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-15423
in-theory        15423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15423.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E and F) -> F)), M:tm-322, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-15424
in-theory        15424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-322 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-15424.        (((A -> (not (B -> A))) -> (not A)) and ((C and D) -> D)), M:tm-322, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-15425
in-theory        15425
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((D and E) -> E))
theorem-size     27
proof            (modus-ponens tm-322 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-15425.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((D and E) -> E)), M:tm-322, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-15426
in-theory        15426
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-322 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15426.        ((((A and B) -> (not A)) -> (not (A and B))) and ((C and D) -> D)), M:tm-322, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-15427
in-theory        15427
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-322 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-15427.        ((((A and B) -> (not B)) -> (not (A and B))) and ((C and D) -> D)), M:tm-322, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-15428
in-theory        15428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-322 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-15428.        (((A -> (not (B -> (A and B)))) -> (not A)) and ((C and D) -> D)), M:tm-322, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-15429
in-theory        15429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-322 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-15429.        (((A -> (not (A or B))) -> (not A)) and ((C and D) -> D)), M:tm-322, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-15430
in-theory        15430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-322 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-15430.        (((A -> (not (B or A))) -> (not A)) and ((C and D) -> D)), M:tm-322, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-15431
in-theory        15431
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-322 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-15431.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((D and E) -> E)), M:tm-322, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-15432
in-theory        15432
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((C and D) -> D))
theorem-size     23
proof            (modus-ponens tm-322 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-15432.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((C and D) -> D)), M:tm-322, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-15433
in-theory        15433
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((D and E) -> E))
theorem-size     29
proof            (modus-ponens tm-322 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-15433.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-15434
in-theory        15434
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15434.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D and E) -> E)), M:tm-322, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-15435
in-theory        15435
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15435.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((D and E) -> E)), M:tm-322, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-15436
in-theory        15436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15436.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((D and E) -> E)), M:tm-322, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-15437
in-theory        15437
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((C and D) -> D))
theorem-size     21
proof            (modus-ponens tm-322 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-15437.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((C and D) -> D)), M:tm-322, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-15438
in-theory        15438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15438.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D and E) -> E)), M:tm-322, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-15439
in-theory        15439
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((B and C) -> C))
theorem-size     17
proof            (modus-ponens tm-322 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-15439.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((B and C) -> C)), M:tm-322, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-15440
in-theory        15440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-322 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-10)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-15440.        (((A -> B) -> (((not (not A)) or A) -> B)) and ((C and D) -> D)), M:tm-322, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-15441
in-theory        15441
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-322 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15441.        ((A or ((not (not B)) -> B)) and ((C and D) -> D)), M:tm-322, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-15442
in-theory        15442
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-322 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15442.        ((((not (not A)) -> A) or B) and ((C and D) -> D)), M:tm-322, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-15443
in-theory        15443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-322 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15443.        ((A -> (((not (not B)) -> B) and A)) and ((C and D) -> D)), M:tm-322, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-15444
in-theory        15444
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((C and D) -> D))
theorem-size     21
proof            (modus-ponens tm-322 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-10)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-15444.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((C and D) -> D)), M:tm-322, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-15445
in-theory        15445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-322 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15445.        ((A -> ((not (not B)) -> B)) and ((C and D) -> D)), M:tm-322, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-15446
in-theory        15446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-15446.        (((A -> (not (B -> (C -> B)))) -> (not A)) and ((D and E) -> E)), M:tm-322, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-15447
in-theory        15447
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-15447.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-15448
in-theory        15448
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15448.        ((A or (B -> (C -> (D -> C)))) and ((E and F) -> F)), M:tm-322, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-15449
in-theory        15449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15449.        (((A -> (B -> (C -> B))) or D) and ((E and F) -> F)), M:tm-322, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-15450
in-theory        15450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15450.        ((A -> ((B -> (C -> (D -> C))) and A)) and ((E and F) -> F)), M:tm-322, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-15451
in-theory        15451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-15451.        (((A -> B) -> (A -> (C -> B))) and ((D and E) -> E)), M:tm-322, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-15452
in-theory        15452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15452.        ((A -> (B -> (C -> (D -> C)))) and ((E and F) -> F)), M:tm-322, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-15453
in-theory        15453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and ((B and C) -> C))
theorem-size     9
proof            (modus-ponens tm-322 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       97
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-15453.        ((A -> A) and ((B and C) -> C)), M:tm-322, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-15454
in-theory        15454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-15454.        (((A -> (B -> C)) -> (A -> (B -> C))) and ((D and E) -> E)), M:tm-322, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-15455
in-theory        15455
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-322 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15455.        (((A and B) -> (A and B)) and ((C and D) -> D)), M:tm-322, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-15456
in-theory        15456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-322 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-15456.        (((A -> B) -> (A -> B)) and ((C and D) -> D)), M:tm-322, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-15457
in-theory        15457
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and ((B and C) -> C))
theorem-size     13
proof            (modus-ponens tm-322 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-10)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-15457.        (((not (not A)) -> (not (not A))) and ((B and C) -> C)), M:tm-322, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-15458
in-theory        15458
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((C and D) -> D))
theorem-size     19
proof            (modus-ponens tm-322 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-15458.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((C and D) -> D)), M:tm-322, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-15459
in-theory        15459
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-15459.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((D and E) -> E)), M:tm-322, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-15460
in-theory        15460
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15460.        ((A or ((B -> C) -> (B -> B))) and ((D and E) -> E)), M:tm-322, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-15461
in-theory        15461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15461.        ((((A -> B) -> (A -> A)) or C) and ((D and E) -> E)), M:tm-322, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-15462
in-theory        15462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15462.        ((A -> (((B -> C) -> (B -> B)) and A)) and ((D and E) -> E)), M:tm-322, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-15463
in-theory        15463
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-322 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-15463.        ((((A -> B) -> A) -> ((A -> B) -> A)) and ((C and D) -> D)), M:tm-322, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-15464
in-theory        15464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15464.        ((A -> ((B -> C) -> (B -> B))) and ((D and E) -> E)), M:tm-322, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-15465
in-theory        15465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-15465.        (((A -> ((B -> A) -> C)) -> (A -> C)) and ((D and E) -> E)), M:tm-322, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-15466
in-theory        15466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-322 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-15466.        (((A -> (A -> B)) -> (A -> B)) and ((C and D) -> D)), M:tm-322, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-15467
in-theory        15467
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-322 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-15467.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((D and E) -> E)), M:tm-322, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-15468
in-theory        15468
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((D and E) -> E))
theorem-size     37
proof            (modus-ponens tm-322 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-15468.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((D and E) -> E)), M:tm-322, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-15469
in-theory        15469
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((E and F) -> F))
theorem-size     39
proof            (modus-ponens tm-322 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-15469.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-15470
in-theory        15470
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15470.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E and F) -> F)), M:tm-322, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-15471
in-theory        15471
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15471.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and ((E and F) -> F)), M:tm-322, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-15472
in-theory        15472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((E and F) -> F))
theorem-size     29
proof            (modus-ponens tm-322 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15472.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((E and F) -> F)), M:tm-322, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-15473
in-theory        15473
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((D and E) -> E))
theorem-size     35
proof            (modus-ponens tm-322 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-15473.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((D and E) -> E)), M:tm-322, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-15474
in-theory        15474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15474.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E and F) -> F)), M:tm-322, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-15475
in-theory        15475
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((E and F) -> F))
theorem-size     29
proof            (modus-ponens tm-322 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-15475.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-15476
in-theory        15476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15476.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((E and F) -> F)), M:tm-322, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-15477
in-theory        15477
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((F and G) -> G))
theorem-size     39
proof            (modus-ponens tm-322 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15477.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((F and G) -> G)), M:tm-322, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-15478
in-theory        15478
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15478.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> G)), M:tm-322, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-15479
in-theory        15479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15479.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F and G) -> G)), M:tm-322, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-15480
in-theory        15480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15480.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F and G) -> G)), M:tm-322, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-15481
in-theory        15481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-15481.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((E and F) -> F)), M:tm-322, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-15482
in-theory        15482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15482.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> G)), M:tm-322, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-15483
in-theory        15483
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-322 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-15483.        ((((A -> B) and A) -> B) and ((C and D) -> D)), M:tm-322, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-15484
in-theory        15484
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-15484.        (((((A -> (B -> A)) -> C) and D) -> C) and ((E and F) -> F)), M:tm-322, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-15485
in-theory        15485
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15485.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((F and G) -> G)), M:tm-322, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-15486
in-theory        15486
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((D and E) -> E))
theorem-size     27
proof            (modus-ponens tm-322 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-15486.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((D and E) -> E)), M:tm-322, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-15487
in-theory        15487
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-15487.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((D and E) -> E)), M:tm-322, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-15488
in-theory        15488
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((D and E) -> E))
theorem-size     31
proof            (modus-ponens tm-322 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-15488.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((D and E) -> E)), M:tm-322, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-15489
in-theory        15489
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((E and F) -> F))
theorem-size     33
proof            (modus-ponens tm-322 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-15489.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-15490
in-theory        15490
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15490.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E and F) -> F)), M:tm-322, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-15491
in-theory        15491
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15491.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((E and F) -> F)), M:tm-322, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-15492
in-theory        15492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15492.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-15493
in-theory        15493
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((D and E) -> E))
theorem-size     29
proof            (modus-ponens tm-322 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-15493.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((D and E) -> E)), M:tm-322, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-15494
in-theory        15494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15494.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E and F) -> F)), M:tm-322, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-15495
in-theory        15495
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-15495.        ((((((A and B) -> A) -> C) and D) -> C) and ((E and F) -> F)), M:tm-322, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-15496
in-theory        15496
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-15496.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-15497
in-theory        15497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15497.        (((A -> (not ((B and C) -> B))) -> (not A)) and ((D and E) -> E)), M:tm-322, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-15498
in-theory        15498
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15498.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-15499
in-theory        15499
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15499.        ((A or (B -> ((C and D) -> C))) and ((E and F) -> F)), M:tm-322, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-15500
in-theory        15500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15500.        (((A -> ((B and C) -> B)) or D) and ((E and F) -> F)), M:tm-322, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-15501
in-theory        15501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15501.        ((A -> ((B -> ((C and D) -> C)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-15502
in-theory        15502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-15502.        (((A -> (B and C)) -> (A -> B)) and ((D and E) -> E)), M:tm-322, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-15503
in-theory        15503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15503.        ((A -> (B -> ((C and D) -> C))) and ((E and F) -> F)), M:tm-322, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-15504
in-theory        15504
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-322 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-15504.        (((A and (A -> B)) -> B) and ((C and D) -> D)), M:tm-322, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-15505
in-theory        15505
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-15505.        (((A and ((B -> (C -> B)) -> D)) -> D) and ((E and F) -> F)), M:tm-322, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-15506
in-theory        15506
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15506.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((F and G) -> G)), M:tm-322, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-15507
in-theory        15507
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-15507.        (((A and (((B and C) -> B) -> D)) -> D) and ((E and F) -> F)), M:tm-322, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-15508
in-theory        15508
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((D and E) -> E))
theorem-size     27
proof            (modus-ponens tm-322 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-15508.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-15509
in-theory        15509
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15509.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((D and E) -> E)), M:tm-322, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-15510
in-theory        15510
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((D and E) -> E))
theorem-size     31
proof            (modus-ponens tm-322 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15510.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((D and E) -> E)), M:tm-322, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-15511
in-theory        15511
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((E and F) -> F))
theorem-size     33
proof            (modus-ponens tm-322 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15511.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-15512
in-theory        15512
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15512.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-15513
in-theory        15513
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15513.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and ((E and F) -> F)), M:tm-322, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-15514
in-theory        15514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15514.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-15515
in-theory        15515
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((D and E) -> E))
theorem-size     29
proof            (modus-ponens tm-322 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-15515.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-15516
in-theory        15516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15516.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-15517
in-theory        15517
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-15517.        (((A and (((B and C) -> C) -> D)) -> D) and ((E and F) -> F)), M:tm-322, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-15518
in-theory        15518
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-15518.        ((((((A and B) -> B) -> C) and D) -> C) and ((E and F) -> F)), M:tm-322, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-15519
in-theory        15519
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-15519.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-15520
in-theory        15520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15520.        (((A -> (not ((B and C) -> C))) -> (not A)) and ((D and E) -> E)), M:tm-322, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-15521
in-theory        15521
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15521.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-15522
in-theory        15522
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15522.        ((A or (B -> ((C and D) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-15523
in-theory        15523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15523.        (((A -> ((B and C) -> C)) or D) and ((E and F) -> F)), M:tm-322, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-15524
in-theory        15524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15524.        ((A -> ((B -> ((C and D) -> D)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-15525
in-theory        15525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-15525.        (((A -> (B and C)) -> (A -> C)) and ((D and E) -> E)), M:tm-322, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-15526
in-theory        15526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15526.        ((A -> (B -> ((C and D) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-15527
in-theory        15527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15527.        (((A -> (B -> A)) and (C -> (D -> C))) and ((E and F) -> F)), M:tm-322, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-15528
in-theory        15528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15528.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-15529
in-theory        15529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15529.        (((A -> (B -> A)) and ((C and D) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-15530
in-theory        15530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15530.        (((A -> (B -> A)) and ((C and D) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-15531
in-theory        15531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15531.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-15532
in-theory        15532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15532.        (((A -> (B -> A)) and (C -> (C or D))) and ((E and F) -> F)), M:tm-322, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-15533
in-theory        15533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15533.        (((A -> (B -> A)) and (C -> (D or C))) and ((E and F) -> F)), M:tm-322, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-15534
in-theory        15534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15534.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-15535
in-theory        15535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15535.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> F)), M:tm-322, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-15536
in-theory        15536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15536.        (((A -> (B -> A)) and ((not (not C)) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-15537
in-theory        15537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15537.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and ((F and G) -> G)), M:tm-322, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-15538
in-theory        15538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15538.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((E and F) -> F)), M:tm-322, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-15539
in-theory        15539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> G))
theorem-size     31
proof            (modus-ponens tm-322 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15539.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-15540
in-theory        15540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15540.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-15541
in-theory        15541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15541.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-15542
in-theory        15542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15542.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-15543
in-theory        15543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15543.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-15544
in-theory        15544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15544.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-15545
in-theory        15545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15545.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-15546
in-theory        15546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-15546.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((D and E) -> E)), M:tm-322, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-15547
in-theory        15547
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-15547.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-15548
in-theory        15548
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15548.        ((A or (B -> ((C -> (D -> C)) and B))) and ((E and F) -> F)), M:tm-322, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-15549
in-theory        15549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15549.        (((A -> ((B -> (C -> B)) and A)) or D) and ((E and F) -> F)), M:tm-322, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-15550
in-theory        15550
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15550.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-15551
in-theory        15551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15551.        ((A -> (B -> ((C -> (D -> C)) and B))) and ((E and F) -> F)), M:tm-322, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-15552
in-theory        15552
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15552.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((F and G) -> G)), M:tm-322, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-15553
in-theory        15553
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G and H) -> H))
theorem-size     33
proof            (modus-ponens tm-322 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15553.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G and H) -> H)), M:tm-322, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-15554
in-theory        15554
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15554.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((F and G) -> G)), M:tm-322, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-15555
in-theory        15555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15555.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((F and G) -> G)), M:tm-322, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-15556
in-theory        15556
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15556.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((F and G) -> G)), M:tm-322, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-15557
in-theory        15557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15557.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((F and G) -> G)), M:tm-322, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-15558
in-theory        15558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15558.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((F and G) -> G)), M:tm-322, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-15559
in-theory        15559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G and H) -> H))
theorem-size     33
proof            (modus-ponens tm-322 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15559.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G and H) -> H)), M:tm-322, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-15560
in-theory        15560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F and G) -> G))
theorem-size     31
proof            (modus-ponens tm-322 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15560.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F and G) -> G)), M:tm-322, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-15561
in-theory        15561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-10)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15561.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-15562
in-theory        15562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15562.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((G and H) -> H)), M:tm-322, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-15563
in-theory        15563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15563.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((F and G) -> G)), M:tm-322, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-15564
in-theory        15564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G and H) -> H))
theorem-size     39
proof            (modus-ponens tm-322 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15564.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G and H) -> H)), M:tm-322, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-15565
in-theory        15565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H and I) -> I))
theorem-size     35
proof            (modus-ponens tm-322 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15565.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H and I) -> I)), M:tm-322, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-15566
in-theory        15566
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G and H) -> H))
theorem-size     35
proof            (modus-ponens tm-322 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15566.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G and H) -> H)), M:tm-322, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-15567
in-theory        15567
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15567.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((G and H) -> H)), M:tm-322, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-15568
in-theory        15568
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G and H) -> H))
theorem-size     35
proof            (modus-ponens tm-322 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15568.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-15569
in-theory        15569
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15569.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-15570
in-theory        15570
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15570.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G and H) -> H)), M:tm-322, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-15571
in-theory        15571
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H and I) -> I))
theorem-size     37
proof            (modus-ponens tm-322 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15571.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H and I) -> I)), M:tm-322, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-15572
in-theory        15572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15572.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> H)), M:tm-322, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-15573
in-theory        15573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-15573.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((E and F) -> F)), M:tm-322, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-15574
in-theory        15574
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((F and G) -> G))
theorem-size     43
proof            (modus-ponens tm-322 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-15574.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((F and G) -> G)), M:tm-322, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-15575
in-theory        15575
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15575.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F and G) -> G)), M:tm-322, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-15576
in-theory        15576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15576.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and ((F and G) -> G)), M:tm-322, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-15577
in-theory        15577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15577.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((F and G) -> G)), M:tm-322, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-15578
in-theory        15578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15578.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F and G) -> G)), M:tm-322, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-15579
in-theory        15579
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15579.        ((((A and B) -> A) and (C -> (D -> C))) and ((E and F) -> F)), M:tm-322, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-15580
in-theory        15580
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15580.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-15581
in-theory        15581
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15581.        ((((A and B) -> A) and ((C and D) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-15582
in-theory        15582
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15582.        ((((A and B) -> A) and ((C and D) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-15583
in-theory        15583
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15583.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-15584
in-theory        15584
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15584.        ((((A and B) -> A) and (C -> (C or D))) and ((E and F) -> F)), M:tm-322, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-15585
in-theory        15585
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15585.        ((((A and B) -> A) and (C -> (D or C))) and ((E and F) -> F)), M:tm-322, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-15586
in-theory        15586
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15586.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-15587
in-theory        15587
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15587.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> F)), M:tm-322, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-15588
in-theory        15588
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15588.        ((((A and B) -> A) and ((not (not C)) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-15589
in-theory        15589
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15589.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((F and G) -> G)), M:tm-322, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-15590
in-theory        15590
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15590.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((E and F) -> F)), M:tm-322, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-15591
in-theory        15591
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> G))
theorem-size     31
proof            (modus-ponens tm-322 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15591.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-15592
in-theory        15592
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15592.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-15593
in-theory        15593
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15593.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-15594
in-theory        15594
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15594.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-15595
in-theory        15595
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15595.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-15596
in-theory        15596
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15596.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-15597
in-theory        15597
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15597.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-15598
in-theory        15598
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15598.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> H)), M:tm-322, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-15599
in-theory        15599
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15599.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((F and G) -> G)), M:tm-322, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-15600
in-theory        15600
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15600.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((G and H) -> H)), M:tm-322, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-15601
in-theory        15601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15601.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and ((F and G) -> G)), M:tm-322, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-15602
in-theory        15602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15602.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((D and E) -> E)), M:tm-322, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-15603
in-theory        15603
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15603.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-15604
in-theory        15604
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15604.        ((A or (B -> (((C and D) -> C) and B))) and ((E and F) -> F)), M:tm-322, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-15605
in-theory        15605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15605.        (((A -> (((B and C) -> B) and A)) or D) and ((E and F) -> F)), M:tm-322, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-15606
in-theory        15606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15606.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-15607
in-theory        15607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15607.        ((A -> (B -> (((C and D) -> C) and B))) and ((E and F) -> F)), M:tm-322, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-15608
in-theory        15608
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15608.        ((((A and B) -> B) and (C -> (D -> C))) and ((E and F) -> F)), M:tm-322, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-15609
in-theory        15609
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15609.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-15610
in-theory        15610
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15610.        ((((A and B) -> B) and ((C and D) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-15611
in-theory        15611
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15611.        ((((A and B) -> B) and ((C and D) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-15612
in-theory        15612
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15612.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-15613
in-theory        15613
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15613.        ((((A and B) -> B) and (C -> (C or D))) and ((E and F) -> F)), M:tm-322, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-15614
in-theory        15614
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15614.        ((((A and B) -> B) and (C -> (D or C))) and ((E and F) -> F)), M:tm-322, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-15615
in-theory        15615
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15615.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-15616
in-theory        15616
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15616.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> F)), M:tm-322, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-15617
in-theory        15617
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15617.        ((((A and B) -> B) and ((not (not C)) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-15618
in-theory        15618
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15618.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((F and G) -> G)), M:tm-322, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-15619
in-theory        15619
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15619.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((E and F) -> F)), M:tm-322, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-15620
in-theory        15620
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> G))
theorem-size     31
proof            (modus-ponens tm-322 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15620.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-15621
in-theory        15621
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15621.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-15622
in-theory        15622
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15622.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-15623
in-theory        15623
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15623.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-15624
in-theory        15624
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15624.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-15625
in-theory        15625
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15625.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-15626
in-theory        15626
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15626.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-15627
in-theory        15627
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15627.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> H)), M:tm-322, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-15628
in-theory        15628
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15628.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((F and G) -> G)), M:tm-322, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-15629
in-theory        15629
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15629.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((F and G) -> G)), M:tm-322, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-15630
in-theory        15630
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15630.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((F and G) -> G)), M:tm-322, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-15631
in-theory        15631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15631.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((G and H) -> H)), M:tm-322, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-15632
in-theory        15632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15632.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and ((F and G) -> G)), M:tm-322, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-15633
in-theory        15633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-15633.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((D and E) -> E)), M:tm-322, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-15634
in-theory        15634
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-15634.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-15635
in-theory        15635
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15635.        ((A or (B -> (((C and D) -> D) and B))) and ((E and F) -> F)), M:tm-322, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-15636
in-theory        15636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15636.        (((A -> (((B and C) -> C) and A)) or D) and ((E and F) -> F)), M:tm-322, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-15637
in-theory        15637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15637.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-15638
in-theory        15638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15638.        ((A -> (B -> (((C and D) -> D) and B))) and ((E and F) -> F)), M:tm-322, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-15639
in-theory        15639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15639.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and ((E and F) -> F)), M:tm-322, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-15640
in-theory        15640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15640.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-15641
in-theory        15641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15641.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-15642
in-theory        15642
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15642.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-15643
in-theory        15643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15643.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-15644
in-theory        15644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15644.        (((A -> (B -> (A and B))) and (C -> (C or D))) and ((E and F) -> F)), M:tm-322, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-15645
in-theory        15645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15645.        (((A -> (B -> (A and B))) and (C -> (D or C))) and ((E and F) -> F)), M:tm-322, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-15646
in-theory        15646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15646.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-15647
in-theory        15647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15647.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> F)), M:tm-322, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-15648
in-theory        15648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15648.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-15649
in-theory        15649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15649.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and ((F and G) -> G)), M:tm-322, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-15650
in-theory        15650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15650.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((E and F) -> F)), M:tm-322, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-15651
in-theory        15651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> G))
theorem-size     33
proof            (modus-ponens tm-322 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15651.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-15652
in-theory        15652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15652.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-15653
in-theory        15653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> G))
theorem-size     29
proof            (modus-ponens tm-322 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15653.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-15654
in-theory        15654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15654.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-15655
in-theory        15655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> G))
theorem-size     29
proof            (modus-ponens tm-322 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15655.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-15656
in-theory        15656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15656.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-15657
in-theory        15657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15657.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-15658
in-theory        15658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> H))
theorem-size     31
proof            (modus-ponens tm-322 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15658.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> H)), M:tm-322, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-15659
in-theory        15659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15659.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and ((F and G) -> G)), M:tm-322, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-15660
in-theory        15660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-15660.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and ((F and G) -> G)), M:tm-322, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-15661
in-theory        15661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15661.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> G)), M:tm-322, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-15662
in-theory        15662
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15662.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> G)), M:tm-322, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-15663
in-theory        15663
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15663.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> G)), M:tm-322, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-15664
in-theory        15664
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G and H) -> H))
theorem-size     31
proof            (modus-ponens tm-322 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15664.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G and H) -> H)), M:tm-322, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-15665
in-theory        15665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15665.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> G)), M:tm-322, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-15666
in-theory        15666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-15666.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((D and E) -> E)), M:tm-322, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-15667
in-theory        15667
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((E and F) -> F))
theorem-size     31
proof            (modus-ponens tm-322 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-15667.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-15668
in-theory        15668
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15668.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((E and F) -> F)), M:tm-322, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-15669
in-theory        15669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15669.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and ((E and F) -> F)), M:tm-322, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-15670
in-theory        15670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15670.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-15671
in-theory        15671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-15671.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((E and F) -> F)), M:tm-322, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-15672
in-theory        15672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-322 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-15672.        ((A -> (A and (B -> A))) and ((C and D) -> D)), M:tm-322, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-15673
in-theory        15673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-322 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-15673.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((D and E) -> E)), M:tm-322, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-15674
in-theory        15674
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-322 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15674.        (((A and B) -> ((A and B) and A)) and ((C and D) -> D)), M:tm-322, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-15675
in-theory        15675
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-322 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-15675.        (((A and B) -> ((A and B) and B)) and ((C and D) -> D)), M:tm-322, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-15676
in-theory        15676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-322 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-15676.        ((A -> (A and (B -> (A and B)))) and ((C and D) -> D)), M:tm-322, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-15677
in-theory        15677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-322 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-15677.        ((A -> (A and (A or B))) and ((C and D) -> D)), M:tm-322, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-15678
in-theory        15678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-322 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-15678.        ((A -> (A and (B or A))) and ((C and D) -> D)), M:tm-322, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-15679
in-theory        15679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-322 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-15679.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((D and E) -> E)), M:tm-322, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-15680
in-theory        15680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((C and D) -> D))
theorem-size     21
proof            (modus-ponens tm-322 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-15680.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((C and D) -> D)), M:tm-322, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-15681
in-theory        15681
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and ((B and C) -> C))
theorem-size     15
proof            (modus-ponens tm-322 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-10)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-15681.        (((not (not A)) -> ((not (not A)) and A)) and ((B and C) -> C)), M:tm-322, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-15682
in-theory        15682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-15682.        ((A -> (A and (B -> (C -> B)))) and ((D and E) -> E)), M:tm-322, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-15683
in-theory        15683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-322 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-15683.        (((A -> B) -> ((A -> B) and (A -> A))) and ((C and D) -> D)), M:tm-322, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-15684
in-theory        15684
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((D and E) -> E))
theorem-size     35
proof            (modus-ponens tm-322 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-15684.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((D and E) -> E)), M:tm-322, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-15685
in-theory        15685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15685.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((E and F) -> F)), M:tm-322, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-15686
in-theory        15686
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((D and E) -> E))
theorem-size     29
proof            (modus-ponens tm-322 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-15686.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((D and E) -> E)), M:tm-322, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-15687
in-theory        15687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15687.        ((A -> (A and ((B and C) -> B))) and ((D and E) -> E)), M:tm-322, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-15688
in-theory        15688
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((D and E) -> E))
theorem-size     29
proof            (modus-ponens tm-322 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15688.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-15689
in-theory        15689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15689.        ((A -> (A and ((B and C) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15690
in-theory        15690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15690.        ((A -> (A and ((B and C) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15691
in-theory        15691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15691.        ((A -> (A and ((B and C) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15692
in-theory        15692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15692.        ((A -> (A and ((B and C) -> C))) and (A -> A)), M:tm-316, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15693
in-theory        15693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15693.        ((A -> (A and ((B and C) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15694
in-theory        15694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and ((A -> (not (A and ((B and C) -> C)))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15694.        ((A -> (A and ((B and C) -> C))) and ((A -> (not (A and ((B and C) -> C)))) -> (not A))), M:tm-313, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15695
in-theory        15695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (((A and ((B and C) -> C)) -> D) -> ((A or (A and ((B and C) -> C))) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15695.        ((A -> (A and ((B and C) -> C))) and (((A and ((B and C) -> C)) -> D) -> ((A or (A and ((B and C) -> C))) -> D))), M:tm-312, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15696
in-theory        15696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (D or (A -> (A and ((B and C) -> C)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15696.        ((A -> (A and ((B and C) -> C))) and (D or (A -> (A and ((B and C) -> C))))), M:tm-311, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15697
in-theory        15697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and ((A -> (A and ((B and C) -> C))) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15697.        ((A -> (A and ((B and C) -> C))) and ((A -> (A and ((B and C) -> C))) or D)), M:tm-310, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15698
in-theory        15698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (D -> ((A -> (A and ((B and C) -> C))) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15698.        ((A -> (A and ((B and C) -> C))) and (D -> ((A -> (A and ((B and C) -> C))) and D))), M:tm-309, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15699
in-theory        15699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (D -> (A -> (A and ((B and C) -> C)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15699.        ((A -> (A and ((B and C) -> C))) and (D -> (A -> (A and ((B and C) -> C))))), M:tm-305, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15700
in-theory        15700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and ((E and F) -> F))))
theorem-size     21
proof            (modus-ponens tm-303 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15700.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and ((E and F) -> F)))), M:tm-303, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15701
in-theory        15701
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and ((D and E) -> E)))
theorem-size     27
proof            (modus-ponens tm-300 tm-322 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15701.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and ((D and E) -> E))), M:tm-300, m:tm-322, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15702
in-theory        15702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-270 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15702.        ((A -> (((B and C) -> C) and A)) and (D -> (D and ((E and F) -> F)))), M:tm-270, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15703
in-theory        15703
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((D and E) -> E)))
theorem-size     23
proof            (modus-ponens tm-267 tm-322 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15703.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((D and E) -> E))), M:tm-267, m:tm-322, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15704
in-theory        15704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-239 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15704.        ((A -> (((B and C) -> B) and A)) and (D -> (D and ((E and F) -> F)))), M:tm-239, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15705
in-theory        15705
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((D and E) -> E)))
theorem-size     23
proof            (modus-ponens tm-236 tm-322 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15705.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((D and E) -> E))), M:tm-236, m:tm-322, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15706
in-theory        15706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and ((F and G) -> G))))
theorem-size     27
proof            (modus-ponens tm-210 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15706.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and ((F and G) -> G)))), M:tm-210, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15707
in-theory        15707
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((E and F) -> F)))
theorem-size     39
proof            (modus-ponens tm-207 tm-322 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15707.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((E and F) -> F))), M:tm-207, m:tm-322, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15708
in-theory        15708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-183 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15708.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and ((E and F) -> F)))), M:tm-183, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15709
in-theory        15709
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and ((D and E) -> E)))
theorem-size     23
proof            (modus-ponens tm-180 tm-322 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15709.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and ((D and E) -> E))), M:tm-180, m:tm-322, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15710
in-theory        15710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-157 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15710.        ((A -> ((B and C) -> C)) and (D -> (D and ((E and F) -> F)))), M:tm-157, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15711
in-theory        15711
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((D and E) -> E)))
theorem-size     19
proof            (modus-ponens tm-154 tm-322 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15711.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((D and E) -> E))), M:tm-154, m:tm-322, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15712
in-theory        15712
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and ((E and F) -> F))))
theorem-size     25
proof            (modus-ponens tm-147 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15712.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and ((E and F) -> F)))), M:tm-147, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15713
in-theory        15713
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((D and E) -> E)))
theorem-size     29
proof            (modus-ponens tm-144 tm-322 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15713.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((D and E) -> E))), M:tm-144, m:tm-322, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15714
in-theory        15714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-134 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15714.        ((A -> ((B and C) -> B)) and (D -> (D and ((E and F) -> F)))), M:tm-134, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15715
in-theory        15715
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((D and E) -> E)))
theorem-size     19
proof            (modus-ponens tm-131 tm-322 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15715.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((D and E) -> E))), M:tm-131, m:tm-322, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15716
in-theory        15716
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and ((E and F) -> F))))
theorem-size     25
proof            (modus-ponens tm-125 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15716.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and ((E and F) -> F)))), M:tm-125, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15717
in-theory        15717
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((D and E) -> E)))
theorem-size     29
proof            (modus-ponens tm-122 tm-322 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15717.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((D and E) -> E))), M:tm-122, m:tm-322, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15718
in-theory        15718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-113 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15718.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F and G) -> G)))), M:tm-113, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15719
in-theory        15719
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> F)))
theorem-size     35
proof            (modus-ponens tm-110 tm-322 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15719.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E and F) -> F))), M:tm-110, m:tm-322, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15720
in-theory        15720
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and ((E and F) -> F))))
theorem-size     29
proof            (modus-ponens tm-105 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15720.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and ((E and F) -> F)))), M:tm-105, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15721
in-theory        15721
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((D and E) -> E)))
theorem-size     35
proof            (modus-ponens tm-102 tm-322 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15721.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((D and E) -> E))), M:tm-102, m:tm-322, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15722
in-theory        15722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and ((D and E) -> E))))
theorem-size     17
proof            (modus-ponens tm-95 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15722.        (((A -> B) -> (A -> A)) and (C -> (C and ((D and E) -> E)))), M:tm-95, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15723
in-theory        15723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and ((C and D) -> D)))
theorem-size     17
proof            (modus-ponens tm-92 tm-322 ((Am (-> A A)) (B (and (-> A A) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15723.        (((A -> B) or (A -> A)) -> ((A -> A) and ((C and D) -> D))), M:tm-92, m:tm-322, u:((Am (-> A A)) (B (and (-> A A) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15724
in-theory        15724
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and ((C and D) -> D))))
theorem-size     11
proof            (modus-ponens tm-84 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15724.        (A -> (B -> (A and ((C and D) -> D)))), M:tm-84, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15725
in-theory        15725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-83 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15725.        ((A -> (B -> (C -> B))) and (D -> (D and ((E and F) -> F)))), M:tm-83, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15726
in-theory        15726
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((D and E) -> E)))
theorem-size     19
proof            (modus-ponens tm-80 tm-322 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15726.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((D and E) -> E))), M:tm-80, m:tm-322, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15727
in-theory        15727
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and ((C and D) -> D))))
theorem-size     15
proof            (modus-ponens tm-76 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15727.        (((not (not A)) -> A) and (B -> (B and ((C and D) -> D)))), M:tm-76, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15728
in-theory        15728
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and ((B and C) -> C)))
theorem-size     13
proof            (modus-ponens tm-73 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15728.        (((not (not A)) or A) -> (A and ((B and C) -> C))), M:tm-73, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15729
in-theory        15729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and ((D and E) -> E))))
theorem-size     21
proof            (modus-ponens tm-69 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15729.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and ((D and E) -> E)))), M:tm-69, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15730
in-theory        15730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((C and D) -> D)))
theorem-size     25
proof            (modus-ponens tm-66 tm-322 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-1 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15730.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((C and D) -> D))), M:tm-66, m:tm-322, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15731
in-theory        15731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and ((E and F) -> F))))
theorem-size     23
proof            (modus-ponens tm-54 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15731.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and ((E and F) -> F)))), M:tm-54, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15732
in-theory        15732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((D and E) -> E)))
theorem-size     29
proof            (modus-ponens tm-51 tm-322 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15732.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((D and E) -> E))), M:tm-51, m:tm-322, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15733
in-theory        15733
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and ((C and D) -> D)))
theorem-size     15
proof            (modus-ponens tm-50 tm-322 ((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15733.        ((A or (B or A)) -> ((B or A) and ((C and D) -> D))), M:tm-50, m:tm-322, u:((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15734
in-theory        15734
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and ((C and D) -> D)))
theorem-size     15
proof            (modus-ponens tm-49 tm-322 ((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15734.        ((A or (A or B)) -> ((A or B) and ((C and D) -> D))), M:tm-49, m:tm-322, u:((Am (or A B)) (C (and (or A B) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15735
in-theory        15735
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((C and D) -> D)))
theorem-size     19
proof            (modus-ponens tm-48 tm-322 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15735.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((C and D) -> D))), M:tm-48, m:tm-322, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15736
in-theory        15736
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and ((C and D) -> D)))
theorem-size     13
proof            (modus-ponens tm-47 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15736.        (((A and B) or B) -> (B and ((C and D) -> D))), M:tm-47, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15737
in-theory        15737
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and ((C and D) -> D)))
theorem-size     13
proof            (modus-ponens tm-46 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15737.        (((A and B) or A) -> (A and ((C and D) -> D))), M:tm-46, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15738
in-theory        15738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D and E) -> E)))
theorem-size     27
proof            (modus-ponens tm-45 tm-322 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15738.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D and E) -> E))), M:tm-45, m:tm-322, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15739
in-theory        15739
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and ((C and D) -> D)))
theorem-size     15
proof            (modus-ponens tm-44 tm-322 ((Am (-> A B)) (C (and (-> A B) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15739.        ((A or (B -> A)) -> ((B -> A) and ((C and D) -> D))), M:tm-44, m:tm-322, u:((Am (-> A B)) (C (and (-> A B) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15740
in-theory        15740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and ((D and E) -> E))))
theorem-size     15
proof            (modus-ponens tm-42 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15740.        ((A -> (B or A)) and (C -> (C and ((D and E) -> E)))), M:tm-42, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15741
in-theory        15741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and ((D and E) -> E))))
theorem-size     15
proof            (modus-ponens tm-32 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15741.        ((A -> (A or B)) and (C -> (C and ((D and E) -> E)))), M:tm-32, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15742
in-theory        15742
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and ((B and C) -> C))))
theorem-size     11
proof            (modus-ponens tm-24 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15742.        (A -> (A and (A and ((B and C) -> C)))), M:tm-24, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15743
in-theory        15743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and ((D and E) -> E))))
theorem-size     17
proof            (modus-ponens tm-23 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15743.        ((A -> (B -> (A and B))) and (C -> (C and ((D and E) -> E)))), M:tm-23, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15744
in-theory        15744
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and ((D and E) -> E))))
theorem-size     15
proof            (modus-ponens tm-22 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15744.        (((A and B) -> B) and (C -> (C and ((D and E) -> E)))), M:tm-22, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15745
in-theory        15745
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and ((D and E) -> E))))
theorem-size     15
proof            (modus-ponens tm-21 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15745.        (((A and B) -> A) and (C -> (C and ((D and E) -> E)))), M:tm-21, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15746
in-theory        15746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and ((E and F) -> F))))
theorem-size     23
proof            (modus-ponens tm-20 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15746.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and ((E and F) -> F)))), M:tm-20, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15747
in-theory        15747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and ((D and E) -> E))))
theorem-size     15
proof            (modus-ponens tm-19 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15747.        ((A -> (B -> A)) and (C -> (C and ((D and E) -> E)))), M:tm-19, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15748
in-theory        15748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and ((B and C) -> C)))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-9 tm-2 tm-5 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15748.        ((A -> (not (A and ((B and C) -> C)))) -> (not A)), M:tm-9, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15749
in-theory        15749
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) -> C)) -> D) -> ((A or (A and ((B and C) -> C))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15749.        (((A and ((B and C) -> C)) -> D) -> ((A or (A and ((B and C) -> C))) -> D)), M:tm-8, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15750
in-theory        15750
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and ((C and D) -> D))))
theorem-size     11
proof            (modus-ponens tm-7 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-7 tm-2 tm-5 tm-1 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15750.        (A or (B -> (B and ((C and D) -> D)))), M:tm-7, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15751
in-theory        15751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-6 tm-2 tm-5 tm-1 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15751.        ((A -> (A and ((B and C) -> C))) or D), M:tm-6, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15752
in-theory        15752
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and ((C and D) -> D))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15752.        (A -> ((B -> (B and ((C and D) -> D))) and A)), M:tm-5, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15753
in-theory        15753
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and ((C and D) -> D))))
theorem-size     11
proof            (modus-ponens tm-1 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-1 tm-2 tm-5 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15753.        (A -> (B -> (B and ((C and D) -> D)))), M:tm-1, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-15754
in-theory        15754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (A -> (B -> A))))
theorem-size     17
proof            (modus-ponens tm-323 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-15754.        ((A -> (B -> A)) and ((C -> (D -> C)) and (A -> (B -> A)))), M:tm-323, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-15755
in-theory        15755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-15755.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))), M:tm-323, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-15756
in-theory        15756
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((A and B) -> A)))
theorem-size     17
proof            (modus-ponens tm-323 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15756.        (((A and B) -> A) and ((C -> (D -> C)) and ((A and B) -> A))), M:tm-323, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-15757
in-theory        15757
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((A and B) -> B)))
theorem-size     17
proof            (modus-ponens tm-323 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-15757.        (((A and B) -> B) and ((C -> (D -> C)) and ((A and B) -> B))), M:tm-323, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-15758
in-theory        15758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (A -> (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-323 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-15758.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (A -> (B -> (A and B))))), M:tm-323, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-15759
in-theory        15759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (A -> (A or B))))
theorem-size     17
proof            (modus-ponens tm-323 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-15759.        ((A -> (A or B)) and ((C -> (D -> C)) and (A -> (A or B)))), M:tm-323, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-15760
in-theory        15760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (A -> (B or A))))
theorem-size     17
proof            (modus-ponens tm-323 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-15760.        ((A -> (B or A)) and ((C -> (D -> C)) and (A -> (B or A)))), M:tm-323, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-15761
in-theory        15761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-15761.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))), M:tm-323, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-15762
in-theory        15762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((A -> B) -> ((A -> (not B)) -> (not A)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-15762.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((A -> B) -> ((A -> (not B)) -> (not A))))), M:tm-323, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-15763
in-theory        15763
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((not (not A)) -> A)))
theorem-size     17
proof            (modus-ponens tm-323 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-15763.        (((not (not A)) -> A) and ((B -> (C -> B)) and ((not (not A)) -> A))), M:tm-323, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-15764
in-theory        15764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (A -> (B -> (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-323 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15764.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (A -> (B -> (C -> B))))), M:tm-323, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-15765
in-theory        15765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((A -> B) -> (A -> A))))
theorem-size     21
proof            (modus-ponens tm-323 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-15765.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((A -> B) -> (A -> A)))), M:tm-323, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-15766
in-theory        15766
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-15766.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-323, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-15767
in-theory        15767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15767.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-323, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-15768
in-theory        15768
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))))
theorem-size     37
proof            (modus-ponens tm-323 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-15768.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)))), M:tm-323, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-15769
in-theory        15769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (A -> ((B and C) -> B))))
theorem-size     21
proof            (modus-ponens tm-323 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15769.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (A -> ((B and C) -> B)))), M:tm-323, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15770
in-theory        15770
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-323 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-15770.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)))), M:tm-323, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-15771
in-theory        15771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (A -> ((B and C) -> C))))
theorem-size     21
proof            (modus-ponens tm-323 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15771.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (A -> ((B and C) -> C)))), M:tm-323, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15772
in-theory        15772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (A -> ((B -> (C -> B)) and A))))
theorem-size     25
proof            (modus-ponens tm-323 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-15772.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (A -> ((B -> (C -> B)) and A)))), M:tm-323, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-15773
in-theory        15773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     41
proof            (modus-ponens tm-323 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15773.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-323, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-15774
in-theory        15774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (A -> (((B and C) -> B) and A))))
theorem-size     25
proof            (modus-ponens tm-323 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15774.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (A -> (((B and C) -> B) and A)))), M:tm-323, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-15775
in-theory        15775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (A -> (((B and C) -> C) and A))))
theorem-size     25
proof            (modus-ponens tm-323 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15775.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (A -> (((B and C) -> C) and A)))), M:tm-323, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-15776
in-theory        15776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (A -> ((B -> (C -> (B and C))) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15776.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (A -> ((B -> (C -> (B and C))) and A)))), M:tm-323, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-15777
in-theory        15777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((A -> B) -> (A -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-15777.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((A -> B) -> (A -> (A and B))))), M:tm-323, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-15778
in-theory        15778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (A -> (B -> (C -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15778.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (A -> (B -> (C -> (B and C)))))), M:tm-323, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-15779
in-theory        15779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((A -> (B -> A)) or C)))
theorem-size     21
proof            (modus-ponens tm-323 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15779.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((A -> (B -> A)) or C))), M:tm-323, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-15780
in-theory        15780
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)))
theorem-size     37
proof            (modus-ponens tm-323 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15780.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D))), M:tm-323, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-15781
in-theory        15781
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((A and B) -> A) or C)))
theorem-size     21
proof            (modus-ponens tm-323 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15781.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((A and B) -> A) or C))), M:tm-323, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-15782
in-theory        15782
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((A and B) -> B) or C)))
theorem-size     21
proof            (modus-ponens tm-323 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15782.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((A and B) -> B) or C))), M:tm-323, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-15783
in-theory        15783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((A -> (B -> (A and B))) or C)))
theorem-size     25
proof            (modus-ponens tm-323 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15783.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((A -> (B -> (A and B))) or C))), M:tm-323, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-15784
in-theory        15784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((A -> (A or B)) or C)))
theorem-size     21
proof            (modus-ponens tm-323 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15784.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((A -> (A or B)) or C))), M:tm-323, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-15785
in-theory        15785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (A -> ((B -> (B or C)) and A))))
theorem-size     25
proof            (modus-ponens tm-323 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15785.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (A -> ((B -> (B or C)) and A)))), M:tm-323, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-15786
in-theory        15786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (A -> (B -> (B or C)))))
theorem-size     21
proof            (modus-ponens tm-323 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15786.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (A -> (B -> (B or C))))), M:tm-323, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-15787
in-theory        15787
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (A or (B -> (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-323 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15787.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (A or (B -> (C -> B))))), M:tm-323, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-15788
in-theory        15788
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15788.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-323, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-15789
in-theory        15789
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (A or ((B and C) -> B))))
theorem-size     21
proof            (modus-ponens tm-323 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15789.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (A or ((B and C) -> B)))), M:tm-323, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-15790
in-theory        15790
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (A or ((B and C) -> C))))
theorem-size     21
proof            (modus-ponens tm-323 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15790.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (A or ((B and C) -> C)))), M:tm-323, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-15791
in-theory        15791
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (A or (B -> (C -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15791.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (A or (B -> (C -> (B and C)))))), M:tm-323, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-15792
in-theory        15792
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (A or (B -> (B or C)))))
theorem-size     21
proof            (modus-ponens tm-323 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15792.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (A or (B -> (B or C))))), M:tm-323, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-15793
in-theory        15793
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (A or (B -> (C or B)))))
theorem-size     21
proof            (modus-ponens tm-323 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15793.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (A or (B -> (C or B))))), M:tm-323, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-15794
in-theory        15794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((A -> (B or A)) or C)))
theorem-size     21
proof            (modus-ponens tm-323 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15794.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((A -> (B or A)) or C))), M:tm-323, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-15795
in-theory        15795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (A -> ((B -> (C or B)) and A))))
theorem-size     25
proof            (modus-ponens tm-323 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15795.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (A -> ((B -> (C or B)) and A)))), M:tm-323, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-15796
in-theory        15796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (A -> (B -> (C or B)))))
theorem-size     21
proof            (modus-ponens tm-323 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15796.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (A -> (B -> (C or B))))), M:tm-323, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-15797
in-theory        15797
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((A -> B) -> C) -> ((B or (A -> B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-323 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-15797.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((A -> B) -> C) -> ((B or (A -> B)) -> C)))), M:tm-323, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-15798
in-theory        15798
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     57
proof            (modus-ponens tm-323 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-15798.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-323, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-15799
in-theory        15799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((A -> B) -> (((A and C) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-323 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15799.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((A -> B) -> (((A and C) or A) -> B)))), M:tm-323, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-15800
in-theory        15800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((A -> B) -> (((C and A) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-323 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-15800.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> D)) and ((A -> B) -> (((C and A) or A) -> B)))), M:tm-323, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-15801
in-theory        15801
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-323 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-15801.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> D)) and (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)))), M:tm-323, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-15802
in-theory        15802
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((A or B) -> C) -> ((A or (A or B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-323 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-15802.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> D)) and (((A or B) -> C) -> ((A or (A or B)) -> C)))), M:tm-323, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-15803
in-theory        15803
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((A or B) -> C) -> ((B or (A or B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-323 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-15803.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> D)) and (((A or B) -> C) -> ((B or (A or B)) -> C)))), M:tm-323, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-15804
in-theory        15804
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     61
proof            (modus-ponens tm-323 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-15804.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> E)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-323, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-15805
in-theory        15805
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15805.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-323, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-15806
in-theory        15806
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)))
theorem-size     37
proof            (modus-ponens tm-323 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15806.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> E)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D))), M:tm-323, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-15807
in-theory        15807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((E -> (F -> E)) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))))
theorem-size     41
proof            (modus-ponens tm-323 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15807.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((E -> (F -> E)) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)))), M:tm-323, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-15808
in-theory        15808
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-15808.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))))), M:tm-323, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-15809
in-theory        15809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15809.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> E)) and (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-323, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-15810
in-theory        15810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and ((C -> (D -> C)) and ((A -> (not (B -> A))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-323 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-15810.        (((A -> (not (B -> A))) -> (not A)) and ((C -> (D -> C)) and ((A -> (not (B -> A))) -> (not A)))), M:tm-323, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-15811
in-theory        15811
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((D -> (E -> D)) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-15811.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((D -> (E -> D)) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))))), M:tm-323, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-15812
in-theory        15812
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and ((C -> (D -> C)) and (((A and B) -> (not A)) -> (not (A and B)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15812.        ((((A and B) -> (not A)) -> (not (A and B))) and ((C -> (D -> C)) and (((A and B) -> (not A)) -> (not (A and B))))), M:tm-323, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-15813
in-theory        15813
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and ((C -> (D -> C)) and (((A and B) -> (not B)) -> (not (A and B)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-15813.        ((((A and B) -> (not B)) -> (not (A and B))) and ((C -> (D -> C)) and (((A and B) -> (not B)) -> (not (A and B))))), M:tm-323, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-15814
in-theory        15814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and ((C -> (D -> C)) and ((A -> (not (B -> (A and B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-15814.        (((A -> (not (B -> (A and B)))) -> (not A)) and ((C -> (D -> C)) and ((A -> (not (B -> (A and B)))) -> (not A)))), M:tm-323, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-15815
in-theory        15815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and ((C -> (D -> C)) and ((A -> (not (A or B))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-323 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-15815.        (((A -> (not (A or B))) -> (not A)) and ((C -> (D -> C)) and ((A -> (not (A or B))) -> (not A)))), M:tm-323, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-15816
in-theory        15816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and ((C -> (D -> C)) and ((A -> (not (B or A))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-323 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-15816.        (((A -> (not (B or A))) -> (not A)) and ((C -> (D -> C)) and ((A -> (not (B or A))) -> (not A)))), M:tm-323, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-15817
in-theory        15817
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((D -> (E -> D)) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-15817.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((D -> (E -> D)) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))))), M:tm-323, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-15818
in-theory        15818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((C -> (D -> C)) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-15818.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((C -> (D -> C)) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))))), M:tm-323, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-15819
in-theory        15819
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((D -> (E -> D)) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))))
theorem-size     53
proof            (modus-ponens tm-323 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-15819.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((D -> (E -> D)) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))), M:tm-323, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-15820
in-theory        15820
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E -> D)) and (A or ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15820.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E -> D)) and (A or ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-323, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-15821
in-theory        15821
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((D -> (E -> D)) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C)))
theorem-size     33
proof            (modus-ponens tm-323 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15821.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((D -> (E -> D)) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C))), M:tm-323, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-15822
in-theory        15822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((D -> (E -> D)) and (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A))))
theorem-size     37
proof            (modus-ponens tm-323 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15822.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((D -> (E -> D)) and (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)))), M:tm-323, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-15823
in-theory        15823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((C -> (D -> C)) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-15823.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((C -> (D -> C)) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))))), M:tm-323, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-15824
in-theory        15824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E -> D)) and (A -> ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15824.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E -> D)) and (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-323, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-15825
in-theory        15825
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((B -> (C -> B)) and (((not (not A)) -> (not A)) -> (not (not (not A))))))
theorem-size     29
proof            (modus-ponens tm-323 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-15825.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((B -> (C -> B)) and (((not (not A)) -> (not A)) -> (not (not (not A)))))), M:tm-323, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-15826
in-theory        15826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and ((C -> (D -> C)) and ((A -> B) -> (((not (not A)) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-323 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-15826.        (((A -> B) -> (((not (not A)) or A) -> B)) and ((C -> (D -> C)) and ((A -> B) -> (((not (not A)) or A) -> B)))), M:tm-323, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-15827
in-theory        15827
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and ((C -> (D -> C)) and (A or ((not (not B)) -> B))))
theorem-size     21
proof            (modus-ponens tm-323 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15827.        ((A or ((not (not B)) -> B)) and ((C -> (D -> C)) and (A or ((not (not B)) -> B)))), M:tm-323, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-15828
in-theory        15828
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and ((C -> (D -> C)) and (((not (not A)) -> A) or B)))
theorem-size     21
proof            (modus-ponens tm-323 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15828.        ((((not (not A)) -> A) or B) and ((C -> (D -> C)) and (((not (not A)) -> A) or B))), M:tm-323, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-15829
in-theory        15829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and ((C -> (D -> C)) and (A -> (((not (not B)) -> B) and A))))
theorem-size     25
proof            (modus-ponens tm-323 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15829.        ((A -> (((not (not B)) -> B) and A)) and ((C -> (D -> C)) and (A -> (((not (not B)) -> B) and A)))), M:tm-323, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-15830
in-theory        15830
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((C -> (D -> C)) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B))))
theorem-size     37
proof            (modus-ponens tm-323 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-15830.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((C -> (D -> C)) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)))), M:tm-323, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-15831
in-theory        15831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and ((C -> (D -> C)) and (A -> ((not (not B)) -> B))))
theorem-size     21
proof            (modus-ponens tm-323 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15831.        ((A -> ((not (not B)) -> B)) and ((C -> (D -> C)) and (A -> ((not (not B)) -> B)))), M:tm-323, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-15832
in-theory        15832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not (B -> (C -> B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-15832.        (((A -> (not (B -> (C -> B)))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not (B -> (C -> B)))) -> (not A)))), M:tm-323, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-15833
in-theory        15833
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((E -> (F -> E)) and (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-323 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-15833.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((E -> (F -> E)) and (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)))), M:tm-323, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-15834
in-theory        15834
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and ((E -> (F -> E)) and (A or (B -> (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15834.        ((A or (B -> (C -> (D -> C)))) and ((E -> (F -> E)) and (A or (B -> (C -> (D -> C)))))), M:tm-323, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-15835
in-theory        15835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and ((E -> (F -> E)) and ((A -> (B -> (C -> B))) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15835.        (((A -> (B -> (C -> B))) or D) and ((E -> (F -> E)) and ((A -> (B -> (C -> B))) or D))), M:tm-323, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-15836
in-theory        15836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and ((E -> (F -> E)) and (A -> ((B -> (C -> (D -> C))) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15836.        ((A -> ((B -> (C -> (D -> C))) and A)) and ((E -> (F -> E)) and (A -> ((B -> (C -> (D -> C))) and A)))), M:tm-323, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-15837
in-theory        15837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and ((D -> (E -> D)) and ((A -> B) -> (A -> (C -> B)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-15837.        (((A -> B) -> (A -> (C -> B))) and ((D -> (E -> D)) and ((A -> B) -> (A -> (C -> B))))), M:tm-323, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-15838
in-theory        15838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and ((E -> (F -> E)) and (A -> (B -> (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15838.        ((A -> (B -> (C -> (D -> C)))) and ((E -> (F -> E)) and (A -> (B -> (C -> (D -> C)))))), M:tm-323, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-15839
in-theory        15839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and ((B -> (C -> B)) and (A -> A)))
theorem-size     13
proof            (modus-ponens tm-323 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-15839.        ((A -> A) and ((B -> (C -> B)) and (A -> A))), M:tm-323, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-15840
in-theory        15840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and ((D -> (E -> D)) and ((A -> (B -> C)) -> (A -> (B -> C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-15840.        (((A -> (B -> C)) -> (A -> (B -> C))) and ((D -> (E -> D)) and ((A -> (B -> C)) -> (A -> (B -> C))))), M:tm-323, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-15841
in-theory        15841
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and ((C -> (D -> C)) and ((A and B) -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-323 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15841.        (((A and B) -> (A and B)) and ((C -> (D -> C)) and ((A and B) -> (A and B)))), M:tm-323, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-15842
in-theory        15842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and ((C -> (D -> C)) and ((A -> B) -> (A -> B))))
theorem-size     21
proof            (modus-ponens tm-323 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-15842.        (((A -> B) -> (A -> B)) and ((C -> (D -> C)) and ((A -> B) -> (A -> B)))), M:tm-323, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-15843
in-theory        15843
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and ((B -> (C -> B)) and ((not (not A)) -> (not (not A)))))
theorem-size     21
proof            (modus-ponens tm-323 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-15843.        (((not (not A)) -> (not (not A))) and ((B -> (C -> B)) and ((not (not A)) -> (not (not A))))), M:tm-323, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-15844
in-theory        15844
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((C -> (D -> C)) and (((A -> B) -> (not (A -> A))) -> (not (A -> B)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-15844.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((C -> (D -> C)) and (((A -> B) -> (not (A -> A))) -> (not (A -> B))))), M:tm-323, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-15845
in-theory        15845
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((D -> (E -> D)) and (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B))))
theorem-size     37
proof            (modus-ponens tm-323 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-15845.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((D -> (E -> D)) and (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)))), M:tm-323, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-15846
in-theory        15846
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and ((D -> (E -> D)) and (A or ((B -> C) -> (B -> B)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15846.        ((A or ((B -> C) -> (B -> B))) and ((D -> (E -> D)) and (A or ((B -> C) -> (B -> B))))), M:tm-323, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-15847
in-theory        15847
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and ((D -> (E -> D)) and (((A -> B) -> (A -> A)) or C)))
theorem-size     25
proof            (modus-ponens tm-323 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15847.        ((((A -> B) -> (A -> A)) or C) and ((D -> (E -> D)) and (((A -> B) -> (A -> A)) or C))), M:tm-323, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-15848
in-theory        15848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and ((D -> (E -> D)) and (A -> (((B -> C) -> (B -> B)) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15848.        ((A -> (((B -> C) -> (B -> B)) and A)) and ((D -> (E -> D)) and (A -> (((B -> C) -> (B -> B)) and A)))), M:tm-323, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-15849
in-theory        15849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and ((C -> (D -> C)) and (((A -> B) -> A) -> ((A -> B) -> A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-15849.        ((((A -> B) -> A) -> ((A -> B) -> A)) and ((C -> (D -> C)) and (((A -> B) -> A) -> ((A -> B) -> A)))), M:tm-323, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-15850
in-theory        15850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and ((D -> (E -> D)) and (A -> ((B -> C) -> (B -> B)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15850.        ((A -> ((B -> C) -> (B -> B))) and ((D -> (E -> D)) and (A -> ((B -> C) -> (B -> B))))), M:tm-323, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-15851
in-theory        15851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and ((D -> (E -> D)) and ((A -> ((B -> A) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-15851.        (((A -> ((B -> A) -> C)) -> (A -> C)) and ((D -> (E -> D)) and ((A -> ((B -> A) -> C)) -> (A -> C)))), M:tm-323, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-15852
in-theory        15852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and ((C -> (D -> C)) and ((A -> (A -> B)) -> (A -> B))))
theorem-size     25
proof            (modus-ponens tm-323 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-15852.        (((A -> (A -> B)) -> (A -> B)) and ((C -> (D -> C)) and ((A -> (A -> B)) -> (A -> B)))), M:tm-323, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-15853
in-theory        15853
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((D -> (E -> D)) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-15853.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((D -> (E -> D)) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))))), M:tm-323, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-15854
in-theory        15854
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((D -> (E -> D)) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B))))))
theorem-size     69
proof            (modus-ponens tm-323 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-15854.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((D -> (E -> D)) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))))), M:tm-323, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-15855
in-theory        15855
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))))
theorem-size     73
proof            (modus-ponens tm-323 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-15855.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))), M:tm-323, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-15856
in-theory        15856
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F -> E)) and (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15856.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F -> E)) and (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-323, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-15857
in-theory        15857
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and ((E -> (F -> E)) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D)))
theorem-size     49
proof            (modus-ponens tm-323 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15857.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and ((E -> (F -> E)) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D))), M:tm-323, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-15858
in-theory        15858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((E -> (F -> E)) and (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))))
theorem-size     53
proof            (modus-ponens tm-323 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15858.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((E -> (F -> E)) and (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)))), M:tm-323, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-15859
in-theory        15859
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((D -> (E -> D)) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-323 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-15859.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((D -> (E -> D)) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))), M:tm-323, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-15860
in-theory        15860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F -> E)) and (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15860.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F -> E)) and (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-323, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-15861
in-theory        15861
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((E -> (F -> E)) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-323 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-15861.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((E -> (F -> E)) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)))), M:tm-323, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-15862
in-theory        15862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((E -> (F -> E)) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A))))
theorem-size     45
proof            (modus-ponens tm-323 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15862.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((E -> (F -> E)) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)))), M:tm-323, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-15863
in-theory        15863
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((F -> (G -> F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))))
theorem-size     73
proof            (modus-ponens tm-323 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15863.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((F -> (G -> F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))), M:tm-323, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-15864
in-theory        15864
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> F)) and (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15864.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> F)) and (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-323, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-15865
in-theory        15865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G -> F)) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-323 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15865.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G -> F)) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-323, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-15866
in-theory        15866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G -> F)) and (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-323 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15866.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G -> F)) and (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-323, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-15867
in-theory        15867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-15867.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))))), M:tm-323, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-15868
in-theory        15868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> F)) and (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15868.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> F)) and (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-323, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-15869
in-theory        15869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and ((C -> (D -> C)) and (((A -> B) and A) -> B)))
theorem-size     21
proof            (modus-ponens tm-323 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-15869.        ((((A -> B) and A) -> B) and ((C -> (D -> C)) and (((A -> B) and A) -> B))), M:tm-323, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-15870
in-theory        15870
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and ((E -> (F -> E)) and ((((A -> (B -> A)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-323 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-15870.        (((((A -> (B -> A)) -> C) and D) -> C) and ((E -> (F -> E)) and ((((A -> (B -> A)) -> C) and D) -> C))), M:tm-323, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-15871
in-theory        15871
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((F -> (G -> F)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D)))
theorem-size     45
proof            (modus-ponens tm-323 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15871.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((F -> (G -> F)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D))), M:tm-323, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-15872
in-theory        15872
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((D -> (E -> D)) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B))))
theorem-size     49
proof            (modus-ponens tm-323 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-15872.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((D -> (E -> D)) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)))), M:tm-323, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-15873
in-theory        15873
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((D -> (E -> D)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A))))
theorem-size     37
proof            (modus-ponens tm-323 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-15873.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((D -> (E -> D)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)))), M:tm-323, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-15874
in-theory        15874
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((D -> (E -> D)) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A)))))
theorem-size     57
proof            (modus-ponens tm-323 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-15874.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((D -> (E -> D)) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))))), M:tm-323, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-15875
in-theory        15875
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((E -> (F -> E)) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))))
theorem-size     61
proof            (modus-ponens tm-323 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-15875.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((E -> (F -> E)) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))), M:tm-323, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-15876
in-theory        15876
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F -> E)) and (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15876.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F -> E)) and (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-323, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-15877
in-theory        15877
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((E -> (F -> E)) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D)))
theorem-size     41
proof            (modus-ponens tm-323 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15877.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((E -> (F -> E)) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D))), M:tm-323, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-15878
in-theory        15878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((E -> (F -> E)) and (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))))
theorem-size     45
proof            (modus-ponens tm-323 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15878.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((E -> (F -> E)) and (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)))), M:tm-323, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-15879
in-theory        15879
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((D -> (E -> D)) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B))))
theorem-size     53
proof            (modus-ponens tm-323 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-15879.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((D -> (E -> D)) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)))), M:tm-323, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-15880
in-theory        15880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F -> E)) and (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15880.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F -> E)) and (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-323, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-15881
in-theory        15881
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and ((E -> (F -> E)) and (((((A and B) -> A) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-323 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-15881.        ((((((A and B) -> A) -> C) and D) -> C) and ((E -> (F -> E)) and (((((A and B) -> A) -> C) and D) -> C))), M:tm-323, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-15882
in-theory        15882
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((D -> (E -> D)) and (((A and B) -> (A -> C)) -> ((A and B) -> C))))
theorem-size     33
proof            (modus-ponens tm-323 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-15882.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((D -> (E -> D)) and (((A and B) -> (A -> C)) -> ((A and B) -> C)))), M:tm-323, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-15883
in-theory        15883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not ((B and C) -> B))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15883.        (((A -> (not ((B and C) -> B))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not ((B and C) -> B))) -> (not A)))), M:tm-323, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-15884
in-theory        15884
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((E -> (F -> E)) and ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C))))
theorem-size     41
proof            (modus-ponens tm-323 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15884.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((E -> (F -> E)) and ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)))), M:tm-323, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-15885
in-theory        15885
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and ((E -> (F -> E)) and (A or (B -> ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15885.        ((A or (B -> ((C and D) -> C))) and ((E -> (F -> E)) and (A or (B -> ((C and D) -> C))))), M:tm-323, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-15886
in-theory        15886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and ((E -> (F -> E)) and ((A -> ((B and C) -> B)) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15886.        (((A -> ((B and C) -> B)) or D) and ((E -> (F -> E)) and ((A -> ((B and C) -> B)) or D))), M:tm-323, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-15887
in-theory        15887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and ((E -> (F -> E)) and (A -> ((B -> ((C and D) -> C)) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15887.        ((A -> ((B -> ((C and D) -> C)) and A)) and ((E -> (F -> E)) and (A -> ((B -> ((C and D) -> C)) and A)))), M:tm-323, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-15888
in-theory        15888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and ((D -> (E -> D)) and ((A -> (B and C)) -> (A -> B))))
theorem-size     25
proof            (modus-ponens tm-323 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-15888.        (((A -> (B and C)) -> (A -> B)) and ((D -> (E -> D)) and ((A -> (B and C)) -> (A -> B)))), M:tm-323, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-15889
in-theory        15889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and ((E -> (F -> E)) and (A -> (B -> ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15889.        ((A -> (B -> ((C and D) -> C))) and ((E -> (F -> E)) and (A -> (B -> ((C and D) -> C))))), M:tm-323, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-15890
in-theory        15890
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and ((C -> (D -> C)) and ((A and (A -> B)) -> B)))
theorem-size     21
proof            (modus-ponens tm-323 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-15890.        (((A and (A -> B)) -> B) and ((C -> (D -> C)) and ((A and (A -> B)) -> B))), M:tm-323, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-15891
in-theory        15891
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and ((E -> (F -> E)) and ((A and ((B -> (C -> B)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-323 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-15891.        (((A and ((B -> (C -> B)) -> D)) -> D) and ((E -> (F -> E)) and ((A and ((B -> (C -> B)) -> D)) -> D))), M:tm-323, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-15892
in-theory        15892
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((F -> (G -> F)) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E)))
theorem-size     45
proof            (modus-ponens tm-323 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-15892.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((F -> (G -> F)) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E))), M:tm-323, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-15893
in-theory        15893
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and ((E -> (F -> E)) and ((A and (((B and C) -> B) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-323 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-15893.        (((A and (((B and C) -> B) -> D)) -> D) and ((E -> (F -> E)) and ((A and (((B and C) -> B) -> D)) -> D))), M:tm-323, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-15894
in-theory        15894
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((D -> (E -> D)) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-323 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-15894.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((D -> (E -> D)) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)))), M:tm-323, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-15895
in-theory        15895
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((D -> (E -> D)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B))))
theorem-size     37
proof            (modus-ponens tm-323 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15895.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((D -> (E -> D)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)))), M:tm-323, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-15896
in-theory        15896
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((D -> (E -> D)) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B)))))
theorem-size     57
proof            (modus-ponens tm-323 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15896.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((D -> (E -> D)) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))))), M:tm-323, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-15897
in-theory        15897
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((E -> (F -> E)) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))))
theorem-size     61
proof            (modus-ponens tm-323 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-15897.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((E -> (F -> E)) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))), M:tm-323, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-15898
in-theory        15898
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F -> E)) and (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15898.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F -> E)) and (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-323, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-15899
in-theory        15899
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and ((E -> (F -> E)) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D)))
theorem-size     41
proof            (modus-ponens tm-323 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15899.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and ((E -> (F -> E)) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D))), M:tm-323, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-15900
in-theory        15900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((E -> (F -> E)) and (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))))
theorem-size     45
proof            (modus-ponens tm-323 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15900.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((E -> (F -> E)) and (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)))), M:tm-323, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-15901
in-theory        15901
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((D -> (E -> D)) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C))))
theorem-size     53
proof            (modus-ponens tm-323 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-15901.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((D -> (E -> D)) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)))), M:tm-323, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-15902
in-theory        15902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F -> E)) and (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15902.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F -> E)) and (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-323, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-15903
in-theory        15903
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and ((E -> (F -> E)) and ((A and (((B and C) -> C) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-323 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-15903.        (((A and (((B and C) -> C) -> D)) -> D) and ((E -> (F -> E)) and ((A and (((B and C) -> C) -> D)) -> D))), M:tm-323, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-15904
in-theory        15904
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and ((E -> (F -> E)) and (((((A and B) -> B) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-323 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-15904.        ((((((A and B) -> B) -> C) and D) -> C) and ((E -> (F -> E)) and (((((A and B) -> B) -> C) and D) -> C))), M:tm-323, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-15905
in-theory        15905
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((D -> (E -> D)) and (((A and B) -> (B -> C)) -> ((A and B) -> C))))
theorem-size     33
proof            (modus-ponens tm-323 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-15905.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((D -> (E -> D)) and (((A and B) -> (B -> C)) -> ((A and B) -> C)))), M:tm-323, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-15906
in-theory        15906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not ((B and C) -> C))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15906.        (((A -> (not ((B and C) -> C))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not ((B and C) -> C))) -> (not A)))), M:tm-323, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-15907
in-theory        15907
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((E -> (F -> E)) and ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C))))
theorem-size     41
proof            (modus-ponens tm-323 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-15907.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((E -> (F -> E)) and ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)))), M:tm-323, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-15908
in-theory        15908
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and ((E -> (F -> E)) and (A or (B -> ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15908.        ((A or (B -> ((C and D) -> D))) and ((E -> (F -> E)) and (A or (B -> ((C and D) -> D))))), M:tm-323, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-15909
in-theory        15909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and ((E -> (F -> E)) and ((A -> ((B and C) -> C)) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15909.        (((A -> ((B and C) -> C)) or D) and ((E -> (F -> E)) and ((A -> ((B and C) -> C)) or D))), M:tm-323, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-15910
in-theory        15910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and ((E -> (F -> E)) and (A -> ((B -> ((C and D) -> D)) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15910.        ((A -> ((B -> ((C and D) -> D)) and A)) and ((E -> (F -> E)) and (A -> ((B -> ((C and D) -> D)) and A)))), M:tm-323, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-15911
in-theory        15911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and ((D -> (E -> D)) and ((A -> (B and C)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-323 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-15911.        (((A -> (B and C)) -> (A -> C)) and ((D -> (E -> D)) and ((A -> (B and C)) -> (A -> C)))), M:tm-323, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-15912
in-theory        15912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and ((E -> (F -> E)) and (A -> (B -> ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15912.        ((A -> (B -> ((C and D) -> D))) and ((E -> (F -> E)) and (A -> (B -> ((C and D) -> D))))), M:tm-323, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-15913
in-theory        15913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and ((E -> (F -> E)) and ((A -> (B -> A)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15913.        (((A -> (B -> A)) and (C -> (D -> C))) and ((E -> (F -> E)) and ((A -> (B -> A)) and (C -> (D -> C))))), M:tm-323, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-15914
in-theory        15914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15914.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-323, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-15915
in-theory        15915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and ((E -> (F -> E)) and ((A -> (B -> A)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15915.        (((A -> (B -> A)) and ((C and D) -> C)) and ((E -> (F -> E)) and ((A -> (B -> A)) and ((C and D) -> C)))), M:tm-323, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-15916
in-theory        15916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and ((E -> (F -> E)) and ((A -> (B -> A)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-323 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15916.        (((A -> (B -> A)) and ((C and D) -> D)) and ((E -> (F -> E)) and ((A -> (B -> A)) and ((C and D) -> D)))), M:tm-323, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-15917
in-theory        15917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A -> (B -> A)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15917.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A -> (B -> A)) and (C -> (D -> (C and D)))))), M:tm-323, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-15918
in-theory        15918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and ((E -> (F -> E)) and ((A -> (B -> A)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15918.        (((A -> (B -> A)) and (C -> (C or D))) and ((E -> (F -> E)) and ((A -> (B -> A)) and (C -> (C or D))))), M:tm-323, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-15919
in-theory        15919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and ((E -> (F -> E)) and ((A -> (B -> A)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15919.        (((A -> (B -> A)) and (C -> (D or C))) and ((E -> (F -> E)) and ((A -> (B -> A)) and (C -> (D or C))))), M:tm-323, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-15920
in-theory        15920
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15920.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-323, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-15921
in-theory        15921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> E)) and ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15921.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> E)) and ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-323, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-15922
in-theory        15922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and ((D -> (E -> D)) and ((A -> (B -> A)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15922.        (((A -> (B -> A)) and ((not (not C)) -> C)) and ((D -> (E -> D)) and ((A -> (B -> A)) and ((not (not C)) -> C)))), M:tm-323, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-15923
in-theory        15923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15923.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> (D -> (E -> D)))))), M:tm-323, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-15924
in-theory        15924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((E -> (F -> E)) and ((A -> (B -> A)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15924.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((E -> (F -> E)) and ((A -> (B -> A)) and ((C -> D) -> (C -> C))))), M:tm-323, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-15925
in-theory        15925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-323 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15925.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-323, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-15926
in-theory        15926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15926.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-323, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-15927
in-theory        15927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15927.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-323, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-15928
in-theory        15928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15928.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> ((D and E) -> D))))), M:tm-323, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-15929
in-theory        15929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15929.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-323, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-15930
in-theory        15930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15930.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> ((D and E) -> E))))), M:tm-323, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-15931
in-theory        15931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15931.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-323, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-15932
in-theory        15932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-15932.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A)))), M:tm-323, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-15933
in-theory        15933
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((E -> (F -> E)) and ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-323 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-15933.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((E -> (F -> E)) and ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)))), M:tm-323, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-15934
in-theory        15934
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and ((E -> (F -> E)) and (A or (B -> ((C -> (D -> C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15934.        ((A or (B -> ((C -> (D -> C)) and B))) and ((E -> (F -> E)) and (A or (B -> ((C -> (D -> C)) and B))))), M:tm-323, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-15935
in-theory        15935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and ((E -> (F -> E)) and ((A -> ((B -> (C -> B)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-323 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15935.        (((A -> ((B -> (C -> B)) and A)) or D) and ((E -> (F -> E)) and ((A -> ((B -> (C -> B)) and A)) or D))), M:tm-323, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-15936
in-theory        15936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((E -> (F -> E)) and (A -> ((B -> ((C -> (D -> C)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15936.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((E -> (F -> E)) and (A -> ((B -> ((C -> (D -> C)) and B)) and A)))), M:tm-323, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-15937
in-theory        15937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and ((E -> (F -> E)) and (A -> (B -> ((C -> (D -> C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15937.        ((A -> (B -> ((C -> (D -> C)) and B))) and ((E -> (F -> E)) and (A -> (B -> ((C -> (D -> C)) and B))))), M:tm-323, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-15938
in-theory        15938
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15938.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))))), M:tm-323, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-15939
in-theory        15939
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15939.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-323, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-15940
in-theory        15940
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-323 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15940.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)))), M:tm-323, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-15941
in-theory        15941
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-323 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15941.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)))), M:tm-323, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-15942
in-theory        15942
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15942.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))))), M:tm-323, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-15943
in-theory        15943
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15943.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))))), M:tm-323, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-15944
in-theory        15944
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15944.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))))), M:tm-323, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-15945
in-theory        15945
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15945.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-323, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-15946
in-theory        15946
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     57
proof            (modus-ponens tm-323 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15946.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-323, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-15947
in-theory        15947
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((E -> (F -> E)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D))))
theorem-size     45
proof            (modus-ponens tm-323 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15947.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((E -> (F -> E)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)))), M:tm-323, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-15948
in-theory        15948
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15948.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))))), M:tm-323, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-15949
in-theory        15949
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15949.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))))), M:tm-323, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-15950
in-theory        15950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     73
proof            (modus-ponens tm-323 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       249
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15950.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-323, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-15951
in-theory        15951
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-323 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15951.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-323, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-15952
in-theory        15952
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     65
proof            (modus-ponens tm-323 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15952.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-323, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-15953
in-theory        15953
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15953.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))))), M:tm-323, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-15954
in-theory        15954
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     65
proof            (modus-ponens tm-323 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15954.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-323, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-15955
in-theory        15955
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15955.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))))), M:tm-323, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-15956
in-theory        15956
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15956.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-323, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-15957
in-theory        15957
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (I -> H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-323 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15957.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (I -> H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-323, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-15958
in-theory        15958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> G)) and ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15958.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> G)) and ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-323, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-15959
in-theory        15959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((E -> (F -> E)) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A))))
theorem-size     49
proof            (modus-ponens tm-323 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-15959.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((E -> (F -> E)) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)))), M:tm-323, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-15960
in-theory        15960
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((F -> (G -> F)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))))
theorem-size     81
proof            (modus-ponens tm-323 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-15960.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((F -> (G -> F)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))), M:tm-323, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-15961
in-theory        15961
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G -> F)) and (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15961.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G -> F)) and (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-323, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-15962
in-theory        15962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and ((F -> (G -> F)) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E)))
theorem-size     45
proof            (modus-ponens tm-323 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15962.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and ((F -> (G -> F)) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E))), M:tm-323, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-15963
in-theory        15963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((F -> (G -> F)) and (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))))
theorem-size     49
proof            (modus-ponens tm-323 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15963.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((F -> (G -> F)) and (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)))), M:tm-323, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-15964
in-theory        15964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G -> F)) and (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15964.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G -> F)) and (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-323, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-15965
in-theory        15965
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and ((E -> (F -> E)) and (((A and B) -> A) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15965.        ((((A and B) -> A) and (C -> (D -> C))) and ((E -> (F -> E)) and (((A and B) -> A) and (C -> (D -> C))))), M:tm-323, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-15966
in-theory        15966
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15966.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-323, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-15967
in-theory        15967
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and ((E -> (F -> E)) and (((A and B) -> A) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15967.        ((((A and B) -> A) and ((C and D) -> C)) and ((E -> (F -> E)) and (((A and B) -> A) and ((C and D) -> C)))), M:tm-323, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-15968
in-theory        15968
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and ((E -> (F -> E)) and (((A and B) -> A) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-323 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15968.        ((((A and B) -> A) and ((C and D) -> D)) and ((E -> (F -> E)) and (((A and B) -> A) and ((C and D) -> D)))), M:tm-323, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-15969
in-theory        15969
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((E -> (F -> E)) and (((A and B) -> A) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15969.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((E -> (F -> E)) and (((A and B) -> A) and (C -> (D -> (C and D)))))), M:tm-323, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-15970
in-theory        15970
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and ((E -> (F -> E)) and (((A and B) -> A) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15970.        ((((A and B) -> A) and (C -> (C or D))) and ((E -> (F -> E)) and (((A and B) -> A) and (C -> (C or D))))), M:tm-323, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-15971
in-theory        15971
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and ((E -> (F -> E)) and (((A and B) -> A) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15971.        ((((A and B) -> A) and (C -> (D or C))) and ((E -> (F -> E)) and (((A and B) -> A) and (C -> (D or C))))), M:tm-323, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-15972
in-theory        15972
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-15972.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-323, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-15973
in-theory        15973
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> E)) and (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-15973.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> E)) and (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-323, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-15974
in-theory        15974
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and ((D -> (E -> D)) and (((A and B) -> A) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-15974.        ((((A and B) -> A) and ((not (not C)) -> C)) and ((D -> (E -> D)) and (((A and B) -> A) and ((not (not C)) -> C)))), M:tm-323, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-15975
in-theory        15975
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-15975.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> (D -> (E -> D)))))), M:tm-323, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-15976
in-theory        15976
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((E -> (F -> E)) and (((A and B) -> A) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-15976.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((E -> (F -> E)) and (((A and B) -> A) and ((C -> D) -> (C -> C))))), M:tm-323, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-15977
in-theory        15977
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> F)) and (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-323 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-15977.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> F)) and (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-323, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-15978
in-theory        15978
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-15978.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-323, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-15979
in-theory        15979
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> F)) and (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-15979.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> F)) and (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-323, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-15980
in-theory        15980
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-15980.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> ((D and E) -> D))))), M:tm-323, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-15981
in-theory        15981
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> F)) and (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-15981.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> F)) and (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-323, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-15982
in-theory        15982
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-15982.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> ((D and E) -> E))))), M:tm-323, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-15983
in-theory        15983
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-15983.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))))), M:tm-323, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-15984
in-theory        15984
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> G)) and (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-15984.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> G)) and (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-323, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-15985
in-theory        15985
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15985.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> (((D and E) -> D) and C))))), M:tm-323, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-15986
in-theory        15986
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15986.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-323, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-15987
in-theory        15987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15987.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))))), M:tm-323, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-15988
in-theory        15988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not (((B and C) -> B) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15988.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not (((B and C) -> B) and A))) -> (not A)))), M:tm-323, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-15989
in-theory        15989
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((E -> (F -> E)) and (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-323 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15989.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((E -> (F -> E)) and (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)))), M:tm-323, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-15990
in-theory        15990
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and ((E -> (F -> E)) and (A or (B -> (((C and D) -> C) and B)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15990.        ((A or (B -> (((C and D) -> C) and B))) and ((E -> (F -> E)) and (A or (B -> (((C and D) -> C) and B))))), M:tm-323, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-15991
in-theory        15991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and ((E -> (F -> E)) and ((A -> (((B and C) -> B) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-323 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15991.        (((A -> (((B and C) -> B) and A)) or D) and ((E -> (F -> E)) and ((A -> (((B and C) -> B) and A)) or D))), M:tm-323, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-15992
in-theory        15992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((E -> (F -> E)) and (A -> ((B -> (((C and D) -> C) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15992.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((E -> (F -> E)) and (A -> ((B -> (((C and D) -> C) and B)) and A)))), M:tm-323, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-15993
in-theory        15993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and ((E -> (F -> E)) and (A -> (B -> (((C and D) -> C) and B)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-15993.        ((A -> (B -> (((C and D) -> C) and B))) and ((E -> (F -> E)) and (A -> (B -> (((C and D) -> C) and B))))), M:tm-323, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-15994
in-theory        15994
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and ((E -> (F -> E)) and (((A and B) -> B) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15994.        ((((A and B) -> B) and (C -> (D -> C))) and ((E -> (F -> E)) and (((A and B) -> B) and (C -> (D -> C))))), M:tm-323, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-15995
in-theory        15995
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15995.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-323, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-15996
in-theory        15996
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and ((E -> (F -> E)) and (((A and B) -> B) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15996.        ((((A and B) -> B) and ((C and D) -> C)) and ((E -> (F -> E)) and (((A and B) -> B) and ((C and D) -> C)))), M:tm-323, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-15997
in-theory        15997
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and ((E -> (F -> E)) and (((A and B) -> B) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-323 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15997.        ((((A and B) -> B) and ((C and D) -> D)) and ((E -> (F -> E)) and (((A and B) -> B) and ((C and D) -> D)))), M:tm-323, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-15998
in-theory        15998
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((E -> (F -> E)) and (((A and B) -> B) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15998.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((E -> (F -> E)) and (((A and B) -> B) and (C -> (D -> (C and D)))))), M:tm-323, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-15999
in-theory        15999
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and ((E -> (F -> E)) and (((A and B) -> B) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15999.        ((((A and B) -> B) and (C -> (C or D))) and ((E -> (F -> E)) and (((A and B) -> B) and (C -> (C or D))))), M:tm-323, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-16000
in-theory        16000
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and ((E -> (F -> E)) and (((A and B) -> B) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16000.        ((((A and B) -> B) and (C -> (D or C))) and ((E -> (F -> E)) and (((A and B) -> B) and (C -> (D or C))))), M:tm-323, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-16001
in-theory        16001
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16001.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-323, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-16002
in-theory        16002
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> E)) and (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16002.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> E)) and (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-323, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-16003
in-theory        16003
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and ((D -> (E -> D)) and (((A and B) -> B) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16003.        ((((A and B) -> B) and ((not (not C)) -> C)) and ((D -> (E -> D)) and (((A and B) -> B) and ((not (not C)) -> C)))), M:tm-323, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-16004
in-theory        16004
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16004.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> (D -> (E -> D)))))), M:tm-323, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-16005
in-theory        16005
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((E -> (F -> E)) and (((A and B) -> B) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16005.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((E -> (F -> E)) and (((A and B) -> B) and ((C -> D) -> (C -> C))))), M:tm-323, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-16006
in-theory        16006
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> F)) and (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-323 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16006.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> F)) and (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-323, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-16007
in-theory        16007
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16007.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-323, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-16008
in-theory        16008
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> F)) and (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16008.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> F)) and (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-323, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-16009
in-theory        16009
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16009.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> ((D and E) -> D))))), M:tm-323, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-16010
in-theory        16010
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> F)) and (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16010.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> F)) and (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-323, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-16011
in-theory        16011
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16011.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> ((D and E) -> E))))), M:tm-323, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-16012
in-theory        16012
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16012.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))))), M:tm-323, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-16013
in-theory        16013
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> G)) and (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16013.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> G)) and (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-323, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-16014
in-theory        16014
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16014.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> (((D and E) -> D) and C))))), M:tm-323, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-16015
in-theory        16015
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16015.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> (((D and E) -> E) and C))))), M:tm-323, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-16016
in-theory        16016
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16016.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> (((D and E) -> E) and C))))), M:tm-323, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-16017
in-theory        16017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16017.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-323, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-16018
in-theory        16018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16018.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))))), M:tm-323, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-16019
in-theory        16019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not (((B and C) -> C) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-16019.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not (((B and C) -> C) and A))) -> (not A)))), M:tm-323, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-16020
in-theory        16020
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((E -> (F -> E)) and (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-323 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-16020.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((E -> (F -> E)) and (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)))), M:tm-323, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-16021
in-theory        16021
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and ((E -> (F -> E)) and (A or (B -> (((C and D) -> D) and B)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16021.        ((A or (B -> (((C and D) -> D) and B))) and ((E -> (F -> E)) and (A or (B -> (((C and D) -> D) and B))))), M:tm-323, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-16022
in-theory        16022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and ((E -> (F -> E)) and ((A -> (((B and C) -> C) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-323 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16022.        (((A -> (((B and C) -> C) and A)) or D) and ((E -> (F -> E)) and ((A -> (((B and C) -> C) and A)) or D))), M:tm-323, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-16023
in-theory        16023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((E -> (F -> E)) and (A -> ((B -> (((C and D) -> D) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16023.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((E -> (F -> E)) and (A -> ((B -> (((C and D) -> D) and B)) and A)))), M:tm-323, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-16024
in-theory        16024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and ((E -> (F -> E)) and (A -> (B -> (((C and D) -> D) and B)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16024.        ((A -> (B -> (((C and D) -> D) and B))) and ((E -> (F -> E)) and (A -> (B -> (((C and D) -> D) and B))))), M:tm-323, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-16025
in-theory        16025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and (C -> (D -> C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16025.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and (C -> (D -> C))))), M:tm-323, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-16026
in-theory        16026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16026.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-323, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-16027
in-theory        16027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and ((C and D) -> C))))
theorem-size     33
proof            (modus-ponens tm-323 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16027.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and ((C and D) -> C)))), M:tm-323, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-16028
in-theory        16028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and ((C and D) -> D))))
theorem-size     33
proof            (modus-ponens tm-323 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16028.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and ((C and D) -> D)))), M:tm-323, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-16029
in-theory        16029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and (C -> (D -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16029.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))))), M:tm-323, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-16030
in-theory        16030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and (C -> (C or D)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16030.        (((A -> (B -> (A and B))) and (C -> (C or D))) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and (C -> (C or D))))), M:tm-323, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-16031
in-theory        16031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and (C -> (D or C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16031.        (((A -> (B -> (A and B))) and (C -> (D or C))) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and (C -> (D or C))))), M:tm-323, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-16032
in-theory        16032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16032.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-323, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-16033
in-theory        16033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16033.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-323, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-16034
in-theory        16034
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((D -> (E -> D)) and ((A -> (B -> (A and B))) and ((not (not C)) -> C))))
theorem-size     33
proof            (modus-ponens tm-323 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16034.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((D -> (E -> D)) and ((A -> (B -> (A and B))) and ((not (not C)) -> C)))), M:tm-323, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-16035
in-theory        16035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16035.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))))), M:tm-323, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-16036
in-theory        16036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16036.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))))), M:tm-323, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-16037
in-theory        16037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16037.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-323, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-16038
in-theory        16038
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     53
proof            (modus-ponens tm-323 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16038.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-323, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-16039
in-theory        16039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16039.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-323, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-16040
in-theory        16040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> D)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16040.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))))), M:tm-323, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-16041
in-theory        16041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16041.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-323, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-16042
in-theory        16042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> E)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16042.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))))), M:tm-323, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-16043
in-theory        16043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16043.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))))), M:tm-323, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-16044
in-theory        16044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> G)) and ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     57
proof            (modus-ponens tm-323 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16044.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> G)) and ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-323, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-16045
in-theory        16045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16045.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))))), M:tm-323, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-16046
in-theory        16046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16046.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))))), M:tm-323, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-16047
in-theory        16047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16047.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-323, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-16048
in-theory        16048
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16048.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-323, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-16049
in-theory        16049
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16049.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-323, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-16050
in-theory        16050
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     57
proof            (modus-ponens tm-323 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16050.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-323, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-16051
in-theory        16051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16051.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-323, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-16052
in-theory        16052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A))))
theorem-size     37
proof            (modus-ponens tm-323 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-16052.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)))), M:tm-323, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-16053
in-theory        16053
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((E -> (F -> E)) and ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-323 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-16053.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((E -> (F -> E)) and ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)))), M:tm-323, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-16054
in-theory        16054
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F -> E)) and (A or (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16054.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F -> E)) and (A or (B -> ((C -> (D -> (C and D))) and B))))), M:tm-323, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-16055
in-theory        16055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and ((E -> (F -> E)) and ((A -> ((B -> (C -> (B and C))) and A)) or D)))
theorem-size     33
proof            (modus-ponens tm-323 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16055.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and ((E -> (F -> E)) and ((A -> ((B -> (C -> (B and C))) and A)) or D))), M:tm-323, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-16056
in-theory        16056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((E -> (F -> E)) and (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A))))
theorem-size     37
proof            (modus-ponens tm-323 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16056.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((E -> (F -> E)) and (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)))), M:tm-323, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-16057
in-theory        16057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F -> E)) and (A -> (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16057.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F -> E)) and (A -> (B -> ((C -> (D -> (C and D))) and B))))), M:tm-323, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-16058
in-theory        16058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and ((C -> (D -> C)) and (A -> (A and (B -> A)))))
theorem-size     21
proof            (modus-ponens tm-323 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16058.        ((A -> (A and (B -> A))) and ((C -> (D -> C)) and (A -> (A and (B -> A))))), M:tm-323, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-16059
in-theory        16059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((D -> (E -> D)) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-16059.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((D -> (E -> D)) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))), M:tm-323, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-16060
in-theory        16060
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and ((C -> (D -> C)) and ((A and B) -> ((A and B) and A))))
theorem-size     25
proof            (modus-ponens tm-323 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16060.        (((A and B) -> ((A and B) and A)) and ((C -> (D -> C)) and ((A and B) -> ((A and B) and A)))), M:tm-323, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-16061
in-theory        16061
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and ((C -> (D -> C)) and ((A and B) -> ((A and B) and B))))
theorem-size     25
proof            (modus-ponens tm-323 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-16061.        (((A and B) -> ((A and B) and B)) and ((C -> (D -> C)) and ((A and B) -> ((A and B) and B)))), M:tm-323, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-16062
in-theory        16062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and ((C -> (D -> C)) and (A -> (A and (B -> (A and B))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-16062.        ((A -> (A and (B -> (A and B)))) and ((C -> (D -> C)) and (A -> (A and (B -> (A and B)))))), M:tm-323, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-16063
in-theory        16063
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and ((C -> (D -> C)) and (A -> (A and (A or B)))))
theorem-size     21
proof            (modus-ponens tm-323 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-16063.        ((A -> (A and (A or B))) and ((C -> (D -> C)) and (A -> (A and (A or B))))), M:tm-323, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-16064
in-theory        16064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and ((C -> (D -> C)) and (A -> (A and (B or A)))))
theorem-size     21
proof            (modus-ponens tm-323 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-16064.        ((A -> (A and (B or A))) and ((C -> (D -> C)) and (A -> (A and (B or A))))), M:tm-323, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-16065
in-theory        16065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((D -> (E -> D)) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-16065.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((D -> (E -> D)) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))))), M:tm-323, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-16066
in-theory        16066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((C -> (D -> C)) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-16066.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((C -> (D -> C)) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))))), M:tm-323, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-16067
in-theory        16067
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and ((B -> (C -> B)) and ((not (not A)) -> ((not (not A)) and A))))
theorem-size     25
proof            (modus-ponens tm-323 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-16067.        (((not (not A)) -> ((not (not A)) and A)) and ((B -> (C -> B)) and ((not (not A)) -> ((not (not A)) and A)))), M:tm-323, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-16068
in-theory        16068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and ((D -> (E -> D)) and (A -> (A and (B -> (C -> B))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-16068.        ((A -> (A and (B -> (C -> B)))) and ((D -> (E -> D)) and (A -> (A and (B -> (C -> B)))))), M:tm-323, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-16069
in-theory        16069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and ((C -> (D -> C)) and ((A -> B) -> ((A -> B) and (A -> A)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-16069.        (((A -> B) -> ((A -> B) and (A -> A))) and ((C -> (D -> C)) and ((A -> B) -> ((A -> B) and (A -> A))))), M:tm-323, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-16070
in-theory        16070
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((D -> (E -> D)) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-323 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-16070.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((D -> (E -> D)) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))), M:tm-323, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-16071
in-theory        16071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((E -> (F -> E)) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-16071.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((E -> (F -> E)) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))), M:tm-323, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-16072
in-theory        16072
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((D -> (E -> D)) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-16072.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((D -> (E -> D)) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))), M:tm-323, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-16073
in-theory        16073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and ((D -> (E -> D)) and (A -> (A and ((B and C) -> B)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-16073.        ((A -> (A and ((B and C) -> B))) and ((D -> (E -> D)) and (A -> (A and ((B and C) -> B))))), M:tm-323, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-16074
in-theory        16074
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((D -> (E -> D)) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-16074.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((D -> (E -> D)) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))), M:tm-323, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-16075
in-theory        16075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and ((D -> (E -> D)) and (A -> (A and ((B and C) -> C)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-16075.        ((A -> (A and ((B and C) -> C))) and ((D -> (E -> D)) and (A -> (A and ((B and C) -> C))))), M:tm-323, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-16076
in-theory        16076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and ((D -> (E -> D)) and (A -> (A and ((B -> (C -> B)) and A)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16076.        ((A -> (A and ((B -> (C -> B)) and A))) and ((D -> (E -> D)) and (A -> (A and ((B -> (C -> B)) and A))))), M:tm-323, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16077
in-theory        16077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16077.        ((A -> (A and ((B -> (C -> B)) and A))) and ((D and E) -> E)), M:tm-322, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16078
in-theory        16078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16078.        ((A -> (A and ((B -> (C -> B)) and A))) and ((D and E) -> D)), M:tm-320, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16079
in-theory        16079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16079.        ((A -> (A and ((B -> (C -> B)) and A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16080
in-theory        16080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16080.        ((A -> (A and ((B -> (C -> B)) and A))) and (A -> A)), M:tm-316, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-16081
in-theory        16081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16081.        ((A -> (A and ((B -> (C -> B)) and A))) and (D -> (E -> D))), M:tm-315, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16082
in-theory        16082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and ((A -> (not (A and ((B -> (C -> B)) and A)))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16082.        ((A -> (A and ((B -> (C -> B)) and A))) and ((A -> (not (A and ((B -> (C -> B)) and A)))) -> (not A))), M:tm-313, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-16083
in-theory        16083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (((A and ((B -> (C -> B)) and A)) -> D) -> ((A or (A and ((B -> (C -> B)) and A))) -> D)))
theorem-size     37
proof            (modus-ponens tm-312 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16083.        ((A -> (A and ((B -> (C -> B)) and A))) and (((A and ((B -> (C -> B)) and A)) -> D) -> ((A or (A and ((B -> (C -> B)) and A))) -> D))), M:tm-312, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-16084
in-theory        16084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (D or (A -> (A and ((B -> (C -> B)) and A)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16084.        ((A -> (A and ((B -> (C -> B)) and A))) and (D or (A -> (A and ((B -> (C -> B)) and A))))), M:tm-311, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16085
in-theory        16085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and ((A -> (A and ((B -> (C -> B)) and A))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16085.        ((A -> (A and ((B -> (C -> B)) and A))) and ((A -> (A and ((B -> (C -> B)) and A))) or D)), M:tm-310, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16086
in-theory        16086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (D -> ((A -> (A and ((B -> (C -> B)) and A))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16086.        ((A -> (A and ((B -> (C -> B)) and A))) and (D -> ((A -> (A and ((B -> (C -> B)) and A))) and D))), M:tm-309, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16087
in-theory        16087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (D -> (A -> (A and ((B -> (C -> B)) and A)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16087.        ((A -> (A and ((B -> (C -> B)) and A))) and (D -> (A -> (A and ((B -> (C -> B)) and A))))), M:tm-305, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16088
in-theory        16088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     23
proof            (modus-ponens tm-303 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16088.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-303, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16089
in-theory        16089
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and ((D -> (E -> D)) and ((B -> (C -> (B and C))) and A))))
theorem-size     37
proof            (modus-ponens tm-300 tm-323 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (and (-> Bm (-> Cm Bm)) (and (-> A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16089.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and ((D -> (E -> D)) and ((B -> (C -> (B and C))) and A)))), M:tm-300, m:tm-323, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (and (-> Bm (-> Cm Bm)) (and (-> A (-> B (and A B))) C)))))
================================================================
tm-name          tm-16090
in-theory        16090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-270 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16090.        ((A -> (((B and C) -> C) and A)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-270, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16091
in-theory        16091
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((D -> (E -> D)) and (((B and C) -> C) and A))))
theorem-size     31
proof            (modus-ponens tm-267 tm-323 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (and (-> Bm (-> Cm Bm)) (and (-> (and A B) B) C))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16091.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((D -> (E -> D)) and (((B and C) -> C) and A)))), M:tm-267, m:tm-323, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (and (-> Bm (-> Cm Bm)) (and (-> (and A B) B) C)))))
================================================================
tm-name          tm-16092
in-theory        16092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-239 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16092.        ((A -> (((B and C) -> B) and A)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-239, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16093
in-theory        16093
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((D -> (E -> D)) and (((B and C) -> B) and A))))
theorem-size     31
proof            (modus-ponens tm-236 tm-323 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (and (-> Bm (-> Cm Bm)) (and (-> (and A B) A) C))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16093.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((D -> (E -> D)) and (((B and C) -> B) and A)))), M:tm-236, m:tm-323, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (and (-> Bm (-> Cm Bm)) (and (-> (and A B) A) C)))))
================================================================
tm-name          tm-16094
in-theory        16094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and ((F -> (G -> F)) and E))))
theorem-size     29
proof            (modus-ponens tm-210 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16094.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and ((F -> (G -> F)) and E)))), M:tm-210, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16095
in-theory        16095
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((E -> (F -> E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     55
proof            (modus-ponens tm-207 tm-323 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (-> Cm Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16095.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((E -> (F -> E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-207, m:tm-323, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (-> Cm Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-16096
in-theory        16096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-183 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16096.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-183, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16097
in-theory        16097
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and ((D -> (E -> D)) and ((B -> (C -> B)) and A))))
theorem-size     31
proof            (modus-ponens tm-180 tm-323 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (and (-> Bm (-> Cm Bm)) (and (-> A (-> B A)) C))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16097.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and ((D -> (E -> D)) and ((B -> (C -> B)) and A)))), M:tm-180, m:tm-323, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (and (-> Bm (-> Cm Bm)) (and (-> A (-> B A)) C)))))
================================================================
tm-name          tm-16098
in-theory        16098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-157 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16098.        ((A -> ((B and C) -> C)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-157, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16099
in-theory        16099
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((D -> (E -> D)) and ((B and C) -> C))))
theorem-size     25
proof            (modus-ponens tm-154 tm-323 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (and (-> Bm (-> Cm Bm)) (-> (and A B) B))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16099.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((D -> (E -> D)) and ((B and C) -> C)))), M:tm-154, m:tm-323, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (and (-> Bm (-> Cm Bm)) (-> (and A B) B)))))
================================================================
tm-name          tm-16100
in-theory        16100
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     27
proof            (modus-ponens tm-147 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16100.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-147, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16101
in-theory        16101
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((D -> (E -> D)) and ((A and (B -> C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-144 tm-323 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (and (-> Bm (-> Cm Bm)) (-> (and A (-> B C)) C))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16101.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((D -> (E -> D)) and ((A and (B -> C)) -> C)))), M:tm-144, m:tm-323, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (and (-> Bm (-> Cm Bm)) (-> (and A (-> B C)) C)))))
================================================================
tm-name          tm-16102
in-theory        16102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-134 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16102.        ((A -> ((B and C) -> B)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-134, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16103
in-theory        16103
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((D -> (E -> D)) and ((B and C) -> B))))
theorem-size     25
proof            (modus-ponens tm-131 tm-323 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (and (-> Bm (-> Cm Bm)) (-> (and A B) A))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16103.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((D -> (E -> D)) and ((B and C) -> B)))), M:tm-131, m:tm-323, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (and (-> Bm (-> Cm Bm)) (-> (and A B) A)))))
================================================================
tm-name          tm-16104
in-theory        16104
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     27
proof            (modus-ponens tm-125 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16104.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-125, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16105
in-theory        16105
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((D -> (E -> D)) and (((A -> B) and C) -> B))))
theorem-size     37
proof            (modus-ponens tm-122 tm-323 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (and (-> Bm (-> Cm Bm)) (-> (and (-> A B) C) B))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16105.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((D -> (E -> D)) and (((A -> B) and C) -> B)))), M:tm-122, m:tm-323, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (and (-> Bm (-> Cm Bm)) (-> (and (-> A B) C) B)))))
================================================================
tm-name          tm-16106
in-theory        16106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-113 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16106.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G -> F)) and E)))), M:tm-113, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16107
in-theory        16107
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-110 tm-323 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (-> Bm (-> Cm Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16107.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-110, m:tm-323, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (-> Bm (-> Cm Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
================================================================
tm-name          tm-16108
in-theory        16108
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     31
proof            (modus-ponens tm-105 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16108.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-105, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16109
in-theory        16109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((D -> (E -> D)) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-102 tm-323 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (and (-> Bm (-> Cm Bm)) (-> (-> A (-> B C)) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16109.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((D -> (E -> D)) and ((A -> (B -> C)) -> (A -> C))))), M:tm-102, m:tm-323, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (and (-> Bm (-> Cm Bm)) (-> (-> A (-> B C)) (-> A C))))))
================================================================
tm-name          tm-16110
in-theory        16110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and ((D -> (E -> D)) and C))))
theorem-size     19
proof            (modus-ponens tm-95 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16110.        (((A -> B) -> (A -> A)) and (C -> (C and ((D -> (E -> D)) and C)))), M:tm-95, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16111
in-theory        16111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and ((C -> (D -> C)) and (A -> A))))
theorem-size     21
proof            (modus-ponens tm-92 tm-323 ((Am (-> A A)) (B (and (-> A A) (and (-> Bm (-> Cm Bm)) (-> A A))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16111.        (((A -> B) or (A -> A)) -> ((A -> A) and ((C -> (D -> C)) and (A -> A)))), M:tm-92, m:tm-323, u:((Am (-> A A)) (B (and (-> A A) (and (-> Bm (-> Cm Bm)) (-> A A)))))
================================================================
tm-name          tm-16112
in-theory        16112
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and ((C -> (D -> C)) and A))))
theorem-size     13
proof            (modus-ponens tm-84 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16112.        (A -> (B -> (A and ((C -> (D -> C)) and A)))), M:tm-84, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-16113
in-theory        16113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-83 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16113.        ((A -> (B -> (C -> B))) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-83, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16114
in-theory        16114
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((D -> (E -> D)) and (B -> (C -> B)))))
theorem-size     25
proof            (modus-ponens tm-80 tm-323 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (and (-> Bm (-> Cm Bm)) (-> A (-> B A)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16114.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((D -> (E -> D)) and (B -> (C -> B))))), M:tm-80, m:tm-323, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (and (-> Bm (-> Cm Bm)) (-> A (-> B A))))))
================================================================
tm-name          tm-16115
in-theory        16115
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and ((C -> (D -> C)) and B))))
theorem-size     17
proof            (modus-ponens tm-76 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16115.        (((not (not A)) -> A) and (B -> (B and ((C -> (D -> C)) and B)))), M:tm-76, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16116
in-theory        16116
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and ((B -> (C -> B)) and A)))
theorem-size     15
proof            (modus-ponens tm-73 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16116.        (((not (not A)) or A) -> (A and ((B -> (C -> B)) and A))), M:tm-73, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-16117
in-theory        16117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and ((D -> (E -> D)) and C))))
theorem-size     23
proof            (modus-ponens tm-69 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16117.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and ((D -> (E -> D)) and C)))), M:tm-69, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16118
in-theory        16118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((C -> (D -> C)) and ((A -> (not B)) -> (not A)))))
theorem-size     33
proof            (modus-ponens tm-66 tm-323 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (and (-> Bm (-> Cm Bm)) (-> (-> A (not B)) (not A)))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16118.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((C -> (D -> C)) and ((A -> (not B)) -> (not A))))), M:tm-66, m:tm-323, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (and (-> Bm (-> Cm Bm)) (-> (-> A (not B)) (not A))))))
================================================================
tm-name          tm-16119
in-theory        16119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     25
proof            (modus-ponens tm-54 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16119.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-54, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16120
in-theory        16120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     39
proof            (modus-ponens tm-51 tm-323 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> (or C A) B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16120.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((D -> (E -> D)) and ((B -> C) -> ((A or B) -> C))))), M:tm-51, m:tm-323, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> (or C A) B))))))
================================================================
tm-name          tm-16121
in-theory        16121
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and ((C -> (D -> C)) and (B or A))))
theorem-size     19
proof            (modus-ponens tm-50 tm-323 ((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm Bm)) (or A B))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16121.        ((A or (B or A)) -> ((B or A) and ((C -> (D -> C)) and (B or A)))), M:tm-50, m:tm-323, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm Bm)) (or A B)))))
================================================================
tm-name          tm-16122
in-theory        16122
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and ((C -> (D -> C)) and (A or B))))
theorem-size     19
proof            (modus-ponens tm-49 tm-323 ((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm Bm)) (or A B))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16122.        ((A or (A or B)) -> ((A or B) and ((C -> (D -> C)) and (A or B)))), M:tm-49, m:tm-323, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm Bm)) (or A B)))))
================================================================
tm-name          tm-16123
in-theory        16123
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((C -> (D -> C)) and (B -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-48 tm-323 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> Bm (-> Cm Bm)) (-> A (and B A)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16123.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((C -> (D -> C)) and (B -> (A and B))))), M:tm-48, m:tm-323, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> Bm (-> Cm Bm)) (-> A (and B A))))))
================================================================
tm-name          tm-16124
in-theory        16124
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and ((C -> (D -> C)) and B)))
theorem-size     15
proof            (modus-ponens tm-47 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16124.        (((A and B) or B) -> (B and ((C -> (D -> C)) and B))), M:tm-47, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-16125
in-theory        16125
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and ((C -> (D -> C)) and A)))
theorem-size     15
proof            (modus-ponens tm-46 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16125.        (((A and B) or A) -> (A and ((C -> (D -> C)) and A))), M:tm-46, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-16126
in-theory        16126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))
theorem-size     35
proof            (modus-ponens tm-45 tm-323 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16126.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E -> D)) and ((A -> B) -> (A -> C))))), M:tm-45, m:tm-323, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-16127
in-theory        16127
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and ((C -> (D -> C)) and (B -> A))))
theorem-size     19
proof            (modus-ponens tm-44 tm-323 ((Am (-> A B)) (C (and (-> A B) (and (-> Bm (-> Cm Bm)) (-> A B))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16127.        ((A or (B -> A)) -> ((B -> A) and ((C -> (D -> C)) and (B -> A)))), M:tm-44, m:tm-323, u:((Am (-> A B)) (C (and (-> A B) (and (-> Bm (-> Cm Bm)) (-> A B)))))
================================================================
tm-name          tm-16128
in-theory        16128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and ((D -> (E -> D)) and C))))
theorem-size     17
proof            (modus-ponens tm-42 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16128.        ((A -> (B or A)) and (C -> (C and ((D -> (E -> D)) and C)))), M:tm-42, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16129
in-theory        16129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and ((D -> (E -> D)) and C))))
theorem-size     17
proof            (modus-ponens tm-32 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16129.        ((A -> (A or B)) and (C -> (C and ((D -> (E -> D)) and C)))), M:tm-32, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16130
in-theory        16130
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and ((B -> (C -> B)) and A))))
theorem-size     13
proof            (modus-ponens tm-24 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16130.        (A -> (A and (A and ((B -> (C -> B)) and A)))), M:tm-24, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-16131
in-theory        16131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and ((D -> (E -> D)) and C))))
theorem-size     19
proof            (modus-ponens tm-23 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16131.        ((A -> (B -> (A and B))) and (C -> (C and ((D -> (E -> D)) and C)))), M:tm-23, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16132
in-theory        16132
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and ((D -> (E -> D)) and C))))
theorem-size     17
proof            (modus-ponens tm-22 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16132.        (((A and B) -> B) and (C -> (C and ((D -> (E -> D)) and C)))), M:tm-22, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16133
in-theory        16133
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and ((D -> (E -> D)) and C))))
theorem-size     17
proof            (modus-ponens tm-21 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16133.        (((A and B) -> A) and (C -> (C and ((D -> (E -> D)) and C)))), M:tm-21, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16134
in-theory        16134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     25
proof            (modus-ponens tm-20 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16134.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-20, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16135
in-theory        16135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and ((D -> (E -> D)) and C))))
theorem-size     17
proof            (modus-ponens tm-19 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16135.        ((A -> (B -> A)) and (C -> (C and ((D -> (E -> D)) and C)))), M:tm-19, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16136
in-theory        16136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and ((B -> (C -> B)) and A)))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-9 tm-2 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16136.        ((A -> (not (A and ((B -> (C -> B)) and A)))) -> (not A)), M:tm-9, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-16137
in-theory        16137
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) and A)) -> D) -> ((A or (A and ((B -> (C -> B)) and A))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16137.        (((A and ((B -> (C -> B)) and A)) -> D) -> ((A or (A and ((B -> (C -> B)) and A))) -> D)), M:tm-8, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-16138
in-theory        16138
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and ((C -> (D -> C)) and B))))
theorem-size     13
proof            (modus-ponens tm-7 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-7 tm-2 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16138.        (A or (B -> (B and ((C -> (D -> C)) and B)))), M:tm-7, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16139
in-theory        16139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-6 tm-2 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16139.        ((A -> (A and ((B -> (C -> B)) and A))) or D), M:tm-6, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16140
in-theory        16140
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and ((C -> (D -> C)) and B))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16140.        (A -> ((B -> (B and ((C -> (D -> C)) and B))) and A)), M:tm-5, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16141
in-theory        16141
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and ((C -> (D -> C)) and B))))
theorem-size     13
proof            (modus-ponens tm-1 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16141.        (A -> (B -> (B and ((C -> (D -> C)) and B)))), M:tm-1, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16142
in-theory        16142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B -> A))))
theorem-size     25
proof            (modus-ponens tm-324 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16142.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B -> A)))), M:tm-324, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-16143
in-theory        16143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16143.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))), M:tm-324, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-16144
in-theory        16144
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and B) -> A)))
theorem-size     25
proof            (modus-ponens tm-324 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-16144.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and B) -> A))), M:tm-324, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-16145
in-theory        16145
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and B) -> B)))
theorem-size     25
proof            (modus-ponens tm-324 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-16145.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and B) -> B))), M:tm-324, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-16146
in-theory        16146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-324 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16146.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B -> (A and B))))), M:tm-324, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-16147
in-theory        16147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A or B))))
theorem-size     25
proof            (modus-ponens tm-324 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-16147.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A or B)))), M:tm-324, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-16148
in-theory        16148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B or A))))
theorem-size     25
proof            (modus-ponens tm-324 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-16148.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B or A)))), M:tm-324, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-16149
in-theory        16149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-16149.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))), M:tm-324, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-16150
in-theory        16150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> ((A -> (not B)) -> (not A)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-16150.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> ((A -> (not B)) -> (not A))))), M:tm-324, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-16151
in-theory        16151
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((not (not A)) -> A)))
theorem-size     25
proof            (modus-ponens tm-324 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-16151.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((not (not A)) -> A))), M:tm-324, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-16152
in-theory        16152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (B -> (C -> B)))))
theorem-size     29
proof            (modus-ponens tm-324 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16152.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (B -> (C -> B))))), M:tm-324, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-16153
in-theory        16153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> (A -> A))))
theorem-size     29
proof            (modus-ponens tm-324 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-16153.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> (A -> A)))), M:tm-324, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-16154
in-theory        16154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-16154.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-324, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-16155
in-theory        16155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16155.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-324, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-16156
in-theory        16156
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))))
theorem-size     45
proof            (modus-ponens tm-324 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16156.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)))), M:tm-324, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-16157
in-theory        16157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B and C) -> B))))
theorem-size     29
proof            (modus-ponens tm-324 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16157.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B and C) -> B)))), M:tm-324, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-16158
in-theory        16158
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))))
theorem-size     45
proof            (modus-ponens tm-324 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-16158.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)))), M:tm-324, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-16159
in-theory        16159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B and C) -> C))))
theorem-size     29
proof            (modus-ponens tm-324 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16159.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B and C) -> C)))), M:tm-324, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-16160
in-theory        16160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B -> (C -> B)) and A))))
theorem-size     33
proof            (modus-ponens tm-324 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16160.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B -> (C -> B)) and A)))), M:tm-324, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-16161
in-theory        16161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     49
proof            (modus-ponens tm-324 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16161.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-324, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16162
in-theory        16162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (((B and C) -> B) and A))))
theorem-size     33
proof            (modus-ponens tm-324 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16162.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (((B and C) -> B) and A)))), M:tm-324, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-16163
in-theory        16163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (((B and C) -> C) and A))))
theorem-size     33
proof            (modus-ponens tm-324 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16163.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (((B and C) -> C) and A)))), M:tm-324, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-16164
in-theory        16164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B -> (C -> (B and C))) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16164.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B -> (C -> (B and C))) and A)))), M:tm-324, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-16165
in-theory        16165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> (A -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16165.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> (A -> (A and B))))), M:tm-324, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-16166
in-theory        16166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (B -> (C -> (B and C))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16166.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (B -> (C -> (B and C)))))), M:tm-324, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-16167
in-theory        16167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> A)) or C)))
theorem-size     29
proof            (modus-ponens tm-324 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16167.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> A)) or C))), M:tm-324, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-16168
in-theory        16168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)))
theorem-size     45
proof            (modus-ponens tm-324 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16168.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D))), M:tm-324, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-16169
in-theory        16169
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> A) or C)))
theorem-size     29
proof            (modus-ponens tm-324 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16169.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> A) or C))), M:tm-324, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-16170
in-theory        16170
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> B) or C)))
theorem-size     29
proof            (modus-ponens tm-324 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16170.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> B) or C))), M:tm-324, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-16171
in-theory        16171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> (A and B))) or C)))
theorem-size     33
proof            (modus-ponens tm-324 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16171.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> (A and B))) or C))), M:tm-324, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-16172
in-theory        16172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (A or B)) or C)))
theorem-size     29
proof            (modus-ponens tm-324 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16172.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (A or B)) or C))), M:tm-324, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-16173
in-theory        16173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B -> (B or C)) and A))))
theorem-size     33
proof            (modus-ponens tm-324 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16173.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B -> (B or C)) and A)))), M:tm-324, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-16174
in-theory        16174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (B -> (B or C)))))
theorem-size     29
proof            (modus-ponens tm-324 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16174.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (B -> (B or C))))), M:tm-324, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-16175
in-theory        16175
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or (B -> (C -> B)))))
theorem-size     29
proof            (modus-ponens tm-324 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16175.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or (B -> (C -> B))))), M:tm-324, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-16176
in-theory        16176
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16176.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-324, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-16177
in-theory        16177
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or ((B and C) -> B))))
theorem-size     29
proof            (modus-ponens tm-324 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16177.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or ((B and C) -> B)))), M:tm-324, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-16178
in-theory        16178
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or ((B and C) -> C))))
theorem-size     29
proof            (modus-ponens tm-324 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16178.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or ((B and C) -> C)))), M:tm-324, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-16179
in-theory        16179
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or (B -> (C -> (B and C))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16179.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or (B -> (C -> (B and C)))))), M:tm-324, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-16180
in-theory        16180
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or (B -> (B or C)))))
theorem-size     29
proof            (modus-ponens tm-324 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16180.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or (B -> (B or C))))), M:tm-324, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-16181
in-theory        16181
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or (B -> (C or B)))))
theorem-size     29
proof            (modus-ponens tm-324 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16181.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or (B -> (C or B))))), M:tm-324, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-16182
in-theory        16182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B or A)) or C)))
theorem-size     29
proof            (modus-ponens tm-324 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16182.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B or A)) or C))), M:tm-324, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-16183
in-theory        16183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B -> (C or B)) and A))))
theorem-size     33
proof            (modus-ponens tm-324 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16183.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B -> (C or B)) and A)))), M:tm-324, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-16184
in-theory        16184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (B -> (C or B)))))
theorem-size     29
proof            (modus-ponens tm-324 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16184.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (B -> (C or B))))), M:tm-324, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-16185
in-theory        16185
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> C) -> ((B or (A -> B)) -> C))))
theorem-size     41
proof            (modus-ponens tm-324 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16185.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> C) -> ((B or (A -> B)) -> C)))), M:tm-324, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-16186
in-theory        16186
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     65
proof            (modus-ponens tm-324 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-16186.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-324, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-16187
in-theory        16187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (((A and C) or A) -> B))))
theorem-size     37
proof            (modus-ponens tm-324 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16187.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (((A and C) or A) -> B)))), M:tm-324, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-16188
in-theory        16188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (((C and A) or A) -> B))))
theorem-size     37
proof            (modus-ponens tm-324 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-16188.        (((A -> B) -> (((C and A) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (((C and A) or A) -> B)))), M:tm-324, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-16189
in-theory        16189
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))))
theorem-size     49
proof            (modus-ponens tm-324 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-16189.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)))), M:tm-324, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-16190
in-theory        16190
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A or B) -> C) -> ((A or (A or B)) -> C))))
theorem-size     41
proof            (modus-ponens tm-324 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-16190.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A or B) -> C) -> ((A or (A or B)) -> C)))), M:tm-324, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-16191
in-theory        16191
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A or B) -> C) -> ((B or (A or B)) -> C))))
theorem-size     41
proof            (modus-ponens tm-324 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-16191.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A or B) -> C) -> ((B or (A or B)) -> C)))), M:tm-324, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-16192
in-theory        16192
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     69
proof            (modus-ponens tm-324 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-16192.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-324, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-16193
in-theory        16193
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16193.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-324, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-16194
in-theory        16194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)))
theorem-size     45
proof            (modus-ponens tm-324 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16194.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D))), M:tm-324, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-16195
in-theory        16195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))))
theorem-size     49
proof            (modus-ponens tm-324 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16195.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)))), M:tm-324, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-16196
in-theory        16196
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-16196.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))))), M:tm-324, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-16197
in-theory        16197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16197.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-324, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-16198
in-theory        16198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> (not (B -> A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-324 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16198.        (((A -> (not (B -> A))) -> (not A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> (not (B -> A))) -> (not A)))), M:tm-324, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-16199
in-theory        16199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-16199.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))))), M:tm-324, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-16200
in-theory        16200
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A and B) -> (not A)) -> (not (A and B)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16200.        ((((A and B) -> (not A)) -> (not (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A and B) -> (not A)) -> (not (A and B))))), M:tm-324, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-16201
in-theory        16201
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A and B) -> (not B)) -> (not (A and B)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-16201.        ((((A and B) -> (not B)) -> (not (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A and B) -> (not B)) -> (not (A and B))))), M:tm-324, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-16202
in-theory        16202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> (not (B -> (A and B)))) -> (not A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-16202.        (((A -> (not (B -> (A and B)))) -> (not A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> (not (B -> (A and B)))) -> (not A)))), M:tm-324, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-16203
in-theory        16203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> (not (A or B))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-324 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-16203.        (((A -> (not (A or B))) -> (not A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> (not (A or B))) -> (not A)))), M:tm-324, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-16204
in-theory        16204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> (not (B or A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-324 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-16204.        (((A -> (not (B or A))) -> (not A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> (not (B or A))) -> (not A)))), M:tm-324, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-16205
in-theory        16205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-16205.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))))), M:tm-324, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-16206
in-theory        16206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-16206.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))))), M:tm-324, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-16207
in-theory        16207
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))))
theorem-size     61
proof            (modus-ponens tm-324 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-16207.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))), M:tm-324, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-16208
in-theory        16208
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16208.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-324, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-16209
in-theory        16209
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C)))
theorem-size     41
proof            (modus-ponens tm-324 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16209.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C))), M:tm-324, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-16210
in-theory        16210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A))))
theorem-size     45
proof            (modus-ponens tm-324 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16210.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)))), M:tm-324, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-16211
in-theory        16211
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-16211.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))))), M:tm-324, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-16212
in-theory        16212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16212.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-324, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-16213
in-theory        16213
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((not (not A)) -> (not A)) -> (not (not (not A))))))
theorem-size     37
proof            (modus-ponens tm-324 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-9 tm-10)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-16213.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((not (not A)) -> (not A)) -> (not (not (not A)))))), M:tm-324, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-16214
in-theory        16214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> (((not (not A)) or A) -> B))))
theorem-size     37
proof            (modus-ponens tm-324 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-16214.        (((A -> B) -> (((not (not A)) or A) -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> (((not (not A)) or A) -> B)))), M:tm-324, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-16215
in-theory        16215
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or ((not (not B)) -> B))))
theorem-size     29
proof            (modus-ponens tm-324 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16215.        ((A or ((not (not B)) -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or ((not (not B)) -> B)))), M:tm-324, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-16216
in-theory        16216
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((not (not A)) -> A) or B)))
theorem-size     29
proof            (modus-ponens tm-324 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16216.        ((((not (not A)) -> A) or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((not (not A)) -> A) or B))), M:tm-324, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-16217
in-theory        16217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (((not (not B)) -> B) and A))))
theorem-size     33
proof            (modus-ponens tm-324 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16217.        ((A -> (((not (not B)) -> B) and A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (((not (not B)) -> B) and A)))), M:tm-324, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-16218
in-theory        16218
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B))))
theorem-size     45
proof            (modus-ponens tm-324 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-16218.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)))), M:tm-324, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-16219
in-theory        16219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> ((not (not B)) -> B))))
theorem-size     29
proof            (modus-ponens tm-324 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16219.        ((A -> ((not (not B)) -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> ((not (not B)) -> B)))), M:tm-324, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-16220
in-theory        16220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not (B -> (C -> B)))) -> (not A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-16220.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not (B -> (C -> B)))) -> (not A)))), M:tm-324, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-16221
in-theory        16221
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C))))
theorem-size     49
proof            (modus-ponens tm-324 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-16221.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)))), M:tm-324, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-16222
in-theory        16222
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> (C -> (D -> C))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16222.        ((A or (B -> (C -> (D -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> (C -> (D -> C)))))), M:tm-324, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-16223
in-theory        16223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (C -> B))) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16223.        (((A -> (B -> (C -> B))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (C -> B))) or D))), M:tm-324, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-16224
in-theory        16224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C -> (D -> C))) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16224.        ((A -> ((B -> (C -> (D -> C))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C -> (D -> C))) and A)))), M:tm-324, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-16225
in-theory        16225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> (C -> B)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-16225.        (((A -> B) -> (A -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> (C -> B))))), M:tm-324, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-16226
in-theory        16226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> (C -> (D -> C))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16226.        ((A -> (B -> (C -> (D -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> (C -> (D -> C)))))), M:tm-324, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-16227
in-theory        16227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (A -> A)))
theorem-size     21
proof            (modus-ponens tm-324 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16227.        ((A -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (A -> A))), M:tm-324, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-16228
in-theory        16228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) -> (A -> (B -> C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-16228.        (((A -> (B -> C)) -> (A -> (B -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) -> (A -> (B -> C))))), M:tm-324, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-16229
in-theory        16229
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and B) -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-324 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16229.        (((A and B) -> (A and B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and B) -> (A and B)))), M:tm-324, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-16230
in-theory        16230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> (A -> B))))
theorem-size     29
proof            (modus-ponens tm-324 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-16230.        (((A -> B) -> (A -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> (A -> B)))), M:tm-324, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-16231
in-theory        16231
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((not (not A)) -> (not (not A)))))
theorem-size     29
proof            (modus-ponens tm-324 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-16231.        (((not (not A)) -> (not (not A))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((not (not A)) -> (not (not A))))), M:tm-324, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-16232
in-theory        16232
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A -> B) -> (not (A -> A))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-16232.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A -> B) -> (not (A -> A))) -> (not (A -> B))))), M:tm-324, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-16233
in-theory        16233
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B))))
theorem-size     45
proof            (modus-ponens tm-324 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-16233.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)))), M:tm-324, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-16234
in-theory        16234
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or ((B -> C) -> (B -> B)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16234.        ((A or ((B -> C) -> (B -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or ((B -> C) -> (B -> B))))), M:tm-324, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-16235
in-theory        16235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> (A -> A)) or C)))
theorem-size     33
proof            (modus-ponens tm-324 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16235.        ((((A -> B) -> (A -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> (A -> A)) or C))), M:tm-324, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-16236
in-theory        16236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (((B -> C) -> (B -> B)) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16236.        ((A -> (((B -> C) -> (B -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (((B -> C) -> (B -> B)) and A)))), M:tm-324, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-16237
in-theory        16237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A -> B) -> A) -> ((A -> B) -> A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-16237.        ((((A -> B) -> A) -> ((A -> B) -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A -> B) -> A) -> ((A -> B) -> A)))), M:tm-324, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-16238
in-theory        16238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B -> C) -> (B -> B)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16238.        ((A -> ((B -> C) -> (B -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B -> C) -> (B -> B))))), M:tm-324, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-16239
in-theory        16239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> ((B -> A) -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-16239.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> ((B -> A) -> C)) -> (A -> C)))), M:tm-324, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-16240
in-theory        16240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> (A -> B)) -> (A -> B))))
theorem-size     33
proof            (modus-ponens tm-324 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-16240.        (((A -> (A -> B)) -> (A -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> (A -> B)) -> (A -> B)))), M:tm-324, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-16241
in-theory        16241
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-16241.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))))), M:tm-324, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-16242
in-theory        16242
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B))))))
theorem-size     77
proof            (modus-ponens tm-324 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-16242.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))))), M:tm-324, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-16243
in-theory        16243
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))))
theorem-size     81
proof            (modus-ponens tm-324 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       257
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-16243.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))), M:tm-324, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-16244
in-theory        16244
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16244.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-324, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-16245
in-theory        16245
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D)))
theorem-size     57
proof            (modus-ponens tm-324 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16245.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D))), M:tm-324, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-16246
in-theory        16246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))))
theorem-size     61
proof            (modus-ponens tm-324 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16246.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)))), M:tm-324, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16247
in-theory        16247
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))))
theorem-size     73
proof            (modus-ponens tm-324 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       245
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-16247.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))), M:tm-324, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-16248
in-theory        16248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16248.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-324, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-16249
in-theory        16249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D))))
theorem-size     61
proof            (modus-ponens tm-324 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       247
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-16249.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)))), M:tm-324, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-16250
in-theory        16250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A))))
theorem-size     53
proof            (modus-ponens tm-324 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-16250.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)))), M:tm-324, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-16251
in-theory        16251
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))))
theorem-size     81
proof            (modus-ponens tm-324 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       245
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-16251.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))), M:tm-324, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-16252
in-theory        16252
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16252.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-324, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-16253
in-theory        16253
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     49
proof            (modus-ponens tm-324 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16253.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-324, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-16254
in-theory        16254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     53
proof            (modus-ponens tm-324 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16254.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-324, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-16255
in-theory        16255
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-16255.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))))), M:tm-324, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-16256
in-theory        16256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16256.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-324, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-16257
in-theory        16257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A -> B) and A) -> B)))
theorem-size     29
proof            (modus-ponens tm-324 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-16257.        ((((A -> B) and A) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A -> B) and A) -> B))), M:tm-324, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-16258
in-theory        16258
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B -> A)) -> C) and D) -> C)))
theorem-size     37
proof            (modus-ponens tm-324 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-16258.        (((((A -> (B -> A)) -> C) and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B -> A)) -> C) and D) -> C))), M:tm-324, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-16259
in-theory        16259
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D)))
theorem-size     53
proof            (modus-ponens tm-324 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       223
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-16259.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D))), M:tm-324, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-16260
in-theory        16260
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B))))
theorem-size     57
proof            (modus-ponens tm-324 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-16260.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)))), M:tm-324, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-16261
in-theory        16261
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A))))
theorem-size     45
proof            (modus-ponens tm-324 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-16261.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)))), M:tm-324, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-16262
in-theory        16262
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A)))))
theorem-size     65
proof            (modus-ponens tm-324 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-16262.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))))), M:tm-324, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-16263
in-theory        16263
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))))
theorem-size     69
proof            (modus-ponens tm-324 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-16263.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))), M:tm-324, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-16264
in-theory        16264
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16264.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-324, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-16265
in-theory        16265
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D)))
theorem-size     49
proof            (modus-ponens tm-324 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16265.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D))), M:tm-324, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-16266
in-theory        16266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))))
theorem-size     53
proof            (modus-ponens tm-324 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16266.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)))), M:tm-324, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-16267
in-theory        16267
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B))))
theorem-size     61
proof            (modus-ponens tm-324 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-16267.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)))), M:tm-324, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-16268
in-theory        16268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16268.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-324, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-16269
in-theory        16269
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A and B) -> A) -> C) and D) -> C)))
theorem-size     37
proof            (modus-ponens tm-324 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-16269.        ((((((A and B) -> A) -> C) and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A and B) -> A) -> C) and D) -> C))), M:tm-324, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-16270
in-theory        16270
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> (A -> C)) -> ((A and B) -> C))))
theorem-size     41
proof            (modus-ponens tm-324 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-16270.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> (A -> C)) -> ((A and B) -> C)))), M:tm-324, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-16271
in-theory        16271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not ((B and C) -> B))) -> (not A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-16271.        (((A -> (not ((B and C) -> B))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not ((B and C) -> B))) -> (not A)))), M:tm-324, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-16272
in-theory        16272
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C))))
theorem-size     49
proof            (modus-ponens tm-324 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-16272.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)))), M:tm-324, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-16273
in-theory        16273
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> ((C and D) -> C)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16273.        ((A or (B -> ((C and D) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> ((C and D) -> C))))), M:tm-324, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-16274
in-theory        16274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> ((B and C) -> B)) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16274.        (((A -> ((B and C) -> B)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> ((B and C) -> B)) or D))), M:tm-324, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-16275
in-theory        16275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> ((C and D) -> C)) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16275.        ((A -> ((B -> ((C and D) -> C)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> ((C and D) -> C)) and A)))), M:tm-324, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-16276
in-theory        16276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B and C)) -> (A -> B))))
theorem-size     33
proof            (modus-ponens tm-324 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-16276.        (((A -> (B and C)) -> (A -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B and C)) -> (A -> B)))), M:tm-324, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-16277
in-theory        16277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> ((C and D) -> C)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16277.        ((A -> (B -> ((C and D) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> ((C and D) -> C))))), M:tm-324, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-16278
in-theory        16278
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and (A -> B)) -> B)))
theorem-size     29
proof            (modus-ponens tm-324 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-16278.        (((A and (A -> B)) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and (A -> B)) -> B))), M:tm-324, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-16279
in-theory        16279
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A and ((B -> (C -> B)) -> D)) -> D)))
theorem-size     37
proof            (modus-ponens tm-324 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-16279.        (((A and ((B -> (C -> B)) -> D)) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A and ((B -> (C -> B)) -> D)) -> D))), M:tm-324, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-16280
in-theory        16280
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E)))
theorem-size     53
proof            (modus-ponens tm-324 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       223
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-16280.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E))), M:tm-324, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-16281
in-theory        16281
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A and (((B and C) -> B) -> D)) -> D)))
theorem-size     37
proof            (modus-ponens tm-324 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-16281.        (((A and (((B and C) -> B) -> D)) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A and (((B and C) -> B) -> D)) -> D))), M:tm-324, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-16282
in-theory        16282
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C))))
theorem-size     57
proof            (modus-ponens tm-324 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-16282.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)))), M:tm-324, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-16283
in-theory        16283
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B))))
theorem-size     45
proof            (modus-ponens tm-324 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-16283.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)))), M:tm-324, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-16284
in-theory        16284
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B)))))
theorem-size     65
proof            (modus-ponens tm-324 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-16284.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))))), M:tm-324, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-16285
in-theory        16285
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))))
theorem-size     69
proof            (modus-ponens tm-324 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-16285.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))), M:tm-324, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-16286
in-theory        16286
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16286.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-324, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-16287
in-theory        16287
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D)))
theorem-size     49
proof            (modus-ponens tm-324 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16287.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D))), M:tm-324, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-16288
in-theory        16288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))))
theorem-size     53
proof            (modus-ponens tm-324 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16288.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)))), M:tm-324, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-16289
in-theory        16289
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C))))
theorem-size     61
proof            (modus-ponens tm-324 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-16289.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)))), M:tm-324, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-16290
in-theory        16290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16290.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-324, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-16291
in-theory        16291
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A and (((B and C) -> C) -> D)) -> D)))
theorem-size     37
proof            (modus-ponens tm-324 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-16291.        (((A and (((B and C) -> C) -> D)) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A and (((B and C) -> C) -> D)) -> D))), M:tm-324, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-16292
in-theory        16292
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A and B) -> B) -> C) and D) -> C)))
theorem-size     37
proof            (modus-ponens tm-324 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-16292.        ((((((A and B) -> B) -> C) and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A and B) -> B) -> C) and D) -> C))), M:tm-324, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-16293
in-theory        16293
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> (B -> C)) -> ((A and B) -> C))))
theorem-size     41
proof            (modus-ponens tm-324 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-16293.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> (B -> C)) -> ((A and B) -> C)))), M:tm-324, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-16294
in-theory        16294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not ((B and C) -> C))) -> (not A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-16294.        (((A -> (not ((B and C) -> C))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not ((B and C) -> C))) -> (not A)))), M:tm-324, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-16295
in-theory        16295
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-324 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-16295.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)))), M:tm-324, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-16296
in-theory        16296
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> ((C and D) -> D)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16296.        ((A or (B -> ((C and D) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> ((C and D) -> D))))), M:tm-324, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-16297
in-theory        16297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> ((B and C) -> C)) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16297.        (((A -> ((B and C) -> C)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> ((B and C) -> C)) or D))), M:tm-324, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-16298
in-theory        16298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> ((C and D) -> D)) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16298.        ((A -> ((B -> ((C and D) -> D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> ((C and D) -> D)) and A)))), M:tm-324, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-16299
in-theory        16299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B and C)) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-324 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-16299.        (((A -> (B and C)) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B and C)) -> (A -> C)))), M:tm-324, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-16300
in-theory        16300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> ((C and D) -> D)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16300.        ((A -> (B -> ((C and D) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> ((C and D) -> D))))), M:tm-324, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-16301
in-theory        16301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and (C -> (D -> C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16301.        (((A -> (B -> A)) and (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and (C -> (D -> C))))), M:tm-324, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-16302
in-theory        16302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16302.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-324, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-16303
in-theory        16303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and ((C and D) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16303.        (((A -> (B -> A)) and ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and ((C and D) -> C)))), M:tm-324, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-16304
in-theory        16304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and ((C and D) -> D))))
theorem-size     37
proof            (modus-ponens tm-324 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16304.        (((A -> (B -> A)) and ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and ((C and D) -> D)))), M:tm-324, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-16305
in-theory        16305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and (C -> (D -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16305.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and (C -> (D -> (C and D)))))), M:tm-324, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-16306
in-theory        16306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and (C -> (C or D)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16306.        (((A -> (B -> A)) and (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and (C -> (C or D))))), M:tm-324, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-16307
in-theory        16307
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and (C -> (D or C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16307.        (((A -> (B -> A)) and (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and (C -> (D or C))))), M:tm-324, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-16308
in-theory        16308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16308.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-324, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-16309
in-theory        16309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16309.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-324, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-16310
in-theory        16310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> A)) and ((not (not C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16310.        (((A -> (B -> A)) and ((not (not C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> A)) and ((not (not C)) -> C)))), M:tm-324, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-16311
in-theory        16311
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> (D -> (E -> D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16311.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> (D -> (E -> D)))))), M:tm-324, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-16312
in-theory        16312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and ((C -> D) -> (C -> C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16312.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and ((C -> D) -> (C -> C))))), M:tm-324, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-16313
in-theory        16313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     65
proof            (modus-ponens tm-324 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16313.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-324, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-16314
in-theory        16314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16314.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-324, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-16315
in-theory        16315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16315.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-324, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-16316
in-theory        16316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> ((D and E) -> D)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16316.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> ((D and E) -> D))))), M:tm-324, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-16317
in-theory        16317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16317.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-324, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-16318
in-theory        16318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> ((D and E) -> E)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16318.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> ((D and E) -> E))))), M:tm-324, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-16319
in-theory        16319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16319.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-324, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-16320
in-theory        16320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16320.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A)))), M:tm-324, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-16321
in-theory        16321
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-324 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16321.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)))), M:tm-324, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-16322
in-theory        16322
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> ((C -> (D -> C)) and B)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16322.        ((A or (B -> ((C -> (D -> C)) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> ((C -> (D -> C)) and B))))), M:tm-324, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-16323
in-theory        16323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> ((B -> (C -> B)) and A)) or D)))
theorem-size     37
proof            (modus-ponens tm-324 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16323.        (((A -> ((B -> (C -> B)) and A)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> ((B -> (C -> B)) and A)) or D))), M:tm-324, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-16324
in-theory        16324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> ((C -> (D -> C)) and B)) and A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16324.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> ((C -> (D -> C)) and B)) and A)))), M:tm-324, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-16325
in-theory        16325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> ((C -> (D -> C)) and B)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16325.        ((A -> (B -> ((C -> (D -> C)) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> ((C -> (D -> C)) and B))))), M:tm-324, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-16326
in-theory        16326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16326.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))))), M:tm-324, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-16327
in-theory        16327
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16327.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-324, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-16328
in-theory        16328
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D))))
theorem-size     53
proof            (modus-ponens tm-324 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16328.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)))), M:tm-324, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-16329
in-theory        16329
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E))))
theorem-size     53
proof            (modus-ponens tm-324 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16329.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)))), M:tm-324, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-16330
in-theory        16330
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16330.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))))), M:tm-324, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-16331
in-theory        16331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16331.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))))), M:tm-324, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-16332
in-theory        16332
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16332.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))))), M:tm-324, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-16333
in-theory        16333
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16333.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-324, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-16334
in-theory        16334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     65
proof            (modus-ponens tm-324 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16334.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-324, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-16335
in-theory        16335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D))))
theorem-size     53
proof            (modus-ponens tm-324 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16335.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)))), M:tm-324, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-16336
in-theory        16336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16336.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))))), M:tm-324, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-16337
in-theory        16337
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16337.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))))), M:tm-324, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-16338
in-theory        16338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     81
proof            (modus-ponens tm-324 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5)
proof-size       281
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16338.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-324, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-16339
in-theory        16339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     73
proof            (modus-ponens tm-324 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       257
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16339.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-324, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-16340
in-theory        16340
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     73
proof            (modus-ponens tm-324 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       257
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16340.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-324, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-16341
in-theory        16341
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16341.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))))), M:tm-324, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-16342
in-theory        16342
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     73
proof            (modus-ponens tm-324 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       257
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16342.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-324, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-16343
in-theory        16343
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16343.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))))), M:tm-324, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-16344
in-theory        16344
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16344.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-324, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-16345
in-theory        16345
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     77
proof            (modus-ponens tm-324 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5)
proof-size       267
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16345.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-324, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-16346
in-theory        16346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16346.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-324, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-16347
in-theory        16347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A))))
theorem-size     57
proof            (modus-ponens tm-324 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16347.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)))), M:tm-324, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-16348
in-theory        16348
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))))
theorem-size     89
proof            (modus-ponens tm-324 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       261
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16348.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))), M:tm-324, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-16349
in-theory        16349
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16349.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-324, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-16350
in-theory        16350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E)))
theorem-size     53
proof            (modus-ponens tm-324 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16350.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E))), M:tm-324, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-16351
in-theory        16351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))))
theorem-size     57
proof            (modus-ponens tm-324 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16351.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)))), M:tm-324, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-16352
in-theory        16352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16352.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-324, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-16353
in-theory        16353
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and (C -> (D -> C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16353.        ((((A and B) -> A) and (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and (C -> (D -> C))))), M:tm-324, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-16354
in-theory        16354
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16354.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-324, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-16355
in-theory        16355
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and ((C and D) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16355.        ((((A and B) -> A) and ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and ((C and D) -> C)))), M:tm-324, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-16356
in-theory        16356
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and ((C and D) -> D))))
theorem-size     37
proof            (modus-ponens tm-324 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16356.        ((((A and B) -> A) and ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and ((C and D) -> D)))), M:tm-324, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-16357
in-theory        16357
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and (C -> (D -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16357.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and (C -> (D -> (C and D)))))), M:tm-324, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-16358
in-theory        16358
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and (C -> (C or D)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16358.        ((((A and B) -> A) and (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and (C -> (C or D))))), M:tm-324, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-16359
in-theory        16359
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and (C -> (D or C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16359.        ((((A and B) -> A) and (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and (C -> (D or C))))), M:tm-324, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-16360
in-theory        16360
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16360.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-324, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-16361
in-theory        16361
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16361.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-324, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-16362
in-theory        16362
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> A) and ((not (not C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-10)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16362.        ((((A and B) -> A) and ((not (not C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> A) and ((not (not C)) -> C)))), M:tm-324, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-16363
in-theory        16363
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> (D -> (E -> D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16363.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> (D -> (E -> D)))))), M:tm-324, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-16364
in-theory        16364
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and ((C -> D) -> (C -> C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16364.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and ((C -> D) -> (C -> C))))), M:tm-324, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-16365
in-theory        16365
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     65
proof            (modus-ponens tm-324 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16365.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-324, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-16366
in-theory        16366
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16366.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-324, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-16367
in-theory        16367
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16367.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-324, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-16368
in-theory        16368
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> ((D and E) -> D)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16368.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> ((D and E) -> D))))), M:tm-324, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-16369
in-theory        16369
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16369.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-324, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-16370
in-theory        16370
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> ((D and E) -> E)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16370.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> ((D and E) -> E))))), M:tm-324, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-16371
in-theory        16371
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16371.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))))), M:tm-324, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-16372
in-theory        16372
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16372.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-324, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-16373
in-theory        16373
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> (((D and E) -> D) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16373.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> (((D and E) -> D) and C))))), M:tm-324, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-16374
in-theory        16374
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16374.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-324, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-16375
in-theory        16375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16375.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))))), M:tm-324, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-16376
in-theory        16376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not (((B and C) -> B) and A))) -> (not A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16376.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not (((B and C) -> B) and A))) -> (not A)))), M:tm-324, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-16377
in-theory        16377
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-324 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16377.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)))), M:tm-324, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-16378
in-theory        16378
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> (((C and D) -> C) and B)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16378.        ((A or (B -> (((C and D) -> C) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> (((C and D) -> C) and B))))), M:tm-324, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-16379
in-theory        16379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (((B and C) -> B) and A)) or D)))
theorem-size     37
proof            (modus-ponens tm-324 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16379.        (((A -> (((B and C) -> B) and A)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (((B and C) -> B) and A)) or D))), M:tm-324, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-16380
in-theory        16380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (((C and D) -> C) and B)) and A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16380.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (((C and D) -> C) and B)) and A)))), M:tm-324, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-16381
in-theory        16381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> (((C and D) -> C) and B)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16381.        ((A -> (B -> (((C and D) -> C) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> (((C and D) -> C) and B))))), M:tm-324, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-16382
in-theory        16382
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and (C -> (D -> C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16382.        ((((A and B) -> B) and (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and (C -> (D -> C))))), M:tm-324, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-16383
in-theory        16383
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16383.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-324, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-16384
in-theory        16384
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and ((C and D) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16384.        ((((A and B) -> B) and ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and ((C and D) -> C)))), M:tm-324, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-16385
in-theory        16385
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and ((C and D) -> D))))
theorem-size     37
proof            (modus-ponens tm-324 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16385.        ((((A and B) -> B) and ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and ((C and D) -> D)))), M:tm-324, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-16386
in-theory        16386
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and (C -> (D -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16386.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and (C -> (D -> (C and D)))))), M:tm-324, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-16387
in-theory        16387
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and (C -> (C or D)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16387.        ((((A and B) -> B) and (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and (C -> (C or D))))), M:tm-324, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-16388
in-theory        16388
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and (C -> (D or C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16388.        ((((A and B) -> B) and (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and (C -> (D or C))))), M:tm-324, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-16389
in-theory        16389
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16389.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-324, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-16390
in-theory        16390
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16390.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-324, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-16391
in-theory        16391
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> B) and ((not (not C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-10)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16391.        ((((A and B) -> B) and ((not (not C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) -> B) and ((not (not C)) -> C)))), M:tm-324, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-16392
in-theory        16392
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> (D -> (E -> D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16392.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> (D -> (E -> D)))))), M:tm-324, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-16393
in-theory        16393
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and ((C -> D) -> (C -> C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16393.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and ((C -> D) -> (C -> C))))), M:tm-324, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-16394
in-theory        16394
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     65
proof            (modus-ponens tm-324 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16394.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-324, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-16395
in-theory        16395
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16395.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-324, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-16396
in-theory        16396
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16396.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-324, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-16397
in-theory        16397
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> ((D and E) -> D)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16397.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> ((D and E) -> D))))), M:tm-324, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-16398
in-theory        16398
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16398.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-324, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-16399
in-theory        16399
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> ((D and E) -> E)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16399.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> ((D and E) -> E))))), M:tm-324, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-16400
in-theory        16400
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16400.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))))), M:tm-324, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-16401
in-theory        16401
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16401.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-324, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-16402
in-theory        16402
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> (((D and E) -> D) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16402.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> (((D and E) -> D) and C))))), M:tm-324, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-16403
in-theory        16403
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> (((D and E) -> E) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16403.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> (((D and E) -> E) and C))))), M:tm-324, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-16404
in-theory        16404
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> (((D and E) -> E) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16404.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> (((D and E) -> E) and C))))), M:tm-324, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-16405
in-theory        16405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16405.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-324, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-16406
in-theory        16406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16406.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))))), M:tm-324, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-16407
in-theory        16407
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not (((B and C) -> C) and A))) -> (not A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-16407.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not (((B and C) -> C) and A))) -> (not A)))), M:tm-324, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-16408
in-theory        16408
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-324 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-16408.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)))), M:tm-324, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-16409
in-theory        16409
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> (((C and D) -> D) and B)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16409.        ((A or (B -> (((C and D) -> D) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> (((C and D) -> D) and B))))), M:tm-324, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-16410
in-theory        16410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (((B and C) -> C) and A)) or D)))
theorem-size     37
proof            (modus-ponens tm-324 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16410.        (((A -> (((B and C) -> C) and A)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (((B and C) -> C) and A)) or D))), M:tm-324, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-16411
in-theory        16411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (((C and D) -> D) and B)) and A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16411.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (((C and D) -> D) and B)) and A)))), M:tm-324, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-16412
in-theory        16412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> (((C and D) -> D) and B)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16412.        ((A -> (B -> (((C and D) -> D) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> (((C and D) -> D) and B))))), M:tm-324, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-16413
in-theory        16413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and (C -> (D -> C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16413.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and (C -> (D -> C))))), M:tm-324, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-16414
in-theory        16414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16414.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-324, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-16415
in-theory        16415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and ((C and D) -> C))))
theorem-size     41
proof            (modus-ponens tm-324 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16415.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and ((C and D) -> C)))), M:tm-324, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-16416
in-theory        16416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and ((C and D) -> D))))
theorem-size     41
proof            (modus-ponens tm-324 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16416.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and ((C and D) -> D)))), M:tm-324, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-16417
in-theory        16417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and (C -> (D -> (C and D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16417.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))))), M:tm-324, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-16418
in-theory        16418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and (C -> (C or D)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16418.        (((A -> (B -> (A and B))) and (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and (C -> (C or D))))), M:tm-324, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-16419
in-theory        16419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and (C -> (D or C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16419.        (((A -> (B -> (A and B))) and (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and (C -> (D or C))))), M:tm-324, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-16420
in-theory        16420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16420.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-324, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-16421
in-theory        16421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16421.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-324, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-16422
in-theory        16422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> (A and B))) and ((not (not C)) -> C))))
theorem-size     41
proof            (modus-ponens tm-324 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16422.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> (A and B))) and ((not (not C)) -> C)))), M:tm-324, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-16423
in-theory        16423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16423.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))))), M:tm-324, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-16424
in-theory        16424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16424.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))))), M:tm-324, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-16425
in-theory        16425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5)
proof-size       251
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16425.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-324, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-16426
in-theory        16426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     61
proof            (modus-ponens tm-324 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16426.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-324, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-16427
in-theory        16427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16427.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-324, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-16428
in-theory        16428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> D)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16428.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))))), M:tm-324, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-16429
in-theory        16429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16429.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-324, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-16430
in-theory        16430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> E)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16430.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))))), M:tm-324, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-16431
in-theory        16431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16431.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))))), M:tm-324, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-16432
in-theory        16432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     65
proof            (modus-ponens tm-324 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       237
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16432.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-324, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-16433
in-theory        16433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16433.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))))), M:tm-324, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-16434
in-theory        16434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16434.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))))), M:tm-324, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-16435
in-theory        16435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16435.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-324, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-16436
in-theory        16436
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16436.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-324, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-16437
in-theory        16437
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16437.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-324, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-16438
in-theory        16438
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     65
proof            (modus-ponens tm-324 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5)
proof-size       237
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16438.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-324, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-16439
in-theory        16439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16439.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-324, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-16440
in-theory        16440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A))))
theorem-size     45
proof            (modus-ponens tm-324 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-16440.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)))), M:tm-324, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-16441
in-theory        16441
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D))))
theorem-size     65
proof            (modus-ponens tm-324 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-16441.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)))), M:tm-324, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-16442
in-theory        16442
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16442.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> ((C -> (D -> (C and D))) and B))))), M:tm-324, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-16443
in-theory        16443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> ((B -> (C -> (B and C))) and A)) or D)))
theorem-size     41
proof            (modus-ponens tm-324 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16443.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> ((B -> (C -> (B and C))) and A)) or D))), M:tm-324, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-16444
in-theory        16444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A))))
theorem-size     45
proof            (modus-ponens tm-324 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16444.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)))), M:tm-324, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-16445
in-theory        16445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16445.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> ((C -> (D -> (C and D))) and B))))), M:tm-324, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-16446
in-theory        16446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A and (B -> A)))))
theorem-size     29
proof            (modus-ponens tm-324 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16446.        ((A -> (A and (B -> A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A and (B -> A))))), M:tm-324, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-16447
in-theory        16447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-16447.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))), M:tm-324, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-16448
in-theory        16448
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and B) -> ((A and B) and A))))
theorem-size     33
proof            (modus-ponens tm-324 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16448.        (((A and B) -> ((A and B) and A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and B) -> ((A and B) and A)))), M:tm-324, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-16449
in-theory        16449
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and B) -> ((A and B) and B))))
theorem-size     33
proof            (modus-ponens tm-324 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-16449.        (((A and B) -> ((A and B) and B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A and B) -> ((A and B) and B)))), M:tm-324, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-16450
in-theory        16450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A and (B -> (A and B))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-16450.        ((A -> (A and (B -> (A and B)))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A and (B -> (A and B)))))), M:tm-324, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-16451
in-theory        16451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A and (A or B)))))
theorem-size     29
proof            (modus-ponens tm-324 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-16451.        ((A -> (A and (A or B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A and (A or B))))), M:tm-324, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-16452
in-theory        16452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A and (B or A)))))
theorem-size     29
proof            (modus-ponens tm-324 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-16452.        ((A -> (A and (B or A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A and (B or A))))), M:tm-324, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-16453
in-theory        16453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-16453.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))))), M:tm-324, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-16454
in-theory        16454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-16454.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))))), M:tm-324, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-16455
in-theory        16455
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((not (not A)) -> ((not (not A)) and A))))
theorem-size     33
proof            (modus-ponens tm-324 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-16455.        (((not (not A)) -> ((not (not A)) and A)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((not (not A)) -> ((not (not A)) and A)))), M:tm-324, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-16456
in-theory        16456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and (B -> (C -> B))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-16456.        ((A -> (A and (B -> (C -> B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and (B -> (C -> B)))))), M:tm-324, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-16457
in-theory        16457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> ((A -> B) and (A -> A)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-16457.        (((A -> B) -> ((A -> B) and (A -> A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> ((A -> B) and (A -> A))))), M:tm-324, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-16458
in-theory        16458
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))))
theorem-size     73
proof            (modus-ponens tm-324 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5)
proof-size       261
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-16458.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))), M:tm-324, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-16459
in-theory        16459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-16459.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))), M:tm-324, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-16460
in-theory        16460
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-16460.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))), M:tm-324, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-16461
in-theory        16461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and ((B and C) -> B)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-16461.        ((A -> (A and ((B and C) -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and ((B and C) -> B))))), M:tm-324, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-16462
in-theory        16462
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-16462.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))), M:tm-324, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-16463
in-theory        16463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and ((B and C) -> C)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-16463.        ((A -> (A and ((B and C) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and ((B and C) -> C))))), M:tm-324, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-16464
in-theory        16464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and ((B -> (C -> B)) and A)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16464.        ((A -> (A and ((B -> (C -> B)) and A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and ((B -> (C -> B)) and A))))), M:tm-324, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16465
in-theory        16465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5)
proof-size       223
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16465.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))), M:tm-324, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16466
in-theory        16466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((E -> (F -> E)) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16466.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((E -> (F -> E)) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))), M:tm-323, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16467
in-theory        16467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16467.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((E and F) -> F)), M:tm-322, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16468
in-theory        16468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16468.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((E and F) -> E)), M:tm-320, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16469
in-theory        16469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16469.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16470
in-theory        16470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (A -> A))
theorem-size     23
proof            (modus-ponens tm-316 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16470.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (A -> A)), M:tm-316, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16471
in-theory        16471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16471.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (E -> (F -> E))), M:tm-315, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16472
in-theory        16472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((A -> (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))) -> (not A)))
theorem-size     43
proof            (modus-ponens tm-313 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16472.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((A -> (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))) -> (not A))), M:tm-313, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16473
in-theory        16473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) -> ((A or (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> E)))
theorem-size     61
proof            (modus-ponens tm-312 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16473.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) -> ((A or (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> E))), M:tm-312, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16474
in-theory        16474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (E or (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16474.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (E or (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))), M:tm-311, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16475
in-theory        16475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16475.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) or E)), M:tm-310, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16476
in-theory        16476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (E -> ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16476.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (E -> ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and E))), M:tm-309, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16477
in-theory        16477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (E -> (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16477.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (E -> (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))), M:tm-305, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16478
in-theory        16478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     31
proof            (modus-ponens tm-303 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16478.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-303, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16479
in-theory        16479
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (C -> (B and C))) and A))))
theorem-size     45
proof            (modus-ponens tm-300 tm-324 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16479.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (C -> (B and C))) and A)))), M:tm-300, m:tm-324, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (-> B (and A B))) C)))))
================================================================
tm-name          tm-16480
in-theory        16480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-270 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16480.        ((A -> (((B and C) -> C) and A)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-270, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16481
in-theory        16481
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((B and C) -> C) and A))))
theorem-size     39
proof            (modus-ponens tm-267 tm-324 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> (and A B) B) C))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16481.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((B and C) -> C) and A)))), M:tm-267, m:tm-324, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> (and A B) B) C)))))
================================================================
tm-name          tm-16482
in-theory        16482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-239 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16482.        ((A -> (((B and C) -> B) and A)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-239, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16483
in-theory        16483
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((B and C) -> B) and A))))
theorem-size     39
proof            (modus-ponens tm-236 tm-324 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> (and A B) A) C))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16483.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((B and C) -> B) and A)))), M:tm-236, m:tm-324, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> (and A B) A) C)))))
================================================================
tm-name          tm-16484
in-theory        16484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     37
proof            (modus-ponens tm-210 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16484.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-210, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16485
in-theory        16485
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     63
proof            (modus-ponens tm-207 tm-324 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16485.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-207, m:tm-324, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-16486
in-theory        16486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-183 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16486.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-183, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16487
in-theory        16487
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (C -> B)) and A))))
theorem-size     39
proof            (modus-ponens tm-180 tm-324 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (-> B A)) C))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16487.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (C -> B)) and A)))), M:tm-180, m:tm-324, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (-> B A)) C)))))
================================================================
tm-name          tm-16488
in-theory        16488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-157 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16488.        ((A -> ((B and C) -> C)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-157, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16489
in-theory        16489
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B and C) -> C))))
theorem-size     33
proof            (modus-ponens tm-154 tm-324 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and A B) B))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16489.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B and C) -> C)))), M:tm-154, m:tm-324, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and A B) B)))))
================================================================
tm-name          tm-16490
in-theory        16490
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     35
proof            (modus-ponens tm-147 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16490.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-147, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16491
in-theory        16491
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A and (B -> C)) -> C))))
theorem-size     45
proof            (modus-ponens tm-144 tm-324 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and A (-> B C)) C))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16491.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A and (B -> C)) -> C)))), M:tm-144, m:tm-324, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and A (-> B C)) C)))))
================================================================
tm-name          tm-16492
in-theory        16492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-134 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16492.        ((A -> ((B and C) -> B)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-134, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16493
in-theory        16493
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B and C) -> B))))
theorem-size     33
proof            (modus-ponens tm-131 tm-324 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and A B) A))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16493.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B and C) -> B)))), M:tm-131, m:tm-324, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and A B) A)))))
================================================================
tm-name          tm-16494
in-theory        16494
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     35
proof            (modus-ponens tm-125 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16494.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-125, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16495
in-theory        16495
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) and C) -> B))))
theorem-size     45
proof            (modus-ponens tm-122 tm-324 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and (-> A B) C) B))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16495.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) and C) -> B)))), M:tm-122, m:tm-324, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (and (-> A B) C) B)))))
================================================================
tm-name          tm-16496
in-theory        16496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-113 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16496.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-113, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16497
in-theory        16497
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     57
proof            (modus-ponens tm-110 tm-324 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16497.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-110, m:tm-324, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
================================================================
tm-name          tm-16498
in-theory        16498
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     39
proof            (modus-ponens tm-105 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16498.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-105, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16499
in-theory        16499
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-102 tm-324 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A (-> B C)) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16499.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) -> (A -> C))))), M:tm-102, m:tm-324, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A (-> B C)) (-> A C))))))
================================================================
tm-name          tm-16500
in-theory        16500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     27
proof            (modus-ponens tm-95 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16500.        (((A -> B) -> (A -> A)) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-95, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16501
in-theory        16501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> A))))
theorem-size     29
proof            (modus-ponens tm-92 tm-324 ((Am (-> A A)) (B (and (-> A A) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A A))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16501.        (((A -> B) or (A -> A)) -> ((A -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> A)))), M:tm-92, m:tm-324, u:((Am (-> A A)) (B (and (-> A A) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A A)))))
================================================================
tm-name          tm-16502
in-theory        16502
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))))
theorem-size     21
proof            (modus-ponens tm-84 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16502.        (A -> (B -> (A and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))), M:tm-84, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16503
in-theory        16503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-83 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16503.        ((A -> (B -> (C -> B))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-83, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16504
in-theory        16504
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (C -> B)))))
theorem-size     33
proof            (modus-ponens tm-80 tm-324 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (-> B A)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16504.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (C -> B))))), M:tm-80, m:tm-324, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (-> B A))))))
================================================================
tm-name          tm-16505
in-theory        16505
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     25
proof            (modus-ponens tm-76 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16505.        (((not (not A)) -> A) and (B -> (B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-76, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16506
in-theory        16506
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     23
proof            (modus-ponens tm-73 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16506.        (((not (not A)) or A) -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-73, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16507
in-theory        16507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     31
proof            (modus-ponens tm-69 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16507.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-69, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16508
in-theory        16508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> (not B)) -> (not A)))))
theorem-size     41
proof            (modus-ponens tm-66 tm-324 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A (not B)) (not A)))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16508.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> (not B)) -> (not A))))), M:tm-66, m:tm-324, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A (not B)) (not A))))))
================================================================
tm-name          tm-16509
in-theory        16509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     33
proof            (modus-ponens tm-54 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16509.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-54, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16510
in-theory        16510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     47
proof            (modus-ponens tm-51 tm-324 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> (or C A) B)))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16510.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> C) -> ((A or B) -> C))))), M:tm-51, m:tm-324, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> (or C A) B))))))
================================================================
tm-name          tm-16511
in-theory        16511
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A))))
theorem-size     27
proof            (modus-ponens tm-50 tm-324 ((Am (or A B)) (C (and (or A B) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A B))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16511.        ((A or (B or A)) -> ((B or A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or A)))), M:tm-50, m:tm-324, u:((Am (or A B)) (C (and (or A B) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A B)))))
================================================================
tm-name          tm-16512
in-theory        16512
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B))))
theorem-size     27
proof            (modus-ponens tm-49 tm-324 ((Am (or A B)) (C (and (or A B) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A B))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16512.        ((A or (A or B)) -> ((A or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A or B)))), M:tm-49, m:tm-324, u:((Am (or A B)) (C (and (or A B) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A B)))))
================================================================
tm-name          tm-16513
in-theory        16513
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-48 tm-324 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (and B A)))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16513.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> (A and B))))), M:tm-48, m:tm-324, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (and B A))))))
================================================================
tm-name          tm-16514
in-theory        16514
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))
theorem-size     23
proof            (modus-ponens tm-47 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16514.        (((A and B) or B) -> (B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-47, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16515
in-theory        16515
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))
theorem-size     23
proof            (modus-ponens tm-46 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16515.        (((A and B) or A) -> (A and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))), M:tm-46, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16516
in-theory        16516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))
theorem-size     43
proof            (modus-ponens tm-45 tm-324 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16516.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))), M:tm-45, m:tm-324, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-16517
in-theory        16517
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))
theorem-size     27
proof            (modus-ponens tm-44 tm-324 ((Am (-> A B)) (C (and (-> A B) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16517.        ((A or (B -> A)) -> ((B -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))), M:tm-44, m:tm-324, u:((Am (-> A B)) (C (and (-> A B) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B)))))
================================================================
tm-name          tm-16518
in-theory        16518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     25
proof            (modus-ponens tm-42 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16518.        ((A -> (B or A)) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-42, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16519
in-theory        16519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     25
proof            (modus-ponens tm-32 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16519.        ((A -> (A or B)) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-32, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16520
in-theory        16520
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     21
proof            (modus-ponens tm-24 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16520.        (A -> (A and (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-24, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16521
in-theory        16521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     27
proof            (modus-ponens tm-23 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16521.        ((A -> (B -> (A and B))) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-23, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16522
in-theory        16522
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     25
proof            (modus-ponens tm-22 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16522.        (((A and B) -> B) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-22, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16523
in-theory        16523
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     25
proof            (modus-ponens tm-21 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16523.        (((A and B) -> A) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-21, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16524
in-theory        16524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     33
proof            (modus-ponens tm-20 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16524.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-20, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16525
in-theory        16525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     25
proof            (modus-ponens tm-19 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16525.        ((A -> (B -> A)) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-19, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16526
in-theory        16526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))) -> (not A))
theorem-size     23
proof            (modus-ponens tm-9 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-9 tm-2 tm-5)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16526.        ((A -> (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))) -> (not A)), M:tm-9, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16527
in-theory        16527
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) -> ((A or (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> E))
theorem-size     41
proof            (modus-ponens tm-8 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16527.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) -> ((A or (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> E)), M:tm-8, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16528
in-theory        16528
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     21
proof            (modus-ponens tm-7 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-7 tm-2 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16528.        (A or (B -> (B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-7, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16529
in-theory        16529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-6 tm-2 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16529.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) or E), M:tm-6, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16530
in-theory        16530
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16530.        (A -> ((B -> (B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and A)), M:tm-5, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16531
in-theory        16531
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     21
proof            (modus-ponens tm-1 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16531.        (A -> (B -> (B and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-1, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16532
in-theory        16532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (A -> (B -> A))))
theorem-size     17
proof            (modus-ponens tm-325 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16532.        ((A -> (B -> A)) and (((C and D) -> C) and (A -> (B -> A)))), M:tm-325, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-16533
in-theory        16533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16533.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))), M:tm-325, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-16534
in-theory        16534
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((A and B) -> A)))
theorem-size     17
proof            (modus-ponens tm-325 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16534.        (((A and B) -> A) and (((C and D) -> C) and ((A and B) -> A))), M:tm-325, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-16535
in-theory        16535
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((A and B) -> B)))
theorem-size     17
proof            (modus-ponens tm-325 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-16535.        (((A and B) -> B) and (((C and D) -> C) and ((A and B) -> B))), M:tm-325, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-16536
in-theory        16536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (A -> (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-325 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16536.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (A -> (B -> (A and B))))), M:tm-325, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-16537
in-theory        16537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (A -> (A or B))))
theorem-size     17
proof            (modus-ponens tm-325 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-16537.        ((A -> (A or B)) and (((C and D) -> C) and (A -> (A or B)))), M:tm-325, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-16538
in-theory        16538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (A -> (B or A))))
theorem-size     17
proof            (modus-ponens tm-325 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-16538.        ((A -> (B or A)) and (((C and D) -> C) and (A -> (B or A)))), M:tm-325, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-16539
in-theory        16539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-16539.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))), M:tm-325, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-16540
in-theory        16540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((A -> B) -> ((A -> (not B)) -> (not A)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-16540.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((A -> B) -> ((A -> (not B)) -> (not A))))), M:tm-325, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-16541
in-theory        16541
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((not (not A)) -> A)))
theorem-size     17
proof            (modus-ponens tm-325 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-3 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-16541.        (((not (not A)) -> A) and (((B and C) -> B) and ((not (not A)) -> A))), M:tm-325, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-16542
in-theory        16542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (A -> (B -> (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-325 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16542.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (A -> (B -> (C -> B))))), M:tm-325, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-16543
in-theory        16543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((A -> B) -> (A -> A))))
theorem-size     21
proof            (modus-ponens tm-325 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-16543.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((A -> B) -> (A -> A)))), M:tm-325, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-16544
in-theory        16544
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-16544.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-325, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-16545
in-theory        16545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16545.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-325, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-16546
in-theory        16546
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))))
theorem-size     37
proof            (modus-ponens tm-325 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16546.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)))), M:tm-325, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-16547
in-theory        16547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (A -> ((B and C) -> B))))
theorem-size     21
proof            (modus-ponens tm-325 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16547.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (A -> ((B and C) -> B)))), M:tm-325, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-16548
in-theory        16548
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-325 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-16548.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)))), M:tm-325, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-16549
in-theory        16549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (A -> ((B and C) -> C))))
theorem-size     21
proof            (modus-ponens tm-325 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16549.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (A -> ((B and C) -> C)))), M:tm-325, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-16550
in-theory        16550
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (A -> ((B -> (C -> B)) and A))))
theorem-size     25
proof            (modus-ponens tm-325 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16550.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (A -> ((B -> (C -> B)) and A)))), M:tm-325, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-16551
in-theory        16551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     41
proof            (modus-ponens tm-325 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16551.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-325, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16552
in-theory        16552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (A -> (((B and C) -> B) and A))))
theorem-size     25
proof            (modus-ponens tm-325 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16552.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (A -> (((B and C) -> B) and A)))), M:tm-325, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-16553
in-theory        16553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (A -> (((B and C) -> C) and A))))
theorem-size     25
proof            (modus-ponens tm-325 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16553.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (A -> (((B and C) -> C) and A)))), M:tm-325, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-16554
in-theory        16554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (A -> ((B -> (C -> (B and C))) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16554.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (A -> ((B -> (C -> (B and C))) and A)))), M:tm-325, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-16555
in-theory        16555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((A -> B) -> (A -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16555.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((A -> B) -> (A -> (A and B))))), M:tm-325, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-16556
in-theory        16556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (A -> (B -> (C -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16556.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (A -> (B -> (C -> (B and C)))))), M:tm-325, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-16557
in-theory        16557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((A -> (B -> A)) or C)))
theorem-size     21
proof            (modus-ponens tm-325 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16557.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((A -> (B -> A)) or C))), M:tm-325, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-16558
in-theory        16558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)))
theorem-size     37
proof            (modus-ponens tm-325 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16558.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D))), M:tm-325, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-16559
in-theory        16559
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (((A and B) -> A) or C)))
theorem-size     21
proof            (modus-ponens tm-325 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16559.        ((((A and B) -> A) or C) and (((D and E) -> D) and (((A and B) -> A) or C))), M:tm-325, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-16560
in-theory        16560
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (((A and B) -> B) or C)))
theorem-size     21
proof            (modus-ponens tm-325 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16560.        ((((A and B) -> B) or C) and (((D and E) -> D) and (((A and B) -> B) or C))), M:tm-325, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-16561
in-theory        16561
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((A -> (B -> (A and B))) or C)))
theorem-size     25
proof            (modus-ponens tm-325 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16561.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((A -> (B -> (A and B))) or C))), M:tm-325, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-16562
in-theory        16562
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((A -> (A or B)) or C)))
theorem-size     21
proof            (modus-ponens tm-325 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16562.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((A -> (A or B)) or C))), M:tm-325, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-16563
in-theory        16563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (A -> ((B -> (B or C)) and A))))
theorem-size     25
proof            (modus-ponens tm-325 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16563.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (A -> ((B -> (B or C)) and A)))), M:tm-325, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-16564
in-theory        16564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (A -> (B -> (B or C)))))
theorem-size     21
proof            (modus-ponens tm-325 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16564.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (A -> (B -> (B or C))))), M:tm-325, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-16565
in-theory        16565
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (A or (B -> (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-325 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16565.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (A or (B -> (C -> B))))), M:tm-325, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-16566
in-theory        16566
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16566.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-325, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-16567
in-theory        16567
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (A or ((B and C) -> B))))
theorem-size     21
proof            (modus-ponens tm-325 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16567.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (A or ((B and C) -> B)))), M:tm-325, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-16568
in-theory        16568
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (A or ((B and C) -> C))))
theorem-size     21
proof            (modus-ponens tm-325 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16568.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (A or ((B and C) -> C)))), M:tm-325, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-16569
in-theory        16569
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (A or (B -> (C -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16569.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (A or (B -> (C -> (B and C)))))), M:tm-325, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-16570
in-theory        16570
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (A or (B -> (B or C)))))
theorem-size     21
proof            (modus-ponens tm-325 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16570.        ((A or (B -> (B or C))) and (((D and E) -> D) and (A or (B -> (B or C))))), M:tm-325, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-16571
in-theory        16571
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (A or (B -> (C or B)))))
theorem-size     21
proof            (modus-ponens tm-325 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16571.        ((A or (B -> (C or B))) and (((D and E) -> D) and (A or (B -> (C or B))))), M:tm-325, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-16572
in-theory        16572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((A -> (B or A)) or C)))
theorem-size     21
proof            (modus-ponens tm-325 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16572.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((A -> (B or A)) or C))), M:tm-325, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-16573
in-theory        16573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (A -> ((B -> (C or B)) and A))))
theorem-size     25
proof            (modus-ponens tm-325 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16573.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (A -> ((B -> (C or B)) and A)))), M:tm-325, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-16574
in-theory        16574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (A -> (B -> (C or B)))))
theorem-size     21
proof            (modus-ponens tm-325 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16574.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (A -> (B -> (C or B))))), M:tm-325, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-16575
in-theory        16575
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((A -> B) -> C) -> ((B or (A -> B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-325 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16575.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((A -> B) -> C) -> ((B or (A -> B)) -> C)))), M:tm-325, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-16576
in-theory        16576
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     57
proof            (modus-ponens tm-325 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-16576.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-325, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-16577
in-theory        16577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((A -> B) -> (((A and C) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-325 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16577.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((A -> B) -> (((A and C) or A) -> B)))), M:tm-325, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-16578
in-theory        16578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((A -> B) -> (((C and A) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-325 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-16578.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> D) and ((A -> B) -> (((C and A) or A) -> B)))), M:tm-325, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-16579
in-theory        16579
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-325 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-16579.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> D) and (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)))), M:tm-325, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-16580
in-theory        16580
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((A or B) -> C) -> ((A or (A or B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-325 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-16580.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> D) and (((A or B) -> C) -> ((A or (A or B)) -> C)))), M:tm-325, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-16581
in-theory        16581
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((A or B) -> C) -> ((B or (A or B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-325 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-16581.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> D) and (((A or B) -> C) -> ((B or (A or B)) -> C)))), M:tm-325, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-16582
in-theory        16582
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     61
proof            (modus-ponens tm-325 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-16582.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> E) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-325, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-16583
in-theory        16583
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16583.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-325, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-16584
in-theory        16584
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)))
theorem-size     37
proof            (modus-ponens tm-325 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16584.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> E) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D))), M:tm-325, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-16585
in-theory        16585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (((E and F) -> E) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))))
theorem-size     41
proof            (modus-ponens tm-325 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16585.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (((E and F) -> E) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)))), M:tm-325, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-16586
in-theory        16586
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((D and E) -> D) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-16586.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((D and E) -> D) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))))), M:tm-325, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-16587
in-theory        16587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16587.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> E) and (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-325, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-16588
in-theory        16588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (((C and D) -> C) and ((A -> (not (B -> A))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-325 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16588.        (((A -> (not (B -> A))) -> (not A)) and (((C and D) -> C) and ((A -> (not (B -> A))) -> (not A)))), M:tm-325, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-16589
in-theory        16589
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((D and E) -> D) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-16589.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((D and E) -> D) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))))), M:tm-325, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-16590
in-theory        16590
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (((C and D) -> C) and (((A and B) -> (not A)) -> (not (A and B)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16590.        ((((A and B) -> (not A)) -> (not (A and B))) and (((C and D) -> C) and (((A and B) -> (not A)) -> (not (A and B))))), M:tm-325, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-16591
in-theory        16591
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (((C and D) -> C) and (((A and B) -> (not B)) -> (not (A and B)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-16591.        ((((A and B) -> (not B)) -> (not (A and B))) and (((C and D) -> C) and (((A and B) -> (not B)) -> (not (A and B))))), M:tm-325, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-16592
in-theory        16592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (((C and D) -> C) and ((A -> (not (B -> (A and B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-16592.        (((A -> (not (B -> (A and B)))) -> (not A)) and (((C and D) -> C) and ((A -> (not (B -> (A and B)))) -> (not A)))), M:tm-325, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-16593
in-theory        16593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (((C and D) -> C) and ((A -> (not (A or B))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-325 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-16593.        (((A -> (not (A or B))) -> (not A)) and (((C and D) -> C) and ((A -> (not (A or B))) -> (not A)))), M:tm-325, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-16594
in-theory        16594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (((C and D) -> C) and ((A -> (not (B or A))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-325 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-16594.        (((A -> (not (B or A))) -> (not A)) and (((C and D) -> C) and ((A -> (not (B or A))) -> (not A)))), M:tm-325, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-16595
in-theory        16595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((D and E) -> D) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-8)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-16595.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((D and E) -> D) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))))), M:tm-325, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-16596
in-theory        16596
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((C and D) -> C) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-16596.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((C and D) -> C) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))))), M:tm-325, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-16597
in-theory        16597
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((D and E) -> D) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))))
theorem-size     53
proof            (modus-ponens tm-325 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-16597.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((D and E) -> D) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))), M:tm-325, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-16598
in-theory        16598
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((D and E) -> D) and (A or ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16598.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((D and E) -> D) and (A or ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-325, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-16599
in-theory        16599
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (((D and E) -> D) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C)))
theorem-size     33
proof            (modus-ponens tm-325 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16599.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (((D and E) -> D) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C))), M:tm-325, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-16600
in-theory        16600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (((D and E) -> D) and (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A))))
theorem-size     37
proof            (modus-ponens tm-325 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16600.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (((D and E) -> D) and (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)))), M:tm-325, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-16601
in-theory        16601
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((C and D) -> C) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-16601.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((C and D) -> C) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))))), M:tm-325, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-16602
in-theory        16602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((D and E) -> D) and (A -> ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16602.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((D and E) -> D) and (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-325, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-16603
in-theory        16603
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((B and C) -> B) and (((not (not A)) -> (not A)) -> (not (not (not A))))))
theorem-size     29
proof            (modus-ponens tm-325 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-16603.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((B and C) -> B) and (((not (not A)) -> (not A)) -> (not (not (not A)))))), M:tm-325, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-16604
in-theory        16604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (((C and D) -> C) and ((A -> B) -> (((not (not A)) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-325 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-16604.        (((A -> B) -> (((not (not A)) or A) -> B)) and (((C and D) -> C) and ((A -> B) -> (((not (not A)) or A) -> B)))), M:tm-325, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-16605
in-theory        16605
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and (((C and D) -> C) and (A or ((not (not B)) -> B))))
theorem-size     21
proof            (modus-ponens tm-325 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16605.        ((A or ((not (not B)) -> B)) and (((C and D) -> C) and (A or ((not (not B)) -> B)))), M:tm-325, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-16606
in-theory        16606
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and (((C and D) -> C) and (((not (not A)) -> A) or B)))
theorem-size     21
proof            (modus-ponens tm-325 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16606.        ((((not (not A)) -> A) or B) and (((C and D) -> C) and (((not (not A)) -> A) or B))), M:tm-325, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-16607
in-theory        16607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (((C and D) -> C) and (A -> (((not (not B)) -> B) and A))))
theorem-size     25
proof            (modus-ponens tm-325 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16607.        ((A -> (((not (not B)) -> B) and A)) and (((C and D) -> C) and (A -> (((not (not B)) -> B) and A)))), M:tm-325, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-16608
in-theory        16608
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (((C and D) -> C) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B))))
theorem-size     37
proof            (modus-ponens tm-325 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-16608.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (((C and D) -> C) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)))), M:tm-325, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-16609
in-theory        16609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and (((C and D) -> C) and (A -> ((not (not B)) -> B))))
theorem-size     21
proof            (modus-ponens tm-325 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16609.        ((A -> ((not (not B)) -> B)) and (((C and D) -> C) and (A -> ((not (not B)) -> B)))), M:tm-325, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-16610
in-theory        16610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (((D and E) -> D) and ((A -> (not (B -> (C -> B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-16610.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (((D and E) -> D) and ((A -> (not (B -> (C -> B)))) -> (not A)))), M:tm-325, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-16611
in-theory        16611
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (((E and F) -> E) and (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-325 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-16611.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (((E and F) -> E) and (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)))), M:tm-325, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-16612
in-theory        16612
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and (((E and F) -> E) and (A or (B -> (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16612.        ((A or (B -> (C -> (D -> C)))) and (((E and F) -> E) and (A or (B -> (C -> (D -> C)))))), M:tm-325, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-16613
in-theory        16613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and (((E and F) -> E) and ((A -> (B -> (C -> B))) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16613.        (((A -> (B -> (C -> B))) or D) and (((E and F) -> E) and ((A -> (B -> (C -> B))) or D))), M:tm-325, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-16614
in-theory        16614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and (((E and F) -> E) and (A -> ((B -> (C -> (D -> C))) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16614.        ((A -> ((B -> (C -> (D -> C))) and A)) and (((E and F) -> E) and (A -> ((B -> (C -> (D -> C))) and A)))), M:tm-325, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-16615
in-theory        16615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (((D and E) -> D) and ((A -> B) -> (A -> (C -> B)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-16615.        (((A -> B) -> (A -> (C -> B))) and (((D and E) -> D) and ((A -> B) -> (A -> (C -> B))))), M:tm-325, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-16616
in-theory        16616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (((E and F) -> E) and (A -> (B -> (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16616.        ((A -> (B -> (C -> (D -> C)))) and (((E and F) -> E) and (A -> (B -> (C -> (D -> C)))))), M:tm-325, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-16617
in-theory        16617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and (((B and C) -> B) and (A -> A)))
theorem-size     13
proof            (modus-ponens tm-325 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16617.        ((A -> A) and (((B and C) -> B) and (A -> A))), M:tm-325, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-16618
in-theory        16618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (((D and E) -> D) and ((A -> (B -> C)) -> (A -> (B -> C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-16618.        (((A -> (B -> C)) -> (A -> (B -> C))) and (((D and E) -> D) and ((A -> (B -> C)) -> (A -> (B -> C))))), M:tm-325, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-16619
in-theory        16619
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and (((C and D) -> C) and ((A and B) -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-325 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16619.        (((A and B) -> (A and B)) and (((C and D) -> C) and ((A and B) -> (A and B)))), M:tm-325, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-16620
in-theory        16620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (((C and D) -> C) and ((A -> B) -> (A -> B))))
theorem-size     21
proof            (modus-ponens tm-325 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-16620.        (((A -> B) -> (A -> B)) and (((C and D) -> C) and ((A -> B) -> (A -> B)))), M:tm-325, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-16621
in-theory        16621
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and (((B and C) -> B) and ((not (not A)) -> (not (not A)))))
theorem-size     21
proof            (modus-ponens tm-325 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-10)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-16621.        (((not (not A)) -> (not (not A))) and (((B and C) -> B) and ((not (not A)) -> (not (not A))))), M:tm-325, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-16622
in-theory        16622
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((C and D) -> C) and (((A -> B) -> (not (A -> A))) -> (not (A -> B)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-16622.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((C and D) -> C) and (((A -> B) -> (not (A -> A))) -> (not (A -> B))))), M:tm-325, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-16623
in-theory        16623
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((D and E) -> D) and (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B))))
theorem-size     37
proof            (modus-ponens tm-325 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-16623.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((D and E) -> D) and (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)))), M:tm-325, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-16624
in-theory        16624
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and (((D and E) -> D) and (A or ((B -> C) -> (B -> B)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16624.        ((A or ((B -> C) -> (B -> B))) and (((D and E) -> D) and (A or ((B -> C) -> (B -> B))))), M:tm-325, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-16625
in-theory        16625
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and (((D and E) -> D) and (((A -> B) -> (A -> A)) or C)))
theorem-size     25
proof            (modus-ponens tm-325 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16625.        ((((A -> B) -> (A -> A)) or C) and (((D and E) -> D) and (((A -> B) -> (A -> A)) or C))), M:tm-325, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-16626
in-theory        16626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (((D and E) -> D) and (A -> (((B -> C) -> (B -> B)) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16626.        ((A -> (((B -> C) -> (B -> B)) and A)) and (((D and E) -> D) and (A -> (((B -> C) -> (B -> B)) and A)))), M:tm-325, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-16627
in-theory        16627
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and (((C and D) -> C) and (((A -> B) -> A) -> ((A -> B) -> A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-16627.        ((((A -> B) -> A) -> ((A -> B) -> A)) and (((C and D) -> C) and (((A -> B) -> A) -> ((A -> B) -> A)))), M:tm-325, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-16628
in-theory        16628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and (((D and E) -> D) and (A -> ((B -> C) -> (B -> B)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16628.        ((A -> ((B -> C) -> (B -> B))) and (((D and E) -> D) and (A -> ((B -> C) -> (B -> B))))), M:tm-325, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-16629
in-theory        16629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (((D and E) -> D) and ((A -> ((B -> A) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-16629.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (((D and E) -> D) and ((A -> ((B -> A) -> C)) -> (A -> C)))), M:tm-325, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-16630
in-theory        16630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (((C and D) -> C) and ((A -> (A -> B)) -> (A -> B))))
theorem-size     25
proof            (modus-ponens tm-325 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-16630.        (((A -> (A -> B)) -> (A -> B)) and (((C and D) -> C) and ((A -> (A -> B)) -> (A -> B)))), M:tm-325, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-16631
in-theory        16631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((D and E) -> D) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-16631.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((D and E) -> D) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))))), M:tm-325, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-16632
in-theory        16632
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((D and E) -> D) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B))))))
theorem-size     69
proof            (modus-ponens tm-325 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-16632.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((D and E) -> D) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))))), M:tm-325, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-16633
in-theory        16633
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (((E and F) -> E) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))))
theorem-size     73
proof            (modus-ponens tm-325 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-16633.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (((E and F) -> E) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))), M:tm-325, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-16634
in-theory        16634
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((E and F) -> E) and (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16634.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((E and F) -> E) and (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-325, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-16635
in-theory        16635
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (((E and F) -> E) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D)))
theorem-size     49
proof            (modus-ponens tm-325 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16635.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (((E and F) -> E) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D))), M:tm-325, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-16636
in-theory        16636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (((E and F) -> E) and (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))))
theorem-size     53
proof            (modus-ponens tm-325 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16636.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (((E and F) -> E) and (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)))), M:tm-325, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16637
in-theory        16637
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((D and E) -> D) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-325 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-16637.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((D and E) -> D) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))), M:tm-325, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-16638
in-theory        16638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((E and F) -> E) and (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16638.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((E and F) -> E) and (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-325, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-16639
in-theory        16639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((E and F) -> E) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-325 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-16639.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((E and F) -> E) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)))), M:tm-325, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-16640
in-theory        16640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((E and F) -> E) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A))))
theorem-size     45
proof            (modus-ponens tm-325 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-16640.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((E and F) -> E) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)))), M:tm-325, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-16641
in-theory        16641
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (((F and G) -> F) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))))
theorem-size     73
proof            (modus-ponens tm-325 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-16641.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (((F and G) -> F) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))), M:tm-325, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-16642
in-theory        16642
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> F) and (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16642.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> F) and (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-325, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-16643
in-theory        16643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((F and G) -> F) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-325 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16643.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((F and G) -> F) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-325, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-16644
in-theory        16644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F and G) -> F) and (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-325 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16644.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F and G) -> F) and (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-325, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-16645
in-theory        16645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-16645.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))))), M:tm-325, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-16646
in-theory        16646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> F) and (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16646.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> F) and (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-325, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-16647
in-theory        16647
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and (((C and D) -> C) and (((A -> B) and A) -> B)))
theorem-size     21
proof            (modus-ponens tm-325 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-16647.        ((((A -> B) and A) -> B) and (((C and D) -> C) and (((A -> B) and A) -> B))), M:tm-325, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-16648
in-theory        16648
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and (((E and F) -> E) and ((((A -> (B -> A)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-325 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-16648.        (((((A -> (B -> A)) -> C) and D) -> C) and (((E and F) -> E) and ((((A -> (B -> A)) -> C) and D) -> C))), M:tm-325, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-16649
in-theory        16649
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (((F and G) -> F) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D)))
theorem-size     45
proof            (modus-ponens tm-325 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-16649.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (((F and G) -> F) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D))), M:tm-325, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-16650
in-theory        16650
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((D and E) -> D) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B))))
theorem-size     49
proof            (modus-ponens tm-325 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-16650.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((D and E) -> D) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)))), M:tm-325, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-16651
in-theory        16651
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((D and E) -> D) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A))))
theorem-size     37
proof            (modus-ponens tm-325 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-16651.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((D and E) -> D) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)))), M:tm-325, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-16652
in-theory        16652
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((D and E) -> D) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A)))))
theorem-size     57
proof            (modus-ponens tm-325 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-16652.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((D and E) -> D) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))))), M:tm-325, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-16653
in-theory        16653
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((E and F) -> E) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))))
theorem-size     61
proof            (modus-ponens tm-325 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-16653.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((E and F) -> E) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))), M:tm-325, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-16654
in-theory        16654
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((E and F) -> E) and (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16654.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((E and F) -> E) and (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-325, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-16655
in-theory        16655
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (((E and F) -> E) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D)))
theorem-size     41
proof            (modus-ponens tm-325 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16655.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (((E and F) -> E) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D))), M:tm-325, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-16656
in-theory        16656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (((E and F) -> E) and (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))))
theorem-size     45
proof            (modus-ponens tm-325 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16656.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (((E and F) -> E) and (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)))), M:tm-325, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-16657
in-theory        16657
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (((D and E) -> D) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B))))
theorem-size     53
proof            (modus-ponens tm-325 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-16657.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (((D and E) -> D) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)))), M:tm-325, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-16658
in-theory        16658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((E and F) -> E) and (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16658.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((E and F) -> E) and (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-325, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-16659
in-theory        16659
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and (((E and F) -> E) and (((((A and B) -> A) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-325 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-16659.        ((((((A and B) -> A) -> C) and D) -> C) and (((E and F) -> E) and (((((A and B) -> A) -> C) and D) -> C))), M:tm-325, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-16660
in-theory        16660
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((D and E) -> D) and (((A and B) -> (A -> C)) -> ((A and B) -> C))))
theorem-size     33
proof            (modus-ponens tm-325 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-16660.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((D and E) -> D) and (((A and B) -> (A -> C)) -> ((A and B) -> C)))), M:tm-325, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-16661
in-theory        16661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (((D and E) -> D) and ((A -> (not ((B and C) -> B))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-16661.        (((A -> (not ((B and C) -> B))) -> (not A)) and (((D and E) -> D) and ((A -> (not ((B and C) -> B))) -> (not A)))), M:tm-325, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-16662
in-theory        16662
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (((E and F) -> E) and ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C))))
theorem-size     41
proof            (modus-ponens tm-325 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-16662.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (((E and F) -> E) and ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)))), M:tm-325, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-16663
in-theory        16663
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and (((E and F) -> E) and (A or (B -> ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16663.        ((A or (B -> ((C and D) -> C))) and (((E and F) -> E) and (A or (B -> ((C and D) -> C))))), M:tm-325, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-16664
in-theory        16664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and (((E and F) -> E) and ((A -> ((B and C) -> B)) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16664.        (((A -> ((B and C) -> B)) or D) and (((E and F) -> E) and ((A -> ((B and C) -> B)) or D))), M:tm-325, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-16665
in-theory        16665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and (((E and F) -> E) and (A -> ((B -> ((C and D) -> C)) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16665.        ((A -> ((B -> ((C and D) -> C)) and A)) and (((E and F) -> E) and (A -> ((B -> ((C and D) -> C)) and A)))), M:tm-325, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-16666
in-theory        16666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (((D and E) -> D) and ((A -> (B and C)) -> (A -> B))))
theorem-size     25
proof            (modus-ponens tm-325 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-16666.        (((A -> (B and C)) -> (A -> B)) and (((D and E) -> D) and ((A -> (B and C)) -> (A -> B)))), M:tm-325, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-16667
in-theory        16667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (((E and F) -> E) and (A -> (B -> ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16667.        ((A -> (B -> ((C and D) -> C))) and (((E and F) -> E) and (A -> (B -> ((C and D) -> C))))), M:tm-325, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-16668
in-theory        16668
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and (((C and D) -> C) and ((A and (A -> B)) -> B)))
theorem-size     21
proof            (modus-ponens tm-325 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-16668.        (((A and (A -> B)) -> B) and (((C and D) -> C) and ((A and (A -> B)) -> B))), M:tm-325, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-16669
in-theory        16669
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and (((E and F) -> E) and ((A and ((B -> (C -> B)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-325 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-16669.        (((A and ((B -> (C -> B)) -> D)) -> D) and (((E and F) -> E) and ((A and ((B -> (C -> B)) -> D)) -> D))), M:tm-325, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-16670
in-theory        16670
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (((F and G) -> F) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E)))
theorem-size     45
proof            (modus-ponens tm-325 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-16670.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (((F and G) -> F) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E))), M:tm-325, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-16671
in-theory        16671
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and (((E and F) -> E) and ((A and (((B and C) -> B) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-325 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-16671.        (((A and (((B and C) -> B) -> D)) -> D) and (((E and F) -> E) and ((A and (((B and C) -> B) -> D)) -> D))), M:tm-325, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-16672
in-theory        16672
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((D and E) -> D) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-325 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-16672.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((D and E) -> D) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)))), M:tm-325, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-16673
in-theory        16673
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (((D and E) -> D) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B))))
theorem-size     37
proof            (modus-ponens tm-325 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-16673.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (((D and E) -> D) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)))), M:tm-325, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-16674
in-theory        16674
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((D and E) -> D) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B)))))
theorem-size     57
proof            (modus-ponens tm-325 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-16674.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((D and E) -> D) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))))), M:tm-325, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-16675
in-theory        16675
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (((E and F) -> E) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))))
theorem-size     61
proof            (modus-ponens tm-325 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-16675.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (((E and F) -> E) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))), M:tm-325, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-16676
in-theory        16676
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((E and F) -> E) and (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16676.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((E and F) -> E) and (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-325, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-16677
in-theory        16677
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (((E and F) -> E) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D)))
theorem-size     41
proof            (modus-ponens tm-325 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16677.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (((E and F) -> E) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D))), M:tm-325, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-16678
in-theory        16678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (((E and F) -> E) and (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))))
theorem-size     45
proof            (modus-ponens tm-325 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16678.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (((E and F) -> E) and (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)))), M:tm-325, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-16679
in-theory        16679
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((D and E) -> D) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C))))
theorem-size     53
proof            (modus-ponens tm-325 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-16679.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((D and E) -> D) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)))), M:tm-325, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-16680
in-theory        16680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((E and F) -> E) and (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16680.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((E and F) -> E) and (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-325, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-16681
in-theory        16681
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and (((E and F) -> E) and ((A and (((B and C) -> C) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-325 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-16681.        (((A and (((B and C) -> C) -> D)) -> D) and (((E and F) -> E) and ((A and (((B and C) -> C) -> D)) -> D))), M:tm-325, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-16682
in-theory        16682
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and (((E and F) -> E) and (((((A and B) -> B) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-325 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-16682.        ((((((A and B) -> B) -> C) and D) -> C) and (((E and F) -> E) and (((((A and B) -> B) -> C) and D) -> C))), M:tm-325, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-16683
in-theory        16683
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((D and E) -> D) and (((A and B) -> (B -> C)) -> ((A and B) -> C))))
theorem-size     33
proof            (modus-ponens tm-325 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-16683.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((D and E) -> D) and (((A and B) -> (B -> C)) -> ((A and B) -> C)))), M:tm-325, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-16684
in-theory        16684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (((D and E) -> D) and ((A -> (not ((B and C) -> C))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-1 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-16684.        (((A -> (not ((B and C) -> C))) -> (not A)) and (((D and E) -> D) and ((A -> (not ((B and C) -> C))) -> (not A)))), M:tm-325, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-16685
in-theory        16685
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (((E and F) -> E) and ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C))))
theorem-size     41
proof            (modus-ponens tm-325 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-16685.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (((E and F) -> E) and ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)))), M:tm-325, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-16686
in-theory        16686
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and (((E and F) -> E) and (A or (B -> ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16686.        ((A or (B -> ((C and D) -> D))) and (((E and F) -> E) and (A or (B -> ((C and D) -> D))))), M:tm-325, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-16687
in-theory        16687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and (((E and F) -> E) and ((A -> ((B and C) -> C)) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16687.        (((A -> ((B and C) -> C)) or D) and (((E and F) -> E) and ((A -> ((B and C) -> C)) or D))), M:tm-325, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-16688
in-theory        16688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and (((E and F) -> E) and (A -> ((B -> ((C and D) -> D)) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16688.        ((A -> ((B -> ((C and D) -> D)) and A)) and (((E and F) -> E) and (A -> ((B -> ((C and D) -> D)) and A)))), M:tm-325, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-16689
in-theory        16689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (((D and E) -> D) and ((A -> (B and C)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-325 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-16689.        (((A -> (B and C)) -> (A -> C)) and (((D and E) -> D) and ((A -> (B and C)) -> (A -> C)))), M:tm-325, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-16690
in-theory        16690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (((E and F) -> E) and (A -> (B -> ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16690.        ((A -> (B -> ((C and D) -> D))) and (((E and F) -> E) and (A -> (B -> ((C and D) -> D))))), M:tm-325, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-16691
in-theory        16691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and (((E and F) -> E) and ((A -> (B -> A)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16691.        (((A -> (B -> A)) and (C -> (D -> C))) and (((E and F) -> E) and ((A -> (B -> A)) and (C -> (D -> C))))), M:tm-325, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-16692
in-theory        16692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16692.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-325, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-16693
in-theory        16693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and (((E and F) -> E) and ((A -> (B -> A)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16693.        (((A -> (B -> A)) and ((C and D) -> C)) and (((E and F) -> E) and ((A -> (B -> A)) and ((C and D) -> C)))), M:tm-325, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-16694
in-theory        16694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and (((E and F) -> E) and ((A -> (B -> A)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-325 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16694.        (((A -> (B -> A)) and ((C and D) -> D)) and (((E and F) -> E) and ((A -> (B -> A)) and ((C and D) -> D)))), M:tm-325, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-16695
in-theory        16695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A -> (B -> A)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16695.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A -> (B -> A)) and (C -> (D -> (C and D)))))), M:tm-325, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-16696
in-theory        16696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and (((E and F) -> E) and ((A -> (B -> A)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16696.        (((A -> (B -> A)) and (C -> (C or D))) and (((E and F) -> E) and ((A -> (B -> A)) and (C -> (C or D))))), M:tm-325, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-16697
in-theory        16697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and (((E and F) -> E) and ((A -> (B -> A)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16697.        (((A -> (B -> A)) and (C -> (D or C))) and (((E and F) -> E) and ((A -> (B -> A)) and (C -> (D or C))))), M:tm-325, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-16698
in-theory        16698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16698.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-325, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-16699
in-theory        16699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> E) and ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16699.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> E) and ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-325, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-16700
in-theory        16700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and (((D and E) -> D) and ((A -> (B -> A)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16700.        (((A -> (B -> A)) and ((not (not C)) -> C)) and (((D and E) -> D) and ((A -> (B -> A)) and ((not (not C)) -> C)))), M:tm-325, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-16701
in-theory        16701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16701.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> (D -> (E -> D)))))), M:tm-325, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-16702
in-theory        16702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (((E and F) -> E) and ((A -> (B -> A)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16702.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (((E and F) -> E) and ((A -> (B -> A)) and ((C -> D) -> (C -> C))))), M:tm-325, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-16703
in-theory        16703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> F) and ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-325 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16703.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> F) and ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-325, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-16704
in-theory        16704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16704.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-325, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-16705
in-theory        16705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> F) and ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16705.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> F) and ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-325, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-16706
in-theory        16706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16706.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> ((D and E) -> D))))), M:tm-325, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-16707
in-theory        16707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> F) and ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16707.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> F) and ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-325, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-16708
in-theory        16708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16708.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> ((D and E) -> E))))), M:tm-325, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-16709
in-theory        16709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16709.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-325, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-16710
in-theory        16710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((D and E) -> D) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16710.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((D and E) -> D) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A)))), M:tm-325, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-16711
in-theory        16711
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (((E and F) -> E) and ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-325 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16711.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (((E and F) -> E) and ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)))), M:tm-325, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-16712
in-theory        16712
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and (((E and F) -> E) and (A or (B -> ((C -> (D -> C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16712.        ((A or (B -> ((C -> (D -> C)) and B))) and (((E and F) -> E) and (A or (B -> ((C -> (D -> C)) and B))))), M:tm-325, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-16713
in-theory        16713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and (((E and F) -> E) and ((A -> ((B -> (C -> B)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-325 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16713.        (((A -> ((B -> (C -> B)) and A)) or D) and (((E and F) -> E) and ((A -> ((B -> (C -> B)) and A)) or D))), M:tm-325, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-16714
in-theory        16714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (((E and F) -> E) and (A -> ((B -> ((C -> (D -> C)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16714.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (((E and F) -> E) and (A -> ((B -> ((C -> (D -> C)) and B)) and A)))), M:tm-325, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-16715
in-theory        16715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (((E and F) -> E) and (A -> (B -> ((C -> (D -> C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16715.        ((A -> (B -> ((C -> (D -> C)) and B))) and (((E and F) -> E) and (A -> (B -> ((C -> (D -> C)) and B))))), M:tm-325, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-16716
in-theory        16716
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16716.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))))), M:tm-325, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-16717
in-theory        16717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16717.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-325, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-16718
in-theory        16718
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-325 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16718.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)))), M:tm-325, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-16719
in-theory        16719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-325 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16719.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)))), M:tm-325, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-16720
in-theory        16720
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16720.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))))), M:tm-325, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-16721
in-theory        16721
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16721.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))))), M:tm-325, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-16722
in-theory        16722
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16722.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))))), M:tm-325, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-16723
in-theory        16723
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16723.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-325, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-16724
in-theory        16724
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     57
proof            (modus-ponens tm-325 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16724.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-325, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-16725
in-theory        16725
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (((E and F) -> E) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D))))
theorem-size     45
proof            (modus-ponens tm-325 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-10)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16725.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (((E and F) -> E) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)))), M:tm-325, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-16726
in-theory        16726
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16726.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))))), M:tm-325, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-16727
in-theory        16727
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16727.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))))), M:tm-325, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-16728
in-theory        16728
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     73
proof            (modus-ponens tm-325 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       249
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16728.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-325, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-16729
in-theory        16729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-325 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16729.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-325, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-16730
in-theory        16730
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     65
proof            (modus-ponens tm-325 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16730.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-325, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-16731
in-theory        16731
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16731.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))))), M:tm-325, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-16732
in-theory        16732
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     65
proof            (modus-ponens tm-325 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16732.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-325, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-16733
in-theory        16733
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16733.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))))), M:tm-325, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-16734
in-theory        16734
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16734.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-325, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-16735
in-theory        16735
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((H and I) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-325 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16735.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((H and I) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-325, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-16736
in-theory        16736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> G) and ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16736.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> G) and ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-325, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-16737
in-theory        16737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((E and F) -> E) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A))))
theorem-size     49
proof            (modus-ponens tm-325 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16737.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((E and F) -> E) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)))), M:tm-325, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-16738
in-theory        16738
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (((F and G) -> F) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))))
theorem-size     81
proof            (modus-ponens tm-325 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16738.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (((F and G) -> F) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))), M:tm-325, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-16739
in-theory        16739
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((F and G) -> F) and (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16739.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((F and G) -> F) and (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-325, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-16740
in-theory        16740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (((F and G) -> F) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E)))
theorem-size     45
proof            (modus-ponens tm-325 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16740.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (((F and G) -> F) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E))), M:tm-325, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-16741
in-theory        16741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (((F and G) -> F) and (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))))
theorem-size     49
proof            (modus-ponens tm-325 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16741.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (((F and G) -> F) and (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)))), M:tm-325, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-16742
in-theory        16742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((F and G) -> F) and (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16742.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((F and G) -> F) and (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-325, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-16743
in-theory        16743
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and (((E and F) -> E) and (((A and B) -> A) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16743.        ((((A and B) -> A) and (C -> (D -> C))) and (((E and F) -> E) and (((A and B) -> A) and (C -> (D -> C))))), M:tm-325, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-16744
in-theory        16744
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16744.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-325, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-16745
in-theory        16745
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and (((E and F) -> E) and (((A and B) -> A) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16745.        ((((A and B) -> A) and ((C and D) -> C)) and (((E and F) -> E) and (((A and B) -> A) and ((C and D) -> C)))), M:tm-325, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-16746
in-theory        16746
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and (((E and F) -> E) and (((A and B) -> A) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-325 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16746.        ((((A and B) -> A) and ((C and D) -> D)) and (((E and F) -> E) and (((A and B) -> A) and ((C and D) -> D)))), M:tm-325, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-16747
in-theory        16747
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and (((E and F) -> E) and (((A and B) -> A) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16747.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and (((E and F) -> E) and (((A and B) -> A) and (C -> (D -> (C and D)))))), M:tm-325, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-16748
in-theory        16748
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and (((E and F) -> E) and (((A and B) -> A) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16748.        ((((A and B) -> A) and (C -> (C or D))) and (((E and F) -> E) and (((A and B) -> A) and (C -> (C or D))))), M:tm-325, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-16749
in-theory        16749
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and (((E and F) -> E) and (((A and B) -> A) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16749.        ((((A and B) -> A) and (C -> (D or C))) and (((E and F) -> E) and (((A and B) -> A) and (C -> (D or C))))), M:tm-325, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-16750
in-theory        16750
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> F) and (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16750.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> F) and (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-325, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-16751
in-theory        16751
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> E) and (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16751.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> E) and (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-325, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-16752
in-theory        16752
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and (((D and E) -> D) and (((A and B) -> A) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16752.        ((((A and B) -> A) and ((not (not C)) -> C)) and (((D and E) -> D) and (((A and B) -> A) and ((not (not C)) -> C)))), M:tm-325, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-16753
in-theory        16753
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (((F and G) -> F) and (((A and B) -> A) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16753.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (((F and G) -> F) and (((A and B) -> A) and (C -> (D -> (E -> D)))))), M:tm-325, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-16754
in-theory        16754
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (((E and F) -> E) and (((A and B) -> A) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16754.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (((E and F) -> E) and (((A and B) -> A) and ((C -> D) -> (C -> C))))), M:tm-325, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-16755
in-theory        16755
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> F) and (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-325 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16755.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> F) and (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-325, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-16756
in-theory        16756
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16756.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-325, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-16757
in-theory        16757
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> F) and (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16757.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> F) and (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-325, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-16758
in-theory        16758
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and (((F and G) -> F) and (((A and B) -> A) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16758.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and (((F and G) -> F) and (((A and B) -> A) and (C -> ((D and E) -> D))))), M:tm-325, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-16759
in-theory        16759
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> F) and (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16759.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> F) and (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-325, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-16760
in-theory        16760
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and (((F and G) -> F) and (((A and B) -> A) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16760.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and (((F and G) -> F) and (((A and B) -> A) and (C -> ((D and E) -> E))))), M:tm-325, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-16761
in-theory        16761
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> F) and (((A and B) -> A) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16761.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> F) and (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))))), M:tm-325, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-16762
in-theory        16762
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> G) and (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16762.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> G) and (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-325, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-16763
in-theory        16763
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (((F and G) -> F) and (((A and B) -> A) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16763.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (((F and G) -> F) and (((A and B) -> A) and (C -> (((D and E) -> D) and C))))), M:tm-325, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-16764
in-theory        16764
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16764.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-325, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-16765
in-theory        16765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16765.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))))), M:tm-325, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-16766
in-theory        16766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((D and E) -> D) and ((A -> (not (((B and C) -> B) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16766.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((D and E) -> D) and ((A -> (not (((B and C) -> B) and A))) -> (not A)))), M:tm-325, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-16767
in-theory        16767
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (((E and F) -> E) and (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-325 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16767.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (((E and F) -> E) and (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)))), M:tm-325, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-16768
in-theory        16768
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and (((E and F) -> E) and (A or (B -> (((C and D) -> C) and B)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16768.        ((A or (B -> (((C and D) -> C) and B))) and (((E and F) -> E) and (A or (B -> (((C and D) -> C) and B))))), M:tm-325, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-16769
in-theory        16769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and (((E and F) -> E) and ((A -> (((B and C) -> B) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-325 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16769.        (((A -> (((B and C) -> B) and A)) or D) and (((E and F) -> E) and ((A -> (((B and C) -> B) and A)) or D))), M:tm-325, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-16770
in-theory        16770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (((E and F) -> E) and (A -> ((B -> (((C and D) -> C) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16770.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (((E and F) -> E) and (A -> ((B -> (((C and D) -> C) and B)) and A)))), M:tm-325, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-16771
in-theory        16771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (((E and F) -> E) and (A -> (B -> (((C and D) -> C) and B)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16771.        ((A -> (B -> (((C and D) -> C) and B))) and (((E and F) -> E) and (A -> (B -> (((C and D) -> C) and B))))), M:tm-325, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-16772
in-theory        16772
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and (((E and F) -> E) and (((A and B) -> B) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16772.        ((((A and B) -> B) and (C -> (D -> C))) and (((E and F) -> E) and (((A and B) -> B) and (C -> (D -> C))))), M:tm-325, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-16773
in-theory        16773
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16773.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-325, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-16774
in-theory        16774
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and (((E and F) -> E) and (((A and B) -> B) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16774.        ((((A and B) -> B) and ((C and D) -> C)) and (((E and F) -> E) and (((A and B) -> B) and ((C and D) -> C)))), M:tm-325, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-16775
in-theory        16775
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and (((E and F) -> E) and (((A and B) -> B) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-325 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16775.        ((((A and B) -> B) and ((C and D) -> D)) and (((E and F) -> E) and (((A and B) -> B) and ((C and D) -> D)))), M:tm-325, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-16776
in-theory        16776
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and (((E and F) -> E) and (((A and B) -> B) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16776.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and (((E and F) -> E) and (((A and B) -> B) and (C -> (D -> (C and D)))))), M:tm-325, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-16777
in-theory        16777
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and (((E and F) -> E) and (((A and B) -> B) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16777.        ((((A and B) -> B) and (C -> (C or D))) and (((E and F) -> E) and (((A and B) -> B) and (C -> (C or D))))), M:tm-325, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-16778
in-theory        16778
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and (((E and F) -> E) and (((A and B) -> B) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16778.        ((((A and B) -> B) and (C -> (D or C))) and (((E and F) -> E) and (((A and B) -> B) and (C -> (D or C))))), M:tm-325, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-16779
in-theory        16779
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> F) and (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16779.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> F) and (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-325, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-16780
in-theory        16780
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> E) and (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16780.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> E) and (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-325, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-16781
in-theory        16781
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and (((D and E) -> D) and (((A and B) -> B) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16781.        ((((A and B) -> B) and ((not (not C)) -> C)) and (((D and E) -> D) and (((A and B) -> B) and ((not (not C)) -> C)))), M:tm-325, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-16782
in-theory        16782
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (((F and G) -> F) and (((A and B) -> B) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16782.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (((F and G) -> F) and (((A and B) -> B) and (C -> (D -> (E -> D)))))), M:tm-325, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-16783
in-theory        16783
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (((E and F) -> E) and (((A and B) -> B) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16783.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (((E and F) -> E) and (((A and B) -> B) and ((C -> D) -> (C -> C))))), M:tm-325, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-16784
in-theory        16784
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> F) and (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-325 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16784.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> F) and (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-325, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-16785
in-theory        16785
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16785.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-325, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-16786
in-theory        16786
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> F) and (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16786.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> F) and (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-325, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-16787
in-theory        16787
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and (((F and G) -> F) and (((A and B) -> B) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16787.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and (((F and G) -> F) and (((A and B) -> B) and (C -> ((D and E) -> D))))), M:tm-325, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-16788
in-theory        16788
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> F) and (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16788.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> F) and (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-325, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-16789
in-theory        16789
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and (((F and G) -> F) and (((A and B) -> B) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16789.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and (((F and G) -> F) and (((A and B) -> B) and (C -> ((D and E) -> E))))), M:tm-325, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-16790
in-theory        16790
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> F) and (((A and B) -> B) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16790.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> F) and (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))))), M:tm-325, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-16791
in-theory        16791
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> G) and (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16791.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> G) and (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-325, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-16792
in-theory        16792
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (((F and G) -> F) and (((A and B) -> B) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16792.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (((F and G) -> F) and (((A and B) -> B) and (C -> (((D and E) -> D) and C))))), M:tm-325, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-16793
in-theory        16793
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (((F and G) -> F) and (((A and B) -> B) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16793.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (((F and G) -> F) and (((A and B) -> B) and (C -> (((D and E) -> E) and C))))), M:tm-325, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-16794
in-theory        16794
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (((F and G) -> F) and (((A and B) -> A) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16794.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (((F and G) -> F) and (((A and B) -> A) and (C -> (((D and E) -> E) and C))))), M:tm-325, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-16795
in-theory        16795
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16795.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-325, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-16796
in-theory        16796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16796.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))))), M:tm-325, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-16797
in-theory        16797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((D and E) -> D) and ((A -> (not (((B and C) -> C) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-16797.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((D and E) -> D) and ((A -> (not (((B and C) -> C) and A))) -> (not A)))), M:tm-325, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-16798
in-theory        16798
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (((E and F) -> E) and (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-325 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-16798.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (((E and F) -> E) and (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)))), M:tm-325, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-16799
in-theory        16799
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and (((E and F) -> E) and (A or (B -> (((C and D) -> D) and B)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16799.        ((A or (B -> (((C and D) -> D) and B))) and (((E and F) -> E) and (A or (B -> (((C and D) -> D) and B))))), M:tm-325, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-16800
in-theory        16800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and (((E and F) -> E) and ((A -> (((B and C) -> C) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-325 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16800.        (((A -> (((B and C) -> C) and A)) or D) and (((E and F) -> E) and ((A -> (((B and C) -> C) and A)) or D))), M:tm-325, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-16801
in-theory        16801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (((E and F) -> E) and (A -> ((B -> (((C and D) -> D) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16801.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (((E and F) -> E) and (A -> ((B -> (((C and D) -> D) and B)) and A)))), M:tm-325, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-16802
in-theory        16802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (((E and F) -> E) and (A -> (B -> (((C and D) -> D) and B)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16802.        ((A -> (B -> (((C and D) -> D) and B))) and (((E and F) -> E) and (A -> (B -> (((C and D) -> D) and B))))), M:tm-325, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-16803
in-theory        16803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and (((E and F) -> E) and ((A -> (B -> (A and B))) and (C -> (D -> C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16803.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and (((E and F) -> E) and ((A -> (B -> (A and B))) and (C -> (D -> C))))), M:tm-325, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-16804
in-theory        16804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16804.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-325, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-16805
in-theory        16805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and (((E and F) -> E) and ((A -> (B -> (A and B))) and ((C and D) -> C))))
theorem-size     33
proof            (modus-ponens tm-325 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16805.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and (((E and F) -> E) and ((A -> (B -> (A and B))) and ((C and D) -> C)))), M:tm-325, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-16806
in-theory        16806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and (((E and F) -> E) and ((A -> (B -> (A and B))) and ((C and D) -> D))))
theorem-size     33
proof            (modus-ponens tm-325 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16806.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and (((E and F) -> E) and ((A -> (B -> (A and B))) and ((C and D) -> D)))), M:tm-325, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-16807
in-theory        16807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A -> (B -> (A and B))) and (C -> (D -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16807.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))))), M:tm-325, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-16808
in-theory        16808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and (((E and F) -> E) and ((A -> (B -> (A and B))) and (C -> (C or D)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16808.        (((A -> (B -> (A and B))) and (C -> (C or D))) and (((E and F) -> E) and ((A -> (B -> (A and B))) and (C -> (C or D))))), M:tm-325, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-16809
in-theory        16809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and (((E and F) -> E) and ((A -> (B -> (A and B))) and (C -> (D or C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16809.        (((A -> (B -> (A and B))) and (C -> (D or C))) and (((E and F) -> E) and ((A -> (B -> (A and B))) and (C -> (D or C))))), M:tm-325, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-16810
in-theory        16810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16810.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-325, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-16811
in-theory        16811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> E) and ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16811.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> E) and ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-325, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-16812
in-theory        16812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (((D and E) -> D) and ((A -> (B -> (A and B))) and ((not (not C)) -> C))))
theorem-size     33
proof            (modus-ponens tm-325 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-10)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16812.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (((D and E) -> D) and ((A -> (B -> (A and B))) and ((not (not C)) -> C)))), M:tm-325, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-16813
in-theory        16813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-16813.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))))), M:tm-325, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-16814
in-theory        16814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (((E and F) -> E) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-16814.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (((E and F) -> E) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))))), M:tm-325, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-16815
in-theory        16815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-16815.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-325, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-16816
in-theory        16816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     53
proof            (modus-ponens tm-325 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-16816.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-325, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-16817
in-theory        16817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-16817.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-325, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-16818
in-theory        16818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> D)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-16818.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))))), M:tm-325, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-16819
in-theory        16819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-16819.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-325, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-16820
in-theory        16820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> E)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-16820.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))))), M:tm-325, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-16821
in-theory        16821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-16821.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))))), M:tm-325, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-16822
in-theory        16822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> G) and ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     57
proof            (modus-ponens tm-325 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-16822.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> G) and ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-325, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-16823
in-theory        16823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-16823.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))))), M:tm-325, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-16824
in-theory        16824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-16824.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))))), M:tm-325, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-16825
in-theory        16825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16825.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-325, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-16826
in-theory        16826
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> F) and (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16826.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> F) and (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-325, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-16827
in-theory        16827
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> F) and (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16827.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> F) and (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-325, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-16828
in-theory        16828
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     57
proof            (modus-ponens tm-325 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16828.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-325, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-16829
in-theory        16829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16829.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-325, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-16830
in-theory        16830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((D and E) -> D) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A))))
theorem-size     37
proof            (modus-ponens tm-325 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-16830.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((D and E) -> D) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)))), M:tm-325, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-16831
in-theory        16831
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (((E and F) -> E) and ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-325 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-16831.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (((E and F) -> E) and ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)))), M:tm-325, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-16832
in-theory        16832
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and (((E and F) -> E) and (A or (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16832.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and (((E and F) -> E) and (A or (B -> ((C -> (D -> (C and D))) and B))))), M:tm-325, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-16833
in-theory        16833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and (((E and F) -> E) and ((A -> ((B -> (C -> (B and C))) and A)) or D)))
theorem-size     33
proof            (modus-ponens tm-325 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16833.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and (((E and F) -> E) and ((A -> ((B -> (C -> (B and C))) and A)) or D))), M:tm-325, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-16834
in-theory        16834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (((E and F) -> E) and (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A))))
theorem-size     37
proof            (modus-ponens tm-325 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16834.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (((E and F) -> E) and (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)))), M:tm-325, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-16835
in-theory        16835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (((E and F) -> E) and (A -> (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-16835.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (((E and F) -> E) and (A -> (B -> ((C -> (D -> (C and D))) and B))))), M:tm-325, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-16836
in-theory        16836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (((C and D) -> C) and (A -> (A and (B -> A)))))
theorem-size     21
proof            (modus-ponens tm-325 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16836.        ((A -> (A and (B -> A))) and (((C and D) -> C) and (A -> (A and (B -> A))))), M:tm-325, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-16837
in-theory        16837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (((D and E) -> D) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-16837.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (((D and E) -> D) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))), M:tm-325, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-16838
in-theory        16838
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and (((C and D) -> C) and ((A and B) -> ((A and B) and A))))
theorem-size     25
proof            (modus-ponens tm-325 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16838.        (((A and B) -> ((A and B) and A)) and (((C and D) -> C) and ((A and B) -> ((A and B) and A)))), M:tm-325, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-16839
in-theory        16839
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and (((C and D) -> C) and ((A and B) -> ((A and B) and B))))
theorem-size     25
proof            (modus-ponens tm-325 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-16839.        (((A and B) -> ((A and B) and B)) and (((C and D) -> C) and ((A and B) -> ((A and B) and B)))), M:tm-325, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-16840
in-theory        16840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (((C and D) -> C) and (A -> (A and (B -> (A and B))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-16840.        ((A -> (A and (B -> (A and B)))) and (((C and D) -> C) and (A -> (A and (B -> (A and B)))))), M:tm-325, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-16841
in-theory        16841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (((C and D) -> C) and (A -> (A and (A or B)))))
theorem-size     21
proof            (modus-ponens tm-325 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-16841.        ((A -> (A and (A or B))) and (((C and D) -> C) and (A -> (A and (A or B))))), M:tm-325, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-16842
in-theory        16842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (((C and D) -> C) and (A -> (A and (B or A)))))
theorem-size     21
proof            (modus-ponens tm-325 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-16842.        ((A -> (A and (B or A))) and (((C and D) -> C) and (A -> (A and (B or A))))), M:tm-325, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-16843
in-theory        16843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (((D and E) -> D) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-16843.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (((D and E) -> D) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))))), M:tm-325, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-16844
in-theory        16844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (((C and D) -> C) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-16844.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (((C and D) -> C) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))))), M:tm-325, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-16845
in-theory        16845
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and (((B and C) -> B) and ((not (not A)) -> ((not (not A)) and A))))
theorem-size     25
proof            (modus-ponens tm-325 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-10)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-16845.        (((not (not A)) -> ((not (not A)) and A)) and (((B and C) -> B) and ((not (not A)) -> ((not (not A)) and A)))), M:tm-325, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-16846
in-theory        16846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (((D and E) -> D) and (A -> (A and (B -> (C -> B))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-16846.        ((A -> (A and (B -> (C -> B)))) and (((D and E) -> D) and (A -> (A and (B -> (C -> B)))))), M:tm-325, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-16847
in-theory        16847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and (((C and D) -> C) and ((A -> B) -> ((A -> B) and (A -> A)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-16847.        (((A -> B) -> ((A -> B) and (A -> A))) and (((C and D) -> C) and ((A -> B) -> ((A -> B) and (A -> A))))), M:tm-325, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-16848
in-theory        16848
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((D and E) -> D) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-325 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-16848.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((D and E) -> D) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))), M:tm-325, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-16849
in-theory        16849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (((E and F) -> E) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-16849.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (((E and F) -> E) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))), M:tm-325, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-16850
in-theory        16850
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (((D and E) -> D) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-16850.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (((D and E) -> D) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))), M:tm-325, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-16851
in-theory        16851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (((D and E) -> D) and (A -> (A and ((B and C) -> B)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-16851.        ((A -> (A and ((B and C) -> B))) and (((D and E) -> D) and (A -> (A and ((B and C) -> B))))), M:tm-325, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-16852
in-theory        16852
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((D and E) -> D) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-16852.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((D and E) -> D) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))), M:tm-325, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-16853
in-theory        16853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (((D and E) -> D) and (A -> (A and ((B and C) -> C)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-16853.        ((A -> (A and ((B and C) -> C))) and (((D and E) -> D) and (A -> (A and ((B and C) -> C))))), M:tm-325, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-16854
in-theory        16854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (((D and E) -> D) and (A -> (A and ((B -> (C -> B)) and A)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-16854.        ((A -> (A and ((B -> (C -> B)) and A))) and (((D and E) -> D) and (A -> (A and ((B -> (C -> B)) and A))))), M:tm-325, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-16855
in-theory        16855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (((E and F) -> E) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-16855.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (((E and F) -> E) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))), M:tm-325, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-16856
in-theory        16856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (((D and E) -> D) and (A -> (A and (((B and C) -> B) and A)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16856.        ((A -> (A and (((B and C) -> B) and A))) and (((D and E) -> D) and (A -> (A and (((B and C) -> B) and A))))), M:tm-325, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16857
in-theory        16857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and (((B and C) -> B) and A)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16857.        ((A -> (A and (((B and C) -> B) and A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and (((B and C) -> B) and A))))), M:tm-324, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16858
in-theory        16858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and ((D -> (E -> D)) and (A -> (A and (((B and C) -> B) and A)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16858.        ((A -> (A and (((B and C) -> B) and A))) and ((D -> (E -> D)) and (A -> (A and (((B and C) -> B) and A))))), M:tm-323, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16859
in-theory        16859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16859.        ((A -> (A and (((B and C) -> B) and A))) and ((D and E) -> E)), M:tm-322, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16860
in-theory        16860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16860.        ((A -> (A and (((B and C) -> B) and A))) and ((D and E) -> D)), M:tm-320, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16861
in-theory        16861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16861.        ((A -> (A and (((B and C) -> B) and A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16862
in-theory        16862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16862.        ((A -> (A and (((B and C) -> B) and A))) and (A -> A)), M:tm-316, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-16863
in-theory        16863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16863.        ((A -> (A and (((B and C) -> B) and A))) and (D -> (E -> D))), M:tm-315, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16864
in-theory        16864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and ((A -> (not (A and (((B and C) -> B) and A)))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16864.        ((A -> (A and (((B and C) -> B) and A))) and ((A -> (not (A and (((B and C) -> B) and A)))) -> (not A))), M:tm-313, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-16865
in-theory        16865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (((A and (((B and C) -> B) and A)) -> D) -> ((A or (A and (((B and C) -> B) and A))) -> D)))
theorem-size     37
proof            (modus-ponens tm-312 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16865.        ((A -> (A and (((B and C) -> B) and A))) and (((A and (((B and C) -> B) and A)) -> D) -> ((A or (A and (((B and C) -> B) and A))) -> D))), M:tm-312, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-16866
in-theory        16866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (D or (A -> (A and (((B and C) -> B) and A)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16866.        ((A -> (A and (((B and C) -> B) and A))) and (D or (A -> (A and (((B and C) -> B) and A))))), M:tm-311, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16867
in-theory        16867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and ((A -> (A and (((B and C) -> B) and A))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16867.        ((A -> (A and (((B and C) -> B) and A))) and ((A -> (A and (((B and C) -> B) and A))) or D)), M:tm-310, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16868
in-theory        16868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (D -> ((A -> (A and (((B and C) -> B) and A))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16868.        ((A -> (A and (((B and C) -> B) and A))) and (D -> ((A -> (A and (((B and C) -> B) and A))) and D))), M:tm-309, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16869
in-theory        16869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (D -> (A -> (A and (((B and C) -> B) and A)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16869.        ((A -> (A and (((B and C) -> B) and A))) and (D -> (A -> (A and (((B and C) -> B) and A))))), M:tm-305, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16870
in-theory        16870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     23
proof            (modus-ponens tm-303 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16870.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-303, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16871
in-theory        16871
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (((D and E) -> D) and ((B -> (C -> (B and C))) and A))))
theorem-size     37
proof            (modus-ponens tm-300 tm-325 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (and (-> (and Bm Cm) Bm) (and (-> A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16871.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (((D and E) -> D) and ((B -> (C -> (B and C))) and A)))), M:tm-300, m:tm-325, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (and (-> (and Bm Cm) Bm) (and (-> A (-> B (and A B))) C)))))
================================================================
tm-name          tm-16872
in-theory        16872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-270 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16872.        ((A -> (((B and C) -> C) and A)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-270, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16873
in-theory        16873
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (((D and E) -> D) and (((B and C) -> C) and A))))
theorem-size     31
proof            (modus-ponens tm-267 tm-325 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (and (-> (and Bm Cm) Bm) (and (-> (and A B) B) C))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16873.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (((D and E) -> D) and (((B and C) -> C) and A)))), M:tm-267, m:tm-325, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (and (-> (and Bm Cm) Bm) (and (-> (and A B) B) C)))))
================================================================
tm-name          tm-16874
in-theory        16874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-239 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16874.        ((A -> (((B and C) -> B) and A)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-239, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16875
in-theory        16875
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (((D and E) -> D) and (((B and C) -> B) and A))))
theorem-size     31
proof            (modus-ponens tm-236 tm-325 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (and (-> (and Bm Cm) Bm) (and (-> (and A B) A) C))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16875.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (((D and E) -> D) and (((B and C) -> B) and A)))), M:tm-236, m:tm-325, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (and (-> (and Bm Cm) Bm) (and (-> (and A B) A) C)))))
================================================================
tm-name          tm-16876
in-theory        16876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (((F and G) -> F) and E))))
theorem-size     29
proof            (modus-ponens tm-210 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16876.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (((F and G) -> F) and E)))), M:tm-210, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16877
in-theory        16877
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (((E and F) -> E) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     55
proof            (modus-ponens tm-207 tm-325 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> (and Bm Cm) Bm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16877.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (((E and F) -> E) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-207, m:tm-325, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> (and Bm Cm) Bm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-16878
in-theory        16878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-183 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16878.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-183, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16879
in-theory        16879
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (((D and E) -> D) and ((B -> (C -> B)) and A))))
theorem-size     31
proof            (modus-ponens tm-180 tm-325 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (and (-> (and Bm Cm) Bm) (and (-> A (-> B A)) C))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16879.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (((D and E) -> D) and ((B -> (C -> B)) and A)))), M:tm-180, m:tm-325, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (and (-> (and Bm Cm) Bm) (and (-> A (-> B A)) C)))))
================================================================
tm-name          tm-16880
in-theory        16880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-157 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16880.        ((A -> ((B and C) -> C)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-157, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16881
in-theory        16881
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and (((D and E) -> D) and ((B and C) -> C))))
theorem-size     25
proof            (modus-ponens tm-154 tm-325 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (and (-> (and Bm Cm) Bm) (-> (and A B) B))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16881.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and (((D and E) -> D) and ((B and C) -> C)))), M:tm-154, m:tm-325, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (and (-> (and Bm Cm) Bm) (-> (and A B) B)))))
================================================================
tm-name          tm-16882
in-theory        16882
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     27
proof            (modus-ponens tm-147 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16882.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-147, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16883
in-theory        16883
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (((D and E) -> D) and ((A and (B -> C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-144 tm-325 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (and (-> (and Bm Cm) Bm) (-> (and A (-> B C)) C))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16883.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (((D and E) -> D) and ((A and (B -> C)) -> C)))), M:tm-144, m:tm-325, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (and (-> (and Bm Cm) Bm) (-> (and A (-> B C)) C)))))
================================================================
tm-name          tm-16884
in-theory        16884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-134 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16884.        ((A -> ((B and C) -> B)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-134, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16885
in-theory        16885
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and (((D and E) -> D) and ((B and C) -> B))))
theorem-size     25
proof            (modus-ponens tm-131 tm-325 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (and (-> (and Bm Cm) Bm) (-> (and A B) A))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16885.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and (((D and E) -> D) and ((B and C) -> B)))), M:tm-131, m:tm-325, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (and (-> (and Bm Cm) Bm) (-> (and A B) A)))))
================================================================
tm-name          tm-16886
in-theory        16886
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     27
proof            (modus-ponens tm-125 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16886.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-125, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16887
in-theory        16887
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (((D and E) -> D) and (((A -> B) and C) -> B))))
theorem-size     37
proof            (modus-ponens tm-122 tm-325 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (and (-> (and Bm Cm) Bm) (-> (and (-> A B) C) B))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16887.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (((D and E) -> D) and (((A -> B) and C) -> B)))), M:tm-122, m:tm-325, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (and (-> (and Bm Cm) Bm) (-> (and (-> A B) C) B)))))
================================================================
tm-name          tm-16888
in-theory        16888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-113 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16888.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (((F and G) -> F) and E)))), M:tm-113, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16889
in-theory        16889
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> E) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-110 tm-325 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (-> (and Bm Cm) Bm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16889.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> E) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-110, m:tm-325, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (-> (and Bm Cm) Bm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
================================================================
tm-name          tm-16890
in-theory        16890
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     31
proof            (modus-ponens tm-105 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16890.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (((E and F) -> E) and D)))), M:tm-105, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16891
in-theory        16891
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((D and E) -> D) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-102 tm-325 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (and (-> (and Bm Cm) Bm) (-> (-> A (-> B C)) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16891.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((D and E) -> D) and ((A -> (B -> C)) -> (A -> C))))), M:tm-102, m:tm-325, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (and (-> (and Bm Cm) Bm) (-> (-> A (-> B C)) (-> A C))))))
================================================================
tm-name          tm-16892
in-theory        16892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and (((D and E) -> D) and C))))
theorem-size     19
proof            (modus-ponens tm-95 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16892.        (((A -> B) -> (A -> A)) and (C -> (C and (((D and E) -> D) and C)))), M:tm-95, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16893
in-theory        16893
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and (((C and D) -> C) and (A -> A))))
theorem-size     21
proof            (modus-ponens tm-92 tm-325 ((Am (-> A A)) (B (and (-> A A) (and (-> (and Bm Cm) Bm) (-> A A))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16893.        (((A -> B) or (A -> A)) -> ((A -> A) and (((C and D) -> C) and (A -> A)))), M:tm-92, m:tm-325, u:((Am (-> A A)) (B (and (-> A A) (and (-> (and Bm Cm) Bm) (-> A A)))))
================================================================
tm-name          tm-16894
in-theory        16894
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and (((C and D) -> C) and A))))
theorem-size     13
proof            (modus-ponens tm-84 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16894.        (A -> (B -> (A and (((C and D) -> C) and A)))), M:tm-84, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-16895
in-theory        16895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-83 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16895.        ((A -> (B -> (C -> B))) and (D -> (D and (((E and F) -> E) and D)))), M:tm-83, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16896
in-theory        16896
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (((D and E) -> D) and (B -> (C -> B)))))
theorem-size     25
proof            (modus-ponens tm-80 tm-325 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (and (-> (and Bm Cm) Bm) (-> A (-> B A)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16896.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (((D and E) -> D) and (B -> (C -> B))))), M:tm-80, m:tm-325, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (and (-> (and Bm Cm) Bm) (-> A (-> B A))))))
================================================================
tm-name          tm-16897
in-theory        16897
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and (((C and D) -> C) and B))))
theorem-size     17
proof            (modus-ponens tm-76 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-10 tm-2 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16897.        (((not (not A)) -> A) and (B -> (B and (((C and D) -> C) and B)))), M:tm-76, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16898
in-theory        16898
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and (((B and C) -> B) and A)))
theorem-size     15
proof            (modus-ponens tm-73 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16898.        (((not (not A)) or A) -> (A and (((B and C) -> B) and A))), M:tm-73, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-16899
in-theory        16899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (((D and E) -> D) and C))))
theorem-size     23
proof            (modus-ponens tm-69 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-9 tm-2 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16899.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (((D and E) -> D) and C)))), M:tm-69, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16900
in-theory        16900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((C and D) -> C) and ((A -> (not B)) -> (not A)))))
theorem-size     33
proof            (modus-ponens tm-66 tm-325 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (and (-> (and Bm Cm) Bm) (-> (-> A (not B)) (not A)))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16900.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((C and D) -> C) and ((A -> (not B)) -> (not A))))), M:tm-66, m:tm-325, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (and (-> (and Bm Cm) Bm) (-> (-> A (not B)) (not A))))))
================================================================
tm-name          tm-16901
in-theory        16901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     25
proof            (modus-ponens tm-54 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16901.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (((E and F) -> E) and D)))), M:tm-54, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16902
in-theory        16902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((D and E) -> D) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     39
proof            (modus-ponens tm-51 tm-325 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> (or C A) B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16902.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((D and E) -> D) and ((B -> C) -> ((A or B) -> C))))), M:tm-51, m:tm-325, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> (or C A) B))))))
================================================================
tm-name          tm-16903
in-theory        16903
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and (((C and D) -> C) and (B or A))))
theorem-size     19
proof            (modus-ponens tm-50 tm-325 ((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Bm) (or A B))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16903.        ((A or (B or A)) -> ((B or A) and (((C and D) -> C) and (B or A)))), M:tm-50, m:tm-325, u:((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Bm) (or A B)))))
================================================================
tm-name          tm-16904
in-theory        16904
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and (((C and D) -> C) and (A or B))))
theorem-size     19
proof            (modus-ponens tm-49 tm-325 ((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Bm) (or A B))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16904.        ((A or (A or B)) -> ((A or B) and (((C and D) -> C) and (A or B)))), M:tm-49, m:tm-325, u:((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Bm) (or A B)))))
================================================================
tm-name          tm-16905
in-theory        16905
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (((C and D) -> C) and (B -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-48 tm-325 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> (and Bm Cm) Bm) (-> A (and B A)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16905.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (((C and D) -> C) and (B -> (A and B))))), M:tm-48, m:tm-325, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> (and Bm Cm) Bm) (-> A (and B A))))))
================================================================
tm-name          tm-16906
in-theory        16906
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (((C and D) -> C) and B)))
theorem-size     15
proof            (modus-ponens tm-47 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16906.        (((A and B) or B) -> (B and (((C and D) -> C) and B))), M:tm-47, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-16907
in-theory        16907
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (((C and D) -> C) and A)))
theorem-size     15
proof            (modus-ponens tm-46 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16907.        (((A and B) or A) -> (A and (((C and D) -> C) and A))), M:tm-46, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-16908
in-theory        16908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D and E) -> D) and ((A -> B) -> (A -> C)))))
theorem-size     35
proof            (modus-ponens tm-45 tm-325 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16908.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D and E) -> D) and ((A -> B) -> (A -> C))))), M:tm-45, m:tm-325, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-16909
in-theory        16909
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (((C and D) -> C) and (B -> A))))
theorem-size     19
proof            (modus-ponens tm-44 tm-325 ((Am (-> A B)) (C (and (-> A B) (and (-> (and Bm Cm) Bm) (-> A B))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16909.        ((A or (B -> A)) -> ((B -> A) and (((C and D) -> C) and (B -> A)))), M:tm-44, m:tm-325, u:((Am (-> A B)) (C (and (-> A B) (and (-> (and Bm Cm) Bm) (-> A B)))))
================================================================
tm-name          tm-16910
in-theory        16910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and (((D and E) -> D) and C))))
theorem-size     17
proof            (modus-ponens tm-42 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16910.        ((A -> (B or A)) and (C -> (C and (((D and E) -> D) and C)))), M:tm-42, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16911
in-theory        16911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and (((D and E) -> D) and C))))
theorem-size     17
proof            (modus-ponens tm-32 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16911.        ((A -> (A or B)) and (C -> (C and (((D and E) -> D) and C)))), M:tm-32, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16912
in-theory        16912
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and (((B and C) -> B) and A))))
theorem-size     13
proof            (modus-ponens tm-24 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16912.        (A -> (A and (A and (((B and C) -> B) and A)))), M:tm-24, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-16913
in-theory        16913
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and (((D and E) -> D) and C))))
theorem-size     19
proof            (modus-ponens tm-23 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16913.        ((A -> (B -> (A and B))) and (C -> (C and (((D and E) -> D) and C)))), M:tm-23, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16914
in-theory        16914
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and (((D and E) -> D) and C))))
theorem-size     17
proof            (modus-ponens tm-22 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16914.        (((A and B) -> B) and (C -> (C and (((D and E) -> D) and C)))), M:tm-22, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16915
in-theory        16915
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and (((D and E) -> D) and C))))
theorem-size     17
proof            (modus-ponens tm-21 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16915.        (((A and B) -> A) and (C -> (C and (((D and E) -> D) and C)))), M:tm-21, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16916
in-theory        16916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     25
proof            (modus-ponens tm-20 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16916.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (((E and F) -> E) and D)))), M:tm-20, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16917
in-theory        16917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and (((D and E) -> D) and C))))
theorem-size     17
proof            (modus-ponens tm-19 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16917.        ((A -> (B -> A)) and (C -> (C and (((D and E) -> D) and C)))), M:tm-19, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16918
in-theory        16918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and (((B and C) -> B) and A)))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-9 tm-2 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16918.        ((A -> (not (A and (((B and C) -> B) and A)))) -> (not A)), M:tm-9, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-16919
in-theory        16919
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) and A)) -> D) -> ((A or (A and (((B and C) -> B) and A))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16919.        (((A and (((B and C) -> B) and A)) -> D) -> ((A or (A and (((B and C) -> B) and A))) -> D)), M:tm-8, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-16920
in-theory        16920
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and (((C and D) -> C) and B))))
theorem-size     13
proof            (modus-ponens tm-7 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-7 tm-2 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16920.        (A or (B -> (B and (((C and D) -> C) and B)))), M:tm-7, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16921
in-theory        16921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-6 tm-2 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16921.        ((A -> (A and (((B and C) -> B) and A))) or D), M:tm-6, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16922
in-theory        16922
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and (((C and D) -> C) and B))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16922.        (A -> ((B -> (B and (((C and D) -> C) and B))) and A)), M:tm-5, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16923
in-theory        16923
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and (((C and D) -> C) and B))))
theorem-size     13
proof            (modus-ponens tm-1 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-1 tm-2 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-16923.        (A -> (B -> (B and (((C and D) -> C) and B)))), M:tm-1, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-16924
in-theory        16924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (A -> (B -> A))))
theorem-size     17
proof            (modus-ponens tm-326 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16924.        ((A -> (B -> A)) and (((C and D) -> D) and (A -> (B -> A)))), M:tm-326, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-16925
in-theory        16925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-16925.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))), M:tm-326, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-16926
in-theory        16926
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((A and B) -> A)))
theorem-size     17
proof            (modus-ponens tm-326 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-16926.        (((A and B) -> A) and (((C and D) -> D) and ((A and B) -> A))), M:tm-326, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-16927
in-theory        16927
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((A and B) -> B)))
theorem-size     17
proof            (modus-ponens tm-326 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-16927.        (((A and B) -> B) and (((C and D) -> D) and ((A and B) -> B))), M:tm-326, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-16928
in-theory        16928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (A -> (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-326 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-16928.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (A -> (B -> (A and B))))), M:tm-326, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-16929
in-theory        16929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (A -> (A or B))))
theorem-size     17
proof            (modus-ponens tm-326 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-16929.        ((A -> (A or B)) and (((C and D) -> D) and (A -> (A or B)))), M:tm-326, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-16930
in-theory        16930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (A -> (B or A))))
theorem-size     17
proof            (modus-ponens tm-326 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-16930.        ((A -> (B or A)) and (((C and D) -> D) and (A -> (B or A)))), M:tm-326, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-16931
in-theory        16931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-16931.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))), M:tm-326, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-16932
in-theory        16932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((A -> B) -> ((A -> (not B)) -> (not A)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-16932.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((A -> B) -> ((A -> (not B)) -> (not A))))), M:tm-326, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-16933
in-theory        16933
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((not (not A)) -> A)))
theorem-size     17
proof            (modus-ponens tm-326 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-4 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-16933.        (((not (not A)) -> A) and (((B and C) -> C) and ((not (not A)) -> A))), M:tm-326, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-16934
in-theory        16934
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (A -> (B -> (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-326 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16934.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (A -> (B -> (C -> B))))), M:tm-326, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-16935
in-theory        16935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((A -> B) -> (A -> A))))
theorem-size     21
proof            (modus-ponens tm-326 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-16935.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((A -> B) -> (A -> A)))), M:tm-326, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-16936
in-theory        16936
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-16936.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-326, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-16937
in-theory        16937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16937.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-326, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-16938
in-theory        16938
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))))
theorem-size     37
proof            (modus-ponens tm-326 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16938.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)))), M:tm-326, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-16939
in-theory        16939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (A -> ((B and C) -> B))))
theorem-size     21
proof            (modus-ponens tm-326 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16939.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (A -> ((B and C) -> B)))), M:tm-326, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-16940
in-theory        16940
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-326 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-16940.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)))), M:tm-326, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-16941
in-theory        16941
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (A -> ((B and C) -> C))))
theorem-size     21
proof            (modus-ponens tm-326 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16941.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (A -> ((B and C) -> C)))), M:tm-326, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-16942
in-theory        16942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (A -> ((B -> (C -> B)) and A))))
theorem-size     25
proof            (modus-ponens tm-326 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16942.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (A -> ((B -> (C -> B)) and A)))), M:tm-326, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-16943
in-theory        16943
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     41
proof            (modus-ponens tm-326 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16943.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-326, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-16944
in-theory        16944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (A -> (((B and C) -> B) and A))))
theorem-size     25
proof            (modus-ponens tm-326 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16944.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (A -> (((B and C) -> B) and A)))), M:tm-326, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-16945
in-theory        16945
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (A -> (((B and C) -> C) and A))))
theorem-size     25
proof            (modus-ponens tm-326 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-16945.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (A -> (((B and C) -> C) and A)))), M:tm-326, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-16946
in-theory        16946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (A -> ((B -> (C -> (B and C))) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16946.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (A -> ((B -> (C -> (B and C))) and A)))), M:tm-326, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-16947
in-theory        16947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((A -> B) -> (A -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-16947.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((A -> B) -> (A -> (A and B))))), M:tm-326, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-16948
in-theory        16948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (A -> (B -> (C -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16948.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (A -> (B -> (C -> (B and C)))))), M:tm-326, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-16949
in-theory        16949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((A -> (B -> A)) or C)))
theorem-size     21
proof            (modus-ponens tm-326 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16949.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((A -> (B -> A)) or C))), M:tm-326, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-16950
in-theory        16950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)))
theorem-size     37
proof            (modus-ponens tm-326 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16950.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D))), M:tm-326, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-16951
in-theory        16951
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (((A and B) -> A) or C)))
theorem-size     21
proof            (modus-ponens tm-326 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16951.        ((((A and B) -> A) or C) and (((D and E) -> E) and (((A and B) -> A) or C))), M:tm-326, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-16952
in-theory        16952
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (((A and B) -> B) or C)))
theorem-size     21
proof            (modus-ponens tm-326 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16952.        ((((A and B) -> B) or C) and (((D and E) -> E) and (((A and B) -> B) or C))), M:tm-326, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-16953
in-theory        16953
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((A -> (B -> (A and B))) or C)))
theorem-size     25
proof            (modus-ponens tm-326 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16953.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((A -> (B -> (A and B))) or C))), M:tm-326, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-16954
in-theory        16954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((A -> (A or B)) or C)))
theorem-size     21
proof            (modus-ponens tm-326 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16954.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((A -> (A or B)) or C))), M:tm-326, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-16955
in-theory        16955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (A -> ((B -> (B or C)) and A))))
theorem-size     25
proof            (modus-ponens tm-326 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16955.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (A -> ((B -> (B or C)) and A)))), M:tm-326, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-16956
in-theory        16956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (A -> (B -> (B or C)))))
theorem-size     21
proof            (modus-ponens tm-326 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16956.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (A -> (B -> (B or C))))), M:tm-326, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-16957
in-theory        16957
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (A or (B -> (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-326 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16957.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (A or (B -> (C -> B))))), M:tm-326, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-16958
in-theory        16958
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-16958.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-326, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-16959
in-theory        16959
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (A or ((B and C) -> B))))
theorem-size     21
proof            (modus-ponens tm-326 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16959.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (A or ((B and C) -> B)))), M:tm-326, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-16960
in-theory        16960
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (A or ((B and C) -> C))))
theorem-size     21
proof            (modus-ponens tm-326 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-16960.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (A or ((B and C) -> C)))), M:tm-326, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-16961
in-theory        16961
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (A or (B -> (C -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-16961.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (A or (B -> (C -> (B and C)))))), M:tm-326, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-16962
in-theory        16962
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (A or (B -> (B or C)))))
theorem-size     21
proof            (modus-ponens tm-326 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-16962.        ((A or (B -> (B or C))) and (((D and E) -> E) and (A or (B -> (B or C))))), M:tm-326, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-16963
in-theory        16963
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (A or (B -> (C or B)))))
theorem-size     21
proof            (modus-ponens tm-326 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16963.        ((A or (B -> (C or B))) and (((D and E) -> E) and (A or (B -> (C or B))))), M:tm-326, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-16964
in-theory        16964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((A -> (B or A)) or C)))
theorem-size     21
proof            (modus-ponens tm-326 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16964.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((A -> (B or A)) or C))), M:tm-326, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-16965
in-theory        16965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (A -> ((B -> (C or B)) and A))))
theorem-size     25
proof            (modus-ponens tm-326 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16965.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (A -> ((B -> (C or B)) and A)))), M:tm-326, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-16966
in-theory        16966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (A -> (B -> (C or B)))))
theorem-size     21
proof            (modus-ponens tm-326 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-16966.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (A -> (B -> (C or B))))), M:tm-326, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-16967
in-theory        16967
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((A -> B) -> C) -> ((B or (A -> B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-326 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16967.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((A -> B) -> C) -> ((B or (A -> B)) -> C)))), M:tm-326, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-16968
in-theory        16968
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     57
proof            (modus-ponens tm-326 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-16968.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-326, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-16969
in-theory        16969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((A -> B) -> (((A and C) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-326 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16969.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((A -> B) -> (((A and C) or A) -> B)))), M:tm-326, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-16970
in-theory        16970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((A -> B) -> (((C and A) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-326 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-16970.        (((A -> B) -> (((C and A) or A) -> B)) and (((D and E) -> E) and ((A -> B) -> (((C and A) or A) -> B)))), M:tm-326, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-16971
in-theory        16971
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-326 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-16971.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((D and E) -> E) and (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)))), M:tm-326, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-16972
in-theory        16972
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((A or B) -> C) -> ((A or (A or B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-326 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-16972.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((D and E) -> E) and (((A or B) -> C) -> ((A or (A or B)) -> C)))), M:tm-326, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-16973
in-theory        16973
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((A or B) -> C) -> ((B or (A or B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-326 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-16973.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((D and E) -> E) and (((A or B) -> C) -> ((B or (A or B)) -> C)))), M:tm-326, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-16974
in-theory        16974
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     61
proof            (modus-ponens tm-326 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-16974.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (((E and F) -> F) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-326, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-16975
in-theory        16975
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16975.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-326, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-16976
in-theory        16976
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)))
theorem-size     37
proof            (modus-ponens tm-326 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16976.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (((E and F) -> F) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D))), M:tm-326, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-16977
in-theory        16977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (((E and F) -> F) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))))
theorem-size     41
proof            (modus-ponens tm-326 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16977.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (((E and F) -> F) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)))), M:tm-326, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-16978
in-theory        16978
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((D and E) -> E) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-16978.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((D and E) -> E) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))))), M:tm-326, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-16979
in-theory        16979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-16979.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((E and F) -> F) and (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-326, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-16980
in-theory        16980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (((C and D) -> D) and ((A -> (not (B -> A))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-326 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16980.        (((A -> (not (B -> A))) -> (not A)) and (((C and D) -> D) and ((A -> (not (B -> A))) -> (not A)))), M:tm-326, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-16981
in-theory        16981
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((D and E) -> E) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-16981.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((D and E) -> E) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))))), M:tm-326, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-16982
in-theory        16982
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (((C and D) -> D) and (((A and B) -> (not A)) -> (not (A and B)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16982.        ((((A and B) -> (not A)) -> (not (A and B))) and (((C and D) -> D) and (((A and B) -> (not A)) -> (not (A and B))))), M:tm-326, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-16983
in-theory        16983
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (((C and D) -> D) and (((A and B) -> (not B)) -> (not (A and B)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-16983.        ((((A and B) -> (not B)) -> (not (A and B))) and (((C and D) -> D) and (((A and B) -> (not B)) -> (not (A and B))))), M:tm-326, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-16984
in-theory        16984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (((C and D) -> D) and ((A -> (not (B -> (A and B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-16984.        (((A -> (not (B -> (A and B)))) -> (not A)) and (((C and D) -> D) and ((A -> (not (B -> (A and B)))) -> (not A)))), M:tm-326, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-16985
in-theory        16985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (((C and D) -> D) and ((A -> (not (A or B))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-326 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-16985.        (((A -> (not (A or B))) -> (not A)) and (((C and D) -> D) and ((A -> (not (A or B))) -> (not A)))), M:tm-326, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-16986
in-theory        16986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (((C and D) -> D) and ((A -> (not (B or A))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-326 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-16986.        (((A -> (not (B or A))) -> (not A)) and (((C and D) -> D) and ((A -> (not (B or A))) -> (not A)))), M:tm-326, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-16987
in-theory        16987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((D and E) -> E) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-8)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-16987.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((D and E) -> E) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))))), M:tm-326, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-16988
in-theory        16988
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((C and D) -> D) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-16988.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((C and D) -> D) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))))), M:tm-326, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-16989
in-theory        16989
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((D and E) -> E) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))))
theorem-size     53
proof            (modus-ponens tm-326 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-16989.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (((D and E) -> E) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))), M:tm-326, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-16990
in-theory        16990
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((D and E) -> E) and (A or ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16990.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((D and E) -> E) and (A or ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-326, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-16991
in-theory        16991
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (((D and E) -> E) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C)))
theorem-size     33
proof            (modus-ponens tm-326 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16991.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (((D and E) -> E) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C))), M:tm-326, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-16992
in-theory        16992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (((D and E) -> E) and (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A))))
theorem-size     37
proof            (modus-ponens tm-326 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16992.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (((D and E) -> E) and (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)))), M:tm-326, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-16993
in-theory        16993
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((C and D) -> D) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-16993.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((C and D) -> D) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))))), M:tm-326, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-16994
in-theory        16994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((D and E) -> E) and (A -> ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-16994.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((D and E) -> E) and (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-326, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-16995
in-theory        16995
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((B and C) -> C) and (((not (not A)) -> (not A)) -> (not (not (not A))))))
theorem-size     29
proof            (modus-ponens tm-326 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-16995.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((B and C) -> C) and (((not (not A)) -> (not A)) -> (not (not (not A)))))), M:tm-326, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-16996
in-theory        16996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (((C and D) -> D) and ((A -> B) -> (((not (not A)) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-326 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-16996.        (((A -> B) -> (((not (not A)) or A) -> B)) and (((C and D) -> D) and ((A -> B) -> (((not (not A)) or A) -> B)))), M:tm-326, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-16997
in-theory        16997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and (((C and D) -> D) and (A or ((not (not B)) -> B))))
theorem-size     21
proof            (modus-ponens tm-326 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16997.        ((A or ((not (not B)) -> B)) and (((C and D) -> D) and (A or ((not (not B)) -> B)))), M:tm-326, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-16998
in-theory        16998
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and (((C and D) -> D) and (((not (not A)) -> A) or B)))
theorem-size     21
proof            (modus-ponens tm-326 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16998.        ((((not (not A)) -> A) or B) and (((C and D) -> D) and (((not (not A)) -> A) or B))), M:tm-326, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-16999
in-theory        16999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (((C and D) -> D) and (A -> (((not (not B)) -> B) and A))))
theorem-size     25
proof            (modus-ponens tm-326 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-16999.        ((A -> (((not (not B)) -> B) and A)) and (((C and D) -> D) and (A -> (((not (not B)) -> B) and A)))), M:tm-326, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-17000
in-theory        17000
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (((C and D) -> D) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B))))
theorem-size     37
proof            (modus-ponens tm-326 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-17000.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (((C and D) -> D) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)))), M:tm-326, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-17001
in-theory        17001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and (((C and D) -> D) and (A -> ((not (not B)) -> B))))
theorem-size     21
proof            (modus-ponens tm-326 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17001.        ((A -> ((not (not B)) -> B)) and (((C and D) -> D) and (A -> ((not (not B)) -> B)))), M:tm-326, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-17002
in-theory        17002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (((D and E) -> E) and ((A -> (not (B -> (C -> B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-17002.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (((D and E) -> E) and ((A -> (not (B -> (C -> B)))) -> (not A)))), M:tm-326, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-17003
in-theory        17003
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (((E and F) -> F) and (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-326 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-17003.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (((E and F) -> F) and (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)))), M:tm-326, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-17004
in-theory        17004
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and (((E and F) -> F) and (A or (B -> (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17004.        ((A or (B -> (C -> (D -> C)))) and (((E and F) -> F) and (A or (B -> (C -> (D -> C)))))), M:tm-326, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-17005
in-theory        17005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and (((E and F) -> F) and ((A -> (B -> (C -> B))) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17005.        (((A -> (B -> (C -> B))) or D) and (((E and F) -> F) and ((A -> (B -> (C -> B))) or D))), M:tm-326, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-17006
in-theory        17006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and (((E and F) -> F) and (A -> ((B -> (C -> (D -> C))) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17006.        ((A -> ((B -> (C -> (D -> C))) and A)) and (((E and F) -> F) and (A -> ((B -> (C -> (D -> C))) and A)))), M:tm-326, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-17007
in-theory        17007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (((D and E) -> E) and ((A -> B) -> (A -> (C -> B)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-17007.        (((A -> B) -> (A -> (C -> B))) and (((D and E) -> E) and ((A -> B) -> (A -> (C -> B))))), M:tm-326, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-17008
in-theory        17008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (((E and F) -> F) and (A -> (B -> (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17008.        ((A -> (B -> (C -> (D -> C)))) and (((E and F) -> F) and (A -> (B -> (C -> (D -> C)))))), M:tm-326, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-17009
in-theory        17009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and (((B and C) -> C) and (A -> A)))
theorem-size     13
proof            (modus-ponens tm-326 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-17009.        ((A -> A) and (((B and C) -> C) and (A -> A))), M:tm-326, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-17010
in-theory        17010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (((D and E) -> E) and ((A -> (B -> C)) -> (A -> (B -> C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-17010.        (((A -> (B -> C)) -> (A -> (B -> C))) and (((D and E) -> E) and ((A -> (B -> C)) -> (A -> (B -> C))))), M:tm-326, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-17011
in-theory        17011
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and (((C and D) -> D) and ((A and B) -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-326 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-17011.        (((A and B) -> (A and B)) and (((C and D) -> D) and ((A and B) -> (A and B)))), M:tm-326, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-17012
in-theory        17012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (((C and D) -> D) and ((A -> B) -> (A -> B))))
theorem-size     21
proof            (modus-ponens tm-326 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-17012.        (((A -> B) -> (A -> B)) and (((C and D) -> D) and ((A -> B) -> (A -> B)))), M:tm-326, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-17013
in-theory        17013
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and (((B and C) -> C) and ((not (not A)) -> (not (not A)))))
theorem-size     21
proof            (modus-ponens tm-326 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-10)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-17013.        (((not (not A)) -> (not (not A))) and (((B and C) -> C) and ((not (not A)) -> (not (not A))))), M:tm-326, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-17014
in-theory        17014
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((C and D) -> D) and (((A -> B) -> (not (A -> A))) -> (not (A -> B)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-17014.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((C and D) -> D) and (((A -> B) -> (not (A -> A))) -> (not (A -> B))))), M:tm-326, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-17015
in-theory        17015
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((D and E) -> E) and (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B))))
theorem-size     37
proof            (modus-ponens tm-326 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-17015.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((D and E) -> E) and (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)))), M:tm-326, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-17016
in-theory        17016
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and (((D and E) -> E) and (A or ((B -> C) -> (B -> B)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17016.        ((A or ((B -> C) -> (B -> B))) and (((D and E) -> E) and (A or ((B -> C) -> (B -> B))))), M:tm-326, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-17017
in-theory        17017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and (((D and E) -> E) and (((A -> B) -> (A -> A)) or C)))
theorem-size     25
proof            (modus-ponens tm-326 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17017.        ((((A -> B) -> (A -> A)) or C) and (((D and E) -> E) and (((A -> B) -> (A -> A)) or C))), M:tm-326, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-17018
in-theory        17018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (((D and E) -> E) and (A -> (((B -> C) -> (B -> B)) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17018.        ((A -> (((B -> C) -> (B -> B)) and A)) and (((D and E) -> E) and (A -> (((B -> C) -> (B -> B)) and A)))), M:tm-326, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-17019
in-theory        17019
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and (((C and D) -> D) and (((A -> B) -> A) -> ((A -> B) -> A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-17019.        ((((A -> B) -> A) -> ((A -> B) -> A)) and (((C and D) -> D) and (((A -> B) -> A) -> ((A -> B) -> A)))), M:tm-326, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-17020
in-theory        17020
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and (((D and E) -> E) and (A -> ((B -> C) -> (B -> B)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17020.        ((A -> ((B -> C) -> (B -> B))) and (((D and E) -> E) and (A -> ((B -> C) -> (B -> B))))), M:tm-326, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-17021
in-theory        17021
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (((D and E) -> E) and ((A -> ((B -> A) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-17021.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (((D and E) -> E) and ((A -> ((B -> A) -> C)) -> (A -> C)))), M:tm-326, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-17022
in-theory        17022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (((C and D) -> D) and ((A -> (A -> B)) -> (A -> B))))
theorem-size     25
proof            (modus-ponens tm-326 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-17022.        (((A -> (A -> B)) -> (A -> B)) and (((C and D) -> D) and ((A -> (A -> B)) -> (A -> B)))), M:tm-326, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-17023
in-theory        17023
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((D and E) -> E) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-17023.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((D and E) -> E) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))))), M:tm-326, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-17024
in-theory        17024
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((D and E) -> E) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B))))))
theorem-size     69
proof            (modus-ponens tm-326 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-17024.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((D and E) -> E) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))))), M:tm-326, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-17025
in-theory        17025
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (((E and F) -> F) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))))
theorem-size     73
proof            (modus-ponens tm-326 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-17025.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (((E and F) -> F) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))), M:tm-326, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-17026
in-theory        17026
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((E and F) -> F) and (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17026.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((E and F) -> F) and (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-326, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-17027
in-theory        17027
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (((E and F) -> F) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D)))
theorem-size     49
proof            (modus-ponens tm-326 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17027.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (((E and F) -> F) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D))), M:tm-326, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-17028
in-theory        17028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (((E and F) -> F) and (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))))
theorem-size     53
proof            (modus-ponens tm-326 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17028.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (((E and F) -> F) and (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)))), M:tm-326, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-17029
in-theory        17029
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((D and E) -> E) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-326 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-17029.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((D and E) -> E) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))), M:tm-326, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-17030
in-theory        17030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((E and F) -> F) and (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17030.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((E and F) -> F) and (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-326, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-17031
in-theory        17031
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((E and F) -> F) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-326 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-17031.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((E and F) -> F) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)))), M:tm-326, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-17032
in-theory        17032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((E and F) -> F) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A))))
theorem-size     45
proof            (modus-ponens tm-326 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17032.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((E and F) -> F) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)))), M:tm-326, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-17033
in-theory        17033
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (((F and G) -> G) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))))
theorem-size     73
proof            (modus-ponens tm-326 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17033.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (((F and G) -> G) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))), M:tm-326, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-17034
in-theory        17034
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> G) and (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17034.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> G) and (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-326, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-17035
in-theory        17035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((F and G) -> G) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-326 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17035.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((F and G) -> G) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-326, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-17036
in-theory        17036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F and G) -> G) and (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-326 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17036.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F and G) -> G) and (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-326, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-17037
in-theory        17037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-17037.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))))), M:tm-326, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-17038
in-theory        17038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> G) and (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17038.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> G) and (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-326, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-17039
in-theory        17039
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and (((C and D) -> D) and (((A -> B) and A) -> B)))
theorem-size     21
proof            (modus-ponens tm-326 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-17039.        ((((A -> B) and A) -> B) and (((C and D) -> D) and (((A -> B) and A) -> B))), M:tm-326, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-17040
in-theory        17040
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and (((E and F) -> F) and ((((A -> (B -> A)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-326 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-17040.        (((((A -> (B -> A)) -> C) and D) -> C) and (((E and F) -> F) and ((((A -> (B -> A)) -> C) and D) -> C))), M:tm-326, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-17041
in-theory        17041
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (((F and G) -> G) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D)))
theorem-size     45
proof            (modus-ponens tm-326 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17041.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (((F and G) -> G) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D))), M:tm-326, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-17042
in-theory        17042
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((D and E) -> E) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B))))
theorem-size     49
proof            (modus-ponens tm-326 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-17042.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((D and E) -> E) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)))), M:tm-326, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-17043
in-theory        17043
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((D and E) -> E) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A))))
theorem-size     37
proof            (modus-ponens tm-326 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-17043.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (((D and E) -> E) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)))), M:tm-326, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-17044
in-theory        17044
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((D and E) -> E) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A)))))
theorem-size     57
proof            (modus-ponens tm-326 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-17044.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((D and E) -> E) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))))), M:tm-326, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-17045
in-theory        17045
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((E and F) -> F) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))))
theorem-size     61
proof            (modus-ponens tm-326 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-17045.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((E and F) -> F) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))), M:tm-326, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-17046
in-theory        17046
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((E and F) -> F) and (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17046.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((E and F) -> F) and (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-326, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-17047
in-theory        17047
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (((E and F) -> F) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D)))
theorem-size     41
proof            (modus-ponens tm-326 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17047.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (((E and F) -> F) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D))), M:tm-326, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-17048
in-theory        17048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (((E and F) -> F) and (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))))
theorem-size     45
proof            (modus-ponens tm-326 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17048.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (((E and F) -> F) and (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)))), M:tm-326, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-17049
in-theory        17049
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (((D and E) -> E) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B))))
theorem-size     53
proof            (modus-ponens tm-326 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-17049.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (((D and E) -> E) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)))), M:tm-326, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-17050
in-theory        17050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((E and F) -> F) and (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17050.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((E and F) -> F) and (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-326, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-17051
in-theory        17051
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and (((E and F) -> F) and (((((A and B) -> A) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-326 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-17051.        ((((((A and B) -> A) -> C) and D) -> C) and (((E and F) -> F) and (((((A and B) -> A) -> C) and D) -> C))), M:tm-326, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-17052
in-theory        17052
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((D and E) -> E) and (((A and B) -> (A -> C)) -> ((A and B) -> C))))
theorem-size     33
proof            (modus-ponens tm-326 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-17052.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((D and E) -> E) and (((A and B) -> (A -> C)) -> ((A and B) -> C)))), M:tm-326, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-17053
in-theory        17053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (((D and E) -> E) and ((A -> (not ((B and C) -> B))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-17053.        (((A -> (not ((B and C) -> B))) -> (not A)) and (((D and E) -> E) and ((A -> (not ((B and C) -> B))) -> (not A)))), M:tm-326, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-17054
in-theory        17054
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (((E and F) -> F) and ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C))))
theorem-size     41
proof            (modus-ponens tm-326 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-17054.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (((E and F) -> F) and ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)))), M:tm-326, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-17055
in-theory        17055
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and (((E and F) -> F) and (A or (B -> ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17055.        ((A or (B -> ((C and D) -> C))) and (((E and F) -> F) and (A or (B -> ((C and D) -> C))))), M:tm-326, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-17056
in-theory        17056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and (((E and F) -> F) and ((A -> ((B and C) -> B)) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17056.        (((A -> ((B and C) -> B)) or D) and (((E and F) -> F) and ((A -> ((B and C) -> B)) or D))), M:tm-326, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-17057
in-theory        17057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and (((E and F) -> F) and (A -> ((B -> ((C and D) -> C)) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17057.        ((A -> ((B -> ((C and D) -> C)) and A)) and (((E and F) -> F) and (A -> ((B -> ((C and D) -> C)) and A)))), M:tm-326, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-17058
in-theory        17058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (((D and E) -> E) and ((A -> (B and C)) -> (A -> B))))
theorem-size     25
proof            (modus-ponens tm-326 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-17058.        (((A -> (B and C)) -> (A -> B)) and (((D and E) -> E) and ((A -> (B and C)) -> (A -> B)))), M:tm-326, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-17059
in-theory        17059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (((E and F) -> F) and (A -> (B -> ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17059.        ((A -> (B -> ((C and D) -> C))) and (((E and F) -> F) and (A -> (B -> ((C and D) -> C))))), M:tm-326, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-17060
in-theory        17060
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and (((C and D) -> D) and ((A and (A -> B)) -> B)))
theorem-size     21
proof            (modus-ponens tm-326 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-17060.        (((A and (A -> B)) -> B) and (((C and D) -> D) and ((A and (A -> B)) -> B))), M:tm-326, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-17061
in-theory        17061
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and (((E and F) -> F) and ((A and ((B -> (C -> B)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-326 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-17061.        (((A and ((B -> (C -> B)) -> D)) -> D) and (((E and F) -> F) and ((A and ((B -> (C -> B)) -> D)) -> D))), M:tm-326, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-17062
in-theory        17062
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (((F and G) -> G) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E)))
theorem-size     45
proof            (modus-ponens tm-326 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17062.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (((F and G) -> G) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E))), M:tm-326, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-17063
in-theory        17063
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and (((E and F) -> F) and ((A and (((B and C) -> B) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-326 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-17063.        (((A and (((B and C) -> B) -> D)) -> D) and (((E and F) -> F) and ((A and (((B and C) -> B) -> D)) -> D))), M:tm-326, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-17064
in-theory        17064
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((D and E) -> E) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-326 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-17064.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((D and E) -> E) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)))), M:tm-326, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-17065
in-theory        17065
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (((D and E) -> E) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B))))
theorem-size     37
proof            (modus-ponens tm-326 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-17065.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (((D and E) -> E) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)))), M:tm-326, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-17066
in-theory        17066
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((D and E) -> E) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B)))))
theorem-size     57
proof            (modus-ponens tm-326 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-17066.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((D and E) -> E) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))))), M:tm-326, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-17067
in-theory        17067
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (((E and F) -> F) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))))
theorem-size     61
proof            (modus-ponens tm-326 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-17067.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (((E and F) -> F) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))), M:tm-326, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-17068
in-theory        17068
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((E and F) -> F) and (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17068.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((E and F) -> F) and (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-326, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-17069
in-theory        17069
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (((E and F) -> F) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D)))
theorem-size     41
proof            (modus-ponens tm-326 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17069.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (((E and F) -> F) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D))), M:tm-326, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-17070
in-theory        17070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (((E and F) -> F) and (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))))
theorem-size     45
proof            (modus-ponens tm-326 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17070.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (((E and F) -> F) and (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)))), M:tm-326, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-17071
in-theory        17071
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((D and E) -> E) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C))))
theorem-size     53
proof            (modus-ponens tm-326 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-17071.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((D and E) -> E) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)))), M:tm-326, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-17072
in-theory        17072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((E and F) -> F) and (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17072.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((E and F) -> F) and (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-326, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-17073
in-theory        17073
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and (((E and F) -> F) and ((A and (((B and C) -> C) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-326 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-17073.        (((A and (((B and C) -> C) -> D)) -> D) and (((E and F) -> F) and ((A and (((B and C) -> C) -> D)) -> D))), M:tm-326, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-17074
in-theory        17074
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and (((E and F) -> F) and (((((A and B) -> B) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-326 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-17074.        ((((((A and B) -> B) -> C) and D) -> C) and (((E and F) -> F) and (((((A and B) -> B) -> C) and D) -> C))), M:tm-326, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-17075
in-theory        17075
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((D and E) -> E) and (((A and B) -> (B -> C)) -> ((A and B) -> C))))
theorem-size     33
proof            (modus-ponens tm-326 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-17075.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((D and E) -> E) and (((A and B) -> (B -> C)) -> ((A and B) -> C)))), M:tm-326, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-17076
in-theory        17076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (((D and E) -> E) and ((A -> (not ((B and C) -> C))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17076.        (((A -> (not ((B and C) -> C))) -> (not A)) and (((D and E) -> E) and ((A -> (not ((B and C) -> C))) -> (not A)))), M:tm-326, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-17077
in-theory        17077
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (((E and F) -> F) and ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C))))
theorem-size     41
proof            (modus-ponens tm-326 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17077.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (((E and F) -> F) and ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)))), M:tm-326, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-17078
in-theory        17078
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and (((E and F) -> F) and (A or (B -> ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17078.        ((A or (B -> ((C and D) -> D))) and (((E and F) -> F) and (A or (B -> ((C and D) -> D))))), M:tm-326, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-17079
in-theory        17079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and (((E and F) -> F) and ((A -> ((B and C) -> C)) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17079.        (((A -> ((B and C) -> C)) or D) and (((E and F) -> F) and ((A -> ((B and C) -> C)) or D))), M:tm-326, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-17080
in-theory        17080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and (((E and F) -> F) and (A -> ((B -> ((C and D) -> D)) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17080.        ((A -> ((B -> ((C and D) -> D)) and A)) and (((E and F) -> F) and (A -> ((B -> ((C and D) -> D)) and A)))), M:tm-326, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-17081
in-theory        17081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (((D and E) -> E) and ((A -> (B and C)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-326 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-17081.        (((A -> (B and C)) -> (A -> C)) and (((D and E) -> E) and ((A -> (B and C)) -> (A -> C)))), M:tm-326, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-17082
in-theory        17082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (((E and F) -> F) and (A -> (B -> ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17082.        ((A -> (B -> ((C and D) -> D))) and (((E and F) -> F) and (A -> (B -> ((C and D) -> D))))), M:tm-326, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-17083
in-theory        17083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and (((E and F) -> F) and ((A -> (B -> A)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17083.        (((A -> (B -> A)) and (C -> (D -> C))) and (((E and F) -> F) and ((A -> (B -> A)) and (C -> (D -> C))))), M:tm-326, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-17084
in-theory        17084
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17084.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-326, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-17085
in-theory        17085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and (((E and F) -> F) and ((A -> (B -> A)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17085.        (((A -> (B -> A)) and ((C and D) -> C)) and (((E and F) -> F) and ((A -> (B -> A)) and ((C and D) -> C)))), M:tm-326, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-17086
in-theory        17086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and (((E and F) -> F) and ((A -> (B -> A)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-326 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17086.        (((A -> (B -> A)) and ((C and D) -> D)) and (((E and F) -> F) and ((A -> (B -> A)) and ((C and D) -> D)))), M:tm-326, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-17087
in-theory        17087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A -> (B -> A)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17087.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A -> (B -> A)) and (C -> (D -> (C and D)))))), M:tm-326, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-17088
in-theory        17088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and (((E and F) -> F) and ((A -> (B -> A)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17088.        (((A -> (B -> A)) and (C -> (C or D))) and (((E and F) -> F) and ((A -> (B -> A)) and (C -> (C or D))))), M:tm-326, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-17089
in-theory        17089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and (((E and F) -> F) and ((A -> (B -> A)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17089.        (((A -> (B -> A)) and (C -> (D or C))) and (((E and F) -> F) and ((A -> (B -> A)) and (C -> (D or C))))), M:tm-326, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-17090
in-theory        17090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17090.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-326, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-17091
in-theory        17091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> F) and ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17091.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> F) and ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-326, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-17092
in-theory        17092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and (((D and E) -> E) and ((A -> (B -> A)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17092.        (((A -> (B -> A)) and ((not (not C)) -> C)) and (((D and E) -> E) and ((A -> (B -> A)) and ((not (not C)) -> C)))), M:tm-326, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-17093
in-theory        17093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17093.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> (D -> (E -> D)))))), M:tm-326, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-17094
in-theory        17094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (((E and F) -> F) and ((A -> (B -> A)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17094.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (((E and F) -> F) and ((A -> (B -> A)) and ((C -> D) -> (C -> C))))), M:tm-326, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-17095
in-theory        17095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> G) and ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-326 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17095.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> G) and ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-326, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-17096
in-theory        17096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17096.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-326, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-17097
in-theory        17097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> G) and ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17097.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> G) and ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-326, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-17098
in-theory        17098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17098.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> ((D and E) -> D))))), M:tm-326, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-17099
in-theory        17099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> G) and ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17099.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> G) and ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-326, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-17100
in-theory        17100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17100.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> ((D and E) -> E))))), M:tm-326, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-17101
in-theory        17101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17101.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-326, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-17102
in-theory        17102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((D and E) -> E) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-17102.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((D and E) -> E) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A)))), M:tm-326, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-17103
in-theory        17103
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (((E and F) -> F) and ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-326 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-17103.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (((E and F) -> F) and ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)))), M:tm-326, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-17104
in-theory        17104
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and (((E and F) -> F) and (A or (B -> ((C -> (D -> C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17104.        ((A or (B -> ((C -> (D -> C)) and B))) and (((E and F) -> F) and (A or (B -> ((C -> (D -> C)) and B))))), M:tm-326, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-17105
in-theory        17105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and (((E and F) -> F) and ((A -> ((B -> (C -> B)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-326 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17105.        (((A -> ((B -> (C -> B)) and A)) or D) and (((E and F) -> F) and ((A -> ((B -> (C -> B)) and A)) or D))), M:tm-326, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-17106
in-theory        17106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (((E and F) -> F) and (A -> ((B -> ((C -> (D -> C)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17106.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (((E and F) -> F) and (A -> ((B -> ((C -> (D -> C)) and B)) and A)))), M:tm-326, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-17107
in-theory        17107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (((E and F) -> F) and (A -> (B -> ((C -> (D -> C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17107.        ((A -> (B -> ((C -> (D -> C)) and B))) and (((E and F) -> F) and (A -> (B -> ((C -> (D -> C)) and B))))), M:tm-326, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-17108
in-theory        17108
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17108.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))))), M:tm-326, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-17109
in-theory        17109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17109.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-326, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-17110
in-theory        17110
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-326 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17110.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)))), M:tm-326, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-17111
in-theory        17111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-326 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17111.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)))), M:tm-326, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-17112
in-theory        17112
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17112.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))))), M:tm-326, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-17113
in-theory        17113
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17113.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))))), M:tm-326, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-17114
in-theory        17114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17114.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))))), M:tm-326, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-17115
in-theory        17115
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17115.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-326, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-17116
in-theory        17116
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     57
proof            (modus-ponens tm-326 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17116.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-326, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-17117
in-theory        17117
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (((E and F) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D))))
theorem-size     45
proof            (modus-ponens tm-326 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-10)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17117.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (((E and F) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)))), M:tm-326, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-17118
in-theory        17118
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17118.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))))), M:tm-326, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-17119
in-theory        17119
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17119.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))))), M:tm-326, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-17120
in-theory        17120
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     73
proof            (modus-ponens tm-326 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       249
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17120.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-326, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-17121
in-theory        17121
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> I) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-326 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17121.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> I) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-326, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-17122
in-theory        17122
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     65
proof            (modus-ponens tm-326 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17122.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-326, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-17123
in-theory        17123
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17123.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))))), M:tm-326, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-17124
in-theory        17124
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     65
proof            (modus-ponens tm-326 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17124.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-326, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-17125
in-theory        17125
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17125.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))))), M:tm-326, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-17126
in-theory        17126
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17126.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-326, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-17127
in-theory        17127
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((H and I) -> I) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-326 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17127.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((H and I) -> I) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-326, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-17128
in-theory        17128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> H) and ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17128.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> H) and ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-326, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-17129
in-theory        17129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((E and F) -> F) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A))))
theorem-size     49
proof            (modus-ponens tm-326 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-17129.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((E and F) -> F) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)))), M:tm-326, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-17130
in-theory        17130
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (((F and G) -> G) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))))
theorem-size     81
proof            (modus-ponens tm-326 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-17130.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (((F and G) -> G) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))), M:tm-326, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-17131
in-theory        17131
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((F and G) -> G) and (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17131.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((F and G) -> G) and (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-326, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-17132
in-theory        17132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (((F and G) -> G) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E)))
theorem-size     45
proof            (modus-ponens tm-326 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17132.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (((F and G) -> G) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E))), M:tm-326, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-17133
in-theory        17133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (((F and G) -> G) and (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))))
theorem-size     49
proof            (modus-ponens tm-326 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17133.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (((F and G) -> G) and (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)))), M:tm-326, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-17134
in-theory        17134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((F and G) -> G) and (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17134.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((F and G) -> G) and (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-326, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-17135
in-theory        17135
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and (((E and F) -> F) and (((A and B) -> A) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17135.        ((((A and B) -> A) and (C -> (D -> C))) and (((E and F) -> F) and (((A and B) -> A) and (C -> (D -> C))))), M:tm-326, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-17136
in-theory        17136
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17136.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-326, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-17137
in-theory        17137
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and (((E and F) -> F) and (((A and B) -> A) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17137.        ((((A and B) -> A) and ((C and D) -> C)) and (((E and F) -> F) and (((A and B) -> A) and ((C and D) -> C)))), M:tm-326, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-17138
in-theory        17138
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and (((E and F) -> F) and (((A and B) -> A) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-326 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17138.        ((((A and B) -> A) and ((C and D) -> D)) and (((E and F) -> F) and (((A and B) -> A) and ((C and D) -> D)))), M:tm-326, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-17139
in-theory        17139
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and (((E and F) -> F) and (((A and B) -> A) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17139.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and (((E and F) -> F) and (((A and B) -> A) and (C -> (D -> (C and D)))))), M:tm-326, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-17140
in-theory        17140
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and (((E and F) -> F) and (((A and B) -> A) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17140.        ((((A and B) -> A) and (C -> (C or D))) and (((E and F) -> F) and (((A and B) -> A) and (C -> (C or D))))), M:tm-326, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-17141
in-theory        17141
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and (((E and F) -> F) and (((A and B) -> A) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17141.        ((((A and B) -> A) and (C -> (D or C))) and (((E and F) -> F) and (((A and B) -> A) and (C -> (D or C))))), M:tm-326, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-17142
in-theory        17142
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> G) and (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17142.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> G) and (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-326, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-17143
in-theory        17143
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> F) and (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17143.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> F) and (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-326, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-17144
in-theory        17144
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and (((D and E) -> E) and (((A and B) -> A) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17144.        ((((A and B) -> A) and ((not (not C)) -> C)) and (((D and E) -> E) and (((A and B) -> A) and ((not (not C)) -> C)))), M:tm-326, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-17145
in-theory        17145
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (((F and G) -> G) and (((A and B) -> A) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17145.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (((F and G) -> G) and (((A and B) -> A) and (C -> (D -> (E -> D)))))), M:tm-326, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-17146
in-theory        17146
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (((E and F) -> F) and (((A and B) -> A) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17146.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (((E and F) -> F) and (((A and B) -> A) and ((C -> D) -> (C -> C))))), M:tm-326, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-17147
in-theory        17147
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> G) and (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-326 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17147.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> G) and (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-326, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-17148
in-theory        17148
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17148.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-326, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-17149
in-theory        17149
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> G) and (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17149.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> G) and (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-326, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-17150
in-theory        17150
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and (((F and G) -> G) and (((A and B) -> A) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17150.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and (((F and G) -> G) and (((A and B) -> A) and (C -> ((D and E) -> D))))), M:tm-326, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-17151
in-theory        17151
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> G) and (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17151.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> G) and (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-326, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-17152
in-theory        17152
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and (((F and G) -> G) and (((A and B) -> A) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17152.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and (((F and G) -> G) and (((A and B) -> A) and (C -> ((D and E) -> E))))), M:tm-326, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-17153
in-theory        17153
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> G) and (((A and B) -> A) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17153.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> G) and (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))))), M:tm-326, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-17154
in-theory        17154
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> H) and (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17154.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> H) and (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-326, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-17155
in-theory        17155
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (((F and G) -> G) and (((A and B) -> A) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17155.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (((F and G) -> G) and (((A and B) -> A) and (C -> (((D and E) -> D) and C))))), M:tm-326, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-17156
in-theory        17156
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17156.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-326, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-17157
in-theory        17157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17157.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))))), M:tm-326, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-17158
in-theory        17158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((D and E) -> E) and ((A -> (not (((B and C) -> B) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-17158.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((D and E) -> E) and ((A -> (not (((B and C) -> B) and A))) -> (not A)))), M:tm-326, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-17159
in-theory        17159
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (((E and F) -> F) and (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-326 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-17159.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (((E and F) -> F) and (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)))), M:tm-326, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-17160
in-theory        17160
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and (((E and F) -> F) and (A or (B -> (((C and D) -> C) and B)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17160.        ((A or (B -> (((C and D) -> C) and B))) and (((E and F) -> F) and (A or (B -> (((C and D) -> C) and B))))), M:tm-326, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-17161
in-theory        17161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and (((E and F) -> F) and ((A -> (((B and C) -> B) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-326 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17161.        (((A -> (((B and C) -> B) and A)) or D) and (((E and F) -> F) and ((A -> (((B and C) -> B) and A)) or D))), M:tm-326, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-17162
in-theory        17162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (((E and F) -> F) and (A -> ((B -> (((C and D) -> C) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17162.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (((E and F) -> F) and (A -> ((B -> (((C and D) -> C) and B)) and A)))), M:tm-326, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-17163
in-theory        17163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (((E and F) -> F) and (A -> (B -> (((C and D) -> C) and B)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17163.        ((A -> (B -> (((C and D) -> C) and B))) and (((E and F) -> F) and (A -> (B -> (((C and D) -> C) and B))))), M:tm-326, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-17164
in-theory        17164
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and (((E and F) -> F) and (((A and B) -> B) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17164.        ((((A and B) -> B) and (C -> (D -> C))) and (((E and F) -> F) and (((A and B) -> B) and (C -> (D -> C))))), M:tm-326, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-17165
in-theory        17165
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17165.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-326, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-17166
in-theory        17166
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and (((E and F) -> F) and (((A and B) -> B) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17166.        ((((A and B) -> B) and ((C and D) -> C)) and (((E and F) -> F) and (((A and B) -> B) and ((C and D) -> C)))), M:tm-326, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-17167
in-theory        17167
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and (((E and F) -> F) and (((A and B) -> B) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-326 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17167.        ((((A and B) -> B) and ((C and D) -> D)) and (((E and F) -> F) and (((A and B) -> B) and ((C and D) -> D)))), M:tm-326, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-17168
in-theory        17168
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and (((E and F) -> F) and (((A and B) -> B) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17168.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and (((E and F) -> F) and (((A and B) -> B) and (C -> (D -> (C and D)))))), M:tm-326, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-17169
in-theory        17169
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and (((E and F) -> F) and (((A and B) -> B) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17169.        ((((A and B) -> B) and (C -> (C or D))) and (((E and F) -> F) and (((A and B) -> B) and (C -> (C or D))))), M:tm-326, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-17170
in-theory        17170
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and (((E and F) -> F) and (((A and B) -> B) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17170.        ((((A and B) -> B) and (C -> (D or C))) and (((E and F) -> F) and (((A and B) -> B) and (C -> (D or C))))), M:tm-326, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-17171
in-theory        17171
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> G) and (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17171.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> G) and (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-326, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-17172
in-theory        17172
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> F) and (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17172.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> F) and (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-326, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-17173
in-theory        17173
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and (((D and E) -> E) and (((A and B) -> B) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17173.        ((((A and B) -> B) and ((not (not C)) -> C)) and (((D and E) -> E) and (((A and B) -> B) and ((not (not C)) -> C)))), M:tm-326, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-17174
in-theory        17174
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (((F and G) -> G) and (((A and B) -> B) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17174.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (((F and G) -> G) and (((A and B) -> B) and (C -> (D -> (E -> D)))))), M:tm-326, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-17175
in-theory        17175
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (((E and F) -> F) and (((A and B) -> B) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17175.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (((E and F) -> F) and (((A and B) -> B) and ((C -> D) -> (C -> C))))), M:tm-326, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-17176
in-theory        17176
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> G) and (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-326 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17176.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> G) and (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-326, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-17177
in-theory        17177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17177.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-326, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-17178
in-theory        17178
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> G) and (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17178.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> G) and (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-326, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-17179
in-theory        17179
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and (((F and G) -> G) and (((A and B) -> B) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17179.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and (((F and G) -> G) and (((A and B) -> B) and (C -> ((D and E) -> D))))), M:tm-326, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-17180
in-theory        17180
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> G) and (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17180.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> G) and (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-326, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-17181
in-theory        17181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and (((F and G) -> G) and (((A and B) -> B) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17181.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and (((F and G) -> G) and (((A and B) -> B) and (C -> ((D and E) -> E))))), M:tm-326, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-17182
in-theory        17182
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> G) and (((A and B) -> B) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17182.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> G) and (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))))), M:tm-326, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-17183
in-theory        17183
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> H) and (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17183.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> H) and (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-326, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-17184
in-theory        17184
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (((F and G) -> G) and (((A and B) -> B) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17184.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (((F and G) -> G) and (((A and B) -> B) and (C -> (((D and E) -> D) and C))))), M:tm-326, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-17185
in-theory        17185
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (((F and G) -> G) and (((A and B) -> B) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17185.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (((F and G) -> G) and (((A and B) -> B) and (C -> (((D and E) -> E) and C))))), M:tm-326, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-17186
in-theory        17186
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (((F and G) -> G) and (((A and B) -> A) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17186.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (((F and G) -> G) and (((A and B) -> A) and (C -> (((D and E) -> E) and C))))), M:tm-326, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-17187
in-theory        17187
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17187.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-326, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-17188
in-theory        17188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17188.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))))), M:tm-326, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-17189
in-theory        17189
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((D and E) -> E) and ((A -> (not (((B and C) -> C) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17189.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((D and E) -> E) and ((A -> (not (((B and C) -> C) and A))) -> (not A)))), M:tm-326, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-17190
in-theory        17190
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (((E and F) -> F) and (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-326 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17190.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (((E and F) -> F) and (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)))), M:tm-326, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-17191
in-theory        17191
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and (((E and F) -> F) and (A or (B -> (((C and D) -> D) and B)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17191.        ((A or (B -> (((C and D) -> D) and B))) and (((E and F) -> F) and (A or (B -> (((C and D) -> D) and B))))), M:tm-326, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-17192
in-theory        17192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and (((E and F) -> F) and ((A -> (((B and C) -> C) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-326 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17192.        (((A -> (((B and C) -> C) and A)) or D) and (((E and F) -> F) and ((A -> (((B and C) -> C) and A)) or D))), M:tm-326, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-17193
in-theory        17193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (((E and F) -> F) and (A -> ((B -> (((C and D) -> D) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17193.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (((E and F) -> F) and (A -> ((B -> (((C and D) -> D) and B)) and A)))), M:tm-326, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-17194
in-theory        17194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (((E and F) -> F) and (A -> (B -> (((C and D) -> D) and B)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17194.        ((A -> (B -> (((C and D) -> D) and B))) and (((E and F) -> F) and (A -> (B -> (((C and D) -> D) and B))))), M:tm-326, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-17195
in-theory        17195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and (((E and F) -> F) and ((A -> (B -> (A and B))) and (C -> (D -> C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17195.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and (((E and F) -> F) and ((A -> (B -> (A and B))) and (C -> (D -> C))))), M:tm-326, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-17196
in-theory        17196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17196.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-326, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-17197
in-theory        17197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and (((E and F) -> F) and ((A -> (B -> (A and B))) and ((C and D) -> C))))
theorem-size     33
proof            (modus-ponens tm-326 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17197.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and (((E and F) -> F) and ((A -> (B -> (A and B))) and ((C and D) -> C)))), M:tm-326, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-17198
in-theory        17198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and (((E and F) -> F) and ((A -> (B -> (A and B))) and ((C and D) -> D))))
theorem-size     33
proof            (modus-ponens tm-326 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17198.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and (((E and F) -> F) and ((A -> (B -> (A and B))) and ((C and D) -> D)))), M:tm-326, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-17199
in-theory        17199
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A -> (B -> (A and B))) and (C -> (D -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17199.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))))), M:tm-326, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-17200
in-theory        17200
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and (((E and F) -> F) and ((A -> (B -> (A and B))) and (C -> (C or D)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17200.        (((A -> (B -> (A and B))) and (C -> (C or D))) and (((E and F) -> F) and ((A -> (B -> (A and B))) and (C -> (C or D))))), M:tm-326, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-17201
in-theory        17201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and (((E and F) -> F) and ((A -> (B -> (A and B))) and (C -> (D or C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17201.        (((A -> (B -> (A and B))) and (C -> (D or C))) and (((E and F) -> F) and ((A -> (B -> (A and B))) and (C -> (D or C))))), M:tm-326, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-17202
in-theory        17202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17202.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-326, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-17203
in-theory        17203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> F) and ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17203.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> F) and ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-326, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-17204
in-theory        17204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (((D and E) -> E) and ((A -> (B -> (A and B))) and ((not (not C)) -> C))))
theorem-size     33
proof            (modus-ponens tm-326 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-10)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17204.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (((D and E) -> E) and ((A -> (B -> (A and B))) and ((not (not C)) -> C)))), M:tm-326, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-17205
in-theory        17205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17205.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))))), M:tm-326, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-17206
in-theory        17206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (((E and F) -> F) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17206.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (((E and F) -> F) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))))), M:tm-326, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-17207
in-theory        17207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17207.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-326, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-17208
in-theory        17208
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     53
proof            (modus-ponens tm-326 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17208.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-326, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-17209
in-theory        17209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17209.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-326, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-17210
in-theory        17210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> D)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17210.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))))), M:tm-326, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-17211
in-theory        17211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17211.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-326, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-17212
in-theory        17212
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> E)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17212.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))))), M:tm-326, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-17213
in-theory        17213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17213.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))))), M:tm-326, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-17214
in-theory        17214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> H) and ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     57
proof            (modus-ponens tm-326 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17214.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> H) and ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-326, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-17215
in-theory        17215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17215.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))))), M:tm-326, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-17216
in-theory        17216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17216.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))))), M:tm-326, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-17217
in-theory        17217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17217.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-326, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-17218
in-theory        17218
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> G) and (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17218.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> G) and (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-326, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-17219
in-theory        17219
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> G) and (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17219.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> G) and (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-326, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-17220
in-theory        17220
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     57
proof            (modus-ponens tm-326 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17220.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-326, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-17221
in-theory        17221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17221.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-326, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-17222
in-theory        17222
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((D and E) -> E) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A))))
theorem-size     37
proof            (modus-ponens tm-326 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17222.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((D and E) -> E) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)))), M:tm-326, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-17223
in-theory        17223
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (((E and F) -> F) and ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-326 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17223.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (((E and F) -> F) and ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)))), M:tm-326, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-17224
in-theory        17224
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and (((E and F) -> F) and (A or (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17224.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and (((E and F) -> F) and (A or (B -> ((C -> (D -> (C and D))) and B))))), M:tm-326, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-17225
in-theory        17225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and (((E and F) -> F) and ((A -> ((B -> (C -> (B and C))) and A)) or D)))
theorem-size     33
proof            (modus-ponens tm-326 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17225.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and (((E and F) -> F) and ((A -> ((B -> (C -> (B and C))) and A)) or D))), M:tm-326, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-17226
in-theory        17226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (((E and F) -> F) and (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A))))
theorem-size     37
proof            (modus-ponens tm-326 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17226.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (((E and F) -> F) and (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)))), M:tm-326, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-17227
in-theory        17227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (((E and F) -> F) and (A -> (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17227.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (((E and F) -> F) and (A -> (B -> ((C -> (D -> (C and D))) and B))))), M:tm-326, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-17228
in-theory        17228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (((C and D) -> D) and (A -> (A and (B -> A)))))
theorem-size     21
proof            (modus-ponens tm-326 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-17228.        ((A -> (A and (B -> A))) and (((C and D) -> D) and (A -> (A and (B -> A))))), M:tm-326, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-17229
in-theory        17229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (((D and E) -> E) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-17229.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (((D and E) -> E) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))), M:tm-326, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-17230
in-theory        17230
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and (((C and D) -> D) and ((A and B) -> ((A and B) and A))))
theorem-size     25
proof            (modus-ponens tm-326 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-17230.        (((A and B) -> ((A and B) and A)) and (((C and D) -> D) and ((A and B) -> ((A and B) and A)))), M:tm-326, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-17231
in-theory        17231
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and (((C and D) -> D) and ((A and B) -> ((A and B) and B))))
theorem-size     25
proof            (modus-ponens tm-326 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17231.        (((A and B) -> ((A and B) and B)) and (((C and D) -> D) and ((A and B) -> ((A and B) and B)))), M:tm-326, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-17232
in-theory        17232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (((C and D) -> D) and (A -> (A and (B -> (A and B))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-17232.        ((A -> (A and (B -> (A and B)))) and (((C and D) -> D) and (A -> (A and (B -> (A and B)))))), M:tm-326, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-17233
in-theory        17233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (((C and D) -> D) and (A -> (A and (A or B)))))
theorem-size     21
proof            (modus-ponens tm-326 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-17233.        ((A -> (A and (A or B))) and (((C and D) -> D) and (A -> (A and (A or B))))), M:tm-326, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-17234
in-theory        17234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (((C and D) -> D) and (A -> (A and (B or A)))))
theorem-size     21
proof            (modus-ponens tm-326 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-17234.        ((A -> (A and (B or A))) and (((C and D) -> D) and (A -> (A and (B or A))))), M:tm-326, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-17235
in-theory        17235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (((D and E) -> E) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-17235.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (((D and E) -> E) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))))), M:tm-326, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-17236
in-theory        17236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (((C and D) -> D) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-17236.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (((C and D) -> D) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))))), M:tm-326, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-17237
in-theory        17237
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and (((B and C) -> C) and ((not (not A)) -> ((not (not A)) and A))))
theorem-size     25
proof            (modus-ponens tm-326 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-10)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-17237.        (((not (not A)) -> ((not (not A)) and A)) and (((B and C) -> C) and ((not (not A)) -> ((not (not A)) and A)))), M:tm-326, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-17238
in-theory        17238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (((D and E) -> E) and (A -> (A and (B -> (C -> B))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-17238.        ((A -> (A and (B -> (C -> B)))) and (((D and E) -> E) and (A -> (A and (B -> (C -> B)))))), M:tm-326, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-17239
in-theory        17239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and (((C and D) -> D) and ((A -> B) -> ((A -> B) and (A -> A)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-17239.        (((A -> B) -> ((A -> B) and (A -> A))) and (((C and D) -> D) and ((A -> B) -> ((A -> B) and (A -> A))))), M:tm-326, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-17240
in-theory        17240
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((D and E) -> E) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-326 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-17240.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((D and E) -> E) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))), M:tm-326, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-17241
in-theory        17241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (((E and F) -> F) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17241.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (((E and F) -> F) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))), M:tm-326, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-17242
in-theory        17242
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (((D and E) -> E) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-17242.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (((D and E) -> E) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))), M:tm-326, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-17243
in-theory        17243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (((D and E) -> E) and (A -> (A and ((B and C) -> B)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-17243.        ((A -> (A and ((B and C) -> B))) and (((D and E) -> E) and (A -> (A and ((B and C) -> B))))), M:tm-326, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-17244
in-theory        17244
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((D and E) -> E) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-17244.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((D and E) -> E) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))), M:tm-326, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-17245
in-theory        17245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (((D and E) -> E) and (A -> (A and ((B and C) -> C)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17245.        ((A -> (A and ((B and C) -> C))) and (((D and E) -> E) and (A -> (A and ((B and C) -> C))))), M:tm-326, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-17246
in-theory        17246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (((D and E) -> E) and (A -> (A and ((B -> (C -> B)) and A)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-17246.        ((A -> (A and ((B -> (C -> B)) and A))) and (((D and E) -> E) and (A -> (A and ((B -> (C -> B)) and A))))), M:tm-326, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-17247
in-theory        17247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (((E and F) -> F) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-17247.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (((E and F) -> F) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))), M:tm-326, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-17248
in-theory        17248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (((D and E) -> E) and (A -> (A and (((B and C) -> B) and A)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-17248.        ((A -> (A and (((B and C) -> B) and A))) and (((D and E) -> E) and (A -> (A and (((B and C) -> B) and A))))), M:tm-326, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-17249
in-theory        17249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (((D and E) -> E) and (A -> (A and (((B and C) -> C) and A)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17249.        ((A -> (A and (((B and C) -> C) and A))) and (((D and E) -> E) and (A -> (A and (((B and C) -> C) and A))))), M:tm-326, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17250
in-theory        17250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (((D and E) -> D) and (A -> (A and (((B and C) -> C) and A)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17250.        ((A -> (A and (((B and C) -> C) and A))) and (((D and E) -> D) and (A -> (A and (((B and C) -> C) and A))))), M:tm-325, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17251
in-theory        17251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and (((B and C) -> C) and A)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17251.        ((A -> (A and (((B and C) -> C) and A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and (((B and C) -> C) and A))))), M:tm-324, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17252
in-theory        17252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and ((D -> (E -> D)) and (A -> (A and (((B and C) -> C) and A)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17252.        ((A -> (A and (((B and C) -> C) and A))) and ((D -> (E -> D)) and (A -> (A and (((B and C) -> C) and A))))), M:tm-323, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17253
in-theory        17253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17253.        ((A -> (A and (((B and C) -> C) and A))) and ((D and E) -> E)), M:tm-322, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17254
in-theory        17254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17254.        ((A -> (A and (((B and C) -> C) and A))) and ((D and E) -> D)), M:tm-320, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17255
in-theory        17255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17255.        ((A -> (A and (((B and C) -> C) and A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17256
in-theory        17256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17256.        ((A -> (A and (((B and C) -> C) and A))) and (A -> A)), M:tm-316, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-17257
in-theory        17257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17257.        ((A -> (A and (((B and C) -> C) and A))) and (D -> (E -> D))), M:tm-315, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17258
in-theory        17258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and ((A -> (not (A and (((B and C) -> C) and A)))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17258.        ((A -> (A and (((B and C) -> C) and A))) and ((A -> (not (A and (((B and C) -> C) and A)))) -> (not A))), M:tm-313, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-17259
in-theory        17259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (((A and (((B and C) -> C) and A)) -> D) -> ((A or (A and (((B and C) -> C) and A))) -> D)))
theorem-size     37
proof            (modus-ponens tm-312 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17259.        ((A -> (A and (((B and C) -> C) and A))) and (((A and (((B and C) -> C) and A)) -> D) -> ((A or (A and (((B and C) -> C) and A))) -> D))), M:tm-312, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-17260
in-theory        17260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (D or (A -> (A and (((B and C) -> C) and A)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17260.        ((A -> (A and (((B and C) -> C) and A))) and (D or (A -> (A and (((B and C) -> C) and A))))), M:tm-311, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17261
in-theory        17261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and ((A -> (A and (((B and C) -> C) and A))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17261.        ((A -> (A and (((B and C) -> C) and A))) and ((A -> (A and (((B and C) -> C) and A))) or D)), M:tm-310, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17262
in-theory        17262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (D -> ((A -> (A and (((B and C) -> C) and A))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17262.        ((A -> (A and (((B and C) -> C) and A))) and (D -> ((A -> (A and (((B and C) -> C) and A))) and D))), M:tm-309, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17263
in-theory        17263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (D -> (A -> (A and (((B and C) -> C) and A)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17263.        ((A -> (A and (((B and C) -> C) and A))) and (D -> (A -> (A and (((B and C) -> C) and A))))), M:tm-305, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17264
in-theory        17264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     23
proof            (modus-ponens tm-303 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17264.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-303, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17265
in-theory        17265
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (((D and E) -> E) and ((B -> (C -> (B and C))) and A))))
theorem-size     37
proof            (modus-ponens tm-300 tm-326 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (and (-> (and Bm Cm) Cm) (and (-> A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17265.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (((D and E) -> E) and ((B -> (C -> (B and C))) and A)))), M:tm-300, m:tm-326, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (and (-> (and Bm Cm) Cm) (and (-> A (-> B (and A B))) C)))))
================================================================
tm-name          tm-17266
in-theory        17266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-270 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17266.        ((A -> (((B and C) -> C) and A)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-270, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17267
in-theory        17267
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (((D and E) -> E) and (((B and C) -> C) and A))))
theorem-size     31
proof            (modus-ponens tm-267 tm-326 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (and (-> (and Bm Cm) Cm) (and (-> (and A B) B) C))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17267.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (((D and E) -> E) and (((B and C) -> C) and A)))), M:tm-267, m:tm-326, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (and (-> (and Bm Cm) Cm) (and (-> (and A B) B) C)))))
================================================================
tm-name          tm-17268
in-theory        17268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-239 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17268.        ((A -> (((B and C) -> B) and A)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-239, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17269
in-theory        17269
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (((D and E) -> E) and (((B and C) -> B) and A))))
theorem-size     31
proof            (modus-ponens tm-236 tm-326 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (and (-> (and Bm Cm) Cm) (and (-> (and A B) A) C))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17269.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (((D and E) -> E) and (((B and C) -> B) and A)))), M:tm-236, m:tm-326, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (and (-> (and Bm Cm) Cm) (and (-> (and A B) A) C)))))
================================================================
tm-name          tm-17270
in-theory        17270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (((F and G) -> G) and E))))
theorem-size     29
proof            (modus-ponens tm-210 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17270.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (((F and G) -> G) and E)))), M:tm-210, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17271
in-theory        17271
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (((E and F) -> F) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     55
proof            (modus-ponens tm-207 tm-326 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> (and Bm Cm) Cm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17271.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (((E and F) -> F) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-207, m:tm-326, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> (and Bm Cm) Cm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-17272
in-theory        17272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-183 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17272.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-183, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17273
in-theory        17273
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (((D and E) -> E) and ((B -> (C -> B)) and A))))
theorem-size     31
proof            (modus-ponens tm-180 tm-326 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (and (-> (and Bm Cm) Cm) (and (-> A (-> B A)) C))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17273.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (((D and E) -> E) and ((B -> (C -> B)) and A)))), M:tm-180, m:tm-326, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (and (-> (and Bm Cm) Cm) (and (-> A (-> B A)) C)))))
================================================================
tm-name          tm-17274
in-theory        17274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-157 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17274.        ((A -> ((B and C) -> C)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-157, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17275
in-theory        17275
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and (((D and E) -> E) and ((B and C) -> C))))
theorem-size     25
proof            (modus-ponens tm-154 tm-326 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (and (-> (and Bm Cm) Cm) (-> (and A B) B))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17275.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and (((D and E) -> E) and ((B and C) -> C)))), M:tm-154, m:tm-326, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (and (-> (and Bm Cm) Cm) (-> (and A B) B)))))
================================================================
tm-name          tm-17276
in-theory        17276
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     27
proof            (modus-ponens tm-147 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17276.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-147, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17277
in-theory        17277
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (((D and E) -> E) and ((A and (B -> C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-144 tm-326 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (and (-> (and Bm Cm) Cm) (-> (and A (-> B C)) C))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17277.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (((D and E) -> E) and ((A and (B -> C)) -> C)))), M:tm-144, m:tm-326, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (and (-> (and Bm Cm) Cm) (-> (and A (-> B C)) C)))))
================================================================
tm-name          tm-17278
in-theory        17278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-134 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17278.        ((A -> ((B and C) -> B)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-134, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17279
in-theory        17279
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and (((D and E) -> E) and ((B and C) -> B))))
theorem-size     25
proof            (modus-ponens tm-131 tm-326 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (and (-> (and Bm Cm) Cm) (-> (and A B) A))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17279.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and (((D and E) -> E) and ((B and C) -> B)))), M:tm-131, m:tm-326, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (and (-> (and Bm Cm) Cm) (-> (and A B) A)))))
================================================================
tm-name          tm-17280
in-theory        17280
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     27
proof            (modus-ponens tm-125 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17280.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-125, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17281
in-theory        17281
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (((D and E) -> E) and (((A -> B) and C) -> B))))
theorem-size     37
proof            (modus-ponens tm-122 tm-326 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (and (-> (and Bm Cm) Cm) (-> (and (-> A B) C) B))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17281.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (((D and E) -> E) and (((A -> B) and C) -> B)))), M:tm-122, m:tm-326, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (and (-> (and Bm Cm) Cm) (-> (and (-> A B) C) B)))))
================================================================
tm-name          tm-17282
in-theory        17282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-113 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17282.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (((F and G) -> G) and E)))), M:tm-113, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17283
in-theory        17283
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> F) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-110 tm-326 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (-> (and Bm Cm) Cm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17283.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> F) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-110, m:tm-326, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (-> (and Bm Cm) Cm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
================================================================
tm-name          tm-17284
in-theory        17284
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     31
proof            (modus-ponens tm-105 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17284.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (((E and F) -> F) and D)))), M:tm-105, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17285
in-theory        17285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((D and E) -> E) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-102 tm-326 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (and (-> (and Bm Cm) Cm) (-> (-> A (-> B C)) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17285.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((D and E) -> E) and ((A -> (B -> C)) -> (A -> C))))), M:tm-102, m:tm-326, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (and (-> (and Bm Cm) Cm) (-> (-> A (-> B C)) (-> A C))))))
================================================================
tm-name          tm-17286
in-theory        17286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and (((D and E) -> E) and C))))
theorem-size     19
proof            (modus-ponens tm-95 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17286.        (((A -> B) -> (A -> A)) and (C -> (C and (((D and E) -> E) and C)))), M:tm-95, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17287
in-theory        17287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and (((C and D) -> D) and (A -> A))))
theorem-size     21
proof            (modus-ponens tm-92 tm-326 ((Am (-> A A)) (B (and (-> A A) (and (-> (and Bm Cm) Cm) (-> A A))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17287.        (((A -> B) or (A -> A)) -> ((A -> A) and (((C and D) -> D) and (A -> A)))), M:tm-92, m:tm-326, u:((Am (-> A A)) (B (and (-> A A) (and (-> (and Bm Cm) Cm) (-> A A)))))
================================================================
tm-name          tm-17288
in-theory        17288
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and (((C and D) -> D) and A))))
theorem-size     13
proof            (modus-ponens tm-84 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17288.        (A -> (B -> (A and (((C and D) -> D) and A)))), M:tm-84, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-17289
in-theory        17289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-83 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17289.        ((A -> (B -> (C -> B))) and (D -> (D and (((E and F) -> F) and D)))), M:tm-83, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17290
in-theory        17290
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (((D and E) -> E) and (B -> (C -> B)))))
theorem-size     25
proof            (modus-ponens tm-80 tm-326 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (and (-> (and Bm Cm) Cm) (-> A (-> B A)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17290.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (((D and E) -> E) and (B -> (C -> B))))), M:tm-80, m:tm-326, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (and (-> (and Bm Cm) Cm) (-> A (-> B A))))))
================================================================
tm-name          tm-17291
in-theory        17291
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and (((C and D) -> D) and B))))
theorem-size     17
proof            (modus-ponens tm-76 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-10 tm-2 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17291.        (((not (not A)) -> A) and (B -> (B and (((C and D) -> D) and B)))), M:tm-76, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17292
in-theory        17292
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and (((B and C) -> C) and A)))
theorem-size     15
proof            (modus-ponens tm-73 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17292.        (((not (not A)) or A) -> (A and (((B and C) -> C) and A))), M:tm-73, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-17293
in-theory        17293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (((D and E) -> E) and C))))
theorem-size     23
proof            (modus-ponens tm-69 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-9 tm-2 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17293.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (((D and E) -> E) and C)))), M:tm-69, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17294
in-theory        17294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((C and D) -> D) and ((A -> (not B)) -> (not A)))))
theorem-size     33
proof            (modus-ponens tm-66 tm-326 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (and (-> (and Bm Cm) Cm) (-> (-> A (not B)) (not A)))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17294.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((C and D) -> D) and ((A -> (not B)) -> (not A))))), M:tm-66, m:tm-326, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (and (-> (and Bm Cm) Cm) (-> (-> A (not B)) (not A))))))
================================================================
tm-name          tm-17295
in-theory        17295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     25
proof            (modus-ponens tm-54 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17295.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (((E and F) -> F) and D)))), M:tm-54, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17296
in-theory        17296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((D and E) -> E) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     39
proof            (modus-ponens tm-51 tm-326 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> (or C A) B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17296.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (((D and E) -> E) and ((B -> C) -> ((A or B) -> C))))), M:tm-51, m:tm-326, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> (or C A) B))))))
================================================================
tm-name          tm-17297
in-theory        17297
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and (((C and D) -> D) and (B or A))))
theorem-size     19
proof            (modus-ponens tm-50 tm-326 ((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Cm) (or A B))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17297.        ((A or (B or A)) -> ((B or A) and (((C and D) -> D) and (B or A)))), M:tm-50, m:tm-326, u:((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Cm) (or A B)))))
================================================================
tm-name          tm-17298
in-theory        17298
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and (((C and D) -> D) and (A or B))))
theorem-size     19
proof            (modus-ponens tm-49 tm-326 ((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Cm) (or A B))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17298.        ((A or (A or B)) -> ((A or B) and (((C and D) -> D) and (A or B)))), M:tm-49, m:tm-326, u:((Am (or A B)) (C (and (or A B) (and (-> (and Bm Cm) Cm) (or A B)))))
================================================================
tm-name          tm-17299
in-theory        17299
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (((C and D) -> D) and (B -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-48 tm-326 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> (and Bm Cm) Cm) (-> A (and B A)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17299.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (((C and D) -> D) and (B -> (A and B))))), M:tm-48, m:tm-326, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> (and Bm Cm) Cm) (-> A (and B A))))))
================================================================
tm-name          tm-17300
in-theory        17300
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (((C and D) -> D) and B)))
theorem-size     15
proof            (modus-ponens tm-47 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17300.        (((A and B) or B) -> (B and (((C and D) -> D) and B))), M:tm-47, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-17301
in-theory        17301
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (((C and D) -> D) and A)))
theorem-size     15
proof            (modus-ponens tm-46 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17301.        (((A and B) or A) -> (A and (((C and D) -> D) and A))), M:tm-46, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-17302
in-theory        17302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D and E) -> E) and ((A -> B) -> (A -> C)))))
theorem-size     35
proof            (modus-ponens tm-45 tm-326 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17302.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D and E) -> E) and ((A -> B) -> (A -> C))))), M:tm-45, m:tm-326, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-17303
in-theory        17303
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (((C and D) -> D) and (B -> A))))
theorem-size     19
proof            (modus-ponens tm-44 tm-326 ((Am (-> A B)) (C (and (-> A B) (and (-> (and Bm Cm) Cm) (-> A B))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17303.        ((A or (B -> A)) -> ((B -> A) and (((C and D) -> D) and (B -> A)))), M:tm-44, m:tm-326, u:((Am (-> A B)) (C (and (-> A B) (and (-> (and Bm Cm) Cm) (-> A B)))))
================================================================
tm-name          tm-17304
in-theory        17304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and (((D and E) -> E) and C))))
theorem-size     17
proof            (modus-ponens tm-42 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17304.        ((A -> (B or A)) and (C -> (C and (((D and E) -> E) and C)))), M:tm-42, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17305
in-theory        17305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and (((D and E) -> E) and C))))
theorem-size     17
proof            (modus-ponens tm-32 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17305.        ((A -> (A or B)) and (C -> (C and (((D and E) -> E) and C)))), M:tm-32, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17306
in-theory        17306
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and (((B and C) -> C) and A))))
theorem-size     13
proof            (modus-ponens tm-24 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17306.        (A -> (A and (A and (((B and C) -> C) and A)))), M:tm-24, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-17307
in-theory        17307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and (((D and E) -> E) and C))))
theorem-size     19
proof            (modus-ponens tm-23 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17307.        ((A -> (B -> (A and B))) and (C -> (C and (((D and E) -> E) and C)))), M:tm-23, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17308
in-theory        17308
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and (((D and E) -> E) and C))))
theorem-size     17
proof            (modus-ponens tm-22 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17308.        (((A and B) -> B) and (C -> (C and (((D and E) -> E) and C)))), M:tm-22, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17309
in-theory        17309
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and (((D and E) -> E) and C))))
theorem-size     17
proof            (modus-ponens tm-21 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17309.        (((A and B) -> A) and (C -> (C and (((D and E) -> E) and C)))), M:tm-21, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17310
in-theory        17310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     25
proof            (modus-ponens tm-20 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17310.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (((E and F) -> F) and D)))), M:tm-20, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17311
in-theory        17311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and (((D and E) -> E) and C))))
theorem-size     17
proof            (modus-ponens tm-19 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17311.        ((A -> (B -> A)) and (C -> (C and (((D and E) -> E) and C)))), M:tm-19, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17312
in-theory        17312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and (((B and C) -> C) and A)))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-9 tm-2 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17312.        ((A -> (not (A and (((B and C) -> C) and A)))) -> (not A)), M:tm-9, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-17313
in-theory        17313
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) and A)) -> D) -> ((A or (A and (((B and C) -> C) and A))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17313.        (((A and (((B and C) -> C) and A)) -> D) -> ((A or (A and (((B and C) -> C) and A))) -> D)), M:tm-8, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-17314
in-theory        17314
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and (((C and D) -> D) and B))))
theorem-size     13
proof            (modus-ponens tm-7 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-7 tm-2 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17314.        (A or (B -> (B and (((C and D) -> D) and B)))), M:tm-7, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17315
in-theory        17315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-6 tm-2 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17315.        ((A -> (A and (((B and C) -> C) and A))) or D), M:tm-6, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17316
in-theory        17316
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and (((C and D) -> D) and B))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17316.        (A -> ((B -> (B and (((C and D) -> D) and B))) and A)), M:tm-5, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17317
in-theory        17317
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and (((C and D) -> D) and B))))
theorem-size     13
proof            (modus-ponens tm-1 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-1 tm-2 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17317.        (A -> (B -> (B and (((C and D) -> D) and B)))), M:tm-1, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17318
in-theory        17318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (A -> (B -> A))))
theorem-size     19
proof            (modus-ponens tm-327 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-17318.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (A -> (B -> A)))), M:tm-327, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-17319
in-theory        17319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17319.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))), M:tm-327, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-17320
in-theory        17320
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((A and B) -> A)))
theorem-size     19
proof            (modus-ponens tm-327 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-17320.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((A and B) -> A))), M:tm-327, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-17321
in-theory        17321
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((A and B) -> B)))
theorem-size     19
proof            (modus-ponens tm-327 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17321.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((A and B) -> B))), M:tm-327, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-17322
in-theory        17322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (A -> (B -> (A and B)))))
theorem-size     23
proof            (modus-ponens tm-327 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17322.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (A -> (B -> (A and B))))), M:tm-327, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-17323
in-theory        17323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (A -> (A or B))))
theorem-size     19
proof            (modus-ponens tm-327 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-17323.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (A -> (A or B)))), M:tm-327, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-17324
in-theory        17324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (A -> (B or A))))
theorem-size     19
proof            (modus-ponens tm-327 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-17324.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (A -> (B or A)))), M:tm-327, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-17325
in-theory        17325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-17325.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))), M:tm-327, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-17326
in-theory        17326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((A -> B) -> ((A -> (not B)) -> (not A)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-17326.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((A -> B) -> ((A -> (not B)) -> (not A))))), M:tm-327, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-17327
in-theory        17327
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((not (not A)) -> A)))
theorem-size     19
proof            (modus-ponens tm-327 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-17327.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((not (not A)) -> A))), M:tm-327, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-17328
in-theory        17328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (A -> (B -> (C -> B)))))
theorem-size     23
proof            (modus-ponens tm-327 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17328.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (A -> (B -> (C -> B))))), M:tm-327, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-17329
in-theory        17329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((A -> B) -> (A -> A))))
theorem-size     23
proof            (modus-ponens tm-327 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-17329.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((A -> B) -> (A -> A)))), M:tm-327, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-17330
in-theory        17330
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-17330.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-327, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-17331
in-theory        17331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17331.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-327, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-17332
in-theory        17332
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))))
theorem-size     39
proof            (modus-ponens tm-327 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-17332.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)))), M:tm-327, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-17333
in-theory        17333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (A -> ((B and C) -> B))))
theorem-size     23
proof            (modus-ponens tm-327 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17333.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (A -> ((B and C) -> B)))), M:tm-327, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-17334
in-theory        17334
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))))
theorem-size     39
proof            (modus-ponens tm-327 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-17334.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)))), M:tm-327, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-17335
in-theory        17335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (A -> ((B and C) -> C))))
theorem-size     23
proof            (modus-ponens tm-327 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17335.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (A -> ((B and C) -> C)))), M:tm-327, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-17336
in-theory        17336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (A -> ((B -> (C -> B)) and A))))
theorem-size     27
proof            (modus-ponens tm-327 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17336.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (A -> ((B -> (C -> B)) and A)))), M:tm-327, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-17337
in-theory        17337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     43
proof            (modus-ponens tm-327 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17337.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-327, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-17338
in-theory        17338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (A -> (((B and C) -> B) and A))))
theorem-size     27
proof            (modus-ponens tm-327 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17338.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (A -> (((B and C) -> B) and A)))), M:tm-327, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-17339
in-theory        17339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (A -> (((B and C) -> C) and A))))
theorem-size     27
proof            (modus-ponens tm-327 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17339.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (A -> (((B and C) -> C) and A)))), M:tm-327, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-17340
in-theory        17340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (A -> ((B -> (C -> (B and C))) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17340.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (A -> ((B -> (C -> (B and C))) and A)))), M:tm-327, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-17341
in-theory        17341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((A -> B) -> (A -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17341.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((A -> B) -> (A -> (A and B))))), M:tm-327, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-17342
in-theory        17342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (A -> (B -> (C -> (B and C))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17342.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (A -> (B -> (C -> (B and C)))))), M:tm-327, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-17343
in-theory        17343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((A -> (B -> A)) or C)))
theorem-size     23
proof            (modus-ponens tm-327 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17343.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((A -> (B -> A)) or C))), M:tm-327, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-17344
in-theory        17344
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)))
theorem-size     39
proof            (modus-ponens tm-327 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17344.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D))), M:tm-327, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-17345
in-theory        17345
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((A and B) -> A) or C)))
theorem-size     23
proof            (modus-ponens tm-327 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17345.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((A and B) -> A) or C))), M:tm-327, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-17346
in-theory        17346
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((A and B) -> B) or C)))
theorem-size     23
proof            (modus-ponens tm-327 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17346.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((A and B) -> B) or C))), M:tm-327, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-17347
in-theory        17347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((A -> (B -> (A and B))) or C)))
theorem-size     27
proof            (modus-ponens tm-327 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17347.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((A -> (B -> (A and B))) or C))), M:tm-327, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-17348
in-theory        17348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((A -> (A or B)) or C)))
theorem-size     23
proof            (modus-ponens tm-327 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17348.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((A -> (A or B)) or C))), M:tm-327, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-17349
in-theory        17349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (A -> ((B -> (B or C)) and A))))
theorem-size     27
proof            (modus-ponens tm-327 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17349.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (A -> ((B -> (B or C)) and A)))), M:tm-327, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-17350
in-theory        17350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (A -> (B -> (B or C)))))
theorem-size     23
proof            (modus-ponens tm-327 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17350.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (A -> (B -> (B or C))))), M:tm-327, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-17351
in-theory        17351
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (A or (B -> (C -> B)))))
theorem-size     23
proof            (modus-ponens tm-327 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17351.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (A or (B -> (C -> B))))), M:tm-327, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-17352
in-theory        17352
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17352.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-327, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-17353
in-theory        17353
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (A or ((B and C) -> B))))
theorem-size     23
proof            (modus-ponens tm-327 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17353.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (A or ((B and C) -> B)))), M:tm-327, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-17354
in-theory        17354
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (A or ((B and C) -> C))))
theorem-size     23
proof            (modus-ponens tm-327 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17354.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (A or ((B and C) -> C)))), M:tm-327, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-17355
in-theory        17355
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (A or (B -> (C -> (B and C))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17355.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (A or (B -> (C -> (B and C)))))), M:tm-327, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-17356
in-theory        17356
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (A or (B -> (B or C)))))
theorem-size     23
proof            (modus-ponens tm-327 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17356.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (A or (B -> (B or C))))), M:tm-327, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-17357
in-theory        17357
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (A or (B -> (C or B)))))
theorem-size     23
proof            (modus-ponens tm-327 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17357.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (A or (B -> (C or B))))), M:tm-327, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-17358
in-theory        17358
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((A -> (B or A)) or C)))
theorem-size     23
proof            (modus-ponens tm-327 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17358.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((A -> (B or A)) or C))), M:tm-327, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-17359
in-theory        17359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (A -> ((B -> (C or B)) and A))))
theorem-size     27
proof            (modus-ponens tm-327 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17359.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (A -> ((B -> (C or B)) and A)))), M:tm-327, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-17360
in-theory        17360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (A -> (B -> (C or B)))))
theorem-size     23
proof            (modus-ponens tm-327 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17360.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (A -> (B -> (C or B))))), M:tm-327, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-17361
in-theory        17361
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((A -> B) -> C) -> ((B or (A -> B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-327 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-17361.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((A -> B) -> C) -> ((B or (A -> B)) -> C)))), M:tm-327, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-17362
in-theory        17362
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     59
proof            (modus-ponens tm-327 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-17362.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-327, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-17363
in-theory        17363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((A -> B) -> (((A and C) or A) -> B))))
theorem-size     31
proof            (modus-ponens tm-327 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-17363.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((A -> B) -> (((A and C) or A) -> B)))), M:tm-327, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-17364
in-theory        17364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((A -> B) -> (((C and A) or A) -> B))))
theorem-size     31
proof            (modus-ponens tm-327 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17364.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E -> (D and E))) and ((A -> B) -> (((C and A) or A) -> B)))), M:tm-327, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-17365
in-theory        17365
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))))
theorem-size     43
proof            (modus-ponens tm-327 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-17365.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E -> (D and E))) and (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)))), M:tm-327, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-17366
in-theory        17366
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((A or B) -> C) -> ((A or (A or B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-327 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-17366.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((A or B) -> C) -> ((A or (A or B)) -> C)))), M:tm-327, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-17367
in-theory        17367
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((A or B) -> C) -> ((B or (A or B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-327 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-17367.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E -> (D and E))) and (((A or B) -> C) -> ((B or (A or B)) -> C)))), M:tm-327, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-17368
in-theory        17368
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     63
proof            (modus-ponens tm-327 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-17368.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F -> (E and F))) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-327, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-17369
in-theory        17369
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17369.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-327, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-17370
in-theory        17370
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)))
theorem-size     39
proof            (modus-ponens tm-327 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17370.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F -> (E and F))) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D))), M:tm-327, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-17371
in-theory        17371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))))
theorem-size     43
proof            (modus-ponens tm-327 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17371.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)))), M:tm-327, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-17372
in-theory        17372
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-17372.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))))), M:tm-327, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-17373
in-theory        17373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17373.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F -> (E and F))) and (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-327, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-17374
in-theory        17374
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and ((C -> (D -> (C and D))) and ((A -> (not (B -> A))) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-327 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-17374.        (((A -> (not (B -> A))) -> (not A)) and ((C -> (D -> (C and D))) and ((A -> (not (B -> A))) -> (not A)))), M:tm-327, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-17375
in-theory        17375
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-17375.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))))), M:tm-327, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-17376
in-theory        17376
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and ((C -> (D -> (C and D))) and (((A and B) -> (not A)) -> (not (A and B)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-17376.        ((((A and B) -> (not A)) -> (not (A and B))) and ((C -> (D -> (C and D))) and (((A and B) -> (not A)) -> (not (A and B))))), M:tm-327, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-17377
in-theory        17377
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and ((C -> (D -> (C and D))) and (((A and B) -> (not B)) -> (not (A and B)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17377.        ((((A and B) -> (not B)) -> (not (A and B))) and ((C -> (D -> (C and D))) and (((A and B) -> (not B)) -> (not (A and B))))), M:tm-327, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-17378
in-theory        17378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and ((C -> (D -> (C and D))) and ((A -> (not (B -> (A and B)))) -> (not A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-17378.        (((A -> (not (B -> (A and B)))) -> (not A)) and ((C -> (D -> (C and D))) and ((A -> (not (B -> (A and B)))) -> (not A)))), M:tm-327, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-17379
in-theory        17379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and ((C -> (D -> (C and D))) and ((A -> (not (A or B))) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-327 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-17379.        (((A -> (not (A or B))) -> (not A)) and ((C -> (D -> (C and D))) and ((A -> (not (A or B))) -> (not A)))), M:tm-327, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-17380
in-theory        17380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and ((C -> (D -> (C and D))) and ((A -> (not (B or A))) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-327 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-17380.        (((A -> (not (B or A))) -> (not A)) and ((C -> (D -> (C and D))) and ((A -> (not (B or A))) -> (not A)))), M:tm-327, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-17381
in-theory        17381
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((D -> (E -> (D and E))) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-17381.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((D -> (E -> (D and E))) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))))), M:tm-327, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-17382
in-theory        17382
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((C -> (D -> (C and D))) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-17382.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((C -> (D -> (C and D))) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))))), M:tm-327, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-17383
in-theory        17383
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((D -> (E -> (D and E))) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))))
theorem-size     55
proof            (modus-ponens tm-327 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-17383.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((D -> (E -> (D and E))) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))), M:tm-327, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-17384
in-theory        17384
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E -> (D and E))) and (A or ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17384.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E -> (D and E))) and (A or ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-327, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-17385
in-theory        17385
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((D -> (E -> (D and E))) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C)))
theorem-size     35
proof            (modus-ponens tm-327 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17385.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((D -> (E -> (D and E))) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C))), M:tm-327, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-17386
in-theory        17386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((D -> (E -> (D and E))) and (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A))))
theorem-size     39
proof            (modus-ponens tm-327 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17386.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((D -> (E -> (D and E))) and (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)))), M:tm-327, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-17387
in-theory        17387
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((C -> (D -> (C and D))) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-17387.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((C -> (D -> (C and D))) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))))), M:tm-327, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-17388
in-theory        17388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E -> (D and E))) and (A -> ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17388.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E -> (D and E))) and (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-327, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-17389
in-theory        17389
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((B -> (C -> (B and C))) and (((not (not A)) -> (not A)) -> (not (not (not A))))))
theorem-size     31
proof            (modus-ponens tm-327 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-9 tm-10)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-17389.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((B -> (C -> (B and C))) and (((not (not A)) -> (not A)) -> (not (not (not A)))))), M:tm-327, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-17390
in-theory        17390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and ((C -> (D -> (C and D))) and ((A -> B) -> (((not (not A)) or A) -> B))))
theorem-size     31
proof            (modus-ponens tm-327 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-17390.        (((A -> B) -> (((not (not A)) or A) -> B)) and ((C -> (D -> (C and D))) and ((A -> B) -> (((not (not A)) or A) -> B)))), M:tm-327, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-17391
in-theory        17391
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and ((C -> (D -> (C and D))) and (A or ((not (not B)) -> B))))
theorem-size     23
proof            (modus-ponens tm-327 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17391.        ((A or ((not (not B)) -> B)) and ((C -> (D -> (C and D))) and (A or ((not (not B)) -> B)))), M:tm-327, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-17392
in-theory        17392
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and ((C -> (D -> (C and D))) and (((not (not A)) -> A) or B)))
theorem-size     23
proof            (modus-ponens tm-327 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17392.        ((((not (not A)) -> A) or B) and ((C -> (D -> (C and D))) and (((not (not A)) -> A) or B))), M:tm-327, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-17393
in-theory        17393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and ((C -> (D -> (C and D))) and (A -> (((not (not B)) -> B) and A))))
theorem-size     27
proof            (modus-ponens tm-327 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17393.        ((A -> (((not (not B)) -> B) and A)) and ((C -> (D -> (C and D))) and (A -> (((not (not B)) -> B) and A)))), M:tm-327, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-17394
in-theory        17394
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((C -> (D -> (C and D))) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B))))
theorem-size     39
proof            (modus-ponens tm-327 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-17394.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((C -> (D -> (C and D))) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)))), M:tm-327, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-17395
in-theory        17395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and ((C -> (D -> (C and D))) and (A -> ((not (not B)) -> B))))
theorem-size     23
proof            (modus-ponens tm-327 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17395.        ((A -> ((not (not B)) -> B)) and ((C -> (D -> (C and D))) and (A -> ((not (not B)) -> B)))), M:tm-327, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-17396
in-theory        17396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not (B -> (C -> B)))) -> (not A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-17396.        (((A -> (not (B -> (C -> B)))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not (B -> (C -> B)))) -> (not A)))), M:tm-327, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-17397
in-theory        17397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((E -> (F -> (E and F))) and (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C))))
theorem-size     43
proof            (modus-ponens tm-327 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-17397.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((E -> (F -> (E and F))) and (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)))), M:tm-327, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-17398
in-theory        17398
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and ((E -> (F -> (E and F))) and (A or (B -> (C -> (D -> C))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17398.        ((A or (B -> (C -> (D -> C)))) and ((E -> (F -> (E and F))) and (A or (B -> (C -> (D -> C)))))), M:tm-327, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-17399
in-theory        17399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and ((E -> (F -> (E and F))) and ((A -> (B -> (C -> B))) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17399.        (((A -> (B -> (C -> B))) or D) and ((E -> (F -> (E and F))) and ((A -> (B -> (C -> B))) or D))), M:tm-327, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-17400
in-theory        17400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> (C -> (D -> C))) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17400.        ((A -> ((B -> (C -> (D -> C))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> (C -> (D -> C))) and A)))), M:tm-327, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-17401
in-theory        17401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> (C -> B)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-17401.        (((A -> B) -> (A -> (C -> B))) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> (C -> B))))), M:tm-327, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-17402
in-theory        17402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and ((E -> (F -> (E and F))) and (A -> (B -> (C -> (D -> C))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17402.        ((A -> (B -> (C -> (D -> C)))) and ((E -> (F -> (E and F))) and (A -> (B -> (C -> (D -> C)))))), M:tm-327, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-17403
in-theory        17403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and ((B -> (C -> (B and C))) and (A -> A)))
theorem-size     15
proof            (modus-ponens tm-327 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-17403.        ((A -> A) and ((B -> (C -> (B and C))) and (A -> A))), M:tm-327, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-17404
in-theory        17404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and ((D -> (E -> (D and E))) and ((A -> (B -> C)) -> (A -> (B -> C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-17404.        (((A -> (B -> C)) -> (A -> (B -> C))) and ((D -> (E -> (D and E))) and ((A -> (B -> C)) -> (A -> (B -> C))))), M:tm-327, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-17405
in-theory        17405
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and ((C -> (D -> (C and D))) and ((A and B) -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-327 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-17405.        (((A and B) -> (A and B)) and ((C -> (D -> (C and D))) and ((A and B) -> (A and B)))), M:tm-327, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-17406
in-theory        17406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and ((C -> (D -> (C and D))) and ((A -> B) -> (A -> B))))
theorem-size     23
proof            (modus-ponens tm-327 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-17406.        (((A -> B) -> (A -> B)) and ((C -> (D -> (C and D))) and ((A -> B) -> (A -> B)))), M:tm-327, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-17407
in-theory        17407
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and ((B -> (C -> (B and C))) and ((not (not A)) -> (not (not A)))))
theorem-size     23
proof            (modus-ponens tm-327 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-17407.        (((not (not A)) -> (not (not A))) and ((B -> (C -> (B and C))) and ((not (not A)) -> (not (not A))))), M:tm-327, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-17408
in-theory        17408
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((C -> (D -> (C and D))) and (((A -> B) -> (not (A -> A))) -> (not (A -> B)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-17408.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((C -> (D -> (C and D))) and (((A -> B) -> (not (A -> A))) -> (not (A -> B))))), M:tm-327, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-17409
in-theory        17409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((D -> (E -> (D and E))) and (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B))))
theorem-size     39
proof            (modus-ponens tm-327 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-17409.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((D -> (E -> (D and E))) and (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)))), M:tm-327, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-17410
in-theory        17410
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and ((D -> (E -> (D and E))) and (A or ((B -> C) -> (B -> B)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17410.        ((A or ((B -> C) -> (B -> B))) and ((D -> (E -> (D and E))) and (A or ((B -> C) -> (B -> B))))), M:tm-327, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-17411
in-theory        17411
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and ((D -> (E -> (D and E))) and (((A -> B) -> (A -> A)) or C)))
theorem-size     27
proof            (modus-ponens tm-327 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17411.        ((((A -> B) -> (A -> A)) or C) and ((D -> (E -> (D and E))) and (((A -> B) -> (A -> A)) or C))), M:tm-327, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-17412
in-theory        17412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and ((D -> (E -> (D and E))) and (A -> (((B -> C) -> (B -> B)) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17412.        ((A -> (((B -> C) -> (B -> B)) and A)) and ((D -> (E -> (D and E))) and (A -> (((B -> C) -> (B -> B)) and A)))), M:tm-327, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-17413
in-theory        17413
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and ((C -> (D -> (C and D))) and (((A -> B) -> A) -> ((A -> B) -> A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-17413.        ((((A -> B) -> A) -> ((A -> B) -> A)) and ((C -> (D -> (C and D))) and (((A -> B) -> A) -> ((A -> B) -> A)))), M:tm-327, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-17414
in-theory        17414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and ((D -> (E -> (D and E))) and (A -> ((B -> C) -> (B -> B)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17414.        ((A -> ((B -> C) -> (B -> B))) and ((D -> (E -> (D and E))) and (A -> ((B -> C) -> (B -> B))))), M:tm-327, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-17415
in-theory        17415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> ((B -> A) -> C)) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-17415.        (((A -> ((B -> A) -> C)) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> ((B -> A) -> C)) -> (A -> C)))), M:tm-327, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-17416
in-theory        17416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and ((C -> (D -> (C and D))) and ((A -> (A -> B)) -> (A -> B))))
theorem-size     27
proof            (modus-ponens tm-327 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-17416.        (((A -> (A -> B)) -> (A -> B)) and ((C -> (D -> (C and D))) and ((A -> (A -> B)) -> (A -> B)))), M:tm-327, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-17417
in-theory        17417
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-17417.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))))), M:tm-327, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-17418
in-theory        17418
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((D -> (E -> (D and E))) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B))))))
theorem-size     71
proof            (modus-ponens tm-327 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-17418.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((D -> (E -> (D and E))) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))))), M:tm-327, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-17419
in-theory        17419
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))))
theorem-size     75
proof            (modus-ponens tm-327 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-17419.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))), M:tm-327, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-17420
in-theory        17420
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F -> (E and F))) and (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17420.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F -> (E and F))) and (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-327, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-17421
in-theory        17421
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D)))
theorem-size     51
proof            (modus-ponens tm-327 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17421.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D))), M:tm-327, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-17422
in-theory        17422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))))
theorem-size     55
proof            (modus-ponens tm-327 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17422.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)))), M:tm-327, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-17423
in-theory        17423
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))))
theorem-size     67
proof            (modus-ponens tm-327 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-17423.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))), M:tm-327, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-17424
in-theory        17424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F -> (E and F))) and (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17424.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F -> (E and F))) and (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-327, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-17425
in-theory        17425
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D))))
theorem-size     55
proof            (modus-ponens tm-327 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       223
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-17425.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)))), M:tm-327, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-17426
in-theory        17426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((E -> (F -> (E and F))) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A))))
theorem-size     47
proof            (modus-ponens tm-327 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17426.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((E -> (F -> (E and F))) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)))), M:tm-327, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-17427
in-theory        17427
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((F -> (G -> (F and G))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))))
theorem-size     75
proof            (modus-ponens tm-327 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17427.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((F -> (G -> (F and G))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))), M:tm-327, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-17428
in-theory        17428
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> (F and G))) and (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17428.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> (F and G))) and (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-327, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-17429
in-theory        17429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G -> (F and G))) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     43
proof            (modus-ponens tm-327 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17429.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G -> (F and G))) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-327, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-17430
in-theory        17430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G -> (F and G))) and (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     47
proof            (modus-ponens tm-327 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17430.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G -> (F and G))) and (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-327, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-17431
in-theory        17431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-17431.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))))), M:tm-327, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-17432
in-theory        17432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> (F and G))) and (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17432.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> (F and G))) and (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-327, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-17433
in-theory        17433
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and ((C -> (D -> (C and D))) and (((A -> B) and A) -> B)))
theorem-size     23
proof            (modus-ponens tm-327 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-17433.        ((((A -> B) and A) -> B) and ((C -> (D -> (C and D))) and (((A -> B) and A) -> B))), M:tm-327, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-17434
in-theory        17434
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and ((E -> (F -> (E and F))) and ((((A -> (B -> A)) -> C) and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-327 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-17434.        (((((A -> (B -> A)) -> C) and D) -> C) and ((E -> (F -> (E and F))) and ((((A -> (B -> A)) -> C) and D) -> C))), M:tm-327, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-17435
in-theory        17435
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((F -> (G -> (F and G))) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D)))
theorem-size     47
proof            (modus-ponens tm-327 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17435.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((F -> (G -> (F and G))) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D))), M:tm-327, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-17436
in-theory        17436
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((D -> (E -> (D and E))) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B))))
theorem-size     51
proof            (modus-ponens tm-327 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-17436.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((D -> (E -> (D and E))) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)))), M:tm-327, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-17437
in-theory        17437
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((D -> (E -> (D and E))) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A))))
theorem-size     39
proof            (modus-ponens tm-327 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-17437.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((D -> (E -> (D and E))) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)))), M:tm-327, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-17438
in-theory        17438
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((D -> (E -> (D and E))) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A)))))
theorem-size     59
proof            (modus-ponens tm-327 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-17438.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((D -> (E -> (D and E))) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))))), M:tm-327, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-17439
in-theory        17439
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((E -> (F -> (E and F))) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))))
theorem-size     63
proof            (modus-ponens tm-327 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-17439.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((E -> (F -> (E and F))) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))), M:tm-327, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-17440
in-theory        17440
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F -> (E and F))) and (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17440.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F -> (E and F))) and (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-327, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-17441
in-theory        17441
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((E -> (F -> (E and F))) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D)))
theorem-size     43
proof            (modus-ponens tm-327 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17441.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((E -> (F -> (E and F))) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D))), M:tm-327, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-17442
in-theory        17442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((E -> (F -> (E and F))) and (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))))
theorem-size     47
proof            (modus-ponens tm-327 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17442.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((E -> (F -> (E and F))) and (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)))), M:tm-327, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-17443
in-theory        17443
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((D -> (E -> (D and E))) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B))))
theorem-size     55
proof            (modus-ponens tm-327 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-17443.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((D -> (E -> (D and E))) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)))), M:tm-327, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-17444
in-theory        17444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F -> (E and F))) and (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17444.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F -> (E and F))) and (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-327, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-17445
in-theory        17445
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and ((E -> (F -> (E and F))) and (((((A and B) -> A) -> C) and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-327 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-17445.        ((((((A and B) -> A) -> C) and D) -> C) and ((E -> (F -> (E and F))) and (((((A and B) -> A) -> C) and D) -> C))), M:tm-327, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-17446
in-theory        17446
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((D -> (E -> (D and E))) and (((A and B) -> (A -> C)) -> ((A and B) -> C))))
theorem-size     35
proof            (modus-ponens tm-327 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-17446.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((D -> (E -> (D and E))) and (((A and B) -> (A -> C)) -> ((A and B) -> C)))), M:tm-327, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-17447
in-theory        17447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not ((B and C) -> B))) -> (not A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-17447.        (((A -> (not ((B and C) -> B))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not ((B and C) -> B))) -> (not A)))), M:tm-327, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-17448
in-theory        17448
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((E -> (F -> (E and F))) and ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C))))
theorem-size     43
proof            (modus-ponens tm-327 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-17448.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((E -> (F -> (E and F))) and ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)))), M:tm-327, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-17449
in-theory        17449
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and ((E -> (F -> (E and F))) and (A or (B -> ((C and D) -> C)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17449.        ((A or (B -> ((C and D) -> C))) and ((E -> (F -> (E and F))) and (A or (B -> ((C and D) -> C))))), M:tm-327, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-17450
in-theory        17450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and ((E -> (F -> (E and F))) and ((A -> ((B and C) -> B)) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17450.        (((A -> ((B and C) -> B)) or D) and ((E -> (F -> (E and F))) and ((A -> ((B and C) -> B)) or D))), M:tm-327, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-17451
in-theory        17451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> ((C and D) -> C)) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17451.        ((A -> ((B -> ((C and D) -> C)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> ((C and D) -> C)) and A)))), M:tm-327, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-17452
in-theory        17452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and ((D -> (E -> (D and E))) and ((A -> (B and C)) -> (A -> B))))
theorem-size     27
proof            (modus-ponens tm-327 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-17452.        (((A -> (B and C)) -> (A -> B)) and ((D -> (E -> (D and E))) and ((A -> (B and C)) -> (A -> B)))), M:tm-327, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-17453
in-theory        17453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and ((E -> (F -> (E and F))) and (A -> (B -> ((C and D) -> C)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17453.        ((A -> (B -> ((C and D) -> C))) and ((E -> (F -> (E and F))) and (A -> (B -> ((C and D) -> C))))), M:tm-327, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-17454
in-theory        17454
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and ((C -> (D -> (C and D))) and ((A and (A -> B)) -> B)))
theorem-size     23
proof            (modus-ponens tm-327 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-17454.        (((A and (A -> B)) -> B) and ((C -> (D -> (C and D))) and ((A and (A -> B)) -> B))), M:tm-327, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-17455
in-theory        17455
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and ((E -> (F -> (E and F))) and ((A and ((B -> (C -> B)) -> D)) -> D)))
theorem-size     31
proof            (modus-ponens tm-327 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-17455.        (((A and ((B -> (C -> B)) -> D)) -> D) and ((E -> (F -> (E and F))) and ((A and ((B -> (C -> B)) -> D)) -> D))), M:tm-327, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-17456
in-theory        17456
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((F -> (G -> (F and G))) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E)))
theorem-size     47
proof            (modus-ponens tm-327 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17456.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((F -> (G -> (F and G))) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E))), M:tm-327, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-17457
in-theory        17457
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and ((E -> (F -> (E and F))) and ((A and (((B and C) -> B) -> D)) -> D)))
theorem-size     31
proof            (modus-ponens tm-327 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-17457.        (((A and (((B and C) -> B) -> D)) -> D) and ((E -> (F -> (E and F))) and ((A and (((B and C) -> B) -> D)) -> D))), M:tm-327, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-17458
in-theory        17458
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((D -> (E -> (D and E))) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C))))
theorem-size     51
proof            (modus-ponens tm-327 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-17458.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((D -> (E -> (D and E))) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)))), M:tm-327, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-17459
in-theory        17459
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((D -> (E -> (D and E))) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B))))
theorem-size     39
proof            (modus-ponens tm-327 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-17459.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((D -> (E -> (D and E))) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)))), M:tm-327, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-17460
in-theory        17460
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((D -> (E -> (D and E))) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B)))))
theorem-size     59
proof            (modus-ponens tm-327 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-17460.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((D -> (E -> (D and E))) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))))), M:tm-327, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-17461
in-theory        17461
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((E -> (F -> (E and F))) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))))
theorem-size     63
proof            (modus-ponens tm-327 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-17461.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((E -> (F -> (E and F))) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))), M:tm-327, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-17462
in-theory        17462
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F -> (E and F))) and (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17462.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F -> (E and F))) and (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-327, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-17463
in-theory        17463
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and ((E -> (F -> (E and F))) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D)))
theorem-size     43
proof            (modus-ponens tm-327 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17463.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and ((E -> (F -> (E and F))) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D))), M:tm-327, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-17464
in-theory        17464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))))
theorem-size     47
proof            (modus-ponens tm-327 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17464.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)))), M:tm-327, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-17465
in-theory        17465
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((D -> (E -> (D and E))) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C))))
theorem-size     55
proof            (modus-ponens tm-327 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-17465.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((D -> (E -> (D and E))) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)))), M:tm-327, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-17466
in-theory        17466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F -> (E and F))) and (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17466.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F -> (E and F))) and (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-327, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-17467
in-theory        17467
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and ((E -> (F -> (E and F))) and ((A and (((B and C) -> C) -> D)) -> D)))
theorem-size     31
proof            (modus-ponens tm-327 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-17467.        (((A and (((B and C) -> C) -> D)) -> D) and ((E -> (F -> (E and F))) and ((A and (((B and C) -> C) -> D)) -> D))), M:tm-327, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-17468
in-theory        17468
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and ((E -> (F -> (E and F))) and (((((A and B) -> B) -> C) and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-327 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-17468.        ((((((A and B) -> B) -> C) and D) -> C) and ((E -> (F -> (E and F))) and (((((A and B) -> B) -> C) and D) -> C))), M:tm-327, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-17469
in-theory        17469
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((D -> (E -> (D and E))) and (((A and B) -> (B -> C)) -> ((A and B) -> C))))
theorem-size     35
proof            (modus-ponens tm-327 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-17469.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((D -> (E -> (D and E))) and (((A and B) -> (B -> C)) -> ((A and B) -> C)))), M:tm-327, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-17470
in-theory        17470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not ((B and C) -> C))) -> (not A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17470.        (((A -> (not ((B and C) -> C))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not ((B and C) -> C))) -> (not A)))), M:tm-327, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-17471
in-theory        17471
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((E -> (F -> (E and F))) and ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C))))
theorem-size     43
proof            (modus-ponens tm-327 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17471.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((E -> (F -> (E and F))) and ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)))), M:tm-327, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-17472
in-theory        17472
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and ((E -> (F -> (E and F))) and (A or (B -> ((C and D) -> D)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17472.        ((A or (B -> ((C and D) -> D))) and ((E -> (F -> (E and F))) and (A or (B -> ((C and D) -> D))))), M:tm-327, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-17473
in-theory        17473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and ((E -> (F -> (E and F))) and ((A -> ((B and C) -> C)) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17473.        (((A -> ((B and C) -> C)) or D) and ((E -> (F -> (E and F))) and ((A -> ((B and C) -> C)) or D))), M:tm-327, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-17474
in-theory        17474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> ((C and D) -> D)) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17474.        ((A -> ((B -> ((C and D) -> D)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> ((C and D) -> D)) and A)))), M:tm-327, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-17475
in-theory        17475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> (B and C)) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-327 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-17475.        (((A -> (B and C)) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> (B and C)) -> (A -> C)))), M:tm-327, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-17476
in-theory        17476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and ((E -> (F -> (E and F))) and (A -> (B -> ((C and D) -> D)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17476.        ((A -> (B -> ((C and D) -> D))) and ((E -> (F -> (E and F))) and (A -> (B -> ((C and D) -> D))))), M:tm-327, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-17477
in-theory        17477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and (C -> (D -> C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17477.        (((A -> (B -> A)) and (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and (C -> (D -> C))))), M:tm-327, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-17478
in-theory        17478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17478.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-327, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-17479
in-theory        17479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and ((C and D) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17479.        (((A -> (B -> A)) and ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and ((C and D) -> C)))), M:tm-327, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-17480
in-theory        17480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and ((C and D) -> D))))
theorem-size     31
proof            (modus-ponens tm-327 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17480.        (((A -> (B -> A)) and ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and ((C and D) -> D)))), M:tm-327, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-17481
in-theory        17481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and (C -> (D -> (C and D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17481.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and (C -> (D -> (C and D)))))), M:tm-327, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-17482
in-theory        17482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and (C -> (C or D)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17482.        (((A -> (B -> A)) and (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and (C -> (C or D))))), M:tm-327, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-17483
in-theory        17483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and (C -> (D or C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17483.        (((A -> (B -> A)) and (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and (C -> (D or C))))), M:tm-327, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-17484
in-theory        17484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17484.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-327, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-17485
in-theory        17485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17485.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-327, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-17486
in-theory        17486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and ((D -> (E -> (D and E))) and ((A -> (B -> A)) and ((not (not C)) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17486.        (((A -> (B -> A)) and ((not (not C)) -> C)) and ((D -> (E -> (D and E))) and ((A -> (B -> A)) and ((not (not C)) -> C)))), M:tm-327, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-17487
in-theory        17487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> (D -> (E -> D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17487.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> (D -> (E -> D)))))), M:tm-327, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-17488
in-theory        17488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and ((C -> D) -> (C -> C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17488.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and ((C -> D) -> (C -> C))))), M:tm-327, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-17489
in-theory        17489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     59
proof            (modus-ponens tm-327 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17489.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-327, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-17490
in-theory        17490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17490.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-327, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-17491
in-theory        17491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17491.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-327, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-17492
in-theory        17492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> ((D and E) -> D)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17492.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> ((D and E) -> D))))), M:tm-327, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-17493
in-theory        17493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17493.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-327, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-17494
in-theory        17494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> ((D and E) -> E)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17494.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> ((D and E) -> E))))), M:tm-327, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-17495
in-theory        17495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17495.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-327, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-17496
in-theory        17496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-17496.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A)))), M:tm-327, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-17497
in-theory        17497
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((E -> (F -> (E and F))) and ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D))))
theorem-size     51
proof            (modus-ponens tm-327 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-17497.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((E -> (F -> (E and F))) and ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)))), M:tm-327, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-17498
in-theory        17498
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and ((E -> (F -> (E and F))) and (A or (B -> ((C -> (D -> C)) and B)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17498.        ((A or (B -> ((C -> (D -> C)) and B))) and ((E -> (F -> (E and F))) and (A or (B -> ((C -> (D -> C)) and B))))), M:tm-327, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-17499
in-theory        17499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and ((E -> (F -> (E and F))) and ((A -> ((B -> (C -> B)) and A)) or D)))
theorem-size     31
proof            (modus-ponens tm-327 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17499.        (((A -> ((B -> (C -> B)) and A)) or D) and ((E -> (F -> (E and F))) and ((A -> ((B -> (C -> B)) and A)) or D))), M:tm-327, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-17500
in-theory        17500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> ((C -> (D -> C)) and B)) and A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17500.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> ((C -> (D -> C)) and B)) and A)))), M:tm-327, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-17501
in-theory        17501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and ((E -> (F -> (E and F))) and (A -> (B -> ((C -> (D -> C)) and B)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17501.        ((A -> (B -> ((C -> (D -> C)) and B))) and ((E -> (F -> (E and F))) and (A -> (B -> ((C -> (D -> C)) and B))))), M:tm-327, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-17502
in-theory        17502
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17502.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))))), M:tm-327, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-17503
in-theory        17503
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17503.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-327, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-17504
in-theory        17504
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D))))
theorem-size     47
proof            (modus-ponens tm-327 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17504.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)))), M:tm-327, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-17505
in-theory        17505
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E))))
theorem-size     47
proof            (modus-ponens tm-327 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17505.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)))), M:tm-327, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-17506
in-theory        17506
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17506.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))))), M:tm-327, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-17507
in-theory        17507
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17507.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))))), M:tm-327, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-17508
in-theory        17508
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17508.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))))), M:tm-327, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-17509
in-theory        17509
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17509.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-327, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-17510
in-theory        17510
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     59
proof            (modus-ponens tm-327 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17510.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-327, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-17511
in-theory        17511
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D))))
theorem-size     47
proof            (modus-ponens tm-327 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17511.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)))), M:tm-327, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-17512
in-theory        17512
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17512.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))))), M:tm-327, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-17513
in-theory        17513
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17513.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))))), M:tm-327, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-17514
in-theory        17514
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     75
proof            (modus-ponens tm-327 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5)
proof-size       257
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17514.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-327, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-17515
in-theory        17515
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> (H and I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     67
proof            (modus-ponens tm-327 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17515.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> (H and I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-327, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-17516
in-theory        17516
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     67
proof            (modus-ponens tm-327 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17516.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-327, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-17517
in-theory        17517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17517.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))))), M:tm-327, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-17518
in-theory        17518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     67
proof            (modus-ponens tm-327 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17518.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-327, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-17519
in-theory        17519
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17519.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))))), M:tm-327, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-17520
in-theory        17520
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17520.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-327, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-17521
in-theory        17521
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (I -> (H and I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     71
proof            (modus-ponens tm-327 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17521.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (I -> (H and I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-327, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-17522
in-theory        17522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17522.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-327, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-17523
in-theory        17523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((E -> (F -> (E and F))) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A))))
theorem-size     51
proof            (modus-ponens tm-327 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-17523.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((E -> (F -> (E and F))) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)))), M:tm-327, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-17524
in-theory        17524
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((F -> (G -> (F and G))) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))))
theorem-size     83
proof            (modus-ponens tm-327 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-17524.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((F -> (G -> (F and G))) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))), M:tm-327, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-17525
in-theory        17525
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G -> (F and G))) and (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17525.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G -> (F and G))) and (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-327, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-17526
in-theory        17526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and ((F -> (G -> (F and G))) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E)))
theorem-size     47
proof            (modus-ponens tm-327 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17526.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and ((F -> (G -> (F and G))) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E))), M:tm-327, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-17527
in-theory        17527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((F -> (G -> (F and G))) and (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))))
theorem-size     51
proof            (modus-ponens tm-327 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17527.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((F -> (G -> (F and G))) and (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)))), M:tm-327, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-17528
in-theory        17528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G -> (F and G))) and (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17528.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G -> (F and G))) and (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-327, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-17529
in-theory        17529
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and ((E -> (F -> (E and F))) and (((A and B) -> A) and (C -> (D -> C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17529.        ((((A and B) -> A) and (C -> (D -> C))) and ((E -> (F -> (E and F))) and (((A and B) -> A) and (C -> (D -> C))))), M:tm-327, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-17530
in-theory        17530
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17530.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-327, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-17531
in-theory        17531
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and ((E -> (F -> (E and F))) and (((A and B) -> A) and ((C and D) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17531.        ((((A and B) -> A) and ((C and D) -> C)) and ((E -> (F -> (E and F))) and (((A and B) -> A) and ((C and D) -> C)))), M:tm-327, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-17532
in-theory        17532
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and ((E -> (F -> (E and F))) and (((A and B) -> A) and ((C and D) -> D))))
theorem-size     31
proof            (modus-ponens tm-327 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17532.        ((((A and B) -> A) and ((C and D) -> D)) and ((E -> (F -> (E and F))) and (((A and B) -> A) and ((C and D) -> D)))), M:tm-327, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-17533
in-theory        17533
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and (((A and B) -> A) and (C -> (D -> (C and D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17533.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and (((A and B) -> A) and (C -> (D -> (C and D)))))), M:tm-327, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-17534
in-theory        17534
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and ((E -> (F -> (E and F))) and (((A and B) -> A) and (C -> (C or D)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17534.        ((((A and B) -> A) and (C -> (C or D))) and ((E -> (F -> (E and F))) and (((A and B) -> A) and (C -> (C or D))))), M:tm-327, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-17535
in-theory        17535
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and ((E -> (F -> (E and F))) and (((A and B) -> A) and (C -> (D or C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17535.        ((((A and B) -> A) and (C -> (D or C))) and ((E -> (F -> (E and F))) and (((A and B) -> A) and (C -> (D or C))))), M:tm-327, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-17536
in-theory        17536
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17536.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-327, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-17537
in-theory        17537
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> (E and F))) and (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17537.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> (E and F))) and (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-327, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-17538
in-theory        17538
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and ((D -> (E -> (D and E))) and (((A and B) -> A) and ((not (not C)) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17538.        ((((A and B) -> A) and ((not (not C)) -> C)) and ((D -> (E -> (D and E))) and (((A and B) -> A) and ((not (not C)) -> C)))), M:tm-327, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-17539
in-theory        17539
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> (D -> (E -> D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17539.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> (D -> (E -> D)))))), M:tm-327, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-17540
in-theory        17540
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((E -> (F -> (E and F))) and (((A and B) -> A) and ((C -> D) -> (C -> C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17540.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((E -> (F -> (E and F))) and (((A and B) -> A) and ((C -> D) -> (C -> C))))), M:tm-327, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-17541
in-theory        17541
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     59
proof            (modus-ponens tm-327 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17541.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-327, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-17542
in-theory        17542
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17542.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-327, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-17543
in-theory        17543
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17543.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-327, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-17544
in-theory        17544
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> ((D and E) -> D)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17544.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> ((D and E) -> D))))), M:tm-327, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-17545
in-theory        17545
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17545.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-327, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-17546
in-theory        17546
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> ((D and E) -> E)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17546.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> ((D and E) -> E))))), M:tm-327, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-17547
in-theory        17547
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17547.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))))), M:tm-327, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-17548
in-theory        17548
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> (G and H))) and (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17548.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> (G and H))) and (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-327, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-17549
in-theory        17549
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> (((D and E) -> D) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17549.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> (((D and E) -> D) and C))))), M:tm-327, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-17550
in-theory        17550
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17550.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-327, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-17551
in-theory        17551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17551.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))))), M:tm-327, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-17552
in-theory        17552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not (((B and C) -> B) and A))) -> (not A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-17552.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not (((B and C) -> B) and A))) -> (not A)))), M:tm-327, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-17553
in-theory        17553
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((E -> (F -> (E and F))) and (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D))))
theorem-size     51
proof            (modus-ponens tm-327 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-17553.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((E -> (F -> (E and F))) and (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)))), M:tm-327, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-17554
in-theory        17554
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and ((E -> (F -> (E and F))) and (A or (B -> (((C and D) -> C) and B)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17554.        ((A or (B -> (((C and D) -> C) and B))) and ((E -> (F -> (E and F))) and (A or (B -> (((C and D) -> C) and B))))), M:tm-327, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-17555
in-theory        17555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and ((E -> (F -> (E and F))) and ((A -> (((B and C) -> B) and A)) or D)))
theorem-size     31
proof            (modus-ponens tm-327 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17555.        (((A -> (((B and C) -> B) and A)) or D) and ((E -> (F -> (E and F))) and ((A -> (((B and C) -> B) and A)) or D))), M:tm-327, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-17556
in-theory        17556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> (((C and D) -> C) and B)) and A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17556.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> (((C and D) -> C) and B)) and A)))), M:tm-327, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-17557
in-theory        17557
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and ((E -> (F -> (E and F))) and (A -> (B -> (((C and D) -> C) and B)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17557.        ((A -> (B -> (((C and D) -> C) and B))) and ((E -> (F -> (E and F))) and (A -> (B -> (((C and D) -> C) and B))))), M:tm-327, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-17558
in-theory        17558
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and ((E -> (F -> (E and F))) and (((A and B) -> B) and (C -> (D -> C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17558.        ((((A and B) -> B) and (C -> (D -> C))) and ((E -> (F -> (E and F))) and (((A and B) -> B) and (C -> (D -> C))))), M:tm-327, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-17559
in-theory        17559
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17559.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-327, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-17560
in-theory        17560
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and ((E -> (F -> (E and F))) and (((A and B) -> B) and ((C and D) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17560.        ((((A and B) -> B) and ((C and D) -> C)) and ((E -> (F -> (E and F))) and (((A and B) -> B) and ((C and D) -> C)))), M:tm-327, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-17561
in-theory        17561
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and ((E -> (F -> (E and F))) and (((A and B) -> B) and ((C and D) -> D))))
theorem-size     31
proof            (modus-ponens tm-327 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17561.        ((((A and B) -> B) and ((C and D) -> D)) and ((E -> (F -> (E and F))) and (((A and B) -> B) and ((C and D) -> D)))), M:tm-327, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-17562
in-theory        17562
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and (((A and B) -> B) and (C -> (D -> (C and D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17562.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and (((A and B) -> B) and (C -> (D -> (C and D)))))), M:tm-327, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-17563
in-theory        17563
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and ((E -> (F -> (E and F))) and (((A and B) -> B) and (C -> (C or D)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17563.        ((((A and B) -> B) and (C -> (C or D))) and ((E -> (F -> (E and F))) and (((A and B) -> B) and (C -> (C or D))))), M:tm-327, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-17564
in-theory        17564
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and ((E -> (F -> (E and F))) and (((A and B) -> B) and (C -> (D or C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17564.        ((((A and B) -> B) and (C -> (D or C))) and ((E -> (F -> (E and F))) and (((A and B) -> B) and (C -> (D or C))))), M:tm-327, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-17565
in-theory        17565
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17565.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-327, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-17566
in-theory        17566
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> (E and F))) and (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17566.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> (E and F))) and (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-327, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-17567
in-theory        17567
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and ((D -> (E -> (D and E))) and (((A and B) -> B) and ((not (not C)) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17567.        ((((A and B) -> B) and ((not (not C)) -> C)) and ((D -> (E -> (D and E))) and (((A and B) -> B) and ((not (not C)) -> C)))), M:tm-327, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-17568
in-theory        17568
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> (D -> (E -> D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17568.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> (D -> (E -> D)))))), M:tm-327, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-17569
in-theory        17569
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((E -> (F -> (E and F))) and (((A and B) -> B) and ((C -> D) -> (C -> C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17569.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((E -> (F -> (E and F))) and (((A and B) -> B) and ((C -> D) -> (C -> C))))), M:tm-327, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-17570
in-theory        17570
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     59
proof            (modus-ponens tm-327 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17570.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-327, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-17571
in-theory        17571
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17571.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-327, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-17572
in-theory        17572
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17572.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-327, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-17573
in-theory        17573
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> ((D and E) -> D)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17573.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> ((D and E) -> D))))), M:tm-327, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-17574
in-theory        17574
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17574.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-327, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-17575
in-theory        17575
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> ((D and E) -> E)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17575.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> ((D and E) -> E))))), M:tm-327, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-17576
in-theory        17576
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17576.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))))), M:tm-327, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-17577
in-theory        17577
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> (G and H))) and (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17577.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> (G and H))) and (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-327, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-17578
in-theory        17578
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> (((D and E) -> D) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17578.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> (((D and E) -> D) and C))))), M:tm-327, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-17579
in-theory        17579
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> (((D and E) -> E) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17579.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> (((D and E) -> E) and C))))), M:tm-327, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-17580
in-theory        17580
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> (((D and E) -> E) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17580.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> (((D and E) -> E) and C))))), M:tm-327, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-17581
in-theory        17581
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17581.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-327, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-17582
in-theory        17582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17582.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))))), M:tm-327, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-17583
in-theory        17583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not (((B and C) -> C) and A))) -> (not A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17583.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not (((B and C) -> C) and A))) -> (not A)))), M:tm-327, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-17584
in-theory        17584
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((E -> (F -> (E and F))) and (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D))))
theorem-size     51
proof            (modus-ponens tm-327 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17584.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((E -> (F -> (E and F))) and (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)))), M:tm-327, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-17585
in-theory        17585
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and ((E -> (F -> (E and F))) and (A or (B -> (((C and D) -> D) and B)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17585.        ((A or (B -> (((C and D) -> D) and B))) and ((E -> (F -> (E and F))) and (A or (B -> (((C and D) -> D) and B))))), M:tm-327, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-17586
in-theory        17586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and ((E -> (F -> (E and F))) and ((A -> (((B and C) -> C) and A)) or D)))
theorem-size     31
proof            (modus-ponens tm-327 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17586.        (((A -> (((B and C) -> C) and A)) or D) and ((E -> (F -> (E and F))) and ((A -> (((B and C) -> C) and A)) or D))), M:tm-327, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-17587
in-theory        17587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> (((C and D) -> D) and B)) and A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17587.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> (((C and D) -> D) and B)) and A)))), M:tm-327, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-17588
in-theory        17588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and ((E -> (F -> (E and F))) and (A -> (B -> (((C and D) -> D) and B)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17588.        ((A -> (B -> (((C and D) -> D) and B))) and ((E -> (F -> (E and F))) and (A -> (B -> (((C and D) -> D) and B))))), M:tm-327, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-17589
in-theory        17589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and (C -> (D -> C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17589.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and (C -> (D -> C))))), M:tm-327, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-17590
in-theory        17590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17590.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-327, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-17591
in-theory        17591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and ((C and D) -> C))))
theorem-size     35
proof            (modus-ponens tm-327 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17591.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and ((C and D) -> C)))), M:tm-327, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-17592
in-theory        17592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and ((C and D) -> D))))
theorem-size     35
proof            (modus-ponens tm-327 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17592.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and ((C and D) -> D)))), M:tm-327, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-17593
in-theory        17593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and (C -> (D -> (C and D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17593.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))))), M:tm-327, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-17594
in-theory        17594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and (C -> (C or D)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17594.        (((A -> (B -> (A and B))) and (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and (C -> (C or D))))), M:tm-327, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-17595
in-theory        17595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and (C -> (D or C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17595.        (((A -> (B -> (A and B))) and (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and (C -> (D or C))))), M:tm-327, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-17596
in-theory        17596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17596.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-327, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-17597
in-theory        17597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17597.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-327, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-17598
in-theory        17598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((D -> (E -> (D and E))) and ((A -> (B -> (A and B))) and ((not (not C)) -> C))))
theorem-size     35
proof            (modus-ponens tm-327 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17598.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((D -> (E -> (D and E))) and ((A -> (B -> (A and B))) and ((not (not C)) -> C)))), M:tm-327, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-17599
in-theory        17599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17599.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))))), M:tm-327, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-17600
in-theory        17600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17600.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))))), M:tm-327, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-17601
in-theory        17601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17601.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-327, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-17602
in-theory        17602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     55
proof            (modus-ponens tm-327 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17602.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-327, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-17603
in-theory        17603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17603.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-327, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-17604
in-theory        17604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> D)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17604.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))))), M:tm-327, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-17605
in-theory        17605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17605.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-327, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-17606
in-theory        17606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> E)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17606.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))))), M:tm-327, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-17607
in-theory        17607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17607.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))))), M:tm-327, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-17608
in-theory        17608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> (G and H))) and ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     59
proof            (modus-ponens tm-327 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17608.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> (G and H))) and ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-327, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-17609
in-theory        17609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17609.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))))), M:tm-327, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-17610
in-theory        17610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17610.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))))), M:tm-327, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-17611
in-theory        17611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17611.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-327, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-17612
in-theory        17612
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17612.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-327, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-17613
in-theory        17613
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17613.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-327, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-17614
in-theory        17614
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     59
proof            (modus-ponens tm-327 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17614.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-327, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-17615
in-theory        17615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17615.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-327, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-17616
in-theory        17616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A))))
theorem-size     39
proof            (modus-ponens tm-327 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17616.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)))), M:tm-327, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-17617
in-theory        17617
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((E -> (F -> (E and F))) and ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D))))
theorem-size     59
proof            (modus-ponens tm-327 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17617.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((E -> (F -> (E and F))) and ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)))), M:tm-327, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-17618
in-theory        17618
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F -> (E and F))) and (A or (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17618.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F -> (E and F))) and (A or (B -> ((C -> (D -> (C and D))) and B))))), M:tm-327, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-17619
in-theory        17619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and ((E -> (F -> (E and F))) and ((A -> ((B -> (C -> (B and C))) and A)) or D)))
theorem-size     35
proof            (modus-ponens tm-327 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17619.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and ((E -> (F -> (E and F))) and ((A -> ((B -> (C -> (B and C))) and A)) or D))), M:tm-327, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-17620
in-theory        17620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A))))
theorem-size     39
proof            (modus-ponens tm-327 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17620.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)))), M:tm-327, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-17621
in-theory        17621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F -> (E and F))) and (A -> (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17621.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F -> (E and F))) and (A -> (B -> ((C -> (D -> (C and D))) and B))))), M:tm-327, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-17622
in-theory        17622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and ((C -> (D -> (C and D))) and (A -> (A and (B -> A)))))
theorem-size     23
proof            (modus-ponens tm-327 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-17622.        ((A -> (A and (B -> A))) and ((C -> (D -> (C and D))) and (A -> (A and (B -> A))))), M:tm-327, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-17623
in-theory        17623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((D -> (E -> (D and E))) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-17623.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((D -> (E -> (D and E))) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))), M:tm-327, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-17624
in-theory        17624
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and ((C -> (D -> (C and D))) and ((A and B) -> ((A and B) and A))))
theorem-size     27
proof            (modus-ponens tm-327 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-17624.        (((A and B) -> ((A and B) and A)) and ((C -> (D -> (C and D))) and ((A and B) -> ((A and B) and A)))), M:tm-327, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-17625
in-theory        17625
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and ((C -> (D -> (C and D))) and ((A and B) -> ((A and B) and B))))
theorem-size     27
proof            (modus-ponens tm-327 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17625.        (((A and B) -> ((A and B) and B)) and ((C -> (D -> (C and D))) and ((A and B) -> ((A and B) and B)))), M:tm-327, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-17626
in-theory        17626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and ((C -> (D -> (C and D))) and (A -> (A and (B -> (A and B))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-17626.        ((A -> (A and (B -> (A and B)))) and ((C -> (D -> (C and D))) and (A -> (A and (B -> (A and B)))))), M:tm-327, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-17627
in-theory        17627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and ((C -> (D -> (C and D))) and (A -> (A and (A or B)))))
theorem-size     23
proof            (modus-ponens tm-327 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-17627.        ((A -> (A and (A or B))) and ((C -> (D -> (C and D))) and (A -> (A and (A or B))))), M:tm-327, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-17628
in-theory        17628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and ((C -> (D -> (C and D))) and (A -> (A and (B or A)))))
theorem-size     23
proof            (modus-ponens tm-327 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-17628.        ((A -> (A and (B or A))) and ((C -> (D -> (C and D))) and (A -> (A and (B or A))))), M:tm-327, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-17629
in-theory        17629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((D -> (E -> (D and E))) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-17629.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((D -> (E -> (D and E))) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))))), M:tm-327, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-17630
in-theory        17630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((C -> (D -> (C and D))) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-17630.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((C -> (D -> (C and D))) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))))), M:tm-327, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-17631
in-theory        17631
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and ((B -> (C -> (B and C))) and ((not (not A)) -> ((not (not A)) and A))))
theorem-size     27
proof            (modus-ponens tm-327 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-17631.        (((not (not A)) -> ((not (not A)) and A)) and ((B -> (C -> (B and C))) and ((not (not A)) -> ((not (not A)) and A)))), M:tm-327, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-17632
in-theory        17632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and ((D -> (E -> (D and E))) and (A -> (A and (B -> (C -> B))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-17632.        ((A -> (A and (B -> (C -> B)))) and ((D -> (E -> (D and E))) and (A -> (A and (B -> (C -> B)))))), M:tm-327, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-17633
in-theory        17633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and ((C -> (D -> (C and D))) and ((A -> B) -> ((A -> B) and (A -> A)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-17633.        (((A -> B) -> ((A -> B) and (A -> A))) and ((C -> (D -> (C and D))) and ((A -> B) -> ((A -> B) and (A -> A))))), M:tm-327, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-17634
in-theory        17634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))))
theorem-size     67
proof            (modus-ponens tm-327 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5)
proof-size       237
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-17634.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))), M:tm-327, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-17635
in-theory        17635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((E -> (F -> (E and F))) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17635.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((E -> (F -> (E and F))) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))), M:tm-327, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-17636
in-theory        17636
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((D -> (E -> (D and E))) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-17636.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((D -> (E -> (D and E))) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))), M:tm-327, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-17637
in-theory        17637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and ((D -> (E -> (D and E))) and (A -> (A and ((B and C) -> B)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-17637.        ((A -> (A and ((B and C) -> B))) and ((D -> (E -> (D and E))) and (A -> (A and ((B and C) -> B))))), M:tm-327, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-17638
in-theory        17638
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((D -> (E -> (D and E))) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-17638.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((D -> (E -> (D and E))) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))), M:tm-327, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-17639
in-theory        17639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and ((D -> (E -> (D and E))) and (A -> (A and ((B and C) -> C)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17639.        ((A -> (A and ((B and C) -> C))) and ((D -> (E -> (D and E))) and (A -> (A and ((B and C) -> C))))), M:tm-327, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-17640
in-theory        17640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and ((D -> (E -> (D and E))) and (A -> (A and ((B -> (C -> B)) and A)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-17640.        ((A -> (A and ((B -> (C -> B)) and A))) and ((D -> (E -> (D and E))) and (A -> (A and ((B -> (C -> B)) and A))))), M:tm-327, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-17641
in-theory        17641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((E -> (F -> (E and F))) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-17641.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((E -> (F -> (E and F))) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))), M:tm-327, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-17642
in-theory        17642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and ((D -> (E -> (D and E))) and (A -> (A and (((B and C) -> B) and A)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-17642.        ((A -> (A and (((B and C) -> B) and A))) and ((D -> (E -> (D and E))) and (A -> (A and (((B and C) -> B) and A))))), M:tm-327, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-17643
in-theory        17643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and ((D -> (E -> (D and E))) and (A -> (A and (((B and C) -> C) and A)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17643.        ((A -> (A and (((B and C) -> C) and A))) and ((D -> (E -> (D and E))) and (A -> (A and (((B and C) -> C) and A))))), M:tm-327, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-17644
in-theory        17644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((D -> (E -> (D and E))) and (A -> (A and ((B -> (C -> (B and C))) and A)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17644.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((D -> (E -> (D and E))) and (A -> (A and ((B -> (C -> (B and C))) and A))))), M:tm-327, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17645
in-theory        17645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (((D and E) -> E) and (A -> (A and ((B -> (C -> (B and C))) and A)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17645.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (((D and E) -> E) and (A -> (A and ((B -> (C -> (B and C))) and A))))), M:tm-326, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17646
in-theory        17646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (((D and E) -> D) and (A -> (A and ((B -> (C -> (B and C))) and A)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17646.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (((D and E) -> D) and (A -> (A and ((B -> (C -> (B and C))) and A))))), M:tm-325, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17647
in-theory        17647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and ((B -> (C -> (B and C))) and A)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17647.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and ((B -> (C -> (B and C))) and A))))), M:tm-324, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17648
in-theory        17648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((D -> (E -> D)) and (A -> (A and ((B -> (C -> (B and C))) and A)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17648.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((D -> (E -> D)) and (A -> (A and ((B -> (C -> (B and C))) and A))))), M:tm-323, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17649
in-theory        17649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17649.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((D and E) -> E)), M:tm-322, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17650
in-theory        17650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17650.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((D and E) -> D)), M:tm-320, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17651
in-theory        17651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17651.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17652
in-theory        17652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (A -> A))
theorem-size     17
proof            (modus-ponens tm-316 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17652.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (A -> A)), M:tm-316, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-17653
in-theory        17653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17653.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (D -> (E -> D))), M:tm-315, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17654
in-theory        17654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((A -> (not (A and ((B -> (C -> (B and C))) and A)))) -> (not A)))
theorem-size     31
proof            (modus-ponens tm-313 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17654.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((A -> (not (A and ((B -> (C -> (B and C))) and A)))) -> (not A))), M:tm-313, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-17655
in-theory        17655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (((A and ((B -> (C -> (B and C))) and A)) -> D) -> ((A or (A and ((B -> (C -> (B and C))) and A))) -> D)))
theorem-size     43
proof            (modus-ponens tm-312 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17655.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (((A and ((B -> (C -> (B and C))) and A)) -> D) -> ((A or (A and ((B -> (C -> (B and C))) and A))) -> D))), M:tm-312, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-17656
in-theory        17656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (D or (A -> (A and ((B -> (C -> (B and C))) and A)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17656.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (D or (A -> (A and ((B -> (C -> (B and C))) and A))))), M:tm-311, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17657
in-theory        17657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((A -> (A and ((B -> (C -> (B and C))) and A))) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17657.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((A -> (A and ((B -> (C -> (B and C))) and A))) or D)), M:tm-310, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17658
in-theory        17658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (D -> ((A -> (A and ((B -> (C -> (B and C))) and A))) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17658.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (D -> ((A -> (A and ((B -> (C -> (B and C))) and A))) and D))), M:tm-309, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17659
in-theory        17659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (D -> (A -> (A and ((B -> (C -> (B and C))) and A)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17659.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (D -> (A -> (A and ((B -> (C -> (B and C))) and A))))), M:tm-305, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17660
in-theory        17660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     25
proof            (modus-ponens tm-303 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17660.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-303, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17661
in-theory        17661
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and ((D -> (E -> (D and E))) and ((B -> (C -> (B and C))) and A))))
theorem-size     39
proof            (modus-ponens tm-300 tm-327 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17661.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and ((D -> (E -> (D and E))) and ((B -> (C -> (B and C))) and A)))), M:tm-300, m:tm-327, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (-> B (and A B))) C)))))
================================================================
tm-name          tm-17662
in-theory        17662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-270 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17662.        ((A -> (((B and C) -> C) and A)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-270, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17663
in-theory        17663
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((D -> (E -> (D and E))) and (((B and C) -> C) and A))))
theorem-size     33
proof            (modus-ponens tm-267 tm-327 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (and (-> Bm (-> Cm (and Bm Cm))) (and (-> (and A B) B) C))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17663.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((D -> (E -> (D and E))) and (((B and C) -> C) and A)))), M:tm-267, m:tm-327, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (and (-> Bm (-> Cm (and Bm Cm))) (and (-> (and A B) B) C)))))
================================================================
tm-name          tm-17664
in-theory        17664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-239 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17664.        ((A -> (((B and C) -> B) and A)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-239, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17665
in-theory        17665
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((D -> (E -> (D and E))) and (((B and C) -> B) and A))))
theorem-size     33
proof            (modus-ponens tm-236 tm-327 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (and (-> Bm (-> Cm (and Bm Cm))) (and (-> (and A B) A) C))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17665.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((D -> (E -> (D and E))) and (((B and C) -> B) and A)))), M:tm-236, m:tm-327, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (and (-> Bm (-> Cm (and Bm Cm))) (and (-> (and A B) A) C)))))
================================================================
tm-name          tm-17666
in-theory        17666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and ((F -> (G -> (F and G))) and E))))
theorem-size     31
proof            (modus-ponens tm-210 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17666.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and ((F -> (G -> (F and G))) and E)))), M:tm-210, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17667
in-theory        17667
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((E -> (F -> (E and F))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     57
proof            (modus-ponens tm-207 tm-327 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (-> Cm (and Bm Cm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17667.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((E -> (F -> (E and F))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-207, m:tm-327, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (-> Cm (and Bm Cm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-17668
in-theory        17668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-183 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17668.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-183, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17669
in-theory        17669
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and ((D -> (E -> (D and E))) and ((B -> (C -> B)) and A))))
theorem-size     33
proof            (modus-ponens tm-180 tm-327 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (-> B A)) C))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17669.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and ((D -> (E -> (D and E))) and ((B -> (C -> B)) and A)))), M:tm-180, m:tm-327, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (-> B A)) C)))))
================================================================
tm-name          tm-17670
in-theory        17670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-157 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17670.        ((A -> ((B and C) -> C)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-157, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17671
in-theory        17671
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((D -> (E -> (D and E))) and ((B and C) -> C))))
theorem-size     27
proof            (modus-ponens tm-154 tm-327 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (and (-> Bm (-> Cm (and Bm Cm))) (-> (and A B) B))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17671.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((D -> (E -> (D and E))) and ((B and C) -> C)))), M:tm-154, m:tm-327, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (and (-> Bm (-> Cm (and Bm Cm))) (-> (and A B) B)))))
================================================================
tm-name          tm-17672
in-theory        17672
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     29
proof            (modus-ponens tm-147 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17672.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-147, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17673
in-theory        17673
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((D -> (E -> (D and E))) and ((A and (B -> C)) -> C))))
theorem-size     39
proof            (modus-ponens tm-144 tm-327 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (and (-> Bm (-> Cm (and Bm Cm))) (-> (and A (-> B C)) C))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17673.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((D -> (E -> (D and E))) and ((A and (B -> C)) -> C)))), M:tm-144, m:tm-327, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (and (-> Bm (-> Cm (and Bm Cm))) (-> (and A (-> B C)) C)))))
================================================================
tm-name          tm-17674
in-theory        17674
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-134 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17674.        ((A -> ((B and C) -> B)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-134, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17675
in-theory        17675
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((D -> (E -> (D and E))) and ((B and C) -> B))))
theorem-size     27
proof            (modus-ponens tm-131 tm-327 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (and (-> Bm (-> Cm (and Bm Cm))) (-> (and A B) A))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17675.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((D -> (E -> (D and E))) and ((B and C) -> B)))), M:tm-131, m:tm-327, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (and (-> Bm (-> Cm (and Bm Cm))) (-> (and A B) A)))))
================================================================
tm-name          tm-17676
in-theory        17676
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     29
proof            (modus-ponens tm-125 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17676.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-125, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17677
in-theory        17677
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((D -> (E -> (D and E))) and (((A -> B) and C) -> B))))
theorem-size     39
proof            (modus-ponens tm-122 tm-327 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (and (-> Bm (-> Cm (and Bm Cm))) (-> (and (-> A B) C) B))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17677.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((D -> (E -> (D and E))) and (((A -> B) and C) -> B)))), M:tm-122, m:tm-327, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (and (-> Bm (-> Cm (and Bm Cm))) (-> (and (-> A B) C) B)))))
================================================================
tm-name          tm-17678
in-theory        17678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-113 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17678.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G -> (F and G))) and E)))), M:tm-113, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17679
in-theory        17679
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> (E and F))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     51
proof            (modus-ponens tm-110 tm-327 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17679.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> (E and F))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-110, m:tm-327, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
================================================================
tm-name          tm-17680
in-theory        17680
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     33
proof            (modus-ponens tm-105 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17680.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-105, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17681
in-theory        17681
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     47
proof            (modus-ponens tm-102 tm-327 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A (-> B C)) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17681.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> (B -> C)) -> (A -> C))))), M:tm-102, m:tm-327, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A (-> B C)) (-> A C))))))
================================================================
tm-name          tm-17682
in-theory        17682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and ((D -> (E -> (D and E))) and C))))
theorem-size     21
proof            (modus-ponens tm-95 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17682.        (((A -> B) -> (A -> A)) and (C -> (C and ((D -> (E -> (D and E))) and C)))), M:tm-95, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17683
in-theory        17683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and ((C -> (D -> (C and D))) and (A -> A))))
theorem-size     23
proof            (modus-ponens tm-92 tm-327 ((Am (-> A A)) (B (and (-> A A) (and (-> Bm (-> Cm (and Bm Cm))) (-> A A))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17683.        (((A -> B) or (A -> A)) -> ((A -> A) and ((C -> (D -> (C and D))) and (A -> A)))), M:tm-92, m:tm-327, u:((Am (-> A A)) (B (and (-> A A) (and (-> Bm (-> Cm (and Bm Cm))) (-> A A)))))
================================================================
tm-name          tm-17684
in-theory        17684
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and ((C -> (D -> (C and D))) and A))))
theorem-size     15
proof            (modus-ponens tm-84 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17684.        (A -> (B -> (A and ((C -> (D -> (C and D))) and A)))), M:tm-84, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-17685
in-theory        17685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-83 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17685.        ((A -> (B -> (C -> B))) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-83, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17686
in-theory        17686
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((D -> (E -> (D and E))) and (B -> (C -> B)))))
theorem-size     27
proof            (modus-ponens tm-80 tm-327 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (and (-> Bm (-> Cm (and Bm Cm))) (-> A (-> B A)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17686.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((D -> (E -> (D and E))) and (B -> (C -> B))))), M:tm-80, m:tm-327, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (and (-> Bm (-> Cm (and Bm Cm))) (-> A (-> B A))))))
================================================================
tm-name          tm-17687
in-theory        17687
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and ((C -> (D -> (C and D))) and B))))
theorem-size     19
proof            (modus-ponens tm-76 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17687.        (((not (not A)) -> A) and (B -> (B and ((C -> (D -> (C and D))) and B)))), M:tm-76, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17688
in-theory        17688
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and ((B -> (C -> (B and C))) and A)))
theorem-size     17
proof            (modus-ponens tm-73 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17688.        (((not (not A)) or A) -> (A and ((B -> (C -> (B and C))) and A))), M:tm-73, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-17689
in-theory        17689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and ((D -> (E -> (D and E))) and C))))
theorem-size     25
proof            (modus-ponens tm-69 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17689.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and ((D -> (E -> (D and E))) and C)))), M:tm-69, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17690
in-theory        17690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((C -> (D -> (C and D))) and ((A -> (not B)) -> (not A)))))
theorem-size     35
proof            (modus-ponens tm-66 tm-327 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A (not B)) (not A)))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17690.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((C -> (D -> (C and D))) and ((A -> (not B)) -> (not A))))), M:tm-66, m:tm-327, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A (not B)) (not A))))))
================================================================
tm-name          tm-17691
in-theory        17691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     27
proof            (modus-ponens tm-54 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17691.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-54, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17692
in-theory        17692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-51 tm-327 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> (or C A) B)))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17692.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((D -> (E -> (D and E))) and ((B -> C) -> ((A or B) -> C))))), M:tm-51, m:tm-327, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> (or C A) B))))))
================================================================
tm-name          tm-17693
in-theory        17693
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and ((C -> (D -> (C and D))) and (B or A))))
theorem-size     21
proof            (modus-ponens tm-50 tm-327 ((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm (and Bm Cm))) (or A B))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17693.        ((A or (B or A)) -> ((B or A) and ((C -> (D -> (C and D))) and (B or A)))), M:tm-50, m:tm-327, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm (and Bm Cm))) (or A B)))))
================================================================
tm-name          tm-17694
in-theory        17694
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and ((C -> (D -> (C and D))) and (A or B))))
theorem-size     21
proof            (modus-ponens tm-49 tm-327 ((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm (and Bm Cm))) (or A B))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17694.        ((A or (A or B)) -> ((A or B) and ((C -> (D -> (C and D))) and (A or B)))), M:tm-49, m:tm-327, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (-> Cm (and Bm Cm))) (or A B)))))
================================================================
tm-name          tm-17695
in-theory        17695
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((C -> (D -> (C and D))) and (B -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-48 tm-327 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> Bm (-> Cm (and Bm Cm))) (-> A (and B A)))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17695.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((C -> (D -> (C and D))) and (B -> (A and B))))), M:tm-48, m:tm-327, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> Bm (-> Cm (and Bm Cm))) (-> A (and B A))))))
================================================================
tm-name          tm-17696
in-theory        17696
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and ((C -> (D -> (C and D))) and B)))
theorem-size     17
proof            (modus-ponens tm-47 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17696.        (((A and B) or B) -> (B and ((C -> (D -> (C and D))) and B))), M:tm-47, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-17697
in-theory        17697
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and ((C -> (D -> (C and D))) and A)))
theorem-size     17
proof            (modus-ponens tm-46 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17697.        (((A and B) or A) -> (A and ((C -> (D -> (C and D))) and A))), M:tm-46, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-17698
in-theory        17698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))
theorem-size     37
proof            (modus-ponens tm-45 tm-327 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17698.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))), M:tm-45, m:tm-327, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-17699
in-theory        17699
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and ((C -> (D -> (C and D))) and (B -> A))))
theorem-size     21
proof            (modus-ponens tm-44 tm-327 ((Am (-> A B)) (C (and (-> A B) (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17699.        ((A or (B -> A)) -> ((B -> A) and ((C -> (D -> (C and D))) and (B -> A)))), M:tm-44, m:tm-327, u:((Am (-> A B)) (C (and (-> A B) (and (-> Bm (-> Cm (and Bm Cm))) (-> A B)))))
================================================================
tm-name          tm-17700
in-theory        17700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and ((D -> (E -> (D and E))) and C))))
theorem-size     19
proof            (modus-ponens tm-42 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17700.        ((A -> (B or A)) and (C -> (C and ((D -> (E -> (D and E))) and C)))), M:tm-42, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17701
in-theory        17701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and ((D -> (E -> (D and E))) and C))))
theorem-size     19
proof            (modus-ponens tm-32 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17701.        ((A -> (A or B)) and (C -> (C and ((D -> (E -> (D and E))) and C)))), M:tm-32, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17702
in-theory        17702
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and ((B -> (C -> (B and C))) and A))))
theorem-size     15
proof            (modus-ponens tm-24 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17702.        (A -> (A and (A and ((B -> (C -> (B and C))) and A)))), M:tm-24, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-17703
in-theory        17703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and ((D -> (E -> (D and E))) and C))))
theorem-size     21
proof            (modus-ponens tm-23 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17703.        ((A -> (B -> (A and B))) and (C -> (C and ((D -> (E -> (D and E))) and C)))), M:tm-23, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17704
in-theory        17704
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and ((D -> (E -> (D and E))) and C))))
theorem-size     19
proof            (modus-ponens tm-22 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17704.        (((A and B) -> B) and (C -> (C and ((D -> (E -> (D and E))) and C)))), M:tm-22, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17705
in-theory        17705
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and ((D -> (E -> (D and E))) and C))))
theorem-size     19
proof            (modus-ponens tm-21 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17705.        (((A and B) -> A) and (C -> (C and ((D -> (E -> (D and E))) and C)))), M:tm-21, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17706
in-theory        17706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     27
proof            (modus-ponens tm-20 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17706.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-20, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17707
in-theory        17707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and ((D -> (E -> (D and E))) and C))))
theorem-size     19
proof            (modus-ponens tm-19 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17707.        ((A -> (B -> A)) and (C -> (C and ((D -> (E -> (D and E))) and C)))), M:tm-19, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17708
in-theory        17708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and ((B -> (C -> (B and C))) and A)))) -> (not A))
theorem-size     17
proof            (modus-ponens tm-9 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-9 tm-2 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17708.        ((A -> (not (A and ((B -> (C -> (B and C))) and A)))) -> (not A)), M:tm-9, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-17709
in-theory        17709
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) and A)) -> D) -> ((A or (A and ((B -> (C -> (B and C))) and A))) -> D))
theorem-size     29
proof            (modus-ponens tm-8 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17709.        (((A and ((B -> (C -> (B and C))) and A)) -> D) -> ((A or (A and ((B -> (C -> (B and C))) and A))) -> D)), M:tm-8, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-17710
in-theory        17710
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and ((C -> (D -> (C and D))) and B))))
theorem-size     15
proof            (modus-ponens tm-7 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-7 tm-2 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17710.        (A or (B -> (B and ((C -> (D -> (C and D))) and B)))), M:tm-7, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17711
in-theory        17711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-6 tm-2 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17711.        ((A -> (A and ((B -> (C -> (B and C))) and A))) or D), M:tm-6, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17712
in-theory        17712
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and ((C -> (D -> (C and D))) and B))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17712.        (A -> ((B -> (B and ((C -> (D -> (C and D))) and B))) and A)), M:tm-5, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17713
in-theory        17713
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and ((C -> (D -> (C and D))) and B))))
theorem-size     15
proof            (modus-ponens tm-1 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17713.        (A -> (B -> (B and ((C -> (D -> (C and D))) and B)))), M:tm-1, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-17714
in-theory        17714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (A -> (A and (B -> A))))
theorem-size     13
proof            (modus-ponens tm-328 tm-1 ((A Am) (B (-> Bm Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-17714.        ((A -> (B -> A)) and (A -> (A and (B -> A)))), M:tm-328, m:tm-1, u:((A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-17715
in-theory        17715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))
theorem-size     33
proof            (modus-ponens tm-328 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17715.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))), M:tm-328, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-17716
in-theory        17716
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((A and B) -> ((A and B) and A)))
theorem-size     15
proof            (modus-ponens tm-328 tm-3 ((A (and Am Bm)) (B Am)))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-17716.        (((A and B) -> A) and ((A and B) -> ((A and B) and A))), M:tm-328, m:tm-3, u:((A (and Am Bm)) (B Am))
================================================================
tm-name          tm-17717
in-theory        17717
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((A and B) -> ((A and B) and B)))
theorem-size     15
proof            (modus-ponens tm-328 tm-4 ((A (and Am Bm)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17717.        (((A and B) -> B) and ((A and B) -> ((A and B) and B))), M:tm-328, m:tm-4, u:((A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-17718
in-theory        17718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (A -> (A and (B -> (A and B)))))
theorem-size     17
proof            (modus-ponens tm-328 tm-5 ((A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-2 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17718.        ((A -> (B -> (A and B))) and (A -> (A and (B -> (A and B))))), M:tm-328, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-17719
in-theory        17719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (A -> (A and (A or B))))
theorem-size     13
proof            (modus-ponens tm-328 tm-6 ((A Am) (B (or Am Bm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-17719.        ((A -> (A or B)) and (A -> (A and (A or B)))), M:tm-328, m:tm-6, u:((A Am) (B (or Am Bm)))
================================================================
tm-name          tm-17720
in-theory        17720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (A -> (A and (B or A))))
theorem-size     13
proof            (modus-ponens tm-328 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-17720.        ((A -> (B or A)) and (A -> (A and (B or A)))), M:tm-328, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-17721
in-theory        17721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     31
proof            (modus-ponens tm-328 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-17721.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))), M:tm-328, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-17722
in-theory        17722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))))
theorem-size     27
proof            (modus-ponens tm-328 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-17722.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A))))), M:tm-328, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-17723
in-theory        17723
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((not (not A)) -> ((not (not A)) and A)))
theorem-size     15
proof            (modus-ponens tm-328 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-17723.        (((not (not A)) -> A) and ((not (not A)) -> ((not (not A)) and A))), M:tm-328, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-17724
in-theory        17724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (A -> (A and (B -> (C -> B)))))
theorem-size     17
proof            (modus-ponens tm-328 tm-11 ((A Am) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17724.        ((A -> (B -> (C -> B))) and (A -> (A and (B -> (C -> B))))), M:tm-328, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-17725
in-theory        17725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((A -> B) -> ((A -> B) and (A -> A))))
theorem-size     19
proof            (modus-ponens tm-328 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-17725.        (((A -> B) -> (A -> A)) and ((A -> B) -> ((A -> B) and (A -> A)))), M:tm-328, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-17726
in-theory        17726
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-328 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-17726.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))), M:tm-328, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-17727
in-theory        17727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     33
proof            (modus-ponens tm-328 tm-14 ((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17727.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-328, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-17728
in-theory        17728
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))
theorem-size     39
proof            (modus-ponens tm-328 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-17728.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))), M:tm-328, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-17729
in-theory        17729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (A -> (A and ((B and C) -> B))))
theorem-size     17
proof            (modus-ponens tm-328 tm-16 ((A Am) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17729.        ((A -> ((B and C) -> B)) and (A -> (A and ((B and C) -> B)))), M:tm-328, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-17730
in-theory        17730
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))
theorem-size     39
proof            (modus-ponens tm-328 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-17730.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))), M:tm-328, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-17731
in-theory        17731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (A -> (A and ((B and C) -> C))))
theorem-size     17
proof            (modus-ponens tm-328 tm-18 ((A Am) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17731.        ((A -> ((B and C) -> C)) and (A -> (A and ((B and C) -> C)))), M:tm-328, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-17732
in-theory        17732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (A -> (A and ((B -> (C -> B)) and A))))
theorem-size     21
proof            (modus-ponens tm-328 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-17732.        ((A -> ((B -> (C -> B)) and A)) and (A -> (A and ((B -> (C -> B)) and A)))), M:tm-328, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-17733
in-theory        17733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     37
proof            (modus-ponens tm-328 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17733.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-328, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-17734
in-theory        17734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (A -> (A and (((B and C) -> B) and A))))
theorem-size     21
proof            (modus-ponens tm-328 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-17734.        ((A -> (((B and C) -> B) and A)) and (A -> (A and (((B and C) -> B) and A)))), M:tm-328, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-17735
in-theory        17735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (A -> (A and (((B and C) -> C) and A))))
theorem-size     21
proof            (modus-ponens tm-328 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17735.        ((A -> (((B and C) -> C) and A)) and (A -> (A and (((B and C) -> C) and A)))), M:tm-328, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-17736
in-theory        17736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (A -> (A and ((B -> (C -> (B and C))) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17736.        ((A -> ((B -> (C -> (B and C))) and A)) and (A -> (A and ((B -> (C -> (B and C))) and A)))), M:tm-328, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-17737
in-theory        17737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((A -> B) -> ((A -> B) and (A -> (A and B)))))
theorem-size     23
proof            (modus-ponens tm-328 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17737.        (((A -> B) -> (A -> (A and B))) and ((A -> B) -> ((A -> B) and (A -> (A and B))))), M:tm-328, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-17738
in-theory        17738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (A -> (A and (B -> (C -> (B and C))))))
theorem-size     21
proof            (modus-ponens tm-328 tm-25 ((A Am) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-17738.        ((A -> (B -> (C -> (B and C)))) and (A -> (A and (B -> (C -> (B and C)))))), M:tm-328, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-17739
in-theory        17739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (A -> (A and ((B -> (B or C)) and A))))
theorem-size     21
proof            (modus-ponens tm-328 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17739.        ((A -> ((B -> (B or C)) and A)) and (A -> (A and ((B -> (B or C)) and A)))), M:tm-328, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-17740
in-theory        17740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (A -> (A and (B -> (B or C)))))
theorem-size     17
proof            (modus-ponens tm-328 tm-33 ((A Am) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17740.        ((A -> (B -> (B or C))) and (A -> (A and (B -> (B or C))))), M:tm-328, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-17741
in-theory        17741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (A -> (A and ((B -> (C or B)) and A))))
theorem-size     21
proof            (modus-ponens tm-328 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17741.        ((A -> ((B -> (C or B)) and A)) and (A -> (A and ((B -> (C or B)) and A)))), M:tm-328, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-17742
in-theory        17742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (A -> (A and (B -> (C or B)))))
theorem-size     17
proof            (modus-ponens tm-328 tm-43 ((A Am) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17742.        ((A -> (B -> (C or B))) and (A -> (A and (B -> (C or B))))), M:tm-328, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-17743
in-theory        17743
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-328 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-17743.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))), M:tm-328, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-17744
in-theory        17744
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     61
proof            (modus-ponens tm-328 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-17744.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-328, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-17745
in-theory        17745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-328 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-17745.        (((A -> B) -> (((A and C) or A) -> B)) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B)))), M:tm-328, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-17746
in-theory        17746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-328 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17746.        (((A -> B) -> (((C and A) or A) -> B)) and ((A -> B) -> ((A -> B) and (((C and A) or A) -> B)))), M:tm-328, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-17747
in-theory        17747
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C))))
theorem-size     43
proof            (modus-ponens tm-328 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-17747.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((A -> (B and A)) -> C) -> (((A -> (B and A)) -> C) and ((B or (A -> (B and A))) -> C)))), M:tm-328, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-17748
in-theory        17748
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-328 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-17748.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((A or B) -> C) -> (((A or B) -> C) and ((A or (A or B)) -> C)))), M:tm-328, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-17749
in-theory        17749
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-328 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-17749.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((A or B) -> C) -> (((A or B) -> C) and ((B or (A or B)) -> C)))), M:tm-328, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-17750
in-theory        17750
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     67
proof            (modus-ponens tm-328 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-17750.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((A -> B) -> ((C or A) -> B)) -> D) and (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-328, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-17751
in-theory        17751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (A -> (A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))))
theorem-size     37
proof            (modus-ponens tm-328 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17751.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (A -> (A and (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)))), M:tm-328, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-17752
in-theory        17752
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((A -> B) -> (B -> C)) -> (((A -> B) -> (B -> C)) and ((A -> B) -> ((A or B) -> C)))))
theorem-size     43
proof            (modus-ponens tm-328 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-17752.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((A -> B) -> (B -> C)) -> (((A -> B) -> (B -> C)) and ((A -> B) -> ((A or B) -> C))))), M:tm-328, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-17753
in-theory        17753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (A -> (A and ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     33
proof            (modus-ponens tm-328 tm-56 ((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-17753.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (A -> (A and ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-328, m:tm-56, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-17754
in-theory        17754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and ((A -> (not (B -> A))) -> ((A -> (not (B -> A))) and (not A))))
theorem-size     26
proof            (modus-ponens tm-328 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       122
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-17754.        (((A -> (not (B -> A))) -> (not A)) and ((A -> (not (B -> A))) -> ((A -> (not (B -> A))) and (not A)))), M:tm-328, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-17755
in-theory        17755
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) and (not (A -> (B -> C))))))
theorem-size     58
proof            (modus-ponens tm-328 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       174
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-17755.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) and (not (A -> (B -> C)))))), M:tm-328, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-17756
in-theory        17756
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (((A and B) -> (not A)) -> (((A and B) -> (not A)) and (not (A and B)))))
theorem-size     30
proof            (modus-ponens tm-328 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-17756.        ((((A and B) -> (not A)) -> (not (A and B))) and (((A and B) -> (not A)) -> (((A and B) -> (not A)) and (not (A and B))))), M:tm-328, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-17757
in-theory        17757
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (((A and B) -> (not B)) -> (((A and B) -> (not B)) and (not (A and B)))))
theorem-size     30
proof            (modus-ponens tm-328 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17757.        ((((A and B) -> (not B)) -> (not (A and B))) and (((A and B) -> (not B)) -> (((A and B) -> (not B)) and (not (A and B))))), M:tm-328, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-17758
in-theory        17758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and ((A -> (not (B -> (A and B)))) -> ((A -> (not (B -> (A and B)))) and (not A))))
theorem-size     32
proof            (modus-ponens tm-328 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       132
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-17758.        (((A -> (not (B -> (A and B)))) -> (not A)) and ((A -> (not (B -> (A and B)))) -> ((A -> (not (B -> (A and B)))) and (not A)))), M:tm-328, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-17759
in-theory        17759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and ((A -> (not (A or B))) -> ((A -> (not (A or B))) and (not A))))
theorem-size     26
proof            (modus-ponens tm-328 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       122
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-17759.        (((A -> (not (A or B))) -> (not A)) and ((A -> (not (A or B))) -> ((A -> (not (A or B))) and (not A)))), M:tm-328, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-17760
in-theory        17760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and ((A -> (not (B or A))) -> ((A -> (not (B or A))) and (not A))))
theorem-size     26
proof            (modus-ponens tm-328 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       122
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-17760.        (((A -> (not (B or A))) -> (not A)) and ((A -> (not (B or A))) -> ((A -> (not (B or A))) and (not A)))), M:tm-328, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-17761
in-theory        17761
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) and (not (A -> B)))))
theorem-size     54
proof            (modus-ponens tm-328 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       168
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-17761.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) and (not (A -> B))))), M:tm-328, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-17762
in-theory        17762
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (((A -> B) -> (not ((A -> (not B)) -> (not A)))) and (not (A -> B)))))
theorem-size     48
proof            (modus-ponens tm-328 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       158
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-17762.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (((A -> B) -> (not ((A -> (not B)) -> (not A)))) and (not (A -> B))))), M:tm-328, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-17763
in-theory        17763
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((((A -> (not B)) -> (not A)) -> C) -> ((((A -> (not B)) -> (not A)) -> C) and (((A -> B) or ((A -> (not B)) -> (not A))) -> C))))
theorem-size     57
proof            (modus-ponens tm-328 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-17763.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((((A -> (not B)) -> (not A)) -> C) -> ((((A -> (not B)) -> (not A)) -> C) and (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))), M:tm-328, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-17764
in-theory        17764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (A -> (A and (((B -> C) -> ((B -> (not C)) -> (not B))) and A))))
theorem-size     33
proof            (modus-ponens tm-328 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17764.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (A -> (A and (((B -> C) -> ((B -> (not C)) -> (not B))) and A)))), M:tm-328, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-17765
in-theory        17765
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((A -> B) -> (A -> (not B))) -> (((A -> B) -> (A -> (not B))) and ((A -> B) -> (not A)))))
theorem-size     40
proof            (modus-ponens tm-328 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       150
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-17765.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((A -> B) -> (A -> (not B))) -> (((A -> B) -> (A -> (not B))) and ((A -> B) -> (not A))))), M:tm-328, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-17766
in-theory        17766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (A -> (A and ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     29
proof            (modus-ponens tm-328 tm-71 ((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-17766.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (A -> (A and ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-328, m:tm-71, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-17767
in-theory        17767
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((not (not A)) -> (not A)) -> (((not (not A)) -> (not A)) and (not (not (not A))))))
theorem-size     30
proof            (modus-ponens tm-328 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-9 tm-10)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-17767.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((not (not A)) -> (not A)) -> (((not (not A)) -> (not A)) and (not (not (not A)))))), M:tm-328, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-17768
in-theory        17768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and ((A -> B) -> ((A -> B) and (((not (not A)) or A) -> B))))
theorem-size     27
proof            (modus-ponens tm-328 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-17768.        (((A -> B) -> (((not (not A)) or A) -> B)) and ((A -> B) -> ((A -> B) and (((not (not A)) or A) -> B)))), M:tm-328, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-17769
in-theory        17769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (A -> (A and (((not (not B)) -> B) and A))))
theorem-size     21
proof            (modus-ponens tm-328 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17769.        ((A -> (((not (not B)) -> B) and A)) and (A -> (A and (((not (not B)) -> B) and A)))), M:tm-328, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-17770
in-theory        17770
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (((not (not (A -> B))) -> A) -> (((not (not (A -> B))) -> A) and ((not (not (A -> B))) -> B))))
theorem-size     39
proof            (modus-ponens tm-328 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-17770.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (((not (not (A -> B))) -> A) -> (((not (not (A -> B))) -> A) and ((not (not (A -> B))) -> B)))), M:tm-328, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-17771
in-theory        17771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and (A -> (A and ((not (not B)) -> B))))
theorem-size     17
proof            (modus-ponens tm-328 tm-78 ((A Am) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-17771.        ((A -> ((not (not B)) -> B)) and (A -> (A and ((not (not B)) -> B)))), M:tm-328, m:tm-78, u:((A Am) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-17772
in-theory        17772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and ((A -> (not (B -> (C -> B)))) -> ((A -> (not (B -> (C -> B)))) and (not A))))
theorem-size     32
proof            (modus-ponens tm-328 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       142
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-17772.        (((A -> (not (B -> (C -> B)))) -> (not A)) and ((A -> (not (B -> (C -> B)))) -> ((A -> (not (B -> (C -> B)))) and (not A)))), M:tm-328, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-17773
in-theory        17773
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (((A -> (B -> A)) -> C) -> (((A -> (B -> A)) -> C) and ((D or (A -> (B -> A))) -> C))))
theorem-size     43
proof            (modus-ponens tm-328 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-17773.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (((A -> (B -> A)) -> C) -> (((A -> (B -> A)) -> C) and ((D or (A -> (B -> A))) -> C)))), M:tm-328, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-17774
in-theory        17774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and (A -> (A and ((B -> (C -> (D -> C))) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17774.        ((A -> ((B -> (C -> (D -> C))) and A)) and (A -> (A and ((B -> (C -> (D -> C))) and A)))), M:tm-328, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-17775
in-theory        17775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and ((A -> B) -> ((A -> B) and (A -> (C -> B)))))
theorem-size     23
proof            (modus-ponens tm-328 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-17775.        (((A -> B) -> (A -> (C -> B))) and ((A -> B) -> ((A -> B) and (A -> (C -> B))))), M:tm-328, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-17776
in-theory        17776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (A -> (A and (B -> (C -> (D -> C))))))
theorem-size     21
proof            (modus-ponens tm-328 tm-85 ((A Am) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-17776.        ((A -> (B -> (C -> (D -> C)))) and (A -> (A and (B -> (C -> (D -> C)))))), M:tm-328, m:tm-85, u:((A Am) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-17777
in-theory        17777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and (A -> (A and A)))
theorem-size     9
proof            (modus-ponens tm-328 tm-86 ((A Am) (B Am)))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-17777.        ((A -> A) and (A -> (A and A))), M:tm-328, m:tm-86, u:((A Am) (B Am))
================================================================
tm-name          tm-17778
in-theory        17778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and ((A -> (B -> C)) -> ((A -> (B -> C)) and (A -> (B -> C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-17778.        (((A -> (B -> C)) -> (A -> (B -> C))) and ((A -> (B -> C)) -> ((A -> (B -> C)) and (A -> (B -> C))))), M:tm-328, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-17779
in-theory        17779
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and ((A and B) -> ((A and B) and (A and B))))
theorem-size     19
proof            (modus-ponens tm-328 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-17779.        (((A and B) -> (A and B)) and ((A and B) -> ((A and B) and (A and B)))), M:tm-328, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-17780
in-theory        17780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and ((A -> B) -> ((A -> B) and (A -> B))))
theorem-size     19
proof            (modus-ponens tm-328 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-17780.        (((A -> B) -> (A -> B)) and ((A -> B) -> ((A -> B) and (A -> B)))), M:tm-328, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-17781
in-theory        17781
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and ((not (not A)) -> ((not (not A)) and (not (not A)))))
theorem-size     19
proof            (modus-ponens tm-328 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-17781.        (((not (not A)) -> (not (not A))) and ((not (not A)) -> ((not (not A)) and (not (not A))))), M:tm-328, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-17782
in-theory        17782
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((A -> B) -> (not (A -> A))) -> (((A -> B) -> (not (A -> A))) and (not (A -> B)))))
theorem-size     36
proof            (modus-ponens tm-328 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       156
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-17782.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((A -> B) -> (not (A -> A))) -> (((A -> B) -> (not (A -> A))) and (not (A -> B))))), M:tm-328, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-17783
in-theory        17783
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((A -> A) -> B) -> (((A -> A) -> B) and (((A -> C) or (A -> A)) -> B))))
theorem-size     37
proof            (modus-ponens tm-328 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-17783.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((A -> A) -> B) -> (((A -> A) -> B) and (((A -> C) or (A -> A)) -> B)))), M:tm-328, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-17784
in-theory        17784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (A -> (A and (((B -> C) -> (B -> B)) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17784.        ((A -> (((B -> C) -> (B -> B)) and A)) and (A -> (A and (((B -> C) -> (B -> B)) and A)))), M:tm-328, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-17785
in-theory        17785
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and (((A -> B) -> A) -> (((A -> B) -> A) and ((A -> B) -> A))))
theorem-size     29
proof            (modus-ponens tm-328 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-17785.        ((((A -> B) -> A) -> ((A -> B) -> A)) and (((A -> B) -> A) -> (((A -> B) -> A) and ((A -> B) -> A)))), M:tm-328, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-17786
in-theory        17786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and (A -> (A and ((B -> C) -> (B -> B)))))
theorem-size     21
proof            (modus-ponens tm-328 tm-97 ((A Am) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-17786.        ((A -> ((B -> C) -> (B -> B))) and (A -> (A and ((B -> C) -> (B -> B))))), M:tm-328, m:tm-97, u:((A Am) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-17787
in-theory        17787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and ((A -> ((B -> A) -> C)) -> ((A -> ((B -> A) -> C)) and (A -> C))))
theorem-size     31
proof            (modus-ponens tm-328 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-17787.        (((A -> ((B -> A) -> C)) -> (A -> C)) and ((A -> ((B -> A) -> C)) -> ((A -> ((B -> A) -> C)) and (A -> C)))), M:tm-328, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-17788
in-theory        17788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and ((A -> (A -> B)) -> ((A -> (A -> B)) and (A -> B))))
theorem-size     25
proof            (modus-ponens tm-328 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-17788.        (((A -> (A -> B)) -> (A -> B)) and ((A -> (A -> B)) -> ((A -> (A -> B)) and (A -> B)))), M:tm-328, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-17789
in-theory        17789
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> B)))))
theorem-size     49
proof            (modus-ponens tm-328 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-17789.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> B))))), M:tm-328, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-17790
in-theory        17790
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) and (not ((A -> (B -> C)) -> (A -> B))))))
theorem-size     84
proof            (modus-ponens tm-328 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       242
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-17790.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) and (not ((A -> (B -> C)) -> (A -> B)))))), M:tm-328, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-17791
in-theory        17791
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> C)) -> D) and ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))))
theorem-size     79
proof            (modus-ponens tm-328 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-17791.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> C)) -> D) and ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))), M:tm-328, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-17792
in-theory        17792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (A -> (A and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))))
theorem-size     49
proof            (modus-ponens tm-328 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17792.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (A -> (A and ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)))), M:tm-328, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-17793
in-theory        17793
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) and (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))))
theorem-size     75
proof            (modus-ponens tm-328 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-17793.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) and (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))), M:tm-328, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-17794
in-theory        17794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (A -> (A and (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     45
proof            (modus-ponens tm-328 tm-107 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-17794.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (A -> (A and (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-328, m:tm-107, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-17795
in-theory        17795
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) and ((A -> (B -> C)) -> D))))
theorem-size     63
proof            (modus-ponens tm-328 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-17795.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) and ((A -> (B -> C)) -> D)))), M:tm-328, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-17796
in-theory        17796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (not A))))
theorem-size     56
proof            (modus-ponens tm-328 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       190
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17796.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (not A)))), M:tm-328, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-17797
in-theory        17797
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))))
theorem-size     83
proof            (modus-ponens tm-328 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17797.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))), M:tm-328, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-17798
in-theory        17798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (A -> (A and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     41
proof            (modus-ponens tm-328 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17798.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (A -> (A and ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-328, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-17799
in-theory        17799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((A -> (B -> (C -> D))) -> ((A -> (B -> (C -> D))) and (A -> ((B -> C) -> (B -> D))))))
theorem-size     43
proof            (modus-ponens tm-328 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-17799.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((A -> (B -> (C -> D))) -> ((A -> (B -> (C -> D))) and (A -> ((B -> C) -> (B -> D)))))), M:tm-328, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-17800
in-theory        17800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (A -> (A and (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     37
proof            (modus-ponens tm-328 tm-115 ((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-17800.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (A -> (A and (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-328, m:tm-115, u:((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-17801
in-theory        17801
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and (((A -> B) and A) -> (((A -> B) and A) and B)))
theorem-size     21
proof            (modus-ponens tm-328 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-17801.        ((((A -> B) and A) -> B) and (((A -> B) and A) -> (((A -> B) and A) and B))), M:tm-328, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-17802
in-theory        17802
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and ((((A -> (B -> A)) -> C) and D) -> ((((A -> (B -> A)) -> C) and D) and C)))
theorem-size     33
proof            (modus-ponens tm-328 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-17802.        (((((A -> (B -> A)) -> C) and D) -> C) and ((((A -> (B -> A)) -> C) and D) -> ((((A -> (B -> A)) -> C) and D) and C))), M:tm-328, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-17803
in-theory        17803
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) and D)))
theorem-size     57
proof            (modus-ponens tm-328 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17803.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) and D))), M:tm-328, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-17804
in-theory        17804
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((((A -> B) -> A) and C) -> (A -> B)) -> (((((A -> B) -> A) and C) -> (A -> B)) and ((((A -> B) -> A) and C) -> B))))
theorem-size     55
proof            (modus-ponens tm-328 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-17804.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((((A -> B) -> A) and C) -> (A -> B)) -> (((((A -> B) -> A) and C) -> (A -> B)) and ((((A -> B) -> A) and C) -> B)))), M:tm-328, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-17805
in-theory        17805
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> A))))
theorem-size     39
proof            (modus-ponens tm-328 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-17805.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> A)))), M:tm-328, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-17806
in-theory        17806
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) and (not (((A -> B) and C) -> A)))))
theorem-size     68
proof            (modus-ponens tm-328 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       208
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-17806.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) and (not (((A -> B) and C) -> A))))), M:tm-328, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-17807
in-theory        17807
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> B) -> D) and (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))))
theorem-size     65
proof            (modus-ponens tm-328 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-17807.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> B) -> D) and (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))), M:tm-328, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-17808
in-theory        17808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (A -> (A and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))))
theorem-size     41
proof            (modus-ponens tm-328 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17808.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (A -> (A and (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)))), M:tm-328, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-17809
in-theory        17809
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (((((A -> B) and C) -> A) -> ((A -> B) and C)) and ((((A -> B) and C) -> A) -> B))))
theorem-size     61
proof            (modus-ponens tm-328 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-17809.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (((((A -> B) and C) -> A) -> ((A -> B) and C)) and ((((A -> B) and C) -> A) -> B)))), M:tm-328, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-17810
in-theory        17810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (A -> (A and ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-127 ((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-17810.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (A -> (A and ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-328, m:tm-127, u:((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-17811
in-theory        17811
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and (((((A and B) -> A) -> C) and D) -> (((((A and B) -> A) -> C) and D) and C)))
theorem-size     33
proof            (modus-ponens tm-328 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-17811.        ((((((A and B) -> A) -> C) and D) -> C) and (((((A and B) -> A) -> C) and D) -> (((((A and B) -> A) -> C) and D) and C))), M:tm-328, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-17812
in-theory        17812
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((A and B) -> (A -> C)) -> (((A and B) -> (A -> C)) and ((A and B) -> C))))
theorem-size     35
proof            (modus-ponens tm-328 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-17812.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((A and B) -> (A -> C)) -> (((A and B) -> (A -> C)) and ((A and B) -> C)))), M:tm-328, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-17813
in-theory        17813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and ((A -> (not ((B and C) -> B))) -> ((A -> (not ((B and C) -> B))) and (not A))))
theorem-size     32
proof            (modus-ponens tm-328 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-3)
proof-size       142
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-17813.        (((A -> (not ((B and C) -> B))) -> (not A)) and ((A -> (not ((B and C) -> B))) -> ((A -> (not ((B and C) -> B))) and (not A)))), M:tm-328, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-17814
in-theory        17814
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((((A and B) -> A) -> C) -> ((((A and B) -> A) -> C) and ((D or ((A and B) -> A)) -> C))))
theorem-size     43
proof            (modus-ponens tm-328 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-17814.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((((A and B) -> A) -> C) -> ((((A and B) -> A) -> C) and ((D or ((A and B) -> A)) -> C)))), M:tm-328, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-17815
in-theory        17815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and (A -> (A and ((B -> ((C and D) -> C)) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17815.        ((A -> ((B -> ((C and D) -> C)) and A)) and (A -> (A and ((B -> ((C and D) -> C)) and A)))), M:tm-328, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-17816
in-theory        17816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and ((A -> (B and C)) -> ((A -> (B and C)) and (A -> B))))
theorem-size     25
proof            (modus-ponens tm-328 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-17816.        (((A -> (B and C)) -> (A -> B)) and ((A -> (B and C)) -> ((A -> (B and C)) and (A -> B)))), M:tm-328, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-17817
in-theory        17817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (A -> (A and (B -> ((C and D) -> C)))))
theorem-size     21
proof            (modus-ponens tm-328 tm-136 ((A Am) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-17817.        ((A -> (B -> ((C and D) -> C))) and (A -> (A and (B -> ((C and D) -> C))))), M:tm-328, m:tm-136, u:((A Am) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-17818
in-theory        17818
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and ((A and (A -> B)) -> ((A and (A -> B)) and B)))
theorem-size     21
proof            (modus-ponens tm-328 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-17818.        (((A and (A -> B)) -> B) and ((A and (A -> B)) -> ((A and (A -> B)) and B))), M:tm-328, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-17819
in-theory        17819
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and ((A and ((B -> (C -> B)) -> D)) -> ((A and ((B -> (C -> B)) -> D)) and D)))
theorem-size     33
proof            (modus-ponens tm-328 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-17819.        (((A and ((B -> (C -> B)) -> D)) -> D) and ((A and ((B -> (C -> B)) -> D)) -> ((A and ((B -> (C -> B)) -> D)) and D))), M:tm-328, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-17820
in-theory        17820
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) and E)))
theorem-size     57
proof            (modus-ponens tm-328 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17820.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) and E))), M:tm-328, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-17821
in-theory        17821
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and ((A and (((B and C) -> B) -> D)) -> ((A and (((B and C) -> B) -> D)) and D)))
theorem-size     33
proof            (modus-ponens tm-328 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-17821.        (((A and (((B and C) -> B) -> D)) -> D) and ((A and (((B and C) -> B) -> D)) -> ((A and (((B and C) -> B) -> D)) and D))), M:tm-328, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-17822
in-theory        17822
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((A and ((B -> C) -> B)) -> (B -> C)) -> (((A and ((B -> C) -> B)) -> (B -> C)) and ((A and ((B -> C) -> B)) -> C))))
theorem-size     55
proof            (modus-ponens tm-328 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-17822.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((A and ((B -> C) -> B)) -> (B -> C)) -> (((A and ((B -> C) -> B)) -> (B -> C)) and ((A and ((B -> C) -> B)) -> C)))), M:tm-328, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-17823
in-theory        17823
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> B))))
theorem-size     39
proof            (modus-ponens tm-328 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-17823.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> B)))), M:tm-328, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-17824
in-theory        17824
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) and (not ((A and (B -> C)) -> B)))))
theorem-size     68
proof            (modus-ponens tm-328 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       208
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-17824.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) and (not ((A and (B -> C)) -> B))))), M:tm-328, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-17825
in-theory        17825
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> C) -> D) and ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))))
theorem-size     65
proof            (modus-ponens tm-328 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-17825.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> C) -> D) and ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))), M:tm-328, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-17826
in-theory        17826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (A -> (A and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-328 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17826.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (A -> (A and ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)))), M:tm-328, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-17827
in-theory        17827
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> ((((A and (B -> C)) -> B) -> (A and (B -> C))) and (((A and (B -> C)) -> B) -> C))))
theorem-size     61
proof            (modus-ponens tm-328 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-17827.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> ((((A and (B -> C)) -> B) -> (A and (B -> C))) and (((A and (B -> C)) -> B) -> C)))), M:tm-328, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-17828
in-theory        17828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (A -> (A and (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-149 ((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-17828.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (A -> (A and (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-328, m:tm-149, u:((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-17829
in-theory        17829
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and ((A and (((B and C) -> C) -> D)) -> ((A and (((B and C) -> C) -> D)) and D)))
theorem-size     33
proof            (modus-ponens tm-328 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-17829.        (((A and (((B and C) -> C) -> D)) -> D) and ((A and (((B and C) -> C) -> D)) -> ((A and (((B and C) -> C) -> D)) and D))), M:tm-328, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-17830
in-theory        17830
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and (((((A and B) -> B) -> C) and D) -> (((((A and B) -> B) -> C) and D) and C)))
theorem-size     33
proof            (modus-ponens tm-328 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-17830.        ((((((A and B) -> B) -> C) and D) -> C) and (((((A and B) -> B) -> C) and D) -> (((((A and B) -> B) -> C) and D) and C))), M:tm-328, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-17831
in-theory        17831
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((A and B) -> (B -> C)) -> (((A and B) -> (B -> C)) and ((A and B) -> C))))
theorem-size     35
proof            (modus-ponens tm-328 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-17831.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((A and B) -> (B -> C)) -> (((A and B) -> (B -> C)) and ((A and B) -> C)))), M:tm-328, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-17832
in-theory        17832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and ((A -> (not ((B and C) -> C))) -> ((A -> (not ((B and C) -> C))) and (not A))))
theorem-size     32
proof            (modus-ponens tm-328 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-4)
proof-size       142
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17832.        (((A -> (not ((B and C) -> C))) -> (not A)) and ((A -> (not ((B and C) -> C))) -> ((A -> (not ((B and C) -> C))) and (not A)))), M:tm-328, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-17833
in-theory        17833
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((((A and B) -> B) -> C) -> ((((A and B) -> B) -> C) and ((D or ((A and B) -> B)) -> C))))
theorem-size     43
proof            (modus-ponens tm-328 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17833.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((((A and B) -> B) -> C) -> ((((A and B) -> B) -> C) and ((D or ((A and B) -> B)) -> C)))), M:tm-328, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-17834
in-theory        17834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and (A -> (A and ((B -> ((C and D) -> D)) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17834.        ((A -> ((B -> ((C and D) -> D)) and A)) and (A -> (A and ((B -> ((C and D) -> D)) and A)))), M:tm-328, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-17835
in-theory        17835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and ((A -> (B and C)) -> ((A -> (B and C)) and (A -> C))))
theorem-size     25
proof            (modus-ponens tm-328 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-17835.        (((A -> (B and C)) -> (A -> C)) and ((A -> (B and C)) -> ((A -> (B and C)) and (A -> C)))), M:tm-328, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-17836
in-theory        17836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (A -> (A and (B -> ((C and D) -> D)))))
theorem-size     21
proof            (modus-ponens tm-328 tm-159 ((A Am) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-17836.        ((A -> (B -> ((C and D) -> D))) and (A -> (A and (B -> ((C and D) -> D))))), M:tm-328, m:tm-159, u:((A Am) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-17837
in-theory        17837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((A -> (not ((B -> (C -> B)) and A))) -> ((A -> (not ((B -> (C -> B)) and A))) and (not A))))
theorem-size     38
proof            (modus-ponens tm-328 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       154
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-17837.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((A -> (not ((B -> (C -> B)) and A))) -> ((A -> (not ((B -> (C -> B)) and A))) and (not A)))), M:tm-328, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-17838
in-theory        17838
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((((A -> (B -> A)) and C) -> D) -> ((((A -> (B -> A)) and C) -> D) and ((C or ((A -> (B -> A)) and C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-328 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-17838.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((((A -> (B -> A)) and C) -> D) -> ((((A -> (B -> A)) and C) -> D) and ((C or ((A -> (B -> A)) and C)) -> D)))), M:tm-328, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-17839
in-theory        17839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (A -> (A and ((B -> ((C -> (D -> C)) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-328 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17839.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (A -> (A and ((B -> ((C -> (D -> C)) and B)) and A)))), M:tm-328, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-17840
in-theory        17840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (A -> (A and (B -> ((C -> (D -> C)) and B)))))
theorem-size     25
proof            (modus-ponens tm-328 tm-184 ((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-17840.        ((A -> (B -> ((C -> (D -> C)) and B))) and (A -> (A and (B -> ((C -> (D -> C)) and B))))), M:tm-328, m:tm-184, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-17841
in-theory        17841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (not A))))
theorem-size     62
proof            (modus-ponens tm-328 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       202
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-17841.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (not A)))), M:tm-328, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-17842
in-theory        17842
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) and ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))))
theorem-size     93
proof            (modus-ponens tm-328 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       251
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-17842.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) and ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))), M:tm-328, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-17843
in-theory        17843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (A -> (A and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))))
theorem-size     45
proof            (modus-ponens tm-328 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-2 tm-5)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17843.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (A -> (A and ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)))), M:tm-328, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-17844
in-theory        17844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (A -> (A and (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     41
proof            (modus-ponens tm-328 tm-211 ((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-17844.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (A -> (A and (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-328, m:tm-211, u:((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-17845
in-theory        17845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((A -> (not (((B and C) -> B) and A))) -> ((A -> (not (((B and C) -> B) and A))) and (not A))))
theorem-size     38
proof            (modus-ponens tm-328 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-3)
proof-size       154
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-17845.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((A -> (not (((B and C) -> B) and A))) -> ((A -> (not (((B and C) -> B) and A))) and (not A)))), M:tm-328, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-17846
in-theory        17846
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (((((A and B) -> A) and C) -> D) -> (((((A and B) -> A) and C) -> D) and ((C or (((A and B) -> A) and C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-328 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-17846.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (((((A and B) -> A) and C) -> D) -> (((((A and B) -> A) and C) -> D) and ((C or (((A and B) -> A) and C)) -> D)))), M:tm-328, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-17847
in-theory        17847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (A -> (A and ((B -> (((C and D) -> C) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-328 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17847.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (A -> (A and ((B -> (((C and D) -> C) and B)) and A)))), M:tm-328, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-17848
in-theory        17848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (A -> (A and (B -> (((C and D) -> C) and B)))))
theorem-size     25
proof            (modus-ponens tm-328 tm-240 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-17848.        ((A -> (B -> (((C and D) -> C) and B))) and (A -> (A and (B -> (((C and D) -> C) and B))))), M:tm-328, m:tm-240, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-17849
in-theory        17849
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((A -> (not (((B and C) -> C) and A))) -> ((A -> (not (((B and C) -> C) and A))) and (not A))))
theorem-size     38
proof            (modus-ponens tm-328 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-4)
proof-size       154
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17849.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((A -> (not (((B and C) -> C) and A))) -> ((A -> (not (((B and C) -> C) and A))) and (not A)))), M:tm-328, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-17850
in-theory        17850
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (((((A and B) -> B) and C) -> D) -> (((((A and B) -> B) and C) -> D) and ((C or (((A and B) -> B) and C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-328 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17850.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (((((A and B) -> B) and C) -> D) -> (((((A and B) -> B) and C) -> D) and ((C or (((A and B) -> B) and C)) -> D)))), M:tm-328, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-17851
in-theory        17851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (A -> (A and ((B -> (((C and D) -> D) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-328 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17851.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (A -> (A and ((B -> (((C and D) -> D) and B)) and A)))), M:tm-328, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-17852
in-theory        17852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (A -> (A and (B -> (((C and D) -> D) and B)))))
theorem-size     25
proof            (modus-ponens tm-328 tm-271 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-17852.        ((A -> (B -> (((C and D) -> D) and B))) and (A -> (A and (B -> (((C and D) -> D) and B))))), M:tm-328, m:tm-271, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-17853
in-theory        17853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> ((A -> (not ((B -> (C -> (B and C))) and A))) and (not A))))
theorem-size     44
proof            (modus-ponens tm-328 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       166
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17853.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> ((A -> (not ((B -> (C -> (B and C))) and A))) and (not A)))), M:tm-328, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-17854
in-theory        17854
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((((A -> (B -> (A and B))) and C) -> D) -> ((((A -> (B -> (A and B))) and C) -> D) and ((C or ((A -> (B -> (A and B))) and C)) -> D))))
theorem-size     63
proof            (modus-ponens tm-328 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17854.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((((A -> (B -> (A and B))) and C) -> D) -> ((((A -> (B -> (A and B))) and C) -> D) and ((C or ((A -> (B -> (A and B))) and C)) -> D)))), M:tm-328, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-17855
in-theory        17855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (A -> (A and ((B -> ((C -> (D -> (C and D))) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-328 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-2 tm-5)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17855.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (A -> (A and ((B -> ((C -> (D -> (C and D))) and B)) and A)))), M:tm-328, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-17856
in-theory        17856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (A -> (A and (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-304 ((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-17856.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (A -> (A and (B -> ((C -> (D -> (C and D))) and B))))), M:tm-328, m:tm-304, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-17857
in-theory        17857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (A -> (A and (A and (B -> A)))))
theorem-size     17
proof            (modus-ponens tm-328 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-17857.        ((A -> (A and (B -> A))) and (A -> (A and (A and (B -> A))))), M:tm-328, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-17858
in-theory        17858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> (B -> C)) and ((A -> B) -> (A -> C))))))
theorem-size     45
proof            (modus-ponens tm-328 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-17858.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))), M:tm-328, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-17859
in-theory        17859
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and ((A and B) -> ((A and B) and ((A and B) and A))))
theorem-size     23
proof            (modus-ponens tm-328 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-17859.        (((A and B) -> ((A and B) and A)) and ((A and B) -> ((A and B) and ((A and B) and A)))), M:tm-328, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-17860
in-theory        17860
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and ((A and B) -> ((A and B) and ((A and B) and B))))
theorem-size     23
proof            (modus-ponens tm-328 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17860.        (((A and B) -> ((A and B) and B)) and ((A and B) -> ((A and B) and ((A and B) and B)))), M:tm-328, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-17861
in-theory        17861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (A -> (A and (A and (B -> (A and B))))))
theorem-size     21
proof            (modus-ponens tm-328 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-17861.        ((A -> (A and (B -> (A and B)))) and (A -> (A and (A and (B -> (A and B)))))), M:tm-328, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-17862
in-theory        17862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (A -> (A and (A and (A or B)))))
theorem-size     17
proof            (modus-ponens tm-328 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-17862.        ((A -> (A and (A or B))) and (A -> (A and (A and (A or B))))), M:tm-328, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-17863
in-theory        17863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (A -> (A and (A and (B or A)))))
theorem-size     17
proof            (modus-ponens tm-328 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-17863.        ((A -> (A and (B or A))) and (A -> (A and (A and (B or A))))), M:tm-328, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-17864
in-theory        17864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((A -> B) -> ((A -> B) and ((A -> B) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     39
proof            (modus-ponens tm-328 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-17864.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((A -> B) -> ((A -> B) and ((A -> B) and ((B -> C) -> ((A or B) -> C)))))), M:tm-328, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-17865
in-theory        17865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((A -> B) -> ((A -> B) and ((A -> B) and ((A -> (not B)) -> (not A))))))
theorem-size     35
proof            (modus-ponens tm-328 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-17865.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((A -> B) -> ((A -> B) and ((A -> B) and ((A -> (not B)) -> (not A)))))), M:tm-328, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-17866
in-theory        17866
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and ((not (not A)) -> ((not (not A)) and ((not (not A)) and A))))
theorem-size     23
proof            (modus-ponens tm-328 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-10)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-17866.        (((not (not A)) -> ((not (not A)) and A)) and ((not (not A)) -> ((not (not A)) and ((not (not A)) and A)))), M:tm-328, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-17867
in-theory        17867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (A -> (A and (A and (B -> (C -> B))))))
theorem-size     21
proof            (modus-ponens tm-328 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-17867.        ((A -> (A and (B -> (C -> B)))) and (A -> (A and (A and (B -> (C -> B)))))), M:tm-328, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-17868
in-theory        17868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and ((A -> B) -> ((A -> B) and ((A -> B) and (A -> A)))))
theorem-size     27
proof            (modus-ponens tm-328 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-17868.        (((A -> B) -> ((A -> B) and (A -> A))) and ((A -> B) -> ((A -> B) and ((A -> B) and (A -> A))))), M:tm-328, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-17869
in-theory        17869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))))
theorem-size     69
proof            (modus-ponens tm-328 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-17869.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))), M:tm-328, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-17870
in-theory        17870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (A -> (A and (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))
theorem-size     37
proof            (modus-ponens tm-328 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-17870.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (A -> (A and (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))), M:tm-328, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-17871
in-theory        17871
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))))
theorem-size     55
proof            (modus-ponens tm-328 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-17871.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))), M:tm-328, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-17872
in-theory        17872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (A -> (A and (A and ((B and C) -> B)))))
theorem-size     21
proof            (modus-ponens tm-328 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-17872.        ((A -> (A and ((B and C) -> B))) and (A -> (A and (A and ((B and C) -> B))))), M:tm-328, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-17873
in-theory        17873
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))))
theorem-size     55
proof            (modus-ponens tm-328 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-17873.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))), M:tm-328, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-17874
in-theory        17874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (A -> (A and (A and ((B and C) -> C)))))
theorem-size     21
proof            (modus-ponens tm-328 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17874.        ((A -> (A and ((B and C) -> C))) and (A -> (A and (A and ((B and C) -> C))))), M:tm-328, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-17875
in-theory        17875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (A -> (A and (A and ((B -> (C -> B)) and A)))))
theorem-size     25
proof            (modus-ponens tm-328 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-17875.        ((A -> (A and ((B -> (C -> B)) and A))) and (A -> (A and (A and ((B -> (C -> B)) and A))))), M:tm-328, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-17876
in-theory        17876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (A -> (A and (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))))
theorem-size     41
proof            (modus-ponens tm-328 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-17876.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (A -> (A and (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))), M:tm-328, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-17877
in-theory        17877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (A -> (A and (A and (((B and C) -> B) and A)))))
theorem-size     25
proof            (modus-ponens tm-328 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-17877.        ((A -> (A and (((B and C) -> B) and A))) and (A -> (A and (A and (((B and C) -> B) and A))))), M:tm-328, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-17878
in-theory        17878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (A -> (A and (A and (((B and C) -> C) and A)))))
theorem-size     25
proof            (modus-ponens tm-328 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17878.        ((A -> (A and (((B and C) -> C) and A))) and (A -> (A and (A and (((B and C) -> C) and A))))), M:tm-328, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-17879
in-theory        17879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (A -> (A and (A and ((B -> (C -> (B and C))) and A)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-17879.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (A -> (A and (A and ((B -> (C -> (B and C))) and A))))), M:tm-328, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-17880
in-theory        17880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((A -> B) -> ((A -> B) and ((A -> B) and (A -> (A and B))))))
theorem-size     31
proof            (modus-ponens tm-328 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17880.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((A -> B) -> ((A -> B) and ((A -> B) and (A -> (A and B)))))), M:tm-328, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-17881
in-theory        17881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((C -> (D -> (C and D))) and ((A -> B) -> ((A -> B) and (A -> (A and B))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17881.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((C -> (D -> (C and D))) and ((A -> B) -> ((A -> B) and (A -> (A and B)))))), M:tm-327, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17882
in-theory        17882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (((C and D) -> D) and ((A -> B) -> ((A -> B) and (A -> (A and B))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17882.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (((C and D) -> D) and ((A -> B) -> ((A -> B) and (A -> (A and B)))))), M:tm-326, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17883
in-theory        17883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (((C and D) -> C) and ((A -> B) -> ((A -> B) and (A -> (A and B))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17883.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (((C and D) -> C) and ((A -> B) -> ((A -> B) and (A -> (A and B)))))), M:tm-325, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17884
in-theory        17884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> ((A -> B) and (A -> (A and B))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17884.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A -> B) -> ((A -> B) and (A -> (A and B)))))), M:tm-324, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17885
in-theory        17885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((C -> (D -> C)) and ((A -> B) -> ((A -> B) and (A -> (A and B))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17885.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((C -> (D -> C)) and ((A -> B) -> ((A -> B) and (A -> (A and B)))))), M:tm-323, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17886
in-theory        17886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((C and D) -> D))
theorem-size     19
proof            (modus-ponens tm-322 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17886.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((C and D) -> D)), M:tm-322, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17887
in-theory        17887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((C and D) -> C))
theorem-size     19
proof            (modus-ponens tm-320 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17887.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((C and D) -> C)), M:tm-320, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17888
in-theory        17888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-318 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17888.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17889
in-theory        17889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((A -> B) -> (A -> B)))
theorem-size     21
proof            (modus-ponens tm-316 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17889.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-17890
in-theory        17890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (C -> (D -> C)))
theorem-size     19
proof            (modus-ponens tm-315 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17890.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (C -> (D -> C))), M:tm-315, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17891
in-theory        17891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (((A -> B) -> (not ((A -> B) and (A -> (A and B))))) -> (not (A -> B))))
theorem-size     33
proof            (modus-ponens tm-313 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17891.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (((A -> B) -> (not ((A -> B) and (A -> (A and B))))) -> (not (A -> B)))), M:tm-313, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-17892
in-theory        17892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((((A -> B) and (A -> (A and B))) -> C) -> (((A -> B) or ((A -> B) and (A -> (A and B)))) -> C)))
theorem-size     41
proof            (modus-ponens tm-312 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17892.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((((A -> B) and (A -> (A and B))) -> C) -> (((A -> B) or ((A -> B) and (A -> (A and B)))) -> C))), M:tm-312, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-17893
in-theory        17893
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (C or ((A -> B) -> ((A -> B) and (A -> (A and B))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17893.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (C or ((A -> B) -> ((A -> B) and (A -> (A and B)))))), M:tm-311, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17894
in-theory        17894
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (((A -> B) -> ((A -> B) and (A -> (A and B)))) or C))
theorem-size     29
proof            (modus-ponens tm-310 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17894.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (((A -> B) -> ((A -> B) and (A -> (A and B)))) or C)), M:tm-310, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17895
in-theory        17895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (C -> (((A -> B) -> ((A -> B) and (A -> (A and B)))) and C)))
theorem-size     31
proof            (modus-ponens tm-309 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17895.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (C -> (((A -> B) -> ((A -> B) and (A -> (A and B)))) and C))), M:tm-309, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17896
in-theory        17896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (C -> ((A -> B) -> ((A -> B) and (A -> (A and B))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17896.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (C -> ((A -> B) -> ((A -> B) and (A -> (A and B)))))), M:tm-305, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17897
in-theory        17897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17897.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-303, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17898
in-theory        17898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17898.        ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-270, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17899
in-theory        17899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17899.        ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-239, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17900
in-theory        17900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((E -> F) and (E -> (E and F)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17900.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((E -> F) and (E -> (E and F))))), M:tm-210, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17901
in-theory        17901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17901.        ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-183, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17902
in-theory        17902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17902.        ((A -> ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-157, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17903
in-theory        17903
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((B and C) -> ((B and C) and C))))
theorem-size     23
proof            (modus-ponens tm-154 tm-328 ((Am (and A Bm)) (B Bm) (C (and (-> (and A Bm) Bm) (-> (and A Bm) (and (and A Bm) Bm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17903.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((B and C) -> ((B and C) and C)))), M:tm-154, m:tm-328, u:((Am (and A Bm)) (B Bm) (C (and (-> (and A Bm) Bm) (-> (and A Bm) (and (and A Bm) Bm)))))
================================================================
tm-name          tm-17904
in-theory        17904
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17904.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-147, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17905
in-theory        17905
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((A and (B -> C)) -> ((A and (B -> C)) and C))))
theorem-size     37
proof            (modus-ponens tm-144 tm-328 ((Am (and A (-> B Bm))) (C Bm) (D (and (-> (and A (-> B Bm)) Bm) (-> (and A (-> B Bm)) (and (and A (-> B Bm)) Bm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17905.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((A and (B -> C)) -> ((A and (B -> C)) and C)))), M:tm-144, m:tm-328, u:((Am (and A (-> B Bm))) (C Bm) (D (and (-> (and A (-> B Bm)) Bm) (-> (and A (-> B Bm)) (and (and A (-> B Bm)) Bm)))))
================================================================
tm-name          tm-17906
in-theory        17906
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17906.        ((A -> ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-134, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17907
in-theory        17907
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((B and C) -> ((B and C) and B))))
theorem-size     23
proof            (modus-ponens tm-131 tm-328 ((Am (and Bm B)) (A Bm) (C (and (-> (and Bm B) Bm) (-> (and Bm B) (and (and Bm B) Bm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17907.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((B and C) -> ((B and C) and B)))), M:tm-131, m:tm-328, u:((Am (and Bm B)) (A Bm) (C (and (-> (and Bm B) Bm) (-> (and Bm B) (and (and Bm B) Bm)))))
================================================================
tm-name          tm-17908
in-theory        17908
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17908.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-125, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17909
in-theory        17909
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (((A -> B) and C) -> (((A -> B) and C) and B))))
theorem-size     37
proof            (modus-ponens tm-122 tm-328 ((Am (and (-> A Bm) C)) (B Bm) (D (and (-> (and (-> A Bm) C) Bm) (-> (and (-> A Bm) C) (and (and (-> A Bm) C) Bm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17909.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (((A -> B) and C) -> (((A -> B) and C) and B)))), M:tm-122, m:tm-328, u:((Am (and (-> A Bm) C)) (B Bm) (D (and (-> (and (-> A Bm) C) Bm) (-> (and (-> A Bm) C) (and (and (-> A Bm) C) Bm)))))
================================================================
tm-name          tm-17910
in-theory        17910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (E -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17910.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (E -> (E and F))))), M:tm-113, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17911
in-theory        17911
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((B -> (C -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-110 tm-328 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (-> A (-> B C)) (and (-> A (-> B C)) (-> (-> A B) (-> A C))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17911.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((B -> (C -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D)))))), M:tm-110, m:tm-328, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (-> A (-> B C)) (and (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
================================================================
tm-name          tm-17912
in-theory        17912
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17912.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-105, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17913
in-theory        17913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((A -> (B -> C)) -> ((A -> (B -> C)) and (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-102 tm-328 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (-> A (-> B C)) (and (-> A (-> B C)) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17913.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((A -> (B -> C)) -> ((A -> (B -> C)) and (A -> C))))), M:tm-102, m:tm-328, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (-> A (-> B C)) (and (-> A (-> B C)) (-> A C))))))
================================================================
tm-name          tm-17914
in-theory        17914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> ((C -> D) and (C -> (C and D)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17914.        (((A -> B) -> (A -> A)) and ((C -> D) -> ((C -> D) and (C -> (C and D))))), M:tm-95, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17915
in-theory        17915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and (A -> (A and A))))
theorem-size     17
proof            (modus-ponens tm-92 tm-328 ((Bm Am) (A Am) (B (and (-> Am Am) (-> Am (and Am Am))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17915.        (((A -> B) or (A -> A)) -> ((A -> A) and (A -> (A and A)))), M:tm-92, m:tm-328, u:((Bm Am) (A Am) (B (and (-> Am Am) (-> Am (and Am Am)))))
================================================================
tm-name          tm-17916
in-theory        17916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((A -> B) and (A -> (A and B)))))
theorem-size     15
proof            (modus-ponens tm-84 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17916.        ((A -> B) -> (C -> ((A -> B) and (A -> (A and B))))), M:tm-84, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-17917
in-theory        17917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17917.        ((A -> (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-83, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17918
in-theory        17918
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (B -> (B and (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-80 tm-328 ((A Am) (Bm (-> B Am)) (C (and (-> Am (-> B Am)) (-> Am (and Am (-> B Am)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17918.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (B -> (B and (C -> B))))), M:tm-80, m:tm-328, u:((A Am) (Bm (-> B Am)) (C (and (-> Am (-> B Am)) (-> Am (and Am (-> B Am))))))
================================================================
tm-name          tm-17919
in-theory        17919
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> ((B -> C) and (B -> (B and C)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17919.        (((not (not A)) -> A) and ((B -> C) -> ((B -> C) and (B -> (B and C))))), M:tm-76, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17920
in-theory        17920
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> ((A -> B) and (A -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-73 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17920.        (((not (not (A -> B))) or (A -> B)) -> ((A -> B) and (A -> (A and B)))), M:tm-73, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-17921
in-theory        17921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((C -> D) and (C -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17921.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((C -> D) and (C -> (C and D))))), M:tm-69, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17922
in-theory        17922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((A -> (not B)) -> ((A -> (not B)) and (not A)))))
theorem-size     32
proof            (modus-ponens tm-66 tm-328 ((Am (-> A (not B))) (Bm (not A)) (C (and (-> (-> A (not B)) (not A)) (-> (-> A (not B)) (and (-> A (not B)) (not A)))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5)
proof-size       150
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17922.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((A -> (not B)) -> ((A -> (not B)) and (not A))))), M:tm-66, m:tm-328, u:((Am (-> A (not B))) (Bm (not A)) (C (and (-> (-> A (not B)) (not A)) (-> (-> A (not B)) (and (-> A (not B)) (not A))))))
================================================================
tm-name          tm-17923
in-theory        17923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17923.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-54, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17924
in-theory        17924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((B -> C) -> ((B -> C) and ((A or B) -> C)))))
theorem-size     37
proof            (modus-ponens tm-51 tm-328 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (-> A B) (and (-> A B) (-> (or C A) B)))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17924.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((B -> C) -> ((B -> C) and ((A or B) -> C))))), M:tm-51, m:tm-328, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (-> A B) (and (-> A B) (-> (or C A) B))))))
================================================================
tm-name          tm-17925
in-theory        17925
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (B -> (B and (A and B)))))
theorem-size     21
proof            (modus-ponens tm-48 tm-328 ((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> Am (and Am (and B Am)))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17925.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (B -> (B and (A and B))))), M:tm-48, m:tm-328, u:((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> Am (and Am (and B Am))))))
================================================================
tm-name          tm-17926
in-theory        17926
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((B -> C) and (B -> (B and C))))
theorem-size     19
proof            (modus-ponens tm-47 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17926.        (((A and (B -> C)) or (B -> C)) -> ((B -> C) and (B -> (B and C)))), M:tm-47, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-17927
in-theory        17927
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((A -> B) and (A -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-46 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17927.        ((((A -> B) and C) or (A -> B)) -> ((A -> B) and (A -> (A and B)))), M:tm-46, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-17928
in-theory        17928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((A -> B) -> ((A -> B) and (A -> C)))))
theorem-size     33
proof            (modus-ponens tm-45 tm-328 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> A B) (and (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17928.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((A -> B) -> ((A -> B) and (A -> C))))), M:tm-45, m:tm-328, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> A B) (and (-> A B) (-> A C))))))
================================================================
tm-name          tm-17929
in-theory        17929
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (B -> (B and A))))
theorem-size     15
proof            (modus-ponens tm-44 tm-328 ((A Am) (B Bm) (C (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17929.        ((A or (B -> A)) -> ((B -> A) and (B -> (B and A)))), M:tm-44, m:tm-328, u:((A Am) (B Bm) (C (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-17930
in-theory        17930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> ((C -> D) and (C -> (C and D)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17930.        ((A -> (B or A)) and ((C -> D) -> ((C -> D) and (C -> (C and D))))), M:tm-42, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17931
in-theory        17931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> ((C -> D) and (C -> (C and D)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17931.        ((A -> (A or B)) and ((C -> D) -> ((C -> D) and (C -> (C and D))))), M:tm-32, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17932
in-theory        17932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((A -> B) and (A -> (A and B)))))
theorem-size     17
proof            (modus-ponens tm-24 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17932.        ((A -> B) -> ((A -> B) and ((A -> B) and (A -> (A and B))))), M:tm-24, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-17933
in-theory        17933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> D) and (C -> (C and D)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-2)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17933.        ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> D) and (C -> (C and D))))), M:tm-23, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17934
in-theory        17934
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> ((C -> D) and (C -> (C and D)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17934.        (((A and B) -> B) and ((C -> D) -> ((C -> D) and (C -> (C and D))))), M:tm-22, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17935
in-theory        17935
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> ((C -> D) and (C -> (C and D)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17935.        (((A and B) -> A) and ((C -> D) -> ((C -> D) and (C -> (C and D))))), M:tm-21, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17936
in-theory        17936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17936.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-20, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17937
in-theory        17937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> ((C -> D) and (C -> (C and D)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17937.        ((A -> (B -> A)) and ((C -> D) -> ((C -> D) and (C -> (C and D))))), M:tm-19, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17938
in-theory        17938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((A -> B) and (A -> (A and B))))) -> (not (A -> B)))
theorem-size     19
proof            (modus-ponens tm-9 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-9 tm-2 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17938.        (((A -> B) -> (not ((A -> B) and (A -> (A and B))))) -> (not (A -> B))), M:tm-9, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-17939
in-theory        17939
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and (A -> (A and B))) -> C) -> (((A -> B) or ((A -> B) and (A -> (A and B)))) -> C))
theorem-size     27
proof            (modus-ponens tm-8 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17939.        ((((A -> B) and (A -> (A and B))) -> C) -> (((A -> B) or ((A -> B) and (A -> (A and B)))) -> C)), M:tm-8, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-17940
in-theory        17940
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> C) -> ((B -> C) and (B -> (B and C)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-7 tm-2 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17940.        (A or ((B -> C) -> ((B -> C) and (B -> (B and C))))), M:tm-7, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17941
in-theory        17941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) or C)
theorem-size     15
proof            (modus-ponens tm-6 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-6 tm-2 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17941.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) or C), M:tm-6, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17942
in-theory        17942
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((B -> C) and (B -> (B and C)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17942.        (A -> (((B -> C) -> ((B -> C) and (B -> (B and C)))) and A)), M:tm-5, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17943
in-theory        17943
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> ((B -> C) and (B -> (B and C)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-17943.        (A -> ((B -> C) -> ((B -> C) and (B -> (B and C))))), M:tm-1, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-17944
in-theory        17944
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17944.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))))), M:tm-327, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17945
in-theory        17945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> F) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17945.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> F) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))))), M:tm-326, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17946
in-theory        17946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> E) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17946.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> E) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))))), M:tm-325, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17947
in-theory        17947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17947.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))))), M:tm-324, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17948
in-theory        17948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17948.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> E)) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))))), M:tm-323, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17949
in-theory        17949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17949.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17950
in-theory        17950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17950.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17951
in-theory        17951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17951.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17952
in-theory        17952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17952.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17953
in-theory        17953
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (E or ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17953.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (E or ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))))), M:tm-311, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17954
in-theory        17954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17954.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) or E)), M:tm-310, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17955
in-theory        17955
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (E -> (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17955.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (E -> (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and E))), M:tm-309, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17956
in-theory        17956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((C -> D) -> (C -> (C and D))))
theorem-size     27
proof            (modus-ponens tm-308 tm-329 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17956.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((C -> D) -> (C -> (C and D)))), M:tm-308, m:tm-329, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))
================================================================
tm-name          tm-17957
in-theory        17957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (A -> (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-307 tm-329 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17957.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-329, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))
================================================================
tm-name          tm-17958
in-theory        17958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (E -> ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17958.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (E -> ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))))), M:tm-305, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17959
in-theory        17959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-303 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17959.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-303, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17960
in-theory        17960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-270 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17960.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-270, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17961
in-theory        17961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-239 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17961.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-239, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17962
in-theory        17962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-210 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17962.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H))))), M:tm-210, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17963
in-theory        17963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-183 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17963.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-183, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17964
in-theory        17964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-157 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17964.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-157, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17965
in-theory        17965
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-147 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17965.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-147, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17966
in-theory        17966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-134 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17966.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-134, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17967
in-theory        17967
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-125 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17967.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-125, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17968
in-theory        17968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-113 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17968.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H))))), M:tm-113, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17969
in-theory        17969
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     37
proof            (modus-ponens tm-105 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17969.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-105, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17970
in-theory        17970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-95 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17970.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F))))), M:tm-95, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17971
in-theory        17971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-83 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17971.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-83, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17972
in-theory        17972
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> E) -> (D -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-76 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17972.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> E) -> (D -> (D and E))))), M:tm-76, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17973
in-theory        17973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-69 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17973.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F))))), M:tm-69, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17974
in-theory        17974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-54 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17974.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-54, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17975
in-theory        17975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-42 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17975.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F))))), M:tm-42, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17976
in-theory        17976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-32 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17976.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F))))), M:tm-32, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17977
in-theory        17977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-23 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17977.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F))))), M:tm-23, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17978
in-theory        17978
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-22 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17978.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F))))), M:tm-22, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17979
in-theory        17979
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-21 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17979.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F))))), M:tm-21, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17980
in-theory        17980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-20 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17980.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-20, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17981
in-theory        17981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-19 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17981.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F))))), M:tm-19, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17982
in-theory        17982
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((D -> E) -> (D -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-7 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17982.        (A or ((B -> (C -> (B and C))) and ((D -> E) -> (D -> (D and E))))), M:tm-7, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17983
in-theory        17983
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17983.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) or E), M:tm-6, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17984
in-theory        17984
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((D -> E) -> (D -> (D and E)))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17984.        (A -> (((B -> (C -> (B and C))) and ((D -> E) -> (D -> (D and E)))) and A)), M:tm-5, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17985
in-theory        17985
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((D -> E) -> (D -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-1 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17985.        (A -> ((B -> (C -> (B and C))) and ((D -> E) -> (D -> (D and E))))), M:tm-1, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17986
in-theory        17986
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> (E and F))) and (((A and B) -> B) and ((C -> D) -> (C -> (C and D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17986.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> (E and F))) and (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))))), M:tm-327, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17987
in-theory        17987
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> F) and (((A and B) -> B) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17987.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> F) and (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))))), M:tm-326, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17988
in-theory        17988
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> E) and (((A and B) -> B) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17988.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> E) and (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))))), M:tm-325, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17989
in-theory        17989
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and ((C -> D) -> (C -> (C and D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17989.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))))), M:tm-324, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17990
in-theory        17990
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> E)) and (((A and B) -> B) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17990.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> E)) and (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))))), M:tm-323, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17991
in-theory        17991
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17991.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17992
in-theory        17992
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17992.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17993
in-theory        17993
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17993.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17994
in-theory        17994
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17994.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17995
in-theory        17995
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (E or (((A and B) -> B) and ((C -> D) -> (C -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17995.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (E or (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))))), M:tm-311, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17996
in-theory        17996
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17996.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) or E)), M:tm-310, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17997
in-theory        17997
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (E -> ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17997.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (E -> ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and E))), M:tm-309, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-17998
in-theory        17998
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((C -> D) -> (C -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-308 tm-330 ((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17998.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((C -> D) -> (C -> (C and D)))), M:tm-308, m:tm-330, u:((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))
================================================================
tm-name          tm-17999
in-theory        17999
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((A and B) -> B))
theorem-size     21
proof            (modus-ponens tm-307 tm-330 ((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-17999.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((A and B) -> B)), M:tm-307, m:tm-330, u:((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))
================================================================
tm-name          tm-18000
in-theory        18000
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (E -> (((A and B) -> B) and ((C -> D) -> (C -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18000.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (E -> (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))))), M:tm-305, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18001
in-theory        18001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18001.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-303, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18002
in-theory        18002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18002.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-270, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18003
in-theory        18003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18003.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-239, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18004
in-theory        18004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18004.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H))))), M:tm-210, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18005
in-theory        18005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18005.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-183, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18006
in-theory        18006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18006.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-157, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18007
in-theory        18007
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18007.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-147, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18008
in-theory        18008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18008.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-134, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18009
in-theory        18009
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18009.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-125, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18010
in-theory        18010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18010.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H))))), M:tm-113, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18011
in-theory        18011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18011.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-105, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18012
in-theory        18012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18012.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F))))), M:tm-95, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18013
in-theory        18013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18013.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-83, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18014
in-theory        18014
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((D -> E) -> (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-4 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18014.        (((not (not A)) -> A) and (((B and C) -> C) and ((D -> E) -> (D -> (D and E))))), M:tm-76, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18015
in-theory        18015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-4 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18015.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F))))), M:tm-69, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18016
in-theory        18016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18016.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-54, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18017
in-theory        18017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18017.        ((A -> (B or A)) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F))))), M:tm-42, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18018
in-theory        18018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18018.        ((A -> (A or B)) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F))))), M:tm-32, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18019
in-theory        18019
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18019.        ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F))))), M:tm-23, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18020
in-theory        18020
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18020.        (((A and B) -> B) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F))))), M:tm-22, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18021
in-theory        18021
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18021.        (((A and B) -> A) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F))))), M:tm-21, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18022
in-theory        18022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18022.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-20, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18023
in-theory        18023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18023.        ((A -> (B -> A)) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F))))), M:tm-19, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18024
in-theory        18024
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-7 tm-5 tm-4 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18024.        (A or (((B and C) -> C) and ((D -> E) -> (D -> (D and E))))), M:tm-7, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18025
in-theory        18025
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-6 tm-5 tm-4 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18025.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) or E), M:tm-6, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18026
in-theory        18026
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((D -> E) -> (D -> (D and E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18026.        (A -> ((((B and C) -> C) and ((D -> E) -> (D -> (D and E)))) and A)), M:tm-5, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18027
in-theory        18027
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-1 tm-5 tm-4 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18027.        (A -> (((B and C) -> C) and ((D -> E) -> (D -> (D and E))))), M:tm-1, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18028
in-theory        18028
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> (E and F))) and (((A and B) -> A) and ((C -> D) -> (C -> (C and D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18028.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> (E and F))) and (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))))), M:tm-327, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18029
in-theory        18029
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> F) and (((A and B) -> A) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18029.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> F) and (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))))), M:tm-326, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18030
in-theory        18030
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> E) and (((A and B) -> A) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18030.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> E) and (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))))), M:tm-325, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18031
in-theory        18031
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and ((C -> D) -> (C -> (C and D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18031.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))))), M:tm-324, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18032
in-theory        18032
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> E)) and (((A and B) -> A) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18032.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> E)) and (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))))), M:tm-323, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18033
in-theory        18033
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18033.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18034
in-theory        18034
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18034.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18035
in-theory        18035
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18035.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18036
in-theory        18036
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18036.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18037
in-theory        18037
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (E or (((A and B) -> A) and ((C -> D) -> (C -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18037.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (E or (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))))), M:tm-311, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18038
in-theory        18038
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18038.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) or E)), M:tm-310, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18039
in-theory        18039
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (E -> ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18039.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (E -> ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and E))), M:tm-309, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18040
in-theory        18040
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((C -> D) -> (C -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-308 tm-331 ((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18040.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((C -> D) -> (C -> (C and D)))), M:tm-308, m:tm-331, u:((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))
================================================================
tm-name          tm-18041
in-theory        18041
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((A and B) -> A))
theorem-size     21
proof            (modus-ponens tm-307 tm-331 ((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18041.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((A and B) -> A)), M:tm-307, m:tm-331, u:((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))
================================================================
tm-name          tm-18042
in-theory        18042
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (E -> (((A and B) -> A) and ((C -> D) -> (C -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18042.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (E -> (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))))), M:tm-305, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18043
in-theory        18043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18043.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-303, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18044
in-theory        18044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18044.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-270, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18045
in-theory        18045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18045.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-239, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18046
in-theory        18046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18046.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H))))), M:tm-210, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18047
in-theory        18047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18047.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-183, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18048
in-theory        18048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18048.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-157, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18049
in-theory        18049
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18049.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-147, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18050
in-theory        18050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18050.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-134, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18051
in-theory        18051
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18051.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-125, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18052
in-theory        18052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18052.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H))))), M:tm-113, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18053
in-theory        18053
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18053.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-105, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18054
in-theory        18054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18054.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F))))), M:tm-95, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18055
in-theory        18055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18055.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-83, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18056
in-theory        18056
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((D -> E) -> (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-3 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18056.        (((not (not A)) -> A) and (((B and C) -> B) and ((D -> E) -> (D -> (D and E))))), M:tm-76, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18057
in-theory        18057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-3 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18057.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F))))), M:tm-69, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18058
in-theory        18058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18058.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-54, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18059
in-theory        18059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18059.        ((A -> (B or A)) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F))))), M:tm-42, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18060
in-theory        18060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18060.        ((A -> (A or B)) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F))))), M:tm-32, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18061
in-theory        18061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18061.        ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F))))), M:tm-23, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18062
in-theory        18062
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18062.        (((A and B) -> B) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F))))), M:tm-22, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18063
in-theory        18063
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18063.        (((A and B) -> A) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F))))), M:tm-21, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18064
in-theory        18064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18064.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-20, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18065
in-theory        18065
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18065.        ((A -> (B -> A)) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F))))), M:tm-19, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18066
in-theory        18066
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-7 tm-5 tm-3 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18066.        (A or (((B and C) -> B) and ((D -> E) -> (D -> (D and E))))), M:tm-7, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18067
in-theory        18067
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-6 tm-5 tm-3 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18067.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) or E), M:tm-6, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18068
in-theory        18068
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((D -> E) -> (D -> (D and E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18068.        (A -> ((((B and C) -> B) and ((D -> E) -> (D -> (D and E)))) and A)), M:tm-5, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18069
in-theory        18069
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-1 tm-5 tm-3 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18069.        (A -> (((B and C) -> B) and ((D -> E) -> (D -> (D and E))))), M:tm-1, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18070
in-theory        18070
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     55
proof            (modus-ponens tm-327 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18070.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-327, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18071
in-theory        18071
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     53
proof            (modus-ponens tm-326 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18071.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (((F and G) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-326, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18072
in-theory        18072
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     53
proof            (modus-ponens tm-325 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18072.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (((F and G) -> F) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-325, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18073
in-theory        18073
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     61
proof            (modus-ponens tm-324 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18073.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-324, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18074
in-theory        18074
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     53
proof            (modus-ponens tm-323 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18074.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G -> F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-323, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18075
in-theory        18075
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F and G) -> G))
theorem-size     29
proof            (modus-ponens tm-322 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18075.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F and G) -> G)), M:tm-322, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18076
in-theory        18076
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F and G) -> F))
theorem-size     29
proof            (modus-ponens tm-320 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18076.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F and G) -> F)), M:tm-320, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18077
in-theory        18077
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-318 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18077.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18078
in-theory        18078
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (G -> F)))
theorem-size     29
proof            (modus-ponens tm-315 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18078.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (G -> F))), M:tm-315, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18079
in-theory        18079
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-311 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18079.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-311, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18080
in-theory        18080
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) or F))
theorem-size     49
proof            (modus-ponens tm-310 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18080.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) or F)), M:tm-310, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18081
in-theory        18081
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and F)))
theorem-size     51
proof            (modus-ponens tm-309 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18081.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and F))), M:tm-309, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18082
in-theory        18082
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((D -> E) -> (D -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-308 tm-332 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> Dm (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18082.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((D -> E) -> (D -> (D and E)))), M:tm-308, m:tm-332, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> Dm (and Dm Em)))))
================================================================
tm-name          tm-18083
in-theory        18083
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-332 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> Dm (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18083.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-332, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> Dm (and Dm Em)))))
================================================================
tm-name          tm-18084
in-theory        18084
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-305 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18084.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-305, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18085
in-theory        18085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-303 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18085.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-303, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18086
in-theory        18086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-270 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18086.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-270, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18087
in-theory        18087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-239 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18087.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-239, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18088
in-theory        18088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> (H and I)))))
theorem-size     41
proof            (modus-ponens tm-210 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18088.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-210, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18089
in-theory        18089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-183 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18089.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-183, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18090
in-theory        18090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-157 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18090.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-157, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18091
in-theory        18091
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-147 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18091.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-147, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18092
in-theory        18092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-134 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18092.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-134, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18093
in-theory        18093
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-125 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18093.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-125, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18094
in-theory        18094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> (H and I)))))
theorem-size     39
proof            (modus-ponens tm-113 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18094.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-113, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18095
in-theory        18095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     43
proof            (modus-ponens tm-105 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18095.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-105, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18096
in-theory        18096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-95 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18096.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-95, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18097
in-theory        18097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-83 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18097.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-83, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18098
in-theory        18098
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-76 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18098.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> (E and F))))), M:tm-76, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18099
in-theory        18099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     35
proof            (modus-ponens tm-69 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18099.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-69, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18100
in-theory        18100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-54 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18100.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-54, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18101
in-theory        18101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-42 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18101.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-42, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18102
in-theory        18102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-32 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18102.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-32, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18103
in-theory        18103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-23 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18103.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-23, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18104
in-theory        18104
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-22 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18104.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-22, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18105
in-theory        18105
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-21 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18105.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-21, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18106
in-theory        18106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-20 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18106.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-20, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18107
in-theory        18107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-19 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18107.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-19, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18108
in-theory        18108
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-7 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18108.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> (E and F))))), M:tm-7, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18109
in-theory        18109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) or F)
theorem-size     25
proof            (modus-ponens tm-6 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18109.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) or F), M:tm-6, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18110
in-theory        18110
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> (E and F)))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18110.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> (E and F)))) and A)), M:tm-5, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18111
in-theory        18111
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-1 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18111.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (E -> (E and F))))), M:tm-1, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18112
in-theory        18112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18112.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-327, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18113
in-theory        18113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> F) and ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18113.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> F) and ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-326, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18114
in-theory        18114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> E) and ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18114.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> E) and ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-325, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18115
in-theory        18115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18115.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-324, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18116
in-theory        18116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> E)) and ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18116.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> E)) and ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-323, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18117
in-theory        18117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18117.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18118
in-theory        18118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18118.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18119
in-theory        18119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18119.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18120
in-theory        18120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18120.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18121
in-theory        18121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (E or ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18121.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (E or ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-311, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18122
in-theory        18122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18122.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) or E)), M:tm-310, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18123
in-theory        18123
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18123.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and E))), M:tm-309, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18124
in-theory        18124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((C -> D) -> (C -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-308 tm-333 ((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18124.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((C -> D) -> (C -> (C and D)))), M:tm-308, m:tm-333, u:((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))
================================================================
tm-name          tm-18125
in-theory        18125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (A -> (B -> A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-333 ((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18125.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (A -> (B -> A))), M:tm-307, m:tm-333, u:((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))
================================================================
tm-name          tm-18126
in-theory        18126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (E -> ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18126.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (E -> ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-305, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18127
in-theory        18127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18127.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-303, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18128
in-theory        18128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18128.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-270, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18129
in-theory        18129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18129.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-239, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18130
in-theory        18130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18130.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H))))), M:tm-210, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18131
in-theory        18131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18131.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-183, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18132
in-theory        18132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18132.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-157, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18133
in-theory        18133
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18133.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-147, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18134
in-theory        18134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18134.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-134, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18135
in-theory        18135
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18135.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-125, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18136
in-theory        18136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18136.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H))))), M:tm-113, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18137
in-theory        18137
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18137.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-105, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18138
in-theory        18138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18138.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F))))), M:tm-95, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18139
in-theory        18139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18139.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-83, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18140
in-theory        18140
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> E) -> (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18140.        (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> E) -> (D -> (D and E))))), M:tm-76, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18141
in-theory        18141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18141.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F))))), M:tm-69, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18142
in-theory        18142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18142.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-54, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18143
in-theory        18143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18143.        ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F))))), M:tm-42, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18144
in-theory        18144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18144.        ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F))))), M:tm-32, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18145
in-theory        18145
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18145.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F))))), M:tm-23, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18146
in-theory        18146
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18146.        (((A and B) -> B) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F))))), M:tm-22, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18147
in-theory        18147
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18147.        (((A and B) -> A) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F))))), M:tm-21, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18148
in-theory        18148
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18148.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-20, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18149
in-theory        18149
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18149.        ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F))))), M:tm-19, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18150
in-theory        18150
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-7 tm-5 tm-1 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18150.        (A or ((B -> (C -> B)) and ((D -> E) -> (D -> (D and E))))), M:tm-7, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18151
in-theory        18151
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-6 tm-5 tm-1 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18151.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) or E), M:tm-6, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18152
in-theory        18152
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((D -> E) -> (D -> (D and E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18152.        (A -> (((B -> (C -> B)) and ((D -> E) -> (D -> (D and E)))) and A)), M:tm-5, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18153
in-theory        18153
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18153.        (A -> ((B -> (C -> B)) and ((D -> E) -> (D -> (D and E))))), M:tm-1, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18154
in-theory        18154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((A -> B) -> (not (A -> (A and B)))) -> (((A -> B) -> (not (A -> (A and B)))) and (not (A -> B)))))
theorem-size     42
proof            (modus-ponens tm-328 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       168
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18154.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((A -> B) -> (not (A -> (A and B)))) -> (((A -> B) -> (not (A -> (A and B)))) and (not (A -> B))))), M:tm-328, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-18155
in-theory        18155
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((C -> (D -> (C and D))) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18155.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((C -> (D -> (C and D))) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))))), M:tm-327, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18156
in-theory        18156
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((C and D) -> D) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18156.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((C and D) -> D) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))))), M:tm-326, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18157
in-theory        18157
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((C and D) -> C) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18157.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((C and D) -> C) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))))), M:tm-325, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18158
in-theory        18158
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18158.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))))), M:tm-324, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18159
in-theory        18159
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((C -> (D -> C)) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18159.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((C -> (D -> C)) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))))), M:tm-323, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18160
in-theory        18160
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((C and D) -> D))
theorem-size     21
proof            (modus-ponens tm-322 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18160.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((C and D) -> D)), M:tm-322, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18161
in-theory        18161
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((C and D) -> C))
theorem-size     21
proof            (modus-ponens tm-320 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18161.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((C and D) -> C)), M:tm-320, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18162
in-theory        18162
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-318 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18162.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18163
in-theory        18163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((A -> B) -> (not (A -> (A and B)))) -> ((A -> B) -> (not (A -> (A and B))))))
theorem-size     37
proof            (modus-ponens tm-316 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18163.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((A -> B) -> (not (A -> (A and B)))) -> ((A -> B) -> (not (A -> (A and B)))))), M:tm-316, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-18164
in-theory        18164
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (C -> (D -> C)))
theorem-size     21
proof            (modus-ponens tm-315 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18164.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (C -> (D -> C))), M:tm-315, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18165
in-theory        18165
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((((A -> B) -> (not (A -> (A and B)))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (A -> (A and B)))))))
theorem-size     44
proof            (modus-ponens tm-313 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18165.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((((A -> B) -> (not (A -> (A and B)))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (A -> (A and B))))))), M:tm-313, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-18166
in-theory        18166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((not (A -> B)) -> C) -> ((((A -> B) -> (not (A -> (A and B)))) or (not (A -> B))) -> C)))
theorem-size     40
proof            (modus-ponens tm-312 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18166.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((not (A -> B)) -> C) -> ((((A -> B) -> (not (A -> (A and B)))) or (not (A -> B))) -> C))), M:tm-312, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-18167
in-theory        18167
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (C or (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18167.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (C or (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))))), M:tm-311, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18168
in-theory        18168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) or C))
theorem-size     33
proof            (modus-ponens tm-310 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18168.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) or C)), M:tm-310, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18169
in-theory        18169
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (C -> ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and C)))
theorem-size     35
proof            (modus-ponens tm-309 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18169.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (C -> ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and C))), M:tm-309, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18170
in-theory        18170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (C -> (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18170.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (C -> (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))))), M:tm-305, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18171
in-theory        18171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-303 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18171.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-303, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18172
in-theory        18172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-270 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18172.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-270, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18173
in-theory        18173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-239 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18173.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-239, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18174
in-theory        18174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-210 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18174.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F)))), M:tm-210, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18175
in-theory        18175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-183 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18175.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-183, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18176
in-theory        18176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-157 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18176.        ((A -> ((B and C) -> C)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-157, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18177
in-theory        18177
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not ((A and B) -> ((A and B) and B)))))
theorem-size     17
proof            (modus-ponens tm-153 tm-334 ((A (-> (-> (and B Bm) Bm) (not (-> (and B Bm) (and (and B Bm) Bm))))) (Am (and B Bm)) (C Bm)))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18177.        (not (((A and B) -> B) -> (not ((A and B) -> ((A and B) and B))))), M:tm-153, m:tm-334, u:((A (-> (-> (and B Bm) Bm) (not (-> (and B Bm) (and (and B Bm) Bm))))) (Am (and B Bm)) (C Bm))
================================================================
tm-name          tm-18178
in-theory        18178
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-147 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18178.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-147, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18179
in-theory        18179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-134 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18179.        ((A -> ((B and C) -> B)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-134, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18180
in-theory        18180
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not ((A and B) -> ((A and B) and A)))))
theorem-size     17
proof            (modus-ponens tm-130 tm-334 ((A (-> (-> (and Bm C) Bm) (not (-> (and Bm C) (and (and Bm C) Bm))))) (Am (and Bm C)) (B Bm)))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18180.        (not (((A and B) -> A) -> (not ((A and B) -> ((A and B) and A))))), M:tm-130, m:tm-334, u:((A (-> (-> (and Bm C) Bm) (not (-> (and Bm C) (and (and Bm C) Bm))))) (Am (and Bm C)) (B Bm))
================================================================
tm-name          tm-18181
in-theory        18181
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-125 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18181.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-125, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18182
in-theory        18182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F))))
theorem-size     31
proof            (modus-ponens tm-113 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18182.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F)))), M:tm-113, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18183
in-theory        18183
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))))
theorem-size     35
proof            (modus-ponens tm-109 tm-334 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (-> B (-> C D)) (and (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> B (-> C D))) (Bm (-> (-> B C) (-> B D)))))
axioms-used      (tm-9 tm-1 tm-2 tm-5)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18183.        (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))))), M:tm-109, m:tm-334, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (-> B (-> C D)) (and (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> B (-> C D))) (Bm (-> (-> B C) (-> B D))))
================================================================
tm-name          tm-18184
in-theory        18184
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     35
proof            (modus-ponens tm-105 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18184.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-105, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18185
in-theory        18185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-95 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18185.        (((A -> B) -> (A -> A)) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D)))), M:tm-95, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18186
in-theory        18186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (A and B)))) -> (C -> (not (A -> B))))
theorem-size     17
proof            (modus-ponens tm-84 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18186.        (((A -> B) -> (not (A -> (A and B)))) -> (C -> (not (A -> B)))), M:tm-84, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-18187
in-theory        18187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-83 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18187.        ((A -> (B -> (C -> B))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-83, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18188
in-theory        18188
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (A -> (A and (B -> A))))))
theorem-size     15
proof            (modus-ponens tm-79 tm-334 ((A (-> (-> Am (-> C Am)) (not (-> Am (and Am (-> C Am)))))) (B Am) (Bm (-> C Am))))
axioms-used      (tm-9 tm-1 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18188.        (not ((A -> (B -> A)) -> (not (A -> (A and (B -> A)))))), M:tm-79, m:tm-334, u:((A (-> (-> Am (-> C Am)) (not (-> Am (and Am (-> C Am)))))) (B Am) (Bm (-> C Am)))
================================================================
tm-name          tm-18189
in-theory        18189
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> (not (B -> (B and C)))) -> (not (B -> C))))
theorem-size     21
proof            (modus-ponens tm-76 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-10 tm-9 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18189.        (((not (not A)) -> A) and (((B -> C) -> (not (B -> (B and C)))) -> (not (B -> C)))), M:tm-76, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18190
in-theory        18190
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> (not (A -> (A and B)))))) or ((A -> B) -> (not (A -> (A and B))))) -> (not (A -> B)))
theorem-size     28
proof            (modus-ponens tm-73 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-10 tm-9 tm-2 tm-5)
proof-size       112
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18190.        (((not (not ((A -> B) -> (not (A -> (A and B)))))) or ((A -> B) -> (not (A -> (A and B))))) -> (not (A -> B))), M:tm-73, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-18191
in-theory        18191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D))))
theorem-size     27
proof            (modus-ponens tm-69 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18191.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D)))), M:tm-69, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18192
in-theory        18192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-54 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-2)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18192.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-54, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18193
in-theory        18193
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> (not (B -> (B and C))))) or ((B -> C) -> (not (B -> (B and C))))) -> (not (B -> C)))
theorem-size     28
proof            (modus-ponens tm-47 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-4 tm-9 tm-2 tm-5)
proof-size       112
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18193.        (((A and ((B -> C) -> (not (B -> (B and C))))) or ((B -> C) -> (not (B -> (B and C))))) -> (not (B -> C))), M:tm-47, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-18194
in-theory        18194
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (not (A -> (A and B)))) and C) or ((A -> B) -> (not (A -> (A and B))))) -> (not (A -> B)))
theorem-size     28
proof            (modus-ponens tm-46 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-3 tm-9 tm-2 tm-5)
proof-size       112
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18194.        (((((A -> B) -> (not (A -> (A and B)))) and C) or ((A -> B) -> (not (A -> (A and B))))) -> (not (A -> B))), M:tm-46, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-18195
in-theory        18195
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> (A and B))) or ((A -> B) -> (not (A -> (A and B))))) -> (not (A -> B)))
theorem-size     22
proof            (modus-ponens tm-44 tm-334 ((A (-> Am Bm)) (B (not (-> Am (and Am Bm)))) (C (not (-> Am Bm)))))
axioms-used      (tm-8 tm-1 tm-9 tm-2 tm-5)
proof-size       108
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18195.        (((not (A -> (A and B))) or ((A -> B) -> (not (A -> (A and B))))) -> (not (A -> B))), M:tm-44, m:tm-334, u:((A (-> Am Bm)) (B (not (-> Am (and Am Bm)))) (C (not (-> Am Bm))))
================================================================
tm-name          tm-18196
in-theory        18196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D))))
theorem-size     21
proof            (modus-ponens tm-42 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18196.        ((A -> (B or A)) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D)))), M:tm-42, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18197
in-theory        18197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D))))
theorem-size     21
proof            (modus-ponens tm-32 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18197.        ((A -> (A or B)) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D)))), M:tm-32, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18198
in-theory        18198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (A and B)))) -> (((A -> B) -> (not (A -> (A and B)))) and (not (A -> B))))
theorem-size     26
proof            (modus-ponens tm-24 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       110
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18198.        (((A -> B) -> (not (A -> (A and B)))) -> (((A -> B) -> (not (A -> (A and B)))) and (not (A -> B)))), M:tm-24, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-18199
in-theory        18199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-23 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18199.        ((A -> (B -> (A and B))) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D)))), M:tm-23, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18200
in-theory        18200
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D))))
theorem-size     21
proof            (modus-ponens tm-22 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18200.        (((A and B) -> B) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D)))), M:tm-22, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18201
in-theory        18201
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D))))
theorem-size     21
proof            (modus-ponens tm-21 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18201.        (((A and B) -> A) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D)))), M:tm-21, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18202
in-theory        18202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-20 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18202.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-20, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18203
in-theory        18203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D))))
theorem-size     21
proof            (modus-ponens tm-19 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18203.        ((A -> (B -> A)) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D)))), M:tm-19, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18204
in-theory        18204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (A and B)))) -> ((A -> B) -> (not (A -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-12 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18204.        (((A -> B) -> (not (A -> (A and B)))) -> ((A -> B) -> (not (A -> (A and B))))), M:tm-12, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-18205
in-theory        18205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (A -> (A and B))))))
theorem-size     28
proof            (modus-ponens tm-9 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-9 tm-2 tm-5)
proof-size       94
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18205.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (A -> (A and B)))))), M:tm-9, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-18206
in-theory        18206
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> B)) -> C) -> ((((A -> B) -> (not (A -> (A and B)))) or (not (A -> B))) -> C))
theorem-size     24
proof            (modus-ponens tm-8 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-9 tm-2 tm-5)
proof-size       92
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18206.        (((not (A -> B)) -> C) -> ((((A -> B) -> (not (A -> (A and B)))) or (not (A -> B))) -> C)), M:tm-8, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-18207
in-theory        18207
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> (not (B -> (B and C)))) -> (not (B -> C))))
theorem-size     17
proof            (modus-ponens tm-7 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-7 tm-9 tm-2 tm-5)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18207.        (A or (((B -> C) -> (not (B -> (B and C)))) -> (not (B -> C)))), M:tm-7, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18208
in-theory        18208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) or C)
theorem-size     17
proof            (modus-ponens tm-6 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-6 tm-9 tm-2 tm-5)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18208.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) or C), M:tm-6, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18209
in-theory        18209
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (not (B -> (B and C)))) -> (not (B -> C))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18209.        (A -> ((((B -> C) -> (not (B -> (B and C)))) -> (not (B -> C))) and A)), M:tm-5, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18210
in-theory        18210
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (not (B -> (B and C)))) -> (not (B -> C))))
theorem-size     17
proof            (modus-ponens tm-1 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-1 tm-9 tm-2 tm-5)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18210.        (A -> (((B -> C) -> (not (B -> (B and C)))) -> (not (B -> C)))), M:tm-1, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18211
in-theory        18211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> (A -> (A and B))))
theorem-size     17
proof            (modus-ponens tm-335 tm-1 ((Am (-> A (and A B))) (C (-> Bm (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-18211.        (((A -> B) or (A -> (A and B))) -> (C -> (A -> (A and B)))), M:tm-335, m:tm-1, u:((Am (-> A (and A B))) (C (-> Bm (-> A (and A B)))))
================================================================
tm-name          tm-18212
in-theory        18212
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> ((A -> (A and B)) and C)))
theorem-size     19
proof            (modus-ponens tm-335 tm-5 ((Am (-> A (and A B))) (C (-> Bm (and (-> A (and A B)) Bm)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18212.        (((A -> B) or (A -> (A and B))) -> (C -> ((A -> (A and B)) and C))), M:tm-335, m:tm-5, u:((Am (-> A (and A B))) (C (-> Bm (and (-> A (and A B)) Bm))))
================================================================
tm-name          tm-18213
in-theory        18213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) or C))
theorem-size     17
proof            (modus-ponens tm-335 tm-6 ((Am (-> A (and A B))) (C (or (-> A (and A B)) Bm))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-18213.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) or C)), M:tm-335, m:tm-6, u:((Am (-> A (and A B))) (C (or (-> A (and A B)) Bm)))
================================================================
tm-name          tm-18214
in-theory        18214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C or (A -> (A and B))))
theorem-size     17
proof            (modus-ponens tm-335 tm-7 ((Am (-> A (and A B))) (C (or Bm (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-18214.        (((A -> B) or (A -> (A and B))) -> (C or (A -> (A and B)))), M:tm-335, m:tm-7, u:((Am (-> A (and A B))) (C (or Bm (-> A (and A B)))))
================================================================
tm-name          tm-18215
in-theory        18215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((A and B) -> C) -> ((A or (A and B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-335 tm-8 ((A Am) (Bm (and Am B)) (C (-> (-> (and Am B) Cm) (-> (or Am (and Am B)) Cm)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18215.        (((A -> B) or (A -> (A and B))) -> (((A and B) -> C) -> ((A or (A and B)) -> C))), M:tm-335, m:tm-8, u:((A Am) (Bm (and Am B)) (C (-> (-> (and Am B) Cm) (-> (or Am (and Am B)) Cm))))
================================================================
tm-name          tm-18216
in-theory        18216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (not (A and B))) -> (not A)))
theorem-size     19
proof            (modus-ponens tm-335 tm-9 ((A Am) (Bm (and Am B)) (C (-> (-> Am (not (and Am B))) (not Am)))))
axioms-used      (tm-8 tm-2 tm-5 tm-9)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-18216.        (((A -> B) or (A -> (A and B))) -> ((A -> (not (A and B))) -> (not A))), M:tm-335, m:tm-9, u:((A Am) (Bm (and Am B)) (C (-> (-> Am (not (and Am B))) (not Am))))
================================================================
tm-name          tm-18217
in-theory        18217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-335 tm-11 ((Am (-> A (and A B))) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18217.        (((A -> B) or (A -> (A and B))) -> (C -> (D -> C))), M:tm-335, m:tm-11, u:((Am (-> A (and A B))) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-18218
in-theory        18218
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (A -> A))
theorem-size     13
proof            (modus-ponens tm-335 tm-12 ((A Am) (Bm (and Am B)) (C (-> Am Am))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-18218.        (((A -> B) or (A -> (A and B))) -> (A -> A)), M:tm-335, m:tm-12, u:((A Am) (Bm (and Am B)) (C (-> Am Am)))
================================================================
tm-name          tm-18219
in-theory        18219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-335 tm-14 ((Am (-> A (and A B))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-18219.        (((A -> B) or (A -> (A and B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-335, m:tm-14, u:((Am (-> A (and A B))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-18220
in-theory        18220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-335 tm-16 ((Am (-> A (and A B))) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-18220.        (((A -> B) or (A -> (A and B))) -> ((C and D) -> C)), M:tm-335, m:tm-16, u:((Am (-> A (and A B))) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-18221
in-theory        18221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-335 tm-18 ((Am (-> A (and A B))) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18221.        (((A -> B) or (A -> (A and B))) -> ((C and D) -> D)), M:tm-335, m:tm-18, u:((Am (-> A (and A B))) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-18222
in-theory        18222
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (D -> C)) and (A -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-335 tm-19 ((Am (-> A (and A B))) (C (and (-> Bm (-> Cm Bm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18222.        (((A -> B) or (A -> (A and B))) -> ((C -> (D -> C)) and (A -> (A and B)))), M:tm-335, m:tm-19, u:((Am (-> A (and A B))) (C (and (-> Bm (-> Cm Bm)) (-> A (and A B)))))
================================================================
tm-name          tm-18223
in-theory        18223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-335 tm-20 ((Am (-> A (and A B))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-18223.        (((A -> B) or (A -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A and B)))), M:tm-335, m:tm-20, u:((Am (-> A (and A B))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (and A B)))))
================================================================
tm-name          tm-18224
in-theory        18224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C and D) -> C) and (A -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-335 tm-21 ((Am (-> A (and A B))) (C (and (-> (and Bm Cm) Bm) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-18224.        (((A -> B) or (A -> (A and B))) -> (((C and D) -> C) and (A -> (A and B)))), M:tm-335, m:tm-21, u:((Am (-> A (and A B))) (C (and (-> (and Bm Cm) Bm) (-> A (and A B)))))
================================================================
tm-name          tm-18225
in-theory        18225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C and D) -> D) and (A -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-335 tm-22 ((Am (-> A (and A B))) (C (and (-> (and Bm Cm) Cm) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18225.        (((A -> B) or (A -> (A and B))) -> (((C and D) -> D) and (A -> (A and B)))), M:tm-335, m:tm-22, u:((Am (-> A (and A B))) (C (and (-> (and Bm Cm) Cm) (-> A (and A B)))))
================================================================
tm-name          tm-18226
in-theory        18226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (D -> (C and D))) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-23 ((Am (-> A (and A B))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-18226.        (((A -> B) or (A -> (A and B))) -> ((C -> (D -> (C and D))) and (A -> (A and B)))), M:tm-335, m:tm-23, u:((Am (-> A (and A B))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (and A B)))))
================================================================
tm-name          tm-18227
in-theory        18227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (A -> (A and (A and B))))
theorem-size     17
proof            (modus-ponens tm-335 tm-24 ((A Am) (Bm (and Am B)) (C (-> Am (and Am (and Am B))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18227.        (((A -> B) or (A -> (A and B))) -> (A -> (A and (A and B)))), M:tm-335, m:tm-24, u:((A Am) (Bm (and Am B)) (C (-> Am (and Am (and Am B)))))
================================================================
tm-name          tm-18228
in-theory        18228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-335 tm-25 ((Am (-> A (and A B))) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-18228.        (((A -> B) or (A -> (A and B))) -> (C -> (D -> (C and D)))), M:tm-335, m:tm-25, u:((Am (-> A (and A B))) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-18229
in-theory        18229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (C or D)) and (A -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-335 tm-32 ((Am (-> A (and A B))) (C (and (-> Bm (or Bm Cm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-18229.        (((A -> B) or (A -> (A and B))) -> ((C -> (C or D)) and (A -> (A and B)))), M:tm-335, m:tm-32, u:((Am (-> A (and A B))) (C (and (-> Bm (or Bm Cm)) (-> A (and A B)))))
================================================================
tm-name          tm-18230
in-theory        18230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-335 tm-33 ((Am (-> A (and A B))) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-18230.        (((A -> B) or (A -> (A and B))) -> (C -> (C or D))), M:tm-335, m:tm-33, u:((Am (-> A (and A B))) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-18231
in-theory        18231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (D or C)) and (A -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-335 tm-42 ((Am (-> A (and A B))) (C (and (-> Bm (or Cm Bm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-18231.        (((A -> B) or (A -> (A and B))) -> ((C -> (D or C)) and (A -> (A and B)))), M:tm-335, m:tm-42, u:((Am (-> A (and A B))) (C (and (-> Bm (or Cm Bm)) (-> A (and A B)))))
================================================================
tm-name          tm-18232
in-theory        18232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-335 tm-43 ((Am (-> A (and A B))) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-18232.        (((A -> B) or (A -> (A and B))) -> (C -> (D or C))), M:tm-335, m:tm-43, u:((Am (-> A (and A B))) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-18233
in-theory        18233
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((A -> B) -> ((A -> B) and C))) -> ((B or (A -> B)) -> ((A -> B) and C)))
theorem-size     27
proof            (modus-ponens tm-335 tm-44 ((A (-> Am Bm)) (Cm (and (-> Am Bm) B)) (C (-> (or Bm (-> Am Bm)) (and (-> Am Bm) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-18233.        ((((A -> B) -> C) or ((A -> B) -> ((A -> B) and C))) -> ((B or (A -> B)) -> ((A -> B) and C))), M:tm-335, m:tm-44, u:((A (-> Am Bm)) (Cm (and (-> Am Bm) B)) (C (-> (or Bm (-> Am Bm)) (and (-> Am Bm) B))))
================================================================
tm-name          tm-18234
in-theory        18234
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and D)))
theorem-size     51
proof            (modus-ponens tm-335 tm-45 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (and (-> (-> Am Bm) (-> Am Cm)) B)) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Am Bm) (-> Am Cm)) B)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-18234.        (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and D))), M:tm-335, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (and (-> (-> Am Bm) (-> Am Cm)) B)) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Am Bm) (-> Am Cm)) B))))
================================================================
tm-name          tm-18235
in-theory        18235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((A and C) or A) -> (A and B)))
theorem-size     19
proof            (modus-ponens tm-335 tm-46 ((A Am) (Bm (and Am B)) (C (-> (or (and Am Cm) Am) (and Am B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-18235.        (((A -> B) or (A -> (A and B))) -> (((A and C) or A) -> (A and B))), M:tm-335, m:tm-46, u:((A Am) (Bm (and Am B)) (C (-> (or (and Am Cm) Am) (and Am B))))
================================================================
tm-name          tm-18236
in-theory        18236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C and A) or A) -> (A and B)))
theorem-size     19
proof            (modus-ponens tm-335 tm-47 ((A Am) (Bm (and Am B)) (C (-> (or (and Cm Am) Am) (and Am B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18236.        (((A -> B) or (A -> (A and B))) -> (((C and A) or A) -> (A and B))), M:tm-335, m:tm-47, u:((A Am) (Bm (and Am B)) (C (-> (or (and Cm Am) Am) (and Am B))))
================================================================
tm-name          tm-18237
in-theory        18237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> ((A -> (B and A)) and C))) -> ((B or (A -> (B and A))) -> ((A -> (B and A)) and C)))
theorem-size     37
proof            (modus-ponens tm-335 tm-48 ((A (-> Am (and Bm Am))) (Cm (and (-> Am (and Bm Am)) B)) (C (-> (or Bm (-> Am (and Bm Am))) (and (-> Am (and Bm Am)) B)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-18237.        ((((A -> (B and A)) -> C) or ((A -> (B and A)) -> ((A -> (B and A)) and C))) -> ((B or (A -> (B and A))) -> ((A -> (B and A)) and C))), M:tm-335, m:tm-48, u:((A (-> Am (and Bm Am))) (Cm (and (-> Am (and Bm Am)) B)) (C (-> (or Bm (-> Am (and Bm Am))) (and (-> Am (and Bm Am)) B))))
================================================================
tm-name          tm-18238
in-theory        18238
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or B) -> ((A or B) and C))) -> ((A or (A or B)) -> ((A or B) and C)))
theorem-size     27
proof            (modus-ponens tm-335 tm-49 ((A (or Am Bm)) (Cm (and (or Am Bm) B)) (C (-> (or Am (or Am Bm)) (and (or Am Bm) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-18238.        ((((A or B) -> C) or ((A or B) -> ((A or B) and C))) -> ((A or (A or B)) -> ((A or B) and C))), M:tm-335, m:tm-49, u:((A (or Am Bm)) (Cm (and (or Am Bm) B)) (C (-> (or Am (or Am Bm)) (and (or Am Bm) B))))
================================================================
tm-name          tm-18239
in-theory        18239
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or ((A or B) -> ((A or B) and C))) -> ((B or (A or B)) -> ((A or B) and C)))
theorem-size     27
proof            (modus-ponens tm-335 tm-50 ((A (or Am Bm)) (Cm (and (or Am Bm) B)) (C (-> (or Bm (or Am Bm)) (and (or Am Bm) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-18239.        ((((A or B) -> C) or ((A or B) -> ((A or B) and C))) -> ((B or (A or B)) -> ((A or B) and C))), M:tm-335, m:tm-50, u:((A (or Am Bm)) (Cm (and (or Am Bm) B)) (C (-> (or Bm (or Am Bm)) (and (or Am Bm) B))))
================================================================
tm-name          tm-18240
in-theory        18240
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) or (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and D))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and D)))
theorem-size     59
proof            (modus-ponens tm-335 tm-51 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-18240.        (((((A -> B) -> ((C or A) -> B)) -> D) or (((A -> B) -> ((C or A) -> B)) -> (((A -> B) -> ((C or A) -> B)) and D))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> (((A -> B) -> ((C or A) -> B)) and D))), M:tm-335, m:tm-51, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))))
================================================================
tm-name          tm-18241
in-theory        18241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-335 tm-54 ((Am (-> A (and A B))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-18241.        (((A -> B) or (A -> (A and B))) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> (A and B)))), M:tm-335, m:tm-54, u:((Am (-> A (and A B))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A (and A B)))))
================================================================
tm-name          tm-18242
in-theory        18242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-335 tm-56 ((Am (-> A (and A B))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-18242.        (((A -> B) or (A -> (A and B))) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-335, m:tm-56, u:((Am (-> A (and A B))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-18243
in-theory        18243
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) or (((A -> (not B)) -> (not A)) -> (((A -> (not B)) -> (not A)) and C))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and C)))
theorem-size     49
proof            (modus-ponens tm-335 tm-66 ((A (-> (-> Am (not Bm)) (not Am))) (Cm (and (-> (-> Am (not Bm)) (not Am)) B)) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (and (-> (-> Am (not Bm)) (not Am)) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-9)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-18243.        (((((A -> (not B)) -> (not A)) -> C) or (((A -> (not B)) -> (not A)) -> (((A -> (not B)) -> (not A)) and C))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and C))), M:tm-335, m:tm-66, u:((A (-> (-> Am (not Bm)) (not Am))) (Cm (and (-> (-> Am (not Bm)) (not Am)) B)) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (and (-> (-> Am (not Bm)) (not Am)) B))))
================================================================
tm-name          tm-18244
in-theory        18244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> (A and B))))
theorem-size     27
proof            (modus-ponens tm-335 tm-69 ((Am (-> A (and A B))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-9)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-18244.        (((A -> B) or (A -> (A and B))) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> (A and B)))), M:tm-335, m:tm-69, u:((Am (-> A (and A B))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A (and A B)))))
================================================================
tm-name          tm-18245
in-theory        18245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     21
proof            (modus-ponens tm-335 tm-71 ((Am (-> A (and A B))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-9)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-18245.        (((A -> B) or (A -> (A and B))) -> ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-335, m:tm-71, u:((Am (-> A (and A B))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-18246
in-theory        18246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((not (not A)) or A) -> (A and B)))
theorem-size     19
proof            (modus-ponens tm-335 tm-73 ((A Am) (Bm (and Am B)) (C (-> (or (not (not Am)) Am) (and Am B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-10)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-18246.        (((A -> B) or (A -> (A and B))) -> (((not (not A)) or A) -> (A and B))), M:tm-335, m:tm-73, u:((A Am) (Bm (and Am B)) (C (-> (or (not (not Am)) Am) (and Am B))))
================================================================
tm-name          tm-18247
in-theory        18247
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((not (not C)) -> C) and (A -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-335 tm-76 ((Am (-> A (and A B))) (C (and (-> (not (not Bm)) Bm) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-10)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-18247.        (((A -> B) or (A -> (A and B))) -> (((not (not C)) -> C) and (A -> (A and B)))), M:tm-335, m:tm-76, u:((Am (-> A (and A B))) (C (and (-> (not (not Bm)) Bm) (-> A (and A B)))))
================================================================
tm-name          tm-18248
in-theory        18248
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((not (not C)) -> C))
theorem-size     15
proof            (modus-ponens tm-335 tm-78 ((Am (-> A (and A B))) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-18248.        (((A -> B) or (A -> (A and B))) -> ((not (not C)) -> C)), M:tm-335, m:tm-78, u:((Am (-> A (and A B))) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-18249
in-theory        18249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) or ((A -> (B -> A)) -> ((A -> (B -> A)) and C))) -> ((D or (A -> (B -> A))) -> ((A -> (B -> A)) and C)))
theorem-size     37
proof            (modus-ponens tm-335 tm-80 ((A (-> Am (-> Bm Am))) (Cm (and (-> Am (-> Bm Am)) B)) (C (-> (or Dm (-> Am (-> Bm Am))) (and (-> Am (-> Bm Am)) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-18249.        ((((A -> (B -> A)) -> C) or ((A -> (B -> A)) -> ((A -> (B -> A)) and C))) -> ((D or (A -> (B -> A))) -> ((A -> (B -> A)) and C))), M:tm-335, m:tm-80, u:((A (-> Am (-> Bm Am))) (Cm (and (-> Am (-> Bm Am)) B)) (C (-> (or Dm (-> Am (-> Bm Am))) (and (-> Am (-> Bm Am)) B))))
================================================================
tm-name          tm-18250
in-theory        18250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (D -> (E -> D))) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-83 ((Am (-> A (and A B))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-18250.        (((A -> B) or (A -> (A and B))) -> ((C -> (D -> (E -> D))) and (A -> (A and B)))), M:tm-335, m:tm-83, u:((Am (-> A (and A B))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (and A B)))))
================================================================
tm-name          tm-18251
in-theory        18251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (A -> (C -> (A and B))))
theorem-size     17
proof            (modus-ponens tm-335 tm-84 ((A Am) (Bm (and Am B)) (C (-> Am (-> Cm (and Am B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-18251.        (((A -> B) or (A -> (A and B))) -> (A -> (C -> (A and B)))), M:tm-335, m:tm-84, u:((A Am) (Bm (and Am B)) (C (-> Am (-> Cm (and Am B)))))
================================================================
tm-name          tm-18252
in-theory        18252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> (D -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-335 tm-85 ((Am (-> A (and A B))) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-18252.        (((A -> B) or (A -> (A and B))) -> (C -> (D -> (E -> D)))), M:tm-335, m:tm-85, u:((Am (-> A (and A B))) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-18253
in-theory        18253
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (A -> (A and B)))
theorem-size     15
proof            (modus-ponens tm-335 tm-86 ((Am (-> A (and A B))) (C (-> A (and A B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-18253.        (((A -> B) or (A -> (A and B))) -> (A -> (A and B))), M:tm-335, m:tm-86, u:((Am (-> A (and A B))) (C (-> A (and A B))))
================================================================
tm-name          tm-18254
in-theory        18254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) or ((A -> A) -> ((A -> A) and B))) -> (((A -> C) or (A -> A)) -> ((A -> A) and B)))
theorem-size     29
proof            (modus-ponens tm-335 tm-92 ((A (-> Am Am)) (Bm (and (-> Am Am) B)) (C (-> (or (-> Am Cm) (-> Am Am)) (and (-> Am Am) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-18254.        ((((A -> A) -> B) or ((A -> A) -> ((A -> A) and B))) -> (((A -> C) or (A -> A)) -> ((A -> A) and B))), M:tm-335, m:tm-92, u:((A (-> Am Am)) (Bm (and (-> Am Am) B)) (C (-> (or (-> Am Cm) (-> Am Am)) (and (-> Am Am) B))))
================================================================
tm-name          tm-18255
in-theory        18255
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> D) -> (C -> C)) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-95 ((Am (-> A (and A B))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-18255.        (((A -> B) or (A -> (A and B))) -> (((C -> D) -> (C -> C)) and (A -> (A and B)))), M:tm-335, m:tm-95, u:((Am (-> A (and A B))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (and A B)))))
================================================================
tm-name          tm-18256
in-theory        18256
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> D) -> (C -> C)))
theorem-size     17
proof            (modus-ponens tm-335 tm-97 ((Am (-> A (and A B))) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-18256.        (((A -> B) or (A -> (A and B))) -> ((C -> D) -> (C -> C))), M:tm-335, m:tm-97, u:((Am (-> A (and A B))) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-18257
in-theory        18257
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) or (((A -> (B -> C)) -> (A -> C)) -> (((A -> (B -> C)) -> (A -> C)) and D))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and D)))
theorem-size     65
proof            (modus-ponens tm-335 tm-102 ((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (Dm (and (-> (-> Am (-> Bm Cm)) (-> Am Cm)) B)) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (and (-> (-> Am (-> Bm Cm)) (-> Am Cm)) B)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-18257.        (((((A -> (B -> C)) -> (A -> C)) -> D) or (((A -> (B -> C)) -> (A -> C)) -> (((A -> (B -> C)) -> (A -> C)) and D))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and D))), M:tm-335, m:tm-102, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (Dm (and (-> (-> Am (-> Bm Cm)) (-> Am Cm)) B)) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (and (-> (-> Am (-> Bm Cm)) (-> Am Cm)) B))))
================================================================
tm-name          tm-18258
in-theory        18258
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> (A and B))))
theorem-size     35
proof            (modus-ponens tm-335 tm-105 ((Am (-> A (and A B))) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-18258.        (((A -> B) or (A -> (A and B))) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> (A and B)))), M:tm-335, m:tm-105, u:((Am (-> A (and A B))) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A (and A B)))))
================================================================
tm-name          tm-18259
in-theory        18259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-335 tm-107 ((Am (-> A (and A B))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-18259.        (((A -> B) or (A -> (A and B))) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-335, m:tm-107, u:((Am (-> A (and A B))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-18260
in-theory        18260
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)))
theorem-size     77
proof            (modus-ponens tm-335 tm-110 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-18260.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))), M:tm-335, m:tm-110, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))))
================================================================
tm-name          tm-18261
in-theory        18261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-335 tm-113 ((Am (-> A (and A B))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-18261.        (((A -> B) or (A -> (A and B))) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (A and B)))), M:tm-335, m:tm-113, u:((Am (-> A (and A B))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (and A B)))))
================================================================
tm-name          tm-18262
in-theory        18262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-335 tm-115 ((Am (-> A (and A B))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-18262.        (((A -> B) or (A -> (A and B))) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-335, m:tm-115, u:((Am (-> A (and A B))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-18263
in-theory        18263
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) or ((((A -> B) and C) -> B) -> ((((A -> B) and C) -> B) and D))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and D)))
theorem-size     53
proof            (modus-ponens tm-335 tm-122 ((A (-> (and (-> Am Bm) Cm) Bm)) (Dm (and (-> (and (-> Am Bm) Cm) Bm) B)) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (and (-> (and (-> Am Bm) Cm) Bm) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-18263.        ((((((A -> B) and C) -> B) -> D) or ((((A -> B) and C) -> B) -> ((((A -> B) and C) -> B) and D))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and D))), M:tm-335, m:tm-122, u:((A (-> (and (-> Am Bm) Cm) Bm)) (Dm (and (-> (and (-> Am Bm) Cm) Bm) B)) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (and (-> (and (-> Am Bm) Cm) Bm) B))))
================================================================
tm-name          tm-18264
in-theory        18264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-335 tm-125 ((Am (-> A (and A B))) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-18264.        (((A -> B) or (A -> (A and B))) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> (A and B)))), M:tm-335, m:tm-125, u:((Am (-> A (and A B))) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A (and A B)))))
================================================================
tm-name          tm-18265
in-theory        18265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     25
proof            (modus-ponens tm-335 tm-127 ((Am (-> A (and A B))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-18265.        (((A -> B) or (A -> (A and B))) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-335, m:tm-127, u:((Am (-> A (and A B))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-18266
in-theory        18266
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) or (((A and B) -> A) -> (((A and B) -> A) and C))) -> ((D or ((A and B) -> A)) -> (((A and B) -> A) and C)))
theorem-size     37
proof            (modus-ponens tm-335 tm-131 ((A (-> (and Am Bm) Am)) (Cm (and (-> (and Am Bm) Am) B)) (C (-> (or Dm (-> (and Am Bm) Am)) (and (-> (and Am Bm) Am) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-18266.        (((((A and B) -> A) -> C) or (((A and B) -> A) -> (((A and B) -> A) and C))) -> ((D or ((A and B) -> A)) -> (((A and B) -> A) and C))), M:tm-335, m:tm-131, u:((A (-> (and Am Bm) Am)) (Cm (and (-> (and Am Bm) Am) B)) (C (-> (or Dm (-> (and Am Bm) Am)) (and (-> (and Am Bm) Am) B))))
================================================================
tm-name          tm-18267
in-theory        18267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> ((D and E) -> D)) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-134 ((Am (-> A (and A B))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-18267.        (((A -> B) or (A -> (A and B))) -> ((C -> ((D and E) -> D)) and (A -> (A and B)))), M:tm-335, m:tm-134, u:((Am (-> A (and A B))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (and A B)))))
================================================================
tm-name          tm-18268
in-theory        18268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> ((D and E) -> D)))
theorem-size     17
proof            (modus-ponens tm-335 tm-136 ((Am (-> A (and A B))) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-18268.        (((A -> B) or (A -> (A and B))) -> (C -> ((D and E) -> D))), M:tm-335, m:tm-136, u:((Am (-> A (and A B))) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-18269
in-theory        18269
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) or (((A and (B -> C)) -> C) -> (((A and (B -> C)) -> C) and D))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and D)))
theorem-size     53
proof            (modus-ponens tm-335 tm-144 ((A (-> (and Am (-> Bm Cm)) Cm)) (Dm (and (-> (and Am (-> Bm Cm)) Cm) B)) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (and (-> (and Am (-> Bm Cm)) Cm) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-18269.        (((((A and (B -> C)) -> C) -> D) or (((A and (B -> C)) -> C) -> (((A and (B -> C)) -> C) and D))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and D))), M:tm-335, m:tm-144, u:((A (-> (and Am (-> Bm Cm)) Cm)) (Dm (and (-> (and Am (-> Bm Cm)) Cm) B)) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (and (-> (and Am (-> Bm Cm)) Cm) B))))
================================================================
tm-name          tm-18270
in-theory        18270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-335 tm-147 ((Am (-> A (and A B))) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-18270.        (((A -> B) or (A -> (A and B))) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> (A and B)))), M:tm-335, m:tm-147, u:((Am (-> A (and A B))) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A (and A B)))))
================================================================
tm-name          tm-18271
in-theory        18271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     25
proof            (modus-ponens tm-335 tm-149 ((Am (-> A (and A B))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-18271.        (((A -> B) or (A -> (A and B))) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-335, m:tm-149, u:((Am (-> A (and A B))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-18272
in-theory        18272
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) or (((A and B) -> B) -> (((A and B) -> B) and C))) -> ((D or ((A and B) -> B)) -> (((A and B) -> B) and C)))
theorem-size     37
proof            (modus-ponens tm-335 tm-154 ((A (-> (and Am Bm) Bm)) (Cm (and (-> (and Am Bm) Bm) B)) (C (-> (or Dm (-> (and Am Bm) Bm)) (and (-> (and Am Bm) Bm) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-18272.        (((((A and B) -> B) -> C) or (((A and B) -> B) -> (((A and B) -> B) and C))) -> ((D or ((A and B) -> B)) -> (((A and B) -> B) and C))), M:tm-335, m:tm-154, u:((A (-> (and Am Bm) Bm)) (Cm (and (-> (and Am Bm) Bm) B)) (C (-> (or Dm (-> (and Am Bm) Bm)) (and (-> (and Am Bm) Bm) B))))
================================================================
tm-name          tm-18273
in-theory        18273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> ((D and E) -> E)) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-157 ((Am (-> A (and A B))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-18273.        (((A -> B) or (A -> (A and B))) -> ((C -> ((D and E) -> E)) and (A -> (A and B)))), M:tm-335, m:tm-157, u:((Am (-> A (and A B))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (and A B)))))
================================================================
tm-name          tm-18274
in-theory        18274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (A -> B))
theorem-size     13
proof            (modus-ponens tm-335 tm-158 ((Bm Am) (A Am) (B Cm) (C (-> Am Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-18274.        (((A -> B) or (A -> (A and B))) -> (A -> B)), M:tm-335, m:tm-158, u:((Bm Am) (A Am) (B Cm) (C (-> Am Cm)))
================================================================
tm-name          tm-18275
in-theory        18275
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> ((D and E) -> E)))
theorem-size     17
proof            (modus-ponens tm-335 tm-159 ((Am (-> A (and A B))) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-18275.        (((A -> B) or (A -> (A and B))) -> (C -> ((D and E) -> E))), M:tm-335, m:tm-159, u:((Am (-> A (and A B))) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-18276
in-theory        18276
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) or (((A -> (B -> A)) and C) -> (((A -> (B -> A)) and C) and D))) -> ((C or ((A -> (B -> A)) and C)) -> (((A -> (B -> A)) and C) and D)))
theorem-size     47
proof            (modus-ponens tm-335 tm-180 ((A (and (-> Am (-> Bm Am)) Cm)) (Dm (and (and (-> Am (-> Bm Am)) Cm) B)) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (and (and (-> Am (-> Bm Am)) Cm) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-18276.        (((((A -> (B -> A)) and C) -> D) or (((A -> (B -> A)) and C) -> (((A -> (B -> A)) and C) and D))) -> ((C or ((A -> (B -> A)) and C)) -> (((A -> (B -> A)) and C) and D))), M:tm-335, m:tm-180, u:((A (and (-> Am (-> Bm Am)) Cm)) (Dm (and (and (-> Am (-> Bm Am)) Cm) B)) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (and (and (-> Am (-> Bm Am)) Cm) B))))
================================================================
tm-name          tm-18277
in-theory        18277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> ((D -> (E -> D)) and C)) and (A -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-335 tm-183 ((Am (-> A (and A B))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-18277.        (((A -> B) or (A -> (A and B))) -> ((C -> ((D -> (E -> D)) and C)) and (A -> (A and B)))), M:tm-335, m:tm-183, u:((Am (-> A (and A B))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (and A B)))))
================================================================
tm-name          tm-18278
in-theory        18278
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> ((D -> (E -> D)) and C)))
theorem-size     19
proof            (modus-ponens tm-335 tm-184 ((Am (-> A (and A B))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-18278.        (((A -> B) or (A -> (A and B))) -> (C -> ((D -> (E -> D)) and C))), M:tm-335, m:tm-184, u:((Am (-> A (and A B))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-18279
in-theory        18279
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) and E))) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) and E)))
theorem-size     87
proof            (modus-ponens tm-335 tm-207 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (and (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B)) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (and (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       235
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-18279.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) and E))) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) and E))), M:tm-335, m:tm-207, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (and (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B)) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (and (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B))))
================================================================
tm-name          tm-18280
in-theory        18280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> (A and B))))
theorem-size     33
proof            (modus-ponens tm-335 tm-210 ((Am (-> A (and A B))) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-18280.        (((A -> B) or (A -> (A and B))) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> (A and B)))), M:tm-335, m:tm-210, u:((Am (-> A (and A B))) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A (and A B)))))
================================================================
tm-name          tm-18281
in-theory        18281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     27
proof            (modus-ponens tm-335 tm-211 ((Am (-> A (and A B))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-18281.        (((A -> B) or (A -> (A and B))) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-335, m:tm-211, u:((Am (-> A (and A B))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-18282
in-theory        18282
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) or ((((A and B) -> A) and C) -> ((((A and B) -> A) and C) and D))) -> ((C or (((A and B) -> A) and C)) -> ((((A and B) -> A) and C) and D)))
theorem-size     47
proof            (modus-ponens tm-335 tm-236 ((A (and (-> (and Am Bm) Am) Cm)) (Dm (and (and (-> (and Am Bm) Am) Cm) B)) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (and (and (-> (and Am Bm) Am) Cm) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-18282.        ((((((A and B) -> A) and C) -> D) or ((((A and B) -> A) and C) -> ((((A and B) -> A) and C) and D))) -> ((C or (((A and B) -> A) and C)) -> ((((A and B) -> A) and C) and D))), M:tm-335, m:tm-236, u:((A (and (-> (and Am Bm) Am) Cm)) (Dm (and (and (-> (and Am Bm) Am) Cm) B)) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (and (and (-> (and Am Bm) Am) Cm) B))))
================================================================
tm-name          tm-18283
in-theory        18283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (((D and E) -> D) and C)) and (A -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-335 tm-239 ((Am (-> A (and A B))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-18283.        (((A -> B) or (A -> (A and B))) -> ((C -> (((D and E) -> D) and C)) and (A -> (A and B)))), M:tm-335, m:tm-239, u:((Am (-> A (and A B))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A (and A B)))))
================================================================
tm-name          tm-18284
in-theory        18284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> (((D and E) -> D) and C)))
theorem-size     19
proof            (modus-ponens tm-335 tm-240 ((Am (-> A (and A B))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-18284.        (((A -> B) or (A -> (A and B))) -> (C -> (((D and E) -> D) and C))), M:tm-335, m:tm-240, u:((Am (-> A (and A B))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-18285
in-theory        18285
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) or ((((A and B) -> B) and C) -> ((((A and B) -> B) and C) and D))) -> ((C or (((A and B) -> B) and C)) -> ((((A and B) -> B) and C) and D)))
theorem-size     47
proof            (modus-ponens tm-335 tm-267 ((A (and (-> (and Am Bm) Bm) Cm)) (Dm (and (and (-> (and Am Bm) Bm) Cm) B)) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (and (and (-> (and Am Bm) Bm) Cm) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-18285.        ((((((A and B) -> B) and C) -> D) or ((((A and B) -> B) and C) -> ((((A and B) -> B) and C) and D))) -> ((C or (((A and B) -> B) and C)) -> ((((A and B) -> B) and C) and D))), M:tm-335, m:tm-267, u:((A (and (-> (and Am Bm) Bm) Cm)) (Dm (and (and (-> (and Am Bm) Bm) Cm) B)) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (and (and (-> (and Am Bm) Bm) Cm) B))))
================================================================
tm-name          tm-18286
in-theory        18286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (((D and E) -> E) and C)) and (A -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-335 tm-270 ((Am (-> A (and A B))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-18286.        (((A -> B) or (A -> (A and B))) -> ((C -> (((D and E) -> E) and C)) and (A -> (A and B)))), M:tm-335, m:tm-270, u:((Am (-> A (and A B))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A (and A B)))))
================================================================
tm-name          tm-18287
in-theory        18287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> (((D and E) -> E) and C)))
theorem-size     19
proof            (modus-ponens tm-335 tm-271 ((Am (-> A (and A B))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-18287.        (((A -> B) or (A -> (A and B))) -> (C -> (((D and E) -> E) and C))), M:tm-335, m:tm-271, u:((Am (-> A (and A B))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-18288
in-theory        18288
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) or (((A -> (B -> (A and B))) and C) -> (((A -> (B -> (A and B))) and C) and D))) -> ((C or ((A -> (B -> (A and B))) and C)) -> (((A -> (B -> (A and B))) and C) and D)))
theorem-size     57
proof            (modus-ponens tm-335 tm-300 ((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (and (and (-> Am (-> Bm (and Am Bm))) Cm) B)) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (and (and (-> Am (-> Bm (and Am Bm))) Cm) B)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-18288.        (((((A -> (B -> (A and B))) and C) -> D) or (((A -> (B -> (A and B))) and C) -> (((A -> (B -> (A and B))) and C) and D))) -> ((C or ((A -> (B -> (A and B))) and C)) -> (((A -> (B -> (A and B))) and C) and D))), M:tm-335, m:tm-300, u:((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (and (and (-> Am (-> Bm (and Am Bm))) Cm) B)) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (and (and (-> Am (-> Bm (and Am Bm))) Cm) B))))
================================================================
tm-name          tm-18289
in-theory        18289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> (A and B))))
theorem-size     27
proof            (modus-ponens tm-335 tm-303 ((Am (-> A (and A B))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-18289.        (((A -> B) or (A -> (A and B))) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> (A and B)))), M:tm-335, m:tm-303, u:((Am (-> A (and A B))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A (and A B)))))
================================================================
tm-name          tm-18290
in-theory        18290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     21
proof            (modus-ponens tm-335 tm-304 ((Am (-> A (and A B))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-18290.        (((A -> B) or (A -> (A and B))) -> (C -> ((D -> (E -> (D and E))) and C))), M:tm-335, m:tm-304, u:((Am (-> A (and A B))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-18291
in-theory        18291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (C -> (A -> (A and B)))))
theorem-size     23
proof            (modus-ponens tm-335 tm-305 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> Bm (-> A (and A B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-18291.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (C -> (A -> (A and B))))), M:tm-335, m:tm-305, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> Bm (-> A (and A B))))))
================================================================
tm-name          tm-18292
in-theory        18292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (C -> ((A -> (A and B)) and C))))
theorem-size     25
proof            (modus-ponens tm-335 tm-309 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> Bm (and (-> A (and A B)) Bm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-18292.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (C -> ((A -> (A and B)) and C)))), M:tm-335, m:tm-309, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> Bm (and (-> A (and A B)) Bm)))))
================================================================
tm-name          tm-18293
in-theory        18293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((A -> (A and B)) or C)))
theorem-size     23
proof            (modus-ponens tm-335 tm-310 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (or (-> A (and A B)) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-18293.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((A -> (A and B)) or C))), M:tm-335, m:tm-310, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (or (-> A (and A B)) Bm))))
================================================================
tm-name          tm-18294
in-theory        18294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (C or (A -> (A and B)))))
theorem-size     23
proof            (modus-ponens tm-335 tm-311 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (or Bm (-> A (and A B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-18294.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (C or (A -> (A and B))))), M:tm-335, m:tm-311, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (or Bm (-> A (and A B))))))
================================================================
tm-name          tm-18295
in-theory        18295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (((A and B) -> C) -> ((A or (A and B)) -> C))))
theorem-size     29
proof            (modus-ponens tm-335 tm-312 ((A Am) (Bm (and Am B)) (C (and (-> Am (and Am B)) (-> (-> (and Am B) Cm) (-> (or Am (and Am B)) Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-18295.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (((A and B) -> C) -> ((A or (A and B)) -> C)))), M:tm-335, m:tm-312, u:((A Am) (Bm (and Am B)) (C (and (-> Am (and Am B)) (-> (-> (and Am B) Cm) (-> (or Am (and Am B)) Cm)))))
================================================================
tm-name          tm-18296
in-theory        18296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((A -> (not (A and B))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-335 tm-313 ((A Am) (Bm (and Am B)) (C (and (-> Am (and Am B)) (-> (-> Am (not (and Am B))) (not Am))))))
axioms-used      (tm-8 tm-2 tm-5 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-18296.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((A -> (not (A and B))) -> (not A)))), M:tm-335, m:tm-313, u:((A Am) (Bm (and Am B)) (C (and (-> Am (and Am B)) (-> (-> Am (not (and Am B))) (not Am)))))
================================================================
tm-name          tm-18297
in-theory        18297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (C -> (D -> C))))
theorem-size     21
proof            (modus-ponens tm-335 tm-315 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-18297.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (C -> (D -> C)))), M:tm-335, m:tm-315, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-18298
in-theory        18298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-335 tm-316 ((A Am) (Bm (and Am B)) (C (and (-> Am (and Am B)) (-> Am Am)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-18298.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (A -> A))), M:tm-335, m:tm-316, u:((A Am) (Bm (and Am B)) (C (and (-> Am (and Am B)) (-> Am Am))))
================================================================
tm-name          tm-18299
in-theory        18299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     29
proof            (modus-ponens tm-335 tm-318 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-18299.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-335, m:tm-318, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-18300
in-theory        18300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((C and D) -> C)))
theorem-size     21
proof            (modus-ponens tm-335 tm-320 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-18300.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((C and D) -> C))), M:tm-335, m:tm-320, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-18301
in-theory        18301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((C and D) -> D)))
theorem-size     21
proof            (modus-ponens tm-335 tm-322 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-18301.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((C and D) -> D))), M:tm-335, m:tm-322, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-18302
in-theory        18302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((C -> (D -> C)) and (A -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-335 tm-323 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (and (-> Bm (-> Cm Bm)) (-> A (and A B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-18302.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((C -> (D -> C)) and (A -> (A and B))))), M:tm-335, m:tm-323, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (and (-> Bm (-> Cm Bm)) (-> A (and A B))))))
================================================================
tm-name          tm-18303
in-theory        18303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A and B)))))
theorem-size     35
proof            (modus-ponens tm-335 tm-324 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (and A B)))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-18303.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A and B))))), M:tm-335, m:tm-324, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (and A B))))))
================================================================
tm-name          tm-18304
in-theory        18304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (((C and D) -> C) and (A -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-335 tm-325 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (and (-> (and Bm Cm) Bm) (-> A (and A B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-18304.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (((C and D) -> C) and (A -> (A and B))))), M:tm-335, m:tm-325, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (and (-> (and Bm Cm) Bm) (-> A (and A B))))))
================================================================
tm-name          tm-18305
in-theory        18305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (((C and D) -> D) and (A -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-335 tm-326 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (and (-> (and Bm Cm) Cm) (-> A (and A B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-18305.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (((C and D) -> D) and (A -> (A and B))))), M:tm-335, m:tm-326, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (and (-> (and Bm Cm) Cm) (-> A (and A B))))))
================================================================
tm-name          tm-18306
in-theory        18306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((C -> (D -> (C and D))) and (A -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-335 tm-327 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (and (-> Bm (-> Cm (and Bm Cm))) (-> A (and A B)))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-18306.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((C -> (D -> (C and D))) and (A -> (A and B))))), M:tm-335, m:tm-327, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (and (-> Bm (-> Cm (and Bm Cm))) (-> A (and A B))))))
================================================================
tm-name          tm-18307
in-theory        18307
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (A -> (A and (A and B)))))
theorem-size     23
proof            (modus-ponens tm-335 tm-328 ((A Am) (Bm (and Am B)) (C (and (-> Am (and Am B)) (-> Am (and Am (and Am B)))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18307.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (A -> (A and (A and B))))), M:tm-335, m:tm-328, u:((A Am) (Bm (and Am B)) (C (and (-> Am (and Am B)) (-> Am (and Am (and Am B))))))
================================================================
tm-name          tm-18308
in-theory        18308
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) or ((A -> (A and B)) -> ((A -> (A and B)) and C))) -> (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and C)))
theorem-size     39
proof            (modus-ponens tm-335 tm-335 ((A (-> Am (and Am Bm))) (Cm (and (-> Am (and Am Bm)) B)) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) (and (-> Am (and Am Bm)) B)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18308.        ((((A -> (A and B)) -> C) or ((A -> (A and B)) -> ((A -> (A and B)) and C))) -> (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and C))), M:tm-335, m:tm-335, u:((A (-> Am (and Am Bm))) (Cm (and (-> Am (and Am Bm)) B)) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) (and (-> Am (and Am Bm)) B))))
================================================================
tm-name          tm-18309
in-theory        18309
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((A -> (A and B)) -> C) -> (((A -> (A and B)) -> C) and (((A -> B) or (A -> (A and B))) -> C))))
theorem-size     47
proof            (modus-ponens tm-328 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18309.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((A -> (A and B)) -> C) -> (((A -> (A and B)) -> C) and (((A -> B) or (A -> (A and B))) -> C)))), M:tm-328, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18310
in-theory        18310
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((D -> (E -> (D and E))) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C))))
theorem-size     47
proof            (modus-ponens tm-327 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18310.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((D -> (E -> (D and E))) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)))), M:tm-327, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18311
in-theory        18311
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((D and E) -> E) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C))))
theorem-size     45
proof            (modus-ponens tm-326 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18311.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((D and E) -> E) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)))), M:tm-326, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18312
in-theory        18312
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((D and E) -> D) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C))))
theorem-size     45
proof            (modus-ponens tm-325 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18312.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((D and E) -> D) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)))), M:tm-325, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18313
in-theory        18313
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C))))
theorem-size     53
proof            (modus-ponens tm-324 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18313.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)))), M:tm-324, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18314
in-theory        18314
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((D -> (E -> D)) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C))))
theorem-size     45
proof            (modus-ponens tm-323 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18314.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((D -> (E -> D)) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)))), M:tm-323, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18315
in-theory        18315
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-322 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18315.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18316
in-theory        18316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-320 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18316.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18317
in-theory        18317
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-318 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18317.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18318
in-theory        18318
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((A -> (A and B)) -> C) -> ((A -> (A and B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-316 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18318.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((A -> (A and B)) -> C) -> ((A -> (A and B)) -> C))), M:tm-316, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18319
in-theory        18319
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-315 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18319.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18320
in-theory        18320
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((((A -> (A and B)) -> C) -> (not (((A -> B) or (A -> (A and B))) -> C))) -> (not ((A -> (A and B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-313 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18320.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((((A -> (A and B)) -> C) -> (not (((A -> B) or (A -> (A and B))) -> C))) -> (not ((A -> (A and B)) -> C)))), M:tm-313, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18321
in-theory        18321
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((((A -> B) or (A -> (A and B))) -> C) -> D) -> ((((A -> (A and B)) -> C) or (((A -> B) or (A -> (A and B))) -> C)) -> D)))
theorem-size     55
proof            (modus-ponens tm-312 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18321.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((((A -> B) or (A -> (A and B))) -> C) -> D) -> ((((A -> (A and B)) -> C) or (((A -> B) or (A -> (A and B))) -> C)) -> D))), M:tm-312, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18322
in-theory        18322
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (D or (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C))))
theorem-size     41
proof            (modus-ponens tm-311 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18322.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (D or (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)))), M:tm-311, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18323
in-theory        18323
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) or D))
theorem-size     41
proof            (modus-ponens tm-310 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18323.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) or D)), M:tm-310, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18324
in-theory        18324
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (D -> ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and D)))
theorem-size     43
proof            (modus-ponens tm-309 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18324.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (D -> ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and D))), M:tm-309, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18325
in-theory        18325
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((((A -> (A and B)) -> C) -> ((A -> B) or (A -> (A and B)))) -> (((A -> (A and B)) -> C) -> C)))
theorem-size     47
proof            (modus-ponens tm-306 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (or (-> Am Bm) (-> Am (and Am Bm)))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18325.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((((A -> (A and B)) -> C) -> ((A -> B) or (A -> (A and B)))) -> (((A -> (A and B)) -> C) -> C))), M:tm-306, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (or (-> Am Bm) (-> Am (and Am Bm)))) (C Cm))
================================================================
tm-name          tm-18326
in-theory        18326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (D -> (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C))))
theorem-size     41
proof            (modus-ponens tm-305 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18326.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (D -> (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)))), M:tm-305, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18327
in-theory        18327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-303 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18327.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-303, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18328
in-theory        18328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     29
proof            (modus-ponens tm-270 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18328.        ((A -> (((B and C) -> C) and A)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-270, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18329
in-theory        18329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     29
proof            (modus-ponens tm-239 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18329.        ((A -> (((B and C) -> B) and A)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-239, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18330
in-theory        18330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G)))
theorem-size     37
proof            (modus-ponens tm-210 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18330.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G))), M:tm-210, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18331
in-theory        18331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     29
proof            (modus-ponens tm-183 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18331.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-183, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18332
in-theory        18332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-157 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18332.        ((A -> ((B and C) -> C)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-157, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18333
in-theory        18333
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     35
proof            (modus-ponens tm-147 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18333.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-147, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18334
in-theory        18334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-134 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18334.        ((A -> ((B and C) -> B)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-134, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18335
in-theory        18335
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     35
proof            (modus-ponens tm-125 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18335.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-125, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18336
in-theory        18336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> (C -> D)) -> ((((A -> B) or (A -> (A and B))) -> C) -> (((A -> B) or (A -> (A and B))) -> D)))
theorem-size     33
proof            (modus-ponens tm-114 tm-335 ((A (-> (-> Am (and Am Bm)) (-> C D))) (B (or (-> Am Bm) (-> Am (and Am Bm)))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18336.        (((A -> (A and B)) -> (C -> D)) -> ((((A -> B) or (A -> (A and B))) -> C) -> (((A -> B) or (A -> (A and B))) -> D))), M:tm-114, m:tm-335, u:((A (-> (-> Am (and Am Bm)) (-> C D))) (B (or (-> Am Bm) (-> Am (and Am Bm)))) (Cm (-> C D)))
================================================================
tm-name          tm-18337
in-theory        18337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-113 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18337.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G))), M:tm-113, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18338
in-theory        18338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     39
proof            (modus-ponens tm-105 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18338.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-105, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18339
in-theory        18339
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E)))
theorem-size     27
proof            (modus-ponens tm-95 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18339.        (((A -> B) -> (A -> A)) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E))), M:tm-95, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18340
in-theory        18340
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) or ((A -> (A and B)) -> (A -> (A and B)))) -> (((A -> B) or (A -> (A and B))) -> (A -> (A and B))))
theorem-size     35
proof            (modus-ponens tm-92 tm-335 ((Cm (-> Am (and Am Bm))) (A (-> Am (and Am Bm))) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) (-> Am (and Am Bm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18340.        ((((A -> (A and B)) -> C) or ((A -> (A and B)) -> (A -> (A and B)))) -> (((A -> B) or (A -> (A and B))) -> (A -> (A and B)))), M:tm-92, m:tm-335, u:((Cm (-> Am (and Am Bm))) (A (-> Am (and Am Bm))) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-18341
in-theory        18341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> C) -> (D -> (((A -> B) or (A -> (A and B))) -> C)))
theorem-size     21
proof            (modus-ponens tm-84 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18341.        (((A -> (A and B)) -> C) -> (D -> (((A -> B) or (A -> (A and B))) -> C))), M:tm-84, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18342
in-theory        18342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-83 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18342.        ((A -> (B -> (C -> B))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-83, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18343
in-theory        18343
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B and C)) -> (D -> (B -> (B and C))))) -> (((B -> C) or (B -> (B and C))) -> (D -> (B -> (B and C)))))
theorem-size     33
proof            (modus-ponens tm-80 tm-335 ((A (-> Am (and Am Bm))) (Cm (-> B (-> Am (and Am Bm)))) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) (-> B (-> Am (and Am Bm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18343.        ((A or ((B -> (B and C)) -> (D -> (B -> (B and C))))) -> (((B -> C) or (B -> (B and C))) -> (D -> (B -> (B and C))))), M:tm-80, m:tm-335, u:((A (-> Am (and Am Bm))) (Cm (-> B (-> Am (and Am Bm)))) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) (-> B (-> Am (and Am Bm))))))
================================================================
tm-name          tm-18344
in-theory        18344
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (B and C)) -> D) -> (((B -> C) or (B -> (B and C))) -> D)))
theorem-size     25
proof            (modus-ponens tm-76 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18344.        (((not (not A)) -> A) and (((B -> (B and C)) -> D) -> (((B -> C) or (B -> (B and C))) -> D))), M:tm-76, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18345
in-theory        18345
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (A and B)) -> C))) or ((A -> (A and B)) -> C)) -> (((A -> B) or (A -> (A and B))) -> C))
theorem-size     29
proof            (modus-ponens tm-73 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18345.        (((not (not ((A -> (A and B)) -> C))) or ((A -> (A and B)) -> C)) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-73, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18346
in-theory        18346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E)))
theorem-size     31
proof            (modus-ponens tm-69 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18346.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E))), M:tm-69, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18347
in-theory        18347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> ((A -> B) or (A -> (A and B)))) -> (((A -> (A and B)) or ((A -> B) or (A -> (A and B)))) -> ((A -> B) or (A -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-55 tm-335 ((A (-> Am (and Am Bm))) (Cm (or (-> Am Bm) (-> Am (and Am Bm)))) (B (or (-> Am Bm) (-> Am (and Am Bm)))) (C (or (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18347.        (((A -> (A and B)) -> ((A -> B) or (A -> (A and B)))) -> (((A -> (A and B)) or ((A -> B) or (A -> (A and B)))) -> ((A -> B) or (A -> (A and B))))), M:tm-55, m:tm-335, u:((A (-> Am (and Am Bm))) (Cm (or (-> Am Bm) (-> Am (and Am Bm)))) (B (or (-> Am Bm) (-> Am (and Am Bm)))) (C (or (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-18348
in-theory        18348
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     33
proof            (modus-ponens tm-54 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18348.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-54, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18349
in-theory        18349
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (B and C)) -> ((A or B) -> (B and C)))) -> (((B -> C) or (B -> (B and C))) -> ((A or B) -> (B and C))))
theorem-size     35
proof            (modus-ponens tm-51 tm-335 ((A Am) (B (and Am Bm)) (Cm (-> (or C Am) (and Am Bm))) (D (-> (or (-> Am Bm) (-> Am (and Am Bm))) (-> (or C Am) (and Am Bm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18349.        (((A -> B) or ((B -> (B and C)) -> ((A or B) -> (B and C)))) -> (((B -> C) or (B -> (B and C))) -> ((A or B) -> (B and C)))), M:tm-51, m:tm-335, u:((A Am) (B (and Am Bm)) (Cm (-> (or C Am) (and Am Bm))) (D (-> (or (-> Am Bm) (-> Am (and Am Bm))) (-> (or C Am) (and Am Bm)))))
================================================================
tm-name          tm-18350
in-theory        18350
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (B and C)) -> (A and (B -> (B and C))))) -> (((B -> C) or (B -> (B and C))) -> (A and (B -> (B and C)))))
theorem-size     33
proof            (modus-ponens tm-48 tm-335 ((A (-> Am (and Am Bm))) (Cm (and B (-> Am (and Am Bm)))) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) (and B (-> Am (and Am Bm)))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18350.        ((A or ((B -> (B and C)) -> (A and (B -> (B and C))))) -> (((B -> C) or (B -> (B and C))) -> (A and (B -> (B and C))))), M:tm-48, m:tm-335, u:((A (-> Am (and Am Bm))) (Cm (and B (-> Am (and Am Bm)))) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) (and B (-> Am (and Am Bm))))))
================================================================
tm-name          tm-18351
in-theory        18351
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((B -> (B and C)) -> D)) or ((B -> (B and C)) -> D)) -> (((B -> C) or (B -> (B and C))) -> D))
theorem-size     29
proof            (modus-ponens tm-47 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18351.        (((A and ((B -> (B and C)) -> D)) or ((B -> (B and C)) -> D)) -> (((B -> C) or (B -> (B and C))) -> D)), M:tm-47, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18352
in-theory        18352
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (A and B)) -> C) and D) or ((A -> (A and B)) -> C)) -> (((A -> B) or (A -> (A and B))) -> C))
theorem-size     29
proof            (modus-ponens tm-46 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18352.        (((((A -> (A and B)) -> C) and D) or ((A -> (A and B)) -> C)) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-46, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18353
in-theory        18353
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((A and B) -> C)) or ((A -> (A and B)) -> (A -> C))) -> (((A -> B) or (A -> (A and B))) -> (A -> C)))
theorem-size     31
proof            (modus-ponens tm-45 tm-335 ((A Am) (B (and Am Bm)) (Cm (-> Am C)) (D (-> (or (-> Am Bm) (-> Am (and Am Bm))) (-> Am C)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18353.        (((A -> ((A and B) -> C)) or ((A -> (A and B)) -> (A -> C))) -> (((A -> B) or (A -> (A and B))) -> (A -> C))), M:tm-45, m:tm-335, u:((A Am) (B (and Am Bm)) (Cm (-> Am C)) (D (-> (or (-> Am Bm) (-> Am (and Am Bm))) (-> Am C))))
================================================================
tm-name          tm-18354
in-theory        18354
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (B and C)) -> A)) -> (((B -> C) or (B -> (B and C))) -> A))
theorem-size     21
proof            (modus-ponens tm-44 tm-335 ((A (-> Am (and Am Bm))) (B Cm) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18354.        ((A or ((B -> (B and C)) -> A)) -> (((B -> C) or (B -> (B and C))) -> A)), M:tm-44, m:tm-335, u:((A (-> Am (and Am Bm))) (B Cm) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18355
in-theory        18355
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E)))
theorem-size     25
proof            (modus-ponens tm-42 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18355.        ((A -> (B or A)) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E))), M:tm-42, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18356
in-theory        18356
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E)))
theorem-size     25
proof            (modus-ponens tm-32 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18356.        ((A -> (A or B)) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E))), M:tm-32, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18357
in-theory        18357
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> C) -> (((A -> (A and B)) -> C) and (((A -> B) or (A -> (A and B))) -> C)))
theorem-size     27
proof            (modus-ponens tm-24 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18357.        (((A -> (A and B)) -> C) -> (((A -> (A and B)) -> C) and (((A -> B) or (A -> (A and B))) -> C))), M:tm-24, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18358
in-theory        18358
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E)))
theorem-size     27
proof            (modus-ponens tm-23 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18358.        ((A -> (B -> (A and B))) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E))), M:tm-23, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18359
in-theory        18359
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E)))
theorem-size     25
proof            (modus-ponens tm-22 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18359.        (((A and B) -> B) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E))), M:tm-22, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18360
in-theory        18360
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E)))
theorem-size     25
proof            (modus-ponens tm-21 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18360.        (((A and B) -> A) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E))), M:tm-21, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18361
in-theory        18361
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     33
proof            (modus-ponens tm-20 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18361.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-20, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18362
in-theory        18362
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E)))
theorem-size     25
proof            (modus-ponens tm-19 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18362.        ((A -> (B -> A)) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E))), M:tm-19, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18363
in-theory        18363
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> C) -> ((A -> (A and B)) -> C))
theorem-size     15
proof            (modus-ponens tm-12 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18363.        (((A -> (A and B)) -> C) -> ((A -> (A and B)) -> C)), M:tm-12, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18364
in-theory        18364
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (not (((A -> B) or (A -> (A and B))) -> C))) -> (not ((A -> (A and B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-9 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-9 tm-8 tm-2 tm-5)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18364.        ((((A -> (A and B)) -> C) -> (not (((A -> B) or (A -> (A and B))) -> C))) -> (not ((A -> (A and B)) -> C))), M:tm-9, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18365
in-theory        18365
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) or (A -> (A and B))) -> C) -> D) -> ((((A -> (A and B)) -> C) or (((A -> B) or (A -> (A and B))) -> C)) -> D))
theorem-size     35
proof            (modus-ponens tm-8 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18365.        (((((A -> B) or (A -> (A and B))) -> C) -> D) -> ((((A -> (A and B)) -> C) or (((A -> B) or (A -> (A and B))) -> C)) -> D)), M:tm-8, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18366
in-theory        18366
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> (B and C)) -> D) -> (((B -> C) or (B -> (B and C))) -> D)))
theorem-size     21
proof            (modus-ponens tm-7 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-7 tm-8 tm-2 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18366.        (A or (((B -> (B and C)) -> D) -> (((B -> C) or (B -> (B and C))) -> D))), M:tm-7, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18367
in-theory        18367
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) or D)
theorem-size     21
proof            (modus-ponens tm-6 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-6 tm-8 tm-2 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18367.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) or D), M:tm-6, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18368
in-theory        18368
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (B and C)) -> D) -> (((B -> C) or (B -> (B and C))) -> D)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18368.        (A -> ((((B -> (B and C)) -> D) -> (((B -> C) or (B -> (B and C))) -> D)) and A)), M:tm-5, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18369
in-theory        18369
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> ((A -> B) or (A -> (A and B)))) -> (((A -> (A and B)) -> C) -> C))
theorem-size     27
proof            (modus-ponens tm-2 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (or (-> Am Bm) (-> Am (and Am Bm)))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18369.        ((((A -> (A and B)) -> C) -> ((A -> B) or (A -> (A and B)))) -> (((A -> (A and B)) -> C) -> C)), M:tm-2, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (or (-> Am Bm) (-> Am (and Am Bm)))) (C Cm))
================================================================
tm-name          tm-18370
in-theory        18370
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (B and C)) -> D) -> (((B -> C) or (B -> (B and C))) -> D)))
theorem-size     21
proof            (modus-ponens tm-1 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-1 tm-8 tm-2 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18370.        (A -> (((B -> (B and C)) -> D) -> (((B -> C) or (B -> (B and C))) -> D))), M:tm-1, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18371
in-theory        18371
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and ((D -> (E -> (D and E))) and (A or ((B -> C) -> (B -> (B and C))))))
theorem-size     31
proof            (modus-ponens tm-327 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18371.        ((A or ((B -> C) -> (B -> (B and C)))) and ((D -> (E -> (D and E))) and (A or ((B -> C) -> (B -> (B and C)))))), M:tm-327, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18372
in-theory        18372
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and (((D and E) -> E) and (A or ((B -> C) -> (B -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-326 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18372.        ((A or ((B -> C) -> (B -> (B and C)))) and (((D and E) -> E) and (A or ((B -> C) -> (B -> (B and C)))))), M:tm-326, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18373
in-theory        18373
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and (((D and E) -> D) and (A or ((B -> C) -> (B -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-325 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18373.        ((A or ((B -> C) -> (B -> (B and C)))) and (((D and E) -> D) and (A or ((B -> C) -> (B -> (B and C)))))), M:tm-325, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18374
in-theory        18374
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or ((B -> C) -> (B -> (B and C))))))
theorem-size     37
proof            (modus-ponens tm-324 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18374.        ((A or ((B -> C) -> (B -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A or ((B -> C) -> (B -> (B and C)))))), M:tm-324, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18375
in-theory        18375
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and ((D -> (E -> D)) and (A or ((B -> C) -> (B -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-323 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18375.        ((A or ((B -> C) -> (B -> (B and C)))) and ((D -> (E -> D)) and (A or ((B -> C) -> (B -> (B and C)))))), M:tm-323, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18376
in-theory        18376
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18376.        ((A or ((B -> C) -> (B -> (B and C)))) and ((D and E) -> E)), M:tm-322, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18377
in-theory        18377
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18377.        ((A or ((B -> C) -> (B -> (B and C)))) and ((D and E) -> D)), M:tm-320, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18378
in-theory        18378
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18378.        ((A or ((B -> C) -> (B -> (B and C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18379
in-theory        18379
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18379.        ((A or ((B -> C) -> (B -> (B and C)))) and (D -> (E -> D))), M:tm-315, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18380
in-theory        18380
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and (D or (A or ((B -> C) -> (B -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-311 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18380.        ((A or ((B -> C) -> (B -> (B and C)))) and (D or (A or ((B -> C) -> (B -> (B and C)))))), M:tm-311, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18381
in-theory        18381
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and ((A or ((B -> C) -> (B -> (B and C)))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18381.        ((A or ((B -> C) -> (B -> (B and C)))) and ((A or ((B -> C) -> (B -> (B and C)))) or D)), M:tm-310, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18382
in-theory        18382
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and (D -> ((A or ((B -> C) -> (B -> (B and C)))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18382.        ((A or ((B -> C) -> (B -> (B and C)))) and (D -> ((A or ((B -> C) -> (B -> (B and C)))) and D))), M:tm-309, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18383
in-theory        18383
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and (D -> (A or ((B -> C) -> (B -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-305 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18383.        ((A or ((B -> C) -> (B -> (B and C)))) and (D -> (A or ((B -> C) -> (B -> (B and C)))))), M:tm-305, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18384
in-theory        18384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-303 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18384.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-303, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18385
in-theory        18385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-270 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18385.        ((A -> (((B and C) -> C) and A)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-270, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18386
in-theory        18386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-239 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18386.        ((A -> (((B and C) -> B) and A)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-239, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18387
in-theory        18387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-210 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18387.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> G) -> (F -> (F and G))))), M:tm-210, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18388
in-theory        18388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-183 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18388.        ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-183, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18389
in-theory        18389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-157 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18389.        ((A -> ((B and C) -> C)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-157, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18390
in-theory        18390
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-147 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18390.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-147, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18391
in-theory        18391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-134 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18391.        ((A -> ((B and C) -> B)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-134, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18392
in-theory        18392
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-125 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18392.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-125, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18393
in-theory        18393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-113 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18393.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (F -> (F and G))))), M:tm-113, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18394
in-theory        18394
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     31
proof            (modus-ponens tm-105 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18394.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-105, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18395
in-theory        18395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((D -> E) -> (D -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-95 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18395.        (((A -> B) -> (A -> A)) and (C or ((D -> E) -> (D -> (D and E))))), M:tm-95, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18396
in-theory        18396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-83 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18396.        ((A -> (B -> (C -> B))) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-83, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18397
in-theory        18397
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((C -> D) -> (C -> (C and D)))))
theorem-size     17
proof            (modus-ponens tm-76 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18397.        (((not (not A)) -> A) and (B or ((C -> D) -> (C -> (C and D))))), M:tm-76, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18398
in-theory        18398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> E) -> (D -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-69 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18398.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> E) -> (D -> (D and E))))), M:tm-69, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18399
in-theory        18399
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-54 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18399.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-54, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18400
in-theory        18400
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-42 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18400.        ((A -> (B or A)) and (C or ((D -> E) -> (D -> (D and E))))), M:tm-42, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18401
in-theory        18401
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-32 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18401.        ((A -> (A or B)) and (C or ((D -> E) -> (D -> (D and E))))), M:tm-32, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18402
in-theory        18402
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((D -> E) -> (D -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-23 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18402.        ((A -> (B -> (A and B))) and (C or ((D -> E) -> (D -> (D and E))))), M:tm-23, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18403
in-theory        18403
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-22 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18403.        (((A and B) -> B) and (C or ((D -> E) -> (D -> (D and E))))), M:tm-22, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18404
in-theory        18404
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-21 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18404.        (((A and B) -> A) and (C or ((D -> E) -> (D -> (D and E))))), M:tm-21, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18405
in-theory        18405
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-20 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18405.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-20, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18406
in-theory        18406
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-19 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18406.        ((A -> (B -> A)) and (C or ((D -> E) -> (D -> (D and E))))), M:tm-19, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18407
in-theory        18407
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or ((C -> D) -> (C -> (C and D)))))
theorem-size     13
proof            (modus-ponens tm-7 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-7 tm-2 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18407.        (A or (B or ((C -> D) -> (C -> (C and D))))), M:tm-7, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18408
in-theory        18408
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-6 tm-7 tm-2 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18408.        ((A or ((B -> C) -> (B -> (B and C)))) or D), M:tm-6, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18409
in-theory        18409
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> D) -> (C -> (C and D)))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18409.        (A -> ((B or ((C -> D) -> (C -> (C and D)))) and A)), M:tm-5, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18410
in-theory        18410
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or ((C -> D) -> (C -> (C and D)))))
theorem-size     13
proof            (modus-ponens tm-1 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-1 tm-7 tm-2 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18410.        (A -> (B or ((C -> D) -> (C -> (C and D))))), M:tm-1, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18411
in-theory        18411
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((A -> B) -> (A -> (A and B))) or C)))
theorem-size     31
proof            (modus-ponens tm-327 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18411.        ((((A -> B) -> (A -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((A -> B) -> (A -> (A and B))) or C))), M:tm-327, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18412
in-theory        18412
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and (((D and E) -> E) and (((A -> B) -> (A -> (A and B))) or C)))
theorem-size     29
proof            (modus-ponens tm-326 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18412.        ((((A -> B) -> (A -> (A and B))) or C) and (((D and E) -> E) and (((A -> B) -> (A -> (A and B))) or C))), M:tm-326, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18413
in-theory        18413
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and (((D and E) -> D) and (((A -> B) -> (A -> (A and B))) or C)))
theorem-size     29
proof            (modus-ponens tm-325 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18413.        ((((A -> B) -> (A -> (A and B))) or C) and (((D and E) -> D) and (((A -> B) -> (A -> (A and B))) or C))), M:tm-325, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18414
in-theory        18414
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> (A -> (A and B))) or C)))
theorem-size     37
proof            (modus-ponens tm-324 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18414.        ((((A -> B) -> (A -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> (A -> (A and B))) or C))), M:tm-324, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18415
in-theory        18415
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and ((D -> (E -> D)) and (((A -> B) -> (A -> (A and B))) or C)))
theorem-size     29
proof            (modus-ponens tm-323 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18415.        ((((A -> B) -> (A -> (A and B))) or C) and ((D -> (E -> D)) and (((A -> B) -> (A -> (A and B))) or C))), M:tm-323, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18416
in-theory        18416
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18416.        ((((A -> B) -> (A -> (A and B))) or C) and ((D and E) -> E)), M:tm-322, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18417
in-theory        18417
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18417.        ((((A -> B) -> (A -> (A and B))) or C) and ((D and E) -> D)), M:tm-320, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18418
in-theory        18418
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18418.        ((((A -> B) -> (A -> (A and B))) or C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18419
in-theory        18419
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18419.        ((((A -> B) -> (A -> (A and B))) or C) and (D -> (E -> D))), M:tm-315, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18420
in-theory        18420
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and (D or (((A -> B) -> (A -> (A and B))) or C)))
theorem-size     25
proof            (modus-ponens tm-311 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18420.        ((((A -> B) -> (A -> (A and B))) or C) and (D or (((A -> B) -> (A -> (A and B))) or C))), M:tm-311, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18421
in-theory        18421
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and ((((A -> B) -> (A -> (A and B))) or C) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18421.        ((((A -> B) -> (A -> (A and B))) or C) and ((((A -> B) -> (A -> (A and B))) or C) or D)), M:tm-310, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18422
in-theory        18422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and (D -> ((((A -> B) -> (A -> (A and B))) or C) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18422.        ((((A -> B) -> (A -> (A and B))) or C) and (D -> ((((A -> B) -> (A -> (A and B))) or C) and D))), M:tm-309, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18423
in-theory        18423
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and (D -> (((A -> B) -> (A -> (A and B))) or C)))
theorem-size     25
proof            (modus-ponens tm-305 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18423.        ((((A -> B) -> (A -> (A and B))) or C) and (D -> (((A -> B) -> (A -> (A and B))) or C))), M:tm-305, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18424
in-theory        18424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     23
proof            (modus-ponens tm-303 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18424.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-303, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18425
in-theory        18425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     21
proof            (modus-ponens tm-270 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18425.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-270, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18426
in-theory        18426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     21
proof            (modus-ponens tm-239 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18426.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-239, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18427
in-theory        18427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (E -> (E and F))) or G))
theorem-size     29
proof            (modus-ponens tm-210 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18427.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (E -> (E and F))) or G)), M:tm-210, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18428
in-theory        18428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     21
proof            (modus-ponens tm-183 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18428.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-183, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18429
in-theory        18429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-157 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18429.        ((A -> ((B and C) -> C)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-157, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18430
in-theory        18430
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     27
proof            (modus-ponens tm-147 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18430.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-147, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18431
in-theory        18431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-134 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18431.        ((A -> ((B and C) -> B)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-134, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18432
in-theory        18432
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     27
proof            (modus-ponens tm-125 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18432.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-125, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18433
in-theory        18433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (E -> (E and F))) or G))
theorem-size     27
proof            (modus-ponens tm-113 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18433.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (E -> (E and F))) or G)), M:tm-113, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18434
in-theory        18434
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     31
proof            (modus-ponens tm-105 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18434.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-105, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18435
in-theory        18435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> (C -> (C and D))) or E))
theorem-size     19
proof            (modus-ponens tm-95 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18435.        (((A -> B) -> (A -> A)) and (((C -> D) -> (C -> (C and D))) or E)), M:tm-95, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18436
in-theory        18436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-83 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18436.        ((A -> (B -> (C -> B))) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-83, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18437
in-theory        18437
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> (B -> (B and C))) or D))
theorem-size     17
proof            (modus-ponens tm-76 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-10 tm-6 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18437.        (((not (not A)) -> A) and (((B -> C) -> (B -> (B and C))) or D)), M:tm-76, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18438
in-theory        18438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (C -> (C and D))) or E))
theorem-size     23
proof            (modus-ponens tm-69 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-9 tm-6 tm-2)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18438.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (C -> (C and D))) or E)), M:tm-69, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18439
in-theory        18439
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     25
proof            (modus-ponens tm-54 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18439.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-54, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18440
in-theory        18440
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> (C -> (C and D))) or E))
theorem-size     17
proof            (modus-ponens tm-42 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18440.        ((A -> (B or A)) and (((C -> D) -> (C -> (C and D))) or E)), M:tm-42, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18441
in-theory        18441
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> (C -> (C and D))) or E))
theorem-size     17
proof            (modus-ponens tm-32 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18441.        ((A -> (A or B)) and (((C -> D) -> (C -> (C and D))) or E)), M:tm-32, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18442
in-theory        18442
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> (C -> (C and D))) or E))
theorem-size     19
proof            (modus-ponens tm-23 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18442.        ((A -> (B -> (A and B))) and (((C -> D) -> (C -> (C and D))) or E)), M:tm-23, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18443
in-theory        18443
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> (C -> (C and D))) or E))
theorem-size     17
proof            (modus-ponens tm-22 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18443.        (((A and B) -> B) and (((C -> D) -> (C -> (C and D))) or E)), M:tm-22, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18444
in-theory        18444
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> (C -> (C and D))) or E))
theorem-size     17
proof            (modus-ponens tm-21 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18444.        (((A and B) -> A) and (((C -> D) -> (C -> (C and D))) or E)), M:tm-21, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18445
in-theory        18445
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     25
proof            (modus-ponens tm-20 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18445.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-20, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18446
in-theory        18446
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> (C -> (C and D))) or E))
theorem-size     17
proof            (modus-ponens tm-19 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18446.        ((A -> (B -> A)) and (((C -> D) -> (C -> (C and D))) or E)), M:tm-19, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18447
in-theory        18447
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> C) -> (B -> (B and C))) or D))
theorem-size     13
proof            (modus-ponens tm-7 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-7 tm-6 tm-2 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18447.        (A or (((B -> C) -> (B -> (B and C))) or D)), M:tm-7, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18448
in-theory        18448
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-6 tm-2 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18448.        ((((A -> B) -> (A -> (A and B))) or C) or D), M:tm-6, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18449
in-theory        18449
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (B -> (B and C))) or D) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18449.        (A -> ((((B -> C) -> (B -> (B and C))) or D) and A)), M:tm-5, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18450
in-theory        18450
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> (B and C))) or D))
theorem-size     13
proof            (modus-ponens tm-1 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-1 tm-6 tm-2 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18450.        (A -> (((B -> C) -> (B -> (B and C))) or D)), M:tm-1, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18451
in-theory        18451
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-338 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18451.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> (C and D)))), M:tm-338, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-18452
in-theory        18452
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-338 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-18452.        (((A -> B) -> (A -> (A and B))) and (C -> (C or D))), M:tm-338, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-18453
in-theory        18453
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-338 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-18453.        (((A -> B) -> (A -> (A and B))) and (C -> (D or C))), M:tm-338, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-18454
in-theory        18454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-18454.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-338, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-18455
in-theory        18455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     21
proof            (modus-ponens tm-338 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-18455.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-338, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-18456
in-theory        18456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((not (not C)) -> C))
theorem-size     15
proof            (modus-ponens tm-338 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-18456.        (((A -> B) -> (A -> (A and B))) and ((not (not C)) -> C)), M:tm-338, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-18457
in-theory        18457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-338 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18457.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-338, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-18458
in-theory        18458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (C -> C)))
theorem-size     17
proof            (modus-ponens tm-338 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-18458.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-338, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-18459
in-theory        18459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-338 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-18459.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-338, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-18460
in-theory        18460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-18460.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-338, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-18461
in-theory        18461
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     25
proof            (modus-ponens tm-338 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-18461.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-338, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-18462
in-theory        18462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D and E) -> D)))
theorem-size     17
proof            (modus-ponens tm-338 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-18462.        (((A -> B) -> (A -> (A and B))) and (C -> ((D and E) -> D))), M:tm-338, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-18463
in-theory        18463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     25
proof            (modus-ponens tm-338 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18463.        (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-338, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-18464
in-theory        18464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D and E) -> E)))
theorem-size     17
proof            (modus-ponens tm-338 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18464.        (((A -> B) -> (A -> (A and B))) and (C -> ((D and E) -> E))), M:tm-338, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-18465
in-theory        18465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> D)) and C)))
theorem-size     19
proof            (modus-ponens tm-338 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18465.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-338, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-18466
in-theory        18466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     27
proof            (modus-ponens tm-338 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-18466.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-338, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-18467
in-theory        18467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D and E) -> D) and C)))
theorem-size     19
proof            (modus-ponens tm-338 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-18467.        (((A -> B) -> (A -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-338, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-18468
in-theory        18468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D and E) -> E) and C)))
theorem-size     19
proof            (modus-ponens tm-338 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18468.        (((A -> B) -> (A -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-338, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-18469
in-theory        18469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-18469.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-338, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18470
in-theory        18470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (C -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-338 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18470.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-338, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-18471
in-theory        18471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-18471.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-338, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-18472
in-theory        18472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) or E))
theorem-size     17
proof            (modus-ponens tm-338 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18472.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-338, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-18473
in-theory        18473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     25
proof            (modus-ponens tm-338 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-18473.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-338, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-18474
in-theory        18474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) or E))
theorem-size     17
proof            (modus-ponens tm-338 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-18474.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) or E)), M:tm-338, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-18475
in-theory        18475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) or E))
theorem-size     17
proof            (modus-ponens tm-338 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18475.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) or E)), M:tm-338, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-18476
in-theory        18476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) or E))
theorem-size     19
proof            (modus-ponens tm-338 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-18476.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-338, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-18477
in-theory        18477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) or E))
theorem-size     17
proof            (modus-ponens tm-338 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-18477.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) or E)), M:tm-338, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-18478
in-theory        18478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (D or E)) and C)))
theorem-size     19
proof            (modus-ponens tm-338 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-18478.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-338, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-18479
in-theory        18479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-338 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-18479.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> (D or E)))), M:tm-338, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-18480
in-theory        18480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-338 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18480.        (((A -> B) -> (A -> (A and B))) and (C or (D -> (E -> D)))), M:tm-338, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-18481
in-theory        18481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-18481.        (((A -> B) -> (A -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-338, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-18482
in-theory        18482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((D and E) -> D)))
theorem-size     17
proof            (modus-ponens tm-338 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-18482.        (((A -> B) -> (A -> (A and B))) and (C or ((D and E) -> D))), M:tm-338, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-18483
in-theory        18483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((D and E) -> E)))
theorem-size     17
proof            (modus-ponens tm-338 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18483.        (((A -> B) -> (A -> (A and B))) and (C or ((D and E) -> E))), M:tm-338, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-18484
in-theory        18484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-18484.        (((A -> B) -> (A -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-338, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-18485
in-theory        18485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-338 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-18485.        (((A -> B) -> (A -> (A and B))) and (C or (D -> (D or E)))), M:tm-338, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-18486
in-theory        18486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-338 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-18486.        (((A -> B) -> (A -> (A and B))) and (C or (D -> (E or D)))), M:tm-338, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-18487
in-theory        18487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) or E))
theorem-size     17
proof            (modus-ponens tm-338 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-18487.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) or E)), M:tm-338, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-18488
in-theory        18488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E or D)) and C)))
theorem-size     19
proof            (modus-ponens tm-338 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-18488.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-338, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-18489
in-theory        18489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-338 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-18489.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> (E or D)))), M:tm-338, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-18490
in-theory        18490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-338 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-18490.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-338, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-18491
in-theory        18491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     35
proof            (modus-ponens tm-338 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-18491.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-338, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-18492
in-theory        18492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     21
proof            (modus-ponens tm-338 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-18492.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-338, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-18493
in-theory        18493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D)))
theorem-size     21
proof            (modus-ponens tm-338 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18493.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (((E and C) or C) -> D))), M:tm-338, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-18494
in-theory        18494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E)))
theorem-size     27
proof            (modus-ponens tm-338 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-18494.        (((A -> B) -> (A -> (A and B))) and (((C -> (D and C)) -> E) -> ((D or (C -> (D and C))) -> E))), M:tm-338, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-18495
in-theory        18495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-338 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-18495.        (((A -> B) -> (A -> (A and B))) and (((C or D) -> E) -> ((C or (C or D)) -> E))), M:tm-338, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-18496
in-theory        18496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-338 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-18496.        (((A -> B) -> (A -> (A and B))) and (((C or D) -> E) -> ((D or (C or D)) -> E))), M:tm-338, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-18497
in-theory        18497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-338 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-18497.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> ((E or C) -> D)) -> F) -> (((E -> C) or ((C -> D) -> ((E or C) -> D))) -> F))), M:tm-338, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-18498
in-theory        18498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-18498.        (((A -> B) -> (A -> (A and B))) and (C or ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-338, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-18499
in-theory        18499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F))
theorem-size     25
proof            (modus-ponens tm-338 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-18499.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((D -> E) -> ((C or D) -> E))) or F)), M:tm-338, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-18500
in-theory        18500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C)))
theorem-size     27
proof            (modus-ponens tm-338 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-18500.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and C))), M:tm-338, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-18501
in-theory        18501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-338 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-18501.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (D -> E)) -> ((C -> D) -> ((C or D) -> E)))), M:tm-338, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-18502
in-theory        18502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-18502.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-338, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-18503
in-theory        18503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not (D -> C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-338 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-18503.        (((A -> B) -> (A -> (A and B))) and ((C -> (not (D -> C))) -> (not C))), M:tm-338, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-18504
in-theory        18504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-18504.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> (not ((C -> D) -> (C -> E)))) -> (not (C -> (D -> E))))), M:tm-338, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-18505
in-theory        18505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> (not C)) -> (not (C and D))))
theorem-size     21
proof            (modus-ponens tm-338 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-18505.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> (not C)) -> (not (C and D)))), M:tm-338, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-18506
in-theory        18506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> (not D)) -> (not (C and D))))
theorem-size     21
proof            (modus-ponens tm-338 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18506.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> (not D)) -> (not (C and D)))), M:tm-338, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-18507
in-theory        18507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not (D -> (C and D)))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-18507.        (((A -> B) -> (A -> (A and B))) and ((C -> (not (D -> (C and D)))) -> (not C))), M:tm-338, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-18508
in-theory        18508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not (C or D))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-338 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-18508.        (((A -> B) -> (A -> (A and B))) and ((C -> (not (C or D))) -> (not C))), M:tm-338, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-18509
in-theory        18509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not (D or C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-338 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-18509.        (((A -> B) -> (A -> (A and B))) and ((C -> (not (D or C))) -> (not C))), M:tm-338, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-18510
in-theory        18510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D))))
theorem-size     29
proof            (modus-ponens tm-338 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-18510.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (not ((D -> E) -> ((C or D) -> E)))) -> (not (C -> D)))), M:tm-338, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18511
in-theory        18511
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D))))
theorem-size     27
proof            (modus-ponens tm-338 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-18511.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (not ((C -> (not D)) -> (not C)))) -> (not (C -> D)))), M:tm-338, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18512
in-theory        18512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-338 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-9)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-18512.        (((A -> B) -> (A -> (A and B))) and ((((C -> (not D)) -> (not C)) -> E) -> (((C -> D) or ((C -> (not D)) -> (not C))) -> E))), M:tm-338, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-18513
in-theory        18513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-18513.        (((A -> B) -> (A -> (A and B))) and (C or ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-338, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-18514
in-theory        18514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E))
theorem-size     23
proof            (modus-ponens tm-338 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-18514.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((C -> (not D)) -> (not C))) or E)), M:tm-338, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-18515
in-theory        18515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C)))
theorem-size     25
proof            (modus-ponens tm-338 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-18515.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> ((D -> (not E)) -> (not D))) and C))), M:tm-338, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-18516
in-theory        18516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C))))
theorem-size     25
proof            (modus-ponens tm-338 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-18516.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (C -> (not D))) -> ((C -> D) -> (not C)))), M:tm-338, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-18517
in-theory        18517
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-18517.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-338, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-18518
in-theory        18518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((not (not C)) -> (not C)) -> (not (not (not C)))))
theorem-size     21
proof            (modus-ponens tm-338 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-2 tm-9 tm-10)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-18518.        (((A -> B) -> (A -> (A and B))) and (((not (not C)) -> (not C)) -> (not (not (not C))))), M:tm-338, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-18519
in-theory        18519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (((not (not C)) or C) -> D)))
theorem-size     21
proof            (modus-ponens tm-338 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-18519.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (((not (not C)) or C) -> D))), M:tm-338, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-18520
in-theory        18520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((not (not D)) -> D)))
theorem-size     17
proof            (modus-ponens tm-338 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-18520.        (((A -> B) -> (A -> (A and B))) and (C or ((not (not D)) -> D))), M:tm-338, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-18521
in-theory        18521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((not (not C)) -> C) or D))
theorem-size     17
proof            (modus-ponens tm-338 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-6 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-18521.        (((A -> B) -> (A -> (A and B))) and (((not (not C)) -> C) or D)), M:tm-338, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-18522
in-theory        18522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((not (not D)) -> D) and C)))
theorem-size     19
proof            (modus-ponens tm-338 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-18522.        (((A -> B) -> (A -> (A and B))) and (C -> (((not (not D)) -> D) and C))), M:tm-338, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-18523
in-theory        18523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D)))
theorem-size     25
proof            (modus-ponens tm-338 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-18523.        (((A -> B) -> (A -> (A and B))) and (((not (not (C -> D))) -> C) -> ((not (not (C -> D))) -> D))), M:tm-338, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-18524
in-theory        18524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((not (not D)) -> D)))
theorem-size     17
proof            (modus-ponens tm-338 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-18524.        (((A -> B) -> (A -> (A and B))) and (C -> ((not (not D)) -> D))), M:tm-338, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-18525
in-theory        18525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not (D -> (E -> D)))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-18525.        (((A -> B) -> (A -> (A and B))) and ((C -> (not (D -> (E -> D)))) -> (not C))), M:tm-338, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-18526
in-theory        18526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E)))
theorem-size     27
proof            (modus-ponens tm-338 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-18526.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> C)) -> E) -> ((F or (C -> (D -> C))) -> E))), M:tm-338, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-18527
in-theory        18527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-18527.        (((A -> B) -> (A -> (A and B))) and (C or (D -> (E -> (F -> E))))), M:tm-338, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-18528
in-theory        18528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (E -> D))) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-18528.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (E -> D))) or F)), M:tm-338, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-18529
in-theory        18529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> (F -> E))) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-18529.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> (F -> E))) and C))), M:tm-338, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-18530
in-theory        18530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (C -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-338 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-18530.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (C -> (E -> D)))), M:tm-338, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-18531
in-theory        18531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-18531.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> (E -> (F -> E))))), M:tm-338, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-18532
in-theory        18532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> C))
theorem-size     13
proof            (modus-ponens tm-338 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-18532.        (((A -> B) -> (A -> (A and B))) and (C -> C)), M:tm-338, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-18533
in-theory        18533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> E)) -> (C -> (D -> E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-18533.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> E)) -> (C -> (D -> E)))), M:tm-338, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-18534
in-theory        18534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C and D) -> (C and D)))
theorem-size     17
proof            (modus-ponens tm-338 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-18534.        (((A -> B) -> (A -> (A and B))) and ((C and D) -> (C and D))), M:tm-338, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-18535
in-theory        18535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (C -> D)))
theorem-size     17
proof            (modus-ponens tm-338 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-18535.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (C -> D))), M:tm-338, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-18536
in-theory        18536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((not (not C)) -> (not (not C))))
theorem-size     17
proof            (modus-ponens tm-338 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-18536.        (((A -> B) -> (A -> (A and B))) and ((not (not C)) -> (not (not C)))), M:tm-338, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-18537
in-theory        18537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (not (C -> C))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-338 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-18537.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (not (C -> C))) -> (not (C -> D)))), M:tm-338, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18538
in-theory        18538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D)))
theorem-size     25
proof            (modus-ponens tm-338 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-18538.        (((A -> B) -> (A -> (A and B))) and (((C -> C) -> D) -> (((C -> E) or (C -> C)) -> D))), M:tm-338, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-18539
in-theory        18539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((D -> E) -> (D -> D))))
theorem-size     19
proof            (modus-ponens tm-338 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-18539.        (((A -> B) -> (A -> (A and B))) and (C or ((D -> E) -> (D -> D)))), M:tm-338, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-18540
in-theory        18540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (C -> C)) or E))
theorem-size     19
proof            (modus-ponens tm-338 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-18540.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (C -> C)) or E)), M:tm-338, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-18541
in-theory        18541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> (D -> D)) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-18541.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> (D -> D)) and C))), M:tm-338, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-18542
in-theory        18542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> C) -> ((C -> D) -> C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-18542.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> C) -> ((C -> D) -> C))), M:tm-338, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-18543
in-theory        18543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> E) -> (D -> D))))
theorem-size     19
proof            (modus-ponens tm-338 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-18543.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> E) -> (D -> D)))), M:tm-338, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-18544
in-theory        18544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> ((D -> C) -> E)) -> (C -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-18544.        (((A -> B) -> (A -> (A and B))) and ((C -> ((D -> C) -> E)) -> (C -> E))), M:tm-338, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-18545
in-theory        18545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C -> D)) -> (C -> D)))
theorem-size     19
proof            (modus-ponens tm-338 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-18545.        (((A -> B) -> (A -> (A and B))) and ((C -> (C -> D)) -> (C -> D))), M:tm-338, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-18546
in-theory        18546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D))))
theorem-size     29
proof            (modus-ponens tm-338 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-18546.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> D)))), M:tm-338, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-18547
in-theory        18547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D)))))
theorem-size     41
proof            (modus-ponens tm-338 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-18547.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> E)) -> (C -> D)) -> (not ((C -> (D -> E)) -> (C -> E)))) -> (not ((C -> (D -> E)) -> (C -> D))))), M:tm-338, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-18548
in-theory        18548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F)))
theorem-size     43
proof            (modus-ponens tm-338 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-18548.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> E)) -> (C -> E)) -> F) -> ((((C -> (D -> E)) -> (C -> D)) or ((C -> (D -> E)) -> (C -> E))) -> F))), M:tm-338, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-18549
in-theory        18549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-18549.        (((A -> B) -> (A -> (A and B))) and (C or (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-338, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-18550
in-theory        18550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F))
theorem-size     31
proof            (modus-ponens tm-338 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-18550.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) or F)), M:tm-338, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-18551
in-theory        18551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C)))
theorem-size     33
proof            (modus-ponens tm-338 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-18551.        (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and C))), M:tm-338, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-18552
in-theory        18552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E))))
theorem-size     39
proof            (modus-ponens tm-338 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-18552.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> E)) -> (C -> D)) -> (C -> (D -> E))) -> (((C -> (D -> E)) -> (C -> D)) -> (C -> E)))), M:tm-338, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-18553
in-theory        18553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-18553.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-338, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-18554
in-theory        18554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-338 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-18554.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> (((C -> D) -> (C -> E)) -> F)) -> ((C -> (D -> E)) -> F))), M:tm-338, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-18555
in-theory        18555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C)))
theorem-size     29
proof            (modus-ponens tm-338 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-18555.        (((A -> B) -> (A -> (A and B))) and ((C -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not C))), M:tm-338, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-18556
in-theory        18556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     43
proof            (modus-ponens tm-338 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-18556.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((G or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-338, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-18557
in-theory        18557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-338 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-18557.        (((A -> B) -> (A -> (A and B))) and (C or (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-338, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-18558
in-theory        18558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     27
proof            (modus-ponens tm-338 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-18558.        (((A -> B) -> (A -> (A and B))) and ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-338, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-18559
in-theory        18559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     29
proof            (modus-ponens tm-338 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-18559.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-338, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-18560
in-theory        18560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-338 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-18560.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (E -> F))) -> (C -> ((D -> E) -> (D -> F))))), M:tm-338, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-18561
in-theory        18561
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-338 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-18561.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-338, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-18562
in-theory        18562
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) and C) -> D))
theorem-size     17
proof            (modus-ponens tm-338 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-18562.        (((A -> B) -> (A -> (A and B))) and (((C -> D) and C) -> D)), M:tm-338, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-18563
in-theory        18563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> C)) -> E) and F) -> E))
theorem-size     21
proof            (modus-ponens tm-338 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-18563.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> C)) -> E) and F) -> E)), M:tm-338, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-18564
in-theory        18564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F))
theorem-size     29
proof            (modus-ponens tm-338 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-18564.        (((A -> B) -> (A -> (A and B))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) and G) -> F)), M:tm-338, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-18565
in-theory        18565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D)))
theorem-size     31
proof            (modus-ponens tm-338 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-18565.        (((A -> B) -> (A -> (A and B))) and (((((C -> D) -> C) and E) -> (C -> D)) -> ((((C -> D) -> C) and E) -> D))), M:tm-338, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-18566
in-theory        18566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C)))
theorem-size     25
proof            (modus-ponens tm-338 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-18566.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> C))), M:tm-338, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-18567
in-theory        18567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C))))
theorem-size     35
proof            (modus-ponens tm-338 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-9 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-18567.        (((A -> B) -> (A -> (A and B))) and (((((C -> D) and E) -> C) -> (not (((C -> D) and E) -> D))) -> (not (((C -> D) and E) -> C)))), M:tm-338, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-18568
in-theory        18568
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F)))
theorem-size     37
proof            (modus-ponens tm-338 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-18568.        (((A -> B) -> (A -> (A and B))) and (((((C -> D) and E) -> D) -> F) -> (((((C -> D) and E) -> C) or (((C -> D) and E) -> D)) -> F))), M:tm-338, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-18569
in-theory        18569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     27
proof            (modus-ponens tm-338 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-18569.        (((A -> B) -> (A -> (A and B))) and (C or ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-338, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-18570
in-theory        18570
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F))
theorem-size     27
proof            (modus-ponens tm-338 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-18570.        (((A -> B) -> (A -> (A and B))) and (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) or F)), M:tm-338, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-18571
in-theory        18571
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C)))
theorem-size     29
proof            (modus-ponens tm-338 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-18571.        (((A -> B) -> (A -> (A and B))) and (C -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and C))), M:tm-338, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-18572
in-theory        18572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D)))
theorem-size     33
proof            (modus-ponens tm-338 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-18572.        (((A -> B) -> (A -> (A and B))) and (((((C -> D) and E) -> C) -> ((C -> D) and E)) -> ((((C -> D) and E) -> C) -> D))), M:tm-338, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-18573
in-theory        18573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     27
proof            (modus-ponens tm-338 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-18573.        (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-338, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-18574
in-theory        18574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C and D) -> C) -> E) and F) -> E))
theorem-size     21
proof            (modus-ponens tm-338 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-18574.        (((A -> B) -> (A -> (A and B))) and (((((C and D) -> C) -> E) and F) -> E)), M:tm-338, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-18575
in-theory        18575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> (C -> E)) -> ((C and D) -> E)))
theorem-size     23
proof            (modus-ponens tm-338 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-18575.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> (C -> E)) -> ((C and D) -> E))), M:tm-338, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-18576
in-theory        18576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not ((D and E) -> D))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-18576.        (((A -> B) -> (A -> (A and B))) and ((C -> (not ((D and E) -> D))) -> (not C))), M:tm-338, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-18577
in-theory        18577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E)))
theorem-size     27
proof            (modus-ponens tm-338 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-18577.        (((A -> B) -> (A -> (A and B))) and ((((C and D) -> C) -> E) -> ((F or ((C and D) -> C)) -> E))), M:tm-338, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-18578
in-theory        18578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-338 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-18578.        (((A -> B) -> (A -> (A and B))) and (C or (D -> ((E and F) -> E)))), M:tm-338, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-18579
in-theory        18579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> ((D and E) -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-18579.        (((A -> B) -> (A -> (A and B))) and ((C -> ((D and E) -> D)) or F)), M:tm-338, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-18580
in-theory        18580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> ((E and F) -> E)) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-18580.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> ((E and F) -> E)) and C))), M:tm-338, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-18581
in-theory        18581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D and E)) -> (C -> D)))
theorem-size     19
proof            (modus-ponens tm-338 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-18581.        (((A -> B) -> (A -> (A and B))) and ((C -> (D and E)) -> (C -> D))), M:tm-338, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-18582
in-theory        18582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-338 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-18582.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> ((E and F) -> E)))), M:tm-338, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-18583
in-theory        18583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C and (C -> D)) -> D))
theorem-size     17
proof            (modus-ponens tm-338 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-18583.        (((A -> B) -> (A -> (A and B))) and ((C and (C -> D)) -> D)), M:tm-338, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-18584
in-theory        18584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C and ((D -> (E -> D)) -> F)) -> F))
theorem-size     21
proof            (modus-ponens tm-338 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-18584.        (((A -> B) -> (A -> (A and B))) and ((C and ((D -> (E -> D)) -> F)) -> F)), M:tm-338, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-18585
in-theory        18585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G))
theorem-size     29
proof            (modus-ponens tm-338 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-18585.        (((A -> B) -> (A -> (A and B))) and ((C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G)) -> G)), M:tm-338, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-18586
in-theory        18586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C and (((D and E) -> D) -> F)) -> F))
theorem-size     21
proof            (modus-ponens tm-338 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-18586.        (((A -> B) -> (A -> (A and B))) and ((C and (((D and E) -> D) -> F)) -> F)), M:tm-338, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-18587
in-theory        18587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-338 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-18587.        (((A -> B) -> (A -> (A and B))) and (((C and ((D -> E) -> D)) -> (D -> E)) -> ((C and ((D -> E) -> D)) -> E))), M:tm-338, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-18588
in-theory        18588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D)))
theorem-size     25
proof            (modus-ponens tm-338 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-18588.        (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> D))), M:tm-338, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-18589
in-theory        18589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D))))
theorem-size     35
proof            (modus-ponens tm-338 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-18589.        (((A -> B) -> (A -> (A and B))) and ((((C and (D -> E)) -> D) -> (not ((C and (D -> E)) -> E))) -> (not ((C and (D -> E)) -> D)))), M:tm-338, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-18590
in-theory        18590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-338 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-18590.        (((A -> B) -> (A -> (A and B))) and ((((C and (D -> E)) -> E) -> F) -> ((((C and (D -> E)) -> D) or ((C and (D -> E)) -> E)) -> F))), M:tm-338, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-18591
in-theory        18591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     27
proof            (modus-ponens tm-338 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-18591.        (((A -> B) -> (A -> (A and B))) and (C or (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-338, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-18592
in-theory        18592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F))
theorem-size     27
proof            (modus-ponens tm-338 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-18592.        (((A -> B) -> (A -> (A and B))) and ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) or F)), M:tm-338, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-18593
in-theory        18593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C)))
theorem-size     29
proof            (modus-ponens tm-338 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-18593.        (((A -> B) -> (A -> (A and B))) and (C -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and C))), M:tm-338, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-18594
in-theory        18594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E)))
theorem-size     33
proof            (modus-ponens tm-338 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-18594.        (((A -> B) -> (A -> (A and B))) and ((((C and (D -> E)) -> D) -> (C and (D -> E))) -> (((C and (D -> E)) -> D) -> E))), M:tm-338, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-18595
in-theory        18595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     27
proof            (modus-ponens tm-338 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-18595.        (((A -> B) -> (A -> (A and B))) and (C -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-338, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-18596
in-theory        18596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C and (((D and E) -> E) -> F)) -> F))
theorem-size     21
proof            (modus-ponens tm-338 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-18596.        (((A -> B) -> (A -> (A and B))) and ((C and (((D and E) -> E) -> F)) -> F)), M:tm-338, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-18597
in-theory        18597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C and D) -> D) -> E) and F) -> E))
theorem-size     21
proof            (modus-ponens tm-338 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-18597.        (((A -> B) -> (A -> (A and B))) and (((((C and D) -> D) -> E) and F) -> E)), M:tm-338, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-18598
in-theory        18598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> (D -> E)) -> ((C and D) -> E)))
theorem-size     23
proof            (modus-ponens tm-338 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-18598.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> (D -> E)) -> ((C and D) -> E))), M:tm-338, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-18599
in-theory        18599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not ((D and E) -> E))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-18599.        (((A -> B) -> (A -> (A and B))) and ((C -> (not ((D and E) -> E))) -> (not C))), M:tm-338, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-18600
in-theory        18600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-338 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-18600.        (((A -> B) -> (A -> (A and B))) and ((((C and D) -> D) -> E) -> ((F or ((C and D) -> D)) -> E))), M:tm-338, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-18601
in-theory        18601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-338 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-18601.        (((A -> B) -> (A -> (A and B))) and (C or (D -> ((E and F) -> F)))), M:tm-338, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-18602
in-theory        18602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> ((D and E) -> E)) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-18602.        (((A -> B) -> (A -> (A and B))) and ((C -> ((D and E) -> E)) or F)), M:tm-338, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-18603
in-theory        18603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> ((E and F) -> F)) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-18603.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> ((E and F) -> F)) and C))), M:tm-338, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-18604
in-theory        18604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D and E)) -> (C -> E)))
theorem-size     19
proof            (modus-ponens tm-338 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-18604.        (((A -> B) -> (A -> (A and B))) and ((C -> (D and E)) -> (C -> E))), M:tm-338, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-18605
in-theory        18605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-338 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-18605.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> ((E and F) -> F)))), M:tm-338, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-18606
in-theory        18606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18606.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> E)))), M:tm-338, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-18607
in-theory        18607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-18607.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-338, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-18608
in-theory        18608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-18608.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E and F) -> E))), M:tm-338, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-18609
in-theory        18609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-338 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18609.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E and F) -> F))), M:tm-338, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-18610
in-theory        18610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-18610.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (E and F))))), M:tm-338, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-18611
in-theory        18611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-338 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-18611.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (E or F)))), M:tm-338, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-18612
in-theory        18612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-18612.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (F or E)))), M:tm-338, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-18613
in-theory        18613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-18613.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-338, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-18614
in-theory        18614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-338 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-18614.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-338, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-18615
in-theory        18615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-18615.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((not (not E)) -> E))), M:tm-338, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-18616
in-theory        18616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-18616.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (G -> F))))), M:tm-338, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-18617
in-theory        18617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-18617.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (E -> E)))), M:tm-338, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-18618
in-theory        18618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-338 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-18618.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-338, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-18619
in-theory        18619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-18619.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-338, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-18620
in-theory        18620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-338 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-18620.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-338, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-18621
in-theory        18621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-338 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-18621.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> ((F and G) -> F)))), M:tm-338, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-18622
in-theory        18622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-338 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-18622.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-338, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-18623
in-theory        18623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-338 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-18623.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> ((F and G) -> G)))), M:tm-338, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-18624
in-theory        18624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-18624.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-338, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-18625
in-theory        18625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-18625.        (((A -> B) -> (A -> (A and B))) and ((C -> (not ((D -> (E -> D)) and C))) -> (not C))), M:tm-338, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-18626
in-theory        18626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-338 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-18626.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> C)) and E) -> F) -> ((E or ((C -> (D -> C)) and E)) -> F))), M:tm-338, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-18627
in-theory        18627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-338 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-18627.        (((A -> B) -> (A -> (A and B))) and (C or (D -> ((E -> (F -> E)) and D)))), M:tm-338, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-18628
in-theory        18628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> ((D -> (E -> D)) and C)) or F))
theorem-size     21
proof            (modus-ponens tm-338 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-18628.        (((A -> B) -> (A -> (A and B))) and ((C -> ((D -> (E -> D)) and C)) or F)), M:tm-338, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-18629
in-theory        18629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> ((E -> (F -> E)) and D)) and C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-18629.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> ((E -> (F -> E)) and D)) and C))), M:tm-338, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-18630
in-theory        18630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-338 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-18630.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> ((E -> (F -> E)) and D)))), M:tm-338, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-18631
in-theory        18631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-338 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18631.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> F)))), M:tm-338, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-18632
in-theory        18632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-18632.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-338, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-18633
in-theory        18633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-338 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-18633.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> F))), M:tm-338, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-18634
in-theory        18634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-338 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18634.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F and G) -> G))), M:tm-338, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-18635
in-theory        18635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-18635.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (F and G))))), M:tm-338, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-18636
in-theory        18636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-18636.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (F or G)))), M:tm-338, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-18637
in-theory        18637
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-338 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-18637.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G or F)))), M:tm-338, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-18638
in-theory        18638
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-18638.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-338, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-18639
in-theory        18639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     35
proof            (modus-ponens tm-338 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-18639.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-338, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-18640
in-theory        18640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-338 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-18640.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((not (not F)) -> F))), M:tm-338, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-18641
in-theory        18641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-18641.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> G))))), M:tm-338, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-18642
in-theory        18642
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F))))
theorem-size     31
proof            (modus-ponens tm-338 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-18642.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> F)))), M:tm-338, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-18643
in-theory        18643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     43
proof            (modus-ponens tm-338 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-18643.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-338, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-18644
in-theory        18644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-338 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-18644.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-338, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-18645
in-theory        18645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     39
proof            (modus-ponens tm-338 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-18645.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-338, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-18646
in-theory        18646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-338 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-18646.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> G)))), M:tm-338, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-18647
in-theory        18647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     39
proof            (modus-ponens tm-338 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-18647.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-338, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-18648
in-theory        18648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-338 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-18648.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G and H) -> H)))), M:tm-338, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-18649
in-theory        18649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     33
proof            (modus-ponens tm-338 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-18649.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-338, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-18650
in-theory        18650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     41
proof            (modus-ponens tm-338 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-2)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-18650.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-338, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-18651
in-theory        18651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-338 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-18651.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-338, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-18652
in-theory        18652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C)))
theorem-size     31
proof            (modus-ponens tm-338 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-18652.        (((A -> B) -> (A -> (A and B))) and ((C -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) -> (not C))), M:tm-338, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-18653
in-theory        18653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G)))
theorem-size     47
proof            (modus-ponens tm-338 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-18653.        (((A -> B) -> (A -> (A and B))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F) -> G) -> ((F or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and F)) -> G))), M:tm-338, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-18654
in-theory        18654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-338 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-18654.        (((A -> B) -> (A -> (A and B))) and (C or (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-338, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-18655
in-theory        18655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G))
theorem-size     29
proof            (modus-ponens tm-338 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-18655.        (((A -> B) -> (A -> (A and B))) and ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) or G)), M:tm-338, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-18656
in-theory        18656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C)))
theorem-size     31
proof            (modus-ponens tm-338 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-18656.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and C))), M:tm-338, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-18657
in-theory        18657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-338 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-18657.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-338, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-18658
in-theory        18658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18658.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (F -> E)))), M:tm-338, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-18659
in-theory        18659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-18659.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-338, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-18660
in-theory        18660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-18660.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E and F) -> E))), M:tm-338, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-18661
in-theory        18661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-338 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18661.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E and F) -> F))), M:tm-338, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-18662
in-theory        18662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-18662.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (F -> (E and F))))), M:tm-338, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-18663
in-theory        18663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-338 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-18663.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (E or F)))), M:tm-338, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-18664
in-theory        18664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-18664.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (F or E)))), M:tm-338, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-18665
in-theory        18665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-18665.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-338, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-18666
in-theory        18666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-338 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-18666.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-338, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-18667
in-theory        18667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-18667.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((not (not E)) -> E))), M:tm-338, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-18668
in-theory        18668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-18668.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (F -> (G -> F))))), M:tm-338, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-18669
in-theory        18669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-18669.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (E -> E)))), M:tm-338, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-18670
in-theory        18670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-338 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-18670.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-338, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-18671
in-theory        18671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-18671.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-338, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-18672
in-theory        18672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-338 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-18672.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-338, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-18673
in-theory        18673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-338 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-18673.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> ((F and G) -> F)))), M:tm-338, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-18674
in-theory        18674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-338 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-18674.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-338, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-18675
in-theory        18675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-338 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-18675.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> ((F and G) -> G)))), M:tm-338, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-18676
in-theory        18676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-18676.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G -> F)) and E)))), M:tm-338, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-18677
in-theory        18677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-338 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-18677.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-338, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-18678
in-theory        18678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-18678.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (((F and G) -> F) and E)))), M:tm-338, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-18679
in-theory        18679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F))))
theorem-size     33
proof            (modus-ponens tm-338 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-18679.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> G) and F)))), M:tm-338, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-18680
in-theory        18680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-18680.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (((F and G) -> F) and E)))), M:tm-338, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-18681
in-theory        18681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not (((D and E) -> D) and C))) -> (not C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-18681.        (((A -> B) -> (A -> (A and B))) and ((C -> (not (((D and E) -> D) and C))) -> (not C))), M:tm-338, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-18682
in-theory        18682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-338 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-18682.        (((A -> B) -> (A -> (A and B))) and (((((C and D) -> C) and E) -> F) -> ((E or (((C and D) -> C) and E)) -> F))), M:tm-338, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-18683
in-theory        18683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-338 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-18683.        (((A -> B) -> (A -> (A and B))) and (C or (D -> (((E and F) -> E) and D)))), M:tm-338, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-18684
in-theory        18684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (((D and E) -> D) and C)) or F))
theorem-size     21
proof            (modus-ponens tm-338 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-18684.        (((A -> B) -> (A -> (A and B))) and ((C -> (((D and E) -> D) and C)) or F)), M:tm-338, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-18685
in-theory        18685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (((E and F) -> E) and D)) and C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-18685.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (((E and F) -> E) and D)) and C))), M:tm-338, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-18686
in-theory        18686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-338 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-18686.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> (((E and F) -> E) and D)))), M:tm-338, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-18687
in-theory        18687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18687.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (F -> E)))), M:tm-338, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-18688
in-theory        18688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-18688.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-338, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-18689
in-theory        18689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-18689.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E and F) -> E))), M:tm-338, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-18690
in-theory        18690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-338 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18690.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E and F) -> F))), M:tm-338, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-18691
in-theory        18691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-18691.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (F -> (E and F))))), M:tm-338, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-18692
in-theory        18692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-338 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-18692.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (E or F)))), M:tm-338, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-18693
in-theory        18693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-18693.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (F or E)))), M:tm-338, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-18694
in-theory        18694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-18694.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-338, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-18695
in-theory        18695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-338 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-18695.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-338, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-18696
in-theory        18696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-18696.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((not (not E)) -> E))), M:tm-338, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-18697
in-theory        18697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-18697.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (F -> (G -> F))))), M:tm-338, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-18698
in-theory        18698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-18698.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (E -> E)))), M:tm-338, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-18699
in-theory        18699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-338 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-18699.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-338, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-18700
in-theory        18700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-18700.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-338, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-18701
in-theory        18701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-338 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-18701.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-338, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-18702
in-theory        18702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-338 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-18702.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> ((F and G) -> F)))), M:tm-338, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-18703
in-theory        18703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-338 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-18703.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-338, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-18704
in-theory        18704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-338 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-18704.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> ((F and G) -> G)))), M:tm-338, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-18705
in-theory        18705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-18705.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G -> F)) and E)))), M:tm-338, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-18706
in-theory        18706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-338 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-18706.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-338, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-18707
in-theory        18707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-18707.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (((F and G) -> F) and E)))), M:tm-338, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-18708
in-theory        18708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-18708.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (((F and G) -> G) and E)))), M:tm-338, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-18709
in-theory        18709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-18709.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (((F and G) -> G) and E)))), M:tm-338, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-18710
in-theory        18710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F))))
theorem-size     33
proof            (modus-ponens tm-338 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-18710.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (((G and H) -> H) and F)))), M:tm-338, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-18711
in-theory        18711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-18711.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (((F and G) -> G) and E)))), M:tm-338, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-18712
in-theory        18712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not (((D and E) -> E) and C))) -> (not C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-18712.        (((A -> B) -> (A -> (A and B))) and ((C -> (not (((D and E) -> E) and C))) -> (not C))), M:tm-338, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-18713
in-theory        18713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-338 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-18713.        (((A -> B) -> (A -> (A and B))) and (((((C and D) -> D) and E) -> F) -> ((E or (((C and D) -> D) and E)) -> F))), M:tm-338, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-18714
in-theory        18714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-338 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-18714.        (((A -> B) -> (A -> (A and B))) and (C or (D -> (((E and F) -> F) and D)))), M:tm-338, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-18715
in-theory        18715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (((D and E) -> E) and C)) or F))
theorem-size     21
proof            (modus-ponens tm-338 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-18715.        (((A -> B) -> (A -> (A and B))) and ((C -> (((D and E) -> E) and C)) or F)), M:tm-338, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-18716
in-theory        18716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (((E and F) -> F) and D)) and C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-18716.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (((E and F) -> F) and D)) and C))), M:tm-338, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-18717
in-theory        18717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-338 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-18717.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> (((E and F) -> F) and D)))), M:tm-338, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-18718
in-theory        18718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18718.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> E)))), M:tm-338, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-18719
in-theory        18719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-18719.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-338, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-18720
in-theory        18720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-338 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-18720.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E and F) -> E))), M:tm-338, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-18721
in-theory        18721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-338 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18721.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E and F) -> F))), M:tm-338, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-18722
in-theory        18722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-18722.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (E and F))))), M:tm-338, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-18723
in-theory        18723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-338 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-18723.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (E or F)))), M:tm-338, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-18724
in-theory        18724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-18724.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F or E)))), M:tm-338, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-18725
in-theory        18725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-18725.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-338, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-18726
in-theory        18726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-18726.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-338, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-18727
in-theory        18727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((not (not E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-338 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-18727.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((not (not E)) -> E))), M:tm-338, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-18728
in-theory        18728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-18728.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> F))))), M:tm-338, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-18729
in-theory        18729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-18729.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> E)))), M:tm-338, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-18730
in-theory        18730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-18730.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-338, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-18731
in-theory        18731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-338 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-18731.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-338, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-18732
in-theory        18732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     33
proof            (modus-ponens tm-338 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-18732.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-338, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-18733
in-theory        18733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-338 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-18733.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> F)))), M:tm-338, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-18734
in-theory        18734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     33
proof            (modus-ponens tm-338 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-18734.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-338, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-18735
in-theory        18735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-338 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-18735.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F and G) -> G)))), M:tm-338, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-18736
in-theory        18736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-338 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-18736.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> F)) and E)))), M:tm-338, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-18737
in-theory        18737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-338 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-18737.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-338, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-18738
in-theory        18738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-338 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-18738.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> F) and E)))), M:tm-338, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-18739
in-theory        18739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-338 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-18739.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (((F and G) -> G) and E)))), M:tm-338, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-18740
in-theory        18740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-338 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-18740.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-338, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-18741
in-theory        18741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-338 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-18741.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-338, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-18742
in-theory        18742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-338 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-18742.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-338, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-18743
in-theory        18743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     35
proof            (modus-ponens tm-338 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-18743.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-338, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-18744
in-theory        18744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-338 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-18744.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-338, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-18745
in-theory        18745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C)))
theorem-size     25
proof            (modus-ponens tm-338 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-18745.        (((A -> B) -> (A -> (A and B))) and ((C -> (not ((D -> (E -> (D and E))) and C))) -> (not C))), M:tm-338, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-18746
in-theory        18746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-338 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-18746.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> (C and D))) and E) -> F) -> ((E or ((C -> (D -> (C and D))) and E)) -> F))), M:tm-338, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-18747
in-theory        18747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-338 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-18747.        (((A -> B) -> (A -> (A and B))) and (C or (D -> ((E -> (F -> (E and F))) and D)))), M:tm-338, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-18748
in-theory        18748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> ((D -> (E -> (D and E))) and C)) or F))
theorem-size     23
proof            (modus-ponens tm-338 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-18748.        (((A -> B) -> (A -> (A and B))) and ((C -> ((D -> (E -> (D and E))) and C)) or F)), M:tm-338, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-18749
in-theory        18749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C)))
theorem-size     25
proof            (modus-ponens tm-338 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-18749.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> ((E -> (F -> (E and F))) and D)) and C))), M:tm-338, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-18750
in-theory        18750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-338 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-18750.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> ((E -> (F -> (E and F))) and D)))), M:tm-338, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-18751
in-theory        18751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and (D -> C))))
theorem-size     17
proof            (modus-ponens tm-338 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-18751.        (((A -> B) -> (A -> (A and B))) and (C -> (C and (D -> C)))), M:tm-338, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-18752
in-theory        18752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-18752.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> E)) -> ((C -> (D -> E)) and ((C -> D) -> (C -> E))))), M:tm-338, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-18753
in-theory        18753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C and D) -> ((C and D) and C)))
theorem-size     19
proof            (modus-ponens tm-338 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-18753.        (((A -> B) -> (A -> (A and B))) and ((C and D) -> ((C and D) and C))), M:tm-338, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-18754
in-theory        18754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C and D) -> ((C and D) and D)))
theorem-size     19
proof            (modus-ponens tm-338 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18754.        (((A -> B) -> (A -> (A and B))) and ((C and D) -> ((C and D) and D))), M:tm-338, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-18755
in-theory        18755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and (D -> (C and D)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-18755.        (((A -> B) -> (A -> (A and B))) and (C -> (C and (D -> (C and D))))), M:tm-338, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-18756
in-theory        18756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and (C or D))))
theorem-size     17
proof            (modus-ponens tm-338 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-18756.        (((A -> B) -> (A -> (A and B))) and (C -> (C and (C or D)))), M:tm-338, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-18757
in-theory        18757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and (D or C))))
theorem-size     17
proof            (modus-ponens tm-338 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-18757.        (((A -> B) -> (A -> (A and B))) and (C -> (C and (D or C)))), M:tm-338, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-18758
in-theory        18758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E)))))
theorem-size     27
proof            (modus-ponens tm-338 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-18758.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((C -> D) and ((D -> E) -> ((C or D) -> E))))), M:tm-338, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-18759
in-theory        18759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-18759.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((C -> D) and ((C -> (not D)) -> (not C))))), M:tm-338, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-18760
in-theory        18760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((not (not C)) -> ((not (not C)) and C)))
theorem-size     19
proof            (modus-ponens tm-338 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-2 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-18760.        (((A -> B) -> (A -> (A and B))) and ((not (not C)) -> ((not (not C)) and C))), M:tm-338, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-18761
in-theory        18761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and (D -> (E -> D)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-18761.        (((A -> B) -> (A -> (A and B))) and (C -> (C and (D -> (E -> D))))), M:tm-338, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-18762
in-theory        18762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((C -> D) and (C -> C))))
theorem-size     21
proof            (modus-ponens tm-338 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-18762.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((C -> D) and (C -> C)))), M:tm-338, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-18763
in-theory        18763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E)))))
theorem-size     39
proof            (modus-ponens tm-338 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-18763.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> (((C -> (D -> E)) -> (C -> D)) and ((C -> (D -> E)) -> (C -> E))))), M:tm-338, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-18764
in-theory        18764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     27
proof            (modus-ponens tm-338 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-18764.        (((A -> B) -> (A -> (A and B))) and (C -> (C and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-338, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-18765
in-theory        18765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D))))
theorem-size     33
proof            (modus-ponens tm-338 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-18765.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) -> C) -> ((((C -> D) and E) -> C) and (((C -> D) and E) -> D)))), M:tm-338, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-18766
in-theory        18766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and ((D and E) -> D))))
theorem-size     19
proof            (modus-ponens tm-338 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-18766.        (((A -> B) -> (A -> (A and B))) and (C -> (C and ((D and E) -> D)))), M:tm-338, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-18767
in-theory        18767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E))))
theorem-size     33
proof            (modus-ponens tm-338 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-18767.        (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) -> D) -> (((C and (D -> E)) -> D) and ((C and (D -> E)) -> E)))), M:tm-338, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-18768
in-theory        18768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and ((D and E) -> E))))
theorem-size     19
proof            (modus-ponens tm-338 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-18768.        (((A -> B) -> (A -> (A and B))) and (C -> (C and ((D and E) -> E)))), M:tm-338, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-18769
in-theory        18769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and ((D -> (E -> D)) and C))))
theorem-size     21
proof            (modus-ponens tm-338 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-18769.        (((A -> B) -> (A -> (A and B))) and (C -> (C and ((D -> (E -> D)) and C)))), M:tm-338, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-18770
in-theory        18770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     29
proof            (modus-ponens tm-338 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-18770.        (((A -> B) -> (A -> (A and B))) and (C -> (C and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-338, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-18771
in-theory        18771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and (((D and E) -> D) and C))))
theorem-size     21
proof            (modus-ponens tm-338 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-18771.        (((A -> B) -> (A -> (A and B))) and (C -> (C and (((D and E) -> D) and C)))), M:tm-338, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-18772
in-theory        18772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and (((D and E) -> E) and C))))
theorem-size     21
proof            (modus-ponens tm-338 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-18772.        (((A -> B) -> (A -> (A and B))) and (C -> (C and (((D and E) -> E) and C)))), M:tm-338, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-18773
in-theory        18773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and ((D -> (E -> (D and E))) and C))))
theorem-size     23
proof            (modus-ponens tm-338 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-18773.        (((A -> B) -> (A -> (A and B))) and (C -> (C and ((D -> (E -> (D and E))) and C)))), M:tm-338, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-18774
in-theory        18774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((C -> D) and (C -> (C and D)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18774.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((C -> D) and (C -> (C and D))))), M:tm-338, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-18775
in-theory        18775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-338 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18775.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (E -> (E and F))))), M:tm-338, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18776
in-theory        18776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18776.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (E -> (E and F))))), M:tm-338, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18777
in-theory        18777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18777.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (E -> (E and F))))), M:tm-338, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18778
in-theory        18778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-338 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18778.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (F -> (F and G))))), M:tm-338, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-18779
in-theory        18779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18779.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (E -> (E and F))))), M:tm-338, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-18780
in-theory        18780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D))))
theorem-size     25
proof            (modus-ponens tm-338 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18780.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (not (C -> (C and D)))) -> (not (C -> D)))), M:tm-338, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-18781
in-theory        18781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E)))
theorem-size     29
proof            (modus-ponens tm-338 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-18781.        (((A -> B) -> (A -> (A and B))) and (((C -> (C and D)) -> E) -> (((C -> D) or (C -> (C and D))) -> E))), M:tm-338, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-18782
in-theory        18782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((D -> E) -> (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-338 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18782.        (((A -> B) -> (A -> (A and B))) and (C or ((D -> E) -> (D -> (D and E))))), M:tm-338, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18783
in-theory        18783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (C -> (C and D))) or E))
theorem-size     21
proof            (modus-ponens tm-338 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18783.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (C -> (C and D))) or E)), M:tm-338, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-18784
in-theory        18784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> (D -> (D and E))) and C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18784.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> (D -> (D and E))) and C))), M:tm-338, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18785
in-theory        18785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> D) -> (C -> (C and D))) and (A -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-335 tm-338 ((Am (-> A (and A B))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18785.        (((A -> B) or (A -> (A and B))) -> (((C -> D) -> (C -> (C and D))) and (A -> (A and B)))), M:tm-335, m:tm-338, u:((Am (-> A (and A B))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (and A B)))))
================================================================
tm-name          tm-18786
in-theory        18786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (A -> (A and (((B -> C) -> (B -> (B and C))) and A))))
theorem-size     29
proof            (modus-ponens tm-328 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-5)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18786.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (A -> (A and (((B -> C) -> (B -> (B and C))) and A)))), M:tm-328, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-18787
in-theory        18787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (A -> (((B -> C) -> (B -> (B and C))) and A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18787.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (A -> (((B -> C) -> (B -> (B and C))) and A)))), M:tm-327, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18788
in-theory        18788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (((D and E) -> E) and (A -> (((B -> C) -> (B -> (B and C))) and A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18788.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (((D and E) -> E) and (A -> (((B -> C) -> (B -> (B and C))) and A)))), M:tm-326, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18789
in-theory        18789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (((D and E) -> D) and (A -> (((B -> C) -> (B -> (B and C))) and A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18789.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (((D and E) -> D) and (A -> (((B -> C) -> (B -> (B and C))) and A)))), M:tm-325, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18790
in-theory        18790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (((B -> C) -> (B -> (B and C))) and A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18790.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (((B -> C) -> (B -> (B and C))) and A)))), M:tm-324, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18791
in-theory        18791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((D -> (E -> D)) and (A -> (((B -> C) -> (B -> (B and C))) and A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18791.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((D -> (E -> D)) and (A -> (((B -> C) -> (B -> (B and C))) and A)))), M:tm-323, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18792
in-theory        18792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18792.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((D and E) -> E)), M:tm-322, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18793
in-theory        18793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18793.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((D and E) -> D)), M:tm-320, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18794
in-theory        18794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18794.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18795
in-theory        18795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (A -> A))
theorem-size     17
proof            (modus-ponens tm-316 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18795.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (A -> A)), M:tm-316, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-18796
in-theory        18796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18796.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (D -> (E -> D))), M:tm-315, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18797
in-theory        18797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((A -> (not (((B -> C) -> (B -> (B and C))) and A))) -> (not A)))
theorem-size     31
proof            (modus-ponens tm-313 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18797.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((A -> (not (((B -> C) -> (B -> (B and C))) and A))) -> (not A))), M:tm-313, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-18798
in-theory        18798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (((((B -> C) -> (B -> (B and C))) and A) -> D) -> ((A or (((B -> C) -> (B -> (B and C))) and A)) -> D)))
theorem-size     43
proof            (modus-ponens tm-312 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18798.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (((((B -> C) -> (B -> (B and C))) and A) -> D) -> ((A or (((B -> C) -> (B -> (B and C))) and A)) -> D))), M:tm-312, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-18799
in-theory        18799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (D or (A -> (((B -> C) -> (B -> (B and C))) and A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18799.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (D or (A -> (((B -> C) -> (B -> (B and C))) and A)))), M:tm-311, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18800
in-theory        18800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((A -> (((B -> C) -> (B -> (B and C))) and A)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18800.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((A -> (((B -> C) -> (B -> (B and C))) and A)) or D)), M:tm-310, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18801
in-theory        18801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (D -> ((A -> (((B -> C) -> (B -> (B and C))) and A)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18801.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (D -> ((A -> (((B -> C) -> (B -> (B and C))) and A)) and D))), M:tm-309, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18802
in-theory        18802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (D -> (A -> (((B -> C) -> (B -> (B and C))) and A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18802.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (D -> (A -> (((B -> C) -> (B -> (B and C))) and A)))), M:tm-305, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18803
in-theory        18803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18803.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-303, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18804
in-theory        18804
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> (D -> (D and E))) and ((B -> (C -> (B and C))) and A)))
theorem-size     31
proof            (modus-ponens tm-300 tm-338 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18804.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> (D -> (D and E))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-338, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-18805
in-theory        18805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18805.        ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-270, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18806
in-theory        18806
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> E) -> (D -> (D and E))) and (((B and C) -> C) and A)))
theorem-size     27
proof            (modus-ponens tm-267 tm-338 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18806.        ((A or (((B and C) -> C) and A)) -> (((D -> E) -> (D -> (D and E))) and (((B and C) -> C) and A))), M:tm-267, m:tm-338, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-18807
in-theory        18807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18807.        ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-239, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18808
in-theory        18808
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> E) -> (D -> (D and E))) and (((B and C) -> B) and A)))
theorem-size     27
proof            (modus-ponens tm-236 tm-338 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18808.        ((A or (((B and C) -> B) and A)) -> (((D -> E) -> (D -> (D and E))) and (((B and C) -> B) and A))), M:tm-236, m:tm-338, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-18809
in-theory        18809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> (F -> (F and G))) and E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18809.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> (F -> (F and G))) and E))), M:tm-210, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18810
in-theory        18810
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> (E -> (E and F))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     43
proof            (modus-ponens tm-207 tm-338 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18810.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> (E -> (E and F))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-338, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-18811
in-theory        18811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18811.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-183, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18812
in-theory        18812
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> (D -> (D and E))) and ((B -> (C -> B)) and A)))
theorem-size     27
proof            (modus-ponens tm-180 tm-338 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18812.        ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> (D -> (D and E))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-338, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-18813
in-theory        18813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18813.        ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-157, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18814
in-theory        18814
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> E) -> (D -> (D and E))) and ((B and C) -> C)))
theorem-size     23
proof            (modus-ponens tm-154 tm-338 ((Am (-> (and A B) B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18814.        ((A or ((B and C) -> C)) -> (((D -> E) -> (D -> (D and E))) and ((B and C) -> C))), M:tm-154, m:tm-338, u:((Am (-> (and A B) B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (and A B) B))))
================================================================
tm-name          tm-18815
in-theory        18815
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18815.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-147, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18816
in-theory        18816
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> (D -> (D and E))) and ((A and (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-144 tm-338 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18816.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> (D -> (D and E))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-338, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-18817
in-theory        18817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18817.        ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-134, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18818
in-theory        18818
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> E) -> (D -> (D and E))) and ((B and C) -> B)))
theorem-size     23
proof            (modus-ponens tm-131 tm-338 ((Am (-> (and A B) A)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18818.        ((A or ((B and C) -> B)) -> (((D -> E) -> (D -> (D and E))) and ((B and C) -> B))), M:tm-131, m:tm-338, u:((Am (-> (and A B) A)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (and A B) A))))
================================================================
tm-name          tm-18819
in-theory        18819
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18819.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-125, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18820
in-theory        18820
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> (D -> (D and E))) and (((A -> B) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-122 tm-338 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18820.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> (D -> (D and E))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-338, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-18821
in-theory        18821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (F -> (F and G))) and E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18821.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (F -> (F and G))) and E))), M:tm-113, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18822
in-theory        18822
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> (E -> (E and F))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     39
proof            (modus-ponens tm-110 tm-338 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18822.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> (E -> (E and F))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-338, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-18823
in-theory        18823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18823.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-105, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18824
in-theory        18824
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> (D -> (D and E))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-102 tm-338 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18824.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> (D -> (D and E))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-338, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-18825
in-theory        18825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> (D -> (D and E))) and C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18825.        (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> (D -> (D and E))) and C))), M:tm-95, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18826
in-theory        18826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> D) -> (C -> (C and D))) and (A -> A)))
theorem-size     21
proof            (modus-ponens tm-92 tm-338 ((Am (-> A A)) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18826.        (((A -> B) or (A -> A)) -> (((C -> D) -> (C -> (C and D))) and (A -> A))), M:tm-92, m:tm-338, u:((Am (-> A A)) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A A))))
================================================================
tm-name          tm-18827
in-theory        18827
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> D) -> (C -> (C and D))) and A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18827.        (A -> (B -> (((C -> D) -> (C -> (C and D))) and A))), M:tm-84, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-18828
in-theory        18828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18828.        ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-83, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18829
in-theory        18829
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> E) -> (D -> (D and E))) and (B -> (C -> B))))
theorem-size     23
proof            (modus-ponens tm-80 tm-338 ((Am (-> A (-> B A))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18829.        ((A or (B -> (C -> B))) -> (((D -> E) -> (D -> (D and E))) and (B -> (C -> B)))), M:tm-80, m:tm-338, u:((Am (-> A (-> B A))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (-> B A)))))
================================================================
tm-name          tm-18830
in-theory        18830
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> D) -> (C -> (C and D))) and B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18830.        (((not (not A)) -> A) and (B -> (((C -> D) -> (C -> (C and D))) and B))), M:tm-76, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18831
in-theory        18831
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> C) -> (B -> (B and C))) and A))
theorem-size     17
proof            (modus-ponens tm-73 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18831.        (((not (not A)) or A) -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-73, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-18832
in-theory        18832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> (D -> (D and E))) and C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18832.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> (D -> (D and E))) and C))), M:tm-69, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18833
in-theory        18833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> (C -> (C and D))) and ((A -> (not B)) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-66 tm-338 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18833.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> (C -> (C and D))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-338, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-18834
in-theory        18834
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18834.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-54, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18835
in-theory        18835
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> (D -> (D and E))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-51 tm-338 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18835.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> (D -> (D and E))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-338, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-18836
in-theory        18836
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> D) -> (C -> (C and D))) and (B or A)))
theorem-size     19
proof            (modus-ponens tm-50 tm-338 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18836.        ((A or (B or A)) -> (((C -> D) -> (C -> (C and D))) and (B or A))), M:tm-50, m:tm-338, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (or A B))))
================================================================
tm-name          tm-18837
in-theory        18837
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> D) -> (C -> (C and D))) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-49 tm-338 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18837.        ((A or (A or B)) -> (((C -> D) -> (C -> (C and D))) and (A or B))), M:tm-49, m:tm-338, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (or A B))))
================================================================
tm-name          tm-18838
in-theory        18838
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> D) -> (C -> (C and D))) and (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-48 tm-338 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18838.        ((A or (B -> (A and B))) -> (((C -> D) -> (C -> (C and D))) and (B -> (A and B)))), M:tm-48, m:tm-338, u:((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-18839
in-theory        18839
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> D) -> (C -> (C and D))) and B))
theorem-size     17
proof            (modus-ponens tm-47 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18839.        (((A and B) or B) -> (((C -> D) -> (C -> (C and D))) and B)), M:tm-47, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-18840
in-theory        18840
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> D) -> (C -> (C and D))) and A))
theorem-size     17
proof            (modus-ponens tm-46 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18840.        (((A and B) or A) -> (((C -> D) -> (C -> (C and D))) and A)), M:tm-46, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-18841
in-theory        18841
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (D -> (D and E))) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-45 tm-338 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18841.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (D -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-338, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-18842
in-theory        18842
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> D) -> (C -> (C and D))) and (B -> A)))
theorem-size     19
proof            (modus-ponens tm-44 tm-338 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18842.        ((A or (B -> A)) -> (((C -> D) -> (C -> (C and D))) and (B -> A))), M:tm-44, m:tm-338, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A B))))
================================================================
tm-name          tm-18843
in-theory        18843
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> E) -> (D -> (D and E))) and C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18843.        ((A -> (B or A)) and (C -> (((D -> E) -> (D -> (D and E))) and C))), M:tm-42, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18844
in-theory        18844
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> E) -> (D -> (D and E))) and C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18844.        ((A -> (A or B)) and (C -> (((D -> E) -> (D -> (D and E))) and C))), M:tm-32, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18845
in-theory        18845
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> C) -> (B -> (B and C))) and A)))
theorem-size     15
proof            (modus-ponens tm-24 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18845.        (A -> (A and (((B -> C) -> (B -> (B and C))) and A))), M:tm-24, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-18846
in-theory        18846
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> E) -> (D -> (D and E))) and C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18846.        ((A -> (B -> (A and B))) and (C -> (((D -> E) -> (D -> (D and E))) and C))), M:tm-23, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18847
in-theory        18847
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> E) -> (D -> (D and E))) and C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18847.        (((A and B) -> B) and (C -> (((D -> E) -> (D -> (D and E))) and C))), M:tm-22, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18848
in-theory        18848
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> E) -> (D -> (D and E))) and C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18848.        (((A and B) -> A) and (C -> (((D -> E) -> (D -> (D and E))) and C))), M:tm-21, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18849
in-theory        18849
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18849.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-20, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18850
in-theory        18850
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> E) -> (D -> (D and E))) and C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18850.        ((A -> (B -> A)) and (C -> (((D -> E) -> (D -> (D and E))) and C))), M:tm-19, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18851
in-theory        18851
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> C) -> (B -> (B and C))) and A))) -> (not A))
theorem-size     17
proof            (modus-ponens tm-9 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-9 tm-5 tm-2)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18851.        ((A -> (not (((B -> C) -> (B -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-18852
in-theory        18852
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> (A and B))) and C) -> D) -> ((C or (((A -> B) -> (A -> (A and B))) and C)) -> D))
theorem-size     29
proof            (modus-ponens tm-8 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18852.        (((((A -> B) -> (A -> (A and B))) and C) -> D) -> ((C or (((A -> B) -> (A -> (A and B))) and C)) -> D)), M:tm-8, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-18853
in-theory        18853
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> D) -> (C -> (C and D))) and B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18853.        (A or (B -> (((C -> D) -> (C -> (C and D))) and B))), M:tm-7, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18854
in-theory        18854
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18854.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) or D), M:tm-6, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18855
in-theory        18855
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> D) -> (C -> (C and D))) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-2)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18855.        (A -> ((B -> (((C -> D) -> (C -> (C and D))) and B)) and A)), M:tm-5, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18856
in-theory        18856
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> D) -> (C -> (C and D))) and B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18856.        (A -> (B -> (((C -> D) -> (C -> (C and D))) and B))), M:tm-1, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-18857
in-theory        18857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> ((A -> (B -> A)) and C))
theorem-size     15
proof            (modus-ponens tm-339 tm-11 ((Am (-> (-> Bm (-> Cm Bm)) B)) (A (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18857.        (((A -> (B -> A)) -> C) -> ((A -> (B -> A)) and C)), M:tm-339, m:tm-11, u:((Am (-> (-> Bm (-> Cm Bm)) B)) (A (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-18858
in-theory        18858
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D))
theorem-size     31
proof            (modus-ponens tm-339 tm-14 ((Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-18858.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)), M:tm-339, m:tm-14, u:((Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-18859
in-theory        18859
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> (((A and B) -> A) and C))
theorem-size     15
proof            (modus-ponens tm-339 tm-16 ((Am (-> (-> (and Bm Cm) Bm) B)) (A (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-18859.        ((((A and B) -> A) -> C) -> (((A and B) -> A) and C)), M:tm-339, m:tm-16, u:((Am (-> (-> (and Bm Cm) Bm) B)) (A (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-18860
in-theory        18860
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> (((A and B) -> B) and C))
theorem-size     15
proof            (modus-ponens tm-339 tm-18 ((Am (-> (-> (and Bm Cm) Cm) B)) (A (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18860.        ((((A and B) -> B) -> C) -> (((A and B) -> B) and C)), M:tm-339, m:tm-18, u:((Am (-> (-> (and Bm Cm) Cm) B)) (A (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-18861
in-theory        18861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> ((A -> (B -> (A and B))) and C))
theorem-size     19
proof            (modus-ponens tm-339 tm-25 ((Am (-> (-> Bm (-> Cm (and Bm Cm))) B)) (A (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-18861.        (((A -> (B -> (A and B))) -> C) -> ((A -> (B -> (A and B))) and C)), M:tm-339, m:tm-25, u:((Am (-> (-> Bm (-> Cm (and Bm Cm))) B)) (A (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-18862
in-theory        18862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> ((A -> (A or B)) and C))
theorem-size     15
proof            (modus-ponens tm-339 tm-33 ((Am (-> (-> Bm (or Bm Cm)) B)) (A (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-18862.        (((A -> (A or B)) -> C) -> ((A -> (A or B)) and C)), M:tm-339, m:tm-33, u:((Am (-> (-> Bm (or Bm Cm)) B)) (A (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-18863
in-theory        18863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> ((A -> (B or A)) and C))
theorem-size     15
proof            (modus-ponens tm-339 tm-43 ((Am (-> (-> Bm (or Cm Bm)) B)) (A (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-18863.        (((A -> (B or A)) -> C) -> ((A -> (B or A)) and C)), M:tm-339, m:tm-43, u:((Am (-> (-> Bm (or Cm Bm)) B)) (A (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-18864
in-theory        18864
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and D))
theorem-size     31
proof            (modus-ponens tm-339 tm-56 ((Am (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B)) (A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-18864.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) -> D) -> (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and D)), M:tm-339, m:tm-56, u:((Am (-> (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) B)) (A (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-18865
in-theory        18865
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) -> C) -> (((A -> B) -> ((A -> (not B)) -> (not A))) and C))
theorem-size     27
proof            (modus-ponens tm-339 tm-71 ((Am (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) B)) (A (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-18865.        ((((A -> B) -> ((A -> (not B)) -> (not A))) -> C) -> (((A -> B) -> ((A -> (not B)) -> (not A))) and C)), M:tm-339, m:tm-71, u:((Am (-> (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) B)) (A (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-18866
in-theory        18866
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) -> B) -> (((not (not A)) -> A) and B))
theorem-size     15
proof            (modus-ponens tm-339 tm-78 ((Am (-> (-> (not (not Bm)) Bm) B)) (A (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-18866.        ((((not (not A)) -> A) -> B) -> (((not (not A)) -> A) and B)), M:tm-339, m:tm-78, u:((Am (-> (-> (not (not Bm)) Bm) B)) (A (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-18867
in-theory        18867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) -> D) -> ((A -> (B -> (C -> B))) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-85 ((Am (-> (-> Bm (-> Cm (-> Dm Cm))) B)) (A (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-18867.        (((A -> (B -> (C -> B))) -> D) -> ((A -> (B -> (C -> B))) and D)), M:tm-339, m:tm-85, u:((Am (-> (-> Bm (-> Cm (-> Dm Cm))) B)) (A (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-18868
in-theory        18868
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) -> C) -> (((A -> B) -> (A -> A)) and C))
theorem-size     19
proof            (modus-ponens tm-339 tm-97 ((Am (-> (-> (-> Bm Cm) (-> Bm Bm)) B)) (A (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-18868.        ((((A -> B) -> (A -> A)) -> C) -> (((A -> B) -> (A -> A)) and C)), M:tm-339, m:tm-97, u:((Am (-> (-> (-> Bm Cm) (-> Bm Bm)) B)) (A (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-18869
in-theory        18869
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) -> ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and D))
theorem-size     43
proof            (modus-ponens tm-339 tm-107 ((Am (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) B)) (A (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-18869.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) -> ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and D)), M:tm-339, m:tm-107, u:((Am (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) B)) (A (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-18870
in-theory        18870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E))
theorem-size     35
proof            (modus-ponens tm-339 tm-115 ((Am (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B)) (A (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-18870.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E)), M:tm-339, m:tm-115, u:((Am (-> (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B)) (A (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-18871
in-theory        18871
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) -> (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and D))
theorem-size     35
proof            (modus-ponens tm-339 tm-127 ((Am (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) B)) (A (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-18871.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) -> (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and D)), M:tm-339, m:tm-127, u:((Am (-> (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) B)) (A (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-18872
in-theory        18872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) -> D) -> ((A -> ((B and C) -> B)) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-136 ((Am (-> (-> Bm (-> (and Cm Dm) Cm)) B)) (A (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-18872.        (((A -> ((B and C) -> B)) -> D) -> ((A -> ((B and C) -> B)) and D)), M:tm-339, m:tm-136, u:((Am (-> (-> Bm (-> (and Cm Dm) Cm)) B)) (A (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-18873
in-theory        18873
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) -> ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and D))
theorem-size     35
proof            (modus-ponens tm-339 tm-149 ((Am (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) B)) (A (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-18873.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) -> ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and D)), M:tm-339, m:tm-149, u:((Am (-> (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) B)) (A (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-18874
in-theory        18874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) -> D) -> ((A -> ((B and C) -> C)) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-159 ((Am (-> (-> Bm (-> (and Cm Dm) Dm)) B)) (A (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-18874.        (((A -> ((B and C) -> C)) -> D) -> ((A -> ((B and C) -> C)) and D)), M:tm-339, m:tm-159, u:((Am (-> (-> Bm (-> (and Cm Dm) Dm)) B)) (A (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-18875
in-theory        18875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) -> D) -> ((A -> ((B -> (C -> B)) and A)) and D))
theorem-size     23
proof            (modus-ponens tm-339 tm-184 ((Am (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) B)) (A (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-18875.        (((A -> ((B -> (C -> B)) and A)) -> D) -> ((A -> ((B -> (C -> B)) and A)) and D)), M:tm-339, m:tm-184, u:((Am (-> (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) B)) (A (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-18876
in-theory        18876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) -> ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and E))
theorem-size     39
proof            (modus-ponens tm-339 tm-211 ((Am (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) B)) (A (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-18876.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> E) -> ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and E)), M:tm-339, m:tm-211, u:((Am (-> (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) B)) (A (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-18877
in-theory        18877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) -> D) -> ((A -> (((B and C) -> B) and A)) and D))
theorem-size     23
proof            (modus-ponens tm-339 tm-240 ((Am (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) B)) (A (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-18877.        (((A -> (((B and C) -> B) and A)) -> D) -> ((A -> (((B and C) -> B) and A)) and D)), M:tm-339, m:tm-240, u:((Am (-> (-> Bm (and (-> (and Cm Dm) Cm) Bm)) B)) (A (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-18878
in-theory        18878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) -> D) -> ((A -> (((B and C) -> C) and A)) and D))
theorem-size     23
proof            (modus-ponens tm-339 tm-271 ((Am (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) B)) (A (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-18878.        (((A -> (((B and C) -> C) and A)) -> D) -> ((A -> (((B and C) -> C) and A)) and D)), M:tm-339, m:tm-271, u:((Am (-> (-> Bm (and (-> (and Cm Dm) Dm) Bm)) B)) (A (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-18879
in-theory        18879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) -> D) -> ((A -> ((B -> (C -> (B and C))) and A)) and D))
theorem-size     27
proof            (modus-ponens tm-339 tm-304 ((Am (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) B)) (A (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-18879.        (((A -> ((B -> (C -> (B and C))) and A)) -> D) -> ((A -> ((B -> (C -> (B and C))) and A)) and D)), M:tm-339, m:tm-304, u:((Am (-> (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) B)) (A (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-18880
in-theory        18880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> C) -> ((C -> D) -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-338 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18880.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> C) -> ((C -> D) -> (C and D)))), M:tm-338, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18881
in-theory        18881
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (((A -> B) -> A) -> (((A -> B) -> A) and ((A -> B) -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-328 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18881.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (((A -> B) -> A) -> (((A -> B) -> A) and ((A -> B) -> (A and B))))), M:tm-328, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-18882
in-theory        18882
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((C -> (D -> (C and D))) and (((A -> B) -> A) -> ((A -> B) -> (A and B)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18882.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((C -> (D -> (C and D))) and (((A -> B) -> A) -> ((A -> B) -> (A and B))))), M:tm-327, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18883
in-theory        18883
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (((C and D) -> D) and (((A -> B) -> A) -> ((A -> B) -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18883.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (((C and D) -> D) and (((A -> B) -> A) -> ((A -> B) -> (A and B))))), M:tm-326, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18884
in-theory        18884
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (((C and D) -> C) and (((A -> B) -> A) -> ((A -> B) -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18884.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (((C and D) -> C) and (((A -> B) -> A) -> ((A -> B) -> (A and B))))), M:tm-325, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18885
in-theory        18885
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A -> B) -> A) -> ((A -> B) -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18885.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A -> B) -> A) -> ((A -> B) -> (A and B))))), M:tm-324, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18886
in-theory        18886
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((C -> (D -> C)) and (((A -> B) -> A) -> ((A -> B) -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18886.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((C -> (D -> C)) and (((A -> B) -> A) -> ((A -> B) -> (A and B))))), M:tm-323, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18887
in-theory        18887
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((C and D) -> D))
theorem-size     19
proof            (modus-ponens tm-322 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18887.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((C and D) -> D)), M:tm-322, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18888
in-theory        18888
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((C and D) -> C))
theorem-size     19
proof            (modus-ponens tm-320 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18888.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((C and D) -> C)), M:tm-320, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18889
in-theory        18889
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-318 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18889.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18890
in-theory        18890
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (((A -> B) -> A) -> ((A -> B) -> A)))
theorem-size     25
proof            (modus-ponens tm-316 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18890.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (((A -> B) -> A) -> ((A -> B) -> A))), M:tm-316, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-18891
in-theory        18891
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (C -> (D -> C)))
theorem-size     19
proof            (modus-ponens tm-315 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18891.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (C -> (D -> C))), M:tm-315, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18892
in-theory        18892
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((((A -> B) -> A) -> (not ((A -> B) -> (A and B)))) -> (not ((A -> B) -> A))))
theorem-size     35
proof            (modus-ponens tm-313 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18892.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((((A -> B) -> A) -> (not ((A -> B) -> (A and B)))) -> (not ((A -> B) -> A)))), M:tm-313, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-18893
in-theory        18893
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((((A -> B) -> (A and B)) -> C) -> ((((A -> B) -> A) or ((A -> B) -> (A and B))) -> C)))
theorem-size     39
proof            (modus-ponens tm-312 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18893.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((((A -> B) -> (A and B)) -> C) -> ((((A -> B) -> A) or ((A -> B) -> (A and B))) -> C))), M:tm-312, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-18894
in-theory        18894
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (C or (((A -> B) -> A) -> ((A -> B) -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18894.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (C or (((A -> B) -> A) -> ((A -> B) -> (A and B))))), M:tm-311, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18895
in-theory        18895
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((((A -> B) -> A) -> ((A -> B) -> (A and B))) or C))
theorem-size     29
proof            (modus-ponens tm-310 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18895.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((((A -> B) -> A) -> ((A -> B) -> (A and B))) or C)), M:tm-310, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18896
in-theory        18896
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (C -> ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and C)))
theorem-size     31
proof            (modus-ponens tm-309 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18896.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (C -> ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and C))), M:tm-309, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18897
in-theory        18897
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((((A -> B) -> A) -> (A -> B)) -> (((A -> B) -> A) -> (A and B))))
theorem-size     33
proof            (modus-ponens tm-306 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> Am Bm)) (C (and Am Bm))))
axioms-used      (tm-2 tm-5)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18897.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((((A -> B) -> A) -> (A -> B)) -> (((A -> B) -> A) -> (A and B)))), M:tm-306, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> Am Bm)) (C (and Am Bm)))
================================================================
tm-name          tm-18898
in-theory        18898
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (C -> (((A -> B) -> A) -> ((A -> B) -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18898.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (C -> (((A -> B) -> A) -> ((A -> B) -> (A and B))))), M:tm-305, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18899
in-theory        18899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-303 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18899.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-303, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18900
in-theory        18900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-270 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18900.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-270, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18901
in-theory        18901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-239 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18901.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-239, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18902
in-theory        18902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> E) -> ((E -> F) -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-210 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18902.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> E) -> ((E -> F) -> (E and F)))), M:tm-210, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18903
in-theory        18903
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-183 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18903.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-183, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18904
in-theory        18904
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-157 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18904.        ((A -> ((B and C) -> C)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-157, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18905
in-theory        18905
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-147 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18905.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-147, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18906
in-theory        18906
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-134 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18906.        ((A -> ((B and C) -> B)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-134, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18907
in-theory        18907
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-125 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18907.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-125, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18908
in-theory        18908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> E) -> ((E -> F) -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-113 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18908.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> E) -> ((E -> F) -> (E and F)))), M:tm-113, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18909
in-theory        18909
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-105 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18909.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-105, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18910
in-theory        18910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> C) -> ((C -> D) -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-95 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18910.        (((A -> B) -> (A -> A)) and (((C -> D) -> C) -> ((C -> D) -> (C and D)))), M:tm-95, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18911
in-theory        18911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> (C -> ((A -> B) -> (A and B))))
theorem-size     15
proof            (modus-ponens tm-84 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18911.        (((A -> B) -> A) -> (C -> ((A -> B) -> (A and B)))), M:tm-84, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-18912
in-theory        18912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-83 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18912.        ((A -> (B -> (C -> B))) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-83, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18913
in-theory        18913
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> B) -> ((B -> C) -> (B and C))))
theorem-size     19
proof            (modus-ponens tm-76 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-10 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18913.        (((not (not A)) -> A) and (((B -> C) -> B) -> ((B -> C) -> (B and C)))), M:tm-76, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18914
in-theory        18914
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> A))) or ((A -> B) -> A)) -> ((A -> B) -> (A and B)))
theorem-size     21
proof            (modus-ponens tm-73 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18914.        (((not (not ((A -> B) -> A))) or ((A -> B) -> A)) -> ((A -> B) -> (A and B))), M:tm-73, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-18915
in-theory        18915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> C) -> ((C -> D) -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-69 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-9 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18915.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> C) -> ((C -> D) -> (C and D)))), M:tm-69, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18916
in-theory        18916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-54 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18916.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-54, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18917
in-theory        18917
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> B)) or ((B -> C) -> B)) -> ((B -> C) -> (B and C)))
theorem-size     21
proof            (modus-ponens tm-47 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18917.        (((A and ((B -> C) -> B)) or ((B -> C) -> B)) -> ((B -> C) -> (B and C))), M:tm-47, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-18918
in-theory        18918
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> A) and C) or ((A -> B) -> A)) -> ((A -> B) -> (A and B)))
theorem-size     21
proof            (modus-ponens tm-46 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18918.        (((((A -> B) -> A) and C) or ((A -> B) -> A)) -> ((A -> B) -> (A and B))), M:tm-46, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-18919
in-theory        18919
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((A -> B) -> A)) -> ((A -> B) -> (A and B)))
theorem-size     15
proof            (modus-ponens tm-44 tm-339 ((A (-> Am Bm)) (B Am) (C (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18919.        ((A or ((A -> B) -> A)) -> ((A -> B) -> (A and B))), M:tm-44, m:tm-339, u:((A (-> Am Bm)) (B Am) (C (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-18920
in-theory        18920
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> C) -> ((C -> D) -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-42 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18920.        ((A -> (B or A)) and (((C -> D) -> C) -> ((C -> D) -> (C and D)))), M:tm-42, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18921
in-theory        18921
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> C) -> ((C -> D) -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-32 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18921.        ((A -> (A or B)) and (((C -> D) -> C) -> ((C -> D) -> (C and D)))), M:tm-32, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18922
in-theory        18922
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> (((A -> B) -> A) and ((A -> B) -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-24 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18922.        (((A -> B) -> A) -> (((A -> B) -> A) and ((A -> B) -> (A and B)))), M:tm-24, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-18923
in-theory        18923
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> C) -> ((C -> D) -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-23 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18923.        ((A -> (B -> (A and B))) and (((C -> D) -> C) -> ((C -> D) -> (C and D)))), M:tm-23, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18924
in-theory        18924
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> C) -> ((C -> D) -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-22 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-4 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18924.        (((A and B) -> B) and (((C -> D) -> C) -> ((C -> D) -> (C and D)))), M:tm-22, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18925
in-theory        18925
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> C) -> ((C -> D) -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-21 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-3 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18925.        (((A and B) -> A) and (((C -> D) -> C) -> ((C -> D) -> (C and D)))), M:tm-21, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18926
in-theory        18926
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-20 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18926.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-20, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18927
in-theory        18927
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> C) -> ((C -> D) -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-19 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18927.        ((A -> (B -> A)) and (((C -> D) -> C) -> ((C -> D) -> (C and D)))), M:tm-19, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18928
in-theory        18928
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> (not ((A -> B) -> (A and B)))) -> (not ((A -> B) -> A)))
theorem-size     21
proof            (modus-ponens tm-9 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-9 tm-2 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18928.        ((((A -> B) -> A) -> (not ((A -> B) -> (A and B)))) -> (not ((A -> B) -> A))), M:tm-9, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-18929
in-theory        18929
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (A and B)) -> C) -> ((((A -> B) -> A) or ((A -> B) -> (A and B))) -> C))
theorem-size     25
proof            (modus-ponens tm-8 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18929.        ((((A -> B) -> (A and B)) -> C) -> ((((A -> B) -> A) or ((A -> B) -> (A and B))) -> C)), M:tm-8, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-18930
in-theory        18930
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> C) -> B) -> ((B -> C) -> (B and C))))
theorem-size     15
proof            (modus-ponens tm-7 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-7 tm-2 tm-5)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18930.        (A or (((B -> C) -> B) -> ((B -> C) -> (B and C)))), M:tm-7, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18931
in-theory        18931
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) or C)
theorem-size     15
proof            (modus-ponens tm-6 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-6 tm-2 tm-5)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18931.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) or C), M:tm-6, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18932
in-theory        18932
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> B) -> ((B -> C) -> (B and C))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18932.        (A -> ((((B -> C) -> B) -> ((B -> C) -> (B and C))) and A)), M:tm-5, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18933
in-theory        18933
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> (A -> B)) -> (((A -> B) -> A) -> (A and B)))
theorem-size     19
proof            (modus-ponens tm-2 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> Am Bm)) (C (and Am Bm))))
axioms-used      (tm-2 tm-5)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18933.        ((((A -> B) -> A) -> (A -> B)) -> (((A -> B) -> A) -> (A and B))), M:tm-2, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> Am Bm)) (C (and Am Bm)))
================================================================
tm-name          tm-18934
in-theory        18934
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> B) -> ((B -> C) -> (B and C))))
theorem-size     15
proof            (modus-ponens tm-1 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-18934.        (A -> (((B -> C) -> B) -> ((B -> C) -> (B and C)))), M:tm-1, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-18935
in-theory        18935
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) -> C) -> (((A -> B) -> (A -> (A and B))) and C))
theorem-size     23
proof            (modus-ponens tm-339 tm-340 ((Am (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) B)) (A (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18935.        ((((A -> B) -> (A -> (A and B))) -> C) -> (((A -> B) -> (A -> (A and B))) and C)), M:tm-339, m:tm-340, u:((Am (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) B)) (A (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18936
in-theory        18936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> E) -> (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-338 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18936.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> E) -> (D -> (D and E))))), M:tm-338, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18937
in-theory        18937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> D) -> (C -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-335 tm-340 ((Am (-> A (and A B))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18937.        (((A -> B) or (A -> (A and B))) -> ((C -> D) -> (C -> (C and D)))), M:tm-335, m:tm-340, u:((Am (-> A (and A B))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18938
in-theory        18938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and (A -> (A and ((B -> C) -> (B -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-328 tm-340 ((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18938.        ((A -> ((B -> C) -> (B -> (B and C)))) and (A -> (A and ((B -> C) -> (B -> (B and C)))))), M:tm-328, m:tm-340, u:((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18939
in-theory        18939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and ((D -> (E -> (D and E))) and (A -> ((B -> C) -> (B -> (B and C))))))
theorem-size     31
proof            (modus-ponens tm-327 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18939.        ((A -> ((B -> C) -> (B -> (B and C)))) and ((D -> (E -> (D and E))) and (A -> ((B -> C) -> (B -> (B and C)))))), M:tm-327, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18940
in-theory        18940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and (((D and E) -> E) and (A -> ((B -> C) -> (B -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-326 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18940.        ((A -> ((B -> C) -> (B -> (B and C)))) and (((D and E) -> E) and (A -> ((B -> C) -> (B -> (B and C)))))), M:tm-326, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18941
in-theory        18941
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and (((D and E) -> D) and (A -> ((B -> C) -> (B -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-325 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18941.        ((A -> ((B -> C) -> (B -> (B and C)))) and (((D and E) -> D) and (A -> ((B -> C) -> (B -> (B and C)))))), M:tm-325, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18942
in-theory        18942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B -> C) -> (B -> (B and C))))))
theorem-size     37
proof            (modus-ponens tm-324 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18942.        ((A -> ((B -> C) -> (B -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> ((B -> C) -> (B -> (B and C)))))), M:tm-324, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18943
in-theory        18943
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and ((D -> (E -> D)) and (A -> ((B -> C) -> (B -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-323 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18943.        ((A -> ((B -> C) -> (B -> (B and C)))) and ((D -> (E -> D)) and (A -> ((B -> C) -> (B -> (B and C)))))), M:tm-323, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18944
in-theory        18944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18944.        ((A -> ((B -> C) -> (B -> (B and C)))) and ((D and E) -> E)), M:tm-322, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18945
in-theory        18945
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (B -> (B and C))) -> D)) -> ((B -> C) -> (B -> (B and C)))) and ((A and (((B -> C) -> (B -> (B and C))) -> D)) -> D))
theorem-size     39
proof            (modus-ponens tm-321 tm-340 ((Am (and A (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) C))) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18945.        (((A and (((B -> C) -> (B -> (B and C))) -> D)) -> ((B -> C) -> (B -> (B and C)))) and ((A and (((B -> C) -> (B -> (B and C))) -> D)) -> D)), M:tm-321, m:tm-340, u:((Am (and A (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) C))) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18946
in-theory        18946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18946.        ((A -> ((B -> C) -> (B -> (B and C)))) and ((D and E) -> D)), M:tm-320, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18947
in-theory        18947
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> (A and B))) -> C) and D) -> ((A -> B) -> (A -> (A and B)))) and (((((A -> B) -> (A -> (A and B))) -> C) and D) -> C))
theorem-size     39
proof            (modus-ponens tm-319 tm-340 ((Am (and (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) B) C)) (A (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18947.        ((((((A -> B) -> (A -> (A and B))) -> C) and D) -> ((A -> B) -> (A -> (A and B)))) and (((((A -> B) -> (A -> (A and B))) -> C) and D) -> C)), M:tm-319, m:tm-340, u:((Am (and (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) B) C)) (A (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18948
in-theory        18948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18948.        ((A -> ((B -> C) -> (B -> (B and C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18949
in-theory        18949
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (A and B)) -> C)) -> ((A -> B) -> (A -> (A and B)))) and (((A -> B) -> ((A -> (A and B)) -> C)) -> ((A -> B) -> C)))
theorem-size     39
proof            (modus-ponens tm-317 tm-340 ((Am (-> (-> Bm Cm) (-> (-> Bm (and Bm Cm)) C))) (A (-> Bm Cm)) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18949.        ((((A -> B) -> ((A -> (A and B)) -> C)) -> ((A -> B) -> (A -> (A and B)))) and (((A -> B) -> ((A -> (A and B)) -> C)) -> ((A -> B) -> C))), M:tm-317, m:tm-340, u:((Am (-> (-> Bm Cm) (-> (-> Bm (and Bm Cm)) C))) (A (-> Bm Cm)) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-18950
in-theory        18950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-340 ((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18950.        ((A -> ((B -> C) -> (B -> (B and C)))) and (A -> A)), M:tm-316, m:tm-340, u:((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18951
in-theory        18951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18951.        ((A -> ((B -> C) -> (B -> (B and C)))) and (D -> (E -> D))), M:tm-315, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18952
in-theory        18952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and ((A -> (not ((B -> C) -> (B -> (B and C))))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-340 ((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18952.        ((A -> ((B -> C) -> (B -> (B and C)))) and ((A -> (not ((B -> C) -> (B -> (B and C))))) -> (not A))), M:tm-313, m:tm-340, u:((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18953
in-theory        18953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and ((((B -> C) -> (B -> (B and C))) -> D) -> ((A or ((B -> C) -> (B -> (B and C)))) -> D)))
theorem-size     37
proof            (modus-ponens tm-312 tm-340 ((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18953.        ((A -> ((B -> C) -> (B -> (B and C)))) and ((((B -> C) -> (B -> (B and C))) -> D) -> ((A or ((B -> C) -> (B -> (B and C)))) -> D))), M:tm-312, m:tm-340, u:((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18954
in-theory        18954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and (D or (A -> ((B -> C) -> (B -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-311 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18954.        ((A -> ((B -> C) -> (B -> (B and C)))) and (D or (A -> ((B -> C) -> (B -> (B and C)))))), M:tm-311, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18955
in-theory        18955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and ((A -> ((B -> C) -> (B -> (B and C)))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18955.        ((A -> ((B -> C) -> (B -> (B and C)))) and ((A -> ((B -> C) -> (B -> (B and C)))) or D)), M:tm-310, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18956
in-theory        18956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and (D -> ((A -> ((B -> C) -> (B -> (B and C)))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18956.        ((A -> ((B -> C) -> (B -> (B and C)))) and (D -> ((A -> ((B -> C) -> (B -> (B and C)))) and D))), M:tm-309, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18957
in-theory        18957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and ((A -> (B -> C)) -> (A -> (B -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-306 tm-340 ((A Am) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18957.        ((A -> ((B -> C) -> (B -> (B and C)))) and ((A -> (B -> C)) -> (A -> (B -> (B and C))))), M:tm-306, m:tm-340, u:((A Am) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-18958
in-theory        18958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and (D -> (A -> ((B -> C) -> (B -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-305 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18958.        ((A -> ((B -> C) -> (B -> (B and C)))) and (D -> (A -> ((B -> C) -> (B -> (B and C)))))), M:tm-305, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18959
in-theory        18959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-303 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18959.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-303, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18960
in-theory        18960
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-300 tm-340 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18960.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> E) -> (D -> (D and E)))), M:tm-300, m:tm-340, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18961
in-theory        18961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-270 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18961.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-270, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18962
in-theory        18962
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-267 tm-340 ((Am (and (-> (and A B) B) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18962.        ((A or (((B and C) -> C) and A)) -> ((D -> E) -> (D -> (D and E)))), M:tm-267, m:tm-340, u:((Am (and (-> (and A B) B) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18963
in-theory        18963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-239 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18963.        ((A -> (((B and C) -> B) and A)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-239, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18964
in-theory        18964
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-236 tm-340 ((Am (and (-> (and A B) A) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18964.        ((A or (((B and C) -> B) and A)) -> ((D -> E) -> (D -> (D and E)))), M:tm-236, m:tm-340, u:((Am (and (-> (and A B) A) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18965
in-theory        18965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-210 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18965.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> G) -> (F -> (F and G))))), M:tm-210, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18966
in-theory        18966
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> F) -> (E -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-207 tm-340 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18966.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> F) -> (E -> (E and F)))), M:tm-207, m:tm-340, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18967
in-theory        18967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-183 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18967.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-183, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18968
in-theory        18968
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-180 tm-340 ((Am (and (-> A (-> B A)) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18968.        ((A or ((B -> (C -> B)) and A)) -> ((D -> E) -> (D -> (D and E)))), M:tm-180, m:tm-340, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18969
in-theory        18969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-157 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18969.        ((A -> ((B and C) -> C)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-157, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18970
in-theory        18970
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-154 tm-340 ((Am (-> (and A B) B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18970.        ((A or ((B and C) -> C)) -> ((D -> E) -> (D -> (D and E)))), M:tm-154, m:tm-340, u:((Am (-> (and A B) B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18971
in-theory        18971
times-derived    1
----------------------------------------------------------------
theorem          ((A and (B -> C)) -> (B -> (B and C)))
theorem-size     11
proof            (modus-ponens tm-152 tm-340 ((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18971.        ((A and (B -> C)) -> (B -> (B and C))), M:tm-152, m:tm-340, u:((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-18972
in-theory        18972
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-147 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18972.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-147, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18973
in-theory        18973
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-144 tm-340 ((Am (-> (and A (-> B C)) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-5)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18973.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> E) -> (D -> (D and E)))), M:tm-144, m:tm-340, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18974
in-theory        18974
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> (B -> (B and C))) -> D)) -> ((B -> C) -> (B -> (B and C))))
theorem-size     23
proof            (modus-ponens tm-142 tm-340 ((Am (and A (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) C))) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18974.        ((A and (((B -> C) -> (B -> (B and C))) -> D)) -> ((B -> C) -> (B -> (B and C)))), M:tm-142, m:tm-340, u:((Am (and A (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) C))) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18975
in-theory        18975
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> (B -> (B and C))) -> (B -> C))) -> (B -> (B and C)))
theorem-size     21
proof            (modus-ponens tm-141 tm-340 ((Am (and A (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> Bm Cm)))) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18975.        ((A and (((B -> C) -> (B -> (B and C))) -> (B -> C))) -> (B -> (B and C))), M:tm-141, m:tm-340, u:((Am (and A (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> Bm Cm)))) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-18976
in-theory        18976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-134 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18976.        ((A -> ((B and C) -> B)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-134, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18977
in-theory        18977
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-131 tm-340 ((Am (-> (and A B) A)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18977.        ((A or ((B and C) -> B)) -> ((D -> E) -> (D -> (D and E)))), M:tm-131, m:tm-340, u:((Am (-> (and A B) A)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18978
in-theory        18978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and C) -> (A -> (A and B)))
theorem-size     11
proof            (modus-ponens tm-129 tm-340 ((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18978.        (((A -> B) and C) -> (A -> (A and B))), M:tm-129, m:tm-340, u:((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-18979
in-theory        18979
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-125 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18979.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-125, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18980
in-theory        18980
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-122 tm-340 ((Am (-> (and (-> A B) C) B)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-5)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18980.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> E) -> (D -> (D and E)))), M:tm-122, m:tm-340, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18981
in-theory        18981
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> (A and B))) -> C) and D) -> ((A -> B) -> (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-120 tm-340 ((Am (and (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) B) C)) (A (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18981.        (((((A -> B) -> (A -> (A and B))) -> C) and D) -> ((A -> B) -> (A -> (A and B)))), M:tm-120, m:tm-340, u:((Am (and (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) B) C)) (A (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18982
in-theory        18982
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> (A and B))) -> (A -> B)) and C) -> (A -> (A and B)))
theorem-size     21
proof            (modus-ponens tm-119 tm-340 ((Am (and (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> Bm Cm)) C)) (A (-> Bm Cm)) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18982.        (((((A -> B) -> (A -> (A and B))) -> (A -> B)) and C) -> (A -> (A and B))), M:tm-119, m:tm-340, u:((Am (and (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> Bm Cm)) C)) (A (-> Bm Cm)) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-18983
in-theory        18983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-113 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18983.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (F -> (F and G))))), M:tm-113, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18984
in-theory        18984
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> F) -> (E -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-110 tm-340 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18984.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> F) -> (E -> (E and F)))), M:tm-110, m:tm-340, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18985
in-theory        18985
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((A -> B) -> ((A -> B) and (A -> C))))
theorem-size     17
proof            (modus-ponens tm-108 tm-340 ((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18985.        ((A -> (B -> C)) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-108, m:tm-340, u:((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
================================================================
tm-name          tm-18986
in-theory        18986
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) -> ((A -> B) -> A)) -> ((A -> B) -> (A and B)))
theorem-size     23
proof            (modus-ponens tm-106 tm-340 ((Am (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> Bm Cm) Bm))) (A (-> Bm Cm)) (B Bm) (C (and Bm Cm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18986.        ((((A -> B) -> (A -> (A and B))) -> ((A -> B) -> A)) -> ((A -> B) -> (A and B))), M:tm-106, m:tm-340, u:((Am (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> Bm Cm) Bm))) (A (-> Bm Cm)) (B Bm) (C (and Bm Cm)))
================================================================
tm-name          tm-18987
in-theory        18987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     31
proof            (modus-ponens tm-105 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18987.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-105, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18988
in-theory        18988
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> E) -> (D -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-102 tm-340 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18988.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> E) -> (D -> (D and E)))), M:tm-102, m:tm-340, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18989
in-theory        18989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (A and B)) -> C)) -> ((A -> B) -> (A -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-100 tm-340 ((Am (-> (-> Bm Cm) (-> (-> Bm (and Bm Cm)) C))) (A (-> Bm Cm)) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18989.        (((A -> B) -> ((A -> (A and B)) -> C)) -> ((A -> B) -> (A -> (A and B)))), M:tm-100, m:tm-340, u:((Am (-> (-> Bm Cm) (-> (-> Bm (and Bm Cm)) C))) (A (-> Bm Cm)) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-18990
in-theory        18990
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and A)))
theorem-size     7
proof            (modus-ponens tm-98 tm-340 ((Cm Am) (B Bm) (A Am) (C (-> Bm (and Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18990.        (A -> (B -> (B and A))), M:tm-98, m:tm-340, u:((Cm Am) (B Bm) (A Am) (C (-> Bm (and Bm Am))))
================================================================
tm-name          tm-18991
in-theory        18991
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) -> C) -> ((A -> B) -> (A -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-96 tm-340 ((Am (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) B)) (A (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18991.        ((((A -> B) -> (A -> (A and B))) -> C) -> ((A -> B) -> (A -> (A and B)))), M:tm-96, m:tm-340, u:((Am (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) B)) (A (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18992
in-theory        18992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> E) -> (D -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-95 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18992.        (((A -> B) -> (A -> A)) and (C -> ((D -> E) -> (D -> (D and E))))), M:tm-95, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18993
in-theory        18993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> D) -> (C -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-92 tm-340 ((Am (-> A A)) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18993.        (((A -> B) or (A -> A)) -> ((C -> D) -> (C -> (C and D)))), M:tm-92, m:tm-340, u:((Am (-> A A)) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18994
in-theory        18994
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> D) -> (C -> (C and D)))))
theorem-size     13
proof            (modus-ponens tm-84 tm-340 ((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18994.        (A -> (B -> ((C -> D) -> (C -> (C and D))))), M:tm-84, m:tm-340, u:((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18995
in-theory        18995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-83 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18995.        ((A -> (B -> (C -> B))) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-83, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18996
in-theory        18996
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-80 tm-340 ((Am (-> A (-> B A))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18996.        ((A or (B -> (C -> B))) -> ((D -> E) -> (D -> (D and E)))), M:tm-80, m:tm-340, u:((Am (-> A (-> B A))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18997
in-theory        18997
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((A -> B) -> (A -> (A and B))) -> C))) -> C)
theorem-size     15
proof            (modus-ponens tm-77 tm-340 ((Am (not (not (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) B)))) (A (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-10 tm-1 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18997.        ((not (not (((A -> B) -> (A -> (A and B))) -> C))) -> C), M:tm-77, m:tm-340, u:((Am (not (not (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) B)))) (A (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-18998
in-theory        18998
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> D) -> (C -> (C and D)))))
theorem-size     17
proof            (modus-ponens tm-76 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18998.        (((not (not A)) -> A) and (B -> ((C -> D) -> (C -> (C and D))))), M:tm-76, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-18999
in-theory        18999
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> C) -> (B -> (B and C))))
theorem-size     15
proof            (modus-ponens tm-73 tm-340 ((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-10 tm-1 tm-2 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-18999.        (((not (not A)) or A) -> ((B -> C) -> (B -> (B and C)))), M:tm-73, m:tm-340, u:((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19000
in-theory        19000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> E) -> (D -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-69 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-2)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19000.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> E) -> (D -> (D and E))))), M:tm-69, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-19001
in-theory        19001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> D) -> (C -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-66 tm-340 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-9 tm-1 tm-2 tm-5)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19001.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> D) -> (C -> (C and D)))), M:tm-66, m:tm-340, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19002
in-theory        19002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((A or (B -> C)) -> (B -> (B and C))))
theorem-size     17
proof            (modus-ponens tm-55 tm-340 ((Am (-> A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19002.        ((A -> (B -> C)) -> ((A or (B -> C)) -> (B -> (B and C)))), M:tm-55, m:tm-340, u:((Am (-> A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-19003
in-theory        19003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-54 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19003.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-54, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-19004
in-theory        19004
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-51 tm-340 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19004.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> (D -> (D and E)))), M:tm-51, m:tm-340, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19005
in-theory        19005
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> D) -> (C -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-50 tm-340 ((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-2 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19005.        ((A or (B or A)) -> ((C -> D) -> (C -> (C and D)))), M:tm-50, m:tm-340, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19006
in-theory        19006
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> D) -> (C -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-49 tm-340 ((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-2 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19006.        ((A or (A or B)) -> ((C -> D) -> (C -> (C and D)))), M:tm-49, m:tm-340, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19007
in-theory        19007
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> D) -> (C -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-48 tm-340 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19007.        ((A or (B -> (A and B))) -> ((C -> D) -> (C -> (C and D)))), M:tm-48, m:tm-340, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19008
in-theory        19008
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> D) -> (C -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-47 tm-340 ((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-2 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19008.        (((A and B) or B) -> ((C -> D) -> (C -> (C and D)))), M:tm-47, m:tm-340, u:((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19009
in-theory        19009
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> D) -> (C -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-46 tm-340 ((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-2 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19009.        (((A and B) or A) -> ((C -> D) -> (C -> (C and D)))), M:tm-46, m:tm-340, u:((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19010
in-theory        19010
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-45 tm-340 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19010.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (D -> (D and E)))), M:tm-45, m:tm-340, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19011
in-theory        19011
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> D) -> (C -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-44 tm-340 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19011.        ((A or (B -> A)) -> ((C -> D) -> (C -> (C and D)))), M:tm-44, m:tm-340, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19012
in-theory        19012
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-42 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19012.        ((A -> (B or A)) and (C -> ((D -> E) -> (D -> (D and E))))), M:tm-42, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-19013
in-theory        19013
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-32 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19013.        ((A -> (A or B)) and (C -> ((D -> E) -> (D -> (D and E))))), M:tm-32, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-19014
in-theory        19014
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> C) -> (B -> (B and C)))))
theorem-size     13
proof            (modus-ponens tm-24 tm-340 ((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19014.        (A -> (A and ((B -> C) -> (B -> (B and C))))), M:tm-24, m:tm-340, u:((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19015
in-theory        19015
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> E) -> (D -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-23 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19015.        ((A -> (B -> (A and B))) and (C -> ((D -> E) -> (D -> (D and E))))), M:tm-23, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-19016
in-theory        19016
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-22 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19016.        (((A and B) -> B) and (C -> ((D -> E) -> (D -> (D and E))))), M:tm-22, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-19017
in-theory        19017
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-21 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19017.        (((A and B) -> A) and (C -> ((D -> E) -> (D -> (D and E))))), M:tm-21, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-19018
in-theory        19018
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-20 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19018.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-20, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-19019
in-theory        19019
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-19 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19019.        ((A -> (B -> A)) and (C -> ((D -> E) -> (D -> (D and E))))), M:tm-19, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-19020
in-theory        19020
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> (B -> (B and C))) -> D)) -> D)
theorem-size     15
proof            (modus-ponens tm-17 tm-340 ((Am (and A (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) C))) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19020.        ((A and (((B -> C) -> (B -> (B and C))) -> D)) -> D), M:tm-17, m:tm-340, u:((Am (and A (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) C))) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19021
in-theory        19021
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> (A and B))) -> C) and D) -> C)
theorem-size     15
proof            (modus-ponens tm-15 tm-340 ((Am (and (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) B) C)) (A (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19021.        (((((A -> B) -> (A -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-340, u:((Am (and (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) B) C)) (A (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19022
in-theory        19022
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (A and B)) -> C)) -> ((A -> B) -> C))
theorem-size     17
proof            (modus-ponens tm-13 tm-340 ((Am (-> (-> Bm Cm) (-> (-> Bm (and Bm Cm)) C))) (A (-> Bm Cm)) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19022.        (((A -> B) -> ((A -> (A and B)) -> C)) -> ((A -> B) -> C)), M:tm-13, m:tm-340, u:((Am (-> (-> Bm Cm) (-> (-> Bm (and Bm Cm)) C))) (A (-> Bm Cm)) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-19023
in-theory        19023
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> C) -> (B -> (B and C))))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-340 ((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-9 tm-1 tm-2 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19023.        ((A -> (not ((B -> C) -> (B -> (B and C))))) -> (not A)), M:tm-9, m:tm-340, u:((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19024
in-theory        19024
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) -> C) -> ((D or ((A -> B) -> (A -> (A and B)))) -> C))
theorem-size     25
proof            (modus-ponens tm-8 tm-340 ((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19024.        ((((A -> B) -> (A -> (A and B))) -> C) -> ((D or ((A -> B) -> (A -> (A and B)))) -> C)), M:tm-8, m:tm-340, u:((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-19025
in-theory        19025
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> D) -> (C -> (C and D)))))
theorem-size     13
proof            (modus-ponens tm-7 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-7 tm-1 tm-2 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19025.        (A or (B -> ((C -> D) -> (C -> (C and D))))), M:tm-7, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-19026
in-theory        19026
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-6 tm-1 tm-2 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19026.        ((A -> ((B -> C) -> (B -> (B and C)))) or D), M:tm-6, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-19027
in-theory        19027
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> D) -> (C -> (C and D)))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19027.        (A -> ((B -> ((C -> D) -> (C -> (C and D)))) and A)), M:tm-5, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-19028
in-theory        19028
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (A -> (B -> (B and C))))
theorem-size     13
proof            (modus-ponens tm-2 tm-340 ((A Am) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19028.        ((A -> (B -> C)) -> (A -> (B -> (B and C)))), M:tm-2, m:tm-340, u:((A Am) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-19029
in-theory        19029
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19029.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19030
in-theory        19030
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-341 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-19030.        (((A -> (B -> A)) or C) and (D -> (E -> (D and E)))), M:tm-341, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-19031
in-theory        19031
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19031.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-19032
in-theory        19032
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-341 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19032.        ((((A and B) -> A) or C) and (D -> (E -> (D and E)))), M:tm-341, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-19033
in-theory        19033
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-341 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19033.        ((((A and B) -> B) or C) and (D -> (E -> (D and E)))), M:tm-341, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-19034
in-theory        19034
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19034.        (((A -> (B -> (A and B))) or C) and (D -> (E -> (D and E)))), M:tm-341, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-19035
in-theory        19035
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-341 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19035.        (((A -> (A or B)) or C) and (D -> (E -> (D and E)))), M:tm-341, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-19036
in-theory        19036
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19036.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-19037
in-theory        19037
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-341 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19037.        ((A -> (B -> (B or C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-19038
in-theory        19038
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-341 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-19038.        ((A or (B -> (C -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-19039
in-theory        19039
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19039.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-19040
in-theory        19040
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-341 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19040.        ((A or ((B and C) -> B)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-19041
in-theory        19041
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-341 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19041.        ((A or ((B and C) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-19042
in-theory        19042
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19042.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19043
in-theory        19043
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-341 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19043.        ((A or (B -> (B or C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-19044
in-theory        19044
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-341 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19044.        ((A or (B -> (C or B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-19045
in-theory        19045
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-341 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19045.        (((A -> (B or A)) or C) and (D -> (E -> (D and E)))), M:tm-341, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-19046
in-theory        19046
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19046.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-19047
in-theory        19047
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-341 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19047.        ((A -> (B -> (C or B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-19048
in-theory        19048
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19048.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-19049
in-theory        19049
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-341 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19049.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-19050
in-theory        19050
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19050.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-19051
in-theory        19051
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19051.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-19052
in-theory        19052
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-341 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-19052.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-19053
in-theory        19053
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-19053.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-19054
in-theory        19054
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-19054.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-19055
in-theory        19055
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-341 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-19055.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-19056
in-theory        19056
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-19056.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-19057
in-theory        19057
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-19057.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-19058
in-theory        19058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-19058.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-19059
in-theory        19059
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-341 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-19059.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-19060
in-theory        19060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-19060.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-19061
in-theory        19061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-341 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19061.        (((A -> (not (B -> A))) -> (not A)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-19062
in-theory        19062
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (D -> (E -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-341 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19062.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-19063
in-theory        19063
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (C -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-341 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19063.        ((((A and B) -> (not A)) -> (not (A and B))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-19064
in-theory        19064
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (C -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-341 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19064.        ((((A and B) -> (not B)) -> (not (A and B))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-19065
in-theory        19065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (C -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-341 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-19065.        (((A -> (not (B -> (A and B)))) -> (not A)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-19066
in-theory        19066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-341 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-19066.        (((A -> (not (A or B))) -> (not A)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-19067
in-theory        19067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-341 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-19067.        (((A -> (not (B or A))) -> (not A)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-19068
in-theory        19068
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (D -> (E -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-341 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-19068.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-19069
in-theory        19069
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (C -> (D -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-341 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-19069.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-19070
in-theory        19070
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (D -> (E -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-341 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-19070.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-19071
in-theory        19071
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-19071.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-19072
in-theory        19072
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-19072.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (D -> (E -> (D and E)))), M:tm-341, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-19073
in-theory        19073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-19073.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-19074
in-theory        19074
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (C -> (D -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-341 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-19074.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-19075
in-theory        19075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-19075.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-19076
in-theory        19076
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (B -> (C -> (B and C))))
theorem-size     19
proof            (modus-ponens tm-341 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-19076.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (B -> (C -> (B and C)))), M:tm-341, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-19077
in-theory        19077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (C -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-341 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-10)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-19077.        (((A -> B) -> (((not (not A)) or A) -> B)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-19078
in-theory        19078
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-341 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-19078.        ((A or ((not (not B)) -> B)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-19079
in-theory        19079
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-341 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-19079.        ((((not (not A)) -> A) or B) and (C -> (D -> (C and D)))), M:tm-341, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-19080
in-theory        19080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-341 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-19080.        ((A -> (((not (not B)) -> B) and A)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-19081
in-theory        19081
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (C -> (D -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-341 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-19081.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-19082
in-theory        19082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-341 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-19082.        ((A -> ((not (not B)) -> B)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-19083
in-theory        19083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19083.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-19084
in-theory        19084
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19084.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-19085
in-theory        19085
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19085.        ((A or (B -> (C -> (D -> C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-19086
in-theory        19086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19086.        (((A -> (B -> (C -> B))) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-19087
in-theory        19087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19087.        ((A -> ((B -> (C -> (D -> C))) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-19088
in-theory        19088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-19088.        (((A -> B) -> (A -> (C -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-19089
in-theory        19089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19089.        ((A -> (B -> (C -> (D -> C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-19090
in-theory        19090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and (B -> (C -> (B and C))))
theorem-size     11
proof            (modus-ponens tm-341 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19090.        ((A -> A) and (B -> (C -> (B and C)))), M:tm-341, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-19091
in-theory        19091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19091.        (((A -> (B -> C)) -> (A -> (B -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-19092
in-theory        19092
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-341 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19092.        (((A and B) -> (A and B)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-19093
in-theory        19093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-341 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-19093.        (((A -> B) -> (A -> B)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-19094
in-theory        19094
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and (B -> (C -> (B and C))))
theorem-size     15
proof            (modus-ponens tm-341 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-19094.        (((not (not A)) -> (not (not A))) and (B -> (C -> (B and C)))), M:tm-341, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-19095
in-theory        19095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-341 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-19095.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-19096
in-theory        19096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-19096.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-19097
in-theory        19097
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19097.        ((A or ((B -> C) -> (B -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-19098
in-theory        19098
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19098.        ((((A -> B) -> (A -> A)) or C) and (D -> (E -> (D and E)))), M:tm-341, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-19099
in-theory        19099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19099.        ((A -> (((B -> C) -> (B -> B)) and A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-19100
in-theory        19100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and (C -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-341 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-19100.        ((((A -> B) -> A) -> ((A -> B) -> A)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-19101
in-theory        19101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19101.        ((A -> ((B -> C) -> (B -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-19102
in-theory        19102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-19102.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19103
in-theory        19103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-341 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-19103.        (((A -> (A -> B)) -> (A -> B)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-19104
in-theory        19104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (D -> (E -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-341 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-19104.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-19105
in-theory        19105
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (D -> (E -> (D and E))))
theorem-size     39
proof            (modus-ponens tm-341 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-19105.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-19106
in-theory        19106
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (E -> (F -> (E and F))))
theorem-size     41
proof            (modus-ponens tm-341 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-19106.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-19107
in-theory        19107
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-19107.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-19108
in-theory        19108
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-19108.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-19109
in-theory        19109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (E -> (F -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-341 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-19109.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-19110
in-theory        19110
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (D -> (E -> (D and E))))
theorem-size     37
proof            (modus-ponens tm-341 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-19110.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-19111
in-theory        19111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-19111.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-19112
in-theory        19112
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-341 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-19112.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-19113
in-theory        19113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19113.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-19114
in-theory        19114
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (F -> (G -> (F and G))))
theorem-size     41
proof            (modus-ponens tm-341 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19114.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-19115
in-theory        19115
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19115.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-19116
in-theory        19116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19116.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (G -> (F and G)))), M:tm-341, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-19117
in-theory        19117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19117.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-19118
in-theory        19118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-19118.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-19119
in-theory        19119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19119.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-19120
in-theory        19120
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-341 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-19120.        ((((A -> B) and A) -> B) and (C -> (D -> (C and D)))), M:tm-341, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-19121
in-theory        19121
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-19121.        (((((A -> (B -> A)) -> C) and D) -> C) and (E -> (F -> (E and F)))), M:tm-341, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-19122
in-theory        19122
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19122.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (F -> (G -> (F and G)))), M:tm-341, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-19123
in-theory        19123
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (D -> (E -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-341 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-19123.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-19124
in-theory        19124
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-19124.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-19125
in-theory        19125
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (D -> (E -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-341 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-19125.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-19126
in-theory        19126
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (E -> (F -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-341 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-19126.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-19127
in-theory        19127
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-19127.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-19128
in-theory        19128
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-19128.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-19129
in-theory        19129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-19129.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-19130
in-theory        19130
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (D -> (E -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-341 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-19130.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-19131
in-theory        19131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-19131.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-19132
in-theory        19132
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-19132.        ((((((A and B) -> A) -> C) and D) -> C) and (E -> (F -> (E and F)))), M:tm-341, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-19133
in-theory        19133
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-19133.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-19134
in-theory        19134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19134.        (((A -> (not ((B and C) -> B))) -> (not A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-19135
in-theory        19135
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19135.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-19136
in-theory        19136
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19136.        ((A or (B -> ((C and D) -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-19137
in-theory        19137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19137.        (((A -> ((B and C) -> B)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-19138
in-theory        19138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19138.        ((A -> ((B -> ((C and D) -> C)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-19139
in-theory        19139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-19139.        (((A -> (B and C)) -> (A -> B)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-19140
in-theory        19140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19140.        ((A -> (B -> ((C and D) -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-19141
in-theory        19141
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-341 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-19141.        (((A and (A -> B)) -> B) and (C -> (D -> (C and D)))), M:tm-341, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-19142
in-theory        19142
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-19142.        (((A and ((B -> (C -> B)) -> D)) -> D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-19143
in-theory        19143
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19143.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (F -> (G -> (F and G)))), M:tm-341, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-19144
in-theory        19144
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-19144.        (((A and (((B and C) -> B) -> D)) -> D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-19145
in-theory        19145
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (D -> (E -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-341 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-19145.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-19146
in-theory        19146
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-19146.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-19147
in-theory        19147
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (D -> (E -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-341 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-19147.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-19148
in-theory        19148
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-341 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-19148.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-19149
in-theory        19149
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-19149.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-19150
in-theory        19150
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-19150.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-19151
in-theory        19151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-19151.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-19152
in-theory        19152
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (D -> (E -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-341 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-19152.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-19153
in-theory        19153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-19153.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-19154
in-theory        19154
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-19154.        (((A and (((B and C) -> C) -> D)) -> D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-19155
in-theory        19155
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-19155.        ((((((A and B) -> B) -> C) and D) -> C) and (E -> (F -> (E and F)))), M:tm-341, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-19156
in-theory        19156
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-19156.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-19157
in-theory        19157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19157.        (((A -> (not ((B and C) -> C))) -> (not A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-19158
in-theory        19158
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19158.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-19159
in-theory        19159
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19159.        ((A or (B -> ((C and D) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-19160
in-theory        19160
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19160.        (((A -> ((B and C) -> C)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-19161
in-theory        19161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19161.        ((A -> ((B -> ((C and D) -> D)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-19162
in-theory        19162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-19162.        (((A -> (B and C)) -> (A -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19163
in-theory        19163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19163.        ((A -> (B -> ((C and D) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-19164
in-theory        19164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-19164.        (((A -> (B -> A)) and (C -> (D -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-19165
in-theory        19165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19165.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-19166
in-theory        19166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19166.        (((A -> (B -> A)) and ((C and D) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-19167
in-theory        19167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19167.        (((A -> (B -> A)) and ((C and D) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-19168
in-theory        19168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19168.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-19169
in-theory        19169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19169.        (((A -> (B -> A)) and (C -> (C or D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-19170
in-theory        19170
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19170.        (((A -> (B -> A)) and (C -> (D or C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-19171
in-theory        19171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-19171.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-19172
in-theory        19172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-19172.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-19173
in-theory        19173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-19173.        (((A -> (B -> A)) and ((not (not C)) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-19174
in-theory        19174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19174.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-19175
in-theory        19175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19175.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-19176
in-theory        19176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     33
proof            (modus-ponens tm-341 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-19176.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-19177
in-theory        19177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19177.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-19178
in-theory        19178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-19178.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-19179
in-theory        19179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19179.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-19180
in-theory        19180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-19180.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-19181
in-theory        19181
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19181.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-19182
in-theory        19182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-19182.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-19183
in-theory        19183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-19183.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-19184
in-theory        19184
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-19184.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-19185
in-theory        19185
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-19185.        ((A or (B -> ((C -> (D -> C)) and B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-19186
in-theory        19186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-19186.        (((A -> ((B -> (C -> B)) and A)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-19187
in-theory        19187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-19187.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-19188
in-theory        19188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-19188.        ((A -> (B -> ((C -> (D -> C)) and B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-19189
in-theory        19189
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-19189.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-19190
in-theory        19190
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H -> (G and H))))
theorem-size     35
proof            (modus-ponens tm-341 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19190.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-19191
in-theory        19191
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19191.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-19192
in-theory        19192
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19192.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-19193
in-theory        19193
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19193.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-19194
in-theory        19194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19194.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-19195
in-theory        19195
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19195.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-19196
in-theory        19196
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (H -> (G and H))))
theorem-size     35
proof            (modus-ponens tm-341 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-19196.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-19197
in-theory        19197
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (G -> (F and G))))
theorem-size     33
proof            (modus-ponens tm-341 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-19197.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-19198
in-theory        19198
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-19198.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-19199
in-theory        19199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19199.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-19200
in-theory        19200
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19200.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-19201
in-theory        19201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (H -> (G and H))))
theorem-size     41
proof            (modus-ponens tm-341 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-19201.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-19202
in-theory        19202
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I -> (H and I))))
theorem-size     37
proof            (modus-ponens tm-341 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19202.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I -> (H and I)))), M:tm-341, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-19203
in-theory        19203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (H -> (G and H))))
theorem-size     37
proof            (modus-ponens tm-341 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-19203.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-19204
in-theory        19204
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19204.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-19205
in-theory        19205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (H -> (G and H))))
theorem-size     37
proof            (modus-ponens tm-341 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-19205.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-19206
in-theory        19206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19206.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-19207
in-theory        19207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-19207.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-19208
in-theory        19208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (I -> (H and I))))
theorem-size     39
proof            (modus-ponens tm-341 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-19208.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (I -> (H and I)))), M:tm-341, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-19209
in-theory        19209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-19209.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-19210
in-theory        19210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-19210.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-19211
in-theory        19211
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (F -> (G -> (F and G))))
theorem-size     45
proof            (modus-ponens tm-341 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-19211.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-19212
in-theory        19212
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-19212.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-19213
in-theory        19213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-19213.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (F -> (G -> (F and G)))), M:tm-341, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-19214
in-theory        19214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-19214.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-19215
in-theory        19215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-19215.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-19216
in-theory        19216
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-19216.        ((((A and B) -> A) and (C -> (D -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-19217
in-theory        19217
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19217.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-19218
in-theory        19218
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19218.        ((((A and B) -> A) and ((C and D) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-19219
in-theory        19219
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19219.        ((((A and B) -> A) and ((C and D) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-19220
in-theory        19220
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19220.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-19221
in-theory        19221
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19221.        ((((A and B) -> A) and (C -> (C or D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-19222
in-theory        19222
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19222.        ((((A and B) -> A) and (C -> (D or C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-19223
in-theory        19223
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-19223.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-19224
in-theory        19224
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-19224.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-19225
in-theory        19225
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-19225.        ((((A and B) -> A) and ((not (not C)) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-19226
in-theory        19226
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19226.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-19227
in-theory        19227
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19227.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-19228
in-theory        19228
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     33
proof            (modus-ponens tm-341 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-19228.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-19229
in-theory        19229
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19229.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-19230
in-theory        19230
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-19230.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-19231
in-theory        19231
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19231.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-19232
in-theory        19232
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-19232.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-19233
in-theory        19233
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19233.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-19234
in-theory        19234
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-19234.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-19235
in-theory        19235
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-19235.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-19236
in-theory        19236
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-19236.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-19237
in-theory        19237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-19237.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-19238
in-theory        19238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-19238.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-19239
in-theory        19239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-19239.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-19240
in-theory        19240
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-19240.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-19241
in-theory        19241
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-19241.        ((A or (B -> (((C and D) -> C) and B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-19242
in-theory        19242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-19242.        (((A -> (((B and C) -> B) and A)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-19243
in-theory        19243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-19243.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-19244
in-theory        19244
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-19244.        ((A -> (B -> (((C and D) -> C) and B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-19245
in-theory        19245
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-19245.        ((((A and B) -> B) and (C -> (D -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-19246
in-theory        19246
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19246.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-19247
in-theory        19247
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19247.        ((((A and B) -> B) and ((C and D) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-19248
in-theory        19248
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19248.        ((((A and B) -> B) and ((C and D) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-19249
in-theory        19249
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19249.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-19250
in-theory        19250
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19250.        ((((A and B) -> B) and (C -> (C or D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-19251
in-theory        19251
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19251.        ((((A and B) -> B) and (C -> (D or C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-19252
in-theory        19252
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-19252.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-19253
in-theory        19253
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-19253.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-19254
in-theory        19254
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-19254.        ((((A and B) -> B) and ((not (not C)) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-19255
in-theory        19255
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19255.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-19256
in-theory        19256
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19256.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-19257
in-theory        19257
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     33
proof            (modus-ponens tm-341 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-19257.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-19258
in-theory        19258
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19258.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-19259
in-theory        19259
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-19259.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-19260
in-theory        19260
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19260.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-19261
in-theory        19261
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-19261.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-19262
in-theory        19262
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19262.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-19263
in-theory        19263
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-19263.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-19264
in-theory        19264
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-19264.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-19265
in-theory        19265
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-19265.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-19266
in-theory        19266
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-19266.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-19267
in-theory        19267
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-19267.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-19268
in-theory        19268
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-19268.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-19269
in-theory        19269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-19269.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-19270
in-theory        19270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-19270.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-19271
in-theory        19271
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-19271.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-19272
in-theory        19272
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-19272.        ((A or (B -> (((C and D) -> D) and B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-19273
in-theory        19273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-19273.        (((A -> (((B and C) -> C) and A)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-19274
in-theory        19274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-19274.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-19275
in-theory        19275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-19275.        ((A -> (B -> (((C and D) -> D) and B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-19276
in-theory        19276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-19276.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-19277
in-theory        19277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19277.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-19278
in-theory        19278
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19278.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-19279
in-theory        19279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19279.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-19280
in-theory        19280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19280.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-19281
in-theory        19281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19281.        (((A -> (B -> (A and B))) and (C -> (C or D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-19282
in-theory        19282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19282.        (((A -> (B -> (A and B))) and (C -> (D or C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-19283
in-theory        19283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-19283.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-19284
in-theory        19284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-19284.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-19285
in-theory        19285
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-19285.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-19286
in-theory        19286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19286.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-19287
in-theory        19287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19287.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-19288
in-theory        19288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     35
proof            (modus-ponens tm-341 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-19288.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-19289
in-theory        19289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19289.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-19290
in-theory        19290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-341 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-19290.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-19291
in-theory        19291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19291.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-19292
in-theory        19292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-341 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-19292.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-19293
in-theory        19293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19293.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-19294
in-theory        19294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-19294.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-19295
in-theory        19295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> (G and H))))
theorem-size     33
proof            (modus-ponens tm-341 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-19295.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-19296
in-theory        19296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-19296.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-19297
in-theory        19297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-19297.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-19298
in-theory        19298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-19298.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-19299
in-theory        19299
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-19299.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-19300
in-theory        19300
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-19300.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-19301
in-theory        19301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (H -> (G and H))))
theorem-size     33
proof            (modus-ponens tm-341 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-19301.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-19302
in-theory        19302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-19302.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-19303
in-theory        19303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-19303.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-19304
in-theory        19304
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-341 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-19304.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-19305
in-theory        19305
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-19305.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-19306
in-theory        19306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-19306.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-19307
in-theory        19307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-19307.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-19308
in-theory        19308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-19308.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-19309
in-theory        19309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-341 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19309.        ((A -> (A and (B -> A))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-19310
in-theory        19310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (D -> (E -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-341 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19310.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-19311
in-theory        19311
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-341 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19311.        (((A and B) -> ((A and B) and A)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-19312
in-theory        19312
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-341 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19312.        (((A and B) -> ((A and B) and B)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-19313
in-theory        19313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-341 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-19313.        ((A -> (A and (B -> (A and B)))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-19314
in-theory        19314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-341 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-19314.        ((A -> (A and (A or B))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-19315
in-theory        19315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-341 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-19315.        ((A -> (A and (B or A))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-19316
in-theory        19316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-341 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-19316.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-19317
in-theory        19317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (C -> (D -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-341 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-19317.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-19318
in-theory        19318
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and (B -> (C -> (B and C))))
theorem-size     17
proof            (modus-ponens tm-341 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-10)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-19318.        (((not (not A)) -> ((not (not A)) and A)) and (B -> (C -> (B and C)))), M:tm-341, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-19319
in-theory        19319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19319.        ((A -> (A and (B -> (C -> B)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-19320
in-theory        19320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and (C -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-341 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-19320.        (((A -> B) -> ((A -> B) and (A -> A))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-19321
in-theory        19321
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (D -> (E -> (D and E))))
theorem-size     37
proof            (modus-ponens tm-341 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-19321.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-19322
in-theory        19322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19322.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-19323
in-theory        19323
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (D -> (E -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-341 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-19323.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-19324
in-theory        19324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19324.        ((A -> (A and ((B and C) -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-19325
in-theory        19325
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (D -> (E -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-341 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-19325.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-19326
in-theory        19326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19326.        ((A -> (A and ((B and C) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-19327
in-theory        19327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-19327.        ((A -> (A and ((B -> (C -> B)) and A))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-19328
in-theory        19328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-19328.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-19329
in-theory        19329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-19329.        ((A -> (A and (((B and C) -> B) and A))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-19330
in-theory        19330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-19330.        ((A -> (A and (((B and C) -> C) and A))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-19331
in-theory        19331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-19331.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-19332
in-theory        19332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-341 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-19332.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-19333
in-theory        19333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19333.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-19334
in-theory        19334
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19334.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-19335
in-theory        19335
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19335.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-19336
in-theory        19336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (G -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-341 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19336.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-19337
in-theory        19337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19337.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-19338
in-theory        19338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (C -> (D -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-341 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-19338.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-19339
in-theory        19339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (D -> (E -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-341 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-19339.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-19340
in-theory        19340
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19340.        ((A or ((B -> C) -> (B -> (B and C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-19341
in-theory        19341
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19341.        ((((A -> B) -> (A -> (A and B))) or C) and (D -> (E -> (D and E)))), M:tm-341, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-19342
in-theory        19342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19342.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-19343
in-theory        19343
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-341 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-19343.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-19344
in-theory        19344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19344.        ((A -> ((B -> C) -> (B -> (B and C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-19345
in-theory        19345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19345.        ((A -> (A and (B -> (C -> (B and C))))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19346
in-theory        19346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and (D -> (E -> (D and E))))))
theorem-size     21
proof            (modus-ponens tm-338 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19346.        (((A -> B) -> (A -> (A and B))) and (C -> (C and (D -> (E -> (D and E)))))), M:tm-338, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19347
in-theory        19347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (C -> (D -> (C and D)))))
theorem-size     23
proof            (modus-ponens tm-335 tm-341 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19347.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (C -> (D -> (C and D))))), M:tm-335, m:tm-341, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19348
in-theory        19348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (A -> (A and (A and (B -> (C -> (B and C)))))))
theorem-size     25
proof            (modus-ponens tm-328 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19348.        ((A -> (A and (B -> (C -> (B and C))))) and (A -> (A and (A and (B -> (C -> (B and C))))))), M:tm-328, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19349
in-theory        19349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and ((D -> (E -> (D and E))) and (A -> (A and (B -> (C -> (B and C)))))))
theorem-size     31
proof            (modus-ponens tm-327 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19349.        ((A -> (A and (B -> (C -> (B and C))))) and ((D -> (E -> (D and E))) and (A -> (A and (B -> (C -> (B and C))))))), M:tm-327, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19350
in-theory        19350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (((D and E) -> E) and (A -> (A and (B -> (C -> (B and C)))))))
theorem-size     29
proof            (modus-ponens tm-326 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19350.        ((A -> (A and (B -> (C -> (B and C))))) and (((D and E) -> E) and (A -> (A and (B -> (C -> (B and C))))))), M:tm-326, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19351
in-theory        19351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (((D and E) -> D) and (A -> (A and (B -> (C -> (B and C)))))))
theorem-size     29
proof            (modus-ponens tm-325 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19351.        ((A -> (A and (B -> (C -> (B and C))))) and (((D and E) -> D) and (A -> (A and (B -> (C -> (B and C))))))), M:tm-325, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19352
in-theory        19352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and (B -> (C -> (B and C)))))))
theorem-size     37
proof            (modus-ponens tm-324 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19352.        ((A -> (A and (B -> (C -> (B and C))))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and (B -> (C -> (B and C))))))), M:tm-324, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19353
in-theory        19353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and ((D -> (E -> D)) and (A -> (A and (B -> (C -> (B and C)))))))
theorem-size     29
proof            (modus-ponens tm-323 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19353.        ((A -> (A and (B -> (C -> (B and C))))) and ((D -> (E -> D)) and (A -> (A and (B -> (C -> (B and C))))))), M:tm-323, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19354
in-theory        19354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19354.        ((A -> (A and (B -> (C -> (B and C))))) and ((D and E) -> E)), M:tm-322, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19355
in-theory        19355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19355.        ((A -> (A and (B -> (C -> (B and C))))) and ((D and E) -> D)), M:tm-320, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19356
in-theory        19356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19356.        ((A -> (A and (B -> (C -> (B and C))))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19357
in-theory        19357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19357.        ((A -> (A and (B -> (C -> (B and C))))) and (A -> A)), M:tm-316, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19358
in-theory        19358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19358.        ((A -> (A and (B -> (C -> (B and C))))) and (D -> (E -> D))), M:tm-315, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19359
in-theory        19359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and ((A -> (not (A and (B -> (C -> (B and C)))))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19359.        ((A -> (A and (B -> (C -> (B and C))))) and ((A -> (not (A and (B -> (C -> (B and C)))))) -> (not A))), M:tm-313, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19360
in-theory        19360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (((A and (B -> (C -> (B and C)))) -> D) -> ((A or (A and (B -> (C -> (B and C))))) -> D)))
theorem-size     37
proof            (modus-ponens tm-312 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19360.        ((A -> (A and (B -> (C -> (B and C))))) and (((A and (B -> (C -> (B and C)))) -> D) -> ((A or (A and (B -> (C -> (B and C))))) -> D))), M:tm-312, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19361
in-theory        19361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (D or (A -> (A and (B -> (C -> (B and C)))))))
theorem-size     25
proof            (modus-ponens tm-311 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19361.        ((A -> (A and (B -> (C -> (B and C))))) and (D or (A -> (A and (B -> (C -> (B and C))))))), M:tm-311, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19362
in-theory        19362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and ((A -> (A and (B -> (C -> (B and C))))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19362.        ((A -> (A and (B -> (C -> (B and C))))) and ((A -> (A and (B -> (C -> (B and C))))) or D)), M:tm-310, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19363
in-theory        19363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (D -> ((A -> (A and (B -> (C -> (B and C))))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19363.        ((A -> (A and (B -> (C -> (B and C))))) and (D -> ((A -> (A and (B -> (C -> (B and C))))) and D))), M:tm-309, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19364
in-theory        19364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (D -> (A -> (A and (B -> (C -> (B and C)))))))
theorem-size     25
proof            (modus-ponens tm-305 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19364.        ((A -> (A and (B -> (C -> (B and C))))) and (D -> (A -> (A and (B -> (C -> (B and C))))))), M:tm-305, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19365
in-theory        19365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     23
proof            (modus-ponens tm-303 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19365.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-303, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19366
in-theory        19366
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (D -> (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-300 tm-341 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19366.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (D -> (E -> (D and E))))), M:tm-300, m:tm-341, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19367
in-theory        19367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-270 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19367.        ((A -> (((B and C) -> C) and A)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-270, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19368
in-theory        19368
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-267 tm-341 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19368.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (D -> (E -> (D and E))))), M:tm-267, m:tm-341, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19369
in-theory        19369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-239 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19369.        ((A -> (((B and C) -> B) and A)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-239, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19370
in-theory        19370
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-236 tm-341 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19370.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (D -> (E -> (D and E))))), M:tm-236, m:tm-341, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19371
in-theory        19371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (F -> (G -> (F and G))))))
theorem-size     29
proof            (modus-ponens tm-210 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19371.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (F -> (G -> (F and G)))))), M:tm-210, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19372
in-theory        19372
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (E -> (F -> (E and F)))))
theorem-size     41
proof            (modus-ponens tm-207 tm-341 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19372.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (E -> (F -> (E and F))))), M:tm-207, m:tm-341, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19373
in-theory        19373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-183 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19373.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-183, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19374
in-theory        19374
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-180 tm-341 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19374.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (D -> (E -> (D and E))))), M:tm-180, m:tm-341, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19375
in-theory        19375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-157 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19375.        ((A -> ((B and C) -> C)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-157, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19376
in-theory        19376
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and (D -> (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-154 tm-341 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19376.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and (D -> (E -> (D and E))))), M:tm-154, m:tm-341, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19377
in-theory        19377
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     27
proof            (modus-ponens tm-147 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19377.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-147, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19378
in-theory        19378
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (D -> (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-144 tm-341 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19378.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (D -> (E -> (D and E))))), M:tm-144, m:tm-341, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19379
in-theory        19379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-134 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19379.        ((A -> ((B and C) -> B)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-134, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19380
in-theory        19380
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and (D -> (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-131 tm-341 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19380.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and (D -> (E -> (D and E))))), M:tm-131, m:tm-341, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19381
in-theory        19381
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     27
proof            (modus-ponens tm-125 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19381.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-125, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19382
in-theory        19382
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (D -> (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-122 tm-341 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19382.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (D -> (E -> (D and E))))), M:tm-122, m:tm-341, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19383
in-theory        19383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-113 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19383.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (G -> (F and G)))))), M:tm-113, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19384
in-theory        19384
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (E and F)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-341 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19384.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (E and F))))), M:tm-110, m:tm-341, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19385
in-theory        19385
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     31
proof            (modus-ponens tm-105 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19385.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-105, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19386
in-theory        19386
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (D -> (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-102 tm-341 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19386.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (D -> (E -> (D and E))))), M:tm-102, m:tm-341, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19387
in-theory        19387
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and (D -> (E -> (D and E))))))
theorem-size     19
proof            (modus-ponens tm-95 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19387.        (((A -> B) -> (A -> A)) and (C -> (C and (D -> (E -> (D and E)))))), M:tm-95, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19388
in-theory        19388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and (C -> (D -> (C and D)))))
theorem-size     19
proof            (modus-ponens tm-92 tm-341 ((Am (-> A A)) (B (and (-> A A) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19388.        (((A -> B) or (A -> A)) -> ((A -> A) and (C -> (D -> (C and D))))), M:tm-92, m:tm-341, u:((Am (-> A A)) (B (and (-> A A) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19389
in-theory        19389
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and (C -> (D -> (C and D))))))
theorem-size     13
proof            (modus-ponens tm-84 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19389.        (A -> (B -> (A and (C -> (D -> (C and D)))))), M:tm-84, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19390
in-theory        19390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-83 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19390.        ((A -> (B -> (C -> B))) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-83, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19391
in-theory        19391
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (D -> (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-80 tm-341 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19391.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (D -> (E -> (D and E))))), M:tm-80, m:tm-341, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19392
in-theory        19392
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and (C -> (D -> (C and D))))))
theorem-size     17
proof            (modus-ponens tm-76 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19392.        (((not (not A)) -> A) and (B -> (B and (C -> (D -> (C and D)))))), M:tm-76, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19393
in-theory        19393
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and (B -> (C -> (B and C)))))
theorem-size     15
proof            (modus-ponens tm-73 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19393.        (((not (not A)) or A) -> (A and (B -> (C -> (B and C))))), M:tm-73, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19394
in-theory        19394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (D -> (E -> (D and E))))))
theorem-size     23
proof            (modus-ponens tm-69 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19394.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (D -> (E -> (D and E)))))), M:tm-69, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19395
in-theory        19395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (C -> (D -> (C and D)))))
theorem-size     27
proof            (modus-ponens tm-66 tm-341 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19395.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (C -> (D -> (C and D))))), M:tm-66, m:tm-341, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19396
in-theory        19396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     25
proof            (modus-ponens tm-54 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19396.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-54, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19397
in-theory        19397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> (E -> (D and E)))))
theorem-size     31
proof            (modus-ponens tm-51 tm-341 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19397.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> (E -> (D and E))))), M:tm-51, m:tm-341, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19398
in-theory        19398
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and (C -> (D -> (C and D)))))
theorem-size     17
proof            (modus-ponens tm-50 tm-341 ((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19398.        ((A or (B or A)) -> ((B or A) and (C -> (D -> (C and D))))), M:tm-50, m:tm-341, u:((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19399
in-theory        19399
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and (C -> (D -> (C and D)))))
theorem-size     17
proof            (modus-ponens tm-49 tm-341 ((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19399.        ((A or (A or B)) -> ((A or B) and (C -> (D -> (C and D))))), M:tm-49, m:tm-341, u:((Am (or A B)) (C (and (or A B) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19400
in-theory        19400
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> (D -> (C and D)))))
theorem-size     21
proof            (modus-ponens tm-48 tm-341 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19400.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> (D -> (C and D))))), M:tm-48, m:tm-341, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19401
in-theory        19401
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (C -> (D -> (C and D)))))
theorem-size     15
proof            (modus-ponens tm-47 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19401.        (((A and B) or B) -> (B and (C -> (D -> (C and D))))), M:tm-47, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19402
in-theory        19402
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (C -> (D -> (C and D)))))
theorem-size     15
proof            (modus-ponens tm-46 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19402.        (((A and B) or A) -> (A and (C -> (D -> (C and D))))), M:tm-46, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19403
in-theory        19403
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-45 tm-341 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19403.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (E -> (D and E))))), M:tm-45, m:tm-341, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19404
in-theory        19404
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (C -> (D -> (C and D)))))
theorem-size     17
proof            (modus-ponens tm-44 tm-341 ((Am (-> A B)) (C (and (-> A B) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19404.        ((A or (B -> A)) -> ((B -> A) and (C -> (D -> (C and D))))), M:tm-44, m:tm-341, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19405
in-theory        19405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and (D -> (E -> (D and E))))))
theorem-size     17
proof            (modus-ponens tm-42 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19405.        ((A -> (B or A)) and (C -> (C and (D -> (E -> (D and E)))))), M:tm-42, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19406
in-theory        19406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and (D -> (E -> (D and E))))))
theorem-size     17
proof            (modus-ponens tm-32 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19406.        ((A -> (A or B)) and (C -> (C and (D -> (E -> (D and E)))))), M:tm-32, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19407
in-theory        19407
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and (B -> (C -> (B and C))))))
theorem-size     13
proof            (modus-ponens tm-24 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19407.        (A -> (A and (A and (B -> (C -> (B and C)))))), M:tm-24, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19408
in-theory        19408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and (D -> (E -> (D and E))))))
theorem-size     19
proof            (modus-ponens tm-23 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19408.        ((A -> (B -> (A and B))) and (C -> (C and (D -> (E -> (D and E)))))), M:tm-23, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19409
in-theory        19409
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and (D -> (E -> (D and E))))))
theorem-size     17
proof            (modus-ponens tm-22 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19409.        (((A and B) -> B) and (C -> (C and (D -> (E -> (D and E)))))), M:tm-22, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19410
in-theory        19410
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and (D -> (E -> (D and E))))))
theorem-size     17
proof            (modus-ponens tm-21 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19410.        (((A and B) -> A) and (C -> (C and (D -> (E -> (D and E)))))), M:tm-21, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19411
in-theory        19411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     25
proof            (modus-ponens tm-20 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19411.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-20, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19412
in-theory        19412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and (D -> (E -> (D and E))))))
theorem-size     17
proof            (modus-ponens tm-19 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19412.        ((A -> (B -> A)) and (C -> (C and (D -> (E -> (D and E)))))), M:tm-19, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19413
in-theory        19413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and (B -> (C -> (B and C)))))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-9 tm-2 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19413.        ((A -> (not (A and (B -> (C -> (B and C)))))) -> (not A)), M:tm-9, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19414
in-theory        19414
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> (B and C)))) -> D) -> ((A or (A and (B -> (C -> (B and C))))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19414.        (((A and (B -> (C -> (B and C)))) -> D) -> ((A or (A and (B -> (C -> (B and C))))) -> D)), M:tm-8, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-19415
in-theory        19415
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and (C -> (D -> (C and D))))))
theorem-size     13
proof            (modus-ponens tm-7 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-7 tm-2 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19415.        (A or (B -> (B and (C -> (D -> (C and D)))))), M:tm-7, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19416
in-theory        19416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-6 tm-2 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19416.        ((A -> (A and (B -> (C -> (B and C))))) or D), M:tm-6, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19417
in-theory        19417
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and (C -> (D -> (C and D))))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19417.        (A -> ((B -> (B and (C -> (D -> (C and D))))) and A)), M:tm-5, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19418
in-theory        19418
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and (C -> (D -> (C and D))))))
theorem-size     13
proof            (modus-ponens tm-1 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19418.        (A -> (B -> (B and (C -> (D -> (C and D)))))), M:tm-1, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19419
in-theory        19419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19419.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19420
in-theory        19420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-338 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19420.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G)))))), M:tm-338, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19421
in-theory        19421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E)))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19421.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))))), M:tm-327, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19422
in-theory        19422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E)))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19422.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))))), M:tm-326, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19423
in-theory        19423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E)))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19423.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))))), M:tm-325, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19424
in-theory        19424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E)))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19424.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))))), M:tm-324, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19425
in-theory        19425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E)))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19425.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))))), M:tm-323, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19426
in-theory        19426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19426.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> G)), M:tm-322, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19427
in-theory        19427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19427.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> F)), M:tm-320, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19428
in-theory        19428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19428.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19429
in-theory        19429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19429.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> F))), M:tm-315, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19430
in-theory        19430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (F or ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19430.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (F or ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))))), M:tm-311, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19431
in-theory        19431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19431.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) or F)), M:tm-310, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19432
in-theory        19432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (F -> (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19432.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (F -> (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and F))), M:tm-309, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19433
in-theory        19433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (C -> (D -> (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-308 tm-342 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19433.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (C -> (D -> (E -> (D and E))))), M:tm-308, m:tm-342, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-19434
in-theory        19434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (A -> (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-307 tm-342 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19434.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-342, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-19435
in-theory        19435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (F -> ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19435.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (F -> ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))))), M:tm-305, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19436
in-theory        19436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-303 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19436.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-303, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19437
in-theory        19437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-270 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19437.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-270, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19438
in-theory        19438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-239 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19438.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-239, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19439
in-theory        19439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     35
proof            (modus-ponens tm-210 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19439.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I)))))), M:tm-210, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19440
in-theory        19440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-183 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19440.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-183, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19441
in-theory        19441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-157 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19441.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-157, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19442
in-theory        19442
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-147 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19442.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-147, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19443
in-theory        19443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-134 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19443.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-134, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19444
in-theory        19444
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-125 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19444.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-125, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19445
in-theory        19445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-113 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19445.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I)))))), M:tm-113, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19446
in-theory        19446
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     37
proof            (modus-ponens tm-105 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19446.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-105, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19447
in-theory        19447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-95 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19447.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G)))))), M:tm-95, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19448
in-theory        19448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-83 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19448.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-83, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19449
in-theory        19449
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (E -> (F -> (E and F))))))
theorem-size     23
proof            (modus-ponens tm-76 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19449.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (E -> (F -> (E and F)))))), M:tm-76, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19450
in-theory        19450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     29
proof            (modus-ponens tm-69 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19450.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G)))))), M:tm-69, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19451
in-theory        19451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-54 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19451.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-54, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19452
in-theory        19452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-42 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19452.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G)))))), M:tm-42, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19453
in-theory        19453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-32 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19453.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G)))))), M:tm-32, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19454
in-theory        19454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-23 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19454.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G)))))), M:tm-23, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19455
in-theory        19455
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-22 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19455.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G)))))), M:tm-22, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19456
in-theory        19456
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-21 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19456.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G)))))), M:tm-21, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19457
in-theory        19457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-20 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19457.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-20, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19458
in-theory        19458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-19 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19458.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G -> (F and G)))))), M:tm-19, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19459
in-theory        19459
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-7 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19459.        (A or ((B -> (C -> (B and C))) and (D -> (E -> (F -> (E and F)))))), M:tm-7, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19460
in-theory        19460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19460.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) or F), M:tm-6, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19461
in-theory        19461
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> (E -> (F -> (E and F))))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19461.        (A -> (((B -> (C -> (B and C))) and (D -> (E -> (F -> (E and F))))) and A)), M:tm-5, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19462
in-theory        19462
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-1 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-1 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19462.        (A -> ((B -> (C -> (B and C))) and (D -> (E -> (F -> (E and F)))))), M:tm-1, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19463
in-theory        19463
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19463.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19464
in-theory        19464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-338 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19464.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (F -> (G -> (F and G)))))), M:tm-338, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19465
in-theory        19465
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> (D -> (E -> (D and E)))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19465.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> (D -> (E -> (D and E))))))), M:tm-327, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19466
in-theory        19466
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> G) and (((A and B) -> B) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19466.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> G) and (((A and B) -> B) and (C -> (D -> (E -> (D and E))))))), M:tm-326, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19467
in-theory        19467
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> F) and (((A and B) -> B) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19467.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> F) and (((A and B) -> B) and (C -> (D -> (E -> (D and E))))))), M:tm-325, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19468
in-theory        19468
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> (D -> (E -> (D and E)))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19468.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> (D -> (E -> (D and E))))))), M:tm-324, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19469
in-theory        19469
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19469.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> (D -> (E -> (D and E))))))), M:tm-323, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19470
in-theory        19470
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19470.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> G)), M:tm-322, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19471
in-theory        19471
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19471.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> F)), M:tm-320, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19472
in-theory        19472
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19472.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19473
in-theory        19473
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19473.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> F))), M:tm-315, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19474
in-theory        19474
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (F or (((A and B) -> B) and (C -> (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19474.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (F or (((A and B) -> B) and (C -> (D -> (E -> (D and E))))))), M:tm-311, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19475
in-theory        19475
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19475.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) or F)), M:tm-310, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19476
in-theory        19476
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (F -> ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19476.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (F -> ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and F))), M:tm-309, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19477
in-theory        19477
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (C -> (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-308 tm-343 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19477.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (C -> (D -> (E -> (D and E))))), M:tm-308, m:tm-343, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-19478
in-theory        19478
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((A and B) -> B))
theorem-size     21
proof            (modus-ponens tm-307 tm-343 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19478.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((A and B) -> B)), M:tm-307, m:tm-343, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-19479
in-theory        19479
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (F -> (((A and B) -> B) and (C -> (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19479.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (F -> (((A and B) -> B) and (C -> (D -> (E -> (D and E))))))), M:tm-305, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19480
in-theory        19480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-303 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19480.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-303, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19481
in-theory        19481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-270 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19481.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-270, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19482
in-theory        19482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-239 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19482.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-239, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19483
in-theory        19483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-210 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19483.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (H -> (I -> (H and I)))))), M:tm-210, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19484
in-theory        19484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-183 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19484.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-183, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19485
in-theory        19485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-157 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19485.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-157, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19486
in-theory        19486
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-147 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19486.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-147, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19487
in-theory        19487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-134 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19487.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-134, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19488
in-theory        19488
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-125 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19488.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-125, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19489
in-theory        19489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-113 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19489.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (I -> (H and I)))))), M:tm-113, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19490
in-theory        19490
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-105 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19490.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-105, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19491
in-theory        19491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-95 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19491.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (F -> (G -> (F and G)))))), M:tm-95, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19492
in-theory        19492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-83 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19492.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-83, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19493
in-theory        19493
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-76 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-10 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19493.        (((not (not A)) -> A) and (((B and C) -> C) and (D -> (E -> (F -> (E and F)))))), M:tm-76, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19494
in-theory        19494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-69 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-9 tm-4 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19494.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (F -> (G -> (F and G)))))), M:tm-69, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19495
in-theory        19495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-54 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19495.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-54, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19496
in-theory        19496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-42 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19496.        ((A -> (B or A)) and (((C and D) -> D) and (E -> (F -> (G -> (F and G)))))), M:tm-42, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19497
in-theory        19497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-32 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19497.        ((A -> (A or B)) and (((C and D) -> D) and (E -> (F -> (G -> (F and G)))))), M:tm-32, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19498
in-theory        19498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-23 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19498.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (F -> (G -> (F and G)))))), M:tm-23, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19499
in-theory        19499
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-22 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19499.        (((A and B) -> B) and (((C and D) -> D) and (E -> (F -> (G -> (F and G)))))), M:tm-22, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19500
in-theory        19500
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-21 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19500.        (((A and B) -> A) and (((C and D) -> D) and (E -> (F -> (G -> (F and G)))))), M:tm-21, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19501
in-theory        19501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-20 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19501.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-20, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19502
in-theory        19502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-19 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19502.        ((A -> (B -> A)) and (((C and D) -> D) and (E -> (F -> (G -> (F and G)))))), M:tm-19, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19503
in-theory        19503
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-7 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-7 tm-5 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19503.        (A or (((B and C) -> C) and (D -> (E -> (F -> (E and F)))))), M:tm-7, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19504
in-theory        19504
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-6 tm-5 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19504.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) or F), M:tm-6, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19505
in-theory        19505
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> (E -> (F -> (E and F))))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19505.        (A -> ((((B and C) -> C) and (D -> (E -> (F -> (E and F))))) and A)), M:tm-5, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19506
in-theory        19506
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-1 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-1 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19506.        (A -> (((B and C) -> C) and (D -> (E -> (F -> (E and F)))))), M:tm-1, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19507
in-theory        19507
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19507.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19508
in-theory        19508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-338 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19508.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (F -> (G -> (F and G)))))), M:tm-338, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19509
in-theory        19509
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> (D -> (E -> (D and E)))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19509.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> (D -> (E -> (D and E))))))), M:tm-327, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19510
in-theory        19510
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> G) and (((A and B) -> A) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19510.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> G) and (((A and B) -> A) and (C -> (D -> (E -> (D and E))))))), M:tm-326, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19511
in-theory        19511
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> F) and (((A and B) -> A) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19511.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> F) and (((A and B) -> A) and (C -> (D -> (E -> (D and E))))))), M:tm-325, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19512
in-theory        19512
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> (D -> (E -> (D and E)))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19512.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> (D -> (E -> (D and E))))))), M:tm-324, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19513
in-theory        19513
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19513.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> (D -> (E -> (D and E))))))), M:tm-323, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19514
in-theory        19514
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19514.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> G)), M:tm-322, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19515
in-theory        19515
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19515.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> F)), M:tm-320, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19516
in-theory        19516
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19516.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19517
in-theory        19517
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19517.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> F))), M:tm-315, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19518
in-theory        19518
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (F or (((A and B) -> A) and (C -> (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19518.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (F or (((A and B) -> A) and (C -> (D -> (E -> (D and E))))))), M:tm-311, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19519
in-theory        19519
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19519.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) or F)), M:tm-310, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19520
in-theory        19520
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (F -> ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19520.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (F -> ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and F))), M:tm-309, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19521
in-theory        19521
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (C -> (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-308 tm-344 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19521.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (C -> (D -> (E -> (D and E))))), M:tm-308, m:tm-344, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-19522
in-theory        19522
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((A and B) -> A))
theorem-size     21
proof            (modus-ponens tm-307 tm-344 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19522.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((A and B) -> A)), M:tm-307, m:tm-344, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-19523
in-theory        19523
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (F -> (((A and B) -> A) and (C -> (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19523.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (F -> (((A and B) -> A) and (C -> (D -> (E -> (D and E))))))), M:tm-305, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19524
in-theory        19524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-303 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19524.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-303, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19525
in-theory        19525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-270 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19525.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-270, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19526
in-theory        19526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-239 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19526.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-239, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19527
in-theory        19527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-210 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19527.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (H -> (I -> (H and I)))))), M:tm-210, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19528
in-theory        19528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-183 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19528.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-183, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19529
in-theory        19529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-157 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19529.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-157, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19530
in-theory        19530
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-147 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19530.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-147, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19531
in-theory        19531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-134 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19531.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-134, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19532
in-theory        19532
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-125 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19532.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-125, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19533
in-theory        19533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-113 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19533.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (I -> (H and I)))))), M:tm-113, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19534
in-theory        19534
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-105 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19534.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-105, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19535
in-theory        19535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-95 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19535.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (F -> (G -> (F and G)))))), M:tm-95, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19536
in-theory        19536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-83 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19536.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-83, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19537
in-theory        19537
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-76 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-10 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19537.        (((not (not A)) -> A) and (((B and C) -> B) and (D -> (E -> (F -> (E and F)))))), M:tm-76, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19538
in-theory        19538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-69 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-9 tm-3 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19538.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (F -> (G -> (F and G)))))), M:tm-69, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19539
in-theory        19539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-54 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19539.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-54, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19540
in-theory        19540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-42 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19540.        ((A -> (B or A)) and (((C and D) -> C) and (E -> (F -> (G -> (F and G)))))), M:tm-42, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19541
in-theory        19541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-32 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19541.        ((A -> (A or B)) and (((C and D) -> C) and (E -> (F -> (G -> (F and G)))))), M:tm-32, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19542
in-theory        19542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-23 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19542.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (F -> (G -> (F and G)))))), M:tm-23, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19543
in-theory        19543
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-22 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19543.        (((A and B) -> B) and (((C and D) -> C) and (E -> (F -> (G -> (F and G)))))), M:tm-22, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19544
in-theory        19544
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-21 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19544.        (((A and B) -> A) and (((C and D) -> C) and (E -> (F -> (G -> (F and G)))))), M:tm-21, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19545
in-theory        19545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-20 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19545.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-20, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19546
in-theory        19546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-19 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19546.        ((A -> (B -> A)) and (((C and D) -> C) and (E -> (F -> (G -> (F and G)))))), M:tm-19, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19547
in-theory        19547
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-7 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-7 tm-5 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19547.        (A or (((B and C) -> B) and (D -> (E -> (F -> (E and F)))))), M:tm-7, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19548
in-theory        19548
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-6 tm-5 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19548.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) or F), M:tm-6, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19549
in-theory        19549
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> (E -> (F -> (E and F))))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19549.        (A -> ((((B and C) -> B) and (D -> (E -> (F -> (E and F))))) and A)), M:tm-5, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19550
in-theory        19550
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-1 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-1 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19550.        (A -> (((B and C) -> B) and (D -> (E -> (F -> (E and F)))))), M:tm-1, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19551
in-theory        19551
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19551.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19552
in-theory        19552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-338 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19552.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-338, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19553
in-theory        19553
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     55
proof            (modus-ponens tm-327 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19553.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-327, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19554
in-theory        19554
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-326 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19554.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-326, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19555
in-theory        19555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-325 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19555.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-325, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19556
in-theory        19556
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     61
proof            (modus-ponens tm-324 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19556.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-324, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19557
in-theory        19557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-323 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19557.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-323, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19558
in-theory        19558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19558.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((G and H) -> H)), M:tm-322, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19559
in-theory        19559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19559.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((G and H) -> G)), M:tm-320, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19560
in-theory        19560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19560.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19561
in-theory        19561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19561.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (H -> G))), M:tm-315, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19562
in-theory        19562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     49
proof            (modus-ponens tm-311 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19562.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-311, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19563
in-theory        19563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19563.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) or G)), M:tm-310, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19564
in-theory        19564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19564.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and G))), M:tm-309, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19565
in-theory        19565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (D -> (E -> (F -> (E and F)))))
theorem-size     33
proof            (modus-ponens tm-308 tm-345 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (-> Fm (and Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19565.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (D -> (E -> (F -> (E and F))))), M:tm-308, m:tm-345, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (-> Fm (and Em Fm))))))
================================================================
tm-name          tm-19566
in-theory        19566
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-345 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (-> Fm (and Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19566.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-345, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (-> Fm (and Em Fm))))))
================================================================
tm-name          tm-19567
in-theory        19567
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     49
proof            (modus-ponens tm-305 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19567.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-305, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19568
in-theory        19568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     35
proof            (modus-ponens tm-303 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19568.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-303, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19569
in-theory        19569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-270 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19569.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-270, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19570
in-theory        19570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-239 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19570.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-239, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19571
in-theory        19571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> (I and J))))))
theorem-size     41
proof            (modus-ponens tm-210 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19571.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-210, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19572
in-theory        19572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-183 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19572.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-183, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19573
in-theory        19573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-157 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19573.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-157, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19574
in-theory        19574
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     39
proof            (modus-ponens tm-147 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19574.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-147, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19575
in-theory        19575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-134 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19575.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-134, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19576
in-theory        19576
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     39
proof            (modus-ponens tm-125 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19576.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-125, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19577
in-theory        19577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-113 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19577.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-113, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19578
in-theory        19578
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-105 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19578.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-105, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19579
in-theory        19579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-95 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19579.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-95, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19580
in-theory        19580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-83 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19580.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-83, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19581
in-theory        19581
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     29
proof            (modus-ponens tm-76 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19581.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> (F and G)))))), M:tm-76, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19582
in-theory        19582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-69 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19582.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-69, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19583
in-theory        19583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-54 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19583.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-54, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19584
in-theory        19584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-42 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19584.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-42, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19585
in-theory        19585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-32 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19585.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-32, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19586
in-theory        19586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-23 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19586.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-23, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19587
in-theory        19587
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-22 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19587.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-22, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19588
in-theory        19588
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-21 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19588.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-21, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19589
in-theory        19589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-20 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19589.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-20, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19590
in-theory        19590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-19 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19590.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H -> (G and H)))))), M:tm-19, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19591
in-theory        19591
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-7 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-7 tm-5 tm-2 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19591.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> (F and G)))))), M:tm-7, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19592
in-theory        19592
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-6 tm-5 tm-2 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19592.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) or G), M:tm-6, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19593
in-theory        19593
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> (F and G))))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19593.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> (F and G))))) and A)), M:tm-5, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19594
in-theory        19594
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-1 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-1 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19594.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G -> (F and G)))))), M:tm-1, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-19595
in-theory        19595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19595.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19596
in-theory        19596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-338 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19596.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G)))))), M:tm-338, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19597
in-theory        19597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19597.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))))), M:tm-327, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19598
in-theory        19598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19598.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))))), M:tm-326, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19599
in-theory        19599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19599.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))))), M:tm-325, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19600
in-theory        19600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19600.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))))), M:tm-324, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19601
in-theory        19601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19601.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))))), M:tm-323, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19602
in-theory        19602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19602.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> G)), M:tm-322, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19603
in-theory        19603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19603.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> F)), M:tm-320, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19604
in-theory        19604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19604.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19605
in-theory        19605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19605.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> F))), M:tm-315, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19606
in-theory        19606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (F or ((A -> (B -> A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19606.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (F or ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))))), M:tm-311, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19607
in-theory        19607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19607.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) or F)), M:tm-310, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19608
in-theory        19608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (F -> (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19608.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (F -> (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and F))), M:tm-309, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19609
in-theory        19609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (C -> (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-308 tm-346 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19609.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (C -> (D -> (E -> (D and E))))), M:tm-308, m:tm-346, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-19610
in-theory        19610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (A -> (B -> A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-346 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19610.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (A -> (B -> A))), M:tm-307, m:tm-346, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-19611
in-theory        19611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (F -> ((A -> (B -> A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19611.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (F -> ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))))), M:tm-305, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19612
in-theory        19612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-303 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19612.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-303, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19613
in-theory        19613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-270 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19613.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-270, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19614
in-theory        19614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-239 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19614.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-239, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19615
in-theory        19615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-210 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19615.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I)))))), M:tm-210, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19616
in-theory        19616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-183 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19616.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-183, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19617
in-theory        19617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-157 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19617.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-157, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19618
in-theory        19618
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-147 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19618.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-147, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19619
in-theory        19619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-134 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19619.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-134, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19620
in-theory        19620
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-125 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19620.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-125, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19621
in-theory        19621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-113 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19621.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I)))))), M:tm-113, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19622
in-theory        19622
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-105 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19622.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-105, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19623
in-theory        19623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-95 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19623.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G)))))), M:tm-95, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19624
in-theory        19624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-83 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19624.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-83, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19625
in-theory        19625
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-76 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19625.        (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (E -> (F -> (E and F)))))), M:tm-76, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19626
in-theory        19626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-69 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19626.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G)))))), M:tm-69, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19627
in-theory        19627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-54 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19627.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-54, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19628
in-theory        19628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-42 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19628.        ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G)))))), M:tm-42, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19629
in-theory        19629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-32 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19629.        ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G)))))), M:tm-32, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19630
in-theory        19630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-23 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19630.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G)))))), M:tm-23, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19631
in-theory        19631
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-22 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19631.        (((A and B) -> B) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G)))))), M:tm-22, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19632
in-theory        19632
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-21 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19632.        (((A and B) -> A) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G)))))), M:tm-21, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19633
in-theory        19633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-20 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19633.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-20, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19634
in-theory        19634
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-19 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19634.        ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (F -> (G -> (F and G)))))), M:tm-19, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19635
in-theory        19635
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-7 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19635.        (A or ((B -> (C -> B)) and (D -> (E -> (F -> (E and F)))))), M:tm-7, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19636
in-theory        19636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19636.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) or F), M:tm-6, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19637
in-theory        19637
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> (E -> (F -> (E and F))))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19637.        (A -> (((B -> (C -> B)) and (D -> (E -> (F -> (E and F))))) and A)), M:tm-5, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19638
in-theory        19638
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-1 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-1 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19638.        (A -> ((B -> (C -> B)) and (D -> (E -> (F -> (E and F)))))), M:tm-1, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-19639
in-theory        19639
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19639.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19640
in-theory        19640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C and ((D -> (E -> (D and E))) -> F)) -> F))
theorem-size     23
proof            (modus-ponens tm-338 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19640.        (((A -> B) -> (A -> (A and B))) and ((C and ((D -> (E -> (D and E))) -> F)) -> F)), M:tm-338, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19641
in-theory        19641
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((A and ((B -> (C -> (B and C))) -> D)) -> ((A and ((B -> (C -> (B and C))) -> D)) and D)))
theorem-size     39
proof            (modus-ponens tm-328 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19641.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((A and ((B -> (C -> (B and C))) -> D)) -> ((A and ((B -> (C -> (B and C))) -> D)) and D))), M:tm-328, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-19642
in-theory        19642
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((E -> (F -> (E and F))) and ((A and ((B -> (C -> (B and C))) -> D)) -> D)))
theorem-size     35
proof            (modus-ponens tm-327 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19642.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((E -> (F -> (E and F))) and ((A and ((B -> (C -> (B and C))) -> D)) -> D))), M:tm-327, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19643
in-theory        19643
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (((E and F) -> F) and ((A and ((B -> (C -> (B and C))) -> D)) -> D)))
theorem-size     33
proof            (modus-ponens tm-326 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19643.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (((E and F) -> F) and ((A and ((B -> (C -> (B and C))) -> D)) -> D))), M:tm-326, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19644
in-theory        19644
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (((E and F) -> E) and ((A and ((B -> (C -> (B and C))) -> D)) -> D)))
theorem-size     33
proof            (modus-ponens tm-325 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19644.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (((E and F) -> E) and ((A and ((B -> (C -> (B and C))) -> D)) -> D))), M:tm-325, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19645
in-theory        19645
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A and ((B -> (C -> (B and C))) -> D)) -> D)))
theorem-size     41
proof            (modus-ponens tm-324 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19645.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A and ((B -> (C -> (B and C))) -> D)) -> D))), M:tm-324, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19646
in-theory        19646
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((E -> (F -> E)) and ((A and ((B -> (C -> (B and C))) -> D)) -> D)))
theorem-size     33
proof            (modus-ponens tm-323 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19646.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((E -> (F -> E)) and ((A and ((B -> (C -> (B and C))) -> D)) -> D))), M:tm-323, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19647
in-theory        19647
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19647.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((E and F) -> F)), M:tm-322, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19648
in-theory        19648
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> (B -> (C -> (B and C))))) -> (B -> (C -> (B and C)))) and ((A and ((B -> (C -> (B and C))) -> (B -> (C -> (B and C))))) -> (B -> (C -> (B and C)))))
theorem-size     51
proof            (modus-ponens tm-321 tm-347 ((A Am) (Dm (-> Bm (-> Cm (and Bm Cm)))) (C (-> Bm (-> Cm (and Bm Cm)))) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19648.        (((A and ((B -> (C -> (B and C))) -> (B -> (C -> (B and C))))) -> (B -> (C -> (B and C)))) and ((A and ((B -> (C -> (B and C))) -> (B -> (C -> (B and C))))) -> (B -> (C -> (B and C))))), M:tm-321, m:tm-347, u:((A Am) (Dm (-> Bm (-> Cm (and Bm Cm)))) (C (-> Bm (-> Cm (and Bm Cm)))) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-19649
in-theory        19649
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19649.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((E and F) -> E)), M:tm-320, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19650
in-theory        19650
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and ((C -> (D -> (C and D))) -> A)) -> A) and (((A -> B) and ((C -> (D -> (C and D))) -> A)) -> B))
theorem-size     31
proof            (modus-ponens tm-319 tm-347 ((Am (-> Dm B)) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (A Dm)))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19650.        ((((A -> B) and ((C -> (D -> (C and D))) -> A)) -> A) and (((A -> B) and ((C -> (D -> (C and D))) -> A)) -> B)), M:tm-319, m:tm-347, u:((Am (-> Dm B)) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (A Dm))
================================================================
tm-name          tm-19651
in-theory        19651
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19651.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19652
in-theory        19652
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((A and ((B -> (C -> (B and C))) -> D)) -> (A and ((B -> (C -> (B and C))) -> D))))
theorem-size     37
proof            (modus-ponens tm-316 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19652.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((A and ((B -> (C -> (B and C))) -> D)) -> (A and ((B -> (C -> (B and C))) -> D)))), M:tm-316, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-19653
in-theory        19653
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19653.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (E -> (F -> E))), M:tm-315, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19654
in-theory        19654
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (((A and ((B -> (C -> (B and C))) -> D)) -> (not D)) -> (not (A and ((B -> (C -> (B and C))) -> D)))))
theorem-size     41
proof            (modus-ponens tm-313 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-9 tm-4 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19654.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (((A and ((B -> (C -> (B and C))) -> D)) -> (not D)) -> (not (A and ((B -> (C -> (B and C))) -> D))))), M:tm-313, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-19655
in-theory        19655
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((D -> E) -> (((A and ((B -> (C -> (B and C))) -> D)) or D) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19655.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((D -> E) -> (((A and ((B -> (C -> (B and C))) -> D)) or D) -> E))), M:tm-312, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-19656
in-theory        19656
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (E or ((A and ((B -> (C -> (B and C))) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-311 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19656.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (E or ((A and ((B -> (C -> (B and C))) -> D)) -> D))), M:tm-311, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19657
in-theory        19657
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (((A and ((B -> (C -> (B and C))) -> D)) -> D) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19657.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (((A and ((B -> (C -> (B and C))) -> D)) -> D) or E)), M:tm-310, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19658
in-theory        19658
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (E -> (((A and ((B -> (C -> (B and C))) -> D)) -> D) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19658.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (E -> (((A and ((B -> (C -> (B and C))) -> D)) -> D) and E))), M:tm-309, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19659
in-theory        19659
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> (D -> E))) -> (D -> E)) and (((A and ((B -> (C -> (B and C))) -> (D -> E))) -> D) -> ((A and ((B -> (C -> (B and C))) -> (D -> E))) -> E)))
theorem-size     49
proof            (modus-ponens tm-306 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19659.        (((A and ((B -> (C -> (B and C))) -> (D -> E))) -> (D -> E)) and (((A and ((B -> (C -> (B and C))) -> (D -> E))) -> D) -> ((A and ((B -> (C -> (B and C))) -> (D -> E))) -> E))), M:tm-306, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-19660
in-theory        19660
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (E -> ((A and ((B -> (C -> (B and C))) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-305 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19660.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (E -> ((A and ((B -> (C -> (B and C))) -> D)) -> D))), M:tm-305, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19661
in-theory        19661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-303 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19661.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-303, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19662
in-theory        19662
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) or ((D -> (E -> (D and E))) and ((A -> (B -> (A and B))) -> C))) -> C)
theorem-size     29
proof            (modus-ponens tm-300 tm-347 ((Am (-> A (-> B (and A B)))) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19662.        ((((A -> (B -> (A and B))) -> C) or ((D -> (E -> (D and E))) and ((A -> (B -> (A and B))) -> C))) -> C), M:tm-300, m:tm-347, u:((Am (-> A (-> B (and A B)))) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (D Dm))
================================================================
tm-name          tm-19663
in-theory        19663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-270 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19663.        ((A -> (((B and C) -> C) and A)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-270, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19664
in-theory        19664
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) or (((D and E) -> E) and ((A -> (B -> (A and B))) -> C))) -> C)
theorem-size     27
proof            (modus-ponens tm-267 tm-347 ((Am (-> (and A B) B)) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19664.        ((((A -> (B -> (A and B))) -> C) or (((D and E) -> E) and ((A -> (B -> (A and B))) -> C))) -> C), M:tm-267, m:tm-347, u:((Am (-> (and A B) B)) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (D Dm))
================================================================
tm-name          tm-19665
in-theory        19665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-239 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19665.        ((A -> (((B and C) -> B) and A)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-239, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19666
in-theory        19666
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) or (((D and E) -> D) and ((A -> (B -> (A and B))) -> C))) -> C)
theorem-size     27
proof            (modus-ponens tm-236 tm-347 ((Am (-> (and A B) A)) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19666.        ((((A -> (B -> (A and B))) -> C) or (((D and E) -> D) and ((A -> (B -> (A and B))) -> C))) -> C), M:tm-236, m:tm-347, u:((Am (-> (and A B) A)) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (D Dm))
================================================================
tm-name          tm-19667
in-theory        19667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and ((F -> (G -> (F and G))) -> H)) -> H))
theorem-size     31
proof            (modus-ponens tm-210 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19667.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and ((F -> (G -> (F and G))) -> H)) -> H)), M:tm-210, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19668
in-theory        19668
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> (A and B))) -> C))) -> C)
theorem-size     35
proof            (modus-ponens tm-207 tm-347 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (E Dm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19668.        ((((A -> (B -> (A and B))) -> C) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> (A and B))) -> C))) -> C), M:tm-207, m:tm-347, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (E Dm))
================================================================
tm-name          tm-19669
in-theory        19669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-183 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19669.        ((A -> ((B -> (C -> B)) and A)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-183, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19670
in-theory        19670
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) or ((D -> (E -> D)) and ((A -> (B -> (A and B))) -> C))) -> C)
theorem-size     27
proof            (modus-ponens tm-180 tm-347 ((Am (-> A (-> B A))) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19670.        ((((A -> (B -> (A and B))) -> C) or ((D -> (E -> D)) and ((A -> (B -> (A and B))) -> C))) -> C), M:tm-180, m:tm-347, u:((Am (-> A (-> B A))) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (D Dm))
================================================================
tm-name          tm-19671
in-theory        19671
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> (D and E))) -> E)
theorem-size     15
proof            (modus-ponens tm-158 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (and B C)))) (Dm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19671.        ((A and ((B -> (C -> (B and C))) -> (D and E))) -> E), M:tm-158, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (and B C)))) (Dm (and B C)))
================================================================
tm-name          tm-19672
in-theory        19672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-157 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19672.        ((A -> ((B and C) -> C)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-157, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19673
in-theory        19673
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> (B and C))) -> (not ((D and E) -> E)))))
theorem-size     17
proof            (modus-ponens tm-153 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (not (-> (and B C) C))))) (Dm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19673.        (not (A and ((B -> (C -> (B and C))) -> (not ((D and E) -> E))))), M:tm-153, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (not (-> (and B C) C))))) (Dm (not (-> (and B C) C))))
================================================================
tm-name          tm-19674
in-theory        19674
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     29
proof            (modus-ponens tm-147 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19674.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-147, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19675
in-theory        19675
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> (B -> (C -> (B and C))))) -> (B -> (C -> (B and C))))
theorem-size     25
proof            (modus-ponens tm-142 tm-347 ((A Am) (Dm (-> Bm (-> Cm (and Bm Cm)))) (C (-> Bm (-> Cm (and Bm Cm)))) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19675.        ((A and ((B -> (C -> (B and C))) -> (B -> (C -> (B and C))))) -> (B -> (C -> (B and C)))), M:tm-142, m:tm-347, u:((A Am) (Dm (-> Bm (-> Cm (and Bm Cm)))) (C (-> Bm (-> Cm (and Bm Cm)))) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-19676
in-theory        19676
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> (D and E))) -> D)
theorem-size     15
proof            (modus-ponens tm-135 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (and B C)))) (Dm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19676.        ((A and ((B -> (C -> (B and C))) -> (D and E))) -> D), M:tm-135, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (and B C)))) (Dm (and B C)))
================================================================
tm-name          tm-19677
in-theory        19677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-134 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19677.        ((A -> ((B and C) -> B)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-134, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19678
in-theory        19678
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> (B and C))) -> (not ((D and E) -> D)))))
theorem-size     17
proof            (modus-ponens tm-130 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (not (-> (and B C) B))))) (Dm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-4 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19678.        (not (A and ((B -> (C -> (B and C))) -> (not ((D and E) -> D))))), M:tm-130, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (not (-> (and B C) B))))) (Dm (not (-> (and B C) B))))
================================================================
tm-name          tm-19679
in-theory        19679
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> (A -> D))) -> D)
theorem-size     15
proof            (modus-ponens tm-129 tm-347 ((A Am) (B (-> (-> Bm (-> Cm (and Bm Cm))) (-> Am C))) (Dm (-> Am C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4 tm-5)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19679.        ((A and ((B -> (C -> (B and C))) -> (A -> D))) -> D), M:tm-129, m:tm-347, u:((A Am) (B (-> (-> Bm (-> Cm (and Bm Cm))) (-> Am C))) (Dm (-> Am C)))
================================================================
tm-name          tm-19680
in-theory        19680
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     29
proof            (modus-ponens tm-125 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19680.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-125, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19681
in-theory        19681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and ((C -> (D -> (C and D))) -> A)) -> A)
theorem-size     15
proof            (modus-ponens tm-120 tm-347 ((Am (-> Dm B)) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (A Dm)))
axioms-used      (tm-2 tm-1 tm-3 tm-4 tm-5)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19681.        (((A -> B) and ((C -> (D -> (C and D))) -> A)) -> A), M:tm-120, m:tm-347, u:((Am (-> Dm B)) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (A Dm))
================================================================
tm-name          tm-19682
in-theory        19682
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) and ((C -> (D -> (C and D))) -> (A -> B))) -> B)
theorem-size     19
proof            (modus-ponens tm-119 tm-347 ((Am (-> (-> A B) A)) (C (-> (-> Bm (-> Cm (and Bm Cm))) (-> A B))) (Dm (-> A B))))
axioms-used      (tm-2 tm-3 tm-4 tm-1 tm-5)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19682.        ((((A -> B) -> A) and ((C -> (D -> (C and D))) -> (A -> B))) -> B), M:tm-119, m:tm-347, u:((Am (-> (-> A B) A)) (C (-> (-> Bm (-> Cm (and Bm Cm))) (-> A B))) (Dm (-> A B)))
================================================================
tm-name          tm-19683
in-theory        19683
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> (D -> (E -> F)))) -> ((D -> E) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-114 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (-> B (-> C D))))) (Dm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19683.        ((A and ((B -> (C -> (B and C))) -> (D -> (E -> F)))) -> ((D -> E) -> (D -> F))), M:tm-114, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (-> B (-> C D))))) (Dm (-> B (-> C D))))
================================================================
tm-name          tm-19684
in-theory        19684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (G -> (F and G))) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-113 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19684.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (G -> (F and G))) -> H)) -> H)), M:tm-113, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19685
in-theory        19685
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> (B and C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     25
proof            (modus-ponens tm-109 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Dm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4 tm-5)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19685.        (not (A and ((B -> (C -> (B and C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-109, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Dm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-19686
in-theory        19686
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     33
proof            (modus-ponens tm-105 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19686.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-105, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19687
in-theory        19687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C and ((D -> (E -> (D and E))) -> F)) -> F))
theorem-size     21
proof            (modus-ponens tm-95 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19687.        (((A -> B) -> (A -> A)) and ((C and ((D -> (E -> (D and E))) -> F)) -> F)), M:tm-95, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19688
in-theory        19688
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> (D -> E))) -> (D -> E))
theorem-size     17
proof            (modus-ponens tm-87 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19688.        ((A and ((B -> (C -> (B and C))) -> (D -> E))) -> (D -> E)), M:tm-87, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-19689
in-theory        19689
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> D)) -> (E -> D))
theorem-size     15
proof            (modus-ponens tm-84 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19689.        ((A and ((B -> (C -> (B and C))) -> D)) -> (E -> D)), M:tm-84, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-19690
in-theory        19690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-83 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19690.        ((A -> (B -> (C -> B))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-83, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19691
in-theory        19691
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> (B and C))) -> (not (D -> (E -> D))))))
theorem-size     17
proof            (modus-ponens tm-79 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (not (-> B (-> C B)))))) (Dm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19691.        (not (A and ((B -> (C -> (B and C))) -> (not (D -> (E -> D)))))), M:tm-79, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (not (-> B (-> C B)))))) (Dm (not (-> B (-> C B)))))
================================================================
tm-name          tm-19692
in-theory        19692
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B and ((C -> (D -> (C and D))) -> E)) -> E))
theorem-size     19
proof            (modus-ponens tm-76 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-10 tm-2 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19692.        (((not (not A)) -> A) and ((B and ((C -> (D -> (C and D))) -> E)) -> E)), M:tm-76, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19693
in-theory        19693
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A and ((B -> (C -> (B and C))) -> D)))) or (A and ((B -> (C -> (B and C))) -> D))) -> D)
theorem-size     27
proof            (modus-ponens tm-73 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-8 tm-10 tm-2 tm-4 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19693.        (((not (not (A and ((B -> (C -> (B and C))) -> D)))) or (A and ((B -> (C -> (B and C))) -> D))) -> D), M:tm-73, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-19694
in-theory        19694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and ((D -> (E -> (D and E))) -> F)) -> F))
theorem-size     25
proof            (modus-ponens tm-69 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-9 tm-2 tm-4 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19694.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and ((D -> (E -> (D and E))) -> F)) -> F)), M:tm-69, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19695
in-theory        19695
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> (B and C))) -> (not A))))
theorem-size     13
proof            (modus-ponens tm-59 tm-347 ((A Am) (B (-> (-> Bm (-> Cm (and Bm Cm))) (not Am))) (Dm (not Am))))
axioms-used      (tm-9 tm-3 tm-2 tm-4 tm-1 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19695.        (not (A and ((B -> (C -> (B and C))) -> (not A)))), M:tm-59, m:tm-347, u:((A Am) (B (-> (-> Bm (-> Cm (and Bm Cm))) (not Am))) (Dm (not Am)))
================================================================
tm-name          tm-19696
in-theory        19696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-54 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19696.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-54, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19697
in-theory        19697
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and ((C -> (D -> (C and D))) -> E))) or (B and ((C -> (D -> (C and D))) -> E))) -> E)
theorem-size     27
proof            (modus-ponens tm-47 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19697.        (((A and (B and ((C -> (D -> (C and D))) -> E))) or (B and ((C -> (D -> (C and D))) -> E))) -> E), M:tm-47, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-19698
in-theory        19698
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> (B and C))) -> D)) and E) or (A and ((B -> (C -> (B and C))) -> D))) -> D)
theorem-size     27
proof            (modus-ponens tm-46 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-8 tm-3 tm-2 tm-4 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19698.        ((((A and ((B -> (C -> (B and C))) -> D)) and E) or (A and ((B -> (C -> (B and C))) -> D))) -> D), M:tm-46, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-19699
in-theory        19699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C and ((D -> (E -> (D and E))) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-42 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19699.        ((A -> (B or A)) and ((C and ((D -> (E -> (D and E))) -> F)) -> F)), M:tm-42, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19700
in-theory        19700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C and ((D -> (E -> (D and E))) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-32 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19700.        ((A -> (A or B)) and ((C and ((D -> (E -> (D and E))) -> F)) -> F)), M:tm-32, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19701
in-theory        19701
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> D)) -> ((A and ((B -> (C -> (B and C))) -> D)) and D))
theorem-size     25
proof            (modus-ponens tm-24 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19701.        ((A and ((B -> (C -> (B and C))) -> D)) -> ((A and ((B -> (C -> (B and C))) -> D)) and D)), M:tm-24, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-19702
in-theory        19702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C and ((D -> (E -> (D and E))) -> F)) -> F))
theorem-size     21
proof            (modus-ponens tm-23 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19702.        ((A -> (B -> (A and B))) and ((C and ((D -> (E -> (D and E))) -> F)) -> F)), M:tm-23, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19703
in-theory        19703
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C and ((D -> (E -> (D and E))) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-22 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19703.        (((A and B) -> B) and ((C and ((D -> (E -> (D and E))) -> F)) -> F)), M:tm-22, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19704
in-theory        19704
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C and ((D -> (E -> (D and E))) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-21 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19704.        (((A and B) -> A) and ((C and ((D -> (E -> (D and E))) -> F)) -> F)), M:tm-21, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19705
in-theory        19705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-20 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19705.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-20, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19706
in-theory        19706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C and ((D -> (E -> (D and E))) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-19 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19706.        ((A -> (B -> A)) and ((C and ((D -> (E -> (D and E))) -> F)) -> F)), M:tm-19, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19707
in-theory        19707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and ((C -> (D -> (C and D))) -> A)) -> B)
theorem-size     15
proof            (modus-ponens tm-15 tm-347 ((Am (-> Dm B)) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (A Dm)))
axioms-used      (tm-2 tm-3 tm-4 tm-1 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19707.        (((A -> B) and ((C -> (D -> (C and D))) -> A)) -> B), M:tm-15, m:tm-347, u:((Am (-> Dm B)) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (A Dm))
================================================================
tm-name          tm-19708
in-theory        19708
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> D)) -> (A and ((B -> (C -> (B and C))) -> D)))
theorem-size     23
proof            (modus-ponens tm-12 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19708.        ((A and ((B -> (C -> (B and C))) -> D)) -> (A and ((B -> (C -> (B and C))) -> D))), M:tm-12, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-19709
in-theory        19709
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> (not D)) -> (not (A and ((B -> (C -> (B and C))) -> D))))
theorem-size     27
proof            (modus-ponens tm-9 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-9 tm-2 tm-4 tm-1 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19709.        (((A and ((B -> (C -> (B and C))) -> D)) -> (not D)) -> (not (A and ((B -> (C -> (B and C))) -> D)))), M:tm-9, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-19710
in-theory        19710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C and ((D -> (E -> (D and E))) -> A)) or A) -> B))
theorem-size     19
proof            (modus-ponens tm-8 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-5)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19710.        ((A -> B) -> (((C and ((D -> (E -> (D and E))) -> A)) or A) -> B)), M:tm-8, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-19711
in-theory        19711
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B and ((C -> (D -> (C and D))) -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-7 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-7 tm-2 tm-4 tm-1 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19711.        (A or ((B and ((C -> (D -> (C and D))) -> E)) -> E)), M:tm-7, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19712
in-theory        19712
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-6 tm-2 tm-4 tm-1 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19712.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) or E), M:tm-6, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19713
in-theory        19713
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and ((C -> (D -> (C and D))) -> E)) -> E) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19713.        (A -> (((B and ((C -> (D -> (C and D))) -> E)) -> E) and A)), M:tm-5, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19714
in-theory        19714
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> (D -> E))) -> D) -> ((A and ((B -> (C -> (B and C))) -> (D -> E))) -> E))
theorem-size     31
proof            (modus-ponens tm-2 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19714.        (((A and ((B -> (C -> (B and C))) -> (D -> E))) -> D) -> ((A and ((B -> (C -> (B and C))) -> (D -> E))) -> E)), M:tm-2, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-19715
in-theory        19715
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B and ((C -> (D -> (C and D))) -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-1 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-1 tm-2 tm-4 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19715.        (A -> ((B and ((C -> (D -> (C and D))) -> E)) -> E)), M:tm-1, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-19716
in-theory        19716
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19716.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and (E -> (F -> (E and F)))), M:tm-341, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19717
in-theory        19717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> (C and D))) -> E) and F) -> E))
theorem-size     23
proof            (modus-ponens tm-338 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19717.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> (C and D))) -> E) and F) -> E)), M:tm-338, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19718
in-theory        19718
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((((A -> (B -> (A and B))) -> C) and D) -> ((((A -> (B -> (A and B))) -> C) and D) and C)))
theorem-size     39
proof            (modus-ponens tm-328 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19718.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((((A -> (B -> (A and B))) -> C) and D) -> ((((A -> (B -> (A and B))) -> C) and D) and C))), M:tm-328, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-19719
in-theory        19719
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((E -> (F -> (E and F))) and ((((A -> (B -> (A and B))) -> C) and D) -> C)))
theorem-size     35
proof            (modus-ponens tm-327 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19719.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((E -> (F -> (E and F))) and ((((A -> (B -> (A and B))) -> C) and D) -> C))), M:tm-327, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19720
in-theory        19720
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and (((E and F) -> F) and ((((A -> (B -> (A and B))) -> C) and D) -> C)))
theorem-size     33
proof            (modus-ponens tm-326 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19720.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and (((E and F) -> F) and ((((A -> (B -> (A and B))) -> C) and D) -> C))), M:tm-326, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19721
in-theory        19721
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and (((E and F) -> E) and ((((A -> (B -> (A and B))) -> C) and D) -> C)))
theorem-size     33
proof            (modus-ponens tm-325 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19721.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and (((E and F) -> E) and ((((A -> (B -> (A and B))) -> C) and D) -> C))), M:tm-325, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19722
in-theory        19722
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B -> (A and B))) -> C) and D) -> C)))
theorem-size     41
proof            (modus-ponens tm-324 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19722.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B -> (A and B))) -> C) and D) -> C))), M:tm-324, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19723
in-theory        19723
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((E -> (F -> E)) and ((((A -> (B -> (A and B))) -> C) and D) -> C)))
theorem-size     33
proof            (modus-ponens tm-323 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19723.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((E -> (F -> E)) and ((((A -> (B -> (A and B))) -> C) and D) -> C))), M:tm-323, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19724
in-theory        19724
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19724.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((E and F) -> F)), M:tm-322, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19725
in-theory        19725
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and (C -> D)) -> C) and ((((A -> (B -> (A and B))) -> C) and (C -> D)) -> D))
theorem-size     31
proof            (modus-ponens tm-321 tm-348 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19725.        (((((A -> (B -> (A and B))) -> C) and (C -> D)) -> C) and ((((A -> (B -> (A and B))) -> C) and (C -> D)) -> D)), M:tm-321, m:tm-348, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-19726
in-theory        19726
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19726.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((E and F) -> E)), M:tm-320, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19727
in-theory        19727
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> (A -> (B -> (A and B)))) and C) -> (A -> (B -> (A and B)))) and ((((A -> (B -> (A and B))) -> (A -> (B -> (A and B)))) and C) -> (A -> (B -> (A and B)))))
theorem-size     51
proof            (modus-ponens tm-319 tm-348 ((Cm (-> Am (-> Bm (and Am Bm)))) (B (-> Am (-> Bm (and Am Bm)))) (C Dm) (A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19727.        (((((A -> (B -> (A and B))) -> (A -> (B -> (A and B)))) and C) -> (A -> (B -> (A and B)))) and ((((A -> (B -> (A and B))) -> (A -> (B -> (A and B)))) and C) -> (A -> (B -> (A and B))))), M:tm-319, m:tm-348, u:((Cm (-> Am (-> Bm (and Am Bm)))) (B (-> Am (-> Bm (and Am Bm)))) (C Dm) (A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-19728
in-theory        19728
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19728.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19729
in-theory        19729
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((((A -> (B -> (A and B))) -> C) and D) -> (((A -> (B -> (A and B))) -> C) and D)))
theorem-size     37
proof            (modus-ponens tm-316 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19729.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((((A -> (B -> (A and B))) -> C) and D) -> (((A -> (B -> (A and B))) -> C) and D))), M:tm-316, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-19730
in-theory        19730
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19730.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and (E -> (F -> E))), M:tm-315, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19731
in-theory        19731
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and (((((A -> (B -> (A and B))) -> C) and D) -> (not C)) -> (not (((A -> (B -> (A and B))) -> C) and D))))
theorem-size     41
proof            (modus-ponens tm-313 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-9 tm-3 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19731.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and (((((A -> (B -> (A and B))) -> C) and D) -> (not C)) -> (not (((A -> (B -> (A and B))) -> C) and D)))), M:tm-313, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-19732
in-theory        19732
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((C -> E) -> (((((A -> (B -> (A and B))) -> C) and D) or C) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19732.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((C -> E) -> (((((A -> (B -> (A and B))) -> C) and D) or C) -> E))), M:tm-312, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-19733
in-theory        19733
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and (E or ((((A -> (B -> (A and B))) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-311 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19733.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and (E or ((((A -> (B -> (A and B))) -> C) and D) -> C))), M:tm-311, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19734
in-theory        19734
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and (((((A -> (B -> (A and B))) -> C) and D) -> C) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19734.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and (((((A -> (B -> (A and B))) -> C) and D) -> C) or E)), M:tm-310, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19735
in-theory        19735
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and (E -> (((((A -> (B -> (A and B))) -> C) and D) -> C) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19735.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and (E -> (((((A -> (B -> (A and B))) -> C) and D) -> C) and E))), M:tm-309, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19736
in-theory        19736
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> (C -> D)) and E) -> (C -> D)) and (((((A -> (B -> (A and B))) -> (C -> D)) and E) -> C) -> ((((A -> (B -> (A and B))) -> (C -> D)) and E) -> D)))
theorem-size     49
proof            (modus-ponens tm-306 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19736.        (((((A -> (B -> (A and B))) -> (C -> D)) and E) -> (C -> D)) and (((((A -> (B -> (A and B))) -> (C -> D)) and E) -> C) -> ((((A -> (B -> (A and B))) -> (C -> D)) and E) -> D))), M:tm-306, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-19737
in-theory        19737
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and (E -> ((((A -> (B -> (A and B))) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-305 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19737.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and (E -> ((((A -> (B -> (A and B))) -> C) and D) -> C))), M:tm-305, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19738
in-theory        19738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-303 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19738.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-303, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19739
in-theory        19739
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> (B and C))) -> (D -> ((B -> (C -> (B and C))) and D))) and A)) -> (D -> ((B -> (C -> (B and C))) and D)))
theorem-size     35
proof            (modus-ponens tm-300 tm-348 ((A (-> Am (-> Bm (and Am Bm)))) (Cm (-> B (and (-> Am (-> Bm (and Am Bm))) B))) (C Dm) (D (-> B (and (-> Am (-> Bm (and Am Bm))) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19739.        ((A or (((B -> (C -> (B and C))) -> (D -> ((B -> (C -> (B and C))) and D))) and A)) -> (D -> ((B -> (C -> (B and C))) and D))), M:tm-300, m:tm-348, u:((A (-> Am (-> Bm (and Am Bm)))) (Cm (-> B (and (-> Am (-> Bm (and Am Bm))) B))) (C Dm) (D (-> B (and (-> Am (-> Bm (and Am Bm))) B))))
================================================================
tm-name          tm-19740
in-theory        19740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-270 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19740.        ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-270, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19741
in-theory        19741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-239 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19741.        ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-239, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19742
in-theory        19742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> (E and F))) -> G) and H) -> G))
theorem-size     31
proof            (modus-ponens tm-210 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19742.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> (E and F))) -> G) and H) -> G)), M:tm-210, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19743
in-theory        19743
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> (B and C))) -> ((B -> C) -> (B -> (B and C)))) and A)) -> ((B -> C) -> (B -> (B and C))))
theorem-size     31
proof            (modus-ponens tm-207 tm-348 ((A Am) (B Bm) (C (and Am Bm)) (Cm (-> (-> Am Bm) (-> Am (and Am Bm)))) (D Dm) (E (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-3 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19743.        ((A or (((B -> (C -> (B and C))) -> ((B -> C) -> (B -> (B and C)))) and A)) -> ((B -> C) -> (B -> (B and C)))), M:tm-207, m:tm-348, u:((A Am) (B Bm) (C (and Am Bm)) (Cm (-> (-> Am Bm) (-> Am (and Am Bm)))) (D Dm) (E (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-19744
in-theory        19744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-183 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19744.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-183, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19745
in-theory        19745
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> (B and C))) -> (D -> (B -> (C -> (B and C))))) and A)) -> (D -> (B -> (C -> (B and C)))))
theorem-size     31
proof            (modus-ponens tm-180 tm-348 ((A (-> Am (-> Bm (and Am Bm)))) (Cm (-> B (-> Am (-> Bm (and Am Bm))))) (C Dm) (D (-> B (-> Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19745.        ((A or (((B -> (C -> (B and C))) -> (D -> (B -> (C -> (B and C))))) and A)) -> (D -> (B -> (C -> (B and C))))), M:tm-180, m:tm-348, u:((A (-> Am (-> Bm (and Am Bm)))) (Cm (-> B (-> Am (-> Bm (and Am Bm))))) (C Dm) (D (-> B (-> Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-19746
in-theory        19746
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> (C and D)) and E) -> D)
theorem-size     15
proof            (modus-ponens tm-158 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) (and B C)) Dm)) (Cm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19746.        ((((A -> (B -> (A and B))) -> (C and D)) and E) -> D), M:tm-158, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) (and B C)) Dm)) (Cm (and B C)))
================================================================
tm-name          tm-19747
in-theory        19747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-157 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19747.        ((A -> ((B and C) -> C)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-157, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19748
in-theory        19748
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> (A and B))) -> (not ((C and D) -> D))) and E))
theorem-size     17
proof            (modus-ponens tm-153 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) (not (-> (and B C) C))) Dm)) (Cm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-3 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19748.        (not (((A -> (B -> (A and B))) -> (not ((C and D) -> D))) and E)), M:tm-153, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) (not (-> (and B C) C))) Dm)) (Cm (not (-> (and B C) C))))
================================================================
tm-name          tm-19749
in-theory        19749
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> (C -> D)) and C) -> D)
theorem-size     15
proof            (modus-ponens tm-152 tm-348 ((A (-> (-> Am (-> Bm (and Am Bm))) (-> Dm C))) (B Dm) (Cm (-> Dm C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3 tm-5)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19749.        ((((A -> (B -> (A and B))) -> (C -> D)) and C) -> D), M:tm-152, m:tm-348, u:((A (-> (-> Am (-> Bm (and Am Bm))) (-> Dm C))) (B Dm) (Cm (-> Dm C)))
================================================================
tm-name          tm-19750
in-theory        19750
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     29
proof            (modus-ponens tm-147 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19750.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-147, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19751
in-theory        19751
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) and (C -> D)) -> C)
theorem-size     15
proof            (modus-ponens tm-142 tm-348 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-4 tm-3 tm-5)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19751.        ((((A -> (B -> (A and B))) -> C) and (C -> D)) -> C), M:tm-142, m:tm-348, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-19752
in-theory        19752
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> (C -> D)) and ((C -> D) -> C)) -> D)
theorem-size     19
proof            (modus-ponens tm-141 tm-348 ((A (-> (-> Am (-> Bm (and Am Bm))) (-> B C))) (Dm (-> (-> B C) B)) (Cm (-> B C))))
axioms-used      (tm-2 tm-4 tm-3 tm-1 tm-5)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19752.        ((((A -> (B -> (A and B))) -> (C -> D)) and ((C -> D) -> C)) -> D), M:tm-141, m:tm-348, u:((A (-> (-> Am (-> Bm (and Am Bm))) (-> B C))) (Dm (-> (-> B C) B)) (Cm (-> B C)))
================================================================
tm-name          tm-19753
in-theory        19753
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> (C and D)) and E) -> C)
theorem-size     15
proof            (modus-ponens tm-135 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) (and B C)) Dm)) (Cm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19753.        ((((A -> (B -> (A and B))) -> (C and D)) and E) -> C), M:tm-135, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) (and B C)) Dm)) (Cm (and B C)))
================================================================
tm-name          tm-19754
in-theory        19754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-134 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19754.        ((A -> ((B and C) -> B)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-134, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19755
in-theory        19755
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> (A and B))) -> (not ((C and D) -> C))) and E))
theorem-size     17
proof            (modus-ponens tm-130 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) (not (-> (and B C) B))) Dm)) (Cm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19755.        (not (((A -> (B -> (A and B))) -> (not ((C and D) -> C))) and E)), M:tm-130, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) (not (-> (and B C) B))) Dm)) (Cm (not (-> (and B C) B))))
================================================================
tm-name          tm-19756
in-theory        19756
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     29
proof            (modus-ponens tm-125 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19756.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-125, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19757
in-theory        19757
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> (A -> (B -> (A and B)))) and C) -> (A -> (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-120 tm-348 ((Cm (-> Am (-> Bm (and Am Bm)))) (B (-> Am (-> Bm (and Am Bm)))) (C Dm) (A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19757.        ((((A -> (B -> (A and B))) -> (A -> (B -> (A and B)))) and C) -> (A -> (B -> (A and B)))), M:tm-120, m:tm-348, u:((Cm (-> Am (-> Bm (and Am Bm)))) (B (-> Am (-> Bm (and Am Bm)))) (C Dm) (A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-19758
in-theory        19758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> (C -> (D -> E))) and F) -> ((C -> D) -> (C -> E)))
theorem-size     23
proof            (modus-ponens tm-114 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) (-> B (-> C D))) Dm)) (Cm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19758.        ((((A -> (B -> (A and B))) -> (C -> (D -> E))) and F) -> ((C -> D) -> (C -> E))), M:tm-114, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) (-> B (-> C D))) Dm)) (Cm (-> B (-> C D))))
================================================================
tm-name          tm-19759
in-theory        19759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> (E and F))) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-113 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19759.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> (E and F))) -> G) and H) -> G)), M:tm-113, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19760
in-theory        19760
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> (A and B))) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F))
theorem-size     25
proof            (modus-ponens tm-109 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Dm)) (Cm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3 tm-5)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19760.        (not (((A -> (B -> (A and B))) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F)), M:tm-109, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Dm)) (Cm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-19761
in-theory        19761
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     33
proof            (modus-ponens tm-105 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19761.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-105, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19762
in-theory        19762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D -> (C and D))) -> E) and F) -> E))
theorem-size     21
proof            (modus-ponens tm-95 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19762.        (((A -> B) -> (A -> A)) and ((((C -> (D -> (C and D))) -> E) and F) -> E)), M:tm-95, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19763
in-theory        19763
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> (C -> D)) and E) -> (C -> D))
theorem-size     17
proof            (modus-ponens tm-87 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19763.        ((((A -> (B -> (A and B))) -> (C -> D)) and E) -> (C -> D)), M:tm-87, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-19764
in-theory        19764
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) and D) -> (E -> C))
theorem-size     15
proof            (modus-ponens tm-84 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19764.        ((((A -> (B -> (A and B))) -> C) and D) -> (E -> C)), M:tm-84, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-19765
in-theory        19765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-83 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19765.        ((A -> (B -> (C -> B))) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-83, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19766
in-theory        19766
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> (A and B))) -> (not (C -> (D -> C)))) and E))
theorem-size     17
proof            (modus-ponens tm-79 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) (not (-> B (-> C B)))) Dm)) (Cm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19766.        (not (((A -> (B -> (A and B))) -> (not (C -> (D -> C)))) and E)), M:tm-79, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) (not (-> B (-> C B)))) Dm)) (Cm (not (-> B (-> C B)))))
================================================================
tm-name          tm-19767
in-theory        19767
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C -> (B and C))) -> D) and E) -> D))
theorem-size     19
proof            (modus-ponens tm-76 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-10 tm-2 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19767.        (((not (not A)) -> A) and ((((B -> (C -> (B and C))) -> D) and E) -> D)), M:tm-76, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19768
in-theory        19768
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (B -> (A and B))) -> C) and D))) or (((A -> (B -> (A and B))) -> C) and D)) -> C)
theorem-size     27
proof            (modus-ponens tm-73 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-10 tm-2 tm-3 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19768.        (((not (not (((A -> (B -> (A and B))) -> C) and D))) or (((A -> (B -> (A and B))) -> C) and D)) -> C), M:tm-73, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-19769
in-theory        19769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> (C and D))) -> E) and F) -> E))
theorem-size     25
proof            (modus-ponens tm-69 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-9 tm-2 tm-3 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19769.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> (C and D))) -> E) and F) -> E)), M:tm-69, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19770
in-theory        19770
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> (A and B))) -> (not C)) and C))
theorem-size     13
proof            (modus-ponens tm-60 tm-348 ((A (-> (-> Am (-> Bm (and Am Bm))) (not Dm))) (B Dm) (Cm (not Dm))))
axioms-used      (tm-9 tm-4 tm-2 tm-3 tm-1 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19770.        (not (((A -> (B -> (A and B))) -> (not C)) and C)), M:tm-60, m:tm-348, u:((A (-> (-> Am (-> Bm (and Am Bm))) (not Dm))) (B Dm) (Cm (not Dm)))
================================================================
tm-name          tm-19771
in-theory        19771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-54 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19771.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-54, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19772
in-theory        19772
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> (B and C))) -> D) and E)) or (((B -> (C -> (B and C))) -> D) and E)) -> D)
theorem-size     27
proof            (modus-ponens tm-47 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-4 tm-2 tm-3 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19772.        (((A and (((B -> (C -> (B and C))) -> D) and E)) or (((B -> (C -> (B and C))) -> D) and E)) -> D), M:tm-47, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-19773
in-theory        19773
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> (A and B))) -> C) and D) and E) or (((A -> (B -> (A and B))) -> C) and D)) -> C)
theorem-size     27
proof            (modus-ponens tm-46 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19773.        ((((((A -> (B -> (A and B))) -> C) and D) and E) or (((A -> (B -> (A and B))) -> C) and D)) -> C), M:tm-46, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-19774
in-theory        19774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D -> (C and D))) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-42 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19774.        ((A -> (B or A)) and ((((C -> (D -> (C and D))) -> E) and F) -> E)), M:tm-42, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19775
in-theory        19775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D -> (C and D))) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-32 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19775.        ((A -> (A or B)) and ((((C -> (D -> (C and D))) -> E) and F) -> E)), M:tm-32, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19776
in-theory        19776
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) and D) -> ((((A -> (B -> (A and B))) -> C) and D) and C))
theorem-size     25
proof            (modus-ponens tm-24 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19776.        ((((A -> (B -> (A and B))) -> C) and D) -> ((((A -> (B -> (A and B))) -> C) and D) and C)), M:tm-24, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-19777
in-theory        19777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D -> (C and D))) -> E) and F) -> E))
theorem-size     21
proof            (modus-ponens tm-23 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19777.        ((A -> (B -> (A and B))) and ((((C -> (D -> (C and D))) -> E) and F) -> E)), M:tm-23, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19778
in-theory        19778
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D -> (C and D))) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-22 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19778.        (((A and B) -> B) and ((((C -> (D -> (C and D))) -> E) and F) -> E)), M:tm-22, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19779
in-theory        19779
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D -> (C and D))) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-21 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19779.        (((A and B) -> A) and ((((C -> (D -> (C and D))) -> E) and F) -> E)), M:tm-21, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19780
in-theory        19780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-20 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19780.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-20, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19781
in-theory        19781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D -> (C and D))) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-19 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19781.        ((A -> (B -> A)) and ((((C -> (D -> (C and D))) -> E) and F) -> E)), M:tm-19, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19782
in-theory        19782
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) and (C -> D)) -> D)
theorem-size     15
proof            (modus-ponens tm-17 tm-348 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-4 tm-3 tm-1 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19782.        ((((A -> (B -> (A and B))) -> C) and (C -> D)) -> D), M:tm-17, m:tm-348, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-19783
in-theory        19783
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) and D) -> (((A -> (B -> (A and B))) -> C) and D))
theorem-size     23
proof            (modus-ponens tm-12 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19783.        ((((A -> (B -> (A and B))) -> C) and D) -> (((A -> (B -> (A and B))) -> C) and D)), M:tm-12, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-19784
in-theory        19784
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> (not C)) -> (not (((A -> (B -> (A and B))) -> C) and D)))
theorem-size     27
proof            (modus-ponens tm-9 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-9 tm-2 tm-3 tm-1 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19784.        (((((A -> (B -> (A and B))) -> C) and D) -> (not C)) -> (not (((A -> (B -> (A and B))) -> C) and D))), M:tm-9, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-19785
in-theory        19785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((((C -> (D -> (C and D))) -> A) and E) or A) -> B))
theorem-size     19
proof            (modus-ponens tm-8 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-5)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19785.        ((A -> B) -> (((((C -> (D -> (C and D))) -> A) and E) or A) -> B)), M:tm-8, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-19786
in-theory        19786
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> (C -> (B and C))) -> D) and E) -> D))
theorem-size     15
proof            (modus-ponens tm-7 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-7 tm-2 tm-3 tm-1 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19786.        (A or ((((B -> (C -> (B and C))) -> D) and E) -> D)), M:tm-7, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19787
in-theory        19787
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-6 tm-2 tm-3 tm-1 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19787.        (((((A -> (B -> (A and B))) -> C) and D) -> C) or E), M:tm-6, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19788
in-theory        19788
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> (B and C))) -> D) and E) -> D) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19788.        (A -> (((((B -> (C -> (B and C))) -> D) and E) -> D) and A)), M:tm-5, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19789
in-theory        19789
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> (C -> D)) and E) -> C) -> ((((A -> (B -> (A and B))) -> (C -> D)) and E) -> D))
theorem-size     31
proof            (modus-ponens tm-2 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19789.        (((((A -> (B -> (A and B))) -> (C -> D)) and E) -> C) -> ((((A -> (B -> (A and B))) -> (C -> D)) and E) -> D)), M:tm-2, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-19790
in-theory        19790
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> (B and C))) -> D) and E) -> D))
theorem-size     15
proof            (modus-ponens tm-1 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-1 tm-2 tm-3 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19790.        (A -> ((((B -> (C -> (B and C))) -> D) and E) -> D)), M:tm-1, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-19791
in-theory        19791
times-derived    2
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (A and C)) and B)))
theorem-size     11
proof            (modus-ponens tm-349 tm-25 ((A Am) (Bm (-> B (and Am B))) (C (-> Cm (and (-> B (and Am B)) Cm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19791.        (A -> (B -> ((C -> (A and C)) and B))), M:tm-349, m:tm-25, u:((A Am) (Bm (-> B (and Am B))) (C (-> Cm (and (-> B (and Am B)) Cm))))
================================================================
tm-name          tm-19792
in-theory        19792
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (A and B)) or C))
theorem-size     9
proof            (modus-ponens tm-349 tm-33 ((A Am) (Bm (-> B (and Am B))) (C (or (-> B (and Am B)) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19792.        (A -> ((B -> (A and B)) or C)), M:tm-349, m:tm-33, u:((A Am) (Bm (-> B (and Am B))) (C (or (-> B (and Am B)) Cm)))
================================================================
tm-name          tm-19793
in-theory        19793
times-derived    2
----------------------------------------------------------------
theorem          (A -> (B or (C -> (A and C))))
theorem-size     9
proof            (modus-ponens tm-349 tm-43 ((A Am) (Bm (-> B (and Am B))) (C (or Cm (-> B (and Am B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19793.        (A -> (B or (C -> (A and C)))), M:tm-349, m:tm-43, u:((A Am) (Bm (-> B (and Am B))) (C (or Cm (-> B (and Am B)))))
================================================================
tm-name          tm-19794
in-theory        19794
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((A and B) -> C) -> ((B or (A and B)) -> C)))
theorem-size     15
proof            (modus-ponens tm-349 tm-56 ((A Am) (B Bm) (Cm (and Am Bm)) (C (-> (-> (and Am Bm) Dm) (-> (or Bm (and Am Bm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-19794.        (A -> (((A and B) -> C) -> ((B or (A and B)) -> C))), M:tm-349, m:tm-56, u:((A Am) (B Bm) (Cm (and Am Bm)) (C (-> (-> (and Am Bm) Dm) (-> (or Bm (and Am Bm)) Dm))))
================================================================
tm-name          tm-19795
in-theory        19795
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not (A and B))) -> (not B)))
theorem-size     11
proof            (modus-ponens tm-349 tm-71 ((A Am) (B Bm) (Cm (and Am Bm)) (C (-> (-> Bm (not (and Am Bm))) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-19795.        (A -> ((B -> (not (A and B))) -> (not B))), M:tm-349, m:tm-71, u:((A Am) (B Bm) (Cm (and Am Bm)) (C (-> (-> Bm (not (and Am Bm))) (not Bm))))
================================================================
tm-name          tm-19796
in-theory        19796
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> (A and D))))
theorem-size     13
proof            (modus-ponens tm-349 tm-184 ((A Am) (Bm (-> B (and Am B))) (C (and (-> Cm (-> Dm Cm)) (-> B (and Am B))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-19796.        (A -> ((B -> (C -> B)) and (D -> (A and D)))), M:tm-349, m:tm-184, u:((A Am) (Bm (-> B (and Am B))) (C (and (-> Cm (-> Dm Cm)) (-> B (and Am B)))))
================================================================
tm-name          tm-19797
in-theory        19797
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (A and E))))
theorem-size     21
proof            (modus-ponens tm-349 tm-211 ((A Am) (Bm (-> B (and Am B))) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> B (and Am B))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-19797.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (A and E)))), M:tm-349, m:tm-211, u:((A Am) (Bm (-> B (and Am B))) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> B (and Am B)))))
================================================================
tm-name          tm-19798
in-theory        19798
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> (A and D))))
theorem-size     13
proof            (modus-ponens tm-349 tm-240 ((A Am) (Bm (-> B (and Am B))) (C (and (-> (and Cm Dm) Cm) (-> B (and Am B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-19798.        (A -> (((B and C) -> B) and (D -> (A and D)))), M:tm-349, m:tm-240, u:((A Am) (Bm (-> B (and Am B))) (C (and (-> (and Cm Dm) Cm) (-> B (and Am B)))))
================================================================
tm-name          tm-19799
in-theory        19799
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> (A and D))))
theorem-size     13
proof            (modus-ponens tm-349 tm-271 ((A Am) (Bm (-> B (and Am B))) (C (and (-> (and Cm Dm) Dm) (-> B (and Am B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-19799.        (A -> (((B and C) -> C) and (D -> (A and D)))), M:tm-349, m:tm-271, u:((A Am) (Bm (-> B (and Am B))) (C (and (-> (and Cm Dm) Dm) (-> B (and Am B)))))
================================================================
tm-name          tm-19800
in-theory        19800
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> (A and D))))
theorem-size     15
proof            (modus-ponens tm-349 tm-304 ((A Am) (Bm (-> B (and Am B))) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> B (and Am B))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-19800.        (A -> ((B -> (C -> (B and C))) and (D -> (A and D)))), M:tm-349, m:tm-304, u:((A Am) (Bm (-> B (and Am B))) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> B (and Am B)))))
================================================================
tm-name          tm-19801
in-theory        19801
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and (A and B))))
theorem-size     9
proof            (modus-ponens tm-349 tm-340 ((A Am) (B Bm) (Cm (and Am Bm)) (C (-> Bm (and Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-19801.        (A -> (B -> (B and (A and B)))), M:tm-349, m:tm-340, u:((A Am) (B Bm) (Cm (and Am Bm)) (C (-> Bm (and Bm (and Am Bm)))))
================================================================
tm-name          tm-19802
in-theory        19802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19802.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19803
in-theory        19803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E)))
theorem-size     23
proof            (modus-ponens tm-338 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19803.        (((A -> B) -> (A -> (A and B))) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E))), M:tm-338, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19804
in-theory        19804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((A -> ((B -> (A and B)) -> C)) -> ((A -> ((B -> (A and B)) -> C)) and (A -> C))))
theorem-size     37
proof            (modus-ponens tm-328 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19804.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((A -> ((B -> (A and B)) -> C)) -> ((A -> ((B -> (A and B)) -> C)) and (A -> C)))), M:tm-328, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-19805
in-theory        19805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-327 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19805.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C)))), M:tm-327, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19806
in-theory        19806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((D and E) -> E) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-326 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19806.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((D and E) -> E) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C)))), M:tm-326, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19807
in-theory        19807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((D and E) -> D) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-325 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19807.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((D and E) -> D) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C)))), M:tm-325, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19808
in-theory        19808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-324 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19808.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C)))), M:tm-324, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19809
in-theory        19809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((D -> (E -> D)) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-323 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19809.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((D -> (E -> D)) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C)))), M:tm-323, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19810
in-theory        19810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19810.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((D and E) -> E)), M:tm-322, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19811
in-theory        19811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19811.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((D and E) -> D)), M:tm-320, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19812
in-theory        19812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19812.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19813
in-theory        19813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> (B -> (A and B)))) -> (A -> (B -> (A and B)))) and ((A -> ((B -> (A and B)) -> (B -> (A and B)))) -> (A -> (B -> (A and B)))))
theorem-size     43
proof            (modus-ponens tm-317 tm-349 ((Cm (-> Bm (and Am Bm))) (C (-> Bm (and Am Bm))) (A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19813.        (((A -> ((B -> (A and B)) -> (B -> (A and B)))) -> (A -> (B -> (A and B)))) and ((A -> ((B -> (A and B)) -> (B -> (A and B)))) -> (A -> (B -> (A and B))))), M:tm-317, m:tm-349, u:((Cm (-> Bm (and Am Bm))) (C (-> Bm (and Am Bm))) (A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-19814
in-theory        19814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((A -> ((B -> (A and B)) -> C)) -> (A -> ((B -> (A and B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-316 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19814.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((A -> ((B -> (A and B)) -> C)) -> (A -> ((B -> (A and B)) -> C)))), M:tm-316, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-19815
in-theory        19815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19815.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (D -> (E -> D))), M:tm-315, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19816
in-theory        19816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((A -> ((B -> (A and B)) -> C)) -> (not (A -> C))) -> (not (A -> ((B -> (A and B)) -> C)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19816.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((A -> ((B -> (A and B)) -> C)) -> (not (A -> C))) -> (not (A -> ((B -> (A and B)) -> C))))), M:tm-313, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-19817
in-theory        19817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((A -> C) -> D) -> (((A -> ((B -> (A and B)) -> C)) or (A -> C)) -> D)))
theorem-size     35
proof            (modus-ponens tm-312 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19817.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((A -> C) -> D) -> (((A -> ((B -> (A and B)) -> C)) or (A -> C)) -> D))), M:tm-312, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-19818
in-theory        19818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (D or ((A -> ((B -> (A and B)) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-311 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19818.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (D or ((A -> ((B -> (A and B)) -> C)) -> (A -> C)))), M:tm-311, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19819
in-theory        19819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19819.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) or D)), M:tm-310, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19820
in-theory        19820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (D -> (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19820.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (D -> (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and D))), M:tm-309, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19821
in-theory        19821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((A -> ((B -> (A and B)) -> C)) -> A) -> ((A -> ((B -> (A and B)) -> C)) -> C)))
theorem-size     37
proof            (modus-ponens tm-306 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B Am) (C Cm)))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19821.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (((A -> ((B -> (A and B)) -> C)) -> A) -> ((A -> ((B -> (A and B)) -> C)) -> C))), M:tm-306, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B Am) (C Cm))
================================================================
tm-name          tm-19822
in-theory        19822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (D -> ((A -> ((B -> (A and B)) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-305 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19822.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (D -> ((A -> ((B -> (A and B)) -> C)) -> (A -> C)))), M:tm-305, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19823
in-theory        19823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-303 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19823.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-303, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19824
in-theory        19824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-270 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19824.        ((A -> (((B and C) -> C) and A)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-270, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19825
in-theory        19825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-239 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19825.        ((A -> (((B and C) -> B) and A)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-239, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19826
in-theory        19826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G)))
theorem-size     31
proof            (modus-ponens tm-210 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19826.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G))), M:tm-210, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19827
in-theory        19827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-183 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19827.        ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-183, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19828
in-theory        19828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-157 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19828.        ((A -> ((B and C) -> C)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-157, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19829
in-theory        19829
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     29
proof            (modus-ponens tm-147 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19829.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-147, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19830
in-theory        19830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-134 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19830.        ((A -> ((B and C) -> B)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-134, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19831
in-theory        19831
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     29
proof            (modus-ponens tm-125 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19831.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-125, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19832
in-theory        19832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (A and B)) -> (C -> D))) -> ((A -> C) -> (A -> D)))
theorem-size     19
proof            (modus-ponens tm-114 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) (-> C D)))) (B Am) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19832.        ((A -> ((B -> (A and B)) -> (C -> D))) -> ((A -> C) -> (A -> D))), M:tm-114, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) (-> C D)))) (B Am) (Cm (-> C D)))
================================================================
tm-name          tm-19833
in-theory        19833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G)))
theorem-size     29
proof            (modus-ponens tm-113 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19833.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G))), M:tm-113, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19834
in-theory        19834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     33
proof            (modus-ponens tm-105 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19834.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-105, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19835
in-theory        19835
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (A and B)) -> (B -> (A and B)))) -> (A -> (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-100 tm-349 ((Cm (-> Bm (and Am Bm))) (C (-> Bm (and Am Bm))) (A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19835.        ((A -> ((B -> (A and B)) -> (B -> (A and B)))) -> (A -> (B -> (A and B)))), M:tm-100, m:tm-349, u:((Cm (-> Bm (and Am Bm))) (C (-> Bm (and Am Bm))) (A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-19836
in-theory        19836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E)))
theorem-size     21
proof            (modus-ponens tm-95 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19836.        (((A -> B) -> (A -> A)) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E))), M:tm-95, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19837
in-theory        19837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (A and B)) -> C)) -> (D -> (A -> C)))
theorem-size     15
proof            (modus-ponens tm-84 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19837.        ((A -> ((B -> (A and B)) -> C)) -> (D -> (A -> C))), M:tm-84, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-19838
in-theory        19838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-83 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19838.        ((A -> (B -> (C -> B))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-83, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19839
in-theory        19839
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (B and C)) -> B))) -> (B -> B))
theorem-size     15
proof            (modus-ponens tm-80 tm-349 ((Cm Am) (B (-> Bm (and Am Bm))) (A Am) (C (-> Am Am))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19839.        ((A or (B -> ((C -> (B and C)) -> B))) -> (B -> B)), M:tm-80, m:tm-349, u:((Cm Am) (B (-> Bm (and Am Bm))) (A Am) (C (-> Am Am)))
================================================================
tm-name          tm-19840
in-theory        19840
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> ((C -> (B and C)) -> D)) -> (B -> D)))
theorem-size     19
proof            (modus-ponens tm-76 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19840.        (((not (not A)) -> A) and ((B -> ((C -> (B and C)) -> D)) -> (B -> D))), M:tm-76, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19841
in-theory        19841
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> ((B -> (A and B)) -> C)))) or (A -> ((B -> (A and B)) -> C))) -> (A -> C))
theorem-size     25
proof            (modus-ponens tm-73 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-5)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19841.        (((not (not (A -> ((B -> (A and B)) -> C)))) or (A -> ((B -> (A and B)) -> C))) -> (A -> C)), M:tm-73, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-19842
in-theory        19842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E)))
theorem-size     25
proof            (modus-ponens tm-69 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19842.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E))), M:tm-69, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19843
in-theory        19843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     27
proof            (modus-ponens tm-54 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19843.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-54, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19844
in-theory        19844
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> ((C -> (B and C)) -> D))) or (B -> ((C -> (B and C)) -> D))) -> (B -> D))
theorem-size     25
proof            (modus-ponens tm-47 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-5)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19844.        (((A and (B -> ((C -> (B and C)) -> D))) or (B -> ((C -> (B and C)) -> D))) -> (B -> D)), M:tm-47, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-19845
in-theory        19845
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> (A and B)) -> C)) and D) or (A -> ((B -> (A and B)) -> C))) -> (A -> C))
theorem-size     25
proof            (modus-ponens tm-46 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-5)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19845.        ((((A -> ((B -> (A and B)) -> C)) and D) or (A -> ((B -> (A and B)) -> C))) -> (A -> C)), M:tm-46, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-19846
in-theory        19846
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) or (B -> ((A -> (B and A)) -> C))) -> (B -> C))
theorem-size     21
proof            (modus-ponens tm-44 tm-349 ((A Am) (B (-> (-> Bm (and Am Bm)) Cm)) (C (-> Am Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19846.        ((((A -> (B and A)) -> C) or (B -> ((A -> (B and A)) -> C))) -> (B -> C)), M:tm-44, m:tm-349, u:((A Am) (B (-> (-> Bm (and Am Bm)) Cm)) (C (-> Am Cm)))
================================================================
tm-name          tm-19847
in-theory        19847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E)))
theorem-size     19
proof            (modus-ponens tm-42 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19847.        ((A -> (B or A)) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E))), M:tm-42, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19848
in-theory        19848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E)))
theorem-size     19
proof            (modus-ponens tm-32 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19848.        ((A -> (A or B)) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E))), M:tm-32, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19849
in-theory        19849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (A and B)) -> C)) -> ((A -> ((B -> (A and B)) -> C)) and (A -> C)))
theorem-size     23
proof            (modus-ponens tm-24 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19849.        ((A -> ((B -> (A and B)) -> C)) -> ((A -> ((B -> (A and B)) -> C)) and (A -> C))), M:tm-24, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-19850
in-theory        19850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E)))
theorem-size     21
proof            (modus-ponens tm-23 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19850.        ((A -> (B -> (A and B))) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E))), M:tm-23, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19851
in-theory        19851
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E)))
theorem-size     19
proof            (modus-ponens tm-22 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19851.        (((A and B) -> B) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E))), M:tm-22, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19852
in-theory        19852
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E)))
theorem-size     19
proof            (modus-ponens tm-21 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19852.        (((A and B) -> A) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E))), M:tm-21, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19853
in-theory        19853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     27
proof            (modus-ponens tm-20 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19853.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-20, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19854
in-theory        19854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E)))
theorem-size     19
proof            (modus-ponens tm-19 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19854.        ((A -> (B -> A)) and ((C -> ((D -> (C and D)) -> E)) -> (C -> E))), M:tm-19, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19855
in-theory        19855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (A and B)) -> C)) -> (A -> ((B -> (A and B)) -> C)))
theorem-size     19
proof            (modus-ponens tm-12 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19855.        ((A -> ((B -> (A and B)) -> C)) -> (A -> ((B -> (A and B)) -> C))), M:tm-12, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-19856
in-theory        19856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (not (A -> C))) -> (not (A -> ((B -> (A and B)) -> C))))
theorem-size     25
proof            (modus-ponens tm-9 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-9 tm-2 tm-1 tm-5)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19856.        (((A -> ((B -> (A and B)) -> C)) -> (not (A -> C))) -> (not (A -> ((B -> (A and B)) -> C)))), M:tm-9, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-19857
in-theory        19857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (((A -> ((D -> (A and D)) -> B)) or (A -> B)) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19857.        (((A -> B) -> C) -> (((A -> ((D -> (A and D)) -> B)) or (A -> B)) -> C)), M:tm-8, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-19858
in-theory        19858
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> ((C -> (B and C)) -> D)) -> (B -> D)))
theorem-size     15
proof            (modus-ponens tm-7 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-7 tm-2 tm-1 tm-5)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19858.        (A or ((B -> ((C -> (B and C)) -> D)) -> (B -> D))), M:tm-7, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19859
in-theory        19859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-6 tm-2 tm-1 tm-5)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19859.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) or D), M:tm-6, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19860
in-theory        19860
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> ((C -> (B and C)) -> D)) -> (B -> D)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19860.        (A -> (((B -> ((C -> (B and C)) -> D)) -> (B -> D)) and A)), M:tm-5, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19861
in-theory        19861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> A) -> ((A -> ((B -> (A and B)) -> C)) -> C))
theorem-size     23
proof            (modus-ponens tm-2 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B Am) (C Cm)))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19861.        (((A -> ((B -> (A and B)) -> C)) -> A) -> ((A -> ((B -> (A and B)) -> C)) -> C)), M:tm-2, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B Am) (C Cm))
================================================================
tm-name          tm-19862
in-theory        19862
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (B and C)) -> D)) -> (B -> D)))
theorem-size     15
proof            (modus-ponens tm-1 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-19862.        (A -> ((B -> ((C -> (B and C)) -> D)) -> (B -> D))), M:tm-1, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-19863
in-theory        19863
times-derived    1
----------------------------------------------------------------
theorem          (not ((not (A -> (B -> (A and B)))) and C))
theorem-size     11
proof            (modus-ponens tm-350 tm-3 ((A (and (not (-> B (-> C (and B C)))) Bm)) (Am (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-19863.        (not ((not (A -> (B -> (A and B)))) and C)), M:tm-350, m:tm-3, u:((A (and (not (-> B (-> C (and B C)))) Bm)) (Am (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19864
in-theory        19864
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (not (B -> (C -> (B and C))))))
theorem-size     11
proof            (modus-ponens tm-350 tm-4 ((A (and Am (not (-> B (-> C (and B C)))))) (Bm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-19864.        (not (A and (not (B -> (C -> (B and C)))))), M:tm-350, m:tm-4, u:((A (and Am (not (-> B (-> C (and B C)))))) (Bm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19865
in-theory        19865
times-derived    1
----------------------------------------------------------------
theorem          (not (not (not (not (A -> (B -> (A and B)))))))
theorem-size     11
proof            (modus-ponens tm-350 tm-10 ((A (not (not (not (-> B (-> C (and B C))))))) (Am (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-10)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-19865.        (not (not (not (not (A -> (B -> (A and B))))))), M:tm-350, m:tm-10, u:((A (not (not (not (-> B (-> C (and B C))))))) (Am (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19866
in-theory        19866
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (C -> (A -> (B -> (A and B)))))))
theorem-size     19
proof            (modus-ponens tm-350 tm-57 ((A (-> (-> B (-> C (and B C))) (not (-> Bm (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19866.        (not ((A -> (B -> (A and B))) -> (not (C -> (A -> (B -> (A and B))))))), M:tm-350, m:tm-57, u:((A (-> (-> B (-> C (and B C))) (not (-> Bm (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-19867
in-theory        19867
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not ((A -> B) -> (A -> (A and B))))))
theorem-size     19
proof            (modus-ponens tm-350 tm-58 ((A (-> (-> Am (-> Bm (and Am Bm))) (not (-> (-> Am Bm) (-> Am (and Am Bm)))))) (B Am) (C Bm) (Cm (and Am Bm))))
axioms-used      (tm-9 tm-1 tm-5 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19867.        (not ((A -> (B -> (A and B))) -> (not ((A -> B) -> (A -> (A and B)))))), M:tm-350, m:tm-58, u:((A (-> (-> Am (-> Bm (and Am Bm))) (not (-> (-> Am Bm) (-> Am (and Am Bm)))))) (B Am) (C Bm) (Cm (and Am Bm)))
================================================================
tm-name          tm-19868
in-theory        19868
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (C -> ((A -> (B -> (A and B))) and C)))))
theorem-size     21
proof            (modus-ponens tm-350 tm-61 ((A (-> (-> B (-> C (and B C))) (not (-> Bm (and (-> B (-> C (and B C))) Bm))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-19868.        (not ((A -> (B -> (A and B))) -> (not (C -> ((A -> (B -> (A and B))) and C))))), M:tm-350, m:tm-61, u:((A (-> (-> B (-> C (and B C))) (not (-> Bm (and (-> B (-> C (and B C))) Bm))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-19869
in-theory        19869
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not ((A -> (B -> (A and B))) or C))))
theorem-size     19
proof            (modus-ponens tm-350 tm-62 ((A (-> (-> B (-> C (and B C))) (not (or (-> B (-> C (and B C))) Bm)))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-19869.        (not ((A -> (B -> (A and B))) -> (not ((A -> (B -> (A and B))) or C)))), M:tm-350, m:tm-62, u:((A (-> (-> B (-> C (and B C))) (not (or (-> B (-> C (and B C))) Bm)))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-19870
in-theory        19870
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (C or (A -> (B -> (A and B)))))))
theorem-size     19
proof            (modus-ponens tm-350 tm-63 ((A (-> (-> B (-> C (and B C))) (not (or Bm (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-19870.        (not ((A -> (B -> (A and B))) -> (not (C or (A -> (B -> (A and B))))))), M:tm-350, m:tm-63, u:((A (-> (-> B (-> C (and B C))) (not (or Bm (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-19871
in-theory        19871
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (((B -> (A and B)) -> C) -> ((A or (B -> (A and B))) -> C)))))
theorem-size     27
proof            (modus-ponens tm-350 tm-64 ((A (-> (-> Am (-> C (and Am C))) (not (-> (-> (-> C (and Am C)) Cm) (-> (or Am (-> C (and Am C))) Cm))))) (B Am) (Bm (-> C (and Am C)))))
axioms-used      (tm-9 tm-1 tm-5 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-19871.        (not ((A -> (B -> (A and B))) -> (not (((B -> (A and B)) -> C) -> ((A or (B -> (A and B))) -> C))))), M:tm-350, m:tm-64, u:((A (-> (-> Am (-> C (and Am C))) (not (-> (-> (-> C (and Am C)) Cm) (-> (or Am (-> C (and Am C))) Cm))))) (B Am) (Bm (-> C (and Am C))))
================================================================
tm-name          tm-19872
in-theory        19872
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not ((A -> (not (B -> (A and B)))) -> (not A)))))
theorem-size     21
proof            (modus-ponens tm-350 tm-65 ((A (-> (-> Am (-> C (and Am C))) (not (-> (-> Am (not (-> C (and Am C)))) (not Am))))) (B Am) (Bm (-> C (and Am C)))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-19872.        (not ((A -> (B -> (A and B))) -> (not ((A -> (not (B -> (A and B)))) -> (not A))))), M:tm-350, m:tm-65, u:((A (-> (-> Am (-> C (and Am C))) (not (-> (-> Am (not (-> C (and Am C)))) (not Am))))) (B Am) (Bm (-> C (and Am C))))
================================================================
tm-name          tm-19873
in-theory        19873
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (C -> (D -> C)))))
theorem-size     15
proof            (modus-ponens tm-350 tm-79 ((A (-> (-> B (-> C (and B C))) (not (-> Bm (-> Cm Bm))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19873.        (not ((A -> (B -> (A and B))) -> (not (C -> (D -> C))))), M:tm-350, m:tm-79, u:((A (-> (-> B (-> C (and B C))) (not (-> Bm (-> Cm Bm))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-19874
in-theory        19874
times-derived    1
----------------------------------------------------------------
theorem          (not (not (A -> (B -> (A and B)))))
theorem-size     9
proof            (modus-ponens tm-350 tm-86 ((A (not (-> B (-> C (and B C))))) (Am (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19874.        (not (not (A -> (B -> (A and B))))), M:tm-350, m:tm-86, u:((A (not (-> B (-> C (and B C))))) (Am (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19875
in-theory        19875
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (A -> A))))
theorem-size     13
proof            (modus-ponens tm-350 tm-91 ((A (-> (-> Am (-> C (and Am C))) (not (-> Am Am)))) (B Am) (Bm (-> C (and Am C)))))
axioms-used      (tm-9 tm-1 tm-5 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-19875.        (not ((A -> (B -> (A and B))) -> (not (A -> A)))), M:tm-350, m:tm-91, u:((A (-> (-> Am (-> C (and Am C))) (not (-> Am Am)))) (B Am) (Bm (-> C (and Am C))))
================================================================
tm-name          tm-19876
in-theory        19876
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     23
proof            (modus-ponens tm-350 tm-109 ((A (-> (-> B (-> C (and B C))) (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19876.        (not ((A -> (B -> (A and B))) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-350, m:tm-109, u:((A (-> (-> B (-> C (and B C))) (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-19877
in-theory        19877
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (not (B -> (C -> (B and C))))) and A))
theorem-size     13
proof            (modus-ponens tm-350 tm-116 ((A (and (-> Am (not (-> B (-> C (and B C))))) Am)) (Bm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-19877.        (not ((A -> (not (B -> (C -> (B and C))))) and A)), M:tm-350, m:tm-116, u:((A (and (-> Am (not (-> B (-> C (and B C))))) Am)) (Bm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19878
in-theory        19878
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> A)) -> (not (C -> (D -> (C and D))))) and E))
theorem-size     17
proof            (modus-ponens tm-350 tm-117 ((A (and (-> (-> Am (-> Bm Am)) (not (-> B (-> C (and B C))))) Dm)) (Cm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-19878.        (not (((A -> (B -> A)) -> (not (C -> (D -> (C and D))))) and E)), M:tm-350, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) (not (-> B (-> C (and B C))))) Dm)) (Cm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19879
in-theory        19879
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (E -> (D and E))))) and F))
theorem-size     25
proof            (modus-ponens tm-350 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not (-> B (-> C (and B C))))) Em)) (Dm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19879.        (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (E -> (D and E))))) and F)), M:tm-350, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not (-> B (-> C (and B C))))) Em)) (Dm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19880
in-theory        19880
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> A) -> (not (C -> (D -> (C and D))))) and E))
theorem-size     17
proof            (modus-ponens tm-350 tm-128 ((A (and (-> (-> (and Am Bm) Am) (not (-> B (-> C (and B C))))) Dm)) (Cm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-19880.        (not ((((A and B) -> A) -> (not (C -> (D -> (C and D))))) and E)), M:tm-350, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) (not (-> B (-> C (and B C))))) Dm)) (Cm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19881
in-theory        19881
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not ((C and D) -> C))))
theorem-size     15
proof            (modus-ponens tm-350 tm-130 ((A (-> (-> B (-> C (and B C))) (not (-> (and Bm Cm) Bm)))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19881.        (not ((A -> (B -> (A and B))) -> (not ((C and D) -> C)))), M:tm-350, m:tm-130, u:((A (-> (-> B (-> C (and B C))) (not (-> (and Bm Cm) Bm)))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-19882
in-theory        19882
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (A -> (not (B -> (C -> (B and C)))))))
theorem-size     13
proof            (modus-ponens tm-350 tm-137 ((A (and Am (-> Am (not (-> B (-> C (and B C))))))) (Bm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-19882.        (not (A and (A -> (not (B -> (C -> (B and C))))))), M:tm-350, m:tm-137, u:((A (and Am (-> Am (not (-> B (-> C (and B C))))))) (Bm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19883
in-theory        19883
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> B)) -> (not (D -> (E -> (D and E)))))))
theorem-size     17
proof            (modus-ponens tm-350 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) (not (-> B (-> C (and B C))))))) (Dm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-19883.        (not (A and ((B -> (C -> B)) -> (not (D -> (E -> (D and E))))))), M:tm-350, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) (not (-> B (-> C (and B C))))))) (Dm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19884
in-theory        19884
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not (E -> (F -> (E and F)))))))
theorem-size     25
proof            (modus-ponens tm-350 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not (-> B (-> C (and B C))))))) (Em (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19884.        (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not (E -> (F -> (E and F))))))), M:tm-350, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not (-> B (-> C (and B C))))))) (Em (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19885
in-theory        19885
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> B) -> (not (D -> (E -> (D and E)))))))
theorem-size     17
proof            (modus-ponens tm-350 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) (not (-> B (-> C (and B C))))))) (Dm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-19885.        (not (A and (((B and C) -> B) -> (not (D -> (E -> (D and E))))))), M:tm-350, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) (not (-> B (-> C (and B C))))))) (Dm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19886
in-theory        19886
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> C) -> (not (D -> (E -> (D and E)))))))
theorem-size     17
proof            (modus-ponens tm-350 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) (not (-> B (-> C (and B C))))))) (Dm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-19886.        (not (A and (((B and C) -> C) -> (not (D -> (E -> (D and E))))))), M:tm-350, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) (not (-> B (-> C (and B C))))))) (Dm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19887
in-theory        19887
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> B) -> (not (C -> (D -> (C and D))))) and E))
theorem-size     17
proof            (modus-ponens tm-350 tm-151 ((A (and (-> (-> (and Am Bm) Bm) (not (-> B (-> C (and B C))))) Dm)) (Cm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-19887.        (not ((((A and B) -> B) -> (not (C -> (D -> (C and D))))) and E)), M:tm-350, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) (not (-> B (-> C (and B C))))) Dm)) (Cm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19888
in-theory        19888
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not ((C and D) -> D))))
theorem-size     15
proof            (modus-ponens tm-350 tm-153 ((A (-> (-> B (-> C (and B C))) (not (-> (and Bm Cm) Cm)))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19888.        (not ((A -> (B -> (A and B))) -> (not ((C and D) -> D)))), M:tm-350, m:tm-153, u:((A (-> (-> B (-> C (and B C))) (not (-> (and Bm Cm) Cm)))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-19889
in-theory        19889
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not ((C -> (D -> C)) and (A -> (B -> (A and B)))))))
theorem-size     23
proof            (modus-ponens tm-350 tm-179 ((A (-> (-> B (-> C (and B C))) (not (and (-> Bm (-> Cm Bm)) (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-19889.        (not ((A -> (B -> (A and B))) -> (not ((C -> (D -> C)) and (A -> (B -> (A and B))))))), M:tm-350, m:tm-179, u:((A (-> (-> B (-> C (and B C))) (not (and (-> Bm (-> Cm Bm)) (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-19890
in-theory        19890
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B -> (A and B)))))))
theorem-size     31
proof            (modus-ponens tm-350 tm-206 ((A (-> (-> B (-> C (and B C))) (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-19890.        (not ((A -> (B -> (A and B))) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B -> (A and B))))))), M:tm-350, m:tm-206, u:((A (-> (-> B (-> C (and B C))) (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-19891
in-theory        19891
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (((C and D) -> C) and (A -> (B -> (A and B)))))))
theorem-size     23
proof            (modus-ponens tm-350 tm-235 ((A (-> (-> B (-> C (and B C))) (not (and (-> (and Bm Cm) Bm) (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-19891.        (not ((A -> (B -> (A and B))) -> (not (((C and D) -> C) and (A -> (B -> (A and B))))))), M:tm-350, m:tm-235, u:((A (-> (-> B (-> C (and B C))) (not (and (-> (and Bm Cm) Bm) (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-19892
in-theory        19892
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (((C and D) -> D) and (A -> (B -> (A and B)))))))
theorem-size     23
proof            (modus-ponens tm-350 tm-266 ((A (-> (-> B (-> C (and B C))) (not (and (-> (and Bm Cm) Cm) (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-19892.        (not ((A -> (B -> (A and B))) -> (not (((C and D) -> D) and (A -> (B -> (A and B))))))), M:tm-350, m:tm-266, u:((A (-> (-> B (-> C (and B C))) (not (and (-> (and Bm Cm) Cm) (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-19893
in-theory        19893
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not ((C -> (D -> (C and D))) and (A -> (B -> (A and B)))))))
theorem-size     25
proof            (modus-ponens tm-350 tm-299 ((A (-> (-> B (-> C (and B C))) (not (and (-> Bm (-> Cm (and Bm Cm))) (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-19893.        (not ((A -> (B -> (A and B))) -> (not ((C -> (D -> (C and D))) and (A -> (B -> (A and B))))))), M:tm-350, m:tm-299, u:((A (-> (-> B (-> C (and B C))) (not (and (-> Bm (-> Cm (and Bm Cm))) (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-19894
in-theory        19894
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (A -> (A and (B -> (A and B)))))))
theorem-size     19
proof            (modus-ponens tm-350 tm-334 ((A (-> (-> Am (-> C (and Am C))) (not (-> Am (and Am (-> C (and Am C))))))) (B Am) (Bm (-> C (and Am C)))))
axioms-used      (tm-9 tm-1 tm-5 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-19894.        (not ((A -> (B -> (A and B))) -> (not (A -> (A and (B -> (A and B))))))), M:tm-350, m:tm-334, u:((A (-> (-> Am (-> C (and Am C))) (not (-> Am (and Am (-> C (and Am C))))))) (B Am) (Bm (-> C (and Am C))))
================================================================
tm-name          tm-19895
in-theory        19895
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> (B and C))) -> (not (D -> (E -> (D and E)))))))
theorem-size     19
proof            (modus-ponens tm-350 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (not (-> B (-> C (and B C))))))) (Dm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19895.        (not (A and ((B -> (C -> (B and C))) -> (not (D -> (E -> (D and E))))))), M:tm-350, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (not (-> B (-> C (and B C))))))) (Dm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19896
in-theory        19896
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> (A and B))) -> (not (C -> (D -> (C and D))))) and E))
theorem-size     19
proof            (modus-ponens tm-350 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) (not (-> B (-> C (and B C))))) Dm)) (Cm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-19896.        (not (((A -> (B -> (A and B))) -> (not (C -> (D -> (C and D))))) and E)), M:tm-350, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) (not (-> B (-> C (and B C))))) Dm)) (Cm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-19897
in-theory        19897
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (C -> (D -> (C and D))))))
theorem-size     17
proof            (modus-ponens tm-350 tm-350 ((A (-> (-> B (-> C (and B C))) (not (-> Bm (-> Cm (and Bm Cm)))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19897.        (not ((A -> (B -> (A and B))) -> (not (C -> (D -> (C and D)))))), M:tm-350, m:tm-350, u:((A (-> (-> B (-> C (and B C))) (not (-> Bm (-> Cm (and Bm Cm)))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-19898
in-theory        19898
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19898.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19899
in-theory        19899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not (D -> (E -> (D and E))))) -> (not C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19899.        (((A -> B) -> (A -> (A and B))) and ((C -> (not (D -> (E -> (D and E))))) -> (not C))), M:tm-338, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19900
in-theory        19900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((A -> (not (B -> (C -> (B and C))))) -> ((A -> (not (B -> (C -> (B and C))))) and (not A))))
theorem-size     38
proof            (modus-ponens tm-328 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       154
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19900.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((A -> (not (B -> (C -> (B and C))))) -> ((A -> (not (B -> (C -> (B and C))))) and (not A)))), M:tm-328, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-19901
in-theory        19901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not (B -> (C -> (B and C))))) -> (not A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19901.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not (B -> (C -> (B and C))))) -> (not A)))), M:tm-327, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19902
in-theory        19902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((D and E) -> E) and ((A -> (not (B -> (C -> (B and C))))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19902.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((D and E) -> E) and ((A -> (not (B -> (C -> (B and C))))) -> (not A)))), M:tm-326, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19903
in-theory        19903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((D and E) -> D) and ((A -> (not (B -> (C -> (B and C))))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19903.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((D and E) -> D) and ((A -> (not (B -> (C -> (B and C))))) -> (not A)))), M:tm-325, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19904
in-theory        19904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not (B -> (C -> (B and C))))) -> (not A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19904.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not (B -> (C -> (B and C))))) -> (not A)))), M:tm-324, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19905
in-theory        19905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not (B -> (C -> (B and C))))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19905.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not (B -> (C -> (B and C))))) -> (not A)))), M:tm-323, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19906
in-theory        19906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19906.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((D and E) -> E)), M:tm-322, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19907
in-theory        19907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19907.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((D and E) -> D)), M:tm-320, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19908
in-theory        19908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19908.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19909
in-theory        19909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((A -> (not (B -> (C -> (B and C))))) -> (A -> (not (B -> (C -> (B and C)))))))
theorem-size     35
proof            (modus-ponens tm-316 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19909.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((A -> (not (B -> (C -> (B and C))))) -> (A -> (not (B -> (C -> (B and C))))))), M:tm-316, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-19910
in-theory        19910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19910.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (D -> (E -> D))), M:tm-315, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19911
in-theory        19911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((A -> (not (B -> (C -> (B and C))))) -> (not (not A))) -> (not (A -> (not (B -> (C -> (B and C))))))))
theorem-size     40
proof            (modus-ponens tm-313 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       140
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19911.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((A -> (not (B -> (C -> (B and C))))) -> (not (not A))) -> (not (A -> (not (B -> (C -> (B and C)))))))), M:tm-313, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-19912
in-theory        19912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((not A) -> D) -> (((A -> (not (B -> (C -> (B and C))))) or (not A)) -> D)))
theorem-size     34
proof            (modus-ponens tm-312 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-1)
proof-size       138
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19912.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((not A) -> D) -> (((A -> (not (B -> (C -> (B and C))))) or (not A)) -> D))), M:tm-312, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-19913
in-theory        19913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (D or ((A -> (not (B -> (C -> (B and C))))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19913.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (D or ((A -> (not (B -> (C -> (B and C))))) -> (not A)))), M:tm-311, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19914
in-theory        19914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((A -> (not (B -> (C -> (B and C))))) -> (not A)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19914.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((A -> (not (B -> (C -> (B and C))))) -> (not A)) or D)), M:tm-310, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19915
in-theory        19915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (D -> (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19915.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (D -> (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and D))), M:tm-309, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19916
in-theory        19916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (D -> ((A -> (not (B -> (C -> (B and C))))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19916.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (D -> ((A -> (not (B -> (C -> (B and C))))) -> (not A)))), M:tm-305, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19917
in-theory        19917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19917.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-303, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19918
in-theory        19918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19918.        ((A -> (((B and C) -> C) and A)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-270, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19919
in-theory        19919
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19919.        ((A -> (((B and C) -> B) and A)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-239, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19920
in-theory        19920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (F -> (G -> (F and G))))) -> (not E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19920.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (F -> (G -> (F and G))))) -> (not E))), M:tm-210, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19921
in-theory        19921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19921.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-183, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19922
in-theory        19922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19922.        ((A -> ((B and C) -> C)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-157, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19923
in-theory        19923
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (not (C -> (D -> (C and D))))) -> (not (C -> (D -> (C and D)))))) -> (not (B and (not (C -> (D -> (C and D)))))))
theorem-size     33
proof            (modus-ponens tm-154 tm-350 ((Am (and A (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not (-> Bm (-> Cm (and Bm Cm))))) (C (not (and A (not (-> Bm (-> Cm (and Bm Cm)))))))))
axioms-used      (tm-8 tm-1 tm-4 tm-9 tm-5)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19923.        ((A or ((B and (not (C -> (D -> (C and D))))) -> (not (C -> (D -> (C and D)))))) -> (not (B and (not (C -> (D -> (C and D))))))), M:tm-154, m:tm-350, u:((Am (and A (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not (-> Bm (-> Cm (and Bm Cm))))) (C (not (and A (not (-> Bm (-> Cm (and Bm Cm))))))))
================================================================
tm-name          tm-19924
in-theory        19924
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not (C -> (D -> (C and D))))))
theorem-size     15
proof            (modus-ponens tm-153 tm-350 ((A (-> (-> (and B C) C) (not (-> Bm (-> Cm (and Bm Cm)))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19924.        (not (((A and B) -> B) -> (not (C -> (D -> (C and D)))))), M:tm-153, m:tm-350, u:((A (-> (-> (and B C) C) (not (-> Bm (-> Cm (and Bm Cm)))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-19925
in-theory        19925
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19925.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-147, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19926
in-theory        19926
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (not (C -> (D -> (C and D)))))) -> B) or ((A and (B -> (not (C -> (D -> (C and D)))))) -> (not (C -> (D -> (C and D)))))) -> (not (A and (B -> (not (C -> (D -> (C and D))))))))
theorem-size     50
proof            (modus-ponens tm-144 tm-350 ((Am (and A (-> B (not (-> Bm (-> Cm (and Bm Cm))))))) (C (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (and A (-> B (not (-> Bm (-> Cm (and Bm Cm))))))))))
axioms-used      (tm-8 tm-2 tm-4 tm-9 tm-1 tm-5)
proof-size       168
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19926.        ((((A and (B -> (not (C -> (D -> (C and D)))))) -> B) or ((A and (B -> (not (C -> (D -> (C and D)))))) -> (not (C -> (D -> (C and D)))))) -> (not (A and (B -> (not (C -> (D -> (C and D)))))))), M:tm-144, m:tm-350, u:((Am (and A (-> B (not (-> Bm (-> Cm (and Bm Cm))))))) (C (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (and A (-> B (not (-> Bm (-> Cm (and Bm Cm)))))))))
================================================================
tm-name          tm-19927
in-theory        19927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19927.        ((A -> ((B and C) -> B)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-134, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19928
in-theory        19928
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((not (B -> (C -> (B and C)))) and D) -> (not (B -> (C -> (B and C)))))) -> (not ((not (B -> (C -> (B and C)))) and D)))
theorem-size     33
proof            (modus-ponens tm-131 tm-350 ((Am (and (not (-> Bm (-> Cm (and Bm Cm)))) B)) (A (not (-> Bm (-> Cm (and Bm Cm))))) (C (not (and (not (-> Bm (-> Cm (and Bm Cm)))) B)))))
axioms-used      (tm-8 tm-1 tm-3 tm-9 tm-5)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19928.        ((A or (((not (B -> (C -> (B and C)))) and D) -> (not (B -> (C -> (B and C)))))) -> (not ((not (B -> (C -> (B and C)))) and D))), M:tm-131, m:tm-350, u:((Am (and (not (-> Bm (-> Cm (and Bm Cm)))) B)) (A (not (-> Bm (-> Cm (and Bm Cm))))) (C (not (and (not (-> Bm (-> Cm (and Bm Cm)))) B))))
================================================================
tm-name          tm-19929
in-theory        19929
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not (C -> (D -> (C and D))))))
theorem-size     15
proof            (modus-ponens tm-130 tm-350 ((A (-> (-> (and B C) B) (not (-> Bm (-> Cm (and Bm Cm)))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19929.        (not (((A and B) -> A) -> (not (C -> (D -> (C and D)))))), M:tm-130, m:tm-350, u:((A (-> (-> (and B C) B) (not (-> Bm (-> Cm (and Bm Cm)))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-19930
in-theory        19930
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19930.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-125, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19931
in-theory        19931
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not (B -> (C -> (B and C))))) and D) -> A) or (((A -> (not (B -> (C -> (B and C))))) and D) -> (not (B -> (C -> (B and C)))))) -> (not ((A -> (not (B -> (C -> (B and C))))) and D)))
theorem-size     50
proof            (modus-ponens tm-122 tm-350 ((Am (and (-> A (not (-> Bm (-> Cm (and Bm Cm))))) C)) (B (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (and (-> A (not (-> Bm (-> Cm (and Bm Cm))))) C)))))
axioms-used      (tm-8 tm-2 tm-3 tm-9 tm-1 tm-5)
proof-size       168
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19931.        (((((A -> (not (B -> (C -> (B and C))))) and D) -> A) or (((A -> (not (B -> (C -> (B and C))))) and D) -> (not (B -> (C -> (B and C)))))) -> (not ((A -> (not (B -> (C -> (B and C))))) and D))), M:tm-122, m:tm-350, u:((Am (and (-> A (not (-> Bm (-> Cm (and Bm Cm))))) C)) (B (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (and (-> A (not (-> Bm (-> Cm (and Bm Cm))))) C))))
================================================================
tm-name          tm-19932
in-theory        19932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (G -> (F and G))))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19932.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (G -> (F and G))))) -> (not E))), M:tm-113, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19933
in-theory        19933
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (E -> (D and E))))))
theorem-size     23
proof            (modus-ponens tm-109 tm-350 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> Bm (-> Cm (and Bm Cm)))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-5)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19933.        (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (E -> (D and E)))))), M:tm-109, m:tm-350, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> Bm (-> Cm (and Bm Cm)))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-19934
in-theory        19934
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19934.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-105, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19935
in-theory        19935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not (D -> (E -> (D and E))))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19935.        (((A -> B) -> (A -> A)) and ((C -> (not (D -> (E -> (D and E))))) -> (not C))), M:tm-95, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19936
in-theory        19936
times-derived    1
----------------------------------------------------------------
theorem          ((((not (A -> (B -> (A and B)))) -> C) or ((not (A -> (B -> (A and B)))) -> (not (A -> (B -> (A and B)))))) -> (not (not (A -> (B -> (A and B))))))
theorem-size     38
proof            (modus-ponens tm-92 tm-350 ((Am (not (-> Bm (-> Cm (and Bm Cm))))) (A (not (-> Bm (-> Cm (and Bm Cm))))) (B (not (not (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-8 tm-2 tm-1 tm-9 tm-5)
proof-size       136
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19936.        ((((not (A -> (B -> (A and B)))) -> C) or ((not (A -> (B -> (A and B)))) -> (not (A -> (B -> (A and B)))))) -> (not (not (A -> (B -> (A and B)))))), M:tm-92, m:tm-350, u:((Am (not (-> Bm (-> Cm (and Bm Cm))))) (A (not (-> Bm (-> Cm (and Bm Cm))))) (B (not (not (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-19937
in-theory        19937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> (B and C))))) -> (D -> (not A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19937.        ((A -> (not (B -> (C -> (B and C))))) -> (D -> (not A))), M:tm-84, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-19938
in-theory        19938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19938.        ((A -> (B -> (C -> B))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-83, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19939
in-theory        19939
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (C -> (D -> (C and D))))))
theorem-size     15
proof            (modus-ponens tm-79 tm-350 ((A (-> (-> B (-> C B)) (not (-> Bm (-> Cm (and Bm Cm)))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19939.        (not ((A -> (B -> A)) -> (not (C -> (D -> (C and D)))))), M:tm-79, m:tm-350, u:((A (-> (-> B (-> C B)) (not (-> Bm (-> Cm (and Bm Cm)))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-19940
in-theory        19940
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not (C -> (D -> (C and D))))) -> (not B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19940.        (((not (not A)) -> A) and ((B -> (not (C -> (D -> (C and D))))) -> (not B))), M:tm-76, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19941
in-theory        19941
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not (B -> (C -> (B and C))))))) or (A -> (not (B -> (C -> (B and C)))))) -> (not A))
theorem-size     26
proof            (modus-ponens tm-73 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-1 tm-5)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19941.        (((not (not (A -> (not (B -> (C -> (B and C))))))) or (A -> (not (B -> (C -> (B and C)))))) -> (not A)), M:tm-73, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-19942
in-theory        19942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (D -> (E -> (D and E))))) -> (not C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19942.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (D -> (E -> (D and E))))) -> (not C))), M:tm-69, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19943
in-theory        19943
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) or (((A -> (B -> (A and B))) -> (not C)) -> (not (A -> (B -> (A and B)))))) -> (not ((A -> (B -> (A and B))) -> (not C))))
theorem-size     41
proof            (modus-ponens tm-66 tm-350 ((Am (-> (-> Bm (-> Cm (and Bm Cm))) (not B))) (A (-> Bm (-> Cm (and Bm Cm)))) (C (not (-> (-> Bm (-> Cm (and Bm Cm))) (not B))))))
axioms-used      (tm-8 tm-9 tm-1 tm-5)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19943.        ((((A -> (B -> (A and B))) -> C) or (((A -> (B -> (A and B))) -> (not C)) -> (not (A -> (B -> (A and B)))))) -> (not ((A -> (B -> (A and B))) -> (not C)))), M:tm-66, m:tm-350, u:((Am (-> (-> Bm (-> Cm (and Bm Cm))) (not B))) (A (-> Bm (-> Cm (and Bm Cm)))) (C (not (-> (-> Bm (-> Cm (and Bm Cm))) (not B)))))
================================================================
tm-name          tm-19944
in-theory        19944
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19944.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-54, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19945
in-theory        19945
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not (C -> (D -> (C and D)))))) or (B -> (not (C -> (D -> (C and D)))))) -> (not B))
theorem-size     26
proof            (modus-ponens tm-47 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-1 tm-5)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19945.        (((A and (B -> (not (C -> (D -> (C and D)))))) or (B -> (not (C -> (D -> (C and D)))))) -> (not B)), M:tm-47, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-19946
in-theory        19946
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not (B -> (C -> (B and C))))) and D) or (A -> (not (B -> (C -> (B and C)))))) -> (not A))
theorem-size     26
proof            (modus-ponens tm-46 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-1 tm-5)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19946.        ((((A -> (not (B -> (C -> (B and C))))) and D) or (A -> (not (B -> (C -> (B and C)))))) -> (not A)), M:tm-46, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-19947
in-theory        19947
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> (B -> (A and B)))) or (C -> (not (A -> (B -> (A and B)))))) -> (not C))
theorem-size     22
proof            (modus-ponens tm-44 tm-350 ((A Am) (B (not (-> Bm (-> Cm (and Bm Cm))))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-5)
proof-size       98
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19947.        (((not (A -> (B -> (A and B)))) or (C -> (not (A -> (B -> (A and B)))))) -> (not C)), M:tm-44, m:tm-350, u:((A Am) (B (not (-> Bm (-> Cm (and Bm Cm))))) (C (not Am)))
================================================================
tm-name          tm-19948
in-theory        19948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not (D -> (E -> (D and E))))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19948.        ((A -> (B or A)) and ((C -> (not (D -> (E -> (D and E))))) -> (not C))), M:tm-42, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19949
in-theory        19949
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not (D -> (E -> (D and E))))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19949.        ((A -> (A or B)) and ((C -> (not (D -> (E -> (D and E))))) -> (not C))), M:tm-32, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19950
in-theory        19950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> (B and C))))) -> ((A -> (not (B -> (C -> (B and C))))) and (not A)))
theorem-size     24
proof            (modus-ponens tm-24 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       98
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19950.        ((A -> (not (B -> (C -> (B and C))))) -> ((A -> (not (B -> (C -> (B and C))))) and (not A))), M:tm-24, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-19951
in-theory        19951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not (D -> (E -> (D and E))))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19951.        ((A -> (B -> (A and B))) and ((C -> (not (D -> (E -> (D and E))))) -> (not C))), M:tm-23, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19952
in-theory        19952
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not (D -> (E -> (D and E))))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19952.        (((A and B) -> B) and ((C -> (not (D -> (E -> (D and E))))) -> (not C))), M:tm-22, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19953
in-theory        19953
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not (D -> (E -> (D and E))))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19953.        (((A and B) -> A) and ((C -> (not (D -> (E -> (D and E))))) -> (not C))), M:tm-21, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19954
in-theory        19954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19954.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-20, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19955
in-theory        19955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not (D -> (E -> (D and E))))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19955.        ((A -> (B -> A)) and ((C -> (not (D -> (E -> (D and E))))) -> (not C))), M:tm-19, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19956
in-theory        19956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> (B and C))))) -> (A -> (not (B -> (C -> (B and C))))))
theorem-size     21
proof            (modus-ponens tm-12 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19956.        ((A -> (not (B -> (C -> (B and C))))) -> (A -> (not (B -> (C -> (B and C)))))), M:tm-12, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-19957
in-theory        19957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not (not A))) -> (not (A -> (not (B -> (C -> (B and C)))))))
theorem-size     26
proof            (modus-ponens tm-9 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       82
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19957.        (((A -> (not (B -> (C -> (B and C))))) -> (not (not A))) -> (not (A -> (not (B -> (C -> (B and C))))))), M:tm-9, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-19958
in-theory        19958
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not (C -> (D -> (C and D))))) or (not A)) -> B))
theorem-size     20
proof            (modus-ponens tm-8 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-1 tm-5)
proof-size       78
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19958.        (((not A) -> B) -> (((A -> (not (C -> (D -> (C and D))))) or (not A)) -> B)), M:tm-8, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-19959
in-theory        19959
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not (C -> (D -> (C and D))))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-1 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19959.        (A or ((B -> (not (C -> (D -> (C and D))))) -> (not B))), M:tm-7, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19960
in-theory        19960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-1 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19960.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) or D), M:tm-6, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19961
in-theory        19961
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not (C -> (D -> (C and D))))) -> (not B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19961.        (A -> (((B -> (not (C -> (D -> (C and D))))) -> (not B)) and A)), M:tm-5, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19962
in-theory        19962
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not (C -> (D -> (C and D))))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19962.        (A -> ((B -> (not (C -> (D -> (C and D))))) -> (not B))), M:tm-1, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-19963
in-theory        19963
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> (B -> (C -> (B and C)))))
theorem-size     19
proof            (modus-ponens tm-351 tm-1 ((Am (-> A (-> B (and A B)))) (C (-> Bm (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19963.        ((A or (B -> (C -> (B and C)))) -> (D -> (B -> (C -> (B and C))))), M:tm-351, m:tm-1, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (-> A (-> B (and A B))))))
================================================================
tm-name          tm-19964
in-theory        19964
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> C) -> (B -> (B and C))))
theorem-size     19
proof            (modus-ponens tm-351 tm-2 ((A Am) (B Bm) (Cm (and Am Bm)) (C (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-19964.        ((A or (B -> (C -> (B and C)))) -> ((B -> C) -> (B -> (B and C)))), M:tm-351, m:tm-2, u:((A Am) (B Bm) (Cm (and Am Bm)) (C (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-19965
in-theory        19965
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> ((B -> (C -> (B and C))) and D)))
theorem-size     21
proof            (modus-ponens tm-351 tm-5 ((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> A (-> B (and A B))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19965.        ((A or (B -> (C -> (B and C)))) -> (D -> ((B -> (C -> (B and C))) and D))), M:tm-351, m:tm-5, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> A (-> B (and A B))) Bm))))
================================================================
tm-name          tm-19966
in-theory        19966
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) or D))
theorem-size     19
proof            (modus-ponens tm-351 tm-6 ((Am (-> A (-> B (and A B)))) (C (or (-> A (-> B (and A B))) Bm))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-19966.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) or D)), M:tm-351, m:tm-6, u:((Am (-> A (-> B (and A B)))) (C (or (-> A (-> B (and A B))) Bm)))
================================================================
tm-name          tm-19967
in-theory        19967
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D or (B -> (C -> (B and C)))))
theorem-size     19
proof            (modus-ponens tm-351 tm-7 ((Am (-> A (-> B (and A B)))) (C (or Bm (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-19967.        ((A or (B -> (C -> (B and C)))) -> (D or (B -> (C -> (B and C))))), M:tm-351, m:tm-7, u:((Am (-> A (-> B (and A B)))) (C (or Bm (-> A (-> B (and A B))))))
================================================================
tm-name          tm-19968
in-theory        19968
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((C -> (B and C)) -> D) -> ((B or (C -> (B and C))) -> D)))
theorem-size     27
proof            (modus-ponens tm-351 tm-8 ((A Am) (Bm (-> B (and Am B))) (C (-> (-> (-> B (and Am B)) Cm) (-> (or Am (-> B (and Am B))) Cm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19968.        ((A or (B -> (C -> (B and C)))) -> (((C -> (B and C)) -> D) -> ((B or (C -> (B and C))) -> D))), M:tm-351, m:tm-8, u:((A Am) (Bm (-> B (and Am B))) (C (-> (-> (-> B (and Am B)) Cm) (-> (or Am (-> B (and Am B))) Cm))))
================================================================
tm-name          tm-19969
in-theory        19969
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (not (C -> (B and C)))) -> (not B)))
theorem-size     21
proof            (modus-ponens tm-351 tm-9 ((A Am) (Bm (-> B (and Am B))) (C (-> (-> Am (not (-> B (and Am B)))) (not Am)))))
axioms-used      (tm-8 tm-1 tm-5 tm-9)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19969.        ((A or (B -> (C -> (B and C)))) -> ((B -> (not (C -> (B and C)))) -> (not B))), M:tm-351, m:tm-9, u:((A Am) (Bm (-> B (and Am B))) (C (-> (-> Am (not (-> B (and Am B)))) (not Am))))
================================================================
tm-name          tm-19970
in-theory        19970
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-351 tm-11 ((Am (-> A (-> B (and A B)))) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-19970.        ((A or (B -> (C -> (B and C)))) -> (D -> (E -> D))), M:tm-351, m:tm-11, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-19971
in-theory        19971
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (B -> B))
theorem-size     13
proof            (modus-ponens tm-351 tm-12 ((A Am) (Bm (-> B (and Am B))) (C (-> Am Am))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-19971.        ((A or (B -> (C -> (B and C)))) -> (B -> B)), M:tm-351, m:tm-12, u:((A Am) (Bm (-> B (and Am B))) (C (-> Am Am)))
================================================================
tm-name          tm-19972
in-theory        19972
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-351 tm-14 ((Am (-> A (-> B (and A B)))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19972.        ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-351, m:tm-14, u:((Am (-> A (-> B (and A B)))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-19973
in-theory        19973
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-351 tm-16 ((Am (-> A (-> B (and A B)))) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19973.        ((A or (B -> (C -> (B and C)))) -> ((D and E) -> D)), M:tm-351, m:tm-16, u:((Am (-> A (-> B (and A B)))) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-19974
in-theory        19974
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-351 tm-18 ((Am (-> A (-> B (and A B)))) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19974.        ((A or (B -> (C -> (B and C)))) -> ((D and E) -> E)), M:tm-351, m:tm-18, u:((Am (-> A (-> B (and A B)))) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-19975
in-theory        19975
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> D)) and (B -> (C -> (B and C)))))
theorem-size     23
proof            (modus-ponens tm-351 tm-19 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> Cm Bm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-19975.        ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> D)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-19, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> Cm Bm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-19976
in-theory        19976
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (C -> (B and C)))))
theorem-size     31
proof            (modus-ponens tm-351 tm-20 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19976.        ((A or (B -> (C -> (B and C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-20, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-19977
in-theory        19977
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D and E) -> D) and (B -> (C -> (B and C)))))
theorem-size     23
proof            (modus-ponens tm-351 tm-21 ((Am (-> A (-> B (and A B)))) (C (and (-> (and Bm Cm) Bm) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19977.        ((A or (B -> (C -> (B and C)))) -> (((D and E) -> D) and (B -> (C -> (B and C))))), M:tm-351, m:tm-21, u:((Am (-> A (-> B (and A B)))) (C (and (-> (and Bm Cm) Bm) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-19978
in-theory        19978
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D and E) -> E) and (B -> (C -> (B and C)))))
theorem-size     23
proof            (modus-ponens tm-351 tm-22 ((Am (-> A (-> B (and A B)))) (C (and (-> (and Bm Cm) Cm) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19978.        ((A or (B -> (C -> (B and C)))) -> (((D and E) -> E) and (B -> (C -> (B and C))))), M:tm-351, m:tm-22, u:((Am (-> A (-> B (and A B)))) (C (and (-> (and Bm Cm) Cm) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-19979
in-theory        19979
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> (D and E))) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-23 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19979.        ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> (D and E))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-23, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-19980
in-theory        19980
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (B -> (B and (C -> (B and C)))))
theorem-size     19
proof            (modus-ponens tm-351 tm-24 ((A Am) (Bm (-> B (and Am B))) (C (-> Am (and Am (-> B (and Am B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19980.        ((A or (B -> (C -> (B and C)))) -> (B -> (B and (C -> (B and C))))), M:tm-351, m:tm-24, u:((A Am) (Bm (-> B (and Am B))) (C (-> Am (and Am (-> B (and Am B))))))
================================================================
tm-name          tm-19981
in-theory        19981
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-351 tm-25 ((Am (-> A (-> B (and A B)))) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19981.        ((A or (B -> (C -> (B and C)))) -> (D -> (E -> (D and E)))), M:tm-351, m:tm-25, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-19982
in-theory        19982
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (D or E)) and (B -> (C -> (B and C)))))
theorem-size     23
proof            (modus-ponens tm-351 tm-32 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (or Bm Cm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19982.        ((A or (B -> (C -> (B and C)))) -> ((D -> (D or E)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-32, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (or Bm Cm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-19983
in-theory        19983
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-351 tm-33 ((Am (-> A (-> B (and A B)))) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19983.        ((A or (B -> (C -> (B and C)))) -> (D -> (D or E))), M:tm-351, m:tm-33, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-19984
in-theory        19984
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (E or D)) and (B -> (C -> (B and C)))))
theorem-size     23
proof            (modus-ponens tm-351 tm-42 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (or Cm Bm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19984.        ((A or (B -> (C -> (B and C)))) -> ((D -> (E or D)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-42, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (or Cm Bm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-19985
in-theory        19985
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-351 tm-43 ((Am (-> A (-> B (and A B)))) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19985.        ((A or (B -> (C -> (B and C)))) -> (D -> (E or D))), M:tm-351, m:tm-43, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-19986
in-theory        19986
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (D -> ((B -> C) and D)))) -> ((C or (B -> C)) -> (D -> ((B -> C) and D))))
theorem-size     27
proof            (modus-ponens tm-351 tm-44 ((A (-> Am Bm)) (Cm (-> B (and (-> Am Bm) B))) (C (-> (or Bm (-> Am Bm)) (-> B (and (-> Am Bm) B))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19986.        ((A or ((B -> C) -> (D -> ((B -> C) and D)))) -> ((C or (B -> C)) -> (D -> ((B -> C) and D)))), M:tm-351, m:tm-44, u:((A (-> Am Bm)) (Cm (-> B (and (-> Am Bm) B))) (C (-> (or Bm (-> Am Bm)) (-> B (and (-> Am Bm) B)))))
================================================================
tm-name          tm-19987
in-theory        19987
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (E -> (((B -> C) -> (B -> D)) and E)))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (((B -> C) -> (B -> D)) and E))))
theorem-size     47
proof            (modus-ponens tm-351 tm-45 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (-> B (and (-> (-> Am Bm) (-> Am Cm)) B))) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B (and (-> (-> Am Bm) (-> Am Cm)) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19987.        ((A or (((B -> C) -> (B -> D)) -> (E -> (((B -> C) -> (B -> D)) and E)))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (((B -> C) -> (B -> D)) and E)))), M:tm-351, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (-> B (and (-> (-> Am Bm) (-> Am Cm)) B))) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B (and (-> (-> Am Bm) (-> Am Cm)) B)))))
================================================================
tm-name          tm-19988
in-theory        19988
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((B and D) or B) -> (C -> (B and C))))
theorem-size     21
proof            (modus-ponens tm-351 tm-46 ((A Am) (Bm (-> B (and Am B))) (C (-> (or (and Am Cm) Am) (-> B (and Am B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19988.        ((A or (B -> (C -> (B and C)))) -> (((B and D) or B) -> (C -> (B and C)))), M:tm-351, m:tm-46, u:((A Am) (Bm (-> B (and Am B))) (C (-> (or (and Am Cm) Am) (-> B (and Am B)))))
================================================================
tm-name          tm-19989
in-theory        19989
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D and B) or B) -> (C -> (B and C))))
theorem-size     21
proof            (modus-ponens tm-351 tm-47 ((A Am) (Bm (-> B (and Am B))) (C (-> (or (and Cm Am) Am) (-> B (and Am B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19989.        ((A or (B -> (C -> (B and C)))) -> (((D and B) or B) -> (C -> (B and C)))), M:tm-351, m:tm-47, u:((A Am) (Bm (-> B (and Am B))) (C (-> (or (and Cm Am) Am) (-> B (and Am B)))))
================================================================
tm-name          tm-19990
in-theory        19990
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (D -> ((B -> (C and B)) and D)))) -> ((C or (B -> (C and B))) -> (D -> ((B -> (C and B)) and D))))
theorem-size     35
proof            (modus-ponens tm-351 tm-48 ((A (-> Am (and Bm Am))) (Cm (-> B (and (-> Am (and Bm Am)) B))) (C (-> (or Bm (-> Am (and Bm Am))) (-> B (and (-> Am (and Bm Am)) B))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-19990.        ((A or ((B -> (C and B)) -> (D -> ((B -> (C and B)) and D)))) -> ((C or (B -> (C and B))) -> (D -> ((B -> (C and B)) and D)))), M:tm-351, m:tm-48, u:((A (-> Am (and Bm Am))) (Cm (-> B (and (-> Am (and Bm Am)) B))) (C (-> (or Bm (-> Am (and Bm Am))) (-> B (and (-> Am (and Bm Am)) B)))))
================================================================
tm-name          tm-19991
in-theory        19991
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D -> ((B or C) and D)))) -> ((B or (B or C)) -> (D -> ((B or C) and D))))
theorem-size     27
proof            (modus-ponens tm-351 tm-49 ((A (or Am Bm)) (Cm (-> B (and (or Am Bm) B))) (C (-> (or Am (or Am Bm)) (-> B (and (or Am Bm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-19991.        ((A or ((B or C) -> (D -> ((B or C) and D)))) -> ((B or (B or C)) -> (D -> ((B or C) and D)))), M:tm-351, m:tm-49, u:((A (or Am Bm)) (Cm (-> B (and (or Am Bm) B))) (C (-> (or Am (or Am Bm)) (-> B (and (or Am Bm) B)))))
================================================================
tm-name          tm-19992
in-theory        19992
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D -> ((B or C) and D)))) -> ((C or (B or C)) -> (D -> ((B or C) and D))))
theorem-size     27
proof            (modus-ponens tm-351 tm-50 ((A (or Am Bm)) (Cm (-> B (and (or Am Bm) B))) (C (-> (or Bm (or Am Bm)) (-> B (and (or Am Bm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-19992.        ((A or ((B or C) -> (D -> ((B or C) and D)))) -> ((C or (B or C)) -> (D -> ((B or C) and D)))), M:tm-351, m:tm-50, u:((A (or Am Bm)) (Cm (-> B (and (or Am Bm) B))) (C (-> (or Bm (or Am Bm)) (-> B (and (or Am Bm) B)))))
================================================================
tm-name          tm-19993
in-theory        19993
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (E -> (((B -> C) -> ((D or B) -> C)) and E)))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (E -> (((B -> C) -> ((D or B) -> C)) and E))))
theorem-size     53
proof            (modus-ponens tm-351 tm-51 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> B (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> B (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-19993.        ((A or (((B -> C) -> ((D or B) -> C)) -> (E -> (((B -> C) -> ((D or B) -> C)) and E)))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (E -> (((B -> C) -> ((D or B) -> C)) and E)))), M:tm-351, m:tm-51, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (-> B (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> B (and (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)))))
================================================================
tm-name          tm-19994
in-theory        19994
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B -> (C -> (B and C)))))
theorem-size     31
proof            (modus-ponens tm-351 tm-54 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-19994.        ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-54, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-19995
in-theory        19995
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (C -> ((B -> C) and C)))) -> ((B -> C) -> ((B or C) -> ((B -> C) and C))))
theorem-size     27
proof            (modus-ponens tm-351 tm-55 ((A (-> Am Bm)) (B Bm) (Cm (and (-> Am Bm) Bm)) (C (-> (-> Am Bm) (-> (or Am Bm) (and (-> Am Bm) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-19995.        ((A or ((B -> C) -> (C -> ((B -> C) and C)))) -> ((B -> C) -> ((B or C) -> ((B -> C) and C)))), M:tm-351, m:tm-55, u:((A (-> Am Bm)) (B Bm) (Cm (and (-> Am Bm) Bm)) (C (-> (-> Am Bm) (-> (or Am Bm) (and (-> Am Bm) Bm)))))
================================================================
tm-name          tm-19996
in-theory        19996
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-351 tm-56 ((Am (-> A (-> B (and A B)))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-19996.        ((A or (B -> (C -> (B and C)))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-351, m:tm-56, u:((Am (-> A (-> B (and A B)))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-19997
in-theory        19997
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (not C)) -> (not B)) -> (D -> (((B -> (not C)) -> (not B)) and D)))) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> (D -> (((B -> (not C)) -> (not B)) and D))))
theorem-size     45
proof            (modus-ponens tm-351 tm-66 ((A (-> (-> Am (not Bm)) (not Am))) (Cm (-> B (and (-> (-> Am (not Bm)) (not Am)) B))) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (-> B (and (-> (-> Am (not Bm)) (not Am)) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-9)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-19997.        ((A or (((B -> (not C)) -> (not B)) -> (D -> (((B -> (not C)) -> (not B)) and D)))) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> (D -> (((B -> (not C)) -> (not B)) and D)))), M:tm-351, m:tm-66, u:((A (-> (-> Am (not Bm)) (not Am))) (Cm (-> B (and (-> (-> Am (not Bm)) (not Am)) B))) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (-> B (and (-> (-> Am (not Bm)) (not Am)) B)))))
================================================================
tm-name          tm-19998
in-theory        19998
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (B -> (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-351 tm-69 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-19998.        ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-69, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-19999
in-theory        19999
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-351 tm-71 ((Am (-> A (-> B (and A B)))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-19999.        ((A or (B -> (C -> (B and C)))) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-351, m:tm-71, u:((Am (-> A (-> B (and A B)))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-20000
in-theory        20000
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((not (not B)) or B) -> (C -> (B and C))))
theorem-size     21
proof            (modus-ponens tm-351 tm-73 ((A Am) (Bm (-> B (and Am B))) (C (-> (or (not (not Am)) Am) (-> B (and Am B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-10)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-20000.        ((A or (B -> (C -> (B and C)))) -> (((not (not B)) or B) -> (C -> (B and C)))), M:tm-351, m:tm-73, u:((A Am) (Bm (-> B (and Am B))) (C (-> (or (not (not Am)) Am) (-> B (and Am B)))))
================================================================
tm-name          tm-20001
in-theory        20001
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((not (not D)) -> D) and (B -> (C -> (B and C)))))
theorem-size     23
proof            (modus-ponens tm-351 tm-76 ((Am (-> A (-> B (and A B)))) (C (and (-> (not (not Bm)) Bm) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-20001.        ((A or (B -> (C -> (B and C)))) -> (((not (not D)) -> D) and (B -> (C -> (B and C))))), M:tm-351, m:tm-76, u:((Am (-> A (-> B (and A B)))) (C (and (-> (not (not Bm)) Bm) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20002
in-theory        20002
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-351 tm-78 ((Am (-> A (-> B (and A B)))) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-5 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-20002.        ((A or (B -> (C -> (B and C)))) -> ((not (not D)) -> D)), M:tm-351, m:tm-78, u:((Am (-> A (-> B (and A B)))) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-20003
in-theory        20003
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) -> (D -> ((B -> (C -> B)) and D)))) -> ((E or (B -> (C -> B))) -> (D -> ((B -> (C -> B)) and D))))
theorem-size     35
proof            (modus-ponens tm-351 tm-80 ((A (-> Am (-> Bm Am))) (Cm (-> B (and (-> Am (-> Bm Am)) B))) (C (-> (or Dm (-> Am (-> Bm Am))) (-> B (and (-> Am (-> Bm Am)) B))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20003.        ((A or ((B -> (C -> B)) -> (D -> ((B -> (C -> B)) and D)))) -> ((E or (B -> (C -> B))) -> (D -> ((B -> (C -> B)) and D)))), M:tm-351, m:tm-80, u:((A (-> Am (-> Bm Am))) (Cm (-> B (and (-> Am (-> Bm Am)) B))) (C (-> (or Dm (-> Am (-> Bm Am))) (-> B (and (-> Am (-> Bm Am)) B)))))
================================================================
tm-name          tm-20004
in-theory        20004
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> (F -> E))) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-83 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-20004.        ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> (F -> E))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-83, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20005
in-theory        20005
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (B -> (D -> (C -> (B and C)))))
theorem-size     19
proof            (modus-ponens tm-351 tm-84 ((A Am) (Bm (-> B (and Am B))) (C (-> Am (-> Cm (-> B (and Am B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-20005.        ((A or (B -> (C -> (B and C)))) -> (B -> (D -> (C -> (B and C))))), M:tm-351, m:tm-84, u:((A Am) (Bm (-> B (and Am B))) (C (-> Am (-> Cm (-> B (and Am B))))))
================================================================
tm-name          tm-20006
in-theory        20006
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-351 tm-85 ((Am (-> A (-> B (and A B)))) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-20006.        ((A or (B -> (C -> (B and C)))) -> (D -> (E -> (F -> E)))), M:tm-351, m:tm-85, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-20007
in-theory        20007
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (B -> (C -> (B and C))))
theorem-size     17
proof            (modus-ponens tm-351 tm-86 ((Am (-> A (-> B (and A B)))) (C (-> A (-> B (and A B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20007.        ((A or (B -> (C -> (B and C)))) -> (B -> (C -> (B and C)))), M:tm-351, m:tm-86, u:((Am (-> A (-> B (and A B)))) (C (-> A (-> B (and A B)))))
================================================================
tm-name          tm-20008
in-theory        20008
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> B) -> (C -> ((B -> B) and C)))) -> (((B -> D) or (B -> B)) -> (C -> ((B -> B) and C))))
theorem-size     29
proof            (modus-ponens tm-351 tm-92 ((A (-> Am Am)) (Bm (-> B (and (-> Am Am) B))) (C (-> (or (-> Am Cm) (-> Am Am)) (-> B (and (-> Am Am) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-20008.        ((A or ((B -> B) -> (C -> ((B -> B) and C)))) -> (((B -> D) or (B -> B)) -> (C -> ((B -> B) and C)))), M:tm-351, m:tm-92, u:((A (-> Am Am)) (Bm (-> B (and (-> Am Am) B))) (C (-> (or (-> Am Cm) (-> Am Am)) (-> B (and (-> Am Am) B)))))
================================================================
tm-name          tm-20009
in-theory        20009
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> (D -> D)) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-95 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20009.        ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> (D -> D)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-95, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20010
in-theory        20010
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-351 tm-97 ((Am (-> A (-> B (and A B)))) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20010.        ((A or (B -> (C -> (B and C)))) -> ((D -> E) -> (D -> D))), M:tm-351, m:tm-97, u:((Am (-> A (-> B (and A B)))) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-20011
in-theory        20011
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> B) -> (B and (C -> B))))) -> (B -> (B and (C -> B))))
theorem-size     21
proof            (modus-ponens tm-351 tm-98 ((A Am) (B (-> Bm Am)) (Cm (and Am (-> Bm Am))) (C (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-20011.        ((A or (B -> ((C -> B) -> (B and (C -> B))))) -> (B -> (B and (C -> B)))), M:tm-351, m:tm-98, u:((A Am) (B (-> Bm Am)) (Cm (and Am (-> Bm Am))) (C (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-20012
in-theory        20012
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B -> (B and B)))) -> (B -> (B and B)))
theorem-size     15
proof            (modus-ponens tm-351 tm-99 ((A Am) (B Am) (Bm (and Am Am)) (C (-> Am (and Am Am)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-20012.        ((A or (B -> (B -> (B and B)))) -> (B -> (B and B))), M:tm-351, m:tm-99, u:((A Am) (B Am) (Bm (and Am Am)) (C (-> Am (and Am Am))))
================================================================
tm-name          tm-20013
in-theory        20013
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> D)) -> (E -> (((B -> (C -> D)) -> (B -> D)) and E)))) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> (E -> (((B -> (C -> D)) -> (B -> D)) and E))))
theorem-size     59
proof            (modus-ponens tm-351 tm-102 ((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (Dm (-> B (and (-> (-> Am (-> Bm Cm)) (-> Am Cm)) B))) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> B (and (-> (-> Am (-> Bm Cm)) (-> Am Cm)) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-20013.        ((A or (((B -> (C -> D)) -> (B -> D)) -> (E -> (((B -> (C -> D)) -> (B -> D)) and E)))) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> (E -> (((B -> (C -> D)) -> (B -> D)) and E)))), M:tm-351, m:tm-102, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (Dm (-> B (and (-> (-> Am (-> Bm Cm)) (-> Am Cm)) B))) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> B (and (-> (-> Am (-> Bm Cm)) (-> Am Cm)) B)))))
================================================================
tm-name          tm-20014
in-theory        20014
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (B -> (C -> (B and C)))))
theorem-size     37
proof            (modus-ponens tm-351 tm-105 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20014.        ((A or (B -> (C -> (B and C)))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-105, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20015
in-theory        20015
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-351 tm-107 ((Am (-> A (-> B (and A B)))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20015.        ((A or (B -> (C -> (B and C)))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-351, m:tm-107, u:((Am (-> A (-> B (and A B)))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-20016
in-theory        20016
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D)))))) -> ((B -> (C -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D)))))
theorem-size     49
proof            (modus-ponens tm-351 tm-108 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-20016.        ((A or ((B -> (C -> D)) -> (((B -> C) -> (B -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D)))))) -> ((B -> (C -> D)) -> ((B -> (C -> D)) and ((B -> C) -> (B -> D))))), M:tm-351, m:tm-108, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-20017
in-theory        20017
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E))))
theorem-size     67
proof            (modus-ponens tm-351 tm-110 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20017.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))), M:tm-351, m:tm-110, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)))))
================================================================
tm-name          tm-20018
in-theory        20018
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (C -> (B and C)))))
theorem-size     33
proof            (modus-ponens tm-351 tm-113 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20018.        ((A or (B -> (C -> (B and C)))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-113, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20019
in-theory        20019
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-115 ((Am (-> A (-> B (and A B)))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20019.        ((A or (B -> (C -> (B and C)))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-351, m:tm-115, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-20020
in-theory        20020
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> C) -> (E -> ((((B -> C) and D) -> C) and E)))) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> (E -> ((((B -> C) and D) -> C) and E))))
theorem-size     49
proof            (modus-ponens tm-351 tm-122 ((A (-> (and (-> Am Bm) Cm) Bm)) (Dm (-> B (and (-> (and (-> Am Bm) Cm) Bm) B))) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (-> B (and (-> (and (-> Am Bm) Cm) Bm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-3)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-20020.        ((A or ((((B -> C) and D) -> C) -> (E -> ((((B -> C) and D) -> C) and E)))) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> (E -> ((((B -> C) and D) -> C) and E)))), M:tm-351, m:tm-122, u:((A (-> (and (-> Am Bm) Cm) Bm)) (Dm (-> B (and (-> (and (-> Am Bm) Cm) Bm) B))) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (-> B (and (-> (and (-> Am Bm) Cm) Bm) B)))))
================================================================
tm-name          tm-20021
in-theory        20021
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (B -> (C -> (B and C)))))
theorem-size     33
proof            (modus-ponens tm-351 tm-125 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20021.        ((A or (B -> (C -> (B and C)))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-125, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20022
in-theory        20022
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-351 tm-127 ((Am (-> A (-> B (and A B)))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20022.        ((A or (B -> (C -> (B and C)))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-351, m:tm-127, u:((Am (-> A (-> B (and A B)))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-20023
in-theory        20023
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> (B -> ((B and C) and B)))) -> ((B and C) -> ((B and C) and B)))
theorem-size     23
proof            (modus-ponens tm-351 tm-129 ((A (and Am Bm)) (B Am) (Cm (and (and Am Bm) Am)) (C (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-20023.        ((A or ((B and C) -> (B -> ((B and C) and B)))) -> ((B and C) -> ((B and C) and B))), M:tm-351, m:tm-129, u:((A (and Am Bm)) (B Am) (Cm (and (and Am Bm) Am)) (C (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-20024
in-theory        20024
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) -> (D -> (((B and C) -> B) and D)))) -> ((E or ((B and C) -> B)) -> (D -> (((B and C) -> B) and D))))
theorem-size     35
proof            (modus-ponens tm-351 tm-131 ((A (-> (and Am Bm) Am)) (Cm (-> B (and (-> (and Am Bm) Am) B))) (C (-> (or Dm (-> (and Am Bm) Am)) (-> B (and (-> (and Am Bm) Am) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20024.        ((A or (((B and C) -> B) -> (D -> (((B and C) -> B) and D)))) -> ((E or ((B and C) -> B)) -> (D -> (((B and C) -> B) and D)))), M:tm-351, m:tm-131, u:((A (-> (and Am Bm) Am)) (Cm (-> B (and (-> (and Am Bm) Am) B))) (C (-> (or Dm (-> (and Am Bm) Am)) (-> B (and (-> (and Am Bm) Am) B)))))
================================================================
tm-name          tm-20025
in-theory        20025
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> ((E and F) -> E)) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-134 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-20025.        ((A or (B -> (C -> (B and C)))) -> ((D -> ((E and F) -> E)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-134, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20026
in-theory        20026
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-351 tm-136 ((Am (-> A (-> B (and A B)))) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-20026.        ((A or (B -> (C -> (B and C)))) -> (D -> ((E and F) -> E))), M:tm-351, m:tm-136, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-20027
in-theory        20027
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> D) -> (E -> (((B and (C -> D)) -> D) and E)))) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> (E -> (((B and (C -> D)) -> D) and E))))
theorem-size     49
proof            (modus-ponens tm-351 tm-144 ((A (-> (and Am (-> Bm Cm)) Cm)) (Dm (-> B (and (-> (and Am (-> Bm Cm)) Cm) B))) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (-> B (and (-> (and Am (-> Bm Cm)) Cm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-4)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-20027.        ((A or (((B and (C -> D)) -> D) -> (E -> (((B and (C -> D)) -> D) and E)))) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> (E -> (((B and (C -> D)) -> D) and E)))), M:tm-351, m:tm-144, u:((A (-> (and Am (-> Bm Cm)) Cm)) (Dm (-> B (and (-> (and Am (-> Bm Cm)) Cm) B))) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (-> B (and (-> (and Am (-> Bm Cm)) Cm) B)))))
================================================================
tm-name          tm-20028
in-theory        20028
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (B -> (C -> (B and C)))))
theorem-size     33
proof            (modus-ponens tm-351 tm-147 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20028.        ((A or (B -> (C -> (B and C)))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-147, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20029
in-theory        20029
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-351 tm-149 ((Am (-> A (-> B (and A B)))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20029.        ((A or (B -> (C -> (B and C)))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-351, m:tm-149, u:((Am (-> A (-> B (and A B)))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-20030
in-theory        20030
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> (C -> ((B and C) and C)))) -> ((B and C) -> ((B and C) and C)))
theorem-size     23
proof            (modus-ponens tm-351 tm-152 ((A (and Am Bm)) (B Bm) (Cm (and (and Am Bm) Bm)) (C (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-20030.        ((A or ((B and C) -> (C -> ((B and C) and C)))) -> ((B and C) -> ((B and C) and C))), M:tm-351, m:tm-152, u:((A (and Am Bm)) (B Bm) (Cm (and (and Am Bm) Bm)) (C (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-20031
in-theory        20031
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) -> (D -> (((B and C) -> C) and D)))) -> ((E or ((B and C) -> C)) -> (D -> (((B and C) -> C) and D))))
theorem-size     35
proof            (modus-ponens tm-351 tm-154 ((A (-> (and Am Bm) Bm)) (Cm (-> B (and (-> (and Am Bm) Bm) B))) (C (-> (or Dm (-> (and Am Bm) Bm)) (-> B (and (-> (and Am Bm) Bm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20031.        ((A or (((B and C) -> C) -> (D -> (((B and C) -> C) and D)))) -> ((E or ((B and C) -> C)) -> (D -> (((B and C) -> C) and D)))), M:tm-351, m:tm-154, u:((A (-> (and Am Bm) Bm)) (Cm (-> B (and (-> (and Am Bm) Bm) B))) (C (-> (or Dm (-> (and Am Bm) Bm)) (-> B (and (-> (and Am Bm) Bm) B)))))
================================================================
tm-name          tm-20032
in-theory        20032
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> ((E and F) -> F)) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-157 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-20032.        ((A or (B -> (C -> (B and C)))) -> ((D -> ((E and F) -> F)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-157, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20033
in-theory        20033
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-351 tm-159 ((Am (-> A (-> B (and A B)))) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-20033.        ((A or (B -> (C -> (B and C)))) -> (D -> ((E and F) -> F))), M:tm-351, m:tm-159, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-20034
in-theory        20034
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> B)) and D) -> (E -> (((B -> (C -> B)) and D) and E)))) -> ((D or ((B -> (C -> B)) and D)) -> (E -> (((B -> (C -> B)) and D) and E))))
theorem-size     43
proof            (modus-ponens tm-351 tm-180 ((A (and (-> Am (-> Bm Am)) Cm)) (Dm (-> B (and (and (-> Am (-> Bm Am)) Cm) B))) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (-> B (and (and (-> Am (-> Bm Am)) Cm) B))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20034.        ((A or (((B -> (C -> B)) and D) -> (E -> (((B -> (C -> B)) and D) and E)))) -> ((D or ((B -> (C -> B)) and D)) -> (E -> (((B -> (C -> B)) and D) and E)))), M:tm-351, m:tm-180, u:((A (and (-> Am (-> Bm Am)) Cm)) (Dm (-> B (and (and (-> Am (-> Bm Am)) Cm) B))) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (-> B (and (and (-> Am (-> Bm Am)) Cm) B)))))
================================================================
tm-name          tm-20035
in-theory        20035
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> ((E -> (F -> E)) and D)) and (B -> (C -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-351 tm-183 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-20035.        ((A or (B -> (C -> (B and C)))) -> ((D -> ((E -> (F -> E)) and D)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-183, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20036
in-theory        20036
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-351 tm-184 ((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-20036.        ((A or (B -> (C -> (B and C)))) -> (D -> ((E -> (F -> E)) and D))), M:tm-351, m:tm-184, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-20037
in-theory        20037
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> (F -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) and F)))) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> (F -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) and F))))
theorem-size     75
proof            (modus-ponens tm-351 tm-207 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> B (and (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B))) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> B (and (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-20037.        ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> (F -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) and F)))) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> (F -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) and F)))), M:tm-351, m:tm-207, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> B (and (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B))) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> B (and (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B)))))
================================================================
tm-name          tm-20038
in-theory        20038
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (B -> (C -> (B and C)))))
theorem-size     35
proof            (modus-ponens tm-351 tm-210 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-20038.        ((A or (B -> (C -> (B and C)))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-210, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20039
in-theory        20039
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-351 tm-211 ((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-20039.        ((A or (B -> (C -> (B and C)))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-351, m:tm-211, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-20040
in-theory        20040
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> B) and D) -> (E -> ((((B and C) -> B) and D) and E)))) -> ((D or (((B and C) -> B) and D)) -> (E -> ((((B and C) -> B) and D) and E))))
theorem-size     43
proof            (modus-ponens tm-351 tm-236 ((A (and (-> (and Am Bm) Am) Cm)) (Dm (-> B (and (and (-> (and Am Bm) Am) Cm) B))) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (-> B (and (and (-> (and Am Bm) Am) Cm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20040.        ((A or ((((B and C) -> B) and D) -> (E -> ((((B and C) -> B) and D) and E)))) -> ((D or (((B and C) -> B) and D)) -> (E -> ((((B and C) -> B) and D) and E)))), M:tm-351, m:tm-236, u:((A (and (-> (and Am Bm) Am) Cm)) (Dm (-> B (and (and (-> (and Am Bm) Am) Cm) B))) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (-> B (and (and (-> (and Am Bm) Am) Cm) B)))))
================================================================
tm-name          tm-20041
in-theory        20041
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (((E and F) -> E) and D)) and (B -> (C -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-351 tm-239 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-20041.        ((A or (B -> (C -> (B and C)))) -> ((D -> (((E and F) -> E) and D)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-239, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20042
in-theory        20042
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-351 tm-240 ((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-20042.        ((A or (B -> (C -> (B and C)))) -> (D -> (((E and F) -> E) and D))), M:tm-351, m:tm-240, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-20043
in-theory        20043
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> C) and D) -> (E -> ((((B and C) -> C) and D) and E)))) -> ((D or (((B and C) -> C) and D)) -> (E -> ((((B and C) -> C) and D) and E))))
theorem-size     43
proof            (modus-ponens tm-351 tm-267 ((A (and (-> (and Am Bm) Bm) Cm)) (Dm (-> B (and (and (-> (and Am Bm) Bm) Cm) B))) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (-> B (and (and (-> (and Am Bm) Bm) Cm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20043.        ((A or ((((B and C) -> C) and D) -> (E -> ((((B and C) -> C) and D) and E)))) -> ((D or (((B and C) -> C) and D)) -> (E -> ((((B and C) -> C) and D) and E)))), M:tm-351, m:tm-267, u:((A (and (-> (and Am Bm) Bm) Cm)) (Dm (-> B (and (and (-> (and Am Bm) Bm) Cm) B))) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (-> B (and (and (-> (and Am Bm) Bm) Cm) B)))))
================================================================
tm-name          tm-20044
in-theory        20044
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (((E and F) -> F) and D)) and (B -> (C -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-351 tm-270 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-20044.        ((A or (B -> (C -> (B and C)))) -> ((D -> (((E and F) -> F) and D)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-270, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20045
in-theory        20045
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-351 tm-271 ((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-20045.        ((A or (B -> (C -> (B and C)))) -> (D -> (((E and F) -> F) and D))), M:tm-351, m:tm-271, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-20046
in-theory        20046
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> (B and C))) and D) -> (E -> (((B -> (C -> (B and C))) and D) and E)))) -> ((D or ((B -> (C -> (B and C))) and D)) -> (E -> (((B -> (C -> (B and C))) and D) and E))))
theorem-size     51
proof            (modus-ponens tm-351 tm-300 ((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (-> B (and (and (-> Am (-> Bm (and Am Bm))) Cm) B))) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (-> B (and (and (-> Am (-> Bm (and Am Bm))) Cm) B))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20046.        ((A or (((B -> (C -> (B and C))) and D) -> (E -> (((B -> (C -> (B and C))) and D) and E)))) -> ((D or ((B -> (C -> (B and C))) and D)) -> (E -> (((B -> (C -> (B and C))) and D) and E)))), M:tm-351, m:tm-300, u:((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (-> B (and (and (-> Am (-> Bm (and Am Bm))) Cm) B))) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (-> B (and (and (-> Am (-> Bm (and Am Bm))) Cm) B)))))
================================================================
tm-name          tm-20047
in-theory        20047
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> ((E -> (F -> (E and F))) and D)) and (B -> (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-351 tm-303 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-20047.        ((A or (B -> (C -> (B and C)))) -> ((D -> ((E -> (F -> (E and F))) and D)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-303, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20048
in-theory        20048
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-351 tm-304 ((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-20048.        ((A or (B -> (C -> (B and C)))) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-351, m:tm-304, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-20049
in-theory        20049
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (D -> (B -> (C -> (B and C))))))
theorem-size     27
proof            (modus-ponens tm-351 tm-305 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> Bm (-> A (-> B (and A B))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20049.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (D -> (B -> (C -> (B and C)))))), M:tm-351, m:tm-305, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> Bm (-> A (-> B (and A B)))))))
================================================================
tm-name          tm-20050
in-theory        20050
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((B -> C) -> (B -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-351 tm-306 ((A Am) (B Bm) (Cm (and Am Bm)) (C (and (-> Am (-> Bm (and Am Bm))) (-> (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20050.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((B -> C) -> (B -> (B and C))))), M:tm-351, m:tm-306, u:((A Am) (B Bm) (Cm (and Am Bm)) (C (and (-> Am (-> Bm (and Am Bm))) (-> (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-20051
in-theory        20051
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (D -> ((B -> (C -> (B and C))) and D))))
theorem-size     29
proof            (modus-ponens tm-351 tm-309 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> Bm (and (-> A (-> B (and A B))) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20051.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (D -> ((B -> (C -> (B and C))) and D)))), M:tm-351, m:tm-309, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> Bm (and (-> A (-> B (and A B))) Bm)))))
================================================================
tm-name          tm-20052
in-theory        20052
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((B -> (C -> (B and C))) or D)))
theorem-size     27
proof            (modus-ponens tm-351 tm-310 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (or (-> A (-> B (and A B))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20052.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((B -> (C -> (B and C))) or D))), M:tm-351, m:tm-310, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (or (-> A (-> B (and A B))) Bm))))
================================================================
tm-name          tm-20053
in-theory        20053
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (D or (B -> (C -> (B and C))))))
theorem-size     27
proof            (modus-ponens tm-351 tm-311 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (or Bm (-> A (-> B (and A B))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20053.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (D or (B -> (C -> (B and C)))))), M:tm-351, m:tm-311, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (or Bm (-> A (-> B (and A B)))))))
================================================================
tm-name          tm-20054
in-theory        20054
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (((C -> (B and C)) -> D) -> ((B or (C -> (B and C))) -> D))))
theorem-size     35
proof            (modus-ponens tm-351 tm-312 ((A Am) (Bm (-> B (and Am B))) (C (and (-> Am (-> B (and Am B))) (-> (-> (-> B (and Am B)) Cm) (-> (or Am (-> B (and Am B))) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-20054.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (((C -> (B and C)) -> D) -> ((B or (C -> (B and C))) -> D)))), M:tm-351, m:tm-312, u:((A Am) (Bm (-> B (and Am B))) (C (and (-> Am (-> B (and Am B))) (-> (-> (-> B (and Am B)) Cm) (-> (or Am (-> B (and Am B))) Cm)))))
================================================================
tm-name          tm-20055
in-theory        20055
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((B -> (not (C -> (B and C)))) -> (not B))))
theorem-size     29
proof            (modus-ponens tm-351 tm-313 ((A Am) (Bm (-> B (and Am B))) (C (and (-> Am (-> B (and Am B))) (-> (-> Am (not (-> B (and Am B)))) (not Am))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-9)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-20055.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((B -> (not (C -> (B and C)))) -> (not B)))), M:tm-351, m:tm-313, u:((A Am) (Bm (-> B (and Am B))) (C (and (-> Am (-> B (and Am B))) (-> (-> Am (not (-> B (and Am B)))) (not Am)))))
================================================================
tm-name          tm-20056
in-theory        20056
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (D -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-351 tm-315 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20056.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (D -> (E -> D)))), M:tm-351, m:tm-315, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-20057
in-theory        20057
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (B -> B)))
theorem-size     21
proof            (modus-ponens tm-351 tm-316 ((A Am) (Bm (-> B (and Am B))) (C (and (-> Am (-> B (and Am B))) (-> Am Am)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-20057.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (B -> B))), M:tm-351, m:tm-316, u:((A Am) (Bm (-> B (and Am B))) (C (and (-> Am (-> B (and Am B))) (-> Am Am))))
================================================================
tm-name          tm-20058
in-theory        20058
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-351 tm-318 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20058.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-351, m:tm-318, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-20059
in-theory        20059
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((D and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-351 tm-320 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20059.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((D and E) -> D))), M:tm-351, m:tm-320, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-20060
in-theory        20060
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((D and E) -> E)))
theorem-size     23
proof            (modus-ponens tm-351 tm-322 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20060.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((D and E) -> E))), M:tm-351, m:tm-322, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-20061
in-theory        20061
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((D -> (E -> D)) and (B -> (C -> (B and C))))))
theorem-size     31
proof            (modus-ponens tm-351 tm-323 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (and (-> Bm (-> Cm Bm)) (-> A (-> B (and A B))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20061.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((D -> (E -> D)) and (B -> (C -> (B and C)))))), M:tm-351, m:tm-323, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (and (-> Bm (-> Cm Bm)) (-> A (-> B (and A B)))))))
================================================================
tm-name          tm-20062
in-theory        20062
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (C -> (B and C))))))
theorem-size     39
proof            (modus-ponens tm-351 tm-324 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (-> B (and A B))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-20062.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (C -> (B and C)))))), M:tm-351, m:tm-324, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (-> B (and A B)))))))
================================================================
tm-name          tm-20063
in-theory        20063
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (((D and E) -> D) and (B -> (C -> (B and C))))))
theorem-size     31
proof            (modus-ponens tm-351 tm-325 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (and (-> (and Bm Cm) Bm) (-> A (-> B (and A B))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20063.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (((D and E) -> D) and (B -> (C -> (B and C)))))), M:tm-351, m:tm-325, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (and (-> (and Bm Cm) Bm) (-> A (-> B (and A B)))))))
================================================================
tm-name          tm-20064
in-theory        20064
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (((D and E) -> E) and (B -> (C -> (B and C))))))
theorem-size     31
proof            (modus-ponens tm-351 tm-326 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (and (-> (and Bm Cm) Cm) (-> A (-> B (and A B))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20064.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (((D and E) -> E) and (B -> (C -> (B and C)))))), M:tm-351, m:tm-326, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (and (-> (and Bm Cm) Cm) (-> A (-> B (and A B)))))))
================================================================
tm-name          tm-20065
in-theory        20065
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((D -> (E -> (D and E))) and (B -> (C -> (B and C))))))
theorem-size     33
proof            (modus-ponens tm-351 tm-327 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (and (-> Bm (-> Cm (and Bm Cm))) (-> A (-> B (and A B))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20065.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((D -> (E -> (D and E))) and (B -> (C -> (B and C)))))), M:tm-351, m:tm-327, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (and (-> Bm (-> Cm (and Bm Cm))) (-> A (-> B (and A B)))))))
================================================================
tm-name          tm-20066
in-theory        20066
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (B -> (B and (C -> (B and C))))))
theorem-size     27
proof            (modus-ponens tm-351 tm-328 ((A Am) (Bm (-> B (and Am B))) (C (and (-> Am (-> B (and Am B))) (-> Am (and Am (-> B (and Am B))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20066.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (B -> (B and (C -> (B and C)))))), M:tm-351, m:tm-328, u:((A Am) (Bm (-> B (and Am B))) (C (and (-> Am (-> B (and Am B))) (-> Am (and Am (-> B (and Am B)))))))
================================================================
tm-name          tm-20067
in-theory        20067
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B and C)) -> (D -> ((B -> (B and C)) and D)))) -> (((B -> C) or (B -> (B and C))) -> (D -> ((B -> (B and C)) and D))))
theorem-size     37
proof            (modus-ponens tm-351 tm-335 ((A (-> Am (and Am Bm))) (Cm (-> B (and (-> Am (and Am Bm)) B))) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) (-> B (and (-> Am (and Am Bm)) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20067.        ((A or ((B -> (B and C)) -> (D -> ((B -> (B and C)) and D)))) -> (((B -> C) or (B -> (B and C))) -> (D -> ((B -> (B and C)) and D)))), M:tm-351, m:tm-335, u:((A (-> Am (and Am Bm))) (Cm (-> B (and (-> Am (and Am Bm)) B))) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) (-> B (and (-> Am (and Am Bm)) B)))))
================================================================
tm-name          tm-20068
in-theory        20068
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> (D -> (D and E))) and (B -> (C -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-351 tm-338 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20068.        ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> (D -> (D and E))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-338, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20069
in-theory        20069
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-351 tm-340 ((Am (-> A (-> B (and A B)))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20069.        ((A or (B -> (C -> (B and C)))) -> ((D -> E) -> (D -> (D and E)))), M:tm-351, m:tm-340, u:((Am (-> A (-> B (and A B)))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-20070
in-theory        20070
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-341 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20070.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (D -> (E -> (D and E))))), M:tm-351, m:tm-341, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20071
in-theory        20071
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (B and C)) -> (B and (C -> (B and C)))))) -> (B -> (B and (C -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-351 tm-349 ((A Am) (B (-> Bm (and Am Bm))) (Cm (and Am (-> Bm (and Am Bm)))) (C (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-20071.        ((A or (B -> ((C -> (B and C)) -> (B and (C -> (B and C)))))) -> (B -> (B and (C -> (B and C))))), M:tm-351, m:tm-349, u:((A Am) (B (-> Bm (and Am Bm))) (Cm (and Am (-> Bm (and Am Bm)))) (C (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-20072
in-theory        20072
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) -> (D -> ((B -> (C -> (B and C))) and D)))) -> ((E or (B -> (C -> (B and C)))) -> (D -> ((B -> (C -> (B and C))) and D))))
theorem-size     43
proof            (modus-ponens tm-351 tm-351 ((A (-> Am (-> Bm (and Am Bm)))) (Cm (-> B (and (-> Am (-> Bm (and Am Bm))) B))) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> B (and (-> Am (-> Bm (and Am Bm))) B))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20072.        ((A or ((B -> (C -> (B and C))) -> (D -> ((B -> (C -> (B and C))) and D)))) -> ((E or (B -> (C -> (B and C)))) -> (D -> ((B -> (C -> (B and C))) and D)))), M:tm-351, m:tm-351, u:((A (-> Am (-> Bm (and Am Bm)))) (Cm (-> B (and (-> Am (-> Bm (and Am Bm))) B))) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> B (and (-> Am (-> Bm (and Am Bm))) B)))))
================================================================
tm-name          tm-20073
in-theory        20073
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20073.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20074
in-theory        20074
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E)))
theorem-size     31
proof            (modus-ponens tm-338 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20074.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E))), M:tm-338, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20075
in-theory        20075
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) or ((A -> (B -> (A and B))) -> ((A -> (B -> (A and B))) and C))) -> ((D or (A -> (B -> (A and B)))) -> ((A -> (B -> (A and B))) and C)))
theorem-size     47
proof            (modus-ponens tm-335 tm-351 ((A (-> Am (-> Bm (and Am Bm)))) (Cm (and (-> Am (-> Bm (and Am Bm))) B)) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (and (-> Am (-> Bm (and Am Bm))) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20075.        ((((A -> (B -> (A and B))) -> C) or ((A -> (B -> (A and B))) -> ((A -> (B -> (A and B))) and C))) -> ((D or (A -> (B -> (A and B)))) -> ((A -> (B -> (A and B))) and C))), M:tm-335, m:tm-351, u:((A (-> Am (-> Bm (and Am Bm)))) (Cm (and (-> Am (-> Bm (and Am Bm))) B)) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (and (-> Am (-> Bm (and Am Bm))) B))))
================================================================
tm-name          tm-20076
in-theory        20076
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (((A -> (B -> (A and B))) -> C) -> (((A -> (B -> (A and B))) -> C) and ((D or (A -> (B -> (A and B)))) -> C))))
theorem-size     53
proof            (modus-ponens tm-328 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20076.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (((A -> (B -> (A and B))) -> C) -> (((A -> (B -> (A and B))) -> C) and ((D or (A -> (B -> (A and B)))) -> C)))), M:tm-328, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-20077
in-theory        20077
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((E -> (F -> (E and F))) and (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C))))
theorem-size     51
proof            (modus-ponens tm-327 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20077.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((E -> (F -> (E and F))) and (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)))), M:tm-327, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20078
in-theory        20078
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (((E and F) -> F) and (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C))))
theorem-size     49
proof            (modus-ponens tm-326 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20078.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (((E and F) -> F) and (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)))), M:tm-326, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20079
in-theory        20079
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (((E and F) -> E) and (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C))))
theorem-size     49
proof            (modus-ponens tm-325 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20079.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (((E and F) -> E) and (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)))), M:tm-325, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20080
in-theory        20080
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C))))
theorem-size     57
proof            (modus-ponens tm-324 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20080.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)))), M:tm-324, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20081
in-theory        20081
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((E -> (F -> E)) and (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C))))
theorem-size     49
proof            (modus-ponens tm-323 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20081.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((E -> (F -> E)) and (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)))), M:tm-323, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20082
in-theory        20082
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20082.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20083
in-theory        20083
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20083.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20084
in-theory        20084
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20084.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20085
in-theory        20085
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (((A -> (B -> (A and B))) -> C) -> ((A -> (B -> (A and B))) -> C)))
theorem-size     41
proof            (modus-ponens tm-316 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20085.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (((A -> (B -> (A and B))) -> C) -> ((A -> (B -> (A and B))) -> C))), M:tm-316, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-20086
in-theory        20086
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20086.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20087
in-theory        20087
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((((A -> (B -> (A and B))) -> C) -> (not ((D or (A -> (B -> (A and B)))) -> C))) -> (not ((A -> (B -> (A and B))) -> C))))
theorem-size     55
proof            (modus-ponens tm-313 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20087.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((((A -> (B -> (A and B))) -> C) -> (not ((D or (A -> (B -> (A and B)))) -> C))) -> (not ((A -> (B -> (A and B))) -> C)))), M:tm-313, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-20088
in-theory        20088
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((((D or (A -> (B -> (A and B)))) -> C) -> E) -> ((((A -> (B -> (A and B))) -> C) or ((D or (A -> (B -> (A and B)))) -> C)) -> E)))
theorem-size     59
proof            (modus-ponens tm-312 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20088.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((((D or (A -> (B -> (A and B)))) -> C) -> E) -> ((((A -> (B -> (A and B))) -> C) or ((D or (A -> (B -> (A and B)))) -> C)) -> E))), M:tm-312, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-20089
in-theory        20089
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (E or (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C))))
theorem-size     45
proof            (modus-ponens tm-311 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20089.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (E or (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)))), M:tm-311, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20090
in-theory        20090
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20090.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) or E)), M:tm-310, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20091
in-theory        20091
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (E -> ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20091.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (E -> ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and E))), M:tm-309, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20092
in-theory        20092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((((A -> (B -> (A and B))) -> C) -> (D or (A -> (B -> (A and B))))) -> (((A -> (B -> (A and B))) -> C) -> C)))
theorem-size     53
proof            (modus-ponens tm-306 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (or Dm (-> Am (-> Bm (and Am Bm))))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20092.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((((A -> (B -> (A and B))) -> C) -> (D or (A -> (B -> (A and B))))) -> (((A -> (B -> (A and B))) -> C) -> C))), M:tm-306, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (or Dm (-> Am (-> Bm (and Am Bm))))) (C Cm))
================================================================
tm-name          tm-20093
in-theory        20093
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (E -> (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C))))
theorem-size     45
proof            (modus-ponens tm-305 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20093.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (E -> (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)))), M:tm-305, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20094
in-theory        20094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     33
proof            (modus-ponens tm-303 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20094.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-303, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20095
in-theory        20095
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     31
proof            (modus-ponens tm-270 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20095.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-270, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20096
in-theory        20096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     31
proof            (modus-ponens tm-239 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20096.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-239, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20097
in-theory        20097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> (E and F))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G)))
theorem-size     39
proof            (modus-ponens tm-210 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20097.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> (E and F))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G))), M:tm-210, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20098
in-theory        20098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     31
proof            (modus-ponens tm-183 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20098.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-183, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20099
in-theory        20099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-157 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20099.        ((A -> ((B and C) -> C)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-157, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20100
in-theory        20100
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     37
proof            (modus-ponens tm-147 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20100.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-147, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20101
in-theory        20101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-134 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20101.        ((A -> ((B and C) -> B)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-134, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20102
in-theory        20102
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     37
proof            (modus-ponens tm-125 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20102.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-125, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20103
in-theory        20103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> (C -> D)) -> (((E or (A -> (B -> (A and B)))) -> C) -> ((E or (A -> (B -> (A and B)))) -> D)))
theorem-size     35
proof            (modus-ponens tm-114 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) (-> C D))) (B (or Dm (-> Am (-> Bm (and Am Bm))))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20103.        (((A -> (B -> (A and B))) -> (C -> D)) -> (((E or (A -> (B -> (A and B)))) -> C) -> ((E or (A -> (B -> (A and B)))) -> D))), M:tm-114, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) (-> C D))) (B (or Dm (-> Am (-> Bm (and Am Bm))))) (Cm (-> C D)))
================================================================
tm-name          tm-20104
in-theory        20104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> (E and F))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G)))
theorem-size     37
proof            (modus-ponens tm-113 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20104.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> (E and F))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G))), M:tm-113, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20105
in-theory        20105
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) -> ((B -> C) -> (B -> (B and C))))) -> ((D or (B -> (C -> (B and C)))) -> ((B -> C) -> (B -> (B and C)))))
theorem-size     39
proof            (modus-ponens tm-110 tm-351 ((A Am) (B Bm) (C (and Am Bm)) (Cm (-> (-> Am Bm) (-> Am (and Am Bm)))) (D (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20105.        ((A or ((B -> (C -> (B and C))) -> ((B -> C) -> (B -> (B and C))))) -> ((D or (B -> (C -> (B and C)))) -> ((B -> C) -> (B -> (B and C))))), M:tm-110, m:tm-351, u:((A Am) (B Bm) (C (and Am Bm)) (Cm (-> (-> Am Bm) (-> Am (and Am Bm)))) (D (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-20106
in-theory        20106
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     41
proof            (modus-ponens tm-105 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20106.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-105, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20107
in-theory        20107
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> (A -> B)) or ((A -> (B -> (A and B))) -> (A -> (A and B)))) -> ((C or (A -> (B -> (A and B)))) -> (A -> (A and B))))
theorem-size     41
proof            (modus-ponens tm-102 tm-351 ((A Am) (B Bm) (C (and Am Bm)) (Cm (-> Am (and Am Bm))) (D (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> Am (and Am Bm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20107.        ((((A -> (B -> (A and B))) -> (A -> B)) or ((A -> (B -> (A and B))) -> (A -> (A and B)))) -> ((C or (A -> (B -> (A and B)))) -> (A -> (A and B)))), M:tm-102, m:tm-351, u:((A Am) (B Bm) (C (and Am Bm)) (Cm (-> Am (and Am Bm))) (D (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-20108
in-theory        20108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E)))
theorem-size     29
proof            (modus-ponens tm-95 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20108.        (((A -> B) -> (A -> A)) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E))), M:tm-95, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20109
in-theory        20109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) or ((A -> (B -> (A and B))) -> (A -> (B -> (A and B))))) -> ((D or (A -> (B -> (A and B)))) -> (A -> (B -> (A and B)))))
theorem-size     43
proof            (modus-ponens tm-92 tm-351 ((Cm (-> Am (-> Bm (and Am Bm)))) (A (-> Am (-> Bm (and Am Bm)))) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20109.        ((((A -> (B -> (A and B))) -> C) or ((A -> (B -> (A and B))) -> (A -> (B -> (A and B))))) -> ((D or (A -> (B -> (A and B)))) -> (A -> (B -> (A and B))))), M:tm-92, m:tm-351, u:((Cm (-> Am (-> Bm (and Am Bm)))) (A (-> Am (-> Bm (and Am Bm)))) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-20110
in-theory        20110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> (D -> ((E or (A -> (B -> (A and B)))) -> C)))
theorem-size     23
proof            (modus-ponens tm-84 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20110.        (((A -> (B -> (A and B))) -> C) -> (D -> ((E or (A -> (B -> (A and B)))) -> C))), M:tm-84, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-20111
in-theory        20111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-83 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20111.        ((A -> (B -> (C -> B))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-83, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20112
in-theory        20112
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) -> (D -> (B -> (C -> (B and C)))))) -> ((E or (B -> (C -> (B and C)))) -> (D -> (B -> (C -> (B and C))))))
theorem-size     39
proof            (modus-ponens tm-80 tm-351 ((A (-> Am (-> Bm (and Am Bm)))) (Cm (-> B (-> Am (-> Bm (and Am Bm))))) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> B (-> Am (-> Bm (and Am Bm))))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20112.        ((A or ((B -> (C -> (B and C))) -> (D -> (B -> (C -> (B and C)))))) -> ((E or (B -> (C -> (B and C)))) -> (D -> (B -> (C -> (B and C)))))), M:tm-80, m:tm-351, u:((A (-> Am (-> Bm (and Am Bm)))) (Cm (-> B (-> Am (-> Bm (and Am Bm))))) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> B (-> Am (-> Bm (and Am Bm)))))))
================================================================
tm-name          tm-20113
in-theory        20113
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> (B and C))) -> D) -> ((E or (B -> (C -> (B and C)))) -> D)))
theorem-size     27
proof            (modus-ponens tm-76 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20113.        (((not (not A)) -> A) and (((B -> (C -> (B and C))) -> D) -> ((E or (B -> (C -> (B and C)))) -> D))), M:tm-76, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20114
in-theory        20114
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> (A and B))) -> C))) or ((A -> (B -> (A and B))) -> C)) -> ((D or (A -> (B -> (A and B)))) -> C))
theorem-size     33
proof            (modus-ponens tm-73 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-8 tm-10 tm-1 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20114.        (((not (not ((A -> (B -> (A and B))) -> C))) or ((A -> (B -> (A and B))) -> C)) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-73, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-20115
in-theory        20115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E)))
theorem-size     33
proof            (modus-ponens tm-69 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20115.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E))), M:tm-69, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20116
in-theory        20116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> (C or (A -> (B -> (A and B))))) -> (((A -> (B -> (A and B))) or (C or (A -> (B -> (A and B))))) -> (C or (A -> (B -> (A and B))))))
theorem-size     45
proof            (modus-ponens tm-55 tm-351 ((A (-> Am (-> Bm (and Am Bm)))) (Cm (or Dm (-> Am (-> Bm (and Am Bm))))) (B (or Dm (-> Am (-> Bm (and Am Bm))))) (C (or Dm (-> Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20116.        (((A -> (B -> (A and B))) -> (C or (A -> (B -> (A and B))))) -> (((A -> (B -> (A and B))) or (C or (A -> (B -> (A and B))))) -> (C or (A -> (B -> (A and B)))))), M:tm-55, m:tm-351, u:((A (-> Am (-> Bm (and Am Bm)))) (Cm (or Dm (-> Am (-> Bm (and Am Bm))))) (B (or Dm (-> Am (-> Bm (and Am Bm))))) (C (or Dm (-> Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-20117
in-theory        20117
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     35
proof            (modus-ponens tm-54 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20117.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-54, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20118
in-theory        20118
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (C -> (B and C))) -> ((A or B) -> (C -> (B and C))))) -> ((D or (B -> (C -> (B and C)))) -> ((A or B) -> (C -> (B and C)))))
theorem-size     41
proof            (modus-ponens tm-51 tm-351 ((A Am) (B (-> Bm (and Am Bm))) (Cm (-> (or C Am) (-> Bm (and Am Bm)))) (D (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> (or C Am) (-> Bm (and Am Bm)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20118.        (((A -> B) or ((B -> (C -> (B and C))) -> ((A or B) -> (C -> (B and C))))) -> ((D or (B -> (C -> (B and C)))) -> ((A or B) -> (C -> (B and C))))), M:tm-51, m:tm-351, u:((A Am) (B (-> Bm (and Am Bm))) (Cm (-> (or C Am) (-> Bm (and Am Bm)))) (D (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> (or C Am) (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-20119
in-theory        20119
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) -> (A and (B -> (C -> (B and C)))))) -> ((D or (B -> (C -> (B and C)))) -> (A and (B -> (C -> (B and C))))))
theorem-size     39
proof            (modus-ponens tm-48 tm-351 ((A (-> Am (-> Bm (and Am Bm)))) (Cm (and B (-> Am (-> Bm (and Am Bm))))) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (and B (-> Am (-> Bm (and Am Bm))))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20119.        ((A or ((B -> (C -> (B and C))) -> (A and (B -> (C -> (B and C)))))) -> ((D or (B -> (C -> (B and C)))) -> (A and (B -> (C -> (B and C)))))), M:tm-48, m:tm-351, u:((A (-> Am (-> Bm (and Am Bm)))) (Cm (and B (-> Am (-> Bm (and Am Bm))))) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (and B (-> Am (-> Bm (and Am Bm)))))))
================================================================
tm-name          tm-20120
in-theory        20120
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) or ((B -> (C -> (B and C))) -> D)) -> ((E or (B -> (C -> (B and C)))) -> D))
theorem-size     33
proof            (modus-ponens tm-47 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-8 tm-4 tm-1 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20120.        (((A and ((B -> (C -> (B and C))) -> D)) or ((B -> (C -> (B and C))) -> D)) -> ((E or (B -> (C -> (B and C)))) -> D)), M:tm-47, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-20121
in-theory        20121
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) or ((A -> (B -> (A and B))) -> C)) -> ((E or (A -> (B -> (A and B)))) -> C))
theorem-size     33
proof            (modus-ponens tm-46 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20121.        (((((A -> (B -> (A and B))) -> C) and D) or ((A -> (B -> (A and B))) -> C)) -> ((E or (A -> (B -> (A and B)))) -> C)), M:tm-46, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-20122
in-theory        20122
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) or ((A -> (B -> (A and B))) -> (A -> C))) -> ((D or (A -> (B -> (A and B)))) -> (A -> C)))
theorem-size     35
proof            (modus-ponens tm-45 tm-351 ((A Am) (B (-> Bm (and Am Bm))) (Cm (-> Am C)) (D (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> Am C)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20122.        (((A -> ((B -> (A and B)) -> C)) or ((A -> (B -> (A and B))) -> (A -> C))) -> ((D or (A -> (B -> (A and B)))) -> (A -> C))), M:tm-45, m:tm-351, u:((A Am) (B (-> Bm (and Am Bm))) (Cm (-> Am C)) (D (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> Am C))))
================================================================
tm-name          tm-20123
in-theory        20123
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) -> A)) -> ((D or (B -> (C -> (B and C)))) -> A))
theorem-size     23
proof            (modus-ponens tm-44 tm-351 ((A (-> Am (-> Bm (and Am Bm)))) (B Cm) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20123.        ((A or ((B -> (C -> (B and C))) -> A)) -> ((D or (B -> (C -> (B and C)))) -> A)), M:tm-44, m:tm-351, u:((A (-> Am (-> Bm (and Am Bm)))) (B Cm) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-20124
in-theory        20124
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E)))
theorem-size     27
proof            (modus-ponens tm-42 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20124.        ((A -> (B or A)) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E))), M:tm-42, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20125
in-theory        20125
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E)))
theorem-size     27
proof            (modus-ponens tm-32 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20125.        ((A -> (A or B)) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E))), M:tm-32, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20126
in-theory        20126
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> (((A -> (B -> (A and B))) -> C) and ((D or (A -> (B -> (A and B)))) -> C)))
theorem-size     31
proof            (modus-ponens tm-24 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20126.        (((A -> (B -> (A and B))) -> C) -> (((A -> (B -> (A and B))) -> C) and ((D or (A -> (B -> (A and B)))) -> C))), M:tm-24, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-20127
in-theory        20127
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E)))
theorem-size     29
proof            (modus-ponens tm-23 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20127.        ((A -> (B -> (A and B))) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E))), M:tm-23, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20128
in-theory        20128
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E)))
theorem-size     27
proof            (modus-ponens tm-22 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20128.        (((A and B) -> B) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E))), M:tm-22, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20129
in-theory        20129
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E)))
theorem-size     27
proof            (modus-ponens tm-21 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20129.        (((A and B) -> A) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E))), M:tm-21, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20130
in-theory        20130
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     35
proof            (modus-ponens tm-20 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20130.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-20, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20131
in-theory        20131
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E)))
theorem-size     27
proof            (modus-ponens tm-19 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20131.        ((A -> (B -> A)) and (((C -> (D -> (C and D))) -> E) -> ((F or (C -> (D -> (C and D)))) -> E))), M:tm-19, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20132
in-theory        20132
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> ((A -> (B -> (A and B))) -> C))
theorem-size     19
proof            (modus-ponens tm-12 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20132.        (((A -> (B -> (A and B))) -> C) -> ((A -> (B -> (A and B))) -> C)), M:tm-12, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-20133
in-theory        20133
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> (not ((D or (A -> (B -> (A and B)))) -> C))) -> (not ((A -> (B -> (A and B))) -> C)))
theorem-size     33
proof            (modus-ponens tm-9 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-9 tm-8 tm-1 tm-5)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20133.        ((((A -> (B -> (A and B))) -> C) -> (not ((D or (A -> (B -> (A and B)))) -> C))) -> (not ((A -> (B -> (A and B))) -> C))), M:tm-9, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-20134
in-theory        20134
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (C -> (B and C)))) -> D) -> E) -> ((((B -> (C -> (B and C))) -> D) or ((A or (B -> (C -> (B and C)))) -> D)) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20134.        ((((A or (B -> (C -> (B and C)))) -> D) -> E) -> ((((B -> (C -> (B and C))) -> D) or ((A or (B -> (C -> (B and C)))) -> D)) -> E)), M:tm-8, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-20135
in-theory        20135
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> (C -> (B and C))) -> D) -> ((E or (B -> (C -> (B and C)))) -> D)))
theorem-size     23
proof            (modus-ponens tm-7 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-7 tm-8 tm-1 tm-5)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20135.        (A or (((B -> (C -> (B and C))) -> D) -> ((E or (B -> (C -> (B and C)))) -> D))), M:tm-7, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20136
in-theory        20136
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-6 tm-8 tm-1 tm-5)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20136.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) or E), M:tm-6, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20137
in-theory        20137
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> (B and C))) -> D) -> ((E or (B -> (C -> (B and C)))) -> D)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20137.        (A -> ((((B -> (C -> (B and C))) -> D) -> ((E or (B -> (C -> (B and C)))) -> D)) and A)), M:tm-5, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20138
in-theory        20138
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> (D or (A -> (B -> (A and B))))) -> (((A -> (B -> (A and B))) -> C) -> C))
theorem-size     31
proof            (modus-ponens tm-2 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (or Dm (-> Am (-> Bm (and Am Bm))))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20138.        ((((A -> (B -> (A and B))) -> C) -> (D or (A -> (B -> (A and B))))) -> (((A -> (B -> (A and B))) -> C) -> C)), M:tm-2, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (or Dm (-> Am (-> Bm (and Am Bm))))) (C Cm))
================================================================
tm-name          tm-20139
in-theory        20139
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) -> D) -> ((E or (B -> (C -> (B and C)))) -> D)))
theorem-size     23
proof            (modus-ponens tm-1 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20139.        (A -> (((B -> (C -> (B and C))) -> D) -> ((E or (B -> (C -> (B and C)))) -> D))), M:tm-1, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20140
in-theory        20140
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20140.        ((A or (B -> (C -> (D -> (C and D))))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20141
in-theory        20141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-338 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20141.        (((A -> B) -> (A -> (A and B))) and (C or (D -> (E -> (F -> (E and F)))))), M:tm-338, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20142
in-theory        20142
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and ((E -> (F -> (E and F))) and (A or (B -> (C -> (D -> (C and D)))))))
theorem-size     31
proof            (modus-ponens tm-327 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20142.        ((A or (B -> (C -> (D -> (C and D))))) and ((E -> (F -> (E and F))) and (A or (B -> (C -> (D -> (C and D))))))), M:tm-327, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20143
in-theory        20143
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and (((E and F) -> F) and (A or (B -> (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-326 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20143.        ((A or (B -> (C -> (D -> (C and D))))) and (((E and F) -> F) and (A or (B -> (C -> (D -> (C and D))))))), M:tm-326, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20144
in-theory        20144
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and (((E and F) -> E) and (A or (B -> (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-325 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20144.        ((A or (B -> (C -> (D -> (C and D))))) and (((E and F) -> E) and (A or (B -> (C -> (D -> (C and D))))))), M:tm-325, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20145
in-theory        20145
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> (C -> (D -> (C and D)))))))
theorem-size     37
proof            (modus-ponens tm-324 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20145.        ((A or (B -> (C -> (D -> (C and D))))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> (C -> (D -> (C and D))))))), M:tm-324, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20146
in-theory        20146
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and ((E -> (F -> E)) and (A or (B -> (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-323 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20146.        ((A or (B -> (C -> (D -> (C and D))))) and ((E -> (F -> E)) and (A or (B -> (C -> (D -> (C and D))))))), M:tm-323, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20147
in-theory        20147
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20147.        ((A or (B -> (C -> (D -> (C and D))))) and ((E and F) -> F)), M:tm-322, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20148
in-theory        20148
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20148.        ((A or (B -> (C -> (D -> (C and D))))) and ((E and F) -> E)), M:tm-320, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20149
in-theory        20149
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20149.        ((A or (B -> (C -> (D -> (C and D))))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20150
in-theory        20150
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20150.        ((A or (B -> (C -> (D -> (C and D))))) and (E -> (F -> E))), M:tm-315, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20151
in-theory        20151
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and (E or (A or (B -> (C -> (D -> (C and D)))))))
theorem-size     25
proof            (modus-ponens tm-311 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20151.        ((A or (B -> (C -> (D -> (C and D))))) and (E or (A or (B -> (C -> (D -> (C and D))))))), M:tm-311, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20152
in-theory        20152
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and ((A or (B -> (C -> (D -> (C and D))))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20152.        ((A or (B -> (C -> (D -> (C and D))))) and ((A or (B -> (C -> (D -> (C and D))))) or E)), M:tm-310, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20153
in-theory        20153
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and (E -> ((A or (B -> (C -> (D -> (C and D))))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20153.        ((A or (B -> (C -> (D -> (C and D))))) and (E -> ((A or (B -> (C -> (D -> (C and D))))) and E))), M:tm-309, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20154
in-theory        20154
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and (E -> (A or (B -> (C -> (D -> (C and D)))))))
theorem-size     25
proof            (modus-ponens tm-305 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20154.        ((A or (B -> (C -> (D -> (C and D))))) and (E -> (A or (B -> (C -> (D -> (C and D))))))), M:tm-305, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20155
in-theory        20155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-303 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20155.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-303, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20156
in-theory        20156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-270 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20156.        ((A -> (((B and C) -> C) and A)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-270, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20157
in-theory        20157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-239 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20157.        ((A -> (((B and C) -> B) and A)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-239, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20158
in-theory        20158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-210 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20158.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (G -> (H -> (G and H)))))), M:tm-210, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20159
in-theory        20159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-183 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20159.        ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-183, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20160
in-theory        20160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-157 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20160.        ((A -> ((B and C) -> C)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-157, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20161
in-theory        20161
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-147 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20161.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-147, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20162
in-theory        20162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-134 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20162.        ((A -> ((B and C) -> B)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-134, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20163
in-theory        20163
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-125 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20163.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-125, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20164
in-theory        20164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-113 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20164.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (H -> (G and H)))))), M:tm-113, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20165
in-theory        20165
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     31
proof            (modus-ponens tm-105 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20165.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-105, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20166
in-theory        20166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-95 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20166.        (((A -> B) -> (A -> A)) and (C or (D -> (E -> (F -> (E and F)))))), M:tm-95, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20167
in-theory        20167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-83 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20167.        ((A -> (B -> (C -> B))) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-83, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20168
in-theory        20168
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> (D -> (E -> (D and E))))))
theorem-size     17
proof            (modus-ponens tm-76 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20168.        (((not (not A)) -> A) and (B or (C -> (D -> (E -> (D and E)))))), M:tm-76, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20169
in-theory        20169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (E -> (F -> (E and F))))))
theorem-size     23
proof            (modus-ponens tm-69 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20169.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (E -> (F -> (E and F)))))), M:tm-69, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20170
in-theory        20170
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-54 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20170.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-54, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20171
in-theory        20171
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-42 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20171.        ((A -> (B or A)) and (C or (D -> (E -> (F -> (E and F)))))), M:tm-42, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20172
in-theory        20172
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-32 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20172.        ((A -> (A or B)) and (C or (D -> (E -> (F -> (E and F)))))), M:tm-32, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20173
in-theory        20173
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-23 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20173.        ((A -> (B -> (A and B))) and (C or (D -> (E -> (F -> (E and F)))))), M:tm-23, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20174
in-theory        20174
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-22 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20174.        (((A and B) -> B) and (C or (D -> (E -> (F -> (E and F)))))), M:tm-22, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20175
in-theory        20175
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-21 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20175.        (((A and B) -> A) and (C or (D -> (E -> (F -> (E and F)))))), M:tm-21, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20176
in-theory        20176
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-20 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20176.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-20, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20177
in-theory        20177
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-19 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20177.        ((A -> (B -> A)) and (C or (D -> (E -> (F -> (E and F)))))), M:tm-19, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20178
in-theory        20178
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C -> (D -> (E -> (D and E))))))
theorem-size     13
proof            (modus-ponens tm-7 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-7 tm-1 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20178.        (A or (B or (C -> (D -> (E -> (D and E)))))), M:tm-7, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20179
in-theory        20179
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-6 tm-7 tm-1 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20179.        ((A or (B -> (C -> (D -> (C and D))))) or E), M:tm-6, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20180
in-theory        20180
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (D -> (E -> (D and E))))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20180.        (A -> ((B or (C -> (D -> (E -> (D and E))))) and A)), M:tm-5, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20181
in-theory        20181
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C -> (D -> (E -> (D and E))))))
theorem-size     13
proof            (modus-ponens tm-1 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-1 tm-7 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20181.        (A -> (B or (C -> (D -> (E -> (D and E)))))), M:tm-1, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20182
in-theory        20182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20182.        (((A -> (B -> (C -> (B and C)))) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20183
in-theory        20183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (E -> (D and E)))) or F))
theorem-size     21
proof            (modus-ponens tm-338 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20183.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (E -> (D and E)))) or F)), M:tm-338, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20184
in-theory        20184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and ((E -> (F -> (E and F))) and ((A -> (B -> (C -> (B and C)))) or D)))
theorem-size     31
proof            (modus-ponens tm-327 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20184.        (((A -> (B -> (C -> (B and C)))) or D) and ((E -> (F -> (E and F))) and ((A -> (B -> (C -> (B and C)))) or D))), M:tm-327, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20185
in-theory        20185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and (((E and F) -> F) and ((A -> (B -> (C -> (B and C)))) or D)))
theorem-size     29
proof            (modus-ponens tm-326 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20185.        (((A -> (B -> (C -> (B and C)))) or D) and (((E and F) -> F) and ((A -> (B -> (C -> (B and C)))) or D))), M:tm-326, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20186
in-theory        20186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and (((E and F) -> E) and ((A -> (B -> (C -> (B and C)))) or D)))
theorem-size     29
proof            (modus-ponens tm-325 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20186.        (((A -> (B -> (C -> (B and C)))) or D) and (((E and F) -> E) and ((A -> (B -> (C -> (B and C)))) or D))), M:tm-325, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20187
in-theory        20187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (C -> (B and C)))) or D)))
theorem-size     37
proof            (modus-ponens tm-324 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20187.        (((A -> (B -> (C -> (B and C)))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (C -> (B and C)))) or D))), M:tm-324, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20188
in-theory        20188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and ((E -> (F -> E)) and ((A -> (B -> (C -> (B and C)))) or D)))
theorem-size     29
proof            (modus-ponens tm-323 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20188.        (((A -> (B -> (C -> (B and C)))) or D) and ((E -> (F -> E)) and ((A -> (B -> (C -> (B and C)))) or D))), M:tm-323, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20189
in-theory        20189
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20189.        (((A -> (B -> (C -> (B and C)))) or D) and ((E and F) -> F)), M:tm-322, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20190
in-theory        20190
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20190.        (((A -> (B -> (C -> (B and C)))) or D) and ((E and F) -> E)), M:tm-320, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20191
in-theory        20191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20191.        (((A -> (B -> (C -> (B and C)))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20192
in-theory        20192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20192.        (((A -> (B -> (C -> (B and C)))) or D) and (E -> (F -> E))), M:tm-315, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20193
in-theory        20193
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and (E or ((A -> (B -> (C -> (B and C)))) or D)))
theorem-size     25
proof            (modus-ponens tm-311 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20193.        (((A -> (B -> (C -> (B and C)))) or D) and (E or ((A -> (B -> (C -> (B and C)))) or D))), M:tm-311, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20194
in-theory        20194
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and (((A -> (B -> (C -> (B and C)))) or D) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20194.        (((A -> (B -> (C -> (B and C)))) or D) and (((A -> (B -> (C -> (B and C)))) or D) or E)), M:tm-310, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20195
in-theory        20195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and (E -> (((A -> (B -> (C -> (B and C)))) or D) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20195.        (((A -> (B -> (C -> (B and C)))) or D) and (E -> (((A -> (B -> (C -> (B and C)))) or D) and E))), M:tm-309, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20196
in-theory        20196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and (E -> ((A -> (B -> (C -> (B and C)))) or D)))
theorem-size     25
proof            (modus-ponens tm-305 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20196.        (((A -> (B -> (C -> (B and C)))) or D) and (E -> ((A -> (B -> (C -> (B and C)))) or D))), M:tm-305, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20197
in-theory        20197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     23
proof            (modus-ponens tm-303 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20197.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-303, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20198
in-theory        20198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-270 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20198.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-270, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20199
in-theory        20199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-239 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20199.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-239, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20200
in-theory        20200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (G -> (F and G)))) or H))
theorem-size     29
proof            (modus-ponens tm-210 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20200.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (G -> (F and G)))) or H)), M:tm-210, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20201
in-theory        20201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-183 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20201.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-183, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20202
in-theory        20202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-157 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20202.        ((A -> ((B and C) -> C)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-157, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20203
in-theory        20203
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     27
proof            (modus-ponens tm-147 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20203.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-147, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20204
in-theory        20204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-134 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20204.        ((A -> ((B and C) -> B)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-134, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20205
in-theory        20205
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     27
proof            (modus-ponens tm-125 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20205.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-125, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20206
in-theory        20206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G -> (F and G)))) or H))
theorem-size     27
proof            (modus-ponens tm-113 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20206.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G -> (F and G)))) or H)), M:tm-113, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20207
in-theory        20207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     31
proof            (modus-ponens tm-105 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20207.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-105, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20208
in-theory        20208
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (E -> (D and E)))) or F))
theorem-size     19
proof            (modus-ponens tm-95 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20208.        (((A -> B) -> (A -> A)) and ((C -> (D -> (E -> (D and E)))) or F)), M:tm-95, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20209
in-theory        20209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-83 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20209.        ((A -> (B -> (C -> B))) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-83, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20210
in-theory        20210
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (D -> (C and D)))) or E))
theorem-size     17
proof            (modus-ponens tm-76 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20210.        (((not (not A)) -> A) and ((B -> (C -> (D -> (C and D)))) or E)), M:tm-76, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20211
in-theory        20211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (E -> (D and E)))) or F))
theorem-size     23
proof            (modus-ponens tm-69 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20211.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (E -> (D and E)))) or F)), M:tm-69, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20212
in-theory        20212
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     25
proof            (modus-ponens tm-54 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20212.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-54, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20213
in-theory        20213
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (E -> (D and E)))) or F))
theorem-size     17
proof            (modus-ponens tm-42 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20213.        ((A -> (B or A)) and ((C -> (D -> (E -> (D and E)))) or F)), M:tm-42, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20214
in-theory        20214
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (E -> (D and E)))) or F))
theorem-size     17
proof            (modus-ponens tm-32 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20214.        ((A -> (A or B)) and ((C -> (D -> (E -> (D and E)))) or F)), M:tm-32, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20215
in-theory        20215
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (E -> (D and E)))) or F))
theorem-size     19
proof            (modus-ponens tm-23 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20215.        ((A -> (B -> (A and B))) and ((C -> (D -> (E -> (D and E)))) or F)), M:tm-23, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20216
in-theory        20216
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (E -> (D and E)))) or F))
theorem-size     17
proof            (modus-ponens tm-22 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20216.        (((A and B) -> B) and ((C -> (D -> (E -> (D and E)))) or F)), M:tm-22, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20217
in-theory        20217
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (E -> (D and E)))) or F))
theorem-size     17
proof            (modus-ponens tm-21 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20217.        (((A and B) -> A) and ((C -> (D -> (E -> (D and E)))) or F)), M:tm-21, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20218
in-theory        20218
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     25
proof            (modus-ponens tm-20 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20218.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-20, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20219
in-theory        20219
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (E -> (D and E)))) or F))
theorem-size     17
proof            (modus-ponens tm-19 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20219.        ((A -> (B -> A)) and ((C -> (D -> (E -> (D and E)))) or F)), M:tm-19, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20220
in-theory        20220
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (D -> (C and D)))) or E))
theorem-size     13
proof            (modus-ponens tm-7 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-7 tm-6 tm-1 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20220.        (A or ((B -> (C -> (D -> (C and D)))) or E)), M:tm-7, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20221
in-theory        20221
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-6 tm-1 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20221.        (((A -> (B -> (C -> (B and C)))) or D) or E), M:tm-6, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20222
in-theory        20222
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (D -> (C and D)))) or E) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20222.        (A -> (((B -> (C -> (D -> (C and D)))) or E) and A)), M:tm-5, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20223
in-theory        20223
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (D -> (C and D)))) or E))
theorem-size     13
proof            (modus-ponens tm-1 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-1 tm-6 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20223.        (A -> ((B -> (C -> (D -> (C and D)))) or E)), M:tm-1, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20224
in-theory        20224
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-354 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-20224.        ((A -> (B -> (C -> (B and C)))) and (D -> (D or E))), M:tm-354, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-20225
in-theory        20225
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-354 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-20225.        ((A -> (B -> (C -> (B and C)))) and (D -> (E or D))), M:tm-354, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-20226
in-theory        20226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20226.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-354, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-20227
in-theory        20227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-354 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20227.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-354, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-20228
in-theory        20228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-354 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-10.           ((not (not A)) -> A), axiom
tm-20228.        ((A -> (B -> (C -> (B and C)))) and ((not (not D)) -> D)), M:tm-354, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-20229
in-theory        20229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-354 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20229.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (F -> E)))), M:tm-354, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-20230
in-theory        20230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-354 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-20230.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (D -> D))), M:tm-354, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-20231
in-theory        20231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-354 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-20231.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-354, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-20232
in-theory        20232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-20232.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-354, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-20233
in-theory        20233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-354 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-20233.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-354, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-20234
in-theory        20234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-354 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20234.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E and F) -> E))), M:tm-354, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-20235
in-theory        20235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-354 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-20235.        ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-354, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-20236
in-theory        20236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-354 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20236.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E and F) -> F))), M:tm-354, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-20237
in-theory        20237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-354 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20237.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> E)) and D))), M:tm-354, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-20238
in-theory        20238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-354 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-20238.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-354, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-20239
in-theory        20239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-354 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20239.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E and F) -> E) and D))), M:tm-354, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-20240
in-theory        20240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-354 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20240.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E and F) -> F) and D))), M:tm-354, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-20241
in-theory        20241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20241.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-354, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-20242
in-theory        20242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-354 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20242.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (D and E)))), M:tm-354, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-20243
in-theory        20243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20243.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (F -> (E and F))))), M:tm-354, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20244
in-theory        20244
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-354 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20244.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) or F)), M:tm-354, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-20245
in-theory        20245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-354 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-20245.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-354, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-20246
in-theory        20246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-354 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20246.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) or F)), M:tm-354, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-20247
in-theory        20247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-354 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20247.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) or F)), M:tm-354, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-20248
in-theory        20248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-354 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20248.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) or F)), M:tm-354, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-20249
in-theory        20249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-354 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20249.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) or F)), M:tm-354, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-20250
in-theory        20250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-354 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20250.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (E or F)) and D))), M:tm-354, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-20251
in-theory        20251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-354 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20251.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (E or F)))), M:tm-354, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-20252
in-theory        20252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-354 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20252.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> (F -> E)))), M:tm-354, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-20253
in-theory        20253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-20253.        ((A -> (B -> (C -> (B and C)))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-354, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-20254
in-theory        20254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-354 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20254.        ((A -> (B -> (C -> (B and C)))) and (D or ((E and F) -> E))), M:tm-354, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-20255
in-theory        20255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-354 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20255.        ((A -> (B -> (C -> (B and C)))) and (D or ((E and F) -> F))), M:tm-354, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-20256
in-theory        20256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20256.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> (F -> (E and F))))), M:tm-354, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20257
in-theory        20257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-354 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20257.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> (E or F)))), M:tm-354, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-20258
in-theory        20258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-354 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20258.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> (F or E)))), M:tm-354, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-20259
in-theory        20259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-354 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20259.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) or F)), M:tm-354, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-20260
in-theory        20260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-354 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20260.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F or E)) and D))), M:tm-354, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-20261
in-theory        20261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-354 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20261.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (F or E)))), M:tm-354, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-20262
in-theory        20262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-354 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20262.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-354, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-20263
in-theory        20263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-354 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20263.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-354, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-20264
in-theory        20264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-354 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20264.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-354, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-20265
in-theory        20265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-354 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20265.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-354, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-20266
in-theory        20266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-354 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20266.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-354, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-20267
in-theory        20267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-354 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20267.        ((A -> (B -> (C -> (B and C)))) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-354, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-20268
in-theory        20268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-354 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20268.        ((A -> (B -> (C -> (B and C)))) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-354, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-20269
in-theory        20269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-354 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-20269.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-354, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-20270
in-theory        20270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-20270.        ((A -> (B -> (C -> (B and C)))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-354, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-20271
in-theory        20271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-354 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-20271.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-354, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-20272
in-theory        20272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-354 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-20272.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-354, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-20273
in-theory        20273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-354 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-20273.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-354, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-20274
in-theory        20274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-20274.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-354, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-20275
in-theory        20275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-354 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20275.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not (E -> D))) -> (not D))), M:tm-354, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-20276
in-theory        20276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20276.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-354, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-20277
in-theory        20277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-354 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20277.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-354, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-20278
in-theory        20278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-354 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20278.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-354, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-20279
in-theory        20279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20279.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-354, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-20280
in-theory        20280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not (D or E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-354 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20280.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not (D or E))) -> (not D))), M:tm-354, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-20281
in-theory        20281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not (E or D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-354 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20281.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not (E or D))) -> (not D))), M:tm-354, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-20282
in-theory        20282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-354 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-20282.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-354, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-20283
in-theory        20283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-354 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-20283.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-354, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-20284
in-theory        20284
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-354 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-20284.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-354, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-20285
in-theory        20285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-20285.        ((A -> (B -> (C -> (B and C)))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-354, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-20286
in-theory        20286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     23
proof            (modus-ponens tm-354 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-20286.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-354, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-20287
in-theory        20287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     25
proof            (modus-ponens tm-354 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-20287.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-354, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-20288
in-theory        20288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-354 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-20288.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-354, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-20289
in-theory        20289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-20289.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-354, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-20290
in-theory        20290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     21
proof            (modus-ponens tm-354 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-1 tm-9 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-20290.        ((A -> (B -> (C -> (B and C)))) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-354, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-20291
in-theory        20291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-354 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-20291.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-354, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-20292
in-theory        20292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-354 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-20292.        ((A -> (B -> (C -> (B and C)))) and (D or ((not (not E)) -> E))), M:tm-354, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-20293
in-theory        20293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((not (not D)) -> D) or E))
theorem-size     17
proof            (modus-ponens tm-354 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-20293.        ((A -> (B -> (C -> (B and C)))) and (((not (not D)) -> D) or E)), M:tm-354, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-20294
in-theory        20294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((not (not E)) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-354 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-20294.        ((A -> (B -> (C -> (B and C)))) and (D -> (((not (not E)) -> E) and D))), M:tm-354, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-20295
in-theory        20295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     25
proof            (modus-ponens tm-354 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-20295.        ((A -> (B -> (C -> (B and C)))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-354, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-20296
in-theory        20296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-354 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-20296.        ((A -> (B -> (C -> (B and C)))) and (D -> ((not (not E)) -> E))), M:tm-354, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-20297
in-theory        20297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20297.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-354, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-20298
in-theory        20298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-354 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20298.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-354, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-20299
in-theory        20299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-20299.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> (F -> (G -> F))))), M:tm-354, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-20300
in-theory        20300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-20300.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (F -> E))) or G)), M:tm-354, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-20301
in-theory        20301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-20301.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-354, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-20302
in-theory        20302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-354 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-20302.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (F -> E)))), M:tm-354, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-20303
in-theory        20303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-20303.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (F -> (G -> F))))), M:tm-354, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-20304
in-theory        20304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> D))
theorem-size     13
proof            (modus-ponens tm-354 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20304.        ((A -> (B -> (C -> (B and C)))) and (D -> D)), M:tm-354, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-20305
in-theory        20305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20305.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-354, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-20306
in-theory        20306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D and E) -> (D and E)))
theorem-size     17
proof            (modus-ponens tm-354 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20306.        ((A -> (B -> (C -> (B and C)))) and ((D and E) -> (D and E))), M:tm-354, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-20307
in-theory        20307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-354 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-20307.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (D -> E))), M:tm-354, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-20308
in-theory        20308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((not (not D)) -> (not (not D))))
theorem-size     17
proof            (modus-ponens tm-354 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-20308.        ((A -> (B -> (C -> (B and C)))) and ((not (not D)) -> (not (not D)))), M:tm-354, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-20309
in-theory        20309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-354 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-20309.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-354, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-20310
in-theory        20310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-354 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-20310.        ((A -> (B -> (C -> (B and C)))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-354, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-20311
in-theory        20311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-354 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20311.        ((A -> (B -> (C -> (B and C)))) and (D or ((E -> F) -> (E -> E)))), M:tm-354, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-20312
in-theory        20312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (D -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-354 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20312.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (D -> D)) or F)), M:tm-354, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-20313
in-theory        20313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20313.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-354, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-20314
in-theory        20314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-20314.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-354, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-20315
in-theory        20315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-354 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20315.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (E -> E)))), M:tm-354, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-20316
in-theory        20316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-20316.        ((A -> (B -> (C -> (B and C)))) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-354, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-20317
in-theory        20317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-354 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-20317.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D -> E)) -> (D -> E))), M:tm-354, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-20318
in-theory        20318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-354 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-20318.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-354, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-20319
in-theory        20319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     41
proof            (modus-ponens tm-354 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-20319.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-354, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-20320
in-theory        20320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-354 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-20320.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-354, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-20321
in-theory        20321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20321.        ((A -> (B -> (C -> (B and C)))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-354, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-20322
in-theory        20322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-354 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20322.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-354, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-20323
in-theory        20323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-354 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20323.        ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-354, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-20324
in-theory        20324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-354 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-20324.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-354, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-20325
in-theory        20325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20325.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-354, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-20326
in-theory        20326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-354 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-20326.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-354, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-20327
in-theory        20327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-354 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20327.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-354, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-20328
in-theory        20328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     43
proof            (modus-ponens tm-354 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20328.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-354, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-20329
in-theory        20329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-354 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20329.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-354, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-20330
in-theory        20330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-354 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20330.        ((A -> (B -> (C -> (B and C)))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-354, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-20331
in-theory        20331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-354 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20331.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-354, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-20332
in-theory        20332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-354 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-20332.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-354, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-20333
in-theory        20333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-354 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20333.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-354, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-20334
in-theory        20334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) and D) -> E))
theorem-size     17
proof            (modus-ponens tm-354 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-20334.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) and D) -> E)), M:tm-354, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-20335
in-theory        20335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-354 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-20335.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-354, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-20336
in-theory        20336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-354 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20336.        ((A -> (B -> (C -> (B and C)))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-354, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-20337
in-theory        20337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-354 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-20337.        ((A -> (B -> (C -> (B and C)))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-354, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-20338
in-theory        20338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     25
proof            (modus-ponens tm-354 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-20338.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-354, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-20339
in-theory        20339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     35
proof            (modus-ponens tm-354 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-20339.        ((A -> (B -> (C -> (B and C)))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-354, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-20340
in-theory        20340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     37
proof            (modus-ponens tm-354 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-20340.        ((A -> (B -> (C -> (B and C)))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-354, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-20341
in-theory        20341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-354 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20341.        ((A -> (B -> (C -> (B and C)))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-354, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-20342
in-theory        20342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-354 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20342.        ((A -> (B -> (C -> (B and C)))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-354, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-20343
in-theory        20343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-354 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20343.        ((A -> (B -> (C -> (B and C)))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-354, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-20344
in-theory        20344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     33
proof            (modus-ponens tm-354 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-20344.        ((A -> (B -> (C -> (B and C)))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-354, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-20345
in-theory        20345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-354 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20345.        ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-354, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-20346
in-theory        20346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-354 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-20346.        ((A -> (B -> (C -> (B and C)))) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-354, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-20347
in-theory        20347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-354 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-20347.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-354, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-20348
in-theory        20348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20348.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-354, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-20349
in-theory        20349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     27
proof            (modus-ponens tm-354 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20349.        ((A -> (B -> (C -> (B and C)))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-354, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-20350
in-theory        20350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-354 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-20350.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> ((F and G) -> F)))), M:tm-354, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-20351
in-theory        20351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-20351.        ((A -> (B -> (C -> (B and C)))) and ((D -> ((E and F) -> E)) or G)), M:tm-354, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-20352
in-theory        20352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-20352.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-354, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-20353
in-theory        20353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E and F)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-354 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-20353.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E and F)) -> (D -> E))), M:tm-354, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-20354
in-theory        20354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-354 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-20354.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> ((F and G) -> F)))), M:tm-354, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-20355
in-theory        20355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D and (D -> E)) -> E))
theorem-size     17
proof            (modus-ponens tm-354 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-20355.        ((A -> (B -> (C -> (B and C)))) and ((D and (D -> E)) -> E)), M:tm-354, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-20356
in-theory        20356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-354 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-20356.        ((A -> (B -> (C -> (B and C)))) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-354, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-20357
in-theory        20357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-354 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20357.        ((A -> (B -> (C -> (B and C)))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-354, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-20358
in-theory        20358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-354 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-20358.        ((A -> (B -> (C -> (B and C)))) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-354, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-20359
in-theory        20359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-354 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-20359.        ((A -> (B -> (C -> (B and C)))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-354, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-20360
in-theory        20360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     25
proof            (modus-ponens tm-354 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-20360.        ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-354, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-20361
in-theory        20361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     35
proof            (modus-ponens tm-354 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-20361.        ((A -> (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-354, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-20362
in-theory        20362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-354 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-20362.        ((A -> (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-354, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-20363
in-theory        20363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-354 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20363.        ((A -> (B -> (C -> (B and C)))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-354, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-20364
in-theory        20364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-354 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20364.        ((A -> (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-354, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-20365
in-theory        20365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-354 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20365.        ((A -> (B -> (C -> (B and C)))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-354, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-20366
in-theory        20366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     33
proof            (modus-ponens tm-354 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-20366.        ((A -> (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-354, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-20367
in-theory        20367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-354 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20367.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-354, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-20368
in-theory        20368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-354 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-20368.        ((A -> (B -> (C -> (B and C)))) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-354, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-20369
in-theory        20369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-354 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-20369.        ((A -> (B -> (C -> (B and C)))) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-354, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-20370
in-theory        20370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-354 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-20370.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-354, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-20371
in-theory        20371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20371.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-354, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-20372
in-theory        20372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-354 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20372.        ((A -> (B -> (C -> (B and C)))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-354, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-20373
in-theory        20373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-354 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-20373.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> ((F and G) -> G)))), M:tm-354, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-20374
in-theory        20374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-20374.        ((A -> (B -> (C -> (B and C)))) and ((D -> ((E and F) -> F)) or G)), M:tm-354, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-20375
in-theory        20375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-20375.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-354, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-20376
in-theory        20376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E and F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-354 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-20376.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E and F)) -> (D -> F))), M:tm-354, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-20377
in-theory        20377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-354 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-20377.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> ((F and G) -> G)))), M:tm-354, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-20378
in-theory        20378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20378.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-354, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-20379
in-theory        20379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-20379.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-354, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-20380
in-theory        20380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20380.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-354, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-20381
in-theory        20381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-354 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20381.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-354, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-20382
in-theory        20382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20382.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-354, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20383
in-theory        20383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-354 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20383.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-354, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-20384
in-theory        20384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20384.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-354, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-20385
in-theory        20385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-20385.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-354, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-20386
in-theory        20386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-354 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-20386.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-354, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-20387
in-theory        20387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-20387.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-354, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-20388
in-theory        20388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-20388.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-354, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-20389
in-theory        20389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20389.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-354, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-20390
in-theory        20390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-354 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20390.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-354, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-20391
in-theory        20391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20391.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-354, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-20392
in-theory        20392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-354 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20392.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-354, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-20393
in-theory        20393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-354 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-20393.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-354, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-20394
in-theory        20394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-354 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20394.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-354, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-20395
in-theory        20395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-354 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-20395.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-354, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-20396
in-theory        20396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-20396.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-354, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-20397
in-theory        20397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20397.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-354, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-20398
in-theory        20398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-354 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20398.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-354, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-20399
in-theory        20399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-354 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-20399.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-354, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-20400
in-theory        20400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-354 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-20400.        ((A -> (B -> (C -> (B and C)))) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-354, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-20401
in-theory        20401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-20401.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-354, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-20402
in-theory        20402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-354 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-20402.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-354, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-20403
in-theory        20403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-354 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20403.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-354, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-20404
in-theory        20404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-20404.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-354, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-20405
in-theory        20405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-354 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20405.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-354, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-20406
in-theory        20406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-354 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20406.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-354, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-20407
in-theory        20407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20407.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-354, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-20408
in-theory        20408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20408.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-354, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-20409
in-theory        20409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-354 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20409.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-354, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-20410
in-theory        20410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-20410.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-354, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-20411
in-theory        20411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-354 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-20411.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-354, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-20412
in-theory        20412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-354 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-20412.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-354, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-20413
in-theory        20413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-20413.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-354, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-20414
in-theory        20414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-354 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20414.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-354, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-20415
in-theory        20415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-354 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20415.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-354, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-20416
in-theory        20416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-354 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20416.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-354, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-20417
in-theory        20417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-354 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20417.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-354, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-20418
in-theory        20418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-354 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-20418.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-354, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-20419
in-theory        20419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-354 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20419.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-354, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-20420
in-theory        20420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-354 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-20420.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-354, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-20421
in-theory        20421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-354 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-20421.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-354, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-20422
in-theory        20422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-354 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-20422.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-354, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-20423
in-theory        20423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-354 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-20423.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-354, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-20424
in-theory        20424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-354 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-20424.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-354, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-20425
in-theory        20425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-354 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-20425.        ((A -> (B -> (C -> (B and C)))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-354, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-20426
in-theory        20426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-354 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-20426.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-354, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-20427
in-theory        20427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     29
proof            (modus-ponens tm-354 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-20427.        ((A -> (B -> (C -> (B and C)))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-354, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-20428
in-theory        20428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-354 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-20428.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-354, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-20429
in-theory        20429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-354 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-20429.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-354, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-20430
in-theory        20430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20430.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-354, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-20431
in-theory        20431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-20431.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-354, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-20432
in-theory        20432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20432.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F and G) -> F))), M:tm-354, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-20433
in-theory        20433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-354 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20433.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F and G) -> G))), M:tm-354, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-20434
in-theory        20434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20434.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-354, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20435
in-theory        20435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-354 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20435.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (F or G)))), M:tm-354, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-20436
in-theory        20436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20436.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G or F)))), M:tm-354, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-20437
in-theory        20437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-20437.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-354, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-20438
in-theory        20438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-354 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-20438.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-354, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-20439
in-theory        20439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-20439.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-354, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-20440
in-theory        20440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-20440.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-354, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-20441
in-theory        20441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20441.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-354, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-20442
in-theory        20442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-354 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20442.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-354, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-20443
in-theory        20443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20443.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-354, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-20444
in-theory        20444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-354 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20444.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-354, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-20445
in-theory        20445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-354 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-20445.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-354, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-20446
in-theory        20446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-354 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20446.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-354, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-20447
in-theory        20447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-354 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-20447.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-354, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-20448
in-theory        20448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-20448.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-354, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-20449
in-theory        20449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-354 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-20449.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-354, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-20450
in-theory        20450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-20450.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-354, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-20451
in-theory        20451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-354 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-20451.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-354, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-20452
in-theory        20452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-20452.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-354, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-20453
in-theory        20453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20453.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-354, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-20454
in-theory        20454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-354 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20454.        ((A -> (B -> (C -> (B and C)))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-354, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-20455
in-theory        20455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-354 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-20455.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> (((F and G) -> F) and E)))), M:tm-354, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-20456
in-theory        20456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-354 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-20456.        ((A -> (B -> (C -> (B and C)))) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-354, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-20457
in-theory        20457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-20457.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-354, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-20458
in-theory        20458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-354 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-20458.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-354, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-20459
in-theory        20459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20459.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-354, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-20460
in-theory        20460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-20460.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-354, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-20461
in-theory        20461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20461.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F and G) -> F))), M:tm-354, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-20462
in-theory        20462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-354 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20462.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F and G) -> G))), M:tm-354, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-20463
in-theory        20463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20463.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-354, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20464
in-theory        20464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-354 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20464.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (F or G)))), M:tm-354, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-20465
in-theory        20465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20465.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G or F)))), M:tm-354, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-20466
in-theory        20466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-20466.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-354, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-20467
in-theory        20467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-354 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-20467.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-354, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-20468
in-theory        20468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-20468.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-354, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-20469
in-theory        20469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-20469.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-354, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-20470
in-theory        20470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20470.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-354, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-20471
in-theory        20471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-354 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20471.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-354, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-20472
in-theory        20472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20472.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-354, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-20473
in-theory        20473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-354 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20473.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-354, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-20474
in-theory        20474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-354 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-20474.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-354, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-20475
in-theory        20475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-354 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20475.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-354, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-20476
in-theory        20476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-354 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-20476.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-354, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-20477
in-theory        20477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-20477.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-354, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-20478
in-theory        20478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-354 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-20478.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-354, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-20479
in-theory        20479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-20479.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-354, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-20480
in-theory        20480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-20480.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-354, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-20481
in-theory        20481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-20481.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-354, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-20482
in-theory        20482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-354 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-20482.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-354, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-20483
in-theory        20483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-20483.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-354, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-20484
in-theory        20484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20484.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-354, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-20485
in-theory        20485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-354 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20485.        ((A -> (B -> (C -> (B and C)))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-354, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-20486
in-theory        20486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-354 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-20486.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> (((F and G) -> G) and E)))), M:tm-354, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-20487
in-theory        20487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-354 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-20487.        ((A -> (B -> (C -> (B and C)))) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-354, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-20488
in-theory        20488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-20488.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-354, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-20489
in-theory        20489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-354 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-20489.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-354, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-20490
in-theory        20490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20490.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-354, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-20491
in-theory        20491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-20491.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-354, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-20492
in-theory        20492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-354 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20492.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-354, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-20493
in-theory        20493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-354 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20493.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-354, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-20494
in-theory        20494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20494.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-354, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20495
in-theory        20495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-354 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20495.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-354, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-20496
in-theory        20496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20496.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-354, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-20497
in-theory        20497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-20497.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-354, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-20498
in-theory        20498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-20498.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-354, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-20499
in-theory        20499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-354 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-20499.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-354, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-20500
in-theory        20500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-20500.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-354, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-20501
in-theory        20501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20501.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-354, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-20502
in-theory        20502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20502.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-354, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-20503
in-theory        20503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-354 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20503.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-354, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-20504
in-theory        20504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-354 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20504.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-354, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-20505
in-theory        20505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-354 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-20505.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-354, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-20506
in-theory        20506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-354 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20506.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-354, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-20507
in-theory        20507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-354 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-20507.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-354, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-20508
in-theory        20508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-354 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-20508.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-354, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-20509
in-theory        20509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-354 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-20509.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-354, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-20510
in-theory        20510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-354 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-20510.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-354, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-20511
in-theory        20511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-354 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-20511.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-354, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-20512
in-theory        20512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-354 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-20512.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-354, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-20513
in-theory        20513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-354 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-20513.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-354, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-20514
in-theory        20514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-354 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-20514.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-354, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-20515
in-theory        20515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-354 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-20515.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-354, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-20516
in-theory        20516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-354 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-20516.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-354, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-20517
in-theory        20517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-354 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20517.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-354, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-20518
in-theory        20518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-354 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20518.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-354, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-20519
in-theory        20519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-354 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-20519.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-354, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-20520
in-theory        20520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-354 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-20520.        ((A -> (B -> (C -> (B and C)))) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-354, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-20521
in-theory        20521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-354 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-20521.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-354, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-20522
in-theory        20522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-354 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-20522.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-354, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-20523
in-theory        20523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and (E -> D))))
theorem-size     17
proof            (modus-ponens tm-354 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20523.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and (E -> D)))), M:tm-354, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-20524
in-theory        20524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20524.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-354, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-20525
in-theory        20525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D and E) -> ((D and E) and D)))
theorem-size     19
proof            (modus-ponens tm-354 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20525.        ((A -> (B -> (C -> (B and C)))) and ((D and E) -> ((D and E) and D))), M:tm-354, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-20526
in-theory        20526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D and E) -> ((D and E) and E)))
theorem-size     19
proof            (modus-ponens tm-354 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20526.        ((A -> (B -> (C -> (B and C)))) and ((D and E) -> ((D and E) and E))), M:tm-354, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-20527
in-theory        20527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20527.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and (E -> (D and E))))), M:tm-354, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-20528
in-theory        20528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and (D or E))))
theorem-size     17
proof            (modus-ponens tm-354 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20528.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and (D or E)))), M:tm-354, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-20529
in-theory        20529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and (E or D))))
theorem-size     17
proof            (modus-ponens tm-354 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20529.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and (E or D)))), M:tm-354, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-20530
in-theory        20530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     27
proof            (modus-ponens tm-354 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-20530.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-354, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-20531
in-theory        20531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-20531.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-354, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-20532
in-theory        20532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     19
proof            (modus-ponens tm-354 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-20532.        ((A -> (B -> (C -> (B and C)))) and ((not (not D)) -> ((not (not D)) and D))), M:tm-354, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-20533
in-theory        20533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20533.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and (E -> (F -> E))))), M:tm-354, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-20534
in-theory        20534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     21
proof            (modus-ponens tm-354 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-20534.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-354, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-20535
in-theory        20535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-354 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-20535.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-354, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-20536
in-theory        20536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-354 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20536.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-354, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-20537
in-theory        20537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     33
proof            (modus-ponens tm-354 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-20537.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-354, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-20538
in-theory        20538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-354 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20538.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and ((E and F) -> E)))), M:tm-354, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-20539
in-theory        20539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     33
proof            (modus-ponens tm-354 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-20539.        ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-354, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-20540
in-theory        20540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-354 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20540.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and ((E and F) -> F)))), M:tm-354, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-20541
in-theory        20541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-354 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20541.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-354, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-20542
in-theory        20542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-354 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-20542.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-354, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-20543
in-theory        20543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-354 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20543.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and (((E and F) -> E) and D)))), M:tm-354, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-20544
in-theory        20544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-354 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20544.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and (((E and F) -> F) and D)))), M:tm-354, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-20545
in-theory        20545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-354 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20545.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-354, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-20546
in-theory        20546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20546.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-354, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-20547
in-theory        20547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-354 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20547.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-354, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-20548
in-theory        20548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20548.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-354, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-20549
in-theory        20549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20549.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-354, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-20550
in-theory        20550
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-354 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20550.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-354, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-20551
in-theory        20551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20551.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-354, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-20552
in-theory        20552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-354 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20552.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-354, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-20553
in-theory        20553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     29
proof            (modus-ponens tm-354 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20553.        ((A -> (B -> (C -> (B and C)))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-354, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-20554
in-theory        20554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-354 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20554.        ((A -> (B -> (C -> (B and C)))) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-354, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-20555
in-theory        20555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     21
proof            (modus-ponens tm-354 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20555.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-354, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-20556
in-theory        20556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20556.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-354, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-20557
in-theory        20557
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-354 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-20557.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-354, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-20558
in-theory        20558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-354 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20558.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-354, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-20559
in-theory        20559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-354 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20559.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-354, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-20560
in-theory        20560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-354 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20560.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-354, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-20561
in-theory        20561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-354 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20561.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-354, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-20562
in-theory        20562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-354 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20562.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-354, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-20563
in-theory        20563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-354 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20563.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-354, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-20564
in-theory        20564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-354 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20564.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-354, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-20565
in-theory        20565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-354 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20565.        ((A -> (B -> (C -> (B and C)))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-354, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-20566
in-theory        20566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-354 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-20566.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-354, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-20567
in-theory        20567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-354 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-20567.        ((A -> (B -> (C -> (B and C)))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-354, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-20568
in-theory        20568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20568.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-354, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-20569
in-theory        20569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     31
proof            (modus-ponens tm-354 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20569.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-354, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-20570
in-theory        20570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-354 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20570.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-354, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20571
in-theory        20571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-354 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20571.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-354, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-20572
in-theory        20572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20572.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-354, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20573
in-theory        20573
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> (F -> (E and F)))) and (B -> (C -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-351 tm-354 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20573.        ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> (F -> (E and F)))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-354, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-20574
in-theory        20574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20574.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20575
in-theory        20575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> (F -> (E and F)))) and C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20575.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> (F -> (E and F)))) and C))), M:tm-338, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20576
in-theory        20576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (D -> (E -> (D and E)))) and (A -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-335 tm-354 ((Am (-> A (and A B))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20576.        (((A -> B) or (A -> (A and B))) -> ((C -> (D -> (E -> (D and E)))) and (A -> (A and B)))), M:tm-335, m:tm-354, u:((Am (-> A (and A B))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (and A B)))))
================================================================
tm-name          tm-20577
in-theory        20577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (A -> (A and ((B -> (C -> (D -> (C and D)))) and A))))
theorem-size     29
proof            (modus-ponens tm-328 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20577.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (A -> (A and ((B -> (C -> (D -> (C and D)))) and A)))), M:tm-328, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-20578
in-theory        20578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> (C -> (D -> (C and D)))) and A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20578.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> (C -> (D -> (C and D)))) and A)))), M:tm-327, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20579
in-theory        20579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (((E and F) -> F) and (A -> ((B -> (C -> (D -> (C and D)))) and A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20579.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (((E and F) -> F) and (A -> ((B -> (C -> (D -> (C and D)))) and A)))), M:tm-326, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20580
in-theory        20580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (((E and F) -> E) and (A -> ((B -> (C -> (D -> (C and D)))) and A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20580.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (((E and F) -> E) and (A -> ((B -> (C -> (D -> (C and D)))) and A)))), M:tm-325, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20581
in-theory        20581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C -> (D -> (C and D)))) and A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20581.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C -> (D -> (C and D)))) and A)))), M:tm-324, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20582
in-theory        20582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((E -> (F -> E)) and (A -> ((B -> (C -> (D -> (C and D)))) and A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20582.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((E -> (F -> E)) and (A -> ((B -> (C -> (D -> (C and D)))) and A)))), M:tm-323, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20583
in-theory        20583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20583.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((E and F) -> F)), M:tm-322, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20584
in-theory        20584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20584.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((E and F) -> E)), M:tm-320, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20585
in-theory        20585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20585.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20586
in-theory        20586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (A -> A))
theorem-size     17
proof            (modus-ponens tm-316 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20586.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (A -> A)), M:tm-316, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-20587
in-theory        20587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20587.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (E -> (F -> E))), M:tm-315, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20588
in-theory        20588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((A -> (not ((B -> (C -> (D -> (C and D)))) and A))) -> (not A)))
theorem-size     31
proof            (modus-ponens tm-313 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20588.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((A -> (not ((B -> (C -> (D -> (C and D)))) and A))) -> (not A))), M:tm-313, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-20589
in-theory        20589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((((B -> (C -> (D -> (C and D)))) and A) -> E) -> ((A or ((B -> (C -> (D -> (C and D)))) and A)) -> E)))
theorem-size     43
proof            (modus-ponens tm-312 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20589.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((((B -> (C -> (D -> (C and D)))) and A) -> E) -> ((A or ((B -> (C -> (D -> (C and D)))) and A)) -> E))), M:tm-312, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-20590
in-theory        20590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (E or (A -> ((B -> (C -> (D -> (C and D)))) and A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20590.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (E or (A -> ((B -> (C -> (D -> (C and D)))) and A)))), M:tm-311, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20591
in-theory        20591
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((A -> ((B -> (C -> (D -> (C and D)))) and A)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20591.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((A -> ((B -> (C -> (D -> (C and D)))) and A)) or E)), M:tm-310, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20592
in-theory        20592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (E -> ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20592.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (E -> ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and E))), M:tm-309, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20593
in-theory        20593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (E -> (A -> ((B -> (C -> (D -> (C and D)))) and A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20593.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (E -> (A -> ((B -> (C -> (D -> (C and D)))) and A)))), M:tm-305, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20594
in-theory        20594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20594.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-303, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20595
in-theory        20595
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> (F -> (E and F)))) and ((B -> (C -> (B and C))) and A)))
theorem-size     31
proof            (modus-ponens tm-300 tm-354 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20595.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> (F -> (E and F)))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-354, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-20596
in-theory        20596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20596.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-270, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20597
in-theory        20597
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (E -> (F -> (E and F)))) and (((B and C) -> C) and A)))
theorem-size     27
proof            (modus-ponens tm-267 tm-354 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20597.        ((A or (((B and C) -> C) and A)) -> ((D -> (E -> (F -> (E and F)))) and (((B and C) -> C) and A))), M:tm-267, m:tm-354, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-20598
in-theory        20598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20598.        ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-239, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20599
in-theory        20599
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (E -> (F -> (E and F)))) and (((B and C) -> B) and A)))
theorem-size     27
proof            (modus-ponens tm-236 tm-354 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20599.        ((A or (((B and C) -> B) and A)) -> ((D -> (E -> (F -> (E and F)))) and (((B and C) -> B) and A))), M:tm-236, m:tm-354, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-20600
in-theory        20600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> (H -> (G and H)))) and E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20600.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> (H -> (G and H)))) and E))), M:tm-210, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20601
in-theory        20601
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> (G -> (F and G)))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     43
proof            (modus-ponens tm-207 tm-354 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20601.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> (G -> (F and G)))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-354, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-20602
in-theory        20602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20602.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-183, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20603
in-theory        20603
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> (F -> (E and F)))) and ((B -> (C -> B)) and A)))
theorem-size     27
proof            (modus-ponens tm-180 tm-354 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20603.        ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> (F -> (E and F)))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-354, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-20604
in-theory        20604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20604.        ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-157, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20605
in-theory        20605
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((B and C) -> C)))
theorem-size     23
proof            (modus-ponens tm-154 tm-354 ((Am (-> (and A B) B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20605.        ((A or ((B and C) -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((B and C) -> C))), M:tm-154, m:tm-354, u:((Am (-> (and A B) B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and A B) B))))
================================================================
tm-name          tm-20606
in-theory        20606
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20606.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-147, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20607
in-theory        20607
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((A and (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-144 tm-354 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20607.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-354, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-20608
in-theory        20608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20608.        ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-134, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20609
in-theory        20609
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (E -> (F -> (E and F)))) and ((B and C) -> B)))
theorem-size     23
proof            (modus-ponens tm-131 tm-354 ((Am (-> (and A B) A)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20609.        ((A or ((B and C) -> B)) -> ((D -> (E -> (F -> (E and F)))) and ((B and C) -> B))), M:tm-131, m:tm-354, u:((Am (-> (and A B) A)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and A B) A))))
================================================================
tm-name          tm-20610
in-theory        20610
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20610.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-125, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20611
in-theory        20611
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> (F -> (E and F)))) and (((A -> B) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-122 tm-354 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20611.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> (F -> (E and F)))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-354, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-20612
in-theory        20612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (H -> (G and H)))) and E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20612.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (H -> (G and H)))) and E))), M:tm-113, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20613
in-theory        20613
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> (G -> (F and G)))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     39
proof            (modus-ponens tm-110 tm-354 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20613.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> (G -> (F and G)))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-354, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-20614
in-theory        20614
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20614.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-105, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20615
in-theory        20615
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> (F -> (E and F)))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-102 tm-354 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20615.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> (F -> (E and F)))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-354, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-20616
in-theory        20616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> (F -> (E and F)))) and C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20616.        (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> (F -> (E and F)))) and C))), M:tm-95, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20617
in-theory        20617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (D -> (E -> (D and E)))) and (A -> A)))
theorem-size     21
proof            (modus-ponens tm-92 tm-354 ((Am (-> A A)) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20617.        (((A -> B) or (A -> A)) -> ((C -> (D -> (E -> (D and E)))) and (A -> A))), M:tm-92, m:tm-354, u:((Am (-> A A)) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A A))))
================================================================
tm-name          tm-20618
in-theory        20618
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> (E -> (D and E)))) and A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20618.        (A -> (B -> ((C -> (D -> (E -> (D and E)))) and A))), M:tm-84, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-20619
in-theory        20619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20619.        ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-83, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20620
in-theory        20620
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (E -> (F -> (E and F)))) and (B -> (C -> B))))
theorem-size     23
proof            (modus-ponens tm-80 tm-354 ((Am (-> A (-> B A))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20620.        ((A or (B -> (C -> B))) -> ((D -> (E -> (F -> (E and F)))) and (B -> (C -> B)))), M:tm-80, m:tm-354, u:((Am (-> A (-> B A))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (-> B A)))))
================================================================
tm-name          tm-20621
in-theory        20621
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (D -> (E -> (D and E)))) and B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20621.        (((not (not A)) -> A) and (B -> ((C -> (D -> (E -> (D and E)))) and B))), M:tm-76, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20622
in-theory        20622
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (C -> (D -> (C and D)))) and A))
theorem-size     17
proof            (modus-ponens tm-73 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20622.        (((not (not A)) or A) -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-73, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-20623
in-theory        20623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> (F -> (E and F)))) and C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20623.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> (F -> (E and F)))) and C))), M:tm-69, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20624
in-theory        20624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> (E -> (D and E)))) and ((A -> (not B)) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-66 tm-354 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20624.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> (E -> (D and E)))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-354, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-20625
in-theory        20625
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20625.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-54, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20626
in-theory        20626
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (F -> (E and F)))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-51 tm-354 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20626.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (F -> (E and F)))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-354, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-20627
in-theory        20627
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (D -> (E -> (D and E)))) and (B or A)))
theorem-size     19
proof            (modus-ponens tm-50 tm-354 ((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20627.        ((A or (B or A)) -> ((C -> (D -> (E -> (D and E)))) and (B or A))), M:tm-50, m:tm-354, u:((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B))))
================================================================
tm-name          tm-20628
in-theory        20628
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (D -> (E -> (D and E)))) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-49 tm-354 ((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20628.        ((A or (A or B)) -> ((C -> (D -> (E -> (D and E)))) and (A or B))), M:tm-49, m:tm-354, u:((Am (or A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B))))
================================================================
tm-name          tm-20629
in-theory        20629
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (D -> (E -> (D and E)))) and (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-48 tm-354 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20629.        ((A or (B -> (A and B))) -> ((C -> (D -> (E -> (D and E)))) and (B -> (A and B)))), M:tm-48, m:tm-354, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (and B A)))))
================================================================
tm-name          tm-20630
in-theory        20630
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (D -> (E -> (D and E)))) and B))
theorem-size     17
proof            (modus-ponens tm-47 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20630.        (((A and B) or B) -> ((C -> (D -> (E -> (D and E)))) and B)), M:tm-47, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-20631
in-theory        20631
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (D -> (E -> (D and E)))) and A))
theorem-size     17
proof            (modus-ponens tm-46 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20631.        (((A and B) or A) -> ((C -> (D -> (E -> (D and E)))) and A)), M:tm-46, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-20632
in-theory        20632
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-45 tm-354 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20632.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-354, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-20633
in-theory        20633
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (D -> (E -> (D and E)))) and (B -> A)))
theorem-size     19
proof            (modus-ponens tm-44 tm-354 ((Am (-> A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20633.        ((A or (B -> A)) -> ((C -> (D -> (E -> (D and E)))) and (B -> A))), M:tm-44, m:tm-354, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A B))))
================================================================
tm-name          tm-20634
in-theory        20634
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (E -> (F -> (E and F)))) and C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20634.        ((A -> (B or A)) and (C -> ((D -> (E -> (F -> (E and F)))) and C))), M:tm-42, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20635
in-theory        20635
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (E -> (F -> (E and F)))) and C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20635.        ((A -> (A or B)) and (C -> ((D -> (E -> (F -> (E and F)))) and C))), M:tm-32, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20636
in-theory        20636
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (C -> (D -> (C and D)))) and A)))
theorem-size     15
proof            (modus-ponens tm-24 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20636.        (A -> (A and ((B -> (C -> (D -> (C and D)))) and A))), M:tm-24, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-20637
in-theory        20637
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (F -> (E and F)))) and C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20637.        ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (F -> (E and F)))) and C))), M:tm-23, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20638
in-theory        20638
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (E -> (F -> (E and F)))) and C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20638.        (((A and B) -> B) and (C -> ((D -> (E -> (F -> (E and F)))) and C))), M:tm-22, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20639
in-theory        20639
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (E -> (F -> (E and F)))) and C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20639.        (((A and B) -> A) and (C -> ((D -> (E -> (F -> (E and F)))) and C))), M:tm-21, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20640
in-theory        20640
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20640.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-20, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20641
in-theory        20641
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (E -> (F -> (E and F)))) and C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20641.        ((A -> (B -> A)) and (C -> ((D -> (E -> (F -> (E and F)))) and C))), M:tm-19, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20642
in-theory        20642
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> (D -> (C and D)))) and A))) -> (not A))
theorem-size     17
proof            (modus-ponens tm-9 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-9 tm-5 tm-1)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20642.        ((A -> (not ((B -> (C -> (D -> (C and D)))) and A))) -> (not A)), M:tm-9, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-20643
in-theory        20643
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (C -> (B and C)))) and D) -> E) -> ((D or ((A -> (B -> (C -> (B and C)))) and D)) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20643.        ((((A -> (B -> (C -> (B and C)))) and D) -> E) -> ((D or ((A -> (B -> (C -> (B and C)))) and D)) -> E)), M:tm-8, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-20644
in-theory        20644
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (D -> (E -> (D and E)))) and B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20644.        (A or (B -> ((C -> (D -> (E -> (D and E)))) and B))), M:tm-7, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20645
in-theory        20645
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20645.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) or E), M:tm-6, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20646
in-theory        20646
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D -> (E -> (D and E)))) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20646.        (A -> ((B -> ((C -> (D -> (E -> (D and E)))) and B)) and A)), M:tm-5, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20647
in-theory        20647
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> (E -> (D and E)))) and B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-1 tm-5)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20647.        (A -> (B -> ((C -> (D -> (E -> (D and E)))) and B))), M:tm-1, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-20648
in-theory        20648
times-derived    2
----------------------------------------------------------------
theorem          (A -> (B -> ((A or C) and B)))
theorem-size     9
proof            (modus-ponens tm-355 tm-6 ((A Am) (B (or Am Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-6.            (A -> (A or B)), axiom
tm-20648.        (A -> (B -> ((A or C) and B))), M:tm-355, m:tm-6, u:((A Am) (B (or Am Bm)))
================================================================
tm-name          tm-20649
in-theory        20649
times-derived    2
----------------------------------------------------------------
theorem          (A -> (B -> ((C or A) and B)))
theorem-size     9
proof            (modus-ponens tm-355 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-20649.        (A -> (B -> ((C or A) and B))), M:tm-355, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-20650
in-theory        20650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (((B -> D) -> ((A or B) -> D)) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20650.        ((A -> B) -> (C -> (((B -> D) -> ((A or B) -> D)) and C))), M:tm-355, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-20651
in-theory        20651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (((A -> (not B)) -> (not A)) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20651.        ((A -> B) -> (C -> (((A -> (not B)) -> (not A)) and C))), M:tm-355, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-20652
in-theory        20652
times-derived    1
----------------------------------------------------------------
theorem          ((not (not A)) -> (B -> (A and B)))
theorem-size     9
proof            (modus-ponens tm-355 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-2 tm-1 tm-5 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-20652.        ((not (not A)) -> (B -> (A and B))), M:tm-355, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-20653
in-theory        20653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((A -> A) and C)))
theorem-size     11
proof            (modus-ponens tm-355 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-20653.        ((A -> B) -> (C -> ((A -> A) and C))), M:tm-355, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-20654
in-theory        20654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (D -> (((A -> (B -> C)) -> (A -> C)) and D)))
theorem-size     23
proof            (modus-ponens tm-355 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-20654.        (((A -> (B -> C)) -> (A -> B)) -> (D -> (((A -> (B -> C)) -> (A -> C)) and D))), M:tm-355, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-20655
in-theory        20655
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> (D -> ((((A -> B) and C) -> B) and D)))
theorem-size     19
proof            (modus-ponens tm-355 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-20655.        ((((A -> B) and C) -> A) -> (D -> ((((A -> B) and C) -> B) and D))), M:tm-355, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-20656
in-theory        20656
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> (D -> (((A and (B -> C)) -> C) and D)))
theorem-size     19
proof            (modus-ponens tm-355 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-20656.        (((A and (B -> C)) -> B) -> (D -> (((A and (B -> C)) -> C) and D))), M:tm-355, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-20657
in-theory        20657
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D -> C)) and A) and B)))
theorem-size     13
proof            (modus-ponens tm-355 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20657.        (A -> (B -> (((C -> (D -> C)) and A) and B))), M:tm-355, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-20658
in-theory        20658
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A) and B)))
theorem-size     21
proof            (modus-ponens tm-355 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-20658.        (A -> (B -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A) and B))), M:tm-355, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-20659
in-theory        20659
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C and D) -> C) and A) and B)))
theorem-size     13
proof            (modus-ponens tm-355 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20659.        (A -> (B -> ((((C and D) -> C) and A) and B))), M:tm-355, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-20660
in-theory        20660
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C and D) -> D) and A) and B)))
theorem-size     13
proof            (modus-ponens tm-355 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20660.        (A -> (B -> ((((C and D) -> D) and A) and B))), M:tm-355, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-20661
in-theory        20661
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D -> (C and D))) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20661.        (A -> (B -> (((C -> (D -> (C and D))) and A) and B))), M:tm-355, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-20662
in-theory        20662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((A -> (A and B)) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20662.        ((A -> B) -> (C -> ((A -> (A and B)) and C))), M:tm-355, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-20663
in-theory        20663
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (C or D)) and A) and B)))
theorem-size     13
proof            (modus-ponens tm-355 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20663.        (A -> (B -> (((C -> (C or D)) and A) and B))), M:tm-355, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-20664
in-theory        20664
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D or C)) and A) and B)))
theorem-size     13
proof            (modus-ponens tm-355 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20664.        (A -> (B -> (((C -> (D or C)) and A) and B))), M:tm-355, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-20665
in-theory        20665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (D -> (((B or (A -> B)) -> C) and D)))
theorem-size     17
proof            (modus-ponens tm-355 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20665.        (((A -> B) -> C) -> (D -> (((B or (A -> B)) -> C) and D))), M:tm-355, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-20666
in-theory        20666
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and E)))
theorem-size     29
proof            (modus-ponens tm-355 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20666.        ((((A -> B) -> (A -> C)) -> D) -> (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and E))), M:tm-355, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-20667
in-theory        20667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((((A and D) or A) -> B) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20667.        ((A -> B) -> (C -> ((((A and D) or A) -> B) and C))), M:tm-355, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-20668
in-theory        20668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((((D and A) or A) -> B) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20668.        ((A -> B) -> (C -> ((((D and A) or A) -> B) and C))), M:tm-355, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-20669
in-theory        20669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> (D -> (((B or (A -> (B and A))) -> C) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20669.        (((A -> (B and A)) -> C) -> (D -> (((B or (A -> (B and A))) -> C) and D))), M:tm-355, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-20670
in-theory        20670
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D -> (((A or (A or B)) -> C) and D)))
theorem-size     17
proof            (modus-ponens tm-355 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20670.        (((A or B) -> C) -> (D -> (((A or (A or B)) -> C) and D))), M:tm-355, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-20671
in-theory        20671
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D -> (((B or (A or B)) -> C) and D)))
theorem-size     17
proof            (modus-ponens tm-355 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20671.        (((A or B) -> C) -> (D -> (((B or (A or B)) -> C) and D))), M:tm-355, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-20672
in-theory        20672
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> (E -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and E)))
theorem-size     31
proof            (modus-ponens tm-355 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-20672.        ((((A -> B) -> ((C or A) -> B)) -> D) -> (E -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) and E))), M:tm-355, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-20673
in-theory        20673
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) and A) and B)))
theorem-size     21
proof            (modus-ponens tm-355 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-20673.        (A -> (B -> ((((C -> D) -> ((D -> E) -> ((C or D) -> E))) and A) and B))), M:tm-355, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-20674
in-theory        20674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (B -> C)) -> (D -> (((A -> B) -> ((A or B) -> C)) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-20674.        (((A -> B) -> (B -> C)) -> (D -> (((A -> B) -> ((A or B) -> C)) and D))), M:tm-355, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-20675
in-theory        20675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> A))) -> (C -> ((not A) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20675.        ((A -> (not (B -> A))) -> (C -> ((not A) and C))), M:tm-355, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-20676
in-theory        20676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (D -> ((not (A -> (B -> C))) and D)))
theorem-size     25
proof            (modus-ponens tm-355 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20676.        (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (D -> ((not (A -> (B -> C))) and D))), M:tm-355, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-20677
in-theory        20677
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not A)) -> (C -> ((not (A and B)) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20677.        (((A and B) -> (not A)) -> (C -> ((not (A and B)) and C))), M:tm-355, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-20678
in-theory        20678
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not B)) -> (C -> ((not (A and B)) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20678.        (((A and B) -> (not B)) -> (C -> ((not (A and B)) and C))), M:tm-355, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-20679
in-theory        20679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (A and B)))) -> (C -> ((not A) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20679.        ((A -> (not (B -> (A and B)))) -> (C -> ((not A) and C))), M:tm-355, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-20680
in-theory        20680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A or B))) -> (C -> ((not A) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20680.        ((A -> (not (A or B))) -> (C -> ((not A) and C))), M:tm-355, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-20681
in-theory        20681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B or A))) -> (C -> ((not A) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20681.        ((A -> (not (B or A))) -> (C -> ((not A) and C))), M:tm-355, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-20682
in-theory        20682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (D -> ((not (A -> B)) and D)))
theorem-size     23
proof            (modus-ponens tm-355 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-20682.        (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (D -> ((not (A -> B)) and D))), M:tm-355, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-20683
in-theory        20683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (C -> ((not (A -> B)) and C)))
theorem-size     21
proof            (modus-ponens tm-355 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-20683.        (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (C -> ((not (A -> B)) and C))), M:tm-355, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-20684
in-theory        20684
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> C) -> (D -> ((((A -> B) or ((A -> (not B)) -> (not A))) -> C) and D)))
theorem-size     27
proof            (modus-ponens tm-355 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-9)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-20684.        ((((A -> (not B)) -> (not A)) -> C) -> (D -> ((((A -> B) or ((A -> (not B)) -> (not A))) -> C) and D))), M:tm-355, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-20685
in-theory        20685
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> D) -> ((C -> (not D)) -> (not C))) and A) and B)))
theorem-size     19
proof            (modus-ponens tm-355 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-20685.        (A -> (B -> ((((C -> D) -> ((C -> (not D)) -> (not C))) and A) and B))), M:tm-355, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-20686
in-theory        20686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (not B))) -> (C -> (((A -> B) -> (not A)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-20686.        (((A -> B) -> (A -> (not B))) -> (C -> (((A -> B) -> (not A)) and C))), M:tm-355, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-20687
in-theory        20687
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not A)) -> (B -> ((not (not (not A))) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-20687.        (((not (not A)) -> (not A)) -> (B -> ((not (not (not A))) and B))), M:tm-355, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-20688
in-theory        20688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((((not (not A)) or A) -> B) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-20688.        ((A -> B) -> (C -> ((((not (not A)) or A) -> B) and C))), M:tm-355, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-20689
in-theory        20689
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((not (not C)) -> C) and A) and B)))
theorem-size     13
proof            (modus-ponens tm-355 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-10)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-20689.        (A -> (B -> ((((not (not C)) -> C) and A) and B))), M:tm-355, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-20690
in-theory        20690
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) -> A) -> (C -> (((not (not (A -> B))) -> B) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-10)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-20690.        (((not (not (A -> B))) -> A) -> (C -> (((not (not (A -> B))) -> B) and C))), M:tm-355, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-20691
in-theory        20691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> B)))) -> (D -> ((not A) and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20691.        ((A -> (not (B -> (C -> B)))) -> (D -> ((not A) and D))), M:tm-355, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-20692
in-theory        20692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> (D -> (((E or (A -> (B -> A))) -> C) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20692.        (((A -> (B -> A)) -> C) -> (D -> (((E or (A -> (B -> A))) -> C) and D))), M:tm-355, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-20693
in-theory        20693
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D -> (E -> D))) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-20693.        (A -> (B -> (((C -> (D -> (E -> D))) and A) and B))), M:tm-355, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-20694
in-theory        20694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((A -> (D -> B)) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-20694.        ((A -> B) -> (C -> ((A -> (D -> B)) and C))), M:tm-355, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-20695
in-theory        20695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (D -> ((A -> (B -> C)) and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20695.        ((A -> (B -> C)) -> (D -> ((A -> (B -> C)) and D))), M:tm-355, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-20696
in-theory        20696
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (C -> ((A and B) and C)))
theorem-size     11
proof            (modus-ponens tm-355 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20696.        ((A and B) -> (C -> ((A and B) and C))), M:tm-355, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-20697
in-theory        20697
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((A -> B) and C)))
theorem-size     11
proof            (modus-ponens tm-355 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-20697.        ((A -> B) -> (C -> ((A -> B) and C))), M:tm-355, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-20698
in-theory        20698
times-derived    1
----------------------------------------------------------------
theorem          ((not (not A)) -> (B -> ((not (not A)) and B)))
theorem-size     11
proof            (modus-ponens tm-355 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-10)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-20698.        ((not (not A)) -> (B -> ((not (not A)) and B))), M:tm-355, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-20699
in-theory        20699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> A))) -> (C -> ((not (A -> B)) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-20699.        (((A -> B) -> (not (A -> A))) -> (C -> ((not (A -> B)) and C))), M:tm-355, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-20700
in-theory        20700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> B) -> (C -> ((((A -> D) or (A -> A)) -> B) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-20700.        (((A -> A) -> B) -> (C -> ((((A -> D) or (A -> A)) -> B) and C))), M:tm-355, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-20701
in-theory        20701
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> D) -> (C -> C)) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20701.        (A -> (B -> ((((C -> D) -> (C -> C)) and A) and B))), M:tm-355, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-20702
in-theory        20702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> (C -> (((A -> B) -> A) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-20702.        (((A -> B) -> A) -> (C -> (((A -> B) -> A) and C))), M:tm-355, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-20703
in-theory        20703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> A) -> C)) -> (D -> ((A -> C) and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-20703.        ((A -> ((B -> A) -> C)) -> (D -> ((A -> C) and D))), M:tm-355, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-20704
in-theory        20704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A -> B)) -> (C -> ((A -> B) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-20704.        ((A -> (A -> B)) -> (C -> ((A -> B) and C))), M:tm-355, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-20705
in-theory        20705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (D -> (((A -> (B -> C)) -> (A -> B)) and D)))
theorem-size     23
proof            (modus-ponens tm-355 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-20705.        (((A -> (B -> C)) -> (A -> B)) -> (D -> (((A -> (B -> C)) -> (A -> B)) and D))), M:tm-355, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-20706
in-theory        20706
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (D -> ((not ((A -> (B -> C)) -> (A -> B))) and D)))
theorem-size     35
proof            (modus-ponens tm-355 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-20706.        ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (D -> ((not ((A -> (B -> C)) -> (A -> B))) and D))), M:tm-355, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-20707
in-theory        20707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> D) -> (E -> (((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D) and E)))
theorem-size     37
proof            (modus-ponens tm-355 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-20707.        ((((A -> (B -> C)) -> (A -> C)) -> D) -> (E -> (((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D) and E))), M:tm-355, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-20708
in-theory        20708
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and A) and B)))
theorem-size     27
proof            (modus-ponens tm-355 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20708.        (A -> (B -> (((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and A) and B))), M:tm-355, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-20709
in-theory        20709
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (D -> ((((A -> (B -> C)) -> (A -> B)) -> (A -> C)) and D)))
theorem-size     33
proof            (modus-ponens tm-355 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-20709.        ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (D -> ((((A -> (B -> C)) -> (A -> B)) -> (A -> C)) and D))), M:tm-355, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-20710
in-theory        20710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (E -> (((A -> (B -> C)) -> D) and E)))
theorem-size     27
proof            (modus-ponens tm-355 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-20710.        (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (E -> (((A -> (B -> C)) -> D) and E))), M:tm-355, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-20711
in-theory        20711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (E -> ((not A) and E)))
theorem-size     23
proof            (modus-ponens tm-355 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20711.        ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (E -> ((not A) and E))), M:tm-355, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-20712
in-theory        20712
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (E -> (((F or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D) and E)))
theorem-size     37
proof            (modus-ponens tm-355 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20712.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (E -> (((F or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D) and E))), M:tm-355, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-20713
in-theory        20713
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A) and B)))
theorem-size     23
proof            (modus-ponens tm-355 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20713.        (A -> (B -> (((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A) and B))), M:tm-355, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-20714
in-theory        20714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> D))) -> (E -> ((A -> ((B -> C) -> (B -> D))) and E)))
theorem-size     21
proof            (modus-ponens tm-355 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-20714.        ((A -> (B -> (C -> D))) -> (E -> ((A -> ((B -> C) -> (B -> D))) and E))), M:tm-355, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-20715
in-theory        20715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and A) -> (C -> (B and C)))
theorem-size     11
proof            (modus-ponens tm-355 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-2 tm-1 tm-5 tm-3 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-20715.        (((A -> B) and A) -> (C -> (B and C))), M:tm-355, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-20716
in-theory        20716
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) and D) -> (E -> (C and E)))
theorem-size     15
proof            (modus-ponens tm-355 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-20716.        ((((A -> (B -> A)) -> C) and D) -> (E -> (C and E))), M:tm-355, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-20717
in-theory        20717
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (F -> (D and F)))
theorem-size     23
proof            (modus-ponens tm-355 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20717.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (F -> (D and F))), M:tm-355, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-20718
in-theory        20718
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> A) and C) -> (A -> B)) -> (D -> (((((A -> B) -> A) and C) -> B) and D)))
theorem-size     25
proof            (modus-ponens tm-355 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-20718.        (((((A -> B) -> A) and C) -> (A -> B)) -> (D -> (((((A -> B) -> A) and C) -> B) and D))), M:tm-355, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-20719
in-theory        20719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> (D -> ((((A -> B) and C) -> A) and D)))
theorem-size     19
proof            (modus-ponens tm-355 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-20719.        ((((A -> B) and C) -> A) -> (D -> ((((A -> B) and C) -> A) and D))), M:tm-355, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-20720
in-theory        20720
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (D -> ((not (((A -> B) and C) -> A)) and D)))
theorem-size     29
proof            (modus-ponens tm-355 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-20720.        (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (D -> ((not (((A -> B) and C) -> A)) and D))), M:tm-355, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-20721
in-theory        20721
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> D) -> (E -> ((((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D) and E)))
theorem-size     31
proof            (modus-ponens tm-355 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-20721.        (((((A -> B) and C) -> B) -> D) -> (E -> ((((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D) and E))), M:tm-355, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-20722
in-theory        20722
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and A) and B)))
theorem-size     23
proof            (modus-ponens tm-355 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20722.        (A -> (B -> ((((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and A) and B))), M:tm-355, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-20723
in-theory        20723
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (D -> (((((A -> B) and C) -> A) -> B) and D)))
theorem-size     27
proof            (modus-ponens tm-355 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-20723.        (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (D -> (((((A -> B) and C) -> A) -> B) and D))), M:tm-355, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-20724
in-theory        20724
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) and D) -> (E -> (C and E)))
theorem-size     15
proof            (modus-ponens tm-355 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-20724.        (((((A and B) -> A) -> C) and D) -> (E -> (C and E))), M:tm-355, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-20725
in-theory        20725
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A -> C)) -> (D -> (((A and B) -> C) and D)))
theorem-size     17
proof            (modus-ponens tm-355 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-20725.        (((A and B) -> (A -> C)) -> (D -> (((A and B) -> C) and D))), M:tm-355, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-20726
in-theory        20726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B and C) -> B))) -> (D -> ((not A) and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20726.        ((A -> (not ((B and C) -> B))) -> (D -> ((not A) and D))), M:tm-355, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-20727
in-theory        20727
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> (D -> (((E or ((A and B) -> A)) -> C) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20727.        ((((A and B) -> A) -> C) -> (D -> (((E or ((A and B) -> A)) -> C) and D))), M:tm-355, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-20728
in-theory        20728
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> ((D and E) -> D)) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-20728.        (A -> (B -> (((C -> ((D and E) -> D)) and A) and B))), M:tm-355, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-20729
in-theory        20729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> (D -> ((A -> B) and D)))
theorem-size     13
proof            (modus-ponens tm-355 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-20729.        ((A -> (B and C)) -> (D -> ((A -> B) and D))), M:tm-355, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-20730
in-theory        20730
times-derived    1
----------------------------------------------------------------
theorem          ((A and (A -> B)) -> (C -> (B and C)))
theorem-size     11
proof            (modus-ponens tm-355 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-5 tm-4 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-20730.        ((A and (A -> B)) -> (C -> (B and C))), M:tm-355, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-20731
in-theory        20731
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> D)) -> (E -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-355 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-20731.        ((A and ((B -> (C -> B)) -> D)) -> (E -> (D and E))), M:tm-355, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-20732
in-theory        20732
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (F -> (E and F)))
theorem-size     23
proof            (modus-ponens tm-355 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20732.        ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (F -> (E and F))), M:tm-355, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-20733
in-theory        20733
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> D)) -> (E -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-355 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-5 tm-4 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-20733.        ((A and (((B and C) -> B) -> D)) -> (E -> (D and E))), M:tm-355, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-20734
in-theory        20734
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> B)) -> (B -> C)) -> (D -> (((A and ((B -> C) -> B)) -> C) and D)))
theorem-size     25
proof            (modus-ponens tm-355 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-20734.        (((A and ((B -> C) -> B)) -> (B -> C)) -> (D -> (((A and ((B -> C) -> B)) -> C) and D))), M:tm-355, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-20735
in-theory        20735
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> (D -> (((A and (B -> C)) -> B) and D)))
theorem-size     19
proof            (modus-ponens tm-355 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-20735.        (((A and (B -> C)) -> B) -> (D -> (((A and (B -> C)) -> B) and D))), M:tm-355, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-20736
in-theory        20736
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (D -> ((not ((A and (B -> C)) -> B)) and D)))
theorem-size     29
proof            (modus-ponens tm-355 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-20736.        ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (D -> ((not ((A and (B -> C)) -> B)) and D))), M:tm-355, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-20737
in-theory        20737
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> D) -> (E -> (((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D) and E)))
theorem-size     31
proof            (modus-ponens tm-355 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-20737.        ((((A and (B -> C)) -> C) -> D) -> (E -> (((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D) and E))), M:tm-355, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-20738
in-theory        20738
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and A) and B)))
theorem-size     23
proof            (modus-ponens tm-355 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20738.        (A -> (B -> (((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and A) and B))), M:tm-355, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-20739
in-theory        20739
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (D -> ((((A and (B -> C)) -> B) -> C) and D)))
theorem-size     27
proof            (modus-ponens tm-355 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-20739.        ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (D -> ((((A and (B -> C)) -> B) -> C) and D))), M:tm-355, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-20740
in-theory        20740
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> D)) -> (E -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-355 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-20740.        ((A and (((B and C) -> C) -> D)) -> (E -> (D and E))), M:tm-355, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-20741
in-theory        20741
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) and D) -> (E -> (C and E)))
theorem-size     15
proof            (modus-ponens tm-355 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-5 tm-3 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-20741.        (((((A and B) -> B) -> C) and D) -> (E -> (C and E))), M:tm-355, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-20742
in-theory        20742
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (B -> C)) -> (D -> (((A and B) -> C) and D)))
theorem-size     17
proof            (modus-ponens tm-355 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-20742.        (((A and B) -> (B -> C)) -> (D -> (((A and B) -> C) and D))), M:tm-355, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-20743
in-theory        20743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B and C) -> C))) -> (D -> ((not A) and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20743.        ((A -> (not ((B and C) -> C))) -> (D -> ((not A) and D))), M:tm-355, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-20744
in-theory        20744
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> (D -> (((E or ((A and B) -> B)) -> C) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20744.        ((((A and B) -> B) -> C) -> (D -> (((E or ((A and B) -> B)) -> C) and D))), M:tm-355, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-20745
in-theory        20745
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> ((D and E) -> E)) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-20745.        (A -> (B -> (((C -> ((D and E) -> E)) and A) and B))), M:tm-355, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-20746
in-theory        20746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> (D -> ((A -> C) and D)))
theorem-size     13
proof            (modus-ponens tm-355 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-20746.        ((A -> (B and C)) -> (D -> ((A -> C) and D))), M:tm-355, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-20747
in-theory        20747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> B)) and A))) -> (D -> ((not A) and D)))
theorem-size     17
proof            (modus-ponens tm-355 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20747.        ((A -> (not ((B -> (C -> B)) and A))) -> (D -> ((not A) and D))), M:tm-355, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-20748
in-theory        20748
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and C) -> D) -> (E -> (((C or ((A -> (B -> A)) and C)) -> D) and E)))
theorem-size     25
proof            (modus-ponens tm-355 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20748.        ((((A -> (B -> A)) and C) -> D) -> (E -> (((C or ((A -> (B -> A)) and C)) -> D) and E))), M:tm-355, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-20749
in-theory        20749
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> ((D -> (E -> D)) and C)) and A) and B)))
theorem-size     17
proof            (modus-ponens tm-355 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-20749.        (A -> (B -> (((C -> ((D -> (E -> D)) and C)) and A) and B))), M:tm-355, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-20750
in-theory        20750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (E -> ((not A) and E)))
theorem-size     25
proof            (modus-ponens tm-355 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-20750.        ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (E -> ((not A) and E))), M:tm-355, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-20751
in-theory        20751
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (F -> (((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E) and F)))
theorem-size     41
proof            (modus-ponens tm-355 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-20751.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (F -> (((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E) and F))), M:tm-355, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-20752
in-theory        20752
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and A) and B)))
theorem-size     25
proof            (modus-ponens tm-355 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-20752.        (A -> (B -> (((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and A) and B))), M:tm-355, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-20753
in-theory        20753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> B) and A))) -> (D -> ((not A) and D)))
theorem-size     17
proof            (modus-ponens tm-355 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20753.        ((A -> (not (((B and C) -> B) and A))) -> (D -> ((not A) and D))), M:tm-355, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-20754
in-theory        20754
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and C) -> D) -> (E -> (((C or (((A and B) -> A) and C)) -> D) and E)))
theorem-size     25
proof            (modus-ponens tm-355 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20754.        (((((A and B) -> A) and C) -> D) -> (E -> (((C or (((A and B) -> A) and C)) -> D) and E))), M:tm-355, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-20755
in-theory        20755
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (((D and E) -> D) and C)) and A) and B)))
theorem-size     17
proof            (modus-ponens tm-355 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-20755.        (A -> (B -> (((C -> (((D and E) -> D) and C)) and A) and B))), M:tm-355, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-20756
in-theory        20756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> C) and A))) -> (D -> ((not A) and D)))
theorem-size     17
proof            (modus-ponens tm-355 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20756.        ((A -> (not (((B and C) -> C) and A))) -> (D -> ((not A) and D))), M:tm-355, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-20757
in-theory        20757
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and C) -> D) -> (E -> (((C or (((A and B) -> B) and C)) -> D) and E)))
theorem-size     25
proof            (modus-ponens tm-355 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20757.        (((((A and B) -> B) and C) -> D) -> (E -> (((C or (((A and B) -> B) and C)) -> D) and E))), M:tm-355, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-20758
in-theory        20758
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (((D and E) -> E) and C)) and A) and B)))
theorem-size     17
proof            (modus-ponens tm-355 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-20758.        (A -> (B -> (((C -> (((D and E) -> E) and C)) and A) and B))), M:tm-355, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-20759
in-theory        20759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (D -> ((not A) and D)))
theorem-size     19
proof            (modus-ponens tm-355 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20759.        ((A -> (not ((B -> (C -> (B and C))) and A))) -> (D -> ((not A) and D))), M:tm-355, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-20760
in-theory        20760
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and C) -> D) -> (E -> (((C or ((A -> (B -> (A and B))) and C)) -> D) and E)))
theorem-size     29
proof            (modus-ponens tm-355 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20760.        ((((A -> (B -> (A and B))) and C) -> D) -> (E -> (((C or ((A -> (B -> (A and B))) and C)) -> D) and E))), M:tm-355, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-20761
in-theory        20761
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> ((D -> (E -> (D and E))) and C)) and A) and B)))
theorem-size     19
proof            (modus-ponens tm-355 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-20761.        (A -> (B -> (((C -> ((D -> (E -> (D and E))) and C)) and A) and B))), M:tm-355, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-20762
in-theory        20762
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and (C -> A)) and B)))
theorem-size     11
proof            (modus-ponens tm-355 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20762.        (A -> (B -> ((A and (C -> A)) and B))), M:tm-355, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-20763
in-theory        20763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (D -> (((A -> (B -> C)) and ((A -> B) -> (A -> C))) and D)))
theorem-size     23
proof            (modus-ponens tm-355 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20763.        ((A -> (B -> C)) -> (D -> (((A -> (B -> C)) and ((A -> B) -> (A -> C))) and D))), M:tm-355, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-20764
in-theory        20764
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (C -> (((A and B) and A) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20764.        ((A and B) -> (C -> (((A and B) and A) and C))), M:tm-355, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-20765
in-theory        20765
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (C -> (((A and B) and B) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20765.        ((A and B) -> (C -> (((A and B) and B) and C))), M:tm-355, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-20766
in-theory        20766
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and (C -> (A and C))) and B)))
theorem-size     13
proof            (modus-ponens tm-355 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20766.        (A -> (B -> ((A and (C -> (A and C))) and B))), M:tm-355, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-20767
in-theory        20767
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and (A or C)) and B)))
theorem-size     11
proof            (modus-ponens tm-355 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20767.        (A -> (B -> ((A and (A or C)) and B))), M:tm-355, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-20768
in-theory        20768
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and (C or A)) and B)))
theorem-size     11
proof            (modus-ponens tm-355 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20768.        (A -> (B -> ((A and (C or A)) and B))), M:tm-355, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-20769
in-theory        20769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (((A -> B) and ((B -> D) -> ((A or B) -> D))) and C)))
theorem-size     21
proof            (modus-ponens tm-355 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-20769.        ((A -> B) -> (C -> (((A -> B) and ((B -> D) -> ((A or B) -> D))) and C))), M:tm-355, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-20770
in-theory        20770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (((A -> B) and ((A -> (not B)) -> (not A))) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-20770.        ((A -> B) -> (C -> (((A -> B) and ((A -> (not B)) -> (not A))) and C))), M:tm-355, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-20771
in-theory        20771
times-derived    1
----------------------------------------------------------------
theorem          ((not (not A)) -> (B -> (((not (not A)) and A) and B)))
theorem-size     13
proof            (modus-ponens tm-355 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-10)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-20771.        ((not (not A)) -> (B -> (((not (not A)) and A) and B))), M:tm-355, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-20772
in-theory        20772
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and (C -> (D -> C))) and B)))
theorem-size     13
proof            (modus-ponens tm-355 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20772.        (A -> (B -> ((A and (C -> (D -> C))) and B))), M:tm-355, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-20773
in-theory        20773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (((A -> B) and (A -> A)) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-20773.        ((A -> B) -> (C -> (((A -> B) and (A -> A)) and C))), M:tm-355, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-20774
in-theory        20774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (D -> ((((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))) and D)))
theorem-size     33
proof            (modus-ponens tm-355 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-20774.        (((A -> (B -> C)) -> (A -> B)) -> (D -> ((((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))) and D))), M:tm-355, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-20775
in-theory        20775
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and B)))
theorem-size     21
proof            (modus-ponens tm-355 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20775.        (A -> (B -> ((A and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and B))), M:tm-355, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-20776
in-theory        20776
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> (D -> (((((A -> B) and C) -> A) and (((A -> B) and C) -> B)) and D)))
theorem-size     27
proof            (modus-ponens tm-355 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-20776.        ((((A -> B) and C) -> A) -> (D -> (((((A -> B) and C) -> A) and (((A -> B) and C) -> B)) and D))), M:tm-355, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-20777
in-theory        20777
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and ((C and D) -> C)) and B)))
theorem-size     13
proof            (modus-ponens tm-355 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20777.        (A -> (B -> ((A and ((C and D) -> C)) and B))), M:tm-355, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-20778
in-theory        20778
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> (D -> ((((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-355 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-20778.        (((A and (B -> C)) -> B) -> (D -> ((((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)) and D))), M:tm-355, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-20779
in-theory        20779
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and ((C and D) -> D)) and B)))
theorem-size     13
proof            (modus-ponens tm-355 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20779.        (A -> (B -> ((A and ((C and D) -> D)) and B))), M:tm-355, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-20780
in-theory        20780
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and ((C -> (D -> C)) and A)) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20780.        (A -> (B -> ((A and ((C -> (D -> C)) and A)) and B))), M:tm-355, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-20781
in-theory        20781
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and B)))
theorem-size     23
proof            (modus-ponens tm-355 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-20781.        (A -> (B -> ((A and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and B))), M:tm-355, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-20782
in-theory        20782
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and (((C and D) -> C) and A)) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20782.        (A -> (B -> ((A and (((C and D) -> C) and A)) and B))), M:tm-355, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-20783
in-theory        20783
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and (((C and D) -> D) and A)) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20783.        (A -> (B -> ((A and (((C and D) -> D) and A)) and B))), M:tm-355, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-20784
in-theory        20784
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and ((C -> (D -> (C and D))) and A)) and B)))
theorem-size     17
proof            (modus-ponens tm-355 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20784.        (A -> (B -> ((A and ((C -> (D -> (C and D))) and A)) and B))), M:tm-355, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-20785
in-theory        20785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (((A -> B) and (A -> (A and B))) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20785.        ((A -> B) -> (C -> (((A -> B) and (A -> (A and B))) and C))), M:tm-355, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-20786
in-theory        20786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (A and B)))) -> (C -> ((not (A -> B)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20786.        (((A -> B) -> (not (A -> (A and B)))) -> (C -> ((not (A -> B)) and C))), M:tm-355, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-20787
in-theory        20787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> C) -> (D -> ((((A -> B) or (A -> (A and B))) -> C) and D)))
theorem-size     23
proof            (modus-ponens tm-355 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-20787.        (((A -> (A and B)) -> C) -> (D -> ((((A -> B) or (A -> (A and B))) -> C) and D))), M:tm-355, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-20788
in-theory        20788
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> D) -> (C -> (C and D))) and A) and B)))
theorem-size     17
proof            (modus-ponens tm-355 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20788.        (A -> (B -> ((((C -> D) -> (C -> (C and D))) and A) and B))), M:tm-355, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-20789
in-theory        20789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> (C -> (((A -> B) -> (A and B)) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-20789.        (((A -> B) -> A) -> (C -> (((A -> B) -> (A and B)) and C))), M:tm-355, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-20790
in-theory        20790
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and (C -> (D -> (C and D)))) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20790.        (A -> (B -> ((A and (C -> (D -> (C and D)))) and B))), M:tm-355, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20791
in-theory        20791
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> D)) -> (E -> (D and E)))
theorem-size     17
proof            (modus-ponens tm-355 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-5 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20791.        ((A and ((B -> (C -> (B and C))) -> D)) -> (E -> (D and E))), M:tm-355, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-20792
in-theory        20792
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) and D) -> (E -> (C and E)))
theorem-size     17
proof            (modus-ponens tm-355 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-5 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-20792.        ((((A -> (B -> (A and B))) -> C) and D) -> (E -> (C and E))), M:tm-355, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-20793
in-theory        20793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (A and B)) -> C)) -> (D -> ((A -> C) and D)))
theorem-size     17
proof            (modus-ponens tm-355 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-20793.        ((A -> ((B -> (A and B)) -> C)) -> (D -> ((A -> C) and D))), M:tm-355, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-20794
in-theory        20794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> (B and C))))) -> (D -> ((not A) and D)))
theorem-size     17
proof            (modus-ponens tm-355 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20794.        ((A -> (not (B -> (C -> (B and C))))) -> (D -> ((not A) and D))), M:tm-355, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-20795
in-theory        20795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> (D -> (((E or (A -> (B -> (A and B)))) -> C) and D)))
theorem-size     25
proof            (modus-ponens tm-355 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20795.        (((A -> (B -> (A and B))) -> C) -> (D -> (((E or (A -> (B -> (A and B)))) -> C) and D))), M:tm-355, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-20796
in-theory        20796
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D -> (E -> (D and E)))) and A) and B)))
theorem-size     17
proof            (modus-ponens tm-355 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20796.        (A -> (B -> (((C -> (D -> (E -> (D and E)))) and A) and B))), M:tm-355, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-20797
in-theory        20797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((A -> (D -> (B and D))) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20797.        ((A -> B) -> (C -> ((A -> (D -> (B and D))) and C))), M:tm-355, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20798
in-theory        20798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-354 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20798.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-354, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20799
in-theory        20799
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (B -> (D -> ((C -> (B and C)) and D))))
theorem-size     21
proof            (modus-ponens tm-351 tm-355 ((A Am) (Bm (-> B (and Am B))) (C (-> Am (-> Cm (and (-> B (and Am B)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20799.        ((A or (B -> (C -> (B and C)))) -> (B -> (D -> ((C -> (B and C)) and D)))), M:tm-351, m:tm-355, u:((A Am) (Bm (-> B (and Am B))) (C (-> Am (-> Cm (and (-> B (and Am B)) Cm)))))
================================================================
tm-name          tm-20800
in-theory        20800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20800.        (((A -> B) -> (A -> (C -> (B and C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20801
in-theory        20801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (C -> (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-338 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20801.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (C -> (E -> (D and E))))), M:tm-338, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20802
in-theory        20802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (A -> (C -> ((A and B) and C))))
theorem-size     19
proof            (modus-ponens tm-335 tm-355 ((A Am) (Bm (and Am B)) (C (-> Am (-> Cm (and (and Am B) Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20802.        (((A -> B) or (A -> (A and B))) -> (A -> (C -> ((A and B) and C)))), M:tm-335, m:tm-355, u:((A Am) (Bm (and Am B)) (C (-> Am (-> Cm (and (and Am B) Cm)))))
================================================================
tm-name          tm-20803
in-theory        20803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and ((A -> B) -> ((A -> B) and (A -> (C -> (B and C))))))
theorem-size     27
proof            (modus-ponens tm-328 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20803.        (((A -> B) -> (A -> (C -> (B and C)))) and ((A -> B) -> ((A -> B) and (A -> (C -> (B and C)))))), M:tm-328, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20804
in-theory        20804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> (C -> (B and C))))))
theorem-size     31
proof            (modus-ponens tm-327 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20804.        (((A -> B) -> (A -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> (C -> (B and C)))))), M:tm-327, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20805
in-theory        20805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (((D and E) -> E) and ((A -> B) -> (A -> (C -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-326 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20805.        (((A -> B) -> (A -> (C -> (B and C)))) and (((D and E) -> E) and ((A -> B) -> (A -> (C -> (B and C)))))), M:tm-326, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20806
in-theory        20806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (((D and E) -> D) and ((A -> B) -> (A -> (C -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-325 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20806.        (((A -> B) -> (A -> (C -> (B and C)))) and (((D and E) -> D) and ((A -> B) -> (A -> (C -> (B and C)))))), M:tm-325, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20807
in-theory        20807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> (C -> (B and C))))))
theorem-size     37
proof            (modus-ponens tm-324 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20807.        (((A -> B) -> (A -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> (C -> (B and C)))))), M:tm-324, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20808
in-theory        20808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and ((D -> (E -> D)) and ((A -> B) -> (A -> (C -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-323 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20808.        (((A -> B) -> (A -> (C -> (B and C)))) and ((D -> (E -> D)) and ((A -> B) -> (A -> (C -> (B and C)))))), M:tm-323, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20809
in-theory        20809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20809.        (((A -> B) -> (A -> (C -> (B and C)))) and ((D and E) -> E)), M:tm-322, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20810
in-theory        20810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20810.        (((A -> B) -> (A -> (C -> (B and C)))) and ((D and E) -> D)), M:tm-320, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20811
in-theory        20811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20811.        (((A -> B) -> (A -> (C -> (B and C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20812
in-theory        20812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and ((A -> B) -> (A -> B)))
theorem-size     19
proof            (modus-ponens tm-316 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20812.        (((A -> B) -> (A -> (C -> (B and C)))) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20813
in-theory        20813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20813.        (((A -> B) -> (A -> (C -> (B and C)))) and (D -> (E -> D))), M:tm-315, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20814
in-theory        20814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (((A -> B) -> (not (A -> (C -> (B and C))))) -> (not (A -> B))))
theorem-size     29
proof            (modus-ponens tm-313 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20814.        (((A -> B) -> (A -> (C -> (B and C)))) and (((A -> B) -> (not (A -> (C -> (B and C))))) -> (not (A -> B)))), M:tm-313, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20815
in-theory        20815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (((A -> (C -> (B and C))) -> D) -> (((A -> B) or (A -> (C -> (B and C)))) -> D)))
theorem-size     35
proof            (modus-ponens tm-312 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20815.        (((A -> B) -> (A -> (C -> (B and C)))) and (((A -> (C -> (B and C))) -> D) -> (((A -> B) or (A -> (C -> (B and C)))) -> D))), M:tm-312, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20816
in-theory        20816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (D or ((A -> B) -> (A -> (C -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-311 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20816.        (((A -> B) -> (A -> (C -> (B and C)))) and (D or ((A -> B) -> (A -> (C -> (B and C)))))), M:tm-311, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20817
in-theory        20817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (((A -> B) -> (A -> (C -> (B and C)))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20817.        (((A -> B) -> (A -> (C -> (B and C)))) and (((A -> B) -> (A -> (C -> (B and C)))) or D)), M:tm-310, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20818
in-theory        20818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (D -> (((A -> B) -> (A -> (C -> (B and C)))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20818.        (((A -> B) -> (A -> (C -> (B and C)))) and (D -> (((A -> B) -> (A -> (C -> (B and C)))) and D))), M:tm-309, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20819
in-theory        20819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (((A -> B) -> A) -> ((A -> B) -> (C -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-306 tm-355 ((A (-> Am Bm)) (B Am) (C (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20819.        (((A -> B) -> (A -> (C -> (B and C)))) and (((A -> B) -> A) -> ((A -> B) -> (C -> (B and C))))), M:tm-306, m:tm-355, u:((A (-> Am Bm)) (B Am) (C (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-20820
in-theory        20820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (D -> ((A -> B) -> (A -> (C -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-305 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20820.        (((A -> B) -> (A -> (C -> (B and C)))) and (D -> ((A -> B) -> (A -> (C -> (B and C)))))), M:tm-305, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20821
in-theory        20821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-303 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20821.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-303, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20822
in-theory        20822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-270 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20822.        ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-270, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20823
in-theory        20823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-239 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20823.        ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-239, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20824
in-theory        20824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (E -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-210 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20824.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (E -> (G -> (F and G))))), M:tm-210, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20825
in-theory        20825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-183 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20825.        ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-183, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20826
in-theory        20826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-157 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20826.        ((A -> ((B and C) -> C)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-157, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20827
in-theory        20827
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((B and C) -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-154 tm-355 ((Am (and A Bm)) (B Bm) (C (-> (and A Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20827.        ((A or ((B and C) -> C)) -> ((B and C) -> (D -> (C and D)))), M:tm-154, m:tm-355, u:((Am (and A Bm)) (B Bm) (C (-> (and A Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20828
in-theory        20828
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-147 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20828.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-147, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20829
in-theory        20829
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> (D -> (C and D))))
theorem-size     27
proof            (modus-ponens tm-144 tm-355 ((Am (and A (-> B Bm))) (C Bm) (D (-> (and A (-> B Bm)) (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-5)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20829.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> (D -> (C and D)))), M:tm-144, m:tm-355, u:((Am (and A (-> B Bm))) (C Bm) (D (-> (and A (-> B Bm)) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20830
in-theory        20830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-134 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20830.        ((A -> ((B and C) -> B)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-134, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20831
in-theory        20831
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((B and C) -> (D -> (B and D))))
theorem-size     17
proof            (modus-ponens tm-131 tm-355 ((Am (and Bm B)) (A Bm) (C (-> (and Bm B) (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20831.        ((A or ((B and C) -> B)) -> ((B and C) -> (D -> (B and D)))), M:tm-131, m:tm-355, u:((Am (and Bm B)) (A Bm) (C (-> (and Bm B) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20832
in-theory        20832
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-125 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20832.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-125, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20833
in-theory        20833
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> (D -> (B and D))))
theorem-size     27
proof            (modus-ponens tm-122 tm-355 ((Am (and (-> A Bm) C)) (B Bm) (D (-> (and (-> A Bm) C) (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-5)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20833.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> (D -> (B and D)))), M:tm-122, m:tm-355, u:((Am (and (-> A Bm) C)) (B Bm) (D (-> (and (-> A Bm) C) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20834
in-theory        20834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> C) -> (A -> (B and C))))
theorem-size     13
proof            (modus-ponens tm-114 tm-355 ((A (-> Am Bm)) (B Am) (C Cm) (D (and Bm Cm))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20834.        ((A -> B) -> ((A -> C) -> (A -> (B and C)))), M:tm-114, m:tm-355, u:((A (-> Am Bm)) (B Am) (C Cm) (D (and Bm Cm)))
================================================================
tm-name          tm-20835
in-theory        20835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-113 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20835.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (G -> (F and G))))), M:tm-113, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20836
in-theory        20836
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> (E -> (((B -> C) -> (B -> D)) and E))))
theorem-size     33
proof            (modus-ponens tm-110 tm-355 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> A (-> B C)) (-> Cm (and (-> (-> A B) (-> A C)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20836.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> (E -> (((B -> C) -> (B -> D)) and E)))), M:tm-110, m:tm-355, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> A (-> B C)) (-> Cm (and (-> (-> A B) (-> A C)) Cm)))))
================================================================
tm-name          tm-20837
in-theory        20837
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     31
proof            (modus-ponens tm-105 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20837.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-105, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20838
in-theory        20838
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> (D -> ((A -> C) and D))))
theorem-size     33
proof            (modus-ponens tm-102 tm-355 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> A (-> B C)) (-> Cm (and (-> A C) Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20838.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> (D -> ((A -> C) and D)))), M:tm-102, m:tm-355, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> A (-> B C)) (-> Cm (and (-> A C) Cm)))))
================================================================
tm-name          tm-20839
in-theory        20839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> (C -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-95 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20839.        (((A -> B) -> (A -> A)) and ((C -> D) -> (C -> (E -> (D and E))))), M:tm-95, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20840
in-theory        20840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (A -> (C -> (A and C))))
theorem-size     15
proof            (modus-ponens tm-92 tm-355 ((Bm Am) (A Am) (B (-> Am (-> Cm (and Am Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20840.        (((A -> B) or (A -> A)) -> (A -> (C -> (A and C)))), M:tm-92, m:tm-355, u:((Bm Am) (A Am) (B (-> Am (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-20841
in-theory        20841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (A -> (D -> (B and D)))))
theorem-size     13
proof            (modus-ponens tm-84 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20841.        ((A -> B) -> (C -> (A -> (D -> (B and D))))), M:tm-84, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20842
in-theory        20842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-83 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20842.        ((A -> (B -> (C -> B))) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-83, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20843
in-theory        20843
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (B -> (D -> ((C -> B) and D))))
theorem-size     17
proof            (modus-ponens tm-80 tm-355 ((A Am) (Bm (-> B Am)) (C (-> Am (-> Cm (and (-> B Am) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20843.        ((A or (B -> (C -> B))) -> (B -> (D -> ((C -> B) and D)))), M:tm-80, m:tm-355, u:((A Am) (Bm (-> B Am)) (C (-> Am (-> Cm (and (-> B Am) Cm)))))
================================================================
tm-name          tm-20844
in-theory        20844
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> (B -> (D -> (C and D)))))
theorem-size     17
proof            (modus-ponens tm-76 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20844.        (((not (not A)) -> A) and ((B -> C) -> (B -> (D -> (C and D))))), M:tm-76, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20845
in-theory        20845
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> (A -> (C -> (B and C))))
theorem-size     17
proof            (modus-ponens tm-73 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20845.        (((not (not (A -> B))) or (A -> B)) -> (A -> (C -> (B and C)))), M:tm-73, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20846
in-theory        20846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (C -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-69 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20846.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (C -> (E -> (D and E))))), M:tm-69, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20847
in-theory        20847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> (C -> ((not A) and C))))
theorem-size     23
proof            (modus-ponens tm-66 tm-355 ((Am (-> A (not B))) (Bm (not A)) (C (-> (-> A (not B)) (-> Cm (and (not A) Cm))))))
axioms-used      (tm-8 tm-9 tm-2 tm-1 tm-5)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20847.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> (C -> ((not A) and C)))), M:tm-66, m:tm-355, u:((Am (-> A (not B))) (Bm (not A)) (C (-> (-> A (not B)) (-> Cm (and (not A) Cm)))))
================================================================
tm-name          tm-20848
in-theory        20848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) -> ((A or A) -> (B -> (A and B))))
theorem-size     13
proof            (modus-ponens tm-55 tm-355 ((A Bm) (Am Bm) (B Bm) (C (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20848.        ((A -> A) -> ((A or A) -> (B -> (A and B)))), M:tm-55, m:tm-355, u:((A Bm) (Am Bm) (B Bm) (C (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-20849
in-theory        20849
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-54 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20849.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-54, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20850
in-theory        20850
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (D -> (((A or B) -> C) and D))))
theorem-size     27
proof            (modus-ponens tm-51 tm-355 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> Cm (and (-> (or C A) B) Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20850.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (D -> (((A or B) -> C) and D)))), M:tm-51, m:tm-355, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (-> Cm (and (-> (or C A) B) Cm)))))
================================================================
tm-name          tm-20851
in-theory        20851
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (B -> (C -> ((A and B) and C))))
theorem-size     17
proof            (modus-ponens tm-48 tm-355 ((A Am) (Bm (and B Am)) (C (-> Am (-> Cm (and (and B Am) Cm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20851.        ((A or (B -> (A and B))) -> (B -> (C -> ((A and B) and C)))), M:tm-48, m:tm-355, u:((A Am) (Bm (and B Am)) (C (-> Am (-> Cm (and (and B Am) Cm)))))
================================================================
tm-name          tm-20852
in-theory        20852
times-derived    2
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (B -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-47 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20852.        (((A and (B -> C)) or (B -> C)) -> (B -> (D -> (C and D)))), M:tm-47, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20853
in-theory        20853
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (A -> (D -> (B and D))))
theorem-size     17
proof            (modus-ponens tm-46 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20853.        ((((A -> B) and C) or (A -> B)) -> (A -> (D -> (B and D)))), M:tm-46, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20854
in-theory        20854
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D -> ((A -> C) and D))))
theorem-size     25
proof            (modus-ponens tm-45 tm-355 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> Cm (and (-> A C) Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20854.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D -> ((A -> C) and D)))), M:tm-45, m:tm-355, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> Cm (and (-> A C) Cm)))))
================================================================
tm-name          tm-20855
in-theory        20855
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (B -> (C -> (A and C))))
theorem-size     13
proof            (modus-ponens tm-44 tm-355 ((A Am) (B Bm) (C (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20855.        ((A or (B -> A)) -> (B -> (C -> (A and C)))), M:tm-44, m:tm-355, u:((A Am) (B Bm) (C (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20856
in-theory        20856
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (C -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-42 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20856.        ((A -> (B or A)) and ((C -> D) -> (C -> (E -> (D and E))))), M:tm-42, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20857
in-theory        20857
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (C -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-32 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20857.        ((A -> (A or B)) and ((C -> D) -> (C -> (E -> (D and E))))), M:tm-32, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20858
in-theory        20858
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (A -> (C -> (B and C)))))
theorem-size     15
proof            (modus-ponens tm-24 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20858.        ((A -> B) -> ((A -> B) and (A -> (C -> (B and C))))), M:tm-24, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20859
in-theory        20859
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-23 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20859.        ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (E -> (D and E))))), M:tm-23, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20860
in-theory        20860
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (C -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-22 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20860.        (((A and B) -> B) and ((C -> D) -> (C -> (E -> (D and E))))), M:tm-22, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20861
in-theory        20861
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (C -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-21 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20861.        (((A and B) -> A) and ((C -> D) -> (C -> (E -> (D and E))))), M:tm-21, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20862
in-theory        20862
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-20 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20862.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-20, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20863
in-theory        20863
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (C -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-19 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20863.        ((A -> (B -> A)) and ((C -> D) -> (C -> (E -> (D and E))))), M:tm-19, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20864
in-theory        20864
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (C -> (B and C))))) -> (not (A -> B)))
theorem-size     17
proof            (modus-ponens tm-9 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-9 tm-2 tm-1 tm-5)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20864.        (((A -> B) -> (not (A -> (C -> (B and C))))) -> (not (A -> B))), M:tm-9, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20865
in-theory        20865
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (C and B))) -> D) -> (((A -> C) or (A -> (B -> (C and B)))) -> D))
theorem-size     23
proof            (modus-ponens tm-8 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20865.        (((A -> (B -> (C and B))) -> D) -> (((A -> C) or (A -> (B -> (C and B)))) -> D)), M:tm-8, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-20866
in-theory        20866
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (B -> (D -> (C and D)))))
theorem-size     13
proof            (modus-ponens tm-7 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-7 tm-2 tm-1 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20866.        (A or ((B -> C) -> (B -> (D -> (C and D))))), M:tm-7, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20867
in-theory        20867
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-6 tm-2 tm-1 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20867.        (((A -> B) -> (A -> (C -> (B and C)))) or D), M:tm-6, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20868
in-theory        20868
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> (D -> (C and D)))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20868.        (A -> (((B -> C) -> (B -> (D -> (C and D)))) and A)), M:tm-5, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20869
in-theory        20869
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> ((A -> B) -> (C -> (B and C))))
theorem-size     15
proof            (modus-ponens tm-2 tm-355 ((A (-> Am Bm)) (B Am) (C (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20869.        (((A -> B) -> A) -> ((A -> B) -> (C -> (B and C)))), M:tm-2, m:tm-355, u:((A (-> Am Bm)) (B Am) (C (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-20870
in-theory        20870
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (B -> (D -> (C and D)))))
theorem-size     13
proof            (modus-ponens tm-1 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-1 tm-2 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-20870.        (A -> ((B -> C) -> (B -> (D -> (C and D))))), M:tm-1, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-20871
in-theory        20871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-354 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20871.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-354, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20872
in-theory        20872
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-351 tm-356 ((Am (-> A (-> B (and A B)))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20872.        ((A or (B -> (C -> (B and C)))) -> (D -> (E -> (F -> (E and F))))), M:tm-351, m:tm-356, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20873
in-theory        20873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20873.        ((A -> (B -> (C -> (D -> (C and D))))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20874
in-theory        20874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) -> D) -> ((A -> (B -> (C -> (B and C)))) and D))
theorem-size     23
proof            (modus-ponens tm-339 tm-356 ((Am (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) B)) (A (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20874.        (((A -> (B -> (C -> (B and C)))) -> D) -> ((A -> (B -> (C -> (B and C)))) and D)), M:tm-339, m:tm-356, u:((Am (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) B)) (A (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20875
in-theory        20875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-338 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20875.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> (E -> (F -> (E and F)))))), M:tm-338, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20876
in-theory        20876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> (D -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-335 tm-356 ((Am (-> A (and A B))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20876.        (((A -> B) or (A -> (A and B))) -> (C -> (D -> (E -> (D and E))))), M:tm-335, m:tm-356, u:((Am (-> A (and A B))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20877
in-theory        20877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (A -> (A and (B -> (C -> (D -> (C and D)))))))
theorem-size     25
proof            (modus-ponens tm-328 tm-356 ((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20877.        ((A -> (B -> (C -> (D -> (C and D))))) and (A -> (A and (B -> (C -> (D -> (C and D))))))), M:tm-328, m:tm-356, u:((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20878
in-theory        20878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and ((E -> (F -> (E and F))) and (A -> (B -> (C -> (D -> (C and D)))))))
theorem-size     31
proof            (modus-ponens tm-327 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20878.        ((A -> (B -> (C -> (D -> (C and D))))) and ((E -> (F -> (E and F))) and (A -> (B -> (C -> (D -> (C and D))))))), M:tm-327, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20879
in-theory        20879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (((E and F) -> F) and (A -> (B -> (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-326 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20879.        ((A -> (B -> (C -> (D -> (C and D))))) and (((E and F) -> F) and (A -> (B -> (C -> (D -> (C and D))))))), M:tm-326, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20880
in-theory        20880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (((E and F) -> E) and (A -> (B -> (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-325 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20880.        ((A -> (B -> (C -> (D -> (C and D))))) and (((E and F) -> E) and (A -> (B -> (C -> (D -> (C and D))))))), M:tm-325, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20881
in-theory        20881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> (C -> (D -> (C and D)))))))
theorem-size     37
proof            (modus-ponens tm-324 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20881.        ((A -> (B -> (C -> (D -> (C and D))))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> (C -> (D -> (C and D))))))), M:tm-324, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20882
in-theory        20882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and ((E -> (F -> E)) and (A -> (B -> (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-323 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20882.        ((A -> (B -> (C -> (D -> (C and D))))) and ((E -> (F -> E)) and (A -> (B -> (C -> (D -> (C and D))))))), M:tm-323, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20883
in-theory        20883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20883.        ((A -> (B -> (C -> (D -> (C and D))))) and ((E and F) -> F)), M:tm-322, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20884
in-theory        20884
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (D -> (C and D)))) -> E)) -> (B -> (C -> (D -> (C and D))))) and ((A and ((B -> (C -> (D -> (C and D)))) -> E)) -> E))
theorem-size     39
proof            (modus-ponens tm-321 tm-356 ((Am (and A (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) C))) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20884.        (((A and ((B -> (C -> (D -> (C and D)))) -> E)) -> (B -> (C -> (D -> (C and D))))) and ((A and ((B -> (C -> (D -> (C and D)))) -> E)) -> E)), M:tm-321, m:tm-356, u:((Am (and A (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) C))) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20885
in-theory        20885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20885.        ((A -> (B -> (C -> (D -> (C and D))))) and ((E and F) -> E)), M:tm-320, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20886
in-theory        20886
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (C -> (B and C)))) -> D) and E) -> (A -> (B -> (C -> (B and C))))) and ((((A -> (B -> (C -> (B and C)))) -> D) and E) -> D))
theorem-size     39
proof            (modus-ponens tm-319 tm-356 ((Am (and (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) B) C)) (A (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20886.        (((((A -> (B -> (C -> (B and C)))) -> D) and E) -> (A -> (B -> (C -> (B and C))))) and ((((A -> (B -> (C -> (B and C)))) -> D) and E) -> D)), M:tm-319, m:tm-356, u:((Am (and (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) B) C)) (A (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20887
in-theory        20887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20887.        ((A -> (B -> (C -> (D -> (C and D))))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20888
in-theory        20888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) -> D)) -> (A -> (B -> (C -> (B and C))))) and ((A -> ((B -> (C -> (B and C))) -> D)) -> (A -> D)))
theorem-size     37
proof            (modus-ponens tm-317 tm-356 ((Am (-> Bm (-> (-> Cm (-> Dm (and Cm Dm))) C))) (A Bm) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20888.        (((A -> ((B -> (C -> (B and C))) -> D)) -> (A -> (B -> (C -> (B and C))))) and ((A -> ((B -> (C -> (B and C))) -> D)) -> (A -> D))), M:tm-317, m:tm-356, u:((Am (-> Bm (-> (-> Cm (-> Dm (and Cm Dm))) C))) (A Bm) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-20889
in-theory        20889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-356 ((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20889.        ((A -> (B -> (C -> (D -> (C and D))))) and (A -> A)), M:tm-316, m:tm-356, u:((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20890
in-theory        20890
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20890.        ((A -> (B -> (C -> (D -> (C and D))))) and (E -> (F -> E))), M:tm-315, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20891
in-theory        20891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and ((A -> (not (B -> (C -> (D -> (C and D)))))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-356 ((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20891.        ((A -> (B -> (C -> (D -> (C and D))))) and ((A -> (not (B -> (C -> (D -> (C and D)))))) -> (not A))), M:tm-313, m:tm-356, u:((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20892
in-theory        20892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (((B -> (C -> (D -> (C and D)))) -> E) -> ((A or (B -> (C -> (D -> (C and D))))) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-356 ((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20892.        ((A -> (B -> (C -> (D -> (C and D))))) and (((B -> (C -> (D -> (C and D)))) -> E) -> ((A or (B -> (C -> (D -> (C and D))))) -> E))), M:tm-312, m:tm-356, u:((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20893
in-theory        20893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (E or (A -> (B -> (C -> (D -> (C and D)))))))
theorem-size     25
proof            (modus-ponens tm-311 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20893.        ((A -> (B -> (C -> (D -> (C and D))))) and (E or (A -> (B -> (C -> (D -> (C and D))))))), M:tm-311, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20894
in-theory        20894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and ((A -> (B -> (C -> (D -> (C and D))))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20894.        ((A -> (B -> (C -> (D -> (C and D))))) and ((A -> (B -> (C -> (D -> (C and D))))) or E)), M:tm-310, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20895
in-theory        20895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (E -> ((A -> (B -> (C -> (D -> (C and D))))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20895.        ((A -> (B -> (C -> (D -> (C and D))))) and (E -> ((A -> (B -> (C -> (D -> (C and D))))) and E))), M:tm-309, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20896
in-theory        20896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and ((A -> B) -> (A -> (C -> (D -> (C and D))))))
theorem-size     25
proof            (modus-ponens tm-306 tm-356 ((A Am) (B Bm) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20896.        ((A -> (B -> (C -> (D -> (C and D))))) and ((A -> B) -> (A -> (C -> (D -> (C and D)))))), M:tm-306, m:tm-356, u:((A Am) (B Bm) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-20897
in-theory        20897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (E -> (A -> (B -> (C -> (D -> (C and D)))))))
theorem-size     25
proof            (modus-ponens tm-305 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20897.        ((A -> (B -> (C -> (D -> (C and D))))) and (E -> (A -> (B -> (C -> (D -> (C and D))))))), M:tm-305, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20898
in-theory        20898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-303 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20898.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-303, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20899
in-theory        20899
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-300 tm-356 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20899.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (E -> (F -> (E and F))))), M:tm-300, m:tm-356, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20900
in-theory        20900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-270 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20900.        ((A -> (((B and C) -> C) and A)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-270, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20901
in-theory        20901
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-267 tm-356 ((Am (and (-> (and A B) B) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20901.        ((A or (((B and C) -> C) and A)) -> (D -> (E -> (F -> (E and F))))), M:tm-267, m:tm-356, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20902
in-theory        20902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-239 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20902.        ((A -> (((B and C) -> B) and A)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-239, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20903
in-theory        20903
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-236 tm-356 ((Am (and (-> (and A B) A) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20903.        ((A or (((B and C) -> B) and A)) -> (D -> (E -> (F -> (E and F))))), M:tm-236, m:tm-356, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20904
in-theory        20904
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-210 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20904.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (G -> (H -> (G and H)))))), M:tm-210, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20905
in-theory        20905
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-207 tm-356 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20905.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (F -> (G -> (F and G))))), M:tm-207, m:tm-356, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20906
in-theory        20906
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-183 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20906.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-183, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20907
in-theory        20907
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-180 tm-356 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20907.        ((A or ((B -> (C -> B)) and A)) -> (D -> (E -> (F -> (E and F))))), M:tm-180, m:tm-356, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20908
in-theory        20908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-157 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20908.        ((A -> ((B and C) -> C)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-157, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20909
in-theory        20909
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-154 tm-356 ((Am (-> (and A B) B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20909.        ((A or ((B and C) -> C)) -> (D -> (E -> (F -> (E and F))))), M:tm-154, m:tm-356, u:((Am (-> (and A B) B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20910
in-theory        20910
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> (C -> (D -> (C and D))))
theorem-size     11
proof            (modus-ponens tm-152 tm-356 ((Am (and A Bm)) (B Bm) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20910.        ((A and B) -> (C -> (D -> (C and D)))), M:tm-152, m:tm-356, u:((Am (and A Bm)) (B Bm) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-20911
in-theory        20911
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-147 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20911.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-147, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20912
in-theory        20912
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-144 tm-356 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20912.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (E -> (F -> (E and F))))), M:tm-144, m:tm-356, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20913
in-theory        20913
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (D -> (C and D)))) -> E)) -> (B -> (C -> (D -> (C and D)))))
theorem-size     23
proof            (modus-ponens tm-142 tm-356 ((Am (and A (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) C))) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-4 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20913.        ((A and ((B -> (C -> (D -> (C and D)))) -> E)) -> (B -> (C -> (D -> (C and D))))), M:tm-142, m:tm-356, u:((Am (and A (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) C))) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20914
in-theory        20914
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (D -> (C and D)))) -> B)) -> (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-141 tm-356 ((Am (and A (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Bm))) (B Bm) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20914.        ((A and ((B -> (C -> (D -> (C and D)))) -> B)) -> (C -> (D -> (C and D)))), M:tm-141, m:tm-356, u:((Am (and A (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Bm))) (B Bm) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-20915
in-theory        20915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-134 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20915.        ((A -> ((B and C) -> B)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-134, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20916
in-theory        20916
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-131 tm-356 ((Am (-> (and A B) A)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20916.        ((A or ((B and C) -> B)) -> (D -> (E -> (F -> (E and F))))), M:tm-131, m:tm-356, u:((Am (-> (and A B) A)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20917
in-theory        20917
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-125 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20917.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-125, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20918
in-theory        20918
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-122 tm-356 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20918.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (E -> (F -> (E and F))))), M:tm-122, m:tm-356, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20919
in-theory        20919
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (C -> (B and C)))) -> D) and E) -> (A -> (B -> (C -> (B and C)))))
theorem-size     23
proof            (modus-ponens tm-120 tm-356 ((Am (and (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) B) C)) (A (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-3 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20919.        ((((A -> (B -> (C -> (B and C)))) -> D) and E) -> (A -> (B -> (C -> (B and C))))), M:tm-120, m:tm-356, u:((Am (and (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) B) C)) (A (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20920
in-theory        20920
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (C -> (B and C)))) -> A) and D) -> (B -> (C -> (B and C))))
theorem-size     21
proof            (modus-ponens tm-119 tm-356 ((Am (and (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Bm) C)) (A Bm) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20920.        ((((A -> (B -> (C -> (B and C)))) -> A) and D) -> (B -> (C -> (B and C)))), M:tm-119, m:tm-356, u:((Am (and (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Bm) C)) (A Bm) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-20921
in-theory        20921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-113 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20921.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (H -> (G and H)))))), M:tm-113, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20922
in-theory        20922
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-110 tm-356 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20922.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (F -> (G -> (F and G))))), M:tm-110, m:tm-356, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20923
in-theory        20923
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (D -> (E -> (D and E))))
theorem-size     13
proof            (modus-ponens tm-108 tm-356 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20923.        ((A -> (B -> C)) -> (D -> (E -> (D and E)))), M:tm-108, m:tm-356, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-20924
in-theory        20924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) -> (A -> B)) -> (A -> (C -> (B and C))))
theorem-size     21
proof            (modus-ponens tm-106 tm-356 ((Am (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> Bm Cm))) (A Bm) (B Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20924.        (((A -> (B -> (C -> (B and C)))) -> (A -> B)) -> (A -> (C -> (B and C)))), M:tm-106, m:tm-356, u:((Am (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> Bm Cm))) (A Bm) (B Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-20925
in-theory        20925
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     31
proof            (modus-ponens tm-105 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20925.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-105, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20926
in-theory        20926
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (E -> (F -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-102 tm-356 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20926.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (E -> (F -> (E and F))))), M:tm-102, m:tm-356, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20927
in-theory        20927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) -> D)) -> (A -> (B -> (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-100 tm-356 ((Am (-> Bm (-> (-> Cm (-> Dm (and Cm Dm))) C))) (A Bm) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20927.        ((A -> ((B -> (C -> (B and C))) -> D)) -> (A -> (B -> (C -> (B and C))))), M:tm-100, m:tm-356, u:((Am (-> Bm (-> (-> Cm (-> Dm (and Cm Dm))) C))) (A Bm) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-20928
in-theory        20928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) -> D) -> (A -> (B -> (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-96 tm-356 ((Am (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) B)) (A (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20928.        (((A -> (B -> (C -> (B and C)))) -> D) -> (A -> (B -> (C -> (B and C))))), M:tm-96, m:tm-356, u:((Am (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) B)) (A (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20929
in-theory        20929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-95 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20929.        (((A -> B) -> (A -> A)) and (C -> (D -> (E -> (F -> (E and F)))))), M:tm-95, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20930
in-theory        20930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> (D -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-92 tm-356 ((Am (-> A A)) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20930.        (((A -> B) or (A -> A)) -> (C -> (D -> (E -> (D and E))))), M:tm-92, m:tm-356, u:((Am (-> A A)) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20931
in-theory        20931
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C -> (D -> (E -> (D and E))))))
theorem-size     13
proof            (modus-ponens tm-84 tm-356 ((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20931.        (A -> (B -> (C -> (D -> (E -> (D and E)))))), M:tm-84, m:tm-356, u:((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20932
in-theory        20932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-83 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20932.        ((A -> (B -> (C -> B))) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-83, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20933
in-theory        20933
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-80 tm-356 ((Am (-> A (-> B A))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20933.        ((A or (B -> (C -> B))) -> (D -> (E -> (F -> (E and F))))), M:tm-80, m:tm-356, u:((Am (-> A (-> B A))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20934
in-theory        20934
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> (B -> (C -> (B and C)))) -> D))) -> D)
theorem-size     15
proof            (modus-ponens tm-77 tm-356 ((Am (not (not (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) B)))) (A (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-10 tm-1 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20934.        ((not (not ((A -> (B -> (C -> (B and C)))) -> D))) -> D), M:tm-77, m:tm-356, u:((Am (not (not (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) B)))) (A (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20935
in-theory        20935
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> (D -> (E -> (D and E))))))
theorem-size     17
proof            (modus-ponens tm-76 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-10 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20935.        (((not (not A)) -> A) and (B -> (C -> (D -> (E -> (D and E)))))), M:tm-76, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20936
in-theory        20936
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> (C -> (D -> (C and D)))))
theorem-size     15
proof            (modus-ponens tm-73 tm-356 ((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-10 tm-1 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20936.        (((not (not A)) or A) -> (B -> (C -> (D -> (C and D))))), M:tm-73, m:tm-356, u:((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20937
in-theory        20937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (E -> (F -> (E and F))))))
theorem-size     23
proof            (modus-ponens tm-69 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-9 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20937.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (E -> (F -> (E and F)))))), M:tm-69, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20938
in-theory        20938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (D -> (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-66 tm-356 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-9 tm-1 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20938.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (D -> (E -> (D and E))))), M:tm-66, m:tm-356, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20939
in-theory        20939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> (C -> (D -> (C and D)))))
theorem-size     15
proof            (modus-ponens tm-55 tm-356 ((Am (-> A Bm)) (B Bm) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20939.        ((A -> B) -> ((A or B) -> (C -> (D -> (C and D))))), M:tm-55, m:tm-356, u:((Am (-> A Bm)) (B Bm) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-20940
in-theory        20940
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-54 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20940.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-54, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20941
in-theory        20941
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-51 tm-356 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20941.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (F -> (E and F))))), M:tm-51, m:tm-356, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20942
in-theory        20942
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-50 tm-356 ((Am (or A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20942.        ((A or (B or A)) -> (C -> (D -> (E -> (D and E))))), M:tm-50, m:tm-356, u:((Am (or A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20943
in-theory        20943
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-49 tm-356 ((Am (or A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20943.        ((A or (A or B)) -> (C -> (D -> (E -> (D and E))))), M:tm-49, m:tm-356, u:((Am (or A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20944
in-theory        20944
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (D -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-48 tm-356 ((Am (-> A (and B A))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20944.        ((A or (B -> (A and B))) -> (C -> (D -> (E -> (D and E))))), M:tm-48, m:tm-356, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20945
in-theory        20945
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-47 tm-356 ((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-4 tm-1 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20945.        (((A and B) or B) -> (C -> (D -> (E -> (D and E))))), M:tm-47, m:tm-356, u:((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20946
in-theory        20946
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-46 tm-356 ((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20946.        (((A and B) or A) -> (C -> (D -> (E -> (D and E))))), M:tm-46, m:tm-356, u:((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20947
in-theory        20947
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-45 tm-356 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20947.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (F -> (E and F))))), M:tm-45, m:tm-356, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20948
in-theory        20948
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-44 tm-356 ((Am (-> A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20948.        ((A or (B -> A)) -> (C -> (D -> (E -> (D and E))))), M:tm-44, m:tm-356, u:((Am (-> A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20949
in-theory        20949
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-42 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20949.        ((A -> (B or A)) and (C -> (D -> (E -> (F -> (E and F)))))), M:tm-42, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20950
in-theory        20950
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-32 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20950.        ((A -> (A or B)) and (C -> (D -> (E -> (F -> (E and F)))))), M:tm-32, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20951
in-theory        20951
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B -> (C -> (D -> (C and D))))))
theorem-size     13
proof            (modus-ponens tm-24 tm-356 ((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20951.        (A -> (A and (B -> (C -> (D -> (C and D)))))), M:tm-24, m:tm-356, u:((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20952
in-theory        20952
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-23 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20952.        ((A -> (B -> (A and B))) and (C -> (D -> (E -> (F -> (E and F)))))), M:tm-23, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20953
in-theory        20953
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-22 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20953.        (((A and B) -> B) and (C -> (D -> (E -> (F -> (E and F)))))), M:tm-22, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20954
in-theory        20954
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-21 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20954.        (((A and B) -> A) and (C -> (D -> (E -> (F -> (E and F)))))), M:tm-21, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20955
in-theory        20955
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-20 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20955.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-20, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20956
in-theory        20956
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-19 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20956.        ((A -> (B -> A)) and (C -> (D -> (E -> (F -> (E and F)))))), M:tm-19, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20957
in-theory        20957
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (D -> (C and D)))) -> E)) -> E)
theorem-size     15
proof            (modus-ponens tm-17 tm-356 ((Am (and A (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) C))) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-4 tm-1 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20957.        ((A and ((B -> (C -> (D -> (C and D)))) -> E)) -> E), M:tm-17, m:tm-356, u:((Am (and A (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) C))) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20958
in-theory        20958
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (C -> (B and C)))) -> D) and E) -> D)
theorem-size     15
proof            (modus-ponens tm-15 tm-356 ((Am (and (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) B) C)) (A (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-3 tm-1 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20958.        ((((A -> (B -> (C -> (B and C)))) -> D) and E) -> D), M:tm-15, m:tm-356, u:((Am (and (-> (-> Bm (-> Cm (-> Dm (and Cm Dm)))) B) C)) (A (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20959
in-theory        20959
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) -> D)) -> (A -> D))
theorem-size     15
proof            (modus-ponens tm-13 tm-356 ((Am (-> Bm (-> (-> Cm (-> Dm (and Cm Dm))) C))) (A Bm) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20959.        ((A -> ((B -> (C -> (B and C))) -> D)) -> (A -> D)), M:tm-13, m:tm-356, u:((Am (-> Bm (-> (-> Cm (-> Dm (and Cm Dm))) C))) (A Bm) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-20960
in-theory        20960
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> (D -> (C and D)))))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-356 ((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-9 tm-1 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20960.        ((A -> (not (B -> (C -> (D -> (C and D)))))) -> (not A)), M:tm-9, m:tm-356, u:((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20961
in-theory        20961
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) -> D) -> ((E or (A -> (B -> (C -> (B and C))))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-356 ((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20961.        (((A -> (B -> (C -> (B and C)))) -> D) -> ((E or (A -> (B -> (C -> (B and C))))) -> D)), M:tm-8, m:tm-356, u:((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-20962
in-theory        20962
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C -> (D -> (E -> (D and E))))))
theorem-size     13
proof            (modus-ponens tm-7 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-7 tm-1 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20962.        (A or (B -> (C -> (D -> (E -> (D and E)))))), M:tm-7, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20963
in-theory        20963
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-6 tm-1 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20963.        ((A -> (B -> (C -> (D -> (C and D))))) or E), M:tm-6, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20964
in-theory        20964
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (D -> (E -> (D and E))))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20964.        (A -> ((B -> (C -> (D -> (E -> (D and E))))) and A)), M:tm-5, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-20965
in-theory        20965
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> (C -> (D -> (C and D)))))
theorem-size     13
proof            (modus-ponens tm-2 tm-356 ((A Am) (B Bm) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-20965.        ((A -> B) -> (A -> (C -> (D -> (C and D))))), M:tm-2, m:tm-356, u:((A Am) (B Bm) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-20966
in-theory        20966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-354 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20966.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-354, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20967
in-theory        20967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20967.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20968
in-theory        20968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G)))
theorem-size     25
proof            (modus-ponens tm-338 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20968.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G))), M:tm-338, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20969
in-theory        20969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E))))
theorem-size     39
proof            (modus-ponens tm-327 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20969.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)))), M:tm-327, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20970
in-theory        20970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E))))
theorem-size     37
proof            (modus-ponens tm-326 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20970.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)))), M:tm-326, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20971
in-theory        20971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E))))
theorem-size     37
proof            (modus-ponens tm-325 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20971.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)))), M:tm-325, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20972
in-theory        20972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E))))
theorem-size     45
proof            (modus-ponens tm-324 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20972.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)))), M:tm-324, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20973
in-theory        20973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E))))
theorem-size     37
proof            (modus-ponens tm-323 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20973.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)))), M:tm-323, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20974
in-theory        20974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20974.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20975
in-theory        20975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20975.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20976
in-theory        20976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20976.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20977
in-theory        20977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20977.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20978
in-theory        20978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (F or ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-311 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20978.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (F or ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)))), M:tm-311, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20979
in-theory        20979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20979.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) or F)), M:tm-310, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20980
in-theory        20980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (F -> (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20980.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (F -> (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and F))), M:tm-309, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20981
in-theory        20981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((C -> (D -> C)) or E))
theorem-size     23
proof            (modus-ponens tm-308 tm-357 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (-> Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20981.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((C -> (D -> C)) or E)), M:tm-308, m:tm-357, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (-> Dm Cm)) Em)))
================================================================
tm-name          tm-20982
in-theory        20982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-357 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (-> Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20982.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (A -> (B -> (A and B)))), M:tm-307, m:tm-357, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (-> Dm Cm)) Em)))
================================================================
tm-name          tm-20983
in-theory        20983
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (F -> ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-305 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20983.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (F -> ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)))), M:tm-305, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20984
in-theory        20984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-303 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20984.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-303, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20985
in-theory        20985
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-270 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20985.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-270, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20986
in-theory        20986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-239 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20986.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-239, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20987
in-theory        20987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I)))
theorem-size     33
proof            (modus-ponens tm-210 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20987.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I))), M:tm-210, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20988
in-theory        20988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-183 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20988.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-183, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20989
in-theory        20989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-157 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20989.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-157, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20990
in-theory        20990
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     31
proof            (modus-ponens tm-147 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20990.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-147, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20991
in-theory        20991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-134 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20991.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-134, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20992
in-theory        20992
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     31
proof            (modus-ponens tm-125 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20992.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-125, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20993
in-theory        20993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-113 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20993.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I))), M:tm-113, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20994
in-theory        20994
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     35
proof            (modus-ponens tm-105 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20994.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-105, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20995
in-theory        20995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-95 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20995.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G))), M:tm-95, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20996
in-theory        20996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-83 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20996.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-83, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20997
in-theory        20997
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> (E -> D)) or F)))
theorem-size     21
proof            (modus-ponens tm-76 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-10 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20997.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> (E -> D)) or F))), M:tm-76, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20998
in-theory        20998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G)))
theorem-size     27
proof            (modus-ponens tm-69 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-9 tm-6 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20998.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G))), M:tm-69, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-20999
in-theory        20999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-54 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-20999.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-54, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21000
in-theory        21000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-42 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21000.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G))), M:tm-42, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21001
in-theory        21001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-32 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21001.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G))), M:tm-32, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21002
in-theory        21002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-23 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21002.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G))), M:tm-23, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21003
in-theory        21003
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-22 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21003.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G))), M:tm-22, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21004
in-theory        21004
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-21 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21004.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G))), M:tm-21, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21005
in-theory        21005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-20 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21005.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-20, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21006
in-theory        21006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-19 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21006.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> (F -> E)) or G))), M:tm-19, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21007
in-theory        21007
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((D -> (E -> D)) or F)))
theorem-size     17
proof            (modus-ponens tm-7 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-7 tm-5 tm-6 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21007.        (A or ((B -> (C -> (B and C))) and ((D -> (E -> D)) or F))), M:tm-7, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21008
in-theory        21008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21008.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) or F), M:tm-6, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21009
in-theory        21009
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((D -> (E -> D)) or F)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21009.        (A -> (((B -> (C -> (B and C))) and ((D -> (E -> D)) or F)) and A)), M:tm-5, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21010
in-theory        21010
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((D -> (E -> D)) or F)))
theorem-size     17
proof            (modus-ponens tm-1 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21010.        (A -> ((B -> (C -> (B and C))) and ((D -> (E -> D)) or F))), M:tm-1, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21011
in-theory        21011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21011.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-354, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21012
in-theory        21012
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21012.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21013
in-theory        21013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21013.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> (F -> E)) or G))), M:tm-338, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21014
in-theory        21014
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> (D -> C)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21014.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> (D -> C)) or E)))), M:tm-327, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21015
in-theory        21015
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (((F and G) -> G) and (((A and B) -> B) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21015.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (((F and G) -> G) and (((A and B) -> B) and ((C -> (D -> C)) or E)))), M:tm-326, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21016
in-theory        21016
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (((F and G) -> F) and (((A and B) -> B) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21016.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (((F and G) -> F) and (((A and B) -> B) and ((C -> (D -> C)) or E)))), M:tm-325, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21017
in-theory        21017
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> (D -> C)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21017.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> (D -> C)) or E)))), M:tm-324, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21018
in-theory        21018
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21018.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> (D -> C)) or E)))), M:tm-323, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21019
in-theory        21019
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21019.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21020
in-theory        21020
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21020.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21021
in-theory        21021
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21021.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21022
in-theory        21022
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21022.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21023
in-theory        21023
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (F or (((A and B) -> B) and ((C -> (D -> C)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21023.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (F or (((A and B) -> B) and ((C -> (D -> C)) or E)))), M:tm-311, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21024
in-theory        21024
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((((A and B) -> B) and ((C -> (D -> C)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21024.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((((A and B) -> B) and ((C -> (D -> C)) or E)) or F)), M:tm-310, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21025
in-theory        21025
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (F -> ((((A and B) -> B) and ((C -> (D -> C)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21025.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (F -> ((((A and B) -> B) and ((C -> (D -> C)) or E)) and F))), M:tm-309, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21026
in-theory        21026
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((C -> (D -> C)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-358 ((A (-> (and Am Bm) Bm)) (B (or (-> Cm (-> Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21026.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((C -> (D -> C)) or E)), M:tm-308, m:tm-358, u:((A (-> (and Am Bm) Bm)) (B (or (-> Cm (-> Dm Cm)) Em)))
================================================================
tm-name          tm-21027
in-theory        21027
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-358 ((A (-> (and Am Bm) Bm)) (B (or (-> Cm (-> Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21027.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((A and B) -> B)), M:tm-307, m:tm-358, u:((A (-> (and Am Bm) Bm)) (B (or (-> Cm (-> Dm Cm)) Em)))
================================================================
tm-name          tm-21028
in-theory        21028
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (F -> (((A and B) -> B) and ((C -> (D -> C)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21028.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (F -> (((A and B) -> B) and ((C -> (D -> C)) or E)))), M:tm-305, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21029
in-theory        21029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21029.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-303, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21030
in-theory        21030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21030.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-270, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21031
in-theory        21031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21031.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-239, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21032
in-theory        21032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21032.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> (H -> G)) or I))), M:tm-210, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21033
in-theory        21033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21033.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-183, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21034
in-theory        21034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21034.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-157, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21035
in-theory        21035
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21035.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-147, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21036
in-theory        21036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21036.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-134, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21037
in-theory        21037
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21037.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-125, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21038
in-theory        21038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21038.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H -> G)) or I))), M:tm-113, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21039
in-theory        21039
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21039.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-105, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21040
in-theory        21040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21040.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> (F -> E)) or G))), M:tm-95, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21041
in-theory        21041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21041.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-83, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21042
in-theory        21042
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((D -> (E -> D)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-10 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21042.        (((not (not A)) -> A) and (((B and C) -> C) and ((D -> (E -> D)) or F))), M:tm-76, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21043
in-theory        21043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> (F -> E)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-9 tm-4 tm-6 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21043.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> (F -> E)) or G))), M:tm-69, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21044
in-theory        21044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21044.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-54, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21045
in-theory        21045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21045.        ((A -> (B or A)) and (((C and D) -> D) and ((E -> (F -> E)) or G))), M:tm-42, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21046
in-theory        21046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21046.        ((A -> (A or B)) and (((C and D) -> D) and ((E -> (F -> E)) or G))), M:tm-32, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21047
in-theory        21047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21047.        ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> (F -> E)) or G))), M:tm-23, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21048
in-theory        21048
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21048.        (((A and B) -> B) and (((C and D) -> D) and ((E -> (F -> E)) or G))), M:tm-22, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21049
in-theory        21049
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21049.        (((A and B) -> A) and (((C and D) -> D) and ((E -> (F -> E)) or G))), M:tm-21, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21050
in-theory        21050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21050.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-20, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21051
in-theory        21051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21051.        ((A -> (B -> A)) and (((C and D) -> D) and ((E -> (F -> E)) or G))), M:tm-19, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21052
in-theory        21052
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-7 tm-5 tm-4 tm-6 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21052.        (A or (((B and C) -> C) and ((D -> (E -> D)) or F))), M:tm-7, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21053
in-theory        21053
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-6 tm-5 tm-4 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21053.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) or F), M:tm-6, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21054
in-theory        21054
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((D -> (E -> D)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21054.        (A -> ((((B and C) -> C) and ((D -> (E -> D)) or F)) and A)), M:tm-5, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21055
in-theory        21055
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-1 tm-5 tm-4 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21055.        (A -> (((B and C) -> C) and ((D -> (E -> D)) or F))), M:tm-1, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21056
in-theory        21056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21056.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-354, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21057
in-theory        21057
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21057.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21058
in-theory        21058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21058.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> (F -> E)) or G))), M:tm-338, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21059
in-theory        21059
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> (D -> C)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21059.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> (D -> C)) or E)))), M:tm-327, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21060
in-theory        21060
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (((F and G) -> G) and (((A and B) -> A) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21060.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (((F and G) -> G) and (((A and B) -> A) and ((C -> (D -> C)) or E)))), M:tm-326, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21061
in-theory        21061
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (((F and G) -> F) and (((A and B) -> A) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21061.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (((F and G) -> F) and (((A and B) -> A) and ((C -> (D -> C)) or E)))), M:tm-325, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21062
in-theory        21062
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> (D -> C)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21062.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> (D -> C)) or E)))), M:tm-324, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21063
in-theory        21063
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21063.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> (D -> C)) or E)))), M:tm-323, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21064
in-theory        21064
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21064.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21065
in-theory        21065
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21065.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21066
in-theory        21066
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21066.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21067
in-theory        21067
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21067.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21068
in-theory        21068
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (F or (((A and B) -> A) and ((C -> (D -> C)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21068.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (F or (((A and B) -> A) and ((C -> (D -> C)) or E)))), M:tm-311, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21069
in-theory        21069
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((((A and B) -> A) and ((C -> (D -> C)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21069.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((((A and B) -> A) and ((C -> (D -> C)) or E)) or F)), M:tm-310, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21070
in-theory        21070
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (F -> ((((A and B) -> A) and ((C -> (D -> C)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21070.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (F -> ((((A and B) -> A) and ((C -> (D -> C)) or E)) and F))), M:tm-309, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21071
in-theory        21071
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((C -> (D -> C)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-359 ((A (-> (and Am Bm) Am)) (B (or (-> Cm (-> Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21071.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((C -> (D -> C)) or E)), M:tm-308, m:tm-359, u:((A (-> (and Am Bm) Am)) (B (or (-> Cm (-> Dm Cm)) Em)))
================================================================
tm-name          tm-21072
in-theory        21072
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-359 ((A (-> (and Am Bm) Am)) (B (or (-> Cm (-> Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21072.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((A and B) -> A)), M:tm-307, m:tm-359, u:((A (-> (and Am Bm) Am)) (B (or (-> Cm (-> Dm Cm)) Em)))
================================================================
tm-name          tm-21073
in-theory        21073
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (F -> (((A and B) -> A) and ((C -> (D -> C)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21073.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (F -> (((A and B) -> A) and ((C -> (D -> C)) or E)))), M:tm-305, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21074
in-theory        21074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21074.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-303, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21075
in-theory        21075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21075.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-270, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21076
in-theory        21076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21076.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-239, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21077
in-theory        21077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21077.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> (H -> G)) or I))), M:tm-210, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21078
in-theory        21078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21078.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-183, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21079
in-theory        21079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21079.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-157, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21080
in-theory        21080
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21080.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-147, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21081
in-theory        21081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21081.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-134, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21082
in-theory        21082
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21082.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-125, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21083
in-theory        21083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21083.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H -> G)) or I))), M:tm-113, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21084
in-theory        21084
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21084.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-105, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21085
in-theory        21085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21085.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> (F -> E)) or G))), M:tm-95, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21086
in-theory        21086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21086.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-83, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21087
in-theory        21087
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((D -> (E -> D)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-10 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21087.        (((not (not A)) -> A) and (((B and C) -> B) and ((D -> (E -> D)) or F))), M:tm-76, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21088
in-theory        21088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> (F -> E)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-9 tm-3 tm-6 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21088.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> (F -> E)) or G))), M:tm-69, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21089
in-theory        21089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21089.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-54, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21090
in-theory        21090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21090.        ((A -> (B or A)) and (((C and D) -> C) and ((E -> (F -> E)) or G))), M:tm-42, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21091
in-theory        21091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21091.        ((A -> (A or B)) and (((C and D) -> C) and ((E -> (F -> E)) or G))), M:tm-32, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21092
in-theory        21092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21092.        ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> (F -> E)) or G))), M:tm-23, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21093
in-theory        21093
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21093.        (((A and B) -> B) and (((C and D) -> C) and ((E -> (F -> E)) or G))), M:tm-22, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21094
in-theory        21094
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21094.        (((A and B) -> A) and (((C and D) -> C) and ((E -> (F -> E)) or G))), M:tm-21, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21095
in-theory        21095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21095.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-20, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21096
in-theory        21096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21096.        ((A -> (B -> A)) and (((C and D) -> C) and ((E -> (F -> E)) or G))), M:tm-19, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21097
in-theory        21097
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-7 tm-5 tm-3 tm-6 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21097.        (A or (((B and C) -> B) and ((D -> (E -> D)) or F))), M:tm-7, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21098
in-theory        21098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-6 tm-5 tm-3 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21098.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) or F), M:tm-6, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21099
in-theory        21099
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((D -> (E -> D)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21099.        (A -> ((((B and C) -> B) and ((D -> (E -> D)) or F)) and A)), M:tm-5, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21100
in-theory        21100
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-1 tm-5 tm-3 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21100.        (A -> (((B and C) -> B) and ((D -> (E -> D)) or F))), M:tm-1, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21101
in-theory        21101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21101.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-354, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21102
in-theory        21102
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21102.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21103
in-theory        21103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21103.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H))), M:tm-338, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21104
in-theory        21104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21104.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)))), M:tm-327, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21105
in-theory        21105
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21105.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)))), M:tm-326, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21106
in-theory        21106
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21106.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)))), M:tm-325, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21107
in-theory        21107
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21107.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)))), M:tm-324, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21108
in-theory        21108
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21108.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)))), M:tm-323, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21109
in-theory        21109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21109.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((G and H) -> H)), M:tm-322, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21110
in-theory        21110
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21110.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((G and H) -> G)), M:tm-320, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21111
in-theory        21111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21111.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21112
in-theory        21112
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21112.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (G -> (H -> G))), M:tm-315, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21113
in-theory        21113
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21113.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)))), M:tm-311, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21114
in-theory        21114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21114.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) or G)), M:tm-310, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21115
in-theory        21115
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21115.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and G))), M:tm-309, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21116
in-theory        21116
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((D -> (E -> D)) or F))
theorem-size     29
proof            (modus-ponens tm-308 tm-360 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (-> Em Dm)) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21116.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((D -> (E -> D)) or F)), M:tm-308, m:tm-360, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (-> Em Dm)) Fm)))
================================================================
tm-name          tm-21117
in-theory        21117
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-360 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (-> Em Dm)) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21117.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-360, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (-> Em Dm)) Fm)))
================================================================
tm-name          tm-21118
in-theory        21118
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21118.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)))), M:tm-305, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21119
in-theory        21119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21119.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-303, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21120
in-theory        21120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21120.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-270, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21121
in-theory        21121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21121.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-239, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21122
in-theory        21122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> H)) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21122.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> H)) or J))), M:tm-210, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21123
in-theory        21123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21123.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-183, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21124
in-theory        21124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21124.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-157, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21125
in-theory        21125
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21125.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-147, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21126
in-theory        21126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21126.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-134, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21127
in-theory        21127
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21127.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-125, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21128
in-theory        21128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> H)) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21128.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> H)) or J))), M:tm-113, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21129
in-theory        21129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21129.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-105, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21130
in-theory        21130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21130.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H))), M:tm-95, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21131
in-theory        21131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21131.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-83, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21132
in-theory        21132
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> E)) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21132.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> E)) or G))), M:tm-76, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21133
in-theory        21133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-6 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21133.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H))), M:tm-69, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21134
in-theory        21134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21134.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-54, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21135
in-theory        21135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21135.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H))), M:tm-42, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21136
in-theory        21136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21136.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H))), M:tm-32, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21137
in-theory        21137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21137.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H))), M:tm-23, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21138
in-theory        21138
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21138.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H))), M:tm-22, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21139
in-theory        21139
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21139.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H))), M:tm-21, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21140
in-theory        21140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21140.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-20, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21141
in-theory        21141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21141.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> F)) or H))), M:tm-19, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21142
in-theory        21142
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-7 tm-5 tm-2 tm-6 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21142.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> E)) or G))), M:tm-7, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21143
in-theory        21143
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-6 tm-5 tm-2 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21143.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) or G), M:tm-6, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21144
in-theory        21144
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> E)) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21144.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> E)) or G)) and A)), M:tm-5, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21145
in-theory        21145
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-1 tm-5 tm-2 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21145.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> E)) or G))), M:tm-1, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21146
in-theory        21146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21146.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-354, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21147
in-theory        21147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21147.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21148
in-theory        21148
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21148.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> (F -> E)) or G))), M:tm-338, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21149
in-theory        21149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> (D -> C)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21149.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> (D -> C)) or E)))), M:tm-327, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21150
in-theory        21150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21150.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> (D -> C)) or E)))), M:tm-326, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21151
in-theory        21151
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21151.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> (D -> C)) or E)))), M:tm-325, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21152
in-theory        21152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> (D -> C)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21152.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> (D -> C)) or E)))), M:tm-324, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21153
in-theory        21153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21153.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> (D -> C)) or E)))), M:tm-323, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21154
in-theory        21154
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21154.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21155
in-theory        21155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21155.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21156
in-theory        21156
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21156.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21157
in-theory        21157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21157.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21158
in-theory        21158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (F or ((A -> (B -> A)) and ((C -> (D -> C)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21158.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (F or ((A -> (B -> A)) and ((C -> (D -> C)) or E)))), M:tm-311, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21159
in-theory        21159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (((A -> (B -> A)) and ((C -> (D -> C)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21159.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (((A -> (B -> A)) and ((C -> (D -> C)) or E)) or F)), M:tm-310, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21160
in-theory        21160
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (F -> (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21160.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (F -> (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and F))), M:tm-309, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21161
in-theory        21161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((C -> (D -> C)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-361 ((A (-> Am (-> Bm Am))) (B (or (-> Cm (-> Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21161.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((C -> (D -> C)) or E)), M:tm-308, m:tm-361, u:((A (-> Am (-> Bm Am))) (B (or (-> Cm (-> Dm Cm)) Em)))
================================================================
tm-name          tm-21162
in-theory        21162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-361 ((A (-> Am (-> Bm Am))) (B (or (-> Cm (-> Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21162.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (A -> (B -> A))), M:tm-307, m:tm-361, u:((A (-> Am (-> Bm Am))) (B (or (-> Cm (-> Dm Cm)) Em)))
================================================================
tm-name          tm-21163
in-theory        21163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (F -> ((A -> (B -> A)) and ((C -> (D -> C)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21163.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (F -> ((A -> (B -> A)) and ((C -> (D -> C)) or E)))), M:tm-305, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21164
in-theory        21164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21164.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-303, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21165
in-theory        21165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21165.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-270, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21166
in-theory        21166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21166.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-239, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21167
in-theory        21167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21167.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> (H -> G)) or I))), M:tm-210, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21168
in-theory        21168
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21168.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-183, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21169
in-theory        21169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21169.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-157, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21170
in-theory        21170
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21170.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-147, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21171
in-theory        21171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21171.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-134, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21172
in-theory        21172
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21172.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-125, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21173
in-theory        21173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21173.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H -> G)) or I))), M:tm-113, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21174
in-theory        21174
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21174.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-105, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21175
in-theory        21175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21175.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> (F -> E)) or G))), M:tm-95, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21176
in-theory        21176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21176.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-83, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21177
in-theory        21177
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> (E -> D)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21177.        (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> (E -> D)) or F))), M:tm-76, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21178
in-theory        21178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> (F -> E)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21178.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> (F -> E)) or G))), M:tm-69, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21179
in-theory        21179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21179.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-54, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21180
in-theory        21180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21180.        ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> (F -> E)) or G))), M:tm-42, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21181
in-theory        21181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21181.        ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> (F -> E)) or G))), M:tm-32, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21182
in-theory        21182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21182.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> (F -> E)) or G))), M:tm-23, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21183
in-theory        21183
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21183.        (((A and B) -> B) and ((C -> (D -> C)) and ((E -> (F -> E)) or G))), M:tm-22, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21184
in-theory        21184
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21184.        (((A and B) -> A) and ((C -> (D -> C)) and ((E -> (F -> E)) or G))), M:tm-21, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21185
in-theory        21185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21185.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-20, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21186
in-theory        21186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21186.        ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> (F -> E)) or G))), M:tm-19, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21187
in-theory        21187
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-7 tm-5 tm-1 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21187.        (A or ((B -> (C -> B)) and ((D -> (E -> D)) or F))), M:tm-7, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21188
in-theory        21188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21188.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) or F), M:tm-6, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21189
in-theory        21189
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((D -> (E -> D)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21189.        (A -> (((B -> (C -> B)) and ((D -> (E -> D)) or F)) and A)), M:tm-5, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21190
in-theory        21190
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21190.        (A -> ((B -> (C -> B)) and ((D -> (E -> D)) or F))), M:tm-1, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21191
in-theory        21191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-354 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21191.        ((A -> (B -> (C -> (B and C)))) and (D or ((E -> (F -> E)) or G))), M:tm-354, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21192
in-theory        21192
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21192.        ((A or ((B -> (C -> B)) or D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21193
in-theory        21193
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((D -> (E -> D)) or F)))
theorem-size     19
proof            (modus-ponens tm-338 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21193.        (((A -> B) -> (A -> (A and B))) and (C or ((D -> (E -> D)) or F))), M:tm-338, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21194
in-theory        21194
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and ((E -> (F -> (E and F))) and (A or ((B -> (C -> B)) or D))))
theorem-size     27
proof            (modus-ponens tm-327 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21194.        ((A or ((B -> (C -> B)) or D)) and ((E -> (F -> (E and F))) and (A or ((B -> (C -> B)) or D)))), M:tm-327, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21195
in-theory        21195
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and (((E and F) -> F) and (A or ((B -> (C -> B)) or D))))
theorem-size     25
proof            (modus-ponens tm-326 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21195.        ((A or ((B -> (C -> B)) or D)) and (((E and F) -> F) and (A or ((B -> (C -> B)) or D)))), M:tm-326, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21196
in-theory        21196
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and (((E and F) -> E) and (A or ((B -> (C -> B)) or D))))
theorem-size     25
proof            (modus-ponens tm-325 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21196.        ((A or ((B -> (C -> B)) or D)) and (((E and F) -> E) and (A or ((B -> (C -> B)) or D)))), M:tm-325, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21197
in-theory        21197
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> (C -> B)) or D))))
theorem-size     33
proof            (modus-ponens tm-324 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21197.        ((A or ((B -> (C -> B)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> (C -> B)) or D)))), M:tm-324, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21198
in-theory        21198
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and ((E -> (F -> E)) and (A or ((B -> (C -> B)) or D))))
theorem-size     25
proof            (modus-ponens tm-323 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21198.        ((A or ((B -> (C -> B)) or D)) and ((E -> (F -> E)) and (A or ((B -> (C -> B)) or D)))), M:tm-323, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21199
in-theory        21199
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21199.        ((A or ((B -> (C -> B)) or D)) and ((E and F) -> F)), M:tm-322, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21200
in-theory        21200
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21200.        ((A or ((B -> (C -> B)) or D)) and ((E and F) -> E)), M:tm-320, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21201
in-theory        21201
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21201.        ((A or ((B -> (C -> B)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21202
in-theory        21202
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21202.        ((A or ((B -> (C -> B)) or D)) and (E -> (F -> E))), M:tm-315, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21203
in-theory        21203
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and (E or (A or ((B -> (C -> B)) or D))))
theorem-size     21
proof            (modus-ponens tm-311 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21203.        ((A or ((B -> (C -> B)) or D)) and (E or (A or ((B -> (C -> B)) or D)))), M:tm-311, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21204
in-theory        21204
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and ((A or ((B -> (C -> B)) or D)) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21204.        ((A or ((B -> (C -> B)) or D)) and ((A or ((B -> (C -> B)) or D)) or E)), M:tm-310, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21205
in-theory        21205
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and (E -> ((A or ((B -> (C -> B)) or D)) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21205.        ((A or ((B -> (C -> B)) or D)) and (E -> ((A or ((B -> (C -> B)) or D)) and E))), M:tm-309, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21206
in-theory        21206
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and (E -> (A or ((B -> (C -> B)) or D))))
theorem-size     21
proof            (modus-ponens tm-305 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21206.        ((A or ((B -> (C -> B)) or D)) and (E -> (A or ((B -> (C -> B)) or D)))), M:tm-305, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21207
in-theory        21207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-303 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21207.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> (F -> E)) or G))), M:tm-303, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21208
in-theory        21208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-270 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21208.        ((A -> (((B and C) -> C) and A)) and (D or ((E -> (F -> E)) or G))), M:tm-270, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21209
in-theory        21209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-239 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21209.        ((A -> (((B and C) -> B) and A)) and (D or ((E -> (F -> E)) or G))), M:tm-239, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21210
in-theory        21210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-210 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21210.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> (G -> F)) or H))), M:tm-210, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21211
in-theory        21211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-183 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21211.        ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> (F -> E)) or G))), M:tm-183, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21212
in-theory        21212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-157 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21212.        ((A -> ((B and C) -> C)) and (D or ((E -> (F -> E)) or G))), M:tm-157, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21213
in-theory        21213
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> (F -> E)) or G)))
theorem-size     25
proof            (modus-ponens tm-147 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21213.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> (F -> E)) or G))), M:tm-147, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21214
in-theory        21214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-134 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21214.        ((A -> ((B and C) -> B)) and (D or ((E -> (F -> E)) or G))), M:tm-134, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21215
in-theory        21215
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> (F -> E)) or G)))
theorem-size     25
proof            (modus-ponens tm-125 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21215.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> (F -> E)) or G))), M:tm-125, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21216
in-theory        21216
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-113 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21216.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G -> F)) or H))), M:tm-113, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21217
in-theory        21217
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> (F -> E)) or G)))
theorem-size     29
proof            (modus-ponens tm-105 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21217.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> (F -> E)) or G))), M:tm-105, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21218
in-theory        21218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((D -> (E -> D)) or F)))
theorem-size     17
proof            (modus-ponens tm-95 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21218.        (((A -> B) -> (A -> A)) and (C or ((D -> (E -> D)) or F))), M:tm-95, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21219
in-theory        21219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-83 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21219.        ((A -> (B -> (C -> B))) and (D or ((E -> (F -> E)) or G))), M:tm-83, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21220
in-theory        21220
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((C -> (D -> C)) or E)))
theorem-size     15
proof            (modus-ponens tm-76 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21220.        (((not (not A)) -> A) and (B or ((C -> (D -> C)) or E))), M:tm-76, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21221
in-theory        21221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> (E -> D)) or F)))
theorem-size     21
proof            (modus-ponens tm-69 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21221.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> (E -> D)) or F))), M:tm-69, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21222
in-theory        21222
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-54 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21222.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> E)) or G))), M:tm-54, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21223
in-theory        21223
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-42 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21223.        ((A -> (B or A)) and (C or ((D -> (E -> D)) or F))), M:tm-42, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21224
in-theory        21224
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-32 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21224.        ((A -> (A or B)) and (C or ((D -> (E -> D)) or F))), M:tm-32, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21225
in-theory        21225
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((D -> (E -> D)) or F)))
theorem-size     17
proof            (modus-ponens tm-23 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21225.        ((A -> (B -> (A and B))) and (C or ((D -> (E -> D)) or F))), M:tm-23, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21226
in-theory        21226
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-22 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21226.        (((A and B) -> B) and (C or ((D -> (E -> D)) or F))), M:tm-22, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21227
in-theory        21227
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-21 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21227.        (((A and B) -> A) and (C or ((D -> (E -> D)) or F))), M:tm-21, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21228
in-theory        21228
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-20 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21228.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> E)) or G))), M:tm-20, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21229
in-theory        21229
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-19 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21229.        ((A -> (B -> A)) and (C or ((D -> (E -> D)) or F))), M:tm-19, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21230
in-theory        21230
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or ((C -> (D -> C)) or E)))
theorem-size     11
proof            (modus-ponens tm-7 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-7 tm-6 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21230.        (A or (B or ((C -> (D -> C)) or E))), M:tm-7, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21231
in-theory        21231
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-6 tm-7 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21231.        ((A or ((B -> (C -> B)) or D)) or E), M:tm-6, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21232
in-theory        21232
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> (D -> C)) or E)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21232.        (A -> ((B or ((C -> (D -> C)) or E)) and A)), M:tm-5, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21233
in-theory        21233
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (D -> C)) or E)))
theorem-size     11
proof            (modus-ponens tm-1 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-1 tm-7 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21233.        (A -> (B or ((C -> (D -> C)) or E))), M:tm-1, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21234
in-theory        21234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21234.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> D)) or F) or G)), M:tm-354, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21235
in-theory        21235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21235.        ((((A -> (B -> A)) or C) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21236
in-theory        21236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> C)) or E) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21236.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> C)) or E) or F)), M:tm-338, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21237
in-theory        21237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and ((E -> (F -> (E and F))) and (((A -> (B -> A)) or C) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21237.        ((((A -> (B -> A)) or C) or D) and ((E -> (F -> (E and F))) and (((A -> (B -> A)) or C) or D))), M:tm-327, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21238
in-theory        21238
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and (((E and F) -> F) and (((A -> (B -> A)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21238.        ((((A -> (B -> A)) or C) or D) and (((E and F) -> F) and (((A -> (B -> A)) or C) or D))), M:tm-326, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21239
in-theory        21239
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and (((E and F) -> E) and (((A -> (B -> A)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21239.        ((((A -> (B -> A)) or C) or D) and (((E and F) -> E) and (((A -> (B -> A)) or C) or D))), M:tm-325, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21240
in-theory        21240
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> A)) or C) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21240.        ((((A -> (B -> A)) or C) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> A)) or C) or D))), M:tm-324, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21241
in-theory        21241
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and ((E -> (F -> E)) and (((A -> (B -> A)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21241.        ((((A -> (B -> A)) or C) or D) and ((E -> (F -> E)) and (((A -> (B -> A)) or C) or D))), M:tm-323, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21242
in-theory        21242
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21242.        ((((A -> (B -> A)) or C) or D) and ((E and F) -> F)), M:tm-322, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21243
in-theory        21243
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21243.        ((((A -> (B -> A)) or C) or D) and ((E and F) -> E)), M:tm-320, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21244
in-theory        21244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21244.        ((((A -> (B -> A)) or C) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21245
in-theory        21245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21245.        ((((A -> (B -> A)) or C) or D) and (E -> (F -> E))), M:tm-315, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21246
in-theory        21246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and (E or (((A -> (B -> A)) or C) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21246.        ((((A -> (B -> A)) or C) or D) and (E or (((A -> (B -> A)) or C) or D))), M:tm-311, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21247
in-theory        21247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and ((((A -> (B -> A)) or C) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21247.        ((((A -> (B -> A)) or C) or D) and ((((A -> (B -> A)) or C) or D) or E)), M:tm-310, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21248
in-theory        21248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and (E -> ((((A -> (B -> A)) or C) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21248.        ((((A -> (B -> A)) or C) or D) and (E -> ((((A -> (B -> A)) or C) or D) and E))), M:tm-309, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21249
in-theory        21249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and (E -> (((A -> (B -> A)) or C) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21249.        ((((A -> (B -> A)) or C) or D) and (E -> (((A -> (B -> A)) or C) or D))), M:tm-305, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21250
in-theory        21250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> D)) or F) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21250.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> D)) or F) or G)), M:tm-303, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21251
in-theory        21251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21251.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> D)) or F) or G)), M:tm-270, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21252
in-theory        21252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21252.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> D)) or F) or G)), M:tm-239, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21253
in-theory        21253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> E)) or G) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21253.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> E)) or G) or H)), M:tm-210, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21254
in-theory        21254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21254.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> D)) or F) or G)), M:tm-183, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21255
in-theory        21255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21255.        ((A -> ((B and C) -> C)) and (((D -> (E -> D)) or F) or G)), M:tm-157, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21256
in-theory        21256
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> D)) or F) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21256.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> D)) or F) or G)), M:tm-147, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21257
in-theory        21257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21257.        ((A -> ((B and C) -> B)) and (((D -> (E -> D)) or F) or G)), M:tm-134, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21258
in-theory        21258
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> D)) or F) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21258.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> D)) or F) or G)), M:tm-125, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21259
in-theory        21259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> E)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21259.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> E)) or G) or H)), M:tm-113, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21260
in-theory        21260
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> D)) or F) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21260.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> D)) or F) or G)), M:tm-105, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21261
in-theory        21261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> C)) or E) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21261.        (((A -> B) -> (A -> A)) and (((C -> (D -> C)) or E) or F)), M:tm-95, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21262
in-theory        21262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21262.        ((A -> (B -> (C -> B))) and (((D -> (E -> D)) or F) or G)), M:tm-83, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21263
in-theory        21263
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> B)) or D) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21263.        (((not (not A)) -> A) and (((B -> (C -> B)) or D) or E)), M:tm-76, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21264
in-theory        21264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> C)) or E) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21264.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> C)) or E) or F)), M:tm-69, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21265
in-theory        21265
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> D)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21265.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> D)) or F) or G)), M:tm-54, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21266
in-theory        21266
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> C)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21266.        ((A -> (B or A)) and (((C -> (D -> C)) or E) or F)), M:tm-42, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21267
in-theory        21267
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> C)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21267.        ((A -> (A or B)) and (((C -> (D -> C)) or E) or F)), M:tm-32, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21268
in-theory        21268
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> C)) or E) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21268.        ((A -> (B -> (A and B))) and (((C -> (D -> C)) or E) or F)), M:tm-23, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21269
in-theory        21269
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> C)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21269.        (((A and B) -> B) and (((C -> (D -> C)) or E) or F)), M:tm-22, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21270
in-theory        21270
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> C)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21270.        (((A and B) -> A) and (((C -> (D -> C)) or E) or F)), M:tm-21, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21271
in-theory        21271
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> D)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21271.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> D)) or F) or G)), M:tm-20, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21272
in-theory        21272
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> C)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21272.        ((A -> (B -> A)) and (((C -> (D -> C)) or E) or F)), M:tm-19, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21273
in-theory        21273
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> (C -> B)) or D) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-7 tm-6 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21273.        (A or (((B -> (C -> B)) or D) or E)), M:tm-7, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21274
in-theory        21274
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-6 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21274.        ((((A -> (B -> A)) or C) or D) or E), M:tm-6, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21275
in-theory        21275
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> B)) or D) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21275.        (A -> ((((B -> (C -> B)) or D) or E) and A)), M:tm-5, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21276
in-theory        21276
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) or D) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-1 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21276.        (A -> (((B -> (C -> B)) or D) or E)), M:tm-1, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21277
in-theory        21277
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-364 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21277.        (((A -> (B -> A)) or C) and (D -> (D or E))), M:tm-364, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-21278
in-theory        21278
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-364 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-21278.        (((A -> (B -> A)) or C) and (D -> (E or D))), M:tm-364, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-21279
in-theory        21279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-21279.        (((A -> (B -> A)) or C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-364, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-21280
in-theory        21280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-364 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-21280.        (((A -> (B -> A)) or C) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-364, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-21281
in-theory        21281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-364 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-21281.        (((A -> (B -> A)) or C) and ((not (not D)) -> D)), M:tm-364, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-21282
in-theory        21282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-364 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21282.        (((A -> (B -> A)) or C) and (D -> (E -> (F -> E)))), M:tm-364, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-21283
in-theory        21283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-364 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-21283.        (((A -> (B -> A)) or C) and ((D -> E) -> (D -> D))), M:tm-364, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-21284
in-theory        21284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-364 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-21284.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-364, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-21285
in-theory        21285
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21285.        (((A -> (B -> A)) or C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-364, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-21286
in-theory        21286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-364 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-21286.        (((A -> (B -> A)) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-364, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-21287
in-theory        21287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-364 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-21287.        (((A -> (B -> A)) or C) and (D -> ((E and F) -> E))), M:tm-364, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-21288
in-theory        21288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-364 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-21288.        (((A -> (B -> A)) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-364, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-21289
in-theory        21289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-364 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21289.        (((A -> (B -> A)) or C) and (D -> ((E and F) -> F))), M:tm-364, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-21290
in-theory        21290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-364 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21290.        (((A -> (B -> A)) or C) and (D -> ((E -> (F -> E)) and D))), M:tm-364, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-21291
in-theory        21291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-364 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21291.        (((A -> (B -> A)) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-364, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-21292
in-theory        21292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-364 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-21292.        (((A -> (B -> A)) or C) and (D -> (((E and F) -> E) and D))), M:tm-364, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-21293
in-theory        21293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-364 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21293.        (((A -> (B -> A)) or C) and (D -> (((E and F) -> F) and D))), M:tm-364, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-21294
in-theory        21294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21294.        (((A -> (B -> A)) or C) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-364, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-21295
in-theory        21295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-364 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-21295.        (((A -> (B -> A)) or C) and ((D -> E) -> (D -> (D and E)))), M:tm-364, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-21296
in-theory        21296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21296.        (((A -> (B -> A)) or C) and (D -> (E -> (F -> (E and F))))), M:tm-364, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-21297
in-theory        21297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-364 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21297.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) or F)), M:tm-364, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-21298
in-theory        21298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-364 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21298.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-364, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-21299
in-theory        21299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-364 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-21299.        (((A -> (B -> A)) or C) and (((D and E) -> D) or F)), M:tm-364, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-21300
in-theory        21300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-364 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21300.        (((A -> (B -> A)) or C) and (((D and E) -> E) or F)), M:tm-364, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-21301
in-theory        21301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-364 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21301.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) or F)), M:tm-364, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-21302
in-theory        21302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-364 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21302.        (((A -> (B -> A)) or C) and ((D -> (D or E)) or F)), M:tm-364, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-21303
in-theory        21303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-364 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21303.        (((A -> (B -> A)) or C) and (D -> ((E -> (E or F)) and D))), M:tm-364, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-21304
in-theory        21304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-364 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21304.        (((A -> (B -> A)) or C) and (D -> (E -> (E or F)))), M:tm-364, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-21305
in-theory        21305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-364 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21305.        (((A -> (B -> A)) or C) and (D or (E -> (F -> E)))), M:tm-364, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-21306
in-theory        21306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21306.        (((A -> (B -> A)) or C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-364, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-21307
in-theory        21307
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-364 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-21307.        (((A -> (B -> A)) or C) and (D or ((E and F) -> E))), M:tm-364, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-21308
in-theory        21308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-364 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21308.        (((A -> (B -> A)) or C) and (D or ((E and F) -> F))), M:tm-364, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-21309
in-theory        21309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21309.        (((A -> (B -> A)) or C) and (D or (E -> (F -> (E and F))))), M:tm-364, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-21310
in-theory        21310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-364 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21310.        (((A -> (B -> A)) or C) and (D or (E -> (E or F)))), M:tm-364, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-21311
in-theory        21311
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-364 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21311.        (((A -> (B -> A)) or C) and (D or (E -> (F or E)))), M:tm-364, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-21312
in-theory        21312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-364 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21312.        (((A -> (B -> A)) or C) and ((D -> (E or D)) or F)), M:tm-364, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-21313
in-theory        21313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-364 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21313.        (((A -> (B -> A)) or C) and (D -> ((E -> (F or E)) and D))), M:tm-364, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-21314
in-theory        21314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-364 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21314.        (((A -> (B -> A)) or C) and (D -> (E -> (F or E)))), M:tm-364, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-21315
in-theory        21315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-364 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-21315.        (((A -> (B -> A)) or C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-364, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-21316
in-theory        21316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-364 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-21316.        (((A -> (B -> A)) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-364, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-21317
in-theory        21317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-364 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21317.        (((A -> (B -> A)) or C) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-364, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-21318
in-theory        21318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-364 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-21318.        (((A -> (B -> A)) or C) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-364, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-21319
in-theory        21319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-364 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-21319.        (((A -> (B -> A)) or C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-364, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-21320
in-theory        21320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-364 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-21320.        (((A -> (B -> A)) or C) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-364, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-21321
in-theory        21321
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-364 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-21321.        (((A -> (B -> A)) or C) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-364, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-21322
in-theory        21322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-364 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-21322.        (((A -> (B -> A)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-364, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-21323
in-theory        21323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-21323.        (((A -> (B -> A)) or C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-364, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-21324
in-theory        21324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-364 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-21324.        (((A -> (B -> A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-364, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-21325
in-theory        21325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-364 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-21325.        (((A -> (B -> A)) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-364, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-21326
in-theory        21326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-364 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-21326.        (((A -> (B -> A)) or C) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-364, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-21327
in-theory        21327
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-21327.        (((A -> (B -> A)) or C) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-364, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-21328
in-theory        21328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-364 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-21328.        (((A -> (B -> A)) or C) and ((D -> (not (E -> D))) -> (not D))), M:tm-364, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-21329
in-theory        21329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-21329.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-364, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-21330
in-theory        21330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-364 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21330.        (((A -> (B -> A)) or C) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-364, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-21331
in-theory        21331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-364 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-21331.        (((A -> (B -> A)) or C) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-364, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-21332
in-theory        21332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-21332.        (((A -> (B -> A)) or C) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-364, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-21333
in-theory        21333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-364 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-21333.        (((A -> (B -> A)) or C) and ((D -> (not (D or E))) -> (not D))), M:tm-364, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-21334
in-theory        21334
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-364 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-21334.        (((A -> (B -> A)) or C) and ((D -> (not (E or D))) -> (not D))), M:tm-364, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-21335
in-theory        21335
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-364 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-21335.        (((A -> (B -> A)) or C) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-364, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-21336
in-theory        21336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-364 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-21336.        (((A -> (B -> A)) or C) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-364, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-21337
in-theory        21337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-364 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-21337.        (((A -> (B -> A)) or C) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-364, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-21338
in-theory        21338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-21338.        (((A -> (B -> A)) or C) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-364, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-21339
in-theory        21339
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-364 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-21339.        (((A -> (B -> A)) or C) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-364, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-21340
in-theory        21340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-364 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-21340.        (((A -> (B -> A)) or C) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-364, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-21341
in-theory        21341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-364 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-21341.        (((A -> (B -> A)) or C) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-364, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-21342
in-theory        21342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-21342.        (((A -> (B -> A)) or C) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-364, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-21343
in-theory        21343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-364 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-21343.        (((A -> (B -> A)) or C) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-364, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-21344
in-theory        21344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-364 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-21344.        (((A -> (B -> A)) or C) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-364, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-21345
in-theory        21345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-364 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-21345.        (((A -> (B -> A)) or C) and (D or ((not (not E)) -> E))), M:tm-364, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-21346
in-theory        21346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-364 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-21346.        (((A -> (B -> A)) or C) and (((not (not D)) -> D) or E)), M:tm-364, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-21347
in-theory        21347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-364 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-21347.        (((A -> (B -> A)) or C) and (D -> (((not (not E)) -> E) and D))), M:tm-364, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-21348
in-theory        21348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-364 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-21348.        (((A -> (B -> A)) or C) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-364, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-21349
in-theory        21349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-364 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-21349.        (((A -> (B -> A)) or C) and (D -> ((not (not E)) -> E))), M:tm-364, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-21350
in-theory        21350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-21350.        (((A -> (B -> A)) or C) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-364, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-21351
in-theory        21351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-364 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-21351.        (((A -> (B -> A)) or C) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-364, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-21352
in-theory        21352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-21352.        (((A -> (B -> A)) or C) and (D or (E -> (F -> (G -> F))))), M:tm-364, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-21353
in-theory        21353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-21353.        (((A -> (B -> A)) or C) and ((D -> (E -> (F -> E))) or G)), M:tm-364, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-21354
in-theory        21354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-21354.        (((A -> (B -> A)) or C) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-364, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-21355
in-theory        21355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-364 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-21355.        (((A -> (B -> A)) or C) and ((D -> E) -> (D -> (F -> E)))), M:tm-364, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-21356
in-theory        21356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-21356.        (((A -> (B -> A)) or C) and (D -> (E -> (F -> (G -> F))))), M:tm-364, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-21357
in-theory        21357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-364 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-21357.        (((A -> (B -> A)) or C) and (D -> D)), M:tm-364, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-21358
in-theory        21358
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-21358.        (((A -> (B -> A)) or C) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-364, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-21359
in-theory        21359
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-364 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21359.        (((A -> (B -> A)) or C) and ((D and E) -> (D and E))), M:tm-364, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-21360
in-theory        21360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-364 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-21360.        (((A -> (B -> A)) or C) and ((D -> E) -> (D -> E))), M:tm-364, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-21361
in-theory        21361
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-364 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-21361.        (((A -> (B -> A)) or C) and ((not (not D)) -> (not (not D)))), M:tm-364, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-21362
in-theory        21362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-364 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-21362.        (((A -> (B -> A)) or C) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-364, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-21363
in-theory        21363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-364 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-21363.        (((A -> (B -> A)) or C) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-364, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-21364
in-theory        21364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-364 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-21364.        (((A -> (B -> A)) or C) and (D or ((E -> F) -> (E -> E)))), M:tm-364, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-21365
in-theory        21365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-364 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-21365.        (((A -> (B -> A)) or C) and (((D -> E) -> (D -> D)) or F)), M:tm-364, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-21366
in-theory        21366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-21366.        (((A -> (B -> A)) or C) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-364, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-21367
in-theory        21367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-21367.        (((A -> (B -> A)) or C) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-364, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-21368
in-theory        21368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-364 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-21368.        (((A -> (B -> A)) or C) and (D -> ((E -> F) -> (E -> E)))), M:tm-364, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-21369
in-theory        21369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-21369.        (((A -> (B -> A)) or C) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-364, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-21370
in-theory        21370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-364 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-21370.        (((A -> (B -> A)) or C) and ((D -> (D -> E)) -> (D -> E))), M:tm-364, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-21371
in-theory        21371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-364 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-21371.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-364, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-21372
in-theory        21372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-364 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-21372.        (((A -> (B -> A)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-364, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-21373
in-theory        21373
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-364 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-21373.        (((A -> (B -> A)) or C) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-364, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-21374
in-theory        21374
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-21374.        (((A -> (B -> A)) or C) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-364, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-21375
in-theory        21375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-364 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-21375.        (((A -> (B -> A)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-364, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-21376
in-theory        21376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-364 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-21376.        (((A -> (B -> A)) or C) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-364, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-21377
in-theory        21377
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-364 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-21377.        (((A -> (B -> A)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-364, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-21378
in-theory        21378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-21378.        (((A -> (B -> A)) or C) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-364, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-21379
in-theory        21379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-364 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-21379.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-364, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-21380
in-theory        21380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-364 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-21380.        (((A -> (B -> A)) or C) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-364, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-21381
in-theory        21381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-364 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-21381.        (((A -> (B -> A)) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-364, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-21382
in-theory        21382
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-364 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-21382.        (((A -> (B -> A)) or C) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-364, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-21383
in-theory        21383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-364 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-21383.        (((A -> (B -> A)) or C) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-364, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-21384
in-theory        21384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-364 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-21384.        (((A -> (B -> A)) or C) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-364, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-21385
in-theory        21385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-364 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-21385.        (((A -> (B -> A)) or C) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-364, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-21386
in-theory        21386
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-364 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-21386.        (((A -> (B -> A)) or C) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-364, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-21387
in-theory        21387
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-364 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-21387.        (((A -> (B -> A)) or C) and (((D -> E) and D) -> E)), M:tm-364, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-21388
in-theory        21388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-364 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-21388.        (((A -> (B -> A)) or C) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-364, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-21389
in-theory        21389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-364 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-21389.        (((A -> (B -> A)) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-364, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-21390
in-theory        21390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-364 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-21390.        (((A -> (B -> A)) or C) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-364, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-21391
in-theory        21391
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-364 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-21391.        (((A -> (B -> A)) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-364, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-21392
in-theory        21392
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-364 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-21392.        (((A -> (B -> A)) or C) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-364, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-21393
in-theory        21393
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-364 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-21393.        (((A -> (B -> A)) or C) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-364, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-21394
in-theory        21394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-364 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21394.        (((A -> (B -> A)) or C) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-364, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-21395
in-theory        21395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-364 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21395.        (((A -> (B -> A)) or C) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-364, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-21396
in-theory        21396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-364 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21396.        (((A -> (B -> A)) or C) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-364, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-21397
in-theory        21397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-364 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-21397.        (((A -> (B -> A)) or C) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-364, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-21398
in-theory        21398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-364 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21398.        (((A -> (B -> A)) or C) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-364, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-21399
in-theory        21399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-364 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-21399.        (((A -> (B -> A)) or C) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-364, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-21400
in-theory        21400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-364 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-21400.        (((A -> (B -> A)) or C) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-364, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-21401
in-theory        21401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21401.        (((A -> (B -> A)) or C) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-364, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-21402
in-theory        21402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-364 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21402.        (((A -> (B -> A)) or C) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-364, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-21403
in-theory        21403
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-364 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21403.        (((A -> (B -> A)) or C) and (D or (E -> ((F and G) -> F)))), M:tm-364, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-21404
in-theory        21404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21404.        (((A -> (B -> A)) or C) and ((D -> ((E and F) -> E)) or G)), M:tm-364, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-21405
in-theory        21405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21405.        (((A -> (B -> A)) or C) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-364, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-21406
in-theory        21406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-364 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-21406.        (((A -> (B -> A)) or C) and ((D -> (E and F)) -> (D -> E))), M:tm-364, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-21407
in-theory        21407
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-364 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21407.        (((A -> (B -> A)) or C) and (D -> (E -> ((F and G) -> F)))), M:tm-364, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-21408
in-theory        21408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-364 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-21408.        (((A -> (B -> A)) or C) and ((D and (D -> E)) -> E)), M:tm-364, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-21409
in-theory        21409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-364 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-21409.        (((A -> (B -> A)) or C) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-364, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-21410
in-theory        21410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-364 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-21410.        (((A -> (B -> A)) or C) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-364, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-21411
in-theory        21411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-364 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-21411.        (((A -> (B -> A)) or C) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-364, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-21412
in-theory        21412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-364 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-21412.        (((A -> (B -> A)) or C) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-364, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-21413
in-theory        21413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-364 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-21413.        (((A -> (B -> A)) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-364, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-21414
in-theory        21414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-364 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-21414.        (((A -> (B -> A)) or C) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-364, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-21415
in-theory        21415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-364 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-21415.        (((A -> (B -> A)) or C) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-364, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-21416
in-theory        21416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-364 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-21416.        (((A -> (B -> A)) or C) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-364, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-21417
in-theory        21417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-364 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-21417.        (((A -> (B -> A)) or C) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-364, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-21418
in-theory        21418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-364 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-21418.        (((A -> (B -> A)) or C) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-364, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-21419
in-theory        21419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-364 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-21419.        (((A -> (B -> A)) or C) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-364, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-21420
in-theory        21420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-364 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-21420.        (((A -> (B -> A)) or C) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-364, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-21421
in-theory        21421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-364 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-21421.        (((A -> (B -> A)) or C) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-364, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-21422
in-theory        21422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-364 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-21422.        (((A -> (B -> A)) or C) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-364, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-21423
in-theory        21423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-364 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-21423.        (((A -> (B -> A)) or C) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-364, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-21424
in-theory        21424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-21424.        (((A -> (B -> A)) or C) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-364, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-21425
in-theory        21425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-364 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-21425.        (((A -> (B -> A)) or C) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-364, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-21426
in-theory        21426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-364 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-21426.        (((A -> (B -> A)) or C) and (D or (E -> ((F and G) -> G)))), M:tm-364, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-21427
in-theory        21427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-21427.        (((A -> (B -> A)) or C) and ((D -> ((E and F) -> F)) or G)), M:tm-364, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-21428
in-theory        21428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-21428.        (((A -> (B -> A)) or C) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-364, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-21429
in-theory        21429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-364 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-21429.        (((A -> (B -> A)) or C) and ((D -> (E and F)) -> (D -> F))), M:tm-364, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-21430
in-theory        21430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-364 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-21430.        (((A -> (B -> A)) or C) and (D -> (E -> ((F and G) -> G)))), M:tm-364, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-21431
in-theory        21431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21431.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-364, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-21432
in-theory        21432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21432.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-364, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-21433
in-theory        21433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-21433.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-364, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-21434
in-theory        21434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-364 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21434.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-364, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-21435
in-theory        21435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21435.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-364, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-21436
in-theory        21436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-364 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21436.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-364, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-21437
in-theory        21437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21437.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-364, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-21438
in-theory        21438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-21438.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-364, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-21439
in-theory        21439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-364 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-21439.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-364, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-21440
in-theory        21440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-21440.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-364, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-21441
in-theory        21441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-21441.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-364, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-21442
in-theory        21442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-21442.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-364, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-21443
in-theory        21443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-364 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-21443.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-364, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-21444
in-theory        21444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-21444.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-364, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-21445
in-theory        21445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-364 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21445.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-364, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-21446
in-theory        21446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-364 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21446.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-364, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-21447
in-theory        21447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-364 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-21447.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-364, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-21448
in-theory        21448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-364 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-21448.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-364, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-21449
in-theory        21449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-21449.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-364, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-21450
in-theory        21450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-21450.        (((A -> (B -> A)) or C) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-364, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-21451
in-theory        21451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-364 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-21451.        (((A -> (B -> A)) or C) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-364, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-21452
in-theory        21452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-364 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-21452.        (((A -> (B -> A)) or C) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-364, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-21453
in-theory        21453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-364 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-21453.        (((A -> (B -> A)) or C) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-364, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-21454
in-theory        21454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-21454.        (((A -> (B -> A)) or C) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-364, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-21455
in-theory        21455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-364 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-21455.        (((A -> (B -> A)) or C) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-364, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-21456
in-theory        21456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-364 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21456.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-364, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-21457
in-theory        21457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21457.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-364, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-21458
in-theory        21458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-364 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-21458.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-364, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-21459
in-theory        21459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-364 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21459.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-364, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-21460
in-theory        21460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21460.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-364, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-21461
in-theory        21461
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21461.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-364, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-21462
in-theory        21462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-364 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21462.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-364, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-21463
in-theory        21463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-21463.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-364, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-21464
in-theory        21464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-364 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-21464.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-364, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-21465
in-theory        21465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-364 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-21465.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-364, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-21466
in-theory        21466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-21466.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-364, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-21467
in-theory        21467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-364 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-21467.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-364, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-21468
in-theory        21468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-364 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-21468.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-364, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-21469
in-theory        21469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-364 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-21469.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-364, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-21470
in-theory        21470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-364 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21470.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-364, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-21471
in-theory        21471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-364 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21471.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-364, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-21472
in-theory        21472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-364 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-21472.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-364, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-21473
in-theory        21473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-364 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-21473.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-364, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-21474
in-theory        21474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-364 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-21474.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-364, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-21475
in-theory        21475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-364 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-21475.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-364, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-21476
in-theory        21476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-364 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-21476.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-364, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-21477
in-theory        21477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-364 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-21477.        (((A -> (B -> A)) or C) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-364, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-21478
in-theory        21478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-364 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-21478.        (((A -> (B -> A)) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-364, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-21479
in-theory        21479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-364 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-21479.        (((A -> (B -> A)) or C) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-364, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-21480
in-theory        21480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-364 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-21480.        (((A -> (B -> A)) or C) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-364, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-21481
in-theory        21481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-364 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-21481.        (((A -> (B -> A)) or C) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-364, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-21482
in-theory        21482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-364 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-21482.        (((A -> (B -> A)) or C) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-364, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-21483
in-theory        21483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21483.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-364, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-21484
in-theory        21484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21484.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-364, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-21485
in-theory        21485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-21485.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F and G) -> F))), M:tm-364, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-21486
in-theory        21486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-364 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21486.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F and G) -> G))), M:tm-364, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-21487
in-theory        21487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21487.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-364, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-21488
in-theory        21488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-364 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21488.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (F or G)))), M:tm-364, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-21489
in-theory        21489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21489.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (G or F)))), M:tm-364, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-21490
in-theory        21490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-21490.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-364, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-21491
in-theory        21491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-364 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-21491.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-364, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-21492
in-theory        21492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-21492.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-364, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-21493
in-theory        21493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-21493.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-364, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-21494
in-theory        21494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-21494.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-364, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-21495
in-theory        21495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-364 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-21495.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-364, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-21496
in-theory        21496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-21496.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-364, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-21497
in-theory        21497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-364 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21497.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-364, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-21498
in-theory        21498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-364 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21498.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-364, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-21499
in-theory        21499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-364 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-21499.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-364, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-21500
in-theory        21500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-364 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-21500.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-364, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-21501
in-theory        21501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-21501.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-364, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-21502
in-theory        21502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-364 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-21502.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-364, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-21503
in-theory        21503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-21503.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-364, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-21504
in-theory        21504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-364 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-21504.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-364, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-21505
in-theory        21505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-21505.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-364, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-21506
in-theory        21506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-21506.        (((A -> (B -> A)) or C) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-364, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-21507
in-theory        21507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-364 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-21507.        (((A -> (B -> A)) or C) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-364, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-21508
in-theory        21508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-364 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-21508.        (((A -> (B -> A)) or C) and (D or (E -> (((F and G) -> F) and E)))), M:tm-364, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-21509
in-theory        21509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-364 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-21509.        (((A -> (B -> A)) or C) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-364, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-21510
in-theory        21510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-21510.        (((A -> (B -> A)) or C) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-364, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-21511
in-theory        21511
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-364 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-21511.        (((A -> (B -> A)) or C) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-364, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-21512
in-theory        21512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21512.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-364, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-21513
in-theory        21513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21513.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-364, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-21514
in-theory        21514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-21514.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F and G) -> F))), M:tm-364, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-21515
in-theory        21515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-364 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21515.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F and G) -> G))), M:tm-364, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-21516
in-theory        21516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21516.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-364, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-21517
in-theory        21517
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-364 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21517.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (F or G)))), M:tm-364, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-21518
in-theory        21518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21518.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (G or F)))), M:tm-364, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-21519
in-theory        21519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-21519.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-364, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-21520
in-theory        21520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-364 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-21520.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-364, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-21521
in-theory        21521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-21521.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-364, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-21522
in-theory        21522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-21522.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-364, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-21523
in-theory        21523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-21523.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-364, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-21524
in-theory        21524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-364 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-21524.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-364, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-21525
in-theory        21525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-21525.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-364, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-21526
in-theory        21526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-364 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21526.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-364, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-21527
in-theory        21527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-364 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21527.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-364, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-21528
in-theory        21528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-364 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-21528.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-364, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-21529
in-theory        21529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-364 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-21529.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-364, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-21530
in-theory        21530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-21530.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-364, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-21531
in-theory        21531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-364 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-21531.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-364, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-21532
in-theory        21532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-21532.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-364, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-21533
in-theory        21533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-21533.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-364, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-21534
in-theory        21534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-21534.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-364, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-21535
in-theory        21535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-364 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-21535.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-364, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-21536
in-theory        21536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-21536.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-364, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-21537
in-theory        21537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-21537.        (((A -> (B -> A)) or C) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-364, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-21538
in-theory        21538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-364 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-21538.        (((A -> (B -> A)) or C) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-364, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-21539
in-theory        21539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-364 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-21539.        (((A -> (B -> A)) or C) and (D or (E -> (((F and G) -> G) and E)))), M:tm-364, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-21540
in-theory        21540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-364 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-21540.        (((A -> (B -> A)) or C) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-364, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-21541
in-theory        21541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-21541.        (((A -> (B -> A)) or C) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-364, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-21542
in-theory        21542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-364 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-21542.        (((A -> (B -> A)) or C) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-364, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-21543
in-theory        21543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21543.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-364, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-21544
in-theory        21544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21544.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-364, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-21545
in-theory        21545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-364 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-21545.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-364, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-21546
in-theory        21546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-364 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21546.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-364, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-21547
in-theory        21547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21547.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-364, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-21548
in-theory        21548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-364 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21548.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-364, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-21549
in-theory        21549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21549.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-364, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-21550
in-theory        21550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-21550.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-364, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-21551
in-theory        21551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-21551.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-364, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-21552
in-theory        21552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-364 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-21552.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-364, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-21553
in-theory        21553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-21553.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-364, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-21554
in-theory        21554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-21554.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-364, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-21555
in-theory        21555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-21555.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-364, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-21556
in-theory        21556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-364 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-21556.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-364, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-21557
in-theory        21557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-364 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21557.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-364, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-21558
in-theory        21558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-364 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21558.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-364, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-21559
in-theory        21559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-364 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-21559.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-364, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-21560
in-theory        21560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-364 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-21560.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-364, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-21561
in-theory        21561
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-364 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-21561.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-364, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-21562
in-theory        21562
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-364 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-21562.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-364, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-21563
in-theory        21563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-364 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-21563.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-364, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-21564
in-theory        21564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-364 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-21564.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-364, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-21565
in-theory        21565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-364 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-21565.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-364, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-21566
in-theory        21566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-364 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-21566.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-364, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-21567
in-theory        21567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-364 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-21567.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-364, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-21568
in-theory        21568
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-364 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-21568.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-364, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-21569
in-theory        21569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-364 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-21569.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-364, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-21570
in-theory        21570
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-364 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-21570.        (((A -> (B -> A)) or C) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-364, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-21571
in-theory        21571
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-364 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-21571.        (((A -> (B -> A)) or C) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-364, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-21572
in-theory        21572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-364 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-21572.        (((A -> (B -> A)) or C) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-364, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-21573
in-theory        21573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-364 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-21573.        (((A -> (B -> A)) or C) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-364, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-21574
in-theory        21574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-364 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-21574.        (((A -> (B -> A)) or C) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-364, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-21575
in-theory        21575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-364 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-21575.        (((A -> (B -> A)) or C) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-364, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-21576
in-theory        21576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-364 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-21576.        (((A -> (B -> A)) or C) and (D -> (D and (E -> D)))), M:tm-364, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-21577
in-theory        21577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-21577.        (((A -> (B -> A)) or C) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-364, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-21578
in-theory        21578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-364 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21578.        (((A -> (B -> A)) or C) and ((D and E) -> ((D and E) and D))), M:tm-364, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-21579
in-theory        21579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-364 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-21579.        (((A -> (B -> A)) or C) and ((D and E) -> ((D and E) and E))), M:tm-364, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-21580
in-theory        21580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-21580.        (((A -> (B -> A)) or C) and (D -> (D and (E -> (D and E))))), M:tm-364, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-21581
in-theory        21581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-364 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-21581.        (((A -> (B -> A)) or C) and (D -> (D and (D or E)))), M:tm-364, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-21582
in-theory        21582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-364 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-21582.        (((A -> (B -> A)) or C) and (D -> (D and (E or D)))), M:tm-364, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-21583
in-theory        21583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-364 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-21583.        (((A -> (B -> A)) or C) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-364, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-21584
in-theory        21584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-21584.        (((A -> (B -> A)) or C) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-364, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-21585
in-theory        21585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-364 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-21585.        (((A -> (B -> A)) or C) and ((not (not D)) -> ((not (not D)) and D))), M:tm-364, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-21586
in-theory        21586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-21586.        (((A -> (B -> A)) or C) and (D -> (D and (E -> (F -> E))))), M:tm-364, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-21587
in-theory        21587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-364 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-21587.        (((A -> (B -> A)) or C) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-364, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-21588
in-theory        21588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-364 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-21588.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-364, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-21589
in-theory        21589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-364 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-21589.        (((A -> (B -> A)) or C) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-364, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-21590
in-theory        21590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-364 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-21590.        (((A -> (B -> A)) or C) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-364, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-21591
in-theory        21591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-364 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21591.        (((A -> (B -> A)) or C) and (D -> (D and ((E and F) -> E)))), M:tm-364, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-21592
in-theory        21592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-364 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-21592.        (((A -> (B -> A)) or C) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-364, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-21593
in-theory        21593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-364 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-21593.        (((A -> (B -> A)) or C) and (D -> (D and ((E and F) -> F)))), M:tm-364, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-21594
in-theory        21594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-364 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-21594.        (((A -> (B -> A)) or C) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-364, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-21595
in-theory        21595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-364 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-21595.        (((A -> (B -> A)) or C) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-364, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-21596
in-theory        21596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-364 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-21596.        (((A -> (B -> A)) or C) and (D -> (D and (((E and F) -> E) and D)))), M:tm-364, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-21597
in-theory        21597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-364 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-21597.        (((A -> (B -> A)) or C) and (D -> (D and (((E and F) -> F) and D)))), M:tm-364, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-21598
in-theory        21598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-364 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-21598.        (((A -> (B -> A)) or C) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-364, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-21599
in-theory        21599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-21599.        (((A -> (B -> A)) or C) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-364, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-21600
in-theory        21600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-364 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-21600.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-364, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-21601
in-theory        21601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-21601.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-364, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-21602
in-theory        21602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-21602.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-364, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-21603
in-theory        21603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-364 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-21603.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-364, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-21604
in-theory        21604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-21604.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-364, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-21605
in-theory        21605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-364 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-21605.        (((A -> (B -> A)) or C) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-364, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-21606
in-theory        21606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-364 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-21606.        (((A -> (B -> A)) or C) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-364, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-21607
in-theory        21607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-364 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-21607.        (((A -> (B -> A)) or C) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-364, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-21608
in-theory        21608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-364 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-21608.        (((A -> (B -> A)) or C) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-364, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-21609
in-theory        21609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-21609.        (((A -> (B -> A)) or C) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-364, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-21610
in-theory        21610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-364 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-21610.        (((A -> (B -> A)) or C) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-364, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-21611
in-theory        21611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-364 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-21611.        (((A -> (B -> A)) or C) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-364, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-21612
in-theory        21612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-364 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-21612.        (((A -> (B -> A)) or C) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-364, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-21613
in-theory        21613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-364 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-21613.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-364, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-21614
in-theory        21614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-364 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-21614.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-364, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-21615
in-theory        21615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-364 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-21615.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-364, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-21616
in-theory        21616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-364 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-21616.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-364, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-21617
in-theory        21617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-364 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-21617.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-364, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-21618
in-theory        21618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-364 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-21618.        (((A -> (B -> A)) or C) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-364, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-21619
in-theory        21619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-364 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-21619.        (((A -> (B -> A)) or C) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-364, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-21620
in-theory        21620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-364 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-21620.        (((A -> (B -> A)) or C) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-364, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-21621
in-theory        21621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-21621.        (((A -> (B -> A)) or C) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-364, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-21622
in-theory        21622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-364 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-21622.        (((A -> (B -> A)) or C) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-364, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-21623
in-theory        21623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-364 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-21623.        (((A -> (B -> A)) or C) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-364, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-21624
in-theory        21624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-364 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-21624.        (((A -> (B -> A)) or C) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-364, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-21625
in-theory        21625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-21625.        (((A -> (B -> A)) or C) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-364, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-21626
in-theory        21626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-364 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-21626.        (((A -> (B -> A)) or C) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-364, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-21627
in-theory        21627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-364 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-21627.        (((A -> (B -> A)) or C) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-364, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-21628
in-theory        21628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-364 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21628.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-364, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21629
in-theory        21629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21629.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-364, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21630
in-theory        21630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21630.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-364, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21631
in-theory        21631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21631.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-364, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-21632
in-theory        21632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21632.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-364, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-21633
in-theory        21633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-364 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21633.        (((A -> (B -> A)) or C) and (D or ((E -> (F -> E)) or G))), M:tm-364, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21634
in-theory        21634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21634.        (((A -> (B -> A)) or C) and (((D -> (E -> D)) or F) or G)), M:tm-364, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-21635
in-theory        21635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21635.        (((A -> (B -> A)) or C) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-364, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21636
in-theory        21636
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> (D -> C)) or E) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21636.        (A -> (B -> ((((C -> (D -> C)) or E) and A) and B))), M:tm-355, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-21637
in-theory        21637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21637.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-354, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21638
in-theory        21638
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> (E -> D)) or F) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-364 ((Am (-> A (-> B (and A B)))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21638.        ((A or (B -> (C -> (B and C)))) -> (((D -> (E -> D)) or F) and (B -> (C -> (B and C))))), M:tm-351, m:tm-364, u:((Am (-> A (-> B (and A B)))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-21639
in-theory        21639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21639.        ((A -> (((B -> (C -> B)) or D) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21640
in-theory        21640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (E -> D)) or F) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21640.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (E -> D)) or F) and C))), M:tm-338, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21641
in-theory        21641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> (D -> C)) or E) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-364 ((Am (-> A (and A B))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21641.        (((A -> B) or (A -> (A and B))) -> (((C -> (D -> C)) or E) and (A -> (A and B)))), M:tm-335, m:tm-364, u:((Am (-> A (and A B))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (and A B)))))
================================================================
tm-name          tm-21642
in-theory        21642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (A -> (A and (((B -> (C -> B)) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21642.        ((A -> (((B -> (C -> B)) or D) and A)) and (A -> (A and (((B -> (C -> B)) or D) and A)))), M:tm-328, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-21643
in-theory        21643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> (C -> B)) or D) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21643.        ((A -> (((B -> (C -> B)) or D) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> (C -> B)) or D) and A)))), M:tm-327, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21644
in-theory        21644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (((E and F) -> F) and (A -> (((B -> (C -> B)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21644.        ((A -> (((B -> (C -> B)) or D) and A)) and (((E and F) -> F) and (A -> (((B -> (C -> B)) or D) and A)))), M:tm-326, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21645
in-theory        21645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (((E and F) -> E) and (A -> (((B -> (C -> B)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21645.        ((A -> (((B -> (C -> B)) or D) and A)) and (((E and F) -> E) and (A -> (((B -> (C -> B)) or D) and A)))), M:tm-325, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21646
in-theory        21646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> (C -> B)) or D) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21646.        ((A -> (((B -> (C -> B)) or D) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> (C -> B)) or D) and A)))), M:tm-324, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21647
in-theory        21647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and ((E -> (F -> E)) and (A -> (((B -> (C -> B)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21647.        ((A -> (((B -> (C -> B)) or D) and A)) and ((E -> (F -> E)) and (A -> (((B -> (C -> B)) or D) and A)))), M:tm-323, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21648
in-theory        21648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21648.        ((A -> (((B -> (C -> B)) or D) and A)) and ((E and F) -> F)), M:tm-322, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21649
in-theory        21649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21649.        ((A -> (((B -> (C -> B)) or D) and A)) and ((E and F) -> E)), M:tm-320, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21650
in-theory        21650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21650.        ((A -> (((B -> (C -> B)) or D) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21651
in-theory        21651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21651.        ((A -> (((B -> (C -> B)) or D) and A)) and (A -> A)), M:tm-316, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-21652
in-theory        21652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21652.        ((A -> (((B -> (C -> B)) or D) and A)) and (E -> (F -> E))), M:tm-315, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21653
in-theory        21653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and ((A -> (not (((B -> (C -> B)) or D) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21653.        ((A -> (((B -> (C -> B)) or D) and A)) and ((A -> (not (((B -> (C -> B)) or D) and A))) -> (not A))), M:tm-313, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-21654
in-theory        21654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (((((B -> (C -> B)) or D) and A) -> E) -> ((A or (((B -> (C -> B)) or D) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21654.        ((A -> (((B -> (C -> B)) or D) and A)) and (((((B -> (C -> B)) or D) and A) -> E) -> ((A or (((B -> (C -> B)) or D) and A)) -> E))), M:tm-312, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-21655
in-theory        21655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (E or (A -> (((B -> (C -> B)) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21655.        ((A -> (((B -> (C -> B)) or D) and A)) and (E or (A -> (((B -> (C -> B)) or D) and A)))), M:tm-311, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21656
in-theory        21656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and ((A -> (((B -> (C -> B)) or D) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21656.        ((A -> (((B -> (C -> B)) or D) and A)) and ((A -> (((B -> (C -> B)) or D) and A)) or E)), M:tm-310, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21657
in-theory        21657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (E -> ((A -> (((B -> (C -> B)) or D) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21657.        ((A -> (((B -> (C -> B)) or D) and A)) and (E -> ((A -> (((B -> (C -> B)) or D) and A)) and E))), M:tm-309, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21658
in-theory        21658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (E -> (A -> (((B -> (C -> B)) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21658.        ((A -> (((B -> (C -> B)) or D) and A)) and (E -> (A -> (((B -> (C -> B)) or D) and A)))), M:tm-305, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21659
in-theory        21659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21659.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-303, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21660
in-theory        21660
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (E -> D)) or F) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-364 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21660.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (E -> D)) or F) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-364, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-21661
in-theory        21661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21661.        ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-270, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21662
in-theory        21662
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> (E -> D)) or F) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-364 ((Am (and (-> (and A B) B) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21662.        ((A or (((B and C) -> C) and A)) -> (((D -> (E -> D)) or F) and (((B and C) -> C) and A))), M:tm-267, m:tm-364, u:((Am (and (-> (and A B) B) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-21663
in-theory        21663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21663.        ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-239, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21664
in-theory        21664
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> (E -> D)) or F) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-364 ((Am (and (-> (and A B) A) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21664.        ((A or (((B and C) -> B) and A)) -> (((D -> (E -> D)) or F) and (((B and C) -> B) and A))), M:tm-236, m:tm-364, u:((Am (and (-> (and A B) A) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-21665
in-theory        21665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (G -> F)) or H) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21665.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (G -> F)) or H) and E))), M:tm-210, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21666
in-theory        21666
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (F -> E)) or G) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-364 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (-> Cm Bm)) Dm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21666.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (F -> E)) or G) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-364, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (-> Cm Bm)) Dm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-21667
in-theory        21667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21667.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-183, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21668
in-theory        21668
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> (E -> D)) or F) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-364 ((Am (and (-> A (-> B A)) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21668.        ((A or ((B -> (C -> B)) and A)) -> (((D -> (E -> D)) or F) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-364, u:((Am (and (-> A (-> B A)) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-21669
in-theory        21669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21669.        ((A -> ((B and C) -> C)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-157, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21670
in-theory        21670
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> (E -> D)) or F) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-364 ((Am (-> (and A B) B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21670.        ((A or ((B and C) -> C)) -> (((D -> (E -> D)) or F) and ((B and C) -> C))), M:tm-154, m:tm-364, u:((Am (-> (and A B) B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> (and A B) B))))
================================================================
tm-name          tm-21671
in-theory        21671
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21671.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-147, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21672
in-theory        21672
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (E -> D)) or F) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-364 ((Am (-> (and A (-> B C)) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-6 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21672.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (E -> D)) or F) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-364, u:((Am (-> (and A (-> B C)) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-21673
in-theory        21673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21673.        ((A -> ((B and C) -> B)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-134, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21674
in-theory        21674
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> (E -> D)) or F) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-364 ((Am (-> (and A B) A)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21674.        ((A or ((B and C) -> B)) -> (((D -> (E -> D)) or F) and ((B and C) -> B))), M:tm-131, m:tm-364, u:((Am (-> (and A B) A)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> (and A B) A))))
================================================================
tm-name          tm-21675
in-theory        21675
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21675.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-125, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21676
in-theory        21676
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (E -> D)) or F) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-364 ((Am (-> (and (-> A B) C) B)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-6 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21676.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (E -> D)) or F) and (((A -> B) and C) -> B))), M:tm-122, m:tm-364, u:((Am (-> (and (-> A B) C) B)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-21677
in-theory        21677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> F)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21677.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> F)) or H) and E))), M:tm-113, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21678
in-theory        21678
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (F -> E)) or G) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-364 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21678.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (F -> E)) or G) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-364, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-21679
in-theory        21679
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21679.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-105, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21680
in-theory        21680
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (E -> D)) or F) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-364 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21680.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (E -> D)) or F) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-364, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-21681
in-theory        21681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> (E -> D)) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21681.        (((A -> B) -> (A -> A)) and (C -> (((D -> (E -> D)) or F) and C))), M:tm-95, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21682
in-theory        21682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> (D -> C)) or E) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-364 ((Am (-> A A)) (B (and (or (-> Bm (-> Cm Bm)) Dm) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21682.        (((A -> B) or (A -> A)) -> (((C -> (D -> C)) or E) and (A -> A))), M:tm-92, m:tm-364, u:((Am (-> A A)) (B (and (or (-> Bm (-> Cm Bm)) Dm) (-> A A))))
================================================================
tm-name          tm-21683
in-theory        21683
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D -> C)) or E) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21683.        (A -> (B -> (((C -> (D -> C)) or E) and A))), M:tm-84, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-21684
in-theory        21684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21684.        ((A -> (B -> (C -> B))) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-83, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21685
in-theory        21685
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> (E -> D)) or F) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-364 ((Am (-> A (-> B A))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21685.        ((A or (B -> (C -> B))) -> (((D -> (E -> D)) or F) and (B -> (C -> B)))), M:tm-80, m:tm-364, u:((Am (-> A (-> B A))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (-> B A)))))
================================================================
tm-name          tm-21686
in-theory        21686
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> (D -> C)) or E) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-10 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21686.        (((not (not A)) -> A) and (B -> (((C -> (D -> C)) or E) and B))), M:tm-76, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21687
in-theory        21687
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> (C -> B)) or D) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-6 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21687.        (((not (not A)) or A) -> (((B -> (C -> B)) or D) and A)), M:tm-73, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-21688
in-theory        21688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (E -> D)) or F) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-9 tm-6 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21688.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (E -> D)) or F) and C))), M:tm-69, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21689
in-theory        21689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (D -> C)) or E) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-364 ((Am (-> (-> A (not B)) (not A))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-6 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21689.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (D -> C)) or E) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-364, u:((Am (-> (-> A (not B)) (not A))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-21690
in-theory        21690
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21690.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-54, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21691
in-theory        21691
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> D)) or F) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-364 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21691.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> D)) or F) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-364, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-21692
in-theory        21692
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> (D -> C)) or E) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-364 ((Am (or A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21692.        ((A or (B or A)) -> (((C -> (D -> C)) or E) and (B or A))), M:tm-50, m:tm-364, u:((Am (or A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (or A B))))
================================================================
tm-name          tm-21693
in-theory        21693
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> (D -> C)) or E) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-364 ((Am (or A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21693.        ((A or (A or B)) -> (((C -> (D -> C)) or E) and (A or B))), M:tm-49, m:tm-364, u:((Am (or A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (or A B))))
================================================================
tm-name          tm-21694
in-theory        21694
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> (D -> C)) or E) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-364 ((Am (-> A (and B A))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21694.        ((A or (B -> (A and B))) -> (((C -> (D -> C)) or E) and (B -> (A and B)))), M:tm-48, m:tm-364, u:((Am (-> A (and B A))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-21695
in-theory        21695
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> (D -> C)) or E) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-6 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21695.        (((A and B) or B) -> (((C -> (D -> C)) or E) and B)), M:tm-47, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-21696
in-theory        21696
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> (D -> C)) or E) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-6 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21696.        (((A and B) or A) -> (((C -> (D -> C)) or E) and A)), M:tm-46, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-21697
in-theory        21697
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> D)) or F) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-364 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21697.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> D)) or F) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-364, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-21698
in-theory        21698
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> (D -> C)) or E) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-364 ((Am (-> A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21698.        ((A or (B -> A)) -> (((C -> (D -> C)) or E) and (B -> A))), M:tm-44, m:tm-364, u:((Am (-> A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A B))))
================================================================
tm-name          tm-21699
in-theory        21699
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> (E -> D)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21699.        ((A -> (B or A)) and (C -> (((D -> (E -> D)) or F) and C))), M:tm-42, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21700
in-theory        21700
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> (E -> D)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21700.        ((A -> (A or B)) and (C -> (((D -> (E -> D)) or F) and C))), M:tm-32, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21701
in-theory        21701
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> (C -> B)) or D) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21701.        (A -> (A and (((B -> (C -> B)) or D) and A))), M:tm-24, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-21702
in-theory        21702
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> D)) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21702.        ((A -> (B -> (A and B))) and (C -> (((D -> (E -> D)) or F) and C))), M:tm-23, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21703
in-theory        21703
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> (E -> D)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21703.        (((A and B) -> B) and (C -> (((D -> (E -> D)) or F) and C))), M:tm-22, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21704
in-theory        21704
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> (E -> D)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21704.        (((A and B) -> A) and (C -> (((D -> (E -> D)) or F) and C))), M:tm-21, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21705
in-theory        21705
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21705.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-20, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21706
in-theory        21706
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> (E -> D)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21706.        ((A -> (B -> A)) and (C -> (((D -> (E -> D)) or F) and C))), M:tm-19, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21707
in-theory        21707
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> (C -> B)) or D) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-9 tm-5 tm-6 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21707.        ((A -> (not (((B -> (C -> B)) or D) and A))) -> (not A)), M:tm-9, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-21708
in-theory        21708
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) or C) and D) -> E) -> ((D or (((A -> (B -> A)) or C) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21708.        (((((A -> (B -> A)) or C) and D) -> E) -> ((D or (((A -> (B -> A)) or C) and D)) -> E)), M:tm-8, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-21709
in-theory        21709
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> (D -> C)) or E) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-7 tm-5 tm-6 tm-1)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21709.        (A or (B -> (((C -> (D -> C)) or E) and B))), M:tm-7, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21710
in-theory        21710
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21710.        ((A -> (((B -> (C -> B)) or D) and A)) or E), M:tm-6, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21711
in-theory        21711
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> (D -> C)) or E) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21711.        (A -> ((B -> (((C -> (D -> C)) or E) and B)) and A)), M:tm-5, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21712
in-theory        21712
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D -> C)) or E) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21712.        (A -> (B -> (((C -> (D -> C)) or E) and B))), M:tm-1, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-21713
in-theory        21713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-364 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21713.        (((A -> (B -> A)) or C) and (D -> ((E -> (F -> E)) or G))), M:tm-364, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21714
in-theory        21714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-354 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21714.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> E)) or G))), M:tm-354, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21715
in-theory        21715
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-351 tm-365 ((Am (-> A (-> B (and A B)))) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21715.        ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> D)) or F)), M:tm-351, m:tm-365, u:((Am (-> A (-> B (and A B)))) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21716
in-theory        21716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21716.        ((A -> ((B -> (C -> B)) or D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21717
in-theory        21717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) -> D) -> (((A -> (B -> A)) or C) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-365 ((Am (-> (or (-> Bm (-> Cm Bm)) Dm) B)) (A (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21717.        ((((A -> (B -> A)) or C) -> D) -> (((A -> (B -> A)) or C) and D)), M:tm-339, m:tm-365, u:((Am (-> (or (-> Bm (-> Cm Bm)) Dm) B)) (A (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21718
in-theory        21718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> D)) or F)))
theorem-size     19
proof            (modus-ponens tm-338 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21718.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> D)) or F))), M:tm-338, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21719
in-theory        21719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (D -> C)) or E))
theorem-size     17
proof            (modus-ponens tm-335 tm-365 ((Am (-> A (and A B))) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21719.        (((A -> B) or (A -> (A and B))) -> ((C -> (D -> C)) or E)), M:tm-335, m:tm-365, u:((Am (-> A (and A B))) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21720
in-theory        21720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and (A -> (A and ((B -> (C -> B)) or D))))
theorem-size     21
proof            (modus-ponens tm-328 tm-365 ((A Am) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21720.        ((A -> ((B -> (C -> B)) or D)) and (A -> (A and ((B -> (C -> B)) or D)))), M:tm-328, m:tm-365, u:((A Am) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21721
in-theory        21721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and ((E -> (F -> (E and F))) and (A -> ((B -> (C -> B)) or D))))
theorem-size     27
proof            (modus-ponens tm-327 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21721.        ((A -> ((B -> (C -> B)) or D)) and ((E -> (F -> (E and F))) and (A -> ((B -> (C -> B)) or D)))), M:tm-327, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21722
in-theory        21722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and (((E and F) -> F) and (A -> ((B -> (C -> B)) or D))))
theorem-size     25
proof            (modus-ponens tm-326 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21722.        ((A -> ((B -> (C -> B)) or D)) and (((E and F) -> F) and (A -> ((B -> (C -> B)) or D)))), M:tm-326, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21723
in-theory        21723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and (((E and F) -> E) and (A -> ((B -> (C -> B)) or D))))
theorem-size     25
proof            (modus-ponens tm-325 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21723.        ((A -> ((B -> (C -> B)) or D)) and (((E and F) -> E) and (A -> ((B -> (C -> B)) or D)))), M:tm-325, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21724
in-theory        21724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C -> B)) or D))))
theorem-size     33
proof            (modus-ponens tm-324 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21724.        ((A -> ((B -> (C -> B)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C -> B)) or D)))), M:tm-324, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21725
in-theory        21725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and ((E -> (F -> E)) and (A -> ((B -> (C -> B)) or D))))
theorem-size     25
proof            (modus-ponens tm-323 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21725.        ((A -> ((B -> (C -> B)) or D)) and ((E -> (F -> E)) and (A -> ((B -> (C -> B)) or D)))), M:tm-323, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21726
in-theory        21726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21726.        ((A -> ((B -> (C -> B)) or D)) and ((E and F) -> F)), M:tm-322, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21727
in-theory        21727
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> B)) or D) -> E)) -> ((B -> (C -> B)) or D)) and ((A and (((B -> (C -> B)) or D) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-365 ((Am (and A (-> (or (-> Bm (-> Cm Bm)) Dm) C))) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21727.        (((A and (((B -> (C -> B)) or D) -> E)) -> ((B -> (C -> B)) or D)) and ((A and (((B -> (C -> B)) or D) -> E)) -> E)), M:tm-321, m:tm-365, u:((Am (and A (-> (or (-> Bm (-> Cm Bm)) Dm) C))) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21728
in-theory        21728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21728.        ((A -> ((B -> (C -> B)) or D)) and ((E and F) -> E)), M:tm-320, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21729
in-theory        21729
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> A)) or C) -> D) and E) -> ((A -> (B -> A)) or C)) and (((((A -> (B -> A)) or C) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-365 ((Am (and (-> (or (-> Bm (-> Cm Bm)) Dm) B) C)) (A (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21729.        ((((((A -> (B -> A)) or C) -> D) and E) -> ((A -> (B -> A)) or C)) and (((((A -> (B -> A)) or C) -> D) and E) -> D)), M:tm-319, m:tm-365, u:((Am (and (-> (or (-> Bm (-> Cm Bm)) Dm) B) C)) (A (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21730
in-theory        21730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21730.        ((A -> ((B -> (C -> B)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21731
in-theory        21731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-365 ((A Am) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21731.        ((A -> ((B -> (C -> B)) or D)) and (A -> A)), M:tm-316, m:tm-365, u:((A Am) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21732
in-theory        21732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21732.        ((A -> ((B -> (C -> B)) or D)) and (E -> (F -> E))), M:tm-315, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21733
in-theory        21733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and ((A -> (not ((B -> (C -> B)) or D))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-365 ((A Am) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21733.        ((A -> ((B -> (C -> B)) or D)) and ((A -> (not ((B -> (C -> B)) or D))) -> (not A))), M:tm-313, m:tm-365, u:((A Am) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21734
in-theory        21734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and ((((B -> (C -> B)) or D) -> E) -> ((A or ((B -> (C -> B)) or D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-365 ((A Am) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21734.        ((A -> ((B -> (C -> B)) or D)) and ((((B -> (C -> B)) or D) -> E) -> ((A or ((B -> (C -> B)) or D)) -> E))), M:tm-312, m:tm-365, u:((A Am) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21735
in-theory        21735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and (E or (A -> ((B -> (C -> B)) or D))))
theorem-size     21
proof            (modus-ponens tm-311 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21735.        ((A -> ((B -> (C -> B)) or D)) and (E or (A -> ((B -> (C -> B)) or D)))), M:tm-311, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21736
in-theory        21736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and ((A -> ((B -> (C -> B)) or D)) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21736.        ((A -> ((B -> (C -> B)) or D)) and ((A -> ((B -> (C -> B)) or D)) or E)), M:tm-310, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21737
in-theory        21737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and (E -> ((A -> ((B -> (C -> B)) or D)) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21737.        ((A -> ((B -> (C -> B)) or D)) and (E -> ((A -> ((B -> (C -> B)) or D)) and E))), M:tm-309, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21738
in-theory        21738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and (E -> (A -> ((B -> (C -> B)) or D))))
theorem-size     21
proof            (modus-ponens tm-305 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21738.        ((A -> ((B -> (C -> B)) or D)) and (E -> (A -> ((B -> (C -> B)) or D)))), M:tm-305, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21739
in-theory        21739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-303 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21739.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> E)) or G))), M:tm-303, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21740
in-theory        21740
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-300 tm-365 ((Am (and (-> A (-> B (and A B))) C)) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21740.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> D)) or F)), M:tm-300, m:tm-365, u:((Am (and (-> A (-> B (and A B))) C)) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21741
in-theory        21741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-270 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21741.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> E)) or G))), M:tm-270, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21742
in-theory        21742
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-267 tm-365 ((Am (and (-> (and A B) B) C)) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21742.        ((A or (((B and C) -> C) and A)) -> ((D -> (E -> D)) or F)), M:tm-267, m:tm-365, u:((Am (and (-> (and A B) B) C)) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21743
in-theory        21743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-239 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21743.        ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> E)) or G))), M:tm-239, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21744
in-theory        21744
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-236 tm-365 ((Am (and (-> (and A B) A) C)) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21744.        ((A or (((B and C) -> B) and A)) -> ((D -> (E -> D)) or F)), M:tm-236, m:tm-365, u:((Am (and (-> (and A B) A) C)) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21745
in-theory        21745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-210 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21745.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> F)) or H))), M:tm-210, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21746
in-theory        21746
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-207 tm-365 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21746.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> E)) or G)), M:tm-207, m:tm-365, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21747
in-theory        21747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-183 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21747.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> E)) or G))), M:tm-183, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21748
in-theory        21748
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-180 tm-365 ((Am (and (-> A (-> B A)) C)) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21748.        ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> D)) or F)), M:tm-180, m:tm-365, u:((Am (and (-> A (-> B A)) C)) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21749
in-theory        21749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-157 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21749.        ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> E)) or G))), M:tm-157, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21750
in-theory        21750
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-154 tm-365 ((Am (-> (and A B) B)) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-4 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21750.        ((A or ((B and C) -> C)) -> ((D -> (E -> D)) or F)), M:tm-154, m:tm-365, u:((Am (-> (and A B) B)) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21751
in-theory        21751
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     25
proof            (modus-ponens tm-147 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21751.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> E)) or G))), M:tm-147, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21752
in-theory        21752
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-144 tm-365 ((Am (-> (and A (-> B C)) C)) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21752.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> D)) or F)), M:tm-144, m:tm-365, u:((Am (-> (and A (-> B C)) C)) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21753
in-theory        21753
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> B)) or D) -> E)) -> ((B -> (C -> B)) or D))
theorem-size     19
proof            (modus-ponens tm-142 tm-365 ((Am (and A (-> (or (-> Bm (-> Cm Bm)) Dm) C))) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21753.        ((A and (((B -> (C -> B)) or D) -> E)) -> ((B -> (C -> B)) or D)), M:tm-142, m:tm-365, u:((Am (and A (-> (or (-> Bm (-> Cm Bm)) Dm) C))) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21754
in-theory        21754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-134 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21754.        ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> E)) or G))), M:tm-134, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21755
in-theory        21755
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-131 tm-365 ((Am (-> (and A B) A)) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-3 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21755.        ((A or ((B and C) -> B)) -> ((D -> (E -> D)) or F)), M:tm-131, m:tm-365, u:((Am (-> (and A B) A)) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21756
in-theory        21756
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     25
proof            (modus-ponens tm-125 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21756.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> E)) or G))), M:tm-125, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21757
in-theory        21757
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-122 tm-365 ((Am (-> (and (-> A B) C) B)) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21757.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> D)) or F)), M:tm-122, m:tm-365, u:((Am (-> (and (-> A B) C) B)) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21758
in-theory        21758
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) or C) -> D) and E) -> ((A -> (B -> A)) or C))
theorem-size     19
proof            (modus-ponens tm-120 tm-365 ((Am (and (-> (or (-> Bm (-> Cm Bm)) Dm) B) C)) (A (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21758.        (((((A -> (B -> A)) or C) -> D) and E) -> ((A -> (B -> A)) or C)), M:tm-120, m:tm-365, u:((Am (and (-> (or (-> Bm (-> Cm Bm)) Dm) B) C)) (A (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21759
in-theory        21759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-113 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21759.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> F)) or H))), M:tm-113, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21760
in-theory        21760
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-110 tm-365 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21760.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> E)) or G)), M:tm-110, m:tm-365, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21761
in-theory        21761
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> E)) or G)))
theorem-size     29
proof            (modus-ponens tm-105 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21761.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> E)) or G))), M:tm-105, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21762
in-theory        21762
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> D)) or F))
theorem-size     27
proof            (modus-ponens tm-102 tm-365 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21762.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> D)) or F)), M:tm-102, m:tm-365, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21763
in-theory        21763
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) -> D) -> ((A -> (B -> A)) or C))
theorem-size     17
proof            (modus-ponens tm-96 tm-365 ((Am (-> (or (-> Bm (-> Cm Bm)) Dm) B)) (A (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21763.        ((((A -> (B -> A)) or C) -> D) -> ((A -> (B -> A)) or C)), M:tm-96, m:tm-365, u:((Am (-> (or (-> Bm (-> Cm Bm)) Dm) B)) (A (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21764
in-theory        21764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> D)) or F)))
theorem-size     17
proof            (modus-ponens tm-95 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21764.        (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> D)) or F))), M:tm-95, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21765
in-theory        21765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (D -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-92 tm-365 ((Am (-> A A)) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21765.        (((A -> B) or (A -> A)) -> ((C -> (D -> C)) or E)), M:tm-92, m:tm-365, u:((Am (-> A A)) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21766
in-theory        21766
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> C)) or E)))
theorem-size     11
proof            (modus-ponens tm-84 tm-365 ((A Am) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21766.        (A -> (B -> ((C -> (D -> C)) or E))), M:tm-84, m:tm-365, u:((A Am) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21767
in-theory        21767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-83 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21767.        ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> E)) or G))), M:tm-83, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21768
in-theory        21768
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-80 tm-365 ((Am (-> A (-> B A))) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21768.        ((A or (B -> (C -> B))) -> ((D -> (E -> D)) or F)), M:tm-80, m:tm-365, u:((Am (-> A (-> B A))) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21769
in-theory        21769
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((A -> (B -> A)) or C) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-365 ((Am (not (not (-> (or (-> Bm (-> Cm Bm)) Dm) B)))) (A (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-10 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21769.        ((not (not (((A -> (B -> A)) or C) -> D))) -> D), M:tm-77, m:tm-365, u:((Am (not (not (-> (or (-> Bm (-> Cm Bm)) Dm) B)))) (A (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21770
in-theory        21770
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (D -> C)) or E)))
theorem-size     15
proof            (modus-ponens tm-76 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21770.        (((not (not A)) -> A) and (B -> ((C -> (D -> C)) or E))), M:tm-76, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21771
in-theory        21771
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (C -> B)) or D))
theorem-size     13
proof            (modus-ponens tm-73 tm-365 ((A Am) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-10 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21771.        (((not (not A)) or A) -> ((B -> (C -> B)) or D)), M:tm-73, m:tm-365, u:((A Am) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21772
in-theory        21772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> D)) or F)))
theorem-size     21
proof            (modus-ponens tm-69 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21772.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> D)) or F))), M:tm-69, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21773
in-theory        21773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> C)) or E))
theorem-size     19
proof            (modus-ponens tm-66 tm-365 ((Am (-> (-> A (not B)) (not A))) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-9 tm-1 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21773.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> C)) or E)), M:tm-66, m:tm-365, u:((Am (-> (-> A (not B)) (not A))) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21774
in-theory        21774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-54 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21774.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> E)) or G))), M:tm-54, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21775
in-theory        21775
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-51 tm-365 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21775.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> D)) or F)), M:tm-51, m:tm-365, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21776
in-theory        21776
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (D -> C)) or E))
theorem-size     13
proof            (modus-ponens tm-50 tm-365 ((Am (or A B)) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21776.        ((A or (B or A)) -> ((C -> (D -> C)) or E)), M:tm-50, m:tm-365, u:((Am (or A B)) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21777
in-theory        21777
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (D -> C)) or E))
theorem-size     13
proof            (modus-ponens tm-49 tm-365 ((Am (or A B)) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21777.        ((A or (A or B)) -> ((C -> (D -> C)) or E)), M:tm-49, m:tm-365, u:((Am (or A B)) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21778
in-theory        21778
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (D -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-48 tm-365 ((Am (-> A (and B A))) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21778.        ((A or (B -> (A and B))) -> ((C -> (D -> C)) or E)), M:tm-48, m:tm-365, u:((Am (-> A (and B A))) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21779
in-theory        21779
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (D -> C)) or E))
theorem-size     13
proof            (modus-ponens tm-47 tm-365 ((A Am) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21779.        (((A and B) or B) -> ((C -> (D -> C)) or E)), M:tm-47, m:tm-365, u:((A Am) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21780
in-theory        21780
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (D -> C)) or E))
theorem-size     13
proof            (modus-ponens tm-46 tm-365 ((A Am) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21780.        (((A and B) or A) -> ((C -> (D -> C)) or E)), M:tm-46, m:tm-365, u:((A Am) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21781
in-theory        21781
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-45 tm-365 ((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21781.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) or F)), M:tm-45, m:tm-365, u:((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21782
in-theory        21782
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (D -> C)) or E))
theorem-size     13
proof            (modus-ponens tm-44 tm-365 ((Am (-> A B)) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21782.        ((A or (B -> A)) -> ((C -> (D -> C)) or E)), M:tm-44, m:tm-365, u:((Am (-> A B)) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21783
in-theory        21783
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-42 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21783.        ((A -> (B or A)) and (C -> ((D -> (E -> D)) or F))), M:tm-42, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21784
in-theory        21784
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-32 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21784.        ((A -> (A or B)) and (C -> ((D -> (E -> D)) or F))), M:tm-32, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21785
in-theory        21785
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (C -> B)) or D)))
theorem-size     11
proof            (modus-ponens tm-24 tm-365 ((A Am) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21785.        (A -> (A and ((B -> (C -> B)) or D))), M:tm-24, m:tm-365, u:((A Am) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21786
in-theory        21786
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) or F)))
theorem-size     17
proof            (modus-ponens tm-23 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21786.        ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) or F))), M:tm-23, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21787
in-theory        21787
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-22 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21787.        (((A and B) -> B) and (C -> ((D -> (E -> D)) or F))), M:tm-22, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21788
in-theory        21788
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-21 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21788.        (((A and B) -> A) and (C -> ((D -> (E -> D)) or F))), M:tm-21, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21789
in-theory        21789
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-20 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21789.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) or G))), M:tm-20, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21790
in-theory        21790
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-19 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21790.        ((A -> (B -> A)) and (C -> ((D -> (E -> D)) or F))), M:tm-19, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21791
in-theory        21791
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> B)) or D) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-365 ((Am (and A (-> (or (-> Bm (-> Cm Bm)) Dm) C))) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-4 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21791.        ((A and (((B -> (C -> B)) or D) -> E)) -> E), M:tm-17, m:tm-365, u:((Am (and A (-> (or (-> Bm (-> Cm Bm)) Dm) C))) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21792
in-theory        21792
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) or C) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-365 ((Am (and (-> (or (-> Bm (-> Cm Bm)) Dm) B) C)) (A (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-3 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21792.        (((((A -> (B -> A)) or C) -> D) and E) -> D), M:tm-15, m:tm-365, u:((Am (and (-> (or (-> Bm (-> Cm Bm)) Dm) B) C)) (A (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21793
in-theory        21793
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> B)) or D))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-365 ((A Am) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-9 tm-1 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21793.        ((A -> (not ((B -> (C -> B)) or D))) -> (not A)), M:tm-9, m:tm-365, u:((A Am) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21794
in-theory        21794
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) -> D) -> ((E or ((A -> (B -> A)) or C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-365 ((A Am) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21794.        ((((A -> (B -> A)) or C) -> D) -> ((E or ((A -> (B -> A)) or C)) -> D)), M:tm-8, m:tm-365, u:((A Am) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-21795
in-theory        21795
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (D -> C)) or E)))
theorem-size     11
proof            (modus-ponens tm-7 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-7 tm-1 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21795.        (A or (B -> ((C -> (D -> C)) or E))), M:tm-7, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21796
in-theory        21796
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-6 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21796.        ((A -> ((B -> (C -> B)) or D)) or E), M:tm-6, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21797
in-theory        21797
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D -> C)) or E)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-21797.        (A -> ((B -> ((C -> (D -> C)) or E)) and A)), M:tm-5, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-21798
in-theory        21798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-364 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21798.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-364, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21799
in-theory        21799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-354 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21799.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-354, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21800
in-theory        21800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21800.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21801
in-theory        21801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     33
proof            (modus-ponens tm-338 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21801.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-338, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21802
in-theory        21802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     55
proof            (modus-ponens tm-327 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21802.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-327, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21803
in-theory        21803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> H) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     53
proof            (modus-ponens tm-326 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21803.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> H) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-326, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21804
in-theory        21804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> G) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     53
proof            (modus-ponens tm-325 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21804.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> G) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-325, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21805
in-theory        21805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     61
proof            (modus-ponens tm-324 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21805.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-324, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21806
in-theory        21806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> G)) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     53
proof            (modus-ponens tm-323 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21806.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> G)) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-323, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21807
in-theory        21807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21807.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> H)), M:tm-322, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21808
in-theory        21808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21808.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> G)), M:tm-320, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21809
in-theory        21809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21809.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21810
in-theory        21810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21810.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> G))), M:tm-315, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21811
in-theory        21811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G or ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-311 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21811.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G or ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-311, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21812
in-theory        21812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21812.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G)), M:tm-310, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21813
in-theory        21813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21813.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and G))), M:tm-309, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21814
in-theory        21814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     39
proof            (modus-ponens tm-308 tm-366 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21814.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-308, m:tm-366, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))
================================================================
tm-name          tm-21815
in-theory        21815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (A -> (B -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-307 tm-366 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21815.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (A -> (B -> (A and B)))), M:tm-307, m:tm-366, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))
================================================================
tm-name          tm-21816
in-theory        21816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-305 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21816.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-305, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21817
in-theory        21817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-303 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21817.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-303, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21818
in-theory        21818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-270 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21818.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-270, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21819
in-theory        21819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-239 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21819.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-239, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21820
in-theory        21820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     41
proof            (modus-ponens tm-210 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21820.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-210, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21821
in-theory        21821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-183 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21821.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-183, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21822
in-theory        21822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-157 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21822.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-157, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21823
in-theory        21823
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-147 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21823.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-147, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21824
in-theory        21824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-134 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21824.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-134, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21825
in-theory        21825
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-125 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21825.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-125, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21826
in-theory        21826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-113 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21826.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-113, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21827
in-theory        21827
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     43
proof            (modus-ponens tm-105 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21827.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-105, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21828
in-theory        21828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-95 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21828.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-95, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21829
in-theory        21829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-83 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21829.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-83, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21830
in-theory        21830
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     29
proof            (modus-ponens tm-76 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-10 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21830.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-76, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21831
in-theory        21831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     35
proof            (modus-ponens tm-69 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-9 tm-6 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21831.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-69, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21832
in-theory        21832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-54 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21832.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-54, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21833
in-theory        21833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-42 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21833.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-42, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21834
in-theory        21834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-32 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21834.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-32, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21835
in-theory        21835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-23 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21835.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-23, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21836
in-theory        21836
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-22 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21836.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-22, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21837
in-theory        21837
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-21 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21837.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-21, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21838
in-theory        21838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-20 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21838.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-20, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21839
in-theory        21839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-19 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21839.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-19, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21840
in-theory        21840
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     25
proof            (modus-ponens tm-7 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-7 tm-5 tm-6 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21840.        (A or ((B -> (C -> (B and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-7, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21841
in-theory        21841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21841.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G), M:tm-6, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21842
in-theory        21842
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21842.        (A -> (((B -> (C -> (B and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and A)), M:tm-5, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21843
in-theory        21843
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     25
proof            (modus-ponens tm-1 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-1 tm-5 tm-6 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21843.        (A -> ((B -> (C -> (B and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-1, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21844
in-theory        21844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21844.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-364, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21845
in-theory        21845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21845.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-354, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21846
in-theory        21846
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21846.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21847
in-theory        21847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21847.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-338, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21848
in-theory        21848
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> (G and H))) and (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21848.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> (G and H))) and (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-327, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21849
in-theory        21849
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> H) and (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21849.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> H) and (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-326, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21850
in-theory        21850
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> G) and (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21850.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> G) and (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-325, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21851
in-theory        21851
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21851.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-324, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21852
in-theory        21852
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> G)) and (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21852.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> G)) and (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-323, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21853
in-theory        21853
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21853.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> H)), M:tm-322, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21854
in-theory        21854
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21854.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> G)), M:tm-320, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21855
in-theory        21855
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21855.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21856
in-theory        21856
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21856.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> G))), M:tm-315, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21857
in-theory        21857
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G or (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21857.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G or (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-311, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21858
in-theory        21858
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21858.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G)), M:tm-310, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21859
in-theory        21859
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21859.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and G))), M:tm-309, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21860
in-theory        21860
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     37
proof            (modus-ponens tm-308 tm-367 ((A (-> (and Am Bm) Bm)) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21860.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-308, m:tm-367, u:((A (-> (and Am Bm) Bm)) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))
================================================================
tm-name          tm-21861
in-theory        21861
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((A and B) -> B))
theorem-size     27
proof            (modus-ponens tm-307 tm-367 ((A (-> (and Am Bm) Bm)) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21861.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((A and B) -> B)), M:tm-307, m:tm-367, u:((A (-> (and Am Bm) Bm)) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))
================================================================
tm-name          tm-21862
in-theory        21862
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21862.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-305, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21863
in-theory        21863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21863.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-303, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21864
in-theory        21864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21864.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-270, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21865
in-theory        21865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21865.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-239, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21866
in-theory        21866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21866.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-210, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21867
in-theory        21867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21867.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-183, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21868
in-theory        21868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21868.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-157, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21869
in-theory        21869
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21869.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-147, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21870
in-theory        21870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21870.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-134, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21871
in-theory        21871
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21871.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-125, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21872
in-theory        21872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21872.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-113, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21873
in-theory        21873
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21873.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-105, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21874
in-theory        21874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21874.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-95, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21875
in-theory        21875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21875.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-83, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21876
in-theory        21876
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-10 tm-4 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21876.        (((not (not A)) -> A) and (((B and C) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-76, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21877
in-theory        21877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-9 tm-4 tm-6 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21877.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-69, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21878
in-theory        21878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21878.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-54, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21879
in-theory        21879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21879.        ((A -> (B or A)) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-42, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21880
in-theory        21880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21880.        ((A -> (A or B)) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-32, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21881
in-theory        21881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21881.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-23, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21882
in-theory        21882
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21882.        (((A and B) -> B) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-22, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21883
in-theory        21883
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21883.        (((A and B) -> A) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-21, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21884
in-theory        21884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21884.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-20, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21885
in-theory        21885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21885.        ((A -> (B -> A)) and (((C and D) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-19, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21886
in-theory        21886
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-7 tm-5 tm-4 tm-6 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21886.        (A or (((B and C) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-7, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21887
in-theory        21887
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-6 tm-5 tm-4 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21887.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G), M:tm-6, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21888
in-theory        21888
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21888.        (A -> ((((B and C) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and A)), M:tm-5, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21889
in-theory        21889
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-1 tm-5 tm-4 tm-6 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21889.        (A -> (((B and C) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-1, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21890
in-theory        21890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21890.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-364, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21891
in-theory        21891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21891.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-354, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21892
in-theory        21892
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21892.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21893
in-theory        21893
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21893.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-338, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21894
in-theory        21894
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> (G and H))) and (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21894.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> (G and H))) and (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-327, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21895
in-theory        21895
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> H) and (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21895.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> H) and (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-326, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21896
in-theory        21896
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> G) and (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21896.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> G) and (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-325, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21897
in-theory        21897
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21897.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-324, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21898
in-theory        21898
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> G)) and (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21898.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> G)) and (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-323, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21899
in-theory        21899
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21899.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> H)), M:tm-322, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21900
in-theory        21900
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21900.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> G)), M:tm-320, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21901
in-theory        21901
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21901.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21902
in-theory        21902
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21902.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> G))), M:tm-315, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21903
in-theory        21903
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G or (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21903.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G or (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-311, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21904
in-theory        21904
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21904.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G)), M:tm-310, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21905
in-theory        21905
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21905.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and G))), M:tm-309, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21906
in-theory        21906
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     37
proof            (modus-ponens tm-308 tm-368 ((A (-> (and Am Bm) Am)) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21906.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-308, m:tm-368, u:((A (-> (and Am Bm) Am)) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))
================================================================
tm-name          tm-21907
in-theory        21907
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((A and B) -> A))
theorem-size     27
proof            (modus-ponens tm-307 tm-368 ((A (-> (and Am Bm) Am)) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21907.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((A and B) -> A)), M:tm-307, m:tm-368, u:((A (-> (and Am Bm) Am)) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))
================================================================
tm-name          tm-21908
in-theory        21908
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21908.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-305, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21909
in-theory        21909
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21909.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-303, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21910
in-theory        21910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21910.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-270, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21911
in-theory        21911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21911.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-239, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21912
in-theory        21912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21912.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-210, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21913
in-theory        21913
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21913.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-183, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21914
in-theory        21914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21914.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-157, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21915
in-theory        21915
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21915.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-147, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21916
in-theory        21916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21916.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-134, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21917
in-theory        21917
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21917.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-125, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21918
in-theory        21918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21918.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-113, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21919
in-theory        21919
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21919.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-105, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21920
in-theory        21920
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21920.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-95, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21921
in-theory        21921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21921.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-83, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21922
in-theory        21922
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-10 tm-3 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21922.        (((not (not A)) -> A) and (((B and C) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-76, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21923
in-theory        21923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-9 tm-3 tm-6 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21923.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-69, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21924
in-theory        21924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21924.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-54, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21925
in-theory        21925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21925.        ((A -> (B or A)) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-42, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21926
in-theory        21926
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21926.        ((A -> (A or B)) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-32, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21927
in-theory        21927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21927.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-23, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21928
in-theory        21928
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21928.        (((A and B) -> B) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-22, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21929
in-theory        21929
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21929.        (((A and B) -> A) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-21, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21930
in-theory        21930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21930.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-20, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21931
in-theory        21931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21931.        ((A -> (B -> A)) and (((C and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-19, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21932
in-theory        21932
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-7 tm-5 tm-3 tm-6 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21932.        (A or (((B and C) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-7, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21933
in-theory        21933
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-6 tm-5 tm-3 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21933.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G), M:tm-6, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21934
in-theory        21934
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21934.        (A -> ((((B and C) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and A)), M:tm-5, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21935
in-theory        21935
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-1 tm-5 tm-3 tm-6 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21935.        (A -> (((B and C) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-1, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21936
in-theory        21936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-364 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21936.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-364, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21937
in-theory        21937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-354 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21937.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-354, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21938
in-theory        21938
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (I -> (H and I))))
theorem-size     37
proof            (modus-ponens tm-341 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21938.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (I -> (H and I)))), M:tm-341, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21939
in-theory        21939
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     39
proof            (modus-ponens tm-338 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21939.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-338, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21940
in-theory        21940
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I -> (H and I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     67
proof            (modus-ponens tm-327 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21940.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I -> (H and I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-327, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21941
in-theory        21941
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((H and I) -> I) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-326 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21941.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((H and I) -> I) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-326, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21942
in-theory        21942
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((H and I) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-325 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21942.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((H and I) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-325, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21943
in-theory        21943
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     73
proof            (modus-ponens tm-324 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       257
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21943.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-324, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21944
in-theory        21944
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I -> H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-323 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21944.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I -> H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-323, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21945
in-theory        21945
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H and I) -> I))
theorem-size     35
proof            (modus-ponens tm-322 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21945.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H and I) -> I)), M:tm-322, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21946
in-theory        21946
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H and I) -> H))
theorem-size     35
proof            (modus-ponens tm-320 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21946.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H and I) -> H)), M:tm-320, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21947
in-theory        21947
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))
theorem-size     43
proof            (modus-ponens tm-318 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21947.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21948
in-theory        21948
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (I -> H)))
theorem-size     35
proof            (modus-ponens tm-315 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21948.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (I -> H))), M:tm-315, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21949
in-theory        21949
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     61
proof            (modus-ponens tm-311 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21949.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-311, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21950
in-theory        21950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) or H))
theorem-size     61
proof            (modus-ponens tm-310 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21950.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) or H)), M:tm-310, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21951
in-theory        21951
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and H)))
theorem-size     63
proof            (modus-ponens tm-309 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21951.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and H))), M:tm-309, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21952
in-theory        21952
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     45
proof            (modus-ponens tm-308 tm-369 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21952.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-308, m:tm-369, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))
================================================================
tm-name          tm-21953
in-theory        21953
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-307 tm-369 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21953.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-369, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))
================================================================
tm-name          tm-21954
in-theory        21954
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     61
proof            (modus-ponens tm-305 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21954.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-305, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21955
in-theory        21955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     41
proof            (modus-ponens tm-303 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21955.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-303, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21956
in-theory        21956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-270 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21956.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-270, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21957
in-theory        21957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-239 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21957.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-239, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21958
in-theory        21958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K)))
theorem-size     47
proof            (modus-ponens tm-210 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21958.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-210, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21959
in-theory        21959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-183 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21959.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-183, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21960
in-theory        21960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-157 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21960.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-157, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21961
in-theory        21961
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     45
proof            (modus-ponens tm-147 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21961.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-147, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21962
in-theory        21962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-134 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21962.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-134, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21963
in-theory        21963
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     45
proof            (modus-ponens tm-125 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21963.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-125, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21964
in-theory        21964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-113 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21964.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-113, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21965
in-theory        21965
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     49
proof            (modus-ponens tm-105 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21965.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-105, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21966
in-theory        21966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-95 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21966.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-95, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21967
in-theory        21967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-83 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21967.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-83, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21968
in-theory        21968
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     35
proof            (modus-ponens tm-76 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21968.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-76, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21969
in-theory        21969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     41
proof            (modus-ponens tm-69 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-6)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21969.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-69, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21970
in-theory        21970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     43
proof            (modus-ponens tm-54 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21970.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-54, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21971
in-theory        21971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-42 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21971.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-42, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21972
in-theory        21972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-32 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21972.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-32, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21973
in-theory        21973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-23 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21973.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-23, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21974
in-theory        21974
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-22 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21974.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-22, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21975
in-theory        21975
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-21 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21975.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-21, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21976
in-theory        21976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     43
proof            (modus-ponens tm-20 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21976.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-20, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21977
in-theory        21977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-19 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21977.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-19, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21978
in-theory        21978
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-7 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-7 tm-5 tm-2 tm-6)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21978.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-7, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21979
in-theory        21979
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) or H)
theorem-size     31
proof            (modus-ponens tm-6 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21979.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) or H), M:tm-6, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21980
in-theory        21980
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21980.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)) and A)), M:tm-5, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21981
in-theory        21981
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-1 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-1 tm-5 tm-2 tm-6)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21981.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-1, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-21982
in-theory        21982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21982.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-364, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21983
in-theory        21983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21983.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-354, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21984
in-theory        21984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21984.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21985
in-theory        21985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21985.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-338, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21986
in-theory        21986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21986.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-327, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21987
in-theory        21987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> H) and ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21987.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> H) and ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-326, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21988
in-theory        21988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> G) and ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21988.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> G) and ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-325, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21989
in-theory        21989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21989.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-324, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21990
in-theory        21990
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> G)) and ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21990.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> G)) and ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-323, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21991
in-theory        21991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21991.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> H)), M:tm-322, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21992
in-theory        21992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21992.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> G)), M:tm-320, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21993
in-theory        21993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21993.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21994
in-theory        21994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21994.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> G))), M:tm-315, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21995
in-theory        21995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G or ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21995.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G or ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-311, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21996
in-theory        21996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21996.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G)), M:tm-310, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21997
in-theory        21997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21997.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and G))), M:tm-309, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-21998
in-theory        21998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     37
proof            (modus-ponens tm-308 tm-370 ((A (-> Am (-> Bm Am))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21998.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-308, m:tm-370, u:((A (-> Am (-> Bm Am))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))
================================================================
tm-name          tm-21999
in-theory        21999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (A -> (B -> A)))
theorem-size     27
proof            (modus-ponens tm-307 tm-370 ((A (-> Am (-> Bm Am))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-21999.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (A -> (B -> A))), M:tm-307, m:tm-370, u:((A (-> Am (-> Bm Am))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))
================================================================
tm-name          tm-22000
in-theory        22000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22000.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-305, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22001
in-theory        22001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22001.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-303, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22002
in-theory        22002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22002.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-270, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22003
in-theory        22003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22003.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-239, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22004
in-theory        22004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22004.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-210, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22005
in-theory        22005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22005.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-183, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22006
in-theory        22006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22006.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-157, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22007
in-theory        22007
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22007.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-147, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22008
in-theory        22008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22008.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-134, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22009
in-theory        22009
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22009.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-125, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22010
in-theory        22010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22010.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-113, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22011
in-theory        22011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22011.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-105, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22012
in-theory        22012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22012.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-95, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22013
in-theory        22013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22013.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-83, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22014
in-theory        22014
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22014.        (((not (not A)) -> A) and ((B -> (C -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-76, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22015
in-theory        22015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22015.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-69, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22016
in-theory        22016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22016.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-54, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22017
in-theory        22017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22017.        ((A -> (B or A)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-42, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22018
in-theory        22018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22018.        ((A -> (A or B)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-32, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22019
in-theory        22019
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22019.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-23, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22020
in-theory        22020
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22020.        (((A and B) -> B) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-22, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22021
in-theory        22021
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22021.        (((A and B) -> A) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-21, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22022
in-theory        22022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22022.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-20, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22023
in-theory        22023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22023.        ((A -> (B -> A)) and ((C -> (D -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-19, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22024
in-theory        22024
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-7 tm-5 tm-1 tm-6 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22024.        (A or ((B -> (C -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-7, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22025
in-theory        22025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-6 tm-5 tm-1 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22025.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G), M:tm-6, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22026
in-theory        22026
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22026.        (A -> (((B -> (C -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and A)), M:tm-5, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22027
in-theory        22027
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-1 tm-5 tm-6 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22027.        (A -> ((B -> (C -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-1, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22028
in-theory        22028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-364 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22028.        (((A -> (B -> A)) or C) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-364, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22029
in-theory        22029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-354 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22029.        ((A -> (B -> (C -> (B and C)))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-354, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22030
in-theory        22030
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22030.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22031
in-theory        22031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     27
proof            (modus-ponens tm-338 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22031.        (((A -> B) -> (A -> (A and B))) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-338, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22032
in-theory        22032
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G -> (F and G))) and (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     43
proof            (modus-ponens tm-327 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22032.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G -> (F and G))) and (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-327, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22033
in-theory        22033
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((F and G) -> G) and (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-326 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22033.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((F and G) -> G) and (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-326, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22034
in-theory        22034
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((F and G) -> F) and (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-325 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22034.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((F and G) -> F) and (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-325, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22035
in-theory        22035
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     49
proof            (modus-ponens tm-324 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22035.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-324, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22036
in-theory        22036
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G -> F)) and (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-323 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22036.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G -> F)) and (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-323, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22037
in-theory        22037
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22037.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F and G) -> G)), M:tm-322, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22038
in-theory        22038
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22038.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F and G) -> F)), M:tm-320, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22039
in-theory        22039
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22039.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22040
in-theory        22040
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22040.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (G -> F))), M:tm-315, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22041
in-theory        22041
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F or (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     37
proof            (modus-ponens tm-311 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22041.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F or (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-311, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22042
in-theory        22042
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22042.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) or F)), M:tm-310, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22043
in-theory        22043
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22043.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and F))), M:tm-309, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22044
in-theory        22044
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     37
proof            (modus-ponens tm-305 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22044.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-305, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22045
in-theory        22045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-303 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22045.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-303, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22046
in-theory        22046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-270 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22046.        ((A -> (((B and C) -> C) and A)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-270, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22047
in-theory        22047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-239 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22047.        ((A -> (((B and C) -> B) and A)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-239, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22048
in-theory        22048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-210 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22048.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-210, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22049
in-theory        22049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-183 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22049.        ((A -> ((B -> (C -> B)) and A)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-183, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22050
in-theory        22050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-157 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22050.        ((A -> ((B and C) -> C)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-157, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22051
in-theory        22051
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     33
proof            (modus-ponens tm-147 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22051.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-147, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22052
in-theory        22052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-134 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22052.        ((A -> ((B and C) -> B)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-134, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22053
in-theory        22053
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     33
proof            (modus-ponens tm-125 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22053.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-125, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22054
in-theory        22054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-113 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22054.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-113, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22055
in-theory        22055
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     37
proof            (modus-ponens tm-105 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22055.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-105, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22056
in-theory        22056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     25
proof            (modus-ponens tm-95 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22056.        (((A -> B) -> (A -> A)) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-95, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22057
in-theory        22057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-83 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22057.        ((A -> (B -> (C -> B))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-83, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22058
in-theory        22058
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))
theorem-size     23
proof            (modus-ponens tm-76 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22058.        (((not (not A)) -> A) and (B or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))), M:tm-76, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22059
in-theory        22059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     29
proof            (modus-ponens tm-69 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22059.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-69, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22060
in-theory        22060
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-54 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22060.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-54, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22061
in-theory        22061
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-42 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22061.        ((A -> (B or A)) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-42, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22062
in-theory        22062
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-32 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22062.        ((A -> (A or B)) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-32, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22063
in-theory        22063
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     25
proof            (modus-ponens tm-23 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22063.        ((A -> (B -> (A and B))) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-23, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22064
in-theory        22064
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-22 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22064.        (((A and B) -> B) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-22, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22065
in-theory        22065
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-21 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22065.        (((A and B) -> A) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-21, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22066
in-theory        22066
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-20 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22066.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-20, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22067
in-theory        22067
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-19 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22067.        ((A -> (B -> A)) and (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-19, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22068
in-theory        22068
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))
theorem-size     19
proof            (modus-ponens tm-7 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-7 tm-6 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22068.        (A or (B or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))), M:tm-7, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22069
in-theory        22069
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-6 tm-7 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22069.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) or F), M:tm-6, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22070
in-theory        22070
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22070.        (A -> ((B or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and A)), M:tm-5, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22071
in-theory        22071
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))
theorem-size     19
proof            (modus-ponens tm-1 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-1 tm-7 tm-6 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22071.        (A -> (B or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))), M:tm-1, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22072
in-theory        22072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-364 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22072.        (((A -> (B -> A)) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-364, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22073
in-theory        22073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-354 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22073.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-354, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22074
in-theory        22074
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22074.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (F -> (G -> (F and G)))), M:tm-341, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22075
in-theory        22075
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G))
theorem-size     27
proof            (modus-ponens tm-338 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22075.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G)), M:tm-338, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22076
in-theory        22076
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and ((F -> (G -> (F and G))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E)))
theorem-size     43
proof            (modus-ponens tm-327 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22076.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and ((F -> (G -> (F and G))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E))), M:tm-327, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22077
in-theory        22077
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (((F and G) -> G) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E)))
theorem-size     41
proof            (modus-ponens tm-326 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22077.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (((F and G) -> G) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E))), M:tm-326, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22078
in-theory        22078
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (((F and G) -> F) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E)))
theorem-size     41
proof            (modus-ponens tm-325 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22078.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (((F and G) -> F) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E))), M:tm-325, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22079
in-theory        22079
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E)))
theorem-size     49
proof            (modus-ponens tm-324 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22079.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E))), M:tm-324, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22080
in-theory        22080
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and ((F -> (G -> F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E)))
theorem-size     41
proof            (modus-ponens tm-323 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22080.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and ((F -> (G -> F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E))), M:tm-323, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22081
in-theory        22081
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22081.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and ((F and G) -> G)), M:tm-322, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22082
in-theory        22082
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22082.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and ((F and G) -> F)), M:tm-320, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22083
in-theory        22083
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22083.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22084
in-theory        22084
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22084.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (F -> (G -> F))), M:tm-315, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22085
in-theory        22085
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (F or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E)))
theorem-size     37
proof            (modus-ponens tm-311 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22085.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (F or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E))), M:tm-311, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22086
in-theory        22086
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22086.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) or F)), M:tm-310, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22087
in-theory        22087
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (F -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22087.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (F -> (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and F))), M:tm-309, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22088
in-theory        22088
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E)))
theorem-size     37
proof            (modus-ponens tm-305 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22088.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (F -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E))), M:tm-305, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22089
in-theory        22089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     29
proof            (modus-ponens tm-303 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22089.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-303, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22090
in-theory        22090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-270 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22090.        ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-270, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22091
in-theory        22091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-239 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22091.        ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-239, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22092
in-theory        22092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) or I))
theorem-size     35
proof            (modus-ponens tm-210 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22092.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) or I)), M:tm-210, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22093
in-theory        22093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-183 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22093.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-183, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22094
in-theory        22094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-157 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22094.        ((A -> ((B and C) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-157, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22095
in-theory        22095
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     33
proof            (modus-ponens tm-147 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22095.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-147, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22096
in-theory        22096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-134 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22096.        ((A -> ((B and C) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-134, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22097
in-theory        22097
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     33
proof            (modus-ponens tm-125 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22097.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-125, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22098
in-theory        22098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) or I))
theorem-size     33
proof            (modus-ponens tm-113 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22098.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) or I)), M:tm-113, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22099
in-theory        22099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     37
proof            (modus-ponens tm-105 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22099.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-105, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22100
in-theory        22100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G))
theorem-size     25
proof            (modus-ponens tm-95 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22100.        (((A -> B) -> (A -> A)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G)), M:tm-95, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22101
in-theory        22101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-83 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22101.        ((A -> (B -> (C -> B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-83, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22102
in-theory        22102
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) or F))
theorem-size     23
proof            (modus-ponens tm-76 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-10 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22102.        (((not (not A)) -> A) and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) or F)), M:tm-76, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22103
in-theory        22103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G))
theorem-size     29
proof            (modus-ponens tm-69 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-9 tm-6 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22103.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G)), M:tm-69, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22104
in-theory        22104
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     31
proof            (modus-ponens tm-54 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22104.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-54, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22105
in-theory        22105
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G))
theorem-size     23
proof            (modus-ponens tm-42 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22105.        ((A -> (B or A)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G)), M:tm-42, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22106
in-theory        22106
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G))
theorem-size     23
proof            (modus-ponens tm-32 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22106.        ((A -> (A or B)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G)), M:tm-32, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22107
in-theory        22107
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G))
theorem-size     25
proof            (modus-ponens tm-23 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22107.        ((A -> (B -> (A and B))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G)), M:tm-23, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22108
in-theory        22108
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G))
theorem-size     23
proof            (modus-ponens tm-22 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22108.        (((A and B) -> B) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G)), M:tm-22, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22109
in-theory        22109
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G))
theorem-size     23
proof            (modus-ponens tm-21 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22109.        (((A and B) -> A) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G)), M:tm-21, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22110
in-theory        22110
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     31
proof            (modus-ponens tm-20 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22110.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-20, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22111
in-theory        22111
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G))
theorem-size     23
proof            (modus-ponens tm-19 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22111.        ((A -> (B -> A)) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) or G)), M:tm-19, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22112
in-theory        22112
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) or F))
theorem-size     19
proof            (modus-ponens tm-7 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-7 tm-6 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22112.        (A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) or F)), M:tm-7, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22113
in-theory        22113
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-6 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22113.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) or F), M:tm-6, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22114
in-theory        22114
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) or F) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22114.        (A -> (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) or F) and A)), M:tm-5, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22115
in-theory        22115
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) or F))
theorem-size     19
proof            (modus-ponens tm-1 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-1 tm-6 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22115.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) or F)), M:tm-1, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22116
in-theory        22116
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-373 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22116.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E or F))), M:tm-373, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-22117
in-theory        22117
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-373 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-22117.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or E))), M:tm-373, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-22118
in-theory        22118
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-22118.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))), M:tm-373, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-22119
in-theory        22119
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((E -> (not F)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-373 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-22119.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((E -> (not F)) -> (not E)))), M:tm-373, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-22120
in-theory        22120
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((not (not E)) -> E))
theorem-size     21
proof            (modus-ponens tm-373 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-10.           ((not (not A)) -> A), axiom
tm-22120.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((not (not E)) -> E)), M:tm-373, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-22121
in-theory        22121
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-373 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22121.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (G -> F)))), M:tm-373, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-22122
in-theory        22122
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-373 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-22122.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (E -> E))), M:tm-373, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-22123
in-theory        22123
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-373 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-22123.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-373, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-22124
in-theory        22124
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22124.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-373, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-22125
in-theory        22125
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-373 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-22125.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))), M:tm-373, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-22126
in-theory        22126
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-373 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22126.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F and G) -> F))), M:tm-373, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-22127
in-theory        22127
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))
theorem-size     31
proof            (modus-ponens tm-373 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-22127.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))), M:tm-373, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-22128
in-theory        22128
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-373 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-22128.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F and G) -> G))), M:tm-373, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-22129
in-theory        22129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> F)) and E)))
theorem-size     25
proof            (modus-ponens tm-373 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22129.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> F)) and E))), M:tm-373, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-22130
in-theory        22130
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     33
proof            (modus-ponens tm-373 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22130.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-373, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-22131
in-theory        22131
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F and G) -> F) and E)))
theorem-size     25
proof            (modus-ponens tm-373 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22131.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F and G) -> F) and E))), M:tm-373, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-22132
in-theory        22132
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F and G) -> G) and E)))
theorem-size     25
proof            (modus-ponens tm-373 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-22132.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F and G) -> G) and E))), M:tm-373, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-22133
in-theory        22133
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> (F and G))) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22133.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> (F and G))) and E))), M:tm-373, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-22134
in-theory        22134
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (E -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-373 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-22134.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (E -> (E and F)))), M:tm-373, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-22135
in-theory        22135
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22135.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (G -> (F and G))))), M:tm-373, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-22136
in-theory        22136
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-373 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22136.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) or G)), M:tm-373, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-22137
in-theory        22137
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))
theorem-size     31
proof            (modus-ponens tm-373 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22137.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)), M:tm-373, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-22138
in-theory        22138
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) or G))
theorem-size     23
proof            (modus-ponens tm-373 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22138.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) or G)), M:tm-373, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-22139
in-theory        22139
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) or G))
theorem-size     23
proof            (modus-ponens tm-373 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-22139.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) or G)), M:tm-373, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-22140
in-theory        22140
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) or G))
theorem-size     25
proof            (modus-ponens tm-373 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22140.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) or G)), M:tm-373, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-22141
in-theory        22141
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) or G))
theorem-size     23
proof            (modus-ponens tm-373 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22141.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) or G)), M:tm-373, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-22142
in-theory        22142
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (F or G)) and E)))
theorem-size     25
proof            (modus-ponens tm-373 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22142.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (F or G)) and E))), M:tm-373, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-22143
in-theory        22143
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-373 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22143.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (F or G)))), M:tm-373, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-22144
in-theory        22144
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-373 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22144.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (G -> F)))), M:tm-373, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-22145
in-theory        22145
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22145.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-373, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-22146
in-theory        22146
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-373 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22146.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F and G) -> F))), M:tm-373, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-22147
in-theory        22147
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-373 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-22147.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F and G) -> G))), M:tm-373, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-22148
in-theory        22148
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22148.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (G -> (F and G))))), M:tm-373, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-22149
in-theory        22149
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-373 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22149.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (F or G)))), M:tm-373, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-22150
in-theory        22150
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-373 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22150.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (G or F)))), M:tm-373, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-22151
in-theory        22151
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) or G))
theorem-size     23
proof            (modus-ponens tm-373 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22151.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) or G)), M:tm-373, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-22152
in-theory        22152
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G or F)) and E)))
theorem-size     25
proof            (modus-ponens tm-373 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22152.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G or F)) and E))), M:tm-373, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-22153
in-theory        22153
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-373 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22153.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (G or F)))), M:tm-373, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-22154
in-theory        22154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-373 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-22154.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))), M:tm-373, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-22155
in-theory        22155
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     41
proof            (modus-ponens tm-373 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-22155.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-373, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-22156
in-theory        22156
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (((E and G) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-373 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-22156.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (((E and G) or E) -> F))), M:tm-373, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-22157
in-theory        22157
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (((G and E) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-373 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22157.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (((G and E) or E) -> F))), M:tm-373, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-22158
in-theory        22158
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-373 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-22158.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))), M:tm-373, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-22159
in-theory        22159
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E or F) -> G) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-373 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-22159.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E or F) -> G) -> ((E or (E or F)) -> G))), M:tm-373, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-22160
in-theory        22160
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E or F) -> G) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-373 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-22160.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E or F) -> G) -> ((F or (E or F)) -> G))), M:tm-373, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-22161
in-theory        22161
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     43
proof            (modus-ponens tm-373 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-22161.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-373, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-22162
in-theory        22162
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-22162.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-373, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-22163
in-theory        22163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))
theorem-size     31
proof            (modus-ponens tm-373 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-22163.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)), M:tm-373, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-22164
in-theory        22164
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E)))
theorem-size     33
proof            (modus-ponens tm-373 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-22164.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E))), M:tm-373, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-22165
in-theory        22165
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-373 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-22165.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G)))), M:tm-373, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-22166
in-theory        22166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-22166.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-373, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-22167
in-theory        22167
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (F -> E))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-373 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-22167.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (F -> E))) -> (not E))), M:tm-373, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-22168
in-theory        22168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-22168.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G))))), M:tm-373, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-22169
in-theory        22169
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> (not E)) -> (not (E and F))))
theorem-size     27
proof            (modus-ponens tm-373 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-22169.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> (not E)) -> (not (E and F)))), M:tm-373, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-22170
in-theory        22170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> (not F)) -> (not (E and F))))
theorem-size     27
proof            (modus-ponens tm-373 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22170.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> (not F)) -> (not (E and F)))), M:tm-373, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-22171
in-theory        22171
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (F -> (E and F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-22171.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (F -> (E and F)))) -> (not E))), M:tm-373, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-22172
in-theory        22172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (E or F))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-373 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-22172.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (E or F))) -> (not E))), M:tm-373, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-22173
in-theory        22173
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (F or E))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-373 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-22173.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (F or E))) -> (not E))), M:tm-373, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-22174
in-theory        22174
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F))))
theorem-size     35
proof            (modus-ponens tm-373 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-8)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-22174.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F)))), M:tm-373, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-22175
in-theory        22175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-373 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-22175.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F)))), M:tm-373, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-22176
in-theory        22176
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G)))
theorem-size     39
proof            (modus-ponens tm-373 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-9)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-22176.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G))), M:tm-373, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-22177
in-theory        22177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-22177.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-373, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-22178
in-theory        22178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G))
theorem-size     29
proof            (modus-ponens tm-373 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-22178.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G)), M:tm-373, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-22179
in-theory        22179
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E)))
theorem-size     31
proof            (modus-ponens tm-373 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-22179.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E))), M:tm-373, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-22180
in-theory        22180
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-373 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-22180.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E)))), M:tm-373, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-22181
in-theory        22181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-22181.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-373, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-22182
in-theory        22182
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((not (not E)) -> (not E)) -> (not (not (not E)))))
theorem-size     27
proof            (modus-ponens tm-373 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-10)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-22182.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((not (not E)) -> (not E)) -> (not (not (not E))))), M:tm-373, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-22183
in-theory        22183
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (((not (not E)) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-373 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-10)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-22183.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (((not (not E)) or E) -> F))), M:tm-373, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-22184
in-theory        22184
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-373 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-22184.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((not (not F)) -> F))), M:tm-373, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-22185
in-theory        22185
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((not (not E)) -> E) or F))
theorem-size     23
proof            (modus-ponens tm-373 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-22185.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((not (not E)) -> E) or F)), M:tm-373, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-22186
in-theory        22186
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((not (not F)) -> F) and E)))
theorem-size     25
proof            (modus-ponens tm-373 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-22186.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((not (not F)) -> F) and E))), M:tm-373, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-22187
in-theory        22187
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F)))
theorem-size     31
proof            (modus-ponens tm-373 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-22187.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F))), M:tm-373, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-22188
in-theory        22188
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-373 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-22188.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((not (not F)) -> F))), M:tm-373, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-22189
in-theory        22189
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (F -> (G -> F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-22189.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (F -> (G -> F)))) -> (not E))), M:tm-373, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-22190
in-theory        22190
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-373 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-22190.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G))), M:tm-373, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-22191
in-theory        22191
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-22191.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (G -> (H -> G))))), M:tm-373, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-22192
in-theory        22192
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (G -> F))) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-22192.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (G -> F))) or H)), M:tm-373, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-22193
in-theory        22193
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> (H -> G))) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-22193.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> (H -> G))) and E))), M:tm-373, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-22194
in-theory        22194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (E -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-373 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-22194.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (E -> (G -> F)))), M:tm-373, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-22195
in-theory        22195
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-22195.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (G -> (H -> G))))), M:tm-373, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-22196
in-theory        22196
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> E))
theorem-size     19
proof            (modus-ponens tm-373 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-22196.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> E)), M:tm-373, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-22197
in-theory        22197
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> G)) -> (E -> (F -> G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-22197.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> G)) -> (E -> (F -> G)))), M:tm-373, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-22198
in-theory        22198
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and F) -> (E and F)))
theorem-size     23
proof            (modus-ponens tm-373 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-22198.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and F) -> (E and F))), M:tm-373, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-22199
in-theory        22199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (E -> F)))
theorem-size     23
proof            (modus-ponens tm-373 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-22199.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (E -> F))), M:tm-373, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-22200
in-theory        22200
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((not (not E)) -> (not (not E))))
theorem-size     23
proof            (modus-ponens tm-373 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-22200.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((not (not E)) -> (not (not E)))), M:tm-373, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-22201
in-theory        22201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (not (E -> E))) -> (not (E -> F))))
theorem-size     29
proof            (modus-ponens tm-373 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-22201.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (not (E -> E))) -> (not (E -> F)))), M:tm-373, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-22202
in-theory        22202
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-373 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-22202.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F))), M:tm-373, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-22203
in-theory        22203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-373 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-22203.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> G) -> (F -> F)))), M:tm-373, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-22204
in-theory        22204
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (E -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-373 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-22204.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (E -> E)) or G)), M:tm-373, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-22205
in-theory        22205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> (F -> F)) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-22205.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> (F -> F)) and E))), M:tm-373, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-22206
in-theory        22206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> E) -> ((E -> F) -> E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-22206.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> E) -> ((E -> F) -> E))), M:tm-373, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-22207
in-theory        22207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-373 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-22207.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> G) -> (F -> F)))), M:tm-373, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-22208
in-theory        22208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F -> E) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-22208.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F -> E) -> G)) -> (E -> G))), M:tm-373, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-22209
in-theory        22209
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E -> F)) -> (E -> F)))
theorem-size     25
proof            (modus-ponens tm-373 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-22209.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E -> F)) -> (E -> F))), M:tm-373, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-22210
in-theory        22210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F))))
theorem-size     35
proof            (modus-ponens tm-373 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-22210.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F)))), M:tm-373, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-22211
in-theory        22211
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> G)) -> (E -> F)) -> (not ((E -> (F -> G)) -> (E -> G)))) -> (not ((E -> (F -> G)) -> (E -> F)))))
theorem-size     47
proof            (modus-ponens tm-373 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-22211.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> G)) -> (E -> F)) -> (not ((E -> (F -> G)) -> (E -> G)))) -> (not ((E -> (F -> G)) -> (E -> F))))), M:tm-373, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-22212
in-theory        22212
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> G)) -> (E -> G)) -> H) -> ((((E -> (F -> G)) -> (E -> F)) or ((E -> (F -> G)) -> (E -> G))) -> H)))
theorem-size     49
proof            (modus-ponens tm-373 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-22212.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> G)) -> (E -> G)) -> H) -> ((((E -> (F -> G)) -> (E -> F)) or ((E -> (F -> G)) -> (E -> G))) -> H))), M:tm-373, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-22213
in-theory        22213
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-22213.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-373, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-22214
in-theory        22214
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H))
theorem-size     37
proof            (modus-ponens tm-373 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-22214.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H)), M:tm-373, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-22215
in-theory        22215
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E)))
theorem-size     39
proof            (modus-ponens tm-373 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-22215.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E))), M:tm-373, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-22216
in-theory        22216
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> G)) -> (E -> F)) -> (E -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-373 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-22216.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> G)) -> (E -> F)) -> (E -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G)))), M:tm-373, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-22217
in-theory        22217
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-22217.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-373, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-22218
in-theory        22218
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> (((E -> F) -> (E -> G)) -> H)) -> ((E -> (F -> G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-373 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-22218.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> (((E -> F) -> (E -> G)) -> H)) -> ((E -> (F -> G)) -> H))), M:tm-373, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-22219
in-theory        22219
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E)))
theorem-size     35
proof            (modus-ponens tm-373 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-22219.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E))), M:tm-373, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-22220
in-theory        22220
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) -> ((I or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) -> H)))
theorem-size     49
proof            (modus-ponens tm-373 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-22220.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) -> ((I or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) -> H))), M:tm-373, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-22221
in-theory        22221
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-373 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-22221.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-373, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-22222
in-theory        22222
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-373 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-22222.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-373, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-22223
in-theory        22223
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-373 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-22223.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-373, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-22224
in-theory        22224
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-373 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-22224.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H))))), M:tm-373, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-22225
in-theory        22225
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-373 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-22225.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-373, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-22226
in-theory        22226
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) and E) -> F))
theorem-size     23
proof            (modus-ponens tm-373 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-22226.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) and E) -> F)), M:tm-373, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-22227
in-theory        22227
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> E)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-373 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-22227.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> E)) -> G) and H) -> G)), M:tm-373, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-22228
in-theory        22228
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) and I) -> H))
theorem-size     35
proof            (modus-ponens tm-373 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-22228.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) and I) -> H)), M:tm-373, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-22229
in-theory        22229
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F)))
theorem-size     37
proof            (modus-ponens tm-373 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-22229.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F))), M:tm-373, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-22230
in-theory        22230
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E)))
theorem-size     31
proof            (modus-ponens tm-373 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-22230.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E))), M:tm-373, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-22231
in-theory        22231
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) and G) -> E) -> (not (((E -> F) and G) -> F))) -> (not (((E -> F) and G) -> E))))
theorem-size     41
proof            (modus-ponens tm-373 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-22231.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) and G) -> E) -> (not (((E -> F) and G) -> F))) -> (not (((E -> F) and G) -> E)))), M:tm-373, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-22232
in-theory        22232
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) and G) -> F) -> H) -> (((((E -> F) and G) -> E) or (((E -> F) and G) -> F)) -> H)))
theorem-size     43
proof            (modus-ponens tm-373 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-22232.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) and G) -> F) -> H) -> (((((E -> F) and G) -> E) or (((E -> F) and G) -> F)) -> H))), M:tm-373, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-22233
in-theory        22233
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-373 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-22233.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-373, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-22234
in-theory        22234
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H))
theorem-size     33
proof            (modus-ponens tm-373 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-22234.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H)), M:tm-373, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-22235
in-theory        22235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E)))
theorem-size     35
proof            (modus-ponens tm-373 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-22235.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E))), M:tm-373, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-22236
in-theory        22236
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F)))
theorem-size     39
proof            (modus-ponens tm-373 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-22236.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F))), M:tm-373, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-22237
in-theory        22237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-373 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-22237.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-373, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-22238
in-theory        22238
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E and F) -> E) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-373 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-22238.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E and F) -> E) -> G) and H) -> G)), M:tm-373, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-22239
in-theory        22239
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> (E -> G)) -> ((E and F) -> G)))
theorem-size     29
proof            (modus-ponens tm-373 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-22239.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> (E -> G)) -> ((E and F) -> G))), M:tm-373, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-22240
in-theory        22240
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not ((F and G) -> F))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-1 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-22240.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not ((F and G) -> F))) -> (not E))), M:tm-373, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-22241
in-theory        22241
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G)))
theorem-size     33
proof            (modus-ponens tm-373 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-22241.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G))), M:tm-373, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-22242
in-theory        22242
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-373 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-22242.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> ((G and H) -> G)))), M:tm-373, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-22243
in-theory        22243
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F and G) -> F)) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-22243.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F and G) -> F)) or H)), M:tm-373, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-22244
in-theory        22244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> ((G and H) -> G)) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-22244.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> ((G and H) -> G)) and E))), M:tm-373, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-22245
in-theory        22245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F and G)) -> (E -> F)))
theorem-size     25
proof            (modus-ponens tm-373 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-22245.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F and G)) -> (E -> F))), M:tm-373, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-22246
in-theory        22246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-373 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-22246.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> ((G and H) -> G)))), M:tm-373, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-22247
in-theory        22247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and (E -> F)) -> F))
theorem-size     23
proof            (modus-ponens tm-373 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-22247.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and (E -> F)) -> F)), M:tm-373, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-22248
in-theory        22248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and ((F -> (G -> F)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-373 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-22248.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and ((F -> (G -> F)) -> H)) -> H)), M:tm-373, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-22249
in-theory        22249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I))
theorem-size     35
proof            (modus-ponens tm-373 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-22249.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I)), M:tm-373, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-22250
in-theory        22250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and (((F and G) -> F) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-373 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-22250.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and (((F and G) -> F) -> H)) -> H)), M:tm-373, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-22251
in-theory        22251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-373 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-22251.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G))), M:tm-373, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-22252
in-theory        22252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F)))
theorem-size     31
proof            (modus-ponens tm-373 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-22252.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F))), M:tm-373, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-22253
in-theory        22253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and (F -> G)) -> F) -> (not ((E and (F -> G)) -> G))) -> (not ((E and (F -> G)) -> F))))
theorem-size     41
proof            (modus-ponens tm-373 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-4)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-22253.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and (F -> G)) -> F) -> (not ((E and (F -> G)) -> G))) -> (not ((E and (F -> G)) -> F)))), M:tm-373, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-22254
in-theory        22254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and (F -> G)) -> G) -> H) -> ((((E and (F -> G)) -> F) or ((E and (F -> G)) -> G)) -> H)))
theorem-size     43
proof            (modus-ponens tm-373 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-22254.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and (F -> G)) -> G) -> H) -> ((((E and (F -> G)) -> F) or ((E and (F -> G)) -> G)) -> H))), M:tm-373, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-22255
in-theory        22255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-373 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22255.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-373, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-22256
in-theory        22256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H))
theorem-size     33
proof            (modus-ponens tm-373 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22256.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H)), M:tm-373, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-22257
in-theory        22257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E)))
theorem-size     35
proof            (modus-ponens tm-373 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22257.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E))), M:tm-373, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-22258
in-theory        22258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and (F -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G)))
theorem-size     39
proof            (modus-ponens tm-373 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-22258.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and (F -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G))), M:tm-373, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-22259
in-theory        22259
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-373 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22259.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-373, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-22260
in-theory        22260
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and (((F and G) -> G) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-373 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-22260.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and (((F and G) -> G) -> H)) -> H)), M:tm-373, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-22261
in-theory        22261
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E and F) -> F) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-373 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-22261.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E and F) -> F) -> G) and H) -> G)), M:tm-373, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-22262
in-theory        22262
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> (F -> G)) -> ((E and F) -> G)))
theorem-size     29
proof            (modus-ponens tm-373 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-22262.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> (F -> G)) -> ((E and F) -> G))), M:tm-373, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-22263
in-theory        22263
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not ((F and G) -> G))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-1 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22263.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not ((F and G) -> G))) -> (not E))), M:tm-373, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-22264
in-theory        22264
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-373 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22264.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G))), M:tm-373, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-22265
in-theory        22265
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-373 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22265.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> ((G and H) -> H)))), M:tm-373, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-22266
in-theory        22266
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F and G) -> G)) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22266.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F and G) -> G)) or H)), M:tm-373, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-22267
in-theory        22267
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> ((G and H) -> H)) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22267.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> ((G and H) -> H)) and E))), M:tm-373, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-22268
in-theory        22268
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F and G)) -> (E -> G)))
theorem-size     25
proof            (modus-ponens tm-373 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-22268.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F and G)) -> (E -> G))), M:tm-373, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-22269
in-theory        22269
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-373 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22269.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> ((G and H) -> H)))), M:tm-373, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-22270
in-theory        22270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22270.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> G)))), M:tm-373, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-22271
in-theory        22271
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22271.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-373, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-22272
in-theory        22272
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22272.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G and H) -> G))), M:tm-373, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-22273
in-theory        22273
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-373 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-22273.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G and H) -> H))), M:tm-373, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-22274
in-theory        22274
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22274.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (G and H))))), M:tm-373, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-22275
in-theory        22275
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-373 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22275.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (G or H)))), M:tm-373, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-22276
in-theory        22276
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22276.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (H or G)))), M:tm-373, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-22277
in-theory        22277
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-22277.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-373, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-22278
in-theory        22278
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-373 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-22278.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-373, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-22279
in-theory        22279
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-22279.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((not (not G)) -> G))), M:tm-373, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-22280
in-theory        22280
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-22280.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (I -> H))))), M:tm-373, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-22281
in-theory        22281
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-22281.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (G -> G)))), M:tm-373, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-22282
in-theory        22282
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-373 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-22282.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-373, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-22283
in-theory        22283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-22283.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-373, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-22284
in-theory        22284
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-373 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-22284.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-373, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-22285
in-theory        22285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-373 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-22285.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> ((H and I) -> H)))), M:tm-373, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-22286
in-theory        22286
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-373 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22286.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-373, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-22287
in-theory        22287
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-373 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22287.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> ((H and I) -> I)))), M:tm-373, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-22288
in-theory        22288
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-22288.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-373, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-22289
in-theory        22289
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-22289.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E))), M:tm-373, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-22290
in-theory        22290
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> E)) and G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-373 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-22290.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> E)) and G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H))), M:tm-373, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-22291
in-theory        22291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-373 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-22291.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> ((G -> (H -> G)) and F)))), M:tm-373, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-22292
in-theory        22292
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F -> (G -> F)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-373 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-22292.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F -> (G -> F)) and E)) or H)), M:tm-373, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-22293
in-theory        22293
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> ((G -> (H -> G)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-22293.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> ((G -> (H -> G)) and F)) and E))), M:tm-373, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-22294
in-theory        22294
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-373 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-22294.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> ((G -> (H -> G)) and F)))), M:tm-373, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-22295
in-theory        22295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-373 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22295.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> H)))), M:tm-373, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-22296
in-theory        22296
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22296.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-373, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-22297
in-theory        22297
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-373 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22297.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> H))), M:tm-373, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-22298
in-theory        22298
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-373 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-22298.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> I))), M:tm-373, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-22299
in-theory        22299
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22299.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (H and I))))), M:tm-373, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-22300
in-theory        22300
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22300.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (H or I)))), M:tm-373, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-22301
in-theory        22301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-373 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22301.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I or H)))), M:tm-373, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-22302
in-theory        22302
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-22302.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-373, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-22303
in-theory        22303
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     41
proof            (modus-ponens tm-373 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-22303.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-373, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-22304
in-theory        22304
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((not (not H)) -> H)))
theorem-size     35
proof            (modus-ponens tm-373 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-22304.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((not (not H)) -> H))), M:tm-373, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-22305
in-theory        22305
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-22305.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> I))))), M:tm-373, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-22306
in-theory        22306
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> H))))
theorem-size     37
proof            (modus-ponens tm-373 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-22306.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> H)))), M:tm-373, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-22307
in-theory        22307
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J)))))
theorem-size     49
proof            (modus-ponens tm-373 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-22307.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-373, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-22308
in-theory        22308
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-373 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-22308.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-373, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-22309
in-theory        22309
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I))))
theorem-size     45
proof            (modus-ponens tm-373 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-22309.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-373, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-22310
in-theory        22310
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-373 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-22310.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> I)))), M:tm-373, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-22311
in-theory        22311
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J))))
theorem-size     45
proof            (modus-ponens tm-373 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22311.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-373, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-22312
in-theory        22312
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-373 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22312.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> J)))), M:tm-373, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-22313
in-theory        22313
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> I)) and H))))
theorem-size     39
proof            (modus-ponens tm-373 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-22313.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-373, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-22314
in-theory        22314
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H))))
theorem-size     47
proof            (modus-ponens tm-373 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-22314.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-373, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-22315
in-theory        22315
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-373 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-22315.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-373, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-22316
in-theory        22316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-373 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-22316.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E))), M:tm-373, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-22317
in-theory        22317
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H) -> I) -> ((H or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H)) -> I)))
theorem-size     53
proof            (modus-ponens tm-373 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-22317.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H) -> I) -> ((H or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H)) -> I))), M:tm-373, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-22318
in-theory        22318
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-373 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-22318.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-373, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-22319
in-theory        22319
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I))
theorem-size     35
proof            (modus-ponens tm-373 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-22319.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I)), M:tm-373, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-22320
in-theory        22320
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E)))
theorem-size     37
proof            (modus-ponens tm-373 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-22320.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E))), M:tm-373, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-22321
in-theory        22321
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-373 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-22321.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-373, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-22322
in-theory        22322
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22322.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (H -> G)))), M:tm-373, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-22323
in-theory        22323
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22323.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-373, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-22324
in-theory        22324
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22324.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G and H) -> G))), M:tm-373, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-22325
in-theory        22325
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-373 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-22325.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G and H) -> H))), M:tm-373, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-22326
in-theory        22326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22326.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (H -> (G and H))))), M:tm-373, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-22327
in-theory        22327
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-373 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22327.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (G or H)))), M:tm-373, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-22328
in-theory        22328
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22328.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (H or G)))), M:tm-373, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-22329
in-theory        22329
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-22329.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-373, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-22330
in-theory        22330
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-373 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-22330.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-373, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-22331
in-theory        22331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-22331.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((not (not G)) -> G))), M:tm-373, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-22332
in-theory        22332
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-22332.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (H -> (I -> H))))), M:tm-373, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-22333
in-theory        22333
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-22333.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (G -> G)))), M:tm-373, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-22334
in-theory        22334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-373 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-22334.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-373, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-22335
in-theory        22335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-22335.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-373, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-22336
in-theory        22336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-373 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-22336.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-373, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-22337
in-theory        22337
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-373 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-22337.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> ((H and I) -> H)))), M:tm-373, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-22338
in-theory        22338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-373 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22338.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-373, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-22339
in-theory        22339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-373 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22339.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> ((H and I) -> I)))), M:tm-373, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-22340
in-theory        22340
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-22340.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G)))), M:tm-373, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-22341
in-theory        22341
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-373 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-22341.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-373, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-22342
in-theory        22342
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-22342.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (((H and I) -> H) and G)))), M:tm-373, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-22343
in-theory        22343
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> I) and H))))
theorem-size     39
proof            (modus-ponens tm-373 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-22343.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-373, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-22344
in-theory        22344
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-22344.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G)))), M:tm-373, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-22345
in-theory        22345
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (((F and G) -> F) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-22345.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (((F and G) -> F) and E))) -> (not E))), M:tm-373, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-22346
in-theory        22346
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E and F) -> E) and G) -> H) -> ((G or (((E and F) -> E) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-373 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-22346.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E and F) -> E) and G) -> H) -> ((G or (((E and F) -> E) and G)) -> H))), M:tm-373, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-22347
in-theory        22347
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-373 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-22347.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (((G and H) -> G) and F)))), M:tm-373, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-22348
in-theory        22348
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (((F and G) -> F) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-373 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-22348.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (((F and G) -> F) and E)) or H)), M:tm-373, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-22349
in-theory        22349
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (((G and H) -> G) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-22349.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (((G and H) -> G) and F)) and E))), M:tm-373, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-22350
in-theory        22350
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-373 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-22350.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (((G and H) -> G) and F)))), M:tm-373, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-22351
in-theory        22351
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22351.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (H -> G)))), M:tm-373, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-22352
in-theory        22352
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22352.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-373, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-22353
in-theory        22353
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22353.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G and H) -> G))), M:tm-373, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-22354
in-theory        22354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-373 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-22354.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G and H) -> H))), M:tm-373, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-22355
in-theory        22355
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22355.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (H -> (G and H))))), M:tm-373, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-22356
in-theory        22356
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-373 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22356.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (G or H)))), M:tm-373, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-22357
in-theory        22357
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22357.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (H or G)))), M:tm-373, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-22358
in-theory        22358
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-22358.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-373, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-22359
in-theory        22359
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-373 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-22359.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-373, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-22360
in-theory        22360
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-22360.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((not (not G)) -> G))), M:tm-373, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-22361
in-theory        22361
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-22361.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (H -> (I -> H))))), M:tm-373, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-22362
in-theory        22362
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-22362.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (G -> G)))), M:tm-373, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-22363
in-theory        22363
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-373 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-22363.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-373, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-22364
in-theory        22364
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-22364.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-373, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-22365
in-theory        22365
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-373 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-22365.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-373, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-22366
in-theory        22366
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-373 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-22366.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> ((H and I) -> H)))), M:tm-373, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-22367
in-theory        22367
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-373 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22367.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-373, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-22368
in-theory        22368
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-373 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22368.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> ((H and I) -> I)))), M:tm-373, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-22369
in-theory        22369
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-22369.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G)))), M:tm-373, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-22370
in-theory        22370
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-373 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-22370.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-373, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-22371
in-theory        22371
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-22371.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (((H and I) -> H) and G)))), M:tm-373, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-22372
in-theory        22372
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-22372.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (((H and I) -> I) and G)))), M:tm-373, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-22373
in-theory        22373
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-22373.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (((H and I) -> I) and G)))), M:tm-373, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-22374
in-theory        22374
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> J) and H))))
theorem-size     39
proof            (modus-ponens tm-373 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-22374.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-373, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-22375
in-theory        22375
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-22375.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G)))), M:tm-373, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-22376
in-theory        22376
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (((F and G) -> G) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-22376.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (((F and G) -> G) and E))) -> (not E))), M:tm-373, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-22377
in-theory        22377
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E and F) -> F) and G) -> H) -> ((G or (((E and F) -> F) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-373 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-22377.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E and F) -> F) and G) -> H) -> ((G or (((E and F) -> F) and G)) -> H))), M:tm-373, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-22378
in-theory        22378
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-373 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-22378.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (((G and H) -> H) and F)))), M:tm-373, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-22379
in-theory        22379
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (((F and G) -> G) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-373 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-22379.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (((F and G) -> G) and E)) or H)), M:tm-373, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-22380
in-theory        22380
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (((G and H) -> H) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-22380.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (((G and H) -> H) and F)) and E))), M:tm-373, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-22381
in-theory        22381
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-373 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-22381.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (((G and H) -> H) and F)))), M:tm-373, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-22382
in-theory        22382
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22382.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> G)))), M:tm-373, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-22383
in-theory        22383
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22383.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-373, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-22384
in-theory        22384
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-373 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22384.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G and H) -> G))), M:tm-373, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-22385
in-theory        22385
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-373 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-22385.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G and H) -> H))), M:tm-373, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-22386
in-theory        22386
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22386.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H))))), M:tm-373, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-22387
in-theory        22387
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-373 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22387.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (G or H)))), M:tm-373, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-22388
in-theory        22388
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22388.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H or G)))), M:tm-373, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-22389
in-theory        22389
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-22389.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-373, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-22390
in-theory        22390
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-22390.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-373, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-22391
in-theory        22391
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-373 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-22391.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((not (not G)) -> G))), M:tm-373, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-22392
in-theory        22392
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-22392.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H))))), M:tm-373, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-22393
in-theory        22393
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-22393.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G)))), M:tm-373, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-22394
in-theory        22394
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-22394.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-373, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-22395
in-theory        22395
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-373 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-22395.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-373, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-22396
in-theory        22396
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-373 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-22396.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-373, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-22397
in-theory        22397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-373 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-22397.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H)))), M:tm-373, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-22398
in-theory        22398
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-373 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22398.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-373, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-22399
in-theory        22399
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-373 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22399.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I)))), M:tm-373, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-22400
in-theory        22400
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-373 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-22400.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-373, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-22401
in-theory        22401
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-373 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-22401.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-373, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-22402
in-theory        22402
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-373 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-22402.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G)))), M:tm-373, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-22403
in-theory        22403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-373 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-22403.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G)))), M:tm-373, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-22404
in-theory        22404
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-373 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-22404.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-373, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-22405
in-theory        22405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-373 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-22405.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-373, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-22406
in-theory        22406
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-373 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-22406.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-373, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-22407
in-theory        22407
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> (I and J))) and H))))
theorem-size     41
proof            (modus-ponens tm-373 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-22407.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-373, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-22408
in-theory        22408
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-373 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-22408.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-373, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-22409
in-theory        22409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E)))
theorem-size     31
proof            (modus-ponens tm-373 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-22409.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E))), M:tm-373, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-22410
in-theory        22410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> (E and F))) and G) -> H) -> ((G or ((E -> (F -> (E and F))) and G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-373 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-22410.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> (E and F))) and G) -> H) -> ((G or ((E -> (F -> (E and F))) and G)) -> H))), M:tm-373, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-22411
in-theory        22411
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-373 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-22411.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> ((G -> (H -> (G and H))) and F)))), M:tm-373, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-22412
in-theory        22412
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F -> (G -> (F and G))) and E)) or H))
theorem-size     29
proof            (modus-ponens tm-373 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-22412.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F -> (G -> (F and G))) and E)) or H)), M:tm-373, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-22413
in-theory        22413
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E)))
theorem-size     31
proof            (modus-ponens tm-373 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-22413.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E))), M:tm-373, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-22414
in-theory        22414
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-373 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-22414.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> ((G -> (H -> (G and H))) and F)))), M:tm-373, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-22415
in-theory        22415
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (F -> E))))
theorem-size     23
proof            (modus-ponens tm-373 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-22415.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (F -> E)))), M:tm-373, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-22416
in-theory        22416
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-22416.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G))))), M:tm-373, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-22417
in-theory        22417
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and F) -> ((E and F) and E)))
theorem-size     25
proof            (modus-ponens tm-373 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-22417.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and F) -> ((E and F) and E))), M:tm-373, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-22418
in-theory        22418
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and F) -> ((E and F) and F)))
theorem-size     25
proof            (modus-ponens tm-373 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22418.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and F) -> ((E and F) and F))), M:tm-373, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-22419
in-theory        22419
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-22419.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (F -> (E and F))))), M:tm-373, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-22420
in-theory        22420
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (E or F))))
theorem-size     23
proof            (modus-ponens tm-373 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-22420.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (E or F)))), M:tm-373, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-22421
in-theory        22421
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (F or E))))
theorem-size     23
proof            (modus-ponens tm-373 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-22421.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (F or E)))), M:tm-373, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-22422
in-theory        22422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     33
proof            (modus-ponens tm-373 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-22422.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G))))), M:tm-373, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-22423
in-theory        22423
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-22423.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E))))), M:tm-373, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-22424
in-theory        22424
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((not (not E)) -> ((not (not E)) and E)))
theorem-size     25
proof            (modus-ponens tm-373 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-22424.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((not (not E)) -> ((not (not E)) and E))), M:tm-373, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-22425
in-theory        22425
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-22425.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (F -> (G -> F))))), M:tm-373, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-22426
in-theory        22426
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((E -> F) and (E -> E))))
theorem-size     27
proof            (modus-ponens tm-373 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-22426.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((E -> F) and (E -> E)))), M:tm-373, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-22427
in-theory        22427
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> (E -> F)) -> (((E -> (F -> G)) -> (E -> F)) and ((E -> (F -> G)) -> (E -> G)))))
theorem-size     45
proof            (modus-ponens tm-373 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-22427.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> (E -> F)) -> (((E -> (F -> G)) -> (E -> F)) and ((E -> (F -> G)) -> (E -> G))))), M:tm-373, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-22428
in-theory        22428
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-373 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-22428.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-373, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-22429
in-theory        22429
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) -> E) -> ((((E -> F) and G) -> E) and (((E -> F) and G) -> F))))
theorem-size     39
proof            (modus-ponens tm-373 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-22429.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) -> E) -> ((((E -> F) and G) -> E) and (((E -> F) and G) -> F)))), M:tm-373, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-22430
in-theory        22430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-373 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-22430.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and ((F and G) -> F)))), M:tm-373, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-22431
in-theory        22431
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) -> F) -> (((E and (F -> G)) -> F) and ((E and (F -> G)) -> G))))
theorem-size     39
proof            (modus-ponens tm-373 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-22431.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) -> F) -> (((E and (F -> G)) -> F) and ((E and (F -> G)) -> G)))), M:tm-373, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-22432
in-theory        22432
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-373 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22432.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and ((F and G) -> G)))), M:tm-373, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-22433
in-theory        22433
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-373 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-22433.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and ((F -> (G -> F)) and E)))), M:tm-373, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-22434
in-theory        22434
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-373 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-22434.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-373, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-22435
in-theory        22435
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-373 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-22435.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (((F and G) -> F) and E)))), M:tm-373, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-22436
in-theory        22436
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-373 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-22436.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (((F and G) -> G) and E)))), M:tm-373, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-22437
in-theory        22437
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-373 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-22437.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and ((F -> (G -> (F and G))) and E)))), M:tm-373, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-22438
in-theory        22438
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((E -> F) and (E -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-22438.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((E -> F) and (E -> (E and F))))), M:tm-373, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-22439
in-theory        22439
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-373 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-22439.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H))))), M:tm-373, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-22440
in-theory        22440
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-22440.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H))))), M:tm-373, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-22441
in-theory        22441
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-22441.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H))))), M:tm-373, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-22442
in-theory        22442
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> (H and I)))))
theorem-size     39
proof            (modus-ponens tm-373 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-22442.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-373, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-22443
in-theory        22443
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-22443.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H))))), M:tm-373, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-22444
in-theory        22444
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F))))
theorem-size     31
proof            (modus-ponens tm-373 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-22444.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F)))), M:tm-373, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-22445
in-theory        22445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-373 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-22445.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G))), M:tm-373, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-22446
in-theory        22446
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-373 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-22446.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> G) -> (F -> (F and G))))), M:tm-373, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-22447
in-theory        22447
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (E -> (E and F))) or G))
theorem-size     27
proof            (modus-ponens tm-373 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-22447.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (E -> (E and F))) or G)), M:tm-373, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-22448
in-theory        22448
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> (F -> (F and G))) and E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-22448.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> (F -> (F and G))) and E))), M:tm-373, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-22449
in-theory        22449
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> E) -> ((E -> F) -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-373 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-22449.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> E) -> ((E -> F) -> (E and F)))), M:tm-373, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-22450
in-theory        22450
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-373 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-22450.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> G) -> (F -> (F and G))))), M:tm-373, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-22451
in-theory        22451
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-373 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-22451.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (F -> (G -> (F and G)))))), M:tm-373, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-22452
in-theory        22452
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-373 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-22452.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I)))))), M:tm-373, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-22453
in-theory        22453
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-373 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-22453.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (H -> (I -> (H and I)))))), M:tm-373, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-22454
in-theory        22454
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-373 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-22454.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (H -> (I -> (H and I)))))), M:tm-373, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-22455
in-theory        22455
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-373 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-22455.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-373, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-22456
in-theory        22456
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-373 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-22456.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I)))))), M:tm-373, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-22457
in-theory        22457
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and ((F -> (G -> (F and G))) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-373 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-22457.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and ((F -> (G -> (F and G))) -> H)) -> H)), M:tm-373, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-22458
in-theory        22458
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> (E and F))) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-373 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-22458.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> (E and F))) -> G) and H) -> G)), M:tm-373, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-22459
in-theory        22459
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G)))
theorem-size     29
proof            (modus-ponens tm-373 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-22459.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G))), M:tm-373, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-22460
in-theory        22460
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (F -> (G -> (F and G))))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-22460.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (F -> (G -> (F and G))))) -> (not E))), M:tm-373, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-22461
in-theory        22461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> (E and F))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G)))
theorem-size     37
proof            (modus-ponens tm-373 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-22461.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> (E and F))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G))), M:tm-373, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-22462
in-theory        22462
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-373 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-22462.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (G -> (H -> (G and H)))))), M:tm-373, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-22463
in-theory        22463
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (G -> (F and G)))) or H))
theorem-size     27
proof            (modus-ponens tm-373 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-22463.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (G -> (F and G)))) or H)), M:tm-373, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-22464
in-theory        22464
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> (H -> (G and H)))) and E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-22464.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> (H -> (G and H)))) and E))), M:tm-373, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-22465
in-theory        22465
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (E -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-373 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-22465.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (E -> (G -> (F and G))))), M:tm-373, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-22466
in-theory        22466
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-373 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-22466.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (G -> (H -> (G and H)))))), M:tm-373, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-22467
in-theory        22467
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-373 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-22467.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I))), M:tm-373, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-22468
in-theory        22468
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-22468.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> (H -> G)) or I))), M:tm-373, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-22469
in-theory        22469
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-22469.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> (H -> G)) or I))), M:tm-373, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-22470
in-theory        22470
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> H)) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-22470.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> H)) or J))), M:tm-373, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-22471
in-theory        22471
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-22471.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> (H -> G)) or I))), M:tm-373, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-22472
in-theory        22472
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-373 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-22472.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> (G -> F)) or H))), M:tm-373, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-22473
in-theory        22473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> E)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-22473.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> E)) or G) or H)), M:tm-373, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-22474
in-theory        22474
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (G -> F)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-22474.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (G -> F)) or H) and E))), M:tm-373, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-22475
in-theory        22475
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-373 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-22475.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> F)) or H))), M:tm-373, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-22476
in-theory        22476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-373 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22476.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-373, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22477
in-theory        22477
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22477.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-373, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22478
in-theory        22478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22478.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-373, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22479
in-theory        22479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-373 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22479.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-373, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-22480
in-theory        22480
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22480.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-373, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-22481
in-theory        22481
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-373 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22481.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-373, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22482
in-theory        22482
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) or I))
theorem-size     33
proof            (modus-ponens tm-373 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22482.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) or I)), M:tm-373, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-22483
in-theory        22483
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E)))
theorem-size     35
proof            (modus-ponens tm-373 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22483.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E))), M:tm-373, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22484
in-theory        22484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-364 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22484.        (((A -> (B -> A)) or C) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-364, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22485
in-theory        22485
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and A) and B)))
theorem-size     23
proof            (modus-ponens tm-355 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22485.        (A -> (B -> (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and A) and B))), M:tm-355, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-22486
in-theory        22486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-354 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22486.        ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-354, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22487
in-theory        22487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (B -> (C -> (B and C)))))
theorem-size     33
proof            (modus-ponens tm-351 tm-373 ((Am (-> A (-> B (and A B)))) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22487.        ((A or (B -> (C -> (B and C)))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (B -> (C -> (B and C))))), M:tm-351, m:tm-373, u:((Am (-> A (-> B (and A B)))) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-22488
in-theory        22488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22488.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22489
in-theory        22489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C)))
theorem-size     29
proof            (modus-ponens tm-338 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22489.        (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C))), M:tm-338, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22490
in-theory        22490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-335 tm-373 ((Am (-> A (and A B))) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22490.        (((A -> B) or (A -> (A and B))) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> (A and B)))), M:tm-335, m:tm-373, u:((Am (-> A (and A B))) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A (and A B)))))
================================================================
tm-name          tm-22491
in-theory        22491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (A -> (A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))))
theorem-size     41
proof            (modus-ponens tm-328 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22491.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (A -> (A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)))), M:tm-328, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-22492
in-theory        22492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((F -> (G -> (F and G))) and (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))))
theorem-size     47
proof            (modus-ponens tm-327 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22492.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((F -> (G -> (F and G))) and (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)))), M:tm-327, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22493
in-theory        22493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (((F and G) -> G) and (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))))
theorem-size     45
proof            (modus-ponens tm-326 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22493.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (((F and G) -> G) and (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)))), M:tm-326, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22494
in-theory        22494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (((F and G) -> F) and (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))))
theorem-size     45
proof            (modus-ponens tm-325 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22494.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (((F and G) -> F) and (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)))), M:tm-325, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22495
in-theory        22495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))))
theorem-size     53
proof            (modus-ponens tm-324 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22495.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)))), M:tm-324, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22496
in-theory        22496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((F -> (G -> F)) and (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))))
theorem-size     45
proof            (modus-ponens tm-323 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22496.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((F -> (G -> F)) and (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)))), M:tm-323, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22497
in-theory        22497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22497.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((F and G) -> G)), M:tm-322, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22498
in-theory        22498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22498.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((F and G) -> F)), M:tm-320, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22499
in-theory        22499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22499.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22500
in-theory        22500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (A -> A))
theorem-size     23
proof            (modus-ponens tm-316 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22500.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (A -> A)), M:tm-316, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-22501
in-theory        22501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22501.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (F -> (G -> F))), M:tm-315, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22502
in-theory        22502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((A -> (not ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))) -> (not A)))
theorem-size     43
proof            (modus-ponens tm-313 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22502.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((A -> (not ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))) -> (not A))), M:tm-313, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-22503
in-theory        22503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A) -> F) -> ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) -> F)))
theorem-size     61
proof            (modus-ponens tm-312 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22503.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A) -> F) -> ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) -> F))), M:tm-312, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-22504
in-theory        22504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (F or (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))))
theorem-size     41
proof            (modus-ponens tm-311 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22504.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (F or (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)))), M:tm-311, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22505
in-theory        22505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22505.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) or F)), M:tm-310, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22506
in-theory        22506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (F -> ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22506.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (F -> ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and F))), M:tm-309, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22507
in-theory        22507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (F -> (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))))
theorem-size     41
proof            (modus-ponens tm-305 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22507.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (F -> (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)))), M:tm-305, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22508
in-theory        22508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     31
proof            (modus-ponens tm-303 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22508.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-303, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22509
in-theory        22509
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B -> (C -> (B and C))) and A)))
theorem-size     37
proof            (modus-ponens tm-300 tm-373 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22509.        ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-373, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-22510
in-theory        22510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-270 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22510.        ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-270, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22511
in-theory        22511
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (((B and C) -> C) and A)))
theorem-size     33
proof            (modus-ponens tm-267 tm-373 ((Am (and (-> (and A B) B) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22511.        ((A or (((B and C) -> C) and A)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (((B and C) -> C) and A))), M:tm-267, m:tm-373, u:((Am (and (-> (and A B) B) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-22512
in-theory        22512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-239 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22512.        ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-239, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22513
in-theory        22513
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (((B and C) -> B) and A)))
theorem-size     33
proof            (modus-ponens tm-236 tm-373 ((Am (and (-> (and A B) A) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22513.        ((A or (((B and C) -> B) and A)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (((B and C) -> B) and A))), M:tm-236, m:tm-373, u:((Am (and (-> (and A B) A) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-22514
in-theory        22514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E)))
theorem-size     37
proof            (modus-ponens tm-210 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22514.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E))), M:tm-210, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22515
in-theory        22515
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     49
proof            (modus-ponens tm-207 tm-373 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22515.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-373, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-22516
in-theory        22516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-183 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22516.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-183, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22517
in-theory        22517
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B -> (C -> B)) and A)))
theorem-size     33
proof            (modus-ponens tm-180 tm-373 ((Am (and (-> A (-> B A)) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22517.        ((A or ((B -> (C -> B)) and A)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-373, u:((Am (and (-> A (-> B A)) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-22518
in-theory        22518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-157 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22518.        ((A -> ((B and C) -> C)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-157, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22519
in-theory        22519
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B and C) -> C)))
theorem-size     29
proof            (modus-ponens tm-154 tm-373 ((Am (-> (and A B) B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22519.        ((A or ((B and C) -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B and C) -> C))), M:tm-154, m:tm-373, u:((Am (-> (and A B) B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (and A B) B))))
================================================================
tm-name          tm-22520
in-theory        22520
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     35
proof            (modus-ponens tm-147 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22520.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-147, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22521
in-theory        22521
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A and (B -> C)) -> C)))
theorem-size     39
proof            (modus-ponens tm-144 tm-373 ((Am (-> (and A (-> B C)) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-6)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22521.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-373, u:((Am (-> (and A (-> B C)) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-22522
in-theory        22522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-134 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22522.        ((A -> ((B and C) -> B)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-134, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22523
in-theory        22523
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B and C) -> B)))
theorem-size     29
proof            (modus-ponens tm-131 tm-373 ((Am (-> (and A B) A)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22523.        ((A or ((B and C) -> B)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B and C) -> B))), M:tm-131, m:tm-373, u:((Am (-> (and A B) A)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (and A B) A))))
================================================================
tm-name          tm-22524
in-theory        22524
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     35
proof            (modus-ponens tm-125 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22524.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-125, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22525
in-theory        22525
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (((A -> B) and C) -> B)))
theorem-size     39
proof            (modus-ponens tm-122 tm-373 ((Am (-> (and (-> A B) C) B)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-6)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22525.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (((A -> B) and C) -> B))), M:tm-122, m:tm-373, u:((Am (-> (and (-> A B) C) B)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-22526
in-theory        22526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E)))
theorem-size     35
proof            (modus-ponens tm-113 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22526.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E))), M:tm-113, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22527
in-theory        22527
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     45
proof            (modus-ponens tm-110 tm-373 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22527.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-373, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-22528
in-theory        22528
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     39
proof            (modus-ponens tm-105 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22528.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-105, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22529
in-theory        22529
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     45
proof            (modus-ponens tm-102 tm-373 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22529.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-373, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-22530
in-theory        22530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C)))
theorem-size     27
proof            (modus-ponens tm-95 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22530.        (((A -> B) -> (A -> A)) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C))), M:tm-95, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22531
in-theory        22531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> A)))
theorem-size     27
proof            (modus-ponens tm-92 tm-373 ((Am (-> A A)) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22531.        (((A -> B) or (A -> A)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> A))), M:tm-92, m:tm-373, u:((Am (-> A A)) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A A))))
================================================================
tm-name          tm-22532
in-theory        22532
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and A)))
theorem-size     21
proof            (modus-ponens tm-84 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22532.        (A -> (B -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and A))), M:tm-84, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-22533
in-theory        22533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-83 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22533.        ((A -> (B -> (C -> B))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-83, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22534
in-theory        22534
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (B -> (C -> B))))
theorem-size     29
proof            (modus-ponens tm-80 tm-373 ((Am (-> A (-> B A))) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22534.        ((A or (B -> (C -> B))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (B -> (C -> B)))), M:tm-80, m:tm-373, u:((Am (-> A (-> B A))) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A (-> B A)))))
================================================================
tm-name          tm-22535
in-theory        22535
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and B)))
theorem-size     25
proof            (modus-ponens tm-76 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-10 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22535.        (((not (not A)) -> A) and (B -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and B))), M:tm-76, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22536
in-theory        22536
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))
theorem-size     23
proof            (modus-ponens tm-73 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-6 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22536.        (((not (not A)) or A) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-73, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-22537
in-theory        22537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C)))
theorem-size     31
proof            (modus-ponens tm-69 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-9 tm-6 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22537.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C))), M:tm-69, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22538
in-theory        22538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and ((A -> (not B)) -> (not A))))
theorem-size     35
proof            (modus-ponens tm-66 tm-373 ((Am (-> (-> A (not B)) (not A))) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-6 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22538.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-373, u:((Am (-> (-> A (not B)) (not A))) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-22539
in-theory        22539
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     33
proof            (modus-ponens tm-54 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22539.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-54, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22540
in-theory        22540
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B -> C) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-51 tm-373 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22540.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-373, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-22541
in-theory        22541
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (B or A)))
theorem-size     25
proof            (modus-ponens tm-50 tm-373 ((Am (or A B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22541.        ((A or (B or A)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (B or A))), M:tm-50, m:tm-373, u:((Am (or A B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (or A B))))
================================================================
tm-name          tm-22542
in-theory        22542
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A or B)))
theorem-size     25
proof            (modus-ponens tm-49 tm-373 ((Am (or A B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22542.        ((A or (A or B)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A or B))), M:tm-49, m:tm-373, u:((Am (or A B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (or A B))))
================================================================
tm-name          tm-22543
in-theory        22543
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-48 tm-373 ((Am (-> A (and B A))) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22543.        ((A or (B -> (A and B))) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (B -> (A and B)))), M:tm-48, m:tm-373, u:((Am (-> A (and B A))) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A (and B A)))))
================================================================
tm-name          tm-22544
in-theory        22544
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and B))
theorem-size     23
proof            (modus-ponens tm-47 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-6 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22544.        (((A and B) or B) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and B)), M:tm-47, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-22545
in-theory        22545
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and A))
theorem-size     23
proof            (modus-ponens tm-46 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-6 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22545.        (((A and B) or A) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and A)), M:tm-46, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-22546
in-theory        22546
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-45 tm-373 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22546.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-373, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-22547
in-theory        22547
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (B -> A)))
theorem-size     25
proof            (modus-ponens tm-44 tm-373 ((Am (-> A B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22547.        ((A or (B -> A)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (B -> A))), M:tm-44, m:tm-373, u:((Am (-> A B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A B))))
================================================================
tm-name          tm-22548
in-theory        22548
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C)))
theorem-size     25
proof            (modus-ponens tm-42 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22548.        ((A -> (B or A)) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C))), M:tm-42, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22549
in-theory        22549
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C)))
theorem-size     25
proof            (modus-ponens tm-32 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22549.        ((A -> (A or B)) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C))), M:tm-32, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22550
in-theory        22550
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)))
theorem-size     21
proof            (modus-ponens tm-24 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22550.        (A -> (A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))), M:tm-24, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-22551
in-theory        22551
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C)))
theorem-size     27
proof            (modus-ponens tm-23 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22551.        ((A -> (B -> (A and B))) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C))), M:tm-23, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22552
in-theory        22552
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C)))
theorem-size     25
proof            (modus-ponens tm-22 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22552.        (((A and B) -> B) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C))), M:tm-22, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22553
in-theory        22553
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C)))
theorem-size     25
proof            (modus-ponens tm-21 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22553.        (((A and B) -> A) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C))), M:tm-21, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22554
in-theory        22554
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     33
proof            (modus-ponens tm-20 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22554.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-20, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22555
in-theory        22555
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C)))
theorem-size     25
proof            (modus-ponens tm-19 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22555.        ((A -> (B -> A)) and (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and C))), M:tm-19, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22556
in-theory        22556
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))) -> (not A))
theorem-size     23
proof            (modus-ponens tm-9 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-9 tm-5 tm-6 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22556.        ((A -> (not ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))) -> (not A)), M:tm-9, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-22557
in-theory        22557
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and E) -> F) -> ((E or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and E)) -> F))
theorem-size     41
proof            (modus-ponens tm-8 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22557.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and E) -> F) -> ((E or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and E)) -> F)), M:tm-8, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-22558
in-theory        22558
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and B)))
theorem-size     21
proof            (modus-ponens tm-7 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-7 tm-5 tm-6 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22558.        (A or (B -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and B))), M:tm-7, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22559
in-theory        22559
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22559.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) or F), M:tm-6, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22560
in-theory        22560
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and B)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22560.        (A -> ((B -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and B)) and A)), M:tm-5, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22561
in-theory        22561
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and B)))
theorem-size     21
proof            (modus-ponens tm-1 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-1 tm-5 tm-6 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22561.        (A -> (B -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and B))), M:tm-1, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-22562
in-theory        22562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-373 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22562.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-373, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22563
in-theory        22563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-364 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22563.        (((A -> (B -> A)) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-364, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22564
in-theory        22564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-354 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22564.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-354, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22565
in-theory        22565
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-351 tm-374 ((Am (-> A (-> B (and A B)))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22565.        ((A or (B -> (C -> (B and C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-351, m:tm-374, u:((Am (-> A (-> B (and A B)))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22566
in-theory        22566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22566.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22567
in-theory        22567
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and E))
theorem-size     35
proof            (modus-ponens tm-339 tm-374 ((Am (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) B)) (A (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22567.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and E)), M:tm-339, m:tm-374, u:((Am (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) B)) (A (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22568
in-theory        22568
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     27
proof            (modus-ponens tm-338 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22568.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-338, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22569
in-theory        22569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     25
proof            (modus-ponens tm-335 tm-374 ((Am (-> A (and A B))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22569.        (((A -> B) or (A -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-335, m:tm-374, u:((Am (-> A (and A B))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22570
in-theory        22570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     37
proof            (modus-ponens tm-328 tm-374 ((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22570.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-328, m:tm-374, u:((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22571
in-theory        22571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G -> (F and G))) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     43
proof            (modus-ponens tm-327 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22571.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G -> (F and G))) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-327, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22572
in-theory        22572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((F and G) -> G) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-326 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22572.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((F and G) -> G) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-326, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22573
in-theory        22573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((F and G) -> F) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-325 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22573.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((F and G) -> F) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-325, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22574
in-theory        22574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     49
proof            (modus-ponens tm-324 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22574.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-324, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22575
in-theory        22575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G -> F)) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-323 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22575.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G -> F)) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-323, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22576
in-theory        22576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22576.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F and G) -> G)), M:tm-322, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22577
in-theory        22577
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) -> F)) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) -> F)) -> F))
theorem-size     57
proof            (modus-ponens tm-321 tm-374 ((Am (and A (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) C))) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22577.        (((A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) -> F)) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) -> F)) -> F)), M:tm-321, m:tm-374, u:((Am (and A (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) C))) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22578
in-theory        22578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22578.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F and G) -> F)), M:tm-320, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22579
in-theory        22579
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) and F) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) and F) -> E))
theorem-size     57
proof            (modus-ponens tm-319 tm-374 ((Am (and (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) B) C)) (A (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22579.        (((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) and F) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) and F) -> E)), M:tm-319, m:tm-374, u:((Am (and (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) B) C)) (A (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22580
in-theory        22580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22580.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22581
in-theory        22581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (A -> A))
theorem-size     21
proof            (modus-ponens tm-316 tm-374 ((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22581.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (A -> A)), M:tm-316, m:tm-374, u:((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22582
in-theory        22582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22582.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (G -> F))), M:tm-315, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22583
in-theory        22583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))) -> (not A)))
theorem-size     39
proof            (modus-ponens tm-313 tm-374 ((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22583.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))) -> (not A))), M:tm-313, m:tm-374, u:((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22584
in-theory        22584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) -> F) -> ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) -> F)))
theorem-size     55
proof            (modus-ponens tm-312 tm-374 ((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22584.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) -> F) -> ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) -> F))), M:tm-312, m:tm-374, u:((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22585
in-theory        22585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F or (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     37
proof            (modus-ponens tm-311 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22585.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F or (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-311, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22586
in-theory        22586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22586.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) or F)), M:tm-310, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22587
in-theory        22587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22587.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and F))), M:tm-309, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22588
in-theory        22588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     37
proof            (modus-ponens tm-305 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22588.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-305, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22589
in-theory        22589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-303 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22589.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-303, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22590
in-theory        22590
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     27
proof            (modus-ponens tm-300 tm-374 ((Am (and (-> A (-> B (and A B))) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22590.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-300, m:tm-374, u:((Am (and (-> A (-> B (and A B))) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22591
in-theory        22591
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-270 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22591.        ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-270, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22592
in-theory        22592
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-267 tm-374 ((Am (and (-> (and A B) B) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22592.        ((A or (((B and C) -> C) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-267, m:tm-374, u:((Am (and (-> (and A B) B) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22593
in-theory        22593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-239 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22593.        ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-239, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22594
in-theory        22594
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-236 tm-374 ((Am (and (-> (and A B) A) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22594.        ((A or (((B and C) -> B) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-236, m:tm-374, u:((Am (and (-> (and A B) A) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22595
in-theory        22595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-210 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22595.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-210, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22596
in-theory        22596
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))
theorem-size     33
proof            (modus-ponens tm-207 tm-374 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22596.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)), M:tm-207, m:tm-374, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22597
in-theory        22597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-183 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22597.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-183, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22598
in-theory        22598
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-180 tm-374 ((Am (and (-> A (-> B A)) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22598.        ((A or ((B -> (C -> B)) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-180, m:tm-374, u:((Am (and (-> A (-> B A)) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22599
in-theory        22599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-157 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22599.        ((A -> ((B and C) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-157, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22600
in-theory        22600
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-154 tm-374 ((Am (-> (and A B) B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-4 tm-6 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22600.        ((A or ((B and C) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-154, m:tm-374, u:((Am (-> (and A B) B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22601
in-theory        22601
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     33
proof            (modus-ponens tm-147 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22601.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-147, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22602
in-theory        22602
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-144 tm-374 ((Am (-> (and A (-> B C)) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-6)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22602.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-144, m:tm-374, u:((Am (-> (and A (-> B C)) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22603
in-theory        22603
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) -> F)) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))
theorem-size     35
proof            (modus-ponens tm-142 tm-374 ((Am (and A (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) C))) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-4 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22603.        ((A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) -> F)) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-142, m:tm-374, u:((Am (and A (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) C))) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22604
in-theory        22604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-134 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22604.        ((A -> ((B and C) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-134, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22605
in-theory        22605
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-131 tm-374 ((Am (-> (and A B) A)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-3 tm-6 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22605.        ((A or ((B and C) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-131, m:tm-374, u:((Am (-> (and A B) A)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22606
in-theory        22606
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     33
proof            (modus-ponens tm-125 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22606.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-125, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22607
in-theory        22607
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-122 tm-374 ((Am (-> (and (-> A B) C) B)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-6)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22607.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-122, m:tm-374, u:((Am (-> (and (-> A B) C) B)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22608
in-theory        22608
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) and F) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D))
theorem-size     35
proof            (modus-ponens tm-120 tm-374 ((Am (and (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) B) C)) (A (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-3 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22608.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) and F) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)), M:tm-120, m:tm-374, u:((Am (and (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) B) C)) (A (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22609
in-theory        22609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-113 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22609.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-113, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22610
in-theory        22610
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))
theorem-size     31
proof            (modus-ponens tm-110 tm-374 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22610.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)), M:tm-110, m:tm-374, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22611
in-theory        22611
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     37
proof            (modus-ponens tm-105 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22611.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-105, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22612
in-theory        22612
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     35
proof            (modus-ponens tm-102 tm-374 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22612.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-102, m:tm-374, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22613
in-theory        22613
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D))
theorem-size     33
proof            (modus-ponens tm-96 tm-374 ((Am (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) B)) (A (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22613.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)), M:tm-96, m:tm-374, u:((Am (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) B)) (A (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22614
in-theory        22614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     25
proof            (modus-ponens tm-95 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22614.        (((A -> B) -> (A -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-95, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22615
in-theory        22615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     23
proof            (modus-ponens tm-92 tm-374 ((Am (-> A A)) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22615.        (((A -> B) or (A -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-92, m:tm-374, u:((Am (-> A A)) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22616
in-theory        22616
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))
theorem-size     19
proof            (modus-ponens tm-84 tm-374 ((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22616.        (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))), M:tm-84, m:tm-374, u:((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22617
in-theory        22617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-83 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22617.        ((A -> (B -> (C -> B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-83, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22618
in-theory        22618
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-80 tm-374 ((Am (-> A (-> B A))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22618.        ((A or (B -> (C -> B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-80, m:tm-374, u:((Am (-> A (-> B A))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22619
in-theory        22619
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E))) -> E)
theorem-size     21
proof            (modus-ponens tm-77 tm-374 ((Am (not (not (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) B)))) (A (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-10 tm-1 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22619.        ((not (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E))) -> E), M:tm-77, m:tm-374, u:((Am (not (not (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) B)))) (A (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22620
in-theory        22620
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))
theorem-size     23
proof            (modus-ponens tm-76 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22620.        (((not (not A)) -> A) and (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))), M:tm-76, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22621
in-theory        22621
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))
theorem-size     21
proof            (modus-ponens tm-73 tm-374 ((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-10 tm-1 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22621.        (((not (not A)) or A) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-73, m:tm-374, u:((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22622
in-theory        22622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     29
proof            (modus-ponens tm-69 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22622.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-69, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22623
in-theory        22623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     27
proof            (modus-ponens tm-66 tm-374 ((Am (-> (-> A (not B)) (not A))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-9 tm-1 tm-6 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22623.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-66, m:tm-374, u:((Am (-> (-> A (not B)) (not A))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22624
in-theory        22624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-54 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22624.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-54, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22625
in-theory        22625
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-51 tm-374 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22625.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-51, m:tm-374, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22626
in-theory        22626
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-50 tm-374 ((Am (or A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-7 tm-1 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22626.        ((A or (B or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-50, m:tm-374, u:((Am (or A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22627
in-theory        22627
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-49 tm-374 ((Am (or A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22627.        ((A or (A or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-49, m:tm-374, u:((Am (or A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22628
in-theory        22628
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     23
proof            (modus-ponens tm-48 tm-374 ((Am (-> A (and B A))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22628.        ((A or (B -> (A and B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-48, m:tm-374, u:((Am (-> A (and B A))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22629
in-theory        22629
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-47 tm-374 ((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-4 tm-1 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22629.        (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-47, m:tm-374, u:((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22630
in-theory        22630
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-46 tm-374 ((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-3 tm-1 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22630.        (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-46, m:tm-374, u:((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22631
in-theory        22631
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-45 tm-374 ((Am (-> (-> A B) (-> A C))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22631.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-45, m:tm-374, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22632
in-theory        22632
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     21
proof            (modus-ponens tm-44 tm-374 ((Am (-> A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22632.        ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-44, m:tm-374, u:((Am (-> A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22633
in-theory        22633
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-42 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22633.        ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-42, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22634
in-theory        22634
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-32 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22634.        ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-32, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22635
in-theory        22635
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))
theorem-size     19
proof            (modus-ponens tm-24 tm-374 ((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22635.        (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))), M:tm-24, m:tm-374, u:((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22636
in-theory        22636
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     25
proof            (modus-ponens tm-23 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22636.        ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-23, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22637
in-theory        22637
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-22 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22637.        (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-22, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22638
in-theory        22638
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-21 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22638.        (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-21, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22639
in-theory        22639
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-20 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22639.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-20, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22640
in-theory        22640
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-19 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22640.        ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-19, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22641
in-theory        22641
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) -> F)) -> F)
theorem-size     21
proof            (modus-ponens tm-17 tm-374 ((Am (and A (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) C))) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-4 tm-1 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22641.        ((A and ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) -> F)) -> F), M:tm-17, m:tm-374, u:((Am (and A (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) C))) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22642
in-theory        22642
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) and F) -> E)
theorem-size     21
proof            (modus-ponens tm-15 tm-374 ((Am (and (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) B) C)) (A (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-3 tm-1 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22642.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) and F) -> E), M:tm-15, m:tm-374, u:((Am (and (-> (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) B) C)) (A (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22643
in-theory        22643
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))) -> (not A))
theorem-size     21
proof            (modus-ponens tm-9 tm-374 ((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-9 tm-1 tm-6 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22643.        ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))) -> (not A)), M:tm-9, m:tm-374, u:((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22644
in-theory        22644
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) -> ((F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-374 ((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22644.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) -> E) -> ((F or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)) -> E)), M:tm-8, m:tm-374, u:((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-22645
in-theory        22645
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))
theorem-size     19
proof            (modus-ponens tm-7 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-7 tm-1 tm-6 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22645.        (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))), M:tm-7, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22646
in-theory        22646
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-6 tm-1 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22646.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) or F), M:tm-6, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22647
in-theory        22647
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-22647.        (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and A)), M:tm-5, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-22648
in-theory        22648
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-373 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22648.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I))), M:tm-373, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22649
in-theory        22649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-364 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22649.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-364, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22650
in-theory        22650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-354 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22650.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-354, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22651
in-theory        22651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22651.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22652
in-theory        22652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G)))
theorem-size     25
proof            (modus-ponens tm-338 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22652.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G))), M:tm-338, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22653
in-theory        22653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C and D) -> C) or E))))
theorem-size     39
proof            (modus-ponens tm-327 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22653.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C and D) -> C) or E)))), M:tm-327, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22654
in-theory        22654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C and D) -> C) or E))))
theorem-size     37
proof            (modus-ponens tm-326 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22654.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C and D) -> C) or E)))), M:tm-326, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22655
in-theory        22655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C and D) -> C) or E))))
theorem-size     37
proof            (modus-ponens tm-325 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22655.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C and D) -> C) or E)))), M:tm-325, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22656
in-theory        22656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C and D) -> C) or E))))
theorem-size     45
proof            (modus-ponens tm-324 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22656.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C and D) -> C) or E)))), M:tm-324, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22657
in-theory        22657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C and D) -> C) or E))))
theorem-size     37
proof            (modus-ponens tm-323 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22657.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C and D) -> C) or E)))), M:tm-323, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22658
in-theory        22658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22658.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and ((F and G) -> G)), M:tm-322, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22659
in-theory        22659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22659.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and ((F and G) -> F)), M:tm-320, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22660
in-theory        22660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22660.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22661
in-theory        22661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22661.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (F -> (G -> F))), M:tm-315, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22662
in-theory        22662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (F or ((A -> (B -> (A and B))) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-311 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22662.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (F or ((A -> (B -> (A and B))) and (((C and D) -> C) or E)))), M:tm-311, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22663
in-theory        22663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22663.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) or F)), M:tm-310, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22664
in-theory        22664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (F -> (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22664.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (F -> (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and F))), M:tm-309, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22665
in-theory        22665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (((C and D) -> C) or E))
theorem-size     23
proof            (modus-ponens tm-308 tm-375 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (and Cm Dm) Cm) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22665.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (((C and D) -> C) or E)), M:tm-308, m:tm-375, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (and Cm Dm) Cm) Em)))
================================================================
tm-name          tm-22666
in-theory        22666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-375 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (and Cm Dm) Cm) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22666.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (A -> (B -> (A and B)))), M:tm-307, m:tm-375, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (and Cm Dm) Cm) Em)))
================================================================
tm-name          tm-22667
in-theory        22667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (F -> ((A -> (B -> (A and B))) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-305 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22667.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (F -> ((A -> (B -> (A and B))) and (((C and D) -> C) or E)))), M:tm-305, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22668
in-theory        22668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-303 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22668.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-303, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22669
in-theory        22669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-270 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22669.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-270, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22670
in-theory        22670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-239 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22670.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-239, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22671
in-theory        22671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I)))
theorem-size     33
proof            (modus-ponens tm-210 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22671.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I))), M:tm-210, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22672
in-theory        22672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-183 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22672.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-183, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22673
in-theory        22673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-157 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22673.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-157, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22674
in-theory        22674
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     31
proof            (modus-ponens tm-147 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22674.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-147, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22675
in-theory        22675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-134 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22675.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-134, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22676
in-theory        22676
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     31
proof            (modus-ponens tm-125 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22676.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-125, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22677
in-theory        22677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-113 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22677.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I))), M:tm-113, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22678
in-theory        22678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     35
proof            (modus-ponens tm-105 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22678.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-105, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22679
in-theory        22679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-95 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22679.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G))), M:tm-95, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22680
in-theory        22680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-83 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22680.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-83, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22681
in-theory        22681
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D and E) -> D) or F)))
theorem-size     21
proof            (modus-ponens tm-76 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-10 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22681.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D and E) -> D) or F))), M:tm-76, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22682
in-theory        22682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G)))
theorem-size     27
proof            (modus-ponens tm-69 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-9 tm-6 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22682.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G))), M:tm-69, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22683
in-theory        22683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-54 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22683.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-54, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22684
in-theory        22684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-42 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22684.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G))), M:tm-42, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22685
in-theory        22685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-32 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22685.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G))), M:tm-32, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22686
in-theory        22686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-23 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22686.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G))), M:tm-23, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22687
in-theory        22687
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-22 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22687.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G))), M:tm-22, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22688
in-theory        22688
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-21 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22688.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G))), M:tm-21, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22689
in-theory        22689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-20 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22689.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-20, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22690
in-theory        22690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-19 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22690.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E and F) -> E) or G))), M:tm-19, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22691
in-theory        22691
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (((D and E) -> D) or F)))
theorem-size     17
proof            (modus-ponens tm-7 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-7 tm-5 tm-6 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22691.        (A or ((B -> (C -> (B and C))) and (((D and E) -> D) or F))), M:tm-7, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22692
in-theory        22692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22692.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) or F), M:tm-6, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22693
in-theory        22693
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (((D and E) -> D) or F)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22693.        (A -> (((B -> (C -> (B and C))) and (((D and E) -> D) or F)) and A)), M:tm-5, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22694
in-theory        22694
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (((D and E) -> D) or F)))
theorem-size     17
proof            (modus-ponens tm-1 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-1 tm-5 tm-6 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22694.        (A -> ((B -> (C -> (B and C))) and (((D and E) -> D) or F))), M:tm-1, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22695
in-theory        22695
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22695.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G and H) -> G) or I))), M:tm-373, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22696
in-theory        22696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22696.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-364, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22697
in-theory        22697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22697.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-354, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22698
in-theory        22698
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22698.        ((((A and B) -> B) and (((C and D) -> C) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22699
in-theory        22699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22699.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E and F) -> E) or G))), M:tm-338, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22700
in-theory        22700
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C and D) -> C) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22700.        ((((A and B) -> B) and (((C and D) -> C) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C and D) -> C) or E)))), M:tm-327, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22701
in-theory        22701
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and (((F and G) -> G) and (((A and B) -> B) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22701.        ((((A and B) -> B) and (((C and D) -> C) or E)) and (((F and G) -> G) and (((A and B) -> B) and (((C and D) -> C) or E)))), M:tm-326, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22702
in-theory        22702
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and (((F and G) -> F) and (((A and B) -> B) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22702.        ((((A and B) -> B) and (((C and D) -> C) or E)) and (((F and G) -> F) and (((A and B) -> B) and (((C and D) -> C) or E)))), M:tm-325, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22703
in-theory        22703
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C and D) -> C) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22703.        ((((A and B) -> B) and (((C and D) -> C) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C and D) -> C) or E)))), M:tm-324, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22704
in-theory        22704
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and ((F -> (G -> F)) and (((A and B) -> B) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22704.        ((((A and B) -> B) and (((C and D) -> C) or E)) and ((F -> (G -> F)) and (((A and B) -> B) and (((C and D) -> C) or E)))), M:tm-323, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22705
in-theory        22705
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22705.        ((((A and B) -> B) and (((C and D) -> C) or E)) and ((F and G) -> G)), M:tm-322, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22706
in-theory        22706
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22706.        ((((A and B) -> B) and (((C and D) -> C) or E)) and ((F and G) -> F)), M:tm-320, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22707
in-theory        22707
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22707.        ((((A and B) -> B) and (((C and D) -> C) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22708
in-theory        22708
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22708.        ((((A and B) -> B) and (((C and D) -> C) or E)) and (F -> (G -> F))), M:tm-315, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22709
in-theory        22709
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and (F or (((A and B) -> B) and (((C and D) -> C) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22709.        ((((A and B) -> B) and (((C and D) -> C) or E)) and (F or (((A and B) -> B) and (((C and D) -> C) or E)))), M:tm-311, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22710
in-theory        22710
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and ((((A and B) -> B) and (((C and D) -> C) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22710.        ((((A and B) -> B) and (((C and D) -> C) or E)) and ((((A and B) -> B) and (((C and D) -> C) or E)) or F)), M:tm-310, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22711
in-theory        22711
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and (F -> ((((A and B) -> B) and (((C and D) -> C) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22711.        ((((A and B) -> B) and (((C and D) -> C) or E)) and (F -> ((((A and B) -> B) and (((C and D) -> C) or E)) and F))), M:tm-309, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22712
in-theory        22712
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and (((C and D) -> C) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-376 ((A (-> (and Am Bm) Bm)) (B (or (-> (and Cm Dm) Cm) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22712.        ((((A and B) -> B) and (((C and D) -> C) or E)) and (((C and D) -> C) or E)), M:tm-308, m:tm-376, u:((A (-> (and Am Bm) Bm)) (B (or (-> (and Cm Dm) Cm) Em)))
================================================================
tm-name          tm-22713
in-theory        22713
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-376 ((A (-> (and Am Bm) Bm)) (B (or (-> (and Cm Dm) Cm) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22713.        ((((A and B) -> B) and (((C and D) -> C) or E)) and ((A and B) -> B)), M:tm-307, m:tm-376, u:((A (-> (and Am Bm) Bm)) (B (or (-> (and Cm Dm) Cm) Em)))
================================================================
tm-name          tm-22714
in-theory        22714
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and (F -> (((A and B) -> B) and (((C and D) -> C) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22714.        ((((A and B) -> B) and (((C and D) -> C) or E)) and (F -> (((A and B) -> B) and (((C and D) -> C) or E)))), M:tm-305, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22715
in-theory        22715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22715.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-303, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22716
in-theory        22716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22716.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-270, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22717
in-theory        22717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22717.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-239, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22718
in-theory        22718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22718.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G and H) -> G) or I))), M:tm-210, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22719
in-theory        22719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22719.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-183, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22720
in-theory        22720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22720.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-157, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22721
in-theory        22721
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22721.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-147, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22722
in-theory        22722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22722.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-134, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22723
in-theory        22723
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22723.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-125, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22724
in-theory        22724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22724.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G and H) -> G) or I))), M:tm-113, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22725
in-theory        22725
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22725.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-105, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22726
in-theory        22726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22726.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E and F) -> E) or G))), M:tm-95, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22727
in-theory        22727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22727.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-83, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22728
in-theory        22728
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (((D and E) -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-10 tm-4 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22728.        (((not (not A)) -> A) and (((B and C) -> C) and (((D and E) -> D) or F))), M:tm-76, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22729
in-theory        22729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E and F) -> E) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-9 tm-4 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22729.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E and F) -> E) or G))), M:tm-69, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22730
in-theory        22730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22730.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-54, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22731
in-theory        22731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22731.        ((A -> (B or A)) and (((C and D) -> D) and (((E and F) -> E) or G))), M:tm-42, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22732
in-theory        22732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22732.        ((A -> (A or B)) and (((C and D) -> D) and (((E and F) -> E) or G))), M:tm-32, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22733
in-theory        22733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22733.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E and F) -> E) or G))), M:tm-23, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22734
in-theory        22734
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22734.        (((A and B) -> B) and (((C and D) -> D) and (((E and F) -> E) or G))), M:tm-22, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22735
in-theory        22735
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22735.        (((A and B) -> A) and (((C and D) -> D) and (((E and F) -> E) or G))), M:tm-21, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22736
in-theory        22736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22736.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-20, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22737
in-theory        22737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22737.        ((A -> (B -> A)) and (((C and D) -> D) and (((E and F) -> E) or G))), M:tm-19, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22738
in-theory        22738
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-7 tm-5 tm-4 tm-6 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22738.        (A or (((B and C) -> C) and (((D and E) -> D) or F))), M:tm-7, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22739
in-theory        22739
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-6 tm-5 tm-4 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22739.        ((((A and B) -> B) and (((C and D) -> C) or E)) or F), M:tm-6, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22740
in-theory        22740
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (((D and E) -> D) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22740.        (A -> ((((B and C) -> C) and (((D and E) -> D) or F)) and A)), M:tm-5, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22741
in-theory        22741
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-1 tm-5 tm-4 tm-6 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22741.        (A -> (((B and C) -> C) and (((D and E) -> D) or F))), M:tm-1, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22742
in-theory        22742
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22742.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G and H) -> G) or I))), M:tm-373, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22743
in-theory        22743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22743.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-364, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22744
in-theory        22744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22744.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-354, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22745
in-theory        22745
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22745.        ((((A and B) -> A) and (((C and D) -> C) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22746
in-theory        22746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22746.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E and F) -> E) or G))), M:tm-338, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22747
in-theory        22747
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C and D) -> C) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22747.        ((((A and B) -> A) and (((C and D) -> C) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C and D) -> C) or E)))), M:tm-327, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22748
in-theory        22748
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and (((F and G) -> G) and (((A and B) -> A) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22748.        ((((A and B) -> A) and (((C and D) -> C) or E)) and (((F and G) -> G) and (((A and B) -> A) and (((C and D) -> C) or E)))), M:tm-326, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22749
in-theory        22749
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and (((F and G) -> F) and (((A and B) -> A) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22749.        ((((A and B) -> A) and (((C and D) -> C) or E)) and (((F and G) -> F) and (((A and B) -> A) and (((C and D) -> C) or E)))), M:tm-325, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22750
in-theory        22750
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C and D) -> C) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22750.        ((((A and B) -> A) and (((C and D) -> C) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C and D) -> C) or E)))), M:tm-324, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22751
in-theory        22751
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and ((F -> (G -> F)) and (((A and B) -> A) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22751.        ((((A and B) -> A) and (((C and D) -> C) or E)) and ((F -> (G -> F)) and (((A and B) -> A) and (((C and D) -> C) or E)))), M:tm-323, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22752
in-theory        22752
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22752.        ((((A and B) -> A) and (((C and D) -> C) or E)) and ((F and G) -> G)), M:tm-322, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22753
in-theory        22753
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22753.        ((((A and B) -> A) and (((C and D) -> C) or E)) and ((F and G) -> F)), M:tm-320, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22754
in-theory        22754
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22754.        ((((A and B) -> A) and (((C and D) -> C) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22755
in-theory        22755
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22755.        ((((A and B) -> A) and (((C and D) -> C) or E)) and (F -> (G -> F))), M:tm-315, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22756
in-theory        22756
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and (F or (((A and B) -> A) and (((C and D) -> C) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22756.        ((((A and B) -> A) and (((C and D) -> C) or E)) and (F or (((A and B) -> A) and (((C and D) -> C) or E)))), M:tm-311, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22757
in-theory        22757
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and ((((A and B) -> A) and (((C and D) -> C) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22757.        ((((A and B) -> A) and (((C and D) -> C) or E)) and ((((A and B) -> A) and (((C and D) -> C) or E)) or F)), M:tm-310, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22758
in-theory        22758
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and (F -> ((((A and B) -> A) and (((C and D) -> C) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22758.        ((((A and B) -> A) and (((C and D) -> C) or E)) and (F -> ((((A and B) -> A) and (((C and D) -> C) or E)) and F))), M:tm-309, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22759
in-theory        22759
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and (((C and D) -> C) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-377 ((A (-> (and Am Bm) Am)) (B (or (-> (and Cm Dm) Cm) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22759.        ((((A and B) -> A) and (((C and D) -> C) or E)) and (((C and D) -> C) or E)), M:tm-308, m:tm-377, u:((A (-> (and Am Bm) Am)) (B (or (-> (and Cm Dm) Cm) Em)))
================================================================
tm-name          tm-22760
in-theory        22760
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-377 ((A (-> (and Am Bm) Am)) (B (or (-> (and Cm Dm) Cm) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22760.        ((((A and B) -> A) and (((C and D) -> C) or E)) and ((A and B) -> A)), M:tm-307, m:tm-377, u:((A (-> (and Am Bm) Am)) (B (or (-> (and Cm Dm) Cm) Em)))
================================================================
tm-name          tm-22761
in-theory        22761
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and (F -> (((A and B) -> A) and (((C and D) -> C) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22761.        ((((A and B) -> A) and (((C and D) -> C) or E)) and (F -> (((A and B) -> A) and (((C and D) -> C) or E)))), M:tm-305, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22762
in-theory        22762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22762.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-303, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22763
in-theory        22763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22763.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-270, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22764
in-theory        22764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22764.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-239, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22765
in-theory        22765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22765.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G and H) -> G) or I))), M:tm-210, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22766
in-theory        22766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22766.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-183, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22767
in-theory        22767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22767.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-157, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22768
in-theory        22768
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22768.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-147, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22769
in-theory        22769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22769.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-134, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22770
in-theory        22770
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22770.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-125, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22771
in-theory        22771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22771.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G and H) -> G) or I))), M:tm-113, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22772
in-theory        22772
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22772.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-105, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22773
in-theory        22773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22773.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E and F) -> E) or G))), M:tm-95, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22774
in-theory        22774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22774.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-83, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22775
in-theory        22775
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (((D and E) -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-10 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22775.        (((not (not A)) -> A) and (((B and C) -> B) and (((D and E) -> D) or F))), M:tm-76, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22776
in-theory        22776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E and F) -> E) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-9 tm-3 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22776.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E and F) -> E) or G))), M:tm-69, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22777
in-theory        22777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22777.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-54, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22778
in-theory        22778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22778.        ((A -> (B or A)) and (((C and D) -> C) and (((E and F) -> E) or G))), M:tm-42, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22779
in-theory        22779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22779.        ((A -> (A or B)) and (((C and D) -> C) and (((E and F) -> E) or G))), M:tm-32, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22780
in-theory        22780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22780.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E and F) -> E) or G))), M:tm-23, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22781
in-theory        22781
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22781.        (((A and B) -> B) and (((C and D) -> C) and (((E and F) -> E) or G))), M:tm-22, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22782
in-theory        22782
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22782.        (((A and B) -> A) and (((C and D) -> C) and (((E and F) -> E) or G))), M:tm-21, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22783
in-theory        22783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22783.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-20, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22784
in-theory        22784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22784.        ((A -> (B -> A)) and (((C and D) -> C) and (((E and F) -> E) or G))), M:tm-19, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22785
in-theory        22785
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-7 tm-5 tm-3 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22785.        (A or (((B and C) -> B) and (((D and E) -> D) or F))), M:tm-7, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22786
in-theory        22786
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22786.        ((((A and B) -> A) and (((C and D) -> C) or E)) or F), M:tm-6, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22787
in-theory        22787
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (((D and E) -> D) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22787.        (A -> ((((B and C) -> B) and (((D and E) -> D) or F)) and A)), M:tm-5, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22788
in-theory        22788
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-1 tm-5 tm-3 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22788.        (A -> (((B and C) -> B) and (((D and E) -> D) or F))), M:tm-1, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22789
in-theory        22789
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> H) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22789.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> H) or J))), M:tm-373, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22790
in-theory        22790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22790.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-364, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22791
in-theory        22791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22791.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-354, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22792
in-theory        22792
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22792.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22793
in-theory        22793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22793.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H))), M:tm-338, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22794
in-theory        22794
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22794.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)))), M:tm-327, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22795
in-theory        22795
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22795.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)))), M:tm-326, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22796
in-theory        22796
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22796.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)))), M:tm-325, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22797
in-theory        22797
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22797.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)))), M:tm-324, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22798
in-theory        22798
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22798.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)))), M:tm-323, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22799
in-theory        22799
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22799.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((G and H) -> H)), M:tm-322, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22800
in-theory        22800
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22800.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((G and H) -> G)), M:tm-320, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22801
in-theory        22801
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22801.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22802
in-theory        22802
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22802.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (G -> (H -> G))), M:tm-315, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22803
in-theory        22803
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22803.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)))), M:tm-311, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22804
in-theory        22804
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22804.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) or G)), M:tm-310, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22805
in-theory        22805
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22805.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and G))), M:tm-309, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22806
in-theory        22806
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (((D and E) -> D) or F))
theorem-size     29
proof            (modus-ponens tm-308 tm-378 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (and Dm Em) Dm) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22806.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (((D and E) -> D) or F)), M:tm-308, m:tm-378, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (and Dm Em) Dm) Fm)))
================================================================
tm-name          tm-22807
in-theory        22807
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-378 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (and Dm Em) Dm) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22807.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-378, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (and Dm Em) Dm) Fm)))
================================================================
tm-name          tm-22808
in-theory        22808
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22808.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)))), M:tm-305, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22809
in-theory        22809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22809.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-303, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22810
in-theory        22810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22810.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-270, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22811
in-theory        22811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22811.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-239, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22812
in-theory        22812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> H) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22812.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> H) or J))), M:tm-210, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22813
in-theory        22813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22813.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-183, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22814
in-theory        22814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22814.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-157, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22815
in-theory        22815
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22815.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-147, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22816
in-theory        22816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22816.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-134, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22817
in-theory        22817
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22817.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-125, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22818
in-theory        22818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> H) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22818.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> H) or J))), M:tm-113, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22819
in-theory        22819
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22819.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-105, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22820
in-theory        22820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22820.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H))), M:tm-95, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22821
in-theory        22821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22821.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-83, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22822
in-theory        22822
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> E) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22822.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> E) or G))), M:tm-76, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22823
in-theory        22823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-6 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22823.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H))), M:tm-69, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22824
in-theory        22824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22824.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-54, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22825
in-theory        22825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22825.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H))), M:tm-42, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22826
in-theory        22826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22826.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H))), M:tm-32, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22827
in-theory        22827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22827.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H))), M:tm-23, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22828
in-theory        22828
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22828.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H))), M:tm-22, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22829
in-theory        22829
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22829.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H))), M:tm-21, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22830
in-theory        22830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22830.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-20, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22831
in-theory        22831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22831.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> F) or H))), M:tm-19, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22832
in-theory        22832
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-7 tm-5 tm-2 tm-6 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22832.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> E) or G))), M:tm-7, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22833
in-theory        22833
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-6 tm-5 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22833.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) or G), M:tm-6, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22834
in-theory        22834
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> E) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22834.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> E) or G)) and A)), M:tm-5, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22835
in-theory        22835
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-1 tm-5 tm-2 tm-6 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22835.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> E) or G))), M:tm-1, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-22836
in-theory        22836
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22836.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G and H) -> G) or I))), M:tm-373, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22837
in-theory        22837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22837.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-364, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22838
in-theory        22838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22838.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-354, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22839
in-theory        22839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22839.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22840
in-theory        22840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22840.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E and F) -> E) or G))), M:tm-338, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22841
in-theory        22841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C and D) -> C) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22841.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C and D) -> C) or E)))), M:tm-327, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22842
in-theory        22842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and (((F and G) -> G) and ((A -> (B -> A)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22842.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and (((F and G) -> G) and ((A -> (B -> A)) and (((C and D) -> C) or E)))), M:tm-326, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22843
in-theory        22843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and (((F and G) -> F) and ((A -> (B -> A)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22843.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and (((F and G) -> F) and ((A -> (B -> A)) and (((C and D) -> C) or E)))), M:tm-325, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22844
in-theory        22844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C and D) -> C) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22844.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C and D) -> C) or E)))), M:tm-324, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22845
in-theory        22845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22845.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C and D) -> C) or E)))), M:tm-323, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22846
in-theory        22846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22846.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and ((F and G) -> G)), M:tm-322, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22847
in-theory        22847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22847.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and ((F and G) -> F)), M:tm-320, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22848
in-theory        22848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22848.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22849
in-theory        22849
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22849.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and (F -> (G -> F))), M:tm-315, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22850
in-theory        22850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and (F or ((A -> (B -> A)) and (((C and D) -> C) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22850.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and (F or ((A -> (B -> A)) and (((C and D) -> C) or E)))), M:tm-311, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22851
in-theory        22851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and (((A -> (B -> A)) and (((C and D) -> C) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22851.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and (((A -> (B -> A)) and (((C and D) -> C) or E)) or F)), M:tm-310, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22852
in-theory        22852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and (F -> (((A -> (B -> A)) and (((C and D) -> C) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22852.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and (F -> (((A -> (B -> A)) and (((C and D) -> C) or E)) and F))), M:tm-309, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22853
in-theory        22853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and (((C and D) -> C) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-379 ((A (-> Am (-> Bm Am))) (B (or (-> (and Cm Dm) Cm) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22853.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and (((C and D) -> C) or E)), M:tm-308, m:tm-379, u:((A (-> Am (-> Bm Am))) (B (or (-> (and Cm Dm) Cm) Em)))
================================================================
tm-name          tm-22854
in-theory        22854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-379 ((A (-> Am (-> Bm Am))) (B (or (-> (and Cm Dm) Cm) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22854.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and (A -> (B -> A))), M:tm-307, m:tm-379, u:((A (-> Am (-> Bm Am))) (B (or (-> (and Cm Dm) Cm) Em)))
================================================================
tm-name          tm-22855
in-theory        22855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and (F -> ((A -> (B -> A)) and (((C and D) -> C) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22855.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and (F -> ((A -> (B -> A)) and (((C and D) -> C) or E)))), M:tm-305, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22856
in-theory        22856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22856.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-303, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22857
in-theory        22857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22857.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-270, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22858
in-theory        22858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22858.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-239, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22859
in-theory        22859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22859.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G and H) -> G) or I))), M:tm-210, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22860
in-theory        22860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22860.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-183, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22861
in-theory        22861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22861.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-157, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22862
in-theory        22862
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22862.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-147, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22863
in-theory        22863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22863.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-134, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22864
in-theory        22864
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22864.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-125, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22865
in-theory        22865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22865.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G and H) -> G) or I))), M:tm-113, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22866
in-theory        22866
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22866.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-105, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22867
in-theory        22867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22867.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E and F) -> E) or G))), M:tm-95, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22868
in-theory        22868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22868.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-83, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22869
in-theory        22869
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (((D and E) -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22869.        (((not (not A)) -> A) and ((B -> (C -> B)) and (((D and E) -> D) or F))), M:tm-76, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22870
in-theory        22870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E and F) -> E) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22870.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E and F) -> E) or G))), M:tm-69, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22871
in-theory        22871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22871.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-54, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22872
in-theory        22872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22872.        ((A -> (B or A)) and ((C -> (D -> C)) and (((E and F) -> E) or G))), M:tm-42, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22873
in-theory        22873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22873.        ((A -> (A or B)) and ((C -> (D -> C)) and (((E and F) -> E) or G))), M:tm-32, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22874
in-theory        22874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22874.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E and F) -> E) or G))), M:tm-23, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22875
in-theory        22875
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22875.        (((A and B) -> B) and ((C -> (D -> C)) and (((E and F) -> E) or G))), M:tm-22, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22876
in-theory        22876
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22876.        (((A and B) -> A) and ((C -> (D -> C)) and (((E and F) -> E) or G))), M:tm-21, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22877
in-theory        22877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22877.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-20, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22878
in-theory        22878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22878.        ((A -> (B -> A)) and ((C -> (D -> C)) and (((E and F) -> E) or G))), M:tm-19, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22879
in-theory        22879
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-7 tm-5 tm-1 tm-6 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22879.        (A or ((B -> (C -> B)) and (((D and E) -> D) or F))), M:tm-7, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22880
in-theory        22880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-6 tm-5 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22880.        (((A -> (B -> A)) and (((C and D) -> C) or E)) or F), M:tm-6, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22881
in-theory        22881
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (((D and E) -> D) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22881.        (A -> (((B -> (C -> B)) and (((D and E) -> D) or F)) and A)), M:tm-5, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22882
in-theory        22882
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-1 tm-5 tm-6 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22882.        (A -> ((B -> (C -> B)) and (((D and E) -> D) or F))), M:tm-1, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-22883
in-theory        22883
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-373 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22883.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F and G) -> F) or H))), M:tm-373, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22884
in-theory        22884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-364 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22884.        (((A -> (B -> A)) or C) and (D or (((E and F) -> E) or G))), M:tm-364, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22885
in-theory        22885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-354 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22885.        ((A -> (B -> (C -> (B and C)))) and (D or (((E and F) -> E) or G))), M:tm-354, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22886
in-theory        22886
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22886.        ((A or (((B and C) -> B) or D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22887
in-theory        22887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (((D and E) -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-338 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22887.        (((A -> B) -> (A -> (A and B))) and (C or (((D and E) -> D) or F))), M:tm-338, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22888
in-theory        22888
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and ((E -> (F -> (E and F))) and (A or (((B and C) -> B) or D))))
theorem-size     27
proof            (modus-ponens tm-327 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22888.        ((A or (((B and C) -> B) or D)) and ((E -> (F -> (E and F))) and (A or (((B and C) -> B) or D)))), M:tm-327, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22889
in-theory        22889
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and (((E and F) -> F) and (A or (((B and C) -> B) or D))))
theorem-size     25
proof            (modus-ponens tm-326 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22889.        ((A or (((B and C) -> B) or D)) and (((E and F) -> F) and (A or (((B and C) -> B) or D)))), M:tm-326, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22890
in-theory        22890
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and (((E and F) -> E) and (A or (((B and C) -> B) or D))))
theorem-size     25
proof            (modus-ponens tm-325 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22890.        ((A or (((B and C) -> B) or D)) and (((E and F) -> E) and (A or (((B and C) -> B) or D)))), M:tm-325, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22891
in-theory        22891
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B and C) -> B) or D))))
theorem-size     33
proof            (modus-ponens tm-324 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22891.        ((A or (((B and C) -> B) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B and C) -> B) or D)))), M:tm-324, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22892
in-theory        22892
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and ((E -> (F -> E)) and (A or (((B and C) -> B) or D))))
theorem-size     25
proof            (modus-ponens tm-323 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22892.        ((A or (((B and C) -> B) or D)) and ((E -> (F -> E)) and (A or (((B and C) -> B) or D)))), M:tm-323, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22893
in-theory        22893
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22893.        ((A or (((B and C) -> B) or D)) and ((E and F) -> F)), M:tm-322, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22894
in-theory        22894
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22894.        ((A or (((B and C) -> B) or D)) and ((E and F) -> E)), M:tm-320, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22895
in-theory        22895
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22895.        ((A or (((B and C) -> B) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22896
in-theory        22896
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22896.        ((A or (((B and C) -> B) or D)) and (E -> (F -> E))), M:tm-315, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22897
in-theory        22897
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and (E or (A or (((B and C) -> B) or D))))
theorem-size     21
proof            (modus-ponens tm-311 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22897.        ((A or (((B and C) -> B) or D)) and (E or (A or (((B and C) -> B) or D)))), M:tm-311, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22898
in-theory        22898
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and ((A or (((B and C) -> B) or D)) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22898.        ((A or (((B and C) -> B) or D)) and ((A or (((B and C) -> B) or D)) or E)), M:tm-310, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22899
in-theory        22899
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and (E -> ((A or (((B and C) -> B) or D)) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22899.        ((A or (((B and C) -> B) or D)) and (E -> ((A or (((B and C) -> B) or D)) and E))), M:tm-309, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22900
in-theory        22900
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and (E -> (A or (((B and C) -> B) or D))))
theorem-size     21
proof            (modus-ponens tm-305 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22900.        ((A or (((B and C) -> B) or D)) and (E -> (A or (((B and C) -> B) or D)))), M:tm-305, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22901
in-theory        22901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-303 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22901.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E and F) -> E) or G))), M:tm-303, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22902
in-theory        22902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-270 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22902.        ((A -> (((B and C) -> C) and A)) and (D or (((E and F) -> E) or G))), M:tm-270, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22903
in-theory        22903
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-239 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22903.        ((A -> (((B and C) -> B) and A)) and (D or (((E and F) -> E) or G))), M:tm-239, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22904
in-theory        22904
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-210 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22904.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F and G) -> F) or H))), M:tm-210, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22905
in-theory        22905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-183 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22905.        ((A -> ((B -> (C -> B)) and A)) and (D or (((E and F) -> E) or G))), M:tm-183, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22906
in-theory        22906
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-157 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22906.        ((A -> ((B and C) -> C)) and (D or (((E and F) -> E) or G))), M:tm-157, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22907
in-theory        22907
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E and F) -> E) or G)))
theorem-size     25
proof            (modus-ponens tm-147 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22907.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E and F) -> E) or G))), M:tm-147, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22908
in-theory        22908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-134 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22908.        ((A -> ((B and C) -> B)) and (D or (((E and F) -> E) or G))), M:tm-134, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22909
in-theory        22909
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E and F) -> E) or G)))
theorem-size     25
proof            (modus-ponens tm-125 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22909.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E and F) -> E) or G))), M:tm-125, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22910
in-theory        22910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-113 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22910.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F and G) -> F) or H))), M:tm-113, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22911
in-theory        22911
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E and F) -> E) or G)))
theorem-size     29
proof            (modus-ponens tm-105 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22911.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E and F) -> E) or G))), M:tm-105, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22912
in-theory        22912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (((D and E) -> D) or F)))
theorem-size     17
proof            (modus-ponens tm-95 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22912.        (((A -> B) -> (A -> A)) and (C or (((D and E) -> D) or F))), M:tm-95, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22913
in-theory        22913
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-83 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22913.        ((A -> (B -> (C -> B))) and (D or (((E and F) -> E) or G))), M:tm-83, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22914
in-theory        22914
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (((C and D) -> C) or E)))
theorem-size     15
proof            (modus-ponens tm-76 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22914.        (((not (not A)) -> A) and (B or (((C and D) -> C) or E))), M:tm-76, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22915
in-theory        22915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D and E) -> D) or F)))
theorem-size     21
proof            (modus-ponens tm-69 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22915.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D and E) -> D) or F))), M:tm-69, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22916
in-theory        22916
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-54 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22916.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E and F) -> E) or G))), M:tm-54, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22917
in-theory        22917
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-42 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22917.        ((A -> (B or A)) and (C or (((D and E) -> D) or F))), M:tm-42, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22918
in-theory        22918
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-32 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22918.        ((A -> (A or B)) and (C or (((D and E) -> D) or F))), M:tm-32, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22919
in-theory        22919
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (((D and E) -> D) or F)))
theorem-size     17
proof            (modus-ponens tm-23 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22919.        ((A -> (B -> (A and B))) and (C or (((D and E) -> D) or F))), M:tm-23, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22920
in-theory        22920
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-22 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22920.        (((A and B) -> B) and (C or (((D and E) -> D) or F))), M:tm-22, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22921
in-theory        22921
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-21 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22921.        (((A and B) -> A) and (C or (((D and E) -> D) or F))), M:tm-21, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22922
in-theory        22922
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-20 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22922.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E and F) -> E) or G))), M:tm-20, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22923
in-theory        22923
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-19 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22923.        ((A -> (B -> A)) and (C or (((D and E) -> D) or F))), M:tm-19, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22924
in-theory        22924
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (((C and D) -> C) or E)))
theorem-size     11
proof            (modus-ponens tm-7 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-7 tm-6 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22924.        (A or (B or (((C and D) -> C) or E))), M:tm-7, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22925
in-theory        22925
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-6 tm-7 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22925.        ((A or (((B and C) -> B) or D)) or E), M:tm-6, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22926
in-theory        22926
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (((C and D) -> C) or E)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22926.        (A -> ((B or (((C and D) -> C) or E)) and A)), M:tm-5, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22927
in-theory        22927
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (((C and D) -> C) or E)))
theorem-size     11
proof            (modus-ponens tm-1 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-1 tm-7 tm-6 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22927.        (A -> (B or (((C and D) -> C) or E))), M:tm-1, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-22928
in-theory        22928
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and F) -> E) or G) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22928.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and F) -> E) or G) or H)), M:tm-373, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22929
in-theory        22929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22929.        (((A -> (B -> A)) or C) and ((((D and E) -> D) or F) or G)), M:tm-364, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22930
in-theory        22930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D and E) -> D) or F) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22930.        ((A -> (B -> (C -> (B and C)))) and ((((D and E) -> D) or F) or G)), M:tm-354, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22931
in-theory        22931
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22931.        (((((A and B) -> A) or C) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22932
in-theory        22932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C and D) -> C) or E) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22932.        (((A -> B) -> (A -> (A and B))) and ((((C and D) -> C) or E) or F)), M:tm-338, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22933
in-theory        22933
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and ((E -> (F -> (E and F))) and ((((A and B) -> A) or C) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22933.        (((((A and B) -> A) or C) or D) and ((E -> (F -> (E and F))) and ((((A and B) -> A) or C) or D))), M:tm-327, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22934
in-theory        22934
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and (((E and F) -> F) and ((((A and B) -> A) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22934.        (((((A and B) -> A) or C) or D) and (((E and F) -> F) and ((((A and B) -> A) or C) or D))), M:tm-326, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22935
in-theory        22935
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and (((E and F) -> E) and ((((A and B) -> A) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22935.        (((((A and B) -> A) or C) or D) and (((E and F) -> E) and ((((A and B) -> A) or C) or D))), M:tm-325, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22936
in-theory        22936
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A and B) -> A) or C) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22936.        (((((A and B) -> A) or C) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A and B) -> A) or C) or D))), M:tm-324, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22937
in-theory        22937
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and ((E -> (F -> E)) and ((((A and B) -> A) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22937.        (((((A and B) -> A) or C) or D) and ((E -> (F -> E)) and ((((A and B) -> A) or C) or D))), M:tm-323, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22938
in-theory        22938
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22938.        (((((A and B) -> A) or C) or D) and ((E and F) -> F)), M:tm-322, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22939
in-theory        22939
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22939.        (((((A and B) -> A) or C) or D) and ((E and F) -> E)), M:tm-320, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22940
in-theory        22940
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22940.        (((((A and B) -> A) or C) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22941
in-theory        22941
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22941.        (((((A and B) -> A) or C) or D) and (E -> (F -> E))), M:tm-315, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22942
in-theory        22942
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and (E or ((((A and B) -> A) or C) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22942.        (((((A and B) -> A) or C) or D) and (E or ((((A and B) -> A) or C) or D))), M:tm-311, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22943
in-theory        22943
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and (((((A and B) -> A) or C) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22943.        (((((A and B) -> A) or C) or D) and (((((A and B) -> A) or C) or D) or E)), M:tm-310, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22944
in-theory        22944
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and (E -> (((((A and B) -> A) or C) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22944.        (((((A and B) -> A) or C) or D) and (E -> (((((A and B) -> A) or C) or D) and E))), M:tm-309, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22945
in-theory        22945
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and (E -> ((((A and B) -> A) or C) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22945.        (((((A and B) -> A) or C) or D) and (E -> ((((A and B) -> A) or C) or D))), M:tm-305, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22946
in-theory        22946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and E) -> D) or F) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22946.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and E) -> D) or F) or G)), M:tm-303, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22947
in-theory        22947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D and E) -> D) or F) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22947.        ((A -> (((B and C) -> C) and A)) and ((((D and E) -> D) or F) or G)), M:tm-270, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22948
in-theory        22948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D and E) -> D) or F) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22948.        ((A -> (((B and C) -> B) and A)) and ((((D and E) -> D) or F) or G)), M:tm-239, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22949
in-theory        22949
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and F) -> E) or G) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22949.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and F) -> E) or G) or H)), M:tm-210, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22950
in-theory        22950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D and E) -> D) or F) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22950.        ((A -> ((B -> (C -> B)) and A)) and ((((D and E) -> D) or F) or G)), M:tm-183, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22951
in-theory        22951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22951.        ((A -> ((B and C) -> C)) and ((((D and E) -> D) or F) or G)), M:tm-157, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22952
in-theory        22952
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and E) -> D) or F) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22952.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and E) -> D) or F) or G)), M:tm-147, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22953
in-theory        22953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22953.        ((A -> ((B and C) -> B)) and ((((D and E) -> D) or F) or G)), M:tm-134, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22954
in-theory        22954
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and E) -> D) or F) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22954.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and E) -> D) or F) or G)), M:tm-125, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22955
in-theory        22955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> E) or G) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22955.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> E) or G) or H)), M:tm-113, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22956
in-theory        22956
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and E) -> D) or F) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22956.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and E) -> D) or F) or G)), M:tm-105, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22957
in-theory        22957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C and D) -> C) or E) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22957.        (((A -> B) -> (A -> A)) and ((((C and D) -> C) or E) or F)), M:tm-95, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22958
in-theory        22958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22958.        ((A -> (B -> (C -> B))) and ((((D and E) -> D) or F) or G)), M:tm-83, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22959
in-theory        22959
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B and C) -> B) or D) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22959.        (((not (not A)) -> A) and ((((B and C) -> B) or D) or E)), M:tm-76, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22960
in-theory        22960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and D) -> C) or E) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22960.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and D) -> C) or E) or F)), M:tm-69, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22961
in-theory        22961
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and E) -> D) or F) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22961.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and E) -> D) or F) or G)), M:tm-54, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22962
in-theory        22962
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C and D) -> C) or E) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22962.        ((A -> (B or A)) and ((((C and D) -> C) or E) or F)), M:tm-42, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22963
in-theory        22963
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C and D) -> C) or E) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22963.        ((A -> (A or B)) and ((((C and D) -> C) or E) or F)), M:tm-32, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22964
in-theory        22964
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C and D) -> C) or E) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22964.        ((A -> (B -> (A and B))) and ((((C and D) -> C) or E) or F)), M:tm-23, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22965
in-theory        22965
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C and D) -> C) or E) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22965.        (((A and B) -> B) and ((((C and D) -> C) or E) or F)), M:tm-22, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22966
in-theory        22966
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C and D) -> C) or E) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22966.        (((A and B) -> A) and ((((C and D) -> C) or E) or F)), M:tm-21, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22967
in-theory        22967
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and E) -> D) or F) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22967.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and E) -> D) or F) or G)), M:tm-20, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22968
in-theory        22968
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C and D) -> C) or E) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22968.        ((A -> (B -> A)) and ((((C and D) -> C) or E) or F)), M:tm-19, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22969
in-theory        22969
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B and C) -> B) or D) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-7 tm-6 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22969.        (A or ((((B and C) -> B) or D) or E)), M:tm-7, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22970
in-theory        22970
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-6 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22970.        (((((A and B) -> A) or C) or D) or E), M:tm-6, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22971
in-theory        22971
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B and C) -> B) or D) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22971.        (A -> (((((B and C) -> B) or D) or E) and A)), M:tm-5, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22972
in-theory        22972
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) or D) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-1 tm-6 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22972.        (A -> ((((B and C) -> B) or D) or E)), M:tm-1, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-22973
in-theory        22973
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-382 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22973.        ((((A and B) -> A) or C) and (D -> (D or E))), M:tm-382, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-22974
in-theory        22974
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-382 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-22974.        ((((A and B) -> A) or C) and (D -> (E or D))), M:tm-382, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-22975
in-theory        22975
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-22975.        ((((A and B) -> A) or C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-382, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-22976
in-theory        22976
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-382 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-22976.        ((((A and B) -> A) or C) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-382, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-22977
in-theory        22977
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-382 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-6 tm-3 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-22977.        ((((A and B) -> A) or C) and ((not (not D)) -> D)), M:tm-382, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-22978
in-theory        22978
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-382 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22978.        ((((A and B) -> A) or C) and (D -> (E -> (F -> E)))), M:tm-382, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-22979
in-theory        22979
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-382 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-22979.        ((((A and B) -> A) or C) and ((D -> E) -> (D -> D))), M:tm-382, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-22980
in-theory        22980
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-382 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-22980.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-382, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-22981
in-theory        22981
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22981.        ((((A and B) -> A) or C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-382, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-22982
in-theory        22982
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-382 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-22982.        ((((A and B) -> A) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-382, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-22983
in-theory        22983
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-382 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22983.        ((((A and B) -> A) or C) and (D -> ((E and F) -> E))), M:tm-382, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-22984
in-theory        22984
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-382 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-22984.        ((((A and B) -> A) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-382, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-22985
in-theory        22985
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-382 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-22985.        ((((A and B) -> A) or C) and (D -> ((E and F) -> F))), M:tm-382, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-22986
in-theory        22986
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-382 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22986.        ((((A and B) -> A) or C) and (D -> ((E -> (F -> E)) and D))), M:tm-382, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-22987
in-theory        22987
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-382 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22987.        ((((A and B) -> A) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-382, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-22988
in-theory        22988
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-382 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22988.        ((((A and B) -> A) or C) and (D -> (((E and F) -> E) and D))), M:tm-382, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-22989
in-theory        22989
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-382 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-22989.        ((((A and B) -> A) or C) and (D -> (((E and F) -> F) and D))), M:tm-382, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-22990
in-theory        22990
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22990.        ((((A and B) -> A) or C) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-382, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-22991
in-theory        22991
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-382 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-22991.        ((((A and B) -> A) or C) and ((D -> E) -> (D -> (D and E)))), M:tm-382, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-22992
in-theory        22992
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22992.        ((((A and B) -> A) or C) and (D -> (E -> (F -> (E and F))))), M:tm-382, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-22993
in-theory        22993
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-382 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22993.        ((((A and B) -> A) or C) and ((D -> (E -> D)) or F)), M:tm-382, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-22994
in-theory        22994
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-382 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22994.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-382, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-22995
in-theory        22995
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-382 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-22995.        ((((A and B) -> A) or C) and (((D and E) -> D) or F)), M:tm-382, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-22996
in-theory        22996
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-382 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-22996.        ((((A and B) -> A) or C) and (((D and E) -> E) or F)), M:tm-382, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-22997
in-theory        22997
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-382 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22997.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) or F)), M:tm-382, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-22998
in-theory        22998
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-382 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22998.        ((((A and B) -> A) or C) and ((D -> (D or E)) or F)), M:tm-382, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-22999
in-theory        22999
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-382 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22999.        ((((A and B) -> A) or C) and (D -> ((E -> (E or F)) and D))), M:tm-382, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-23000
in-theory        23000
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-382 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23000.        ((((A and B) -> A) or C) and (D -> (E -> (E or F)))), M:tm-382, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-23001
in-theory        23001
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-382 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23001.        ((((A and B) -> A) or C) and (D or (E -> (F -> E)))), M:tm-382, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-23002
in-theory        23002
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23002.        ((((A and B) -> A) or C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-382, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-23003
in-theory        23003
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-382 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23003.        ((((A and B) -> A) or C) and (D or ((E and F) -> E))), M:tm-382, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-23004
in-theory        23004
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-382 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23004.        ((((A and B) -> A) or C) and (D or ((E and F) -> F))), M:tm-382, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-23005
in-theory        23005
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-23005.        ((((A and B) -> A) or C) and (D or (E -> (F -> (E and F))))), M:tm-382, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-23006
in-theory        23006
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-382 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23006.        ((((A and B) -> A) or C) and (D or (E -> (E or F)))), M:tm-382, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-23007
in-theory        23007
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-382 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23007.        ((((A and B) -> A) or C) and (D or (E -> (F or E)))), M:tm-382, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-23008
in-theory        23008
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-382 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23008.        ((((A and B) -> A) or C) and ((D -> (E or D)) or F)), M:tm-382, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-23009
in-theory        23009
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-382 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23009.        ((((A and B) -> A) or C) and (D -> ((E -> (F or E)) and D))), M:tm-382, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-23010
in-theory        23010
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-382 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23010.        ((((A and B) -> A) or C) and (D -> (E -> (F or E)))), M:tm-382, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-23011
in-theory        23011
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-382 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23011.        ((((A and B) -> A) or C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-382, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-23012
in-theory        23012
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-382 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23012.        ((((A and B) -> A) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-382, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-23013
in-theory        23013
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-382 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23013.        ((((A and B) -> A) or C) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-382, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-23014
in-theory        23014
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-382 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23014.        ((((A and B) -> A) or C) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-382, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-23015
in-theory        23015
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-382 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23015.        ((((A and B) -> A) or C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-382, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-23016
in-theory        23016
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-382 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23016.        ((((A and B) -> A) or C) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-382, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-23017
in-theory        23017
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-382 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23017.        ((((A and B) -> A) or C) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-382, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-23018
in-theory        23018
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-382 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-23018.        ((((A and B) -> A) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-382, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-23019
in-theory        23019
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23019.        ((((A and B) -> A) or C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-382, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-23020
in-theory        23020
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-382 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23020.        ((((A and B) -> A) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-382, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-23021
in-theory        23021
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-382 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23021.        ((((A and B) -> A) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-382, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-23022
in-theory        23022
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-382 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-23022.        ((((A and B) -> A) or C) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-382, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-23023
in-theory        23023
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23023.        ((((A and B) -> A) or C) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-382, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-23024
in-theory        23024
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-382 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23024.        ((((A and B) -> A) or C) and ((D -> (not (E -> D))) -> (not D))), M:tm-382, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-23025
in-theory        23025
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23025.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-382, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-23026
in-theory        23026
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-382 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23026.        ((((A and B) -> A) or C) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-382, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-23027
in-theory        23027
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-382 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23027.        ((((A and B) -> A) or C) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-382, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-23028
in-theory        23028
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23028.        ((((A and B) -> A) or C) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-382, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-23029
in-theory        23029
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-382 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23029.        ((((A and B) -> A) or C) and ((D -> (not (D or E))) -> (not D))), M:tm-382, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-23030
in-theory        23030
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-382 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23030.        ((((A and B) -> A) or C) and ((D -> (not (E or D))) -> (not D))), M:tm-382, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-23031
in-theory        23031
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-382 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-23031.        ((((A and B) -> A) or C) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-382, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-23032
in-theory        23032
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-382 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-23032.        ((((A and B) -> A) or C) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-382, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-23033
in-theory        23033
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-382 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-23033.        ((((A and B) -> A) or C) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-382, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-23034
in-theory        23034
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23034.        ((((A and B) -> A) or C) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-382, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-23035
in-theory        23035
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-382 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23035.        ((((A and B) -> A) or C) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-382, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-23036
in-theory        23036
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-382 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23036.        ((((A and B) -> A) or C) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-382, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-23037
in-theory        23037
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-382 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-23037.        ((((A and B) -> A) or C) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-382, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-23038
in-theory        23038
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23038.        ((((A and B) -> A) or C) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-382, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-23039
in-theory        23039
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-382 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-23039.        ((((A and B) -> A) or C) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-382, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-23040
in-theory        23040
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-382 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-23040.        ((((A and B) -> A) or C) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-382, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-23041
in-theory        23041
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-382 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23041.        ((((A and B) -> A) or C) and (D or ((not (not E)) -> E))), M:tm-382, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-23042
in-theory        23042
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-382 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-3 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23042.        ((((A and B) -> A) or C) and (((not (not D)) -> D) or E)), M:tm-382, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-23043
in-theory        23043
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-382 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23043.        ((((A and B) -> A) or C) and (D -> (((not (not E)) -> E) and D))), M:tm-382, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-23044
in-theory        23044
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-382 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-23044.        ((((A and B) -> A) or C) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-382, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-23045
in-theory        23045
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-382 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23045.        ((((A and B) -> A) or C) and (D -> ((not (not E)) -> E))), M:tm-382, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-23046
in-theory        23046
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23046.        ((((A and B) -> A) or C) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-382, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-23047
in-theory        23047
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-382 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23047.        ((((A and B) -> A) or C) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-382, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-23048
in-theory        23048
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23048.        ((((A and B) -> A) or C) and (D or (E -> (F -> (G -> F))))), M:tm-382, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-23049
in-theory        23049
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23049.        ((((A and B) -> A) or C) and ((D -> (E -> (F -> E))) or G)), M:tm-382, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-23050
in-theory        23050
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23050.        ((((A and B) -> A) or C) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-382, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-23051
in-theory        23051
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-382 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-23051.        ((((A and B) -> A) or C) and ((D -> E) -> (D -> (F -> E)))), M:tm-382, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-23052
in-theory        23052
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23052.        ((((A and B) -> A) or C) and (D -> (E -> (F -> (G -> F))))), M:tm-382, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-23053
in-theory        23053
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-382 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23053.        ((((A and B) -> A) or C) and (D -> D)), M:tm-382, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-23054
in-theory        23054
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23054.        ((((A and B) -> A) or C) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-382, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-23055
in-theory        23055
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-382 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23055.        ((((A and B) -> A) or C) and ((D and E) -> (D and E))), M:tm-382, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-23056
in-theory        23056
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-382 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-23056.        ((((A and B) -> A) or C) and ((D -> E) -> (D -> E))), M:tm-382, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-23057
in-theory        23057
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-382 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-23057.        ((((A and B) -> A) or C) and ((not (not D)) -> (not (not D)))), M:tm-382, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-23058
in-theory        23058
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-382 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-23058.        ((((A and B) -> A) or C) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-382, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-23059
in-theory        23059
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-382 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-23059.        ((((A and B) -> A) or C) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-382, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-23060
in-theory        23060
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-382 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23060.        ((((A and B) -> A) or C) and (D or ((E -> F) -> (E -> E)))), M:tm-382, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-23061
in-theory        23061
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-382 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23061.        ((((A and B) -> A) or C) and (((D -> E) -> (D -> D)) or F)), M:tm-382, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-23062
in-theory        23062
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23062.        ((((A and B) -> A) or C) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-382, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-23063
in-theory        23063
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-23063.        ((((A and B) -> A) or C) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-382, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-23064
in-theory        23064
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-382 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23064.        ((((A and B) -> A) or C) and (D -> ((E -> F) -> (E -> E)))), M:tm-382, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-23065
in-theory        23065
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-23065.        ((((A and B) -> A) or C) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-382, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-23066
in-theory        23066
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-382 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-23066.        ((((A and B) -> A) or C) and ((D -> (D -> E)) -> (D -> E))), M:tm-382, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-23067
in-theory        23067
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-382 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-23067.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-382, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-23068
in-theory        23068
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-382 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-23068.        ((((A and B) -> A) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-382, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-23069
in-theory        23069
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-382 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-23069.        ((((A and B) -> A) or C) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-382, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-23070
in-theory        23070
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23070.        ((((A and B) -> A) or C) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-382, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-23071
in-theory        23071
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-382 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23071.        ((((A and B) -> A) or C) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-382, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-23072
in-theory        23072
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-382 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23072.        ((((A and B) -> A) or C) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-382, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-23073
in-theory        23073
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-382 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-23073.        ((((A and B) -> A) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-382, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-23074
in-theory        23074
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23074.        ((((A and B) -> A) or C) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-382, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-23075
in-theory        23075
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-382 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-23075.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-382, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-23076
in-theory        23076
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-382 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23076.        ((((A and B) -> A) or C) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-382, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-23077
in-theory        23077
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-382 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23077.        ((((A and B) -> A) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-382, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-23078
in-theory        23078
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-382 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23078.        ((((A and B) -> A) or C) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-382, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-23079
in-theory        23079
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-382 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23079.        ((((A and B) -> A) or C) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-382, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-23080
in-theory        23080
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-382 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23080.        ((((A and B) -> A) or C) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-382, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-23081
in-theory        23081
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-382 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-23081.        ((((A and B) -> A) or C) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-382, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-23082
in-theory        23082
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-382 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23082.        ((((A and B) -> A) or C) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-382, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-23083
in-theory        23083
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-382 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-23083.        ((((A and B) -> A) or C) and (((D -> E) and D) -> E)), M:tm-382, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-23084
in-theory        23084
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-382 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-23084.        ((((A and B) -> A) or C) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-382, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-23085
in-theory        23085
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-382 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23085.        ((((A and B) -> A) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-382, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-23086
in-theory        23086
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-382 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-23086.        ((((A and B) -> A) or C) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-382, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-23087
in-theory        23087
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-382 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-23087.        ((((A and B) -> A) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-382, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-23088
in-theory        23088
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-382 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-23088.        ((((A and B) -> A) or C) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-382, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-23089
in-theory        23089
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-382 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-23089.        ((((A and B) -> A) or C) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-382, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-23090
in-theory        23090
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-382 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23090.        ((((A and B) -> A) or C) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-382, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-23091
in-theory        23091
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-382 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23091.        ((((A and B) -> A) or C) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-382, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-23092
in-theory        23092
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-382 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23092.        ((((A and B) -> A) or C) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-382, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-23093
in-theory        23093
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-382 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-23093.        ((((A and B) -> A) or C) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-382, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-23094
in-theory        23094
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-382 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23094.        ((((A and B) -> A) or C) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-382, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-23095
in-theory        23095
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-382 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-23095.        ((((A and B) -> A) or C) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-382, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-23096
in-theory        23096
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-382 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-23096.        ((((A and B) -> A) or C) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-382, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-23097
in-theory        23097
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23097.        ((((A and B) -> A) or C) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-382, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-23098
in-theory        23098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-382 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23098.        ((((A and B) -> A) or C) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-382, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-23099
in-theory        23099
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-382 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23099.        ((((A and B) -> A) or C) and (D or (E -> ((F and G) -> F)))), M:tm-382, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-23100
in-theory        23100
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23100.        ((((A and B) -> A) or C) and ((D -> ((E and F) -> E)) or G)), M:tm-382, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-23101
in-theory        23101
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23101.        ((((A and B) -> A) or C) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-382, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-23102
in-theory        23102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-382 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-23102.        ((((A and B) -> A) or C) and ((D -> (E and F)) -> (D -> E))), M:tm-382, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-23103
in-theory        23103
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-382 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23103.        ((((A and B) -> A) or C) and (D -> (E -> ((F and G) -> F)))), M:tm-382, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-23104
in-theory        23104
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-382 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-23104.        ((((A and B) -> A) or C) and ((D and (D -> E)) -> E)), M:tm-382, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-23105
in-theory        23105
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-382 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-23105.        ((((A and B) -> A) or C) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-382, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-23106
in-theory        23106
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-382 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23106.        ((((A and B) -> A) or C) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-382, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-23107
in-theory        23107
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-382 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-23107.        ((((A and B) -> A) or C) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-382, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-23108
in-theory        23108
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-382 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-23108.        ((((A and B) -> A) or C) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-382, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-23109
in-theory        23109
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-382 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-23109.        ((((A and B) -> A) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-382, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-23110
in-theory        23110
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-382 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-23110.        ((((A and B) -> A) or C) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-382, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-23111
in-theory        23111
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-382 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-23111.        ((((A and B) -> A) or C) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-382, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-23112
in-theory        23112
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-382 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23112.        ((((A and B) -> A) or C) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-382, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-23113
in-theory        23113
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-382 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23113.        ((((A and B) -> A) or C) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-382, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-23114
in-theory        23114
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-382 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23114.        ((((A and B) -> A) or C) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-382, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-23115
in-theory        23115
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-382 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-23115.        ((((A and B) -> A) or C) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-382, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-23116
in-theory        23116
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-382 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23116.        ((((A and B) -> A) or C) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-382, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-23117
in-theory        23117
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-382 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-23117.        ((((A and B) -> A) or C) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-382, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-23118
in-theory        23118
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-382 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-23118.        ((((A and B) -> A) or C) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-382, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-23119
in-theory        23119
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-382 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-23119.        ((((A and B) -> A) or C) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-382, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-23120
in-theory        23120
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23120.        ((((A and B) -> A) or C) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-382, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-23121
in-theory        23121
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-382 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23121.        ((((A and B) -> A) or C) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-382, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-23122
in-theory        23122
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-382 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23122.        ((((A and B) -> A) or C) and (D or (E -> ((F and G) -> G)))), M:tm-382, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-23123
in-theory        23123
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23123.        ((((A and B) -> A) or C) and ((D -> ((E and F) -> F)) or G)), M:tm-382, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-23124
in-theory        23124
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23124.        ((((A and B) -> A) or C) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-382, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-23125
in-theory        23125
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-382 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-23125.        ((((A and B) -> A) or C) and ((D -> (E and F)) -> (D -> F))), M:tm-382, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-23126
in-theory        23126
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-382 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23126.        ((((A and B) -> A) or C) and (D -> (E -> ((F and G) -> G)))), M:tm-382, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-23127
in-theory        23127
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23127.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-382, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-23128
in-theory        23128
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23128.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-382, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-23129
in-theory        23129
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23129.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-382, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-23130
in-theory        23130
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-382 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23130.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-382, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-23131
in-theory        23131
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-23131.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-382, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-23132
in-theory        23132
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-382 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23132.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-382, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-23133
in-theory        23133
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23133.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-382, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-23134
in-theory        23134
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23134.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-382, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-23135
in-theory        23135
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-382 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23135.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-382, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-23136
in-theory        23136
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23136.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-382, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-23137
in-theory        23137
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23137.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-382, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-23138
in-theory        23138
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23138.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-382, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-23139
in-theory        23139
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-382 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23139.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-382, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-23140
in-theory        23140
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23140.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-382, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-23141
in-theory        23141
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-382 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23141.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-382, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-23142
in-theory        23142
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-382 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23142.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-382, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-23143
in-theory        23143
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-382 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23143.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-382, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-23144
in-theory        23144
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-382 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23144.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-382, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-23145
in-theory        23145
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23145.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-382, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-23146
in-theory        23146
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23146.        ((((A and B) -> A) or C) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-382, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-23147
in-theory        23147
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-382 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23147.        ((((A and B) -> A) or C) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-382, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-23148
in-theory        23148
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-382 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23148.        ((((A and B) -> A) or C) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-382, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-23149
in-theory        23149
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-382 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23149.        ((((A and B) -> A) or C) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-382, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-23150
in-theory        23150
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23150.        ((((A and B) -> A) or C) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-382, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-23151
in-theory        23151
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-382 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23151.        ((((A and B) -> A) or C) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-382, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-23152
in-theory        23152
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-382 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23152.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-382, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-23153
in-theory        23153
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23153.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-382, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-23154
in-theory        23154
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-382 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23154.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-382, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-23155
in-theory        23155
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-382 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23155.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-382, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-23156
in-theory        23156
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-23156.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-382, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-23157
in-theory        23157
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23157.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-382, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-23158
in-theory        23158
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-382 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23158.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-382, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-23159
in-theory        23159
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23159.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-382, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-23160
in-theory        23160
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-382 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23160.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-382, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-23161
in-theory        23161
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-382 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23161.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-382, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-23162
in-theory        23162
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23162.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-382, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-23163
in-theory        23163
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-382 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23163.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-382, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-23164
in-theory        23164
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-382 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23164.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-382, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-23165
in-theory        23165
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-382 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23165.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-382, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-23166
in-theory        23166
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-382 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23166.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-382, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-23167
in-theory        23167
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-382 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23167.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-382, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-23168
in-theory        23168
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-382 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23168.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-382, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-23169
in-theory        23169
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-382 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23169.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-382, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-23170
in-theory        23170
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-382 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23170.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-382, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-23171
in-theory        23171
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-382 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23171.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-382, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-23172
in-theory        23172
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-382 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23172.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-382, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-23173
in-theory        23173
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-382 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23173.        ((((A and B) -> A) or C) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-382, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-23174
in-theory        23174
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-382 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23174.        ((((A and B) -> A) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-382, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-23175
in-theory        23175
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-382 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23175.        ((((A and B) -> A) or C) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-382, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-23176
in-theory        23176
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-382 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23176.        ((((A and B) -> A) or C) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-382, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-23177
in-theory        23177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-382 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23177.        ((((A and B) -> A) or C) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-382, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-23178
in-theory        23178
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-382 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23178.        ((((A and B) -> A) or C) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-382, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-23179
in-theory        23179
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23179.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-382, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-23180
in-theory        23180
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23180.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-382, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-23181
in-theory        23181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23181.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((F and G) -> F))), M:tm-382, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-23182
in-theory        23182
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-382 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23182.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((F and G) -> G))), M:tm-382, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-23183
in-theory        23183
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-23183.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-382, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-23184
in-theory        23184
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-382 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23184.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (F or G)))), M:tm-382, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-23185
in-theory        23185
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23185.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (G or F)))), M:tm-382, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-23186
in-theory        23186
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23186.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-382, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-23187
in-theory        23187
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-382 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23187.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-382, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-23188
in-theory        23188
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23188.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-382, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-23189
in-theory        23189
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23189.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-382, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-23190
in-theory        23190
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23190.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-382, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-23191
in-theory        23191
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-382 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23191.        ((((A and B) -> A) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-382, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-23192
in-theory        23192
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23192.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-382, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-23193
in-theory        23193
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-382 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23193.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-382, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-23194
in-theory        23194
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-382 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23194.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-382, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-23195
in-theory        23195
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-382 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23195.        ((((A and B) -> A) or C) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-382, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-23196
in-theory        23196
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-382 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23196.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-382, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-23197
in-theory        23197
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23197.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-382, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-23198
in-theory        23198
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-382 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23198.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-382, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-23199
in-theory        23199
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23199.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-382, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-23200
in-theory        23200
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-382 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23200.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-382, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-23201
in-theory        23201
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23201.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-382, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-23202
in-theory        23202
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23202.        ((((A and B) -> A) or C) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-382, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-23203
in-theory        23203
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-382 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23203.        ((((A and B) -> A) or C) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-382, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-23204
in-theory        23204
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-382 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23204.        ((((A and B) -> A) or C) and (D or (E -> (((F and G) -> F) and E)))), M:tm-382, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-23205
in-theory        23205
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-382 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23205.        ((((A and B) -> A) or C) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-382, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-23206
in-theory        23206
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23206.        ((((A and B) -> A) or C) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-382, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-23207
in-theory        23207
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-382 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23207.        ((((A and B) -> A) or C) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-382, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-23208
in-theory        23208
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23208.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-382, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-23209
in-theory        23209
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23209.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-382, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-23210
in-theory        23210
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23210.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((F and G) -> F))), M:tm-382, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-23211
in-theory        23211
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-382 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23211.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((F and G) -> G))), M:tm-382, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-23212
in-theory        23212
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-23212.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-382, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-23213
in-theory        23213
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-382 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23213.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (F or G)))), M:tm-382, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-23214
in-theory        23214
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23214.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (G or F)))), M:tm-382, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-23215
in-theory        23215
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23215.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-382, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-23216
in-theory        23216
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-382 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23216.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-382, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-23217
in-theory        23217
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23217.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-382, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-23218
in-theory        23218
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23218.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-382, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-23219
in-theory        23219
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23219.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-382, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-23220
in-theory        23220
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-382 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23220.        ((((A and B) -> A) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-382, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-23221
in-theory        23221
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23221.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-382, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-23222
in-theory        23222
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-382 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23222.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-382, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-23223
in-theory        23223
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-382 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23223.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-382, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-23224
in-theory        23224
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-382 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23224.        ((((A and B) -> A) or C) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-382, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-23225
in-theory        23225
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-382 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23225.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-382, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-23226
in-theory        23226
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23226.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-382, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-23227
in-theory        23227
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-382 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23227.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-382, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-23228
in-theory        23228
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23228.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-382, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-23229
in-theory        23229
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23229.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-382, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-23230
in-theory        23230
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23230.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-382, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-23231
in-theory        23231
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-382 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23231.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-382, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-23232
in-theory        23232
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23232.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-382, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-23233
in-theory        23233
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23233.        ((((A and B) -> A) or C) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-382, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-23234
in-theory        23234
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-382 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23234.        ((((A and B) -> A) or C) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-382, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-23235
in-theory        23235
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-382 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23235.        ((((A and B) -> A) or C) and (D or (E -> (((F and G) -> G) and E)))), M:tm-382, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-23236
in-theory        23236
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-382 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23236.        ((((A and B) -> A) or C) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-382, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-23237
in-theory        23237
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23237.        ((((A and B) -> A) or C) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-382, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-23238
in-theory        23238
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-382 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23238.        ((((A and B) -> A) or C) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-382, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-23239
in-theory        23239
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23239.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-382, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-23240
in-theory        23240
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23240.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-382, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-23241
in-theory        23241
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-382 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23241.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-382, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-23242
in-theory        23242
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-382 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23242.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-382, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-23243
in-theory        23243
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-23243.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-382, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-23244
in-theory        23244
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-382 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23244.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-382, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-23245
in-theory        23245
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23245.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-382, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-23246
in-theory        23246
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23246.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-382, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-23247
in-theory        23247
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23247.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-382, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-23248
in-theory        23248
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-382 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23248.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-382, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-23249
in-theory        23249
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23249.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-382, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-23250
in-theory        23250
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23250.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-382, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-23251
in-theory        23251
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23251.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-382, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-23252
in-theory        23252
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-382 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23252.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-382, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-23253
in-theory        23253
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-382 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23253.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-382, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-23254
in-theory        23254
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-382 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23254.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-382, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-23255
in-theory        23255
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-382 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23255.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-382, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-23256
in-theory        23256
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-382 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23256.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-382, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-23257
in-theory        23257
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-382 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23257.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-382, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-23258
in-theory        23258
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-382 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23258.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-382, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-23259
in-theory        23259
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-382 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23259.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-382, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-23260
in-theory        23260
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-382 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23260.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-382, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-23261
in-theory        23261
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-382 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-23261.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-382, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-23262
in-theory        23262
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-382 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-23262.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-382, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-23263
in-theory        23263
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-382 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-23263.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-382, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-23264
in-theory        23264
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-382 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-23264.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-382, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-23265
in-theory        23265
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-382 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-23265.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-382, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-23266
in-theory        23266
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-382 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-23266.        ((((A and B) -> A) or C) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-382, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-23267
in-theory        23267
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-382 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-23267.        ((((A and B) -> A) or C) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-382, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-23268
in-theory        23268
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-382 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-23268.        ((((A and B) -> A) or C) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-382, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-23269
in-theory        23269
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-382 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-23269.        ((((A and B) -> A) or C) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-382, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-23270
in-theory        23270
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-382 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-23270.        ((((A and B) -> A) or C) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-382, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-23271
in-theory        23271
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-382 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-23271.        ((((A and B) -> A) or C) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-382, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-23272
in-theory        23272
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-382 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23272.        ((((A and B) -> A) or C) and (D -> (D and (E -> D)))), M:tm-382, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-23273
in-theory        23273
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23273.        ((((A and B) -> A) or C) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-382, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-23274
in-theory        23274
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-382 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23274.        ((((A and B) -> A) or C) and ((D and E) -> ((D and E) and D))), M:tm-382, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-23275
in-theory        23275
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-382 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23275.        ((((A and B) -> A) or C) and ((D and E) -> ((D and E) and E))), M:tm-382, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-23276
in-theory        23276
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23276.        ((((A and B) -> A) or C) and (D -> (D and (E -> (D and E))))), M:tm-382, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-23277
in-theory        23277
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-382 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23277.        ((((A and B) -> A) or C) and (D -> (D and (D or E)))), M:tm-382, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-23278
in-theory        23278
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-382 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23278.        ((((A and B) -> A) or C) and (D -> (D and (E or D)))), M:tm-382, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-23279
in-theory        23279
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-382 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-23279.        ((((A and B) -> A) or C) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-382, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-23280
in-theory        23280
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-23280.        ((((A and B) -> A) or C) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-382, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-23281
in-theory        23281
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-382 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-23281.        ((((A and B) -> A) or C) and ((not (not D)) -> ((not (not D)) and D))), M:tm-382, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-23282
in-theory        23282
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23282.        ((((A and B) -> A) or C) and (D -> (D and (E -> (F -> E))))), M:tm-382, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-23283
in-theory        23283
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-382 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-23283.        ((((A and B) -> A) or C) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-382, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-23284
in-theory        23284
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-382 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-23284.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-382, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-23285
in-theory        23285
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-382 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23285.        ((((A and B) -> A) or C) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-382, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-23286
in-theory        23286
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-382 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-23286.        ((((A and B) -> A) or C) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-382, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-23287
in-theory        23287
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-382 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23287.        ((((A and B) -> A) or C) and (D -> (D and ((E and F) -> E)))), M:tm-382, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-23288
in-theory        23288
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-382 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-23288.        ((((A and B) -> A) or C) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-382, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-23289
in-theory        23289
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-382 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23289.        ((((A and B) -> A) or C) and (D -> (D and ((E and F) -> F)))), M:tm-382, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-23290
in-theory        23290
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-382 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23290.        ((((A and B) -> A) or C) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-382, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-23291
in-theory        23291
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-382 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23291.        ((((A and B) -> A) or C) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-382, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-23292
in-theory        23292
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-382 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23292.        ((((A and B) -> A) or C) and (D -> (D and (((E and F) -> E) and D)))), M:tm-382, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-23293
in-theory        23293
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-382 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23293.        ((((A and B) -> A) or C) and (D -> (D and (((E and F) -> F) and D)))), M:tm-382, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-23294
in-theory        23294
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-382 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-23294.        ((((A and B) -> A) or C) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-382, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-23295
in-theory        23295
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-23295.        ((((A and B) -> A) or C) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-382, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-23296
in-theory        23296
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-382 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23296.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-382, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-23297
in-theory        23297
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23297.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-382, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-23298
in-theory        23298
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23298.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-382, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-23299
in-theory        23299
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-382 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23299.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-382, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-23300
in-theory        23300
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23300.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-382, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-23301
in-theory        23301
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-382 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-23301.        ((((A and B) -> A) or C) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-382, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-23302
in-theory        23302
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-382 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-23302.        ((((A and B) -> A) or C) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-382, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-23303
in-theory        23303
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-382 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23303.        ((((A and B) -> A) or C) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-382, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-23304
in-theory        23304
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-382 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23304.        ((((A and B) -> A) or C) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-382, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-23305
in-theory        23305
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23305.        ((((A and B) -> A) or C) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-382, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-23306
in-theory        23306
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-382 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-23306.        ((((A and B) -> A) or C) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-382, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-23307
in-theory        23307
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-382 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23307.        ((((A and B) -> A) or C) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-382, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-23308
in-theory        23308
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-382 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23308.        ((((A and B) -> A) or C) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-382, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-23309
in-theory        23309
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-382 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23309.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-382, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-23310
in-theory        23310
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-382 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23310.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-382, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-23311
in-theory        23311
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-382 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23311.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-382, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-23312
in-theory        23312
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-382 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23312.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-382, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-23313
in-theory        23313
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-382 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23313.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-382, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-23314
in-theory        23314
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-382 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23314.        ((((A and B) -> A) or C) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-382, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-23315
in-theory        23315
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-382 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-23315.        ((((A and B) -> A) or C) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-382, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-23316
in-theory        23316
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-382 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-23316.        ((((A and B) -> A) or C) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-382, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-23317
in-theory        23317
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23317.        ((((A and B) -> A) or C) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-382, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-23318
in-theory        23318
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-382 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23318.        ((((A and B) -> A) or C) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-382, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-23319
in-theory        23319
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-382 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23319.        ((((A and B) -> A) or C) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-382, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-23320
in-theory        23320
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-382 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23320.        ((((A and B) -> A) or C) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-382, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-23321
in-theory        23321
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23321.        ((((A and B) -> A) or C) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-382, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-23322
in-theory        23322
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-382 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-23322.        ((((A and B) -> A) or C) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-382, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-23323
in-theory        23323
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-382 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23323.        ((((A and B) -> A) or C) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-382, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-23324
in-theory        23324
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-382 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23324.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-382, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-23325
in-theory        23325
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23325.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-382, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-23326
in-theory        23326
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23326.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-382, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-23327
in-theory        23327
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23327.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-382, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-23328
in-theory        23328
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23328.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-382, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-23329
in-theory        23329
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-382 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23329.        ((((A and B) -> A) or C) and (D or ((E -> (F -> E)) or G))), M:tm-382, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-23330
in-theory        23330
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23330.        ((((A and B) -> A) or C) and (((D -> (E -> D)) or F) or G)), M:tm-382, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-23331
in-theory        23331
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23331.        ((((A and B) -> A) or C) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-382, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-23332
in-theory        23332
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-382 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23332.        ((((A and B) -> A) or C) and (D -> ((E -> (F -> E)) or G))), M:tm-382, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-23333
in-theory        23333
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-382 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23333.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-382, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-23334
in-theory        23334
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23334.        ((((A and B) -> A) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-382, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-23335
in-theory        23335
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23335.        ((((A and B) -> A) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-382, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-23336
in-theory        23336
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-382 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23336.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-382, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-23337
in-theory        23337
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23337.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-382, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-23338
in-theory        23338
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-382 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23338.        ((((A and B) -> A) or C) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-382, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-23339
in-theory        23339
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-382 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23339.        ((((A and B) -> A) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-382, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-23340
in-theory        23340
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-382 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23340.        ((((A and B) -> A) or C) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-382, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-23341
in-theory        23341
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-382 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23341.        ((((A and B) -> A) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-382, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-23342
in-theory        23342
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-382 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23342.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-382, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-23343
in-theory        23343
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23343.        ((((A and B) -> A) or C) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-382, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-23344
in-theory        23344
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23344.        ((((A and B) -> A) or C) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-382, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-23345
in-theory        23345
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23345.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-382, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-23346
in-theory        23346
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23346.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-382, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-23347
in-theory        23347
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-382 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23347.        ((((A and B) -> A) or C) and (D or (((E and F) -> E) or G))), M:tm-382, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23348
in-theory        23348
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23348.        ((((A and B) -> A) or C) and ((((D and E) -> D) or F) or G)), M:tm-382, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-23349
in-theory        23349
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23349.        ((((A and B) -> A) or C) and (D -> ((((E and F) -> E) or G) and D))), M:tm-382, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23350
in-theory        23350
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F and G) -> F) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23350.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F and G) -> F) or H) and E))), M:tm-373, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23351
in-theory        23351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23351.        (((A -> (B -> A)) or C) and (D -> ((((E and F) -> E) or G) and D))), M:tm-364, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23352
in-theory        23352
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((((C and D) -> C) or E) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23352.        (A -> (B -> (((((C and D) -> C) or E) and A) and B))), M:tm-355, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-23353
in-theory        23353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23353.        ((A -> (B -> (C -> (B and C)))) and (D -> ((((E and F) -> E) or G) and D))), M:tm-354, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23354
in-theory        23354
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((((D and E) -> D) or F) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-382 ((Am (-> A (-> B (and A B)))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23354.        ((A or (B -> (C -> (B and C)))) -> ((((D and E) -> D) or F) and (B -> (C -> (B and C))))), M:tm-351, m:tm-382, u:((Am (-> A (-> B (and A B)))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-23355
in-theory        23355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23355.        ((A -> ((((B and C) -> B) or D) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23356
in-theory        23356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((((D and E) -> D) or F) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23356.        (((A -> B) -> (A -> (A and B))) and (C -> ((((D and E) -> D) or F) and C))), M:tm-338, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23357
in-theory        23357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((((C and D) -> C) or E) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-382 ((Am (-> A (and A B))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23357.        (((A -> B) or (A -> (A and B))) -> ((((C and D) -> C) or E) and (A -> (A and B)))), M:tm-335, m:tm-382, u:((Am (-> A (and A B))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (and A B)))))
================================================================
tm-name          tm-23358
in-theory        23358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and (A -> (A and ((((B and C) -> B) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23358.        ((A -> ((((B and C) -> B) or D) and A)) and (A -> (A and ((((B and C) -> B) or D) and A)))), M:tm-328, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-23359
in-theory        23359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B and C) -> B) or D) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23359.        ((A -> ((((B and C) -> B) or D) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B and C) -> B) or D) and A)))), M:tm-327, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23360
in-theory        23360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and (((E and F) -> F) and (A -> ((((B and C) -> B) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23360.        ((A -> ((((B and C) -> B) or D) and A)) and (((E and F) -> F) and (A -> ((((B and C) -> B) or D) and A)))), M:tm-326, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23361
in-theory        23361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and (((E and F) -> E) and (A -> ((((B and C) -> B) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23361.        ((A -> ((((B and C) -> B) or D) and A)) and (((E and F) -> E) and (A -> ((((B and C) -> B) or D) and A)))), M:tm-325, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23362
in-theory        23362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B and C) -> B) or D) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23362.        ((A -> ((((B and C) -> B) or D) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B and C) -> B) or D) and A)))), M:tm-324, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23363
in-theory        23363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and ((E -> (F -> E)) and (A -> ((((B and C) -> B) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23363.        ((A -> ((((B and C) -> B) or D) and A)) and ((E -> (F -> E)) and (A -> ((((B and C) -> B) or D) and A)))), M:tm-323, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23364
in-theory        23364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23364.        ((A -> ((((B and C) -> B) or D) and A)) and ((E and F) -> F)), M:tm-322, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23365
in-theory        23365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23365.        ((A -> ((((B and C) -> B) or D) and A)) and ((E and F) -> E)), M:tm-320, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23366
in-theory        23366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23366.        ((A -> ((((B and C) -> B) or D) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23367
in-theory        23367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23367.        ((A -> ((((B and C) -> B) or D) and A)) and (A -> A)), M:tm-316, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-23368
in-theory        23368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23368.        ((A -> ((((B and C) -> B) or D) and A)) and (E -> (F -> E))), M:tm-315, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23369
in-theory        23369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and ((A -> (not ((((B and C) -> B) or D) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23369.        ((A -> ((((B and C) -> B) or D) and A)) and ((A -> (not ((((B and C) -> B) or D) and A))) -> (not A))), M:tm-313, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-23370
in-theory        23370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and ((((((B and C) -> B) or D) and A) -> E) -> ((A or ((((B and C) -> B) or D) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23370.        ((A -> ((((B and C) -> B) or D) and A)) and ((((((B and C) -> B) or D) and A) -> E) -> ((A or ((((B and C) -> B) or D) and A)) -> E))), M:tm-312, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-23371
in-theory        23371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and (E or (A -> ((((B and C) -> B) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23371.        ((A -> ((((B and C) -> B) or D) and A)) and (E or (A -> ((((B and C) -> B) or D) and A)))), M:tm-311, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23372
in-theory        23372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and ((A -> ((((B and C) -> B) or D) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23372.        ((A -> ((((B and C) -> B) or D) and A)) and ((A -> ((((B and C) -> B) or D) and A)) or E)), M:tm-310, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23373
in-theory        23373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and (E -> ((A -> ((((B and C) -> B) or D) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23373.        ((A -> ((((B and C) -> B) or D) and A)) and (E -> ((A -> ((((B and C) -> B) or D) and A)) and E))), M:tm-309, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23374
in-theory        23374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and (E -> (A -> ((((B and C) -> B) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23374.        ((A -> ((((B and C) -> B) or D) and A)) and (E -> (A -> ((((B and C) -> B) or D) and A)))), M:tm-305, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23375
in-theory        23375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23375.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-303, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23376
in-theory        23376
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((((D and E) -> D) or F) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-382 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23376.        ((A or ((B -> (C -> (B and C))) and A)) -> ((((D and E) -> D) or F) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-382, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-23377
in-theory        23377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23377.        ((A -> (((B and C) -> C) and A)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-270, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23378
in-theory        23378
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((D and E) -> D) or F) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-382 ((Am (and (-> (and A B) B) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23378.        ((A or (((B and C) -> C) and A)) -> ((((D and E) -> D) or F) and (((B and C) -> C) and A))), M:tm-267, m:tm-382, u:((Am (and (-> (and A B) B) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-23379
in-theory        23379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23379.        ((A -> (((B and C) -> B) and A)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-239, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23380
in-theory        23380
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((D and E) -> D) or F) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-382 ((Am (and (-> (and A B) A) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23380.        ((A or (((B and C) -> B) and A)) -> ((((D and E) -> D) or F) and (((B and C) -> B) and A))), M:tm-236, m:tm-382, u:((Am (and (-> (and A B) A) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-23381
in-theory        23381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F and G) -> F) or H) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23381.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F and G) -> F) or H) and E))), M:tm-210, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23382
in-theory        23382
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E and F) -> E) or G) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-382 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (and Bm Cm) Bm) Dm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23382.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E and F) -> E) or G) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-382, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (and Bm Cm) Bm) Dm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-23383
in-theory        23383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23383.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-183, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23384
in-theory        23384
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((((D and E) -> D) or F) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-382 ((Am (and (-> A (-> B A)) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23384.        ((A or ((B -> (C -> B)) and A)) -> ((((D and E) -> D) or F) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-382, u:((Am (and (-> A (-> B A)) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-23385
in-theory        23385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23385.        ((A -> ((B and C) -> C)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-157, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23386
in-theory        23386
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((((D and E) -> D) or F) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-382 ((Am (-> (and A B) B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23386.        ((A or ((B and C) -> C)) -> ((((D and E) -> D) or F) and ((B and C) -> C))), M:tm-154, m:tm-382, u:((Am (-> (and A B) B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> (and A B) B))))
================================================================
tm-name          tm-23387
in-theory        23387
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23387.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-147, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23388
in-theory        23388
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D and E) -> D) or F) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-382 ((Am (-> (and A (-> B C)) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-6 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23388.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D and E) -> D) or F) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-382, u:((Am (-> (and A (-> B C)) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-23389
in-theory        23389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23389.        ((A -> ((B and C) -> B)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-134, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23390
in-theory        23390
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((((D and E) -> D) or F) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-382 ((Am (-> (and A B) A)) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23390.        ((A or ((B and C) -> B)) -> ((((D and E) -> D) or F) and ((B and C) -> B))), M:tm-131, m:tm-382, u:((Am (-> (and A B) A)) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> (and A B) A))))
================================================================
tm-name          tm-23391
in-theory        23391
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23391.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-125, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23392
in-theory        23392
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D and E) -> D) or F) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-382 ((Am (-> (and (-> A B) C) B)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23392.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D and E) -> D) or F) and (((A -> B) and C) -> B))), M:tm-122, m:tm-382, u:((Am (-> (and (-> A B) C) B)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-23393
in-theory        23393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F and G) -> F) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23393.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F and G) -> F) or H) and E))), M:tm-113, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23394
in-theory        23394
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E and F) -> E) or G) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-382 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23394.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E and F) -> E) or G) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-382, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-23395
in-theory        23395
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23395.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E and F) -> E) or G) and D))), M:tm-105, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23396
in-theory        23396
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D and E) -> D) or F) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-382 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23396.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D and E) -> D) or F) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-382, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-23397
in-theory        23397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((((D and E) -> D) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23397.        (((A -> B) -> (A -> A)) and (C -> ((((D and E) -> D) or F) and C))), M:tm-95, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23398
in-theory        23398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((((C and D) -> C) or E) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-382 ((Am (-> A A)) (B (and (or (-> (and Bm Cm) Bm) Dm) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23398.        (((A -> B) or (A -> A)) -> ((((C and D) -> C) or E) and (A -> A))), M:tm-92, m:tm-382, u:((Am (-> A A)) (B (and (or (-> (and Bm Cm) Bm) Dm) (-> A A))))
================================================================
tm-name          tm-23399
in-theory        23399
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C and D) -> C) or E) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23399.        (A -> (B -> ((((C and D) -> C) or E) and A))), M:tm-84, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-23400
in-theory        23400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23400.        ((A -> (B -> (C -> B))) and (D -> ((((E and F) -> E) or G) and D))), M:tm-83, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23401
in-theory        23401
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((((D and E) -> D) or F) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-382 ((Am (-> A (-> B A))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23401.        ((A or (B -> (C -> B))) -> ((((D and E) -> D) or F) and (B -> (C -> B)))), M:tm-80, m:tm-382, u:((Am (-> A (-> B A))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (-> B A)))))
================================================================
tm-name          tm-23402
in-theory        23402
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((((C and D) -> C) or E) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-10 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23402.        (((not (not A)) -> A) and (B -> ((((C and D) -> C) or E) and B))), M:tm-76, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23403
in-theory        23403
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((((B and C) -> B) or D) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-6 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23403.        (((not (not A)) or A) -> ((((B and C) -> B) or D) and A)), M:tm-73, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-23404
in-theory        23404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D and E) -> D) or F) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-9 tm-6 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23404.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D and E) -> D) or F) and C))), M:tm-69, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23405
in-theory        23405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C and D) -> C) or E) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-382 ((Am (-> (-> A (not B)) (not A))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-6 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23405.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C and D) -> C) or E) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-382, u:((Am (-> (-> A (not B)) (not A))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-23406
in-theory        23406
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23406.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E and F) -> E) or G) and D))), M:tm-54, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23407
in-theory        23407
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D and E) -> D) or F) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-382 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-6 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23407.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D and E) -> D) or F) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-382, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-23408
in-theory        23408
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C and D) -> C) or E) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-382 ((Am (or A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23408.        ((A or (B or A)) -> ((((C and D) -> C) or E) and (B or A))), M:tm-50, m:tm-382, u:((Am (or A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (or A B))))
================================================================
tm-name          tm-23409
in-theory        23409
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C and D) -> C) or E) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-382 ((Am (or A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23409.        ((A or (A or B)) -> ((((C and D) -> C) or E) and (A or B))), M:tm-49, m:tm-382, u:((Am (or A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (or A B))))
================================================================
tm-name          tm-23410
in-theory        23410
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C and D) -> C) or E) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-382 ((Am (-> A (and B A))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-6 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23410.        ((A or (B -> (A and B))) -> ((((C and D) -> C) or E) and (B -> (A and B)))), M:tm-48, m:tm-382, u:((Am (-> A (and B A))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-23411
in-theory        23411
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C and D) -> C) or E) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-6 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23411.        (((A and B) or B) -> ((((C and D) -> C) or E) and B)), M:tm-47, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-23412
in-theory        23412
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C and D) -> C) or E) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23412.        (((A and B) or A) -> ((((C and D) -> C) or E) and A)), M:tm-46, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-23413
in-theory        23413
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and E) -> D) or F) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-382 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23413.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and E) -> D) or F) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-382, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-23414
in-theory        23414
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C and D) -> C) or E) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-382 ((Am (-> A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23414.        ((A or (B -> A)) -> ((((C and D) -> C) or E) and (B -> A))), M:tm-44, m:tm-382, u:((Am (-> A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A B))))
================================================================
tm-name          tm-23415
in-theory        23415
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((((D and E) -> D) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23415.        ((A -> (B or A)) and (C -> ((((D and E) -> D) or F) and C))), M:tm-42, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23416
in-theory        23416
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((((D and E) -> D) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23416.        ((A -> (A or B)) and (C -> ((((D and E) -> D) or F) and C))), M:tm-32, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23417
in-theory        23417
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((((B and C) -> B) or D) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23417.        (A -> (A and ((((B and C) -> B) or D) and A))), M:tm-24, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-23418
in-theory        23418
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((((D and E) -> D) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23418.        ((A -> (B -> (A and B))) and (C -> ((((D and E) -> D) or F) and C))), M:tm-23, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23419
in-theory        23419
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((((D and E) -> D) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23419.        (((A and B) -> B) and (C -> ((((D and E) -> D) or F) and C))), M:tm-22, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23420
in-theory        23420
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((((D and E) -> D) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23420.        (((A and B) -> A) and (C -> ((((D and E) -> D) or F) and C))), M:tm-21, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23421
in-theory        23421
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23421.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E and F) -> E) or G) and D))), M:tm-20, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23422
in-theory        23422
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((((D and E) -> D) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23422.        ((A -> (B -> A)) and (C -> ((((D and E) -> D) or F) and C))), M:tm-19, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23423
in-theory        23423
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((((B and C) -> B) or D) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-9 tm-5 tm-6 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23423.        ((A -> (not ((((B and C) -> B) or D) and A))) -> (not A)), M:tm-9, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-23424
in-theory        23424
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) -> A) or C) and D) -> E) -> ((D or ((((A and B) -> A) or C) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-8 tm-5 tm-6 tm-3)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23424.        ((((((A and B) -> A) or C) and D) -> E) -> ((D or ((((A and B) -> A) or C) and D)) -> E)), M:tm-8, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-23425
in-theory        23425
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((((C and D) -> C) or E) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-7 tm-5 tm-6 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23425.        (A or (B -> ((((C and D) -> C) or E) and B))), M:tm-7, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23426
in-theory        23426
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23426.        ((A -> ((((B and C) -> B) or D) and A)) or E), M:tm-6, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23427
in-theory        23427
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((((C and D) -> C) or E) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23427.        (A -> ((B -> ((((C and D) -> C) or E) and B)) and A)), M:tm-5, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23428
in-theory        23428
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((((C and D) -> C) or E) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-1 tm-5 tm-6 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23428.        (A -> (B -> ((((C and D) -> C) or E) and B))), M:tm-1, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-23429
in-theory        23429
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-382 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23429.        ((((A and B) -> A) or C) and (D -> (((E and F) -> E) or G))), M:tm-382, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23430
in-theory        23430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-373 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23430.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F and G) -> F) or H))), M:tm-373, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23431
in-theory        23431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-364 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23431.        (((A -> (B -> A)) or C) and (D -> (((E and F) -> E) or G))), M:tm-364, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23432
in-theory        23432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-354 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23432.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E and F) -> E) or G))), M:tm-354, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23433
in-theory        23433
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-351 tm-383 ((Am (-> A (-> B (and A B)))) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23433.        ((A or (B -> (C -> (B and C)))) -> (((D and E) -> D) or F)), M:tm-351, m:tm-383, u:((Am (-> A (-> B (and A B)))) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23434
in-theory        23434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23434.        ((A -> (((B and C) -> B) or D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23435
in-theory        23435
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) -> D) -> ((((A and B) -> A) or C) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-383 ((Am (-> (or (-> (and Bm Cm) Bm) Dm) B)) (A (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23435.        (((((A and B) -> A) or C) -> D) -> ((((A and B) -> A) or C) and D)), M:tm-339, m:tm-383, u:((Am (-> (or (-> (and Bm Cm) Bm) Dm) B)) (A (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23436
in-theory        23436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D and E) -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-338 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23436.        (((A -> B) -> (A -> (A and B))) and (C -> (((D and E) -> D) or F))), M:tm-338, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23437
in-theory        23437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C and D) -> C) or E))
theorem-size     17
proof            (modus-ponens tm-335 tm-383 ((Am (-> A (and A B))) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23437.        (((A -> B) or (A -> (A and B))) -> (((C and D) -> C) or E)), M:tm-335, m:tm-383, u:((Am (-> A (and A B))) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23438
in-theory        23438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (A -> (A and (((B and C) -> B) or D))))
theorem-size     21
proof            (modus-ponens tm-328 tm-383 ((A Am) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23438.        ((A -> (((B and C) -> B) or D)) and (A -> (A and (((B and C) -> B) or D)))), M:tm-328, m:tm-383, u:((A Am) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23439
in-theory        23439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and ((E -> (F -> (E and F))) and (A -> (((B and C) -> B) or D))))
theorem-size     27
proof            (modus-ponens tm-327 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23439.        ((A -> (((B and C) -> B) or D)) and ((E -> (F -> (E and F))) and (A -> (((B and C) -> B) or D)))), M:tm-327, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23440
in-theory        23440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (((E and F) -> F) and (A -> (((B and C) -> B) or D))))
theorem-size     25
proof            (modus-ponens tm-326 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23440.        ((A -> (((B and C) -> B) or D)) and (((E and F) -> F) and (A -> (((B and C) -> B) or D)))), M:tm-326, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23441
in-theory        23441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (((E and F) -> E) and (A -> (((B and C) -> B) or D))))
theorem-size     25
proof            (modus-ponens tm-325 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23441.        ((A -> (((B and C) -> B) or D)) and (((E and F) -> E) and (A -> (((B and C) -> B) or D)))), M:tm-325, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23442
in-theory        23442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B and C) -> B) or D))))
theorem-size     33
proof            (modus-ponens tm-324 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23442.        ((A -> (((B and C) -> B) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B and C) -> B) or D)))), M:tm-324, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23443
in-theory        23443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and ((E -> (F -> E)) and (A -> (((B and C) -> B) or D))))
theorem-size     25
proof            (modus-ponens tm-323 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23443.        ((A -> (((B and C) -> B) or D)) and ((E -> (F -> E)) and (A -> (((B and C) -> B) or D)))), M:tm-323, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23444
in-theory        23444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23444.        ((A -> (((B and C) -> B) or D)) and ((E and F) -> F)), M:tm-322, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23445
in-theory        23445
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B and C) -> B) or D) -> E)) -> (((B and C) -> B) or D)) and ((A and ((((B and C) -> B) or D) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-383 ((Am (and A (-> (or (-> (and Bm Cm) Bm) Dm) C))) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23445.        (((A and ((((B and C) -> B) or D) -> E)) -> (((B and C) -> B) or D)) and ((A and ((((B and C) -> B) or D) -> E)) -> E)), M:tm-321, m:tm-383, u:((Am (and A (-> (or (-> (and Bm Cm) Bm) Dm) C))) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23446
in-theory        23446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23446.        ((A -> (((B and C) -> B) or D)) and ((E and F) -> E)), M:tm-320, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23447
in-theory        23447
times-derived    1
----------------------------------------------------------------
theorem          (((((((A and B) -> A) or C) -> D) and E) -> (((A and B) -> A) or C)) and ((((((A and B) -> A) or C) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-383 ((Am (and (-> (or (-> (and Bm Cm) Bm) Dm) B) C)) (A (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23447.        (((((((A and B) -> A) or C) -> D) and E) -> (((A and B) -> A) or C)) and ((((((A and B) -> A) or C) -> D) and E) -> D)), M:tm-319, m:tm-383, u:((Am (and (-> (or (-> (and Bm Cm) Bm) Dm) B) C)) (A (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23448
in-theory        23448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23448.        ((A -> (((B and C) -> B) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23449
in-theory        23449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-383 ((A Am) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23449.        ((A -> (((B and C) -> B) or D)) and (A -> A)), M:tm-316, m:tm-383, u:((A Am) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23450
in-theory        23450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23450.        ((A -> (((B and C) -> B) or D)) and (E -> (F -> E))), M:tm-315, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23451
in-theory        23451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and ((A -> (not (((B and C) -> B) or D))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-383 ((A Am) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23451.        ((A -> (((B and C) -> B) or D)) and ((A -> (not (((B and C) -> B) or D))) -> (not A))), M:tm-313, m:tm-383, u:((A Am) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23452
in-theory        23452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (((((B and C) -> B) or D) -> E) -> ((A or (((B and C) -> B) or D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-383 ((A Am) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23452.        ((A -> (((B and C) -> B) or D)) and (((((B and C) -> B) or D) -> E) -> ((A or (((B and C) -> B) or D)) -> E))), M:tm-312, m:tm-383, u:((A Am) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23453
in-theory        23453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (E or (A -> (((B and C) -> B) or D))))
theorem-size     21
proof            (modus-ponens tm-311 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23453.        ((A -> (((B and C) -> B) or D)) and (E or (A -> (((B and C) -> B) or D)))), M:tm-311, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23454
in-theory        23454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and ((A -> (((B and C) -> B) or D)) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23454.        ((A -> (((B and C) -> B) or D)) and ((A -> (((B and C) -> B) or D)) or E)), M:tm-310, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23455
in-theory        23455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (E -> ((A -> (((B and C) -> B) or D)) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23455.        ((A -> (((B and C) -> B) or D)) and (E -> ((A -> (((B and C) -> B) or D)) and E))), M:tm-309, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23456
in-theory        23456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (E -> (A -> (((B and C) -> B) or D))))
theorem-size     21
proof            (modus-ponens tm-305 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23456.        ((A -> (((B and C) -> B) or D)) and (E -> (A -> (((B and C) -> B) or D)))), M:tm-305, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23457
in-theory        23457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-303 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23457.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E and F) -> E) or G))), M:tm-303, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23458
in-theory        23458
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D and E) -> D) or F))
theorem-size     19
proof            (modus-ponens tm-300 tm-383 ((Am (and (-> A (-> B (and A B))) C)) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23458.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D and E) -> D) or F)), M:tm-300, m:tm-383, u:((Am (and (-> A (-> B (and A B))) C)) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23459
in-theory        23459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-270 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23459.        ((A -> (((B and C) -> C) and A)) and (D -> (((E and F) -> E) or G))), M:tm-270, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23460
in-theory        23460
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-267 tm-383 ((Am (and (-> (and A B) B) C)) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23460.        ((A or (((B and C) -> C) and A)) -> (((D and E) -> D) or F)), M:tm-267, m:tm-383, u:((Am (and (-> (and A B) B) C)) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23461
in-theory        23461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-239 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23461.        ((A -> (((B and C) -> B) and A)) and (D -> (((E and F) -> E) or G))), M:tm-239, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23462
in-theory        23462
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-236 tm-383 ((Am (and (-> (and A B) A) C)) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23462.        ((A or (((B and C) -> B) and A)) -> (((D and E) -> D) or F)), M:tm-236, m:tm-383, u:((Am (and (-> (and A B) A) C)) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23463
in-theory        23463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-210 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23463.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F and G) -> F) or H))), M:tm-210, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23464
in-theory        23464
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E and F) -> E) or G))
theorem-size     25
proof            (modus-ponens tm-207 tm-383 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23464.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E and F) -> E) or G)), M:tm-207, m:tm-383, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23465
in-theory        23465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-183 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23465.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E and F) -> E) or G))), M:tm-183, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23466
in-theory        23466
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-180 tm-383 ((Am (and (-> A (-> B A)) C)) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23466.        ((A or ((B -> (C -> B)) and A)) -> (((D and E) -> D) or F)), M:tm-180, m:tm-383, u:((Am (and (-> A (-> B A)) C)) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23467
in-theory        23467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-157 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23467.        ((A -> ((B and C) -> C)) and (D -> (((E and F) -> E) or G))), M:tm-157, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23468
in-theory        23468
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-154 tm-383 ((Am (-> (and A B) B)) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-1 tm-4 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23468.        ((A or ((B and C) -> C)) -> (((D and E) -> D) or F)), M:tm-154, m:tm-383, u:((Am (-> (and A B) B)) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23469
in-theory        23469
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E and F) -> E) or G)))
theorem-size     25
proof            (modus-ponens tm-147 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23469.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E and F) -> E) or G))), M:tm-147, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23470
in-theory        23470
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D and E) -> D) or F))
theorem-size     23
proof            (modus-ponens tm-144 tm-383 ((Am (-> (and A (-> B C)) C)) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-6 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23470.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D and E) -> D) or F)), M:tm-144, m:tm-383, u:((Am (-> (and A (-> B C)) C)) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23471
in-theory        23471
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B and C) -> B) or D) -> E)) -> (((B and C) -> B) or D))
theorem-size     19
proof            (modus-ponens tm-142 tm-383 ((Am (and A (-> (or (-> (and Bm Cm) Bm) Dm) C))) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-1 tm-4 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23471.        ((A and ((((B and C) -> B) or D) -> E)) -> (((B and C) -> B) or D)), M:tm-142, m:tm-383, u:((Am (and A (-> (or (-> (and Bm Cm) Bm) Dm) C))) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23472
in-theory        23472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-134 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23472.        ((A -> ((B and C) -> B)) and (D -> (((E and F) -> E) or G))), M:tm-134, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23473
in-theory        23473
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-131 tm-383 ((Am (-> (and A B) A)) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-1 tm-3 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23473.        ((A or ((B and C) -> B)) -> (((D and E) -> D) or F)), M:tm-131, m:tm-383, u:((Am (-> (and A B) A)) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23474
in-theory        23474
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E and F) -> E) or G)))
theorem-size     25
proof            (modus-ponens tm-125 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23474.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E and F) -> E) or G))), M:tm-125, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23475
in-theory        23475
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D and E) -> D) or F))
theorem-size     23
proof            (modus-ponens tm-122 tm-383 ((Am (-> (and (-> A B) C) B)) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23475.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D and E) -> D) or F)), M:tm-122, m:tm-383, u:((Am (-> (and (-> A B) C) B)) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23476
in-theory        23476
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) or C) -> D) and E) -> (((A and B) -> A) or C))
theorem-size     19
proof            (modus-ponens tm-120 tm-383 ((Am (and (-> (or (-> (and Bm Cm) Bm) Dm) B) C)) (A (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-1 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23476.        ((((((A and B) -> A) or C) -> D) and E) -> (((A and B) -> A) or C)), M:tm-120, m:tm-383, u:((Am (and (-> (or (-> (and Bm Cm) Bm) Dm) B) C)) (A (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23477
in-theory        23477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-113 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23477.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> F) or H))), M:tm-113, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23478
in-theory        23478
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E and F) -> E) or G))
theorem-size     23
proof            (modus-ponens tm-110 tm-383 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23478.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E and F) -> E) or G)), M:tm-110, m:tm-383, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23479
in-theory        23479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E and F) -> E) or G)))
theorem-size     29
proof            (modus-ponens tm-105 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23479.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E and F) -> E) or G))), M:tm-105, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23480
in-theory        23480
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D and E) -> D) or F))
theorem-size     27
proof            (modus-ponens tm-102 tm-383 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23480.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D and E) -> D) or F)), M:tm-102, m:tm-383, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23481
in-theory        23481
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) -> D) -> (((A and B) -> A) or C))
theorem-size     17
proof            (modus-ponens tm-96 tm-383 ((Am (-> (or (-> (and Bm Cm) Bm) Dm) B)) (A (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23481.        (((((A and B) -> A) or C) -> D) -> (((A and B) -> A) or C)), M:tm-96, m:tm-383, u:((Am (-> (or (-> (and Bm Cm) Bm) Dm) B)) (A (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23482
in-theory        23482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D and E) -> D) or F)))
theorem-size     17
proof            (modus-ponens tm-95 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23482.        (((A -> B) -> (A -> A)) and (C -> (((D and E) -> D) or F))), M:tm-95, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23483
in-theory        23483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C and D) -> C) or E))
theorem-size     15
proof            (modus-ponens tm-92 tm-383 ((Am (-> A A)) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23483.        (((A -> B) or (A -> A)) -> (((C and D) -> C) or E)), M:tm-92, m:tm-383, u:((Am (-> A A)) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23484
in-theory        23484
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C and D) -> C) or E)))
theorem-size     11
proof            (modus-ponens tm-84 tm-383 ((A Am) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-3)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23484.        (A -> (B -> (((C and D) -> C) or E))), M:tm-84, m:tm-383, u:((A Am) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23485
in-theory        23485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-83 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23485.        ((A -> (B -> (C -> B))) and (D -> (((E and F) -> E) or G))), M:tm-83, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23486
in-theory        23486
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-80 tm-383 ((Am (-> A (-> B A))) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23486.        ((A or (B -> (C -> B))) -> (((D and E) -> D) or F)), M:tm-80, m:tm-383, u:((Am (-> A (-> B A))) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23487
in-theory        23487
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((((A and B) -> A) or C) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-383 ((Am (not (not (-> (or (-> (and Bm Cm) Bm) Dm) B)))) (A (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-10 tm-1 tm-6 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23487.        ((not (not ((((A and B) -> A) or C) -> D))) -> D), M:tm-77, m:tm-383, u:((Am (not (not (-> (or (-> (and Bm Cm) Bm) Dm) B)))) (A (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23488
in-theory        23488
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C and D) -> C) or E)))
theorem-size     15
proof            (modus-ponens tm-76 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23488.        (((not (not A)) -> A) and (B -> (((C and D) -> C) or E))), M:tm-76, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23489
in-theory        23489
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B and C) -> B) or D))
theorem-size     13
proof            (modus-ponens tm-73 tm-383 ((A Am) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-10 tm-1 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23489.        (((not (not A)) or A) -> (((B and C) -> B) or D)), M:tm-73, m:tm-383, u:((A Am) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23490
in-theory        23490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D and E) -> D) or F)))
theorem-size     21
proof            (modus-ponens tm-69 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23490.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D and E) -> D) or F))), M:tm-69, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23491
in-theory        23491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C and D) -> C) or E))
theorem-size     19
proof            (modus-ponens tm-66 tm-383 ((Am (-> (-> A (not B)) (not A))) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-9 tm-1 tm-6 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23491.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C and D) -> C) or E)), M:tm-66, m:tm-383, u:((Am (-> (-> A (not B)) (not A))) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23492
in-theory        23492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-54 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23492.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> E) or G))), M:tm-54, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23493
in-theory        23493
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) or F))
theorem-size     21
proof            (modus-ponens tm-51 tm-383 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23493.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> D) or F)), M:tm-51, m:tm-383, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23494
in-theory        23494
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C and D) -> C) or E))
theorem-size     13
proof            (modus-ponens tm-50 tm-383 ((Am (or A B)) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23494.        ((A or (B or A)) -> (((C and D) -> C) or E)), M:tm-50, m:tm-383, u:((Am (or A B)) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23495
in-theory        23495
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C and D) -> C) or E))
theorem-size     13
proof            (modus-ponens tm-49 tm-383 ((Am (or A B)) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-6 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23495.        ((A or (A or B)) -> (((C and D) -> C) or E)), M:tm-49, m:tm-383, u:((Am (or A B)) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23496
in-theory        23496
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C and D) -> C) or E))
theorem-size     15
proof            (modus-ponens tm-48 tm-383 ((Am (-> A (and B A))) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23496.        ((A or (B -> (A and B))) -> (((C and D) -> C) or E)), M:tm-48, m:tm-383, u:((Am (-> A (and B A))) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23497
in-theory        23497
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C and D) -> C) or E))
theorem-size     13
proof            (modus-ponens tm-47 tm-383 ((A Am) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-4 tm-1 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23497.        (((A and B) or B) -> (((C and D) -> C) or E)), M:tm-47, m:tm-383, u:((A Am) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23498
in-theory        23498
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C and D) -> C) or E))
theorem-size     13
proof            (modus-ponens tm-46 tm-383 ((A Am) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23498.        (((A and B) or A) -> (((C and D) -> C) or E)), M:tm-46, m:tm-383, u:((A Am) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23499
in-theory        23499
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) or F))
theorem-size     21
proof            (modus-ponens tm-45 tm-383 ((Am (-> (-> A B) (-> A C))) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23499.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) or F)), M:tm-45, m:tm-383, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23500
in-theory        23500
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C and D) -> C) or E))
theorem-size     13
proof            (modus-ponens tm-44 tm-383 ((Am (-> A B)) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23500.        ((A or (B -> A)) -> (((C and D) -> C) or E)), M:tm-44, m:tm-383, u:((Am (-> A B)) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23501
in-theory        23501
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-42 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23501.        ((A -> (B or A)) and (C -> (((D and E) -> D) or F))), M:tm-42, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23502
in-theory        23502
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-32 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23502.        ((A -> (A or B)) and (C -> (((D and E) -> D) or F))), M:tm-32, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23503
in-theory        23503
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B and C) -> B) or D)))
theorem-size     11
proof            (modus-ponens tm-24 tm-383 ((A Am) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23503.        (A -> (A and (((B and C) -> B) or D))), M:tm-24, m:tm-383, u:((A Am) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23504
in-theory        23504
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) or F)))
theorem-size     17
proof            (modus-ponens tm-23 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23504.        ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) or F))), M:tm-23, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23505
in-theory        23505
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-22 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23505.        (((A and B) -> B) and (C -> (((D and E) -> D) or F))), M:tm-22, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23506
in-theory        23506
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-21 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23506.        (((A and B) -> A) and (C -> (((D and E) -> D) or F))), M:tm-21, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23507
in-theory        23507
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-20 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23507.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) or G))), M:tm-20, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23508
in-theory        23508
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-19 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23508.        ((A -> (B -> A)) and (C -> (((D and E) -> D) or F))), M:tm-19, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23509
in-theory        23509
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((((B and C) -> B) or D) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-383 ((Am (and A (-> (or (-> (and Bm Cm) Bm) Dm) C))) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-4 tm-1 tm-6 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23509.        ((A and ((((B and C) -> B) or D) -> E)) -> E), M:tm-17, m:tm-383, u:((Am (and A (-> (or (-> (and Bm Cm) Bm) Dm) C))) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23510
in-theory        23510
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) -> A) or C) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-383 ((Am (and (-> (or (-> (and Bm Cm) Bm) Dm) B) C)) (A (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-3 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23510.        ((((((A and B) -> A) or C) -> D) and E) -> D), M:tm-15, m:tm-383, u:((Am (and (-> (or (-> (and Bm Cm) Bm) Dm) B) C)) (A (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23511
in-theory        23511
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> B) or D))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-383 ((A Am) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-9 tm-1 tm-6 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23511.        ((A -> (not (((B and C) -> B) or D))) -> (not A)), M:tm-9, m:tm-383, u:((A Am) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23512
in-theory        23512
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) -> D) -> ((E or (((A and B) -> A) or C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-383 ((A Am) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23512.        (((((A and B) -> A) or C) -> D) -> ((E or (((A and B) -> A) or C)) -> D)), M:tm-8, m:tm-383, u:((A Am) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-23513
in-theory        23513
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C and D) -> C) or E)))
theorem-size     11
proof            (modus-ponens tm-7 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-7 tm-1 tm-6 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23513.        (A or (B -> (((C and D) -> C) or E))), M:tm-7, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23514
in-theory        23514
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-6 tm-1 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23514.        ((A -> (((B and C) -> B) or D)) or E), M:tm-6, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23515
in-theory        23515
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C and D) -> C) or E)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23515.        (A -> ((B -> (((C and D) -> C) or E)) and A)), M:tm-5, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-23516
in-theory        23516
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-382 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23516.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-382, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23517
in-theory        23517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-373 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23517.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I))), M:tm-373, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23518
in-theory        23518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-364 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23518.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-364, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23519
in-theory        23519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-354 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23519.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-354, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23520
in-theory        23520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23520.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23521
in-theory        23521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G)))
theorem-size     25
proof            (modus-ponens tm-338 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23521.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G))), M:tm-338, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23522
in-theory        23522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C and D) -> D) or E))))
theorem-size     39
proof            (modus-ponens tm-327 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23522.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C and D) -> D) or E)))), M:tm-327, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23523
in-theory        23523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C and D) -> D) or E))))
theorem-size     37
proof            (modus-ponens tm-326 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23523.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C and D) -> D) or E)))), M:tm-326, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23524
in-theory        23524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C and D) -> D) or E))))
theorem-size     37
proof            (modus-ponens tm-325 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23524.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C and D) -> D) or E)))), M:tm-325, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23525
in-theory        23525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C and D) -> D) or E))))
theorem-size     45
proof            (modus-ponens tm-324 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23525.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C and D) -> D) or E)))), M:tm-324, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23526
in-theory        23526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C and D) -> D) or E))))
theorem-size     37
proof            (modus-ponens tm-323 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23526.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C and D) -> D) or E)))), M:tm-323, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23527
in-theory        23527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23527.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and ((F and G) -> G)), M:tm-322, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23528
in-theory        23528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23528.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and ((F and G) -> F)), M:tm-320, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23529
in-theory        23529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23529.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23530
in-theory        23530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23530.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (F -> (G -> F))), M:tm-315, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23531
in-theory        23531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (F or ((A -> (B -> (A and B))) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-311 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23531.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (F or ((A -> (B -> (A and B))) and (((C and D) -> D) or E)))), M:tm-311, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23532
in-theory        23532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23532.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) or F)), M:tm-310, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23533
in-theory        23533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (F -> (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23533.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (F -> (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and F))), M:tm-309, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23534
in-theory        23534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (((C and D) -> D) or E))
theorem-size     23
proof            (modus-ponens tm-308 tm-384 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (and Cm Dm) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23534.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (((C and D) -> D) or E)), M:tm-308, m:tm-384, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (and Cm Dm) Dm) Em)))
================================================================
tm-name          tm-23535
in-theory        23535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-384 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (and Cm Dm) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23535.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (A -> (B -> (A and B)))), M:tm-307, m:tm-384, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> (and Cm Dm) Dm) Em)))
================================================================
tm-name          tm-23536
in-theory        23536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (F -> ((A -> (B -> (A and B))) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-305 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23536.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (F -> ((A -> (B -> (A and B))) and (((C and D) -> D) or E)))), M:tm-305, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23537
in-theory        23537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-303 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23537.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-303, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23538
in-theory        23538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-270 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23538.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-270, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23539
in-theory        23539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-239 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23539.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-239, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23540
in-theory        23540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I)))
theorem-size     33
proof            (modus-ponens tm-210 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23540.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I))), M:tm-210, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23541
in-theory        23541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-183 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23541.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-183, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23542
in-theory        23542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-157 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23542.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-157, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23543
in-theory        23543
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     31
proof            (modus-ponens tm-147 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23543.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-147, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23544
in-theory        23544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-134 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23544.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-134, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23545
in-theory        23545
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     31
proof            (modus-ponens tm-125 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23545.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-125, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23546
in-theory        23546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-113 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23546.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I))), M:tm-113, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23547
in-theory        23547
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     35
proof            (modus-ponens tm-105 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23547.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-105, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23548
in-theory        23548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-95 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23548.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G))), M:tm-95, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23549
in-theory        23549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-83 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23549.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-83, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23550
in-theory        23550
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D and E) -> E) or F)))
theorem-size     21
proof            (modus-ponens tm-76 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-10 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23550.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D and E) -> E) or F))), M:tm-76, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23551
in-theory        23551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G)))
theorem-size     27
proof            (modus-ponens tm-69 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-9 tm-6 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23551.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G))), M:tm-69, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23552
in-theory        23552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-54 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23552.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-54, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23553
in-theory        23553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-42 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23553.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G))), M:tm-42, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23554
in-theory        23554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-32 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23554.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G))), M:tm-32, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23555
in-theory        23555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-23 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23555.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G))), M:tm-23, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23556
in-theory        23556
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-22 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23556.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G))), M:tm-22, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23557
in-theory        23557
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-21 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23557.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G))), M:tm-21, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23558
in-theory        23558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-20 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23558.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-20, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23559
in-theory        23559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-19 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23559.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E and F) -> F) or G))), M:tm-19, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23560
in-theory        23560
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (((D and E) -> E) or F)))
theorem-size     17
proof            (modus-ponens tm-7 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-7 tm-5 tm-6 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23560.        (A or ((B -> (C -> (B and C))) and (((D and E) -> E) or F))), M:tm-7, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23561
in-theory        23561
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23561.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) or F), M:tm-6, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23562
in-theory        23562
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (((D and E) -> E) or F)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23562.        (A -> (((B -> (C -> (B and C))) and (((D and E) -> E) or F)) and A)), M:tm-5, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23563
in-theory        23563
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (((D and E) -> E) or F)))
theorem-size     17
proof            (modus-ponens tm-1 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-1 tm-5 tm-6 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23563.        (A -> ((B -> (C -> (B and C))) and (((D and E) -> E) or F))), M:tm-1, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23564
in-theory        23564
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23564.        ((((A and B) -> A) or C) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-382, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23565
in-theory        23565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23565.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G and H) -> H) or I))), M:tm-373, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23566
in-theory        23566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23566.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-364, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23567
in-theory        23567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23567.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-354, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23568
in-theory        23568
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23568.        ((((A and B) -> B) and (((C and D) -> D) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23569
in-theory        23569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23569.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E and F) -> F) or G))), M:tm-338, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23570
in-theory        23570
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C and D) -> D) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23570.        ((((A and B) -> B) and (((C and D) -> D) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C and D) -> D) or E)))), M:tm-327, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23571
in-theory        23571
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and (((F and G) -> G) and (((A and B) -> B) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23571.        ((((A and B) -> B) and (((C and D) -> D) or E)) and (((F and G) -> G) and (((A and B) -> B) and (((C and D) -> D) or E)))), M:tm-326, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23572
in-theory        23572
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and (((F and G) -> F) and (((A and B) -> B) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23572.        ((((A and B) -> B) and (((C and D) -> D) or E)) and (((F and G) -> F) and (((A and B) -> B) and (((C and D) -> D) or E)))), M:tm-325, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23573
in-theory        23573
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C and D) -> D) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23573.        ((((A and B) -> B) and (((C and D) -> D) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C and D) -> D) or E)))), M:tm-324, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23574
in-theory        23574
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and ((F -> (G -> F)) and (((A and B) -> B) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23574.        ((((A and B) -> B) and (((C and D) -> D) or E)) and ((F -> (G -> F)) and (((A and B) -> B) and (((C and D) -> D) or E)))), M:tm-323, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23575
in-theory        23575
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23575.        ((((A and B) -> B) and (((C and D) -> D) or E)) and ((F and G) -> G)), M:tm-322, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23576
in-theory        23576
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23576.        ((((A and B) -> B) and (((C and D) -> D) or E)) and ((F and G) -> F)), M:tm-320, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23577
in-theory        23577
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23577.        ((((A and B) -> B) and (((C and D) -> D) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23578
in-theory        23578
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23578.        ((((A and B) -> B) and (((C and D) -> D) or E)) and (F -> (G -> F))), M:tm-315, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23579
in-theory        23579
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and (F or (((A and B) -> B) and (((C and D) -> D) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23579.        ((((A and B) -> B) and (((C and D) -> D) or E)) and (F or (((A and B) -> B) and (((C and D) -> D) or E)))), M:tm-311, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23580
in-theory        23580
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and ((((A and B) -> B) and (((C and D) -> D) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23580.        ((((A and B) -> B) and (((C and D) -> D) or E)) and ((((A and B) -> B) and (((C and D) -> D) or E)) or F)), M:tm-310, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23581
in-theory        23581
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and (F -> ((((A and B) -> B) and (((C and D) -> D) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23581.        ((((A and B) -> B) and (((C and D) -> D) or E)) and (F -> ((((A and B) -> B) and (((C and D) -> D) or E)) and F))), M:tm-309, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23582
in-theory        23582
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and (((C and D) -> D) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-385 ((A (-> (and Am Bm) Bm)) (B (or (-> (and Cm Dm) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23582.        ((((A and B) -> B) and (((C and D) -> D) or E)) and (((C and D) -> D) or E)), M:tm-308, m:tm-385, u:((A (-> (and Am Bm) Bm)) (B (or (-> (and Cm Dm) Dm) Em)))
================================================================
tm-name          tm-23583
in-theory        23583
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-385 ((A (-> (and Am Bm) Bm)) (B (or (-> (and Cm Dm) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23583.        ((((A and B) -> B) and (((C and D) -> D) or E)) and ((A and B) -> B)), M:tm-307, m:tm-385, u:((A (-> (and Am Bm) Bm)) (B (or (-> (and Cm Dm) Dm) Em)))
================================================================
tm-name          tm-23584
in-theory        23584
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and (F -> (((A and B) -> B) and (((C and D) -> D) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23584.        ((((A and B) -> B) and (((C and D) -> D) or E)) and (F -> (((A and B) -> B) and (((C and D) -> D) or E)))), M:tm-305, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23585
in-theory        23585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23585.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-303, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23586
in-theory        23586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23586.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-270, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23587
in-theory        23587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23587.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-239, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23588
in-theory        23588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23588.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G and H) -> H) or I))), M:tm-210, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23589
in-theory        23589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23589.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-183, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23590
in-theory        23590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23590.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-157, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23591
in-theory        23591
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23591.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-147, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23592
in-theory        23592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23592.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-134, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23593
in-theory        23593
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23593.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-125, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23594
in-theory        23594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23594.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G and H) -> H) or I))), M:tm-113, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23595
in-theory        23595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23595.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-105, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23596
in-theory        23596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23596.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E and F) -> F) or G))), M:tm-95, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23597
in-theory        23597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23597.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-83, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23598
in-theory        23598
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (((D and E) -> E) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-10 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23598.        (((not (not A)) -> A) and (((B and C) -> C) and (((D and E) -> E) or F))), M:tm-76, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23599
in-theory        23599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E and F) -> F) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-9 tm-4 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23599.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E and F) -> F) or G))), M:tm-69, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23600
in-theory        23600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23600.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-54, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23601
in-theory        23601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23601.        ((A -> (B or A)) and (((C and D) -> D) and (((E and F) -> F) or G))), M:tm-42, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23602
in-theory        23602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23602.        ((A -> (A or B)) and (((C and D) -> D) and (((E and F) -> F) or G))), M:tm-32, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23603
in-theory        23603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23603.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E and F) -> F) or G))), M:tm-23, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23604
in-theory        23604
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23604.        (((A and B) -> B) and (((C and D) -> D) and (((E and F) -> F) or G))), M:tm-22, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23605
in-theory        23605
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23605.        (((A and B) -> A) and (((C and D) -> D) and (((E and F) -> F) or G))), M:tm-21, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23606
in-theory        23606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23606.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-20, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23607
in-theory        23607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23607.        ((A -> (B -> A)) and (((C and D) -> D) and (((E and F) -> F) or G))), M:tm-19, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23608
in-theory        23608
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-7 tm-5 tm-4 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23608.        (A or (((B and C) -> C) and (((D and E) -> E) or F))), M:tm-7, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23609
in-theory        23609
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23609.        ((((A and B) -> B) and (((C and D) -> D) or E)) or F), M:tm-6, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23610
in-theory        23610
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (((D and E) -> E) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23610.        (A -> ((((B and C) -> C) and (((D and E) -> E) or F)) and A)), M:tm-5, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23611
in-theory        23611
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-1 tm-5 tm-4 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23611.        (A -> (((B and C) -> C) and (((D and E) -> E) or F))), M:tm-1, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23612
in-theory        23612
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23612.        ((((A and B) -> A) or C) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-382, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23613
in-theory        23613
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23613.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G and H) -> H) or I))), M:tm-373, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23614
in-theory        23614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23614.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-364, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23615
in-theory        23615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23615.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-354, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23616
in-theory        23616
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23616.        ((((A and B) -> A) and (((C and D) -> D) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23617
in-theory        23617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23617.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E and F) -> F) or G))), M:tm-338, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23618
in-theory        23618
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C and D) -> D) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23618.        ((((A and B) -> A) and (((C and D) -> D) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C and D) -> D) or E)))), M:tm-327, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23619
in-theory        23619
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and (((F and G) -> G) and (((A and B) -> A) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23619.        ((((A and B) -> A) and (((C and D) -> D) or E)) and (((F and G) -> G) and (((A and B) -> A) and (((C and D) -> D) or E)))), M:tm-326, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23620
in-theory        23620
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and (((F and G) -> F) and (((A and B) -> A) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23620.        ((((A and B) -> A) and (((C and D) -> D) or E)) and (((F and G) -> F) and (((A and B) -> A) and (((C and D) -> D) or E)))), M:tm-325, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23621
in-theory        23621
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C and D) -> D) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23621.        ((((A and B) -> A) and (((C and D) -> D) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C and D) -> D) or E)))), M:tm-324, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23622
in-theory        23622
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and ((F -> (G -> F)) and (((A and B) -> A) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23622.        ((((A and B) -> A) and (((C and D) -> D) or E)) and ((F -> (G -> F)) and (((A and B) -> A) and (((C and D) -> D) or E)))), M:tm-323, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23623
in-theory        23623
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23623.        ((((A and B) -> A) and (((C and D) -> D) or E)) and ((F and G) -> G)), M:tm-322, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23624
in-theory        23624
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23624.        ((((A and B) -> A) and (((C and D) -> D) or E)) and ((F and G) -> F)), M:tm-320, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23625
in-theory        23625
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23625.        ((((A and B) -> A) and (((C and D) -> D) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23626
in-theory        23626
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23626.        ((((A and B) -> A) and (((C and D) -> D) or E)) and (F -> (G -> F))), M:tm-315, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23627
in-theory        23627
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and (F or (((A and B) -> A) and (((C and D) -> D) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23627.        ((((A and B) -> A) and (((C and D) -> D) or E)) and (F or (((A and B) -> A) and (((C and D) -> D) or E)))), M:tm-311, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23628
in-theory        23628
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and ((((A and B) -> A) and (((C and D) -> D) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23628.        ((((A and B) -> A) and (((C and D) -> D) or E)) and ((((A and B) -> A) and (((C and D) -> D) or E)) or F)), M:tm-310, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23629
in-theory        23629
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and (F -> ((((A and B) -> A) and (((C and D) -> D) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23629.        ((((A and B) -> A) and (((C and D) -> D) or E)) and (F -> ((((A and B) -> A) and (((C and D) -> D) or E)) and F))), M:tm-309, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23630
in-theory        23630
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and (((C and D) -> D) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-386 ((A (-> (and Am Bm) Am)) (B (or (-> (and Cm Dm) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23630.        ((((A and B) -> A) and (((C and D) -> D) or E)) and (((C and D) -> D) or E)), M:tm-308, m:tm-386, u:((A (-> (and Am Bm) Am)) (B (or (-> (and Cm Dm) Dm) Em)))
================================================================
tm-name          tm-23631
in-theory        23631
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-386 ((A (-> (and Am Bm) Am)) (B (or (-> (and Cm Dm) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23631.        ((((A and B) -> A) and (((C and D) -> D) or E)) and ((A and B) -> A)), M:tm-307, m:tm-386, u:((A (-> (and Am Bm) Am)) (B (or (-> (and Cm Dm) Dm) Em)))
================================================================
tm-name          tm-23632
in-theory        23632
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and (F -> (((A and B) -> A) and (((C and D) -> D) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23632.        ((((A and B) -> A) and (((C and D) -> D) or E)) and (F -> (((A and B) -> A) and (((C and D) -> D) or E)))), M:tm-305, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23633
in-theory        23633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23633.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-303, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23634
in-theory        23634
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23634.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-270, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23635
in-theory        23635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23635.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-239, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23636
in-theory        23636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23636.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G and H) -> H) or I))), M:tm-210, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23637
in-theory        23637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23637.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-183, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23638
in-theory        23638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23638.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-157, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23639
in-theory        23639
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23639.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-147, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23640
in-theory        23640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23640.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-134, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23641
in-theory        23641
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23641.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-125, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23642
in-theory        23642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23642.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G and H) -> H) or I))), M:tm-113, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23643
in-theory        23643
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23643.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-105, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23644
in-theory        23644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23644.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E and F) -> F) or G))), M:tm-95, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23645
in-theory        23645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23645.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-83, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23646
in-theory        23646
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (((D and E) -> E) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-10 tm-3 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23646.        (((not (not A)) -> A) and (((B and C) -> B) and (((D and E) -> E) or F))), M:tm-76, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23647
in-theory        23647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E and F) -> F) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-9 tm-3 tm-6 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23647.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E and F) -> F) or G))), M:tm-69, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23648
in-theory        23648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23648.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-54, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23649
in-theory        23649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23649.        ((A -> (B or A)) and (((C and D) -> C) and (((E and F) -> F) or G))), M:tm-42, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23650
in-theory        23650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23650.        ((A -> (A or B)) and (((C and D) -> C) and (((E and F) -> F) or G))), M:tm-32, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23651
in-theory        23651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23651.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E and F) -> F) or G))), M:tm-23, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23652
in-theory        23652
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23652.        (((A and B) -> B) and (((C and D) -> C) and (((E and F) -> F) or G))), M:tm-22, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23653
in-theory        23653
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23653.        (((A and B) -> A) and (((C and D) -> C) and (((E and F) -> F) or G))), M:tm-21, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23654
in-theory        23654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23654.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-20, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23655
in-theory        23655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23655.        ((A -> (B -> A)) and (((C and D) -> C) and (((E and F) -> F) or G))), M:tm-19, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23656
in-theory        23656
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-7 tm-5 tm-3 tm-6 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23656.        (A or (((B and C) -> B) and (((D and E) -> E) or F))), M:tm-7, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23657
in-theory        23657
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-6 tm-5 tm-3 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23657.        ((((A and B) -> A) and (((C and D) -> D) or E)) or F), M:tm-6, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23658
in-theory        23658
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (((D and E) -> E) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23658.        (A -> ((((B and C) -> B) and (((D and E) -> E) or F)) and A)), M:tm-5, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23659
in-theory        23659
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-1 tm-5 tm-3 tm-6 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23659.        (A -> (((B and C) -> B) and (((D and E) -> E) or F))), M:tm-1, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23660
in-theory        23660
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23660.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-382, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23661
in-theory        23661
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> I) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23661.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> I) or J))), M:tm-373, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23662
in-theory        23662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23662.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-364, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23663
in-theory        23663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23663.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-354, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23664
in-theory        23664
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23664.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23665
in-theory        23665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23665.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H))), M:tm-338, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23666
in-theory        23666
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23666.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)))), M:tm-327, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23667
in-theory        23667
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23667.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)))), M:tm-326, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23668
in-theory        23668
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23668.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)))), M:tm-325, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23669
in-theory        23669
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23669.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)))), M:tm-324, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23670
in-theory        23670
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23670.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)))), M:tm-323, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23671
in-theory        23671
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23671.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((G and H) -> H)), M:tm-322, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23672
in-theory        23672
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23672.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((G and H) -> G)), M:tm-320, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23673
in-theory        23673
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23673.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23674
in-theory        23674
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23674.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (G -> (H -> G))), M:tm-315, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23675
in-theory        23675
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23675.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)))), M:tm-311, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23676
in-theory        23676
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23676.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) or G)), M:tm-310, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23677
in-theory        23677
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23677.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and G))), M:tm-309, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23678
in-theory        23678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (((D and E) -> E) or F))
theorem-size     29
proof            (modus-ponens tm-308 tm-387 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (and Dm Em) Em) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23678.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (((D and E) -> E) or F)), M:tm-308, m:tm-387, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (and Dm Em) Em) Fm)))
================================================================
tm-name          tm-23679
in-theory        23679
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-387 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (and Dm Em) Em) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23679.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-387, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (and Dm Em) Em) Fm)))
================================================================
tm-name          tm-23680
in-theory        23680
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23680.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)))), M:tm-305, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23681
in-theory        23681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23681.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-303, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23682
in-theory        23682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23682.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-270, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23683
in-theory        23683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23683.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-239, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23684
in-theory        23684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> I) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23684.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> I) or J))), M:tm-210, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23685
in-theory        23685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23685.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-183, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23686
in-theory        23686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23686.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-157, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23687
in-theory        23687
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23687.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-147, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23688
in-theory        23688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23688.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-134, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23689
in-theory        23689
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23689.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-125, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23690
in-theory        23690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> I) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23690.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> I) or J))), M:tm-113, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23691
in-theory        23691
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23691.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-105, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23692
in-theory        23692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23692.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H))), M:tm-95, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23693
in-theory        23693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23693.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-83, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23694
in-theory        23694
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> F) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23694.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> F) or G))), M:tm-76, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23695
in-theory        23695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-6 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23695.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H))), M:tm-69, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23696
in-theory        23696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23696.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-54, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23697
in-theory        23697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23697.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H))), M:tm-42, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23698
in-theory        23698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23698.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H))), M:tm-32, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23699
in-theory        23699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23699.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H))), M:tm-23, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23700
in-theory        23700
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23700.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H))), M:tm-22, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23701
in-theory        23701
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23701.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H))), M:tm-21, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23702
in-theory        23702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23702.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-20, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23703
in-theory        23703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23703.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F and G) -> G) or H))), M:tm-19, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23704
in-theory        23704
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-7 tm-5 tm-2 tm-6 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23704.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> F) or G))), M:tm-7, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23705
in-theory        23705
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-6 tm-5 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23705.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) or G), M:tm-6, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23706
in-theory        23706
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> F) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23706.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> F) or G)) and A)), M:tm-5, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23707
in-theory        23707
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-1 tm-5 tm-2 tm-6 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23707.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E and F) -> F) or G))), M:tm-1, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-23708
in-theory        23708
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23708.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-382, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23709
in-theory        23709
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23709.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G and H) -> H) or I))), M:tm-373, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23710
in-theory        23710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23710.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-364, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23711
in-theory        23711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23711.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-354, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23712
in-theory        23712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23712.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23713
in-theory        23713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23713.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E and F) -> F) or G))), M:tm-338, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23714
in-theory        23714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C and D) -> D) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23714.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C and D) -> D) or E)))), M:tm-327, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23715
in-theory        23715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and (((F and G) -> G) and ((A -> (B -> A)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23715.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and (((F and G) -> G) and ((A -> (B -> A)) and (((C and D) -> D) or E)))), M:tm-326, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23716
in-theory        23716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and (((F and G) -> F) and ((A -> (B -> A)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23716.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and (((F and G) -> F) and ((A -> (B -> A)) and (((C and D) -> D) or E)))), M:tm-325, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23717
in-theory        23717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C and D) -> D) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23717.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C and D) -> D) or E)))), M:tm-324, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23718
in-theory        23718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23718.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C and D) -> D) or E)))), M:tm-323, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23719
in-theory        23719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23719.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and ((F and G) -> G)), M:tm-322, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23720
in-theory        23720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23720.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and ((F and G) -> F)), M:tm-320, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23721
in-theory        23721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23721.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23722
in-theory        23722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23722.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and (F -> (G -> F))), M:tm-315, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23723
in-theory        23723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and (F or ((A -> (B -> A)) and (((C and D) -> D) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23723.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and (F or ((A -> (B -> A)) and (((C and D) -> D) or E)))), M:tm-311, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23724
in-theory        23724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and (((A -> (B -> A)) and (((C and D) -> D) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23724.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and (((A -> (B -> A)) and (((C and D) -> D) or E)) or F)), M:tm-310, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23725
in-theory        23725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and (F -> (((A -> (B -> A)) and (((C and D) -> D) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23725.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and (F -> (((A -> (B -> A)) and (((C and D) -> D) or E)) and F))), M:tm-309, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23726
in-theory        23726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and (((C and D) -> D) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-388 ((A (-> Am (-> Bm Am))) (B (or (-> (and Cm Dm) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23726.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and (((C and D) -> D) or E)), M:tm-308, m:tm-388, u:((A (-> Am (-> Bm Am))) (B (or (-> (and Cm Dm) Dm) Em)))
================================================================
tm-name          tm-23727
in-theory        23727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-388 ((A (-> Am (-> Bm Am))) (B (or (-> (and Cm Dm) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23727.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and (A -> (B -> A))), M:tm-307, m:tm-388, u:((A (-> Am (-> Bm Am))) (B (or (-> (and Cm Dm) Dm) Em)))
================================================================
tm-name          tm-23728
in-theory        23728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and (F -> ((A -> (B -> A)) and (((C and D) -> D) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23728.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and (F -> ((A -> (B -> A)) and (((C and D) -> D) or E)))), M:tm-305, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23729
in-theory        23729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23729.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-303, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23730
in-theory        23730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23730.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-270, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23731
in-theory        23731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23731.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-239, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23732
in-theory        23732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23732.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G and H) -> H) or I))), M:tm-210, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23733
in-theory        23733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23733.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-183, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23734
in-theory        23734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23734.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-157, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23735
in-theory        23735
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23735.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-147, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23736
in-theory        23736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23736.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-134, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23737
in-theory        23737
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23737.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-125, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23738
in-theory        23738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23738.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G and H) -> H) or I))), M:tm-113, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23739
in-theory        23739
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23739.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-105, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23740
in-theory        23740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23740.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E and F) -> F) or G))), M:tm-95, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23741
in-theory        23741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23741.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-83, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23742
in-theory        23742
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (((D and E) -> E) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23742.        (((not (not A)) -> A) and ((B -> (C -> B)) and (((D and E) -> E) or F))), M:tm-76, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23743
in-theory        23743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E and F) -> F) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23743.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E and F) -> F) or G))), M:tm-69, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23744
in-theory        23744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23744.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-54, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23745
in-theory        23745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23745.        ((A -> (B or A)) and ((C -> (D -> C)) and (((E and F) -> F) or G))), M:tm-42, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23746
in-theory        23746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23746.        ((A -> (A or B)) and ((C -> (D -> C)) and (((E and F) -> F) or G))), M:tm-32, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23747
in-theory        23747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23747.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E and F) -> F) or G))), M:tm-23, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23748
in-theory        23748
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23748.        (((A and B) -> B) and ((C -> (D -> C)) and (((E and F) -> F) or G))), M:tm-22, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23749
in-theory        23749
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23749.        (((A and B) -> A) and ((C -> (D -> C)) and (((E and F) -> F) or G))), M:tm-21, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23750
in-theory        23750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23750.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-20, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23751
in-theory        23751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23751.        ((A -> (B -> A)) and ((C -> (D -> C)) and (((E and F) -> F) or G))), M:tm-19, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23752
in-theory        23752
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-7 tm-5 tm-1 tm-6 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23752.        (A or ((B -> (C -> B)) and (((D and E) -> E) or F))), M:tm-7, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23753
in-theory        23753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-6 tm-5 tm-1 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23753.        (((A -> (B -> A)) and (((C and D) -> D) or E)) or F), M:tm-6, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23754
in-theory        23754
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (((D and E) -> E) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23754.        (A -> (((B -> (C -> B)) and (((D and E) -> E) or F)) and A)), M:tm-5, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23755
in-theory        23755
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-1 tm-5 tm-6 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23755.        (A -> ((B -> (C -> B)) and (((D and E) -> E) or F))), M:tm-1, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-23756
in-theory        23756
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-382 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23756.        ((((A and B) -> A) or C) and (D or (((E and F) -> F) or G))), M:tm-382, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23757
in-theory        23757
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-373 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23757.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F and G) -> G) or H))), M:tm-373, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23758
in-theory        23758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-364 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23758.        (((A -> (B -> A)) or C) and (D or (((E and F) -> F) or G))), M:tm-364, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23759
in-theory        23759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-354 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23759.        ((A -> (B -> (C -> (B and C)))) and (D or (((E and F) -> F) or G))), M:tm-354, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23760
in-theory        23760
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23760.        ((A or (((B and C) -> C) or D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23761
in-theory        23761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (((D and E) -> E) or F)))
theorem-size     19
proof            (modus-ponens tm-338 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23761.        (((A -> B) -> (A -> (A and B))) and (C or (((D and E) -> E) or F))), M:tm-338, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23762
in-theory        23762
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and ((E -> (F -> (E and F))) and (A or (((B and C) -> C) or D))))
theorem-size     27
proof            (modus-ponens tm-327 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23762.        ((A or (((B and C) -> C) or D)) and ((E -> (F -> (E and F))) and (A or (((B and C) -> C) or D)))), M:tm-327, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23763
in-theory        23763
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and (((E and F) -> F) and (A or (((B and C) -> C) or D))))
theorem-size     25
proof            (modus-ponens tm-326 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23763.        ((A or (((B and C) -> C) or D)) and (((E and F) -> F) and (A or (((B and C) -> C) or D)))), M:tm-326, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23764
in-theory        23764
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and (((E and F) -> E) and (A or (((B and C) -> C) or D))))
theorem-size     25
proof            (modus-ponens tm-325 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23764.        ((A or (((B and C) -> C) or D)) and (((E and F) -> E) and (A or (((B and C) -> C) or D)))), M:tm-325, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23765
in-theory        23765
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B and C) -> C) or D))))
theorem-size     33
proof            (modus-ponens tm-324 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23765.        ((A or (((B and C) -> C) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B and C) -> C) or D)))), M:tm-324, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23766
in-theory        23766
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and ((E -> (F -> E)) and (A or (((B and C) -> C) or D))))
theorem-size     25
proof            (modus-ponens tm-323 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23766.        ((A or (((B and C) -> C) or D)) and ((E -> (F -> E)) and (A or (((B and C) -> C) or D)))), M:tm-323, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23767
in-theory        23767
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23767.        ((A or (((B and C) -> C) or D)) and ((E and F) -> F)), M:tm-322, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23768
in-theory        23768
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23768.        ((A or (((B and C) -> C) or D)) and ((E and F) -> E)), M:tm-320, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23769
in-theory        23769
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23769.        ((A or (((B and C) -> C) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23770
in-theory        23770
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23770.        ((A or (((B and C) -> C) or D)) and (E -> (F -> E))), M:tm-315, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23771
in-theory        23771
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and (E or (A or (((B and C) -> C) or D))))
theorem-size     21
proof            (modus-ponens tm-311 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23771.        ((A or (((B and C) -> C) or D)) and (E or (A or (((B and C) -> C) or D)))), M:tm-311, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23772
in-theory        23772
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and ((A or (((B and C) -> C) or D)) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23772.        ((A or (((B and C) -> C) or D)) and ((A or (((B and C) -> C) or D)) or E)), M:tm-310, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23773
in-theory        23773
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and (E -> ((A or (((B and C) -> C) or D)) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23773.        ((A or (((B and C) -> C) or D)) and (E -> ((A or (((B and C) -> C) or D)) and E))), M:tm-309, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23774
in-theory        23774
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and (E -> (A or (((B and C) -> C) or D))))
theorem-size     21
proof            (modus-ponens tm-305 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23774.        ((A or (((B and C) -> C) or D)) and (E -> (A or (((B and C) -> C) or D)))), M:tm-305, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23775
in-theory        23775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-303 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23775.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E and F) -> F) or G))), M:tm-303, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23776
in-theory        23776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-270 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23776.        ((A -> (((B and C) -> C) and A)) and (D or (((E and F) -> F) or G))), M:tm-270, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23777
in-theory        23777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-239 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23777.        ((A -> (((B and C) -> B) and A)) and (D or (((E and F) -> F) or G))), M:tm-239, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23778
in-theory        23778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-210 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23778.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F and G) -> G) or H))), M:tm-210, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23779
in-theory        23779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-183 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23779.        ((A -> ((B -> (C -> B)) and A)) and (D or (((E and F) -> F) or G))), M:tm-183, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23780
in-theory        23780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-157 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23780.        ((A -> ((B and C) -> C)) and (D or (((E and F) -> F) or G))), M:tm-157, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23781
in-theory        23781
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E and F) -> F) or G)))
theorem-size     25
proof            (modus-ponens tm-147 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23781.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E and F) -> F) or G))), M:tm-147, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23782
in-theory        23782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-134 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23782.        ((A -> ((B and C) -> B)) and (D or (((E and F) -> F) or G))), M:tm-134, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23783
in-theory        23783
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E and F) -> F) or G)))
theorem-size     25
proof            (modus-ponens tm-125 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23783.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E and F) -> F) or G))), M:tm-125, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23784
in-theory        23784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-113 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23784.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F and G) -> G) or H))), M:tm-113, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23785
in-theory        23785
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E and F) -> F) or G)))
theorem-size     29
proof            (modus-ponens tm-105 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23785.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E and F) -> F) or G))), M:tm-105, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23786
in-theory        23786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (((D and E) -> E) or F)))
theorem-size     17
proof            (modus-ponens tm-95 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23786.        (((A -> B) -> (A -> A)) and (C or (((D and E) -> E) or F))), M:tm-95, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23787
in-theory        23787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-83 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23787.        ((A -> (B -> (C -> B))) and (D or (((E and F) -> F) or G))), M:tm-83, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23788
in-theory        23788
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (((C and D) -> D) or E)))
theorem-size     15
proof            (modus-ponens tm-76 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23788.        (((not (not A)) -> A) and (B or (((C and D) -> D) or E))), M:tm-76, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23789
in-theory        23789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D and E) -> E) or F)))
theorem-size     21
proof            (modus-ponens tm-69 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23789.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D and E) -> E) or F))), M:tm-69, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23790
in-theory        23790
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-54 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23790.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E and F) -> F) or G))), M:tm-54, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23791
in-theory        23791
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-42 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23791.        ((A -> (B or A)) and (C or (((D and E) -> E) or F))), M:tm-42, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23792
in-theory        23792
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-32 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23792.        ((A -> (A or B)) and (C or (((D and E) -> E) or F))), M:tm-32, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23793
in-theory        23793
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (((D and E) -> E) or F)))
theorem-size     17
proof            (modus-ponens tm-23 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23793.        ((A -> (B -> (A and B))) and (C or (((D and E) -> E) or F))), M:tm-23, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23794
in-theory        23794
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-22 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23794.        (((A and B) -> B) and (C or (((D and E) -> E) or F))), M:tm-22, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23795
in-theory        23795
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-21 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23795.        (((A and B) -> A) and (C or (((D and E) -> E) or F))), M:tm-21, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23796
in-theory        23796
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-20 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23796.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E and F) -> F) or G))), M:tm-20, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23797
in-theory        23797
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-19 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23797.        ((A -> (B -> A)) and (C or (((D and E) -> E) or F))), M:tm-19, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23798
in-theory        23798
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (((C and D) -> D) or E)))
theorem-size     11
proof            (modus-ponens tm-7 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-7 tm-6 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23798.        (A or (B or (((C and D) -> D) or E))), M:tm-7, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23799
in-theory        23799
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-6 tm-7 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23799.        ((A or (((B and C) -> C) or D)) or E), M:tm-6, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23800
in-theory        23800
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (((C and D) -> D) or E)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23800.        (A -> ((B or (((C and D) -> D) or E)) and A)), M:tm-5, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23801
in-theory        23801
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (((C and D) -> D) or E)))
theorem-size     11
proof            (modus-ponens tm-1 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-1 tm-7 tm-6 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23801.        (A -> (B or (((C and D) -> D) or E))), M:tm-1, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-23802
in-theory        23802
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23802.        ((((A and B) -> A) or C) and ((((D and E) -> E) or F) or G)), M:tm-382, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23803
in-theory        23803
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and F) -> F) or G) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23803.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and F) -> F) or G) or H)), M:tm-373, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23804
in-theory        23804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23804.        (((A -> (B -> A)) or C) and ((((D and E) -> E) or F) or G)), M:tm-364, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23805
in-theory        23805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D and E) -> E) or F) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23805.        ((A -> (B -> (C -> (B and C)))) and ((((D and E) -> E) or F) or G)), M:tm-354, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23806
in-theory        23806
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23806.        (((((A and B) -> B) or C) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23807
in-theory        23807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C and D) -> D) or E) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23807.        (((A -> B) -> (A -> (A and B))) and ((((C and D) -> D) or E) or F)), M:tm-338, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23808
in-theory        23808
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and ((E -> (F -> (E and F))) and ((((A and B) -> B) or C) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23808.        (((((A and B) -> B) or C) or D) and ((E -> (F -> (E and F))) and ((((A and B) -> B) or C) or D))), M:tm-327, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23809
in-theory        23809
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and (((E and F) -> F) and ((((A and B) -> B) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23809.        (((((A and B) -> B) or C) or D) and (((E and F) -> F) and ((((A and B) -> B) or C) or D))), M:tm-326, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23810
in-theory        23810
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and (((E and F) -> E) and ((((A and B) -> B) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23810.        (((((A and B) -> B) or C) or D) and (((E and F) -> E) and ((((A and B) -> B) or C) or D))), M:tm-325, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23811
in-theory        23811
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A and B) -> B) or C) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23811.        (((((A and B) -> B) or C) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A and B) -> B) or C) or D))), M:tm-324, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23812
in-theory        23812
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and ((E -> (F -> E)) and ((((A and B) -> B) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23812.        (((((A and B) -> B) or C) or D) and ((E -> (F -> E)) and ((((A and B) -> B) or C) or D))), M:tm-323, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23813
in-theory        23813
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23813.        (((((A and B) -> B) or C) or D) and ((E and F) -> F)), M:tm-322, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23814
in-theory        23814
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23814.        (((((A and B) -> B) or C) or D) and ((E and F) -> E)), M:tm-320, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23815
in-theory        23815
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23815.        (((((A and B) -> B) or C) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23816
in-theory        23816
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23816.        (((((A and B) -> B) or C) or D) and (E -> (F -> E))), M:tm-315, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23817
in-theory        23817
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and (E or ((((A and B) -> B) or C) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23817.        (((((A and B) -> B) or C) or D) and (E or ((((A and B) -> B) or C) or D))), M:tm-311, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23818
in-theory        23818
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and (((((A and B) -> B) or C) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23818.        (((((A and B) -> B) or C) or D) and (((((A and B) -> B) or C) or D) or E)), M:tm-310, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23819
in-theory        23819
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and (E -> (((((A and B) -> B) or C) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23819.        (((((A and B) -> B) or C) or D) and (E -> (((((A and B) -> B) or C) or D) and E))), M:tm-309, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23820
in-theory        23820
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and (E -> ((((A and B) -> B) or C) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23820.        (((((A and B) -> B) or C) or D) and (E -> ((((A and B) -> B) or C) or D))), M:tm-305, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23821
in-theory        23821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and E) -> E) or F) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23821.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and E) -> E) or F) or G)), M:tm-303, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23822
in-theory        23822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D and E) -> E) or F) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23822.        ((A -> (((B and C) -> C) and A)) and ((((D and E) -> E) or F) or G)), M:tm-270, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23823
in-theory        23823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D and E) -> E) or F) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23823.        ((A -> (((B and C) -> B) and A)) and ((((D and E) -> E) or F) or G)), M:tm-239, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23824
in-theory        23824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and F) -> F) or G) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23824.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and F) -> F) or G) or H)), M:tm-210, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23825
in-theory        23825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D and E) -> E) or F) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23825.        ((A -> ((B -> (C -> B)) and A)) and ((((D and E) -> E) or F) or G)), M:tm-183, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23826
in-theory        23826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23826.        ((A -> ((B and C) -> C)) and ((((D and E) -> E) or F) or G)), M:tm-157, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23827
in-theory        23827
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and E) -> E) or F) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23827.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and E) -> E) or F) or G)), M:tm-147, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23828
in-theory        23828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23828.        ((A -> ((B and C) -> B)) and ((((D and E) -> E) or F) or G)), M:tm-134, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23829
in-theory        23829
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and E) -> E) or F) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23829.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and E) -> E) or F) or G)), M:tm-125, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23830
in-theory        23830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> F) or G) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23830.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> F) or G) or H)), M:tm-113, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23831
in-theory        23831
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and E) -> E) or F) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23831.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and E) -> E) or F) or G)), M:tm-105, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23832
in-theory        23832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C and D) -> D) or E) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23832.        (((A -> B) -> (A -> A)) and ((((C and D) -> D) or E) or F)), M:tm-95, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23833
in-theory        23833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23833.        ((A -> (B -> (C -> B))) and ((((D and E) -> E) or F) or G)), M:tm-83, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23834
in-theory        23834
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B and C) -> C) or D) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23834.        (((not (not A)) -> A) and ((((B and C) -> C) or D) or E)), M:tm-76, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23835
in-theory        23835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and D) -> D) or E) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23835.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and D) -> D) or E) or F)), M:tm-69, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23836
in-theory        23836
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and E) -> E) or F) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23836.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and E) -> E) or F) or G)), M:tm-54, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23837
in-theory        23837
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C and D) -> D) or E) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23837.        ((A -> (B or A)) and ((((C and D) -> D) or E) or F)), M:tm-42, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23838
in-theory        23838
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C and D) -> D) or E) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23838.        ((A -> (A or B)) and ((((C and D) -> D) or E) or F)), M:tm-32, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23839
in-theory        23839
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C and D) -> D) or E) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23839.        ((A -> (B -> (A and B))) and ((((C and D) -> D) or E) or F)), M:tm-23, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23840
in-theory        23840
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C and D) -> D) or E) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23840.        (((A and B) -> B) and ((((C and D) -> D) or E) or F)), M:tm-22, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23841
in-theory        23841
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C and D) -> D) or E) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23841.        (((A and B) -> A) and ((((C and D) -> D) or E) or F)), M:tm-21, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23842
in-theory        23842
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and E) -> E) or F) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23842.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and E) -> E) or F) or G)), M:tm-20, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23843
in-theory        23843
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C and D) -> D) or E) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23843.        ((A -> (B -> A)) and ((((C and D) -> D) or E) or F)), M:tm-19, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23844
in-theory        23844
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B and C) -> C) or D) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-7 tm-6 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23844.        (A or ((((B and C) -> C) or D) or E)), M:tm-7, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23845
in-theory        23845
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-6 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23845.        (((((A and B) -> B) or C) or D) or E), M:tm-6, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23846
in-theory        23846
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B and C) -> C) or D) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23846.        (A -> (((((B and C) -> C) or D) or E) and A)), M:tm-5, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23847
in-theory        23847
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) or D) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-1 tm-6 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23847.        (A -> ((((B and C) -> C) or D) or E)), M:tm-1, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-23848
in-theory        23848
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-391 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23848.        ((((A and B) -> B) or C) and (D -> (D or E))), M:tm-391, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-23849
in-theory        23849
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-391 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-23849.        ((((A and B) -> B) or C) and (D -> (E or D))), M:tm-391, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-23850
in-theory        23850
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23850.        ((((A and B) -> B) or C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-391, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-23851
in-theory        23851
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-391 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23851.        ((((A and B) -> B) or C) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-391, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-23852
in-theory        23852
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-391 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-6 tm-4 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-23852.        ((((A and B) -> B) or C) and ((not (not D)) -> D)), M:tm-391, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-23853
in-theory        23853
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-391 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23853.        ((((A and B) -> B) or C) and (D -> (E -> (F -> E)))), M:tm-391, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-23854
in-theory        23854
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-391 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-23854.        ((((A and B) -> B) or C) and ((D -> E) -> (D -> D))), M:tm-391, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-23855
in-theory        23855
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-391 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-23855.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-391, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-23856
in-theory        23856
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23856.        ((((A and B) -> B) or C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-391, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-23857
in-theory        23857
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-391 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-23857.        ((((A and B) -> B) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-391, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-23858
in-theory        23858
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-391 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23858.        ((((A and B) -> B) or C) and (D -> ((E and F) -> E))), M:tm-391, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-23859
in-theory        23859
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-391 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-23859.        ((((A and B) -> B) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-391, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-23860
in-theory        23860
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-391 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23860.        ((((A and B) -> B) or C) and (D -> ((E and F) -> F))), M:tm-391, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-23861
in-theory        23861
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-391 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23861.        ((((A and B) -> B) or C) and (D -> ((E -> (F -> E)) and D))), M:tm-391, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-23862
in-theory        23862
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-391 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23862.        ((((A and B) -> B) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-391, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-23863
in-theory        23863
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-391 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23863.        ((((A and B) -> B) or C) and (D -> (((E and F) -> E) and D))), M:tm-391, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-23864
in-theory        23864
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-391 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23864.        ((((A and B) -> B) or C) and (D -> (((E and F) -> F) and D))), M:tm-391, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-23865
in-theory        23865
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-23865.        ((((A and B) -> B) or C) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-391, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-23866
in-theory        23866
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-391 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23866.        ((((A and B) -> B) or C) and ((D -> E) -> (D -> (D and E)))), M:tm-391, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-23867
in-theory        23867
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-23867.        ((((A and B) -> B) or C) and (D -> (E -> (F -> (E and F))))), M:tm-391, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-23868
in-theory        23868
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-391 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23868.        ((((A and B) -> B) or C) and ((D -> (E -> D)) or F)), M:tm-391, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-23869
in-theory        23869
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-391 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23869.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-391, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-23870
in-theory        23870
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-391 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23870.        ((((A and B) -> B) or C) and (((D and E) -> D) or F)), M:tm-391, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-23871
in-theory        23871
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-391 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23871.        ((((A and B) -> B) or C) and (((D and E) -> E) or F)), M:tm-391, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-23872
in-theory        23872
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-391 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-23872.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) or F)), M:tm-391, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-23873
in-theory        23873
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-391 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23873.        ((((A and B) -> B) or C) and ((D -> (D or E)) or F)), M:tm-391, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-23874
in-theory        23874
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-391 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23874.        ((((A and B) -> B) or C) and (D -> ((E -> (E or F)) and D))), M:tm-391, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-23875
in-theory        23875
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-391 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23875.        ((((A and B) -> B) or C) and (D -> (E -> (E or F)))), M:tm-391, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-23876
in-theory        23876
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-391 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23876.        ((((A and B) -> B) or C) and (D or (E -> (F -> E)))), M:tm-391, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-23877
in-theory        23877
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23877.        ((((A and B) -> B) or C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-391, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-23878
in-theory        23878
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-391 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23878.        ((((A and B) -> B) or C) and (D or ((E and F) -> E))), M:tm-391, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-23879
in-theory        23879
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-391 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23879.        ((((A and B) -> B) or C) and (D or ((E and F) -> F))), M:tm-391, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-23880
in-theory        23880
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-23880.        ((((A and B) -> B) or C) and (D or (E -> (F -> (E and F))))), M:tm-391, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-23881
in-theory        23881
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-391 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23881.        ((((A and B) -> B) or C) and (D or (E -> (E or F)))), M:tm-391, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-23882
in-theory        23882
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-391 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23882.        ((((A and B) -> B) or C) and (D or (E -> (F or E)))), M:tm-391, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-23883
in-theory        23883
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-391 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23883.        ((((A and B) -> B) or C) and ((D -> (E or D)) or F)), M:tm-391, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-23884
in-theory        23884
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-391 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23884.        ((((A and B) -> B) or C) and (D -> ((E -> (F or E)) and D))), M:tm-391, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-23885
in-theory        23885
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-391 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23885.        ((((A and B) -> B) or C) and (D -> (E -> (F or E)))), M:tm-391, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-23886
in-theory        23886
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-391 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23886.        ((((A and B) -> B) or C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-391, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-23887
in-theory        23887
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-391 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23887.        ((((A and B) -> B) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-391, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-23888
in-theory        23888
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-391 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23888.        ((((A and B) -> B) or C) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-391, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-23889
in-theory        23889
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-391 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23889.        ((((A and B) -> B) or C) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-391, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-23890
in-theory        23890
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-391 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23890.        ((((A and B) -> B) or C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-391, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-23891
in-theory        23891
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-391 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23891.        ((((A and B) -> B) or C) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-391, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-23892
in-theory        23892
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-391 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23892.        ((((A and B) -> B) or C) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-391, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-23893
in-theory        23893
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-391 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-23893.        ((((A and B) -> B) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-391, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-23894
in-theory        23894
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23894.        ((((A and B) -> B) or C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-391, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-23895
in-theory        23895
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-391 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23895.        ((((A and B) -> B) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-391, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-23896
in-theory        23896
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-391 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23896.        ((((A and B) -> B) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-391, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-23897
in-theory        23897
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-391 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-23897.        ((((A and B) -> B) or C) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-391, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-23898
in-theory        23898
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23898.        ((((A and B) -> B) or C) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-391, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-23899
in-theory        23899
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-391 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23899.        ((((A and B) -> B) or C) and ((D -> (not (E -> D))) -> (not D))), M:tm-391, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-23900
in-theory        23900
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23900.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-391, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-23901
in-theory        23901
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-391 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23901.        ((((A and B) -> B) or C) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-391, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-23902
in-theory        23902
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-391 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23902.        ((((A and B) -> B) or C) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-391, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-23903
in-theory        23903
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23903.        ((((A and B) -> B) or C) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-391, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-23904
in-theory        23904
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-391 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23904.        ((((A and B) -> B) or C) and ((D -> (not (D or E))) -> (not D))), M:tm-391, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-23905
in-theory        23905
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-391 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23905.        ((((A and B) -> B) or C) and ((D -> (not (E or D))) -> (not D))), M:tm-391, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-23906
in-theory        23906
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-391 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-23906.        ((((A and B) -> B) or C) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-391, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-23907
in-theory        23907
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-391 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-23907.        ((((A and B) -> B) or C) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-391, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-23908
in-theory        23908
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-391 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-23908.        ((((A and B) -> B) or C) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-391, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-23909
in-theory        23909
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23909.        ((((A and B) -> B) or C) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-391, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-23910
in-theory        23910
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-391 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23910.        ((((A and B) -> B) or C) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-391, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-23911
in-theory        23911
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-391 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23911.        ((((A and B) -> B) or C) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-391, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-23912
in-theory        23912
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-391 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-23912.        ((((A and B) -> B) or C) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-391, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-23913
in-theory        23913
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23913.        ((((A and B) -> B) or C) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-391, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-23914
in-theory        23914
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-391 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-23914.        ((((A and B) -> B) or C) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-391, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-23915
in-theory        23915
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-391 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-23915.        ((((A and B) -> B) or C) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-391, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-23916
in-theory        23916
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-391 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23916.        ((((A and B) -> B) or C) and (D or ((not (not E)) -> E))), M:tm-391, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-23917
in-theory        23917
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-391 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-4 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23917.        ((((A and B) -> B) or C) and (((not (not D)) -> D) or E)), M:tm-391, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-23918
in-theory        23918
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-391 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23918.        ((((A and B) -> B) or C) and (D -> (((not (not E)) -> E) and D))), M:tm-391, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-23919
in-theory        23919
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-391 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-23919.        ((((A and B) -> B) or C) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-391, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-23920
in-theory        23920
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-391 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23920.        ((((A and B) -> B) or C) and (D -> ((not (not E)) -> E))), M:tm-391, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-23921
in-theory        23921
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23921.        ((((A and B) -> B) or C) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-391, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-23922
in-theory        23922
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-391 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23922.        ((((A and B) -> B) or C) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-391, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-23923
in-theory        23923
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23923.        ((((A and B) -> B) or C) and (D or (E -> (F -> (G -> F))))), M:tm-391, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-23924
in-theory        23924
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23924.        ((((A and B) -> B) or C) and ((D -> (E -> (F -> E))) or G)), M:tm-391, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-23925
in-theory        23925
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23925.        ((((A and B) -> B) or C) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-391, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-23926
in-theory        23926
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-391 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-23926.        ((((A and B) -> B) or C) and ((D -> E) -> (D -> (F -> E)))), M:tm-391, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-23927
in-theory        23927
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23927.        ((((A and B) -> B) or C) and (D -> (E -> (F -> (G -> F))))), M:tm-391, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-23928
in-theory        23928
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-391 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23928.        ((((A and B) -> B) or C) and (D -> D)), M:tm-391, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-23929
in-theory        23929
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23929.        ((((A and B) -> B) or C) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-391, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-23930
in-theory        23930
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-391 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23930.        ((((A and B) -> B) or C) and ((D and E) -> (D and E))), M:tm-391, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-23931
in-theory        23931
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-391 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-23931.        ((((A and B) -> B) or C) and ((D -> E) -> (D -> E))), M:tm-391, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-23932
in-theory        23932
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-391 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-23932.        ((((A and B) -> B) or C) and ((not (not D)) -> (not (not D)))), M:tm-391, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-23933
in-theory        23933
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-391 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-23933.        ((((A and B) -> B) or C) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-391, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-23934
in-theory        23934
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-391 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-23934.        ((((A and B) -> B) or C) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-391, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-23935
in-theory        23935
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-391 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23935.        ((((A and B) -> B) or C) and (D or ((E -> F) -> (E -> E)))), M:tm-391, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-23936
in-theory        23936
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-391 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23936.        ((((A and B) -> B) or C) and (((D -> E) -> (D -> D)) or F)), M:tm-391, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-23937
in-theory        23937
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23937.        ((((A and B) -> B) or C) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-391, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-23938
in-theory        23938
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-23938.        ((((A and B) -> B) or C) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-391, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-23939
in-theory        23939
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-391 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23939.        ((((A and B) -> B) or C) and (D -> ((E -> F) -> (E -> E)))), M:tm-391, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-23940
in-theory        23940
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-23940.        ((((A and B) -> B) or C) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-391, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-23941
in-theory        23941
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-391 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-23941.        ((((A and B) -> B) or C) and ((D -> (D -> E)) -> (D -> E))), M:tm-391, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-23942
in-theory        23942
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-391 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-23942.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-391, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-23943
in-theory        23943
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-391 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-23943.        ((((A and B) -> B) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-391, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-23944
in-theory        23944
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-391 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-23944.        ((((A and B) -> B) or C) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-391, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-23945
in-theory        23945
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23945.        ((((A and B) -> B) or C) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-391, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-23946
in-theory        23946
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-391 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23946.        ((((A and B) -> B) or C) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-391, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-23947
in-theory        23947
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-391 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23947.        ((((A and B) -> B) or C) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-391, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-23948
in-theory        23948
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-391 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-23948.        ((((A and B) -> B) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-391, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-23949
in-theory        23949
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23949.        ((((A and B) -> B) or C) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-391, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-23950
in-theory        23950
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-391 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-23950.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-391, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-23951
in-theory        23951
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-391 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23951.        ((((A and B) -> B) or C) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-391, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-23952
in-theory        23952
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-391 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23952.        ((((A and B) -> B) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-391, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-23953
in-theory        23953
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-391 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23953.        ((((A and B) -> B) or C) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-391, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-23954
in-theory        23954
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-391 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23954.        ((((A and B) -> B) or C) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-391, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-23955
in-theory        23955
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-391 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23955.        ((((A and B) -> B) or C) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-391, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-23956
in-theory        23956
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-391 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-23956.        ((((A and B) -> B) or C) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-391, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-23957
in-theory        23957
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-391 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23957.        ((((A and B) -> B) or C) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-391, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-23958
in-theory        23958
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-391 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-23958.        ((((A and B) -> B) or C) and (((D -> E) and D) -> E)), M:tm-391, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-23959
in-theory        23959
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-391 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-23959.        ((((A and B) -> B) or C) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-391, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-23960
in-theory        23960
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-391 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23960.        ((((A and B) -> B) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-391, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-23961
in-theory        23961
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-391 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-23961.        ((((A and B) -> B) or C) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-391, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-23962
in-theory        23962
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-391 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-23962.        ((((A and B) -> B) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-391, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-23963
in-theory        23963
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-391 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-23963.        ((((A and B) -> B) or C) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-391, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-23964
in-theory        23964
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-391 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-23964.        ((((A and B) -> B) or C) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-391, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-23965
in-theory        23965
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-391 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23965.        ((((A and B) -> B) or C) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-391, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-23966
in-theory        23966
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-391 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23966.        ((((A and B) -> B) or C) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-391, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-23967
in-theory        23967
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-391 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23967.        ((((A and B) -> B) or C) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-391, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-23968
in-theory        23968
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-391 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-23968.        ((((A and B) -> B) or C) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-391, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-23969
in-theory        23969
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-391 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23969.        ((((A and B) -> B) or C) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-391, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-23970
in-theory        23970
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-391 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-23970.        ((((A and B) -> B) or C) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-391, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-23971
in-theory        23971
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-391 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-23971.        ((((A and B) -> B) or C) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-391, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-23972
in-theory        23972
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23972.        ((((A and B) -> B) or C) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-391, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-23973
in-theory        23973
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-391 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23973.        ((((A and B) -> B) or C) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-391, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-23974
in-theory        23974
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-391 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23974.        ((((A and B) -> B) or C) and (D or (E -> ((F and G) -> F)))), M:tm-391, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-23975
in-theory        23975
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23975.        ((((A and B) -> B) or C) and ((D -> ((E and F) -> E)) or G)), M:tm-391, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-23976
in-theory        23976
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23976.        ((((A and B) -> B) or C) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-391, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-23977
in-theory        23977
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-391 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-23977.        ((((A and B) -> B) or C) and ((D -> (E and F)) -> (D -> E))), M:tm-391, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-23978
in-theory        23978
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-391 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23978.        ((((A and B) -> B) or C) and (D -> (E -> ((F and G) -> F)))), M:tm-391, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-23979
in-theory        23979
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-391 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-23979.        ((((A and B) -> B) or C) and ((D and (D -> E)) -> E)), M:tm-391, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-23980
in-theory        23980
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-391 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-23980.        ((((A and B) -> B) or C) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-391, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-23981
in-theory        23981
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-391 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23981.        ((((A and B) -> B) or C) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-391, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-23982
in-theory        23982
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-391 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-23982.        ((((A and B) -> B) or C) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-391, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-23983
in-theory        23983
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-391 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-23983.        ((((A and B) -> B) or C) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-391, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-23984
in-theory        23984
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-391 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-23984.        ((((A and B) -> B) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-391, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-23985
in-theory        23985
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-391 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-23985.        ((((A and B) -> B) or C) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-391, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-23986
in-theory        23986
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-391 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-23986.        ((((A and B) -> B) or C) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-391, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-23987
in-theory        23987
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-391 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23987.        ((((A and B) -> B) or C) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-391, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-23988
in-theory        23988
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-391 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23988.        ((((A and B) -> B) or C) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-391, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-23989
in-theory        23989
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-391 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23989.        ((((A and B) -> B) or C) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-391, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-23990
in-theory        23990
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-391 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-23990.        ((((A and B) -> B) or C) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-391, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-23991
in-theory        23991
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-391 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23991.        ((((A and B) -> B) or C) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-391, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-23992
in-theory        23992
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-391 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-23992.        ((((A and B) -> B) or C) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-391, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-23993
in-theory        23993
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-391 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-23993.        ((((A and B) -> B) or C) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-391, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-23994
in-theory        23994
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-391 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-23994.        ((((A and B) -> B) or C) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-391, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-23995
in-theory        23995
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23995.        ((((A and B) -> B) or C) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-391, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-23996
in-theory        23996
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-391 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23996.        ((((A and B) -> B) or C) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-391, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-23997
in-theory        23997
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-391 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23997.        ((((A and B) -> B) or C) and (D or (E -> ((F and G) -> G)))), M:tm-391, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-23998
in-theory        23998
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23998.        ((((A and B) -> B) or C) and ((D -> ((E and F) -> F)) or G)), M:tm-391, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-23999
in-theory        23999
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23999.        ((((A and B) -> B) or C) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-391, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-24000
in-theory        24000
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-391 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-24000.        ((((A and B) -> B) or C) and ((D -> (E and F)) -> (D -> F))), M:tm-391, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-24001
in-theory        24001
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-391 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-24001.        ((((A and B) -> B) or C) and (D -> (E -> ((F and G) -> G)))), M:tm-391, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-24002
in-theory        24002
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24002.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-391, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-24003
in-theory        24003
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24003.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-391, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-24004
in-theory        24004
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24004.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-391, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-24005
in-theory        24005
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-391 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24005.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-391, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-24006
in-theory        24006
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24006.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-391, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-24007
in-theory        24007
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-391 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24007.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-391, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-24008
in-theory        24008
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24008.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-391, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-24009
in-theory        24009
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-24009.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-391, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-24010
in-theory        24010
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-391 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-24010.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-391, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-24011
in-theory        24011
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-24011.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-391, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-24012
in-theory        24012
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-24012.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-391, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-24013
in-theory        24013
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24013.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-391, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-24014
in-theory        24014
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-391 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24014.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-391, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-24015
in-theory        24015
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24015.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-391, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-24016
in-theory        24016
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-391 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24016.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-391, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-24017
in-theory        24017
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-391 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-24017.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-391, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-24018
in-theory        24018
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-391 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24018.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-391, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-24019
in-theory        24019
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-391 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-24019.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-391, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-24020
in-theory        24020
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24020.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-391, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-24021
in-theory        24021
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-24021.        ((((A and B) -> B) or C) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-391, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-24022
in-theory        24022
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-391 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-24022.        ((((A and B) -> B) or C) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-391, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-24023
in-theory        24023
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-391 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24023.        ((((A and B) -> B) or C) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-391, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-24024
in-theory        24024
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-391 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24024.        ((((A and B) -> B) or C) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-391, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-24025
in-theory        24025
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24025.        ((((A and B) -> B) or C) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-391, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-24026
in-theory        24026
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-391 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24026.        ((((A and B) -> B) or C) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-391, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-24027
in-theory        24027
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-391 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24027.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-391, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-24028
in-theory        24028
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24028.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-391, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-24029
in-theory        24029
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-391 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24029.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-391, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-24030
in-theory        24030
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-391 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24030.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-391, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-24031
in-theory        24031
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24031.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-391, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-24032
in-theory        24032
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24032.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-391, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-24033
in-theory        24033
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-391 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24033.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-391, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-24034
in-theory        24034
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-24034.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-391, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-24035
in-theory        24035
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-391 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-24035.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-391, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-24036
in-theory        24036
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-391 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-24036.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-391, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-24037
in-theory        24037
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-24037.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-391, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-24038
in-theory        24038
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-391 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24038.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-391, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-24039
in-theory        24039
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-391 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24039.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-391, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-24040
in-theory        24040
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-391 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24040.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-391, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-24041
in-theory        24041
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-391 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24041.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-391, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-24042
in-theory        24042
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-391 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-24042.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-391, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-24043
in-theory        24043
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-391 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24043.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-391, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-24044
in-theory        24044
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-391 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-24044.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-391, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-24045
in-theory        24045
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-391 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24045.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-391, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-24046
in-theory        24046
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-391 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24046.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-391, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-24047
in-theory        24047
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-391 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24047.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-391, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-24048
in-theory        24048
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-391 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24048.        ((((A and B) -> B) or C) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-391, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-24049
in-theory        24049
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-391 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24049.        ((((A and B) -> B) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-391, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-24050
in-theory        24050
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-391 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24050.        ((((A and B) -> B) or C) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-391, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-24051
in-theory        24051
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-391 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24051.        ((((A and B) -> B) or C) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-391, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-24052
in-theory        24052
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-391 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24052.        ((((A and B) -> B) or C) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-391, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-24053
in-theory        24053
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-391 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24053.        ((((A and B) -> B) or C) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-391, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-24054
in-theory        24054
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24054.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-391, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-24055
in-theory        24055
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24055.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-391, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-24056
in-theory        24056
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24056.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((F and G) -> F))), M:tm-391, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-24057
in-theory        24057
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-391 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24057.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((F and G) -> G))), M:tm-391, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-24058
in-theory        24058
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24058.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-391, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-24059
in-theory        24059
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-391 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24059.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (F or G)))), M:tm-391, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-24060
in-theory        24060
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24060.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (G or F)))), M:tm-391, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-24061
in-theory        24061
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-24061.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-391, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-24062
in-theory        24062
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-391 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-24062.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-391, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-24063
in-theory        24063
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-24063.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-391, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-24064
in-theory        24064
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-24064.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-391, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-24065
in-theory        24065
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24065.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-391, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-24066
in-theory        24066
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-391 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24066.        ((((A and B) -> B) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-391, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-24067
in-theory        24067
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24067.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-391, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-24068
in-theory        24068
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-391 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24068.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-391, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-24069
in-theory        24069
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-391 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-24069.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-391, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-24070
in-theory        24070
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-391 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24070.        ((((A and B) -> B) or C) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-391, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-24071
in-theory        24071
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-391 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-24071.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-391, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-24072
in-theory        24072
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24072.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-391, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-24073
in-theory        24073
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-391 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24073.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-391, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-24074
in-theory        24074
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24074.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-391, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-24075
in-theory        24075
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-391 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24075.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-391, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-24076
in-theory        24076
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24076.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-391, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-24077
in-theory        24077
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-24077.        ((((A and B) -> B) or C) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-391, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-24078
in-theory        24078
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-391 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-24078.        ((((A and B) -> B) or C) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-391, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-24079
in-theory        24079
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-391 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24079.        ((((A and B) -> B) or C) and (D or (E -> (((F and G) -> F) and E)))), M:tm-391, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-24080
in-theory        24080
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-391 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24080.        ((((A and B) -> B) or C) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-391, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-24081
in-theory        24081
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24081.        ((((A and B) -> B) or C) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-391, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-24082
in-theory        24082
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-391 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24082.        ((((A and B) -> B) or C) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-391, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-24083
in-theory        24083
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24083.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-391, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-24084
in-theory        24084
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24084.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-391, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-24085
in-theory        24085
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24085.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((F and G) -> F))), M:tm-391, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-24086
in-theory        24086
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-391 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24086.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((F and G) -> G))), M:tm-391, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-24087
in-theory        24087
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24087.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-391, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-24088
in-theory        24088
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-391 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24088.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (F or G)))), M:tm-391, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-24089
in-theory        24089
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24089.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (G or F)))), M:tm-391, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-24090
in-theory        24090
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-24090.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-391, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-24091
in-theory        24091
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-391 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-24091.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-391, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-24092
in-theory        24092
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-24092.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-391, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-24093
in-theory        24093
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-24093.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-391, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-24094
in-theory        24094
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24094.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-391, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-24095
in-theory        24095
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-391 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24095.        ((((A and B) -> B) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-391, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-24096
in-theory        24096
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24096.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-391, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-24097
in-theory        24097
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-391 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24097.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-391, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-24098
in-theory        24098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-391 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-24098.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-391, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-24099
in-theory        24099
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-391 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24099.        ((((A and B) -> B) or C) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-391, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-24100
in-theory        24100
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-391 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-24100.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-391, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-24101
in-theory        24101
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24101.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-391, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-24102
in-theory        24102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-391 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24102.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-391, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-24103
in-theory        24103
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24103.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-391, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-24104
in-theory        24104
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-24104.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-391, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-24105
in-theory        24105
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-24105.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-391, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-24106
in-theory        24106
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-391 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-24106.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-391, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-24107
in-theory        24107
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-24107.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-391, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-24108
in-theory        24108
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-24108.        ((((A and B) -> B) or C) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-391, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-24109
in-theory        24109
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-391 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-24109.        ((((A and B) -> B) or C) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-391, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-24110
in-theory        24110
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-391 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-24110.        ((((A and B) -> B) or C) and (D or (E -> (((F and G) -> G) and E)))), M:tm-391, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-24111
in-theory        24111
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-391 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-24111.        ((((A and B) -> B) or C) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-391, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-24112
in-theory        24112
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-24112.        ((((A and B) -> B) or C) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-391, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-24113
in-theory        24113
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-391 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-24113.        ((((A and B) -> B) or C) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-391, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-24114
in-theory        24114
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24114.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-391, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-24115
in-theory        24115
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24115.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-391, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-24116
in-theory        24116
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-391 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24116.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-391, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-24117
in-theory        24117
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-391 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24117.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-391, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-24118
in-theory        24118
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24118.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-391, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-24119
in-theory        24119
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-391 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24119.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-391, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-24120
in-theory        24120
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24120.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-391, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-24121
in-theory        24121
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-24121.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-391, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-24122
in-theory        24122
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-24122.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-391, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-24123
in-theory        24123
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-391 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-24123.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-391, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-24124
in-theory        24124
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-24124.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-391, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-24125
in-theory        24125
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24125.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-391, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-24126
in-theory        24126
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24126.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-391, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-24127
in-theory        24127
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-391 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24127.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-391, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-24128
in-theory        24128
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-391 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24128.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-391, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-24129
in-theory        24129
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-391 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-24129.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-391, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-24130
in-theory        24130
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-391 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24130.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-391, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-24131
in-theory        24131
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-391 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-24131.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-391, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-24132
in-theory        24132
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-391 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24132.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-391, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-24133
in-theory        24133
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-391 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24133.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-391, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-24134
in-theory        24134
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-391 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24134.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-391, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-24135
in-theory        24135
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-391 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-24135.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-391, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-24136
in-theory        24136
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-391 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-24136.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-391, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-24137
in-theory        24137
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-391 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-24137.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-391, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-24138
in-theory        24138
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-391 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-24138.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-391, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-24139
in-theory        24139
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-391 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-24139.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-391, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-24140
in-theory        24140
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-391 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-24140.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-391, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-24141
in-theory        24141
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-391 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-24141.        ((((A and B) -> B) or C) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-391, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-24142
in-theory        24142
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-391 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-24142.        ((((A and B) -> B) or C) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-391, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-24143
in-theory        24143
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-391 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-24143.        ((((A and B) -> B) or C) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-391, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-24144
in-theory        24144
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-391 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-24144.        ((((A and B) -> B) or C) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-391, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-24145
in-theory        24145
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-391 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-24145.        ((((A and B) -> B) or C) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-391, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-24146
in-theory        24146
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-391 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-24146.        ((((A and B) -> B) or C) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-391, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-24147
in-theory        24147
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-391 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24147.        ((((A and B) -> B) or C) and (D -> (D and (E -> D)))), M:tm-391, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-24148
in-theory        24148
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24148.        ((((A and B) -> B) or C) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-391, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-24149
in-theory        24149
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-391 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24149.        ((((A and B) -> B) or C) and ((D and E) -> ((D and E) and D))), M:tm-391, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-24150
in-theory        24150
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-391 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-24150.        ((((A and B) -> B) or C) and ((D and E) -> ((D and E) and E))), M:tm-391, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-24151
in-theory        24151
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-24151.        ((((A and B) -> B) or C) and (D -> (D and (E -> (D and E))))), M:tm-391, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-24152
in-theory        24152
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-391 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-24152.        ((((A and B) -> B) or C) and (D -> (D and (D or E)))), M:tm-391, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-24153
in-theory        24153
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-391 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-24153.        ((((A and B) -> B) or C) and (D -> (D and (E or D)))), M:tm-391, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-24154
in-theory        24154
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-391 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-24154.        ((((A and B) -> B) or C) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-391, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-24155
in-theory        24155
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-24155.        ((((A and B) -> B) or C) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-391, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-24156
in-theory        24156
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-391 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-24156.        ((((A and B) -> B) or C) and ((not (not D)) -> ((not (not D)) and D))), M:tm-391, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-24157
in-theory        24157
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-24157.        ((((A and B) -> B) or C) and (D -> (D and (E -> (F -> E))))), M:tm-391, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-24158
in-theory        24158
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-391 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-24158.        ((((A and B) -> B) or C) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-391, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-24159
in-theory        24159
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-391 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-24159.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-391, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-24160
in-theory        24160
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-391 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-24160.        ((((A and B) -> B) or C) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-391, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-24161
in-theory        24161
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-391 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-24161.        ((((A and B) -> B) or C) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-391, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-24162
in-theory        24162
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-391 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-24162.        ((((A and B) -> B) or C) and (D -> (D and ((E and F) -> E)))), M:tm-391, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-24163
in-theory        24163
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-391 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-24163.        ((((A and B) -> B) or C) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-391, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-24164
in-theory        24164
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-391 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-24164.        ((((A and B) -> B) or C) and (D -> (D and ((E and F) -> F)))), M:tm-391, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-24165
in-theory        24165
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-391 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-24165.        ((((A and B) -> B) or C) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-391, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-24166
in-theory        24166
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-391 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24166.        ((((A and B) -> B) or C) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-391, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-24167
in-theory        24167
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-391 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-24167.        ((((A and B) -> B) or C) and (D -> (D and (((E and F) -> E) and D)))), M:tm-391, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-24168
in-theory        24168
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-391 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-24168.        ((((A and B) -> B) or C) and (D -> (D and (((E and F) -> F) and D)))), M:tm-391, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-24169
in-theory        24169
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-391 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-24169.        ((((A and B) -> B) or C) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-391, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-24170
in-theory        24170
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-24170.        ((((A and B) -> B) or C) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-391, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-24171
in-theory        24171
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-391 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-24171.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-391, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-24172
in-theory        24172
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-24172.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-391, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-24173
in-theory        24173
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-24173.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-391, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-24174
in-theory        24174
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-391 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-24174.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-391, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-24175
in-theory        24175
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-24175.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-391, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-24176
in-theory        24176
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-391 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-24176.        ((((A and B) -> B) or C) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-391, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-24177
in-theory        24177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-391 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-24177.        ((((A and B) -> B) or C) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-391, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-24178
in-theory        24178
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-391 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-24178.        ((((A and B) -> B) or C) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-391, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-24179
in-theory        24179
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-391 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-24179.        ((((A and B) -> B) or C) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-391, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-24180
in-theory        24180
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-24180.        ((((A and B) -> B) or C) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-391, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-24181
in-theory        24181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-391 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-24181.        ((((A and B) -> B) or C) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-391, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-24182
in-theory        24182
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-391 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-24182.        ((((A and B) -> B) or C) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-391, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-24183
in-theory        24183
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-391 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-24183.        ((((A and B) -> B) or C) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-391, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-24184
in-theory        24184
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-391 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-24184.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-391, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-24185
in-theory        24185
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-391 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-24185.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-391, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-24186
in-theory        24186
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-391 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-24186.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-391, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-24187
in-theory        24187
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-391 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-24187.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-391, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-24188
in-theory        24188
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-391 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-24188.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-391, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-24189
in-theory        24189
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-391 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-24189.        ((((A and B) -> B) or C) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-391, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-24190
in-theory        24190
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-391 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-24190.        ((((A and B) -> B) or C) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-391, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-24191
in-theory        24191
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-391 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-24191.        ((((A and B) -> B) or C) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-391, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-24192
in-theory        24192
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-24192.        ((((A and B) -> B) or C) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-391, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-24193
in-theory        24193
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-391 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-24193.        ((((A and B) -> B) or C) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-391, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-24194
in-theory        24194
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-391 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-24194.        ((((A and B) -> B) or C) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-391, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-24195
in-theory        24195
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-391 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-24195.        ((((A and B) -> B) or C) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-391, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-24196
in-theory        24196
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-24196.        ((((A and B) -> B) or C) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-391, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-24197
in-theory        24197
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-391 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24197.        ((((A and B) -> B) or C) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-391, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-24198
in-theory        24198
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-391 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-24198.        ((((A and B) -> B) or C) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-391, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-24199
in-theory        24199
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-391 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-24199.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-391, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-24200
in-theory        24200
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-24200.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-391, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-24201
in-theory        24201
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-24201.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-391, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-24202
in-theory        24202
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-24202.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-391, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-24203
in-theory        24203
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-24203.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-391, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-24204
in-theory        24204
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-391 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-24204.        ((((A and B) -> B) or C) and (D or ((E -> (F -> E)) or G))), M:tm-391, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-24205
in-theory        24205
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-24205.        ((((A and B) -> B) or C) and (((D -> (E -> D)) or F) or G)), M:tm-391, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-24206
in-theory        24206
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-24206.        ((((A and B) -> B) or C) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-391, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-24207
in-theory        24207
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-391 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-24207.        ((((A and B) -> B) or C) and (D -> ((E -> (F -> E)) or G))), M:tm-391, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-24208
in-theory        24208
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-391 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24208.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-391, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-24209
in-theory        24209
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24209.        ((((A and B) -> B) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-391, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-24210
in-theory        24210
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24210.        ((((A and B) -> B) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-391, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-24211
in-theory        24211
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-391 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24211.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-391, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-24212
in-theory        24212
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24212.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-391, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-24213
in-theory        24213
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-391 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24213.        ((((A and B) -> B) or C) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-391, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-24214
in-theory        24214
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-391 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24214.        ((((A and B) -> B) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-391, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-24215
in-theory        24215
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-391 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24215.        ((((A and B) -> B) or C) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-391, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-24216
in-theory        24216
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-391 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24216.        ((((A and B) -> B) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-391, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-24217
in-theory        24217
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-391 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-24217.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-391, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-24218
in-theory        24218
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-24218.        ((((A and B) -> B) or C) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-391, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-24219
in-theory        24219
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-24219.        ((((A and B) -> B) or C) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-391, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-24220
in-theory        24220
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-24220.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-391, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-24221
in-theory        24221
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-24221.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-391, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-24222
in-theory        24222
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-391 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-24222.        ((((A and B) -> B) or C) and (D or (((E and F) -> E) or G))), M:tm-391, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-24223
in-theory        24223
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-24223.        ((((A and B) -> B) or C) and ((((D and E) -> D) or F) or G)), M:tm-391, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-24224
in-theory        24224
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-24224.        ((((A and B) -> B) or C) and (D -> ((((E and F) -> E) or G) and D))), M:tm-391, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-24225
in-theory        24225
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-391 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-24225.        ((((A and B) -> B) or C) and (D -> (((E and F) -> E) or G))), M:tm-391, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-24226
in-theory        24226
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-391 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24226.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-391, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-24227
in-theory        24227
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24227.        ((((A and B) -> B) or C) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-391, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-24228
in-theory        24228
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24228.        ((((A and B) -> B) or C) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-391, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-24229
in-theory        24229
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24229.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-391, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-24230
in-theory        24230
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24230.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-391, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-24231
in-theory        24231
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-391 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24231.        ((((A and B) -> B) or C) and (D or (((E and F) -> F) or G))), M:tm-391, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24232
in-theory        24232
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24232.        ((((A and B) -> B) or C) and ((((D and E) -> E) or F) or G)), M:tm-391, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-24233
in-theory        24233
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24233.        ((((A and B) -> B) or C) and (D -> ((((E and F) -> F) or G) and D))), M:tm-391, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24234
in-theory        24234
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24234.        ((((A and B) -> A) or C) and (D -> ((((E and F) -> F) or G) and D))), M:tm-382, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24235
in-theory        24235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F and G) -> G) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24235.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F and G) -> G) or H) and E))), M:tm-373, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24236
in-theory        24236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24236.        (((A -> (B -> A)) or C) and (D -> ((((E and F) -> F) or G) and D))), M:tm-364, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24237
in-theory        24237
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((((C and D) -> D) or E) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24237.        (A -> (B -> (((((C and D) -> D) or E) and A) and B))), M:tm-355, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-24238
in-theory        24238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24238.        ((A -> (B -> (C -> (B and C)))) and (D -> ((((E and F) -> F) or G) and D))), M:tm-354, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24239
in-theory        24239
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((((D and E) -> E) or F) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-391 ((Am (-> A (-> B (and A B)))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24239.        ((A or (B -> (C -> (B and C)))) -> ((((D and E) -> E) or F) and (B -> (C -> (B and C))))), M:tm-351, m:tm-391, u:((Am (-> A (-> B (and A B)))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-24240
in-theory        24240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24240.        ((A -> ((((B and C) -> C) or D) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24241
in-theory        24241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((((D and E) -> E) or F) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24241.        (((A -> B) -> (A -> (A and B))) and (C -> ((((D and E) -> E) or F) and C))), M:tm-338, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24242
in-theory        24242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((((C and D) -> D) or E) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-391 ((Am (-> A (and A B))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24242.        (((A -> B) or (A -> (A and B))) -> ((((C and D) -> D) or E) and (A -> (A and B)))), M:tm-335, m:tm-391, u:((Am (-> A (and A B))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (and A B)))))
================================================================
tm-name          tm-24243
in-theory        24243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and (A -> (A and ((((B and C) -> C) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24243.        ((A -> ((((B and C) -> C) or D) and A)) and (A -> (A and ((((B and C) -> C) or D) and A)))), M:tm-328, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-24244
in-theory        24244
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B and C) -> C) or D) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24244.        ((A -> ((((B and C) -> C) or D) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B and C) -> C) or D) and A)))), M:tm-327, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24245
in-theory        24245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and (((E and F) -> F) and (A -> ((((B and C) -> C) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24245.        ((A -> ((((B and C) -> C) or D) and A)) and (((E and F) -> F) and (A -> ((((B and C) -> C) or D) and A)))), M:tm-326, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24246
in-theory        24246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and (((E and F) -> E) and (A -> ((((B and C) -> C) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24246.        ((A -> ((((B and C) -> C) or D) and A)) and (((E and F) -> E) and (A -> ((((B and C) -> C) or D) and A)))), M:tm-325, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24247
in-theory        24247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B and C) -> C) or D) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24247.        ((A -> ((((B and C) -> C) or D) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B and C) -> C) or D) and A)))), M:tm-324, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24248
in-theory        24248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and ((E -> (F -> E)) and (A -> ((((B and C) -> C) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24248.        ((A -> ((((B and C) -> C) or D) and A)) and ((E -> (F -> E)) and (A -> ((((B and C) -> C) or D) and A)))), M:tm-323, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24249
in-theory        24249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24249.        ((A -> ((((B and C) -> C) or D) and A)) and ((E and F) -> F)), M:tm-322, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24250
in-theory        24250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24250.        ((A -> ((((B and C) -> C) or D) and A)) and ((E and F) -> E)), M:tm-320, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24251
in-theory        24251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24251.        ((A -> ((((B and C) -> C) or D) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24252
in-theory        24252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24252.        ((A -> ((((B and C) -> C) or D) and A)) and (A -> A)), M:tm-316, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-24253
in-theory        24253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24253.        ((A -> ((((B and C) -> C) or D) and A)) and (E -> (F -> E))), M:tm-315, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24254
in-theory        24254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and ((A -> (not ((((B and C) -> C) or D) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24254.        ((A -> ((((B and C) -> C) or D) and A)) and ((A -> (not ((((B and C) -> C) or D) and A))) -> (not A))), M:tm-313, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-24255
in-theory        24255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and ((((((B and C) -> C) or D) and A) -> E) -> ((A or ((((B and C) -> C) or D) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24255.        ((A -> ((((B and C) -> C) or D) and A)) and ((((((B and C) -> C) or D) and A) -> E) -> ((A or ((((B and C) -> C) or D) and A)) -> E))), M:tm-312, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-24256
in-theory        24256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and (E or (A -> ((((B and C) -> C) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24256.        ((A -> ((((B and C) -> C) or D) and A)) and (E or (A -> ((((B and C) -> C) or D) and A)))), M:tm-311, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24257
in-theory        24257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and ((A -> ((((B and C) -> C) or D) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24257.        ((A -> ((((B and C) -> C) or D) and A)) and ((A -> ((((B and C) -> C) or D) and A)) or E)), M:tm-310, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24258
in-theory        24258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and (E -> ((A -> ((((B and C) -> C) or D) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24258.        ((A -> ((((B and C) -> C) or D) and A)) and (E -> ((A -> ((((B and C) -> C) or D) and A)) and E))), M:tm-309, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24259
in-theory        24259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and (E -> (A -> ((((B and C) -> C) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24259.        ((A -> ((((B and C) -> C) or D) and A)) and (E -> (A -> ((((B and C) -> C) or D) and A)))), M:tm-305, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24260
in-theory        24260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24260.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-303, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24261
in-theory        24261
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((((D and E) -> E) or F) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-391 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24261.        ((A or ((B -> (C -> (B and C))) and A)) -> ((((D and E) -> E) or F) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-391, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-24262
in-theory        24262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24262.        ((A -> (((B and C) -> C) and A)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-270, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24263
in-theory        24263
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((D and E) -> E) or F) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-391 ((Am (and (-> (and A B) B) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24263.        ((A or (((B and C) -> C) and A)) -> ((((D and E) -> E) or F) and (((B and C) -> C) and A))), M:tm-267, m:tm-391, u:((Am (and (-> (and A B) B) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-24264
in-theory        24264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24264.        ((A -> (((B and C) -> B) and A)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-239, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24265
in-theory        24265
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((D and E) -> E) or F) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-391 ((Am (and (-> (and A B) A) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24265.        ((A or (((B and C) -> B) and A)) -> ((((D and E) -> E) or F) and (((B and C) -> B) and A))), M:tm-236, m:tm-391, u:((Am (and (-> (and A B) A) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-24266
in-theory        24266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F and G) -> G) or H) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24266.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F and G) -> G) or H) and E))), M:tm-210, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24267
in-theory        24267
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E and F) -> F) or G) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-391 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (and Bm Cm) Cm) Dm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24267.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E and F) -> F) or G) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-391, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (and Bm Cm) Cm) Dm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-24268
in-theory        24268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24268.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-183, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24269
in-theory        24269
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((((D and E) -> E) or F) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-391 ((Am (and (-> A (-> B A)) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24269.        ((A or ((B -> (C -> B)) and A)) -> ((((D and E) -> E) or F) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-391, u:((Am (and (-> A (-> B A)) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-24270
in-theory        24270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24270.        ((A -> ((B and C) -> C)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-157, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24271
in-theory        24271
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((((D and E) -> E) or F) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-391 ((Am (-> (and A B) B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24271.        ((A or ((B and C) -> C)) -> ((((D and E) -> E) or F) and ((B and C) -> C))), M:tm-154, m:tm-391, u:((Am (-> (and A B) B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> (and A B) B))))
================================================================
tm-name          tm-24272
in-theory        24272
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24272.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-147, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24273
in-theory        24273
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D and E) -> E) or F) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-391 ((Am (-> (and A (-> B C)) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24273.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D and E) -> E) or F) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-391, u:((Am (-> (and A (-> B C)) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-24274
in-theory        24274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24274.        ((A -> ((B and C) -> B)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-134, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24275
in-theory        24275
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((((D and E) -> E) or F) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-391 ((Am (-> (and A B) A)) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24275.        ((A or ((B and C) -> B)) -> ((((D and E) -> E) or F) and ((B and C) -> B))), M:tm-131, m:tm-391, u:((Am (-> (and A B) A)) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> (and A B) A))))
================================================================
tm-name          tm-24276
in-theory        24276
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24276.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-125, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24277
in-theory        24277
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D and E) -> E) or F) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-391 ((Am (-> (and (-> A B) C) B)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-6 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24277.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D and E) -> E) or F) and (((A -> B) and C) -> B))), M:tm-122, m:tm-391, u:((Am (-> (and (-> A B) C) B)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-24278
in-theory        24278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F and G) -> G) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24278.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F and G) -> G) or H) and E))), M:tm-113, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24279
in-theory        24279
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E and F) -> F) or G) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-391 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24279.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E and F) -> F) or G) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-391, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-24280
in-theory        24280
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24280.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E and F) -> F) or G) and D))), M:tm-105, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24281
in-theory        24281
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D and E) -> E) or F) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-391 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24281.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D and E) -> E) or F) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-391, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-24282
in-theory        24282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((((D and E) -> E) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24282.        (((A -> B) -> (A -> A)) and (C -> ((((D and E) -> E) or F) and C))), M:tm-95, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24283
in-theory        24283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((((C and D) -> D) or E) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-391 ((Am (-> A A)) (B (and (or (-> (and Bm Cm) Cm) Dm) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24283.        (((A -> B) or (A -> A)) -> ((((C and D) -> D) or E) and (A -> A))), M:tm-92, m:tm-391, u:((Am (-> A A)) (B (and (or (-> (and Bm Cm) Cm) Dm) (-> A A))))
================================================================
tm-name          tm-24284
in-theory        24284
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C and D) -> D) or E) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6 tm-4)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24284.        (A -> (B -> ((((C and D) -> D) or E) and A))), M:tm-84, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-24285
in-theory        24285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24285.        ((A -> (B -> (C -> B))) and (D -> ((((E and F) -> F) or G) and D))), M:tm-83, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24286
in-theory        24286
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((((D and E) -> E) or F) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-391 ((Am (-> A (-> B A))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24286.        ((A or (B -> (C -> B))) -> ((((D and E) -> E) or F) and (B -> (C -> B)))), M:tm-80, m:tm-391, u:((Am (-> A (-> B A))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (-> B A)))))
================================================================
tm-name          tm-24287
in-theory        24287
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((((C and D) -> D) or E) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-10 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24287.        (((not (not A)) -> A) and (B -> ((((C and D) -> D) or E) and B))), M:tm-76, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24288
in-theory        24288
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((((B and C) -> C) or D) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-6 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24288.        (((not (not A)) or A) -> ((((B and C) -> C) or D) and A)), M:tm-73, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-24289
in-theory        24289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D and E) -> E) or F) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-9 tm-6 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24289.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D and E) -> E) or F) and C))), M:tm-69, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24290
in-theory        24290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C and D) -> D) or E) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-391 ((Am (-> (-> A (not B)) (not A))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-6 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24290.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C and D) -> D) or E) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-391, u:((Am (-> (-> A (not B)) (not A))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-24291
in-theory        24291
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24291.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E and F) -> F) or G) and D))), M:tm-54, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24292
in-theory        24292
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D and E) -> E) or F) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-391 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-6 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24292.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D and E) -> E) or F) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-391, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-24293
in-theory        24293
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C and D) -> D) or E) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-391 ((Am (or A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24293.        ((A or (B or A)) -> ((((C and D) -> D) or E) and (B or A))), M:tm-50, m:tm-391, u:((Am (or A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (or A B))))
================================================================
tm-name          tm-24294
in-theory        24294
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C and D) -> D) or E) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-391 ((Am (or A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24294.        ((A or (A or B)) -> ((((C and D) -> D) or E) and (A or B))), M:tm-49, m:tm-391, u:((Am (or A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (or A B))))
================================================================
tm-name          tm-24295
in-theory        24295
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C and D) -> D) or E) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-391 ((Am (-> A (and B A))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-6 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24295.        ((A or (B -> (A and B))) -> ((((C and D) -> D) or E) and (B -> (A and B)))), M:tm-48, m:tm-391, u:((Am (-> A (and B A))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-24296
in-theory        24296
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C and D) -> D) or E) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24296.        (((A and B) or B) -> ((((C and D) -> D) or E) and B)), M:tm-47, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-24297
in-theory        24297
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C and D) -> D) or E) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-6 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24297.        (((A and B) or A) -> ((((C and D) -> D) or E) and A)), M:tm-46, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-24298
in-theory        24298
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and E) -> E) or F) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-391 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24298.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and E) -> E) or F) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-391, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-24299
in-theory        24299
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C and D) -> D) or E) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-391 ((Am (-> A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24299.        ((A or (B -> A)) -> ((((C and D) -> D) or E) and (B -> A))), M:tm-44, m:tm-391, u:((Am (-> A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A B))))
================================================================
tm-name          tm-24300
in-theory        24300
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((((D and E) -> E) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24300.        ((A -> (B or A)) and (C -> ((((D and E) -> E) or F) and C))), M:tm-42, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24301
in-theory        24301
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((((D and E) -> E) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24301.        ((A -> (A or B)) and (C -> ((((D and E) -> E) or F) and C))), M:tm-32, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24302
in-theory        24302
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((((B and C) -> C) or D) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24302.        (A -> (A and ((((B and C) -> C) or D) and A))), M:tm-24, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-24303
in-theory        24303
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((((D and E) -> E) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24303.        ((A -> (B -> (A and B))) and (C -> ((((D and E) -> E) or F) and C))), M:tm-23, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24304
in-theory        24304
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((((D and E) -> E) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24304.        (((A and B) -> B) and (C -> ((((D and E) -> E) or F) and C))), M:tm-22, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24305
in-theory        24305
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((((D and E) -> E) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24305.        (((A and B) -> A) and (C -> ((((D and E) -> E) or F) and C))), M:tm-21, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24306
in-theory        24306
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24306.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E and F) -> F) or G) and D))), M:tm-20, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24307
in-theory        24307
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((((D and E) -> E) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24307.        ((A -> (B -> A)) and (C -> ((((D and E) -> E) or F) and C))), M:tm-19, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24308
in-theory        24308
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((((B and C) -> C) or D) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-9 tm-5 tm-6 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24308.        ((A -> (not ((((B and C) -> C) or D) and A))) -> (not A)), M:tm-9, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-24309
in-theory        24309
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) -> B) or C) and D) -> E) -> ((D or ((((A and B) -> B) or C) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-8 tm-5 tm-6 tm-4)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24309.        ((((((A and B) -> B) or C) and D) -> E) -> ((D or ((((A and B) -> B) or C) and D)) -> E)), M:tm-8, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-24310
in-theory        24310
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((((C and D) -> D) or E) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-7 tm-5 tm-6 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24310.        (A or (B -> ((((C and D) -> D) or E) and B))), M:tm-7, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24311
in-theory        24311
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24311.        ((A -> ((((B and C) -> C) or D) and A)) or E), M:tm-6, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24312
in-theory        24312
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((((C and D) -> D) or E) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24312.        (A -> ((B -> ((((C and D) -> D) or E) and B)) and A)), M:tm-5, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24313
in-theory        24313
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((((C and D) -> D) or E) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-1 tm-5 tm-6 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24313.        (A -> (B -> ((((C and D) -> D) or E) and B))), M:tm-1, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-24314
in-theory        24314
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-391 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24314.        ((((A and B) -> B) or C) and (D -> (((E and F) -> F) or G))), M:tm-391, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24315
in-theory        24315
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-382 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24315.        ((((A and B) -> A) or C) and (D -> (((E and F) -> F) or G))), M:tm-382, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24316
in-theory        24316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-373 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24316.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F and G) -> G) or H))), M:tm-373, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24317
in-theory        24317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-364 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24317.        (((A -> (B -> A)) or C) and (D -> (((E and F) -> F) or G))), M:tm-364, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24318
in-theory        24318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-354 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24318.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E and F) -> F) or G))), M:tm-354, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24319
in-theory        24319
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-351 tm-392 ((Am (-> A (-> B (and A B)))) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24319.        ((A or (B -> (C -> (B and C)))) -> (((D and E) -> E) or F)), M:tm-351, m:tm-392, u:((Am (-> A (-> B (and A B)))) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24320
in-theory        24320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24320.        ((A -> (((B and C) -> C) or D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24321
in-theory        24321
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) -> D) -> ((((A and B) -> B) or C) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-392 ((Am (-> (or (-> (and Bm Cm) Cm) Dm) B)) (A (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24321.        (((((A and B) -> B) or C) -> D) -> ((((A and B) -> B) or C) and D)), M:tm-339, m:tm-392, u:((Am (-> (or (-> (and Bm Cm) Cm) Dm) B)) (A (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24322
in-theory        24322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D and E) -> E) or F)))
theorem-size     19
proof            (modus-ponens tm-338 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24322.        (((A -> B) -> (A -> (A and B))) and (C -> (((D and E) -> E) or F))), M:tm-338, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24323
in-theory        24323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C and D) -> D) or E))
theorem-size     17
proof            (modus-ponens tm-335 tm-392 ((Am (-> A (and A B))) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24323.        (((A -> B) or (A -> (A and B))) -> (((C and D) -> D) or E)), M:tm-335, m:tm-392, u:((Am (-> A (and A B))) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24324
in-theory        24324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (A -> (A and (((B and C) -> C) or D))))
theorem-size     21
proof            (modus-ponens tm-328 tm-392 ((A Am) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24324.        ((A -> (((B and C) -> C) or D)) and (A -> (A and (((B and C) -> C) or D)))), M:tm-328, m:tm-392, u:((A Am) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24325
in-theory        24325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and ((E -> (F -> (E and F))) and (A -> (((B and C) -> C) or D))))
theorem-size     27
proof            (modus-ponens tm-327 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24325.        ((A -> (((B and C) -> C) or D)) and ((E -> (F -> (E and F))) and (A -> (((B and C) -> C) or D)))), M:tm-327, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24326
in-theory        24326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (((E and F) -> F) and (A -> (((B and C) -> C) or D))))
theorem-size     25
proof            (modus-ponens tm-326 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24326.        ((A -> (((B and C) -> C) or D)) and (((E and F) -> F) and (A -> (((B and C) -> C) or D)))), M:tm-326, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24327
in-theory        24327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (((E and F) -> E) and (A -> (((B and C) -> C) or D))))
theorem-size     25
proof            (modus-ponens tm-325 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24327.        ((A -> (((B and C) -> C) or D)) and (((E and F) -> E) and (A -> (((B and C) -> C) or D)))), M:tm-325, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24328
in-theory        24328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B and C) -> C) or D))))
theorem-size     33
proof            (modus-ponens tm-324 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24328.        ((A -> (((B and C) -> C) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B and C) -> C) or D)))), M:tm-324, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24329
in-theory        24329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and ((E -> (F -> E)) and (A -> (((B and C) -> C) or D))))
theorem-size     25
proof            (modus-ponens tm-323 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24329.        ((A -> (((B and C) -> C) or D)) and ((E -> (F -> E)) and (A -> (((B and C) -> C) or D)))), M:tm-323, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24330
in-theory        24330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24330.        ((A -> (((B and C) -> C) or D)) and ((E and F) -> F)), M:tm-322, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24331
in-theory        24331
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B and C) -> C) or D) -> E)) -> (((B and C) -> C) or D)) and ((A and ((((B and C) -> C) or D) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-392 ((Am (and A (-> (or (-> (and Bm Cm) Cm) Dm) C))) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24331.        (((A and ((((B and C) -> C) or D) -> E)) -> (((B and C) -> C) or D)) and ((A and ((((B and C) -> C) or D) -> E)) -> E)), M:tm-321, m:tm-392, u:((Am (and A (-> (or (-> (and Bm Cm) Cm) Dm) C))) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24332
in-theory        24332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24332.        ((A -> (((B and C) -> C) or D)) and ((E and F) -> E)), M:tm-320, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24333
in-theory        24333
times-derived    1
----------------------------------------------------------------
theorem          (((((((A and B) -> B) or C) -> D) and E) -> (((A and B) -> B) or C)) and ((((((A and B) -> B) or C) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-392 ((Am (and (-> (or (-> (and Bm Cm) Cm) Dm) B) C)) (A (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24333.        (((((((A and B) -> B) or C) -> D) and E) -> (((A and B) -> B) or C)) and ((((((A and B) -> B) or C) -> D) and E) -> D)), M:tm-319, m:tm-392, u:((Am (and (-> (or (-> (and Bm Cm) Cm) Dm) B) C)) (A (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24334
in-theory        24334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24334.        ((A -> (((B and C) -> C) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24335
in-theory        24335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-392 ((A Am) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24335.        ((A -> (((B and C) -> C) or D)) and (A -> A)), M:tm-316, m:tm-392, u:((A Am) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24336
in-theory        24336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24336.        ((A -> (((B and C) -> C) or D)) and (E -> (F -> E))), M:tm-315, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24337
in-theory        24337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and ((A -> (not (((B and C) -> C) or D))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-392 ((A Am) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24337.        ((A -> (((B and C) -> C) or D)) and ((A -> (not (((B and C) -> C) or D))) -> (not A))), M:tm-313, m:tm-392, u:((A Am) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24338
in-theory        24338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (((((B and C) -> C) or D) -> E) -> ((A or (((B and C) -> C) or D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-392 ((A Am) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24338.        ((A -> (((B and C) -> C) or D)) and (((((B and C) -> C) or D) -> E) -> ((A or (((B and C) -> C) or D)) -> E))), M:tm-312, m:tm-392, u:((A Am) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24339
in-theory        24339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (E or (A -> (((B and C) -> C) or D))))
theorem-size     21
proof            (modus-ponens tm-311 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24339.        ((A -> (((B and C) -> C) or D)) and (E or (A -> (((B and C) -> C) or D)))), M:tm-311, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24340
in-theory        24340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and ((A -> (((B and C) -> C) or D)) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24340.        ((A -> (((B and C) -> C) or D)) and ((A -> (((B and C) -> C) or D)) or E)), M:tm-310, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24341
in-theory        24341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (E -> ((A -> (((B and C) -> C) or D)) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24341.        ((A -> (((B and C) -> C) or D)) and (E -> ((A -> (((B and C) -> C) or D)) and E))), M:tm-309, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24342
in-theory        24342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (E -> (A -> (((B and C) -> C) or D))))
theorem-size     21
proof            (modus-ponens tm-305 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24342.        ((A -> (((B and C) -> C) or D)) and (E -> (A -> (((B and C) -> C) or D)))), M:tm-305, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24343
in-theory        24343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-303 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24343.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E and F) -> F) or G))), M:tm-303, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24344
in-theory        24344
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D and E) -> E) or F))
theorem-size     19
proof            (modus-ponens tm-300 tm-392 ((Am (and (-> A (-> B (and A B))) C)) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24344.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D and E) -> E) or F)), M:tm-300, m:tm-392, u:((Am (and (-> A (-> B (and A B))) C)) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24345
in-theory        24345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-270 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24345.        ((A -> (((B and C) -> C) and A)) and (D -> (((E and F) -> F) or G))), M:tm-270, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24346
in-theory        24346
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-267 tm-392 ((Am (and (-> (and A B) B) C)) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24346.        ((A or (((B and C) -> C) and A)) -> (((D and E) -> E) or F)), M:tm-267, m:tm-392, u:((Am (and (-> (and A B) B) C)) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24347
in-theory        24347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-239 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24347.        ((A -> (((B and C) -> B) and A)) and (D -> (((E and F) -> F) or G))), M:tm-239, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24348
in-theory        24348
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-236 tm-392 ((Am (and (-> (and A B) A) C)) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24348.        ((A or (((B and C) -> B) and A)) -> (((D and E) -> E) or F)), M:tm-236, m:tm-392, u:((Am (and (-> (and A B) A) C)) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24349
in-theory        24349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-210 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24349.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F and G) -> G) or H))), M:tm-210, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24350
in-theory        24350
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E and F) -> F) or G))
theorem-size     25
proof            (modus-ponens tm-207 tm-392 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24350.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E and F) -> F) or G)), M:tm-207, m:tm-392, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24351
in-theory        24351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-183 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24351.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E and F) -> F) or G))), M:tm-183, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24352
in-theory        24352
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-180 tm-392 ((Am (and (-> A (-> B A)) C)) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24352.        ((A or ((B -> (C -> B)) and A)) -> (((D and E) -> E) or F)), M:tm-180, m:tm-392, u:((Am (and (-> A (-> B A)) C)) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24353
in-theory        24353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-157 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24353.        ((A -> ((B and C) -> C)) and (D -> (((E and F) -> F) or G))), M:tm-157, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24354
in-theory        24354
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-154 tm-392 ((Am (-> (and A B) B)) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-1 tm-4 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24354.        ((A or ((B and C) -> C)) -> (((D and E) -> E) or F)), M:tm-154, m:tm-392, u:((Am (-> (and A B) B)) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24355
in-theory        24355
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E and F) -> F) or G)))
theorem-size     25
proof            (modus-ponens tm-147 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24355.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E and F) -> F) or G))), M:tm-147, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24356
in-theory        24356
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D and E) -> E) or F))
theorem-size     23
proof            (modus-ponens tm-144 tm-392 ((Am (-> (and A (-> B C)) C)) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24356.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D and E) -> E) or F)), M:tm-144, m:tm-392, u:((Am (-> (and A (-> B C)) C)) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24357
in-theory        24357
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B and C) -> C) or D) -> E)) -> (((B and C) -> C) or D))
theorem-size     19
proof            (modus-ponens tm-142 tm-392 ((Am (and A (-> (or (-> (and Bm Cm) Cm) Dm) C))) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-1 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24357.        ((A and ((((B and C) -> C) or D) -> E)) -> (((B and C) -> C) or D)), M:tm-142, m:tm-392, u:((Am (and A (-> (or (-> (and Bm Cm) Cm) Dm) C))) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24358
in-theory        24358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-134 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24358.        ((A -> ((B and C) -> B)) and (D -> (((E and F) -> F) or G))), M:tm-134, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24359
in-theory        24359
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-131 tm-392 ((Am (-> (and A B) A)) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-1 tm-3 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24359.        ((A or ((B and C) -> B)) -> (((D and E) -> E) or F)), M:tm-131, m:tm-392, u:((Am (-> (and A B) A)) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24360
in-theory        24360
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E and F) -> F) or G)))
theorem-size     25
proof            (modus-ponens tm-125 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24360.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E and F) -> F) or G))), M:tm-125, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24361
in-theory        24361
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D and E) -> E) or F))
theorem-size     23
proof            (modus-ponens tm-122 tm-392 ((Am (-> (and (-> A B) C) B)) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-6 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24361.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D and E) -> E) or F)), M:tm-122, m:tm-392, u:((Am (-> (and (-> A B) C) B)) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24362
in-theory        24362
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) or C) -> D) and E) -> (((A and B) -> B) or C))
theorem-size     19
proof            (modus-ponens tm-120 tm-392 ((Am (and (-> (or (-> (and Bm Cm) Cm) Dm) B) C)) (A (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-1 tm-3 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24362.        ((((((A and B) -> B) or C) -> D) and E) -> (((A and B) -> B) or C)), M:tm-120, m:tm-392, u:((Am (and (-> (or (-> (and Bm Cm) Cm) Dm) B) C)) (A (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24363
in-theory        24363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-113 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24363.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> G) or H))), M:tm-113, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24364
in-theory        24364
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E and F) -> F) or G))
theorem-size     23
proof            (modus-ponens tm-110 tm-392 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24364.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E and F) -> F) or G)), M:tm-110, m:tm-392, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24365
in-theory        24365
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E and F) -> F) or G)))
theorem-size     29
proof            (modus-ponens tm-105 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24365.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E and F) -> F) or G))), M:tm-105, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24366
in-theory        24366
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D and E) -> E) or F))
theorem-size     27
proof            (modus-ponens tm-102 tm-392 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24366.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D and E) -> E) or F)), M:tm-102, m:tm-392, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24367
in-theory        24367
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) -> D) -> (((A and B) -> B) or C))
theorem-size     17
proof            (modus-ponens tm-96 tm-392 ((Am (-> (or (-> (and Bm Cm) Cm) Dm) B)) (A (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24367.        (((((A and B) -> B) or C) -> D) -> (((A and B) -> B) or C)), M:tm-96, m:tm-392, u:((Am (-> (or (-> (and Bm Cm) Cm) Dm) B)) (A (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24368
in-theory        24368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D and E) -> E) or F)))
theorem-size     17
proof            (modus-ponens tm-95 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24368.        (((A -> B) -> (A -> A)) and (C -> (((D and E) -> E) or F))), M:tm-95, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24369
in-theory        24369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C and D) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-92 tm-392 ((Am (-> A A)) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24369.        (((A -> B) or (A -> A)) -> (((C and D) -> D) or E)), M:tm-92, m:tm-392, u:((Am (-> A A)) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24370
in-theory        24370
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C and D) -> D) or E)))
theorem-size     11
proof            (modus-ponens tm-84 tm-392 ((A Am) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-4)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24370.        (A -> (B -> (((C and D) -> D) or E))), M:tm-84, m:tm-392, u:((A Am) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24371
in-theory        24371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-83 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24371.        ((A -> (B -> (C -> B))) and (D -> (((E and F) -> F) or G))), M:tm-83, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24372
in-theory        24372
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-80 tm-392 ((Am (-> A (-> B A))) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24372.        ((A or (B -> (C -> B))) -> (((D and E) -> E) or F)), M:tm-80, m:tm-392, u:((Am (-> A (-> B A))) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24373
in-theory        24373
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((((A and B) -> B) or C) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-392 ((Am (not (not (-> (or (-> (and Bm Cm) Cm) Dm) B)))) (A (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-10 tm-1 tm-6 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24373.        ((not (not ((((A and B) -> B) or C) -> D))) -> D), M:tm-77, m:tm-392, u:((Am (not (not (-> (or (-> (and Bm Cm) Cm) Dm) B)))) (A (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24374
in-theory        24374
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C and D) -> D) or E)))
theorem-size     15
proof            (modus-ponens tm-76 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24374.        (((not (not A)) -> A) and (B -> (((C and D) -> D) or E))), M:tm-76, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24375
in-theory        24375
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B and C) -> C) or D))
theorem-size     13
proof            (modus-ponens tm-73 tm-392 ((A Am) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-10 tm-1 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24375.        (((not (not A)) or A) -> (((B and C) -> C) or D)), M:tm-73, m:tm-392, u:((A Am) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24376
in-theory        24376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D and E) -> E) or F)))
theorem-size     21
proof            (modus-ponens tm-69 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24376.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D and E) -> E) or F))), M:tm-69, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24377
in-theory        24377
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C and D) -> D) or E))
theorem-size     19
proof            (modus-ponens tm-66 tm-392 ((Am (-> (-> A (not B)) (not A))) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-9 tm-1 tm-6 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24377.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C and D) -> D) or E)), M:tm-66, m:tm-392, u:((Am (-> (-> A (not B)) (not A))) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24378
in-theory        24378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-54 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24378.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E and F) -> F) or G))), M:tm-54, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24379
in-theory        24379
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) or F))
theorem-size     21
proof            (modus-ponens tm-51 tm-392 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24379.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D and E) -> E) or F)), M:tm-51, m:tm-392, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24380
in-theory        24380
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C and D) -> D) or E))
theorem-size     13
proof            (modus-ponens tm-50 tm-392 ((Am (or A B)) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24380.        ((A or (B or A)) -> (((C and D) -> D) or E)), M:tm-50, m:tm-392, u:((Am (or A B)) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24381
in-theory        24381
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C and D) -> D) or E))
theorem-size     13
proof            (modus-ponens tm-49 tm-392 ((Am (or A B)) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-6 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24381.        ((A or (A or B)) -> (((C and D) -> D) or E)), M:tm-49, m:tm-392, u:((Am (or A B)) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24382
in-theory        24382
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C and D) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-48 tm-392 ((Am (-> A (and B A))) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24382.        ((A or (B -> (A and B))) -> (((C and D) -> D) or E)), M:tm-48, m:tm-392, u:((Am (-> A (and B A))) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24383
in-theory        24383
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C and D) -> D) or E))
theorem-size     13
proof            (modus-ponens tm-47 tm-392 ((A Am) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24383.        (((A and B) or B) -> (((C and D) -> D) or E)), M:tm-47, m:tm-392, u:((A Am) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24384
in-theory        24384
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C and D) -> D) or E))
theorem-size     13
proof            (modus-ponens tm-46 tm-392 ((A Am) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24384.        (((A and B) or A) -> (((C and D) -> D) or E)), M:tm-46, m:tm-392, u:((A Am) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24385
in-theory        24385
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) or F))
theorem-size     21
proof            (modus-ponens tm-45 tm-392 ((Am (-> (-> A B) (-> A C))) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24385.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) or F)), M:tm-45, m:tm-392, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24386
in-theory        24386
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C and D) -> D) or E))
theorem-size     13
proof            (modus-ponens tm-44 tm-392 ((Am (-> A B)) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24386.        ((A or (B -> A)) -> (((C and D) -> D) or E)), M:tm-44, m:tm-392, u:((Am (-> A B)) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24387
in-theory        24387
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-42 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24387.        ((A -> (B or A)) and (C -> (((D and E) -> E) or F))), M:tm-42, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24388
in-theory        24388
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-32 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24388.        ((A -> (A or B)) and (C -> (((D and E) -> E) or F))), M:tm-32, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24389
in-theory        24389
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B and C) -> C) or D)))
theorem-size     11
proof            (modus-ponens tm-24 tm-392 ((A Am) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24389.        (A -> (A and (((B and C) -> C) or D))), M:tm-24, m:tm-392, u:((A Am) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24390
in-theory        24390
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) or F)))
theorem-size     17
proof            (modus-ponens tm-23 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24390.        ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) or F))), M:tm-23, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24391
in-theory        24391
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-22 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24391.        (((A and B) -> B) and (C -> (((D and E) -> E) or F))), M:tm-22, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24392
in-theory        24392
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-21 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24392.        (((A and B) -> A) and (C -> (((D and E) -> E) or F))), M:tm-21, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24393
in-theory        24393
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-20 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24393.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) or G))), M:tm-20, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24394
in-theory        24394
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-19 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24394.        ((A -> (B -> A)) and (C -> (((D and E) -> E) or F))), M:tm-19, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24395
in-theory        24395
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((((B and C) -> C) or D) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-392 ((Am (and A (-> (or (-> (and Bm Cm) Cm) Dm) C))) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-4 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24395.        ((A and ((((B and C) -> C) or D) -> E)) -> E), M:tm-17, m:tm-392, u:((Am (and A (-> (or (-> (and Bm Cm) Cm) Dm) C))) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24396
in-theory        24396
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) -> B) or C) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-392 ((Am (and (-> (or (-> (and Bm Cm) Cm) Dm) B) C)) (A (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-3 tm-1 tm-6 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24396.        ((((((A and B) -> B) or C) -> D) and E) -> D), M:tm-15, m:tm-392, u:((Am (and (-> (or (-> (and Bm Cm) Cm) Dm) B) C)) (A (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24397
in-theory        24397
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> C) or D))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-392 ((A Am) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-9 tm-1 tm-6 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24397.        ((A -> (not (((B and C) -> C) or D))) -> (not A)), M:tm-9, m:tm-392, u:((A Am) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24398
in-theory        24398
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) -> D) -> ((E or (((A and B) -> B) or C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-392 ((A Am) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24398.        (((((A and B) -> B) or C) -> D) -> ((E or (((A and B) -> B) or C)) -> D)), M:tm-8, m:tm-392, u:((A Am) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-24399
in-theory        24399
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C and D) -> D) or E)))
theorem-size     11
proof            (modus-ponens tm-7 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-7 tm-1 tm-6 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24399.        (A or (B -> (((C and D) -> D) or E))), M:tm-7, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24400
in-theory        24400
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-6 tm-1 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24400.        ((A -> (((B and C) -> C) or D)) or E), M:tm-6, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24401
in-theory        24401
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C and D) -> D) or E)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-24401.        (A -> ((B -> (((C and D) -> D) or E)) and A)), M:tm-5, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-24402
in-theory        24402
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-391 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24402.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-391, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24403
in-theory        24403
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-382 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24403.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-382, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24404
in-theory        24404
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-373 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24404.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I))), M:tm-373, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24405
in-theory        24405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-364 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24405.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-364, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24406
in-theory        24406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-354 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24406.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-354, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24407
in-theory        24407
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24407.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24408
in-theory        24408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     27
proof            (modus-ponens tm-338 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24408.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G))), M:tm-338, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24409
in-theory        24409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E))))
theorem-size     43
proof            (modus-ponens tm-327 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24409.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)))), M:tm-327, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24410
in-theory        24410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E))))
theorem-size     41
proof            (modus-ponens tm-326 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24410.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)))), M:tm-326, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24411
in-theory        24411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E))))
theorem-size     41
proof            (modus-ponens tm-325 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24411.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)))), M:tm-325, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24412
in-theory        24412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E))))
theorem-size     49
proof            (modus-ponens tm-324 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24412.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)))), M:tm-324, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24413
in-theory        24413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E))))
theorem-size     41
proof            (modus-ponens tm-323 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24413.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)))), M:tm-323, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24414
in-theory        24414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24414.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> G)), M:tm-322, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24415
in-theory        24415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24415.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> F)), M:tm-320, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24416
in-theory        24416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24416.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24417
in-theory        24417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24417.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> F))), M:tm-315, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24418
in-theory        24418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (F or ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-311 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24418.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (F or ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)))), M:tm-311, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24419
in-theory        24419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24419.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) or F)), M:tm-310, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24420
in-theory        24420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (F -> (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24420.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (F -> (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and F))), M:tm-309, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24421
in-theory        24421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((C -> (D -> (C and D))) or E))
theorem-size     27
proof            (modus-ponens tm-308 tm-393 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24421.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((C -> (D -> (C and D))) or E)), M:tm-308, m:tm-393, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em)))
================================================================
tm-name          tm-24422
in-theory        24422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (A -> (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-307 tm-393 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24422.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (A -> (B -> (A and B)))), M:tm-307, m:tm-393, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em)))
================================================================
tm-name          tm-24423
in-theory        24423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (F -> ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-305 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24423.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (F -> ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)))), M:tm-305, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24424
in-theory        24424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-303 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24424.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-303, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24425
in-theory        24425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-270 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24425.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-270, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24426
in-theory        24426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-239 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24426.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-239, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24427
in-theory        24427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     35
proof            (modus-ponens tm-210 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24427.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I))), M:tm-210, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24428
in-theory        24428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-183 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24428.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-183, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24429
in-theory        24429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-157 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24429.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-157, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24430
in-theory        24430
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     33
proof            (modus-ponens tm-147 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24430.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-147, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24431
in-theory        24431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-134 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24431.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-134, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24432
in-theory        24432
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     33
proof            (modus-ponens tm-125 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24432.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-125, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24433
in-theory        24433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-113 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24433.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I))), M:tm-113, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24434
in-theory        24434
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     37
proof            (modus-ponens tm-105 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24434.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-105, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24435
in-theory        24435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-95 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24435.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G))), M:tm-95, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24436
in-theory        24436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-83 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24436.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-83, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24437
in-theory        24437
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> (E -> (D and E))) or F)))
theorem-size     23
proof            (modus-ponens tm-76 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24437.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> (E -> (D and E))) or F))), M:tm-76, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24438
in-theory        24438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     29
proof            (modus-ponens tm-69 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24438.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G))), M:tm-69, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24439
in-theory        24439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-54 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24439.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-54, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24440
in-theory        24440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-42 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24440.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G))), M:tm-42, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24441
in-theory        24441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-32 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24441.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G))), M:tm-32, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24442
in-theory        24442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-23 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24442.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G))), M:tm-23, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24443
in-theory        24443
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-22 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24443.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G))), M:tm-22, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24444
in-theory        24444
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-21 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24444.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G))), M:tm-21, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24445
in-theory        24445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-20 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24445.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-20, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24446
in-theory        24446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-19 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24446.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> (F -> (E and F))) or G))), M:tm-19, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24447
in-theory        24447
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((D -> (E -> (D and E))) or F)))
theorem-size     19
proof            (modus-ponens tm-7 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24447.        (A or ((B -> (C -> (B and C))) and ((D -> (E -> (D and E))) or F))), M:tm-7, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24448
in-theory        24448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-6 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24448.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) or F), M:tm-6, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24449
in-theory        24449
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((D -> (E -> (D and E))) or F)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24449.        (A -> (((B -> (C -> (B and C))) and ((D -> (E -> (D and E))) or F)) and A)), M:tm-5, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24450
in-theory        24450
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((D -> (E -> (D and E))) or F)))
theorem-size     19
proof            (modus-ponens tm-1 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24450.        (A -> ((B -> (C -> (B and C))) and ((D -> (E -> (D and E))) or F))), M:tm-1, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24451
in-theory        24451
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-391 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24451.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-391, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24452
in-theory        24452
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-382 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24452.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-382, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24453
in-theory        24453
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-373 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24453.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I))), M:tm-373, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24454
in-theory        24454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-364 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24454.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-364, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24455
in-theory        24455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-354 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24455.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-354, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24456
in-theory        24456
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24456.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24457
in-theory        24457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-338 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24457.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G))), M:tm-338, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24458
in-theory        24458
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> (D -> (C and D))) or E))))
theorem-size     39
proof            (modus-ponens tm-327 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24458.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> (D -> (C and D))) or E)))), M:tm-327, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24459
in-theory        24459
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> G) and (((A and B) -> B) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-326 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24459.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> G) and (((A and B) -> B) and ((C -> (D -> (C and D))) or E)))), M:tm-326, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24460
in-theory        24460
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> F) and (((A and B) -> B) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-325 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24460.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> F) and (((A and B) -> B) and ((C -> (D -> (C and D))) or E)))), M:tm-325, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24461
in-theory        24461
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> (D -> (C and D))) or E))))
theorem-size     45
proof            (modus-ponens tm-324 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24461.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> (D -> (C and D))) or E)))), M:tm-324, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24462
in-theory        24462
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-323 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24462.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> (D -> (C and D))) or E)))), M:tm-323, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24463
in-theory        24463
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24463.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> G)), M:tm-322, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24464
in-theory        24464
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24464.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> F)), M:tm-320, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24465
in-theory        24465
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24465.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24466
in-theory        24466
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24466.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> F))), M:tm-315, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24467
in-theory        24467
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (F or (((A and B) -> B) and ((C -> (D -> (C and D))) or E))))
theorem-size     33
proof            (modus-ponens tm-311 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24467.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (F or (((A and B) -> B) and ((C -> (D -> (C and D))) or E)))), M:tm-311, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24468
in-theory        24468
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24468.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) or F)), M:tm-310, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24469
in-theory        24469
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (F -> ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24469.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (F -> ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and F))), M:tm-309, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24470
in-theory        24470
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((C -> (D -> (C and D))) or E))
theorem-size     25
proof            (modus-ponens tm-308 tm-394 ((A (-> (and Am Bm) Bm)) (B (or (-> Cm (-> Dm (and Cm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24470.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((C -> (D -> (C and D))) or E)), M:tm-308, m:tm-394, u:((A (-> (and Am Bm) Bm)) (B (or (-> Cm (-> Dm (and Cm Dm))) Em)))
================================================================
tm-name          tm-24471
in-theory        24471
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((A and B) -> B))
theorem-size     21
proof            (modus-ponens tm-307 tm-394 ((A (-> (and Am Bm) Bm)) (B (or (-> Cm (-> Dm (and Cm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24471.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((A and B) -> B)), M:tm-307, m:tm-394, u:((A (-> (and Am Bm) Bm)) (B (or (-> Cm (-> Dm (and Cm Dm))) Em)))
================================================================
tm-name          tm-24472
in-theory        24472
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (F -> (((A and B) -> B) and ((C -> (D -> (C and D))) or E))))
theorem-size     33
proof            (modus-ponens tm-305 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24472.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (F -> (((A and B) -> B) and ((C -> (D -> (C and D))) or E)))), M:tm-305, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24473
in-theory        24473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-303 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24473.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-303, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24474
in-theory        24474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-270 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24474.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-270, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24475
in-theory        24475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-239 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24475.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-239, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24476
in-theory        24476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-210 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24476.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I))), M:tm-210, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24477
in-theory        24477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-183 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24477.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-183, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24478
in-theory        24478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-157 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24478.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-157, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24479
in-theory        24479
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-147 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24479.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-147, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24480
in-theory        24480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-134 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24480.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-134, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24481
in-theory        24481
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-125 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24481.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-125, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24482
in-theory        24482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-113 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24482.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I))), M:tm-113, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24483
in-theory        24483
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     35
proof            (modus-ponens tm-105 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24483.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-105, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24484
in-theory        24484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-95 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24484.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G))), M:tm-95, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24485
in-theory        24485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-83 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24485.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-83, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24486
in-theory        24486
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((D -> (E -> (D and E))) or F)))
theorem-size     21
proof            (modus-ponens tm-76 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-10 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24486.        (((not (not A)) -> A) and (((B and C) -> C) and ((D -> (E -> (D and E))) or F))), M:tm-76, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24487
in-theory        24487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G)))
theorem-size     27
proof            (modus-ponens tm-69 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-9 tm-4 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24487.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G))), M:tm-69, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24488
in-theory        24488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-54 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24488.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-54, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24489
in-theory        24489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-42 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24489.        ((A -> (B or A)) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G))), M:tm-42, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24490
in-theory        24490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-32 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24490.        ((A -> (A or B)) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G))), M:tm-32, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24491
in-theory        24491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-23 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24491.        ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G))), M:tm-23, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24492
in-theory        24492
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-22 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24492.        (((A and B) -> B) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G))), M:tm-22, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24493
in-theory        24493
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-21 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24493.        (((A and B) -> A) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G))), M:tm-21, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24494
in-theory        24494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-20 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24494.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-20, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24495
in-theory        24495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-19 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24495.        ((A -> (B -> A)) and (((C and D) -> D) and ((E -> (F -> (E and F))) or G))), M:tm-19, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24496
in-theory        24496
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-7 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-7 tm-5 tm-4 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24496.        (A or (((B and C) -> C) and ((D -> (E -> (D and E))) or F))), M:tm-7, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24497
in-theory        24497
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24497.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) or F), M:tm-6, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24498
in-theory        24498
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((D -> (E -> (D and E))) or F)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24498.        (A -> ((((B and C) -> C) and ((D -> (E -> (D and E))) or F)) and A)), M:tm-5, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24499
in-theory        24499
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-1 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-1 tm-5 tm-4 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24499.        (A -> (((B and C) -> C) and ((D -> (E -> (D and E))) or F))), M:tm-1, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24500
in-theory        24500
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-391 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24500.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-391, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24501
in-theory        24501
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-382 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24501.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-382, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24502
in-theory        24502
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-373 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24502.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I))), M:tm-373, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24503
in-theory        24503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-364 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24503.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-364, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24504
in-theory        24504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-354 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24504.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-354, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24505
in-theory        24505
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24505.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24506
in-theory        24506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-338 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24506.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G))), M:tm-338, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24507
in-theory        24507
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> (D -> (C and D))) or E))))
theorem-size     39
proof            (modus-ponens tm-327 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24507.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> (D -> (C and D))) or E)))), M:tm-327, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24508
in-theory        24508
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> G) and (((A and B) -> A) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-326 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24508.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> G) and (((A and B) -> A) and ((C -> (D -> (C and D))) or E)))), M:tm-326, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24509
in-theory        24509
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> F) and (((A and B) -> A) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-325 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24509.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> F) and (((A and B) -> A) and ((C -> (D -> (C and D))) or E)))), M:tm-325, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24510
in-theory        24510
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> (D -> (C and D))) or E))))
theorem-size     45
proof            (modus-ponens tm-324 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24510.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> (D -> (C and D))) or E)))), M:tm-324, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24511
in-theory        24511
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-323 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24511.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> (D -> (C and D))) or E)))), M:tm-323, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24512
in-theory        24512
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24512.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> G)), M:tm-322, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24513
in-theory        24513
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24513.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> F)), M:tm-320, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24514
in-theory        24514
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24514.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24515
in-theory        24515
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24515.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> F))), M:tm-315, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24516
in-theory        24516
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (F or (((A and B) -> A) and ((C -> (D -> (C and D))) or E))))
theorem-size     33
proof            (modus-ponens tm-311 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24516.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (F or (((A and B) -> A) and ((C -> (D -> (C and D))) or E)))), M:tm-311, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24517
in-theory        24517
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24517.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) or F)), M:tm-310, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24518
in-theory        24518
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (F -> ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24518.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (F -> ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and F))), M:tm-309, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24519
in-theory        24519
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((C -> (D -> (C and D))) or E))
theorem-size     25
proof            (modus-ponens tm-308 tm-395 ((A (-> (and Am Bm) Am)) (B (or (-> Cm (-> Dm (and Cm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24519.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((C -> (D -> (C and D))) or E)), M:tm-308, m:tm-395, u:((A (-> (and Am Bm) Am)) (B (or (-> Cm (-> Dm (and Cm Dm))) Em)))
================================================================
tm-name          tm-24520
in-theory        24520
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((A and B) -> A))
theorem-size     21
proof            (modus-ponens tm-307 tm-395 ((A (-> (and Am Bm) Am)) (B (or (-> Cm (-> Dm (and Cm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24520.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((A and B) -> A)), M:tm-307, m:tm-395, u:((A (-> (and Am Bm) Am)) (B (or (-> Cm (-> Dm (and Cm Dm))) Em)))
================================================================
tm-name          tm-24521
in-theory        24521
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (F -> (((A and B) -> A) and ((C -> (D -> (C and D))) or E))))
theorem-size     33
proof            (modus-ponens tm-305 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24521.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (F -> (((A and B) -> A) and ((C -> (D -> (C and D))) or E)))), M:tm-305, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24522
in-theory        24522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-303 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24522.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-303, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24523
in-theory        24523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-270 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24523.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-270, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24524
in-theory        24524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-239 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24524.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-239, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24525
in-theory        24525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-210 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24525.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I))), M:tm-210, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24526
in-theory        24526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-183 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24526.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-183, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24527
in-theory        24527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-157 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24527.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-157, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24528
in-theory        24528
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-147 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24528.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-147, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24529
in-theory        24529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-134 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24529.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-134, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24530
in-theory        24530
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-125 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24530.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-125, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24531
in-theory        24531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-113 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24531.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I))), M:tm-113, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24532
in-theory        24532
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     35
proof            (modus-ponens tm-105 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24532.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-105, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24533
in-theory        24533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-95 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24533.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G))), M:tm-95, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24534
in-theory        24534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-83 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24534.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-83, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24535
in-theory        24535
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((D -> (E -> (D and E))) or F)))
theorem-size     21
proof            (modus-ponens tm-76 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-10 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24535.        (((not (not A)) -> A) and (((B and C) -> B) and ((D -> (E -> (D and E))) or F))), M:tm-76, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24536
in-theory        24536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G)))
theorem-size     27
proof            (modus-ponens tm-69 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-9 tm-3 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24536.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G))), M:tm-69, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24537
in-theory        24537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-54 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24537.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-54, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24538
in-theory        24538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-42 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24538.        ((A -> (B or A)) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G))), M:tm-42, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24539
in-theory        24539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-32 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24539.        ((A -> (A or B)) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G))), M:tm-32, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24540
in-theory        24540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-23 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24540.        ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G))), M:tm-23, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24541
in-theory        24541
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-22 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24541.        (((A and B) -> B) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G))), M:tm-22, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24542
in-theory        24542
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-21 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24542.        (((A and B) -> A) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G))), M:tm-21, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24543
in-theory        24543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-20 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24543.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-20, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24544
in-theory        24544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-19 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24544.        ((A -> (B -> A)) and (((C and D) -> C) and ((E -> (F -> (E and F))) or G))), M:tm-19, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24545
in-theory        24545
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-7 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-7 tm-5 tm-3 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24545.        (A or (((B and C) -> B) and ((D -> (E -> (D and E))) or F))), M:tm-7, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24546
in-theory        24546
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24546.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) or F), M:tm-6, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24547
in-theory        24547
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((D -> (E -> (D and E))) or F)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24547.        (A -> ((((B and C) -> B) and ((D -> (E -> (D and E))) or F)) and A)), M:tm-5, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24548
in-theory        24548
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-1 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-1 tm-5 tm-3 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24548.        (A -> (((B and C) -> B) and ((D -> (E -> (D and E))) or F))), M:tm-1, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24549
in-theory        24549
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-391 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24549.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-391, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24550
in-theory        24550
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-382 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24550.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-382, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24551
in-theory        24551
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> (H and I))) or J)))
theorem-size     39
proof            (modus-ponens tm-373 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24551.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-373, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24552
in-theory        24552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-364 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24552.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-364, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24553
in-theory        24553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-354 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24553.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-354, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24554
in-theory        24554
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24554.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24555
in-theory        24555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     33
proof            (modus-ponens tm-338 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24555.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-338, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24556
in-theory        24556
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     55
proof            (modus-ponens tm-327 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24556.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-327, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24557
in-theory        24557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     53
proof            (modus-ponens tm-326 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24557.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-326, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24558
in-theory        24558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     53
proof            (modus-ponens tm-325 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24558.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-325, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24559
in-theory        24559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     61
proof            (modus-ponens tm-324 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24559.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-324, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24560
in-theory        24560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     53
proof            (modus-ponens tm-323 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24560.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-323, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24561
in-theory        24561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24561.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((G and H) -> H)), M:tm-322, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24562
in-theory        24562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24562.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((G and H) -> G)), M:tm-320, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24563
in-theory        24563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24563.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24564
in-theory        24564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24564.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (H -> G))), M:tm-315, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24565
in-theory        24565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     49
proof            (modus-ponens tm-311 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24565.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-311, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24566
in-theory        24566
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24566.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) or G)), M:tm-310, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24567
in-theory        24567
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24567.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and G))), M:tm-309, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24568
in-theory        24568
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((D -> (E -> (D and E))) or F))
theorem-size     33
proof            (modus-ponens tm-308 tm-396 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (-> Em (and Dm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24568.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((D -> (E -> (D and E))) or F)), M:tm-308, m:tm-396, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (-> Em (and Dm Em))) Fm)))
================================================================
tm-name          tm-24569
in-theory        24569
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-396 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (-> Em (and Dm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24569.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-396, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (-> Em (and Dm Em))) Fm)))
================================================================
tm-name          tm-24570
in-theory        24570
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     49
proof            (modus-ponens tm-305 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24570.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-305, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24571
in-theory        24571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     35
proof            (modus-ponens tm-303 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24571.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-303, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24572
in-theory        24572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-270 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24572.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-270, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24573
in-theory        24573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-239 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24573.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-239, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24574
in-theory        24574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> (H and I))) or J)))
theorem-size     41
proof            (modus-ponens tm-210 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24574.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-210, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24575
in-theory        24575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-183 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24575.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-183, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24576
in-theory        24576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-157 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24576.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-157, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24577
in-theory        24577
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     39
proof            (modus-ponens tm-147 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24577.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-147, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24578
in-theory        24578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-134 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24578.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-134, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24579
in-theory        24579
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     39
proof            (modus-ponens tm-125 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24579.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-125, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24580
in-theory        24580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> (H and I))) or J)))
theorem-size     39
proof            (modus-ponens tm-113 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24580.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-113, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24581
in-theory        24581
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     43
proof            (modus-ponens tm-105 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24581.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-105, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24582
in-theory        24582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-95 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24582.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-95, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24583
in-theory        24583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-83 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24583.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-83, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24584
in-theory        24584
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     29
proof            (modus-ponens tm-76 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24584.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> (E and F))) or G))), M:tm-76, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24585
in-theory        24585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     35
proof            (modus-ponens tm-69 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24585.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-69, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24586
in-theory        24586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     37
proof            (modus-ponens tm-54 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24586.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-54, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24587
in-theory        24587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-42 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24587.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-42, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24588
in-theory        24588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-32 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24588.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-32, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24589
in-theory        24589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-23 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24589.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-23, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24590
in-theory        24590
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-22 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24590.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-22, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24591
in-theory        24591
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-21 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24591.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-21, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24592
in-theory        24592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     37
proof            (modus-ponens tm-20 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24592.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-20, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24593
in-theory        24593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-19 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24593.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G -> (F and G))) or H))), M:tm-19, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24594
in-theory        24594
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-7 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-7 tm-5 tm-2 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24594.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> (E and F))) or G))), M:tm-7, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24595
in-theory        24595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24595.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) or G), M:tm-6, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24596
in-theory        24596
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> (E and F))) or G)) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24596.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> (E and F))) or G)) and A)), M:tm-5, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24597
in-theory        24597
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-1 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-1 tm-5 tm-2 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24597.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F -> (E and F))) or G))), M:tm-1, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-24598
in-theory        24598
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-391 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24598.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-391, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24599
in-theory        24599
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-382 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24599.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-382, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24600
in-theory        24600
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-373 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24600.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I))), M:tm-373, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24601
in-theory        24601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-364 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24601.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-364, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24602
in-theory        24602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-354 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24602.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-354, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24603
in-theory        24603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24603.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24604
in-theory        24604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-338 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24604.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G))), M:tm-338, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24605
in-theory        24605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     39
proof            (modus-ponens tm-327 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24605.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)))), M:tm-327, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24606
in-theory        24606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-326 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24606.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)))), M:tm-326, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24607
in-theory        24607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-325 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24607.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)))), M:tm-325, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24608
in-theory        24608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     45
proof            (modus-ponens tm-324 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24608.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)))), M:tm-324, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24609
in-theory        24609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-323 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24609.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)))), M:tm-323, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24610
in-theory        24610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24610.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> G)), M:tm-322, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24611
in-theory        24611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24611.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> F)), M:tm-320, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24612
in-theory        24612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24612.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24613
in-theory        24613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24613.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> F))), M:tm-315, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24614
in-theory        24614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (F or ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     33
proof            (modus-ponens tm-311 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24614.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (F or ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)))), M:tm-311, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24615
in-theory        24615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24615.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) or F)), M:tm-310, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24616
in-theory        24616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (F -> (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24616.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (F -> (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and F))), M:tm-309, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24617
in-theory        24617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((C -> (D -> (C and D))) or E))
theorem-size     25
proof            (modus-ponens tm-308 tm-397 ((A (-> Am (-> Bm Am))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24617.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((C -> (D -> (C and D))) or E)), M:tm-308, m:tm-397, u:((A (-> Am (-> Bm Am))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em)))
================================================================
tm-name          tm-24618
in-theory        24618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (A -> (B -> A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-397 ((A (-> Am (-> Bm Am))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24618.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (A -> (B -> A))), M:tm-307, m:tm-397, u:((A (-> Am (-> Bm Am))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em)))
================================================================
tm-name          tm-24619
in-theory        24619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (F -> ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     33
proof            (modus-ponens tm-305 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24619.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (F -> ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)))), M:tm-305, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24620
in-theory        24620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-303 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24620.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-303, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24621
in-theory        24621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-270 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24621.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-270, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24622
in-theory        24622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-239 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24622.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-239, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24623
in-theory        24623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-210 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24623.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I))), M:tm-210, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24624
in-theory        24624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-183 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24624.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-183, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24625
in-theory        24625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-157 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24625.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-157, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24626
in-theory        24626
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-147 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24626.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-147, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24627
in-theory        24627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-134 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24627.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-134, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24628
in-theory        24628
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-125 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24628.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-125, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24629
in-theory        24629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-113 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24629.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I))), M:tm-113, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24630
in-theory        24630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     35
proof            (modus-ponens tm-105 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24630.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-105, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24631
in-theory        24631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-95 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24631.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G))), M:tm-95, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24632
in-theory        24632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-83 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24632.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-83, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24633
in-theory        24633
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> (E -> (D and E))) or F)))
theorem-size     21
proof            (modus-ponens tm-76 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24633.        (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> (E -> (D and E))) or F))), M:tm-76, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24634
in-theory        24634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     27
proof            (modus-ponens tm-69 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24634.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G))), M:tm-69, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24635
in-theory        24635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-54 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24635.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-54, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24636
in-theory        24636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-42 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24636.        ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G))), M:tm-42, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24637
in-theory        24637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-32 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24637.        ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G))), M:tm-32, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24638
in-theory        24638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-23 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24638.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G))), M:tm-23, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24639
in-theory        24639
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-22 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24639.        (((A and B) -> B) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G))), M:tm-22, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24640
in-theory        24640
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-21 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24640.        (((A and B) -> A) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G))), M:tm-21, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24641
in-theory        24641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-20 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24641.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-20, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24642
in-theory        24642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-19 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24642.        ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> (F -> (E and F))) or G))), M:tm-19, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24643
in-theory        24643
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-7 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-7 tm-5 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24643.        (A or ((B -> (C -> B)) and ((D -> (E -> (D and E))) or F))), M:tm-7, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24644
in-theory        24644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24644.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) or F), M:tm-6, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24645
in-theory        24645
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((D -> (E -> (D and E))) or F)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24645.        (A -> (((B -> (C -> B)) and ((D -> (E -> (D and E))) or F)) and A)), M:tm-5, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24646
in-theory        24646
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-1 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24646.        (A -> ((B -> (C -> B)) and ((D -> (E -> (D and E))) or F))), M:tm-1, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-24647
in-theory        24647
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-391 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24647.        ((((A and B) -> B) or C) and (D or ((E -> (F -> (E and F))) or G))), M:tm-391, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24648
in-theory        24648
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-382 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24648.        ((((A and B) -> A) or C) and (D or ((E -> (F -> (E and F))) or G))), M:tm-382, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24649
in-theory        24649
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-373 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24649.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> (G -> (F and G))) or H))), M:tm-373, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24650
in-theory        24650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-364 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24650.        (((A -> (B -> A)) or C) and (D or ((E -> (F -> (E and F))) or G))), M:tm-364, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24651
in-theory        24651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-354 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24651.        ((A -> (B -> (C -> (B and C)))) and (D or ((E -> (F -> (E and F))) or G))), M:tm-354, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24652
in-theory        24652
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24652.        ((A or ((B -> (C -> (B and C))) or D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24653
in-theory        24653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((D -> (E -> (D and E))) or F)))
theorem-size     21
proof            (modus-ponens tm-338 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24653.        (((A -> B) -> (A -> (A and B))) and (C or ((D -> (E -> (D and E))) or F))), M:tm-338, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24654
in-theory        24654
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and ((E -> (F -> (E and F))) and (A or ((B -> (C -> (B and C))) or D))))
theorem-size     31
proof            (modus-ponens tm-327 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24654.        ((A or ((B -> (C -> (B and C))) or D)) and ((E -> (F -> (E and F))) and (A or ((B -> (C -> (B and C))) or D)))), M:tm-327, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24655
in-theory        24655
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and (((E and F) -> F) and (A or ((B -> (C -> (B and C))) or D))))
theorem-size     29
proof            (modus-ponens tm-326 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24655.        ((A or ((B -> (C -> (B and C))) or D)) and (((E and F) -> F) and (A or ((B -> (C -> (B and C))) or D)))), M:tm-326, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24656
in-theory        24656
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and (((E and F) -> E) and (A or ((B -> (C -> (B and C))) or D))))
theorem-size     29
proof            (modus-ponens tm-325 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24656.        ((A or ((B -> (C -> (B and C))) or D)) and (((E and F) -> E) and (A or ((B -> (C -> (B and C))) or D)))), M:tm-325, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24657
in-theory        24657
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> (C -> (B and C))) or D))))
theorem-size     37
proof            (modus-ponens tm-324 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24657.        ((A or ((B -> (C -> (B and C))) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> (C -> (B and C))) or D)))), M:tm-324, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24658
in-theory        24658
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and ((E -> (F -> E)) and (A or ((B -> (C -> (B and C))) or D))))
theorem-size     29
proof            (modus-ponens tm-323 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24658.        ((A or ((B -> (C -> (B and C))) or D)) and ((E -> (F -> E)) and (A or ((B -> (C -> (B and C))) or D)))), M:tm-323, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24659
in-theory        24659
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24659.        ((A or ((B -> (C -> (B and C))) or D)) and ((E and F) -> F)), M:tm-322, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24660
in-theory        24660
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24660.        ((A or ((B -> (C -> (B and C))) or D)) and ((E and F) -> E)), M:tm-320, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24661
in-theory        24661
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24661.        ((A or ((B -> (C -> (B and C))) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24662
in-theory        24662
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24662.        ((A or ((B -> (C -> (B and C))) or D)) and (E -> (F -> E))), M:tm-315, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24663
in-theory        24663
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and (E or (A or ((B -> (C -> (B and C))) or D))))
theorem-size     25
proof            (modus-ponens tm-311 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24663.        ((A or ((B -> (C -> (B and C))) or D)) and (E or (A or ((B -> (C -> (B and C))) or D)))), M:tm-311, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24664
in-theory        24664
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and ((A or ((B -> (C -> (B and C))) or D)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24664.        ((A or ((B -> (C -> (B and C))) or D)) and ((A or ((B -> (C -> (B and C))) or D)) or E)), M:tm-310, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24665
in-theory        24665
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and (E -> ((A or ((B -> (C -> (B and C))) or D)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24665.        ((A or ((B -> (C -> (B and C))) or D)) and (E -> ((A or ((B -> (C -> (B and C))) or D)) and E))), M:tm-309, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24666
in-theory        24666
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and (E -> (A or ((B -> (C -> (B and C))) or D))))
theorem-size     25
proof            (modus-ponens tm-305 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24666.        ((A or ((B -> (C -> (B and C))) or D)) and (E -> (A or ((B -> (C -> (B and C))) or D)))), M:tm-305, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24667
in-theory        24667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-303 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24667.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-303, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24668
in-theory        24668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-270 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24668.        ((A -> (((B and C) -> C) and A)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-270, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24669
in-theory        24669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-239 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24669.        ((A -> (((B and C) -> B) and A)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-239, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24670
in-theory        24670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-210 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24670.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> (G -> (F and G))) or H))), M:tm-210, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24671
in-theory        24671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-183 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24671.        ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-183, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24672
in-theory        24672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-157 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24672.        ((A -> ((B and C) -> C)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-157, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24673
in-theory        24673
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     27
proof            (modus-ponens tm-147 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24673.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-147, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24674
in-theory        24674
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-134 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24674.        ((A -> ((B and C) -> B)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-134, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24675
in-theory        24675
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     27
proof            (modus-ponens tm-125 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24675.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-125, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24676
in-theory        24676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-113 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24676.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G -> (F and G))) or H))), M:tm-113, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24677
in-theory        24677
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     31
proof            (modus-ponens tm-105 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24677.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> (F -> (E and F))) or G))), M:tm-105, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24678
in-theory        24678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((D -> (E -> (D and E))) or F)))
theorem-size     19
proof            (modus-ponens tm-95 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24678.        (((A -> B) -> (A -> A)) and (C or ((D -> (E -> (D and E))) or F))), M:tm-95, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24679
in-theory        24679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-83 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24679.        ((A -> (B -> (C -> B))) and (D or ((E -> (F -> (E and F))) or G))), M:tm-83, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24680
in-theory        24680
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((C -> (D -> (C and D))) or E)))
theorem-size     17
proof            (modus-ponens tm-76 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24680.        (((not (not A)) -> A) and (B or ((C -> (D -> (C and D))) or E))), M:tm-76, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24681
in-theory        24681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> (E -> (D and E))) or F)))
theorem-size     23
proof            (modus-ponens tm-69 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24681.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> (E -> (D and E))) or F))), M:tm-69, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24682
in-theory        24682
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-54 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24682.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F -> (E and F))) or G))), M:tm-54, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24683
in-theory        24683
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-42 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24683.        ((A -> (B or A)) and (C or ((D -> (E -> (D and E))) or F))), M:tm-42, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24684
in-theory        24684
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-32 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24684.        ((A -> (A or B)) and (C or ((D -> (E -> (D and E))) or F))), M:tm-32, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24685
in-theory        24685
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((D -> (E -> (D and E))) or F)))
theorem-size     19
proof            (modus-ponens tm-23 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24685.        ((A -> (B -> (A and B))) and (C or ((D -> (E -> (D and E))) or F))), M:tm-23, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24686
in-theory        24686
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-22 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24686.        (((A and B) -> B) and (C or ((D -> (E -> (D and E))) or F))), M:tm-22, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24687
in-theory        24687
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-21 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24687.        (((A and B) -> A) and (C or ((D -> (E -> (D and E))) or F))), M:tm-21, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24688
in-theory        24688
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-20 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24688.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> (E and F))) or G))), M:tm-20, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24689
in-theory        24689
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-19 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24689.        ((A -> (B -> A)) and (C or ((D -> (E -> (D and E))) or F))), M:tm-19, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24690
in-theory        24690
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or ((C -> (D -> (C and D))) or E)))
theorem-size     13
proof            (modus-ponens tm-7 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-7 tm-6 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24690.        (A or (B or ((C -> (D -> (C and D))) or E))), M:tm-7, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24691
in-theory        24691
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-6 tm-7 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24691.        ((A or ((B -> (C -> (B and C))) or D)) or E), M:tm-6, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24692
in-theory        24692
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> (D -> (C and D))) or E)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24692.        (A -> ((B or ((C -> (D -> (C and D))) or E)) and A)), M:tm-5, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24693
in-theory        24693
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (D -> (C and D))) or E)))
theorem-size     13
proof            (modus-ponens tm-1 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-1 tm-7 tm-6 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24693.        (A -> (B or ((C -> (D -> (C and D))) or E))), M:tm-1, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-24694
in-theory        24694
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-391 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24694.        ((((A and B) -> B) or C) and (((D -> (E -> (D and E))) or F) or G)), M:tm-391, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24695
in-theory        24695
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-382 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24695.        ((((A and B) -> A) or C) and (((D -> (E -> (D and E))) or F) or G)), M:tm-382, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24696
in-theory        24696
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> (E and F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-373 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24696.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> (E and F))) or G) or H)), M:tm-373, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24697
in-theory        24697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-364 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24697.        (((A -> (B -> A)) or C) and (((D -> (E -> (D and E))) or F) or G)), M:tm-364, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24698
in-theory        24698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     21
proof            (modus-ponens tm-354 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24698.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> (D and E))) or F) or G)), M:tm-354, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24699
in-theory        24699
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24699.        ((((A -> (B -> (A and B))) or C) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24700
in-theory        24700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> (C and D))) or E) or F))
theorem-size     21
proof            (modus-ponens tm-338 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24700.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> (C and D))) or E) or F)), M:tm-338, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24701
in-theory        24701
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and ((E -> (F -> (E and F))) and (((A -> (B -> (A and B))) or C) or D)))
theorem-size     31
proof            (modus-ponens tm-327 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24701.        ((((A -> (B -> (A and B))) or C) or D) and ((E -> (F -> (E and F))) and (((A -> (B -> (A and B))) or C) or D))), M:tm-327, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24702
in-theory        24702
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and (((E and F) -> F) and (((A -> (B -> (A and B))) or C) or D)))
theorem-size     29
proof            (modus-ponens tm-326 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24702.        ((((A -> (B -> (A and B))) or C) or D) and (((E and F) -> F) and (((A -> (B -> (A and B))) or C) or D))), M:tm-326, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24703
in-theory        24703
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and (((E and F) -> E) and (((A -> (B -> (A and B))) or C) or D)))
theorem-size     29
proof            (modus-ponens tm-325 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24703.        ((((A -> (B -> (A and B))) or C) or D) and (((E and F) -> E) and (((A -> (B -> (A and B))) or C) or D))), M:tm-325, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24704
in-theory        24704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> (A and B))) or C) or D)))
theorem-size     37
proof            (modus-ponens tm-324 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24704.        ((((A -> (B -> (A and B))) or C) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> (A and B))) or C) or D))), M:tm-324, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24705
in-theory        24705
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and ((E -> (F -> E)) and (((A -> (B -> (A and B))) or C) or D)))
theorem-size     29
proof            (modus-ponens tm-323 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24705.        ((((A -> (B -> (A and B))) or C) or D) and ((E -> (F -> E)) and (((A -> (B -> (A and B))) or C) or D))), M:tm-323, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24706
in-theory        24706
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24706.        ((((A -> (B -> (A and B))) or C) or D) and ((E and F) -> F)), M:tm-322, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24707
in-theory        24707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24707.        ((((A -> (B -> (A and B))) or C) or D) and ((E and F) -> E)), M:tm-320, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24708
in-theory        24708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24708.        ((((A -> (B -> (A and B))) or C) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24709
in-theory        24709
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24709.        ((((A -> (B -> (A and B))) or C) or D) and (E -> (F -> E))), M:tm-315, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24710
in-theory        24710
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and (E or (((A -> (B -> (A and B))) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-311 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24710.        ((((A -> (B -> (A and B))) or C) or D) and (E or (((A -> (B -> (A and B))) or C) or D))), M:tm-311, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24711
in-theory        24711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and ((((A -> (B -> (A and B))) or C) or D) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24711.        ((((A -> (B -> (A and B))) or C) or D) and ((((A -> (B -> (A and B))) or C) or D) or E)), M:tm-310, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24712
in-theory        24712
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and (E -> ((((A -> (B -> (A and B))) or C) or D) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24712.        ((((A -> (B -> (A and B))) or C) or D) and (E -> ((((A -> (B -> (A and B))) or C) or D) and E))), M:tm-309, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24713
in-theory        24713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and (E -> (((A -> (B -> (A and B))) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-305 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24713.        ((((A -> (B -> (A and B))) or C) or D) and (E -> (((A -> (B -> (A and B))) or C) or D))), M:tm-305, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24714
in-theory        24714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     23
proof            (modus-ponens tm-303 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24714.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-303, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24715
in-theory        24715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     21
proof            (modus-ponens tm-270 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24715.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-270, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24716
in-theory        24716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     21
proof            (modus-ponens tm-239 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24716.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-239, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24717
in-theory        24717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> (E and F))) or G) or H))
theorem-size     29
proof            (modus-ponens tm-210 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24717.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> (E and F))) or G) or H)), M:tm-210, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24718
in-theory        24718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     21
proof            (modus-ponens tm-183 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24718.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-183, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24719
in-theory        24719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-157 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24719.        ((A -> ((B and C) -> C)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-157, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24720
in-theory        24720
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     27
proof            (modus-ponens tm-147 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24720.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-147, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24721
in-theory        24721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-134 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24721.        ((A -> ((B and C) -> B)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-134, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24722
in-theory        24722
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     27
proof            (modus-ponens tm-125 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24722.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-125, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24723
in-theory        24723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> (E and F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-113 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24723.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> (E and F))) or G) or H)), M:tm-113, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24724
in-theory        24724
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     31
proof            (modus-ponens tm-105 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24724.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> (D and E))) or F) or G)), M:tm-105, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24725
in-theory        24725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> (C and D))) or E) or F))
theorem-size     19
proof            (modus-ponens tm-95 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24725.        (((A -> B) -> (A -> A)) and (((C -> (D -> (C and D))) or E) or F)), M:tm-95, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24726
in-theory        24726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-83 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24726.        ((A -> (B -> (C -> B))) and (((D -> (E -> (D and E))) or F) or G)), M:tm-83, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24727
in-theory        24727
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> (B and C))) or D) or E))
theorem-size     17
proof            (modus-ponens tm-76 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24727.        (((not (not A)) -> A) and (((B -> (C -> (B and C))) or D) or E)), M:tm-76, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24728
in-theory        24728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> (C and D))) or E) or F))
theorem-size     23
proof            (modus-ponens tm-69 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24728.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> (C and D))) or E) or F)), M:tm-69, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24729
in-theory        24729
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     25
proof            (modus-ponens tm-54 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24729.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> (D and E))) or F) or G)), M:tm-54, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24730
in-theory        24730
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> (C and D))) or E) or F))
theorem-size     17
proof            (modus-ponens tm-42 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24730.        ((A -> (B or A)) and (((C -> (D -> (C and D))) or E) or F)), M:tm-42, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24731
in-theory        24731
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> (C and D))) or E) or F))
theorem-size     17
proof            (modus-ponens tm-32 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24731.        ((A -> (A or B)) and (((C -> (D -> (C and D))) or E) or F)), M:tm-32, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24732
in-theory        24732
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> (C and D))) or E) or F))
theorem-size     19
proof            (modus-ponens tm-23 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24732.        ((A -> (B -> (A and B))) and (((C -> (D -> (C and D))) or E) or F)), M:tm-23, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24733
in-theory        24733
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> (C and D))) or E) or F))
theorem-size     17
proof            (modus-ponens tm-22 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24733.        (((A and B) -> B) and (((C -> (D -> (C and D))) or E) or F)), M:tm-22, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24734
in-theory        24734
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> (C and D))) or E) or F))
theorem-size     17
proof            (modus-ponens tm-21 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24734.        (((A and B) -> A) and (((C -> (D -> (C and D))) or E) or F)), M:tm-21, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24735
in-theory        24735
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     25
proof            (modus-ponens tm-20 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24735.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> (D and E))) or F) or G)), M:tm-20, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24736
in-theory        24736
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> (C and D))) or E) or F))
theorem-size     17
proof            (modus-ponens tm-19 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24736.        ((A -> (B -> A)) and (((C -> (D -> (C and D))) or E) or F)), M:tm-19, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24737
in-theory        24737
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> (C -> (B and C))) or D) or E))
theorem-size     13
proof            (modus-ponens tm-7 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-7 tm-6 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24737.        (A or (((B -> (C -> (B and C))) or D) or E)), M:tm-7, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24738
in-theory        24738
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-6 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24738.        ((((A -> (B -> (A and B))) or C) or D) or E), M:tm-6, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24739
in-theory        24739
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> (B and C))) or D) or E) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24739.        (A -> ((((B -> (C -> (B and C))) or D) or E) and A)), M:tm-5, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24740
in-theory        24740
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) or D) or E))
theorem-size     13
proof            (modus-ponens tm-1 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-1 tm-6 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24740.        (A -> (((B -> (C -> (B and C))) or D) or E)), M:tm-1, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-24741
in-theory        24741
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-400 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24741.        (((A -> (B -> (A and B))) or C) and (D -> (D or E))), M:tm-400, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-24742
in-theory        24742
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-400 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-24742.        (((A -> (B -> (A and B))) or C) and (D -> (E or D))), M:tm-400, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-24743
in-theory        24743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-24743.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-400, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-24744
in-theory        24744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-400 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-24744.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-400, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-24745
in-theory        24745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-400 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-24745.        (((A -> (B -> (A and B))) or C) and ((not (not D)) -> D)), M:tm-400, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-24746
in-theory        24746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-400 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24746.        (((A -> (B -> (A and B))) or C) and (D -> (E -> (F -> E)))), M:tm-400, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-24747
in-theory        24747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-400 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-24747.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> (D -> D))), M:tm-400, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-24748
in-theory        24748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-400 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-24748.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-400, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-24749
in-theory        24749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24749.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-400, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-24750
in-theory        24750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-400 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-24750.        (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-400, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-24751
in-theory        24751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-400 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24751.        (((A -> (B -> (A and B))) or C) and (D -> ((E and F) -> E))), M:tm-400, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-24752
in-theory        24752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-400 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-24752.        (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-400, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-24753
in-theory        24753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-400 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24753.        (((A -> (B -> (A and B))) or C) and (D -> ((E and F) -> F))), M:tm-400, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-24754
in-theory        24754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-400 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24754.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> E)) and D))), M:tm-400, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-24755
in-theory        24755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-400 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24755.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-400, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-24756
in-theory        24756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-400 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24756.        (((A -> (B -> (A and B))) or C) and (D -> (((E and F) -> E) and D))), M:tm-400, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-24757
in-theory        24757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-400 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24757.        (((A -> (B -> (A and B))) or C) and (D -> (((E and F) -> F) and D))), M:tm-400, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-24758
in-theory        24758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24758.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-400, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-24759
in-theory        24759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-400 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-24759.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> (D -> (D and E)))), M:tm-400, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-24760
in-theory        24760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24760.        (((A -> (B -> (A and B))) or C) and (D -> (E -> (F -> (E and F))))), M:tm-400, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-24761
in-theory        24761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-400 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24761.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) or F)), M:tm-400, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-24762
in-theory        24762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-400 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24762.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-400, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-24763
in-theory        24763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-400 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24763.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) or F)), M:tm-400, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-24764
in-theory        24764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-400 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24764.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) or F)), M:tm-400, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-24765
in-theory        24765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-400 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-24765.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) or F)), M:tm-400, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-24766
in-theory        24766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-400 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24766.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) or F)), M:tm-400, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-24767
in-theory        24767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-400 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24767.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (E or F)) and D))), M:tm-400, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-24768
in-theory        24768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-400 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24768.        (((A -> (B -> (A and B))) or C) and (D -> (E -> (E or F)))), M:tm-400, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-24769
in-theory        24769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-400 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24769.        (((A -> (B -> (A and B))) or C) and (D or (E -> (F -> E)))), M:tm-400, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-24770
in-theory        24770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24770.        (((A -> (B -> (A and B))) or C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-400, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-24771
in-theory        24771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-400 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24771.        (((A -> (B -> (A and B))) or C) and (D or ((E and F) -> E))), M:tm-400, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-24772
in-theory        24772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-400 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24772.        (((A -> (B -> (A and B))) or C) and (D or ((E and F) -> F))), M:tm-400, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-24773
in-theory        24773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24773.        (((A -> (B -> (A and B))) or C) and (D or (E -> (F -> (E and F))))), M:tm-400, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-24774
in-theory        24774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-400 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24774.        (((A -> (B -> (A and B))) or C) and (D or (E -> (E or F)))), M:tm-400, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-24775
in-theory        24775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-400 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24775.        (((A -> (B -> (A and B))) or C) and (D or (E -> (F or E)))), M:tm-400, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-24776
in-theory        24776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-400 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24776.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) or F)), M:tm-400, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-24777
in-theory        24777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-400 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24777.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F or E)) and D))), M:tm-400, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-24778
in-theory        24778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-400 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24778.        (((A -> (B -> (A and B))) or C) and (D -> (E -> (F or E)))), M:tm-400, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-24779
in-theory        24779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-400 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24779.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-400, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-24780
in-theory        24780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-400 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24780.        (((A -> (B -> (A and B))) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-400, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-24781
in-theory        24781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-400 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24781.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-400, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-24782
in-theory        24782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-400 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-24782.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-400, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-24783
in-theory        24783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-400 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-24783.        (((A -> (B -> (A and B))) or C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-400, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-24784
in-theory        24784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-400 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-24784.        (((A -> (B -> (A and B))) or C) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-400, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-24785
in-theory        24785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-400 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-24785.        (((A -> (B -> (A and B))) or C) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-400, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-24786
in-theory        24786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-400 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-24786.        (((A -> (B -> (A and B))) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-400, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-24787
in-theory        24787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-24787.        (((A -> (B -> (A and B))) or C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-400, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-24788
in-theory        24788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-400 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-24788.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-400, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-24789
in-theory        24789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-400 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-24789.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-400, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-24790
in-theory        24790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-400 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-24790.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-400, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-24791
in-theory        24791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-24791.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-400, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-24792
in-theory        24792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-400 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24792.        (((A -> (B -> (A and B))) or C) and ((D -> (not (E -> D))) -> (not D))), M:tm-400, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-24793
in-theory        24793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24793.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-400, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-24794
in-theory        24794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-400 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24794.        (((A -> (B -> (A and B))) or C) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-400, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-24795
in-theory        24795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-400 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-24795.        (((A -> (B -> (A and B))) or C) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-400, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-24796
in-theory        24796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-24796.        (((A -> (B -> (A and B))) or C) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-400, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-24797
in-theory        24797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not (D or E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-400 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-24797.        (((A -> (B -> (A and B))) or C) and ((D -> (not (D or E))) -> (not D))), M:tm-400, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-24798
in-theory        24798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not (E or D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-400 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-24798.        (((A -> (B -> (A and B))) or C) and ((D -> (not (E or D))) -> (not D))), M:tm-400, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-24799
in-theory        24799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-400 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-24799.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-400, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-24800
in-theory        24800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-400 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-24800.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-400, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-24801
in-theory        24801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-400 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-24801.        (((A -> (B -> (A and B))) or C) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-400, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-24802
in-theory        24802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-24802.        (((A -> (B -> (A and B))) or C) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-400, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-24803
in-theory        24803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     23
proof            (modus-ponens tm-400 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-24803.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-400, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-24804
in-theory        24804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     25
proof            (modus-ponens tm-400 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-24804.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-400, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-24805
in-theory        24805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-400 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-24805.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-400, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-24806
in-theory        24806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-24806.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-400, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-24807
in-theory        24807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     21
proof            (modus-ponens tm-400 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-6 tm-9 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-24807.        (((A -> (B -> (A and B))) or C) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-400, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-24808
in-theory        24808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-400 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-24808.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-400, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-24809
in-theory        24809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-400 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-24809.        (((A -> (B -> (A and B))) or C) and (D or ((not (not E)) -> E))), M:tm-400, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-24810
in-theory        24810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((not (not D)) -> D) or E))
theorem-size     17
proof            (modus-ponens tm-400 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-24810.        (((A -> (B -> (A and B))) or C) and (((not (not D)) -> D) or E)), M:tm-400, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-24811
in-theory        24811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((not (not E)) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-400 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-24811.        (((A -> (B -> (A and B))) or C) and (D -> (((not (not E)) -> E) and D))), M:tm-400, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-24812
in-theory        24812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     25
proof            (modus-ponens tm-400 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-24812.        (((A -> (B -> (A and B))) or C) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-400, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-24813
in-theory        24813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-400 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-24813.        (((A -> (B -> (A and B))) or C) and (D -> ((not (not E)) -> E))), M:tm-400, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-24814
in-theory        24814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-24814.        (((A -> (B -> (A and B))) or C) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-400, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-24815
in-theory        24815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-400 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-24815.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-400, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-24816
in-theory        24816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-24816.        (((A -> (B -> (A and B))) or C) and (D or (E -> (F -> (G -> F))))), M:tm-400, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-24817
in-theory        24817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-24817.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (F -> E))) or G)), M:tm-400, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-24818
in-theory        24818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-24818.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-400, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-24819
in-theory        24819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> (D -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-400 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-24819.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> (D -> (F -> E)))), M:tm-400, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-24820
in-theory        24820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-24820.        (((A -> (B -> (A and B))) or C) and (D -> (E -> (F -> (G -> F))))), M:tm-400, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-24821
in-theory        24821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> D))
theorem-size     13
proof            (modus-ponens tm-400 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24821.        (((A -> (B -> (A and B))) or C) and (D -> D)), M:tm-400, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-24822
in-theory        24822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24822.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-400, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-24823
in-theory        24823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D and E) -> (D and E)))
theorem-size     17
proof            (modus-ponens tm-400 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24823.        (((A -> (B -> (A and B))) or C) and ((D and E) -> (D and E))), M:tm-400, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-24824
in-theory        24824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-400 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-24824.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> (D -> E))), M:tm-400, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-24825
in-theory        24825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((not (not D)) -> (not (not D))))
theorem-size     17
proof            (modus-ponens tm-400 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-24825.        (((A -> (B -> (A and B))) or C) and ((not (not D)) -> (not (not D)))), M:tm-400, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-24826
in-theory        24826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-400 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-24826.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-400, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-24827
in-theory        24827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-400 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-24827.        (((A -> (B -> (A and B))) or C) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-400, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-24828
in-theory        24828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-400 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24828.        (((A -> (B -> (A and B))) or C) and (D or ((E -> F) -> (E -> E)))), M:tm-400, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-24829
in-theory        24829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> (D -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-400 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24829.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> (D -> D)) or F)), M:tm-400, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-24830
in-theory        24830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24830.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-400, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-24831
in-theory        24831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-24831.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-400, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-24832
in-theory        24832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-400 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24832.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> F) -> (E -> E)))), M:tm-400, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-24833
in-theory        24833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-24833.        (((A -> (B -> (A and B))) or C) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-400, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-24834
in-theory        24834
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-400 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-24834.        (((A -> (B -> (A and B))) or C) and ((D -> (D -> E)) -> (D -> E))), M:tm-400, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-24835
in-theory        24835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-400 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-24835.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-400, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-24836
in-theory        24836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     41
proof            (modus-ponens tm-400 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-24836.        (((A -> (B -> (A and B))) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-400, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-24837
in-theory        24837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-400 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-24837.        (((A -> (B -> (A and B))) or C) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-400, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-24838
in-theory        24838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24838.        (((A -> (B -> (A and B))) or C) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-400, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-24839
in-theory        24839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-400 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24839.        (((A -> (B -> (A and B))) or C) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-400, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-24840
in-theory        24840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-400 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24840.        (((A -> (B -> (A and B))) or C) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-400, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-24841
in-theory        24841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-400 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-24841.        (((A -> (B -> (A and B))) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-400, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-24842
in-theory        24842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24842.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-400, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-24843
in-theory        24843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-400 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-24843.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-400, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-24844
in-theory        24844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-400 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-24844.        (((A -> (B -> (A and B))) or C) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-400, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-24845
in-theory        24845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     43
proof            (modus-ponens tm-400 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-24845.        (((A -> (B -> (A and B))) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-400, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-24846
in-theory        24846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-400 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24846.        (((A -> (B -> (A and B))) or C) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-400, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-24847
in-theory        24847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-400 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24847.        (((A -> (B -> (A and B))) or C) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-400, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-24848
in-theory        24848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-400 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24848.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-400, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-24849
in-theory        24849
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-400 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-24849.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-400, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-24850
in-theory        24850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-400 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24850.        (((A -> (B -> (A and B))) or C) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-400, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-24851
in-theory        24851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) and D) -> E))
theorem-size     17
proof            (modus-ponens tm-400 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-24851.        (((A -> (B -> (A and B))) or C) and (((D -> E) and D) -> E)), M:tm-400, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-24852
in-theory        24852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-400 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-24852.        (((A -> (B -> (A and B))) or C) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-400, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-24853
in-theory        24853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-400 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-24853.        (((A -> (B -> (A and B))) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-400, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-24854
in-theory        24854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-400 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-24854.        (((A -> (B -> (A and B))) or C) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-400, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-24855
in-theory        24855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     25
proof            (modus-ponens tm-400 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-24855.        (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-400, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-24856
in-theory        24856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     35
proof            (modus-ponens tm-400 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-24856.        (((A -> (B -> (A and B))) or C) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-400, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-24857
in-theory        24857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     37
proof            (modus-ponens tm-400 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-24857.        (((A -> (B -> (A and B))) or C) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-400, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-24858
in-theory        24858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-400 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24858.        (((A -> (B -> (A and B))) or C) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-400, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-24859
in-theory        24859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-400 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24859.        (((A -> (B -> (A and B))) or C) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-400, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-24860
in-theory        24860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-400 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24860.        (((A -> (B -> (A and B))) or C) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-400, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-24861
in-theory        24861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     33
proof            (modus-ponens tm-400 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-24861.        (((A -> (B -> (A and B))) or C) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-400, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-24862
in-theory        24862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-400 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24862.        (((A -> (B -> (A and B))) or C) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-400, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-24863
in-theory        24863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-400 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-24863.        (((A -> (B -> (A and B))) or C) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-400, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-24864
in-theory        24864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-400 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-24864.        (((A -> (B -> (A and B))) or C) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-400, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-24865
in-theory        24865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-24865.        (((A -> (B -> (A and B))) or C) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-400, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-24866
in-theory        24866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     27
proof            (modus-ponens tm-400 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-24866.        (((A -> (B -> (A and B))) or C) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-400, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-24867
in-theory        24867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-400 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-24867.        (((A -> (B -> (A and B))) or C) and (D or (E -> ((F and G) -> F)))), M:tm-400, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-24868
in-theory        24868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-24868.        (((A -> (B -> (A and B))) or C) and ((D -> ((E and F) -> E)) or G)), M:tm-400, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-24869
in-theory        24869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-24869.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-400, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-24870
in-theory        24870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E and F)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-400 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-24870.        (((A -> (B -> (A and B))) or C) and ((D -> (E and F)) -> (D -> E))), M:tm-400, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-24871
in-theory        24871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-400 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-24871.        (((A -> (B -> (A and B))) or C) and (D -> (E -> ((F and G) -> F)))), M:tm-400, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-24872
in-theory        24872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D and (D -> E)) -> E))
theorem-size     17
proof            (modus-ponens tm-400 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-24872.        (((A -> (B -> (A and B))) or C) and ((D and (D -> E)) -> E)), M:tm-400, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-24873
in-theory        24873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-400 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-24873.        (((A -> (B -> (A and B))) or C) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-400, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-24874
in-theory        24874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-400 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-24874.        (((A -> (B -> (A and B))) or C) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-400, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-24875
in-theory        24875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-400 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-24875.        (((A -> (B -> (A and B))) or C) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-400, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-24876
in-theory        24876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-400 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-24876.        (((A -> (B -> (A and B))) or C) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-400, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-24877
in-theory        24877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     25
proof            (modus-ponens tm-400 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-24877.        (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-400, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-24878
in-theory        24878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     35
proof            (modus-ponens tm-400 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-24878.        (((A -> (B -> (A and B))) or C) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-400, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-24879
in-theory        24879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-400 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-24879.        (((A -> (B -> (A and B))) or C) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-400, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-24880
in-theory        24880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-400 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24880.        (((A -> (B -> (A and B))) or C) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-400, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-24881
in-theory        24881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-400 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24881.        (((A -> (B -> (A and B))) or C) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-400, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-24882
in-theory        24882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-400 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24882.        (((A -> (B -> (A and B))) or C) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-400, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-24883
in-theory        24883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     33
proof            (modus-ponens tm-400 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-24883.        (((A -> (B -> (A and B))) or C) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-400, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-24884
in-theory        24884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-400 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24884.        (((A -> (B -> (A and B))) or C) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-400, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-24885
in-theory        24885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-400 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-24885.        (((A -> (B -> (A and B))) or C) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-400, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-24886
in-theory        24886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-400 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-24886.        (((A -> (B -> (A and B))) or C) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-400, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-24887
in-theory        24887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-400 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-24887.        (((A -> (B -> (A and B))) or C) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-400, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-24888
in-theory        24888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-24888.        (((A -> (B -> (A and B))) or C) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-400, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-24889
in-theory        24889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-400 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-24889.        (((A -> (B -> (A and B))) or C) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-400, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-24890
in-theory        24890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-400 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-24890.        (((A -> (B -> (A and B))) or C) and (D or (E -> ((F and G) -> G)))), M:tm-400, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-24891
in-theory        24891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-24891.        (((A -> (B -> (A and B))) or C) and ((D -> ((E and F) -> F)) or G)), M:tm-400, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-24892
in-theory        24892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-24892.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-400, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-24893
in-theory        24893
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E and F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-400 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-24893.        (((A -> (B -> (A and B))) or C) and ((D -> (E and F)) -> (D -> F))), M:tm-400, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-24894
in-theory        24894
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-400 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-24894.        (((A -> (B -> (A and B))) or C) and (D -> (E -> ((F and G) -> G)))), M:tm-400, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-24895
in-theory        24895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24895.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-400, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-24896
in-theory        24896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24896.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-400, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-24897
in-theory        24897
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24897.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-400, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-24898
in-theory        24898
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-400 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24898.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-400, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-24899
in-theory        24899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24899.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-400, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-24900
in-theory        24900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-400 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24900.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-400, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-24901
in-theory        24901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24901.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-400, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-24902
in-theory        24902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-24902.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-400, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-24903
in-theory        24903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-400 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-24903.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-400, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-24904
in-theory        24904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-24904.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-400, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-24905
in-theory        24905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-24905.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-400, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-24906
in-theory        24906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24906.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-400, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-24907
in-theory        24907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-400 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24907.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-400, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-24908
in-theory        24908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24908.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-400, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-24909
in-theory        24909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-400 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24909.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-400, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-24910
in-theory        24910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-400 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-24910.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-400, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-24911
in-theory        24911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-400 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24911.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-400, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-24912
in-theory        24912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-400 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-24912.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-400, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-24913
in-theory        24913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24913.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-400, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-24914
in-theory        24914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-24914.        (((A -> (B -> (A and B))) or C) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-400, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-24915
in-theory        24915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-400 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-24915.        (((A -> (B -> (A and B))) or C) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-400, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-24916
in-theory        24916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-400 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24916.        (((A -> (B -> (A and B))) or C) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-400, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-24917
in-theory        24917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-400 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24917.        (((A -> (B -> (A and B))) or C) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-400, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-24918
in-theory        24918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24918.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-400, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-24919
in-theory        24919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-400 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24919.        (((A -> (B -> (A and B))) or C) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-400, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-24920
in-theory        24920
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-400 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24920.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-400, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-24921
in-theory        24921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24921.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-400, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-24922
in-theory        24922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-400 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24922.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-400, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-24923
in-theory        24923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-400 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24923.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-400, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-24924
in-theory        24924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24924.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-400, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-24925
in-theory        24925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24925.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-400, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-24926
in-theory        24926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-400 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24926.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-400, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-24927
in-theory        24927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-24927.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-400, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-24928
in-theory        24928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-400 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-24928.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-400, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-24929
in-theory        24929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-400 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-24929.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-400, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-24930
in-theory        24930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-24930.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-400, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-24931
in-theory        24931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-400 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24931.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-400, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-24932
in-theory        24932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-400 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24932.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-400, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-24933
in-theory        24933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-400 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24933.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-400, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-24934
in-theory        24934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-400 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24934.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-400, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-24935
in-theory        24935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-400 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-24935.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-400, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-24936
in-theory        24936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-400 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24936.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-400, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-24937
in-theory        24937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-400 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-24937.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-400, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-24938
in-theory        24938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-400 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24938.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-400, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-24939
in-theory        24939
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-400 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24939.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-400, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-24940
in-theory        24940
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-400 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24940.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-400, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-24941
in-theory        24941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-400 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24941.        (((A -> (B -> (A and B))) or C) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-400, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-24942
in-theory        24942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-400 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24942.        (((A -> (B -> (A and B))) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-400, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-24943
in-theory        24943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-400 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24943.        (((A -> (B -> (A and B))) or C) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-400, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-24944
in-theory        24944
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     29
proof            (modus-ponens tm-400 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24944.        (((A -> (B -> (A and B))) or C) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-400, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-24945
in-theory        24945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-400 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24945.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-400, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-24946
in-theory        24946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-400 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24946.        (((A -> (B -> (A and B))) or C) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-400, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-24947
in-theory        24947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24947.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-400, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-24948
in-theory        24948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24948.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-400, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-24949
in-theory        24949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24949.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F and G) -> F))), M:tm-400, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-24950
in-theory        24950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-400 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24950.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F and G) -> G))), M:tm-400, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-24951
in-theory        24951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24951.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-400, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-24952
in-theory        24952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-400 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24952.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (F or G)))), M:tm-400, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-24953
in-theory        24953
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24953.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (G or F)))), M:tm-400, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-24954
in-theory        24954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-24954.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-400, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-24955
in-theory        24955
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-400 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-24955.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-400, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-24956
in-theory        24956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-24956.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-400, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-24957
in-theory        24957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-24957.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-400, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-24958
in-theory        24958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24958.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-400, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-24959
in-theory        24959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-400 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24959.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-400, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-24960
in-theory        24960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24960.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-400, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-24961
in-theory        24961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-400 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24961.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-400, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-24962
in-theory        24962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-400 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-24962.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-400, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-24963
in-theory        24963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-400 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24963.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-400, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-24964
in-theory        24964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-400 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-24964.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-400, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-24965
in-theory        24965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24965.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-400, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-24966
in-theory        24966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-400 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24966.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-400, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-24967
in-theory        24967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24967.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-400, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-24968
in-theory        24968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-400 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24968.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-400, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-24969
in-theory        24969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24969.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-400, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-24970
in-theory        24970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-24970.        (((A -> (B -> (A and B))) or C) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-400, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-24971
in-theory        24971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-400 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-24971.        (((A -> (B -> (A and B))) or C) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-400, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-24972
in-theory        24972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-400 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24972.        (((A -> (B -> (A and B))) or C) and (D or (E -> (((F and G) -> F) and E)))), M:tm-400, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-24973
in-theory        24973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-400 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24973.        (((A -> (B -> (A and B))) or C) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-400, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-24974
in-theory        24974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24974.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-400, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-24975
in-theory        24975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-400 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24975.        (((A -> (B -> (A and B))) or C) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-400, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-24976
in-theory        24976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24976.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-400, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-24977
in-theory        24977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24977.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-400, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-24978
in-theory        24978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24978.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F and G) -> F))), M:tm-400, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-24979
in-theory        24979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-400 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24979.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F and G) -> G))), M:tm-400, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-24980
in-theory        24980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24980.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-400, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-24981
in-theory        24981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-400 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24981.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (F or G)))), M:tm-400, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-24982
in-theory        24982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24982.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (G or F)))), M:tm-400, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-24983
in-theory        24983
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-24983.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-400, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-24984
in-theory        24984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-400 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-24984.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-400, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-24985
in-theory        24985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-24985.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-400, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-24986
in-theory        24986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-24986.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-400, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-24987
in-theory        24987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24987.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-400, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-24988
in-theory        24988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-400 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24988.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-400, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-24989
in-theory        24989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24989.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-400, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-24990
in-theory        24990
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-400 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24990.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-400, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-24991
in-theory        24991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-400 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-24991.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-400, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-24992
in-theory        24992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-400 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24992.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-400, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-24993
in-theory        24993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-400 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-24993.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-400, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-24994
in-theory        24994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-24994.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-400, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-24995
in-theory        24995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-400 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24995.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-400, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-24996
in-theory        24996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-24996.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-400, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-24997
in-theory        24997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-24997.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-400, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-24998
in-theory        24998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-24998.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-400, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-24999
in-theory        24999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-400 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-24999.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-400, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-25000
in-theory        25000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25000.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-400, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-25001
in-theory        25001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-25001.        (((A -> (B -> (A and B))) or C) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-400, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-25002
in-theory        25002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-400 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-25002.        (((A -> (B -> (A and B))) or C) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-400, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-25003
in-theory        25003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-400 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25003.        (((A -> (B -> (A and B))) or C) and (D or (E -> (((F and G) -> G) and E)))), M:tm-400, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-25004
in-theory        25004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-400 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25004.        (((A -> (B -> (A and B))) or C) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-400, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-25005
in-theory        25005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25005.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-400, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-25006
in-theory        25006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-400 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25006.        (((A -> (B -> (A and B))) or C) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-400, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-25007
in-theory        25007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25007.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-400, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-25008
in-theory        25008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25008.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-400, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-25009
in-theory        25009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-400 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25009.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-400, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-25010
in-theory        25010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-400 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25010.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-400, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-25011
in-theory        25011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25011.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-400, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-25012
in-theory        25012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-400 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25012.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-400, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-25013
in-theory        25013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25013.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-400, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-25014
in-theory        25014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-25014.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-400, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-25015
in-theory        25015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-25015.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-400, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-25016
in-theory        25016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-400 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-25016.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-400, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-25017
in-theory        25017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-25017.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-400, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-25018
in-theory        25018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-25018.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-400, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-25019
in-theory        25019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-25019.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-400, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-25020
in-theory        25020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-400 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-25020.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-400, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-25021
in-theory        25021
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-400 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-25021.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-400, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-25022
in-theory        25022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-400 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-25022.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-400, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-25023
in-theory        25023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-400 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-25023.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-400, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-25024
in-theory        25024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-400 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-25024.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-400, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-25025
in-theory        25025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-400 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-25025.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-400, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-25026
in-theory        25026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-400 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-25026.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-400, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-25027
in-theory        25027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-400 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-25027.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-400, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-25028
in-theory        25028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-400 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25028.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-400, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-25029
in-theory        25029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-400 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25029.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-400, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-25030
in-theory        25030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-400 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25030.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-400, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-25031
in-theory        25031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-400 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25031.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-400, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-25032
in-theory        25032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-400 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25032.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-400, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-25033
in-theory        25033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-400 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25033.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-400, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-25034
in-theory        25034
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-400 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-25034.        (((A -> (B -> (A and B))) or C) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-400, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-25035
in-theory        25035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-400 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-25035.        (((A -> (B -> (A and B))) or C) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-400, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-25036
in-theory        25036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-400 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25036.        (((A -> (B -> (A and B))) or C) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-400, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-25037
in-theory        25037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-400 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25037.        (((A -> (B -> (A and B))) or C) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-400, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-25038
in-theory        25038
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-400 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25038.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-400, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-25039
in-theory        25039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-400 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25039.        (((A -> (B -> (A and B))) or C) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-400, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-25040
in-theory        25040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and (E -> D))))
theorem-size     17
proof            (modus-ponens tm-400 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25040.        (((A -> (B -> (A and B))) or C) and (D -> (D and (E -> D)))), M:tm-400, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-25041
in-theory        25041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25041.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-400, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-25042
in-theory        25042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D and E) -> ((D and E) and D)))
theorem-size     19
proof            (modus-ponens tm-400 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25042.        (((A -> (B -> (A and B))) or C) and ((D and E) -> ((D and E) and D))), M:tm-400, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-25043
in-theory        25043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D and E) -> ((D and E) and E)))
theorem-size     19
proof            (modus-ponens tm-400 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-25043.        (((A -> (B -> (A and B))) or C) and ((D and E) -> ((D and E) and E))), M:tm-400, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-25044
in-theory        25044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-25044.        (((A -> (B -> (A and B))) or C) and (D -> (D and (E -> (D and E))))), M:tm-400, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-25045
in-theory        25045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and (D or E))))
theorem-size     17
proof            (modus-ponens tm-400 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-25045.        (((A -> (B -> (A and B))) or C) and (D -> (D and (D or E)))), M:tm-400, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-25046
in-theory        25046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and (E or D))))
theorem-size     17
proof            (modus-ponens tm-400 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-25046.        (((A -> (B -> (A and B))) or C) and (D -> (D and (E or D)))), M:tm-400, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-25047
in-theory        25047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     27
proof            (modus-ponens tm-400 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-25047.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-400, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-25048
in-theory        25048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-25048.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-400, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-25049
in-theory        25049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     19
proof            (modus-ponens tm-400 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-25049.        (((A -> (B -> (A and B))) or C) and ((not (not D)) -> ((not (not D)) and D))), M:tm-400, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-25050
in-theory        25050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-25050.        (((A -> (B -> (A and B))) or C) and (D -> (D and (E -> (F -> E))))), M:tm-400, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-25051
in-theory        25051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     21
proof            (modus-ponens tm-400 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-25051.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-400, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-25052
in-theory        25052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-400 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-25052.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-400, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-25053
in-theory        25053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-400 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-25053.        (((A -> (B -> (A and B))) or C) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-400, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-25054
in-theory        25054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     33
proof            (modus-ponens tm-400 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-25054.        (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-400, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-25055
in-theory        25055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-400 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-25055.        (((A -> (B -> (A and B))) or C) and (D -> (D and ((E and F) -> E)))), M:tm-400, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-25056
in-theory        25056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     33
proof            (modus-ponens tm-400 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-25056.        (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-400, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-25057
in-theory        25057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-400 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-25057.        (((A -> (B -> (A and B))) or C) and (D -> (D and ((E and F) -> F)))), M:tm-400, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-25058
in-theory        25058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-400 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-25058.        (((A -> (B -> (A and B))) or C) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-400, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-25059
in-theory        25059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-400 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-25059.        (((A -> (B -> (A and B))) or C) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-400, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-25060
in-theory        25060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-400 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-25060.        (((A -> (B -> (A and B))) or C) and (D -> (D and (((E and F) -> E) and D)))), M:tm-400, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-25061
in-theory        25061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-400 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-25061.        (((A -> (B -> (A and B))) or C) and (D -> (D and (((E and F) -> F) and D)))), M:tm-400, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-25062
in-theory        25062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-400 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-25062.        (((A -> (B -> (A and B))) or C) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-400, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-25063
in-theory        25063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-25063.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-400, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-25064
in-theory        25064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-400 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25064.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-400, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-25065
in-theory        25065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25065.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-400, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-25066
in-theory        25066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25066.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-400, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-25067
in-theory        25067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-400 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25067.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-400, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-25068
in-theory        25068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25068.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-400, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-25069
in-theory        25069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-400 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-25069.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-400, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-25070
in-theory        25070
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     29
proof            (modus-ponens tm-400 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-25070.        (((A -> (B -> (A and B))) or C) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-400, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-25071
in-theory        25071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-400 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25071.        (((A -> (B -> (A and B))) or C) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-400, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-25072
in-theory        25072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     21
proof            (modus-ponens tm-400 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25072.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-400, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-25073
in-theory        25073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25073.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-400, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-25074
in-theory        25074
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-400 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-25074.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-400, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-25075
in-theory        25075
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-400 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25075.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-400, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-25076
in-theory        25076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-400 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-25076.        (((A -> (B -> (A and B))) or C) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-400, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-25077
in-theory        25077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-400 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25077.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-400, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-25078
in-theory        25078
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-400 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25078.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-400, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-25079
in-theory        25079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-400 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25079.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-400, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-25080
in-theory        25080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-400 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25080.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-400, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-25081
in-theory        25081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-400 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25081.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-400, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-25082
in-theory        25082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-400 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-25082.        (((A -> (B -> (A and B))) or C) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-400, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-25083
in-theory        25083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-400 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-25083.        (((A -> (B -> (A and B))) or C) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-400, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-25084
in-theory        25084
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-400 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-25084.        (((A -> (B -> (A and B))) or C) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-400, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-25085
in-theory        25085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-25085.        (((A -> (B -> (A and B))) or C) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-400, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-25086
in-theory        25086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     31
proof            (modus-ponens tm-400 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-25086.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-400, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-25087
in-theory        25087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-400 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25087.        (((A -> (B -> (A and B))) or C) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-400, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-25088
in-theory        25088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-400 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25088.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-400, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-25089
in-theory        25089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25089.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-400, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-25090
in-theory        25090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-400 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-25090.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-400, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-25091
in-theory        25091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-400 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25091.        (((A -> (B -> (A and B))) or C) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-400, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-25092
in-theory        25092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-400 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-25092.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-400, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-25093
in-theory        25093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-25093.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-400, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-25094
in-theory        25094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-25094.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-400, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-25095
in-theory        25095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-25095.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-400, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-25096
in-theory        25096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-25096.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-400, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-25097
in-theory        25097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-400 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-25097.        (((A -> (B -> (A and B))) or C) and (D or ((E -> (F -> E)) or G))), M:tm-400, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-25098
in-theory        25098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-25098.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> D)) or F) or G)), M:tm-400, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-25099
in-theory        25099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-25099.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-400, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-25100
in-theory        25100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-400 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-25100.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> E)) or G))), M:tm-400, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-25101
in-theory        25101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-400 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-25101.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-400, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-25102
in-theory        25102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-25102.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-400, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-25103
in-theory        25103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-25103.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-400, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-25104
in-theory        25104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-400 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-25104.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-400, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-25105
in-theory        25105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-25105.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-400, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-25106
in-theory        25106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-400 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-25106.        (((A -> (B -> (A and B))) or C) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-400, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-25107
in-theory        25107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-400 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-25107.        (((A -> (B -> (A and B))) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-400, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-25108
in-theory        25108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-400 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-25108.        (((A -> (B -> (A and B))) or C) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-400, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-25109
in-theory        25109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-400 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-25109.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-400, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-25110
in-theory        25110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-400 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-25110.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-400, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-25111
in-theory        25111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-25111.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-400, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-25112
in-theory        25112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-25112.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-400, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-25113
in-theory        25113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-25113.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-400, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-25114
in-theory        25114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-25114.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-400, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-25115
in-theory        25115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-400 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-25115.        (((A -> (B -> (A and B))) or C) and (D or (((E and F) -> E) or G))), M:tm-400, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-25116
in-theory        25116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D and E) -> D) or F) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-25116.        (((A -> (B -> (A and B))) or C) and ((((D and E) -> D) or F) or G)), M:tm-400, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-25117
in-theory        25117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-25117.        (((A -> (B -> (A and B))) or C) and (D -> ((((E and F) -> E) or G) and D))), M:tm-400, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-25118
in-theory        25118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-400 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-25118.        (((A -> (B -> (A and B))) or C) and (D -> (((E and F) -> E) or G))), M:tm-400, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-25119
in-theory        25119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-400 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-25119.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-400, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-25120
in-theory        25120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-25120.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-400, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-25121
in-theory        25121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-25121.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-400, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-25122
in-theory        25122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-25122.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-400, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-25123
in-theory        25123
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-25123.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-400, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-25124
in-theory        25124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-400 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-25124.        (((A -> (B -> (A and B))) or C) and (D or (((E and F) -> F) or G))), M:tm-400, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-25125
in-theory        25125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D and E) -> E) or F) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-25125.        (((A -> (B -> (A and B))) or C) and ((((D and E) -> E) or F) or G)), M:tm-400, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-25126
in-theory        25126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-25126.        (((A -> (B -> (A and B))) or C) and (D -> ((((E and F) -> F) or G) and D))), M:tm-400, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-25127
in-theory        25127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-400 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-25127.        (((A -> (B -> (A and B))) or C) and (D -> (((E and F) -> F) or G))), M:tm-400, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-25128
in-theory        25128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-400 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25128.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-400, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-25129
in-theory        25129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-400 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25129.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-400, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-25130
in-theory        25130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-400 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25130.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-400, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-25131
in-theory        25131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-400 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25131.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-400, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-25132
in-theory        25132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-400 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25132.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-400, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-25133
in-theory        25133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-400 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25133.        (((A -> (B -> (A and B))) or C) and (D or ((E -> (F -> (E and F))) or G))), M:tm-400, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25134
in-theory        25134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     21
proof            (modus-ponens tm-400 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25134.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> (D and E))) or F) or G)), M:tm-400, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-25135
in-theory        25135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25135.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-400, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25136
in-theory        25136
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25136.        ((((A and B) -> B) or C) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-391, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25137
in-theory        25137
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25137.        ((((A and B) -> A) or C) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-382, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25138
in-theory        25138
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (G -> (F and G))) or H) and E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25138.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (G -> (F and G))) or H) and E))), M:tm-373, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25139
in-theory        25139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25139.        (((A -> (B -> A)) or C) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-364, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25140
in-theory        25140
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> (D -> (C and D))) or E) and A) and B)))
theorem-size     17
proof            (modus-ponens tm-355 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25140.        (A -> (B -> ((((C -> (D -> (C and D))) or E) and A) and B))), M:tm-355, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-25141
in-theory        25141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25141.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-354, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25142
in-theory        25142
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> (E -> (D and E))) or F) and (B -> (C -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-351 tm-400 ((Am (-> A (-> B (and A B)))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25142.        ((A or (B -> (C -> (B and C)))) -> (((D -> (E -> (D and E))) or F) and (B -> (C -> (B and C))))), M:tm-351, m:tm-400, u:((Am (-> A (-> B (and A B)))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-25143
in-theory        25143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25143.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25144
in-theory        25144
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (E -> (D and E))) or F) and C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25144.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (E -> (D and E))) or F) and C))), M:tm-338, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25145
in-theory        25145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> (D -> (C and D))) or E) and (A -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-335 tm-400 ((Am (-> A (and A B))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25145.        (((A -> B) or (A -> (A and B))) -> (((C -> (D -> (C and D))) or E) and (A -> (A and B)))), M:tm-335, m:tm-400, u:((Am (-> A (and A B))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A (and A B)))))
================================================================
tm-name          tm-25146
in-theory        25146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (A -> (A and (((B -> (C -> (B and C))) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-328 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25146.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (A -> (A and (((B -> (C -> (B and C))) or D) and A)))), M:tm-328, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-25147
in-theory        25147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> (C -> (B and C))) or D) and A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25147.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> (C -> (B and C))) or D) and A)))), M:tm-327, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25148
in-theory        25148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (((E and F) -> F) and (A -> (((B -> (C -> (B and C))) or D) and A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25148.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (((E and F) -> F) and (A -> (((B -> (C -> (B and C))) or D) and A)))), M:tm-326, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25149
in-theory        25149
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (((E and F) -> E) and (A -> (((B -> (C -> (B and C))) or D) and A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25149.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (((E and F) -> E) and (A -> (((B -> (C -> (B and C))) or D) and A)))), M:tm-325, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25150
in-theory        25150
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> (C -> (B and C))) or D) and A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25150.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> (C -> (B and C))) or D) and A)))), M:tm-324, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25151
in-theory        25151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((E -> (F -> E)) and (A -> (((B -> (C -> (B and C))) or D) and A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25151.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((E -> (F -> E)) and (A -> (((B -> (C -> (B and C))) or D) and A)))), M:tm-323, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25152
in-theory        25152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25152.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((E and F) -> F)), M:tm-322, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25153
in-theory        25153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25153.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((E and F) -> E)), M:tm-320, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25154
in-theory        25154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25154.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25155
in-theory        25155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (A -> A))
theorem-size     17
proof            (modus-ponens tm-316 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25155.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (A -> A)), M:tm-316, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-25156
in-theory        25156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25156.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (E -> (F -> E))), M:tm-315, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25157
in-theory        25157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((A -> (not (((B -> (C -> (B and C))) or D) and A))) -> (not A)))
theorem-size     31
proof            (modus-ponens tm-313 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25157.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((A -> (not (((B -> (C -> (B and C))) or D) and A))) -> (not A))), M:tm-313, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-25158
in-theory        25158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (((((B -> (C -> (B and C))) or D) and A) -> E) -> ((A or (((B -> (C -> (B and C))) or D) and A)) -> E)))
theorem-size     43
proof            (modus-ponens tm-312 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25158.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (((((B -> (C -> (B and C))) or D) and A) -> E) -> ((A or (((B -> (C -> (B and C))) or D) and A)) -> E))), M:tm-312, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-25159
in-theory        25159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (E or (A -> (((B -> (C -> (B and C))) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25159.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (E or (A -> (((B -> (C -> (B and C))) or D) and A)))), M:tm-311, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25160
in-theory        25160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((A -> (((B -> (C -> (B and C))) or D) and A)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25160.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((A -> (((B -> (C -> (B and C))) or D) and A)) or E)), M:tm-310, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25161
in-theory        25161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (E -> ((A -> (((B -> (C -> (B and C))) or D) and A)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25161.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (E -> ((A -> (((B -> (C -> (B and C))) or D) and A)) and E))), M:tm-309, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25162
in-theory        25162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (E -> (A -> (((B -> (C -> (B and C))) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25162.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (E -> (A -> (((B -> (C -> (B and C))) or D) and A)))), M:tm-305, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25163
in-theory        25163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25163.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-303, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25164
in-theory        25164
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (E -> (D and E))) or F) and ((B -> (C -> (B and C))) and A)))
theorem-size     31
proof            (modus-ponens tm-300 tm-400 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25164.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (E -> (D and E))) or F) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-400, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-25165
in-theory        25165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25165.        ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-270, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25166
in-theory        25166
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> (E -> (D and E))) or F) and (((B and C) -> C) and A)))
theorem-size     27
proof            (modus-ponens tm-267 tm-400 ((Am (and (-> (and A B) B) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25166.        ((A or (((B and C) -> C) and A)) -> (((D -> (E -> (D and E))) or F) and (((B and C) -> C) and A))), M:tm-267, m:tm-400, u:((Am (and (-> (and A B) B) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-25167
in-theory        25167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25167.        ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-239, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25168
in-theory        25168
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> (E -> (D and E))) or F) and (((B and C) -> B) and A)))
theorem-size     27
proof            (modus-ponens tm-236 tm-400 ((Am (and (-> (and A B) A) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25168.        ((A or (((B and C) -> B) and A)) -> (((D -> (E -> (D and E))) or F) and (((B and C) -> B) and A))), M:tm-236, m:tm-400, u:((Am (and (-> (and A B) A) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-25169
in-theory        25169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (G -> (F and G))) or H) and E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25169.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (G -> (F and G))) or H) and E))), M:tm-210, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25170
in-theory        25170
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (F -> (E and F))) or G) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     43
proof            (modus-ponens tm-207 tm-400 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25170.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (F -> (E and F))) or G) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-400, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-25171
in-theory        25171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25171.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-183, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25172
in-theory        25172
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> (E -> (D and E))) or F) and ((B -> (C -> B)) and A)))
theorem-size     27
proof            (modus-ponens tm-180 tm-400 ((Am (and (-> A (-> B A)) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25172.        ((A or ((B -> (C -> B)) and A)) -> (((D -> (E -> (D and E))) or F) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-400, u:((Am (and (-> A (-> B A)) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-25173
in-theory        25173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25173.        ((A -> ((B and C) -> C)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-157, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25174
in-theory        25174
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> (E -> (D and E))) or F) and ((B and C) -> C)))
theorem-size     23
proof            (modus-ponens tm-154 tm-400 ((Am (-> (and A B) B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25174.        ((A or ((B and C) -> C)) -> (((D -> (E -> (D and E))) or F) and ((B and C) -> C))), M:tm-154, m:tm-400, u:((Am (-> (and A B) B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (and A B) B))))
================================================================
tm-name          tm-25175
in-theory        25175
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25175.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-147, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25176
in-theory        25176
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (E -> (D and E))) or F) and ((A and (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-144 tm-400 ((Am (-> (and A (-> B C)) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25176.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (E -> (D and E))) or F) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-400, u:((Am (-> (and A (-> B C)) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-25177
in-theory        25177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25177.        ((A -> ((B and C) -> B)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-134, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25178
in-theory        25178
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> (E -> (D and E))) or F) and ((B and C) -> B)))
theorem-size     23
proof            (modus-ponens tm-131 tm-400 ((Am (-> (and A B) A)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25178.        ((A or ((B and C) -> B)) -> (((D -> (E -> (D and E))) or F) and ((B and C) -> B))), M:tm-131, m:tm-400, u:((Am (-> (and A B) A)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (and A B) A))))
================================================================
tm-name          tm-25179
in-theory        25179
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25179.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-125, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25180
in-theory        25180
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (E -> (D and E))) or F) and (((A -> B) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-122 tm-400 ((Am (-> (and (-> A B) C) B)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25180.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (E -> (D and E))) or F) and (((A -> B) and C) -> B))), M:tm-122, m:tm-400, u:((Am (-> (and (-> A B) C) B)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-25181
in-theory        25181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> (F and G))) or H) and E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25181.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> (F and G))) or H) and E))), M:tm-113, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25182
in-theory        25182
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (F -> (E and F))) or G) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     39
proof            (modus-ponens tm-110 tm-400 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25182.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (F -> (E and F))) or G) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-400, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-25183
in-theory        25183
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25183.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-105, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25184
in-theory        25184
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (E -> (D and E))) or F) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-102 tm-400 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25184.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (E -> (D and E))) or F) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-400, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-25185
in-theory        25185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> (E -> (D and E))) or F) and C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25185.        (((A -> B) -> (A -> A)) and (C -> (((D -> (E -> (D and E))) or F) and C))), M:tm-95, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25186
in-theory        25186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> (D -> (C and D))) or E) and (A -> A)))
theorem-size     21
proof            (modus-ponens tm-92 tm-400 ((Am (-> A A)) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25186.        (((A -> B) or (A -> A)) -> (((C -> (D -> (C and D))) or E) and (A -> A))), M:tm-92, m:tm-400, u:((Am (-> A A)) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A A))))
================================================================
tm-name          tm-25187
in-theory        25187
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D -> (C and D))) or E) and A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25187.        (A -> (B -> (((C -> (D -> (C and D))) or E) and A))), M:tm-84, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-25188
in-theory        25188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25188.        ((A -> (B -> (C -> B))) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-83, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25189
in-theory        25189
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> (E -> (D and E))) or F) and (B -> (C -> B))))
theorem-size     23
proof            (modus-ponens tm-80 tm-400 ((Am (-> A (-> B A))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25189.        ((A or (B -> (C -> B))) -> (((D -> (E -> (D and E))) or F) and (B -> (C -> B)))), M:tm-80, m:tm-400, u:((Am (-> A (-> B A))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A (-> B A)))))
================================================================
tm-name          tm-25190
in-theory        25190
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> (D -> (C and D))) or E) and B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25190.        (((not (not A)) -> A) and (B -> (((C -> (D -> (C and D))) or E) and B))), M:tm-76, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25191
in-theory        25191
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> (C -> (B and C))) or D) and A))
theorem-size     17
proof            (modus-ponens tm-73 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25191.        (((not (not A)) or A) -> (((B -> (C -> (B and C))) or D) and A)), M:tm-73, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-25192
in-theory        25192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (E -> (D and E))) or F) and C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25192.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (E -> (D and E))) or F) and C))), M:tm-69, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25193
in-theory        25193
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (D -> (C and D))) or E) and ((A -> (not B)) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-66 tm-400 ((Am (-> (-> A (not B)) (not A))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-6)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25193.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (D -> (C and D))) or E) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-400, u:((Am (-> (-> A (not B)) (not A))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-25194
in-theory        25194
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25194.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-54, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25195
in-theory        25195
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> (D and E))) or F) and ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-51 tm-400 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25195.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E -> (D and E))) or F) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-400, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-25196
in-theory        25196
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> (D -> (C and D))) or E) and (B or A)))
theorem-size     19
proof            (modus-ponens tm-50 tm-400 ((Am (or A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25196.        ((A or (B or A)) -> (((C -> (D -> (C and D))) or E) and (B or A))), M:tm-50, m:tm-400, u:((Am (or A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (or A B))))
================================================================
tm-name          tm-25197
in-theory        25197
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> (D -> (C and D))) or E) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-49 tm-400 ((Am (or A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25197.        ((A or (A or B)) -> (((C -> (D -> (C and D))) or E) and (A or B))), M:tm-49, m:tm-400, u:((Am (or A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (or A B))))
================================================================
tm-name          tm-25198
in-theory        25198
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> (D -> (C and D))) or E) and (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-48 tm-400 ((Am (-> A (and B A))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25198.        ((A or (B -> (A and B))) -> (((C -> (D -> (C and D))) or E) and (B -> (A and B)))), M:tm-48, m:tm-400, u:((Am (-> A (and B A))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-25199
in-theory        25199
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> (D -> (C and D))) or E) and B))
theorem-size     17
proof            (modus-ponens tm-47 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25199.        (((A and B) or B) -> (((C -> (D -> (C and D))) or E) and B)), M:tm-47, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-25200
in-theory        25200
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> (D -> (C and D))) or E) and A))
theorem-size     17
proof            (modus-ponens tm-46 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25200.        (((A and B) or A) -> (((C -> (D -> (C and D))) or E) and A)), M:tm-46, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-25201
in-theory        25201
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> (D and E))) or F) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-45 tm-400 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25201.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> (D and E))) or F) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-400, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-25202
in-theory        25202
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> (D -> (C and D))) or E) and (B -> A)))
theorem-size     19
proof            (modus-ponens tm-44 tm-400 ((Am (-> A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25202.        ((A or (B -> A)) -> (((C -> (D -> (C and D))) or E) and (B -> A))), M:tm-44, m:tm-400, u:((Am (-> A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A B))))
================================================================
tm-name          tm-25203
in-theory        25203
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> (E -> (D and E))) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25203.        ((A -> (B or A)) and (C -> (((D -> (E -> (D and E))) or F) and C))), M:tm-42, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25204
in-theory        25204
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> (E -> (D and E))) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25204.        ((A -> (A or B)) and (C -> (((D -> (E -> (D and E))) or F) and C))), M:tm-32, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25205
in-theory        25205
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> (C -> (B and C))) or D) and A)))
theorem-size     15
proof            (modus-ponens tm-24 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25205.        (A -> (A and (((B -> (C -> (B and C))) or D) and A))), M:tm-24, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-25206
in-theory        25206
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> (D and E))) or F) and C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25206.        ((A -> (B -> (A and B))) and (C -> (((D -> (E -> (D and E))) or F) and C))), M:tm-23, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25207
in-theory        25207
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> (E -> (D and E))) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25207.        (((A and B) -> B) and (C -> (((D -> (E -> (D and E))) or F) and C))), M:tm-22, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25208
in-theory        25208
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> (E -> (D and E))) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25208.        (((A and B) -> A) and (C -> (((D -> (E -> (D and E))) or F) and C))), M:tm-21, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25209
in-theory        25209
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25209.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-20, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25210
in-theory        25210
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> (E -> (D and E))) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25210.        ((A -> (B -> A)) and (C -> (((D -> (E -> (D and E))) or F) and C))), M:tm-19, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25211
in-theory        25211
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> (C -> (B and C))) or D) and A))) -> (not A))
theorem-size     17
proof            (modus-ponens tm-9 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-9 tm-5 tm-6)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25211.        ((A -> (not (((B -> (C -> (B and C))) or D) and A))) -> (not A)), M:tm-9, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-25212
in-theory        25212
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) or C) and D) -> E) -> ((D or (((A -> (B -> (A and B))) or C) and D)) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25212.        (((((A -> (B -> (A and B))) or C) and D) -> E) -> ((D or (((A -> (B -> (A and B))) or C) and D)) -> E)), M:tm-8, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-25213
in-theory        25213
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> (D -> (C and D))) or E) and B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25213.        (A or (B -> (((C -> (D -> (C and D))) or E) and B))), M:tm-7, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25214
in-theory        25214
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-6 tm-5)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25214.        ((A -> (((B -> (C -> (B and C))) or D) and A)) or E), M:tm-6, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25215
in-theory        25215
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> (D -> (C and D))) or E) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25215.        (A -> ((B -> (((C -> (D -> (C and D))) or E) and B)) and A)), M:tm-5, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25216
in-theory        25216
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D -> (C and D))) or E) and B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25216.        (A -> (B -> (((C -> (D -> (C and D))) or E) and B))), M:tm-1, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-25217
in-theory        25217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-400 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25217.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-400, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25218
in-theory        25218
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-391 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25218.        ((((A and B) -> B) or C) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-391, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25219
in-theory        25219
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-382 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25219.        ((((A and B) -> A) or C) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-382, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25220
in-theory        25220
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-373 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25220.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> (F and G))) or H))), M:tm-373, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25221
in-theory        25221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-364 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25221.        (((A -> (B -> A)) or C) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-364, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25222
in-theory        25222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-354 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25222.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-354, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25223
in-theory        25223
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-351 tm-401 ((Am (-> A (-> B (and A B)))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25223.        ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> (D and E))) or F)), M:tm-351, m:tm-401, u:((Am (-> A (-> B (and A B)))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25224
in-theory        25224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25224.        ((A -> ((B -> (C -> (B and C))) or D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25225
in-theory        25225
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) -> D) -> (((A -> (B -> (A and B))) or C) and D))
theorem-size     23
proof            (modus-ponens tm-339 tm-401 ((Am (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) B)) (A (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25225.        ((((A -> (B -> (A and B))) or C) -> D) -> (((A -> (B -> (A and B))) or C) and D)), M:tm-339, m:tm-401, u:((Am (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) B)) (A (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25226
in-theory        25226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> (D and E))) or F)))
theorem-size     21
proof            (modus-ponens tm-338 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25226.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> (D and E))) or F))), M:tm-338, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25227
in-theory        25227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (D -> (C and D))) or E))
theorem-size     19
proof            (modus-ponens tm-335 tm-401 ((Am (-> A (and A B))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25227.        (((A -> B) or (A -> (A and B))) -> ((C -> (D -> (C and D))) or E)), M:tm-335, m:tm-401, u:((Am (-> A (and A B))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25228
in-theory        25228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and (A -> (A and ((B -> (C -> (B and C))) or D))))
theorem-size     25
proof            (modus-ponens tm-328 tm-401 ((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25228.        ((A -> ((B -> (C -> (B and C))) or D)) and (A -> (A and ((B -> (C -> (B and C))) or D)))), M:tm-328, m:tm-401, u:((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25229
in-theory        25229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and ((E -> (F -> (E and F))) and (A -> ((B -> (C -> (B and C))) or D))))
theorem-size     31
proof            (modus-ponens tm-327 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25229.        ((A -> ((B -> (C -> (B and C))) or D)) and ((E -> (F -> (E and F))) and (A -> ((B -> (C -> (B and C))) or D)))), M:tm-327, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25230
in-theory        25230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and (((E and F) -> F) and (A -> ((B -> (C -> (B and C))) or D))))
theorem-size     29
proof            (modus-ponens tm-326 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25230.        ((A -> ((B -> (C -> (B and C))) or D)) and (((E and F) -> F) and (A -> ((B -> (C -> (B and C))) or D)))), M:tm-326, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25231
in-theory        25231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and (((E and F) -> E) and (A -> ((B -> (C -> (B and C))) or D))))
theorem-size     29
proof            (modus-ponens tm-325 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25231.        ((A -> ((B -> (C -> (B and C))) or D)) and (((E and F) -> E) and (A -> ((B -> (C -> (B and C))) or D)))), M:tm-325, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25232
in-theory        25232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C -> (B and C))) or D))))
theorem-size     37
proof            (modus-ponens tm-324 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25232.        ((A -> ((B -> (C -> (B and C))) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C -> (B and C))) or D)))), M:tm-324, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25233
in-theory        25233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and ((E -> (F -> E)) and (A -> ((B -> (C -> (B and C))) or D))))
theorem-size     29
proof            (modus-ponens tm-323 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25233.        ((A -> ((B -> (C -> (B and C))) or D)) and ((E -> (F -> E)) and (A -> ((B -> (C -> (B and C))) or D)))), M:tm-323, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25234
in-theory        25234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25234.        ((A -> ((B -> (C -> (B and C))) or D)) and ((E and F) -> F)), M:tm-322, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25235
in-theory        25235
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> (B and C))) or D) -> E)) -> ((B -> (C -> (B and C))) or D)) and ((A and (((B -> (C -> (B and C))) or D) -> E)) -> E))
theorem-size     39
proof            (modus-ponens tm-321 tm-401 ((Am (and A (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) C))) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25235.        (((A and (((B -> (C -> (B and C))) or D) -> E)) -> ((B -> (C -> (B and C))) or D)) and ((A and (((B -> (C -> (B and C))) or D) -> E)) -> E)), M:tm-321, m:tm-401, u:((Am (and A (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) C))) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25236
in-theory        25236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25236.        ((A -> ((B -> (C -> (B and C))) or D)) and ((E and F) -> E)), M:tm-320, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25237
in-theory        25237
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> (A and B))) or C) -> D) and E) -> ((A -> (B -> (A and B))) or C)) and (((((A -> (B -> (A and B))) or C) -> D) and E) -> D))
theorem-size     39
proof            (modus-ponens tm-319 tm-401 ((Am (and (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) B) C)) (A (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25237.        ((((((A -> (B -> (A and B))) or C) -> D) and E) -> ((A -> (B -> (A and B))) or C)) and (((((A -> (B -> (A and B))) or C) -> D) and E) -> D)), M:tm-319, m:tm-401, u:((Am (and (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) B) C)) (A (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25238
in-theory        25238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25238.        ((A -> ((B -> (C -> (B and C))) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25239
in-theory        25239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-401 ((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25239.        ((A -> ((B -> (C -> (B and C))) or D)) and (A -> A)), M:tm-316, m:tm-401, u:((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25240
in-theory        25240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25240.        ((A -> ((B -> (C -> (B and C))) or D)) and (E -> (F -> E))), M:tm-315, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25241
in-theory        25241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and ((A -> (not ((B -> (C -> (B and C))) or D))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-401 ((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25241.        ((A -> ((B -> (C -> (B and C))) or D)) and ((A -> (not ((B -> (C -> (B and C))) or D))) -> (not A))), M:tm-313, m:tm-401, u:((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25242
in-theory        25242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and ((((B -> (C -> (B and C))) or D) -> E) -> ((A or ((B -> (C -> (B and C))) or D)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-401 ((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25242.        ((A -> ((B -> (C -> (B and C))) or D)) and ((((B -> (C -> (B and C))) or D) -> E) -> ((A or ((B -> (C -> (B and C))) or D)) -> E))), M:tm-312, m:tm-401, u:((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25243
in-theory        25243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and (E or (A -> ((B -> (C -> (B and C))) or D))))
theorem-size     25
proof            (modus-ponens tm-311 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25243.        ((A -> ((B -> (C -> (B and C))) or D)) and (E or (A -> ((B -> (C -> (B and C))) or D)))), M:tm-311, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25244
in-theory        25244
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and ((A -> ((B -> (C -> (B and C))) or D)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25244.        ((A -> ((B -> (C -> (B and C))) or D)) and ((A -> ((B -> (C -> (B and C))) or D)) or E)), M:tm-310, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25245
in-theory        25245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and (E -> ((A -> ((B -> (C -> (B and C))) or D)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25245.        ((A -> ((B -> (C -> (B and C))) or D)) and (E -> ((A -> ((B -> (C -> (B and C))) or D)) and E))), M:tm-309, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25246
in-theory        25246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and (E -> (A -> ((B -> (C -> (B and C))) or D))))
theorem-size     25
proof            (modus-ponens tm-305 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25246.        ((A -> ((B -> (C -> (B and C))) or D)) and (E -> (A -> ((B -> (C -> (B and C))) or D)))), M:tm-305, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25247
in-theory        25247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-303 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25247.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-303, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25248
in-theory        25248
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> (D and E))) or F))
theorem-size     21
proof            (modus-ponens tm-300 tm-401 ((Am (and (-> A (-> B (and A B))) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25248.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> (D and E))) or F)), M:tm-300, m:tm-401, u:((Am (and (-> A (-> B (and A B))) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25249
in-theory        25249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-270 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25249.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-270, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25250
in-theory        25250
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-267 tm-401 ((Am (and (-> (and A B) B) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25250.        ((A or (((B and C) -> C) and A)) -> ((D -> (E -> (D and E))) or F)), M:tm-267, m:tm-401, u:((Am (and (-> (and A B) B) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25251
in-theory        25251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-239 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25251.        ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-239, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25252
in-theory        25252
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-236 tm-401 ((Am (and (-> (and A B) A) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25252.        ((A or (((B and C) -> B) and A)) -> ((D -> (E -> (D and E))) or F)), M:tm-236, m:tm-401, u:((Am (and (-> (and A B) A) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25253
in-theory        25253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-210 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25253.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> (F and G))) or H))), M:tm-210, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25254
in-theory        25254
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> (E and F))) or G))
theorem-size     27
proof            (modus-ponens tm-207 tm-401 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25254.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> (E and F))) or G)), M:tm-207, m:tm-401, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25255
in-theory        25255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-183 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25255.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-183, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25256
in-theory        25256
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-180 tm-401 ((Am (and (-> A (-> B A)) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25256.        ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> (D and E))) or F)), M:tm-180, m:tm-401, u:((Am (and (-> A (-> B A)) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25257
in-theory        25257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-157 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25257.        ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-157, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25258
in-theory        25258
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-154 tm-401 ((Am (-> (and A B) B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-1 tm-4 tm-6 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25258.        ((A or ((B and C) -> C)) -> ((D -> (E -> (D and E))) or F)), M:tm-154, m:tm-401, u:((Am (-> (and A B) B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25259
in-theory        25259
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     27
proof            (modus-ponens tm-147 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25259.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-147, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25260
in-theory        25260
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> (D and E))) or F))
theorem-size     25
proof            (modus-ponens tm-144 tm-401 ((Am (-> (and A (-> B C)) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-6 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25260.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> (D and E))) or F)), M:tm-144, m:tm-401, u:((Am (-> (and A (-> B C)) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25261
in-theory        25261
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> (B and C))) or D) -> E)) -> ((B -> (C -> (B and C))) or D))
theorem-size     23
proof            (modus-ponens tm-142 tm-401 ((Am (and A (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) C))) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-4 tm-6 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25261.        ((A and (((B -> (C -> (B and C))) or D) -> E)) -> ((B -> (C -> (B and C))) or D)), M:tm-142, m:tm-401, u:((Am (and A (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) C))) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25262
in-theory        25262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-134 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25262.        ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-134, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25263
in-theory        25263
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-131 tm-401 ((Am (-> (and A B) A)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-1 tm-3 tm-6 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25263.        ((A or ((B and C) -> B)) -> ((D -> (E -> (D and E))) or F)), M:tm-131, m:tm-401, u:((Am (-> (and A B) A)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25264
in-theory        25264
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     27
proof            (modus-ponens tm-125 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25264.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-125, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25265
in-theory        25265
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> (D and E))) or F))
theorem-size     25
proof            (modus-ponens tm-122 tm-401 ((Am (-> (and (-> A B) C) B)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-6 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25265.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> (D and E))) or F)), M:tm-122, m:tm-401, u:((Am (-> (and (-> A B) C) B)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25266
in-theory        25266
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) or C) -> D) and E) -> ((A -> (B -> (A and B))) or C))
theorem-size     23
proof            (modus-ponens tm-120 tm-401 ((Am (and (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) B) C)) (A (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-3 tm-6 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25266.        (((((A -> (B -> (A and B))) or C) -> D) and E) -> ((A -> (B -> (A and B))) or C)), M:tm-120, m:tm-401, u:((Am (and (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) B) C)) (A (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25267
in-theory        25267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-113 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25267.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (F and G))) or H))), M:tm-113, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25268
in-theory        25268
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> (E and F))) or G))
theorem-size     25
proof            (modus-ponens tm-110 tm-401 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25268.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> (E and F))) or G)), M:tm-110, m:tm-401, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25269
in-theory        25269
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     31
proof            (modus-ponens tm-105 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25269.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-105, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25270
in-theory        25270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> (D and E))) or F))
theorem-size     29
proof            (modus-ponens tm-102 tm-401 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-5)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25270.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> (D and E))) or F)), M:tm-102, m:tm-401, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25271
in-theory        25271
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) -> D) -> ((A -> (B -> (A and B))) or C))
theorem-size     21
proof            (modus-ponens tm-96 tm-401 ((Am (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) B)) (A (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25271.        ((((A -> (B -> (A and B))) or C) -> D) -> ((A -> (B -> (A and B))) or C)), M:tm-96, m:tm-401, u:((Am (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) B)) (A (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25272
in-theory        25272
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> (D and E))) or F)))
theorem-size     19
proof            (modus-ponens tm-95 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25272.        (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> (D and E))) or F))), M:tm-95, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25273
in-theory        25273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (D -> (C and D))) or E))
theorem-size     17
proof            (modus-ponens tm-92 tm-401 ((Am (-> A A)) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25273.        (((A -> B) or (A -> A)) -> ((C -> (D -> (C and D))) or E)), M:tm-92, m:tm-401, u:((Am (-> A A)) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25274
in-theory        25274
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> (C and D))) or E)))
theorem-size     13
proof            (modus-ponens tm-84 tm-401 ((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25274.        (A -> (B -> ((C -> (D -> (C and D))) or E))), M:tm-84, m:tm-401, u:((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25275
in-theory        25275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-83 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25275.        ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-83, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25276
in-theory        25276
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-80 tm-401 ((Am (-> A (-> B A))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25276.        ((A or (B -> (C -> B))) -> ((D -> (E -> (D and E))) or F)), M:tm-80, m:tm-401, u:((Am (-> A (-> B A))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25277
in-theory        25277
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((A -> (B -> (A and B))) or C) -> D))) -> D)
theorem-size     15
proof            (modus-ponens tm-77 tm-401 ((Am (not (not (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) B)))) (A (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-10 tm-1 tm-6 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25277.        ((not (not (((A -> (B -> (A and B))) or C) -> D))) -> D), M:tm-77, m:tm-401, u:((Am (not (not (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) B)))) (A (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25278
in-theory        25278
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (D -> (C and D))) or E)))
theorem-size     17
proof            (modus-ponens tm-76 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25278.        (((not (not A)) -> A) and (B -> ((C -> (D -> (C and D))) or E))), M:tm-76, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25279
in-theory        25279
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (C -> (B and C))) or D))
theorem-size     15
proof            (modus-ponens tm-73 tm-401 ((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-10 tm-1 tm-6 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25279.        (((not (not A)) or A) -> ((B -> (C -> (B and C))) or D)), M:tm-73, m:tm-401, u:((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25280
in-theory        25280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> (D and E))) or F)))
theorem-size     23
proof            (modus-ponens tm-69 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25280.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> (D and E))) or F))), M:tm-69, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25281
in-theory        25281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> (C and D))) or E))
theorem-size     21
proof            (modus-ponens tm-66 tm-401 ((Am (-> (-> A (not B)) (not A))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-9 tm-1 tm-6 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25281.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> (C and D))) or E)), M:tm-66, m:tm-401, u:((Am (-> (-> A (not B)) (not A))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25282
in-theory        25282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-54 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25282.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-54, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25283
in-theory        25283
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) or F))
theorem-size     23
proof            (modus-ponens tm-51 tm-401 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25283.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (D and E))) or F)), M:tm-51, m:tm-401, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25284
in-theory        25284
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (D -> (C and D))) or E))
theorem-size     15
proof            (modus-ponens tm-50 tm-401 ((Am (or A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25284.        ((A or (B or A)) -> ((C -> (D -> (C and D))) or E)), M:tm-50, m:tm-401, u:((Am (or A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25285
in-theory        25285
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (D -> (C and D))) or E))
theorem-size     15
proof            (modus-ponens tm-49 tm-401 ((Am (or A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25285.        ((A or (A or B)) -> ((C -> (D -> (C and D))) or E)), M:tm-49, m:tm-401, u:((Am (or A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25286
in-theory        25286
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) or E))
theorem-size     17
proof            (modus-ponens tm-48 tm-401 ((Am (-> A (and B A))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25286.        ((A or (B -> (A and B))) -> ((C -> (D -> (C and D))) or E)), M:tm-48, m:tm-401, u:((Am (-> A (and B A))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25287
in-theory        25287
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (D -> (C and D))) or E))
theorem-size     15
proof            (modus-ponens tm-47 tm-401 ((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-4 tm-1 tm-6 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25287.        (((A and B) or B) -> ((C -> (D -> (C and D))) or E)), M:tm-47, m:tm-401, u:((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25288
in-theory        25288
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (D -> (C and D))) or E))
theorem-size     15
proof            (modus-ponens tm-46 tm-401 ((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-6 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25288.        (((A and B) or A) -> ((C -> (D -> (C and D))) or E)), M:tm-46, m:tm-401, u:((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25289
in-theory        25289
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) or F))
theorem-size     23
proof            (modus-ponens tm-45 tm-401 ((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25289.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) or F)), M:tm-45, m:tm-401, u:((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25290
in-theory        25290
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (D -> (C and D))) or E))
theorem-size     15
proof            (modus-ponens tm-44 tm-401 ((Am (-> A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25290.        ((A or (B -> A)) -> ((C -> (D -> (C and D))) or E)), M:tm-44, m:tm-401, u:((Am (-> A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25291
in-theory        25291
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-42 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25291.        ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) or F))), M:tm-42, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25292
in-theory        25292
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-32 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25292.        ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) or F))), M:tm-32, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25293
in-theory        25293
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (C -> (B and C))) or D)))
theorem-size     13
proof            (modus-ponens tm-24 tm-401 ((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25293.        (A -> (A and ((B -> (C -> (B and C))) or D))), M:tm-24, m:tm-401, u:((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25294
in-theory        25294
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) or F)))
theorem-size     19
proof            (modus-ponens tm-23 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25294.        ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) or F))), M:tm-23, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25295
in-theory        25295
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-22 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25295.        (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) or F))), M:tm-22, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25296
in-theory        25296
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-21 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25296.        (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) or F))), M:tm-21, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25297
in-theory        25297
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-20 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25297.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-20, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25298
in-theory        25298
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-19 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25298.        ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) or F))), M:tm-19, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25299
in-theory        25299
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> (B and C))) or D) -> E)) -> E)
theorem-size     15
proof            (modus-ponens tm-17 tm-401 ((Am (and A (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) C))) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-4 tm-1 tm-6 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25299.        ((A and (((B -> (C -> (B and C))) or D) -> E)) -> E), M:tm-17, m:tm-401, u:((Am (and A (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) C))) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25300
in-theory        25300
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) or C) -> D) and E) -> D)
theorem-size     15
proof            (modus-ponens tm-15 tm-401 ((Am (and (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) B) C)) (A (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-3 tm-1 tm-6 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25300.        (((((A -> (B -> (A and B))) or C) -> D) and E) -> D), M:tm-15, m:tm-401, u:((Am (and (-> (or (-> Bm (-> Cm (and Bm Cm))) Dm) B) C)) (A (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25301
in-theory        25301
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> (B and C))) or D))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-401 ((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-9 tm-1 tm-6 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25301.        ((A -> (not ((B -> (C -> (B and C))) or D))) -> (not A)), M:tm-9, m:tm-401, u:((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25302
in-theory        25302
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) -> D) -> ((E or ((A -> (B -> (A and B))) or C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-401 ((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25302.        ((((A -> (B -> (A and B))) or C) -> D) -> ((E or ((A -> (B -> (A and B))) or C)) -> D)), M:tm-8, m:tm-401, u:((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-25303
in-theory        25303
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (D -> (C and D))) or E)))
theorem-size     13
proof            (modus-ponens tm-7 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-7 tm-1 tm-6 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25303.        (A or (B -> ((C -> (D -> (C and D))) or E))), M:tm-7, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25304
in-theory        25304
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-6 tm-1 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25304.        ((A -> ((B -> (C -> (B and C))) or D)) or E), M:tm-6, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25305
in-theory        25305
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D -> (C and D))) or E)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-25305.        (A -> ((B -> ((C -> (D -> (C and D))) or E)) and A)), M:tm-5, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-25306
in-theory        25306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-400 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25306.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-400, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25307
in-theory        25307
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-391 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25307.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-391, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25308
in-theory        25308
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-382 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25308.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-382, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25309
in-theory        25309
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-373 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25309.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I))), M:tm-373, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25310
in-theory        25310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-364 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25310.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-364, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25311
in-theory        25311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-354 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25311.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-354, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25312
in-theory        25312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25312.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25313
in-theory        25313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G)))
theorem-size     25
proof            (modus-ponens tm-338 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25313.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G))), M:tm-338, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25314
in-theory        25314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> (C or D)) or E))))
theorem-size     39
proof            (modus-ponens tm-327 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25314.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)))), M:tm-327, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25315
in-theory        25315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> (C or D)) or E))))
theorem-size     37
proof            (modus-ponens tm-326 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25315.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)))), M:tm-326, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25316
in-theory        25316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> (C or D)) or E))))
theorem-size     37
proof            (modus-ponens tm-325 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25316.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)))), M:tm-325, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25317
in-theory        25317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> (C or D)) or E))))
theorem-size     45
proof            (modus-ponens tm-324 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25317.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)))), M:tm-324, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25318
in-theory        25318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> (C or D)) or E))))
theorem-size     37
proof            (modus-ponens tm-323 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25318.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)))), M:tm-323, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25319
in-theory        25319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25319.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25320
in-theory        25320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25320.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25321
in-theory        25321
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25321.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25322
in-theory        25322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25322.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25323
in-theory        25323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (F or ((A -> (B -> (A and B))) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-311 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25323.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (F or ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)))), M:tm-311, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25324
in-theory        25324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25324.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) or F)), M:tm-310, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25325
in-theory        25325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (F -> (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25325.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (F -> (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and F))), M:tm-309, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25326
in-theory        25326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((C -> (C or D)) or E))
theorem-size     23
proof            (modus-ponens tm-308 tm-402 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (or Cm Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25326.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((C -> (C or D)) or E)), M:tm-308, m:tm-402, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (or Cm Dm)) Em)))
================================================================
tm-name          tm-25327
in-theory        25327
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-402 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (or Cm Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25327.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (A -> (B -> (A and B)))), M:tm-307, m:tm-402, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (or Cm Dm)) Em)))
================================================================
tm-name          tm-25328
in-theory        25328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (F -> ((A -> (B -> (A and B))) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-305 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25328.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (F -> ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)))), M:tm-305, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25329
in-theory        25329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-303 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25329.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-303, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25330
in-theory        25330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-270 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25330.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-270, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25331
in-theory        25331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-239 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25331.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-239, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25332
in-theory        25332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I)))
theorem-size     33
proof            (modus-ponens tm-210 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25332.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I))), M:tm-210, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25333
in-theory        25333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-183 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25333.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-183, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25334
in-theory        25334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-157 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25334.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-157, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25335
in-theory        25335
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     31
proof            (modus-ponens tm-147 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25335.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-147, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25336
in-theory        25336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-134 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25336.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-134, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25337
in-theory        25337
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     31
proof            (modus-ponens tm-125 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25337.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-125, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25338
in-theory        25338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-113 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25338.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I))), M:tm-113, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25339
in-theory        25339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     35
proof            (modus-ponens tm-105 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25339.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-105, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25340
in-theory        25340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-95 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25340.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G))), M:tm-95, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25341
in-theory        25341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-83 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25341.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-83, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25342
in-theory        25342
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> (D or E)) or F)))
theorem-size     21
proof            (modus-ponens tm-76 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25342.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> (D or E)) or F))), M:tm-76, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25343
in-theory        25343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G)))
theorem-size     27
proof            (modus-ponens tm-69 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25343.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G))), M:tm-69, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25344
in-theory        25344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-54 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25344.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-54, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25345
in-theory        25345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-42 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25345.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G))), M:tm-42, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25346
in-theory        25346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-32 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25346.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G))), M:tm-32, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25347
in-theory        25347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-23 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25347.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G))), M:tm-23, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25348
in-theory        25348
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-22 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25348.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G))), M:tm-22, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25349
in-theory        25349
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-21 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25349.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G))), M:tm-21, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25350
in-theory        25350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-20 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25350.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-20, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25351
in-theory        25351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-19 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25351.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> (E or F)) or G))), M:tm-19, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25352
in-theory        25352
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((D -> (D or E)) or F)))
theorem-size     17
proof            (modus-ponens tm-7 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25352.        (A or ((B -> (C -> (B and C))) and ((D -> (D or E)) or F))), M:tm-7, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25353
in-theory        25353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-6 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25353.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) or F), M:tm-6, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25354
in-theory        25354
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((D -> (D or E)) or F)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25354.        (A -> (((B -> (C -> (B and C))) and ((D -> (D or E)) or F)) and A)), M:tm-5, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25355
in-theory        25355
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((D -> (D or E)) or F)))
theorem-size     17
proof            (modus-ponens tm-1 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25355.        (A -> ((B -> (C -> (B and C))) and ((D -> (D or E)) or F))), M:tm-1, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25356
in-theory        25356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25356.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-400, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25357
in-theory        25357
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25357.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-391, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25358
in-theory        25358
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25358.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-382, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25359
in-theory        25359
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25359.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> (G or H)) or I))), M:tm-373, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25360
in-theory        25360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25360.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-364, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25361
in-theory        25361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25361.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-354, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25362
in-theory        25362
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25362.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25363
in-theory        25363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25363.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> (E or F)) or G))), M:tm-338, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25364
in-theory        25364
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> (C or D)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25364.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> (C or D)) or E)))), M:tm-327, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25365
in-theory        25365
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and (((F and G) -> G) and (((A and B) -> B) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25365.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and (((F and G) -> G) and (((A and B) -> B) and ((C -> (C or D)) or E)))), M:tm-326, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25366
in-theory        25366
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and (((F and G) -> F) and (((A and B) -> B) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25366.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and (((F and G) -> F) and (((A and B) -> B) and ((C -> (C or D)) or E)))), M:tm-325, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25367
in-theory        25367
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> (C or D)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25367.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> (C or D)) or E)))), M:tm-324, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25368
in-theory        25368
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25368.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> (C or D)) or E)))), M:tm-323, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25369
in-theory        25369
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25369.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25370
in-theory        25370
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25370.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25371
in-theory        25371
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25371.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25372
in-theory        25372
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25372.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25373
in-theory        25373
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and (F or (((A and B) -> B) and ((C -> (C or D)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25373.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and (F or (((A and B) -> B) and ((C -> (C or D)) or E)))), M:tm-311, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25374
in-theory        25374
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((((A and B) -> B) and ((C -> (C or D)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25374.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((((A and B) -> B) and ((C -> (C or D)) or E)) or F)), M:tm-310, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25375
in-theory        25375
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and (F -> ((((A and B) -> B) and ((C -> (C or D)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25375.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and (F -> ((((A and B) -> B) and ((C -> (C or D)) or E)) and F))), M:tm-309, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25376
in-theory        25376
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((C -> (C or D)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-403 ((A (-> (and Am Bm) Bm)) (B (or (-> Cm (or Cm Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25376.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((C -> (C or D)) or E)), M:tm-308, m:tm-403, u:((A (-> (and Am Bm) Bm)) (B (or (-> Cm (or Cm Dm)) Em)))
================================================================
tm-name          tm-25377
in-theory        25377
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-403 ((A (-> (and Am Bm) Bm)) (B (or (-> Cm (or Cm Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25377.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((A and B) -> B)), M:tm-307, m:tm-403, u:((A (-> (and Am Bm) Bm)) (B (or (-> Cm (or Cm Dm)) Em)))
================================================================
tm-name          tm-25378
in-theory        25378
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and (F -> (((A and B) -> B) and ((C -> (C or D)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25378.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and (F -> (((A and B) -> B) and ((C -> (C or D)) or E)))), M:tm-305, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25379
in-theory        25379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25379.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-303, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25380
in-theory        25380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25380.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-270, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25381
in-theory        25381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25381.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-239, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25382
in-theory        25382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25382.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> (G or H)) or I))), M:tm-210, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25383
in-theory        25383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25383.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-183, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25384
in-theory        25384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25384.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-157, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25385
in-theory        25385
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25385.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-147, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25386
in-theory        25386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25386.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-134, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25387
in-theory        25387
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25387.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-125, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25388
in-theory        25388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25388.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (G or H)) or I))), M:tm-113, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25389
in-theory        25389
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25389.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-105, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25390
in-theory        25390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25390.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> (E or F)) or G))), M:tm-95, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25391
in-theory        25391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25391.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-83, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25392
in-theory        25392
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((D -> (D or E)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-10 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25392.        (((not (not A)) -> A) and (((B and C) -> C) and ((D -> (D or E)) or F))), M:tm-76, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25393
in-theory        25393
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> (E or F)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-9 tm-4 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25393.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> (E or F)) or G))), M:tm-69, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25394
in-theory        25394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25394.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-54, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25395
in-theory        25395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25395.        ((A -> (B or A)) and (((C and D) -> D) and ((E -> (E or F)) or G))), M:tm-42, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25396
in-theory        25396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25396.        ((A -> (A or B)) and (((C and D) -> D) and ((E -> (E or F)) or G))), M:tm-32, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25397
in-theory        25397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25397.        ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> (E or F)) or G))), M:tm-23, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25398
in-theory        25398
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25398.        (((A and B) -> B) and (((C and D) -> D) and ((E -> (E or F)) or G))), M:tm-22, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25399
in-theory        25399
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25399.        (((A and B) -> A) and (((C and D) -> D) and ((E -> (E or F)) or G))), M:tm-21, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25400
in-theory        25400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25400.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-20, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25401
in-theory        25401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25401.        ((A -> (B -> A)) and (((C and D) -> D) and ((E -> (E or F)) or G))), M:tm-19, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25402
in-theory        25402
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-7 tm-5 tm-4 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25402.        (A or (((B and C) -> C) and ((D -> (D or E)) or F))), M:tm-7, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25403
in-theory        25403
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25403.        ((((A and B) -> B) and ((C -> (C or D)) or E)) or F), M:tm-6, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25404
in-theory        25404
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((D -> (D or E)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25404.        (A -> ((((B and C) -> C) and ((D -> (D or E)) or F)) and A)), M:tm-5, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25405
in-theory        25405
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-1 tm-5 tm-4 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25405.        (A -> (((B and C) -> C) and ((D -> (D or E)) or F))), M:tm-1, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25406
in-theory        25406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25406.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-400, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25407
in-theory        25407
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25407.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-391, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25408
in-theory        25408
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25408.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-382, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25409
in-theory        25409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25409.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> (G or H)) or I))), M:tm-373, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25410
in-theory        25410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25410.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-364, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25411
in-theory        25411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25411.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-354, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25412
in-theory        25412
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25412.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25413
in-theory        25413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25413.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> (E or F)) or G))), M:tm-338, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25414
in-theory        25414
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> (C or D)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25414.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> (C or D)) or E)))), M:tm-327, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25415
in-theory        25415
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and (((F and G) -> G) and (((A and B) -> A) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25415.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and (((F and G) -> G) and (((A and B) -> A) and ((C -> (C or D)) or E)))), M:tm-326, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25416
in-theory        25416
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and (((F and G) -> F) and (((A and B) -> A) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25416.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and (((F and G) -> F) and (((A and B) -> A) and ((C -> (C or D)) or E)))), M:tm-325, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25417
in-theory        25417
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> (C or D)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25417.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> (C or D)) or E)))), M:tm-324, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25418
in-theory        25418
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25418.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> (C or D)) or E)))), M:tm-323, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25419
in-theory        25419
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25419.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25420
in-theory        25420
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25420.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25421
in-theory        25421
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25421.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25422
in-theory        25422
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25422.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25423
in-theory        25423
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and (F or (((A and B) -> A) and ((C -> (C or D)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25423.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and (F or (((A and B) -> A) and ((C -> (C or D)) or E)))), M:tm-311, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25424
in-theory        25424
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((((A and B) -> A) and ((C -> (C or D)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25424.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((((A and B) -> A) and ((C -> (C or D)) or E)) or F)), M:tm-310, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25425
in-theory        25425
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and (F -> ((((A and B) -> A) and ((C -> (C or D)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25425.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and (F -> ((((A and B) -> A) and ((C -> (C or D)) or E)) and F))), M:tm-309, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25426
in-theory        25426
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((C -> (C or D)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-404 ((A (-> (and Am Bm) Am)) (B (or (-> Cm (or Cm Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25426.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((C -> (C or D)) or E)), M:tm-308, m:tm-404, u:((A (-> (and Am Bm) Am)) (B (or (-> Cm (or Cm Dm)) Em)))
================================================================
tm-name          tm-25427
in-theory        25427
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-404 ((A (-> (and Am Bm) Am)) (B (or (-> Cm (or Cm Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25427.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((A and B) -> A)), M:tm-307, m:tm-404, u:((A (-> (and Am Bm) Am)) (B (or (-> Cm (or Cm Dm)) Em)))
================================================================
tm-name          tm-25428
in-theory        25428
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and (F -> (((A and B) -> A) and ((C -> (C or D)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25428.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and (F -> (((A and B) -> A) and ((C -> (C or D)) or E)))), M:tm-305, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25429
in-theory        25429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25429.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-303, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25430
in-theory        25430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25430.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-270, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25431
in-theory        25431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25431.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-239, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25432
in-theory        25432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25432.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> (G or H)) or I))), M:tm-210, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25433
in-theory        25433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25433.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-183, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25434
in-theory        25434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25434.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-157, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25435
in-theory        25435
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25435.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-147, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25436
in-theory        25436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25436.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-134, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25437
in-theory        25437
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25437.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-125, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25438
in-theory        25438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25438.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (G or H)) or I))), M:tm-113, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25439
in-theory        25439
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25439.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-105, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25440
in-theory        25440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25440.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> (E or F)) or G))), M:tm-95, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25441
in-theory        25441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25441.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-83, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25442
in-theory        25442
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((D -> (D or E)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-10 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25442.        (((not (not A)) -> A) and (((B and C) -> B) and ((D -> (D or E)) or F))), M:tm-76, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25443
in-theory        25443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> (E or F)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-9 tm-3 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25443.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> (E or F)) or G))), M:tm-69, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25444
in-theory        25444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25444.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-54, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25445
in-theory        25445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25445.        ((A -> (B or A)) and (((C and D) -> C) and ((E -> (E or F)) or G))), M:tm-42, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25446
in-theory        25446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25446.        ((A -> (A or B)) and (((C and D) -> C) and ((E -> (E or F)) or G))), M:tm-32, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25447
in-theory        25447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25447.        ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> (E or F)) or G))), M:tm-23, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25448
in-theory        25448
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25448.        (((A and B) -> B) and (((C and D) -> C) and ((E -> (E or F)) or G))), M:tm-22, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25449
in-theory        25449
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25449.        (((A and B) -> A) and (((C and D) -> C) and ((E -> (E or F)) or G))), M:tm-21, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25450
in-theory        25450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25450.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-20, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25451
in-theory        25451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25451.        ((A -> (B -> A)) and (((C and D) -> C) and ((E -> (E or F)) or G))), M:tm-19, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25452
in-theory        25452
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-7 tm-5 tm-3 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25452.        (A or (((B and C) -> B) and ((D -> (D or E)) or F))), M:tm-7, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25453
in-theory        25453
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25453.        ((((A and B) -> A) and ((C -> (C or D)) or E)) or F), M:tm-6, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25454
in-theory        25454
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((D -> (D or E)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25454.        (A -> ((((B and C) -> B) and ((D -> (D or E)) or F)) and A)), M:tm-5, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25455
in-theory        25455
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-1 tm-5 tm-3 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25455.        (A -> (((B and C) -> B) and ((D -> (D or E)) or F))), M:tm-1, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25456
in-theory        25456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25456.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-400, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25457
in-theory        25457
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25457.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-391, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25458
in-theory        25458
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25458.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-382, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25459
in-theory        25459
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (H or I)) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25459.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (H or I)) or J))), M:tm-373, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25460
in-theory        25460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25460.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-364, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25461
in-theory        25461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25461.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-354, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25462
in-theory        25462
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25462.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25463
in-theory        25463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25463.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H))), M:tm-338, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25464
in-theory        25464
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25464.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)))), M:tm-327, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25465
in-theory        25465
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25465.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)))), M:tm-326, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25466
in-theory        25466
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25466.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)))), M:tm-325, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25467
in-theory        25467
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25467.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)))), M:tm-324, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25468
in-theory        25468
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25468.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)))), M:tm-323, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25469
in-theory        25469
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25469.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((G and H) -> H)), M:tm-322, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25470
in-theory        25470
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25470.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((G and H) -> G)), M:tm-320, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25471
in-theory        25471
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25471.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25472
in-theory        25472
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25472.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (G -> (H -> G))), M:tm-315, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25473
in-theory        25473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25473.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)))), M:tm-311, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25474
in-theory        25474
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25474.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) or G)), M:tm-310, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25475
in-theory        25475
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25475.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and G))), M:tm-309, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25476
in-theory        25476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((D -> (D or E)) or F))
theorem-size     29
proof            (modus-ponens tm-308 tm-405 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (or Dm Em)) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25476.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((D -> (D or E)) or F)), M:tm-308, m:tm-405, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (or Dm Em)) Fm)))
================================================================
tm-name          tm-25477
in-theory        25477
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-405 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (or Dm Em)) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25477.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-405, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (or Dm Em)) Fm)))
================================================================
tm-name          tm-25478
in-theory        25478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25478.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)))), M:tm-305, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25479
in-theory        25479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25479.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-303, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25480
in-theory        25480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25480.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-270, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25481
in-theory        25481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25481.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-239, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25482
in-theory        25482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (H or I)) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25482.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (H or I)) or J))), M:tm-210, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25483
in-theory        25483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25483.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-183, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25484
in-theory        25484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25484.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-157, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25485
in-theory        25485
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25485.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-147, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25486
in-theory        25486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25486.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-134, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25487
in-theory        25487
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25487.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-125, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25488
in-theory        25488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (H or I)) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25488.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (H or I)) or J))), M:tm-113, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25489
in-theory        25489
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25489.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-105, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25490
in-theory        25490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25490.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H))), M:tm-95, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25491
in-theory        25491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25491.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-83, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25492
in-theory        25492
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (E or F)) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25492.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (E or F)) or G))), M:tm-76, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25493
in-theory        25493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25493.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H))), M:tm-69, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25494
in-theory        25494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25494.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-54, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25495
in-theory        25495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25495.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H))), M:tm-42, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25496
in-theory        25496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25496.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H))), M:tm-32, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25497
in-theory        25497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25497.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H))), M:tm-23, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25498
in-theory        25498
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25498.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H))), M:tm-22, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25499
in-theory        25499
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25499.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H))), M:tm-21, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25500
in-theory        25500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25500.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-20, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25501
in-theory        25501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25501.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (F or G)) or H))), M:tm-19, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25502
in-theory        25502
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-7 tm-5 tm-2 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25502.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (E or F)) or G))), M:tm-7, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25503
in-theory        25503
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25503.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) or G), M:tm-6, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25504
in-theory        25504
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (E or F)) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25504.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (E or F)) or G)) and A)), M:tm-5, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25505
in-theory        25505
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-1 tm-5 tm-2 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25505.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (E or F)) or G))), M:tm-1, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-25506
in-theory        25506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25506.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-400, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25507
in-theory        25507
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25507.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-391, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25508
in-theory        25508
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25508.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-382, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25509
in-theory        25509
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25509.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> (G or H)) or I))), M:tm-373, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25510
in-theory        25510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25510.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-364, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25511
in-theory        25511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25511.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-354, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25512
in-theory        25512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25512.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25513
in-theory        25513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25513.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> (E or F)) or G))), M:tm-338, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25514
in-theory        25514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> (C or D)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25514.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> (C or D)) or E)))), M:tm-327, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25515
in-theory        25515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25515.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> (C or D)) or E)))), M:tm-326, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25516
in-theory        25516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25516.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> (C or D)) or E)))), M:tm-325, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25517
in-theory        25517
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> (C or D)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25517.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> (C or D)) or E)))), M:tm-324, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25518
in-theory        25518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25518.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> (C or D)) or E)))), M:tm-323, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25519
in-theory        25519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25519.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25520
in-theory        25520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25520.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25521
in-theory        25521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25521.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25522
in-theory        25522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25522.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25523
in-theory        25523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (F or ((A -> (B -> A)) and ((C -> (C or D)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25523.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (F or ((A -> (B -> A)) and ((C -> (C or D)) or E)))), M:tm-311, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25524
in-theory        25524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (((A -> (B -> A)) and ((C -> (C or D)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25524.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (((A -> (B -> A)) and ((C -> (C or D)) or E)) or F)), M:tm-310, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25525
in-theory        25525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (F -> (((A -> (B -> A)) and ((C -> (C or D)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25525.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (F -> (((A -> (B -> A)) and ((C -> (C or D)) or E)) and F))), M:tm-309, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25526
in-theory        25526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((C -> (C or D)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-406 ((A (-> Am (-> Bm Am))) (B (or (-> Cm (or Cm Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25526.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((C -> (C or D)) or E)), M:tm-308, m:tm-406, u:((A (-> Am (-> Bm Am))) (B (or (-> Cm (or Cm Dm)) Em)))
================================================================
tm-name          tm-25527
in-theory        25527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-406 ((A (-> Am (-> Bm Am))) (B (or (-> Cm (or Cm Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25527.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (A -> (B -> A))), M:tm-307, m:tm-406, u:((A (-> Am (-> Bm Am))) (B (or (-> Cm (or Cm Dm)) Em)))
================================================================
tm-name          tm-25528
in-theory        25528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (F -> ((A -> (B -> A)) and ((C -> (C or D)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25528.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (F -> ((A -> (B -> A)) and ((C -> (C or D)) or E)))), M:tm-305, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25529
in-theory        25529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25529.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-303, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25530
in-theory        25530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25530.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-270, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25531
in-theory        25531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25531.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-239, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25532
in-theory        25532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25532.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> (G or H)) or I))), M:tm-210, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25533
in-theory        25533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25533.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-183, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25534
in-theory        25534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25534.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-157, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25535
in-theory        25535
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25535.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-147, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25536
in-theory        25536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25536.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-134, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25537
in-theory        25537
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25537.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-125, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25538
in-theory        25538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25538.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (G or H)) or I))), M:tm-113, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25539
in-theory        25539
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25539.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-105, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25540
in-theory        25540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25540.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> (E or F)) or G))), M:tm-95, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25541
in-theory        25541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25541.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-83, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25542
in-theory        25542
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> (D or E)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25542.        (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> (D or E)) or F))), M:tm-76, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25543
in-theory        25543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> (E or F)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25543.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> (E or F)) or G))), M:tm-69, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25544
in-theory        25544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25544.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-54, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25545
in-theory        25545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25545.        ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> (E or F)) or G))), M:tm-42, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25546
in-theory        25546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25546.        ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> (E or F)) or G))), M:tm-32, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25547
in-theory        25547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25547.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> (E or F)) or G))), M:tm-23, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25548
in-theory        25548
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25548.        (((A and B) -> B) and ((C -> (D -> C)) and ((E -> (E or F)) or G))), M:tm-22, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25549
in-theory        25549
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25549.        (((A and B) -> A) and ((C -> (D -> C)) and ((E -> (E or F)) or G))), M:tm-21, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25550
in-theory        25550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25550.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-20, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25551
in-theory        25551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25551.        ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> (E or F)) or G))), M:tm-19, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25552
in-theory        25552
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-7 tm-5 tm-1 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25552.        (A or ((B -> (C -> B)) and ((D -> (D or E)) or F))), M:tm-7, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25553
in-theory        25553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25553.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) or F), M:tm-6, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25554
in-theory        25554
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((D -> (D or E)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25554.        (A -> (((B -> (C -> B)) and ((D -> (D or E)) or F)) and A)), M:tm-5, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25555
in-theory        25555
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25555.        (A -> ((B -> (C -> B)) and ((D -> (D or E)) or F))), M:tm-1, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-25556
in-theory        25556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-400 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25556.        (((A -> (B -> (A and B))) or C) and (D or ((E -> (E or F)) or G))), M:tm-400, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25557
in-theory        25557
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-391 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25557.        ((((A and B) -> B) or C) and (D or ((E -> (E or F)) or G))), M:tm-391, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25558
in-theory        25558
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-382 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25558.        ((((A and B) -> A) or C) and (D or ((E -> (E or F)) or G))), M:tm-382, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25559
in-theory        25559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-373 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25559.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> (F or G)) or H))), M:tm-373, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25560
in-theory        25560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-364 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25560.        (((A -> (B -> A)) or C) and (D or ((E -> (E or F)) or G))), M:tm-364, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25561
in-theory        25561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-354 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25561.        ((A -> (B -> (C -> (B and C)))) and (D or ((E -> (E or F)) or G))), M:tm-354, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25562
in-theory        25562
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25562.        ((A or ((B -> (B or C)) or D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25563
in-theory        25563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((D -> (D or E)) or F)))
theorem-size     19
proof            (modus-ponens tm-338 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25563.        (((A -> B) -> (A -> (A and B))) and (C or ((D -> (D or E)) or F))), M:tm-338, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25564
in-theory        25564
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and ((E -> (F -> (E and F))) and (A or ((B -> (B or C)) or D))))
theorem-size     27
proof            (modus-ponens tm-327 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25564.        ((A or ((B -> (B or C)) or D)) and ((E -> (F -> (E and F))) and (A or ((B -> (B or C)) or D)))), M:tm-327, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25565
in-theory        25565
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and (((E and F) -> F) and (A or ((B -> (B or C)) or D))))
theorem-size     25
proof            (modus-ponens tm-326 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25565.        ((A or ((B -> (B or C)) or D)) and (((E and F) -> F) and (A or ((B -> (B or C)) or D)))), M:tm-326, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25566
in-theory        25566
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and (((E and F) -> E) and (A or ((B -> (B or C)) or D))))
theorem-size     25
proof            (modus-ponens tm-325 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25566.        ((A or ((B -> (B or C)) or D)) and (((E and F) -> E) and (A or ((B -> (B or C)) or D)))), M:tm-325, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25567
in-theory        25567
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> (B or C)) or D))))
theorem-size     33
proof            (modus-ponens tm-324 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25567.        ((A or ((B -> (B or C)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> (B or C)) or D)))), M:tm-324, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25568
in-theory        25568
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and ((E -> (F -> E)) and (A or ((B -> (B or C)) or D))))
theorem-size     25
proof            (modus-ponens tm-323 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25568.        ((A or ((B -> (B or C)) or D)) and ((E -> (F -> E)) and (A or ((B -> (B or C)) or D)))), M:tm-323, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25569
in-theory        25569
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25569.        ((A or ((B -> (B or C)) or D)) and ((E and F) -> F)), M:tm-322, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25570
in-theory        25570
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25570.        ((A or ((B -> (B or C)) or D)) and ((E and F) -> E)), M:tm-320, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25571
in-theory        25571
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25571.        ((A or ((B -> (B or C)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25572
in-theory        25572
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25572.        ((A or ((B -> (B or C)) or D)) and (E -> (F -> E))), M:tm-315, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25573
in-theory        25573
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and (E or (A or ((B -> (B or C)) or D))))
theorem-size     21
proof            (modus-ponens tm-311 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25573.        ((A or ((B -> (B or C)) or D)) and (E or (A or ((B -> (B or C)) or D)))), M:tm-311, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25574
in-theory        25574
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and ((A or ((B -> (B or C)) or D)) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25574.        ((A or ((B -> (B or C)) or D)) and ((A or ((B -> (B or C)) or D)) or E)), M:tm-310, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25575
in-theory        25575
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and (E -> ((A or ((B -> (B or C)) or D)) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25575.        ((A or ((B -> (B or C)) or D)) and (E -> ((A or ((B -> (B or C)) or D)) and E))), M:tm-309, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25576
in-theory        25576
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and (E -> (A or ((B -> (B or C)) or D))))
theorem-size     21
proof            (modus-ponens tm-305 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25576.        ((A or ((B -> (B or C)) or D)) and (E -> (A or ((B -> (B or C)) or D)))), M:tm-305, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25577
in-theory        25577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-303 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25577.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> (E or F)) or G))), M:tm-303, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25578
in-theory        25578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-270 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25578.        ((A -> (((B and C) -> C) and A)) and (D or ((E -> (E or F)) or G))), M:tm-270, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25579
in-theory        25579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-239 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25579.        ((A -> (((B and C) -> B) and A)) and (D or ((E -> (E or F)) or G))), M:tm-239, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25580
in-theory        25580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-210 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25580.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> (F or G)) or H))), M:tm-210, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25581
in-theory        25581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-183 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25581.        ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> (E or F)) or G))), M:tm-183, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25582
in-theory        25582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-157 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25582.        ((A -> ((B and C) -> C)) and (D or ((E -> (E or F)) or G))), M:tm-157, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25583
in-theory        25583
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> (E or F)) or G)))
theorem-size     25
proof            (modus-ponens tm-147 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25583.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> (E or F)) or G))), M:tm-147, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25584
in-theory        25584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-134 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25584.        ((A -> ((B and C) -> B)) and (D or ((E -> (E or F)) or G))), M:tm-134, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25585
in-theory        25585
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> (E or F)) or G)))
theorem-size     25
proof            (modus-ponens tm-125 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25585.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> (E or F)) or G))), M:tm-125, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25586
in-theory        25586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-113 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25586.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (F or G)) or H))), M:tm-113, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25587
in-theory        25587
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> (E or F)) or G)))
theorem-size     29
proof            (modus-ponens tm-105 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25587.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> (E or F)) or G))), M:tm-105, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25588
in-theory        25588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((D -> (D or E)) or F)))
theorem-size     17
proof            (modus-ponens tm-95 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25588.        (((A -> B) -> (A -> A)) and (C or ((D -> (D or E)) or F))), M:tm-95, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25589
in-theory        25589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-83 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25589.        ((A -> (B -> (C -> B))) and (D or ((E -> (E or F)) or G))), M:tm-83, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25590
in-theory        25590
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((C -> (C or D)) or E)))
theorem-size     15
proof            (modus-ponens tm-76 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25590.        (((not (not A)) -> A) and (B or ((C -> (C or D)) or E))), M:tm-76, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25591
in-theory        25591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> (D or E)) or F)))
theorem-size     21
proof            (modus-ponens tm-69 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25591.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> (D or E)) or F))), M:tm-69, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25592
in-theory        25592
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-54 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25592.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (E or F)) or G))), M:tm-54, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25593
in-theory        25593
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-42 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25593.        ((A -> (B or A)) and (C or ((D -> (D or E)) or F))), M:tm-42, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25594
in-theory        25594
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-32 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25594.        ((A -> (A or B)) and (C or ((D -> (D or E)) or F))), M:tm-32, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25595
in-theory        25595
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((D -> (D or E)) or F)))
theorem-size     17
proof            (modus-ponens tm-23 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25595.        ((A -> (B -> (A and B))) and (C or ((D -> (D or E)) or F))), M:tm-23, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25596
in-theory        25596
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-22 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25596.        (((A and B) -> B) and (C or ((D -> (D or E)) or F))), M:tm-22, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25597
in-theory        25597
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-21 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25597.        (((A and B) -> A) and (C or ((D -> (D or E)) or F))), M:tm-21, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25598
in-theory        25598
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-20 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25598.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (E or F)) or G))), M:tm-20, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25599
in-theory        25599
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-19 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25599.        ((A -> (B -> A)) and (C or ((D -> (D or E)) or F))), M:tm-19, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25600
in-theory        25600
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or ((C -> (C or D)) or E)))
theorem-size     11
proof            (modus-ponens tm-7 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-7 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25600.        (A or (B or ((C -> (C or D)) or E))), M:tm-7, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25601
in-theory        25601
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-6 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25601.        ((A or ((B -> (B or C)) or D)) or E), M:tm-6, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25602
in-theory        25602
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> (C or D)) or E)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25602.        (A -> ((B or ((C -> (C or D)) or E)) and A)), M:tm-5, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25603
in-theory        25603
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (C or D)) or E)))
theorem-size     11
proof            (modus-ponens tm-1 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-1 tm-7 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25603.        (A -> (B or ((C -> (C or D)) or E))), M:tm-1, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-25604
in-theory        25604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (D or E)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25604.        (((A -> (B -> (A and B))) or C) and (((D -> (D or E)) or F) or G)), M:tm-400, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25605
in-theory        25605
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25605.        ((((A and B) -> B) or C) and (((D -> (D or E)) or F) or G)), M:tm-391, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25606
in-theory        25606
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25606.        ((((A and B) -> A) or C) and (((D -> (D or E)) or F) or G)), M:tm-382, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25607
in-theory        25607
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (E or F)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25607.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (E or F)) or G) or H)), M:tm-373, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25608
in-theory        25608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25608.        (((A -> (B -> A)) or C) and (((D -> (D or E)) or F) or G)), M:tm-364, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25609
in-theory        25609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (D or E)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25609.        ((A -> (B -> (C -> (B and C)))) and (((D -> (D or E)) or F) or G)), M:tm-354, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25610
in-theory        25610
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25610.        ((((A -> (A or B)) or C) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25611
in-theory        25611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (C or D)) or E) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25611.        (((A -> B) -> (A -> (A and B))) and (((C -> (C or D)) or E) or F)), M:tm-338, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25612
in-theory        25612
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and ((E -> (F -> (E and F))) and (((A -> (A or B)) or C) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25612.        ((((A -> (A or B)) or C) or D) and ((E -> (F -> (E and F))) and (((A -> (A or B)) or C) or D))), M:tm-327, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25613
in-theory        25613
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and (((E and F) -> F) and (((A -> (A or B)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25613.        ((((A -> (A or B)) or C) or D) and (((E and F) -> F) and (((A -> (A or B)) or C) or D))), M:tm-326, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25614
in-theory        25614
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and (((E and F) -> E) and (((A -> (A or B)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25614.        ((((A -> (A or B)) or C) or D) and (((E and F) -> E) and (((A -> (A or B)) or C) or D))), M:tm-325, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25615
in-theory        25615
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (A or B)) or C) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25615.        ((((A -> (A or B)) or C) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (A or B)) or C) or D))), M:tm-324, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25616
in-theory        25616
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and ((E -> (F -> E)) and (((A -> (A or B)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25616.        ((((A -> (A or B)) or C) or D) and ((E -> (F -> E)) and (((A -> (A or B)) or C) or D))), M:tm-323, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25617
in-theory        25617
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25617.        ((((A -> (A or B)) or C) or D) and ((E and F) -> F)), M:tm-322, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25618
in-theory        25618
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25618.        ((((A -> (A or B)) or C) or D) and ((E and F) -> E)), M:tm-320, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25619
in-theory        25619
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25619.        ((((A -> (A or B)) or C) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25620
in-theory        25620
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25620.        ((((A -> (A or B)) or C) or D) and (E -> (F -> E))), M:tm-315, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25621
in-theory        25621
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and (E or (((A -> (A or B)) or C) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25621.        ((((A -> (A or B)) or C) or D) and (E or (((A -> (A or B)) or C) or D))), M:tm-311, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25622
in-theory        25622
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and ((((A -> (A or B)) or C) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25622.        ((((A -> (A or B)) or C) or D) and ((((A -> (A or B)) or C) or D) or E)), M:tm-310, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25623
in-theory        25623
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and (E -> ((((A -> (A or B)) or C) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25623.        ((((A -> (A or B)) or C) or D) and (E -> ((((A -> (A or B)) or C) or D) and E))), M:tm-309, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25624
in-theory        25624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and (E -> (((A -> (A or B)) or C) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25624.        ((((A -> (A or B)) or C) or D) and (E -> (((A -> (A or B)) or C) or D))), M:tm-305, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25625
in-theory        25625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (D or E)) or F) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25625.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (D or E)) or F) or G)), M:tm-303, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25626
in-theory        25626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (D or E)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25626.        ((A -> (((B and C) -> C) and A)) and (((D -> (D or E)) or F) or G)), M:tm-270, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25627
in-theory        25627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (D or E)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25627.        ((A -> (((B and C) -> B) and A)) and (((D -> (D or E)) or F) or G)), M:tm-239, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25628
in-theory        25628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (E or F)) or G) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25628.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (E or F)) or G) or H)), M:tm-210, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25629
in-theory        25629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (D or E)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25629.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (D or E)) or F) or G)), M:tm-183, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25630
in-theory        25630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25630.        ((A -> ((B and C) -> C)) and (((D -> (D or E)) or F) or G)), M:tm-157, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25631
in-theory        25631
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (D or E)) or F) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25631.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (D or E)) or F) or G)), M:tm-147, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25632
in-theory        25632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25632.        ((A -> ((B and C) -> B)) and (((D -> (D or E)) or F) or G)), M:tm-134, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25633
in-theory        25633
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (D or E)) or F) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25633.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (D or E)) or F) or G)), M:tm-125, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25634
in-theory        25634
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (E or F)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25634.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (E or F)) or G) or H)), M:tm-113, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25635
in-theory        25635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (D or E)) or F) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25635.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (D or E)) or F) or G)), M:tm-105, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25636
in-theory        25636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (C or D)) or E) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25636.        (((A -> B) -> (A -> A)) and (((C -> (C or D)) or E) or F)), M:tm-95, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25637
in-theory        25637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25637.        ((A -> (B -> (C -> B))) and (((D -> (D or E)) or F) or G)), M:tm-83, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25638
in-theory        25638
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (B or C)) or D) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25638.        (((not (not A)) -> A) and (((B -> (B or C)) or D) or E)), M:tm-76, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25639
in-theory        25639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (C or D)) or E) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25639.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (C or D)) or E) or F)), M:tm-69, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25640
in-theory        25640
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (D or E)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25640.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (D or E)) or F) or G)), M:tm-54, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25641
in-theory        25641
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (C or D)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25641.        ((A -> (B or A)) and (((C -> (C or D)) or E) or F)), M:tm-42, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25642
in-theory        25642
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (C or D)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25642.        ((A -> (A or B)) and (((C -> (C or D)) or E) or F)), M:tm-32, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25643
in-theory        25643
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (C or D)) or E) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25643.        ((A -> (B -> (A and B))) and (((C -> (C or D)) or E) or F)), M:tm-23, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25644
in-theory        25644
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (C or D)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25644.        (((A and B) -> B) and (((C -> (C or D)) or E) or F)), M:tm-22, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25645
in-theory        25645
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (C or D)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25645.        (((A and B) -> A) and (((C -> (C or D)) or E) or F)), M:tm-21, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25646
in-theory        25646
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (D or E)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25646.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (D or E)) or F) or G)), M:tm-20, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25647
in-theory        25647
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (C or D)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25647.        ((A -> (B -> A)) and (((C -> (C or D)) or E) or F)), M:tm-19, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25648
in-theory        25648
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> (B or C)) or D) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-7 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25648.        (A or (((B -> (B or C)) or D) or E)), M:tm-7, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25649
in-theory        25649
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25649.        ((((A -> (A or B)) or C) or D) or E), M:tm-6, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25650
in-theory        25650
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (B or C)) or D) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25650.        (A -> ((((B -> (B or C)) or D) or E) and A)), M:tm-5, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25651
in-theory        25651
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) or D) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-1 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25651.        (A -> (((B -> (B or C)) or D) or E)), M:tm-1, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-25652
in-theory        25652
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-409 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-6)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25652.        (((A -> (A or B)) or C) and (D -> (D or E))), M:tm-409, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-25653
in-theory        25653
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-409 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-25653.        (((A -> (A or B)) or C) and (D -> (E or D))), M:tm-409, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-25654
in-theory        25654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25654.        (((A -> (A or B)) or C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-409, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-25655
in-theory        25655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-409 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25655.        (((A -> (A or B)) or C) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-409, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-25656
in-theory        25656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-409 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-25656.        (((A -> (A or B)) or C) and ((not (not D)) -> D)), M:tm-409, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-25657
in-theory        25657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-409 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25657.        (((A -> (A or B)) or C) and (D -> (E -> (F -> E)))), M:tm-409, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-25658
in-theory        25658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-409 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-25658.        (((A -> (A or B)) or C) and ((D -> E) -> (D -> D))), M:tm-409, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-25659
in-theory        25659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-409 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25659.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-409, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-25660
in-theory        25660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25660.        (((A -> (A or B)) or C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-409, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-25661
in-theory        25661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-409 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25661.        (((A -> (A or B)) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-409, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-25662
in-theory        25662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-409 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25662.        (((A -> (A or B)) or C) and (D -> ((E and F) -> E))), M:tm-409, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-25663
in-theory        25663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-409 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25663.        (((A -> (A or B)) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-409, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-25664
in-theory        25664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-409 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25664.        (((A -> (A or B)) or C) and (D -> ((E and F) -> F))), M:tm-409, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-25665
in-theory        25665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-409 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25665.        (((A -> (A or B)) or C) and (D -> ((E -> (F -> E)) and D))), M:tm-409, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-25666
in-theory        25666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-409 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25666.        (((A -> (A or B)) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-409, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-25667
in-theory        25667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-409 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25667.        (((A -> (A or B)) or C) and (D -> (((E and F) -> E) and D))), M:tm-409, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-25668
in-theory        25668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-409 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25668.        (((A -> (A or B)) or C) and (D -> (((E and F) -> F) and D))), M:tm-409, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-25669
in-theory        25669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25669.        (((A -> (A or B)) or C) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-409, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-25670
in-theory        25670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-409 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25670.        (((A -> (A or B)) or C) and ((D -> E) -> (D -> (D and E)))), M:tm-409, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-25671
in-theory        25671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25671.        (((A -> (A or B)) or C) and (D -> (E -> (F -> (E and F))))), M:tm-409, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-25672
in-theory        25672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-409 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25672.        (((A -> (A or B)) or C) and ((D -> (E -> D)) or F)), M:tm-409, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-25673
in-theory        25673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-409 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25673.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-409, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-25674
in-theory        25674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-409 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25674.        (((A -> (A or B)) or C) and (((D and E) -> D) or F)), M:tm-409, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-25675
in-theory        25675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-409 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25675.        (((A -> (A or B)) or C) and (((D and E) -> E) or F)), M:tm-409, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-25676
in-theory        25676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-409 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25676.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) or F)), M:tm-409, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-25677
in-theory        25677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-409 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-25677.        (((A -> (A or B)) or C) and ((D -> (D or E)) or F)), M:tm-409, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-25678
in-theory        25678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-409 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25678.        (((A -> (A or B)) or C) and (D -> ((E -> (E or F)) and D))), M:tm-409, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-25679
in-theory        25679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-409 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25679.        (((A -> (A or B)) or C) and (D -> (E -> (E or F)))), M:tm-409, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-25680
in-theory        25680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-409 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25680.        (((A -> (A or B)) or C) and (D or (E -> (F -> E)))), M:tm-409, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-25681
in-theory        25681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25681.        (((A -> (A or B)) or C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-409, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-25682
in-theory        25682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-409 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25682.        (((A -> (A or B)) or C) and (D or ((E and F) -> E))), M:tm-409, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-25683
in-theory        25683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-409 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25683.        (((A -> (A or B)) or C) and (D or ((E and F) -> F))), M:tm-409, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-25684
in-theory        25684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25684.        (((A -> (A or B)) or C) and (D or (E -> (F -> (E and F))))), M:tm-409, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-25685
in-theory        25685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-409 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25685.        (((A -> (A or B)) or C) and (D or (E -> (E or F)))), M:tm-409, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-25686
in-theory        25686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-409 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25686.        (((A -> (A or B)) or C) and (D or (E -> (F or E)))), M:tm-409, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-25687
in-theory        25687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-409 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25687.        (((A -> (A or B)) or C) and ((D -> (E or D)) or F)), M:tm-409, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-25688
in-theory        25688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-409 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25688.        (((A -> (A or B)) or C) and (D -> ((E -> (F or E)) and D))), M:tm-409, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-25689
in-theory        25689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-409 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25689.        (((A -> (A or B)) or C) and (D -> (E -> (F or E)))), M:tm-409, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-25690
in-theory        25690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-409 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25690.        (((A -> (A or B)) or C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-409, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-25691
in-theory        25691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-409 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25691.        (((A -> (A or B)) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-409, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-25692
in-theory        25692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-409 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25692.        (((A -> (A or B)) or C) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-409, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-25693
in-theory        25693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-409 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-25693.        (((A -> (A or B)) or C) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-409, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-25694
in-theory        25694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-409 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-25694.        (((A -> (A or B)) or C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-409, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-25695
in-theory        25695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-409 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-25695.        (((A -> (A or B)) or C) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-409, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-25696
in-theory        25696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-409 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-25696.        (((A -> (A or B)) or C) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-409, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-25697
in-theory        25697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-409 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-25697.        (((A -> (A or B)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-409, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-25698
in-theory        25698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-25698.        (((A -> (A or B)) or C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-409, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-25699
in-theory        25699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-409 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-25699.        (((A -> (A or B)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-409, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-25700
in-theory        25700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-409 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-25700.        (((A -> (A or B)) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-409, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-25701
in-theory        25701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-409 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-25701.        (((A -> (A or B)) or C) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-409, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-25702
in-theory        25702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-25702.        (((A -> (A or B)) or C) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-409, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-25703
in-theory        25703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-409 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25703.        (((A -> (A or B)) or C) and ((D -> (not (E -> D))) -> (not D))), M:tm-409, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-25704
in-theory        25704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25704.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-409, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-25705
in-theory        25705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-409 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25705.        (((A -> (A or B)) or C) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-409, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-25706
in-theory        25706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-409 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-25706.        (((A -> (A or B)) or C) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-409, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-25707
in-theory        25707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-25707.        (((A -> (A or B)) or C) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-409, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-25708
in-theory        25708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-409 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-25708.        (((A -> (A or B)) or C) and ((D -> (not (D or E))) -> (not D))), M:tm-409, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-25709
in-theory        25709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-409 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-25709.        (((A -> (A or B)) or C) and ((D -> (not (E or D))) -> (not D))), M:tm-409, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-25710
in-theory        25710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-409 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-25710.        (((A -> (A or B)) or C) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-409, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-25711
in-theory        25711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-409 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-25711.        (((A -> (A or B)) or C) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-409, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-25712
in-theory        25712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-409 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-25712.        (((A -> (A or B)) or C) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-409, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-25713
in-theory        25713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-25713.        (((A -> (A or B)) or C) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-409, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-25714
in-theory        25714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-409 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-25714.        (((A -> (A or B)) or C) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-409, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-25715
in-theory        25715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-409 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-25715.        (((A -> (A or B)) or C) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-409, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-25716
in-theory        25716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-409 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-25716.        (((A -> (A or B)) or C) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-409, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-25717
in-theory        25717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-25717.        (((A -> (A or B)) or C) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-409, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-25718
in-theory        25718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-409 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-6 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-25718.        (((A -> (A or B)) or C) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-409, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-25719
in-theory        25719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-409 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-25719.        (((A -> (A or B)) or C) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-409, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-25720
in-theory        25720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-409 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-25720.        (((A -> (A or B)) or C) and (D or ((not (not E)) -> E))), M:tm-409, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-25721
in-theory        25721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-409 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-25721.        (((A -> (A or B)) or C) and (((not (not D)) -> D) or E)), M:tm-409, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-25722
in-theory        25722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-409 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-25722.        (((A -> (A or B)) or C) and (D -> (((not (not E)) -> E) and D))), M:tm-409, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-25723
in-theory        25723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-409 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-25723.        (((A -> (A or B)) or C) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-409, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-25724
in-theory        25724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-409 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-25724.        (((A -> (A or B)) or C) and (D -> ((not (not E)) -> E))), M:tm-409, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-25725
in-theory        25725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-25725.        (((A -> (A or B)) or C) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-409, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-25726
in-theory        25726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-409 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-25726.        (((A -> (A or B)) or C) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-409, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-25727
in-theory        25727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-25727.        (((A -> (A or B)) or C) and (D or (E -> (F -> (G -> F))))), M:tm-409, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-25728
in-theory        25728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-25728.        (((A -> (A or B)) or C) and ((D -> (E -> (F -> E))) or G)), M:tm-409, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-25729
in-theory        25729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-25729.        (((A -> (A or B)) or C) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-409, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-25730
in-theory        25730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-409 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-25730.        (((A -> (A or B)) or C) and ((D -> E) -> (D -> (F -> E)))), M:tm-409, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-25731
in-theory        25731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-25731.        (((A -> (A or B)) or C) and (D -> (E -> (F -> (G -> F))))), M:tm-409, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-25732
in-theory        25732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-409 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25732.        (((A -> (A or B)) or C) and (D -> D)), M:tm-409, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-25733
in-theory        25733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25733.        (((A -> (A or B)) or C) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-409, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-25734
in-theory        25734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-409 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25734.        (((A -> (A or B)) or C) and ((D and E) -> (D and E))), M:tm-409, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-25735
in-theory        25735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-409 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-25735.        (((A -> (A or B)) or C) and ((D -> E) -> (D -> E))), M:tm-409, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-25736
in-theory        25736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-409 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-25736.        (((A -> (A or B)) or C) and ((not (not D)) -> (not (not D)))), M:tm-409, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-25737
in-theory        25737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-409 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-25737.        (((A -> (A or B)) or C) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-409, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-25738
in-theory        25738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-409 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-25738.        (((A -> (A or B)) or C) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-409, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-25739
in-theory        25739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-409 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-25739.        (((A -> (A or B)) or C) and (D or ((E -> F) -> (E -> E)))), M:tm-409, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-25740
in-theory        25740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-409 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-25740.        (((A -> (A or B)) or C) and (((D -> E) -> (D -> D)) or F)), M:tm-409, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-25741
in-theory        25741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-25741.        (((A -> (A or B)) or C) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-409, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-25742
in-theory        25742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-25742.        (((A -> (A or B)) or C) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-409, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-25743
in-theory        25743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-409 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-25743.        (((A -> (A or B)) or C) and (D -> ((E -> F) -> (E -> E)))), M:tm-409, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-25744
in-theory        25744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-25744.        (((A -> (A or B)) or C) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-409, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-25745
in-theory        25745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-409 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-25745.        (((A -> (A or B)) or C) and ((D -> (D -> E)) -> (D -> E))), M:tm-409, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-25746
in-theory        25746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-409 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-25746.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-409, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-25747
in-theory        25747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-409 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-25747.        (((A -> (A or B)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-409, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-25748
in-theory        25748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-409 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-25748.        (((A -> (A or B)) or C) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-409, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-25749
in-theory        25749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-25749.        (((A -> (A or B)) or C) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-409, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-25750
in-theory        25750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-409 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-25750.        (((A -> (A or B)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-409, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-25751
in-theory        25751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-409 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-25751.        (((A -> (A or B)) or C) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-409, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-25752
in-theory        25752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-409 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-25752.        (((A -> (A or B)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-409, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-25753
in-theory        25753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-25753.        (((A -> (A or B)) or C) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-409, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-25754
in-theory        25754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-409 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-25754.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-409, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-25755
in-theory        25755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-409 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-25755.        (((A -> (A or B)) or C) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-409, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-25756
in-theory        25756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-409 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-25756.        (((A -> (A or B)) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-409, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-25757
in-theory        25757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-409 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-25757.        (((A -> (A or B)) or C) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-409, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-25758
in-theory        25758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-409 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-25758.        (((A -> (A or B)) or C) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-409, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-25759
in-theory        25759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-409 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-25759.        (((A -> (A or B)) or C) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-409, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-25760
in-theory        25760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-409 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-25760.        (((A -> (A or B)) or C) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-409, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-25761
in-theory        25761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-409 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-25761.        (((A -> (A or B)) or C) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-409, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-25762
in-theory        25762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-409 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-25762.        (((A -> (A or B)) or C) and (((D -> E) and D) -> E)), M:tm-409, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-25763
in-theory        25763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-409 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-25763.        (((A -> (A or B)) or C) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-409, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-25764
in-theory        25764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-409 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-25764.        (((A -> (A or B)) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-409, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-25765
in-theory        25765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-409 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-25765.        (((A -> (A or B)) or C) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-409, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-25766
in-theory        25766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-409 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-25766.        (((A -> (A or B)) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-409, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-25767
in-theory        25767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-409 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-25767.        (((A -> (A or B)) or C) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-409, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-25768
in-theory        25768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-409 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-25768.        (((A -> (A or B)) or C) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-409, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-25769
in-theory        25769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-409 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-25769.        (((A -> (A or B)) or C) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-409, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-25770
in-theory        25770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-409 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-25770.        (((A -> (A or B)) or C) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-409, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-25771
in-theory        25771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-409 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-25771.        (((A -> (A or B)) or C) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-409, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-25772
in-theory        25772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-409 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-25772.        (((A -> (A or B)) or C) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-409, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-25773
in-theory        25773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-409 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-25773.        (((A -> (A or B)) or C) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-409, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-25774
in-theory        25774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-409 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-25774.        (((A -> (A or B)) or C) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-409, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-25775
in-theory        25775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-409 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-25775.        (((A -> (A or B)) or C) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-409, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-25776
in-theory        25776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-25776.        (((A -> (A or B)) or C) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-409, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-25777
in-theory        25777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-409 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-25777.        (((A -> (A or B)) or C) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-409, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-25778
in-theory        25778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-409 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-25778.        (((A -> (A or B)) or C) and (D or (E -> ((F and G) -> F)))), M:tm-409, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-25779
in-theory        25779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-25779.        (((A -> (A or B)) or C) and ((D -> ((E and F) -> E)) or G)), M:tm-409, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-25780
in-theory        25780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-25780.        (((A -> (A or B)) or C) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-409, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-25781
in-theory        25781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-409 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-25781.        (((A -> (A or B)) or C) and ((D -> (E and F)) -> (D -> E))), M:tm-409, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-25782
in-theory        25782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-409 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-25782.        (((A -> (A or B)) or C) and (D -> (E -> ((F and G) -> F)))), M:tm-409, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-25783
in-theory        25783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-409 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-25783.        (((A -> (A or B)) or C) and ((D and (D -> E)) -> E)), M:tm-409, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-25784
in-theory        25784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-409 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-25784.        (((A -> (A or B)) or C) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-409, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-25785
in-theory        25785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-409 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-25785.        (((A -> (A or B)) or C) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-409, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-25786
in-theory        25786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-409 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-25786.        (((A -> (A or B)) or C) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-409, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-25787
in-theory        25787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-409 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-25787.        (((A -> (A or B)) or C) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-409, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-25788
in-theory        25788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-409 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-25788.        (((A -> (A or B)) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-409, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-25789
in-theory        25789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-409 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-25789.        (((A -> (A or B)) or C) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-409, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-25790
in-theory        25790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-409 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-25790.        (((A -> (A or B)) or C) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-409, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-25791
in-theory        25791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-409 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-25791.        (((A -> (A or B)) or C) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-409, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-25792
in-theory        25792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-409 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-25792.        (((A -> (A or B)) or C) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-409, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-25793
in-theory        25793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-409 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-25793.        (((A -> (A or B)) or C) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-409, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-25794
in-theory        25794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-409 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-25794.        (((A -> (A or B)) or C) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-409, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-25795
in-theory        25795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-409 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-25795.        (((A -> (A or B)) or C) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-409, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-25796
in-theory        25796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-409 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-25796.        (((A -> (A or B)) or C) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-409, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-25797
in-theory        25797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-409 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-25797.        (((A -> (A or B)) or C) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-409, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-25798
in-theory        25798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-409 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-25798.        (((A -> (A or B)) or C) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-409, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-25799
in-theory        25799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-25799.        (((A -> (A or B)) or C) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-409, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-25800
in-theory        25800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-409 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-25800.        (((A -> (A or B)) or C) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-409, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-25801
in-theory        25801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-409 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-25801.        (((A -> (A or B)) or C) and (D or (E -> ((F and G) -> G)))), M:tm-409, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-25802
in-theory        25802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-25802.        (((A -> (A or B)) or C) and ((D -> ((E and F) -> F)) or G)), M:tm-409, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-25803
in-theory        25803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-25803.        (((A -> (A or B)) or C) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-409, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-25804
in-theory        25804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-409 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-25804.        (((A -> (A or B)) or C) and ((D -> (E and F)) -> (D -> F))), M:tm-409, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-25805
in-theory        25805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-409 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-25805.        (((A -> (A or B)) or C) and (D -> (E -> ((F and G) -> G)))), M:tm-409, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-25806
in-theory        25806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25806.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-409, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-25807
in-theory        25807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25807.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-409, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-25808
in-theory        25808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25808.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-409, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-25809
in-theory        25809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-409 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25809.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-409, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-25810
in-theory        25810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25810.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-409, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-25811
in-theory        25811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-409 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25811.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-409, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-25812
in-theory        25812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25812.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-409, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-25813
in-theory        25813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-25813.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-409, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-25814
in-theory        25814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-409 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-25814.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-409, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-25815
in-theory        25815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-25815.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-409, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-25816
in-theory        25816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-25816.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-409, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-25817
in-theory        25817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-25817.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-409, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-25818
in-theory        25818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-409 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-25818.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-409, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-25819
in-theory        25819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-25819.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-409, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-25820
in-theory        25820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-409 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-25820.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-409, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-25821
in-theory        25821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-409 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-25821.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-409, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-25822
in-theory        25822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-409 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-25822.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-409, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-25823
in-theory        25823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-409 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-25823.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-409, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-25824
in-theory        25824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-25824.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-409, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-25825
in-theory        25825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-25825.        (((A -> (A or B)) or C) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-409, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-25826
in-theory        25826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-409 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-25826.        (((A -> (A or B)) or C) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-409, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-25827
in-theory        25827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-409 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-25827.        (((A -> (A or B)) or C) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-409, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-25828
in-theory        25828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-409 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-25828.        (((A -> (A or B)) or C) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-409, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-25829
in-theory        25829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-25829.        (((A -> (A or B)) or C) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-409, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-25830
in-theory        25830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-409 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-25830.        (((A -> (A or B)) or C) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-409, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-25831
in-theory        25831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-409 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25831.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-409, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-25832
in-theory        25832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25832.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-409, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-25833
in-theory        25833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-409 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25833.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-409, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-25834
in-theory        25834
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-409 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25834.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-409, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-25835
in-theory        25835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25835.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-409, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-25836
in-theory        25836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25836.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-409, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-25837
in-theory        25837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-409 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25837.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-409, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-25838
in-theory        25838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-25838.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-409, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-25839
in-theory        25839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-409 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-25839.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-409, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-25840
in-theory        25840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-409 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-25840.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-409, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-25841
in-theory        25841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-25841.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-409, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-25842
in-theory        25842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-409 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-25842.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-409, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-25843
in-theory        25843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-409 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-25843.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-409, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-25844
in-theory        25844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-409 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-25844.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-409, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-25845
in-theory        25845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-409 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-25845.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-409, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-25846
in-theory        25846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-409 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-25846.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-409, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-25847
in-theory        25847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-409 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-25847.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-409, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-25848
in-theory        25848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-409 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-25848.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-409, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-25849
in-theory        25849
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-409 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-25849.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-409, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-25850
in-theory        25850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-409 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-25850.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-409, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-25851
in-theory        25851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-409 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-25851.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-409, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-25852
in-theory        25852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-409 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-25852.        (((A -> (A or B)) or C) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-409, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-25853
in-theory        25853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-409 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-25853.        (((A -> (A or B)) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-409, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-25854
in-theory        25854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-409 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-25854.        (((A -> (A or B)) or C) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-409, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-25855
in-theory        25855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-409 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-25855.        (((A -> (A or B)) or C) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-409, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-25856
in-theory        25856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-409 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-25856.        (((A -> (A or B)) or C) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-409, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-25857
in-theory        25857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-409 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-25857.        (((A -> (A or B)) or C) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-409, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-25858
in-theory        25858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25858.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-409, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-25859
in-theory        25859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25859.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-409, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-25860
in-theory        25860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25860.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((F and G) -> F))), M:tm-409, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-25861
in-theory        25861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-409 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25861.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((F and G) -> G))), M:tm-409, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-25862
in-theory        25862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25862.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-409, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-25863
in-theory        25863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-409 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25863.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (F or G)))), M:tm-409, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-25864
in-theory        25864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25864.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (G or F)))), M:tm-409, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-25865
in-theory        25865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-25865.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-409, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-25866
in-theory        25866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-409 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-25866.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-409, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-25867
in-theory        25867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-25867.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-409, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-25868
in-theory        25868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-25868.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-409, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-25869
in-theory        25869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-25869.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-409, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-25870
in-theory        25870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-409 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-25870.        (((A -> (A or B)) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-409, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-25871
in-theory        25871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-25871.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-409, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-25872
in-theory        25872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-409 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-25872.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-409, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-25873
in-theory        25873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-409 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-25873.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-409, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-25874
in-theory        25874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-409 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-25874.        (((A -> (A or B)) or C) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-409, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-25875
in-theory        25875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-409 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-25875.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-409, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-25876
in-theory        25876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-25876.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-409, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-25877
in-theory        25877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-409 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-25877.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-409, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-25878
in-theory        25878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-25878.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-409, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-25879
in-theory        25879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-409 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-25879.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-409, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-25880
in-theory        25880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-25880.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-409, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-25881
in-theory        25881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-25881.        (((A -> (A or B)) or C) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-409, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-25882
in-theory        25882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-409 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-25882.        (((A -> (A or B)) or C) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-409, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-25883
in-theory        25883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-409 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-25883.        (((A -> (A or B)) or C) and (D or (E -> (((F and G) -> F) and E)))), M:tm-409, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-25884
in-theory        25884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-409 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-25884.        (((A -> (A or B)) or C) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-409, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-25885
in-theory        25885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-25885.        (((A -> (A or B)) or C) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-409, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-25886
in-theory        25886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-409 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-25886.        (((A -> (A or B)) or C) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-409, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-25887
in-theory        25887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25887.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-409, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-25888
in-theory        25888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25888.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-409, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-25889
in-theory        25889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25889.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((F and G) -> F))), M:tm-409, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-25890
in-theory        25890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-409 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25890.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((F and G) -> G))), M:tm-409, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-25891
in-theory        25891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25891.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-409, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-25892
in-theory        25892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-409 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25892.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (F or G)))), M:tm-409, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-25893
in-theory        25893
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25893.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (G or F)))), M:tm-409, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-25894
in-theory        25894
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-25894.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-409, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-25895
in-theory        25895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-409 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-25895.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-409, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-25896
in-theory        25896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-25896.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-409, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-25897
in-theory        25897
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-25897.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-409, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-25898
in-theory        25898
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-25898.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-409, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-25899
in-theory        25899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-409 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-25899.        (((A -> (A or B)) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-409, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-25900
in-theory        25900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-25900.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-409, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-25901
in-theory        25901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-409 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-25901.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-409, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-25902
in-theory        25902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-409 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-25902.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-409, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-25903
in-theory        25903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-409 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-25903.        (((A -> (A or B)) or C) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-409, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-25904
in-theory        25904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-409 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-25904.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-409, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-25905
in-theory        25905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-25905.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-409, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-25906
in-theory        25906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-409 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-25906.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-409, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-25907
in-theory        25907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-25907.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-409, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-25908
in-theory        25908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25908.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-409, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-25909
in-theory        25909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25909.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-409, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-25910
in-theory        25910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-409 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25910.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-409, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-25911
in-theory        25911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25911.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-409, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-25912
in-theory        25912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-25912.        (((A -> (A or B)) or C) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-409, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-25913
in-theory        25913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-409 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-25913.        (((A -> (A or B)) or C) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-409, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-25914
in-theory        25914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-409 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25914.        (((A -> (A or B)) or C) and (D or (E -> (((F and G) -> G) and E)))), M:tm-409, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-25915
in-theory        25915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-409 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25915.        (((A -> (A or B)) or C) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-409, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-25916
in-theory        25916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25916.        (((A -> (A or B)) or C) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-409, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-25917
in-theory        25917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-409 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25917.        (((A -> (A or B)) or C) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-409, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-25918
in-theory        25918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25918.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-409, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-25919
in-theory        25919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25919.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-409, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-25920
in-theory        25920
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-409 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25920.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-409, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-25921
in-theory        25921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-409 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25921.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-409, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-25922
in-theory        25922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25922.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-409, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-25923
in-theory        25923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-409 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25923.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-409, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-25924
in-theory        25924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25924.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-409, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-25925
in-theory        25925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-25925.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-409, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-25926
in-theory        25926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-25926.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-409, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-25927
in-theory        25927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-409 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-25927.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-409, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-25928
in-theory        25928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-25928.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-409, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-25929
in-theory        25929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-25929.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-409, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-25930
in-theory        25930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-25930.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-409, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-25931
in-theory        25931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-409 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-25931.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-409, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-25932
in-theory        25932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-409 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-25932.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-409, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-25933
in-theory        25933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-409 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-25933.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-409, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-25934
in-theory        25934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-409 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-25934.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-409, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-25935
in-theory        25935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-409 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-25935.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-409, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-25936
in-theory        25936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-409 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-25936.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-409, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-25937
in-theory        25937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-409 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-25937.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-409, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-25938
in-theory        25938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-409 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-25938.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-409, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-25939
in-theory        25939
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-409 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-25939.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-409, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-25940
in-theory        25940
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-409 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25940.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-409, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-25941
in-theory        25941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-409 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25941.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-409, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-25942
in-theory        25942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-409 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25942.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-409, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-25943
in-theory        25943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-409 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25943.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-409, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-25944
in-theory        25944
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-409 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25944.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-409, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-25945
in-theory        25945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-409 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-25945.        (((A -> (A or B)) or C) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-409, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-25946
in-theory        25946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-409 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-25946.        (((A -> (A or B)) or C) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-409, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-25947
in-theory        25947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-409 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25947.        (((A -> (A or B)) or C) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-409, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-25948
in-theory        25948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-409 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25948.        (((A -> (A or B)) or C) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-409, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-25949
in-theory        25949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-409 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25949.        (((A -> (A or B)) or C) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-409, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-25950
in-theory        25950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-409 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-25950.        (((A -> (A or B)) or C) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-409, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-25951
in-theory        25951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-409 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25951.        (((A -> (A or B)) or C) and (D -> (D and (E -> D)))), M:tm-409, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-25952
in-theory        25952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25952.        (((A -> (A or B)) or C) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-409, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-25953
in-theory        25953
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-409 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25953.        (((A -> (A or B)) or C) and ((D and E) -> ((D and E) and D))), M:tm-409, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-25954
in-theory        25954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-409 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-25954.        (((A -> (A or B)) or C) and ((D and E) -> ((D and E) and E))), M:tm-409, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-25955
in-theory        25955
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-25955.        (((A -> (A or B)) or C) and (D -> (D and (E -> (D and E))))), M:tm-409, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-25956
in-theory        25956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-409 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-25956.        (((A -> (A or B)) or C) and (D -> (D and (D or E)))), M:tm-409, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-25957
in-theory        25957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-409 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-25957.        (((A -> (A or B)) or C) and (D -> (D and (E or D)))), M:tm-409, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-25958
in-theory        25958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-409 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-25958.        (((A -> (A or B)) or C) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-409, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-25959
in-theory        25959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-25959.        (((A -> (A or B)) or C) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-409, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-25960
in-theory        25960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-409 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-25960.        (((A -> (A or B)) or C) and ((not (not D)) -> ((not (not D)) and D))), M:tm-409, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-25961
in-theory        25961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-25961.        (((A -> (A or B)) or C) and (D -> (D and (E -> (F -> E))))), M:tm-409, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-25962
in-theory        25962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-409 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-25962.        (((A -> (A or B)) or C) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-409, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-25963
in-theory        25963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-409 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-25963.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-409, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-25964
in-theory        25964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-409 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-25964.        (((A -> (A or B)) or C) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-409, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-25965
in-theory        25965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-409 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-25965.        (((A -> (A or B)) or C) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-409, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-25966
in-theory        25966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-409 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-25966.        (((A -> (A or B)) or C) and (D -> (D and ((E and F) -> E)))), M:tm-409, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-25967
in-theory        25967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-409 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-25967.        (((A -> (A or B)) or C) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-409, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-25968
in-theory        25968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-409 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-25968.        (((A -> (A or B)) or C) and (D -> (D and ((E and F) -> F)))), M:tm-409, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-25969
in-theory        25969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-409 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-25969.        (((A -> (A or B)) or C) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-409, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-25970
in-theory        25970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-409 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-25970.        (((A -> (A or B)) or C) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-409, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-25971
in-theory        25971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-409 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-25971.        (((A -> (A or B)) or C) and (D -> (D and (((E and F) -> E) and D)))), M:tm-409, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-25972
in-theory        25972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-409 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-25972.        (((A -> (A or B)) or C) and (D -> (D and (((E and F) -> F) and D)))), M:tm-409, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-25973
in-theory        25973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-409 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-25973.        (((A -> (A or B)) or C) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-409, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-25974
in-theory        25974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-25974.        (((A -> (A or B)) or C) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-409, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-25975
in-theory        25975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-409 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25975.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-409, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-25976
in-theory        25976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25976.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-409, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-25977
in-theory        25977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25977.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-409, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-25978
in-theory        25978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-409 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25978.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-409, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-25979
in-theory        25979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25979.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-409, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-25980
in-theory        25980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-409 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-25980.        (((A -> (A or B)) or C) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-409, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-25981
in-theory        25981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-409 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-25981.        (((A -> (A or B)) or C) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-409, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-25982
in-theory        25982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-409 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25982.        (((A -> (A or B)) or C) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-409, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-25983
in-theory        25983
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-409 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25983.        (((A -> (A or B)) or C) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-409, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-25984
in-theory        25984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25984.        (((A -> (A or B)) or C) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-409, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-25985
in-theory        25985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-409 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-25985.        (((A -> (A or B)) or C) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-409, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-25986
in-theory        25986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-409 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-25986.        (((A -> (A or B)) or C) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-409, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-25987
in-theory        25987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-409 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-25987.        (((A -> (A or B)) or C) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-409, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-25988
in-theory        25988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-409 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25988.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-409, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-25989
in-theory        25989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-409 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25989.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-409, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-25990
in-theory        25990
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-409 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25990.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-409, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-25991
in-theory        25991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-409 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25991.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-409, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-25992
in-theory        25992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-409 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25992.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-409, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-25993
in-theory        25993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-409 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-25993.        (((A -> (A or B)) or C) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-409, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-25994
in-theory        25994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-409 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-25994.        (((A -> (A or B)) or C) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-409, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-25995
in-theory        25995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-409 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-25995.        (((A -> (A or B)) or C) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-409, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-25996
in-theory        25996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-25996.        (((A -> (A or B)) or C) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-409, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-25997
in-theory        25997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-409 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-25997.        (((A -> (A or B)) or C) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-409, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-25998
in-theory        25998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-409 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25998.        (((A -> (A or B)) or C) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-409, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-25999
in-theory        25999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-409 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-25999.        (((A -> (A or B)) or C) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-409, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-26000
in-theory        26000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-26000.        (((A -> (A or B)) or C) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-409, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-26001
in-theory        26001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-409 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-26001.        (((A -> (A or B)) or C) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-409, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-26002
in-theory        26002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-409 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-26002.        (((A -> (A or B)) or C) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-409, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-26003
in-theory        26003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-409 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-26003.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-409, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-26004
in-theory        26004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-26004.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-409, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-26005
in-theory        26005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-26005.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-409, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-26006
in-theory        26006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-26006.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-409, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-26007
in-theory        26007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-26007.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-409, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-26008
in-theory        26008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-409 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-26008.        (((A -> (A or B)) or C) and (D or ((E -> (F -> E)) or G))), M:tm-409, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-26009
in-theory        26009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-26009.        (((A -> (A or B)) or C) and (((D -> (E -> D)) or F) or G)), M:tm-409, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-26010
in-theory        26010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-26010.        (((A -> (A or B)) or C) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-409, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-26011
in-theory        26011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-409 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-26011.        (((A -> (A or B)) or C) and (D -> ((E -> (F -> E)) or G))), M:tm-409, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-26012
in-theory        26012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-409 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-26012.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-409, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-26013
in-theory        26013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-26013.        (((A -> (A or B)) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-409, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-26014
in-theory        26014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-26014.        (((A -> (A or B)) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-409, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-26015
in-theory        26015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-409 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-26015.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-409, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-26016
in-theory        26016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-26016.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-409, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-26017
in-theory        26017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-409 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-26017.        (((A -> (A or B)) or C) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-409, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-26018
in-theory        26018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-409 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-26018.        (((A -> (A or B)) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-409, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-26019
in-theory        26019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-409 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-26019.        (((A -> (A or B)) or C) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-409, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-26020
in-theory        26020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-409 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-26020.        (((A -> (A or B)) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-409, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-26021
in-theory        26021
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-409 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-26021.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-409, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-26022
in-theory        26022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-26022.        (((A -> (A or B)) or C) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-409, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-26023
in-theory        26023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-26023.        (((A -> (A or B)) or C) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-409, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-26024
in-theory        26024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-26024.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-409, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-26025
in-theory        26025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-26025.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-409, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-26026
in-theory        26026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-409 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-26026.        (((A -> (A or B)) or C) and (D or (((E and F) -> E) or G))), M:tm-409, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-26027
in-theory        26027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-26027.        (((A -> (A or B)) or C) and ((((D and E) -> D) or F) or G)), M:tm-409, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-26028
in-theory        26028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-26028.        (((A -> (A or B)) or C) and (D -> ((((E and F) -> E) or G) and D))), M:tm-409, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-26029
in-theory        26029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-409 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-26029.        (((A -> (A or B)) or C) and (D -> (((E and F) -> E) or G))), M:tm-409, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-26030
in-theory        26030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-409 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-26030.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-409, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-26031
in-theory        26031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-26031.        (((A -> (A or B)) or C) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-409, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-26032
in-theory        26032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-26032.        (((A -> (A or B)) or C) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-409, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-26033
in-theory        26033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-26033.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-409, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-26034
in-theory        26034
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-26034.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-409, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-26035
in-theory        26035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-409 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-26035.        (((A -> (A or B)) or C) and (D or (((E and F) -> F) or G))), M:tm-409, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-26036
in-theory        26036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-26036.        (((A -> (A or B)) or C) and ((((D and E) -> E) or F) or G)), M:tm-409, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-26037
in-theory        26037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-26037.        (((A -> (A or B)) or C) and (D -> ((((E and F) -> F) or G) and D))), M:tm-409, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-26038
in-theory        26038
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-409 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-26038.        (((A -> (A or B)) or C) and (D -> (((E and F) -> F) or G))), M:tm-409, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-26039
in-theory        26039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-409 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-26039.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-409, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-26040
in-theory        26040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-409 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-26040.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-409, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-26041
in-theory        26041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-409 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-26041.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-409, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-26042
in-theory        26042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-409 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-26042.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-409, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-26043
in-theory        26043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-409 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-26043.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-409, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-26044
in-theory        26044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-409 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-26044.        (((A -> (A or B)) or C) and (D or ((E -> (F -> (E and F))) or G))), M:tm-409, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-26045
in-theory        26045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-409 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-26045.        (((A -> (A or B)) or C) and (((D -> (E -> (D and E))) or F) or G)), M:tm-409, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-26046
in-theory        26046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-26046.        (((A -> (A or B)) or C) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-409, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-26047
in-theory        26047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-409 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-26047.        (((A -> (A or B)) or C) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-409, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-26048
in-theory        26048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-409 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26048.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-409, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-26049
in-theory        26049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26049.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-409, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-26050
in-theory        26050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26050.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-409, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-26051
in-theory        26051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26051.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-409, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-26052
in-theory        26052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26052.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-409, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-26053
in-theory        26053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-409 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26053.        (((A -> (A or B)) or C) and (D or ((E -> (E or F)) or G))), M:tm-409, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26054
in-theory        26054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26054.        (((A -> (A or B)) or C) and (((D -> (D or E)) or F) or G)), M:tm-409, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-26055
in-theory        26055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26055.        (((A -> (A or B)) or C) and (D -> (((E -> (E or F)) or G) and D))), M:tm-409, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26056
in-theory        26056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26056.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> (E or F)) or G) and D))), M:tm-400, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26057
in-theory        26057
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26057.        ((((A and B) -> B) or C) and (D -> (((E -> (E or F)) or G) and D))), M:tm-391, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26058
in-theory        26058
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26058.        ((((A and B) -> A) or C) and (D -> (((E -> (E or F)) or G) and D))), M:tm-382, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26059
in-theory        26059
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (F or G)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26059.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (F or G)) or H) and E))), M:tm-373, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26060
in-theory        26060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26060.        (((A -> (B -> A)) or C) and (D -> (((E -> (E or F)) or G) and D))), M:tm-364, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26061
in-theory        26061
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> (C or D)) or E) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26061.        (A -> (B -> ((((C -> (C or D)) or E) and A) and B))), M:tm-355, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-26062
in-theory        26062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26062.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (E or F)) or G) and D))), M:tm-354, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26063
in-theory        26063
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> (D or E)) or F) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-409 ((Am (-> A (-> B (and A B)))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26063.        ((A or (B -> (C -> (B and C)))) -> (((D -> (D or E)) or F) and (B -> (C -> (B and C))))), M:tm-351, m:tm-409, u:((Am (-> A (-> B (and A B)))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-26064
in-theory        26064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26064.        ((A -> (((B -> (B or C)) or D) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26065
in-theory        26065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (D or E)) or F) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26065.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (D or E)) or F) and C))), M:tm-338, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26066
in-theory        26066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> (C or D)) or E) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-409 ((Am (-> A (and A B))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26066.        (((A -> B) or (A -> (A and B))) -> (((C -> (C or D)) or E) and (A -> (A and B)))), M:tm-335, m:tm-409, u:((Am (-> A (and A B))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (and A B)))))
================================================================
tm-name          tm-26067
in-theory        26067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (A -> (A and (((B -> (B or C)) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26067.        ((A -> (((B -> (B or C)) or D) and A)) and (A -> (A and (((B -> (B or C)) or D) and A)))), M:tm-328, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-26068
in-theory        26068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> (B or C)) or D) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26068.        ((A -> (((B -> (B or C)) or D) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> (B or C)) or D) and A)))), M:tm-327, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26069
in-theory        26069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (((E and F) -> F) and (A -> (((B -> (B or C)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26069.        ((A -> (((B -> (B or C)) or D) and A)) and (((E and F) -> F) and (A -> (((B -> (B or C)) or D) and A)))), M:tm-326, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26070
in-theory        26070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (((E and F) -> E) and (A -> (((B -> (B or C)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26070.        ((A -> (((B -> (B or C)) or D) and A)) and (((E and F) -> E) and (A -> (((B -> (B or C)) or D) and A)))), M:tm-325, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26071
in-theory        26071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> (B or C)) or D) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26071.        ((A -> (((B -> (B or C)) or D) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> (B or C)) or D) and A)))), M:tm-324, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26072
in-theory        26072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and ((E -> (F -> E)) and (A -> (((B -> (B or C)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26072.        ((A -> (((B -> (B or C)) or D) and A)) and ((E -> (F -> E)) and (A -> (((B -> (B or C)) or D) and A)))), M:tm-323, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26073
in-theory        26073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26073.        ((A -> (((B -> (B or C)) or D) and A)) and ((E and F) -> F)), M:tm-322, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26074
in-theory        26074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26074.        ((A -> (((B -> (B or C)) or D) and A)) and ((E and F) -> E)), M:tm-320, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26075
in-theory        26075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26075.        ((A -> (((B -> (B or C)) or D) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26076
in-theory        26076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26076.        ((A -> (((B -> (B or C)) or D) and A)) and (A -> A)), M:tm-316, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-26077
in-theory        26077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26077.        ((A -> (((B -> (B or C)) or D) and A)) and (E -> (F -> E))), M:tm-315, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26078
in-theory        26078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and ((A -> (not (((B -> (B or C)) or D) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26078.        ((A -> (((B -> (B or C)) or D) and A)) and ((A -> (not (((B -> (B or C)) or D) and A))) -> (not A))), M:tm-313, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-26079
in-theory        26079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (((((B -> (B or C)) or D) and A) -> E) -> ((A or (((B -> (B or C)) or D) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26079.        ((A -> (((B -> (B or C)) or D) and A)) and (((((B -> (B or C)) or D) and A) -> E) -> ((A or (((B -> (B or C)) or D) and A)) -> E))), M:tm-312, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-26080
in-theory        26080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (E or (A -> (((B -> (B or C)) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26080.        ((A -> (((B -> (B or C)) or D) and A)) and (E or (A -> (((B -> (B or C)) or D) and A)))), M:tm-311, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26081
in-theory        26081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and ((A -> (((B -> (B or C)) or D) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26081.        ((A -> (((B -> (B or C)) or D) and A)) and ((A -> (((B -> (B or C)) or D) and A)) or E)), M:tm-310, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26082
in-theory        26082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (E -> ((A -> (((B -> (B or C)) or D) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26082.        ((A -> (((B -> (B or C)) or D) and A)) and (E -> ((A -> (((B -> (B or C)) or D) and A)) and E))), M:tm-309, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26083
in-theory        26083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (E -> (A -> (((B -> (B or C)) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26083.        ((A -> (((B -> (B or C)) or D) and A)) and (E -> (A -> (((B -> (B or C)) or D) and A)))), M:tm-305, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26084
in-theory        26084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26084.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-303, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26085
in-theory        26085
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (D or E)) or F) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-409 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26085.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (D or E)) or F) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-409, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-26086
in-theory        26086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26086.        ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-270, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26087
in-theory        26087
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> (D or E)) or F) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-409 ((Am (and (-> (and A B) B) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26087.        ((A or (((B and C) -> C) and A)) -> (((D -> (D or E)) or F) and (((B and C) -> C) and A))), M:tm-267, m:tm-409, u:((Am (and (-> (and A B) B) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-26088
in-theory        26088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26088.        ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-239, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26089
in-theory        26089
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> (D or E)) or F) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-409 ((Am (and (-> (and A B) A) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26089.        ((A or (((B and C) -> B) and A)) -> (((D -> (D or E)) or F) and (((B and C) -> B) and A))), M:tm-236, m:tm-409, u:((Am (and (-> (and A B) A) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-26090
in-theory        26090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (F or G)) or H) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26090.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (F or G)) or H) and E))), M:tm-210, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26091
in-theory        26091
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (E or F)) or G) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-409 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (or Bm Cm)) Dm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26091.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (E or F)) or G) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-409, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (or Bm Cm)) Dm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-26092
in-theory        26092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26092.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-183, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26093
in-theory        26093
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> (D or E)) or F) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-409 ((Am (and (-> A (-> B A)) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26093.        ((A or ((B -> (C -> B)) and A)) -> (((D -> (D or E)) or F) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-409, u:((Am (and (-> A (-> B A)) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-26094
in-theory        26094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26094.        ((A -> ((B and C) -> C)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-157, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26095
in-theory        26095
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> (D or E)) or F) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-409 ((Am (-> (and A B) B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26095.        ((A or ((B and C) -> C)) -> (((D -> (D or E)) or F) and ((B and C) -> C))), M:tm-154, m:tm-409, u:((Am (-> (and A B) B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> (and A B) B))))
================================================================
tm-name          tm-26096
in-theory        26096
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26096.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-147, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26097
in-theory        26097
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (D or E)) or F) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-409 ((Am (-> (and A (-> B C)) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26097.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (D or E)) or F) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-409, u:((Am (-> (and A (-> B C)) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-26098
in-theory        26098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26098.        ((A -> ((B and C) -> B)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-134, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26099
in-theory        26099
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> (D or E)) or F) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-409 ((Am (-> (and A B) A)) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26099.        ((A or ((B and C) -> B)) -> (((D -> (D or E)) or F) and ((B and C) -> B))), M:tm-131, m:tm-409, u:((Am (-> (and A B) A)) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> (and A B) A))))
================================================================
tm-name          tm-26100
in-theory        26100
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26100.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-125, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26101
in-theory        26101
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (D or E)) or F) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-409 ((Am (-> (and (-> A B) C) B)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26101.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (D or E)) or F) and (((A -> B) and C) -> B))), M:tm-122, m:tm-409, u:((Am (-> (and (-> A B) C) B)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-26102
in-theory        26102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (F or G)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26102.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (F or G)) or H) and E))), M:tm-113, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26103
in-theory        26103
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (E or F)) or G) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-409 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26103.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (E or F)) or G) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-409, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-26104
in-theory        26104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26104.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (E or F)) or G) and D))), M:tm-105, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26105
in-theory        26105
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (D or E)) or F) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-409 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26105.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (D or E)) or F) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-409, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-26106
in-theory        26106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> (D or E)) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26106.        (((A -> B) -> (A -> A)) and (C -> (((D -> (D or E)) or F) and C))), M:tm-95, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26107
in-theory        26107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> (C or D)) or E) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-409 ((Am (-> A A)) (B (and (or (-> Bm (or Bm Cm)) Dm) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26107.        (((A -> B) or (A -> A)) -> (((C -> (C or D)) or E) and (A -> A))), M:tm-92, m:tm-409, u:((Am (-> A A)) (B (and (or (-> Bm (or Bm Cm)) Dm) (-> A A))))
================================================================
tm-name          tm-26108
in-theory        26108
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (C or D)) or E) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26108.        (A -> (B -> (((C -> (C or D)) or E) and A))), M:tm-84, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-26109
in-theory        26109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26109.        ((A -> (B -> (C -> B))) and (D -> (((E -> (E or F)) or G) and D))), M:tm-83, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26110
in-theory        26110
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> (D or E)) or F) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-409 ((Am (-> A (-> B A))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26110.        ((A or (B -> (C -> B))) -> (((D -> (D or E)) or F) and (B -> (C -> B)))), M:tm-80, m:tm-409, u:((Am (-> A (-> B A))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (-> B A)))))
================================================================
tm-name          tm-26111
in-theory        26111
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> (C or D)) or E) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26111.        (((not (not A)) -> A) and (B -> (((C -> (C or D)) or E) and B))), M:tm-76, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26112
in-theory        26112
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> (B or C)) or D) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26112.        (((not (not A)) or A) -> (((B -> (B or C)) or D) and A)), M:tm-73, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-26113
in-theory        26113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (D or E)) or F) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26113.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (D or E)) or F) and C))), M:tm-69, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26114
in-theory        26114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (C or D)) or E) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-409 ((Am (-> (-> A (not B)) (not A))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26114.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (C or D)) or E) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-409, u:((Am (-> (-> A (not B)) (not A))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-26115
in-theory        26115
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26115.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (E or F)) or G) and D))), M:tm-54, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26116
in-theory        26116
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (D or E)) or F) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-409 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26116.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (D or E)) or F) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-409, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-26117
in-theory        26117
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> (C or D)) or E) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-409 ((Am (or A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26117.        ((A or (B or A)) -> (((C -> (C or D)) or E) and (B or A))), M:tm-50, m:tm-409, u:((Am (or A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (or A B))))
================================================================
tm-name          tm-26118
in-theory        26118
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> (C or D)) or E) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-409 ((Am (or A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26118.        ((A or (A or B)) -> (((C -> (C or D)) or E) and (A or B))), M:tm-49, m:tm-409, u:((Am (or A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (or A B))))
================================================================
tm-name          tm-26119
in-theory        26119
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> (C or D)) or E) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-409 ((Am (-> A (and B A))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26119.        ((A or (B -> (A and B))) -> (((C -> (C or D)) or E) and (B -> (A and B)))), M:tm-48, m:tm-409, u:((Am (-> A (and B A))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-26120
in-theory        26120
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> (C or D)) or E) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26120.        (((A and B) or B) -> (((C -> (C or D)) or E) and B)), M:tm-47, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-26121
in-theory        26121
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> (C or D)) or E) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26121.        (((A and B) or A) -> (((C -> (C or D)) or E) and A)), M:tm-46, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-26122
in-theory        26122
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (D or E)) or F) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-409 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26122.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (D or E)) or F) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-409, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-26123
in-theory        26123
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> (C or D)) or E) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-409 ((Am (-> A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26123.        ((A or (B -> A)) -> (((C -> (C or D)) or E) and (B -> A))), M:tm-44, m:tm-409, u:((Am (-> A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A B))))
================================================================
tm-name          tm-26124
in-theory        26124
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> (D or E)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26124.        ((A -> (B or A)) and (C -> (((D -> (D or E)) or F) and C))), M:tm-42, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26125
in-theory        26125
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> (D or E)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26125.        ((A -> (A or B)) and (C -> (((D -> (D or E)) or F) and C))), M:tm-32, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26126
in-theory        26126
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> (B or C)) or D) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26126.        (A -> (A and (((B -> (B or C)) or D) and A))), M:tm-24, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-26127
in-theory        26127
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> (D or E)) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26127.        ((A -> (B -> (A and B))) and (C -> (((D -> (D or E)) or F) and C))), M:tm-23, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26128
in-theory        26128
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> (D or E)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26128.        (((A and B) -> B) and (C -> (((D -> (D or E)) or F) and C))), M:tm-22, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26129
in-theory        26129
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> (D or E)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26129.        (((A and B) -> A) and (C -> (((D -> (D or E)) or F) and C))), M:tm-21, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26130
in-theory        26130
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26130.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (E or F)) or G) and D))), M:tm-20, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26131
in-theory        26131
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> (D or E)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26131.        ((A -> (B -> A)) and (C -> (((D -> (D or E)) or F) and C))), M:tm-19, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26132
in-theory        26132
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> (B or C)) or D) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-9 tm-5 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26132.        ((A -> (not (((B -> (B or C)) or D) and A))) -> (not A)), M:tm-9, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-26133
in-theory        26133
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (A or B)) or C) and D) -> E) -> ((D or (((A -> (A or B)) or C) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26133.        (((((A -> (A or B)) or C) and D) -> E) -> ((D or (((A -> (A or B)) or C) and D)) -> E)), M:tm-8, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-26134
in-theory        26134
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> (C or D)) or E) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26134.        (A or (B -> (((C -> (C or D)) or E) and B))), M:tm-7, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26135
in-theory        26135
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-6 tm-5)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26135.        ((A -> (((B -> (B or C)) or D) and A)) or E), M:tm-6, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26136
in-theory        26136
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> (C or D)) or E) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26136.        (A -> ((B -> (((C -> (C or D)) or E) and B)) and A)), M:tm-5, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26137
in-theory        26137
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (C or D)) or E) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26137.        (A -> (B -> (((C -> (C or D)) or E) and B))), M:tm-1, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-26138
in-theory        26138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-409 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26138.        (((A -> (A or B)) or C) and (D -> ((E -> (E or F)) or G))), M:tm-409, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26139
in-theory        26139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-400 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26139.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (E or F)) or G))), M:tm-400, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26140
in-theory        26140
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-391 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26140.        ((((A and B) -> B) or C) and (D -> ((E -> (E or F)) or G))), M:tm-391, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26141
in-theory        26141
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-382 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26141.        ((((A and B) -> A) or C) and (D -> ((E -> (E or F)) or G))), M:tm-382, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26142
in-theory        26142
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-373 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26142.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (F or G)) or H))), M:tm-373, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26143
in-theory        26143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-364 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26143.        (((A -> (B -> A)) or C) and (D -> ((E -> (E or F)) or G))), M:tm-364, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26144
in-theory        26144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-354 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26144.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (E or F)) or G))), M:tm-354, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26145
in-theory        26145
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-351 tm-410 ((Am (-> A (-> B (and A B)))) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26145.        ((A or (B -> (C -> (B and C)))) -> ((D -> (D or E)) or F)), M:tm-351, m:tm-410, u:((Am (-> A (-> B (and A B)))) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26146
in-theory        26146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26146.        ((A -> ((B -> (B or C)) or D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26147
in-theory        26147
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) -> D) -> (((A -> (A or B)) or C) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-410 ((Am (-> (or (-> Bm (or Bm Cm)) Dm) B)) (A (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26147.        ((((A -> (A or B)) or C) -> D) -> (((A -> (A or B)) or C) and D)), M:tm-339, m:tm-410, u:((Am (-> (or (-> Bm (or Bm Cm)) Dm) B)) (A (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26148
in-theory        26148
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (D or E)) or F)))
theorem-size     19
proof            (modus-ponens tm-338 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26148.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (D or E)) or F))), M:tm-338, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26149
in-theory        26149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (C or D)) or E))
theorem-size     17
proof            (modus-ponens tm-335 tm-410 ((Am (-> A (and A B))) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26149.        (((A -> B) or (A -> (A and B))) -> ((C -> (C or D)) or E)), M:tm-335, m:tm-410, u:((Am (-> A (and A B))) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26150
in-theory        26150
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and (A -> (A and ((B -> (B or C)) or D))))
theorem-size     21
proof            (modus-ponens tm-328 tm-410 ((A Am) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26150.        ((A -> ((B -> (B or C)) or D)) and (A -> (A and ((B -> (B or C)) or D)))), M:tm-328, m:tm-410, u:((A Am) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26151
in-theory        26151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and ((E -> (F -> (E and F))) and (A -> ((B -> (B or C)) or D))))
theorem-size     27
proof            (modus-ponens tm-327 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26151.        ((A -> ((B -> (B or C)) or D)) and ((E -> (F -> (E and F))) and (A -> ((B -> (B or C)) or D)))), M:tm-327, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26152
in-theory        26152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and (((E and F) -> F) and (A -> ((B -> (B or C)) or D))))
theorem-size     25
proof            (modus-ponens tm-326 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26152.        ((A -> ((B -> (B or C)) or D)) and (((E and F) -> F) and (A -> ((B -> (B or C)) or D)))), M:tm-326, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26153
in-theory        26153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and (((E and F) -> E) and (A -> ((B -> (B or C)) or D))))
theorem-size     25
proof            (modus-ponens tm-325 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26153.        ((A -> ((B -> (B or C)) or D)) and (((E and F) -> E) and (A -> ((B -> (B or C)) or D)))), M:tm-325, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26154
in-theory        26154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (B or C)) or D))))
theorem-size     33
proof            (modus-ponens tm-324 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26154.        ((A -> ((B -> (B or C)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (B or C)) or D)))), M:tm-324, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26155
in-theory        26155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and ((E -> (F -> E)) and (A -> ((B -> (B or C)) or D))))
theorem-size     25
proof            (modus-ponens tm-323 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26155.        ((A -> ((B -> (B or C)) or D)) and ((E -> (F -> E)) and (A -> ((B -> (B or C)) or D)))), M:tm-323, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26156
in-theory        26156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26156.        ((A -> ((B -> (B or C)) or D)) and ((E and F) -> F)), M:tm-322, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26157
in-theory        26157
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (B or C)) or D) -> E)) -> ((B -> (B or C)) or D)) and ((A and (((B -> (B or C)) or D) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-410 ((Am (and A (-> (or (-> Bm (or Bm Cm)) Dm) C))) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26157.        (((A and (((B -> (B or C)) or D) -> E)) -> ((B -> (B or C)) or D)) and ((A and (((B -> (B or C)) or D) -> E)) -> E)), M:tm-321, m:tm-410, u:((Am (and A (-> (or (-> Bm (or Bm Cm)) Dm) C))) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26158
in-theory        26158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26158.        ((A -> ((B -> (B or C)) or D)) and ((E and F) -> E)), M:tm-320, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26159
in-theory        26159
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (A or B)) or C) -> D) and E) -> ((A -> (A or B)) or C)) and (((((A -> (A or B)) or C) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-410 ((Am (and (-> (or (-> Bm (or Bm Cm)) Dm) B) C)) (A (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26159.        ((((((A -> (A or B)) or C) -> D) and E) -> ((A -> (A or B)) or C)) and (((((A -> (A or B)) or C) -> D) and E) -> D)), M:tm-319, m:tm-410, u:((Am (and (-> (or (-> Bm (or Bm Cm)) Dm) B) C)) (A (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26160
in-theory        26160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26160.        ((A -> ((B -> (B or C)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26161
in-theory        26161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-410 ((A Am) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26161.        ((A -> ((B -> (B or C)) or D)) and (A -> A)), M:tm-316, m:tm-410, u:((A Am) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26162
in-theory        26162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26162.        ((A -> ((B -> (B or C)) or D)) and (E -> (F -> E))), M:tm-315, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26163
in-theory        26163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and ((A -> (not ((B -> (B or C)) or D))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-410 ((A Am) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26163.        ((A -> ((B -> (B or C)) or D)) and ((A -> (not ((B -> (B or C)) or D))) -> (not A))), M:tm-313, m:tm-410, u:((A Am) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26164
in-theory        26164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and ((((B -> (B or C)) or D) -> E) -> ((A or ((B -> (B or C)) or D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-410 ((A Am) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26164.        ((A -> ((B -> (B or C)) or D)) and ((((B -> (B or C)) or D) -> E) -> ((A or ((B -> (B or C)) or D)) -> E))), M:tm-312, m:tm-410, u:((A Am) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26165
in-theory        26165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and (E or (A -> ((B -> (B or C)) or D))))
theorem-size     21
proof            (modus-ponens tm-311 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26165.        ((A -> ((B -> (B or C)) or D)) and (E or (A -> ((B -> (B or C)) or D)))), M:tm-311, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26166
in-theory        26166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and ((A -> ((B -> (B or C)) or D)) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26166.        ((A -> ((B -> (B or C)) or D)) and ((A -> ((B -> (B or C)) or D)) or E)), M:tm-310, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26167
in-theory        26167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and (E -> ((A -> ((B -> (B or C)) or D)) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26167.        ((A -> ((B -> (B or C)) or D)) and (E -> ((A -> ((B -> (B or C)) or D)) and E))), M:tm-309, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26168
in-theory        26168
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and (E -> (A -> ((B -> (B or C)) or D))))
theorem-size     21
proof            (modus-ponens tm-305 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26168.        ((A -> ((B -> (B or C)) or D)) and (E -> (A -> ((B -> (B or C)) or D)))), M:tm-305, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26169
in-theory        26169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-303 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26169.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (E or F)) or G))), M:tm-303, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26170
in-theory        26170
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (D or E)) or F))
theorem-size     19
proof            (modus-ponens tm-300 tm-410 ((Am (and (-> A (-> B (and A B))) C)) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26170.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (D or E)) or F)), M:tm-300, m:tm-410, u:((Am (and (-> A (-> B (and A B))) C)) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26171
in-theory        26171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-270 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26171.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (E or F)) or G))), M:tm-270, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26172
in-theory        26172
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-267 tm-410 ((Am (and (-> (and A B) B) C)) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26172.        ((A or (((B and C) -> C) and A)) -> ((D -> (D or E)) or F)), M:tm-267, m:tm-410, u:((Am (and (-> (and A B) B) C)) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26173
in-theory        26173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-239 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26173.        ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (E or F)) or G))), M:tm-239, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26174
in-theory        26174
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-236 tm-410 ((Am (and (-> (and A B) A) C)) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26174.        ((A or (((B and C) -> B) and A)) -> ((D -> (D or E)) or F)), M:tm-236, m:tm-410, u:((Am (and (-> (and A B) A) C)) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26175
in-theory        26175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-210 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26175.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (F or G)) or H))), M:tm-210, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26176
in-theory        26176
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (E or F)) or G))
theorem-size     25
proof            (modus-ponens tm-207 tm-410 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26176.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (E or F)) or G)), M:tm-207, m:tm-410, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26177
in-theory        26177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-183 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26177.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (E or F)) or G))), M:tm-183, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26178
in-theory        26178
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-180 tm-410 ((Am (and (-> A (-> B A)) C)) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26178.        ((A or ((B -> (C -> B)) and A)) -> ((D -> (D or E)) or F)), M:tm-180, m:tm-410, u:((Am (and (-> A (-> B A)) C)) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26179
in-theory        26179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-157 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26179.        ((A -> ((B and C) -> C)) and (D -> ((E -> (E or F)) or G))), M:tm-157, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26180
in-theory        26180
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-154 tm-410 ((Am (-> (and A B) B)) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-4 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26180.        ((A or ((B and C) -> C)) -> ((D -> (D or E)) or F)), M:tm-154, m:tm-410, u:((Am (-> (and A B) B)) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26181
in-theory        26181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (E or F)) or G)))
theorem-size     25
proof            (modus-ponens tm-147 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26181.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (E or F)) or G))), M:tm-147, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26182
in-theory        26182
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (D or E)) or F))
theorem-size     23
proof            (modus-ponens tm-144 tm-410 ((Am (-> (and A (-> B C)) C)) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26182.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (D or E)) or F)), M:tm-144, m:tm-410, u:((Am (-> (and A (-> B C)) C)) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26183
in-theory        26183
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (B or C)) or D) -> E)) -> ((B -> (B or C)) or D))
theorem-size     19
proof            (modus-ponens tm-142 tm-410 ((Am (and A (-> (or (-> Bm (or Bm Cm)) Dm) C))) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26183.        ((A and (((B -> (B or C)) or D) -> E)) -> ((B -> (B or C)) or D)), M:tm-142, m:tm-410, u:((Am (and A (-> (or (-> Bm (or Bm Cm)) Dm) C))) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26184
in-theory        26184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-134 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26184.        ((A -> ((B and C) -> B)) and (D -> ((E -> (E or F)) or G))), M:tm-134, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26185
in-theory        26185
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-131 tm-410 ((Am (-> (and A B) A)) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-3 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26185.        ((A or ((B and C) -> B)) -> ((D -> (D or E)) or F)), M:tm-131, m:tm-410, u:((Am (-> (and A B) A)) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26186
in-theory        26186
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (E or F)) or G)))
theorem-size     25
proof            (modus-ponens tm-125 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26186.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (E or F)) or G))), M:tm-125, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26187
in-theory        26187
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (D or E)) or F))
theorem-size     23
proof            (modus-ponens tm-122 tm-410 ((Am (-> (and (-> A B) C) B)) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26187.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (D or E)) or F)), M:tm-122, m:tm-410, u:((Am (-> (and (-> A B) C) B)) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26188
in-theory        26188
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) or C) -> D) and E) -> ((A -> (A or B)) or C))
theorem-size     19
proof            (modus-ponens tm-120 tm-410 ((Am (and (-> (or (-> Bm (or Bm Cm)) Dm) B) C)) (A (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26188.        (((((A -> (A or B)) or C) -> D) and E) -> ((A -> (A or B)) or C)), M:tm-120, m:tm-410, u:((Am (and (-> (or (-> Bm (or Bm Cm)) Dm) B) C)) (A (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26189
in-theory        26189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-113 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26189.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (F or G)) or H))), M:tm-113, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26190
in-theory        26190
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (E or F)) or G))
theorem-size     23
proof            (modus-ponens tm-110 tm-410 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26190.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (E or F)) or G)), M:tm-110, m:tm-410, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26191
in-theory        26191
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (E or F)) or G)))
theorem-size     29
proof            (modus-ponens tm-105 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26191.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (E or F)) or G))), M:tm-105, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26192
in-theory        26192
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (D or E)) or F))
theorem-size     27
proof            (modus-ponens tm-102 tm-410 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26192.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (D or E)) or F)), M:tm-102, m:tm-410, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26193
in-theory        26193
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) -> D) -> ((A -> (A or B)) or C))
theorem-size     17
proof            (modus-ponens tm-96 tm-410 ((Am (-> (or (-> Bm (or Bm Cm)) Dm) B)) (A (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26193.        ((((A -> (A or B)) or C) -> D) -> ((A -> (A or B)) or C)), M:tm-96, m:tm-410, u:((Am (-> (or (-> Bm (or Bm Cm)) Dm) B)) (A (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26194
in-theory        26194
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (D or E)) or F)))
theorem-size     17
proof            (modus-ponens tm-95 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26194.        (((A -> B) -> (A -> A)) and (C -> ((D -> (D or E)) or F))), M:tm-95, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26195
in-theory        26195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (C or D)) or E))
theorem-size     15
proof            (modus-ponens tm-92 tm-410 ((Am (-> A A)) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26195.        (((A -> B) or (A -> A)) -> ((C -> (C or D)) or E)), M:tm-92, m:tm-410, u:((Am (-> A A)) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26196
in-theory        26196
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (C or D)) or E)))
theorem-size     11
proof            (modus-ponens tm-84 tm-410 ((A Am) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26196.        (A -> (B -> ((C -> (C or D)) or E))), M:tm-84, m:tm-410, u:((A Am) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26197
in-theory        26197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-83 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26197.        ((A -> (B -> (C -> B))) and (D -> ((E -> (E or F)) or G))), M:tm-83, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26198
in-theory        26198
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-80 tm-410 ((Am (-> A (-> B A))) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26198.        ((A or (B -> (C -> B))) -> ((D -> (D or E)) or F)), M:tm-80, m:tm-410, u:((Am (-> A (-> B A))) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26199
in-theory        26199
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((A -> (A or B)) or C) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-410 ((Am (not (not (-> (or (-> Bm (or Bm Cm)) Dm) B)))) (A (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-10 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26199.        ((not (not (((A -> (A or B)) or C) -> D))) -> D), M:tm-77, m:tm-410, u:((Am (not (not (-> (or (-> Bm (or Bm Cm)) Dm) B)))) (A (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26200
in-theory        26200
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (C or D)) or E)))
theorem-size     15
proof            (modus-ponens tm-76 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26200.        (((not (not A)) -> A) and (B -> ((C -> (C or D)) or E))), M:tm-76, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26201
in-theory        26201
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (B or C)) or D))
theorem-size     13
proof            (modus-ponens tm-73 tm-410 ((A Am) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26201.        (((not (not A)) or A) -> ((B -> (B or C)) or D)), M:tm-73, m:tm-410, u:((A Am) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26202
in-theory        26202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (D or E)) or F)))
theorem-size     21
proof            (modus-ponens tm-69 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26202.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (D or E)) or F))), M:tm-69, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26203
in-theory        26203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (C or D)) or E))
theorem-size     19
proof            (modus-ponens tm-66 tm-410 ((Am (-> (-> A (not B)) (not A))) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-9 tm-1 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26203.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (C or D)) or E)), M:tm-66, m:tm-410, u:((Am (-> (-> A (not B)) (not A))) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26204
in-theory        26204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-54 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26204.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (E or F)) or G))), M:tm-54, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26205
in-theory        26205
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) or F))
theorem-size     21
proof            (modus-ponens tm-51 tm-410 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26205.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (D or E)) or F)), M:tm-51, m:tm-410, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26206
in-theory        26206
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (C or D)) or E))
theorem-size     13
proof            (modus-ponens tm-50 tm-410 ((Am (or A B)) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26206.        ((A or (B or A)) -> ((C -> (C or D)) or E)), M:tm-50, m:tm-410, u:((Am (or A B)) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26207
in-theory        26207
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (C or D)) or E))
theorem-size     13
proof            (modus-ponens tm-49 tm-410 ((Am (or A B)) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26207.        ((A or (A or B)) -> ((C -> (C or D)) or E)), M:tm-49, m:tm-410, u:((Am (or A B)) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26208
in-theory        26208
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (C or D)) or E))
theorem-size     15
proof            (modus-ponens tm-48 tm-410 ((Am (-> A (and B A))) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26208.        ((A or (B -> (A and B))) -> ((C -> (C or D)) or E)), M:tm-48, m:tm-410, u:((Am (-> A (and B A))) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26209
in-theory        26209
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (C or D)) or E))
theorem-size     13
proof            (modus-ponens tm-47 tm-410 ((A Am) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26209.        (((A and B) or B) -> ((C -> (C or D)) or E)), M:tm-47, m:tm-410, u:((A Am) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26210
in-theory        26210
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (C or D)) or E))
theorem-size     13
proof            (modus-ponens tm-46 tm-410 ((A Am) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26210.        (((A and B) or A) -> ((C -> (C or D)) or E)), M:tm-46, m:tm-410, u:((A Am) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26211
in-theory        26211
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) or F))
theorem-size     21
proof            (modus-ponens tm-45 tm-410 ((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26211.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) or F)), M:tm-45, m:tm-410, u:((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26212
in-theory        26212
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (C or D)) or E))
theorem-size     13
proof            (modus-ponens tm-44 tm-410 ((Am (-> A B)) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26212.        ((A or (B -> A)) -> ((C -> (C or D)) or E)), M:tm-44, m:tm-410, u:((Am (-> A B)) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26213
in-theory        26213
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-42 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26213.        ((A -> (B or A)) and (C -> ((D -> (D or E)) or F))), M:tm-42, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26214
in-theory        26214
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-32 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26214.        ((A -> (A or B)) and (C -> ((D -> (D or E)) or F))), M:tm-32, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26215
in-theory        26215
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (B or C)) or D)))
theorem-size     11
proof            (modus-ponens tm-24 tm-410 ((A Am) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26215.        (A -> (A and ((B -> (B or C)) or D))), M:tm-24, m:tm-410, u:((A Am) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26216
in-theory        26216
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) or F)))
theorem-size     17
proof            (modus-ponens tm-23 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26216.        ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) or F))), M:tm-23, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26217
in-theory        26217
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-22 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26217.        (((A and B) -> B) and (C -> ((D -> (D or E)) or F))), M:tm-22, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26218
in-theory        26218
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-21 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26218.        (((A and B) -> A) and (C -> ((D -> (D or E)) or F))), M:tm-21, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26219
in-theory        26219
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-20 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26219.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) or G))), M:tm-20, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26220
in-theory        26220
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-19 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26220.        ((A -> (B -> A)) and (C -> ((D -> (D or E)) or F))), M:tm-19, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26221
in-theory        26221
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((B -> (B or C)) or D) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-410 ((Am (and A (-> (or (-> Bm (or Bm Cm)) Dm) C))) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-4 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26221.        ((A and (((B -> (B or C)) or D) -> E)) -> E), M:tm-17, m:tm-410, u:((Am (and A (-> (or (-> Bm (or Bm Cm)) Dm) C))) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26222
in-theory        26222
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (A or B)) or C) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-410 ((Am (and (-> (or (-> Bm (or Bm Cm)) Dm) B) C)) (A (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-3 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26222.        (((((A -> (A or B)) or C) -> D) and E) -> D), M:tm-15, m:tm-410, u:((Am (and (-> (or (-> Bm (or Bm Cm)) Dm) B) C)) (A (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26223
in-theory        26223
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (B or C)) or D))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-410 ((A Am) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-9 tm-1 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26223.        ((A -> (not ((B -> (B or C)) or D))) -> (not A)), M:tm-9, m:tm-410, u:((A Am) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26224
in-theory        26224
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) -> D) -> ((E or ((A -> (A or B)) or C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-410 ((A Am) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26224.        ((((A -> (A or B)) or C) -> D) -> ((E or ((A -> (A or B)) or C)) -> D)), M:tm-8, m:tm-410, u:((A Am) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-26225
in-theory        26225
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (C or D)) or E)))
theorem-size     11
proof            (modus-ponens tm-7 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-7 tm-1 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26225.        (A or (B -> ((C -> (C or D)) or E))), M:tm-7, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26226
in-theory        26226
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-6 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26226.        ((A -> ((B -> (B or C)) or D)) or E), M:tm-6, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26227
in-theory        26227
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (C or D)) or E)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-26227.        (A -> ((B -> ((C -> (C or D)) or E)) and A)), M:tm-5, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-26228
in-theory        26228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26228.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-409, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26229
in-theory        26229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26229.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-400, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26230
in-theory        26230
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26230.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-391, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26231
in-theory        26231
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26231.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-382, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26232
in-theory        26232
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26232.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (H -> G)))), M:tm-373, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26233
in-theory        26233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26233.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-364, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26234
in-theory        26234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26234.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-354, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26235
in-theory        26235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26235.        (((A -> (A or B)) and (C -> (D -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26236
in-theory        26236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26236.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (F -> E)))), M:tm-338, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26237
in-theory        26237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and (C -> (D -> C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26237.        (((A -> (A or B)) and (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and (C -> (D -> C))))), M:tm-327, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26238
in-theory        26238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and (((E and F) -> F) and ((A -> (A or B)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26238.        (((A -> (A or B)) and (C -> (D -> C))) and (((E and F) -> F) and ((A -> (A or B)) and (C -> (D -> C))))), M:tm-326, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26239
in-theory        26239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and (((E and F) -> E) and ((A -> (A or B)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26239.        (((A -> (A or B)) and (C -> (D -> C))) and (((E and F) -> E) and ((A -> (A or B)) and (C -> (D -> C))))), M:tm-325, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26240
in-theory        26240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and (C -> (D -> C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26240.        (((A -> (A or B)) and (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and (C -> (D -> C))))), M:tm-324, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26241
in-theory        26241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and ((E -> (F -> E)) and ((A -> (A or B)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26241.        (((A -> (A or B)) and (C -> (D -> C))) and ((E -> (F -> E)) and ((A -> (A or B)) and (C -> (D -> C))))), M:tm-323, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26242
in-theory        26242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26242.        (((A -> (A or B)) and (C -> (D -> C))) and ((E and F) -> F)), M:tm-322, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26243
in-theory        26243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26243.        (((A -> (A or B)) and (C -> (D -> C))) and ((E and F) -> E)), M:tm-320, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26244
in-theory        26244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26244.        (((A -> (A or B)) and (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26245
in-theory        26245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26245.        (((A -> (A or B)) and (C -> (D -> C))) and (E -> (F -> E))), M:tm-315, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26246
in-theory        26246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and (E or ((A -> (A or B)) and (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26246.        (((A -> (A or B)) and (C -> (D -> C))) and (E or ((A -> (A or B)) and (C -> (D -> C))))), M:tm-311, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26247
in-theory        26247
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and (((A -> (A or B)) and (C -> (D -> C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26247.        (((A -> (A or B)) and (C -> (D -> C))) and (((A -> (A or B)) and (C -> (D -> C))) or E)), M:tm-310, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26248
in-theory        26248
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and (E -> (((A -> (A or B)) and (C -> (D -> C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26248.        (((A -> (A or B)) and (C -> (D -> C))) and (E -> (((A -> (A or B)) and (C -> (D -> C))) and E))), M:tm-309, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26249
in-theory        26249
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-308 tm-411 ((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26249.        (((A -> (A or B)) and (C -> (D -> C))) and (C -> (D -> C))), M:tm-308, m:tm-411, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-26250
in-theory        26250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and (A -> (A or B)))
theorem-size     17
proof            (modus-ponens tm-307 tm-411 ((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26250.        (((A -> (A or B)) and (C -> (D -> C))) and (A -> (A or B))), M:tm-307, m:tm-411, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-26251
in-theory        26251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and (E -> ((A -> (A or B)) and (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26251.        (((A -> (A or B)) and (C -> (D -> C))) and (E -> ((A -> (A or B)) and (C -> (D -> C))))), M:tm-305, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26252
in-theory        26252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26252.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-303, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26253
in-theory        26253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26253.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-270, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26254
in-theory        26254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26254.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-239, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26255
in-theory        26255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26255.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (H -> G)))), M:tm-210, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26256
in-theory        26256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26256.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-183, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26257
in-theory        26257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26257.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-157, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26258
in-theory        26258
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26258.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-147, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26259
in-theory        26259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26259.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-134, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26260
in-theory        26260
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26260.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-125, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26261
in-theory        26261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26261.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> G)))), M:tm-113, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26262
in-theory        26262
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26262.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-105, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26263
in-theory        26263
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26263.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (F -> E)))), M:tm-95, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26264
in-theory        26264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26264.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-83, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26265
in-theory        26265
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26265.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (E -> D)))), M:tm-76, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26266
in-theory        26266
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-6 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26266.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (F -> E)))), M:tm-69, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26267
in-theory        26267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26267.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-54, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26268
in-theory        26268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26268.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> (F -> E)))), M:tm-42, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26269
in-theory        26269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26269.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> (F -> E)))), M:tm-32, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26270
in-theory        26270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26270.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (F -> E)))), M:tm-23, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26271
in-theory        26271
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26271.        (((A and B) -> B) and ((C -> (C or D)) and (E -> (F -> E)))), M:tm-22, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26272
in-theory        26272
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26272.        (((A and B) -> A) and ((C -> (C or D)) and (E -> (F -> E)))), M:tm-21, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26273
in-theory        26273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26273.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-20, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26274
in-theory        26274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26274.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (F -> E)))), M:tm-19, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26275
in-theory        26275
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-7 tm-5 tm-6 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26275.        (A or ((B -> (B or C)) and (D -> (E -> D)))), M:tm-7, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26276
in-theory        26276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26276.        (((A -> (A or B)) and (C -> (D -> C))) or E), M:tm-6, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26277
in-theory        26277
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> (E -> D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26277.        (A -> (((B -> (B or C)) and (D -> (E -> D))) and A)), M:tm-5, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26278
in-theory        26278
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26278.        (A -> ((B -> (B or C)) and (D -> (E -> D)))), M:tm-1, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-26279
in-theory        26279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26279.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-409, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26280
in-theory        26280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26280.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-400, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26281
in-theory        26281
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26281.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-391, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26282
in-theory        26282
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26282.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-382, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26283
in-theory        26283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26283.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-373, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26284
in-theory        26284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26284.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-364, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26285
in-theory        26285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26285.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-354, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26286
in-theory        26286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26286.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26287
in-theory        26287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26287.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-338, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26288
in-theory        26288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26288.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-327, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26289
in-theory        26289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26289.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-326, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26290
in-theory        26290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26290.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-325, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26291
in-theory        26291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26291.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-324, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26292
in-theory        26292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26292.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-323, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26293
in-theory        26293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26293.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26294
in-theory        26294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26294.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26295
in-theory        26295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26295.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26296
in-theory        26296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26296.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26297
in-theory        26297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26297.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-311, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26298
in-theory        26298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26298.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-310, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26299
in-theory        26299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26299.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F))), M:tm-309, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26300
in-theory        26300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-308 tm-412 ((A (-> Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26300.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-308, m:tm-412, u:((A (-> Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-26301
in-theory        26301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (A -> (A or B)))
theorem-size     25
proof            (modus-ponens tm-307 tm-412 ((A (-> Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26301.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (A -> (A or B))), M:tm-307, m:tm-412, u:((A (-> Am (or Am Bm))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-26302
in-theory        26302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26302.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-305, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26303
in-theory        26303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26303.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-303, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26304
in-theory        26304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26304.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-270, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26305
in-theory        26305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26305.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-239, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26306
in-theory        26306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26306.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-210, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26307
in-theory        26307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26307.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-183, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26308
in-theory        26308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26308.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-157, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26309
in-theory        26309
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26309.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-147, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26310
in-theory        26310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26310.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-134, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26311
in-theory        26311
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26311.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-125, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26312
in-theory        26312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26312.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-113, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26313
in-theory        26313
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26313.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-105, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26314
in-theory        26314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26314.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-95, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26315
in-theory        26315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26315.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-83, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26316
in-theory        26316
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26316.        (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-76, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26317
in-theory        26317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-6 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26317.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-69, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26318
in-theory        26318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26318.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-54, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26319
in-theory        26319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26319.        ((A -> (B or A)) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-42, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26320
in-theory        26320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26320.        ((A -> (A or B)) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-32, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26321
in-theory        26321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26321.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-23, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26322
in-theory        26322
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26322.        (((A and B) -> B) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-22, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26323
in-theory        26323
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26323.        (((A and B) -> A) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-21, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26324
in-theory        26324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26324.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-20, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26325
in-theory        26325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26325.        ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-19, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26326
in-theory        26326
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-7 tm-5 tm-6 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26326.        (A or ((B -> (B or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-7, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26327
in-theory        26327
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26327.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F), M:tm-6, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26328
in-theory        26328
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26328.        (A -> (((B -> (B or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)), M:tm-5, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26329
in-theory        26329
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-1 tm-5 tm-6 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26329.        (A -> ((B -> (B or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-1, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-26330
in-theory        26330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26330.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-409, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26331
in-theory        26331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26331.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-400, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26332
in-theory        26332
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26332.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-391, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26333
in-theory        26333
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26333.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-382, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26334
in-theory        26334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26334.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G and H) -> G))), M:tm-373, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26335
in-theory        26335
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26335.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-364, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26336
in-theory        26336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26336.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-354, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26337
in-theory        26337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26337.        (((A -> (A or B)) and ((C and D) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26338
in-theory        26338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26338.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E and F) -> E))), M:tm-338, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26339
in-theory        26339
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and ((C and D) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26339.        (((A -> (A or B)) and ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and ((C and D) -> C)))), M:tm-327, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26340
in-theory        26340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and (((E and F) -> F) and ((A -> (A or B)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26340.        (((A -> (A or B)) and ((C and D) -> C)) and (((E and F) -> F) and ((A -> (A or B)) and ((C and D) -> C)))), M:tm-326, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26341
in-theory        26341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and (((E and F) -> E) and ((A -> (A or B)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26341.        (((A -> (A or B)) and ((C and D) -> C)) and (((E and F) -> E) and ((A -> (A or B)) and ((C and D) -> C)))), M:tm-325, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26342
in-theory        26342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and ((C and D) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26342.        (((A -> (A or B)) and ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and ((C and D) -> C)))), M:tm-324, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26343
in-theory        26343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and ((E -> (F -> E)) and ((A -> (A or B)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26343.        (((A -> (A or B)) and ((C and D) -> C)) and ((E -> (F -> E)) and ((A -> (A or B)) and ((C and D) -> C)))), M:tm-323, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26344
in-theory        26344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26344.        (((A -> (A or B)) and ((C and D) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26345
in-theory        26345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26345.        (((A -> (A or B)) and ((C and D) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26346
in-theory        26346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26346.        (((A -> (A or B)) and ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26347
in-theory        26347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26347.        (((A -> (A or B)) and ((C and D) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26348
in-theory        26348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and (E or ((A -> (A or B)) and ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26348.        (((A -> (A or B)) and ((C and D) -> C)) and (E or ((A -> (A or B)) and ((C and D) -> C)))), M:tm-311, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26349
in-theory        26349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and (((A -> (A or B)) and ((C and D) -> C)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26349.        (((A -> (A or B)) and ((C and D) -> C)) and (((A -> (A or B)) and ((C and D) -> C)) or E)), M:tm-310, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26350
in-theory        26350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and (E -> (((A -> (A or B)) and ((C and D) -> C)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26350.        (((A -> (A or B)) and ((C and D) -> C)) and (E -> (((A -> (A or B)) and ((C and D) -> C)) and E))), M:tm-309, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26351
in-theory        26351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-308 tm-413 ((A (-> Am (or Am Bm))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26351.        (((A -> (A or B)) and ((C and D) -> C)) and ((C and D) -> C)), M:tm-308, m:tm-413, u:((A (-> Am (or Am Bm))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-26352
in-theory        26352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and (A -> (A or B)))
theorem-size     17
proof            (modus-ponens tm-307 tm-413 ((A (-> Am (or Am Bm))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26352.        (((A -> (A or B)) and ((C and D) -> C)) and (A -> (A or B))), M:tm-307, m:tm-413, u:((A (-> Am (or Am Bm))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-26353
in-theory        26353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and (E -> ((A -> (A or B)) and ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26353.        (((A -> (A or B)) and ((C and D) -> C)) and (E -> ((A -> (A or B)) and ((C and D) -> C)))), M:tm-305, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26354
in-theory        26354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26354.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-303, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26355
in-theory        26355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26355.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-270, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26356
in-theory        26356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26356.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-239, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26357
in-theory        26357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26357.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G and H) -> G))), M:tm-210, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26358
in-theory        26358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26358.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-183, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26359
in-theory        26359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26359.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-157, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26360
in-theory        26360
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26360.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-147, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26361
in-theory        26361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26361.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-134, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26362
in-theory        26362
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26362.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-125, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26363
in-theory        26363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26363.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G and H) -> G))), M:tm-113, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26364
in-theory        26364
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26364.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-105, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26365
in-theory        26365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26365.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E and F) -> E))), M:tm-95, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26366
in-theory        26366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26366.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-83, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26367
in-theory        26367
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((D and E) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-10 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26367.        (((not (not A)) -> A) and ((B -> (B or C)) and ((D and E) -> D))), M:tm-76, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26368
in-theory        26368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-9 tm-6 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26368.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E and F) -> E))), M:tm-69, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26369
in-theory        26369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26369.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-54, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26370
in-theory        26370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26370.        ((A -> (B or A)) and ((C -> (C or D)) and ((E and F) -> E))), M:tm-42, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26371
in-theory        26371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26371.        ((A -> (A or B)) and ((C -> (C or D)) and ((E and F) -> E))), M:tm-32, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26372
in-theory        26372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26372.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E and F) -> E))), M:tm-23, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26373
in-theory        26373
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26373.        (((A and B) -> B) and ((C -> (C or D)) and ((E and F) -> E))), M:tm-22, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26374
in-theory        26374
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26374.        (((A and B) -> A) and ((C -> (C or D)) and ((E and F) -> E))), M:tm-21, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26375
in-theory        26375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26375.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-20, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26376
in-theory        26376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26376.        ((A -> (B -> A)) and ((C -> (C or D)) and ((E and F) -> E))), M:tm-19, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26377
in-theory        26377
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-7 tm-5 tm-6 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26377.        (A or ((B -> (B or C)) and ((D and E) -> D))), M:tm-7, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26378
in-theory        26378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26378.        (((A -> (A or B)) and ((C and D) -> C)) or E), M:tm-6, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26379
in-theory        26379
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((D and E) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26379.        (A -> (((B -> (B or C)) and ((D and E) -> D)) and A)), M:tm-5, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26380
in-theory        26380
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-1 tm-5 tm-6 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26380.        (A -> ((B -> (B or C)) and ((D and E) -> D))), M:tm-1, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-26381
in-theory        26381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-409 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26381.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-409, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26382
in-theory        26382
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-400 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26382.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-400, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26383
in-theory        26383
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-391 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26383.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-391, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26384
in-theory        26384
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-382 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26384.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-382, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26385
in-theory        26385
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-373 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26385.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G and H) -> H))), M:tm-373, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26386
in-theory        26386
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-364 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26386.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-364, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26387
in-theory        26387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-354 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26387.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-354, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26388
in-theory        26388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26388.        (((A -> (A or B)) and ((C and D) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26389
in-theory        26389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-338 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26389.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E and F) -> F))), M:tm-338, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26390
in-theory        26390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and ((C and D) -> D))))
theorem-size     31
proof            (modus-ponens tm-327 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26390.        (((A -> (A or B)) and ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and ((C and D) -> D)))), M:tm-327, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26391
in-theory        26391
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and (((E and F) -> F) and ((A -> (A or B)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-326 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26391.        (((A -> (A or B)) and ((C and D) -> D)) and (((E and F) -> F) and ((A -> (A or B)) and ((C and D) -> D)))), M:tm-326, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26392
in-theory        26392
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and (((E and F) -> E) and ((A -> (A or B)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-325 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26392.        (((A -> (A or B)) and ((C and D) -> D)) and (((E and F) -> E) and ((A -> (A or B)) and ((C and D) -> D)))), M:tm-325, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26393
in-theory        26393
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and ((C and D) -> D))))
theorem-size     37
proof            (modus-ponens tm-324 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26393.        (((A -> (A or B)) and ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and ((C and D) -> D)))), M:tm-324, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26394
in-theory        26394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and ((E -> (F -> E)) and ((A -> (A or B)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-323 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26394.        (((A -> (A or B)) and ((C and D) -> D)) and ((E -> (F -> E)) and ((A -> (A or B)) and ((C and D) -> D)))), M:tm-323, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26395
in-theory        26395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26395.        (((A -> (A or B)) and ((C and D) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26396
in-theory        26396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26396.        (((A -> (A or B)) and ((C and D) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26397
in-theory        26397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26397.        (((A -> (A or B)) and ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26398
in-theory        26398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26398.        (((A -> (A or B)) and ((C and D) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26399
in-theory        26399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and (E or ((A -> (A or B)) and ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-311 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26399.        (((A -> (A or B)) and ((C and D) -> D)) and (E or ((A -> (A or B)) and ((C and D) -> D)))), M:tm-311, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26400
in-theory        26400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and (((A -> (A or B)) and ((C and D) -> D)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26400.        (((A -> (A or B)) and ((C and D) -> D)) and (((A -> (A or B)) and ((C and D) -> D)) or E)), M:tm-310, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26401
in-theory        26401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and (E -> (((A -> (A or B)) and ((C and D) -> D)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26401.        (((A -> (A or B)) and ((C and D) -> D)) and (E -> (((A -> (A or B)) and ((C and D) -> D)) and E))), M:tm-309, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26402
in-theory        26402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-308 tm-414 ((A (-> Am (or Am Bm))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26402.        (((A -> (A or B)) and ((C and D) -> D)) and ((C and D) -> D)), M:tm-308, m:tm-414, u:((A (-> Am (or Am Bm))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-26403
in-theory        26403
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and (A -> (A or B)))
theorem-size     17
proof            (modus-ponens tm-307 tm-414 ((A (-> Am (or Am Bm))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26403.        (((A -> (A or B)) and ((C and D) -> D)) and (A -> (A or B))), M:tm-307, m:tm-414, u:((A (-> Am (or Am Bm))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-26404
in-theory        26404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and (E -> ((A -> (A or B)) and ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-305 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26404.        (((A -> (A or B)) and ((C and D) -> D)) and (E -> ((A -> (A or B)) and ((C and D) -> D)))), M:tm-305, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26405
in-theory        26405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-303 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26405.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-303, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26406
in-theory        26406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-270 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26406.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-270, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26407
in-theory        26407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-239 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26407.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-239, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26408
in-theory        26408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-210 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26408.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G and H) -> H))), M:tm-210, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26409
in-theory        26409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-183 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26409.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-183, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26410
in-theory        26410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-157 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26410.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-157, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26411
in-theory        26411
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-147 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26411.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-147, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26412
in-theory        26412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-134 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26412.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-134, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26413
in-theory        26413
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-125 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26413.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-125, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26414
in-theory        26414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-113 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26414.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G and H) -> H))), M:tm-113, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26415
in-theory        26415
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-105 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26415.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-105, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26416
in-theory        26416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-95 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26416.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E and F) -> F))), M:tm-95, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26417
in-theory        26417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-83 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26417.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-83, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26418
in-theory        26418
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((D and E) -> E)))
theorem-size     17
proof            (modus-ponens tm-76 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-10 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26418.        (((not (not A)) -> A) and ((B -> (B or C)) and ((D and E) -> E))), M:tm-76, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26419
in-theory        26419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-69 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-9 tm-6 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26419.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E and F) -> F))), M:tm-69, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26420
in-theory        26420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-54 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26420.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-54, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26421
in-theory        26421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-42 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26421.        ((A -> (B or A)) and ((C -> (C or D)) and ((E and F) -> F))), M:tm-42, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26422
in-theory        26422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-32 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26422.        ((A -> (A or B)) and ((C -> (C or D)) and ((E and F) -> F))), M:tm-32, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26423
in-theory        26423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-23 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26423.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E and F) -> F))), M:tm-23, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26424
in-theory        26424
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-22 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26424.        (((A and B) -> B) and ((C -> (C or D)) and ((E and F) -> F))), M:tm-22, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26425
in-theory        26425
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-21 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26425.        (((A and B) -> A) and ((C -> (C or D)) and ((E and F) -> F))), M:tm-21, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26426
in-theory        26426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-20 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26426.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-20, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26427
in-theory        26427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-19 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26427.        ((A -> (B -> A)) and ((C -> (C or D)) and ((E and F) -> F))), M:tm-19, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26428
in-theory        26428
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-7 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-7 tm-5 tm-6 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26428.        (A or ((B -> (B or C)) and ((D and E) -> E))), M:tm-7, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26429
in-theory        26429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26429.        (((A -> (A or B)) and ((C and D) -> D)) or E), M:tm-6, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26430
in-theory        26430
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((D and E) -> E)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26430.        (A -> (((B -> (B or C)) and ((D and E) -> E)) and A)), M:tm-5, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26431
in-theory        26431
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-1 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-1 tm-5 tm-6 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26431.        (A -> ((B -> (B or C)) and ((D and E) -> E))), M:tm-1, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-26432
in-theory        26432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26432.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-409, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26433
in-theory        26433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26433.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-400, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26434
in-theory        26434
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26434.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-391, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26435
in-theory        26435
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26435.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-382, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26436
in-theory        26436
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26436.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (G and H))))), M:tm-373, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26437
in-theory        26437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26437.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-364, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26438
in-theory        26438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26438.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-354, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26439
in-theory        26439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26439.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26440
in-theory        26440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26440.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (E and F))))), M:tm-338, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26441
in-theory        26441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and (C -> (D -> (C and D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26441.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and (C -> (D -> (C and D)))))), M:tm-327, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26442
in-theory        26442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A -> (A or B)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26442.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A -> (A or B)) and (C -> (D -> (C and D)))))), M:tm-326, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26443
in-theory        26443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A -> (A or B)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26443.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A -> (A or B)) and (C -> (D -> (C and D)))))), M:tm-325, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26444
in-theory        26444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and (C -> (D -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26444.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and (C -> (D -> (C and D)))))), M:tm-324, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26445
in-theory        26445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A -> (A or B)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26445.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A -> (A or B)) and (C -> (D -> (C and D)))))), M:tm-323, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26446
in-theory        26446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26446.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26447
in-theory        26447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26447.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26448
in-theory        26448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26448.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26449
in-theory        26449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26449.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26450
in-theory        26450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and (E or ((A -> (A or B)) and (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26450.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and (E or ((A -> (A or B)) and (C -> (D -> (C and D)))))), M:tm-311, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26451
in-theory        26451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and (((A -> (A or B)) and (C -> (D -> (C and D)))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26451.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and (((A -> (A or B)) and (C -> (D -> (C and D)))) or E)), M:tm-310, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26452
in-theory        26452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and (E -> (((A -> (A or B)) and (C -> (D -> (C and D)))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26452.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and (E -> (((A -> (A or B)) and (C -> (D -> (C and D)))) and E))), M:tm-309, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26453
in-theory        26453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-415 ((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26453.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and (C -> (D -> (C and D)))), M:tm-308, m:tm-415, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-26454
in-theory        26454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-415 ((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26454.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and (A -> (A or B))), M:tm-307, m:tm-415, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-26455
in-theory        26455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and (E -> ((A -> (A or B)) and (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26455.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and (E -> ((A -> (A or B)) and (C -> (D -> (C and D)))))), M:tm-305, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26456
in-theory        26456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26456.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-303, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26457
in-theory        26457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26457.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-270, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26458
in-theory        26458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26458.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-239, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26459
in-theory        26459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26459.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (H -> (G and H))))), M:tm-210, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26460
in-theory        26460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26460.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-183, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26461
in-theory        26461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26461.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-157, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26462
in-theory        26462
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26462.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-147, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26463
in-theory        26463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26463.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-134, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26464
in-theory        26464
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26464.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-125, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26465
in-theory        26465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26465.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (G and H))))), M:tm-113, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26466
in-theory        26466
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26466.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-105, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26467
in-theory        26467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26467.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (F -> (E and F))))), M:tm-95, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26468
in-theory        26468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26468.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-83, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26469
in-theory        26469
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26469.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (E -> (D and E))))), M:tm-76, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26470
in-theory        26470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26470.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (F -> (E and F))))), M:tm-69, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26471
in-theory        26471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26471.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-54, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26472
in-theory        26472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26472.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> (F -> (E and F))))), M:tm-42, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26473
in-theory        26473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26473.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> (F -> (E and F))))), M:tm-32, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26474
in-theory        26474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26474.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (E and F))))), M:tm-23, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26475
in-theory        26475
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26475.        (((A and B) -> B) and ((C -> (C or D)) and (E -> (F -> (E and F))))), M:tm-22, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26476
in-theory        26476
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26476.        (((A and B) -> A) and ((C -> (C or D)) and (E -> (F -> (E and F))))), M:tm-21, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26477
in-theory        26477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26477.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-20, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26478
in-theory        26478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26478.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (F -> (E and F))))), M:tm-19, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26479
in-theory        26479
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26479.        (A or ((B -> (B or C)) and (D -> (E -> (D and E))))), M:tm-7, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26480
in-theory        26480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-6 tm-5)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26480.        (((A -> (A or B)) and (C -> (D -> (C and D)))) or E), M:tm-6, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26481
in-theory        26481
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> (E -> (D and E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26481.        (A -> (((B -> (B or C)) and (D -> (E -> (D and E)))) and A)), M:tm-5, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26482
in-theory        26482
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26482.        (A -> ((B -> (B or C)) and (D -> (E -> (D and E))))), M:tm-1, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-26483
in-theory        26483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-409 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26483.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-409, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26484
in-theory        26484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-400 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26484.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-400, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26485
in-theory        26485
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-391 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26485.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-391, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26486
in-theory        26486
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-382 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26486.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-382, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26487
in-theory        26487
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-373 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26487.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (G or H)))), M:tm-373, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26488
in-theory        26488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-364 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26488.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-364, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26489
in-theory        26489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-354 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26489.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-354, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26490
in-theory        26490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26490.        (((A -> (A or B)) and (C -> (C or D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26491
in-theory        26491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-338 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26491.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (E or F)))), M:tm-338, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26492
in-theory        26492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and (C -> (C or D)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26492.        (((A -> (A or B)) and (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and (C -> (C or D))))), M:tm-327, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26493
in-theory        26493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and (((E and F) -> F) and ((A -> (A or B)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26493.        (((A -> (A or B)) and (C -> (C or D))) and (((E and F) -> F) and ((A -> (A or B)) and (C -> (C or D))))), M:tm-326, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26494
in-theory        26494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and (((E and F) -> E) and ((A -> (A or B)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26494.        (((A -> (A or B)) and (C -> (C or D))) and (((E and F) -> E) and ((A -> (A or B)) and (C -> (C or D))))), M:tm-325, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26495
in-theory        26495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and (C -> (C or D)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26495.        (((A -> (A or B)) and (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and (C -> (C or D))))), M:tm-324, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26496
in-theory        26496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and ((E -> (F -> E)) and ((A -> (A or B)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26496.        (((A -> (A or B)) and (C -> (C or D))) and ((E -> (F -> E)) and ((A -> (A or B)) and (C -> (C or D))))), M:tm-323, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26497
in-theory        26497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26497.        (((A -> (A or B)) and (C -> (C or D))) and ((E and F) -> F)), M:tm-322, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26498
in-theory        26498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26498.        (((A -> (A or B)) and (C -> (C or D))) and ((E and F) -> E)), M:tm-320, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26499
in-theory        26499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26499.        (((A -> (A or B)) and (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26500
in-theory        26500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26500.        (((A -> (A or B)) and (C -> (C or D))) and (E -> (F -> E))), M:tm-315, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26501
in-theory        26501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and (E or ((A -> (A or B)) and (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26501.        (((A -> (A or B)) and (C -> (C or D))) and (E or ((A -> (A or B)) and (C -> (C or D))))), M:tm-311, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26502
in-theory        26502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and (((A -> (A or B)) and (C -> (C or D))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26502.        (((A -> (A or B)) and (C -> (C or D))) and (((A -> (A or B)) and (C -> (C or D))) or E)), M:tm-310, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26503
in-theory        26503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and (E -> (((A -> (A or B)) and (C -> (C or D))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26503.        (((A -> (A or B)) and (C -> (C or D))) and (E -> (((A -> (A or B)) and (C -> (C or D))) and E))), M:tm-309, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26504
in-theory        26504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-308 tm-416 ((A (-> Am (or Am Bm))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26504.        (((A -> (A or B)) and (C -> (C or D))) and (C -> (C or D))), M:tm-308, m:tm-416, u:((A (-> Am (or Am Bm))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-26505
in-theory        26505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and (A -> (A or B)))
theorem-size     17
proof            (modus-ponens tm-307 tm-416 ((A (-> Am (or Am Bm))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26505.        (((A -> (A or B)) and (C -> (C or D))) and (A -> (A or B))), M:tm-307, m:tm-416, u:((A (-> Am (or Am Bm))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-26506
in-theory        26506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and (E -> ((A -> (A or B)) and (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26506.        (((A -> (A or B)) and (C -> (C or D))) and (E -> ((A -> (A or B)) and (C -> (C or D))))), M:tm-305, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26507
in-theory        26507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-303 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26507.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-303, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26508
in-theory        26508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-270 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26508.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-270, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26509
in-theory        26509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-239 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26509.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-239, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26510
in-theory        26510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-210 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26510.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (G or H)))), M:tm-210, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26511
in-theory        26511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-183 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26511.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-183, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26512
in-theory        26512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-157 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26512.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-157, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26513
in-theory        26513
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-147 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26513.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-147, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26514
in-theory        26514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-134 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26514.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-134, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26515
in-theory        26515
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-125 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26515.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-125, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26516
in-theory        26516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-113 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26516.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (G or H)))), M:tm-113, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26517
in-theory        26517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-105 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26517.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-105, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26518
in-theory        26518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-95 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26518.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (E or F)))), M:tm-95, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26519
in-theory        26519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-83 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26519.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-83, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26520
in-theory        26520
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-76 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26520.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (D or E)))), M:tm-76, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26521
in-theory        26521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-69 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26521.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (E or F)))), M:tm-69, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26522
in-theory        26522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-54 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26522.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-54, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26523
in-theory        26523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-42 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26523.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> (E or F)))), M:tm-42, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26524
in-theory        26524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-32 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26524.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> (E or F)))), M:tm-32, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26525
in-theory        26525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-23 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26525.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (E or F)))), M:tm-23, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26526
in-theory        26526
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-22 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26526.        (((A and B) -> B) and ((C -> (C or D)) and (E -> (E or F)))), M:tm-22, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26527
in-theory        26527
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-21 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26527.        (((A and B) -> A) and ((C -> (C or D)) and (E -> (E or F)))), M:tm-21, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26528
in-theory        26528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-20 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26528.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-20, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26529
in-theory        26529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-19 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26529.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (E or F)))), M:tm-19, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26530
in-theory        26530
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-7 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26530.        (A or ((B -> (B or C)) and (D -> (D or E)))), M:tm-7, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26531
in-theory        26531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-6 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26531.        (((A -> (A or B)) and (C -> (C or D))) or E), M:tm-6, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26532
in-theory        26532
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> (D or E))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26532.        (A -> (((B -> (B or C)) and (D -> (D or E))) and A)), M:tm-5, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26533
in-theory        26533
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-1 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26533.        (A -> ((B -> (B or C)) and (D -> (D or E)))), M:tm-1, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-26534
in-theory        26534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26534.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-409, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26535
in-theory        26535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26535.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-400, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26536
in-theory        26536
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26536.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-391, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26537
in-theory        26537
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26537.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-382, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26538
in-theory        26538
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26538.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (H or G)))), M:tm-373, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26539
in-theory        26539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26539.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-364, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26540
in-theory        26540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26540.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-354, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26541
in-theory        26541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26541.        (((A -> (A or B)) and (C -> (D or C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26542
in-theory        26542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26542.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (F or E)))), M:tm-338, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26543
in-theory        26543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and (C -> (D or C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26543.        (((A -> (A or B)) and (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and (C -> (D or C))))), M:tm-327, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26544
in-theory        26544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and (((E and F) -> F) and ((A -> (A or B)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26544.        (((A -> (A or B)) and (C -> (D or C))) and (((E and F) -> F) and ((A -> (A or B)) and (C -> (D or C))))), M:tm-326, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26545
in-theory        26545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and (((E and F) -> E) and ((A -> (A or B)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26545.        (((A -> (A or B)) and (C -> (D or C))) and (((E and F) -> E) and ((A -> (A or B)) and (C -> (D or C))))), M:tm-325, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26546
in-theory        26546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and (C -> (D or C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26546.        (((A -> (A or B)) and (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and (C -> (D or C))))), M:tm-324, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26547
in-theory        26547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and ((E -> (F -> E)) and ((A -> (A or B)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26547.        (((A -> (A or B)) and (C -> (D or C))) and ((E -> (F -> E)) and ((A -> (A or B)) and (C -> (D or C))))), M:tm-323, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26548
in-theory        26548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26548.        (((A -> (A or B)) and (C -> (D or C))) and ((E and F) -> F)), M:tm-322, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26549
in-theory        26549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26549.        (((A -> (A or B)) and (C -> (D or C))) and ((E and F) -> E)), M:tm-320, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26550
in-theory        26550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26550.        (((A -> (A or B)) and (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26551
in-theory        26551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26551.        (((A -> (A or B)) and (C -> (D or C))) and (E -> (F -> E))), M:tm-315, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26552
in-theory        26552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and (E or ((A -> (A or B)) and (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26552.        (((A -> (A or B)) and (C -> (D or C))) and (E or ((A -> (A or B)) and (C -> (D or C))))), M:tm-311, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26553
in-theory        26553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and (((A -> (A or B)) and (C -> (D or C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26553.        (((A -> (A or B)) and (C -> (D or C))) and (((A -> (A or B)) and (C -> (D or C))) or E)), M:tm-310, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26554
in-theory        26554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and (E -> (((A -> (A or B)) and (C -> (D or C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26554.        (((A -> (A or B)) and (C -> (D or C))) and (E -> (((A -> (A or B)) and (C -> (D or C))) and E))), M:tm-309, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26555
in-theory        26555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-308 tm-417 ((A (-> Am (or Am Bm))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26555.        (((A -> (A or B)) and (C -> (D or C))) and (C -> (D or C))), M:tm-308, m:tm-417, u:((A (-> Am (or Am Bm))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-26556
in-theory        26556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and (A -> (A or B)))
theorem-size     17
proof            (modus-ponens tm-307 tm-417 ((A (-> Am (or Am Bm))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26556.        (((A -> (A or B)) and (C -> (D or C))) and (A -> (A or B))), M:tm-307, m:tm-417, u:((A (-> Am (or Am Bm))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-26557
in-theory        26557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and (E -> ((A -> (A or B)) and (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26557.        (((A -> (A or B)) and (C -> (D or C))) and (E -> ((A -> (A or B)) and (C -> (D or C))))), M:tm-305, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26558
in-theory        26558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26558.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-303, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26559
in-theory        26559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26559.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-270, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26560
in-theory        26560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26560.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-239, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26561
in-theory        26561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26561.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (H or G)))), M:tm-210, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26562
in-theory        26562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26562.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-183, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26563
in-theory        26563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26563.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-157, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26564
in-theory        26564
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26564.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-147, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26565
in-theory        26565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26565.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-134, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26566
in-theory        26566
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26566.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-125, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26567
in-theory        26567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26567.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H or G)))), M:tm-113, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26568
in-theory        26568
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26568.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-105, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26569
in-theory        26569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26569.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (F or E)))), M:tm-95, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26570
in-theory        26570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26570.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-83, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26571
in-theory        26571
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26571.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (E or D)))), M:tm-76, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26572
in-theory        26572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-6 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26572.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (F or E)))), M:tm-69, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26573
in-theory        26573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26573.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-54, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26574
in-theory        26574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26574.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> (F or E)))), M:tm-42, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26575
in-theory        26575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26575.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> (F or E)))), M:tm-32, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26576
in-theory        26576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26576.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (F or E)))), M:tm-23, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26577
in-theory        26577
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26577.        (((A and B) -> B) and ((C -> (C or D)) and (E -> (F or E)))), M:tm-22, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26578
in-theory        26578
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26578.        (((A and B) -> A) and ((C -> (C or D)) and (E -> (F or E)))), M:tm-21, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26579
in-theory        26579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26579.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-20, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26580
in-theory        26580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26580.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (F or E)))), M:tm-19, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26581
in-theory        26581
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26581.        (A or ((B -> (B or C)) and (D -> (E or D)))), M:tm-7, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26582
in-theory        26582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26582.        (((A -> (A or B)) and (C -> (D or C))) or E), M:tm-6, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26583
in-theory        26583
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> (E or D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26583.        (A -> (((B -> (B or C)) and (D -> (E or D))) and A)), M:tm-5, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26584
in-theory        26584
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-1 tm-5 tm-6 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26584.        (A -> ((B -> (B or C)) and (D -> (E or D)))), M:tm-1, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-26585
in-theory        26585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26585.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-409, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26586
in-theory        26586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26586.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-400, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26587
in-theory        26587
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26587.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-391, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26588
in-theory        26588
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26588.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-382, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26589
in-theory        26589
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26589.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-373, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26590
in-theory        26590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26590.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-364, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26591
in-theory        26591
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26591.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-354, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26592
in-theory        26592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26592.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26593
in-theory        26593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26593.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-338, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26594
in-theory        26594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26594.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-327, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26595
in-theory        26595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26595.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-326, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26596
in-theory        26596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26596.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-325, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26597
in-theory        26597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26597.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-324, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26598
in-theory        26598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26598.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-323, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26599
in-theory        26599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26599.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26600
in-theory        26600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26600.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26601
in-theory        26601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26601.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26602
in-theory        26602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26602.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26603
in-theory        26603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F or ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26603.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F or ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-311, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26604
in-theory        26604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26604.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)), M:tm-310, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26605
in-theory        26605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26605.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and F))), M:tm-309, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26606
in-theory        26606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     33
proof            (modus-ponens tm-308 tm-418 ((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26606.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-308, m:tm-418, u:((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))
================================================================
tm-name          tm-26607
in-theory        26607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (A -> (A or B)))
theorem-size     25
proof            (modus-ponens tm-307 tm-418 ((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26607.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (A -> (A or B))), M:tm-307, m:tm-418, u:((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))
================================================================
tm-name          tm-26608
in-theory        26608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26608.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-305, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26609
in-theory        26609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26609.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-303, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26610
in-theory        26610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26610.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-270, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26611
in-theory        26611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26611.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-239, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26612
in-theory        26612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26612.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-210, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26613
in-theory        26613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26613.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-183, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26614
in-theory        26614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26614.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-157, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26615
in-theory        26615
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26615.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-147, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26616
in-theory        26616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26616.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-134, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26617
in-theory        26617
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26617.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-125, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26618
in-theory        26618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26618.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-113, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26619
in-theory        26619
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26619.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-105, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26620
in-theory        26620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26620.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-95, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26621
in-theory        26621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26621.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-83, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26622
in-theory        26622
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-10 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26622.        (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-76, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26623
in-theory        26623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-9 tm-6 tm-8)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26623.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-69, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26624
in-theory        26624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26624.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-54, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26625
in-theory        26625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26625.        ((A -> (B or A)) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-42, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26626
in-theory        26626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26626.        ((A -> (A or B)) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-32, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26627
in-theory        26627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26627.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-23, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26628
in-theory        26628
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26628.        (((A and B) -> B) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-22, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26629
in-theory        26629
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26629.        (((A and B) -> A) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-21, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26630
in-theory        26630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26630.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-20, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26631
in-theory        26631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26631.        ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-19, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26632
in-theory        26632
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-7 tm-5 tm-6 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26632.        (A or ((B -> (B or C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-7, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26633
in-theory        26633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-6 tm-5 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26633.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F), M:tm-6, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26634
in-theory        26634
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26634.        (A -> (((B -> (B or C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A)), M:tm-5, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26635
in-theory        26635
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-1 tm-5 tm-6 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-26635.        (A -> ((B -> (B or C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-1, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-26636
in-theory        26636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-409 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26636.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-409, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26637
in-theory        26637
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-400 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26637.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-400, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26638
in-theory        26638
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-391 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26638.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-391, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26639
in-theory        26639
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-382 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26639.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-382, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26640
in-theory        26640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-373 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26640.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-373, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26641
in-theory        26641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-364 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26641.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-364, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26642
in-theory        26642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-354 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26642.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-354, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26643
in-theory        26643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26643.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26644
in-theory        26644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-338 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26644.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-338, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26645
in-theory        26645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26645.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-327, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26646
in-theory        26646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> F) and ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26646.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> F) and ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-326, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26647
in-theory        26647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> E) and ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26647.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> E) and ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-325, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26648
in-theory        26648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26648.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-324, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26649
in-theory        26649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> E)) and ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26649.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> E)) and ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-323, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26650
in-theory        26650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26650.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> F)), M:tm-322, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26651
in-theory        26651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26651.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> E)), M:tm-320, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26652
in-theory        26652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26652.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26653
in-theory        26653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26653.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> E))), M:tm-315, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26654
in-theory        26654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E or ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26654.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E or ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-311, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26655
in-theory        26655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26655.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E)), M:tm-310, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26656
in-theory        26656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26656.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and E))), M:tm-309, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26657
in-theory        26657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     29
proof            (modus-ponens tm-308 tm-419 ((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26657.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-308, m:tm-419, u:((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))
================================================================
tm-name          tm-26658
in-theory        26658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (A -> (A or B)))
theorem-size     23
proof            (modus-ponens tm-307 tm-419 ((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26658.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (A -> (A or B))), M:tm-307, m:tm-419, u:((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))
================================================================
tm-name          tm-26659
in-theory        26659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26659.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-305, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26660
in-theory        26660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-303 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26660.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-303, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26661
in-theory        26661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-270 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26661.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-270, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26662
in-theory        26662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-239 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26662.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-239, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26663
in-theory        26663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-210 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26663.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-210, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26664
in-theory        26664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-183 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26664.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-183, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26665
in-theory        26665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-157 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26665.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-157, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26666
in-theory        26666
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-147 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26666.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-147, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26667
in-theory        26667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-134 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26667.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-134, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26668
in-theory        26668
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-125 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26668.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-125, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26669
in-theory        26669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-113 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26669.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-113, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26670
in-theory        26670
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     37
proof            (modus-ponens tm-105 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26670.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-105, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26671
in-theory        26671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-95 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26671.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-95, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26672
in-theory        26672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-83 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26672.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-83, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26673
in-theory        26673
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-76 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-10 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26673.        (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-76, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26674
in-theory        26674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     29
proof            (modus-ponens tm-69 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26674.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-69, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26675
in-theory        26675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-54 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26675.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-54, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26676
in-theory        26676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-42 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26676.        ((A -> (B or A)) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-42, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26677
in-theory        26677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-32 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26677.        ((A -> (A or B)) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-32, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26678
in-theory        26678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-23 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26678.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-23, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26679
in-theory        26679
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-22 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26679.        (((A and B) -> B) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-22, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26680
in-theory        26680
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-21 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26680.        (((A and B) -> A) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-21, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26681
in-theory        26681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-20 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26681.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-20, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26682
in-theory        26682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-19 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26682.        ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-19, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26683
in-theory        26683
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-7 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-7 tm-5 tm-6 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26683.        (A or ((B -> (B or C)) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-7, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26684
in-theory        26684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-6 tm-5 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26684.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E), M:tm-6, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26685
in-theory        26685
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26685.        (A -> (((B -> (B or C)) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and A)), M:tm-5, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26686
in-theory        26686
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-1 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-1 tm-5 tm-6 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-26686.        (A -> ((B -> (B or C)) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-1, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-26687
in-theory        26687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26687.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-409, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26688
in-theory        26688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26688.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-400, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26689
in-theory        26689
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26689.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-391, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26690
in-theory        26690
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26690.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-382, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26691
in-theory        26691
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26691.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((not (not G)) -> G))), M:tm-373, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26692
in-theory        26692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26692.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-364, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26693
in-theory        26693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26693.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-354, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26694
in-theory        26694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26694.        (((A -> (A or B)) and ((not (not C)) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26695
in-theory        26695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26695.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((not (not E)) -> E))), M:tm-338, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26696
in-theory        26696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and ((D -> (E -> (D and E))) and ((A -> (A or B)) and ((not (not C)) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26696.        (((A -> (A or B)) and ((not (not C)) -> C)) and ((D -> (E -> (D and E))) and ((A -> (A or B)) and ((not (not C)) -> C)))), M:tm-327, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26697
in-theory        26697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and (((D and E) -> E) and ((A -> (A or B)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26697.        (((A -> (A or B)) and ((not (not C)) -> C)) and (((D and E) -> E) and ((A -> (A or B)) and ((not (not C)) -> C)))), M:tm-326, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26698
in-theory        26698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and (((D and E) -> D) and ((A -> (A or B)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26698.        (((A -> (A or B)) and ((not (not C)) -> C)) and (((D and E) -> D) and ((A -> (A or B)) and ((not (not C)) -> C)))), M:tm-325, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26699
in-theory        26699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (A or B)) and ((not (not C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26699.        (((A -> (A or B)) and ((not (not C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (A or B)) and ((not (not C)) -> C)))), M:tm-324, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26700
in-theory        26700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and ((D -> (E -> D)) and ((A -> (A or B)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26700.        (((A -> (A or B)) and ((not (not C)) -> C)) and ((D -> (E -> D)) and ((A -> (A or B)) and ((not (not C)) -> C)))), M:tm-323, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26701
in-theory        26701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26701.        (((A -> (A or B)) and ((not (not C)) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26702
in-theory        26702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26702.        (((A -> (A or B)) and ((not (not C)) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26703
in-theory        26703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26703.        (((A -> (A or B)) and ((not (not C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26704
in-theory        26704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26704.        (((A -> (A or B)) and ((not (not C)) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26705
in-theory        26705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and (D or ((A -> (A or B)) and ((not (not C)) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26705.        (((A -> (A or B)) and ((not (not C)) -> C)) and (D or ((A -> (A or B)) and ((not (not C)) -> C)))), M:tm-311, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26706
in-theory        26706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and (((A -> (A or B)) and ((not (not C)) -> C)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26706.        (((A -> (A or B)) and ((not (not C)) -> C)) and (((A -> (A or B)) and ((not (not C)) -> C)) or D)), M:tm-310, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26707
in-theory        26707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and (D -> (((A -> (A or B)) and ((not (not C)) -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26707.        (((A -> (A or B)) and ((not (not C)) -> C)) and (D -> (((A -> (A or B)) and ((not (not C)) -> C)) and D))), M:tm-309, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26708
in-theory        26708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and ((not (not C)) -> C))
theorem-size     17
proof            (modus-ponens tm-308 tm-420 ((A (-> Am (or Am Bm))) (B (-> (not (not Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26708.        (((A -> (A or B)) and ((not (not C)) -> C)) and ((not (not C)) -> C)), M:tm-308, m:tm-420, u:((A (-> Am (or Am Bm))) (B (-> (not (not Cm)) Cm)))
================================================================
tm-name          tm-26709
in-theory        26709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and (A -> (A or B)))
theorem-size     17
proof            (modus-ponens tm-307 tm-420 ((A (-> Am (or Am Bm))) (B (-> (not (not Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26709.        (((A -> (A or B)) and ((not (not C)) -> C)) and (A -> (A or B))), M:tm-307, m:tm-420, u:((A (-> Am (or Am Bm))) (B (-> (not (not Cm)) Cm)))
================================================================
tm-name          tm-26710
in-theory        26710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and (D -> ((A -> (A or B)) and ((not (not C)) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26710.        (((A -> (A or B)) and ((not (not C)) -> C)) and (D -> ((A -> (A or B)) and ((not (not C)) -> C)))), M:tm-305, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26711
in-theory        26711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26711.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-303, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26712
in-theory        26712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26712.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-270, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26713
in-theory        26713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26713.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-239, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26714
in-theory        26714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26714.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((not (not G)) -> G))), M:tm-210, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26715
in-theory        26715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26715.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-183, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26716
in-theory        26716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26716.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-157, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26717
in-theory        26717
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26717.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-147, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26718
in-theory        26718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26718.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-134, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26719
in-theory        26719
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26719.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-125, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26720
in-theory        26720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26720.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((not (not G)) -> G))), M:tm-113, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26721
in-theory        26721
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-10)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26721.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-105, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26722
in-theory        26722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26722.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((not (not E)) -> E))), M:tm-95, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26723
in-theory        26723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26723.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-83, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26724
in-theory        26724
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((not (not D)) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26724.        (((not (not A)) -> A) and ((B -> (B or C)) and ((not (not D)) -> D))), M:tm-76, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26725
in-theory        26725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((not (not E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-6 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26725.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((not (not E)) -> E))), M:tm-69, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26726
in-theory        26726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26726.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-54, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26727
in-theory        26727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26727.        ((A -> (B or A)) and ((C -> (C or D)) and ((not (not E)) -> E))), M:tm-42, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26728
in-theory        26728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26728.        ((A -> (A or B)) and ((C -> (C or D)) and ((not (not E)) -> E))), M:tm-32, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26729
in-theory        26729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26729.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((not (not E)) -> E))), M:tm-23, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26730
in-theory        26730
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26730.        (((A and B) -> B) and ((C -> (C or D)) and ((not (not E)) -> E))), M:tm-22, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26731
in-theory        26731
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26731.        (((A and B) -> A) and ((C -> (C or D)) and ((not (not E)) -> E))), M:tm-21, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26732
in-theory        26732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26732.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-20, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26733
in-theory        26733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26733.        ((A -> (B -> A)) and ((C -> (C or D)) and ((not (not E)) -> E))), M:tm-19, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26734
in-theory        26734
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-7 tm-5 tm-6 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26734.        (A or ((B -> (B or C)) and ((not (not D)) -> D))), M:tm-7, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26735
in-theory        26735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-6 tm-5 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26735.        (((A -> (A or B)) and ((not (not C)) -> C)) or D), M:tm-6, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26736
in-theory        26736
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((not (not D)) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26736.        (A -> (((B -> (B or C)) and ((not (not D)) -> D)) and A)), M:tm-5, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26737
in-theory        26737
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-1 tm-5 tm-6 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-26737.        (A -> ((B -> (B or C)) and ((not (not D)) -> D))), M:tm-1, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-26738
in-theory        26738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26738.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-409, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26739
in-theory        26739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26739.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-400, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26740
in-theory        26740
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26740.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-391, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26741
in-theory        26741
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26741.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-382, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26742
in-theory        26742
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26742.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (I -> H))))), M:tm-373, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26743
in-theory        26743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26743.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-364, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26744
in-theory        26744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26744.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-354, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26745
in-theory        26745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26745.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26746
in-theory        26746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26746.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (G -> F))))), M:tm-338, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26747
in-theory        26747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> (D -> (E -> D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26747.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> (D -> (E -> D)))))), M:tm-327, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26748
in-theory        26748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26748.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> (D -> (E -> D)))))), M:tm-326, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26749
in-theory        26749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26749.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> (D -> (E -> D)))))), M:tm-325, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26750
in-theory        26750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> (D -> (E -> D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26750.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> (D -> (E -> D)))))), M:tm-324, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26751
in-theory        26751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26751.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> (D -> (E -> D)))))), M:tm-323, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26752
in-theory        26752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26752.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and ((F and G) -> G)), M:tm-322, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26753
in-theory        26753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26753.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and ((F and G) -> F)), M:tm-320, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26754
in-theory        26754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26754.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26755
in-theory        26755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26755.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (F -> (G -> F))), M:tm-315, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26756
in-theory        26756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (F or ((A -> (A or B)) and (C -> (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26756.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (F or ((A -> (A or B)) and (C -> (D -> (E -> D)))))), M:tm-311, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26757
in-theory        26757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (((A -> (A or B)) and (C -> (D -> (E -> D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26757.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (((A -> (A or B)) and (C -> (D -> (E -> D)))) or F)), M:tm-310, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26758
in-theory        26758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (F -> (((A -> (A or B)) and (C -> (D -> (E -> D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26758.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (F -> (((A -> (A or B)) and (C -> (D -> (E -> D)))) and F))), M:tm-309, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26759
in-theory        26759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (C -> (D -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-421 ((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26759.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (C -> (D -> (E -> D)))), M:tm-308, m:tm-421, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-26760
in-theory        26760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-421 ((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26760.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (A -> (A or B))), M:tm-307, m:tm-421, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-26761
in-theory        26761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (F -> ((A -> (A or B)) and (C -> (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26761.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (F -> ((A -> (A or B)) and (C -> (D -> (E -> D)))))), M:tm-305, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26762
in-theory        26762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26762.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-303, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26763
in-theory        26763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26763.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-270, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26764
in-theory        26764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26764.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-239, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26765
in-theory        26765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26765.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (H -> (I -> H))))), M:tm-210, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26766
in-theory        26766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26766.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-183, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26767
in-theory        26767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26767.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-157, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26768
in-theory        26768
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26768.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-147, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26769
in-theory        26769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26769.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-134, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26770
in-theory        26770
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26770.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-125, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26771
in-theory        26771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26771.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (I -> H))))), M:tm-113, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26772
in-theory        26772
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26772.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-105, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26773
in-theory        26773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26773.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (F -> (G -> F))))), M:tm-95, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26774
in-theory        26774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26774.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-83, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26775
in-theory        26775
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26775.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (E -> (F -> E))))), M:tm-76, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26776
in-theory        26776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-6 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26776.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (F -> (G -> F))))), M:tm-69, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26777
in-theory        26777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26777.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-54, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26778
in-theory        26778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26778.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> (F -> (G -> F))))), M:tm-42, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26779
in-theory        26779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26779.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> (F -> (G -> F))))), M:tm-32, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26780
in-theory        26780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26780.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (G -> F))))), M:tm-23, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26781
in-theory        26781
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26781.        (((A and B) -> B) and ((C -> (C or D)) and (E -> (F -> (G -> F))))), M:tm-22, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26782
in-theory        26782
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26782.        (((A and B) -> A) and ((C -> (C or D)) and (E -> (F -> (G -> F))))), M:tm-21, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26783
in-theory        26783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26783.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-20, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26784
in-theory        26784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26784.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (F -> (G -> F))))), M:tm-19, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26785
in-theory        26785
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-6 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26785.        (A or ((B -> (B or C)) and (D -> (E -> (F -> E))))), M:tm-7, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26786
in-theory        26786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26786.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) or F), M:tm-6, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26787
in-theory        26787
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> (E -> (F -> E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26787.        (A -> (((B -> (B or C)) and (D -> (E -> (F -> E)))) and A)), M:tm-5, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26788
in-theory        26788
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-26788.        (A -> ((B -> (B or C)) and (D -> (E -> (F -> E))))), M:tm-1, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-26789
in-theory        26789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26789.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-409, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26790
in-theory        26790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26790.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-400, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26791
in-theory        26791
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26791.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-391, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26792
in-theory        26792
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26792.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-382, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26793
in-theory        26793
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26793.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (G -> G)))), M:tm-373, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26794
in-theory        26794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26794.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-364, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26795
in-theory        26795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26795.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-354, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26796
in-theory        26796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26796.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26797
in-theory        26797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26797.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (E -> E)))), M:tm-338, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26798
in-theory        26798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and ((C -> D) -> (C -> C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26798.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and ((C -> D) -> (C -> C))))), M:tm-327, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26799
in-theory        26799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (((E and F) -> F) and ((A -> (A or B)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26799.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (((E and F) -> F) and ((A -> (A or B)) and ((C -> D) -> (C -> C))))), M:tm-326, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26800
in-theory        26800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (((E and F) -> E) and ((A -> (A or B)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26800.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (((E and F) -> E) and ((A -> (A or B)) and ((C -> D) -> (C -> C))))), M:tm-325, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26801
in-theory        26801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and ((C -> D) -> (C -> C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26801.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and ((C -> D) -> (C -> C))))), M:tm-324, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26802
in-theory        26802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((E -> (F -> E)) and ((A -> (A or B)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26802.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((E -> (F -> E)) and ((A -> (A or B)) and ((C -> D) -> (C -> C))))), M:tm-323, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26803
in-theory        26803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26803.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((E and F) -> F)), M:tm-322, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26804
in-theory        26804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26804.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((E and F) -> E)), M:tm-320, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26805
in-theory        26805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26805.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26806
in-theory        26806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26806.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (E -> (F -> E))), M:tm-315, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26807
in-theory        26807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (E or ((A -> (A or B)) and ((C -> D) -> (C -> C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26807.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (E or ((A -> (A or B)) and ((C -> D) -> (C -> C))))), M:tm-311, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26808
in-theory        26808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (((A -> (A or B)) and ((C -> D) -> (C -> C))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26808.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (((A -> (A or B)) and ((C -> D) -> (C -> C))) or E)), M:tm-310, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26809
in-theory        26809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (E -> (((A -> (A or B)) and ((C -> D) -> (C -> C))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26809.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (E -> (((A -> (A or B)) and ((C -> D) -> (C -> C))) and E))), M:tm-309, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26810
in-theory        26810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((C -> D) -> (C -> C)))
theorem-size     21
proof            (modus-ponens tm-308 tm-422 ((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> Cm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26810.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((C -> D) -> (C -> C))), M:tm-308, m:tm-422, u:((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> Cm Cm))))
================================================================
tm-name          tm-26811
in-theory        26811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-422 ((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> Cm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26811.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (A -> (A or B))), M:tm-307, m:tm-422, u:((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> Cm Cm))))
================================================================
tm-name          tm-26812
in-theory        26812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (E -> ((A -> (A or B)) and ((C -> D) -> (C -> C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26812.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (E -> ((A -> (A or B)) and ((C -> D) -> (C -> C))))), M:tm-305, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26813
in-theory        26813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26813.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-303, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26814
in-theory        26814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26814.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-270, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26815
in-theory        26815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26815.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-239, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26816
in-theory        26816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26816.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> H) -> (G -> G)))), M:tm-210, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26817
in-theory        26817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26817.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-183, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26818
in-theory        26818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26818.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-157, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26819
in-theory        26819
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26819.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-147, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26820
in-theory        26820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26820.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-134, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26821
in-theory        26821
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26821.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-125, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26822
in-theory        26822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26822.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (G -> G)))), M:tm-113, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26823
in-theory        26823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26823.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-105, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26824
in-theory        26824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26824.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> F) -> (E -> E)))), M:tm-95, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26825
in-theory        26825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26825.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-83, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26826
in-theory        26826
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> E) -> (D -> D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-10 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26826.        (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> E) -> (D -> D)))), M:tm-76, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26827
in-theory        26827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> F) -> (E -> E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-9 tm-6 tm-2 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26827.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> F) -> (E -> E)))), M:tm-69, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26828
in-theory        26828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26828.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-54, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26829
in-theory        26829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26829.        ((A -> (B or A)) and ((C -> (C or D)) and ((E -> F) -> (E -> E)))), M:tm-42, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26830
in-theory        26830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26830.        ((A -> (A or B)) and ((C -> (C or D)) and ((E -> F) -> (E -> E)))), M:tm-32, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26831
in-theory        26831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26831.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (E -> E)))), M:tm-23, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26832
in-theory        26832
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26832.        (((A and B) -> B) and ((C -> (C or D)) and ((E -> F) -> (E -> E)))), M:tm-22, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26833
in-theory        26833
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26833.        (((A and B) -> A) and ((C -> (C or D)) and ((E -> F) -> (E -> E)))), M:tm-21, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26834
in-theory        26834
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26834.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-20, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26835
in-theory        26835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26835.        ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> F) -> (E -> E)))), M:tm-19, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26836
in-theory        26836
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-7 tm-5 tm-6 tm-2 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26836.        (A or ((B -> (B or C)) and ((D -> E) -> (D -> D)))), M:tm-7, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26837
in-theory        26837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26837.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) or E), M:tm-6, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26838
in-theory        26838
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((D -> E) -> (D -> D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26838.        (A -> (((B -> (B or C)) and ((D -> E) -> (D -> D))) and A)), M:tm-5, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26839
in-theory        26839
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-1 tm-5 tm-6 tm-2)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-26839.        (A -> ((B -> (B or C)) and ((D -> E) -> (D -> D)))), M:tm-1, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-26840
in-theory        26840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-409 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26840.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-409, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26841
in-theory        26841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-400 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26841.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-400, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26842
in-theory        26842
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-391 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26842.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-391, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26843
in-theory        26843
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-382 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26843.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-382, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26844
in-theory        26844
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-373 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26844.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-373, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26845
in-theory        26845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-364 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26845.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-364, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26846
in-theory        26846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-354 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26846.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-354, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26847
in-theory        26847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     33
proof            (modus-ponens tm-341 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26847.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26848
in-theory        26848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-338 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26848.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-338, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26849
in-theory        26849
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     59
proof            (modus-ponens tm-327 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26849.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-327, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26850
in-theory        26850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> G) and ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-326 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26850.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> G) and ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-326, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26851
in-theory        26851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> F) and ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-325 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26851.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> F) and ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-325, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26852
in-theory        26852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     65
proof            (modus-ponens tm-324 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26852.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-324, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26853
in-theory        26853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-323 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26853.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-323, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26854
in-theory        26854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> G))
theorem-size     31
proof            (modus-ponens tm-322 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26854.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26855
in-theory        26855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> F))
theorem-size     31
proof            (modus-ponens tm-320 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26855.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26856
in-theory        26856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     39
proof            (modus-ponens tm-318 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26856.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26857
in-theory        26857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     31
proof            (modus-ponens tm-315 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26857.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26858
in-theory        26858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F or ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-311 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26858.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F or ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-311, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26859
in-theory        26859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F))
theorem-size     53
proof            (modus-ponens tm-310 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26859.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F)), M:tm-310, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26860
in-theory        26860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and F)))
theorem-size     55
proof            (modus-ponens tm-309 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26860.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and F))), M:tm-309, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26861
in-theory        26861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     45
proof            (modus-ponens tm-308 tm-423 ((A (-> Am (or Am Bm))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26861.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-308, m:tm-423, u:((A (-> Am (or Am Bm))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))
================================================================
tm-name          tm-26862
in-theory        26862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (A -> (A or B)))
theorem-size     31
proof            (modus-ponens tm-307 tm-423 ((A (-> Am (or Am Bm))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26862.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (A -> (A or B))), M:tm-307, m:tm-423, u:((A (-> Am (or Am Bm))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))
================================================================
tm-name          tm-26863
in-theory        26863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-305 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26863.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-305, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26864
in-theory        26864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-303 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26864.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-303, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26865
in-theory        26865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-270 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26865.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-270, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26866
in-theory        26866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-239 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26866.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-239, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26867
in-theory        26867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-210 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26867.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-210, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26868
in-theory        26868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-183 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26868.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-183, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26869
in-theory        26869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-157 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26869.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-157, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26870
in-theory        26870
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-147 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26870.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-147, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26871
in-theory        26871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-134 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26871.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-134, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26872
in-theory        26872
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-125 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26872.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-125, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26873
in-theory        26873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-113 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26873.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-113, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26874
in-theory        26874
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     45
proof            (modus-ponens tm-105 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26874.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-105, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26875
in-theory        26875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-95 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26875.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-95, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26876
in-theory        26876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-83 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26876.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-83, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26877
in-theory        26877
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-76 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26877.        (((not (not A)) -> A) and ((B -> (B or C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-76, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26878
in-theory        26878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     37
proof            (modus-ponens tm-69 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-6 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26878.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-69, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26879
in-theory        26879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-54 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26879.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-54, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26880
in-theory        26880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-42 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26880.        ((A -> (B or A)) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-42, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26881
in-theory        26881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-32 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26881.        ((A -> (A or B)) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-32, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26882
in-theory        26882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-23 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26882.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-23, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26883
in-theory        26883
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-22 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26883.        (((A and B) -> B) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-22, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26884
in-theory        26884
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-21 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26884.        (((A and B) -> A) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-21, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26885
in-theory        26885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-20 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26885.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-20, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26886
in-theory        26886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-19 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26886.        ((A -> (B -> A)) and ((C -> (C or D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-19, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26887
in-theory        26887
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-7 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-7 tm-5 tm-6 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26887.        (A or ((B -> (B or C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-7, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26888
in-theory        26888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F)
theorem-size     27
proof            (modus-ponens tm-6 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26888.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F), M:tm-6, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26889
in-theory        26889
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26889.        (A -> (((B -> (B or C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and A)), M:tm-5, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26890
in-theory        26890
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-1 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-1 tm-5 tm-6 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-26890.        (A -> ((B -> (B or C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-1, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-26891
in-theory        26891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26891.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-409, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26892
in-theory        26892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26892.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-400, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26893
in-theory        26893
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26893.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-391, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26894
in-theory        26894
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26894.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-382, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26895
in-theory        26895
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26895.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-373, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26896
in-theory        26896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26896.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-364, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26897
in-theory        26897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26897.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-354, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26898
in-theory        26898
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26898.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26899
in-theory        26899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26899.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-338, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26900
in-theory        26900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26900.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-327, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26901
in-theory        26901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26901.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-326, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26902
in-theory        26902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26902.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-325, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26903
in-theory        26903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26903.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-324, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26904
in-theory        26904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26904.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-323, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26905
in-theory        26905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26905.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26906
in-theory        26906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26906.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26907
in-theory        26907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26907.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26908
in-theory        26908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26908.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26909
in-theory        26909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26909.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-311, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26910
in-theory        26910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26910.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)), M:tm-310, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26911
in-theory        26911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26911.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G))), M:tm-309, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26912
in-theory        26912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-424 ((A (-> Am (or Am Bm))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26912.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-308, m:tm-424, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-26913
in-theory        26913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (A or B)))
theorem-size     27
proof            (modus-ponens tm-307 tm-424 ((A (-> Am (or Am Bm))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26913.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (A or B))), M:tm-307, m:tm-424, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-26914
in-theory        26914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26914.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-305, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26915
in-theory        26915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26915.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-303, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26916
in-theory        26916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26916.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-270, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26917
in-theory        26917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26917.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-239, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26918
in-theory        26918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26918.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-210, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26919
in-theory        26919
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26919.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-183, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26920
in-theory        26920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26920.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-157, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26921
in-theory        26921
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26921.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-147, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26922
in-theory        26922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26922.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-134, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26923
in-theory        26923
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26923.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-125, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26924
in-theory        26924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26924.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-113, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26925
in-theory        26925
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26925.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-105, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26926
in-theory        26926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26926.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-95, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26927
in-theory        26927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26927.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-83, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26928
in-theory        26928
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-10 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26928.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-76, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26929
in-theory        26929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-9 tm-6 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26929.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-69, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26930
in-theory        26930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26930.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-54, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26931
in-theory        26931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26931.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-42, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26932
in-theory        26932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26932.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-32, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26933
in-theory        26933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26933.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-23, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26934
in-theory        26934
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26934.        (((A and B) -> B) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-22, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26935
in-theory        26935
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26935.        (((A and B) -> A) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-21, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26936
in-theory        26936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26936.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-20, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26937
in-theory        26937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26937.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-19, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26938
in-theory        26938
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-7 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-7 tm-5 tm-6 tm-1 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26938.        (A or ((B -> (B or C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-7, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26939
in-theory        26939
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-6 tm-5 tm-1 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26939.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G), M:tm-6, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26940
in-theory        26940
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26940.        (A -> (((B -> (B or C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A)), M:tm-5, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26941
in-theory        26941
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-1 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-1 tm-5 tm-6 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-26941.        (A -> ((B -> (B or C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-1, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-26942
in-theory        26942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-409 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26942.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-409, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26943
in-theory        26943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-400 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26943.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-400, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26944
in-theory        26944
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-391 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26944.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-391, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26945
in-theory        26945
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-382 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26945.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-382, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26946
in-theory        26946
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-373 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26946.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-373, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26947
in-theory        26947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-364 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26947.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-364, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26948
in-theory        26948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-354 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26948.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-354, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26949
in-theory        26949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26949.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26950
in-theory        26950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-338 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26950.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-338, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26951
in-theory        26951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26951.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-327, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26952
in-theory        26952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> G) and ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26952.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> G) and ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-326, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26953
in-theory        26953
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> F) and ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26953.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> F) and ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-325, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26954
in-theory        26954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26954.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-324, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26955
in-theory        26955
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> F)) and ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26955.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> F)) and ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-323, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26956
in-theory        26956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26956.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26957
in-theory        26957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26957.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26958
in-theory        26958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26958.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26959
in-theory        26959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26959.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26960
in-theory        26960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F or ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26960.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F or ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-311, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26961
in-theory        26961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26961.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F)), M:tm-310, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26962
in-theory        26962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26962.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and F))), M:tm-309, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26963
in-theory        26963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     37
proof            (modus-ponens tm-308 tm-425 ((A (-> Am (or Am Bm))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26963.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-308, m:tm-425, u:((A (-> Am (or Am Bm))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))
================================================================
tm-name          tm-26964
in-theory        26964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (A -> (A or B)))
theorem-size     27
proof            (modus-ponens tm-307 tm-425 ((A (-> Am (or Am Bm))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26964.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (A -> (A or B))), M:tm-307, m:tm-425, u:((A (-> Am (or Am Bm))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))
================================================================
tm-name          tm-26965
in-theory        26965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26965.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-305, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26966
in-theory        26966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-303 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26966.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-303, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26967
in-theory        26967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-270 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26967.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-270, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26968
in-theory        26968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-239 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26968.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-239, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26969
in-theory        26969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-210 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26969.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-210, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26970
in-theory        26970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-183 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26970.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-183, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26971
in-theory        26971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-157 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26971.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-157, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26972
in-theory        26972
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-147 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26972.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-147, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26973
in-theory        26973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-134 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26973.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-134, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26974
in-theory        26974
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-125 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26974.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-125, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26975
in-theory        26975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-113 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26975.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-113, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26976
in-theory        26976
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     41
proof            (modus-ponens tm-105 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26976.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-105, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26977
in-theory        26977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-95 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26977.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-95, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26978
in-theory        26978
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-83 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26978.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-83, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26979
in-theory        26979
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     27
proof            (modus-ponens tm-76 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26979.        (((not (not A)) -> A) and ((B -> (B or C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-76, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26980
in-theory        26980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     33
proof            (modus-ponens tm-69 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-6 tm-2 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26980.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-69, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26981
in-theory        26981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-54 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26981.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-54, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26982
in-theory        26982
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-42 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26982.        ((A -> (B or A)) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-42, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26983
in-theory        26983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-32 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26983.        ((A -> (A or B)) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-32, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26984
in-theory        26984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-23 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26984.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-23, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26985
in-theory        26985
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-22 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26985.        (((A and B) -> B) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-22, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26986
in-theory        26986
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-21 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26986.        (((A and B) -> A) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-21, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26987
in-theory        26987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-20 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26987.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-20, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26988
in-theory        26988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-19 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26988.        ((A -> (B -> A)) and ((C -> (C or D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-19, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26989
in-theory        26989
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-7 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-6 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26989.        (A or ((B -> (B or C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-7, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26990
in-theory        26990
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26990.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F), M:tm-6, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26991
in-theory        26991
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26991.        (A -> (((B -> (B or C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and A)), M:tm-5, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26992
in-theory        26992
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-1 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-6 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-26992.        (A -> ((B -> (B or C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-1, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-26993
in-theory        26993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-409 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-26993.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-409, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-26994
in-theory        26994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-400 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-26994.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-400, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-26995
in-theory        26995
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-391 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-26995.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-391, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-26996
in-theory        26996
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-382 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-26996.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-382, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-26997
in-theory        26997
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-373 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-26997.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> ((H and I) -> H)))), M:tm-373, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-26998
in-theory        26998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-364 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-26998.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-364, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-26999
in-theory        26999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-354 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-26999.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-354, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27000
in-theory        27000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27000.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27001
in-theory        27001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-338 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27001.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> ((F and G) -> F)))), M:tm-338, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27002
in-theory        27002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> ((D and E) -> D)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27002.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> ((D and E) -> D))))), M:tm-327, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27003
in-theory        27003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27003.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> ((D and E) -> D))))), M:tm-326, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27004
in-theory        27004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27004.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> ((D and E) -> D))))), M:tm-325, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27005
in-theory        27005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> ((D and E) -> D)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27005.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> ((D and E) -> D))))), M:tm-324, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27006
in-theory        27006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27006.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> ((D and E) -> D))))), M:tm-323, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27007
in-theory        27007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27007.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27008
in-theory        27008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27008.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27009
in-theory        27009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27009.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27010
in-theory        27010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27010.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27011
in-theory        27011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and (F or ((A -> (A or B)) and (C -> ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27011.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and (F or ((A -> (A or B)) and (C -> ((D and E) -> D))))), M:tm-311, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27012
in-theory        27012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and (((A -> (A or B)) and (C -> ((D and E) -> D))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27012.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and (((A -> (A or B)) and (C -> ((D and E) -> D))) or F)), M:tm-310, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27013
in-theory        27013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and (F -> (((A -> (A or B)) and (C -> ((D and E) -> D))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27013.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and (F -> (((A -> (A or B)) and (C -> ((D and E) -> D))) and F))), M:tm-309, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27014
in-theory        27014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and (C -> ((D and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-308 tm-426 ((A (-> Am (or Am Bm))) (B (-> Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27014.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and (C -> ((D and E) -> D))), M:tm-308, m:tm-426, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-27015
in-theory        27015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-426 ((A (-> Am (or Am Bm))) (B (-> Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27015.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and (A -> (A or B))), M:tm-307, m:tm-426, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-27016
in-theory        27016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and (F -> ((A -> (A or B)) and (C -> ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27016.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and (F -> ((A -> (A or B)) and (C -> ((D and E) -> D))))), M:tm-305, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27017
in-theory        27017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-303 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27017.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-303, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27018
in-theory        27018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-270 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27018.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-270, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27019
in-theory        27019
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-239 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27019.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-239, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27020
in-theory        27020
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-210 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27020.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> ((H and I) -> H)))), M:tm-210, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27021
in-theory        27021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-183 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27021.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-183, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27022
in-theory        27022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-157 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27022.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-157, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27023
in-theory        27023
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-147 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27023.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-147, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27024
in-theory        27024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-134 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27024.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-134, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27025
in-theory        27025
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-125 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27025.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-125, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27026
in-theory        27026
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-113 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27026.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H and I) -> H)))), M:tm-113, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27027
in-theory        27027
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-105 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27027.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-105, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27028
in-theory        27028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-95 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27028.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> ((F and G) -> F)))), M:tm-95, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27029
in-theory        27029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-83 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27029.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-83, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27030
in-theory        27030
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-76 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27030.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> ((E and F) -> E)))), M:tm-76, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27031
in-theory        27031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-69 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-6 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27031.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> ((F and G) -> F)))), M:tm-69, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27032
in-theory        27032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-54 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27032.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-54, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27033
in-theory        27033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-42 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27033.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> ((F and G) -> F)))), M:tm-42, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27034
in-theory        27034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-32 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27034.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> ((F and G) -> F)))), M:tm-32, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27035
in-theory        27035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-23 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27035.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> ((F and G) -> F)))), M:tm-23, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27036
in-theory        27036
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-22 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27036.        (((A and B) -> B) and ((C -> (C or D)) and (E -> ((F and G) -> F)))), M:tm-22, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27037
in-theory        27037
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-21 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27037.        (((A and B) -> A) and ((C -> (C or D)) and (E -> ((F and G) -> F)))), M:tm-21, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27038
in-theory        27038
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-20 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27038.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-20, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27039
in-theory        27039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-19 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27039.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> ((F and G) -> F)))), M:tm-19, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27040
in-theory        27040
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-7 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-6 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27040.        (A or ((B -> (B or C)) and (D -> ((E and F) -> E)))), M:tm-7, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27041
in-theory        27041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27041.        (((A -> (A or B)) and (C -> ((D and E) -> D))) or F), M:tm-6, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27042
in-theory        27042
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> ((E and F) -> E))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27042.        (A -> (((B -> (B or C)) and (D -> ((E and F) -> E))) and A)), M:tm-5, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27043
in-theory        27043
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-1 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-6 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27043.        (A -> ((B -> (B or C)) and (D -> ((E and F) -> E)))), M:tm-1, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-27044
in-theory        27044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-409 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27044.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-409, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27045
in-theory        27045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-400 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27045.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-400, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27046
in-theory        27046
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-391 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27046.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-391, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27047
in-theory        27047
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-382 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27047.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-382, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27048
in-theory        27048
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-373 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27048.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-373, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27049
in-theory        27049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-364 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27049.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-364, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27050
in-theory        27050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-354 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27050.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-354, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27051
in-theory        27051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27051.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27052
in-theory        27052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-338 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27052.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-338, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27053
in-theory        27053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27053.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-327, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27054
in-theory        27054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> G) and ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27054.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> G) and ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-326, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27055
in-theory        27055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> F) and ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27055.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> F) and ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-325, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27056
in-theory        27056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27056.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-324, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27057
in-theory        27057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27057.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-323, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27058
in-theory        27058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27058.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27059
in-theory        27059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27059.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27060
in-theory        27060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27060.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27061
in-theory        27061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27061.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27062
in-theory        27062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F or ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27062.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F or ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-311, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27063
in-theory        27063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27063.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F)), M:tm-310, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27064
in-theory        27064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27064.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and F))), M:tm-309, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27065
in-theory        27065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     37
proof            (modus-ponens tm-308 tm-427 ((A (-> Am (or Am Bm))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27065.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-308, m:tm-427, u:((A (-> Am (or Am Bm))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))
================================================================
tm-name          tm-27066
in-theory        27066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (A -> (A or B)))
theorem-size     27
proof            (modus-ponens tm-307 tm-427 ((A (-> Am (or Am Bm))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27066.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (A -> (A or B))), M:tm-307, m:tm-427, u:((A (-> Am (or Am Bm))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))
================================================================
tm-name          tm-27067
in-theory        27067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27067.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-305, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27068
in-theory        27068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-303 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27068.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-303, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27069
in-theory        27069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-270 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27069.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-270, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27070
in-theory        27070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-239 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27070.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-239, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27071
in-theory        27071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-210 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27071.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-210, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27072
in-theory        27072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-183 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27072.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-183, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27073
in-theory        27073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-157 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27073.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-157, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27074
in-theory        27074
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-147 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27074.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-147, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27075
in-theory        27075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-134 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27075.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-134, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27076
in-theory        27076
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-125 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27076.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-125, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27077
in-theory        27077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-113 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27077.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-113, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27078
in-theory        27078
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     41
proof            (modus-ponens tm-105 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27078.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-105, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27079
in-theory        27079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-95 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27079.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-95, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27080
in-theory        27080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-83 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27080.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-83, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27081
in-theory        27081
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     27
proof            (modus-ponens tm-76 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-10 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27081.        (((not (not A)) -> A) and ((B -> (B or C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-76, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27082
in-theory        27082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     33
proof            (modus-ponens tm-69 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-9 tm-6 tm-2 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27082.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-69, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27083
in-theory        27083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-54 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27083.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-54, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27084
in-theory        27084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-42 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27084.        ((A -> (B or A)) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-42, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27085
in-theory        27085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-32 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27085.        ((A -> (A or B)) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-32, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27086
in-theory        27086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-23 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27086.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-23, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27087
in-theory        27087
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-22 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27087.        (((A and B) -> B) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-22, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27088
in-theory        27088
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-21 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27088.        (((A and B) -> A) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-21, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27089
in-theory        27089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-20 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27089.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-20, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27090
in-theory        27090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-19 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27090.        ((A -> (B -> A)) and ((C -> (C or D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-19, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27091
in-theory        27091
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-7 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-7 tm-5 tm-6 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27091.        (A or ((B -> (B or C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-7, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27092
in-theory        27092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-6 tm-5 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27092.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F), M:tm-6, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27093
in-theory        27093
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27093.        (A -> (((B -> (B or C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and A)), M:tm-5, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27094
in-theory        27094
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-1 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-1 tm-5 tm-6 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-27094.        (A -> ((B -> (B or C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-1, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-27095
in-theory        27095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-409 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27095.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-409, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27096
in-theory        27096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-400 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27096.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-400, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27097
in-theory        27097
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-391 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27097.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-391, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27098
in-theory        27098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-382 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27098.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-382, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27099
in-theory        27099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-373 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27099.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> ((H and I) -> I)))), M:tm-373, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27100
in-theory        27100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-364 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27100.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-364, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27101
in-theory        27101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-354 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27101.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-354, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27102
in-theory        27102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27102.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27103
in-theory        27103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-338 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27103.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> ((F and G) -> G)))), M:tm-338, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27104
in-theory        27104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> ((D and E) -> E)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27104.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> ((D and E) -> E))))), M:tm-327, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27105
in-theory        27105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27105.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> ((D and E) -> E))))), M:tm-326, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27106
in-theory        27106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27106.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> ((D and E) -> E))))), M:tm-325, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27107
in-theory        27107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> ((D and E) -> E)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27107.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> ((D and E) -> E))))), M:tm-324, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27108
in-theory        27108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27108.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> ((D and E) -> E))))), M:tm-323, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27109
in-theory        27109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27109.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27110
in-theory        27110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27110.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27111
in-theory        27111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27111.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27112
in-theory        27112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27112.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27113
in-theory        27113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and (F or ((A -> (A or B)) and (C -> ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27113.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and (F or ((A -> (A or B)) and (C -> ((D and E) -> E))))), M:tm-311, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27114
in-theory        27114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and (((A -> (A or B)) and (C -> ((D and E) -> E))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27114.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and (((A -> (A or B)) and (C -> ((D and E) -> E))) or F)), M:tm-310, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27115
in-theory        27115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and (F -> (((A -> (A or B)) and (C -> ((D and E) -> E))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27115.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and (F -> (((A -> (A or B)) and (C -> ((D and E) -> E))) and F))), M:tm-309, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27116
in-theory        27116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and (C -> ((D and E) -> E)))
theorem-size     21
proof            (modus-ponens tm-308 tm-428 ((A (-> Am (or Am Bm))) (B (-> Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27116.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and (C -> ((D and E) -> E))), M:tm-308, m:tm-428, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-27117
in-theory        27117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-428 ((A (-> Am (or Am Bm))) (B (-> Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27117.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and (A -> (A or B))), M:tm-307, m:tm-428, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-27118
in-theory        27118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and (F -> ((A -> (A or B)) and (C -> ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27118.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and (F -> ((A -> (A or B)) and (C -> ((D and E) -> E))))), M:tm-305, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27119
in-theory        27119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-303 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27119.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-303, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27120
in-theory        27120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-270 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27120.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-270, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27121
in-theory        27121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-239 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27121.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-239, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27122
in-theory        27122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-210 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27122.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> ((H and I) -> I)))), M:tm-210, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27123
in-theory        27123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-183 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27123.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-183, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27124
in-theory        27124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-157 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27124.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-157, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27125
in-theory        27125
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-147 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27125.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-147, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27126
in-theory        27126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-134 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27126.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-134, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27127
in-theory        27127
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-125 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27127.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-125, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27128
in-theory        27128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-113 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27128.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H and I) -> I)))), M:tm-113, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27129
in-theory        27129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-105 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27129.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-105, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27130
in-theory        27130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-95 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27130.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> ((F and G) -> G)))), M:tm-95, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27131
in-theory        27131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-83 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27131.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-83, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27132
in-theory        27132
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-76 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-10 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27132.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> ((E and F) -> F)))), M:tm-76, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27133
in-theory        27133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-69 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-9 tm-6 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27133.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> ((F and G) -> G)))), M:tm-69, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27134
in-theory        27134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-54 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27134.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-54, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27135
in-theory        27135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-42 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27135.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> ((F and G) -> G)))), M:tm-42, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27136
in-theory        27136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-32 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27136.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> ((F and G) -> G)))), M:tm-32, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27137
in-theory        27137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-23 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27137.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> ((F and G) -> G)))), M:tm-23, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27138
in-theory        27138
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-22 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27138.        (((A and B) -> B) and ((C -> (C or D)) and (E -> ((F and G) -> G)))), M:tm-22, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27139
in-theory        27139
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-21 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27139.        (((A and B) -> A) and ((C -> (C or D)) and (E -> ((F and G) -> G)))), M:tm-21, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27140
in-theory        27140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-20 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27140.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-20, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27141
in-theory        27141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-19 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27141.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> ((F and G) -> G)))), M:tm-19, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27142
in-theory        27142
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-7 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-7 tm-5 tm-6 tm-1 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27142.        (A or ((B -> (B or C)) and (D -> ((E and F) -> F)))), M:tm-7, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27143
in-theory        27143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-6 tm-5 tm-1 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27143.        (((A -> (A or B)) and (C -> ((D and E) -> E))) or F), M:tm-6, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27144
in-theory        27144
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> ((E and F) -> F))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27144.        (A -> (((B -> (B or C)) and (D -> ((E and F) -> F))) and A)), M:tm-5, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27145
in-theory        27145
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-1 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-1 tm-5 tm-6 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-27145.        (A -> ((B -> (B or C)) and (D -> ((E and F) -> F)))), M:tm-1, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-27146
in-theory        27146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27146.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-409, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27147
in-theory        27147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27147.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-400, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27148
in-theory        27148
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27148.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-391, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27149
in-theory        27149
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27149.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-382, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27150
in-theory        27150
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27150.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G)))), M:tm-373, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27151
in-theory        27151
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27151.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-364, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27152
in-theory        27152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27152.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-354, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27153
in-theory        27153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27153.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27154
in-theory        27154
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27154.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E)))), M:tm-338, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27155
in-theory        27155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27155.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))))), M:tm-327, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27156
in-theory        27156
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27156.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))))), M:tm-326, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27157
in-theory        27157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27157.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))))), M:tm-325, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27158
in-theory        27158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27158.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))))), M:tm-324, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27159
in-theory        27159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27159.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))))), M:tm-323, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27160
in-theory        27160
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27160.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27161
in-theory        27161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27161.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27162
in-theory        27162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27162.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27163
in-theory        27163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27163.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27164
in-theory        27164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (F or ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27164.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (F or ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))))), M:tm-311, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27165
in-theory        27165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27165.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) or F)), M:tm-310, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27166
in-theory        27166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (F -> (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27166.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (F -> (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and F))), M:tm-309, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27167
in-theory        27167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (C -> ((D -> (E -> D)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-429 ((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27167.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (C -> ((D -> (E -> D)) and C))), M:tm-308, m:tm-429, u:((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm))))
================================================================
tm-name          tm-27168
in-theory        27168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (A -> (A or B)))
theorem-size     21
proof            (modus-ponens tm-307 tm-429 ((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27168.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (A -> (A or B))), M:tm-307, m:tm-429, u:((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm))))
================================================================
tm-name          tm-27169
in-theory        27169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (F -> ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27169.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (F -> ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))))), M:tm-305, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27170
in-theory        27170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27170.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-303, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27171
in-theory        27171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27171.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-270, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27172
in-theory        27172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27172.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-239, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27173
in-theory        27173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27173.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G)))), M:tm-210, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27174
in-theory        27174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27174.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-183, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27175
in-theory        27175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27175.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-157, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27176
in-theory        27176
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27176.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-147, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27177
in-theory        27177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27177.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-134, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27178
in-theory        27178
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27178.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-125, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27179
in-theory        27179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27179.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G)))), M:tm-113, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27180
in-theory        27180
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27180.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-105, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27181
in-theory        27181
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27181.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E)))), M:tm-95, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27182
in-theory        27182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27182.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-83, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27183
in-theory        27183
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27183.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> ((E -> (F -> E)) and D)))), M:tm-76, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27184
in-theory        27184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-6 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27184.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E)))), M:tm-69, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27185
in-theory        27185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27185.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-54, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27186
in-theory        27186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27186.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E)))), M:tm-42, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27187
in-theory        27187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27187.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E)))), M:tm-32, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27188
in-theory        27188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27188.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E)))), M:tm-23, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27189
in-theory        27189
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27189.        (((A and B) -> B) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E)))), M:tm-22, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27190
in-theory        27190
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27190.        (((A and B) -> A) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E)))), M:tm-21, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27191
in-theory        27191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27191.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-20, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27192
in-theory        27192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27192.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> ((F -> (G -> F)) and E)))), M:tm-19, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27193
in-theory        27193
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-7 tm-5 tm-6 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27193.        (A or ((B -> (B or C)) and (D -> ((E -> (F -> E)) and D)))), M:tm-7, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27194
in-theory        27194
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27194.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) or F), M:tm-6, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27195
in-theory        27195
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> ((E -> (F -> E)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27195.        (A -> (((B -> (B or C)) and (D -> ((E -> (F -> E)) and D))) and A)), M:tm-5, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27196
in-theory        27196
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-27196.        (A -> ((B -> (B or C)) and (D -> ((E -> (F -> E)) and D)))), M:tm-1, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-27197
in-theory        27197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-409 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27197.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-409, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27198
in-theory        27198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-400 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27198.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-400, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27199
in-theory        27199
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-391 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27199.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-391, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27200
in-theory        27200
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-382 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27200.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-382, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27201
in-theory        27201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-373 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27201.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-373, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27202
in-theory        27202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-364 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27202.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-364, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27203
in-theory        27203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-354 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27203.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-354, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27204
in-theory        27204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27204.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27205
in-theory        27205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-338 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27205.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-338, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27206
in-theory        27206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27206.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-327, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27207
in-theory        27207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> H) and ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27207.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> H) and ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-326, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27208
in-theory        27208
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> G) and ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27208.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> G) and ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-325, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27209
in-theory        27209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27209.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-324, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27210
in-theory        27210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> G)) and ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27210.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> G)) and ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-323, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27211
in-theory        27211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27211.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> H)), M:tm-322, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27212
in-theory        27212
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27212.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> G)), M:tm-320, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27213
in-theory        27213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27213.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27214
in-theory        27214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27214.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> G))), M:tm-315, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27215
in-theory        27215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G or ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27215.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G or ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-311, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27216
in-theory        27216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27216.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G)), M:tm-310, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27217
in-theory        27217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27217.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and G))), M:tm-309, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27218
in-theory        27218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     41
proof            (modus-ponens tm-308 tm-430 ((A (-> Am (or Am Bm))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27218.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-308, m:tm-430, u:((A (-> Am (or Am Bm))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))
================================================================
tm-name          tm-27219
in-theory        27219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (A -> (A or B)))
theorem-size     29
proof            (modus-ponens tm-307 tm-430 ((A (-> Am (or Am Bm))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27219.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (A -> (A or B))), M:tm-307, m:tm-430, u:((A (-> Am (or Am Bm))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))
================================================================
tm-name          tm-27220
in-theory        27220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27220.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-305, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27221
in-theory        27221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-303 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27221.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-303, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27222
in-theory        27222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-270 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27222.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-270, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27223
in-theory        27223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-239 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27223.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-239, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27224
in-theory        27224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-210 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27224.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-210, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27225
in-theory        27225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-183 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27225.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-183, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27226
in-theory        27226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-157 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27226.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-157, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27227
in-theory        27227
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-147 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27227.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-147, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27228
in-theory        27228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-134 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27228.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-134, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27229
in-theory        27229
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-125 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27229.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-125, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27230
in-theory        27230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-113 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27230.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-113, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27231
in-theory        27231
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     43
proof            (modus-ponens tm-105 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27231.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-105, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27232
in-theory        27232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-95 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27232.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-95, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27233
in-theory        27233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-83 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27233.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-83, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27234
in-theory        27234
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-76 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-10 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27234.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-76, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27235
in-theory        27235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-69 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-9 tm-6 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27235.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-69, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27236
in-theory        27236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-54 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27236.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-54, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27237
in-theory        27237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-42 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27237.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-42, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27238
in-theory        27238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-32 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27238.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-32, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27239
in-theory        27239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-23 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27239.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-23, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27240
in-theory        27240
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-22 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27240.        (((A and B) -> B) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-22, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27241
in-theory        27241
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-21 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27241.        (((A and B) -> A) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-21, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27242
in-theory        27242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-20 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27242.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-20, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27243
in-theory        27243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-19 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27243.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-19, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27244
in-theory        27244
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-7 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-7 tm-5 tm-6 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27244.        (A or ((B -> (B or C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-7, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27245
in-theory        27245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27245.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G), M:tm-6, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27246
in-theory        27246
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27246.        (A -> (((B -> (B or C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and A)), M:tm-5, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27247
in-theory        27247
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-1 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-1 tm-5 tm-6 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-27247.        (A -> ((B -> (B or C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-1, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-27248
in-theory        27248
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27248.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-409, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27249
in-theory        27249
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27249.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-400, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27250
in-theory        27250
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27250.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-391, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27251
in-theory        27251
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27251.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-382, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27252
in-theory        27252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27252.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G)))), M:tm-373, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27253
in-theory        27253
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27253.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-364, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27254
in-theory        27254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27254.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-354, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27255
in-theory        27255
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27255.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27256
in-theory        27256
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27256.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E)))), M:tm-338, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27257
in-theory        27257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> (((D and E) -> D) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27257.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> (((D and E) -> D) and C))))), M:tm-327, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27258
in-theory        27258
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27258.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> (((D and E) -> D) and C))))), M:tm-326, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27259
in-theory        27259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27259.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> (((D and E) -> D) and C))))), M:tm-325, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27260
in-theory        27260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> (((D and E) -> D) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27260.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> (((D and E) -> D) and C))))), M:tm-324, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27261
in-theory        27261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27261.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> (((D and E) -> D) and C))))), M:tm-323, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27262
in-theory        27262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27262.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and ((F and G) -> G)), M:tm-322, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27263
in-theory        27263
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27263.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and ((F and G) -> F)), M:tm-320, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27264
in-theory        27264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27264.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27265
in-theory        27265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27265.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (F -> (G -> F))), M:tm-315, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27266
in-theory        27266
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (F or ((A -> (A or B)) and (C -> (((D and E) -> D) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27266.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (F or ((A -> (A or B)) and (C -> (((D and E) -> D) and C))))), M:tm-311, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27267
in-theory        27267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27267.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) or F)), M:tm-310, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27268
in-theory        27268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (F -> (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27268.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (F -> (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and F))), M:tm-309, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27269
in-theory        27269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (C -> (((D and E) -> D) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-431 ((A (-> Am (or Am Bm))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27269.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (C -> (((D and E) -> D) and C))), M:tm-308, m:tm-431, u:((A (-> Am (or Am Bm))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm))))
================================================================
tm-name          tm-27270
in-theory        27270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (A -> (A or B)))
theorem-size     21
proof            (modus-ponens tm-307 tm-431 ((A (-> Am (or Am Bm))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27270.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (A -> (A or B))), M:tm-307, m:tm-431, u:((A (-> Am (or Am Bm))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm))))
================================================================
tm-name          tm-27271
in-theory        27271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (F -> ((A -> (A or B)) and (C -> (((D and E) -> D) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27271.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (F -> ((A -> (A or B)) and (C -> (((D and E) -> D) and C))))), M:tm-305, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27272
in-theory        27272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27272.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-303, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27273
in-theory        27273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27273.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-270, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27274
in-theory        27274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27274.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-239, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27275
in-theory        27275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27275.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G)))), M:tm-210, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27276
in-theory        27276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27276.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-183, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27277
in-theory        27277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27277.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-157, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27278
in-theory        27278
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27278.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-147, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27279
in-theory        27279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27279.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-134, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27280
in-theory        27280
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27280.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-125, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27281
in-theory        27281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27281.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G)))), M:tm-113, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27282
in-theory        27282
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27282.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-105, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27283
in-theory        27283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27283.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E)))), M:tm-95, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27284
in-theory        27284
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27284.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-83, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27285
in-theory        27285
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-10 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27285.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (((E and F) -> E) and D)))), M:tm-76, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27286
in-theory        27286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-9 tm-6 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27286.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E)))), M:tm-69, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27287
in-theory        27287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27287.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-54, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27288
in-theory        27288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27288.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E)))), M:tm-42, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27289
in-theory        27289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27289.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E)))), M:tm-32, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27290
in-theory        27290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27290.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E)))), M:tm-23, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27291
in-theory        27291
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27291.        (((A and B) -> B) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E)))), M:tm-22, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27292
in-theory        27292
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27292.        (((A and B) -> A) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E)))), M:tm-21, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27293
in-theory        27293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27293.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-20, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27294
in-theory        27294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27294.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (((F and G) -> F) and E)))), M:tm-19, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27295
in-theory        27295
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-7 tm-5 tm-6 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27295.        (A or ((B -> (B or C)) and (D -> (((E and F) -> E) and D)))), M:tm-7, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27296
in-theory        27296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27296.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) or F), M:tm-6, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27297
in-theory        27297
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> (((E and F) -> E) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27297.        (A -> (((B -> (B or C)) and (D -> (((E and F) -> E) and D))) and A)), M:tm-5, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27298
in-theory        27298
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-1 tm-5 tm-6 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-27298.        (A -> ((B -> (B or C)) and (D -> (((E and F) -> E) and D)))), M:tm-1, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-27299
in-theory        27299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27299.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-409, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27300
in-theory        27300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27300.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-400, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27301
in-theory        27301
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27301.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-391, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27302
in-theory        27302
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27302.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-382, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27303
in-theory        27303
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27303.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G)))), M:tm-373, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27304
in-theory        27304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27304.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-364, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27305
in-theory        27305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27305.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-354, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27306
in-theory        27306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27306.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27307
in-theory        27307
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27307.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E)))), M:tm-338, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27308
in-theory        27308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> (((D and E) -> E) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27308.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> (((D and E) -> E) and C))))), M:tm-327, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27309
in-theory        27309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27309.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> (((D and E) -> E) and C))))), M:tm-326, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27310
in-theory        27310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27310.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> (((D and E) -> E) and C))))), M:tm-325, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27311
in-theory        27311
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> (((D and E) -> E) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27311.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> (((D and E) -> E) and C))))), M:tm-324, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27312
in-theory        27312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27312.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> (((D and E) -> E) and C))))), M:tm-323, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27313
in-theory        27313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27313.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and ((F and G) -> G)), M:tm-322, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27314
in-theory        27314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27314.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and ((F and G) -> F)), M:tm-320, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27315
in-theory        27315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27315.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27316
in-theory        27316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27316.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (F -> (G -> F))), M:tm-315, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27317
in-theory        27317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (F or ((A -> (A or B)) and (C -> (((D and E) -> E) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27317.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (F or ((A -> (A or B)) and (C -> (((D and E) -> E) and C))))), M:tm-311, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27318
in-theory        27318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27318.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) or F)), M:tm-310, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27319
in-theory        27319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (F -> (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27319.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (F -> (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and F))), M:tm-309, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27320
in-theory        27320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (C -> (((D and E) -> E) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-432 ((A (-> Am (or Am Bm))) (B (-> Cm (and (-> (and Dm Em) Em) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27320.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (C -> (((D and E) -> E) and C))), M:tm-308, m:tm-432, u:((A (-> Am (or Am Bm))) (B (-> Cm (and (-> (and Dm Em) Em) Cm))))
================================================================
tm-name          tm-27321
in-theory        27321
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (A -> (A or B)))
theorem-size     21
proof            (modus-ponens tm-307 tm-432 ((A (-> Am (or Am Bm))) (B (-> Cm (and (-> (and Dm Em) Em) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27321.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (A -> (A or B))), M:tm-307, m:tm-432, u:((A (-> Am (or Am Bm))) (B (-> Cm (and (-> (and Dm Em) Em) Cm))))
================================================================
tm-name          tm-27322
in-theory        27322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (F -> ((A -> (A or B)) and (C -> (((D and E) -> E) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27322.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (F -> ((A -> (A or B)) and (C -> (((D and E) -> E) and C))))), M:tm-305, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27323
in-theory        27323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27323.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-303, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27324
in-theory        27324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27324.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-270, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27325
in-theory        27325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27325.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-239, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27326
in-theory        27326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27326.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G)))), M:tm-210, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27327
in-theory        27327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27327.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-183, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27328
in-theory        27328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27328.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-157, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27329
in-theory        27329
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27329.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-147, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27330
in-theory        27330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27330.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-134, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27331
in-theory        27331
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27331.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-125, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27332
in-theory        27332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27332.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G)))), M:tm-113, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27333
in-theory        27333
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27333.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-105, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27334
in-theory        27334
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27334.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E)))), M:tm-95, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27335
in-theory        27335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27335.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-83, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27336
in-theory        27336
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-10 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27336.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (((E and F) -> F) and D)))), M:tm-76, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27337
in-theory        27337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-9 tm-6 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27337.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E)))), M:tm-69, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27338
in-theory        27338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27338.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-54, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27339
in-theory        27339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27339.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E)))), M:tm-42, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27340
in-theory        27340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27340.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E)))), M:tm-32, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27341
in-theory        27341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27341.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E)))), M:tm-23, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27342
in-theory        27342
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27342.        (((A and B) -> B) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E)))), M:tm-22, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27343
in-theory        27343
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27343.        (((A and B) -> A) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E)))), M:tm-21, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27344
in-theory        27344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27344.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-20, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27345
in-theory        27345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27345.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (((F and G) -> G) and E)))), M:tm-19, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27346
in-theory        27346
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-7 tm-5 tm-6 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27346.        (A or ((B -> (B or C)) and (D -> (((E and F) -> F) and D)))), M:tm-7, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27347
in-theory        27347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27347.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) or F), M:tm-6, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27348
in-theory        27348
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> (((E and F) -> F) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27348.        (A -> (((B -> (B or C)) and (D -> (((E and F) -> F) and D))) and A)), M:tm-5, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27349
in-theory        27349
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-1 tm-5 tm-6 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-27349.        (A -> ((B -> (B or C)) and (D -> (((E and F) -> F) and D)))), M:tm-1, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-27350
in-theory        27350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-409 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27350.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-409, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27351
in-theory        27351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-400 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27351.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-400, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27352
in-theory        27352
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-391 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27352.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-391, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27353
in-theory        27353
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-382 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27353.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-382, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27354
in-theory        27354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-373 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27354.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-373, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27355
in-theory        27355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-364 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27355.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-364, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27356
in-theory        27356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-354 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27356.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-354, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27357
in-theory        27357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27357.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27358
in-theory        27358
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-338 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27358.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-338, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27359
in-theory        27359
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27359.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-327, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27360
in-theory        27360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27360.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-326, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27361
in-theory        27361
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27361.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-325, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27362
in-theory        27362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27362.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-324, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27363
in-theory        27363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27363.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-323, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27364
in-theory        27364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27364.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> G)), M:tm-322, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27365
in-theory        27365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27365.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> F)), M:tm-320, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27366
in-theory        27366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27366.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27367
in-theory        27367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27367.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> F))), M:tm-315, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27368
in-theory        27368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (F or ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27368.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (F or ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-311, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27369
in-theory        27369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27369.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) or F)), M:tm-310, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27370
in-theory        27370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27370.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and F))), M:tm-309, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27371
in-theory        27371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     29
proof            (modus-ponens tm-308 tm-433 ((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27371.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-308, m:tm-433, u:((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))
================================================================
tm-name          tm-27372
in-theory        27372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (A -> (A or B)))
theorem-size     23
proof            (modus-ponens tm-307 tm-433 ((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27372.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (A -> (A or B))), M:tm-307, m:tm-433, u:((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))
================================================================
tm-name          tm-27373
in-theory        27373
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27373.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-305, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27374
in-theory        27374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-303 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27374.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-303, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27375
in-theory        27375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-270 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27375.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-270, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27376
in-theory        27376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-239 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27376.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-239, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27377
in-theory        27377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-210 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27377.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-210, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27378
in-theory        27378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-183 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27378.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-183, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27379
in-theory        27379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-157 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27379.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-157, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27380
in-theory        27380
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-147 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27380.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-147, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27381
in-theory        27381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-134 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27381.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-134, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27382
in-theory        27382
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-125 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27382.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-125, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27383
in-theory        27383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-113 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27383.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-113, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27384
in-theory        27384
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     37
proof            (modus-ponens tm-105 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27384.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-105, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27385
in-theory        27385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-95 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27385.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-95, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27386
in-theory        27386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-83 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27386.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-83, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27387
in-theory        27387
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-76 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27387.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-76, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27388
in-theory        27388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-69 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27388.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-69, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27389
in-theory        27389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-54 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27389.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-54, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27390
in-theory        27390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-42 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27390.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-42, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27391
in-theory        27391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-32 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27391.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-32, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27392
in-theory        27392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-23 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27392.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-23, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27393
in-theory        27393
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-22 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27393.        (((A and B) -> B) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-22, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27394
in-theory        27394
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-21 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27394.        (((A and B) -> A) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-21, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27395
in-theory        27395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-20 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27395.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-20, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27396
in-theory        27396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-19 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27396.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-19, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27397
in-theory        27397
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-7 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27397.        (A or ((B -> (B or C)) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-7, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27398
in-theory        27398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-6 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27398.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) or F), M:tm-6, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27399
in-theory        27399
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> ((E -> (F -> (E and F))) and D))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27399.        (A -> (((B -> (B or C)) and (D -> ((E -> (F -> (E and F))) and D))) and A)), M:tm-5, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27400
in-theory        27400
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-1 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-27400.        (A -> ((B -> (B or C)) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-1, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-27401
in-theory        27401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27401.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-409, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27402
in-theory        27402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27402.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-400, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27403
in-theory        27403
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27403.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-391, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27404
in-theory        27404
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27404.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-382, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27405
in-theory        27405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27405.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H))))), M:tm-373, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27406
in-theory        27406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27406.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-364, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27407
in-theory        27407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27407.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-354, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27408
in-theory        27408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27408.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27409
in-theory        27409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27409.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F))))), M:tm-338, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27410
in-theory        27410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27410.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))))), M:tm-327, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27411
in-theory        27411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> F) and ((A -> (A or B)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27411.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> F) and ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))))), M:tm-326, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27412
in-theory        27412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> E) and ((A -> (A or B)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27412.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> E) and ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))))), M:tm-325, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27413
in-theory        27413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27413.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))))), M:tm-324, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27414
in-theory        27414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> E)) and ((A -> (A or B)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27414.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> E)) and ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))))), M:tm-323, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27415
in-theory        27415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27415.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27416
in-theory        27416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27416.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27417
in-theory        27417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27417.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27418
in-theory        27418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27418.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27419
in-theory        27419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (E or ((A -> (A or B)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27419.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (E or ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))))), M:tm-311, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27420
in-theory        27420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27420.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) or E)), M:tm-310, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27421
in-theory        27421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (E -> (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27421.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (E -> (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and E))), M:tm-309, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27422
in-theory        27422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((C -> D) -> (C -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-308 tm-434 ((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27422.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((C -> D) -> (C -> (C and D)))), M:tm-308, m:tm-434, u:((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))
================================================================
tm-name          tm-27423
in-theory        27423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (A -> (A or B)))
theorem-size     21
proof            (modus-ponens tm-307 tm-434 ((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27423.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (A -> (A or B))), M:tm-307, m:tm-434, u:((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))
================================================================
tm-name          tm-27424
in-theory        27424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (E -> ((A -> (A or B)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27424.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (E -> ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))))), M:tm-305, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27425
in-theory        27425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27425.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-303, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27426
in-theory        27426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27426.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-270, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27427
in-theory        27427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27427.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-239, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27428
in-theory        27428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27428.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H))))), M:tm-210, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27429
in-theory        27429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27429.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-183, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27430
in-theory        27430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27430.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-157, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27431
in-theory        27431
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27431.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-147, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27432
in-theory        27432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27432.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-134, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27433
in-theory        27433
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27433.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-125, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27434
in-theory        27434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27434.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H))))), M:tm-113, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27435
in-theory        27435
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27435.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-105, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27436
in-theory        27436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27436.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F))))), M:tm-95, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27437
in-theory        27437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27437.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-83, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27438
in-theory        27438
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> E) -> (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27438.        (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> E) -> (D -> (D and E))))), M:tm-76, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27439
in-theory        27439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-6 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27439.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F))))), M:tm-69, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27440
in-theory        27440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27440.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-54, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27441
in-theory        27441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27441.        ((A -> (B or A)) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F))))), M:tm-42, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27442
in-theory        27442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27442.        ((A -> (A or B)) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F))))), M:tm-32, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27443
in-theory        27443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27443.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F))))), M:tm-23, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27444
in-theory        27444
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27444.        (((A and B) -> B) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F))))), M:tm-22, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27445
in-theory        27445
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27445.        (((A and B) -> A) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F))))), M:tm-21, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27446
in-theory        27446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27446.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-20, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27447
in-theory        27447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27447.        ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> F) -> (E -> (E and F))))), M:tm-19, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27448
in-theory        27448
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-7 tm-5 tm-6 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27448.        (A or ((B -> (B or C)) and ((D -> E) -> (D -> (D and E))))), M:tm-7, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27449
in-theory        27449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27449.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) or E), M:tm-6, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27450
in-theory        27450
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((D -> E) -> (D -> (D and E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27450.        (A -> (((B -> (B or C)) and ((D -> E) -> (D -> (D and E)))) and A)), M:tm-5, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27451
in-theory        27451
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-1 tm-5 tm-6 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-27451.        (A -> ((B -> (B or C)) and ((D -> E) -> (D -> (D and E))))), M:tm-1, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-27452
in-theory        27452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-409 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27452.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-409, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27453
in-theory        27453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-400 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27453.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-400, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27454
in-theory        27454
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-391 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27454.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-391, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27455
in-theory        27455
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-382 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27455.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-382, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27456
in-theory        27456
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-373 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27456.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I)))))), M:tm-373, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27457
in-theory        27457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-364 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27457.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-364, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27458
in-theory        27458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-354 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27458.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-354, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27459
in-theory        27459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27459.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27460
in-theory        27460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-338 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27460.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G)))))), M:tm-338, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27461
in-theory        27461
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27461.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))))), M:tm-327, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27462
in-theory        27462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27462.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))))), M:tm-326, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27463
in-theory        27463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27463.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))))), M:tm-325, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27464
in-theory        27464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27464.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))))), M:tm-324, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27465
in-theory        27465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27465.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))))), M:tm-323, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27466
in-theory        27466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27466.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> G)), M:tm-322, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27467
in-theory        27467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27467.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> F)), M:tm-320, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27468
in-theory        27468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27468.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27469
in-theory        27469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27469.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> F))), M:tm-315, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27470
in-theory        27470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (F or ((A -> (A or B)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27470.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (F or ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))))), M:tm-311, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27471
in-theory        27471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27471.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) or F)), M:tm-310, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27472
in-theory        27472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (F -> (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27472.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (F -> (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and F))), M:tm-309, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27473
in-theory        27473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (C -> (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-308 tm-435 ((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27473.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (C -> (D -> (E -> (D and E))))), M:tm-308, m:tm-435, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-27474
in-theory        27474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (A -> (A or B)))
theorem-size     21
proof            (modus-ponens tm-307 tm-435 ((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27474.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (A -> (A or B))), M:tm-307, m:tm-435, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-27475
in-theory        27475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (F -> ((A -> (A or B)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27475.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (F -> ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))))), M:tm-305, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27476
in-theory        27476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-303 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27476.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-303, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27477
in-theory        27477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-270 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27477.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-270, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27478
in-theory        27478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-239 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27478.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-239, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27479
in-theory        27479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-210 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27479.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I)))))), M:tm-210, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27480
in-theory        27480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-183 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27480.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-183, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27481
in-theory        27481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-157 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27481.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-157, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27482
in-theory        27482
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-147 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27482.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-147, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27483
in-theory        27483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-134 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27483.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-134, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27484
in-theory        27484
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-125 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27484.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-125, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27485
in-theory        27485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-113 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27485.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I)))))), M:tm-113, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27486
in-theory        27486
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-105 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27486.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-105, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27487
in-theory        27487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-95 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27487.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G)))))), M:tm-95, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27488
in-theory        27488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-83 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27488.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-83, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27489
in-theory        27489
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-76 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-10 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27489.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (E -> (F -> (E and F)))))), M:tm-76, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27490
in-theory        27490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-69 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-9 tm-6 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27490.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G)))))), M:tm-69, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27491
in-theory        27491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-54 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27491.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-54, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27492
in-theory        27492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-42 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27492.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G)))))), M:tm-42, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27493
in-theory        27493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-32 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27493.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G)))))), M:tm-32, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27494
in-theory        27494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-23 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27494.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G)))))), M:tm-23, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27495
in-theory        27495
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-22 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27495.        (((A and B) -> B) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G)))))), M:tm-22, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27496
in-theory        27496
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-21 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27496.        (((A and B) -> A) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G)))))), M:tm-21, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27497
in-theory        27497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-20 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27497.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-20, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27498
in-theory        27498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-19 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27498.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (F -> (G -> (F and G)))))), M:tm-19, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27499
in-theory        27499
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-7 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-7 tm-5 tm-6 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27499.        (A or ((B -> (B or C)) and (D -> (E -> (F -> (E and F)))))), M:tm-7, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27500
in-theory        27500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27500.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) or F), M:tm-6, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27501
in-theory        27501
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> (E -> (F -> (E and F))))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27501.        (A -> (((B -> (B or C)) and (D -> (E -> (F -> (E and F))))) and A)), M:tm-5, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27502
in-theory        27502
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-1 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-27502.        (A -> ((B -> (B or C)) and (D -> (E -> (F -> (E and F)))))), M:tm-1, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-27503
in-theory        27503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27503.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-409, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27504
in-theory        27504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27504.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-400, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27505
in-theory        27505
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27505.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-391, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27506
in-theory        27506
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27506.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-382, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27507
in-theory        27507
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27507.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> (H -> G)) or I))), M:tm-373, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27508
in-theory        27508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27508.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-364, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27509
in-theory        27509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27509.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-354, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27510
in-theory        27510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27510.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27511
in-theory        27511
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27511.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> (F -> E)) or G))), M:tm-338, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27512
in-theory        27512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> (D -> C)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27512.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> (D -> C)) or E)))), M:tm-327, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27513
in-theory        27513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27513.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> (D -> C)) or E)))), M:tm-326, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27514
in-theory        27514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27514.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> (D -> C)) or E)))), M:tm-325, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27515
in-theory        27515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> (D -> C)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27515.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> (D -> C)) or E)))), M:tm-324, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27516
in-theory        27516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27516.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> (D -> C)) or E)))), M:tm-323, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27517
in-theory        27517
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27517.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27518
in-theory        27518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27518.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27519
in-theory        27519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27519.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27520
in-theory        27520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27520.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27521
in-theory        27521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (F or ((A -> (A or B)) and ((C -> (D -> C)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27521.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (F or ((A -> (A or B)) and ((C -> (D -> C)) or E)))), M:tm-311, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27522
in-theory        27522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (((A -> (A or B)) and ((C -> (D -> C)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27522.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (((A -> (A or B)) and ((C -> (D -> C)) or E)) or F)), M:tm-310, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27523
in-theory        27523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (F -> (((A -> (A or B)) and ((C -> (D -> C)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27523.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (F -> (((A -> (A or B)) and ((C -> (D -> C)) or E)) and F))), M:tm-309, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27524
in-theory        27524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((C -> (D -> C)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-436 ((A (-> Am (or Am Bm))) (B (or (-> Cm (-> Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27524.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((C -> (D -> C)) or E)), M:tm-308, m:tm-436, u:((A (-> Am (or Am Bm))) (B (or (-> Cm (-> Dm Cm)) Em)))
================================================================
tm-name          tm-27525
in-theory        27525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-436 ((A (-> Am (or Am Bm))) (B (or (-> Cm (-> Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27525.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (A -> (A or B))), M:tm-307, m:tm-436, u:((A (-> Am (or Am Bm))) (B (or (-> Cm (-> Dm Cm)) Em)))
================================================================
tm-name          tm-27526
in-theory        27526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (F -> ((A -> (A or B)) and ((C -> (D -> C)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27526.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (F -> ((A -> (A or B)) and ((C -> (D -> C)) or E)))), M:tm-305, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27527
in-theory        27527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27527.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-303, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27528
in-theory        27528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27528.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-270, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27529
in-theory        27529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27529.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-239, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27530
in-theory        27530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27530.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> (H -> G)) or I))), M:tm-210, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27531
in-theory        27531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27531.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-183, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27532
in-theory        27532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27532.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-157, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27533
in-theory        27533
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27533.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-147, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27534
in-theory        27534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27534.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-134, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27535
in-theory        27535
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27535.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-125, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27536
in-theory        27536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27536.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H -> G)) or I))), M:tm-113, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27537
in-theory        27537
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27537.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-105, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27538
in-theory        27538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27538.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> (F -> E)) or G))), M:tm-95, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27539
in-theory        27539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27539.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-83, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27540
in-theory        27540
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> (E -> D)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-10 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27540.        (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> (E -> D)) or F))), M:tm-76, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27541
in-theory        27541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> (F -> E)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-9 tm-6 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27541.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> (F -> E)) or G))), M:tm-69, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27542
in-theory        27542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27542.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-54, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27543
in-theory        27543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27543.        ((A -> (B or A)) and ((C -> (C or D)) and ((E -> (F -> E)) or G))), M:tm-42, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27544
in-theory        27544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27544.        ((A -> (A or B)) and ((C -> (C or D)) and ((E -> (F -> E)) or G))), M:tm-32, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27545
in-theory        27545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27545.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> (F -> E)) or G))), M:tm-23, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27546
in-theory        27546
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27546.        (((A and B) -> B) and ((C -> (C or D)) and ((E -> (F -> E)) or G))), M:tm-22, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27547
in-theory        27547
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27547.        (((A and B) -> A) and ((C -> (C or D)) and ((E -> (F -> E)) or G))), M:tm-21, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27548
in-theory        27548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27548.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-20, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27549
in-theory        27549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27549.        ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> (F -> E)) or G))), M:tm-19, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27550
in-theory        27550
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-7 tm-5 tm-6 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27550.        (A or ((B -> (B or C)) and ((D -> (E -> D)) or F))), M:tm-7, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27551
in-theory        27551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27551.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) or F), M:tm-6, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27552
in-theory        27552
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((D -> (E -> D)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27552.        (A -> (((B -> (B or C)) and ((D -> (E -> D)) or F)) and A)), M:tm-5, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27553
in-theory        27553
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-27553.        (A -> ((B -> (B or C)) and ((D -> (E -> D)) or F))), M:tm-1, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-27554
in-theory        27554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27554.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-409, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27555
in-theory        27555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27555.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-400, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27556
in-theory        27556
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27556.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-391, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27557
in-theory        27557
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27557.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-382, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27558
in-theory        27558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27558.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-373, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27559
in-theory        27559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27559.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-364, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27560
in-theory        27560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27560.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-354, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27561
in-theory        27561
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27561.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27562
in-theory        27562
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27562.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-338, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27563
in-theory        27563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27563.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-327, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27564
in-theory        27564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> H) and ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27564.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> H) and ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-326, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27565
in-theory        27565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> G) and ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27565.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> G) and ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-325, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27566
in-theory        27566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27566.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-324, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27567
in-theory        27567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> G)) and ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27567.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> G)) and ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-323, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27568
in-theory        27568
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27568.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> H)), M:tm-322, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27569
in-theory        27569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27569.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> G)), M:tm-320, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27570
in-theory        27570
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27570.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27571
in-theory        27571
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27571.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> G))), M:tm-315, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27572
in-theory        27572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G or ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27572.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G or ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-311, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27573
in-theory        27573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27573.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G)), M:tm-310, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27574
in-theory        27574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27574.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and G))), M:tm-309, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27575
in-theory        27575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     37
proof            (modus-ponens tm-308 tm-437 ((A (-> Am (or Am Bm))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27575.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-308, m:tm-437, u:((A (-> Am (or Am Bm))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))
================================================================
tm-name          tm-27576
in-theory        27576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (A -> (A or B)))
theorem-size     27
proof            (modus-ponens tm-307 tm-437 ((A (-> Am (or Am Bm))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27576.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (A -> (A or B))), M:tm-307, m:tm-437, u:((A (-> Am (or Am Bm))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))
================================================================
tm-name          tm-27577
in-theory        27577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27577.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-305, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27578
in-theory        27578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27578.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-303, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27579
in-theory        27579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27579.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-270, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27580
in-theory        27580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27580.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-239, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27581
in-theory        27581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27581.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-210, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27582
in-theory        27582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27582.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-183, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27583
in-theory        27583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27583.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-157, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27584
in-theory        27584
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27584.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-147, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27585
in-theory        27585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27585.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-134, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27586
in-theory        27586
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27586.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-125, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27587
in-theory        27587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27587.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-113, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27588
in-theory        27588
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27588.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-105, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27589
in-theory        27589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27589.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-95, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27590
in-theory        27590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27590.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-83, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27591
in-theory        27591
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-10 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27591.        (((not (not A)) -> A) and ((B -> (B or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-76, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27592
in-theory        27592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-9 tm-6 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27592.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-69, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27593
in-theory        27593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27593.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-54, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27594
in-theory        27594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27594.        ((A -> (B or A)) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-42, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27595
in-theory        27595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27595.        ((A -> (A or B)) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-32, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27596
in-theory        27596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27596.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-23, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27597
in-theory        27597
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27597.        (((A and B) -> B) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-22, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27598
in-theory        27598
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27598.        (((A and B) -> A) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-21, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27599
in-theory        27599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27599.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-20, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27600
in-theory        27600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27600.        ((A -> (B -> A)) and ((C -> (C or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-19, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27601
in-theory        27601
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-7 tm-5 tm-6 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27601.        (A or ((B -> (B or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-7, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27602
in-theory        27602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27602.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G), M:tm-6, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27603
in-theory        27603
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27603.        (A -> (((B -> (B or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and A)), M:tm-5, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27604
in-theory        27604
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-1 tm-5 tm-6 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-27604.        (A -> ((B -> (B or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-1, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-27605
in-theory        27605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27605.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-409, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27606
in-theory        27606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27606.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-400, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27607
in-theory        27607
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27607.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-391, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27608
in-theory        27608
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27608.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-382, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27609
in-theory        27609
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27609.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G and H) -> G) or I))), M:tm-373, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27610
in-theory        27610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27610.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-364, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27611
in-theory        27611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27611.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-354, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27612
in-theory        27612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27612.        (((A -> (A or B)) and (((C and D) -> C) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27613
in-theory        27613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27613.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E and F) -> E) or G))), M:tm-338, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27614
in-theory        27614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C and D) -> C) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27614.        (((A -> (A or B)) and (((C and D) -> C) or E)) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C and D) -> C) or E)))), M:tm-327, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27615
in-theory        27615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and (((F and G) -> G) and ((A -> (A or B)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27615.        (((A -> (A or B)) and (((C and D) -> C) or E)) and (((F and G) -> G) and ((A -> (A or B)) and (((C and D) -> C) or E)))), M:tm-326, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27616
in-theory        27616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and (((F and G) -> F) and ((A -> (A or B)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27616.        (((A -> (A or B)) and (((C and D) -> C) or E)) and (((F and G) -> F) and ((A -> (A or B)) and (((C and D) -> C) or E)))), M:tm-325, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27617
in-theory        27617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C and D) -> C) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27617.        (((A -> (A or B)) and (((C and D) -> C) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C and D) -> C) or E)))), M:tm-324, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27618
in-theory        27618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27618.        (((A -> (A or B)) and (((C and D) -> C) or E)) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C and D) -> C) or E)))), M:tm-323, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27619
in-theory        27619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27619.        (((A -> (A or B)) and (((C and D) -> C) or E)) and ((F and G) -> G)), M:tm-322, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27620
in-theory        27620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27620.        (((A -> (A or B)) and (((C and D) -> C) or E)) and ((F and G) -> F)), M:tm-320, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27621
in-theory        27621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27621.        (((A -> (A or B)) and (((C and D) -> C) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27622
in-theory        27622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27622.        (((A -> (A or B)) and (((C and D) -> C) or E)) and (F -> (G -> F))), M:tm-315, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27623
in-theory        27623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and (F or ((A -> (A or B)) and (((C and D) -> C) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27623.        (((A -> (A or B)) and (((C and D) -> C) or E)) and (F or ((A -> (A or B)) and (((C and D) -> C) or E)))), M:tm-311, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27624
in-theory        27624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and (((A -> (A or B)) and (((C and D) -> C) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27624.        (((A -> (A or B)) and (((C and D) -> C) or E)) and (((A -> (A or B)) and (((C and D) -> C) or E)) or F)), M:tm-310, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27625
in-theory        27625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and (F -> (((A -> (A or B)) and (((C and D) -> C) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27625.        (((A -> (A or B)) and (((C and D) -> C) or E)) and (F -> (((A -> (A or B)) and (((C and D) -> C) or E)) and F))), M:tm-309, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27626
in-theory        27626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and (((C and D) -> C) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-438 ((A (-> Am (or Am Bm))) (B (or (-> (and Cm Dm) Cm) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27626.        (((A -> (A or B)) and (((C and D) -> C) or E)) and (((C and D) -> C) or E)), M:tm-308, m:tm-438, u:((A (-> Am (or Am Bm))) (B (or (-> (and Cm Dm) Cm) Em)))
================================================================
tm-name          tm-27627
in-theory        27627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-438 ((A (-> Am (or Am Bm))) (B (or (-> (and Cm Dm) Cm) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27627.        (((A -> (A or B)) and (((C and D) -> C) or E)) and (A -> (A or B))), M:tm-307, m:tm-438, u:((A (-> Am (or Am Bm))) (B (or (-> (and Cm Dm) Cm) Em)))
================================================================
tm-name          tm-27628
in-theory        27628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and (F -> ((A -> (A or B)) and (((C and D) -> C) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27628.        (((A -> (A or B)) and (((C and D) -> C) or E)) and (F -> ((A -> (A or B)) and (((C and D) -> C) or E)))), M:tm-305, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27629
in-theory        27629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27629.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-303, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27630
in-theory        27630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27630.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-270, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27631
in-theory        27631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27631.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-239, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27632
in-theory        27632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27632.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G and H) -> G) or I))), M:tm-210, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27633
in-theory        27633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27633.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-183, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27634
in-theory        27634
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27634.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-157, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27635
in-theory        27635
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27635.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-147, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27636
in-theory        27636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27636.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-134, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27637
in-theory        27637
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27637.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-125, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27638
in-theory        27638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27638.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G and H) -> G) or I))), M:tm-113, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27639
in-theory        27639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27639.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-105, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27640
in-theory        27640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27640.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E and F) -> E) or G))), M:tm-95, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27641
in-theory        27641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27641.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-83, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27642
in-theory        27642
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (((D and E) -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-10 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27642.        (((not (not A)) -> A) and ((B -> (B or C)) and (((D and E) -> D) or F))), M:tm-76, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27643
in-theory        27643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E and F) -> E) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-9 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27643.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E and F) -> E) or G))), M:tm-69, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27644
in-theory        27644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27644.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-54, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27645
in-theory        27645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27645.        ((A -> (B or A)) and ((C -> (C or D)) and (((E and F) -> E) or G))), M:tm-42, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27646
in-theory        27646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27646.        ((A -> (A or B)) and ((C -> (C or D)) and (((E and F) -> E) or G))), M:tm-32, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27647
in-theory        27647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27647.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E and F) -> E) or G))), M:tm-23, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27648
in-theory        27648
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27648.        (((A and B) -> B) and ((C -> (C or D)) and (((E and F) -> E) or G))), M:tm-22, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27649
in-theory        27649
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27649.        (((A and B) -> A) and ((C -> (C or D)) and (((E and F) -> E) or G))), M:tm-21, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27650
in-theory        27650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27650.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-20, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27651
in-theory        27651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27651.        ((A -> (B -> A)) and ((C -> (C or D)) and (((E and F) -> E) or G))), M:tm-19, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27652
in-theory        27652
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-7 tm-5 tm-6 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27652.        (A or ((B -> (B or C)) and (((D and E) -> D) or F))), M:tm-7, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27653
in-theory        27653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27653.        (((A -> (A or B)) and (((C and D) -> C) or E)) or F), M:tm-6, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27654
in-theory        27654
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (((D and E) -> D) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27654.        (A -> (((B -> (B or C)) and (((D and E) -> D) or F)) and A)), M:tm-5, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27655
in-theory        27655
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-1 tm-5 tm-6 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-27655.        (A -> ((B -> (B or C)) and (((D and E) -> D) or F))), M:tm-1, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-27656
in-theory        27656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27656.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-409, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27657
in-theory        27657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27657.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-400, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27658
in-theory        27658
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27658.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-391, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27659
in-theory        27659
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27659.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-382, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27660
in-theory        27660
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27660.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G and H) -> H) or I))), M:tm-373, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27661
in-theory        27661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27661.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-364, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27662
in-theory        27662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27662.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-354, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27663
in-theory        27663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27663.        (((A -> (A or B)) and (((C and D) -> D) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27664
in-theory        27664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27664.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E and F) -> F) or G))), M:tm-338, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27665
in-theory        27665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C and D) -> D) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27665.        (((A -> (A or B)) and (((C and D) -> D) or E)) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C and D) -> D) or E)))), M:tm-327, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27666
in-theory        27666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and (((F and G) -> G) and ((A -> (A or B)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27666.        (((A -> (A or B)) and (((C and D) -> D) or E)) and (((F and G) -> G) and ((A -> (A or B)) and (((C and D) -> D) or E)))), M:tm-326, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27667
in-theory        27667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and (((F and G) -> F) and ((A -> (A or B)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27667.        (((A -> (A or B)) and (((C and D) -> D) or E)) and (((F and G) -> F) and ((A -> (A or B)) and (((C and D) -> D) or E)))), M:tm-325, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27668
in-theory        27668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C and D) -> D) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27668.        (((A -> (A or B)) and (((C and D) -> D) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C and D) -> D) or E)))), M:tm-324, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27669
in-theory        27669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27669.        (((A -> (A or B)) and (((C and D) -> D) or E)) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C and D) -> D) or E)))), M:tm-323, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27670
in-theory        27670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27670.        (((A -> (A or B)) and (((C and D) -> D) or E)) and ((F and G) -> G)), M:tm-322, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27671
in-theory        27671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27671.        (((A -> (A or B)) and (((C and D) -> D) or E)) and ((F and G) -> F)), M:tm-320, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27672
in-theory        27672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27672.        (((A -> (A or B)) and (((C and D) -> D) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27673
in-theory        27673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27673.        (((A -> (A or B)) and (((C and D) -> D) or E)) and (F -> (G -> F))), M:tm-315, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27674
in-theory        27674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and (F or ((A -> (A or B)) and (((C and D) -> D) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27674.        (((A -> (A or B)) and (((C and D) -> D) or E)) and (F or ((A -> (A or B)) and (((C and D) -> D) or E)))), M:tm-311, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27675
in-theory        27675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and (((A -> (A or B)) and (((C and D) -> D) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27675.        (((A -> (A or B)) and (((C and D) -> D) or E)) and (((A -> (A or B)) and (((C and D) -> D) or E)) or F)), M:tm-310, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27676
in-theory        27676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and (F -> (((A -> (A or B)) and (((C and D) -> D) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27676.        (((A -> (A or B)) and (((C and D) -> D) or E)) and (F -> (((A -> (A or B)) and (((C and D) -> D) or E)) and F))), M:tm-309, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27677
in-theory        27677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and (((C and D) -> D) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-439 ((A (-> Am (or Am Bm))) (B (or (-> (and Cm Dm) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27677.        (((A -> (A or B)) and (((C and D) -> D) or E)) and (((C and D) -> D) or E)), M:tm-308, m:tm-439, u:((A (-> Am (or Am Bm))) (B (or (-> (and Cm Dm) Dm) Em)))
================================================================
tm-name          tm-27678
in-theory        27678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-439 ((A (-> Am (or Am Bm))) (B (or (-> (and Cm Dm) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27678.        (((A -> (A or B)) and (((C and D) -> D) or E)) and (A -> (A or B))), M:tm-307, m:tm-439, u:((A (-> Am (or Am Bm))) (B (or (-> (and Cm Dm) Dm) Em)))
================================================================
tm-name          tm-27679
in-theory        27679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and (F -> ((A -> (A or B)) and (((C and D) -> D) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27679.        (((A -> (A or B)) and (((C and D) -> D) or E)) and (F -> ((A -> (A or B)) and (((C and D) -> D) or E)))), M:tm-305, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27680
in-theory        27680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27680.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-303, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27681
in-theory        27681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27681.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-270, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27682
in-theory        27682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27682.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-239, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27683
in-theory        27683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27683.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G and H) -> H) or I))), M:tm-210, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27684
in-theory        27684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27684.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-183, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27685
in-theory        27685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27685.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-157, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27686
in-theory        27686
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27686.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-147, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27687
in-theory        27687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27687.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-134, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27688
in-theory        27688
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27688.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-125, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27689
in-theory        27689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27689.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G and H) -> H) or I))), M:tm-113, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27690
in-theory        27690
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27690.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-105, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27691
in-theory        27691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27691.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E and F) -> F) or G))), M:tm-95, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27692
in-theory        27692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27692.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-83, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27693
in-theory        27693
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (((D and E) -> E) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-10 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27693.        (((not (not A)) -> A) and ((B -> (B or C)) and (((D and E) -> E) or F))), M:tm-76, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27694
in-theory        27694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E and F) -> F) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-9 tm-6 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27694.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E and F) -> F) or G))), M:tm-69, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27695
in-theory        27695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27695.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-54, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27696
in-theory        27696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27696.        ((A -> (B or A)) and ((C -> (C or D)) and (((E and F) -> F) or G))), M:tm-42, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27697
in-theory        27697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27697.        ((A -> (A or B)) and ((C -> (C or D)) and (((E and F) -> F) or G))), M:tm-32, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27698
in-theory        27698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27698.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E and F) -> F) or G))), M:tm-23, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27699
in-theory        27699
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27699.        (((A and B) -> B) and ((C -> (C or D)) and (((E and F) -> F) or G))), M:tm-22, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27700
in-theory        27700
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27700.        (((A and B) -> A) and ((C -> (C or D)) and (((E and F) -> F) or G))), M:tm-21, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27701
in-theory        27701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27701.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-20, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27702
in-theory        27702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27702.        ((A -> (B -> A)) and ((C -> (C or D)) and (((E and F) -> F) or G))), M:tm-19, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27703
in-theory        27703
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-7 tm-5 tm-6 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27703.        (A or ((B -> (B or C)) and (((D and E) -> E) or F))), M:tm-7, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27704
in-theory        27704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27704.        (((A -> (A or B)) and (((C and D) -> D) or E)) or F), M:tm-6, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27705
in-theory        27705
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (((D and E) -> E) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27705.        (A -> (((B -> (B or C)) and (((D and E) -> E) or F)) and A)), M:tm-5, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27706
in-theory        27706
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-1 tm-5 tm-6 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-27706.        (A -> ((B -> (B or C)) and (((D and E) -> E) or F))), M:tm-1, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-27707
in-theory        27707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-409 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27707.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-409, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27708
in-theory        27708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-400 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27708.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-400, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27709
in-theory        27709
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-391 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27709.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-391, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27710
in-theory        27710
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-382 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27710.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-382, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27711
in-theory        27711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-373 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27711.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I))), M:tm-373, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27712
in-theory        27712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-364 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27712.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-364, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27713
in-theory        27713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-354 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27713.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-354, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27714
in-theory        27714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27714.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27715
in-theory        27715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-338 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27715.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G))), M:tm-338, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27716
in-theory        27716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> (D -> (C and D))) or E))))
theorem-size     39
proof            (modus-ponens tm-327 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27716.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)))), M:tm-327, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27717
in-theory        27717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-326 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27717.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)))), M:tm-326, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27718
in-theory        27718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-325 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27718.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)))), M:tm-325, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27719
in-theory        27719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> (D -> (C and D))) or E))))
theorem-size     45
proof            (modus-ponens tm-324 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27719.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)))), M:tm-324, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27720
in-theory        27720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-323 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27720.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)))), M:tm-323, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27721
in-theory        27721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27721.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> G)), M:tm-322, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27722
in-theory        27722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27722.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> F)), M:tm-320, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27723
in-theory        27723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27723.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27724
in-theory        27724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27724.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> F))), M:tm-315, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27725
in-theory        27725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (F or ((A -> (A or B)) and ((C -> (D -> (C and D))) or E))))
theorem-size     33
proof            (modus-ponens tm-311 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27725.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (F or ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)))), M:tm-311, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27726
in-theory        27726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27726.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) or F)), M:tm-310, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27727
in-theory        27727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (F -> (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27727.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (F -> (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and F))), M:tm-309, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27728
in-theory        27728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((C -> (D -> (C and D))) or E))
theorem-size     25
proof            (modus-ponens tm-308 tm-440 ((A (-> Am (or Am Bm))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27728.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((C -> (D -> (C and D))) or E)), M:tm-308, m:tm-440, u:((A (-> Am (or Am Bm))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em)))
================================================================
tm-name          tm-27729
in-theory        27729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (A -> (A or B)))
theorem-size     21
proof            (modus-ponens tm-307 tm-440 ((A (-> Am (or Am Bm))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27729.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (A -> (A or B))), M:tm-307, m:tm-440, u:((A (-> Am (or Am Bm))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em)))
================================================================
tm-name          tm-27730
in-theory        27730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (F -> ((A -> (A or B)) and ((C -> (D -> (C and D))) or E))))
theorem-size     33
proof            (modus-ponens tm-305 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27730.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (F -> ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)))), M:tm-305, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27731
in-theory        27731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-303 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27731.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-303, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27732
in-theory        27732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-270 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27732.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-270, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27733
in-theory        27733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-239 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27733.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-239, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27734
in-theory        27734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-210 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27734.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I))), M:tm-210, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27735
in-theory        27735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-183 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27735.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-183, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27736
in-theory        27736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-157 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27736.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-157, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27737
in-theory        27737
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-147 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27737.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-147, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27738
in-theory        27738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-134 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27738.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-134, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27739
in-theory        27739
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-125 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27739.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-125, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27740
in-theory        27740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-113 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27740.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I))), M:tm-113, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27741
in-theory        27741
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     35
proof            (modus-ponens tm-105 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27741.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-105, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27742
in-theory        27742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-95 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27742.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G))), M:tm-95, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27743
in-theory        27743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-83 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27743.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-83, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27744
in-theory        27744
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> (E -> (D and E))) or F)))
theorem-size     21
proof            (modus-ponens tm-76 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27744.        (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> (E -> (D and E))) or F))), M:tm-76, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27745
in-theory        27745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G)))
theorem-size     27
proof            (modus-ponens tm-69 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27745.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G))), M:tm-69, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27746
in-theory        27746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-54 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27746.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-54, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27747
in-theory        27747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-42 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27747.        ((A -> (B or A)) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G))), M:tm-42, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27748
in-theory        27748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-32 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27748.        ((A -> (A or B)) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G))), M:tm-32, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27749
in-theory        27749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-23 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27749.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G))), M:tm-23, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27750
in-theory        27750
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-22 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27750.        (((A and B) -> B) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G))), M:tm-22, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27751
in-theory        27751
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-21 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27751.        (((A and B) -> A) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G))), M:tm-21, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27752
in-theory        27752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-20 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27752.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-20, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27753
in-theory        27753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-19 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27753.        ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> (F -> (E and F))) or G))), M:tm-19, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27754
in-theory        27754
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-7 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27754.        (A or ((B -> (B or C)) and ((D -> (E -> (D and E))) or F))), M:tm-7, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27755
in-theory        27755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-6 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27755.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) or F), M:tm-6, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27756
in-theory        27756
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((D -> (E -> (D and E))) or F)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27756.        (A -> (((B -> (B or C)) and ((D -> (E -> (D and E))) or F)) and A)), M:tm-5, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27757
in-theory        27757
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-1 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-27757.        (A -> ((B -> (B or C)) and ((D -> (E -> (D and E))) or F))), M:tm-1, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-27758
in-theory        27758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27758.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-409, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27759
in-theory        27759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27759.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-400, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27760
in-theory        27760
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27760.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-391, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27761
in-theory        27761
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27761.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-382, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27762
in-theory        27762
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27762.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> (G or H)) or I))), M:tm-373, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27763
in-theory        27763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27763.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-364, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27764
in-theory        27764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27764.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-354, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27765
in-theory        27765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27765.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27766
in-theory        27766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27766.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> (E or F)) or G))), M:tm-338, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27767
in-theory        27767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> (C or D)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27767.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> (C or D)) or E)))), M:tm-327, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27768
in-theory        27768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27768.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> (C or D)) or E)))), M:tm-326, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27769
in-theory        27769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27769.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> (C or D)) or E)))), M:tm-325, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27770
in-theory        27770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> (C or D)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27770.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> (C or D)) or E)))), M:tm-324, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27771
in-theory        27771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27771.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> (C or D)) or E)))), M:tm-323, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27772
in-theory        27772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27772.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27773
in-theory        27773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27773.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27774
in-theory        27774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27774.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27775
in-theory        27775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27775.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27776
in-theory        27776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and (F or ((A -> (A or B)) and ((C -> (C or D)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27776.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and (F or ((A -> (A or B)) and ((C -> (C or D)) or E)))), M:tm-311, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27777
in-theory        27777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and (((A -> (A or B)) and ((C -> (C or D)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27777.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and (((A -> (A or B)) and ((C -> (C or D)) or E)) or F)), M:tm-310, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27778
in-theory        27778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and (F -> (((A -> (A or B)) and ((C -> (C or D)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27778.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and (F -> (((A -> (A or B)) and ((C -> (C or D)) or E)) and F))), M:tm-309, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27779
in-theory        27779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((C -> (C or D)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-441 ((A (-> Am (or Am Bm))) (B (or (-> Cm (or Cm Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27779.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((C -> (C or D)) or E)), M:tm-308, m:tm-441, u:((A (-> Am (or Am Bm))) (B (or (-> Cm (or Cm Dm)) Em)))
================================================================
tm-name          tm-27780
in-theory        27780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-441 ((A (-> Am (or Am Bm))) (B (or (-> Cm (or Cm Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27780.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and (A -> (A or B))), M:tm-307, m:tm-441, u:((A (-> Am (or Am Bm))) (B (or (-> Cm (or Cm Dm)) Em)))
================================================================
tm-name          tm-27781
in-theory        27781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and (F -> ((A -> (A or B)) and ((C -> (C or D)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27781.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and (F -> ((A -> (A or B)) and ((C -> (C or D)) or E)))), M:tm-305, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27782
in-theory        27782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27782.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-303, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27783
in-theory        27783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27783.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-270, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27784
in-theory        27784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27784.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-239, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27785
in-theory        27785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27785.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> (G or H)) or I))), M:tm-210, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27786
in-theory        27786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27786.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-183, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27787
in-theory        27787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27787.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-157, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27788
in-theory        27788
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27788.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-147, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27789
in-theory        27789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27789.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-134, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27790
in-theory        27790
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27790.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-125, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27791
in-theory        27791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27791.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (G or H)) or I))), M:tm-113, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27792
in-theory        27792
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27792.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-105, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27793
in-theory        27793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27793.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> (E or F)) or G))), M:tm-95, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27794
in-theory        27794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27794.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-83, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27795
in-theory        27795
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> (D or E)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27795.        (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> (D or E)) or F))), M:tm-76, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27796
in-theory        27796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> (E or F)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27796.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> (E or F)) or G))), M:tm-69, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27797
in-theory        27797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27797.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-54, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27798
in-theory        27798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27798.        ((A -> (B or A)) and ((C -> (C or D)) and ((E -> (E or F)) or G))), M:tm-42, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27799
in-theory        27799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27799.        ((A -> (A or B)) and ((C -> (C or D)) and ((E -> (E or F)) or G))), M:tm-32, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27800
in-theory        27800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27800.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> (E or F)) or G))), M:tm-23, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27801
in-theory        27801
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27801.        (((A and B) -> B) and ((C -> (C or D)) and ((E -> (E or F)) or G))), M:tm-22, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27802
in-theory        27802
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27802.        (((A and B) -> A) and ((C -> (C or D)) and ((E -> (E or F)) or G))), M:tm-21, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27803
in-theory        27803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27803.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-20, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27804
in-theory        27804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27804.        ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> (E or F)) or G))), M:tm-19, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27805
in-theory        27805
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27805.        (A or ((B -> (B or C)) and ((D -> (D or E)) or F))), M:tm-7, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27806
in-theory        27806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-6 tm-5)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27806.        (((A -> (A or B)) and ((C -> (C or D)) or E)) or F), M:tm-6, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27807
in-theory        27807
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((D -> (D or E)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27807.        (A -> (((B -> (B or C)) and ((D -> (D or E)) or F)) and A)), M:tm-5, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27808
in-theory        27808
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-27808.        (A -> ((B -> (B or C)) and ((D -> (D or E)) or F))), M:tm-1, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-27809
in-theory        27809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27809.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-409, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27810
in-theory        27810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27810.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-400, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27811
in-theory        27811
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27811.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-391, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27812
in-theory        27812
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27812.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-382, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27813
in-theory        27813
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27813.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G)))), M:tm-373, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27814
in-theory        27814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27814.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-364, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27815
in-theory        27815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27815.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-354, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27816
in-theory        27816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27816.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27817
in-theory        27817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27817.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E)))), M:tm-338, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27818
in-theory        27818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27818.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))))), M:tm-327, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27819
in-theory        27819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27819.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))))), M:tm-326, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27820
in-theory        27820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27820.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))))), M:tm-325, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27821
in-theory        27821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27821.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))))), M:tm-324, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27822
in-theory        27822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27822.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))))), M:tm-323, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27823
in-theory        27823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27823.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27824
in-theory        27824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27824.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27825
in-theory        27825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27825.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27826
in-theory        27826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27826.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27827
in-theory        27827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (F or ((A -> (A or B)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27827.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (F or ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))))), M:tm-311, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27828
in-theory        27828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27828.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) or F)), M:tm-310, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27829
in-theory        27829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (F -> (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27829.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (F -> (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and F))), M:tm-309, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27830
in-theory        27830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (C -> ((D -> (D or E)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-442 ((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27830.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (C -> ((D -> (D or E)) and C))), M:tm-308, m:tm-442, u:((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm))))
================================================================
tm-name          tm-27831
in-theory        27831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (A -> (A or B)))
theorem-size     21
proof            (modus-ponens tm-307 tm-442 ((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27831.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (A -> (A or B))), M:tm-307, m:tm-442, u:((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm))))
================================================================
tm-name          tm-27832
in-theory        27832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (F -> ((A -> (A or B)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27832.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (F -> ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))))), M:tm-305, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27833
in-theory        27833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27833.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-303, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27834
in-theory        27834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27834.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-270, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27835
in-theory        27835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27835.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-239, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27836
in-theory        27836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27836.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G)))), M:tm-210, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27837
in-theory        27837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27837.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-183, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27838
in-theory        27838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27838.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-157, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27839
in-theory        27839
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27839.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-147, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27840
in-theory        27840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27840.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-134, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27841
in-theory        27841
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27841.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-125, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27842
in-theory        27842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27842.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G)))), M:tm-113, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27843
in-theory        27843
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27843.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-105, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27844
in-theory        27844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27844.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E)))), M:tm-95, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27845
in-theory        27845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27845.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-83, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27846
in-theory        27846
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27846.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> ((E -> (E or F)) and D)))), M:tm-76, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27847
in-theory        27847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27847.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E)))), M:tm-69, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27848
in-theory        27848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27848.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-54, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27849
in-theory        27849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27849.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E)))), M:tm-42, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27850
in-theory        27850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27850.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E)))), M:tm-32, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27851
in-theory        27851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27851.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E)))), M:tm-23, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27852
in-theory        27852
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27852.        (((A and B) -> B) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E)))), M:tm-22, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27853
in-theory        27853
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27853.        (((A and B) -> A) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E)))), M:tm-21, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27854
in-theory        27854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27854.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-20, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27855
in-theory        27855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27855.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> ((F -> (F or G)) and E)))), M:tm-19, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27856
in-theory        27856
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27856.        (A or ((B -> (B or C)) and (D -> ((E -> (E or F)) and D)))), M:tm-7, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27857
in-theory        27857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-6 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27857.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) or F), M:tm-6, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27858
in-theory        27858
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> ((E -> (E or F)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27858.        (A -> (((B -> (B or C)) and (D -> ((E -> (E or F)) and D))) and A)), M:tm-5, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27859
in-theory        27859
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-27859.        (A -> ((B -> (B or C)) and (D -> ((E -> (E or F)) and D)))), M:tm-1, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-27860
in-theory        27860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (A -> (B -> A))))
theorem-size     17
proof            (modus-ponens tm-443 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-27860.        ((A -> (B -> A)) and ((C -> (C or D)) and (A -> (B -> A)))), M:tm-443, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-27861
in-theory        27861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-27861.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))), M:tm-443, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-27862
in-theory        27862
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((A and B) -> A)))
theorem-size     17
proof            (modus-ponens tm-443 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-27862.        (((A and B) -> A) and ((C -> (C or D)) and ((A and B) -> A))), M:tm-443, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-27863
in-theory        27863
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((A and B) -> B)))
theorem-size     17
proof            (modus-ponens tm-443 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-27863.        (((A and B) -> B) and ((C -> (C or D)) and ((A and B) -> B))), M:tm-443, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-27864
in-theory        27864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (A -> (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-443 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-27864.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (A -> (B -> (A and B))))), M:tm-443, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-27865
in-theory        27865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (A -> (A or B))))
theorem-size     17
proof            (modus-ponens tm-443 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-27865.        ((A -> (A or B)) and ((C -> (C or D)) and (A -> (A or B)))), M:tm-443, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-27866
in-theory        27866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (A -> (B or A))))
theorem-size     17
proof            (modus-ponens tm-443 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-27866.        ((A -> (B or A)) and ((C -> (C or D)) and (A -> (B or A)))), M:tm-443, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-27867
in-theory        27867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-27867.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))), M:tm-443, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-27868
in-theory        27868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((A -> B) -> ((A -> (not B)) -> (not A)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-27868.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((A -> B) -> ((A -> (not B)) -> (not A))))), M:tm-443, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-27869
in-theory        27869
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((not (not A)) -> A)))
theorem-size     17
proof            (modus-ponens tm-443 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-27869.        (((not (not A)) -> A) and ((B -> (B or C)) and ((not (not A)) -> A))), M:tm-443, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-27870
in-theory        27870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (A -> (B -> (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-443 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-27870.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (A -> (B -> (C -> B))))), M:tm-443, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-27871
in-theory        27871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((A -> B) -> (A -> A))))
theorem-size     21
proof            (modus-ponens tm-443 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-27871.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((A -> B) -> (A -> A)))), M:tm-443, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-27872
in-theory        27872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-27872.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-443, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-27873
in-theory        27873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27873.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-443, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-27874
in-theory        27874
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))))
theorem-size     37
proof            (modus-ponens tm-443 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-27874.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)))), M:tm-443, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-27875
in-theory        27875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (A -> ((B and C) -> B))))
theorem-size     21
proof            (modus-ponens tm-443 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-27875.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (A -> ((B and C) -> B)))), M:tm-443, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-27876
in-theory        27876
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-443 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-27876.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)))), M:tm-443, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-27877
in-theory        27877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (A -> ((B and C) -> C))))
theorem-size     21
proof            (modus-ponens tm-443 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-27877.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (A -> ((B and C) -> C)))), M:tm-443, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-27878
in-theory        27878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (A -> ((B -> (C -> B)) and A))))
theorem-size     25
proof            (modus-ponens tm-443 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-27878.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (A -> ((B -> (C -> B)) and A)))), M:tm-443, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-27879
in-theory        27879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     41
proof            (modus-ponens tm-443 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27879.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-443, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-27880
in-theory        27880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (A -> (((B and C) -> B) and A))))
theorem-size     25
proof            (modus-ponens tm-443 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-27880.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (A -> (((B and C) -> B) and A)))), M:tm-443, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-27881
in-theory        27881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (A -> (((B and C) -> C) and A))))
theorem-size     25
proof            (modus-ponens tm-443 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-27881.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (A -> (((B and C) -> C) and A)))), M:tm-443, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-27882
in-theory        27882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (A -> ((B -> (C -> (B and C))) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-27882.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (A -> ((B -> (C -> (B and C))) and A)))), M:tm-443, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-27883
in-theory        27883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((A -> B) -> (A -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-27883.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((A -> B) -> (A -> (A and B))))), M:tm-443, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-27884
in-theory        27884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (A -> (B -> (C -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-27884.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (A -> (B -> (C -> (B and C)))))), M:tm-443, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-27885
in-theory        27885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((A -> (B -> A)) or C)))
theorem-size     21
proof            (modus-ponens tm-443 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-27885.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((A -> (B -> A)) or C))), M:tm-443, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-27886
in-theory        27886
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)))
theorem-size     37
proof            (modus-ponens tm-443 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27886.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D))), M:tm-443, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-27887
in-theory        27887
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (((A and B) -> A) or C)))
theorem-size     21
proof            (modus-ponens tm-443 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-27887.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (((A and B) -> A) or C))), M:tm-443, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-27888
in-theory        27888
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (((A and B) -> B) or C)))
theorem-size     21
proof            (modus-ponens tm-443 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-27888.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (((A and B) -> B) or C))), M:tm-443, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-27889
in-theory        27889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((A -> (B -> (A and B))) or C)))
theorem-size     25
proof            (modus-ponens tm-443 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-27889.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((A -> (B -> (A and B))) or C))), M:tm-443, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-27890
in-theory        27890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((A -> (A or B)) or C)))
theorem-size     21
proof            (modus-ponens tm-443 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27890.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((A -> (A or B)) or C))), M:tm-443, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-27891
in-theory        27891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (A -> ((B -> (B or C)) and A))))
theorem-size     25
proof            (modus-ponens tm-443 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-27891.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (A -> ((B -> (B or C)) and A)))), M:tm-443, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-27892
in-theory        27892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (A -> (B -> (B or C)))))
theorem-size     21
proof            (modus-ponens tm-443 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27892.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (A -> (B -> (B or C))))), M:tm-443, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-27893
in-theory        27893
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (A or (B -> (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-443 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-27893.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (A or (B -> (C -> B))))), M:tm-443, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-27894
in-theory        27894
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27894.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-443, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-27895
in-theory        27895
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (A or ((B and C) -> B))))
theorem-size     21
proof            (modus-ponens tm-443 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-27895.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (A or ((B and C) -> B)))), M:tm-443, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-27896
in-theory        27896
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (A or ((B and C) -> C))))
theorem-size     21
proof            (modus-ponens tm-443 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-27896.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (A or ((B and C) -> C)))), M:tm-443, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-27897
in-theory        27897
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (A or (B -> (C -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-27897.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (A or (B -> (C -> (B and C)))))), M:tm-443, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-27898
in-theory        27898
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (A or (B -> (B or C)))))
theorem-size     21
proof            (modus-ponens tm-443 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27898.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (A or (B -> (B or C))))), M:tm-443, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-27899
in-theory        27899
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (A or (B -> (C or B)))))
theorem-size     21
proof            (modus-ponens tm-443 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-27899.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (A or (B -> (C or B))))), M:tm-443, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-27900
in-theory        27900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((A -> (B or A)) or C)))
theorem-size     21
proof            (modus-ponens tm-443 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-27900.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((A -> (B or A)) or C))), M:tm-443, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-27901
in-theory        27901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (A -> ((B -> (C or B)) and A))))
theorem-size     25
proof            (modus-ponens tm-443 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-27901.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (A -> ((B -> (C or B)) and A)))), M:tm-443, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-27902
in-theory        27902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (A -> (B -> (C or B)))))
theorem-size     21
proof            (modus-ponens tm-443 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-27902.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (A -> (B -> (C or B))))), M:tm-443, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-27903
in-theory        27903
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((A -> B) -> C) -> ((B or (A -> B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-443 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-27903.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((A -> B) -> C) -> ((B or (A -> B)) -> C)))), M:tm-443, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-27904
in-theory        27904
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     57
proof            (modus-ponens tm-443 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-27904.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-443, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-27905
in-theory        27905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((A -> B) -> (((A and C) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-443 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-27905.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((A -> B) -> (((A and C) or A) -> B)))), M:tm-443, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-27906
in-theory        27906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((A -> B) -> (((C and A) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-443 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-27906.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (D or E)) and ((A -> B) -> (((C and A) or A) -> B)))), M:tm-443, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-27907
in-theory        27907
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-443 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-27907.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (D or E)) and (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)))), M:tm-443, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-27908
in-theory        27908
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((A or B) -> C) -> ((A or (A or B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-443 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-27908.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (D or E)) and (((A or B) -> C) -> ((A or (A or B)) -> C)))), M:tm-443, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-27909
in-theory        27909
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((A or B) -> C) -> ((B or (A or B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-443 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-27909.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (D or E)) and (((A or B) -> C) -> ((B or (A or B)) -> C)))), M:tm-443, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-27910
in-theory        27910
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     61
proof            (modus-ponens tm-443 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-27910.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (E or F)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-443, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-27911
in-theory        27911
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-27911.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-443, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-27912
in-theory        27912
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)))
theorem-size     37
proof            (modus-ponens tm-443 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-27912.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (E or F)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D))), M:tm-443, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-27913
in-theory        27913
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((E -> (E or F)) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))))
theorem-size     41
proof            (modus-ponens tm-443 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-27913.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((E -> (E or F)) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)))), M:tm-443, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-27914
in-theory        27914
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((D -> (D or E)) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-27914.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((D -> (D or E)) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))))), M:tm-443, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-27915
in-theory        27915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-27915.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (E or F)) and (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-443, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-27916
in-theory        27916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and ((C -> (C or D)) and ((A -> (not (B -> A))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-443 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-27916.        (((A -> (not (B -> A))) -> (not A)) and ((C -> (C or D)) and ((A -> (not (B -> A))) -> (not A)))), M:tm-443, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-27917
in-theory        27917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((D -> (D or E)) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-27917.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((D -> (D or E)) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))))), M:tm-443, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-27918
in-theory        27918
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and ((C -> (C or D)) and (((A and B) -> (not A)) -> (not (A and B)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-27918.        ((((A and B) -> (not A)) -> (not (A and B))) and ((C -> (C or D)) and (((A and B) -> (not A)) -> (not (A and B))))), M:tm-443, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-27919
in-theory        27919
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and ((C -> (C or D)) and (((A and B) -> (not B)) -> (not (A and B)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-27919.        ((((A and B) -> (not B)) -> (not (A and B))) and ((C -> (C or D)) and (((A and B) -> (not B)) -> (not (A and B))))), M:tm-443, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-27920
in-theory        27920
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and ((C -> (C or D)) and ((A -> (not (B -> (A and B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-27920.        (((A -> (not (B -> (A and B)))) -> (not A)) and ((C -> (C or D)) and ((A -> (not (B -> (A and B)))) -> (not A)))), M:tm-443, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-27921
in-theory        27921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and ((C -> (C or D)) and ((A -> (not (A or B))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-443 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-27921.        (((A -> (not (A or B))) -> (not A)) and ((C -> (C or D)) and ((A -> (not (A or B))) -> (not A)))), M:tm-443, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-27922
in-theory        27922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and ((C -> (C or D)) and ((A -> (not (B or A))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-443 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-27922.        (((A -> (not (B or A))) -> (not A)) and ((C -> (C or D)) and ((A -> (not (B or A))) -> (not A)))), M:tm-443, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-27923
in-theory        27923
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((D -> (D or E)) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-8)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-27923.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((D -> (D or E)) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))))), M:tm-443, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-27924
in-theory        27924
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((C -> (C or D)) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-27924.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((C -> (C or D)) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))))), M:tm-443, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-27925
in-theory        27925
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((D -> (D or E)) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))))
theorem-size     53
proof            (modus-ponens tm-443 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-27925.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((D -> (D or E)) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))), M:tm-443, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-27926
in-theory        27926
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (D or E)) and (A or ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-27926.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (D or E)) and (A or ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-443, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-27927
in-theory        27927
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((D -> (D or E)) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C)))
theorem-size     33
proof            (modus-ponens tm-443 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-27927.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((D -> (D or E)) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C))), M:tm-443, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-27928
in-theory        27928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((D -> (D or E)) and (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A))))
theorem-size     37
proof            (modus-ponens tm-443 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-27928.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((D -> (D or E)) and (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)))), M:tm-443, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-27929
in-theory        27929
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((C -> (C or D)) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-27929.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((C -> (C or D)) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))))), M:tm-443, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-27930
in-theory        27930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (D or E)) and (A -> ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-27930.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (D or E)) and (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-443, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-27931
in-theory        27931
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((B -> (B or C)) and (((not (not A)) -> (not A)) -> (not (not (not A))))))
theorem-size     29
proof            (modus-ponens tm-443 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-27931.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((B -> (B or C)) and (((not (not A)) -> (not A)) -> (not (not (not A)))))), M:tm-443, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-27932
in-theory        27932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and ((C -> (C or D)) and ((A -> B) -> (((not (not A)) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-443 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-27932.        (((A -> B) -> (((not (not A)) or A) -> B)) and ((C -> (C or D)) and ((A -> B) -> (((not (not A)) or A) -> B)))), M:tm-443, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-27933
in-theory        27933
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and ((C -> (C or D)) and (A or ((not (not B)) -> B))))
theorem-size     21
proof            (modus-ponens tm-443 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-27933.        ((A or ((not (not B)) -> B)) and ((C -> (C or D)) and (A or ((not (not B)) -> B)))), M:tm-443, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-27934
in-theory        27934
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and ((C -> (C or D)) and (((not (not A)) -> A) or B)))
theorem-size     21
proof            (modus-ponens tm-443 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-27934.        ((((not (not A)) -> A) or B) and ((C -> (C or D)) and (((not (not A)) -> A) or B))), M:tm-443, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-27935
in-theory        27935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and ((C -> (C or D)) and (A -> (((not (not B)) -> B) and A))))
theorem-size     25
proof            (modus-ponens tm-443 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-27935.        ((A -> (((not (not B)) -> B) and A)) and ((C -> (C or D)) and (A -> (((not (not B)) -> B) and A)))), M:tm-443, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-27936
in-theory        27936
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((C -> (C or D)) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B))))
theorem-size     37
proof            (modus-ponens tm-443 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-27936.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((C -> (C or D)) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)))), M:tm-443, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-27937
in-theory        27937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and ((C -> (C or D)) and (A -> ((not (not B)) -> B))))
theorem-size     21
proof            (modus-ponens tm-443 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-27937.        ((A -> ((not (not B)) -> B)) and ((C -> (C or D)) and (A -> ((not (not B)) -> B)))), M:tm-443, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-27938
in-theory        27938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and ((D -> (D or E)) and ((A -> (not (B -> (C -> B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-27938.        (((A -> (not (B -> (C -> B)))) -> (not A)) and ((D -> (D or E)) and ((A -> (not (B -> (C -> B)))) -> (not A)))), M:tm-443, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-27939
in-theory        27939
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((E -> (E or F)) and (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-443 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-27939.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((E -> (E or F)) and (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)))), M:tm-443, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-27940
in-theory        27940
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and ((E -> (E or F)) and (A or (B -> (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-27940.        ((A or (B -> (C -> (D -> C)))) and ((E -> (E or F)) and (A or (B -> (C -> (D -> C)))))), M:tm-443, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-27941
in-theory        27941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and ((E -> (E or F)) and ((A -> (B -> (C -> B))) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-27941.        (((A -> (B -> (C -> B))) or D) and ((E -> (E or F)) and ((A -> (B -> (C -> B))) or D))), M:tm-443, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-27942
in-theory        27942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and ((E -> (E or F)) and (A -> ((B -> (C -> (D -> C))) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-27942.        ((A -> ((B -> (C -> (D -> C))) and A)) and ((E -> (E or F)) and (A -> ((B -> (C -> (D -> C))) and A)))), M:tm-443, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-27943
in-theory        27943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and ((D -> (D or E)) and ((A -> B) -> (A -> (C -> B)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-27943.        (((A -> B) -> (A -> (C -> B))) and ((D -> (D or E)) and ((A -> B) -> (A -> (C -> B))))), M:tm-443, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-27944
in-theory        27944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and ((E -> (E or F)) and (A -> (B -> (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-27944.        ((A -> (B -> (C -> (D -> C)))) and ((E -> (E or F)) and (A -> (B -> (C -> (D -> C)))))), M:tm-443, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-27945
in-theory        27945
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and ((B -> (B or C)) and (A -> A)))
theorem-size     13
proof            (modus-ponens tm-443 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-27945.        ((A -> A) and ((B -> (B or C)) and (A -> A))), M:tm-443, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-27946
in-theory        27946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and ((D -> (D or E)) and ((A -> (B -> C)) -> (A -> (B -> C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-27946.        (((A -> (B -> C)) -> (A -> (B -> C))) and ((D -> (D or E)) and ((A -> (B -> C)) -> (A -> (B -> C))))), M:tm-443, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-27947
in-theory        27947
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and ((C -> (C or D)) and ((A and B) -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-443 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-27947.        (((A and B) -> (A and B)) and ((C -> (C or D)) and ((A and B) -> (A and B)))), M:tm-443, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-27948
in-theory        27948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and ((C -> (C or D)) and ((A -> B) -> (A -> B))))
theorem-size     21
proof            (modus-ponens tm-443 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-27948.        (((A -> B) -> (A -> B)) and ((C -> (C or D)) and ((A -> B) -> (A -> B)))), M:tm-443, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-27949
in-theory        27949
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and ((B -> (B or C)) and ((not (not A)) -> (not (not A)))))
theorem-size     21
proof            (modus-ponens tm-443 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-10)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-27949.        (((not (not A)) -> (not (not A))) and ((B -> (B or C)) and ((not (not A)) -> (not (not A))))), M:tm-443, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-27950
in-theory        27950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((C -> (C or D)) and (((A -> B) -> (not (A -> A))) -> (not (A -> B)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-27950.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((C -> (C or D)) and (((A -> B) -> (not (A -> A))) -> (not (A -> B))))), M:tm-443, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-27951
in-theory        27951
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((D -> (D or E)) and (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B))))
theorem-size     37
proof            (modus-ponens tm-443 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-27951.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((D -> (D or E)) and (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)))), M:tm-443, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-27952
in-theory        27952
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and ((D -> (D or E)) and (A or ((B -> C) -> (B -> B)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-27952.        ((A or ((B -> C) -> (B -> B))) and ((D -> (D or E)) and (A or ((B -> C) -> (B -> B))))), M:tm-443, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-27953
in-theory        27953
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and ((D -> (D or E)) and (((A -> B) -> (A -> A)) or C)))
theorem-size     25
proof            (modus-ponens tm-443 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-27953.        ((((A -> B) -> (A -> A)) or C) and ((D -> (D or E)) and (((A -> B) -> (A -> A)) or C))), M:tm-443, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-27954
in-theory        27954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and ((D -> (D or E)) and (A -> (((B -> C) -> (B -> B)) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-27954.        ((A -> (((B -> C) -> (B -> B)) and A)) and ((D -> (D or E)) and (A -> (((B -> C) -> (B -> B)) and A)))), M:tm-443, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-27955
in-theory        27955
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and ((C -> (C or D)) and (((A -> B) -> A) -> ((A -> B) -> A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-27955.        ((((A -> B) -> A) -> ((A -> B) -> A)) and ((C -> (C or D)) and (((A -> B) -> A) -> ((A -> B) -> A)))), M:tm-443, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-27956
in-theory        27956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and ((D -> (D or E)) and (A -> ((B -> C) -> (B -> B)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-27956.        ((A -> ((B -> C) -> (B -> B))) and ((D -> (D or E)) and (A -> ((B -> C) -> (B -> B))))), M:tm-443, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-27957
in-theory        27957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and ((D -> (D or E)) and ((A -> ((B -> A) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-27957.        (((A -> ((B -> A) -> C)) -> (A -> C)) and ((D -> (D or E)) and ((A -> ((B -> A) -> C)) -> (A -> C)))), M:tm-443, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-27958
in-theory        27958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and ((C -> (C or D)) and ((A -> (A -> B)) -> (A -> B))))
theorem-size     25
proof            (modus-ponens tm-443 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-27958.        (((A -> (A -> B)) -> (A -> B)) and ((C -> (C or D)) and ((A -> (A -> B)) -> (A -> B)))), M:tm-443, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-27959
in-theory        27959
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((D -> (D or E)) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-27959.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((D -> (D or E)) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))))), M:tm-443, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-27960
in-theory        27960
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((D -> (D or E)) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B))))))
theorem-size     69
proof            (modus-ponens tm-443 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-27960.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((D -> (D or E)) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))))), M:tm-443, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-27961
in-theory        27961
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))))
theorem-size     73
proof            (modus-ponens tm-443 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-27961.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))), M:tm-443, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-27962
in-theory        27962
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (E or F)) and (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-27962.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (E or F)) and (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-443, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-27963
in-theory        27963
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and ((E -> (E or F)) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D)))
theorem-size     49
proof            (modus-ponens tm-443 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-27963.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and ((E -> (E or F)) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D))), M:tm-443, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-27964
in-theory        27964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((E -> (E or F)) and (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))))
theorem-size     53
proof            (modus-ponens tm-443 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-27964.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((E -> (E or F)) and (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)))), M:tm-443, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-27965
in-theory        27965
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((D -> (D or E)) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-443 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-27965.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((D -> (D or E)) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))), M:tm-443, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-27966
in-theory        27966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (E or F)) and (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-27966.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (E or F)) and (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-443, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-27967
in-theory        27967
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((E -> (E or F)) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-443 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-27967.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((E -> (E or F)) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)))), M:tm-443, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-27968
in-theory        27968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((E -> (E or F)) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A))))
theorem-size     45
proof            (modus-ponens tm-443 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-27968.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((E -> (E or F)) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)))), M:tm-443, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-27969
in-theory        27969
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((F -> (F or G)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))))
theorem-size     73
proof            (modus-ponens tm-443 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-27969.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((F -> (F or G)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))), M:tm-443, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-27970
in-theory        27970
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (F or G)) and (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-27970.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (F or G)) and (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-443, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-27971
in-theory        27971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (F or G)) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-443 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-27971.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (F or G)) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-443, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-27972
in-theory        27972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (F or G)) and (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-443 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-27972.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (F or G)) and (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-443, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-27973
in-theory        27973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-27973.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))))), M:tm-443, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-27974
in-theory        27974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (F or G)) and (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-27974.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (F or G)) and (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-443, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-27975
in-theory        27975
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and ((C -> (C or D)) and (((A -> B) and A) -> B)))
theorem-size     21
proof            (modus-ponens tm-443 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-27975.        ((((A -> B) and A) -> B) and ((C -> (C or D)) and (((A -> B) and A) -> B))), M:tm-443, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-27976
in-theory        27976
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and ((E -> (E or F)) and ((((A -> (B -> A)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-443 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-27976.        (((((A -> (B -> A)) -> C) and D) -> C) and ((E -> (E or F)) and ((((A -> (B -> A)) -> C) and D) -> C))), M:tm-443, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-27977
in-theory        27977
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((F -> (F or G)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D)))
theorem-size     45
proof            (modus-ponens tm-443 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-27977.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((F -> (F or G)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D))), M:tm-443, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-27978
in-theory        27978
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((D -> (D or E)) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B))))
theorem-size     49
proof            (modus-ponens tm-443 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-27978.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((D -> (D or E)) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)))), M:tm-443, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-27979
in-theory        27979
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((D -> (D or E)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A))))
theorem-size     37
proof            (modus-ponens tm-443 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-27979.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((D -> (D or E)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)))), M:tm-443, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-27980
in-theory        27980
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((D -> (D or E)) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A)))))
theorem-size     57
proof            (modus-ponens tm-443 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-27980.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((D -> (D or E)) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))))), M:tm-443, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-27981
in-theory        27981
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((E -> (E or F)) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))))
theorem-size     61
proof            (modus-ponens tm-443 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-27981.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((E -> (E or F)) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))), M:tm-443, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-27982
in-theory        27982
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (E or F)) and (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-27982.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (E or F)) and (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-443, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-27983
in-theory        27983
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((E -> (E or F)) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D)))
theorem-size     41
proof            (modus-ponens tm-443 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-27983.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((E -> (E or F)) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D))), M:tm-443, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-27984
in-theory        27984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((E -> (E or F)) and (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))))
theorem-size     45
proof            (modus-ponens tm-443 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-27984.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((E -> (E or F)) and (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)))), M:tm-443, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-27985
in-theory        27985
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((D -> (D or E)) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B))))
theorem-size     53
proof            (modus-ponens tm-443 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-27985.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((D -> (D or E)) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)))), M:tm-443, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-27986
in-theory        27986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (E or F)) and (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-27986.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (E or F)) and (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-443, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-27987
in-theory        27987
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and ((E -> (E or F)) and (((((A and B) -> A) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-443 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-27987.        ((((((A and B) -> A) -> C) and D) -> C) and ((E -> (E or F)) and (((((A and B) -> A) -> C) and D) -> C))), M:tm-443, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-27988
in-theory        27988
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((D -> (D or E)) and (((A and B) -> (A -> C)) -> ((A and B) -> C))))
theorem-size     33
proof            (modus-ponens tm-443 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-27988.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((D -> (D or E)) and (((A and B) -> (A -> C)) -> ((A and B) -> C)))), M:tm-443, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-27989
in-theory        27989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and ((D -> (D or E)) and ((A -> (not ((B and C) -> B))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-27989.        (((A -> (not ((B and C) -> B))) -> (not A)) and ((D -> (D or E)) and ((A -> (not ((B and C) -> B))) -> (not A)))), M:tm-443, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-27990
in-theory        27990
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((E -> (E or F)) and ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C))))
theorem-size     41
proof            (modus-ponens tm-443 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-27990.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((E -> (E or F)) and ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)))), M:tm-443, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-27991
in-theory        27991
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and ((E -> (E or F)) and (A or (B -> ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27991.        ((A or (B -> ((C and D) -> C))) and ((E -> (E or F)) and (A or (B -> ((C and D) -> C))))), M:tm-443, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-27992
in-theory        27992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and ((E -> (E or F)) and ((A -> ((B and C) -> B)) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27992.        (((A -> ((B and C) -> B)) or D) and ((E -> (E or F)) and ((A -> ((B and C) -> B)) or D))), M:tm-443, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-27993
in-theory        27993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and ((E -> (E or F)) and (A -> ((B -> ((C and D) -> C)) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27993.        ((A -> ((B -> ((C and D) -> C)) and A)) and ((E -> (E or F)) and (A -> ((B -> ((C and D) -> C)) and A)))), M:tm-443, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-27994
in-theory        27994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and ((D -> (D or E)) and ((A -> (B and C)) -> (A -> B))))
theorem-size     25
proof            (modus-ponens tm-443 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-27994.        (((A -> (B and C)) -> (A -> B)) and ((D -> (D or E)) and ((A -> (B and C)) -> (A -> B)))), M:tm-443, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-27995
in-theory        27995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and ((E -> (E or F)) and (A -> (B -> ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-27995.        ((A -> (B -> ((C and D) -> C))) and ((E -> (E or F)) and (A -> (B -> ((C and D) -> C))))), M:tm-443, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-27996
in-theory        27996
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and ((C -> (C or D)) and ((A and (A -> B)) -> B)))
theorem-size     21
proof            (modus-ponens tm-443 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-27996.        (((A and (A -> B)) -> B) and ((C -> (C or D)) and ((A and (A -> B)) -> B))), M:tm-443, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-27997
in-theory        27997
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and ((E -> (E or F)) and ((A and ((B -> (C -> B)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-443 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-27997.        (((A and ((B -> (C -> B)) -> D)) -> D) and ((E -> (E or F)) and ((A and ((B -> (C -> B)) -> D)) -> D))), M:tm-443, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-27998
in-theory        27998
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((F -> (F or G)) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E)))
theorem-size     45
proof            (modus-ponens tm-443 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-27998.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((F -> (F or G)) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E))), M:tm-443, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-27999
in-theory        27999
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and ((E -> (E or F)) and ((A and (((B and C) -> B) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-443 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-27999.        (((A and (((B and C) -> B) -> D)) -> D) and ((E -> (E or F)) and ((A and (((B and C) -> B) -> D)) -> D))), M:tm-443, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-28000
in-theory        28000
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((D -> (D or E)) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-443 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-28000.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((D -> (D or E)) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)))), M:tm-443, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-28001
in-theory        28001
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((D -> (D or E)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B))))
theorem-size     37
proof            (modus-ponens tm-443 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-28001.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((D -> (D or E)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)))), M:tm-443, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-28002
in-theory        28002
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((D -> (D or E)) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B)))))
theorem-size     57
proof            (modus-ponens tm-443 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-28002.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((D -> (D or E)) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))))), M:tm-443, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-28003
in-theory        28003
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((E -> (E or F)) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))))
theorem-size     61
proof            (modus-ponens tm-443 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-28003.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((E -> (E or F)) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))), M:tm-443, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-28004
in-theory        28004
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (E or F)) and (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-28004.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (E or F)) and (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-443, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-28005
in-theory        28005
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and ((E -> (E or F)) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D)))
theorem-size     41
proof            (modus-ponens tm-443 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-28005.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and ((E -> (E or F)) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D))), M:tm-443, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-28006
in-theory        28006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((E -> (E or F)) and (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))))
theorem-size     45
proof            (modus-ponens tm-443 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-28006.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((E -> (E or F)) and (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)))), M:tm-443, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-28007
in-theory        28007
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((D -> (D or E)) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C))))
theorem-size     53
proof            (modus-ponens tm-443 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-28007.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((D -> (D or E)) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)))), M:tm-443, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-28008
in-theory        28008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (E or F)) and (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-28008.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (E or F)) and (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-443, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-28009
in-theory        28009
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and ((E -> (E or F)) and ((A and (((B and C) -> C) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-443 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-28009.        (((A and (((B and C) -> C) -> D)) -> D) and ((E -> (E or F)) and ((A and (((B and C) -> C) -> D)) -> D))), M:tm-443, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-28010
in-theory        28010
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and ((E -> (E or F)) and (((((A and B) -> B) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-443 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-28010.        ((((((A and B) -> B) -> C) and D) -> C) and ((E -> (E or F)) and (((((A and B) -> B) -> C) and D) -> C))), M:tm-443, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-28011
in-theory        28011
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((D -> (D or E)) and (((A and B) -> (B -> C)) -> ((A and B) -> C))))
theorem-size     33
proof            (modus-ponens tm-443 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-28011.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((D -> (D or E)) and (((A and B) -> (B -> C)) -> ((A and B) -> C)))), M:tm-443, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-28012
in-theory        28012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and ((D -> (D or E)) and ((A -> (not ((B and C) -> C))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-28012.        (((A -> (not ((B and C) -> C))) -> (not A)) and ((D -> (D or E)) and ((A -> (not ((B and C) -> C))) -> (not A)))), M:tm-443, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-28013
in-theory        28013
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((E -> (E or F)) and ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C))))
theorem-size     41
proof            (modus-ponens tm-443 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-28013.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((E -> (E or F)) and ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)))), M:tm-443, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-28014
in-theory        28014
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and ((E -> (E or F)) and (A or (B -> ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-28014.        ((A or (B -> ((C and D) -> D))) and ((E -> (E or F)) and (A or (B -> ((C and D) -> D))))), M:tm-443, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-28015
in-theory        28015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and ((E -> (E or F)) and ((A -> ((B and C) -> C)) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-28015.        (((A -> ((B and C) -> C)) or D) and ((E -> (E or F)) and ((A -> ((B and C) -> C)) or D))), M:tm-443, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-28016
in-theory        28016
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and ((E -> (E or F)) and (A -> ((B -> ((C and D) -> D)) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-28016.        ((A -> ((B -> ((C and D) -> D)) and A)) and ((E -> (E or F)) and (A -> ((B -> ((C and D) -> D)) and A)))), M:tm-443, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-28017
in-theory        28017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and ((D -> (D or E)) and ((A -> (B and C)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-443 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-28017.        (((A -> (B and C)) -> (A -> C)) and ((D -> (D or E)) and ((A -> (B and C)) -> (A -> C)))), M:tm-443, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-28018
in-theory        28018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and ((E -> (E or F)) and (A -> (B -> ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-28018.        ((A -> (B -> ((C and D) -> D))) and ((E -> (E or F)) and (A -> (B -> ((C and D) -> D))))), M:tm-443, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-28019
in-theory        28019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and ((E -> (E or F)) and ((A -> (B -> A)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-28019.        (((A -> (B -> A)) and (C -> (D -> C))) and ((E -> (E or F)) and ((A -> (B -> A)) and (C -> (D -> C))))), M:tm-443, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-28020
in-theory        28020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-28020.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-443, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-28021
in-theory        28021
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and ((E -> (E or F)) and ((A -> (B -> A)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28021.        (((A -> (B -> A)) and ((C and D) -> C)) and ((E -> (E or F)) and ((A -> (B -> A)) and ((C and D) -> C)))), M:tm-443, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-28022
in-theory        28022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and ((E -> (E or F)) and ((A -> (B -> A)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-443 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-28022.        (((A -> (B -> A)) and ((C and D) -> D)) and ((E -> (E or F)) and ((A -> (B -> A)) and ((C and D) -> D)))), M:tm-443, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-28023
in-theory        28023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A -> (B -> A)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-28023.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A -> (B -> A)) and (C -> (D -> (C and D)))))), M:tm-443, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-28024
in-theory        28024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and ((E -> (E or F)) and ((A -> (B -> A)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28024.        (((A -> (B -> A)) and (C -> (C or D))) and ((E -> (E or F)) and ((A -> (B -> A)) and (C -> (C or D))))), M:tm-443, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-28025
in-theory        28025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and ((E -> (E or F)) and ((A -> (B -> A)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-28025.        (((A -> (B -> A)) and (C -> (D or C))) and ((E -> (E or F)) and ((A -> (B -> A)) and (C -> (D or C))))), M:tm-443, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-28026
in-theory        28026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-28026.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-443, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-28027
in-theory        28027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (E or F)) and ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-28027.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (E or F)) and ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-443, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-28028
in-theory        28028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and ((D -> (D or E)) and ((A -> (B -> A)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-28028.        (((A -> (B -> A)) and ((not (not C)) -> C)) and ((D -> (D or E)) and ((A -> (B -> A)) and ((not (not C)) -> C)))), M:tm-443, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-28029
in-theory        28029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-28029.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> (D -> (E -> D)))))), M:tm-443, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-28030
in-theory        28030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((E -> (E or F)) and ((A -> (B -> A)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-28030.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((E -> (E or F)) and ((A -> (B -> A)) and ((C -> D) -> (C -> C))))), M:tm-443, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-28031
in-theory        28031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-443 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-28031.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-443, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-28032
in-theory        28032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-28032.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-443, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-28033
in-theory        28033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (F or G)) and ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-28033.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (F or G)) and ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-443, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-28034
in-theory        28034
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-28034.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> ((D and E) -> D))))), M:tm-443, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-28035
in-theory        28035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-28035.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-443, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-28036
in-theory        28036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-28036.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> ((D and E) -> E))))), M:tm-443, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-28037
in-theory        28037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-28037.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-443, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-28038
in-theory        28038
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((D -> (D or E)) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-28038.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((D -> (D or E)) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A)))), M:tm-443, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-28039
in-theory        28039
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((E -> (E or F)) and ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-443 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-28039.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((E -> (E or F)) and ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)))), M:tm-443, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-28040
in-theory        28040
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and ((E -> (E or F)) and (A or (B -> ((C -> (D -> C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-28040.        ((A or (B -> ((C -> (D -> C)) and B))) and ((E -> (E or F)) and (A or (B -> ((C -> (D -> C)) and B))))), M:tm-443, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-28041
in-theory        28041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and ((E -> (E or F)) and ((A -> ((B -> (C -> B)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-443 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-28041.        (((A -> ((B -> (C -> B)) and A)) or D) and ((E -> (E or F)) and ((A -> ((B -> (C -> B)) and A)) or D))), M:tm-443, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-28042
in-theory        28042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((E -> (E or F)) and (A -> ((B -> ((C -> (D -> C)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-28042.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((E -> (E or F)) and (A -> ((B -> ((C -> (D -> C)) and B)) and A)))), M:tm-443, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-28043
in-theory        28043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and ((E -> (E or F)) and (A -> (B -> ((C -> (D -> C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-28043.        ((A -> (B -> ((C -> (D -> C)) and B))) and ((E -> (E or F)) and (A -> (B -> ((C -> (D -> C)) and B))))), M:tm-443, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-28044
in-theory        28044
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-28044.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))))), M:tm-443, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-28045
in-theory        28045
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-28045.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-443, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-28046
in-theory        28046
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-443 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28046.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)))), M:tm-443, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-28047
in-theory        28047
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-443 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-28047.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)))), M:tm-443, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-28048
in-theory        28048
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-28048.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))))), M:tm-443, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-28049
in-theory        28049
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28049.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))))), M:tm-443, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-28050
in-theory        28050
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-28050.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))))), M:tm-443, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-28051
in-theory        28051
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-28051.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-443, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-28052
in-theory        28052
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     57
proof            (modus-ponens tm-443 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-28052.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-443, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-28053
in-theory        28053
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((E -> (E or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D))))
theorem-size     45
proof            (modus-ponens tm-443 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-28053.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((E -> (E or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)))), M:tm-443, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-28054
in-theory        28054
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-28054.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))))), M:tm-443, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-28055
in-theory        28055
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-28055.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))))), M:tm-443, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-28056
in-theory        28056
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     73
proof            (modus-ponens tm-443 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       249
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-28056.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-443, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-28057
in-theory        28057
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (H or I)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-443 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-28057.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (H or I)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-443, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-28058
in-theory        28058
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     65
proof            (modus-ponens tm-443 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-28058.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-443, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-28059
in-theory        28059
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-28059.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))))), M:tm-443, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-28060
in-theory        28060
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     65
proof            (modus-ponens tm-443 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-28060.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-443, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-28061
in-theory        28061
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-28061.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))))), M:tm-443, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-28062
in-theory        28062
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-28062.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-443, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-28063
in-theory        28063
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (H or I)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-443 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-28063.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (H or I)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-443, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-28064
in-theory        28064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (G or H)) and ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-28064.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (G or H)) and ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-443, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-28065
in-theory        28065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((E -> (E or F)) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A))))
theorem-size     49
proof            (modus-ponens tm-443 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-28065.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((E -> (E or F)) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)))), M:tm-443, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-28066
in-theory        28066
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((F -> (F or G)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))))
theorem-size     81
proof            (modus-ponens tm-443 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-28066.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((F -> (F or G)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))), M:tm-443, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-28067
in-theory        28067
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (F or G)) and (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-28067.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (F or G)) and (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-443, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-28068
in-theory        28068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and ((F -> (F or G)) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E)))
theorem-size     45
proof            (modus-ponens tm-443 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-28068.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and ((F -> (F or G)) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E))), M:tm-443, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-28069
in-theory        28069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((F -> (F or G)) and (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))))
theorem-size     49
proof            (modus-ponens tm-443 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-28069.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((F -> (F or G)) and (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)))), M:tm-443, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-28070
in-theory        28070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (F or G)) and (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-28070.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (F or G)) and (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-443, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-28071
in-theory        28071
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and ((E -> (E or F)) and (((A and B) -> A) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-28071.        ((((A and B) -> A) and (C -> (D -> C))) and ((E -> (E or F)) and (((A and B) -> A) and (C -> (D -> C))))), M:tm-443, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-28072
in-theory        28072
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-28072.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-443, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-28073
in-theory        28073
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and ((E -> (E or F)) and (((A and B) -> A) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28073.        ((((A and B) -> A) and ((C and D) -> C)) and ((E -> (E or F)) and (((A and B) -> A) and ((C and D) -> C)))), M:tm-443, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-28074
in-theory        28074
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and ((E -> (E or F)) and (((A and B) -> A) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-443 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-28074.        ((((A and B) -> A) and ((C and D) -> D)) and ((E -> (E or F)) and (((A and B) -> A) and ((C and D) -> D)))), M:tm-443, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-28075
in-theory        28075
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((E -> (E or F)) and (((A and B) -> A) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-28075.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((E -> (E or F)) and (((A and B) -> A) and (C -> (D -> (C and D)))))), M:tm-443, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-28076
in-theory        28076
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and ((E -> (E or F)) and (((A and B) -> A) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28076.        ((((A and B) -> A) and (C -> (C or D))) and ((E -> (E or F)) and (((A and B) -> A) and (C -> (C or D))))), M:tm-443, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-28077
in-theory        28077
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and ((E -> (E or F)) and (((A and B) -> A) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-28077.        ((((A and B) -> A) and (C -> (D or C))) and ((E -> (E or F)) and (((A and B) -> A) and (C -> (D or C))))), M:tm-443, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-28078
in-theory        28078
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-28078.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-443, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-28079
in-theory        28079
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (E or F)) and (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-28079.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (E or F)) and (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-443, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-28080
in-theory        28080
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and ((D -> (D or E)) and (((A and B) -> A) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-28080.        ((((A and B) -> A) and ((not (not C)) -> C)) and ((D -> (D or E)) and (((A and B) -> A) and ((not (not C)) -> C)))), M:tm-443, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-28081
in-theory        28081
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-28081.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> (D -> (E -> D)))))), M:tm-443, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-28082
in-theory        28082
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((E -> (E or F)) and (((A and B) -> A) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-28082.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((E -> (E or F)) and (((A and B) -> A) and ((C -> D) -> (C -> C))))), M:tm-443, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-28083
in-theory        28083
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (F or G)) and (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-443 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-28083.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (F or G)) and (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-443, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-28084
in-theory        28084
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-28084.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-443, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-28085
in-theory        28085
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (F or G)) and (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-28085.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (F or G)) and (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-443, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-28086
in-theory        28086
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-28086.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> ((D and E) -> D))))), M:tm-443, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-28087
in-theory        28087
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (F or G)) and (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-28087.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (F or G)) and (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-443, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-28088
in-theory        28088
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-28088.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> ((D and E) -> E))))), M:tm-443, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-28089
in-theory        28089
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-28089.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))))), M:tm-443, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-28090
in-theory        28090
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (G or H)) and (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-28090.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (G or H)) and (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-443, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-28091
in-theory        28091
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-28091.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> (((D and E) -> D) and C))))), M:tm-443, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-28092
in-theory        28092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-28092.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-443, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-28093
in-theory        28093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-28093.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))))), M:tm-443, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-28094
in-theory        28094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((D -> (D or E)) and ((A -> (not (((B and C) -> B) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-28094.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((D -> (D or E)) and ((A -> (not (((B and C) -> B) and A))) -> (not A)))), M:tm-443, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-28095
in-theory        28095
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((E -> (E or F)) and (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-443 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-28095.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((E -> (E or F)) and (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)))), M:tm-443, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-28096
in-theory        28096
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and ((E -> (E or F)) and (A or (B -> (((C and D) -> C) and B)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-28096.        ((A or (B -> (((C and D) -> C) and B))) and ((E -> (E or F)) and (A or (B -> (((C and D) -> C) and B))))), M:tm-443, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-28097
in-theory        28097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and ((E -> (E or F)) and ((A -> (((B and C) -> B) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-443 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-28097.        (((A -> (((B and C) -> B) and A)) or D) and ((E -> (E or F)) and ((A -> (((B and C) -> B) and A)) or D))), M:tm-443, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-28098
in-theory        28098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((E -> (E or F)) and (A -> ((B -> (((C and D) -> C) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-28098.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((E -> (E or F)) and (A -> ((B -> (((C and D) -> C) and B)) and A)))), M:tm-443, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-28099
in-theory        28099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and ((E -> (E or F)) and (A -> (B -> (((C and D) -> C) and B)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-28099.        ((A -> (B -> (((C and D) -> C) and B))) and ((E -> (E or F)) and (A -> (B -> (((C and D) -> C) and B))))), M:tm-443, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-28100
in-theory        28100
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and ((E -> (E or F)) and (((A and B) -> B) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-28100.        ((((A and B) -> B) and (C -> (D -> C))) and ((E -> (E or F)) and (((A and B) -> B) and (C -> (D -> C))))), M:tm-443, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-28101
in-theory        28101
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-28101.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-443, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-28102
in-theory        28102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and ((E -> (E or F)) and (((A and B) -> B) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28102.        ((((A and B) -> B) and ((C and D) -> C)) and ((E -> (E or F)) and (((A and B) -> B) and ((C and D) -> C)))), M:tm-443, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-28103
in-theory        28103
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and ((E -> (E or F)) and (((A and B) -> B) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-443 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-28103.        ((((A and B) -> B) and ((C and D) -> D)) and ((E -> (E or F)) and (((A and B) -> B) and ((C and D) -> D)))), M:tm-443, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-28104
in-theory        28104
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((E -> (E or F)) and (((A and B) -> B) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-28104.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((E -> (E or F)) and (((A and B) -> B) and (C -> (D -> (C and D)))))), M:tm-443, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-28105
in-theory        28105
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and ((E -> (E or F)) and (((A and B) -> B) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28105.        ((((A and B) -> B) and (C -> (C or D))) and ((E -> (E or F)) and (((A and B) -> B) and (C -> (C or D))))), M:tm-443, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-28106
in-theory        28106
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and ((E -> (E or F)) and (((A and B) -> B) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-28106.        ((((A and B) -> B) and (C -> (D or C))) and ((E -> (E or F)) and (((A and B) -> B) and (C -> (D or C))))), M:tm-443, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-28107
in-theory        28107
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-28107.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-443, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-28108
in-theory        28108
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (E or F)) and (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-28108.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (E or F)) and (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-443, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-28109
in-theory        28109
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and ((D -> (D or E)) and (((A and B) -> B) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-28109.        ((((A and B) -> B) and ((not (not C)) -> C)) and ((D -> (D or E)) and (((A and B) -> B) and ((not (not C)) -> C)))), M:tm-443, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-28110
in-theory        28110
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-28110.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> (D -> (E -> D)))))), M:tm-443, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-28111
in-theory        28111
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((E -> (E or F)) and (((A and B) -> B) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-28111.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((E -> (E or F)) and (((A and B) -> B) and ((C -> D) -> (C -> C))))), M:tm-443, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-28112
in-theory        28112
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (F or G)) and (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-443 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-28112.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (F or G)) and (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-443, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-28113
in-theory        28113
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-28113.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-443, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-28114
in-theory        28114
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (F or G)) and (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-28114.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (F or G)) and (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-443, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-28115
in-theory        28115
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-28115.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> ((D and E) -> D))))), M:tm-443, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-28116
in-theory        28116
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (F or G)) and (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-28116.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (F or G)) and (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-443, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-28117
in-theory        28117
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-28117.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> ((D and E) -> E))))), M:tm-443, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-28118
in-theory        28118
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-28118.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))))), M:tm-443, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-28119
in-theory        28119
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (G or H)) and (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-28119.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (G or H)) and (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-443, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-28120
in-theory        28120
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-28120.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> (((D and E) -> D) and C))))), M:tm-443, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-28121
in-theory        28121
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-28121.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> (((D and E) -> E) and C))))), M:tm-443, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-28122
in-theory        28122
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-28122.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> (((D and E) -> E) and C))))), M:tm-443, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-28123
in-theory        28123
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-28123.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-443, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-28124
in-theory        28124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-28124.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))))), M:tm-443, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-28125
in-theory        28125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((D -> (D or E)) and ((A -> (not (((B and C) -> C) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-28125.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((D -> (D or E)) and ((A -> (not (((B and C) -> C) and A))) -> (not A)))), M:tm-443, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-28126
in-theory        28126
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((E -> (E or F)) and (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-443 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-28126.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((E -> (E or F)) and (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)))), M:tm-443, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-28127
in-theory        28127
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and ((E -> (E or F)) and (A or (B -> (((C and D) -> D) and B)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-28127.        ((A or (B -> (((C and D) -> D) and B))) and ((E -> (E or F)) and (A or (B -> (((C and D) -> D) and B))))), M:tm-443, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-28128
in-theory        28128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and ((E -> (E or F)) and ((A -> (((B and C) -> C) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-443 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-28128.        (((A -> (((B and C) -> C) and A)) or D) and ((E -> (E or F)) and ((A -> (((B and C) -> C) and A)) or D))), M:tm-443, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-28129
in-theory        28129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((E -> (E or F)) and (A -> ((B -> (((C and D) -> D) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-28129.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((E -> (E or F)) and (A -> ((B -> (((C and D) -> D) and B)) and A)))), M:tm-443, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-28130
in-theory        28130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and ((E -> (E or F)) and (A -> (B -> (((C and D) -> D) and B)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-28130.        ((A -> (B -> (((C and D) -> D) and B))) and ((E -> (E or F)) and (A -> (B -> (((C and D) -> D) and B))))), M:tm-443, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-28131
in-theory        28131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and (C -> (D -> C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-28131.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and (C -> (D -> C))))), M:tm-443, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-28132
in-theory        28132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-28132.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-443, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-28133
in-theory        28133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and ((C and D) -> C))))
theorem-size     33
proof            (modus-ponens tm-443 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28133.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and ((C and D) -> C)))), M:tm-443, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-28134
in-theory        28134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and ((C and D) -> D))))
theorem-size     33
proof            (modus-ponens tm-443 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-28134.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and ((C and D) -> D)))), M:tm-443, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-28135
in-theory        28135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and (C -> (D -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-28135.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))))), M:tm-443, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-28136
in-theory        28136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and (C -> (C or D)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28136.        (((A -> (B -> (A and B))) and (C -> (C or D))) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and (C -> (C or D))))), M:tm-443, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-28137
in-theory        28137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and (C -> (D or C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-28137.        (((A -> (B -> (A and B))) and (C -> (D or C))) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and (C -> (D or C))))), M:tm-443, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-28138
in-theory        28138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-28138.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-443, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-28139
in-theory        28139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-28139.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-443, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-28140
in-theory        28140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((D -> (D or E)) and ((A -> (B -> (A and B))) and ((not (not C)) -> C))))
theorem-size     33
proof            (modus-ponens tm-443 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-28140.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((D -> (D or E)) and ((A -> (B -> (A and B))) and ((not (not C)) -> C)))), M:tm-443, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-28141
in-theory        28141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-28141.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))))), M:tm-443, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-28142
in-theory        28142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-28142.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))))), M:tm-443, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-28143
in-theory        28143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-28143.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-443, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-28144
in-theory        28144
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     53
proof            (modus-ponens tm-443 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-28144.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-443, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-28145
in-theory        28145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-28145.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-443, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-28146
in-theory        28146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> D)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-28146.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))))), M:tm-443, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-28147
in-theory        28147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-28147.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-443, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-28148
in-theory        28148
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> E)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-28148.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))))), M:tm-443, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-28149
in-theory        28149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-28149.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))))), M:tm-443, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-28150
in-theory        28150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (G or H)) and ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     57
proof            (modus-ponens tm-443 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-28150.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (G or H)) and ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-443, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-28151
in-theory        28151
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-28151.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))))), M:tm-443, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-28152
in-theory        28152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-28152.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))))), M:tm-443, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-28153
in-theory        28153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-28153.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-443, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-28154
in-theory        28154
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-28154.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-443, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-28155
in-theory        28155
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-28155.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-443, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-28156
in-theory        28156
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     57
proof            (modus-ponens tm-443 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-28156.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-443, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-28157
in-theory        28157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-28157.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-443, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-28158
in-theory        28158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((D -> (D or E)) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A))))
theorem-size     37
proof            (modus-ponens tm-443 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-28158.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((D -> (D or E)) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)))), M:tm-443, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-28159
in-theory        28159
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((E -> (E or F)) and ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-443 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-28159.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((E -> (E or F)) and ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)))), M:tm-443, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-28160
in-theory        28160
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (E or F)) and (A or (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-28160.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (E or F)) and (A or (B -> ((C -> (D -> (C and D))) and B))))), M:tm-443, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-28161
in-theory        28161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and ((E -> (E or F)) and ((A -> ((B -> (C -> (B and C))) and A)) or D)))
theorem-size     33
proof            (modus-ponens tm-443 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-28161.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and ((E -> (E or F)) and ((A -> ((B -> (C -> (B and C))) and A)) or D))), M:tm-443, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-28162
in-theory        28162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((E -> (E or F)) and (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A))))
theorem-size     37
proof            (modus-ponens tm-443 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-28162.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((E -> (E or F)) and (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)))), M:tm-443, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-28163
in-theory        28163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (E or F)) and (A -> (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-28163.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (E or F)) and (A -> (B -> ((C -> (D -> (C and D))) and B))))), M:tm-443, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-28164
in-theory        28164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and ((C -> (C or D)) and (A -> (A and (B -> A)))))
theorem-size     21
proof            (modus-ponens tm-443 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-28164.        ((A -> (A and (B -> A))) and ((C -> (C or D)) and (A -> (A and (B -> A))))), M:tm-443, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-28165
in-theory        28165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((D -> (D or E)) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-28165.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((D -> (D or E)) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))), M:tm-443, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-28166
in-theory        28166
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and ((C -> (C or D)) and ((A and B) -> ((A and B) and A))))
theorem-size     25
proof            (modus-ponens tm-443 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-28166.        (((A and B) -> ((A and B) and A)) and ((C -> (C or D)) and ((A and B) -> ((A and B) and A)))), M:tm-443, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-28167
in-theory        28167
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and ((C -> (C or D)) and ((A and B) -> ((A and B) and B))))
theorem-size     25
proof            (modus-ponens tm-443 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-28167.        (((A and B) -> ((A and B) and B)) and ((C -> (C or D)) and ((A and B) -> ((A and B) and B)))), M:tm-443, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-28168
in-theory        28168
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and ((C -> (C or D)) and (A -> (A and (B -> (A and B))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-28168.        ((A -> (A and (B -> (A and B)))) and ((C -> (C or D)) and (A -> (A and (B -> (A and B)))))), M:tm-443, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-28169
in-theory        28169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and ((C -> (C or D)) and (A -> (A and (A or B)))))
theorem-size     21
proof            (modus-ponens tm-443 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-28169.        ((A -> (A and (A or B))) and ((C -> (C or D)) and (A -> (A and (A or B))))), M:tm-443, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-28170
in-theory        28170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and ((C -> (C or D)) and (A -> (A and (B or A)))))
theorem-size     21
proof            (modus-ponens tm-443 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-28170.        ((A -> (A and (B or A))) and ((C -> (C or D)) and (A -> (A and (B or A))))), M:tm-443, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-28171
in-theory        28171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((D -> (D or E)) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-28171.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((D -> (D or E)) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))))), M:tm-443, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-28172
in-theory        28172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((C -> (C or D)) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-28172.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((C -> (C or D)) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))))), M:tm-443, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-28173
in-theory        28173
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and ((B -> (B or C)) and ((not (not A)) -> ((not (not A)) and A))))
theorem-size     25
proof            (modus-ponens tm-443 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-28173.        (((not (not A)) -> ((not (not A)) and A)) and ((B -> (B or C)) and ((not (not A)) -> ((not (not A)) and A)))), M:tm-443, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-28174
in-theory        28174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and ((D -> (D or E)) and (A -> (A and (B -> (C -> B))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-28174.        ((A -> (A and (B -> (C -> B)))) and ((D -> (D or E)) and (A -> (A and (B -> (C -> B)))))), M:tm-443, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-28175
in-theory        28175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and ((C -> (C or D)) and ((A -> B) -> ((A -> B) and (A -> A)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-28175.        (((A -> B) -> ((A -> B) and (A -> A))) and ((C -> (C or D)) and ((A -> B) -> ((A -> B) and (A -> A))))), M:tm-443, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-28176
in-theory        28176
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((D -> (D or E)) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-443 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-28176.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((D -> (D or E)) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))), M:tm-443, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-28177
in-theory        28177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((E -> (E or F)) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-28177.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((E -> (E or F)) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))), M:tm-443, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-28178
in-theory        28178
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((D -> (D or E)) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-28178.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((D -> (D or E)) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))), M:tm-443, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-28179
in-theory        28179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and ((D -> (D or E)) and (A -> (A and ((B and C) -> B)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-28179.        ((A -> (A and ((B and C) -> B))) and ((D -> (D or E)) and (A -> (A and ((B and C) -> B))))), M:tm-443, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-28180
in-theory        28180
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((D -> (D or E)) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-28180.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((D -> (D or E)) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))), M:tm-443, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-28181
in-theory        28181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and ((D -> (D or E)) and (A -> (A and ((B and C) -> C)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-28181.        ((A -> (A and ((B and C) -> C))) and ((D -> (D or E)) and (A -> (A and ((B and C) -> C))))), M:tm-443, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-28182
in-theory        28182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and ((D -> (D or E)) and (A -> (A and ((B -> (C -> B)) and A)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-28182.        ((A -> (A and ((B -> (C -> B)) and A))) and ((D -> (D or E)) and (A -> (A and ((B -> (C -> B)) and A))))), M:tm-443, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-28183
in-theory        28183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((E -> (E or F)) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-28183.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((E -> (E or F)) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))), M:tm-443, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-28184
in-theory        28184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and ((D -> (D or E)) and (A -> (A and (((B and C) -> B) and A)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-28184.        ((A -> (A and (((B and C) -> B) and A))) and ((D -> (D or E)) and (A -> (A and (((B and C) -> B) and A))))), M:tm-443, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-28185
in-theory        28185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and ((D -> (D or E)) and (A -> (A and (((B and C) -> C) and A)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-28185.        ((A -> (A and (((B and C) -> C) and A))) and ((D -> (D or E)) and (A -> (A and (((B and C) -> C) and A))))), M:tm-443, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-28186
in-theory        28186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((D -> (D or E)) and (A -> (A and ((B -> (C -> (B and C))) and A)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-28186.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((D -> (D or E)) and (A -> (A and ((B -> (C -> (B and C))) and A))))), M:tm-443, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-28187
in-theory        28187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((C -> (C or D)) and ((A -> B) -> ((A -> B) and (A -> (A and B))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-28187.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((C -> (C or D)) and ((A -> B) -> ((A -> B) and (A -> (A and B)))))), M:tm-443, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-28188
in-theory        28188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-28188.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((E -> (E or F)) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))))), M:tm-443, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-28189
in-theory        28189
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((E -> (E or F)) and (((A and B) -> B) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-28189.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((E -> (E or F)) and (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))))), M:tm-443, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-28190
in-theory        28190
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((E -> (E or F)) and (((A and B) -> A) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-28190.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((E -> (E or F)) and (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))))), M:tm-443, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-28191
in-theory        28191
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     53
proof            (modus-ponens tm-443 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-28191.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (F or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-443, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-28192
in-theory        28192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (E or F)) and ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-28192.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (E or F)) and ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-443, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-28193
in-theory        28193
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((C -> (C or D)) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-28193.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((C -> (C or D)) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))))), M:tm-443, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-28194
in-theory        28194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((D -> (D or E)) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C))))
theorem-size     45
proof            (modus-ponens tm-443 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-28194.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((D -> (D or E)) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)))), M:tm-443, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-28195
in-theory        28195
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and ((D -> (D or E)) and (A or ((B -> C) -> (B -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-443 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-28195.        ((A or ((B -> C) -> (B -> (B and C)))) and ((D -> (D or E)) and (A or ((B -> C) -> (B -> (B and C)))))), M:tm-443, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-28196
in-theory        28196
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and ((D -> (D or E)) and (((A -> B) -> (A -> (A and B))) or C)))
theorem-size     29
proof            (modus-ponens tm-443 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-28196.        ((((A -> B) -> (A -> (A and B))) or C) and ((D -> (D or E)) and (((A -> B) -> (A -> (A and B))) or C))), M:tm-443, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-28197
in-theory        28197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((D -> (D or E)) and (A -> (((B -> C) -> (B -> (B and C))) and A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-28197.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((D -> (D or E)) and (A -> (((B -> C) -> (B -> (B and C))) and A)))), M:tm-443, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-28198
in-theory        28198
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((C -> (C or D)) and (((A -> B) -> A) -> ((A -> B) -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-28198.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((C -> (C or D)) and (((A -> B) -> A) -> ((A -> B) -> (A and B))))), M:tm-443, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-28199
in-theory        28199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and ((D -> (D or E)) and (A -> ((B -> C) -> (B -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-443 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-28199.        ((A -> ((B -> C) -> (B -> (B and C)))) and ((D -> (D or E)) and (A -> ((B -> C) -> (B -> (B and C)))))), M:tm-443, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-28200
in-theory        28200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and ((D -> (D or E)) and (A -> (A and (B -> (C -> (B and C)))))))
theorem-size     29
proof            (modus-ponens tm-443 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-28200.        ((A -> (A and (B -> (C -> (B and C))))) and ((D -> (D or E)) and (A -> (A and (B -> (C -> (B and C))))))), M:tm-443, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-28201
in-theory        28201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E)))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-28201.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))))), M:tm-443, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-28202
in-theory        28202
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-28202.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> (D -> (E -> (D and E))))))), M:tm-443, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-28203
in-theory        28203
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-28203.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> (D -> (E -> (D and E))))))), M:tm-443, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-28204
in-theory        28204
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-443 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-28204.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-443, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-28205
in-theory        28205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-28205.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))))), M:tm-443, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-28206
in-theory        28206
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((E -> (E or F)) and ((A and ((B -> (C -> (B and C))) -> D)) -> D)))
theorem-size     33
proof            (modus-ponens tm-443 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-28206.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((E -> (E or F)) and ((A and ((B -> (C -> (B and C))) -> D)) -> D))), M:tm-443, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-28207
in-theory        28207
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((E -> (E or F)) and ((((A -> (B -> (A and B))) -> C) and D) -> C)))
theorem-size     33
proof            (modus-ponens tm-443 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-28207.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((E -> (E or F)) and ((((A -> (B -> (A and B))) -> C) and D) -> C))), M:tm-443, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-28208
in-theory        28208
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((D -> (D or E)) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-443 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-28208.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((D -> (D or E)) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C)))), M:tm-443, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-28209
in-theory        28209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((D -> (D or E)) and ((A -> (not (B -> (C -> (B and C))))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-28209.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((D -> (D or E)) and ((A -> (not (B -> (C -> (B and C))))) -> (not A)))), M:tm-443, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-28210
in-theory        28210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((E -> (E or F)) and (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C))))
theorem-size     49
proof            (modus-ponens tm-443 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-28210.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((E -> (E or F)) and (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)))), M:tm-443, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-28211
in-theory        28211
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and ((E -> (E or F)) and (A or (B -> (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-443 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-28211.        ((A or (B -> (C -> (D -> (C and D))))) and ((E -> (E or F)) and (A or (B -> (C -> (D -> (C and D))))))), M:tm-443, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-28212
in-theory        28212
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and ((E -> (E or F)) and ((A -> (B -> (C -> (B and C)))) or D)))
theorem-size     29
proof            (modus-ponens tm-443 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-28212.        (((A -> (B -> (C -> (B and C)))) or D) and ((E -> (E or F)) and ((A -> (B -> (C -> (B and C)))) or D))), M:tm-443, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-28213
in-theory        28213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((E -> (E or F)) and (A -> ((B -> (C -> (D -> (C and D)))) and A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-28213.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((E -> (E or F)) and (A -> ((B -> (C -> (D -> (C and D)))) and A)))), M:tm-443, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-28214
in-theory        28214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and ((D -> (D or E)) and ((A -> B) -> (A -> (C -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-443 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-28214.        (((A -> B) -> (A -> (C -> (B and C)))) and ((D -> (D or E)) and ((A -> B) -> (A -> (C -> (B and C)))))), M:tm-443, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-28215
in-theory        28215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and ((E -> (E or F)) and (A -> (B -> (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-443 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-28215.        ((A -> (B -> (C -> (D -> (C and D))))) and ((E -> (E or F)) and (A -> (B -> (C -> (D -> (C and D))))))), M:tm-443, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-28216
in-theory        28216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E))))
theorem-size     37
proof            (modus-ponens tm-443 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-28216.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)))), M:tm-443, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-28217
in-theory        28217
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-28217.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> (D -> C)) or E)))), M:tm-443, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-28218
in-theory        28218
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-28218.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> (D -> C)) or E)))), M:tm-443, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-28219
in-theory        28219
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-28219.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)))), M:tm-443, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-28220
in-theory        28220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-28220.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> (D -> C)) or E)))), M:tm-443, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-28221
in-theory        28221
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and ((E -> (E or F)) and (A or ((B -> (C -> B)) or D))))
theorem-size     25
proof            (modus-ponens tm-443 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-28221.        ((A or ((B -> (C -> B)) or D)) and ((E -> (E or F)) and (A or ((B -> (C -> B)) or D)))), M:tm-443, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-28222
in-theory        28222
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and ((E -> (E or F)) and (((A -> (B -> A)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-28222.        ((((A -> (B -> A)) or C) or D) and ((E -> (E or F)) and (((A -> (B -> A)) or C) or D))), M:tm-443, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-28223
in-theory        28223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and ((E -> (E or F)) and (A -> (((B -> (C -> B)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-28223.        ((A -> (((B -> (C -> B)) or D) and A)) and ((E -> (E or F)) and (A -> (((B -> (C -> B)) or D) and A)))), M:tm-443, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-28224
in-theory        28224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and ((E -> (E or F)) and (A -> ((B -> (C -> B)) or D))))
theorem-size     25
proof            (modus-ponens tm-443 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-28224.        ((A -> ((B -> (C -> B)) or D)) and ((E -> (E or F)) and (A -> ((B -> (C -> B)) or D)))), M:tm-443, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-28225
in-theory        28225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (G or H)) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     53
proof            (modus-ponens tm-443 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-28225.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (G or H)) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-443, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-28226
in-theory        28226
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (G or H)) and (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-28226.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (G or H)) and (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-443, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-28227
in-theory        28227
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (G or H)) and (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-28227.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (G or H)) and (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-443, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-28228
in-theory        28228
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (H or I)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-443 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-28228.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (H or I)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-443, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-28229
in-theory        28229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (G or H)) and ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-28229.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (G or H)) and ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-443, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-28230
in-theory        28230
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (F or G)) and (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-443 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-28230.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (F or G)) and (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-443, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-28231
in-theory        28231
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and ((F -> (F or G)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E)))
theorem-size     41
proof            (modus-ponens tm-443 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-28231.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and ((F -> (F or G)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E))), M:tm-443, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-28232
in-theory        28232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((F -> (F or G)) and (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))))
theorem-size     45
proof            (modus-ponens tm-443 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-28232.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((F -> (F or G)) and (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)))), M:tm-443, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-28233
in-theory        28233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (F or G)) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-443 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-28233.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (F or G)) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-443, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-28234
in-theory        28234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C and D) -> C) or E))))
theorem-size     37
proof            (modus-ponens tm-443 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-28234.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C and D) -> C) or E)))), M:tm-443, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-28235
in-theory        28235
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and ((F -> (F or G)) and (((A and B) -> B) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-28235.        ((((A and B) -> B) and (((C and D) -> C) or E)) and ((F -> (F or G)) and (((A and B) -> B) and (((C and D) -> C) or E)))), M:tm-443, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-28236
in-theory        28236
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and ((F -> (F or G)) and (((A and B) -> A) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-28236.        ((((A and B) -> A) and (((C and D) -> C) or E)) and ((F -> (F or G)) and (((A and B) -> A) and (((C and D) -> C) or E)))), M:tm-443, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-28237
in-theory        28237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-28237.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)))), M:tm-443, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-28238
in-theory        28238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-28238.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C and D) -> C) or E)))), M:tm-443, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-28239
in-theory        28239
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and ((E -> (E or F)) and (A or (((B and C) -> B) or D))))
theorem-size     25
proof            (modus-ponens tm-443 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-28239.        ((A or (((B and C) -> B) or D)) and ((E -> (E or F)) and (A or (((B and C) -> B) or D)))), M:tm-443, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-28240
in-theory        28240
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and ((E -> (E or F)) and ((((A and B) -> A) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-28240.        (((((A and B) -> A) or C) or D) and ((E -> (E or F)) and ((((A and B) -> A) or C) or D))), M:tm-443, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-28241
in-theory        28241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and ((E -> (E or F)) and (A -> ((((B and C) -> B) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-28241.        ((A -> ((((B and C) -> B) or D) and A)) and ((E -> (E or F)) and (A -> ((((B and C) -> B) or D) and A)))), M:tm-443, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-28242
in-theory        28242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and ((E -> (E or F)) and (A -> (((B and C) -> B) or D))))
theorem-size     25
proof            (modus-ponens tm-443 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-28242.        ((A -> (((B and C) -> B) or D)) and ((E -> (E or F)) and (A -> (((B and C) -> B) or D)))), M:tm-443, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-28243
in-theory        28243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C and D) -> D) or E))))
theorem-size     37
proof            (modus-ponens tm-443 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-28243.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C and D) -> D) or E)))), M:tm-443, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-28244
in-theory        28244
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and ((F -> (F or G)) and (((A and B) -> B) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-28244.        ((((A and B) -> B) and (((C and D) -> D) or E)) and ((F -> (F or G)) and (((A and B) -> B) and (((C and D) -> D) or E)))), M:tm-443, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-28245
in-theory        28245
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and ((F -> (F or G)) and (((A and B) -> A) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-28245.        ((((A and B) -> A) and (((C and D) -> D) or E)) and ((F -> (F or G)) and (((A and B) -> A) and (((C and D) -> D) or E)))), M:tm-443, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-28246
in-theory        28246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-28246.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)))), M:tm-443, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-28247
in-theory        28247
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-28247.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C and D) -> D) or E)))), M:tm-443, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-28248
in-theory        28248
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and ((E -> (E or F)) and (A or (((B and C) -> C) or D))))
theorem-size     25
proof            (modus-ponens tm-443 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-28248.        ((A or (((B and C) -> C) or D)) and ((E -> (E or F)) and (A or (((B and C) -> C) or D)))), M:tm-443, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-28249
in-theory        28249
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and ((E -> (E or F)) and ((((A and B) -> B) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-28249.        (((((A and B) -> B) or C) or D) and ((E -> (E or F)) and ((((A and B) -> B) or C) or D))), M:tm-443, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-28250
in-theory        28250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and ((E -> (E or F)) and (A -> ((((B and C) -> C) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-28250.        ((A -> ((((B and C) -> C) or D) and A)) and ((E -> (E or F)) and (A -> ((((B and C) -> C) or D) and A)))), M:tm-443, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-28251
in-theory        28251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and ((E -> (E or F)) and (A -> (((B and C) -> C) or D))))
theorem-size     25
proof            (modus-ponens tm-443 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-28251.        ((A -> (((B and C) -> C) or D)) and ((E -> (E or F)) and (A -> (((B and C) -> C) or D)))), M:tm-443, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-28252
in-theory        28252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E))))
theorem-size     41
proof            (modus-ponens tm-443 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-28252.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)))), M:tm-443, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-28253
in-theory        28253
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-443 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-28253.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> (D -> (C and D))) or E)))), M:tm-443, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-28254
in-theory        28254
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-443 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-28254.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> (D -> (C and D))) or E)))), M:tm-443, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-28255
in-theory        28255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     53
proof            (modus-ponens tm-443 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-28255.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-443, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-28256
in-theory        28256
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-443 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-28256.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)))), M:tm-443, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-28257
in-theory        28257
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and ((E -> (E or F)) and (A or ((B -> (C -> (B and C))) or D))))
theorem-size     29
proof            (modus-ponens tm-443 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-28257.        ((A or ((B -> (C -> (B and C))) or D)) and ((E -> (E or F)) and (A or ((B -> (C -> (B and C))) or D)))), M:tm-443, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-28258
in-theory        28258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and ((E -> (E or F)) and (((A -> (B -> (A and B))) or C) or D)))
theorem-size     29
proof            (modus-ponens tm-443 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-28258.        ((((A -> (B -> (A and B))) or C) or D) and ((E -> (E or F)) and (((A -> (B -> (A and B))) or C) or D))), M:tm-443, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-28259
in-theory        28259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((E -> (E or F)) and (A -> (((B -> (C -> (B and C))) or D) and A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-28259.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((E -> (E or F)) and (A -> (((B -> (C -> (B and C))) or D) and A)))), M:tm-443, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-28260
in-theory        28260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and ((E -> (E or F)) and (A -> ((B -> (C -> (B and C))) or D))))
theorem-size     29
proof            (modus-ponens tm-443 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-28260.        ((A -> ((B -> (C -> (B and C))) or D)) and ((E -> (E or F)) and (A -> ((B -> (C -> (B and C))) or D)))), M:tm-443, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-28261
in-theory        28261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> (C or D)) or E))))
theorem-size     37
proof            (modus-ponens tm-443 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-28261.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)))), M:tm-443, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-28262
in-theory        28262
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-28262.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> (C or D)) or E)))), M:tm-443, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-28263
in-theory        28263
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-28263.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> (C or D)) or E)))), M:tm-443, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-28264
in-theory        28264
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-28264.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)))), M:tm-443, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-28265
in-theory        28265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-28265.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> (C or D)) or E)))), M:tm-443, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-28266
in-theory        28266
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and ((E -> (E or F)) and (A or ((B -> (B or C)) or D))))
theorem-size     25
proof            (modus-ponens tm-443 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-28266.        ((A or ((B -> (B or C)) or D)) and ((E -> (E or F)) and (A or ((B -> (B or C)) or D)))), M:tm-443, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-28267
in-theory        28267
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and ((E -> (E or F)) and (((A -> (A or B)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-28267.        ((((A -> (A or B)) or C) or D) and ((E -> (E or F)) and (((A -> (A or B)) or C) or D))), M:tm-443, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-28268
in-theory        28268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and ((E -> (E or F)) and (A -> (((B -> (B or C)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-28268.        ((A -> (((B -> (B or C)) or D) and A)) and ((E -> (E or F)) and (A -> (((B -> (B or C)) or D) and A)))), M:tm-443, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-28269
in-theory        28269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and ((E -> (E or F)) and (A -> ((B -> (B or C)) or D))))
theorem-size     25
proof            (modus-ponens tm-443 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-28269.        ((A -> ((B -> (B or C)) or D)) and ((E -> (E or F)) and (A -> ((B -> (B or C)) or D)))), M:tm-443, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-28270
in-theory        28270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and ((E -> (E or F)) and ((A -> (A or B)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-28270.        (((A -> (A or B)) and (C -> (D -> C))) and ((E -> (E or F)) and ((A -> (A or B)) and (C -> (D -> C))))), M:tm-443, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-28271
in-theory        28271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-28271.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-443, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-28272
in-theory        28272
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and ((E -> (E or F)) and ((A -> (A or B)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28272.        (((A -> (A or B)) and ((C and D) -> C)) and ((E -> (E or F)) and ((A -> (A or B)) and ((C and D) -> C)))), M:tm-443, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-28273
in-theory        28273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and ((E -> (E or F)) and ((A -> (A or B)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-443 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-28273.        (((A -> (A or B)) and ((C and D) -> D)) and ((E -> (E or F)) and ((A -> (A or B)) and ((C and D) -> D)))), M:tm-443, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-28274
in-theory        28274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A -> (A or B)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-28274.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A -> (A or B)) and (C -> (D -> (C and D)))))), M:tm-443, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-28275
in-theory        28275
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and ((E -> (E or F)) and ((A -> (A or B)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28275.        (((A -> (A or B)) and (C -> (C or D))) and ((E -> (E or F)) and ((A -> (A or B)) and (C -> (C or D))))), M:tm-443, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-28276
in-theory        28276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and ((E -> (E or F)) and ((A -> (A or B)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-28276.        (((A -> (A or B)) and (C -> (D or C))) and ((E -> (E or F)) and ((A -> (A or B)) and (C -> (D or C))))), M:tm-443, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-28277
in-theory        28277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-28277.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-443, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-28278
in-theory        28278
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (E or F)) and ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-28278.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (E or F)) and ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-443, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-28279
in-theory        28279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and ((D -> (D or E)) and ((A -> (A or B)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-28279.        (((A -> (A or B)) and ((not (not C)) -> C)) and ((D -> (D or E)) and ((A -> (A or B)) and ((not (not C)) -> C)))), M:tm-443, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-28280
in-theory        28280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-28280.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> (D -> (E -> D)))))), M:tm-443, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-28281
in-theory        28281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((E -> (E or F)) and ((A -> (A or B)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-28281.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((E -> (E or F)) and ((A -> (A or B)) and ((C -> D) -> (C -> C))))), M:tm-443, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-28282
in-theory        28282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-443 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-28282.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-443, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-28283
in-theory        28283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-28283.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-443, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-28284
in-theory        28284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (F or G)) and ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-28284.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (F or G)) and ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-443, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-28285
in-theory        28285
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-28285.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> ((D and E) -> D))))), M:tm-443, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-28286
in-theory        28286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (F or G)) and ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-28286.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (F or G)) and ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-443, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-28287
in-theory        28287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-28287.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> ((D and E) -> E))))), M:tm-443, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-28288
in-theory        28288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-28288.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))))), M:tm-443, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-28289
in-theory        28289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (G or H)) and ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-28289.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (G or H)) and ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-443, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-28290
in-theory        28290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-28290.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> (((D and E) -> D) and C))))), M:tm-443, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-28291
in-theory        28291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-28291.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> (((D and E) -> E) and C))))), M:tm-443, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-28292
in-theory        28292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-28292.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-443, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-28293
in-theory        28293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (E or F)) and ((A -> (A or B)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-28293.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (E or F)) and ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))))), M:tm-443, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-28294
in-theory        28294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-28294.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))))), M:tm-443, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-28295
in-theory        28295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-28295.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> (D -> C)) or E)))), M:tm-443, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-28296
in-theory        28296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (G or H)) and ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-28296.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (G or H)) and ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-443, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-28297
in-theory        28297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and ((F -> (F or G)) and ((A -> (A or B)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-28297.        (((A -> (A or B)) and (((C and D) -> C) or E)) and ((F -> (F or G)) and ((A -> (A or B)) and (((C and D) -> C) or E)))), M:tm-443, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-28298
in-theory        28298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and ((F -> (F or G)) and ((A -> (A or B)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-28298.        (((A -> (A or B)) and (((C and D) -> D) or E)) and ((F -> (F or G)) and ((A -> (A or B)) and (((C and D) -> D) or E)))), M:tm-443, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-28299
in-theory        28299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-443 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-28299.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)))), M:tm-443, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-28300
in-theory        28300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-28300.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> (C or D)) or E)))), M:tm-443, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-28301
in-theory        28301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28301.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))))), M:tm-443, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28302
in-theory        28302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and ((D -> (D or E)) and (A -> (A and ((B -> (B or C)) and A)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28302.        ((A -> (A and ((B -> (B or C)) and A))) and ((D -> (D or E)) and (A -> (A and ((B -> (B or C)) and A))))), M:tm-443, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28303
in-theory        28303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-409 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28303.        (((A -> (A or B)) or C) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-409, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28304
in-theory        28304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-400 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28304.        (((A -> (B -> (A and B))) or C) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-400, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28305
in-theory        28305
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-391 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28305.        ((((A and B) -> B) or C) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-391, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28306
in-theory        28306
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-382 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28306.        ((((A and B) -> A) or C) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-382, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28307
in-theory        28307
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-373 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28307.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and ((F -> (F or G)) and E)))), M:tm-373, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28308
in-theory        28308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-364 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28308.        (((A -> (B -> A)) or C) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-364, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28309
in-theory        28309
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and ((C -> (C or D)) and A)) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28309.        (A -> (B -> ((A and ((C -> (C or D)) and A)) and B))), M:tm-355, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-28310
in-theory        28310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-354 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28310.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-354, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28311
in-theory        28311
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((D -> (D or E)) and (B -> (C -> (B and C))))))
theorem-size     31
proof            (modus-ponens tm-351 tm-443 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (and (-> Bm (or Bm Cm)) (-> A (-> B (and A B))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28311.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((D -> (D or E)) and (B -> (C -> (B and C)))))), M:tm-351, m:tm-443, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (and (-> Bm (or Bm Cm)) (-> A (-> B (and A B)))))))
================================================================
tm-name          tm-28312
in-theory        28312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28312.        ((A -> (A and ((B -> (B or C)) and A))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28313
in-theory        28313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and ((D -> (D or E)) and C))))
theorem-size     21
proof            (modus-ponens tm-338 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28313.        (((A -> B) -> (A -> (A and B))) and (C -> (C and ((D -> (D or E)) and C)))), M:tm-338, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28314
in-theory        28314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((C -> (C or D)) and (A -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-335 tm-443 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (and (-> Bm (or Bm Cm)) (-> A (and A B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28314.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((C -> (C or D)) and (A -> (A and B))))), M:tm-335, m:tm-443, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (and (-> Bm (or Bm Cm)) (-> A (and A B))))))
================================================================
tm-name          tm-28315
in-theory        28315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (A -> (A and (A and ((B -> (B or C)) and A)))))
theorem-size     25
proof            (modus-ponens tm-328 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28315.        ((A -> (A and ((B -> (B or C)) and A))) and (A -> (A and (A and ((B -> (B or C)) and A))))), M:tm-328, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-28316
in-theory        28316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and ((D -> (E -> (D and E))) and (A -> (A and ((B -> (B or C)) and A)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28316.        ((A -> (A and ((B -> (B or C)) and A))) and ((D -> (E -> (D and E))) and (A -> (A and ((B -> (B or C)) and A))))), M:tm-327, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28317
in-theory        28317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (((D and E) -> E) and (A -> (A and ((B -> (B or C)) and A)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28317.        ((A -> (A and ((B -> (B or C)) and A))) and (((D and E) -> E) and (A -> (A and ((B -> (B or C)) and A))))), M:tm-326, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28318
in-theory        28318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (((D and E) -> D) and (A -> (A and ((B -> (B or C)) and A)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28318.        ((A -> (A and ((B -> (B or C)) and A))) and (((D and E) -> D) and (A -> (A and ((B -> (B or C)) and A))))), M:tm-325, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28319
in-theory        28319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and ((B -> (B or C)) and A)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28319.        ((A -> (A and ((B -> (B or C)) and A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and ((B -> (B or C)) and A))))), M:tm-324, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28320
in-theory        28320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and ((D -> (E -> D)) and (A -> (A and ((B -> (B or C)) and A)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28320.        ((A -> (A and ((B -> (B or C)) and A))) and ((D -> (E -> D)) and (A -> (A and ((B -> (B or C)) and A))))), M:tm-323, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28321
in-theory        28321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28321.        ((A -> (A and ((B -> (B or C)) and A))) and ((D and E) -> E)), M:tm-322, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28322
in-theory        28322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28322.        ((A -> (A and ((B -> (B or C)) and A))) and ((D and E) -> D)), M:tm-320, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28323
in-theory        28323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28323.        ((A -> (A and ((B -> (B or C)) and A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28324
in-theory        28324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28324.        ((A -> (A and ((B -> (B or C)) and A))) and (A -> A)), M:tm-316, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-28325
in-theory        28325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28325.        ((A -> (A and ((B -> (B or C)) and A))) and (D -> (E -> D))), M:tm-315, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28326
in-theory        28326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and ((A -> (not (A and ((B -> (B or C)) and A)))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28326.        ((A -> (A and ((B -> (B or C)) and A))) and ((A -> (not (A and ((B -> (B or C)) and A)))) -> (not A))), M:tm-313, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-28327
in-theory        28327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (((A and ((B -> (B or C)) and A)) -> D) -> ((A or (A and ((B -> (B or C)) and A))) -> D)))
theorem-size     37
proof            (modus-ponens tm-312 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28327.        ((A -> (A and ((B -> (B or C)) and A))) and (((A and ((B -> (B or C)) and A)) -> D) -> ((A or (A and ((B -> (B or C)) and A))) -> D))), M:tm-312, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-28328
in-theory        28328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (D or (A -> (A and ((B -> (B or C)) and A)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28328.        ((A -> (A and ((B -> (B or C)) and A))) and (D or (A -> (A and ((B -> (B or C)) and A))))), M:tm-311, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28329
in-theory        28329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and ((A -> (A and ((B -> (B or C)) and A))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28329.        ((A -> (A and ((B -> (B or C)) and A))) and ((A -> (A and ((B -> (B or C)) and A))) or D)), M:tm-310, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28330
in-theory        28330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (D -> ((A -> (A and ((B -> (B or C)) and A))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28330.        ((A -> (A and ((B -> (B or C)) and A))) and (D -> ((A -> (A and ((B -> (B or C)) and A))) and D))), M:tm-309, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28331
in-theory        28331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (D -> (A -> (A and ((B -> (B or C)) and A)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28331.        ((A -> (A and ((B -> (B or C)) and A))) and (D -> (A -> (A and ((B -> (B or C)) and A))))), M:tm-305, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28332
in-theory        28332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     23
proof            (modus-ponens tm-303 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28332.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-303, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28333
in-theory        28333
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and ((D -> (D or E)) and ((B -> (C -> (B and C))) and A))))
theorem-size     37
proof            (modus-ponens tm-300 tm-443 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (and (-> Bm (or Bm Cm)) (and (-> A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28333.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and ((D -> (D or E)) and ((B -> (C -> (B and C))) and A)))), M:tm-300, m:tm-443, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (and (-> Bm (or Bm Cm)) (and (-> A (-> B (and A B))) C)))))
================================================================
tm-name          tm-28334
in-theory        28334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-270 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28334.        ((A -> (((B and C) -> C) and A)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-270, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28335
in-theory        28335
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((D -> (D or E)) and (((B and C) -> C) and A))))
theorem-size     31
proof            (modus-ponens tm-267 tm-443 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (and (-> Bm (or Bm Cm)) (and (-> (and A B) B) C))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28335.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((D -> (D or E)) and (((B and C) -> C) and A)))), M:tm-267, m:tm-443, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (and (-> Bm (or Bm Cm)) (and (-> (and A B) B) C)))))
================================================================
tm-name          tm-28336
in-theory        28336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-239 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28336.        ((A -> (((B and C) -> B) and A)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-239, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28337
in-theory        28337
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((D -> (D or E)) and (((B and C) -> B) and A))))
theorem-size     31
proof            (modus-ponens tm-236 tm-443 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (and (-> Bm (or Bm Cm)) (and (-> (and A B) A) C))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28337.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((D -> (D or E)) and (((B and C) -> B) and A)))), M:tm-236, m:tm-443, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (and (-> Bm (or Bm Cm)) (and (-> (and A B) A) C)))))
================================================================
tm-name          tm-28338
in-theory        28338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and ((F -> (F or G)) and E))))
theorem-size     29
proof            (modus-ponens tm-210 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28338.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and ((F -> (F or G)) and E)))), M:tm-210, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28339
in-theory        28339
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((E -> (E or F)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     55
proof            (modus-ponens tm-207 tm-443 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (or Bm Cm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28339.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((E -> (E or F)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-207, m:tm-443, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (or Bm Cm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-28340
in-theory        28340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-183 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28340.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-183, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28341
in-theory        28341
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and ((D -> (D or E)) and ((B -> (C -> B)) and A))))
theorem-size     31
proof            (modus-ponens tm-180 tm-443 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (and (-> Bm (or Bm Cm)) (and (-> A (-> B A)) C))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28341.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and ((D -> (D or E)) and ((B -> (C -> B)) and A)))), M:tm-180, m:tm-443, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (and (-> Bm (or Bm Cm)) (and (-> A (-> B A)) C)))))
================================================================
tm-name          tm-28342
in-theory        28342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-157 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28342.        ((A -> ((B and C) -> C)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-157, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28343
in-theory        28343
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((D -> (D or E)) and ((B and C) -> C))))
theorem-size     25
proof            (modus-ponens tm-154 tm-443 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (and (-> Bm (or Bm Cm)) (-> (and A B) B))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28343.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((D -> (D or E)) and ((B and C) -> C)))), M:tm-154, m:tm-443, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (and (-> Bm (or Bm Cm)) (-> (and A B) B)))))
================================================================
tm-name          tm-28344
in-theory        28344
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     27
proof            (modus-ponens tm-147 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28344.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-147, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28345
in-theory        28345
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((D -> (D or E)) and ((A and (B -> C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-144 tm-443 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (and (-> Bm (or Bm Cm)) (-> (and A (-> B C)) C))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28345.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((D -> (D or E)) and ((A and (B -> C)) -> C)))), M:tm-144, m:tm-443, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (and (-> Bm (or Bm Cm)) (-> (and A (-> B C)) C)))))
================================================================
tm-name          tm-28346
in-theory        28346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-134 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28346.        ((A -> ((B and C) -> B)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-134, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28347
in-theory        28347
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((D -> (D or E)) and ((B and C) -> B))))
theorem-size     25
proof            (modus-ponens tm-131 tm-443 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (and (-> Bm (or Bm Cm)) (-> (and A B) A))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28347.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((D -> (D or E)) and ((B and C) -> B)))), M:tm-131, m:tm-443, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (and (-> Bm (or Bm Cm)) (-> (and A B) A)))))
================================================================
tm-name          tm-28348
in-theory        28348
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     27
proof            (modus-ponens tm-125 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28348.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-125, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28349
in-theory        28349
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((D -> (D or E)) and (((A -> B) and C) -> B))))
theorem-size     37
proof            (modus-ponens tm-122 tm-443 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (and (-> Bm (or Bm Cm)) (-> (and (-> A B) C) B))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28349.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((D -> (D or E)) and (((A -> B) and C) -> B)))), M:tm-122, m:tm-443, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (and (-> Bm (or Bm Cm)) (-> (and (-> A B) C) B)))))
================================================================
tm-name          tm-28350
in-theory        28350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-113 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28350.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (F or G)) and E)))), M:tm-113, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28351
in-theory        28351
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (E or F)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-110 tm-443 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (-> Bm (or Bm Cm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28351.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (E or F)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-110, m:tm-443, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (-> Bm (or Bm Cm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
================================================================
tm-name          tm-28352
in-theory        28352
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     31
proof            (modus-ponens tm-105 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28352.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-105, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28353
in-theory        28353
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((D -> (D or E)) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-102 tm-443 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (and (-> Bm (or Bm Cm)) (-> (-> A (-> B C)) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28353.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((D -> (D or E)) and ((A -> (B -> C)) -> (A -> C))))), M:tm-102, m:tm-443, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (and (-> Bm (or Bm Cm)) (-> (-> A (-> B C)) (-> A C))))))
================================================================
tm-name          tm-28354
in-theory        28354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and ((D -> (D or E)) and C))))
theorem-size     19
proof            (modus-ponens tm-95 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28354.        (((A -> B) -> (A -> A)) and (C -> (C and ((D -> (D or E)) and C)))), M:tm-95, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28355
in-theory        28355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and ((C -> (C or D)) and (A -> A))))
theorem-size     21
proof            (modus-ponens tm-92 tm-443 ((Am (-> A A)) (B (and (-> A A) (and (-> Bm (or Bm Cm)) (-> A A))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28355.        (((A -> B) or (A -> A)) -> ((A -> A) and ((C -> (C or D)) and (A -> A)))), M:tm-92, m:tm-443, u:((Am (-> A A)) (B (and (-> A A) (and (-> Bm (or Bm Cm)) (-> A A)))))
================================================================
tm-name          tm-28356
in-theory        28356
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and ((C -> (C or D)) and A))))
theorem-size     13
proof            (modus-ponens tm-84 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28356.        (A -> (B -> (A and ((C -> (C or D)) and A)))), M:tm-84, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-28357
in-theory        28357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-83 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28357.        ((A -> (B -> (C -> B))) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-83, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28358
in-theory        28358
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((D -> (D or E)) and (B -> (C -> B)))))
theorem-size     25
proof            (modus-ponens tm-80 tm-443 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (and (-> Bm (or Bm Cm)) (-> A (-> B A)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28358.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((D -> (D or E)) and (B -> (C -> B))))), M:tm-80, m:tm-443, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (and (-> Bm (or Bm Cm)) (-> A (-> B A))))))
================================================================
tm-name          tm-28359
in-theory        28359
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and ((C -> (C or D)) and B))))
theorem-size     17
proof            (modus-ponens tm-76 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-10 tm-2 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28359.        (((not (not A)) -> A) and (B -> (B and ((C -> (C or D)) and B)))), M:tm-76, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28360
in-theory        28360
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and ((B -> (B or C)) and A)))
theorem-size     15
proof            (modus-ponens tm-73 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28360.        (((not (not A)) or A) -> (A and ((B -> (B or C)) and A))), M:tm-73, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-28361
in-theory        28361
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and ((D -> (D or E)) and C))))
theorem-size     23
proof            (modus-ponens tm-69 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-9 tm-2 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28361.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and ((D -> (D or E)) and C)))), M:tm-69, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28362
in-theory        28362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((C -> (C or D)) and ((A -> (not B)) -> (not A)))))
theorem-size     33
proof            (modus-ponens tm-66 tm-443 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (and (-> Bm (or Bm Cm)) (-> (-> A (not B)) (not A)))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28362.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((C -> (C or D)) and ((A -> (not B)) -> (not A))))), M:tm-66, m:tm-443, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (and (-> Bm (or Bm Cm)) (-> (-> A (not B)) (not A))))))
================================================================
tm-name          tm-28363
in-theory        28363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     25
proof            (modus-ponens tm-54 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28363.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-54, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28364
in-theory        28364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     39
proof            (modus-ponens tm-51 tm-443 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> (or C A) B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28364.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((D -> (D or E)) and ((B -> C) -> ((A or B) -> C))))), M:tm-51, m:tm-443, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> (or C A) B))))))
================================================================
tm-name          tm-28365
in-theory        28365
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and ((C -> (C or D)) and (B or A))))
theorem-size     19
proof            (modus-ponens tm-50 tm-443 ((Am (or A B)) (C (and (or A B) (and (-> Bm (or Bm Cm)) (or A B))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28365.        ((A or (B or A)) -> ((B or A) and ((C -> (C or D)) and (B or A)))), M:tm-50, m:tm-443, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (or Bm Cm)) (or A B)))))
================================================================
tm-name          tm-28366
in-theory        28366
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and ((C -> (C or D)) and (A or B))))
theorem-size     19
proof            (modus-ponens tm-49 tm-443 ((Am (or A B)) (C (and (or A B) (and (-> Bm (or Bm Cm)) (or A B))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28366.        ((A or (A or B)) -> ((A or B) and ((C -> (C or D)) and (A or B)))), M:tm-49, m:tm-443, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (or Bm Cm)) (or A B)))))
================================================================
tm-name          tm-28367
in-theory        28367
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((C -> (C or D)) and (B -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-48 tm-443 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> Bm (or Bm Cm)) (-> A (and B A)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28367.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((C -> (C or D)) and (B -> (A and B))))), M:tm-48, m:tm-443, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> Bm (or Bm Cm)) (-> A (and B A))))))
================================================================
tm-name          tm-28368
in-theory        28368
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and ((C -> (C or D)) and B)))
theorem-size     15
proof            (modus-ponens tm-47 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28368.        (((A and B) or B) -> (B and ((C -> (C or D)) and B))), M:tm-47, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-28369
in-theory        28369
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and ((C -> (C or D)) and A)))
theorem-size     15
proof            (modus-ponens tm-46 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28369.        (((A and B) or A) -> (A and ((C -> (C or D)) and A))), M:tm-46, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-28370
in-theory        28370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (D or E)) and ((A -> B) -> (A -> C)))))
theorem-size     35
proof            (modus-ponens tm-45 tm-443 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28370.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (D or E)) and ((A -> B) -> (A -> C))))), M:tm-45, m:tm-443, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-28371
in-theory        28371
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and ((C -> (C or D)) and (B -> A))))
theorem-size     19
proof            (modus-ponens tm-44 tm-443 ((Am (-> A B)) (C (and (-> A B) (and (-> Bm (or Bm Cm)) (-> A B))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28371.        ((A or (B -> A)) -> ((B -> A) and ((C -> (C or D)) and (B -> A)))), M:tm-44, m:tm-443, u:((Am (-> A B)) (C (and (-> A B) (and (-> Bm (or Bm Cm)) (-> A B)))))
================================================================
tm-name          tm-28372
in-theory        28372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and ((D -> (D or E)) and C))))
theorem-size     17
proof            (modus-ponens tm-42 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28372.        ((A -> (B or A)) and (C -> (C and ((D -> (D or E)) and C)))), M:tm-42, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28373
in-theory        28373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and ((D -> (D or E)) and C))))
theorem-size     17
proof            (modus-ponens tm-32 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28373.        ((A -> (A or B)) and (C -> (C and ((D -> (D or E)) and C)))), M:tm-32, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28374
in-theory        28374
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and ((B -> (B or C)) and A))))
theorem-size     13
proof            (modus-ponens tm-24 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28374.        (A -> (A and (A and ((B -> (B or C)) and A)))), M:tm-24, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-28375
in-theory        28375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and ((D -> (D or E)) and C))))
theorem-size     19
proof            (modus-ponens tm-23 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28375.        ((A -> (B -> (A and B))) and (C -> (C and ((D -> (D or E)) and C)))), M:tm-23, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28376
in-theory        28376
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and ((D -> (D or E)) and C))))
theorem-size     17
proof            (modus-ponens tm-22 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28376.        (((A and B) -> B) and (C -> (C and ((D -> (D or E)) and C)))), M:tm-22, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28377
in-theory        28377
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and ((D -> (D or E)) and C))))
theorem-size     17
proof            (modus-ponens tm-21 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28377.        (((A and B) -> A) and (C -> (C and ((D -> (D or E)) and C)))), M:tm-21, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28378
in-theory        28378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     25
proof            (modus-ponens tm-20 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28378.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-20, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28379
in-theory        28379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and ((D -> (D or E)) and C))))
theorem-size     17
proof            (modus-ponens tm-19 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28379.        ((A -> (B -> A)) and (C -> (C and ((D -> (D or E)) and C)))), M:tm-19, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28380
in-theory        28380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and ((B -> (B or C)) and A)))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-9 tm-2 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28380.        ((A -> (not (A and ((B -> (B or C)) and A)))) -> (not A)), M:tm-9, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-28381
in-theory        28381
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) and A)) -> D) -> ((A or (A and ((B -> (B or C)) and A))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28381.        (((A and ((B -> (B or C)) and A)) -> D) -> ((A or (A and ((B -> (B or C)) and A))) -> D)), M:tm-8, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-28382
in-theory        28382
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and ((C -> (C or D)) and B))))
theorem-size     13
proof            (modus-ponens tm-7 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-7 tm-2 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28382.        (A or (B -> (B and ((C -> (C or D)) and B)))), M:tm-7, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28383
in-theory        28383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-6 tm-2 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28383.        ((A -> (A and ((B -> (B or C)) and A))) or D), M:tm-6, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28384
in-theory        28384
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and ((C -> (C or D)) and B))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28384.        (A -> ((B -> (B and ((C -> (C or D)) and B))) and A)), M:tm-5, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28385
in-theory        28385
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and ((C -> (C or D)) and B))))
theorem-size     13
proof            (modus-ponens tm-1 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-1 tm-2 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28385.        (A -> (B -> (B and ((C -> (C or D)) and B)))), M:tm-1, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-28386
in-theory        28386
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28386.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))))), M:tm-443, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28387
in-theory        28387
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-409 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28387.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-409, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28388
in-theory        28388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-400 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28388.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-400, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28389
in-theory        28389
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-391 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28389.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-391, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28390
in-theory        28390
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-382 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28390.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-382, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28391
in-theory        28391
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-373 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28391.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G)))), M:tm-373, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28392
in-theory        28392
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-364 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28392.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-364, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28393
in-theory        28393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-354 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28393.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-354, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28394
in-theory        28394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28394.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28395
in-theory        28395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-338 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28395.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E)))), M:tm-338, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28396
in-theory        28396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28396.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))))), M:tm-327, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28397
in-theory        28397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28397.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))))), M:tm-326, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28398
in-theory        28398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28398.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))))), M:tm-325, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28399
in-theory        28399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28399.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))))), M:tm-324, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28400
in-theory        28400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28400.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))))), M:tm-323, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28401
in-theory        28401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28401.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28402
in-theory        28402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28402.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28403
in-theory        28403
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28403.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28404
in-theory        28404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28404.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28405
in-theory        28405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (F or ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28405.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (F or ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))))), M:tm-311, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28406
in-theory        28406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28406.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) or F)), M:tm-310, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28407
in-theory        28407
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (F -> (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28407.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (F -> (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and F))), M:tm-309, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28408
in-theory        28408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (C -> ((D -> (D or E)) and C)))
theorem-size     27
proof            (modus-ponens tm-308 tm-444 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28408.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (C -> ((D -> (D or E)) and C))), M:tm-308, m:tm-444, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm))))
================================================================
tm-name          tm-28409
in-theory        28409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (A -> (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-307 tm-444 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28409.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-444, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm))))
================================================================
tm-name          tm-28410
in-theory        28410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (F -> ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28410.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (F -> ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))))), M:tm-305, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28411
in-theory        28411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-303 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28411.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-303, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28412
in-theory        28412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-270 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28412.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-270, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28413
in-theory        28413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-239 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28413.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-239, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28414
in-theory        28414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     35
proof            (modus-ponens tm-210 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28414.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G)))), M:tm-210, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28415
in-theory        28415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-183 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28415.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-183, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28416
in-theory        28416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-157 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28416.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-157, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28417
in-theory        28417
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     33
proof            (modus-ponens tm-147 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28417.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-147, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28418
in-theory        28418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-134 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28418.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-134, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28419
in-theory        28419
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     33
proof            (modus-ponens tm-125 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28419.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-125, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28420
in-theory        28420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-113 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28420.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G)))), M:tm-113, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28421
in-theory        28421
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     37
proof            (modus-ponens tm-105 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28421.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-105, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28422
in-theory        28422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-95 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28422.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E)))), M:tm-95, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28423
in-theory        28423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-83 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28423.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-83, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28424
in-theory        28424
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> ((E -> (E or F)) and D))))
theorem-size     23
proof            (modus-ponens tm-76 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28424.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> ((E -> (E or F)) and D)))), M:tm-76, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28425
in-theory        28425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     29
proof            (modus-ponens tm-69 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28425.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E)))), M:tm-69, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28426
in-theory        28426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-54 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28426.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-54, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28427
in-theory        28427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-42 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28427.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E)))), M:tm-42, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28428
in-theory        28428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-32 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28428.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E)))), M:tm-32, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28429
in-theory        28429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-23 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28429.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E)))), M:tm-23, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28430
in-theory        28430
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-22 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28430.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E)))), M:tm-22, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28431
in-theory        28431
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-21 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28431.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E)))), M:tm-21, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28432
in-theory        28432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-20 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28432.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-20, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28433
in-theory        28433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-19 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28433.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (F or G)) and E)))), M:tm-19, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28434
in-theory        28434
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-7 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28434.        (A or ((B -> (C -> (B and C))) and (D -> ((E -> (E or F)) and D)))), M:tm-7, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28435
in-theory        28435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-6 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28435.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) or F), M:tm-6, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28436
in-theory        28436
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> ((E -> (E or F)) and D))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28436.        (A -> (((B -> (C -> (B and C))) and (D -> ((E -> (E or F)) and D))) and A)), M:tm-5, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28437
in-theory        28437
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-1 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28437.        (A -> ((B -> (C -> (B and C))) and (D -> ((E -> (E or F)) and D)))), M:tm-1, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28438
in-theory        28438
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28438.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> ((D -> (D or E)) and C))))), M:tm-443, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28439
in-theory        28439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28439.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-409, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28440
in-theory        28440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28440.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-400, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28441
in-theory        28441
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28441.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-391, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28442
in-theory        28442
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28442.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-382, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28443
in-theory        28443
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28443.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G)))), M:tm-373, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28444
in-theory        28444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28444.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-364, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28445
in-theory        28445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28445.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-354, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28446
in-theory        28446
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28446.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28447
in-theory        28447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28447.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E)))), M:tm-338, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28448
in-theory        28448
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> ((D -> (D or E)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28448.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> ((D -> (D or E)) and C))))), M:tm-327, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28449
in-theory        28449
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> G) and (((A and B) -> B) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28449.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> G) and (((A and B) -> B) and (C -> ((D -> (D or E)) and C))))), M:tm-326, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28450
in-theory        28450
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> F) and (((A and B) -> B) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28450.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> F) and (((A and B) -> B) and (C -> ((D -> (D or E)) and C))))), M:tm-325, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28451
in-theory        28451
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> ((D -> (D or E)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28451.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> ((D -> (D or E)) and C))))), M:tm-324, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28452
in-theory        28452
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28452.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> ((D -> (D or E)) and C))))), M:tm-323, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28453
in-theory        28453
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28453.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28454
in-theory        28454
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28454.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28455
in-theory        28455
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28455.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28456
in-theory        28456
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28456.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28457
in-theory        28457
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (F or (((A and B) -> B) and (C -> ((D -> (D or E)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28457.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (F or (((A and B) -> B) and (C -> ((D -> (D or E)) and C))))), M:tm-311, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28458
in-theory        28458
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28458.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) or F)), M:tm-310, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28459
in-theory        28459
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (F -> ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28459.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (F -> ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and F))), M:tm-309, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28460
in-theory        28460
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (C -> ((D -> (D or E)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-445 ((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28460.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (C -> ((D -> (D or E)) and C))), M:tm-308, m:tm-445, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (or Dm Em)) Cm))))
================================================================
tm-name          tm-28461
in-theory        28461
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((A and B) -> B))
theorem-size     21
proof            (modus-ponens tm-307 tm-445 ((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28461.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((A and B) -> B)), M:tm-307, m:tm-445, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (or Dm Em)) Cm))))
================================================================
tm-name          tm-28462
in-theory        28462
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (F -> (((A and B) -> B) and (C -> ((D -> (D or E)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28462.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (F -> (((A and B) -> B) and (C -> ((D -> (D or E)) and C))))), M:tm-305, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28463
in-theory        28463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28463.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-303, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28464
in-theory        28464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28464.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-270, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28465
in-theory        28465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28465.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-239, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28466
in-theory        28466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28466.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G)))), M:tm-210, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28467
in-theory        28467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28467.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-183, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28468
in-theory        28468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28468.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-157, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28469
in-theory        28469
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28469.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-147, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28470
in-theory        28470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28470.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-134, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28471
in-theory        28471
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28471.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-125, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28472
in-theory        28472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28472.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G)))), M:tm-113, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28473
in-theory        28473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28473.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-105, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28474
in-theory        28474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28474.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E)))), M:tm-95, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28475
in-theory        28475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28475.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-83, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28476
in-theory        28476
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28476.        (((not (not A)) -> A) and (((B and C) -> C) and (D -> ((E -> (E or F)) and D)))), M:tm-76, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28477
in-theory        28477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28477.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E)))), M:tm-69, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28478
in-theory        28478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28478.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-54, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28479
in-theory        28479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28479.        ((A -> (B or A)) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E)))), M:tm-42, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28480
in-theory        28480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28480.        ((A -> (A or B)) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E)))), M:tm-32, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28481
in-theory        28481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28481.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E)))), M:tm-23, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28482
in-theory        28482
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28482.        (((A and B) -> B) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E)))), M:tm-22, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28483
in-theory        28483
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28483.        (((A and B) -> A) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E)))), M:tm-21, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28484
in-theory        28484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28484.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-20, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28485
in-theory        28485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28485.        ((A -> (B -> A)) and (((C and D) -> D) and (E -> ((F -> (F or G)) and E)))), M:tm-19, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28486
in-theory        28486
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-7 tm-5 tm-4 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28486.        (A or (((B and C) -> C) and (D -> ((E -> (E or F)) and D)))), M:tm-7, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28487
in-theory        28487
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-6 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28487.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) or F), M:tm-6, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28488
in-theory        28488
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> ((E -> (E or F)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28488.        (A -> ((((B and C) -> C) and (D -> ((E -> (E or F)) and D))) and A)), M:tm-5, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28489
in-theory        28489
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-1 tm-5 tm-4 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28489.        (A -> (((B and C) -> C) and (D -> ((E -> (E or F)) and D)))), M:tm-1, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28490
in-theory        28490
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28490.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> ((D -> (D or E)) and C))))), M:tm-443, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28491
in-theory        28491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28491.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-409, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28492
in-theory        28492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28492.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-400, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28493
in-theory        28493
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28493.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-391, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28494
in-theory        28494
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28494.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-382, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28495
in-theory        28495
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28495.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G)))), M:tm-373, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28496
in-theory        28496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28496.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-364, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28497
in-theory        28497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28497.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-354, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28498
in-theory        28498
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28498.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28499
in-theory        28499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28499.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E)))), M:tm-338, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28500
in-theory        28500
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> ((D -> (D or E)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28500.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> ((D -> (D or E)) and C))))), M:tm-327, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28501
in-theory        28501
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> G) and (((A and B) -> A) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28501.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> G) and (((A and B) -> A) and (C -> ((D -> (D or E)) and C))))), M:tm-326, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28502
in-theory        28502
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> F) and (((A and B) -> A) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28502.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> F) and (((A and B) -> A) and (C -> ((D -> (D or E)) and C))))), M:tm-325, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28503
in-theory        28503
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> ((D -> (D or E)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28503.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> ((D -> (D or E)) and C))))), M:tm-324, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28504
in-theory        28504
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28504.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> ((D -> (D or E)) and C))))), M:tm-323, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28505
in-theory        28505
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28505.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28506
in-theory        28506
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28506.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28507
in-theory        28507
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28507.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28508
in-theory        28508
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28508.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28509
in-theory        28509
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (F or (((A and B) -> A) and (C -> ((D -> (D or E)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28509.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (F or (((A and B) -> A) and (C -> ((D -> (D or E)) and C))))), M:tm-311, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28510
in-theory        28510
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28510.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) or F)), M:tm-310, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28511
in-theory        28511
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (F -> ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28511.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (F -> ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and F))), M:tm-309, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28512
in-theory        28512
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (C -> ((D -> (D or E)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-446 ((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28512.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (C -> ((D -> (D or E)) and C))), M:tm-308, m:tm-446, u:((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (or Dm Em)) Cm))))
================================================================
tm-name          tm-28513
in-theory        28513
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((A and B) -> A))
theorem-size     21
proof            (modus-ponens tm-307 tm-446 ((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28513.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((A and B) -> A)), M:tm-307, m:tm-446, u:((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (or Dm Em)) Cm))))
================================================================
tm-name          tm-28514
in-theory        28514
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (F -> (((A and B) -> A) and (C -> ((D -> (D or E)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28514.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (F -> (((A and B) -> A) and (C -> ((D -> (D or E)) and C))))), M:tm-305, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28515
in-theory        28515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28515.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-303, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28516
in-theory        28516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28516.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-270, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28517
in-theory        28517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28517.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-239, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28518
in-theory        28518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28518.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G)))), M:tm-210, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28519
in-theory        28519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28519.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-183, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28520
in-theory        28520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28520.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-157, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28521
in-theory        28521
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28521.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-147, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28522
in-theory        28522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28522.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-134, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28523
in-theory        28523
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28523.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-125, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28524
in-theory        28524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28524.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G)))), M:tm-113, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28525
in-theory        28525
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28525.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-105, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28526
in-theory        28526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28526.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E)))), M:tm-95, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28527
in-theory        28527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28527.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-83, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28528
in-theory        28528
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28528.        (((not (not A)) -> A) and (((B and C) -> B) and (D -> ((E -> (E or F)) and D)))), M:tm-76, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28529
in-theory        28529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28529.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E)))), M:tm-69, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28530
in-theory        28530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28530.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-54, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28531
in-theory        28531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28531.        ((A -> (B or A)) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E)))), M:tm-42, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28532
in-theory        28532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28532.        ((A -> (A or B)) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E)))), M:tm-32, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28533
in-theory        28533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28533.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E)))), M:tm-23, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28534
in-theory        28534
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28534.        (((A and B) -> B) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E)))), M:tm-22, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28535
in-theory        28535
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28535.        (((A and B) -> A) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E)))), M:tm-21, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28536
in-theory        28536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28536.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-20, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28537
in-theory        28537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28537.        ((A -> (B -> A)) and (((C and D) -> C) and (E -> ((F -> (F or G)) and E)))), M:tm-19, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28538
in-theory        28538
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-7 tm-5 tm-3 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28538.        (A or (((B and C) -> B) and (D -> ((E -> (E or F)) and D)))), M:tm-7, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28539
in-theory        28539
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-6 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28539.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) or F), M:tm-6, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28540
in-theory        28540
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> ((E -> (E or F)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28540.        (A -> ((((B and C) -> B) and (D -> ((E -> (E or F)) and D))) and A)), M:tm-5, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28541
in-theory        28541
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-1 tm-5 tm-3 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28541.        (A -> (((B and C) -> B) and (D -> ((E -> (E or F)) and D)))), M:tm-1, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28542
in-theory        28542
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28542.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-443, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28543
in-theory        28543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-409 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28543.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-409, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28544
in-theory        28544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-400 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28544.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-400, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28545
in-theory        28545
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-391 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28545.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-391, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28546
in-theory        28546
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-382 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28546.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-382, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28547
in-theory        28547
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (I or J)) and H))))
theorem-size     39
proof            (modus-ponens tm-373 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28547.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-373, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28548
in-theory        28548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-364 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28548.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-364, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28549
in-theory        28549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-354 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28549.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-354, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28550
in-theory        28550
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28550.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28551
in-theory        28551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     33
proof            (modus-ponens tm-338 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28551.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-338, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28552
in-theory        28552
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28552.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-327, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28553
in-theory        28553
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28553.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-326, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28554
in-theory        28554
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28554.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-325, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28555
in-theory        28555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28555.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-324, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28556
in-theory        28556
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28556.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-323, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28557
in-theory        28557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28557.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((G and H) -> H)), M:tm-322, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28558
in-theory        28558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28558.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((G and H) -> G)), M:tm-320, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28559
in-theory        28559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28559.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28560
in-theory        28560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28560.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (H -> G))), M:tm-315, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28561
in-theory        28561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28561.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-311, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28562
in-theory        28562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28562.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) or G)), M:tm-310, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28563
in-theory        28563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28563.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and G))), M:tm-309, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28564
in-theory        28564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (D -> ((E -> (E or F)) and D)))
theorem-size     33
proof            (modus-ponens tm-308 tm-447 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (or Em Fm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28564.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (D -> ((E -> (E or F)) and D))), M:tm-308, m:tm-447, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (or Em Fm)) Dm))))
================================================================
tm-name          tm-28565
in-theory        28565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-447 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (or Em Fm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28565.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-447, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (or Em Fm)) Dm))))
================================================================
tm-name          tm-28566
in-theory        28566
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28566.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-305, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28567
in-theory        28567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     35
proof            (modus-ponens tm-303 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28567.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-303, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28568
in-theory        28568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-270 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28568.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-270, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28569
in-theory        28569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-239 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28569.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-239, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28570
in-theory        28570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (I or J)) and H))))
theorem-size     41
proof            (modus-ponens tm-210 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28570.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-210, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28571
in-theory        28571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-183 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28571.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-183, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28572
in-theory        28572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-157 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28572.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-157, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28573
in-theory        28573
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     39
proof            (modus-ponens tm-147 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28573.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-147, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28574
in-theory        28574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-134 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28574.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-134, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28575
in-theory        28575
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     39
proof            (modus-ponens tm-125 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28575.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-125, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28576
in-theory        28576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (I or J)) and H))))
theorem-size     39
proof            (modus-ponens tm-113 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28576.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-113, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28577
in-theory        28577
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     43
proof            (modus-ponens tm-105 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28577.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-105, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28578
in-theory        28578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-95 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28578.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-95, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28579
in-theory        28579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-83 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28579.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-83, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28580
in-theory        28580
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     29
proof            (modus-ponens tm-76 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28580.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (F or G)) and E)))), M:tm-76, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28581
in-theory        28581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     35
proof            (modus-ponens tm-69 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28581.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-69, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28582
in-theory        28582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     37
proof            (modus-ponens tm-54 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28582.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-54, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28583
in-theory        28583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-42 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28583.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-42, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28584
in-theory        28584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-32 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28584.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-32, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28585
in-theory        28585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-23 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28585.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-23, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28586
in-theory        28586
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-22 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28586.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-22, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28587
in-theory        28587
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-21 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28587.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-21, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28588
in-theory        28588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     37
proof            (modus-ponens tm-20 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28588.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-20, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28589
in-theory        28589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-19 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28589.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (G or H)) and F)))), M:tm-19, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28590
in-theory        28590
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-7 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28590.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (F or G)) and E)))), M:tm-7, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28591
in-theory        28591
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-6 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28591.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) or G), M:tm-6, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28592
in-theory        28592
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (F or G)) and E))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28592.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (F or G)) and E))) and A)), M:tm-5, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28593
in-theory        28593
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-1 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28593.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (F or G)) and E)))), M:tm-1, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-28594
in-theory        28594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28594.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))))), M:tm-443, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28595
in-theory        28595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28595.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-409, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28596
in-theory        28596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28596.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-400, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28597
in-theory        28597
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28597.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-391, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28598
in-theory        28598
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28598.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-382, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28599
in-theory        28599
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28599.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G)))), M:tm-373, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28600
in-theory        28600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28600.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-364, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28601
in-theory        28601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28601.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-354, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28602
in-theory        28602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28602.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28603
in-theory        28603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28603.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E)))), M:tm-338, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28604
in-theory        28604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28604.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))))), M:tm-327, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28605
in-theory        28605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28605.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))))), M:tm-326, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28606
in-theory        28606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28606.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))))), M:tm-325, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28607
in-theory        28607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28607.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))))), M:tm-324, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28608
in-theory        28608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28608.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))))), M:tm-323, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28609
in-theory        28609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28609.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28610
in-theory        28610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28610.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28611
in-theory        28611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28611.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28612
in-theory        28612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28612.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28613
in-theory        28613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (F or ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28613.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (F or ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))))), M:tm-311, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28614
in-theory        28614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28614.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) or F)), M:tm-310, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28615
in-theory        28615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (F -> (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28615.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (F -> (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and F))), M:tm-309, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28616
in-theory        28616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (C -> ((D -> (D or E)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-448 ((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28616.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (C -> ((D -> (D or E)) and C))), M:tm-308, m:tm-448, u:((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm))))
================================================================
tm-name          tm-28617
in-theory        28617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (A -> (B -> A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-448 ((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28617.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (A -> (B -> A))), M:tm-307, m:tm-448, u:((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm))))
================================================================
tm-name          tm-28618
in-theory        28618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (F -> ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28618.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (F -> ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))))), M:tm-305, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28619
in-theory        28619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28619.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-303, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28620
in-theory        28620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28620.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-270, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28621
in-theory        28621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28621.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-239, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28622
in-theory        28622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28622.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G)))), M:tm-210, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28623
in-theory        28623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28623.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-183, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28624
in-theory        28624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28624.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-157, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28625
in-theory        28625
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28625.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-147, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28626
in-theory        28626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28626.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-134, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28627
in-theory        28627
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28627.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-125, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28628
in-theory        28628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28628.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G)))), M:tm-113, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28629
in-theory        28629
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28629.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-105, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28630
in-theory        28630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28630.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E)))), M:tm-95, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28631
in-theory        28631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28631.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-83, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28632
in-theory        28632
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28632.        (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> ((E -> (E or F)) and D)))), M:tm-76, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28633
in-theory        28633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28633.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E)))), M:tm-69, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28634
in-theory        28634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28634.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-54, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28635
in-theory        28635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28635.        ((A -> (B or A)) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E)))), M:tm-42, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28636
in-theory        28636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28636.        ((A -> (A or B)) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E)))), M:tm-32, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28637
in-theory        28637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28637.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E)))), M:tm-23, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28638
in-theory        28638
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28638.        (((A and B) -> B) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E)))), M:tm-22, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28639
in-theory        28639
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28639.        (((A and B) -> A) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E)))), M:tm-21, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28640
in-theory        28640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28640.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-20, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28641
in-theory        28641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28641.        ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> ((F -> (F or G)) and E)))), M:tm-19, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28642
in-theory        28642
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28642.        (A or ((B -> (C -> B)) and (D -> ((E -> (E or F)) and D)))), M:tm-7, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28643
in-theory        28643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28643.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) or F), M:tm-6, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28644
in-theory        28644
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> ((E -> (E or F)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28644.        (A -> (((B -> (C -> B)) and (D -> ((E -> (E or F)) and D))) and A)), M:tm-5, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28645
in-theory        28645
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28645.        (A -> ((B -> (C -> B)) and (D -> ((E -> (E or F)) and D)))), M:tm-1, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-28646
in-theory        28646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((D -> (D or E)) and ((A -> (not ((B -> (B or C)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28646.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((D -> (D or E)) and ((A -> (not ((B -> (B or C)) and A))) -> (not A)))), M:tm-443, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28647
in-theory        28647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28647.        (((A -> (A or B)) or C) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-409, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28648
in-theory        28648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28648.        (((A -> (B -> (A and B))) or C) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-400, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28649
in-theory        28649
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28649.        ((((A and B) -> B) or C) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-391, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28650
in-theory        28650
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28650.        ((((A and B) -> A) or C) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-382, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28651
in-theory        28651
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not ((F -> (F or G)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28651.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not ((F -> (F or G)) and E))) -> (not E))), M:tm-373, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28652
in-theory        28652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28652.        (((A -> (B -> A)) or C) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-364, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28653
in-theory        28653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (B or C)) and A))) -> (D -> ((not A) and D)))
theorem-size     17
proof            (modus-ponens tm-355 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28653.        ((A -> (not ((B -> (B or C)) and A))) -> (D -> ((not A) and D))), M:tm-355, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-28654
in-theory        28654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28654.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-354, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28655
in-theory        28655
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not ((C -> (C or D)) and (A -> (B -> (A and B)))))))
theorem-size     23
proof            (modus-ponens tm-350 tm-449 ((A (-> (-> B (-> C (and B C))) (not (and (-> Bm (or Bm Cm)) (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28655.        (not ((A -> (B -> (A and B))) -> (not ((C -> (C or D)) and (A -> (B -> (A and B))))))), M:tm-350, m:tm-449, u:((A (-> (-> B (-> C (and B C))) (not (and (-> Bm (or Bm Cm)) (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-28656
in-theory        28656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28656.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28657
in-theory        28657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not ((D -> (D or E)) and C))) -> (not C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28657.        (((A -> B) -> (A -> (A and B))) and ((C -> (not ((D -> (D or E)) and C))) -> (not C))), M:tm-338, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28658
in-theory        28658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((A -> (not ((B -> (B or C)) and A))) -> ((A -> (not ((B -> (B or C)) and A))) and (not A))))
theorem-size     38
proof            (modus-ponens tm-328 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       154
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28658.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((A -> (not ((B -> (B or C)) and A))) -> ((A -> (not ((B -> (B or C)) and A))) and (not A)))), M:tm-328, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-28659
in-theory        28659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not ((B -> (B or C)) and A))) -> (not A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28659.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not ((B -> (B or C)) and A))) -> (not A)))), M:tm-327, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28660
in-theory        28660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((D and E) -> E) and ((A -> (not ((B -> (B or C)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28660.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((D and E) -> E) and ((A -> (not ((B -> (B or C)) and A))) -> (not A)))), M:tm-326, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28661
in-theory        28661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((D and E) -> D) and ((A -> (not ((B -> (B or C)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28661.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((D and E) -> D) and ((A -> (not ((B -> (B or C)) and A))) -> (not A)))), M:tm-325, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28662
in-theory        28662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not ((B -> (B or C)) and A))) -> (not A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28662.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not ((B -> (B or C)) and A))) -> (not A)))), M:tm-324, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28663
in-theory        28663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not ((B -> (B or C)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28663.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not ((B -> (B or C)) and A))) -> (not A)))), M:tm-323, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28664
in-theory        28664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28664.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((D and E) -> E)), M:tm-322, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28665
in-theory        28665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28665.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((D and E) -> D)), M:tm-320, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28666
in-theory        28666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28666.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28667
in-theory        28667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((A -> (not ((B -> (B or C)) and A))) -> (A -> (not ((B -> (B or C)) and A)))))
theorem-size     35
proof            (modus-ponens tm-316 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28667.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((A -> (not ((B -> (B or C)) and A))) -> (A -> (not ((B -> (B or C)) and A))))), M:tm-316, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-28668
in-theory        28668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28668.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (D -> (E -> D))), M:tm-315, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28669
in-theory        28669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((A -> (not ((B -> (B or C)) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (B or C)) and A))))))
theorem-size     40
proof            (modus-ponens tm-313 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       140
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28669.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((A -> (not ((B -> (B or C)) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (B or C)) and A)))))), M:tm-313, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-28670
in-theory        28670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((not A) -> D) -> (((A -> (not ((B -> (B or C)) and A))) or (not A)) -> D)))
theorem-size     34
proof            (modus-ponens tm-312 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-6)
proof-size       138
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28670.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((not A) -> D) -> (((A -> (not ((B -> (B or C)) and A))) or (not A)) -> D))), M:tm-312, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-28671
in-theory        28671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (D or ((A -> (not ((B -> (B or C)) and A))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28671.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (D or ((A -> (not ((B -> (B or C)) and A))) -> (not A)))), M:tm-311, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28672
in-theory        28672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((A -> (not ((B -> (B or C)) and A))) -> (not A)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28672.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((A -> (not ((B -> (B or C)) and A))) -> (not A)) or D)), M:tm-310, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28673
in-theory        28673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (D -> (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28673.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (D -> (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and D))), M:tm-309, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28674
in-theory        28674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (D -> ((A -> (not ((B -> (B or C)) and A))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28674.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (D -> ((A -> (not ((B -> (B or C)) and A))) -> (not A)))), M:tm-305, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28675
in-theory        28675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28675.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-303, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28676
in-theory        28676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28676.        ((A -> (((B and C) -> C) and A)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-270, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28677
in-theory        28677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28677.        ((A -> (((B and C) -> B) and A)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-239, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28678
in-theory        28678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not ((F -> (F or G)) and E))) -> (not E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28678.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not ((F -> (F or G)) and E))) -> (not E))), M:tm-210, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28679
in-theory        28679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28679.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-183, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28680
in-theory        28680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28680.        ((A -> ((B and C) -> C)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-157, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28681
in-theory        28681
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not ((C -> (C or D)) and ((A and B) -> B)))))
theorem-size     19
proof            (modus-ponens tm-153 tm-449 ((A (-> (-> (and B C) C) (not (and (-> Bm (or Bm Cm)) (-> (and B C) C))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28681.        (not (((A and B) -> B) -> (not ((C -> (C or D)) and ((A and B) -> B))))), M:tm-153, m:tm-449, u:((A (-> (-> (and B C) C) (not (and (-> Bm (or Bm Cm)) (-> (and B C) C))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-28682
in-theory        28682
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28682.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-147, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28683
in-theory        28683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28683.        ((A -> ((B and C) -> B)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-134, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28684
in-theory        28684
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not ((C -> (C or D)) and ((A and B) -> A)))))
theorem-size     19
proof            (modus-ponens tm-130 tm-449 ((A (-> (-> (and B C) B) (not (and (-> Bm (or Bm Cm)) (-> (and B C) B))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28684.        (not (((A and B) -> A) -> (not ((C -> (C or D)) and ((A and B) -> A))))), M:tm-130, m:tm-449, u:((A (-> (-> (and B C) B) (not (and (-> Bm (or Bm Cm)) (-> (and B C) B))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-28685
in-theory        28685
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28685.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-125, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28686
in-theory        28686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (F or G)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28686.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (F or G)) and E))) -> (not E))), M:tm-113, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28687
in-theory        28687
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D -> (D or E)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))))
theorem-size     35
proof            (modus-ponens tm-109 tm-449 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (and (-> Bm (or Bm Cm)) (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-5 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28687.        (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D -> (D or E)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))), M:tm-109, m:tm-449, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (and (-> Bm (or Bm Cm)) (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-28688
in-theory        28688
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28688.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-105, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28689
in-theory        28689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not ((D -> (D or E)) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28689.        (((A -> B) -> (A -> A)) and ((C -> (not ((D -> (D or E)) and C))) -> (not C))), M:tm-95, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28690
in-theory        28690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (B or C)) and A))) -> (D -> (not A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28690.        ((A -> (not ((B -> (B or C)) and A))) -> (D -> (not A))), M:tm-84, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-28691
in-theory        28691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28691.        ((A -> (B -> (C -> B))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-83, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28692
in-theory        28692
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not ((C -> (C or D)) and (A -> (B -> A))))))
theorem-size     19
proof            (modus-ponens tm-79 tm-449 ((A (-> (-> B (-> C B)) (not (and (-> Bm (or Bm Cm)) (-> B (-> C B)))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28692.        (not ((A -> (B -> A)) -> (not ((C -> (C or D)) and (A -> (B -> A)))))), M:tm-79, m:tm-449, u:((A (-> (-> B (-> C B)) (not (and (-> Bm (or Bm Cm)) (-> B (-> C B)))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-28693
in-theory        28693
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not ((C -> (C or D)) and B))) -> (not B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28693.        (((not (not A)) -> A) and ((B -> (not ((C -> (C or D)) and B))) -> (not B))), M:tm-76, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28694
in-theory        28694
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not ((B -> (B or C)) and A))))) or (A -> (not ((B -> (B or C)) and A)))) -> (not A))
theorem-size     26
proof            (modus-ponens tm-73 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-5 tm-6)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28694.        (((not (not (A -> (not ((B -> (B or C)) and A))))) or (A -> (not ((B -> (B or C)) and A)))) -> (not A)), M:tm-73, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-28695
in-theory        28695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not ((D -> (D or E)) and C))) -> (not C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28695.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not ((D -> (D or E)) and C))) -> (not C))), M:tm-69, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28696
in-theory        28696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28696.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-54, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28697
in-theory        28697
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not ((C -> (C or D)) and B)))) or (B -> (not ((C -> (C or D)) and B)))) -> (not B))
theorem-size     26
proof            (modus-ponens tm-47 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-5 tm-6)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28697.        (((A and (B -> (not ((C -> (C or D)) and B)))) or (B -> (not ((C -> (C or D)) and B)))) -> (not B)), M:tm-47, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-28698
in-theory        28698
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not ((B -> (B or C)) and A))) and D) or (A -> (not ((B -> (B or C)) and A)))) -> (not A))
theorem-size     26
proof            (modus-ponens tm-46 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-5 tm-6)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28698.        ((((A -> (not ((B -> (B or C)) and A))) and D) or (A -> (not ((B -> (B or C)) and A)))) -> (not A)), M:tm-46, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-28699
in-theory        28699
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A -> (A or B)) and C)) or (C -> (not ((A -> (A or B)) and C)))) -> (not C))
theorem-size     22
proof            (modus-ponens tm-44 tm-449 ((A Am) (B (not (and (-> Bm (or Bm Cm)) Am))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-5 tm-6)
proof-size       98
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28699.        (((not ((A -> (A or B)) and C)) or (C -> (not ((A -> (A or B)) and C)))) -> (not C)), M:tm-44, m:tm-449, u:((A Am) (B (not (and (-> Bm (or Bm Cm)) Am))) (C (not Am)))
================================================================
tm-name          tm-28700
in-theory        28700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not ((D -> (D or E)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28700.        ((A -> (B or A)) and ((C -> (not ((D -> (D or E)) and C))) -> (not C))), M:tm-42, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28701
in-theory        28701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not ((D -> (D or E)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28701.        ((A -> (A or B)) and ((C -> (not ((D -> (D or E)) and C))) -> (not C))), M:tm-32, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28702
in-theory        28702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (B or C)) and A))) -> ((A -> (not ((B -> (B or C)) and A))) and (not A)))
theorem-size     24
proof            (modus-ponens tm-24 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       98
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28702.        ((A -> (not ((B -> (B or C)) and A))) -> ((A -> (not ((B -> (B or C)) and A))) and (not A))), M:tm-24, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-28703
in-theory        28703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not ((D -> (D or E)) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28703.        ((A -> (B -> (A and B))) and ((C -> (not ((D -> (D or E)) and C))) -> (not C))), M:tm-23, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28704
in-theory        28704
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not ((D -> (D or E)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28704.        (((A and B) -> B) and ((C -> (not ((D -> (D or E)) and C))) -> (not C))), M:tm-22, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28705
in-theory        28705
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not ((D -> (D or E)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28705.        (((A and B) -> A) and ((C -> (not ((D -> (D or E)) and C))) -> (not C))), M:tm-21, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28706
in-theory        28706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28706.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-20, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28707
in-theory        28707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not ((D -> (D or E)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28707.        ((A -> (B -> A)) and ((C -> (not ((D -> (D or E)) and C))) -> (not C))), M:tm-19, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28708
in-theory        28708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (B or C)) and A))) -> (A -> (not ((B -> (B or C)) and A))))
theorem-size     21
proof            (modus-ponens tm-12 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28708.        ((A -> (not ((B -> (B or C)) and A))) -> (A -> (not ((B -> (B or C)) and A)))), M:tm-12, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-28709
in-theory        28709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (B or C)) and A)))))
theorem-size     26
proof            (modus-ponens tm-9 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-9 tm-5 tm-6)
proof-size       82
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28709.        (((A -> (not ((B -> (B or C)) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (B or C)) and A))))), M:tm-9, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-28710
in-theory        28710
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not ((C -> (C or D)) and A))) or (not A)) -> B))
theorem-size     20
proof            (modus-ponens tm-8 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-5 tm-6)
proof-size       78
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28710.        (((not A) -> B) -> (((A -> (not ((C -> (C or D)) and A))) or (not A)) -> B)), M:tm-8, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-28711
in-theory        28711
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not ((C -> (C or D)) and B))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-5 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28711.        (A or ((B -> (not ((C -> (C or D)) and B))) -> (not B))), M:tm-7, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28712
in-theory        28712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28712.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) or D), M:tm-6, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28713
in-theory        28713
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not ((C -> (C or D)) and B))) -> (not B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28713.        (A -> (((B -> (not ((C -> (C or D)) and B))) -> (not B)) and A)), M:tm-5, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28714
in-theory        28714
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not ((C -> (C or D)) and B))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-5 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28714.        (A -> ((B -> (not ((C -> (C or D)) and B))) -> (not B))), M:tm-1, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-28715
in-theory        28715
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> ((B -> (B or C)) and A)))
theorem-size     19
proof            (modus-ponens tm-450 tm-1 ((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-28715.        ((A or ((B -> (B or C)) and A)) -> (D -> ((B -> (B or C)) and A))), M:tm-450, m:tm-1, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28716
in-theory        28716
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (B -> (B or C)))
theorem-size     15
proof            (modus-ponens tm-450 tm-3 ((Am (-> A (or A B))) (C Bm) (D (-> A (or A B)))))
axioms-used      (tm-8 tm-5 tm-6 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-28716.        ((A or ((B -> (B or C)) and A)) -> (B -> (B or C))), M:tm-450, m:tm-3, u:((Am (-> A (or A B))) (C Bm) (D (-> A (or A B))))
================================================================
tm-name          tm-28717
in-theory        28717
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> A)
theorem-size     11
proof            (modus-ponens tm-450 tm-4 ((Am (-> A (or A B))) (C Bm) (D Bm)))
axioms-used      (tm-8 tm-5 tm-6 tm-4)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-28717.        ((A or ((B -> (B or C)) and A)) -> A), M:tm-450, m:tm-4, u:((Am (-> A (or A B))) (C Bm) (D Bm))
================================================================
tm-name          tm-28718
in-theory        28718
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> (((B -> (B or C)) and A) and D)))
theorem-size     21
proof            (modus-ponens tm-450 tm-5 ((Am (and (-> A (or A B)) C)) (D (-> Bm (and (and (-> A (or A B)) C) Bm)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28718.        ((A or ((B -> (B or C)) and A)) -> (D -> (((B -> (B or C)) and A) and D))), M:tm-450, m:tm-5, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (and (and (-> A (or A B)) C) Bm))))
================================================================
tm-name          tm-28719
in-theory        28719
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) or D))
theorem-size     19
proof            (modus-ponens tm-450 tm-6 ((Am (and (-> A (or A B)) C)) (D (or (and (-> A (or A B)) C) Bm))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28719.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) or D)), M:tm-450, m:tm-6, u:((Am (and (-> A (or A B)) C)) (D (or (and (-> A (or A B)) C) Bm)))
================================================================
tm-name          tm-28720
in-theory        28720
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D or ((B -> (B or C)) and A)))
theorem-size     19
proof            (modus-ponens tm-450 tm-7 ((Am (and (-> A (or A B)) C)) (D (or Bm (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-28720.        ((A or ((B -> (B or C)) and A)) -> (D or ((B -> (B or C)) and A))), M:tm-450, m:tm-7, u:((Am (and (-> A (or A B)) C)) (D (or Bm (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28721
in-theory        28721
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-450 tm-11 ((Am (and (-> A (or A B)) C)) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-28721.        ((A or ((B -> (B or C)) and A)) -> (D -> (E -> D))), M:tm-450, m:tm-11, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-28722
in-theory        28722
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-450 tm-14 ((Am (and (-> A (or A B)) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-28722.        ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-450, m:tm-14, u:((Am (and (-> A (or A B)) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-28723
in-theory        28723
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-450 tm-16 ((Am (and (-> A (or A B)) C)) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28723.        ((A or ((B -> (B or C)) and A)) -> ((D and E) -> D)), M:tm-450, m:tm-16, u:((Am (and (-> A (or A B)) C)) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-28724
in-theory        28724
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-450 tm-18 ((Am (and (-> A (or A B)) C)) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-28724.        ((A or ((B -> (B or C)) and A)) -> ((D and E) -> E)), M:tm-450, m:tm-18, u:((Am (and (-> A (or A B)) C)) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-28725
in-theory        28725
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> D)) and ((B -> (B or C)) and A)))
theorem-size     23
proof            (modus-ponens tm-450 tm-19 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> Cm Bm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-28725.        ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> D)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-19, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> Cm Bm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28726
in-theory        28726
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (B or C)) and A)))
theorem-size     31
proof            (modus-ponens tm-450 tm-20 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-28726.        ((A or ((B -> (B or C)) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-20, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28727
in-theory        28727
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D and E) -> D) and ((B -> (B or C)) and A)))
theorem-size     23
proof            (modus-ponens tm-450 tm-21 ((Am (and (-> A (or A B)) C)) (D (and (-> (and Bm Cm) Bm) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28727.        ((A or ((B -> (B or C)) and A)) -> (((D and E) -> D) and ((B -> (B or C)) and A))), M:tm-450, m:tm-21, u:((Am (and (-> A (or A B)) C)) (D (and (-> (and Bm Cm) Bm) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28728
in-theory        28728
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D and E) -> E) and ((B -> (B or C)) and A)))
theorem-size     23
proof            (modus-ponens tm-450 tm-22 ((Am (and (-> A (or A B)) C)) (D (and (-> (and Bm Cm) Cm) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-28728.        ((A or ((B -> (B or C)) and A)) -> (((D and E) -> E) and ((B -> (B or C)) and A))), M:tm-450, m:tm-22, u:((Am (and (-> A (or A B)) C)) (D (and (-> (and Bm Cm) Cm) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28729
in-theory        28729
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> (D and E))) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-23 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-28729.        ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> (D and E))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-23, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28730
in-theory        28730
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-450 tm-25 ((Am (and (-> A (or A B)) C)) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-28730.        ((A or ((B -> (B or C)) and A)) -> (D -> (E -> (D and E)))), M:tm-450, m:tm-25, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-28731
in-theory        28731
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (D or E)) and ((B -> (B or C)) and A)))
theorem-size     23
proof            (modus-ponens tm-450 tm-32 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (or Bm Cm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28731.        ((A or ((B -> (B or C)) and A)) -> ((D -> (D or E)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-32, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (or Bm Cm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28732
in-theory        28732
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-450 tm-33 ((Am (and (-> A (or A B)) C)) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28732.        ((A or ((B -> (B or C)) and A)) -> (D -> (D or E))), M:tm-450, m:tm-33, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-28733
in-theory        28733
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (E or D)) and ((B -> (B or C)) and A)))
theorem-size     23
proof            (modus-ponens tm-450 tm-42 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (or Cm Bm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-28733.        ((A or ((B -> (B or C)) and A)) -> ((D -> (E or D)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-42, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (or Cm Bm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28734
in-theory        28734
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-450 tm-43 ((Am (and (-> A (or A B)) C)) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-28734.        ((A or ((B -> (B or C)) and A)) -> (D -> (E or D))), M:tm-450, m:tm-43, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-28735
in-theory        28735
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> (B or C)) and A)))
theorem-size     31
proof            (modus-ponens tm-450 tm-54 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-28735.        ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-54, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28736
in-theory        28736
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-450 tm-56 ((Am (and (-> A (or A B)) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-28736.        ((A or ((B -> (B or C)) and A)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-450, m:tm-56, u:((Am (and (-> A (or A B)) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-28737
in-theory        28737
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B -> (B or C)) and A)))
theorem-size     29
proof            (modus-ponens tm-450 tm-69 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-28737.        ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-69, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28738
in-theory        28738
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-450 tm-71 ((Am (and (-> A (or A B)) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-28738.        ((A or ((B -> (B or C)) and A)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-450, m:tm-71, u:((Am (and (-> A (or A B)) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-28739
in-theory        28739
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((not (not D)) -> D) and ((B -> (B or C)) and A)))
theorem-size     23
proof            (modus-ponens tm-450 tm-76 ((Am (and (-> A (or A B)) C)) (D (and (-> (not (not Bm)) Bm) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-28739.        ((A or ((B -> (B or C)) and A)) -> (((not (not D)) -> D) and ((B -> (B or C)) and A))), M:tm-450, m:tm-76, u:((Am (and (-> A (or A B)) C)) (D (and (-> (not (not Bm)) Bm) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28740
in-theory        28740
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-450 tm-78 ((Am (and (-> A (or A B)) C)) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-28740.        ((A or ((B -> (B or C)) and A)) -> ((not (not D)) -> D)), M:tm-450, m:tm-78, u:((Am (and (-> A (or A B)) C)) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-28741
in-theory        28741
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> (F -> E))) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-83 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-28741.        ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> (F -> E))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-83, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28742
in-theory        28742
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-450 tm-85 ((Am (and (-> A (or A B)) C)) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-28742.        ((A or ((B -> (B or C)) and A)) -> (D -> (E -> (F -> E)))), M:tm-450, m:tm-85, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-28743
in-theory        28743
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((B -> (B or C)) and A))
theorem-size     17
proof            (modus-ponens tm-450 tm-86 ((Am (and (-> A (or A B)) C)) (D (and (-> A (or A B)) C))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-28743.        ((A or ((B -> (B or C)) and A)) -> ((B -> (B or C)) and A)), M:tm-450, m:tm-86, u:((Am (and (-> A (or A B)) C)) (D (and (-> A (or A B)) C)))
================================================================
tm-name          tm-28744
in-theory        28744
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> (D -> D)) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-95 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-28744.        ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> (D -> D)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-95, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28745
in-theory        28745
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-450 tm-97 ((Am (and (-> A (or A B)) C)) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-28745.        ((A or ((B -> (B or C)) and A)) -> ((D -> E) -> (D -> D))), M:tm-450, m:tm-97, u:((Am (and (-> A (or A B)) C)) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-28746
in-theory        28746
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B -> (B or C)) and A)))
theorem-size     37
proof            (modus-ponens tm-450 tm-105 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-28746.        ((A or ((B -> (B or C)) and A)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-105, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28747
in-theory        28747
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-450 tm-107 ((Am (and (-> A (or A B)) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-28747.        ((A or ((B -> (B or C)) and A)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-450, m:tm-107, u:((Am (and (-> A (or A B)) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-28748
in-theory        28748
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (B or C)) and A)))
theorem-size     33
proof            (modus-ponens tm-450 tm-113 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-28748.        ((A or ((B -> (B or C)) and A)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-113, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28749
in-theory        28749
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-450 tm-115 ((Am (and (-> A (or A B)) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-28749.        ((A or ((B -> (B or C)) and A)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-450, m:tm-115, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-28750
in-theory        28750
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A -> (A or B)) and A)) -> (A or B))
theorem-size     13
proof            (modus-ponens tm-450 tm-116 ((A Am) (Bm (or Am B)) (C Am) (D (or Am B))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-3 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-28750.        ((A or ((A -> (A or B)) and A)) -> (A or B)), M:tm-450, m:tm-116, u:((A Am) (Bm (or Am B)) (C Am) (D (or Am B)))
================================================================
tm-name          tm-28751
in-theory        28751
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> B)) -> ((B -> (C -> B)) or D)) and A)) -> ((B -> (C -> B)) or D))
theorem-size     25
proof            (modus-ponens tm-450 tm-117 ((A (-> Am (-> Bm Am))) (Cm (or (-> Am (-> Bm Am)) B)) (C Dm) (D (or (-> Am (-> Bm Am)) B))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-28751.        ((A or (((B -> (C -> B)) -> ((B -> (C -> B)) or D)) and A)) -> ((B -> (C -> B)) or D)), M:tm-450, m:tm-117, u:((A (-> Am (-> Bm Am))) (Cm (or (-> Am (-> Bm Am)) B)) (C Dm) (D (or (-> Am (-> Bm Am)) B)))
================================================================
tm-name          tm-28752
in-theory        28752
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and A)) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))
theorem-size     49
proof            (modus-ponens tm-450 tm-118 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C Em) (D (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-28752.        ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and A)) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-450, m:tm-118, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C Em) (D (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)))
================================================================
tm-name          tm-28753
in-theory        28753
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B -> (B or C)) and A)))
theorem-size     33
proof            (modus-ponens tm-450 tm-125 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-28753.        ((A or ((B -> (B or C)) and A)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-125, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28754
in-theory        28754
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-450 tm-127 ((Am (and (-> A (or A B)) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-28754.        ((A or ((B -> (B or C)) and A)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-450, m:tm-127, u:((Am (and (-> A (or A B)) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-28755
in-theory        28755
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> B) -> (((B and C) -> B) or D)) and A)) -> (((B and C) -> B) or D))
theorem-size     25
proof            (modus-ponens tm-450 tm-128 ((A (-> (and Am Bm) Am)) (Cm (or (-> (and Am Bm) Am) B)) (C Dm) (D (or (-> (and Am Bm) Am) B))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-28755.        ((A or ((((B and C) -> B) -> (((B and C) -> B) or D)) and A)) -> (((B and C) -> B) or D)), M:tm-450, m:tm-128, u:((A (-> (and Am Bm) Am)) (Cm (or (-> (and Am Bm) Am) B)) (C Dm) (D (or (-> (and Am Bm) Am) B)))
================================================================
tm-name          tm-28756
in-theory        28756
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> ((E and F) -> E)) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-134 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-28756.        ((A or ((B -> (B or C)) and A)) -> ((D -> ((E and F) -> E)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-134, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28757
in-theory        28757
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-450 tm-136 ((Am (and (-> A (or A B)) C)) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-28757.        ((A or ((B -> (B or C)) and A)) -> (D -> ((E and F) -> E))), M:tm-450, m:tm-136, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-28758
in-theory        28758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) or ((A -> (A or B)) and ((A -> (A or B)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-450 tm-137 ((Am (-> A (or A B))) (C (-> (-> A (or A B)) Bm)) (D Bm)))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-4 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-28758.        ((((A -> (A or B)) -> C) or ((A -> (A or B)) and ((A -> (A or B)) -> C))) -> C), M:tm-450, m:tm-137, u:((Am (-> A (or A B))) (C (-> (-> A (or A B)) Bm)) (D Bm))
================================================================
tm-name          tm-28759
in-theory        28759
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) or ((D -> (D or E)) and ((A -> (B -> A)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-450 tm-138 ((Am (-> A (or A B))) (C (-> (-> Bm (-> Cm Bm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-28759.        ((((A -> (B -> A)) -> C) or ((D -> (D or E)) and ((A -> (B -> A)) -> C))) -> C), M:tm-450, m:tm-138, u:((Am (-> A (or A B))) (C (-> (-> Bm (-> Cm Bm)) Dm)) (D Dm))
================================================================
tm-name          tm-28760
in-theory        28760
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or ((E -> (E or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D)
theorem-size     39
proof            (modus-ponens tm-450 tm-139 ((Am (-> A (or A B))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (D Em)))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-28760.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or ((E -> (E or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D), M:tm-450, m:tm-139, u:((Am (-> A (or A B))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (D Em))
================================================================
tm-name          tm-28761
in-theory        28761
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) or ((D -> (D or E)) and (((A and B) -> A) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-450 tm-140 ((Am (-> A (or A B))) (C (-> (-> (and Bm Cm) Bm) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-4 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-28761.        (((((A and B) -> A) -> C) or ((D -> (D or E)) and (((A and B) -> A) -> C))) -> C), M:tm-450, m:tm-140, u:((Am (-> A (or A B))) (C (-> (-> (and Bm Cm) Bm) Dm)) (D Dm))
================================================================
tm-name          tm-28762
in-theory        28762
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B -> (B or C)) and A)))
theorem-size     33
proof            (modus-ponens tm-450 tm-147 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-28762.        ((A or ((B -> (B or C)) and A)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-147, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28763
in-theory        28763
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-450 tm-149 ((Am (and (-> A (or A B)) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-28763.        ((A or ((B -> (B or C)) and A)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-450, m:tm-149, u:((Am (and (-> A (or A B)) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-28764
in-theory        28764
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) or ((D -> (D or E)) and (((A and B) -> B) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-450 tm-150 ((Am (-> A (or A B))) (C (-> (-> (and Bm Cm) Cm) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-28764.        (((((A and B) -> B) -> C) or ((D -> (D or E)) and (((A and B) -> B) -> C))) -> C), M:tm-450, m:tm-150, u:((Am (-> A (or A B))) (C (-> (-> (and Bm Cm) Cm) Dm)) (D Dm))
================================================================
tm-name          tm-28765
in-theory        28765
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> C) -> (((B and C) -> C) or D)) and A)) -> (((B and C) -> C) or D))
theorem-size     25
proof            (modus-ponens tm-450 tm-151 ((A (-> (and Am Bm) Bm)) (Cm (or (-> (and Am Bm) Bm) B)) (C Dm) (D (or (-> (and Am Bm) Bm) B))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-3 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-28765.        ((A or ((((B and C) -> C) -> (((B and C) -> C) or D)) and A)) -> (((B and C) -> C) or D)), M:tm-450, m:tm-151, u:((A (-> (and Am Bm) Bm)) (Cm (or (-> (and Am Bm) Bm) B)) (C Dm) (D (or (-> (and Am Bm) Bm) B)))
================================================================
tm-name          tm-28766
in-theory        28766
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> ((E and F) -> F)) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-157 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-28766.        ((A or ((B -> (B or C)) and A)) -> ((D -> ((E and F) -> F)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-157, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28767
in-theory        28767
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-450 tm-159 ((Am (and (-> A (or A B)) C)) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-28767.        ((A or ((B -> (B or C)) and A)) -> (D -> ((E and F) -> F))), M:tm-450, m:tm-159, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-28768
in-theory        28768
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> ((E -> (F -> E)) and D)) and ((B -> (B or C)) and A)))
theorem-size     27
proof            (modus-ponens tm-450 tm-183 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-28768.        ((A or ((B -> (B or C)) and A)) -> ((D -> ((E -> (F -> E)) and D)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-183, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28769
in-theory        28769
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-450 tm-184 ((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-28769.        ((A or ((B -> (B or C)) and A)) -> (D -> ((E -> (F -> E)) and D))), M:tm-450, m:tm-184, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-28770
in-theory        28770
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B -> (B or C)) and A)))
theorem-size     35
proof            (modus-ponens tm-450 tm-210 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-28770.        ((A or ((B -> (B or C)) and A)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-210, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28771
in-theory        28771
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-450 tm-211 ((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-28771.        ((A or ((B -> (B or C)) and A)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-450, m:tm-211, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-28772
in-theory        28772
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (((E and F) -> E) and D)) and ((B -> (B or C)) and A)))
theorem-size     27
proof            (modus-ponens tm-450 tm-239 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-28772.        ((A or ((B -> (B or C)) and A)) -> ((D -> (((E and F) -> E) and D)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-239, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28773
in-theory        28773
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-450 tm-240 ((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-28773.        ((A or ((B -> (B or C)) and A)) -> (D -> (((E and F) -> E) and D))), M:tm-450, m:tm-240, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-28774
in-theory        28774
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (((E and F) -> F) and D)) and ((B -> (B or C)) and A)))
theorem-size     27
proof            (modus-ponens tm-450 tm-270 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-28774.        ((A or ((B -> (B or C)) and A)) -> ((D -> (((E and F) -> F) and D)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-270, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28775
in-theory        28775
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-450 tm-271 ((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-28775.        ((A or ((B -> (B or C)) and A)) -> (D -> (((E and F) -> F) and D))), M:tm-450, m:tm-271, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-28776
in-theory        28776
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B -> (B or C)) and A)))
theorem-size     29
proof            (modus-ponens tm-450 tm-303 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-28776.        ((A or ((B -> (B or C)) and A)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-303, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28777
in-theory        28777
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-450 tm-304 ((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-28777.        ((A or ((B -> (B or C)) and A)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-450, m:tm-304, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-28778
in-theory        28778
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (D -> ((B -> (B or C)) and A))))
theorem-size     27
proof            (modus-ponens tm-450 tm-305 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> Bm (and (-> A (or A B)) C))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-28778.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (D -> ((B -> (B or C)) and A)))), M:tm-450, m:tm-305, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> Bm (and (-> A (or A B)) C)))))
================================================================
tm-name          tm-28779
in-theory        28779
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (B -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-450 tm-307 ((Am (-> A (or A B))) (C Bm) (D (and (and (-> A (or A B)) Bm) (-> A (or A B))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-28779.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (B -> (B or C)))), M:tm-450, m:tm-307, u:((Am (-> A (or A B))) (C Bm) (D (and (and (-> A (or A B)) Bm) (-> A (or A B)))))
================================================================
tm-name          tm-28780
in-theory        28780
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and A))
theorem-size     19
proof            (modus-ponens tm-450 tm-308 ((Am (-> A (or A B))) (C Bm) (D (and (and (-> A (or A B)) Bm) Bm))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-28780.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and A)), M:tm-450, m:tm-308, u:((Am (-> A (or A B))) (C Bm) (D (and (and (-> A (or A B)) Bm) Bm)))
================================================================
tm-name          tm-28781
in-theory        28781
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (D -> (((B -> (B or C)) and A) and D))))
theorem-size     29
proof            (modus-ponens tm-450 tm-309 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> Bm (and (and (-> A (or A B)) C) Bm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-28781.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (D -> (((B -> (B or C)) and A) and D)))), M:tm-450, m:tm-309, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> Bm (and (and (-> A (or A B)) C) Bm)))))
================================================================
tm-name          tm-28782
in-theory        28782
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (((B -> (B or C)) and A) or D)))
theorem-size     27
proof            (modus-ponens tm-450 tm-310 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (or (and (-> A (or A B)) C) Bm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-28782.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (((B -> (B or C)) and A) or D))), M:tm-450, m:tm-310, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (or (and (-> A (or A B)) C) Bm))))
================================================================
tm-name          tm-28783
in-theory        28783
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (D or ((B -> (B or C)) and A))))
theorem-size     27
proof            (modus-ponens tm-450 tm-311 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (or Bm (and (-> A (or A B)) C))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-28783.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (D or ((B -> (B or C)) and A)))), M:tm-450, m:tm-311, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (or Bm (and (-> A (or A B)) C)))))
================================================================
tm-name          tm-28784
in-theory        28784
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (D -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-450 tm-315 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-28784.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (D -> (E -> D)))), M:tm-450, m:tm-315, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-28785
in-theory        28785
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-450 tm-318 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-28785.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-450, m:tm-318, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-28786
in-theory        28786
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and ((D and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-450 tm-320 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-28786.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and ((D and E) -> D))), M:tm-450, m:tm-320, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-28787
in-theory        28787
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and ((D and E) -> E)))
theorem-size     23
proof            (modus-ponens tm-450 tm-322 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-28787.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and ((D and E) -> E))), M:tm-450, m:tm-322, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-28788
in-theory        28788
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and ((D -> (E -> D)) and ((B -> (B or C)) and A))))
theorem-size     31
proof            (modus-ponens tm-450 tm-323 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (and (-> Bm (-> Cm Bm)) (and (-> A (or A B)) C))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-28788.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and ((D -> (E -> D)) and ((B -> (B or C)) and A)))), M:tm-450, m:tm-323, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (and (-> Bm (-> Cm Bm)) (and (-> A (or A B)) C)))))
================================================================
tm-name          tm-28789
in-theory        28789
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (B or C)) and A))))
theorem-size     39
proof            (modus-ponens tm-450 tm-324 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (or A B)) C))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-28789.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (B or C)) and A)))), M:tm-450, m:tm-324, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (or A B)) C)))))
================================================================
tm-name          tm-28790
in-theory        28790
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (((D and E) -> D) and ((B -> (B or C)) and A))))
theorem-size     31
proof            (modus-ponens tm-450 tm-325 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (and (-> (and Bm Cm) Bm) (and (-> A (or A B)) C))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-28790.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (((D and E) -> D) and ((B -> (B or C)) and A)))), M:tm-450, m:tm-325, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (and (-> (and Bm Cm) Bm) (and (-> A (or A B)) C)))))
================================================================
tm-name          tm-28791
in-theory        28791
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (((D and E) -> E) and ((B -> (B or C)) and A))))
theorem-size     31
proof            (modus-ponens tm-450 tm-326 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (and (-> (and Bm Cm) Cm) (and (-> A (or A B)) C))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-28791.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (((D and E) -> E) and ((B -> (B or C)) and A)))), M:tm-450, m:tm-326, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (and (-> (and Bm Cm) Cm) (and (-> A (or A B)) C)))))
================================================================
tm-name          tm-28792
in-theory        28792
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and ((D -> (E -> (D and E))) and ((B -> (B or C)) and A))))
theorem-size     33
proof            (modus-ponens tm-450 tm-327 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (or A B)) C))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-28792.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and ((D -> (E -> (D and E))) and ((B -> (B or C)) and A)))), M:tm-450, m:tm-327, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (or A B)) C)))))
================================================================
tm-name          tm-28793
in-theory        28793
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> (D -> (D and E))) and ((B -> (B or C)) and A)))
theorem-size     27
proof            (modus-ponens tm-450 tm-338 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-28793.        ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> (D -> (D and E))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-338, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28794
in-theory        28794
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-450 tm-340 ((Am (and (-> A (or A B)) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-28794.        ((A or ((B -> (B or C)) and A)) -> ((D -> E) -> (D -> (D and E)))), M:tm-450, m:tm-340, u:((Am (and (-> A (or A B)) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-28795
in-theory        28795
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-450 tm-341 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-28795.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (D -> (E -> (D and E))))), M:tm-450, m:tm-341, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-28796
in-theory        28796
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) or ((D -> (D or E)) and ((A -> (B -> (A and B))) -> C))) -> C)
theorem-size     27
proof            (modus-ponens tm-450 tm-347 ((Am (-> A (or A B))) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-28796.        ((((A -> (B -> (A and B))) -> C) or ((D -> (D or E)) and ((A -> (B -> (A and B))) -> C))) -> C), M:tm-450, m:tm-347, u:((Am (-> A (or A B))) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (D Dm))
================================================================
tm-name          tm-28797
in-theory        28797
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> (B and C))) -> ((B -> (C -> (B and C))) or D)) and A)) -> ((B -> (C -> (B and C))) or D))
theorem-size     31
proof            (modus-ponens tm-450 tm-348 ((A (-> Am (-> Bm (and Am Bm)))) (Cm (or (-> Am (-> Bm (and Am Bm))) B)) (C Dm) (D (or (-> Am (-> Bm (and Am Bm))) B))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-28797.        ((A or (((B -> (C -> (B and C))) -> ((B -> (C -> (B and C))) or D)) and A)) -> ((B -> (C -> (B and C))) or D)), M:tm-450, m:tm-348, u:((A (-> Am (-> Bm (and Am Bm)))) (Cm (or (-> Am (-> Bm (and Am Bm))) B)) (C Dm) (D (or (-> Am (-> Bm (and Am Bm))) B)))
================================================================
tm-name          tm-28798
in-theory        28798
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> (F -> (E and F)))) and ((B -> (B or C)) and A)))
theorem-size     27
proof            (modus-ponens tm-450 tm-354 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-28798.        ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> (F -> (E and F)))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-354, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28799
in-theory        28799
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-450 tm-356 ((Am (and (-> A (or A B)) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-28799.        ((A or ((B -> (B or C)) and A)) -> (D -> (E -> (F -> (E and F))))), M:tm-450, m:tm-356, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-28800
in-theory        28800
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> (E -> D)) or F) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-364 ((Am (and (-> A (or A B)) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-28800.        ((A or ((B -> (B or C)) and A)) -> (((D -> (E -> D)) or F) and ((B -> (B or C)) and A))), M:tm-450, m:tm-364, u:((Am (and (-> A (or A B)) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28801
in-theory        28801
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-450 tm-365 ((Am (and (-> A (or A B)) C)) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-28801.        ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> D)) or F)), M:tm-450, m:tm-365, u:((Am (and (-> A (or A B)) C)) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-28802
in-theory        28802
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B -> (B or C)) and A)))
theorem-size     33
proof            (modus-ponens tm-450 tm-373 ((Am (and (-> A (or A B)) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-28802.        ((A or ((B -> (B or C)) and A)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B -> (B or C)) and A))), M:tm-450, m:tm-373, u:((Am (and (-> A (or A B)) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28803
in-theory        28803
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-450 tm-374 ((Am (and (-> A (or A B)) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-28803.        ((A or ((B -> (B or C)) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-450, m:tm-374, u:((Am (and (-> A (or A B)) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-28804
in-theory        28804
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((((D and E) -> D) or F) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-382 ((Am (and (-> A (or A B)) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-28804.        ((A or ((B -> (B or C)) and A)) -> ((((D and E) -> D) or F) and ((B -> (B or C)) and A))), M:tm-450, m:tm-382, u:((Am (and (-> A (or A B)) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28805
in-theory        28805
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-450 tm-383 ((Am (and (-> A (or A B)) C)) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-28805.        ((A or ((B -> (B or C)) and A)) -> (((D and E) -> D) or F)), M:tm-450, m:tm-383, u:((Am (and (-> A (or A B)) C)) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-28806
in-theory        28806
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((((D and E) -> E) or F) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-391 ((Am (and (-> A (or A B)) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-28806.        ((A or ((B -> (B or C)) and A)) -> ((((D and E) -> E) or F) and ((B -> (B or C)) and A))), M:tm-450, m:tm-391, u:((Am (and (-> A (or A B)) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28807
in-theory        28807
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-450 tm-392 ((Am (and (-> A (or A B)) C)) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-28807.        ((A or ((B -> (B or C)) and A)) -> (((D and E) -> E) or F)), M:tm-450, m:tm-392, u:((Am (and (-> A (or A B)) C)) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-28808
in-theory        28808
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> (E -> (D and E))) or F) and ((B -> (B or C)) and A)))
theorem-size     27
proof            (modus-ponens tm-450 tm-400 ((Am (and (-> A (or A B)) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-28808.        ((A or ((B -> (B or C)) and A)) -> (((D -> (E -> (D and E))) or F) and ((B -> (B or C)) and A))), M:tm-450, m:tm-400, u:((Am (and (-> A (or A B)) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28809
in-theory        28809
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-450 tm-401 ((Am (and (-> A (or A B)) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-28809.        ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> (D and E))) or F)), M:tm-450, m:tm-401, u:((Am (and (-> A (or A B)) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-28810
in-theory        28810
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> (D or E)) or F) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-409 ((Am (and (-> A (or A B)) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-28810.        ((A or ((B -> (B or C)) and A)) -> (((D -> (D or E)) or F) and ((B -> (B or C)) and A))), M:tm-450, m:tm-409, u:((Am (and (-> A (or A B)) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-28811
in-theory        28811
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-450 tm-410 ((Am (and (-> A (or A B)) C)) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-28811.        ((A or ((B -> (B or C)) and A)) -> ((D -> (D or E)) or F)), M:tm-450, m:tm-410, u:((Am (and (-> A (or A B)) C)) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-28812
in-theory        28812
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and ((D -> (D or E)) and ((B -> (B or C)) and A))))
theorem-size     31
proof            (modus-ponens tm-450 tm-443 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (and (-> Bm (or Bm Cm)) (and (-> A (or A B)) C))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28812.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and ((D -> (D or E)) and ((B -> (B or C)) and A)))), M:tm-450, m:tm-443, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (and (-> Bm (or Bm Cm)) (and (-> A (or A B)) C)))))
================================================================
tm-name          tm-28813
in-theory        28813
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((E -> (E or F)) and ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-443 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28813.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((E -> (E or F)) and ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)))), M:tm-443, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28814
in-theory        28814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-409 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28814.        (((A -> (A or B)) or C) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-409, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28815
in-theory        28815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-400 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28815.        (((A -> (B -> (A and B))) or C) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-400, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28816
in-theory        28816
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-391 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28816.        ((((A and B) -> B) or C) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-391, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28817
in-theory        28817
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-382 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28817.        ((((A and B) -> A) or C) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-382, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28818
in-theory        28818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (E or F)) and G) -> H) -> ((G or ((E -> (E or F)) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-373 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28818.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (E or F)) and G) -> H) -> ((G or ((E -> (E or F)) and G)) -> H))), M:tm-373, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28819
in-theory        28819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-364 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28819.        (((A -> (B -> A)) or C) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-364, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28820
in-theory        28820
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and C) -> D) -> (E -> (((C or ((A -> (A or B)) and C)) -> D) and E)))
theorem-size     25
proof            (modus-ponens tm-355 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28820.        ((((A -> (A or B)) and C) -> D) -> (E -> (((C or ((A -> (A or B)) and C)) -> D) and E))), M:tm-355, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-28821
in-theory        28821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-354 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28821.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-354, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28822
in-theory        28822
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (B or C)) and D) -> (E -> (((B -> (B or C)) and D) and E)))) -> ((D or ((B -> (B or C)) and D)) -> (E -> (((B -> (B or C)) and D) and E))))
theorem-size     43
proof            (modus-ponens tm-351 tm-450 ((A (and (-> Am (or Am Bm)) Cm)) (Dm (-> B (and (and (-> Am (or Am Bm)) Cm) B))) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (-> B (and (and (-> Am (or Am Bm)) Cm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28822.        ((A or (((B -> (B or C)) and D) -> (E -> (((B -> (B or C)) and D) and E)))) -> ((D or ((B -> (B or C)) and D)) -> (E -> (((B -> (B or C)) and D) and E)))), M:tm-351, m:tm-450, u:((A (and (-> Am (or Am Bm)) Cm)) (Dm (-> B (and (and (-> Am (or Am Bm)) Cm) B))) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (-> B (and (and (-> Am (or Am Bm)) Cm) B)))))
================================================================
tm-name          tm-28823
in-theory        28823
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28823.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28824
in-theory        28824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-338 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28824.        (((A -> B) -> (A -> (A and B))) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F))), M:tm-338, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28825
in-theory        28825
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) or (((A -> (A or B)) and C) -> (((A -> (A or B)) and C) and D))) -> ((C or ((A -> (A or B)) and C)) -> (((A -> (A or B)) and C) and D)))
theorem-size     47
proof            (modus-ponens tm-335 tm-450 ((A (and (-> Am (or Am Bm)) Cm)) (Dm (and (and (-> Am (or Am Bm)) Cm) B)) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (and (and (-> Am (or Am Bm)) Cm) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28825.        (((((A -> (A or B)) and C) -> D) or (((A -> (A or B)) and C) -> (((A -> (A or B)) and C) and D))) -> ((C or ((A -> (A or B)) and C)) -> (((A -> (A or B)) and C) and D))), M:tm-335, m:tm-450, u:((A (and (-> Am (or Am Bm)) Cm)) (Dm (and (and (-> Am (or Am Bm)) Cm) B)) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (and (and (-> Am (or Am Bm)) Cm) B))))
================================================================
tm-name          tm-28826
in-theory        28826
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((((A -> (A or B)) and C) -> D) -> ((((A -> (A or B)) and C) -> D) and ((C or ((A -> (A or B)) and C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-328 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28826.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((((A -> (A or B)) and C) -> D) -> ((((A -> (A or B)) and C) -> D) and ((C or ((A -> (A or B)) and C)) -> D)))), M:tm-328, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-28827
in-theory        28827
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((E -> (F -> (E and F))) and ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D))))
theorem-size     51
proof            (modus-ponens tm-327 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28827.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((E -> (F -> (E and F))) and ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)))), M:tm-327, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28828
in-theory        28828
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (((E and F) -> F) and ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-326 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28828.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (((E and F) -> F) and ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)))), M:tm-326, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28829
in-theory        28829
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (((E and F) -> E) and ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-325 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28829.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (((E and F) -> E) and ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)))), M:tm-325, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28830
in-theory        28830
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-324 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28830.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)))), M:tm-324, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28831
in-theory        28831
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((E -> (F -> E)) and ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-323 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28831.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((E -> (F -> E)) and ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)))), M:tm-323, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28832
in-theory        28832
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28832.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28833
in-theory        28833
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28833.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28834
in-theory        28834
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28834.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28835
in-theory        28835
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((((A -> (A or B)) and C) -> D) -> (((A -> (A or B)) and C) -> D)))
theorem-size     41
proof            (modus-ponens tm-316 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28835.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((((A -> (A or B)) and C) -> D) -> (((A -> (A or B)) and C) -> D))), M:tm-316, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-28836
in-theory        28836
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28836.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28837
in-theory        28837
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (((((A -> (A or B)) and C) -> D) -> (not ((C or ((A -> (A or B)) and C)) -> D))) -> (not (((A -> (A or B)) and C) -> D))))
theorem-size     55
proof            (modus-ponens tm-313 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-6)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28837.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (((((A -> (A or B)) and C) -> D) -> (not ((C or ((A -> (A or B)) and C)) -> D))) -> (not (((A -> (A or B)) and C) -> D)))), M:tm-313, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-28838
in-theory        28838
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((((C or ((A -> (A or B)) and C)) -> D) -> E) -> (((((A -> (A or B)) and C) -> D) or ((C or ((A -> (A or B)) and C)) -> D)) -> E)))
theorem-size     59
proof            (modus-ponens tm-312 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28838.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((((C or ((A -> (A or B)) and C)) -> D) -> E) -> (((((A -> (A or B)) and C) -> D) or ((C or ((A -> (A or B)) and C)) -> D)) -> E))), M:tm-312, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-28839
in-theory        28839
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (E or ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-311 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28839.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (E or ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)))), M:tm-311, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28840
in-theory        28840
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28840.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) or E)), M:tm-310, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28841
in-theory        28841
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (E -> (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28841.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (E -> (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and E))), M:tm-309, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28842
in-theory        28842
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (((((A -> (A or B)) and C) -> D) -> (C or ((A -> (A or B)) and C))) -> ((((A -> (A or B)) and C) -> D) -> D)))
theorem-size     53
proof            (modus-ponens tm-306 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (or Cm (and (-> Am (or Am Bm)) Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28842.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (((((A -> (A or B)) and C) -> D) -> (C or ((A -> (A or B)) and C))) -> ((((A -> (A or B)) and C) -> D) -> D))), M:tm-306, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (or Cm (and (-> Am (or Am Bm)) Cm))) (C Dm))
================================================================
tm-name          tm-28843
in-theory        28843
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (E -> ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-305 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28843.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (E -> ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)))), M:tm-305, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28844
in-theory        28844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-303 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28844.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-303, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28845
in-theory        28845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-270 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28845.        ((A -> (((B and C) -> C) and A)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-270, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28846
in-theory        28846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-239 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28846.        ((A -> (((B and C) -> B) and A)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-239, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28847
in-theory        28847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (E or F)) and G) -> H) -> ((G or ((E -> (E or F)) and G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-210 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28847.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (E or F)) and G) -> H) -> ((G or ((E -> (E or F)) and G)) -> H))), M:tm-210, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28848
in-theory        28848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-183 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28848.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-183, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28849
in-theory        28849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-157 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28849.        ((A -> ((B and C) -> C)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-157, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28850
in-theory        28850
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (B or C)) and D) -> D)) -> ((D or ((B -> (B or C)) and D)) -> D))
theorem-size     23
proof            (modus-ponens tm-154 tm-450 ((A (-> Am (or Am Bm))) (Dm Cm) (B Cm) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Cm))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28850.        ((A or (((B -> (B or C)) and D) -> D)) -> ((D or ((B -> (B or C)) and D)) -> D)), M:tm-154, m:tm-450, u:((A (-> Am (or Am Bm))) (Dm Cm) (B Cm) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Cm)))
================================================================
tm-name          tm-28851
in-theory        28851
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-147 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28851.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-147, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28852
in-theory        28852
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and (C -> D)) -> C) or (((A -> (A or B)) and (C -> D)) -> D)) -> (((C -> D) or ((A -> (A or B)) and (C -> D))) -> D))
theorem-size     39
proof            (modus-ponens tm-144 tm-450 ((A (-> Am (or Am Bm))) (Cm (-> B Dm)) (C Dm) (D (-> (or (-> B Dm) (and (-> Am (or Am Bm)) (-> B Dm))) Dm))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-6)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28852.        (((((A -> (A or B)) and (C -> D)) -> C) or (((A -> (A or B)) and (C -> D)) -> D)) -> (((C -> D) or ((A -> (A or B)) and (C -> D))) -> D)), M:tm-144, m:tm-450, u:((A (-> Am (or Am Bm))) (Cm (-> B Dm)) (C Dm) (D (-> (or (-> B Dm) (and (-> Am (or Am Bm)) (-> B Dm))) Dm)))
================================================================
tm-name          tm-28853
in-theory        28853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-134 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28853.        ((A -> ((B and C) -> B)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-134, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28854
in-theory        28854
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (B or C)) and D) -> (B -> (B or C)))) -> ((D or ((B -> (B or C)) and D)) -> (B -> (B or C))))
theorem-size     31
proof            (modus-ponens tm-131 tm-450 ((Dm (-> Am (or Am Bm))) (B Cm) (A (-> Am (or Am Bm))) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (-> Am (or Am Bm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28854.        ((A or (((B -> (B or C)) and D) -> (B -> (B or C)))) -> ((D or ((B -> (B or C)) and D)) -> (B -> (B or C)))), M:tm-131, m:tm-450, u:((Dm (-> Am (or Am Bm))) (B Cm) (A (-> Am (or Am Bm))) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (-> Am (or Am Bm)))))
================================================================
tm-name          tm-28855
in-theory        28855
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-125 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28855.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-125, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28856
in-theory        28856
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> A) or (((A -> (A or B)) and C) -> (A or B))) -> ((C or ((A -> (A or B)) and C)) -> (A or B)))
theorem-size     35
proof            (modus-ponens tm-122 tm-450 ((A Am) (Dm (or Am Bm)) (C Cm) (B (or Am Bm)) (D (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (or Am Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-6)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28856.        (((((A -> (A or B)) and C) -> A) or (((A -> (A or B)) and C) -> (A or B))) -> ((C or ((A -> (A or B)) and C)) -> (A or B))), M:tm-122, m:tm-450, u:((A Am) (Dm (or Am Bm)) (C Cm) (B (or Am Bm)) (D (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (or Am Bm))))
================================================================
tm-name          tm-28857
in-theory        28857
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and C) -> (D -> E)) -> (((C or ((A -> (A or B)) and C)) -> D) -> ((C or ((A -> (A or B)) and C)) -> E)))
theorem-size     35
proof            (modus-ponens tm-114 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) (-> C D))) (B (or Cm (and (-> Am (or Am Bm)) Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28857.        ((((A -> (A or B)) and C) -> (D -> E)) -> (((C or ((A -> (A or B)) and C)) -> D) -> ((C or ((A -> (A or B)) and C)) -> E))), M:tm-114, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) (-> C D))) (B (or Cm (and (-> Am (or Am Bm)) Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-28858
in-theory        28858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (E or F)) and G) -> H) -> ((G or ((E -> (E or F)) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-113 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28858.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (E or F)) and G) -> H) -> ((G or ((E -> (E or F)) and G)) -> H))), M:tm-113, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28859
in-theory        28859
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-105 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28859.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-105, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28860
in-theory        28860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-95 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28860.        (((A -> B) -> (A -> A)) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F))), M:tm-95, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28861
in-theory        28861
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) or (((A -> (A or B)) and C) -> ((A -> (A or B)) and C))) -> ((C or ((A -> (A or B)) and C)) -> ((A -> (A or B)) and C)))
theorem-size     43
proof            (modus-ponens tm-92 tm-450 ((Dm (and (-> Am (or Am Bm)) Cm)) (A (and (-> Am (or Am Bm)) Cm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (and (-> Am (or Am Bm)) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28861.        (((((A -> (A or B)) and C) -> D) or (((A -> (A or B)) and C) -> ((A -> (A or B)) and C))) -> ((C or ((A -> (A or B)) and C)) -> ((A -> (A or B)) and C))), M:tm-92, m:tm-450, u:((Dm (and (-> Am (or Am Bm)) Cm)) (A (and (-> Am (or Am Bm)) Cm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (and (-> Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-28862
in-theory        28862
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and C) -> D) -> (E -> ((C or ((A -> (A or B)) and C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-84 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28862.        ((((A -> (A or B)) and C) -> D) -> (E -> ((C or ((A -> (A or B)) and C)) -> D))), M:tm-84, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-28863
in-theory        28863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-83 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28863.        ((A -> (B -> (C -> B))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-83, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28864
in-theory        28864
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (B or C)) and D) -> (E -> ((B -> (B or C)) and D)))) -> ((D or ((B -> (B or C)) and D)) -> (E -> ((B -> (B or C)) and D))))
theorem-size     39
proof            (modus-ponens tm-80 tm-450 ((A (and (-> Am (or Am Bm)) Cm)) (Dm (-> B (and (-> Am (or Am Bm)) Cm))) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (-> B (and (-> Am (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28864.        ((A or (((B -> (B or C)) and D) -> (E -> ((B -> (B or C)) and D)))) -> ((D or ((B -> (B or C)) and D)) -> (E -> ((B -> (B or C)) and D)))), M:tm-80, m:tm-450, u:((A (and (-> Am (or Am Bm)) Cm)) (Dm (-> B (and (-> Am (or Am Bm)) Cm))) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (-> B (and (-> Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-28865
in-theory        28865
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (B or C)) and D) -> E) -> ((D or ((B -> (B or C)) and D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-76 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28865.        (((not (not A)) -> A) and ((((B -> (B or C)) and D) -> E) -> ((D or ((B -> (B or C)) and D)) -> E))), M:tm-76, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28866
in-theory        28866
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (A or B)) and C) -> D))) or (((A -> (A or B)) and C) -> D)) -> ((C or ((A -> (A or B)) and C)) -> D))
theorem-size     33
proof            (modus-ponens tm-73 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-5 tm-6)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28866.        (((not (not (((A -> (A or B)) and C) -> D))) or (((A -> (A or B)) and C) -> D)) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-73, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-28867
in-theory        28867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-69 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-6)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28867.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F))), M:tm-69, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28868
in-theory        28868
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and C) -> (C or ((A -> (A or B)) and C))) -> ((((A -> (A or B)) and C) or (C or ((A -> (A or B)) and C))) -> (C or ((A -> (A or B)) and C))))
theorem-size     45
proof            (modus-ponens tm-55 tm-450 ((A (and (-> Am (or Am Bm)) Cm)) (Dm (or Cm (and (-> Am (or Am Bm)) Cm))) (B (or Cm (and (-> Am (or Am Bm)) Cm))) (C (or Cm (and (-> Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-8 tm-5 tm-6)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28868.        ((((A -> (A or B)) and C) -> (C or ((A -> (A or B)) and C))) -> ((((A -> (A or B)) and C) or (C or ((A -> (A or B)) and C))) -> (C or ((A -> (A or B)) and C)))), M:tm-55, m:tm-450, u:((A (and (-> Am (or Am Bm)) Cm)) (Dm (or Cm (and (-> Am (or Am Bm)) Cm))) (B (or Cm (and (-> Am (or Am Bm)) Cm))) (C (or Cm (and (-> Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-28869
in-theory        28869
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-54 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28869.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-54, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28870
in-theory        28870
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (B or C)) and D) -> (A and ((B -> (B or C)) and D)))) -> ((D or ((B -> (B or C)) and D)) -> (A and ((B -> (B or C)) and D))))
theorem-size     39
proof            (modus-ponens tm-48 tm-450 ((A (and (-> Am (or Am Bm)) Cm)) (Dm (and B (and (-> Am (or Am Bm)) Cm))) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (and B (and (-> Am (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28870.        ((A or (((B -> (B or C)) and D) -> (A and ((B -> (B or C)) and D)))) -> ((D or ((B -> (B or C)) and D)) -> (A and ((B -> (B or C)) and D)))), M:tm-48, m:tm-450, u:((A (and (-> Am (or Am Bm)) Cm)) (Dm (and B (and (-> Am (or Am Bm)) Cm))) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (and B (and (-> Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-28871
in-theory        28871
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B -> (B or C)) and D) -> E)) or (((B -> (B or C)) and D) -> E)) -> ((D or ((B -> (B or C)) and D)) -> E))
theorem-size     33
proof            (modus-ponens tm-47 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28871.        (((A and (((B -> (B or C)) and D) -> E)) or (((B -> (B or C)) and D) -> E)) -> ((D or ((B -> (B or C)) and D)) -> E)), M:tm-47, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-28872
in-theory        28872
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (A or B)) and C) -> D) and E) or (((A -> (A or B)) and C) -> D)) -> ((C or ((A -> (A or B)) and C)) -> D))
theorem-size     33
proof            (modus-ponens tm-46 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28872.        ((((((A -> (A or B)) and C) -> D) and E) or (((A -> (A or B)) and C) -> D)) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-46, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-28873
in-theory        28873
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (B or C)) and D) -> A)) -> ((D or ((B -> (B or C)) and D)) -> A))
theorem-size     23
proof            (modus-ponens tm-44 tm-450 ((A (and (-> Am (or Am Bm)) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28873.        ((A or (((B -> (B or C)) and D) -> A)) -> ((D or ((B -> (B or C)) and D)) -> A)), M:tm-44, m:tm-450, u:((A (and (-> Am (or Am Bm)) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-28874
in-theory        28874
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-42 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28874.        ((A -> (B or A)) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F))), M:tm-42, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28875
in-theory        28875
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-32 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28875.        ((A -> (A or B)) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F))), M:tm-32, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28876
in-theory        28876
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and C) -> D) -> ((((A -> (A or B)) and C) -> D) and ((C or ((A -> (A or B)) and C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-24 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28876.        ((((A -> (A or B)) and C) -> D) -> ((((A -> (A or B)) and C) -> D) and ((C or ((A -> (A or B)) and C)) -> D))), M:tm-24, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-28877
in-theory        28877
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-23 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28877.        ((A -> (B -> (A and B))) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F))), M:tm-23, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28878
in-theory        28878
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-22 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28878.        (((A and B) -> B) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F))), M:tm-22, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28879
in-theory        28879
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-21 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28879.        (((A and B) -> A) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F))), M:tm-21, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28880
in-theory        28880
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-20 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28880.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-20, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28881
in-theory        28881
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-19 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28881.        ((A -> (B -> A)) and ((((C -> (C or D)) and E) -> F) -> ((E or ((C -> (C or D)) and E)) -> F))), M:tm-19, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28882
in-theory        28882
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and C) -> D) -> (((A -> (A or B)) and C) -> D))
theorem-size     19
proof            (modus-ponens tm-12 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28882.        ((((A -> (A or B)) and C) -> D) -> (((A -> (A or B)) and C) -> D)), M:tm-12, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-28883
in-theory        28883
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> (not ((C or ((A -> (A or B)) and C)) -> D))) -> (not (((A -> (A or B)) and C) -> D)))
theorem-size     33
proof            (modus-ponens tm-9 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-5 tm-6)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28883.        (((((A -> (A or B)) and C) -> D) -> (not ((C or ((A -> (A or B)) and C)) -> D))) -> (not (((A -> (A or B)) and C) -> D))), M:tm-9, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-28884
in-theory        28884
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B -> (B or C)) and A)) -> D) -> E) -> (((((B -> (B or C)) and A) -> D) or ((A or ((B -> (B or C)) and A)) -> D)) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28884.        ((((A or ((B -> (B or C)) and A)) -> D) -> E) -> (((((B -> (B or C)) and A) -> D) or ((A or ((B -> (B or C)) and A)) -> D)) -> E)), M:tm-8, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-28885
in-theory        28885
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> (B or C)) and D) -> E) -> ((D or ((B -> (B or C)) and D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-7 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-5 tm-6)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28885.        (A or ((((B -> (B or C)) and D) -> E) -> ((D or ((B -> (B or C)) and D)) -> E))), M:tm-7, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28886
in-theory        28886
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-5)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28886.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) or E), M:tm-6, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28887
in-theory        28887
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> (B or C)) and D) -> E) -> ((D or ((B -> (B or C)) and D)) -> E)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28887.        (A -> (((((B -> (B or C)) and D) -> E) -> ((D or ((B -> (B or C)) and D)) -> E)) and A)), M:tm-5, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28888
in-theory        28888
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> (C or ((A -> (A or B)) and C))) -> ((((A -> (A or B)) and C) -> D) -> D))
theorem-size     31
proof            (modus-ponens tm-2 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (or Cm (and (-> Am (or Am Bm)) Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-5 tm-6)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28888.        (((((A -> (A or B)) and C) -> D) -> (C or ((A -> (A or B)) and C))) -> ((((A -> (A or B)) and C) -> D) -> D)), M:tm-2, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (or Cm (and (-> Am (or Am Bm)) Cm))) (C Dm))
================================================================
tm-name          tm-28889
in-theory        28889
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (B or C)) and D) -> E) -> ((D or ((B -> (B or C)) and D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-1 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-5 tm-6)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-28889.        (A -> ((((B -> (B or C)) and D) -> E) -> ((D or ((B -> (B or C)) and D)) -> E))), M:tm-1, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-28890
in-theory        28890
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and ((E -> (E or F)) and (A or (B -> ((C -> (C or D)) and B)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28890.        ((A or (B -> ((C -> (C or D)) and B))) and ((E -> (E or F)) and (A or (B -> ((C -> (C or D)) and B))))), M:tm-443, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28891
in-theory        28891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-409 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28891.        (((A -> (A or B)) or C) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-409, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28892
in-theory        28892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-400 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28892.        (((A -> (B -> (A and B))) or C) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-400, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28893
in-theory        28893
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-391 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28893.        ((((A and B) -> B) or C) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-391, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28894
in-theory        28894
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-382 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28894.        ((((A and B) -> A) or C) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-382, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28895
in-theory        28895
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-373 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28895.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> ((G -> (G or H)) and F)))), M:tm-373, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28896
in-theory        28896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-364 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28896.        (((A -> (B -> A)) or C) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-364, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28897
in-theory        28897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-354 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28897.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-354, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28898
in-theory        28898
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28898.        ((A or (B -> ((C -> (C or D)) and B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28899
in-theory        28899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-338 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28899.        (((A -> B) -> (A -> (A and B))) and (C or (D -> ((E -> (E or F)) and D)))), M:tm-338, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28900
in-theory        28900
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and ((E -> (F -> (E and F))) and (A or (B -> ((C -> (C or D)) and B)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28900.        ((A or (B -> ((C -> (C or D)) and B))) and ((E -> (F -> (E and F))) and (A or (B -> ((C -> (C or D)) and B))))), M:tm-327, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28901
in-theory        28901
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and (((E and F) -> F) and (A or (B -> ((C -> (C or D)) and B)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28901.        ((A or (B -> ((C -> (C or D)) and B))) and (((E and F) -> F) and (A or (B -> ((C -> (C or D)) and B))))), M:tm-326, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28902
in-theory        28902
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and (((E and F) -> E) and (A or (B -> ((C -> (C or D)) and B)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28902.        ((A or (B -> ((C -> (C or D)) and B))) and (((E and F) -> E) and (A or (B -> ((C -> (C or D)) and B))))), M:tm-325, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28903
in-theory        28903
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> ((C -> (C or D)) and B)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28903.        ((A or (B -> ((C -> (C or D)) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> ((C -> (C or D)) and B))))), M:tm-324, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28904
in-theory        28904
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and ((E -> (F -> E)) and (A or (B -> ((C -> (C or D)) and B)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28904.        ((A or (B -> ((C -> (C or D)) and B))) and ((E -> (F -> E)) and (A or (B -> ((C -> (C or D)) and B))))), M:tm-323, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28905
in-theory        28905
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28905.        ((A or (B -> ((C -> (C or D)) and B))) and ((E and F) -> F)), M:tm-322, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28906
in-theory        28906
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28906.        ((A or (B -> ((C -> (C or D)) and B))) and ((E and F) -> E)), M:tm-320, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28907
in-theory        28907
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28907.        ((A or (B -> ((C -> (C or D)) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28908
in-theory        28908
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28908.        ((A or (B -> ((C -> (C or D)) and B))) and (E -> (F -> E))), M:tm-315, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28909
in-theory        28909
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and (E or (A or (B -> ((C -> (C or D)) and B)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28909.        ((A or (B -> ((C -> (C or D)) and B))) and (E or (A or (B -> ((C -> (C or D)) and B))))), M:tm-311, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28910
in-theory        28910
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and ((A or (B -> ((C -> (C or D)) and B))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28910.        ((A or (B -> ((C -> (C or D)) and B))) and ((A or (B -> ((C -> (C or D)) and B))) or E)), M:tm-310, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28911
in-theory        28911
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and (E -> ((A or (B -> ((C -> (C or D)) and B))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28911.        ((A or (B -> ((C -> (C or D)) and B))) and (E -> ((A or (B -> ((C -> (C or D)) and B))) and E))), M:tm-309, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28912
in-theory        28912
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and (E -> (A or (B -> ((C -> (C or D)) and B)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28912.        ((A or (B -> ((C -> (C or D)) and B))) and (E -> (A or (B -> ((C -> (C or D)) and B))))), M:tm-305, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28913
in-theory        28913
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-303 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28913.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-303, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28914
in-theory        28914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-270 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28914.        ((A -> (((B and C) -> C) and A)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-270, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28915
in-theory        28915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-239 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28915.        ((A -> (((B and C) -> B) and A)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-239, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28916
in-theory        28916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-210 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28916.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> ((G -> (G or H)) and F)))), M:tm-210, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28917
in-theory        28917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-183 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28917.        ((A -> ((B -> (C -> B)) and A)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-183, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28918
in-theory        28918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-157 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28918.        ((A -> ((B and C) -> C)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-157, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28919
in-theory        28919
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-147 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28919.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-147, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28920
in-theory        28920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-134 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28920.        ((A -> ((B and C) -> B)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-134, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28921
in-theory        28921
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-125 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28921.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-125, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28922
in-theory        28922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-113 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28922.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (G or H)) and F)))), M:tm-113, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28923
in-theory        28923
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     31
proof            (modus-ponens tm-105 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28923.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-105, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28924
in-theory        28924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-95 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28924.        (((A -> B) -> (A -> A)) and (C or (D -> ((E -> (E or F)) and D)))), M:tm-95, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28925
in-theory        28925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-83 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28925.        ((A -> (B -> (C -> B))) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-83, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28926
in-theory        28926
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> ((D -> (D or E)) and C))))
theorem-size     17
proof            (modus-ponens tm-76 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28926.        (((not (not A)) -> A) and (B or (C -> ((D -> (D or E)) and C)))), M:tm-76, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28927
in-theory        28927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> ((E -> (E or F)) and D))))
theorem-size     23
proof            (modus-ponens tm-69 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28927.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> ((E -> (E or F)) and D)))), M:tm-69, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28928
in-theory        28928
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-54 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28928.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-54, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28929
in-theory        28929
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-42 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28929.        ((A -> (B or A)) and (C or (D -> ((E -> (E or F)) and D)))), M:tm-42, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28930
in-theory        28930
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-32 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28930.        ((A -> (A or B)) and (C or (D -> ((E -> (E or F)) and D)))), M:tm-32, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28931
in-theory        28931
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-23 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28931.        ((A -> (B -> (A and B))) and (C or (D -> ((E -> (E or F)) and D)))), M:tm-23, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28932
in-theory        28932
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-22 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28932.        (((A and B) -> B) and (C or (D -> ((E -> (E or F)) and D)))), M:tm-22, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28933
in-theory        28933
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-21 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28933.        (((A and B) -> A) and (C or (D -> ((E -> (E or F)) and D)))), M:tm-21, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28934
in-theory        28934
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-20 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28934.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-20, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28935
in-theory        28935
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-19 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28935.        ((A -> (B -> A)) and (C or (D -> ((E -> (E or F)) and D)))), M:tm-19, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28936
in-theory        28936
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C -> ((D -> (D or E)) and C))))
theorem-size     13
proof            (modus-ponens tm-7 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28936.        (A or (B or (C -> ((D -> (D or E)) and C)))), M:tm-7, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28937
in-theory        28937
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-6 tm-7 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28937.        ((A or (B -> ((C -> (C or D)) and B))) or E), M:tm-6, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28938
in-theory        28938
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C -> ((D -> (D or E)) and C))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28938.        (A -> ((B or (C -> ((D -> (D or E)) and C))) and A)), M:tm-5, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28939
in-theory        28939
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C -> ((D -> (D or E)) and C))))
theorem-size     13
proof            (modus-ponens tm-1 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-1 tm-7 tm-5 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28939.        (A -> (B or (C -> ((D -> (D or E)) and C)))), M:tm-1, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-28940
in-theory        28940
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and ((E -> (E or F)) and ((A -> ((B -> (B or C)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-443 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28940.        (((A -> ((B -> (B or C)) and A)) or D) and ((E -> (E or F)) and ((A -> ((B -> (B or C)) and A)) or D))), M:tm-443, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28941
in-theory        28941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-409 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28941.        (((A -> (A or B)) or C) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-409, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28942
in-theory        28942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-400 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28942.        (((A -> (B -> (A and B))) or C) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-400, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28943
in-theory        28943
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-391 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28943.        ((((A and B) -> B) or C) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-391, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28944
in-theory        28944
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-382 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28944.        ((((A and B) -> A) or C) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-382, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28945
in-theory        28945
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F -> (F or G)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-373 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28945.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F -> (F or G)) and E)) or H)), M:tm-373, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28946
in-theory        28946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-364 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28946.        (((A -> (B -> A)) or C) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-364, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28947
in-theory        28947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-354 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28947.        ((A -> (B -> (C -> (B and C)))) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-354, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28948
in-theory        28948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28948.        (((A -> ((B -> (B or C)) and A)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28949
in-theory        28949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> ((D -> (D or E)) and C)) or F))
theorem-size     21
proof            (modus-ponens tm-338 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28949.        (((A -> B) -> (A -> (A and B))) and ((C -> ((D -> (D or E)) and C)) or F)), M:tm-338, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28950
in-theory        28950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and ((E -> (F -> (E and F))) and ((A -> ((B -> (B or C)) and A)) or D)))
theorem-size     31
proof            (modus-ponens tm-327 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28950.        (((A -> ((B -> (B or C)) and A)) or D) and ((E -> (F -> (E and F))) and ((A -> ((B -> (B or C)) and A)) or D))), M:tm-327, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28951
in-theory        28951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and (((E and F) -> F) and ((A -> ((B -> (B or C)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-326 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28951.        (((A -> ((B -> (B or C)) and A)) or D) and (((E and F) -> F) and ((A -> ((B -> (B or C)) and A)) or D))), M:tm-326, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28952
in-theory        28952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and (((E and F) -> E) and ((A -> ((B -> (B or C)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-325 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28952.        (((A -> ((B -> (B or C)) and A)) or D) and (((E and F) -> E) and ((A -> ((B -> (B or C)) and A)) or D))), M:tm-325, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28953
in-theory        28953
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> ((B -> (B or C)) and A)) or D)))
theorem-size     37
proof            (modus-ponens tm-324 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28953.        (((A -> ((B -> (B or C)) and A)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> ((B -> (B or C)) and A)) or D))), M:tm-324, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28954
in-theory        28954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and ((E -> (F -> E)) and ((A -> ((B -> (B or C)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-323 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28954.        (((A -> ((B -> (B or C)) and A)) or D) and ((E -> (F -> E)) and ((A -> ((B -> (B or C)) and A)) or D))), M:tm-323, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28955
in-theory        28955
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28955.        (((A -> ((B -> (B or C)) and A)) or D) and ((E and F) -> F)), M:tm-322, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28956
in-theory        28956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28956.        (((A -> ((B -> (B or C)) and A)) or D) and ((E and F) -> E)), M:tm-320, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28957
in-theory        28957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28957.        (((A -> ((B -> (B or C)) and A)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28958
in-theory        28958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28958.        (((A -> ((B -> (B or C)) and A)) or D) and (E -> (F -> E))), M:tm-315, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28959
in-theory        28959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and (E or ((A -> ((B -> (B or C)) and A)) or D)))
theorem-size     25
proof            (modus-ponens tm-311 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28959.        (((A -> ((B -> (B or C)) and A)) or D) and (E or ((A -> ((B -> (B or C)) and A)) or D))), M:tm-311, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28960
in-theory        28960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and (((A -> ((B -> (B or C)) and A)) or D) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28960.        (((A -> ((B -> (B or C)) and A)) or D) and (((A -> ((B -> (B or C)) and A)) or D) or E)), M:tm-310, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28961
in-theory        28961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and (E -> (((A -> ((B -> (B or C)) and A)) or D) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28961.        (((A -> ((B -> (B or C)) and A)) or D) and (E -> (((A -> ((B -> (B or C)) and A)) or D) and E))), M:tm-309, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28962
in-theory        28962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and (E -> ((A -> ((B -> (B or C)) and A)) or D)))
theorem-size     25
proof            (modus-ponens tm-305 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28962.        (((A -> ((B -> (B or C)) and A)) or D) and (E -> ((A -> ((B -> (B or C)) and A)) or D))), M:tm-305, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28963
in-theory        28963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-303 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28963.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-303, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28964
in-theory        28964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-270 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28964.        ((A -> (((B and C) -> C) and A)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-270, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28965
in-theory        28965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-239 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28965.        ((A -> (((B and C) -> B) and A)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-239, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28966
in-theory        28966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F -> (F or G)) and E)) or H))
theorem-size     29
proof            (modus-ponens tm-210 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28966.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F -> (F or G)) and E)) or H)), M:tm-210, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28967
in-theory        28967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-183 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28967.        ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-183, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28968
in-theory        28968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-157 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28968.        ((A -> ((B and C) -> C)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-157, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28969
in-theory        28969
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-147 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28969.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-147, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28970
in-theory        28970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-134 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28970.        ((A -> ((B and C) -> B)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-134, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28971
in-theory        28971
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-125 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28971.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-125, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28972
in-theory        28972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (F or G)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-113 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28972.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (F or G)) and E)) or H)), M:tm-113, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28973
in-theory        28973
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     31
proof            (modus-ponens tm-105 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28973.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-105, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28974
in-theory        28974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> ((D -> (D or E)) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-95 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28974.        (((A -> B) -> (A -> A)) and ((C -> ((D -> (D or E)) and C)) or F)), M:tm-95, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28975
in-theory        28975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-83 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28975.        ((A -> (B -> (C -> B))) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-83, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28976
in-theory        28976
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> ((C -> (C or D)) and B)) or E))
theorem-size     17
proof            (modus-ponens tm-76 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28976.        (((not (not A)) -> A) and ((B -> ((C -> (C or D)) and B)) or E)), M:tm-76, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28977
in-theory        28977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D -> (D or E)) and C)) or F))
theorem-size     23
proof            (modus-ponens tm-69 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28977.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D -> (D or E)) and C)) or F)), M:tm-69, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28978
in-theory        28978
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-54 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28978.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-54, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28979
in-theory        28979
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> ((D -> (D or E)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-42 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28979.        ((A -> (B or A)) and ((C -> ((D -> (D or E)) and C)) or F)), M:tm-42, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28980
in-theory        28980
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> ((D -> (D or E)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-32 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28980.        ((A -> (A or B)) and ((C -> ((D -> (D or E)) and C)) or F)), M:tm-32, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28981
in-theory        28981
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> ((D -> (D or E)) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-23 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28981.        ((A -> (B -> (A and B))) and ((C -> ((D -> (D or E)) and C)) or F)), M:tm-23, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28982
in-theory        28982
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> ((D -> (D or E)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-22 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28982.        (((A and B) -> B) and ((C -> ((D -> (D or E)) and C)) or F)), M:tm-22, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28983
in-theory        28983
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> ((D -> (D or E)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-21 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28983.        (((A and B) -> A) and ((C -> ((D -> (D or E)) and C)) or F)), M:tm-21, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28984
in-theory        28984
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-20 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28984.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-20, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28985
in-theory        28985
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> ((D -> (D or E)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-19 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28985.        ((A -> (B -> A)) and ((C -> ((D -> (D or E)) and C)) or F)), M:tm-19, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28986
in-theory        28986
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> ((C -> (C or D)) and B)) or E))
theorem-size     13
proof            (modus-ponens tm-7 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-7 tm-6 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28986.        (A or ((B -> ((C -> (C or D)) and B)) or E)), M:tm-7, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28987
in-theory        28987
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-6 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28987.        (((A -> ((B -> (B or C)) and A)) or D) or E), M:tm-6, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28988
in-theory        28988
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> ((C -> (C or D)) and B)) or E) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28988.        (A -> (((B -> ((C -> (C or D)) and B)) or E) and A)), M:tm-5, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28989
in-theory        28989
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (C or D)) and B)) or E))
theorem-size     13
proof            (modus-ponens tm-1 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-1 tm-6 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28989.        (A -> ((B -> ((C -> (C or D)) and B)) or E)), M:tm-1, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-28990
in-theory        28990
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-453 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-5 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-28990.        ((A -> ((B -> (B or C)) and A)) and (D -> (D or E))), M:tm-453, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-28991
in-theory        28991
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-453 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-28991.        ((A -> ((B -> (B or C)) and A)) and (D -> (E or D))), M:tm-453, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-28992
in-theory        28992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-28992.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-453, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-28993
in-theory        28993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-453 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-28993.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-453, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-28994
in-theory        28994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-453 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-28994.        ((A -> ((B -> (B or C)) and A)) and ((not (not D)) -> D)), M:tm-453, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-28995
in-theory        28995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-453 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-28995.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (F -> E)))), M:tm-453, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-28996
in-theory        28996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-453 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-28996.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (D -> D))), M:tm-453, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-28997
in-theory        28997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-453 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-28997.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-453, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-28998
in-theory        28998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-28998.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-453, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-28999
in-theory        28999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-453 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-28999.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-453, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-29000
in-theory        29000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-453 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29000.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E and F) -> E))), M:tm-453, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-29001
in-theory        29001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-453 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-29001.        ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-453, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-29002
in-theory        29002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-453 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29002.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E and F) -> F))), M:tm-453, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-29003
in-theory        29003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-453 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29003.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> E)) and D))), M:tm-453, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-29004
in-theory        29004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-453 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29004.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-453, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-29005
in-theory        29005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-453 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29005.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E and F) -> E) and D))), M:tm-453, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-29006
in-theory        29006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-453 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29006.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E and F) -> F) and D))), M:tm-453, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-29007
in-theory        29007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29007.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-453, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-29008
in-theory        29008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-453 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-29008.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (D -> (D and E)))), M:tm-453, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-29009
in-theory        29009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29009.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (F -> (E and F))))), M:tm-453, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-29010
in-theory        29010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-453 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29010.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) or F)), M:tm-453, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-29011
in-theory        29011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-453 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29011.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-453, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-29012
in-theory        29012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-453 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29012.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) or F)), M:tm-453, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-29013
in-theory        29013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-453 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29013.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) or F)), M:tm-453, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-29014
in-theory        29014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-453 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29014.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) or F)), M:tm-453, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-29015
in-theory        29015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-453 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29015.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) or F)), M:tm-453, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-29016
in-theory        29016
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-453 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29016.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (E or F)) and D))), M:tm-453, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-29017
in-theory        29017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-453 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29017.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (E or F)))), M:tm-453, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-29018
in-theory        29018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-453 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29018.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> (F -> E)))), M:tm-453, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-29019
in-theory        29019
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29019.        ((A -> ((B -> (B or C)) and A)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-453, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-29020
in-theory        29020
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-453 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29020.        ((A -> ((B -> (B or C)) and A)) and (D or ((E and F) -> E))), M:tm-453, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-29021
in-theory        29021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-453 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29021.        ((A -> ((B -> (B or C)) and A)) and (D or ((E and F) -> F))), M:tm-453, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-29022
in-theory        29022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29022.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> (F -> (E and F))))), M:tm-453, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-29023
in-theory        29023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-453 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29023.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> (E or F)))), M:tm-453, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-29024
in-theory        29024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-453 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29024.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> (F or E)))), M:tm-453, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-29025
in-theory        29025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-453 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29025.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) or F)), M:tm-453, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-29026
in-theory        29026
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-453 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29026.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F or E)) and D))), M:tm-453, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-29027
in-theory        29027
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-453 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29027.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (F or E)))), M:tm-453, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-29028
in-theory        29028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-453 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-29028.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-453, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-29029
in-theory        29029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-453 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-29029.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-453, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-29030
in-theory        29030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-453 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-29030.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-453, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-29031
in-theory        29031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-453 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-29031.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-453, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-29032
in-theory        29032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-453 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-29032.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-453, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-29033
in-theory        29033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-453 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-29033.        ((A -> ((B -> (B or C)) and A)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-453, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-29034
in-theory        29034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-453 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-29034.        ((A -> ((B -> (B or C)) and A)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-453, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-29035
in-theory        29035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-453 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-29035.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-453, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-29036
in-theory        29036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29036.        ((A -> ((B -> (B or C)) and A)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-453, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-29037
in-theory        29037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-453 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29037.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-453, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-29038
in-theory        29038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-453 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29038.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-453, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-29039
in-theory        29039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-453 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-29039.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-453, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-29040
in-theory        29040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29040.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-453, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-29041
in-theory        29041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-453 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-29041.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not (E -> D))) -> (not D))), M:tm-453, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-29042
in-theory        29042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-29042.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-453, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-29043
in-theory        29043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-453 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-29043.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-453, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-29044
in-theory        29044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-453 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-29044.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-453, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-29045
in-theory        29045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-29045.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-453, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-29046
in-theory        29046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-453 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-29046.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not (D or E))) -> (not D))), M:tm-453, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-29047
in-theory        29047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-453 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-29047.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not (E or D))) -> (not D))), M:tm-453, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-29048
in-theory        29048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-453 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-29048.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-453, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-29049
in-theory        29049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-453 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-29049.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-453, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-29050
in-theory        29050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-453 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-9)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-29050.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-453, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-29051
in-theory        29051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29051.        ((A -> ((B -> (B or C)) and A)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-453, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-29052
in-theory        29052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     23
proof            (modus-ponens tm-453 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29052.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-453, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-29053
in-theory        29053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     25
proof            (modus-ponens tm-453 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29053.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-453, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-29054
in-theory        29054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-453 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-29054.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-453, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-29055
in-theory        29055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29055.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-453, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-29056
in-theory        29056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     21
proof            (modus-ponens tm-453 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-6 tm-9 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-29056.        ((A -> ((B -> (B or C)) and A)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-453, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-29057
in-theory        29057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-453 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-29057.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-453, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-29058
in-theory        29058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-453 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29058.        ((A -> ((B -> (B or C)) and A)) and (D or ((not (not E)) -> E))), M:tm-453, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-29059
in-theory        29059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((not (not D)) -> D) or E))
theorem-size     17
proof            (modus-ponens tm-453 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29059.        ((A -> ((B -> (B or C)) and A)) and (((not (not D)) -> D) or E)), M:tm-453, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-29060
in-theory        29060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-453 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29060.        ((A -> ((B -> (B or C)) and A)) and (D -> (((not (not E)) -> E) and D))), M:tm-453, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-29061
in-theory        29061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     25
proof            (modus-ponens tm-453 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-29061.        ((A -> ((B -> (B or C)) and A)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-453, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-29062
in-theory        29062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-453 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29062.        ((A -> ((B -> (B or C)) and A)) and (D -> ((not (not E)) -> E))), M:tm-453, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-29063
in-theory        29063
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-29063.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-453, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-29064
in-theory        29064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-453 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-29064.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-453, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-29065
in-theory        29065
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29065.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> (F -> (G -> F))))), M:tm-453, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-29066
in-theory        29066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29066.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (F -> E))) or G)), M:tm-453, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-29067
in-theory        29067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29067.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-453, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-29068
in-theory        29068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-453 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-29068.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (D -> (F -> E)))), M:tm-453, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-29069
in-theory        29069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29069.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (F -> (G -> F))))), M:tm-453, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-29070
in-theory        29070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> D))
theorem-size     13
proof            (modus-ponens tm-453 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-29070.        ((A -> ((B -> (B or C)) and A)) and (D -> D)), M:tm-453, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-29071
in-theory        29071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-29071.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-453, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-29072
in-theory        29072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D and E) -> (D and E)))
theorem-size     17
proof            (modus-ponens tm-453 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-29072.        ((A -> ((B -> (B or C)) and A)) and ((D and E) -> (D and E))), M:tm-453, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-29073
in-theory        29073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-453 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-29073.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (D -> E))), M:tm-453, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-29074
in-theory        29074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((not (not D)) -> (not (not D))))
theorem-size     17
proof            (modus-ponens tm-453 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-29074.        ((A -> ((B -> (B or C)) and A)) and ((not (not D)) -> (not (not D)))), M:tm-453, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-29075
in-theory        29075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-453 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-29075.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-453, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-29076
in-theory        29076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-453 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-29076.        ((A -> ((B -> (B or C)) and A)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-453, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-29077
in-theory        29077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-453 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29077.        ((A -> ((B -> (B or C)) and A)) and (D or ((E -> F) -> (E -> E)))), M:tm-453, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-29078
in-theory        29078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (D -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-453 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29078.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (D -> D)) or F)), M:tm-453, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-29079
in-theory        29079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29079.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-453, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-29080
in-theory        29080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-29080.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-453, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-29081
in-theory        29081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-453 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29081.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> F) -> (E -> E)))), M:tm-453, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-29082
in-theory        29082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-29082.        ((A -> ((B -> (B or C)) and A)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-453, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-29083
in-theory        29083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-453 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-29083.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D -> E)) -> (D -> E))), M:tm-453, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-29084
in-theory        29084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-453 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-29084.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-453, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-29085
in-theory        29085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     41
proof            (modus-ponens tm-453 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-29085.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-453, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-29086
in-theory        29086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-453 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-29086.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-453, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-29087
in-theory        29087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29087.        ((A -> ((B -> (B or C)) and A)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-453, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-29088
in-theory        29088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-453 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29088.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-453, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-29089
in-theory        29089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-453 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29089.        ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-453, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-29090
in-theory        29090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-453 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-29090.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-453, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-29091
in-theory        29091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29091.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-453, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-29092
in-theory        29092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-453 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-29092.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-453, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-29093
in-theory        29093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-453 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-29093.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-453, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-29094
in-theory        29094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     43
proof            (modus-ponens tm-453 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-29094.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-453, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-29095
in-theory        29095
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-453 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29095.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-453, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-29096
in-theory        29096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-453 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29096.        ((A -> ((B -> (B or C)) and A)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-453, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-29097
in-theory        29097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-453 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29097.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-453, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-29098
in-theory        29098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-453 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-29098.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-453, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-29099
in-theory        29099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-453 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29099.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-453, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-29100
in-theory        29100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) and D) -> E))
theorem-size     17
proof            (modus-ponens tm-453 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-29100.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) and D) -> E)), M:tm-453, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-29101
in-theory        29101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-453 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-29101.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-453, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-29102
in-theory        29102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-453 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-29102.        ((A -> ((B -> (B or C)) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-453, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-29103
in-theory        29103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-453 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-29103.        ((A -> ((B -> (B or C)) and A)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-453, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-29104
in-theory        29104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     25
proof            (modus-ponens tm-453 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-29104.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-453, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-29105
in-theory        29105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     35
proof            (modus-ponens tm-453 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-29105.        ((A -> ((B -> (B or C)) and A)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-453, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-29106
in-theory        29106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     37
proof            (modus-ponens tm-453 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-29106.        ((A -> ((B -> (B or C)) and A)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-453, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-29107
in-theory        29107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-453 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29107.        ((A -> ((B -> (B or C)) and A)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-453, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-29108
in-theory        29108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-453 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29108.        ((A -> ((B -> (B or C)) and A)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-453, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-29109
in-theory        29109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-453 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29109.        ((A -> ((B -> (B or C)) and A)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-453, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-29110
in-theory        29110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     33
proof            (modus-ponens tm-453 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-29110.        ((A -> ((B -> (B or C)) and A)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-453, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-29111
in-theory        29111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-453 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29111.        ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-453, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-29112
in-theory        29112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-453 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-29112.        ((A -> ((B -> (B or C)) and A)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-453, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-29113
in-theory        29113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-453 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-29113.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-453, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-29114
in-theory        29114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-29114.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-453, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-29115
in-theory        29115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     27
proof            (modus-ponens tm-453 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-29115.        ((A -> ((B -> (B or C)) and A)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-453, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-29116
in-theory        29116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-453 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29116.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> ((F and G) -> F)))), M:tm-453, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-29117
in-theory        29117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29117.        ((A -> ((B -> (B or C)) and A)) and ((D -> ((E and F) -> E)) or G)), M:tm-453, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-29118
in-theory        29118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29118.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-453, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-29119
in-theory        29119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-453 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-29119.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E and F)) -> (D -> E))), M:tm-453, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-29120
in-theory        29120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-453 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29120.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> ((F and G) -> F)))), M:tm-453, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-29121
in-theory        29121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D and (D -> E)) -> E))
theorem-size     17
proof            (modus-ponens tm-453 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-29121.        ((A -> ((B -> (B or C)) and A)) and ((D and (D -> E)) -> E)), M:tm-453, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-29122
in-theory        29122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-453 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-29122.        ((A -> ((B -> (B or C)) and A)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-453, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-29123
in-theory        29123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-453 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-29123.        ((A -> ((B -> (B or C)) and A)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-453, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-29124
in-theory        29124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-453 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-29124.        ((A -> ((B -> (B or C)) and A)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-453, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-29125
in-theory        29125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-453 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-29125.        ((A -> ((B -> (B or C)) and A)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-453, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-29126
in-theory        29126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     25
proof            (modus-ponens tm-453 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-29126.        ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-453, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-29127
in-theory        29127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     35
proof            (modus-ponens tm-453 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-29127.        ((A -> ((B -> (B or C)) and A)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-453, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-29128
in-theory        29128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-453 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-29128.        ((A -> ((B -> (B or C)) and A)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-453, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-29129
in-theory        29129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-453 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29129.        ((A -> ((B -> (B or C)) and A)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-453, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-29130
in-theory        29130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-453 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29130.        ((A -> ((B -> (B or C)) and A)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-453, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-29131
in-theory        29131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-453 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29131.        ((A -> ((B -> (B or C)) and A)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-453, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-29132
in-theory        29132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     33
proof            (modus-ponens tm-453 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-29132.        ((A -> ((B -> (B or C)) and A)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-453, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-29133
in-theory        29133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-453 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29133.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-453, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-29134
in-theory        29134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-453 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-29134.        ((A -> ((B -> (B or C)) and A)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-453, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-29135
in-theory        29135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-453 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-29135.        ((A -> ((B -> (B or C)) and A)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-453, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-29136
in-theory        29136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-453 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-29136.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-453, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-29137
in-theory        29137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-29137.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-453, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-29138
in-theory        29138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-453 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-29138.        ((A -> ((B -> (B or C)) and A)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-453, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-29139
in-theory        29139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-453 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29139.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> ((F and G) -> G)))), M:tm-453, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-29140
in-theory        29140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29140.        ((A -> ((B -> (B or C)) and A)) and ((D -> ((E and F) -> F)) or G)), M:tm-453, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-29141
in-theory        29141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29141.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-453, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-29142
in-theory        29142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-453 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-29142.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E and F)) -> (D -> F))), M:tm-453, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-29143
in-theory        29143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-453 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29143.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> ((F and G) -> G)))), M:tm-453, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-29144
in-theory        29144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29144.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-453, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-29145
in-theory        29145
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29145.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-453, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-29146
in-theory        29146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29146.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-453, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-29147
in-theory        29147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-453 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29147.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-453, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-29148
in-theory        29148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29148.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-453, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-29149
in-theory        29149
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-453 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29149.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-453, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-29150
in-theory        29150
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29150.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-453, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-29151
in-theory        29151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29151.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-453, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-29152
in-theory        29152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-453 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29152.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-453, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-29153
in-theory        29153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29153.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-453, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-29154
in-theory        29154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29154.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-453, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-29155
in-theory        29155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29155.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-453, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-29156
in-theory        29156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-453 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29156.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-453, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-29157
in-theory        29157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29157.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-453, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-29158
in-theory        29158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-453 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29158.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-453, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-29159
in-theory        29159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-453 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29159.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-453, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-29160
in-theory        29160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-453 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29160.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-453, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-29161
in-theory        29161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-453 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29161.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-453, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-29162
in-theory        29162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29162.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-453, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-29163
in-theory        29163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-29163.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-453, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-29164
in-theory        29164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-453 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-29164.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-453, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-29165
in-theory        29165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-453 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29165.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-453, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-29166
in-theory        29166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-453 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29166.        ((A -> ((B -> (B or C)) and A)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-453, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-29167
in-theory        29167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29167.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-453, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-29168
in-theory        29168
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-453 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29168.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-453, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-29169
in-theory        29169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-453 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29169.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-453, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-29170
in-theory        29170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29170.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-453, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-29171
in-theory        29171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-453 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29171.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-453, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-29172
in-theory        29172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-453 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29172.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-453, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-29173
in-theory        29173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29173.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-453, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-29174
in-theory        29174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29174.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-453, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-29175
in-theory        29175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-453 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29175.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-453, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-29176
in-theory        29176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29176.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-453, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-29177
in-theory        29177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-453 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29177.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-453, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-29178
in-theory        29178
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-453 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29178.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-453, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-29179
in-theory        29179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29179.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-453, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-29180
in-theory        29180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-453 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29180.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-453, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-29181
in-theory        29181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-453 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29181.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-453, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-29182
in-theory        29182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-453 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29182.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-453, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-29183
in-theory        29183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-453 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29183.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-453, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-29184
in-theory        29184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-453 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29184.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-453, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-29185
in-theory        29185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-453 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29185.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-453, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-29186
in-theory        29186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-453 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29186.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-453, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-29187
in-theory        29187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-453 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29187.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-453, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-29188
in-theory        29188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-453 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29188.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-453, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-29189
in-theory        29189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-453 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29189.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-453, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-29190
in-theory        29190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-453 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-29190.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-453, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-29191
in-theory        29191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-453 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-29191.        ((A -> ((B -> (B or C)) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-453, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-29192
in-theory        29192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-453 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29192.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-453, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-29193
in-theory        29193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     29
proof            (modus-ponens tm-453 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29193.        ((A -> ((B -> (B or C)) and A)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-453, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-29194
in-theory        29194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-453 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29194.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-453, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-29195
in-theory        29195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-453 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29195.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-453, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-29196
in-theory        29196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29196.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-453, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-29197
in-theory        29197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29197.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-453, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-29198
in-theory        29198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29198.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-453, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-29199
in-theory        29199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-453 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29199.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-453, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-29200
in-theory        29200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29200.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-453, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-29201
in-theory        29201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-453 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29201.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-453, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-29202
in-theory        29202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29202.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-453, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-29203
in-theory        29203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29203.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-453, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-29204
in-theory        29204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-453 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29204.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-453, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-29205
in-theory        29205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29205.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-453, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-29206
in-theory        29206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29206.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-453, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-29207
in-theory        29207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29207.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-453, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-29208
in-theory        29208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-453 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29208.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-453, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-29209
in-theory        29209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29209.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-453, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-29210
in-theory        29210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-453 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29210.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-453, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-29211
in-theory        29211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-453 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29211.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-453, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-29212
in-theory        29212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-453 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29212.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-453, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-29213
in-theory        29213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-453 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29213.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-453, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-29214
in-theory        29214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29214.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-453, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-29215
in-theory        29215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-453 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29215.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-453, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-29216
in-theory        29216
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29216.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-453, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-29217
in-theory        29217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-453 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29217.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-453, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-29218
in-theory        29218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29218.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-453, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-29219
in-theory        29219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-29219.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-453, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-29220
in-theory        29220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-453 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-29220.        ((A -> ((B -> (B or C)) and A)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-453, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-29221
in-theory        29221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-453 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29221.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-453, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-29222
in-theory        29222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-453 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29222.        ((A -> ((B -> (B or C)) and A)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-453, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-29223
in-theory        29223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29223.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-453, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-29224
in-theory        29224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-453 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29224.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-453, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-29225
in-theory        29225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29225.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-453, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-29226
in-theory        29226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29226.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-453, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-29227
in-theory        29227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29227.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-453, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-29228
in-theory        29228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-453 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29228.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-453, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-29229
in-theory        29229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29229.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-453, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-29230
in-theory        29230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-453 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29230.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-453, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-29231
in-theory        29231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29231.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-453, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-29232
in-theory        29232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29232.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-453, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-29233
in-theory        29233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-453 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29233.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-453, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-29234
in-theory        29234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29234.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-453, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-29235
in-theory        29235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29235.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-453, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-29236
in-theory        29236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29236.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-453, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-29237
in-theory        29237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-453 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29237.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-453, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-29238
in-theory        29238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29238.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-453, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-29239
in-theory        29239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-453 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29239.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-453, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-29240
in-theory        29240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-453 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29240.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-453, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-29241
in-theory        29241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-453 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29241.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-453, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-29242
in-theory        29242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-453 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29242.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-453, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-29243
in-theory        29243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29243.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-453, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-29244
in-theory        29244
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-453 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29244.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-453, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-29245
in-theory        29245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29245.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-453, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-29246
in-theory        29246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29246.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-453, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-29247
in-theory        29247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29247.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-453, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-29248
in-theory        29248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-453 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29248.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-453, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-29249
in-theory        29249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29249.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-453, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-29250
in-theory        29250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-29250.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-453, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-29251
in-theory        29251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-453 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-29251.        ((A -> ((B -> (B or C)) and A)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-453, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-29252
in-theory        29252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-453 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29252.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-453, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-29253
in-theory        29253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-453 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29253.        ((A -> ((B -> (B or C)) and A)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-453, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-29254
in-theory        29254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29254.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-453, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-29255
in-theory        29255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-453 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29255.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-453, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-29256
in-theory        29256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29256.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-453, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-29257
in-theory        29257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29257.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-453, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-29258
in-theory        29258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-453 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29258.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-453, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-29259
in-theory        29259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-453 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29259.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-453, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-29260
in-theory        29260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29260.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-453, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-29261
in-theory        29261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-453 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29261.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-453, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-29262
in-theory        29262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29262.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-453, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-29263
in-theory        29263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29263.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-453, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-29264
in-theory        29264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29264.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-453, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-29265
in-theory        29265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-453 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29265.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-453, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-29266
in-theory        29266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29266.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-453, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-29267
in-theory        29267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29267.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-453, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-29268
in-theory        29268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29268.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-453, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-29269
in-theory        29269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-453 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29269.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-453, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-29270
in-theory        29270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-453 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29270.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-453, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-29271
in-theory        29271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-453 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29271.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-453, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-29272
in-theory        29272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-453 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29272.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-453, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-29273
in-theory        29273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-453 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29273.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-453, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-29274
in-theory        29274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-453 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29274.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-453, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-29275
in-theory        29275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-453 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29275.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-453, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-29276
in-theory        29276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-453 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29276.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-453, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-29277
in-theory        29277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-453 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29277.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-453, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-29278
in-theory        29278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-453 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29278.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-453, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-29279
in-theory        29279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-453 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29279.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-453, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-29280
in-theory        29280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-453 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29280.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-453, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-29281
in-theory        29281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-453 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29281.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-453, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-29282
in-theory        29282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-453 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29282.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-453, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-29283
in-theory        29283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-453 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-29283.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-453, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-29284
in-theory        29284
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-453 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-29284.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-453, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-29285
in-theory        29285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-453 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29285.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-453, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-29286
in-theory        29286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-453 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29286.        ((A -> ((B -> (B or C)) and A)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-453, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-29287
in-theory        29287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-453 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29287.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-453, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-29288
in-theory        29288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-453 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29288.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-453, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-29289
in-theory        29289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and (E -> D))))
theorem-size     17
proof            (modus-ponens tm-453 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-29289.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and (E -> D)))), M:tm-453, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-29290
in-theory        29290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-29290.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-453, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-29291
in-theory        29291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D and E) -> ((D and E) and D)))
theorem-size     19
proof            (modus-ponens tm-453 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-29291.        ((A -> ((B -> (B or C)) and A)) and ((D and E) -> ((D and E) and D))), M:tm-453, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-29292
in-theory        29292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D and E) -> ((D and E) and E)))
theorem-size     19
proof            (modus-ponens tm-453 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-29292.        ((A -> ((B -> (B or C)) and A)) and ((D and E) -> ((D and E) and E))), M:tm-453, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-29293
in-theory        29293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-29293.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and (E -> (D and E))))), M:tm-453, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-29294
in-theory        29294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and (D or E))))
theorem-size     17
proof            (modus-ponens tm-453 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-29294.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and (D or E)))), M:tm-453, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-29295
in-theory        29295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and (E or D))))
theorem-size     17
proof            (modus-ponens tm-453 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-29295.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and (E or D)))), M:tm-453, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-29296
in-theory        29296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     27
proof            (modus-ponens tm-453 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-29296.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-453, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-29297
in-theory        29297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-29297.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-453, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-29298
in-theory        29298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     19
proof            (modus-ponens tm-453 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-29298.        ((A -> ((B -> (B or C)) and A)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-453, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-29299
in-theory        29299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-29299.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and (E -> (F -> E))))), M:tm-453, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-29300
in-theory        29300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     21
proof            (modus-ponens tm-453 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-29300.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-453, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-29301
in-theory        29301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-453 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-29301.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-453, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-29302
in-theory        29302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-453 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-29302.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-453, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-29303
in-theory        29303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     33
proof            (modus-ponens tm-453 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-29303.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-453, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-29304
in-theory        29304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-453 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-29304.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and ((E and F) -> E)))), M:tm-453, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-29305
in-theory        29305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     33
proof            (modus-ponens tm-453 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-29305.        ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-453, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-29306
in-theory        29306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-453 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-29306.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and ((E and F) -> F)))), M:tm-453, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-29307
in-theory        29307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-453 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-29307.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-453, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-29308
in-theory        29308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-453 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-29308.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-453, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-29309
in-theory        29309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-453 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-29309.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-453, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-29310
in-theory        29310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-453 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-29310.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-453, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-29311
in-theory        29311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-453 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-29311.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-453, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-29312
in-theory        29312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-29312.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-453, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-29313
in-theory        29313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-453 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29313.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-453, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-29314
in-theory        29314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29314.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-453, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-29315
in-theory        29315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29315.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-453, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-29316
in-theory        29316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-453 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29316.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-453, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-29317
in-theory        29317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29317.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-453, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-29318
in-theory        29318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-453 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-29318.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-453, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-29319
in-theory        29319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     29
proof            (modus-ponens tm-453 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-29319.        ((A -> ((B -> (B or C)) and A)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-453, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-29320
in-theory        29320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-453 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29320.        ((A -> ((B -> (B or C)) and A)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-453, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-29321
in-theory        29321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     21
proof            (modus-ponens tm-453 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29321.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-453, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-29322
in-theory        29322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29322.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-453, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-29323
in-theory        29323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-453 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-29323.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-453, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-29324
in-theory        29324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-453 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29324.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-453, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-29325
in-theory        29325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-453 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-29325.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-453, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-29326
in-theory        29326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-453 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29326.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-453, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-29327
in-theory        29327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-453 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29327.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-453, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-29328
in-theory        29328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-453 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29328.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-453, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-29329
in-theory        29329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-453 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29329.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-453, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-29330
in-theory        29330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-453 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29330.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-453, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-29331
in-theory        29331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-453 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-29331.        ((A -> ((B -> (B or C)) and A)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-453, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-29332
in-theory        29332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-453 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-29332.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-453, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-29333
in-theory        29333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-453 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-29333.        ((A -> ((B -> (B or C)) and A)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-453, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-29334
in-theory        29334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-29334.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-453, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-29335
in-theory        29335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     31
proof            (modus-ponens tm-453 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-29335.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-453, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-29336
in-theory        29336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-453 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29336.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-453, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-29337
in-theory        29337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-453 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29337.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-453, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-29338
in-theory        29338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29338.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-453, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-29339
in-theory        29339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-453 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-29339.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-453, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-29340
in-theory        29340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-453 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29340.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-453, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-29341
in-theory        29341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-453 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-29341.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-453, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-29342
in-theory        29342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-29342.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-453, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-29343
in-theory        29343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-29343.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-453, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-29344
in-theory        29344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-29344.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-453, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-29345
in-theory        29345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-29345.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-453, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-29346
in-theory        29346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-453 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-29346.        ((A -> ((B -> (B or C)) and A)) and (D or ((E -> (F -> E)) or G))), M:tm-453, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-29347
in-theory        29347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-29347.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> D)) or F) or G)), M:tm-453, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-29348
in-theory        29348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-29348.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-453, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-29349
in-theory        29349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-453 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-29349.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> E)) or G))), M:tm-453, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-29350
in-theory        29350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-453 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-29350.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-453, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-29351
in-theory        29351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-29351.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-453, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-29352
in-theory        29352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-29352.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-453, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-29353
in-theory        29353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-453 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-29353.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-453, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-29354
in-theory        29354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-29354.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-453, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-29355
in-theory        29355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-453 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-29355.        ((A -> ((B -> (B or C)) and A)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-453, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-29356
in-theory        29356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-453 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-29356.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-453, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-29357
in-theory        29357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-453 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-29357.        ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-453, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-29358
in-theory        29358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-453 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-29358.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-453, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-29359
in-theory        29359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-453 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-29359.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-453, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-29360
in-theory        29360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-29360.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-453, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-29361
in-theory        29361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-29361.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-453, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-29362
in-theory        29362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-29362.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-453, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-29363
in-theory        29363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-29363.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-453, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-29364
in-theory        29364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-453 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-29364.        ((A -> ((B -> (B or C)) and A)) and (D or (((E and F) -> E) or G))), M:tm-453, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-29365
in-theory        29365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D and E) -> D) or F) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-29365.        ((A -> ((B -> (B or C)) and A)) and ((((D and E) -> D) or F) or G)), M:tm-453, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-29366
in-theory        29366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-29366.        ((A -> ((B -> (B or C)) and A)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-453, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-29367
in-theory        29367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-453 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-29367.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E and F) -> E) or G))), M:tm-453, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-29368
in-theory        29368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-453 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-29368.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-453, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-29369
in-theory        29369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-29369.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-453, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-29370
in-theory        29370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-29370.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-453, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-29371
in-theory        29371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-29371.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-453, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-29372
in-theory        29372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-29372.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-453, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-29373
in-theory        29373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-453 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-29373.        ((A -> ((B -> (B or C)) and A)) and (D or (((E and F) -> F) or G))), M:tm-453, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-29374
in-theory        29374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D and E) -> E) or F) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-29374.        ((A -> ((B -> (B or C)) and A)) and ((((D and E) -> E) or F) or G)), M:tm-453, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-29375
in-theory        29375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-29375.        ((A -> ((B -> (B or C)) and A)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-453, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-29376
in-theory        29376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-453 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-29376.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E and F) -> F) or G))), M:tm-453, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-29377
in-theory        29377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-453 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-29377.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-453, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-29378
in-theory        29378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-453 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-29378.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-453, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-29379
in-theory        29379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-453 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-29379.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-453, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-29380
in-theory        29380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-453 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-29380.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-453, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-29381
in-theory        29381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-453 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-29381.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-453, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-29382
in-theory        29382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-453 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-29382.        ((A -> ((B -> (B or C)) and A)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-453, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-29383
in-theory        29383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     21
proof            (modus-ponens tm-453 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-29383.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-453, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-29384
in-theory        29384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-29384.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-453, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-29385
in-theory        29385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-453 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-29385.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-453, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-29386
in-theory        29386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-453 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-29386.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-453, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-29387
in-theory        29387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-29387.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-453, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-29388
in-theory        29388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-29388.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-453, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-29389
in-theory        29389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-29389.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-453, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-29390
in-theory        29390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-29390.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-453, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-29391
in-theory        29391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-453 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-29391.        ((A -> ((B -> (B or C)) and A)) and (D or ((E -> (E or F)) or G))), M:tm-453, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-29392
in-theory        29392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (D or E)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-29392.        ((A -> ((B -> (B or C)) and A)) and (((D -> (D or E)) or F) or G)), M:tm-453, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-29393
in-theory        29393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-29393.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-453, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-29394
in-theory        29394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-453 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-29394.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (E or F)) or G))), M:tm-453, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-29395
in-theory        29395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29395.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-453, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-29396
in-theory        29396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29396.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-453, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-29397
in-theory        29397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29397.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-453, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-29398
in-theory        29398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-453 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29398.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-453, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-29399
in-theory        29399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29399.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-453, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-29400
in-theory        29400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-453 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29400.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-453, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-29401
in-theory        29401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29401.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-453, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-29402
in-theory        29402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29402.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-453, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-29403
in-theory        29403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-453 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29403.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-453, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-29404
in-theory        29404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29404.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-453, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-29405
in-theory        29405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29405.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-453, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-29406
in-theory        29406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29406.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-453, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-29407
in-theory        29407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-453 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29407.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-453, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-29408
in-theory        29408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29408.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-453, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-29409
in-theory        29409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-453 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29409.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-453, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-29410
in-theory        29410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-453 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29410.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-453, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-29411
in-theory        29411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-453 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29411.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-453, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-29412
in-theory        29412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-453 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29412.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-453, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-29413
in-theory        29413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29413.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-453, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-29414
in-theory        29414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-453 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29414.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-453, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-29415
in-theory        29415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29415.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-453, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-29416
in-theory        29416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29416.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-453, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-29417
in-theory        29417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-453 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29417.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-453, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-29418
in-theory        29418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29418.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-453, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-29419
in-theory        29419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-453 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29419.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-453, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-29420
in-theory        29420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-29420.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-453, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-29421
in-theory        29421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-29421.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-453, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-29422
in-theory        29422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-29422.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-453, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-29423
in-theory        29423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-29423.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-453, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-29424
in-theory        29424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-453 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-29424.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-453, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-29425
in-theory        29425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-29425.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-453, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-29426
in-theory        29426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29426.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-453, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-29427
in-theory        29427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-453 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-29427.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-453, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-29428
in-theory        29428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-453 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29428.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-453, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-29429
in-theory        29429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29429.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-453, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-29430
in-theory        29430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29430.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-453, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-29431
in-theory        29431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-453 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29431.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-453, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-29432
in-theory        29432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29432.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-453, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-29433
in-theory        29433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-29433.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-453, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-29434
in-theory        29434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-453 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-29434.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-453, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-29435
in-theory        29435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-453 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29435.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-453, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29436
in-theory        29436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-453 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29436.        ((A -> ((B -> (B or C)) and A)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-453, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-29437
in-theory        29437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29437.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-453, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29438
in-theory        29438
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> ((E -> (E or F)) and D)) and ((B -> (B or C)) and A)))
theorem-size     27
proof            (modus-ponens tm-450 tm-453 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29438.        ((A or ((B -> (B or C)) and A)) -> ((D -> ((E -> (E or F)) and D)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-453, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-29439
in-theory        29439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((E -> (E or F)) and (A -> ((B -> ((C -> (C or D)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29439.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((E -> (E or F)) and (A -> ((B -> ((C -> (C or D)) and B)) and A)))), M:tm-443, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29440
in-theory        29440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29440.        (((A -> (A or B)) or C) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-409, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29441
in-theory        29441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29441.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-400, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29442
in-theory        29442
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29442.        ((((A and B) -> B) or C) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-391, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29443
in-theory        29443
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29443.        ((((A and B) -> A) or C) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-382, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29444
in-theory        29444
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> ((G -> (G or H)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29444.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> ((G -> (G or H)) and F)) and E))), M:tm-373, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29445
in-theory        29445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29445.        (((A -> (B -> A)) or C) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-364, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29446
in-theory        29446
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> ((D -> (D or E)) and C)) and A) and B)))
theorem-size     17
proof            (modus-ponens tm-355 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29446.        (A -> (B -> (((C -> ((D -> (D or E)) and C)) and A) and B))), M:tm-355, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-29447
in-theory        29447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29447.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-354, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29448
in-theory        29448
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> ((E -> (E or F)) and D)) and (B -> (C -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-351 tm-453 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29448.        ((A or (B -> (C -> (B and C)))) -> ((D -> ((E -> (E or F)) and D)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-453, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-29449
in-theory        29449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29449.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29450
in-theory        29450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> ((E -> (E or F)) and D)) and C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29450.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> ((E -> (E or F)) and D)) and C))), M:tm-338, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29451
in-theory        29451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> ((D -> (D or E)) and C)) and (A -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-335 tm-453 ((Am (-> A (and A B))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29451.        (((A -> B) or (A -> (A and B))) -> ((C -> ((D -> (D or E)) and C)) and (A -> (A and B)))), M:tm-335, m:tm-453, u:((Am (-> A (and A B))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A (and A B)))))
================================================================
tm-name          tm-29452
in-theory        29452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (A -> (A and ((B -> ((C -> (C or D)) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-328 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29452.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (A -> (A and ((B -> ((C -> (C or D)) and B)) and A)))), M:tm-328, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-29453
in-theory        29453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> ((C -> (C or D)) and B)) and A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29453.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> ((C -> (C or D)) and B)) and A)))), M:tm-327, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29454
in-theory        29454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (((E and F) -> F) and (A -> ((B -> ((C -> (C or D)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29454.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (((E and F) -> F) and (A -> ((B -> ((C -> (C or D)) and B)) and A)))), M:tm-326, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29455
in-theory        29455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (((E and F) -> E) and (A -> ((B -> ((C -> (C or D)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29455.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (((E and F) -> E) and (A -> ((B -> ((C -> (C or D)) and B)) and A)))), M:tm-325, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29456
in-theory        29456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> ((C -> (C or D)) and B)) and A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29456.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> ((C -> (C or D)) and B)) and A)))), M:tm-324, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29457
in-theory        29457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((E -> (F -> E)) and (A -> ((B -> ((C -> (C or D)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29457.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((E -> (F -> E)) and (A -> ((B -> ((C -> (C or D)) and B)) and A)))), M:tm-323, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29458
in-theory        29458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29458.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29459
in-theory        29459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29459.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29460
in-theory        29460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29460.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29461
in-theory        29461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (A -> A))
theorem-size     17
proof            (modus-ponens tm-316 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29461.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (A -> A)), M:tm-316, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-29462
in-theory        29462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29462.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29463
in-theory        29463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((A -> (not ((B -> ((C -> (C or D)) and B)) and A))) -> (not A)))
theorem-size     31
proof            (modus-ponens tm-313 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29463.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((A -> (not ((B -> ((C -> (C or D)) and B)) and A))) -> (not A))), M:tm-313, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-29464
in-theory        29464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((((B -> ((C -> (C or D)) and B)) and A) -> E) -> ((A or ((B -> ((C -> (C or D)) and B)) and A)) -> E)))
theorem-size     43
proof            (modus-ponens tm-312 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29464.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((((B -> ((C -> (C or D)) and B)) and A) -> E) -> ((A or ((B -> ((C -> (C or D)) and B)) and A)) -> E))), M:tm-312, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-29465
in-theory        29465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (E or (A -> ((B -> ((C -> (C or D)) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29465.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (E or (A -> ((B -> ((C -> (C or D)) and B)) and A)))), M:tm-311, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29466
in-theory        29466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((A -> ((B -> ((C -> (C or D)) and B)) and A)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29466.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((A -> ((B -> ((C -> (C or D)) and B)) and A)) or E)), M:tm-310, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29467
in-theory        29467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (E -> ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29467.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (E -> ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and E))), M:tm-309, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29468
in-theory        29468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (E -> (A -> ((B -> ((C -> (C or D)) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29468.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (E -> (A -> ((B -> ((C -> (C or D)) and B)) and A)))), M:tm-305, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29469
in-theory        29469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29469.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-303, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29470
in-theory        29470
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> ((E -> (E or F)) and D)) and ((B -> (C -> (B and C))) and A)))
theorem-size     31
proof            (modus-ponens tm-300 tm-453 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29470.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> ((E -> (E or F)) and D)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-453, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-29471
in-theory        29471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29471.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-270, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29472
in-theory        29472
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> ((E -> (E or F)) and D)) and (((B and C) -> C) and A)))
theorem-size     27
proof            (modus-ponens tm-267 tm-453 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29472.        ((A or (((B and C) -> C) and A)) -> ((D -> ((E -> (E or F)) and D)) and (((B and C) -> C) and A))), M:tm-267, m:tm-453, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-29473
in-theory        29473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29473.        ((A -> (((B and C) -> B) and A)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-239, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29474
in-theory        29474
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> ((E -> (E or F)) and D)) and (((B and C) -> B) and A)))
theorem-size     27
proof            (modus-ponens tm-236 tm-453 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29474.        ((A or (((B and C) -> B) and A)) -> ((D -> ((E -> (E or F)) and D)) and (((B and C) -> B) and A))), M:tm-236, m:tm-453, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-29475
in-theory        29475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> ((G -> (G or H)) and F)) and E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29475.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> ((G -> (G or H)) and F)) and E))), M:tm-210, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29476
in-theory        29476
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> ((F -> (F or G)) and E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     43
proof            (modus-ponens tm-207 tm-453 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29476.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> ((F -> (F or G)) and E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-453, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-29477
in-theory        29477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29477.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-183, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29478
in-theory        29478
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> ((E -> (E or F)) and D)) and ((B -> (C -> B)) and A)))
theorem-size     27
proof            (modus-ponens tm-180 tm-453 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29478.        ((A or ((B -> (C -> B)) and A)) -> ((D -> ((E -> (E or F)) and D)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-453, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-29479
in-theory        29479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29479.        ((A -> ((B and C) -> C)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-157, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29480
in-theory        29480
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((B and C) -> C)))
theorem-size     23
proof            (modus-ponens tm-154 tm-453 ((Am (-> (and A B) B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29480.        ((A or ((B and C) -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((B and C) -> C))), M:tm-154, m:tm-453, u:((Am (-> (and A B) B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (and A B) B))))
================================================================
tm-name          tm-29481
in-theory        29481
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29481.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-147, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29482
in-theory        29482
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((A and (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-144 tm-453 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29482.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-453, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-29483
in-theory        29483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29483.        ((A -> ((B and C) -> B)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-134, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29484
in-theory        29484
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> ((E -> (E or F)) and D)) and ((B and C) -> B)))
theorem-size     23
proof            (modus-ponens tm-131 tm-453 ((Am (-> (and A B) A)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29484.        ((A or ((B and C) -> B)) -> ((D -> ((E -> (E or F)) and D)) and ((B and C) -> B))), M:tm-131, m:tm-453, u:((Am (-> (and A B) A)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (and A B) A))))
================================================================
tm-name          tm-29485
in-theory        29485
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29485.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-125, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29486
in-theory        29486
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> ((E -> (E or F)) and D)) and (((A -> B) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-122 tm-453 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29486.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> ((E -> (E or F)) and D)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-453, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-29487
in-theory        29487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (G or H)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29487.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (G or H)) and F)) and E))), M:tm-113, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29488
in-theory        29488
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> ((F -> (F or G)) and E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     39
proof            (modus-ponens tm-110 tm-453 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29488.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> ((F -> (F or G)) and E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-453, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-29489
in-theory        29489
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29489.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-105, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29490
in-theory        29490
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> ((E -> (E or F)) and D)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-102 tm-453 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29490.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> ((E -> (E or F)) and D)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-453, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-29491
in-theory        29491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> ((E -> (E or F)) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29491.        (((A -> B) -> (A -> A)) and (C -> ((D -> ((E -> (E or F)) and D)) and C))), M:tm-95, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29492
in-theory        29492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> ((D -> (D or E)) and C)) and (A -> A)))
theorem-size     21
proof            (modus-ponens tm-92 tm-453 ((Am (-> A A)) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29492.        (((A -> B) or (A -> A)) -> ((C -> ((D -> (D or E)) and C)) and (A -> A))), M:tm-92, m:tm-453, u:((Am (-> A A)) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A A))))
================================================================
tm-name          tm-29493
in-theory        29493
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> ((D -> (D or E)) and C)) and A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29493.        (A -> (B -> ((C -> ((D -> (D or E)) and C)) and A))), M:tm-84, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-29494
in-theory        29494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29494.        ((A -> (B -> (C -> B))) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-83, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29495
in-theory        29495
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> ((E -> (E or F)) and D)) and (B -> (C -> B))))
theorem-size     23
proof            (modus-ponens tm-80 tm-453 ((Am (-> A (-> B A))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29495.        ((A or (B -> (C -> B))) -> ((D -> ((E -> (E or F)) and D)) and (B -> (C -> B)))), M:tm-80, m:tm-453, u:((Am (-> A (-> B A))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A (-> B A)))))
================================================================
tm-name          tm-29496
in-theory        29496
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> ((D -> (D or E)) and C)) and B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-10 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29496.        (((not (not A)) -> A) and (B -> ((C -> ((D -> (D or E)) and C)) and B))), M:tm-76, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29497
in-theory        29497
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> ((C -> (C or D)) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-73 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29497.        (((not (not A)) or A) -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-73, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-29498
in-theory        29498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> ((E -> (E or F)) and D)) and C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-9 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29498.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> ((E -> (E or F)) and D)) and C))), M:tm-69, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29499
in-theory        29499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> ((D -> (D or E)) and C)) and ((A -> (not B)) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-66 tm-453 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-6)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29499.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> ((D -> (D or E)) and C)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-453, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-29500
in-theory        29500
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29500.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-54, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29501
in-theory        29501
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((E -> (E or F)) and D)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-51 tm-453 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29501.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((E -> (E or F)) and D)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-453, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-29502
in-theory        29502
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> ((D -> (D or E)) and C)) and (B or A)))
theorem-size     19
proof            (modus-ponens tm-50 tm-453 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29502.        ((A or (B or A)) -> ((C -> ((D -> (D or E)) and C)) and (B or A))), M:tm-50, m:tm-453, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (or A B))))
================================================================
tm-name          tm-29503
in-theory        29503
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> ((D -> (D or E)) and C)) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-49 tm-453 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29503.        ((A or (A or B)) -> ((C -> ((D -> (D or E)) and C)) and (A or B))), M:tm-49, m:tm-453, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (or A B))))
================================================================
tm-name          tm-29504
in-theory        29504
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> ((D -> (D or E)) and C)) and (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-48 tm-453 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29504.        ((A or (B -> (A and B))) -> ((C -> ((D -> (D or E)) and C)) and (B -> (A and B)))), M:tm-48, m:tm-453, u:((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-29505
in-theory        29505
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> ((D -> (D or E)) and C)) and B))
theorem-size     17
proof            (modus-ponens tm-47 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29505.        (((A and B) or B) -> ((C -> ((D -> (D or E)) and C)) and B)), M:tm-47, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-29506
in-theory        29506
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> ((D -> (D or E)) and C)) and A))
theorem-size     17
proof            (modus-ponens tm-46 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29506.        (((A and B) or A) -> ((C -> ((D -> (D or E)) and C)) and A)), M:tm-46, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-29507
in-theory        29507
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (E or F)) and D)) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-45 tm-453 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29507.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (E or F)) and D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-453, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-29508
in-theory        29508
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> ((D -> (D or E)) and C)) and (B -> A)))
theorem-size     19
proof            (modus-ponens tm-44 tm-453 ((Am (-> A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29508.        ((A or (B -> A)) -> ((C -> ((D -> (D or E)) and C)) and (B -> A))), M:tm-44, m:tm-453, u:((Am (-> A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A B))))
================================================================
tm-name          tm-29509
in-theory        29509
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> ((E -> (E or F)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29509.        ((A -> (B or A)) and (C -> ((D -> ((E -> (E or F)) and D)) and C))), M:tm-42, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29510
in-theory        29510
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> ((E -> (E or F)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29510.        ((A -> (A or B)) and (C -> ((D -> ((E -> (E or F)) and D)) and C))), M:tm-32, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29511
in-theory        29511
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> ((C -> (C or D)) and B)) and A)))
theorem-size     15
proof            (modus-ponens tm-24 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29511.        (A -> (A and ((B -> ((C -> (C or D)) and B)) and A))), M:tm-24, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-29512
in-theory        29512
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> ((E -> (E or F)) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29512.        ((A -> (B -> (A and B))) and (C -> ((D -> ((E -> (E or F)) and D)) and C))), M:tm-23, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29513
in-theory        29513
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> ((E -> (E or F)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29513.        (((A and B) -> B) and (C -> ((D -> ((E -> (E or F)) and D)) and C))), M:tm-22, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29514
in-theory        29514
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> ((E -> (E or F)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29514.        (((A and B) -> A) and (C -> ((D -> ((E -> (E or F)) and D)) and C))), M:tm-21, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29515
in-theory        29515
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29515.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-20, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29516
in-theory        29516
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> ((E -> (E or F)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29516.        ((A -> (B -> A)) and (C -> ((D -> ((E -> (E or F)) and D)) and C))), M:tm-19, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29517
in-theory        29517
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> ((C -> (C or D)) and B)) and A))) -> (not A))
theorem-size     17
proof            (modus-ponens tm-9 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-9 tm-5 tm-6)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29517.        ((A -> (not ((B -> ((C -> (C or D)) and B)) and A))) -> (not A)), M:tm-9, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-29518
in-theory        29518
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> ((B -> (B or C)) and A)) and D) -> E) -> ((D or ((A -> ((B -> (B or C)) and A)) and D)) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-8 tm-5 tm-6)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29518.        ((((A -> ((B -> (B or C)) and A)) and D) -> E) -> ((D or ((A -> ((B -> (B or C)) and A)) and D)) -> E)), M:tm-8, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-29519
in-theory        29519
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> ((D -> (D or E)) and C)) and B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29519.        (A or (B -> ((C -> ((D -> (D or E)) and C)) and B))), M:tm-7, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29520
in-theory        29520
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-6 tm-5)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29520.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) or E), M:tm-6, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29521
in-theory        29521
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> ((D -> (D or E)) and C)) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29521.        (A -> ((B -> ((C -> ((D -> (D or E)) and C)) and B)) and A)), M:tm-5, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29522
in-theory        29522
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> ((D -> (D or E)) and C)) and B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29522.        (A -> (B -> ((C -> ((D -> (D or E)) and C)) and B))), M:tm-1, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-29523
in-theory        29523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-453 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29523.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-453, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29524
in-theory        29524
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-450 tm-454 ((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29524.        ((A or ((B -> (B or C)) and A)) -> (D -> ((E -> (E or F)) and D))), M:tm-450, m:tm-454, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29525
in-theory        29525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and ((E -> (E or F)) and (A -> (B -> ((C -> (C or D)) and B)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29525.        ((A -> (B -> ((C -> (C or D)) and B))) and ((E -> (E or F)) and (A -> (B -> ((C -> (C or D)) and B))))), M:tm-443, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29526
in-theory        29526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-409 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29526.        (((A -> (A or B)) or C) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-409, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29527
in-theory        29527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-400 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29527.        (((A -> (B -> (A and B))) or C) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-400, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29528
in-theory        29528
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-391 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29528.        ((((A and B) -> B) or C) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-391, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29529
in-theory        29529
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-382 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29529.        ((((A and B) -> A) or C) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-382, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29530
in-theory        29530
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-373 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29530.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> ((G -> (G or H)) and F)))), M:tm-373, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29531
in-theory        29531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-364 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29531.        (((A -> (B -> A)) or C) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-364, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29532
in-theory        29532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-354 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29532.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-354, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29533
in-theory        29533
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-351 tm-454 ((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29533.        ((A or (B -> (C -> (B and C)))) -> (D -> ((E -> (E or F)) and D))), M:tm-351, m:tm-454, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29534
in-theory        29534
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> (A and D))))
theorem-size     13
proof            (modus-ponens tm-349 tm-454 ((A Am) (Bm (-> B (and Am B))) (C (and (-> Cm (or Cm Dm)) (-> B (and Am B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29534.        (A -> ((B -> (B or C)) and (D -> (A and D)))), M:tm-349, m:tm-454, u:((A Am) (Bm (-> B (and Am B))) (C (and (-> Cm (or Cm Dm)) (-> B (and Am B)))))
================================================================
tm-name          tm-29535
in-theory        29535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29535.        ((A -> (B -> ((C -> (C or D)) and B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29536
in-theory        29536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) -> D) -> ((A -> ((B -> (B or C)) and A)) and D))
theorem-size     23
proof            (modus-ponens tm-339 tm-454 ((Am (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) B)) (A (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29536.        (((A -> ((B -> (B or C)) and A)) -> D) -> ((A -> ((B -> (B or C)) and A)) and D)), M:tm-339, m:tm-454, u:((Am (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) B)) (A (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29537
in-theory        29537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-338 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29537.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> ((E -> (E or F)) and D)))), M:tm-338, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29538
in-theory        29538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> ((D -> (D or E)) and C)))
theorem-size     19
proof            (modus-ponens tm-335 tm-454 ((Am (-> A (and A B))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29538.        (((A -> B) or (A -> (A and B))) -> (C -> ((D -> (D or E)) and C))), M:tm-335, m:tm-454, u:((Am (-> A (and A B))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29539
in-theory        29539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (A -> (A and (B -> ((C -> (C or D)) and B)))))
theorem-size     25
proof            (modus-ponens tm-328 tm-454 ((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29539.        ((A -> (B -> ((C -> (C or D)) and B))) and (A -> (A and (B -> ((C -> (C or D)) and B))))), M:tm-328, m:tm-454, u:((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29540
in-theory        29540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and ((E -> (F -> (E and F))) and (A -> (B -> ((C -> (C or D)) and B)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29540.        ((A -> (B -> ((C -> (C or D)) and B))) and ((E -> (F -> (E and F))) and (A -> (B -> ((C -> (C or D)) and B))))), M:tm-327, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29541
in-theory        29541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (((E and F) -> F) and (A -> (B -> ((C -> (C or D)) and B)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29541.        ((A -> (B -> ((C -> (C or D)) and B))) and (((E and F) -> F) and (A -> (B -> ((C -> (C or D)) and B))))), M:tm-326, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29542
in-theory        29542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (((E and F) -> E) and (A -> (B -> ((C -> (C or D)) and B)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29542.        ((A -> (B -> ((C -> (C or D)) and B))) and (((E and F) -> E) and (A -> (B -> ((C -> (C or D)) and B))))), M:tm-325, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29543
in-theory        29543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> ((C -> (C or D)) and B)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29543.        ((A -> (B -> ((C -> (C or D)) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> ((C -> (C or D)) and B))))), M:tm-324, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29544
in-theory        29544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and ((E -> (F -> E)) and (A -> (B -> ((C -> (C or D)) and B)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29544.        ((A -> (B -> ((C -> (C or D)) and B))) and ((E -> (F -> E)) and (A -> (B -> ((C -> (C or D)) and B))))), M:tm-323, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29545
in-theory        29545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29545.        ((A -> (B -> ((C -> (C or D)) and B))) and ((E and F) -> F)), M:tm-322, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29546
in-theory        29546
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> ((C -> (C or D)) and B)) -> E)) -> (B -> ((C -> (C or D)) and B))) and ((A and ((B -> ((C -> (C or D)) and B)) -> E)) -> E))
theorem-size     39
proof            (modus-ponens tm-321 tm-454 ((Am (and A (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) C))) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29546.        (((A and ((B -> ((C -> (C or D)) and B)) -> E)) -> (B -> ((C -> (C or D)) and B))) and ((A and ((B -> ((C -> (C or D)) and B)) -> E)) -> E)), M:tm-321, m:tm-454, u:((Am (and A (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) C))) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29547
in-theory        29547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29547.        ((A -> (B -> ((C -> (C or D)) and B))) and ((E and F) -> E)), M:tm-320, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29548
in-theory        29548
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> ((B -> (B or C)) and A)) -> D) and E) -> (A -> ((B -> (B or C)) and A))) and ((((A -> ((B -> (B or C)) and A)) -> D) and E) -> D))
theorem-size     39
proof            (modus-ponens tm-319 tm-454 ((Am (and (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29548.        (((((A -> ((B -> (B or C)) and A)) -> D) and E) -> (A -> ((B -> (B or C)) and A))) and ((((A -> ((B -> (B or C)) and A)) -> D) and E) -> D)), M:tm-319, m:tm-454, u:((Am (and (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29549
in-theory        29549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29549.        ((A -> (B -> ((C -> (C or D)) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29550
in-theory        29550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (B or C)) and A) -> D)) -> (A -> ((B -> (B or C)) and A))) and ((A -> (((B -> (B or C)) and A) -> D)) -> (A -> D)))
theorem-size     37
proof            (modus-ponens tm-317 tm-454 ((Am (-> Bm (-> (and (-> Cm (or Cm Dm)) Bm) C))) (A Bm) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29550.        (((A -> (((B -> (B or C)) and A) -> D)) -> (A -> ((B -> (B or C)) and A))) and ((A -> (((B -> (B or C)) and A) -> D)) -> (A -> D))), M:tm-317, m:tm-454, u:((Am (-> Bm (-> (and (-> Cm (or Cm Dm)) Bm) C))) (A Bm) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-29551
in-theory        29551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-454 ((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29551.        ((A -> (B -> ((C -> (C or D)) and B))) and (A -> A)), M:tm-316, m:tm-454, u:((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29552
in-theory        29552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29552.        ((A -> (B -> ((C -> (C or D)) and B))) and (E -> (F -> E))), M:tm-315, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29553
in-theory        29553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and ((A -> (not (B -> ((C -> (C or D)) and B)))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-454 ((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29553.        ((A -> (B -> ((C -> (C or D)) and B))) and ((A -> (not (B -> ((C -> (C or D)) and B)))) -> (not A))), M:tm-313, m:tm-454, u:((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29554
in-theory        29554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (((B -> ((C -> (C or D)) and B)) -> E) -> ((A or (B -> ((C -> (C or D)) and B))) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-454 ((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29554.        ((A -> (B -> ((C -> (C or D)) and B))) and (((B -> ((C -> (C or D)) and B)) -> E) -> ((A or (B -> ((C -> (C or D)) and B))) -> E))), M:tm-312, m:tm-454, u:((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29555
in-theory        29555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (E or (A -> (B -> ((C -> (C or D)) and B)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29555.        ((A -> (B -> ((C -> (C or D)) and B))) and (E or (A -> (B -> ((C -> (C or D)) and B))))), M:tm-311, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29556
in-theory        29556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and ((A -> (B -> ((C -> (C or D)) and B))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29556.        ((A -> (B -> ((C -> (C or D)) and B))) and ((A -> (B -> ((C -> (C or D)) and B))) or E)), M:tm-310, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29557
in-theory        29557
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (E -> ((A -> (B -> ((C -> (C or D)) and B))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29557.        ((A -> (B -> ((C -> (C or D)) and B))) and (E -> ((A -> (B -> ((C -> (C or D)) and B))) and E))), M:tm-309, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29558
in-theory        29558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and ((A -> B) -> (A -> ((C -> (C or D)) and B))))
theorem-size     25
proof            (modus-ponens tm-306 tm-454 ((A Am) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29558.        ((A -> (B -> ((C -> (C or D)) and B))) and ((A -> B) -> (A -> ((C -> (C or D)) and B)))), M:tm-306, m:tm-454, u:((A Am) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-29559
in-theory        29559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (E -> (A -> (B -> ((C -> (C or D)) and B)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29559.        ((A -> (B -> ((C -> (C or D)) and B))) and (E -> (A -> (B -> ((C -> (C or D)) and B))))), M:tm-305, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29560
in-theory        29560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-303 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29560.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-303, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29561
in-theory        29561
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-300 tm-454 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29561.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((E -> (E or F)) and D))), M:tm-300, m:tm-454, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29562
in-theory        29562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-270 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29562.        ((A -> (((B and C) -> C) and A)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-270, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29563
in-theory        29563
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-267 tm-454 ((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29563.        ((A or (((B and C) -> C) and A)) -> (D -> ((E -> (E or F)) and D))), M:tm-267, m:tm-454, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29564
in-theory        29564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-239 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29564.        ((A -> (((B and C) -> B) and A)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-239, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29565
in-theory        29565
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-236 tm-454 ((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29565.        ((A or (((B and C) -> B) and A)) -> (D -> ((E -> (E or F)) and D))), M:tm-236, m:tm-454, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29566
in-theory        29566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-210 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29566.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> ((G -> (G or H)) and F)))), M:tm-210, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29567
in-theory        29567
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((F -> (F or G)) and E)))
theorem-size     27
proof            (modus-ponens tm-207 tm-454 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29567.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((F -> (F or G)) and E))), M:tm-207, m:tm-454, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29568
in-theory        29568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-183 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29568.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-183, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29569
in-theory        29569
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-180 tm-454 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29569.        ((A or ((B -> (C -> B)) and A)) -> (D -> ((E -> (E or F)) and D))), M:tm-180, m:tm-454, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29570
in-theory        29570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-157 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29570.        ((A -> ((B and C) -> C)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-157, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29571
in-theory        29571
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-154 tm-454 ((Am (-> (and A B) B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29571.        ((A or ((B and C) -> C)) -> (D -> ((E -> (E or F)) and D))), M:tm-154, m:tm-454, u:((Am (-> (and A B) B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29572
in-theory        29572
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> ((C -> (C or D)) and B))
theorem-size     11
proof            (modus-ponens tm-152 tm-454 ((Am (and A Bm)) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-1 tm-4 tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29572.        ((A and B) -> ((C -> (C or D)) and B)), M:tm-152, m:tm-454, u:((Am (and A Bm)) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-29573
in-theory        29573
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-147 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29573.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-147, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29574
in-theory        29574
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     25
proof            (modus-ponens tm-144 tm-454 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-5 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29574.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((E -> (E or F)) and D))), M:tm-144, m:tm-454, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29575
in-theory        29575
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (C or D)) and B)) -> E)) -> (B -> ((C -> (C or D)) and B)))
theorem-size     23
proof            (modus-ponens tm-142 tm-454 ((Am (and A (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) C))) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-5 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29575.        ((A and ((B -> ((C -> (C or D)) and B)) -> E)) -> (B -> ((C -> (C or D)) and B))), M:tm-142, m:tm-454, u:((Am (and A (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) C))) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29576
in-theory        29576
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (C or D)) and B)) -> B)) -> ((C -> (C or D)) and B))
theorem-size     21
proof            (modus-ponens tm-141 tm-454 ((Am (and A (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Bm))) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-4 tm-1 tm-5 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29576.        ((A and ((B -> ((C -> (C or D)) and B)) -> B)) -> ((C -> (C or D)) and B)), M:tm-141, m:tm-454, u:((Am (and A (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Bm))) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-29577
in-theory        29577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-134 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29577.        ((A -> ((B and C) -> B)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-134, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29578
in-theory        29578
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-131 tm-454 ((Am (-> (and A B) A)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29578.        ((A or ((B and C) -> B)) -> (D -> ((E -> (E or F)) and D))), M:tm-131, m:tm-454, u:((Am (-> (and A B) A)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29579
in-theory        29579
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> ((C -> (C or D)) and A))
theorem-size     11
proof            (modus-ponens tm-129 tm-454 ((Am (and Bm B)) (A Bm) (C (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-1 tm-3 tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29579.        ((A and B) -> ((C -> (C or D)) and A)), M:tm-129, m:tm-454, u:((Am (and Bm B)) (A Bm) (C (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-29580
in-theory        29580
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-125 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29580.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-125, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29581
in-theory        29581
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     25
proof            (modus-ponens tm-122 tm-454 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-5 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29581.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((E -> (E or F)) and D))), M:tm-122, m:tm-454, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29582
in-theory        29582
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> (B or C)) and A)) -> D) and E) -> (A -> ((B -> (B or C)) and A)))
theorem-size     23
proof            (modus-ponens tm-120 tm-454 ((Am (and (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-5 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29582.        ((((A -> ((B -> (B or C)) and A)) -> D) and E) -> (A -> ((B -> (B or C)) and A))), M:tm-120, m:tm-454, u:((Am (and (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29583
in-theory        29583
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> (B or C)) and A)) -> A) and D) -> ((B -> (B or C)) and A))
theorem-size     21
proof            (modus-ponens tm-119 tm-454 ((Am (and (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Bm) C)) (A Bm) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-3 tm-1 tm-5 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29583.        ((((A -> ((B -> (B or C)) and A)) -> A) and D) -> ((B -> (B or C)) and A)), M:tm-119, m:tm-454, u:((Am (and (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Bm) C)) (A Bm) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-29584
in-theory        29584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-113 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29584.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (G or H)) and F)))), M:tm-113, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29585
in-theory        29585
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((F -> (F or G)) and E)))
theorem-size     25
proof            (modus-ponens tm-110 tm-454 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29585.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((F -> (F or G)) and E))), M:tm-110, m:tm-454, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29586
in-theory        29586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))
theorem-size     19
proof            (modus-ponens tm-108 tm-454 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> Cm (or Cm Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29586.        ((A -> (B -> C)) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-108, m:tm-454, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> Cm (or Cm Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-29587
in-theory        29587
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     31
proof            (modus-ponens tm-105 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29587.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-105, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29588
in-theory        29588
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((E -> (E or F)) and D)))
theorem-size     29
proof            (modus-ponens tm-102 tm-454 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29588.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((E -> (E or F)) and D))), M:tm-102, m:tm-454, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29589
in-theory        29589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) and A) -> D)) -> (A -> ((B -> (B or C)) and A)))
theorem-size     21
proof            (modus-ponens tm-100 tm-454 ((Am (-> Bm (-> (and (-> Cm (or Cm Dm)) Bm) C))) (A Bm) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29589.        ((A -> (((B -> (B or C)) and A) -> D)) -> (A -> ((B -> (B or C)) and A))), M:tm-100, m:tm-454, u:((Am (-> Bm (-> (and (-> Cm (or Cm Dm)) Bm) C))) (A Bm) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-29590
in-theory        29590
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> A)))
theorem-size     11
proof            (modus-ponens tm-98 tm-454 ((A Am) (Bm (-> B Am)) (C (and (-> Cm (or Cm Dm)) (-> B Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29590.        (A -> ((B -> (B or C)) and (D -> A))), M:tm-98, m:tm-454, u:((A Am) (Bm (-> B Am)) (C (and (-> Cm (or Cm Dm)) (-> B Am))))
================================================================
tm-name          tm-29591
in-theory        29591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) -> D) -> (A -> ((B -> (B or C)) and A)))
theorem-size     21
proof            (modus-ponens tm-96 tm-454 ((Am (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) B)) (A (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29591.        (((A -> ((B -> (B or C)) and A)) -> D) -> (A -> ((B -> (B or C)) and A))), M:tm-96, m:tm-454, u:((Am (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) B)) (A (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29592
in-theory        29592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-95 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29592.        (((A -> B) -> (A -> A)) and (C -> (D -> ((E -> (E or F)) and D)))), M:tm-95, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29593
in-theory        29593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> ((D -> (D or E)) and C)))
theorem-size     17
proof            (modus-ponens tm-92 tm-454 ((Am (-> A A)) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29593.        (((A -> B) or (A -> A)) -> (C -> ((D -> (D or E)) and C))), M:tm-92, m:tm-454, u:((Am (-> A A)) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29594
in-theory        29594
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C -> ((D -> (D or E)) and C))))
theorem-size     13
proof            (modus-ponens tm-84 tm-454 ((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29594.        (A -> (B -> (C -> ((D -> (D or E)) and C)))), M:tm-84, m:tm-454, u:((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29595
in-theory        29595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-83 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29595.        ((A -> (B -> (C -> B))) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-83, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29596
in-theory        29596
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-80 tm-454 ((Am (-> A (-> B A))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29596.        ((A or (B -> (C -> B))) -> (D -> ((E -> (E or F)) and D))), M:tm-80, m:tm-454, u:((Am (-> A (-> B A))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29597
in-theory        29597
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> ((B -> (B or C)) and A)) -> D))) -> D)
theorem-size     15
proof            (modus-ponens tm-77 tm-454 ((Am (not (not (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) B)))) (A (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-5 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29597.        ((not (not ((A -> ((B -> (B or C)) and A)) -> D))) -> D), M:tm-77, m:tm-454, u:((Am (not (not (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) B)))) (A (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29598
in-theory        29598
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> ((D -> (D or E)) and C))))
theorem-size     17
proof            (modus-ponens tm-76 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29598.        (((not (not A)) -> A) and (B -> (C -> ((D -> (D or E)) and C)))), M:tm-76, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29599
in-theory        29599
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> ((C -> (C or D)) and B)))
theorem-size     15
proof            (modus-ponens tm-73 tm-454 ((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29599.        (((not (not A)) or A) -> (B -> ((C -> (C or D)) and B))), M:tm-73, m:tm-454, u:((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29600
in-theory        29600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> ((E -> (E or F)) and D))))
theorem-size     23
proof            (modus-ponens tm-69 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29600.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> ((E -> (E or F)) and D)))), M:tm-69, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29601
in-theory        29601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((D -> (D or E)) and C)))
theorem-size     21
proof            (modus-ponens tm-66 tm-454 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-5 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29601.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((D -> (D or E)) and C))), M:tm-66, m:tm-454, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29602
in-theory        29602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> ((C -> (C or D)) and B)))
theorem-size     15
proof            (modus-ponens tm-55 tm-454 ((Am (-> A Bm)) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-8 tm-1 tm-5 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29602.        ((A -> B) -> ((A or B) -> ((C -> (C or D)) and B))), M:tm-55, m:tm-454, u:((Am (-> A Bm)) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-29603
in-theory        29603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-54 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29603.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-54, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29604
in-theory        29604
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (E or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-51 tm-454 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29604.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (E or F)) and D))), M:tm-51, m:tm-454, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29605
in-theory        29605
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D -> (D or E)) and C)))
theorem-size     15
proof            (modus-ponens tm-50 tm-454 ((Am (or A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29605.        ((A or (B or A)) -> (C -> ((D -> (D or E)) and C))), M:tm-50, m:tm-454, u:((Am (or A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29606
in-theory        29606
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D -> (D or E)) and C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-454 ((Am (or A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29606.        ((A or (A or B)) -> (C -> ((D -> (D or E)) and C))), M:tm-49, m:tm-454, u:((Am (or A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29607
in-theory        29607
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D -> (D or E)) and C)))
theorem-size     17
proof            (modus-ponens tm-48 tm-454 ((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29607.        ((A or (B -> (A and B))) -> (C -> ((D -> (D or E)) and C))), M:tm-48, m:tm-454, u:((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29608
in-theory        29608
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D -> (D or E)) and C)))
theorem-size     15
proof            (modus-ponens tm-47 tm-454 ((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29608.        (((A and B) or B) -> (C -> ((D -> (D or E)) and C))), M:tm-47, m:tm-454, u:((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29609
in-theory        29609
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D -> (D or E)) and C)))
theorem-size     15
proof            (modus-ponens tm-46 tm-454 ((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29609.        (((A and B) or A) -> (C -> ((D -> (D or E)) and C))), M:tm-46, m:tm-454, u:((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29610
in-theory        29610
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (E or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-45 tm-454 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29610.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (E or F)) and D))), M:tm-45, m:tm-454, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29611
in-theory        29611
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D -> (D or E)) and C)))
theorem-size     15
proof            (modus-ponens tm-44 tm-454 ((Am (-> A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29611.        ((A or (B -> A)) -> (C -> ((D -> (D or E)) and C))), M:tm-44, m:tm-454, u:((Am (-> A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29612
in-theory        29612
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-42 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29612.        ((A -> (B or A)) and (C -> (D -> ((E -> (E or F)) and D)))), M:tm-42, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29613
in-theory        29613
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-32 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29613.        ((A -> (A or B)) and (C -> (D -> ((E -> (E or F)) and D)))), M:tm-32, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29614
in-theory        29614
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B -> ((C -> (C or D)) and B))))
theorem-size     13
proof            (modus-ponens tm-24 tm-454 ((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29614.        (A -> (A and (B -> ((C -> (C or D)) and B)))), M:tm-24, m:tm-454, u:((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29615
in-theory        29615
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-23 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29615.        ((A -> (B -> (A and B))) and (C -> (D -> ((E -> (E or F)) and D)))), M:tm-23, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29616
in-theory        29616
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-22 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29616.        (((A and B) -> B) and (C -> (D -> ((E -> (E or F)) and D)))), M:tm-22, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29617
in-theory        29617
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-21 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29617.        (((A and B) -> A) and (C -> (D -> ((E -> (E or F)) and D)))), M:tm-21, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29618
in-theory        29618
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-20 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29618.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-20, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29619
in-theory        29619
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-19 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29619.        ((A -> (B -> A)) and (C -> (D -> ((E -> (E or F)) and D)))), M:tm-19, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29620
in-theory        29620
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (C or D)) and B)) -> E)) -> E)
theorem-size     15
proof            (modus-ponens tm-17 tm-454 ((Am (and A (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) C))) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-5 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29620.        ((A and ((B -> ((C -> (C or D)) and B)) -> E)) -> E), M:tm-17, m:tm-454, u:((Am (and A (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) C))) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29621
in-theory        29621
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> ((B -> (B or C)) and A)) -> D) and E) -> D)
theorem-size     15
proof            (modus-ponens tm-15 tm-454 ((Am (and (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-5 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29621.        ((((A -> ((B -> (B or C)) and A)) -> D) and E) -> D), M:tm-15, m:tm-454, u:((Am (and (-> (-> Bm (and (-> Cm (or Cm Dm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29622
in-theory        29622
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) and A) -> D)) -> (A -> D))
theorem-size     15
proof            (modus-ponens tm-13 tm-454 ((Am (-> Bm (-> (and (-> Cm (or Cm Dm)) Bm) C))) (A Bm) (B (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29622.        ((A -> (((B -> (B or C)) and A) -> D)) -> (A -> D)), M:tm-13, m:tm-454, u:((Am (-> Bm (-> (and (-> Cm (or Cm Dm)) Bm) C))) (A Bm) (B (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-29623
in-theory        29623
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B -> ((C -> (C or D)) and B)))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-454 ((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-9 tm-1 tm-5 tm-6)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29623.        ((A -> (not (B -> ((C -> (C or D)) and B)))) -> (not A)), M:tm-9, m:tm-454, u:((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29624
in-theory        29624
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) -> D) -> ((E or (A -> ((B -> (B or C)) and A))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-454 ((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29624.        (((A -> ((B -> (B or C)) and A)) -> D) -> ((E or (A -> ((B -> (B or C)) and A))) -> D)), M:tm-8, m:tm-454, u:((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-29625
in-theory        29625
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C -> ((D -> (D or E)) and C))))
theorem-size     13
proof            (modus-ponens tm-7 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-7 tm-1 tm-5 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29625.        (A or (B -> (C -> ((D -> (D or E)) and C)))), M:tm-7, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29626
in-theory        29626
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-6 tm-1 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29626.        ((A -> (B -> ((C -> (C or D)) and B))) or E), M:tm-6, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29627
in-theory        29627
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> ((D -> (D or E)) and C))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29627.        (A -> ((B -> (C -> ((D -> (D or E)) and C))) and A)), M:tm-5, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-29628
in-theory        29628
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> ((C -> (C or D)) and B)))
theorem-size     13
proof            (modus-ponens tm-2 tm-454 ((A Am) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-29628.        ((A -> B) -> (A -> ((C -> (C or D)) and B))), M:tm-2, m:tm-454, u:((A Am) (B Bm) (C (and (-> Cm (or Cm Dm)) Bm)))
================================================================
tm-name          tm-29629
in-theory        29629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29629.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-453, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29630
in-theory        29630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29630.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> (D -> (D or E)))))), M:tm-443, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29631
in-theory        29631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29631.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-409, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29632
in-theory        29632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29632.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-400, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29633
in-theory        29633
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29633.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-391, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29634
in-theory        29634
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29634.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-382, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29635
in-theory        29635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29635.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (H or I))))), M:tm-373, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29636
in-theory        29636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29636.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-364, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29637
in-theory        29637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29637.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-354, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29638
in-theory        29638
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29638.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29639
in-theory        29639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29639.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (F or G))))), M:tm-338, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29640
in-theory        29640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> (D -> (D or E))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29640.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> (D -> (D or E)))))), M:tm-327, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29641
in-theory        29641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29641.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> (D -> (D or E)))))), M:tm-326, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29642
in-theory        29642
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29642.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> (D -> (D or E)))))), M:tm-325, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29643
in-theory        29643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> (D -> (D or E))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29643.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> (D -> (D or E)))))), M:tm-324, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29644
in-theory        29644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29644.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> (D -> (D or E)))))), M:tm-323, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29645
in-theory        29645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29645.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and ((F and G) -> G)), M:tm-322, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29646
in-theory        29646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29646.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and ((F and G) -> F)), M:tm-320, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29647
in-theory        29647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29647.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29648
in-theory        29648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29648.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and (F -> (G -> F))), M:tm-315, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29649
in-theory        29649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and (F or ((A -> (A or B)) and (C -> (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29649.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and (F or ((A -> (A or B)) and (C -> (D -> (D or E)))))), M:tm-311, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29650
in-theory        29650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and (((A -> (A or B)) and (C -> (D -> (D or E)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29650.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and (((A -> (A or B)) and (C -> (D -> (D or E)))) or F)), M:tm-310, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29651
in-theory        29651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and (F -> (((A -> (A or B)) and (C -> (D -> (D or E)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29651.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and (F -> (((A -> (A or B)) and (C -> (D -> (D or E)))) and F))), M:tm-309, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29652
in-theory        29652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and (C -> (D -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-308 tm-455 ((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29652.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and (C -> (D -> (D or E)))), M:tm-308, m:tm-455, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-29653
in-theory        29653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-455 ((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29653.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and (A -> (A or B))), M:tm-307, m:tm-455, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-29654
in-theory        29654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and (F -> ((A -> (A or B)) and (C -> (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29654.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and (F -> ((A -> (A or B)) and (C -> (D -> (D or E)))))), M:tm-305, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29655
in-theory        29655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29655.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-303, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29656
in-theory        29656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29656.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-270, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29657
in-theory        29657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29657.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-239, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29658
in-theory        29658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29658.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (H -> (H or I))))), M:tm-210, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29659
in-theory        29659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29659.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-183, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29660
in-theory        29660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29660.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-157, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29661
in-theory        29661
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29661.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-147, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29662
in-theory        29662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29662.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-134, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29663
in-theory        29663
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29663.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-125, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29664
in-theory        29664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29664.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (H or I))))), M:tm-113, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29665
in-theory        29665
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29665.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-105, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29666
in-theory        29666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29666.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (F -> (F or G))))), M:tm-95, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29667
in-theory        29667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29667.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-83, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29668
in-theory        29668
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29668.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (E -> (E or F))))), M:tm-76, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29669
in-theory        29669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-6 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29669.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (F -> (F or G))))), M:tm-69, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29670
in-theory        29670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29670.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-54, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29671
in-theory        29671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29671.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> (F -> (F or G))))), M:tm-42, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29672
in-theory        29672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29672.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> (F -> (F or G))))), M:tm-32, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29673
in-theory        29673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29673.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (F or G))))), M:tm-23, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29674
in-theory        29674
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29674.        (((A and B) -> B) and ((C -> (C or D)) and (E -> (F -> (F or G))))), M:tm-22, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29675
in-theory        29675
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29675.        (((A and B) -> A) and ((C -> (C or D)) and (E -> (F -> (F or G))))), M:tm-21, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29676
in-theory        29676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29676.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-20, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29677
in-theory        29677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29677.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (F -> (F or G))))), M:tm-19, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29678
in-theory        29678
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-6 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29678.        (A or ((B -> (B or C)) and (D -> (E -> (E or F))))), M:tm-7, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29679
in-theory        29679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29679.        (((A -> (A or B)) and (C -> (D -> (D or E)))) or F), M:tm-6, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29680
in-theory        29680
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> (E -> (E or F)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29680.        (A -> (((B -> (B or C)) and (D -> (E -> (E or F)))) and A)), M:tm-5, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29681
in-theory        29681
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-29681.        (A -> ((B -> (B or C)) and (D -> (E -> (E or F))))), M:tm-1, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-29682
in-theory        29682
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-456 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-29682.        ((A -> (B -> (B or C))) and (D -> (D or E))), M:tm-456, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-29683
in-theory        29683
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-456 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29683.        ((A or (B -> (C -> B))) and (D -> (D or E))), M:tm-456, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-29684
in-theory        29684
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29684.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E or F))), M:tm-456, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-29685
in-theory        29685
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-456 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29685.        ((A or ((B and C) -> B)) and (D -> (D or E))), M:tm-456, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-29686
in-theory        29686
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-456 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29686.        ((A or ((B and C) -> C)) and (D -> (D or E))), M:tm-456, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-29687
in-theory        29687
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29687.        ((A or (B -> (C -> (B and C)))) and (D -> (D or E))), M:tm-456, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-29688
in-theory        29688
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-456 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29688.        ((A or (B -> (B or C))) and (D -> (D or E))), M:tm-456, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-29689
in-theory        29689
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-456 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29689.        ((A or (B -> (C or B))) and (D -> (D or E))), M:tm-456, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-29690
in-theory        29690
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-456 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29690.        (((A -> (B or A)) or C) and (D -> (D or E))), M:tm-456, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-29691
in-theory        29691
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29691.        ((A -> ((B -> (C or B)) and A)) and (D -> (D or E))), M:tm-456, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-29692
in-theory        29692
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-456 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29692.        ((A -> (B -> (C or B))) and (D -> (D or E))), M:tm-456, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-29693
in-theory        29693
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-29693.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D or E))), M:tm-456, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-29694
in-theory        29694
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E or F)))
theorem-size     31
proof            (modus-ponens tm-456 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-29694.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E or F))), M:tm-456, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-29695
in-theory        29695
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-29695.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D or E))), M:tm-456, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-29696
in-theory        29696
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-29696.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (D or E))), M:tm-456, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-29697
in-theory        29697
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-456 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-29697.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (D or E))), M:tm-456, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-29698
in-theory        29698
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-29698.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (D or E))), M:tm-456, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-29699
in-theory        29699
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-29699.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (D or E))), M:tm-456, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-29700
in-theory        29700
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E or F)))
theorem-size     33
proof            (modus-ponens tm-456 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-29700.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (E or F))), M:tm-456, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-29701
in-theory        29701
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29701.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E or F))), M:tm-456, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-29702
in-theory        29702
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29702.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (E or F))), M:tm-456, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-29703
in-theory        29703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29703.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (E -> (E or F))), M:tm-456, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-29704
in-theory        29704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-456 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-29704.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (D -> (D or E))), M:tm-456, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-29705
in-theory        29705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29705.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (E or F))), M:tm-456, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-29706
in-theory        29706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-456 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-29706.        (((A -> (not (B -> A))) -> (not A)) and (C -> (C or D))), M:tm-456, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-29707
in-theory        29707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (D -> (D or E)))
theorem-size     27
proof            (modus-ponens tm-456 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-29707.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (D -> (D or E))), M:tm-456, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-29708
in-theory        29708
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-456 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-29708.        ((((A and B) -> (not A)) -> (not (A and B))) and (C -> (C or D))), M:tm-456, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-29709
in-theory        29709
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-456 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-29709.        ((((A and B) -> (not B)) -> (not (A and B))) and (C -> (C or D))), M:tm-456, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-29710
in-theory        29710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-456 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-29710.        (((A -> (not (B -> (A and B)))) -> (not A)) and (C -> (C or D))), M:tm-456, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-29711
in-theory        29711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-456 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-29711.        (((A -> (not (A or B))) -> (not A)) and (C -> (C or D))), M:tm-456, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-29712
in-theory        29712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-456 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-29712.        (((A -> (not (B or A))) -> (not A)) and (C -> (C or D))), M:tm-456, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-29713
in-theory        29713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-456 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-29713.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (D -> (D or E))), M:tm-456, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-29714
in-theory        29714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (C -> (C or D)))
theorem-size     23
proof            (modus-ponens tm-456 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-29714.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (C -> (C or D))), M:tm-456, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-29715
in-theory        29715
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (D -> (D or E)))
theorem-size     29
proof            (modus-ponens tm-456 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-29715.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (D -> (D or E))), M:tm-456, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-29716
in-theory        29716
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29716.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (D or E))), M:tm-456, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-29717
in-theory        29717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29717.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (D -> (D or E))), M:tm-456, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-29718
in-theory        29718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29718.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (D -> (D or E))), M:tm-456, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-29719
in-theory        29719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (C -> (C or D)))
theorem-size     21
proof            (modus-ponens tm-456 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-29719.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (C -> (C or D))), M:tm-456, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-29720
in-theory        29720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29720.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (D or E))), M:tm-456, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-29721
in-theory        29721
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (B -> (B or C)))
theorem-size     17
proof            (modus-ponens tm-456 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-29721.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (B -> (B or C))), M:tm-456, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-29722
in-theory        29722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-456 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-10)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-29722.        (((A -> B) -> (((not (not A)) or A) -> B)) and (C -> (C or D))), M:tm-456, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-29723
in-theory        29723
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-456 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29723.        ((A or ((not (not B)) -> B)) and (C -> (C or D))), M:tm-456, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-29724
in-theory        29724
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-456 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29724.        ((((not (not A)) -> A) or B) and (C -> (C or D))), M:tm-456, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-29725
in-theory        29725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-456 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29725.        ((A -> (((not (not B)) -> B) and A)) and (C -> (C or D))), M:tm-456, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-29726
in-theory        29726
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (C -> (C or D)))
theorem-size     21
proof            (modus-ponens tm-456 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-29726.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (C -> (C or D))), M:tm-456, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-29727
in-theory        29727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-456 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29727.        ((A -> ((not (not B)) -> B)) and (C -> (C or D))), M:tm-456, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-29728
in-theory        29728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-29728.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (D -> (D or E))), M:tm-456, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-29729
in-theory        29729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-29729.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (E -> (E or F))), M:tm-456, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-29730
in-theory        29730
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29730.        ((A or (B -> (C -> (D -> C)))) and (E -> (E or F))), M:tm-456, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-29731
in-theory        29731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29731.        (((A -> (B -> (C -> B))) or D) and (E -> (E or F))), M:tm-456, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-29732
in-theory        29732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29732.        ((A -> ((B -> (C -> (D -> C))) and A)) and (E -> (E or F))), M:tm-456, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-29733
in-theory        29733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-29733.        (((A -> B) -> (A -> (C -> B))) and (D -> (D or E))), M:tm-456, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-29734
in-theory        29734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29734.        ((A -> (B -> (C -> (D -> C)))) and (E -> (E or F))), M:tm-456, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-29735
in-theory        29735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and (B -> (B or C)))
theorem-size     9
proof            (modus-ponens tm-456 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       97
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-29735.        ((A -> A) and (B -> (B or C))), M:tm-456, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-29736
in-theory        29736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-29736.        (((A -> (B -> C)) -> (A -> (B -> C))) and (D -> (D or E))), M:tm-456, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-29737
in-theory        29737
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-456 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-29737.        (((A and B) -> (A and B)) and (C -> (C or D))), M:tm-456, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-29738
in-theory        29738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-456 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-29738.        (((A -> B) -> (A -> B)) and (C -> (C or D))), M:tm-456, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-29739
in-theory        29739
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and (B -> (B or C)))
theorem-size     13
proof            (modus-ponens tm-456 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-29739.        (((not (not A)) -> (not (not A))) and (B -> (B or C))), M:tm-456, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-29740
in-theory        29740
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (C -> (C or D)))
theorem-size     19
proof            (modus-ponens tm-456 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-29740.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (C -> (C or D))), M:tm-456, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-29741
in-theory        29741
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-29741.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (D -> (D or E))), M:tm-456, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-29742
in-theory        29742
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29742.        ((A or ((B -> C) -> (B -> B))) and (D -> (D or E))), M:tm-456, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-29743
in-theory        29743
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29743.        ((((A -> B) -> (A -> A)) or C) and (D -> (D or E))), M:tm-456, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-29744
in-theory        29744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29744.        ((A -> (((B -> C) -> (B -> B)) and A)) and (D -> (D or E))), M:tm-456, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-29745
in-theory        29745
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-456 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-29745.        ((((A -> B) -> A) -> ((A -> B) -> A)) and (C -> (C or D))), M:tm-456, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-29746
in-theory        29746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29746.        ((A -> ((B -> C) -> (B -> B))) and (D -> (D or E))), M:tm-456, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-29747
in-theory        29747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-29747.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (D -> (D or E))), M:tm-456, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-29748
in-theory        29748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-456 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-29748.        (((A -> (A -> B)) -> (A -> B)) and (C -> (C or D))), M:tm-456, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-29749
in-theory        29749
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-456 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-29749.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (D -> (D or E))), M:tm-456, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-29750
in-theory        29750
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (D -> (D or E)))
theorem-size     37
proof            (modus-ponens tm-456 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-29750.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (D -> (D or E))), M:tm-456, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-29751
in-theory        29751
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (E -> (E or F)))
theorem-size     39
proof            (modus-ponens tm-456 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-29751.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (E -> (E or F))), M:tm-456, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-29752
in-theory        29752
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29752.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (E or F))), M:tm-456, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-29753
in-theory        29753
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29753.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (E -> (E or F))), M:tm-456, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-29754
in-theory        29754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (E -> (E or F)))
theorem-size     29
proof            (modus-ponens tm-456 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29754.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (E -> (E or F))), M:tm-456, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-29755
in-theory        29755
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (D -> (D or E)))
theorem-size     35
proof            (modus-ponens tm-456 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-29755.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (D -> (D or E))), M:tm-456, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-29756
in-theory        29756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29756.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (E or F))), M:tm-456, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-29757
in-theory        29757
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (E -> (E or F)))
theorem-size     29
proof            (modus-ponens tm-456 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-29757.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-29758
in-theory        29758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-29758.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (E -> (E or F))), M:tm-456, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-29759
in-theory        29759
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (F -> (F or G)))
theorem-size     39
proof            (modus-ponens tm-456 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-29759.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (F -> (F or G))), M:tm-456, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-29760
in-theory        29760
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29760.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (F or G))), M:tm-456, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-29761
in-theory        29761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29761.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (F or G))), M:tm-456, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-29762
in-theory        29762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29762.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (F or G))), M:tm-456, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-29763
in-theory        29763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-29763.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (E -> (E or F))), M:tm-456, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-29764
in-theory        29764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29764.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (F or G))), M:tm-456, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-29765
in-theory        29765
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-456 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-29765.        ((((A -> B) and A) -> B) and (C -> (C or D))), M:tm-456, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-29766
in-theory        29766
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-29766.        (((((A -> (B -> A)) -> C) and D) -> C) and (E -> (E or F))), M:tm-456, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-29767
in-theory        29767
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-29767.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (F -> (F or G))), M:tm-456, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-29768
in-theory        29768
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (D -> (D or E)))
theorem-size     27
proof            (modus-ponens tm-456 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-29768.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (D -> (D or E))), M:tm-456, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-29769
in-theory        29769
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-29769.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (D -> (D or E))), M:tm-456, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-29770
in-theory        29770
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (D -> (D or E)))
theorem-size     31
proof            (modus-ponens tm-456 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-29770.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (D -> (D or E))), M:tm-456, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-29771
in-theory        29771
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (E -> (E or F)))
theorem-size     33
proof            (modus-ponens tm-456 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-29771.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-29772
in-theory        29772
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29772.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (E or F))), M:tm-456, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-29773
in-theory        29773
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29773.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (E -> (E or F))), M:tm-456, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-29774
in-theory        29774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29774.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (E -> (E or F))), M:tm-456, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-29775
in-theory        29775
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (D -> (D or E)))
theorem-size     29
proof            (modus-ponens tm-456 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-29775.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (D -> (D or E))), M:tm-456, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-29776
in-theory        29776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29776.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (E or F))), M:tm-456, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-29777
in-theory        29777
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-29777.        ((((((A and B) -> A) -> C) and D) -> C) and (E -> (E or F))), M:tm-456, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-29778
in-theory        29778
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-29778.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (D -> (D or E))), M:tm-456, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-29779
in-theory        29779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-29779.        (((A -> (not ((B and C) -> B))) -> (not A)) and (D -> (D or E))), M:tm-456, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-29780
in-theory        29780
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-29780.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (E -> (E or F))), M:tm-456, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-29781
in-theory        29781
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29781.        ((A or (B -> ((C and D) -> C))) and (E -> (E or F))), M:tm-456, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-29782
in-theory        29782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29782.        (((A -> ((B and C) -> B)) or D) and (E -> (E or F))), M:tm-456, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-29783
in-theory        29783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29783.        ((A -> ((B -> ((C and D) -> C)) and A)) and (E -> (E or F))), M:tm-456, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-29784
in-theory        29784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-29784.        (((A -> (B and C)) -> (A -> B)) and (D -> (D or E))), M:tm-456, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-29785
in-theory        29785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29785.        ((A -> (B -> ((C and D) -> C))) and (E -> (E or F))), M:tm-456, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-29786
in-theory        29786
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-456 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-29786.        (((A and (A -> B)) -> B) and (C -> (C or D))), M:tm-456, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-29787
in-theory        29787
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-29787.        (((A and ((B -> (C -> B)) -> D)) -> D) and (E -> (E or F))), M:tm-456, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-29788
in-theory        29788
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-29788.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (F -> (F or G))), M:tm-456, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-29789
in-theory        29789
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-29789.        (((A and (((B and C) -> B) -> D)) -> D) and (E -> (E or F))), M:tm-456, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-29790
in-theory        29790
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (D -> (D or E)))
theorem-size     27
proof            (modus-ponens tm-456 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-29790.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (D -> (D or E))), M:tm-456, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-29791
in-theory        29791
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-29791.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (D -> (D or E))), M:tm-456, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-29792
in-theory        29792
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (D -> (D or E)))
theorem-size     31
proof            (modus-ponens tm-456 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-29792.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (D -> (D or E))), M:tm-456, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-29793
in-theory        29793
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (E -> (E or F)))
theorem-size     33
proof            (modus-ponens tm-456 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-29793.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-29794
in-theory        29794
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29794.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (E or F))), M:tm-456, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-29795
in-theory        29795
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29795.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (E -> (E or F))), M:tm-456, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-29796
in-theory        29796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29796.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (E -> (E or F))), M:tm-456, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-29797
in-theory        29797
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (D -> (D or E)))
theorem-size     29
proof            (modus-ponens tm-456 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-29797.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (D -> (D or E))), M:tm-456, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-29798
in-theory        29798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29798.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (E or F))), M:tm-456, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-29799
in-theory        29799
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-29799.        (((A and (((B and C) -> C) -> D)) -> D) and (E -> (E or F))), M:tm-456, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-29800
in-theory        29800
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-29800.        ((((((A and B) -> B) -> C) and D) -> C) and (E -> (E or F))), M:tm-456, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-29801
in-theory        29801
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-29801.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (D -> (D or E))), M:tm-456, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-29802
in-theory        29802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-29802.        (((A -> (not ((B and C) -> C))) -> (not A)) and (D -> (D or E))), M:tm-456, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-29803
in-theory        29803
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-29803.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (E -> (E or F))), M:tm-456, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-29804
in-theory        29804
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29804.        ((A or (B -> ((C and D) -> D))) and (E -> (E or F))), M:tm-456, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-29805
in-theory        29805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29805.        (((A -> ((B and C) -> C)) or D) and (E -> (E or F))), M:tm-456, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-29806
in-theory        29806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29806.        ((A -> ((B -> ((C and D) -> D)) and A)) and (E -> (E or F))), M:tm-456, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-29807
in-theory        29807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-29807.        (((A -> (B and C)) -> (A -> C)) and (D -> (D or E))), M:tm-456, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-29808
in-theory        29808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29808.        ((A -> (B -> ((C and D) -> D))) and (E -> (E or F))), M:tm-456, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-29809
in-theory        29809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29809.        (((A -> (B -> A)) and (C -> (D -> C))) and (E -> (E or F))), M:tm-456, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-29810
in-theory        29810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29810.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-29811
in-theory        29811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29811.        (((A -> (B -> A)) and ((C and D) -> C)) and (E -> (E or F))), M:tm-456, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-29812
in-theory        29812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29812.        (((A -> (B -> A)) and ((C and D) -> D)) and (E -> (E or F))), M:tm-456, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-29813
in-theory        29813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29813.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-29814
in-theory        29814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29814.        (((A -> (B -> A)) and (C -> (C or D))) and (E -> (E or F))), M:tm-456, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-29815
in-theory        29815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29815.        (((A -> (B -> A)) and (C -> (D or C))) and (E -> (E or F))), M:tm-456, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-29816
in-theory        29816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29816.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (F or G))), M:tm-456, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-29817
in-theory        29817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29817.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (E or F))), M:tm-456, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-29818
in-theory        29818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29818.        (((A -> (B -> A)) and ((not (not C)) -> C)) and (D -> (D or E))), M:tm-456, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-29819
in-theory        29819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29819.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (F -> (F or G))), M:tm-456, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-29820
in-theory        29820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29820.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (E -> (E or F))), M:tm-456, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-29821
in-theory        29821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (F or G)))
theorem-size     31
proof            (modus-ponens tm-456 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29821.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-29822
in-theory        29822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29822.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H))), M:tm-456, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-29823
in-theory        29823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29823.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-29824
in-theory        29824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29824.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-29825
in-theory        29825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29825.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-29826
in-theory        29826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29826.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (F -> (F or G))), M:tm-456, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-29827
in-theory        29827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29827.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (F or G))), M:tm-456, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-29828
in-theory        29828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-29828.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (D -> (D or E))), M:tm-456, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-29829
in-theory        29829
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-29829.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-29830
in-theory        29830
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29830.        ((A or (B -> ((C -> (D -> C)) and B))) and (E -> (E or F))), M:tm-456, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-29831
in-theory        29831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29831.        (((A -> ((B -> (C -> B)) and A)) or D) and (E -> (E or F))), M:tm-456, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-29832
in-theory        29832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29832.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (E -> (E or F))), M:tm-456, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-29833
in-theory        29833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29833.        ((A -> (B -> ((C -> (D -> C)) and B))) and (E -> (E or F))), M:tm-456, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-29834
in-theory        29834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29834.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (F -> (F or G))), M:tm-456, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-29835
in-theory        29835
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (G or H)))
theorem-size     33
proof            (modus-ponens tm-456 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29835.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (G or H))), M:tm-456, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-29836
in-theory        29836
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29836.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (F -> (F or G))), M:tm-456, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-29837
in-theory        29837
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29837.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (F -> (F or G))), M:tm-456, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-29838
in-theory        29838
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29838.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (F -> (F or G))), M:tm-456, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-29839
in-theory        29839
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29839.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (F -> (F or G))), M:tm-456, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-29840
in-theory        29840
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29840.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (F -> (F or G))), M:tm-456, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-29841
in-theory        29841
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (G or H)))
theorem-size     33
proof            (modus-ponens tm-456 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29841.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (G or H))), M:tm-456, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-29842
in-theory        29842
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (F or G)))
theorem-size     31
proof            (modus-ponens tm-456 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29842.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (F or G))), M:tm-456, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-29843
in-theory        29843
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29843.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-29844
in-theory        29844
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29844.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (G -> (G or H))), M:tm-456, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-29845
in-theory        29845
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29845.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (F -> (F or G))), M:tm-456, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-29846
in-theory        29846
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (G or H)))
theorem-size     39
proof            (modus-ponens tm-456 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29846.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (G or H))), M:tm-456, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-29847
in-theory        29847
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (H or I)))
theorem-size     35
proof            (modus-ponens tm-456 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29847.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (H or I))), M:tm-456, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-29848
in-theory        29848
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (G or H)))
theorem-size     35
proof            (modus-ponens tm-456 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29848.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (G or H))), M:tm-456, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-29849
in-theory        29849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29849.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (G -> (G or H))), M:tm-456, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-29850
in-theory        29850
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (G or H)))
theorem-size     35
proof            (modus-ponens tm-456 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29850.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (G or H))), M:tm-456, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-29851
in-theory        29851
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29851.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (G -> (G or H))), M:tm-456, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-29852
in-theory        29852
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29852.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (G or H))), M:tm-456, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-29853
in-theory        29853
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (H or I)))
theorem-size     37
proof            (modus-ponens tm-456 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29853.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (H or I))), M:tm-456, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-29854
in-theory        29854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29854.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (G or H))), M:tm-456, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-29855
in-theory        29855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-29855.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (E -> (E or F))), M:tm-456, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-29856
in-theory        29856
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (F -> (F or G)))
theorem-size     43
proof            (modus-ponens tm-456 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-29856.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (F -> (F or G))), M:tm-456, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-29857
in-theory        29857
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29857.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (F or G))), M:tm-456, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-29858
in-theory        29858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29858.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (F -> (F or G))), M:tm-456, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-29859
in-theory        29859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29859.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (F -> (F or G))), M:tm-456, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-29860
in-theory        29860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29860.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (F or G))), M:tm-456, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-29861
in-theory        29861
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29861.        ((((A and B) -> A) and (C -> (D -> C))) and (E -> (E or F))), M:tm-456, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-29862
in-theory        29862
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29862.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-29863
in-theory        29863
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29863.        ((((A and B) -> A) and ((C and D) -> C)) and (E -> (E or F))), M:tm-456, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-29864
in-theory        29864
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29864.        ((((A and B) -> A) and ((C and D) -> D)) and (E -> (E or F))), M:tm-456, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-29865
in-theory        29865
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29865.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-29866
in-theory        29866
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29866.        ((((A and B) -> A) and (C -> (C or D))) and (E -> (E or F))), M:tm-456, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-29867
in-theory        29867
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29867.        ((((A and B) -> A) and (C -> (D or C))) and (E -> (E or F))), M:tm-456, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-29868
in-theory        29868
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29868.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (F or G))), M:tm-456, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-29869
in-theory        29869
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29869.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (E or F))), M:tm-456, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-29870
in-theory        29870
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29870.        ((((A and B) -> A) and ((not (not C)) -> C)) and (D -> (D or E))), M:tm-456, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-29871
in-theory        29871
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29871.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (F -> (F or G))), M:tm-456, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-29872
in-theory        29872
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29872.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (E -> (E or F))), M:tm-456, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-29873
in-theory        29873
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (F or G)))
theorem-size     31
proof            (modus-ponens tm-456 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29873.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-29874
in-theory        29874
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29874.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H))), M:tm-456, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-29875
in-theory        29875
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29875.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-29876
in-theory        29876
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29876.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-29877
in-theory        29877
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29877.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-29878
in-theory        29878
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29878.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and (F -> (F or G))), M:tm-456, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-29879
in-theory        29879
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29879.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (F -> (F or G))), M:tm-456, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-29880
in-theory        29880
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29880.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (G or H))), M:tm-456, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-29881
in-theory        29881
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29881.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (F -> (F or G))), M:tm-456, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-29882
in-theory        29882
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29882.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (G or H))), M:tm-456, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-29883
in-theory        29883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29883.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (F -> (F or G))), M:tm-456, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-29884
in-theory        29884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-29884.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (D -> (D or E))), M:tm-456, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-29885
in-theory        29885
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-29885.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-29886
in-theory        29886
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29886.        ((A or (B -> (((C and D) -> C) and B))) and (E -> (E or F))), M:tm-456, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-29887
in-theory        29887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29887.        (((A -> (((B and C) -> B) and A)) or D) and (E -> (E or F))), M:tm-456, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-29888
in-theory        29888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29888.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (E -> (E or F))), M:tm-456, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-29889
in-theory        29889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29889.        ((A -> (B -> (((C and D) -> C) and B))) and (E -> (E or F))), M:tm-456, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-29890
in-theory        29890
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29890.        ((((A and B) -> B) and (C -> (D -> C))) and (E -> (E or F))), M:tm-456, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-29891
in-theory        29891
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29891.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-29892
in-theory        29892
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29892.        ((((A and B) -> B) and ((C and D) -> C)) and (E -> (E or F))), M:tm-456, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-29893
in-theory        29893
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29893.        ((((A and B) -> B) and ((C and D) -> D)) and (E -> (E or F))), M:tm-456, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-29894
in-theory        29894
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29894.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-29895
in-theory        29895
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29895.        ((((A and B) -> B) and (C -> (C or D))) and (E -> (E or F))), M:tm-456, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-29896
in-theory        29896
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29896.        ((((A and B) -> B) and (C -> (D or C))) and (E -> (E or F))), M:tm-456, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-29897
in-theory        29897
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29897.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (F or G))), M:tm-456, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-29898
in-theory        29898
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29898.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (E or F))), M:tm-456, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-29899
in-theory        29899
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29899.        ((((A and B) -> B) and ((not (not C)) -> C)) and (D -> (D or E))), M:tm-456, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-29900
in-theory        29900
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29900.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (F -> (F or G))), M:tm-456, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-29901
in-theory        29901
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29901.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (E -> (E or F))), M:tm-456, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-29902
in-theory        29902
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (F or G)))
theorem-size     31
proof            (modus-ponens tm-456 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29902.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-29903
in-theory        29903
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29903.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H))), M:tm-456, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-29904
in-theory        29904
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29904.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-29905
in-theory        29905
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29905.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-29906
in-theory        29906
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29906.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-29907
in-theory        29907
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29907.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and (F -> (F or G))), M:tm-456, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-29908
in-theory        29908
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29908.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (F -> (F or G))), M:tm-456, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-29909
in-theory        29909
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29909.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (G or H))), M:tm-456, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-29910
in-theory        29910
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29910.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (F -> (F or G))), M:tm-456, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-29911
in-theory        29911
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29911.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (F -> (F or G))), M:tm-456, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-29912
in-theory        29912
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29912.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (F -> (F or G))), M:tm-456, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-29913
in-theory        29913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29913.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (G or H))), M:tm-456, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-29914
in-theory        29914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29914.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (F -> (F or G))), M:tm-456, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-29915
in-theory        29915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-29915.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (D -> (D or E))), M:tm-456, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-29916
in-theory        29916
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-29916.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-29917
in-theory        29917
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29917.        ((A or (B -> (((C and D) -> D) and B))) and (E -> (E or F))), M:tm-456, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-29918
in-theory        29918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29918.        (((A -> (((B and C) -> C) and A)) or D) and (E -> (E or F))), M:tm-456, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-29919
in-theory        29919
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29919.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (E -> (E or F))), M:tm-456, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-29920
in-theory        29920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29920.        ((A -> (B -> (((C and D) -> D) and B))) and (E -> (E or F))), M:tm-456, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-29921
in-theory        29921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-29921.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and (E -> (E or F))), M:tm-456, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-29922
in-theory        29922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-29922.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-29923
in-theory        29923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-29923.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and (E -> (E or F))), M:tm-456, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-29924
in-theory        29924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29924.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and (E -> (E or F))), M:tm-456, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-29925
in-theory        29925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-29925.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-29926
in-theory        29926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29926.        (((A -> (B -> (A and B))) and (C -> (C or D))) and (E -> (E or F))), M:tm-456, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-29927
in-theory        29927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-29927.        (((A -> (B -> (A and B))) and (C -> (D or C))) and (E -> (E or F))), M:tm-456, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-29928
in-theory        29928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-29928.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (F or G))), M:tm-456, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-29929
in-theory        29929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-29929.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (E or F))), M:tm-456, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-29930
in-theory        29930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-29930.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (D -> (D or E))), M:tm-456, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-29931
in-theory        29931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-29931.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (F -> (F or G))), M:tm-456, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-29932
in-theory        29932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-29932.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (E -> (E or F))), M:tm-456, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-29933
in-theory        29933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (F or G)))
theorem-size     33
proof            (modus-ponens tm-456 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-29933.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-29934
in-theory        29934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-29934.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H))), M:tm-456, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-29935
in-theory        29935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (F or G)))
theorem-size     29
proof            (modus-ponens tm-456 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-29935.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-29936
in-theory        29936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-29936.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-29937
in-theory        29937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (F or G)))
theorem-size     29
proof            (modus-ponens tm-456 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-29937.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-29938
in-theory        29938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-29938.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (F -> (F or G))), M:tm-456, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-29939
in-theory        29939
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-29939.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (F -> (F or G))), M:tm-456, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-29940
in-theory        29940
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (G or H)))
theorem-size     31
proof            (modus-ponens tm-456 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-29940.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (G or H))), M:tm-456, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-29941
in-theory        29941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-29941.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (F -> (F or G))), M:tm-456, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-29942
in-theory        29942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-29942.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (F -> (F or G))), M:tm-456, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-29943
in-theory        29943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29943.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (F or G))), M:tm-456, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-29944
in-theory        29944
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29944.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (F or G))), M:tm-456, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-29945
in-theory        29945
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29945.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (F or G))), M:tm-456, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-29946
in-theory        29946
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (G or H)))
theorem-size     31
proof            (modus-ponens tm-456 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29946.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (G or H))), M:tm-456, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-29947
in-theory        29947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29947.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (F or G))), M:tm-456, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-29948
in-theory        29948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-29948.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (D -> (D or E))), M:tm-456, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-29949
in-theory        29949
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (E -> (E or F)))
theorem-size     31
proof            (modus-ponens tm-456 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-29949.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-29950
in-theory        29950
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29950.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and (E -> (E or F))), M:tm-456, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-29951
in-theory        29951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29951.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and (E -> (E or F))), M:tm-456, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-29952
in-theory        29952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29952.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (E -> (E or F))), M:tm-456, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-29953
in-theory        29953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-29953.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (E -> (E or F))), M:tm-456, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-29954
in-theory        29954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-456 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-29954.        ((A -> (A and (B -> A))) and (C -> (C or D))), M:tm-456, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-29955
in-theory        29955
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-456 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-29955.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (D -> (D or E))), M:tm-456, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-29956
in-theory        29956
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-456 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-29956.        (((A and B) -> ((A and B) and A)) and (C -> (C or D))), M:tm-456, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-29957
in-theory        29957
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-456 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-29957.        (((A and B) -> ((A and B) and B)) and (C -> (C or D))), M:tm-456, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-29958
in-theory        29958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-456 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-29958.        ((A -> (A and (B -> (A and B)))) and (C -> (C or D))), M:tm-456, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-29959
in-theory        29959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-456 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-29959.        ((A -> (A and (A or B))) and (C -> (C or D))), M:tm-456, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-29960
in-theory        29960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-456 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-29960.        ((A -> (A and (B or A))) and (C -> (C or D))), M:tm-456, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-29961
in-theory        29961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-456 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-29961.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (D -> (D or E))), M:tm-456, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-29962
in-theory        29962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (C -> (C or D)))
theorem-size     21
proof            (modus-ponens tm-456 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-29962.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (C -> (C or D))), M:tm-456, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-29963
in-theory        29963
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and (B -> (B or C)))
theorem-size     15
proof            (modus-ponens tm-456 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-29963.        (((not (not A)) -> ((not (not A)) and A)) and (B -> (B or C))), M:tm-456, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-29964
in-theory        29964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-29964.        ((A -> (A and (B -> (C -> B)))) and (D -> (D or E))), M:tm-456, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-29965
in-theory        29965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-456 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-29965.        (((A -> B) -> ((A -> B) and (A -> A))) and (C -> (C or D))), M:tm-456, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-29966
in-theory        29966
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (D -> (D or E)))
theorem-size     35
proof            (modus-ponens tm-456 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-29966.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (D -> (D or E))), M:tm-456, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-29967
in-theory        29967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-29967.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (E -> (E or F))), M:tm-456, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-29968
in-theory        29968
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (D -> (D or E)))
theorem-size     29
proof            (modus-ponens tm-456 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-29968.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (D -> (D or E))), M:tm-456, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-29969
in-theory        29969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-29969.        ((A -> (A and ((B and C) -> B))) and (D -> (D or E))), M:tm-456, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-29970
in-theory        29970
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (D -> (D or E)))
theorem-size     29
proof            (modus-ponens tm-456 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-29970.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (D -> (D or E))), M:tm-456, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-29971
in-theory        29971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-29971.        ((A -> (A and ((B and C) -> C))) and (D -> (D or E))), M:tm-456, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-29972
in-theory        29972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-29972.        ((A -> (A and ((B -> (C -> B)) and A))) and (D -> (D or E))), M:tm-456, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-29973
in-theory        29973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-29973.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (E -> (E or F))), M:tm-456, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-29974
in-theory        29974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-29974.        ((A -> (A and (((B and C) -> B) and A))) and (D -> (D or E))), M:tm-456, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-29975
in-theory        29975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-29975.        ((A -> (A and (((B and C) -> C) and A))) and (D -> (D or E))), M:tm-456, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-29976
in-theory        29976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-29976.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (D -> (D or E))), M:tm-456, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-29977
in-theory        29977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (C -> (C or D)))
theorem-size     19
proof            (modus-ponens tm-456 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-29977.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (C -> (C or D))), M:tm-456, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-29978
in-theory        29978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29978.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-29979
in-theory        29979
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29979.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-29980
in-theory        29980
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29980.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-29981
in-theory        29981
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (F or G)))
theorem-size     29
proof            (modus-ponens tm-456 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29981.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (F or G))), M:tm-456, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-29982
in-theory        29982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29982.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-29983
in-theory        29983
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (C -> (C or D)))
theorem-size     21
proof            (modus-ponens tm-456 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-29983.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (C -> (C or D))), M:tm-456, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-29984
in-theory        29984
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-456 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-29984.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (D -> (D or E))), M:tm-456, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-29985
in-theory        29985
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29985.        ((A or ((B -> C) -> (B -> (B and C)))) and (D -> (D or E))), M:tm-456, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-29986
in-theory        29986
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29986.        ((((A -> B) -> (A -> (A and B))) or C) and (D -> (D or E))), M:tm-456, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-29987
in-theory        29987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29987.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (D -> (D or E))), M:tm-456, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-29988
in-theory        29988
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (C -> (C or D)))
theorem-size     19
proof            (modus-ponens tm-456 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-29988.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (C -> (C or D))), M:tm-456, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-29989
in-theory        29989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-29989.        ((A -> ((B -> C) -> (B -> (B and C)))) and (D -> (D or E))), M:tm-456, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-29990
in-theory        29990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-29990.        ((A -> (A and (B -> (C -> (B and C))))) and (D -> (D or E))), M:tm-456, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-29991
in-theory        29991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29991.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (F -> (F or G))), M:tm-456, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-29992
in-theory        29992
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29992.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (F -> (F or G))), M:tm-456, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-29993
in-theory        29993
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29993.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (F -> (F or G))), M:tm-456, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-29994
in-theory        29994
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29994.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (G or H))), M:tm-456, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-29995
in-theory        29995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-29995.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (F -> (F or G))), M:tm-456, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-29996
in-theory        29996
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-29996.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (E -> (E or F))), M:tm-456, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-29997
in-theory        29997
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-29997.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and (E -> (E or F))), M:tm-456, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-29998
in-theory        29998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-29998.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (D -> (D or E))), M:tm-456, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-29999
in-theory        29999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-29999.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (D -> (D or E))), M:tm-456, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-30000
in-theory        30000
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-30000.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (E -> (E or F))), M:tm-456, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-30001
in-theory        30001
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-30001.        ((A or (B -> (C -> (D -> (C and D))))) and (E -> (E or F))), M:tm-456, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-30002
in-theory        30002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-30002.        (((A -> (B -> (C -> (B and C)))) or D) and (E -> (E or F))), M:tm-456, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-30003
in-theory        30003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-30003.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (E -> (E or F))), M:tm-456, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-30004
in-theory        30004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-30004.        (((A -> B) -> (A -> (C -> (B and C)))) and (D -> (D or E))), M:tm-456, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-30005
in-theory        30005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-30005.        ((A -> (B -> (C -> (D -> (C and D))))) and (E -> (E or F))), M:tm-456, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-30006
in-theory        30006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30006.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (F -> (F or G))), M:tm-456, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-30007
in-theory        30007
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30007.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (F -> (F or G))), M:tm-456, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-30008
in-theory        30008
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30008.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (F -> (F or G))), M:tm-456, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-30009
in-theory        30009
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30009.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (G -> (G or H))), M:tm-456, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-30010
in-theory        30010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30010.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (F -> (F or G))), M:tm-456, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-30011
in-theory        30011
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30011.        ((A or ((B -> (C -> B)) or D)) and (E -> (E or F))), M:tm-456, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-30012
in-theory        30012
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30012.        ((((A -> (B -> A)) or C) or D) and (E -> (E or F))), M:tm-456, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-30013
in-theory        30013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30013.        ((A -> (((B -> (C -> B)) or D) and A)) and (E -> (E or F))), M:tm-456, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-30014
in-theory        30014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30014.        ((A -> ((B -> (C -> B)) or D)) and (E -> (E or F))), M:tm-456, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-30015
in-theory        30015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30015.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (G or H))), M:tm-456, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-30016
in-theory        30016
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30016.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (G or H))), M:tm-456, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-30017
in-theory        30017
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30017.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (G or H))), M:tm-456, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-30018
in-theory        30018
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (H or I)))
theorem-size     35
proof            (modus-ponens tm-456 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30018.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (H or I))), M:tm-456, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-30019
in-theory        30019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30019.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (G or H))), M:tm-456, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-30020
in-theory        30020
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30020.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (F or G))), M:tm-456, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-30021
in-theory        30021
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30021.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (F -> (F or G))), M:tm-456, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-30022
in-theory        30022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30022.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (F -> (F or G))), M:tm-456, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-30023
in-theory        30023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30023.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (F or G))), M:tm-456, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-30024
in-theory        30024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30024.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (F -> (F or G))), M:tm-456, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-30025
in-theory        30025
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30025.        ((((A and B) -> B) and (((C and D) -> C) or E)) and (F -> (F or G))), M:tm-456, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-30026
in-theory        30026
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30026.        ((((A and B) -> A) and (((C and D) -> C) or E)) and (F -> (F or G))), M:tm-456, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-30027
in-theory        30027
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30027.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (G -> (G or H))), M:tm-456, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-30028
in-theory        30028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30028.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and (F -> (F or G))), M:tm-456, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-30029
in-theory        30029
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30029.        ((A or (((B and C) -> B) or D)) and (E -> (E or F))), M:tm-456, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-30030
in-theory        30030
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30030.        (((((A and B) -> A) or C) or D) and (E -> (E or F))), M:tm-456, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-30031
in-theory        30031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30031.        ((A -> ((((B and C) -> B) or D) and A)) and (E -> (E or F))), M:tm-456, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-30032
in-theory        30032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30032.        ((A -> (((B and C) -> B) or D)) and (E -> (E or F))), M:tm-456, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-30033
in-theory        30033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30033.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (F -> (F or G))), M:tm-456, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-30034
in-theory        30034
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30034.        ((((A and B) -> B) and (((C and D) -> D) or E)) and (F -> (F or G))), M:tm-456, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-30035
in-theory        30035
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30035.        ((((A and B) -> A) and (((C and D) -> D) or E)) and (F -> (F or G))), M:tm-456, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-30036
in-theory        30036
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30036.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (G -> (G or H))), M:tm-456, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-30037
in-theory        30037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30037.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and (F -> (F or G))), M:tm-456, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-30038
in-theory        30038
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30038.        ((A or (((B and C) -> C) or D)) and (E -> (E or F))), M:tm-456, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-30039
in-theory        30039
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30039.        (((((A and B) -> B) or C) or D) and (E -> (E or F))), M:tm-456, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-30040
in-theory        30040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30040.        ((A -> ((((B and C) -> C) or D) and A)) and (E -> (E or F))), M:tm-456, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-30041
in-theory        30041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30041.        ((A -> (((B and C) -> C) or D)) and (E -> (E or F))), M:tm-456, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-30042
in-theory        30042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-30042.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (F -> (F or G))), M:tm-456, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-30043
in-theory        30043
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-30043.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (F -> (F or G))), M:tm-456, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-30044
in-theory        30044
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-30044.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (F -> (F or G))), M:tm-456, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-30045
in-theory        30045
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-30045.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (G or H))), M:tm-456, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-30046
in-theory        30046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-30046.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (F -> (F or G))), M:tm-456, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-30047
in-theory        30047
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-30047.        ((A or ((B -> (C -> (B and C))) or D)) and (E -> (E or F))), M:tm-456, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-30048
in-theory        30048
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-30048.        ((((A -> (B -> (A and B))) or C) or D) and (E -> (E or F))), M:tm-456, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-30049
in-theory        30049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-30049.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (E -> (E or F))), M:tm-456, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-30050
in-theory        30050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-30050.        ((A -> ((B -> (C -> (B and C))) or D)) and (E -> (E or F))), M:tm-456, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-30051
in-theory        30051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30051.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (F -> (F or G))), M:tm-456, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-30052
in-theory        30052
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30052.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and (F -> (F or G))), M:tm-456, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-30053
in-theory        30053
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30053.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and (F -> (F or G))), M:tm-456, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-30054
in-theory        30054
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30054.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (G -> (G or H))), M:tm-456, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-30055
in-theory        30055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30055.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (F -> (F or G))), M:tm-456, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-30056
in-theory        30056
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30056.        ((A or ((B -> (B or C)) or D)) and (E -> (E or F))), M:tm-456, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-30057
in-theory        30057
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30057.        ((((A -> (A or B)) or C) or D) and (E -> (E or F))), M:tm-456, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-30058
in-theory        30058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30058.        ((A -> (((B -> (B or C)) or D) and A)) and (E -> (E or F))), M:tm-456, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-30059
in-theory        30059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30059.        ((A -> ((B -> (B or C)) or D)) and (E -> (E or F))), M:tm-456, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-30060
in-theory        30060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30060.        (((A -> (A or B)) and (C -> (D -> C))) and (E -> (E or F))), M:tm-456, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-30061
in-theory        30061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30061.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-30062
in-theory        30062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30062.        (((A -> (A or B)) and ((C and D) -> C)) and (E -> (E or F))), M:tm-456, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-30063
in-theory        30063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30063.        (((A -> (A or B)) and ((C and D) -> D)) and (E -> (E or F))), M:tm-456, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-30064
in-theory        30064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30064.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-30065
in-theory        30065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30065.        (((A -> (A or B)) and (C -> (C or D))) and (E -> (E or F))), M:tm-456, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-30066
in-theory        30066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30066.        (((A -> (A or B)) and (C -> (D or C))) and (E -> (E or F))), M:tm-456, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-30067
in-theory        30067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-30067.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (F or G))), M:tm-456, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-30068
in-theory        30068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-30068.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (E or F))), M:tm-456, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-30069
in-theory        30069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-30069.        (((A -> (A or B)) and ((not (not C)) -> C)) and (D -> (D or E))), M:tm-456, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-30070
in-theory        30070
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-30070.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (F -> (F or G))), M:tm-456, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-30071
in-theory        30071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-30071.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (E -> (E or F))), M:tm-456, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-30072
in-theory        30072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (F or G)))
theorem-size     31
proof            (modus-ponens tm-456 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-30072.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-30073
in-theory        30073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-30073.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H))), M:tm-456, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-30074
in-theory        30074
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-30074.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-30075
in-theory        30075
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-30075.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-30076
in-theory        30076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-30076.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-30077
in-theory        30077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-30077.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and (F -> (F or G))), M:tm-456, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-30078
in-theory        30078
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-30078.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (F -> (F or G))), M:tm-456, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-30079
in-theory        30079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-30079.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (G or H))), M:tm-456, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-30080
in-theory        30080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-30080.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (F -> (F or G))), M:tm-456, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-30081
in-theory        30081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-30081.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (F -> (F or G))), M:tm-456, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-30082
in-theory        30082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-30082.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (F or G))), M:tm-456, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-30083
in-theory        30083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-30083.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-30084
in-theory        30084
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-30084.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (F -> (F or G))), M:tm-456, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-30085
in-theory        30085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30085.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (F -> (F or G))), M:tm-456, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-30086
in-theory        30086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30086.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (G or H))), M:tm-456, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-30087
in-theory        30087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30087.        (((A -> (A or B)) and (((C and D) -> C) or E)) and (F -> (F or G))), M:tm-456, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-30088
in-theory        30088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30088.        (((A -> (A or B)) and (((C and D) -> D) or E)) and (F -> (F or G))), M:tm-456, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-30089
in-theory        30089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-30089.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (F -> (F or G))), M:tm-456, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-30090
in-theory        30090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30090.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and (F -> (F or G))), M:tm-456, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-30091
in-theory        30091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30091.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (F -> (F or G))), M:tm-456, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-30092
in-theory        30092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-30092.        ((A -> (A and ((B -> (B or C)) and A))) and (D -> (D or E))), M:tm-456, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-30093
in-theory        30093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30093.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (F -> (F or G))), M:tm-456, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-30094
in-theory        30094
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30094.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (F -> (F or G))), M:tm-456, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-30095
in-theory        30095
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30095.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (F -> (F or G))), M:tm-456, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-30096
in-theory        30096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30096.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (G or H))), M:tm-456, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-30097
in-theory        30097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30097.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (F -> (F or G))), M:tm-456, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-30098
in-theory        30098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-30098.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (D -> (D or E))), M:tm-456, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-30099
in-theory        30099
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-30099.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-30100
in-theory        30100
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30100.        ((A or (B -> ((C -> (C or D)) and B))) and (E -> (E or F))), M:tm-456, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-30101
in-theory        30101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30101.        (((A -> ((B -> (B or C)) and A)) or D) and (E -> (E or F))), M:tm-456, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-30102
in-theory        30102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30102.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (E -> (E or F))), M:tm-456, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-30103
in-theory        30103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30103.        ((A -> (B -> ((C -> (C or D)) and B))) and (E -> (E or F))), M:tm-456, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-30104
in-theory        30104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30104.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and (F -> (F or G))), M:tm-456, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30105
in-theory        30105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30105.        ((A -> (A and (B -> (B or C)))) and (D -> (D or E))), M:tm-456, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30106
in-theory        30106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30106.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and (E -> (E or F))))), M:tm-453, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30107
in-theory        30107
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (D -> (D or E))))
theorem-size     23
proof            (modus-ponens tm-450 tm-456 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30107.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (D -> (D or E)))), M:tm-450, m:tm-456, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30108
in-theory        30108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and ((D -> (D or E)) and (A -> (A and (B -> (B or C))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30108.        ((A -> (A and (B -> (B or C)))) and ((D -> (D or E)) and (A -> (A and (B -> (B or C)))))), M:tm-443, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30109
in-theory        30109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30109.        (((A -> (A or B)) or C) and (D -> (D and (E -> (E or F))))), M:tm-409, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30110
in-theory        30110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30110.        (((A -> (B -> (A and B))) or C) and (D -> (D and (E -> (E or F))))), M:tm-400, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30111
in-theory        30111
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30111.        ((((A and B) -> B) or C) and (D -> (D and (E -> (E or F))))), M:tm-391, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30112
in-theory        30112
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30112.        ((((A and B) -> A) or C) and (D -> (D and (E -> (E or F))))), M:tm-382, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30113
in-theory        30113
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30113.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (F -> (F or G))))), M:tm-373, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30114
in-theory        30114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30114.        (((A -> (B -> A)) or C) and (D -> (D and (E -> (E or F))))), M:tm-364, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30115
in-theory        30115
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and (C -> (C or D))) and B)))
theorem-size     13
proof            (modus-ponens tm-355 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30115.        (A -> (B -> ((A and (C -> (C or D))) and B))), M:tm-355, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30116
in-theory        30116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30116.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and (E -> (E or F))))), M:tm-354, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30117
in-theory        30117
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (D -> (D or E))))
theorem-size     23
proof            (modus-ponens tm-351 tm-456 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30117.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (D -> (D or E)))), M:tm-351, m:tm-456, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30118
in-theory        30118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30118.        ((A -> (A and (B -> (B or C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30119
in-theory        30119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and (D -> (D or E)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30119.        (((A -> B) -> (A -> (A and B))) and (C -> (C and (D -> (D or E))))), M:tm-338, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30120
in-theory        30120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (C -> (C or D))))
theorem-size     21
proof            (modus-ponens tm-335 tm-456 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30120.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (C -> (C or D)))), M:tm-335, m:tm-456, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30121
in-theory        30121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (A -> (A and (A and (B -> (B or C))))))
theorem-size     21
proof            (modus-ponens tm-328 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30121.        ((A -> (A and (B -> (B or C)))) and (A -> (A and (A and (B -> (B or C)))))), M:tm-328, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30122
in-theory        30122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and ((D -> (E -> (D and E))) and (A -> (A and (B -> (B or C))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30122.        ((A -> (A and (B -> (B or C)))) and ((D -> (E -> (D and E))) and (A -> (A and (B -> (B or C)))))), M:tm-327, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30123
in-theory        30123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (((D and E) -> E) and (A -> (A and (B -> (B or C))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30123.        ((A -> (A and (B -> (B or C)))) and (((D and E) -> E) and (A -> (A and (B -> (B or C)))))), M:tm-326, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30124
in-theory        30124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (((D and E) -> D) and (A -> (A and (B -> (B or C))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30124.        ((A -> (A and (B -> (B or C)))) and (((D and E) -> D) and (A -> (A and (B -> (B or C)))))), M:tm-325, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30125
in-theory        30125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and (B -> (B or C))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30125.        ((A -> (A and (B -> (B or C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and (B -> (B or C)))))), M:tm-324, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30126
in-theory        30126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and ((D -> (E -> D)) and (A -> (A and (B -> (B or C))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30126.        ((A -> (A and (B -> (B or C)))) and ((D -> (E -> D)) and (A -> (A and (B -> (B or C)))))), M:tm-323, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30127
in-theory        30127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30127.        ((A -> (A and (B -> (B or C)))) and ((D and E) -> E)), M:tm-322, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30128
in-theory        30128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30128.        ((A -> (A and (B -> (B or C)))) and ((D and E) -> D)), M:tm-320, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30129
in-theory        30129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30129.        ((A -> (A and (B -> (B or C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30130
in-theory        30130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30130.        ((A -> (A and (B -> (B or C)))) and (A -> A)), M:tm-316, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30131
in-theory        30131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30131.        ((A -> (A and (B -> (B or C)))) and (D -> (E -> D))), M:tm-315, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30132
in-theory        30132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and ((A -> (not (A and (B -> (B or C))))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30132.        ((A -> (A and (B -> (B or C)))) and ((A -> (not (A and (B -> (B or C))))) -> (not A))), M:tm-313, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30133
in-theory        30133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (((A and (B -> (B or C))) -> D) -> ((A or (A and (B -> (B or C)))) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30133.        ((A -> (A and (B -> (B or C)))) and (((A and (B -> (B or C))) -> D) -> ((A or (A and (B -> (B or C)))) -> D))), M:tm-312, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30134
in-theory        30134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (D or (A -> (A and (B -> (B or C))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30134.        ((A -> (A and (B -> (B or C)))) and (D or (A -> (A and (B -> (B or C)))))), M:tm-311, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30135
in-theory        30135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and ((A -> (A and (B -> (B or C)))) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30135.        ((A -> (A and (B -> (B or C)))) and ((A -> (A and (B -> (B or C)))) or D)), M:tm-310, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30136
in-theory        30136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (D -> ((A -> (A and (B -> (B or C)))) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30136.        ((A -> (A and (B -> (B or C)))) and (D -> ((A -> (A and (B -> (B or C)))) and D))), M:tm-309, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30137
in-theory        30137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (D -> (A -> (A and (B -> (B or C))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30137.        ((A -> (A and (B -> (B or C)))) and (D -> (A -> (A and (B -> (B or C)))))), M:tm-305, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30138
in-theory        30138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (E -> (E or F)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30138.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (E -> (E or F))))), M:tm-303, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30139
in-theory        30139
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (D -> (D or E))))
theorem-size     27
proof            (modus-ponens tm-300 tm-456 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30139.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (D -> (D or E)))), M:tm-300, m:tm-456, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30140
in-theory        30140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30140.        ((A -> (((B and C) -> C) and A)) and (D -> (D and (E -> (E or F))))), M:tm-270, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30141
in-theory        30141
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (D -> (D or E))))
theorem-size     23
proof            (modus-ponens tm-267 tm-456 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30141.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (D -> (D or E)))), M:tm-267, m:tm-456, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30142
in-theory        30142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30142.        ((A -> (((B and C) -> B) and A)) and (D -> (D and (E -> (E or F))))), M:tm-239, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30143
in-theory        30143
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (D -> (D or E))))
theorem-size     23
proof            (modus-ponens tm-236 tm-456 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30143.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (D -> (D or E)))), M:tm-236, m:tm-456, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30144
in-theory        30144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (F -> (F or G)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30144.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (F -> (F or G))))), M:tm-210, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30145
in-theory        30145
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (E -> (E or F))))
theorem-size     39
proof            (modus-ponens tm-207 tm-456 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30145.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (E -> (E or F)))), M:tm-207, m:tm-456, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30146
in-theory        30146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30146.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (E -> (E or F))))), M:tm-183, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30147
in-theory        30147
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (D -> (D or E))))
theorem-size     23
proof            (modus-ponens tm-180 tm-456 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30147.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (D -> (D or E)))), M:tm-180, m:tm-456, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30148
in-theory        30148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30148.        ((A -> ((B and C) -> C)) and (D -> (D and (E -> (E or F))))), M:tm-157, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30149
in-theory        30149
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and (D -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-154 tm-456 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30149.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and (D -> (D or E)))), M:tm-154, m:tm-456, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30150
in-theory        30150
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (E -> (E or F)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30150.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (E -> (E or F))))), M:tm-147, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30151
in-theory        30151
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (D -> (D or E))))
theorem-size     29
proof            (modus-ponens tm-144 tm-456 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30151.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (D -> (D or E)))), M:tm-144, m:tm-456, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30152
in-theory        30152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30152.        ((A -> ((B and C) -> B)) and (D -> (D and (E -> (E or F))))), M:tm-134, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30153
in-theory        30153
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and (D -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-131 tm-456 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30153.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and (D -> (D or E)))), M:tm-131, m:tm-456, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30154
in-theory        30154
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (E -> (E or F)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30154.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (E -> (E or F))))), M:tm-125, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30155
in-theory        30155
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (D -> (D or E))))
theorem-size     29
proof            (modus-ponens tm-122 tm-456 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30155.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (D -> (D or E)))), M:tm-122, m:tm-456, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30156
in-theory        30156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30156.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (F or G))))), M:tm-113, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30157
in-theory        30157
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (E or F))))
theorem-size     35
proof            (modus-ponens tm-110 tm-456 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30157.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (E or F)))), M:tm-110, m:tm-456, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30158
in-theory        30158
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (E -> (E or F)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30158.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (E -> (E or F))))), M:tm-105, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30159
in-theory        30159
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (D -> (D or E))))
theorem-size     35
proof            (modus-ponens tm-102 tm-456 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30159.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (D -> (D or E)))), M:tm-102, m:tm-456, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30160
in-theory        30160
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and (D -> (D or E)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30160.        (((A -> B) -> (A -> A)) and (C -> (C and (D -> (D or E))))), M:tm-95, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30161
in-theory        30161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and (C -> (C or D))))
theorem-size     17
proof            (modus-ponens tm-92 tm-456 ((Am (-> A A)) (B (and (-> A A) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30161.        (((A -> B) or (A -> A)) -> ((A -> A) and (C -> (C or D)))), M:tm-92, m:tm-456, u:((Am (-> A A)) (B (and (-> A A) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30162
in-theory        30162
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and (C -> (C or D)))))
theorem-size     11
proof            (modus-ponens tm-84 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30162.        (A -> (B -> (A and (C -> (C or D))))), M:tm-84, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30163
in-theory        30163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30163.        ((A -> (B -> (C -> B))) and (D -> (D and (E -> (E or F))))), M:tm-83, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30164
in-theory        30164
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (D -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-80 tm-456 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30164.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (D -> (D or E)))), M:tm-80, m:tm-456, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30165
in-theory        30165
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and (C -> (C or D)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30165.        (((not (not A)) -> A) and (B -> (B and (C -> (C or D))))), M:tm-76, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30166
in-theory        30166
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and (B -> (B or C))))
theorem-size     13
proof            (modus-ponens tm-73 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30166.        (((not (not A)) or A) -> (A and (B -> (B or C)))), M:tm-73, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30167
in-theory        30167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (D -> (D or E)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30167.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (D -> (D or E))))), M:tm-69, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30168
in-theory        30168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (C -> (C or D))))
theorem-size     25
proof            (modus-ponens tm-66 tm-456 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30168.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (C -> (C or D)))), M:tm-66, m:tm-456, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30169
in-theory        30169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (E -> (E or F)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30169.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (E -> (E or F))))), M:tm-54, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30170
in-theory        30170
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> (D or E))))
theorem-size     29
proof            (modus-ponens tm-51 tm-456 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30170.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> (D or E)))), M:tm-51, m:tm-456, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30171
in-theory        30171
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and (C -> (C or D))))
theorem-size     15
proof            (modus-ponens tm-50 tm-456 ((Am (or A B)) (C (and (or A B) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30171.        ((A or (B or A)) -> ((B or A) and (C -> (C or D)))), M:tm-50, m:tm-456, u:((Am (or A B)) (C (and (or A B) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30172
in-theory        30172
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and (C -> (C or D))))
theorem-size     15
proof            (modus-ponens tm-49 tm-456 ((Am (or A B)) (C (and (or A B) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30172.        ((A or (A or B)) -> ((A or B) and (C -> (C or D)))), M:tm-49, m:tm-456, u:((Am (or A B)) (C (and (or A B) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30173
in-theory        30173
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> (C or D))))
theorem-size     19
proof            (modus-ponens tm-48 tm-456 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30173.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> (C or D)))), M:tm-48, m:tm-456, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30174
in-theory        30174
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (C -> (C or D))))
theorem-size     13
proof            (modus-ponens tm-47 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30174.        (((A and B) or B) -> (B and (C -> (C or D)))), M:tm-47, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30175
in-theory        30175
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (C -> (C or D))))
theorem-size     13
proof            (modus-ponens tm-46 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30175.        (((A and B) or A) -> (A and (C -> (C or D)))), M:tm-46, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30176
in-theory        30176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (D or E))))
theorem-size     27
proof            (modus-ponens tm-45 tm-456 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30176.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (D or E)))), M:tm-45, m:tm-456, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30177
in-theory        30177
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (C -> (C or D))))
theorem-size     15
proof            (modus-ponens tm-44 tm-456 ((Am (-> A B)) (C (and (-> A B) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30177.        ((A or (B -> A)) -> ((B -> A) and (C -> (C or D)))), M:tm-44, m:tm-456, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30178
in-theory        30178
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and (D -> (D or E)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30178.        ((A -> (B or A)) and (C -> (C and (D -> (D or E))))), M:tm-42, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30179
in-theory        30179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and (D -> (D or E)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30179.        ((A -> (A or B)) and (C -> (C and (D -> (D or E))))), M:tm-32, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30180
in-theory        30180
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and (B -> (B or C)))))
theorem-size     11
proof            (modus-ponens tm-24 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30180.        (A -> (A and (A and (B -> (B or C))))), M:tm-24, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30181
in-theory        30181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and (D -> (D or E)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30181.        ((A -> (B -> (A and B))) and (C -> (C and (D -> (D or E))))), M:tm-23, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30182
in-theory        30182
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and (D -> (D or E)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30182.        (((A and B) -> B) and (C -> (C and (D -> (D or E))))), M:tm-22, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30183
in-theory        30183
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and (D -> (D or E)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30183.        (((A and B) -> A) and (C -> (C and (D -> (D or E))))), M:tm-21, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30184
in-theory        30184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (E -> (E or F)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30184.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (E -> (E or F))))), M:tm-20, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30185
in-theory        30185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and (D -> (D or E)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30185.        ((A -> (B -> A)) and (C -> (C and (D -> (D or E))))), M:tm-19, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30186
in-theory        30186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and (B -> (B or C))))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-9 tm-2 tm-5 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30186.        ((A -> (not (A and (B -> (B or C))))) -> (not A)), M:tm-9, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30187
in-theory        30187
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (B or C))) -> D) -> ((A or (A and (B -> (B or C)))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30187.        (((A and (B -> (B or C))) -> D) -> ((A or (A and (B -> (B or C)))) -> D)), M:tm-8, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30188
in-theory        30188
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and (C -> (C or D)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-7 tm-2 tm-5 tm-1 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30188.        (A or (B -> (B and (C -> (C or D))))), M:tm-7, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30189
in-theory        30189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-6 tm-2 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30189.        ((A -> (A and (B -> (B or C)))) or D), M:tm-6, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30190
in-theory        30190
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and (C -> (C or D)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30190.        (A -> ((B -> (B and (C -> (C or D)))) and A)), M:tm-5, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30191
in-theory        30191
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and (C -> (C or D)))))
theorem-size     11
proof            (modus-ponens tm-1 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-1 tm-2 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30191.        (A -> (B -> (B and (C -> (C or D))))), M:tm-1, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30192
in-theory        30192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30192.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (F -> (F or G))), M:tm-456, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30193
in-theory        30193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30193.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-453, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30194
in-theory        30194
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> (D -> (D or E))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30194.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))))), M:tm-443, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30195
in-theory        30195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30195.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-409, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30196
in-theory        30196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30196.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-400, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30197
in-theory        30197
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30197.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-391, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30198
in-theory        30198
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30198.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-382, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30199
in-theory        30199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30199.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I))))), M:tm-373, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30200
in-theory        30200
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30200.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-364, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30201
in-theory        30201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30201.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-354, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30202
in-theory        30202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30202.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30203
in-theory        30203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30203.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G))))), M:tm-338, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30204
in-theory        30204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> (D -> (D or E))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30204.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))))), M:tm-327, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30205
in-theory        30205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> (D -> (D or E))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30205.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))))), M:tm-326, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30206
in-theory        30206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> (D -> (D or E))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30206.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))))), M:tm-325, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30207
in-theory        30207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> (D -> (D or E))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30207.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))))), M:tm-324, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30208
in-theory        30208
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> (D -> (D or E))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30208.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))))), M:tm-323, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30209
in-theory        30209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30209.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and ((F and G) -> G)), M:tm-322, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30210
in-theory        30210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30210.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and ((F and G) -> F)), M:tm-320, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30211
in-theory        30211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30211.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30212
in-theory        30212
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30212.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (F -> (G -> F))), M:tm-315, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30213
in-theory        30213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (F or ((A -> (B -> (A and B))) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30213.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (F or ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))))), M:tm-311, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30214
in-theory        30214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30214.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) or F)), M:tm-310, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30215
in-theory        30215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (F -> (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30215.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (F -> (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and F))), M:tm-309, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30216
in-theory        30216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (C -> (D -> (D or E))))
theorem-size     23
proof            (modus-ponens tm-308 tm-457 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30216.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (C -> (D -> (D or E)))), M:tm-308, m:tm-457, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-30217
in-theory        30217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-457 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30217.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-457, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-30218
in-theory        30218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (F -> ((A -> (B -> (A and B))) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30218.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (F -> ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))))), M:tm-305, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30219
in-theory        30219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30219.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-303, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30220
in-theory        30220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30220.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-270, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30221
in-theory        30221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30221.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-239, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30222
in-theory        30222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30222.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I))))), M:tm-210, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30223
in-theory        30223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30223.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-183, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30224
in-theory        30224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30224.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-157, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30225
in-theory        30225
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30225.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-147, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30226
in-theory        30226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30226.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-134, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30227
in-theory        30227
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30227.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-125, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30228
in-theory        30228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30228.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I))))), M:tm-113, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30229
in-theory        30229
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30229.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-105, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30230
in-theory        30230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30230.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G))))), M:tm-95, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30231
in-theory        30231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30231.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-83, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30232
in-theory        30232
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (E -> (E or F)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30232.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (E -> (E or F))))), M:tm-76, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30233
in-theory        30233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30233.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G))))), M:tm-69, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30234
in-theory        30234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30234.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-54, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30235
in-theory        30235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30235.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G))))), M:tm-42, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30236
in-theory        30236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30236.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G))))), M:tm-32, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30237
in-theory        30237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30237.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G))))), M:tm-23, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30238
in-theory        30238
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30238.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G))))), M:tm-22, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30239
in-theory        30239
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30239.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G))))), M:tm-21, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30240
in-theory        30240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30240.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-20, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30241
in-theory        30241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30241.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (F or G))))), M:tm-19, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30242
in-theory        30242
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30242.        (A or ((B -> (C -> (B and C))) and (D -> (E -> (E or F))))), M:tm-7, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30243
in-theory        30243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30243.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) or F), M:tm-6, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30244
in-theory        30244
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> (E -> (E or F)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30244.        (A -> (((B -> (C -> (B and C))) and (D -> (E -> (E or F)))) and A)), M:tm-5, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30245
in-theory        30245
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30245.        (A -> ((B -> (C -> (B and C))) and (D -> (E -> (E or F))))), M:tm-1, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30246
in-theory        30246
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30246.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and (F -> (F or G))), M:tm-456, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30247
in-theory        30247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30247.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-453, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30248
in-theory        30248
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30248.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> (D -> (D or E)))))), M:tm-443, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30249
in-theory        30249
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30249.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-409, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30250
in-theory        30250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30250.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-400, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30251
in-theory        30251
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30251.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-391, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30252
in-theory        30252
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30252.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-382, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30253
in-theory        30253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30253.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (H -> (H or I))))), M:tm-373, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30254
in-theory        30254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30254.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-364, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30255
in-theory        30255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30255.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-354, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30256
in-theory        30256
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30256.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30257
in-theory        30257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30257.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (F -> (F or G))))), M:tm-338, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30258
in-theory        30258
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> (D -> (D or E))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30258.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> (D -> (D or E)))))), M:tm-327, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30259
in-theory        30259
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and (((F and G) -> G) and (((A and B) -> B) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30259.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and (((F and G) -> G) and (((A and B) -> B) and (C -> (D -> (D or E)))))), M:tm-326, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30260
in-theory        30260
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and (((F and G) -> F) and (((A and B) -> B) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30260.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and (((F and G) -> F) and (((A and B) -> B) and (C -> (D -> (D or E)))))), M:tm-325, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30261
in-theory        30261
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> (D -> (D or E))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30261.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> (D -> (D or E)))))), M:tm-324, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30262
in-theory        30262
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30262.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> (D -> (D or E)))))), M:tm-323, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30263
in-theory        30263
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30263.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((F and G) -> G)), M:tm-322, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30264
in-theory        30264
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30264.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((F and G) -> F)), M:tm-320, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30265
in-theory        30265
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30265.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30266
in-theory        30266
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30266.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and (F -> (G -> F))), M:tm-315, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30267
in-theory        30267
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and (F or (((A and B) -> B) and (C -> (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30267.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and (F or (((A and B) -> B) and (C -> (D -> (D or E)))))), M:tm-311, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30268
in-theory        30268
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((((A and B) -> B) and (C -> (D -> (D or E)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30268.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((((A and B) -> B) and (C -> (D -> (D or E)))) or F)), M:tm-310, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30269
in-theory        30269
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and (F -> ((((A and B) -> B) and (C -> (D -> (D or E)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30269.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and (F -> ((((A and B) -> B) and (C -> (D -> (D or E)))) and F))), M:tm-309, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30270
in-theory        30270
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and (C -> (D -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-308 tm-458 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30270.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and (C -> (D -> (D or E)))), M:tm-308, m:tm-458, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-30271
in-theory        30271
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-458 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30271.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((A and B) -> B)), M:tm-307, m:tm-458, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-30272
in-theory        30272
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and (F -> (((A and B) -> B) and (C -> (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30272.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and (F -> (((A and B) -> B) and (C -> (D -> (D or E)))))), M:tm-305, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30273
in-theory        30273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30273.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-303, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30274
in-theory        30274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30274.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-270, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30275
in-theory        30275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30275.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-239, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30276
in-theory        30276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30276.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (H -> (H or I))))), M:tm-210, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30277
in-theory        30277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30277.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-183, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30278
in-theory        30278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30278.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-157, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30279
in-theory        30279
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30279.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-147, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30280
in-theory        30280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30280.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-134, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30281
in-theory        30281
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30281.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-125, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30282
in-theory        30282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30282.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (H or I))))), M:tm-113, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30283
in-theory        30283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30283.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-105, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30284
in-theory        30284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30284.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (F -> (F or G))))), M:tm-95, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30285
in-theory        30285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30285.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-83, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30286
in-theory        30286
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30286.        (((not (not A)) -> A) and (((B and C) -> C) and (D -> (E -> (E or F))))), M:tm-76, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30287
in-theory        30287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-4 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30287.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (F -> (F or G))))), M:tm-69, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30288
in-theory        30288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30288.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-54, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30289
in-theory        30289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30289.        ((A -> (B or A)) and (((C and D) -> D) and (E -> (F -> (F or G))))), M:tm-42, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30290
in-theory        30290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30290.        ((A -> (A or B)) and (((C and D) -> D) and (E -> (F -> (F or G))))), M:tm-32, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30291
in-theory        30291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30291.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (F -> (F or G))))), M:tm-23, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30292
in-theory        30292
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30292.        (((A and B) -> B) and (((C and D) -> D) and (E -> (F -> (F or G))))), M:tm-22, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30293
in-theory        30293
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30293.        (((A and B) -> A) and (((C and D) -> D) and (E -> (F -> (F or G))))), M:tm-21, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30294
in-theory        30294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30294.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-20, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30295
in-theory        30295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30295.        ((A -> (B -> A)) and (((C and D) -> D) and (E -> (F -> (F or G))))), M:tm-19, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30296
in-theory        30296
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-4 tm-1 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30296.        (A or (((B and C) -> C) and (D -> (E -> (E or F))))), M:tm-7, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30297
in-theory        30297
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-4 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30297.        ((((A and B) -> B) and (C -> (D -> (D or E)))) or F), M:tm-6, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30298
in-theory        30298
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> (E -> (E or F)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30298.        (A -> ((((B and C) -> C) and (D -> (E -> (E or F)))) and A)), M:tm-5, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30299
in-theory        30299
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-4 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30299.        (A -> (((B and C) -> C) and (D -> (E -> (E or F))))), M:tm-1, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30300
in-theory        30300
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30300.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and (F -> (F or G))), M:tm-456, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30301
in-theory        30301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30301.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-453, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30302
in-theory        30302
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30302.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> (D -> (D or E)))))), M:tm-443, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30303
in-theory        30303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30303.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-409, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30304
in-theory        30304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30304.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-400, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30305
in-theory        30305
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30305.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-391, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30306
in-theory        30306
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30306.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-382, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30307
in-theory        30307
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30307.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (H -> (H or I))))), M:tm-373, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30308
in-theory        30308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30308.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-364, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30309
in-theory        30309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30309.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-354, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30310
in-theory        30310
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30310.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30311
in-theory        30311
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30311.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (F -> (F or G))))), M:tm-338, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30312
in-theory        30312
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> (D -> (D or E))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30312.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> (D -> (D or E)))))), M:tm-327, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30313
in-theory        30313
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and (((F and G) -> G) and (((A and B) -> A) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30313.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and (((F and G) -> G) and (((A and B) -> A) and (C -> (D -> (D or E)))))), M:tm-326, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30314
in-theory        30314
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and (((F and G) -> F) and (((A and B) -> A) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30314.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and (((F and G) -> F) and (((A and B) -> A) and (C -> (D -> (D or E)))))), M:tm-325, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30315
in-theory        30315
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> (D -> (D or E))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30315.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> (D -> (D or E)))))), M:tm-324, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30316
in-theory        30316
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30316.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> (D -> (D or E)))))), M:tm-323, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30317
in-theory        30317
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30317.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((F and G) -> G)), M:tm-322, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30318
in-theory        30318
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30318.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((F and G) -> F)), M:tm-320, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30319
in-theory        30319
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30319.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30320
in-theory        30320
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30320.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and (F -> (G -> F))), M:tm-315, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30321
in-theory        30321
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and (F or (((A and B) -> A) and (C -> (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30321.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and (F or (((A and B) -> A) and (C -> (D -> (D or E)))))), M:tm-311, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30322
in-theory        30322
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((((A and B) -> A) and (C -> (D -> (D or E)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30322.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((((A and B) -> A) and (C -> (D -> (D or E)))) or F)), M:tm-310, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30323
in-theory        30323
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and (F -> ((((A and B) -> A) and (C -> (D -> (D or E)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30323.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and (F -> ((((A and B) -> A) and (C -> (D -> (D or E)))) and F))), M:tm-309, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30324
in-theory        30324
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and (C -> (D -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-308 tm-459 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30324.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and (C -> (D -> (D or E)))), M:tm-308, m:tm-459, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-30325
in-theory        30325
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-459 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30325.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((A and B) -> A)), M:tm-307, m:tm-459, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-30326
in-theory        30326
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and (F -> (((A and B) -> A) and (C -> (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30326.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and (F -> (((A and B) -> A) and (C -> (D -> (D or E)))))), M:tm-305, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30327
in-theory        30327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30327.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-303, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30328
in-theory        30328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30328.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-270, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30329
in-theory        30329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30329.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-239, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30330
in-theory        30330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30330.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (H -> (H or I))))), M:tm-210, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30331
in-theory        30331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30331.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-183, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30332
in-theory        30332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30332.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-157, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30333
in-theory        30333
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30333.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-147, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30334
in-theory        30334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30334.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-134, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30335
in-theory        30335
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30335.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-125, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30336
in-theory        30336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30336.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (H or I))))), M:tm-113, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30337
in-theory        30337
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30337.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-105, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30338
in-theory        30338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30338.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (F -> (F or G))))), M:tm-95, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30339
in-theory        30339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30339.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-83, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30340
in-theory        30340
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30340.        (((not (not A)) -> A) and (((B and C) -> B) and (D -> (E -> (E or F))))), M:tm-76, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30341
in-theory        30341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-3 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30341.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (F -> (F or G))))), M:tm-69, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30342
in-theory        30342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30342.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-54, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30343
in-theory        30343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30343.        ((A -> (B or A)) and (((C and D) -> C) and (E -> (F -> (F or G))))), M:tm-42, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30344
in-theory        30344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30344.        ((A -> (A or B)) and (((C and D) -> C) and (E -> (F -> (F or G))))), M:tm-32, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30345
in-theory        30345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30345.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (F -> (F or G))))), M:tm-23, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30346
in-theory        30346
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30346.        (((A and B) -> B) and (((C and D) -> C) and (E -> (F -> (F or G))))), M:tm-22, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30347
in-theory        30347
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30347.        (((A and B) -> A) and (((C and D) -> C) and (E -> (F -> (F or G))))), M:tm-21, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30348
in-theory        30348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30348.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-20, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30349
in-theory        30349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30349.        ((A -> (B -> A)) and (((C and D) -> C) and (E -> (F -> (F or G))))), M:tm-19, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30350
in-theory        30350
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-3 tm-1 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30350.        (A or (((B and C) -> B) and (D -> (E -> (E or F))))), M:tm-7, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30351
in-theory        30351
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-3 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30351.        ((((A and B) -> A) and (C -> (D -> (D or E)))) or F), M:tm-6, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30352
in-theory        30352
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> (E -> (E or F)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30352.        (A -> ((((B and C) -> B) and (D -> (E -> (E or F)))) and A)), M:tm-5, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30353
in-theory        30353
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-3 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30353.        (A -> (((B and C) -> B) and (D -> (E -> (E or F))))), M:tm-1, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30354
in-theory        30354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30354.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (G -> (G or H))), M:tm-456, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30355
in-theory        30355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30355.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-453, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30356
in-theory        30356
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30356.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))))), M:tm-443, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30357
in-theory        30357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30357.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-409, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30358
in-theory        30358
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30358.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-400, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30359
in-theory        30359
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30359.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-391, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30360
in-theory        30360
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30360.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-382, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30361
in-theory        30361
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30361.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (I or J))))), M:tm-373, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30362
in-theory        30362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30362.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-364, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30363
in-theory        30363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30363.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-354, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30364
in-theory        30364
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30364.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30365
in-theory        30365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30365.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H))))), M:tm-338, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30366
in-theory        30366
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30366.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))))), M:tm-327, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30367
in-theory        30367
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30367.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))))), M:tm-326, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30368
in-theory        30368
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30368.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))))), M:tm-325, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30369
in-theory        30369
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30369.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))))), M:tm-324, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30370
in-theory        30370
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30370.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))))), M:tm-323, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30371
in-theory        30371
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30371.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((G and H) -> H)), M:tm-322, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30372
in-theory        30372
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30372.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((G and H) -> G)), M:tm-320, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30373
in-theory        30373
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30373.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30374
in-theory        30374
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30374.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (G -> (H -> G))), M:tm-315, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30375
in-theory        30375
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30375.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))))), M:tm-311, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30376
in-theory        30376
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30376.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) or G)), M:tm-310, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30377
in-theory        30377
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30377.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and G))), M:tm-309, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30378
in-theory        30378
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (D -> (E -> (E or F))))
theorem-size     29
proof            (modus-ponens tm-308 tm-460 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (or Em Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30378.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (D -> (E -> (E or F)))), M:tm-308, m:tm-460, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (or Em Fm)))))
================================================================
tm-name          tm-30379
in-theory        30379
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-460 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (or Em Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30379.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-460, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (or Em Fm)))))
================================================================
tm-name          tm-30380
in-theory        30380
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30380.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))))), M:tm-305, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30381
in-theory        30381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30381.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-303, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30382
in-theory        30382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30382.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-270, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30383
in-theory        30383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30383.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-239, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30384
in-theory        30384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (I or J)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30384.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (I or J))))), M:tm-210, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30385
in-theory        30385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30385.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-183, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30386
in-theory        30386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30386.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-157, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30387
in-theory        30387
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30387.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-147, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30388
in-theory        30388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30388.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-134, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30389
in-theory        30389
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30389.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-125, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30390
in-theory        30390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30390.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (I or J))))), M:tm-113, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30391
in-theory        30391
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30391.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-105, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30392
in-theory        30392
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30392.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H))))), M:tm-95, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30393
in-theory        30393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30393.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-83, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30394
in-theory        30394
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (F or G)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30394.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (F or G))))), M:tm-76, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30395
in-theory        30395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30395.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H))))), M:tm-69, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30396
in-theory        30396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30396.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-54, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30397
in-theory        30397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30397.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H))))), M:tm-42, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30398
in-theory        30398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30398.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H))))), M:tm-32, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30399
in-theory        30399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30399.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H))))), M:tm-23, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30400
in-theory        30400
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30400.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H))))), M:tm-22, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30401
in-theory        30401
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30401.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H))))), M:tm-21, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30402
in-theory        30402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30402.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-20, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30403
in-theory        30403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30403.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (G or H))))), M:tm-19, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30404
in-theory        30404
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-7 tm-5 tm-2 tm-1 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30404.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (F or G))))), M:tm-7, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30405
in-theory        30405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-6 tm-5 tm-2 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30405.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) or G), M:tm-6, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30406
in-theory        30406
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (F or G)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30406.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (F or G)))) and A)), M:tm-5, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30407
in-theory        30407
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-1 tm-5 tm-2 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30407.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (F or G))))), M:tm-1, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-30408
in-theory        30408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30408.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (F -> (F or G))), M:tm-456, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30409
in-theory        30409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30409.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-453, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30410
in-theory        30410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30410.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> (D -> (D or E)))))), M:tm-443, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30411
in-theory        30411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30411.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-409, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30412
in-theory        30412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30412.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-400, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30413
in-theory        30413
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30413.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-391, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30414
in-theory        30414
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30414.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-382, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30415
in-theory        30415
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30415.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (H or I))))), M:tm-373, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30416
in-theory        30416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30416.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-364, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30417
in-theory        30417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30417.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-354, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30418
in-theory        30418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30418.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30419
in-theory        30419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30419.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (F or G))))), M:tm-338, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30420
in-theory        30420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> (D -> (D or E))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30420.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> (D -> (D or E)))))), M:tm-327, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30421
in-theory        30421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30421.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> (D -> (D or E)))))), M:tm-326, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30422
in-theory        30422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30422.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> (D -> (D or E)))))), M:tm-325, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30423
in-theory        30423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> (D -> (D or E))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30423.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> (D -> (D or E)))))), M:tm-324, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30424
in-theory        30424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30424.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> (D -> (D or E)))))), M:tm-323, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30425
in-theory        30425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30425.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and ((F and G) -> G)), M:tm-322, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30426
in-theory        30426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30426.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and ((F and G) -> F)), M:tm-320, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30427
in-theory        30427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30427.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30428
in-theory        30428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30428.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (F -> (G -> F))), M:tm-315, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30429
in-theory        30429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (F or ((A -> (B -> A)) and (C -> (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30429.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (F or ((A -> (B -> A)) and (C -> (D -> (D or E)))))), M:tm-311, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30430
in-theory        30430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (((A -> (B -> A)) and (C -> (D -> (D or E)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30430.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (((A -> (B -> A)) and (C -> (D -> (D or E)))) or F)), M:tm-310, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30431
in-theory        30431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (F -> (((A -> (B -> A)) and (C -> (D -> (D or E)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30431.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (F -> (((A -> (B -> A)) and (C -> (D -> (D or E)))) and F))), M:tm-309, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30432
in-theory        30432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (C -> (D -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-308 tm-461 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30432.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (C -> (D -> (D or E)))), M:tm-308, m:tm-461, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-30433
in-theory        30433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-461 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30433.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (A -> (B -> A))), M:tm-307, m:tm-461, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-30434
in-theory        30434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (F -> ((A -> (B -> A)) and (C -> (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30434.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (F -> ((A -> (B -> A)) and (C -> (D -> (D or E)))))), M:tm-305, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30435
in-theory        30435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30435.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-303, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30436
in-theory        30436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30436.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-270, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30437
in-theory        30437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30437.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-239, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30438
in-theory        30438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30438.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (H -> (H or I))))), M:tm-210, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30439
in-theory        30439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30439.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-183, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30440
in-theory        30440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30440.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-157, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30441
in-theory        30441
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30441.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-147, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30442
in-theory        30442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30442.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-134, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30443
in-theory        30443
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30443.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-125, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30444
in-theory        30444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30444.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (H or I))))), M:tm-113, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30445
in-theory        30445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30445.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-105, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30446
in-theory        30446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30446.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (F -> (F or G))))), M:tm-95, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30447
in-theory        30447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30447.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-83, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30448
in-theory        30448
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30448.        (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (E -> (E or F))))), M:tm-76, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30449
in-theory        30449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30449.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (F -> (F or G))))), M:tm-69, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30450
in-theory        30450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30450.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-54, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30451
in-theory        30451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30451.        ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (F -> (F or G))))), M:tm-42, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30452
in-theory        30452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30452.        ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (F -> (F or G))))), M:tm-32, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30453
in-theory        30453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30453.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (F or G))))), M:tm-23, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30454
in-theory        30454
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30454.        (((A and B) -> B) and ((C -> (D -> C)) and (E -> (F -> (F or G))))), M:tm-22, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30455
in-theory        30455
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30455.        (((A and B) -> A) and ((C -> (D -> C)) and (E -> (F -> (F or G))))), M:tm-21, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30456
in-theory        30456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30456.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-20, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30457
in-theory        30457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30457.        ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (F -> (F or G))))), M:tm-19, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30458
in-theory        30458
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-1 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30458.        (A or ((B -> (C -> B)) and (D -> (E -> (E or F))))), M:tm-7, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30459
in-theory        30459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30459.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) or F), M:tm-6, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30460
in-theory        30460
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> (E -> (E or F)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30460.        (A -> (((B -> (C -> B)) and (D -> (E -> (E or F)))) and A)), M:tm-5, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30461
in-theory        30461
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30461.        (A -> ((B -> (C -> B)) and (D -> (E -> (E or F))))), M:tm-1, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-30462
in-theory        30462
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30462.        (((A and ((B -> (B or C)) -> D)) -> D) and (E -> (E or F))), M:tm-456, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30463
in-theory        30463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-453 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30463.        ((A -> ((B -> (B or C)) and A)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-453, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30464
in-theory        30464
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) or ((D -> (D or E)) and ((A -> (A or B)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-450 tm-462 ((Am (-> A (or A B))) (C (-> (-> Bm (or Bm Cm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30464.        ((((A -> (A or B)) -> C) or ((D -> (D or E)) and ((A -> (A or B)) -> C))) -> C), M:tm-450, m:tm-462, u:((Am (-> A (or A B))) (C (-> (-> Bm (or Bm Cm)) Dm)) (D Dm))
================================================================
tm-name          tm-30465
in-theory        30465
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and ((E -> (E or F)) and ((A and ((B -> (B or C)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-443 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30465.        (((A and ((B -> (B or C)) -> D)) -> D) and ((E -> (E or F)) and ((A and ((B -> (B or C)) -> D)) -> D))), M:tm-443, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30466
in-theory        30466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-409 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30466.        (((A -> (A or B)) or C) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-409, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30467
in-theory        30467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-400 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30467.        (((A -> (B -> (A and B))) or C) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-400, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30468
in-theory        30468
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-391 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30468.        ((((A and B) -> B) or C) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-391, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30469
in-theory        30469
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-382 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30469.        ((((A and B) -> A) or C) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-382, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30470
in-theory        30470
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and ((F -> (F or G)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-373 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30470.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and ((F -> (F or G)) -> H)) -> H)), M:tm-373, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30471
in-theory        30471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-364 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30471.        (((A -> (B -> A)) or C) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-364, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30472
in-theory        30472
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> D)) -> (E -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-355 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-5 tm-4 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30472.        ((A and ((B -> (B or C)) -> D)) -> (E -> (D and E))), M:tm-355, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-30473
in-theory        30473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-354 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30473.        ((A -> (B -> (C -> (B and C)))) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-354, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30474
in-theory        30474
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (B or C)) -> (not (D -> (E -> (D and E)))))))
theorem-size     17
proof            (modus-ponens tm-350 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) (not (-> B (-> C (and B C))))))) (Dm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30474.        (not (A and ((B -> (B or C)) -> (not (D -> (E -> (D and E))))))), M:tm-350, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) (not (-> B (-> C (and B C))))))) (Dm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-30475
in-theory        30475
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30475.        (((A and ((B -> (B or C)) -> D)) -> D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30476
in-theory        30476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C and ((D -> (D or E)) -> F)) -> F))
theorem-size     21
proof            (modus-ponens tm-338 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30476.        (((A -> B) -> (A -> (A and B))) and ((C and ((D -> (D or E)) -> F)) -> F)), M:tm-338, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30477
in-theory        30477
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and ((A and ((B -> (B or C)) -> D)) -> ((A and ((B -> (B or C)) -> D)) and D)))
theorem-size     33
proof            (modus-ponens tm-328 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30477.        (((A and ((B -> (B or C)) -> D)) -> D) and ((A and ((B -> (B or C)) -> D)) -> ((A and ((B -> (B or C)) -> D)) and D))), M:tm-328, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-30478
in-theory        30478
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and ((E -> (F -> (E and F))) and ((A and ((B -> (B or C)) -> D)) -> D)))
theorem-size     31
proof            (modus-ponens tm-327 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30478.        (((A and ((B -> (B or C)) -> D)) -> D) and ((E -> (F -> (E and F))) and ((A and ((B -> (B or C)) -> D)) -> D))), M:tm-327, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30479
in-theory        30479
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and (((E and F) -> F) and ((A and ((B -> (B or C)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-326 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30479.        (((A and ((B -> (B or C)) -> D)) -> D) and (((E and F) -> F) and ((A and ((B -> (B or C)) -> D)) -> D))), M:tm-326, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30480
in-theory        30480
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and (((E and F) -> E) and ((A and ((B -> (B or C)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-325 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30480.        (((A and ((B -> (B or C)) -> D)) -> D) and (((E and F) -> E) and ((A and ((B -> (B or C)) -> D)) -> D))), M:tm-325, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30481
in-theory        30481
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A and ((B -> (B or C)) -> D)) -> D)))
theorem-size     37
proof            (modus-ponens tm-324 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30481.        (((A and ((B -> (B or C)) -> D)) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A and ((B -> (B or C)) -> D)) -> D))), M:tm-324, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30482
in-theory        30482
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and ((E -> (F -> E)) and ((A and ((B -> (B or C)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-323 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30482.        (((A and ((B -> (B or C)) -> D)) -> D) and ((E -> (F -> E)) and ((A and ((B -> (B or C)) -> D)) -> D))), M:tm-323, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30483
in-theory        30483
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30483.        (((A and ((B -> (B or C)) -> D)) -> D) and ((E and F) -> F)), M:tm-322, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30484
in-theory        30484
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> (B -> (B or C)))) -> (B -> (B or C))) and ((A and ((B -> (B or C)) -> (B -> (B or C)))) -> (B -> (B or C))))
theorem-size     39
proof            (modus-ponens tm-321 tm-462 ((A Am) (Dm (-> Bm (or Bm Cm))) (C (-> Bm (or Bm Cm))) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30484.        (((A and ((B -> (B or C)) -> (B -> (B or C)))) -> (B -> (B or C))) and ((A and ((B -> (B or C)) -> (B -> (B or C)))) -> (B -> (B or C)))), M:tm-321, m:tm-462, u:((A Am) (Dm (-> Bm (or Bm Cm))) (C (-> Bm (or Bm Cm))) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-30485
in-theory        30485
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30485.        (((A and ((B -> (B or C)) -> D)) -> D) and ((E and F) -> E)), M:tm-320, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30486
in-theory        30486
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and ((C -> (C or D)) -> A)) -> A) and (((A -> B) and ((C -> (C or D)) -> A)) -> B))
theorem-size     27
proof            (modus-ponens tm-319 tm-462 ((Am (-> Dm B)) (C (-> (-> Bm (or Bm Cm)) Dm)) (A Dm)))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30486.        ((((A -> B) and ((C -> (C or D)) -> A)) -> A) and (((A -> B) and ((C -> (C or D)) -> A)) -> B)), M:tm-319, m:tm-462, u:((Am (-> Dm B)) (C (-> (-> Bm (or Bm Cm)) Dm)) (A Dm))
================================================================
tm-name          tm-30487
in-theory        30487
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30487.        (((A and ((B -> (B or C)) -> D)) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30488
in-theory        30488
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and ((A and ((B -> (B or C)) -> D)) -> (A and ((B -> (B or C)) -> D))))
theorem-size     31
proof            (modus-ponens tm-316 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30488.        (((A and ((B -> (B or C)) -> D)) -> D) and ((A and ((B -> (B or C)) -> D)) -> (A and ((B -> (B or C)) -> D)))), M:tm-316, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-30489
in-theory        30489
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30489.        (((A and ((B -> (B or C)) -> D)) -> D) and (E -> (F -> E))), M:tm-315, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30490
in-theory        30490
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and (((A and ((B -> (B or C)) -> D)) -> (not D)) -> (not (A and ((B -> (B or C)) -> D)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-9 tm-4 tm-1 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30490.        (((A and ((B -> (B or C)) -> D)) -> D) and (((A and ((B -> (B or C)) -> D)) -> (not D)) -> (not (A and ((B -> (B or C)) -> D))))), M:tm-313, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-30491
in-theory        30491
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and ((D -> E) -> (((A and ((B -> (B or C)) -> D)) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-312 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30491.        (((A and ((B -> (B or C)) -> D)) -> D) and ((D -> E) -> (((A and ((B -> (B or C)) -> D)) or D) -> E))), M:tm-312, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-30492
in-theory        30492
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and (E or ((A and ((B -> (B or C)) -> D)) -> D)))
theorem-size     25
proof            (modus-ponens tm-311 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30492.        (((A and ((B -> (B or C)) -> D)) -> D) and (E or ((A and ((B -> (B or C)) -> D)) -> D))), M:tm-311, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30493
in-theory        30493
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and (((A and ((B -> (B or C)) -> D)) -> D) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30493.        (((A and ((B -> (B or C)) -> D)) -> D) and (((A and ((B -> (B or C)) -> D)) -> D) or E)), M:tm-310, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30494
in-theory        30494
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and (E -> (((A and ((B -> (B or C)) -> D)) -> D) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30494.        (((A and ((B -> (B or C)) -> D)) -> D) and (E -> (((A and ((B -> (B or C)) -> D)) -> D) and E))), M:tm-309, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30495
in-theory        30495
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> (D -> E))) -> (D -> E)) and (((A and ((B -> (B or C)) -> (D -> E))) -> D) -> ((A and ((B -> (B or C)) -> (D -> E))) -> E)))
theorem-size     43
proof            (modus-ponens tm-306 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30495.        (((A and ((B -> (B or C)) -> (D -> E))) -> (D -> E)) and (((A and ((B -> (B or C)) -> (D -> E))) -> D) -> ((A and ((B -> (B or C)) -> (D -> E))) -> E))), M:tm-306, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-30496
in-theory        30496
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and (E -> ((A and ((B -> (B or C)) -> D)) -> D)))
theorem-size     25
proof            (modus-ponens tm-305 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30496.        (((A and ((B -> (B or C)) -> D)) -> D) and (E -> ((A and ((B -> (B or C)) -> D)) -> D))), M:tm-305, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30497
in-theory        30497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-303 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30497.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-303, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30498
in-theory        30498
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) or ((D -> (E -> (D and E))) and ((A -> (A or B)) -> C))) -> C)
theorem-size     25
proof            (modus-ponens tm-300 tm-462 ((Am (-> A (-> B (and A B)))) (C (-> (-> Bm (or Bm Cm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30498.        ((((A -> (A or B)) -> C) or ((D -> (E -> (D and E))) and ((A -> (A or B)) -> C))) -> C), M:tm-300, m:tm-462, u:((Am (-> A (-> B (and A B)))) (C (-> (-> Bm (or Bm Cm)) Dm)) (D Dm))
================================================================
tm-name          tm-30499
in-theory        30499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-270 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30499.        ((A -> (((B and C) -> C) and A)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-270, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30500
in-theory        30500
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) or (((D and E) -> E) and ((A -> (A or B)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-267 tm-462 ((Am (-> (and A B) B)) (C (-> (-> Bm (or Bm Cm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30500.        ((((A -> (A or B)) -> C) or (((D and E) -> E) and ((A -> (A or B)) -> C))) -> C), M:tm-267, m:tm-462, u:((Am (-> (and A B) B)) (C (-> (-> Bm (or Bm Cm)) Dm)) (D Dm))
================================================================
tm-name          tm-30501
in-theory        30501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-239 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30501.        ((A -> (((B and C) -> B) and A)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-239, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30502
in-theory        30502
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) or (((D and E) -> D) and ((A -> (A or B)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-236 tm-462 ((Am (-> (and A B) A)) (C (-> (-> Bm (or Bm Cm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-4 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30502.        ((((A -> (A or B)) -> C) or (((D and E) -> D) and ((A -> (A or B)) -> C))) -> C), M:tm-236, m:tm-462, u:((Am (-> (and A B) A)) (C (-> (-> Bm (or Bm Cm)) Dm)) (D Dm))
================================================================
tm-name          tm-30503
in-theory        30503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and ((F -> (F or G)) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-210 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30503.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and ((F -> (F or G)) -> H)) -> H)), M:tm-210, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30504
in-theory        30504
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (A or B)) -> C))) -> C)
theorem-size     31
proof            (modus-ponens tm-207 tm-462 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm (or Bm Cm)) Dm)) (E Dm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30504.        ((((A -> (A or B)) -> C) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (A or B)) -> C))) -> C), M:tm-207, m:tm-462, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm (or Bm Cm)) Dm)) (E Dm))
================================================================
tm-name          tm-30505
in-theory        30505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-183 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30505.        ((A -> ((B -> (C -> B)) and A)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-183, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30506
in-theory        30506
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) or ((D -> (E -> D)) and ((A -> (A or B)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-180 tm-462 ((Am (-> A (-> B A))) (C (-> (-> Bm (or Bm Cm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30506.        ((((A -> (A or B)) -> C) or ((D -> (E -> D)) and ((A -> (A or B)) -> C))) -> C), M:tm-180, m:tm-462, u:((Am (-> A (-> B A))) (C (-> (-> Bm (or Bm Cm)) Dm)) (D Dm))
================================================================
tm-name          tm-30507
in-theory        30507
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> (D and E))) -> E)
theorem-size     13
proof            (modus-ponens tm-158 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) (and B C)))) (Dm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30507.        ((A and ((B -> (B or C)) -> (D and E))) -> E), M:tm-158, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) (and B C)))) (Dm (and B C)))
================================================================
tm-name          tm-30508
in-theory        30508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-157 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30508.        ((A -> ((B and C) -> C)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-157, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30509
in-theory        30509
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (B or C)) -> (not ((D and E) -> E)))))
theorem-size     15
proof            (modus-ponens tm-153 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) (not (-> (and B C) C))))) (Dm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30509.        (not (A and ((B -> (B or C)) -> (not ((D and E) -> E))))), M:tm-153, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) (not (-> (and B C) C))))) (Dm (not (-> (and B C) C))))
================================================================
tm-name          tm-30510
in-theory        30510
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-147 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30510.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-147, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30511
in-theory        30511
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> (B -> (B or C)))) -> (B -> (B or C)))
theorem-size     19
proof            (modus-ponens tm-142 tm-462 ((A Am) (Dm (-> Bm (or Bm Cm))) (C (-> Bm (or Bm Cm))) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30511.        ((A and ((B -> (B or C)) -> (B -> (B or C)))) -> (B -> (B or C))), M:tm-142, m:tm-462, u:((A Am) (Dm (-> Bm (or Bm Cm))) (C (-> Bm (or Bm Cm))) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-30512
in-theory        30512
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> (D and E))) -> D)
theorem-size     13
proof            (modus-ponens tm-135 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) (and B C)))) (Dm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30512.        ((A and ((B -> (B or C)) -> (D and E))) -> D), M:tm-135, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) (and B C)))) (Dm (and B C)))
================================================================
tm-name          tm-30513
in-theory        30513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-134 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30513.        ((A -> ((B and C) -> B)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-134, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30514
in-theory        30514
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (B or C)) -> (not ((D and E) -> D)))))
theorem-size     15
proof            (modus-ponens tm-130 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) (not (-> (and B C) B))))) (Dm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30514.        (not (A and ((B -> (B or C)) -> (not ((D and E) -> D))))), M:tm-130, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) (not (-> (and B C) B))))) (Dm (not (-> (and B C) B))))
================================================================
tm-name          tm-30515
in-theory        30515
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> (A -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-129 tm-462 ((A Am) (B (-> (-> Bm (or Bm Cm)) (-> Am C))) (Dm (-> Am C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30515.        ((A and ((B -> (B or C)) -> (A -> D))) -> D), M:tm-129, m:tm-462, u:((A Am) (B (-> (-> Bm (or Bm Cm)) (-> Am C))) (Dm (-> Am C)))
================================================================
tm-name          tm-30516
in-theory        30516
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-125 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30516.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-125, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30517
in-theory        30517
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and ((C -> (C or D)) -> A)) -> A)
theorem-size     13
proof            (modus-ponens tm-120 tm-462 ((Am (-> Dm B)) (C (-> (-> Bm (or Bm Cm)) Dm)) (A Dm)))
axioms-used      (tm-2 tm-1 tm-3 tm-4 tm-6)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30517.        (((A -> B) and ((C -> (C or D)) -> A)) -> A), M:tm-120, m:tm-462, u:((Am (-> Dm B)) (C (-> (-> Bm (or Bm Cm)) Dm)) (A Dm))
================================================================
tm-name          tm-30518
in-theory        30518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) and ((C -> (C or D)) -> (A -> B))) -> B)
theorem-size     17
proof            (modus-ponens tm-119 tm-462 ((Am (-> (-> A B) A)) (C (-> (-> Bm (or Bm Cm)) (-> A B))) (Dm (-> A B))))
axioms-used      (tm-2 tm-3 tm-4 tm-1 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30518.        ((((A -> B) -> A) and ((C -> (C or D)) -> (A -> B))) -> B), M:tm-119, m:tm-462, u:((Am (-> (-> A B) A)) (C (-> (-> Bm (or Bm Cm)) (-> A B))) (Dm (-> A B)))
================================================================
tm-name          tm-30519
in-theory        30519
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> (D -> (E -> F)))) -> ((D -> E) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-114 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) (-> B (-> C D))))) (Dm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-4 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30519.        ((A and ((B -> (B or C)) -> (D -> (E -> F)))) -> ((D -> E) -> (D -> F))), M:tm-114, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) (-> B (-> C D))))) (Dm (-> B (-> C D))))
================================================================
tm-name          tm-30520
in-theory        30520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (F or G)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-113 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30520.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (F or G)) -> H)) -> H)), M:tm-113, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30521
in-theory        30521
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (B or C)) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     23
proof            (modus-ponens tm-109 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Dm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30521.        (not (A and ((B -> (B or C)) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-109, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Dm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-30522
in-theory        30522
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     31
proof            (modus-ponens tm-105 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30522.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-105, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30523
in-theory        30523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C and ((D -> (D or E)) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-95 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30523.        (((A -> B) -> (A -> A)) and ((C and ((D -> (D or E)) -> F)) -> F)), M:tm-95, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30524
in-theory        30524
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> (D -> E))) -> (D -> E))
theorem-size     15
proof            (modus-ponens tm-87 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30524.        ((A and ((B -> (B or C)) -> (D -> E))) -> (D -> E)), M:tm-87, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-30525
in-theory        30525
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> D)) -> (E -> D))
theorem-size     13
proof            (modus-ponens tm-84 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-4 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30525.        ((A and ((B -> (B or C)) -> D)) -> (E -> D)), M:tm-84, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-30526
in-theory        30526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-83 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30526.        ((A -> (B -> (C -> B))) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-83, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30527
in-theory        30527
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (B or C)) -> (not (D -> (E -> D))))))
theorem-size     15
proof            (modus-ponens tm-79 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) (not (-> B (-> C B)))))) (Dm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30527.        (not (A and ((B -> (B or C)) -> (not (D -> (E -> D)))))), M:tm-79, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) (not (-> B (-> C B)))))) (Dm (not (-> B (-> C B)))))
================================================================
tm-name          tm-30528
in-theory        30528
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B and ((C -> (C or D)) -> E)) -> E))
theorem-size     17
proof            (modus-ponens tm-76 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-10 tm-2 tm-4 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30528.        (((not (not A)) -> A) and ((B and ((C -> (C or D)) -> E)) -> E)), M:tm-76, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30529
in-theory        30529
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A and ((B -> (B or C)) -> D)))) or (A and ((B -> (B or C)) -> D))) -> D)
theorem-size     23
proof            (modus-ponens tm-73 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-8 tm-10 tm-2 tm-4 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30529.        (((not (not (A and ((B -> (B or C)) -> D)))) or (A and ((B -> (B or C)) -> D))) -> D), M:tm-73, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-30530
in-theory        30530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and ((D -> (D or E)) -> F)) -> F))
theorem-size     23
proof            (modus-ponens tm-69 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-9 tm-2 tm-4 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30530.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and ((D -> (D or E)) -> F)) -> F)), M:tm-69, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30531
in-theory        30531
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (B or C)) -> (not A))))
theorem-size     11
proof            (modus-ponens tm-59 tm-462 ((A Am) (B (-> (-> Bm (or Bm Cm)) (not Am))) (Dm (not Am))))
axioms-used      (tm-9 tm-3 tm-2 tm-4 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30531.        (not (A and ((B -> (B or C)) -> (not A)))), M:tm-59, m:tm-462, u:((A Am) (B (-> (-> Bm (or Bm Cm)) (not Am))) (Dm (not Am)))
================================================================
tm-name          tm-30532
in-theory        30532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-54 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30532.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-54, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30533
in-theory        30533
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and ((C -> (C or D)) -> E))) or (B and ((C -> (C or D)) -> E))) -> E)
theorem-size     23
proof            (modus-ponens tm-47 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30533.        (((A and (B and ((C -> (C or D)) -> E))) or (B and ((C -> (C or D)) -> E))) -> E), M:tm-47, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-30534
in-theory        30534
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (B or C)) -> D)) and E) or (A and ((B -> (B or C)) -> D))) -> D)
theorem-size     23
proof            (modus-ponens tm-46 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-8 tm-3 tm-2 tm-4 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30534.        ((((A and ((B -> (B or C)) -> D)) and E) or (A and ((B -> (B or C)) -> D))) -> D), M:tm-46, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-30535
in-theory        30535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C and ((D -> (D or E)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-42 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30535.        ((A -> (B or A)) and ((C and ((D -> (D or E)) -> F)) -> F)), M:tm-42, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30536
in-theory        30536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C and ((D -> (D or E)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-32 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30536.        ((A -> (A or B)) and ((C and ((D -> (D or E)) -> F)) -> F)), M:tm-32, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30537
in-theory        30537
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> D)) -> ((A and ((B -> (B or C)) -> D)) and D))
theorem-size     21
proof            (modus-ponens tm-24 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30537.        ((A and ((B -> (B or C)) -> D)) -> ((A and ((B -> (B or C)) -> D)) and D)), M:tm-24, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-30538
in-theory        30538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C and ((D -> (D or E)) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-23 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30538.        ((A -> (B -> (A and B))) and ((C and ((D -> (D or E)) -> F)) -> F)), M:tm-23, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30539
in-theory        30539
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C and ((D -> (D or E)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-22 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30539.        (((A and B) -> B) and ((C and ((D -> (D or E)) -> F)) -> F)), M:tm-22, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30540
in-theory        30540
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C and ((D -> (D or E)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-21 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30540.        (((A and B) -> A) and ((C and ((D -> (D or E)) -> F)) -> F)), M:tm-21, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30541
in-theory        30541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-20 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30541.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-20, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30542
in-theory        30542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C and ((D -> (D or E)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-19 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30542.        ((A -> (B -> A)) and ((C and ((D -> (D or E)) -> F)) -> F)), M:tm-19, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30543
in-theory        30543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and ((C -> (C or D)) -> A)) -> B)
theorem-size     13
proof            (modus-ponens tm-15 tm-462 ((Am (-> Dm B)) (C (-> (-> Bm (or Bm Cm)) Dm)) (A Dm)))
axioms-used      (tm-2 tm-3 tm-4 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30543.        (((A -> B) and ((C -> (C or D)) -> A)) -> B), M:tm-15, m:tm-462, u:((Am (-> Dm B)) (C (-> (-> Bm (or Bm Cm)) Dm)) (A Dm))
================================================================
tm-name          tm-30544
in-theory        30544
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> D)) -> (A and ((B -> (B or C)) -> D)))
theorem-size     19
proof            (modus-ponens tm-12 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-4 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30544.        ((A and ((B -> (B or C)) -> D)) -> (A and ((B -> (B or C)) -> D))), M:tm-12, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-30545
in-theory        30545
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> (not D)) -> (not (A and ((B -> (B or C)) -> D))))
theorem-size     23
proof            (modus-ponens tm-9 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-9 tm-2 tm-4 tm-1 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30545.        (((A and ((B -> (B or C)) -> D)) -> (not D)) -> (not (A and ((B -> (B or C)) -> D)))), M:tm-9, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-30546
in-theory        30546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C and ((D -> (D or E)) -> A)) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30546.        ((A -> B) -> (((C and ((D -> (D or E)) -> A)) or A) -> B)), M:tm-8, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-30547
in-theory        30547
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B and ((C -> (C or D)) -> E)) -> E))
theorem-size     13
proof            (modus-ponens tm-7 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-7 tm-2 tm-4 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30547.        (A or ((B and ((C -> (C or D)) -> E)) -> E)), M:tm-7, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30548
in-theory        30548
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-6 tm-2 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30548.        (((A and ((B -> (B or C)) -> D)) -> D) or E), M:tm-6, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30549
in-theory        30549
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and ((C -> (C or D)) -> E)) -> E) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30549.        (A -> (((B and ((C -> (C or D)) -> E)) -> E) and A)), M:tm-5, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30550
in-theory        30550
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> (D -> E))) -> D) -> ((A and ((B -> (B or C)) -> (D -> E))) -> E))
theorem-size     27
proof            (modus-ponens tm-2 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-4 tm-1 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30550.        (((A and ((B -> (B or C)) -> (D -> E))) -> D) -> ((A and ((B -> (B or C)) -> (D -> E))) -> E)), M:tm-2, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-30551
in-theory        30551
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B and ((C -> (C or D)) -> E)) -> E))
theorem-size     13
proof            (modus-ponens tm-1 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-1 tm-2 tm-4 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30551.        (A -> ((B and ((C -> (C or D)) -> E)) -> E)), M:tm-1, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-30552
in-theory        30552
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30552.        (((((A -> (A or B)) -> C) and D) -> C) and (E -> (E or F))), M:tm-456, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30553
in-theory        30553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-453 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30553.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-453, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30554
in-theory        30554
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (B or C)) -> ((B -> (B or C)) or D)) and A)) -> ((B -> (B or C)) or D))
theorem-size     25
proof            (modus-ponens tm-450 tm-463 ((A (-> Am (or Am Bm))) (Cm (or (-> Am (or Am Bm)) B)) (C Dm) (D (or (-> Am (or Am Bm)) B))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30554.        ((A or (((B -> (B or C)) -> ((B -> (B or C)) or D)) and A)) -> ((B -> (B or C)) or D)), M:tm-450, m:tm-463, u:((A (-> Am (or Am Bm))) (Cm (or (-> Am (or Am Bm)) B)) (C Dm) (D (or (-> Am (or Am Bm)) B)))
================================================================
tm-name          tm-30555
in-theory        30555
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and ((E -> (E or F)) and ((((A -> (A or B)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-443 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30555.        (((((A -> (A or B)) -> C) and D) -> C) and ((E -> (E or F)) and ((((A -> (A or B)) -> C) and D) -> C))), M:tm-443, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30556
in-theory        30556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-409 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30556.        (((A -> (A or B)) or C) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-409, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30557
in-theory        30557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-400 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30557.        (((A -> (B -> (A and B))) or C) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-400, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30558
in-theory        30558
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-391 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30558.        ((((A and B) -> B) or C) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-391, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30559
in-theory        30559
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-382 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30559.        ((((A and B) -> A) or C) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-382, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30560
in-theory        30560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (E or F)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-373 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30560.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (E or F)) -> G) and H) -> G)), M:tm-373, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30561
in-theory        30561
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-364 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30561.        (((A -> (B -> A)) or C) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-364, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30562
in-theory        30562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) and D) -> (E -> (C and E)))
theorem-size     15
proof            (modus-ponens tm-355 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-5 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30562.        ((((A -> (A or B)) -> C) and D) -> (E -> (C and E))), M:tm-355, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-30563
in-theory        30563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-354 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30563.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-354, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30564
in-theory        30564
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (A or B)) -> (not (C -> (D -> (C and D))))) and E))
theorem-size     17
proof            (modus-ponens tm-350 tm-463 ((A (and (-> (-> Am (or Am Bm)) (not (-> B (-> C (and B C))))) Dm)) (Cm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30564.        (not (((A -> (A or B)) -> (not (C -> (D -> (C and D))))) and E)), M:tm-350, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) (not (-> B (-> C (and B C))))) Dm)) (Cm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-30565
in-theory        30565
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30565.        (((((A -> (A or B)) -> C) and D) -> C) and (E -> (F -> (E and F)))), M:tm-341, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30566
in-theory        30566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (C or D)) -> E) and F) -> E))
theorem-size     21
proof            (modus-ponens tm-338 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30566.        (((A -> B) -> (A -> (A and B))) and ((((C -> (C or D)) -> E) and F) -> E)), M:tm-338, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30567
in-theory        30567
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and ((((A -> (A or B)) -> C) and D) -> ((((A -> (A or B)) -> C) and D) and C)))
theorem-size     33
proof            (modus-ponens tm-328 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30567.        (((((A -> (A or B)) -> C) and D) -> C) and ((((A -> (A or B)) -> C) and D) -> ((((A -> (A or B)) -> C) and D) and C))), M:tm-328, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-30568
in-theory        30568
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and ((E -> (F -> (E and F))) and ((((A -> (A or B)) -> C) and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-327 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30568.        (((((A -> (A or B)) -> C) and D) -> C) and ((E -> (F -> (E and F))) and ((((A -> (A or B)) -> C) and D) -> C))), M:tm-327, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30569
in-theory        30569
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and (((E and F) -> F) and ((((A -> (A or B)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-326 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30569.        (((((A -> (A or B)) -> C) and D) -> C) and (((E and F) -> F) and ((((A -> (A or B)) -> C) and D) -> C))), M:tm-326, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30570
in-theory        30570
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and (((E and F) -> E) and ((((A -> (A or B)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-325 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30570.        (((((A -> (A or B)) -> C) and D) -> C) and (((E and F) -> E) and ((((A -> (A or B)) -> C) and D) -> C))), M:tm-325, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30571
in-theory        30571
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (A or B)) -> C) and D) -> C)))
theorem-size     37
proof            (modus-ponens tm-324 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30571.        (((((A -> (A or B)) -> C) and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (A or B)) -> C) and D) -> C))), M:tm-324, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30572
in-theory        30572
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and ((E -> (F -> E)) and ((((A -> (A or B)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-323 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30572.        (((((A -> (A or B)) -> C) and D) -> C) and ((E -> (F -> E)) and ((((A -> (A or B)) -> C) and D) -> C))), M:tm-323, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30573
in-theory        30573
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30573.        (((((A -> (A or B)) -> C) and D) -> C) and ((E and F) -> F)), M:tm-322, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30574
in-theory        30574
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and (C -> D)) -> C) and ((((A -> (A or B)) -> C) and (C -> D)) -> D))
theorem-size     27
proof            (modus-ponens tm-321 tm-463 ((A (-> (-> Am (or Am Bm)) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30574.        (((((A -> (A or B)) -> C) and (C -> D)) -> C) and ((((A -> (A or B)) -> C) and (C -> D)) -> D)), M:tm-321, m:tm-463, u:((A (-> (-> Am (or Am Bm)) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-30575
in-theory        30575
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30575.        (((((A -> (A or B)) -> C) and D) -> C) and ((E and F) -> E)), M:tm-320, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30576
in-theory        30576
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> (A -> (A or B))) and C) -> (A -> (A or B))) and ((((A -> (A or B)) -> (A -> (A or B))) and C) -> (A -> (A or B))))
theorem-size     39
proof            (modus-ponens tm-319 tm-463 ((Cm (-> Am (or Am Bm))) (B (-> Am (or Am Bm))) (C Dm) (A (-> Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30576.        (((((A -> (A or B)) -> (A -> (A or B))) and C) -> (A -> (A or B))) and ((((A -> (A or B)) -> (A -> (A or B))) and C) -> (A -> (A or B)))), M:tm-319, m:tm-463, u:((Cm (-> Am (or Am Bm))) (B (-> Am (or Am Bm))) (C Dm) (A (-> Am (or Am Bm))))
================================================================
tm-name          tm-30577
in-theory        30577
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30577.        (((((A -> (A or B)) -> C) and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30578
in-theory        30578
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and ((((A -> (A or B)) -> C) and D) -> (((A -> (A or B)) -> C) and D)))
theorem-size     31
proof            (modus-ponens tm-316 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30578.        (((((A -> (A or B)) -> C) and D) -> C) and ((((A -> (A or B)) -> C) and D) -> (((A -> (A or B)) -> C) and D))), M:tm-316, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-30579
in-theory        30579
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30579.        (((((A -> (A or B)) -> C) and D) -> C) and (E -> (F -> E))), M:tm-315, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30580
in-theory        30580
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and (((((A -> (A or B)) -> C) and D) -> (not C)) -> (not (((A -> (A or B)) -> C) and D))))
theorem-size     35
proof            (modus-ponens tm-313 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-9 tm-3 tm-1 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30580.        (((((A -> (A or B)) -> C) and D) -> C) and (((((A -> (A or B)) -> C) and D) -> (not C)) -> (not (((A -> (A or B)) -> C) and D)))), M:tm-313, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-30581
in-theory        30581
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and ((C -> E) -> (((((A -> (A or B)) -> C) and D) or C) -> E)))
theorem-size     29
proof            (modus-ponens tm-312 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30581.        (((((A -> (A or B)) -> C) and D) -> C) and ((C -> E) -> (((((A -> (A or B)) -> C) and D) or C) -> E))), M:tm-312, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-30582
in-theory        30582
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and (E or ((((A -> (A or B)) -> C) and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-311 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30582.        (((((A -> (A or B)) -> C) and D) -> C) and (E or ((((A -> (A or B)) -> C) and D) -> C))), M:tm-311, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30583
in-theory        30583
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and (((((A -> (A or B)) -> C) and D) -> C) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30583.        (((((A -> (A or B)) -> C) and D) -> C) and (((((A -> (A or B)) -> C) and D) -> C) or E)), M:tm-310, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30584
in-theory        30584
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and (E -> (((((A -> (A or B)) -> C) and D) -> C) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30584.        (((((A -> (A or B)) -> C) and D) -> C) and (E -> (((((A -> (A or B)) -> C) and D) -> C) and E))), M:tm-309, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30585
in-theory        30585
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> (C -> D)) and E) -> (C -> D)) and (((((A -> (A or B)) -> (C -> D)) and E) -> C) -> ((((A -> (A or B)) -> (C -> D)) and E) -> D)))
theorem-size     43
proof            (modus-ponens tm-306 tm-463 ((A (and (-> (-> Am (or Am Bm)) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30585.        (((((A -> (A or B)) -> (C -> D)) and E) -> (C -> D)) and (((((A -> (A or B)) -> (C -> D)) and E) -> C) -> ((((A -> (A or B)) -> (C -> D)) and E) -> D))), M:tm-306, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-30586
in-theory        30586
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and (E -> ((((A -> (A or B)) -> C) and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-305 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30586.        (((((A -> (A or B)) -> C) and D) -> C) and (E -> ((((A -> (A or B)) -> C) and D) -> C))), M:tm-305, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30587
in-theory        30587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-303 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30587.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-303, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30588
in-theory        30588
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (B or C)) -> (D -> ((B -> (B or C)) and D))) and A)) -> (D -> ((B -> (B or C)) and D)))
theorem-size     29
proof            (modus-ponens tm-300 tm-463 ((A (-> Am (or Am Bm))) (Cm (-> B (and (-> Am (or Am Bm)) B))) (C Dm) (D (-> B (and (-> Am (or Am Bm)) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30588.        ((A or (((B -> (B or C)) -> (D -> ((B -> (B or C)) and D))) and A)) -> (D -> ((B -> (B or C)) and D))), M:tm-300, m:tm-463, u:((A (-> Am (or Am Bm))) (Cm (-> B (and (-> Am (or Am Bm)) B))) (C Dm) (D (-> B (and (-> Am (or Am Bm)) B))))
================================================================
tm-name          tm-30589
in-theory        30589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-270 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30589.        ((A -> (((B and C) -> C) and A)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-270, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30590
in-theory        30590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-239 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30590.        ((A -> (((B and C) -> B) and A)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-239, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30591
in-theory        30591
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (E or F)) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-210 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30591.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (E or F)) -> G) and H) -> G)), M:tm-210, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30592
in-theory        30592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-183 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30592.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-183, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30593
in-theory        30593
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (B or C)) -> (D -> (B -> (B or C)))) and A)) -> (D -> (B -> (B or C))))
theorem-size     25
proof            (modus-ponens tm-180 tm-463 ((A (-> Am (or Am Bm))) (Cm (-> B (-> Am (or Am Bm)))) (C Dm) (D (-> B (-> Am (or Am Bm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30593.        ((A or (((B -> (B or C)) -> (D -> (B -> (B or C)))) and A)) -> (D -> (B -> (B or C)))), M:tm-180, m:tm-463, u:((A (-> Am (or Am Bm))) (Cm (-> B (-> Am (or Am Bm)))) (C Dm) (D (-> B (-> Am (or Am Bm)))))
================================================================
tm-name          tm-30594
in-theory        30594
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> (C and D)) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-158 tm-463 ((A (and (-> (-> Am (or Am Bm)) (and B C)) Dm)) (Cm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30594.        ((((A -> (A or B)) -> (C and D)) and E) -> D), M:tm-158, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) (and B C)) Dm)) (Cm (and B C)))
================================================================
tm-name          tm-30595
in-theory        30595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-157 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30595.        ((A -> ((B and C) -> C)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-157, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30596
in-theory        30596
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (A or B)) -> (not ((C and D) -> D))) and E))
theorem-size     15
proof            (modus-ponens tm-153 tm-463 ((A (and (-> (-> Am (or Am Bm)) (not (-> (and B C) C))) Dm)) (Cm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30596.        (not (((A -> (A or B)) -> (not ((C and D) -> D))) and E)), M:tm-153, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) (not (-> (and B C) C))) Dm)) (Cm (not (-> (and B C) C))))
================================================================
tm-name          tm-30597
in-theory        30597
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> (C -> D)) and C) -> D)
theorem-size     13
proof            (modus-ponens tm-152 tm-463 ((A (-> (-> Am (or Am Bm)) (-> Dm C))) (B Dm) (Cm (-> Dm C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30597.        ((((A -> (A or B)) -> (C -> D)) and C) -> D), M:tm-152, m:tm-463, u:((A (-> (-> Am (or Am Bm)) (-> Dm C))) (B Dm) (Cm (-> Dm C)))
================================================================
tm-name          tm-30598
in-theory        30598
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-147 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30598.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-147, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30599
in-theory        30599
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) and (C -> D)) -> C)
theorem-size     13
proof            (modus-ponens tm-142 tm-463 ((A (-> (-> Am (or Am Bm)) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-4 tm-3 tm-6)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30599.        ((((A -> (A or B)) -> C) and (C -> D)) -> C), M:tm-142, m:tm-463, u:((A (-> (-> Am (or Am Bm)) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-30600
in-theory        30600
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> (C -> D)) and ((C -> D) -> C)) -> D)
theorem-size     17
proof            (modus-ponens tm-141 tm-463 ((A (-> (-> Am (or Am Bm)) (-> B C))) (Dm (-> (-> B C) B)) (Cm (-> B C))))
axioms-used      (tm-2 tm-4 tm-3 tm-1 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30600.        ((((A -> (A or B)) -> (C -> D)) and ((C -> D) -> C)) -> D), M:tm-141, m:tm-463, u:((A (-> (-> Am (or Am Bm)) (-> B C))) (Dm (-> (-> B C) B)) (Cm (-> B C)))
================================================================
tm-name          tm-30601
in-theory        30601
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> (C and D)) and E) -> C)
theorem-size     13
proof            (modus-ponens tm-135 tm-463 ((A (and (-> (-> Am (or Am Bm)) (and B C)) Dm)) (Cm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30601.        ((((A -> (A or B)) -> (C and D)) and E) -> C), M:tm-135, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) (and B C)) Dm)) (Cm (and B C)))
================================================================
tm-name          tm-30602
in-theory        30602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-134 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30602.        ((A -> ((B and C) -> B)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-134, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30603
in-theory        30603
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (A or B)) -> (not ((C and D) -> C))) and E))
theorem-size     15
proof            (modus-ponens tm-130 tm-463 ((A (and (-> (-> Am (or Am Bm)) (not (-> (and B C) B))) Dm)) (Cm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30603.        (not (((A -> (A or B)) -> (not ((C and D) -> C))) and E)), M:tm-130, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) (not (-> (and B C) B))) Dm)) (Cm (not (-> (and B C) B))))
================================================================
tm-name          tm-30604
in-theory        30604
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-125 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30604.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-125, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30605
in-theory        30605
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> (A -> (A or B))) and C) -> (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-120 tm-463 ((Cm (-> Am (or Am Bm))) (B (-> Am (or Am Bm))) (C Dm) (A (-> Am (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30605.        ((((A -> (A or B)) -> (A -> (A or B))) and C) -> (A -> (A or B))), M:tm-120, m:tm-463, u:((Cm (-> Am (or Am Bm))) (B (-> Am (or Am Bm))) (C Dm) (A (-> Am (or Am Bm))))
================================================================
tm-name          tm-30606
in-theory        30606
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> (C -> (D -> E))) and F) -> ((C -> D) -> (C -> E)))
theorem-size     21
proof            (modus-ponens tm-114 tm-463 ((A (and (-> (-> Am (or Am Bm)) (-> B (-> C D))) Dm)) (Cm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-3 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30606.        ((((A -> (A or B)) -> (C -> (D -> E))) and F) -> ((C -> D) -> (C -> E))), M:tm-114, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) (-> B (-> C D))) Dm)) (Cm (-> B (-> C D))))
================================================================
tm-name          tm-30607
in-theory        30607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (E or F)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-113 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30607.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (E or F)) -> G) and H) -> G)), M:tm-113, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30608
in-theory        30608
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (A or B)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F))
theorem-size     23
proof            (modus-ponens tm-109 tm-463 ((A (and (-> (-> Am (or Am Bm)) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Dm)) (Cm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30608.        (not (((A -> (A or B)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F)), M:tm-109, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Dm)) (Cm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-30609
in-theory        30609
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     31
proof            (modus-ponens tm-105 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30609.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-105, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30610
in-theory        30610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (C or D)) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-95 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30610.        (((A -> B) -> (A -> A)) and ((((C -> (C or D)) -> E) and F) -> E)), M:tm-95, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30611
in-theory        30611
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> (C -> D)) and E) -> (C -> D))
theorem-size     15
proof            (modus-ponens tm-87 tm-463 ((A (and (-> (-> Am (or Am Bm)) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30611.        ((((A -> (A or B)) -> (C -> D)) and E) -> (C -> D)), M:tm-87, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-30612
in-theory        30612
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) and D) -> (E -> C))
theorem-size     13
proof            (modus-ponens tm-84 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-3 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30612.        ((((A -> (A or B)) -> C) and D) -> (E -> C)), M:tm-84, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-30613
in-theory        30613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-83 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30613.        ((A -> (B -> (C -> B))) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-83, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30614
in-theory        30614
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (A or B)) -> (not (C -> (D -> C)))) and E))
theorem-size     15
proof            (modus-ponens tm-79 tm-463 ((A (and (-> (-> Am (or Am Bm)) (not (-> B (-> C B)))) Dm)) (Cm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30614.        (not (((A -> (A or B)) -> (not (C -> (D -> C)))) and E)), M:tm-79, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) (not (-> B (-> C B)))) Dm)) (Cm (not (-> B (-> C B)))))
================================================================
tm-name          tm-30615
in-theory        30615
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (B or C)) -> D) and E) -> D))
theorem-size     17
proof            (modus-ponens tm-76 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-10 tm-2 tm-3 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30615.        (((not (not A)) -> A) and ((((B -> (B or C)) -> D) and E) -> D)), M:tm-76, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30616
in-theory        30616
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (A or B)) -> C) and D))) or (((A -> (A or B)) -> C) and D)) -> C)
theorem-size     23
proof            (modus-ponens tm-73 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-10 tm-2 tm-3 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30616.        (((not (not (((A -> (A or B)) -> C) and D))) or (((A -> (A or B)) -> C) and D)) -> C), M:tm-73, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-30617
in-theory        30617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (C or D)) -> E) and F) -> E))
theorem-size     23
proof            (modus-ponens tm-69 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-9 tm-2 tm-3 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30617.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (C or D)) -> E) and F) -> E)), M:tm-69, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30618
in-theory        30618
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (A or B)) -> (not C)) and C))
theorem-size     11
proof            (modus-ponens tm-60 tm-463 ((A (-> (-> Am (or Am Bm)) (not Dm))) (B Dm) (Cm (not Dm))))
axioms-used      (tm-9 tm-4 tm-2 tm-3 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30618.        (not (((A -> (A or B)) -> (not C)) and C)), M:tm-60, m:tm-463, u:((A (-> (-> Am (or Am Bm)) (not Dm))) (B Dm) (Cm (not Dm)))
================================================================
tm-name          tm-30619
in-theory        30619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-54 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30619.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-54, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30620
in-theory        30620
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (B or C)) -> D) and E)) or (((B -> (B or C)) -> D) and E)) -> D)
theorem-size     23
proof            (modus-ponens tm-47 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-4 tm-2 tm-3 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30620.        (((A and (((B -> (B or C)) -> D) and E)) or (((B -> (B or C)) -> D) and E)) -> D), M:tm-47, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-30621
in-theory        30621
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (A or B)) -> C) and D) and E) or (((A -> (A or B)) -> C) and D)) -> C)
theorem-size     23
proof            (modus-ponens tm-46 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30621.        ((((((A -> (A or B)) -> C) and D) and E) or (((A -> (A or B)) -> C) and D)) -> C), M:tm-46, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-30622
in-theory        30622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (C or D)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-42 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30622.        ((A -> (B or A)) and ((((C -> (C or D)) -> E) and F) -> E)), M:tm-42, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30623
in-theory        30623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (C or D)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-32 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30623.        ((A -> (A or B)) and ((((C -> (C or D)) -> E) and F) -> E)), M:tm-32, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30624
in-theory        30624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) and D) -> ((((A -> (A or B)) -> C) and D) and C))
theorem-size     21
proof            (modus-ponens tm-24 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30624.        ((((A -> (A or B)) -> C) and D) -> ((((A -> (A or B)) -> C) and D) and C)), M:tm-24, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-30625
in-theory        30625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (C or D)) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-23 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30625.        ((A -> (B -> (A and B))) and ((((C -> (C or D)) -> E) and F) -> E)), M:tm-23, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30626
in-theory        30626
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (C or D)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-22 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30626.        (((A and B) -> B) and ((((C -> (C or D)) -> E) and F) -> E)), M:tm-22, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30627
in-theory        30627
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (C or D)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-21 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30627.        (((A and B) -> A) and ((((C -> (C or D)) -> E) and F) -> E)), M:tm-21, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30628
in-theory        30628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-20 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30628.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-20, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30629
in-theory        30629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (C or D)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-19 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30629.        ((A -> (B -> A)) and ((((C -> (C or D)) -> E) and F) -> E)), M:tm-19, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30630
in-theory        30630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) and (C -> D)) -> D)
theorem-size     13
proof            (modus-ponens tm-17 tm-463 ((A (-> (-> Am (or Am Bm)) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-4 tm-3 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30630.        ((((A -> (A or B)) -> C) and (C -> D)) -> D), M:tm-17, m:tm-463, u:((A (-> (-> Am (or Am Bm)) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-30631
in-theory        30631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) and D) -> (((A -> (A or B)) -> C) and D))
theorem-size     19
proof            (modus-ponens tm-12 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-3 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30631.        ((((A -> (A or B)) -> C) and D) -> (((A -> (A or B)) -> C) and D)), M:tm-12, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-30632
in-theory        30632
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> (not C)) -> (not (((A -> (A or B)) -> C) and D)))
theorem-size     23
proof            (modus-ponens tm-9 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-9 tm-2 tm-3 tm-1 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30632.        (((((A -> (A or B)) -> C) and D) -> (not C)) -> (not (((A -> (A or B)) -> C) and D))), M:tm-9, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-30633
in-theory        30633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((((C -> (C or D)) -> A) and E) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30633.        ((A -> B) -> (((((C -> (C or D)) -> A) and E) or A) -> B)), M:tm-8, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-30634
in-theory        30634
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> (B or C)) -> D) and E) -> D))
theorem-size     13
proof            (modus-ponens tm-7 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-7 tm-2 tm-3 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30634.        (A or ((((B -> (B or C)) -> D) and E) -> D)), M:tm-7, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30635
in-theory        30635
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-6 tm-2 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30635.        (((((A -> (A or B)) -> C) and D) -> C) or E), M:tm-6, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30636
in-theory        30636
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> (B or C)) -> D) and E) -> D) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30636.        (A -> (((((B -> (B or C)) -> D) and E) -> D) and A)), M:tm-5, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30637
in-theory        30637
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> (C -> D)) and E) -> C) -> ((((A -> (A or B)) -> (C -> D)) and E) -> D))
theorem-size     27
proof            (modus-ponens tm-2 tm-463 ((A (and (-> (-> Am (or Am Bm)) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-3 tm-1 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30637.        (((((A -> (A or B)) -> (C -> D)) and E) -> C) -> ((((A -> (A or B)) -> (C -> D)) and E) -> D)), M:tm-2, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-30638
in-theory        30638
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (B or C)) -> D) and E) -> D))
theorem-size     13
proof            (modus-ponens tm-1 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-1 tm-2 tm-3 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30638.        (A -> ((((B -> (B or C)) -> D) and E) -> D)), M:tm-1, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-30639
in-theory        30639
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((A or B) or C))
theorem-size     7
proof            (modus-ponens tm-464 tm-33 ((A Am) (Bm (or Am B)) (C (or (or Am B) Cm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30639.        (A -> ((A or B) or C)), M:tm-464, m:tm-33, u:((A Am) (Bm (or Am B)) (C (or (or Am B) Cm)))
================================================================
tm-name          tm-30640
in-theory        30640
times-derived    2
----------------------------------------------------------------
theorem          (A -> (B or (A or C)))
theorem-size     7
proof            (modus-ponens tm-464 tm-43 ((A Am) (Bm (or Am B)) (C (or Cm (or Am B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30640.        (A -> (B or (A or C))), M:tm-464, m:tm-43, u:((A Am) (Bm (or Am B)) (C (or Cm (or Am B))))
================================================================
tm-name          tm-30641
in-theory        30641
times-derived    4
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> C)
theorem-size     9
proof            (modus-ponens tm-464 tm-80 ((Dm (-> (-> Am (-> Bm Am)) Cm)) (A (-> (-> Am (-> Bm Am)) Cm)) (B (-> Am (-> Bm Am))) (C Cm)))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-30641.        (((A -> (B -> A)) -> C) -> C), M:tm-464, m:tm-80, u:((Dm (-> (-> Am (-> Bm Am)) Cm)) (A (-> (-> Am (-> Bm Am)) Cm)) (B (-> Am (-> Bm Am))) (C Cm))
================================================================
tm-name          tm-30642
in-theory        30642
times-derived    4
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> D)
theorem-size     17
proof            (modus-ponens tm-464 tm-110 ((Em (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm)))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-30642.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> D), M:tm-464, m:tm-110, u:((Em (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
================================================================
tm-name          tm-30643
in-theory        30643
times-derived    4
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> C)
theorem-size     9
proof            (modus-ponens tm-464 tm-131 ((Dm (-> (-> (and Am Bm) Am) Cm)) (A (-> (-> (and Am Bm) Am) Cm)) (B (-> (and Am Bm) Am)) (C Cm)))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-30643.        ((((A and B) -> A) -> C) -> C), M:tm-464, m:tm-131, u:((Dm (-> (-> (and Am Bm) Am) Cm)) (A (-> (-> (and Am Bm) Am) Cm)) (B (-> (and Am Bm) Am)) (C Cm))
================================================================
tm-name          tm-30644
in-theory        30644
times-derived    4
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> C)
theorem-size     9
proof            (modus-ponens tm-464 tm-154 ((Dm (-> (-> (and Am Bm) Bm) Cm)) (A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (and Am Bm) Bm)) (C Cm)))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-30644.        ((((A and B) -> B) -> C) -> C), M:tm-464, m:tm-154, u:((Dm (-> (-> (and Am Bm) Bm) Cm)) (A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (and Am Bm) Bm)) (C Cm))
================================================================
tm-name          tm-30645
in-theory        30645
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (A or D)))
theorem-size     11
proof            (modus-ponens tm-464 tm-184 ((A Am) (Bm (or Am B)) (C (and (-> Cm (-> Dm Cm)) (or Am B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-30645.        (A -> ((B -> (C -> B)) and (A or D))), M:tm-464, m:tm-184, u:((A Am) (Bm (or Am B)) (C (and (-> Cm (-> Dm Cm)) (or Am B))))
================================================================
tm-name          tm-30646
in-theory        30646
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (A or E)))
theorem-size     19
proof            (modus-ponens tm-464 tm-211 ((A Am) (Bm (or Am B)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-30646.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (A or E))), M:tm-464, m:tm-211, u:((A Am) (Bm (or Am B)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or Am B))))
================================================================
tm-name          tm-30647
in-theory        30647
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (A or D)))
theorem-size     11
proof            (modus-ponens tm-464 tm-240 ((A Am) (Bm (or Am B)) (C (and (-> (and Cm Dm) Cm) (or Am B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-30647.        (A -> (((B and C) -> B) and (A or D))), M:tm-464, m:tm-240, u:((A Am) (Bm (or Am B)) (C (and (-> (and Cm Dm) Cm) (or Am B))))
================================================================
tm-name          tm-30648
in-theory        30648
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (A or D)))
theorem-size     11
proof            (modus-ponens tm-464 tm-271 ((A Am) (Bm (or Am B)) (C (and (-> (and Cm Dm) Dm) (or Am B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-30648.        (A -> (((B and C) -> C) and (A or D))), M:tm-464, m:tm-271, u:((A Am) (Bm (or Am B)) (C (and (-> (and Cm Dm) Dm) (or Am B))))
================================================================
tm-name          tm-30649
in-theory        30649
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (A or D)))
theorem-size     13
proof            (modus-ponens tm-464 tm-304 ((A Am) (Bm (or Am B)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Am B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-30649.        (A -> ((B -> (C -> (B and C))) and (A or D))), M:tm-464, m:tm-304, u:((A Am) (Bm (or Am B)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or Am B))))
================================================================
tm-name          tm-30650
in-theory        30650
times-derived    4
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> C)
theorem-size     11
proof            (modus-ponens tm-464 tm-351 ((Dm (-> (-> Am (-> Bm (and Am Bm))) Cm)) (A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> Am (-> Bm (and Am Bm)))) (C Cm)))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-30650.        (((A -> (B -> (A and B))) -> C) -> C), M:tm-464, m:tm-351, u:((Dm (-> (-> Am (-> Bm (and Am Bm))) Cm)) (A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> Am (-> Bm (and Am Bm)))) (C Cm))
================================================================
tm-name          tm-30651
in-theory        30651
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (A or D)))
theorem-size     11
proof            (modus-ponens tm-464 tm-454 ((A Am) (Bm (or Am B)) (C (and (-> Cm (or Cm Dm)) (or Am B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30651.        (A -> ((B -> (B or C)) and (A or D))), M:tm-464, m:tm-454, u:((A Am) (Bm (or Am B)) (C (and (-> Cm (or Cm Dm)) (or Am B))))
================================================================
tm-name          tm-30652
in-theory        30652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30652.        (((A -> ((A or B) -> C)) -> (A -> C)) and (D -> (D or E))), M:tm-456, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30653
in-theory        30653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30653.        ((A -> ((B -> (B or C)) and A)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-453, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30654
in-theory        30654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and ((D -> (D or E)) and ((A -> ((A or B) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30654.        (((A -> ((A or B) -> C)) -> (A -> C)) and ((D -> (D or E)) and ((A -> ((A or B) -> C)) -> (A -> C)))), M:tm-443, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30655
in-theory        30655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30655.        (((A -> (A or B)) or C) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-409, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30656
in-theory        30656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30656.        (((A -> (B -> (A and B))) or C) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-400, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30657
in-theory        30657
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30657.        ((((A and B) -> B) or C) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-391, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30658
in-theory        30658
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30658.        ((((A and B) -> A) or C) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-382, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30659
in-theory        30659
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((E or F) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30659.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((E or F) -> G)) -> (E -> G))), M:tm-373, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30660
in-theory        30660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30660.        (((A -> (B -> A)) or C) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-364, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30661
in-theory        30661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((A or B) -> C)) -> (D -> ((A -> C) and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30661.        ((A -> ((A or B) -> C)) -> (D -> ((A -> C) and D))), M:tm-355, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-30662
in-theory        30662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30662.        ((A -> (B -> (C -> (B and C)))) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-354, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30663
in-theory        30663
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((B or C) -> (B and (B or C))))) -> (B -> (B and (B or C))))
theorem-size     21
proof            (modus-ponens tm-351 tm-464 ((A Am) (B (or Am Bm)) (Cm (and Am (or Am Bm))) (C (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30663.        ((A or (B -> ((B or C) -> (B and (B or C))))) -> (B -> (B and (B or C)))), M:tm-351, m:tm-464, u:((A Am) (B (or Am Bm)) (Cm (and Am (or Am Bm))) (C (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-30664
in-theory        30664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30664.        (((A -> ((A or B) -> C)) -> (A -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30665
in-theory        30665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> ((C or D) -> E)) -> (C -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30665.        (((A -> B) -> (A -> (A and B))) and ((C -> ((C or D) -> E)) -> (C -> E))), M:tm-338, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30666
in-theory        30666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and ((A -> ((A or B) -> C)) -> ((A -> ((A or B) -> C)) and (A -> C))))
theorem-size     31
proof            (modus-ponens tm-328 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30666.        (((A -> ((A or B) -> C)) -> (A -> C)) and ((A -> ((A or B) -> C)) -> ((A -> ((A or B) -> C)) and (A -> C)))), M:tm-328, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-30667
in-theory        30667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> ((A or B) -> C)) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30667.        (((A -> ((A or B) -> C)) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> ((A or B) -> C)) -> (A -> C)))), M:tm-327, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30668
in-theory        30668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (((D and E) -> E) and ((A -> ((A or B) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30668.        (((A -> ((A or B) -> C)) -> (A -> C)) and (((D and E) -> E) and ((A -> ((A or B) -> C)) -> (A -> C)))), M:tm-326, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30669
in-theory        30669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (((D and E) -> D) and ((A -> ((A or B) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30669.        (((A -> ((A or B) -> C)) -> (A -> C)) and (((D and E) -> D) and ((A -> ((A or B) -> C)) -> (A -> C)))), M:tm-325, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30670
in-theory        30670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> ((A or B) -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30670.        (((A -> ((A or B) -> C)) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> ((A or B) -> C)) -> (A -> C)))), M:tm-324, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30671
in-theory        30671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and ((D -> (E -> D)) and ((A -> ((A or B) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30671.        (((A -> ((A or B) -> C)) -> (A -> C)) and ((D -> (E -> D)) and ((A -> ((A or B) -> C)) -> (A -> C)))), M:tm-323, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30672
in-theory        30672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30672.        (((A -> ((A or B) -> C)) -> (A -> C)) and ((D and E) -> E)), M:tm-322, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30673
in-theory        30673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30673.        (((A -> ((A or B) -> C)) -> (A -> C)) and ((D and E) -> D)), M:tm-320, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30674
in-theory        30674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30674.        (((A -> ((A or B) -> C)) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30675
in-theory        30675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> (A or B))) -> (A -> (A or B))) and ((A -> ((A or B) -> (A or B))) -> (A -> (A or B))))
theorem-size     31
proof            (modus-ponens tm-317 tm-464 ((Cm (or Am Bm)) (C (or Am Bm)) (A Am) (B (or Am Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30675.        (((A -> ((A or B) -> (A or B))) -> (A -> (A or B))) and ((A -> ((A or B) -> (A or B))) -> (A -> (A or B)))), M:tm-317, m:tm-464, u:((Cm (or Am Bm)) (C (or Am Bm)) (A Am) (B (or Am Bm)))
================================================================
tm-name          tm-30676
in-theory        30676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and ((A -> ((A or B) -> C)) -> (A -> ((A or B) -> C))))
theorem-size     27
proof            (modus-ponens tm-316 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30676.        (((A -> ((A or B) -> C)) -> (A -> C)) and ((A -> ((A or B) -> C)) -> (A -> ((A or B) -> C)))), M:tm-316, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-30677
in-theory        30677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30677.        (((A -> ((A or B) -> C)) -> (A -> C)) and (D -> (E -> D))), M:tm-315, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30678
in-theory        30678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (((A -> ((A or B) -> C)) -> (not (A -> C))) -> (not (A -> ((A or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-313 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30678.        (((A -> ((A or B) -> C)) -> (A -> C)) and (((A -> ((A or B) -> C)) -> (not (A -> C))) -> (not (A -> ((A or B) -> C))))), M:tm-313, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-30679
in-theory        30679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (((A -> C) -> D) -> (((A -> ((A or B) -> C)) or (A -> C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30679.        (((A -> ((A or B) -> C)) -> (A -> C)) and (((A -> C) -> D) -> (((A -> ((A or B) -> C)) or (A -> C)) -> D))), M:tm-312, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-30680
in-theory        30680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (D or ((A -> ((A or B) -> C)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30680.        (((A -> ((A or B) -> C)) -> (A -> C)) and (D or ((A -> ((A or B) -> C)) -> (A -> C)))), M:tm-311, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30681
in-theory        30681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (((A -> ((A or B) -> C)) -> (A -> C)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30681.        (((A -> ((A or B) -> C)) -> (A -> C)) and (((A -> ((A or B) -> C)) -> (A -> C)) or D)), M:tm-310, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30682
in-theory        30682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (D -> (((A -> ((A or B) -> C)) -> (A -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30682.        (((A -> ((A or B) -> C)) -> (A -> C)) and (D -> (((A -> ((A or B) -> C)) -> (A -> C)) and D))), M:tm-309, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30683
in-theory        30683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (((A -> ((A or B) -> C)) -> A) -> ((A -> ((A or B) -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-306 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B Am) (C Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30683.        (((A -> ((A or B) -> C)) -> (A -> C)) and (((A -> ((A or B) -> C)) -> A) -> ((A -> ((A or B) -> C)) -> C))), M:tm-306, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B Am) (C Cm))
================================================================
tm-name          tm-30684
in-theory        30684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (D -> ((A -> ((A or B) -> C)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30684.        (((A -> ((A or B) -> C)) -> (A -> C)) and (D -> ((A -> ((A or B) -> C)) -> (A -> C)))), M:tm-305, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30685
in-theory        30685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30685.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-303, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30686
in-theory        30686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30686.        ((A -> (((B and C) -> C) and A)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-270, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30687
in-theory        30687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30687.        ((A -> (((B and C) -> B) and A)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-239, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30688
in-theory        30688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((E or F) -> G)) -> (E -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30688.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((E or F) -> G)) -> (E -> G))), M:tm-210, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30689
in-theory        30689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30689.        ((A -> ((B -> (C -> B)) and A)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-183, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30690
in-theory        30690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30690.        ((A -> ((B and C) -> C)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-157, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30691
in-theory        30691
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30691.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-147, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30692
in-theory        30692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30692.        ((A -> ((B and C) -> B)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-134, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30693
in-theory        30693
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30693.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-125, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30694
in-theory        30694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((A or B) -> (C -> D))) -> ((A -> C) -> (A -> D)))
theorem-size     17
proof            (modus-ponens tm-114 tm-464 ((A (-> Am (-> (or Am Bm) (-> C D)))) (B Am) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30694.        ((A -> ((A or B) -> (C -> D))) -> ((A -> C) -> (A -> D))), M:tm-114, m:tm-464, u:((A (-> Am (-> (or Am Bm) (-> C D)))) (B Am) (Cm (-> C D)))
================================================================
tm-name          tm-30695
in-theory        30695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((E or F) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30695.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((E or F) -> G)) -> (E -> G))), M:tm-113, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30696
in-theory        30696
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30696.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-105, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30697
in-theory        30697
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((A or B) -> (A or B))) -> (A -> (A or B)))
theorem-size     15
proof            (modus-ponens tm-100 tm-464 ((Cm (or Am Bm)) (C (or Am Bm)) (A Am) (B (or Am Bm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30697.        ((A -> ((A or B) -> (A or B))) -> (A -> (A or B))), M:tm-100, m:tm-464, u:((Cm (or Am Bm)) (C (or Am Bm)) (A Am) (B (or Am Bm)))
================================================================
tm-name          tm-30698
in-theory        30698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> ((C or D) -> E)) -> (C -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30698.        (((A -> B) -> (A -> A)) and ((C -> ((C or D) -> E)) -> (C -> E))), M:tm-95, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30699
in-theory        30699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((A or B) -> C)) -> (D -> (A -> C)))
theorem-size     13
proof            (modus-ponens tm-84 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30699.        ((A -> ((A or B) -> C)) -> (D -> (A -> C))), M:tm-84, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-30700
in-theory        30700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30700.        ((A -> (B -> (C -> B))) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-83, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30701
in-theory        30701
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((B or C) -> B))) -> (B -> B))
theorem-size     13
proof            (modus-ponens tm-80 tm-464 ((Cm Am) (B (or Am Bm)) (A Am) (C (-> Am Am))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30701.        ((A or (B -> ((B or C) -> B))) -> (B -> B)), M:tm-80, m:tm-464, u:((Cm Am) (B (or Am Bm)) (A Am) (C (-> Am Am)))
================================================================
tm-name          tm-30702
in-theory        30702
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> ((B or C) -> D)) -> (B -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30702.        (((not (not A)) -> A) and ((B -> ((B or C) -> D)) -> (B -> D))), M:tm-76, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30703
in-theory        30703
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> ((A or B) -> C)))) or (A -> ((A or B) -> C))) -> (A -> C))
theorem-size     21
proof            (modus-ponens tm-73 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30703.        (((not (not (A -> ((A or B) -> C)))) or (A -> ((A or B) -> C))) -> (A -> C)), M:tm-73, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-30704
in-theory        30704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((C or D) -> E)) -> (C -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30704.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((C or D) -> E)) -> (C -> E))), M:tm-69, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30705
in-theory        30705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30705.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-54, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30706
in-theory        30706
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) or ((A -> B) -> (((A -> B) or A) -> B))) -> ((A -> B) -> B))
theorem-size     23
proof            (modus-ponens tm-51 tm-464 ((Am (-> Bm Cm)) (C (-> Bm Cm)) (A Bm) (B Cm) (D (-> (-> Bm Cm) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30706.        ((((A -> B) -> A) or ((A -> B) -> (((A -> B) or A) -> B))) -> ((A -> B) -> B)), M:tm-51, m:tm-464, u:((Am (-> Bm Cm)) (C (-> Bm Cm)) (A Bm) (B Cm) (D (-> (-> Bm Cm) Cm)))
================================================================
tm-name          tm-30707
in-theory        30707
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> ((B or C) -> D))) or (B -> ((B or C) -> D))) -> (B -> D))
theorem-size     21
proof            (modus-ponens tm-47 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30707.        (((A and (B -> ((B or C) -> D))) or (B -> ((B or C) -> D))) -> (B -> D)), M:tm-47, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-30708
in-theory        30708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((A or B) -> C)) and D) or (A -> ((A or B) -> C))) -> (A -> C))
theorem-size     21
proof            (modus-ponens tm-46 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30708.        ((((A -> ((A or B) -> C)) and D) or (A -> ((A or B) -> C))) -> (A -> C)), M:tm-46, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-30709
in-theory        30709
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or (A -> ((A or B) -> C))) -> (A -> C))
theorem-size     17
proof            (modus-ponens tm-44 tm-464 ((A Am) (B (-> (or Am Bm) Cm)) (C (-> Am Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30709.        ((((A or B) -> C) or (A -> ((A or B) -> C))) -> (A -> C)), M:tm-44, m:tm-464, u:((A Am) (B (-> (or Am Bm) Cm)) (C (-> Am Cm)))
================================================================
tm-name          tm-30710
in-theory        30710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> ((C or D) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30710.        ((A -> (B or A)) and ((C -> ((C or D) -> E)) -> (C -> E))), M:tm-42, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30711
in-theory        30711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> ((C or D) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30711.        ((A -> (A or B)) and ((C -> ((C or D) -> E)) -> (C -> E))), M:tm-32, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30712
in-theory        30712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((A or B) -> C)) -> ((A -> ((A or B) -> C)) and (A -> C)))
theorem-size     19
proof            (modus-ponens tm-24 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30712.        ((A -> ((A or B) -> C)) -> ((A -> ((A or B) -> C)) and (A -> C))), M:tm-24, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-30713
in-theory        30713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> ((C or D) -> E)) -> (C -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30713.        ((A -> (B -> (A and B))) and ((C -> ((C or D) -> E)) -> (C -> E))), M:tm-23, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30714
in-theory        30714
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> ((C or D) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30714.        (((A and B) -> B) and ((C -> ((C or D) -> E)) -> (C -> E))), M:tm-22, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30715
in-theory        30715
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> ((C or D) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30715.        (((A and B) -> A) and ((C -> ((C or D) -> E)) -> (C -> E))), M:tm-21, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30716
in-theory        30716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30716.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-20, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30717
in-theory        30717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> ((C or D) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30717.        ((A -> (B -> A)) and ((C -> ((C or D) -> E)) -> (C -> E))), M:tm-19, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30718
in-theory        30718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((A or B) -> C)) -> (A -> ((A or B) -> C)))
theorem-size     15
proof            (modus-ponens tm-12 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30718.        ((A -> ((A or B) -> C)) -> (A -> ((A or B) -> C))), M:tm-12, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-30719
in-theory        30719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (not (A -> C))) -> (not (A -> ((A or B) -> C))))
theorem-size     21
proof            (modus-ponens tm-9 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-9 tm-2 tm-1 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30719.        (((A -> ((A or B) -> C)) -> (not (A -> C))) -> (not (A -> ((A or B) -> C)))), M:tm-9, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-30720
in-theory        30720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (((A -> ((A or D) -> B)) or (A -> B)) -> C))
theorem-size     19
proof            (modus-ponens tm-8 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30720.        (((A -> B) -> C) -> (((A -> ((A or D) -> B)) or (A -> B)) -> C)), M:tm-8, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-30721
in-theory        30721
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> ((B or C) -> D)) -> (B -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-7 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30721.        (A or ((B -> ((B or C) -> D)) -> (B -> D))), M:tm-7, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30722
in-theory        30722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-6 tm-2 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30722.        (((A -> ((A or B) -> C)) -> (A -> C)) or D), M:tm-6, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30723
in-theory        30723
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> ((B or C) -> D)) -> (B -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30723.        (A -> (((B -> ((B or C) -> D)) -> (B -> D)) and A)), M:tm-5, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30724
in-theory        30724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> A) -> ((A -> ((A or B) -> C)) -> C))
theorem-size     19
proof            (modus-ponens tm-2 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B Am) (C Cm)))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30724.        (((A -> ((A or B) -> C)) -> A) -> ((A -> ((A or B) -> C)) -> C)), M:tm-2, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B Am) (C Cm))
================================================================
tm-name          tm-30725
in-theory        30725
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> ((B or C) -> D)) -> (B -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-1 tm-2 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-30725.        (A -> ((B -> ((B or C) -> D)) -> (B -> D))), M:tm-1, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-30726
in-theory        30726
times-derived    1
----------------------------------------------------------------
theorem          (not ((not (A -> (A or B))) and C))
theorem-size     9
proof            (modus-ponens tm-465 tm-3 ((A (and (not (-> B (or B C))) Bm)) (Am (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-30726.        (not ((not (A -> (A or B))) and C)), M:tm-465, m:tm-3, u:((A (and (not (-> B (or B C))) Bm)) (Am (not (-> B (or B C)))))
================================================================
tm-name          tm-30727
in-theory        30727
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (not (B -> (B or C)))))
theorem-size     9
proof            (modus-ponens tm-465 tm-4 ((A (and Am (not (-> B (or B C))))) (Bm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-30727.        (not (A and (not (B -> (B or C))))), M:tm-465, m:tm-4, u:((A (and Am (not (-> B (or B C))))) (Bm (not (-> B (or B C)))))
================================================================
tm-name          tm-30728
in-theory        30728
times-derived    1
----------------------------------------------------------------
theorem          (not (not (not (not (A -> (A or B))))))
theorem-size     9
proof            (modus-ponens tm-465 tm-10 ((A (not (not (not (-> B (or B C)))))) (Am (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-30728.        (not (not (not (not (A -> (A or B)))))), M:tm-465, m:tm-10, u:((A (not (not (not (-> B (or B C)))))) (Am (not (-> B (or B C)))))
================================================================
tm-name          tm-30729
in-theory        30729
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (C -> (A -> (A or B))))))
theorem-size     15
proof            (modus-ponens tm-465 tm-57 ((A (-> (-> B (or B C)) (not (-> Bm (-> B (or B C)))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-30729.        (not ((A -> (A or B)) -> (not (C -> (A -> (A or B)))))), M:tm-465, m:tm-57, u:((A (-> (-> B (or B C)) (not (-> Bm (-> B (or B C)))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30730
in-theory        30730
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (C -> ((A -> (A or B)) and C)))))
theorem-size     17
proof            (modus-ponens tm-465 tm-61 ((A (-> (-> B (or B C)) (not (-> Bm (and (-> B (or B C)) Bm))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-30730.        (not ((A -> (A or B)) -> (not (C -> ((A -> (A or B)) and C))))), M:tm-465, m:tm-61, u:((A (-> (-> B (or B C)) (not (-> Bm (and (-> B (or B C)) Bm))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30731
in-theory        30731
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not ((A -> (A or B)) or C))))
theorem-size     15
proof            (modus-ponens tm-465 tm-62 ((A (-> (-> B (or B C)) (not (or (-> B (or B C)) Bm)))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-30731.        (not ((A -> (A or B)) -> (not ((A -> (A or B)) or C)))), M:tm-465, m:tm-62, u:((A (-> (-> B (or B C)) (not (or (-> B (or B C)) Bm)))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30732
in-theory        30732
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (C or (A -> (A or B))))))
theorem-size     15
proof            (modus-ponens tm-465 tm-63 ((A (-> (-> B (or B C)) (not (or Bm (-> B (or B C)))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-30732.        (not ((A -> (A or B)) -> (not (C or (A -> (A or B)))))), M:tm-465, m:tm-63, u:((A (-> (-> B (or B C)) (not (or Bm (-> B (or B C)))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30733
in-theory        30733
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (((A or B) -> C) -> ((A or (A or B)) -> C)))))
theorem-size     21
proof            (modus-ponens tm-465 tm-64 ((A (-> (-> Am (or Am C)) (not (-> (-> (or Am C) Cm) (-> (or Am (or Am C)) Cm))))) (B Am) (Bm (or Am C))))
axioms-used      (tm-9 tm-1 tm-6 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-30733.        (not ((A -> (A or B)) -> (not (((A or B) -> C) -> ((A or (A or B)) -> C))))), M:tm-465, m:tm-64, u:((A (-> (-> Am (or Am C)) (not (-> (-> (or Am C) Cm) (-> (or Am (or Am C)) Cm))))) (B Am) (Bm (or Am C)))
================================================================
tm-name          tm-30734
in-theory        30734
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not ((A -> (not (A or B))) -> (not A)))))
theorem-size     17
proof            (modus-ponens tm-465 tm-65 ((A (-> (-> Am (or Am C)) (not (-> (-> Am (not (or Am C))) (not Am))))) (B Am) (Bm (or Am C))))
axioms-used      (tm-9 tm-1 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-30734.        (not ((A -> (A or B)) -> (not ((A -> (not (A or B))) -> (not A))))), M:tm-465, m:tm-65, u:((A (-> (-> Am (or Am C)) (not (-> (-> Am (not (or Am C))) (not Am))))) (B Am) (Bm (or Am C)))
================================================================
tm-name          tm-30735
in-theory        30735
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (C -> (D -> C)))))
theorem-size     13
proof            (modus-ponens tm-465 tm-79 ((A (-> (-> B (or B C)) (not (-> Bm (-> Cm Bm))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-30735.        (not ((A -> (A or B)) -> (not (C -> (D -> C))))), M:tm-465, m:tm-79, u:((A (-> (-> B (or B C)) (not (-> Bm (-> Cm Bm))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30736
in-theory        30736
times-derived    1
----------------------------------------------------------------
theorem          (not (not (A -> (A or B))))
theorem-size     7
proof            (modus-ponens tm-465 tm-86 ((A (not (-> B (or B C)))) (Am (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-30736.        (not (not (A -> (A or B)))), M:tm-465, m:tm-86, u:((A (not (-> B (or B C)))) (Am (not (-> B (or B C)))))
================================================================
tm-name          tm-30737
in-theory        30737
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (A -> A))))
theorem-size     11
proof            (modus-ponens tm-465 tm-91 ((A (-> (-> Am (or Am C)) (not (-> Am Am)))) (B Am) (Bm (or Am C))))
axioms-used      (tm-9 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-30737.        (not ((A -> (A or B)) -> (not (A -> A)))), M:tm-465, m:tm-91, u:((A (-> (-> Am (or Am C)) (not (-> Am Am)))) (B Am) (Bm (or Am C)))
================================================================
tm-name          tm-30738
in-theory        30738
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     21
proof            (modus-ponens tm-465 tm-109 ((A (-> (-> B (or B C)) (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-30738.        (not ((A -> (A or B)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-465, m:tm-109, u:((A (-> (-> B (or B C)) (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30739
in-theory        30739
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (not (B -> (B or C)))) and A))
theorem-size     11
proof            (modus-ponens tm-465 tm-116 ((A (and (-> Am (not (-> B (or B C)))) Am)) (Bm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-3 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-30739.        (not ((A -> (not (B -> (B or C)))) and A)), M:tm-465, m:tm-116, u:((A (and (-> Am (not (-> B (or B C)))) Am)) (Bm (not (-> B (or B C)))))
================================================================
tm-name          tm-30740
in-theory        30740
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> A)) -> (not (C -> (C or D)))) and E))
theorem-size     15
proof            (modus-ponens tm-465 tm-117 ((A (and (-> (-> Am (-> Bm Am)) (not (-> B (or B C)))) Dm)) (Cm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-30740.        (not (((A -> (B -> A)) -> (not (C -> (C or D)))) and E)), M:tm-465, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) (not (-> B (or B C)))) Dm)) (Cm (not (-> B (or B C)))))
================================================================
tm-name          tm-30741
in-theory        30741
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (D or E)))) and F))
theorem-size     23
proof            (modus-ponens tm-465 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not (-> B (or B C)))) Em)) (Dm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-30741.        (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (D or E)))) and F)), M:tm-465, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not (-> B (or B C)))) Em)) (Dm (not (-> B (or B C)))))
================================================================
tm-name          tm-30742
in-theory        30742
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> A) -> (not (C -> (C or D)))) and E))
theorem-size     15
proof            (modus-ponens tm-465 tm-128 ((A (and (-> (-> (and Am Bm) Am) (not (-> B (or B C)))) Dm)) (Cm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-30742.        (not ((((A and B) -> A) -> (not (C -> (C or D)))) and E)), M:tm-465, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) (not (-> B (or B C)))) Dm)) (Cm (not (-> B (or B C)))))
================================================================
tm-name          tm-30743
in-theory        30743
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not ((C and D) -> C))))
theorem-size     13
proof            (modus-ponens tm-465 tm-130 ((A (-> (-> B (or B C)) (not (-> (and Bm Cm) Bm)))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-30743.        (not ((A -> (A or B)) -> (not ((C and D) -> C)))), M:tm-465, m:tm-130, u:((A (-> (-> B (or B C)) (not (-> (and Bm Cm) Bm)))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30744
in-theory        30744
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (A -> (not (B -> (B or C))))))
theorem-size     11
proof            (modus-ponens tm-465 tm-137 ((A (and Am (-> Am (not (-> B (or B C)))))) (Bm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-4 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-30744.        (not (A and (A -> (not (B -> (B or C)))))), M:tm-465, m:tm-137, u:((A (and Am (-> Am (not (-> B (or B C)))))) (Bm (not (-> B (or B C)))))
================================================================
tm-name          tm-30745
in-theory        30745
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> B)) -> (not (D -> (D or E))))))
theorem-size     15
proof            (modus-ponens tm-465 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) (not (-> B (or B C)))))) (Dm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-30745.        (not (A and ((B -> (C -> B)) -> (not (D -> (D or E)))))), M:tm-465, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) (not (-> B (or B C)))))) (Dm (not (-> B (or B C)))))
================================================================
tm-name          tm-30746
in-theory        30746
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not (E -> (E or F))))))
theorem-size     23
proof            (modus-ponens tm-465 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not (-> B (or B C)))))) (Em (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-30746.        (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not (E -> (E or F)))))), M:tm-465, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not (-> B (or B C)))))) (Em (not (-> B (or B C)))))
================================================================
tm-name          tm-30747
in-theory        30747
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> B) -> (not (D -> (D or E))))))
theorem-size     15
proof            (modus-ponens tm-465 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) (not (-> B (or B C)))))) (Dm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-30747.        (not (A and (((B and C) -> B) -> (not (D -> (D or E)))))), M:tm-465, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) (not (-> B (or B C)))))) (Dm (not (-> B (or B C)))))
================================================================
tm-name          tm-30748
in-theory        30748
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> C) -> (not (D -> (D or E))))))
theorem-size     15
proof            (modus-ponens tm-465 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) (not (-> B (or B C)))))) (Dm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-30748.        (not (A and (((B and C) -> C) -> (not (D -> (D or E)))))), M:tm-465, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) (not (-> B (or B C)))))) (Dm (not (-> B (or B C)))))
================================================================
tm-name          tm-30749
in-theory        30749
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> B) -> (not (C -> (C or D)))) and E))
theorem-size     15
proof            (modus-ponens tm-465 tm-151 ((A (and (-> (-> (and Am Bm) Bm) (not (-> B (or B C)))) Dm)) (Cm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-30749.        (not ((((A and B) -> B) -> (not (C -> (C or D)))) and E)), M:tm-465, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) (not (-> B (or B C)))) Dm)) (Cm (not (-> B (or B C)))))
================================================================
tm-name          tm-30750
in-theory        30750
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not ((C and D) -> D))))
theorem-size     13
proof            (modus-ponens tm-465 tm-153 ((A (-> (-> B (or B C)) (not (-> (and Bm Cm) Cm)))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-30750.        (not ((A -> (A or B)) -> (not ((C and D) -> D)))), M:tm-465, m:tm-153, u:((A (-> (-> B (or B C)) (not (-> (and Bm Cm) Cm)))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30751
in-theory        30751
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not ((C -> (D -> C)) and (A -> (A or B))))))
theorem-size     19
proof            (modus-ponens tm-465 tm-179 ((A (-> (-> B (or B C)) (not (and (-> Bm (-> Cm Bm)) (-> B (or B C)))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-30751.        (not ((A -> (A or B)) -> (not ((C -> (D -> C)) and (A -> (A or B)))))), M:tm-465, m:tm-179, u:((A (-> (-> B (or B C)) (not (and (-> Bm (-> Cm Bm)) (-> B (or B C)))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30752
in-theory        30752
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A or B))))))
theorem-size     27
proof            (modus-ponens tm-465 tm-206 ((A (-> (-> B (or B C)) (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B (or B C)))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-30752.        (not ((A -> (A or B)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (A or B)))))), M:tm-465, m:tm-206, u:((A (-> (-> B (or B C)) (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B (or B C)))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30753
in-theory        30753
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (((C and D) -> C) and (A -> (A or B))))))
theorem-size     19
proof            (modus-ponens tm-465 tm-235 ((A (-> (-> B (or B C)) (not (and (-> (and Bm Cm) Bm) (-> B (or B C)))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6 tm-5 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-30753.        (not ((A -> (A or B)) -> (not (((C and D) -> C) and (A -> (A or B)))))), M:tm-465, m:tm-235, u:((A (-> (-> B (or B C)) (not (and (-> (and Bm Cm) Bm) (-> B (or B C)))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30754
in-theory        30754
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (((C and D) -> D) and (A -> (A or B))))))
theorem-size     19
proof            (modus-ponens tm-465 tm-266 ((A (-> (-> B (or B C)) (not (and (-> (and Bm Cm) Cm) (-> B (or B C)))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6 tm-5 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-30754.        (not ((A -> (A or B)) -> (not (((C and D) -> D) and (A -> (A or B)))))), M:tm-465, m:tm-266, u:((A (-> (-> B (or B C)) (not (and (-> (and Bm Cm) Cm) (-> B (or B C)))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30755
in-theory        30755
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not ((C -> (D -> (C and D))) and (A -> (A or B))))))
theorem-size     21
proof            (modus-ponens tm-465 tm-299 ((A (-> (-> B (or B C)) (not (and (-> Bm (-> Cm (and Bm Cm))) (-> B (or B C)))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-30755.        (not ((A -> (A or B)) -> (not ((C -> (D -> (C and D))) and (A -> (A or B)))))), M:tm-465, m:tm-299, u:((A (-> (-> B (or B C)) (not (and (-> Bm (-> Cm (and Bm Cm))) (-> B (or B C)))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30756
in-theory        30756
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (A -> (A and (A or B))))))
theorem-size     15
proof            (modus-ponens tm-465 tm-334 ((A (-> (-> Am (or Am C)) (not (-> Am (and Am (or Am C)))))) (B Am) (Bm (or Am C))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-30756.        (not ((A -> (A or B)) -> (not (A -> (A and (A or B)))))), M:tm-465, m:tm-334, u:((A (-> (-> Am (or Am C)) (not (-> Am (and Am (or Am C)))))) (B Am) (Bm (or Am C)))
================================================================
tm-name          tm-30757
in-theory        30757
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> (B and C))) -> (not (D -> (D or E))))))
theorem-size     17
proof            (modus-ponens tm-465 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (not (-> B (or B C)))))) (Dm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-4 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-30757.        (not (A and ((B -> (C -> (B and C))) -> (not (D -> (D or E)))))), M:tm-465, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (not (-> B (or B C)))))) (Dm (not (-> B (or B C)))))
================================================================
tm-name          tm-30758
in-theory        30758
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> (A and B))) -> (not (C -> (C or D)))) and E))
theorem-size     17
proof            (modus-ponens tm-465 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) (not (-> B (or B C)))) Dm)) (Cm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-3 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-30758.        (not (((A -> (B -> (A and B))) -> (not (C -> (C or D)))) and E)), M:tm-465, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) (not (-> B (or B C)))) Dm)) (Cm (not (-> B (or B C)))))
================================================================
tm-name          tm-30759
in-theory        30759
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (C -> (D -> (C and D))))))
theorem-size     15
proof            (modus-ponens tm-465 tm-350 ((A (-> (-> B (or B C)) (not (-> Bm (-> Cm (and Bm Cm)))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-30759.        (not ((A -> (A or B)) -> (not (C -> (D -> (C and D)))))), M:tm-465, m:tm-350, u:((A (-> (-> B (or B C)) (not (-> Bm (-> Cm (and Bm Cm)))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30760
in-theory        30760
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not ((C -> (C or D)) and (A -> (A or B))))))
theorem-size     19
proof            (modus-ponens tm-465 tm-449 ((A (-> (-> B (or B C)) (not (and (-> Bm (or Bm Cm)) (-> B (or B C)))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-30760.        (not ((A -> (A or B)) -> (not ((C -> (C or D)) and (A -> (A or B)))))), M:tm-465, m:tm-449, u:((A (-> (-> B (or B C)) (not (and (-> Bm (or Bm Cm)) (-> B (or B C)))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30761
in-theory        30761
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (B or C)) -> (not (D -> (D or E))))))
theorem-size     15
proof            (modus-ponens tm-465 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) (not (-> B (or B C)))))) (Dm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-30761.        (not (A and ((B -> (B or C)) -> (not (D -> (D or E)))))), M:tm-465, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) (not (-> B (or B C)))))) (Dm (not (-> B (or B C)))))
================================================================
tm-name          tm-30762
in-theory        30762
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (A or B)) -> (not (C -> (C or D)))) and E))
theorem-size     15
proof            (modus-ponens tm-465 tm-463 ((A (and (-> (-> Am (or Am Bm)) (not (-> B (or B C)))) Dm)) (Cm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-30762.        (not (((A -> (A or B)) -> (not (C -> (C or D)))) and E)), M:tm-465, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) (not (-> B (or B C)))) Dm)) (Cm (not (-> B (or B C)))))
================================================================
tm-name          tm-30763
in-theory        30763
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (C -> (C or D)))))
theorem-size     13
proof            (modus-ponens tm-465 tm-465 ((A (-> (-> B (or B C)) (not (-> Bm (or Bm Cm))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30763.        (not ((A -> (A or B)) -> (not (C -> (C or D))))), M:tm-465, m:tm-465, u:((A (-> (-> B (or B C)) (not (-> Bm (or Bm Cm))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-30764
in-theory        30764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30764.        (((A -> (not (B -> (B or C)))) -> (not A)) and (D -> (D or E))), M:tm-456, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30765
in-theory        30765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30765.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-453, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30766
in-theory        30766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and ((D -> (D or E)) and ((A -> (not (B -> (B or C)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30766.        (((A -> (not (B -> (B or C)))) -> (not A)) and ((D -> (D or E)) and ((A -> (not (B -> (B or C)))) -> (not A)))), M:tm-443, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30767
in-theory        30767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30767.        (((A -> (A or B)) or C) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-409, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30768
in-theory        30768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30768.        (((A -> (B -> (A and B))) or C) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-400, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30769
in-theory        30769
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30769.        ((((A and B) -> B) or C) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-391, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30770
in-theory        30770
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30770.        ((((A and B) -> A) or C) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-382, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30771
in-theory        30771
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (F -> (F or G)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30771.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (F -> (F or G)))) -> (not E))), M:tm-373, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30772
in-theory        30772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30772.        (((A -> (B -> A)) or C) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-364, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30773
in-theory        30773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (B or C)))) -> (D -> ((not A) and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30773.        ((A -> (not (B -> (B or C)))) -> (D -> ((not A) and D))), M:tm-355, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-30774
in-theory        30774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30774.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-354, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30775
in-theory        30775
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (C -> (C or D)))))
theorem-size     15
proof            (modus-ponens tm-350 tm-465 ((A (-> (-> B (-> C (and B C))) (not (-> Bm (or Bm Cm))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30775.        (not ((A -> (B -> (A and B))) -> (not (C -> (C or D))))), M:tm-350, m:tm-465, u:((A (-> (-> B (-> C (and B C))) (not (-> Bm (or Bm Cm))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-30776
in-theory        30776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30776.        (((A -> (not (B -> (B or C)))) -> (not A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30777
in-theory        30777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not (D -> (D or E)))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30777.        (((A -> B) -> (A -> (A and B))) and ((C -> (not (D -> (D or E)))) -> (not C))), M:tm-338, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30778
in-theory        30778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and ((A -> (not (B -> (B or C)))) -> ((A -> (not (B -> (B or C)))) and (not A))))
theorem-size     32
proof            (modus-ponens tm-328 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       142
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30778.        (((A -> (not (B -> (B or C)))) -> (not A)) and ((A -> (not (B -> (B or C)))) -> ((A -> (not (B -> (B or C)))) and (not A)))), M:tm-328, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-30779
in-theory        30779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not (B -> (B or C)))) -> (not A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30779.        (((A -> (not (B -> (B or C)))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not (B -> (B or C)))) -> (not A)))), M:tm-327, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30780
in-theory        30780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (((D and E) -> E) and ((A -> (not (B -> (B or C)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-1 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30780.        (((A -> (not (B -> (B or C)))) -> (not A)) and (((D and E) -> E) and ((A -> (not (B -> (B or C)))) -> (not A)))), M:tm-326, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30781
in-theory        30781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (((D and E) -> D) and ((A -> (not (B -> (B or C)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-1 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30781.        (((A -> (not (B -> (B or C)))) -> (not A)) and (((D and E) -> D) and ((A -> (not (B -> (B or C)))) -> (not A)))), M:tm-325, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30782
in-theory        30782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not (B -> (B or C)))) -> (not A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30782.        (((A -> (not (B -> (B or C)))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not (B -> (B or C)))) -> (not A)))), M:tm-324, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30783
in-theory        30783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not (B -> (B or C)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30783.        (((A -> (not (B -> (B or C)))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not (B -> (B or C)))) -> (not A)))), M:tm-323, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30784
in-theory        30784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-6)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30784.        (((A -> (not (B -> (B or C)))) -> (not A)) and ((D and E) -> E)), M:tm-322, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30785
in-theory        30785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-6)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30785.        (((A -> (not (B -> (B or C)))) -> (not A)) and ((D and E) -> D)), M:tm-320, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30786
in-theory        30786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30786.        (((A -> (not (B -> (B or C)))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30787
in-theory        30787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and ((A -> (not (B -> (B or C)))) -> (A -> (not (B -> (B or C))))))
theorem-size     29
proof            (modus-ponens tm-316 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30787.        (((A -> (not (B -> (B or C)))) -> (not A)) and ((A -> (not (B -> (B or C)))) -> (A -> (not (B -> (B or C)))))), M:tm-316, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-30788
in-theory        30788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30788.        (((A -> (not (B -> (B or C)))) -> (not A)) and (D -> (E -> D))), M:tm-315, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30789
in-theory        30789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (((A -> (not (B -> (B or C)))) -> (not (not A))) -> (not (A -> (not (B -> (B or C)))))))
theorem-size     34
proof            (modus-ponens tm-313 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30789.        (((A -> (not (B -> (B or C)))) -> (not A)) and (((A -> (not (B -> (B or C)))) -> (not (not A))) -> (not (A -> (not (B -> (B or C))))))), M:tm-313, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-30790
in-theory        30790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (((not A) -> D) -> (((A -> (not (B -> (B or C)))) or (not A)) -> D)))
theorem-size     30
proof            (modus-ponens tm-312 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-1 tm-6)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30790.        (((A -> (not (B -> (B or C)))) -> (not A)) and (((not A) -> D) -> (((A -> (not (B -> (B or C)))) or (not A)) -> D))), M:tm-312, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-30791
in-theory        30791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (D or ((A -> (not (B -> (B or C)))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30791.        (((A -> (not (B -> (B or C)))) -> (not A)) and (D or ((A -> (not (B -> (B or C)))) -> (not A)))), M:tm-311, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30792
in-theory        30792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (((A -> (not (B -> (B or C)))) -> (not A)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30792.        (((A -> (not (B -> (B or C)))) -> (not A)) and (((A -> (not (B -> (B or C)))) -> (not A)) or D)), M:tm-310, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30793
in-theory        30793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (D -> (((A -> (not (B -> (B or C)))) -> (not A)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30793.        (((A -> (not (B -> (B or C)))) -> (not A)) and (D -> (((A -> (not (B -> (B or C)))) -> (not A)) and D))), M:tm-309, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30794
in-theory        30794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (D -> ((A -> (not (B -> (B or C)))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30794.        (((A -> (not (B -> (B or C)))) -> (not A)) and (D -> ((A -> (not (B -> (B or C)))) -> (not A)))), M:tm-305, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30795
in-theory        30795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30795.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-303, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30796
in-theory        30796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30796.        ((A -> (((B and C) -> C) and A)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-270, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30797
in-theory        30797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30797.        ((A -> (((B and C) -> B) and A)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-239, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30798
in-theory        30798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (F -> (F or G)))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30798.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (F -> (F or G)))) -> (not E))), M:tm-210, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30799
in-theory        30799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30799.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-183, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30800
in-theory        30800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30800.        ((A -> ((B and C) -> C)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-157, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30801
in-theory        30801
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (not (C -> (C or D)))) -> (not (C -> (C or D))))) -> (not (B and (not (C -> (C or D))))))
theorem-size     27
proof            (modus-ponens tm-154 tm-465 ((Am (and A (not (-> Bm (or Bm Cm))))) (B (not (-> Bm (or Bm Cm)))) (C (not (and A (not (-> Bm (or Bm Cm))))))))
axioms-used      (tm-8 tm-1 tm-4 tm-9 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30801.        ((A or ((B and (not (C -> (C or D)))) -> (not (C -> (C or D))))) -> (not (B and (not (C -> (C or D)))))), M:tm-154, m:tm-465, u:((Am (and A (not (-> Bm (or Bm Cm))))) (B (not (-> Bm (or Bm Cm)))) (C (not (and A (not (-> Bm (or Bm Cm)))))))
================================================================
tm-name          tm-30802
in-theory        30802
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not (C -> (C or D)))))
theorem-size     13
proof            (modus-ponens tm-153 tm-465 ((A (-> (-> (and B C) C) (not (-> Bm (or Bm Cm))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30802.        (not (((A and B) -> B) -> (not (C -> (C or D))))), M:tm-153, m:tm-465, u:((A (-> (-> (and B C) C) (not (-> Bm (or Bm Cm))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-30803
in-theory        30803
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-1 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30803.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-147, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30804
in-theory        30804
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (not (C -> (C or D))))) -> B) or ((A and (B -> (not (C -> (C or D))))) -> (not (C -> (C or D))))) -> (not (A and (B -> (not (C -> (C or D)))))))
theorem-size     42
proof            (modus-ponens tm-144 tm-465 ((Am (and A (-> B (not (-> Bm (or Bm Cm)))))) (C (not (-> Bm (or Bm Cm)))) (D (not (and A (-> B (not (-> Bm (or Bm Cm)))))))))
axioms-used      (tm-8 tm-2 tm-4 tm-9 tm-1 tm-6)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30804.        ((((A and (B -> (not (C -> (C or D))))) -> B) or ((A and (B -> (not (C -> (C or D))))) -> (not (C -> (C or D))))) -> (not (A and (B -> (not (C -> (C or D))))))), M:tm-144, m:tm-465, u:((Am (and A (-> B (not (-> Bm (or Bm Cm)))))) (C (not (-> Bm (or Bm Cm)))) (D (not (and A (-> B (not (-> Bm (or Bm Cm))))))))
================================================================
tm-name          tm-30805
in-theory        30805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30805.        ((A -> ((B and C) -> B)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-134, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30806
in-theory        30806
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((not (B -> (B or C))) and D) -> (not (B -> (B or C))))) -> (not ((not (B -> (B or C))) and D)))
theorem-size     27
proof            (modus-ponens tm-131 tm-465 ((Am (and (not (-> Bm (or Bm Cm))) B)) (A (not (-> Bm (or Bm Cm)))) (C (not (and (not (-> Bm (or Bm Cm))) B)))))
axioms-used      (tm-8 tm-1 tm-3 tm-9 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30806.        ((A or (((not (B -> (B or C))) and D) -> (not (B -> (B or C))))) -> (not ((not (B -> (B or C))) and D))), M:tm-131, m:tm-465, u:((Am (and (not (-> Bm (or Bm Cm))) B)) (A (not (-> Bm (or Bm Cm)))) (C (not (and (not (-> Bm (or Bm Cm))) B))))
================================================================
tm-name          tm-30807
in-theory        30807
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not (C -> (C or D)))))
theorem-size     13
proof            (modus-ponens tm-130 tm-465 ((A (-> (-> (and B C) B) (not (-> Bm (or Bm Cm))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30807.        (not (((A and B) -> A) -> (not (C -> (C or D))))), M:tm-130, m:tm-465, u:((A (-> (-> (and B C) B) (not (-> Bm (or Bm Cm))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-30808
in-theory        30808
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-1 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30808.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-125, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30809
in-theory        30809
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not (B -> (B or C)))) and D) -> A) or (((A -> (not (B -> (B or C)))) and D) -> (not (B -> (B or C))))) -> (not ((A -> (not (B -> (B or C)))) and D)))
theorem-size     42
proof            (modus-ponens tm-122 tm-465 ((Am (and (-> A (not (-> Bm (or Bm Cm)))) C)) (B (not (-> Bm (or Bm Cm)))) (D (not (and (-> A (not (-> Bm (or Bm Cm)))) C)))))
axioms-used      (tm-8 tm-2 tm-3 tm-9 tm-1 tm-6)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30809.        (((((A -> (not (B -> (B or C)))) and D) -> A) or (((A -> (not (B -> (B or C)))) and D) -> (not (B -> (B or C))))) -> (not ((A -> (not (B -> (B or C)))) and D))), M:tm-122, m:tm-465, u:((Am (and (-> A (not (-> Bm (or Bm Cm)))) C)) (B (not (-> Bm (or Bm Cm)))) (D (not (and (-> A (not (-> Bm (or Bm Cm)))) C))))
================================================================
tm-name          tm-30810
in-theory        30810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (F or G)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30810.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (F or G)))) -> (not E))), M:tm-113, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30811
in-theory        30811
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (D or E)))))
theorem-size     21
proof            (modus-ponens tm-109 tm-465 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> Bm (or Bm Cm))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30811.        (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (D or E))))), M:tm-109, m:tm-465, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> Bm (or Bm Cm))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-30812
in-theory        30812
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30812.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-105, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30813
in-theory        30813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not (D -> (D or E)))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30813.        (((A -> B) -> (A -> A)) and ((C -> (not (D -> (D or E)))) -> (not C))), M:tm-95, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30814
in-theory        30814
times-derived    1
----------------------------------------------------------------
theorem          ((((not (A -> (A or B))) -> C) or ((not (A -> (A or B))) -> (not (A -> (A or B))))) -> (not (not (A -> (A or B)))))
theorem-size     30
proof            (modus-ponens tm-92 tm-465 ((Am (not (-> Bm (or Bm Cm)))) (A (not (-> Bm (or Bm Cm)))) (B (not (not (-> Bm (or Bm Cm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-9 tm-6)
proof-size       122
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30814.        ((((not (A -> (A or B))) -> C) or ((not (A -> (A or B))) -> (not (A -> (A or B))))) -> (not (not (A -> (A or B))))), M:tm-92, m:tm-465, u:((Am (not (-> Bm (or Bm Cm)))) (A (not (-> Bm (or Bm Cm)))) (B (not (not (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-30815
in-theory        30815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (B or C)))) -> (D -> (not A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30815.        ((A -> (not (B -> (B or C)))) -> (D -> (not A))), M:tm-84, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-30816
in-theory        30816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30816.        ((A -> (B -> (C -> B))) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-83, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30817
in-theory        30817
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (C -> (C or D)))))
theorem-size     13
proof            (modus-ponens tm-79 tm-465 ((A (-> (-> B (-> C B)) (not (-> Bm (or Bm Cm))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30817.        (not ((A -> (B -> A)) -> (not (C -> (C or D))))), M:tm-79, m:tm-465, u:((A (-> (-> B (-> C B)) (not (-> Bm (or Bm Cm))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-30818
in-theory        30818
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not (C -> (C or D)))) -> (not B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30818.        (((not (not A)) -> A) and ((B -> (not (C -> (C or D)))) -> (not B))), M:tm-76, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30819
in-theory        30819
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not (B -> (B or C)))))) or (A -> (not (B -> (B or C))))) -> (not A))
theorem-size     22
proof            (modus-ponens tm-73 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-1 tm-6)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30819.        (((not (not (A -> (not (B -> (B or C)))))) or (A -> (not (B -> (B or C))))) -> (not A)), M:tm-73, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-30820
in-theory        30820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (D -> (D or E)))) -> (not C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30820.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (D -> (D or E)))) -> (not C))), M:tm-69, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30821
in-theory        30821
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) or (((A -> (A or B)) -> (not C)) -> (not (A -> (A or B))))) -> (not ((A -> (A or B)) -> (not C))))
theorem-size     33
proof            (modus-ponens tm-66 tm-465 ((Am (-> (-> Bm (or Bm Cm)) (not B))) (A (-> Bm (or Bm Cm))) (C (not (-> (-> Bm (or Bm Cm)) (not B))))))
axioms-used      (tm-8 tm-9 tm-1 tm-6)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30821.        ((((A -> (A or B)) -> C) or (((A -> (A or B)) -> (not C)) -> (not (A -> (A or B))))) -> (not ((A -> (A or B)) -> (not C)))), M:tm-66, m:tm-465, u:((Am (-> (-> Bm (or Bm Cm)) (not B))) (A (-> Bm (or Bm Cm))) (C (not (-> (-> Bm (or Bm Cm)) (not B)))))
================================================================
tm-name          tm-30822
in-theory        30822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-1 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30822.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-54, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30823
in-theory        30823
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not (C -> (C or D))))) or (B -> (not (C -> (C or D))))) -> (not B))
theorem-size     22
proof            (modus-ponens tm-47 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-1 tm-6)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30823.        (((A and (B -> (not (C -> (C or D))))) or (B -> (not (C -> (C or D))))) -> (not B)), M:tm-47, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-30824
in-theory        30824
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not (B -> (B or C)))) and D) or (A -> (not (B -> (B or C))))) -> (not A))
theorem-size     22
proof            (modus-ponens tm-46 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-1 tm-6)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30824.        ((((A -> (not (B -> (B or C)))) and D) or (A -> (not (B -> (B or C))))) -> (not A)), M:tm-46, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-30825
in-theory        30825
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> (A or B))) or (C -> (not (A -> (A or B))))) -> (not C))
theorem-size     18
proof            (modus-ponens tm-44 tm-465 ((A Am) (B (not (-> Bm (or Bm Cm)))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-6)
proof-size       88
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30825.        (((not (A -> (A or B))) or (C -> (not (A -> (A or B))))) -> (not C)), M:tm-44, m:tm-465, u:((A Am) (B (not (-> Bm (or Bm Cm)))) (C (not Am)))
================================================================
tm-name          tm-30826
in-theory        30826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not (D -> (D or E)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30826.        ((A -> (B or A)) and ((C -> (not (D -> (D or E)))) -> (not C))), M:tm-42, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30827
in-theory        30827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not (D -> (D or E)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30827.        ((A -> (A or B)) and ((C -> (not (D -> (D or E)))) -> (not C))), M:tm-32, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30828
in-theory        30828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (B or C)))) -> ((A -> (not (B -> (B or C)))) and (not A)))
theorem-size     20
proof            (modus-ponens tm-24 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       88
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30828.        ((A -> (not (B -> (B or C)))) -> ((A -> (not (B -> (B or C)))) and (not A))), M:tm-24, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-30829
in-theory        30829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not (D -> (D or E)))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30829.        ((A -> (B -> (A and B))) and ((C -> (not (D -> (D or E)))) -> (not C))), M:tm-23, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30830
in-theory        30830
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not (D -> (D or E)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30830.        (((A and B) -> B) and ((C -> (not (D -> (D or E)))) -> (not C))), M:tm-22, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30831
in-theory        30831
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not (D -> (D or E)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30831.        (((A and B) -> A) and ((C -> (not (D -> (D or E)))) -> (not C))), M:tm-21, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30832
in-theory        30832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30832.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-20, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30833
in-theory        30833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not (D -> (D or E)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30833.        ((A -> (B -> A)) and ((C -> (not (D -> (D or E)))) -> (not C))), M:tm-19, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30834
in-theory        30834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (B or C)))) -> (A -> (not (B -> (B or C)))))
theorem-size     17
proof            (modus-ponens tm-12 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30834.        ((A -> (not (B -> (B or C)))) -> (A -> (not (B -> (B or C))))), M:tm-12, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-30835
in-theory        30835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not (not A))) -> (not (A -> (not (B -> (B or C))))))
theorem-size     22
proof            (modus-ponens tm-9 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-9 tm-1 tm-6)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30835.        (((A -> (not (B -> (B or C)))) -> (not (not A))) -> (not (A -> (not (B -> (B or C)))))), M:tm-9, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-30836
in-theory        30836
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not (C -> (C or D)))) or (not A)) -> B))
theorem-size     18
proof            (modus-ponens tm-8 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-1 tm-6)
proof-size       70
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30836.        (((not A) -> B) -> (((A -> (not (C -> (C or D)))) or (not A)) -> B)), M:tm-8, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-30837
in-theory        30837
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not (C -> (C or D)))) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-1 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30837.        (A or ((B -> (not (C -> (C or D)))) -> (not B))), M:tm-7, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30838
in-theory        30838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30838.        (((A -> (not (B -> (B or C)))) -> (not A)) or D), M:tm-6, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30839
in-theory        30839
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not (C -> (C or D)))) -> (not B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30839.        (A -> (((B -> (not (C -> (C or D)))) -> (not B)) and A)), M:tm-5, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30840
in-theory        30840
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not (C -> (C or D)))) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30840.        (A -> ((B -> (not (C -> (C or D)))) -> (not B))), M:tm-1, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-30841
in-theory        30841
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> (B -> (B or C))))
theorem-size     15
proof            (modus-ponens tm-466 tm-1 ((Am (-> A (or A B))) (C (-> Bm (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30841.        ((A or (B -> (B or C))) -> (D -> (B -> (B or C)))), M:tm-466, m:tm-1, u:((Am (-> A (or A B))) (C (-> Bm (-> A (or A B)))))
================================================================
tm-name          tm-30842
in-theory        30842
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> ((B -> (B or C)) and D)))
theorem-size     17
proof            (modus-ponens tm-466 tm-5 ((Am (-> A (or A B))) (C (-> Bm (and (-> A (or A B)) Bm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-30842.        ((A or (B -> (B or C))) -> (D -> ((B -> (B or C)) and D))), M:tm-466, m:tm-5, u:((Am (-> A (or A B))) (C (-> Bm (and (-> A (or A B)) Bm))))
================================================================
tm-name          tm-30843
in-theory        30843
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) or D))
theorem-size     15
proof            (modus-ponens tm-466 tm-6 ((Am (-> A (or A B))) (C (or (-> A (or A B)) Bm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30843.        ((A or (B -> (B or C))) -> ((B -> (B or C)) or D)), M:tm-466, m:tm-6, u:((Am (-> A (or A B))) (C (or (-> A (or A B)) Bm)))
================================================================
tm-name          tm-30844
in-theory        30844
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D or (B -> (B or C))))
theorem-size     15
proof            (modus-ponens tm-466 tm-7 ((Am (-> A (or A B))) (C (or Bm (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-30844.        ((A or (B -> (B or C))) -> (D or (B -> (B or C)))), M:tm-466, m:tm-7, u:((Am (-> A (or A B))) (C (or Bm (-> A (or A B)))))
================================================================
tm-name          tm-30845
in-theory        30845
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((B or C) -> D) -> ((B or (B or C)) -> D)))
theorem-size     21
proof            (modus-ponens tm-466 tm-8 ((A Am) (Bm (or Am B)) (C (-> (-> (or Am B) Cm) (-> (or Am (or Am B)) Cm)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30845.        ((A or (B -> (B or C))) -> (((B or C) -> D) -> ((B or (B or C)) -> D))), M:tm-466, m:tm-8, u:((A Am) (Bm (or Am B)) (C (-> (-> (or Am B) Cm) (-> (or Am (or Am B)) Cm))))
================================================================
tm-name          tm-30846
in-theory        30846
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (not (B or C))) -> (not B)))
theorem-size     17
proof            (modus-ponens tm-466 tm-9 ((A Am) (Bm (or Am B)) (C (-> (-> Am (not (or Am B))) (not Am)))))
axioms-used      (tm-8 tm-1 tm-6 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-30846.        ((A or (B -> (B or C))) -> ((B -> (not (B or C))) -> (not B))), M:tm-466, m:tm-9, u:((A Am) (Bm (or Am B)) (C (-> (-> Am (not (or Am B))) (not Am))))
================================================================
tm-name          tm-30847
in-theory        30847
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-466 tm-11 ((Am (-> A (or A B))) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30847.        ((A or (B -> (B or C))) -> (D -> (E -> D))), M:tm-466, m:tm-11, u:((Am (-> A (or A B))) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-30848
in-theory        30848
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (B -> B))
theorem-size     11
proof            (modus-ponens tm-466 tm-12 ((A Am) (Bm (or Am B)) (C (-> Am Am))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-30848.        ((A or (B -> (B or C))) -> (B -> B)), M:tm-466, m:tm-12, u:((A Am) (Bm (or Am B)) (C (-> Am Am)))
================================================================
tm-name          tm-30849
in-theory        30849
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-466 tm-14 ((Am (-> A (or A B))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30849.        ((A or (B -> (B or C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-466, m:tm-14, u:((Am (-> A (or A B))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-30850
in-theory        30850
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-466 tm-16 ((Am (-> A (or A B))) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30850.        ((A or (B -> (B or C))) -> ((D and E) -> D)), M:tm-466, m:tm-16, u:((Am (-> A (or A B))) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-30851
in-theory        30851
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-466 tm-18 ((Am (-> A (or A B))) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-1 tm-6 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30851.        ((A or (B -> (B or C))) -> ((D and E) -> E)), M:tm-466, m:tm-18, u:((Am (-> A (or A B))) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-30852
in-theory        30852
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (E -> D)) and (B -> (B or C))))
theorem-size     19
proof            (modus-ponens tm-466 tm-19 ((Am (-> A (or A B))) (C (and (-> Bm (-> Cm Bm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30852.        ((A or (B -> (B or C))) -> ((D -> (E -> D)) and (B -> (B or C)))), M:tm-466, m:tm-19, u:((Am (-> A (or A B))) (C (and (-> Bm (-> Cm Bm)) (-> A (or A B)))))
================================================================
tm-name          tm-30853
in-theory        30853
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (B or C))))
theorem-size     27
proof            (modus-ponens tm-466 tm-20 ((Am (-> A (or A B))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30853.        ((A or (B -> (B or C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (B or C)))), M:tm-466, m:tm-20, u:((Am (-> A (or A B))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (or A B)))))
================================================================
tm-name          tm-30854
in-theory        30854
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D and E) -> D) and (B -> (B or C))))
theorem-size     19
proof            (modus-ponens tm-466 tm-21 ((Am (-> A (or A B))) (C (and (-> (and Bm Cm) Bm) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30854.        ((A or (B -> (B or C))) -> (((D and E) -> D) and (B -> (B or C)))), M:tm-466, m:tm-21, u:((Am (-> A (or A B))) (C (and (-> (and Bm Cm) Bm) (-> A (or A B)))))
================================================================
tm-name          tm-30855
in-theory        30855
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D and E) -> E) and (B -> (B or C))))
theorem-size     19
proof            (modus-ponens tm-466 tm-22 ((Am (-> A (or A B))) (C (and (-> (and Bm Cm) Cm) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30855.        ((A or (B -> (B or C))) -> (((D and E) -> E) and (B -> (B or C)))), M:tm-466, m:tm-22, u:((Am (-> A (or A B))) (C (and (-> (and Bm Cm) Cm) (-> A (or A B)))))
================================================================
tm-name          tm-30856
in-theory        30856
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (E -> (D and E))) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-23 ((Am (-> A (or A B))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30856.        ((A or (B -> (B or C))) -> ((D -> (E -> (D and E))) and (B -> (B or C)))), M:tm-466, m:tm-23, u:((Am (-> A (or A B))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (or A B)))))
================================================================
tm-name          tm-30857
in-theory        30857
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (B -> (B and (B or C))))
theorem-size     15
proof            (modus-ponens tm-466 tm-24 ((A Am) (Bm (or Am B)) (C (-> Am (and Am (or Am B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-30857.        ((A or (B -> (B or C))) -> (B -> (B and (B or C)))), M:tm-466, m:tm-24, u:((A Am) (Bm (or Am B)) (C (-> Am (and Am (or Am B)))))
================================================================
tm-name          tm-30858
in-theory        30858
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-466 tm-25 ((Am (-> A (or A B))) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30858.        ((A or (B -> (B or C))) -> (D -> (E -> (D and E)))), M:tm-466, m:tm-25, u:((Am (-> A (or A B))) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-30859
in-theory        30859
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (D or E)) and (B -> (B or C))))
theorem-size     19
proof            (modus-ponens tm-466 tm-32 ((Am (-> A (or A B))) (C (and (-> Bm (or Bm Cm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30859.        ((A or (B -> (B or C))) -> ((D -> (D or E)) and (B -> (B or C)))), M:tm-466, m:tm-32, u:((Am (-> A (or A B))) (C (and (-> Bm (or Bm Cm)) (-> A (or A B)))))
================================================================
tm-name          tm-30860
in-theory        30860
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-466 tm-33 ((Am (-> A (or A B))) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30860.        ((A or (B -> (B or C))) -> (D -> (D or E))), M:tm-466, m:tm-33, u:((Am (-> A (or A B))) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-30861
in-theory        30861
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (E or D)) and (B -> (B or C))))
theorem-size     19
proof            (modus-ponens tm-466 tm-42 ((Am (-> A (or A B))) (C (and (-> Bm (or Cm Bm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30861.        ((A or (B -> (B or C))) -> ((D -> (E or D)) and (B -> (B or C)))), M:tm-466, m:tm-42, u:((Am (-> A (or A B))) (C (and (-> Bm (or Cm Bm)) (-> A (or A B)))))
================================================================
tm-name          tm-30862
in-theory        30862
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-466 tm-43 ((Am (-> A (or A B))) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30862.        ((A or (B -> (B or C))) -> (D -> (E or D))), M:tm-466, m:tm-43, u:((Am (-> A (or A B))) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-30863
in-theory        30863
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> C) or D))) -> ((C or (B -> C)) -> ((B -> C) or D)))
theorem-size     23
proof            (modus-ponens tm-466 tm-44 ((A (-> Am Bm)) (Cm (or (-> Am Bm) B)) (C (-> (or Bm (-> Am Bm)) (or (-> Am Bm) B)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-30863.        ((A or ((B -> C) -> ((B -> C) or D))) -> ((C or (B -> C)) -> ((B -> C) or D))), M:tm-466, m:tm-44, u:((A (-> Am Bm)) (Cm (or (-> Am Bm) B)) (C (-> (or Bm (-> Am Bm)) (or (-> Am Bm) B))))
================================================================
tm-name          tm-30864
in-theory        30864
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (((B -> C) -> (B -> D)) or E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (B -> D)) or E)))
theorem-size     43
proof            (modus-ponens tm-466 tm-45 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (or (-> (-> Am Bm) (-> Am Cm)) B)) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-30864.        ((A or (((B -> C) -> (B -> D)) -> (((B -> C) -> (B -> D)) or E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (B -> D)) or E))), M:tm-466, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (or (-> (-> Am Bm) (-> Am Cm)) B)) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) B))))
================================================================
tm-name          tm-30865
in-theory        30865
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((B and D) or B) -> (B or C)))
theorem-size     17
proof            (modus-ponens tm-466 tm-46 ((A Am) (Bm (or Am B)) (C (-> (or (and Am Cm) Am) (or Am B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-30865.        ((A or (B -> (B or C))) -> (((B and D) or B) -> (B or C))), M:tm-466, m:tm-46, u:((A Am) (Bm (or Am B)) (C (-> (or (and Am Cm) Am) (or Am B))))
================================================================
tm-name          tm-30866
in-theory        30866
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D and B) or B) -> (B or C)))
theorem-size     17
proof            (modus-ponens tm-466 tm-47 ((A Am) (Bm (or Am B)) (C (-> (or (and Cm Am) Am) (or Am B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-30866.        ((A or (B -> (B or C))) -> (((D and B) or B) -> (B or C))), M:tm-466, m:tm-47, u:((A Am) (Bm (or Am B)) (C (-> (or (and Cm Am) Am) (or Am B))))
================================================================
tm-name          tm-30867
in-theory        30867
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> ((B -> (C and B)) or D))) -> ((C or (B -> (C and B))) -> ((B -> (C and B)) or D)))
theorem-size     31
proof            (modus-ponens tm-466 tm-48 ((A (-> Am (and Bm Am))) (Cm (or (-> Am (and Bm Am)) B)) (C (-> (or Bm (-> Am (and Bm Am))) (or (-> Am (and Bm Am)) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-30867.        ((A or ((B -> (C and B)) -> ((B -> (C and B)) or D))) -> ((C or (B -> (C and B))) -> ((B -> (C and B)) or D))), M:tm-466, m:tm-48, u:((A (-> Am (and Bm Am))) (Cm (or (-> Am (and Bm Am)) B)) (C (-> (or Bm (-> Am (and Bm Am))) (or (-> Am (and Bm Am)) B))))
================================================================
tm-name          tm-30868
in-theory        30868
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> ((B or C) or D))) -> ((B or (B or C)) -> ((B or C) or D)))
theorem-size     23
proof            (modus-ponens tm-466 tm-49 ((A (or Am Bm)) (Cm (or (or Am Bm) B)) (C (-> (or Am (or Am Bm)) (or (or Am Bm) B)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-30868.        ((A or ((B or C) -> ((B or C) or D))) -> ((B or (B or C)) -> ((B or C) or D))), M:tm-466, m:tm-49, u:((A (or Am Bm)) (Cm (or (or Am Bm) B)) (C (-> (or Am (or Am Bm)) (or (or Am Bm) B))))
================================================================
tm-name          tm-30869
in-theory        30869
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> ((B or C) or D))) -> ((C or (B or C)) -> ((B or C) or D)))
theorem-size     23
proof            (modus-ponens tm-466 tm-50 ((A (or Am Bm)) (Cm (or (or Am Bm) B)) (C (-> (or Bm (or Am Bm)) (or (or Am Bm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-30869.        ((A or ((B or C) -> ((B or C) or D))) -> ((C or (B or C)) -> ((B or C) or D))), M:tm-466, m:tm-50, u:((A (or Am Bm)) (Cm (or (or Am Bm) B)) (C (-> (or Bm (or Am Bm)) (or (or Am Bm) B))))
================================================================
tm-name          tm-30870
in-theory        30870
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> ((D or B) -> C)) or E))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (((B -> C) -> ((D or B) -> C)) or E)))
theorem-size     49
proof            (modus-ponens tm-466 tm-51 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-30870.        ((A or (((B -> C) -> ((D or B) -> C)) -> (((B -> C) -> ((D or B) -> C)) or E))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (((B -> C) -> ((D or B) -> C)) or E))), M:tm-466, m:tm-51, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) B)) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (or (-> (-> Am Bm) (-> (or Cm Am) Bm)) B))))
================================================================
tm-name          tm-30871
in-theory        30871
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B -> (B or C))))
theorem-size     27
proof            (modus-ponens tm-466 tm-54 ((Am (-> A (or A B))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-30871.        ((A or (B -> (B or C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B -> (B or C)))), M:tm-466, m:tm-54, u:((Am (-> A (or A B))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A (or A B)))))
================================================================
tm-name          tm-30872
in-theory        30872
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-466 tm-56 ((Am (-> A (or A B))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-30872.        ((A or (B -> (B or C))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-466, m:tm-56, u:((Am (-> A (or A B))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-30873
in-theory        30873
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (not C)) -> (not B)) -> (((B -> (not C)) -> (not B)) or D))) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> (((B -> (not C)) -> (not B)) or D)))
theorem-size     41
proof            (modus-ponens tm-466 tm-66 ((A (-> (-> Am (not Bm)) (not Am))) (Cm (or (-> (-> Am (not Bm)) (not Am)) B)) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (or (-> (-> Am (not Bm)) (not Am)) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-9)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-30873.        ((A or (((B -> (not C)) -> (not B)) -> (((B -> (not C)) -> (not B)) or D))) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> (((B -> (not C)) -> (not B)) or D))), M:tm-466, m:tm-66, u:((A (-> (-> Am (not Bm)) (not Am))) (Cm (or (-> (-> Am (not Bm)) (not Am)) B)) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (or (-> (-> Am (not Bm)) (not Am)) B))))
================================================================
tm-name          tm-30874
in-theory        30874
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (B -> (B or C))))
theorem-size     25
proof            (modus-ponens tm-466 tm-69 ((Am (-> A (or A B))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-30874.        ((A or (B -> (B or C))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (B -> (B or C)))), M:tm-466, m:tm-69, u:((Am (-> A (or A B))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A (or A B)))))
================================================================
tm-name          tm-30875
in-theory        30875
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-466 tm-71 ((Am (-> A (or A B))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-30875.        ((A or (B -> (B or C))) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-466, m:tm-71, u:((Am (-> A (or A B))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-30876
in-theory        30876
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((not (not B)) or B) -> (B or C)))
theorem-size     17
proof            (modus-ponens tm-466 tm-73 ((A Am) (Bm (or Am B)) (C (-> (or (not (not Am)) Am) (or Am B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-30876.        ((A or (B -> (B or C))) -> (((not (not B)) or B) -> (B or C))), M:tm-466, m:tm-73, u:((A Am) (Bm (or Am B)) (C (-> (or (not (not Am)) Am) (or Am B))))
================================================================
tm-name          tm-30877
in-theory        30877
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((not (not D)) -> D) and (B -> (B or C))))
theorem-size     19
proof            (modus-ponens tm-466 tm-76 ((Am (-> A (or A B))) (C (and (-> (not (not Bm)) Bm) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-30877.        ((A or (B -> (B or C))) -> (((not (not D)) -> D) and (B -> (B or C)))), M:tm-466, m:tm-76, u:((Am (-> A (or A B))) (C (and (-> (not (not Bm)) Bm) (-> A (or A B)))))
================================================================
tm-name          tm-30878
in-theory        30878
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-466 tm-78 ((Am (-> A (or A B))) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-6 tm-10)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-30878.        ((A or (B -> (B or C))) -> ((not (not D)) -> D)), M:tm-466, m:tm-78, u:((Am (-> A (or A B))) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-30879
in-theory        30879
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) -> ((B -> (C -> B)) or D))) -> ((E or (B -> (C -> B))) -> ((B -> (C -> B)) or D)))
theorem-size     31
proof            (modus-ponens tm-466 tm-80 ((A (-> Am (-> Bm Am))) (Cm (or (-> Am (-> Bm Am)) B)) (C (-> (or Dm (-> Am (-> Bm Am))) (or (-> Am (-> Bm Am)) B)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-30879.        ((A or ((B -> (C -> B)) -> ((B -> (C -> B)) or D))) -> ((E or (B -> (C -> B))) -> ((B -> (C -> B)) or D))), M:tm-466, m:tm-80, u:((A (-> Am (-> Bm Am))) (Cm (or (-> Am (-> Bm Am)) B)) (C (-> (or Dm (-> Am (-> Bm Am))) (or (-> Am (-> Bm Am)) B))))
================================================================
tm-name          tm-30880
in-theory        30880
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (E -> (F -> E))) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-83 ((Am (-> A (or A B))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-30880.        ((A or (B -> (B or C))) -> ((D -> (E -> (F -> E))) and (B -> (B or C)))), M:tm-466, m:tm-83, u:((Am (-> A (or A B))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (or A B)))))
================================================================
tm-name          tm-30881
in-theory        30881
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (B -> (D -> (B or C))))
theorem-size     15
proof            (modus-ponens tm-466 tm-84 ((A Am) (Bm (or Am B)) (C (-> Am (-> Cm (or Am B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-30881.        ((A or (B -> (B or C))) -> (B -> (D -> (B or C)))), M:tm-466, m:tm-84, u:((A Am) (Bm (or Am B)) (C (-> Am (-> Cm (or Am B)))))
================================================================
tm-name          tm-30882
in-theory        30882
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-466 tm-85 ((Am (-> A (or A B))) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-30882.        ((A or (B -> (B or C))) -> (D -> (E -> (F -> E)))), M:tm-466, m:tm-85, u:((Am (-> A (or A B))) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-30883
in-theory        30883
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (B -> (B or C)))
theorem-size     13
proof            (modus-ponens tm-466 tm-86 ((Am (-> A (or A B))) (C (-> A (or A B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-30883.        ((A or (B -> (B or C))) -> (B -> (B or C))), M:tm-466, m:tm-86, u:((Am (-> A (or A B))) (C (-> A (or A B))))
================================================================
tm-name          tm-30884
in-theory        30884
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> B) -> ((B -> B) or C))) -> (((B -> D) or (B -> B)) -> ((B -> B) or C)))
theorem-size     25
proof            (modus-ponens tm-466 tm-92 ((A (-> Am Am)) (Bm (or (-> Am Am) B)) (C (-> (or (-> Am Cm) (-> Am Am)) (or (-> Am Am) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-30884.        ((A or ((B -> B) -> ((B -> B) or C))) -> (((B -> D) or (B -> B)) -> ((B -> B) or C))), M:tm-466, m:tm-92, u:((A (-> Am Am)) (Bm (or (-> Am Am) B)) (C (-> (or (-> Am Cm) (-> Am Am)) (or (-> Am Am) B))))
================================================================
tm-name          tm-30885
in-theory        30885
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> E) -> (D -> D)) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-95 ((Am (-> A (or A B))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-30885.        ((A or (B -> (B or C))) -> (((D -> E) -> (D -> D)) and (B -> (B or C)))), M:tm-466, m:tm-95, u:((Am (-> A (or A B))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (or A B)))))
================================================================
tm-name          tm-30886
in-theory        30886
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-466 tm-97 ((Am (-> A (or A B))) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-30886.        ((A or (B -> (B or C))) -> ((D -> E) -> (D -> D))), M:tm-466, m:tm-97, u:((Am (-> A (or A B))) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-30887
in-theory        30887
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> D)) -> (((B -> (C -> D)) -> (B -> D)) or E))) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> (((B -> (C -> D)) -> (B -> D)) or E)))
theorem-size     55
proof            (modus-ponens tm-466 tm-102 ((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (Dm (or (-> (-> Am (-> Bm Cm)) (-> Am Cm)) B)) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (or (-> (-> Am (-> Bm Cm)) (-> Am Cm)) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-30887.        ((A or (((B -> (C -> D)) -> (B -> D)) -> (((B -> (C -> D)) -> (B -> D)) or E))) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> (((B -> (C -> D)) -> (B -> D)) or E))), M:tm-466, m:tm-102, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (Dm (or (-> (-> Am (-> Bm Cm)) (-> Am Cm)) B)) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (or (-> (-> Am (-> Bm Cm)) (-> Am Cm)) B))))
================================================================
tm-name          tm-30888
in-theory        30888
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (B -> (B or C))))
theorem-size     33
proof            (modus-ponens tm-466 tm-105 ((Am (-> A (or A B))) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-30888.        ((A or (B -> (B or C))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (B -> (B or C)))), M:tm-466, m:tm-105, u:((Am (-> A (or A B))) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A (or A B)))))
================================================================
tm-name          tm-30889
in-theory        30889
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-466 tm-107 ((Am (-> A (or A B))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-30889.        ((A or (B -> (B or C))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-466, m:tm-107, u:((Am (-> A (or A B))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-30890
in-theory        30890
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))
theorem-size     63
proof            (modus-ponens tm-466 tm-110 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-30890.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))), M:tm-466, m:tm-110, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))))
================================================================
tm-name          tm-30891
in-theory        30891
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (B or C))))
theorem-size     29
proof            (modus-ponens tm-466 tm-113 ((Am (-> A (or A B))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-30891.        ((A or (B -> (B or C))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (B or C)))), M:tm-466, m:tm-113, u:((Am (-> A (or A B))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (or A B)))))
================================================================
tm-name          tm-30892
in-theory        30892
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-466 tm-115 ((Am (-> A (or A B))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-30892.        ((A or (B -> (B or C))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-466, m:tm-115, u:((Am (-> A (or A B))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-30893
in-theory        30893
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> C) -> ((((B -> C) and D) -> C) or E))) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> ((((B -> C) and D) -> C) or E)))
theorem-size     45
proof            (modus-ponens tm-466 tm-122 ((A (-> (and (-> Am Bm) Cm) Bm)) (Dm (or (-> (and (-> Am Bm) Cm) Bm) B)) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (or (-> (and (-> Am Bm) Cm) Bm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-30893.        ((A or ((((B -> C) and D) -> C) -> ((((B -> C) and D) -> C) or E))) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> ((((B -> C) and D) -> C) or E))), M:tm-466, m:tm-122, u:((A (-> (and (-> Am Bm) Cm) Bm)) (Dm (or (-> (and (-> Am Bm) Cm) Bm) B)) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (or (-> (and (-> Am Bm) Cm) Bm) B))))
================================================================
tm-name          tm-30894
in-theory        30894
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (B -> (B or C))))
theorem-size     29
proof            (modus-ponens tm-466 tm-125 ((Am (-> A (or A B))) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-30894.        ((A or (B -> (B or C))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (B -> (B or C)))), M:tm-466, m:tm-125, u:((Am (-> A (or A B))) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A (or A B)))))
================================================================
tm-name          tm-30895
in-theory        30895
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-466 tm-127 ((Am (-> A (or A B))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-30895.        ((A or (B -> (B or C))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-466, m:tm-127, u:((Am (-> A (or A B))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-30896
in-theory        30896
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) -> (((B and C) -> B) or D))) -> ((E or ((B and C) -> B)) -> (((B and C) -> B) or D)))
theorem-size     31
proof            (modus-ponens tm-466 tm-131 ((A (-> (and Am Bm) Am)) (Cm (or (-> (and Am Bm) Am) B)) (C (-> (or Dm (-> (and Am Bm) Am)) (or (-> (and Am Bm) Am) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-30896.        ((A or (((B and C) -> B) -> (((B and C) -> B) or D))) -> ((E or ((B and C) -> B)) -> (((B and C) -> B) or D))), M:tm-466, m:tm-131, u:((A (-> (and Am Bm) Am)) (Cm (or (-> (and Am Bm) Am) B)) (C (-> (or Dm (-> (and Am Bm) Am)) (or (-> (and Am Bm) Am) B))))
================================================================
tm-name          tm-30897
in-theory        30897
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> ((E and F) -> E)) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-134 ((Am (-> A (or A B))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-30897.        ((A or (B -> (B or C))) -> ((D -> ((E and F) -> E)) and (B -> (B or C)))), M:tm-466, m:tm-134, u:((Am (-> A (or A B))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (or A B)))))
================================================================
tm-name          tm-30898
in-theory        30898
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-466 tm-136 ((Am (-> A (or A B))) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-30898.        ((A or (B -> (B or C))) -> (D -> ((E and F) -> E))), M:tm-466, m:tm-136, u:((Am (-> A (or A B))) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-30899
in-theory        30899
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> D) -> (((B and (C -> D)) -> D) or E))) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> (((B and (C -> D)) -> D) or E)))
theorem-size     45
proof            (modus-ponens tm-466 tm-144 ((A (-> (and Am (-> Bm Cm)) Cm)) (Dm (or (-> (and Am (-> Bm Cm)) Cm) B)) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (or (-> (and Am (-> Bm Cm)) Cm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-4)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-30899.        ((A or (((B and (C -> D)) -> D) -> (((B and (C -> D)) -> D) or E))) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> (((B and (C -> D)) -> D) or E))), M:tm-466, m:tm-144, u:((A (-> (and Am (-> Bm Cm)) Cm)) (Dm (or (-> (and Am (-> Bm Cm)) Cm) B)) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (or (-> (and Am (-> Bm Cm)) Cm) B))))
================================================================
tm-name          tm-30900
in-theory        30900
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (B -> (B or C))))
theorem-size     29
proof            (modus-ponens tm-466 tm-147 ((Am (-> A (or A B))) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-30900.        ((A or (B -> (B or C))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (B -> (B or C)))), M:tm-466, m:tm-147, u:((Am (-> A (or A B))) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A (or A B)))))
================================================================
tm-name          tm-30901
in-theory        30901
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-466 tm-149 ((Am (-> A (or A B))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-30901.        ((A or (B -> (B or C))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-466, m:tm-149, u:((Am (-> A (or A B))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-30902
in-theory        30902
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) -> (((B and C) -> C) or D))) -> ((E or ((B and C) -> C)) -> (((B and C) -> C) or D)))
theorem-size     31
proof            (modus-ponens tm-466 tm-154 ((A (-> (and Am Bm) Bm)) (Cm (or (-> (and Am Bm) Bm) B)) (C (-> (or Dm (-> (and Am Bm) Bm)) (or (-> (and Am Bm) Bm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-30902.        ((A or (((B and C) -> C) -> (((B and C) -> C) or D))) -> ((E or ((B and C) -> C)) -> (((B and C) -> C) or D))), M:tm-466, m:tm-154, u:((A (-> (and Am Bm) Bm)) (Cm (or (-> (and Am Bm) Bm) B)) (C (-> (or Dm (-> (and Am Bm) Bm)) (or (-> (and Am Bm) Bm) B))))
================================================================
tm-name          tm-30903
in-theory        30903
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> ((E and F) -> F)) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-157 ((Am (-> A (or A B))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-30903.        ((A or (B -> (B or C))) -> ((D -> ((E and F) -> F)) and (B -> (B or C)))), M:tm-466, m:tm-157, u:((Am (-> A (or A B))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (or A B)))))
================================================================
tm-name          tm-30904
in-theory        30904
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-466 tm-159 ((Am (-> A (or A B))) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-30904.        ((A or (B -> (B or C))) -> (D -> ((E and F) -> F))), M:tm-466, m:tm-159, u:((Am (-> A (or A B))) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-30905
in-theory        30905
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> B)) and D) -> (((B -> (C -> B)) and D) or E))) -> ((D or ((B -> (C -> B)) and D)) -> (((B -> (C -> B)) and D) or E)))
theorem-size     39
proof            (modus-ponens tm-466 tm-180 ((A (and (-> Am (-> Bm Am)) Cm)) (Dm (or (and (-> Am (-> Bm Am)) Cm) B)) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (or (and (-> Am (-> Bm Am)) Cm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-30905.        ((A or (((B -> (C -> B)) and D) -> (((B -> (C -> B)) and D) or E))) -> ((D or ((B -> (C -> B)) and D)) -> (((B -> (C -> B)) and D) or E))), M:tm-466, m:tm-180, u:((A (and (-> Am (-> Bm Am)) Cm)) (Dm (or (and (-> Am (-> Bm Am)) Cm) B)) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (or (and (-> Am (-> Bm Am)) Cm) B))))
================================================================
tm-name          tm-30906
in-theory        30906
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> ((E -> (F -> E)) and D)) and (B -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-466 tm-183 ((Am (-> A (or A B))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-30906.        ((A or (B -> (B or C))) -> ((D -> ((E -> (F -> E)) and D)) and (B -> (B or C)))), M:tm-466, m:tm-183, u:((Am (-> A (or A B))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (or A B)))))
================================================================
tm-name          tm-30907
in-theory        30907
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-466 tm-184 ((Am (-> A (or A B))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-30907.        ((A or (B -> (B or C))) -> (D -> ((E -> (F -> E)) and D))), M:tm-466, m:tm-184, u:((Am (-> A (or A B))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-30908
in-theory        30908
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) or F))) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) or F)))
theorem-size     71
proof            (modus-ponens tm-466 tm-207 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (or (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B)) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (or (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-2)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-30908.        ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) or F))) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) or F))), M:tm-466, m:tm-207, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (or (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B)) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (or (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B))))
================================================================
tm-name          tm-30909
in-theory        30909
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (B -> (B or C))))
theorem-size     31
proof            (modus-ponens tm-466 tm-210 ((Am (-> A (or A B))) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-30909.        ((A or (B -> (B or C))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (B -> (B or C)))), M:tm-466, m:tm-210, u:((Am (-> A (or A B))) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A (or A B)))))
================================================================
tm-name          tm-30910
in-theory        30910
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-466 tm-211 ((Am (-> A (or A B))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-30910.        ((A or (B -> (B or C))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-466, m:tm-211, u:((Am (-> A (or A B))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-30911
in-theory        30911
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> B) and D) -> ((((B and C) -> B) and D) or E))) -> ((D or (((B and C) -> B) and D)) -> ((((B and C) -> B) and D) or E)))
theorem-size     39
proof            (modus-ponens tm-466 tm-236 ((A (and (-> (and Am Bm) Am) Cm)) (Dm (or (and (-> (and Am Bm) Am) Cm) B)) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (or (and (-> (and Am Bm) Am) Cm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-30911.        ((A or ((((B and C) -> B) and D) -> ((((B and C) -> B) and D) or E))) -> ((D or (((B and C) -> B) and D)) -> ((((B and C) -> B) and D) or E))), M:tm-466, m:tm-236, u:((A (and (-> (and Am Bm) Am) Cm)) (Dm (or (and (-> (and Am Bm) Am) Cm) B)) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (or (and (-> (and Am Bm) Am) Cm) B))))
================================================================
tm-name          tm-30912
in-theory        30912
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (((E and F) -> E) and D)) and (B -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-466 tm-239 ((Am (-> A (or A B))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-30912.        ((A or (B -> (B or C))) -> ((D -> (((E and F) -> E) and D)) and (B -> (B or C)))), M:tm-466, m:tm-239, u:((Am (-> A (or A B))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A (or A B)))))
================================================================
tm-name          tm-30913
in-theory        30913
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-466 tm-240 ((Am (-> A (or A B))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-30913.        ((A or (B -> (B or C))) -> (D -> (((E and F) -> E) and D))), M:tm-466, m:tm-240, u:((Am (-> A (or A B))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-30914
in-theory        30914
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> C) and D) -> ((((B and C) -> C) and D) or E))) -> ((D or (((B and C) -> C) and D)) -> ((((B and C) -> C) and D) or E)))
theorem-size     39
proof            (modus-ponens tm-466 tm-267 ((A (and (-> (and Am Bm) Bm) Cm)) (Dm (or (and (-> (and Am Bm) Bm) Cm) B)) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (or (and (-> (and Am Bm) Bm) Cm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-30914.        ((A or ((((B and C) -> C) and D) -> ((((B and C) -> C) and D) or E))) -> ((D or (((B and C) -> C) and D)) -> ((((B and C) -> C) and D) or E))), M:tm-466, m:tm-267, u:((A (and (-> (and Am Bm) Bm) Cm)) (Dm (or (and (-> (and Am Bm) Bm) Cm) B)) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (or (and (-> (and Am Bm) Bm) Cm) B))))
================================================================
tm-name          tm-30915
in-theory        30915
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (((E and F) -> F) and D)) and (B -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-466 tm-270 ((Am (-> A (or A B))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-30915.        ((A or (B -> (B or C))) -> ((D -> (((E and F) -> F) and D)) and (B -> (B or C)))), M:tm-466, m:tm-270, u:((Am (-> A (or A B))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A (or A B)))))
================================================================
tm-name          tm-30916
in-theory        30916
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-466 tm-271 ((Am (-> A (or A B))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-30916.        ((A or (B -> (B or C))) -> (D -> (((E and F) -> F) and D))), M:tm-466, m:tm-271, u:((Am (-> A (or A B))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-30917
in-theory        30917
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> (B and C))) and D) -> (((B -> (C -> (B and C))) and D) or E))) -> ((D or ((B -> (C -> (B and C))) and D)) -> (((B -> (C -> (B and C))) and D) or E)))
theorem-size     47
proof            (modus-ponens tm-466 tm-300 ((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (or (and (-> Am (-> Bm (and Am Bm))) Cm) B)) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (or (and (-> Am (-> Bm (and Am Bm))) Cm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-30917.        ((A or (((B -> (C -> (B and C))) and D) -> (((B -> (C -> (B and C))) and D) or E))) -> ((D or ((B -> (C -> (B and C))) and D)) -> (((B -> (C -> (B and C))) and D) or E))), M:tm-466, m:tm-300, u:((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (or (and (-> Am (-> Bm (and Am Bm))) Cm) B)) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (or (and (-> Am (-> Bm (and Am Bm))) Cm) B))))
================================================================
tm-name          tm-30918
in-theory        30918
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> ((E -> (F -> (E and F))) and D)) and (B -> (B or C))))
theorem-size     25
proof            (modus-ponens tm-466 tm-303 ((Am (-> A (or A B))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-30918.        ((A or (B -> (B or C))) -> ((D -> ((E -> (F -> (E and F))) and D)) and (B -> (B or C)))), M:tm-466, m:tm-303, u:((Am (-> A (or A B))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A (or A B)))))
================================================================
tm-name          tm-30919
in-theory        30919
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-466 tm-304 ((Am (-> A (or A B))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-30919.        ((A or (B -> (B or C))) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-466, m:tm-304, u:((Am (-> A (or A B))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-30920
in-theory        30920
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (D -> (B -> (B or C)))))
theorem-size     21
proof            (modus-ponens tm-466 tm-305 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> Bm (-> A (or A B)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-30920.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (D -> (B -> (B or C))))), M:tm-466, m:tm-305, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> Bm (-> A (or A B))))))
================================================================
tm-name          tm-30921
in-theory        30921
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (D -> ((B -> (B or C)) and D))))
theorem-size     23
proof            (modus-ponens tm-466 tm-309 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> Bm (and (-> A (or A B)) Bm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-30921.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (D -> ((B -> (B or C)) and D)))), M:tm-466, m:tm-309, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> Bm (and (-> A (or A B)) Bm)))))
================================================================
tm-name          tm-30922
in-theory        30922
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((B -> (B or C)) or D)))
theorem-size     21
proof            (modus-ponens tm-466 tm-310 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (or (-> A (or A B)) Bm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-30922.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((B -> (B or C)) or D))), M:tm-466, m:tm-310, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (or (-> A (or A B)) Bm))))
================================================================
tm-name          tm-30923
in-theory        30923
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (D or (B -> (B or C)))))
theorem-size     21
proof            (modus-ponens tm-466 tm-311 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (or Bm (-> A (or A B)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-30923.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (D or (B -> (B or C))))), M:tm-466, m:tm-311, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (or Bm (-> A (or A B))))))
================================================================
tm-name          tm-30924
in-theory        30924
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (((B or C) -> D) -> ((B or (B or C)) -> D))))
theorem-size     27
proof            (modus-ponens tm-466 tm-312 ((A Am) (Bm (or Am B)) (C (and (-> Am (or Am B)) (-> (-> (or Am B) Cm) (-> (or Am (or Am B)) Cm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-30924.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (((B or C) -> D) -> ((B or (B or C)) -> D)))), M:tm-466, m:tm-312, u:((A Am) (Bm (or Am B)) (C (and (-> Am (or Am B)) (-> (-> (or Am B) Cm) (-> (or Am (or Am B)) Cm)))))
================================================================
tm-name          tm-30925
in-theory        30925
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((B -> (not (B or C))) -> (not B))))
theorem-size     23
proof            (modus-ponens tm-466 tm-313 ((A Am) (Bm (or Am B)) (C (and (-> Am (or Am B)) (-> (-> Am (not (or Am B))) (not Am))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-30925.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((B -> (not (B or C))) -> (not B)))), M:tm-466, m:tm-313, u:((A Am) (Bm (or Am B)) (C (and (-> Am (or Am B)) (-> (-> Am (not (or Am B))) (not Am)))))
================================================================
tm-name          tm-30926
in-theory        30926
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (D -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-466 tm-315 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-30926.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (D -> (E -> D)))), M:tm-466, m:tm-315, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-30927
in-theory        30927
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (B -> B)))
theorem-size     17
proof            (modus-ponens tm-466 tm-316 ((A Am) (Bm (or Am B)) (C (and (-> Am (or Am B)) (-> Am Am)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-30927.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (B -> B))), M:tm-466, m:tm-316, u:((A Am) (Bm (or Am B)) (C (and (-> Am (or Am B)) (-> Am Am))))
================================================================
tm-name          tm-30928
in-theory        30928
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-466 tm-318 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-30928.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-466, m:tm-318, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-30929
in-theory        30929
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((D and E) -> D)))
theorem-size     19
proof            (modus-ponens tm-466 tm-320 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-30929.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((D and E) -> D))), M:tm-466, m:tm-320, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-30930
in-theory        30930
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((D and E) -> E)))
theorem-size     19
proof            (modus-ponens tm-466 tm-322 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-30930.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((D and E) -> E))), M:tm-466, m:tm-322, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-30931
in-theory        30931
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((D -> (E -> D)) and (B -> (B or C)))))
theorem-size     25
proof            (modus-ponens tm-466 tm-323 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (and (-> Bm (-> Cm Bm)) (-> A (or A B)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-30931.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((D -> (E -> D)) and (B -> (B or C))))), M:tm-466, m:tm-323, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (and (-> Bm (-> Cm Bm)) (-> A (or A B))))))
================================================================
tm-name          tm-30932
in-theory        30932
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (B or C)))))
theorem-size     33
proof            (modus-ponens tm-466 tm-324 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (or A B)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-30932.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (B or C))))), M:tm-466, m:tm-324, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (or A B))))))
================================================================
tm-name          tm-30933
in-theory        30933
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (((D and E) -> D) and (B -> (B or C)))))
theorem-size     25
proof            (modus-ponens tm-466 tm-325 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (and (-> (and Bm Cm) Bm) (-> A (or A B)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-30933.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (((D and E) -> D) and (B -> (B or C))))), M:tm-466, m:tm-325, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (and (-> (and Bm Cm) Bm) (-> A (or A B))))))
================================================================
tm-name          tm-30934
in-theory        30934
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (((D and E) -> E) and (B -> (B or C)))))
theorem-size     25
proof            (modus-ponens tm-466 tm-326 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (and (-> (and Bm Cm) Cm) (-> A (or A B)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-30934.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (((D and E) -> E) and (B -> (B or C))))), M:tm-466, m:tm-326, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (and (-> (and Bm Cm) Cm) (-> A (or A B))))))
================================================================
tm-name          tm-30935
in-theory        30935
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((D -> (E -> (D and E))) and (B -> (B or C)))))
theorem-size     27
proof            (modus-ponens tm-466 tm-327 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (and (-> Bm (-> Cm (and Bm Cm))) (-> A (or A B)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-30935.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((D -> (E -> (D and E))) and (B -> (B or C))))), M:tm-466, m:tm-327, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (and (-> Bm (-> Cm (and Bm Cm))) (-> A (or A B))))))
================================================================
tm-name          tm-30936
in-theory        30936
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (B -> (B and (B or C)))))
theorem-size     21
proof            (modus-ponens tm-466 tm-328 ((A Am) (Bm (or Am B)) (C (and (-> Am (or Am B)) (-> Am (and Am (or Am B)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-30936.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (B -> (B and (B or C))))), M:tm-466, m:tm-328, u:((A Am) (Bm (or Am B)) (C (and (-> Am (or Am B)) (-> Am (and Am (or Am B))))))
================================================================
tm-name          tm-30937
in-theory        30937
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B and C)) -> ((B -> (B and C)) or D))) -> (((B -> C) or (B -> (B and C))) -> ((B -> (B and C)) or D)))
theorem-size     33
proof            (modus-ponens tm-466 tm-335 ((A (-> Am (and Am Bm))) (Cm (or (-> Am (and Am Bm)) B)) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) (or (-> Am (and Am Bm)) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-30937.        ((A or ((B -> (B and C)) -> ((B -> (B and C)) or D))) -> (((B -> C) or (B -> (B and C))) -> ((B -> (B and C)) or D))), M:tm-466, m:tm-335, u:((A (-> Am (and Am Bm))) (Cm (or (-> Am (and Am Bm)) B)) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) (or (-> Am (and Am Bm)) B))))
================================================================
tm-name          tm-30938
in-theory        30938
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> E) -> (D -> (D and E))) and (B -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-466 tm-338 ((Am (-> A (or A B))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-30938.        ((A or (B -> (B or C))) -> (((D -> E) -> (D -> (D and E))) and (B -> (B or C)))), M:tm-466, m:tm-338, u:((Am (-> A (or A B))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (or A B)))))
================================================================
tm-name          tm-30939
in-theory        30939
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-466 tm-340 ((Am (-> A (or A B))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-30939.        ((A or (B -> (B or C))) -> ((D -> E) -> (D -> (D and E)))), M:tm-466, m:tm-340, u:((Am (-> A (or A B))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-30940
in-theory        30940
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (D -> (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-466 tm-341 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-30940.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (D -> (E -> (D and E))))), M:tm-466, m:tm-341, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-30941
in-theory        30941
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) -> ((B -> (C -> (B and C))) or D))) -> ((E or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) or D)))
theorem-size     39
proof            (modus-ponens tm-466 tm-351 ((A (-> Am (-> Bm (and Am Bm)))) (Cm (or (-> Am (-> Bm (and Am Bm))) B)) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (or (-> Am (-> Bm (and Am Bm))) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-30941.        ((A or ((B -> (C -> (B and C))) -> ((B -> (C -> (B and C))) or D))) -> ((E or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) or D))), M:tm-466, m:tm-351, u:((A (-> Am (-> Bm (and Am Bm)))) (Cm (or (-> Am (-> Bm (and Am Bm))) B)) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (or (-> Am (-> Bm (and Am Bm))) B))))
================================================================
tm-name          tm-30942
in-theory        30942
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (E -> (F -> (E and F)))) and (B -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-466 tm-354 ((Am (-> A (or A B))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-30942.        ((A or (B -> (B or C))) -> ((D -> (E -> (F -> (E and F)))) and (B -> (B or C)))), M:tm-466, m:tm-354, u:((Am (-> A (or A B))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (or A B)))))
================================================================
tm-name          tm-30943
in-theory        30943
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (B -> (D -> ((B or C) and D))))
theorem-size     17
proof            (modus-ponens tm-466 tm-355 ((A Am) (Bm (or Am B)) (C (-> Am (-> Cm (and (or Am B) Cm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-30943.        ((A or (B -> (B or C))) -> (B -> (D -> ((B or C) and D)))), M:tm-466, m:tm-355, u:((A Am) (Bm (or Am B)) (C (-> Am (-> Cm (and (or Am B) Cm)))))
================================================================
tm-name          tm-30944
in-theory        30944
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-466 tm-356 ((Am (-> A (or A B))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-30944.        ((A or (B -> (B or C))) -> (D -> (E -> (F -> (E and F))))), M:tm-466, m:tm-356, u:((Am (-> A (or A B))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-30945
in-theory        30945
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> (E -> D)) or F) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-364 ((Am (-> A (or A B))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30945.        ((A or (B -> (B or C))) -> (((D -> (E -> D)) or F) and (B -> (B or C)))), M:tm-466, m:tm-364, u:((Am (-> A (or A B))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (or A B)))))
================================================================
tm-name          tm-30946
in-theory        30946
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-466 tm-365 ((Am (-> A (or A B))) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-30946.        ((A or (B -> (B or C))) -> ((D -> (E -> D)) or F)), M:tm-466, m:tm-365, u:((Am (-> A (or A B))) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-30947
in-theory        30947
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (B -> (B or C))))
theorem-size     29
proof            (modus-ponens tm-466 tm-373 ((Am (-> A (or A B))) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30947.        ((A or (B -> (B or C))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (B -> (B or C)))), M:tm-466, m:tm-373, u:((Am (-> A (or A B))) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A (or A B)))))
================================================================
tm-name          tm-30948
in-theory        30948
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-466 tm-374 ((Am (-> A (or A B))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-30948.        ((A or (B -> (B or C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-466, m:tm-374, u:((Am (-> A (or A B))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-30949
in-theory        30949
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((((D and E) -> D) or F) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-382 ((Am (-> A (or A B))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30949.        ((A or (B -> (B or C))) -> ((((D and E) -> D) or F) and (B -> (B or C)))), M:tm-466, m:tm-382, u:((Am (-> A (or A B))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (or A B)))))
================================================================
tm-name          tm-30950
in-theory        30950
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-466 tm-383 ((Am (-> A (or A B))) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-30950.        ((A or (B -> (B or C))) -> (((D and E) -> D) or F)), M:tm-466, m:tm-383, u:((Am (-> A (or A B))) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-30951
in-theory        30951
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((((D and E) -> E) or F) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-391 ((Am (-> A (or A B))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30951.        ((A or (B -> (B or C))) -> ((((D and E) -> E) or F) and (B -> (B or C)))), M:tm-466, m:tm-391, u:((Am (-> A (or A B))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (or A B)))))
================================================================
tm-name          tm-30952
in-theory        30952
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-466 tm-392 ((Am (-> A (or A B))) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-30952.        ((A or (B -> (B or C))) -> (((D and E) -> E) or F)), M:tm-466, m:tm-392, u:((Am (-> A (or A B))) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-30953
in-theory        30953
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> (E -> (D and E))) or F) and (B -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-466 tm-400 ((Am (-> A (or A B))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-30953.        ((A or (B -> (B or C))) -> (((D -> (E -> (D and E))) or F) and (B -> (B or C)))), M:tm-466, m:tm-400, u:((Am (-> A (or A B))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A (or A B)))))
================================================================
tm-name          tm-30954
in-theory        30954
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-466 tm-401 ((Am (-> A (or A B))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-30954.        ((A or (B -> (B or C))) -> ((D -> (E -> (D and E))) or F)), M:tm-466, m:tm-401, u:((Am (-> A (or A B))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-30955
in-theory        30955
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> (D or E)) or F) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-409 ((Am (-> A (or A B))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30955.        ((A or (B -> (B or C))) -> (((D -> (D or E)) or F) and (B -> (B or C)))), M:tm-466, m:tm-409, u:((Am (-> A (or A B))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (or A B)))))
================================================================
tm-name          tm-30956
in-theory        30956
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-466 tm-410 ((Am (-> A (or A B))) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-30956.        ((A or (B -> (B or C))) -> ((D -> (D or E)) or F)), M:tm-466, m:tm-410, u:((Am (-> A (or A B))) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-30957
in-theory        30957
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((D -> (D or E)) and (B -> (B or C)))))
theorem-size     25
proof            (modus-ponens tm-466 tm-443 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (and (-> Bm (or Bm Cm)) (-> A (or A B)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-30957.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((D -> (D or E)) and (B -> (B or C))))), M:tm-466, m:tm-443, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (and (-> Bm (or Bm Cm)) (-> A (or A B))))))
================================================================
tm-name          tm-30958
in-theory        30958
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (B or C)) and D) -> (((B -> (B or C)) and D) or E))) -> ((D or ((B -> (B or C)) and D)) -> (((B -> (B or C)) and D) or E)))
theorem-size     39
proof            (modus-ponens tm-466 tm-450 ((A (and (-> Am (or Am Bm)) Cm)) (Dm (or (and (-> Am (or Am Bm)) Cm) B)) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (or (and (-> Am (or Am Bm)) Cm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-30958.        ((A or (((B -> (B or C)) and D) -> (((B -> (B or C)) and D) or E))) -> ((D or ((B -> (B or C)) and D)) -> (((B -> (B or C)) and D) or E))), M:tm-466, m:tm-450, u:((A (and (-> Am (or Am Bm)) Cm)) (Dm (or (and (-> Am (or Am Bm)) Cm) B)) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (or (and (-> Am (or Am Bm)) Cm) B))))
================================================================
tm-name          tm-30959
in-theory        30959
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> ((E -> (E or F)) and D)) and (B -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-466 tm-453 ((Am (-> A (or A B))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30959.        ((A or (B -> (B or C))) -> ((D -> ((E -> (E or F)) and D)) and (B -> (B or C)))), M:tm-466, m:tm-453, u:((Am (-> A (or A B))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A (or A B)))))
================================================================
tm-name          tm-30960
in-theory        30960
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-466 tm-454 ((Am (-> A (or A B))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-30960.        ((A or (B -> (B or C))) -> (D -> ((E -> (E or F)) and D))), M:tm-466, m:tm-454, u:((Am (-> A (or A B))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-30961
in-theory        30961
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (D -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-466 tm-456 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30961.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (D -> (D or E)))), M:tm-466, m:tm-456, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-30962
in-theory        30962
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) -> ((B -> (B or C)) or D))) -> ((E or (B -> (B or C))) -> ((B -> (B or C)) or D)))
theorem-size     31
proof            (modus-ponens tm-466 tm-466 ((A (-> Am (or Am Bm))) (Cm (or (-> Am (or Am Bm)) B)) (C (-> (or Dm (-> Am (or Am Bm))) (or (-> Am (or Am Bm)) B)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30962.        ((A or ((B -> (B or C)) -> ((B -> (B or C)) or D))) -> ((E or (B -> (B or C))) -> ((B -> (B or C)) or D))), M:tm-466, m:tm-466, u:((A (-> Am (or Am Bm))) (Cm (or (-> Am (or Am Bm)) B)) (C (-> (or Dm (-> Am (or Am Bm))) (or (-> Am (or Am Bm)) B))))
================================================================
tm-name          tm-30963
in-theory        30963
times-derived    4
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> C)
theorem-size     9
proof            (modus-ponens tm-464 tm-466 ((Dm (-> (-> Am (or Am Bm)) Cm)) (A (-> (-> Am (or Am Bm)) Cm)) (B (-> Am (or Am Bm))) (C Cm)))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30963.        (((A -> (A or B)) -> C) -> C), M:tm-464, m:tm-466, u:((Dm (-> (-> Am (or Am Bm)) Cm)) (A (-> (-> Am (or Am Bm)) Cm)) (B (-> Am (or Am Bm))) (C Cm))
================================================================
tm-name          tm-30964
in-theory        30964
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30964.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (E -> (E or F))), M:tm-456, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30965
in-theory        30965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-453 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30965.        ((A -> ((B -> (B or C)) and A)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-453, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30966
in-theory        30966
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((E -> (E or F)) and (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C))))
theorem-size     41
proof            (modus-ponens tm-443 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30966.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((E -> (E or F)) and (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)))), M:tm-443, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30967
in-theory        30967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-409 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30967.        (((A -> (A or B)) or C) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-409, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30968
in-theory        30968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-400 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30968.        (((A -> (B -> (A and B))) or C) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-400, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30969
in-theory        30969
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-391 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30969.        ((((A and B) -> B) or C) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-391, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30970
in-theory        30970
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-382 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30970.        ((((A and B) -> A) or C) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-382, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30971
in-theory        30971
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-373 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30971.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G))), M:tm-373, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30972
in-theory        30972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-364 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30972.        (((A -> (B -> A)) or C) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-364, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30973
in-theory        30973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> (D -> (((E or (A -> (A or B))) -> C) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30973.        (((A -> (A or B)) -> C) -> (D -> (((E or (A -> (A or B))) -> C) and D))), M:tm-355, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-30974
in-theory        30974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-354 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30974.        ((A -> (B -> (C -> (B and C)))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-354, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30975
in-theory        30975
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) -> (D -> ((B -> (B or C)) and D)))) -> ((E or (B -> (B or C))) -> (D -> ((B -> (B or C)) and D))))
theorem-size     35
proof            (modus-ponens tm-351 tm-466 ((A (-> Am (or Am Bm))) (Cm (-> B (and (-> Am (or Am Bm)) B))) (C (-> (or Dm (-> Am (or Am Bm))) (-> B (and (-> Am (or Am Bm)) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30975.        ((A or ((B -> (B or C)) -> (D -> ((B -> (B or C)) and D)))) -> ((E or (B -> (B or C))) -> (D -> ((B -> (B or C)) and D)))), M:tm-351, m:tm-466, u:((A (-> Am (or Am Bm))) (Cm (-> B (and (-> Am (or Am Bm)) B))) (C (-> (or Dm (-> Am (or Am Bm))) (-> B (and (-> Am (or Am Bm)) B)))))
================================================================
tm-name          tm-30976
in-theory        30976
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30976.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30977
in-theory        30977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E)))
theorem-size     27
proof            (modus-ponens tm-338 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30977.        (((A -> B) -> (A -> (A and B))) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E))), M:tm-338, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30978
in-theory        30978
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) or ((A -> (A or B)) -> ((A -> (A or B)) and C))) -> ((D or (A -> (A or B))) -> ((A -> (A or B)) and C)))
theorem-size     37
proof            (modus-ponens tm-335 tm-466 ((A (-> Am (or Am Bm))) (Cm (and (-> Am (or Am Bm)) B)) (C (-> (or Dm (-> Am (or Am Bm))) (and (-> Am (or Am Bm)) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30978.        ((((A -> (A or B)) -> C) or ((A -> (A or B)) -> ((A -> (A or B)) and C))) -> ((D or (A -> (A or B))) -> ((A -> (A or B)) and C))), M:tm-335, m:tm-466, u:((A (-> Am (or Am Bm))) (Cm (and (-> Am (or Am Bm)) B)) (C (-> (or Dm (-> Am (or Am Bm))) (and (-> Am (or Am Bm)) B))))
================================================================
tm-name          tm-30979
in-theory        30979
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (((A -> (A or B)) -> C) -> (((A -> (A or B)) -> C) and ((D or (A -> (A or B))) -> C))))
theorem-size     43
proof            (modus-ponens tm-328 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30979.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (((A -> (A or B)) -> C) -> (((A -> (A or B)) -> C) and ((D or (A -> (A or B))) -> C)))), M:tm-328, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-30980
in-theory        30980
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((E -> (F -> (E and F))) and (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C))))
theorem-size     43
proof            (modus-ponens tm-327 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30980.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((E -> (F -> (E and F))) and (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)))), M:tm-327, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30981
in-theory        30981
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (((E and F) -> F) and (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C))))
theorem-size     41
proof            (modus-ponens tm-326 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30981.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (((E and F) -> F) and (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)))), M:tm-326, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30982
in-theory        30982
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (((E and F) -> E) and (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C))))
theorem-size     41
proof            (modus-ponens tm-325 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30982.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (((E and F) -> E) and (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)))), M:tm-325, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30983
in-theory        30983
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C))))
theorem-size     49
proof            (modus-ponens tm-324 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30983.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)))), M:tm-324, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30984
in-theory        30984
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((E -> (F -> E)) and (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C))))
theorem-size     41
proof            (modus-ponens tm-323 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30984.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((E -> (F -> E)) and (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)))), M:tm-323, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30985
in-theory        30985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30985.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30986
in-theory        30986
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30986.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30987
in-theory        30987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30987.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30988
in-theory        30988
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (((A -> (A or B)) -> C) -> ((A -> (A or B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-316 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30988.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (((A -> (A or B)) -> C) -> ((A -> (A or B)) -> C))), M:tm-316, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-30989
in-theory        30989
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30989.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30990
in-theory        30990
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((((A -> (A or B)) -> C) -> (not ((D or (A -> (A or B))) -> C))) -> (not ((A -> (A or B)) -> C))))
theorem-size     45
proof            (modus-ponens tm-313 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30990.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((((A -> (A or B)) -> C) -> (not ((D or (A -> (A or B))) -> C))) -> (not ((A -> (A or B)) -> C)))), M:tm-313, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-30991
in-theory        30991
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((((D or (A -> (A or B))) -> C) -> E) -> ((((A -> (A or B)) -> C) or ((D or (A -> (A or B))) -> C)) -> E)))
theorem-size     49
proof            (modus-ponens tm-312 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30991.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((((D or (A -> (A or B))) -> C) -> E) -> ((((A -> (A or B)) -> C) or ((D or (A -> (A or B))) -> C)) -> E))), M:tm-312, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-30992
in-theory        30992
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (E or (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C))))
theorem-size     37
proof            (modus-ponens tm-311 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30992.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (E or (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)))), M:tm-311, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30993
in-theory        30993
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30993.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) or E)), M:tm-310, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30994
in-theory        30994
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (E -> ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30994.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (E -> ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and E))), M:tm-309, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30995
in-theory        30995
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((((A -> (A or B)) -> C) -> (D or (A -> (A or B)))) -> (((A -> (A or B)) -> C) -> C)))
theorem-size     43
proof            (modus-ponens tm-306 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (or Dm (-> Am (or Am Bm)))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30995.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((((A -> (A or B)) -> C) -> (D or (A -> (A or B)))) -> (((A -> (A or B)) -> C) -> C))), M:tm-306, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (or Dm (-> Am (or Am Bm)))) (C Cm))
================================================================
tm-name          tm-30996
in-theory        30996
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (E -> (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C))))
theorem-size     37
proof            (modus-ponens tm-305 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30996.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (E -> (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)))), M:tm-305, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30997
in-theory        30997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     29
proof            (modus-ponens tm-303 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30997.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-303, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30998
in-theory        30998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-270 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30998.        ((A -> (((B and C) -> C) and A)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-270, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-30999
in-theory        30999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-239 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-30999.        ((A -> (((B and C) -> B) and A)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-239, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31000
in-theory        31000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-210 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31000.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G))), M:tm-210, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31001
in-theory        31001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-183 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31001.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-183, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31002
in-theory        31002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-157 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31002.        ((A -> ((B and C) -> C)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-157, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31003
in-theory        31003
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     33
proof            (modus-ponens tm-147 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31003.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-147, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31004
in-theory        31004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-134 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31004.        ((A -> ((B and C) -> B)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-134, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31005
in-theory        31005
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     33
proof            (modus-ponens tm-125 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31005.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-125, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31006
in-theory        31006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> (C -> D)) -> (((E or (A -> (A or B))) -> C) -> ((E or (A -> (A or B))) -> D)))
theorem-size     29
proof            (modus-ponens tm-114 tm-466 ((A (-> (-> Am (or Am Bm)) (-> C D))) (B (or Dm (-> Am (or Am Bm)))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31006.        (((A -> (A or B)) -> (C -> D)) -> (((E or (A -> (A or B))) -> C) -> ((E or (A -> (A or B))) -> D))), M:tm-114, m:tm-466, u:((A (-> (-> Am (or Am Bm)) (-> C D))) (B (or Dm (-> Am (or Am Bm)))) (Cm (-> C D)))
================================================================
tm-name          tm-31007
in-theory        31007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-113 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31007.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G))), M:tm-113, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31008
in-theory        31008
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     37
proof            (modus-ponens tm-105 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31008.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-105, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31009
in-theory        31009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E)))
theorem-size     25
proof            (modus-ponens tm-95 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31009.        (((A -> B) -> (A -> A)) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E))), M:tm-95, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31010
in-theory        31010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) or ((A -> (A or B)) -> (A -> (A or B)))) -> ((D or (A -> (A or B))) -> (A -> (A or B))))
theorem-size     33
proof            (modus-ponens tm-92 tm-466 ((Cm (-> Am (or Am Bm))) (A (-> Am (or Am Bm))) (B (-> (or Dm (-> Am (or Am Bm))) (-> Am (or Am Bm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31010.        ((((A -> (A or B)) -> C) or ((A -> (A or B)) -> (A -> (A or B)))) -> ((D or (A -> (A or B))) -> (A -> (A or B)))), M:tm-92, m:tm-466, u:((Cm (-> Am (or Am Bm))) (A (-> Am (or Am Bm))) (B (-> (or Dm (-> Am (or Am Bm))) (-> Am (or Am Bm)))))
================================================================
tm-name          tm-31011
in-theory        31011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> (D -> ((E or (A -> (A or B))) -> C)))
theorem-size     19
proof            (modus-ponens tm-84 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31011.        (((A -> (A or B)) -> C) -> (D -> ((E or (A -> (A or B))) -> C))), M:tm-84, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-31012
in-theory        31012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-83 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31012.        ((A -> (B -> (C -> B))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-83, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31013
in-theory        31013
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) -> (D -> (B -> (B or C))))) -> ((E or (B -> (B or C))) -> (D -> (B -> (B or C)))))
theorem-size     31
proof            (modus-ponens tm-80 tm-466 ((A (-> Am (or Am Bm))) (Cm (-> B (-> Am (or Am Bm)))) (C (-> (or Dm (-> Am (or Am Bm))) (-> B (-> Am (or Am Bm)))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31013.        ((A or ((B -> (B or C)) -> (D -> (B -> (B or C))))) -> ((E or (B -> (B or C))) -> (D -> (B -> (B or C))))), M:tm-80, m:tm-466, u:((A (-> Am (or Am Bm))) (Cm (-> B (-> Am (or Am Bm)))) (C (-> (or Dm (-> Am (or Am Bm))) (-> B (-> Am (or Am Bm))))))
================================================================
tm-name          tm-31014
in-theory        31014
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (B or C)) -> D) -> ((E or (B -> (B or C))) -> D)))
theorem-size     23
proof            (modus-ponens tm-76 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31014.        (((not (not A)) -> A) and (((B -> (B or C)) -> D) -> ((E or (B -> (B or C))) -> D))), M:tm-76, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31015
in-theory        31015
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (A or B)) -> C))) or ((A -> (A or B)) -> C)) -> ((D or (A -> (A or B))) -> C))
theorem-size     27
proof            (modus-ponens tm-73 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-8 tm-10 tm-1 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31015.        (((not (not ((A -> (A or B)) -> C))) or ((A -> (A or B)) -> C)) -> ((D or (A -> (A or B))) -> C)), M:tm-73, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-31016
in-theory        31016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E)))
theorem-size     29
proof            (modus-ponens tm-69 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31016.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E))), M:tm-69, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31017
in-theory        31017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> (C or (A -> (A or B)))) -> (((A -> (A or B)) or (C or (A -> (A or B)))) -> (C or (A -> (A or B)))))
theorem-size     35
proof            (modus-ponens tm-55 tm-466 ((A (-> Am (or Am Bm))) (Cm (or Dm (-> Am (or Am Bm)))) (B (or Dm (-> Am (or Am Bm)))) (C (or Dm (-> Am (or Am Bm))))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31017.        (((A -> (A or B)) -> (C or (A -> (A or B)))) -> (((A -> (A or B)) or (C or (A -> (A or B)))) -> (C or (A -> (A or B))))), M:tm-55, m:tm-466, u:((A (-> Am (or Am Bm))) (Cm (or Dm (-> Am (or Am Bm)))) (B (or Dm (-> Am (or Am Bm)))) (C (or Dm (-> Am (or Am Bm)))))
================================================================
tm-name          tm-31018
in-theory        31018
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-54 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31018.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-54, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31019
in-theory        31019
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (B or C)) -> ((A or B) -> (B or C)))) -> ((D or (B -> (B or C))) -> ((A or B) -> (B or C))))
theorem-size     33
proof            (modus-ponens tm-51 tm-466 ((A Am) (B (or Am Bm)) (Cm (-> (or C Am) (or Am Bm))) (D (-> (or Dm (-> Am (or Am Bm))) (-> (or C Am) (or Am Bm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31019.        (((A -> B) or ((B -> (B or C)) -> ((A or B) -> (B or C)))) -> ((D or (B -> (B or C))) -> ((A or B) -> (B or C)))), M:tm-51, m:tm-466, u:((A Am) (B (or Am Bm)) (Cm (-> (or C Am) (or Am Bm))) (D (-> (or Dm (-> Am (or Am Bm))) (-> (or C Am) (or Am Bm)))))
================================================================
tm-name          tm-31020
in-theory        31020
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) -> (A and (B -> (B or C))))) -> ((D or (B -> (B or C))) -> (A and (B -> (B or C)))))
theorem-size     31
proof            (modus-ponens tm-48 tm-466 ((A (-> Am (or Am Bm))) (Cm (and B (-> Am (or Am Bm)))) (C (-> (or Dm (-> Am (or Am Bm))) (and B (-> Am (or Am Bm)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31020.        ((A or ((B -> (B or C)) -> (A and (B -> (B or C))))) -> ((D or (B -> (B or C))) -> (A and (B -> (B or C))))), M:tm-48, m:tm-466, u:((A (-> Am (or Am Bm))) (Cm (and B (-> Am (or Am Bm)))) (C (-> (or Dm (-> Am (or Am Bm))) (and B (-> Am (or Am Bm))))))
================================================================
tm-name          tm-31021
in-theory        31021
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) or ((B -> (B or C)) -> D)) -> ((E or (B -> (B or C))) -> D))
theorem-size     27
proof            (modus-ponens tm-47 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31021.        (((A and ((B -> (B or C)) -> D)) or ((B -> (B or C)) -> D)) -> ((E or (B -> (B or C))) -> D)), M:tm-47, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-31022
in-theory        31022
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) or ((A -> (A or B)) -> C)) -> ((E or (A -> (A or B))) -> C))
theorem-size     27
proof            (modus-ponens tm-46 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31022.        (((((A -> (A or B)) -> C) and D) or ((A -> (A or B)) -> C)) -> ((E or (A -> (A or B))) -> C)), M:tm-46, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-31023
in-theory        31023
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) or ((A -> (A or B)) -> (A -> C))) -> ((D or (A -> (A or B))) -> (A -> C)))
theorem-size     29
proof            (modus-ponens tm-45 tm-466 ((A Am) (B (or Am Bm)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (or Am Bm))) (-> Am C)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31023.        (((A -> ((A or B) -> C)) or ((A -> (A or B)) -> (A -> C))) -> ((D or (A -> (A or B))) -> (A -> C))), M:tm-45, m:tm-466, u:((A Am) (B (or Am Bm)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (or Am Bm))) (-> Am C))))
================================================================
tm-name          tm-31024
in-theory        31024
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) -> A)) -> ((D or (B -> (B or C))) -> A))
theorem-size     19
proof            (modus-ponens tm-44 tm-466 ((A (-> Am (or Am Bm))) (B Cm) (C (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31024.        ((A or ((B -> (B or C)) -> A)) -> ((D or (B -> (B or C))) -> A)), M:tm-44, m:tm-466, u:((A (-> Am (or Am Bm))) (B Cm) (C (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-31025
in-theory        31025
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E)))
theorem-size     23
proof            (modus-ponens tm-42 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31025.        ((A -> (B or A)) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E))), M:tm-42, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31026
in-theory        31026
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E)))
theorem-size     23
proof            (modus-ponens tm-32 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31026.        ((A -> (A or B)) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E))), M:tm-32, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31027
in-theory        31027
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> (((A -> (A or B)) -> C) and ((D or (A -> (A or B))) -> C)))
theorem-size     25
proof            (modus-ponens tm-24 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31027.        (((A -> (A or B)) -> C) -> (((A -> (A or B)) -> C) and ((D or (A -> (A or B))) -> C))), M:tm-24, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-31028
in-theory        31028
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E)))
theorem-size     25
proof            (modus-ponens tm-23 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31028.        ((A -> (B -> (A and B))) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E))), M:tm-23, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31029
in-theory        31029
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E)))
theorem-size     23
proof            (modus-ponens tm-22 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31029.        (((A and B) -> B) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E))), M:tm-22, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31030
in-theory        31030
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E)))
theorem-size     23
proof            (modus-ponens tm-21 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31030.        (((A and B) -> A) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E))), M:tm-21, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31031
in-theory        31031
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-20 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31031.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-20, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31032
in-theory        31032
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E)))
theorem-size     23
proof            (modus-ponens tm-19 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31032.        ((A -> (B -> A)) and (((C -> (C or D)) -> E) -> ((F or (C -> (C or D))) -> E))), M:tm-19, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31033
in-theory        31033
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> ((A -> (A or B)) -> C))
theorem-size     15
proof            (modus-ponens tm-12 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31033.        (((A -> (A or B)) -> C) -> ((A -> (A or B)) -> C)), M:tm-12, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-31034
in-theory        31034
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> (not ((D or (A -> (A or B))) -> C))) -> (not ((A -> (A or B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-9 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-9 tm-8 tm-1 tm-6)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31034.        ((((A -> (A or B)) -> C) -> (not ((D or (A -> (A or B))) -> C))) -> (not ((A -> (A or B)) -> C))), M:tm-9, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-31035
in-theory        31035
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (B or C))) -> D) -> E) -> ((((B -> (B or C)) -> D) or ((A or (B -> (B or C))) -> D)) -> E))
theorem-size     31
proof            (modus-ponens tm-8 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31035.        ((((A or (B -> (B or C))) -> D) -> E) -> ((((B -> (B or C)) -> D) or ((A or (B -> (B or C))) -> D)) -> E)), M:tm-8, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-31036
in-theory        31036
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> (B or C)) -> D) -> ((E or (B -> (B or C))) -> D)))
theorem-size     19
proof            (modus-ponens tm-7 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-7 tm-8 tm-1 tm-6)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31036.        (A or (((B -> (B or C)) -> D) -> ((E or (B -> (B or C))) -> D))), M:tm-7, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31037
in-theory        31037
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-6 tm-8 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31037.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) or E), M:tm-6, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31038
in-theory        31038
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (B or C)) -> D) -> ((E or (B -> (B or C))) -> D)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31038.        (A -> ((((B -> (B or C)) -> D) -> ((E or (B -> (B or C))) -> D)) and A)), M:tm-5, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31039
in-theory        31039
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> (D or (A -> (A or B)))) -> (((A -> (A or B)) -> C) -> C))
theorem-size     25
proof            (modus-ponens tm-2 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (or Dm (-> Am (or Am Bm)))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31039.        ((((A -> (A or B)) -> C) -> (D or (A -> (A or B)))) -> (((A -> (A or B)) -> C) -> C)), M:tm-2, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (or Dm (-> Am (or Am Bm)))) (C Cm))
================================================================
tm-name          tm-31040
in-theory        31040
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) -> D) -> ((E or (B -> (B or C))) -> D)))
theorem-size     19
proof            (modus-ponens tm-1 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-1 tm-8 tm-6)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31040.        (A -> (((B -> (B or C)) -> D) -> ((E or (B -> (B or C))) -> D))), M:tm-1, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31041
in-theory        31041
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31041.        ((A or (B -> (C -> (C or D)))) and (E -> (E or F))), M:tm-456, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31042
in-theory        31042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31042.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> (F -> (F or G))))), M:tm-453, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31043
in-theory        31043
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and ((E -> (E or F)) and (A or (B -> (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31043.        ((A or (B -> (C -> (C or D)))) and ((E -> (E or F)) and (A or (B -> (C -> (C or D)))))), M:tm-443, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31044
in-theory        31044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31044.        (((A -> (A or B)) or C) and (D or (E -> (F -> (F or G))))), M:tm-409, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31045
in-theory        31045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31045.        (((A -> (B -> (A and B))) or C) and (D or (E -> (F -> (F or G))))), M:tm-400, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31046
in-theory        31046
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31046.        ((((A and B) -> B) or C) and (D or (E -> (F -> (F or G))))), M:tm-391, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31047
in-theory        31047
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31047.        ((((A and B) -> A) or C) and (D or (E -> (F -> (F or G))))), M:tm-382, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31048
in-theory        31048
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31048.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (G -> (G or H))))), M:tm-373, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31049
in-theory        31049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31049.        (((A -> (B -> A)) or C) and (D or (E -> (F -> (F or G))))), M:tm-364, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31050
in-theory        31050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31050.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> (F -> (F or G))))), M:tm-354, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31051
in-theory        31051
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31051.        ((A or (B -> (C -> (C or D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31052
in-theory        31052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31052.        (((A -> B) -> (A -> (A and B))) and (C or (D -> (E -> (E or F))))), M:tm-338, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31053
in-theory        31053
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and ((E -> (F -> (E and F))) and (A or (B -> (C -> (C or D))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31053.        ((A or (B -> (C -> (C or D)))) and ((E -> (F -> (E and F))) and (A or (B -> (C -> (C or D)))))), M:tm-327, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31054
in-theory        31054
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and (((E and F) -> F) and (A or (B -> (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31054.        ((A or (B -> (C -> (C or D)))) and (((E and F) -> F) and (A or (B -> (C -> (C or D)))))), M:tm-326, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31055
in-theory        31055
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and (((E and F) -> E) and (A or (B -> (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31055.        ((A or (B -> (C -> (C or D)))) and (((E and F) -> E) and (A or (B -> (C -> (C or D)))))), M:tm-325, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31056
in-theory        31056
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> (C -> (C or D))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31056.        ((A or (B -> (C -> (C or D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> (C -> (C or D)))))), M:tm-324, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31057
in-theory        31057
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and ((E -> (F -> E)) and (A or (B -> (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31057.        ((A or (B -> (C -> (C or D)))) and ((E -> (F -> E)) and (A or (B -> (C -> (C or D)))))), M:tm-323, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31058
in-theory        31058
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31058.        ((A or (B -> (C -> (C or D)))) and ((E and F) -> F)), M:tm-322, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31059
in-theory        31059
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31059.        ((A or (B -> (C -> (C or D)))) and ((E and F) -> E)), M:tm-320, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31060
in-theory        31060
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31060.        ((A or (B -> (C -> (C or D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31061
in-theory        31061
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31061.        ((A or (B -> (C -> (C or D)))) and (E -> (F -> E))), M:tm-315, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31062
in-theory        31062
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and (E or (A or (B -> (C -> (C or D))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31062.        ((A or (B -> (C -> (C or D)))) and (E or (A or (B -> (C -> (C or D)))))), M:tm-311, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31063
in-theory        31063
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and ((A or (B -> (C -> (C or D)))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31063.        ((A or (B -> (C -> (C or D)))) and ((A or (B -> (C -> (C or D)))) or E)), M:tm-310, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31064
in-theory        31064
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and (E -> ((A or (B -> (C -> (C or D)))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31064.        ((A or (B -> (C -> (C or D)))) and (E -> ((A or (B -> (C -> (C or D)))) and E))), M:tm-309, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31065
in-theory        31065
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and (E -> (A or (B -> (C -> (C or D))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31065.        ((A or (B -> (C -> (C or D)))) and (E -> (A or (B -> (C -> (C or D)))))), M:tm-305, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31066
in-theory        31066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31066.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (F -> (F or G))))), M:tm-303, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31067
in-theory        31067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31067.        ((A -> (((B and C) -> C) and A)) and (D or (E -> (F -> (F or G))))), M:tm-270, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31068
in-theory        31068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31068.        ((A -> (((B and C) -> B) and A)) and (D or (E -> (F -> (F or G))))), M:tm-239, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31069
in-theory        31069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31069.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (G -> (G or H))))), M:tm-210, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31070
in-theory        31070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31070.        ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (F -> (F or G))))), M:tm-183, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31071
in-theory        31071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31071.        ((A -> ((B and C) -> C)) and (D or (E -> (F -> (F or G))))), M:tm-157, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31072
in-theory        31072
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31072.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (F -> (F or G))))), M:tm-147, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31073
in-theory        31073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31073.        ((A -> ((B and C) -> B)) and (D or (E -> (F -> (F or G))))), M:tm-134, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31074
in-theory        31074
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31074.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (F -> (F or G))))), M:tm-125, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31075
in-theory        31075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31075.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (G or H))))), M:tm-113, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31076
in-theory        31076
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (F -> (F or G)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31076.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (F -> (F or G))))), M:tm-105, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31077
in-theory        31077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31077.        (((A -> B) -> (A -> A)) and (C or (D -> (E -> (E or F))))), M:tm-95, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31078
in-theory        31078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31078.        ((A -> (B -> (C -> B))) and (D or (E -> (F -> (F or G))))), M:tm-83, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31079
in-theory        31079
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> (D -> (D or E)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31079.        (((not (not A)) -> A) and (B or (C -> (D -> (D or E))))), M:tm-76, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31080
in-theory        31080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (E -> (E or F)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31080.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (E -> (E or F))))), M:tm-69, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31081
in-theory        31081
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31081.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (F or G))))), M:tm-54, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31082
in-theory        31082
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31082.        ((A -> (B or A)) and (C or (D -> (E -> (E or F))))), M:tm-42, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31083
in-theory        31083
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31083.        ((A -> (A or B)) and (C or (D -> (E -> (E or F))))), M:tm-32, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31084
in-theory        31084
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31084.        ((A -> (B -> (A and B))) and (C or (D -> (E -> (E or F))))), M:tm-23, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31085
in-theory        31085
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31085.        (((A and B) -> B) and (C or (D -> (E -> (E or F))))), M:tm-22, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31086
in-theory        31086
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31086.        (((A and B) -> A) and (C or (D -> (E -> (E or F))))), M:tm-21, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31087
in-theory        31087
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31087.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (F or G))))), M:tm-20, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31088
in-theory        31088
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31088.        ((A -> (B -> A)) and (C or (D -> (E -> (E or F))))), M:tm-19, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31089
in-theory        31089
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C -> (D -> (D or E)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-7 tm-1 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31089.        (A or (B or (C -> (D -> (D or E))))), M:tm-7, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31090
in-theory        31090
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-6 tm-7 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31090.        ((A or (B -> (C -> (C or D)))) or E), M:tm-6, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31091
in-theory        31091
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (D -> (D or E)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31091.        (A -> ((B or (C -> (D -> (D or E)))) and A)), M:tm-5, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31092
in-theory        31092
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C -> (D -> (D or E)))))
theorem-size     11
proof            (modus-ponens tm-1 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-1 tm-7 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31092.        (A -> (B or (C -> (D -> (D or E))))), M:tm-1, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31093
in-theory        31093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31093.        (((A -> (B -> (B or C))) or D) and (E -> (E or F))), M:tm-456, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31094
in-theory        31094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31094.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (E or F))) or G)), M:tm-453, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31095
in-theory        31095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and ((E -> (E or F)) and ((A -> (B -> (B or C))) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31095.        (((A -> (B -> (B or C))) or D) and ((E -> (E or F)) and ((A -> (B -> (B or C))) or D))), M:tm-443, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31096
in-theory        31096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31096.        (((A -> (A or B)) or C) and ((D -> (E -> (E or F))) or G)), M:tm-409, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31097
in-theory        31097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31097.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (E or F))) or G)), M:tm-400, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31098
in-theory        31098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31098.        ((((A and B) -> B) or C) and ((D -> (E -> (E or F))) or G)), M:tm-391, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31099
in-theory        31099
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31099.        ((((A and B) -> A) or C) and ((D -> (E -> (E or F))) or G)), M:tm-382, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31100
in-theory        31100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (F or G))) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31100.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (F or G))) or H)), M:tm-373, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31101
in-theory        31101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31101.        (((A -> (B -> A)) or C) and ((D -> (E -> (E or F))) or G)), M:tm-364, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31102
in-theory        31102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31102.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (E or F))) or G)), M:tm-354, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31103
in-theory        31103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31103.        (((A -> (B -> (B or C))) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31104
in-theory        31104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (D or E))) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31104.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (D or E))) or F)), M:tm-338, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31105
in-theory        31105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and ((E -> (F -> (E and F))) and ((A -> (B -> (B or C))) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31105.        (((A -> (B -> (B or C))) or D) and ((E -> (F -> (E and F))) and ((A -> (B -> (B or C))) or D))), M:tm-327, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31106
in-theory        31106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and (((E and F) -> F) and ((A -> (B -> (B or C))) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31106.        (((A -> (B -> (B or C))) or D) and (((E and F) -> F) and ((A -> (B -> (B or C))) or D))), M:tm-326, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31107
in-theory        31107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and (((E and F) -> E) and ((A -> (B -> (B or C))) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31107.        (((A -> (B -> (B or C))) or D) and (((E and F) -> E) and ((A -> (B -> (B or C))) or D))), M:tm-325, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31108
in-theory        31108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (B or C))) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31108.        (((A -> (B -> (B or C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (B or C))) or D))), M:tm-324, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31109
in-theory        31109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and ((E -> (F -> E)) and ((A -> (B -> (B or C))) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31109.        (((A -> (B -> (B or C))) or D) and ((E -> (F -> E)) and ((A -> (B -> (B or C))) or D))), M:tm-323, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31110
in-theory        31110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31110.        (((A -> (B -> (B or C))) or D) and ((E and F) -> F)), M:tm-322, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31111
in-theory        31111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31111.        (((A -> (B -> (B or C))) or D) and ((E and F) -> E)), M:tm-320, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31112
in-theory        31112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31112.        (((A -> (B -> (B or C))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31113
in-theory        31113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31113.        (((A -> (B -> (B or C))) or D) and (E -> (F -> E))), M:tm-315, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31114
in-theory        31114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and (E or ((A -> (B -> (B or C))) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31114.        (((A -> (B -> (B or C))) or D) and (E or ((A -> (B -> (B or C))) or D))), M:tm-311, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31115
in-theory        31115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and (((A -> (B -> (B or C))) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31115.        (((A -> (B -> (B or C))) or D) and (((A -> (B -> (B or C))) or D) or E)), M:tm-310, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31116
in-theory        31116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and (E -> (((A -> (B -> (B or C))) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31116.        (((A -> (B -> (B or C))) or D) and (E -> (((A -> (B -> (B or C))) or D) and E))), M:tm-309, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31117
in-theory        31117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and (E -> ((A -> (B -> (B or C))) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31117.        (((A -> (B -> (B or C))) or D) and (E -> ((A -> (B -> (B or C))) or D))), M:tm-305, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31118
in-theory        31118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (E or F))) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31118.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (E or F))) or G)), M:tm-303, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31119
in-theory        31119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31119.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (E or F))) or G)), M:tm-270, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31120
in-theory        31120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31120.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (E or F))) or G)), M:tm-239, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31121
in-theory        31121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (F or G))) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31121.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (F or G))) or H)), M:tm-210, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31122
in-theory        31122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31122.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (E or F))) or G)), M:tm-183, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31123
in-theory        31123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31123.        ((A -> ((B and C) -> C)) and ((D -> (E -> (E or F))) or G)), M:tm-157, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31124
in-theory        31124
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (E or F))) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31124.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (E or F))) or G)), M:tm-147, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31125
in-theory        31125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31125.        ((A -> ((B and C) -> B)) and ((D -> (E -> (E or F))) or G)), M:tm-134, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31126
in-theory        31126
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (E or F))) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31126.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (E or F))) or G)), M:tm-125, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31127
in-theory        31127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (F or G))) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31127.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (F or G))) or H)), M:tm-113, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31128
in-theory        31128
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (E or F))) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31128.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (E or F))) or G)), M:tm-105, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31129
in-theory        31129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (D or E))) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31129.        (((A -> B) -> (A -> A)) and ((C -> (D -> (D or E))) or F)), M:tm-95, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31130
in-theory        31130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31130.        ((A -> (B -> (C -> B))) and ((D -> (E -> (E or F))) or G)), M:tm-83, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31131
in-theory        31131
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (C or D))) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31131.        (((not (not A)) -> A) and ((B -> (C -> (C or D))) or E)), M:tm-76, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31132
in-theory        31132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (D or E))) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31132.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (D or E))) or F)), M:tm-69, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31133
in-theory        31133
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (E or F))) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31133.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (E or F))) or G)), M:tm-54, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31134
in-theory        31134
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (D or E))) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31134.        ((A -> (B or A)) and ((C -> (D -> (D or E))) or F)), M:tm-42, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31135
in-theory        31135
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (D or E))) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31135.        ((A -> (A or B)) and ((C -> (D -> (D or E))) or F)), M:tm-32, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31136
in-theory        31136
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (D or E))) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31136.        ((A -> (B -> (A and B))) and ((C -> (D -> (D or E))) or F)), M:tm-23, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31137
in-theory        31137
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (D or E))) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31137.        (((A and B) -> B) and ((C -> (D -> (D or E))) or F)), M:tm-22, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31138
in-theory        31138
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (D or E))) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31138.        (((A and B) -> A) and ((C -> (D -> (D or E))) or F)), M:tm-21, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31139
in-theory        31139
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (E or F))) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31139.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (E or F))) or G)), M:tm-20, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31140
in-theory        31140
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (D or E))) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31140.        ((A -> (B -> A)) and ((C -> (D -> (D or E))) or F)), M:tm-19, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31141
in-theory        31141
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (C or D))) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-7 tm-6 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31141.        (A or ((B -> (C -> (C or D))) or E)), M:tm-7, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31142
in-theory        31142
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-6 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31142.        (((A -> (B -> (B or C))) or D) or E), M:tm-6, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31143
in-theory        31143
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (C or D))) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31143.        (A -> (((B -> (C -> (C or D))) or E) and A)), M:tm-5, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31144
in-theory        31144
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (C or D))) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-1 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31144.        (A -> ((B -> (C -> (C or D))) or E)), M:tm-1, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31145
in-theory        31145
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-469 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-31145.        ((A -> (B -> (B or C))) and (D -> (E or D))), M:tm-469, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-31146
in-theory        31146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-31146.        ((A -> (B -> (B or C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-469, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-31147
in-theory        31147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-469 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-31147.        ((A -> (B -> (B or C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-469, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-31148
in-theory        31148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-469 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-31148.        ((A -> (B -> (B or C))) and ((not (not D)) -> D)), M:tm-469, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-31149
in-theory        31149
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-469 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31149.        ((A -> (B -> (B or C))) and (D -> (E -> (F -> E)))), M:tm-469, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-31150
in-theory        31150
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-469 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-31150.        ((A -> (B -> (B or C))) and ((D -> E) -> (D -> D))), M:tm-469, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-31151
in-theory        31151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-469 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-31151.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-469, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-31152
in-theory        31152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31152.        ((A -> (B -> (B or C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-469, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-31153
in-theory        31153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-469 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-31153.        ((A -> (B -> (B or C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-469, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-31154
in-theory        31154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-469 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31154.        ((A -> (B -> (B or C))) and (D -> ((E and F) -> E))), M:tm-469, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-31155
in-theory        31155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-469 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-31155.        ((A -> (B -> (B or C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-469, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-31156
in-theory        31156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-469 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31156.        ((A -> (B -> (B or C))) and (D -> ((E and F) -> F))), M:tm-469, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-31157
in-theory        31157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-469 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31157.        ((A -> (B -> (B or C))) and (D -> ((E -> (F -> E)) and D))), M:tm-469, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-31158
in-theory        31158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-469 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31158.        ((A -> (B -> (B or C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-469, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-31159
in-theory        31159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-469 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31159.        ((A -> (B -> (B or C))) and (D -> (((E and F) -> E) and D))), M:tm-469, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-31160
in-theory        31160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-469 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31160.        ((A -> (B -> (B or C))) and (D -> (((E and F) -> F) and D))), M:tm-469, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-31161
in-theory        31161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31161.        ((A -> (B -> (B or C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-469, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-31162
in-theory        31162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-469 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-31162.        ((A -> (B -> (B or C))) and ((D -> E) -> (D -> (D and E)))), M:tm-469, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-31163
in-theory        31163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31163.        ((A -> (B -> (B or C))) and (D -> (E -> (F -> (E and F))))), M:tm-469, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-31164
in-theory        31164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-469 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31164.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) or F)), M:tm-469, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-31165
in-theory        31165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-469 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31165.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-469, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-31166
in-theory        31166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-469 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31166.        ((A -> (B -> (B or C))) and (((D and E) -> D) or F)), M:tm-469, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-31167
in-theory        31167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-469 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31167.        ((A -> (B -> (B or C))) and (((D and E) -> E) or F)), M:tm-469, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-31168
in-theory        31168
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-469 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31168.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) or F)), M:tm-469, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-31169
in-theory        31169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-469 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31169.        ((A -> (B -> (B or C))) and ((D -> (D or E)) or F)), M:tm-469, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-31170
in-theory        31170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-469 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31170.        ((A -> (B -> (B or C))) and (D -> ((E -> (E or F)) and D))), M:tm-469, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-31171
in-theory        31171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-469 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31171.        ((A -> (B -> (B or C))) and (D -> (E -> (E or F)))), M:tm-469, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-31172
in-theory        31172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-469 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31172.        ((A -> (B -> (B or C))) and (D or (E -> (F -> E)))), M:tm-469, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-31173
in-theory        31173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31173.        ((A -> (B -> (B or C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-469, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-31174
in-theory        31174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-469 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31174.        ((A -> (B -> (B or C))) and (D or ((E and F) -> E))), M:tm-469, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-31175
in-theory        31175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-469 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31175.        ((A -> (B -> (B or C))) and (D or ((E and F) -> F))), M:tm-469, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-31176
in-theory        31176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31176.        ((A -> (B -> (B or C))) and (D or (E -> (F -> (E and F))))), M:tm-469, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-31177
in-theory        31177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-469 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31177.        ((A -> (B -> (B or C))) and (D or (E -> (E or F)))), M:tm-469, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-31178
in-theory        31178
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-469 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31178.        ((A -> (B -> (B or C))) and (D or (E -> (F or E)))), M:tm-469, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-31179
in-theory        31179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-469 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31179.        ((A -> (B -> (B or C))) and ((D -> (E or D)) or F)), M:tm-469, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-31180
in-theory        31180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-469 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31180.        ((A -> (B -> (B or C))) and (D -> ((E -> (F or E)) and D))), M:tm-469, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-31181
in-theory        31181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-469 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31181.        ((A -> (B -> (B or C))) and (D -> (E -> (F or E)))), M:tm-469, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-31182
in-theory        31182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-469 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-31182.        ((A -> (B -> (B or C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-469, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-31183
in-theory        31183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-469 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-31183.        ((A -> (B -> (B or C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-469, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-31184
in-theory        31184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-469 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-31184.        ((A -> (B -> (B or C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-469, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-31185
in-theory        31185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-469 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-31185.        ((A -> (B -> (B or C))) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-469, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-31186
in-theory        31186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-469 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-31186.        ((A -> (B -> (B or C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-469, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-31187
in-theory        31187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-469 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-31187.        ((A -> (B -> (B or C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-469, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-31188
in-theory        31188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-469 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-31188.        ((A -> (B -> (B or C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-469, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-31189
in-theory        31189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-469 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-31189.        ((A -> (B -> (B or C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-469, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-31190
in-theory        31190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-31190.        ((A -> (B -> (B or C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-469, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-31191
in-theory        31191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-469 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-31191.        ((A -> (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-469, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-31192
in-theory        31192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-469 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-31192.        ((A -> (B -> (B or C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-469, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-31193
in-theory        31193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-469 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-31193.        ((A -> (B -> (B or C))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-469, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-31194
in-theory        31194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-31194.        ((A -> (B -> (B or C))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-469, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-31195
in-theory        31195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-469 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-31195.        ((A -> (B -> (B or C))) and ((D -> (not (E -> D))) -> (not D))), M:tm-469, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-31196
in-theory        31196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-31196.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-469, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-31197
in-theory        31197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-469 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-31197.        ((A -> (B -> (B or C))) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-469, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-31198
in-theory        31198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-469 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-31198.        ((A -> (B -> (B or C))) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-469, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-31199
in-theory        31199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-31199.        ((A -> (B -> (B or C))) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-469, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-31200
in-theory        31200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-469 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-31200.        ((A -> (B -> (B or C))) and ((D -> (not (D or E))) -> (not D))), M:tm-469, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-31201
in-theory        31201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-469 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-31201.        ((A -> (B -> (B or C))) and ((D -> (not (E or D))) -> (not D))), M:tm-469, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-31202
in-theory        31202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-469 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-31202.        ((A -> (B -> (B or C))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-469, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-31203
in-theory        31203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-469 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-31203.        ((A -> (B -> (B or C))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-469, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-31204
in-theory        31204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-469 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-31204.        ((A -> (B -> (B or C))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-469, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-31205
in-theory        31205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-31205.        ((A -> (B -> (B or C))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-469, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-31206
in-theory        31206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-469 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-31206.        ((A -> (B -> (B or C))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-469, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-31207
in-theory        31207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-469 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-31207.        ((A -> (B -> (B or C))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-469, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-31208
in-theory        31208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-469 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-31208.        ((A -> (B -> (B or C))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-469, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-31209
in-theory        31209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-31209.        ((A -> (B -> (B or C))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-469, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-31210
in-theory        31210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-469 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-31210.        ((A -> (B -> (B or C))) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-469, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-31211
in-theory        31211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-469 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-31211.        ((A -> (B -> (B or C))) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-469, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-31212
in-theory        31212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-469 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-31212.        ((A -> (B -> (B or C))) and (D or ((not (not E)) -> E))), M:tm-469, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-31213
in-theory        31213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-469 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-31213.        ((A -> (B -> (B or C))) and (((not (not D)) -> D) or E)), M:tm-469, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-31214
in-theory        31214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-469 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-31214.        ((A -> (B -> (B or C))) and (D -> (((not (not E)) -> E) and D))), M:tm-469, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-31215
in-theory        31215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-469 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-31215.        ((A -> (B -> (B or C))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-469, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-31216
in-theory        31216
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-469 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-31216.        ((A -> (B -> (B or C))) and (D -> ((not (not E)) -> E))), M:tm-469, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-31217
in-theory        31217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-31217.        ((A -> (B -> (B or C))) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-469, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-31218
in-theory        31218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-469 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-31218.        ((A -> (B -> (B or C))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-469, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-31219
in-theory        31219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-31219.        ((A -> (B -> (B or C))) and (D or (E -> (F -> (G -> F))))), M:tm-469, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-31220
in-theory        31220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-31220.        ((A -> (B -> (B or C))) and ((D -> (E -> (F -> E))) or G)), M:tm-469, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-31221
in-theory        31221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-31221.        ((A -> (B -> (B or C))) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-469, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-31222
in-theory        31222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-469 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-31222.        ((A -> (B -> (B or C))) and ((D -> E) -> (D -> (F -> E)))), M:tm-469, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-31223
in-theory        31223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-31223.        ((A -> (B -> (B or C))) and (D -> (E -> (F -> (G -> F))))), M:tm-469, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-31224
in-theory        31224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-469 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-31224.        ((A -> (B -> (B or C))) and (D -> D)), M:tm-469, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-31225
in-theory        31225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-31225.        ((A -> (B -> (B or C))) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-469, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-31226
in-theory        31226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-469 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-31226.        ((A -> (B -> (B or C))) and ((D and E) -> (D and E))), M:tm-469, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-31227
in-theory        31227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-469 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-31227.        ((A -> (B -> (B or C))) and ((D -> E) -> (D -> E))), M:tm-469, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-31228
in-theory        31228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-469 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-31228.        ((A -> (B -> (B or C))) and ((not (not D)) -> (not (not D)))), M:tm-469, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-31229
in-theory        31229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-469 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-31229.        ((A -> (B -> (B or C))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-469, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-31230
in-theory        31230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-469 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-31230.        ((A -> (B -> (B or C))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-469, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-31231
in-theory        31231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-469 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-31231.        ((A -> (B -> (B or C))) and (D or ((E -> F) -> (E -> E)))), M:tm-469, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-31232
in-theory        31232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-469 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-31232.        ((A -> (B -> (B or C))) and (((D -> E) -> (D -> D)) or F)), M:tm-469, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-31233
in-theory        31233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-31233.        ((A -> (B -> (B or C))) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-469, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-31234
in-theory        31234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-31234.        ((A -> (B -> (B or C))) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-469, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-31235
in-theory        31235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-469 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-31235.        ((A -> (B -> (B or C))) and (D -> ((E -> F) -> (E -> E)))), M:tm-469, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-31236
in-theory        31236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-31236.        ((A -> (B -> (B or C))) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-469, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-31237
in-theory        31237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-469 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-31237.        ((A -> (B -> (B or C))) and ((D -> (D -> E)) -> (D -> E))), M:tm-469, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-31238
in-theory        31238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-469 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-31238.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-469, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-31239
in-theory        31239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-469 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-31239.        ((A -> (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-469, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-31240
in-theory        31240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-469 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-31240.        ((A -> (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-469, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-31241
in-theory        31241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-31241.        ((A -> (B -> (B or C))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-469, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-31242
in-theory        31242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-469 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-31242.        ((A -> (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-469, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-31243
in-theory        31243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-469 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-31243.        ((A -> (B -> (B or C))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-469, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-31244
in-theory        31244
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-469 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-31244.        ((A -> (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-469, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-31245
in-theory        31245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-31245.        ((A -> (B -> (B or C))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-469, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-31246
in-theory        31246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-469 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-31246.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-469, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-31247
in-theory        31247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-469 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-31247.        ((A -> (B -> (B or C))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-469, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-31248
in-theory        31248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-469 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-31248.        ((A -> (B -> (B or C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-469, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-31249
in-theory        31249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-469 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-31249.        ((A -> (B -> (B or C))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-469, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-31250
in-theory        31250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-469 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-31250.        ((A -> (B -> (B or C))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-469, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-31251
in-theory        31251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-469 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-31251.        ((A -> (B -> (B or C))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-469, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-31252
in-theory        31252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-469 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-31252.        ((A -> (B -> (B or C))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-469, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-31253
in-theory        31253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-469 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-31253.        ((A -> (B -> (B or C))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-469, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-31254
in-theory        31254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-469 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-31254.        ((A -> (B -> (B or C))) and (((D -> E) and D) -> E)), M:tm-469, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-31255
in-theory        31255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-469 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-31255.        ((A -> (B -> (B or C))) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-469, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-31256
in-theory        31256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-469 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-31256.        ((A -> (B -> (B or C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-469, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-31257
in-theory        31257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-469 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-31257.        ((A -> (B -> (B or C))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-469, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-31258
in-theory        31258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-469 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-31258.        ((A -> (B -> (B or C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-469, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-31259
in-theory        31259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-469 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-31259.        ((A -> (B -> (B or C))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-469, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-31260
in-theory        31260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-469 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-31260.        ((A -> (B -> (B or C))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-469, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-31261
in-theory        31261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-469 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-31261.        ((A -> (B -> (B or C))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-469, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-31262
in-theory        31262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-469 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-31262.        ((A -> (B -> (B or C))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-469, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-31263
in-theory        31263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-469 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-31263.        ((A -> (B -> (B or C))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-469, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-31264
in-theory        31264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-469 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-31264.        ((A -> (B -> (B or C))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-469, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-31265
in-theory        31265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-469 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-31265.        ((A -> (B -> (B or C))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-469, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-31266
in-theory        31266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-469 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-31266.        ((A -> (B -> (B or C))) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-469, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-31267
in-theory        31267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-469 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-31267.        ((A -> (B -> (B or C))) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-469, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-31268
in-theory        31268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-31268.        ((A -> (B -> (B or C))) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-469, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-31269
in-theory        31269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-469 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-31269.        ((A -> (B -> (B or C))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-469, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-31270
in-theory        31270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-469 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-31270.        ((A -> (B -> (B or C))) and (D or (E -> ((F and G) -> F)))), M:tm-469, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-31271
in-theory        31271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-31271.        ((A -> (B -> (B or C))) and ((D -> ((E and F) -> E)) or G)), M:tm-469, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-31272
in-theory        31272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-31272.        ((A -> (B -> (B or C))) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-469, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-31273
in-theory        31273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-469 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-31273.        ((A -> (B -> (B or C))) and ((D -> (E and F)) -> (D -> E))), M:tm-469, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-31274
in-theory        31274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-469 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-31274.        ((A -> (B -> (B or C))) and (D -> (E -> ((F and G) -> F)))), M:tm-469, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-31275
in-theory        31275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-469 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-31275.        ((A -> (B -> (B or C))) and ((D and (D -> E)) -> E)), M:tm-469, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-31276
in-theory        31276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-469 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-31276.        ((A -> (B -> (B or C))) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-469, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-31277
in-theory        31277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-469 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-31277.        ((A -> (B -> (B or C))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-469, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-31278
in-theory        31278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-469 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-31278.        ((A -> (B -> (B or C))) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-469, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-31279
in-theory        31279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-469 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-31279.        ((A -> (B -> (B or C))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-469, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-31280
in-theory        31280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-469 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-31280.        ((A -> (B -> (B or C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-469, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-31281
in-theory        31281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-469 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-31281.        ((A -> (B -> (B or C))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-469, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-31282
in-theory        31282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-469 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-31282.        ((A -> (B -> (B or C))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-469, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-31283
in-theory        31283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-469 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-31283.        ((A -> (B -> (B or C))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-469, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-31284
in-theory        31284
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-469 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-31284.        ((A -> (B -> (B or C))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-469, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-31285
in-theory        31285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-469 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-31285.        ((A -> (B -> (B or C))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-469, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-31286
in-theory        31286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-469 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-31286.        ((A -> (B -> (B or C))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-469, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-31287
in-theory        31287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-469 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-31287.        ((A -> (B -> (B or C))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-469, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-31288
in-theory        31288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-469 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-31288.        ((A -> (B -> (B or C))) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-469, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-31289
in-theory        31289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-469 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-31289.        ((A -> (B -> (B or C))) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-469, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-31290
in-theory        31290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-469 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-31290.        ((A -> (B -> (B or C))) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-469, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-31291
in-theory        31291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-31291.        ((A -> (B -> (B or C))) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-469, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-31292
in-theory        31292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-469 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-31292.        ((A -> (B -> (B or C))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-469, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-31293
in-theory        31293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-469 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-31293.        ((A -> (B -> (B or C))) and (D or (E -> ((F and G) -> G)))), M:tm-469, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-31294
in-theory        31294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-31294.        ((A -> (B -> (B or C))) and ((D -> ((E and F) -> F)) or G)), M:tm-469, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-31295
in-theory        31295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-31295.        ((A -> (B -> (B or C))) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-469, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-31296
in-theory        31296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-469 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-31296.        ((A -> (B -> (B or C))) and ((D -> (E and F)) -> (D -> F))), M:tm-469, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-31297
in-theory        31297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-469 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-31297.        ((A -> (B -> (B or C))) and (D -> (E -> ((F and G) -> G)))), M:tm-469, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-31298
in-theory        31298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31298.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-469, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-31299
in-theory        31299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31299.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-469, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-31300
in-theory        31300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31300.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-469, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-31301
in-theory        31301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-469 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31301.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-469, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-31302
in-theory        31302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31302.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-469, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-31303
in-theory        31303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-469 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31303.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-469, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31304
in-theory        31304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31304.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-469, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-31305
in-theory        31305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-31305.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-469, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-31306
in-theory        31306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-469 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-31306.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-469, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-31307
in-theory        31307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-31307.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-469, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-31308
in-theory        31308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-31308.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-469, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-31309
in-theory        31309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-31309.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-469, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-31310
in-theory        31310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-469 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-31310.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-469, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-31311
in-theory        31311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-31311.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-469, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-31312
in-theory        31312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-469 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-31312.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-469, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-31313
in-theory        31313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-469 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-31313.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-469, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-31314
in-theory        31314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-469 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-31314.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-469, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-31315
in-theory        31315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-469 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-31315.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-469, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-31316
in-theory        31316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-31316.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-469, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-31317
in-theory        31317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-31317.        ((A -> (B -> (B or C))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-469, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-31318
in-theory        31318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-469 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-31318.        ((A -> (B -> (B or C))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-469, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-31319
in-theory        31319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-469 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-31319.        ((A -> (B -> (B or C))) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-469, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-31320
in-theory        31320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-469 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-31320.        ((A -> (B -> (B or C))) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-469, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-31321
in-theory        31321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-31321.        ((A -> (B -> (B or C))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-469, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-31322
in-theory        31322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-469 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-31322.        ((A -> (B -> (B or C))) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-469, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-31323
in-theory        31323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-469 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31323.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-469, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-31324
in-theory        31324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31324.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-469, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-31325
in-theory        31325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-469 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31325.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-469, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-31326
in-theory        31326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-469 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31326.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-469, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-31327
in-theory        31327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31327.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-469, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-31328
in-theory        31328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31328.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-469, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-31329
in-theory        31329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-469 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31329.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-469, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-31330
in-theory        31330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-31330.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-469, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-31331
in-theory        31331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-469 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-31331.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-469, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-31332
in-theory        31332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-469 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-31332.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-469, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-31333
in-theory        31333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-31333.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-469, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-31334
in-theory        31334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-469 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-31334.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-469, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-31335
in-theory        31335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-469 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-31335.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-469, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-31336
in-theory        31336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-469 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-31336.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-469, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-31337
in-theory        31337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-469 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-31337.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-469, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-31338
in-theory        31338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-469 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-31338.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-469, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-31339
in-theory        31339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-469 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-31339.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-469, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-31340
in-theory        31340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-469 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-31340.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-469, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-31341
in-theory        31341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-469 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-31341.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-469, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-31342
in-theory        31342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-469 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-31342.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-469, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-31343
in-theory        31343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-469 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-31343.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-469, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-31344
in-theory        31344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-469 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-31344.        ((A -> (B -> (B or C))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-469, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-31345
in-theory        31345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-469 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-31345.        ((A -> (B -> (B or C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-469, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-31346
in-theory        31346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-469 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-31346.        ((A -> (B -> (B or C))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-469, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-31347
in-theory        31347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-469 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-31347.        ((A -> (B -> (B or C))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-469, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-31348
in-theory        31348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-469 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-31348.        ((A -> (B -> (B or C))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-469, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-31349
in-theory        31349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-469 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-31349.        ((A -> (B -> (B or C))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-469, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-31350
in-theory        31350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31350.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-469, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-31351
in-theory        31351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31351.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-469, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-31352
in-theory        31352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31352.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F and G) -> F))), M:tm-469, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-31353
in-theory        31353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-469 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31353.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F and G) -> G))), M:tm-469, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-31354
in-theory        31354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31354.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-469, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-31355
in-theory        31355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-469 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31355.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (F or G)))), M:tm-469, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31356
in-theory        31356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31356.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (G or F)))), M:tm-469, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-31357
in-theory        31357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-31357.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-469, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-31358
in-theory        31358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-469 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-31358.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-469, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-31359
in-theory        31359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-31359.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-469, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-31360
in-theory        31360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-31360.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-469, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-31361
in-theory        31361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-31361.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-469, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-31362
in-theory        31362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-469 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-31362.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-469, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-31363
in-theory        31363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-31363.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-469, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-31364
in-theory        31364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-469 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-31364.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-469, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-31365
in-theory        31365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-469 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-31365.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-469, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-31366
in-theory        31366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-469 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-31366.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-469, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-31367
in-theory        31367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-469 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-31367.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-469, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-31368
in-theory        31368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-31368.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-469, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-31369
in-theory        31369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-469 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-31369.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-469, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-31370
in-theory        31370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-31370.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-469, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-31371
in-theory        31371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-469 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-31371.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-469, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-31372
in-theory        31372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-31372.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-469, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-31373
in-theory        31373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-31373.        ((A -> (B -> (B or C))) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-469, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-31374
in-theory        31374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-469 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-31374.        ((A -> (B -> (B or C))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-469, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-31375
in-theory        31375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-469 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-31375.        ((A -> (B -> (B or C))) and (D or (E -> (((F and G) -> F) and E)))), M:tm-469, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-31376
in-theory        31376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-469 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-31376.        ((A -> (B -> (B or C))) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-469, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-31377
in-theory        31377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-31377.        ((A -> (B -> (B or C))) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-469, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-31378
in-theory        31378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-469 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-31378.        ((A -> (B -> (B or C))) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-469, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-31379
in-theory        31379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31379.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-469, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-31380
in-theory        31380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31380.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-469, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-31381
in-theory        31381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31381.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F and G) -> F))), M:tm-469, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-31382
in-theory        31382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-469 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31382.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F and G) -> G))), M:tm-469, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-31383
in-theory        31383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31383.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-469, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-31384
in-theory        31384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-469 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31384.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (F or G)))), M:tm-469, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31385
in-theory        31385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31385.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (G or F)))), M:tm-469, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-31386
in-theory        31386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-31386.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-469, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-31387
in-theory        31387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-469 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-31387.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-469, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-31388
in-theory        31388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-31388.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-469, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-31389
in-theory        31389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-31389.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-469, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-31390
in-theory        31390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-31390.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-469, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-31391
in-theory        31391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-469 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-31391.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-469, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-31392
in-theory        31392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-31392.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-469, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-31393
in-theory        31393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-469 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-31393.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-469, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-31394
in-theory        31394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-469 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-31394.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-469, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-31395
in-theory        31395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-469 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-31395.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-469, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-31396
in-theory        31396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-469 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-31396.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-469, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-31397
in-theory        31397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-31397.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-469, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-31398
in-theory        31398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-469 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-31398.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-469, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-31399
in-theory        31399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-31399.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-469, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-31400
in-theory        31400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-31400.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-469, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-31401
in-theory        31401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-31401.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-469, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-31402
in-theory        31402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-469 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-31402.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-469, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-31403
in-theory        31403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-31403.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-469, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-31404
in-theory        31404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-31404.        ((A -> (B -> (B or C))) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-469, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-31405
in-theory        31405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-469 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-31405.        ((A -> (B -> (B or C))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-469, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-31406
in-theory        31406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-469 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-31406.        ((A -> (B -> (B or C))) and (D or (E -> (((F and G) -> G) and E)))), M:tm-469, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-31407
in-theory        31407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-469 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-31407.        ((A -> (B -> (B or C))) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-469, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-31408
in-theory        31408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-31408.        ((A -> (B -> (B or C))) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-469, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-31409
in-theory        31409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-469 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-31409.        ((A -> (B -> (B or C))) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-469, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-31410
in-theory        31410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31410.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-469, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-31411
in-theory        31411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31411.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-469, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-31412
in-theory        31412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-469 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31412.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-469, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-31413
in-theory        31413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-469 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31413.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-469, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-31414
in-theory        31414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31414.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-469, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-31415
in-theory        31415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-469 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31415.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-469, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31416
in-theory        31416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31416.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-469, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-31417
in-theory        31417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-31417.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-469, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-31418
in-theory        31418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-31418.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-469, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-31419
in-theory        31419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-469 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-31419.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-469, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-31420
in-theory        31420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-31420.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-469, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-31421
in-theory        31421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-31421.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-469, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-31422
in-theory        31422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-31422.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-469, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-31423
in-theory        31423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-469 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-31423.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-469, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-31424
in-theory        31424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-469 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-31424.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-469, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-31425
in-theory        31425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-469 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-31425.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-469, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-31426
in-theory        31426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-469 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-31426.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-469, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-31427
in-theory        31427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-469 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-31427.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-469, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-31428
in-theory        31428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-469 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-31428.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-469, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-31429
in-theory        31429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-469 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-31429.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-469, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-31430
in-theory        31430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-469 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-31430.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-469, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-31431
in-theory        31431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-469 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-31431.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-469, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-31432
in-theory        31432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-469 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-31432.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-469, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-31433
in-theory        31433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-469 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-31433.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-469, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-31434
in-theory        31434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-469 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-31434.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-469, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-31435
in-theory        31435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-469 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-31435.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-469, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-31436
in-theory        31436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-469 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-31436.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-469, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-31437
in-theory        31437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-469 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-31437.        ((A -> (B -> (B or C))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-469, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-31438
in-theory        31438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-469 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-31438.        ((A -> (B -> (B or C))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-469, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-31439
in-theory        31439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-469 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-31439.        ((A -> (B -> (B or C))) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-469, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-31440
in-theory        31440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-469 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-31440.        ((A -> (B -> (B or C))) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-469, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-31441
in-theory        31441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-469 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-31441.        ((A -> (B -> (B or C))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-469, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-31442
in-theory        31442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-469 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-31442.        ((A -> (B -> (B or C))) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-469, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-31443
in-theory        31443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-469 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-31443.        ((A -> (B -> (B or C))) and (D -> (D and (E -> D)))), M:tm-469, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-31444
in-theory        31444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-31444.        ((A -> (B -> (B or C))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-469, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-31445
in-theory        31445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-469 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-31445.        ((A -> (B -> (B or C))) and ((D and E) -> ((D and E) and D))), M:tm-469, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-31446
in-theory        31446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-469 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-31446.        ((A -> (B -> (B or C))) and ((D and E) -> ((D and E) and E))), M:tm-469, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-31447
in-theory        31447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-31447.        ((A -> (B -> (B or C))) and (D -> (D and (E -> (D and E))))), M:tm-469, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-31448
in-theory        31448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-469 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-31448.        ((A -> (B -> (B or C))) and (D -> (D and (D or E)))), M:tm-469, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-31449
in-theory        31449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-469 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-31449.        ((A -> (B -> (B or C))) and (D -> (D and (E or D)))), M:tm-469, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-31450
in-theory        31450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-469 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-31450.        ((A -> (B -> (B or C))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-469, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-31451
in-theory        31451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-31451.        ((A -> (B -> (B or C))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-469, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-31452
in-theory        31452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-469 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-31452.        ((A -> (B -> (B or C))) and ((not (not D)) -> ((not (not D)) and D))), M:tm-469, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-31453
in-theory        31453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-31453.        ((A -> (B -> (B or C))) and (D -> (D and (E -> (F -> E))))), M:tm-469, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-31454
in-theory        31454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-469 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-31454.        ((A -> (B -> (B or C))) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-469, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-31455
in-theory        31455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-469 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-31455.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-469, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-31456
in-theory        31456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-469 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-31456.        ((A -> (B -> (B or C))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-469, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-31457
in-theory        31457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-469 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-31457.        ((A -> (B -> (B or C))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-469, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-31458
in-theory        31458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-469 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-31458.        ((A -> (B -> (B or C))) and (D -> (D and ((E and F) -> E)))), M:tm-469, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-31459
in-theory        31459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-469 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-31459.        ((A -> (B -> (B or C))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-469, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-31460
in-theory        31460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-469 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-31460.        ((A -> (B -> (B or C))) and (D -> (D and ((E and F) -> F)))), M:tm-469, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-31461
in-theory        31461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-469 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-31461.        ((A -> (B -> (B or C))) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-469, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-31462
in-theory        31462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-469 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-31462.        ((A -> (B -> (B or C))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-469, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-31463
in-theory        31463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-469 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-31463.        ((A -> (B -> (B or C))) and (D -> (D and (((E and F) -> E) and D)))), M:tm-469, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-31464
in-theory        31464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-469 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-31464.        ((A -> (B -> (B or C))) and (D -> (D and (((E and F) -> F) and D)))), M:tm-469, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-31465
in-theory        31465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-469 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-31465.        ((A -> (B -> (B or C))) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-469, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-31466
in-theory        31466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-31466.        ((A -> (B -> (B or C))) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-469, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-31467
in-theory        31467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-469 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-31467.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-469, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-31468
in-theory        31468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-31468.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-469, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-31469
in-theory        31469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-31469.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-469, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-31470
in-theory        31470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-469 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-31470.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-469, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-31471
in-theory        31471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-31471.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-469, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-31472
in-theory        31472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-469 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-31472.        ((A -> (B -> (B or C))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-469, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-31473
in-theory        31473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-469 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-31473.        ((A -> (B -> (B or C))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-469, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-31474
in-theory        31474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-469 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-31474.        ((A -> (B -> (B or C))) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-469, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-31475
in-theory        31475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-469 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-31475.        ((A -> (B -> (B or C))) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-469, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-31476
in-theory        31476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-31476.        ((A -> (B -> (B or C))) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-469, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-31477
in-theory        31477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-469 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-31477.        ((A -> (B -> (B or C))) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-469, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-31478
in-theory        31478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-469 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-31478.        ((A -> (B -> (B or C))) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-469, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-31479
in-theory        31479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-469 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-31479.        ((A -> (B -> (B or C))) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-469, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-31480
in-theory        31480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-469 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-31480.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-469, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-31481
in-theory        31481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-469 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-31481.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-469, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-31482
in-theory        31482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-469 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-31482.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-469, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-31483
in-theory        31483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-469 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-31483.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-469, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-31484
in-theory        31484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-469 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-31484.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-469, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-31485
in-theory        31485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-469 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-31485.        ((A -> (B -> (B or C))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-469, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-31486
in-theory        31486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-469 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-31486.        ((A -> (B -> (B or C))) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-469, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-31487
in-theory        31487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-469 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-31487.        ((A -> (B -> (B or C))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-469, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-31488
in-theory        31488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-31488.        ((A -> (B -> (B or C))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-469, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-31489
in-theory        31489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-469 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-31489.        ((A -> (B -> (B or C))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-469, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-31490
in-theory        31490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-469 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-31490.        ((A -> (B -> (B or C))) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-469, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-31491
in-theory        31491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-469 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-31491.        ((A -> (B -> (B or C))) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-469, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-31492
in-theory        31492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-31492.        ((A -> (B -> (B or C))) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-469, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-31493
in-theory        31493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-469 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-31493.        ((A -> (B -> (B or C))) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-469, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-31494
in-theory        31494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-469 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-31494.        ((A -> (B -> (B or C))) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-469, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-31495
in-theory        31495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-469 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31495.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-469, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-31496
in-theory        31496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31496.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-469, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-31497
in-theory        31497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31497.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-469, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-31498
in-theory        31498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31498.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-469, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-31499
in-theory        31499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31499.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-469, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-31500
in-theory        31500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-469 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31500.        ((A -> (B -> (B or C))) and (D or ((E -> (F -> E)) or G))), M:tm-469, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-31501
in-theory        31501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31501.        ((A -> (B -> (B or C))) and (((D -> (E -> D)) or F) or G)), M:tm-469, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-31502
in-theory        31502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31502.        ((A -> (B -> (B or C))) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-469, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-31503
in-theory        31503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-469 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31503.        ((A -> (B -> (B or C))) and (D -> ((E -> (F -> E)) or G))), M:tm-469, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-31504
in-theory        31504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-469 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-31504.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-469, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-31505
in-theory        31505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-31505.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-469, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-31506
in-theory        31506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-31506.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-469, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-31507
in-theory        31507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-469 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-31507.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-469, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-31508
in-theory        31508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-31508.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-469, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-31509
in-theory        31509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-469 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-31509.        ((A -> (B -> (B or C))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-469, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-31510
in-theory        31510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-469 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-31510.        ((A -> (B -> (B or C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-469, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-31511
in-theory        31511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-469 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-31511.        ((A -> (B -> (B or C))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-469, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-31512
in-theory        31512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-469 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-31512.        ((A -> (B -> (B or C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-469, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-31513
in-theory        31513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-469 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-31513.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-469, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-31514
in-theory        31514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-31514.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-469, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-31515
in-theory        31515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-31515.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-469, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-31516
in-theory        31516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-31516.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-469, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-31517
in-theory        31517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-31517.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-469, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-31518
in-theory        31518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-469 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-31518.        ((A -> (B -> (B or C))) and (D or (((E and F) -> E) or G))), M:tm-469, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-31519
in-theory        31519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-31519.        ((A -> (B -> (B or C))) and ((((D and E) -> D) or F) or G)), M:tm-469, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-31520
in-theory        31520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-31520.        ((A -> (B -> (B or C))) and (D -> ((((E and F) -> E) or G) and D))), M:tm-469, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-31521
in-theory        31521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-469 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-31521.        ((A -> (B -> (B or C))) and (D -> (((E and F) -> E) or G))), M:tm-469, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-31522
in-theory        31522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-469 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-31522.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-469, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-31523
in-theory        31523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-31523.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-469, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-31524
in-theory        31524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-31524.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-469, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-31525
in-theory        31525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-31525.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-469, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-31526
in-theory        31526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-31526.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-469, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-31527
in-theory        31527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-469 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-31527.        ((A -> (B -> (B or C))) and (D or (((E and F) -> F) or G))), M:tm-469, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-31528
in-theory        31528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-31528.        ((A -> (B -> (B or C))) and ((((D and E) -> E) or F) or G)), M:tm-469, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-31529
in-theory        31529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-31529.        ((A -> (B -> (B or C))) and (D -> ((((E and F) -> F) or G) and D))), M:tm-469, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-31530
in-theory        31530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-469 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-31530.        ((A -> (B -> (B or C))) and (D -> (((E and F) -> F) or G))), M:tm-469, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-31531
in-theory        31531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-469 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-31531.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-469, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-31532
in-theory        31532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-469 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-31532.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-469, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-31533
in-theory        31533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-469 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-31533.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-469, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-31534
in-theory        31534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-469 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-31534.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-469, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-31535
in-theory        31535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-469 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-31535.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-469, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-31536
in-theory        31536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-469 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-31536.        ((A -> (B -> (B or C))) and (D or ((E -> (F -> (E and F))) or G))), M:tm-469, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-31537
in-theory        31537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-469 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-31537.        ((A -> (B -> (B or C))) and (((D -> (E -> (D and E))) or F) or G)), M:tm-469, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-31538
in-theory        31538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-31538.        ((A -> (B -> (B or C))) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-469, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-31539
in-theory        31539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-469 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-31539.        ((A -> (B -> (B or C))) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-469, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-31540
in-theory        31540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-469 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-31540.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-469, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-31541
in-theory        31541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-31541.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-469, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-31542
in-theory        31542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-31542.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-469, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-31543
in-theory        31543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-31543.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-469, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-31544
in-theory        31544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-31544.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-469, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-31545
in-theory        31545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-469 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-31545.        ((A -> (B -> (B or C))) and (D or ((E -> (E or F)) or G))), M:tm-469, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-31546
in-theory        31546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-31546.        ((A -> (B -> (B or C))) and (((D -> (D or E)) or F) or G)), M:tm-469, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-31547
in-theory        31547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-31547.        ((A -> (B -> (B or C))) and (D -> (((E -> (E or F)) or G) and D))), M:tm-469, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-31548
in-theory        31548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-469 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-31548.        ((A -> (B -> (B or C))) and (D -> ((E -> (E or F)) or G))), M:tm-469, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-31549
in-theory        31549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31549.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-469, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-31550
in-theory        31550
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31550.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-469, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-31551
in-theory        31551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31551.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-469, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-31552
in-theory        31552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-469 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31552.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-469, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-31553
in-theory        31553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31553.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-469, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-31554
in-theory        31554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-469 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31554.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-469, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31555
in-theory        31555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31555.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-469, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-31556
in-theory        31556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-31556.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-469, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-31557
in-theory        31557
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-469 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-31557.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-469, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-31558
in-theory        31558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-31558.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-469, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-31559
in-theory        31559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-31559.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-469, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-31560
in-theory        31560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-31560.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-469, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-31561
in-theory        31561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-469 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-31561.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-469, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-31562
in-theory        31562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-31562.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-469, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-31563
in-theory        31563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-469 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-31563.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-469, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-31564
in-theory        31564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-469 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-31564.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-469, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-31565
in-theory        31565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-469 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-31565.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-469, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-31566
in-theory        31566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-469 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-31566.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-469, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-31567
in-theory        31567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-31567.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-469, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-31568
in-theory        31568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-469 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-31568.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-469, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-31569
in-theory        31569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-31569.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-469, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-31570
in-theory        31570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-31570.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-469, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-31571
in-theory        31571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-469 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-31571.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-469, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-31572
in-theory        31572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-31572.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-469, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-31573
in-theory        31573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-469 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-31573.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-469, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-31574
in-theory        31574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31574.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-469, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-31575
in-theory        31575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-31575.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-469, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-31576
in-theory        31576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-31576.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-469, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-31577
in-theory        31577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-31577.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-469, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-31578
in-theory        31578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-469 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-31578.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-469, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-31579
in-theory        31579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-31579.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-469, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-31580
in-theory        31580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31580.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-469, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-31581
in-theory        31581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-469 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-31581.        ((A -> (B -> (B or C))) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-469, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-31582
in-theory        31582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-469 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31582.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-469, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-31583
in-theory        31583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31583.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-469, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-31584
in-theory        31584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31584.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-469, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-31585
in-theory        31585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-469 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31585.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-469, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-31586
in-theory        31586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31586.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-469, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-31587
in-theory        31587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-31587.        ((A -> (B -> (B or C))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-469, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-31588
in-theory        31588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-469 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-31588.        ((A -> (B -> (B or C))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-469, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-31589
in-theory        31589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-469 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31589.        ((A -> (B -> (B or C))) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-469, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-31590
in-theory        31590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-469 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31590.        ((A -> (B -> (B or C))) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-469, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-31591
in-theory        31591
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31591.        ((A -> (B -> (B or C))) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-469, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-31592
in-theory        31592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-469 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31592.        ((A -> (B -> (B or C))) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-469, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-31593
in-theory        31593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31593.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-469, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-31594
in-theory        31594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31594.        ((A -> (B -> (B or C))) and (D -> (D and (E -> (E or F))))), M:tm-469, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-31595
in-theory        31595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31595.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-469, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-31596
in-theory        31596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31596.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-469, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-31597
in-theory        31597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31597.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-469, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-31598
in-theory        31598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31598.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-469, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-31599
in-theory        31599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31599.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-469, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-31600
in-theory        31600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-469 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-31600.        ((A -> (B -> (B or C))) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-469, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-31601
in-theory        31601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-469 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-31601.        ((A -> (B -> (B or C))) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-469, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-31602
in-theory        31602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-31602.        ((A -> (B -> (B or C))) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-469, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-31603
in-theory        31603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31603.        ((A -> (B -> (B or C))) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-469, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-31604
in-theory        31604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-469 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31604.        ((A -> (B -> (B or C))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-469, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-31605
in-theory        31605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31605.        ((A -> (B -> (B or C))) and (D or (E -> (F -> (F or G))))), M:tm-469, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31606
in-theory        31606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31606.        ((A -> (B -> (B or C))) and ((D -> (E -> (E or F))) or G)), M:tm-469, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-31607
in-theory        31607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31607.        ((A -> (B -> (B or C))) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-469, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31608
in-theory        31608
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (E -> (E or F))) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-469 ((Am (-> A (or A B))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31608.        ((A or (B -> (B or C))) -> ((D -> (E -> (E or F))) and (B -> (B or C)))), M:tm-466, m:tm-469, u:((Am (-> A (or A B))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (or A B)))))
================================================================
tm-name          tm-31609
in-theory        31609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31609.        ((A -> ((B -> (C -> (C or D))) and A)) and (E -> (E or F))), M:tm-456, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31610
in-theory        31610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31610.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-453, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31611
in-theory        31611
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> (E or F))) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-469 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31611.        ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> (E or F))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-469, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-31612
in-theory        31612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and ((E -> (E or F)) and (A -> ((B -> (C -> (C or D))) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31612.        ((A -> ((B -> (C -> (C or D))) and A)) and ((E -> (E or F)) and (A -> ((B -> (C -> (C or D))) and A)))), M:tm-443, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31613
in-theory        31613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31613.        (((A -> (A or B)) or C) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-409, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31614
in-theory        31614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31614.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-400, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31615
in-theory        31615
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31615.        ((((A and B) -> B) or C) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-391, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31616
in-theory        31616
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31616.        ((((A and B) -> A) or C) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-382, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31617
in-theory        31617
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> (G or H))) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31617.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> (G or H))) and E))), M:tm-373, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31618
in-theory        31618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31618.        (((A -> (B -> A)) or C) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-364, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31619
in-theory        31619
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D -> (D or E))) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31619.        (A -> (B -> (((C -> (D -> (D or E))) and A) and B))), M:tm-355, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-31620
in-theory        31620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31620.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-354, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31621
in-theory        31621
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> (E or F))) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-469 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31621.        ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> (E or F))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-469, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-31622
in-theory        31622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31622.        ((A -> ((B -> (C -> (C or D))) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31623
in-theory        31623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> (E or F))) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31623.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> (E or F))) and C))), M:tm-338, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31624
in-theory        31624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (D -> (D or E))) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-469 ((Am (-> A (and A B))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31624.        (((A -> B) or (A -> (A and B))) -> ((C -> (D -> (D or E))) and (A -> (A and B)))), M:tm-335, m:tm-469, u:((Am (-> A (and A B))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (and A B)))))
================================================================
tm-name          tm-31625
in-theory        31625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and (A -> (A and ((B -> (C -> (C or D))) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31625.        ((A -> ((B -> (C -> (C or D))) and A)) and (A -> (A and ((B -> (C -> (C or D))) and A)))), M:tm-328, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-31626
in-theory        31626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> (C -> (C or D))) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31626.        ((A -> ((B -> (C -> (C or D))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> (C -> (C or D))) and A)))), M:tm-327, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31627
in-theory        31627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and (((E and F) -> F) and (A -> ((B -> (C -> (C or D))) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31627.        ((A -> ((B -> (C -> (C or D))) and A)) and (((E and F) -> F) and (A -> ((B -> (C -> (C or D))) and A)))), M:tm-326, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31628
in-theory        31628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and (((E and F) -> E) and (A -> ((B -> (C -> (C or D))) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31628.        ((A -> ((B -> (C -> (C or D))) and A)) and (((E and F) -> E) and (A -> ((B -> (C -> (C or D))) and A)))), M:tm-325, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31629
in-theory        31629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C -> (C or D))) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31629.        ((A -> ((B -> (C -> (C or D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C -> (C or D))) and A)))), M:tm-324, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31630
in-theory        31630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and ((E -> (F -> E)) and (A -> ((B -> (C -> (C or D))) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31630.        ((A -> ((B -> (C -> (C or D))) and A)) and ((E -> (F -> E)) and (A -> ((B -> (C -> (C or D))) and A)))), M:tm-323, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31631
in-theory        31631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31631.        ((A -> ((B -> (C -> (C or D))) and A)) and ((E and F) -> F)), M:tm-322, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31632
in-theory        31632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31632.        ((A -> ((B -> (C -> (C or D))) and A)) and ((E and F) -> E)), M:tm-320, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31633
in-theory        31633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31633.        ((A -> ((B -> (C -> (C or D))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31634
in-theory        31634
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31634.        ((A -> ((B -> (C -> (C or D))) and A)) and (A -> A)), M:tm-316, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-31635
in-theory        31635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31635.        ((A -> ((B -> (C -> (C or D))) and A)) and (E -> (F -> E))), M:tm-315, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31636
in-theory        31636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and ((A -> (not ((B -> (C -> (C or D))) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31636.        ((A -> ((B -> (C -> (C or D))) and A)) and ((A -> (not ((B -> (C -> (C or D))) and A))) -> (not A))), M:tm-313, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-31637
in-theory        31637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and ((((B -> (C -> (C or D))) and A) -> E) -> ((A or ((B -> (C -> (C or D))) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31637.        ((A -> ((B -> (C -> (C or D))) and A)) and ((((B -> (C -> (C or D))) and A) -> E) -> ((A or ((B -> (C -> (C or D))) and A)) -> E))), M:tm-312, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-31638
in-theory        31638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and (E or (A -> ((B -> (C -> (C or D))) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31638.        ((A -> ((B -> (C -> (C or D))) and A)) and (E or (A -> ((B -> (C -> (C or D))) and A)))), M:tm-311, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31639
in-theory        31639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and ((A -> ((B -> (C -> (C or D))) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31639.        ((A -> ((B -> (C -> (C or D))) and A)) and ((A -> ((B -> (C -> (C or D))) and A)) or E)), M:tm-310, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31640
in-theory        31640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and (E -> ((A -> ((B -> (C -> (C or D))) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31640.        ((A -> ((B -> (C -> (C or D))) and A)) and (E -> ((A -> ((B -> (C -> (C or D))) and A)) and E))), M:tm-309, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31641
in-theory        31641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and (E -> (A -> ((B -> (C -> (C or D))) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31641.        ((A -> ((B -> (C -> (C or D))) and A)) and (E -> (A -> ((B -> (C -> (C or D))) and A)))), M:tm-305, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31642
in-theory        31642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31642.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-303, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31643
in-theory        31643
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> (E or F))) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-469 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31643.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> (E or F))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-469, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-31644
in-theory        31644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31644.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-270, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31645
in-theory        31645
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (E -> (E or F))) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-469 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31645.        ((A or (((B and C) -> C) and A)) -> ((D -> (E -> (E or F))) and (((B and C) -> C) and A))), M:tm-267, m:tm-469, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-31646
in-theory        31646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31646.        ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-239, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31647
in-theory        31647
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (E -> (E or F))) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-469 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31647.        ((A or (((B and C) -> B) and A)) -> ((D -> (E -> (E or F))) and (((B and C) -> B) and A))), M:tm-236, m:tm-469, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-31648
in-theory        31648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> (G or H))) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31648.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> (G or H))) and E))), M:tm-210, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31649
in-theory        31649
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> (F or G))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-469 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (or Cm Dm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31649.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> (F or G))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-469, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (or Cm Dm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-31650
in-theory        31650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31650.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-183, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31651
in-theory        31651
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> (E or F))) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-469 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31651.        ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> (E or F))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-469, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-31652
in-theory        31652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31652.        ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-157, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31653
in-theory        31653
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (E -> (E or F))) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-469 ((Am (-> (and A B) B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31653.        ((A or ((B and C) -> C)) -> ((D -> (E -> (E or F))) and ((B and C) -> C))), M:tm-154, m:tm-469, u:((Am (-> (and A B) B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> (and A B) B))))
================================================================
tm-name          tm-31654
in-theory        31654
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31654.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-147, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31655
in-theory        31655
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> (E or F))) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-469 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31655.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> (E or F))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-469, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-31656
in-theory        31656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31656.        ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-134, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31657
in-theory        31657
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (E -> (E or F))) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-469 ((Am (-> (and A B) A)) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31657.        ((A or ((B and C) -> B)) -> ((D -> (E -> (E or F))) and ((B and C) -> B))), M:tm-131, m:tm-469, u:((Am (-> (and A B) A)) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> (and A B) A))))
================================================================
tm-name          tm-31658
in-theory        31658
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31658.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-125, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31659
in-theory        31659
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> (E or F))) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-469 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31659.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> (E or F))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-469, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-31660
in-theory        31660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (G or H))) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31660.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (G or H))) and E))), M:tm-113, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31661
in-theory        31661
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> (F or G))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-469 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31661.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> (F or G))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-469, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-31662
in-theory        31662
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31662.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-105, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31663
in-theory        31663
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> (E or F))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-469 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31663.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> (E or F))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-469, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-31664
in-theory        31664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> (E or F))) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31664.        (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> (E or F))) and C))), M:tm-95, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31665
in-theory        31665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (D -> (D or E))) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-469 ((Am (-> A A)) (B (and (-> Bm (-> Cm (or Cm Dm))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31665.        (((A -> B) or (A -> A)) -> ((C -> (D -> (D or E))) and (A -> A))), M:tm-92, m:tm-469, u:((Am (-> A A)) (B (and (-> Bm (-> Cm (or Cm Dm))) (-> A A))))
================================================================
tm-name          tm-31666
in-theory        31666
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> (D or E))) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31666.        (A -> (B -> ((C -> (D -> (D or E))) and A))), M:tm-84, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-31667
in-theory        31667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31667.        ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-83, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31668
in-theory        31668
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (E -> (E or F))) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-469 ((Am (-> A (-> B A))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31668.        ((A or (B -> (C -> B))) -> ((D -> (E -> (E or F))) and (B -> (C -> B)))), M:tm-80, m:tm-469, u:((Am (-> A (-> B A))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (-> B A)))))
================================================================
tm-name          tm-31669
in-theory        31669
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (D -> (D or E))) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31669.        (((not (not A)) -> A) and (B -> ((C -> (D -> (D or E))) and B))), M:tm-76, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31670
in-theory        31670
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (C -> (C or D))) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31670.        (((not (not A)) or A) -> ((B -> (C -> (C or D))) and A)), M:tm-73, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-31671
in-theory        31671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> (E or F))) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31671.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> (E or F))) and C))), M:tm-69, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31672
in-theory        31672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> (D or E))) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-469 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31672.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> (D or E))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-469, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-31673
in-theory        31673
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31673.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-54, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31674
in-theory        31674
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (E or F))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-469 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31674.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (E or F))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-469, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-31675
in-theory        31675
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (D -> (D or E))) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-469 ((Am (or A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31675.        ((A or (B or A)) -> ((C -> (D -> (D or E))) and (B or A))), M:tm-50, m:tm-469, u:((Am (or A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (or A B))))
================================================================
tm-name          tm-31676
in-theory        31676
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (D -> (D or E))) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-469 ((Am (or A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31676.        ((A or (A or B)) -> ((C -> (D -> (D or E))) and (A or B))), M:tm-49, m:tm-469, u:((Am (or A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (or A B))))
================================================================
tm-name          tm-31677
in-theory        31677
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (D -> (D or E))) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-469 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31677.        ((A or (B -> (A and B))) -> ((C -> (D -> (D or E))) and (B -> (A and B)))), M:tm-48, m:tm-469, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (and B A)))))
================================================================
tm-name          tm-31678
in-theory        31678
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (D -> (D or E))) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31678.        (((A and B) or B) -> ((C -> (D -> (D or E))) and B)), M:tm-47, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-31679
in-theory        31679
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (D -> (D or E))) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31679.        (((A and B) or A) -> ((C -> (D -> (D or E))) and A)), M:tm-46, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-31680
in-theory        31680
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (E or F))) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-469 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31680.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (E or F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-469, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-31681
in-theory        31681
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (D -> (D or E))) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-469 ((Am (-> A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31681.        ((A or (B -> A)) -> ((C -> (D -> (D or E))) and (B -> A))), M:tm-44, m:tm-469, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A B))))
================================================================
tm-name          tm-31682
in-theory        31682
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (E -> (E or F))) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31682.        ((A -> (B or A)) and (C -> ((D -> (E -> (E or F))) and C))), M:tm-42, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31683
in-theory        31683
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (E -> (E or F))) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31683.        ((A -> (A or B)) and (C -> ((D -> (E -> (E or F))) and C))), M:tm-32, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31684
in-theory        31684
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (C -> (C or D))) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31684.        (A -> (A and ((B -> (C -> (C or D))) and A))), M:tm-24, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-31685
in-theory        31685
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (E or F))) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31685.        ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (E or F))) and C))), M:tm-23, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31686
in-theory        31686
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (E -> (E or F))) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31686.        (((A and B) -> B) and (C -> ((D -> (E -> (E or F))) and C))), M:tm-22, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31687
in-theory        31687
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (E -> (E or F))) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31687.        (((A and B) -> A) and (C -> ((D -> (E -> (E or F))) and C))), M:tm-21, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31688
in-theory        31688
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31688.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-20, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31689
in-theory        31689
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (E -> (E or F))) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31689.        ((A -> (B -> A)) and (C -> ((D -> (E -> (E or F))) and C))), M:tm-19, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31690
in-theory        31690
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> (C or D))) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-9 tm-5 tm-1 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31690.        ((A -> (not ((B -> (C -> (C or D))) and A))) -> (not A)), M:tm-9, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-31691
in-theory        31691
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (B or C))) and D) -> E) -> ((D or ((A -> (B -> (B or C))) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31691.        ((((A -> (B -> (B or C))) and D) -> E) -> ((D or ((A -> (B -> (B or C))) and D)) -> E)), M:tm-8, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-31692
in-theory        31692
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (D -> (D or E))) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-7 tm-5 tm-1 tm-6)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31692.        (A or (B -> ((C -> (D -> (D or E))) and B))), M:tm-7, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31693
in-theory        31693
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-6 tm-5 tm-1)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31693.        ((A -> ((B -> (C -> (C or D))) and A)) or E), M:tm-6, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31694
in-theory        31694
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D -> (D or E))) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31694.        (A -> ((B -> ((C -> (D -> (D or E))) and B)) and A)), M:tm-5, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31695
in-theory        31695
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> (D or E))) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-1 tm-5 tm-6)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31695.        (A -> (B -> ((C -> (D -> (D or E))) and B))), M:tm-1, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-31696
in-theory        31696
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or A) or C))
theorem-size     7
proof            (modus-ponens tm-470 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-7.            (A -> (B or A)), axiom
tm-31696.        (A -> ((B or A) or C)), M:tm-470, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-31697
in-theory        31697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((B -> C) -> ((A or B) -> C)) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-31697.        ((A -> B) -> (((B -> C) -> ((A or B) -> C)) or D)), M:tm-470, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-31698
in-theory        31698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((A -> (not B)) -> (not A)) or C))
theorem-size     13
proof            (modus-ponens tm-470 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-31698.        ((A -> B) -> (((A -> (not B)) -> (not A)) or C)), M:tm-470, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-31699
in-theory        31699
times-derived    1
----------------------------------------------------------------
theorem          ((not (not A)) -> (A or B))
theorem-size     7
proof            (modus-ponens tm-470 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-2 tm-1 tm-6 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-31699.        ((not (not A)) -> (A or B)), M:tm-470, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-31700
in-theory        31700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> A) or C))
theorem-size     9
proof            (modus-ponens tm-470 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-31700.        ((A -> B) -> ((A -> A) or C)), M:tm-470, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-31701
in-theory        31701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> C)) or D))
theorem-size     21
proof            (modus-ponens tm-470 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-31701.        (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> C)) or D)), M:tm-470, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-31702
in-theory        31702
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> B) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-31702.        ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> B) or D)), M:tm-470, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-31703
in-theory        31703
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> C) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-31703.        (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> C) or D)), M:tm-470, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-31704
in-theory        31704
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and A) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31704.        (A -> (((B -> (C -> B)) and A) or D)), M:tm-470, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-31705
in-theory        31705
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31705.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) or E)), M:tm-470, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-31706
in-theory        31706
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and A) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31706.        (A -> ((((B and C) -> B) and A) or D)), M:tm-470, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-31707
in-theory        31707
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and A) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31707.        (A -> ((((B and C) -> C) and A) or D)), M:tm-470, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-31708
in-theory        31708
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and A) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31708.        (A -> (((B -> (C -> (B and C))) and A) or D)), M:tm-470, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-31709
in-theory        31709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> (A and B)) or C))
theorem-size     11
proof            (modus-ponens tm-470 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-31709.        ((A -> B) -> ((A -> (A and B)) or C)), M:tm-470, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-31710
in-theory        31710
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and A) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31710.        (A -> (((B -> (B or C)) and A) or D)), M:tm-470, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-31711
in-theory        31711
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and A) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31711.        (A -> (((B -> (C or B)) and A) or D)), M:tm-470, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-31712
in-theory        31712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (((B or (A -> B)) -> C) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-31712.        (((A -> B) -> C) -> (((B or (A -> B)) -> C) or D)), M:tm-470, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-31713
in-theory        31713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) or E))
theorem-size     27
proof            (modus-ponens tm-470 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-31713.        ((((A -> B) -> (A -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) or E)), M:tm-470, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-31714
in-theory        31714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((A and C) or A) -> B) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-31714.        ((A -> B) -> ((((A and C) or A) -> B) or D)), M:tm-470, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-31715
in-theory        31715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C and A) or A) -> B) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-31715.        ((A -> B) -> ((((C and A) or A) -> B) or D)), M:tm-470, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-31716
in-theory        31716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> (((B or (A -> (B and A))) -> C) or D))
theorem-size     19
proof            (modus-ponens tm-470 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-31716.        (((A -> (B and A)) -> C) -> (((B or (A -> (B and A))) -> C) or D)), M:tm-470, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-31717
in-theory        31717
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (((A or (A or B)) -> C) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-31717.        (((A or B) -> C) -> (((A or (A or B)) -> C) or D)), M:tm-470, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-31718
in-theory        31718
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (((B or (A or B)) -> C) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-31718.        (((A or B) -> C) -> (((B or (A or B)) -> C) or D)), M:tm-470, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-31719
in-theory        31719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) or E))
theorem-size     29
proof            (modus-ponens tm-470 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-31719.        ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D) or E)), M:tm-470, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-31720
in-theory        31720
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-8)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-31720.        (A -> ((((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A) or E)), M:tm-470, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-31721
in-theory        31721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (B -> C)) -> (((A -> B) -> ((A or B) -> C)) or D))
theorem-size     19
proof            (modus-ponens tm-470 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-31721.        (((A -> B) -> (B -> C)) -> (((A -> B) -> ((A or B) -> C)) or D)), M:tm-470, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-31722
in-theory        31722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> A))) -> ((not A) or C))
theorem-size     11
proof            (modus-ponens tm-470 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-31722.        ((A -> (not (B -> A))) -> ((not A) or C)), M:tm-470, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-31723
in-theory        31723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> ((not (A -> (B -> C))) or D))
theorem-size     23
proof            (modus-ponens tm-470 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-31723.        (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> ((not (A -> (B -> C))) or D)), M:tm-470, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-31724
in-theory        31724
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not A)) -> ((not (A and B)) or C))
theorem-size     13
proof            (modus-ponens tm-470 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-31724.        (((A and B) -> (not A)) -> ((not (A and B)) or C)), M:tm-470, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-31725
in-theory        31725
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not B)) -> ((not (A and B)) or C))
theorem-size     13
proof            (modus-ponens tm-470 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-31725.        (((A and B) -> (not B)) -> ((not (A and B)) or C)), M:tm-470, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-31726
in-theory        31726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (A and B)))) -> ((not A) or C))
theorem-size     13
proof            (modus-ponens tm-470 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-31726.        ((A -> (not (B -> (A and B)))) -> ((not A) or C)), M:tm-470, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-31727
in-theory        31727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A or B))) -> ((not A) or C))
theorem-size     11
proof            (modus-ponens tm-470 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-31727.        ((A -> (not (A or B))) -> ((not A) or C)), M:tm-470, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-31728
in-theory        31728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B or A))) -> ((not A) or C))
theorem-size     11
proof            (modus-ponens tm-470 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-31728.        ((A -> (not (B or A))) -> ((not A) or C)), M:tm-470, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-31729
in-theory        31729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> ((not (A -> B)) or D))
theorem-size     21
proof            (modus-ponens tm-470 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-31729.        (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> ((not (A -> B)) or D)), M:tm-470, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-31730
in-theory        31730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> ((not (A -> B)) or C))
theorem-size     19
proof            (modus-ponens tm-470 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-31730.        (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> ((not (A -> B)) or C)), M:tm-470, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-31731
in-theory        31731
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> C) -> ((((A -> B) or ((A -> (not B)) -> (not A))) -> C) or D))
theorem-size     25
proof            (modus-ponens tm-470 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-9)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-31731.        ((((A -> (not B)) -> (not A)) -> C) -> ((((A -> B) or ((A -> (not B)) -> (not A))) -> C) or D)), M:tm-470, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-31732
in-theory        31732
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((B -> (not C)) -> (not B))) and A) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-9)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-31732.        (A -> ((((B -> C) -> ((B -> (not C)) -> (not B))) and A) or D)), M:tm-470, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-31733
in-theory        31733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (not B))) -> (((A -> B) -> (not A)) or C))
theorem-size     17
proof            (modus-ponens tm-470 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-31733.        (((A -> B) -> (A -> (not B))) -> (((A -> B) -> (not A)) or C)), M:tm-470, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-31734
in-theory        31734
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not A)) -> ((not (not (not A))) or B))
theorem-size     13
proof            (modus-ponens tm-470 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-10)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-31734.        (((not (not A)) -> (not A)) -> ((not (not (not A))) or B)), M:tm-470, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-31735
in-theory        31735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((not (not A)) or A) -> B) or C))
theorem-size     13
proof            (modus-ponens tm-470 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-31735.        ((A -> B) -> ((((not (not A)) or A) -> B) or C)), M:tm-470, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-31736
in-theory        31736
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((not (not B)) -> B) and A) or C))
theorem-size     11
proof            (modus-ponens tm-470 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-10)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-31736.        (A -> ((((not (not B)) -> B) and A) or C)), M:tm-470, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-31737
in-theory        31737
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) -> A) -> (((not (not (A -> B))) -> B) or C))
theorem-size     17
proof            (modus-ponens tm-470 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-31737.        (((not (not (A -> B))) -> A) -> (((not (not (A -> B))) -> B) or C)), M:tm-470, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-31738
in-theory        31738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> B)))) -> ((not A) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-31738.        ((A -> (not (B -> (C -> B)))) -> ((not A) or D)), M:tm-470, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-31739
in-theory        31739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> (((D or (A -> (B -> A))) -> C) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-31739.        (((A -> (B -> A)) -> C) -> (((D or (A -> (B -> A))) -> C) or E)), M:tm-470, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-31740
in-theory        31740
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (D -> C))) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-31740.        (A -> (((B -> (C -> (D -> C))) and A) or E)), M:tm-470, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-31741
in-theory        31741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> (C -> B)) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-31741.        ((A -> B) -> ((A -> (C -> B)) or D)), M:tm-470, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-31742
in-theory        31742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((A -> (B -> C)) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-31742.        ((A -> (B -> C)) -> ((A -> (B -> C)) or D)), M:tm-470, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-31743
in-theory        31743
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> ((A and B) or C))
theorem-size     9
proof            (modus-ponens tm-470 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-3)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-31743.        ((A and B) -> ((A and B) or C)), M:tm-470, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-31744
in-theory        31744
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) or C))
theorem-size     9
proof            (modus-ponens tm-470 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-31744.        ((A -> B) -> ((A -> B) or C)), M:tm-470, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-31745
in-theory        31745
times-derived    1
----------------------------------------------------------------
theorem          ((not (not A)) -> ((not (not A)) or B))
theorem-size     9
proof            (modus-ponens tm-470 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-31745.        ((not (not A)) -> ((not (not A)) or B)), M:tm-470, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-31746
in-theory        31746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> A))) -> ((not (A -> B)) or C))
theorem-size     15
proof            (modus-ponens tm-470 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-31746.        (((A -> B) -> (not (A -> A))) -> ((not (A -> B)) or C)), M:tm-470, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-31747
in-theory        31747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> B) -> ((((A -> C) or (A -> A)) -> B) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-31747.        (((A -> A) -> B) -> ((((A -> C) or (A -> A)) -> B) or D)), M:tm-470, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-31748
in-theory        31748
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (B -> B)) and A) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-31748.        (A -> ((((B -> C) -> (B -> B)) and A) or D)), M:tm-470, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-31749
in-theory        31749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> (((A -> B) -> A) or C))
theorem-size     13
proof            (modus-ponens tm-470 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-31749.        (((A -> B) -> A) -> (((A -> B) -> A) or C)), M:tm-470, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-31750
in-theory        31750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> A) -> C)) -> ((A -> C) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-31750.        ((A -> ((B -> A) -> C)) -> ((A -> C) or D)), M:tm-470, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-31751
in-theory        31751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A -> B)) -> ((A -> B) or C))
theorem-size     11
proof            (modus-ponens tm-470 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-31751.        ((A -> (A -> B)) -> ((A -> B) or C)), M:tm-470, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-31752
in-theory        31752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) or D))
theorem-size     21
proof            (modus-ponens tm-470 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-31752.        (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) or D)), M:tm-470, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-31753
in-theory        31753
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> ((not ((A -> (B -> C)) -> (A -> B))) or D))
theorem-size     33
proof            (modus-ponens tm-470 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-31753.        ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> ((not ((A -> (B -> C)) -> (A -> B))) or D)), M:tm-470, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-31754
in-theory        31754
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> D) -> (((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D) or E))
theorem-size     35
proof            (modus-ponens tm-470 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-31754.        ((((A -> (B -> C)) -> (A -> C)) -> D) -> (((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D) or E)), M:tm-470, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-31755
in-theory        31755
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A) or E))
theorem-size     25
proof            (modus-ponens tm-470 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-31755.        (A -> (((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A) or E)), M:tm-470, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-31756
in-theory        31756
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> ((((A -> (B -> C)) -> (A -> B)) -> (A -> C)) or D))
theorem-size     31
proof            (modus-ponens tm-470 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-31756.        ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> ((((A -> (B -> C)) -> (A -> B)) -> (A -> C)) or D)), M:tm-470, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-31757
in-theory        31757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) -> D) or E))
theorem-size     25
proof            (modus-ponens tm-470 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-31757.        (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) -> D) or E)), M:tm-470, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-31758
in-theory        31758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> ((not A) or E))
theorem-size     21
proof            (modus-ponens tm-470 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-31758.        ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> ((not A) or E)), M:tm-470, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-31759
in-theory        31759
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D) or F))
theorem-size     35
proof            (modus-ponens tm-470 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-31759.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D) or F)), M:tm-470, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-31760
in-theory        31760
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A) or F))
theorem-size     21
proof            (modus-ponens tm-470 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-31760.        (A -> (((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A) or F)), M:tm-470, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-31761
in-theory        31761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> D))) -> ((A -> ((B -> C) -> (B -> D))) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-31761.        ((A -> (B -> (C -> D))) -> ((A -> ((B -> C) -> (B -> D))) or E)), M:tm-470, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-31762
in-theory        31762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and A) -> (B or C))
theorem-size     9
proof            (modus-ponens tm-470 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-2 tm-1 tm-6 tm-3 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-31762.        (((A -> B) and A) -> (B or C)), M:tm-470, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-31763
in-theory        31763
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) and D) -> (C or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-6 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-31763.        ((((A -> (B -> A)) -> C) and D) -> (C or E)), M:tm-470, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-31764
in-theory        31764
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (D or F))
theorem-size     21
proof            (modus-ponens tm-470 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-2 tm-1 tm-6 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-31764.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (D or F)), M:tm-470, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-31765
in-theory        31765
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> A) and C) -> (A -> B)) -> (((((A -> B) -> A) and C) -> B) or D))
theorem-size     23
proof            (modus-ponens tm-470 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-31765.        (((((A -> B) -> A) and C) -> (A -> B)) -> (((((A -> B) -> A) and C) -> B) or D)), M:tm-470, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-31766
in-theory        31766
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-31766.        ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) or D)), M:tm-470, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-31767
in-theory        31767
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> ((not (((A -> B) and C) -> A)) or D))
theorem-size     27
proof            (modus-ponens tm-470 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-31767.        (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> ((not (((A -> B) and C) -> A)) or D)), M:tm-470, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-31768
in-theory        31768
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> D) -> ((((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D) or E))
theorem-size     29
proof            (modus-ponens tm-470 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-31768.        (((((A -> B) and C) -> B) -> D) -> ((((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D) or E)), M:tm-470, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-31769
in-theory        31769
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A) or E))
theorem-size     21
proof            (modus-ponens tm-470 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-31769.        (A -> ((((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A) or E)), M:tm-470, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-31770
in-theory        31770
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (((((A -> B) and C) -> A) -> B) or D))
theorem-size     25
proof            (modus-ponens tm-470 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-31770.        (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (((((A -> B) and C) -> A) -> B) or D)), M:tm-470, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-31771
in-theory        31771
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) and D) -> (C or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-6 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-31771.        (((((A and B) -> A) -> C) and D) -> (C or E)), M:tm-470, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-31772
in-theory        31772
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A -> C)) -> (((A and B) -> C) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-31772.        (((A and B) -> (A -> C)) -> (((A and B) -> C) or D)), M:tm-470, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-31773
in-theory        31773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B and C) -> B))) -> ((not A) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-31773.        ((A -> (not ((B and C) -> B))) -> ((not A) or D)), M:tm-470, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-31774
in-theory        31774
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> (((D or ((A and B) -> A)) -> C) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-31774.        ((((A and B) -> A) -> C) -> (((D or ((A and B) -> A)) -> C) or E)), M:tm-470, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-31775
in-theory        31775
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> ((C and D) -> C)) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-31775.        (A -> (((B -> ((C and D) -> C)) and A) or E)), M:tm-470, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-31776
in-theory        31776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> ((A -> B) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-31776.        ((A -> (B and C)) -> ((A -> B) or D)), M:tm-470, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-31777
in-theory        31777
times-derived    1
----------------------------------------------------------------
theorem          ((A and (A -> B)) -> (B or C))
theorem-size     9
proof            (modus-ponens tm-470 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-6 tm-4 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-31777.        ((A and (A -> B)) -> (B or C)), M:tm-470, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-31778
in-theory        31778
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> D)) -> (D or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-6 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-31778.        ((A and ((B -> (C -> B)) -> D)) -> (D or E)), M:tm-470, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-31779
in-theory        31779
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (E or F))
theorem-size     21
proof            (modus-ponens tm-470 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-2 tm-1 tm-6 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-31779.        ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (E or F)), M:tm-470, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-31780
in-theory        31780
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> D)) -> (D or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-6 tm-4 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-31780.        ((A and (((B and C) -> B) -> D)) -> (D or E)), M:tm-470, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-31781
in-theory        31781
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> B)) -> (B -> C)) -> (((A and ((B -> C) -> B)) -> C) or D))
theorem-size     23
proof            (modus-ponens tm-470 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-31781.        (((A and ((B -> C) -> B)) -> (B -> C)) -> (((A and ((B -> C) -> B)) -> C) or D)), M:tm-470, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-31782
in-theory        31782
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-31782.        (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) or D)), M:tm-470, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-31783
in-theory        31783
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> ((not ((A and (B -> C)) -> B)) or D))
theorem-size     27
proof            (modus-ponens tm-470 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-31783.        ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> ((not ((A and (B -> C)) -> B)) or D)), M:tm-470, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-31784
in-theory        31784
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> D) -> (((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D) or E))
theorem-size     29
proof            (modus-ponens tm-470 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-31784.        ((((A and (B -> C)) -> C) -> D) -> (((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D) or E)), M:tm-470, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-31785
in-theory        31785
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A) or E))
theorem-size     21
proof            (modus-ponens tm-470 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-31785.        (A -> (((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A) or E)), M:tm-470, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-31786
in-theory        31786
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> ((((A and (B -> C)) -> B) -> C) or D))
theorem-size     25
proof            (modus-ponens tm-470 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-31786.        ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> ((((A and (B -> C)) -> B) -> C) or D)), M:tm-470, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-31787
in-theory        31787
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> D)) -> (D or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-6 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-31787.        ((A and (((B and C) -> C) -> D)) -> (D or E)), M:tm-470, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-31788
in-theory        31788
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) and D) -> (C or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-6 tm-3 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-31788.        (((((A and B) -> B) -> C) and D) -> (C or E)), M:tm-470, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-31789
in-theory        31789
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (B -> C)) -> (((A and B) -> C) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-31789.        (((A and B) -> (B -> C)) -> (((A and B) -> C) or D)), M:tm-470, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-31790
in-theory        31790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B and C) -> C))) -> ((not A) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-31790.        ((A -> (not ((B and C) -> C))) -> ((not A) or D)), M:tm-470, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-31791
in-theory        31791
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> (((D or ((A and B) -> B)) -> C) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-31791.        ((((A and B) -> B) -> C) -> (((D or ((A and B) -> B)) -> C) or E)), M:tm-470, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-31792
in-theory        31792
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> ((C and D) -> D)) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-4)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-31792.        (A -> (((B -> ((C and D) -> D)) and A) or E)), M:tm-470, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-31793
in-theory        31793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> ((A -> C) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-31793.        ((A -> (B and C)) -> ((A -> C) or D)), M:tm-470, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-31794
in-theory        31794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> B)) and A))) -> ((not A) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-31794.        ((A -> (not ((B -> (C -> B)) and A))) -> ((not A) or D)), M:tm-470, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-31795
in-theory        31795
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and C) -> D) -> (((C or ((A -> (B -> A)) and C)) -> D) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-31795.        ((((A -> (B -> A)) and C) -> D) -> (((C or ((A -> (B -> A)) and C)) -> D) or E)), M:tm-470, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-31796
in-theory        31796
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> ((C -> (D -> C)) and B)) and A) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-31796.        (A -> (((B -> ((C -> (D -> C)) and B)) and A) or E)), M:tm-470, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-31797
in-theory        31797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> ((not A) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-5)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-31797.        ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> ((not A) or E)), M:tm-470, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-31798
in-theory        31798
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E) or F))
theorem-size     39
proof            (modus-ponens tm-470 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-31798.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E) or F)), M:tm-470, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-31799
in-theory        31799
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A) or F))
theorem-size     23
proof            (modus-ponens tm-470 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-31799.        (A -> (((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A) or F)), M:tm-470, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-31800
in-theory        31800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> B) and A))) -> ((not A) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-5 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-31800.        ((A -> (not (((B and C) -> B) and A))) -> ((not A) or D)), M:tm-470, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-31801
in-theory        31801
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and C) -> D) -> (((C or (((A and B) -> A) and C)) -> D) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-31801.        (((((A and B) -> A) and C) -> D) -> (((C or (((A and B) -> A) and C)) -> D) or E)), M:tm-470, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-31802
in-theory        31802
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (((C and D) -> C) and B)) and A) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-31802.        (A -> (((B -> (((C and D) -> C) and B)) and A) or E)), M:tm-470, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-31803
in-theory        31803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> C) and A))) -> ((not A) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-5 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-31803.        ((A -> (not (((B and C) -> C) and A))) -> ((not A) or D)), M:tm-470, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-31804
in-theory        31804
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and C) -> D) -> (((C or (((A and B) -> B) and C)) -> D) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-31804.        (((((A and B) -> B) and C) -> D) -> (((C or (((A and B) -> B) and C)) -> D) or E)), M:tm-470, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-31805
in-theory        31805
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (((C and D) -> D) and B)) and A) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-31805.        (A -> (((B -> (((C and D) -> D) and B)) and A) or E)), M:tm-470, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-31806
in-theory        31806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> (B and C))) and A))) -> ((not A) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-31806.        ((A -> (not ((B -> (C -> (B and C))) and A))) -> ((not A) or D)), M:tm-470, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-31807
in-theory        31807
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and C) -> D) -> (((C or ((A -> (B -> (A and B))) and C)) -> D) or E))
theorem-size     27
proof            (modus-ponens tm-470 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-31807.        ((((A -> (B -> (A and B))) and C) -> D) -> (((C or ((A -> (B -> (A and B))) and C)) -> D) or E)), M:tm-470, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-31808
in-theory        31808
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> ((C -> (D -> (C and D))) and B)) and A) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-31808.        (A -> (((B -> ((C -> (D -> (C and D))) and B)) and A) or E)), M:tm-470, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-31809
in-theory        31809
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and (B -> A)) or C))
theorem-size     9
proof            (modus-ponens tm-470 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-31809.        (A -> ((A and (B -> A)) or C)), M:tm-470, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-31810
in-theory        31810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (((A -> (B -> C)) and ((A -> B) -> (A -> C))) or D))
theorem-size     21
proof            (modus-ponens tm-470 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-31810.        ((A -> (B -> C)) -> (((A -> (B -> C)) and ((A -> B) -> (A -> C))) or D)), M:tm-470, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-31811
in-theory        31811
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (((A and B) and A) or C))
theorem-size     11
proof            (modus-ponens tm-470 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-31811.        ((A and B) -> (((A and B) and A) or C)), M:tm-470, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-31812
in-theory        31812
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (((A and B) and B) or C))
theorem-size     11
proof            (modus-ponens tm-470 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-31812.        ((A and B) -> (((A and B) and B) or C)), M:tm-470, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-31813
in-theory        31813
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and (B -> (A and B))) or C))
theorem-size     11
proof            (modus-ponens tm-470 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-31813.        (A -> ((A and (B -> (A and B))) or C)), M:tm-470, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-31814
in-theory        31814
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and (A or B)) or C))
theorem-size     9
proof            (modus-ponens tm-470 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-31814.        (A -> ((A and (A or B)) or C)), M:tm-470, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-31815
in-theory        31815
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and (B or A)) or C))
theorem-size     9
proof            (modus-ponens tm-470 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-31815.        (A -> ((A and (B or A)) or C)), M:tm-470, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-31816
in-theory        31816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((A -> B) and ((B -> C) -> ((A or B) -> C))) or D))
theorem-size     19
proof            (modus-ponens tm-470 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-31816.        ((A -> B) -> (((A -> B) and ((B -> C) -> ((A or B) -> C))) or D)), M:tm-470, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-31817
in-theory        31817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((A -> B) and ((A -> (not B)) -> (not A))) or C))
theorem-size     17
proof            (modus-ponens tm-470 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-31817.        ((A -> B) -> (((A -> B) and ((A -> (not B)) -> (not A))) or C)), M:tm-470, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-31818
in-theory        31818
times-derived    1
----------------------------------------------------------------
theorem          ((not (not A)) -> (((not (not A)) and A) or B))
theorem-size     11
proof            (modus-ponens tm-470 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-10)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-31818.        ((not (not A)) -> (((not (not A)) and A) or B)), M:tm-470, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-31819
in-theory        31819
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and (B -> (C -> B))) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-31819.        (A -> ((A and (B -> (C -> B))) or D)), M:tm-470, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-31820
in-theory        31820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((A -> B) and (A -> A)) or C))
theorem-size     13
proof            (modus-ponens tm-470 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-31820.        ((A -> B) -> (((A -> B) and (A -> A)) or C)), M:tm-470, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-31821
in-theory        31821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> ((((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))) or D))
theorem-size     31
proof            (modus-ponens tm-470 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-31821.        (((A -> (B -> C)) -> (A -> B)) -> ((((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))) or D)), M:tm-470, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-31822
in-theory        31822
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-31822.        (A -> ((A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)), M:tm-470, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-31823
in-theory        31823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> (((((A -> B) and C) -> A) and (((A -> B) and C) -> B)) or D))
theorem-size     25
proof            (modus-ponens tm-470 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-31823.        ((((A -> B) and C) -> A) -> (((((A -> B) and C) -> A) and (((A -> B) and C) -> B)) or D)), M:tm-470, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-31824
in-theory        31824
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and ((B and C) -> B)) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-3)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-31824.        (A -> ((A and ((B and C) -> B)) or D)), M:tm-470, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-31825
in-theory        31825
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> ((((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)) or D))
theorem-size     25
proof            (modus-ponens tm-470 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-31825.        (((A and (B -> C)) -> B) -> ((((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)) or D)), M:tm-470, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-31826
in-theory        31826
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and ((B and C) -> C)) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-4)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-31826.        (A -> ((A and ((B and C) -> C)) or D)), M:tm-470, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-31827
in-theory        31827
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and ((B -> (C -> B)) and A)) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-31827.        (A -> ((A and ((B -> (C -> B)) and A)) or D)), M:tm-470, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-31828
in-theory        31828
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E))
theorem-size     21
proof            (modus-ponens tm-470 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-31828.        (A -> ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E)), M:tm-470, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-31829
in-theory        31829
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and (((B and C) -> B) and A)) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-31829.        (A -> ((A and (((B and C) -> B) and A)) or D)), M:tm-470, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-31830
in-theory        31830
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and (((B and C) -> C) and A)) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-31830.        (A -> ((A and (((B and C) -> C) and A)) or D)), M:tm-470, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-31831
in-theory        31831
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and ((B -> (C -> (B and C))) and A)) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-31831.        (A -> ((A and ((B -> (C -> (B and C))) and A)) or D)), M:tm-470, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-31832
in-theory        31832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((A -> B) and (A -> (A and B))) or C))
theorem-size     15
proof            (modus-ponens tm-470 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-31832.        ((A -> B) -> (((A -> B) and (A -> (A and B))) or C)), M:tm-470, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-31833
in-theory        31833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (A and B)))) -> ((not (A -> B)) or C))
theorem-size     17
proof            (modus-ponens tm-470 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-31833.        (((A -> B) -> (not (A -> (A and B)))) -> ((not (A -> B)) or C)), M:tm-470, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-31834
in-theory        31834
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> C) -> ((((A -> B) or (A -> (A and B))) -> C) or D))
theorem-size     21
proof            (modus-ponens tm-470 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-31834.        (((A -> (A and B)) -> C) -> ((((A -> B) or (A -> (A and B))) -> C) or D)), M:tm-470, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-31835
in-theory        31835
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (B -> (B and C))) and A) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-31835.        (A -> ((((B -> C) -> (B -> (B and C))) and A) or D)), M:tm-470, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-31836
in-theory        31836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> (((A -> B) -> (A and B)) or C))
theorem-size     15
proof            (modus-ponens tm-470 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-31836.        (((A -> B) -> A) -> (((A -> B) -> (A and B)) or C)), M:tm-470, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-31837
in-theory        31837
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and (B -> (C -> (B and C)))) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-31837.        (A -> ((A and (B -> (C -> (B and C)))) or D)), M:tm-470, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-31838
in-theory        31838
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> D)) -> (D or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-6 tm-4 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-31838.        ((A and ((B -> (C -> (B and C))) -> D)) -> (D or E)), M:tm-470, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-31839
in-theory        31839
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) and D) -> (C or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-6 tm-3 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-31839.        ((((A -> (B -> (A and B))) -> C) and D) -> (C or E)), M:tm-470, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-31840
in-theory        31840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (A and B)) -> C)) -> ((A -> C) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-31840.        ((A -> ((B -> (A and B)) -> C)) -> ((A -> C) or D)), M:tm-470, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-31841
in-theory        31841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> (B and C))))) -> ((not A) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-31841.        ((A -> (not (B -> (C -> (B and C))))) -> ((not A) or D)), M:tm-470, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-31842
in-theory        31842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> (((D or (A -> (B -> (A and B)))) -> C) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-31842.        (((A -> (B -> (A and B))) -> C) -> (((D or (A -> (B -> (A and B)))) -> C) or E)), M:tm-470, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-31843
in-theory        31843
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (D -> (C and D)))) and A) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-31843.        (A -> (((B -> (C -> (D -> (C and D)))) and A) or E)), M:tm-470, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-31844
in-theory        31844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> (C -> (B and C))) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-31844.        ((A -> B) -> ((A -> (C -> (B and C))) or D)), M:tm-470, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-31845
in-theory        31845
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> B)) or D) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-31845.        (A -> ((((B -> (C -> B)) or D) and A) or E)), M:tm-470, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-31846
in-theory        31846
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A) or F))
theorem-size     21
proof            (modus-ponens tm-470 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-31846.        (A -> (((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A) or F)), M:tm-470, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-31847
in-theory        31847
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B and C) -> B) or D) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-31847.        (A -> (((((B and C) -> B) or D) and A) or E)), M:tm-470, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-31848
in-theory        31848
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B and C) -> C) or D) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-4)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-31848.        (A -> (((((B and C) -> C) or D) and A) or E)), M:tm-470, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-31849
in-theory        31849
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> (B and C))) or D) and A) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-31849.        (A -> ((((B -> (C -> (B and C))) or D) and A) or E)), M:tm-470, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-31850
in-theory        31850
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (B or C)) or D) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-31850.        (A -> ((((B -> (B or C)) or D) and A) or E)), M:tm-470, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-31851
in-theory        31851
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and ((B -> (B or C)) and A)) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-31851.        (A -> ((A and ((B -> (B or C)) and A)) or D)), M:tm-470, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-31852
in-theory        31852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (B or C)) and A))) -> ((not A) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-31852.        ((A -> (not ((B -> (B or C)) and A))) -> ((not A) or D)), M:tm-470, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-31853
in-theory        31853
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and C) -> D) -> (((C or ((A -> (A or B)) and C)) -> D) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-31853.        ((((A -> (A or B)) and C) -> D) -> (((C or ((A -> (A or B)) and C)) -> D) or E)), M:tm-470, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-31854
in-theory        31854
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> ((C -> (C or D)) and B)) and A) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-31854.        (A -> (((B -> ((C -> (C or D)) and B)) and A) or E)), M:tm-470, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-31855
in-theory        31855
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and (B -> (B or C))) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31855.        (A -> ((A and (B -> (B or C))) or D)), M:tm-470, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-31856
in-theory        31856
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> D)) -> (D or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-6 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-31856.        ((A and ((B -> (B or C)) -> D)) -> (D or E)), M:tm-470, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-31857
in-theory        31857
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) and D) -> (C or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-6 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-31857.        ((((A -> (A or B)) -> C) and D) -> (C or E)), M:tm-470, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-31858
in-theory        31858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((A or B) -> C)) -> ((A -> C) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-31858.        ((A -> ((A or B) -> C)) -> ((A -> C) or D)), M:tm-470, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-31859
in-theory        31859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (B or C)))) -> ((not A) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31859.        ((A -> (not (B -> (B or C)))) -> ((not A) or D)), M:tm-470, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-31860
in-theory        31860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> (((D or (A -> (A or B))) -> C) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-31860.        (((A -> (A or B)) -> C) -> (((D or (A -> (A or B))) -> C) or E)), M:tm-470, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-31861
in-theory        31861
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (C or D))) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31861.        (A -> (((B -> (C -> (C or D))) and A) or E)), M:tm-470, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-31862
in-theory        31862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> (B or C)) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31862.        ((A -> B) -> ((A -> (B or C)) or D)), M:tm-470, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-31863
in-theory        31863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-469 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31863.        ((A -> (B -> (B or C))) and ((D -> E) -> (D -> (E or F)))), M:tm-469, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31864
in-theory        31864
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (B -> ((B or C) or D)))
theorem-size     15
proof            (modus-ponens tm-466 tm-470 ((A Am) (Bm (or Am B)) (C (-> Am (or (or Am B) Cm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31864.        ((A or (B -> (B or C))) -> (B -> ((B or C) or D))), M:tm-466, m:tm-470, u:((A Am) (Bm (or Am B)) (C (-> Am (or (or Am B) Cm))))
================================================================
tm-name          tm-31865
in-theory        31865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31865.        (((A -> B) -> (A -> (B or C))) and (D -> (D or E))), M:tm-456, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31866
in-theory        31866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (D -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-453 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31866.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (D -> (E or F)))), M:tm-453, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31867
in-theory        31867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and ((D -> (D or E)) and ((A -> B) -> (A -> (B or C)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31867.        (((A -> B) -> (A -> (B or C))) and ((D -> (D or E)) and ((A -> B) -> (A -> (B or C))))), M:tm-443, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31868
in-theory        31868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-409 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31868.        (((A -> (A or B)) or C) and ((D -> E) -> (D -> (E or F)))), M:tm-409, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31869
in-theory        31869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> (D -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-400 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31869.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> (D -> (E or F)))), M:tm-400, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31870
in-theory        31870
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-391 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31870.        ((((A and B) -> B) or C) and ((D -> E) -> (D -> (E or F)))), M:tm-391, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31871
in-theory        31871
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-382 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31871.        ((((A and B) -> A) or C) and ((D -> E) -> (D -> (E or F)))), M:tm-382, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31872
in-theory        31872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (E -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-373 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31872.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (E -> (F or G)))), M:tm-373, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31873
in-theory        31873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-364 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31873.        (((A -> (B -> A)) or C) and ((D -> E) -> (D -> (E or F)))), M:tm-364, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31874
in-theory        31874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((A -> (B or D)) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31874.        ((A -> B) -> (C -> ((A -> (B or D)) and C))), M:tm-355, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-31875
in-theory        31875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-354 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31875.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (E or F)))), M:tm-354, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31876
in-theory        31876
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (B -> ((C -> (B and C)) or D)))
theorem-size     19
proof            (modus-ponens tm-351 tm-470 ((A Am) (Bm (-> B (and Am B))) (C (-> Am (or (-> B (and Am B)) Cm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31876.        ((A or (B -> (C -> (B and C)))) -> (B -> ((C -> (B and C)) or D))), M:tm-351, m:tm-470, u:((A Am) (Bm (-> B (and Am B))) (C (-> Am (or (-> B (and Am B)) Cm))))
================================================================
tm-name          tm-31877
in-theory        31877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31877.        (((A -> B) -> (A -> (B or C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31878
in-theory        31878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (C -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-338 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31878.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (C -> (D or E)))), M:tm-338, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31879
in-theory        31879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (A -> ((A and B) or C)))
theorem-size     17
proof            (modus-ponens tm-335 tm-470 ((A Am) (Bm (and Am B)) (C (-> Am (or (and Am B) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31879.        (((A -> B) or (A -> (A and B))) -> (A -> ((A and B) or C))), M:tm-335, m:tm-470, u:((A Am) (Bm (and Am B)) (C (-> Am (or (and Am B) Cm))))
================================================================
tm-name          tm-31880
in-theory        31880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and ((A -> B) -> ((A -> B) and (A -> (B or C)))))
theorem-size     23
proof            (modus-ponens tm-328 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31880.        (((A -> B) -> (A -> (B or C))) and ((A -> B) -> ((A -> B) and (A -> (B or C))))), M:tm-328, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-31881
in-theory        31881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> (B or C)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31881.        (((A -> B) -> (A -> (B or C))) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> (B or C))))), M:tm-327, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31882
in-theory        31882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (((D and E) -> E) and ((A -> B) -> (A -> (B or C)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31882.        (((A -> B) -> (A -> (B or C))) and (((D and E) -> E) and ((A -> B) -> (A -> (B or C))))), M:tm-326, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31883
in-theory        31883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (((D and E) -> D) and ((A -> B) -> (A -> (B or C)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31883.        (((A -> B) -> (A -> (B or C))) and (((D and E) -> D) and ((A -> B) -> (A -> (B or C))))), M:tm-325, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31884
in-theory        31884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> (B or C)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31884.        (((A -> B) -> (A -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> (B or C))))), M:tm-324, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31885
in-theory        31885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and ((D -> (E -> D)) and ((A -> B) -> (A -> (B or C)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31885.        (((A -> B) -> (A -> (B or C))) and ((D -> (E -> D)) and ((A -> B) -> (A -> (B or C))))), M:tm-323, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31886
in-theory        31886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31886.        (((A -> B) -> (A -> (B or C))) and ((D and E) -> E)), M:tm-322, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31887
in-theory        31887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31887.        (((A -> B) -> (A -> (B or C))) and ((D and E) -> D)), M:tm-320, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31888
in-theory        31888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31888.        (((A -> B) -> (A -> (B or C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31889
in-theory        31889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and ((A -> B) -> (A -> B)))
theorem-size     17
proof            (modus-ponens tm-316 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31889.        (((A -> B) -> (A -> (B or C))) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-31890
in-theory        31890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31890.        (((A -> B) -> (A -> (B or C))) and (D -> (E -> D))), M:tm-315, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31891
in-theory        31891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (((A -> B) -> (not (A -> (B or C)))) -> (not (A -> B))))
theorem-size     25
proof            (modus-ponens tm-313 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31891.        (((A -> B) -> (A -> (B or C))) and (((A -> B) -> (not (A -> (B or C)))) -> (not (A -> B)))), M:tm-313, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-31892
in-theory        31892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (((A -> (B or C)) -> D) -> (((A -> B) or (A -> (B or C))) -> D)))
theorem-size     29
proof            (modus-ponens tm-312 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31892.        (((A -> B) -> (A -> (B or C))) and (((A -> (B or C)) -> D) -> (((A -> B) or (A -> (B or C))) -> D))), M:tm-312, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-31893
in-theory        31893
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (D or ((A -> B) -> (A -> (B or C)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31893.        (((A -> B) -> (A -> (B or C))) and (D or ((A -> B) -> (A -> (B or C))))), M:tm-311, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31894
in-theory        31894
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (((A -> B) -> (A -> (B or C))) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31894.        (((A -> B) -> (A -> (B or C))) and (((A -> B) -> (A -> (B or C))) or D)), M:tm-310, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31895
in-theory        31895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (D -> (((A -> B) -> (A -> (B or C))) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31895.        (((A -> B) -> (A -> (B or C))) and (D -> (((A -> B) -> (A -> (B or C))) and D))), M:tm-309, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31896
in-theory        31896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (((A -> B) -> A) -> ((A -> B) -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-306 tm-470 ((A (-> Am Bm)) (B Am) (C (or Bm Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31896.        (((A -> B) -> (A -> (B or C))) and (((A -> B) -> A) -> ((A -> B) -> (B or C)))), M:tm-306, m:tm-470, u:((A (-> Am Bm)) (B Am) (C (or Bm Cm)))
================================================================
tm-name          tm-31897
in-theory        31897
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (D -> ((A -> B) -> (A -> (B or C)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31897.        (((A -> B) -> (A -> (B or C))) and (D -> ((A -> B) -> (A -> (B or C))))), M:tm-305, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31898
in-theory        31898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (D -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-303 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31898.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (D -> (E or F)))), M:tm-303, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31899
in-theory        31899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (D -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-270 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31899.        ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (D -> (E or F)))), M:tm-270, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31900
in-theory        31900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (D -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-239 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31900.        ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (D -> (E or F)))), M:tm-239, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31901
in-theory        31901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (E -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-210 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31901.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (E -> (F or G)))), M:tm-210, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31902
in-theory        31902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (D -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-183 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31902.        ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (D -> (E or F)))), M:tm-183, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31903
in-theory        31903
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-157 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31903.        ((A -> ((B and C) -> C)) and ((D -> E) -> (D -> (E or F)))), M:tm-157, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31904
in-theory        31904
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((B and C) -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-154 tm-470 ((Am (and A Bm)) (B Bm) (C (-> (and A Bm) (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31904.        ((A or ((B and C) -> C)) -> ((B and C) -> (C or D))), M:tm-154, m:tm-470, u:((Am (and A Bm)) (B Bm) (C (-> (and A Bm) (or Bm Cm))))
================================================================
tm-name          tm-31905
in-theory        31905
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (D -> (E or F))))
theorem-size     25
proof            (modus-ponens tm-147 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31905.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (D -> (E or F)))), M:tm-147, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31906
in-theory        31906
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> (C or D)))
theorem-size     25
proof            (modus-ponens tm-144 tm-470 ((Am (and A (-> B Bm))) (C Bm) (D (-> (and A (-> B Bm)) (or Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31906.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> (C or D))), M:tm-144, m:tm-470, u:((Am (and A (-> B Bm))) (C Bm) (D (-> (and A (-> B Bm)) (or Bm Cm))))
================================================================
tm-name          tm-31907
in-theory        31907
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-134 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31907.        ((A -> ((B and C) -> B)) and ((D -> E) -> (D -> (E or F)))), M:tm-134, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31908
in-theory        31908
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((B and C) -> (B or D)))
theorem-size     15
proof            (modus-ponens tm-131 tm-470 ((Am (and Bm B)) (A Bm) (C (-> (and Bm B) (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31908.        ((A or ((B and C) -> B)) -> ((B and C) -> (B or D))), M:tm-131, m:tm-470, u:((Am (and Bm B)) (A Bm) (C (-> (and Bm B) (or Bm Cm))))
================================================================
tm-name          tm-31909
in-theory        31909
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (D -> (E or F))))
theorem-size     25
proof            (modus-ponens tm-125 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31909.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (D -> (E or F)))), M:tm-125, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31910
in-theory        31910
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> (B or D)))
theorem-size     25
proof            (modus-ponens tm-122 tm-470 ((Am (and (-> A Bm) C)) (B Bm) (D (-> (and (-> A Bm) C) (or Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31910.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> (B or D))), M:tm-122, m:tm-470, u:((Am (and (-> A Bm) C)) (B Bm) (D (-> (and (-> A Bm) C) (or Bm Cm))))
================================================================
tm-name          tm-31911
in-theory        31911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-113 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31911.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (F or G)))), M:tm-113, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31912
in-theory        31912
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> (((B -> C) -> (B -> D)) or E)))
theorem-size     31
proof            (modus-ponens tm-110 tm-470 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> A (-> B C)) (or (-> (-> A B) (-> A C)) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31912.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> (((B -> C) -> (B -> D)) or E))), M:tm-110, m:tm-470, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> A (-> B C)) (or (-> (-> A B) (-> A C)) Cm))))
================================================================
tm-name          tm-31913
in-theory        31913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (D -> (E or F))))
theorem-size     29
proof            (modus-ponens tm-105 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31913.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (D -> (E or F)))), M:tm-105, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31914
in-theory        31914
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> ((A -> C) or D)))
theorem-size     31
proof            (modus-ponens tm-102 tm-470 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> A (-> B C)) (or (-> A C) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31914.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> ((A -> C) or D))), M:tm-102, m:tm-470, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> A (-> B C)) (or (-> A C) Cm))))
================================================================
tm-name          tm-31915
in-theory        31915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> (C -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-95 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31915.        (((A -> B) -> (A -> A)) and ((C -> D) -> (C -> (D or E)))), M:tm-95, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31916
in-theory        31916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (A -> (A or C)))
theorem-size     13
proof            (modus-ponens tm-92 tm-470 ((Bm Am) (A Am) (B (-> Am (or Am Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31916.        (((A -> B) or (A -> A)) -> (A -> (A or C))), M:tm-92, m:tm-470, u:((Bm Am) (A Am) (B (-> Am (or Am Cm))))
================================================================
tm-name          tm-31917
in-theory        31917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (A -> (B or D))))
theorem-size     11
proof            (modus-ponens tm-84 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31917.        ((A -> B) -> (C -> (A -> (B or D)))), M:tm-84, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-31918
in-theory        31918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-83 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31918.        ((A -> (B -> (C -> B))) and ((D -> E) -> (D -> (E or F)))), M:tm-83, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31919
in-theory        31919
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (B -> ((C -> B) or D)))
theorem-size     15
proof            (modus-ponens tm-80 tm-470 ((A Am) (Bm (-> B Am)) (C (-> Am (or (-> B Am) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31919.        ((A or (B -> (C -> B))) -> (B -> ((C -> B) or D))), M:tm-80, m:tm-470, u:((A Am) (Bm (-> B Am)) (C (-> Am (or (-> B Am) Cm))))
================================================================
tm-name          tm-31920
in-theory        31920
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> (B -> (C or D))))
theorem-size     15
proof            (modus-ponens tm-76 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31920.        (((not (not A)) -> A) and ((B -> C) -> (B -> (C or D)))), M:tm-76, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31921
in-theory        31921
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> (A -> (B or C)))
theorem-size     15
proof            (modus-ponens tm-73 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31921.        (((not (not (A -> B))) or (A -> B)) -> (A -> (B or C))), M:tm-73, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-31922
in-theory        31922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (C -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-69 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31922.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (C -> (D or E)))), M:tm-69, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31923
in-theory        31923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> ((not A) or C)))
theorem-size     21
proof            (modus-ponens tm-66 tm-470 ((Am (-> A (not B))) (Bm (not A)) (C (-> (-> A (not B)) (or (not A) Cm)))))
axioms-used      (tm-8 tm-9 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31923.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> ((not A) or C))), M:tm-66, m:tm-470, u:((Am (-> A (not B))) (Bm (not A)) (C (-> (-> A (not B)) (or (not A) Cm))))
================================================================
tm-name          tm-31924
in-theory        31924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) -> ((A or A) -> (A or B)))
theorem-size     11
proof            (modus-ponens tm-55 tm-470 ((A Bm) (Am Bm) (B Bm) (C (or Bm Cm))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31924.        ((A -> A) -> ((A or A) -> (A or B))), M:tm-55, m:tm-470, u:((A Bm) (Am Bm) (B Bm) (C (or Bm Cm)))
================================================================
tm-name          tm-31925
in-theory        31925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-54 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31925.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (E or F)))), M:tm-54, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31926
in-theory        31926
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (((A or B) -> C) or D)))
theorem-size     25
proof            (modus-ponens tm-51 tm-470 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (or (-> (or C A) B) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31926.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (((A or B) -> C) or D))), M:tm-51, m:tm-470, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (or (-> (or C A) B) Cm))))
================================================================
tm-name          tm-31927
in-theory        31927
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (B -> ((A and B) or C)))
theorem-size     15
proof            (modus-ponens tm-48 tm-470 ((A Am) (Bm (and B Am)) (C (-> Am (or (and B Am) Cm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31927.        ((A or (B -> (A and B))) -> (B -> ((A and B) or C))), M:tm-48, m:tm-470, u:((A Am) (Bm (and B Am)) (C (-> Am (or (and B Am) Cm))))
================================================================
tm-name          tm-31928
in-theory        31928
times-derived    2
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (B -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-47 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31928.        (((A and (B -> C)) or (B -> C)) -> (B -> (C or D))), M:tm-47, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-31929
in-theory        31929
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (A -> (B or D)))
theorem-size     15
proof            (modus-ponens tm-46 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31929.        ((((A -> B) and C) or (A -> B)) -> (A -> (B or D))), M:tm-46, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-31930
in-theory        31930
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> C) or D)))
theorem-size     23
proof            (modus-ponens tm-45 tm-470 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (or (-> A C) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31930.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> C) or D))), M:tm-45, m:tm-470, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (or (-> A C) Cm))))
================================================================
tm-name          tm-31931
in-theory        31931
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (B -> (A or C)))
theorem-size     11
proof            (modus-ponens tm-44 tm-470 ((A Am) (B Bm) (C (-> Am (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31931.        ((A or (B -> A)) -> (B -> (A or C))), M:tm-44, m:tm-470, u:((A Am) (B Bm) (C (-> Am (or Bm Cm))))
================================================================
tm-name          tm-31932
in-theory        31932
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (C -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-42 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31932.        ((A -> (B or A)) and ((C -> D) -> (C -> (D or E)))), M:tm-42, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31933
in-theory        31933
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (C -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-32 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31933.        ((A -> (A or B)) and ((C -> D) -> (C -> (D or E)))), M:tm-32, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31934
in-theory        31934
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (A -> (B or C))))
theorem-size     13
proof            (modus-ponens tm-24 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31934.        ((A -> B) -> ((A -> B) and (A -> (B or C)))), M:tm-24, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-31935
in-theory        31935
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-23 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31935.        ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (D or E)))), M:tm-23, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31936
in-theory        31936
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (C -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-22 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31936.        (((A and B) -> B) and ((C -> D) -> (C -> (D or E)))), M:tm-22, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31937
in-theory        31937
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (C -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-21 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31937.        (((A and B) -> A) and ((C -> D) -> (C -> (D or E)))), M:tm-21, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31938
in-theory        31938
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-20 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31938.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (E or F)))), M:tm-20, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31939
in-theory        31939
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (C -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-19 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31939.        ((A -> (B -> A)) and ((C -> D) -> (C -> (D or E)))), M:tm-19, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31940
in-theory        31940
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (B or C)))) -> (not (A -> B)))
theorem-size     15
proof            (modus-ponens tm-9 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-9 tm-2 tm-1 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31940.        (((A -> B) -> (not (A -> (B or C)))) -> (not (A -> B))), M:tm-9, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-31941
in-theory        31941
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or C)) -> D) -> (((A -> B) or (A -> (B or C))) -> D))
theorem-size     19
proof            (modus-ponens tm-8 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31941.        (((A -> (B or C)) -> D) -> (((A -> B) or (A -> (B or C))) -> D)), M:tm-8, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-31942
in-theory        31942
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (B -> (C or D))))
theorem-size     11
proof            (modus-ponens tm-7 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-7 tm-2 tm-1 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31942.        (A or ((B -> C) -> (B -> (C or D)))), M:tm-7, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31943
in-theory        31943
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-6 tm-2 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31943.        (((A -> B) -> (A -> (B or C))) or D), M:tm-6, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31944
in-theory        31944
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> (C or D))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31944.        (A -> (((B -> C) -> (B -> (C or D))) and A)), M:tm-5, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31945
in-theory        31945
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> ((A -> B) -> (B or C)))
theorem-size     13
proof            (modus-ponens tm-2 tm-470 ((A (-> Am Bm)) (B Am) (C (or Bm Cm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31945.        (((A -> B) -> A) -> ((A -> B) -> (B or C))), M:tm-2, m:tm-470, u:((A (-> Am Bm)) (B Am) (C (or Bm Cm)))
================================================================
tm-name          tm-31946
in-theory        31946
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (B -> (C or D))))
theorem-size     11
proof            (modus-ponens tm-1 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-1 tm-2 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-31946.        (A -> ((B -> C) -> (B -> (C or D)))), M:tm-1, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-31947
in-theory        31947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31947.        ((A -> (B -> (B or C))) and (D -> (E -> (F -> (F or G))))), M:tm-469, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31948
in-theory        31948
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-466 tm-471 ((Am (-> A (or A B))) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31948.        ((A or (B -> (B or C))) -> (D -> (E -> (E or F)))), M:tm-466, m:tm-471, u:((Am (-> A (or A B))) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31949
in-theory        31949
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31949.        ((A -> (B -> (C -> (C or D)))) and (E -> (E or F))), M:tm-456, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31950
in-theory        31950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31950.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (F -> (F or G))))), M:tm-453, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31951
in-theory        31951
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-450 tm-471 ((Am (and (-> A (or A B)) C)) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31951.        ((A or ((B -> (B or C)) and A)) -> (D -> (E -> (E or F)))), M:tm-450, m:tm-471, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31952
in-theory        31952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and ((E -> (E or F)) and (A -> (B -> (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31952.        ((A -> (B -> (C -> (C or D)))) and ((E -> (E or F)) and (A -> (B -> (C -> (C or D)))))), M:tm-443, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31953
in-theory        31953
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31953.        (((A -> (A or B)) or C) and (D -> (E -> (F -> (F or G))))), M:tm-409, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31954
in-theory        31954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31954.        (((A -> (B -> (A and B))) or C) and (D -> (E -> (F -> (F or G))))), M:tm-400, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31955
in-theory        31955
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31955.        ((((A and B) -> B) or C) and (D -> (E -> (F -> (F or G))))), M:tm-391, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31956
in-theory        31956
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31956.        ((((A and B) -> A) or C) and (D -> (E -> (F -> (F or G))))), M:tm-382, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31957
in-theory        31957
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31957.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (G -> (G or H))))), M:tm-373, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31958
in-theory        31958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31958.        (((A -> (B -> A)) or C) and (D -> (E -> (F -> (F or G))))), M:tm-364, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31959
in-theory        31959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31959.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (F -> (F or G))))), M:tm-354, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31960
in-theory        31960
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-351 tm-471 ((Am (-> A (-> B (and A B)))) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31960.        ((A or (B -> (C -> (B and C)))) -> (D -> (E -> (E or F)))), M:tm-351, m:tm-471, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31961
in-theory        31961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31961.        ((A -> (B -> (C -> (C or D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31962
in-theory        31962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) -> D) -> ((A -> (B -> (B or C))) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-471 ((Am (-> (-> Bm (-> Cm (or Cm Dm))) B)) (A (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31962.        (((A -> (B -> (B or C))) -> D) -> ((A -> (B -> (B or C))) and D)), M:tm-339, m:tm-471, u:((Am (-> (-> Bm (-> Cm (or Cm Dm))) B)) (A (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31963
in-theory        31963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31963.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> (E -> (E or F))))), M:tm-338, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31964
in-theory        31964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> (D -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-335 tm-471 ((Am (-> A (and A B))) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31964.        (((A -> B) or (A -> (A and B))) -> (C -> (D -> (D or E)))), M:tm-335, m:tm-471, u:((Am (-> A (and A B))) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31965
in-theory        31965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (A -> (A and (B -> (C -> (C or D))))))
theorem-size     21
proof            (modus-ponens tm-328 tm-471 ((A Am) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31965.        ((A -> (B -> (C -> (C or D)))) and (A -> (A and (B -> (C -> (C or D)))))), M:tm-328, m:tm-471, u:((A Am) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31966
in-theory        31966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and ((E -> (F -> (E and F))) and (A -> (B -> (C -> (C or D))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31966.        ((A -> (B -> (C -> (C or D)))) and ((E -> (F -> (E and F))) and (A -> (B -> (C -> (C or D)))))), M:tm-327, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31967
in-theory        31967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (((E and F) -> F) and (A -> (B -> (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31967.        ((A -> (B -> (C -> (C or D)))) and (((E and F) -> F) and (A -> (B -> (C -> (C or D)))))), M:tm-326, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31968
in-theory        31968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (((E and F) -> E) and (A -> (B -> (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31968.        ((A -> (B -> (C -> (C or D)))) and (((E and F) -> E) and (A -> (B -> (C -> (C or D)))))), M:tm-325, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31969
in-theory        31969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> (C -> (C or D))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31969.        ((A -> (B -> (C -> (C or D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> (C -> (C or D)))))), M:tm-324, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31970
in-theory        31970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and ((E -> (F -> E)) and (A -> (B -> (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31970.        ((A -> (B -> (C -> (C or D)))) and ((E -> (F -> E)) and (A -> (B -> (C -> (C or D)))))), M:tm-323, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31971
in-theory        31971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31971.        ((A -> (B -> (C -> (C or D)))) and ((E and F) -> F)), M:tm-322, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31972
in-theory        31972
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (C or D))) -> E)) -> (B -> (C -> (C or D)))) and ((A and ((B -> (C -> (C or D))) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-471 ((Am (and A (-> (-> Bm (-> Cm (or Cm Dm))) C))) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31972.        (((A and ((B -> (C -> (C or D))) -> E)) -> (B -> (C -> (C or D)))) and ((A and ((B -> (C -> (C or D))) -> E)) -> E)), M:tm-321, m:tm-471, u:((Am (and A (-> (-> Bm (-> Cm (or Cm Dm))) C))) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31973
in-theory        31973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31973.        ((A -> (B -> (C -> (C or D)))) and ((E and F) -> E)), M:tm-320, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31974
in-theory        31974
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (B or C))) -> D) and E) -> (A -> (B -> (B or C)))) and ((((A -> (B -> (B or C))) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-471 ((Am (and (-> (-> Bm (-> Cm (or Cm Dm))) B) C)) (A (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31974.        (((((A -> (B -> (B or C))) -> D) and E) -> (A -> (B -> (B or C)))) and ((((A -> (B -> (B or C))) -> D) and E) -> D)), M:tm-319, m:tm-471, u:((Am (and (-> (-> Bm (-> Cm (or Cm Dm))) B) C)) (A (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31975
in-theory        31975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31975.        ((A -> (B -> (C -> (C or D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31976
in-theory        31976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) -> D)) -> (A -> (B -> (B or C)))) and ((A -> ((B -> (B or C)) -> D)) -> (A -> D)))
theorem-size     31
proof            (modus-ponens tm-317 tm-471 ((Am (-> Bm (-> (-> Cm (or Cm Dm)) C))) (A Bm) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31976.        (((A -> ((B -> (B or C)) -> D)) -> (A -> (B -> (B or C)))) and ((A -> ((B -> (B or C)) -> D)) -> (A -> D))), M:tm-317, m:tm-471, u:((Am (-> Bm (-> (-> Cm (or Cm Dm)) C))) (A Bm) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-31977
in-theory        31977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-471 ((A Am) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31977.        ((A -> (B -> (C -> (C or D)))) and (A -> A)), M:tm-316, m:tm-471, u:((A Am) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31978
in-theory        31978
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31978.        ((A -> (B -> (C -> (C or D)))) and (E -> (F -> E))), M:tm-315, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31979
in-theory        31979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and ((A -> (not (B -> (C -> (C or D))))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-471 ((A Am) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31979.        ((A -> (B -> (C -> (C or D)))) and ((A -> (not (B -> (C -> (C or D))))) -> (not A))), M:tm-313, m:tm-471, u:((A Am) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31980
in-theory        31980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (((B -> (C -> (C or D))) -> E) -> ((A or (B -> (C -> (C or D)))) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-471 ((A Am) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31980.        ((A -> (B -> (C -> (C or D)))) and (((B -> (C -> (C or D))) -> E) -> ((A or (B -> (C -> (C or D)))) -> E))), M:tm-312, m:tm-471, u:((A Am) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31981
in-theory        31981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (E or (A -> (B -> (C -> (C or D))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31981.        ((A -> (B -> (C -> (C or D)))) and (E or (A -> (B -> (C -> (C or D)))))), M:tm-311, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31982
in-theory        31982
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and ((A -> (B -> (C -> (C or D)))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31982.        ((A -> (B -> (C -> (C or D)))) and ((A -> (B -> (C -> (C or D)))) or E)), M:tm-310, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31983
in-theory        31983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (E -> ((A -> (B -> (C -> (C or D)))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31983.        ((A -> (B -> (C -> (C or D)))) and (E -> ((A -> (B -> (C -> (C or D)))) and E))), M:tm-309, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31984
in-theory        31984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and ((A -> B) -> (A -> (C -> (C or D)))))
theorem-size     21
proof            (modus-ponens tm-306 tm-471 ((A Am) (B Bm) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31984.        ((A -> (B -> (C -> (C or D)))) and ((A -> B) -> (A -> (C -> (C or D))))), M:tm-306, m:tm-471, u:((A Am) (B Bm) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-31985
in-theory        31985
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (E -> (A -> (B -> (C -> (C or D))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31985.        ((A -> (B -> (C -> (C or D)))) and (E -> (A -> (B -> (C -> (C or D)))))), M:tm-305, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31986
in-theory        31986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31986.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (F -> (F or G))))), M:tm-303, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31987
in-theory        31987
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-300 tm-471 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31987.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (E -> (E or F)))), M:tm-300, m:tm-471, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31988
in-theory        31988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31988.        ((A -> (((B and C) -> C) and A)) and (D -> (E -> (F -> (F or G))))), M:tm-270, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31989
in-theory        31989
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-267 tm-471 ((Am (and (-> (and A B) B) C)) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31989.        ((A or (((B and C) -> C) and A)) -> (D -> (E -> (E or F)))), M:tm-267, m:tm-471, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31990
in-theory        31990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31990.        ((A -> (((B and C) -> B) and A)) and (D -> (E -> (F -> (F or G))))), M:tm-239, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31991
in-theory        31991
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-236 tm-471 ((Am (and (-> (and A B) A) C)) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31991.        ((A or (((B and C) -> B) and A)) -> (D -> (E -> (E or F)))), M:tm-236, m:tm-471, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31992
in-theory        31992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31992.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (G -> (G or H))))), M:tm-210, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31993
in-theory        31993
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-207 tm-471 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31993.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (F -> (F or G)))), M:tm-207, m:tm-471, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31994
in-theory        31994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31994.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (F -> (F or G))))), M:tm-183, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31995
in-theory        31995
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-180 tm-471 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31995.        ((A or ((B -> (C -> B)) and A)) -> (D -> (E -> (E or F)))), M:tm-180, m:tm-471, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31996
in-theory        31996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31996.        ((A -> ((B and C) -> C)) and (D -> (E -> (F -> (F or G))))), M:tm-157, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-31997
in-theory        31997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-154 tm-471 ((Am (-> (and A B) B)) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31997.        ((A or ((B and C) -> C)) -> (D -> (E -> (E or F)))), M:tm-154, m:tm-471, u:((Am (-> (and A B) B)) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-31998
in-theory        31998
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> (C -> (C or D)))
theorem-size     9
proof            (modus-ponens tm-152 tm-471 ((Am (and A Bm)) (B Bm) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31998.        ((A and B) -> (C -> (C or D))), M:tm-152, m:tm-471, u:((Am (and A Bm)) (B Bm) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-31999
in-theory        31999
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-31999.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (F -> (F or G))))), M:tm-147, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32000
in-theory        32000
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-144 tm-471 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32000.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (E -> (E or F)))), M:tm-144, m:tm-471, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32001
in-theory        32001
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (C or D))) -> E)) -> (B -> (C -> (C or D))))
theorem-size     19
proof            (modus-ponens tm-142 tm-471 ((Am (and A (-> (-> Bm (-> Cm (or Cm Dm))) C))) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32001.        ((A and ((B -> (C -> (C or D))) -> E)) -> (B -> (C -> (C or D)))), M:tm-142, m:tm-471, u:((Am (and A (-> (-> Bm (-> Cm (or Cm Dm))) C))) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32002
in-theory        32002
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (C or D))) -> B)) -> (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-141 tm-471 ((Am (and A (-> (-> Bm (-> Cm (or Cm Dm))) Bm))) (B Bm) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32002.        ((A and ((B -> (C -> (C or D))) -> B)) -> (C -> (C or D))), M:tm-141, m:tm-471, u:((Am (and A (-> (-> Bm (-> Cm (or Cm Dm))) Bm))) (B Bm) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-32003
in-theory        32003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32003.        ((A -> ((B and C) -> B)) and (D -> (E -> (F -> (F or G))))), M:tm-134, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32004
in-theory        32004
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-131 tm-471 ((Am (-> (and A B) A)) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32004.        ((A or ((B and C) -> B)) -> (D -> (E -> (E or F)))), M:tm-131, m:tm-471, u:((Am (-> (and A B) A)) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32005
in-theory        32005
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32005.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (F -> (F or G))))), M:tm-125, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32006
in-theory        32006
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-122 tm-471 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32006.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (E -> (E or F)))), M:tm-122, m:tm-471, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32007
in-theory        32007
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (B or C))) -> D) and E) -> (A -> (B -> (B or C))))
theorem-size     19
proof            (modus-ponens tm-120 tm-471 ((Am (and (-> (-> Bm (-> Cm (or Cm Dm))) B) C)) (A (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32007.        ((((A -> (B -> (B or C))) -> D) and E) -> (A -> (B -> (B or C)))), M:tm-120, m:tm-471, u:((Am (and (-> (-> Bm (-> Cm (or Cm Dm))) B) C)) (A (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32008
in-theory        32008
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (B or C))) -> A) and D) -> (B -> (B or C)))
theorem-size     17
proof            (modus-ponens tm-119 tm-471 ((Am (and (-> (-> Bm (-> Cm (or Cm Dm))) Bm) C)) (A Bm) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32008.        ((((A -> (B -> (B or C))) -> A) and D) -> (B -> (B or C))), M:tm-119, m:tm-471, u:((Am (and (-> (-> Bm (-> Cm (or Cm Dm))) Bm) C)) (A Bm) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-32009
in-theory        32009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32009.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (G or H))))), M:tm-113, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32010
in-theory        32010
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-110 tm-471 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32010.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (F -> (F or G)))), M:tm-110, m:tm-471, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32011
in-theory        32011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (D -> (D or E)))
theorem-size     11
proof            (modus-ponens tm-108 tm-471 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32011.        ((A -> (B -> C)) -> (D -> (D or E))), M:tm-108, m:tm-471, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-32012
in-theory        32012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) -> (A -> B)) -> (A -> (B or C)))
theorem-size     17
proof            (modus-ponens tm-106 tm-471 ((Am (-> (-> Bm (-> Cm (or Cm Dm))) (-> Bm Cm))) (A Bm) (B Cm) (C (or Cm Dm))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32012.        (((A -> (B -> (B or C))) -> (A -> B)) -> (A -> (B or C))), M:tm-106, m:tm-471, u:((Am (-> (-> Bm (-> Cm (or Cm Dm))) (-> Bm Cm))) (A Bm) (B Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-32013
in-theory        32013
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (F -> (F or G)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32013.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (F -> (F or G))))), M:tm-105, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32014
in-theory        32014
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (E -> (E or F))))
theorem-size     27
proof            (modus-ponens tm-102 tm-471 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32014.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (E -> (E or F)))), M:tm-102, m:tm-471, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32015
in-theory        32015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) -> D)) -> (A -> (B -> (B or C))))
theorem-size     17
proof            (modus-ponens tm-100 tm-471 ((Am (-> Bm (-> (-> Cm (or Cm Dm)) C))) (A Bm) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32015.        ((A -> ((B -> (B or C)) -> D)) -> (A -> (B -> (B or C)))), M:tm-100, m:tm-471, u:((Am (-> Bm (-> (-> Cm (or Cm Dm)) C))) (A Bm) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-32016
in-theory        32016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) -> D) -> (A -> (B -> (B or C))))
theorem-size     17
proof            (modus-ponens tm-96 tm-471 ((Am (-> (-> Bm (-> Cm (or Cm Dm))) B)) (A (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32016.        (((A -> (B -> (B or C))) -> D) -> (A -> (B -> (B or C)))), M:tm-96, m:tm-471, u:((Am (-> (-> Bm (-> Cm (or Cm Dm))) B)) (A (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32017
in-theory        32017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32017.        (((A -> B) -> (A -> A)) and (C -> (D -> (E -> (E or F))))), M:tm-95, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32018
in-theory        32018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> (D -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-92 tm-471 ((Am (-> A A)) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32018.        (((A -> B) or (A -> A)) -> (C -> (D -> (D or E)))), M:tm-92, m:tm-471, u:((Am (-> A A)) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32019
in-theory        32019
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C -> (D -> (D or E)))))
theorem-size     11
proof            (modus-ponens tm-84 tm-471 ((A Am) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32019.        (A -> (B -> (C -> (D -> (D or E))))), M:tm-84, m:tm-471, u:((A Am) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32020
in-theory        32020
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32020.        ((A -> (B -> (C -> B))) and (D -> (E -> (F -> (F or G))))), M:tm-83, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32021
in-theory        32021
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-80 tm-471 ((Am (-> A (-> B A))) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32021.        ((A or (B -> (C -> B))) -> (D -> (E -> (E or F)))), M:tm-80, m:tm-471, u:((Am (-> A (-> B A))) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32022
in-theory        32022
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> (B -> (B or C))) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-471 ((Am (not (not (-> (-> Bm (-> Cm (or Cm Dm))) B)))) (A (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-10 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32022.        ((not (not ((A -> (B -> (B or C))) -> D))) -> D), M:tm-77, m:tm-471, u:((Am (not (not (-> (-> Bm (-> Cm (or Cm Dm))) B)))) (A (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32023
in-theory        32023
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> (D -> (D or E)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32023.        (((not (not A)) -> A) and (B -> (C -> (D -> (D or E))))), M:tm-76, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32024
in-theory        32024
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> (C -> (C or D))))
theorem-size     13
proof            (modus-ponens tm-73 tm-471 ((A Am) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-10 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32024.        (((not (not A)) or A) -> (B -> (C -> (C or D)))), M:tm-73, m:tm-471, u:((A Am) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32025
in-theory        32025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (E -> (E or F)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32025.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (E -> (E or F))))), M:tm-69, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32026
in-theory        32026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (D -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-66 tm-471 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-9 tm-1 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32026.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (D -> (D or E)))), M:tm-66, m:tm-471, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32027
in-theory        32027
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> (C -> (C or D))))
theorem-size     13
proof            (modus-ponens tm-55 tm-471 ((Am (-> A Bm)) (B Bm) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32027.        ((A -> B) -> ((A or B) -> (C -> (C or D)))), M:tm-55, m:tm-471, u:((Am (-> A Bm)) (B Bm) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-32028
in-theory        32028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32028.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (F or G))))), M:tm-54, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32029
in-theory        32029
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-51 tm-471 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32029.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (E or F)))), M:tm-51, m:tm-471, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32030
in-theory        32030
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-50 tm-471 ((Am (or A B)) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32030.        ((A or (B or A)) -> (C -> (D -> (D or E)))), M:tm-50, m:tm-471, u:((Am (or A B)) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32031
in-theory        32031
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-49 tm-471 ((Am (or A B)) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32031.        ((A or (A or B)) -> (C -> (D -> (D or E)))), M:tm-49, m:tm-471, u:((Am (or A B)) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32032
in-theory        32032
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (D -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-48 tm-471 ((Am (-> A (and B A))) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32032.        ((A or (B -> (A and B))) -> (C -> (D -> (D or E)))), M:tm-48, m:tm-471, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32033
in-theory        32033
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-47 tm-471 ((A Am) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32033.        (((A and B) or B) -> (C -> (D -> (D or E)))), M:tm-47, m:tm-471, u:((A Am) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32034
in-theory        32034
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-46 tm-471 ((A Am) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32034.        (((A and B) or A) -> (C -> (D -> (D or E)))), M:tm-46, m:tm-471, u:((A Am) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32035
in-theory        32035
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-45 tm-471 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32035.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (E or F)))), M:tm-45, m:tm-471, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32036
in-theory        32036
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-44 tm-471 ((Am (-> A B)) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32036.        ((A or (B -> A)) -> (C -> (D -> (D or E)))), M:tm-44, m:tm-471, u:((Am (-> A B)) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32037
in-theory        32037
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32037.        ((A -> (B or A)) and (C -> (D -> (E -> (E or F))))), M:tm-42, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32038
in-theory        32038
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32038.        ((A -> (A or B)) and (C -> (D -> (E -> (E or F))))), M:tm-32, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32039
in-theory        32039
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B -> (C -> (C or D)))))
theorem-size     11
proof            (modus-ponens tm-24 tm-471 ((A Am) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32039.        (A -> (A and (B -> (C -> (C or D))))), M:tm-24, m:tm-471, u:((A Am) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32040
in-theory        32040
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32040.        ((A -> (B -> (A and B))) and (C -> (D -> (E -> (E or F))))), M:tm-23, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32041
in-theory        32041
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32041.        (((A and B) -> B) and (C -> (D -> (E -> (E or F))))), M:tm-22, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32042
in-theory        32042
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32042.        (((A and B) -> A) and (C -> (D -> (E -> (E or F))))), M:tm-21, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32043
in-theory        32043
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32043.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (F or G))))), M:tm-20, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32044
in-theory        32044
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32044.        ((A -> (B -> A)) and (C -> (D -> (E -> (E or F))))), M:tm-19, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32045
in-theory        32045
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (C or D))) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-471 ((Am (and A (-> (-> Bm (-> Cm (or Cm Dm))) C))) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-4 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32045.        ((A and ((B -> (C -> (C or D))) -> E)) -> E), M:tm-17, m:tm-471, u:((Am (and A (-> (-> Bm (-> Cm (or Cm Dm))) C))) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32046
in-theory        32046
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (B or C))) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-471 ((Am (and (-> (-> Bm (-> Cm (or Cm Dm))) B) C)) (A (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-3 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32046.        ((((A -> (B -> (B or C))) -> D) and E) -> D), M:tm-15, m:tm-471, u:((Am (and (-> (-> Bm (-> Cm (or Cm Dm))) B) C)) (A (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32047
in-theory        32047
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) -> D)) -> (A -> D))
theorem-size     13
proof            (modus-ponens tm-13 tm-471 ((Am (-> Bm (-> (-> Cm (or Cm Dm)) C))) (A Bm) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32047.        ((A -> ((B -> (B or C)) -> D)) -> (A -> D)), M:tm-13, m:tm-471, u:((Am (-> Bm (-> (-> Cm (or Cm Dm)) C))) (A Bm) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-32048
in-theory        32048
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> (C or D))))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-471 ((A Am) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-9 tm-1 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32048.        ((A -> (not (B -> (C -> (C or D))))) -> (not A)), M:tm-9, m:tm-471, u:((A Am) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32049
in-theory        32049
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) -> D) -> ((E or (A -> (B -> (B or C)))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-471 ((A Am) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32049.        (((A -> (B -> (B or C))) -> D) -> ((E or (A -> (B -> (B or C)))) -> D)), M:tm-8, m:tm-471, u:((A Am) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32050
in-theory        32050
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C -> (D -> (D or E)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-7 tm-1 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32050.        (A or (B -> (C -> (D -> (D or E))))), M:tm-7, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32051
in-theory        32051
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-6 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32051.        ((A -> (B -> (C -> (C or D)))) or E), M:tm-6, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32052
in-theory        32052
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (D -> (D or E)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32052.        (A -> ((B -> (C -> (D -> (D or E)))) and A)), M:tm-5, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32053
in-theory        32053
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> (C -> (C or D))))
theorem-size     11
proof            (modus-ponens tm-2 tm-471 ((A Am) (B Bm) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-1 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32053.        ((A -> B) -> (A -> (C -> (C or D)))), M:tm-2, m:tm-471, u:((A Am) (B Bm) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-32054
in-theory        32054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32054.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-469, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32055
in-theory        32055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32055.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and (F -> (F or G))), M:tm-456, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32056
in-theory        32056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32056.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-453, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32057
in-theory        32057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (A or B)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32057.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (A or B)) and (C or (D -> (E -> D)))))), M:tm-443, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32058
in-theory        32058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32058.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-409, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32059
in-theory        32059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32059.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-400, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32060
in-theory        32060
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32060.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-391, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32061
in-theory        32061
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32061.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-382, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32062
in-theory        32062
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32062.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or (H -> (I -> H))))), M:tm-373, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32063
in-theory        32063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32063.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-364, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32064
in-theory        32064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32064.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-354, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32065
in-theory        32065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32065.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32066
in-theory        32066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32066.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or (F -> (G -> F))))), M:tm-338, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32067
in-theory        32067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C or (D -> (E -> D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32067.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C or (D -> (E -> D)))))), M:tm-327, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32068
in-theory        32068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (A or B)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32068.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (A or B)) and (C or (D -> (E -> D)))))), M:tm-326, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32069
in-theory        32069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (A or B)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32069.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (A or B)) and (C or (D -> (E -> D)))))), M:tm-325, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32070
in-theory        32070
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C or (D -> (E -> D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32070.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C or (D -> (E -> D)))))), M:tm-324, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32071
in-theory        32071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32071.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C or (D -> (E -> D)))))), M:tm-323, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32072
in-theory        32072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32072.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and ((F and G) -> G)), M:tm-322, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32073
in-theory        32073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32073.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and ((F and G) -> F)), M:tm-320, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32074
in-theory        32074
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32074.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32075
in-theory        32075
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32075.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and (F -> (G -> F))), M:tm-315, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32076
in-theory        32076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and (F or ((A -> (A or B)) and (C or (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32076.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and (F or ((A -> (A or B)) and (C or (D -> (E -> D)))))), M:tm-311, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32077
in-theory        32077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and (((A -> (A or B)) and (C or (D -> (E -> D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32077.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and (((A -> (A or B)) and (C or (D -> (E -> D)))) or F)), M:tm-310, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32078
in-theory        32078
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and (F -> (((A -> (A or B)) and (C or (D -> (E -> D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32078.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and (F -> (((A -> (A or B)) and (C or (D -> (E -> D)))) and F))), M:tm-309, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32079
in-theory        32079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and (C or (D -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-472 ((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32079.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and (C or (D -> (E -> D)))), M:tm-308, m:tm-472, u:((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-32080
in-theory        32080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-472 ((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32080.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and (A -> (A or B))), M:tm-307, m:tm-472, u:((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-32081
in-theory        32081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and (F -> ((A -> (A or B)) and (C or (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32081.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and (F -> ((A -> (A or B)) and (C or (D -> (E -> D)))))), M:tm-305, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32082
in-theory        32082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32082.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-303, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32083
in-theory        32083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32083.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-270, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32084
in-theory        32084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32084.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-239, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32085
in-theory        32085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32085.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or (H -> (I -> H))))), M:tm-210, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32086
in-theory        32086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32086.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-183, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32087
in-theory        32087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32087.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-157, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32088
in-theory        32088
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32088.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-147, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32089
in-theory        32089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32089.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-134, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32090
in-theory        32090
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32090.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-125, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32091
in-theory        32091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32091.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (I -> H))))), M:tm-113, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32092
in-theory        32092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32092.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-105, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32093
in-theory        32093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32093.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or (F -> (G -> F))))), M:tm-95, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32094
in-theory        32094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32094.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-83, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32095
in-theory        32095
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D or (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32095.        (((not (not A)) -> A) and ((B -> (B or C)) and (D or (E -> (F -> E))))), M:tm-76, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32096
in-theory        32096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-6 tm-7 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32096.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or (F -> (G -> F))))), M:tm-69, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32097
in-theory        32097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32097.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-54, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32098
in-theory        32098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32098.        ((A -> (B or A)) and ((C -> (C or D)) and (E or (F -> (G -> F))))), M:tm-42, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32099
in-theory        32099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32099.        ((A -> (A or B)) and ((C -> (C or D)) and (E or (F -> (G -> F))))), M:tm-32, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32100
in-theory        32100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32100.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or (F -> (G -> F))))), M:tm-23, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32101
in-theory        32101
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32101.        (((A and B) -> B) and ((C -> (C or D)) and (E or (F -> (G -> F))))), M:tm-22, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32102
in-theory        32102
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32102.        (((A and B) -> A) and ((C -> (C or D)) and (E or (F -> (G -> F))))), M:tm-21, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32103
in-theory        32103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32103.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-20, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32104
in-theory        32104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32104.        ((A -> (B -> A)) and ((C -> (C or D)) and (E or (F -> (G -> F))))), M:tm-19, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32105
in-theory        32105
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-6 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32105.        (A or ((B -> (B or C)) and (D or (E -> (F -> E))))), M:tm-7, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32106
in-theory        32106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-7 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32106.        (((A -> (A or B)) and (C or (D -> (E -> D)))) or F), M:tm-6, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32107
in-theory        32107
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D or (E -> (F -> E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32107.        (A -> (((B -> (B or C)) and (D or (E -> (F -> E)))) and A)), M:tm-5, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32108
in-theory        32108
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-6 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32108.        (A -> ((B -> (B or C)) and (D or (E -> (F -> E))))), M:tm-1, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32109
in-theory        32109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32109.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-469, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32110
in-theory        32110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32110.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (F -> (F or G))), M:tm-456, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32111
in-theory        32111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32111.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-453, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32112
in-theory        32112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C or (D -> (E -> D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32112.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))))), M:tm-443, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32113
in-theory        32113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32113.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-409, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32114
in-theory        32114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32114.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-400, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32115
in-theory        32115
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32115.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-391, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32116
in-theory        32116
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32116.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-382, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32117
in-theory        32117
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32117.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H))))), M:tm-373, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32118
in-theory        32118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32118.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-364, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32119
in-theory        32119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32119.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-354, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32120
in-theory        32120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32120.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32121
in-theory        32121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32121.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F))))), M:tm-338, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32122
in-theory        32122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C or (D -> (E -> D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32122.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))))), M:tm-327, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32123
in-theory        32123
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C or (D -> (E -> D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32123.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))))), M:tm-326, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32124
in-theory        32124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C or (D -> (E -> D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32124.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))))), M:tm-325, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32125
in-theory        32125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C or (D -> (E -> D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32125.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))))), M:tm-324, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32126
in-theory        32126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C or (D -> (E -> D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32126.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))))), M:tm-323, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32127
in-theory        32127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32127.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and ((F and G) -> G)), M:tm-322, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32128
in-theory        32128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32128.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and ((F and G) -> F)), M:tm-320, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32129
in-theory        32129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32129.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32130
in-theory        32130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32130.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (F -> (G -> F))), M:tm-315, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32131
in-theory        32131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (F or ((A -> (B -> (A and B))) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32131.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (F or ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))))), M:tm-311, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32132
in-theory        32132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32132.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) or F)), M:tm-310, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32133
in-theory        32133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (F -> (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32133.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (F -> (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and F))), M:tm-309, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32134
in-theory        32134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (C or (D -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-308 tm-473 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32134.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (C or (D -> (E -> D)))), M:tm-308, m:tm-473, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-32135
in-theory        32135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-473 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32135.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-473, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-32136
in-theory        32136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (F -> ((A -> (B -> (A and B))) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32136.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (F -> ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))))), M:tm-305, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32137
in-theory        32137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32137.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-303, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32138
in-theory        32138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32138.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-270, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32139
in-theory        32139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32139.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-239, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32140
in-theory        32140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32140.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H))))), M:tm-210, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32141
in-theory        32141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32141.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-183, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32142
in-theory        32142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32142.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-157, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32143
in-theory        32143
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32143.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-147, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32144
in-theory        32144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32144.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-134, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32145
in-theory        32145
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32145.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-125, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32146
in-theory        32146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32146.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H))))), M:tm-113, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32147
in-theory        32147
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32147.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-105, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32148
in-theory        32148
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32148.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F))))), M:tm-95, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32149
in-theory        32149
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32149.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-83, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32150
in-theory        32150
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or (E -> (F -> E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32150.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or (E -> (F -> E))))), M:tm-76, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32151
in-theory        32151
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32151.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F))))), M:tm-69, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32152
in-theory        32152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32152.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-54, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32153
in-theory        32153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32153.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F))))), M:tm-42, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32154
in-theory        32154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32154.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F))))), M:tm-32, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32155
in-theory        32155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32155.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F))))), M:tm-23, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32156
in-theory        32156
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32156.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F))))), M:tm-22, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32157
in-theory        32157
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32157.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F))))), M:tm-21, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32158
in-theory        32158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32158.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-20, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32159
in-theory        32159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32159.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> F))))), M:tm-19, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32160
in-theory        32160
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D or (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32160.        (A or ((B -> (C -> (B and C))) and (D or (E -> (F -> E))))), M:tm-7, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32161
in-theory        32161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-7 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32161.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) or F), M:tm-6, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32162
in-theory        32162
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D or (E -> (F -> E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32162.        (A -> (((B -> (C -> (B and C))) and (D or (E -> (F -> E)))) and A)), M:tm-5, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32163
in-theory        32163
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D or (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32163.        (A -> ((B -> (C -> (B and C))) and (D or (E -> (F -> E))))), M:tm-1, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32164
in-theory        32164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32164.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-469, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32165
in-theory        32165
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32165.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and (F -> (F or G))), M:tm-456, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32166
in-theory        32166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32166.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-453, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32167
in-theory        32167
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((F -> (F or G)) and (((A and B) -> B) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32167.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((F -> (F or G)) and (((A and B) -> B) and (C or (D -> (E -> D)))))), M:tm-443, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32168
in-theory        32168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32168.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-409, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32169
in-theory        32169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32169.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-400, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32170
in-theory        32170
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32170.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-391, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32171
in-theory        32171
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32171.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-382, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32172
in-theory        32172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32172.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or (H -> (I -> H))))), M:tm-373, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32173
in-theory        32173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32173.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-364, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32174
in-theory        32174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32174.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-354, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32175
in-theory        32175
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32175.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32176
in-theory        32176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32176.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or (F -> (G -> F))))), M:tm-338, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32177
in-theory        32177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C or (D -> (E -> D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32177.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C or (D -> (E -> D)))))), M:tm-327, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32178
in-theory        32178
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and (((F and G) -> G) and (((A and B) -> B) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32178.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and (((F and G) -> G) and (((A and B) -> B) and (C or (D -> (E -> D)))))), M:tm-326, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32179
in-theory        32179
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and (((F and G) -> F) and (((A and B) -> B) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32179.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and (((F and G) -> F) and (((A and B) -> B) and (C or (D -> (E -> D)))))), M:tm-325, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32180
in-theory        32180
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C or (D -> (E -> D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32180.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C or (D -> (E -> D)))))), M:tm-324, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32181
in-theory        32181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((F -> (G -> F)) and (((A and B) -> B) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32181.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((F -> (G -> F)) and (((A and B) -> B) and (C or (D -> (E -> D)))))), M:tm-323, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32182
in-theory        32182
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32182.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((F and G) -> G)), M:tm-322, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32183
in-theory        32183
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32183.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((F and G) -> F)), M:tm-320, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32184
in-theory        32184
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32184.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32185
in-theory        32185
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32185.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and (F -> (G -> F))), M:tm-315, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32186
in-theory        32186
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and (F or (((A and B) -> B) and (C or (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32186.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and (F or (((A and B) -> B) and (C or (D -> (E -> D)))))), M:tm-311, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32187
in-theory        32187
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((((A and B) -> B) and (C or (D -> (E -> D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32187.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((((A and B) -> B) and (C or (D -> (E -> D)))) or F)), M:tm-310, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32188
in-theory        32188
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and (F -> ((((A and B) -> B) and (C or (D -> (E -> D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32188.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and (F -> ((((A and B) -> B) and (C or (D -> (E -> D)))) and F))), M:tm-309, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32189
in-theory        32189
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and (C or (D -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-474 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32189.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and (C or (D -> (E -> D)))), M:tm-308, m:tm-474, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-32190
in-theory        32190
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-474 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32190.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((A and B) -> B)), M:tm-307, m:tm-474, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-32191
in-theory        32191
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and (F -> (((A and B) -> B) and (C or (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32191.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and (F -> (((A and B) -> B) and (C or (D -> (E -> D)))))), M:tm-305, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32192
in-theory        32192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32192.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-303, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32193
in-theory        32193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32193.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-270, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32194
in-theory        32194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32194.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-239, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32195
in-theory        32195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32195.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or (H -> (I -> H))))), M:tm-210, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32196
in-theory        32196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32196.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-183, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32197
in-theory        32197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32197.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-157, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32198
in-theory        32198
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32198.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-147, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32199
in-theory        32199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32199.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-134, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32200
in-theory        32200
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32200.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-125, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32201
in-theory        32201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32201.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (I -> H))))), M:tm-113, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32202
in-theory        32202
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32202.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-105, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32203
in-theory        32203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32203.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or (F -> (G -> F))))), M:tm-95, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32204
in-theory        32204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32204.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-83, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32205
in-theory        32205
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D or (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32205.        (((not (not A)) -> A) and (((B and C) -> C) and (D or (E -> (F -> E))))), M:tm-76, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32206
in-theory        32206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-4 tm-7 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32206.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or (F -> (G -> F))))), M:tm-69, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32207
in-theory        32207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32207.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-54, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32208
in-theory        32208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32208.        ((A -> (B or A)) and (((C and D) -> D) and (E or (F -> (G -> F))))), M:tm-42, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32209
in-theory        32209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32209.        ((A -> (A or B)) and (((C and D) -> D) and (E or (F -> (G -> F))))), M:tm-32, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32210
in-theory        32210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32210.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or (F -> (G -> F))))), M:tm-23, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32211
in-theory        32211
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32211.        (((A and B) -> B) and (((C and D) -> D) and (E or (F -> (G -> F))))), M:tm-22, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32212
in-theory        32212
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32212.        (((A and B) -> A) and (((C and D) -> D) and (E or (F -> (G -> F))))), M:tm-21, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32213
in-theory        32213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32213.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-20, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32214
in-theory        32214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32214.        ((A -> (B -> A)) and (((C and D) -> D) and (E or (F -> (G -> F))))), M:tm-19, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32215
in-theory        32215
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-4 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32215.        (A or (((B and C) -> C) and (D or (E -> (F -> E))))), M:tm-7, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32216
in-theory        32216
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-4 tm-7 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32216.        ((((A and B) -> B) and (C or (D -> (E -> D)))) or F), M:tm-6, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32217
in-theory        32217
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D or (E -> (F -> E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32217.        (A -> ((((B and C) -> C) and (D or (E -> (F -> E)))) and A)), M:tm-5, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32218
in-theory        32218
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-4 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32218.        (A -> (((B and C) -> C) and (D or (E -> (F -> E))))), M:tm-1, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32219
in-theory        32219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32219.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-469, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32220
in-theory        32220
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32220.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and (F -> (F or G))), M:tm-456, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32221
in-theory        32221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32221.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-453, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32222
in-theory        32222
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((F -> (F or G)) and (((A and B) -> A) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32222.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((F -> (F or G)) and (((A and B) -> A) and (C or (D -> (E -> D)))))), M:tm-443, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32223
in-theory        32223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32223.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-409, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32224
in-theory        32224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32224.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-400, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32225
in-theory        32225
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32225.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-391, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32226
in-theory        32226
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32226.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-382, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32227
in-theory        32227
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32227.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or (H -> (I -> H))))), M:tm-373, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32228
in-theory        32228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32228.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-364, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32229
in-theory        32229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32229.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-354, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32230
in-theory        32230
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32230.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32231
in-theory        32231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32231.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or (F -> (G -> F))))), M:tm-338, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32232
in-theory        32232
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C or (D -> (E -> D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32232.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C or (D -> (E -> D)))))), M:tm-327, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32233
in-theory        32233
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and (((F and G) -> G) and (((A and B) -> A) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32233.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and (((F and G) -> G) and (((A and B) -> A) and (C or (D -> (E -> D)))))), M:tm-326, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32234
in-theory        32234
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and (((F and G) -> F) and (((A and B) -> A) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32234.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and (((F and G) -> F) and (((A and B) -> A) and (C or (D -> (E -> D)))))), M:tm-325, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32235
in-theory        32235
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C or (D -> (E -> D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32235.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C or (D -> (E -> D)))))), M:tm-324, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32236
in-theory        32236
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((F -> (G -> F)) and (((A and B) -> A) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32236.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((F -> (G -> F)) and (((A and B) -> A) and (C or (D -> (E -> D)))))), M:tm-323, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32237
in-theory        32237
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32237.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((F and G) -> G)), M:tm-322, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32238
in-theory        32238
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32238.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((F and G) -> F)), M:tm-320, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32239
in-theory        32239
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32239.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32240
in-theory        32240
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32240.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and (F -> (G -> F))), M:tm-315, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32241
in-theory        32241
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and (F or (((A and B) -> A) and (C or (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32241.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and (F or (((A and B) -> A) and (C or (D -> (E -> D)))))), M:tm-311, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32242
in-theory        32242
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((((A and B) -> A) and (C or (D -> (E -> D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32242.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((((A and B) -> A) and (C or (D -> (E -> D)))) or F)), M:tm-310, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32243
in-theory        32243
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and (F -> ((((A and B) -> A) and (C or (D -> (E -> D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32243.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and (F -> ((((A and B) -> A) and (C or (D -> (E -> D)))) and F))), M:tm-309, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32244
in-theory        32244
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and (C or (D -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-475 ((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32244.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and (C or (D -> (E -> D)))), M:tm-308, m:tm-475, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-32245
in-theory        32245
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-475 ((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32245.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((A and B) -> A)), M:tm-307, m:tm-475, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-32246
in-theory        32246
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and (F -> (((A and B) -> A) and (C or (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32246.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and (F -> (((A and B) -> A) and (C or (D -> (E -> D)))))), M:tm-305, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32247
in-theory        32247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32247.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-303, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32248
in-theory        32248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32248.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-270, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32249
in-theory        32249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32249.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-239, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32250
in-theory        32250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32250.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or (H -> (I -> H))))), M:tm-210, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32251
in-theory        32251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32251.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-183, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32252
in-theory        32252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32252.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-157, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32253
in-theory        32253
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32253.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-147, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32254
in-theory        32254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32254.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-134, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32255
in-theory        32255
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32255.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-125, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32256
in-theory        32256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32256.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (I -> H))))), M:tm-113, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32257
in-theory        32257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32257.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-105, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32258
in-theory        32258
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32258.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or (F -> (G -> F))))), M:tm-95, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32259
in-theory        32259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32259.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-83, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32260
in-theory        32260
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D or (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32260.        (((not (not A)) -> A) and (((B and C) -> B) and (D or (E -> (F -> E))))), M:tm-76, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32261
in-theory        32261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-3 tm-7 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32261.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or (F -> (G -> F))))), M:tm-69, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32262
in-theory        32262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32262.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-54, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32263
in-theory        32263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32263.        ((A -> (B or A)) and (((C and D) -> C) and (E or (F -> (G -> F))))), M:tm-42, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32264
in-theory        32264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32264.        ((A -> (A or B)) and (((C and D) -> C) and (E or (F -> (G -> F))))), M:tm-32, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32265
in-theory        32265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32265.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or (F -> (G -> F))))), M:tm-23, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32266
in-theory        32266
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32266.        (((A and B) -> B) and (((C and D) -> C) and (E or (F -> (G -> F))))), M:tm-22, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32267
in-theory        32267
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32267.        (((A and B) -> A) and (((C and D) -> C) and (E or (F -> (G -> F))))), M:tm-21, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32268
in-theory        32268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32268.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-20, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32269
in-theory        32269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32269.        ((A -> (B -> A)) and (((C and D) -> C) and (E or (F -> (G -> F))))), M:tm-19, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32270
in-theory        32270
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-3 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32270.        (A or (((B and C) -> B) and (D or (E -> (F -> E))))), M:tm-7, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32271
in-theory        32271
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-3 tm-7 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32271.        ((((A and B) -> A) and (C or (D -> (E -> D)))) or F), M:tm-6, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32272
in-theory        32272
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D or (E -> (F -> E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32272.        (A -> ((((B and C) -> B) and (D or (E -> (F -> E)))) and A)), M:tm-5, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32273
in-theory        32273
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-3 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32273.        (A -> (((B and C) -> B) and (D or (E -> (F -> E))))), M:tm-1, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32274
in-theory        32274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32274.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-469, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32275
in-theory        32275
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32275.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (G -> (G or H))), M:tm-456, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32276
in-theory        32276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32276.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-453, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32277
in-theory        32277
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32277.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))))), M:tm-443, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32278
in-theory        32278
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32278.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-409, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32279
in-theory        32279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32279.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-400, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32280
in-theory        32280
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32280.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-391, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32281
in-theory        32281
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32281.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-382, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32282
in-theory        32282
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32282.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> I))))), M:tm-373, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32283
in-theory        32283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32283.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-364, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32284
in-theory        32284
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32284.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-354, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32285
in-theory        32285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32285.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32286
in-theory        32286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32286.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G))))), M:tm-338, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32287
in-theory        32287
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32287.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))))), M:tm-327, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32288
in-theory        32288
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32288.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))))), M:tm-326, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32289
in-theory        32289
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32289.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))))), M:tm-325, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32290
in-theory        32290
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32290.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))))), M:tm-324, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32291
in-theory        32291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32291.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))))), M:tm-323, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32292
in-theory        32292
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32292.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((G and H) -> H)), M:tm-322, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32293
in-theory        32293
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32293.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((G and H) -> G)), M:tm-320, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32294
in-theory        32294
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32294.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32295
in-theory        32295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32295.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (G -> (H -> G))), M:tm-315, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32296
in-theory        32296
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32296.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))))), M:tm-311, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32297
in-theory        32297
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32297.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) or G)), M:tm-310, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32298
in-theory        32298
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32298.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and G))), M:tm-309, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32299
in-theory        32299
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (D or (E -> (F -> E))))
theorem-size     29
proof            (modus-ponens tm-308 tm-476 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (-> Fm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32299.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (D or (E -> (F -> E)))), M:tm-308, m:tm-476, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (-> Fm Em)))))
================================================================
tm-name          tm-32300
in-theory        32300
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-476 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (-> Fm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32300.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-476, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (-> Fm Em)))))
================================================================
tm-name          tm-32301
in-theory        32301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32301.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))))), M:tm-305, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32302
in-theory        32302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32302.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-303, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32303
in-theory        32303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32303.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-270, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32304
in-theory        32304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32304.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-239, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32305
in-theory        32305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32305.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> I))))), M:tm-210, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32306
in-theory        32306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32306.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-183, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32307
in-theory        32307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32307.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-157, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32308
in-theory        32308
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32308.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-147, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32309
in-theory        32309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32309.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-134, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32310
in-theory        32310
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32310.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-125, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32311
in-theory        32311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32311.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> I))))), M:tm-113, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32312
in-theory        32312
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32312.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-105, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32313
in-theory        32313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32313.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G))))), M:tm-95, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32314
in-theory        32314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32314.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-83, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32315
in-theory        32315
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32315.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> F))))), M:tm-76, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32316
in-theory        32316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-9 tm-2 tm-7 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32316.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G))))), M:tm-69, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32317
in-theory        32317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32317.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-54, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32318
in-theory        32318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32318.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G))))), M:tm-42, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32319
in-theory        32319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32319.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G))))), M:tm-32, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32320
in-theory        32320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32320.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G))))), M:tm-23, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32321
in-theory        32321
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32321.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G))))), M:tm-22, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32322
in-theory        32322
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32322.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G))))), M:tm-21, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32323
in-theory        32323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32323.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-20, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32324
in-theory        32324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32324.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> G))))), M:tm-19, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32325
in-theory        32325
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-7 tm-5 tm-2 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32325.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> F))))), M:tm-7, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32326
in-theory        32326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-6 tm-5 tm-2 tm-7 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32326.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) or G), M:tm-6, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32327
in-theory        32327
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32327.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> F)))) and A)), M:tm-5, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32328
in-theory        32328
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-1 tm-5 tm-2 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32328.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> F))))), M:tm-1, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32329
in-theory        32329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32329.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-469, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32330
in-theory        32330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32330.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (F -> (F or G))), M:tm-456, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32331
in-theory        32331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32331.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-453, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32332
in-theory        32332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32332.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C or (D -> (E -> D)))))), M:tm-443, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32333
in-theory        32333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32333.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-409, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32334
in-theory        32334
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32334.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-400, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32335
in-theory        32335
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32335.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-391, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32336
in-theory        32336
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32336.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-382, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32337
in-theory        32337
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32337.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (I -> H))))), M:tm-373, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32338
in-theory        32338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32338.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-364, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32339
in-theory        32339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32339.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-354, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32340
in-theory        32340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32340.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32341
in-theory        32341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32341.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (G -> F))))), M:tm-338, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32342
in-theory        32342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C or (D -> (E -> D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32342.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C or (D -> (E -> D)))))), M:tm-327, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32343
in-theory        32343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (B -> A)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32343.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (B -> A)) and (C or (D -> (E -> D)))))), M:tm-326, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32344
in-theory        32344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (B -> A)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32344.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (B -> A)) and (C or (D -> (E -> D)))))), M:tm-325, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32345
in-theory        32345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C or (D -> (E -> D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32345.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C or (D -> (E -> D)))))), M:tm-324, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32346
in-theory        32346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32346.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C or (D -> (E -> D)))))), M:tm-323, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32347
in-theory        32347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32347.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and ((F and G) -> G)), M:tm-322, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32348
in-theory        32348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32348.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and ((F and G) -> F)), M:tm-320, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32349
in-theory        32349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32349.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32350
in-theory        32350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32350.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (F -> (G -> F))), M:tm-315, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32351
in-theory        32351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (F or ((A -> (B -> A)) and (C or (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32351.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (F or ((A -> (B -> A)) and (C or (D -> (E -> D)))))), M:tm-311, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32352
in-theory        32352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (((A -> (B -> A)) and (C or (D -> (E -> D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32352.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (((A -> (B -> A)) and (C or (D -> (E -> D)))) or F)), M:tm-310, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32353
in-theory        32353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (F -> (((A -> (B -> A)) and (C or (D -> (E -> D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32353.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (F -> (((A -> (B -> A)) and (C or (D -> (E -> D)))) and F))), M:tm-309, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32354
in-theory        32354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (C or (D -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-477 ((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32354.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (C or (D -> (E -> D)))), M:tm-308, m:tm-477, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-32355
in-theory        32355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-477 ((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32355.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (A -> (B -> A))), M:tm-307, m:tm-477, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-32356
in-theory        32356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (F -> ((A -> (B -> A)) and (C or (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32356.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (F -> ((A -> (B -> A)) and (C or (D -> (E -> D)))))), M:tm-305, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32357
in-theory        32357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32357.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-303, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32358
in-theory        32358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32358.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-270, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32359
in-theory        32359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32359.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-239, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32360
in-theory        32360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32360.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or (H -> (I -> H))))), M:tm-210, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32361
in-theory        32361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32361.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-183, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32362
in-theory        32362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32362.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-157, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32363
in-theory        32363
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32363.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-147, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32364
in-theory        32364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32364.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-134, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32365
in-theory        32365
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32365.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-125, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32366
in-theory        32366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32366.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (I -> H))))), M:tm-113, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32367
in-theory        32367
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32367.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-105, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32368
in-theory        32368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32368.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or (F -> (G -> F))))), M:tm-95, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32369
in-theory        32369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32369.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-83, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32370
in-theory        32370
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D or (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32370.        (((not (not A)) -> A) and ((B -> (C -> B)) and (D or (E -> (F -> E))))), M:tm-76, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32371
in-theory        32371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32371.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or (F -> (G -> F))))), M:tm-69, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32372
in-theory        32372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32372.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-54, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32373
in-theory        32373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32373.        ((A -> (B or A)) and ((C -> (D -> C)) and (E or (F -> (G -> F))))), M:tm-42, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32374
in-theory        32374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32374.        ((A -> (A or B)) and ((C -> (D -> C)) and (E or (F -> (G -> F))))), M:tm-32, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32375
in-theory        32375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32375.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (G -> F))))), M:tm-23, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32376
in-theory        32376
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32376.        (((A and B) -> B) and ((C -> (D -> C)) and (E or (F -> (G -> F))))), M:tm-22, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32377
in-theory        32377
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32377.        (((A and B) -> A) and ((C -> (D -> C)) and (E or (F -> (G -> F))))), M:tm-21, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32378
in-theory        32378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32378.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-20, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32379
in-theory        32379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32379.        ((A -> (B -> A)) and ((C -> (D -> C)) and (E or (F -> (G -> F))))), M:tm-19, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32380
in-theory        32380
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32380.        (A or ((B -> (C -> B)) and (D or (E -> (F -> E))))), M:tm-7, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32381
in-theory        32381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-1 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32381.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) or F), M:tm-6, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32382
in-theory        32382
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D or (E -> (F -> E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32382.        (A -> (((B -> (C -> B)) and (D or (E -> (F -> E)))) and A)), M:tm-5, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32383
in-theory        32383
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32383.        (A -> ((B -> (C -> B)) and (D or (E -> (F -> E))))), M:tm-1, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32384
in-theory        32384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32384.        ((A -> (B -> (B or C))) and (D or (E or (F -> (G -> F))))), M:tm-469, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32385
in-theory        32385
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32385.        ((A or (B or (C -> (D -> C)))) and (E -> (E or F))), M:tm-456, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32386
in-theory        32386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32386.        ((A -> ((B -> (B or C)) and A)) and (D or (E or (F -> (G -> F))))), M:tm-453, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32387
in-theory        32387
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and ((E -> (E or F)) and (A or (B or (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32387.        ((A or (B or (C -> (D -> C)))) and ((E -> (E or F)) and (A or (B or (C -> (D -> C)))))), M:tm-443, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32388
in-theory        32388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32388.        (((A -> (A or B)) or C) and (D or (E or (F -> (G -> F))))), M:tm-409, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32389
in-theory        32389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32389.        (((A -> (B -> (A and B))) or C) and (D or (E or (F -> (G -> F))))), M:tm-400, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32390
in-theory        32390
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32390.        ((((A and B) -> B) or C) and (D or (E or (F -> (G -> F))))), M:tm-391, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32391
in-theory        32391
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32391.        ((((A and B) -> A) or C) and (D or (E or (F -> (G -> F))))), M:tm-382, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32392
in-theory        32392
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32392.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or (G -> (H -> G))))), M:tm-373, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32393
in-theory        32393
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32393.        (((A -> (B -> A)) or C) and (D or (E or (F -> (G -> F))))), M:tm-364, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32394
in-theory        32394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32394.        ((A -> (B -> (C -> (B and C)))) and (D or (E or (F -> (G -> F))))), M:tm-354, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32395
in-theory        32395
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32395.        ((A or (B or (C -> (D -> C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32396
in-theory        32396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D or (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32396.        (((A -> B) -> (A -> (A and B))) and (C or (D or (E -> (F -> E))))), M:tm-338, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32397
in-theory        32397
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and ((E -> (F -> (E and F))) and (A or (B or (C -> (D -> C))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32397.        ((A or (B or (C -> (D -> C)))) and ((E -> (F -> (E and F))) and (A or (B or (C -> (D -> C)))))), M:tm-327, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32398
in-theory        32398
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and (((E and F) -> F) and (A or (B or (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32398.        ((A or (B or (C -> (D -> C)))) and (((E and F) -> F) and (A or (B or (C -> (D -> C)))))), M:tm-326, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32399
in-theory        32399
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and (((E and F) -> E) and (A or (B or (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32399.        ((A or (B or (C -> (D -> C)))) and (((E and F) -> E) and (A or (B or (C -> (D -> C)))))), M:tm-325, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32400
in-theory        32400
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B or (C -> (D -> C))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32400.        ((A or (B or (C -> (D -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B or (C -> (D -> C)))))), M:tm-324, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32401
in-theory        32401
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and ((E -> (F -> E)) and (A or (B or (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32401.        ((A or (B or (C -> (D -> C)))) and ((E -> (F -> E)) and (A or (B or (C -> (D -> C)))))), M:tm-323, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32402
in-theory        32402
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32402.        ((A or (B or (C -> (D -> C)))) and ((E and F) -> F)), M:tm-322, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32403
in-theory        32403
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32403.        ((A or (B or (C -> (D -> C)))) and ((E and F) -> E)), M:tm-320, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32404
in-theory        32404
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32404.        ((A or (B or (C -> (D -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32405
in-theory        32405
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32405.        ((A or (B or (C -> (D -> C)))) and (E -> (F -> E))), M:tm-315, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32406
in-theory        32406
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and (E or (A or (B or (C -> (D -> C))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32406.        ((A or (B or (C -> (D -> C)))) and (E or (A or (B or (C -> (D -> C)))))), M:tm-311, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32407
in-theory        32407
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and ((A or (B or (C -> (D -> C)))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32407.        ((A or (B or (C -> (D -> C)))) and ((A or (B or (C -> (D -> C)))) or E)), M:tm-310, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32408
in-theory        32408
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and (E -> ((A or (B or (C -> (D -> C)))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32408.        ((A or (B or (C -> (D -> C)))) and (E -> ((A or (B or (C -> (D -> C)))) and E))), M:tm-309, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32409
in-theory        32409
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and (E -> (A or (B or (C -> (D -> C))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32409.        ((A or (B or (C -> (D -> C)))) and (E -> (A or (B or (C -> (D -> C)))))), M:tm-305, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32410
in-theory        32410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32410.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or (F -> (G -> F))))), M:tm-303, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32411
in-theory        32411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32411.        ((A -> (((B and C) -> C) and A)) and (D or (E or (F -> (G -> F))))), M:tm-270, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32412
in-theory        32412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32412.        ((A -> (((B and C) -> B) and A)) and (D or (E or (F -> (G -> F))))), M:tm-239, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32413
in-theory        32413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32413.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or (G -> (H -> G))))), M:tm-210, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32414
in-theory        32414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32414.        ((A -> ((B -> (C -> B)) and A)) and (D or (E or (F -> (G -> F))))), M:tm-183, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32415
in-theory        32415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32415.        ((A -> ((B and C) -> C)) and (D or (E or (F -> (G -> F))))), M:tm-157, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32416
in-theory        32416
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32416.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or (F -> (G -> F))))), M:tm-147, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32417
in-theory        32417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32417.        ((A -> ((B and C) -> B)) and (D or (E or (F -> (G -> F))))), M:tm-134, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32418
in-theory        32418
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32418.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or (F -> (G -> F))))), M:tm-125, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32419
in-theory        32419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32419.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (H -> G))))), M:tm-113, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32420
in-theory        32420
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or (F -> (G -> F)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32420.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or (F -> (G -> F))))), M:tm-105, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32421
in-theory        32421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D or (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32421.        (((A -> B) -> (A -> A)) and (C or (D or (E -> (F -> E))))), M:tm-95, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32422
in-theory        32422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32422.        ((A -> (B -> (C -> B))) and (D or (E or (F -> (G -> F))))), M:tm-83, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32423
in-theory        32423
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C or (D -> (E -> D)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32423.        (((not (not A)) -> A) and (B or (C or (D -> (E -> D))))), M:tm-76, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32424
in-theory        32424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or (E -> (F -> E)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32424.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or (E -> (F -> E))))), M:tm-69, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32425
in-theory        32425
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32425.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or (F -> (G -> F))))), M:tm-54, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32426
in-theory        32426
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32426.        ((A -> (B or A)) and (C or (D or (E -> (F -> E))))), M:tm-42, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32427
in-theory        32427
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32427.        ((A -> (A or B)) and (C or (D or (E -> (F -> E))))), M:tm-32, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32428
in-theory        32428
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D or (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32428.        ((A -> (B -> (A and B))) and (C or (D or (E -> (F -> E))))), M:tm-23, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32429
in-theory        32429
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32429.        (((A and B) -> B) and (C or (D or (E -> (F -> E))))), M:tm-22, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32430
in-theory        32430
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32430.        (((A and B) -> A) and (C or (D or (E -> (F -> E))))), M:tm-21, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32431
in-theory        32431
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32431.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or (F -> (G -> F))))), M:tm-20, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32432
in-theory        32432
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32432.        ((A -> (B -> A)) and (C or (D or (E -> (F -> E))))), M:tm-19, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32433
in-theory        32433
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C or (D -> (E -> D)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-7 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32433.        (A or (B or (C or (D -> (E -> D))))), M:tm-7, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32434
in-theory        32434
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-6 tm-7 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32434.        ((A or (B or (C -> (D -> C)))) or E), M:tm-6, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32435
in-theory        32435
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C or (D -> (E -> D)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32435.        (A -> ((B or (C or (D -> (E -> D)))) and A)), M:tm-5, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32436
in-theory        32436
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C or (D -> (E -> D)))))
theorem-size     11
proof            (modus-ponens tm-1 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-1 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32436.        (A -> (B or (C or (D -> (E -> D))))), M:tm-1, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32437
in-theory        32437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32437.        ((A -> (B -> (B or C))) and ((D or (E -> (F -> E))) or G)), M:tm-469, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32438
in-theory        32438
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32438.        (((A or (B -> (C -> B))) or D) and (E -> (E or F))), M:tm-456, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32439
in-theory        32439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32439.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (F -> E))) or G)), M:tm-453, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32440
in-theory        32440
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and ((E -> (E or F)) and ((A or (B -> (C -> B))) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32440.        (((A or (B -> (C -> B))) or D) and ((E -> (E or F)) and ((A or (B -> (C -> B))) or D))), M:tm-443, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32441
in-theory        32441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32441.        (((A -> (A or B)) or C) and ((D or (E -> (F -> E))) or G)), M:tm-409, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32442
in-theory        32442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32442.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (F -> E))) or G)), M:tm-400, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32443
in-theory        32443
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32443.        ((((A and B) -> B) or C) and ((D or (E -> (F -> E))) or G)), M:tm-391, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32444
in-theory        32444
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32444.        ((((A and B) -> A) or C) and ((D or (E -> (F -> E))) or G)), M:tm-382, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32445
in-theory        32445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (G -> F))) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32445.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (G -> F))) or H)), M:tm-373, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32446
in-theory        32446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32446.        (((A -> (B -> A)) or C) and ((D or (E -> (F -> E))) or G)), M:tm-364, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32447
in-theory        32447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32447.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (F -> E))) or G)), M:tm-354, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32448
in-theory        32448
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32448.        (((A or (B -> (C -> B))) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32449
in-theory        32449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (E -> D))) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32449.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (E -> D))) or F)), M:tm-338, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32450
in-theory        32450
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and ((E -> (F -> (E and F))) and ((A or (B -> (C -> B))) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32450.        (((A or (B -> (C -> B))) or D) and ((E -> (F -> (E and F))) and ((A or (B -> (C -> B))) or D))), M:tm-327, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32451
in-theory        32451
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and (((E and F) -> F) and ((A or (B -> (C -> B))) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32451.        (((A or (B -> (C -> B))) or D) and (((E and F) -> F) and ((A or (B -> (C -> B))) or D))), M:tm-326, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32452
in-theory        32452
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and (((E and F) -> E) and ((A or (B -> (C -> B))) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32452.        (((A or (B -> (C -> B))) or D) and (((E and F) -> E) and ((A or (B -> (C -> B))) or D))), M:tm-325, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32453
in-theory        32453
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (C -> B))) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32453.        (((A or (B -> (C -> B))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (C -> B))) or D))), M:tm-324, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32454
in-theory        32454
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and ((E -> (F -> E)) and ((A or (B -> (C -> B))) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32454.        (((A or (B -> (C -> B))) or D) and ((E -> (F -> E)) and ((A or (B -> (C -> B))) or D))), M:tm-323, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32455
in-theory        32455
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32455.        (((A or (B -> (C -> B))) or D) and ((E and F) -> F)), M:tm-322, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32456
in-theory        32456
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32456.        (((A or (B -> (C -> B))) or D) and ((E and F) -> E)), M:tm-320, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32457
in-theory        32457
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32457.        (((A or (B -> (C -> B))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32458
in-theory        32458
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32458.        (((A or (B -> (C -> B))) or D) and (E -> (F -> E))), M:tm-315, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32459
in-theory        32459
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and (E or ((A or (B -> (C -> B))) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32459.        (((A or (B -> (C -> B))) or D) and (E or ((A or (B -> (C -> B))) or D))), M:tm-311, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32460
in-theory        32460
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and (((A or (B -> (C -> B))) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32460.        (((A or (B -> (C -> B))) or D) and (((A or (B -> (C -> B))) or D) or E)), M:tm-310, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32461
in-theory        32461
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and (E -> (((A or (B -> (C -> B))) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32461.        (((A or (B -> (C -> B))) or D) and (E -> (((A or (B -> (C -> B))) or D) and E))), M:tm-309, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32462
in-theory        32462
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and (E -> ((A or (B -> (C -> B))) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32462.        (((A or (B -> (C -> B))) or D) and (E -> ((A or (B -> (C -> B))) or D))), M:tm-305, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32463
in-theory        32463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (F -> E))) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32463.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (F -> E))) or G)), M:tm-303, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32464
in-theory        32464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32464.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (F -> E))) or G)), M:tm-270, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32465
in-theory        32465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32465.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (F -> E))) or G)), M:tm-239, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32466
in-theory        32466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (G -> F))) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32466.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (G -> F))) or H)), M:tm-210, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32467
in-theory        32467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32467.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (F -> E))) or G)), M:tm-183, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32468
in-theory        32468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32468.        ((A -> ((B and C) -> C)) and ((D or (E -> (F -> E))) or G)), M:tm-157, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32469
in-theory        32469
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (F -> E))) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32469.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (F -> E))) or G)), M:tm-147, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32470
in-theory        32470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32470.        ((A -> ((B and C) -> B)) and ((D or (E -> (F -> E))) or G)), M:tm-134, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32471
in-theory        32471
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (F -> E))) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32471.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (F -> E))) or G)), M:tm-125, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32472
in-theory        32472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (G -> F))) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32472.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (G -> F))) or H)), M:tm-113, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32473
in-theory        32473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (F -> E))) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32473.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (F -> E))) or G)), M:tm-105, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32474
in-theory        32474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (E -> D))) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32474.        (((A -> B) -> (A -> A)) and ((C or (D -> (E -> D))) or F)), M:tm-95, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32475
in-theory        32475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32475.        ((A -> (B -> (C -> B))) and ((D or (E -> (F -> E))) or G)), M:tm-83, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32476
in-theory        32476
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (D -> C))) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32476.        (((not (not A)) -> A) and ((B or (C -> (D -> C))) or E)), M:tm-76, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32477
in-theory        32477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (E -> D))) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-7 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32477.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (E -> D))) or F)), M:tm-69, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32478
in-theory        32478
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (F -> E))) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32478.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (F -> E))) or G)), M:tm-54, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32479
in-theory        32479
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (E -> D))) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32479.        ((A -> (B or A)) and ((C or (D -> (E -> D))) or F)), M:tm-42, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32480
in-theory        32480
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (E -> D))) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32480.        ((A -> (A or B)) and ((C or (D -> (E -> D))) or F)), M:tm-32, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32481
in-theory        32481
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (E -> D))) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32481.        ((A -> (B -> (A and B))) and ((C or (D -> (E -> D))) or F)), M:tm-23, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32482
in-theory        32482
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (E -> D))) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32482.        (((A and B) -> B) and ((C or (D -> (E -> D))) or F)), M:tm-22, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32483
in-theory        32483
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (E -> D))) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32483.        (((A and B) -> A) and ((C or (D -> (E -> D))) or F)), M:tm-21, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32484
in-theory        32484
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (F -> E))) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32484.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (F -> E))) or G)), M:tm-20, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32485
in-theory        32485
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (E -> D))) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32485.        ((A -> (B -> A)) and ((C or (D -> (E -> D))) or F)), M:tm-19, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32486
in-theory        32486
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B or (C -> (D -> C))) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-7 tm-6 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32486.        (A or ((B or (C -> (D -> C))) or E)), M:tm-7, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32487
in-theory        32487
times-derived    2
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-6 tm-7 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32487.        (((A or (B -> (C -> B))) or D) or E), M:tm-6, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32488
in-theory        32488
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (D -> C))) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32488.        (A -> (((B or (C -> (D -> C))) or E) and A)), M:tm-5, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32489
in-theory        32489
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (D -> C))) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-1 tm-6 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32489.        (A -> ((B or (C -> (D -> C))) or E)), M:tm-1, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32490
in-theory        32490
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-480 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32490.        ((A or (B -> (C -> B))) and (D -> (E or D))), M:tm-480, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-32491
in-theory        32491
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-32491.        ((A or (B -> (C -> B))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-480, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-32492
in-theory        32492
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-480 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-32492.        ((A or (B -> (C -> B))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-480, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-32493
in-theory        32493
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-480 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-32493.        ((A or (B -> (C -> B))) and ((not (not D)) -> D)), M:tm-480, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-32494
in-theory        32494
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-480 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32494.        ((A or (B -> (C -> B))) and (D -> (E -> (F -> E)))), M:tm-480, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-32495
in-theory        32495
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-480 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-32495.        ((A or (B -> (C -> B))) and ((D -> E) -> (D -> D))), M:tm-480, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-32496
in-theory        32496
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-480 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-32496.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-480, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-32497
in-theory        32497
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32497.        ((A or (B -> (C -> B))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-480, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-32498
in-theory        32498
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-480 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-32498.        ((A or (B -> (C -> B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-480, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-32499
in-theory        32499
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-480 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32499.        ((A or (B -> (C -> B))) and (D -> ((E and F) -> E))), M:tm-480, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-32500
in-theory        32500
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-480 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-32500.        ((A or (B -> (C -> B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-480, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-32501
in-theory        32501
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-480 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32501.        ((A or (B -> (C -> B))) and (D -> ((E and F) -> F))), M:tm-480, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-32502
in-theory        32502
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-480 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32502.        ((A or (B -> (C -> B))) and (D -> ((E -> (F -> E)) and D))), M:tm-480, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-32503
in-theory        32503
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-480 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32503.        ((A or (B -> (C -> B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-480, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-32504
in-theory        32504
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-480 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32504.        ((A or (B -> (C -> B))) and (D -> (((E and F) -> E) and D))), M:tm-480, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-32505
in-theory        32505
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-480 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32505.        ((A or (B -> (C -> B))) and (D -> (((E and F) -> F) and D))), M:tm-480, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-32506
in-theory        32506
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32506.        ((A or (B -> (C -> B))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-480, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-32507
in-theory        32507
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-480 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-32507.        ((A or (B -> (C -> B))) and ((D -> E) -> (D -> (D and E)))), M:tm-480, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-32508
in-theory        32508
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32508.        ((A or (B -> (C -> B))) and (D -> (E -> (F -> (E and F))))), M:tm-480, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-32509
in-theory        32509
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-480 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32509.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) or F)), M:tm-480, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-32510
in-theory        32510
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-480 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32510.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-480, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-32511
in-theory        32511
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-480 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32511.        ((A or (B -> (C -> B))) and (((D and E) -> D) or F)), M:tm-480, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-32512
in-theory        32512
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-480 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32512.        ((A or (B -> (C -> B))) and (((D and E) -> E) or F)), M:tm-480, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-32513
in-theory        32513
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-480 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32513.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) or F)), M:tm-480, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-32514
in-theory        32514
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-480 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-32514.        ((A or (B -> (C -> B))) and ((D -> (D or E)) or F)), M:tm-480, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-32515
in-theory        32515
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-480 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-32515.        ((A or (B -> (C -> B))) and (D -> ((E -> (E or F)) and D))), M:tm-480, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-32516
in-theory        32516
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-480 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-32516.        ((A or (B -> (C -> B))) and (D -> (E -> (E or F)))), M:tm-480, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-32517
in-theory        32517
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-480 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32517.        ((A or (B -> (C -> B))) and (D or (E -> (F -> E)))), M:tm-480, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-32518
in-theory        32518
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32518.        ((A or (B -> (C -> B))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-480, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-32519
in-theory        32519
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-480 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32519.        ((A or (B -> (C -> B))) and (D or ((E and F) -> E))), M:tm-480, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-32520
in-theory        32520
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-480 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32520.        ((A or (B -> (C -> B))) and (D or ((E and F) -> F))), M:tm-480, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-32521
in-theory        32521
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32521.        ((A or (B -> (C -> B))) and (D or (E -> (F -> (E and F))))), M:tm-480, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-32522
in-theory        32522
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-480 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-32522.        ((A or (B -> (C -> B))) and (D or (E -> (E or F)))), M:tm-480, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-32523
in-theory        32523
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-480 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32523.        ((A or (B -> (C -> B))) and (D or (E -> (F or E)))), M:tm-480, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-32524
in-theory        32524
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-480 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32524.        ((A or (B -> (C -> B))) and ((D -> (E or D)) or F)), M:tm-480, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-32525
in-theory        32525
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-480 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32525.        ((A or (B -> (C -> B))) and (D -> ((E -> (F or E)) and D))), M:tm-480, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-32526
in-theory        32526
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-480 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32526.        ((A or (B -> (C -> B))) and (D -> (E -> (F or E)))), M:tm-480, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-32527
in-theory        32527
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-480 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32527.        ((A or (B -> (C -> B))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-480, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-32528
in-theory        32528
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-480 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32528.        ((A or (B -> (C -> B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-480, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-32529
in-theory        32529
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-480 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32529.        ((A or (B -> (C -> B))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-480, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-32530
in-theory        32530
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-480 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-32530.        ((A or (B -> (C -> B))) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-480, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-32531
in-theory        32531
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-480 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-32531.        ((A or (B -> (C -> B))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-480, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-32532
in-theory        32532
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-480 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32532.        ((A or (B -> (C -> B))) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-480, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-32533
in-theory        32533
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-480 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-32533.        ((A or (B -> (C -> B))) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-480, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-32534
in-theory        32534
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-480 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-32534.        ((A or (B -> (C -> B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-480, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-32535
in-theory        32535
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-32535.        ((A or (B -> (C -> B))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-480, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-32536
in-theory        32536
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-480 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-32536.        ((A or (B -> (C -> B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-480, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-32537
in-theory        32537
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-480 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-32537.        ((A or (B -> (C -> B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-480, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-32538
in-theory        32538
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-480 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-32538.        ((A or (B -> (C -> B))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-480, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-32539
in-theory        32539
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-32539.        ((A or (B -> (C -> B))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-480, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-32540
in-theory        32540
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-480 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32540.        ((A or (B -> (C -> B))) and ((D -> (not (E -> D))) -> (not D))), M:tm-480, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-32541
in-theory        32541
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32541.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-480, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-32542
in-theory        32542
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-480 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32542.        ((A or (B -> (C -> B))) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-480, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-32543
in-theory        32543
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-480 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-32543.        ((A or (B -> (C -> B))) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-480, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-32544
in-theory        32544
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-32544.        ((A or (B -> (C -> B))) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-480, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-32545
in-theory        32545
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-480 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32545.        ((A or (B -> (C -> B))) and ((D -> (not (D or E))) -> (not D))), M:tm-480, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-32546
in-theory        32546
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-480 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-32546.        ((A or (B -> (C -> B))) and ((D -> (not (E or D))) -> (not D))), M:tm-480, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-32547
in-theory        32547
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-480 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-32547.        ((A or (B -> (C -> B))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-480, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-32548
in-theory        32548
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-480 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-32548.        ((A or (B -> (C -> B))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-480, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-32549
in-theory        32549
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-480 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-32549.        ((A or (B -> (C -> B))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-480, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-32550
in-theory        32550
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-32550.        ((A or (B -> (C -> B))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-480, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-32551
in-theory        32551
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-480 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-32551.        ((A or (B -> (C -> B))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-480, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-32552
in-theory        32552
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-480 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-32552.        ((A or (B -> (C -> B))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-480, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-32553
in-theory        32553
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-480 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-32553.        ((A or (B -> (C -> B))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-480, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-32554
in-theory        32554
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-32554.        ((A or (B -> (C -> B))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-480, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-32555
in-theory        32555
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-480 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-32555.        ((A or (B -> (C -> B))) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-480, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-32556
in-theory        32556
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-480 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-32556.        ((A or (B -> (C -> B))) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-480, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-32557
in-theory        32557
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-480 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-32557.        ((A or (B -> (C -> B))) and (D or ((not (not E)) -> E))), M:tm-480, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-32558
in-theory        32558
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-480 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-32558.        ((A or (B -> (C -> B))) and (((not (not D)) -> D) or E)), M:tm-480, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-32559
in-theory        32559
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-480 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-32559.        ((A or (B -> (C -> B))) and (D -> (((not (not E)) -> E) and D))), M:tm-480, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-32560
in-theory        32560
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-480 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-32560.        ((A or (B -> (C -> B))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-480, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-32561
in-theory        32561
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-480 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-32561.        ((A or (B -> (C -> B))) and (D -> ((not (not E)) -> E))), M:tm-480, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-32562
in-theory        32562
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-32562.        ((A or (B -> (C -> B))) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-480, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-32563
in-theory        32563
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-480 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-32563.        ((A or (B -> (C -> B))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-480, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-32564
in-theory        32564
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-32564.        ((A or (B -> (C -> B))) and (D or (E -> (F -> (G -> F))))), M:tm-480, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32565
in-theory        32565
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-32565.        ((A or (B -> (C -> B))) and ((D -> (E -> (F -> E))) or G)), M:tm-480, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32566
in-theory        32566
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-32566.        ((A or (B -> (C -> B))) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-480, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32567
in-theory        32567
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-480 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-32567.        ((A or (B -> (C -> B))) and ((D -> E) -> (D -> (F -> E)))), M:tm-480, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-32568
in-theory        32568
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-32568.        ((A or (B -> (C -> B))) and (D -> (E -> (F -> (G -> F))))), M:tm-480, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32569
in-theory        32569
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-480 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32569.        ((A or (B -> (C -> B))) and (D -> D)), M:tm-480, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-32570
in-theory        32570
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32570.        ((A or (B -> (C -> B))) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-480, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-32571
in-theory        32571
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-480 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32571.        ((A or (B -> (C -> B))) and ((D and E) -> (D and E))), M:tm-480, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-32572
in-theory        32572
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-480 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-32572.        ((A or (B -> (C -> B))) and ((D -> E) -> (D -> E))), M:tm-480, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-32573
in-theory        32573
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-480 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-32573.        ((A or (B -> (C -> B))) and ((not (not D)) -> (not (not D)))), M:tm-480, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-32574
in-theory        32574
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-480 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-32574.        ((A or (B -> (C -> B))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-480, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-32575
in-theory        32575
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-480 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-32575.        ((A or (B -> (C -> B))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-480, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-32576
in-theory        32576
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-480 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-32576.        ((A or (B -> (C -> B))) and (D or ((E -> F) -> (E -> E)))), M:tm-480, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-32577
in-theory        32577
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-480 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-32577.        ((A or (B -> (C -> B))) and (((D -> E) -> (D -> D)) or F)), M:tm-480, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-32578
in-theory        32578
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-32578.        ((A or (B -> (C -> B))) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-480, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-32579
in-theory        32579
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-32579.        ((A or (B -> (C -> B))) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-480, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-32580
in-theory        32580
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-480 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-32580.        ((A or (B -> (C -> B))) and (D -> ((E -> F) -> (E -> E)))), M:tm-480, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-32581
in-theory        32581
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-32581.        ((A or (B -> (C -> B))) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-480, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-32582
in-theory        32582
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-480 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-32582.        ((A or (B -> (C -> B))) and ((D -> (D -> E)) -> (D -> E))), M:tm-480, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-32583
in-theory        32583
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-480 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-32583.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-480, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-32584
in-theory        32584
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-480 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-32584.        ((A or (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-480, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-32585
in-theory        32585
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-480 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-32585.        ((A or (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-480, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-32586
in-theory        32586
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-32586.        ((A or (B -> (C -> B))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-480, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-32587
in-theory        32587
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-480 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-32587.        ((A or (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-480, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-32588
in-theory        32588
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-480 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-32588.        ((A or (B -> (C -> B))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-480, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-32589
in-theory        32589
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-480 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-32589.        ((A or (B -> (C -> B))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-480, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-32590
in-theory        32590
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-32590.        ((A or (B -> (C -> B))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-480, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-32591
in-theory        32591
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-480 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-32591.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-480, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-32592
in-theory        32592
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-480 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-32592.        ((A or (B -> (C -> B))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-480, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-32593
in-theory        32593
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-480 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-32593.        ((A or (B -> (C -> B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-480, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-32594
in-theory        32594
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-480 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-32594.        ((A or (B -> (C -> B))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-480, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-32595
in-theory        32595
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-480 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-32595.        ((A or (B -> (C -> B))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-480, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-32596
in-theory        32596
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-480 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-32596.        ((A or (B -> (C -> B))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-480, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-32597
in-theory        32597
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-480 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-32597.        ((A or (B -> (C -> B))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-480, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-32598
in-theory        32598
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-480 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-32598.        ((A or (B -> (C -> B))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-480, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-32599
in-theory        32599
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-480 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-32599.        ((A or (B -> (C -> B))) and (((D -> E) and D) -> E)), M:tm-480, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-32600
in-theory        32600
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-480 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-32600.        ((A or (B -> (C -> B))) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-480, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-32601
in-theory        32601
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-480 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-32601.        ((A or (B -> (C -> B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-480, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-32602
in-theory        32602
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-480 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-32602.        ((A or (B -> (C -> B))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-480, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-32603
in-theory        32603
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-480 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-32603.        ((A or (B -> (C -> B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-480, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-32604
in-theory        32604
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-480 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-32604.        ((A or (B -> (C -> B))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-480, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-32605
in-theory        32605
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-480 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-32605.        ((A or (B -> (C -> B))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-480, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-32606
in-theory        32606
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-480 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-32606.        ((A or (B -> (C -> B))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-480, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-32607
in-theory        32607
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-480 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-32607.        ((A or (B -> (C -> B))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-480, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-32608
in-theory        32608
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-480 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-32608.        ((A or (B -> (C -> B))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-480, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-32609
in-theory        32609
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-480 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-32609.        ((A or (B -> (C -> B))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-480, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-32610
in-theory        32610
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-480 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-32610.        ((A or (B -> (C -> B))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-480, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-32611
in-theory        32611
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-480 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-32611.        ((A or (B -> (C -> B))) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-480, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-32612
in-theory        32612
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-480 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-32612.        ((A or (B -> (C -> B))) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-480, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-32613
in-theory        32613
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-32613.        ((A or (B -> (C -> B))) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-480, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-32614
in-theory        32614
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-480 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-32614.        ((A or (B -> (C -> B))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-480, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-32615
in-theory        32615
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-480 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-32615.        ((A or (B -> (C -> B))) and (D or (E -> ((F and G) -> F)))), M:tm-480, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-32616
in-theory        32616
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-32616.        ((A or (B -> (C -> B))) and ((D -> ((E and F) -> E)) or G)), M:tm-480, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-32617
in-theory        32617
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-32617.        ((A or (B -> (C -> B))) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-480, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-32618
in-theory        32618
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-480 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-32618.        ((A or (B -> (C -> B))) and ((D -> (E and F)) -> (D -> E))), M:tm-480, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-32619
in-theory        32619
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-480 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-32619.        ((A or (B -> (C -> B))) and (D -> (E -> ((F and G) -> F)))), M:tm-480, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-32620
in-theory        32620
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-480 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-32620.        ((A or (B -> (C -> B))) and ((D and (D -> E)) -> E)), M:tm-480, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-32621
in-theory        32621
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-480 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-32621.        ((A or (B -> (C -> B))) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-480, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-32622
in-theory        32622
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-480 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-32622.        ((A or (B -> (C -> B))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-480, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-32623
in-theory        32623
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-480 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-32623.        ((A or (B -> (C -> B))) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-480, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-32624
in-theory        32624
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-480 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-32624.        ((A or (B -> (C -> B))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-480, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-32625
in-theory        32625
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-480 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-32625.        ((A or (B -> (C -> B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-480, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-32626
in-theory        32626
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-480 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-32626.        ((A or (B -> (C -> B))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-480, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-32627
in-theory        32627
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-480 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-32627.        ((A or (B -> (C -> B))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-480, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-32628
in-theory        32628
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-480 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-32628.        ((A or (B -> (C -> B))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-480, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-32629
in-theory        32629
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-480 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-32629.        ((A or (B -> (C -> B))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-480, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-32630
in-theory        32630
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-480 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-32630.        ((A or (B -> (C -> B))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-480, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-32631
in-theory        32631
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-480 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-32631.        ((A or (B -> (C -> B))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-480, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-32632
in-theory        32632
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-480 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-32632.        ((A or (B -> (C -> B))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-480, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-32633
in-theory        32633
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-480 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-32633.        ((A or (B -> (C -> B))) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-480, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-32634
in-theory        32634
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-480 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-32634.        ((A or (B -> (C -> B))) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-480, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-32635
in-theory        32635
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-480 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-32635.        ((A or (B -> (C -> B))) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-480, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-32636
in-theory        32636
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-32636.        ((A or (B -> (C -> B))) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-480, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-32637
in-theory        32637
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-480 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-32637.        ((A or (B -> (C -> B))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-480, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-32638
in-theory        32638
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-480 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-32638.        ((A or (B -> (C -> B))) and (D or (E -> ((F and G) -> G)))), M:tm-480, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-32639
in-theory        32639
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-32639.        ((A or (B -> (C -> B))) and ((D -> ((E and F) -> F)) or G)), M:tm-480, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-32640
in-theory        32640
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-32640.        ((A or (B -> (C -> B))) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-480, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-32641
in-theory        32641
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-480 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-32641.        ((A or (B -> (C -> B))) and ((D -> (E and F)) -> (D -> F))), M:tm-480, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-32642
in-theory        32642
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-480 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-32642.        ((A or (B -> (C -> B))) and (D -> (E -> ((F and G) -> G)))), M:tm-480, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-32643
in-theory        32643
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32643.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-480, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-32644
in-theory        32644
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32644.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-480, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-32645
in-theory        32645
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32645.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-480, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-32646
in-theory        32646
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-480 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32646.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-480, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-32647
in-theory        32647
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32647.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-480, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-32648
in-theory        32648
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-480 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-32648.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-480, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32649
in-theory        32649
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32649.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-480, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-32650
in-theory        32650
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-32650.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-480, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-32651
in-theory        32651
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-480 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-32651.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-480, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-32652
in-theory        32652
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-32652.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-480, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-32653
in-theory        32653
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-32653.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-480, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32654
in-theory        32654
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-32654.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-480, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-32655
in-theory        32655
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-480 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-32655.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-480, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-32656
in-theory        32656
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-32656.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-480, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-32657
in-theory        32657
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-480 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-32657.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-480, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-32658
in-theory        32658
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-480 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-32658.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-480, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-32659
in-theory        32659
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-480 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-32659.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-480, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-32660
in-theory        32660
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-480 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-32660.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-480, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-32661
in-theory        32661
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-32661.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-480, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-32662
in-theory        32662
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-32662.        ((A or (B -> (C -> B))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-480, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-32663
in-theory        32663
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-480 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-32663.        ((A or (B -> (C -> B))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-480, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-32664
in-theory        32664
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-480 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-32664.        ((A or (B -> (C -> B))) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-480, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-32665
in-theory        32665
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-480 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-32665.        ((A or (B -> (C -> B))) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-480, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-32666
in-theory        32666
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-32666.        ((A or (B -> (C -> B))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-480, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-32667
in-theory        32667
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-480 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-32667.        ((A or (B -> (C -> B))) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-480, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-32668
in-theory        32668
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-480 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32668.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-480, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-32669
in-theory        32669
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32669.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-480, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-32670
in-theory        32670
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-480 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32670.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-480, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-32671
in-theory        32671
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-480 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32671.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-480, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-32672
in-theory        32672
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32672.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-480, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-32673
in-theory        32673
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-32673.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-480, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-32674
in-theory        32674
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-480 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32674.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-480, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-32675
in-theory        32675
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-32675.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-480, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-32676
in-theory        32676
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-480 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-32676.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-480, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-32677
in-theory        32677
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-480 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-32677.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-480, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-32678
in-theory        32678
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-32678.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-480, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32679
in-theory        32679
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-480 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-32679.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-480, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-32680
in-theory        32680
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-480 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-32680.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-480, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-32681
in-theory        32681
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-480 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-32681.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-480, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-32682
in-theory        32682
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-480 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-32682.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-480, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-32683
in-theory        32683
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-480 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-32683.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-480, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-32684
in-theory        32684
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-480 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-32684.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-480, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-32685
in-theory        32685
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-480 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-32685.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-480, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-32686
in-theory        32686
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-480 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-32686.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-480, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-32687
in-theory        32687
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-480 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-32687.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-480, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-32688
in-theory        32688
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-480 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-32688.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-480, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-32689
in-theory        32689
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-480 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-32689.        ((A or (B -> (C -> B))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-480, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-32690
in-theory        32690
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-480 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-32690.        ((A or (B -> (C -> B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-480, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-32691
in-theory        32691
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-480 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-32691.        ((A or (B -> (C -> B))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-480, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-32692
in-theory        32692
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-480 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-32692.        ((A or (B -> (C -> B))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-480, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-32693
in-theory        32693
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-480 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-32693.        ((A or (B -> (C -> B))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-480, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-32694
in-theory        32694
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-480 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-32694.        ((A or (B -> (C -> B))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-480, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-32695
in-theory        32695
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32695.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-480, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-32696
in-theory        32696
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32696.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-480, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-32697
in-theory        32697
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32697.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F and G) -> F))), M:tm-480, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-32698
in-theory        32698
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-480 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32698.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F and G) -> G))), M:tm-480, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-32699
in-theory        32699
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32699.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-480, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-32700
in-theory        32700
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-480 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-32700.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (F or G)))), M:tm-480, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32701
in-theory        32701
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32701.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (G or F)))), M:tm-480, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-32702
in-theory        32702
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-32702.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-480, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-32703
in-theory        32703
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-480 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-32703.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-480, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-32704
in-theory        32704
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-32704.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-480, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-32705
in-theory        32705
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-32705.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-480, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32706
in-theory        32706
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-32706.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-480, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-32707
in-theory        32707
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-480 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-32707.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-480, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-32708
in-theory        32708
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-32708.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-480, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-32709
in-theory        32709
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-480 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-32709.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-480, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-32710
in-theory        32710
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-480 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-32710.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-480, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-32711
in-theory        32711
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-480 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-32711.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-480, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-32712
in-theory        32712
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-480 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-32712.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-480, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-32713
in-theory        32713
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-32713.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-480, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-32714
in-theory        32714
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-480 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-32714.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-480, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-32715
in-theory        32715
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-32715.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-480, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-32716
in-theory        32716
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-480 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-32716.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-480, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-32717
in-theory        32717
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-32717.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-480, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-32718
in-theory        32718
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-32718.        ((A or (B -> (C -> B))) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-480, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-32719
in-theory        32719
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-480 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-32719.        ((A or (B -> (C -> B))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-480, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-32720
in-theory        32720
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-480 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-32720.        ((A or (B -> (C -> B))) and (D or (E -> (((F and G) -> F) and E)))), M:tm-480, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-32721
in-theory        32721
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-480 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-32721.        ((A or (B -> (C -> B))) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-480, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-32722
in-theory        32722
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-32722.        ((A or (B -> (C -> B))) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-480, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-32723
in-theory        32723
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-480 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-32723.        ((A or (B -> (C -> B))) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-480, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-32724
in-theory        32724
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32724.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-480, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-32725
in-theory        32725
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32725.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-480, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-32726
in-theory        32726
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32726.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F and G) -> F))), M:tm-480, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-32727
in-theory        32727
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-480 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32727.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F and G) -> G))), M:tm-480, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-32728
in-theory        32728
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32728.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-480, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-32729
in-theory        32729
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-480 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-32729.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (F or G)))), M:tm-480, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32730
in-theory        32730
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32730.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (G or F)))), M:tm-480, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-32731
in-theory        32731
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-32731.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-480, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-32732
in-theory        32732
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-480 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-32732.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-480, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-32733
in-theory        32733
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-32733.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-480, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-32734
in-theory        32734
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-32734.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-480, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32735
in-theory        32735
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-32735.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-480, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-32736
in-theory        32736
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-480 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-32736.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-480, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-32737
in-theory        32737
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-32737.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-480, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-32738
in-theory        32738
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-480 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-32738.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-480, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-32739
in-theory        32739
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-480 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-32739.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-480, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-32740
in-theory        32740
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-480 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-32740.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-480, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-32741
in-theory        32741
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-480 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-32741.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-480, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-32742
in-theory        32742
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-32742.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-480, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-32743
in-theory        32743
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-480 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-32743.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-480, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-32744
in-theory        32744
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-32744.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-480, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-32745
in-theory        32745
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-32745.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-480, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-32746
in-theory        32746
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-32746.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-480, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-32747
in-theory        32747
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-480 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-32747.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-480, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-32748
in-theory        32748
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-32748.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-480, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-32749
in-theory        32749
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-32749.        ((A or (B -> (C -> B))) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-480, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-32750
in-theory        32750
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-480 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-32750.        ((A or (B -> (C -> B))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-480, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-32751
in-theory        32751
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-480 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-32751.        ((A or (B -> (C -> B))) and (D or (E -> (((F and G) -> G) and E)))), M:tm-480, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-32752
in-theory        32752
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-480 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-32752.        ((A or (B -> (C -> B))) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-480, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-32753
in-theory        32753
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-32753.        ((A or (B -> (C -> B))) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-480, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-32754
in-theory        32754
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-480 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-32754.        ((A or (B -> (C -> B))) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-480, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-32755
in-theory        32755
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32755.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-480, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-32756
in-theory        32756
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32756.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-480, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-32757
in-theory        32757
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-480 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32757.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-480, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-32758
in-theory        32758
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-480 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32758.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-480, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-32759
in-theory        32759
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32759.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-480, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-32760
in-theory        32760
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-480 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-32760.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-480, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32761
in-theory        32761
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32761.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-480, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-32762
in-theory        32762
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-32762.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-480, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-32763
in-theory        32763
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-32763.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-480, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-32764
in-theory        32764
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-480 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-32764.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-480, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-32765
in-theory        32765
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-32765.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-480, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32766
in-theory        32766
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-32766.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-480, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-32767
in-theory        32767
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-32767.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-480, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-32768
in-theory        32768
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-480 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-32768.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-480, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-32769
in-theory        32769
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-480 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-32769.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-480, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-32770
in-theory        32770
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-480 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-32770.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-480, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-32771
in-theory        32771
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-480 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-32771.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-480, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-32772
in-theory        32772
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-480 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-32772.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-480, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-32773
in-theory        32773
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-480 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-32773.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-480, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-32774
in-theory        32774
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-480 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-32774.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-480, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-32775
in-theory        32775
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-480 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-32775.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-480, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-32776
in-theory        32776
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-480 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-32776.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-480, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-32777
in-theory        32777
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-480 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-32777.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-480, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-32778
in-theory        32778
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-480 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-32778.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-480, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-32779
in-theory        32779
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-480 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-32779.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-480, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-32780
in-theory        32780
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-480 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-32780.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-480, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-32781
in-theory        32781
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-480 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-32781.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-480, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-32782
in-theory        32782
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-480 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-32782.        ((A or (B -> (C -> B))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-480, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-32783
in-theory        32783
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-480 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-32783.        ((A or (B -> (C -> B))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-480, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-32784
in-theory        32784
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-480 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-32784.        ((A or (B -> (C -> B))) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-480, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-32785
in-theory        32785
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-480 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-32785.        ((A or (B -> (C -> B))) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-480, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-32786
in-theory        32786
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-480 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-32786.        ((A or (B -> (C -> B))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-480, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-32787
in-theory        32787
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-480 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-32787.        ((A or (B -> (C -> B))) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-480, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-32788
in-theory        32788
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-480 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32788.        ((A or (B -> (C -> B))) and (D -> (D and (E -> D)))), M:tm-480, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-32789
in-theory        32789
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32789.        ((A or (B -> (C -> B))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-480, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-32790
in-theory        32790
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-480 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32790.        ((A or (B -> (C -> B))) and ((D and E) -> ((D and E) and D))), M:tm-480, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-32791
in-theory        32791
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-480 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-32791.        ((A or (B -> (C -> B))) and ((D and E) -> ((D and E) and E))), M:tm-480, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-32792
in-theory        32792
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-32792.        ((A or (B -> (C -> B))) and (D -> (D and (E -> (D and E))))), M:tm-480, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-32793
in-theory        32793
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-480 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32793.        ((A or (B -> (C -> B))) and (D -> (D and (D or E)))), M:tm-480, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-32794
in-theory        32794
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-480 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-32794.        ((A or (B -> (C -> B))) and (D -> (D and (E or D)))), M:tm-480, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-32795
in-theory        32795
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-480 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-32795.        ((A or (B -> (C -> B))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-480, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-32796
in-theory        32796
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-32796.        ((A or (B -> (C -> B))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-480, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-32797
in-theory        32797
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-480 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-32797.        ((A or (B -> (C -> B))) and ((not (not D)) -> ((not (not D)) and D))), M:tm-480, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-32798
in-theory        32798
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-32798.        ((A or (B -> (C -> B))) and (D -> (D and (E -> (F -> E))))), M:tm-480, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-32799
in-theory        32799
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-480 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-32799.        ((A or (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-480, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-32800
in-theory        32800
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-480 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-32800.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-480, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-32801
in-theory        32801
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-480 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-32801.        ((A or (B -> (C -> B))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-480, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-32802
in-theory        32802
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-480 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-32802.        ((A or (B -> (C -> B))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-480, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-32803
in-theory        32803
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-480 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-32803.        ((A or (B -> (C -> B))) and (D -> (D and ((E and F) -> E)))), M:tm-480, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-32804
in-theory        32804
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-480 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-32804.        ((A or (B -> (C -> B))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-480, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-32805
in-theory        32805
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-480 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-32805.        ((A or (B -> (C -> B))) and (D -> (D and ((E and F) -> F)))), M:tm-480, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-32806
in-theory        32806
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-480 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-32806.        ((A or (B -> (C -> B))) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-480, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-32807
in-theory        32807
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-480 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-32807.        ((A or (B -> (C -> B))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-480, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-32808
in-theory        32808
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-480 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-32808.        ((A or (B -> (C -> B))) and (D -> (D and (((E and F) -> E) and D)))), M:tm-480, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-32809
in-theory        32809
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-480 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-32809.        ((A or (B -> (C -> B))) and (D -> (D and (((E and F) -> F) and D)))), M:tm-480, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-32810
in-theory        32810
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-480 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-32810.        ((A or (B -> (C -> B))) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-480, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-32811
in-theory        32811
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-32811.        ((A or (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-480, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-32812
in-theory        32812
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-480 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-32812.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-480, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-32813
in-theory        32813
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-32813.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-480, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-32814
in-theory        32814
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-32814.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-480, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-32815
in-theory        32815
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-480 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-32815.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-480, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-32816
in-theory        32816
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-32816.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-480, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-32817
in-theory        32817
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-480 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-32817.        ((A or (B -> (C -> B))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-480, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-32818
in-theory        32818
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-480 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-32818.        ((A or (B -> (C -> B))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-480, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-32819
in-theory        32819
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-480 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-32819.        ((A or (B -> (C -> B))) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-480, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-32820
in-theory        32820
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-480 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-32820.        ((A or (B -> (C -> B))) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-480, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-32821
in-theory        32821
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-32821.        ((A or (B -> (C -> B))) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-480, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-32822
in-theory        32822
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-480 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-32822.        ((A or (B -> (C -> B))) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-480, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-32823
in-theory        32823
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-480 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-32823.        ((A or (B -> (C -> B))) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-480, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-32824
in-theory        32824
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-480 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-32824.        ((A or (B -> (C -> B))) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-480, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-32825
in-theory        32825
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-480 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-32825.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-480, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-32826
in-theory        32826
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-480 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-32826.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-480, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-32827
in-theory        32827
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-480 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-32827.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-480, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-32828
in-theory        32828
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-480 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-32828.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-480, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-32829
in-theory        32829
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-480 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-32829.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-480, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-32830
in-theory        32830
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-480 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-32830.        ((A or (B -> (C -> B))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-480, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-32831
in-theory        32831
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-480 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-32831.        ((A or (B -> (C -> B))) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-480, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-32832
in-theory        32832
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-480 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-32832.        ((A or (B -> (C -> B))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-480, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-32833
in-theory        32833
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-32833.        ((A or (B -> (C -> B))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-480, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-32834
in-theory        32834
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-480 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-32834.        ((A or (B -> (C -> B))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-480, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-32835
in-theory        32835
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-480 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-32835.        ((A or (B -> (C -> B))) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-480, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-32836
in-theory        32836
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-480 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-32836.        ((A or (B -> (C -> B))) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-480, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-32837
in-theory        32837
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-32837.        ((A or (B -> (C -> B))) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-480, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-32838
in-theory        32838
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-480 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-32838.        ((A or (B -> (C -> B))) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-480, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-32839
in-theory        32839
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-480 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-32839.        ((A or (B -> (C -> B))) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-480, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-32840
in-theory        32840
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-480 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32840.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-480, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-32841
in-theory        32841
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32841.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-480, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-32842
in-theory        32842
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32842.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-480, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-32843
in-theory        32843
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32843.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-480, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-32844
in-theory        32844
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32844.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-480, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-32845
in-theory        32845
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-480 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32845.        ((A or (B -> (C -> B))) and (D or ((E -> (F -> E)) or G))), M:tm-480, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-32846
in-theory        32846
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32846.        ((A or (B -> (C -> B))) and (((D -> (E -> D)) or F) or G)), M:tm-480, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-32847
in-theory        32847
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32847.        ((A or (B -> (C -> B))) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-480, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-32848
in-theory        32848
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-480 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32848.        ((A or (B -> (C -> B))) and (D -> ((E -> (F -> E)) or G))), M:tm-480, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-32849
in-theory        32849
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-480 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32849.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-480, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-32850
in-theory        32850
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32850.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-480, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-32851
in-theory        32851
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32851.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-480, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-32852
in-theory        32852
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-480 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32852.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-480, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-32853
in-theory        32853
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32853.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-480, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-32854
in-theory        32854
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-480 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32854.        ((A or (B -> (C -> B))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-480, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-32855
in-theory        32855
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-480 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32855.        ((A or (B -> (C -> B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-480, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-32856
in-theory        32856
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-480 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32856.        ((A or (B -> (C -> B))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-480, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-32857
in-theory        32857
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-480 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32857.        ((A or (B -> (C -> B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-480, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-32858
in-theory        32858
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-480 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32858.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-480, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-32859
in-theory        32859
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32859.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-480, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-32860
in-theory        32860
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32860.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-480, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-32861
in-theory        32861
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32861.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-480, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-32862
in-theory        32862
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32862.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-480, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-32863
in-theory        32863
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-480 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32863.        ((A or (B -> (C -> B))) and (D or (((E and F) -> E) or G))), M:tm-480, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-32864
in-theory        32864
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32864.        ((A or (B -> (C -> B))) and ((((D and E) -> D) or F) or G)), M:tm-480, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-32865
in-theory        32865
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32865.        ((A or (B -> (C -> B))) and (D -> ((((E and F) -> E) or G) and D))), M:tm-480, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-32866
in-theory        32866
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-480 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32866.        ((A or (B -> (C -> B))) and (D -> (((E and F) -> E) or G))), M:tm-480, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-32867
in-theory        32867
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-480 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32867.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-480, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-32868
in-theory        32868
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32868.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-480, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-32869
in-theory        32869
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32869.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-480, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-32870
in-theory        32870
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32870.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-480, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-32871
in-theory        32871
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32871.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-480, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-32872
in-theory        32872
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-480 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32872.        ((A or (B -> (C -> B))) and (D or (((E and F) -> F) or G))), M:tm-480, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-32873
in-theory        32873
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32873.        ((A or (B -> (C -> B))) and ((((D and E) -> E) or F) or G)), M:tm-480, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-32874
in-theory        32874
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32874.        ((A or (B -> (C -> B))) and (D -> ((((E and F) -> F) or G) and D))), M:tm-480, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-32875
in-theory        32875
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-480 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32875.        ((A or (B -> (C -> B))) and (D -> (((E and F) -> F) or G))), M:tm-480, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-32876
in-theory        32876
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-480 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32876.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-480, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-32877
in-theory        32877
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-480 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32877.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-480, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-32878
in-theory        32878
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-480 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32878.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-480, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-32879
in-theory        32879
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-480 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32879.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-480, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-32880
in-theory        32880
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-480 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32880.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-480, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-32881
in-theory        32881
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-480 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32881.        ((A or (B -> (C -> B))) and (D or ((E -> (F -> (E and F))) or G))), M:tm-480, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-32882
in-theory        32882
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-480 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32882.        ((A or (B -> (C -> B))) and (((D -> (E -> (D and E))) or F) or G)), M:tm-480, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-32883
in-theory        32883
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32883.        ((A or (B -> (C -> B))) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-480, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-32884
in-theory        32884
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-480 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32884.        ((A or (B -> (C -> B))) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-480, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-32885
in-theory        32885
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-480 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32885.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-480, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-32886
in-theory        32886
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32886.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-480, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-32887
in-theory        32887
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32887.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-480, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-32888
in-theory        32888
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32888.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-480, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-32889
in-theory        32889
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32889.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-480, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-32890
in-theory        32890
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-480 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32890.        ((A or (B -> (C -> B))) and (D or ((E -> (E or F)) or G))), M:tm-480, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-32891
in-theory        32891
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32891.        ((A or (B -> (C -> B))) and (((D -> (D or E)) or F) or G)), M:tm-480, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-32892
in-theory        32892
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32892.        ((A or (B -> (C -> B))) and (D -> (((E -> (E or F)) or G) and D))), M:tm-480, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-32893
in-theory        32893
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-480 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32893.        ((A or (B -> (C -> B))) and (D -> ((E -> (E or F)) or G))), M:tm-480, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-32894
in-theory        32894
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32894.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-480, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-32895
in-theory        32895
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32895.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-480, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-32896
in-theory        32896
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32896.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-480, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-32897
in-theory        32897
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-480 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32897.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-480, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-32898
in-theory        32898
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32898.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-480, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-32899
in-theory        32899
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-480 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-32899.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-480, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-32900
in-theory        32900
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32900.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-480, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-32901
in-theory        32901
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-32901.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-480, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-32902
in-theory        32902
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-480 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-32902.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-480, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-32903
in-theory        32903
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-32903.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-480, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-32904
in-theory        32904
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-32904.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-480, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32905
in-theory        32905
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-32905.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-480, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-32906
in-theory        32906
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-480 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-32906.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-480, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-32907
in-theory        32907
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-32907.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-480, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-32908
in-theory        32908
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-480 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-32908.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-480, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-32909
in-theory        32909
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-480 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-32909.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-480, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-32910
in-theory        32910
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-480 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-32910.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-480, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-32911
in-theory        32911
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-480 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-32911.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-480, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-32912
in-theory        32912
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-32912.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-480, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-32913
in-theory        32913
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-480 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-32913.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-480, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-32914
in-theory        32914
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-32914.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-480, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-32915
in-theory        32915
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-32915.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-480, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-32916
in-theory        32916
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-480 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-32916.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-480, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-32917
in-theory        32917
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-32917.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-480, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-32918
in-theory        32918
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-480 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-32918.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-480, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-32919
in-theory        32919
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32919.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-480, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-32920
in-theory        32920
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32920.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-480, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-32921
in-theory        32921
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32921.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-480, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-32922
in-theory        32922
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32922.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-480, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-32923
in-theory        32923
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-480 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32923.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-480, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-32924
in-theory        32924
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32924.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-480, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-32925
in-theory        32925
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-32925.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-480, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-32926
in-theory        32926
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-480 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-32926.        ((A or (B -> (C -> B))) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-480, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-32927
in-theory        32927
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-480 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-32927.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-480, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-32928
in-theory        32928
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-32928.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-480, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-32929
in-theory        32929
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-32929.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-480, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-32930
in-theory        32930
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-480 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-32930.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-480, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-32931
in-theory        32931
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-32931.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-480, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-32932
in-theory        32932
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-32932.        ((A or (B -> (C -> B))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-480, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-32933
in-theory        32933
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-480 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-32933.        ((A or (B -> (C -> B))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-480, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-32934
in-theory        32934
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-480 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-32934.        ((A or (B -> (C -> B))) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-480, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-32935
in-theory        32935
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-480 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-32935.        ((A or (B -> (C -> B))) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-480, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-32936
in-theory        32936
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-32936.        ((A or (B -> (C -> B))) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-480, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-32937
in-theory        32937
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-480 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-32937.        ((A or (B -> (C -> B))) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-480, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-32938
in-theory        32938
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32938.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-480, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-32939
in-theory        32939
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32939.        ((A or (B -> (C -> B))) and (D -> (D and (E -> (E or F))))), M:tm-480, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-32940
in-theory        32940
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32940.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-480, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-32941
in-theory        32941
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32941.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-480, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-32942
in-theory        32942
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32942.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-480, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-32943
in-theory        32943
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32943.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-480, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-32944
in-theory        32944
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32944.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-480, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-32945
in-theory        32945
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-480 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-32945.        ((A or (B -> (C -> B))) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-480, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-32946
in-theory        32946
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-480 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-32946.        ((A or (B -> (C -> B))) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-480, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-32947
in-theory        32947
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-32947.        ((A or (B -> (C -> B))) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-480, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-32948
in-theory        32948
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32948.        ((A or (B -> (C -> B))) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-480, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-32949
in-theory        32949
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-480 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32949.        ((A or (B -> (C -> B))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-480, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-32950
in-theory        32950
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32950.        ((A or (B -> (C -> B))) and (D or (E -> (F -> (F or G))))), M:tm-480, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32951
in-theory        32951
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32951.        ((A or (B -> (C -> B))) and ((D -> (E -> (E or F))) or G)), M:tm-480, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-32952
in-theory        32952
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32952.        ((A or (B -> (C -> B))) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-480, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-32953
in-theory        32953
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-480 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-32953.        ((A or (B -> (C -> B))) and ((D -> E) -> (D -> (E or F)))), M:tm-480, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-32954
in-theory        32954
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32954.        ((A or (B -> (C -> B))) and (D -> (E -> (F -> (F or G))))), M:tm-480, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-32955
in-theory        32955
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32955.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-480, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32956
in-theory        32956
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32956.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-480, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32957
in-theory        32957
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32957.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-480, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32958
in-theory        32958
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32958.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-480, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32959
in-theory        32959
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32959.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-480, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-32960
in-theory        32960
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32960.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-480, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-32961
in-theory        32961
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32961.        ((A or (B -> (C -> B))) and (D or (E or (F -> (G -> F))))), M:tm-480, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-32962
in-theory        32962
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32962.        ((A or (B -> (C -> B))) and ((D or (E -> (F -> E))) or G)), M:tm-480, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-32963
in-theory        32963
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32963.        ((A or (B -> (C -> B))) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-480, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32964
in-theory        32964
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (D -> C))) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32964.        (A -> (((B or (C -> (D -> C))) and A) or E)), M:tm-470, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-32965
in-theory        32965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32965.        ((A -> (B -> (B or C))) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-469, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32966
in-theory        32966
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D or (E -> (F -> E))) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-480 ((Am (-> A (or A B))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32966.        ((A or (B -> (B or C))) -> ((D or (E -> (F -> E))) and (B -> (B or C)))), M:tm-466, m:tm-480, u:((Am (-> A (or A B))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (or A B)))))
================================================================
tm-name          tm-32967
in-theory        32967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32967.        ((A -> ((B or (C -> (D -> C))) and A)) and (E -> (E or F))), M:tm-456, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32968
in-theory        32968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32968.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-453, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32969
in-theory        32969
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D or (E -> (F -> E))) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-480 ((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32969.        ((A or ((B -> (B or C)) and A)) -> ((D or (E -> (F -> E))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-480, u:((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-32970
in-theory        32970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and ((E -> (E or F)) and (A -> ((B or (C -> (D -> C))) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32970.        ((A -> ((B or (C -> (D -> C))) and A)) and ((E -> (E or F)) and (A -> ((B or (C -> (D -> C))) and A)))), M:tm-443, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32971
in-theory        32971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32971.        (((A -> (A or B)) or C) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-409, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32972
in-theory        32972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32972.        (((A -> (B -> (A and B))) or C) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-400, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32973
in-theory        32973
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32973.        ((((A and B) -> B) or C) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-391, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32974
in-theory        32974
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32974.        ((((A and B) -> A) or C) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-382, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32975
in-theory        32975
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or (G -> (H -> G))) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32975.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or (G -> (H -> G))) and E))), M:tm-373, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32976
in-theory        32976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32976.        (((A -> (B -> A)) or C) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-364, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32977
in-theory        32977
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C or (D -> (E -> D))) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32977.        (A -> (B -> (((C or (D -> (E -> D))) and A) and B))), M:tm-355, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-32978
in-theory        32978
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32978.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-354, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32979
in-theory        32979
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D or (E -> (F -> E))) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-480 ((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32979.        ((A or (B -> (C -> (B and C)))) -> ((D or (E -> (F -> E))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-480, u:((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-32980
in-theory        32980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32980.        ((A -> ((B or (C -> (D -> C))) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32981
in-theory        32981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D or (E -> (F -> E))) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32981.        (((A -> B) -> (A -> (A and B))) and (C -> ((D or (E -> (F -> E))) and C))), M:tm-338, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32982
in-theory        32982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C or (D -> (E -> D))) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-480 ((Am (-> A (and A B))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32982.        (((A -> B) or (A -> (A and B))) -> ((C or (D -> (E -> D))) and (A -> (A and B)))), M:tm-335, m:tm-480, u:((Am (-> A (and A B))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (and A B)))))
================================================================
tm-name          tm-32983
in-theory        32983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and (A -> (A and ((B or (C -> (D -> C))) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32983.        ((A -> ((B or (C -> (D -> C))) and A)) and (A -> (A and ((B or (C -> (D -> C))) and A)))), M:tm-328, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-32984
in-theory        32984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B or (C -> (D -> C))) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32984.        ((A -> ((B or (C -> (D -> C))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B or (C -> (D -> C))) and A)))), M:tm-327, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32985
in-theory        32985
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and (((E and F) -> F) and (A -> ((B or (C -> (D -> C))) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32985.        ((A -> ((B or (C -> (D -> C))) and A)) and (((E and F) -> F) and (A -> ((B or (C -> (D -> C))) and A)))), M:tm-326, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32986
in-theory        32986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and (((E and F) -> E) and (A -> ((B or (C -> (D -> C))) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32986.        ((A -> ((B or (C -> (D -> C))) and A)) and (((E and F) -> E) and (A -> ((B or (C -> (D -> C))) and A)))), M:tm-325, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32987
in-theory        32987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B or (C -> (D -> C))) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32987.        ((A -> ((B or (C -> (D -> C))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B or (C -> (D -> C))) and A)))), M:tm-324, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32988
in-theory        32988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and ((E -> (F -> E)) and (A -> ((B or (C -> (D -> C))) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32988.        ((A -> ((B or (C -> (D -> C))) and A)) and ((E -> (F -> E)) and (A -> ((B or (C -> (D -> C))) and A)))), M:tm-323, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32989
in-theory        32989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32989.        ((A -> ((B or (C -> (D -> C))) and A)) and ((E and F) -> F)), M:tm-322, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32990
in-theory        32990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32990.        ((A -> ((B or (C -> (D -> C))) and A)) and ((E and F) -> E)), M:tm-320, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32991
in-theory        32991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32991.        ((A -> ((B or (C -> (D -> C))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32992
in-theory        32992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32992.        ((A -> ((B or (C -> (D -> C))) and A)) and (A -> A)), M:tm-316, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-32993
in-theory        32993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32993.        ((A -> ((B or (C -> (D -> C))) and A)) and (E -> (F -> E))), M:tm-315, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32994
in-theory        32994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and ((A -> (not ((B or (C -> (D -> C))) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32994.        ((A -> ((B or (C -> (D -> C))) and A)) and ((A -> (not ((B or (C -> (D -> C))) and A))) -> (not A))), M:tm-313, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-32995
in-theory        32995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and ((((B or (C -> (D -> C))) and A) -> E) -> ((A or ((B or (C -> (D -> C))) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32995.        ((A -> ((B or (C -> (D -> C))) and A)) and ((((B or (C -> (D -> C))) and A) -> E) -> ((A or ((B or (C -> (D -> C))) and A)) -> E))), M:tm-312, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-32996
in-theory        32996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and (E or (A -> ((B or (C -> (D -> C))) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32996.        ((A -> ((B or (C -> (D -> C))) and A)) and (E or (A -> ((B or (C -> (D -> C))) and A)))), M:tm-311, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32997
in-theory        32997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and ((A -> ((B or (C -> (D -> C))) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32997.        ((A -> ((B or (C -> (D -> C))) and A)) and ((A -> ((B or (C -> (D -> C))) and A)) or E)), M:tm-310, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32998
in-theory        32998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and (E -> ((A -> ((B or (C -> (D -> C))) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32998.        ((A -> ((B or (C -> (D -> C))) and A)) and (E -> ((A -> ((B or (C -> (D -> C))) and A)) and E))), M:tm-309, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-32999
in-theory        32999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and (E -> (A -> ((B or (C -> (D -> C))) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-32999.        ((A -> ((B or (C -> (D -> C))) and A)) and (E -> (A -> ((B or (C -> (D -> C))) and A)))), M:tm-305, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33000
in-theory        33000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33000.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-303, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33001
in-theory        33001
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D or (E -> (F -> E))) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-480 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33001.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D or (E -> (F -> E))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-480, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-33002
in-theory        33002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33002.        ((A -> (((B and C) -> C) and A)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-270, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33003
in-theory        33003
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D or (E -> (F -> E))) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-480 ((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33003.        ((A or (((B and C) -> C) and A)) -> ((D or (E -> (F -> E))) and (((B and C) -> C) and A))), M:tm-267, m:tm-480, u:((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-33004
in-theory        33004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33004.        ((A -> (((B and C) -> B) and A)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-239, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33005
in-theory        33005
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D or (E -> (F -> E))) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-480 ((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33005.        ((A or (((B and C) -> B) and A)) -> ((D or (E -> (F -> E))) and (((B and C) -> B) and A))), M:tm-236, m:tm-480, u:((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-33006
in-theory        33006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or (G -> (H -> G))) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33006.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or (G -> (H -> G))) and E))), M:tm-210, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33007
in-theory        33007
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or (F -> (G -> F))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-480 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (-> Dm Cm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-7 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33007.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or (F -> (G -> F))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-480, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (-> Dm Cm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-33008
in-theory        33008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33008.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-183, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33009
in-theory        33009
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D or (E -> (F -> E))) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-480 ((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33009.        ((A or ((B -> (C -> B)) and A)) -> ((D or (E -> (F -> E))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-480, u:((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-33010
in-theory        33010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33010.        ((A -> ((B and C) -> C)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-157, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33011
in-theory        33011
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D or (E -> (F -> E))) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-480 ((Am (-> (and A B) B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33011.        ((A or ((B and C) -> C)) -> ((D or (E -> (F -> E))) and ((B and C) -> C))), M:tm-154, m:tm-480, u:((Am (-> (and A B) B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> (and A B) B))))
================================================================
tm-name          tm-33012
in-theory        33012
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33012.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-147, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33013
in-theory        33013
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or (E -> (F -> E))) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-480 ((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-7 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33013.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or (E -> (F -> E))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-480, u:((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-33014
in-theory        33014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33014.        ((A -> ((B and C) -> B)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-134, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33015
in-theory        33015
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D or (E -> (F -> E))) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-480 ((Am (-> (and A B) A)) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33015.        ((A or ((B and C) -> B)) -> ((D or (E -> (F -> E))) and ((B and C) -> B))), M:tm-131, m:tm-480, u:((Am (-> (and A B) A)) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> (and A B) A))))
================================================================
tm-name          tm-33016
in-theory        33016
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33016.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-125, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33017
in-theory        33017
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or (E -> (F -> E))) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-480 ((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-7 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33017.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or (E -> (F -> E))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-480, u:((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-33018
in-theory        33018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (H -> G))) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33018.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (H -> G))) and E))), M:tm-113, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33019
in-theory        33019
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or (F -> (G -> F))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-480 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33019.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or (F -> (G -> F))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-480, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-33020
in-theory        33020
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33020.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-105, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33021
in-theory        33021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or (E -> (F -> E))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-480 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33021.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or (E -> (F -> E))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-480, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-33022
in-theory        33022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D or (E -> (F -> E))) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33022.        (((A -> B) -> (A -> A)) and (C -> ((D or (E -> (F -> E))) and C))), M:tm-95, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33023
in-theory        33023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C or (D -> (E -> D))) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-480 ((Am (-> A A)) (B (and (or Bm (-> Cm (-> Dm Cm))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33023.        (((A -> B) or (A -> A)) -> ((C or (D -> (E -> D))) and (A -> A))), M:tm-92, m:tm-480, u:((Am (-> A A)) (B (and (or Bm (-> Cm (-> Dm Cm))) (-> A A))))
================================================================
tm-name          tm-33024
in-theory        33024
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C or (D -> (E -> D))) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33024.        (A -> (B -> ((C or (D -> (E -> D))) and A))), M:tm-84, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-33025
in-theory        33025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33025.        ((A -> (B -> (C -> B))) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-83, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33026
in-theory        33026
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D or (E -> (F -> E))) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-480 ((Am (-> A (-> B A))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33026.        ((A or (B -> (C -> B))) -> ((D or (E -> (F -> E))) and (B -> (C -> B)))), M:tm-80, m:tm-480, u:((Am (-> A (-> B A))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (-> B A)))))
================================================================
tm-name          tm-33027
in-theory        33027
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C or (D -> (E -> D))) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-10 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33027.        (((not (not A)) -> A) and (B -> ((C or (D -> (E -> D))) and B))), M:tm-76, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33028
in-theory        33028
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B or (C -> (D -> C))) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-7 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33028.        (((not (not A)) or A) -> ((B or (C -> (D -> C))) and A)), M:tm-73, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-33029
in-theory        33029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or (E -> (F -> E))) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-9 tm-7 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33029.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or (E -> (F -> E))) and C))), M:tm-69, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33030
in-theory        33030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or (D -> (E -> D))) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-480 ((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-7 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33030.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or (D -> (E -> D))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-480, u:((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-33031
in-theory        33031
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33031.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-54, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33032
in-theory        33032
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or (E -> (F -> E))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-480 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33032.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or (E -> (F -> E))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-480, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-33033
in-theory        33033
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C or (D -> (E -> D))) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-480 ((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33033.        ((A or (B or A)) -> ((C or (D -> (E -> D))) and (B or A))), M:tm-50, m:tm-480, u:((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (or A B))))
================================================================
tm-name          tm-33034
in-theory        33034
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C or (D -> (E -> D))) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-480 ((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33034.        ((A or (A or B)) -> ((C or (D -> (E -> D))) and (A or B))), M:tm-49, m:tm-480, u:((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (or A B))))
================================================================
tm-name          tm-33035
in-theory        33035
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C or (D -> (E -> D))) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-480 ((Am (-> A (and B A))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33035.        ((A or (B -> (A and B))) -> ((C or (D -> (E -> D))) and (B -> (A and B)))), M:tm-48, m:tm-480, u:((Am (-> A (and B A))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-33036
in-theory        33036
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C or (D -> (E -> D))) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-7 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33036.        (((A and B) or B) -> ((C or (D -> (E -> D))) and B)), M:tm-47, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-33037
in-theory        33037
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C or (D -> (E -> D))) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-7 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33037.        (((A and B) or A) -> ((C or (D -> (E -> D))) and A)), M:tm-46, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-33038
in-theory        33038
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (F -> E))) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-480 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33038.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (F -> E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-480, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-33039
in-theory        33039
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C or (D -> (E -> D))) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-480 ((Am (-> A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33039.        ((A or (B -> A)) -> ((C or (D -> (E -> D))) and (B -> A))), M:tm-44, m:tm-480, u:((Am (-> A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A B))))
================================================================
tm-name          tm-33040
in-theory        33040
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D or (E -> (F -> E))) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33040.        ((A -> (B or A)) and (C -> ((D or (E -> (F -> E))) and C))), M:tm-42, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33041
in-theory        33041
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D or (E -> (F -> E))) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33041.        ((A -> (A or B)) and (C -> ((D or (E -> (F -> E))) and C))), M:tm-32, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33042
in-theory        33042
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B or (C -> (D -> C))) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33042.        (A -> (A and ((B or (C -> (D -> C))) and A))), M:tm-24, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-33043
in-theory        33043
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D or (E -> (F -> E))) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33043.        ((A -> (B -> (A and B))) and (C -> ((D or (E -> (F -> E))) and C))), M:tm-23, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33044
in-theory        33044
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D or (E -> (F -> E))) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33044.        (((A and B) -> B) and (C -> ((D or (E -> (F -> E))) and C))), M:tm-22, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33045
in-theory        33045
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D or (E -> (F -> E))) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33045.        (((A and B) -> A) and (C -> ((D or (E -> (F -> E))) and C))), M:tm-21, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33046
in-theory        33046
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33046.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-20, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33047
in-theory        33047
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D or (E -> (F -> E))) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33047.        ((A -> (B -> A)) and (C -> ((D or (E -> (F -> E))) and C))), M:tm-19, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33048
in-theory        33048
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B or (C -> (D -> C))) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-9 tm-5 tm-7 tm-1)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33048.        ((A -> (not ((B or (C -> (D -> C))) and A))) -> (not A)), M:tm-9, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-33049
in-theory        33049
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (C -> B))) and D) -> E) -> ((D or ((A or (B -> (C -> B))) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33049.        ((((A or (B -> (C -> B))) and D) -> E) -> ((D or ((A or (B -> (C -> B))) and D)) -> E)), M:tm-8, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-33050
in-theory        33050
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C or (D -> (E -> D))) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33050.        (A or (B -> ((C or (D -> (E -> D))) and B))), M:tm-7, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33051
in-theory        33051
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-6 tm-5 tm-7 tm-1)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33051.        ((A -> ((B or (C -> (D -> C))) and A)) or E), M:tm-6, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33052
in-theory        33052
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C or (D -> (E -> D))) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33052.        (A -> ((B -> ((C or (D -> (E -> D))) and B)) and A)), M:tm-5, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33053
in-theory        33053
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C or (D -> (E -> D))) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33053.        (A -> (B -> ((C or (D -> (E -> D))) and B))), M:tm-1, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33054
in-theory        33054
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33054.        ((A or (B -> (C -> B))) and (D -> (E or (F -> (G -> F))))), M:tm-480, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33055
in-theory        33055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33055.        ((A -> (B -> (B or C))) and (D -> (E or (F -> (G -> F))))), M:tm-469, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33056
in-theory        33056
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-466 tm-481 ((Am (-> A (or A B))) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33056.        ((A or (B -> (B or C))) -> (D or (E -> (F -> E)))), M:tm-466, m:tm-481, u:((Am (-> A (or A B))) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33057
in-theory        33057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33057.        ((A -> (B or (C -> (D -> C)))) and (E -> (E or F))), M:tm-456, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33058
in-theory        33058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33058.        ((A -> ((B -> (B or C)) and A)) and (D -> (E or (F -> (G -> F))))), M:tm-453, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33059
in-theory        33059
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-450 tm-481 ((Am (and (-> A (or A B)) C)) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33059.        ((A or ((B -> (B or C)) and A)) -> (D or (E -> (F -> E)))), M:tm-450, m:tm-481, u:((Am (and (-> A (or A B)) C)) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33060
in-theory        33060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and ((E -> (E or F)) and (A -> (B or (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33060.        ((A -> (B or (C -> (D -> C)))) and ((E -> (E or F)) and (A -> (B or (C -> (D -> C)))))), M:tm-443, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33061
in-theory        33061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33061.        (((A -> (A or B)) or C) and (D -> (E or (F -> (G -> F))))), M:tm-409, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33062
in-theory        33062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33062.        (((A -> (B -> (A and B))) or C) and (D -> (E or (F -> (G -> F))))), M:tm-400, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33063
in-theory        33063
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33063.        ((((A and B) -> B) or C) and (D -> (E or (F -> (G -> F))))), M:tm-391, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33064
in-theory        33064
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33064.        ((((A and B) -> A) or C) and (D -> (E or (F -> (G -> F))))), M:tm-382, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33065
in-theory        33065
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33065.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or (G -> (H -> G))))), M:tm-373, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33066
in-theory        33066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33066.        (((A -> (B -> A)) or C) and (D -> (E or (F -> (G -> F))))), M:tm-364, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33067
in-theory        33067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33067.        ((A -> (B -> (C -> (B and C)))) and (D -> (E or (F -> (G -> F))))), M:tm-354, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33068
in-theory        33068
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-351 tm-481 ((Am (-> A (-> B (and A B)))) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33068.        ((A or (B -> (C -> (B and C)))) -> (D or (E -> (F -> E)))), M:tm-351, m:tm-481, u:((Am (-> A (-> B (and A B)))) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33069
in-theory        33069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33069.        ((A -> (B or (C -> (D -> C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33070
in-theory        33070
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) -> D) -> ((A or (B -> (C -> B))) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-481 ((Am (-> (or Bm (-> Cm (-> Dm Cm))) B)) (A (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33070.        (((A or (B -> (C -> B))) -> D) -> ((A or (B -> (C -> B))) and D)), M:tm-339, m:tm-481, u:((Am (-> (or Bm (-> Cm (-> Dm Cm))) B)) (A (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33071
in-theory        33071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D or (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33071.        (((A -> B) -> (A -> (A and B))) and (C -> (D or (E -> (F -> E))))), M:tm-338, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33072
in-theory        33072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C or (D -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-335 tm-481 ((Am (-> A (and A B))) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33072.        (((A -> B) or (A -> (A and B))) -> (C or (D -> (E -> D)))), M:tm-335, m:tm-481, u:((Am (-> A (and A B))) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33073
in-theory        33073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (A -> (A and (B or (C -> (D -> C))))))
theorem-size     21
proof            (modus-ponens tm-328 tm-481 ((A Am) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33073.        ((A -> (B or (C -> (D -> C)))) and (A -> (A and (B or (C -> (D -> C)))))), M:tm-328, m:tm-481, u:((A Am) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33074
in-theory        33074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and ((E -> (F -> (E and F))) and (A -> (B or (C -> (D -> C))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33074.        ((A -> (B or (C -> (D -> C)))) and ((E -> (F -> (E and F))) and (A -> (B or (C -> (D -> C)))))), M:tm-327, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33075
in-theory        33075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (((E and F) -> F) and (A -> (B or (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33075.        ((A -> (B or (C -> (D -> C)))) and (((E and F) -> F) and (A -> (B or (C -> (D -> C)))))), M:tm-326, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33076
in-theory        33076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (((E and F) -> E) and (A -> (B or (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33076.        ((A -> (B or (C -> (D -> C)))) and (((E and F) -> E) and (A -> (B or (C -> (D -> C)))))), M:tm-325, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33077
in-theory        33077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B or (C -> (D -> C))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33077.        ((A -> (B or (C -> (D -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B or (C -> (D -> C)))))), M:tm-324, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33078
in-theory        33078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and ((E -> (F -> E)) and (A -> (B or (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33078.        ((A -> (B or (C -> (D -> C)))) and ((E -> (F -> E)) and (A -> (B or (C -> (D -> C)))))), M:tm-323, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33079
in-theory        33079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33079.        ((A -> (B or (C -> (D -> C)))) and ((E and F) -> F)), M:tm-322, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33080
in-theory        33080
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or (C -> (D -> C))) -> E)) -> (B or (C -> (D -> C)))) and ((A and ((B or (C -> (D -> C))) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-481 ((Am (and A (-> (or Bm (-> Cm (-> Dm Cm))) C))) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33080.        (((A and ((B or (C -> (D -> C))) -> E)) -> (B or (C -> (D -> C)))) and ((A and ((B or (C -> (D -> C))) -> E)) -> E)), M:tm-321, m:tm-481, u:((Am (and A (-> (or Bm (-> Cm (-> Dm Cm))) C))) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33081
in-theory        33081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33081.        ((A -> (B or (C -> (D -> C)))) and ((E and F) -> E)), M:tm-320, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33082
in-theory        33082
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (C -> B))) -> D) and E) -> (A or (B -> (C -> B)))) and ((((A or (B -> (C -> B))) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-481 ((Am (and (-> (or Bm (-> Cm (-> Dm Cm))) B) C)) (A (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33082.        (((((A or (B -> (C -> B))) -> D) and E) -> (A or (B -> (C -> B)))) and ((((A or (B -> (C -> B))) -> D) and E) -> D)), M:tm-319, m:tm-481, u:((Am (and (-> (or Bm (-> Cm (-> Dm Cm))) B) C)) (A (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33083
in-theory        33083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33083.        ((A -> (B or (C -> (D -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33084
in-theory        33084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-481 ((A Am) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33084.        ((A -> (B or (C -> (D -> C)))) and (A -> A)), M:tm-316, m:tm-481, u:((A Am) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33085
in-theory        33085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33085.        ((A -> (B or (C -> (D -> C)))) and (E -> (F -> E))), M:tm-315, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33086
in-theory        33086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and ((A -> (not (B or (C -> (D -> C))))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-481 ((A Am) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33086.        ((A -> (B or (C -> (D -> C)))) and ((A -> (not (B or (C -> (D -> C))))) -> (not A))), M:tm-313, m:tm-481, u:((A Am) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33087
in-theory        33087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (((B or (C -> (D -> C))) -> E) -> ((A or (B or (C -> (D -> C)))) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-481 ((A Am) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33087.        ((A -> (B or (C -> (D -> C)))) and (((B or (C -> (D -> C))) -> E) -> ((A or (B or (C -> (D -> C)))) -> E))), M:tm-312, m:tm-481, u:((A Am) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33088
in-theory        33088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (E or (A -> (B or (C -> (D -> C))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33088.        ((A -> (B or (C -> (D -> C)))) and (E or (A -> (B or (C -> (D -> C)))))), M:tm-311, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33089
in-theory        33089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and ((A -> (B or (C -> (D -> C)))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33089.        ((A -> (B or (C -> (D -> C)))) and ((A -> (B or (C -> (D -> C)))) or E)), M:tm-310, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33090
in-theory        33090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (E -> ((A -> (B or (C -> (D -> C)))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33090.        ((A -> (B or (C -> (D -> C)))) and (E -> ((A -> (B or (C -> (D -> C)))) and E))), M:tm-309, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33091
in-theory        33091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (E -> (A -> (B or (C -> (D -> C))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33091.        ((A -> (B or (C -> (D -> C)))) and (E -> (A -> (B or (C -> (D -> C)))))), M:tm-305, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33092
in-theory        33092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33092.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or (F -> (G -> F))))), M:tm-303, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33093
in-theory        33093
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D or (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-300 tm-481 ((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33093.        ((A or ((B -> (C -> (B and C))) and A)) -> (D or (E -> (F -> E)))), M:tm-300, m:tm-481, u:((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33094
in-theory        33094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33094.        ((A -> (((B and C) -> C) and A)) and (D -> (E or (F -> (G -> F))))), M:tm-270, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33095
in-theory        33095
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-267 tm-481 ((Am (and (-> (and A B) B) C)) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33095.        ((A or (((B and C) -> C) and A)) -> (D or (E -> (F -> E)))), M:tm-267, m:tm-481, u:((Am (and (-> (and A B) B) C)) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33096
in-theory        33096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33096.        ((A -> (((B and C) -> B) and A)) and (D -> (E or (F -> (G -> F))))), M:tm-239, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33097
in-theory        33097
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-236 tm-481 ((Am (and (-> (and A B) A) C)) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33097.        ((A or (((B and C) -> B) and A)) -> (D or (E -> (F -> E)))), M:tm-236, m:tm-481, u:((Am (and (-> (and A B) A) C)) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33098
in-theory        33098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33098.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or (G -> (H -> G))))), M:tm-210, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33099
in-theory        33099
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-207 tm-481 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33099.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or (F -> (G -> F)))), M:tm-207, m:tm-481, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33100
in-theory        33100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33100.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E or (F -> (G -> F))))), M:tm-183, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33101
in-theory        33101
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-180 tm-481 ((Am (and (-> A (-> B A)) C)) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33101.        ((A or ((B -> (C -> B)) and A)) -> (D or (E -> (F -> E)))), M:tm-180, m:tm-481, u:((Am (and (-> A (-> B A)) C)) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33102
in-theory        33102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33102.        ((A -> ((B and C) -> C)) and (D -> (E or (F -> (G -> F))))), M:tm-157, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33103
in-theory        33103
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-154 tm-481 ((Am (-> (and A B) B)) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33103.        ((A or ((B and C) -> C)) -> (D or (E -> (F -> E)))), M:tm-154, m:tm-481, u:((Am (-> (and A B) B)) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33104
in-theory        33104
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33104.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or (F -> (G -> F))))), M:tm-147, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33105
in-theory        33105
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-144 tm-481 ((Am (-> (and A (-> B C)) C)) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33105.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or (E -> (F -> E)))), M:tm-144, m:tm-481, u:((Am (-> (and A (-> B C)) C)) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33106
in-theory        33106
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B or (C -> (D -> C))) -> E)) -> (B or (C -> (D -> C))))
theorem-size     19
proof            (modus-ponens tm-142 tm-481 ((Am (and A (-> (or Bm (-> Cm (-> Dm Cm))) C))) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33106.        ((A and ((B or (C -> (D -> C))) -> E)) -> (B or (C -> (D -> C)))), M:tm-142, m:tm-481, u:((Am (and A (-> (or Bm (-> Cm (-> Dm Cm))) C))) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33107
in-theory        33107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33107.        ((A -> ((B and C) -> B)) and (D -> (E or (F -> (G -> F))))), M:tm-134, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33108
in-theory        33108
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-131 tm-481 ((Am (-> (and A B) A)) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33108.        ((A or ((B and C) -> B)) -> (D or (E -> (F -> E)))), M:tm-131, m:tm-481, u:((Am (-> (and A B) A)) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33109
in-theory        33109
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33109.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or (F -> (G -> F))))), M:tm-125, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33110
in-theory        33110
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-122 tm-481 ((Am (-> (and (-> A B) C) B)) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33110.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or (E -> (F -> E)))), M:tm-122, m:tm-481, u:((Am (-> (and (-> A B) C) B)) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33111
in-theory        33111
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (C -> B))) -> D) and E) -> (A or (B -> (C -> B))))
theorem-size     19
proof            (modus-ponens tm-120 tm-481 ((Am (and (-> (or Bm (-> Cm (-> Dm Cm))) B) C)) (A (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33111.        ((((A or (B -> (C -> B))) -> D) and E) -> (A or (B -> (C -> B)))), M:tm-120, m:tm-481, u:((Am (and (-> (or Bm (-> Cm (-> Dm Cm))) B) C)) (A (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33112
in-theory        33112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33112.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (H -> G))))), M:tm-113, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33113
in-theory        33113
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-110 tm-481 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33113.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or (F -> (G -> F)))), M:tm-110, m:tm-481, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33114
in-theory        33114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or (F -> (G -> F)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33114.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or (F -> (G -> F))))), M:tm-105, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33115
in-theory        33115
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or (E -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-102 tm-481 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33115.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or (E -> (F -> E)))), M:tm-102, m:tm-481, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33116
in-theory        33116
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) -> D) -> (A or (B -> (C -> B))))
theorem-size     17
proof            (modus-ponens tm-96 tm-481 ((Am (-> (or Bm (-> Cm (-> Dm Cm))) B)) (A (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33116.        (((A or (B -> (C -> B))) -> D) -> (A or (B -> (C -> B)))), M:tm-96, m:tm-481, u:((Am (-> (or Bm (-> Cm (-> Dm Cm))) B)) (A (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33117
in-theory        33117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D or (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33117.        (((A -> B) -> (A -> A)) and (C -> (D or (E -> (F -> E))))), M:tm-95, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33118
in-theory        33118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C or (D -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-92 tm-481 ((Am (-> A A)) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33118.        (((A -> B) or (A -> A)) -> (C or (D -> (E -> D)))), M:tm-92, m:tm-481, u:((Am (-> A A)) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33119
in-theory        33119
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C or (D -> (E -> D)))))
theorem-size     11
proof            (modus-ponens tm-84 tm-481 ((A Am) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33119.        (A -> (B -> (C or (D -> (E -> D))))), M:tm-84, m:tm-481, u:((A Am) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33120
in-theory        33120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33120.        ((A -> (B -> (C -> B))) and (D -> (E or (F -> (G -> F))))), M:tm-83, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33121
in-theory        33121
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-80 tm-481 ((Am (-> A (-> B A))) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33121.        ((A or (B -> (C -> B))) -> (D or (E -> (F -> E)))), M:tm-80, m:tm-481, u:((Am (-> A (-> B A))) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33122
in-theory        33122
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A or (B -> (C -> B))) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-481 ((Am (not (not (-> (or Bm (-> Cm (-> Dm Cm))) B)))) (A (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-10 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33122.        ((not (not ((A or (B -> (C -> B))) -> D))) -> D), M:tm-77, m:tm-481, u:((Am (not (not (-> (or Bm (-> Cm (-> Dm Cm))) B)))) (A (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33123
in-theory        33123
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C or (D -> (E -> D)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33123.        (((not (not A)) -> A) and (B -> (C or (D -> (E -> D))))), M:tm-76, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33124
in-theory        33124
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B or (C -> (D -> C))))
theorem-size     13
proof            (modus-ponens tm-73 tm-481 ((A Am) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-10 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33124.        (((not (not A)) or A) -> (B or (C -> (D -> C)))), M:tm-73, m:tm-481, u:((A Am) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33125
in-theory        33125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or (E -> (F -> E)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33125.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or (E -> (F -> E))))), M:tm-69, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33126
in-theory        33126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or (D -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-66 tm-481 ((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-9 tm-1 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33126.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or (D -> (E -> D)))), M:tm-66, m:tm-481, u:((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33127
in-theory        33127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33127.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or (F -> (G -> F))))), M:tm-54, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33128
in-theory        33128
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-51 tm-481 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33128.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> (F -> E)))), M:tm-51, m:tm-481, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33129
in-theory        33129
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-50 tm-481 ((Am (or A B)) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33129.        ((A or (B or A)) -> (C or (D -> (E -> D)))), M:tm-50, m:tm-481, u:((Am (or A B)) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33130
in-theory        33130
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-49 tm-481 ((Am (or A B)) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33130.        ((A or (A or B)) -> (C or (D -> (E -> D)))), M:tm-49, m:tm-481, u:((Am (or A B)) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33131
in-theory        33131
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (D -> (E -> D))))
theorem-size     15
proof            (modus-ponens tm-48 tm-481 ((Am (-> A (and B A))) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33131.        ((A or (B -> (A and B))) -> (C or (D -> (E -> D)))), M:tm-48, m:tm-481, u:((Am (-> A (and B A))) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33132
in-theory        33132
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-47 tm-481 ((A Am) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33132.        (((A and B) or B) -> (C or (D -> (E -> D)))), M:tm-47, m:tm-481, u:((A Am) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33133
in-theory        33133
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-46 tm-481 ((A Am) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33133.        (((A and B) or A) -> (C or (D -> (E -> D)))), M:tm-46, m:tm-481, u:((A Am) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33134
in-theory        33134
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-45 tm-481 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33134.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (F -> E)))), M:tm-45, m:tm-481, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33135
in-theory        33135
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-44 tm-481 ((Am (-> A B)) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33135.        ((A or (B -> A)) -> (C or (D -> (E -> D)))), M:tm-44, m:tm-481, u:((Am (-> A B)) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33136
in-theory        33136
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33136.        ((A -> (B or A)) and (C -> (D or (E -> (F -> E))))), M:tm-42, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33137
in-theory        33137
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33137.        ((A -> (A or B)) and (C -> (D or (E -> (F -> E))))), M:tm-32, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33138
in-theory        33138
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B or (C -> (D -> C)))))
theorem-size     11
proof            (modus-ponens tm-24 tm-481 ((A Am) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33138.        (A -> (A and (B or (C -> (D -> C))))), M:tm-24, m:tm-481, u:((A Am) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33139
in-theory        33139
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D or (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33139.        ((A -> (B -> (A and B))) and (C -> (D or (E -> (F -> E))))), M:tm-23, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33140
in-theory        33140
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33140.        (((A and B) -> B) and (C -> (D or (E -> (F -> E))))), M:tm-22, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33141
in-theory        33141
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33141.        (((A and B) -> A) and (C -> (D or (E -> (F -> E))))), M:tm-21, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33142
in-theory        33142
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33142.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or (F -> (G -> F))))), M:tm-20, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33143
in-theory        33143
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33143.        ((A -> (B -> A)) and (C -> (D or (E -> (F -> E))))), M:tm-19, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33144
in-theory        33144
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B or (C -> (D -> C))) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-481 ((Am (and A (-> (or Bm (-> Cm (-> Dm Cm))) C))) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-4 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33144.        ((A and ((B or (C -> (D -> C))) -> E)) -> E), M:tm-17, m:tm-481, u:((Am (and A (-> (or Bm (-> Cm (-> Dm Cm))) C))) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33145
in-theory        33145
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (C -> B))) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-481 ((Am (and (-> (or Bm (-> Cm (-> Dm Cm))) B) C)) (A (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-3 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33145.        ((((A or (B -> (C -> B))) -> D) and E) -> D), M:tm-15, m:tm-481, u:((Am (and (-> (or Bm (-> Cm (-> Dm Cm))) B) C)) (A (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33146
in-theory        33146
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B or (C -> (D -> C))))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-481 ((A Am) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-9 tm-1 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33146.        ((A -> (not (B or (C -> (D -> C))))) -> (not A)), M:tm-9, m:tm-481, u:((A Am) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33147
in-theory        33147
times-derived    2
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) -> D) -> ((E or (A or (B -> (C -> B)))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-481 ((A Am) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33147.        (((A or (B -> (C -> B))) -> D) -> ((E or (A or (B -> (C -> B)))) -> D)), M:tm-8, m:tm-481, u:((A Am) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33148
in-theory        33148
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C or (D -> (E -> D)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-7 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33148.        (A or (B -> (C or (D -> (E -> D))))), M:tm-7, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33149
in-theory        33149
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-6 tm-1 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33149.        ((A -> (B or (C -> (D -> C)))) or E), M:tm-6, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33150
in-theory        33150
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C or (D -> (E -> D)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-33150.        (A -> ((B -> (C or (D -> (E -> D)))) and A)), M:tm-5, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33151
in-theory        33151
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33151.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-480, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33152
in-theory        33152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33152.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-469, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33153
in-theory        33153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33153.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H))), M:tm-456, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33154
in-theory        33154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33154.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-453, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33155
in-theory        33155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33155.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-443, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33156
in-theory        33156
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33156.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-409, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33157
in-theory        33157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33157.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-400, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33158
in-theory        33158
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33158.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-391, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33159
in-theory        33159
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33159.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-382, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33160
in-theory        33160
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33160.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-373, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33161
in-theory        33161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33161.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-364, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33162
in-theory        33162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33162.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-354, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33163
in-theory        33163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33163.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33164
in-theory        33164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33164.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-338, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33165
in-theory        33165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33165.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-327, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33166
in-theory        33166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33166.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-326, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33167
in-theory        33167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33167.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-325, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33168
in-theory        33168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33168.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-324, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33169
in-theory        33169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33169.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-323, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33170
in-theory        33170
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33170.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33171
in-theory        33171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33171.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33172
in-theory        33172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33172.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33173
in-theory        33173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33173.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33174
in-theory        33174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33174.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-311, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33175
in-theory        33175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33175.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)), M:tm-310, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33176
in-theory        33176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33176.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G))), M:tm-309, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33177
in-theory        33177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-482 ((A (-> Am (or Am Bm))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33177.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-308, m:tm-482, u:((A (-> Am (or Am Bm))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-33178
in-theory        33178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (A or B)))
theorem-size     27
proof            (modus-ponens tm-307 tm-482 ((A (-> Am (or Am Bm))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33178.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (A or B))), M:tm-307, m:tm-482, u:((A (-> Am (or Am Bm))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-33179
in-theory        33179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33179.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-305, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33180
in-theory        33180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33180.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-303, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33181
in-theory        33181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33181.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-270, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33182
in-theory        33182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33182.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-239, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33183
in-theory        33183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33183.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-210, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33184
in-theory        33184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33184.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-183, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33185
in-theory        33185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33185.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-157, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33186
in-theory        33186
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33186.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-147, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33187
in-theory        33187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33187.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-134, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33188
in-theory        33188
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33188.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-125, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33189
in-theory        33189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33189.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-113, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33190
in-theory        33190
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33190.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-105, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33191
in-theory        33191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33191.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-95, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33192
in-theory        33192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33192.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-83, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33193
in-theory        33193
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-10 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33193.        (((not (not A)) -> A) and ((B -> (B or C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-76, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33194
in-theory        33194
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-9 tm-6 tm-7 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33194.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-69, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33195
in-theory        33195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33195.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-54, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33196
in-theory        33196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33196.        ((A -> (B or A)) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-42, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33197
in-theory        33197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33197.        ((A -> (A or B)) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-32, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33198
in-theory        33198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33198.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-23, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33199
in-theory        33199
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33199.        (((A and B) -> B) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-22, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33200
in-theory        33200
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33200.        (((A and B) -> A) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-21, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33201
in-theory        33201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33201.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-20, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33202
in-theory        33202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33202.        ((A -> (B -> A)) and ((C -> (C or D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-19, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33203
in-theory        33203
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-7 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-7 tm-5 tm-6 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33203.        (A or ((B -> (B or C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-7, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33204
in-theory        33204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-6 tm-5 tm-7 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33204.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G), M:tm-6, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33205
in-theory        33205
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33205.        (A -> (((B -> (B or C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A)), M:tm-5, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33206
in-theory        33206
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-1 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-1 tm-5 tm-6 tm-7 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33206.        (A -> ((B -> (B or C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-1, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33207
in-theory        33207
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-480 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33207.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-480, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33208
in-theory        33208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-469 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33208.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-469, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33209
in-theory        33209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33209.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H))), M:tm-456, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33210
in-theory        33210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-453 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33210.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-453, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33211
in-theory        33211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     53
proof            (modus-ponens tm-443 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33211.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-443, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33212
in-theory        33212
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-409 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33212.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-409, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33213
in-theory        33213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-400 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33213.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-400, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33214
in-theory        33214
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-391 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33214.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-391, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33215
in-theory        33215
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-382 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33215.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-382, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33216
in-theory        33216
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-373 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33216.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-373, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33217
in-theory        33217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-364 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33217.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-364, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33218
in-theory        33218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-354 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33218.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-354, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33219
in-theory        33219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33219.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33220
in-theory        33220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-338 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33220.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-338, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33221
in-theory        33221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     55
proof            (modus-ponens tm-327 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33221.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-327, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33222
in-theory        33222
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     53
proof            (modus-ponens tm-326 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33222.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-326, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33223
in-theory        33223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     53
proof            (modus-ponens tm-325 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33223.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-325, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33224
in-theory        33224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     61
proof            (modus-ponens tm-324 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33224.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-324, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33225
in-theory        33225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     53
proof            (modus-ponens tm-323 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33225.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-323, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33226
in-theory        33226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33226.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33227
in-theory        33227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33227.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33228
in-theory        33228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33228.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33229
in-theory        33229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33229.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33230
in-theory        33230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-311 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33230.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-311, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33231
in-theory        33231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33231.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)), M:tm-310, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33232
in-theory        33232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33232.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G))), M:tm-309, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33233
in-theory        33233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-308 tm-483 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33233.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-308, m:tm-483, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-33234
in-theory        33234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (B -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-307 tm-483 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33234.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-483, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-33235
in-theory        33235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-305 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33235.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-305, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33236
in-theory        33236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-303 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33236.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-303, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33237
in-theory        33237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-270 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33237.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-270, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33238
in-theory        33238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-239 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33238.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-239, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33239
in-theory        33239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     41
proof            (modus-ponens tm-210 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33239.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-210, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33240
in-theory        33240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-183 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33240.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-183, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33241
in-theory        33241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-157 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33241.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-157, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33242
in-theory        33242
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-147 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33242.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-147, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33243
in-theory        33243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-134 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33243.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-134, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33244
in-theory        33244
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-125 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33244.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-125, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33245
in-theory        33245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-113 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33245.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-113, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33246
in-theory        33246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     43
proof            (modus-ponens tm-105 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33246.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-105, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33247
in-theory        33247
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-95 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33247.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-95, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33248
in-theory        33248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-83 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33248.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-83, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33249
in-theory        33249
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     29
proof            (modus-ponens tm-76 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33249.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-76, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33250
in-theory        33250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     35
proof            (modus-ponens tm-69 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33250.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-69, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33251
in-theory        33251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-54 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33251.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-54, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33252
in-theory        33252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-42 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33252.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-42, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33253
in-theory        33253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-32 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33253.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-32, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33254
in-theory        33254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-23 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33254.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-23, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33255
in-theory        33255
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-22 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33255.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-22, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33256
in-theory        33256
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-21 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33256.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-21, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33257
in-theory        33257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-20 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33257.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-20, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33258
in-theory        33258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-19 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33258.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-19, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33259
in-theory        33259
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-7 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33259.        (A or ((B -> (C -> (B and C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-7, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33260
in-theory        33260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-6 tm-5 tm-7 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33260.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G), M:tm-6, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33261
in-theory        33261
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33261.        (A -> (((B -> (C -> (B and C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A)), M:tm-5, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33262
in-theory        33262
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-1 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-1 tm-5 tm-7 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33262.        (A -> ((B -> (C -> (B and C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-1, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33263
in-theory        33263
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33263.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-480, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33264
in-theory        33264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33264.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-469, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33265
in-theory        33265
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33265.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H))), M:tm-456, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33266
in-theory        33266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33266.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-453, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33267
in-theory        33267
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33267.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-443, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33268
in-theory        33268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33268.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-409, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33269
in-theory        33269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33269.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-400, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33270
in-theory        33270
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33270.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-391, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33271
in-theory        33271
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33271.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-382, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33272
in-theory        33272
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33272.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-373, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33273
in-theory        33273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33273.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-364, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33274
in-theory        33274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33274.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-354, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33275
in-theory        33275
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33275.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33276
in-theory        33276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33276.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-338, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33277
in-theory        33277
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33277.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-327, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33278
in-theory        33278
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33278.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-326, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33279
in-theory        33279
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33279.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-325, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33280
in-theory        33280
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33280.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-324, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33281
in-theory        33281
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33281.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-323, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33282
in-theory        33282
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33282.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33283
in-theory        33283
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33283.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33284
in-theory        33284
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33284.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33285
in-theory        33285
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33285.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33286
in-theory        33286
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33286.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-311, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33287
in-theory        33287
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33287.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)), M:tm-310, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33288
in-theory        33288
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33288.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G))), M:tm-309, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33289
in-theory        33289
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-484 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33289.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-308, m:tm-484, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-33290
in-theory        33290
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((A and B) -> B))
theorem-size     27
proof            (modus-ponens tm-307 tm-484 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33290.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((A and B) -> B)), M:tm-307, m:tm-484, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-33291
in-theory        33291
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33291.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-305, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33292
in-theory        33292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33292.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-303, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33293
in-theory        33293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33293.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-270, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33294
in-theory        33294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33294.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-239, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33295
in-theory        33295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33295.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-210, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33296
in-theory        33296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33296.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-183, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33297
in-theory        33297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33297.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-157, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33298
in-theory        33298
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33298.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-147, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33299
in-theory        33299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33299.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-134, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33300
in-theory        33300
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33300.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-125, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33301
in-theory        33301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33301.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-113, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33302
in-theory        33302
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33302.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-105, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33303
in-theory        33303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33303.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-95, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33304
in-theory        33304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33304.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-83, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33305
in-theory        33305
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-10 tm-4 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33305.        (((not (not A)) -> A) and (((B and C) -> C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-76, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33306
in-theory        33306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-9 tm-4 tm-7 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33306.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-69, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33307
in-theory        33307
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33307.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-54, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33308
in-theory        33308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33308.        ((A -> (B or A)) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-42, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33309
in-theory        33309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33309.        ((A -> (A or B)) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-32, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33310
in-theory        33310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33310.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-23, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33311
in-theory        33311
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33311.        (((A and B) -> B) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-22, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33312
in-theory        33312
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33312.        (((A and B) -> A) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-21, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33313
in-theory        33313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33313.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-20, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33314
in-theory        33314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33314.        ((A -> (B -> A)) and (((C and D) -> D) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-19, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33315
in-theory        33315
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-7 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-7 tm-5 tm-4 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33315.        (A or (((B and C) -> C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-7, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33316
in-theory        33316
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-6 tm-5 tm-4 tm-7 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33316.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G), M:tm-6, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33317
in-theory        33317
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33317.        (A -> ((((B and C) -> C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A)), M:tm-5, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33318
in-theory        33318
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-1 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-1 tm-5 tm-4 tm-7 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33318.        (A -> (((B and C) -> C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-1, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33319
in-theory        33319
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33319.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-480, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33320
in-theory        33320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33320.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-469, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33321
in-theory        33321
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33321.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H))), M:tm-456, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33322
in-theory        33322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33322.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-453, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33323
in-theory        33323
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33323.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-443, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33324
in-theory        33324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33324.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-409, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33325
in-theory        33325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33325.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-400, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33326
in-theory        33326
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33326.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-391, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33327
in-theory        33327
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33327.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-382, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33328
in-theory        33328
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33328.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-373, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33329
in-theory        33329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33329.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-364, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33330
in-theory        33330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33330.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-354, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33331
in-theory        33331
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33331.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33332
in-theory        33332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33332.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-338, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33333
in-theory        33333
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33333.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-327, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33334
in-theory        33334
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33334.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-326, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33335
in-theory        33335
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33335.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-325, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33336
in-theory        33336
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33336.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-324, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33337
in-theory        33337
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33337.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-323, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33338
in-theory        33338
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33338.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33339
in-theory        33339
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33339.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33340
in-theory        33340
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33340.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33341
in-theory        33341
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33341.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33342
in-theory        33342
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33342.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-311, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33343
in-theory        33343
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33343.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)), M:tm-310, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33344
in-theory        33344
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33344.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G))), M:tm-309, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33345
in-theory        33345
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-485 ((A (-> (and Am Bm) Am)) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33345.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-308, m:tm-485, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-33346
in-theory        33346
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((A and B) -> A))
theorem-size     27
proof            (modus-ponens tm-307 tm-485 ((A (-> (and Am Bm) Am)) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33346.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((A and B) -> A)), M:tm-307, m:tm-485, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-33347
in-theory        33347
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33347.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-305, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33348
in-theory        33348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33348.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-303, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33349
in-theory        33349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33349.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-270, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33350
in-theory        33350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33350.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-239, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33351
in-theory        33351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33351.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-210, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33352
in-theory        33352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33352.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-183, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33353
in-theory        33353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33353.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-157, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33354
in-theory        33354
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33354.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-147, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33355
in-theory        33355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33355.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-134, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33356
in-theory        33356
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33356.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-125, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33357
in-theory        33357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33357.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-113, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33358
in-theory        33358
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33358.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-105, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33359
in-theory        33359
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33359.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-95, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33360
in-theory        33360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33360.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-83, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33361
in-theory        33361
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-10 tm-3 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33361.        (((not (not A)) -> A) and (((B and C) -> B) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-76, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33362
in-theory        33362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-9 tm-3 tm-7 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33362.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-69, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33363
in-theory        33363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33363.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-54, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33364
in-theory        33364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33364.        ((A -> (B or A)) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-42, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33365
in-theory        33365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33365.        ((A -> (A or B)) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-32, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33366
in-theory        33366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33366.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-23, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33367
in-theory        33367
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33367.        (((A and B) -> B) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-22, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33368
in-theory        33368
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33368.        (((A and B) -> A) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-21, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33369
in-theory        33369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33369.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-20, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33370
in-theory        33370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33370.        ((A -> (B -> A)) and (((C and D) -> C) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-19, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33371
in-theory        33371
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-7 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-7 tm-5 tm-3 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33371.        (A or (((B and C) -> B) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-7, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33372
in-theory        33372
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-6 tm-5 tm-3 tm-7 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33372.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G), M:tm-6, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33373
in-theory        33373
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33373.        (A -> ((((B and C) -> B) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A)), M:tm-5, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33374
in-theory        33374
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-1 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-1 tm-5 tm-3 tm-7 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33374.        (A -> (((B and C) -> B) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-1, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33375
in-theory        33375
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-480 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33375.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-480, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33376
in-theory        33376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-469 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33376.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-469, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33377
in-theory        33377
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (H or I)))
theorem-size     35
proof            (modus-ponens tm-456 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33377.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (H or I))), M:tm-456, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33378
in-theory        33378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-453 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33378.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-453, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33379
in-theory        33379
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (H or I)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-443 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33379.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (H or I)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-443, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33380
in-theory        33380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-409 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33380.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-409, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33381
in-theory        33381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-400 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33381.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-400, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33382
in-theory        33382
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-391 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33382.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-391, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33383
in-theory        33383
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-382 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33383.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-382, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33384
in-theory        33384
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-373 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33384.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-373, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33385
in-theory        33385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-364 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33385.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-364, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33386
in-theory        33386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-354 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33386.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-354, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33387
in-theory        33387
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I -> (H and I))))
theorem-size     37
proof            (modus-ponens tm-341 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33387.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I -> (H and I)))), M:tm-341, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33388
in-theory        33388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     39
proof            (modus-ponens tm-338 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33388.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-338, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33389
in-theory        33389
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> (H and I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     67
proof            (modus-ponens tm-327 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33389.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> (H and I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-327, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33390
in-theory        33390
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> I) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-326 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33390.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> I) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-326, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33391
in-theory        33391
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-325 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33391.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H and I) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-325, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33392
in-theory        33392
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     73
proof            (modus-ponens tm-324 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       257
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33392.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-324, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33393
in-theory        33393
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-323 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33393.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-323, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33394
in-theory        33394
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H and I) -> I))
theorem-size     35
proof            (modus-ponens tm-322 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33394.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H and I) -> I)), M:tm-322, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33395
in-theory        33395
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H and I) -> H))
theorem-size     35
proof            (modus-ponens tm-320 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33395.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H and I) -> H)), M:tm-320, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33396
in-theory        33396
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))
theorem-size     43
proof            (modus-ponens tm-318 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33396.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33397
in-theory        33397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I -> H)))
theorem-size     35
proof            (modus-ponens tm-315 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33397.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I -> H))), M:tm-315, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33398
in-theory        33398
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     61
proof            (modus-ponens tm-311 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33398.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-311, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33399
in-theory        33399
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) or H))
theorem-size     61
proof            (modus-ponens tm-310 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33399.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) or H)), M:tm-310, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33400
in-theory        33400
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and H)))
theorem-size     63
proof            (modus-ponens tm-309 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33400.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and H))), M:tm-309, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33401
in-theory        33401
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     45
proof            (modus-ponens tm-308 tm-486 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33401.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-308, m:tm-486, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))
================================================================
tm-name          tm-33402
in-theory        33402
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-307 tm-486 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33402.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-486, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))
================================================================
tm-name          tm-33403
in-theory        33403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     61
proof            (modus-ponens tm-305 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33403.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-305, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33404
in-theory        33404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     41
proof            (modus-ponens tm-303 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33404.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-303, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33405
in-theory        33405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-270 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33405.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-270, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33406
in-theory        33406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-239 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33406.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-239, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33407
in-theory        33407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     47
proof            (modus-ponens tm-210 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33407.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-210, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33408
in-theory        33408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-183 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33408.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-183, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33409
in-theory        33409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-157 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33409.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-157, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33410
in-theory        33410
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     45
proof            (modus-ponens tm-147 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33410.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-147, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33411
in-theory        33411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-134 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33411.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-134, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33412
in-theory        33412
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     45
proof            (modus-ponens tm-125 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33412.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-125, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33413
in-theory        33413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-113 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33413.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-113, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33414
in-theory        33414
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-105 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33414.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-105, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33415
in-theory        33415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-95 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33415.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-95, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33416
in-theory        33416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-83 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33416.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-83, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33417
in-theory        33417
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     35
proof            (modus-ponens tm-76 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-10 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33417.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-76, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33418
in-theory        33418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-69 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-9 tm-2 tm-7)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33418.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-69, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33419
in-theory        33419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-54 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33419.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-54, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33420
in-theory        33420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-42 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33420.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-42, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33421
in-theory        33421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-32 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33421.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-32, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33422
in-theory        33422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-23 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33422.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-23, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33423
in-theory        33423
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-22 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33423.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-22, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33424
in-theory        33424
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-21 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33424.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-21, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33425
in-theory        33425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-20 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33425.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-20, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33426
in-theory        33426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-19 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33426.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-19, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33427
in-theory        33427
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-7 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33427.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-7, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33428
in-theory        33428
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) or H)
theorem-size     31
proof            (modus-ponens tm-6 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-6 tm-5 tm-2 tm-7)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33428.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) or H), M:tm-6, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33429
in-theory        33429
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33429.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) and A)), M:tm-5, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33430
in-theory        33430
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-1 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-1 tm-5 tm-2 tm-7)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33430.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-1, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33431
in-theory        33431
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33431.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-480, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33432
in-theory        33432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33432.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-469, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33433
in-theory        33433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33433.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H))), M:tm-456, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33434
in-theory        33434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33434.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-453, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33435
in-theory        33435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33435.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-443, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33436
in-theory        33436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33436.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-409, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33437
in-theory        33437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33437.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-400, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33438
in-theory        33438
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33438.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-391, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33439
in-theory        33439
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33439.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-382, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33440
in-theory        33440
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33440.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-373, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33441
in-theory        33441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33441.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-364, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33442
in-theory        33442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33442.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-354, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33443
in-theory        33443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33443.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33444
in-theory        33444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33444.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-338, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33445
in-theory        33445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33445.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-327, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33446
in-theory        33446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33446.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-326, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33447
in-theory        33447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33447.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-325, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33448
in-theory        33448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33448.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-324, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33449
in-theory        33449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33449.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-323, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33450
in-theory        33450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33450.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33451
in-theory        33451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33451.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33452
in-theory        33452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33452.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33453
in-theory        33453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33453.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33454
in-theory        33454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33454.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-311, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33455
in-theory        33455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33455.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)), M:tm-310, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33456
in-theory        33456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33456.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G))), M:tm-309, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33457
in-theory        33457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-487 ((A (-> Am (-> Bm Am))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33457.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-308, m:tm-487, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-33458
in-theory        33458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (B -> A)))
theorem-size     27
proof            (modus-ponens tm-307 tm-487 ((A (-> Am (-> Bm Am))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33458.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (B -> A))), M:tm-307, m:tm-487, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-33459
in-theory        33459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33459.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-305, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33460
in-theory        33460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33460.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-303, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33461
in-theory        33461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33461.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-270, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33462
in-theory        33462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33462.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-239, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33463
in-theory        33463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33463.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-210, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33464
in-theory        33464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33464.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-183, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33465
in-theory        33465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33465.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-157, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33466
in-theory        33466
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33466.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-147, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33467
in-theory        33467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33467.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-134, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33468
in-theory        33468
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33468.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-125, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33469
in-theory        33469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33469.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-113, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33470
in-theory        33470
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33470.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-105, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33471
in-theory        33471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33471.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-95, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33472
in-theory        33472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33472.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-83, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33473
in-theory        33473
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33473.        (((not (not A)) -> A) and ((B -> (C -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-76, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33474
in-theory        33474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33474.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-69, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33475
in-theory        33475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33475.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-54, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33476
in-theory        33476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33476.        ((A -> (B or A)) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-42, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33477
in-theory        33477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33477.        ((A -> (A or B)) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-32, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33478
in-theory        33478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33478.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-23, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33479
in-theory        33479
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33479.        (((A and B) -> B) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-22, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33480
in-theory        33480
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33480.        (((A and B) -> A) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-21, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33481
in-theory        33481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33481.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-20, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33482
in-theory        33482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33482.        ((A -> (B -> A)) and ((C -> (D -> C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-19, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33483
in-theory        33483
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-7 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-7 tm-5 tm-1 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33483.        (A or ((B -> (C -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-7, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33484
in-theory        33484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-6 tm-5 tm-1 tm-7 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33484.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G), M:tm-6, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33485
in-theory        33485
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33485.        (A -> (((B -> (C -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A)), M:tm-5, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33486
in-theory        33486
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-1 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-1 tm-5 tm-7 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33486.        (A -> ((B -> (C -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-1, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33487
in-theory        33487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-480 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33487.        ((A or (B -> (C -> B))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-480, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33488
in-theory        33488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-469 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33488.        ((A -> (B -> (B or C))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-469, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33489
in-theory        33489
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33489.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (F or G))), M:tm-456, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33490
in-theory        33490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-453 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33490.        ((A -> ((B -> (B or C)) and A)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-453, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33491
in-theory        33491
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (F or G)) and (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33491.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (F or G)) and (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-443, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33492
in-theory        33492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-409 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33492.        (((A -> (A or B)) or C) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-409, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33493
in-theory        33493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-400 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33493.        (((A -> (B -> (A and B))) or C) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-400, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33494
in-theory        33494
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-391 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33494.        ((((A and B) -> B) or C) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-391, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33495
in-theory        33495
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-382 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33495.        ((((A and B) -> A) or C) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-382, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33496
in-theory        33496
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-373 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33496.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-373, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33497
in-theory        33497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-364 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33497.        (((A -> (B -> A)) or C) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-364, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33498
in-theory        33498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-354 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33498.        ((A -> (B -> (C -> (B and C)))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-354, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33499
in-theory        33499
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33499.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33500
in-theory        33500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-338 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33500.        (((A -> B) -> (A -> (A and B))) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-338, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33501
in-theory        33501
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> (F and G))) and (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33501.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> (F and G))) and (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-327, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33502
in-theory        33502
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> G) and (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33502.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> G) and (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-326, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33503
in-theory        33503
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> F) and (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33503.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> F) and (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-325, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33504
in-theory        33504
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33504.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-324, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33505
in-theory        33505
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> F)) and (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33505.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> F)) and (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-323, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33506
in-theory        33506
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33506.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> G)), M:tm-322, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33507
in-theory        33507
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33507.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> F)), M:tm-320, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33508
in-theory        33508
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33508.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33509
in-theory        33509
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33509.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> F))), M:tm-315, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33510
in-theory        33510
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F or (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33510.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F or (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-311, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33511
in-theory        33511
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33511.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F)), M:tm-310, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33512
in-theory        33512
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33512.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F))), M:tm-309, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33513
in-theory        33513
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33513.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-305, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33514
in-theory        33514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-303 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33514.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-303, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33515
in-theory        33515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-270 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33515.        ((A -> (((B and C) -> C) and A)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-270, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33516
in-theory        33516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-239 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33516.        ((A -> (((B and C) -> B) and A)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-239, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33517
in-theory        33517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-210 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33517.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-210, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33518
in-theory        33518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-183 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33518.        ((A -> ((B -> (C -> B)) and A)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-183, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33519
in-theory        33519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-157 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33519.        ((A -> ((B and C) -> C)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-157, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33520
in-theory        33520
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-147 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33520.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-147, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33521
in-theory        33521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-134 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33521.        ((A -> ((B and C) -> B)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-134, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33522
in-theory        33522
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-125 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33522.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-125, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33523
in-theory        33523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-113 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33523.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-113, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33524
in-theory        33524
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     37
proof            (modus-ponens tm-105 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33524.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-105, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33525
in-theory        33525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-95 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33525.        (((A -> B) -> (A -> A)) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-95, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33526
in-theory        33526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-83 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33526.        ((A -> (B -> (C -> B))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-83, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33527
in-theory        33527
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     23
proof            (modus-ponens tm-76 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33527.        (((not (not A)) -> A) and (B or (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-76, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33528
in-theory        33528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     29
proof            (modus-ponens tm-69 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33528.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-69, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33529
in-theory        33529
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-54 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33529.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-54, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33530
in-theory        33530
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-42 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33530.        ((A -> (B or A)) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-42, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33531
in-theory        33531
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-32 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33531.        ((A -> (A or B)) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-32, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33532
in-theory        33532
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-23 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33532.        ((A -> (B -> (A and B))) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-23, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33533
in-theory        33533
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-22 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33533.        (((A and B) -> B) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-22, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33534
in-theory        33534
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-21 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33534.        (((A and B) -> A) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-21, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33535
in-theory        33535
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-20 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33535.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-20, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33536
in-theory        33536
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-19 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33536.        ((A -> (B -> A)) and (C or (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-19, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33537
in-theory        33537
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     19
proof            (modus-ponens tm-7 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-7 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33537.        (A or (B or (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-7, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33538
in-theory        33538
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-6 tm-7 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33538.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F), M:tm-6, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33539
in-theory        33539
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33539.        (A -> ((B or (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and A)), M:tm-5, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33540
in-theory        33540
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     19
proof            (modus-ponens tm-1 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-1 tm-7 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33540.        (A -> (B or (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-1, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33541
in-theory        33541
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-480 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33541.        ((A or (B -> (C -> B))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-480, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33542
in-theory        33542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-469 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33542.        ((A -> (B -> (B or C))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-469, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33543
in-theory        33543
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33543.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (F or G))), M:tm-456, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33544
in-theory        33544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-453 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33544.        ((A -> ((B -> (B or C)) and A)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-453, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33545
in-theory        33545
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (F or G)) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-443 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33545.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (F or G)) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-443, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33546
in-theory        33546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-409 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33546.        (((A -> (A or B)) or C) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-409, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33547
in-theory        33547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-400 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33547.        (((A -> (B -> (A and B))) or C) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-400, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33548
in-theory        33548
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-391 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33548.        ((((A and B) -> B) or C) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-391, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33549
in-theory        33549
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-382 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33549.        ((((A and B) -> A) or C) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-382, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33550
in-theory        33550
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-373 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33550.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-373, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33551
in-theory        33551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-364 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33551.        (((A -> (B -> A)) or C) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-364, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33552
in-theory        33552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-354 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33552.        ((A -> (B -> (C -> (B and C)))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-354, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33553
in-theory        33553
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33553.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (G -> (F and G)))), M:tm-341, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33554
in-theory        33554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     27
proof            (modus-ponens tm-338 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33554.        (((A -> B) -> (A -> (A and B))) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-338, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33555
in-theory        33555
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G -> (F and G))) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     43
proof            (modus-ponens tm-327 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33555.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G -> (F and G))) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-327, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33556
in-theory        33556
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((F and G) -> G) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-326 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33556.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((F and G) -> G) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-326, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33557
in-theory        33557
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((F and G) -> F) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-325 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33557.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((F and G) -> F) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-325, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33558
in-theory        33558
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     49
proof            (modus-ponens tm-324 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33558.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-324, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33559
in-theory        33559
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G -> F)) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-323 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33559.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G -> F)) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-323, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33560
in-theory        33560
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33560.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F and G) -> G)), M:tm-322, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33561
in-theory        33561
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33561.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F and G) -> F)), M:tm-320, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33562
in-theory        33562
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33562.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33563
in-theory        33563
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33563.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (G -> F))), M:tm-315, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33564
in-theory        33564
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F or ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     37
proof            (modus-ponens tm-311 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33564.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F or ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-311, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33565
in-theory        33565
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33565.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) or F)), M:tm-310, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33566
in-theory        33566
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33566.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and F))), M:tm-309, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33567
in-theory        33567
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     37
proof            (modus-ponens tm-305 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33567.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-305, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33568
in-theory        33568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     29
proof            (modus-ponens tm-303 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33568.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-303, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33569
in-theory        33569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-270 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-4 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33569.        ((A -> (((B and C) -> C) and A)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-270, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33570
in-theory        33570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-239 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-3 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33570.        ((A -> (((B and C) -> B) and A)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-239, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33571
in-theory        33571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     35
proof            (modus-ponens tm-210 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33571.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-210, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33572
in-theory        33572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-183 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33572.        ((A -> ((B -> (C -> B)) and A)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-183, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33573
in-theory        33573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-157 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33573.        ((A -> ((B and C) -> C)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-157, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33574
in-theory        33574
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     33
proof            (modus-ponens tm-147 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33574.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-147, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33575
in-theory        33575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-134 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33575.        ((A -> ((B and C) -> B)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-134, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33576
in-theory        33576
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     33
proof            (modus-ponens tm-125 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33576.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-125, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33577
in-theory        33577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-113 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33577.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-113, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33578
in-theory        33578
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     37
proof            (modus-ponens tm-105 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33578.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-105, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33579
in-theory        33579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     25
proof            (modus-ponens tm-95 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33579.        (((A -> B) -> (A -> A)) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-95, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33580
in-theory        33580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-83 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33580.        ((A -> (B -> (C -> B))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-83, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33581
in-theory        33581
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     23
proof            (modus-ponens tm-76 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-10 tm-6 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33581.        (((not (not A)) -> A) and ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-76, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33582
in-theory        33582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     29
proof            (modus-ponens tm-69 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-9 tm-6 tm-7 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33582.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-69, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33583
in-theory        33583
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-54 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33583.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-54, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33584
in-theory        33584
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-42 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33584.        ((A -> (B or A)) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-42, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33585
in-theory        33585
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-32 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33585.        ((A -> (A or B)) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-32, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33586
in-theory        33586
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     25
proof            (modus-ponens tm-23 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33586.        ((A -> (B -> (A and B))) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-23, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33587
in-theory        33587
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-22 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-4 tm-6 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33587.        (((A and B) -> B) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-22, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33588
in-theory        33588
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-21 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-3 tm-6 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33588.        (((A and B) -> A) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-21, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33589
in-theory        33589
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-20 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33589.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-20, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33590
in-theory        33590
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     23
proof            (modus-ponens tm-19 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33590.        ((A -> (B -> A)) and ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-19, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33591
in-theory        33591
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     19
proof            (modus-ponens tm-7 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-7 tm-6 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33591.        (A or ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-7, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33592
in-theory        33592
times-derived    2
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-6 tm-7 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33592.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) or F), M:tm-6, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33593
in-theory        33593
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33593.        (A -> (((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F) and A)), M:tm-5, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33594
in-theory        33594
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     19
proof            (modus-ponens tm-1 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-1 tm-6 tm-7 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33594.        (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-1, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33595
in-theory        33595
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-490 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33595.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or E))), M:tm-490, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-33596
in-theory        33596
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-33596.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))), M:tm-490, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-33597
in-theory        33597
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> (not F)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-490 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-33597.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> (not F)) -> (not E)))), M:tm-490, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-33598
in-theory        33598
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((not (not E)) -> E))
theorem-size     21
proof            (modus-ponens tm-490 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10.           ((not (not A)) -> A), axiom
tm-33598.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((not (not E)) -> E)), M:tm-490, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-33599
in-theory        33599
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-490 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33599.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> F)))), M:tm-490, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-33600
in-theory        33600
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-490 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-33600.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> E))), M:tm-490, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-33601
in-theory        33601
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-490 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-33601.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-490, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-33602
in-theory        33602
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-33602.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-490, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-33603
in-theory        33603
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-490 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-33603.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))), M:tm-490, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-33604
in-theory        33604
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-490 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-33604.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F and G) -> F))), M:tm-490, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-33605
in-theory        33605
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))
theorem-size     31
proof            (modus-ponens tm-490 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-33605.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))), M:tm-490, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-33606
in-theory        33606
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-490 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-33606.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F and G) -> G))), M:tm-490, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-33607
in-theory        33607
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> F)) and E)))
theorem-size     25
proof            (modus-ponens tm-490 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33607.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> F)) and E))), M:tm-490, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-33608
in-theory        33608
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     33
proof            (modus-ponens tm-490 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-33608.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-490, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-33609
in-theory        33609
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> F) and E)))
theorem-size     25
proof            (modus-ponens tm-490 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-33609.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> F) and E))), M:tm-490, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-33610
in-theory        33610
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> G) and E)))
theorem-size     25
proof            (modus-ponens tm-490 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-33610.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> G) and E))), M:tm-490, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-33611
in-theory        33611
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (F and G))) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-33611.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (F and G))) and E))), M:tm-490, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-33612
in-theory        33612
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-490 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-33612.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (E and F)))), M:tm-490, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-33613
in-theory        33613
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-33613.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (F and G))))), M:tm-490, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-33614
in-theory        33614
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-490 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33614.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) or G)), M:tm-490, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-33615
in-theory        33615
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))
theorem-size     31
proof            (modus-ponens tm-490 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-33615.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)), M:tm-490, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-33616
in-theory        33616
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) or G))
theorem-size     23
proof            (modus-ponens tm-490 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-33616.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) or G)), M:tm-490, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-33617
in-theory        33617
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) or G))
theorem-size     23
proof            (modus-ponens tm-490 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-33617.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) or G)), M:tm-490, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-33618
in-theory        33618
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) or G))
theorem-size     25
proof            (modus-ponens tm-490 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-33618.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) or G)), M:tm-490, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-33619
in-theory        33619
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) or G))
theorem-size     23
proof            (modus-ponens tm-490 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33619.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) or G)), M:tm-490, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-33620
in-theory        33620
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (F or G)) and E)))
theorem-size     25
proof            (modus-ponens tm-490 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33620.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (F or G)) and E))), M:tm-490, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-33621
in-theory        33621
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-490 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33621.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (F or G)))), M:tm-490, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-33622
in-theory        33622
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-490 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33622.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> F)))), M:tm-490, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-33623
in-theory        33623
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33623.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-490, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-33624
in-theory        33624
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-490 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-33624.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F and G) -> F))), M:tm-490, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-33625
in-theory        33625
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-490 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-33625.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F and G) -> G))), M:tm-490, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-33626
in-theory        33626
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-33626.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (F and G))))), M:tm-490, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-33627
in-theory        33627
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-490 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33627.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (F or G)))), M:tm-490, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-33628
in-theory        33628
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-490 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-33628.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G or F)))), M:tm-490, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-33629
in-theory        33629
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) or G))
theorem-size     23
proof            (modus-ponens tm-490 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-33629.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) or G)), M:tm-490, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-33630
in-theory        33630
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G or F)) and E)))
theorem-size     25
proof            (modus-ponens tm-490 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-33630.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G or F)) and E))), M:tm-490, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-33631
in-theory        33631
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-490 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-33631.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G or F)))), M:tm-490, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-33632
in-theory        33632
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-490 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33632.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))), M:tm-490, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-33633
in-theory        33633
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     41
proof            (modus-ponens tm-490 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-33633.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-490, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-33634
in-theory        33634
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (((E and G) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-490 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-33634.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (((E and G) or E) -> F))), M:tm-490, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-33635
in-theory        33635
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (((G and E) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-490 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-33635.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (((G and E) or E) -> F))), M:tm-490, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-33636
in-theory        33636
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-490 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-33636.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))), M:tm-490, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-33637
in-theory        33637
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> ((E or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-490 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-33637.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> ((E or (E or F)) -> G))), M:tm-490, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-33638
in-theory        33638
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> ((F or (E or F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-490 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-33638.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E or F) -> G) -> ((F or (E or F)) -> G))), M:tm-490, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-33639
in-theory        33639
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     43
proof            (modus-ponens tm-490 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-33639.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-490, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-33640
in-theory        33640
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-33640.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-490, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-33641
in-theory        33641
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))
theorem-size     31
proof            (modus-ponens tm-490 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-33641.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)), M:tm-490, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-33642
in-theory        33642
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E)))
theorem-size     33
proof            (modus-ponens tm-490 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-33642.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E))), M:tm-490, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-33643
in-theory        33643
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-490 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-33643.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G)))), M:tm-490, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-33644
in-theory        33644
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-33644.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-490, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-33645
in-theory        33645
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> E))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-490 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33645.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> E))) -> (not E))), M:tm-490, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-33646
in-theory        33646
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-33646.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G))))), M:tm-490, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-33647
in-theory        33647
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (not E)) -> (not (E and F))))
theorem-size     27
proof            (modus-ponens tm-490 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-33647.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (not E)) -> (not (E and F)))), M:tm-490, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-33648
in-theory        33648
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (not F)) -> (not (E and F))))
theorem-size     27
proof            (modus-ponens tm-490 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-33648.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (not F)) -> (not (E and F)))), M:tm-490, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-33649
in-theory        33649
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (E and F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-33649.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (E and F)))) -> (not E))), M:tm-490, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-33650
in-theory        33650
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (E or F))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-490 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-33650.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (E or F))) -> (not E))), M:tm-490, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-33651
in-theory        33651
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F or E))) -> (not E)))
theorem-size     25
proof            (modus-ponens tm-490 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-33651.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F or E))) -> (not E))), M:tm-490, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-33652
in-theory        33652
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F))))
theorem-size     35
proof            (modus-ponens tm-490 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-8)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-33652.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F)))), M:tm-490, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-33653
in-theory        33653
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-490 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-33653.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F)))), M:tm-490, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-33654
in-theory        33654
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G)))
theorem-size     39
proof            (modus-ponens tm-490 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-9)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-33654.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G))), M:tm-490, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-33655
in-theory        33655
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-33655.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-490, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-33656
in-theory        33656
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G))
theorem-size     29
proof            (modus-ponens tm-490 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-33656.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G)), M:tm-490, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-33657
in-theory        33657
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E)))
theorem-size     31
proof            (modus-ponens tm-490 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-33657.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E))), M:tm-490, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-33658
in-theory        33658
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-490 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-33658.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E)))), M:tm-490, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-33659
in-theory        33659
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-33659.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-490, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-33660
in-theory        33660
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((not (not E)) -> (not E)) -> (not (not (not E)))))
theorem-size     27
proof            (modus-ponens tm-490 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-10)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-33660.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((not (not E)) -> (not E)) -> (not (not (not E))))), M:tm-490, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-33661
in-theory        33661
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (((not (not E)) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-490 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-10)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-33661.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (((not (not E)) or E) -> F))), M:tm-490, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-33662
in-theory        33662
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-490 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-33662.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((not (not F)) -> F))), M:tm-490, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-33663
in-theory        33663
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((not (not E)) -> E) or F))
theorem-size     23
proof            (modus-ponens tm-490 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-33663.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((not (not E)) -> E) or F)), M:tm-490, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-33664
in-theory        33664
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((not (not F)) -> F) and E)))
theorem-size     25
proof            (modus-ponens tm-490 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-33664.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((not (not F)) -> F) and E))), M:tm-490, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-33665
in-theory        33665
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F)))
theorem-size     31
proof            (modus-ponens tm-490 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-33665.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F))), M:tm-490, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-33666
in-theory        33666
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-490 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-33666.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((not (not F)) -> F))), M:tm-490, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-33667
in-theory        33667
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (G -> F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-33667.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (G -> F)))) -> (not E))), M:tm-490, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-33668
in-theory        33668
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-490 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-33668.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G))), M:tm-490, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-33669
in-theory        33669
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-33669.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (H -> G))))), M:tm-490, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33670
in-theory        33670
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G -> F))) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-33670.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G -> F))) or H)), M:tm-490, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-33671
in-theory        33671
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (H -> G))) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-33671.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (H -> G))) and E))), M:tm-490, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-33672
in-theory        33672
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-490 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-33672.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (G -> F)))), M:tm-490, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-33673
in-theory        33673
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-33673.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (H -> G))))), M:tm-490, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-33674
in-theory        33674
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> E))
theorem-size     19
proof            (modus-ponens tm-490 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33674.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> E)), M:tm-490, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-33675
in-theory        33675
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> G)) -> (E -> (F -> G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-33675.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> G)) -> (E -> (F -> G)))), M:tm-490, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-33676
in-theory        33676
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> (E and F)))
theorem-size     23
proof            (modus-ponens tm-490 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-33676.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> (E and F))), M:tm-490, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-33677
in-theory        33677
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> F)))
theorem-size     23
proof            (modus-ponens tm-490 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-33677.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> F))), M:tm-490, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-33678
in-theory        33678
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((not (not E)) -> (not (not E))))
theorem-size     23
proof            (modus-ponens tm-490 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-33678.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((not (not E)) -> (not (not E)))), M:tm-490, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-33679
in-theory        33679
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (E -> E))) -> (not (E -> F))))
theorem-size     29
proof            (modus-ponens tm-490 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-33679.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (E -> E))) -> (not (E -> F)))), M:tm-490, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-33680
in-theory        33680
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-490 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-33680.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F))), M:tm-490, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-33681
in-theory        33681
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-490 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-33681.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (F -> F)))), M:tm-490, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-33682
in-theory        33682
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (E -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-490 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-33682.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (E -> E)) or G)), M:tm-490, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-33683
in-theory        33683
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (F -> F)) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-33683.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (F -> F)) and E))), M:tm-490, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-33684
in-theory        33684
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> E) -> ((E -> F) -> E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-33684.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> E) -> ((E -> F) -> E))), M:tm-490, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-33685
in-theory        33685
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-490 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-33685.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (F -> F)))), M:tm-490, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-33686
in-theory        33686
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> E) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-33686.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> E) -> G)) -> (E -> G))), M:tm-490, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-33687
in-theory        33687
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E -> F)) -> (E -> F)))
theorem-size     25
proof            (modus-ponens tm-490 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-33687.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E -> F)) -> (E -> F))), M:tm-490, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-33688
in-theory        33688
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F))))
theorem-size     35
proof            (modus-ponens tm-490 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-33688.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F)))), M:tm-490, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-33689
in-theory        33689
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> (not ((E -> (F -> G)) -> (E -> G)))) -> (not ((E -> (F -> G)) -> (E -> F)))))
theorem-size     47
proof            (modus-ponens tm-490 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-33689.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> (not ((E -> (F -> G)) -> (E -> G)))) -> (not ((E -> (F -> G)) -> (E -> F))))), M:tm-490, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-33690
in-theory        33690
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> G)) -> H) -> ((((E -> (F -> G)) -> (E -> F)) or ((E -> (F -> G)) -> (E -> G))) -> H)))
theorem-size     49
proof            (modus-ponens tm-490 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-33690.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> G)) -> H) -> ((((E -> (F -> G)) -> (E -> F)) or ((E -> (F -> G)) -> (E -> G))) -> H))), M:tm-490, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-33691
in-theory        33691
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-33691.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-490, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-33692
in-theory        33692
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H))
theorem-size     37
proof            (modus-ponens tm-490 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-33692.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H)), M:tm-490, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-33693
in-theory        33693
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E)))
theorem-size     39
proof            (modus-ponens tm-490 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-33693.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E))), M:tm-490, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-33694
in-theory        33694
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> (E -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-490 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-33694.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> (E -> F)) -> (E -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G)))), M:tm-490, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-33695
in-theory        33695
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-33695.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-490, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-33696
in-theory        33696
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (((E -> F) -> (E -> G)) -> H)) -> ((E -> (F -> G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-490 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-33696.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (((E -> F) -> (E -> G)) -> H)) -> ((E -> (F -> G)) -> H))), M:tm-490, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-33697
in-theory        33697
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E)))
theorem-size     35
proof            (modus-ponens tm-490 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-33697.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E))), M:tm-490, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-33698
in-theory        33698
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) -> ((I or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) -> H)))
theorem-size     49
proof            (modus-ponens tm-490 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-33698.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) -> ((I or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) -> H))), M:tm-490, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-33699
in-theory        33699
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-490 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33699.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-490, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33700
in-theory        33700
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-490 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33700.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-490, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-33701
in-theory        33701
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-490 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33701.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-490, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-33702
in-theory        33702
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-490 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-33702.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H))))), M:tm-490, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-33703
in-theory        33703
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-490 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33703.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-490, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-33704
in-theory        33704
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) and E) -> F))
theorem-size     23
proof            (modus-ponens tm-490 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-33704.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) and E) -> F)), M:tm-490, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-33705
in-theory        33705
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> E)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-490 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-33705.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> E)) -> G) and H) -> G)), M:tm-490, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-33706
in-theory        33706
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) and I) -> H))
theorem-size     35
proof            (modus-ponens tm-490 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-33706.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) and I) -> H)), M:tm-490, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-33707
in-theory        33707
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F)))
theorem-size     37
proof            (modus-ponens tm-490 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-33707.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F))), M:tm-490, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-33708
in-theory        33708
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E)))
theorem-size     31
proof            (modus-ponens tm-490 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-33708.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E))), M:tm-490, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-33709
in-theory        33709
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> E) -> (not (((E -> F) and G) -> F))) -> (not (((E -> F) and G) -> E))))
theorem-size     41
proof            (modus-ponens tm-490 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-33709.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> E) -> (not (((E -> F) and G) -> F))) -> (not (((E -> F) and G) -> E)))), M:tm-490, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-33710
in-theory        33710
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> F) -> H) -> (((((E -> F) and G) -> E) or (((E -> F) and G) -> F)) -> H)))
theorem-size     43
proof            (modus-ponens tm-490 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-33710.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> F) -> H) -> (((((E -> F) and G) -> E) or (((E -> F) and G) -> F)) -> H))), M:tm-490, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-33711
in-theory        33711
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-490 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-33711.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-490, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-33712
in-theory        33712
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H))
theorem-size     33
proof            (modus-ponens tm-490 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-33712.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H)), M:tm-490, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-33713
in-theory        33713
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E)))
theorem-size     35
proof            (modus-ponens tm-490 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-33713.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E))), M:tm-490, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-33714
in-theory        33714
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F)))
theorem-size     39
proof            (modus-ponens tm-490 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-33714.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F))), M:tm-490, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-33715
in-theory        33715
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-490 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-33715.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-490, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-33716
in-theory        33716
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> E) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-490 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-33716.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> E) -> G) and H) -> G)), M:tm-490, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-33717
in-theory        33717
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (E -> G)) -> ((E and F) -> G)))
theorem-size     29
proof            (modus-ponens tm-490 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-33717.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (E -> G)) -> ((E and F) -> G))), M:tm-490, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-33718
in-theory        33718
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F and G) -> F))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-1 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-33718.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F and G) -> F))) -> (not E))), M:tm-490, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-33719
in-theory        33719
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G)))
theorem-size     33
proof            (modus-ponens tm-490 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-33719.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G))), M:tm-490, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-33720
in-theory        33720
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-490 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-33720.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G and H) -> G)))), M:tm-490, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-33721
in-theory        33721
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F and G) -> F)) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-33721.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F and G) -> F)) or H)), M:tm-490, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-33722
in-theory        33722
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G and H) -> G)) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-33722.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G and H) -> G)) and E))), M:tm-490, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-33723
in-theory        33723
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F and G)) -> (E -> F)))
theorem-size     25
proof            (modus-ponens tm-490 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-33723.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F and G)) -> (E -> F))), M:tm-490, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-33724
in-theory        33724
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-490 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-33724.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G and H) -> G)))), M:tm-490, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-33725
in-theory        33725
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (E -> F)) -> F))
theorem-size     23
proof            (modus-ponens tm-490 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-33725.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (E -> F)) -> F)), M:tm-490, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-33726
in-theory        33726
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (G -> F)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-490 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-33726.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (G -> F)) -> H)) -> H)), M:tm-490, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-33727
in-theory        33727
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I))
theorem-size     35
proof            (modus-ponens tm-490 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-33727.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I)), M:tm-490, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-33728
in-theory        33728
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (((F and G) -> F) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-490 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-33728.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (((F and G) -> F) -> H)) -> H)), M:tm-490, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-33729
in-theory        33729
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-490 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-33729.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G))), M:tm-490, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-33730
in-theory        33730
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F)))
theorem-size     31
proof            (modus-ponens tm-490 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-33730.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F))), M:tm-490, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-33731
in-theory        33731
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> F) -> (not ((E and (F -> G)) -> G))) -> (not ((E and (F -> G)) -> F))))
theorem-size     41
proof            (modus-ponens tm-490 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-4)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-33731.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> F) -> (not ((E and (F -> G)) -> G))) -> (not ((E and (F -> G)) -> F)))), M:tm-490, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-33732
in-theory        33732
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> G) -> H) -> ((((E and (F -> G)) -> F) or ((E and (F -> G)) -> G)) -> H)))
theorem-size     43
proof            (modus-ponens tm-490 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-33732.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> G) -> H) -> ((((E and (F -> G)) -> F) or ((E and (F -> G)) -> G)) -> H))), M:tm-490, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-33733
in-theory        33733
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-490 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-33733.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-490, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-33734
in-theory        33734
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H))
theorem-size     33
proof            (modus-ponens tm-490 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-33734.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H)), M:tm-490, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-33735
in-theory        33735
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E)))
theorem-size     35
proof            (modus-ponens tm-490 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-33735.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E))), M:tm-490, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-33736
in-theory        33736
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G)))
theorem-size     39
proof            (modus-ponens tm-490 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-33736.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and (F -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G))), M:tm-490, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-33737
in-theory        33737
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-490 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-33737.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-490, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-33738
in-theory        33738
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (((F and G) -> G) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-490 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-33738.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and (((F and G) -> G) -> H)) -> H)), M:tm-490, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-33739
in-theory        33739
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> F) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-490 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-33739.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> F) -> G) and H) -> G)), M:tm-490, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-33740
in-theory        33740
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (F -> G)) -> ((E and F) -> G)))
theorem-size     29
proof            (modus-ponens tm-490 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-33740.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> (F -> G)) -> ((E and F) -> G))), M:tm-490, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-33741
in-theory        33741
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F and G) -> G))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-1 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-33741.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F and G) -> G))) -> (not E))), M:tm-490, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-33742
in-theory        33742
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-490 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-33742.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G))), M:tm-490, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-33743
in-theory        33743
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-490 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-33743.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G and H) -> H)))), M:tm-490, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-33744
in-theory        33744
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F and G) -> G)) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-33744.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F and G) -> G)) or H)), M:tm-490, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-33745
in-theory        33745
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G and H) -> H)) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-33745.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G and H) -> H)) and E))), M:tm-490, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-33746
in-theory        33746
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F and G)) -> (E -> G)))
theorem-size     25
proof            (modus-ponens tm-490 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-33746.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F and G)) -> (E -> G))), M:tm-490, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-33747
in-theory        33747
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-490 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-33747.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G and H) -> H)))), M:tm-490, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-33748
in-theory        33748
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33748.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> G)))), M:tm-490, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33749
in-theory        33749
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-33749.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-490, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-33750
in-theory        33750
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-33750.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G and H) -> G))), M:tm-490, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-33751
in-theory        33751
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-490 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-33751.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G and H) -> H))), M:tm-490, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-33752
in-theory        33752
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-33752.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (G and H))))), M:tm-490, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-33753
in-theory        33753
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-490 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33753.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (G or H)))), M:tm-490, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-33754
in-theory        33754
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-33754.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H or G)))), M:tm-490, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-33755
in-theory        33755
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-33755.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-490, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-33756
in-theory        33756
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-490 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-33756.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-490, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-33757
in-theory        33757
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-33757.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((not (not G)) -> G))), M:tm-490, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-33758
in-theory        33758
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-33758.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I -> H))))), M:tm-490, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-33759
in-theory        33759
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-33759.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (G -> G)))), M:tm-490, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-33760
in-theory        33760
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-490 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-33760.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-490, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-33761
in-theory        33761
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33761.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-490, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33762
in-theory        33762
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-490 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-33762.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-490, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-33763
in-theory        33763
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-490 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-33763.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H and I) -> H)))), M:tm-490, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-33764
in-theory        33764
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-490 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-33764.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-490, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-33765
in-theory        33765
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-490 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-33765.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H and I) -> I)))), M:tm-490, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-33766
in-theory        33766
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-33766.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-490, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-33767
in-theory        33767
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-33767.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E))), M:tm-490, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-33768
in-theory        33768
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> E)) and G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-490 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-33768.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> E)) and G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H))), M:tm-490, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-33769
in-theory        33769
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-490 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-33769.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H -> G)) and F)))), M:tm-490, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-33770
in-theory        33770
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G -> F)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-490 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-33770.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G -> F)) and E)) or H)), M:tm-490, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-33771
in-theory        33771
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H -> G)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-33771.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H -> G)) and F)) and E))), M:tm-490, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-33772
in-theory        33772
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-490 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-33772.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H -> G)) and F)))), M:tm-490, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-33773
in-theory        33773
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-490 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33773.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> H)))), M:tm-490, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-33774
in-theory        33774
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-33774.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-490, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-33775
in-theory        33775
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-490 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-33775.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> H))), M:tm-490, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-33776
in-theory        33776
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-490 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-33776.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> I))), M:tm-490, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-33777
in-theory        33777
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-33777.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (H and I))))), M:tm-490, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-33778
in-theory        33778
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33778.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (H or I)))), M:tm-490, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-33779
in-theory        33779
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-490 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-33779.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I or H)))), M:tm-490, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-33780
in-theory        33780
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-33780.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-490, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-33781
in-theory        33781
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     41
proof            (modus-ponens tm-490 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-33781.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-490, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-33782
in-theory        33782
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((not (not H)) -> H)))
theorem-size     35
proof            (modus-ponens tm-490 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-33782.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((not (not H)) -> H))), M:tm-490, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-33783
in-theory        33783
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-33783.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> I))))), M:tm-490, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-33784
in-theory        33784
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> H))))
theorem-size     37
proof            (modus-ponens tm-490 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-33784.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> H)))), M:tm-490, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-33785
in-theory        33785
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J)))))
theorem-size     49
proof            (modus-ponens tm-490 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-33785.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-490, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-33786
in-theory        33786
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-490 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33786.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-490, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-33787
in-theory        33787
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I))))
theorem-size     45
proof            (modus-ponens tm-490 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-33787.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-490, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-33788
in-theory        33788
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-490 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-33788.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> I)))), M:tm-490, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-33789
in-theory        33789
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J))))
theorem-size     45
proof            (modus-ponens tm-490 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-33789.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-490, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-33790
in-theory        33790
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-490 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-33790.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> J)))), M:tm-490, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-33791
in-theory        33791
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> I)) and H))))
theorem-size     39
proof            (modus-ponens tm-490 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-33791.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-490, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-33792
in-theory        33792
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H))))
theorem-size     47
proof            (modus-ponens tm-490 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-33792.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-490, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-33793
in-theory        33793
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-490 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-33793.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-490, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-33794
in-theory        33794
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-490 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-33794.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E))), M:tm-490, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-33795
in-theory        33795
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H) -> I) -> ((H or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H)) -> I)))
theorem-size     53
proof            (modus-ponens tm-490 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-33795.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H) -> I) -> ((H or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H)) -> I))), M:tm-490, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-33796
in-theory        33796
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-490 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-33796.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-490, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-33797
in-theory        33797
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I))
theorem-size     35
proof            (modus-ponens tm-490 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-33797.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I)), M:tm-490, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-33798
in-theory        33798
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E)))
theorem-size     37
proof            (modus-ponens tm-490 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-33798.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E))), M:tm-490, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-33799
in-theory        33799
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-490 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-33799.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-490, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-33800
in-theory        33800
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33800.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> G)))), M:tm-490, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33801
in-theory        33801
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-33801.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-490, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-33802
in-theory        33802
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-33802.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G and H) -> G))), M:tm-490, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-33803
in-theory        33803
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-490 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-33803.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G and H) -> H))), M:tm-490, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-33804
in-theory        33804
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-33804.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (G and H))))), M:tm-490, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-33805
in-theory        33805
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-490 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33805.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (G or H)))), M:tm-490, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-33806
in-theory        33806
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-33806.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H or G)))), M:tm-490, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-33807
in-theory        33807
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-33807.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-490, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-33808
in-theory        33808
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-490 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-33808.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-490, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-33809
in-theory        33809
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-33809.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((not (not G)) -> G))), M:tm-490, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-33810
in-theory        33810
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-33810.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (I -> H))))), M:tm-490, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-33811
in-theory        33811
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-33811.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (G -> G)))), M:tm-490, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-33812
in-theory        33812
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-490 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-33812.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-490, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-33813
in-theory        33813
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33813.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-490, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33814
in-theory        33814
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-490 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-33814.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-490, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-33815
in-theory        33815
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-490 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-33815.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H and I) -> H)))), M:tm-490, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-33816
in-theory        33816
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-490 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-33816.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-490, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-33817
in-theory        33817
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-490 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-33817.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H and I) -> I)))), M:tm-490, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-33818
in-theory        33818
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-33818.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G)))), M:tm-490, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-33819
in-theory        33819
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-490 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-33819.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-490, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-33820
in-theory        33820
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-33820.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (((H and I) -> H) and G)))), M:tm-490, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-33821
in-theory        33821
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> I) and H))))
theorem-size     39
proof            (modus-ponens tm-490 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-33821.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-490, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-33822
in-theory        33822
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-33822.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G)))), M:tm-490, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-33823
in-theory        33823
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (((F and G) -> F) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-33823.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (((F and G) -> F) and E))) -> (not E))), M:tm-490, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-33824
in-theory        33824
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> E) and G) -> H) -> ((G or (((E and F) -> E) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-490 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-33824.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> E) and G) -> H) -> ((G or (((E and F) -> E) and G)) -> H))), M:tm-490, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-33825
in-theory        33825
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-490 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-33825.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (((G and H) -> G) and F)))), M:tm-490, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-33826
in-theory        33826
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (((F and G) -> F) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-490 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-33826.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (((F and G) -> F) and E)) or H)), M:tm-490, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-33827
in-theory        33827
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (((G and H) -> G) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-33827.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (((G and H) -> G) and F)) and E))), M:tm-490, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-33828
in-theory        33828
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-490 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-33828.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (((G and H) -> G) and F)))), M:tm-490, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-33829
in-theory        33829
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33829.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> G)))), M:tm-490, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33830
in-theory        33830
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-33830.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-490, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-33831
in-theory        33831
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-33831.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G and H) -> G))), M:tm-490, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-33832
in-theory        33832
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-490 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-33832.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G and H) -> H))), M:tm-490, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-33833
in-theory        33833
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-33833.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (G and H))))), M:tm-490, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-33834
in-theory        33834
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-490 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33834.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (G or H)))), M:tm-490, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-33835
in-theory        33835
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-33835.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H or G)))), M:tm-490, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-33836
in-theory        33836
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-33836.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-490, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-33837
in-theory        33837
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-490 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-33837.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-490, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-33838
in-theory        33838
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-33838.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((not (not G)) -> G))), M:tm-490, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-33839
in-theory        33839
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-33839.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (I -> H))))), M:tm-490, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-33840
in-theory        33840
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-33840.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (G -> G)))), M:tm-490, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-33841
in-theory        33841
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-490 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-33841.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-490, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-33842
in-theory        33842
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33842.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-490, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33843
in-theory        33843
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-490 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-33843.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-490, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-33844
in-theory        33844
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-490 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-33844.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H and I) -> H)))), M:tm-490, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-33845
in-theory        33845
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-490 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-33845.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-490, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-33846
in-theory        33846
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-490 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-33846.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H and I) -> I)))), M:tm-490, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-33847
in-theory        33847
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-33847.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G)))), M:tm-490, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-33848
in-theory        33848
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-490 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-33848.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-490, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-33849
in-theory        33849
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-33849.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (((H and I) -> H) and G)))), M:tm-490, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-33850
in-theory        33850
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-33850.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (((H and I) -> I) and G)))), M:tm-490, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-33851
in-theory        33851
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-33851.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (((H and I) -> I) and G)))), M:tm-490, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-33852
in-theory        33852
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> J) and H))))
theorem-size     39
proof            (modus-ponens tm-490 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-33852.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-490, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-33853
in-theory        33853
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-33853.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G)))), M:tm-490, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-33854
in-theory        33854
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (((F and G) -> G) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-33854.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (((F and G) -> G) and E))) -> (not E))), M:tm-490, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-33855
in-theory        33855
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> F) and G) -> H) -> ((G or (((E and F) -> F) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-490 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-33855.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) -> F) and G) -> H) -> ((G or (((E and F) -> F) and G)) -> H))), M:tm-490, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-33856
in-theory        33856
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-490 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-33856.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (((G and H) -> H) and F)))), M:tm-490, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-33857
in-theory        33857
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (((F and G) -> G) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-490 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-33857.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (((F and G) -> G) and E)) or H)), M:tm-490, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-33858
in-theory        33858
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (((G and H) -> H) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-33858.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (((G and H) -> H) and F)) and E))), M:tm-490, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-33859
in-theory        33859
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-490 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-33859.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (((G and H) -> H) and F)))), M:tm-490, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-33860
in-theory        33860
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33860.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> G)))), M:tm-490, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-33861
in-theory        33861
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-33861.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-490, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-33862
in-theory        33862
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-490 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-33862.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G and H) -> G))), M:tm-490, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-33863
in-theory        33863
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-490 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-33863.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G and H) -> H))), M:tm-490, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-33864
in-theory        33864
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-33864.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H))))), M:tm-490, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-33865
in-theory        33865
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-490 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33865.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (G or H)))), M:tm-490, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-33866
in-theory        33866
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-33866.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H or G)))), M:tm-490, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-33867
in-theory        33867
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-33867.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-490, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-33868
in-theory        33868
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-33868.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-490, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-33869
in-theory        33869
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-490 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-33869.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((not (not G)) -> G))), M:tm-490, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-33870
in-theory        33870
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-33870.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H))))), M:tm-490, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-33871
in-theory        33871
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-33871.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G)))), M:tm-490, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-33872
in-theory        33872
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-33872.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-490, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-33873
in-theory        33873
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-490 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-33873.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-490, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-33874
in-theory        33874
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-490 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-33874.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-490, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-33875
in-theory        33875
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-490 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-33875.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H)))), M:tm-490, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-33876
in-theory        33876
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-490 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-33876.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-490, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-33877
in-theory        33877
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-490 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-33877.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I)))), M:tm-490, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-33878
in-theory        33878
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-490 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-33878.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-490, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-33879
in-theory        33879
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-490 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-33879.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-490, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-33880
in-theory        33880
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-490 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-33880.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G)))), M:tm-490, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-33881
in-theory        33881
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-490 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-33881.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G)))), M:tm-490, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-33882
in-theory        33882
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-490 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-33882.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-490, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-33883
in-theory        33883
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-490 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-33883.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-490, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-33884
in-theory        33884
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-490 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-33884.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-490, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-33885
in-theory        33885
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> (I and J))) and H))))
theorem-size     41
proof            (modus-ponens tm-490 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-33885.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-490, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-33886
in-theory        33886
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-490 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-33886.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-490, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-33887
in-theory        33887
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E)))
theorem-size     31
proof            (modus-ponens tm-490 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-33887.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E))), M:tm-490, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-33888
in-theory        33888
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> (E and F))) and G) -> H) -> ((G or ((E -> (F -> (E and F))) and G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-490 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-33888.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> (E and F))) and G) -> H) -> ((G or ((E -> (F -> (E and F))) and G)) -> H))), M:tm-490, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-33889
in-theory        33889
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-490 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-33889.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H -> (G and H))) and F)))), M:tm-490, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-33890
in-theory        33890
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G -> (F and G))) and E)) or H))
theorem-size     29
proof            (modus-ponens tm-490 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-33890.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G -> (F and G))) and E)) or H)), M:tm-490, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-33891
in-theory        33891
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E)))
theorem-size     31
proof            (modus-ponens tm-490 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-33891.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E))), M:tm-490, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-33892
in-theory        33892
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-490 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-33892.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H -> (G and H))) and F)))), M:tm-490, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-33893
in-theory        33893
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> E))))
theorem-size     23
proof            (modus-ponens tm-490 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33893.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> E)))), M:tm-490, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-33894
in-theory        33894
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-33894.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G))))), M:tm-490, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-33895
in-theory        33895
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> ((E and F) and E)))
theorem-size     25
proof            (modus-ponens tm-490 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-33895.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> ((E and F) and E))), M:tm-490, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-33896
in-theory        33896
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> ((E and F) and F)))
theorem-size     25
proof            (modus-ponens tm-490 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-33896.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and F) -> ((E and F) and F))), M:tm-490, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-33897
in-theory        33897
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-33897.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (E and F))))), M:tm-490, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-33898
in-theory        33898
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (E or F))))
theorem-size     23
proof            (modus-ponens tm-490 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-33898.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (E or F)))), M:tm-490, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-33899
in-theory        33899
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F or E))))
theorem-size     23
proof            (modus-ponens tm-490 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-33899.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F or E)))), M:tm-490, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-33900
in-theory        33900
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     33
proof            (modus-ponens tm-490 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-33900.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G))))), M:tm-490, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-33901
in-theory        33901
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-33901.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E))))), M:tm-490, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-33902
in-theory        33902
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((not (not E)) -> ((not (not E)) and E)))
theorem-size     25
proof            (modus-ponens tm-490 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-33902.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((not (not E)) -> ((not (not E)) and E))), M:tm-490, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-33903
in-theory        33903
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-33903.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (G -> F))))), M:tm-490, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-33904
in-theory        33904
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (E -> E))))
theorem-size     27
proof            (modus-ponens tm-490 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-33904.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (E -> E)))), M:tm-490, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-33905
in-theory        33905
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> (((E -> (F -> G)) -> (E -> F)) and ((E -> (F -> G)) -> (E -> G)))))
theorem-size     45
proof            (modus-ponens tm-490 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-33905.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> (E -> F)) -> (((E -> (F -> G)) -> (E -> F)) and ((E -> (F -> G)) -> (E -> G))))), M:tm-490, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-33906
in-theory        33906
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-490 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-33906.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-490, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-33907
in-theory        33907
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) -> E) -> ((((E -> F) and G) -> E) and (((E -> F) and G) -> F))))
theorem-size     39
proof            (modus-ponens tm-490 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-33907.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) -> E) -> ((((E -> F) and G) -> E) and (((E -> F) and G) -> F)))), M:tm-490, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-33908
in-theory        33908
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-490 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-33908.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F and G) -> F)))), M:tm-490, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-33909
in-theory        33909
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) -> F) -> (((E and (F -> G)) -> F) and ((E and (F -> G)) -> G))))
theorem-size     39
proof            (modus-ponens tm-490 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-33909.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) -> F) -> (((E and (F -> G)) -> F) and ((E and (F -> G)) -> G)))), M:tm-490, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-33910
in-theory        33910
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-490 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-33910.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F and G) -> G)))), M:tm-490, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-33911
in-theory        33911
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-490 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-33911.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G -> F)) and E)))), M:tm-490, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-33912
in-theory        33912
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-490 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-33912.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-490, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-33913
in-theory        33913
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-490 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-33913.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (((F and G) -> F) and E)))), M:tm-490, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-33914
in-theory        33914
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-490 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-33914.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (((F and G) -> G) and E)))), M:tm-490, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-33915
in-theory        33915
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-490 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-33915.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G -> (F and G))) and E)))), M:tm-490, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-33916
in-theory        33916
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (E -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-33916.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (E -> (E and F))))), M:tm-490, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-33917
in-theory        33917
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-490 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-33917.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H))))), M:tm-490, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-33918
in-theory        33918
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-33918.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H))))), M:tm-490, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-33919
in-theory        33919
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-33919.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H))))), M:tm-490, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-33920
in-theory        33920
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> (H and I)))))
theorem-size     39
proof            (modus-ponens tm-490 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-33920.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-490, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-33921
in-theory        33921
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-33921.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H))))), M:tm-490, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-33922
in-theory        33922
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F))))
theorem-size     31
proof            (modus-ponens tm-490 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-33922.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F)))), M:tm-490, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-33923
in-theory        33923
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-490 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-33923.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G))), M:tm-490, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-33924
in-theory        33924
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-490 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-33924.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (F -> (F and G))))), M:tm-490, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-33925
in-theory        33925
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (E -> (E and F))) or G))
theorem-size     27
proof            (modus-ponens tm-490 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-33925.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (E -> (E and F))) or G)), M:tm-490, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-33926
in-theory        33926
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (F -> (F and G))) and E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-33926.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (F -> (F and G))) and E))), M:tm-490, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-33927
in-theory        33927
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> E) -> ((E -> F) -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-490 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-33927.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> E) -> ((E -> F) -> (E and F)))), M:tm-490, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-33928
in-theory        33928
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-490 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-33928.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (F -> (F and G))))), M:tm-490, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-33929
in-theory        33929
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-490 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-33929.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (G -> (F and G)))))), M:tm-490, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-33930
in-theory        33930
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-490 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-33930.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I)))))), M:tm-490, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-33931
in-theory        33931
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-490 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-33931.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (I -> (H and I)))))), M:tm-490, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-33932
in-theory        33932
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-490 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-33932.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (I -> (H and I)))))), M:tm-490, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-33933
in-theory        33933
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-490 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-33933.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-490, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-33934
in-theory        33934
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-490 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-33934.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I)))))), M:tm-490, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-33935
in-theory        33935
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (G -> (F and G))) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-490 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-33935.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (G -> (F and G))) -> H)) -> H)), M:tm-490, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-33936
in-theory        33936
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> (E and F))) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-490 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-33936.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> (E and F))) -> G) and H) -> G)), M:tm-490, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-33937
in-theory        33937
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G)))
theorem-size     29
proof            (modus-ponens tm-490 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-33937.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G))), M:tm-490, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-33938
in-theory        33938
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (G -> (F and G))))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-33938.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (G -> (F and G))))) -> (not E))), M:tm-490, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-33939
in-theory        33939
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> (E and F))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G)))
theorem-size     37
proof            (modus-ponens tm-490 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-33939.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> (E and F))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G))), M:tm-490, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-33940
in-theory        33940
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-490 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-33940.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (H -> (G and H)))))), M:tm-490, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-33941
in-theory        33941
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G -> (F and G)))) or H))
theorem-size     27
proof            (modus-ponens tm-490 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-33941.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G -> (F and G)))) or H)), M:tm-490, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-33942
in-theory        33942
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (H -> (G and H)))) and E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-33942.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (H -> (G and H)))) and E))), M:tm-490, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-33943
in-theory        33943
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-490 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-33943.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (G -> (F and G))))), M:tm-490, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-33944
in-theory        33944
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-490 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-33944.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (H -> (G and H)))))), M:tm-490, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-33945
in-theory        33945
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-490 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-33945.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I))), M:tm-490, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-33946
in-theory        33946
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-33946.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H -> G)) or I))), M:tm-490, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-33947
in-theory        33947
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-33947.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H -> G)) or I))), M:tm-490, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-33948
in-theory        33948
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> H)) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-33948.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> H)) or J))), M:tm-490, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-33949
in-theory        33949
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-33949.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H -> G)) or I))), M:tm-490, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-33950
in-theory        33950
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-490 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-33950.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G -> F)) or H))), M:tm-490, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-33951
in-theory        33951
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> E)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-33951.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> E)) or G) or H)), M:tm-490, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-33952
in-theory        33952
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> F)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-33952.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> F)) or H) and E))), M:tm-490, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-33953
in-theory        33953
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-490 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-33953.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> F)) or H))), M:tm-490, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-33954
in-theory        33954
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-490 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-33954.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-490, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-33955
in-theory        33955
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-33955.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-490, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-33956
in-theory        33956
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-33956.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-490, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-33957
in-theory        33957
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K)))
theorem-size     45
proof            (modus-ponens tm-490 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-33957.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-490, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-33958
in-theory        33958
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-33958.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-490, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-33959
in-theory        33959
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-490 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-33959.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-490, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-33960
in-theory        33960
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) or I))
theorem-size     33
proof            (modus-ponens tm-490 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-33960.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) or I)), M:tm-490, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-33961
in-theory        33961
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E)))
theorem-size     35
proof            (modus-ponens tm-490 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-33961.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E))), M:tm-490, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-33962
in-theory        33962
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-490 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-33962.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-490, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-33963
in-theory        33963
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-490 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-33963.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I))), M:tm-490, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-33964
in-theory        33964
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-33964.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G and H) -> G) or I))), M:tm-490, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-33965
in-theory        33965
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-33965.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G and H) -> G) or I))), M:tm-490, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-33966
in-theory        33966
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> H) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-33966.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> H) or J))), M:tm-490, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-33967
in-theory        33967
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-33967.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G and H) -> G) or I))), M:tm-490, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-33968
in-theory        33968
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-490 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-33968.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F and G) -> F) or H))), M:tm-490, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-33969
in-theory        33969
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> E) or G) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-33969.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> E) or G) or H)), M:tm-490, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-33970
in-theory        33970
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F and G) -> F) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-33970.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F and G) -> F) or H) and E))), M:tm-490, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-33971
in-theory        33971
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-490 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-33971.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> F) or H))), M:tm-490, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-33972
in-theory        33972
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-490 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-33972.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I))), M:tm-490, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-33973
in-theory        33973
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-33973.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G and H) -> H) or I))), M:tm-490, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-33974
in-theory        33974
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-33974.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G and H) -> H) or I))), M:tm-490, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-33975
in-theory        33975
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> I) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-33975.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> I) or J))), M:tm-490, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-33976
in-theory        33976
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-33976.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G and H) -> H) or I))), M:tm-490, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-33977
in-theory        33977
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-490 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-33977.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F and G) -> G) or H))), M:tm-490, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-33978
in-theory        33978
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> F) or G) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-33978.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) -> F) or G) or H)), M:tm-490, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-33979
in-theory        33979
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F and G) -> G) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-33979.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F and G) -> G) or H) and E))), M:tm-490, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-33980
in-theory        33980
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-490 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-33980.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F and G) -> G) or H))), M:tm-490, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-33981
in-theory        33981
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-490 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-33981.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I))), M:tm-490, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-33982
in-theory        33982
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-490 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-33982.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I))), M:tm-490, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-33983
in-theory        33983
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-490 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-33983.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I))), M:tm-490, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-33984
in-theory        33984
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> (H and I))) or J)))
theorem-size     39
proof            (modus-ponens tm-490 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-33984.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-490, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-33985
in-theory        33985
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-490 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-33985.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I))), M:tm-490, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-33986
in-theory        33986
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-490 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-33986.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G -> (F and G))) or H))), M:tm-490, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-33987
in-theory        33987
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> (E and F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-490 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-33987.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> (E and F))) or G) or H)), M:tm-490, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-33988
in-theory        33988
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> (F and G))) or H) and E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-33988.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G -> (F and G))) or H) and E))), M:tm-490, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-33989
in-theory        33989
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-490 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-33989.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (F and G))) or H))), M:tm-490, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-33990
in-theory        33990
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-490 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-33990.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I))), M:tm-490, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-33991
in-theory        33991
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-33991.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (G or H)) or I))), M:tm-490, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-33992
in-theory        33992
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-33992.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (G or H)) or I))), M:tm-490, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-33993
in-theory        33993
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (H or I)) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-33993.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (H or I)) or J))), M:tm-490, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-33994
in-theory        33994
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-33994.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (G or H)) or I))), M:tm-490, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-33995
in-theory        33995
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-490 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-33995.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (F or G)) or H))), M:tm-490, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-33996
in-theory        33996
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (E or F)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-33996.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (E or F)) or G) or H)), M:tm-490, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-33997
in-theory        33997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (F or G)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-33997.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (F or G)) or H) and E))), M:tm-490, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-33998
in-theory        33998
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-490 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-33998.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (F or G)) or H))), M:tm-490, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-33999
in-theory        33999
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33999.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> G)))), M:tm-490, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-34000
in-theory        34000
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-34000.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-490, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34001
in-theory        34001
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-34001.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G and H) -> G))), M:tm-490, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-34002
in-theory        34002
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-490 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-34002.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G and H) -> H))), M:tm-490, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-34003
in-theory        34003
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-34003.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (G and H))))), M:tm-490, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-34004
in-theory        34004
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-490 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-34004.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (G or H)))), M:tm-490, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-34005
in-theory        34005
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34005.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H or G)))), M:tm-490, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-34006
in-theory        34006
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-34006.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-490, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-34007
in-theory        34007
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-490 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-34007.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-490, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-34008
in-theory        34008
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-34008.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((not (not G)) -> G))), M:tm-490, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-34009
in-theory        34009
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-34009.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (I -> H))))), M:tm-490, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-34010
in-theory        34010
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-34010.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (G -> G)))), M:tm-490, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-34011
in-theory        34011
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-490 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-34011.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-490, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-34012
in-theory        34012
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34012.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-490, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-34013
in-theory        34013
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-490 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-34013.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-490, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-34014
in-theory        34014
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-490 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-34014.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H and I) -> H)))), M:tm-490, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34015
in-theory        34015
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-490 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-34015.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-490, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-34016
in-theory        34016
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-490 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-34016.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H and I) -> I)))), M:tm-490, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-34017
in-theory        34017
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-34017.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G)))), M:tm-490, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-34018
in-theory        34018
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-490 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-34018.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-490, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-34019
in-theory        34019
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-34019.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G)))), M:tm-490, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-34020
in-theory        34020
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-34020.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G)))), M:tm-490, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-34021
in-theory        34021
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-490 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-34021.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-490, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-34022
in-theory        34022
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-34022.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H))))), M:tm-490, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-34023
in-theory        34023
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-490 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-34023.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I)))))), M:tm-490, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-34024
in-theory        34024
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-34024.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H -> G)) or I))), M:tm-490, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-34025
in-theory        34025
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-34025.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-490, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-34026
in-theory        34026
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-34026.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G and H) -> G) or I))), M:tm-490, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-34027
in-theory        34027
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-34027.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G and H) -> H) or I))), M:tm-490, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-34028
in-theory        34028
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-490 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-34028.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I))), M:tm-490, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-34029
in-theory        34029
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-34029.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (G or H)) or I))), M:tm-490, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-34030
in-theory        34030
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-34030.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G)))), M:tm-490, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-34031
in-theory        34031
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-490 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-34031.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (F or G)) and E)))), M:tm-490, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-34032
in-theory        34032
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-490 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-34032.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G)))), M:tm-490, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-34033
in-theory        34033
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-34033.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G)))), M:tm-490, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-34034
in-theory        34034
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-34034.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G)))), M:tm-490, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-34035
in-theory        34035
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (I or J)) and H))))
theorem-size     39
proof            (modus-ponens tm-490 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-34035.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-490, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-34036
in-theory        34036
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-34036.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G)))), M:tm-490, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-34037
in-theory        34037
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (F or G)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-34037.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (F or G)) and E))) -> (not E))), M:tm-490, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-34038
in-theory        34038
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (E or F)) and G) -> H) -> ((G or ((E -> (E or F)) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-490 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-34038.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (E or F)) and G) -> H) -> ((G or ((E -> (E or F)) and G)) -> H))), M:tm-490, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-34039
in-theory        34039
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-490 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-34039.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (G or H)) and F)))), M:tm-490, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-34040
in-theory        34040
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (F or G)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-490 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-34040.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (F or G)) and E)) or H)), M:tm-490, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-34041
in-theory        34041
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (G or H)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-34041.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (G or H)) and F)) and E))), M:tm-490, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-34042
in-theory        34042
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-490 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-34042.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (G or H)) and F)))), M:tm-490, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-34043
in-theory        34043
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-34043.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (H or I))))), M:tm-490, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-34044
in-theory        34044
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-34044.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (F or G))))), M:tm-490, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-34045
in-theory        34045
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-34045.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I))))), M:tm-490, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-34046
in-theory        34046
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-34046.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (H or I))))), M:tm-490, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-34047
in-theory        34047
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-34047.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (H or I))))), M:tm-490, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-34048
in-theory        34048
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-34048.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (I or J))))), M:tm-490, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-34049
in-theory        34049
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-34049.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (H or I))))), M:tm-490, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-34050
in-theory        34050
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (F or G)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-490 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-34050.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (F or G)) -> H)) -> H)), M:tm-490, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-34051
in-theory        34051
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (E or F)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-490 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-34051.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (E or F)) -> G) and H) -> G)), M:tm-490, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-34052
in-theory        34052
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((E or F) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-34052.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((E or F) -> G)) -> (E -> G))), M:tm-490, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-34053
in-theory        34053
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (F or G)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-1 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-34053.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (F or G)))) -> (not E))), M:tm-490, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-34054
in-theory        34054
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-490 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-34054.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G))), M:tm-490, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-34055
in-theory        34055
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-34055.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (G or H))))), M:tm-490, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-34056
in-theory        34056
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (F or G))) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-34056.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (F or G))) or H)), M:tm-490, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-34057
in-theory        34057
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (G or H))) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-34057.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (G or H))) and E))), M:tm-490, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-34058
in-theory        34058
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-490 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-34058.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (F or G)))), M:tm-490, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-34059
in-theory        34059
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-34059.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (G or H))))), M:tm-490, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-34060
in-theory        34060
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-34060.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (I -> H))))), M:tm-490, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-34061
in-theory        34061
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-34061.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H))))), M:tm-490, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-34062
in-theory        34062
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-34062.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (I -> H))))), M:tm-490, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-34063
in-theory        34063
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-34063.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (I -> H))))), M:tm-490, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-34064
in-theory        34064
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-34064.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> I))))), M:tm-490, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-34065
in-theory        34065
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-34065.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (I -> H))))), M:tm-490, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-34066
in-theory        34066
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-34066.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (H -> G))))), M:tm-490, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-34067
in-theory        34067
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (G -> F))) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-34067.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (G -> F))) or H)), M:tm-490, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-34068
in-theory        34068
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (H -> G))) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-34068.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (H -> G))) and E))), M:tm-490, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-34069
in-theory        34069
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-34069.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (H -> G))))), M:tm-490, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-34070
in-theory        34070
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34070.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-490, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-34071
in-theory        34071
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-490 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34071.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-490, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-34072
in-theory        34072
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34072.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-490, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-34073
in-theory        34073
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34073.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-490, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-34074
in-theory        34074
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     45
proof            (modus-ponens tm-490 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34074.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-490, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-34075
in-theory        34075
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34075.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-490, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-34076
in-theory        34076
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-490 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34076.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-490, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34077
in-theory        34077
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     33
proof            (modus-ponens tm-490 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34077.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-490, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-34078
in-theory        34078
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-490 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34078.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-490, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34079
in-theory        34079
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-480 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34079.        ((A or (B -> (C -> B))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-480, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34080
in-theory        34080
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A) or F))
theorem-size     21
proof            (modus-ponens tm-470 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34080.        (A -> (((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A) or F)), M:tm-470, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-34081
in-theory        34081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-469 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34081.        ((A -> (B -> (B or C))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-469, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34082
in-theory        34082
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (B or C))))
theorem-size     29
proof            (modus-ponens tm-466 tm-490 ((Am (-> A (or A B))) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34082.        ((A or (B -> (B or C))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (B or C)))), M:tm-466, m:tm-490, u:((Am (-> A (or A B))) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (or A B)))))
================================================================
tm-name          tm-34083
in-theory        34083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34083.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (F or G))), M:tm-456, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34084
in-theory        34084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-453 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34084.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-453, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34085
in-theory        34085
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (B or C)) and A)))
theorem-size     33
proof            (modus-ponens tm-450 tm-490 ((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34085.        ((A or ((B -> (B or C)) and A)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-490, u:((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-34086
in-theory        34086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (F or G)) and (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-443 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34086.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (F or G)) and (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-443, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34087
in-theory        34087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-409 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34087.        (((A -> (A or B)) or C) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-409, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34088
in-theory        34088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-400 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34088.        (((A -> (B -> (A and B))) or C) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-400, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34089
in-theory        34089
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-391 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34089.        ((((A and B) -> B) or C) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-391, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34090
in-theory        34090
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-382 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34090.        ((((A and B) -> A) or C) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-382, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34091
in-theory        34091
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-373 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34091.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-373, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34092
in-theory        34092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-364 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34092.        (((A -> (B -> A)) or C) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-364, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34093
in-theory        34093
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A) and B)))
theorem-size     23
proof            (modus-ponens tm-355 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34093.        (A -> (B -> (((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A) and B))), M:tm-355, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-34094
in-theory        34094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-354 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34094.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-354, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34095
in-theory        34095
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (C -> (B and C)))))
theorem-size     33
proof            (modus-ponens tm-351 tm-490 ((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34095.        ((A or (B -> (C -> (B and C)))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-490, u:((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-34096
in-theory        34096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34096.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34097
in-theory        34097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     29
proof            (modus-ponens tm-338 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34097.        (((A -> B) -> (A -> (A and B))) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-338, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34098
in-theory        34098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (A and B))))
theorem-size     31
proof            (modus-ponens tm-335 tm-490 ((Am (-> A (and A B))) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34098.        (((A -> B) or (A -> (A and B))) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> (A and B)))), M:tm-335, m:tm-490, u:((Am (-> A (and A B))) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (and A B)))))
================================================================
tm-name          tm-34099
in-theory        34099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (A -> (A and ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     41
proof            (modus-ponens tm-328 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34099.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (A -> (A and ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-328, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-34100
in-theory        34100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G -> (F and G))) and (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     47
proof            (modus-ponens tm-327 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34100.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G -> (F and G))) and (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-327, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34101
in-theory        34101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F and G) -> G) and (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-326 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34101.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F and G) -> G) and (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-326, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34102
in-theory        34102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F and G) -> F) and (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-325 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34102.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F and G) -> F) and (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-325, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34103
in-theory        34103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     53
proof            (modus-ponens tm-324 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34103.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-324, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34104
in-theory        34104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G -> F)) and (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-323 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34104.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G -> F)) and (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-323, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34105
in-theory        34105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34105.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F and G) -> G)), M:tm-322, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34106
in-theory        34106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34106.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F and G) -> F)), M:tm-320, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34107
in-theory        34107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34107.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34108
in-theory        34108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (A -> A))
theorem-size     23
proof            (modus-ponens tm-316 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34108.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (A -> A)), M:tm-316, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-34109
in-theory        34109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34109.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (G -> F))), M:tm-315, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34110
in-theory        34110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((A -> (not ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))) -> (not A)))
theorem-size     43
proof            (modus-ponens tm-313 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34110.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((A -> (not ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))) -> (not A))), M:tm-313, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-34111
in-theory        34111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A) -> F) -> ((A or ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) -> F)))
theorem-size     61
proof            (modus-ponens tm-312 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34111.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A) -> F) -> ((A or ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) -> F))), M:tm-312, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-34112
in-theory        34112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F or (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     41
proof            (modus-ponens tm-311 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34112.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F or (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-311, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34113
in-theory        34113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34113.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) or F)), M:tm-310, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34114
in-theory        34114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34114.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and F))), M:tm-309, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34115
in-theory        34115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     41
proof            (modus-ponens tm-305 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34115.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-305, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34116
in-theory        34116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     31
proof            (modus-ponens tm-303 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34116.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-303, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34117
in-theory        34117
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (C -> (B and C))) and A)))
theorem-size     37
proof            (modus-ponens tm-300 tm-490 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34117.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-490, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-34118
in-theory        34118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-270 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34118.        ((A -> (((B and C) -> C) and A)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-270, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34119
in-theory        34119
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((B and C) -> C) and A)))
theorem-size     33
proof            (modus-ponens tm-267 tm-490 ((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34119.        ((A or (((B and C) -> C) and A)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((B and C) -> C) and A))), M:tm-267, m:tm-490, u:((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-34120
in-theory        34120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-239 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34120.        ((A -> (((B and C) -> B) and A)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-239, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34121
in-theory        34121
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((B and C) -> B) and A)))
theorem-size     33
proof            (modus-ponens tm-236 tm-490 ((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34121.        ((A or (((B and C) -> B) and A)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((B and C) -> B) and A))), M:tm-236, m:tm-490, u:((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-34122
in-theory        34122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     37
proof            (modus-ponens tm-210 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34122.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-210, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34123
in-theory        34123
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     49
proof            (modus-ponens tm-207 tm-490 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34123.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-490, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-34124
in-theory        34124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-183 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34124.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-183, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34125
in-theory        34125
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (C -> B)) and A)))
theorem-size     33
proof            (modus-ponens tm-180 tm-490 ((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34125.        ((A or ((B -> (C -> B)) and A)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-490, u:((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-34126
in-theory        34126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-157 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34126.        ((A -> ((B and C) -> C)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-157, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34127
in-theory        34127
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B and C) -> C)))
theorem-size     29
proof            (modus-ponens tm-154 tm-490 ((Am (-> (and A B) B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34127.        ((A or ((B and C) -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B and C) -> C))), M:tm-154, m:tm-490, u:((Am (-> (and A B) B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and A B) B))))
================================================================
tm-name          tm-34128
in-theory        34128
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     35
proof            (modus-ponens tm-147 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34128.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-147, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34129
in-theory        34129
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A and (B -> C)) -> C)))
theorem-size     39
proof            (modus-ponens tm-144 tm-490 ((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-7)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34129.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-490, u:((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-34130
in-theory        34130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-134 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34130.        ((A -> ((B and C) -> B)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-134, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34131
in-theory        34131
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B and C) -> B)))
theorem-size     29
proof            (modus-ponens tm-131 tm-490 ((Am (-> (and A B) A)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34131.        ((A or ((B and C) -> B)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B and C) -> B))), M:tm-131, m:tm-490, u:((Am (-> (and A B) A)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and A B) A))))
================================================================
tm-name          tm-34132
in-theory        34132
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     35
proof            (modus-ponens tm-125 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34132.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-125, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34133
in-theory        34133
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((A -> B) and C) -> B)))
theorem-size     39
proof            (modus-ponens tm-122 tm-490 ((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-7)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34133.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-490, u:((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-34134
in-theory        34134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     35
proof            (modus-ponens tm-113 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34134.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-113, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34135
in-theory        34135
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     45
proof            (modus-ponens tm-110 tm-490 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34135.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-490, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-34136
in-theory        34136
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     39
proof            (modus-ponens tm-105 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34136.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-105, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34137
in-theory        34137
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     45
proof            (modus-ponens tm-102 tm-490 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34137.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-490, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-34138
in-theory        34138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     27
proof            (modus-ponens tm-95 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34138.        (((A -> B) -> (A -> A)) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-95, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34139
in-theory        34139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> A)))
theorem-size     27
proof            (modus-ponens tm-92 tm-490 ((Am (-> A A)) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34139.        (((A -> B) or (A -> A)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> A))), M:tm-92, m:tm-490, u:((Am (-> A A)) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A A))))
================================================================
tm-name          tm-34140
in-theory        34140
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)))
theorem-size     21
proof            (modus-ponens tm-84 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34140.        (A -> (B -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))), M:tm-84, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-34141
in-theory        34141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-83 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34141.        ((A -> (B -> (C -> B))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-83, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34142
in-theory        34142
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (C -> B))))
theorem-size     29
proof            (modus-ponens tm-80 tm-490 ((Am (-> A (-> B A))) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34142.        ((A or (B -> (C -> B))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (C -> B)))), M:tm-80, m:tm-490, u:((Am (-> A (-> B A))) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (-> B A)))))
================================================================
tm-name          tm-34143
in-theory        34143
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B)))
theorem-size     25
proof            (modus-ponens tm-76 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-10 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34143.        (((not (not A)) -> A) and (B -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B))), M:tm-76, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34144
in-theory        34144
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))
theorem-size     23
proof            (modus-ponens tm-73 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-7 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34144.        (((not (not A)) or A) -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-73, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-34145
in-theory        34145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     31
proof            (modus-ponens tm-69 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-9 tm-7 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34145.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-69, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34146
in-theory        34146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((A -> (not B)) -> (not A))))
theorem-size     35
proof            (modus-ponens tm-66 tm-490 ((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-7 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34146.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-490, u:((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-34147
in-theory        34147
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-54 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34147.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-54, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34148
in-theory        34148
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-51 tm-490 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34148.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-490, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-34149
in-theory        34149
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (B or A)))
theorem-size     25
proof            (modus-ponens tm-50 tm-490 ((Am (or A B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34149.        ((A or (B or A)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (B or A))), M:tm-50, m:tm-490, u:((Am (or A B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B))))
================================================================
tm-name          tm-34150
in-theory        34150
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B)))
theorem-size     25
proof            (modus-ponens tm-49 tm-490 ((Am (or A B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34150.        ((A or (A or B)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A or B))), M:tm-49, m:tm-490, u:((Am (or A B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (or A B))))
================================================================
tm-name          tm-34151
in-theory        34151
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-48 tm-490 ((Am (-> A (and B A))) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34151.        ((A or (B -> (A and B))) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (B -> (A and B)))), M:tm-48, m:tm-490, u:((Am (-> A (and B A))) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (and B A)))))
================================================================
tm-name          tm-34152
in-theory        34152
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B))
theorem-size     23
proof            (modus-ponens tm-47 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-7 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34152.        (((A and B) or B) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B)), M:tm-47, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-34153
in-theory        34153
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-46 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-7 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34153.        (((A and B) or A) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)), M:tm-46, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-34154
in-theory        34154
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-45 tm-490 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34154.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-490, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-34155
in-theory        34155
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (B -> A)))
theorem-size     25
proof            (modus-ponens tm-44 tm-490 ((Am (-> A B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34155.        ((A or (B -> A)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (B -> A))), M:tm-44, m:tm-490, u:((Am (-> A B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A B))))
================================================================
tm-name          tm-34156
in-theory        34156
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-42 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34156.        ((A -> (B or A)) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-42, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34157
in-theory        34157
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-32 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34157.        ((A -> (A or B)) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-32, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34158
in-theory        34158
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))
theorem-size     21
proof            (modus-ponens tm-24 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34158.        (A -> (A and ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))), M:tm-24, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-34159
in-theory        34159
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     27
proof            (modus-ponens tm-23 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34159.        ((A -> (B -> (A and B))) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-23, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34160
in-theory        34160
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-22 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34160.        (((A and B) -> B) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-22, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34161
in-theory        34161
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-21 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34161.        (((A and B) -> A) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-21, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34162
in-theory        34162
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-20 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34162.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-20, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34163
in-theory        34163
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C)))
theorem-size     25
proof            (modus-ponens tm-19 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34163.        ((A -> (B -> A)) and (C -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and C))), M:tm-19, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34164
in-theory        34164
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))) -> (not A))
theorem-size     23
proof            (modus-ponens tm-9 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-9 tm-5 tm-7 tm-2)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34164.        ((A -> (not ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))) -> (not A)), M:tm-9, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-34165
in-theory        34165
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E) -> F) -> ((E or ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E)) -> F))
theorem-size     41
proof            (modus-ponens tm-8 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34165.        ((((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E) -> F) -> ((E or ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E)) -> F)), M:tm-8, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-34166
in-theory        34166
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B)))
theorem-size     21
proof            (modus-ponens tm-7 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34166.        (A or (B -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B))), M:tm-7, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34167
in-theory        34167
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-6 tm-5 tm-7 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34167.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) or F), M:tm-6, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34168
in-theory        34168
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34168.        (A -> ((B -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B)) and A)), M:tm-5, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34169
in-theory        34169
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B)))
theorem-size     21
proof            (modus-ponens tm-1 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-1 tm-5 tm-7 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34169.        (A -> (B -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and B))), M:tm-1, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34170
in-theory        34170
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-490 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34170.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-490, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34171
in-theory        34171
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-480 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34171.        ((A or (B -> (C -> B))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-480, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34172
in-theory        34172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-469 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34172.        ((A -> (B -> (B or C))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-469, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34173
in-theory        34173
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-466 tm-491 ((Am (-> A (or A B))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-7 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34173.        ((A or (B -> (B or C))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-466, m:tm-491, u:((Am (-> A (or A B))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34174
in-theory        34174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34174.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (F or G))), M:tm-456, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34175
in-theory        34175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-453 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34175.        ((A -> ((B -> (B or C)) and A)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-453, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34176
in-theory        34176
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-450 tm-491 ((Am (and (-> A (or A B)) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34176.        ((A or ((B -> (B or C)) and A)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-450, m:tm-491, u:((Am (and (-> A (or A B)) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34177
in-theory        34177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (F or G)) and (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34177.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (F or G)) and (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-443, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34178
in-theory        34178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-409 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34178.        (((A -> (A or B)) or C) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-409, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34179
in-theory        34179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-400 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34179.        (((A -> (B -> (A and B))) or C) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-400, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34180
in-theory        34180
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-391 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34180.        ((((A and B) -> B) or C) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-391, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34181
in-theory        34181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-382 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34181.        ((((A and B) -> A) or C) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-382, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34182
in-theory        34182
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-373 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34182.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-373, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34183
in-theory        34183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-364 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34183.        (((A -> (B -> A)) or C) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-364, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34184
in-theory        34184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-354 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34184.        ((A -> (B -> (C -> (B and C)))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-354, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34185
in-theory        34185
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-491 ((Am (-> A (-> B (and A B)))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34185.        ((A or (B -> (C -> (B and C)))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-351, m:tm-491, u:((Am (-> A (-> B (and A B)))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34186
in-theory        34186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34186.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34187
in-theory        34187
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E))
theorem-size     35
proof            (modus-ponens tm-339 tm-491 ((Am (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B)) (A (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34187.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E)), M:tm-339, m:tm-491, u:((Am (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B)) (A (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34188
in-theory        34188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-338 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34188.        (((A -> B) -> (A -> (A and B))) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-338, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34189
in-theory        34189
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-335 tm-491 ((Am (-> A (and A B))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34189.        (((A -> B) or (A -> (A and B))) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-335, m:tm-491, u:((Am (-> A (and A B))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34190
in-theory        34190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (A -> (A and (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     37
proof            (modus-ponens tm-328 tm-491 ((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34190.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (A -> (A and (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-328, m:tm-491, u:((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34191
in-theory        34191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> (F and G))) and (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34191.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> (F and G))) and (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-327, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34192
in-theory        34192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> G) and (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34192.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> G) and (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-326, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34193
in-theory        34193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> F) and (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34193.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F and G) -> F) and (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-325, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34194
in-theory        34194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34194.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-324, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34195
in-theory        34195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> F)) and (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34195.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> F)) and (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-323, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34196
in-theory        34196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34196.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> G)), M:tm-322, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34197
in-theory        34197
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A and ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> F))
theorem-size     57
proof            (modus-ponens tm-321 tm-491 ((Am (and A (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) C))) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34197.        (((A and ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A and ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> F)), M:tm-321, m:tm-491, u:((Am (and A (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) C))) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34198
in-theory        34198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34198.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F and G) -> F)), M:tm-320, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34199
in-theory        34199
times-derived    1
----------------------------------------------------------------
theorem          (((((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> E))
theorem-size     57
proof            (modus-ponens tm-319 tm-491 ((Am (and (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B) C)) (A (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34199.        (((((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> E)), M:tm-319, m:tm-491, u:((Am (and (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B) C)) (A (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34200
in-theory        34200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34200.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34201
in-theory        34201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (A -> A))
theorem-size     21
proof            (modus-ponens tm-316 tm-491 ((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34201.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (A -> A)), M:tm-316, m:tm-491, u:((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34202
in-theory        34202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34202.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G -> F))), M:tm-315, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34203
in-theory        34203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A -> (not (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not A)))
theorem-size     39
proof            (modus-ponens tm-313 tm-491 ((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34203.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A -> (not (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not A))), M:tm-313, m:tm-491, u:((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34204
in-theory        34204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F) -> ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> F)))
theorem-size     55
proof            (modus-ponens tm-312 tm-491 ((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34204.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F) -> ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> F))), M:tm-312, m:tm-491, u:((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34205
in-theory        34205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F or (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34205.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F or (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-311, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34206
in-theory        34206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34206.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F)), M:tm-310, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34207
in-theory        34207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34207.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F))), M:tm-309, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34208
in-theory        34208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34208.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-305, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34209
in-theory        34209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-303 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34209.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-303, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34210
in-theory        34210
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-300 tm-491 ((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34210.        ((A or ((B -> (C -> (B and C))) and A)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-300, m:tm-491, u:((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34211
in-theory        34211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-270 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34211.        ((A -> (((B and C) -> C) and A)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-270, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34212
in-theory        34212
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-267 tm-491 ((Am (and (-> (and A B) B) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34212.        ((A or (((B and C) -> C) and A)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-267, m:tm-491, u:((Am (and (-> (and A B) B) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34213
in-theory        34213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-239 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34213.        ((A -> (((B and C) -> B) and A)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-239, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34214
in-theory        34214
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-236 tm-491 ((Am (and (-> (and A B) A) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34214.        ((A or (((B and C) -> B) and A)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-236, m:tm-491, u:((Am (and (-> (and A B) A) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34215
in-theory        34215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-210 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34215.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-210, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34216
in-theory        34216
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-207 tm-491 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34216.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-207, m:tm-491, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34217
in-theory        34217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-183 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34217.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-183, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34218
in-theory        34218
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-180 tm-491 ((Am (and (-> A (-> B A)) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34218.        ((A or ((B -> (C -> B)) and A)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-180, m:tm-491, u:((Am (and (-> A (-> B A)) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34219
in-theory        34219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-157 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34219.        ((A -> ((B and C) -> C)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-157, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34220
in-theory        34220
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-154 tm-491 ((Am (-> (and A B) B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-4 tm-7 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34220.        ((A or ((B and C) -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-154, m:tm-491, u:((Am (-> (and A B) B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34221
in-theory        34221
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-147 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34221.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-147, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34222
in-theory        34222
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-144 tm-491 ((Am (-> (and A (-> B C)) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-7)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34222.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-144, m:tm-491, u:((Am (-> (and A (-> B C)) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34223
in-theory        34223
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-142 tm-491 ((Am (and A (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) C))) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-1 tm-4 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34223.        ((A and ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-142, m:tm-491, u:((Am (and A (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) C))) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34224
in-theory        34224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-134 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34224.        ((A -> ((B and C) -> B)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-134, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34225
in-theory        34225
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-131 tm-491 ((Am (-> (and A B) A)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-3 tm-7 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34225.        ((A or ((B and C) -> B)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-131, m:tm-491, u:((Am (-> (and A B) A)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34226
in-theory        34226
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-125 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34226.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-125, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34227
in-theory        34227
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-122 tm-491 ((Am (-> (and (-> A B) C) B)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-7)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34227.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-122, m:tm-491, u:((Am (-> (and (-> A B) C) B)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34228
in-theory        34228
times-derived    1
----------------------------------------------------------------
theorem          ((((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     35
proof            (modus-ponens tm-120 tm-491 ((Am (and (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B) C)) (A (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-1 tm-3 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34228.        ((((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-120, m:tm-491, u:((Am (and (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B) C)) (A (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34229
in-theory        34229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-113 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34229.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-113, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34230
in-theory        34230
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-110 tm-491 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-7)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34230.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-110, m:tm-491, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34231
in-theory        34231
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     37
proof            (modus-ponens tm-105 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34231.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-105, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34232
in-theory        34232
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-102 tm-491 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34232.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-102, m:tm-491, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34233
in-theory        34233
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     33
proof            (modus-ponens tm-96 tm-491 ((Am (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B)) (A (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34233.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-96, m:tm-491, u:((Am (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B)) (A (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34234
in-theory        34234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-95 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34234.        (((A -> B) -> (A -> A)) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-95, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34235
in-theory        34235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-92 tm-491 ((Am (-> A A)) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34235.        (((A -> B) or (A -> A)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-92, m:tm-491, u:((Am (-> A A)) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34236
in-theory        34236
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     19
proof            (modus-ponens tm-84 tm-491 ((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34236.        (A -> (B -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-84, m:tm-491, u:((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34237
in-theory        34237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-83 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34237.        ((A -> (B -> (C -> B))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-83, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34238
in-theory        34238
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-80 tm-491 ((Am (-> A (-> B A))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34238.        ((A or (B -> (C -> B))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-80, m:tm-491, u:((Am (-> A (-> B A))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34239
in-theory        34239
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E))) -> E)
theorem-size     21
proof            (modus-ponens tm-77 tm-491 ((Am (not (not (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B)))) (A (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-10 tm-1 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34239.        ((not (not ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E))) -> E), M:tm-77, m:tm-491, u:((Am (not (not (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B)))) (A (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34240
in-theory        34240
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     23
proof            (modus-ponens tm-76 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34240.        (((not (not A)) -> A) and (B -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-76, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34241
in-theory        34241
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     21
proof            (modus-ponens tm-73 tm-491 ((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-10 tm-1 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34241.        (((not (not A)) or A) -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-73, m:tm-491, u:((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34242
in-theory        34242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     29
proof            (modus-ponens tm-69 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34242.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-69, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34243
in-theory        34243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-66 tm-491 ((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-9 tm-1 tm-7 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34243.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-66, m:tm-491, u:((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34244
in-theory        34244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-54 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34244.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-54, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34245
in-theory        34245
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-51 tm-491 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34245.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-51, m:tm-491, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34246
in-theory        34246
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-50 tm-491 ((Am (or A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34246.        ((A or (B or A)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-50, m:tm-491, u:((Am (or A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34247
in-theory        34247
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-49 tm-491 ((Am (or A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-6 tm-1 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34247.        ((A or (A or B)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-49, m:tm-491, u:((Am (or A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34248
in-theory        34248
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     23
proof            (modus-ponens tm-48 tm-491 ((Am (-> A (and B A))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34248.        ((A or (B -> (A and B))) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-48, m:tm-491, u:((Am (-> A (and B A))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34249
in-theory        34249
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-47 tm-491 ((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-4 tm-1 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34249.        (((A and B) or B) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-47, m:tm-491, u:((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34250
in-theory        34250
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-46 tm-491 ((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-3 tm-1 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34250.        (((A and B) or A) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-46, m:tm-491, u:((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34251
in-theory        34251
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-45 tm-491 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34251.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-45, m:tm-491, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34252
in-theory        34252
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-44 tm-491 ((Am (-> A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34252.        ((A or (B -> A)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-44, m:tm-491, u:((Am (-> A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34253
in-theory        34253
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-42 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34253.        ((A -> (B or A)) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-42, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34254
in-theory        34254
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-32 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34254.        ((A -> (A or B)) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-32, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34255
in-theory        34255
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     19
proof            (modus-ponens tm-24 tm-491 ((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34255.        (A -> (A and (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-24, m:tm-491, u:((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34256
in-theory        34256
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-23 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34256.        ((A -> (B -> (A and B))) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-23, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34257
in-theory        34257
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-22 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34257.        (((A and B) -> B) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-22, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34258
in-theory        34258
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-21 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34258.        (((A and B) -> A) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-21, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34259
in-theory        34259
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-20 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34259.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-20, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34260
in-theory        34260
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-19 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34260.        ((A -> (B -> A)) and (C -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-19, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34261
in-theory        34261
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> F)
theorem-size     21
proof            (modus-ponens tm-17 tm-491 ((Am (and A (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) C))) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-4 tm-1 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34261.        ((A and ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)) -> F), M:tm-17, m:tm-491, u:((Am (and A (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) C))) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34262
in-theory        34262
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> E)
theorem-size     21
proof            (modus-ponens tm-15 tm-491 ((Am (and (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B) C)) (A (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-3 tm-1 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34262.        ((((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) and F) -> E), M:tm-15, m:tm-491, u:((Am (and (-> (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) B) C)) (A (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34263
in-theory        34263
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not A))
theorem-size     21
proof            (modus-ponens tm-9 tm-491 ((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34263.        ((A -> (not (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not A)), M:tm-9, m:tm-491, u:((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34264
in-theory        34264
times-derived    2
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> ((F or (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-491 ((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34264.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> ((F or (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> E)), M:tm-8, m:tm-491, u:((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34265
in-theory        34265
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     19
proof            (modus-ponens tm-7 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-7 tm-1 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34265.        (A or (B -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-7, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34266
in-theory        34266
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-6 tm-1 tm-7 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34266.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or F), M:tm-6, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34267
in-theory        34267
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34267.        (A -> ((B -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and A)), M:tm-5, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34268
in-theory        34268
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-490 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34268.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H and I) -> H)))), M:tm-490, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34269
in-theory        34269
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-480 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34269.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-480, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34270
in-theory        34270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-469 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34270.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-469, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34271
in-theory        34271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34271.        (((A -> (A or B)) and (C or ((D and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34272
in-theory        34272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-453 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34272.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-453, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34273
in-theory        34273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (A or B)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34273.        (((A -> (A or B)) and (C or ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (A or B)) and (C or ((D and E) -> D))))), M:tm-443, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34274
in-theory        34274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-409 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34274.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-409, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34275
in-theory        34275
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-400 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34275.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-400, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34276
in-theory        34276
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-391 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34276.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-391, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34277
in-theory        34277
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-382 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34277.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-382, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34278
in-theory        34278
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-373 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34278.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or ((H and I) -> H)))), M:tm-373, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34279
in-theory        34279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-364 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34279.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-364, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34280
in-theory        34280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-354 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34280.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-354, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34281
in-theory        34281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34281.        (((A -> (A or B)) and (C or ((D and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34282
in-theory        34282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-338 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34282.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or ((F and G) -> F)))), M:tm-338, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34283
in-theory        34283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C or ((D and E) -> D)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34283.        (((A -> (A or B)) and (C or ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C or ((D and E) -> D))))), M:tm-327, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34284
in-theory        34284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and (((F and G) -> G) and ((A -> (A or B)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34284.        (((A -> (A or B)) and (C or ((D and E) -> D))) and (((F and G) -> G) and ((A -> (A or B)) and (C or ((D and E) -> D))))), M:tm-326, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34285
in-theory        34285
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and (((F and G) -> F) and ((A -> (A or B)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34285.        (((A -> (A or B)) and (C or ((D and E) -> D))) and (((F and G) -> F) and ((A -> (A or B)) and (C or ((D and E) -> D))))), M:tm-325, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34286
in-theory        34286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C or ((D and E) -> D)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34286.        (((A -> (A or B)) and (C or ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C or ((D and E) -> D))))), M:tm-324, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34287
in-theory        34287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34287.        (((A -> (A or B)) and (C or ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C or ((D and E) -> D))))), M:tm-323, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34288
in-theory        34288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34288.        (((A -> (A or B)) and (C or ((D and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34289
in-theory        34289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34289.        (((A -> (A or B)) and (C or ((D and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34290
in-theory        34290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34290.        (((A -> (A or B)) and (C or ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34291
in-theory        34291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34291.        (((A -> (A or B)) and (C or ((D and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34292
in-theory        34292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and (F or ((A -> (A or B)) and (C or ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34292.        (((A -> (A or B)) and (C or ((D and E) -> D))) and (F or ((A -> (A or B)) and (C or ((D and E) -> D))))), M:tm-311, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34293
in-theory        34293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and (((A -> (A or B)) and (C or ((D and E) -> D))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34293.        (((A -> (A or B)) and (C or ((D and E) -> D))) and (((A -> (A or B)) and (C or ((D and E) -> D))) or F)), M:tm-310, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34294
in-theory        34294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and (F -> (((A -> (A or B)) and (C or ((D and E) -> D))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34294.        (((A -> (A or B)) and (C or ((D and E) -> D))) and (F -> (((A -> (A or B)) and (C or ((D and E) -> D))) and F))), M:tm-309, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34295
in-theory        34295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and (C or ((D and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-308 tm-492 ((A (-> Am (or Am Bm))) (B (or Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34295.        (((A -> (A or B)) and (C or ((D and E) -> D))) and (C or ((D and E) -> D))), M:tm-308, m:tm-492, u:((A (-> Am (or Am Bm))) (B (or Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-34296
in-theory        34296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-492 ((A (-> Am (or Am Bm))) (B (or Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34296.        (((A -> (A or B)) and (C or ((D and E) -> D))) and (A -> (A or B))), M:tm-307, m:tm-492, u:((A (-> Am (or Am Bm))) (B (or Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-34297
in-theory        34297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and (F -> ((A -> (A or B)) and (C or ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34297.        (((A -> (A or B)) and (C or ((D and E) -> D))) and (F -> ((A -> (A or B)) and (C or ((D and E) -> D))))), M:tm-305, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34298
in-theory        34298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-303 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34298.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-303, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34299
in-theory        34299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-270 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34299.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-270, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34300
in-theory        34300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-239 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34300.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-239, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34301
in-theory        34301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-210 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34301.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or ((H and I) -> H)))), M:tm-210, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34302
in-theory        34302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-183 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34302.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-183, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34303
in-theory        34303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-157 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34303.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-157, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34304
in-theory        34304
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-147 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34304.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-147, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34305
in-theory        34305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-134 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34305.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-134, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34306
in-theory        34306
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-125 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34306.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-125, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34307
in-theory        34307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-113 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34307.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H and I) -> H)))), M:tm-113, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34308
in-theory        34308
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-105 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34308.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-105, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34309
in-theory        34309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-95 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34309.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or ((F and G) -> F)))), M:tm-95, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34310
in-theory        34310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-83 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34310.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-83, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34311
in-theory        34311
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D or ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-76 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34311.        (((not (not A)) -> A) and ((B -> (B or C)) and (D or ((E and F) -> E)))), M:tm-76, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34312
in-theory        34312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-69 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-6 tm-7 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34312.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or ((F and G) -> F)))), M:tm-69, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34313
in-theory        34313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-54 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34313.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-54, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34314
in-theory        34314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-42 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34314.        ((A -> (B or A)) and ((C -> (C or D)) and (E or ((F and G) -> F)))), M:tm-42, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34315
in-theory        34315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-32 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34315.        ((A -> (A or B)) and ((C -> (C or D)) and (E or ((F and G) -> F)))), M:tm-32, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34316
in-theory        34316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-23 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34316.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or ((F and G) -> F)))), M:tm-23, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34317
in-theory        34317
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-22 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34317.        (((A and B) -> B) and ((C -> (C or D)) and (E or ((F and G) -> F)))), M:tm-22, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34318
in-theory        34318
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-21 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34318.        (((A and B) -> A) and ((C -> (C or D)) and (E or ((F and G) -> F)))), M:tm-21, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34319
in-theory        34319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-20 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34319.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-20, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34320
in-theory        34320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-19 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34320.        ((A -> (B -> A)) and ((C -> (C or D)) and (E or ((F and G) -> F)))), M:tm-19, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34321
in-theory        34321
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-7 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-6 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34321.        (A or ((B -> (B or C)) and (D or ((E and F) -> E)))), M:tm-7, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34322
in-theory        34322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34322.        (((A -> (A or B)) and (C or ((D and E) -> D))) or F), M:tm-6, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34323
in-theory        34323
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D or ((E and F) -> E))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34323.        (A -> (((B -> (B or C)) and (D or ((E and F) -> E))) and A)), M:tm-5, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34324
in-theory        34324
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-1 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-6 tm-7 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34324.        (A -> ((B -> (B or C)) and (D or ((E and F) -> E)))), M:tm-1, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34325
in-theory        34325
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-490 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34325.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H)))), M:tm-490, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34326
in-theory        34326
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-480 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34326.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-480, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34327
in-theory        34327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-469 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34327.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-469, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34328
in-theory        34328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34328.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34329
in-theory        34329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-453 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34329.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-453, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34330
in-theory        34330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C or ((D and E) -> D)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34330.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C or ((D and E) -> D))))), M:tm-443, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34331
in-theory        34331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-409 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34331.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-409, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34332
in-theory        34332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-400 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34332.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-400, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34333
in-theory        34333
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-391 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34333.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-391, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34334
in-theory        34334
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-382 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34334.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-382, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34335
in-theory        34335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-373 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34335.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H)))), M:tm-373, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34336
in-theory        34336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-364 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34336.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-364, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34337
in-theory        34337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-354 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34337.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-354, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34338
in-theory        34338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34338.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34339
in-theory        34339
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-338 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34339.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F)))), M:tm-338, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34340
in-theory        34340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C or ((D and E) -> D)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34340.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C or ((D and E) -> D))))), M:tm-327, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34341
in-theory        34341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C or ((D and E) -> D)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34341.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C or ((D and E) -> D))))), M:tm-326, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34342
in-theory        34342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C or ((D and E) -> D)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34342.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C or ((D and E) -> D))))), M:tm-325, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34343
in-theory        34343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C or ((D and E) -> D)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34343.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C or ((D and E) -> D))))), M:tm-324, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34344
in-theory        34344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C or ((D and E) -> D)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34344.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C or ((D and E) -> D))))), M:tm-323, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34345
in-theory        34345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34345.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34346
in-theory        34346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34346.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34347
in-theory        34347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34347.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34348
in-theory        34348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34348.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34349
in-theory        34349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (F or ((A -> (B -> (A and B))) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34349.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (F or ((A -> (B -> (A and B))) and (C or ((D and E) -> D))))), M:tm-311, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34350
in-theory        34350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34350.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) or F)), M:tm-310, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34351
in-theory        34351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (F -> (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34351.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (F -> (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and F))), M:tm-309, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34352
in-theory        34352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (C or ((D and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-308 tm-493 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34352.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (C or ((D and E) -> D))), M:tm-308, m:tm-493, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-34353
in-theory        34353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-493 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34353.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-493, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-34354
in-theory        34354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (F -> ((A -> (B -> (A and B))) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34354.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (F -> ((A -> (B -> (A and B))) and (C or ((D and E) -> D))))), M:tm-305, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34355
in-theory        34355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-303 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34355.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-303, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34356
in-theory        34356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-270 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34356.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-270, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34357
in-theory        34357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-239 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34357.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-239, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34358
in-theory        34358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H))))
theorem-size     33
proof            (modus-ponens tm-210 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34358.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H)))), M:tm-210, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34359
in-theory        34359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-183 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34359.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-183, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34360
in-theory        34360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-157 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34360.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-157, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34361
in-theory        34361
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-147 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34361.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-147, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34362
in-theory        34362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-134 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34362.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-134, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34363
in-theory        34363
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-125 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34363.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-125, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34364
in-theory        34364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-113 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34364.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H)))), M:tm-113, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34365
in-theory        34365
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-105 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34365.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-105, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34366
in-theory        34366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-95 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34366.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F)))), M:tm-95, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34367
in-theory        34367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-83 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34367.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-83, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34368
in-theory        34368
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or ((E and F) -> E))))
theorem-size     21
proof            (modus-ponens tm-76 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34368.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or ((E and F) -> E)))), M:tm-76, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34369
in-theory        34369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-69 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34369.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F)))), M:tm-69, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34370
in-theory        34370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-54 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34370.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-54, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34371
in-theory        34371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-42 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34371.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F)))), M:tm-42, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34372
in-theory        34372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-32 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34372.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F)))), M:tm-32, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34373
in-theory        34373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-23 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34373.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F)))), M:tm-23, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34374
in-theory        34374
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-22 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34374.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F)))), M:tm-22, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34375
in-theory        34375
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-21 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34375.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F)))), M:tm-21, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34376
in-theory        34376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-20 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34376.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-20, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34377
in-theory        34377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-19 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34377.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> F)))), M:tm-19, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34378
in-theory        34378
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D or ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-7 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34378.        (A or ((B -> (C -> (B and C))) and (D or ((E and F) -> E)))), M:tm-7, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34379
in-theory        34379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34379.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) or F), M:tm-6, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34380
in-theory        34380
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D or ((E and F) -> E))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34380.        (A -> (((B -> (C -> (B and C))) and (D or ((E and F) -> E))) and A)), M:tm-5, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34381
in-theory        34381
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D or ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-1 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34381.        (A -> ((B -> (C -> (B and C))) and (D or ((E and F) -> E)))), M:tm-1, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34382
in-theory        34382
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-490 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34382.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H and I) -> H)))), M:tm-490, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34383
in-theory        34383
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-480 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34383.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-480, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34384
in-theory        34384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-469 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34384.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-469, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34385
in-theory        34385
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34385.        ((((A and B) -> B) and (C or ((D and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34386
in-theory        34386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-453 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34386.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-453, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34387
in-theory        34387
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and ((F -> (F or G)) and (((A and B) -> B) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34387.        ((((A and B) -> B) and (C or ((D and E) -> D))) and ((F -> (F or G)) and (((A and B) -> B) and (C or ((D and E) -> D))))), M:tm-443, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34388
in-theory        34388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-409 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34388.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-409, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34389
in-theory        34389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-400 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34389.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-400, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34390
in-theory        34390
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-391 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34390.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-391, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34391
in-theory        34391
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-382 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34391.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-382, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34392
in-theory        34392
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-373 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34392.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or ((H and I) -> H)))), M:tm-373, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34393
in-theory        34393
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-364 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34393.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-364, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34394
in-theory        34394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-354 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34394.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-354, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34395
in-theory        34395
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34395.        ((((A and B) -> B) and (C or ((D and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34396
in-theory        34396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-338 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34396.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or ((F and G) -> F)))), M:tm-338, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34397
in-theory        34397
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C or ((D and E) -> D)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34397.        ((((A and B) -> B) and (C or ((D and E) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C or ((D and E) -> D))))), M:tm-327, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34398
in-theory        34398
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and (((F and G) -> G) and (((A and B) -> B) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34398.        ((((A and B) -> B) and (C or ((D and E) -> D))) and (((F and G) -> G) and (((A and B) -> B) and (C or ((D and E) -> D))))), M:tm-326, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34399
in-theory        34399
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and (((F and G) -> F) and (((A and B) -> B) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34399.        ((((A and B) -> B) and (C or ((D and E) -> D))) and (((F and G) -> F) and (((A and B) -> B) and (C or ((D and E) -> D))))), M:tm-325, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34400
in-theory        34400
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C or ((D and E) -> D)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34400.        ((((A and B) -> B) and (C or ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C or ((D and E) -> D))))), M:tm-324, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34401
in-theory        34401
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and ((F -> (G -> F)) and (((A and B) -> B) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34401.        ((((A and B) -> B) and (C or ((D and E) -> D))) and ((F -> (G -> F)) and (((A and B) -> B) and (C or ((D and E) -> D))))), M:tm-323, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34402
in-theory        34402
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34402.        ((((A and B) -> B) and (C or ((D and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34403
in-theory        34403
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34403.        ((((A and B) -> B) and (C or ((D and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34404
in-theory        34404
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34404.        ((((A and B) -> B) and (C or ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34405
in-theory        34405
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34405.        ((((A and B) -> B) and (C or ((D and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34406
in-theory        34406
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and (F or (((A and B) -> B) and (C or ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34406.        ((((A and B) -> B) and (C or ((D and E) -> D))) and (F or (((A and B) -> B) and (C or ((D and E) -> D))))), M:tm-311, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34407
in-theory        34407
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and ((((A and B) -> B) and (C or ((D and E) -> D))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34407.        ((((A and B) -> B) and (C or ((D and E) -> D))) and ((((A and B) -> B) and (C or ((D and E) -> D))) or F)), M:tm-310, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34408
in-theory        34408
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and (F -> ((((A and B) -> B) and (C or ((D and E) -> D))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34408.        ((((A and B) -> B) and (C or ((D and E) -> D))) and (F -> ((((A and B) -> B) and (C or ((D and E) -> D))) and F))), M:tm-309, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34409
in-theory        34409
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and (C or ((D and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-308 tm-494 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34409.        ((((A and B) -> B) and (C or ((D and E) -> D))) and (C or ((D and E) -> D))), M:tm-308, m:tm-494, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-34410
in-theory        34410
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-494 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34410.        ((((A and B) -> B) and (C or ((D and E) -> D))) and ((A and B) -> B)), M:tm-307, m:tm-494, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-34411
in-theory        34411
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and (F -> (((A and B) -> B) and (C or ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34411.        ((((A and B) -> B) and (C or ((D and E) -> D))) and (F -> (((A and B) -> B) and (C or ((D and E) -> D))))), M:tm-305, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34412
in-theory        34412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-303 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34412.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-303, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34413
in-theory        34413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-270 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34413.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-270, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34414
in-theory        34414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-239 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34414.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-239, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34415
in-theory        34415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-210 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34415.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or ((H and I) -> H)))), M:tm-210, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34416
in-theory        34416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-183 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34416.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-183, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34417
in-theory        34417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-157 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34417.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-157, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34418
in-theory        34418
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-147 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34418.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-147, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34419
in-theory        34419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-134 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34419.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-134, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34420
in-theory        34420
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-125 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34420.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-125, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34421
in-theory        34421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-113 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34421.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H and I) -> H)))), M:tm-113, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34422
in-theory        34422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-105 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34422.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-105, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34423
in-theory        34423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-95 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34423.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or ((F and G) -> F)))), M:tm-95, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34424
in-theory        34424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-83 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34424.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-83, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34425
in-theory        34425
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D or ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-76 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34425.        (((not (not A)) -> A) and (((B and C) -> C) and (D or ((E and F) -> E)))), M:tm-76, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34426
in-theory        34426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-69 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-7 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34426.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or ((F and G) -> F)))), M:tm-69, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34427
in-theory        34427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-54 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34427.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-54, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34428
in-theory        34428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-42 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34428.        ((A -> (B or A)) and (((C and D) -> D) and (E or ((F and G) -> F)))), M:tm-42, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34429
in-theory        34429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-32 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34429.        ((A -> (A or B)) and (((C and D) -> D) and (E or ((F and G) -> F)))), M:tm-32, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34430
in-theory        34430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-23 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34430.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or ((F and G) -> F)))), M:tm-23, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34431
in-theory        34431
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-22 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34431.        (((A and B) -> B) and (((C and D) -> D) and (E or ((F and G) -> F)))), M:tm-22, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34432
in-theory        34432
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-21 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34432.        (((A and B) -> A) and (((C and D) -> D) and (E or ((F and G) -> F)))), M:tm-21, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34433
in-theory        34433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-20 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34433.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-20, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34434
in-theory        34434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-19 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34434.        ((A -> (B -> A)) and (((C and D) -> D) and (E or ((F and G) -> F)))), M:tm-19, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34435
in-theory        34435
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-7 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-4 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34435.        (A or (((B and C) -> C) and (D or ((E and F) -> E)))), M:tm-7, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34436
in-theory        34436
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-4 tm-7 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34436.        ((((A and B) -> B) and (C or ((D and E) -> D))) or F), M:tm-6, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34437
in-theory        34437
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D or ((E and F) -> E))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34437.        (A -> ((((B and C) -> C) and (D or ((E and F) -> E))) and A)), M:tm-5, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34438
in-theory        34438
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-1 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-4 tm-7 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34438.        (A -> (((B and C) -> C) and (D or ((E and F) -> E)))), M:tm-1, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34439
in-theory        34439
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-490 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34439.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H and I) -> H)))), M:tm-490, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34440
in-theory        34440
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-480 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34440.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-480, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34441
in-theory        34441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-469 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34441.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-469, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34442
in-theory        34442
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34442.        ((((A and B) -> A) and (C or ((D and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34443
in-theory        34443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-453 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34443.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-453, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34444
in-theory        34444
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and ((F -> (F or G)) and (((A and B) -> A) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34444.        ((((A and B) -> A) and (C or ((D and E) -> D))) and ((F -> (F or G)) and (((A and B) -> A) and (C or ((D and E) -> D))))), M:tm-443, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34445
in-theory        34445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-409 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34445.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-409, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34446
in-theory        34446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-400 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34446.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-400, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34447
in-theory        34447
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-391 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34447.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-391, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34448
in-theory        34448
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-382 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34448.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-382, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34449
in-theory        34449
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-373 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34449.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or ((H and I) -> H)))), M:tm-373, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34450
in-theory        34450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-364 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34450.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-364, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34451
in-theory        34451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-354 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34451.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-354, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34452
in-theory        34452
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34452.        ((((A and B) -> A) and (C or ((D and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34453
in-theory        34453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-338 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34453.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or ((F and G) -> F)))), M:tm-338, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34454
in-theory        34454
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C or ((D and E) -> D)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34454.        ((((A and B) -> A) and (C or ((D and E) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C or ((D and E) -> D))))), M:tm-327, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34455
in-theory        34455
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and (((F and G) -> G) and (((A and B) -> A) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34455.        ((((A and B) -> A) and (C or ((D and E) -> D))) and (((F and G) -> G) and (((A and B) -> A) and (C or ((D and E) -> D))))), M:tm-326, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34456
in-theory        34456
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and (((F and G) -> F) and (((A and B) -> A) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34456.        ((((A and B) -> A) and (C or ((D and E) -> D))) and (((F and G) -> F) and (((A and B) -> A) and (C or ((D and E) -> D))))), M:tm-325, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34457
in-theory        34457
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C or ((D and E) -> D)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34457.        ((((A and B) -> A) and (C or ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C or ((D and E) -> D))))), M:tm-324, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34458
in-theory        34458
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and ((F -> (G -> F)) and (((A and B) -> A) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34458.        ((((A and B) -> A) and (C or ((D and E) -> D))) and ((F -> (G -> F)) and (((A and B) -> A) and (C or ((D and E) -> D))))), M:tm-323, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34459
in-theory        34459
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34459.        ((((A and B) -> A) and (C or ((D and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34460
in-theory        34460
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34460.        ((((A and B) -> A) and (C or ((D and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34461
in-theory        34461
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34461.        ((((A and B) -> A) and (C or ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34462
in-theory        34462
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34462.        ((((A and B) -> A) and (C or ((D and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34463
in-theory        34463
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and (F or (((A and B) -> A) and (C or ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34463.        ((((A and B) -> A) and (C or ((D and E) -> D))) and (F or (((A and B) -> A) and (C or ((D and E) -> D))))), M:tm-311, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34464
in-theory        34464
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and ((((A and B) -> A) and (C or ((D and E) -> D))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34464.        ((((A and B) -> A) and (C or ((D and E) -> D))) and ((((A and B) -> A) and (C or ((D and E) -> D))) or F)), M:tm-310, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34465
in-theory        34465
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and (F -> ((((A and B) -> A) and (C or ((D and E) -> D))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34465.        ((((A and B) -> A) and (C or ((D and E) -> D))) and (F -> ((((A and B) -> A) and (C or ((D and E) -> D))) and F))), M:tm-309, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34466
in-theory        34466
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and (C or ((D and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-308 tm-495 ((A (-> (and Am Bm) Am)) (B (or Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34466.        ((((A and B) -> A) and (C or ((D and E) -> D))) and (C or ((D and E) -> D))), M:tm-308, m:tm-495, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-34467
in-theory        34467
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-495 ((A (-> (and Am Bm) Am)) (B (or Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34467.        ((((A and B) -> A) and (C or ((D and E) -> D))) and ((A and B) -> A)), M:tm-307, m:tm-495, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-34468
in-theory        34468
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and (F -> (((A and B) -> A) and (C or ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34468.        ((((A and B) -> A) and (C or ((D and E) -> D))) and (F -> (((A and B) -> A) and (C or ((D and E) -> D))))), M:tm-305, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34469
in-theory        34469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-303 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34469.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-303, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34470
in-theory        34470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-270 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34470.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-270, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34471
in-theory        34471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-239 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34471.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-239, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34472
in-theory        34472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-210 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34472.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or ((H and I) -> H)))), M:tm-210, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34473
in-theory        34473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-183 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34473.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-183, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34474
in-theory        34474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-157 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34474.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-157, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34475
in-theory        34475
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-147 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34475.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-147, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34476
in-theory        34476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-134 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34476.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-134, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34477
in-theory        34477
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-125 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34477.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-125, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34478
in-theory        34478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-113 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34478.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H and I) -> H)))), M:tm-113, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34479
in-theory        34479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-105 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34479.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-105, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34480
in-theory        34480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-95 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34480.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or ((F and G) -> F)))), M:tm-95, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34481
in-theory        34481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-83 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34481.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-83, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34482
in-theory        34482
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D or ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-76 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34482.        (((not (not A)) -> A) and (((B and C) -> B) and (D or ((E and F) -> E)))), M:tm-76, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34483
in-theory        34483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-69 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34483.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or ((F and G) -> F)))), M:tm-69, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34484
in-theory        34484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-54 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34484.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-54, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34485
in-theory        34485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-42 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34485.        ((A -> (B or A)) and (((C and D) -> C) and (E or ((F and G) -> F)))), M:tm-42, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34486
in-theory        34486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-32 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34486.        ((A -> (A or B)) and (((C and D) -> C) and (E or ((F and G) -> F)))), M:tm-32, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34487
in-theory        34487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-23 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34487.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or ((F and G) -> F)))), M:tm-23, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34488
in-theory        34488
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-22 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34488.        (((A and B) -> B) and (((C and D) -> C) and (E or ((F and G) -> F)))), M:tm-22, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34489
in-theory        34489
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-21 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34489.        (((A and B) -> A) and (((C and D) -> C) and (E or ((F and G) -> F)))), M:tm-21, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34490
in-theory        34490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-20 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34490.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-20, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34491
in-theory        34491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-19 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34491.        ((A -> (B -> A)) and (((C and D) -> C) and (E or ((F and G) -> F)))), M:tm-19, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34492
in-theory        34492
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-7 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34492.        (A or (((B and C) -> B) and (D or ((E and F) -> E)))), M:tm-7, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34493
in-theory        34493
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-3 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34493.        ((((A and B) -> A) and (C or ((D and E) -> D))) or F), M:tm-6, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34494
in-theory        34494
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D or ((E and F) -> E))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34494.        (A -> ((((B and C) -> B) and (D or ((E and F) -> E))) and A)), M:tm-5, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34495
in-theory        34495
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-1 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-3 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34495.        (A -> (((B and C) -> B) and (D or ((E and F) -> E)))), M:tm-1, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34496
in-theory        34496
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-490 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34496.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> I)))), M:tm-490, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34497
in-theory        34497
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-480 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34497.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-480, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34498
in-theory        34498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-469 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34498.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-469, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34499
in-theory        34499
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34499.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (G -> (G or H))), M:tm-456, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34500
in-theory        34500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-453 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34500.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-453, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34501
in-theory        34501
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34501.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))))), M:tm-443, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34502
in-theory        34502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-409 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34502.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-409, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34503
in-theory        34503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-400 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34503.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-400, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34504
in-theory        34504
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-391 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34504.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-391, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34505
in-theory        34505
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-382 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34505.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-382, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34506
in-theory        34506
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-373 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34506.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> I)))), M:tm-373, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34507
in-theory        34507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-364 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34507.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-364, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34508
in-theory        34508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-354 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34508.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-354, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34509
in-theory        34509
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34509.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34510
in-theory        34510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-338 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34510.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G)))), M:tm-338, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34511
in-theory        34511
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34511.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))))), M:tm-327, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34512
in-theory        34512
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34512.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))))), M:tm-326, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34513
in-theory        34513
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34513.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))))), M:tm-325, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34514
in-theory        34514
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34514.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))))), M:tm-324, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34515
in-theory        34515
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34515.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))))), M:tm-323, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34516
in-theory        34516
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34516.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((G and H) -> H)), M:tm-322, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34517
in-theory        34517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34517.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((G and H) -> G)), M:tm-320, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34518
in-theory        34518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34518.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34519
in-theory        34519
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34519.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (G -> (H -> G))), M:tm-315, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34520
in-theory        34520
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34520.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))))), M:tm-311, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34521
in-theory        34521
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34521.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) or G)), M:tm-310, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34522
in-theory        34522
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34522.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and G))), M:tm-309, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34523
in-theory        34523
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (D or ((E and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-308 tm-496 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (and Em Fm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34523.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (D or ((E and F) -> E))), M:tm-308, m:tm-496, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (and Em Fm) Em))))
================================================================
tm-name          tm-34524
in-theory        34524
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-496 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (and Em Fm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34524.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-496, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (and Em Fm) Em))))
================================================================
tm-name          tm-34525
in-theory        34525
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34525.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))))), M:tm-305, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34526
in-theory        34526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     33
proof            (modus-ponens tm-303 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34526.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-303, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34527
in-theory        34527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-270 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34527.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-270, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34528
in-theory        34528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-239 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34528.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-239, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34529
in-theory        34529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> I))))
theorem-size     39
proof            (modus-ponens tm-210 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34529.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> I)))), M:tm-210, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34530
in-theory        34530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-183 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34530.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-183, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34531
in-theory        34531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-157 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34531.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-157, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34532
in-theory        34532
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-147 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34532.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-147, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34533
in-theory        34533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-134 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34533.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-134, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34534
in-theory        34534
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-125 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34534.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-125, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34535
in-theory        34535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> I))))
theorem-size     37
proof            (modus-ponens tm-113 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34535.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> I)))), M:tm-113, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34536
in-theory        34536
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-105 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34536.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-105, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34537
in-theory        34537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-95 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34537.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G)))), M:tm-95, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34538
in-theory        34538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-83 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34538.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-83, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34539
in-theory        34539
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-76 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-10 tm-2 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34539.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> F)))), M:tm-76, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34540
in-theory        34540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-69 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-9 tm-2 tm-7 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34540.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G)))), M:tm-69, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34541
in-theory        34541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-54 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34541.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-54, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34542
in-theory        34542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-42 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34542.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G)))), M:tm-42, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34543
in-theory        34543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-32 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34543.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G)))), M:tm-32, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34544
in-theory        34544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-23 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34544.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G)))), M:tm-23, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34545
in-theory        34545
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-22 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34545.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G)))), M:tm-22, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34546
in-theory        34546
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-21 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34546.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G)))), M:tm-21, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34547
in-theory        34547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-20 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34547.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-20, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34548
in-theory        34548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-19 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34548.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> G)))), M:tm-19, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34549
in-theory        34549
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-7 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-7 tm-5 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34549.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> F)))), M:tm-7, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34550
in-theory        34550
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-6 tm-5 tm-2 tm-7 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34550.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) or G), M:tm-6, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34551
in-theory        34551
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> F))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34551.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> F))) and A)), M:tm-5, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34552
in-theory        34552
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-1 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-1 tm-5 tm-2 tm-7 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34552.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> F)))), M:tm-1, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34553
in-theory        34553
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-490 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34553.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H and I) -> H)))), M:tm-490, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34554
in-theory        34554
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-480 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34554.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-480, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34555
in-theory        34555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-469 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34555.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-469, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34556
in-theory        34556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34556.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34557
in-theory        34557
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-453 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34557.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-453, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34558
in-theory        34558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34558.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C or ((D and E) -> D))))), M:tm-443, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34559
in-theory        34559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-409 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34559.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-409, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34560
in-theory        34560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-400 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34560.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-400, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34561
in-theory        34561
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-391 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34561.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-391, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34562
in-theory        34562
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-382 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34562.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-382, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34563
in-theory        34563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-373 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34563.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or ((H and I) -> H)))), M:tm-373, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34564
in-theory        34564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-364 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34564.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-364, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34565
in-theory        34565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-354 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34565.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-354, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34566
in-theory        34566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34566.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34567
in-theory        34567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-338 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34567.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or ((F and G) -> F)))), M:tm-338, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34568
in-theory        34568
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C or ((D and E) -> D)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34568.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C or ((D and E) -> D))))), M:tm-327, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34569
in-theory        34569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and (((F and G) -> G) and ((A -> (B -> A)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34569.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and (((F and G) -> G) and ((A -> (B -> A)) and (C or ((D and E) -> D))))), M:tm-326, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34570
in-theory        34570
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and (((F and G) -> F) and ((A -> (B -> A)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34570.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and (((F and G) -> F) and ((A -> (B -> A)) and (C or ((D and E) -> D))))), M:tm-325, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34571
in-theory        34571
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C or ((D and E) -> D)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34571.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C or ((D and E) -> D))))), M:tm-324, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34572
in-theory        34572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34572.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C or ((D and E) -> D))))), M:tm-323, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34573
in-theory        34573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34573.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34574
in-theory        34574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34574.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34575
in-theory        34575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34575.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34576
in-theory        34576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34576.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34577
in-theory        34577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and (F or ((A -> (B -> A)) and (C or ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34577.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and (F or ((A -> (B -> A)) and (C or ((D and E) -> D))))), M:tm-311, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34578
in-theory        34578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and (((A -> (B -> A)) and (C or ((D and E) -> D))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34578.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and (((A -> (B -> A)) and (C or ((D and E) -> D))) or F)), M:tm-310, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34579
in-theory        34579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and (F -> (((A -> (B -> A)) and (C or ((D and E) -> D))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34579.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and (F -> (((A -> (B -> A)) and (C or ((D and E) -> D))) and F))), M:tm-309, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34580
in-theory        34580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and (C or ((D and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-308 tm-497 ((A (-> Am (-> Bm Am))) (B (or Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34580.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and (C or ((D and E) -> D))), M:tm-308, m:tm-497, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-34581
in-theory        34581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-497 ((A (-> Am (-> Bm Am))) (B (or Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34581.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and (A -> (B -> A))), M:tm-307, m:tm-497, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-34582
in-theory        34582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and (F -> ((A -> (B -> A)) and (C or ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34582.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and (F -> ((A -> (B -> A)) and (C or ((D and E) -> D))))), M:tm-305, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34583
in-theory        34583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-303 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34583.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-303, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34584
in-theory        34584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-270 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34584.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-270, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34585
in-theory        34585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-239 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34585.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-239, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34586
in-theory        34586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-210 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34586.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or ((H and I) -> H)))), M:tm-210, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34587
in-theory        34587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-183 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34587.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-183, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34588
in-theory        34588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-157 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34588.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-157, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34589
in-theory        34589
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-147 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34589.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-147, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34590
in-theory        34590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-134 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34590.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-134, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34591
in-theory        34591
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-125 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34591.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-125, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34592
in-theory        34592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-113 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34592.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H and I) -> H)))), M:tm-113, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34593
in-theory        34593
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-105 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34593.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-105, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34594
in-theory        34594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-95 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34594.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or ((F and G) -> F)))), M:tm-95, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34595
in-theory        34595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-83 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34595.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-83, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34596
in-theory        34596
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D or ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-76 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34596.        (((not (not A)) -> A) and ((B -> (C -> B)) and (D or ((E and F) -> E)))), M:tm-76, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34597
in-theory        34597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-69 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34597.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or ((F and G) -> F)))), M:tm-69, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34598
in-theory        34598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-54 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34598.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-54, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34599
in-theory        34599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-42 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34599.        ((A -> (B or A)) and ((C -> (D -> C)) and (E or ((F and G) -> F)))), M:tm-42, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34600
in-theory        34600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-32 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34600.        ((A -> (A or B)) and ((C -> (D -> C)) and (E or ((F and G) -> F)))), M:tm-32, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34601
in-theory        34601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-23 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34601.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or ((F and G) -> F)))), M:tm-23, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34602
in-theory        34602
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-22 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34602.        (((A and B) -> B) and ((C -> (D -> C)) and (E or ((F and G) -> F)))), M:tm-22, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34603
in-theory        34603
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-21 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34603.        (((A and B) -> A) and ((C -> (D -> C)) and (E or ((F and G) -> F)))), M:tm-21, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34604
in-theory        34604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-20 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34604.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-20, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34605
in-theory        34605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-19 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34605.        ((A -> (B -> A)) and ((C -> (D -> C)) and (E or ((F and G) -> F)))), M:tm-19, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34606
in-theory        34606
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-7 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34606.        (A or ((B -> (C -> B)) and (D or ((E and F) -> E)))), M:tm-7, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34607
in-theory        34607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-7 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34607.        (((A -> (B -> A)) and (C or ((D and E) -> D))) or F), M:tm-6, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34608
in-theory        34608
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D or ((E and F) -> E))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34608.        (A -> (((B -> (C -> B)) and (D or ((E and F) -> E))) and A)), M:tm-5, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34609
in-theory        34609
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-1 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34609.        (A -> ((B -> (C -> B)) and (D or ((E and F) -> E)))), M:tm-1, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34610
in-theory        34610
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-490 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34610.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G and H) -> G)))), M:tm-490, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34611
in-theory        34611
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-480 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34611.        ((A or (B -> (C -> B))) and (D or (E or ((F and G) -> F)))), M:tm-480, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34612
in-theory        34612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-469 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34612.        ((A -> (B -> (B or C))) and (D or (E or ((F and G) -> F)))), M:tm-469, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34613
in-theory        34613
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34613.        ((A or (B or ((C and D) -> C))) and (E -> (E or F))), M:tm-456, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34614
in-theory        34614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-453 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34614.        ((A -> ((B -> (B or C)) and A)) and (D or (E or ((F and G) -> F)))), M:tm-453, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34615
in-theory        34615
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and ((E -> (E or F)) and (A or (B or ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34615.        ((A or (B or ((C and D) -> C))) and ((E -> (E or F)) and (A or (B or ((C and D) -> C))))), M:tm-443, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34616
in-theory        34616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-409 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34616.        (((A -> (A or B)) or C) and (D or (E or ((F and G) -> F)))), M:tm-409, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34617
in-theory        34617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-400 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34617.        (((A -> (B -> (A and B))) or C) and (D or (E or ((F and G) -> F)))), M:tm-400, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34618
in-theory        34618
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-391 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34618.        ((((A and B) -> B) or C) and (D or (E or ((F and G) -> F)))), M:tm-391, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34619
in-theory        34619
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-382 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34619.        ((((A and B) -> A) or C) and (D or (E or ((F and G) -> F)))), M:tm-382, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34620
in-theory        34620
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-373 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34620.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or ((G and H) -> G)))), M:tm-373, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34621
in-theory        34621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-364 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34621.        (((A -> (B -> A)) or C) and (D or (E or ((F and G) -> F)))), M:tm-364, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34622
in-theory        34622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-354 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34622.        ((A -> (B -> (C -> (B and C)))) and (D or (E or ((F and G) -> F)))), M:tm-354, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34623
in-theory        34623
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34623.        ((A or (B or ((C and D) -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34624
in-theory        34624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D or ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-338 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34624.        (((A -> B) -> (A -> (A and B))) and (C or (D or ((E and F) -> E)))), M:tm-338, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34625
in-theory        34625
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and ((E -> (F -> (E and F))) and (A or (B or ((C and D) -> C)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34625.        ((A or (B or ((C and D) -> C))) and ((E -> (F -> (E and F))) and (A or (B or ((C and D) -> C))))), M:tm-327, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34626
in-theory        34626
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and (((E and F) -> F) and (A or (B or ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34626.        ((A or (B or ((C and D) -> C))) and (((E and F) -> F) and (A or (B or ((C and D) -> C))))), M:tm-326, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34627
in-theory        34627
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and (((E and F) -> E) and (A or (B or ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34627.        ((A or (B or ((C and D) -> C))) and (((E and F) -> E) and (A or (B or ((C and D) -> C))))), M:tm-325, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34628
in-theory        34628
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B or ((C and D) -> C)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34628.        ((A or (B or ((C and D) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B or ((C and D) -> C))))), M:tm-324, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34629
in-theory        34629
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and ((E -> (F -> E)) and (A or (B or ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34629.        ((A or (B or ((C and D) -> C))) and ((E -> (F -> E)) and (A or (B or ((C and D) -> C))))), M:tm-323, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34630
in-theory        34630
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34630.        ((A or (B or ((C and D) -> C))) and ((E and F) -> F)), M:tm-322, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34631
in-theory        34631
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34631.        ((A or (B or ((C and D) -> C))) and ((E and F) -> E)), M:tm-320, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34632
in-theory        34632
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34632.        ((A or (B or ((C and D) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34633
in-theory        34633
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34633.        ((A or (B or ((C and D) -> C))) and (E -> (F -> E))), M:tm-315, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34634
in-theory        34634
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and (E or (A or (B or ((C and D) -> C)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34634.        ((A or (B or ((C and D) -> C))) and (E or (A or (B or ((C and D) -> C))))), M:tm-311, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34635
in-theory        34635
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and ((A or (B or ((C and D) -> C))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34635.        ((A or (B or ((C and D) -> C))) and ((A or (B or ((C and D) -> C))) or E)), M:tm-310, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34636
in-theory        34636
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and (E -> ((A or (B or ((C and D) -> C))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34636.        ((A or (B or ((C and D) -> C))) and (E -> ((A or (B or ((C and D) -> C))) and E))), M:tm-309, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34637
in-theory        34637
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and (E -> (A or (B or ((C and D) -> C)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34637.        ((A or (B or ((C and D) -> C))) and (E -> (A or (B or ((C and D) -> C))))), M:tm-305, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34638
in-theory        34638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-303 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34638.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or ((F and G) -> F)))), M:tm-303, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34639
in-theory        34639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-270 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34639.        ((A -> (((B and C) -> C) and A)) and (D or (E or ((F and G) -> F)))), M:tm-270, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34640
in-theory        34640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-239 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34640.        ((A -> (((B and C) -> B) and A)) and (D or (E or ((F and G) -> F)))), M:tm-239, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34641
in-theory        34641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-210 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34641.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or ((G and H) -> G)))), M:tm-210, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34642
in-theory        34642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-183 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34642.        ((A -> ((B -> (C -> B)) and A)) and (D or (E or ((F and G) -> F)))), M:tm-183, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34643
in-theory        34643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-157 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34643.        ((A -> ((B and C) -> C)) and (D or (E or ((F and G) -> F)))), M:tm-157, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34644
in-theory        34644
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-147 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34644.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or ((F and G) -> F)))), M:tm-147, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34645
in-theory        34645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-134 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34645.        ((A -> ((B and C) -> B)) and (D or (E or ((F and G) -> F)))), M:tm-134, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34646
in-theory        34646
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-125 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34646.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or ((F and G) -> F)))), M:tm-125, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34647
in-theory        34647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-113 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34647.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G and H) -> G)))), M:tm-113, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34648
in-theory        34648
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or ((F and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-105 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34648.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or ((F and G) -> F)))), M:tm-105, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34649
in-theory        34649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D or ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-95 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34649.        (((A -> B) -> (A -> A)) and (C or (D or ((E and F) -> E)))), M:tm-95, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34650
in-theory        34650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-83 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34650.        ((A -> (B -> (C -> B))) and (D or (E or ((F and G) -> F)))), M:tm-83, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34651
in-theory        34651
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C or ((D and E) -> D))))
theorem-size     15
proof            (modus-ponens tm-76 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34651.        (((not (not A)) -> A) and (B or (C or ((D and E) -> D)))), M:tm-76, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34652
in-theory        34652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or ((E and F) -> E))))
theorem-size     21
proof            (modus-ponens tm-69 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34652.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or ((E and F) -> E)))), M:tm-69, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34653
in-theory        34653
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-54 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34653.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or ((F and G) -> F)))), M:tm-54, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34654
in-theory        34654
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-42 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34654.        ((A -> (B or A)) and (C or (D or ((E and F) -> E)))), M:tm-42, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34655
in-theory        34655
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-32 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34655.        ((A -> (A or B)) and (C or (D or ((E and F) -> E)))), M:tm-32, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34656
in-theory        34656
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D or ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-23 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34656.        ((A -> (B -> (A and B))) and (C or (D or ((E and F) -> E)))), M:tm-23, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34657
in-theory        34657
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-22 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34657.        (((A and B) -> B) and (C or (D or ((E and F) -> E)))), M:tm-22, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34658
in-theory        34658
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-21 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34658.        (((A and B) -> A) and (C or (D or ((E and F) -> E)))), M:tm-21, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34659
in-theory        34659
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-20 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34659.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or ((F and G) -> F)))), M:tm-20, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34660
in-theory        34660
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-19 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34660.        ((A -> (B -> A)) and (C or (D or ((E and F) -> E)))), M:tm-19, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34661
in-theory        34661
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C or ((D and E) -> D))))
theorem-size     11
proof            (modus-ponens tm-7 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-7 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34661.        (A or (B or (C or ((D and E) -> D)))), M:tm-7, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34662
in-theory        34662
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-6 tm-7 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34662.        ((A or (B or ((C and D) -> C))) or E), M:tm-6, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34663
in-theory        34663
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C or ((D and E) -> D))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34663.        (A -> ((B or (C or ((D and E) -> D))) and A)), M:tm-5, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34664
in-theory        34664
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C or ((D and E) -> D))))
theorem-size     11
proof            (modus-ponens tm-1 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-1 tm-7 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34664.        (A -> (B or (C or ((D and E) -> D)))), M:tm-1, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34665
in-theory        34665
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F and G) -> F)) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34665.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F and G) -> F)) or H)), M:tm-490, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34666
in-theory        34666
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34666.        ((A or (B -> (C -> B))) and ((D or ((E and F) -> E)) or G)), M:tm-480, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34667
in-theory        34667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34667.        ((A -> (B -> (B or C))) and ((D or ((E and F) -> E)) or G)), M:tm-469, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34668
in-theory        34668
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34668.        (((A or ((B and C) -> B)) or D) and (E -> (E or F))), M:tm-456, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34669
in-theory        34669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34669.        ((A -> ((B -> (B or C)) and A)) and ((D or ((E and F) -> E)) or G)), M:tm-453, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34670
in-theory        34670
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and ((E -> (E or F)) and ((A or ((B and C) -> B)) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34670.        (((A or ((B and C) -> B)) or D) and ((E -> (E or F)) and ((A or ((B and C) -> B)) or D))), M:tm-443, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34671
in-theory        34671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34671.        (((A -> (A or B)) or C) and ((D or ((E and F) -> E)) or G)), M:tm-409, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34672
in-theory        34672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34672.        (((A -> (B -> (A and B))) or C) and ((D or ((E and F) -> E)) or G)), M:tm-400, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34673
in-theory        34673
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34673.        ((((A and B) -> B) or C) and ((D or ((E and F) -> E)) or G)), M:tm-391, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34674
in-theory        34674
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34674.        ((((A and B) -> A) or C) and ((D or ((E and F) -> E)) or G)), M:tm-382, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34675
in-theory        34675
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F and G) -> F)) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34675.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F and G) -> F)) or H)), M:tm-373, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34676
in-theory        34676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34676.        (((A -> (B -> A)) or C) and ((D or ((E and F) -> E)) or G)), M:tm-364, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34677
in-theory        34677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34677.        ((A -> (B -> (C -> (B and C)))) and ((D or ((E and F) -> E)) or G)), M:tm-354, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34678
in-theory        34678
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34678.        (((A or ((B and C) -> B)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34679
in-theory        34679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or ((D and E) -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34679.        (((A -> B) -> (A -> (A and B))) and ((C or ((D and E) -> D)) or F)), M:tm-338, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34680
in-theory        34680
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and ((E -> (F -> (E and F))) and ((A or ((B and C) -> B)) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34680.        (((A or ((B and C) -> B)) or D) and ((E -> (F -> (E and F))) and ((A or ((B and C) -> B)) or D))), M:tm-327, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34681
in-theory        34681
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and (((E and F) -> F) and ((A or ((B and C) -> B)) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34681.        (((A or ((B and C) -> B)) or D) and (((E and F) -> F) and ((A or ((B and C) -> B)) or D))), M:tm-326, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34682
in-theory        34682
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and (((E and F) -> E) and ((A or ((B and C) -> B)) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34682.        (((A or ((B and C) -> B)) or D) and (((E and F) -> E) and ((A or ((B and C) -> B)) or D))), M:tm-325, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34683
in-theory        34683
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or ((B and C) -> B)) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34683.        (((A or ((B and C) -> B)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or ((B and C) -> B)) or D))), M:tm-324, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34684
in-theory        34684
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and ((E -> (F -> E)) and ((A or ((B and C) -> B)) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34684.        (((A or ((B and C) -> B)) or D) and ((E -> (F -> E)) and ((A or ((B and C) -> B)) or D))), M:tm-323, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34685
in-theory        34685
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34685.        (((A or ((B and C) -> B)) or D) and ((E and F) -> F)), M:tm-322, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34686
in-theory        34686
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34686.        (((A or ((B and C) -> B)) or D) and ((E and F) -> E)), M:tm-320, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34687
in-theory        34687
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34687.        (((A or ((B and C) -> B)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34688
in-theory        34688
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34688.        (((A or ((B and C) -> B)) or D) and (E -> (F -> E))), M:tm-315, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34689
in-theory        34689
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and (E or ((A or ((B and C) -> B)) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34689.        (((A or ((B and C) -> B)) or D) and (E or ((A or ((B and C) -> B)) or D))), M:tm-311, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34690
in-theory        34690
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and (((A or ((B and C) -> B)) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34690.        (((A or ((B and C) -> B)) or D) and (((A or ((B and C) -> B)) or D) or E)), M:tm-310, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34691
in-theory        34691
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and (E -> (((A or ((B and C) -> B)) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34691.        (((A or ((B and C) -> B)) or D) and (E -> (((A or ((B and C) -> B)) or D) and E))), M:tm-309, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34692
in-theory        34692
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and (E -> ((A or ((B and C) -> B)) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34692.        (((A or ((B and C) -> B)) or D) and (E -> ((A or ((B and C) -> B)) or D))), M:tm-305, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34693
in-theory        34693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E and F) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34693.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E and F) -> E)) or G)), M:tm-303, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34694
in-theory        34694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34694.        ((A -> (((B and C) -> C) and A)) and ((D or ((E and F) -> E)) or G)), M:tm-270, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34695
in-theory        34695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34695.        ((A -> (((B and C) -> B) and A)) and ((D or ((E and F) -> E)) or G)), M:tm-239, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34696
in-theory        34696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F and G) -> F)) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34696.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F and G) -> F)) or H)), M:tm-210, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34697
in-theory        34697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34697.        ((A -> ((B -> (C -> B)) and A)) and ((D or ((E and F) -> E)) or G)), M:tm-183, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34698
in-theory        34698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34698.        ((A -> ((B and C) -> C)) and ((D or ((E and F) -> E)) or G)), M:tm-157, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34699
in-theory        34699
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34699.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E and F) -> E)) or G)), M:tm-147, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34700
in-theory        34700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34700.        ((A -> ((B and C) -> B)) and ((D or ((E and F) -> E)) or G)), M:tm-134, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34701
in-theory        34701
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34701.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E and F) -> E)) or G)), M:tm-125, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34702
in-theory        34702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F and G) -> F)) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34702.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F and G) -> F)) or H)), M:tm-113, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34703
in-theory        34703
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E and F) -> E)) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34703.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E and F) -> E)) or G)), M:tm-105, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34704
in-theory        34704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or ((D and E) -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34704.        (((A -> B) -> (A -> A)) and ((C or ((D and E) -> D)) or F)), M:tm-95, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34705
in-theory        34705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34705.        ((A -> (B -> (C -> B))) and ((D or ((E and F) -> E)) or G)), M:tm-83, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34706
in-theory        34706
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or ((C and D) -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34706.        (((not (not A)) -> A) and ((B or ((C and D) -> C)) or E)), M:tm-76, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34707
in-theory        34707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D and E) -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-7 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34707.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D and E) -> D)) or F)), M:tm-69, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34708
in-theory        34708
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E and F) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34708.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E and F) -> E)) or G)), M:tm-54, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34709
in-theory        34709
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or ((D and E) -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34709.        ((A -> (B or A)) and ((C or ((D and E) -> D)) or F)), M:tm-42, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34710
in-theory        34710
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or ((D and E) -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34710.        ((A -> (A or B)) and ((C or ((D and E) -> D)) or F)), M:tm-32, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34711
in-theory        34711
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or ((D and E) -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34711.        ((A -> (B -> (A and B))) and ((C or ((D and E) -> D)) or F)), M:tm-23, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34712
in-theory        34712
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or ((D and E) -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34712.        (((A and B) -> B) and ((C or ((D and E) -> D)) or F)), M:tm-22, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34713
in-theory        34713
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or ((D and E) -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34713.        (((A and B) -> A) and ((C or ((D and E) -> D)) or F)), M:tm-21, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34714
in-theory        34714
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E and F) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34714.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E and F) -> E)) or G)), M:tm-20, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34715
in-theory        34715
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or ((D and E) -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34715.        ((A -> (B -> A)) and ((C or ((D and E) -> D)) or F)), M:tm-19, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34716
in-theory        34716
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B or ((C and D) -> C)) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-7 tm-6 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34716.        (A or ((B or ((C and D) -> C)) or E)), M:tm-7, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34717
in-theory        34717
times-derived    2
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-6 tm-7 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34717.        (((A or ((B and C) -> B)) or D) or E), M:tm-6, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34718
in-theory        34718
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B or ((C and D) -> C)) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34718.        (A -> (((B or ((C and D) -> C)) or E) and A)), M:tm-5, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34719
in-theory        34719
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B or ((C and D) -> C)) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-1 tm-6 tm-7 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34719.        (A -> ((B or ((C and D) -> C)) or E)), M:tm-1, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34720
in-theory        34720
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-500 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34720.        ((A or ((B and C) -> B)) and (D -> (E or D))), M:tm-500, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-34721
in-theory        34721
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-34721.        ((A or ((B and C) -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-500, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-34722
in-theory        34722
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-500 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-34722.        ((A or ((B and C) -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-500, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-34723
in-theory        34723
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-500 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-7 tm-3 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-34723.        ((A or ((B and C) -> B)) and ((not (not D)) -> D)), M:tm-500, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-34724
in-theory        34724
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-500 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34724.        ((A or ((B and C) -> B)) and (D -> (E -> (F -> E)))), M:tm-500, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-34725
in-theory        34725
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-500 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-34725.        ((A or ((B and C) -> B)) and ((D -> E) -> (D -> D))), M:tm-500, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-34726
in-theory        34726
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-500 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-34726.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-500, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-34727
in-theory        34727
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-34727.        ((A or ((B and C) -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-500, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-34728
in-theory        34728
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-500 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-34728.        ((A or ((B and C) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-500, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-34729
in-theory        34729
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-500 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-34729.        ((A or ((B and C) -> B)) and (D -> ((E and F) -> E))), M:tm-500, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-34730
in-theory        34730
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-500 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-34730.        ((A or ((B and C) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-500, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-34731
in-theory        34731
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-500 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-34731.        ((A or ((B and C) -> B)) and (D -> ((E and F) -> F))), M:tm-500, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-34732
in-theory        34732
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-500 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34732.        ((A or ((B and C) -> B)) and (D -> ((E -> (F -> E)) and D))), M:tm-500, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-34733
in-theory        34733
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-500 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-34733.        ((A or ((B and C) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-500, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-34734
in-theory        34734
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-500 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-34734.        ((A or ((B and C) -> B)) and (D -> (((E and F) -> E) and D))), M:tm-500, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-34735
in-theory        34735
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-500 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-34735.        ((A or ((B and C) -> B)) and (D -> (((E and F) -> F) and D))), M:tm-500, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-34736
in-theory        34736
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-34736.        ((A or ((B and C) -> B)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-500, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-34737
in-theory        34737
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-500 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-34737.        ((A or ((B and C) -> B)) and ((D -> E) -> (D -> (D and E)))), M:tm-500, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-34738
in-theory        34738
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-34738.        ((A or ((B and C) -> B)) and (D -> (E -> (F -> (E and F))))), M:tm-500, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-34739
in-theory        34739
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-500 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34739.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) or F)), M:tm-500, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-34740
in-theory        34740
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-500 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-34740.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-500, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-34741
in-theory        34741
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-500 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-34741.        ((A or ((B and C) -> B)) and (((D and E) -> D) or F)), M:tm-500, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-34742
in-theory        34742
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-500 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-34742.        ((A or ((B and C) -> B)) and (((D and E) -> E) or F)), M:tm-500, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-34743
in-theory        34743
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-500 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-34743.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) or F)), M:tm-500, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-34744
in-theory        34744
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-500 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-34744.        ((A or ((B and C) -> B)) and ((D -> (D or E)) or F)), M:tm-500, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-34745
in-theory        34745
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-500 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-34745.        ((A or ((B and C) -> B)) and (D -> ((E -> (E or F)) and D))), M:tm-500, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-34746
in-theory        34746
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-500 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-34746.        ((A or ((B and C) -> B)) and (D -> (E -> (E or F)))), M:tm-500, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-34747
in-theory        34747
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-500 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34747.        ((A or ((B and C) -> B)) and (D or (E -> (F -> E)))), M:tm-500, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-34748
in-theory        34748
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-34748.        ((A or ((B and C) -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-500, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-34749
in-theory        34749
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-500 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-34749.        ((A or ((B and C) -> B)) and (D or ((E and F) -> E))), M:tm-500, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-34750
in-theory        34750
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-500 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-34750.        ((A or ((B and C) -> B)) and (D or ((E and F) -> F))), M:tm-500, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-34751
in-theory        34751
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-34751.        ((A or ((B and C) -> B)) and (D or (E -> (F -> (E and F))))), M:tm-500, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-34752
in-theory        34752
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-500 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-34752.        ((A or ((B and C) -> B)) and (D or (E -> (E or F)))), M:tm-500, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-34753
in-theory        34753
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-500 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34753.        ((A or ((B and C) -> B)) and (D or (E -> (F or E)))), M:tm-500, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-34754
in-theory        34754
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-500 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34754.        ((A or ((B and C) -> B)) and ((D -> (E or D)) or F)), M:tm-500, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-34755
in-theory        34755
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-500 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34755.        ((A or ((B and C) -> B)) and (D -> ((E -> (F or E)) and D))), M:tm-500, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-34756
in-theory        34756
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-500 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34756.        ((A or ((B and C) -> B)) and (D -> (E -> (F or E)))), M:tm-500, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-34757
in-theory        34757
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-500 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-34757.        ((A or ((B and C) -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-500, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-34758
in-theory        34758
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-500 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-34758.        ((A or ((B and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-500, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-34759
in-theory        34759
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-500 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-34759.        ((A or ((B and C) -> B)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-500, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-34760
in-theory        34760
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-500 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-34760.        ((A or ((B and C) -> B)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-500, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-34761
in-theory        34761
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-500 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-34761.        ((A or ((B and C) -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-500, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-34762
in-theory        34762
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-500 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-34762.        ((A or ((B and C) -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-500, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-34763
in-theory        34763
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-500 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-34763.        ((A or ((B and C) -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-500, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-34764
in-theory        34764
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-500 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-34764.        ((A or ((B and C) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-500, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-34765
in-theory        34765
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-34765.        ((A or ((B and C) -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-500, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-34766
in-theory        34766
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-500 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-34766.        ((A or ((B and C) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-500, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-34767
in-theory        34767
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-500 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-34767.        ((A or ((B and C) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-500, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-34768
in-theory        34768
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-500 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-34768.        ((A or ((B and C) -> B)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-500, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-34769
in-theory        34769
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-34769.        ((A or ((B and C) -> B)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-500, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-34770
in-theory        34770
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-500 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-34770.        ((A or ((B and C) -> B)) and ((D -> (not (E -> D))) -> (not D))), M:tm-500, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-34771
in-theory        34771
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-34771.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-500, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-34772
in-theory        34772
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-500 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-34772.        ((A or ((B and C) -> B)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-500, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-34773
in-theory        34773
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-500 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-34773.        ((A or ((B and C) -> B)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-500, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-34774
in-theory        34774
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-34774.        ((A or ((B and C) -> B)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-500, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-34775
in-theory        34775
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-500 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-34775.        ((A or ((B and C) -> B)) and ((D -> (not (D or E))) -> (not D))), M:tm-500, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-34776
in-theory        34776
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-500 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-34776.        ((A or ((B and C) -> B)) and ((D -> (not (E or D))) -> (not D))), M:tm-500, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-34777
in-theory        34777
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-500 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-34777.        ((A or ((B and C) -> B)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-500, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-34778
in-theory        34778
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-500 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-34778.        ((A or ((B and C) -> B)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-500, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-34779
in-theory        34779
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-500 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-34779.        ((A or ((B and C) -> B)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-500, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-34780
in-theory        34780
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-34780.        ((A or ((B and C) -> B)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-500, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-34781
in-theory        34781
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-500 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-34781.        ((A or ((B and C) -> B)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-500, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-34782
in-theory        34782
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-500 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-34782.        ((A or ((B and C) -> B)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-500, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-34783
in-theory        34783
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-500 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-34783.        ((A or ((B and C) -> B)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-500, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-34784
in-theory        34784
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-34784.        ((A or ((B and C) -> B)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-500, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-34785
in-theory        34785
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-500 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-34785.        ((A or ((B and C) -> B)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-500, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-34786
in-theory        34786
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-500 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-34786.        ((A or ((B and C) -> B)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-500, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-34787
in-theory        34787
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-500 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-34787.        ((A or ((B and C) -> B)) and (D or ((not (not E)) -> E))), M:tm-500, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-34788
in-theory        34788
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-500 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-34788.        ((A or ((B and C) -> B)) and (((not (not D)) -> D) or E)), M:tm-500, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-34789
in-theory        34789
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-500 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-34789.        ((A or ((B and C) -> B)) and (D -> (((not (not E)) -> E) and D))), M:tm-500, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-34790
in-theory        34790
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-500 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-34790.        ((A or ((B and C) -> B)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-500, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-34791
in-theory        34791
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-500 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-34791.        ((A or ((B and C) -> B)) and (D -> ((not (not E)) -> E))), M:tm-500, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-34792
in-theory        34792
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-34792.        ((A or ((B and C) -> B)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-500, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-34793
in-theory        34793
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-500 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-34793.        ((A or ((B and C) -> B)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-500, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-34794
in-theory        34794
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-34794.        ((A or ((B and C) -> B)) and (D or (E -> (F -> (G -> F))))), M:tm-500, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-34795
in-theory        34795
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-34795.        ((A or ((B and C) -> B)) and ((D -> (E -> (F -> E))) or G)), M:tm-500, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-34796
in-theory        34796
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-34796.        ((A or ((B and C) -> B)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-500, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-34797
in-theory        34797
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-500 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-34797.        ((A or ((B and C) -> B)) and ((D -> E) -> (D -> (F -> E)))), M:tm-500, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-34798
in-theory        34798
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-34798.        ((A or ((B and C) -> B)) and (D -> (E -> (F -> (G -> F))))), M:tm-500, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-34799
in-theory        34799
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-500 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-34799.        ((A or ((B and C) -> B)) and (D -> D)), M:tm-500, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-34800
in-theory        34800
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-34800.        ((A or ((B and C) -> B)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-500, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-34801
in-theory        34801
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-500 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-34801.        ((A or ((B and C) -> B)) and ((D and E) -> (D and E))), M:tm-500, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-34802
in-theory        34802
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-500 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-34802.        ((A or ((B and C) -> B)) and ((D -> E) -> (D -> E))), M:tm-500, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-34803
in-theory        34803
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-500 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-34803.        ((A or ((B and C) -> B)) and ((not (not D)) -> (not (not D)))), M:tm-500, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-34804
in-theory        34804
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-500 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-34804.        ((A or ((B and C) -> B)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-500, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-34805
in-theory        34805
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-500 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-34805.        ((A or ((B and C) -> B)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-500, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-34806
in-theory        34806
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-500 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-34806.        ((A or ((B and C) -> B)) and (D or ((E -> F) -> (E -> E)))), M:tm-500, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-34807
in-theory        34807
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-500 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-34807.        ((A or ((B and C) -> B)) and (((D -> E) -> (D -> D)) or F)), M:tm-500, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-34808
in-theory        34808
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-34808.        ((A or ((B and C) -> B)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-500, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-34809
in-theory        34809
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-34809.        ((A or ((B and C) -> B)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-500, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-34810
in-theory        34810
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-500 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-34810.        ((A or ((B and C) -> B)) and (D -> ((E -> F) -> (E -> E)))), M:tm-500, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-34811
in-theory        34811
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-34811.        ((A or ((B and C) -> B)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-500, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-34812
in-theory        34812
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-500 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-34812.        ((A or ((B and C) -> B)) and ((D -> (D -> E)) -> (D -> E))), M:tm-500, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-34813
in-theory        34813
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-500 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-34813.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-500, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-34814
in-theory        34814
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-500 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-34814.        ((A or ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-500, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-34815
in-theory        34815
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-500 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-34815.        ((A or ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-500, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-34816
in-theory        34816
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-34816.        ((A or ((B and C) -> B)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-500, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-34817
in-theory        34817
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-500 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-34817.        ((A or ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-500, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-34818
in-theory        34818
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-500 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-34818.        ((A or ((B and C) -> B)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-500, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-34819
in-theory        34819
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-500 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-34819.        ((A or ((B and C) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-500, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-34820
in-theory        34820
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-34820.        ((A or ((B and C) -> B)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-500, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-34821
in-theory        34821
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-500 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-34821.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-500, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-34822
in-theory        34822
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-500 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-34822.        ((A or ((B and C) -> B)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-500, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-34823
in-theory        34823
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-500 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-34823.        ((A or ((B and C) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-500, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-34824
in-theory        34824
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-500 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34824.        ((A or ((B and C) -> B)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-500, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34825
in-theory        34825
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-500 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34825.        ((A or ((B and C) -> B)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-500, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-34826
in-theory        34826
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-500 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34826.        ((A or ((B and C) -> B)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-500, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-34827
in-theory        34827
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-500 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-34827.        ((A or ((B and C) -> B)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-500, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-34828
in-theory        34828
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-500 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34828.        ((A or ((B and C) -> B)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-500, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-34829
in-theory        34829
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-500 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-34829.        ((A or ((B and C) -> B)) and (((D -> E) and D) -> E)), M:tm-500, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-34830
in-theory        34830
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-500 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-34830.        ((A or ((B and C) -> B)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-500, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-34831
in-theory        34831
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-500 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-34831.        ((A or ((B and C) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-500, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-34832
in-theory        34832
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-500 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-34832.        ((A or ((B and C) -> B)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-500, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-34833
in-theory        34833
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-500 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-34833.        ((A or ((B and C) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-500, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-34834
in-theory        34834
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-500 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-34834.        ((A or ((B and C) -> B)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-500, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-34835
in-theory        34835
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-500 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-34835.        ((A or ((B and C) -> B)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-500, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-34836
in-theory        34836
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-500 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-34836.        ((A or ((B and C) -> B)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-500, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-34837
in-theory        34837
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-500 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-34837.        ((A or ((B and C) -> B)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-500, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-34838
in-theory        34838
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-500 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-34838.        ((A or ((B and C) -> B)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-500, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-34839
in-theory        34839
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-500 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-34839.        ((A or ((B and C) -> B)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-500, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-34840
in-theory        34840
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-500 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-34840.        ((A or ((B and C) -> B)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-500, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-34841
in-theory        34841
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-500 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-34841.        ((A or ((B and C) -> B)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-500, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-34842
in-theory        34842
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-500 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-34842.        ((A or ((B and C) -> B)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-500, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-34843
in-theory        34843
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-34843.        ((A or ((B and C) -> B)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-500, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-34844
in-theory        34844
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-500 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-34844.        ((A or ((B and C) -> B)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-500, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-34845
in-theory        34845
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-500 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-34845.        ((A or ((B and C) -> B)) and (D or (E -> ((F and G) -> F)))), M:tm-500, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34846
in-theory        34846
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-34846.        ((A or ((B and C) -> B)) and ((D -> ((E and F) -> E)) or G)), M:tm-500, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-34847
in-theory        34847
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-34847.        ((A or ((B and C) -> B)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-500, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-34848
in-theory        34848
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-500 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-34848.        ((A or ((B and C) -> B)) and ((D -> (E and F)) -> (D -> E))), M:tm-500, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-34849
in-theory        34849
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-500 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-34849.        ((A or ((B and C) -> B)) and (D -> (E -> ((F and G) -> F)))), M:tm-500, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-34850
in-theory        34850
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-500 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-34850.        ((A or ((B and C) -> B)) and ((D and (D -> E)) -> E)), M:tm-500, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-34851
in-theory        34851
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-500 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-34851.        ((A or ((B and C) -> B)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-500, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-34852
in-theory        34852
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-500 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-34852.        ((A or ((B and C) -> B)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-500, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-34853
in-theory        34853
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-500 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-34853.        ((A or ((B and C) -> B)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-500, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-34854
in-theory        34854
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-500 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-34854.        ((A or ((B and C) -> B)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-500, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-34855
in-theory        34855
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-500 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-34855.        ((A or ((B and C) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-500, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-34856
in-theory        34856
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-500 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-34856.        ((A or ((B and C) -> B)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-500, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-34857
in-theory        34857
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-500 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-34857.        ((A or ((B and C) -> B)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-500, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-34858
in-theory        34858
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-500 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-34858.        ((A or ((B and C) -> B)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-500, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-34859
in-theory        34859
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-500 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-34859.        ((A or ((B and C) -> B)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-500, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-34860
in-theory        34860
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-500 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-34860.        ((A or ((B and C) -> B)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-500, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-34861
in-theory        34861
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-500 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-34861.        ((A or ((B and C) -> B)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-500, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-34862
in-theory        34862
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-500 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-34862.        ((A or ((B and C) -> B)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-500, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-34863
in-theory        34863
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-500 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-34863.        ((A or ((B and C) -> B)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-500, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-34864
in-theory        34864
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-500 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-34864.        ((A or ((B and C) -> B)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-500, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-34865
in-theory        34865
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-500 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-34865.        ((A or ((B and C) -> B)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-500, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-34866
in-theory        34866
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-34866.        ((A or ((B and C) -> B)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-500, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-34867
in-theory        34867
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-500 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-34867.        ((A or ((B and C) -> B)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-500, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-34868
in-theory        34868
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-500 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-34868.        ((A or ((B and C) -> B)) and (D or (E -> ((F and G) -> G)))), M:tm-500, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-34869
in-theory        34869
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-34869.        ((A or ((B and C) -> B)) and ((D -> ((E and F) -> F)) or G)), M:tm-500, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-34870
in-theory        34870
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-34870.        ((A or ((B and C) -> B)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-500, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-34871
in-theory        34871
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-500 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-34871.        ((A or ((B and C) -> B)) and ((D -> (E and F)) -> (D -> F))), M:tm-500, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-34872
in-theory        34872
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-500 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-34872.        ((A or ((B and C) -> B)) and (D -> (E -> ((F and G) -> G)))), M:tm-500, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-34873
in-theory        34873
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34873.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-500, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-34874
in-theory        34874
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-34874.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-500, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34875
in-theory        34875
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-34875.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-500, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-34876
in-theory        34876
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-500 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-34876.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-500, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-34877
in-theory        34877
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-34877.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-500, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-34878
in-theory        34878
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-500 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-34878.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-500, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-34879
in-theory        34879
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34879.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-500, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-34880
in-theory        34880
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-34880.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-500, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-34881
in-theory        34881
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-500 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-34881.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-500, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-34882
in-theory        34882
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-34882.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-500, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-34883
in-theory        34883
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-34883.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-500, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-34884
in-theory        34884
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-34884.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-500, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-34885
in-theory        34885
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-500 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-34885.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-500, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-34886
in-theory        34886
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34886.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-500, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-34887
in-theory        34887
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-500 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-34887.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-500, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-34888
in-theory        34888
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-500 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-34888.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-500, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34889
in-theory        34889
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-500 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-34889.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-500, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-34890
in-theory        34890
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-500 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-34890.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-500, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-34891
in-theory        34891
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-34891.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-500, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-34892
in-theory        34892
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-34892.        ((A or ((B and C) -> B)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-500, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-34893
in-theory        34893
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-500 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-34893.        ((A or ((B and C) -> B)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-500, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-34894
in-theory        34894
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-500 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-34894.        ((A or ((B and C) -> B)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-500, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-34895
in-theory        34895
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-500 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-34895.        ((A or ((B and C) -> B)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-500, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-34896
in-theory        34896
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-34896.        ((A or ((B and C) -> B)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-500, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-34897
in-theory        34897
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-500 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-34897.        ((A or ((B and C) -> B)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-500, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-34898
in-theory        34898
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-500 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34898.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-500, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-34899
in-theory        34899
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-34899.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-500, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-34900
in-theory        34900
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-500 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-34900.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-500, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-34901
in-theory        34901
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-500 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-34901.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-500, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-34902
in-theory        34902
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-34902.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-500, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-34903
in-theory        34903
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-34903.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-500, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-34904
in-theory        34904
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-500 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34904.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-500, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-34905
in-theory        34905
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-34905.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-500, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-34906
in-theory        34906
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-500 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-34906.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-500, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-34907
in-theory        34907
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-500 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-34907.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-500, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-34908
in-theory        34908
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-34908.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-500, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-34909
in-theory        34909
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-500 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-34909.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-500, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-34910
in-theory        34910
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-500 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-34910.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-500, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-34911
in-theory        34911
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-500 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34911.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-500, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-34912
in-theory        34912
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-500 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-34912.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-500, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-34913
in-theory        34913
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-500 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-34913.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-500, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-34914
in-theory        34914
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-500 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-34914.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-500, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-34915
in-theory        34915
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-500 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-34915.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-500, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-34916
in-theory        34916
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-500 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-34916.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-500, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-34917
in-theory        34917
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-500 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-34917.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-500, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-34918
in-theory        34918
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-500 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-34918.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-500, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-34919
in-theory        34919
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-500 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-34919.        ((A or ((B and C) -> B)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-500, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-34920
in-theory        34920
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-500 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-34920.        ((A or ((B and C) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-500, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-34921
in-theory        34921
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-500 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-34921.        ((A or ((B and C) -> B)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-500, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-34922
in-theory        34922
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-500 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-34922.        ((A or ((B and C) -> B)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-500, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-34923
in-theory        34923
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-500 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-34923.        ((A or ((B and C) -> B)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-500, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-34924
in-theory        34924
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-500 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-34924.        ((A or ((B and C) -> B)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-500, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-34925
in-theory        34925
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34925.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-500, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-34926
in-theory        34926
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-34926.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-500, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34927
in-theory        34927
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-34927.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-500, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-34928
in-theory        34928
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-500 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-34928.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-500, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-34929
in-theory        34929
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-34929.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-500, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-34930
in-theory        34930
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-500 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-34930.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-500, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-34931
in-theory        34931
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34931.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-500, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-34932
in-theory        34932
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-34932.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-500, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-34933
in-theory        34933
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-500 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-34933.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-500, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-34934
in-theory        34934
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-34934.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-500, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-34935
in-theory        34935
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-34935.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-500, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-34936
in-theory        34936
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-34936.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-500, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-34937
in-theory        34937
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-500 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-34937.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-500, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-34938
in-theory        34938
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34938.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-500, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-34939
in-theory        34939
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-500 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-34939.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-500, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-34940
in-theory        34940
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-500 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-34940.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-500, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34941
in-theory        34941
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-500 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-34941.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-500, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-34942
in-theory        34942
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-500 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-34942.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-500, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-34943
in-theory        34943
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-34943.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-500, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-34944
in-theory        34944
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-500 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-34944.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-500, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-34945
in-theory        34945
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-34945.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-500, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-34946
in-theory        34946
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-500 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-34946.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-500, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-34947
in-theory        34947
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-34947.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-500, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-34948
in-theory        34948
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-34948.        ((A or ((B and C) -> B)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-500, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-34949
in-theory        34949
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-500 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-34949.        ((A or ((B and C) -> B)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-500, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-34950
in-theory        34950
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-500 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-34950.        ((A or ((B and C) -> B)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-500, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-34951
in-theory        34951
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-500 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-34951.        ((A or ((B and C) -> B)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-500, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-34952
in-theory        34952
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-34952.        ((A or ((B and C) -> B)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-500, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-34953
in-theory        34953
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-500 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-34953.        ((A or ((B and C) -> B)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-500, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-34954
in-theory        34954
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34954.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-500, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-34955
in-theory        34955
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-34955.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-500, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34956
in-theory        34956
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-34956.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-500, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-34957
in-theory        34957
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-500 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-34957.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-500, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-34958
in-theory        34958
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-34958.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-500, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-34959
in-theory        34959
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-500 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-34959.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-500, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-34960
in-theory        34960
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34960.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-500, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-34961
in-theory        34961
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-34961.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-500, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-34962
in-theory        34962
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-500 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-34962.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-500, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-34963
in-theory        34963
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-34963.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-500, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-34964
in-theory        34964
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-34964.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-500, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-34965
in-theory        34965
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-34965.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-500, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-34966
in-theory        34966
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-500 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-34966.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-500, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-34967
in-theory        34967
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34967.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-500, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-34968
in-theory        34968
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-500 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-34968.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-500, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-34969
in-theory        34969
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-500 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-34969.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-500, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-34970
in-theory        34970
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-500 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-34970.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-500, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-34971
in-theory        34971
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-500 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-34971.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-500, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-34972
in-theory        34972
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-34972.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-500, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-34973
in-theory        34973
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-500 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-34973.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-500, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-34974
in-theory        34974
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-34974.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-500, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-34975
in-theory        34975
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-34975.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-500, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-34976
in-theory        34976
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-34976.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-500, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-34977
in-theory        34977
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-500 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-34977.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-500, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-34978
in-theory        34978
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-34978.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-500, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-34979
in-theory        34979
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-34979.        ((A or ((B and C) -> B)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-500, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-34980
in-theory        34980
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-500 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-34980.        ((A or ((B and C) -> B)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-500, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-34981
in-theory        34981
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-500 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-34981.        ((A or ((B and C) -> B)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-500, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-34982
in-theory        34982
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-500 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-34982.        ((A or ((B and C) -> B)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-500, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-34983
in-theory        34983
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-34983.        ((A or ((B and C) -> B)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-500, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-34984
in-theory        34984
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-500 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-34984.        ((A or ((B and C) -> B)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-500, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-34985
in-theory        34985
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34985.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-500, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-34986
in-theory        34986
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-34986.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-500, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-34987
in-theory        34987
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-500 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-34987.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-500, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-34988
in-theory        34988
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-500 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-34988.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-500, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-34989
in-theory        34989
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-34989.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-500, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-34990
in-theory        34990
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-500 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-34990.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-500, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-34991
in-theory        34991
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34991.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-500, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-34992
in-theory        34992
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-34992.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-500, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-34993
in-theory        34993
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-34993.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-500, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-34994
in-theory        34994
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-500 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-34994.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-500, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-34995
in-theory        34995
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-34995.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-500, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-34996
in-theory        34996
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-34996.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-500, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-34997
in-theory        34997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-34997.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-500, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-34998
in-theory        34998
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-500 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-34998.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-500, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-34999
in-theory        34999
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-500 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-34999.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-500, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-35000
in-theory        35000
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-500 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-35000.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-500, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-35001
in-theory        35001
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-500 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-35001.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-500, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-35002
in-theory        35002
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-500 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-35002.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-500, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35003
in-theory        35003
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-500 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-35003.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-500, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-35004
in-theory        35004
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-500 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-35004.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-500, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-35005
in-theory        35005
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-500 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-35005.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-500, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-35006
in-theory        35006
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-500 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-35006.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-500, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-35007
in-theory        35007
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-500 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-35007.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-500, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-35008
in-theory        35008
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-500 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-35008.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-500, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-35009
in-theory        35009
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-500 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-35009.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-500, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-35010
in-theory        35010
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-500 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-35010.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-500, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-35011
in-theory        35011
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-500 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-35011.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-500, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-35012
in-theory        35012
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-500 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-35012.        ((A or ((B and C) -> B)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-500, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-35013
in-theory        35013
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-500 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-35013.        ((A or ((B and C) -> B)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-500, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-35014
in-theory        35014
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-500 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-35014.        ((A or ((B and C) -> B)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-500, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-35015
in-theory        35015
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-500 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-35015.        ((A or ((B and C) -> B)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-500, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-35016
in-theory        35016
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-500 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-35016.        ((A or ((B and C) -> B)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-500, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-35017
in-theory        35017
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-500 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-35017.        ((A or ((B and C) -> B)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-500, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-35018
in-theory        35018
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-500 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-35018.        ((A or ((B and C) -> B)) and (D -> (D and (E -> D)))), M:tm-500, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-35019
in-theory        35019
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-35019.        ((A or ((B and C) -> B)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-500, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-35020
in-theory        35020
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-500 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-35020.        ((A or ((B and C) -> B)) and ((D and E) -> ((D and E) and D))), M:tm-500, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-35021
in-theory        35021
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-500 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-35021.        ((A or ((B and C) -> B)) and ((D and E) -> ((D and E) and E))), M:tm-500, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-35022
in-theory        35022
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-35022.        ((A or ((B and C) -> B)) and (D -> (D and (E -> (D and E))))), M:tm-500, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-35023
in-theory        35023
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-500 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-35023.        ((A or ((B and C) -> B)) and (D -> (D and (D or E)))), M:tm-500, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-35024
in-theory        35024
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-500 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-35024.        ((A or ((B and C) -> B)) and (D -> (D and (E or D)))), M:tm-500, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-35025
in-theory        35025
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-500 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-35025.        ((A or ((B and C) -> B)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-500, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-35026
in-theory        35026
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-35026.        ((A or ((B and C) -> B)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-500, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-35027
in-theory        35027
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-500 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-35027.        ((A or ((B and C) -> B)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-500, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-35028
in-theory        35028
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-35028.        ((A or ((B and C) -> B)) and (D -> (D and (E -> (F -> E))))), M:tm-500, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-35029
in-theory        35029
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-500 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-35029.        ((A or ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-500, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-35030
in-theory        35030
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-500 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-35030.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-500, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-35031
in-theory        35031
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-500 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-35031.        ((A or ((B and C) -> B)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-500, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-35032
in-theory        35032
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-500 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-35032.        ((A or ((B and C) -> B)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-500, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-35033
in-theory        35033
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-500 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-35033.        ((A or ((B and C) -> B)) and (D -> (D and ((E and F) -> E)))), M:tm-500, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-35034
in-theory        35034
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-500 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-35034.        ((A or ((B and C) -> B)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-500, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-35035
in-theory        35035
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-500 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-35035.        ((A or ((B and C) -> B)) and (D -> (D and ((E and F) -> F)))), M:tm-500, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-35036
in-theory        35036
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-500 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-35036.        ((A or ((B and C) -> B)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-500, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-35037
in-theory        35037
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-500 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-35037.        ((A or ((B and C) -> B)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-500, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-35038
in-theory        35038
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-500 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-35038.        ((A or ((B and C) -> B)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-500, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-35039
in-theory        35039
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-500 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-35039.        ((A or ((B and C) -> B)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-500, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-35040
in-theory        35040
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-500 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-35040.        ((A or ((B and C) -> B)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-500, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-35041
in-theory        35041
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-35041.        ((A or ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-500, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-35042
in-theory        35042
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-500 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-35042.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-500, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-35043
in-theory        35043
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-35043.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-500, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-35044
in-theory        35044
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-35044.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-500, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-35045
in-theory        35045
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-500 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-35045.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-500, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-35046
in-theory        35046
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-35046.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-500, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-35047
in-theory        35047
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-500 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-35047.        ((A or ((B and C) -> B)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-500, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-35048
in-theory        35048
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-500 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-35048.        ((A or ((B and C) -> B)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-500, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-35049
in-theory        35049
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-500 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-35049.        ((A or ((B and C) -> B)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-500, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-35050
in-theory        35050
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-500 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-35050.        ((A or ((B and C) -> B)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-500, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-35051
in-theory        35051
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-35051.        ((A or ((B and C) -> B)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-500, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-35052
in-theory        35052
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-500 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-35052.        ((A or ((B and C) -> B)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-500, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-35053
in-theory        35053
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-500 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-35053.        ((A or ((B and C) -> B)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-500, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-35054
in-theory        35054
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-500 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-35054.        ((A or ((B and C) -> B)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-500, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-35055
in-theory        35055
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-500 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-35055.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-500, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-35056
in-theory        35056
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-500 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-35056.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-500, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-35057
in-theory        35057
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-500 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-35057.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-500, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-35058
in-theory        35058
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-500 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-35058.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-500, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-35059
in-theory        35059
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-500 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-35059.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-500, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-35060
in-theory        35060
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-500 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-35060.        ((A or ((B and C) -> B)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-500, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-35061
in-theory        35061
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-500 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-35061.        ((A or ((B and C) -> B)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-500, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-35062
in-theory        35062
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-500 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-35062.        ((A or ((B and C) -> B)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-500, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-35063
in-theory        35063
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-35063.        ((A or ((B and C) -> B)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-500, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-35064
in-theory        35064
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-500 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-35064.        ((A or ((B and C) -> B)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-500, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-35065
in-theory        35065
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-500 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-35065.        ((A or ((B and C) -> B)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-500, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-35066
in-theory        35066
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-500 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-35066.        ((A or ((B and C) -> B)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-500, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-35067
in-theory        35067
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-35067.        ((A or ((B and C) -> B)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-500, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-35068
in-theory        35068
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-500 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-35068.        ((A or ((B and C) -> B)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-500, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-35069
in-theory        35069
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-500 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-35069.        ((A or ((B and C) -> B)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-500, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-35070
in-theory        35070
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-500 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-35070.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-500, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-35071
in-theory        35071
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-35071.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-500, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-35072
in-theory        35072
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-35072.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-500, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-35073
in-theory        35073
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-35073.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-500, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-35074
in-theory        35074
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-35074.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-500, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-35075
in-theory        35075
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-500 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-35075.        ((A or ((B and C) -> B)) and (D or ((E -> (F -> E)) or G))), M:tm-500, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-35076
in-theory        35076
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-35076.        ((A or ((B and C) -> B)) and (((D -> (E -> D)) or F) or G)), M:tm-500, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-35077
in-theory        35077
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-35077.        ((A or ((B and C) -> B)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-500, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-35078
in-theory        35078
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-500 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-35078.        ((A or ((B and C) -> B)) and (D -> ((E -> (F -> E)) or G))), M:tm-500, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-35079
in-theory        35079
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-500 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-35079.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-500, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-35080
in-theory        35080
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-35080.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-500, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-35081
in-theory        35081
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-35081.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-500, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-35082
in-theory        35082
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-500 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-35082.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-500, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-35083
in-theory        35083
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-35083.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-500, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-35084
in-theory        35084
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-500 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-35084.        ((A or ((B and C) -> B)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-500, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-35085
in-theory        35085
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-500 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-35085.        ((A or ((B and C) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-500, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-35086
in-theory        35086
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-500 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-35086.        ((A or ((B and C) -> B)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-500, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-35087
in-theory        35087
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-500 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-35087.        ((A or ((B and C) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-500, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-35088
in-theory        35088
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-500 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-35088.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-500, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-35089
in-theory        35089
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-35089.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-500, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-35090
in-theory        35090
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-35090.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-500, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-35091
in-theory        35091
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-35091.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-500, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-35092
in-theory        35092
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-35092.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-500, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-35093
in-theory        35093
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-500 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-35093.        ((A or ((B and C) -> B)) and (D or (((E and F) -> E) or G))), M:tm-500, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-35094
in-theory        35094
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-35094.        ((A or ((B and C) -> B)) and ((((D and E) -> D) or F) or G)), M:tm-500, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-35095
in-theory        35095
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-35095.        ((A or ((B and C) -> B)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-500, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-35096
in-theory        35096
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-500 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-35096.        ((A or ((B and C) -> B)) and (D -> (((E and F) -> E) or G))), M:tm-500, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-35097
in-theory        35097
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-500 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-35097.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-500, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-35098
in-theory        35098
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-35098.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-500, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-35099
in-theory        35099
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-35099.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-500, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-35100
in-theory        35100
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-35100.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-500, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-35101
in-theory        35101
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-35101.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-500, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-35102
in-theory        35102
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-500 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-35102.        ((A or ((B and C) -> B)) and (D or (((E and F) -> F) or G))), M:tm-500, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-35103
in-theory        35103
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-35103.        ((A or ((B and C) -> B)) and ((((D and E) -> E) or F) or G)), M:tm-500, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-35104
in-theory        35104
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-35104.        ((A or ((B and C) -> B)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-500, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-35105
in-theory        35105
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-500 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-35105.        ((A or ((B and C) -> B)) and (D -> (((E and F) -> F) or G))), M:tm-500, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-35106
in-theory        35106
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-500 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-35106.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-500, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-35107
in-theory        35107
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-500 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-35107.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-500, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-35108
in-theory        35108
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-500 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-35108.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-500, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-35109
in-theory        35109
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-500 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-35109.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-500, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-35110
in-theory        35110
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-500 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-35110.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-500, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-35111
in-theory        35111
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-500 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-35111.        ((A or ((B and C) -> B)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-500, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-35112
in-theory        35112
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-500 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-35112.        ((A or ((B and C) -> B)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-500, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-35113
in-theory        35113
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-35113.        ((A or ((B and C) -> B)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-500, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-35114
in-theory        35114
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-500 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-35114.        ((A or ((B and C) -> B)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-500, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-35115
in-theory        35115
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-500 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-35115.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-500, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-35116
in-theory        35116
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-35116.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-500, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-35117
in-theory        35117
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-35117.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-500, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-35118
in-theory        35118
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-35118.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-500, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-35119
in-theory        35119
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-35119.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-500, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-35120
in-theory        35120
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-500 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-35120.        ((A or ((B and C) -> B)) and (D or ((E -> (E or F)) or G))), M:tm-500, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-35121
in-theory        35121
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-35121.        ((A or ((B and C) -> B)) and (((D -> (D or E)) or F) or G)), M:tm-500, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-35122
in-theory        35122
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-35122.        ((A or ((B and C) -> B)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-500, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-35123
in-theory        35123
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-500 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-35123.        ((A or ((B and C) -> B)) and (D -> ((E -> (E or F)) or G))), M:tm-500, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-35124
in-theory        35124
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-35124.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-500, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-35125
in-theory        35125
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35125.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-500, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-35126
in-theory        35126
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-35126.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-500, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35127
in-theory        35127
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-500 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-35127.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-500, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-35128
in-theory        35128
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-35128.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-500, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-35129
in-theory        35129
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-500 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-35129.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-500, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-35130
in-theory        35130
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35130.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-500, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-35131
in-theory        35131
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-35131.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-500, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-35132
in-theory        35132
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-500 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-35132.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-500, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-35133
in-theory        35133
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-35133.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-500, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-35134
in-theory        35134
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-35134.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-500, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-35135
in-theory        35135
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-35135.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-500, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-35136
in-theory        35136
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-500 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-35136.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-500, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-35137
in-theory        35137
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35137.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-500, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-35138
in-theory        35138
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-500 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-35138.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-500, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-35139
in-theory        35139
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-500 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-35139.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-500, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-35140
in-theory        35140
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-500 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-35140.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-500, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-35141
in-theory        35141
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-500 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-35141.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-500, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35142
in-theory        35142
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-35142.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-500, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-35143
in-theory        35143
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-500 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-35143.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-500, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-35144
in-theory        35144
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-35144.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-500, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-35145
in-theory        35145
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-35145.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-500, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-35146
in-theory        35146
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-500 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-35146.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-500, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-35147
in-theory        35147
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-35147.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-500, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-35148
in-theory        35148
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-500 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-35148.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-500, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-35149
in-theory        35149
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-35149.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-500, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-35150
in-theory        35150
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-35150.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-500, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-35151
in-theory        35151
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-35151.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-500, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-35152
in-theory        35152
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-35152.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-500, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-35153
in-theory        35153
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-500 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-35153.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-500, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-35154
in-theory        35154
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-35154.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-500, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-35155
in-theory        35155
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-35155.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-500, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-35156
in-theory        35156
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-500 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-35156.        ((A or ((B and C) -> B)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-500, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-35157
in-theory        35157
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-500 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-35157.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-500, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-35158
in-theory        35158
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-35158.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-500, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-35159
in-theory        35159
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-35159.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-500, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-35160
in-theory        35160
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-500 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-35160.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-500, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-35161
in-theory        35161
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-35161.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-500, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-35162
in-theory        35162
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-35162.        ((A or ((B and C) -> B)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-500, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-35163
in-theory        35163
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-500 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-35163.        ((A or ((B and C) -> B)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-500, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-35164
in-theory        35164
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-500 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-35164.        ((A or ((B and C) -> B)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-500, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-35165
in-theory        35165
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-500 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-35165.        ((A or ((B and C) -> B)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-500, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-35166
in-theory        35166
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-35166.        ((A or ((B and C) -> B)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-500, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-35167
in-theory        35167
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-500 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-35167.        ((A or ((B and C) -> B)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-500, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-35168
in-theory        35168
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-35168.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-500, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-35169
in-theory        35169
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-35169.        ((A or ((B and C) -> B)) and (D -> (D and (E -> (E or F))))), M:tm-500, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-35170
in-theory        35170
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-35170.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-500, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-35171
in-theory        35171
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-35171.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-500, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-35172
in-theory        35172
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-35172.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-500, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-35173
in-theory        35173
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-35173.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-500, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-35174
in-theory        35174
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-35174.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-500, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-35175
in-theory        35175
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-500 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-35175.        ((A or ((B and C) -> B)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-500, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-35176
in-theory        35176
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-500 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-35176.        ((A or ((B and C) -> B)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-500, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-35177
in-theory        35177
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-35177.        ((A or ((B and C) -> B)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-500, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-35178
in-theory        35178
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-35178.        ((A or ((B and C) -> B)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-500, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-35179
in-theory        35179
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-500 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-35179.        ((A or ((B and C) -> B)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-500, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-35180
in-theory        35180
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-35180.        ((A or ((B and C) -> B)) and (D or (E -> (F -> (F or G))))), M:tm-500, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-35181
in-theory        35181
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-35181.        ((A or ((B and C) -> B)) and ((D -> (E -> (E or F))) or G)), M:tm-500, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-35182
in-theory        35182
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-35182.        ((A or ((B and C) -> B)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-500, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-35183
in-theory        35183
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-500 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-35183.        ((A or ((B and C) -> B)) and ((D -> E) -> (D -> (E or F)))), M:tm-500, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-35184
in-theory        35184
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-35184.        ((A or ((B and C) -> B)) and (D -> (E -> (F -> (F or G))))), M:tm-500, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-35185
in-theory        35185
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-35185.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-500, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-35186
in-theory        35186
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-35186.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-500, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-35187
in-theory        35187
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-35187.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-500, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-35188
in-theory        35188
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-35188.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-500, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-35189
in-theory        35189
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-35189.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-500, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-35190
in-theory        35190
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-35190.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-500, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-35191
in-theory        35191
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-35191.        ((A or ((B and C) -> B)) and (D or (E or (F -> (G -> F))))), M:tm-500, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-35192
in-theory        35192
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-35192.        ((A or ((B and C) -> B)) and ((D or (E -> (F -> E))) or G)), M:tm-500, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-35193
in-theory        35193
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-35193.        ((A or ((B and C) -> B)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-500, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-35194
in-theory        35194
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-35194.        ((A or ((B and C) -> B)) and (D -> (E or (F -> (G -> F))))), M:tm-500, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-35195
in-theory        35195
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35195.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-500, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-35196
in-theory        35196
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-500 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35196.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-500, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-35197
in-theory        35197
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35197.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-500, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-35198
in-theory        35198
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35198.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-500, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-35199
in-theory        35199
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-500 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35199.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-500, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-35200
in-theory        35200
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35200.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-500, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-35201
in-theory        35201
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-500 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35201.        ((A or ((B and C) -> B)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-500, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-35202
in-theory        35202
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-500 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35202.        ((A or ((B and C) -> B)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-500, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-35203
in-theory        35203
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-500 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35203.        ((A or ((B and C) -> B)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-500, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-35204
in-theory        35204
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-500 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35204.        ((A or ((B and C) -> B)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-500, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-35205
in-theory        35205
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-500 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35205.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-500, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-35206
in-theory        35206
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-500 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35206.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-500, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-35207
in-theory        35207
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-500 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35207.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-500, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-35208
in-theory        35208
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-500 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35208.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-500, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-35209
in-theory        35209
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-500 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35209.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-500, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-35210
in-theory        35210
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-500 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35210.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-500, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-35211
in-theory        35211
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-500 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35211.        ((A or ((B and C) -> B)) and (D or (E or ((F and G) -> F)))), M:tm-500, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35212
in-theory        35212
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35212.        ((A or ((B and C) -> B)) and ((D or ((E and F) -> E)) or G)), M:tm-500, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-35213
in-theory        35213
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35213.        ((A or ((B and C) -> B)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-500, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35214
in-theory        35214
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G and H) -> G)) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35214.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G and H) -> G)) and E))), M:tm-490, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35215
in-theory        35215
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35215.        ((A or (B -> (C -> B))) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-480, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35216
in-theory        35216
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or ((C and D) -> C)) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35216.        (A -> (((B or ((C and D) -> C)) and A) or E)), M:tm-470, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-35217
in-theory        35217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35217.        ((A -> (B -> (B or C))) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-469, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35218
in-theory        35218
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D or ((E and F) -> E)) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-500 ((Am (-> A (or A B))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35218.        ((A or (B -> (B or C))) -> ((D or ((E and F) -> E)) and (B -> (B or C)))), M:tm-466, m:tm-500, u:((Am (-> A (or A B))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (or A B)))))
================================================================
tm-name          tm-35219
in-theory        35219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35219.        ((A -> ((B or ((C and D) -> C)) and A)) and (E -> (E or F))), M:tm-456, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35220
in-theory        35220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35220.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-453, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35221
in-theory        35221
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D or ((E and F) -> E)) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-500 ((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35221.        ((A or ((B -> (B or C)) and A)) -> ((D or ((E and F) -> E)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-500, u:((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-35222
in-theory        35222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and ((E -> (E or F)) and (A -> ((B or ((C and D) -> C)) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35222.        ((A -> ((B or ((C and D) -> C)) and A)) and ((E -> (E or F)) and (A -> ((B or ((C and D) -> C)) and A)))), M:tm-443, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35223
in-theory        35223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35223.        (((A -> (A or B)) or C) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-409, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35224
in-theory        35224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35224.        (((A -> (B -> (A and B))) or C) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-400, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35225
in-theory        35225
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35225.        ((((A and B) -> B) or C) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-391, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35226
in-theory        35226
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35226.        ((((A and B) -> A) or C) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-382, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35227
in-theory        35227
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or ((G and H) -> G)) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35227.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or ((G and H) -> G)) and E))), M:tm-373, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35228
in-theory        35228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35228.        (((A -> (B -> A)) or C) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-364, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35229
in-theory        35229
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C or ((D and E) -> D)) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35229.        (A -> (B -> (((C or ((D and E) -> D)) and A) and B))), M:tm-355, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-35230
in-theory        35230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35230.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-354, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35231
in-theory        35231
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D or ((E and F) -> E)) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-500 ((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35231.        ((A or (B -> (C -> (B and C)))) -> ((D or ((E and F) -> E)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-500, u:((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-35232
in-theory        35232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35232.        ((A -> ((B or ((C and D) -> C)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35233
in-theory        35233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D or ((E and F) -> E)) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35233.        (((A -> B) -> (A -> (A and B))) and (C -> ((D or ((E and F) -> E)) and C))), M:tm-338, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35234
in-theory        35234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C or ((D and E) -> D)) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-500 ((Am (-> A (and A B))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35234.        (((A -> B) or (A -> (A and B))) -> ((C or ((D and E) -> D)) and (A -> (A and B)))), M:tm-335, m:tm-500, u:((Am (-> A (and A B))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (and A B)))))
================================================================
tm-name          tm-35235
in-theory        35235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and (A -> (A and ((B or ((C and D) -> C)) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35235.        ((A -> ((B or ((C and D) -> C)) and A)) and (A -> (A and ((B or ((C and D) -> C)) and A)))), M:tm-328, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-35236
in-theory        35236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B or ((C and D) -> C)) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35236.        ((A -> ((B or ((C and D) -> C)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B or ((C and D) -> C)) and A)))), M:tm-327, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35237
in-theory        35237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and (((E and F) -> F) and (A -> ((B or ((C and D) -> C)) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35237.        ((A -> ((B or ((C and D) -> C)) and A)) and (((E and F) -> F) and (A -> ((B or ((C and D) -> C)) and A)))), M:tm-326, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35238
in-theory        35238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and (((E and F) -> E) and (A -> ((B or ((C and D) -> C)) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35238.        ((A -> ((B or ((C and D) -> C)) and A)) and (((E and F) -> E) and (A -> ((B or ((C and D) -> C)) and A)))), M:tm-325, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35239
in-theory        35239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B or ((C and D) -> C)) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35239.        ((A -> ((B or ((C and D) -> C)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B or ((C and D) -> C)) and A)))), M:tm-324, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35240
in-theory        35240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and ((E -> (F -> E)) and (A -> ((B or ((C and D) -> C)) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35240.        ((A -> ((B or ((C and D) -> C)) and A)) and ((E -> (F -> E)) and (A -> ((B or ((C and D) -> C)) and A)))), M:tm-323, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35241
in-theory        35241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35241.        ((A -> ((B or ((C and D) -> C)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35242
in-theory        35242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35242.        ((A -> ((B or ((C and D) -> C)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35243
in-theory        35243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35243.        ((A -> ((B or ((C and D) -> C)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35244
in-theory        35244
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35244.        ((A -> ((B or ((C and D) -> C)) and A)) and (A -> A)), M:tm-316, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-35245
in-theory        35245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35245.        ((A -> ((B or ((C and D) -> C)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35246
in-theory        35246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and ((A -> (not ((B or ((C and D) -> C)) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35246.        ((A -> ((B or ((C and D) -> C)) and A)) and ((A -> (not ((B or ((C and D) -> C)) and A))) -> (not A))), M:tm-313, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-35247
in-theory        35247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and ((((B or ((C and D) -> C)) and A) -> E) -> ((A or ((B or ((C and D) -> C)) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35247.        ((A -> ((B or ((C and D) -> C)) and A)) and ((((B or ((C and D) -> C)) and A) -> E) -> ((A or ((B or ((C and D) -> C)) and A)) -> E))), M:tm-312, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-35248
in-theory        35248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and (E or (A -> ((B or ((C and D) -> C)) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35248.        ((A -> ((B or ((C and D) -> C)) and A)) and (E or (A -> ((B or ((C and D) -> C)) and A)))), M:tm-311, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35249
in-theory        35249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and ((A -> ((B or ((C and D) -> C)) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35249.        ((A -> ((B or ((C and D) -> C)) and A)) and ((A -> ((B or ((C and D) -> C)) and A)) or E)), M:tm-310, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35250
in-theory        35250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and (E -> ((A -> ((B or ((C and D) -> C)) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35250.        ((A -> ((B or ((C and D) -> C)) and A)) and (E -> ((A -> ((B or ((C and D) -> C)) and A)) and E))), M:tm-309, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35251
in-theory        35251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and (E -> (A -> ((B or ((C and D) -> C)) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35251.        ((A -> ((B or ((C and D) -> C)) and A)) and (E -> (A -> ((B or ((C and D) -> C)) and A)))), M:tm-305, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35252
in-theory        35252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35252.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-303, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35253
in-theory        35253
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D or ((E and F) -> E)) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-500 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35253.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D or ((E and F) -> E)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-500, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-35254
in-theory        35254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35254.        ((A -> (((B and C) -> C) and A)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-270, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35255
in-theory        35255
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D or ((E and F) -> E)) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-500 ((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35255.        ((A or (((B and C) -> C) and A)) -> ((D or ((E and F) -> E)) and (((B and C) -> C) and A))), M:tm-267, m:tm-500, u:((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-35256
in-theory        35256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35256.        ((A -> (((B and C) -> B) and A)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-239, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35257
in-theory        35257
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D or ((E and F) -> E)) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-500 ((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35257.        ((A or (((B and C) -> B) and A)) -> ((D or ((E and F) -> E)) and (((B and C) -> B) and A))), M:tm-236, m:tm-500, u:((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-35258
in-theory        35258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or ((G and H) -> G)) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35258.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or ((G and H) -> G)) and E))), M:tm-210, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35259
in-theory        35259
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or ((F and G) -> F)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-500 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (and Cm Dm) Cm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-7 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35259.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or ((F and G) -> F)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-500, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (and Cm Dm) Cm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-35260
in-theory        35260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35260.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-183, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35261
in-theory        35261
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D or ((E and F) -> E)) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-500 ((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35261.        ((A or ((B -> (C -> B)) and A)) -> ((D or ((E and F) -> E)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-500, u:((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-35262
in-theory        35262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35262.        ((A -> ((B and C) -> C)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-157, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35263
in-theory        35263
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D or ((E and F) -> E)) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-500 ((Am (-> (and A B) B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35263.        ((A or ((B and C) -> C)) -> ((D or ((E and F) -> E)) and ((B and C) -> C))), M:tm-154, m:tm-500, u:((Am (-> (and A B) B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> (and A B) B))))
================================================================
tm-name          tm-35264
in-theory        35264
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35264.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-147, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35265
in-theory        35265
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or ((E and F) -> E)) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-500 ((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-7 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35265.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or ((E and F) -> E)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-500, u:((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-35266
in-theory        35266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35266.        ((A -> ((B and C) -> B)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-134, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35267
in-theory        35267
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D or ((E and F) -> E)) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-500 ((Am (-> (and A B) A)) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35267.        ((A or ((B and C) -> B)) -> ((D or ((E and F) -> E)) and ((B and C) -> B))), M:tm-131, m:tm-500, u:((Am (-> (and A B) A)) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> (and A B) A))))
================================================================
tm-name          tm-35268
in-theory        35268
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35268.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-125, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35269
in-theory        35269
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or ((E and F) -> E)) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-500 ((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35269.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or ((E and F) -> E)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-500, u:((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-35270
in-theory        35270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G and H) -> G)) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35270.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G and H) -> G)) and E))), M:tm-113, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35271
in-theory        35271
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or ((F and G) -> F)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-500 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35271.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or ((F and G) -> F)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-500, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-35272
in-theory        35272
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35272.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-105, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35273
in-theory        35273
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or ((E and F) -> E)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-500 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35273.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or ((E and F) -> E)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-500, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-35274
in-theory        35274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D or ((E and F) -> E)) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35274.        (((A -> B) -> (A -> A)) and (C -> ((D or ((E and F) -> E)) and C))), M:tm-95, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35275
in-theory        35275
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C or ((D and E) -> D)) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-500 ((Am (-> A A)) (B (and (or Bm (-> (and Cm Dm) Cm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35275.        (((A -> B) or (A -> A)) -> ((C or ((D and E) -> D)) and (A -> A))), M:tm-92, m:tm-500, u:((Am (-> A A)) (B (and (or Bm (-> (and Cm Dm) Cm)) (-> A A))))
================================================================
tm-name          tm-35276
in-theory        35276
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C or ((D and E) -> D)) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35276.        (A -> (B -> ((C or ((D and E) -> D)) and A))), M:tm-84, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-35277
in-theory        35277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35277.        ((A -> (B -> (C -> B))) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-83, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35278
in-theory        35278
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D or ((E and F) -> E)) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-500 ((Am (-> A (-> B A))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35278.        ((A or (B -> (C -> B))) -> ((D or ((E and F) -> E)) and (B -> (C -> B)))), M:tm-80, m:tm-500, u:((Am (-> A (-> B A))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (-> B A)))))
================================================================
tm-name          tm-35279
in-theory        35279
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C or ((D and E) -> D)) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-10 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35279.        (((not (not A)) -> A) and (B -> ((C or ((D and E) -> D)) and B))), M:tm-76, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35280
in-theory        35280
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B or ((C and D) -> C)) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-7 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35280.        (((not (not A)) or A) -> ((B or ((C and D) -> C)) and A)), M:tm-73, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-35281
in-theory        35281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or ((E and F) -> E)) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-9 tm-7 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35281.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or ((E and F) -> E)) and C))), M:tm-69, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35282
in-theory        35282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or ((D and E) -> D)) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-500 ((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-7 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35282.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or ((D and E) -> D)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-500, u:((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-35283
in-theory        35283
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35283.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-54, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35284
in-theory        35284
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or ((E and F) -> E)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-500 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-7 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35284.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or ((E and F) -> E)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-500, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-35285
in-theory        35285
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C or ((D and E) -> D)) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-500 ((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35285.        ((A or (B or A)) -> ((C or ((D and E) -> D)) and (B or A))), M:tm-50, m:tm-500, u:((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (or A B))))
================================================================
tm-name          tm-35286
in-theory        35286
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C or ((D and E) -> D)) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-500 ((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35286.        ((A or (A or B)) -> ((C or ((D and E) -> D)) and (A or B))), M:tm-49, m:tm-500, u:((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (or A B))))
================================================================
tm-name          tm-35287
in-theory        35287
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C or ((D and E) -> D)) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-500 ((Am (-> A (and B A))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-7 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35287.        ((A or (B -> (A and B))) -> ((C or ((D and E) -> D)) and (B -> (A and B)))), M:tm-48, m:tm-500, u:((Am (-> A (and B A))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (and B A)))))
================================================================
tm-name          tm-35288
in-theory        35288
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C or ((D and E) -> D)) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-7 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35288.        (((A and B) or B) -> ((C or ((D and E) -> D)) and B)), M:tm-47, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-35289
in-theory        35289
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C or ((D and E) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35289.        (((A and B) or A) -> ((C or ((D and E) -> D)) and A)), M:tm-46, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-35290
in-theory        35290
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E and F) -> E)) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-500 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35290.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E and F) -> E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-500, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-35291
in-theory        35291
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C or ((D and E) -> D)) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-500 ((Am (-> A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35291.        ((A or (B -> A)) -> ((C or ((D and E) -> D)) and (B -> A))), M:tm-44, m:tm-500, u:((Am (-> A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A B))))
================================================================
tm-name          tm-35292
in-theory        35292
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D or ((E and F) -> E)) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35292.        ((A -> (B or A)) and (C -> ((D or ((E and F) -> E)) and C))), M:tm-42, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35293
in-theory        35293
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D or ((E and F) -> E)) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35293.        ((A -> (A or B)) and (C -> ((D or ((E and F) -> E)) and C))), M:tm-32, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35294
in-theory        35294
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B or ((C and D) -> C)) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35294.        (A -> (A and ((B or ((C and D) -> C)) and A))), M:tm-24, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-35295
in-theory        35295
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D or ((E and F) -> E)) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35295.        ((A -> (B -> (A and B))) and (C -> ((D or ((E and F) -> E)) and C))), M:tm-23, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35296
in-theory        35296
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D or ((E and F) -> E)) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35296.        (((A and B) -> B) and (C -> ((D or ((E and F) -> E)) and C))), M:tm-22, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35297
in-theory        35297
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D or ((E and F) -> E)) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35297.        (((A and B) -> A) and (C -> ((D or ((E and F) -> E)) and C))), M:tm-21, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35298
in-theory        35298
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35298.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-20, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35299
in-theory        35299
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D or ((E and F) -> E)) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35299.        ((A -> (B -> A)) and (C -> ((D or ((E and F) -> E)) and C))), M:tm-19, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35300
in-theory        35300
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B or ((C and D) -> C)) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-9 tm-5 tm-7 tm-3)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35300.        ((A -> (not ((B or ((C and D) -> C)) and A))) -> (not A)), M:tm-9, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-35301
in-theory        35301
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B and C) -> B)) and D) -> E) -> ((D or ((A or ((B and C) -> B)) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-8 tm-5 tm-7 tm-3)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35301.        ((((A or ((B and C) -> B)) and D) -> E) -> ((D or ((A or ((B and C) -> B)) and D)) -> E)), M:tm-8, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-35302
in-theory        35302
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C or ((D and E) -> D)) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35302.        (A or (B -> ((C or ((D and E) -> D)) and B))), M:tm-7, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35303
in-theory        35303
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-6 tm-5 tm-7 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35303.        ((A -> ((B or ((C and D) -> C)) and A)) or E), M:tm-6, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35304
in-theory        35304
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C or ((D and E) -> D)) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35304.        (A -> ((B -> ((C or ((D and E) -> D)) and B)) and A)), M:tm-5, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35305
in-theory        35305
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C or ((D and E) -> D)) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-1 tm-5 tm-7 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35305.        (A -> (B -> ((C or ((D and E) -> D)) and B))), M:tm-1, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35306
in-theory        35306
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-500 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35306.        ((A or ((B and C) -> B)) and (D -> (E or ((F and G) -> F)))), M:tm-500, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35307
in-theory        35307
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-490 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35307.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G and H) -> G)))), M:tm-490, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35308
in-theory        35308
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-480 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35308.        ((A or (B -> (C -> B))) and (D -> (E or ((F and G) -> F)))), M:tm-480, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35309
in-theory        35309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-469 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35309.        ((A -> (B -> (B or C))) and (D -> (E or ((F and G) -> F)))), M:tm-469, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35310
in-theory        35310
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-466 tm-501 ((Am (-> A (or A B))) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35310.        ((A or (B -> (B or C))) -> (D or ((E and F) -> E))), M:tm-466, m:tm-501, u:((Am (-> A (or A B))) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35311
in-theory        35311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35311.        ((A -> (B or ((C and D) -> C))) and (E -> (E or F))), M:tm-456, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35312
in-theory        35312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-453 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35312.        ((A -> ((B -> (B or C)) and A)) and (D -> (E or ((F and G) -> F)))), M:tm-453, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35313
in-theory        35313
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-450 tm-501 ((Am (and (-> A (or A B)) C)) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35313.        ((A or ((B -> (B or C)) and A)) -> (D or ((E and F) -> E))), M:tm-450, m:tm-501, u:((Am (and (-> A (or A B)) C)) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35314
in-theory        35314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and ((E -> (E or F)) and (A -> (B or ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35314.        ((A -> (B or ((C and D) -> C))) and ((E -> (E or F)) and (A -> (B or ((C and D) -> C))))), M:tm-443, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35315
in-theory        35315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-409 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35315.        (((A -> (A or B)) or C) and (D -> (E or ((F and G) -> F)))), M:tm-409, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35316
in-theory        35316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-400 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35316.        (((A -> (B -> (A and B))) or C) and (D -> (E or ((F and G) -> F)))), M:tm-400, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35317
in-theory        35317
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-391 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35317.        ((((A and B) -> B) or C) and (D -> (E or ((F and G) -> F)))), M:tm-391, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35318
in-theory        35318
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-382 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35318.        ((((A and B) -> A) or C) and (D -> (E or ((F and G) -> F)))), M:tm-382, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35319
in-theory        35319
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-373 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35319.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or ((G and H) -> G)))), M:tm-373, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35320
in-theory        35320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-364 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35320.        (((A -> (B -> A)) or C) and (D -> (E or ((F and G) -> F)))), M:tm-364, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35321
in-theory        35321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-354 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35321.        ((A -> (B -> (C -> (B and C)))) and (D -> (E or ((F and G) -> F)))), M:tm-354, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35322
in-theory        35322
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-351 tm-501 ((Am (-> A (-> B (and A B)))) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35322.        ((A or (B -> (C -> (B and C)))) -> (D or ((E and F) -> E))), M:tm-351, m:tm-501, u:((Am (-> A (-> B (and A B)))) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35323
in-theory        35323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35323.        ((A -> (B or ((C and D) -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35324
in-theory        35324
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) -> D) -> ((A or ((B and C) -> B)) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-501 ((Am (-> (or Bm (-> (and Cm Dm) Cm)) B)) (A (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35324.        (((A or ((B and C) -> B)) -> D) -> ((A or ((B and C) -> B)) and D)), M:tm-339, m:tm-501, u:((Am (-> (or Bm (-> (and Cm Dm) Cm)) B)) (A (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35325
in-theory        35325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D or ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-338 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35325.        (((A -> B) -> (A -> (A and B))) and (C -> (D or ((E and F) -> E)))), M:tm-338, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35326
in-theory        35326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C or ((D and E) -> D)))
theorem-size     17
proof            (modus-ponens tm-335 tm-501 ((Am (-> A (and A B))) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35326.        (((A -> B) or (A -> (A and B))) -> (C or ((D and E) -> D))), M:tm-335, m:tm-501, u:((Am (-> A (and A B))) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35327
in-theory        35327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (A -> (A and (B or ((C and D) -> C)))))
theorem-size     21
proof            (modus-ponens tm-328 tm-501 ((A Am) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35327.        ((A -> (B or ((C and D) -> C))) and (A -> (A and (B or ((C and D) -> C))))), M:tm-328, m:tm-501, u:((A Am) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35328
in-theory        35328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and ((E -> (F -> (E and F))) and (A -> (B or ((C and D) -> C)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35328.        ((A -> (B or ((C and D) -> C))) and ((E -> (F -> (E and F))) and (A -> (B or ((C and D) -> C))))), M:tm-327, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35329
in-theory        35329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (((E and F) -> F) and (A -> (B or ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35329.        ((A -> (B or ((C and D) -> C))) and (((E and F) -> F) and (A -> (B or ((C and D) -> C))))), M:tm-326, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35330
in-theory        35330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (((E and F) -> E) and (A -> (B or ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35330.        ((A -> (B or ((C and D) -> C))) and (((E and F) -> E) and (A -> (B or ((C and D) -> C))))), M:tm-325, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35331
in-theory        35331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B or ((C and D) -> C)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35331.        ((A -> (B or ((C and D) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B or ((C and D) -> C))))), M:tm-324, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35332
in-theory        35332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and ((E -> (F -> E)) and (A -> (B or ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35332.        ((A -> (B or ((C and D) -> C))) and ((E -> (F -> E)) and (A -> (B or ((C and D) -> C))))), M:tm-323, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35333
in-theory        35333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35333.        ((A -> (B or ((C and D) -> C))) and ((E and F) -> F)), M:tm-322, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35334
in-theory        35334
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or ((C and D) -> C)) -> E)) -> (B or ((C and D) -> C))) and ((A and ((B or ((C and D) -> C)) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-501 ((Am (and A (-> (or Bm (-> (and Cm Dm) Cm)) C))) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35334.        (((A and ((B or ((C and D) -> C)) -> E)) -> (B or ((C and D) -> C))) and ((A and ((B or ((C and D) -> C)) -> E)) -> E)), M:tm-321, m:tm-501, u:((Am (and A (-> (or Bm (-> (and Cm Dm) Cm)) C))) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35335
in-theory        35335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35335.        ((A -> (B or ((C and D) -> C))) and ((E and F) -> E)), M:tm-320, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35336
in-theory        35336
times-derived    1
----------------------------------------------------------------
theorem          (((((A or ((B and C) -> B)) -> D) and E) -> (A or ((B and C) -> B))) and ((((A or ((B and C) -> B)) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-501 ((Am (and (-> (or Bm (-> (and Cm Dm) Cm)) B) C)) (A (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35336.        (((((A or ((B and C) -> B)) -> D) and E) -> (A or ((B and C) -> B))) and ((((A or ((B and C) -> B)) -> D) and E) -> D)), M:tm-319, m:tm-501, u:((Am (and (-> (or Bm (-> (and Cm Dm) Cm)) B) C)) (A (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35337
in-theory        35337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35337.        ((A -> (B or ((C and D) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35338
in-theory        35338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-501 ((A Am) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35338.        ((A -> (B or ((C and D) -> C))) and (A -> A)), M:tm-316, m:tm-501, u:((A Am) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35339
in-theory        35339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35339.        ((A -> (B or ((C and D) -> C))) and (E -> (F -> E))), M:tm-315, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35340
in-theory        35340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and ((A -> (not (B or ((C and D) -> C)))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-501 ((A Am) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35340.        ((A -> (B or ((C and D) -> C))) and ((A -> (not (B or ((C and D) -> C)))) -> (not A))), M:tm-313, m:tm-501, u:((A Am) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35341
in-theory        35341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (((B or ((C and D) -> C)) -> E) -> ((A or (B or ((C and D) -> C))) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-501 ((A Am) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35341.        ((A -> (B or ((C and D) -> C))) and (((B or ((C and D) -> C)) -> E) -> ((A or (B or ((C and D) -> C))) -> E))), M:tm-312, m:tm-501, u:((A Am) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35342
in-theory        35342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (E or (A -> (B or ((C and D) -> C)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35342.        ((A -> (B or ((C and D) -> C))) and (E or (A -> (B or ((C and D) -> C))))), M:tm-311, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35343
in-theory        35343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and ((A -> (B or ((C and D) -> C))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35343.        ((A -> (B or ((C and D) -> C))) and ((A -> (B or ((C and D) -> C))) or E)), M:tm-310, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35344
in-theory        35344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (E -> ((A -> (B or ((C and D) -> C))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35344.        ((A -> (B or ((C and D) -> C))) and (E -> ((A -> (B or ((C and D) -> C))) and E))), M:tm-309, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35345
in-theory        35345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (E -> (A -> (B or ((C and D) -> C)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35345.        ((A -> (B or ((C and D) -> C))) and (E -> (A -> (B or ((C and D) -> C))))), M:tm-305, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35346
in-theory        35346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-303 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35346.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or ((F and G) -> F)))), M:tm-303, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35347
in-theory        35347
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D or ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-300 tm-501 ((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35347.        ((A or ((B -> (C -> (B and C))) and A)) -> (D or ((E and F) -> E))), M:tm-300, m:tm-501, u:((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35348
in-theory        35348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-270 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35348.        ((A -> (((B and C) -> C) and A)) and (D -> (E or ((F and G) -> F)))), M:tm-270, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35349
in-theory        35349
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-267 tm-501 ((Am (and (-> (and A B) B) C)) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35349.        ((A or (((B and C) -> C) and A)) -> (D or ((E and F) -> E))), M:tm-267, m:tm-501, u:((Am (and (-> (and A B) B) C)) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35350
in-theory        35350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-239 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35350.        ((A -> (((B and C) -> B) and A)) and (D -> (E or ((F and G) -> F)))), M:tm-239, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35351
in-theory        35351
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-236 tm-501 ((Am (and (-> (and A B) A) C)) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35351.        ((A or (((B and C) -> B) and A)) -> (D or ((E and F) -> E))), M:tm-236, m:tm-501, u:((Am (and (-> (and A B) A) C)) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35352
in-theory        35352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-210 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35352.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or ((G and H) -> G)))), M:tm-210, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35353
in-theory        35353
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-207 tm-501 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35353.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or ((F and G) -> F))), M:tm-207, m:tm-501, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35354
in-theory        35354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-183 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35354.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E or ((F and G) -> F)))), M:tm-183, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35355
in-theory        35355
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-180 tm-501 ((Am (and (-> A (-> B A)) C)) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35355.        ((A or ((B -> (C -> B)) and A)) -> (D or ((E and F) -> E))), M:tm-180, m:tm-501, u:((Am (and (-> A (-> B A)) C)) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35356
in-theory        35356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-157 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35356.        ((A -> ((B and C) -> C)) and (D -> (E or ((F and G) -> F)))), M:tm-157, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35357
in-theory        35357
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-154 tm-501 ((Am (-> (and A B) B)) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35357.        ((A or ((B and C) -> C)) -> (D or ((E and F) -> E))), M:tm-154, m:tm-501, u:((Am (-> (and A B) B)) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35358
in-theory        35358
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-147 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35358.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or ((F and G) -> F)))), M:tm-147, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35359
in-theory        35359
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-144 tm-501 ((Am (-> (and A (-> B C)) C)) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-7 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35359.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or ((E and F) -> E))), M:tm-144, m:tm-501, u:((Am (-> (and A (-> B C)) C)) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35360
in-theory        35360
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B or ((C and D) -> C)) -> E)) -> (B or ((C and D) -> C)))
theorem-size     19
proof            (modus-ponens tm-142 tm-501 ((Am (and A (-> (or Bm (-> (and Cm Dm) Cm)) C))) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35360.        ((A and ((B or ((C and D) -> C)) -> E)) -> (B or ((C and D) -> C))), M:tm-142, m:tm-501, u:((Am (and A (-> (or Bm (-> (and Cm Dm) Cm)) C))) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35361
in-theory        35361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-134 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35361.        ((A -> ((B and C) -> B)) and (D -> (E or ((F and G) -> F)))), M:tm-134, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35362
in-theory        35362
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-131 tm-501 ((Am (-> (and A B) A)) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35362.        ((A or ((B and C) -> B)) -> (D or ((E and F) -> E))), M:tm-131, m:tm-501, u:((Am (-> (and A B) A)) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35363
in-theory        35363
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-125 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35363.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or ((F and G) -> F)))), M:tm-125, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35364
in-theory        35364
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-122 tm-501 ((Am (-> (and (-> A B) C) B)) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35364.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or ((E and F) -> E))), M:tm-122, m:tm-501, u:((Am (-> (and (-> A B) C) B)) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35365
in-theory        35365
times-derived    1
----------------------------------------------------------------
theorem          ((((A or ((B and C) -> B)) -> D) and E) -> (A or ((B and C) -> B)))
theorem-size     19
proof            (modus-ponens tm-120 tm-501 ((Am (and (-> (or Bm (-> (and Cm Dm) Cm)) B) C)) (A (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35365.        ((((A or ((B and C) -> B)) -> D) and E) -> (A or ((B and C) -> B))), M:tm-120, m:tm-501, u:((Am (and (-> (or Bm (-> (and Cm Dm) Cm)) B) C)) (A (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35366
in-theory        35366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-113 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35366.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G and H) -> G)))), M:tm-113, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35367
in-theory        35367
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-110 tm-501 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-7 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35367.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or ((F and G) -> F))), M:tm-110, m:tm-501, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35368
in-theory        35368
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or ((F and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-105 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35368.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or ((F and G) -> F)))), M:tm-105, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35369
in-theory        35369
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or ((E and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-102 tm-501 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35369.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or ((E and F) -> E))), M:tm-102, m:tm-501, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35370
in-theory        35370
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) -> D) -> (A or ((B and C) -> B)))
theorem-size     17
proof            (modus-ponens tm-96 tm-501 ((Am (-> (or Bm (-> (and Cm Dm) Cm)) B)) (A (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35370.        (((A or ((B and C) -> B)) -> D) -> (A or ((B and C) -> B))), M:tm-96, m:tm-501, u:((Am (-> (or Bm (-> (and Cm Dm) Cm)) B)) (A (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35371
in-theory        35371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D or ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-95 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35371.        (((A -> B) -> (A -> A)) and (C -> (D or ((E and F) -> E)))), M:tm-95, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35372
in-theory        35372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C or ((D and E) -> D)))
theorem-size     15
proof            (modus-ponens tm-92 tm-501 ((Am (-> A A)) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35372.        (((A -> B) or (A -> A)) -> (C or ((D and E) -> D))), M:tm-92, m:tm-501, u:((Am (-> A A)) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35373
in-theory        35373
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C or ((D and E) -> D))))
theorem-size     11
proof            (modus-ponens tm-84 tm-501 ((A Am) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-3)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35373.        (A -> (B -> (C or ((D and E) -> D)))), M:tm-84, m:tm-501, u:((A Am) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35374
in-theory        35374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-83 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35374.        ((A -> (B -> (C -> B))) and (D -> (E or ((F and G) -> F)))), M:tm-83, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35375
in-theory        35375
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-80 tm-501 ((Am (-> A (-> B A))) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35375.        ((A or (B -> (C -> B))) -> (D or ((E and F) -> E))), M:tm-80, m:tm-501, u:((Am (-> A (-> B A))) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35376
in-theory        35376
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A or ((B and C) -> B)) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-501 ((Am (not (not (-> (or Bm (-> (and Cm Dm) Cm)) B)))) (A (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-7 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35376.        ((not (not ((A or ((B and C) -> B)) -> D))) -> D), M:tm-77, m:tm-501, u:((Am (not (not (-> (or Bm (-> (and Cm Dm) Cm)) B)))) (A (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35377
in-theory        35377
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C or ((D and E) -> D))))
theorem-size     15
proof            (modus-ponens tm-76 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35377.        (((not (not A)) -> A) and (B -> (C or ((D and E) -> D)))), M:tm-76, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35378
in-theory        35378
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B or ((C and D) -> C)))
theorem-size     13
proof            (modus-ponens tm-73 tm-501 ((A Am) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35378.        (((not (not A)) or A) -> (B or ((C and D) -> C))), M:tm-73, m:tm-501, u:((A Am) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35379
in-theory        35379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or ((E and F) -> E))))
theorem-size     21
proof            (modus-ponens tm-69 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35379.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or ((E and F) -> E)))), M:tm-69, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35380
in-theory        35380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or ((D and E) -> D)))
theorem-size     19
proof            (modus-ponens tm-66 tm-501 ((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-7 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35380.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or ((D and E) -> D))), M:tm-66, m:tm-501, u:((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35381
in-theory        35381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-54 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35381.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or ((F and G) -> F)))), M:tm-54, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35382
in-theory        35382
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-51 tm-501 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35382.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((E and F) -> E))), M:tm-51, m:tm-501, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35383
in-theory        35383
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-50 tm-501 ((Am (or A B)) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35383.        ((A or (B or A)) -> (C or ((D and E) -> D))), M:tm-50, m:tm-501, u:((Am (or A B)) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35384
in-theory        35384
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-49 tm-501 ((Am (or A B)) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35384.        ((A or (A or B)) -> (C or ((D and E) -> D))), M:tm-49, m:tm-501, u:((Am (or A B)) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35385
in-theory        35385
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or ((D and E) -> D)))
theorem-size     15
proof            (modus-ponens tm-48 tm-501 ((Am (-> A (and B A))) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35385.        ((A or (B -> (A and B))) -> (C or ((D and E) -> D))), M:tm-48, m:tm-501, u:((Am (-> A (and B A))) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35386
in-theory        35386
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-47 tm-501 ((A Am) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35386.        (((A and B) or B) -> (C or ((D and E) -> D))), M:tm-47, m:tm-501, u:((A Am) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35387
in-theory        35387
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-46 tm-501 ((A Am) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35387.        (((A and B) or A) -> (C or ((D and E) -> D))), M:tm-46, m:tm-501, u:((A Am) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35388
in-theory        35388
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-45 tm-501 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35388.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E and F) -> E))), M:tm-45, m:tm-501, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35389
in-theory        35389
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-44 tm-501 ((Am (-> A B)) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35389.        ((A or (B -> A)) -> (C or ((D and E) -> D))), M:tm-44, m:tm-501, u:((Am (-> A B)) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35390
in-theory        35390
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-42 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35390.        ((A -> (B or A)) and (C -> (D or ((E and F) -> E)))), M:tm-42, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35391
in-theory        35391
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-32 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35391.        ((A -> (A or B)) and (C -> (D or ((E and F) -> E)))), M:tm-32, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35392
in-theory        35392
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B or ((C and D) -> C))))
theorem-size     11
proof            (modus-ponens tm-24 tm-501 ((A Am) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35392.        (A -> (A and (B or ((C and D) -> C)))), M:tm-24, m:tm-501, u:((A Am) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35393
in-theory        35393
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D or ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-23 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35393.        ((A -> (B -> (A and B))) and (C -> (D or ((E and F) -> E)))), M:tm-23, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35394
in-theory        35394
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-22 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35394.        (((A and B) -> B) and (C -> (D or ((E and F) -> E)))), M:tm-22, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35395
in-theory        35395
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-21 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35395.        (((A and B) -> A) and (C -> (D or ((E and F) -> E)))), M:tm-21, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35396
in-theory        35396
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-20 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35396.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or ((F and G) -> F)))), M:tm-20, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35397
in-theory        35397
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-19 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35397.        ((A -> (B -> A)) and (C -> (D or ((E and F) -> E)))), M:tm-19, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35398
in-theory        35398
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B or ((C and D) -> C)) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-501 ((Am (and A (-> (or Bm (-> (and Cm Dm) Cm)) C))) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-7 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35398.        ((A and ((B or ((C and D) -> C)) -> E)) -> E), M:tm-17, m:tm-501, u:((Am (and A (-> (or Bm (-> (and Cm Dm) Cm)) C))) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35399
in-theory        35399
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B and C) -> B)) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-501 ((Am (and (-> (or Bm (-> (and Cm Dm) Cm)) B) C)) (A (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35399.        ((((A or ((B and C) -> B)) -> D) and E) -> D), M:tm-15, m:tm-501, u:((Am (and (-> (or Bm (-> (and Cm Dm) Cm)) B) C)) (A (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35400
in-theory        35400
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B or ((C and D) -> C)))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-501 ((A Am) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-9 tm-1 tm-7 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35400.        ((A -> (not (B or ((C and D) -> C)))) -> (not A)), M:tm-9, m:tm-501, u:((A Am) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35401
in-theory        35401
times-derived    2
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) -> D) -> ((E or (A or ((B and C) -> B))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-501 ((A Am) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-3)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35401.        (((A or ((B and C) -> B)) -> D) -> ((E or (A or ((B and C) -> B))) -> D)), M:tm-8, m:tm-501, u:((A Am) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-35402
in-theory        35402
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C or ((D and E) -> D))))
theorem-size     11
proof            (modus-ponens tm-7 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-7 tm-1 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35402.        (A or (B -> (C or ((D and E) -> D)))), M:tm-7, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35403
in-theory        35403
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-6 tm-1 tm-7 tm-3)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35403.        ((A -> (B or ((C and D) -> C))) or E), M:tm-6, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35404
in-theory        35404
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C or ((D and E) -> D))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-35404.        (A -> ((B -> (C or ((D and E) -> D))) and A)), M:tm-5, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35405
in-theory        35405
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-500 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35405.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-500, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35406
in-theory        35406
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-490 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35406.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H and I) -> I)))), M:tm-490, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35407
in-theory        35407
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-480 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35407.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-480, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35408
in-theory        35408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-469 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35408.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-469, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35409
in-theory        35409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35409.        (((A -> (A or B)) and (C or ((D and E) -> E))) and (F -> (F or G))), M:tm-456, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35410
in-theory        35410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-453 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35410.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-453, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35411
in-theory        35411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (A or B)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35411.        (((A -> (A or B)) and (C or ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (A or B)) and (C or ((D and E) -> E))))), M:tm-443, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35412
in-theory        35412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-409 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35412.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-409, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35413
in-theory        35413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-400 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35413.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-400, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35414
in-theory        35414
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-391 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35414.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-391, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35415
in-theory        35415
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-382 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35415.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-382, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35416
in-theory        35416
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-373 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35416.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or ((H and I) -> I)))), M:tm-373, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35417
in-theory        35417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-364 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35417.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-364, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35418
in-theory        35418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-354 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35418.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-354, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35419
in-theory        35419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35419.        (((A -> (A or B)) and (C or ((D and E) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35420
in-theory        35420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-338 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35420.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or ((F and G) -> G)))), M:tm-338, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35421
in-theory        35421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C or ((D and E) -> E)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35421.        (((A -> (A or B)) and (C or ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C or ((D and E) -> E))))), M:tm-327, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35422
in-theory        35422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and (((F and G) -> G) and ((A -> (A or B)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35422.        (((A -> (A or B)) and (C or ((D and E) -> E))) and (((F and G) -> G) and ((A -> (A or B)) and (C or ((D and E) -> E))))), M:tm-326, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35423
in-theory        35423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and (((F and G) -> F) and ((A -> (A or B)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35423.        (((A -> (A or B)) and (C or ((D and E) -> E))) and (((F and G) -> F) and ((A -> (A or B)) and (C or ((D and E) -> E))))), M:tm-325, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35424
in-theory        35424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C or ((D and E) -> E)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35424.        (((A -> (A or B)) and (C or ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C or ((D and E) -> E))))), M:tm-324, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35425
in-theory        35425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35425.        (((A -> (A or B)) and (C or ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C or ((D and E) -> E))))), M:tm-323, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35426
in-theory        35426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35426.        (((A -> (A or B)) and (C or ((D and E) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35427
in-theory        35427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35427.        (((A -> (A or B)) and (C or ((D and E) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35428
in-theory        35428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35428.        (((A -> (A or B)) and (C or ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35429
in-theory        35429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35429.        (((A -> (A or B)) and (C or ((D and E) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35430
in-theory        35430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and (F or ((A -> (A or B)) and (C or ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35430.        (((A -> (A or B)) and (C or ((D and E) -> E))) and (F or ((A -> (A or B)) and (C or ((D and E) -> E))))), M:tm-311, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35431
in-theory        35431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and (((A -> (A or B)) and (C or ((D and E) -> E))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35431.        (((A -> (A or B)) and (C or ((D and E) -> E))) and (((A -> (A or B)) and (C or ((D and E) -> E))) or F)), M:tm-310, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35432
in-theory        35432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and (F -> (((A -> (A or B)) and (C or ((D and E) -> E))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35432.        (((A -> (A or B)) and (C or ((D and E) -> E))) and (F -> (((A -> (A or B)) and (C or ((D and E) -> E))) and F))), M:tm-309, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35433
in-theory        35433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and (C or ((D and E) -> E)))
theorem-size     21
proof            (modus-ponens tm-308 tm-502 ((A (-> Am (or Am Bm))) (B (or Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35433.        (((A -> (A or B)) and (C or ((D and E) -> E))) and (C or ((D and E) -> E))), M:tm-308, m:tm-502, u:((A (-> Am (or Am Bm))) (B (or Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-35434
in-theory        35434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-502 ((A (-> Am (or Am Bm))) (B (or Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35434.        (((A -> (A or B)) and (C or ((D and E) -> E))) and (A -> (A or B))), M:tm-307, m:tm-502, u:((A (-> Am (or Am Bm))) (B (or Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-35435
in-theory        35435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and (F -> ((A -> (A or B)) and (C or ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35435.        (((A -> (A or B)) and (C or ((D and E) -> E))) and (F -> ((A -> (A or B)) and (C or ((D and E) -> E))))), M:tm-305, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35436
in-theory        35436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-303 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35436.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-303, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35437
in-theory        35437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-270 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35437.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-270, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35438
in-theory        35438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-239 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35438.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-239, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35439
in-theory        35439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-210 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35439.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or ((H and I) -> I)))), M:tm-210, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35440
in-theory        35440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-183 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35440.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-183, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35441
in-theory        35441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-157 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35441.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-157, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35442
in-theory        35442
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-147 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35442.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-147, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35443
in-theory        35443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-134 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35443.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-134, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35444
in-theory        35444
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-125 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35444.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-125, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35445
in-theory        35445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-113 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35445.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or ((H and I) -> I)))), M:tm-113, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35446
in-theory        35446
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-105 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35446.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-105, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35447
in-theory        35447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-95 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35447.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or ((F and G) -> G)))), M:tm-95, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35448
in-theory        35448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-83 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35448.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-83, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35449
in-theory        35449
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D or ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-76 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-10 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35449.        (((not (not A)) -> A) and ((B -> (B or C)) and (D or ((E and F) -> F)))), M:tm-76, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35450
in-theory        35450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-69 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-9 tm-6 tm-7 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35450.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or ((F and G) -> G)))), M:tm-69, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35451
in-theory        35451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-54 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35451.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-54, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35452
in-theory        35452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-42 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35452.        ((A -> (B or A)) and ((C -> (C or D)) and (E or ((F and G) -> G)))), M:tm-42, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35453
in-theory        35453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-32 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35453.        ((A -> (A or B)) and ((C -> (C or D)) and (E or ((F and G) -> G)))), M:tm-32, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35454
in-theory        35454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-23 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35454.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or ((F and G) -> G)))), M:tm-23, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35455
in-theory        35455
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-22 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35455.        (((A and B) -> B) and ((C -> (C or D)) and (E or ((F and G) -> G)))), M:tm-22, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35456
in-theory        35456
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-21 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35456.        (((A and B) -> A) and ((C -> (C or D)) and (E or ((F and G) -> G)))), M:tm-21, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35457
in-theory        35457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-20 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35457.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-20, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35458
in-theory        35458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-19 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35458.        ((A -> (B -> A)) and ((C -> (C or D)) and (E or ((F and G) -> G)))), M:tm-19, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35459
in-theory        35459
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-7 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-7 tm-5 tm-6 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35459.        (A or ((B -> (B or C)) and (D or ((E and F) -> F)))), M:tm-7, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35460
in-theory        35460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-6 tm-5 tm-7 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35460.        (((A -> (A or B)) and (C or ((D and E) -> E))) or F), M:tm-6, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35461
in-theory        35461
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D or ((E and F) -> F))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35461.        (A -> (((B -> (B or C)) and (D or ((E and F) -> F))) and A)), M:tm-5, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35462
in-theory        35462
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-1 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-1 tm-5 tm-6 tm-7 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35462.        (A -> ((B -> (B or C)) and (D or ((E and F) -> F)))), M:tm-1, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35463
in-theory        35463
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-500 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35463.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-500, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35464
in-theory        35464
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-490 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35464.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I)))), M:tm-490, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35465
in-theory        35465
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-480 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35465.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-480, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35466
in-theory        35466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-469 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35466.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-469, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35467
in-theory        35467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35467.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (F -> (F or G))), M:tm-456, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35468
in-theory        35468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-453 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35468.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-453, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35469
in-theory        35469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C or ((D and E) -> E)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35469.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C or ((D and E) -> E))))), M:tm-443, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35470
in-theory        35470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-409 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35470.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-409, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35471
in-theory        35471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-400 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35471.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-400, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35472
in-theory        35472
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-391 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35472.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-391, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35473
in-theory        35473
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-382 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35473.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-382, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35474
in-theory        35474
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-373 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35474.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I)))), M:tm-373, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35475
in-theory        35475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-364 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35475.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-364, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35476
in-theory        35476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-354 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35476.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-354, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35477
in-theory        35477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35477.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35478
in-theory        35478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-338 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35478.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G)))), M:tm-338, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35479
in-theory        35479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C or ((D and E) -> E)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35479.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C or ((D and E) -> E))))), M:tm-327, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35480
in-theory        35480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C or ((D and E) -> E)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35480.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C or ((D and E) -> E))))), M:tm-326, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35481
in-theory        35481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C or ((D and E) -> E)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35481.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C or ((D and E) -> E))))), M:tm-325, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35482
in-theory        35482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C or ((D and E) -> E)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35482.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C or ((D and E) -> E))))), M:tm-324, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35483
in-theory        35483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C or ((D and E) -> E)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35483.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C or ((D and E) -> E))))), M:tm-323, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35484
in-theory        35484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35484.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35485
in-theory        35485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35485.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35486
in-theory        35486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35486.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35487
in-theory        35487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35487.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35488
in-theory        35488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (F or ((A -> (B -> (A and B))) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35488.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (F or ((A -> (B -> (A and B))) and (C or ((D and E) -> E))))), M:tm-311, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35489
in-theory        35489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35489.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) or F)), M:tm-310, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35490
in-theory        35490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (F -> (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35490.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (F -> (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and F))), M:tm-309, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35491
in-theory        35491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (C or ((D and E) -> E)))
theorem-size     23
proof            (modus-ponens tm-308 tm-503 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35491.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (C or ((D and E) -> E))), M:tm-308, m:tm-503, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-35492
in-theory        35492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-503 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35492.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-503, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-35493
in-theory        35493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (F -> ((A -> (B -> (A and B))) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35493.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (F -> ((A -> (B -> (A and B))) and (C or ((D and E) -> E))))), M:tm-305, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35494
in-theory        35494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-303 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35494.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-303, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35495
in-theory        35495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-270 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35495.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-270, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35496
in-theory        35496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-239 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35496.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-239, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35497
in-theory        35497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I))))
theorem-size     33
proof            (modus-ponens tm-210 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35497.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I)))), M:tm-210, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35498
in-theory        35498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-183 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35498.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-183, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35499
in-theory        35499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-157 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35499.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-157, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35500
in-theory        35500
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-147 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35500.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-147, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35501
in-theory        35501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-134 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35501.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-134, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35502
in-theory        35502
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-125 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35502.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-125, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35503
in-theory        35503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-113 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35503.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I)))), M:tm-113, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35504
in-theory        35504
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     35
proof            (modus-ponens tm-105 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35504.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-105, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35505
in-theory        35505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-95 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35505.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G)))), M:tm-95, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35506
in-theory        35506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-83 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35506.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-83, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35507
in-theory        35507
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or ((E and F) -> F))))
theorem-size     21
proof            (modus-ponens tm-76 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-10 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35507.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or ((E and F) -> F)))), M:tm-76, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35508
in-theory        35508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G))))
theorem-size     27
proof            (modus-ponens tm-69 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-9 tm-7 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35508.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G)))), M:tm-69, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35509
in-theory        35509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-54 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35509.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-54, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35510
in-theory        35510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-42 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35510.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G)))), M:tm-42, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35511
in-theory        35511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-32 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35511.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G)))), M:tm-32, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35512
in-theory        35512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-23 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35512.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G)))), M:tm-23, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35513
in-theory        35513
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-22 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35513.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G)))), M:tm-22, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35514
in-theory        35514
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-21 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35514.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G)))), M:tm-21, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35515
in-theory        35515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-20 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35515.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-20, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35516
in-theory        35516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-19 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35516.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or ((F and G) -> G)))), M:tm-19, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35517
in-theory        35517
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D or ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-7 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35517.        (A or ((B -> (C -> (B and C))) and (D or ((E and F) -> F)))), M:tm-7, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35518
in-theory        35518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-6 tm-5 tm-7 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35518.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) or F), M:tm-6, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35519
in-theory        35519
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D or ((E and F) -> F))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35519.        (A -> (((B -> (C -> (B and C))) and (D or ((E and F) -> F))) and A)), M:tm-5, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35520
in-theory        35520
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D or ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-1 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-1 tm-5 tm-7 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35520.        (A -> ((B -> (C -> (B and C))) and (D or ((E and F) -> F)))), M:tm-1, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35521
in-theory        35521
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-500 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35521.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-500, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35522
in-theory        35522
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-490 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35522.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H and I) -> I)))), M:tm-490, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35523
in-theory        35523
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-480 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35523.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-480, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35524
in-theory        35524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-469 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35524.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-469, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35525
in-theory        35525
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35525.        ((((A and B) -> B) and (C or ((D and E) -> E))) and (F -> (F or G))), M:tm-456, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35526
in-theory        35526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-453 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35526.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-453, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35527
in-theory        35527
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and ((F -> (F or G)) and (((A and B) -> B) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35527.        ((((A and B) -> B) and (C or ((D and E) -> E))) and ((F -> (F or G)) and (((A and B) -> B) and (C or ((D and E) -> E))))), M:tm-443, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35528
in-theory        35528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-409 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35528.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-409, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35529
in-theory        35529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-400 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35529.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-400, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35530
in-theory        35530
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-391 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35530.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-391, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35531
in-theory        35531
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-382 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35531.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-382, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35532
in-theory        35532
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-373 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35532.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or ((H and I) -> I)))), M:tm-373, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35533
in-theory        35533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-364 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35533.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-364, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35534
in-theory        35534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-354 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35534.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-354, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35535
in-theory        35535
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35535.        ((((A and B) -> B) and (C or ((D and E) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35536
in-theory        35536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-338 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35536.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or ((F and G) -> G)))), M:tm-338, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35537
in-theory        35537
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C or ((D and E) -> E)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35537.        ((((A and B) -> B) and (C or ((D and E) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C or ((D and E) -> E))))), M:tm-327, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35538
in-theory        35538
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and (((F and G) -> G) and (((A and B) -> B) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35538.        ((((A and B) -> B) and (C or ((D and E) -> E))) and (((F and G) -> G) and (((A and B) -> B) and (C or ((D and E) -> E))))), M:tm-326, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35539
in-theory        35539
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and (((F and G) -> F) and (((A and B) -> B) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35539.        ((((A and B) -> B) and (C or ((D and E) -> E))) and (((F and G) -> F) and (((A and B) -> B) and (C or ((D and E) -> E))))), M:tm-325, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35540
in-theory        35540
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C or ((D and E) -> E)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35540.        ((((A and B) -> B) and (C or ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C or ((D and E) -> E))))), M:tm-324, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35541
in-theory        35541
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and ((F -> (G -> F)) and (((A and B) -> B) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35541.        ((((A and B) -> B) and (C or ((D and E) -> E))) and ((F -> (G -> F)) and (((A and B) -> B) and (C or ((D and E) -> E))))), M:tm-323, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35542
in-theory        35542
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35542.        ((((A and B) -> B) and (C or ((D and E) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35543
in-theory        35543
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35543.        ((((A and B) -> B) and (C or ((D and E) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35544
in-theory        35544
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35544.        ((((A and B) -> B) and (C or ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35545
in-theory        35545
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35545.        ((((A and B) -> B) and (C or ((D and E) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35546
in-theory        35546
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and (F or (((A and B) -> B) and (C or ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35546.        ((((A and B) -> B) and (C or ((D and E) -> E))) and (F or (((A and B) -> B) and (C or ((D and E) -> E))))), M:tm-311, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35547
in-theory        35547
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and ((((A and B) -> B) and (C or ((D and E) -> E))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35547.        ((((A and B) -> B) and (C or ((D and E) -> E))) and ((((A and B) -> B) and (C or ((D and E) -> E))) or F)), M:tm-310, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35548
in-theory        35548
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and (F -> ((((A and B) -> B) and (C or ((D and E) -> E))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35548.        ((((A and B) -> B) and (C or ((D and E) -> E))) and (F -> ((((A and B) -> B) and (C or ((D and E) -> E))) and F))), M:tm-309, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35549
in-theory        35549
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and (C or ((D and E) -> E)))
theorem-size     21
proof            (modus-ponens tm-308 tm-504 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35549.        ((((A and B) -> B) and (C or ((D and E) -> E))) and (C or ((D and E) -> E))), M:tm-308, m:tm-504, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-35550
in-theory        35550
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-504 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35550.        ((((A and B) -> B) and (C or ((D and E) -> E))) and ((A and B) -> B)), M:tm-307, m:tm-504, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-35551
in-theory        35551
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and (F -> (((A and B) -> B) and (C or ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35551.        ((((A and B) -> B) and (C or ((D and E) -> E))) and (F -> (((A and B) -> B) and (C or ((D and E) -> E))))), M:tm-305, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35552
in-theory        35552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-303 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35552.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-303, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35553
in-theory        35553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-270 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35553.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-270, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35554
in-theory        35554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-239 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35554.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-239, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35555
in-theory        35555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-210 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35555.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or ((H and I) -> I)))), M:tm-210, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35556
in-theory        35556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-183 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35556.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-183, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35557
in-theory        35557
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-157 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35557.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-157, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35558
in-theory        35558
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-147 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35558.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-147, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35559
in-theory        35559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-134 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35559.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-134, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35560
in-theory        35560
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-125 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35560.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-125, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35561
in-theory        35561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-113 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35561.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or ((H and I) -> I)))), M:tm-113, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35562
in-theory        35562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-105 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35562.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-105, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35563
in-theory        35563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-95 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35563.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or ((F and G) -> G)))), M:tm-95, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35564
in-theory        35564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-83 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35564.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-83, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35565
in-theory        35565
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D or ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-76 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-10 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35565.        (((not (not A)) -> A) and (((B and C) -> C) and (D or ((E and F) -> F)))), M:tm-76, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35566
in-theory        35566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-69 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-9 tm-4 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35566.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or ((F and G) -> G)))), M:tm-69, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35567
in-theory        35567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-54 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35567.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-54, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35568
in-theory        35568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-42 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35568.        ((A -> (B or A)) and (((C and D) -> D) and (E or ((F and G) -> G)))), M:tm-42, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35569
in-theory        35569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-32 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35569.        ((A -> (A or B)) and (((C and D) -> D) and (E or ((F and G) -> G)))), M:tm-32, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35570
in-theory        35570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-23 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35570.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or ((F and G) -> G)))), M:tm-23, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35571
in-theory        35571
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-22 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35571.        (((A and B) -> B) and (((C and D) -> D) and (E or ((F and G) -> G)))), M:tm-22, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35572
in-theory        35572
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-21 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35572.        (((A and B) -> A) and (((C and D) -> D) and (E or ((F and G) -> G)))), M:tm-21, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35573
in-theory        35573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-20 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35573.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-20, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35574
in-theory        35574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-19 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35574.        ((A -> (B -> A)) and (((C and D) -> D) and (E or ((F and G) -> G)))), M:tm-19, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35575
in-theory        35575
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-7 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35575.        (A or (((B and C) -> C) and (D or ((E and F) -> F)))), M:tm-7, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35576
in-theory        35576
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-6 tm-5 tm-4 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35576.        ((((A and B) -> B) and (C or ((D and E) -> E))) or F), M:tm-6, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35577
in-theory        35577
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D or ((E and F) -> F))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35577.        (A -> ((((B and C) -> C) and (D or ((E and F) -> F))) and A)), M:tm-5, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35578
in-theory        35578
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-1 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-1 tm-5 tm-4 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35578.        (A -> (((B and C) -> C) and (D or ((E and F) -> F)))), M:tm-1, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35579
in-theory        35579
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-500 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35579.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-500, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35580
in-theory        35580
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-490 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35580.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H and I) -> I)))), M:tm-490, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35581
in-theory        35581
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-480 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35581.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-480, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35582
in-theory        35582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-469 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35582.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-469, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35583
in-theory        35583
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35583.        ((((A and B) -> A) and (C or ((D and E) -> E))) and (F -> (F or G))), M:tm-456, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35584
in-theory        35584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-453 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35584.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-453, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35585
in-theory        35585
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and ((F -> (F or G)) and (((A and B) -> A) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35585.        ((((A and B) -> A) and (C or ((D and E) -> E))) and ((F -> (F or G)) and (((A and B) -> A) and (C or ((D and E) -> E))))), M:tm-443, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35586
in-theory        35586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-409 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35586.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-409, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35587
in-theory        35587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-400 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35587.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-400, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35588
in-theory        35588
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-391 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35588.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-391, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35589
in-theory        35589
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-382 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35589.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-382, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35590
in-theory        35590
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-373 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35590.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or ((H and I) -> I)))), M:tm-373, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35591
in-theory        35591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-364 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35591.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-364, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35592
in-theory        35592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-354 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35592.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-354, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35593
in-theory        35593
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35593.        ((((A and B) -> A) and (C or ((D and E) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35594
in-theory        35594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-338 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35594.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or ((F and G) -> G)))), M:tm-338, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35595
in-theory        35595
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C or ((D and E) -> E)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35595.        ((((A and B) -> A) and (C or ((D and E) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C or ((D and E) -> E))))), M:tm-327, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35596
in-theory        35596
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and (((F and G) -> G) and (((A and B) -> A) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35596.        ((((A and B) -> A) and (C or ((D and E) -> E))) and (((F and G) -> G) and (((A and B) -> A) and (C or ((D and E) -> E))))), M:tm-326, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35597
in-theory        35597
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and (((F and G) -> F) and (((A and B) -> A) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35597.        ((((A and B) -> A) and (C or ((D and E) -> E))) and (((F and G) -> F) and (((A and B) -> A) and (C or ((D and E) -> E))))), M:tm-325, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35598
in-theory        35598
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C or ((D and E) -> E)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35598.        ((((A and B) -> A) and (C or ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C or ((D and E) -> E))))), M:tm-324, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35599
in-theory        35599
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and ((F -> (G -> F)) and (((A and B) -> A) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35599.        ((((A and B) -> A) and (C or ((D and E) -> E))) and ((F -> (G -> F)) and (((A and B) -> A) and (C or ((D and E) -> E))))), M:tm-323, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35600
in-theory        35600
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35600.        ((((A and B) -> A) and (C or ((D and E) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35601
in-theory        35601
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35601.        ((((A and B) -> A) and (C or ((D and E) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35602
in-theory        35602
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35602.        ((((A and B) -> A) and (C or ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35603
in-theory        35603
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35603.        ((((A and B) -> A) and (C or ((D and E) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35604
in-theory        35604
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and (F or (((A and B) -> A) and (C or ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35604.        ((((A and B) -> A) and (C or ((D and E) -> E))) and (F or (((A and B) -> A) and (C or ((D and E) -> E))))), M:tm-311, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35605
in-theory        35605
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and ((((A and B) -> A) and (C or ((D and E) -> E))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35605.        ((((A and B) -> A) and (C or ((D and E) -> E))) and ((((A and B) -> A) and (C or ((D and E) -> E))) or F)), M:tm-310, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35606
in-theory        35606
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and (F -> ((((A and B) -> A) and (C or ((D and E) -> E))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35606.        ((((A and B) -> A) and (C or ((D and E) -> E))) and (F -> ((((A and B) -> A) and (C or ((D and E) -> E))) and F))), M:tm-309, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35607
in-theory        35607
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and (C or ((D and E) -> E)))
theorem-size     21
proof            (modus-ponens tm-308 tm-505 ((A (-> (and Am Bm) Am)) (B (or Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35607.        ((((A and B) -> A) and (C or ((D and E) -> E))) and (C or ((D and E) -> E))), M:tm-308, m:tm-505, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-35608
in-theory        35608
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-505 ((A (-> (and Am Bm) Am)) (B (or Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35608.        ((((A and B) -> A) and (C or ((D and E) -> E))) and ((A and B) -> A)), M:tm-307, m:tm-505, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-35609
in-theory        35609
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and (F -> (((A and B) -> A) and (C or ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35609.        ((((A and B) -> A) and (C or ((D and E) -> E))) and (F -> (((A and B) -> A) and (C or ((D and E) -> E))))), M:tm-305, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35610
in-theory        35610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-303 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35610.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-303, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35611
in-theory        35611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-270 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35611.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-270, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35612
in-theory        35612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-239 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35612.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-239, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35613
in-theory        35613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-210 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35613.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or ((H and I) -> I)))), M:tm-210, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35614
in-theory        35614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-183 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35614.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-183, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35615
in-theory        35615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-157 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35615.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-157, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35616
in-theory        35616
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-147 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35616.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-147, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35617
in-theory        35617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-134 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35617.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-134, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35618
in-theory        35618
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-125 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35618.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-125, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35619
in-theory        35619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-113 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35619.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or ((H and I) -> I)))), M:tm-113, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35620
in-theory        35620
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-105 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35620.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-105, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35621
in-theory        35621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-95 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35621.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or ((F and G) -> G)))), M:tm-95, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35622
in-theory        35622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-83 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35622.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-83, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35623
in-theory        35623
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D or ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-76 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-10 tm-3 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35623.        (((not (not A)) -> A) and (((B and C) -> B) and (D or ((E and F) -> F)))), M:tm-76, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35624
in-theory        35624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-69 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-9 tm-3 tm-7 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35624.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or ((F and G) -> G)))), M:tm-69, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35625
in-theory        35625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-54 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35625.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-54, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35626
in-theory        35626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-42 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35626.        ((A -> (B or A)) and (((C and D) -> C) and (E or ((F and G) -> G)))), M:tm-42, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35627
in-theory        35627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-32 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35627.        ((A -> (A or B)) and (((C and D) -> C) and (E or ((F and G) -> G)))), M:tm-32, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35628
in-theory        35628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-23 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35628.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or ((F and G) -> G)))), M:tm-23, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35629
in-theory        35629
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-22 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35629.        (((A and B) -> B) and (((C and D) -> C) and (E or ((F and G) -> G)))), M:tm-22, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35630
in-theory        35630
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-21 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35630.        (((A and B) -> A) and (((C and D) -> C) and (E or ((F and G) -> G)))), M:tm-21, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35631
in-theory        35631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-20 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35631.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-20, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35632
in-theory        35632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-19 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35632.        ((A -> (B -> A)) and (((C and D) -> C) and (E or ((F and G) -> G)))), M:tm-19, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35633
in-theory        35633
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-7 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-7 tm-5 tm-3 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35633.        (A or (((B and C) -> B) and (D or ((E and F) -> F)))), M:tm-7, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35634
in-theory        35634
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-6 tm-5 tm-3 tm-7 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35634.        ((((A and B) -> A) and (C or ((D and E) -> E))) or F), M:tm-6, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35635
in-theory        35635
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D or ((E and F) -> F))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35635.        (A -> ((((B and C) -> B) and (D or ((E and F) -> F))) and A)), M:tm-5, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35636
in-theory        35636
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-1 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-1 tm-5 tm-3 tm-7 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35636.        (A -> (((B and C) -> B) and (D or ((E and F) -> F)))), M:tm-1, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35637
in-theory        35637
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-500 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35637.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-500, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35638
in-theory        35638
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-490 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35638.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> J)))), M:tm-490, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35639
in-theory        35639
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-480 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35639.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-480, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35640
in-theory        35640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-469 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35640.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-469, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35641
in-theory        35641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35641.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (G -> (G or H))), M:tm-456, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35642
in-theory        35642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-453 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35642.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-453, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35643
in-theory        35643
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35643.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))))), M:tm-443, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35644
in-theory        35644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-409 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35644.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-409, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35645
in-theory        35645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-400 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35645.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-400, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35646
in-theory        35646
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-391 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35646.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-391, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35647
in-theory        35647
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-382 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35647.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-382, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35648
in-theory        35648
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-373 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35648.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> J)))), M:tm-373, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35649
in-theory        35649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-364 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35649.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-364, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35650
in-theory        35650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-354 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35650.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-354, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35651
in-theory        35651
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35651.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35652
in-theory        35652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H))))
theorem-size     31
proof            (modus-ponens tm-338 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35652.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H)))), M:tm-338, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35653
in-theory        35653
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35653.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))))), M:tm-327, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35654
in-theory        35654
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35654.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))))), M:tm-326, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35655
in-theory        35655
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35655.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))))), M:tm-325, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35656
in-theory        35656
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35656.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))))), M:tm-324, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35657
in-theory        35657
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35657.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))))), M:tm-323, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35658
in-theory        35658
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35658.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35659
in-theory        35659
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35659.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35660
in-theory        35660
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35660.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35661
in-theory        35661
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35661.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35662
in-theory        35662
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35662.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))))), M:tm-311, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35663
in-theory        35663
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35663.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) or G)), M:tm-310, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35664
in-theory        35664
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35664.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and G))), M:tm-309, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35665
in-theory        35665
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (D or ((E and F) -> F)))
theorem-size     29
proof            (modus-ponens tm-308 tm-506 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (and Em Fm) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35665.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (D or ((E and F) -> F))), M:tm-308, m:tm-506, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (and Em Fm) Fm))))
================================================================
tm-name          tm-35666
in-theory        35666
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-506 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (and Em Fm) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35666.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-506, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (and Em Fm) Fm))))
================================================================
tm-name          tm-35667
in-theory        35667
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35667.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))))), M:tm-305, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35668
in-theory        35668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     33
proof            (modus-ponens tm-303 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35668.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-303, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35669
in-theory        35669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-270 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35669.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-270, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35670
in-theory        35670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-239 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35670.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-239, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35671
in-theory        35671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> J))))
theorem-size     39
proof            (modus-ponens tm-210 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35671.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> J)))), M:tm-210, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35672
in-theory        35672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-183 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35672.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-183, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35673
in-theory        35673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-157 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35673.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-157, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35674
in-theory        35674
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     37
proof            (modus-ponens tm-147 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35674.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-147, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35675
in-theory        35675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-134 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35675.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-134, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35676
in-theory        35676
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     37
proof            (modus-ponens tm-125 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35676.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-125, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35677
in-theory        35677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> J))))
theorem-size     37
proof            (modus-ponens tm-113 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35677.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> J)))), M:tm-113, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35678
in-theory        35678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-105 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35678.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-105, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35679
in-theory        35679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-95 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35679.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H)))), M:tm-95, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35680
in-theory        35680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-83 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35680.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-83, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35681
in-theory        35681
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> G))))
theorem-size     27
proof            (modus-ponens tm-76 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35681.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> G)))), M:tm-76, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35682
in-theory        35682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-69 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-7 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35682.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H)))), M:tm-69, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35683
in-theory        35683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-54 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35683.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-54, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35684
in-theory        35684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-42 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35684.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H)))), M:tm-42, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35685
in-theory        35685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-32 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35685.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H)))), M:tm-32, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35686
in-theory        35686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-23 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35686.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H)))), M:tm-23, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35687
in-theory        35687
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-22 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35687.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H)))), M:tm-22, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35688
in-theory        35688
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-21 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35688.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H)))), M:tm-21, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35689
in-theory        35689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-20 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35689.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-20, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35690
in-theory        35690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-19 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35690.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or ((G and H) -> H)))), M:tm-19, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35691
in-theory        35691
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-7 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35691.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> G)))), M:tm-7, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35692
in-theory        35692
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-7 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35692.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) or G), M:tm-6, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35693
in-theory        35693
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> G))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35693.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> G))) and A)), M:tm-5, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35694
in-theory        35694
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-1 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-7 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35694.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or ((F and G) -> G)))), M:tm-1, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-35695
in-theory        35695
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-500 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35695.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-500, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35696
in-theory        35696
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-490 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35696.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H and I) -> I)))), M:tm-490, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35697
in-theory        35697
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-480 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35697.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-480, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35698
in-theory        35698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-469 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35698.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-469, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35699
in-theory        35699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35699.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and (F -> (F or G))), M:tm-456, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35700
in-theory        35700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-453 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35700.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-453, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35701
in-theory        35701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35701.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C or ((D and E) -> E))))), M:tm-443, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35702
in-theory        35702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-409 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35702.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-409, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35703
in-theory        35703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-400 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35703.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-400, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35704
in-theory        35704
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-391 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35704.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-391, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35705
in-theory        35705
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-382 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35705.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-382, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35706
in-theory        35706
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-373 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35706.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or ((H and I) -> I)))), M:tm-373, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35707
in-theory        35707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-364 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35707.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-364, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35708
in-theory        35708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-354 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35708.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-354, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35709
in-theory        35709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35709.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35710
in-theory        35710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-338 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35710.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or ((F and G) -> G)))), M:tm-338, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35711
in-theory        35711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C or ((D and E) -> E)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35711.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C or ((D and E) -> E))))), M:tm-327, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35712
in-theory        35712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and (((F and G) -> G) and ((A -> (B -> A)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35712.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and (((F and G) -> G) and ((A -> (B -> A)) and (C or ((D and E) -> E))))), M:tm-326, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35713
in-theory        35713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and (((F and G) -> F) and ((A -> (B -> A)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35713.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and (((F and G) -> F) and ((A -> (B -> A)) and (C or ((D and E) -> E))))), M:tm-325, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35714
in-theory        35714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C or ((D and E) -> E)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35714.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C or ((D and E) -> E))))), M:tm-324, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35715
in-theory        35715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35715.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C or ((D and E) -> E))))), M:tm-323, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35716
in-theory        35716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35716.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35717
in-theory        35717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35717.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35718
in-theory        35718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35718.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35719
in-theory        35719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35719.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35720
in-theory        35720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and (F or ((A -> (B -> A)) and (C or ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35720.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and (F or ((A -> (B -> A)) and (C or ((D and E) -> E))))), M:tm-311, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35721
in-theory        35721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and (((A -> (B -> A)) and (C or ((D and E) -> E))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35721.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and (((A -> (B -> A)) and (C or ((D and E) -> E))) or F)), M:tm-310, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35722
in-theory        35722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and (F -> (((A -> (B -> A)) and (C or ((D and E) -> E))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35722.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and (F -> (((A -> (B -> A)) and (C or ((D and E) -> E))) and F))), M:tm-309, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35723
in-theory        35723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and (C or ((D and E) -> E)))
theorem-size     21
proof            (modus-ponens tm-308 tm-507 ((A (-> Am (-> Bm Am))) (B (or Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35723.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and (C or ((D and E) -> E))), M:tm-308, m:tm-507, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-35724
in-theory        35724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-507 ((A (-> Am (-> Bm Am))) (B (or Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35724.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and (A -> (B -> A))), M:tm-307, m:tm-507, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-35725
in-theory        35725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and (F -> ((A -> (B -> A)) and (C or ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35725.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and (F -> ((A -> (B -> A)) and (C or ((D and E) -> E))))), M:tm-305, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35726
in-theory        35726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-303 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35726.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-303, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35727
in-theory        35727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-270 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35727.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-270, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35728
in-theory        35728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-239 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35728.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-239, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35729
in-theory        35729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-210 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35729.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or ((H and I) -> I)))), M:tm-210, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35730
in-theory        35730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-183 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35730.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-183, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35731
in-theory        35731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-157 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35731.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-157, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35732
in-theory        35732
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-147 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35732.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-147, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35733
in-theory        35733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-134 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35733.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-134, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35734
in-theory        35734
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-125 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35734.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-125, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35735
in-theory        35735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-113 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35735.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or ((H and I) -> I)))), M:tm-113, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35736
in-theory        35736
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-105 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35736.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-105, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35737
in-theory        35737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-95 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35737.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or ((F and G) -> G)))), M:tm-95, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35738
in-theory        35738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-83 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35738.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-83, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35739
in-theory        35739
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D or ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-76 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35739.        (((not (not A)) -> A) and ((B -> (C -> B)) and (D or ((E and F) -> F)))), M:tm-76, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35740
in-theory        35740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-69 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35740.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or ((F and G) -> G)))), M:tm-69, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35741
in-theory        35741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-54 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35741.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-54, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35742
in-theory        35742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-42 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35742.        ((A -> (B or A)) and ((C -> (D -> C)) and (E or ((F and G) -> G)))), M:tm-42, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35743
in-theory        35743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-32 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35743.        ((A -> (A or B)) and ((C -> (D -> C)) and (E or ((F and G) -> G)))), M:tm-32, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35744
in-theory        35744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-23 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35744.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or ((F and G) -> G)))), M:tm-23, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35745
in-theory        35745
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-22 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35745.        (((A and B) -> B) and ((C -> (D -> C)) and (E or ((F and G) -> G)))), M:tm-22, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35746
in-theory        35746
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-21 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35746.        (((A and B) -> A) and ((C -> (D -> C)) and (E or ((F and G) -> G)))), M:tm-21, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35747
in-theory        35747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-20 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35747.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-20, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35748
in-theory        35748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-19 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35748.        ((A -> (B -> A)) and ((C -> (D -> C)) and (E or ((F and G) -> G)))), M:tm-19, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35749
in-theory        35749
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-7 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-7 tm-5 tm-1 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35749.        (A or ((B -> (C -> B)) and (D or ((E and F) -> F)))), M:tm-7, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35750
in-theory        35750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-6 tm-5 tm-1 tm-7 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35750.        (((A -> (B -> A)) and (C or ((D and E) -> E))) or F), M:tm-6, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35751
in-theory        35751
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D or ((E and F) -> F))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35751.        (A -> (((B -> (C -> B)) and (D or ((E and F) -> F))) and A)), M:tm-5, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35752
in-theory        35752
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-1 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-1 tm-5 tm-7 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35752.        (A -> ((B -> (C -> B)) and (D or ((E and F) -> F)))), M:tm-1, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-35753
in-theory        35753
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-500 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35753.        ((A or ((B and C) -> B)) and (D or (E or ((F and G) -> G)))), M:tm-500, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35754
in-theory        35754
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-490 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35754.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G and H) -> H)))), M:tm-490, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35755
in-theory        35755
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-480 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35755.        ((A or (B -> (C -> B))) and (D or (E or ((F and G) -> G)))), M:tm-480, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35756
in-theory        35756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-469 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35756.        ((A -> (B -> (B or C))) and (D or (E or ((F and G) -> G)))), M:tm-469, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35757
in-theory        35757
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35757.        ((A or (B or ((C and D) -> D))) and (E -> (E or F))), M:tm-456, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35758
in-theory        35758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-453 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35758.        ((A -> ((B -> (B or C)) and A)) and (D or (E or ((F and G) -> G)))), M:tm-453, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35759
in-theory        35759
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and ((E -> (E or F)) and (A or (B or ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35759.        ((A or (B or ((C and D) -> D))) and ((E -> (E or F)) and (A or (B or ((C and D) -> D))))), M:tm-443, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35760
in-theory        35760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-409 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35760.        (((A -> (A or B)) or C) and (D or (E or ((F and G) -> G)))), M:tm-409, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35761
in-theory        35761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-400 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35761.        (((A -> (B -> (A and B))) or C) and (D or (E or ((F and G) -> G)))), M:tm-400, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35762
in-theory        35762
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-391 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35762.        ((((A and B) -> B) or C) and (D or (E or ((F and G) -> G)))), M:tm-391, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35763
in-theory        35763
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-382 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35763.        ((((A and B) -> A) or C) and (D or (E or ((F and G) -> G)))), M:tm-382, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35764
in-theory        35764
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-373 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35764.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or ((G and H) -> H)))), M:tm-373, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35765
in-theory        35765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-364 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35765.        (((A -> (B -> A)) or C) and (D or (E or ((F and G) -> G)))), M:tm-364, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35766
in-theory        35766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-354 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35766.        ((A -> (B -> (C -> (B and C)))) and (D or (E or ((F and G) -> G)))), M:tm-354, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35767
in-theory        35767
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35767.        ((A or (B or ((C and D) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35768
in-theory        35768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D or ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-338 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35768.        (((A -> B) -> (A -> (A and B))) and (C or (D or ((E and F) -> F)))), M:tm-338, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35769
in-theory        35769
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and ((E -> (F -> (E and F))) and (A or (B or ((C and D) -> D)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35769.        ((A or (B or ((C and D) -> D))) and ((E -> (F -> (E and F))) and (A or (B or ((C and D) -> D))))), M:tm-327, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35770
in-theory        35770
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and (((E and F) -> F) and (A or (B or ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35770.        ((A or (B or ((C and D) -> D))) and (((E and F) -> F) and (A or (B or ((C and D) -> D))))), M:tm-326, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35771
in-theory        35771
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and (((E and F) -> E) and (A or (B or ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35771.        ((A or (B or ((C and D) -> D))) and (((E and F) -> E) and (A or (B or ((C and D) -> D))))), M:tm-325, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35772
in-theory        35772
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B or ((C and D) -> D)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35772.        ((A or (B or ((C and D) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B or ((C and D) -> D))))), M:tm-324, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35773
in-theory        35773
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and ((E -> (F -> E)) and (A or (B or ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35773.        ((A or (B or ((C and D) -> D))) and ((E -> (F -> E)) and (A or (B or ((C and D) -> D))))), M:tm-323, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35774
in-theory        35774
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35774.        ((A or (B or ((C and D) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35775
in-theory        35775
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35775.        ((A or (B or ((C and D) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35776
in-theory        35776
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35776.        ((A or (B or ((C and D) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35777
in-theory        35777
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35777.        ((A or (B or ((C and D) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35778
in-theory        35778
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and (E or (A or (B or ((C and D) -> D)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35778.        ((A or (B or ((C and D) -> D))) and (E or (A or (B or ((C and D) -> D))))), M:tm-311, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35779
in-theory        35779
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and ((A or (B or ((C and D) -> D))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35779.        ((A or (B or ((C and D) -> D))) and ((A or (B or ((C and D) -> D))) or E)), M:tm-310, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35780
in-theory        35780
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and (E -> ((A or (B or ((C and D) -> D))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35780.        ((A or (B or ((C and D) -> D))) and (E -> ((A or (B or ((C and D) -> D))) and E))), M:tm-309, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35781
in-theory        35781
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and (E -> (A or (B or ((C and D) -> D)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35781.        ((A or (B or ((C and D) -> D))) and (E -> (A or (B or ((C and D) -> D))))), M:tm-305, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35782
in-theory        35782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-303 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35782.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or ((F and G) -> G)))), M:tm-303, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35783
in-theory        35783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-270 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35783.        ((A -> (((B and C) -> C) and A)) and (D or (E or ((F and G) -> G)))), M:tm-270, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35784
in-theory        35784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-239 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35784.        ((A -> (((B and C) -> B) and A)) and (D or (E or ((F and G) -> G)))), M:tm-239, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35785
in-theory        35785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-210 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35785.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or ((G and H) -> H)))), M:tm-210, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35786
in-theory        35786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-183 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35786.        ((A -> ((B -> (C -> B)) and A)) and (D or (E or ((F and G) -> G)))), M:tm-183, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35787
in-theory        35787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-157 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35787.        ((A -> ((B and C) -> C)) and (D or (E or ((F and G) -> G)))), M:tm-157, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35788
in-theory        35788
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-147 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35788.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or ((F and G) -> G)))), M:tm-147, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35789
in-theory        35789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-134 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35789.        ((A -> ((B and C) -> B)) and (D or (E or ((F and G) -> G)))), M:tm-134, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35790
in-theory        35790
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-125 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35790.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or ((F and G) -> G)))), M:tm-125, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35791
in-theory        35791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-113 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35791.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or ((G and H) -> H)))), M:tm-113, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35792
in-theory        35792
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or ((F and G) -> G))))
theorem-size     29
proof            (modus-ponens tm-105 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35792.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or ((F and G) -> G)))), M:tm-105, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35793
in-theory        35793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D or ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-95 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35793.        (((A -> B) -> (A -> A)) and (C or (D or ((E and F) -> F)))), M:tm-95, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35794
in-theory        35794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-83 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35794.        ((A -> (B -> (C -> B))) and (D or (E or ((F and G) -> G)))), M:tm-83, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35795
in-theory        35795
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C or ((D and E) -> E))))
theorem-size     15
proof            (modus-ponens tm-76 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35795.        (((not (not A)) -> A) and (B or (C or ((D and E) -> E)))), M:tm-76, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35796
in-theory        35796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or ((E and F) -> F))))
theorem-size     21
proof            (modus-ponens tm-69 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35796.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or ((E and F) -> F)))), M:tm-69, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35797
in-theory        35797
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-54 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35797.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or ((F and G) -> G)))), M:tm-54, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35798
in-theory        35798
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-42 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35798.        ((A -> (B or A)) and (C or (D or ((E and F) -> F)))), M:tm-42, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35799
in-theory        35799
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-32 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35799.        ((A -> (A or B)) and (C or (D or ((E and F) -> F)))), M:tm-32, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35800
in-theory        35800
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D or ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-23 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35800.        ((A -> (B -> (A and B))) and (C or (D or ((E and F) -> F)))), M:tm-23, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35801
in-theory        35801
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-22 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35801.        (((A and B) -> B) and (C or (D or ((E and F) -> F)))), M:tm-22, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35802
in-theory        35802
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-21 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35802.        (((A and B) -> A) and (C or (D or ((E and F) -> F)))), M:tm-21, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35803
in-theory        35803
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-20 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35803.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or ((F and G) -> G)))), M:tm-20, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35804
in-theory        35804
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-19 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35804.        ((A -> (B -> A)) and (C or (D or ((E and F) -> F)))), M:tm-19, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35805
in-theory        35805
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C or ((D and E) -> E))))
theorem-size     11
proof            (modus-ponens tm-7 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-7 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35805.        (A or (B or (C or ((D and E) -> E)))), M:tm-7, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35806
in-theory        35806
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-6 tm-7 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35806.        ((A or (B or ((C and D) -> D))) or E), M:tm-6, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35807
in-theory        35807
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C or ((D and E) -> E))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35807.        (A -> ((B or (C or ((D and E) -> E))) and A)), M:tm-5, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35808
in-theory        35808
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C or ((D and E) -> E))))
theorem-size     11
proof            (modus-ponens tm-1 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-1 tm-7 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35808.        (A -> (B or (C or ((D and E) -> E)))), M:tm-1, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-35809
in-theory        35809
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35809.        ((A or ((B and C) -> B)) and ((D or ((E and F) -> F)) or G)), M:tm-500, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35810
in-theory        35810
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F and G) -> G)) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35810.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F and G) -> G)) or H)), M:tm-490, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35811
in-theory        35811
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35811.        ((A or (B -> (C -> B))) and ((D or ((E and F) -> F)) or G)), M:tm-480, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35812
in-theory        35812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35812.        ((A -> (B -> (B or C))) and ((D or ((E and F) -> F)) or G)), M:tm-469, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35813
in-theory        35813
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35813.        (((A or ((B and C) -> C)) or D) and (E -> (E or F))), M:tm-456, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35814
in-theory        35814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35814.        ((A -> ((B -> (B or C)) and A)) and ((D or ((E and F) -> F)) or G)), M:tm-453, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35815
in-theory        35815
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and ((E -> (E or F)) and ((A or ((B and C) -> C)) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35815.        (((A or ((B and C) -> C)) or D) and ((E -> (E or F)) and ((A or ((B and C) -> C)) or D))), M:tm-443, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35816
in-theory        35816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35816.        (((A -> (A or B)) or C) and ((D or ((E and F) -> F)) or G)), M:tm-409, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35817
in-theory        35817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35817.        (((A -> (B -> (A and B))) or C) and ((D or ((E and F) -> F)) or G)), M:tm-400, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35818
in-theory        35818
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35818.        ((((A and B) -> B) or C) and ((D or ((E and F) -> F)) or G)), M:tm-391, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35819
in-theory        35819
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35819.        ((((A and B) -> A) or C) and ((D or ((E and F) -> F)) or G)), M:tm-382, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35820
in-theory        35820
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F and G) -> G)) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35820.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F and G) -> G)) or H)), M:tm-373, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35821
in-theory        35821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35821.        (((A -> (B -> A)) or C) and ((D or ((E and F) -> F)) or G)), M:tm-364, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35822
in-theory        35822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35822.        ((A -> (B -> (C -> (B and C)))) and ((D or ((E and F) -> F)) or G)), M:tm-354, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35823
in-theory        35823
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35823.        (((A or ((B and C) -> C)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35824
in-theory        35824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or ((D and E) -> E)) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35824.        (((A -> B) -> (A -> (A and B))) and ((C or ((D and E) -> E)) or F)), M:tm-338, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35825
in-theory        35825
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and ((E -> (F -> (E and F))) and ((A or ((B and C) -> C)) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35825.        (((A or ((B and C) -> C)) or D) and ((E -> (F -> (E and F))) and ((A or ((B and C) -> C)) or D))), M:tm-327, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35826
in-theory        35826
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and (((E and F) -> F) and ((A or ((B and C) -> C)) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35826.        (((A or ((B and C) -> C)) or D) and (((E and F) -> F) and ((A or ((B and C) -> C)) or D))), M:tm-326, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35827
in-theory        35827
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and (((E and F) -> E) and ((A or ((B and C) -> C)) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35827.        (((A or ((B and C) -> C)) or D) and (((E and F) -> E) and ((A or ((B and C) -> C)) or D))), M:tm-325, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35828
in-theory        35828
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or ((B and C) -> C)) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35828.        (((A or ((B and C) -> C)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or ((B and C) -> C)) or D))), M:tm-324, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35829
in-theory        35829
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and ((E -> (F -> E)) and ((A or ((B and C) -> C)) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35829.        (((A or ((B and C) -> C)) or D) and ((E -> (F -> E)) and ((A or ((B and C) -> C)) or D))), M:tm-323, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35830
in-theory        35830
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35830.        (((A or ((B and C) -> C)) or D) and ((E and F) -> F)), M:tm-322, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35831
in-theory        35831
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35831.        (((A or ((B and C) -> C)) or D) and ((E and F) -> E)), M:tm-320, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35832
in-theory        35832
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35832.        (((A or ((B and C) -> C)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35833
in-theory        35833
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35833.        (((A or ((B and C) -> C)) or D) and (E -> (F -> E))), M:tm-315, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35834
in-theory        35834
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and (E or ((A or ((B and C) -> C)) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35834.        (((A or ((B and C) -> C)) or D) and (E or ((A or ((B and C) -> C)) or D))), M:tm-311, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35835
in-theory        35835
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and (((A or ((B and C) -> C)) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35835.        (((A or ((B and C) -> C)) or D) and (((A or ((B and C) -> C)) or D) or E)), M:tm-310, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35836
in-theory        35836
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and (E -> (((A or ((B and C) -> C)) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35836.        (((A or ((B and C) -> C)) or D) and (E -> (((A or ((B and C) -> C)) or D) and E))), M:tm-309, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35837
in-theory        35837
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and (E -> ((A or ((B and C) -> C)) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35837.        (((A or ((B and C) -> C)) or D) and (E -> ((A or ((B and C) -> C)) or D))), M:tm-305, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35838
in-theory        35838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E and F) -> F)) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35838.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E and F) -> F)) or G)), M:tm-303, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35839
in-theory        35839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35839.        ((A -> (((B and C) -> C) and A)) and ((D or ((E and F) -> F)) or G)), M:tm-270, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35840
in-theory        35840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35840.        ((A -> (((B and C) -> B) and A)) and ((D or ((E and F) -> F)) or G)), M:tm-239, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35841
in-theory        35841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F and G) -> G)) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35841.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F and G) -> G)) or H)), M:tm-210, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35842
in-theory        35842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35842.        ((A -> ((B -> (C -> B)) and A)) and ((D or ((E and F) -> F)) or G)), M:tm-183, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35843
in-theory        35843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35843.        ((A -> ((B and C) -> C)) and ((D or ((E and F) -> F)) or G)), M:tm-157, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35844
in-theory        35844
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E and F) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35844.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E and F) -> F)) or G)), M:tm-147, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35845
in-theory        35845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35845.        ((A -> ((B and C) -> B)) and ((D or ((E and F) -> F)) or G)), M:tm-134, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35846
in-theory        35846
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E and F) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35846.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E and F) -> F)) or G)), M:tm-125, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35847
in-theory        35847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F and G) -> G)) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35847.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F and G) -> G)) or H)), M:tm-113, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35848
in-theory        35848
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E and F) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35848.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E and F) -> F)) or G)), M:tm-105, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35849
in-theory        35849
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or ((D and E) -> E)) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35849.        (((A -> B) -> (A -> A)) and ((C or ((D and E) -> E)) or F)), M:tm-95, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35850
in-theory        35850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35850.        ((A -> (B -> (C -> B))) and ((D or ((E and F) -> F)) or G)), M:tm-83, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35851
in-theory        35851
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or ((C and D) -> D)) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35851.        (((not (not A)) -> A) and ((B or ((C and D) -> D)) or E)), M:tm-76, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35852
in-theory        35852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D and E) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-7 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35852.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D and E) -> E)) or F)), M:tm-69, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35853
in-theory        35853
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E and F) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35853.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E and F) -> F)) or G)), M:tm-54, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35854
in-theory        35854
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or ((D and E) -> E)) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35854.        ((A -> (B or A)) and ((C or ((D and E) -> E)) or F)), M:tm-42, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35855
in-theory        35855
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or ((D and E) -> E)) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35855.        ((A -> (A or B)) and ((C or ((D and E) -> E)) or F)), M:tm-32, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35856
in-theory        35856
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or ((D and E) -> E)) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35856.        ((A -> (B -> (A and B))) and ((C or ((D and E) -> E)) or F)), M:tm-23, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35857
in-theory        35857
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or ((D and E) -> E)) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35857.        (((A and B) -> B) and ((C or ((D and E) -> E)) or F)), M:tm-22, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35858
in-theory        35858
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or ((D and E) -> E)) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35858.        (((A and B) -> A) and ((C or ((D and E) -> E)) or F)), M:tm-21, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35859
in-theory        35859
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E and F) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35859.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E and F) -> F)) or G)), M:tm-20, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35860
in-theory        35860
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or ((D and E) -> E)) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35860.        ((A -> (B -> A)) and ((C or ((D and E) -> E)) or F)), M:tm-19, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35861
in-theory        35861
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B or ((C and D) -> D)) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-7 tm-6 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35861.        (A or ((B or ((C and D) -> D)) or E)), M:tm-7, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35862
in-theory        35862
times-derived    2
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-6 tm-7 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35862.        (((A or ((B and C) -> C)) or D) or E), M:tm-6, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35863
in-theory        35863
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B or ((C and D) -> D)) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35863.        (A -> (((B or ((C and D) -> D)) or E) and A)), M:tm-5, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35864
in-theory        35864
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B or ((C and D) -> D)) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-1 tm-6 tm-7 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35864.        (A -> ((B or ((C and D) -> D)) or E)), M:tm-1, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-35865
in-theory        35865
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-510 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35865.        ((A or ((B and C) -> C)) and (D -> (E or D))), M:tm-510, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-35866
in-theory        35866
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-35866.        ((A or ((B and C) -> C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-510, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-35867
in-theory        35867
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-510 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-35867.        ((A or ((B and C) -> C)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-510, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-35868
in-theory        35868
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-510 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-7 tm-4 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-35868.        ((A or ((B and C) -> C)) and ((not (not D)) -> D)), M:tm-510, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-35869
in-theory        35869
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-510 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-35869.        ((A or ((B and C) -> C)) and (D -> (E -> (F -> E)))), M:tm-510, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-35870
in-theory        35870
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-510 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-35870.        ((A or ((B and C) -> C)) and ((D -> E) -> (D -> D))), M:tm-510, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-35871
in-theory        35871
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-510 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-35871.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-510, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-35872
in-theory        35872
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35872.        ((A or ((B and C) -> C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-510, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-35873
in-theory        35873
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-510 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-35873.        ((A or ((B and C) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-510, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-35874
in-theory        35874
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-510 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-35874.        ((A or ((B and C) -> C)) and (D -> ((E and F) -> E))), M:tm-510, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-35875
in-theory        35875
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-510 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-35875.        ((A or ((B and C) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-510, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-35876
in-theory        35876
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-510 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-35876.        ((A or ((B and C) -> C)) and (D -> ((E and F) -> F))), M:tm-510, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-35877
in-theory        35877
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-510 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-35877.        ((A or ((B and C) -> C)) and (D -> ((E -> (F -> E)) and D))), M:tm-510, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-35878
in-theory        35878
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-510 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35878.        ((A or ((B and C) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-510, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-35879
in-theory        35879
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-510 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-35879.        ((A or ((B and C) -> C)) and (D -> (((E and F) -> E) and D))), M:tm-510, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-35880
in-theory        35880
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-510 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-35880.        ((A or ((B and C) -> C)) and (D -> (((E and F) -> F) and D))), M:tm-510, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-35881
in-theory        35881
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-35881.        ((A or ((B and C) -> C)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-510, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-35882
in-theory        35882
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-510 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-35882.        ((A or ((B and C) -> C)) and ((D -> E) -> (D -> (D and E)))), M:tm-510, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-35883
in-theory        35883
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-35883.        ((A or ((B and C) -> C)) and (D -> (E -> (F -> (E and F))))), M:tm-510, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-35884
in-theory        35884
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-510 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-35884.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) or F)), M:tm-510, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-35885
in-theory        35885
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-510 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35885.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-510, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-35886
in-theory        35886
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-510 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-35886.        ((A or ((B and C) -> C)) and (((D and E) -> D) or F)), M:tm-510, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-35887
in-theory        35887
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-510 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-35887.        ((A or ((B and C) -> C)) and (((D and E) -> E) or F)), M:tm-510, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-35888
in-theory        35888
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-510 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-35888.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) or F)), M:tm-510, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-35889
in-theory        35889
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-510 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-35889.        ((A or ((B and C) -> C)) and ((D -> (D or E)) or F)), M:tm-510, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-35890
in-theory        35890
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-510 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-35890.        ((A or ((B and C) -> C)) and (D -> ((E -> (E or F)) and D))), M:tm-510, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-35891
in-theory        35891
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-510 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-35891.        ((A or ((B and C) -> C)) and (D -> (E -> (E or F)))), M:tm-510, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-35892
in-theory        35892
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-510 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-35892.        ((A or ((B and C) -> C)) and (D or (E -> (F -> E)))), M:tm-510, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-35893
in-theory        35893
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35893.        ((A or ((B and C) -> C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-510, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-35894
in-theory        35894
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-510 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-35894.        ((A or ((B and C) -> C)) and (D or ((E and F) -> E))), M:tm-510, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-35895
in-theory        35895
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-510 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-35895.        ((A or ((B and C) -> C)) and (D or ((E and F) -> F))), M:tm-510, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-35896
in-theory        35896
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-35896.        ((A or ((B and C) -> C)) and (D or (E -> (F -> (E and F))))), M:tm-510, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-35897
in-theory        35897
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-510 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-35897.        ((A or ((B and C) -> C)) and (D or (E -> (E or F)))), M:tm-510, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-35898
in-theory        35898
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-510 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35898.        ((A or ((B and C) -> C)) and (D or (E -> (F or E)))), M:tm-510, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-35899
in-theory        35899
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-510 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35899.        ((A or ((B and C) -> C)) and ((D -> (E or D)) or F)), M:tm-510, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-35900
in-theory        35900
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-510 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35900.        ((A or ((B and C) -> C)) and (D -> ((E -> (F or E)) and D))), M:tm-510, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-35901
in-theory        35901
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-510 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35901.        ((A or ((B and C) -> C)) and (D -> (E -> (F or E)))), M:tm-510, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-35902
in-theory        35902
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-510 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-35902.        ((A or ((B and C) -> C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-510, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-35903
in-theory        35903
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-510 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-35903.        ((A or ((B and C) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-510, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-35904
in-theory        35904
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-510 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-35904.        ((A or ((B and C) -> C)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-510, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-35905
in-theory        35905
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-510 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-35905.        ((A or ((B and C) -> C)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-510, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-35906
in-theory        35906
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-510 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-35906.        ((A or ((B and C) -> C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-510, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-35907
in-theory        35907
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-510 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-35907.        ((A or ((B and C) -> C)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-510, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-35908
in-theory        35908
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-510 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-35908.        ((A or ((B and C) -> C)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-510, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-35909
in-theory        35909
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-510 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-35909.        ((A or ((B and C) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-510, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-35910
in-theory        35910
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-35910.        ((A or ((B and C) -> C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-510, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-35911
in-theory        35911
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-510 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-35911.        ((A or ((B and C) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-510, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-35912
in-theory        35912
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-510 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-35912.        ((A or ((B and C) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-510, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-35913
in-theory        35913
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-510 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-35913.        ((A or ((B and C) -> C)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-510, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-35914
in-theory        35914
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-35914.        ((A or ((B and C) -> C)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-510, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-35915
in-theory        35915
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-510 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-35915.        ((A or ((B and C) -> C)) and ((D -> (not (E -> D))) -> (not D))), M:tm-510, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-35916
in-theory        35916
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-35916.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-510, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-35917
in-theory        35917
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-510 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-35917.        ((A or ((B and C) -> C)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-510, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-35918
in-theory        35918
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-510 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-35918.        ((A or ((B and C) -> C)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-510, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-35919
in-theory        35919
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-35919.        ((A or ((B and C) -> C)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-510, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-35920
in-theory        35920
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-510 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-35920.        ((A or ((B and C) -> C)) and ((D -> (not (D or E))) -> (not D))), M:tm-510, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-35921
in-theory        35921
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-510 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-35921.        ((A or ((B and C) -> C)) and ((D -> (not (E or D))) -> (not D))), M:tm-510, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-35922
in-theory        35922
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-510 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-35922.        ((A or ((B and C) -> C)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-510, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-35923
in-theory        35923
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-510 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-35923.        ((A or ((B and C) -> C)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-510, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-35924
in-theory        35924
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-510 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-35924.        ((A or ((B and C) -> C)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-510, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-35925
in-theory        35925
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-35925.        ((A or ((B and C) -> C)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-510, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-35926
in-theory        35926
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-510 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-35926.        ((A or ((B and C) -> C)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-510, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-35927
in-theory        35927
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-510 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-35927.        ((A or ((B and C) -> C)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-510, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-35928
in-theory        35928
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-510 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-35928.        ((A or ((B and C) -> C)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-510, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-35929
in-theory        35929
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-35929.        ((A or ((B and C) -> C)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-510, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-35930
in-theory        35930
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-510 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-35930.        ((A or ((B and C) -> C)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-510, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-35931
in-theory        35931
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-510 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-35931.        ((A or ((B and C) -> C)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-510, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-35932
in-theory        35932
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-510 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-35932.        ((A or ((B and C) -> C)) and (D or ((not (not E)) -> E))), M:tm-510, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-35933
in-theory        35933
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-510 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-35933.        ((A or ((B and C) -> C)) and (((not (not D)) -> D) or E)), M:tm-510, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-35934
in-theory        35934
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-510 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-35934.        ((A or ((B and C) -> C)) and (D -> (((not (not E)) -> E) and D))), M:tm-510, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-35935
in-theory        35935
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-510 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-35935.        ((A or ((B and C) -> C)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-510, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-35936
in-theory        35936
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-510 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-35936.        ((A or ((B and C) -> C)) and (D -> ((not (not E)) -> E))), M:tm-510, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-35937
in-theory        35937
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-35937.        ((A or ((B and C) -> C)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-510, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-35938
in-theory        35938
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-510 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-35938.        ((A or ((B and C) -> C)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-510, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-35939
in-theory        35939
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-35939.        ((A or ((B and C) -> C)) and (D or (E -> (F -> (G -> F))))), M:tm-510, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-35940
in-theory        35940
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-35940.        ((A or ((B and C) -> C)) and ((D -> (E -> (F -> E))) or G)), M:tm-510, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-35941
in-theory        35941
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-35941.        ((A or ((B and C) -> C)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-510, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-35942
in-theory        35942
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-510 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-35942.        ((A or ((B and C) -> C)) and ((D -> E) -> (D -> (F -> E)))), M:tm-510, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-35943
in-theory        35943
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-35943.        ((A or ((B and C) -> C)) and (D -> (E -> (F -> (G -> F))))), M:tm-510, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-35944
in-theory        35944
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-510 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-35944.        ((A or ((B and C) -> C)) and (D -> D)), M:tm-510, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-35945
in-theory        35945
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-35945.        ((A or ((B and C) -> C)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-510, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-35946
in-theory        35946
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-510 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-35946.        ((A or ((B and C) -> C)) and ((D and E) -> (D and E))), M:tm-510, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-35947
in-theory        35947
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-510 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-35947.        ((A or ((B and C) -> C)) and ((D -> E) -> (D -> E))), M:tm-510, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-35948
in-theory        35948
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-510 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-35948.        ((A or ((B and C) -> C)) and ((not (not D)) -> (not (not D)))), M:tm-510, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-35949
in-theory        35949
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-510 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-35949.        ((A or ((B and C) -> C)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-510, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-35950
in-theory        35950
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-510 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-35950.        ((A or ((B and C) -> C)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-510, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-35951
in-theory        35951
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-510 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-35951.        ((A or ((B and C) -> C)) and (D or ((E -> F) -> (E -> E)))), M:tm-510, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-35952
in-theory        35952
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-510 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-35952.        ((A or ((B and C) -> C)) and (((D -> E) -> (D -> D)) or F)), M:tm-510, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-35953
in-theory        35953
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-35953.        ((A or ((B and C) -> C)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-510, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-35954
in-theory        35954
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-35954.        ((A or ((B and C) -> C)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-510, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-35955
in-theory        35955
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-510 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-35955.        ((A or ((B and C) -> C)) and (D -> ((E -> F) -> (E -> E)))), M:tm-510, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-35956
in-theory        35956
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-35956.        ((A or ((B and C) -> C)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-510, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-35957
in-theory        35957
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-510 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-35957.        ((A or ((B and C) -> C)) and ((D -> (D -> E)) -> (D -> E))), M:tm-510, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-35958
in-theory        35958
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-510 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-35958.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-510, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-35959
in-theory        35959
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-510 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-35959.        ((A or ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-510, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-35960
in-theory        35960
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-510 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-35960.        ((A or ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-510, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-35961
in-theory        35961
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-35961.        ((A or ((B and C) -> C)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-510, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-35962
in-theory        35962
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-510 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-35962.        ((A or ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-510, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-35963
in-theory        35963
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-510 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-35963.        ((A or ((B and C) -> C)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-510, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-35964
in-theory        35964
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-510 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-35964.        ((A or ((B and C) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-510, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-35965
in-theory        35965
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-35965.        ((A or ((B and C) -> C)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-510, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-35966
in-theory        35966
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-510 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-35966.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-510, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-35967
in-theory        35967
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-510 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-35967.        ((A or ((B and C) -> C)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-510, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-35968
in-theory        35968
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-510 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-35968.        ((A or ((B and C) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-510, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-35969
in-theory        35969
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-510 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35969.        ((A or ((B and C) -> C)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-510, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-35970
in-theory        35970
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-510 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35970.        ((A or ((B and C) -> C)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-510, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-35971
in-theory        35971
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-510 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35971.        ((A or ((B and C) -> C)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-510, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-35972
in-theory        35972
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-510 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-35972.        ((A or ((B and C) -> C)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-510, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-35973
in-theory        35973
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-510 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-35973.        ((A or ((B and C) -> C)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-510, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-35974
in-theory        35974
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-510 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-35974.        ((A or ((B and C) -> C)) and (((D -> E) and D) -> E)), M:tm-510, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-35975
in-theory        35975
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-510 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-35975.        ((A or ((B and C) -> C)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-510, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-35976
in-theory        35976
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-510 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-35976.        ((A or ((B and C) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-510, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-35977
in-theory        35977
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-510 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-35977.        ((A or ((B and C) -> C)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-510, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-35978
in-theory        35978
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-510 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-35978.        ((A or ((B and C) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-510, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-35979
in-theory        35979
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-510 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-35979.        ((A or ((B and C) -> C)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-510, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-35980
in-theory        35980
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-510 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-35980.        ((A or ((B and C) -> C)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-510, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-35981
in-theory        35981
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-510 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-35981.        ((A or ((B and C) -> C)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-510, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-35982
in-theory        35982
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-510 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-35982.        ((A or ((B and C) -> C)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-510, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-35983
in-theory        35983
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-510 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-35983.        ((A or ((B and C) -> C)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-510, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-35984
in-theory        35984
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-510 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-35984.        ((A or ((B and C) -> C)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-510, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-35985
in-theory        35985
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-510 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-35985.        ((A or ((B and C) -> C)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-510, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-35986
in-theory        35986
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-510 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-35986.        ((A or ((B and C) -> C)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-510, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-35987
in-theory        35987
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-510 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-35987.        ((A or ((B and C) -> C)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-510, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-35988
in-theory        35988
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-35988.        ((A or ((B and C) -> C)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-510, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-35989
in-theory        35989
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-510 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-35989.        ((A or ((B and C) -> C)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-510, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-35990
in-theory        35990
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-510 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-35990.        ((A or ((B and C) -> C)) and (D or (E -> ((F and G) -> F)))), M:tm-510, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35991
in-theory        35991
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-35991.        ((A or ((B and C) -> C)) and ((D -> ((E and F) -> E)) or G)), M:tm-510, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-35992
in-theory        35992
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-35992.        ((A or ((B and C) -> C)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-510, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-35993
in-theory        35993
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-510 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-35993.        ((A or ((B and C) -> C)) and ((D -> (E and F)) -> (D -> E))), M:tm-510, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-35994
in-theory        35994
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-510 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-35994.        ((A or ((B and C) -> C)) and (D -> (E -> ((F and G) -> F)))), M:tm-510, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-35995
in-theory        35995
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-510 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-35995.        ((A or ((B and C) -> C)) and ((D and (D -> E)) -> E)), M:tm-510, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-35996
in-theory        35996
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-510 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-35996.        ((A or ((B and C) -> C)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-510, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-35997
in-theory        35997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-510 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-35997.        ((A or ((B and C) -> C)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-510, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-35998
in-theory        35998
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-510 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-35998.        ((A or ((B and C) -> C)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-510, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-35999
in-theory        35999
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-510 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-35999.        ((A or ((B and C) -> C)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-510, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-36000
in-theory        36000
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-510 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-36000.        ((A or ((B and C) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-510, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-36001
in-theory        36001
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-510 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-36001.        ((A or ((B and C) -> C)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-510, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-36002
in-theory        36002
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-510 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-36002.        ((A or ((B and C) -> C)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-510, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-36003
in-theory        36003
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-510 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-36003.        ((A or ((B and C) -> C)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-510, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-36004
in-theory        36004
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-510 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-36004.        ((A or ((B and C) -> C)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-510, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-36005
in-theory        36005
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-510 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-36005.        ((A or ((B and C) -> C)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-510, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-36006
in-theory        36006
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-510 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-36006.        ((A or ((B and C) -> C)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-510, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-36007
in-theory        36007
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-510 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-36007.        ((A or ((B and C) -> C)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-510, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-36008
in-theory        36008
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-510 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-36008.        ((A or ((B and C) -> C)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-510, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-36009
in-theory        36009
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-510 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-36009.        ((A or ((B and C) -> C)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-510, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-36010
in-theory        36010
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-510 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-36010.        ((A or ((B and C) -> C)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-510, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-36011
in-theory        36011
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-36011.        ((A or ((B and C) -> C)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-510, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-36012
in-theory        36012
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-510 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-36012.        ((A or ((B and C) -> C)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-510, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-36013
in-theory        36013
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-510 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-36013.        ((A or ((B and C) -> C)) and (D or (E -> ((F and G) -> G)))), M:tm-510, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36014
in-theory        36014
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-36014.        ((A or ((B and C) -> C)) and ((D -> ((E and F) -> F)) or G)), M:tm-510, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-36015
in-theory        36015
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-36015.        ((A or ((B and C) -> C)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-510, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36016
in-theory        36016
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-510 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-36016.        ((A or ((B and C) -> C)) and ((D -> (E and F)) -> (D -> F))), M:tm-510, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-36017
in-theory        36017
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-510 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-36017.        ((A or ((B and C) -> C)) and (D -> (E -> ((F and G) -> G)))), M:tm-510, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36018
in-theory        36018
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-36018.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-510, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-36019
in-theory        36019
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-36019.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-510, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-36020
in-theory        36020
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36020.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-510, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-36021
in-theory        36021
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-510 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-36021.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-510, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36022
in-theory        36022
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-36022.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-510, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-36023
in-theory        36023
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-510 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-36023.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-510, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-36024
in-theory        36024
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36024.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-510, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-36025
in-theory        36025
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-36025.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-510, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-36026
in-theory        36026
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-510 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-36026.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-510, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-36027
in-theory        36027
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-36027.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-510, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-36028
in-theory        36028
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-36028.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-510, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-36029
in-theory        36029
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-36029.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-510, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-36030
in-theory        36030
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-510 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-36030.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-510, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-36031
in-theory        36031
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36031.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-510, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-36032
in-theory        36032
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-510 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-36032.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-510, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-36033
in-theory        36033
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-510 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-36033.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-510, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-36034
in-theory        36034
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-510 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-36034.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-510, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-36035
in-theory        36035
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-510 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-36035.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-510, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-36036
in-theory        36036
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-36036.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-510, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-36037
in-theory        36037
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-36037.        ((A or ((B and C) -> C)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-510, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-36038
in-theory        36038
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-510 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-36038.        ((A or ((B and C) -> C)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-510, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-36039
in-theory        36039
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-510 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-36039.        ((A or ((B and C) -> C)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-510, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-36040
in-theory        36040
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-510 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-36040.        ((A or ((B and C) -> C)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-510, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-36041
in-theory        36041
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-36041.        ((A or ((B and C) -> C)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-510, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-36042
in-theory        36042
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-510 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-36042.        ((A or ((B and C) -> C)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-510, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-36043
in-theory        36043
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-510 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-36043.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-510, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-36044
in-theory        36044
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-36044.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-510, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-36045
in-theory        36045
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-510 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36045.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-510, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-36046
in-theory        36046
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-510 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-36046.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-510, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-36047
in-theory        36047
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-36047.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-510, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-36048
in-theory        36048
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-36048.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-510, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-36049
in-theory        36049
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-510 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36049.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-510, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-36050
in-theory        36050
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-36050.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-510, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-36051
in-theory        36051
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-510 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-36051.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-510, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-36052
in-theory        36052
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-510 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-36052.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-510, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-36053
in-theory        36053
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-36053.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-510, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-36054
in-theory        36054
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-510 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-36054.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-510, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-36055
in-theory        36055
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-510 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-36055.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-510, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-36056
in-theory        36056
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-510 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36056.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-510, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-36057
in-theory        36057
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-510 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-36057.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-510, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-36058
in-theory        36058
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-510 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-36058.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-510, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-36059
in-theory        36059
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-510 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-36059.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-510, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-36060
in-theory        36060
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-510 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-36060.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-510, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-36061
in-theory        36061
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-510 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-36061.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-510, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-36062
in-theory        36062
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-510 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-36062.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-510, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-36063
in-theory        36063
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-510 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-36063.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-510, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-36064
in-theory        36064
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-510 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-36064.        ((A or ((B and C) -> C)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-510, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-36065
in-theory        36065
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-510 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-36065.        ((A or ((B and C) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-510, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-36066
in-theory        36066
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-510 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-36066.        ((A or ((B and C) -> C)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-510, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-36067
in-theory        36067
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-510 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-36067.        ((A or ((B and C) -> C)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-510, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-36068
in-theory        36068
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-510 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-36068.        ((A or ((B and C) -> C)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-510, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-36069
in-theory        36069
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-510 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-36069.        ((A or ((B and C) -> C)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-510, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-36070
in-theory        36070
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-36070.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-510, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-36071
in-theory        36071
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-36071.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-510, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-36072
in-theory        36072
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36072.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-510, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-36073
in-theory        36073
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-510 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-36073.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-510, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36074
in-theory        36074
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-36074.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-510, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-36075
in-theory        36075
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-510 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-36075.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-510, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-36076
in-theory        36076
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36076.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-510, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-36077
in-theory        36077
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-36077.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-510, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-36078
in-theory        36078
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-510 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-36078.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-510, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-36079
in-theory        36079
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-36079.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-510, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-36080
in-theory        36080
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-36080.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-510, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-36081
in-theory        36081
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-36081.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-510, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-36082
in-theory        36082
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-510 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-36082.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-510, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-36083
in-theory        36083
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36083.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-510, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-36084
in-theory        36084
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-510 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-36084.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-510, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-36085
in-theory        36085
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-510 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-36085.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-510, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-36086
in-theory        36086
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-510 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-36086.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-510, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-36087
in-theory        36087
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-510 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-36087.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-510, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-36088
in-theory        36088
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-36088.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-510, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-36089
in-theory        36089
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-510 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-36089.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-510, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-36090
in-theory        36090
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-36090.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-510, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-36091
in-theory        36091
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-510 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-36091.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-510, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-36092
in-theory        36092
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-36092.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-510, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-36093
in-theory        36093
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-36093.        ((A or ((B and C) -> C)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-510, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-36094
in-theory        36094
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-510 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-36094.        ((A or ((B and C) -> C)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-510, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-36095
in-theory        36095
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-510 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-36095.        ((A or ((B and C) -> C)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-510, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-36096
in-theory        36096
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-510 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-36096.        ((A or ((B and C) -> C)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-510, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-36097
in-theory        36097
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-36097.        ((A or ((B and C) -> C)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-510, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-36098
in-theory        36098
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-510 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-36098.        ((A or ((B and C) -> C)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-510, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-36099
in-theory        36099
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-36099.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-510, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-36100
in-theory        36100
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-36100.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-510, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-36101
in-theory        36101
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36101.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-510, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-36102
in-theory        36102
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-510 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-36102.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-510, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36103
in-theory        36103
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-36103.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-510, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-36104
in-theory        36104
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-510 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-36104.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-510, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-36105
in-theory        36105
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36105.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-510, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-36106
in-theory        36106
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-36106.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-510, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-36107
in-theory        36107
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-510 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-36107.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-510, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-36108
in-theory        36108
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-36108.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-510, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-36109
in-theory        36109
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-36109.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-510, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-36110
in-theory        36110
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-36110.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-510, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-36111
in-theory        36111
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-510 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-36111.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-510, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-36112
in-theory        36112
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36112.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-510, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-36113
in-theory        36113
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-510 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-36113.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-510, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-36114
in-theory        36114
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-510 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-36114.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-510, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-36115
in-theory        36115
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-510 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-36115.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-510, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-36116
in-theory        36116
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-510 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-36116.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-510, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-36117
in-theory        36117
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-36117.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-510, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-36118
in-theory        36118
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-510 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-36118.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-510, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-36119
in-theory        36119
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-36119.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-510, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-36120
in-theory        36120
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-36120.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-510, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-36121
in-theory        36121
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-36121.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-510, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-36122
in-theory        36122
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-510 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-36122.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-510, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-36123
in-theory        36123
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-36123.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-510, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-36124
in-theory        36124
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-36124.        ((A or ((B and C) -> C)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-510, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-36125
in-theory        36125
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-510 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-36125.        ((A or ((B and C) -> C)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-510, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-36126
in-theory        36126
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-510 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-36126.        ((A or ((B and C) -> C)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-510, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-36127
in-theory        36127
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-510 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-36127.        ((A or ((B and C) -> C)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-510, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-36128
in-theory        36128
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-36128.        ((A or ((B and C) -> C)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-510, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-36129
in-theory        36129
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-510 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-36129.        ((A or ((B and C) -> C)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-510, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-36130
in-theory        36130
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-36130.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-510, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-36131
in-theory        36131
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-36131.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-510, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-36132
in-theory        36132
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-510 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36132.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-510, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-36133
in-theory        36133
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-510 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-36133.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-510, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36134
in-theory        36134
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-36134.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-510, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-36135
in-theory        36135
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-510 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-36135.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-510, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-36136
in-theory        36136
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36136.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-510, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-36137
in-theory        36137
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-36137.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-510, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-36138
in-theory        36138
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-36138.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-510, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-36139
in-theory        36139
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-510 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-36139.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-510, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-36140
in-theory        36140
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-36140.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-510, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-36141
in-theory        36141
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-36141.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-510, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-36142
in-theory        36142
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-36142.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-510, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-36143
in-theory        36143
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-510 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36143.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-510, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-36144
in-theory        36144
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-510 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-36144.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-510, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-36145
in-theory        36145
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-510 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-36145.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-510, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-36146
in-theory        36146
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-510 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-36146.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-510, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-36147
in-theory        36147
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-510 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-36147.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-510, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-36148
in-theory        36148
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-510 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-36148.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-510, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-36149
in-theory        36149
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-510 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-36149.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-510, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-36150
in-theory        36150
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-510 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-36150.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-510, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-36151
in-theory        36151
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-510 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-36151.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-510, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-36152
in-theory        36152
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-510 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-36152.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-510, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-36153
in-theory        36153
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-510 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-36153.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-510, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-36154
in-theory        36154
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-510 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-36154.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-510, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-36155
in-theory        36155
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-510 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-36155.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-510, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-36156
in-theory        36156
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-510 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-36156.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-510, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-36157
in-theory        36157
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-510 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-36157.        ((A or ((B and C) -> C)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-510, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-36158
in-theory        36158
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-510 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-36158.        ((A or ((B and C) -> C)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-510, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-36159
in-theory        36159
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-510 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-36159.        ((A or ((B and C) -> C)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-510, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-36160
in-theory        36160
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-510 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-36160.        ((A or ((B and C) -> C)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-510, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-36161
in-theory        36161
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-510 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-36161.        ((A or ((B and C) -> C)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-510, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-36162
in-theory        36162
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-510 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-36162.        ((A or ((B and C) -> C)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-510, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-36163
in-theory        36163
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-510 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-36163.        ((A or ((B and C) -> C)) and (D -> (D and (E -> D)))), M:tm-510, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-36164
in-theory        36164
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-36164.        ((A or ((B and C) -> C)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-510, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-36165
in-theory        36165
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-510 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-36165.        ((A or ((B and C) -> C)) and ((D and E) -> ((D and E) and D))), M:tm-510, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-36166
in-theory        36166
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-510 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-36166.        ((A or ((B and C) -> C)) and ((D and E) -> ((D and E) and E))), M:tm-510, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-36167
in-theory        36167
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-36167.        ((A or ((B and C) -> C)) and (D -> (D and (E -> (D and E))))), M:tm-510, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-36168
in-theory        36168
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-510 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-36168.        ((A or ((B and C) -> C)) and (D -> (D and (D or E)))), M:tm-510, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-36169
in-theory        36169
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-510 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-36169.        ((A or ((B and C) -> C)) and (D -> (D and (E or D)))), M:tm-510, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-36170
in-theory        36170
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-510 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-36170.        ((A or ((B and C) -> C)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-510, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-36171
in-theory        36171
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-36171.        ((A or ((B and C) -> C)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-510, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-36172
in-theory        36172
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-510 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-36172.        ((A or ((B and C) -> C)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-510, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-36173
in-theory        36173
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-36173.        ((A or ((B and C) -> C)) and (D -> (D and (E -> (F -> E))))), M:tm-510, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-36174
in-theory        36174
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-510 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-36174.        ((A or ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-510, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-36175
in-theory        36175
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-510 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-36175.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-510, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-36176
in-theory        36176
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-510 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-36176.        ((A or ((B and C) -> C)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-510, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-36177
in-theory        36177
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-510 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-36177.        ((A or ((B and C) -> C)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-510, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-36178
in-theory        36178
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-510 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-36178.        ((A or ((B and C) -> C)) and (D -> (D and ((E and F) -> E)))), M:tm-510, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-36179
in-theory        36179
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-510 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-36179.        ((A or ((B and C) -> C)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-510, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-36180
in-theory        36180
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-510 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-36180.        ((A or ((B and C) -> C)) and (D -> (D and ((E and F) -> F)))), M:tm-510, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-36181
in-theory        36181
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-510 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-36181.        ((A or ((B and C) -> C)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-510, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-36182
in-theory        36182
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-510 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-36182.        ((A or ((B and C) -> C)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-510, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-36183
in-theory        36183
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-510 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-36183.        ((A or ((B and C) -> C)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-510, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-36184
in-theory        36184
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-510 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-36184.        ((A or ((B and C) -> C)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-510, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-36185
in-theory        36185
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-510 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-36185.        ((A or ((B and C) -> C)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-510, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-36186
in-theory        36186
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-36186.        ((A or ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-510, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-36187
in-theory        36187
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-510 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-36187.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-510, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-36188
in-theory        36188
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-36188.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-510, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-36189
in-theory        36189
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-36189.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-510, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-36190
in-theory        36190
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-510 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-36190.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-510, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-36191
in-theory        36191
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-36191.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-510, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-36192
in-theory        36192
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-510 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-36192.        ((A or ((B and C) -> C)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-510, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-36193
in-theory        36193
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-510 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-36193.        ((A or ((B and C) -> C)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-510, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-36194
in-theory        36194
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-510 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-36194.        ((A or ((B and C) -> C)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-510, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-36195
in-theory        36195
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-510 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-36195.        ((A or ((B and C) -> C)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-510, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-36196
in-theory        36196
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-36196.        ((A or ((B and C) -> C)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-510, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-36197
in-theory        36197
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-510 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-36197.        ((A or ((B and C) -> C)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-510, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-36198
in-theory        36198
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-510 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-36198.        ((A or ((B and C) -> C)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-510, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-36199
in-theory        36199
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-510 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-36199.        ((A or ((B and C) -> C)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-510, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-36200
in-theory        36200
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-510 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36200.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-510, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36201
in-theory        36201
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-510 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36201.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-510, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36202
in-theory        36202
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-510 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36202.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-510, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36203
in-theory        36203
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-510 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36203.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-510, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36204
in-theory        36204
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-510 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36204.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-510, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36205
in-theory        36205
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-510 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-36205.        ((A or ((B and C) -> C)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-510, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-36206
in-theory        36206
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-510 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-36206.        ((A or ((B and C) -> C)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-510, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-36207
in-theory        36207
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-510 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-36207.        ((A or ((B and C) -> C)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-510, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-36208
in-theory        36208
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-36208.        ((A or ((B and C) -> C)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-510, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-36209
in-theory        36209
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-510 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-36209.        ((A or ((B and C) -> C)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-510, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-36210
in-theory        36210
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-510 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36210.        ((A or ((B and C) -> C)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-510, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36211
in-theory        36211
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-510 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36211.        ((A or ((B and C) -> C)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-510, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36212
in-theory        36212
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36212.        ((A or ((B and C) -> C)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-510, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-36213
in-theory        36213
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-510 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-36213.        ((A or ((B and C) -> C)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-510, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-36214
in-theory        36214
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-510 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36214.        ((A or ((B and C) -> C)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-510, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36215
in-theory        36215
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-510 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-36215.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-510, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-36216
in-theory        36216
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-36216.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-510, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-36217
in-theory        36217
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-36217.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-510, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-36218
in-theory        36218
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-36218.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-510, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-36219
in-theory        36219
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-36219.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-510, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-36220
in-theory        36220
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-510 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-36220.        ((A or ((B and C) -> C)) and (D or ((E -> (F -> E)) or G))), M:tm-510, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-36221
in-theory        36221
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-36221.        ((A or ((B and C) -> C)) and (((D -> (E -> D)) or F) or G)), M:tm-510, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-36222
in-theory        36222
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-36222.        ((A or ((B and C) -> C)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-510, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-36223
in-theory        36223
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-510 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-36223.        ((A or ((B and C) -> C)) and (D -> ((E -> (F -> E)) or G))), M:tm-510, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-36224
in-theory        36224
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-510 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-36224.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-510, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-36225
in-theory        36225
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-36225.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-510, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-36226
in-theory        36226
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-36226.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-510, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-36227
in-theory        36227
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-510 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-36227.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-510, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-36228
in-theory        36228
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-36228.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-510, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-36229
in-theory        36229
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-510 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-36229.        ((A or ((B and C) -> C)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-510, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-36230
in-theory        36230
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-510 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-36230.        ((A or ((B and C) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-510, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-36231
in-theory        36231
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-510 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-36231.        ((A or ((B and C) -> C)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-510, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-36232
in-theory        36232
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-510 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-36232.        ((A or ((B and C) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-510, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-36233
in-theory        36233
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-510 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-36233.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-510, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-36234
in-theory        36234
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-36234.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-510, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-36235
in-theory        36235
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-36235.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-510, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-36236
in-theory        36236
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-36236.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-510, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-36237
in-theory        36237
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-36237.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-510, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-36238
in-theory        36238
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-510 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-36238.        ((A or ((B and C) -> C)) and (D or (((E and F) -> E) or G))), M:tm-510, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-36239
in-theory        36239
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-36239.        ((A or ((B and C) -> C)) and ((((D and E) -> D) or F) or G)), M:tm-510, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-36240
in-theory        36240
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-36240.        ((A or ((B and C) -> C)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-510, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-36241
in-theory        36241
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-510 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-36241.        ((A or ((B and C) -> C)) and (D -> (((E and F) -> E) or G))), M:tm-510, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-36242
in-theory        36242
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-510 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-36242.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-510, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-36243
in-theory        36243
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-36243.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-510, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-36244
in-theory        36244
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-36244.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-510, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-36245
in-theory        36245
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-36245.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-510, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-36246
in-theory        36246
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-36246.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-510, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-36247
in-theory        36247
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-510 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-36247.        ((A or ((B and C) -> C)) and (D or (((E and F) -> F) or G))), M:tm-510, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-36248
in-theory        36248
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-36248.        ((A or ((B and C) -> C)) and ((((D and E) -> E) or F) or G)), M:tm-510, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-36249
in-theory        36249
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-36249.        ((A or ((B and C) -> C)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-510, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-36250
in-theory        36250
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-510 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-36250.        ((A or ((B and C) -> C)) and (D -> (((E and F) -> F) or G))), M:tm-510, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-36251
in-theory        36251
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-510 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-36251.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-510, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-36252
in-theory        36252
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-510 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-36252.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-510, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-36253
in-theory        36253
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-510 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-36253.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-510, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-36254
in-theory        36254
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-510 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-36254.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-510, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-36255
in-theory        36255
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-510 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-36255.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-510, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-36256
in-theory        36256
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-510 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-36256.        ((A or ((B and C) -> C)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-510, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-36257
in-theory        36257
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-510 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-36257.        ((A or ((B and C) -> C)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-510, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-36258
in-theory        36258
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-36258.        ((A or ((B and C) -> C)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-510, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-36259
in-theory        36259
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-510 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-36259.        ((A or ((B and C) -> C)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-510, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-36260
in-theory        36260
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-510 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-36260.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-510, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-36261
in-theory        36261
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-36261.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-510, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-36262
in-theory        36262
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-36262.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-510, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-36263
in-theory        36263
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-36263.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-510, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-36264
in-theory        36264
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-36264.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-510, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-36265
in-theory        36265
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-510 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-36265.        ((A or ((B and C) -> C)) and (D or ((E -> (E or F)) or G))), M:tm-510, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-36266
in-theory        36266
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-36266.        ((A or ((B and C) -> C)) and (((D -> (D or E)) or F) or G)), M:tm-510, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-36267
in-theory        36267
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-36267.        ((A or ((B and C) -> C)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-510, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-36268
in-theory        36268
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-510 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-36268.        ((A or ((B and C) -> C)) and (D -> ((E -> (E or F)) or G))), M:tm-510, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-36269
in-theory        36269
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-36269.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-510, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-36270
in-theory        36270
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-36270.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-510, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-36271
in-theory        36271
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36271.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-510, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-36272
in-theory        36272
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-510 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-36272.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-510, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36273
in-theory        36273
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-36273.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-510, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-36274
in-theory        36274
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-510 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-36274.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-510, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-36275
in-theory        36275
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36275.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-510, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-36276
in-theory        36276
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-36276.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-510, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-36277
in-theory        36277
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-510 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-36277.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-510, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-36278
in-theory        36278
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-36278.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-510, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-36279
in-theory        36279
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-36279.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-510, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-36280
in-theory        36280
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-36280.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-510, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-36281
in-theory        36281
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-510 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-36281.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-510, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-36282
in-theory        36282
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36282.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-510, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-36283
in-theory        36283
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-510 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-36283.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-510, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-36284
in-theory        36284
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-510 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-36284.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-510, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-36285
in-theory        36285
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-510 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-36285.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-510, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-36286
in-theory        36286
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-510 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-36286.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-510, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-36287
in-theory        36287
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-36287.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-510, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-36288
in-theory        36288
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-510 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-36288.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-510, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-36289
in-theory        36289
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-36289.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-510, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-36290
in-theory        36290
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-36290.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-510, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-36291
in-theory        36291
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-510 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-36291.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-510, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-36292
in-theory        36292
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-36292.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-510, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-36293
in-theory        36293
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-510 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36293.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-510, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36294
in-theory        36294
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-36294.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-510, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-36295
in-theory        36295
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-36295.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-510, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-36296
in-theory        36296
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-36296.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-510, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-36297
in-theory        36297
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-36297.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-510, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-36298
in-theory        36298
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-510 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-36298.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-510, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-36299
in-theory        36299
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-36299.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-510, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-36300
in-theory        36300
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-36300.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-510, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-36301
in-theory        36301
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-510 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-36301.        ((A or ((B and C) -> C)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-510, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-36302
in-theory        36302
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-510 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-36302.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-510, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-36303
in-theory        36303
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-36303.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-510, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-36304
in-theory        36304
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-36304.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-510, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-36305
in-theory        36305
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-510 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-36305.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-510, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-36306
in-theory        36306
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-36306.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-510, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-36307
in-theory        36307
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-36307.        ((A or ((B and C) -> C)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-510, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-36308
in-theory        36308
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-510 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-36308.        ((A or ((B and C) -> C)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-510, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-36309
in-theory        36309
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-510 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-36309.        ((A or ((B and C) -> C)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-510, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-36310
in-theory        36310
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-510 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-36310.        ((A or ((B and C) -> C)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-510, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-36311
in-theory        36311
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-36311.        ((A or ((B and C) -> C)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-510, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-36312
in-theory        36312
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-510 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-36312.        ((A or ((B and C) -> C)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-510, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-36313
in-theory        36313
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-36313.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-510, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-36314
in-theory        36314
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-36314.        ((A or ((B and C) -> C)) and (D -> (D and (E -> (E or F))))), M:tm-510, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-36315
in-theory        36315
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-36315.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-510, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-36316
in-theory        36316
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-36316.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-510, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-36317
in-theory        36317
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-36317.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-510, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-36318
in-theory        36318
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-36318.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-510, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-36319
in-theory        36319
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-36319.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-510, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-36320
in-theory        36320
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-510 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-36320.        ((A or ((B and C) -> C)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-510, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-36321
in-theory        36321
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-510 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-36321.        ((A or ((B and C) -> C)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-510, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-36322
in-theory        36322
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-36322.        ((A or ((B and C) -> C)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-510, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-36323
in-theory        36323
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-36323.        ((A or ((B and C) -> C)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-510, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-36324
in-theory        36324
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-510 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-36324.        ((A or ((B and C) -> C)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-510, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-36325
in-theory        36325
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-36325.        ((A or ((B and C) -> C)) and (D or (E -> (F -> (F or G))))), M:tm-510, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-36326
in-theory        36326
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-36326.        ((A or ((B and C) -> C)) and ((D -> (E -> (E or F))) or G)), M:tm-510, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-36327
in-theory        36327
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-36327.        ((A or ((B and C) -> C)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-510, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-36328
in-theory        36328
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-510 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-36328.        ((A or ((B and C) -> C)) and ((D -> E) -> (D -> (E or F)))), M:tm-510, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-36329
in-theory        36329
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-36329.        ((A or ((B and C) -> C)) and (D -> (E -> (F -> (F or G))))), M:tm-510, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-36330
in-theory        36330
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-36330.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-510, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-36331
in-theory        36331
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-36331.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-510, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-36332
in-theory        36332
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-36332.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-510, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-36333
in-theory        36333
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-36333.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-510, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-36334
in-theory        36334
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-36334.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-510, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-36335
in-theory        36335
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-36335.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-510, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-36336
in-theory        36336
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-36336.        ((A or ((B and C) -> C)) and (D or (E or (F -> (G -> F))))), M:tm-510, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-36337
in-theory        36337
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-36337.        ((A or ((B and C) -> C)) and ((D or (E -> (F -> E))) or G)), M:tm-510, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-36338
in-theory        36338
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-36338.        ((A or ((B and C) -> C)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-510, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-36339
in-theory        36339
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-36339.        ((A or ((B and C) -> C)) and (D -> (E or (F -> (G -> F))))), M:tm-510, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-36340
in-theory        36340
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36340.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-510, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-36341
in-theory        36341
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-510 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36341.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-510, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-36342
in-theory        36342
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36342.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-510, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-36343
in-theory        36343
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36343.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-510, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-36344
in-theory        36344
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-510 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36344.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-510, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-36345
in-theory        36345
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36345.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-510, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-36346
in-theory        36346
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-510 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36346.        ((A or ((B and C) -> C)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-510, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-36347
in-theory        36347
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-510 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36347.        ((A or ((B and C) -> C)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-510, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-36348
in-theory        36348
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-510 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36348.        ((A or ((B and C) -> C)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-510, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-36349
in-theory        36349
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-510 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-36349.        ((A or ((B and C) -> C)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-510, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-36350
in-theory        36350
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-510 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-36350.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-510, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-36351
in-theory        36351
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-510 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-36351.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-510, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-36352
in-theory        36352
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-510 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-36352.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-510, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-36353
in-theory        36353
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-510 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-36353.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-510, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-36354
in-theory        36354
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-510 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-36354.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-510, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-36355
in-theory        36355
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-510 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-36355.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-510, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-36356
in-theory        36356
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-510 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-36356.        ((A or ((B and C) -> C)) and (D or (E or ((F and G) -> F)))), M:tm-510, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-36357
in-theory        36357
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-36357.        ((A or ((B and C) -> C)) and ((D or ((E and F) -> E)) or G)), M:tm-510, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-36358
in-theory        36358
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-36358.        ((A or ((B and C) -> C)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-510, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-36359
in-theory        36359
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-510 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-36359.        ((A or ((B and C) -> C)) and (D -> (E or ((F and G) -> F)))), M:tm-510, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-36360
in-theory        36360
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-510 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36360.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-510, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-36361
in-theory        36361
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-510 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36361.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-510, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-36362
in-theory        36362
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-510 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36362.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-510, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-36363
in-theory        36363
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-510 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36363.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-510, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-36364
in-theory        36364
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-510 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36364.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-510, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-36365
in-theory        36365
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-510 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36365.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-510, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-36366
in-theory        36366
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-510 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36366.        ((A or ((B and C) -> C)) and (D or (E or ((F and G) -> G)))), M:tm-510, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36367
in-theory        36367
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36367.        ((A or ((B and C) -> C)) and ((D or ((E and F) -> F)) or G)), M:tm-510, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-36368
in-theory        36368
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36368.        ((A or ((B and C) -> C)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-510, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36369
in-theory        36369
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36369.        ((A or ((B and C) -> B)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-500, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36370
in-theory        36370
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G and H) -> H)) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36370.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G and H) -> H)) and E))), M:tm-490, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36371
in-theory        36371
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36371.        ((A or (B -> (C -> B))) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-480, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36372
in-theory        36372
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or ((C and D) -> D)) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7 tm-4)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36372.        (A -> (((B or ((C and D) -> D)) and A) or E)), M:tm-470, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-36373
in-theory        36373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36373.        ((A -> (B -> (B or C))) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-469, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36374
in-theory        36374
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D or ((E and F) -> F)) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-510 ((Am (-> A (or A B))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36374.        ((A or (B -> (B or C))) -> ((D or ((E and F) -> F)) and (B -> (B or C)))), M:tm-466, m:tm-510, u:((Am (-> A (or A B))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (or A B)))))
================================================================
tm-name          tm-36375
in-theory        36375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36375.        ((A -> ((B or ((C and D) -> D)) and A)) and (E -> (E or F))), M:tm-456, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36376
in-theory        36376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36376.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-453, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36377
in-theory        36377
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D or ((E and F) -> F)) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-510 ((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36377.        ((A or ((B -> (B or C)) and A)) -> ((D or ((E and F) -> F)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-510, u:((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-36378
in-theory        36378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and ((E -> (E or F)) and (A -> ((B or ((C and D) -> D)) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36378.        ((A -> ((B or ((C and D) -> D)) and A)) and ((E -> (E or F)) and (A -> ((B or ((C and D) -> D)) and A)))), M:tm-443, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36379
in-theory        36379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36379.        (((A -> (A or B)) or C) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-409, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36380
in-theory        36380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36380.        (((A -> (B -> (A and B))) or C) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-400, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36381
in-theory        36381
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36381.        ((((A and B) -> B) or C) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-391, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36382
in-theory        36382
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36382.        ((((A and B) -> A) or C) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-382, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36383
in-theory        36383
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or ((G and H) -> H)) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36383.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or ((G and H) -> H)) and E))), M:tm-373, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36384
in-theory        36384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36384.        (((A -> (B -> A)) or C) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-364, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36385
in-theory        36385
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C or ((D and E) -> E)) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36385.        (A -> (B -> (((C or ((D and E) -> E)) and A) and B))), M:tm-355, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-36386
in-theory        36386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36386.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-354, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36387
in-theory        36387
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D or ((E and F) -> F)) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-510 ((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36387.        ((A or (B -> (C -> (B and C)))) -> ((D or ((E and F) -> F)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-510, u:((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-36388
in-theory        36388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36388.        ((A -> ((B or ((C and D) -> D)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36389
in-theory        36389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D or ((E and F) -> F)) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36389.        (((A -> B) -> (A -> (A and B))) and (C -> ((D or ((E and F) -> F)) and C))), M:tm-338, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36390
in-theory        36390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C or ((D and E) -> E)) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-510 ((Am (-> A (and A B))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36390.        (((A -> B) or (A -> (A and B))) -> ((C or ((D and E) -> E)) and (A -> (A and B)))), M:tm-335, m:tm-510, u:((Am (-> A (and A B))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (and A B)))))
================================================================
tm-name          tm-36391
in-theory        36391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and (A -> (A and ((B or ((C and D) -> D)) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36391.        ((A -> ((B or ((C and D) -> D)) and A)) and (A -> (A and ((B or ((C and D) -> D)) and A)))), M:tm-328, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-36392
in-theory        36392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B or ((C and D) -> D)) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36392.        ((A -> ((B or ((C and D) -> D)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B or ((C and D) -> D)) and A)))), M:tm-327, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36393
in-theory        36393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and (((E and F) -> F) and (A -> ((B or ((C and D) -> D)) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36393.        ((A -> ((B or ((C and D) -> D)) and A)) and (((E and F) -> F) and (A -> ((B or ((C and D) -> D)) and A)))), M:tm-326, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36394
in-theory        36394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and (((E and F) -> E) and (A -> ((B or ((C and D) -> D)) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36394.        ((A -> ((B or ((C and D) -> D)) and A)) and (((E and F) -> E) and (A -> ((B or ((C and D) -> D)) and A)))), M:tm-325, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36395
in-theory        36395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B or ((C and D) -> D)) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36395.        ((A -> ((B or ((C and D) -> D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B or ((C and D) -> D)) and A)))), M:tm-324, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36396
in-theory        36396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and ((E -> (F -> E)) and (A -> ((B or ((C and D) -> D)) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36396.        ((A -> ((B or ((C and D) -> D)) and A)) and ((E -> (F -> E)) and (A -> ((B or ((C and D) -> D)) and A)))), M:tm-323, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36397
in-theory        36397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36397.        ((A -> ((B or ((C and D) -> D)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36398
in-theory        36398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36398.        ((A -> ((B or ((C and D) -> D)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36399
in-theory        36399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36399.        ((A -> ((B or ((C and D) -> D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36400
in-theory        36400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36400.        ((A -> ((B or ((C and D) -> D)) and A)) and (A -> A)), M:tm-316, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-36401
in-theory        36401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36401.        ((A -> ((B or ((C and D) -> D)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36402
in-theory        36402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and ((A -> (not ((B or ((C and D) -> D)) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36402.        ((A -> ((B or ((C and D) -> D)) and A)) and ((A -> (not ((B or ((C and D) -> D)) and A))) -> (not A))), M:tm-313, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-36403
in-theory        36403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and ((((B or ((C and D) -> D)) and A) -> E) -> ((A or ((B or ((C and D) -> D)) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36403.        ((A -> ((B or ((C and D) -> D)) and A)) and ((((B or ((C and D) -> D)) and A) -> E) -> ((A or ((B or ((C and D) -> D)) and A)) -> E))), M:tm-312, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-36404
in-theory        36404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and (E or (A -> ((B or ((C and D) -> D)) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36404.        ((A -> ((B or ((C and D) -> D)) and A)) and (E or (A -> ((B or ((C and D) -> D)) and A)))), M:tm-311, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36405
in-theory        36405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and ((A -> ((B or ((C and D) -> D)) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36405.        ((A -> ((B or ((C and D) -> D)) and A)) and ((A -> ((B or ((C and D) -> D)) and A)) or E)), M:tm-310, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36406
in-theory        36406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and (E -> ((A -> ((B or ((C and D) -> D)) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36406.        ((A -> ((B or ((C and D) -> D)) and A)) and (E -> ((A -> ((B or ((C and D) -> D)) and A)) and E))), M:tm-309, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36407
in-theory        36407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and (E -> (A -> ((B or ((C and D) -> D)) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36407.        ((A -> ((B or ((C and D) -> D)) and A)) and (E -> (A -> ((B or ((C and D) -> D)) and A)))), M:tm-305, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36408
in-theory        36408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36408.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-303, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36409
in-theory        36409
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D or ((E and F) -> F)) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-510 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36409.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D or ((E and F) -> F)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-510, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-36410
in-theory        36410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36410.        ((A -> (((B and C) -> C) and A)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-270, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36411
in-theory        36411
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D or ((E and F) -> F)) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-510 ((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36411.        ((A or (((B and C) -> C) and A)) -> ((D or ((E and F) -> F)) and (((B and C) -> C) and A))), M:tm-267, m:tm-510, u:((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-36412
in-theory        36412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36412.        ((A -> (((B and C) -> B) and A)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-239, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36413
in-theory        36413
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D or ((E and F) -> F)) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-510 ((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36413.        ((A or (((B and C) -> B) and A)) -> ((D or ((E and F) -> F)) and (((B and C) -> B) and A))), M:tm-236, m:tm-510, u:((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-36414
in-theory        36414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or ((G and H) -> H)) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36414.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or ((G and H) -> H)) and E))), M:tm-210, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36415
in-theory        36415
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or ((F and G) -> G)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-510 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (and Cm Dm) Dm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-7 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36415.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or ((F and G) -> G)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-510, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (and Cm Dm) Dm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-36416
in-theory        36416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36416.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-183, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36417
in-theory        36417
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D or ((E and F) -> F)) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-510 ((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36417.        ((A or ((B -> (C -> B)) and A)) -> ((D or ((E and F) -> F)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-510, u:((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-36418
in-theory        36418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36418.        ((A -> ((B and C) -> C)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-157, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36419
in-theory        36419
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D or ((E and F) -> F)) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-510 ((Am (-> (and A B) B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36419.        ((A or ((B and C) -> C)) -> ((D or ((E and F) -> F)) and ((B and C) -> C))), M:tm-154, m:tm-510, u:((Am (-> (and A B) B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> (and A B) B))))
================================================================
tm-name          tm-36420
in-theory        36420
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36420.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-147, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36421
in-theory        36421
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or ((E and F) -> F)) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-510 ((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36421.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or ((E and F) -> F)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-510, u:((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-36422
in-theory        36422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36422.        ((A -> ((B and C) -> B)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-134, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36423
in-theory        36423
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D or ((E and F) -> F)) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-510 ((Am (-> (and A B) A)) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36423.        ((A or ((B and C) -> B)) -> ((D or ((E and F) -> F)) and ((B and C) -> B))), M:tm-131, m:tm-510, u:((Am (-> (and A B) A)) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> (and A B) A))))
================================================================
tm-name          tm-36424
in-theory        36424
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36424.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-125, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36425
in-theory        36425
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or ((E and F) -> F)) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-510 ((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-7 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36425.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or ((E and F) -> F)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-510, u:((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-36426
in-theory        36426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G and H) -> H)) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36426.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or ((G and H) -> H)) and E))), M:tm-113, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36427
in-theory        36427
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or ((F and G) -> G)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-510 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36427.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or ((F and G) -> G)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-510, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-36428
in-theory        36428
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36428.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-105, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36429
in-theory        36429
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or ((E and F) -> F)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-510 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36429.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or ((E and F) -> F)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-510, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-36430
in-theory        36430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D or ((E and F) -> F)) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36430.        (((A -> B) -> (A -> A)) and (C -> ((D or ((E and F) -> F)) and C))), M:tm-95, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36431
in-theory        36431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C or ((D and E) -> E)) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-510 ((Am (-> A A)) (B (and (or Bm (-> (and Cm Dm) Dm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36431.        (((A -> B) or (A -> A)) -> ((C or ((D and E) -> E)) and (A -> A))), M:tm-92, m:tm-510, u:((Am (-> A A)) (B (and (or Bm (-> (and Cm Dm) Dm)) (-> A A))))
================================================================
tm-name          tm-36432
in-theory        36432
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C or ((D and E) -> E)) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7 tm-4)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36432.        (A -> (B -> ((C or ((D and E) -> E)) and A))), M:tm-84, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-36433
in-theory        36433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36433.        ((A -> (B -> (C -> B))) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-83, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36434
in-theory        36434
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D or ((E and F) -> F)) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-510 ((Am (-> A (-> B A))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36434.        ((A or (B -> (C -> B))) -> ((D or ((E and F) -> F)) and (B -> (C -> B)))), M:tm-80, m:tm-510, u:((Am (-> A (-> B A))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (-> B A)))))
================================================================
tm-name          tm-36435
in-theory        36435
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C or ((D and E) -> E)) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-10 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36435.        (((not (not A)) -> A) and (B -> ((C or ((D and E) -> E)) and B))), M:tm-76, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36436
in-theory        36436
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B or ((C and D) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-7 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36436.        (((not (not A)) or A) -> ((B or ((C and D) -> D)) and A)), M:tm-73, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-36437
in-theory        36437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or ((E and F) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-9 tm-7 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36437.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or ((E and F) -> F)) and C))), M:tm-69, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36438
in-theory        36438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or ((D and E) -> E)) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-510 ((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-7 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36438.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or ((D and E) -> E)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-510, u:((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-36439
in-theory        36439
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36439.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-54, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36440
in-theory        36440
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or ((E and F) -> F)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-510 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-7 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36440.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or ((E and F) -> F)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-510, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-36441
in-theory        36441
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C or ((D and E) -> E)) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-510 ((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36441.        ((A or (B or A)) -> ((C or ((D and E) -> E)) and (B or A))), M:tm-50, m:tm-510, u:((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (or A B))))
================================================================
tm-name          tm-36442
in-theory        36442
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C or ((D and E) -> E)) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-510 ((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36442.        ((A or (A or B)) -> ((C or ((D and E) -> E)) and (A or B))), M:tm-49, m:tm-510, u:((Am (or A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (or A B))))
================================================================
tm-name          tm-36443
in-theory        36443
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C or ((D and E) -> E)) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-510 ((Am (-> A (and B A))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-7 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36443.        ((A or (B -> (A and B))) -> ((C or ((D and E) -> E)) and (B -> (A and B)))), M:tm-48, m:tm-510, u:((Am (-> A (and B A))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (and B A)))))
================================================================
tm-name          tm-36444
in-theory        36444
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C or ((D and E) -> E)) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36444.        (((A and B) or B) -> ((C or ((D and E) -> E)) and B)), M:tm-47, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-36445
in-theory        36445
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C or ((D and E) -> E)) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-7 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36445.        (((A and B) or A) -> ((C or ((D and E) -> E)) and A)), M:tm-46, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-36446
in-theory        36446
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E and F) -> F)) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-510 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36446.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E and F) -> F)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-510, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-36447
in-theory        36447
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C or ((D and E) -> E)) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-510 ((Am (-> A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36447.        ((A or (B -> A)) -> ((C or ((D and E) -> E)) and (B -> A))), M:tm-44, m:tm-510, u:((Am (-> A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A B))))
================================================================
tm-name          tm-36448
in-theory        36448
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D or ((E and F) -> F)) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36448.        ((A -> (B or A)) and (C -> ((D or ((E and F) -> F)) and C))), M:tm-42, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36449
in-theory        36449
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D or ((E and F) -> F)) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36449.        ((A -> (A or B)) and (C -> ((D or ((E and F) -> F)) and C))), M:tm-32, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36450
in-theory        36450
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B or ((C and D) -> D)) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36450.        (A -> (A and ((B or ((C and D) -> D)) and A))), M:tm-24, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-36451
in-theory        36451
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D or ((E and F) -> F)) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36451.        ((A -> (B -> (A and B))) and (C -> ((D or ((E and F) -> F)) and C))), M:tm-23, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36452
in-theory        36452
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D or ((E and F) -> F)) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36452.        (((A and B) -> B) and (C -> ((D or ((E and F) -> F)) and C))), M:tm-22, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36453
in-theory        36453
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D or ((E and F) -> F)) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36453.        (((A and B) -> A) and (C -> ((D or ((E and F) -> F)) and C))), M:tm-21, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36454
in-theory        36454
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36454.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-20, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36455
in-theory        36455
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D or ((E and F) -> F)) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36455.        ((A -> (B -> A)) and (C -> ((D or ((E and F) -> F)) and C))), M:tm-19, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36456
in-theory        36456
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B or ((C and D) -> D)) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-9 tm-5 tm-7 tm-4)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36456.        ((A -> (not ((B or ((C and D) -> D)) and A))) -> (not A)), M:tm-9, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-36457
in-theory        36457
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B and C) -> C)) and D) -> E) -> ((D or ((A or ((B and C) -> C)) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-8 tm-5 tm-7 tm-4)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36457.        ((((A or ((B and C) -> C)) and D) -> E) -> ((D or ((A or ((B and C) -> C)) and D)) -> E)), M:tm-8, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-36458
in-theory        36458
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C or ((D and E) -> E)) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36458.        (A or (B -> ((C or ((D and E) -> E)) and B))), M:tm-7, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36459
in-theory        36459
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-6 tm-5 tm-7 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36459.        ((A -> ((B or ((C and D) -> D)) and A)) or E), M:tm-6, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36460
in-theory        36460
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C or ((D and E) -> E)) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36460.        (A -> ((B -> ((C or ((D and E) -> E)) and B)) and A)), M:tm-5, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36461
in-theory        36461
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C or ((D and E) -> E)) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-1 tm-5 tm-7 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36461.        (A -> (B -> ((C or ((D and E) -> E)) and B))), M:tm-1, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-36462
in-theory        36462
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-510 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36462.        ((A or ((B and C) -> C)) and (D -> (E or ((F and G) -> G)))), M:tm-510, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36463
in-theory        36463
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-500 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36463.        ((A or ((B and C) -> B)) and (D -> (E or ((F and G) -> G)))), M:tm-500, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36464
in-theory        36464
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-490 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36464.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G and H) -> H)))), M:tm-490, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36465
in-theory        36465
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-480 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36465.        ((A or (B -> (C -> B))) and (D -> (E or ((F and G) -> G)))), M:tm-480, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36466
in-theory        36466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-469 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36466.        ((A -> (B -> (B or C))) and (D -> (E or ((F and G) -> G)))), M:tm-469, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36467
in-theory        36467
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-466 tm-511 ((Am (-> A (or A B))) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36467.        ((A or (B -> (B or C))) -> (D or ((E and F) -> F))), M:tm-466, m:tm-511, u:((Am (-> A (or A B))) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36468
in-theory        36468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36468.        ((A -> (B or ((C and D) -> D))) and (E -> (E or F))), M:tm-456, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36469
in-theory        36469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-453 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36469.        ((A -> ((B -> (B or C)) and A)) and (D -> (E or ((F and G) -> G)))), M:tm-453, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36470
in-theory        36470
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-450 tm-511 ((Am (and (-> A (or A B)) C)) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36470.        ((A or ((B -> (B or C)) and A)) -> (D or ((E and F) -> F))), M:tm-450, m:tm-511, u:((Am (and (-> A (or A B)) C)) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36471
in-theory        36471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and ((E -> (E or F)) and (A -> (B or ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36471.        ((A -> (B or ((C and D) -> D))) and ((E -> (E or F)) and (A -> (B or ((C and D) -> D))))), M:tm-443, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36472
in-theory        36472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-409 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36472.        (((A -> (A or B)) or C) and (D -> (E or ((F and G) -> G)))), M:tm-409, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36473
in-theory        36473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-400 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36473.        (((A -> (B -> (A and B))) or C) and (D -> (E or ((F and G) -> G)))), M:tm-400, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36474
in-theory        36474
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-391 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36474.        ((((A and B) -> B) or C) and (D -> (E or ((F and G) -> G)))), M:tm-391, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36475
in-theory        36475
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-382 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36475.        ((((A and B) -> A) or C) and (D -> (E or ((F and G) -> G)))), M:tm-382, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36476
in-theory        36476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-373 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36476.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or ((G and H) -> H)))), M:tm-373, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36477
in-theory        36477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-364 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36477.        (((A -> (B -> A)) or C) and (D -> (E or ((F and G) -> G)))), M:tm-364, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36478
in-theory        36478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-354 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36478.        ((A -> (B -> (C -> (B and C)))) and (D -> (E or ((F and G) -> G)))), M:tm-354, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36479
in-theory        36479
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-351 tm-511 ((Am (-> A (-> B (and A B)))) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36479.        ((A or (B -> (C -> (B and C)))) -> (D or ((E and F) -> F))), M:tm-351, m:tm-511, u:((Am (-> A (-> B (and A B)))) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36480
in-theory        36480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36480.        ((A -> (B or ((C and D) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36481
in-theory        36481
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) -> D) -> ((A or ((B and C) -> C)) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-511 ((Am (-> (or Bm (-> (and Cm Dm) Dm)) B)) (A (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36481.        (((A or ((B and C) -> C)) -> D) -> ((A or ((B and C) -> C)) and D)), M:tm-339, m:tm-511, u:((Am (-> (or Bm (-> (and Cm Dm) Dm)) B)) (A (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36482
in-theory        36482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D or ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-338 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36482.        (((A -> B) -> (A -> (A and B))) and (C -> (D or ((E and F) -> F)))), M:tm-338, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36483
in-theory        36483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C or ((D and E) -> E)))
theorem-size     17
proof            (modus-ponens tm-335 tm-511 ((Am (-> A (and A B))) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36483.        (((A -> B) or (A -> (A and B))) -> (C or ((D and E) -> E))), M:tm-335, m:tm-511, u:((Am (-> A (and A B))) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36484
in-theory        36484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (A -> (A and (B or ((C and D) -> D)))))
theorem-size     21
proof            (modus-ponens tm-328 tm-511 ((A Am) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36484.        ((A -> (B or ((C and D) -> D))) and (A -> (A and (B or ((C and D) -> D))))), M:tm-328, m:tm-511, u:((A Am) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36485
in-theory        36485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and ((E -> (F -> (E and F))) and (A -> (B or ((C and D) -> D)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36485.        ((A -> (B or ((C and D) -> D))) and ((E -> (F -> (E and F))) and (A -> (B or ((C and D) -> D))))), M:tm-327, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36486
in-theory        36486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (((E and F) -> F) and (A -> (B or ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36486.        ((A -> (B or ((C and D) -> D))) and (((E and F) -> F) and (A -> (B or ((C and D) -> D))))), M:tm-326, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36487
in-theory        36487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (((E and F) -> E) and (A -> (B or ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36487.        ((A -> (B or ((C and D) -> D))) and (((E and F) -> E) and (A -> (B or ((C and D) -> D))))), M:tm-325, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36488
in-theory        36488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B or ((C and D) -> D)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36488.        ((A -> (B or ((C and D) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B or ((C and D) -> D))))), M:tm-324, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36489
in-theory        36489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and ((E -> (F -> E)) and (A -> (B or ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36489.        ((A -> (B or ((C and D) -> D))) and ((E -> (F -> E)) and (A -> (B or ((C and D) -> D))))), M:tm-323, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36490
in-theory        36490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36490.        ((A -> (B or ((C and D) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36491
in-theory        36491
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or ((C and D) -> D)) -> E)) -> (B or ((C and D) -> D))) and ((A and ((B or ((C and D) -> D)) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-511 ((Am (and A (-> (or Bm (-> (and Cm Dm) Dm)) C))) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36491.        (((A and ((B or ((C and D) -> D)) -> E)) -> (B or ((C and D) -> D))) and ((A and ((B or ((C and D) -> D)) -> E)) -> E)), M:tm-321, m:tm-511, u:((Am (and A (-> (or Bm (-> (and Cm Dm) Dm)) C))) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36492
in-theory        36492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36492.        ((A -> (B or ((C and D) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36493
in-theory        36493
times-derived    1
----------------------------------------------------------------
theorem          (((((A or ((B and C) -> C)) -> D) and E) -> (A or ((B and C) -> C))) and ((((A or ((B and C) -> C)) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-511 ((Am (and (-> (or Bm (-> (and Cm Dm) Dm)) B) C)) (A (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36493.        (((((A or ((B and C) -> C)) -> D) and E) -> (A or ((B and C) -> C))) and ((((A or ((B and C) -> C)) -> D) and E) -> D)), M:tm-319, m:tm-511, u:((Am (and (-> (or Bm (-> (and Cm Dm) Dm)) B) C)) (A (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36494
in-theory        36494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36494.        ((A -> (B or ((C and D) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36495
in-theory        36495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-511 ((A Am) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36495.        ((A -> (B or ((C and D) -> D))) and (A -> A)), M:tm-316, m:tm-511, u:((A Am) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36496
in-theory        36496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36496.        ((A -> (B or ((C and D) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36497
in-theory        36497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and ((A -> (not (B or ((C and D) -> D)))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-511 ((A Am) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36497.        ((A -> (B or ((C and D) -> D))) and ((A -> (not (B or ((C and D) -> D)))) -> (not A))), M:tm-313, m:tm-511, u:((A Am) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36498
in-theory        36498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (((B or ((C and D) -> D)) -> E) -> ((A or (B or ((C and D) -> D))) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-511 ((A Am) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36498.        ((A -> (B or ((C and D) -> D))) and (((B or ((C and D) -> D)) -> E) -> ((A or (B or ((C and D) -> D))) -> E))), M:tm-312, m:tm-511, u:((A Am) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36499
in-theory        36499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (E or (A -> (B or ((C and D) -> D)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36499.        ((A -> (B or ((C and D) -> D))) and (E or (A -> (B or ((C and D) -> D))))), M:tm-311, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36500
in-theory        36500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and ((A -> (B or ((C and D) -> D))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36500.        ((A -> (B or ((C and D) -> D))) and ((A -> (B or ((C and D) -> D))) or E)), M:tm-310, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36501
in-theory        36501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (E -> ((A -> (B or ((C and D) -> D))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36501.        ((A -> (B or ((C and D) -> D))) and (E -> ((A -> (B or ((C and D) -> D))) and E))), M:tm-309, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36502
in-theory        36502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (E -> (A -> (B or ((C and D) -> D)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36502.        ((A -> (B or ((C and D) -> D))) and (E -> (A -> (B or ((C and D) -> D))))), M:tm-305, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36503
in-theory        36503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-303 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36503.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or ((F and G) -> G)))), M:tm-303, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36504
in-theory        36504
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D or ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-300 tm-511 ((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36504.        ((A or ((B -> (C -> (B and C))) and A)) -> (D or ((E and F) -> F))), M:tm-300, m:tm-511, u:((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36505
in-theory        36505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-270 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36505.        ((A -> (((B and C) -> C) and A)) and (D -> (E or ((F and G) -> G)))), M:tm-270, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36506
in-theory        36506
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-267 tm-511 ((Am (and (-> (and A B) B) C)) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36506.        ((A or (((B and C) -> C) and A)) -> (D or ((E and F) -> F))), M:tm-267, m:tm-511, u:((Am (and (-> (and A B) B) C)) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36507
in-theory        36507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-239 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36507.        ((A -> (((B and C) -> B) and A)) and (D -> (E or ((F and G) -> G)))), M:tm-239, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36508
in-theory        36508
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-236 tm-511 ((Am (and (-> (and A B) A) C)) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36508.        ((A or (((B and C) -> B) and A)) -> (D or ((E and F) -> F))), M:tm-236, m:tm-511, u:((Am (and (-> (and A B) A) C)) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36509
in-theory        36509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-210 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36509.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or ((G and H) -> H)))), M:tm-210, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36510
in-theory        36510
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-207 tm-511 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36510.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or ((F and G) -> G))), M:tm-207, m:tm-511, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36511
in-theory        36511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-183 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36511.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E or ((F and G) -> G)))), M:tm-183, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36512
in-theory        36512
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-180 tm-511 ((Am (and (-> A (-> B A)) C)) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36512.        ((A or ((B -> (C -> B)) and A)) -> (D or ((E and F) -> F))), M:tm-180, m:tm-511, u:((Am (and (-> A (-> B A)) C)) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36513
in-theory        36513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-157 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36513.        ((A -> ((B and C) -> C)) and (D -> (E or ((F and G) -> G)))), M:tm-157, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36514
in-theory        36514
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-154 tm-511 ((Am (-> (and A B) B)) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36514.        ((A or ((B and C) -> C)) -> (D or ((E and F) -> F))), M:tm-154, m:tm-511, u:((Am (-> (and A B) B)) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36515
in-theory        36515
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-147 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36515.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or ((F and G) -> G)))), M:tm-147, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36516
in-theory        36516
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-144 tm-511 ((Am (-> (and A (-> B C)) C)) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36516.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or ((E and F) -> F))), M:tm-144, m:tm-511, u:((Am (-> (and A (-> B C)) C)) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36517
in-theory        36517
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B or ((C and D) -> D)) -> E)) -> (B or ((C and D) -> D)))
theorem-size     19
proof            (modus-ponens tm-142 tm-511 ((Am (and A (-> (or Bm (-> (and Cm Dm) Dm)) C))) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36517.        ((A and ((B or ((C and D) -> D)) -> E)) -> (B or ((C and D) -> D))), M:tm-142, m:tm-511, u:((Am (and A (-> (or Bm (-> (and Cm Dm) Dm)) C))) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36518
in-theory        36518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-134 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36518.        ((A -> ((B and C) -> B)) and (D -> (E or ((F and G) -> G)))), M:tm-134, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36519
in-theory        36519
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-131 tm-511 ((Am (-> (and A B) A)) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36519.        ((A or ((B and C) -> B)) -> (D or ((E and F) -> F))), M:tm-131, m:tm-511, u:((Am (-> (and A B) A)) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36520
in-theory        36520
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-125 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36520.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or ((F and G) -> G)))), M:tm-125, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36521
in-theory        36521
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-122 tm-511 ((Am (-> (and (-> A B) C) B)) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-7 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36521.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or ((E and F) -> F))), M:tm-122, m:tm-511, u:((Am (-> (and (-> A B) C) B)) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36522
in-theory        36522
times-derived    1
----------------------------------------------------------------
theorem          ((((A or ((B and C) -> C)) -> D) and E) -> (A or ((B and C) -> C)))
theorem-size     19
proof            (modus-ponens tm-120 tm-511 ((Am (and (-> (or Bm (-> (and Cm Dm) Dm)) B) C)) (A (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36522.        ((((A or ((B and C) -> C)) -> D) and E) -> (A or ((B and C) -> C))), M:tm-120, m:tm-511, u:((Am (and (-> (or Bm (-> (and Cm Dm) Dm)) B) C)) (A (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36523
in-theory        36523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-113 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36523.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or ((G and H) -> H)))), M:tm-113, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36524
in-theory        36524
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-110 tm-511 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-7 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36524.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or ((F and G) -> G))), M:tm-110, m:tm-511, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36525
in-theory        36525
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or ((F and G) -> G))))
theorem-size     29
proof            (modus-ponens tm-105 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36525.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or ((F and G) -> G)))), M:tm-105, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36526
in-theory        36526
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or ((E and F) -> F)))
theorem-size     27
proof            (modus-ponens tm-102 tm-511 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36526.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or ((E and F) -> F))), M:tm-102, m:tm-511, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36527
in-theory        36527
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) -> D) -> (A or ((B and C) -> C)))
theorem-size     17
proof            (modus-ponens tm-96 tm-511 ((Am (-> (or Bm (-> (and Cm Dm) Dm)) B)) (A (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36527.        (((A or ((B and C) -> C)) -> D) -> (A or ((B and C) -> C))), M:tm-96, m:tm-511, u:((Am (-> (or Bm (-> (and Cm Dm) Dm)) B)) (A (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36528
in-theory        36528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D or ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-95 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36528.        (((A -> B) -> (A -> A)) and (C -> (D or ((E and F) -> F)))), M:tm-95, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36529
in-theory        36529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C or ((D and E) -> E)))
theorem-size     15
proof            (modus-ponens tm-92 tm-511 ((Am (-> A A)) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36529.        (((A -> B) or (A -> A)) -> (C or ((D and E) -> E))), M:tm-92, m:tm-511, u:((Am (-> A A)) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36530
in-theory        36530
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C or ((D and E) -> E))))
theorem-size     11
proof            (modus-ponens tm-84 tm-511 ((A Am) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-4)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36530.        (A -> (B -> (C or ((D and E) -> E)))), M:tm-84, m:tm-511, u:((A Am) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36531
in-theory        36531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-83 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36531.        ((A -> (B -> (C -> B))) and (D -> (E or ((F and G) -> G)))), M:tm-83, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36532
in-theory        36532
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-80 tm-511 ((Am (-> A (-> B A))) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36532.        ((A or (B -> (C -> B))) -> (D or ((E and F) -> F))), M:tm-80, m:tm-511, u:((Am (-> A (-> B A))) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36533
in-theory        36533
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A or ((B and C) -> C)) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-511 ((Am (not (not (-> (or Bm (-> (and Cm Dm) Dm)) B)))) (A (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-7 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36533.        ((not (not ((A or ((B and C) -> C)) -> D))) -> D), M:tm-77, m:tm-511, u:((Am (not (not (-> (or Bm (-> (and Cm Dm) Dm)) B)))) (A (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36534
in-theory        36534
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C or ((D and E) -> E))))
theorem-size     15
proof            (modus-ponens tm-76 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36534.        (((not (not A)) -> A) and (B -> (C or ((D and E) -> E)))), M:tm-76, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36535
in-theory        36535
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B or ((C and D) -> D)))
theorem-size     13
proof            (modus-ponens tm-73 tm-511 ((A Am) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36535.        (((not (not A)) or A) -> (B or ((C and D) -> D))), M:tm-73, m:tm-511, u:((A Am) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36536
in-theory        36536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or ((E and F) -> F))))
theorem-size     21
proof            (modus-ponens tm-69 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36536.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or ((E and F) -> F)))), M:tm-69, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36537
in-theory        36537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or ((D and E) -> E)))
theorem-size     19
proof            (modus-ponens tm-66 tm-511 ((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-7 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36537.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or ((D and E) -> E))), M:tm-66, m:tm-511, u:((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36538
in-theory        36538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-54 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36538.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or ((F and G) -> G)))), M:tm-54, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36539
in-theory        36539
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-51 tm-511 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36539.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or ((E and F) -> F))), M:tm-51, m:tm-511, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36540
in-theory        36540
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-50 tm-511 ((Am (or A B)) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36540.        ((A or (B or A)) -> (C or ((D and E) -> E))), M:tm-50, m:tm-511, u:((Am (or A B)) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36541
in-theory        36541
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-49 tm-511 ((Am (or A B)) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36541.        ((A or (A or B)) -> (C or ((D and E) -> E))), M:tm-49, m:tm-511, u:((Am (or A B)) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36542
in-theory        36542
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or ((D and E) -> E)))
theorem-size     15
proof            (modus-ponens tm-48 tm-511 ((Am (-> A (and B A))) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36542.        ((A or (B -> (A and B))) -> (C or ((D and E) -> E))), M:tm-48, m:tm-511, u:((Am (-> A (and B A))) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36543
in-theory        36543
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-47 tm-511 ((A Am) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36543.        (((A and B) or B) -> (C or ((D and E) -> E))), M:tm-47, m:tm-511, u:((A Am) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36544
in-theory        36544
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-46 tm-511 ((A Am) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36544.        (((A and B) or A) -> (C or ((D and E) -> E))), M:tm-46, m:tm-511, u:((A Am) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36545
in-theory        36545
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-45 tm-511 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36545.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E and F) -> F))), M:tm-45, m:tm-511, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36546
in-theory        36546
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-44 tm-511 ((Am (-> A B)) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36546.        ((A or (B -> A)) -> (C or ((D and E) -> E))), M:tm-44, m:tm-511, u:((Am (-> A B)) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36547
in-theory        36547
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-42 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36547.        ((A -> (B or A)) and (C -> (D or ((E and F) -> F)))), M:tm-42, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36548
in-theory        36548
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-32 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36548.        ((A -> (A or B)) and (C -> (D or ((E and F) -> F)))), M:tm-32, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36549
in-theory        36549
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B or ((C and D) -> D))))
theorem-size     11
proof            (modus-ponens tm-24 tm-511 ((A Am) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36549.        (A -> (A and (B or ((C and D) -> D)))), M:tm-24, m:tm-511, u:((A Am) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36550
in-theory        36550
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D or ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-23 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36550.        ((A -> (B -> (A and B))) and (C -> (D or ((E and F) -> F)))), M:tm-23, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36551
in-theory        36551
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-22 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36551.        (((A and B) -> B) and (C -> (D or ((E and F) -> F)))), M:tm-22, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36552
in-theory        36552
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-21 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36552.        (((A and B) -> A) and (C -> (D or ((E and F) -> F)))), M:tm-21, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36553
in-theory        36553
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-20 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36553.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or ((F and G) -> G)))), M:tm-20, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36554
in-theory        36554
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-19 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36554.        ((A -> (B -> A)) and (C -> (D or ((E and F) -> F)))), M:tm-19, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36555
in-theory        36555
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B or ((C and D) -> D)) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-511 ((Am (and A (-> (or Bm (-> (and Cm Dm) Dm)) C))) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36555.        ((A and ((B or ((C and D) -> D)) -> E)) -> E), M:tm-17, m:tm-511, u:((Am (and A (-> (or Bm (-> (and Cm Dm) Dm)) C))) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36556
in-theory        36556
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B and C) -> C)) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-511 ((Am (and (-> (or Bm (-> (and Cm Dm) Dm)) B) C)) (A (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-7 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36556.        ((((A or ((B and C) -> C)) -> D) and E) -> D), M:tm-15, m:tm-511, u:((Am (and (-> (or Bm (-> (and Cm Dm) Dm)) B) C)) (A (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36557
in-theory        36557
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B or ((C and D) -> D)))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-511 ((A Am) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-9 tm-1 tm-7 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36557.        ((A -> (not (B or ((C and D) -> D)))) -> (not A)), M:tm-9, m:tm-511, u:((A Am) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36558
in-theory        36558
times-derived    2
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) -> D) -> ((E or (A or ((B and C) -> C))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-511 ((A Am) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-4)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36558.        (((A or ((B and C) -> C)) -> D) -> ((E or (A or ((B and C) -> C))) -> D)), M:tm-8, m:tm-511, u:((A Am) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-36559
in-theory        36559
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C or ((D and E) -> E))))
theorem-size     11
proof            (modus-ponens tm-7 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-7 tm-1 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36559.        (A or (B -> (C or ((D and E) -> E)))), M:tm-7, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36560
in-theory        36560
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-6 tm-1 tm-7 tm-4)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36560.        ((A -> (B or ((C and D) -> D))) or E), M:tm-6, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36561
in-theory        36561
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C or ((D and E) -> E))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-36561.        (A -> ((B -> (C or ((D and E) -> E))) and A)), M:tm-5, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-36562
in-theory        36562
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-510 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36562.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-510, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36563
in-theory        36563
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-500 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36563.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-500, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36564
in-theory        36564
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-490 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36564.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (I -> (H and I)))))), M:tm-490, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36565
in-theory        36565
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-480 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36565.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-480, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36566
in-theory        36566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-469 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36566.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-469, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36567
in-theory        36567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36567.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (F -> (F or G))), M:tm-456, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36568
in-theory        36568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-453 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36568.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-453, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36569
in-theory        36569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (A or B)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36569.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (A or B)) and (C or (D -> (E -> (D and E))))))), M:tm-443, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36570
in-theory        36570
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-409 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36570.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-409, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36571
in-theory        36571
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-400 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36571.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-400, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36572
in-theory        36572
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-391 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36572.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-391, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36573
in-theory        36573
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-382 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36573.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-382, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36574
in-theory        36574
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-373 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36574.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or (H -> (I -> (H and I)))))), M:tm-373, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36575
in-theory        36575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-364 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36575.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-364, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36576
in-theory        36576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-354 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36576.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-354, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36577
in-theory        36577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36577.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36578
in-theory        36578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-338 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36578.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or (F -> (G -> (F and G)))))), M:tm-338, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36579
in-theory        36579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C or (D -> (E -> (D and E)))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36579.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C or (D -> (E -> (D and E))))))), M:tm-327, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36580
in-theory        36580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (A or B)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36580.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (A or B)) and (C or (D -> (E -> (D and E))))))), M:tm-326, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36581
in-theory        36581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (A or B)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36581.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (A or B)) and (C or (D -> (E -> (D and E))))))), M:tm-325, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36582
in-theory        36582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C or (D -> (E -> (D and E)))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36582.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C or (D -> (E -> (D and E))))))), M:tm-324, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36583
in-theory        36583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36583.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C or (D -> (E -> (D and E))))))), M:tm-323, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36584
in-theory        36584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36584.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and ((F and G) -> G)), M:tm-322, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36585
in-theory        36585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36585.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and ((F and G) -> F)), M:tm-320, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36586
in-theory        36586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36586.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36587
in-theory        36587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36587.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (F -> (G -> F))), M:tm-315, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36588
in-theory        36588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (F or ((A -> (A or B)) and (C or (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36588.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (F or ((A -> (A or B)) and (C or (D -> (E -> (D and E))))))), M:tm-311, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36589
in-theory        36589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36589.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) or F)), M:tm-310, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36590
in-theory        36590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (F -> (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36590.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (F -> (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and F))), M:tm-309, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36591
in-theory        36591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (C or (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-308 tm-512 ((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36591.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (C or (D -> (E -> (D and E))))), M:tm-308, m:tm-512, u:((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-36592
in-theory        36592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (A -> (A or B)))
theorem-size     21
proof            (modus-ponens tm-307 tm-512 ((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36592.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (A -> (A or B))), M:tm-307, m:tm-512, u:((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-36593
in-theory        36593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (F -> ((A -> (A or B)) and (C or (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36593.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (F -> ((A -> (A or B)) and (C or (D -> (E -> (D and E))))))), M:tm-305, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36594
in-theory        36594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-303 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36594.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-303, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36595
in-theory        36595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-270 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36595.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-270, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36596
in-theory        36596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-239 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36596.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-239, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36597
in-theory        36597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-210 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36597.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or (H -> (I -> (H and I)))))), M:tm-210, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36598
in-theory        36598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-183 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36598.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-183, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36599
in-theory        36599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-157 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36599.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-157, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36600
in-theory        36600
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-147 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36600.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-147, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36601
in-theory        36601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-134 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36601.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-134, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36602
in-theory        36602
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-125 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36602.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-125, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36603
in-theory        36603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-113 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36603.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (I -> (H and I)))))), M:tm-113, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36604
in-theory        36604
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-105 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36604.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-105, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36605
in-theory        36605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-95 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36605.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or (F -> (G -> (F and G)))))), M:tm-95, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36606
in-theory        36606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-83 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36606.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-83, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36607
in-theory        36607
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D or (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-76 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-10 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36607.        (((not (not A)) -> A) and ((B -> (B or C)) and (D or (E -> (F -> (E and F)))))), M:tm-76, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36608
in-theory        36608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-69 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-9 tm-6 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36608.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or (F -> (G -> (F and G)))))), M:tm-69, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36609
in-theory        36609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-54 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36609.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-54, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36610
in-theory        36610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-42 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36610.        ((A -> (B or A)) and ((C -> (C or D)) and (E or (F -> (G -> (F and G)))))), M:tm-42, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36611
in-theory        36611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-32 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36611.        ((A -> (A or B)) and ((C -> (C or D)) and (E or (F -> (G -> (F and G)))))), M:tm-32, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36612
in-theory        36612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-23 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36612.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or (F -> (G -> (F and G)))))), M:tm-23, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36613
in-theory        36613
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-22 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36613.        (((A and B) -> B) and ((C -> (C or D)) and (E or (F -> (G -> (F and G)))))), M:tm-22, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36614
in-theory        36614
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-21 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36614.        (((A and B) -> A) and ((C -> (C or D)) and (E or (F -> (G -> (F and G)))))), M:tm-21, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36615
in-theory        36615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-20 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36615.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-20, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36616
in-theory        36616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-19 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36616.        ((A -> (B -> A)) and ((C -> (C or D)) and (E or (F -> (G -> (F and G)))))), M:tm-19, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36617
in-theory        36617
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-7 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36617.        (A or ((B -> (B or C)) and (D or (E -> (F -> (E and F)))))), M:tm-7, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36618
in-theory        36618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36618.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) or F), M:tm-6, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36619
in-theory        36619
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D or (E -> (F -> (E and F))))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36619.        (A -> (((B -> (B or C)) and (D or (E -> (F -> (E and F))))) and A)), M:tm-5, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36620
in-theory        36620
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-1 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-1 tm-5 tm-6 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36620.        (A -> ((B -> (B or C)) and (D or (E -> (F -> (E and F)))))), M:tm-1, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36621
in-theory        36621
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-510 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36621.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-510, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36622
in-theory        36622
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-500 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36622.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-500, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36623
in-theory        36623
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-490 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36623.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I)))))), M:tm-490, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36624
in-theory        36624
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-480 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36624.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-480, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36625
in-theory        36625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-469 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36625.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-469, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36626
in-theory        36626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36626.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (F -> (F or G))), M:tm-456, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36627
in-theory        36627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-453 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36627.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-453, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36628
in-theory        36628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E)))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36628.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))))), M:tm-443, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36629
in-theory        36629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-409 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36629.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-409, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36630
in-theory        36630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-400 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36630.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-400, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36631
in-theory        36631
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-391 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36631.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-391, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36632
in-theory        36632
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-382 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36632.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-382, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36633
in-theory        36633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-373 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36633.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I)))))), M:tm-373, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36634
in-theory        36634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-364 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36634.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-364, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36635
in-theory        36635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-354 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36635.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-354, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36636
in-theory        36636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36636.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36637
in-theory        36637
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-338 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36637.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G)))))), M:tm-338, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36638
in-theory        36638
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E)))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36638.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))))), M:tm-327, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36639
in-theory        36639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E)))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36639.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))))), M:tm-326, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36640
in-theory        36640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E)))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36640.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))))), M:tm-325, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36641
in-theory        36641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E)))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36641.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))))), M:tm-324, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36642
in-theory        36642
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E)))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36642.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))))), M:tm-323, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36643
in-theory        36643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36643.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and ((F and G) -> G)), M:tm-322, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36644
in-theory        36644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36644.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and ((F and G) -> F)), M:tm-320, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36645
in-theory        36645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36645.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36646
in-theory        36646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36646.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (F -> (G -> F))), M:tm-315, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36647
in-theory        36647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (F or ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36647.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (F or ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))))), M:tm-311, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36648
in-theory        36648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36648.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) or F)), M:tm-310, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36649
in-theory        36649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (F -> (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36649.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (F -> (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and F))), M:tm-309, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36650
in-theory        36650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (C or (D -> (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-308 tm-513 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36650.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (C or (D -> (E -> (D and E))))), M:tm-308, m:tm-513, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-36651
in-theory        36651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (A -> (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-307 tm-513 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36651.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-513, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-36652
in-theory        36652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (F -> ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36652.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (F -> ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))))), M:tm-305, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36653
in-theory        36653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-303 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36653.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-303, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36654
in-theory        36654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-270 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36654.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-270, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36655
in-theory        36655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-239 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36655.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-239, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36656
in-theory        36656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I))))))
theorem-size     35
proof            (modus-ponens tm-210 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36656.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I)))))), M:tm-210, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36657
in-theory        36657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-183 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36657.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-183, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36658
in-theory        36658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-157 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36658.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-157, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36659
in-theory        36659
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-147 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36659.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-147, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36660
in-theory        36660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-134 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36660.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-134, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36661
in-theory        36661
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-125 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36661.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-125, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36662
in-theory        36662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-113 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36662.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I)))))), M:tm-113, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36663
in-theory        36663
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     37
proof            (modus-ponens tm-105 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36663.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-105, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36664
in-theory        36664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-95 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36664.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G)))))), M:tm-95, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36665
in-theory        36665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-83 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36665.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-83, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36666
in-theory        36666
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or (E -> (F -> (E and F))))))
theorem-size     23
proof            (modus-ponens tm-76 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36666.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or (E -> (F -> (E and F)))))), M:tm-76, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36667
in-theory        36667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G))))))
theorem-size     29
proof            (modus-ponens tm-69 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36667.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G)))))), M:tm-69, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36668
in-theory        36668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-54 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36668.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-54, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36669
in-theory        36669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-42 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36669.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G)))))), M:tm-42, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36670
in-theory        36670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-32 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36670.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G)))))), M:tm-32, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36671
in-theory        36671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-23 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36671.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G)))))), M:tm-23, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36672
in-theory        36672
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-22 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36672.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G)))))), M:tm-22, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36673
in-theory        36673
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-21 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36673.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G)))))), M:tm-21, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36674
in-theory        36674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-20 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36674.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-20, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36675
in-theory        36675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-19 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36675.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (G -> (F and G)))))), M:tm-19, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36676
in-theory        36676
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D or (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-7 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-7 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36676.        (A or ((B -> (C -> (B and C))) and (D or (E -> (F -> (E and F)))))), M:tm-7, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36677
in-theory        36677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36677.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) or F), M:tm-6, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36678
in-theory        36678
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D or (E -> (F -> (E and F))))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36678.        (A -> (((B -> (C -> (B and C))) and (D or (E -> (F -> (E and F))))) and A)), M:tm-5, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36679
in-theory        36679
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D or (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-1 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36679.        (A -> ((B -> (C -> (B and C))) and (D or (E -> (F -> (E and F)))))), M:tm-1, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36680
in-theory        36680
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-510 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36680.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-510, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36681
in-theory        36681
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-500 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36681.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-500, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36682
in-theory        36682
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-490 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36682.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (I -> (H and I)))))), M:tm-490, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36683
in-theory        36683
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-480 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36683.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-480, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36684
in-theory        36684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-469 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36684.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-469, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36685
in-theory        36685
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36685.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (F -> (F or G))), M:tm-456, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36686
in-theory        36686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-453 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36686.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-453, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36687
in-theory        36687
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((F -> (F or G)) and (((A and B) -> B) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36687.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((F -> (F or G)) and (((A and B) -> B) and (C or (D -> (E -> (D and E))))))), M:tm-443, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36688
in-theory        36688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-409 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36688.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-409, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36689
in-theory        36689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-400 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36689.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-400, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36690
in-theory        36690
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-391 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36690.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-391, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36691
in-theory        36691
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-382 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36691.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-382, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36692
in-theory        36692
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-373 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36692.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or (H -> (I -> (H and I)))))), M:tm-373, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36693
in-theory        36693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-364 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36693.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-364, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36694
in-theory        36694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-354 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36694.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-354, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36695
in-theory        36695
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36695.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36696
in-theory        36696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-338 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36696.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or (F -> (G -> (F and G)))))), M:tm-338, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36697
in-theory        36697
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C or (D -> (E -> (D and E)))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36697.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C or (D -> (E -> (D and E))))))), M:tm-327, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36698
in-theory        36698
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (((F and G) -> G) and (((A and B) -> B) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36698.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (((F and G) -> G) and (((A and B) -> B) and (C or (D -> (E -> (D and E))))))), M:tm-326, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36699
in-theory        36699
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (((F and G) -> F) and (((A and B) -> B) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36699.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (((F and G) -> F) and (((A and B) -> B) and (C or (D -> (E -> (D and E))))))), M:tm-325, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36700
in-theory        36700
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C or (D -> (E -> (D and E)))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36700.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C or (D -> (E -> (D and E))))))), M:tm-324, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36701
in-theory        36701
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> F)) and (((A and B) -> B) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36701.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> F)) and (((A and B) -> B) and (C or (D -> (E -> (D and E))))))), M:tm-323, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36702
in-theory        36702
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36702.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((F and G) -> G)), M:tm-322, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36703
in-theory        36703
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36703.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((F and G) -> F)), M:tm-320, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36704
in-theory        36704
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36704.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36705
in-theory        36705
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36705.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (F -> (G -> F))), M:tm-315, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36706
in-theory        36706
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (F or (((A and B) -> B) and (C or (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36706.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (F or (((A and B) -> B) and (C or (D -> (E -> (D and E))))))), M:tm-311, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36707
in-theory        36707
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36707.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) or F)), M:tm-310, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36708
in-theory        36708
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (F -> ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36708.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (F -> ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and F))), M:tm-309, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36709
in-theory        36709
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (C or (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-308 tm-514 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36709.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (C or (D -> (E -> (D and E))))), M:tm-308, m:tm-514, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-36710
in-theory        36710
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((A and B) -> B))
theorem-size     21
proof            (modus-ponens tm-307 tm-514 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36710.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((A and B) -> B)), M:tm-307, m:tm-514, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-36711
in-theory        36711
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (F -> (((A and B) -> B) and (C or (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36711.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (F -> (((A and B) -> B) and (C or (D -> (E -> (D and E))))))), M:tm-305, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36712
in-theory        36712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-303 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36712.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-303, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36713
in-theory        36713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-270 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36713.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-270, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36714
in-theory        36714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-239 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36714.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-239, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36715
in-theory        36715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-210 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36715.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or (H -> (I -> (H and I)))))), M:tm-210, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36716
in-theory        36716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-183 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36716.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-183, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36717
in-theory        36717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-157 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36717.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-157, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36718
in-theory        36718
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-147 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36718.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-147, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36719
in-theory        36719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-134 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36719.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-134, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36720
in-theory        36720
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-125 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36720.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-125, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36721
in-theory        36721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-113 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36721.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (I -> (H and I)))))), M:tm-113, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36722
in-theory        36722
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-105 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36722.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-105, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36723
in-theory        36723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-95 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36723.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or (F -> (G -> (F and G)))))), M:tm-95, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36724
in-theory        36724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-83 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36724.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-83, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36725
in-theory        36725
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D or (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-76 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-10 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36725.        (((not (not A)) -> A) and (((B and C) -> C) and (D or (E -> (F -> (E and F)))))), M:tm-76, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36726
in-theory        36726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-69 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-9 tm-4 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36726.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or (F -> (G -> (F and G)))))), M:tm-69, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36727
in-theory        36727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-54 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36727.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-54, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36728
in-theory        36728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-42 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36728.        ((A -> (B or A)) and (((C and D) -> D) and (E or (F -> (G -> (F and G)))))), M:tm-42, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36729
in-theory        36729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-32 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36729.        ((A -> (A or B)) and (((C and D) -> D) and (E or (F -> (G -> (F and G)))))), M:tm-32, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36730
in-theory        36730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-23 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36730.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or (F -> (G -> (F and G)))))), M:tm-23, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36731
in-theory        36731
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-22 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36731.        (((A and B) -> B) and (((C and D) -> D) and (E or (F -> (G -> (F and G)))))), M:tm-22, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36732
in-theory        36732
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-21 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36732.        (((A and B) -> A) and (((C and D) -> D) and (E or (F -> (G -> (F and G)))))), M:tm-21, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36733
in-theory        36733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-20 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36733.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-20, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36734
in-theory        36734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-19 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36734.        ((A -> (B -> A)) and (((C and D) -> D) and (E or (F -> (G -> (F and G)))))), M:tm-19, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36735
in-theory        36735
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-7 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36735.        (A or (((B and C) -> C) and (D or (E -> (F -> (E and F)))))), M:tm-7, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36736
in-theory        36736
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-6 tm-5 tm-4 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36736.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) or F), M:tm-6, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36737
in-theory        36737
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D or (E -> (F -> (E and F))))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36737.        (A -> ((((B and C) -> C) and (D or (E -> (F -> (E and F))))) and A)), M:tm-5, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36738
in-theory        36738
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-1 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-1 tm-5 tm-4 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36738.        (A -> (((B and C) -> C) and (D or (E -> (F -> (E and F)))))), M:tm-1, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36739
in-theory        36739
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-510 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36739.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-510, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36740
in-theory        36740
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-500 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36740.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-500, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36741
in-theory        36741
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-490 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36741.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (I -> (H and I)))))), M:tm-490, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36742
in-theory        36742
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-480 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36742.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-480, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36743
in-theory        36743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-469 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36743.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-469, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36744
in-theory        36744
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36744.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (F -> (F or G))), M:tm-456, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36745
in-theory        36745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-453 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36745.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-453, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36746
in-theory        36746
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((F -> (F or G)) and (((A and B) -> A) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36746.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((F -> (F or G)) and (((A and B) -> A) and (C or (D -> (E -> (D and E))))))), M:tm-443, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36747
in-theory        36747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-409 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36747.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-409, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36748
in-theory        36748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-400 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36748.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-400, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36749
in-theory        36749
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-391 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36749.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-391, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36750
in-theory        36750
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-382 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36750.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-382, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36751
in-theory        36751
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-373 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36751.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or (H -> (I -> (H and I)))))), M:tm-373, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36752
in-theory        36752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-364 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36752.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-364, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36753
in-theory        36753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-354 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36753.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-354, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36754
in-theory        36754
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36754.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36755
in-theory        36755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-338 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36755.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or (F -> (G -> (F and G)))))), M:tm-338, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36756
in-theory        36756
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C or (D -> (E -> (D and E)))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36756.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C or (D -> (E -> (D and E))))))), M:tm-327, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36757
in-theory        36757
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (((F and G) -> G) and (((A and B) -> A) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36757.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (((F and G) -> G) and (((A and B) -> A) and (C or (D -> (E -> (D and E))))))), M:tm-326, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36758
in-theory        36758
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (((F and G) -> F) and (((A and B) -> A) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36758.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (((F and G) -> F) and (((A and B) -> A) and (C or (D -> (E -> (D and E))))))), M:tm-325, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36759
in-theory        36759
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C or (D -> (E -> (D and E)))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36759.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C or (D -> (E -> (D and E))))))), M:tm-324, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36760
in-theory        36760
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> F)) and (((A and B) -> A) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36760.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> F)) and (((A and B) -> A) and (C or (D -> (E -> (D and E))))))), M:tm-323, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36761
in-theory        36761
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36761.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((F and G) -> G)), M:tm-322, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36762
in-theory        36762
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36762.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((F and G) -> F)), M:tm-320, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36763
in-theory        36763
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36763.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36764
in-theory        36764
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36764.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (F -> (G -> F))), M:tm-315, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36765
in-theory        36765
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (F or (((A and B) -> A) and (C or (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36765.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (F or (((A and B) -> A) and (C or (D -> (E -> (D and E))))))), M:tm-311, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36766
in-theory        36766
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36766.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) or F)), M:tm-310, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36767
in-theory        36767
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (F -> ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36767.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (F -> ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and F))), M:tm-309, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36768
in-theory        36768
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (C or (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-308 tm-515 ((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36768.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (C or (D -> (E -> (D and E))))), M:tm-308, m:tm-515, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-36769
in-theory        36769
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((A and B) -> A))
theorem-size     21
proof            (modus-ponens tm-307 tm-515 ((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36769.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((A and B) -> A)), M:tm-307, m:tm-515, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-36770
in-theory        36770
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (F -> (((A and B) -> A) and (C or (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36770.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (F -> (((A and B) -> A) and (C or (D -> (E -> (D and E))))))), M:tm-305, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36771
in-theory        36771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-303 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36771.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-303, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36772
in-theory        36772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-270 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36772.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-270, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36773
in-theory        36773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-239 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36773.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-239, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36774
in-theory        36774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-210 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36774.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or (H -> (I -> (H and I)))))), M:tm-210, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36775
in-theory        36775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-183 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36775.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-183, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36776
in-theory        36776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-157 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36776.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-157, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36777
in-theory        36777
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-147 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36777.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-147, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36778
in-theory        36778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-134 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36778.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-134, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36779
in-theory        36779
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-125 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36779.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-125, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36780
in-theory        36780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-113 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36780.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (I -> (H and I)))))), M:tm-113, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36781
in-theory        36781
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-105 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36781.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-105, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36782
in-theory        36782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-95 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36782.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or (F -> (G -> (F and G)))))), M:tm-95, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36783
in-theory        36783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-83 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36783.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-83, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36784
in-theory        36784
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D or (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-76 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-10 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36784.        (((not (not A)) -> A) and (((B and C) -> B) and (D or (E -> (F -> (E and F)))))), M:tm-76, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36785
in-theory        36785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-69 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-9 tm-3 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36785.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or (F -> (G -> (F and G)))))), M:tm-69, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36786
in-theory        36786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-54 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36786.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-54, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36787
in-theory        36787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-42 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36787.        ((A -> (B or A)) and (((C and D) -> C) and (E or (F -> (G -> (F and G)))))), M:tm-42, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36788
in-theory        36788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-32 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36788.        ((A -> (A or B)) and (((C and D) -> C) and (E or (F -> (G -> (F and G)))))), M:tm-32, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36789
in-theory        36789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-23 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36789.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or (F -> (G -> (F and G)))))), M:tm-23, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36790
in-theory        36790
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-22 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36790.        (((A and B) -> B) and (((C and D) -> C) and (E or (F -> (G -> (F and G)))))), M:tm-22, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36791
in-theory        36791
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-21 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36791.        (((A and B) -> A) and (((C and D) -> C) and (E or (F -> (G -> (F and G)))))), M:tm-21, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36792
in-theory        36792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-20 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36792.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-20, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36793
in-theory        36793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-19 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36793.        ((A -> (B -> A)) and (((C and D) -> C) and (E or (F -> (G -> (F and G)))))), M:tm-19, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36794
in-theory        36794
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-7 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36794.        (A or (((B and C) -> B) and (D or (E -> (F -> (E and F)))))), M:tm-7, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36795
in-theory        36795
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-6 tm-5 tm-3 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36795.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) or F), M:tm-6, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36796
in-theory        36796
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D or (E -> (F -> (E and F))))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36796.        (A -> ((((B and C) -> B) and (D or (E -> (F -> (E and F))))) and A)), M:tm-5, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36797
in-theory        36797
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-1 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-1 tm-5 tm-3 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36797.        (A -> (((B and C) -> B) and (D or (E -> (F -> (E and F)))))), M:tm-1, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36798
in-theory        36798
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-510 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36798.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-510, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36799
in-theory        36799
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-500 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36799.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-500, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36800
in-theory        36800
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-490 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36800.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-490, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36801
in-theory        36801
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-480 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36801.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-480, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36802
in-theory        36802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-469 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36802.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-469, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36803
in-theory        36803
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36803.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (G or H))), M:tm-456, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36804
in-theory        36804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-453 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36804.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-453, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36805
in-theory        36805
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-443 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36805.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-443, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36806
in-theory        36806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-409 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36806.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-409, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36807
in-theory        36807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-400 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36807.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-400, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36808
in-theory        36808
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-391 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36808.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-391, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36809
in-theory        36809
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-382 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36809.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-382, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36810
in-theory        36810
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-373 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36810.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-373, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36811
in-theory        36811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-364 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36811.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-364, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36812
in-theory        36812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-354 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36812.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-354, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36813
in-theory        36813
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36813.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36814
in-theory        36814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     33
proof            (modus-ponens tm-338 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36814.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-338, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36815
in-theory        36815
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     55
proof            (modus-ponens tm-327 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36815.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-327, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36816
in-theory        36816
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-326 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36816.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-326, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36817
in-theory        36817
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-325 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36817.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-325, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36818
in-theory        36818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     61
proof            (modus-ponens tm-324 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36818.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-324, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36819
in-theory        36819
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-323 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36819.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-323, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36820
in-theory        36820
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36820.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((G and H) -> H)), M:tm-322, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36821
in-theory        36821
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36821.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((G and H) -> G)), M:tm-320, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36822
in-theory        36822
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36822.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36823
in-theory        36823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36823.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (H -> G))), M:tm-315, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36824
in-theory        36824
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     49
proof            (modus-ponens tm-311 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36824.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-311, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36825
in-theory        36825
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36825.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) or G)), M:tm-310, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36826
in-theory        36826
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36826.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and G))), M:tm-309, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36827
in-theory        36827
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (D or (E -> (F -> (E and F)))))
theorem-size     33
proof            (modus-ponens tm-308 tm-516 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (-> Fm (and Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36827.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (D or (E -> (F -> (E and F))))), M:tm-308, m:tm-516, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (-> Fm (and Em Fm))))))
================================================================
tm-name          tm-36828
in-theory        36828
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-516 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (-> Fm (and Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36828.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-516, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (-> Fm (and Em Fm))))))
================================================================
tm-name          tm-36829
in-theory        36829
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     49
proof            (modus-ponens tm-305 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36829.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-305, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36830
in-theory        36830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     35
proof            (modus-ponens tm-303 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36830.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-303, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36831
in-theory        36831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-270 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36831.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-270, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36832
in-theory        36832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-239 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36832.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-239, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36833
in-theory        36833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> (I and J))))))
theorem-size     41
proof            (modus-ponens tm-210 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36833.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-210, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36834
in-theory        36834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-183 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36834.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-183, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36835
in-theory        36835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-157 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36835.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-157, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36836
in-theory        36836
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     39
proof            (modus-ponens tm-147 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36836.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-147, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36837
in-theory        36837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-134 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36837.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-134, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36838
in-theory        36838
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     39
proof            (modus-ponens tm-125 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36838.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-125, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36839
in-theory        36839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> (I and J))))))
theorem-size     39
proof            (modus-ponens tm-113 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36839.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-113, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36840
in-theory        36840
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-105 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36840.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-105, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36841
in-theory        36841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-95 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36841.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-95, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36842
in-theory        36842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-83 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36842.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-83, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36843
in-theory        36843
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> (F and G))))))
theorem-size     29
proof            (modus-ponens tm-76 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-10 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36843.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> (F and G)))))), M:tm-76, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36844
in-theory        36844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-69 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-9 tm-2 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36844.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-69, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36845
in-theory        36845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-54 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36845.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-54, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36846
in-theory        36846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-42 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36846.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-42, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36847
in-theory        36847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-32 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36847.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-32, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36848
in-theory        36848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-23 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36848.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-23, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36849
in-theory        36849
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-22 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36849.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-22, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36850
in-theory        36850
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-21 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36850.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-21, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36851
in-theory        36851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-20 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36851.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-20, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36852
in-theory        36852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-19 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36852.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H -> (G and H)))))), M:tm-19, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36853
in-theory        36853
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-7 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36853.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> (F and G)))))), M:tm-7, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36854
in-theory        36854
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-6 tm-5 tm-2 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36854.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) or G), M:tm-6, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36855
in-theory        36855
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> (F and G))))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36855.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> (F and G))))) and A)), M:tm-5, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36856
in-theory        36856
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-1 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-1 tm-5 tm-2 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36856.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G -> (F and G)))))), M:tm-1, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-36857
in-theory        36857
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-510 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36857.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-510, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36858
in-theory        36858
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-500 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36858.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-500, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36859
in-theory        36859
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-490 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36859.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I)))))), M:tm-490, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36860
in-theory        36860
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-480 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36860.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-480, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36861
in-theory        36861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-469 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36861.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-469, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36862
in-theory        36862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36862.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (F -> (F or G))), M:tm-456, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36863
in-theory        36863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-453 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36863.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-453, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36864
in-theory        36864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36864.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))))), M:tm-443, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36865
in-theory        36865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-409 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36865.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-409, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36866
in-theory        36866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-400 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36866.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-400, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36867
in-theory        36867
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-391 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36867.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-391, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36868
in-theory        36868
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-382 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36868.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-382, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36869
in-theory        36869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-373 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36869.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I)))))), M:tm-373, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36870
in-theory        36870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-364 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36870.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-364, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36871
in-theory        36871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-354 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36871.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-354, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36872
in-theory        36872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36872.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36873
in-theory        36873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-338 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36873.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G)))))), M:tm-338, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36874
in-theory        36874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36874.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))))), M:tm-327, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36875
in-theory        36875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (B -> A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36875.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))))), M:tm-326, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36876
in-theory        36876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (B -> A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36876.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))))), M:tm-325, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36877
in-theory        36877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36877.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))))), M:tm-324, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36878
in-theory        36878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36878.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))))), M:tm-323, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36879
in-theory        36879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36879.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and ((F and G) -> G)), M:tm-322, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36880
in-theory        36880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36880.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and ((F and G) -> F)), M:tm-320, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36881
in-theory        36881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36881.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36882
in-theory        36882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36882.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (F -> (G -> F))), M:tm-315, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36883
in-theory        36883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (F or ((A -> (B -> A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36883.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (F or ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))))), M:tm-311, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36884
in-theory        36884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36884.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) or F)), M:tm-310, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36885
in-theory        36885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (F -> (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36885.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (F -> (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and F))), M:tm-309, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36886
in-theory        36886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (C or (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-308 tm-517 ((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36886.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (C or (D -> (E -> (D and E))))), M:tm-308, m:tm-517, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-36887
in-theory        36887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (A -> (B -> A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-517 ((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36887.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (A -> (B -> A))), M:tm-307, m:tm-517, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-36888
in-theory        36888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (F -> ((A -> (B -> A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36888.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (F -> ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))))), M:tm-305, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36889
in-theory        36889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-303 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36889.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-303, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36890
in-theory        36890
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-270 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36890.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-270, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36891
in-theory        36891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-239 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36891.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-239, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36892
in-theory        36892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-210 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36892.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I)))))), M:tm-210, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36893
in-theory        36893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-183 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36893.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-183, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36894
in-theory        36894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-157 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36894.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-157, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36895
in-theory        36895
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-147 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36895.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-147, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36896
in-theory        36896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-134 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36896.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-134, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36897
in-theory        36897
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-125 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36897.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-125, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36898
in-theory        36898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-113 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36898.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I)))))), M:tm-113, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36899
in-theory        36899
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-105 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36899.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-105, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36900
in-theory        36900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-95 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36900.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G)))))), M:tm-95, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36901
in-theory        36901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-83 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36901.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-83, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36902
in-theory        36902
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D or (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-76 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36902.        (((not (not A)) -> A) and ((B -> (C -> B)) and (D or (E -> (F -> (E and F)))))), M:tm-76, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36903
in-theory        36903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-69 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36903.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G)))))), M:tm-69, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36904
in-theory        36904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-54 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36904.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-54, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36905
in-theory        36905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-42 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36905.        ((A -> (B or A)) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G)))))), M:tm-42, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36906
in-theory        36906
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-32 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36906.        ((A -> (A or B)) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G)))))), M:tm-32, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36907
in-theory        36907
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-23 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36907.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G)))))), M:tm-23, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36908
in-theory        36908
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-22 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36908.        (((A and B) -> B) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G)))))), M:tm-22, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36909
in-theory        36909
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-21 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36909.        (((A and B) -> A) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G)))))), M:tm-21, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36910
in-theory        36910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-20 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36910.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-20, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36911
in-theory        36911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-19 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36911.        ((A -> (B -> A)) and ((C -> (D -> C)) and (E or (F -> (G -> (F and G)))))), M:tm-19, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36912
in-theory        36912
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-7 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36912.        (A or ((B -> (C -> B)) and (D or (E -> (F -> (E and F)))))), M:tm-7, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36913
in-theory        36913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-6 tm-5 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36913.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) or F), M:tm-6, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36914
in-theory        36914
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D or (E -> (F -> (E and F))))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36914.        (A -> (((B -> (C -> B)) and (D or (E -> (F -> (E and F))))) and A)), M:tm-5, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36915
in-theory        36915
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-1 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36915.        (A -> ((B -> (C -> B)) and (D or (E -> (F -> (E and F)))))), M:tm-1, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-36916
in-theory        36916
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-510 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36916.        ((A or ((B and C) -> C)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-510, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36917
in-theory        36917
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-500 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36917.        ((A or ((B and C) -> B)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-500, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36918
in-theory        36918
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-490 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36918.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (H -> (G and H)))))), M:tm-490, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36919
in-theory        36919
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-480 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36919.        ((A or (B -> (C -> B))) and (D or (E or (F -> (G -> (F and G)))))), M:tm-480, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36920
in-theory        36920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-469 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36920.        ((A -> (B -> (B or C))) and (D or (E or (F -> (G -> (F and G)))))), M:tm-469, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36921
in-theory        36921
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36921.        ((A or (B or (C -> (D -> (C and D))))) and (E -> (E or F))), M:tm-456, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36922
in-theory        36922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-453 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36922.        ((A -> ((B -> (B or C)) and A)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-453, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36923
in-theory        36923
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and ((E -> (E or F)) and (A or (B or (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-443 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36923.        ((A or (B or (C -> (D -> (C and D))))) and ((E -> (E or F)) and (A or (B or (C -> (D -> (C and D))))))), M:tm-443, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36924
in-theory        36924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-409 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36924.        (((A -> (A or B)) or C) and (D or (E or (F -> (G -> (F and G)))))), M:tm-409, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36925
in-theory        36925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-400 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36925.        (((A -> (B -> (A and B))) or C) and (D or (E or (F -> (G -> (F and G)))))), M:tm-400, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36926
in-theory        36926
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-391 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36926.        ((((A and B) -> B) or C) and (D or (E or (F -> (G -> (F and G)))))), M:tm-391, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36927
in-theory        36927
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-382 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36927.        ((((A and B) -> A) or C) and (D or (E or (F -> (G -> (F and G)))))), M:tm-382, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36928
in-theory        36928
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-373 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36928.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or (G -> (H -> (G and H)))))), M:tm-373, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36929
in-theory        36929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-364 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36929.        (((A -> (B -> A)) or C) and (D or (E or (F -> (G -> (F and G)))))), M:tm-364, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36930
in-theory        36930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-354 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36930.        ((A -> (B -> (C -> (B and C)))) and (D or (E or (F -> (G -> (F and G)))))), M:tm-354, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36931
in-theory        36931
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36931.        ((A or (B or (C -> (D -> (C and D))))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36932
in-theory        36932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D or (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-338 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36932.        (((A -> B) -> (A -> (A and B))) and (C or (D or (E -> (F -> (E and F)))))), M:tm-338, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36933
in-theory        36933
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and ((E -> (F -> (E and F))) and (A or (B or (C -> (D -> (C and D)))))))
theorem-size     31
proof            (modus-ponens tm-327 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36933.        ((A or (B or (C -> (D -> (C and D))))) and ((E -> (F -> (E and F))) and (A or (B or (C -> (D -> (C and D))))))), M:tm-327, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36934
in-theory        36934
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and (((E and F) -> F) and (A or (B or (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-326 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36934.        ((A or (B or (C -> (D -> (C and D))))) and (((E and F) -> F) and (A or (B or (C -> (D -> (C and D))))))), M:tm-326, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36935
in-theory        36935
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and (((E and F) -> E) and (A or (B or (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-325 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36935.        ((A or (B or (C -> (D -> (C and D))))) and (((E and F) -> E) and (A or (B or (C -> (D -> (C and D))))))), M:tm-325, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36936
in-theory        36936
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B or (C -> (D -> (C and D)))))))
theorem-size     37
proof            (modus-ponens tm-324 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36936.        ((A or (B or (C -> (D -> (C and D))))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B or (C -> (D -> (C and D))))))), M:tm-324, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36937
in-theory        36937
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and ((E -> (F -> E)) and (A or (B or (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-323 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36937.        ((A or (B or (C -> (D -> (C and D))))) and ((E -> (F -> E)) and (A or (B or (C -> (D -> (C and D))))))), M:tm-323, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36938
in-theory        36938
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36938.        ((A or (B or (C -> (D -> (C and D))))) and ((E and F) -> F)), M:tm-322, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36939
in-theory        36939
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36939.        ((A or (B or (C -> (D -> (C and D))))) and ((E and F) -> E)), M:tm-320, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36940
in-theory        36940
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36940.        ((A or (B or (C -> (D -> (C and D))))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36941
in-theory        36941
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36941.        ((A or (B or (C -> (D -> (C and D))))) and (E -> (F -> E))), M:tm-315, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36942
in-theory        36942
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and (E or (A or (B or (C -> (D -> (C and D)))))))
theorem-size     25
proof            (modus-ponens tm-311 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36942.        ((A or (B or (C -> (D -> (C and D))))) and (E or (A or (B or (C -> (D -> (C and D))))))), M:tm-311, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36943
in-theory        36943
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and ((A or (B or (C -> (D -> (C and D))))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36943.        ((A or (B or (C -> (D -> (C and D))))) and ((A or (B or (C -> (D -> (C and D))))) or E)), M:tm-310, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36944
in-theory        36944
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and (E -> ((A or (B or (C -> (D -> (C and D))))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36944.        ((A or (B or (C -> (D -> (C and D))))) and (E -> ((A or (B or (C -> (D -> (C and D))))) and E))), M:tm-309, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36945
in-theory        36945
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and (E -> (A or (B or (C -> (D -> (C and D)))))))
theorem-size     25
proof            (modus-ponens tm-305 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36945.        ((A or (B or (C -> (D -> (C and D))))) and (E -> (A or (B or (C -> (D -> (C and D))))))), M:tm-305, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36946
in-theory        36946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-303 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36946.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-303, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36947
in-theory        36947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-270 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36947.        ((A -> (((B and C) -> C) and A)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-270, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36948
in-theory        36948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-239 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36948.        ((A -> (((B and C) -> B) and A)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-239, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36949
in-theory        36949
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-210 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36949.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or (G -> (H -> (G and H)))))), M:tm-210, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36950
in-theory        36950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-183 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36950.        ((A -> ((B -> (C -> B)) and A)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-183, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36951
in-theory        36951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-157 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36951.        ((A -> ((B and C) -> C)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-157, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36952
in-theory        36952
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-147 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36952.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-147, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36953
in-theory        36953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-134 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36953.        ((A -> ((B and C) -> B)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-134, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36954
in-theory        36954
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-125 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36954.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-125, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36955
in-theory        36955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-113 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36955.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (H -> (G and H)))))), M:tm-113, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36956
in-theory        36956
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     31
proof            (modus-ponens tm-105 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36956.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or (F -> (G -> (F and G)))))), M:tm-105, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36957
in-theory        36957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D or (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-95 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36957.        (((A -> B) -> (A -> A)) and (C or (D or (E -> (F -> (E and F)))))), M:tm-95, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36958
in-theory        36958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-83 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36958.        ((A -> (B -> (C -> B))) and (D or (E or (F -> (G -> (F and G)))))), M:tm-83, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36959
in-theory        36959
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C or (D -> (E -> (D and E))))))
theorem-size     17
proof            (modus-ponens tm-76 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36959.        (((not (not A)) -> A) and (B or (C or (D -> (E -> (D and E)))))), M:tm-76, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36960
in-theory        36960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or (E -> (F -> (E and F))))))
theorem-size     23
proof            (modus-ponens tm-69 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36960.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or (E -> (F -> (E and F)))))), M:tm-69, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36961
in-theory        36961
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-54 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36961.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or (F -> (G -> (F and G)))))), M:tm-54, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36962
in-theory        36962
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-42 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36962.        ((A -> (B or A)) and (C or (D or (E -> (F -> (E and F)))))), M:tm-42, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36963
in-theory        36963
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-32 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36963.        ((A -> (A or B)) and (C or (D or (E -> (F -> (E and F)))))), M:tm-32, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36964
in-theory        36964
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D or (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-23 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36964.        ((A -> (B -> (A and B))) and (C or (D or (E -> (F -> (E and F)))))), M:tm-23, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36965
in-theory        36965
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-22 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36965.        (((A and B) -> B) and (C or (D or (E -> (F -> (E and F)))))), M:tm-22, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36966
in-theory        36966
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-21 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36966.        (((A and B) -> A) and (C or (D or (E -> (F -> (E and F)))))), M:tm-21, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36967
in-theory        36967
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-20 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36967.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or (F -> (G -> (F and G)))))), M:tm-20, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36968
in-theory        36968
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-19 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36968.        ((A -> (B -> A)) and (C or (D or (E -> (F -> (E and F)))))), M:tm-19, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36969
in-theory        36969
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C or (D -> (E -> (D and E))))))
theorem-size     13
proof            (modus-ponens tm-7 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-7 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36969.        (A or (B or (C or (D -> (E -> (D and E)))))), M:tm-7, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36970
in-theory        36970
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-6 tm-7 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36970.        ((A or (B or (C -> (D -> (C and D))))) or E), M:tm-6, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36971
in-theory        36971
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C or (D -> (E -> (D and E))))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36971.        (A -> ((B or (C or (D -> (E -> (D and E))))) and A)), M:tm-5, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36972
in-theory        36972
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C or (D -> (E -> (D and E))))))
theorem-size     13
proof            (modus-ponens tm-1 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-1 tm-7 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36972.        (A -> (B or (C or (D -> (E -> (D and E)))))), M:tm-1, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-36973
in-theory        36973
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-510 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36973.        ((A or ((B and C) -> C)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-510, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36974
in-theory        36974
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-500 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36974.        ((A or ((B and C) -> B)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-500, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36975
in-theory        36975
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (G -> (F and G)))) or H))
theorem-size     27
proof            (modus-ponens tm-490 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36975.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (G -> (F and G)))) or H)), M:tm-490, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36976
in-theory        36976
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-480 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36976.        ((A or (B -> (C -> B))) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-480, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36977
in-theory        36977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-469 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36977.        ((A -> (B -> (B or C))) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-469, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36978
in-theory        36978
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36978.        (((A or (B -> (C -> (B and C)))) or D) and (E -> (E or F))), M:tm-456, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36979
in-theory        36979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-453 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36979.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-453, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36980
in-theory        36980
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and ((E -> (E or F)) and ((A or (B -> (C -> (B and C)))) or D)))
theorem-size     29
proof            (modus-ponens tm-443 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36980.        (((A or (B -> (C -> (B and C)))) or D) and ((E -> (E or F)) and ((A or (B -> (C -> (B and C)))) or D))), M:tm-443, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36981
in-theory        36981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-409 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36981.        (((A -> (A or B)) or C) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-409, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36982
in-theory        36982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-400 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36982.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-400, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36983
in-theory        36983
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-391 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36983.        ((((A and B) -> B) or C) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-391, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36984
in-theory        36984
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-382 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36984.        ((((A and B) -> A) or C) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-382, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36985
in-theory        36985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (G -> (F and G)))) or H))
theorem-size     27
proof            (modus-ponens tm-373 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36985.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (G -> (F and G)))) or H)), M:tm-373, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36986
in-theory        36986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-364 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36986.        (((A -> (B -> A)) or C) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-364, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36987
in-theory        36987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-354 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36987.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-354, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36988
in-theory        36988
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36988.        (((A or (B -> (C -> (B and C)))) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36989
in-theory        36989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (E -> (D and E)))) or F))
theorem-size     21
proof            (modus-ponens tm-338 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36989.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (E -> (D and E)))) or F)), M:tm-338, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36990
in-theory        36990
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and ((E -> (F -> (E and F))) and ((A or (B -> (C -> (B and C)))) or D)))
theorem-size     31
proof            (modus-ponens tm-327 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36990.        (((A or (B -> (C -> (B and C)))) or D) and ((E -> (F -> (E and F))) and ((A or (B -> (C -> (B and C)))) or D))), M:tm-327, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36991
in-theory        36991
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and (((E and F) -> F) and ((A or (B -> (C -> (B and C)))) or D)))
theorem-size     29
proof            (modus-ponens tm-326 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36991.        (((A or (B -> (C -> (B and C)))) or D) and (((E and F) -> F) and ((A or (B -> (C -> (B and C)))) or D))), M:tm-326, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36992
in-theory        36992
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and (((E and F) -> E) and ((A or (B -> (C -> (B and C)))) or D)))
theorem-size     29
proof            (modus-ponens tm-325 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36992.        (((A or (B -> (C -> (B and C)))) or D) and (((E and F) -> E) and ((A or (B -> (C -> (B and C)))) or D))), M:tm-325, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36993
in-theory        36993
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (C -> (B and C)))) or D)))
theorem-size     37
proof            (modus-ponens tm-324 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36993.        (((A or (B -> (C -> (B and C)))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (C -> (B and C)))) or D))), M:tm-324, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36994
in-theory        36994
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and ((E -> (F -> E)) and ((A or (B -> (C -> (B and C)))) or D)))
theorem-size     29
proof            (modus-ponens tm-323 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36994.        (((A or (B -> (C -> (B and C)))) or D) and ((E -> (F -> E)) and ((A or (B -> (C -> (B and C)))) or D))), M:tm-323, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36995
in-theory        36995
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36995.        (((A or (B -> (C -> (B and C)))) or D) and ((E and F) -> F)), M:tm-322, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36996
in-theory        36996
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36996.        (((A or (B -> (C -> (B and C)))) or D) and ((E and F) -> E)), M:tm-320, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36997
in-theory        36997
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36997.        (((A or (B -> (C -> (B and C)))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36998
in-theory        36998
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36998.        (((A or (B -> (C -> (B and C)))) or D) and (E -> (F -> E))), M:tm-315, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-36999
in-theory        36999
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and (E or ((A or (B -> (C -> (B and C)))) or D)))
theorem-size     25
proof            (modus-ponens tm-311 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-36999.        (((A or (B -> (C -> (B and C)))) or D) and (E or ((A or (B -> (C -> (B and C)))) or D))), M:tm-311, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37000
in-theory        37000
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and (((A or (B -> (C -> (B and C)))) or D) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37000.        (((A or (B -> (C -> (B and C)))) or D) and (((A or (B -> (C -> (B and C)))) or D) or E)), M:tm-310, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37001
in-theory        37001
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and (E -> (((A or (B -> (C -> (B and C)))) or D) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37001.        (((A or (B -> (C -> (B and C)))) or D) and (E -> (((A or (B -> (C -> (B and C)))) or D) and E))), M:tm-309, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37002
in-theory        37002
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and (E -> ((A or (B -> (C -> (B and C)))) or D)))
theorem-size     25
proof            (modus-ponens tm-305 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37002.        (((A or (B -> (C -> (B and C)))) or D) and (E -> ((A or (B -> (C -> (B and C)))) or D))), M:tm-305, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37003
in-theory        37003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     23
proof            (modus-ponens tm-303 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37003.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-303, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37004
in-theory        37004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-270 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37004.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-270, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37005
in-theory        37005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-239 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37005.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-239, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37006
in-theory        37006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (G -> (F and G)))) or H))
theorem-size     29
proof            (modus-ponens tm-210 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37006.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (G -> (F and G)))) or H)), M:tm-210, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37007
in-theory        37007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-183 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37007.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-183, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37008
in-theory        37008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-157 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37008.        ((A -> ((B and C) -> C)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-157, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37009
in-theory        37009
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     27
proof            (modus-ponens tm-147 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37009.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-147, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37010
in-theory        37010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-134 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37010.        ((A -> ((B and C) -> B)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-134, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37011
in-theory        37011
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     27
proof            (modus-ponens tm-125 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37011.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-125, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37012
in-theory        37012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (G -> (F and G)))) or H))
theorem-size     27
proof            (modus-ponens tm-113 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37012.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (G -> (F and G)))) or H)), M:tm-113, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37013
in-theory        37013
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     31
proof            (modus-ponens tm-105 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37013.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-105, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37014
in-theory        37014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (E -> (D and E)))) or F))
theorem-size     19
proof            (modus-ponens tm-95 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37014.        (((A -> B) -> (A -> A)) and ((C or (D -> (E -> (D and E)))) or F)), M:tm-95, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37015
in-theory        37015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-83 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37015.        ((A -> (B -> (C -> B))) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-83, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37016
in-theory        37016
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (D -> (C and D)))) or E))
theorem-size     17
proof            (modus-ponens tm-76 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37016.        (((not (not A)) -> A) and ((B or (C -> (D -> (C and D)))) or E)), M:tm-76, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37017
in-theory        37017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (E -> (D and E)))) or F))
theorem-size     23
proof            (modus-ponens tm-69 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37017.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (E -> (D and E)))) or F)), M:tm-69, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37018
in-theory        37018
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     25
proof            (modus-ponens tm-54 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37018.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-54, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37019
in-theory        37019
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (E -> (D and E)))) or F))
theorem-size     17
proof            (modus-ponens tm-42 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37019.        ((A -> (B or A)) and ((C or (D -> (E -> (D and E)))) or F)), M:tm-42, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37020
in-theory        37020
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (E -> (D and E)))) or F))
theorem-size     17
proof            (modus-ponens tm-32 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37020.        ((A -> (A or B)) and ((C or (D -> (E -> (D and E)))) or F)), M:tm-32, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37021
in-theory        37021
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (E -> (D and E)))) or F))
theorem-size     19
proof            (modus-ponens tm-23 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37021.        ((A -> (B -> (A and B))) and ((C or (D -> (E -> (D and E)))) or F)), M:tm-23, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37022
in-theory        37022
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (E -> (D and E)))) or F))
theorem-size     17
proof            (modus-ponens tm-22 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37022.        (((A and B) -> B) and ((C or (D -> (E -> (D and E)))) or F)), M:tm-22, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37023
in-theory        37023
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (E -> (D and E)))) or F))
theorem-size     17
proof            (modus-ponens tm-21 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37023.        (((A and B) -> A) and ((C or (D -> (E -> (D and E)))) or F)), M:tm-21, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37024
in-theory        37024
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     25
proof            (modus-ponens tm-20 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37024.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-20, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37025
in-theory        37025
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (E -> (D and E)))) or F))
theorem-size     17
proof            (modus-ponens tm-19 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37025.        ((A -> (B -> A)) and ((C or (D -> (E -> (D and E)))) or F)), M:tm-19, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37026
in-theory        37026
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B or (C -> (D -> (C and D)))) or E))
theorem-size     13
proof            (modus-ponens tm-7 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-7 tm-6 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37026.        (A or ((B or (C -> (D -> (C and D)))) or E)), M:tm-7, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37027
in-theory        37027
times-derived    2
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-6 tm-7 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37027.        (((A or (B -> (C -> (B and C)))) or D) or E), M:tm-6, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37028
in-theory        37028
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (D -> (C and D)))) or E) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37028.        (A -> (((B or (C -> (D -> (C and D)))) or E) and A)), M:tm-5, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37029
in-theory        37029
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (D -> (C and D)))) or E))
theorem-size     13
proof            (modus-ponens tm-1 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-1 tm-6 tm-7 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37029.        (A -> ((B or (C -> (D -> (C and D)))) or E)), M:tm-1, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37030
in-theory        37030
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-520 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37030.        ((A or (B -> (C -> (B and C)))) and (D -> (E or D))), M:tm-520, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-37031
in-theory        37031
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-37031.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-520, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-37032
in-theory        37032
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-520 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-37032.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-520, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-37033
in-theory        37033
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-520 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-10.           ((not (not A)) -> A), axiom
tm-37033.        ((A or (B -> (C -> (B and C)))) and ((not (not D)) -> D)), M:tm-520, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-37034
in-theory        37034
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-520 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-37034.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> (F -> E)))), M:tm-520, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-37035
in-theory        37035
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-520 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-37035.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (D -> D))), M:tm-520, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-37036
in-theory        37036
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-520 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-37036.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-520, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-37037
in-theory        37037
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-37037.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-520, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-37038
in-theory        37038
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-520 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-37038.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-520, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-37039
in-theory        37039
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-520 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-37039.        ((A or (B -> (C -> (B and C)))) and (D -> ((E and F) -> E))), M:tm-520, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-37040
in-theory        37040
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-520 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-37040.        ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-520, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-37041
in-theory        37041
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-520 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37041.        ((A or (B -> (C -> (B and C)))) and (D -> ((E and F) -> F))), M:tm-520, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-37042
in-theory        37042
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-520 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-37042.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> E)) and D))), M:tm-520, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-37043
in-theory        37043
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-520 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-37043.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-520, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-37044
in-theory        37044
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-520 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-37044.        ((A or (B -> (C -> (B and C)))) and (D -> (((E and F) -> E) and D))), M:tm-520, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-37045
in-theory        37045
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-520 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37045.        ((A or (B -> (C -> (B and C)))) and (D -> (((E and F) -> F) and D))), M:tm-520, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-37046
in-theory        37046
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-37046.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-520, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-37047
in-theory        37047
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-520 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-37047.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (D and E)))), M:tm-520, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-37048
in-theory        37048
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-37048.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> (F -> (E and F))))), M:tm-520, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-37049
in-theory        37049
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-520 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-37049.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) or F)), M:tm-520, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-37050
in-theory        37050
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-520 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-37050.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-520, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-37051
in-theory        37051
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-520 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-37051.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) or F)), M:tm-520, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-37052
in-theory        37052
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-520 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37052.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) or F)), M:tm-520, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-37053
in-theory        37053
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-520 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-37053.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) or F)), M:tm-520, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-37054
in-theory        37054
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-520 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-37054.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) or F)), M:tm-520, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-37055
in-theory        37055
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-520 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-37055.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (E or F)) and D))), M:tm-520, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-37056
in-theory        37056
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-520 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-37056.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> (E or F)))), M:tm-520, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-37057
in-theory        37057
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-520 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-37057.        ((A or (B -> (C -> (B and C)))) and (D or (E -> (F -> E)))), M:tm-520, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-37058
in-theory        37058
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-37058.        ((A or (B -> (C -> (B and C)))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-520, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-37059
in-theory        37059
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-520 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-37059.        ((A or (B -> (C -> (B and C)))) and (D or ((E and F) -> E))), M:tm-520, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-37060
in-theory        37060
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-520 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37060.        ((A or (B -> (C -> (B and C)))) and (D or ((E and F) -> F))), M:tm-520, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-37061
in-theory        37061
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37061.        ((A or (B -> (C -> (B and C)))) and (D or (E -> (F -> (E and F))))), M:tm-520, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-37062
in-theory        37062
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-520 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-37062.        ((A or (B -> (C -> (B and C)))) and (D or (E -> (E or F)))), M:tm-520, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-37063
in-theory        37063
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-520 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37063.        ((A or (B -> (C -> (B and C)))) and (D or (E -> (F or E)))), M:tm-520, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-37064
in-theory        37064
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-520 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37064.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) or F)), M:tm-520, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-37065
in-theory        37065
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-520 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37065.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F or E)) and D))), M:tm-520, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-37066
in-theory        37066
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-520 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37066.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> (F or E)))), M:tm-520, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-37067
in-theory        37067
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-520 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-37067.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-520, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-37068
in-theory        37068
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-520 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-37068.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-520, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-37069
in-theory        37069
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-520 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-37069.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-520, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-37070
in-theory        37070
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-520 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-37070.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-520, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-37071
in-theory        37071
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-520 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-37071.        ((A or (B -> (C -> (B and C)))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-520, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-37072
in-theory        37072
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-520 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-37072.        ((A or (B -> (C -> (B and C)))) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-520, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-37073
in-theory        37073
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-520 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-37073.        ((A or (B -> (C -> (B and C)))) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-520, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-37074
in-theory        37074
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-520 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-37074.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-520, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-37075
in-theory        37075
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-37075.        ((A or (B -> (C -> (B and C)))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-520, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-37076
in-theory        37076
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-520 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-37076.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-520, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-37077
in-theory        37077
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-520 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-37077.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-520, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-37078
in-theory        37078
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-520 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-37078.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-520, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-37079
in-theory        37079
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-37079.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-520, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-37080
in-theory        37080
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-520 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-37080.        ((A or (B -> (C -> (B and C)))) and ((D -> (not (E -> D))) -> (not D))), M:tm-520, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-37081
in-theory        37081
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-37081.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-520, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-37082
in-theory        37082
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-520 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-37082.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-520, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-37083
in-theory        37083
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-520 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-37083.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-520, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-37084
in-theory        37084
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-37084.        ((A or (B -> (C -> (B and C)))) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-520, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-37085
in-theory        37085
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not (D or E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-520 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-37085.        ((A or (B -> (C -> (B and C)))) and ((D -> (not (D or E))) -> (not D))), M:tm-520, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-37086
in-theory        37086
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not (E or D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-520 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-37086.        ((A or (B -> (C -> (B and C)))) and ((D -> (not (E or D))) -> (not D))), M:tm-520, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-37087
in-theory        37087
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-520 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-37087.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-520, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-37088
in-theory        37088
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-520 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-37088.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-520, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-37089
in-theory        37089
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-520 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-37089.        ((A or (B -> (C -> (B and C)))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-520, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-37090
in-theory        37090
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-37090.        ((A or (B -> (C -> (B and C)))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-520, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-37091
in-theory        37091
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     23
proof            (modus-ponens tm-520 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-37091.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-520, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-37092
in-theory        37092
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     25
proof            (modus-ponens tm-520 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-37092.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-520, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-37093
in-theory        37093
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-520 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-37093.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-520, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-37094
in-theory        37094
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-37094.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-520, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-37095
in-theory        37095
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     21
proof            (modus-ponens tm-520 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-7 tm-9 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-37095.        ((A or (B -> (C -> (B and C)))) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-520, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-37096
in-theory        37096
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-520 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-37096.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-520, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-37097
in-theory        37097
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-520 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-37097.        ((A or (B -> (C -> (B and C)))) and (D or ((not (not E)) -> E))), M:tm-520, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-37098
in-theory        37098
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((not (not D)) -> D) or E))
theorem-size     17
proof            (modus-ponens tm-520 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-37098.        ((A or (B -> (C -> (B and C)))) and (((not (not D)) -> D) or E)), M:tm-520, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-37099
in-theory        37099
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((not (not E)) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-520 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-37099.        ((A or (B -> (C -> (B and C)))) and (D -> (((not (not E)) -> E) and D))), M:tm-520, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-37100
in-theory        37100
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     25
proof            (modus-ponens tm-520 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-37100.        ((A or (B -> (C -> (B and C)))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-520, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-37101
in-theory        37101
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-520 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-37101.        ((A or (B -> (C -> (B and C)))) and (D -> ((not (not E)) -> E))), M:tm-520, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-37102
in-theory        37102
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-37102.        ((A or (B -> (C -> (B and C)))) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-520, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-37103
in-theory        37103
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-520 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-37103.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-520, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-37104
in-theory        37104
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-37104.        ((A or (B -> (C -> (B and C)))) and (D or (E -> (F -> (G -> F))))), M:tm-520, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-37105
in-theory        37105
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-37105.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (F -> E))) or G)), M:tm-520, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-37106
in-theory        37106
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-37106.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-520, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-37107
in-theory        37107
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-520 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-37107.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (F -> E)))), M:tm-520, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-37108
in-theory        37108
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-37108.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> (F -> (G -> F))))), M:tm-520, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-37109
in-theory        37109
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> D))
theorem-size     13
proof            (modus-ponens tm-520 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-37109.        ((A or (B -> (C -> (B and C)))) and (D -> D)), M:tm-520, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-37110
in-theory        37110
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-37110.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-520, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-37111
in-theory        37111
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D and E) -> (D and E)))
theorem-size     17
proof            (modus-ponens tm-520 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-37111.        ((A or (B -> (C -> (B and C)))) and ((D and E) -> (D and E))), M:tm-520, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-37112
in-theory        37112
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-520 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-37112.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (D -> E))), M:tm-520, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-37113
in-theory        37113
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((not (not D)) -> (not (not D))))
theorem-size     17
proof            (modus-ponens tm-520 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-37113.        ((A or (B -> (C -> (B and C)))) and ((not (not D)) -> (not (not D)))), M:tm-520, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-37114
in-theory        37114
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-520 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-37114.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-520, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-37115
in-theory        37115
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-520 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-37115.        ((A or (B -> (C -> (B and C)))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-520, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-37116
in-theory        37116
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-520 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-37116.        ((A or (B -> (C -> (B and C)))) and (D or ((E -> F) -> (E -> E)))), M:tm-520, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-37117
in-theory        37117
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (D -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-520 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-37117.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (D -> D)) or F)), M:tm-520, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-37118
in-theory        37118
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-37118.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-520, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-37119
in-theory        37119
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-37119.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-520, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-37120
in-theory        37120
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-520 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-37120.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (E -> E)))), M:tm-520, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-37121
in-theory        37121
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-37121.        ((A or (B -> (C -> (B and C)))) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-520, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-37122
in-theory        37122
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-520 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-37122.        ((A or (B -> (C -> (B and C)))) and ((D -> (D -> E)) -> (D -> E))), M:tm-520, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-37123
in-theory        37123
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-520 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-37123.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-520, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-37124
in-theory        37124
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     41
proof            (modus-ponens tm-520 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-37124.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-520, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-37125
in-theory        37125
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-520 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-37125.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-520, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-37126
in-theory        37126
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-37126.        ((A or (B -> (C -> (B and C)))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-520, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-37127
in-theory        37127
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-520 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-37127.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-520, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-37128
in-theory        37128
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-520 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-37128.        ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-520, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-37129
in-theory        37129
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-520 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-37129.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-520, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-37130
in-theory        37130
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-37130.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-520, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-37131
in-theory        37131
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-520 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-37131.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-520, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-37132
in-theory        37132
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-520 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-37132.        ((A or (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-520, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-37133
in-theory        37133
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     43
proof            (modus-ponens tm-520 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-37133.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-520, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-37134
in-theory        37134
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-520 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37134.        ((A or (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-520, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-37135
in-theory        37135
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-520 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37135.        ((A or (B -> (C -> (B and C)))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-520, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-37136
in-theory        37136
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-520 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37136.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-520, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-37137
in-theory        37137
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-520 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-37137.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-520, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-37138
in-theory        37138
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-520 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37138.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-520, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-37139
in-theory        37139
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) and D) -> E))
theorem-size     17
proof            (modus-ponens tm-520 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-37139.        ((A or (B -> (C -> (B and C)))) and (((D -> E) and D) -> E)), M:tm-520, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-37140
in-theory        37140
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-520 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-37140.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-520, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-37141
in-theory        37141
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-520 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-37141.        ((A or (B -> (C -> (B and C)))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-520, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-37142
in-theory        37142
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-520 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-37142.        ((A or (B -> (C -> (B and C)))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-520, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-37143
in-theory        37143
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     25
proof            (modus-ponens tm-520 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-37143.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-520, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-37144
in-theory        37144
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     35
proof            (modus-ponens tm-520 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-37144.        ((A or (B -> (C -> (B and C)))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-520, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-37145
in-theory        37145
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     37
proof            (modus-ponens tm-520 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-37145.        ((A or (B -> (C -> (B and C)))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-520, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-37146
in-theory        37146
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-520 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-37146.        ((A or (B -> (C -> (B and C)))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-520, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-37147
in-theory        37147
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-520 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-37147.        ((A or (B -> (C -> (B and C)))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-520, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-37148
in-theory        37148
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-520 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-37148.        ((A or (B -> (C -> (B and C)))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-520, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-37149
in-theory        37149
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     33
proof            (modus-ponens tm-520 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-37149.        ((A or (B -> (C -> (B and C)))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-520, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-37150
in-theory        37150
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-520 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-37150.        ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-520, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-37151
in-theory        37151
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-520 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-37151.        ((A or (B -> (C -> (B and C)))) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-520, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-37152
in-theory        37152
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-520 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-37152.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-520, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-37153
in-theory        37153
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-37153.        ((A or (B -> (C -> (B and C)))) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-520, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-37154
in-theory        37154
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     27
proof            (modus-ponens tm-520 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-37154.        ((A or (B -> (C -> (B and C)))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-520, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-37155
in-theory        37155
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-520 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-37155.        ((A or (B -> (C -> (B and C)))) and (D or (E -> ((F and G) -> F)))), M:tm-520, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-37156
in-theory        37156
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-37156.        ((A or (B -> (C -> (B and C)))) and ((D -> ((E and F) -> E)) or G)), M:tm-520, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-37157
in-theory        37157
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-37157.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-520, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-37158
in-theory        37158
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E and F)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-520 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-37158.        ((A or (B -> (C -> (B and C)))) and ((D -> (E and F)) -> (D -> E))), M:tm-520, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-37159
in-theory        37159
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-520 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-37159.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> ((F and G) -> F)))), M:tm-520, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-37160
in-theory        37160
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D and (D -> E)) -> E))
theorem-size     17
proof            (modus-ponens tm-520 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-37160.        ((A or (B -> (C -> (B and C)))) and ((D and (D -> E)) -> E)), M:tm-520, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-37161
in-theory        37161
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-520 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-37161.        ((A or (B -> (C -> (B and C)))) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-520, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-37162
in-theory        37162
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-520 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-37162.        ((A or (B -> (C -> (B and C)))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-520, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-37163
in-theory        37163
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-520 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-37163.        ((A or (B -> (C -> (B and C)))) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-520, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-37164
in-theory        37164
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-520 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-37164.        ((A or (B -> (C -> (B and C)))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-520, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-37165
in-theory        37165
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     25
proof            (modus-ponens tm-520 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-37165.        ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-520, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-37166
in-theory        37166
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     35
proof            (modus-ponens tm-520 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-37166.        ((A or (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-520, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-37167
in-theory        37167
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-520 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-37167.        ((A or (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-520, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-37168
in-theory        37168
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-520 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-37168.        ((A or (B -> (C -> (B and C)))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-520, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-37169
in-theory        37169
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-520 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-37169.        ((A or (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-520, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-37170
in-theory        37170
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-520 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-37170.        ((A or (B -> (C -> (B and C)))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-520, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-37171
in-theory        37171
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     33
proof            (modus-ponens tm-520 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-37171.        ((A or (B -> (C -> (B and C)))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-520, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-37172
in-theory        37172
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-520 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-37172.        ((A or (B -> (C -> (B and C)))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-520, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-37173
in-theory        37173
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-520 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-37173.        ((A or (B -> (C -> (B and C)))) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-520, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-37174
in-theory        37174
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-520 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-37174.        ((A or (B -> (C -> (B and C)))) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-520, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-37175
in-theory        37175
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-520 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-37175.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-520, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-37176
in-theory        37176
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-37176.        ((A or (B -> (C -> (B and C)))) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-520, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-37177
in-theory        37177
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-520 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-37177.        ((A or (B -> (C -> (B and C)))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-520, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-37178
in-theory        37178
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-520 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-37178.        ((A or (B -> (C -> (B and C)))) and (D or (E -> ((F and G) -> G)))), M:tm-520, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-37179
in-theory        37179
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-37179.        ((A or (B -> (C -> (B and C)))) and ((D -> ((E and F) -> F)) or G)), M:tm-520, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-37180
in-theory        37180
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-37180.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-520, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-37181
in-theory        37181
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E and F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-520 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-37181.        ((A or (B -> (C -> (B and C)))) and ((D -> (E and F)) -> (D -> F))), M:tm-520, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-37182
in-theory        37182
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-520 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-37182.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> ((F and G) -> G)))), M:tm-520, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-37183
in-theory        37183
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-37183.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-520, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-37184
in-theory        37184
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-37184.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-520, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-37185
in-theory        37185
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-37185.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-520, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-37186
in-theory        37186
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-520 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37186.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-520, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-37187
in-theory        37187
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-37187.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-520, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37188
in-theory        37188
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-520 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-37188.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-520, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-37189
in-theory        37189
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37189.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-520, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-37190
in-theory        37190
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-37190.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-520, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-37191
in-theory        37191
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-520 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-37191.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-520, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-37192
in-theory        37192
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-37192.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-520, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-37193
in-theory        37193
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-37193.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-520, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-37194
in-theory        37194
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-37194.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-520, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-37195
in-theory        37195
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-520 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-37195.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-520, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-37196
in-theory        37196
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37196.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-520, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-37197
in-theory        37197
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-520 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-37197.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-520, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-37198
in-theory        37198
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-520 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-37198.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-520, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-37199
in-theory        37199
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-520 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-37199.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-520, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-37200
in-theory        37200
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-520 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-37200.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-520, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-37201
in-theory        37201
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-37201.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-520, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-37202
in-theory        37202
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-37202.        ((A or (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-520, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-37203
in-theory        37203
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-520 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-37203.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-520, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-37204
in-theory        37204
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-520 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-37204.        ((A or (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-520, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-37205
in-theory        37205
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-520 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-37205.        ((A or (B -> (C -> (B and C)))) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-520, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-37206
in-theory        37206
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-37206.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-520, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-37207
in-theory        37207
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-520 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-37207.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-520, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-37208
in-theory        37208
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-520 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-37208.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-520, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-37209
in-theory        37209
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-37209.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-520, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-37210
in-theory        37210
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-520 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-37210.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-520, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-37211
in-theory        37211
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-520 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37211.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-520, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-37212
in-theory        37212
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-37212.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-520, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-37213
in-theory        37213
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-37213.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-520, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-37214
in-theory        37214
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-520 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37214.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-520, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-37215
in-theory        37215
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-37215.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-520, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-37216
in-theory        37216
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-520 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-37216.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-520, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-37217
in-theory        37217
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-520 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-37217.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-520, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-37218
in-theory        37218
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-37218.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-520, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-37219
in-theory        37219
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-520 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-37219.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-520, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-37220
in-theory        37220
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-520 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-37220.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-520, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-37221
in-theory        37221
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-520 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37221.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-520, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-37222
in-theory        37222
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-520 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-37222.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-520, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-37223
in-theory        37223
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-520 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-37223.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-520, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-37224
in-theory        37224
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-520 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-37224.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-520, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-37225
in-theory        37225
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-520 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-37225.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-520, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-37226
in-theory        37226
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-520 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-37226.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-520, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-37227
in-theory        37227
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-520 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-37227.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-520, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-37228
in-theory        37228
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-520 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-37228.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-520, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-37229
in-theory        37229
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-520 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-37229.        ((A or (B -> (C -> (B and C)))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-520, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-37230
in-theory        37230
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-520 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-37230.        ((A or (B -> (C -> (B and C)))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-520, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-37231
in-theory        37231
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-520 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-37231.        ((A or (B -> (C -> (B and C)))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-520, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-37232
in-theory        37232
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     29
proof            (modus-ponens tm-520 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-37232.        ((A or (B -> (C -> (B and C)))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-520, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-37233
in-theory        37233
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-520 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-37233.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-520, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-37234
in-theory        37234
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-520 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-37234.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-520, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-37235
in-theory        37235
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-37235.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-520, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-37236
in-theory        37236
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-37236.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-520, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-37237
in-theory        37237
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-37237.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F and G) -> F))), M:tm-520, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-37238
in-theory        37238
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-520 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37238.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F and G) -> G))), M:tm-520, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-37239
in-theory        37239
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-37239.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-520, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37240
in-theory        37240
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-520 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-37240.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (F or G)))), M:tm-520, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-37241
in-theory        37241
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37241.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G or F)))), M:tm-520, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-37242
in-theory        37242
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-37242.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-520, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-37243
in-theory        37243
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-520 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-37243.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-520, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-37244
in-theory        37244
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-37244.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-520, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-37245
in-theory        37245
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-37245.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-520, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-37246
in-theory        37246
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-37246.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-520, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-37247
in-theory        37247
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-520 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-37247.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-520, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-37248
in-theory        37248
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37248.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-520, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-37249
in-theory        37249
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-520 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-37249.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-520, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-37250
in-theory        37250
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-520 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-37250.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-520, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-37251
in-theory        37251
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-520 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-37251.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-520, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-37252
in-theory        37252
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-520 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-37252.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-520, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-37253
in-theory        37253
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-37253.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-520, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-37254
in-theory        37254
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-520 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-37254.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-520, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-37255
in-theory        37255
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-37255.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-520, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-37256
in-theory        37256
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-520 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-37256.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-520, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-37257
in-theory        37257
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-37257.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-520, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-37258
in-theory        37258
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-37258.        ((A or (B -> (C -> (B and C)))) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-520, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-37259
in-theory        37259
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-520 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-37259.        ((A or (B -> (C -> (B and C)))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-520, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-37260
in-theory        37260
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-520 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-37260.        ((A or (B -> (C -> (B and C)))) and (D or (E -> (((F and G) -> F) and E)))), M:tm-520, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-37261
in-theory        37261
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-520 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-37261.        ((A or (B -> (C -> (B and C)))) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-520, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-37262
in-theory        37262
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-37262.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-520, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-37263
in-theory        37263
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-520 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-37263.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-520, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-37264
in-theory        37264
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-37264.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-520, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-37265
in-theory        37265
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-37265.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-520, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-37266
in-theory        37266
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-37266.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F and G) -> F))), M:tm-520, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-37267
in-theory        37267
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-520 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37267.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F and G) -> G))), M:tm-520, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-37268
in-theory        37268
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-37268.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-520, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37269
in-theory        37269
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-520 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-37269.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (F or G)))), M:tm-520, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-37270
in-theory        37270
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37270.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G or F)))), M:tm-520, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-37271
in-theory        37271
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-37271.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-520, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-37272
in-theory        37272
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-520 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-37272.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-520, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-37273
in-theory        37273
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-37273.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-520, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-37274
in-theory        37274
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-37274.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-520, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-37275
in-theory        37275
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-37275.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-520, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-37276
in-theory        37276
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-520 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-37276.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-520, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-37277
in-theory        37277
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37277.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-520, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-37278
in-theory        37278
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-520 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-37278.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-520, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-37279
in-theory        37279
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-520 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-37279.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-520, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-37280
in-theory        37280
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-520 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-37280.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-520, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-37281
in-theory        37281
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-520 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-37281.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-520, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-37282
in-theory        37282
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-37282.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-520, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-37283
in-theory        37283
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-520 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-37283.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-520, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-37284
in-theory        37284
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-37284.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-520, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-37285
in-theory        37285
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-37285.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-520, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-37286
in-theory        37286
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-37286.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-520, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-37287
in-theory        37287
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-520 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-37287.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-520, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-37288
in-theory        37288
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-37288.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-520, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-37289
in-theory        37289
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-37289.        ((A or (B -> (C -> (B and C)))) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-520, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-37290
in-theory        37290
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-520 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-37290.        ((A or (B -> (C -> (B and C)))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-520, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-37291
in-theory        37291
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-520 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-37291.        ((A or (B -> (C -> (B and C)))) and (D or (E -> (((F and G) -> G) and E)))), M:tm-520, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-37292
in-theory        37292
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-520 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-37292.        ((A or (B -> (C -> (B and C)))) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-520, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-37293
in-theory        37293
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-37293.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-520, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-37294
in-theory        37294
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-520 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-37294.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-520, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-37295
in-theory        37295
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-37295.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-520, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-37296
in-theory        37296
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-37296.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-520, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-37297
in-theory        37297
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-520 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-37297.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-520, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-37298
in-theory        37298
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-520 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37298.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-520, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-37299
in-theory        37299
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-37299.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-520, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37300
in-theory        37300
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-520 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-37300.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-520, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-37301
in-theory        37301
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37301.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-520, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-37302
in-theory        37302
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-37302.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-520, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-37303
in-theory        37303
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-37303.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-520, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-37304
in-theory        37304
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-520 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-37304.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-520, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-37305
in-theory        37305
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-37305.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-520, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-37306
in-theory        37306
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-37306.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-520, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-37307
in-theory        37307
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-37307.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-520, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-37308
in-theory        37308
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-520 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37308.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-520, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-37309
in-theory        37309
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-520 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-37309.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-520, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-37310
in-theory        37310
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-520 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-37310.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-520, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-37311
in-theory        37311
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-520 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-37311.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-520, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-37312
in-theory        37312
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-520 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-37312.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-520, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-37313
in-theory        37313
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-520 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-37313.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-520, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-37314
in-theory        37314
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-520 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-37314.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-520, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-37315
in-theory        37315
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-520 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-37315.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-520, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-37316
in-theory        37316
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-520 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-37316.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-520, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-37317
in-theory        37317
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-520 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-37317.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-520, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-37318
in-theory        37318
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-520 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-37318.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-520, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-37319
in-theory        37319
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-520 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-37319.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-520, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-37320
in-theory        37320
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-520 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-37320.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-520, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-37321
in-theory        37321
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-520 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-37321.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-520, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-37322
in-theory        37322
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-520 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-37322.        ((A or (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-520, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-37323
in-theory        37323
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-520 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-37323.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-520, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-37324
in-theory        37324
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-520 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-37324.        ((A or (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-520, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-37325
in-theory        37325
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-520 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-37325.        ((A or (B -> (C -> (B and C)))) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-520, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-37326
in-theory        37326
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-520 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-37326.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-520, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-37327
in-theory        37327
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-520 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-37327.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-520, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-37328
in-theory        37328
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and (E -> D))))
theorem-size     17
proof            (modus-ponens tm-520 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-37328.        ((A or (B -> (C -> (B and C)))) and (D -> (D and (E -> D)))), M:tm-520, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-37329
in-theory        37329
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-37329.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-520, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-37330
in-theory        37330
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D and E) -> ((D and E) and D)))
theorem-size     19
proof            (modus-ponens tm-520 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-37330.        ((A or (B -> (C -> (B and C)))) and ((D and E) -> ((D and E) and D))), M:tm-520, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-37331
in-theory        37331
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D and E) -> ((D and E) and E)))
theorem-size     19
proof            (modus-ponens tm-520 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-37331.        ((A or (B -> (C -> (B and C)))) and ((D and E) -> ((D and E) and E))), M:tm-520, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-37332
in-theory        37332
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-37332.        ((A or (B -> (C -> (B and C)))) and (D -> (D and (E -> (D and E))))), M:tm-520, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-37333
in-theory        37333
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and (D or E))))
theorem-size     17
proof            (modus-ponens tm-520 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-37333.        ((A or (B -> (C -> (B and C)))) and (D -> (D and (D or E)))), M:tm-520, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-37334
in-theory        37334
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and (E or D))))
theorem-size     17
proof            (modus-ponens tm-520 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-37334.        ((A or (B -> (C -> (B and C)))) and (D -> (D and (E or D)))), M:tm-520, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-37335
in-theory        37335
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     27
proof            (modus-ponens tm-520 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-37335.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-520, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-37336
in-theory        37336
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-37336.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-520, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-37337
in-theory        37337
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     19
proof            (modus-ponens tm-520 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-37337.        ((A or (B -> (C -> (B and C)))) and ((not (not D)) -> ((not (not D)) and D))), M:tm-520, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-37338
in-theory        37338
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-37338.        ((A or (B -> (C -> (B and C)))) and (D -> (D and (E -> (F -> E))))), M:tm-520, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-37339
in-theory        37339
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     21
proof            (modus-ponens tm-520 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-37339.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-520, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-37340
in-theory        37340
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-520 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-37340.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-520, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-37341
in-theory        37341
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-520 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-37341.        ((A or (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-520, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-37342
in-theory        37342
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     33
proof            (modus-ponens tm-520 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-37342.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-520, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-37343
in-theory        37343
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-520 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-37343.        ((A or (B -> (C -> (B and C)))) and (D -> (D and ((E and F) -> E)))), M:tm-520, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-37344
in-theory        37344
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     33
proof            (modus-ponens tm-520 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-37344.        ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-520, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-37345
in-theory        37345
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-520 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-37345.        ((A or (B -> (C -> (B and C)))) and (D -> (D and ((E and F) -> F)))), M:tm-520, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-37346
in-theory        37346
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-520 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-37346.        ((A or (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-520, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-37347
in-theory        37347
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-520 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-37347.        ((A or (B -> (C -> (B and C)))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-520, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-37348
in-theory        37348
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-520 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-37348.        ((A or (B -> (C -> (B and C)))) and (D -> (D and (((E and F) -> E) and D)))), M:tm-520, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-37349
in-theory        37349
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-520 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-37349.        ((A or (B -> (C -> (B and C)))) and (D -> (D and (((E and F) -> F) and D)))), M:tm-520, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-37350
in-theory        37350
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-520 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-37350.        ((A or (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-520, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-37351
in-theory        37351
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-37351.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-520, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-37352
in-theory        37352
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-520 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-37352.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-520, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-37353
in-theory        37353
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-37353.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-520, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-37354
in-theory        37354
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-37354.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-520, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-37355
in-theory        37355
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-520 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-37355.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-520, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-37356
in-theory        37356
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-37356.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-520, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-37357
in-theory        37357
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-520 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-37357.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-520, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-37358
in-theory        37358
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     29
proof            (modus-ponens tm-520 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-37358.        ((A or (B -> (C -> (B and C)))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-520, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-37359
in-theory        37359
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-520 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-37359.        ((A or (B -> (C -> (B and C)))) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-520, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-37360
in-theory        37360
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     21
proof            (modus-ponens tm-520 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-37360.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-520, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-37361
in-theory        37361
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-37361.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-520, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-37362
in-theory        37362
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-520 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-37362.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-520, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-37363
in-theory        37363
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-520 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-37363.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-520, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-37364
in-theory        37364
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-520 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-37364.        ((A or (B -> (C -> (B and C)))) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-520, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-37365
in-theory        37365
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-520 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37365.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-520, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-37366
in-theory        37366
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-520 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37366.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-520, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-37367
in-theory        37367
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-520 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37367.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-520, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-37368
in-theory        37368
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-520 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37368.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-520, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-37369
in-theory        37369
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-520 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37369.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-520, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-37370
in-theory        37370
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-520 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-37370.        ((A or (B -> (C -> (B and C)))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-520, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-37371
in-theory        37371
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-520 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-37371.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-520, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-37372
in-theory        37372
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-520 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-37372.        ((A or (B -> (C -> (B and C)))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-520, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-37373
in-theory        37373
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-37373.        ((A or (B -> (C -> (B and C)))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-520, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-37374
in-theory        37374
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     31
proof            (modus-ponens tm-520 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-37374.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-520, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-37375
in-theory        37375
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-520 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37375.        ((A or (B -> (C -> (B and C)))) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-520, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37376
in-theory        37376
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-520 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37376.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-520, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37377
in-theory        37377
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37377.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-520, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37378
in-theory        37378
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-520 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-37378.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-520, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-37379
in-theory        37379
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-520 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37379.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-520, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37380
in-theory        37380
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-520 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-37380.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-520, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-37381
in-theory        37381
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-37381.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-520, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-37382
in-theory        37382
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-37382.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-520, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-37383
in-theory        37383
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-37383.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-520, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-37384
in-theory        37384
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-37384.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-520, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-37385
in-theory        37385
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-520 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-37385.        ((A or (B -> (C -> (B and C)))) and (D or ((E -> (F -> E)) or G))), M:tm-520, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-37386
in-theory        37386
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-37386.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> D)) or F) or G)), M:tm-520, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-37387
in-theory        37387
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-37387.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-520, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-37388
in-theory        37388
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-520 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-37388.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> E)) or G))), M:tm-520, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-37389
in-theory        37389
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-520 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-37389.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-520, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-37390
in-theory        37390
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-37390.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-520, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-37391
in-theory        37391
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-37391.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-520, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-37392
in-theory        37392
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-520 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-37392.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-520, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-37393
in-theory        37393
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-37393.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-520, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-37394
in-theory        37394
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-520 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-37394.        ((A or (B -> (C -> (B and C)))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-520, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-37395
in-theory        37395
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-520 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-37395.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-520, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-37396
in-theory        37396
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-520 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-37396.        ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-520, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-37397
in-theory        37397
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-520 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-37397.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-520, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-37398
in-theory        37398
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-520 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-37398.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-520, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-37399
in-theory        37399
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-37399.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-520, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-37400
in-theory        37400
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-37400.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-520, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-37401
in-theory        37401
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-37401.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-520, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-37402
in-theory        37402
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-37402.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-520, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-37403
in-theory        37403
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-520 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-37403.        ((A or (B -> (C -> (B and C)))) and (D or (((E and F) -> E) or G))), M:tm-520, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-37404
in-theory        37404
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D and E) -> D) or F) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-37404.        ((A or (B -> (C -> (B and C)))) and ((((D and E) -> D) or F) or G)), M:tm-520, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-37405
in-theory        37405
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-37405.        ((A or (B -> (C -> (B and C)))) and (D -> ((((E and F) -> E) or G) and D))), M:tm-520, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-37406
in-theory        37406
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-520 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-37406.        ((A or (B -> (C -> (B and C)))) and (D -> (((E and F) -> E) or G))), M:tm-520, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-37407
in-theory        37407
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-520 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-37407.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-520, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-37408
in-theory        37408
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-37408.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-520, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-37409
in-theory        37409
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-37409.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-520, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-37410
in-theory        37410
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-37410.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-520, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-37411
in-theory        37411
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-37411.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-520, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-37412
in-theory        37412
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-520 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-37412.        ((A or (B -> (C -> (B and C)))) and (D or (((E and F) -> F) or G))), M:tm-520, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-37413
in-theory        37413
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D and E) -> E) or F) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-37413.        ((A or (B -> (C -> (B and C)))) and ((((D and E) -> E) or F) or G)), M:tm-520, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-37414
in-theory        37414
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-37414.        ((A or (B -> (C -> (B and C)))) and (D -> ((((E and F) -> F) or G) and D))), M:tm-520, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-37415
in-theory        37415
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-520 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-37415.        ((A or (B -> (C -> (B and C)))) and (D -> (((E and F) -> F) or G))), M:tm-520, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-37416
in-theory        37416
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-520 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-37416.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-520, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-37417
in-theory        37417
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-520 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-37417.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-520, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-37418
in-theory        37418
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-520 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-37418.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-520, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-37419
in-theory        37419
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-520 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-37419.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-520, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-37420
in-theory        37420
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-520 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-37420.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-520, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-37421
in-theory        37421
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-520 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-37421.        ((A or (B -> (C -> (B and C)))) and (D or ((E -> (F -> (E and F))) or G))), M:tm-520, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-37422
in-theory        37422
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     21
proof            (modus-ponens tm-520 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-37422.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> (D and E))) or F) or G)), M:tm-520, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-37423
in-theory        37423
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-37423.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-520, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-37424
in-theory        37424
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-520 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-37424.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-520, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-37425
in-theory        37425
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-520 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-37425.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-520, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-37426
in-theory        37426
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-37426.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-520, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-37427
in-theory        37427
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-37427.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-520, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-37428
in-theory        37428
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-37428.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-520, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-37429
in-theory        37429
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-37429.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-520, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-37430
in-theory        37430
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-520 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-37430.        ((A or (B -> (C -> (B and C)))) and (D or ((E -> (E or F)) or G))), M:tm-520, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-37431
in-theory        37431
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (D or E)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-37431.        ((A or (B -> (C -> (B and C)))) and (((D -> (D or E)) or F) or G)), M:tm-520, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-37432
in-theory        37432
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-37432.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (E or F)) or G) and D))), M:tm-520, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-37433
in-theory        37433
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-520 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-37433.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (E or F)) or G))), M:tm-520, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-37434
in-theory        37434
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-37434.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-520, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-37435
in-theory        37435
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-37435.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-520, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-37436
in-theory        37436
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-37436.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-520, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-37437
in-theory        37437
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-520 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37437.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-520, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-37438
in-theory        37438
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-37438.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-520, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37439
in-theory        37439
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-520 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-37439.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-520, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-37440
in-theory        37440
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37440.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-520, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-37441
in-theory        37441
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-37441.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-520, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-37442
in-theory        37442
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-520 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-37442.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-520, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-37443
in-theory        37443
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-37443.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-520, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-37444
in-theory        37444
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-37444.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-520, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-37445
in-theory        37445
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-37445.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-520, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-37446
in-theory        37446
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-520 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-37446.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-520, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-37447
in-theory        37447
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37447.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-520, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-37448
in-theory        37448
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-520 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-37448.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-520, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-37449
in-theory        37449
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-520 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-37449.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-520, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-37450
in-theory        37450
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-520 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-37450.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-520, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-37451
in-theory        37451
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-520 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-37451.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-520, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-37452
in-theory        37452
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-37452.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-520, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-37453
in-theory        37453
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-520 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-37453.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-520, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-37454
in-theory        37454
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-37454.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-520, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-37455
in-theory        37455
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-37455.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-520, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-37456
in-theory        37456
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-520 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-37456.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-520, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-37457
in-theory        37457
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-37457.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-520, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-37458
in-theory        37458
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-520 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37458.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-520, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-37459
in-theory        37459
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-37459.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-520, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-37460
in-theory        37460
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-37460.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-520, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-37461
in-theory        37461
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-37461.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-520, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-37462
in-theory        37462
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-37462.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-520, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-37463
in-theory        37463
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-520 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-37463.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-520, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-37464
in-theory        37464
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-37464.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-520, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-37465
in-theory        37465
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-37465.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-520, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-37466
in-theory        37466
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-520 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-37466.        ((A or (B -> (C -> (B and C)))) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-520, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-37467
in-theory        37467
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-520 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-37467.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-520, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-37468
in-theory        37468
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-37468.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-520, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-37469
in-theory        37469
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-37469.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-520, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-37470
in-theory        37470
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-520 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-37470.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-520, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-37471
in-theory        37471
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-37471.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-520, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-37472
in-theory        37472
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-37472.        ((A or (B -> (C -> (B and C)))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-520, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-37473
in-theory        37473
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-520 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-37473.        ((A or (B -> (C -> (B and C)))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-520, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-37474
in-theory        37474
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-520 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-37474.        ((A or (B -> (C -> (B and C)))) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-520, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-37475
in-theory        37475
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-520 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-37475.        ((A or (B -> (C -> (B and C)))) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-520, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-37476
in-theory        37476
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-37476.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-520, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-37477
in-theory        37477
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-520 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-37477.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-520, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-37478
in-theory        37478
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-37478.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-520, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37479
in-theory        37479
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-37479.        ((A or (B -> (C -> (B and C)))) and (D -> (D and (E -> (E or F))))), M:tm-520, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-37480
in-theory        37480
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-37480.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-520, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37481
in-theory        37481
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-37481.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-520, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37482
in-theory        37482
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-37482.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-520, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37483
in-theory        37483
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-37483.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-520, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37484
in-theory        37484
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-37484.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-520, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37485
in-theory        37485
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-520 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-37485.        ((A or (B -> (C -> (B and C)))) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-520, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-37486
in-theory        37486
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-520 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-37486.        ((A or (B -> (C -> (B and C)))) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-520, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-37487
in-theory        37487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-37487.        ((A or (B -> (C -> (B and C)))) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-520, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-37488
in-theory        37488
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-37488.        ((A or (B -> (C -> (B and C)))) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-520, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-37489
in-theory        37489
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-520 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-37489.        ((A or (B -> (C -> (B and C)))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-520, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-37490
in-theory        37490
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-37490.        ((A or (B -> (C -> (B and C)))) and (D or (E -> (F -> (F or G))))), M:tm-520, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-37491
in-theory        37491
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-37491.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (E or F))) or G)), M:tm-520, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-37492
in-theory        37492
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-37492.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-520, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-37493
in-theory        37493
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-520 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-37493.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (E or F)))), M:tm-520, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-37494
in-theory        37494
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-37494.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> (F -> (F or G))))), M:tm-520, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-37495
in-theory        37495
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-37495.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-520, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-37496
in-theory        37496
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-37496.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-520, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-37497
in-theory        37497
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-37497.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-520, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-37498
in-theory        37498
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-37498.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-520, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-37499
in-theory        37499
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-37499.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-520, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-37500
in-theory        37500
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-37500.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-520, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-37501
in-theory        37501
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-37501.        ((A or (B -> (C -> (B and C)))) and (D or (E or (F -> (G -> F))))), M:tm-520, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-37502
in-theory        37502
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-37502.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (F -> E))) or G)), M:tm-520, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-37503
in-theory        37503
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-37503.        ((A or (B -> (C -> (B and C)))) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-520, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-37504
in-theory        37504
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-37504.        ((A or (B -> (C -> (B and C)))) and (D -> (E or (F -> (G -> F))))), M:tm-520, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-37505
in-theory        37505
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37505.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-520, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-37506
in-theory        37506
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-520 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37506.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-520, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-37507
in-theory        37507
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37507.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-520, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-37508
in-theory        37508
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37508.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-520, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-37509
in-theory        37509
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-520 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37509.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-520, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-37510
in-theory        37510
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37510.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-520, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-37511
in-theory        37511
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-520 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37511.        ((A or (B -> (C -> (B and C)))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-520, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-37512
in-theory        37512
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-520 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37512.        ((A or (B -> (C -> (B and C)))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-520, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-37513
in-theory        37513
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-520 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37513.        ((A or (B -> (C -> (B and C)))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-520, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-37514
in-theory        37514
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-520 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-37514.        ((A or (B -> (C -> (B and C)))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-520, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-37515
in-theory        37515
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-520 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-37515.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-520, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-37516
in-theory        37516
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-520 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-37516.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-520, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-37517
in-theory        37517
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-520 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-37517.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-520, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-37518
in-theory        37518
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-520 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-37518.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-520, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-37519
in-theory        37519
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-520 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-37519.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-520, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-37520
in-theory        37520
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-520 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-37520.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-520, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-37521
in-theory        37521
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-520 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-37521.        ((A or (B -> (C -> (B and C)))) and (D or (E or ((F and G) -> F)))), M:tm-520, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-37522
in-theory        37522
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-37522.        ((A or (B -> (C -> (B and C)))) and ((D or ((E and F) -> E)) or G)), M:tm-520, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-37523
in-theory        37523
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-37523.        ((A or (B -> (C -> (B and C)))) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-520, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-37524
in-theory        37524
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-520 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-37524.        ((A or (B -> (C -> (B and C)))) and (D -> (E or ((F and G) -> F)))), M:tm-520, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-37525
in-theory        37525
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-520 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-37525.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-520, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-37526
in-theory        37526
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-520 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-37526.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-520, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-37527
in-theory        37527
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-520 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-37527.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-520, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-37528
in-theory        37528
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-520 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-37528.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-520, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-37529
in-theory        37529
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-520 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-37529.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-520, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-37530
in-theory        37530
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-520 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-37530.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-520, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-37531
in-theory        37531
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-520 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-37531.        ((A or (B -> (C -> (B and C)))) and (D or (E or ((F and G) -> G)))), M:tm-520, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-37532
in-theory        37532
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-37532.        ((A or (B -> (C -> (B and C)))) and ((D or ((E and F) -> F)) or G)), M:tm-520, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-37533
in-theory        37533
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-37533.        ((A or (B -> (C -> (B and C)))) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-520, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-37534
in-theory        37534
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-520 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-37534.        ((A or (B -> (C -> (B and C)))) and (D -> (E or ((F and G) -> G)))), M:tm-520, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-37535
in-theory        37535
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-520 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37535.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-520, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-37536
in-theory        37536
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-520 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37536.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-520, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-37537
in-theory        37537
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-520 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37537.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-520, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-37538
in-theory        37538
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-520 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37538.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-520, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-37539
in-theory        37539
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-520 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37539.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-520, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-37540
in-theory        37540
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-520 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37540.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-520, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-37541
in-theory        37541
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-520 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37541.        ((A or (B -> (C -> (B and C)))) and (D or (E or (F -> (G -> (F and G)))))), M:tm-520, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37542
in-theory        37542
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-520 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37542.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-520, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-37543
in-theory        37543
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37543.        ((A or (B -> (C -> (B and C)))) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-520, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37544
in-theory        37544
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37544.        ((A or ((B and C) -> C)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-510, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37545
in-theory        37545
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37545.        ((A or ((B and C) -> B)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-500, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37546
in-theory        37546
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (H -> (G and H)))) and E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37546.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (H -> (G and H)))) and E))), M:tm-490, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37547
in-theory        37547
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37547.        ((A or (B -> (C -> B))) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-480, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37548
in-theory        37548
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (D -> (C and D)))) and A) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37548.        (A -> (((B or (C -> (D -> (C and D)))) and A) or E)), M:tm-470, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-37549
in-theory        37549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37549.        ((A -> (B -> (B or C))) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-469, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37550
in-theory        37550
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D or (E -> (F -> (E and F)))) and (B -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-466 tm-520 ((Am (-> A (or A B))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37550.        ((A or (B -> (B or C))) -> ((D or (E -> (F -> (E and F)))) and (B -> (B or C)))), M:tm-466, m:tm-520, u:((Am (-> A (or A B))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (or A B)))))
================================================================
tm-name          tm-37551
in-theory        37551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37551.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (E -> (E or F))), M:tm-456, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37552
in-theory        37552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37552.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-453, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37553
in-theory        37553
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D or (E -> (F -> (E and F)))) and ((B -> (B or C)) and A)))
theorem-size     27
proof            (modus-ponens tm-450 tm-520 ((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37553.        ((A or ((B -> (B or C)) and A)) -> ((D or (E -> (F -> (E and F)))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-520, u:((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-37554
in-theory        37554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((E -> (E or F)) and (A -> ((B or (C -> (D -> (C and D)))) and A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37554.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((E -> (E or F)) and (A -> ((B or (C -> (D -> (C and D)))) and A)))), M:tm-443, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37555
in-theory        37555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37555.        (((A -> (A or B)) or C) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-409, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37556
in-theory        37556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37556.        (((A -> (B -> (A and B))) or C) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-400, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37557
in-theory        37557
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37557.        ((((A and B) -> B) or C) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-391, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37558
in-theory        37558
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37558.        ((((A and B) -> A) or C) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-382, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37559
in-theory        37559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or (G -> (H -> (G and H)))) and E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37559.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or (G -> (H -> (G and H)))) and E))), M:tm-373, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37560
in-theory        37560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37560.        (((A -> (B -> A)) or C) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-364, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37561
in-theory        37561
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C or (D -> (E -> (D and E)))) and A) and B)))
theorem-size     17
proof            (modus-ponens tm-355 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37561.        (A -> (B -> (((C or (D -> (E -> (D and E)))) and A) and B))), M:tm-355, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-37562
in-theory        37562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37562.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-354, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37563
in-theory        37563
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D or (E -> (F -> (E and F)))) and (B -> (C -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-351 tm-520 ((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37563.        ((A or (B -> (C -> (B and C)))) -> ((D or (E -> (F -> (E and F)))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-520, u:((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-37564
in-theory        37564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37564.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37565
in-theory        37565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D or (E -> (F -> (E and F)))) and C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37565.        (((A -> B) -> (A -> (A and B))) and (C -> ((D or (E -> (F -> (E and F)))) and C))), M:tm-338, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37566
in-theory        37566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C or (D -> (E -> (D and E)))) and (A -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-335 tm-520 ((Am (-> A (and A B))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37566.        (((A -> B) or (A -> (A and B))) -> ((C or (D -> (E -> (D and E)))) and (A -> (A and B)))), M:tm-335, m:tm-520, u:((Am (-> A (and A B))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (and A B)))))
================================================================
tm-name          tm-37567
in-theory        37567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (A -> (A and ((B or (C -> (D -> (C and D)))) and A))))
theorem-size     29
proof            (modus-ponens tm-328 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37567.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (A -> (A and ((B or (C -> (D -> (C and D)))) and A)))), M:tm-328, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-37568
in-theory        37568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B or (C -> (D -> (C and D)))) and A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37568.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B or (C -> (D -> (C and D)))) and A)))), M:tm-327, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37569
in-theory        37569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (((E and F) -> F) and (A -> ((B or (C -> (D -> (C and D)))) and A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37569.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (((E and F) -> F) and (A -> ((B or (C -> (D -> (C and D)))) and A)))), M:tm-326, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37570
in-theory        37570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (((E and F) -> E) and (A -> ((B or (C -> (D -> (C and D)))) and A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37570.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (((E and F) -> E) and (A -> ((B or (C -> (D -> (C and D)))) and A)))), M:tm-325, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37571
in-theory        37571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B or (C -> (D -> (C and D)))) and A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37571.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B or (C -> (D -> (C and D)))) and A)))), M:tm-324, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37572
in-theory        37572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((E -> (F -> E)) and (A -> ((B or (C -> (D -> (C and D)))) and A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37572.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((E -> (F -> E)) and (A -> ((B or (C -> (D -> (C and D)))) and A)))), M:tm-323, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37573
in-theory        37573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37573.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((E and F) -> F)), M:tm-322, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37574
in-theory        37574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37574.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((E and F) -> E)), M:tm-320, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37575
in-theory        37575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37575.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37576
in-theory        37576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (A -> A))
theorem-size     17
proof            (modus-ponens tm-316 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37576.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (A -> A)), M:tm-316, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-37577
in-theory        37577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37577.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (E -> (F -> E))), M:tm-315, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37578
in-theory        37578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((A -> (not ((B or (C -> (D -> (C and D)))) and A))) -> (not A)))
theorem-size     31
proof            (modus-ponens tm-313 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37578.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((A -> (not ((B or (C -> (D -> (C and D)))) and A))) -> (not A))), M:tm-313, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-37579
in-theory        37579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((((B or (C -> (D -> (C and D)))) and A) -> E) -> ((A or ((B or (C -> (D -> (C and D)))) and A)) -> E)))
theorem-size     43
proof            (modus-ponens tm-312 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37579.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((((B or (C -> (D -> (C and D)))) and A) -> E) -> ((A or ((B or (C -> (D -> (C and D)))) and A)) -> E))), M:tm-312, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-37580
in-theory        37580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (E or (A -> ((B or (C -> (D -> (C and D)))) and A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37580.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (E or (A -> ((B or (C -> (D -> (C and D)))) and A)))), M:tm-311, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37581
in-theory        37581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((A -> ((B or (C -> (D -> (C and D)))) and A)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37581.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((A -> ((B or (C -> (D -> (C and D)))) and A)) or E)), M:tm-310, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37582
in-theory        37582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (E -> ((A -> ((B or (C -> (D -> (C and D)))) and A)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37582.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (E -> ((A -> ((B or (C -> (D -> (C and D)))) and A)) and E))), M:tm-309, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37583
in-theory        37583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (E -> (A -> ((B or (C -> (D -> (C and D)))) and A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37583.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (E -> (A -> ((B or (C -> (D -> (C and D)))) and A)))), M:tm-305, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37584
in-theory        37584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37584.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-303, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37585
in-theory        37585
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D or (E -> (F -> (E and F)))) and ((B -> (C -> (B and C))) and A)))
theorem-size     31
proof            (modus-ponens tm-300 tm-520 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37585.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D or (E -> (F -> (E and F)))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-520, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-37586
in-theory        37586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37586.        ((A -> (((B and C) -> C) and A)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-270, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37587
in-theory        37587
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D or (E -> (F -> (E and F)))) and (((B and C) -> C) and A)))
theorem-size     27
proof            (modus-ponens tm-267 tm-520 ((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37587.        ((A or (((B and C) -> C) and A)) -> ((D or (E -> (F -> (E and F)))) and (((B and C) -> C) and A))), M:tm-267, m:tm-520, u:((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-37588
in-theory        37588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37588.        ((A -> (((B and C) -> B) and A)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-239, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37589
in-theory        37589
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D or (E -> (F -> (E and F)))) and (((B and C) -> B) and A)))
theorem-size     27
proof            (modus-ponens tm-236 tm-520 ((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37589.        ((A or (((B and C) -> B) and A)) -> ((D or (E -> (F -> (E and F)))) and (((B and C) -> B) and A))), M:tm-236, m:tm-520, u:((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-37590
in-theory        37590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or (G -> (H -> (G and H)))) and E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37590.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or (G -> (H -> (G and H)))) and E))), M:tm-210, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37591
in-theory        37591
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or (F -> (G -> (F and G)))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     43
proof            (modus-ponens tm-207 tm-520 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37591.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or (F -> (G -> (F and G)))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-520, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-37592
in-theory        37592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37592.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-183, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37593
in-theory        37593
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D or (E -> (F -> (E and F)))) and ((B -> (C -> B)) and A)))
theorem-size     27
proof            (modus-ponens tm-180 tm-520 ((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37593.        ((A or ((B -> (C -> B)) and A)) -> ((D or (E -> (F -> (E and F)))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-520, u:((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-37594
in-theory        37594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37594.        ((A -> ((B and C) -> C)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-157, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37595
in-theory        37595
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D or (E -> (F -> (E and F)))) and ((B and C) -> C)))
theorem-size     23
proof            (modus-ponens tm-154 tm-520 ((Am (-> (and A B) B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37595.        ((A or ((B and C) -> C)) -> ((D or (E -> (F -> (E and F)))) and ((B and C) -> C))), M:tm-154, m:tm-520, u:((Am (-> (and A B) B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and A B) B))))
================================================================
tm-name          tm-37596
in-theory        37596
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37596.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-147, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37597
in-theory        37597
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or (E -> (F -> (E and F)))) and ((A and (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-144 tm-520 ((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37597.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or (E -> (F -> (E and F)))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-520, u:((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-37598
in-theory        37598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37598.        ((A -> ((B and C) -> B)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-134, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37599
in-theory        37599
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D or (E -> (F -> (E and F)))) and ((B and C) -> B)))
theorem-size     23
proof            (modus-ponens tm-131 tm-520 ((Am (-> (and A B) A)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37599.        ((A or ((B and C) -> B)) -> ((D or (E -> (F -> (E and F)))) and ((B and C) -> B))), M:tm-131, m:tm-520, u:((Am (-> (and A B) A)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and A B) A))))
================================================================
tm-name          tm-37600
in-theory        37600
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37600.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-125, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37601
in-theory        37601
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or (E -> (F -> (E and F)))) and (((A -> B) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-122 tm-520 ((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37601.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or (E -> (F -> (E and F)))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-520, u:((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-37602
in-theory        37602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (H -> (G and H)))) and E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37602.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (H -> (G and H)))) and E))), M:tm-113, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37603
in-theory        37603
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or (F -> (G -> (F and G)))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     39
proof            (modus-ponens tm-110 tm-520 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37603.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or (F -> (G -> (F and G)))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-520, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-37604
in-theory        37604
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37604.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-105, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37605
in-theory        37605
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or (E -> (F -> (E and F)))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-102 tm-520 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37605.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or (E -> (F -> (E and F)))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-520, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-37606
in-theory        37606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D or (E -> (F -> (E and F)))) and C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37606.        (((A -> B) -> (A -> A)) and (C -> ((D or (E -> (F -> (E and F)))) and C))), M:tm-95, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37607
in-theory        37607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C or (D -> (E -> (D and E)))) and (A -> A)))
theorem-size     21
proof            (modus-ponens tm-92 tm-520 ((Am (-> A A)) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37607.        (((A -> B) or (A -> A)) -> ((C or (D -> (E -> (D and E)))) and (A -> A))), M:tm-92, m:tm-520, u:((Am (-> A A)) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A A))))
================================================================
tm-name          tm-37608
in-theory        37608
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C or (D -> (E -> (D and E)))) and A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37608.        (A -> (B -> ((C or (D -> (E -> (D and E)))) and A))), M:tm-84, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-37609
in-theory        37609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37609.        ((A -> (B -> (C -> B))) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-83, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37610
in-theory        37610
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D or (E -> (F -> (E and F)))) and (B -> (C -> B))))
theorem-size     23
proof            (modus-ponens tm-80 tm-520 ((Am (-> A (-> B A))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37610.        ((A or (B -> (C -> B))) -> ((D or (E -> (F -> (E and F)))) and (B -> (C -> B)))), M:tm-80, m:tm-520, u:((Am (-> A (-> B A))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (-> B A)))))
================================================================
tm-name          tm-37611
in-theory        37611
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C or (D -> (E -> (D and E)))) and B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37611.        (((not (not A)) -> A) and (B -> ((C or (D -> (E -> (D and E)))) and B))), M:tm-76, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37612
in-theory        37612
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B or (C -> (D -> (C and D)))) and A))
theorem-size     17
proof            (modus-ponens tm-73 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37612.        (((not (not A)) or A) -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-73, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-37613
in-theory        37613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or (E -> (F -> (E and F)))) and C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37613.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or (E -> (F -> (E and F)))) and C))), M:tm-69, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37614
in-theory        37614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or (D -> (E -> (D and E)))) and ((A -> (not B)) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-66 tm-520 ((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37614.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or (D -> (E -> (D and E)))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-520, u:((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-37615
in-theory        37615
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37615.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-54, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37616
in-theory        37616
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or (E -> (F -> (E and F)))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-51 tm-520 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37616.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or (E -> (F -> (E and F)))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-520, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-37617
in-theory        37617
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C or (D -> (E -> (D and E)))) and (B or A)))
theorem-size     19
proof            (modus-ponens tm-50 tm-520 ((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37617.        ((A or (B or A)) -> ((C or (D -> (E -> (D and E)))) and (B or A))), M:tm-50, m:tm-520, u:((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B))))
================================================================
tm-name          tm-37618
in-theory        37618
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C or (D -> (E -> (D and E)))) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-49 tm-520 ((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37618.        ((A or (A or B)) -> ((C or (D -> (E -> (D and E)))) and (A or B))), M:tm-49, m:tm-520, u:((Am (or A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (or A B))))
================================================================
tm-name          tm-37619
in-theory        37619
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C or (D -> (E -> (D and E)))) and (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-48 tm-520 ((Am (-> A (and B A))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37619.        ((A or (B -> (A and B))) -> ((C or (D -> (E -> (D and E)))) and (B -> (A and B)))), M:tm-48, m:tm-520, u:((Am (-> A (and B A))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (and B A)))))
================================================================
tm-name          tm-37620
in-theory        37620
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C or (D -> (E -> (D and E)))) and B))
theorem-size     17
proof            (modus-ponens tm-47 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37620.        (((A and B) or B) -> ((C or (D -> (E -> (D and E)))) and B)), M:tm-47, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-37621
in-theory        37621
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C or (D -> (E -> (D and E)))) and A))
theorem-size     17
proof            (modus-ponens tm-46 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37621.        (((A and B) or A) -> ((C or (D -> (E -> (D and E)))) and A)), M:tm-46, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-37622
in-theory        37622
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-45 tm-520 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37622.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-520, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-37623
in-theory        37623
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C or (D -> (E -> (D and E)))) and (B -> A)))
theorem-size     19
proof            (modus-ponens tm-44 tm-520 ((Am (-> A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37623.        ((A or (B -> A)) -> ((C or (D -> (E -> (D and E)))) and (B -> A))), M:tm-44, m:tm-520, u:((Am (-> A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A B))))
================================================================
tm-name          tm-37624
in-theory        37624
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D or (E -> (F -> (E and F)))) and C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37624.        ((A -> (B or A)) and (C -> ((D or (E -> (F -> (E and F)))) and C))), M:tm-42, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37625
in-theory        37625
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D or (E -> (F -> (E and F)))) and C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37625.        ((A -> (A or B)) and (C -> ((D or (E -> (F -> (E and F)))) and C))), M:tm-32, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37626
in-theory        37626
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B or (C -> (D -> (C and D)))) and A)))
theorem-size     15
proof            (modus-ponens tm-24 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37626.        (A -> (A and ((B or (C -> (D -> (C and D)))) and A))), M:tm-24, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-37627
in-theory        37627
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D or (E -> (F -> (E and F)))) and C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37627.        ((A -> (B -> (A and B))) and (C -> ((D or (E -> (F -> (E and F)))) and C))), M:tm-23, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37628
in-theory        37628
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D or (E -> (F -> (E and F)))) and C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37628.        (((A and B) -> B) and (C -> ((D or (E -> (F -> (E and F)))) and C))), M:tm-22, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37629
in-theory        37629
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D or (E -> (F -> (E and F)))) and C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37629.        (((A and B) -> A) and (C -> ((D or (E -> (F -> (E and F)))) and C))), M:tm-21, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37630
in-theory        37630
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37630.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-20, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37631
in-theory        37631
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D or (E -> (F -> (E and F)))) and C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37631.        ((A -> (B -> A)) and (C -> ((D or (E -> (F -> (E and F)))) and C))), M:tm-19, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37632
in-theory        37632
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B or (C -> (D -> (C and D)))) and A))) -> (not A))
theorem-size     17
proof            (modus-ponens tm-9 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-9 tm-5 tm-7)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37632.        ((A -> (not ((B or (C -> (D -> (C and D)))) and A))) -> (not A)), M:tm-9, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-37633
in-theory        37633
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (C -> (B and C)))) and D) -> E) -> ((D or ((A or (B -> (C -> (B and C)))) and D)) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37633.        ((((A or (B -> (C -> (B and C)))) and D) -> E) -> ((D or ((A or (B -> (C -> (B and C)))) and D)) -> E)), M:tm-8, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-37634
in-theory        37634
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C or (D -> (E -> (D and E)))) and B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-7 tm-5)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37634.        (A or (B -> ((C or (D -> (E -> (D and E)))) and B))), M:tm-7, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37635
in-theory        37635
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37635.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) or E), M:tm-6, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37636
in-theory        37636
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C or (D -> (E -> (D and E)))) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37636.        (A -> ((B -> ((C or (D -> (E -> (D and E)))) and B)) and A)), M:tm-5, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37637
in-theory        37637
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C or (D -> (E -> (D and E)))) and B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37637.        (A -> (B -> ((C or (D -> (E -> (D and E)))) and B))), M:tm-1, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-37638
in-theory        37638
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-520 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37638.        ((A or (B -> (C -> (B and C)))) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-520, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37639
in-theory        37639
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-510 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37639.        ((A or ((B and C) -> C)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-510, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37640
in-theory        37640
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-500 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37640.        ((A or ((B and C) -> B)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-500, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37641
in-theory        37641
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-490 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37641.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (H -> (G and H)))))), M:tm-490, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37642
in-theory        37642
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-480 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37642.        ((A or (B -> (C -> B))) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-480, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37643
in-theory        37643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-469 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37643.        ((A -> (B -> (B or C))) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-469, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37644
in-theory        37644
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-466 tm-521 ((Am (-> A (or A B))) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-7 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37644.        ((A or (B -> (B or C))) -> (D or (E -> (F -> (E and F))))), M:tm-466, m:tm-521, u:((Am (-> A (or A B))) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37645
in-theory        37645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37645.        ((A -> (B or (C -> (D -> (C and D))))) and (E -> (E or F))), M:tm-456, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37646
in-theory        37646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-453 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37646.        ((A -> ((B -> (B or C)) and A)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-453, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37647
in-theory        37647
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-450 tm-521 ((Am (and (-> A (or A B)) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37647.        ((A or ((B -> (B or C)) and A)) -> (D or (E -> (F -> (E and F))))), M:tm-450, m:tm-521, u:((Am (and (-> A (or A B)) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37648
in-theory        37648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and ((E -> (E or F)) and (A -> (B or (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-443 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37648.        ((A -> (B or (C -> (D -> (C and D))))) and ((E -> (E or F)) and (A -> (B or (C -> (D -> (C and D))))))), M:tm-443, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37649
in-theory        37649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-409 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37649.        (((A -> (A or B)) or C) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-409, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37650
in-theory        37650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-400 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37650.        (((A -> (B -> (A and B))) or C) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-400, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37651
in-theory        37651
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-391 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37651.        ((((A and B) -> B) or C) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-391, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37652
in-theory        37652
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-382 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37652.        ((((A and B) -> A) or C) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-382, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37653
in-theory        37653
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-373 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37653.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or (G -> (H -> (G and H)))))), M:tm-373, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37654
in-theory        37654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-364 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37654.        (((A -> (B -> A)) or C) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-364, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37655
in-theory        37655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-354 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37655.        ((A -> (B -> (C -> (B and C)))) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-354, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37656
in-theory        37656
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-351 tm-521 ((Am (-> A (-> B (and A B)))) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37656.        ((A or (B -> (C -> (B and C)))) -> (D or (E -> (F -> (E and F))))), M:tm-351, m:tm-521, u:((Am (-> A (-> B (and A B)))) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37657
in-theory        37657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37657.        ((A -> (B or (C -> (D -> (C and D))))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37658
in-theory        37658
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) -> D) -> ((A or (B -> (C -> (B and C)))) and D))
theorem-size     23
proof            (modus-ponens tm-339 tm-521 ((Am (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) B)) (A (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37658.        (((A or (B -> (C -> (B and C)))) -> D) -> ((A or (B -> (C -> (B and C)))) and D)), M:tm-339, m:tm-521, u:((Am (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) B)) (A (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37659
in-theory        37659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D or (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-338 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37659.        (((A -> B) -> (A -> (A and B))) and (C -> (D or (E -> (F -> (E and F)))))), M:tm-338, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37660
in-theory        37660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C or (D -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-335 tm-521 ((Am (-> A (and A B))) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37660.        (((A -> B) or (A -> (A and B))) -> (C or (D -> (E -> (D and E))))), M:tm-335, m:tm-521, u:((Am (-> A (and A B))) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37661
in-theory        37661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (A -> (A and (B or (C -> (D -> (C and D)))))))
theorem-size     25
proof            (modus-ponens tm-328 tm-521 ((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37661.        ((A -> (B or (C -> (D -> (C and D))))) and (A -> (A and (B or (C -> (D -> (C and D))))))), M:tm-328, m:tm-521, u:((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37662
in-theory        37662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and ((E -> (F -> (E and F))) and (A -> (B or (C -> (D -> (C and D)))))))
theorem-size     31
proof            (modus-ponens tm-327 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37662.        ((A -> (B or (C -> (D -> (C and D))))) and ((E -> (F -> (E and F))) and (A -> (B or (C -> (D -> (C and D))))))), M:tm-327, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37663
in-theory        37663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (((E and F) -> F) and (A -> (B or (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-326 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37663.        ((A -> (B or (C -> (D -> (C and D))))) and (((E and F) -> F) and (A -> (B or (C -> (D -> (C and D))))))), M:tm-326, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37664
in-theory        37664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (((E and F) -> E) and (A -> (B or (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-325 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37664.        ((A -> (B or (C -> (D -> (C and D))))) and (((E and F) -> E) and (A -> (B or (C -> (D -> (C and D))))))), M:tm-325, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37665
in-theory        37665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B or (C -> (D -> (C and D)))))))
theorem-size     37
proof            (modus-ponens tm-324 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37665.        ((A -> (B or (C -> (D -> (C and D))))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B or (C -> (D -> (C and D))))))), M:tm-324, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37666
in-theory        37666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and ((E -> (F -> E)) and (A -> (B or (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-323 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37666.        ((A -> (B or (C -> (D -> (C and D))))) and ((E -> (F -> E)) and (A -> (B or (C -> (D -> (C and D))))))), M:tm-323, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37667
in-theory        37667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37667.        ((A -> (B or (C -> (D -> (C and D))))) and ((E and F) -> F)), M:tm-322, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37668
in-theory        37668
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or (C -> (D -> (C and D)))) -> E)) -> (B or (C -> (D -> (C and D))))) and ((A and ((B or (C -> (D -> (C and D)))) -> E)) -> E))
theorem-size     39
proof            (modus-ponens tm-321 tm-521 ((Am (and A (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) C))) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37668.        (((A and ((B or (C -> (D -> (C and D)))) -> E)) -> (B or (C -> (D -> (C and D))))) and ((A and ((B or (C -> (D -> (C and D)))) -> E)) -> E)), M:tm-321, m:tm-521, u:((Am (and A (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) C))) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37669
in-theory        37669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37669.        ((A -> (B or (C -> (D -> (C and D))))) and ((E and F) -> E)), M:tm-320, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37670
in-theory        37670
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (C -> (B and C)))) -> D) and E) -> (A or (B -> (C -> (B and C))))) and ((((A or (B -> (C -> (B and C)))) -> D) and E) -> D))
theorem-size     39
proof            (modus-ponens tm-319 tm-521 ((Am (and (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) B) C)) (A (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37670.        (((((A or (B -> (C -> (B and C)))) -> D) and E) -> (A or (B -> (C -> (B and C))))) and ((((A or (B -> (C -> (B and C)))) -> D) and E) -> D)), M:tm-319, m:tm-521, u:((Am (and (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) B) C)) (A (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37671
in-theory        37671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37671.        ((A -> (B or (C -> (D -> (C and D))))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37672
in-theory        37672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-521 ((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37672.        ((A -> (B or (C -> (D -> (C and D))))) and (A -> A)), M:tm-316, m:tm-521, u:((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37673
in-theory        37673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37673.        ((A -> (B or (C -> (D -> (C and D))))) and (E -> (F -> E))), M:tm-315, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37674
in-theory        37674
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and ((A -> (not (B or (C -> (D -> (C and D)))))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-521 ((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37674.        ((A -> (B or (C -> (D -> (C and D))))) and ((A -> (not (B or (C -> (D -> (C and D)))))) -> (not A))), M:tm-313, m:tm-521, u:((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37675
in-theory        37675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (((B or (C -> (D -> (C and D)))) -> E) -> ((A or (B or (C -> (D -> (C and D))))) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-521 ((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37675.        ((A -> (B or (C -> (D -> (C and D))))) and (((B or (C -> (D -> (C and D)))) -> E) -> ((A or (B or (C -> (D -> (C and D))))) -> E))), M:tm-312, m:tm-521, u:((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37676
in-theory        37676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (E or (A -> (B or (C -> (D -> (C and D)))))))
theorem-size     25
proof            (modus-ponens tm-311 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37676.        ((A -> (B or (C -> (D -> (C and D))))) and (E or (A -> (B or (C -> (D -> (C and D))))))), M:tm-311, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37677
in-theory        37677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and ((A -> (B or (C -> (D -> (C and D))))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37677.        ((A -> (B or (C -> (D -> (C and D))))) and ((A -> (B or (C -> (D -> (C and D))))) or E)), M:tm-310, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37678
in-theory        37678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (E -> ((A -> (B or (C -> (D -> (C and D))))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37678.        ((A -> (B or (C -> (D -> (C and D))))) and (E -> ((A -> (B or (C -> (D -> (C and D))))) and E))), M:tm-309, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37679
in-theory        37679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (E -> (A -> (B or (C -> (D -> (C and D)))))))
theorem-size     25
proof            (modus-ponens tm-305 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37679.        ((A -> (B or (C -> (D -> (C and D))))) and (E -> (A -> (B or (C -> (D -> (C and D))))))), M:tm-305, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37680
in-theory        37680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-303 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37680.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-303, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37681
in-theory        37681
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D or (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-300 tm-521 ((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37681.        ((A or ((B -> (C -> (B and C))) and A)) -> (D or (E -> (F -> (E and F))))), M:tm-300, m:tm-521, u:((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37682
in-theory        37682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-270 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37682.        ((A -> (((B and C) -> C) and A)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-270, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37683
in-theory        37683
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-267 tm-521 ((Am (and (-> (and A B) B) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37683.        ((A or (((B and C) -> C) and A)) -> (D or (E -> (F -> (E and F))))), M:tm-267, m:tm-521, u:((Am (and (-> (and A B) B) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37684
in-theory        37684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-239 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37684.        ((A -> (((B and C) -> B) and A)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-239, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37685
in-theory        37685
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-236 tm-521 ((Am (and (-> (and A B) A) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37685.        ((A or (((B and C) -> B) and A)) -> (D or (E -> (F -> (E and F))))), M:tm-236, m:tm-521, u:((Am (and (-> (and A B) A) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37686
in-theory        37686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-210 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37686.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or (G -> (H -> (G and H)))))), M:tm-210, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37687
in-theory        37687
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-207 tm-521 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37687.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or (F -> (G -> (F and G))))), M:tm-207, m:tm-521, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37688
in-theory        37688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-183 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37688.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-183, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37689
in-theory        37689
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-180 tm-521 ((Am (and (-> A (-> B A)) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37689.        ((A or ((B -> (C -> B)) and A)) -> (D or (E -> (F -> (E and F))))), M:tm-180, m:tm-521, u:((Am (and (-> A (-> B A)) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37690
in-theory        37690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-157 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37690.        ((A -> ((B and C) -> C)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-157, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37691
in-theory        37691
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-154 tm-521 ((Am (-> (and A B) B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-4 tm-7 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37691.        ((A or ((B and C) -> C)) -> (D or (E -> (F -> (E and F))))), M:tm-154, m:tm-521, u:((Am (-> (and A B) B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37692
in-theory        37692
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-147 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37692.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-147, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37693
in-theory        37693
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-144 tm-521 ((Am (-> (and A (-> B C)) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-7 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37693.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or (E -> (F -> (E and F))))), M:tm-144, m:tm-521, u:((Am (-> (and A (-> B C)) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37694
in-theory        37694
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B or (C -> (D -> (C and D)))) -> E)) -> (B or (C -> (D -> (C and D)))))
theorem-size     23
proof            (modus-ponens tm-142 tm-521 ((Am (and A (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) C))) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-4 tm-7 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37694.        ((A and ((B or (C -> (D -> (C and D)))) -> E)) -> (B or (C -> (D -> (C and D))))), M:tm-142, m:tm-521, u:((Am (and A (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) C))) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37695
in-theory        37695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-134 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37695.        ((A -> ((B and C) -> B)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-134, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37696
in-theory        37696
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-131 tm-521 ((Am (-> (and A B) A)) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-3 tm-7 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37696.        ((A or ((B and C) -> B)) -> (D or (E -> (F -> (E and F))))), M:tm-131, m:tm-521, u:((Am (-> (and A B) A)) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37697
in-theory        37697
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-125 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37697.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-125, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37698
in-theory        37698
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-122 tm-521 ((Am (-> (and (-> A B) C) B)) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-7 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37698.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or (E -> (F -> (E and F))))), M:tm-122, m:tm-521, u:((Am (-> (and (-> A B) C) B)) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37699
in-theory        37699
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (C -> (B and C)))) -> D) and E) -> (A or (B -> (C -> (B and C)))))
theorem-size     23
proof            (modus-ponens tm-120 tm-521 ((Am (and (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) B) C)) (A (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-3 tm-7 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37699.        ((((A or (B -> (C -> (B and C)))) -> D) and E) -> (A or (B -> (C -> (B and C))))), M:tm-120, m:tm-521, u:((Am (and (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) B) C)) (A (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37700
in-theory        37700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-113 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37700.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (H -> (G and H)))))), M:tm-113, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37701
in-theory        37701
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-110 tm-521 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-7 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37701.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or (F -> (G -> (F and G))))), M:tm-110, m:tm-521, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37702
in-theory        37702
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     31
proof            (modus-ponens tm-105 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37702.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-105, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37703
in-theory        37703
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or (E -> (F -> (E and F)))))
theorem-size     29
proof            (modus-ponens tm-102 tm-521 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-5)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37703.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or (E -> (F -> (E and F))))), M:tm-102, m:tm-521, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37704
in-theory        37704
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) -> D) -> (A or (B -> (C -> (B and C)))))
theorem-size     21
proof            (modus-ponens tm-96 tm-521 ((Am (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) B)) (A (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37704.        (((A or (B -> (C -> (B and C)))) -> D) -> (A or (B -> (C -> (B and C))))), M:tm-96, m:tm-521, u:((Am (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) B)) (A (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37705
in-theory        37705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D or (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-95 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37705.        (((A -> B) -> (A -> A)) and (C -> (D or (E -> (F -> (E and F)))))), M:tm-95, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37706
in-theory        37706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C or (D -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-92 tm-521 ((Am (-> A A)) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37706.        (((A -> B) or (A -> A)) -> (C or (D -> (E -> (D and E))))), M:tm-92, m:tm-521, u:((Am (-> A A)) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37707
in-theory        37707
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C or (D -> (E -> (D and E))))))
theorem-size     13
proof            (modus-ponens tm-84 tm-521 ((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37707.        (A -> (B -> (C or (D -> (E -> (D and E)))))), M:tm-84, m:tm-521, u:((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37708
in-theory        37708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-83 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37708.        ((A -> (B -> (C -> B))) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-83, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37709
in-theory        37709
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-80 tm-521 ((Am (-> A (-> B A))) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37709.        ((A or (B -> (C -> B))) -> (D or (E -> (F -> (E and F))))), M:tm-80, m:tm-521, u:((Am (-> A (-> B A))) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37710
in-theory        37710
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A or (B -> (C -> (B and C)))) -> D))) -> D)
theorem-size     15
proof            (modus-ponens tm-77 tm-521 ((Am (not (not (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) B)))) (A (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-10 tm-1 tm-7 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37710.        ((not (not ((A or (B -> (C -> (B and C)))) -> D))) -> D), M:tm-77, m:tm-521, u:((Am (not (not (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) B)))) (A (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37711
in-theory        37711
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C or (D -> (E -> (D and E))))))
theorem-size     17
proof            (modus-ponens tm-76 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37711.        (((not (not A)) -> A) and (B -> (C or (D -> (E -> (D and E)))))), M:tm-76, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37712
in-theory        37712
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B or (C -> (D -> (C and D)))))
theorem-size     15
proof            (modus-ponens tm-73 tm-521 ((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-10 tm-1 tm-7 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37712.        (((not (not A)) or A) -> (B or (C -> (D -> (C and D))))), M:tm-73, m:tm-521, u:((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37713
in-theory        37713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or (E -> (F -> (E and F))))))
theorem-size     23
proof            (modus-ponens tm-69 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37713.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or (E -> (F -> (E and F)))))), M:tm-69, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37714
in-theory        37714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or (D -> (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-66 tm-521 ((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-9 tm-1 tm-7 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37714.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or (D -> (E -> (D and E))))), M:tm-66, m:tm-521, u:((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37715
in-theory        37715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-54 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37715.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-54, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37716
in-theory        37716
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-51 tm-521 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37716.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> (F -> (E and F))))), M:tm-51, m:tm-521, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37717
in-theory        37717
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-50 tm-521 ((Am (or A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37717.        ((A or (B or A)) -> (C or (D -> (E -> (D and E))))), M:tm-50, m:tm-521, u:((Am (or A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37718
in-theory        37718
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-49 tm-521 ((Am (or A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-6 tm-1 tm-7 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37718.        ((A or (A or B)) -> (C or (D -> (E -> (D and E))))), M:tm-49, m:tm-521, u:((Am (or A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37719
in-theory        37719
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (D -> (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-48 tm-521 ((Am (-> A (and B A))) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37719.        ((A or (B -> (A and B))) -> (C or (D -> (E -> (D and E))))), M:tm-48, m:tm-521, u:((Am (-> A (and B A))) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37720
in-theory        37720
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-47 tm-521 ((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-4 tm-1 tm-7 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37720.        (((A and B) or B) -> (C or (D -> (E -> (D and E))))), M:tm-47, m:tm-521, u:((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37721
in-theory        37721
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-46 tm-521 ((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-3 tm-1 tm-7 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37721.        (((A and B) or A) -> (C or (D -> (E -> (D and E))))), M:tm-46, m:tm-521, u:((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37722
in-theory        37722
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-45 tm-521 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37722.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (F -> (E and F))))), M:tm-45, m:tm-521, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37723
in-theory        37723
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-44 tm-521 ((Am (-> A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37723.        ((A or (B -> A)) -> (C or (D -> (E -> (D and E))))), M:tm-44, m:tm-521, u:((Am (-> A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37724
in-theory        37724
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-42 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37724.        ((A -> (B or A)) and (C -> (D or (E -> (F -> (E and F)))))), M:tm-42, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37725
in-theory        37725
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-32 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37725.        ((A -> (A or B)) and (C -> (D or (E -> (F -> (E and F)))))), M:tm-32, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37726
in-theory        37726
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B or (C -> (D -> (C and D))))))
theorem-size     13
proof            (modus-ponens tm-24 tm-521 ((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37726.        (A -> (A and (B or (C -> (D -> (C and D)))))), M:tm-24, m:tm-521, u:((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37727
in-theory        37727
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D or (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-23 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37727.        ((A -> (B -> (A and B))) and (C -> (D or (E -> (F -> (E and F)))))), M:tm-23, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37728
in-theory        37728
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-22 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37728.        (((A and B) -> B) and (C -> (D or (E -> (F -> (E and F)))))), M:tm-22, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37729
in-theory        37729
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-21 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37729.        (((A and B) -> A) and (C -> (D or (E -> (F -> (E and F)))))), M:tm-21, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37730
in-theory        37730
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-20 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37730.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-20, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37731
in-theory        37731
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-19 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37731.        ((A -> (B -> A)) and (C -> (D or (E -> (F -> (E and F)))))), M:tm-19, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37732
in-theory        37732
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B or (C -> (D -> (C and D)))) -> E)) -> E)
theorem-size     15
proof            (modus-ponens tm-17 tm-521 ((Am (and A (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) C))) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-4 tm-1 tm-7 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37732.        ((A and ((B or (C -> (D -> (C and D)))) -> E)) -> E), M:tm-17, m:tm-521, u:((Am (and A (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) C))) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37733
in-theory        37733
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (C -> (B and C)))) -> D) and E) -> D)
theorem-size     15
proof            (modus-ponens tm-15 tm-521 ((Am (and (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) B) C)) (A (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-3 tm-1 tm-7 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37733.        ((((A or (B -> (C -> (B and C)))) -> D) and E) -> D), M:tm-15, m:tm-521, u:((Am (and (-> (or Bm (-> Cm (-> Dm (and Cm Dm)))) B) C)) (A (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37734
in-theory        37734
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B or (C -> (D -> (C and D)))))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-521 ((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-9 tm-1 tm-7 tm-5)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37734.        ((A -> (not (B or (C -> (D -> (C and D)))))) -> (not A)), M:tm-9, m:tm-521, u:((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37735
in-theory        37735
times-derived    2
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) -> D) -> ((E or (A or (B -> (C -> (B and C))))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-521 ((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37735.        (((A or (B -> (C -> (B and C)))) -> D) -> ((E or (A or (B -> (C -> (B and C))))) -> D)), M:tm-8, m:tm-521, u:((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-37736
in-theory        37736
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C or (D -> (E -> (D and E))))))
theorem-size     13
proof            (modus-ponens tm-7 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-7 tm-1 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37736.        (A or (B -> (C or (D -> (E -> (D and E)))))), M:tm-7, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37737
in-theory        37737
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-6 tm-1 tm-7 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37737.        ((A -> (B or (C -> (D -> (C and D))))) or E), M:tm-6, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37738
in-theory        37738
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C or (D -> (E -> (D and E))))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-37738.        (A -> ((B -> (C or (D -> (E -> (D and E))))) and A)), M:tm-5, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-37739
in-theory        37739
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37739.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-520, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37740
in-theory        37740
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37740.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-510, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37741
in-theory        37741
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37741.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-500, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37742
in-theory        37742
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37742.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (H or I))))), M:tm-490, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37743
in-theory        37743
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37743.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-480, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37744
in-theory        37744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37744.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-469, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37745
in-theory        37745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37745.        (((A -> (A or B)) and (C or (D -> (D or E)))) and (F -> (F or G))), M:tm-456, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37746
in-theory        37746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37746.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-453, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37747
in-theory        37747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (A or B)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37747.        (((A -> (A or B)) and (C or (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (A or B)) and (C or (D -> (D or E)))))), M:tm-443, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37748
in-theory        37748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37748.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-409, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37749
in-theory        37749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37749.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-400, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37750
in-theory        37750
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37750.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-391, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37751
in-theory        37751
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37751.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-382, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37752
in-theory        37752
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37752.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or (H -> (H or I))))), M:tm-373, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37753
in-theory        37753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37753.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-364, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37754
in-theory        37754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37754.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-354, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37755
in-theory        37755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37755.        (((A -> (A or B)) and (C or (D -> (D or E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37756
in-theory        37756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37756.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or (F -> (F or G))))), M:tm-338, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37757
in-theory        37757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C or (D -> (D or E))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37757.        (((A -> (A or B)) and (C or (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C or (D -> (D or E)))))), M:tm-327, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37758
in-theory        37758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and (((F and G) -> G) and ((A -> (A or B)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37758.        (((A -> (A or B)) and (C or (D -> (D or E)))) and (((F and G) -> G) and ((A -> (A or B)) and (C or (D -> (D or E)))))), M:tm-326, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37759
in-theory        37759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and (((F and G) -> F) and ((A -> (A or B)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37759.        (((A -> (A or B)) and (C or (D -> (D or E)))) and (((F and G) -> F) and ((A -> (A or B)) and (C or (D -> (D or E)))))), M:tm-325, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37760
in-theory        37760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C or (D -> (D or E))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37760.        (((A -> (A or B)) and (C or (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C or (D -> (D or E)))))), M:tm-324, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37761
in-theory        37761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37761.        (((A -> (A or B)) and (C or (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C or (D -> (D or E)))))), M:tm-323, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37762
in-theory        37762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37762.        (((A -> (A or B)) and (C or (D -> (D or E)))) and ((F and G) -> G)), M:tm-322, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37763
in-theory        37763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37763.        (((A -> (A or B)) and (C or (D -> (D or E)))) and ((F and G) -> F)), M:tm-320, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37764
in-theory        37764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37764.        (((A -> (A or B)) and (C or (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37765
in-theory        37765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37765.        (((A -> (A or B)) and (C or (D -> (D or E)))) and (F -> (G -> F))), M:tm-315, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37766
in-theory        37766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and (F or ((A -> (A or B)) and (C or (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37766.        (((A -> (A or B)) and (C or (D -> (D or E)))) and (F or ((A -> (A or B)) and (C or (D -> (D or E)))))), M:tm-311, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37767
in-theory        37767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and (((A -> (A or B)) and (C or (D -> (D or E)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37767.        (((A -> (A or B)) and (C or (D -> (D or E)))) and (((A -> (A or B)) and (C or (D -> (D or E)))) or F)), M:tm-310, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37768
in-theory        37768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and (F -> (((A -> (A or B)) and (C or (D -> (D or E)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37768.        (((A -> (A or B)) and (C or (D -> (D or E)))) and (F -> (((A -> (A or B)) and (C or (D -> (D or E)))) and F))), M:tm-309, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37769
in-theory        37769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and (C or (D -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-308 tm-522 ((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37769.        (((A -> (A or B)) and (C or (D -> (D or E)))) and (C or (D -> (D or E)))), M:tm-308, m:tm-522, u:((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-37770
in-theory        37770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-522 ((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37770.        (((A -> (A or B)) and (C or (D -> (D or E)))) and (A -> (A or B))), M:tm-307, m:tm-522, u:((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-37771
in-theory        37771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and (F -> ((A -> (A or B)) and (C or (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37771.        (((A -> (A or B)) and (C or (D -> (D or E)))) and (F -> ((A -> (A or B)) and (C or (D -> (D or E)))))), M:tm-305, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37772
in-theory        37772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37772.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-303, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37773
in-theory        37773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37773.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-270, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37774
in-theory        37774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37774.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-239, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37775
in-theory        37775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37775.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or (H -> (H or I))))), M:tm-210, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37776
in-theory        37776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37776.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-183, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37777
in-theory        37777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37777.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-157, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37778
in-theory        37778
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37778.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-147, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37779
in-theory        37779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37779.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-134, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37780
in-theory        37780
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37780.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-125, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37781
in-theory        37781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37781.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (H or I))))), M:tm-113, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37782
in-theory        37782
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37782.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-105, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37783
in-theory        37783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37783.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or (F -> (F or G))))), M:tm-95, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37784
in-theory        37784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37784.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-83, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37785
in-theory        37785
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D or (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37785.        (((not (not A)) -> A) and ((B -> (B or C)) and (D or (E -> (E or F))))), M:tm-76, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37786
in-theory        37786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37786.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or (F -> (F or G))))), M:tm-69, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37787
in-theory        37787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37787.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-54, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37788
in-theory        37788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37788.        ((A -> (B or A)) and ((C -> (C or D)) and (E or (F -> (F or G))))), M:tm-42, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37789
in-theory        37789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37789.        ((A -> (A or B)) and ((C -> (C or D)) and (E or (F -> (F or G))))), M:tm-32, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37790
in-theory        37790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37790.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or (F -> (F or G))))), M:tm-23, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37791
in-theory        37791
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37791.        (((A and B) -> B) and ((C -> (C or D)) and (E or (F -> (F or G))))), M:tm-22, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37792
in-theory        37792
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37792.        (((A and B) -> A) and ((C -> (C or D)) and (E or (F -> (F or G))))), M:tm-21, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37793
in-theory        37793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37793.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-20, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37794
in-theory        37794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37794.        ((A -> (B -> A)) and ((C -> (C or D)) and (E or (F -> (F or G))))), M:tm-19, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37795
in-theory        37795
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37795.        (A or ((B -> (B or C)) and (D or (E -> (E or F))))), M:tm-7, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37796
in-theory        37796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37796.        (((A -> (A or B)) and (C or (D -> (D or E)))) or F), M:tm-6, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37797
in-theory        37797
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D or (E -> (E or F)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37797.        (A -> (((B -> (B or C)) and (D or (E -> (E or F)))) and A)), M:tm-5, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37798
in-theory        37798
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-6 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37798.        (A -> ((B -> (B or C)) and (D or (E -> (E or F))))), M:tm-1, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37799
in-theory        37799
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37799.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-520, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37800
in-theory        37800
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37800.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-510, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37801
in-theory        37801
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37801.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-500, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37802
in-theory        37802
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37802.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (H or I))))), M:tm-490, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37803
in-theory        37803
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37803.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-480, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37804
in-theory        37804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37804.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-469, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37805
in-theory        37805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37805.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (F -> (F or G))), M:tm-456, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37806
in-theory        37806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37806.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-453, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37807
in-theory        37807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C or (D -> (D or E))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37807.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C or (D -> (D or E)))))), M:tm-443, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37808
in-theory        37808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37808.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-409, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37809
in-theory        37809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37809.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-400, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37810
in-theory        37810
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37810.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-391, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37811
in-theory        37811
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37811.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-382, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37812
in-theory        37812
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37812.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (H or I))))), M:tm-373, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37813
in-theory        37813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37813.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-364, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37814
in-theory        37814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37814.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-354, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37815
in-theory        37815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37815.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37816
in-theory        37816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37816.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (F or G))))), M:tm-338, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37817
in-theory        37817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C or (D -> (D or E))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37817.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C or (D -> (D or E)))))), M:tm-327, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37818
in-theory        37818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C or (D -> (D or E))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37818.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C or (D -> (D or E)))))), M:tm-326, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37819
in-theory        37819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C or (D -> (D or E))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37819.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C or (D -> (D or E)))))), M:tm-325, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37820
in-theory        37820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C or (D -> (D or E))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37820.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C or (D -> (D or E)))))), M:tm-324, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37821
in-theory        37821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C or (D -> (D or E))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37821.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C or (D -> (D or E)))))), M:tm-323, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37822
in-theory        37822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37822.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and ((F and G) -> G)), M:tm-322, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37823
in-theory        37823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37823.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and ((F and G) -> F)), M:tm-320, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37824
in-theory        37824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37824.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37825
in-theory        37825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37825.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (F -> (G -> F))), M:tm-315, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37826
in-theory        37826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (F or ((A -> (B -> (A and B))) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37826.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (F or ((A -> (B -> (A and B))) and (C or (D -> (D or E)))))), M:tm-311, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37827
in-theory        37827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37827.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) or F)), M:tm-310, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37828
in-theory        37828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (F -> (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37828.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (F -> (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and F))), M:tm-309, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37829
in-theory        37829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (C or (D -> (D or E))))
theorem-size     23
proof            (modus-ponens tm-308 tm-523 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37829.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (C or (D -> (D or E)))), M:tm-308, m:tm-523, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-37830
in-theory        37830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-523 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37830.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-523, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-37831
in-theory        37831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (F -> ((A -> (B -> (A and B))) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37831.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (F -> ((A -> (B -> (A and B))) and (C or (D -> (D or E)))))), M:tm-305, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37832
in-theory        37832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37832.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-303, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37833
in-theory        37833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37833.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-270, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37834
in-theory        37834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37834.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-239, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37835
in-theory        37835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or (H -> (H or I)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37835.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or (H -> (H or I))))), M:tm-210, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37836
in-theory        37836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37836.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-183, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37837
in-theory        37837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37837.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-157, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37838
in-theory        37838
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37838.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-147, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37839
in-theory        37839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37839.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-134, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37840
in-theory        37840
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37840.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-125, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37841
in-theory        37841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37841.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (H or I))))), M:tm-113, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37842
in-theory        37842
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37842.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-105, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37843
in-theory        37843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37843.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (F or G))))), M:tm-95, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37844
in-theory        37844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37844.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-83, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37845
in-theory        37845
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or (E -> (E or F)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37845.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or (E -> (E or F))))), M:tm-76, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37846
in-theory        37846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or (F -> (F or G)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37846.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or (F -> (F or G))))), M:tm-69, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37847
in-theory        37847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37847.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-54, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37848
in-theory        37848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37848.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or (F -> (F or G))))), M:tm-42, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37849
in-theory        37849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37849.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or (F -> (F or G))))), M:tm-32, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37850
in-theory        37850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37850.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (F or G))))), M:tm-23, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37851
in-theory        37851
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37851.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or (F -> (F or G))))), M:tm-22, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37852
in-theory        37852
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37852.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or (F -> (F or G))))), M:tm-21, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37853
in-theory        37853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37853.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-20, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37854
in-theory        37854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37854.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (F or G))))), M:tm-19, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37855
in-theory        37855
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D or (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37855.        (A or ((B -> (C -> (B and C))) and (D or (E -> (E or F))))), M:tm-7, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37856
in-theory        37856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37856.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) or F), M:tm-6, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37857
in-theory        37857
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D or (E -> (E or F)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37857.        (A -> (((B -> (C -> (B and C))) and (D or (E -> (E or F)))) and A)), M:tm-5, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37858
in-theory        37858
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D or (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-7 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37858.        (A -> ((B -> (C -> (B and C))) and (D or (E -> (E or F))))), M:tm-1, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37859
in-theory        37859
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37859.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-520, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37860
in-theory        37860
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37860.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-510, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37861
in-theory        37861
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37861.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-500, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37862
in-theory        37862
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37862.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (H or I))))), M:tm-490, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37863
in-theory        37863
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37863.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-480, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37864
in-theory        37864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37864.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-469, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37865
in-theory        37865
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37865.        ((((A and B) -> B) and (C or (D -> (D or E)))) and (F -> (F or G))), M:tm-456, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37866
in-theory        37866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37866.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-453, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37867
in-theory        37867
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and ((F -> (F or G)) and (((A and B) -> B) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37867.        ((((A and B) -> B) and (C or (D -> (D or E)))) and ((F -> (F or G)) and (((A and B) -> B) and (C or (D -> (D or E)))))), M:tm-443, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37868
in-theory        37868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37868.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-409, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37869
in-theory        37869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37869.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-400, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37870
in-theory        37870
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37870.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-391, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37871
in-theory        37871
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37871.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-382, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37872
in-theory        37872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37872.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or (H -> (H or I))))), M:tm-373, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37873
in-theory        37873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37873.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-364, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37874
in-theory        37874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37874.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-354, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37875
in-theory        37875
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37875.        ((((A and B) -> B) and (C or (D -> (D or E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37876
in-theory        37876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37876.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or (F -> (F or G))))), M:tm-338, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37877
in-theory        37877
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C or (D -> (D or E))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37877.        ((((A and B) -> B) and (C or (D -> (D or E)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C or (D -> (D or E)))))), M:tm-327, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37878
in-theory        37878
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and (((F and G) -> G) and (((A and B) -> B) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37878.        ((((A and B) -> B) and (C or (D -> (D or E)))) and (((F and G) -> G) and (((A and B) -> B) and (C or (D -> (D or E)))))), M:tm-326, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37879
in-theory        37879
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and (((F and G) -> F) and (((A and B) -> B) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37879.        ((((A and B) -> B) and (C or (D -> (D or E)))) and (((F and G) -> F) and (((A and B) -> B) and (C or (D -> (D or E)))))), M:tm-325, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37880
in-theory        37880
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C or (D -> (D or E))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37880.        ((((A and B) -> B) and (C or (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C or (D -> (D or E)))))), M:tm-324, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37881
in-theory        37881
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and ((F -> (G -> F)) and (((A and B) -> B) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37881.        ((((A and B) -> B) and (C or (D -> (D or E)))) and ((F -> (G -> F)) and (((A and B) -> B) and (C or (D -> (D or E)))))), M:tm-323, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37882
in-theory        37882
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37882.        ((((A and B) -> B) and (C or (D -> (D or E)))) and ((F and G) -> G)), M:tm-322, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37883
in-theory        37883
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37883.        ((((A and B) -> B) and (C or (D -> (D or E)))) and ((F and G) -> F)), M:tm-320, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37884
in-theory        37884
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37884.        ((((A and B) -> B) and (C or (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37885
in-theory        37885
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37885.        ((((A and B) -> B) and (C or (D -> (D or E)))) and (F -> (G -> F))), M:tm-315, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37886
in-theory        37886
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and (F or (((A and B) -> B) and (C or (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37886.        ((((A and B) -> B) and (C or (D -> (D or E)))) and (F or (((A and B) -> B) and (C or (D -> (D or E)))))), M:tm-311, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37887
in-theory        37887
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and ((((A and B) -> B) and (C or (D -> (D or E)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37887.        ((((A and B) -> B) and (C or (D -> (D or E)))) and ((((A and B) -> B) and (C or (D -> (D or E)))) or F)), M:tm-310, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37888
in-theory        37888
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and (F -> ((((A and B) -> B) and (C or (D -> (D or E)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37888.        ((((A and B) -> B) and (C or (D -> (D or E)))) and (F -> ((((A and B) -> B) and (C or (D -> (D or E)))) and F))), M:tm-309, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37889
in-theory        37889
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and (C or (D -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-308 tm-524 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37889.        ((((A and B) -> B) and (C or (D -> (D or E)))) and (C or (D -> (D or E)))), M:tm-308, m:tm-524, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-37890
in-theory        37890
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-524 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37890.        ((((A and B) -> B) and (C or (D -> (D or E)))) and ((A and B) -> B)), M:tm-307, m:tm-524, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-37891
in-theory        37891
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and (F -> (((A and B) -> B) and (C or (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37891.        ((((A and B) -> B) and (C or (D -> (D or E)))) and (F -> (((A and B) -> B) and (C or (D -> (D or E)))))), M:tm-305, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37892
in-theory        37892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37892.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-303, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37893
in-theory        37893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37893.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-270, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37894
in-theory        37894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37894.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-239, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37895
in-theory        37895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37895.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or (H -> (H or I))))), M:tm-210, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37896
in-theory        37896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37896.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-183, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37897
in-theory        37897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37897.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-157, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37898
in-theory        37898
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37898.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-147, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37899
in-theory        37899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37899.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-134, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37900
in-theory        37900
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37900.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-125, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37901
in-theory        37901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37901.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (H or I))))), M:tm-113, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37902
in-theory        37902
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37902.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-105, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37903
in-theory        37903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37903.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or (F -> (F or G))))), M:tm-95, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37904
in-theory        37904
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37904.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-83, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37905
in-theory        37905
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D or (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37905.        (((not (not A)) -> A) and (((B and C) -> C) and (D or (E -> (E or F))))), M:tm-76, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37906
in-theory        37906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-4 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37906.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or (F -> (F or G))))), M:tm-69, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37907
in-theory        37907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37907.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-54, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37908
in-theory        37908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37908.        ((A -> (B or A)) and (((C and D) -> D) and (E or (F -> (F or G))))), M:tm-42, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37909
in-theory        37909
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37909.        ((A -> (A or B)) and (((C and D) -> D) and (E or (F -> (F or G))))), M:tm-32, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37910
in-theory        37910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37910.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or (F -> (F or G))))), M:tm-23, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37911
in-theory        37911
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37911.        (((A and B) -> B) and (((C and D) -> D) and (E or (F -> (F or G))))), M:tm-22, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37912
in-theory        37912
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37912.        (((A and B) -> A) and (((C and D) -> D) and (E or (F -> (F or G))))), M:tm-21, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37913
in-theory        37913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37913.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-20, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37914
in-theory        37914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37914.        ((A -> (B -> A)) and (((C and D) -> D) and (E or (F -> (F or G))))), M:tm-19, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37915
in-theory        37915
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-4 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37915.        (A or (((B and C) -> C) and (D or (E -> (E or F))))), M:tm-7, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37916
in-theory        37916
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-4 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37916.        ((((A and B) -> B) and (C or (D -> (D or E)))) or F), M:tm-6, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37917
in-theory        37917
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D or (E -> (E or F)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37917.        (A -> ((((B and C) -> C) and (D or (E -> (E or F)))) and A)), M:tm-5, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37918
in-theory        37918
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-4 tm-7 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37918.        (A -> (((B and C) -> C) and (D or (E -> (E or F))))), M:tm-1, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37919
in-theory        37919
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37919.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-520, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37920
in-theory        37920
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37920.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-510, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37921
in-theory        37921
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37921.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-500, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37922
in-theory        37922
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37922.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (H or I))))), M:tm-490, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37923
in-theory        37923
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37923.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-480, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37924
in-theory        37924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37924.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-469, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37925
in-theory        37925
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37925.        ((((A and B) -> A) and (C or (D -> (D or E)))) and (F -> (F or G))), M:tm-456, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37926
in-theory        37926
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37926.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-453, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37927
in-theory        37927
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and ((F -> (F or G)) and (((A and B) -> A) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37927.        ((((A and B) -> A) and (C or (D -> (D or E)))) and ((F -> (F or G)) and (((A and B) -> A) and (C or (D -> (D or E)))))), M:tm-443, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37928
in-theory        37928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37928.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-409, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37929
in-theory        37929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37929.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-400, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37930
in-theory        37930
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37930.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-391, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37931
in-theory        37931
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37931.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-382, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37932
in-theory        37932
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37932.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or (H -> (H or I))))), M:tm-373, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37933
in-theory        37933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37933.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-364, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37934
in-theory        37934
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37934.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-354, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37935
in-theory        37935
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37935.        ((((A and B) -> A) and (C or (D -> (D or E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37936
in-theory        37936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37936.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or (F -> (F or G))))), M:tm-338, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37937
in-theory        37937
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C or (D -> (D or E))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37937.        ((((A and B) -> A) and (C or (D -> (D or E)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C or (D -> (D or E)))))), M:tm-327, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37938
in-theory        37938
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and (((F and G) -> G) and (((A and B) -> A) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37938.        ((((A and B) -> A) and (C or (D -> (D or E)))) and (((F and G) -> G) and (((A and B) -> A) and (C or (D -> (D or E)))))), M:tm-326, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37939
in-theory        37939
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and (((F and G) -> F) and (((A and B) -> A) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37939.        ((((A and B) -> A) and (C or (D -> (D or E)))) and (((F and G) -> F) and (((A and B) -> A) and (C or (D -> (D or E)))))), M:tm-325, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37940
in-theory        37940
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C or (D -> (D or E))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37940.        ((((A and B) -> A) and (C or (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C or (D -> (D or E)))))), M:tm-324, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37941
in-theory        37941
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and ((F -> (G -> F)) and (((A and B) -> A) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37941.        ((((A and B) -> A) and (C or (D -> (D or E)))) and ((F -> (G -> F)) and (((A and B) -> A) and (C or (D -> (D or E)))))), M:tm-323, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37942
in-theory        37942
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37942.        ((((A and B) -> A) and (C or (D -> (D or E)))) and ((F and G) -> G)), M:tm-322, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37943
in-theory        37943
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37943.        ((((A and B) -> A) and (C or (D -> (D or E)))) and ((F and G) -> F)), M:tm-320, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37944
in-theory        37944
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37944.        ((((A and B) -> A) and (C or (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37945
in-theory        37945
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37945.        ((((A and B) -> A) and (C or (D -> (D or E)))) and (F -> (G -> F))), M:tm-315, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37946
in-theory        37946
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and (F or (((A and B) -> A) and (C or (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37946.        ((((A and B) -> A) and (C or (D -> (D or E)))) and (F or (((A and B) -> A) and (C or (D -> (D or E)))))), M:tm-311, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37947
in-theory        37947
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and ((((A and B) -> A) and (C or (D -> (D or E)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37947.        ((((A and B) -> A) and (C or (D -> (D or E)))) and ((((A and B) -> A) and (C or (D -> (D or E)))) or F)), M:tm-310, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37948
in-theory        37948
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and (F -> ((((A and B) -> A) and (C or (D -> (D or E)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37948.        ((((A and B) -> A) and (C or (D -> (D or E)))) and (F -> ((((A and B) -> A) and (C or (D -> (D or E)))) and F))), M:tm-309, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37949
in-theory        37949
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and (C or (D -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-308 tm-525 ((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37949.        ((((A and B) -> A) and (C or (D -> (D or E)))) and (C or (D -> (D or E)))), M:tm-308, m:tm-525, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-37950
in-theory        37950
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-525 ((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37950.        ((((A and B) -> A) and (C or (D -> (D or E)))) and ((A and B) -> A)), M:tm-307, m:tm-525, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-37951
in-theory        37951
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and (F -> (((A and B) -> A) and (C or (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37951.        ((((A and B) -> A) and (C or (D -> (D or E)))) and (F -> (((A and B) -> A) and (C or (D -> (D or E)))))), M:tm-305, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37952
in-theory        37952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37952.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-303, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37953
in-theory        37953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37953.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-270, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37954
in-theory        37954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37954.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-239, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37955
in-theory        37955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37955.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or (H -> (H or I))))), M:tm-210, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37956
in-theory        37956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37956.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-183, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37957
in-theory        37957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37957.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-157, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37958
in-theory        37958
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37958.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-147, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37959
in-theory        37959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37959.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-134, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37960
in-theory        37960
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37960.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-125, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37961
in-theory        37961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37961.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (H or I))))), M:tm-113, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37962
in-theory        37962
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37962.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-105, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37963
in-theory        37963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37963.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or (F -> (F or G))))), M:tm-95, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37964
in-theory        37964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37964.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-83, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37965
in-theory        37965
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D or (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37965.        (((not (not A)) -> A) and (((B and C) -> B) and (D or (E -> (E or F))))), M:tm-76, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37966
in-theory        37966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-3 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37966.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or (F -> (F or G))))), M:tm-69, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37967
in-theory        37967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37967.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-54, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37968
in-theory        37968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37968.        ((A -> (B or A)) and (((C and D) -> C) and (E or (F -> (F or G))))), M:tm-42, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37969
in-theory        37969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37969.        ((A -> (A or B)) and (((C and D) -> C) and (E or (F -> (F or G))))), M:tm-32, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37970
in-theory        37970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37970.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or (F -> (F or G))))), M:tm-23, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37971
in-theory        37971
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37971.        (((A and B) -> B) and (((C and D) -> C) and (E or (F -> (F or G))))), M:tm-22, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37972
in-theory        37972
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37972.        (((A and B) -> A) and (((C and D) -> C) and (E or (F -> (F or G))))), M:tm-21, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37973
in-theory        37973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37973.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-20, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37974
in-theory        37974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37974.        ((A -> (B -> A)) and (((C and D) -> C) and (E or (F -> (F or G))))), M:tm-19, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37975
in-theory        37975
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-3 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37975.        (A or (((B and C) -> B) and (D or (E -> (E or F))))), M:tm-7, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37976
in-theory        37976
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-3 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37976.        ((((A and B) -> A) and (C or (D -> (D or E)))) or F), M:tm-6, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37977
in-theory        37977
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D or (E -> (E or F)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37977.        (A -> ((((B and C) -> B) and (D or (E -> (E or F)))) and A)), M:tm-5, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37978
in-theory        37978
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-3 tm-7 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37978.        (A -> (((B and C) -> B) and (D or (E -> (E or F))))), M:tm-1, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-37979
in-theory        37979
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37979.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-520, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37980
in-theory        37980
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37980.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-510, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37981
in-theory        37981
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37981.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-500, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37982
in-theory        37982
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37982.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (I or J))))), M:tm-490, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37983
in-theory        37983
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37983.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-480, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37984
in-theory        37984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37984.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-469, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37985
in-theory        37985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37985.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (G -> (G or H))), M:tm-456, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37986
in-theory        37986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37986.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-453, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37987
in-theory        37987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37987.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))))), M:tm-443, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37988
in-theory        37988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37988.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-409, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37989
in-theory        37989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37989.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-400, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37990
in-theory        37990
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37990.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-391, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37991
in-theory        37991
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37991.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-382, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37992
in-theory        37992
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37992.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (I or J))))), M:tm-373, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37993
in-theory        37993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37993.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-364, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37994
in-theory        37994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37994.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-354, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37995
in-theory        37995
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37995.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37996
in-theory        37996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37996.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H))))), M:tm-338, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37997
in-theory        37997
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37997.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))))), M:tm-327, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37998
in-theory        37998
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37998.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))))), M:tm-326, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-37999
in-theory        37999
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-37999.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))))), M:tm-325, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38000
in-theory        38000
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38000.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))))), M:tm-324, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38001
in-theory        38001
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38001.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))))), M:tm-323, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38002
in-theory        38002
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38002.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((G and H) -> H)), M:tm-322, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38003
in-theory        38003
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38003.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((G and H) -> G)), M:tm-320, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38004
in-theory        38004
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38004.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38005
in-theory        38005
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38005.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (G -> (H -> G))), M:tm-315, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38006
in-theory        38006
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38006.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))))), M:tm-311, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38007
in-theory        38007
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38007.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) or G)), M:tm-310, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38008
in-theory        38008
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38008.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and G))), M:tm-309, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38009
in-theory        38009
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (D or (E -> (E or F))))
theorem-size     29
proof            (modus-ponens tm-308 tm-526 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (or Em Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38009.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (D or (E -> (E or F)))), M:tm-308, m:tm-526, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (or Em Fm)))))
================================================================
tm-name          tm-38010
in-theory        38010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-526 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (or Em Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38010.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-526, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (or Em Fm)))))
================================================================
tm-name          tm-38011
in-theory        38011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38011.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))))), M:tm-305, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38012
in-theory        38012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38012.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-303, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38013
in-theory        38013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38013.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-270, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38014
in-theory        38014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38014.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-239, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38015
in-theory        38015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (I or J)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38015.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (I or J))))), M:tm-210, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38016
in-theory        38016
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38016.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-183, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38017
in-theory        38017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38017.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-157, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38018
in-theory        38018
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38018.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-147, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38019
in-theory        38019
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38019.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-134, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38020
in-theory        38020
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38020.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-125, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38021
in-theory        38021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (I or J)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38021.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (I or J))))), M:tm-113, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38022
in-theory        38022
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38022.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-105, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38023
in-theory        38023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38023.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H))))), M:tm-95, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38024
in-theory        38024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38024.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-83, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38025
in-theory        38025
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (F or G)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38025.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (F or G))))), M:tm-76, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38026
in-theory        38026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-9 tm-2 tm-7 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38026.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H))))), M:tm-69, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38027
in-theory        38027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38027.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-54, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38028
in-theory        38028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38028.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H))))), M:tm-42, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38029
in-theory        38029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38029.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H))))), M:tm-32, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38030
in-theory        38030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38030.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H))))), M:tm-23, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38031
in-theory        38031
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38031.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H))))), M:tm-22, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38032
in-theory        38032
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38032.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H))))), M:tm-21, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38033
in-theory        38033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38033.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-20, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38034
in-theory        38034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38034.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (G or H))))), M:tm-19, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38035
in-theory        38035
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-7 tm-5 tm-2 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38035.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (F or G))))), M:tm-7, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38036
in-theory        38036
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-6 tm-5 tm-2 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38036.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) or G), M:tm-6, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38037
in-theory        38037
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (F or G)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38037.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (F or G)))) and A)), M:tm-5, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38038
in-theory        38038
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-1 tm-5 tm-2 tm-7 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38038.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (F or G))))), M:tm-1, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38039
in-theory        38039
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38039.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-520, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38040
in-theory        38040
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38040.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-510, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38041
in-theory        38041
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38041.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-500, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38042
in-theory        38042
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38042.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (H or I))))), M:tm-490, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38043
in-theory        38043
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38043.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-480, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38044
in-theory        38044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38044.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-469, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38045
in-theory        38045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38045.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and (F -> (F or G))), M:tm-456, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38046
in-theory        38046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38046.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-453, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38047
in-theory        38047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38047.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C or (D -> (D or E)))))), M:tm-443, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38048
in-theory        38048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38048.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-409, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38049
in-theory        38049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38049.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-400, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38050
in-theory        38050
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38050.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-391, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38051
in-theory        38051
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38051.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-382, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38052
in-theory        38052
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38052.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (H or I))))), M:tm-373, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38053
in-theory        38053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38053.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-364, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38054
in-theory        38054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38054.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-354, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38055
in-theory        38055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38055.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38056
in-theory        38056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38056.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (F or G))))), M:tm-338, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38057
in-theory        38057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C or (D -> (D or E))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38057.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C or (D -> (D or E)))))), M:tm-327, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38058
in-theory        38058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and (((F and G) -> G) and ((A -> (B -> A)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38058.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and (((F and G) -> G) and ((A -> (B -> A)) and (C or (D -> (D or E)))))), M:tm-326, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38059
in-theory        38059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and (((F and G) -> F) and ((A -> (B -> A)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38059.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and (((F and G) -> F) and ((A -> (B -> A)) and (C or (D -> (D or E)))))), M:tm-325, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38060
in-theory        38060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C or (D -> (D or E))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38060.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C or (D -> (D or E)))))), M:tm-324, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38061
in-theory        38061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38061.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C or (D -> (D or E)))))), M:tm-323, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38062
in-theory        38062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38062.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and ((F and G) -> G)), M:tm-322, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38063
in-theory        38063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38063.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and ((F and G) -> F)), M:tm-320, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38064
in-theory        38064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38064.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38065
in-theory        38065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38065.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and (F -> (G -> F))), M:tm-315, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38066
in-theory        38066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and (F or ((A -> (B -> A)) and (C or (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38066.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and (F or ((A -> (B -> A)) and (C or (D -> (D or E)))))), M:tm-311, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38067
in-theory        38067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and (((A -> (B -> A)) and (C or (D -> (D or E)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38067.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and (((A -> (B -> A)) and (C or (D -> (D or E)))) or F)), M:tm-310, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38068
in-theory        38068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and (F -> (((A -> (B -> A)) and (C or (D -> (D or E)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38068.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and (F -> (((A -> (B -> A)) and (C or (D -> (D or E)))) and F))), M:tm-309, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38069
in-theory        38069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and (C or (D -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-308 tm-527 ((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38069.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and (C or (D -> (D or E)))), M:tm-308, m:tm-527, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-38070
in-theory        38070
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-527 ((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38070.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and (A -> (B -> A))), M:tm-307, m:tm-527, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-38071
in-theory        38071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and (F -> ((A -> (B -> A)) and (C or (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38071.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and (F -> ((A -> (B -> A)) and (C or (D -> (D or E)))))), M:tm-305, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38072
in-theory        38072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38072.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-303, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38073
in-theory        38073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38073.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-270, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38074
in-theory        38074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38074.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-239, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38075
in-theory        38075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38075.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or (H -> (H or I))))), M:tm-210, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38076
in-theory        38076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38076.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-183, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38077
in-theory        38077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38077.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-157, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38078
in-theory        38078
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38078.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-147, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38079
in-theory        38079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38079.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-134, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38080
in-theory        38080
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38080.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-125, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38081
in-theory        38081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38081.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (H or I))))), M:tm-113, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38082
in-theory        38082
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38082.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-105, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38083
in-theory        38083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38083.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or (F -> (F or G))))), M:tm-95, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38084
in-theory        38084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38084.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-83, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38085
in-theory        38085
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D or (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38085.        (((not (not A)) -> A) and ((B -> (C -> B)) and (D or (E -> (E or F))))), M:tm-76, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38086
in-theory        38086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38086.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or (F -> (F or G))))), M:tm-69, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38087
in-theory        38087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38087.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-54, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38088
in-theory        38088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38088.        ((A -> (B or A)) and ((C -> (D -> C)) and (E or (F -> (F or G))))), M:tm-42, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38089
in-theory        38089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38089.        ((A -> (A or B)) and ((C -> (D -> C)) and (E or (F -> (F or G))))), M:tm-32, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38090
in-theory        38090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38090.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (F or G))))), M:tm-23, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38091
in-theory        38091
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38091.        (((A and B) -> B) and ((C -> (D -> C)) and (E or (F -> (F or G))))), M:tm-22, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38092
in-theory        38092
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38092.        (((A and B) -> A) and ((C -> (D -> C)) and (E or (F -> (F or G))))), M:tm-21, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38093
in-theory        38093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38093.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-20, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38094
in-theory        38094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38094.        ((A -> (B -> A)) and ((C -> (D -> C)) and (E or (F -> (F or G))))), M:tm-19, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38095
in-theory        38095
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-1 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38095.        (A or ((B -> (C -> B)) and (D or (E -> (E or F))))), M:tm-7, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38096
in-theory        38096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-1 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38096.        (((A -> (B -> A)) and (C or (D -> (D or E)))) or F), M:tm-6, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38097
in-theory        38097
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D or (E -> (E or F)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38097.        (A -> (((B -> (C -> B)) and (D or (E -> (E or F)))) and A)), M:tm-5, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38098
in-theory        38098
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-7 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38098.        (A -> ((B -> (C -> B)) and (D or (E -> (E or F))))), M:tm-1, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38099
in-theory        38099
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38099.        ((A or (B -> (C -> (B and C)))) and (D or (E or (F -> (F or G))))), M:tm-520, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38100
in-theory        38100
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38100.        ((A or ((B and C) -> C)) and (D or (E or (F -> (F or G))))), M:tm-510, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38101
in-theory        38101
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38101.        ((A or ((B and C) -> B)) and (D or (E or (F -> (F or G))))), M:tm-500, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38102
in-theory        38102
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38102.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (G or H))))), M:tm-490, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38103
in-theory        38103
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38103.        ((A or (B -> (C -> B))) and (D or (E or (F -> (F or G))))), M:tm-480, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38104
in-theory        38104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38104.        ((A -> (B -> (B or C))) and (D or (E or (F -> (F or G))))), M:tm-469, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38105
in-theory        38105
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38105.        ((A or (B or (C -> (C or D)))) and (E -> (E or F))), M:tm-456, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38106
in-theory        38106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38106.        ((A -> ((B -> (B or C)) and A)) and (D or (E or (F -> (F or G))))), M:tm-453, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38107
in-theory        38107
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and ((E -> (E or F)) and (A or (B or (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38107.        ((A or (B or (C -> (C or D)))) and ((E -> (E or F)) and (A or (B or (C -> (C or D)))))), M:tm-443, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38108
in-theory        38108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38108.        (((A -> (A or B)) or C) and (D or (E or (F -> (F or G))))), M:tm-409, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38109
in-theory        38109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38109.        (((A -> (B -> (A and B))) or C) and (D or (E or (F -> (F or G))))), M:tm-400, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38110
in-theory        38110
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38110.        ((((A and B) -> B) or C) and (D or (E or (F -> (F or G))))), M:tm-391, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38111
in-theory        38111
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38111.        ((((A and B) -> A) or C) and (D or (E or (F -> (F or G))))), M:tm-382, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38112
in-theory        38112
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38112.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or (G -> (G or H))))), M:tm-373, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38113
in-theory        38113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38113.        (((A -> (B -> A)) or C) and (D or (E or (F -> (F or G))))), M:tm-364, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38114
in-theory        38114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38114.        ((A -> (B -> (C -> (B and C)))) and (D or (E or (F -> (F or G))))), M:tm-354, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38115
in-theory        38115
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38115.        ((A or (B or (C -> (C or D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38116
in-theory        38116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D or (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38116.        (((A -> B) -> (A -> (A and B))) and (C or (D or (E -> (E or F))))), M:tm-338, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38117
in-theory        38117
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and ((E -> (F -> (E and F))) and (A or (B or (C -> (C or D))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38117.        ((A or (B or (C -> (C or D)))) and ((E -> (F -> (E and F))) and (A or (B or (C -> (C or D)))))), M:tm-327, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38118
in-theory        38118
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and (((E and F) -> F) and (A or (B or (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38118.        ((A or (B or (C -> (C or D)))) and (((E and F) -> F) and (A or (B or (C -> (C or D)))))), M:tm-326, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38119
in-theory        38119
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and (((E and F) -> E) and (A or (B or (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38119.        ((A or (B or (C -> (C or D)))) and (((E and F) -> E) and (A or (B or (C -> (C or D)))))), M:tm-325, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38120
in-theory        38120
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B or (C -> (C or D))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38120.        ((A or (B or (C -> (C or D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B or (C -> (C or D)))))), M:tm-324, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38121
in-theory        38121
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and ((E -> (F -> E)) and (A or (B or (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38121.        ((A or (B or (C -> (C or D)))) and ((E -> (F -> E)) and (A or (B or (C -> (C or D)))))), M:tm-323, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38122
in-theory        38122
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38122.        ((A or (B or (C -> (C or D)))) and ((E and F) -> F)), M:tm-322, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38123
in-theory        38123
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38123.        ((A or (B or (C -> (C or D)))) and ((E and F) -> E)), M:tm-320, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38124
in-theory        38124
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38124.        ((A or (B or (C -> (C or D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38125
in-theory        38125
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38125.        ((A or (B or (C -> (C or D)))) and (E -> (F -> E))), M:tm-315, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38126
in-theory        38126
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and (E or (A or (B or (C -> (C or D))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38126.        ((A or (B or (C -> (C or D)))) and (E or (A or (B or (C -> (C or D)))))), M:tm-311, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38127
in-theory        38127
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and ((A or (B or (C -> (C or D)))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38127.        ((A or (B or (C -> (C or D)))) and ((A or (B or (C -> (C or D)))) or E)), M:tm-310, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38128
in-theory        38128
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and (E -> ((A or (B or (C -> (C or D)))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38128.        ((A or (B or (C -> (C or D)))) and (E -> ((A or (B or (C -> (C or D)))) and E))), M:tm-309, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38129
in-theory        38129
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and (E -> (A or (B or (C -> (C or D))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38129.        ((A or (B or (C -> (C or D)))) and (E -> (A or (B or (C -> (C or D)))))), M:tm-305, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38130
in-theory        38130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38130.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or (F -> (F or G))))), M:tm-303, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38131
in-theory        38131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38131.        ((A -> (((B and C) -> C) and A)) and (D or (E or (F -> (F or G))))), M:tm-270, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38132
in-theory        38132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38132.        ((A -> (((B and C) -> B) and A)) and (D or (E or (F -> (F or G))))), M:tm-239, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38133
in-theory        38133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38133.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or (G -> (G or H))))), M:tm-210, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38134
in-theory        38134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38134.        ((A -> ((B -> (C -> B)) and A)) and (D or (E or (F -> (F or G))))), M:tm-183, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38135
in-theory        38135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38135.        ((A -> ((B and C) -> C)) and (D or (E or (F -> (F or G))))), M:tm-157, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38136
in-theory        38136
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38136.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or (F -> (F or G))))), M:tm-147, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38137
in-theory        38137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38137.        ((A -> ((B and C) -> B)) and (D or (E or (F -> (F or G))))), M:tm-134, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38138
in-theory        38138
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38138.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or (F -> (F or G))))), M:tm-125, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38139
in-theory        38139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38139.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (G or H))))), M:tm-113, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38140
in-theory        38140
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or (F -> (F or G)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38140.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or (F -> (F or G))))), M:tm-105, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38141
in-theory        38141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D or (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38141.        (((A -> B) -> (A -> A)) and (C or (D or (E -> (E or F))))), M:tm-95, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38142
in-theory        38142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38142.        ((A -> (B -> (C -> B))) and (D or (E or (F -> (F or G))))), M:tm-83, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38143
in-theory        38143
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C or (D -> (D or E)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38143.        (((not (not A)) -> A) and (B or (C or (D -> (D or E))))), M:tm-76, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38144
in-theory        38144
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or (E -> (E or F)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38144.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or (E -> (E or F))))), M:tm-69, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38145
in-theory        38145
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38145.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or (F -> (F or G))))), M:tm-54, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38146
in-theory        38146
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38146.        ((A -> (B or A)) and (C or (D or (E -> (E or F))))), M:tm-42, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38147
in-theory        38147
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38147.        ((A -> (A or B)) and (C or (D or (E -> (E or F))))), M:tm-32, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38148
in-theory        38148
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D or (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38148.        ((A -> (B -> (A and B))) and (C or (D or (E -> (E or F))))), M:tm-23, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38149
in-theory        38149
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38149.        (((A and B) -> B) and (C or (D or (E -> (E or F))))), M:tm-22, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38150
in-theory        38150
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38150.        (((A and B) -> A) and (C or (D or (E -> (E or F))))), M:tm-21, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38151
in-theory        38151
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38151.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or (F -> (F or G))))), M:tm-20, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38152
in-theory        38152
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38152.        ((A -> (B -> A)) and (C or (D or (E -> (E or F))))), M:tm-19, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38153
in-theory        38153
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C or (D -> (D or E)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-7 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38153.        (A or (B or (C or (D -> (D or E))))), M:tm-7, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38154
in-theory        38154
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-6 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38154.        ((A or (B or (C -> (C or D)))) or E), M:tm-6, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38155
in-theory        38155
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C or (D -> (D or E)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38155.        (A -> ((B or (C or (D -> (D or E)))) and A)), M:tm-5, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38156
in-theory        38156
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C or (D -> (D or E)))))
theorem-size     11
proof            (modus-ponens tm-1 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-1 tm-7 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38156.        (A -> (B or (C or (D -> (D or E))))), M:tm-1, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38157
in-theory        38157
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38157.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (E or F))) or G)), M:tm-520, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38158
in-theory        38158
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38158.        ((A or ((B and C) -> C)) and ((D or (E -> (E or F))) or G)), M:tm-510, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38159
in-theory        38159
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38159.        ((A or ((B and C) -> B)) and ((D or (E -> (E or F))) or G)), M:tm-500, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38160
in-theory        38160
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (F or G))) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38160.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (F or G))) or H)), M:tm-490, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38161
in-theory        38161
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38161.        ((A or (B -> (C -> B))) and ((D or (E -> (E or F))) or G)), M:tm-480, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38162
in-theory        38162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38162.        ((A -> (B -> (B or C))) and ((D or (E -> (E or F))) or G)), M:tm-469, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38163
in-theory        38163
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38163.        (((A or (B -> (B or C))) or D) and (E -> (E or F))), M:tm-456, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38164
in-theory        38164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38164.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (E or F))) or G)), M:tm-453, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38165
in-theory        38165
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and ((E -> (E or F)) and ((A or (B -> (B or C))) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38165.        (((A or (B -> (B or C))) or D) and ((E -> (E or F)) and ((A or (B -> (B or C))) or D))), M:tm-443, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38166
in-theory        38166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38166.        (((A -> (A or B)) or C) and ((D or (E -> (E or F))) or G)), M:tm-409, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38167
in-theory        38167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38167.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (E or F))) or G)), M:tm-400, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38168
in-theory        38168
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38168.        ((((A and B) -> B) or C) and ((D or (E -> (E or F))) or G)), M:tm-391, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38169
in-theory        38169
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38169.        ((((A and B) -> A) or C) and ((D or (E -> (E or F))) or G)), M:tm-382, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38170
in-theory        38170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (F or G))) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38170.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (F or G))) or H)), M:tm-373, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38171
in-theory        38171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38171.        (((A -> (B -> A)) or C) and ((D or (E -> (E or F))) or G)), M:tm-364, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38172
in-theory        38172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38172.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (E or F))) or G)), M:tm-354, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38173
in-theory        38173
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38173.        (((A or (B -> (B or C))) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38174
in-theory        38174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (D or E))) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38174.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (D or E))) or F)), M:tm-338, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38175
in-theory        38175
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and ((E -> (F -> (E and F))) and ((A or (B -> (B or C))) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38175.        (((A or (B -> (B or C))) or D) and ((E -> (F -> (E and F))) and ((A or (B -> (B or C))) or D))), M:tm-327, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38176
in-theory        38176
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and (((E and F) -> F) and ((A or (B -> (B or C))) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38176.        (((A or (B -> (B or C))) or D) and (((E and F) -> F) and ((A or (B -> (B or C))) or D))), M:tm-326, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38177
in-theory        38177
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and (((E and F) -> E) and ((A or (B -> (B or C))) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38177.        (((A or (B -> (B or C))) or D) and (((E and F) -> E) and ((A or (B -> (B or C))) or D))), M:tm-325, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38178
in-theory        38178
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (B or C))) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38178.        (((A or (B -> (B or C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (B or C))) or D))), M:tm-324, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38179
in-theory        38179
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and ((E -> (F -> E)) and ((A or (B -> (B or C))) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38179.        (((A or (B -> (B or C))) or D) and ((E -> (F -> E)) and ((A or (B -> (B or C))) or D))), M:tm-323, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38180
in-theory        38180
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38180.        (((A or (B -> (B or C))) or D) and ((E and F) -> F)), M:tm-322, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38181
in-theory        38181
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38181.        (((A or (B -> (B or C))) or D) and ((E and F) -> E)), M:tm-320, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38182
in-theory        38182
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38182.        (((A or (B -> (B or C))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38183
in-theory        38183
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38183.        (((A or (B -> (B or C))) or D) and (E -> (F -> E))), M:tm-315, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38184
in-theory        38184
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and (E or ((A or (B -> (B or C))) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38184.        (((A or (B -> (B or C))) or D) and (E or ((A or (B -> (B or C))) or D))), M:tm-311, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38185
in-theory        38185
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and (((A or (B -> (B or C))) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38185.        (((A or (B -> (B or C))) or D) and (((A or (B -> (B or C))) or D) or E)), M:tm-310, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38186
in-theory        38186
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and (E -> (((A or (B -> (B or C))) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38186.        (((A or (B -> (B or C))) or D) and (E -> (((A or (B -> (B or C))) or D) and E))), M:tm-309, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38187
in-theory        38187
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and (E -> ((A or (B -> (B or C))) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38187.        (((A or (B -> (B or C))) or D) and (E -> ((A or (B -> (B or C))) or D))), M:tm-305, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38188
in-theory        38188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (E or F))) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38188.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (E or F))) or G)), M:tm-303, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38189
in-theory        38189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38189.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (E or F))) or G)), M:tm-270, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38190
in-theory        38190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38190.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (E or F))) or G)), M:tm-239, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38191
in-theory        38191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (F or G))) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38191.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (F or G))) or H)), M:tm-210, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38192
in-theory        38192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38192.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (E or F))) or G)), M:tm-183, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38193
in-theory        38193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38193.        ((A -> ((B and C) -> C)) and ((D or (E -> (E or F))) or G)), M:tm-157, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38194
in-theory        38194
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (E or F))) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38194.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (E or F))) or G)), M:tm-147, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38195
in-theory        38195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38195.        ((A -> ((B and C) -> B)) and ((D or (E -> (E or F))) or G)), M:tm-134, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38196
in-theory        38196
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (E or F))) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38196.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (E or F))) or G)), M:tm-125, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38197
in-theory        38197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (F or G))) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38197.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (F or G))) or H)), M:tm-113, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38198
in-theory        38198
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (E or F))) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38198.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (E or F))) or G)), M:tm-105, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38199
in-theory        38199
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (D or E))) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38199.        (((A -> B) -> (A -> A)) and ((C or (D -> (D or E))) or F)), M:tm-95, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38200
in-theory        38200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38200.        ((A -> (B -> (C -> B))) and ((D or (E -> (E or F))) or G)), M:tm-83, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38201
in-theory        38201
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (C or D))) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38201.        (((not (not A)) -> A) and ((B or (C -> (C or D))) or E)), M:tm-76, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38202
in-theory        38202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (D or E))) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38202.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (D or E))) or F)), M:tm-69, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38203
in-theory        38203
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (E or F))) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38203.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (E or F))) or G)), M:tm-54, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38204
in-theory        38204
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (D or E))) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38204.        ((A -> (B or A)) and ((C or (D -> (D or E))) or F)), M:tm-42, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38205
in-theory        38205
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (D or E))) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38205.        ((A -> (A or B)) and ((C or (D -> (D or E))) or F)), M:tm-32, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38206
in-theory        38206
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (D or E))) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38206.        ((A -> (B -> (A and B))) and ((C or (D -> (D or E))) or F)), M:tm-23, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38207
in-theory        38207
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (D or E))) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38207.        (((A and B) -> B) and ((C or (D -> (D or E))) or F)), M:tm-22, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38208
in-theory        38208
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (D or E))) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38208.        (((A and B) -> A) and ((C or (D -> (D or E))) or F)), M:tm-21, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38209
in-theory        38209
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (E or F))) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38209.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (E or F))) or G)), M:tm-20, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38210
in-theory        38210
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (D or E))) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38210.        ((A -> (B -> A)) and ((C or (D -> (D or E))) or F)), M:tm-19, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38211
in-theory        38211
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B or (C -> (C or D))) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-7 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38211.        (A or ((B or (C -> (C or D))) or E)), M:tm-7, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38212
in-theory        38212
times-derived    2
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-6 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38212.        (((A or (B -> (B or C))) or D) or E), M:tm-6, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38213
in-theory        38213
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (C or D))) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38213.        (A -> (((B or (C -> (C or D))) or E) and A)), M:tm-5, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38214
in-theory        38214
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (C or D))) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-1 tm-6 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38214.        (A -> ((B or (C -> (C or D))) or E)), M:tm-1, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38215
in-theory        38215
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-530 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38215.        ((A or (B -> (B or C))) and (D -> (E or D))), M:tm-530, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-38216
in-theory        38216
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-38216.        ((A or (B -> (B or C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-530, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-38217
in-theory        38217
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-530 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-38217.        ((A or (B -> (B or C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-530, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-38218
in-theory        38218
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-530 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-38218.        ((A or (B -> (B or C))) and ((not (not D)) -> D)), M:tm-530, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-38219
in-theory        38219
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-530 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38219.        ((A or (B -> (B or C))) and (D -> (E -> (F -> E)))), M:tm-530, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-38220
in-theory        38220
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-530 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-38220.        ((A or (B -> (B or C))) and ((D -> E) -> (D -> D))), M:tm-530, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-38221
in-theory        38221
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-530 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-38221.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-530, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-38222
in-theory        38222
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38222.        ((A or (B -> (B or C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-530, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-38223
in-theory        38223
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-530 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-38223.        ((A or (B -> (B or C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-530, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-38224
in-theory        38224
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-530 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38224.        ((A or (B -> (B or C))) and (D -> ((E and F) -> E))), M:tm-530, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-38225
in-theory        38225
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-530 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-38225.        ((A or (B -> (B or C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-530, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-38226
in-theory        38226
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-530 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38226.        ((A or (B -> (B or C))) and (D -> ((E and F) -> F))), M:tm-530, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-38227
in-theory        38227
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-530 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38227.        ((A or (B -> (B or C))) and (D -> ((E -> (F -> E)) and D))), M:tm-530, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-38228
in-theory        38228
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-530 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38228.        ((A or (B -> (B or C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-530, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-38229
in-theory        38229
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-530 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38229.        ((A or (B -> (B or C))) and (D -> (((E and F) -> E) and D))), M:tm-530, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-38230
in-theory        38230
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-530 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38230.        ((A or (B -> (B or C))) and (D -> (((E and F) -> F) and D))), M:tm-530, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-38231
in-theory        38231
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38231.        ((A or (B -> (B or C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-530, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-38232
in-theory        38232
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-530 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-38232.        ((A or (B -> (B or C))) and ((D -> E) -> (D -> (D and E)))), M:tm-530, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-38233
in-theory        38233
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38233.        ((A or (B -> (B or C))) and (D -> (E -> (F -> (E and F))))), M:tm-530, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-38234
in-theory        38234
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-530 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38234.        ((A or (B -> (B or C))) and ((D -> (E -> D)) or F)), M:tm-530, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-38235
in-theory        38235
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-530 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38235.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-530, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-38236
in-theory        38236
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-530 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38236.        ((A or (B -> (B or C))) and (((D and E) -> D) or F)), M:tm-530, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-38237
in-theory        38237
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-530 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38237.        ((A or (B -> (B or C))) and (((D and E) -> E) or F)), M:tm-530, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-38238
in-theory        38238
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-530 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38238.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) or F)), M:tm-530, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-38239
in-theory        38239
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-530 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38239.        ((A or (B -> (B or C))) and ((D -> (D or E)) or F)), M:tm-530, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-38240
in-theory        38240
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-530 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38240.        ((A or (B -> (B or C))) and (D -> ((E -> (E or F)) and D))), M:tm-530, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-38241
in-theory        38241
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-530 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38241.        ((A or (B -> (B or C))) and (D -> (E -> (E or F)))), M:tm-530, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-38242
in-theory        38242
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-530 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38242.        ((A or (B -> (B or C))) and (D or (E -> (F -> E)))), M:tm-530, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-38243
in-theory        38243
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38243.        ((A or (B -> (B or C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-530, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-38244
in-theory        38244
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-530 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38244.        ((A or (B -> (B or C))) and (D or ((E and F) -> E))), M:tm-530, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-38245
in-theory        38245
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-530 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38245.        ((A or (B -> (B or C))) and (D or ((E and F) -> F))), M:tm-530, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-38246
in-theory        38246
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38246.        ((A or (B -> (B or C))) and (D or (E -> (F -> (E and F))))), M:tm-530, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-38247
in-theory        38247
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-530 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38247.        ((A or (B -> (B or C))) and (D or (E -> (E or F)))), M:tm-530, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-38248
in-theory        38248
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-530 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38248.        ((A or (B -> (B or C))) and (D or (E -> (F or E)))), M:tm-530, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-38249
in-theory        38249
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-530 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38249.        ((A or (B -> (B or C))) and ((D -> (E or D)) or F)), M:tm-530, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-38250
in-theory        38250
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-530 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38250.        ((A or (B -> (B or C))) and (D -> ((E -> (F or E)) and D))), M:tm-530, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-38251
in-theory        38251
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-530 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38251.        ((A or (B -> (B or C))) and (D -> (E -> (F or E)))), M:tm-530, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-38252
in-theory        38252
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-530 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-38252.        ((A or (B -> (B or C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-530, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-38253
in-theory        38253
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-530 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-38253.        ((A or (B -> (B or C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-530, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-38254
in-theory        38254
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-530 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-38254.        ((A or (B -> (B or C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-530, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-38255
in-theory        38255
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-530 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-38255.        ((A or (B -> (B or C))) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-530, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-38256
in-theory        38256
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-530 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-38256.        ((A or (B -> (B or C))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-530, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-38257
in-theory        38257
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-530 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-38257.        ((A or (B -> (B or C))) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-530, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-38258
in-theory        38258
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-530 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-38258.        ((A or (B -> (B or C))) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-530, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-38259
in-theory        38259
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-530 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-38259.        ((A or (B -> (B or C))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-530, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-38260
in-theory        38260
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-38260.        ((A or (B -> (B or C))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-530, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-38261
in-theory        38261
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-530 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-38261.        ((A or (B -> (B or C))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-530, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-38262
in-theory        38262
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-530 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-38262.        ((A or (B -> (B or C))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-530, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-38263
in-theory        38263
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-530 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-38263.        ((A or (B -> (B or C))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-530, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-38264
in-theory        38264
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-38264.        ((A or (B -> (B or C))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-530, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-38265
in-theory        38265
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-530 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-38265.        ((A or (B -> (B or C))) and ((D -> (not (E -> D))) -> (not D))), M:tm-530, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-38266
in-theory        38266
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-38266.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-530, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-38267
in-theory        38267
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-530 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-38267.        ((A or (B -> (B or C))) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-530, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-38268
in-theory        38268
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-530 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-38268.        ((A or (B -> (B or C))) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-530, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-38269
in-theory        38269
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-38269.        ((A or (B -> (B or C))) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-530, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-38270
in-theory        38270
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-530 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-38270.        ((A or (B -> (B or C))) and ((D -> (not (D or E))) -> (not D))), M:tm-530, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-38271
in-theory        38271
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-530 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-38271.        ((A or (B -> (B or C))) and ((D -> (not (E or D))) -> (not D))), M:tm-530, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-38272
in-theory        38272
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-530 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-38272.        ((A or (B -> (B or C))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-530, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-38273
in-theory        38273
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-530 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-38273.        ((A or (B -> (B or C))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-530, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-38274
in-theory        38274
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-530 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-38274.        ((A or (B -> (B or C))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-530, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-38275
in-theory        38275
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-38275.        ((A or (B -> (B or C))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-530, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-38276
in-theory        38276
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-530 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-38276.        ((A or (B -> (B or C))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-530, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-38277
in-theory        38277
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-530 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-38277.        ((A or (B -> (B or C))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-530, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-38278
in-theory        38278
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-530 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-38278.        ((A or (B -> (B or C))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-530, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-38279
in-theory        38279
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-38279.        ((A or (B -> (B or C))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-530, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-38280
in-theory        38280
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-530 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-38280.        ((A or (B -> (B or C))) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-530, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-38281
in-theory        38281
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-530 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-38281.        ((A or (B -> (B or C))) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-530, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-38282
in-theory        38282
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-530 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-38282.        ((A or (B -> (B or C))) and (D or ((not (not E)) -> E))), M:tm-530, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-38283
in-theory        38283
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-530 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-38283.        ((A or (B -> (B or C))) and (((not (not D)) -> D) or E)), M:tm-530, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-38284
in-theory        38284
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-530 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-38284.        ((A or (B -> (B or C))) and (D -> (((not (not E)) -> E) and D))), M:tm-530, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-38285
in-theory        38285
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-530 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-38285.        ((A or (B -> (B or C))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-530, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-38286
in-theory        38286
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-530 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-38286.        ((A or (B -> (B or C))) and (D -> ((not (not E)) -> E))), M:tm-530, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-38287
in-theory        38287
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-38287.        ((A or (B -> (B or C))) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-530, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-38288
in-theory        38288
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-530 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-38288.        ((A or (B -> (B or C))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-530, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-38289
in-theory        38289
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-38289.        ((A or (B -> (B or C))) and (D or (E -> (F -> (G -> F))))), M:tm-530, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-38290
in-theory        38290
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-38290.        ((A or (B -> (B or C))) and ((D -> (E -> (F -> E))) or G)), M:tm-530, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-38291
in-theory        38291
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-38291.        ((A or (B -> (B or C))) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-530, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-38292
in-theory        38292
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-530 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-38292.        ((A or (B -> (B or C))) and ((D -> E) -> (D -> (F -> E)))), M:tm-530, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-38293
in-theory        38293
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-38293.        ((A or (B -> (B or C))) and (D -> (E -> (F -> (G -> F))))), M:tm-530, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-38294
in-theory        38294
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-530 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-38294.        ((A or (B -> (B or C))) and (D -> D)), M:tm-530, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-38295
in-theory        38295
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-38295.        ((A or (B -> (B or C))) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-530, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-38296
in-theory        38296
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-530 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-38296.        ((A or (B -> (B or C))) and ((D and E) -> (D and E))), M:tm-530, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-38297
in-theory        38297
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-530 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-38297.        ((A or (B -> (B or C))) and ((D -> E) -> (D -> E))), M:tm-530, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-38298
in-theory        38298
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-530 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-38298.        ((A or (B -> (B or C))) and ((not (not D)) -> (not (not D)))), M:tm-530, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-38299
in-theory        38299
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-530 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-38299.        ((A or (B -> (B or C))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-530, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-38300
in-theory        38300
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-530 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-38300.        ((A or (B -> (B or C))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-530, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-38301
in-theory        38301
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-530 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-38301.        ((A or (B -> (B or C))) and (D or ((E -> F) -> (E -> E)))), M:tm-530, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-38302
in-theory        38302
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-530 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-38302.        ((A or (B -> (B or C))) and (((D -> E) -> (D -> D)) or F)), M:tm-530, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-38303
in-theory        38303
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-38303.        ((A or (B -> (B or C))) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-530, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-38304
in-theory        38304
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-38304.        ((A or (B -> (B or C))) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-530, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-38305
in-theory        38305
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-530 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-38305.        ((A or (B -> (B or C))) and (D -> ((E -> F) -> (E -> E)))), M:tm-530, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-38306
in-theory        38306
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-38306.        ((A or (B -> (B or C))) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-530, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-38307
in-theory        38307
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-530 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-38307.        ((A or (B -> (B or C))) and ((D -> (D -> E)) -> (D -> E))), M:tm-530, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-38308
in-theory        38308
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-530 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-38308.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-530, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-38309
in-theory        38309
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-530 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-38309.        ((A or (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-530, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-38310
in-theory        38310
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-530 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-38310.        ((A or (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-530, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-38311
in-theory        38311
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-38311.        ((A or (B -> (B or C))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-530, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-38312
in-theory        38312
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-530 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-38312.        ((A or (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-530, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-38313
in-theory        38313
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-530 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-38313.        ((A or (B -> (B or C))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-530, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-38314
in-theory        38314
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-530 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-38314.        ((A or (B -> (B or C))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-530, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-38315
in-theory        38315
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-38315.        ((A or (B -> (B or C))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-530, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-38316
in-theory        38316
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-530 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-38316.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-530, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-38317
in-theory        38317
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-530 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-38317.        ((A or (B -> (B or C))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-530, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-38318
in-theory        38318
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-530 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-38318.        ((A or (B -> (B or C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-530, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-38319
in-theory        38319
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-530 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38319.        ((A or (B -> (B or C))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-530, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-38320
in-theory        38320
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-530 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38320.        ((A or (B -> (B or C))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-530, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-38321
in-theory        38321
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-530 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38321.        ((A or (B -> (B or C))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-530, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-38322
in-theory        38322
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-530 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-38322.        ((A or (B -> (B or C))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-530, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-38323
in-theory        38323
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-530 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38323.        ((A or (B -> (B or C))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-530, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-38324
in-theory        38324
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-530 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-38324.        ((A or (B -> (B or C))) and (((D -> E) and D) -> E)), M:tm-530, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-38325
in-theory        38325
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-530 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-38325.        ((A or (B -> (B or C))) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-530, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-38326
in-theory        38326
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-530 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-38326.        ((A or (B -> (B or C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-530, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-38327
in-theory        38327
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-530 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-38327.        ((A or (B -> (B or C))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-530, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-38328
in-theory        38328
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-530 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-38328.        ((A or (B -> (B or C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-530, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-38329
in-theory        38329
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-530 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-38329.        ((A or (B -> (B or C))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-530, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-38330
in-theory        38330
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-530 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-38330.        ((A or (B -> (B or C))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-530, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-38331
in-theory        38331
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-530 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-38331.        ((A or (B -> (B or C))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-530, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-38332
in-theory        38332
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-530 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-38332.        ((A or (B -> (B or C))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-530, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-38333
in-theory        38333
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-530 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-38333.        ((A or (B -> (B or C))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-530, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-38334
in-theory        38334
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-530 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-38334.        ((A or (B -> (B or C))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-530, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-38335
in-theory        38335
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-530 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-38335.        ((A or (B -> (B or C))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-530, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-38336
in-theory        38336
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-530 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-38336.        ((A or (B -> (B or C))) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-530, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-38337
in-theory        38337
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-530 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-38337.        ((A or (B -> (B or C))) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-530, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-38338
in-theory        38338
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-38338.        ((A or (B -> (B or C))) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-530, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-38339
in-theory        38339
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-530 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-38339.        ((A or (B -> (B or C))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-530, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-38340
in-theory        38340
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-530 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-38340.        ((A or (B -> (B or C))) and (D or (E -> ((F and G) -> F)))), M:tm-530, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-38341
in-theory        38341
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-38341.        ((A or (B -> (B or C))) and ((D -> ((E and F) -> E)) or G)), M:tm-530, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-38342
in-theory        38342
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-38342.        ((A or (B -> (B or C))) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-530, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-38343
in-theory        38343
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-530 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-38343.        ((A or (B -> (B or C))) and ((D -> (E and F)) -> (D -> E))), M:tm-530, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-38344
in-theory        38344
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-530 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-38344.        ((A or (B -> (B or C))) and (D -> (E -> ((F and G) -> F)))), M:tm-530, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-38345
in-theory        38345
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-530 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-38345.        ((A or (B -> (B or C))) and ((D and (D -> E)) -> E)), M:tm-530, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-38346
in-theory        38346
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-530 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-38346.        ((A or (B -> (B or C))) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-530, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-38347
in-theory        38347
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-530 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-38347.        ((A or (B -> (B or C))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-530, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-38348
in-theory        38348
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-530 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-38348.        ((A or (B -> (B or C))) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-530, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-38349
in-theory        38349
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-530 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-38349.        ((A or (B -> (B or C))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-530, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-38350
in-theory        38350
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-530 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-38350.        ((A or (B -> (B or C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-530, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-38351
in-theory        38351
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-530 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-38351.        ((A or (B -> (B or C))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-530, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-38352
in-theory        38352
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-530 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-38352.        ((A or (B -> (B or C))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-530, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-38353
in-theory        38353
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-530 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-38353.        ((A or (B -> (B or C))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-530, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-38354
in-theory        38354
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-530 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-38354.        ((A or (B -> (B or C))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-530, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-38355
in-theory        38355
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-530 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-38355.        ((A or (B -> (B or C))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-530, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-38356
in-theory        38356
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-530 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-38356.        ((A or (B -> (B or C))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-530, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-38357
in-theory        38357
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-530 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-38357.        ((A or (B -> (B or C))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-530, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-38358
in-theory        38358
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-530 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-38358.        ((A or (B -> (B or C))) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-530, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-38359
in-theory        38359
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-530 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-38359.        ((A or (B -> (B or C))) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-530, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-38360
in-theory        38360
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-530 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-38360.        ((A or (B -> (B or C))) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-530, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-38361
in-theory        38361
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-38361.        ((A or (B -> (B or C))) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-530, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-38362
in-theory        38362
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-530 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-38362.        ((A or (B -> (B or C))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-530, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-38363
in-theory        38363
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-530 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-38363.        ((A or (B -> (B or C))) and (D or (E -> ((F and G) -> G)))), M:tm-530, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-38364
in-theory        38364
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-38364.        ((A or (B -> (B or C))) and ((D -> ((E and F) -> F)) or G)), M:tm-530, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-38365
in-theory        38365
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-38365.        ((A or (B -> (B or C))) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-530, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-38366
in-theory        38366
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-530 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-38366.        ((A or (B -> (B or C))) and ((D -> (E and F)) -> (D -> F))), M:tm-530, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-38367
in-theory        38367
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-530 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-38367.        ((A or (B -> (B or C))) and (D -> (E -> ((F and G) -> G)))), M:tm-530, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-38368
in-theory        38368
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38368.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-530, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-38369
in-theory        38369
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38369.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-530, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-38370
in-theory        38370
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38370.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-530, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-38371
in-theory        38371
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-530 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38371.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-530, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-38372
in-theory        38372
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38372.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-530, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-38373
in-theory        38373
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-530 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38373.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-530, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38374
in-theory        38374
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38374.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-530, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-38375
in-theory        38375
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-38375.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-530, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-38376
in-theory        38376
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-530 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-38376.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-530, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-38377
in-theory        38377
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-38377.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-530, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-38378
in-theory        38378
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-38378.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-530, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-38379
in-theory        38379
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-38379.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-530, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-38380
in-theory        38380
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-530 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-38380.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-530, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-38381
in-theory        38381
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38381.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-530, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-38382
in-theory        38382
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-530 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-38382.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-530, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-38383
in-theory        38383
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-530 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-38383.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-530, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-38384
in-theory        38384
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-530 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-38384.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-530, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-38385
in-theory        38385
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-530 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-38385.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-530, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-38386
in-theory        38386
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-38386.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-530, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-38387
in-theory        38387
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-38387.        ((A or (B -> (B or C))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-530, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-38388
in-theory        38388
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-530 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-38388.        ((A or (B -> (B or C))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-530, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-38389
in-theory        38389
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-530 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-38389.        ((A or (B -> (B or C))) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-530, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-38390
in-theory        38390
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-530 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-38390.        ((A or (B -> (B or C))) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-530, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-38391
in-theory        38391
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-38391.        ((A or (B -> (B or C))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-530, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-38392
in-theory        38392
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-530 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-38392.        ((A or (B -> (B or C))) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-530, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-38393
in-theory        38393
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-530 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38393.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-530, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-38394
in-theory        38394
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38394.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-530, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-38395
in-theory        38395
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-530 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38395.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-530, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-38396
in-theory        38396
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-530 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38396.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-530, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-38397
in-theory        38397
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38397.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-530, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-38398
in-theory        38398
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38398.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-530, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-38399
in-theory        38399
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-530 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38399.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-530, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-38400
in-theory        38400
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-38400.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-530, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-38401
in-theory        38401
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-530 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-38401.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-530, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-38402
in-theory        38402
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-530 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-38402.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-530, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-38403
in-theory        38403
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-38403.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-530, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-38404
in-theory        38404
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-530 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-38404.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-530, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-38405
in-theory        38405
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-530 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-38405.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-530, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-38406
in-theory        38406
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-530 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38406.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-530, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-38407
in-theory        38407
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-530 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-38407.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-530, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-38408
in-theory        38408
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-530 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-38408.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-530, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-38409
in-theory        38409
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-530 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-38409.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-530, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-38410
in-theory        38410
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-530 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-38410.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-530, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-38411
in-theory        38411
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-530 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-38411.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-530, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-38412
in-theory        38412
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-530 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-38412.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-530, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-38413
in-theory        38413
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-530 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-38413.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-530, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-38414
in-theory        38414
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-530 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-38414.        ((A or (B -> (B or C))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-530, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-38415
in-theory        38415
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-530 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-38415.        ((A or (B -> (B or C))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-530, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-38416
in-theory        38416
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-530 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-38416.        ((A or (B -> (B or C))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-530, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-38417
in-theory        38417
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-530 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-38417.        ((A or (B -> (B or C))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-530, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-38418
in-theory        38418
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-530 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-38418.        ((A or (B -> (B or C))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-530, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-38419
in-theory        38419
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-530 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-38419.        ((A or (B -> (B or C))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-530, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-38420
in-theory        38420
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38420.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-530, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-38421
in-theory        38421
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38421.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-530, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-38422
in-theory        38422
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38422.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((F and G) -> F))), M:tm-530, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-38423
in-theory        38423
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-530 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38423.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((F and G) -> G))), M:tm-530, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-38424
in-theory        38424
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38424.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-530, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-38425
in-theory        38425
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-530 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38425.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (F or G)))), M:tm-530, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38426
in-theory        38426
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38426.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (G or F)))), M:tm-530, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-38427
in-theory        38427
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-38427.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-530, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-38428
in-theory        38428
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-530 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-38428.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-530, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-38429
in-theory        38429
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-38429.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-530, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-38430
in-theory        38430
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-38430.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-530, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-38431
in-theory        38431
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-38431.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-530, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-38432
in-theory        38432
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-530 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-38432.        ((A or (B -> (B or C))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-530, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-38433
in-theory        38433
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38433.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-530, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-38434
in-theory        38434
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-530 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-38434.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-530, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-38435
in-theory        38435
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-530 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-38435.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-530, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-38436
in-theory        38436
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-530 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-38436.        ((A or (B -> (B or C))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-530, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-38437
in-theory        38437
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-530 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-38437.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-530, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-38438
in-theory        38438
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-38438.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-530, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-38439
in-theory        38439
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-530 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-38439.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-530, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-38440
in-theory        38440
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-38440.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-530, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-38441
in-theory        38441
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-530 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-38441.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-530, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-38442
in-theory        38442
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-38442.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-530, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-38443
in-theory        38443
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-38443.        ((A or (B -> (B or C))) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-530, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-38444
in-theory        38444
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-530 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-38444.        ((A or (B -> (B or C))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-530, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-38445
in-theory        38445
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-530 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-38445.        ((A or (B -> (B or C))) and (D or (E -> (((F and G) -> F) and E)))), M:tm-530, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-38446
in-theory        38446
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-530 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-38446.        ((A or (B -> (B or C))) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-530, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-38447
in-theory        38447
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-38447.        ((A or (B -> (B or C))) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-530, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-38448
in-theory        38448
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-530 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-38448.        ((A or (B -> (B or C))) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-530, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-38449
in-theory        38449
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38449.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-530, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-38450
in-theory        38450
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38450.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-530, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-38451
in-theory        38451
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38451.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((F and G) -> F))), M:tm-530, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-38452
in-theory        38452
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-530 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38452.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((F and G) -> G))), M:tm-530, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-38453
in-theory        38453
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38453.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-530, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-38454
in-theory        38454
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-530 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38454.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (F or G)))), M:tm-530, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38455
in-theory        38455
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38455.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (G or F)))), M:tm-530, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-38456
in-theory        38456
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-38456.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-530, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-38457
in-theory        38457
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-530 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-38457.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-530, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-38458
in-theory        38458
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-38458.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-530, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-38459
in-theory        38459
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-38459.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-530, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-38460
in-theory        38460
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-38460.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-530, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-38461
in-theory        38461
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-530 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-38461.        ((A or (B -> (B or C))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-530, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-38462
in-theory        38462
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38462.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-530, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-38463
in-theory        38463
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-530 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-38463.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-530, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-38464
in-theory        38464
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-530 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-38464.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-530, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-38465
in-theory        38465
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-530 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-38465.        ((A or (B -> (B or C))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-530, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-38466
in-theory        38466
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-530 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-38466.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-530, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-38467
in-theory        38467
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-38467.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-530, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-38468
in-theory        38468
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-530 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-38468.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-530, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-38469
in-theory        38469
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-38469.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-530, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-38470
in-theory        38470
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-38470.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-530, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-38471
in-theory        38471
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-38471.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-530, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-38472
in-theory        38472
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-530 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-38472.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-530, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-38473
in-theory        38473
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-38473.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-530, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-38474
in-theory        38474
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-38474.        ((A or (B -> (B or C))) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-530, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-38475
in-theory        38475
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-530 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-38475.        ((A or (B -> (B or C))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-530, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-38476
in-theory        38476
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-530 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-38476.        ((A or (B -> (B or C))) and (D or (E -> (((F and G) -> G) and E)))), M:tm-530, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-38477
in-theory        38477
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-530 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-38477.        ((A or (B -> (B or C))) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-530, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-38478
in-theory        38478
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-38478.        ((A or (B -> (B or C))) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-530, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-38479
in-theory        38479
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-530 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-38479.        ((A or (B -> (B or C))) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-530, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-38480
in-theory        38480
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38480.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-530, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-38481
in-theory        38481
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38481.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-530, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-38482
in-theory        38482
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-530 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38482.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-530, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-38483
in-theory        38483
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-530 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38483.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-530, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-38484
in-theory        38484
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38484.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-530, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-38485
in-theory        38485
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-530 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38485.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-530, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38486
in-theory        38486
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38486.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-530, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-38487
in-theory        38487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-38487.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-530, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-38488
in-theory        38488
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-38488.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-530, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-38489
in-theory        38489
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-530 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-38489.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-530, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-38490
in-theory        38490
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-38490.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-530, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-38491
in-theory        38491
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-38491.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-530, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-38492
in-theory        38492
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-38492.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-530, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-38493
in-theory        38493
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-530 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38493.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-530, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-38494
in-theory        38494
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-530 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-38494.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-530, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-38495
in-theory        38495
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-530 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-38495.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-530, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-38496
in-theory        38496
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-530 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-38496.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-530, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-38497
in-theory        38497
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-530 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-38497.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-530, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-38498
in-theory        38498
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-530 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-38498.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-530, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-38499
in-theory        38499
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-530 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-38499.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-530, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-38500
in-theory        38500
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-530 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-38500.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-530, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-38501
in-theory        38501
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-530 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-38501.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-530, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-38502
in-theory        38502
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-530 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-38502.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-530, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-38503
in-theory        38503
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-530 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-38503.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-530, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-38504
in-theory        38504
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-530 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-38504.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-530, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-38505
in-theory        38505
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-530 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-38505.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-530, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-38506
in-theory        38506
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-530 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-38506.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-530, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-38507
in-theory        38507
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-530 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-38507.        ((A or (B -> (B or C))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-530, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-38508
in-theory        38508
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-530 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-38508.        ((A or (B -> (B or C))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-530, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-38509
in-theory        38509
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-530 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-38509.        ((A or (B -> (B or C))) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-530, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-38510
in-theory        38510
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-530 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-38510.        ((A or (B -> (B or C))) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-530, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-38511
in-theory        38511
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-530 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-38511.        ((A or (B -> (B or C))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-530, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-38512
in-theory        38512
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-530 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-38512.        ((A or (B -> (B or C))) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-530, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-38513
in-theory        38513
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-530 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-38513.        ((A or (B -> (B or C))) and (D -> (D and (E -> D)))), M:tm-530, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-38514
in-theory        38514
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-38514.        ((A or (B -> (B or C))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-530, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-38515
in-theory        38515
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-530 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-38515.        ((A or (B -> (B or C))) and ((D and E) -> ((D and E) and D))), M:tm-530, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-38516
in-theory        38516
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-530 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-38516.        ((A or (B -> (B or C))) and ((D and E) -> ((D and E) and E))), M:tm-530, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-38517
in-theory        38517
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-38517.        ((A or (B -> (B or C))) and (D -> (D and (E -> (D and E))))), M:tm-530, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-38518
in-theory        38518
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-530 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-38518.        ((A or (B -> (B or C))) and (D -> (D and (D or E)))), M:tm-530, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-38519
in-theory        38519
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-530 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-38519.        ((A or (B -> (B or C))) and (D -> (D and (E or D)))), M:tm-530, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-38520
in-theory        38520
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-530 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-38520.        ((A or (B -> (B or C))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-530, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-38521
in-theory        38521
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-38521.        ((A or (B -> (B or C))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-530, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-38522
in-theory        38522
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-530 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-38522.        ((A or (B -> (B or C))) and ((not (not D)) -> ((not (not D)) and D))), M:tm-530, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-38523
in-theory        38523
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-38523.        ((A or (B -> (B or C))) and (D -> (D and (E -> (F -> E))))), M:tm-530, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-38524
in-theory        38524
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-530 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-38524.        ((A or (B -> (B or C))) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-530, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-38525
in-theory        38525
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-530 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-38525.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-530, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-38526
in-theory        38526
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-530 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-38526.        ((A or (B -> (B or C))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-530, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-38527
in-theory        38527
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-530 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-38527.        ((A or (B -> (B or C))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-530, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-38528
in-theory        38528
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-530 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-38528.        ((A or (B -> (B or C))) and (D -> (D and ((E and F) -> E)))), M:tm-530, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-38529
in-theory        38529
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-530 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-38529.        ((A or (B -> (B or C))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-530, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-38530
in-theory        38530
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-530 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-38530.        ((A or (B -> (B or C))) and (D -> (D and ((E and F) -> F)))), M:tm-530, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-38531
in-theory        38531
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-530 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-38531.        ((A or (B -> (B or C))) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-530, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-38532
in-theory        38532
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-530 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-38532.        ((A or (B -> (B or C))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-530, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-38533
in-theory        38533
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-530 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-38533.        ((A or (B -> (B or C))) and (D -> (D and (((E and F) -> E) and D)))), M:tm-530, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-38534
in-theory        38534
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-530 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-38534.        ((A or (B -> (B or C))) and (D -> (D and (((E and F) -> F) and D)))), M:tm-530, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-38535
in-theory        38535
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-530 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-38535.        ((A or (B -> (B or C))) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-530, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-38536
in-theory        38536
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-38536.        ((A or (B -> (B or C))) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-530, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-38537
in-theory        38537
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-530 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-38537.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-530, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-38538
in-theory        38538
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-38538.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-530, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-38539
in-theory        38539
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-38539.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-530, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-38540
in-theory        38540
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-530 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-38540.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-530, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-38541
in-theory        38541
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-38541.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-530, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-38542
in-theory        38542
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-530 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-38542.        ((A or (B -> (B or C))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-530, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-38543
in-theory        38543
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-530 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-38543.        ((A or (B -> (B or C))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-530, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-38544
in-theory        38544
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-530 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-38544.        ((A or (B -> (B or C))) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-530, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-38545
in-theory        38545
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-530 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-38545.        ((A or (B -> (B or C))) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-530, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-38546
in-theory        38546
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-38546.        ((A or (B -> (B or C))) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-530, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-38547
in-theory        38547
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-530 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-38547.        ((A or (B -> (B or C))) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-530, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-38548
in-theory        38548
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-530 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-38548.        ((A or (B -> (B or C))) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-530, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-38549
in-theory        38549
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-530 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-38549.        ((A or (B -> (B or C))) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-530, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-38550
in-theory        38550
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-530 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38550.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-530, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-38551
in-theory        38551
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-530 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38551.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-530, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-38552
in-theory        38552
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-530 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38552.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-530, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-38553
in-theory        38553
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-530 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38553.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-530, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-38554
in-theory        38554
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-530 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38554.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-530, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-38555
in-theory        38555
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-530 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-38555.        ((A or (B -> (B or C))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-530, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-38556
in-theory        38556
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-530 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-38556.        ((A or (B -> (B or C))) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-530, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-38557
in-theory        38557
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-530 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-38557.        ((A or (B -> (B or C))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-530, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-38558
in-theory        38558
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-38558.        ((A or (B -> (B or C))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-530, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-38559
in-theory        38559
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-530 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-38559.        ((A or (B -> (B or C))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-530, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-38560
in-theory        38560
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-530 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38560.        ((A or (B -> (B or C))) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-530, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-38561
in-theory        38561
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-530 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38561.        ((A or (B -> (B or C))) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-530, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-38562
in-theory        38562
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38562.        ((A or (B -> (B or C))) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-530, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-38563
in-theory        38563
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-530 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-38563.        ((A or (B -> (B or C))) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-530, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-38564
in-theory        38564
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-530 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38564.        ((A or (B -> (B or C))) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-530, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-38565
in-theory        38565
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-530 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-38565.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-530, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-38566
in-theory        38566
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-38566.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-530, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-38567
in-theory        38567
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-38567.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-530, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-38568
in-theory        38568
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-38568.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-530, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-38569
in-theory        38569
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-38569.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-530, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-38570
in-theory        38570
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-530 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-38570.        ((A or (B -> (B or C))) and (D or ((E -> (F -> E)) or G))), M:tm-530, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-38571
in-theory        38571
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-38571.        ((A or (B -> (B or C))) and (((D -> (E -> D)) or F) or G)), M:tm-530, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-38572
in-theory        38572
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-38572.        ((A or (B -> (B or C))) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-530, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-38573
in-theory        38573
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-530 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-38573.        ((A or (B -> (B or C))) and (D -> ((E -> (F -> E)) or G))), M:tm-530, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-38574
in-theory        38574
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-530 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-38574.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-530, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-38575
in-theory        38575
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-38575.        ((A or (B -> (B or C))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-530, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-38576
in-theory        38576
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-38576.        ((A or (B -> (B or C))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-530, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-38577
in-theory        38577
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-530 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-38577.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-530, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-38578
in-theory        38578
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-38578.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-530, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-38579
in-theory        38579
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-530 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-38579.        ((A or (B -> (B or C))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-530, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-38580
in-theory        38580
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-530 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-38580.        ((A or (B -> (B or C))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-530, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-38581
in-theory        38581
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-530 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-38581.        ((A or (B -> (B or C))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-530, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-38582
in-theory        38582
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-530 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-38582.        ((A or (B -> (B or C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-530, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-38583
in-theory        38583
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-530 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-38583.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-530, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-38584
in-theory        38584
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-38584.        ((A or (B -> (B or C))) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-530, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-38585
in-theory        38585
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-38585.        ((A or (B -> (B or C))) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-530, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-38586
in-theory        38586
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-38586.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-530, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-38587
in-theory        38587
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-38587.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-530, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-38588
in-theory        38588
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-530 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-38588.        ((A or (B -> (B or C))) and (D or (((E and F) -> E) or G))), M:tm-530, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-38589
in-theory        38589
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-38589.        ((A or (B -> (B or C))) and ((((D and E) -> D) or F) or G)), M:tm-530, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-38590
in-theory        38590
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-38590.        ((A or (B -> (B or C))) and (D -> ((((E and F) -> E) or G) and D))), M:tm-530, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-38591
in-theory        38591
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-530 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-38591.        ((A or (B -> (B or C))) and (D -> (((E and F) -> E) or G))), M:tm-530, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-38592
in-theory        38592
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-530 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-38592.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-530, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-38593
in-theory        38593
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-38593.        ((A or (B -> (B or C))) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-530, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-38594
in-theory        38594
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-38594.        ((A or (B -> (B or C))) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-530, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-38595
in-theory        38595
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-38595.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-530, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-38596
in-theory        38596
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-38596.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-530, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-38597
in-theory        38597
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-530 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-38597.        ((A or (B -> (B or C))) and (D or (((E and F) -> F) or G))), M:tm-530, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-38598
in-theory        38598
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-38598.        ((A or (B -> (B or C))) and ((((D and E) -> E) or F) or G)), M:tm-530, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-38599
in-theory        38599
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-38599.        ((A or (B -> (B or C))) and (D -> ((((E and F) -> F) or G) and D))), M:tm-530, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-38600
in-theory        38600
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-530 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-38600.        ((A or (B -> (B or C))) and (D -> (((E and F) -> F) or G))), M:tm-530, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-38601
in-theory        38601
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-530 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-38601.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-530, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-38602
in-theory        38602
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-530 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-38602.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-530, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-38603
in-theory        38603
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-530 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-38603.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-530, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-38604
in-theory        38604
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-530 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-38604.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-530, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-38605
in-theory        38605
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-530 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-38605.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-530, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-38606
in-theory        38606
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-530 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-38606.        ((A or (B -> (B or C))) and (D or ((E -> (F -> (E and F))) or G))), M:tm-530, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-38607
in-theory        38607
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-530 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-38607.        ((A or (B -> (B or C))) and (((D -> (E -> (D and E))) or F) or G)), M:tm-530, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-38608
in-theory        38608
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-38608.        ((A or (B -> (B or C))) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-530, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-38609
in-theory        38609
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-530 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-38609.        ((A or (B -> (B or C))) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-530, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-38610
in-theory        38610
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-530 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-38610.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-530, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-38611
in-theory        38611
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-38611.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-530, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-38612
in-theory        38612
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-38612.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-530, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-38613
in-theory        38613
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-38613.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-530, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-38614
in-theory        38614
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-38614.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-530, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-38615
in-theory        38615
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-530 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-38615.        ((A or (B -> (B or C))) and (D or ((E -> (E or F)) or G))), M:tm-530, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-38616
in-theory        38616
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-38616.        ((A or (B -> (B or C))) and (((D -> (D or E)) or F) or G)), M:tm-530, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-38617
in-theory        38617
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-38617.        ((A or (B -> (B or C))) and (D -> (((E -> (E or F)) or G) and D))), M:tm-530, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-38618
in-theory        38618
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-530 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-38618.        ((A or (B -> (B or C))) and (D -> ((E -> (E or F)) or G))), M:tm-530, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-38619
in-theory        38619
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38619.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-530, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-38620
in-theory        38620
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38620.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-530, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-38621
in-theory        38621
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38621.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-530, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-38622
in-theory        38622
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-530 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38622.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-530, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-38623
in-theory        38623
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38623.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-530, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-38624
in-theory        38624
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-530 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38624.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-530, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38625
in-theory        38625
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38625.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-530, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-38626
in-theory        38626
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-38626.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-530, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-38627
in-theory        38627
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-530 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-38627.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-530, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-38628
in-theory        38628
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-38628.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-530, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-38629
in-theory        38629
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-38629.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-530, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-38630
in-theory        38630
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-38630.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-530, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-38631
in-theory        38631
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-530 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-38631.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-530, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-38632
in-theory        38632
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38632.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-530, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-38633
in-theory        38633
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-530 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-38633.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-530, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-38634
in-theory        38634
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-530 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-38634.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-530, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-38635
in-theory        38635
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-530 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-38635.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-530, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-38636
in-theory        38636
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-530 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-38636.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-530, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-38637
in-theory        38637
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-38637.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-530, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-38638
in-theory        38638
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-530 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-38638.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-530, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-38639
in-theory        38639
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-38639.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-530, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-38640
in-theory        38640
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-38640.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-530, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-38641
in-theory        38641
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-530 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-38641.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-530, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-38642
in-theory        38642
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-38642.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-530, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-38643
in-theory        38643
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-530 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38643.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-530, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-38644
in-theory        38644
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-38644.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-530, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-38645
in-theory        38645
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-38645.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-530, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-38646
in-theory        38646
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-38646.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-530, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-38647
in-theory        38647
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-38647.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-530, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-38648
in-theory        38648
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-530 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-38648.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-530, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-38649
in-theory        38649
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-38649.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-530, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-38650
in-theory        38650
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-38650.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-530, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-38651
in-theory        38651
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-530 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-38651.        ((A or (B -> (B or C))) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-530, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-38652
in-theory        38652
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-530 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-38652.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-530, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-38653
in-theory        38653
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-38653.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-530, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-38654
in-theory        38654
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-38654.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-530, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-38655
in-theory        38655
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-530 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-38655.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-530, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-38656
in-theory        38656
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-38656.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-530, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-38657
in-theory        38657
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-38657.        ((A or (B -> (B or C))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-530, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-38658
in-theory        38658
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-530 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-38658.        ((A or (B -> (B or C))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-530, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-38659
in-theory        38659
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-530 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-38659.        ((A or (B -> (B or C))) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-530, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-38660
in-theory        38660
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-530 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-38660.        ((A or (B -> (B or C))) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-530, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-38661
in-theory        38661
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-38661.        ((A or (B -> (B or C))) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-530, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-38662
in-theory        38662
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-530 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-38662.        ((A or (B -> (B or C))) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-530, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-38663
in-theory        38663
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-38663.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-530, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38664
in-theory        38664
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-38664.        ((A or (B -> (B or C))) and (D -> (D and (E -> (E or F))))), M:tm-530, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-38665
in-theory        38665
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-38665.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-530, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38666
in-theory        38666
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-38666.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-530, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38667
in-theory        38667
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-38667.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-530, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38668
in-theory        38668
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-38668.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-530, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38669
in-theory        38669
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-38669.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-530, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38670
in-theory        38670
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-530 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-38670.        ((A or (B -> (B or C))) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-530, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-38671
in-theory        38671
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-530 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-38671.        ((A or (B -> (B or C))) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-530, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-38672
in-theory        38672
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-38672.        ((A or (B -> (B or C))) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-530, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-38673
in-theory        38673
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-38673.        ((A or (B -> (B or C))) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-530, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-38674
in-theory        38674
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-530 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-38674.        ((A or (B -> (B or C))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-530, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-38675
in-theory        38675
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-38675.        ((A or (B -> (B or C))) and (D or (E -> (F -> (F or G))))), M:tm-530, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38676
in-theory        38676
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-38676.        ((A or (B -> (B or C))) and ((D -> (E -> (E or F))) or G)), M:tm-530, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38677
in-theory        38677
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-38677.        ((A or (B -> (B or C))) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-530, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38678
in-theory        38678
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-530 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-38678.        ((A or (B -> (B or C))) and ((D -> E) -> (D -> (E or F)))), M:tm-530, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-38679
in-theory        38679
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-38679.        ((A or (B -> (B or C))) and (D -> (E -> (F -> (F or G))))), M:tm-530, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38680
in-theory        38680
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-38680.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-530, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-38681
in-theory        38681
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-38681.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-530, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-38682
in-theory        38682
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-38682.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-530, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-38683
in-theory        38683
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-38683.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-530, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-38684
in-theory        38684
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-38684.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-530, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-38685
in-theory        38685
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-38685.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-530, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-38686
in-theory        38686
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-38686.        ((A or (B -> (B or C))) and (D or (E or (F -> (G -> F))))), M:tm-530, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-38687
in-theory        38687
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-38687.        ((A or (B -> (B or C))) and ((D or (E -> (F -> E))) or G)), M:tm-530, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-38688
in-theory        38688
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-38688.        ((A or (B -> (B or C))) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-530, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-38689
in-theory        38689
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-38689.        ((A or (B -> (B or C))) and (D -> (E or (F -> (G -> F))))), M:tm-530, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-38690
in-theory        38690
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38690.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-530, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-38691
in-theory        38691
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-530 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38691.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-530, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-38692
in-theory        38692
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38692.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-530, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-38693
in-theory        38693
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38693.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-530, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-38694
in-theory        38694
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-530 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38694.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-530, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-38695
in-theory        38695
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38695.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-530, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-38696
in-theory        38696
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-530 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38696.        ((A or (B -> (B or C))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-530, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-38697
in-theory        38697
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-530 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38697.        ((A or (B -> (B or C))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-530, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-38698
in-theory        38698
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-530 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38698.        ((A or (B -> (B or C))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-530, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-38699
in-theory        38699
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-530 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-38699.        ((A or (B -> (B or C))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-530, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-38700
in-theory        38700
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-530 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-38700.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-530, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-38701
in-theory        38701
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-530 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-38701.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-530, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-38702
in-theory        38702
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-530 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-38702.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-530, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-38703
in-theory        38703
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-530 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-38703.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-530, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-38704
in-theory        38704
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-530 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-38704.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-530, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-38705
in-theory        38705
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-530 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-38705.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-530, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-38706
in-theory        38706
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-530 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-38706.        ((A or (B -> (B or C))) and (D or (E or ((F and G) -> F)))), M:tm-530, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-38707
in-theory        38707
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-38707.        ((A or (B -> (B or C))) and ((D or ((E and F) -> E)) or G)), M:tm-530, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-38708
in-theory        38708
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-38708.        ((A or (B -> (B or C))) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-530, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-38709
in-theory        38709
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-530 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-38709.        ((A or (B -> (B or C))) and (D -> (E or ((F and G) -> F)))), M:tm-530, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-38710
in-theory        38710
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-530 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-38710.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-530, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-38711
in-theory        38711
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-530 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-38711.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-530, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-38712
in-theory        38712
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-530 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-38712.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-530, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-38713
in-theory        38713
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-530 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-38713.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-530, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-38714
in-theory        38714
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-530 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-38714.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-530, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-38715
in-theory        38715
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-530 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-38715.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-530, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-38716
in-theory        38716
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-530 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-38716.        ((A or (B -> (B or C))) and (D or (E or ((F and G) -> G)))), M:tm-530, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-38717
in-theory        38717
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-38717.        ((A or (B -> (B or C))) and ((D or ((E and F) -> F)) or G)), M:tm-530, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-38718
in-theory        38718
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-38718.        ((A or (B -> (B or C))) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-530, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-38719
in-theory        38719
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-530 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-38719.        ((A or (B -> (B or C))) and (D -> (E or ((F and G) -> G)))), M:tm-530, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-38720
in-theory        38720
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-530 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38720.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-530, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-38721
in-theory        38721
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-530 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38721.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-530, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-38722
in-theory        38722
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-530 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38722.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-530, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-38723
in-theory        38723
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-530 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38723.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-530, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-38724
in-theory        38724
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-530 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38724.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-530, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-38725
in-theory        38725
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-530 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38725.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-530, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-38726
in-theory        38726
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-530 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38726.        ((A or (B -> (B or C))) and (D or (E or (F -> (G -> (F and G)))))), M:tm-530, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-38727
in-theory        38727
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-530 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38727.        ((A or (B -> (B or C))) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-530, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-38728
in-theory        38728
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38728.        ((A or (B -> (B or C))) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-530, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-38729
in-theory        38729
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-530 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-38729.        ((A or (B -> (B or C))) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-530, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-38730
in-theory        38730
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38730.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-530, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38731
in-theory        38731
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38731.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-530, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38732
in-theory        38732
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38732.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-530, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38733
in-theory        38733
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38733.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-530, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38734
in-theory        38734
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38734.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-530, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-38735
in-theory        38735
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38735.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-530, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-38736
in-theory        38736
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38736.        ((A or (B -> (B or C))) and (D or (E or (F -> (F or G))))), M:tm-530, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38737
in-theory        38737
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38737.        ((A or (B -> (B or C))) and ((D or (E -> (E or F))) or G)), M:tm-530, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-38738
in-theory        38738
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38738.        ((A or (B -> (B or C))) and (D -> ((E or (F -> (F or G))) and D))), M:tm-530, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38739
in-theory        38739
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38739.        ((A or (B -> (C -> (B and C)))) and (D -> ((E or (F -> (F or G))) and D))), M:tm-520, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38740
in-theory        38740
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38740.        ((A or ((B and C) -> C)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-510, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38741
in-theory        38741
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38741.        ((A or ((B and C) -> B)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-500, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38742
in-theory        38742
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (G or H))) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38742.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (G or H))) and E))), M:tm-490, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38743
in-theory        38743
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38743.        ((A or (B -> (C -> B))) and (D -> ((E or (F -> (F or G))) and D))), M:tm-480, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38744
in-theory        38744
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (C or D))) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38744.        (A -> (((B or (C -> (C or D))) and A) or E)), M:tm-470, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-38745
in-theory        38745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38745.        ((A -> (B -> (B or C))) and (D -> ((E or (F -> (F or G))) and D))), M:tm-469, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38746
in-theory        38746
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D or (E -> (E or F))) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-530 ((Am (-> A (or A B))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38746.        ((A or (B -> (B or C))) -> ((D or (E -> (E or F))) and (B -> (B or C)))), M:tm-466, m:tm-530, u:((Am (-> A (or A B))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (or A B)))))
================================================================
tm-name          tm-38747
in-theory        38747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38747.        ((A -> ((B or (C -> (C or D))) and A)) and (E -> (E or F))), M:tm-456, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38748
in-theory        38748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38748.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-453, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38749
in-theory        38749
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D or (E -> (E or F))) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-530 ((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38749.        ((A or ((B -> (B or C)) and A)) -> ((D or (E -> (E or F))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-530, u:((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-38750
in-theory        38750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and ((E -> (E or F)) and (A -> ((B or (C -> (C or D))) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38750.        ((A -> ((B or (C -> (C or D))) and A)) and ((E -> (E or F)) and (A -> ((B or (C -> (C or D))) and A)))), M:tm-443, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38751
in-theory        38751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38751.        (((A -> (A or B)) or C) and (D -> ((E or (F -> (F or G))) and D))), M:tm-409, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38752
in-theory        38752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38752.        (((A -> (B -> (A and B))) or C) and (D -> ((E or (F -> (F or G))) and D))), M:tm-400, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38753
in-theory        38753
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38753.        ((((A and B) -> B) or C) and (D -> ((E or (F -> (F or G))) and D))), M:tm-391, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38754
in-theory        38754
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38754.        ((((A and B) -> A) or C) and (D -> ((E or (F -> (F or G))) and D))), M:tm-382, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38755
in-theory        38755
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or (G -> (G or H))) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38755.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or (G -> (G or H))) and E))), M:tm-373, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38756
in-theory        38756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38756.        (((A -> (B -> A)) or C) and (D -> ((E or (F -> (F or G))) and D))), M:tm-364, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38757
in-theory        38757
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C or (D -> (D or E))) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38757.        (A -> (B -> (((C or (D -> (D or E))) and A) and B))), M:tm-355, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-38758
in-theory        38758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38758.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E or (F -> (F or G))) and D))), M:tm-354, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38759
in-theory        38759
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D or (E -> (E or F))) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-530 ((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38759.        ((A or (B -> (C -> (B and C)))) -> ((D or (E -> (E or F))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-530, u:((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-38760
in-theory        38760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38760.        ((A -> ((B or (C -> (C or D))) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38761
in-theory        38761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D or (E -> (E or F))) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38761.        (((A -> B) -> (A -> (A and B))) and (C -> ((D or (E -> (E or F))) and C))), M:tm-338, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38762
in-theory        38762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C or (D -> (D or E))) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-530 ((Am (-> A (and A B))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38762.        (((A -> B) or (A -> (A and B))) -> ((C or (D -> (D or E))) and (A -> (A and B)))), M:tm-335, m:tm-530, u:((Am (-> A (and A B))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (and A B)))))
================================================================
tm-name          tm-38763
in-theory        38763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and (A -> (A and ((B or (C -> (C or D))) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38763.        ((A -> ((B or (C -> (C or D))) and A)) and (A -> (A and ((B or (C -> (C or D))) and A)))), M:tm-328, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-38764
in-theory        38764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B or (C -> (C or D))) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38764.        ((A -> ((B or (C -> (C or D))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B or (C -> (C or D))) and A)))), M:tm-327, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38765
in-theory        38765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and (((E and F) -> F) and (A -> ((B or (C -> (C or D))) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38765.        ((A -> ((B or (C -> (C or D))) and A)) and (((E and F) -> F) and (A -> ((B or (C -> (C or D))) and A)))), M:tm-326, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38766
in-theory        38766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and (((E and F) -> E) and (A -> ((B or (C -> (C or D))) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38766.        ((A -> ((B or (C -> (C or D))) and A)) and (((E and F) -> E) and (A -> ((B or (C -> (C or D))) and A)))), M:tm-325, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38767
in-theory        38767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B or (C -> (C or D))) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38767.        ((A -> ((B or (C -> (C or D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B or (C -> (C or D))) and A)))), M:tm-324, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38768
in-theory        38768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and ((E -> (F -> E)) and (A -> ((B or (C -> (C or D))) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38768.        ((A -> ((B or (C -> (C or D))) and A)) and ((E -> (F -> E)) and (A -> ((B or (C -> (C or D))) and A)))), M:tm-323, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38769
in-theory        38769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38769.        ((A -> ((B or (C -> (C or D))) and A)) and ((E and F) -> F)), M:tm-322, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38770
in-theory        38770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38770.        ((A -> ((B or (C -> (C or D))) and A)) and ((E and F) -> E)), M:tm-320, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38771
in-theory        38771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38771.        ((A -> ((B or (C -> (C or D))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38772
in-theory        38772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38772.        ((A -> ((B or (C -> (C or D))) and A)) and (A -> A)), M:tm-316, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-38773
in-theory        38773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38773.        ((A -> ((B or (C -> (C or D))) and A)) and (E -> (F -> E))), M:tm-315, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38774
in-theory        38774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and ((A -> (not ((B or (C -> (C or D))) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38774.        ((A -> ((B or (C -> (C or D))) and A)) and ((A -> (not ((B or (C -> (C or D))) and A))) -> (not A))), M:tm-313, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-38775
in-theory        38775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and ((((B or (C -> (C or D))) and A) -> E) -> ((A or ((B or (C -> (C or D))) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38775.        ((A -> ((B or (C -> (C or D))) and A)) and ((((B or (C -> (C or D))) and A) -> E) -> ((A or ((B or (C -> (C or D))) and A)) -> E))), M:tm-312, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-38776
in-theory        38776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and (E or (A -> ((B or (C -> (C or D))) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38776.        ((A -> ((B or (C -> (C or D))) and A)) and (E or (A -> ((B or (C -> (C or D))) and A)))), M:tm-311, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38777
in-theory        38777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and ((A -> ((B or (C -> (C or D))) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38777.        ((A -> ((B or (C -> (C or D))) and A)) and ((A -> ((B or (C -> (C or D))) and A)) or E)), M:tm-310, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38778
in-theory        38778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and (E -> ((A -> ((B or (C -> (C or D))) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38778.        ((A -> ((B or (C -> (C or D))) and A)) and (E -> ((A -> ((B or (C -> (C or D))) and A)) and E))), M:tm-309, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38779
in-theory        38779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and (E -> (A -> ((B or (C -> (C or D))) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38779.        ((A -> ((B or (C -> (C or D))) and A)) and (E -> (A -> ((B or (C -> (C or D))) and A)))), M:tm-305, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38780
in-theory        38780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38780.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-303, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38781
in-theory        38781
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D or (E -> (E or F))) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-530 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38781.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D or (E -> (E or F))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-530, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-38782
in-theory        38782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38782.        ((A -> (((B and C) -> C) and A)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-270, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38783
in-theory        38783
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D or (E -> (E or F))) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-530 ((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38783.        ((A or (((B and C) -> C) and A)) -> ((D or (E -> (E or F))) and (((B and C) -> C) and A))), M:tm-267, m:tm-530, u:((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-38784
in-theory        38784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38784.        ((A -> (((B and C) -> B) and A)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-239, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38785
in-theory        38785
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D or (E -> (E or F))) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-530 ((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38785.        ((A or (((B and C) -> B) and A)) -> ((D or (E -> (E or F))) and (((B and C) -> B) and A))), M:tm-236, m:tm-530, u:((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-38786
in-theory        38786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or (G -> (G or H))) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38786.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or (G -> (G or H))) and E))), M:tm-210, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38787
in-theory        38787
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or (F -> (F or G))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-530 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (or Cm Dm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-7 tm-6)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38787.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or (F -> (F or G))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-530, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (or Cm Dm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-38788
in-theory        38788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38788.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-183, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38789
in-theory        38789
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D or (E -> (E or F))) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-530 ((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38789.        ((A or ((B -> (C -> B)) and A)) -> ((D or (E -> (E or F))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-530, u:((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-38790
in-theory        38790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38790.        ((A -> ((B and C) -> C)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-157, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38791
in-theory        38791
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D or (E -> (E or F))) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-530 ((Am (-> (and A B) B)) (C (and (or Bm (-> Cm (or Cm Dm))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38791.        ((A or ((B and C) -> C)) -> ((D or (E -> (E or F))) and ((B and C) -> C))), M:tm-154, m:tm-530, u:((Am (-> (and A B) B)) (C (and (or Bm (-> Cm (or Cm Dm))) (-> (and A B) B))))
================================================================
tm-name          tm-38792
in-theory        38792
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38792.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-147, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38793
in-theory        38793
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or (E -> (E or F))) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-530 ((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-7 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38793.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or (E -> (E or F))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-530, u:((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-38794
in-theory        38794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38794.        ((A -> ((B and C) -> B)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-134, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38795
in-theory        38795
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D or (E -> (E or F))) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-530 ((Am (-> (and A B) A)) (C (and (or Bm (-> Cm (or Cm Dm))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38795.        ((A or ((B and C) -> B)) -> ((D or (E -> (E or F))) and ((B and C) -> B))), M:tm-131, m:tm-530, u:((Am (-> (and A B) A)) (C (and (or Bm (-> Cm (or Cm Dm))) (-> (and A B) A))))
================================================================
tm-name          tm-38796
in-theory        38796
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38796.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-125, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38797
in-theory        38797
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or (E -> (E or F))) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-530 ((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-7 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38797.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or (E -> (E or F))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-530, u:((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-38798
in-theory        38798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (G or H))) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38798.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (G or H))) and E))), M:tm-113, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38799
in-theory        38799
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or (F -> (F or G))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-530 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38799.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or (F -> (F or G))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-530, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-38800
in-theory        38800
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38800.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or (F -> (F or G))) and D))), M:tm-105, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38801
in-theory        38801
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or (E -> (E or F))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-530 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-6)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38801.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or (E -> (E or F))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-530, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-38802
in-theory        38802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D or (E -> (E or F))) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38802.        (((A -> B) -> (A -> A)) and (C -> ((D or (E -> (E or F))) and C))), M:tm-95, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38803
in-theory        38803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C or (D -> (D or E))) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-530 ((Am (-> A A)) (B (and (or Bm (-> Cm (or Cm Dm))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38803.        (((A -> B) or (A -> A)) -> ((C or (D -> (D or E))) and (A -> A))), M:tm-92, m:tm-530, u:((Am (-> A A)) (B (and (or Bm (-> Cm (or Cm Dm))) (-> A A))))
================================================================
tm-name          tm-38804
in-theory        38804
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C or (D -> (D or E))) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7 tm-6)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38804.        (A -> (B -> ((C or (D -> (D or E))) and A))), M:tm-84, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-38805
in-theory        38805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38805.        ((A -> (B -> (C -> B))) and (D -> ((E or (F -> (F or G))) and D))), M:tm-83, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38806
in-theory        38806
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D or (E -> (E or F))) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-530 ((Am (-> A (-> B A))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38806.        ((A or (B -> (C -> B))) -> ((D or (E -> (E or F))) and (B -> (C -> B)))), M:tm-80, m:tm-530, u:((Am (-> A (-> B A))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (-> B A)))))
================================================================
tm-name          tm-38807
in-theory        38807
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C or (D -> (D or E))) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38807.        (((not (not A)) -> A) and (B -> ((C or (D -> (D or E))) and B))), M:tm-76, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38808
in-theory        38808
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B or (C -> (C or D))) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-7 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38808.        (((not (not A)) or A) -> ((B or (C -> (C or D))) and A)), M:tm-73, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-38809
in-theory        38809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or (E -> (E or F))) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38809.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or (E -> (E or F))) and C))), M:tm-69, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38810
in-theory        38810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or (D -> (D or E))) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-530 ((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-7 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38810.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or (D -> (D or E))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-530, u:((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-38811
in-theory        38811
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38811.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or (F -> (F or G))) and D))), M:tm-54, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38812
in-theory        38812
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or (E -> (E or F))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-530 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38812.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or (E -> (E or F))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-530, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-38813
in-theory        38813
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C or (D -> (D or E))) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-530 ((Am (or A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38813.        ((A or (B or A)) -> ((C or (D -> (D or E))) and (B or A))), M:tm-50, m:tm-530, u:((Am (or A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (or A B))))
================================================================
tm-name          tm-38814
in-theory        38814
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C or (D -> (D or E))) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-530 ((Am (or A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38814.        ((A or (A or B)) -> ((C or (D -> (D or E))) and (A or B))), M:tm-49, m:tm-530, u:((Am (or A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (or A B))))
================================================================
tm-name          tm-38815
in-theory        38815
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C or (D -> (D or E))) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-530 ((Am (-> A (and B A))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38815.        ((A or (B -> (A and B))) -> ((C or (D -> (D or E))) and (B -> (A and B)))), M:tm-48, m:tm-530, u:((Am (-> A (and B A))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (and B A)))))
================================================================
tm-name          tm-38816
in-theory        38816
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C or (D -> (D or E))) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-7 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38816.        (((A and B) or B) -> ((C or (D -> (D or E))) and B)), M:tm-47, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-38817
in-theory        38817
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C or (D -> (D or E))) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-7 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38817.        (((A and B) or A) -> ((C or (D -> (D or E))) and A)), M:tm-46, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-38818
in-theory        38818
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (E or F))) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-530 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-6)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38818.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (E or F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-530, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-38819
in-theory        38819
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C or (D -> (D or E))) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-530 ((Am (-> A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38819.        ((A or (B -> A)) -> ((C or (D -> (D or E))) and (B -> A))), M:tm-44, m:tm-530, u:((Am (-> A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A B))))
================================================================
tm-name          tm-38820
in-theory        38820
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D or (E -> (E or F))) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38820.        ((A -> (B or A)) and (C -> ((D or (E -> (E or F))) and C))), M:tm-42, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38821
in-theory        38821
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D or (E -> (E or F))) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38821.        ((A -> (A or B)) and (C -> ((D or (E -> (E or F))) and C))), M:tm-32, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38822
in-theory        38822
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B or (C -> (C or D))) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38822.        (A -> (A and ((B or (C -> (C or D))) and A))), M:tm-24, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-38823
in-theory        38823
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D or (E -> (E or F))) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38823.        ((A -> (B -> (A and B))) and (C -> ((D or (E -> (E or F))) and C))), M:tm-23, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38824
in-theory        38824
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D or (E -> (E or F))) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38824.        (((A and B) -> B) and (C -> ((D or (E -> (E or F))) and C))), M:tm-22, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38825
in-theory        38825
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D or (E -> (E or F))) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38825.        (((A and B) -> A) and (C -> ((D or (E -> (E or F))) and C))), M:tm-21, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38826
in-theory        38826
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38826.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or (F -> (F or G))) and D))), M:tm-20, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38827
in-theory        38827
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D or (E -> (E or F))) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38827.        ((A -> (B -> A)) and (C -> ((D or (E -> (E or F))) and C))), M:tm-19, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38828
in-theory        38828
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B or (C -> (C or D))) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-9 tm-5 tm-7 tm-6)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38828.        ((A -> (not ((B or (C -> (C or D))) and A))) -> (not A)), M:tm-9, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-38829
in-theory        38829
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (B or C))) and D) -> E) -> ((D or ((A or (B -> (B or C))) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38829.        ((((A or (B -> (B or C))) and D) -> E) -> ((D or ((A or (B -> (B or C))) and D)) -> E)), M:tm-8, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-38830
in-theory        38830
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C or (D -> (D or E))) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38830.        (A or (B -> ((C or (D -> (D or E))) and B))), M:tm-7, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38831
in-theory        38831
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38831.        ((A -> ((B or (C -> (C or D))) and A)) or E), M:tm-6, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38832
in-theory        38832
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C or (D -> (D or E))) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38832.        (A -> ((B -> ((C or (D -> (D or E))) and B)) and A)), M:tm-5, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38833
in-theory        38833
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C or (D -> (D or E))) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-1 tm-5 tm-7 tm-6)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38833.        (A -> (B -> ((C or (D -> (D or E))) and B))), M:tm-1, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-38834
in-theory        38834
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38834.        ((A or (B -> (B or C))) and (D -> (E or (F -> (F or G))))), M:tm-530, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38835
in-theory        38835
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38835.        ((A or (B -> (C -> (B and C)))) and (D -> (E or (F -> (F or G))))), M:tm-520, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38836
in-theory        38836
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38836.        ((A or ((B and C) -> C)) and (D -> (E or (F -> (F or G))))), M:tm-510, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38837
in-theory        38837
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38837.        ((A or ((B and C) -> B)) and (D -> (E or (F -> (F or G))))), M:tm-500, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38838
in-theory        38838
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38838.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (G or H))))), M:tm-490, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38839
in-theory        38839
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38839.        ((A or (B -> (C -> B))) and (D -> (E or (F -> (F or G))))), M:tm-480, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38840
in-theory        38840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38840.        ((A -> (B -> (B or C))) and (D -> (E or (F -> (F or G))))), M:tm-469, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38841
in-theory        38841
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-466 tm-531 ((Am (-> A (or A B))) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38841.        ((A or (B -> (B or C))) -> (D or (E -> (E or F)))), M:tm-466, m:tm-531, u:((Am (-> A (or A B))) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38842
in-theory        38842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38842.        ((A -> (B or (C -> (C or D)))) and (E -> (E or F))), M:tm-456, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38843
in-theory        38843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38843.        ((A -> ((B -> (B or C)) and A)) and (D -> (E or (F -> (F or G))))), M:tm-453, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38844
in-theory        38844
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-450 tm-531 ((Am (and (-> A (or A B)) C)) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38844.        ((A or ((B -> (B or C)) and A)) -> (D or (E -> (E or F)))), M:tm-450, m:tm-531, u:((Am (and (-> A (or A B)) C)) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38845
in-theory        38845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and ((E -> (E or F)) and (A -> (B or (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38845.        ((A -> (B or (C -> (C or D)))) and ((E -> (E or F)) and (A -> (B or (C -> (C or D)))))), M:tm-443, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38846
in-theory        38846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38846.        (((A -> (A or B)) or C) and (D -> (E or (F -> (F or G))))), M:tm-409, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38847
in-theory        38847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38847.        (((A -> (B -> (A and B))) or C) and (D -> (E or (F -> (F or G))))), M:tm-400, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38848
in-theory        38848
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38848.        ((((A and B) -> B) or C) and (D -> (E or (F -> (F or G))))), M:tm-391, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38849
in-theory        38849
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38849.        ((((A and B) -> A) or C) and (D -> (E or (F -> (F or G))))), M:tm-382, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38850
in-theory        38850
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38850.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or (G -> (G or H))))), M:tm-373, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38851
in-theory        38851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38851.        (((A -> (B -> A)) or C) and (D -> (E or (F -> (F or G))))), M:tm-364, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38852
in-theory        38852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38852.        ((A -> (B -> (C -> (B and C)))) and (D -> (E or (F -> (F or G))))), M:tm-354, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38853
in-theory        38853
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-351 tm-531 ((Am (-> A (-> B (and A B)))) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38853.        ((A or (B -> (C -> (B and C)))) -> (D or (E -> (E or F)))), M:tm-351, m:tm-531, u:((Am (-> A (-> B (and A B)))) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38854
in-theory        38854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38854.        ((A -> (B or (C -> (C or D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38855
in-theory        38855
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) -> D) -> ((A or (B -> (B or C))) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-531 ((Am (-> (or Bm (-> Cm (or Cm Dm))) B)) (A (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38855.        (((A or (B -> (B or C))) -> D) -> ((A or (B -> (B or C))) and D)), M:tm-339, m:tm-531, u:((Am (-> (or Bm (-> Cm (or Cm Dm))) B)) (A (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38856
in-theory        38856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D or (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38856.        (((A -> B) -> (A -> (A and B))) and (C -> (D or (E -> (E or F))))), M:tm-338, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38857
in-theory        38857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C or (D -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-335 tm-531 ((Am (-> A (and A B))) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38857.        (((A -> B) or (A -> (A and B))) -> (C or (D -> (D or E)))), M:tm-335, m:tm-531, u:((Am (-> A (and A B))) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38858
in-theory        38858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (A -> (A and (B or (C -> (C or D))))))
theorem-size     21
proof            (modus-ponens tm-328 tm-531 ((A Am) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38858.        ((A -> (B or (C -> (C or D)))) and (A -> (A and (B or (C -> (C or D)))))), M:tm-328, m:tm-531, u:((A Am) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38859
in-theory        38859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and ((E -> (F -> (E and F))) and (A -> (B or (C -> (C or D))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38859.        ((A -> (B or (C -> (C or D)))) and ((E -> (F -> (E and F))) and (A -> (B or (C -> (C or D)))))), M:tm-327, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38860
in-theory        38860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (((E and F) -> F) and (A -> (B or (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38860.        ((A -> (B or (C -> (C or D)))) and (((E and F) -> F) and (A -> (B or (C -> (C or D)))))), M:tm-326, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38861
in-theory        38861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (((E and F) -> E) and (A -> (B or (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38861.        ((A -> (B or (C -> (C or D)))) and (((E and F) -> E) and (A -> (B or (C -> (C or D)))))), M:tm-325, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38862
in-theory        38862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B or (C -> (C or D))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38862.        ((A -> (B or (C -> (C or D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B or (C -> (C or D)))))), M:tm-324, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38863
in-theory        38863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and ((E -> (F -> E)) and (A -> (B or (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38863.        ((A -> (B or (C -> (C or D)))) and ((E -> (F -> E)) and (A -> (B or (C -> (C or D)))))), M:tm-323, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38864
in-theory        38864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38864.        ((A -> (B or (C -> (C or D)))) and ((E and F) -> F)), M:tm-322, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38865
in-theory        38865
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or (C -> (C or D))) -> E)) -> (B or (C -> (C or D)))) and ((A and ((B or (C -> (C or D))) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-531 ((Am (and A (-> (or Bm (-> Cm (or Cm Dm))) C))) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38865.        (((A and ((B or (C -> (C or D))) -> E)) -> (B or (C -> (C or D)))) and ((A and ((B or (C -> (C or D))) -> E)) -> E)), M:tm-321, m:tm-531, u:((Am (and A (-> (or Bm (-> Cm (or Cm Dm))) C))) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38866
in-theory        38866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38866.        ((A -> (B or (C -> (C or D)))) and ((E and F) -> E)), M:tm-320, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38867
in-theory        38867
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (B or C))) -> D) and E) -> (A or (B -> (B or C)))) and ((((A or (B -> (B or C))) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-531 ((Am (and (-> (or Bm (-> Cm (or Cm Dm))) B) C)) (A (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38867.        (((((A or (B -> (B or C))) -> D) and E) -> (A or (B -> (B or C)))) and ((((A or (B -> (B or C))) -> D) and E) -> D)), M:tm-319, m:tm-531, u:((Am (and (-> (or Bm (-> Cm (or Cm Dm))) B) C)) (A (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38868
in-theory        38868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38868.        ((A -> (B or (C -> (C or D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38869
in-theory        38869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-531 ((A Am) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38869.        ((A -> (B or (C -> (C or D)))) and (A -> A)), M:tm-316, m:tm-531, u:((A Am) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38870
in-theory        38870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38870.        ((A -> (B or (C -> (C or D)))) and (E -> (F -> E))), M:tm-315, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38871
in-theory        38871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and ((A -> (not (B or (C -> (C or D))))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-531 ((A Am) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38871.        ((A -> (B or (C -> (C or D)))) and ((A -> (not (B or (C -> (C or D))))) -> (not A))), M:tm-313, m:tm-531, u:((A Am) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38872
in-theory        38872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (((B or (C -> (C or D))) -> E) -> ((A or (B or (C -> (C or D)))) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-531 ((A Am) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38872.        ((A -> (B or (C -> (C or D)))) and (((B or (C -> (C or D))) -> E) -> ((A or (B or (C -> (C or D)))) -> E))), M:tm-312, m:tm-531, u:((A Am) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38873
in-theory        38873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (E or (A -> (B or (C -> (C or D))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38873.        ((A -> (B or (C -> (C or D)))) and (E or (A -> (B or (C -> (C or D)))))), M:tm-311, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38874
in-theory        38874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and ((A -> (B or (C -> (C or D)))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38874.        ((A -> (B or (C -> (C or D)))) and ((A -> (B or (C -> (C or D)))) or E)), M:tm-310, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38875
in-theory        38875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (E -> ((A -> (B or (C -> (C or D)))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38875.        ((A -> (B or (C -> (C or D)))) and (E -> ((A -> (B or (C -> (C or D)))) and E))), M:tm-309, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38876
in-theory        38876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (E -> (A -> (B or (C -> (C or D))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38876.        ((A -> (B or (C -> (C or D)))) and (E -> (A -> (B or (C -> (C or D)))))), M:tm-305, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38877
in-theory        38877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38877.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or (F -> (F or G))))), M:tm-303, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38878
in-theory        38878
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D or (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-300 tm-531 ((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38878.        ((A or ((B -> (C -> (B and C))) and A)) -> (D or (E -> (E or F)))), M:tm-300, m:tm-531, u:((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38879
in-theory        38879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38879.        ((A -> (((B and C) -> C) and A)) and (D -> (E or (F -> (F or G))))), M:tm-270, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38880
in-theory        38880
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-267 tm-531 ((Am (and (-> (and A B) B) C)) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38880.        ((A or (((B and C) -> C) and A)) -> (D or (E -> (E or F)))), M:tm-267, m:tm-531, u:((Am (and (-> (and A B) B) C)) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38881
in-theory        38881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38881.        ((A -> (((B and C) -> B) and A)) and (D -> (E or (F -> (F or G))))), M:tm-239, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38882
in-theory        38882
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-236 tm-531 ((Am (and (-> (and A B) A) C)) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38882.        ((A or (((B and C) -> B) and A)) -> (D or (E -> (E or F)))), M:tm-236, m:tm-531, u:((Am (and (-> (and A B) A) C)) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38883
in-theory        38883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38883.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or (G -> (G or H))))), M:tm-210, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38884
in-theory        38884
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-207 tm-531 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38884.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or (F -> (F or G)))), M:tm-207, m:tm-531, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38885
in-theory        38885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38885.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E or (F -> (F or G))))), M:tm-183, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38886
in-theory        38886
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-180 tm-531 ((Am (and (-> A (-> B A)) C)) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38886.        ((A or ((B -> (C -> B)) and A)) -> (D or (E -> (E or F)))), M:tm-180, m:tm-531, u:((Am (and (-> A (-> B A)) C)) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38887
in-theory        38887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38887.        ((A -> ((B and C) -> C)) and (D -> (E or (F -> (F or G))))), M:tm-157, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38888
in-theory        38888
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-154 tm-531 ((Am (-> (and A B) B)) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38888.        ((A or ((B and C) -> C)) -> (D or (E -> (E or F)))), M:tm-154, m:tm-531, u:((Am (-> (and A B) B)) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38889
in-theory        38889
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38889.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or (F -> (F or G))))), M:tm-147, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38890
in-theory        38890
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-144 tm-531 ((Am (-> (and A (-> B C)) C)) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-7 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38890.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or (E -> (E or F)))), M:tm-144, m:tm-531, u:((Am (-> (and A (-> B C)) C)) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38891
in-theory        38891
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B or (C -> (C or D))) -> E)) -> (B or (C -> (C or D))))
theorem-size     19
proof            (modus-ponens tm-142 tm-531 ((Am (and A (-> (or Bm (-> Cm (or Cm Dm))) C))) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-4 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38891.        ((A and ((B or (C -> (C or D))) -> E)) -> (B or (C -> (C or D)))), M:tm-142, m:tm-531, u:((Am (and A (-> (or Bm (-> Cm (or Cm Dm))) C))) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38892
in-theory        38892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38892.        ((A -> ((B and C) -> B)) and (D -> (E or (F -> (F or G))))), M:tm-134, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38893
in-theory        38893
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-131 tm-531 ((Am (-> (and A B) A)) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38893.        ((A or ((B and C) -> B)) -> (D or (E -> (E or F)))), M:tm-131, m:tm-531, u:((Am (-> (and A B) A)) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38894
in-theory        38894
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38894.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or (F -> (F or G))))), M:tm-125, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38895
in-theory        38895
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-122 tm-531 ((Am (-> (and (-> A B) C) B)) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-7 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38895.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or (E -> (E or F)))), M:tm-122, m:tm-531, u:((Am (-> (and (-> A B) C) B)) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38896
in-theory        38896
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (B or C))) -> D) and E) -> (A or (B -> (B or C))))
theorem-size     19
proof            (modus-ponens tm-120 tm-531 ((Am (and (-> (or Bm (-> Cm (or Cm Dm))) B) C)) (A (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-3 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38896.        ((((A or (B -> (B or C))) -> D) and E) -> (A or (B -> (B or C)))), M:tm-120, m:tm-531, u:((Am (and (-> (or Bm (-> Cm (or Cm Dm))) B) C)) (A (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38897
in-theory        38897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38897.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (G or H))))), M:tm-113, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38898
in-theory        38898
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-110 tm-531 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-7 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38898.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or (F -> (F or G)))), M:tm-110, m:tm-531, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38899
in-theory        38899
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or (F -> (F or G)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38899.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or (F -> (F or G))))), M:tm-105, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38900
in-theory        38900
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or (E -> (E or F))))
theorem-size     27
proof            (modus-ponens tm-102 tm-531 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38900.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or (E -> (E or F)))), M:tm-102, m:tm-531, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38901
in-theory        38901
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) -> D) -> (A or (B -> (B or C))))
theorem-size     17
proof            (modus-ponens tm-96 tm-531 ((Am (-> (or Bm (-> Cm (or Cm Dm))) B)) (A (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38901.        (((A or (B -> (B or C))) -> D) -> (A or (B -> (B or C)))), M:tm-96, m:tm-531, u:((Am (-> (or Bm (-> Cm (or Cm Dm))) B)) (A (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38902
in-theory        38902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D or (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38902.        (((A -> B) -> (A -> A)) and (C -> (D or (E -> (E or F))))), M:tm-95, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38903
in-theory        38903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C or (D -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-92 tm-531 ((Am (-> A A)) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38903.        (((A -> B) or (A -> A)) -> (C or (D -> (D or E)))), M:tm-92, m:tm-531, u:((Am (-> A A)) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38904
in-theory        38904
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C or (D -> (D or E)))))
theorem-size     11
proof            (modus-ponens tm-84 tm-531 ((A Am) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-6)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38904.        (A -> (B -> (C or (D -> (D or E))))), M:tm-84, m:tm-531, u:((A Am) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38905
in-theory        38905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38905.        ((A -> (B -> (C -> B))) and (D -> (E or (F -> (F or G))))), M:tm-83, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38906
in-theory        38906
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-80 tm-531 ((Am (-> A (-> B A))) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38906.        ((A or (B -> (C -> B))) -> (D or (E -> (E or F)))), M:tm-80, m:tm-531, u:((Am (-> A (-> B A))) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38907
in-theory        38907
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A or (B -> (B or C))) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-531 ((Am (not (not (-> (or Bm (-> Cm (or Cm Dm))) B)))) (A (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-10 tm-1 tm-7 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38907.        ((not (not ((A or (B -> (B or C))) -> D))) -> D), M:tm-77, m:tm-531, u:((Am (not (not (-> (or Bm (-> Cm (or Cm Dm))) B)))) (A (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38908
in-theory        38908
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C or (D -> (D or E)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38908.        (((not (not A)) -> A) and (B -> (C or (D -> (D or E))))), M:tm-76, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38909
in-theory        38909
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B or (C -> (C or D))))
theorem-size     13
proof            (modus-ponens tm-73 tm-531 ((A Am) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-10 tm-1 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38909.        (((not (not A)) or A) -> (B or (C -> (C or D)))), M:tm-73, m:tm-531, u:((A Am) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38910
in-theory        38910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or (E -> (E or F)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38910.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or (E -> (E or F))))), M:tm-69, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38911
in-theory        38911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or (D -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-66 tm-531 ((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-9 tm-1 tm-7 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38911.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or (D -> (D or E)))), M:tm-66, m:tm-531, u:((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38912
in-theory        38912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38912.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or (F -> (F or G))))), M:tm-54, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38913
in-theory        38913
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-51 tm-531 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38913.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> (E or F)))), M:tm-51, m:tm-531, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38914
in-theory        38914
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-50 tm-531 ((Am (or A B)) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38914.        ((A or (B or A)) -> (C or (D -> (D or E)))), M:tm-50, m:tm-531, u:((Am (or A B)) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38915
in-theory        38915
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-49 tm-531 ((Am (or A B)) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38915.        ((A or (A or B)) -> (C or (D -> (D or E)))), M:tm-49, m:tm-531, u:((Am (or A B)) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38916
in-theory        38916
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (D -> (D or E))))
theorem-size     15
proof            (modus-ponens tm-48 tm-531 ((Am (-> A (and B A))) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38916.        ((A or (B -> (A and B))) -> (C or (D -> (D or E)))), M:tm-48, m:tm-531, u:((Am (-> A (and B A))) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38917
in-theory        38917
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-47 tm-531 ((A Am) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38917.        (((A and B) or B) -> (C or (D -> (D or E)))), M:tm-47, m:tm-531, u:((A Am) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38918
in-theory        38918
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-46 tm-531 ((A Am) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38918.        (((A and B) or A) -> (C or (D -> (D or E)))), M:tm-46, m:tm-531, u:((A Am) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38919
in-theory        38919
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-45 tm-531 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38919.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (E or F)))), M:tm-45, m:tm-531, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38920
in-theory        38920
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-44 tm-531 ((Am (-> A B)) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38920.        ((A or (B -> A)) -> (C or (D -> (D or E)))), M:tm-44, m:tm-531, u:((Am (-> A B)) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38921
in-theory        38921
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38921.        ((A -> (B or A)) and (C -> (D or (E -> (E or F))))), M:tm-42, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38922
in-theory        38922
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38922.        ((A -> (A or B)) and (C -> (D or (E -> (E or F))))), M:tm-32, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38923
in-theory        38923
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B or (C -> (C or D)))))
theorem-size     11
proof            (modus-ponens tm-24 tm-531 ((A Am) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38923.        (A -> (A and (B or (C -> (C or D))))), M:tm-24, m:tm-531, u:((A Am) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38924
in-theory        38924
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D or (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38924.        ((A -> (B -> (A and B))) and (C -> (D or (E -> (E or F))))), M:tm-23, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38925
in-theory        38925
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38925.        (((A and B) -> B) and (C -> (D or (E -> (E or F))))), M:tm-22, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38926
in-theory        38926
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38926.        (((A and B) -> A) and (C -> (D or (E -> (E or F))))), M:tm-21, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38927
in-theory        38927
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38927.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or (F -> (F or G))))), M:tm-20, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38928
in-theory        38928
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38928.        ((A -> (B -> A)) and (C -> (D or (E -> (E or F))))), M:tm-19, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38929
in-theory        38929
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B or (C -> (C or D))) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-531 ((Am (and A (-> (or Bm (-> Cm (or Cm Dm))) C))) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-4 tm-1 tm-7 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38929.        ((A and ((B or (C -> (C or D))) -> E)) -> E), M:tm-17, m:tm-531, u:((Am (and A (-> (or Bm (-> Cm (or Cm Dm))) C))) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38930
in-theory        38930
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (B or C))) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-531 ((Am (and (-> (or Bm (-> Cm (or Cm Dm))) B) C)) (A (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-3 tm-1 tm-7 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38930.        ((((A or (B -> (B or C))) -> D) and E) -> D), M:tm-15, m:tm-531, u:((Am (and (-> (or Bm (-> Cm (or Cm Dm))) B) C)) (A (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38931
in-theory        38931
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B or (C -> (C or D))))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-531 ((A Am) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-9 tm-1 tm-7 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38931.        ((A -> (not (B or (C -> (C or D))))) -> (not A)), M:tm-9, m:tm-531, u:((A Am) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38932
in-theory        38932
times-derived    2
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) -> D) -> ((E or (A or (B -> (B or C)))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-531 ((A Am) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38932.        (((A or (B -> (B or C))) -> D) -> ((E or (A or (B -> (B or C)))) -> D)), M:tm-8, m:tm-531, u:((A Am) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-38933
in-theory        38933
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C or (D -> (D or E)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-7 tm-1 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38933.        (A or (B -> (C or (D -> (D or E))))), M:tm-7, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38934
in-theory        38934
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-6 tm-1 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38934.        ((A -> (B or (C -> (C or D)))) or E), M:tm-6, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38935
in-theory        38935
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C or (D -> (D or E)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-38935.        (A -> ((B -> (C or (D -> (D or E)))) and A)), M:tm-5, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-38936
in-theory        38936
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38936.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-530, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38937
in-theory        38937
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38937.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-520, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38938
in-theory        38938
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38938.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-510, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38939
in-theory        38939
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38939.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-500, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38940
in-theory        38940
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38940.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (I or H))))), M:tm-490, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38941
in-theory        38941
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38941.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-480, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38942
in-theory        38942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38942.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-469, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38943
in-theory        38943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38943.        (((A -> (A or B)) and (C or (D -> (E or D)))) and (F -> (F or G))), M:tm-456, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38944
in-theory        38944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38944.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-453, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38945
in-theory        38945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (A or B)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38945.        (((A -> (A or B)) and (C or (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (A or B)) and (C or (D -> (E or D)))))), M:tm-443, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38946
in-theory        38946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38946.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-409, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38947
in-theory        38947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38947.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-400, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38948
in-theory        38948
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38948.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-391, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38949
in-theory        38949
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38949.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-382, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38950
in-theory        38950
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38950.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G or (H -> (I or H))))), M:tm-373, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38951
in-theory        38951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38951.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-364, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38952
in-theory        38952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38952.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-354, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38953
in-theory        38953
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38953.        (((A -> (A or B)) and (C or (D -> (E or D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38954
in-theory        38954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38954.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E or (F -> (G or F))))), M:tm-338, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38955
in-theory        38955
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C or (D -> (E or D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38955.        (((A -> (A or B)) and (C or (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C or (D -> (E or D)))))), M:tm-327, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38956
in-theory        38956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and (((F and G) -> G) and ((A -> (A or B)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38956.        (((A -> (A or B)) and (C or (D -> (E or D)))) and (((F and G) -> G) and ((A -> (A or B)) and (C or (D -> (E or D)))))), M:tm-326, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38957
in-theory        38957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and (((F and G) -> F) and ((A -> (A or B)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38957.        (((A -> (A or B)) and (C or (D -> (E or D)))) and (((F and G) -> F) and ((A -> (A or B)) and (C or (D -> (E or D)))))), M:tm-325, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38958
in-theory        38958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C or (D -> (E or D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38958.        (((A -> (A or B)) and (C or (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C or (D -> (E or D)))))), M:tm-324, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38959
in-theory        38959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38959.        (((A -> (A or B)) and (C or (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C or (D -> (E or D)))))), M:tm-323, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38960
in-theory        38960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38960.        (((A -> (A or B)) and (C or (D -> (E or D)))) and ((F and G) -> G)), M:tm-322, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38961
in-theory        38961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38961.        (((A -> (A or B)) and (C or (D -> (E or D)))) and ((F and G) -> F)), M:tm-320, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38962
in-theory        38962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38962.        (((A -> (A or B)) and (C or (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38963
in-theory        38963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38963.        (((A -> (A or B)) and (C or (D -> (E or D)))) and (F -> (G -> F))), M:tm-315, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38964
in-theory        38964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and (F or ((A -> (A or B)) and (C or (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38964.        (((A -> (A or B)) and (C or (D -> (E or D)))) and (F or ((A -> (A or B)) and (C or (D -> (E or D)))))), M:tm-311, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38965
in-theory        38965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and (((A -> (A or B)) and (C or (D -> (E or D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38965.        (((A -> (A or B)) and (C or (D -> (E or D)))) and (((A -> (A or B)) and (C or (D -> (E or D)))) or F)), M:tm-310, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38966
in-theory        38966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and (F -> (((A -> (A or B)) and (C or (D -> (E or D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38966.        (((A -> (A or B)) and (C or (D -> (E or D)))) and (F -> (((A -> (A or B)) and (C or (D -> (E or D)))) and F))), M:tm-309, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38967
in-theory        38967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and (C or (D -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-532 ((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38967.        (((A -> (A or B)) and (C or (D -> (E or D)))) and (C or (D -> (E or D)))), M:tm-308, m:tm-532, u:((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-38968
in-theory        38968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-532 ((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38968.        (((A -> (A or B)) and (C or (D -> (E or D)))) and (A -> (A or B))), M:tm-307, m:tm-532, u:((A (-> Am (or Am Bm))) (B (or Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-38969
in-theory        38969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and (F -> ((A -> (A or B)) and (C or (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38969.        (((A -> (A or B)) and (C or (D -> (E or D)))) and (F -> ((A -> (A or B)) and (C or (D -> (E or D)))))), M:tm-305, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38970
in-theory        38970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38970.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-303, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38971
in-theory        38971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38971.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-270, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38972
in-theory        38972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38972.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-239, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38973
in-theory        38973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38973.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G or (H -> (I or H))))), M:tm-210, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38974
in-theory        38974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38974.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-183, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38975
in-theory        38975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38975.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-157, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38976
in-theory        38976
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38976.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-147, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38977
in-theory        38977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38977.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-134, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38978
in-theory        38978
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38978.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-125, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38979
in-theory        38979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38979.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G or (H -> (I or H))))), M:tm-113, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38980
in-theory        38980
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38980.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-105, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38981
in-theory        38981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38981.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E or (F -> (G or F))))), M:tm-95, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38982
in-theory        38982
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38982.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-83, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38983
in-theory        38983
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D or (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38983.        (((not (not A)) -> A) and ((B -> (B or C)) and (D or (E -> (F or E))))), M:tm-76, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38984
in-theory        38984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38984.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E or (F -> (G or F))))), M:tm-69, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38985
in-theory        38985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38985.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-54, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38986
in-theory        38986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38986.        ((A -> (B or A)) and ((C -> (C or D)) and (E or (F -> (G or F))))), M:tm-42, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38987
in-theory        38987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38987.        ((A -> (A or B)) and ((C -> (C or D)) and (E or (F -> (G or F))))), M:tm-32, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38988
in-theory        38988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38988.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E or (F -> (G or F))))), M:tm-23, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38989
in-theory        38989
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38989.        (((A and B) -> B) and ((C -> (C or D)) and (E or (F -> (G or F))))), M:tm-22, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38990
in-theory        38990
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38990.        (((A and B) -> A) and ((C -> (C or D)) and (E or (F -> (G or F))))), M:tm-21, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38991
in-theory        38991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38991.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-20, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38992
in-theory        38992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38992.        ((A -> (B -> A)) and ((C -> (C or D)) and (E or (F -> (G or F))))), M:tm-19, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38993
in-theory        38993
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38993.        (A or ((B -> (B or C)) and (D or (E -> (F or E))))), M:tm-7, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38994
in-theory        38994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38994.        (((A -> (A or B)) and (C or (D -> (E or D)))) or F), M:tm-6, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38995
in-theory        38995
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D or (E -> (F or E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38995.        (A -> (((B -> (B or C)) and (D or (E -> (F or E)))) and A)), M:tm-5, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38996
in-theory        38996
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-6 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38996.        (A -> ((B -> (B or C)) and (D or (E -> (F or E))))), M:tm-1, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38997
in-theory        38997
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38997.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-530, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38998
in-theory        38998
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38998.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-520, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-38999
in-theory        38999
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38999.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-510, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39000
in-theory        39000
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39000.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-500, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39001
in-theory        39001
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39001.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I or H))))), M:tm-490, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39002
in-theory        39002
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39002.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-480, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39003
in-theory        39003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39003.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-469, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39004
in-theory        39004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39004.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (F -> (F or G))), M:tm-456, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39005
in-theory        39005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39005.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-453, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39006
in-theory        39006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C or (D -> (E or D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39006.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C or (D -> (E or D)))))), M:tm-443, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39007
in-theory        39007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39007.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-409, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39008
in-theory        39008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39008.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-400, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39009
in-theory        39009
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39009.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-391, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39010
in-theory        39010
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39010.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-382, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39011
in-theory        39011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39011.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G or (H -> (I or H))))), M:tm-373, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39012
in-theory        39012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39012.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-364, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39013
in-theory        39013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39013.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-354, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39014
in-theory        39014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39014.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39015
in-theory        39015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39015.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (G or F))))), M:tm-338, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39016
in-theory        39016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C or (D -> (E or D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39016.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C or (D -> (E or D)))))), M:tm-327, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39017
in-theory        39017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C or (D -> (E or D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39017.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C or (D -> (E or D)))))), M:tm-326, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39018
in-theory        39018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C or (D -> (E or D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39018.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C or (D -> (E or D)))))), M:tm-325, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39019
in-theory        39019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C or (D -> (E or D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39019.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C or (D -> (E or D)))))), M:tm-324, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39020
in-theory        39020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C or (D -> (E or D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39020.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C or (D -> (E or D)))))), M:tm-323, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39021
in-theory        39021
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39021.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and ((F and G) -> G)), M:tm-322, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39022
in-theory        39022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39022.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and ((F and G) -> F)), M:tm-320, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39023
in-theory        39023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39023.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39024
in-theory        39024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39024.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (F -> (G -> F))), M:tm-315, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39025
in-theory        39025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (F or ((A -> (B -> (A and B))) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39025.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (F or ((A -> (B -> (A and B))) and (C or (D -> (E or D)))))), M:tm-311, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39026
in-theory        39026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39026.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) or F)), M:tm-310, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39027
in-theory        39027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (F -> (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39027.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (F -> (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and F))), M:tm-309, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39028
in-theory        39028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (C or (D -> (E or D))))
theorem-size     23
proof            (modus-ponens tm-308 tm-533 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39028.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (C or (D -> (E or D)))), M:tm-308, m:tm-533, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-39029
in-theory        39029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-533 ((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39029.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-533, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-39030
in-theory        39030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (F -> ((A -> (B -> (A and B))) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39030.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (F -> ((A -> (B -> (A and B))) and (C or (D -> (E or D)))))), M:tm-305, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39031
in-theory        39031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39031.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-303, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39032
in-theory        39032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39032.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-270, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39033
in-theory        39033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39033.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-239, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39034
in-theory        39034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or (H -> (I or H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39034.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G or (H -> (I or H))))), M:tm-210, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39035
in-theory        39035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39035.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-183, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39036
in-theory        39036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39036.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-157, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39037
in-theory        39037
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39037.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-147, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39038
in-theory        39038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39038.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-134, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39039
in-theory        39039
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39039.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-125, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39040
in-theory        39040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39040.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G or (H -> (I or H))))), M:tm-113, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39041
in-theory        39041
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39041.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-105, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39042
in-theory        39042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39042.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (G or F))))), M:tm-95, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39043
in-theory        39043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39043.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-83, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39044
in-theory        39044
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or (E -> (F or E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39044.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D or (E -> (F or E))))), M:tm-76, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39045
in-theory        39045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or (F -> (G or F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39045.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E or (F -> (G or F))))), M:tm-69, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39046
in-theory        39046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39046.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-54, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39047
in-theory        39047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39047.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E or (F -> (G or F))))), M:tm-42, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39048
in-theory        39048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39048.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E or (F -> (G or F))))), M:tm-32, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39049
in-theory        39049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39049.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E or (F -> (G or F))))), M:tm-23, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39050
in-theory        39050
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39050.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E or (F -> (G or F))))), M:tm-22, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39051
in-theory        39051
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39051.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E or (F -> (G or F))))), M:tm-21, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39052
in-theory        39052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39052.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-20, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39053
in-theory        39053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39053.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E or (F -> (G or F))))), M:tm-19, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39054
in-theory        39054
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D or (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-7 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39054.        (A or ((B -> (C -> (B and C))) and (D or (E -> (F or E))))), M:tm-7, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39055
in-theory        39055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39055.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) or F), M:tm-6, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39056
in-theory        39056
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D or (E -> (F or E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39056.        (A -> (((B -> (C -> (B and C))) and (D or (E -> (F or E)))) and A)), M:tm-5, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39057
in-theory        39057
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D or (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39057.        (A -> ((B -> (C -> (B and C))) and (D or (E -> (F or E))))), M:tm-1, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39058
in-theory        39058
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39058.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-530, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39059
in-theory        39059
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39059.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-520, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39060
in-theory        39060
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39060.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-510, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39061
in-theory        39061
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39061.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-500, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39062
in-theory        39062
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39062.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (I or H))))), M:tm-490, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39063
in-theory        39063
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39063.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-480, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39064
in-theory        39064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39064.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-469, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39065
in-theory        39065
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39065.        ((((A and B) -> B) and (C or (D -> (E or D)))) and (F -> (F or G))), M:tm-456, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39066
in-theory        39066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39066.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-453, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39067
in-theory        39067
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and ((F -> (F or G)) and (((A and B) -> B) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39067.        ((((A and B) -> B) and (C or (D -> (E or D)))) and ((F -> (F or G)) and (((A and B) -> B) and (C or (D -> (E or D)))))), M:tm-443, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39068
in-theory        39068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39068.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-409, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39069
in-theory        39069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39069.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-400, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39070
in-theory        39070
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39070.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-391, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39071
in-theory        39071
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39071.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-382, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39072
in-theory        39072
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39072.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G or (H -> (I or H))))), M:tm-373, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39073
in-theory        39073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39073.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-364, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39074
in-theory        39074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39074.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-354, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39075
in-theory        39075
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39075.        ((((A and B) -> B) and (C or (D -> (E or D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39076
in-theory        39076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39076.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E or (F -> (G or F))))), M:tm-338, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39077
in-theory        39077
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C or (D -> (E or D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39077.        ((((A and B) -> B) and (C or (D -> (E or D)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C or (D -> (E or D)))))), M:tm-327, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39078
in-theory        39078
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and (((F and G) -> G) and (((A and B) -> B) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39078.        ((((A and B) -> B) and (C or (D -> (E or D)))) and (((F and G) -> G) and (((A and B) -> B) and (C or (D -> (E or D)))))), M:tm-326, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39079
in-theory        39079
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and (((F and G) -> F) and (((A and B) -> B) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39079.        ((((A and B) -> B) and (C or (D -> (E or D)))) and (((F and G) -> F) and (((A and B) -> B) and (C or (D -> (E or D)))))), M:tm-325, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39080
in-theory        39080
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C or (D -> (E or D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39080.        ((((A and B) -> B) and (C or (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C or (D -> (E or D)))))), M:tm-324, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39081
in-theory        39081
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and ((F -> (G -> F)) and (((A and B) -> B) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39081.        ((((A and B) -> B) and (C or (D -> (E or D)))) and ((F -> (G -> F)) and (((A and B) -> B) and (C or (D -> (E or D)))))), M:tm-323, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39082
in-theory        39082
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39082.        ((((A and B) -> B) and (C or (D -> (E or D)))) and ((F and G) -> G)), M:tm-322, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39083
in-theory        39083
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39083.        ((((A and B) -> B) and (C or (D -> (E or D)))) and ((F and G) -> F)), M:tm-320, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39084
in-theory        39084
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39084.        ((((A and B) -> B) and (C or (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39085
in-theory        39085
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39085.        ((((A and B) -> B) and (C or (D -> (E or D)))) and (F -> (G -> F))), M:tm-315, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39086
in-theory        39086
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and (F or (((A and B) -> B) and (C or (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39086.        ((((A and B) -> B) and (C or (D -> (E or D)))) and (F or (((A and B) -> B) and (C or (D -> (E or D)))))), M:tm-311, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39087
in-theory        39087
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and ((((A and B) -> B) and (C or (D -> (E or D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39087.        ((((A and B) -> B) and (C or (D -> (E or D)))) and ((((A and B) -> B) and (C or (D -> (E or D)))) or F)), M:tm-310, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39088
in-theory        39088
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and (F -> ((((A and B) -> B) and (C or (D -> (E or D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39088.        ((((A and B) -> B) and (C or (D -> (E or D)))) and (F -> ((((A and B) -> B) and (C or (D -> (E or D)))) and F))), M:tm-309, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39089
in-theory        39089
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and (C or (D -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-534 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39089.        ((((A and B) -> B) and (C or (D -> (E or D)))) and (C or (D -> (E or D)))), M:tm-308, m:tm-534, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-39090
in-theory        39090
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-534 ((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39090.        ((((A and B) -> B) and (C or (D -> (E or D)))) and ((A and B) -> B)), M:tm-307, m:tm-534, u:((A (-> (and Am Bm) Bm)) (B (or Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-39091
in-theory        39091
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and (F -> (((A and B) -> B) and (C or (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39091.        ((((A and B) -> B) and (C or (D -> (E or D)))) and (F -> (((A and B) -> B) and (C or (D -> (E or D)))))), M:tm-305, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39092
in-theory        39092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39092.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-303, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39093
in-theory        39093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39093.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-270, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39094
in-theory        39094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39094.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-239, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39095
in-theory        39095
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39095.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G or (H -> (I or H))))), M:tm-210, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39096
in-theory        39096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39096.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-183, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39097
in-theory        39097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39097.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-157, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39098
in-theory        39098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39098.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-147, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39099
in-theory        39099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39099.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-134, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39100
in-theory        39100
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39100.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-125, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39101
in-theory        39101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39101.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G or (H -> (I or H))))), M:tm-113, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39102
in-theory        39102
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39102.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-105, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39103
in-theory        39103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39103.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E or (F -> (G or F))))), M:tm-95, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39104
in-theory        39104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39104.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-83, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39105
in-theory        39105
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D or (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39105.        (((not (not A)) -> A) and (((B and C) -> C) and (D or (E -> (F or E))))), M:tm-76, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39106
in-theory        39106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-4 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39106.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E or (F -> (G or F))))), M:tm-69, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39107
in-theory        39107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39107.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-54, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39108
in-theory        39108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39108.        ((A -> (B or A)) and (((C and D) -> D) and (E or (F -> (G or F))))), M:tm-42, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39109
in-theory        39109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39109.        ((A -> (A or B)) and (((C and D) -> D) and (E or (F -> (G or F))))), M:tm-32, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39110
in-theory        39110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39110.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (E or (F -> (G or F))))), M:tm-23, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39111
in-theory        39111
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39111.        (((A and B) -> B) and (((C and D) -> D) and (E or (F -> (G or F))))), M:tm-22, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39112
in-theory        39112
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39112.        (((A and B) -> A) and (((C and D) -> D) and (E or (F -> (G or F))))), M:tm-21, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39113
in-theory        39113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39113.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-20, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39114
in-theory        39114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39114.        ((A -> (B -> A)) and (((C and D) -> D) and (E or (F -> (G or F))))), M:tm-19, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39115
in-theory        39115
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39115.        (A or (((B and C) -> C) and (D or (E -> (F or E))))), M:tm-7, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39116
in-theory        39116
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-4 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39116.        ((((A and B) -> B) and (C or (D -> (E or D)))) or F), M:tm-6, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39117
in-theory        39117
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D or (E -> (F or E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39117.        (A -> ((((B and C) -> C) and (D or (E -> (F or E)))) and A)), M:tm-5, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39118
in-theory        39118
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-4 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39118.        (A -> (((B and C) -> C) and (D or (E -> (F or E))))), M:tm-1, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39119
in-theory        39119
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39119.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-530, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39120
in-theory        39120
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39120.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-520, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39121
in-theory        39121
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39121.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-510, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39122
in-theory        39122
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39122.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-500, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39123
in-theory        39123
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39123.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (I or H))))), M:tm-490, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39124
in-theory        39124
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39124.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-480, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39125
in-theory        39125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39125.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-469, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39126
in-theory        39126
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39126.        ((((A and B) -> A) and (C or (D -> (E or D)))) and (F -> (F or G))), M:tm-456, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39127
in-theory        39127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39127.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-453, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39128
in-theory        39128
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and ((F -> (F or G)) and (((A and B) -> A) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39128.        ((((A and B) -> A) and (C or (D -> (E or D)))) and ((F -> (F or G)) and (((A and B) -> A) and (C or (D -> (E or D)))))), M:tm-443, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39129
in-theory        39129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39129.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-409, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39130
in-theory        39130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39130.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-400, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39131
in-theory        39131
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39131.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-391, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39132
in-theory        39132
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39132.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-382, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39133
in-theory        39133
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39133.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G or (H -> (I or H))))), M:tm-373, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39134
in-theory        39134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39134.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-364, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39135
in-theory        39135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39135.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-354, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39136
in-theory        39136
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39136.        ((((A and B) -> A) and (C or (D -> (E or D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39137
in-theory        39137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39137.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E or (F -> (G or F))))), M:tm-338, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39138
in-theory        39138
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C or (D -> (E or D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39138.        ((((A and B) -> A) and (C or (D -> (E or D)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C or (D -> (E or D)))))), M:tm-327, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39139
in-theory        39139
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and (((F and G) -> G) and (((A and B) -> A) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39139.        ((((A and B) -> A) and (C or (D -> (E or D)))) and (((F and G) -> G) and (((A and B) -> A) and (C or (D -> (E or D)))))), M:tm-326, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39140
in-theory        39140
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and (((F and G) -> F) and (((A and B) -> A) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39140.        ((((A and B) -> A) and (C or (D -> (E or D)))) and (((F and G) -> F) and (((A and B) -> A) and (C or (D -> (E or D)))))), M:tm-325, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39141
in-theory        39141
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C or (D -> (E or D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39141.        ((((A and B) -> A) and (C or (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C or (D -> (E or D)))))), M:tm-324, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39142
in-theory        39142
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and ((F -> (G -> F)) and (((A and B) -> A) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39142.        ((((A and B) -> A) and (C or (D -> (E or D)))) and ((F -> (G -> F)) and (((A and B) -> A) and (C or (D -> (E or D)))))), M:tm-323, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39143
in-theory        39143
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39143.        ((((A and B) -> A) and (C or (D -> (E or D)))) and ((F and G) -> G)), M:tm-322, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39144
in-theory        39144
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39144.        ((((A and B) -> A) and (C or (D -> (E or D)))) and ((F and G) -> F)), M:tm-320, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39145
in-theory        39145
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39145.        ((((A and B) -> A) and (C or (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39146
in-theory        39146
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39146.        ((((A and B) -> A) and (C or (D -> (E or D)))) and (F -> (G -> F))), M:tm-315, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39147
in-theory        39147
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and (F or (((A and B) -> A) and (C or (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39147.        ((((A and B) -> A) and (C or (D -> (E or D)))) and (F or (((A and B) -> A) and (C or (D -> (E or D)))))), M:tm-311, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39148
in-theory        39148
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and ((((A and B) -> A) and (C or (D -> (E or D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39148.        ((((A and B) -> A) and (C or (D -> (E or D)))) and ((((A and B) -> A) and (C or (D -> (E or D)))) or F)), M:tm-310, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39149
in-theory        39149
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and (F -> ((((A and B) -> A) and (C or (D -> (E or D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39149.        ((((A and B) -> A) and (C or (D -> (E or D)))) and (F -> ((((A and B) -> A) and (C or (D -> (E or D)))) and F))), M:tm-309, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39150
in-theory        39150
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and (C or (D -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-535 ((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39150.        ((((A and B) -> A) and (C or (D -> (E or D)))) and (C or (D -> (E or D)))), M:tm-308, m:tm-535, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-39151
in-theory        39151
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-535 ((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39151.        ((((A and B) -> A) and (C or (D -> (E or D)))) and ((A and B) -> A)), M:tm-307, m:tm-535, u:((A (-> (and Am Bm) Am)) (B (or Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-39152
in-theory        39152
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and (F -> (((A and B) -> A) and (C or (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39152.        ((((A and B) -> A) and (C or (D -> (E or D)))) and (F -> (((A and B) -> A) and (C or (D -> (E or D)))))), M:tm-305, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39153
in-theory        39153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39153.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-303, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39154
in-theory        39154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39154.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-270, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39155
in-theory        39155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39155.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-239, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39156
in-theory        39156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39156.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G or (H -> (I or H))))), M:tm-210, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39157
in-theory        39157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39157.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-183, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39158
in-theory        39158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39158.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-157, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39159
in-theory        39159
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39159.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-147, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39160
in-theory        39160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39160.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-134, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39161
in-theory        39161
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39161.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-125, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39162
in-theory        39162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39162.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G or (H -> (I or H))))), M:tm-113, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39163
in-theory        39163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39163.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-105, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39164
in-theory        39164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39164.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E or (F -> (G or F))))), M:tm-95, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39165
in-theory        39165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39165.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-83, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39166
in-theory        39166
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D or (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39166.        (((not (not A)) -> A) and (((B and C) -> B) and (D or (E -> (F or E))))), M:tm-76, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39167
in-theory        39167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-3 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39167.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E or (F -> (G or F))))), M:tm-69, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39168
in-theory        39168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39168.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-54, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39169
in-theory        39169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39169.        ((A -> (B or A)) and (((C and D) -> C) and (E or (F -> (G or F))))), M:tm-42, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39170
in-theory        39170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39170.        ((A -> (A or B)) and (((C and D) -> C) and (E or (F -> (G or F))))), M:tm-32, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39171
in-theory        39171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39171.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (E or (F -> (G or F))))), M:tm-23, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39172
in-theory        39172
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39172.        (((A and B) -> B) and (((C and D) -> C) and (E or (F -> (G or F))))), M:tm-22, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39173
in-theory        39173
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39173.        (((A and B) -> A) and (((C and D) -> C) and (E or (F -> (G or F))))), M:tm-21, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39174
in-theory        39174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39174.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-20, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39175
in-theory        39175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39175.        ((A -> (B -> A)) and (((C and D) -> C) and (E or (F -> (G or F))))), M:tm-19, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39176
in-theory        39176
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39176.        (A or (((B and C) -> B) and (D or (E -> (F or E))))), M:tm-7, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39177
in-theory        39177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-3 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39177.        ((((A and B) -> A) and (C or (D -> (E or D)))) or F), M:tm-6, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39178
in-theory        39178
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D or (E -> (F or E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39178.        (A -> ((((B and C) -> B) and (D or (E -> (F or E)))) and A)), M:tm-5, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39179
in-theory        39179
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-3 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39179.        (A -> (((B and C) -> B) and (D or (E -> (F or E))))), M:tm-1, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39180
in-theory        39180
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39180.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-530, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39181
in-theory        39181
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39181.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-520, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39182
in-theory        39182
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39182.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-510, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39183
in-theory        39183
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39183.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-500, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39184
in-theory        39184
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39184.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J or I))))), M:tm-490, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39185
in-theory        39185
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39185.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-480, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39186
in-theory        39186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39186.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-469, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39187
in-theory        39187
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39187.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (G -> (G or H))), M:tm-456, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39188
in-theory        39188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39188.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-453, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39189
in-theory        39189
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39189.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))))), M:tm-443, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39190
in-theory        39190
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39190.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-409, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39191
in-theory        39191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39191.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-400, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39192
in-theory        39192
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39192.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-391, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39193
in-theory        39193
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39193.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-382, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39194
in-theory        39194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39194.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J or I))))), M:tm-373, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39195
in-theory        39195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39195.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-364, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39196
in-theory        39196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39196.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-354, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39197
in-theory        39197
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39197.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39198
in-theory        39198
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39198.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G))))), M:tm-338, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39199
in-theory        39199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39199.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))))), M:tm-327, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39200
in-theory        39200
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39200.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))))), M:tm-326, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39201
in-theory        39201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39201.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))))), M:tm-325, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39202
in-theory        39202
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39202.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))))), M:tm-324, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39203
in-theory        39203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39203.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))))), M:tm-323, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39204
in-theory        39204
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39204.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((G and H) -> H)), M:tm-322, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39205
in-theory        39205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39205.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((G and H) -> G)), M:tm-320, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39206
in-theory        39206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39206.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39207
in-theory        39207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39207.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (G -> (H -> G))), M:tm-315, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39208
in-theory        39208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39208.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))))), M:tm-311, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39209
in-theory        39209
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39209.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) or G)), M:tm-310, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39210
in-theory        39210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39210.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and G))), M:tm-309, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39211
in-theory        39211
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (D or (E -> (F or E))))
theorem-size     29
proof            (modus-ponens tm-308 tm-536 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (or Fm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39211.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (D or (E -> (F or E)))), M:tm-308, m:tm-536, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (or Fm Em)))))
================================================================
tm-name          tm-39212
in-theory        39212
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-536 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (or Fm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39212.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-536, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> Em (or Fm Em)))))
================================================================
tm-name          tm-39213
in-theory        39213
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39213.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))))), M:tm-305, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39214
in-theory        39214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39214.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-303, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39215
in-theory        39215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39215.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-270, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39216
in-theory        39216
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39216.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-239, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39217
in-theory        39217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J or I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39217.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J or I))))), M:tm-210, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39218
in-theory        39218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39218.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-183, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39219
in-theory        39219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39219.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-157, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39220
in-theory        39220
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39220.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-147, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39221
in-theory        39221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39221.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-134, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39222
in-theory        39222
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39222.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-125, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39223
in-theory        39223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39223.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J or I))))), M:tm-113, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39224
in-theory        39224
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39224.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-105, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39225
in-theory        39225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39225.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G))))), M:tm-95, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39226
in-theory        39226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39226.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-83, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39227
in-theory        39227
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G or F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39227.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G or F))))), M:tm-76, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39228
in-theory        39228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-9 tm-2 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39228.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G))))), M:tm-69, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39229
in-theory        39229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39229.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-54, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39230
in-theory        39230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39230.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G))))), M:tm-42, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39231
in-theory        39231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39231.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G))))), M:tm-32, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39232
in-theory        39232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39232.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G))))), M:tm-23, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39233
in-theory        39233
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39233.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G))))), M:tm-22, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39234
in-theory        39234
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39234.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G))))), M:tm-21, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39235
in-theory        39235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39235.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-20, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39236
in-theory        39236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39236.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F or (G -> (H or G))))), M:tm-19, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39237
in-theory        39237
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39237.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G or F))))), M:tm-7, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39238
in-theory        39238
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-6 tm-5 tm-2 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39238.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) or G), M:tm-6, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39239
in-theory        39239
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G or F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39239.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G or F)))) and A)), M:tm-5, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39240
in-theory        39240
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-1 tm-5 tm-2 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39240.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or (F -> (G or F))))), M:tm-1, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39241
in-theory        39241
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39241.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-530, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39242
in-theory        39242
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39242.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-520, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39243
in-theory        39243
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39243.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-510, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39244
in-theory        39244
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39244.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-500, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39245
in-theory        39245
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39245.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (I or H))))), M:tm-490, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39246
in-theory        39246
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39246.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-480, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39247
in-theory        39247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39247.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-469, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39248
in-theory        39248
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39248.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and (F -> (F or G))), M:tm-456, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39249
in-theory        39249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39249.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-453, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39250
in-theory        39250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39250.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C or (D -> (E or D)))))), M:tm-443, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39251
in-theory        39251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39251.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-409, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39252
in-theory        39252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39252.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-400, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39253
in-theory        39253
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39253.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-391, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39254
in-theory        39254
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39254.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-382, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39255
in-theory        39255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39255.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G or (H -> (I or H))))), M:tm-373, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39256
in-theory        39256
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39256.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-364, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39257
in-theory        39257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39257.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-354, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39258
in-theory        39258
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39258.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39259
in-theory        39259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39259.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (G or F))))), M:tm-338, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39260
in-theory        39260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C or (D -> (E or D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39260.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C or (D -> (E or D)))))), M:tm-327, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39261
in-theory        39261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and (((F and G) -> G) and ((A -> (B -> A)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39261.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and (((F and G) -> G) and ((A -> (B -> A)) and (C or (D -> (E or D)))))), M:tm-326, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39262
in-theory        39262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and (((F and G) -> F) and ((A -> (B -> A)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39262.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and (((F and G) -> F) and ((A -> (B -> A)) and (C or (D -> (E or D)))))), M:tm-325, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39263
in-theory        39263
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C or (D -> (E or D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39263.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C or (D -> (E or D)))))), M:tm-324, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39264
in-theory        39264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39264.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C or (D -> (E or D)))))), M:tm-323, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39265
in-theory        39265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39265.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and ((F and G) -> G)), M:tm-322, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39266
in-theory        39266
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39266.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and ((F and G) -> F)), M:tm-320, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39267
in-theory        39267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39267.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39268
in-theory        39268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39268.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and (F -> (G -> F))), M:tm-315, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39269
in-theory        39269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and (F or ((A -> (B -> A)) and (C or (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39269.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and (F or ((A -> (B -> A)) and (C or (D -> (E or D)))))), M:tm-311, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39270
in-theory        39270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and (((A -> (B -> A)) and (C or (D -> (E or D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39270.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and (((A -> (B -> A)) and (C or (D -> (E or D)))) or F)), M:tm-310, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39271
in-theory        39271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and (F -> (((A -> (B -> A)) and (C or (D -> (E or D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39271.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and (F -> (((A -> (B -> A)) and (C or (D -> (E or D)))) and F))), M:tm-309, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39272
in-theory        39272
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and (C or (D -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-537 ((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39272.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and (C or (D -> (E or D)))), M:tm-308, m:tm-537, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-39273
in-theory        39273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-537 ((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39273.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and (A -> (B -> A))), M:tm-307, m:tm-537, u:((A (-> Am (-> Bm Am))) (B (or Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-39274
in-theory        39274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and (F -> ((A -> (B -> A)) and (C or (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39274.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and (F -> ((A -> (B -> A)) and (C or (D -> (E or D)))))), M:tm-305, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39275
in-theory        39275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39275.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-303, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39276
in-theory        39276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39276.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-270, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39277
in-theory        39277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39277.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-239, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39278
in-theory        39278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39278.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G or (H -> (I or H))))), M:tm-210, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39279
in-theory        39279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39279.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-183, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39280
in-theory        39280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39280.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-157, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39281
in-theory        39281
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39281.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-147, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39282
in-theory        39282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39282.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-134, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39283
in-theory        39283
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39283.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-125, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39284
in-theory        39284
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39284.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G or (H -> (I or H))))), M:tm-113, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39285
in-theory        39285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39285.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-105, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39286
in-theory        39286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39286.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E or (F -> (G or F))))), M:tm-95, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39287
in-theory        39287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39287.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-83, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39288
in-theory        39288
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D or (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39288.        (((not (not A)) -> A) and ((B -> (C -> B)) and (D or (E -> (F or E))))), M:tm-76, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39289
in-theory        39289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39289.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E or (F -> (G or F))))), M:tm-69, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39290
in-theory        39290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39290.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-54, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39291
in-theory        39291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39291.        ((A -> (B or A)) and ((C -> (D -> C)) and (E or (F -> (G or F))))), M:tm-42, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39292
in-theory        39292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39292.        ((A -> (A or B)) and ((C -> (D -> C)) and (E or (F -> (G or F))))), M:tm-32, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39293
in-theory        39293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39293.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E or (F -> (G or F))))), M:tm-23, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39294
in-theory        39294
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39294.        (((A and B) -> B) and ((C -> (D -> C)) and (E or (F -> (G or F))))), M:tm-22, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39295
in-theory        39295
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39295.        (((A and B) -> A) and ((C -> (D -> C)) and (E or (F -> (G or F))))), M:tm-21, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39296
in-theory        39296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39296.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-20, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39297
in-theory        39297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39297.        ((A -> (B -> A)) and ((C -> (D -> C)) and (E or (F -> (G or F))))), M:tm-19, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39298
in-theory        39298
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39298.        (A or ((B -> (C -> B)) and (D or (E -> (F or E))))), M:tm-7, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39299
in-theory        39299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-1 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39299.        (((A -> (B -> A)) and (C or (D -> (E or D)))) or F), M:tm-6, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39300
in-theory        39300
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D or (E -> (F or E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39300.        (A -> (((B -> (C -> B)) and (D or (E -> (F or E)))) and A)), M:tm-5, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39301
in-theory        39301
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39301.        (A -> ((B -> (C -> B)) and (D or (E -> (F or E))))), M:tm-1, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39302
in-theory        39302
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39302.        ((A or (B -> (B or C))) and (D or (E or (F -> (G or F))))), M:tm-530, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39303
in-theory        39303
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39303.        ((A or (B -> (C -> (B and C)))) and (D or (E or (F -> (G or F))))), M:tm-520, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39304
in-theory        39304
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39304.        ((A or ((B and C) -> C)) and (D or (E or (F -> (G or F))))), M:tm-510, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39305
in-theory        39305
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39305.        ((A or ((B and C) -> B)) and (D or (E or (F -> (G or F))))), M:tm-500, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39306
in-theory        39306
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39306.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (H or G))))), M:tm-490, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39307
in-theory        39307
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39307.        ((A or (B -> (C -> B))) and (D or (E or (F -> (G or F))))), M:tm-480, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39308
in-theory        39308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39308.        ((A -> (B -> (B or C))) and (D or (E or (F -> (G or F))))), M:tm-469, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39309
in-theory        39309
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39309.        ((A or (B or (C -> (D or C)))) and (E -> (E or F))), M:tm-456, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39310
in-theory        39310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39310.        ((A -> ((B -> (B or C)) and A)) and (D or (E or (F -> (G or F))))), M:tm-453, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39311
in-theory        39311
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and ((E -> (E or F)) and (A or (B or (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39311.        ((A or (B or (C -> (D or C)))) and ((E -> (E or F)) and (A or (B or (C -> (D or C)))))), M:tm-443, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39312
in-theory        39312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39312.        (((A -> (A or B)) or C) and (D or (E or (F -> (G or F))))), M:tm-409, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39313
in-theory        39313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39313.        (((A -> (B -> (A and B))) or C) and (D or (E or (F -> (G or F))))), M:tm-400, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39314
in-theory        39314
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39314.        ((((A and B) -> B) or C) and (D or (E or (F -> (G or F))))), M:tm-391, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39315
in-theory        39315
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39315.        ((((A and B) -> A) or C) and (D or (E or (F -> (G or F))))), M:tm-382, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39316
in-theory        39316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39316.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F or (G -> (H or G))))), M:tm-373, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39317
in-theory        39317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39317.        (((A -> (B -> A)) or C) and (D or (E or (F -> (G or F))))), M:tm-364, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39318
in-theory        39318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39318.        ((A -> (B -> (C -> (B and C)))) and (D or (E or (F -> (G or F))))), M:tm-354, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39319
in-theory        39319
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39319.        ((A or (B or (C -> (D or C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39320
in-theory        39320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D or (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39320.        (((A -> B) -> (A -> (A and B))) and (C or (D or (E -> (F or E))))), M:tm-338, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39321
in-theory        39321
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and ((E -> (F -> (E and F))) and (A or (B or (C -> (D or C))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39321.        ((A or (B or (C -> (D or C)))) and ((E -> (F -> (E and F))) and (A or (B or (C -> (D or C)))))), M:tm-327, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39322
in-theory        39322
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and (((E and F) -> F) and (A or (B or (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39322.        ((A or (B or (C -> (D or C)))) and (((E and F) -> F) and (A or (B or (C -> (D or C)))))), M:tm-326, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39323
in-theory        39323
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and (((E and F) -> E) and (A or (B or (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39323.        ((A or (B or (C -> (D or C)))) and (((E and F) -> E) and (A or (B or (C -> (D or C)))))), M:tm-325, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39324
in-theory        39324
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B or (C -> (D or C))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39324.        ((A or (B or (C -> (D or C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B or (C -> (D or C)))))), M:tm-324, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39325
in-theory        39325
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and ((E -> (F -> E)) and (A or (B or (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39325.        ((A or (B or (C -> (D or C)))) and ((E -> (F -> E)) and (A or (B or (C -> (D or C)))))), M:tm-323, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39326
in-theory        39326
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39326.        ((A or (B or (C -> (D or C)))) and ((E and F) -> F)), M:tm-322, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39327
in-theory        39327
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39327.        ((A or (B or (C -> (D or C)))) and ((E and F) -> E)), M:tm-320, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39328
in-theory        39328
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39328.        ((A or (B or (C -> (D or C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39329
in-theory        39329
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39329.        ((A or (B or (C -> (D or C)))) and (E -> (F -> E))), M:tm-315, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39330
in-theory        39330
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and (E or (A or (B or (C -> (D or C))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39330.        ((A or (B or (C -> (D or C)))) and (E or (A or (B or (C -> (D or C)))))), M:tm-311, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39331
in-theory        39331
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and ((A or (B or (C -> (D or C)))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39331.        ((A or (B or (C -> (D or C)))) and ((A or (B or (C -> (D or C)))) or E)), M:tm-310, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39332
in-theory        39332
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and (E -> ((A or (B or (C -> (D or C)))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39332.        ((A or (B or (C -> (D or C)))) and (E -> ((A or (B or (C -> (D or C)))) and E))), M:tm-309, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39333
in-theory        39333
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and (E -> (A or (B or (C -> (D or C))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39333.        ((A or (B or (C -> (D or C)))) and (E -> (A or (B or (C -> (D or C)))))), M:tm-305, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39334
in-theory        39334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39334.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E or (F -> (G or F))))), M:tm-303, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39335
in-theory        39335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39335.        ((A -> (((B and C) -> C) and A)) and (D or (E or (F -> (G or F))))), M:tm-270, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39336
in-theory        39336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39336.        ((A -> (((B and C) -> B) and A)) and (D or (E or (F -> (G or F))))), M:tm-239, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39337
in-theory        39337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39337.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F or (G -> (H or G))))), M:tm-210, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39338
in-theory        39338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39338.        ((A -> ((B -> (C -> B)) and A)) and (D or (E or (F -> (G or F))))), M:tm-183, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39339
in-theory        39339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39339.        ((A -> ((B and C) -> C)) and (D or (E or (F -> (G or F))))), M:tm-157, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39340
in-theory        39340
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39340.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E or (F -> (G or F))))), M:tm-147, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39341
in-theory        39341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39341.        ((A -> ((B and C) -> B)) and (D or (E or (F -> (G or F))))), M:tm-134, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39342
in-theory        39342
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39342.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E or (F -> (G or F))))), M:tm-125, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39343
in-theory        39343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39343.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F or (G -> (H or G))))), M:tm-113, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39344
in-theory        39344
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or (F -> (G or F)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39344.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E or (F -> (G or F))))), M:tm-105, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39345
in-theory        39345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D or (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39345.        (((A -> B) -> (A -> A)) and (C or (D or (E -> (F or E))))), M:tm-95, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39346
in-theory        39346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39346.        ((A -> (B -> (C -> B))) and (D or (E or (F -> (G or F))))), M:tm-83, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39347
in-theory        39347
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C or (D -> (E or D)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39347.        (((not (not A)) -> A) and (B or (C or (D -> (E or D))))), M:tm-76, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39348
in-theory        39348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or (E -> (F or E)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39348.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D or (E -> (F or E))))), M:tm-69, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39349
in-theory        39349
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39349.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E or (F -> (G or F))))), M:tm-54, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39350
in-theory        39350
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39350.        ((A -> (B or A)) and (C or (D or (E -> (F or E))))), M:tm-42, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39351
in-theory        39351
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39351.        ((A -> (A or B)) and (C or (D or (E -> (F or E))))), M:tm-32, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39352
in-theory        39352
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D or (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39352.        ((A -> (B -> (A and B))) and (C or (D or (E -> (F or E))))), M:tm-23, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39353
in-theory        39353
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39353.        (((A and B) -> B) and (C or (D or (E -> (F or E))))), M:tm-22, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39354
in-theory        39354
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39354.        (((A and B) -> A) and (C or (D or (E -> (F or E))))), M:tm-21, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39355
in-theory        39355
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39355.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E or (F -> (G or F))))), M:tm-20, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39356
in-theory        39356
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39356.        ((A -> (B -> A)) and (C or (D or (E -> (F or E))))), M:tm-19, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39357
in-theory        39357
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C or (D -> (E or D)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39357.        (A or (B or (C or (D -> (E or D))))), M:tm-7, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39358
in-theory        39358
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-6 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39358.        ((A or (B or (C -> (D or C)))) or E), M:tm-6, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39359
in-theory        39359
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C or (D -> (E or D)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39359.        (A -> ((B or (C or (D -> (E or D)))) and A)), M:tm-5, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39360
in-theory        39360
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C or (D -> (E or D)))))
theorem-size     11
proof            (modus-ponens tm-1 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-1 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39360.        (A -> (B or (C or (D -> (E or D))))), M:tm-1, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39361
in-theory        39361
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39361.        ((A or (B -> (B or C))) and ((D or (E -> (F or E))) or G)), M:tm-530, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39362
in-theory        39362
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39362.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> (F or E))) or G)), M:tm-520, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39363
in-theory        39363
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39363.        ((A or ((B and C) -> C)) and ((D or (E -> (F or E))) or G)), M:tm-510, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39364
in-theory        39364
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39364.        ((A or ((B and C) -> B)) and ((D or (E -> (F or E))) or G)), M:tm-500, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39365
in-theory        39365
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (G or F))) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39365.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (G or F))) or H)), M:tm-490, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39366
in-theory        39366
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39366.        ((A or (B -> (C -> B))) and ((D or (E -> (F or E))) or G)), M:tm-480, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39367
in-theory        39367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39367.        ((A -> (B -> (B or C))) and ((D or (E -> (F or E))) or G)), M:tm-469, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39368
in-theory        39368
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39368.        (((A or (B -> (C or B))) or D) and (E -> (E or F))), M:tm-456, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39369
in-theory        39369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39369.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> (F or E))) or G)), M:tm-453, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39370
in-theory        39370
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and ((E -> (E or F)) and ((A or (B -> (C or B))) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39370.        (((A or (B -> (C or B))) or D) and ((E -> (E or F)) and ((A or (B -> (C or B))) or D))), M:tm-443, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39371
in-theory        39371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39371.        (((A -> (A or B)) or C) and ((D or (E -> (F or E))) or G)), M:tm-409, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39372
in-theory        39372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39372.        (((A -> (B -> (A and B))) or C) and ((D or (E -> (F or E))) or G)), M:tm-400, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39373
in-theory        39373
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39373.        ((((A and B) -> B) or C) and ((D or (E -> (F or E))) or G)), M:tm-391, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39374
in-theory        39374
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39374.        ((((A and B) -> A) or C) and ((D or (E -> (F or E))) or G)), M:tm-382, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39375
in-theory        39375
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (G or F))) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39375.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> (G or F))) or H)), M:tm-373, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39376
in-theory        39376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39376.        (((A -> (B -> A)) or C) and ((D or (E -> (F or E))) or G)), M:tm-364, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39377
in-theory        39377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39377.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> (F or E))) or G)), M:tm-354, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39378
in-theory        39378
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39378.        (((A or (B -> (C or B))) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39379
in-theory        39379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> (E or D))) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39379.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> (E or D))) or F)), M:tm-338, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39380
in-theory        39380
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and ((E -> (F -> (E and F))) and ((A or (B -> (C or B))) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39380.        (((A or (B -> (C or B))) or D) and ((E -> (F -> (E and F))) and ((A or (B -> (C or B))) or D))), M:tm-327, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39381
in-theory        39381
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and (((E and F) -> F) and ((A or (B -> (C or B))) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39381.        (((A or (B -> (C or B))) or D) and (((E and F) -> F) and ((A or (B -> (C or B))) or D))), M:tm-326, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39382
in-theory        39382
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and (((E and F) -> E) and ((A or (B -> (C or B))) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39382.        (((A or (B -> (C or B))) or D) and (((E and F) -> E) and ((A or (B -> (C or B))) or D))), M:tm-325, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39383
in-theory        39383
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (C or B))) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39383.        (((A or (B -> (C or B))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> (C or B))) or D))), M:tm-324, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39384
in-theory        39384
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and ((E -> (F -> E)) and ((A or (B -> (C or B))) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39384.        (((A or (B -> (C or B))) or D) and ((E -> (F -> E)) and ((A or (B -> (C or B))) or D))), M:tm-323, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39385
in-theory        39385
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39385.        (((A or (B -> (C or B))) or D) and ((E and F) -> F)), M:tm-322, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39386
in-theory        39386
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39386.        (((A or (B -> (C or B))) or D) and ((E and F) -> E)), M:tm-320, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39387
in-theory        39387
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39387.        (((A or (B -> (C or B))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39388
in-theory        39388
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39388.        (((A or (B -> (C or B))) or D) and (E -> (F -> E))), M:tm-315, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39389
in-theory        39389
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and (E or ((A or (B -> (C or B))) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39389.        (((A or (B -> (C or B))) or D) and (E or ((A or (B -> (C or B))) or D))), M:tm-311, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39390
in-theory        39390
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and (((A or (B -> (C or B))) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39390.        (((A or (B -> (C or B))) or D) and (((A or (B -> (C or B))) or D) or E)), M:tm-310, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39391
in-theory        39391
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and (E -> (((A or (B -> (C or B))) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39391.        (((A or (B -> (C or B))) or D) and (E -> (((A or (B -> (C or B))) or D) and E))), M:tm-309, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39392
in-theory        39392
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and (E -> ((A or (B -> (C or B))) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39392.        (((A or (B -> (C or B))) or D) and (E -> ((A or (B -> (C or B))) or D))), M:tm-305, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39393
in-theory        39393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (F or E))) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39393.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> (F or E))) or G)), M:tm-303, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39394
in-theory        39394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39394.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> (F or E))) or G)), M:tm-270, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39395
in-theory        39395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39395.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> (F or E))) or G)), M:tm-239, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39396
in-theory        39396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (G or F))) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39396.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> (G or F))) or H)), M:tm-210, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39397
in-theory        39397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39397.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> (F or E))) or G)), M:tm-183, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39398
in-theory        39398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39398.        ((A -> ((B and C) -> C)) and ((D or (E -> (F or E))) or G)), M:tm-157, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39399
in-theory        39399
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (F or E))) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39399.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> (F or E))) or G)), M:tm-147, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39400
in-theory        39400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39400.        ((A -> ((B and C) -> B)) and ((D or (E -> (F or E))) or G)), M:tm-134, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39401
in-theory        39401
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (F or E))) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39401.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> (F or E))) or G)), M:tm-125, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39402
in-theory        39402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (G or F))) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39402.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> (G or F))) or H)), M:tm-113, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39403
in-theory        39403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (F or E))) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39403.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> (F or E))) or G)), M:tm-105, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39404
in-theory        39404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> (E or D))) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39404.        (((A -> B) -> (A -> A)) and ((C or (D -> (E or D))) or F)), M:tm-95, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39405
in-theory        39405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39405.        ((A -> (B -> (C -> B))) and ((D or (E -> (F or E))) or G)), M:tm-83, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39406
in-theory        39406
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> (D or C))) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39406.        (((not (not A)) -> A) and ((B or (C -> (D or C))) or E)), M:tm-76, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39407
in-theory        39407
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (E or D))) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39407.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> (E or D))) or F)), M:tm-69, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39408
in-theory        39408
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (F or E))) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39408.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> (F or E))) or G)), M:tm-54, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39409
in-theory        39409
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> (E or D))) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39409.        ((A -> (B or A)) and ((C or (D -> (E or D))) or F)), M:tm-42, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39410
in-theory        39410
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> (E or D))) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39410.        ((A -> (A or B)) and ((C or (D -> (E or D))) or F)), M:tm-32, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39411
in-theory        39411
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> (E or D))) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39411.        ((A -> (B -> (A and B))) and ((C or (D -> (E or D))) or F)), M:tm-23, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39412
in-theory        39412
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> (E or D))) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39412.        (((A and B) -> B) and ((C or (D -> (E or D))) or F)), M:tm-22, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39413
in-theory        39413
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> (E or D))) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39413.        (((A and B) -> A) and ((C or (D -> (E or D))) or F)), M:tm-21, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39414
in-theory        39414
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (F or E))) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39414.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> (F or E))) or G)), M:tm-20, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39415
in-theory        39415
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> (E or D))) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39415.        ((A -> (B -> A)) and ((C or (D -> (E or D))) or F)), M:tm-19, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39416
in-theory        39416
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B or (C -> (D or C))) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-7 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39416.        (A or ((B or (C -> (D or C))) or E)), M:tm-7, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39417
in-theory        39417
times-derived    2
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-6 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39417.        (((A or (B -> (C or B))) or D) or E), M:tm-6, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39418
in-theory        39418
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (D or C))) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39418.        (A -> (((B or (C -> (D or C))) or E) and A)), M:tm-5, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39419
in-theory        39419
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (D or C))) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-1 tm-6 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39419.        (A -> ((B or (C -> (D or C))) or E)), M:tm-1, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39420
in-theory        39420
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-540 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39420.        ((A or (B -> (C or B))) and (D -> (E or D))), M:tm-540, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-39421
in-theory        39421
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-39421.        ((A or (B -> (C or B))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-540, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-39422
in-theory        39422
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-540 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-39422.        ((A or (B -> (C or B))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-540, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-39423
in-theory        39423
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-540 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-39423.        ((A or (B -> (C or B))) and ((not (not D)) -> D)), M:tm-540, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-39424
in-theory        39424
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-540 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-39424.        ((A or (B -> (C or B))) and (D -> (E -> (F -> E)))), M:tm-540, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-39425
in-theory        39425
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-540 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-39425.        ((A or (B -> (C or B))) and ((D -> E) -> (D -> D))), M:tm-540, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-39426
in-theory        39426
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-540 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-39426.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-540, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-39427
in-theory        39427
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-39427.        ((A or (B -> (C or B))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-540, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-39428
in-theory        39428
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-540 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-39428.        ((A or (B -> (C or B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-540, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-39429
in-theory        39429
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-540 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-39429.        ((A or (B -> (C or B))) and (D -> ((E and F) -> E))), M:tm-540, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-39430
in-theory        39430
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-540 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-39430.        ((A or (B -> (C or B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-540, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-39431
in-theory        39431
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-540 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-39431.        ((A or (B -> (C or B))) and (D -> ((E and F) -> F))), M:tm-540, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-39432
in-theory        39432
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-540 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-39432.        ((A or (B -> (C or B))) and (D -> ((E -> (F -> E)) and D))), M:tm-540, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-39433
in-theory        39433
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-540 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-39433.        ((A or (B -> (C or B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-540, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-39434
in-theory        39434
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-540 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-39434.        ((A or (B -> (C or B))) and (D -> (((E and F) -> E) and D))), M:tm-540, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-39435
in-theory        39435
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-540 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-39435.        ((A or (B -> (C or B))) and (D -> (((E and F) -> F) and D))), M:tm-540, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-39436
in-theory        39436
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-39436.        ((A or (B -> (C or B))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-540, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-39437
in-theory        39437
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-540 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-39437.        ((A or (B -> (C or B))) and ((D -> E) -> (D -> (D and E)))), M:tm-540, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-39438
in-theory        39438
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-39438.        ((A or (B -> (C or B))) and (D -> (E -> (F -> (E and F))))), M:tm-540, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-39439
in-theory        39439
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-540 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-39439.        ((A or (B -> (C or B))) and ((D -> (E -> D)) or F)), M:tm-540, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-39440
in-theory        39440
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-540 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-39440.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-540, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-39441
in-theory        39441
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-540 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-39441.        ((A or (B -> (C or B))) and (((D and E) -> D) or F)), M:tm-540, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-39442
in-theory        39442
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-540 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-39442.        ((A or (B -> (C or B))) and (((D and E) -> E) or F)), M:tm-540, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-39443
in-theory        39443
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-540 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-39443.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) or F)), M:tm-540, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-39444
in-theory        39444
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-540 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39444.        ((A or (B -> (C or B))) and ((D -> (D or E)) or F)), M:tm-540, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-39445
in-theory        39445
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-540 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39445.        ((A or (B -> (C or B))) and (D -> ((E -> (E or F)) and D))), M:tm-540, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-39446
in-theory        39446
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-540 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39446.        ((A or (B -> (C or B))) and (D -> (E -> (E or F)))), M:tm-540, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-39447
in-theory        39447
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-540 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-39447.        ((A or (B -> (C or B))) and (D or (E -> (F -> E)))), M:tm-540, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-39448
in-theory        39448
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-39448.        ((A or (B -> (C or B))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-540, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-39449
in-theory        39449
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-540 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-39449.        ((A or (B -> (C or B))) and (D or ((E and F) -> E))), M:tm-540, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-39450
in-theory        39450
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-540 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-39450.        ((A or (B -> (C or B))) and (D or ((E and F) -> F))), M:tm-540, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-39451
in-theory        39451
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-39451.        ((A or (B -> (C or B))) and (D or (E -> (F -> (E and F))))), M:tm-540, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-39452
in-theory        39452
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-540 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39452.        ((A or (B -> (C or B))) and (D or (E -> (E or F)))), M:tm-540, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-39453
in-theory        39453
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-540 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39453.        ((A or (B -> (C or B))) and (D or (E -> (F or E)))), M:tm-540, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-39454
in-theory        39454
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-540 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39454.        ((A or (B -> (C or B))) and ((D -> (E or D)) or F)), M:tm-540, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-39455
in-theory        39455
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-540 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39455.        ((A or (B -> (C or B))) and (D -> ((E -> (F or E)) and D))), M:tm-540, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-39456
in-theory        39456
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-540 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39456.        ((A or (B -> (C or B))) and (D -> (E -> (F or E)))), M:tm-540, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-39457
in-theory        39457
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-540 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-39457.        ((A or (B -> (C or B))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-540, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-39458
in-theory        39458
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-540 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-39458.        ((A or (B -> (C or B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-540, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-39459
in-theory        39459
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-540 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-39459.        ((A or (B -> (C or B))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-540, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-39460
in-theory        39460
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-540 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-39460.        ((A or (B -> (C or B))) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-540, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-39461
in-theory        39461
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-540 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-39461.        ((A or (B -> (C or B))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-540, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-39462
in-theory        39462
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-540 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-39462.        ((A or (B -> (C or B))) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-540, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-39463
in-theory        39463
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-540 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-39463.        ((A or (B -> (C or B))) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-540, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-39464
in-theory        39464
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-540 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-39464.        ((A or (B -> (C or B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-540, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-39465
in-theory        39465
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-39465.        ((A or (B -> (C or B))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-540, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-39466
in-theory        39466
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-540 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-39466.        ((A or (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-540, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-39467
in-theory        39467
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-540 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-39467.        ((A or (B -> (C or B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-540, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-39468
in-theory        39468
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-540 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-39468.        ((A or (B -> (C or B))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-540, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-39469
in-theory        39469
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-39469.        ((A or (B -> (C or B))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-540, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-39470
in-theory        39470
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-540 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-39470.        ((A or (B -> (C or B))) and ((D -> (not (E -> D))) -> (not D))), M:tm-540, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-39471
in-theory        39471
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-39471.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-540, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-39472
in-theory        39472
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-540 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-39472.        ((A or (B -> (C or B))) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-540, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-39473
in-theory        39473
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-540 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-39473.        ((A or (B -> (C or B))) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-540, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-39474
in-theory        39474
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-39474.        ((A or (B -> (C or B))) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-540, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-39475
in-theory        39475
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-540 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-39475.        ((A or (B -> (C or B))) and ((D -> (not (D or E))) -> (not D))), M:tm-540, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-39476
in-theory        39476
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-540 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-39476.        ((A or (B -> (C or B))) and ((D -> (not (E or D))) -> (not D))), M:tm-540, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-39477
in-theory        39477
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-540 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-39477.        ((A or (B -> (C or B))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-540, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-39478
in-theory        39478
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-540 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-39478.        ((A or (B -> (C or B))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-540, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-39479
in-theory        39479
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-540 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-39479.        ((A or (B -> (C or B))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-540, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-39480
in-theory        39480
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-39480.        ((A or (B -> (C or B))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-540, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-39481
in-theory        39481
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-540 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-39481.        ((A or (B -> (C or B))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-540, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-39482
in-theory        39482
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-540 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-39482.        ((A or (B -> (C or B))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-540, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-39483
in-theory        39483
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-540 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-39483.        ((A or (B -> (C or B))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-540, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-39484
in-theory        39484
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-39484.        ((A or (B -> (C or B))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-540, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-39485
in-theory        39485
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-540 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-7 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-39485.        ((A or (B -> (C or B))) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-540, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-39486
in-theory        39486
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-540 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-39486.        ((A or (B -> (C or B))) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-540, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-39487
in-theory        39487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-540 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-39487.        ((A or (B -> (C or B))) and (D or ((not (not E)) -> E))), M:tm-540, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-39488
in-theory        39488
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-540 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-39488.        ((A or (B -> (C or B))) and (((not (not D)) -> D) or E)), M:tm-540, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-39489
in-theory        39489
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-540 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-39489.        ((A or (B -> (C or B))) and (D -> (((not (not E)) -> E) and D))), M:tm-540, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-39490
in-theory        39490
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-540 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-39490.        ((A or (B -> (C or B))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-540, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-39491
in-theory        39491
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-540 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-39491.        ((A or (B -> (C or B))) and (D -> ((not (not E)) -> E))), M:tm-540, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-39492
in-theory        39492
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-39492.        ((A or (B -> (C or B))) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-540, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-39493
in-theory        39493
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-540 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-39493.        ((A or (B -> (C or B))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-540, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-39494
in-theory        39494
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-39494.        ((A or (B -> (C or B))) and (D or (E -> (F -> (G -> F))))), M:tm-540, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-39495
in-theory        39495
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-39495.        ((A or (B -> (C or B))) and ((D -> (E -> (F -> E))) or G)), M:tm-540, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-39496
in-theory        39496
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-39496.        ((A or (B -> (C or B))) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-540, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-39497
in-theory        39497
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-540 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-39497.        ((A or (B -> (C or B))) and ((D -> E) -> (D -> (F -> E)))), M:tm-540, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-39498
in-theory        39498
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-39498.        ((A or (B -> (C or B))) and (D -> (E -> (F -> (G -> F))))), M:tm-540, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-39499
in-theory        39499
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-540 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-39499.        ((A or (B -> (C or B))) and (D -> D)), M:tm-540, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-39500
in-theory        39500
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-39500.        ((A or (B -> (C or B))) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-540, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-39501
in-theory        39501
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-540 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-39501.        ((A or (B -> (C or B))) and ((D and E) -> (D and E))), M:tm-540, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-39502
in-theory        39502
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-540 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-39502.        ((A or (B -> (C or B))) and ((D -> E) -> (D -> E))), M:tm-540, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-39503
in-theory        39503
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-540 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-39503.        ((A or (B -> (C or B))) and ((not (not D)) -> (not (not D)))), M:tm-540, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-39504
in-theory        39504
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-540 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-39504.        ((A or (B -> (C or B))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-540, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-39505
in-theory        39505
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-540 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-39505.        ((A or (B -> (C or B))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-540, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-39506
in-theory        39506
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-540 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-39506.        ((A or (B -> (C or B))) and (D or ((E -> F) -> (E -> E)))), M:tm-540, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-39507
in-theory        39507
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-540 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-39507.        ((A or (B -> (C or B))) and (((D -> E) -> (D -> D)) or F)), M:tm-540, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-39508
in-theory        39508
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-39508.        ((A or (B -> (C or B))) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-540, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-39509
in-theory        39509
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-39509.        ((A or (B -> (C or B))) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-540, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-39510
in-theory        39510
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-540 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-39510.        ((A or (B -> (C or B))) and (D -> ((E -> F) -> (E -> E)))), M:tm-540, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-39511
in-theory        39511
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-39511.        ((A or (B -> (C or B))) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-540, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-39512
in-theory        39512
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-540 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-39512.        ((A or (B -> (C or B))) and ((D -> (D -> E)) -> (D -> E))), M:tm-540, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-39513
in-theory        39513
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-540 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-39513.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-540, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-39514
in-theory        39514
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-540 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-39514.        ((A or (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-540, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-39515
in-theory        39515
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-540 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-39515.        ((A or (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-540, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-39516
in-theory        39516
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-39516.        ((A or (B -> (C or B))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-540, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-39517
in-theory        39517
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-540 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-39517.        ((A or (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-540, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-39518
in-theory        39518
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-540 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-39518.        ((A or (B -> (C or B))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-540, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-39519
in-theory        39519
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-540 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-39519.        ((A or (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-540, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-39520
in-theory        39520
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-39520.        ((A or (B -> (C or B))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-540, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-39521
in-theory        39521
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-540 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-39521.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-540, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-39522
in-theory        39522
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-540 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-39522.        ((A or (B -> (C or B))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-540, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-39523
in-theory        39523
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-540 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-39523.        ((A or (B -> (C or B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-540, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-39524
in-theory        39524
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-540 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39524.        ((A or (B -> (C or B))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-540, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-39525
in-theory        39525
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-540 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39525.        ((A or (B -> (C or B))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-540, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-39526
in-theory        39526
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-540 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39526.        ((A or (B -> (C or B))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-540, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-39527
in-theory        39527
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-540 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-39527.        ((A or (B -> (C or B))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-540, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-39528
in-theory        39528
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-540 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39528.        ((A or (B -> (C or B))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-540, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-39529
in-theory        39529
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-540 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-39529.        ((A or (B -> (C or B))) and (((D -> E) and D) -> E)), M:tm-540, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-39530
in-theory        39530
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-540 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-39530.        ((A or (B -> (C or B))) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-540, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-39531
in-theory        39531
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-540 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-39531.        ((A or (B -> (C or B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-540, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-39532
in-theory        39532
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-540 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-39532.        ((A or (B -> (C or B))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-540, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-39533
in-theory        39533
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-540 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-39533.        ((A or (B -> (C or B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-540, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-39534
in-theory        39534
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-540 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-39534.        ((A or (B -> (C or B))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-540, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-39535
in-theory        39535
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-540 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-39535.        ((A or (B -> (C or B))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-540, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-39536
in-theory        39536
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-540 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-39536.        ((A or (B -> (C or B))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-540, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-39537
in-theory        39537
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-540 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-39537.        ((A or (B -> (C or B))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-540, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-39538
in-theory        39538
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-540 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-39538.        ((A or (B -> (C or B))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-540, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-39539
in-theory        39539
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-540 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-39539.        ((A or (B -> (C or B))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-540, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-39540
in-theory        39540
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-540 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-39540.        ((A or (B -> (C or B))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-540, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-39541
in-theory        39541
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-540 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-39541.        ((A or (B -> (C or B))) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-540, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-39542
in-theory        39542
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-540 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-39542.        ((A or (B -> (C or B))) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-540, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-39543
in-theory        39543
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-39543.        ((A or (B -> (C or B))) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-540, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-39544
in-theory        39544
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-540 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-39544.        ((A or (B -> (C or B))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-540, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-39545
in-theory        39545
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-540 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-39545.        ((A or (B -> (C or B))) and (D or (E -> ((F and G) -> F)))), M:tm-540, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-39546
in-theory        39546
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-39546.        ((A or (B -> (C or B))) and ((D -> ((E and F) -> E)) or G)), M:tm-540, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-39547
in-theory        39547
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-39547.        ((A or (B -> (C or B))) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-540, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-39548
in-theory        39548
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-540 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-39548.        ((A or (B -> (C or B))) and ((D -> (E and F)) -> (D -> E))), M:tm-540, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-39549
in-theory        39549
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-540 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-39549.        ((A or (B -> (C or B))) and (D -> (E -> ((F and G) -> F)))), M:tm-540, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-39550
in-theory        39550
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-540 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-39550.        ((A or (B -> (C or B))) and ((D and (D -> E)) -> E)), M:tm-540, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-39551
in-theory        39551
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-540 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-39551.        ((A or (B -> (C or B))) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-540, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-39552
in-theory        39552
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-540 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-39552.        ((A or (B -> (C or B))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-540, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-39553
in-theory        39553
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-540 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-39553.        ((A or (B -> (C or B))) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-540, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-39554
in-theory        39554
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-540 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-39554.        ((A or (B -> (C or B))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-540, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-39555
in-theory        39555
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-540 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-39555.        ((A or (B -> (C or B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-540, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-39556
in-theory        39556
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-540 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-39556.        ((A or (B -> (C or B))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-540, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-39557
in-theory        39557
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-540 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-39557.        ((A or (B -> (C or B))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-540, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-39558
in-theory        39558
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-540 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-39558.        ((A or (B -> (C or B))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-540, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-39559
in-theory        39559
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-540 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-39559.        ((A or (B -> (C or B))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-540, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-39560
in-theory        39560
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-540 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-39560.        ((A or (B -> (C or B))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-540, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-39561
in-theory        39561
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-540 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-39561.        ((A or (B -> (C or B))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-540, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-39562
in-theory        39562
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-540 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-39562.        ((A or (B -> (C or B))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-540, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-39563
in-theory        39563
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-540 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-39563.        ((A or (B -> (C or B))) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-540, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-39564
in-theory        39564
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-540 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-39564.        ((A or (B -> (C or B))) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-540, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-39565
in-theory        39565
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-540 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-39565.        ((A or (B -> (C or B))) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-540, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-39566
in-theory        39566
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-39566.        ((A or (B -> (C or B))) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-540, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-39567
in-theory        39567
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-540 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-39567.        ((A or (B -> (C or B))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-540, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-39568
in-theory        39568
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-540 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-39568.        ((A or (B -> (C or B))) and (D or (E -> ((F and G) -> G)))), M:tm-540, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-39569
in-theory        39569
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-39569.        ((A or (B -> (C or B))) and ((D -> ((E and F) -> F)) or G)), M:tm-540, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-39570
in-theory        39570
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-39570.        ((A or (B -> (C or B))) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-540, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-39571
in-theory        39571
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-540 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-39571.        ((A or (B -> (C or B))) and ((D -> (E and F)) -> (D -> F))), M:tm-540, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-39572
in-theory        39572
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-540 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-39572.        ((A or (B -> (C or B))) and (D -> (E -> ((F and G) -> G)))), M:tm-540, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-39573
in-theory        39573
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-39573.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-540, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-39574
in-theory        39574
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-39574.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-540, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-39575
in-theory        39575
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-39575.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-540, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-39576
in-theory        39576
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-540 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-39576.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-540, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-39577
in-theory        39577
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-39577.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-540, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-39578
in-theory        39578
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-540 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39578.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-540, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-39579
in-theory        39579
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39579.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-540, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-39580
in-theory        39580
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-39580.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-540, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-39581
in-theory        39581
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-540 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-39581.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-540, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-39582
in-theory        39582
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-39582.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-540, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-39583
in-theory        39583
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-39583.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-540, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-39584
in-theory        39584
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-39584.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-540, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-39585
in-theory        39585
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-540 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-39585.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-540, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-39586
in-theory        39586
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39586.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-540, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-39587
in-theory        39587
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-540 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-39587.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-540, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-39588
in-theory        39588
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-540 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-39588.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-540, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-39589
in-theory        39589
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-540 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-39589.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-540, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-39590
in-theory        39590
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-540 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-39590.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-540, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-39591
in-theory        39591
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-39591.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-540, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-39592
in-theory        39592
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-39592.        ((A or (B -> (C or B))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-540, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-39593
in-theory        39593
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-540 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-39593.        ((A or (B -> (C or B))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-540, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-39594
in-theory        39594
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-540 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-39594.        ((A or (B -> (C or B))) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-540, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-39595
in-theory        39595
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-540 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-39595.        ((A or (B -> (C or B))) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-540, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-39596
in-theory        39596
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-39596.        ((A or (B -> (C or B))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-540, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-39597
in-theory        39597
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-540 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-39597.        ((A or (B -> (C or B))) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-540, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-39598
in-theory        39598
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-540 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-39598.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-540, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-39599
in-theory        39599
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-39599.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-540, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-39600
in-theory        39600
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-540 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-39600.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-540, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-39601
in-theory        39601
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-540 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-39601.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-540, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-39602
in-theory        39602
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-39602.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-540, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-39603
in-theory        39603
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39603.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-540, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-39604
in-theory        39604
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-540 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39604.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-540, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-39605
in-theory        39605
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-39605.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-540, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-39606
in-theory        39606
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-540 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-39606.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-540, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-39607
in-theory        39607
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-540 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-39607.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-540, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-39608
in-theory        39608
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-39608.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-540, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-39609
in-theory        39609
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-540 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-39609.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-540, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-39610
in-theory        39610
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-540 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-39610.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-540, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-39611
in-theory        39611
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-540 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39611.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-540, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-39612
in-theory        39612
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-540 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-39612.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-540, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-39613
in-theory        39613
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-540 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-39613.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-540, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-39614
in-theory        39614
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-540 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-39614.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-540, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-39615
in-theory        39615
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-540 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-39615.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-540, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-39616
in-theory        39616
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-540 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-39616.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-540, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-39617
in-theory        39617
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-540 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-39617.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-540, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-39618
in-theory        39618
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-540 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-39618.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-540, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-39619
in-theory        39619
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-540 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-39619.        ((A or (B -> (C or B))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-540, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-39620
in-theory        39620
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-540 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-39620.        ((A or (B -> (C or B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-540, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-39621
in-theory        39621
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-540 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-39621.        ((A or (B -> (C or B))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-540, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-39622
in-theory        39622
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-540 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-39622.        ((A or (B -> (C or B))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-540, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-39623
in-theory        39623
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-540 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-39623.        ((A or (B -> (C or B))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-540, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-39624
in-theory        39624
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-540 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-39624.        ((A or (B -> (C or B))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-540, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-39625
in-theory        39625
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-39625.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-540, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-39626
in-theory        39626
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-39626.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-540, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-39627
in-theory        39627
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-39627.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((F and G) -> F))), M:tm-540, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-39628
in-theory        39628
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-540 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-39628.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((F and G) -> G))), M:tm-540, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-39629
in-theory        39629
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-39629.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-540, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-39630
in-theory        39630
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-540 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39630.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (F or G)))), M:tm-540, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-39631
in-theory        39631
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39631.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (G or F)))), M:tm-540, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-39632
in-theory        39632
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-39632.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-540, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-39633
in-theory        39633
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-540 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-39633.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-540, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-39634
in-theory        39634
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-39634.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-540, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-39635
in-theory        39635
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-39635.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-540, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-39636
in-theory        39636
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-39636.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-540, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-39637
in-theory        39637
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-540 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-39637.        ((A or (B -> (C or B))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-540, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-39638
in-theory        39638
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39638.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-540, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-39639
in-theory        39639
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-540 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-39639.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-540, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-39640
in-theory        39640
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-540 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-39640.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-540, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-39641
in-theory        39641
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-540 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-39641.        ((A or (B -> (C or B))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-540, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-39642
in-theory        39642
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-540 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-39642.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-540, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-39643
in-theory        39643
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-39643.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-540, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-39644
in-theory        39644
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-540 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-39644.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-540, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-39645
in-theory        39645
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-39645.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-540, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-39646
in-theory        39646
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-540 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-39646.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-540, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-39647
in-theory        39647
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-39647.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-540, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-39648
in-theory        39648
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-39648.        ((A or (B -> (C or B))) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-540, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-39649
in-theory        39649
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-540 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-39649.        ((A or (B -> (C or B))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-540, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-39650
in-theory        39650
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-540 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-39650.        ((A or (B -> (C or B))) and (D or (E -> (((F and G) -> F) and E)))), M:tm-540, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-39651
in-theory        39651
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-540 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-39651.        ((A or (B -> (C or B))) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-540, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-39652
in-theory        39652
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-39652.        ((A or (B -> (C or B))) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-540, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-39653
in-theory        39653
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-540 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-39653.        ((A or (B -> (C or B))) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-540, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-39654
in-theory        39654
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-39654.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-540, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-39655
in-theory        39655
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-39655.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-540, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-39656
in-theory        39656
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-39656.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((F and G) -> F))), M:tm-540, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-39657
in-theory        39657
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-540 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-39657.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((F and G) -> G))), M:tm-540, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-39658
in-theory        39658
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-39658.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-540, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-39659
in-theory        39659
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-540 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39659.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (F or G)))), M:tm-540, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-39660
in-theory        39660
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39660.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (G or F)))), M:tm-540, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-39661
in-theory        39661
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-39661.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-540, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-39662
in-theory        39662
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-540 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-39662.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-540, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-39663
in-theory        39663
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-39663.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-540, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-39664
in-theory        39664
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-39664.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-540, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-39665
in-theory        39665
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-39665.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-540, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-39666
in-theory        39666
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-540 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-39666.        ((A or (B -> (C or B))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-540, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-39667
in-theory        39667
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39667.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-540, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-39668
in-theory        39668
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-540 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-39668.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-540, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-39669
in-theory        39669
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-540 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-39669.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-540, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-39670
in-theory        39670
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-540 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-39670.        ((A or (B -> (C or B))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-540, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-39671
in-theory        39671
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-540 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-39671.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-540, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-39672
in-theory        39672
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-39672.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-540, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-39673
in-theory        39673
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-540 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-39673.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-540, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-39674
in-theory        39674
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-39674.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-540, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-39675
in-theory        39675
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-39675.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-540, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-39676
in-theory        39676
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-39676.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-540, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-39677
in-theory        39677
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-540 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-39677.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-540, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-39678
in-theory        39678
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-39678.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-540, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-39679
in-theory        39679
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-39679.        ((A or (B -> (C or B))) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-540, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-39680
in-theory        39680
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-540 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-39680.        ((A or (B -> (C or B))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-540, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-39681
in-theory        39681
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-540 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-39681.        ((A or (B -> (C or B))) and (D or (E -> (((F and G) -> G) and E)))), M:tm-540, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-39682
in-theory        39682
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-540 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-39682.        ((A or (B -> (C or B))) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-540, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-39683
in-theory        39683
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-39683.        ((A or (B -> (C or B))) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-540, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-39684
in-theory        39684
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-540 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-39684.        ((A or (B -> (C or B))) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-540, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-39685
in-theory        39685
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-39685.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-540, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-39686
in-theory        39686
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-39686.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-540, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-39687
in-theory        39687
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-540 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-39687.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-540, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-39688
in-theory        39688
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-540 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-39688.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-540, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-39689
in-theory        39689
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-39689.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-540, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-39690
in-theory        39690
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-540 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39690.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-540, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-39691
in-theory        39691
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39691.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-540, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-39692
in-theory        39692
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-39692.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-540, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-39693
in-theory        39693
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-39693.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-540, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-39694
in-theory        39694
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-540 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-39694.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-540, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-39695
in-theory        39695
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-39695.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-540, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-39696
in-theory        39696
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-39696.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-540, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-39697
in-theory        39697
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-39697.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-540, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-39698
in-theory        39698
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-540 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39698.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-540, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-39699
in-theory        39699
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-540 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-39699.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-540, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-39700
in-theory        39700
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-540 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-39700.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-540, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-39701
in-theory        39701
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-540 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-39701.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-540, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-39702
in-theory        39702
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-540 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-39702.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-540, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-39703
in-theory        39703
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-540 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-39703.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-540, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-39704
in-theory        39704
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-540 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-39704.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-540, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-39705
in-theory        39705
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-540 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-39705.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-540, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-39706
in-theory        39706
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-540 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-39706.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-540, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-39707
in-theory        39707
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-540 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-39707.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-540, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-39708
in-theory        39708
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-540 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-39708.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-540, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-39709
in-theory        39709
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-540 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-39709.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-540, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-39710
in-theory        39710
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-540 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-39710.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-540, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-39711
in-theory        39711
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-540 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-39711.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-540, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-39712
in-theory        39712
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-540 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-39712.        ((A or (B -> (C or B))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-540, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-39713
in-theory        39713
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-540 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-39713.        ((A or (B -> (C or B))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-540, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-39714
in-theory        39714
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-540 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-39714.        ((A or (B -> (C or B))) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-540, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-39715
in-theory        39715
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-540 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-39715.        ((A or (B -> (C or B))) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-540, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-39716
in-theory        39716
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-540 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-39716.        ((A or (B -> (C or B))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-540, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-39717
in-theory        39717
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-540 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-39717.        ((A or (B -> (C or B))) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-540, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-39718
in-theory        39718
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-540 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-39718.        ((A or (B -> (C or B))) and (D -> (D and (E -> D)))), M:tm-540, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-39719
in-theory        39719
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-39719.        ((A or (B -> (C or B))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-540, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-39720
in-theory        39720
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-540 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-39720.        ((A or (B -> (C or B))) and ((D and E) -> ((D and E) and D))), M:tm-540, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-39721
in-theory        39721
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-540 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-39721.        ((A or (B -> (C or B))) and ((D and E) -> ((D and E) and E))), M:tm-540, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-39722
in-theory        39722
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-39722.        ((A or (B -> (C or B))) and (D -> (D and (E -> (D and E))))), M:tm-540, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-39723
in-theory        39723
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-540 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-39723.        ((A or (B -> (C or B))) and (D -> (D and (D or E)))), M:tm-540, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-39724
in-theory        39724
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-540 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-39724.        ((A or (B -> (C or B))) and (D -> (D and (E or D)))), M:tm-540, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-39725
in-theory        39725
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-540 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-39725.        ((A or (B -> (C or B))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-540, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-39726
in-theory        39726
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-39726.        ((A or (B -> (C or B))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-540, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-39727
in-theory        39727
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-540 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-39727.        ((A or (B -> (C or B))) and ((not (not D)) -> ((not (not D)) and D))), M:tm-540, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-39728
in-theory        39728
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-39728.        ((A or (B -> (C or B))) and (D -> (D and (E -> (F -> E))))), M:tm-540, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-39729
in-theory        39729
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-540 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-39729.        ((A or (B -> (C or B))) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-540, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-39730
in-theory        39730
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-540 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-39730.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-540, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-39731
in-theory        39731
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-540 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-39731.        ((A or (B -> (C or B))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-540, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-39732
in-theory        39732
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-540 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-39732.        ((A or (B -> (C or B))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-540, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-39733
in-theory        39733
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-540 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-39733.        ((A or (B -> (C or B))) and (D -> (D and ((E and F) -> E)))), M:tm-540, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-39734
in-theory        39734
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-540 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-39734.        ((A or (B -> (C or B))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-540, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-39735
in-theory        39735
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-540 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-39735.        ((A or (B -> (C or B))) and (D -> (D and ((E and F) -> F)))), M:tm-540, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-39736
in-theory        39736
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-540 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-39736.        ((A or (B -> (C or B))) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-540, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-39737
in-theory        39737
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-540 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-39737.        ((A or (B -> (C or B))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-540, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-39738
in-theory        39738
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-540 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-39738.        ((A or (B -> (C or B))) and (D -> (D and (((E and F) -> E) and D)))), M:tm-540, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-39739
in-theory        39739
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-540 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-39739.        ((A or (B -> (C or B))) and (D -> (D and (((E and F) -> F) and D)))), M:tm-540, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-39740
in-theory        39740
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-540 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-39740.        ((A or (B -> (C or B))) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-540, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-39741
in-theory        39741
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-39741.        ((A or (B -> (C or B))) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-540, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-39742
in-theory        39742
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-540 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-39742.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-540, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-39743
in-theory        39743
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-39743.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-540, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-39744
in-theory        39744
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-39744.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-540, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-39745
in-theory        39745
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-540 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-39745.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-540, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-39746
in-theory        39746
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-39746.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-540, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-39747
in-theory        39747
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-540 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-39747.        ((A or (B -> (C or B))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-540, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-39748
in-theory        39748
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-540 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-39748.        ((A or (B -> (C or B))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-540, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-39749
in-theory        39749
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-540 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-39749.        ((A or (B -> (C or B))) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-540, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-39750
in-theory        39750
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-540 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-39750.        ((A or (B -> (C or B))) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-540, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-39751
in-theory        39751
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-39751.        ((A or (B -> (C or B))) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-540, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-39752
in-theory        39752
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-540 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-39752.        ((A or (B -> (C or B))) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-540, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-39753
in-theory        39753
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-540 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-39753.        ((A or (B -> (C or B))) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-540, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-39754
in-theory        39754
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-540 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-39754.        ((A or (B -> (C or B))) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-540, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-39755
in-theory        39755
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-540 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39755.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-540, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-39756
in-theory        39756
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-540 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39756.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-540, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-39757
in-theory        39757
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-540 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39757.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-540, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-39758
in-theory        39758
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-540 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39758.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-540, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-39759
in-theory        39759
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-540 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39759.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-540, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-39760
in-theory        39760
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-540 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-39760.        ((A or (B -> (C or B))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-540, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-39761
in-theory        39761
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-540 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-39761.        ((A or (B -> (C or B))) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-540, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-39762
in-theory        39762
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-540 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-39762.        ((A or (B -> (C or B))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-540, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-39763
in-theory        39763
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-39763.        ((A or (B -> (C or B))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-540, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-39764
in-theory        39764
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-540 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-39764.        ((A or (B -> (C or B))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-540, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-39765
in-theory        39765
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-540 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39765.        ((A or (B -> (C or B))) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-540, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-39766
in-theory        39766
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-540 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39766.        ((A or (B -> (C or B))) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-540, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-39767
in-theory        39767
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39767.        ((A or (B -> (C or B))) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-540, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-39768
in-theory        39768
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-540 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-39768.        ((A or (B -> (C or B))) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-540, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-39769
in-theory        39769
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-540 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39769.        ((A or (B -> (C or B))) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-540, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-39770
in-theory        39770
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-540 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-39770.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-540, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-39771
in-theory        39771
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-39771.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-540, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-39772
in-theory        39772
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-39772.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-540, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-39773
in-theory        39773
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-39773.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-540, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-39774
in-theory        39774
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-39774.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-540, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-39775
in-theory        39775
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-540 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-39775.        ((A or (B -> (C or B))) and (D or ((E -> (F -> E)) or G))), M:tm-540, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-39776
in-theory        39776
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-39776.        ((A or (B -> (C or B))) and (((D -> (E -> D)) or F) or G)), M:tm-540, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-39777
in-theory        39777
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-39777.        ((A or (B -> (C or B))) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-540, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-39778
in-theory        39778
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-540 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-39778.        ((A or (B -> (C or B))) and (D -> ((E -> (F -> E)) or G))), M:tm-540, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-39779
in-theory        39779
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-540 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-39779.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-540, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-39780
in-theory        39780
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-39780.        ((A or (B -> (C or B))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-540, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-39781
in-theory        39781
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-39781.        ((A or (B -> (C or B))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-540, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-39782
in-theory        39782
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-540 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-39782.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-540, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-39783
in-theory        39783
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-39783.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-540, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-39784
in-theory        39784
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-540 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-39784.        ((A or (B -> (C or B))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-540, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-39785
in-theory        39785
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-540 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-39785.        ((A or (B -> (C or B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-540, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-39786
in-theory        39786
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-540 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-39786.        ((A or (B -> (C or B))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-540, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-39787
in-theory        39787
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-540 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-39787.        ((A or (B -> (C or B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-540, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-39788
in-theory        39788
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-540 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-39788.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-540, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-39789
in-theory        39789
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-39789.        ((A or (B -> (C or B))) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-540, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-39790
in-theory        39790
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-39790.        ((A or (B -> (C or B))) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-540, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-39791
in-theory        39791
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-39791.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-540, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-39792
in-theory        39792
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-39792.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-540, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-39793
in-theory        39793
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-540 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-39793.        ((A or (B -> (C or B))) and (D or (((E and F) -> E) or G))), M:tm-540, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-39794
in-theory        39794
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-39794.        ((A or (B -> (C or B))) and ((((D and E) -> D) or F) or G)), M:tm-540, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-39795
in-theory        39795
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-39795.        ((A or (B -> (C or B))) and (D -> ((((E and F) -> E) or G) and D))), M:tm-540, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-39796
in-theory        39796
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-540 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-39796.        ((A or (B -> (C or B))) and (D -> (((E and F) -> E) or G))), M:tm-540, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-39797
in-theory        39797
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-540 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-39797.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-540, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-39798
in-theory        39798
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-39798.        ((A or (B -> (C or B))) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-540, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-39799
in-theory        39799
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-39799.        ((A or (B -> (C or B))) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-540, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-39800
in-theory        39800
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-39800.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-540, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-39801
in-theory        39801
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-39801.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-540, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-39802
in-theory        39802
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-540 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-39802.        ((A or (B -> (C or B))) and (D or (((E and F) -> F) or G))), M:tm-540, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-39803
in-theory        39803
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-39803.        ((A or (B -> (C or B))) and ((((D and E) -> E) or F) or G)), M:tm-540, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-39804
in-theory        39804
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-39804.        ((A or (B -> (C or B))) and (D -> ((((E and F) -> F) or G) and D))), M:tm-540, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-39805
in-theory        39805
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-540 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-39805.        ((A or (B -> (C or B))) and (D -> (((E and F) -> F) or G))), M:tm-540, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-39806
in-theory        39806
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-540 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-39806.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-540, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-39807
in-theory        39807
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-540 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-39807.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-540, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-39808
in-theory        39808
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-540 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-39808.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-540, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-39809
in-theory        39809
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-540 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-39809.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-540, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-39810
in-theory        39810
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-540 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-39810.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-540, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-39811
in-theory        39811
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-540 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-39811.        ((A or (B -> (C or B))) and (D or ((E -> (F -> (E and F))) or G))), M:tm-540, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-39812
in-theory        39812
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-540 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-39812.        ((A or (B -> (C or B))) and (((D -> (E -> (D and E))) or F) or G)), M:tm-540, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-39813
in-theory        39813
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-39813.        ((A or (B -> (C or B))) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-540, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-39814
in-theory        39814
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-540 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-39814.        ((A or (B -> (C or B))) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-540, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-39815
in-theory        39815
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-540 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-39815.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-540, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-39816
in-theory        39816
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-39816.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-540, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-39817
in-theory        39817
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-39817.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-540, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-39818
in-theory        39818
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-39818.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-540, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-39819
in-theory        39819
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-39819.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-540, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-39820
in-theory        39820
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-540 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-39820.        ((A or (B -> (C or B))) and (D or ((E -> (E or F)) or G))), M:tm-540, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-39821
in-theory        39821
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-39821.        ((A or (B -> (C or B))) and (((D -> (D or E)) or F) or G)), M:tm-540, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-39822
in-theory        39822
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-39822.        ((A or (B -> (C or B))) and (D -> (((E -> (E or F)) or G) and D))), M:tm-540, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-39823
in-theory        39823
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-540 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-39823.        ((A or (B -> (C or B))) and (D -> ((E -> (E or F)) or G))), M:tm-540, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-39824
in-theory        39824
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-39824.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-540, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-39825
in-theory        39825
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-39825.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-540, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-39826
in-theory        39826
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-39826.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-540, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-39827
in-theory        39827
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-540 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-39827.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-540, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-39828
in-theory        39828
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-39828.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-540, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-39829
in-theory        39829
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-540 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39829.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-540, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-39830
in-theory        39830
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39830.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-540, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-39831
in-theory        39831
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-39831.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-540, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-39832
in-theory        39832
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-540 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-39832.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-540, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-39833
in-theory        39833
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-39833.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-540, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-39834
in-theory        39834
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-39834.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-540, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-39835
in-theory        39835
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-39835.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-540, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-39836
in-theory        39836
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-540 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-39836.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-540, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-39837
in-theory        39837
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39837.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-540, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-39838
in-theory        39838
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-540 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-39838.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-540, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-39839
in-theory        39839
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-540 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-39839.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-540, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-39840
in-theory        39840
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-540 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-39840.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-540, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-39841
in-theory        39841
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-540 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-39841.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-540, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-39842
in-theory        39842
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-39842.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-540, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-39843
in-theory        39843
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-540 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-39843.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-540, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-39844
in-theory        39844
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-39844.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-540, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-39845
in-theory        39845
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-39845.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-540, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-39846
in-theory        39846
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-540 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-39846.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-540, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-39847
in-theory        39847
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-39847.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-540, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-39848
in-theory        39848
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-540 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39848.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-540, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-39849
in-theory        39849
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-39849.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-540, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-39850
in-theory        39850
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-39850.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-540, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-39851
in-theory        39851
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-39851.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-540, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-39852
in-theory        39852
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-39852.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-540, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-39853
in-theory        39853
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-540 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-39853.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-540, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-39854
in-theory        39854
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-39854.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-540, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-39855
in-theory        39855
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-39855.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-540, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-39856
in-theory        39856
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-540 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-39856.        ((A or (B -> (C or B))) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-540, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-39857
in-theory        39857
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-540 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-39857.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-540, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-39858
in-theory        39858
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-39858.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-540, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-39859
in-theory        39859
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-39859.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-540, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-39860
in-theory        39860
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-540 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-39860.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-540, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-39861
in-theory        39861
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-39861.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-540, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-39862
in-theory        39862
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-39862.        ((A or (B -> (C or B))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-540, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-39863
in-theory        39863
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-540 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-39863.        ((A or (B -> (C or B))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-540, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-39864
in-theory        39864
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-540 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-39864.        ((A or (B -> (C or B))) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-540, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-39865
in-theory        39865
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-540 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-39865.        ((A or (B -> (C or B))) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-540, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-39866
in-theory        39866
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-39866.        ((A or (B -> (C or B))) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-540, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-39867
in-theory        39867
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-540 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-39867.        ((A or (B -> (C or B))) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-540, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-39868
in-theory        39868
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-39868.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-540, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-39869
in-theory        39869
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-39869.        ((A or (B -> (C or B))) and (D -> (D and (E -> (E or F))))), M:tm-540, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-39870
in-theory        39870
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-39870.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-540, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-39871
in-theory        39871
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-39871.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-540, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-39872
in-theory        39872
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-39872.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-540, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-39873
in-theory        39873
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-39873.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-540, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-39874
in-theory        39874
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-39874.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-540, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-39875
in-theory        39875
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-540 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-39875.        ((A or (B -> (C or B))) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-540, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-39876
in-theory        39876
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-540 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-39876.        ((A or (B -> (C or B))) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-540, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-39877
in-theory        39877
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-39877.        ((A or (B -> (C or B))) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-540, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-39878
in-theory        39878
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-39878.        ((A or (B -> (C or B))) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-540, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-39879
in-theory        39879
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-540 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-39879.        ((A or (B -> (C or B))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-540, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-39880
in-theory        39880
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-39880.        ((A or (B -> (C or B))) and (D or (E -> (F -> (F or G))))), M:tm-540, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-39881
in-theory        39881
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-39881.        ((A or (B -> (C or B))) and ((D -> (E -> (E or F))) or G)), M:tm-540, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-39882
in-theory        39882
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-39882.        ((A or (B -> (C or B))) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-540, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-39883
in-theory        39883
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-540 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-39883.        ((A or (B -> (C or B))) and ((D -> E) -> (D -> (E or F)))), M:tm-540, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-39884
in-theory        39884
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-39884.        ((A or (B -> (C or B))) and (D -> (E -> (F -> (F or G))))), M:tm-540, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-39885
in-theory        39885
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-39885.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-540, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-39886
in-theory        39886
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-39886.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-540, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-39887
in-theory        39887
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-39887.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-540, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-39888
in-theory        39888
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-39888.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-540, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-39889
in-theory        39889
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-39889.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-540, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-39890
in-theory        39890
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-39890.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-540, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-39891
in-theory        39891
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-39891.        ((A or (B -> (C or B))) and (D or (E or (F -> (G -> F))))), M:tm-540, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-39892
in-theory        39892
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-39892.        ((A or (B -> (C or B))) and ((D or (E -> (F -> E))) or G)), M:tm-540, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-39893
in-theory        39893
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-39893.        ((A or (B -> (C or B))) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-540, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-39894
in-theory        39894
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-39894.        ((A or (B -> (C or B))) and (D -> (E or (F -> (G -> F))))), M:tm-540, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-39895
in-theory        39895
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39895.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-540, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-39896
in-theory        39896
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-540 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39896.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-540, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-39897
in-theory        39897
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39897.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-540, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-39898
in-theory        39898
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39898.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-540, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-39899
in-theory        39899
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-540 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39899.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-540, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-39900
in-theory        39900
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39900.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-540, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-39901
in-theory        39901
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-540 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39901.        ((A or (B -> (C or B))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-540, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-39902
in-theory        39902
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-540 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39902.        ((A or (B -> (C or B))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-540, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-39903
in-theory        39903
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-540 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39903.        ((A or (B -> (C or B))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-540, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-39904
in-theory        39904
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-540 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-39904.        ((A or (B -> (C or B))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-540, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-39905
in-theory        39905
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-540 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-39905.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-540, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-39906
in-theory        39906
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-540 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-39906.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-540, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-39907
in-theory        39907
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-540 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-39907.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-540, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-39908
in-theory        39908
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-540 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-39908.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-540, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-39909
in-theory        39909
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-540 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-39909.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-540, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-39910
in-theory        39910
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-540 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-39910.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-540, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-39911
in-theory        39911
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-540 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-39911.        ((A or (B -> (C or B))) and (D or (E or ((F and G) -> F)))), M:tm-540, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-39912
in-theory        39912
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-39912.        ((A or (B -> (C or B))) and ((D or ((E and F) -> E)) or G)), M:tm-540, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-39913
in-theory        39913
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-39913.        ((A or (B -> (C or B))) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-540, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-39914
in-theory        39914
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-540 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-39914.        ((A or (B -> (C or B))) and (D -> (E or ((F and G) -> F)))), M:tm-540, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-39915
in-theory        39915
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-540 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-39915.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-540, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-39916
in-theory        39916
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-540 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-39916.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-540, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-39917
in-theory        39917
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-540 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-39917.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-540, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-39918
in-theory        39918
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-540 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-39918.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-540, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-39919
in-theory        39919
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-540 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-39919.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-540, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-39920
in-theory        39920
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-540 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-39920.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-540, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-39921
in-theory        39921
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-540 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-39921.        ((A or (B -> (C or B))) and (D or (E or ((F and G) -> G)))), M:tm-540, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-39922
in-theory        39922
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-39922.        ((A or (B -> (C or B))) and ((D or ((E and F) -> F)) or G)), M:tm-540, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-39923
in-theory        39923
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-39923.        ((A or (B -> (C or B))) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-540, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-39924
in-theory        39924
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-540 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-39924.        ((A or (B -> (C or B))) and (D -> (E or ((F and G) -> G)))), M:tm-540, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-39925
in-theory        39925
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-540 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39925.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-540, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-39926
in-theory        39926
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-540 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39926.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-540, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-39927
in-theory        39927
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-540 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39927.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-540, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-39928
in-theory        39928
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-540 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39928.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-540, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-39929
in-theory        39929
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-540 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39929.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-540, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-39930
in-theory        39930
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-540 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39930.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-540, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-39931
in-theory        39931
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-540 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39931.        ((A or (B -> (C or B))) and (D or (E or (F -> (G -> (F and G)))))), M:tm-540, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-39932
in-theory        39932
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-540 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39932.        ((A or (B -> (C or B))) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-540, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-39933
in-theory        39933
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39933.        ((A or (B -> (C or B))) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-540, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-39934
in-theory        39934
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-540 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-39934.        ((A or (B -> (C or B))) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-540, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-39935
in-theory        39935
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-39935.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-540, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-39936
in-theory        39936
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-39936.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-540, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-39937
in-theory        39937
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-39937.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-540, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-39938
in-theory        39938
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-39938.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-540, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-39939
in-theory        39939
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-39939.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-540, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-39940
in-theory        39940
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-39940.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-540, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-39941
in-theory        39941
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-39941.        ((A or (B -> (C or B))) and (D or (E or (F -> (F or G))))), M:tm-540, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-39942
in-theory        39942
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-39942.        ((A or (B -> (C or B))) and ((D or (E -> (E or F))) or G)), M:tm-540, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-39943
in-theory        39943
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-39943.        ((A or (B -> (C or B))) and (D -> ((E or (F -> (F or G))) and D))), M:tm-540, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-39944
in-theory        39944
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-39944.        ((A or (B -> (C or B))) and (D -> (E or (F -> (F or G))))), M:tm-540, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-39945
in-theory        39945
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39945.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-540, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39946
in-theory        39946
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39946.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-540, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39947
in-theory        39947
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39947.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-540, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39948
in-theory        39948
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39948.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-540, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39949
in-theory        39949
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39949.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-540, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-39950
in-theory        39950
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39950.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-540, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-39951
in-theory        39951
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39951.        ((A or (B -> (C or B))) and (D or (E or (F -> (G or F))))), M:tm-540, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-39952
in-theory        39952
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39952.        ((A or (B -> (C or B))) and ((D or (E -> (F or E))) or G)), M:tm-540, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-39953
in-theory        39953
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39953.        ((A or (B -> (C or B))) and (D -> ((E or (F -> (G or F))) and D))), M:tm-540, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39954
in-theory        39954
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39954.        ((A or (B -> (B or C))) and (D -> ((E or (F -> (G or F))) and D))), M:tm-530, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39955
in-theory        39955
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39955.        ((A or (B -> (C -> (B and C)))) and (D -> ((E or (F -> (G or F))) and D))), M:tm-520, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39956
in-theory        39956
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39956.        ((A or ((B and C) -> C)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-510, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39957
in-theory        39957
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39957.        ((A or ((B and C) -> B)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-500, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39958
in-theory        39958
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (H or G))) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39958.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (H or G))) and E))), M:tm-490, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39959
in-theory        39959
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39959.        ((A or (B -> (C -> B))) and (D -> ((E or (F -> (G or F))) and D))), M:tm-480, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39960
in-theory        39960
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> (D or C))) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39960.        (A -> (((B or (C -> (D or C))) and A) or E)), M:tm-470, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-39961
in-theory        39961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39961.        ((A -> (B -> (B or C))) and (D -> ((E or (F -> (G or F))) and D))), M:tm-469, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39962
in-theory        39962
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D or (E -> (F or E))) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-540 ((Am (-> A (or A B))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39962.        ((A or (B -> (B or C))) -> ((D or (E -> (F or E))) and (B -> (B or C)))), M:tm-466, m:tm-540, u:((Am (-> A (or A B))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (or A B)))))
================================================================
tm-name          tm-39963
in-theory        39963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39963.        ((A -> ((B or (C -> (D or C))) and A)) and (E -> (E or F))), M:tm-456, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39964
in-theory        39964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39964.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-453, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39965
in-theory        39965
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D or (E -> (F or E))) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-540 ((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39965.        ((A or ((B -> (B or C)) and A)) -> ((D or (E -> (F or E))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-540, u:((Am (and (-> A (or A B)) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-39966
in-theory        39966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and ((E -> (E or F)) and (A -> ((B or (C -> (D or C))) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39966.        ((A -> ((B or (C -> (D or C))) and A)) and ((E -> (E or F)) and (A -> ((B or (C -> (D or C))) and A)))), M:tm-443, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39967
in-theory        39967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39967.        (((A -> (A or B)) or C) and (D -> ((E or (F -> (G or F))) and D))), M:tm-409, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39968
in-theory        39968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39968.        (((A -> (B -> (A and B))) or C) and (D -> ((E or (F -> (G or F))) and D))), M:tm-400, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39969
in-theory        39969
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39969.        ((((A and B) -> B) or C) and (D -> ((E or (F -> (G or F))) and D))), M:tm-391, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39970
in-theory        39970
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39970.        ((((A and B) -> A) or C) and (D -> ((E or (F -> (G or F))) and D))), M:tm-382, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39971
in-theory        39971
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or (G -> (H or G))) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39971.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F or (G -> (H or G))) and E))), M:tm-373, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39972
in-theory        39972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39972.        (((A -> (B -> A)) or C) and (D -> ((E or (F -> (G or F))) and D))), M:tm-364, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39973
in-theory        39973
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C or (D -> (E or D))) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39973.        (A -> (B -> (((C or (D -> (E or D))) and A) and B))), M:tm-355, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-39974
in-theory        39974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39974.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E or (F -> (G or F))) and D))), M:tm-354, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39975
in-theory        39975
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D or (E -> (F or E))) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-540 ((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39975.        ((A or (B -> (C -> (B and C)))) -> ((D or (E -> (F or E))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-540, u:((Am (-> A (-> B (and A B)))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-39976
in-theory        39976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39976.        ((A -> ((B or (C -> (D or C))) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39977
in-theory        39977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D or (E -> (F or E))) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39977.        (((A -> B) -> (A -> (A and B))) and (C -> ((D or (E -> (F or E))) and C))), M:tm-338, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39978
in-theory        39978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C or (D -> (E or D))) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-540 ((Am (-> A (and A B))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39978.        (((A -> B) or (A -> (A and B))) -> ((C or (D -> (E or D))) and (A -> (A and B)))), M:tm-335, m:tm-540, u:((Am (-> A (and A B))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (and A B)))))
================================================================
tm-name          tm-39979
in-theory        39979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and (A -> (A and ((B or (C -> (D or C))) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39979.        ((A -> ((B or (C -> (D or C))) and A)) and (A -> (A and ((B or (C -> (D or C))) and A)))), M:tm-328, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-39980
in-theory        39980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B or (C -> (D or C))) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39980.        ((A -> ((B or (C -> (D or C))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B or (C -> (D or C))) and A)))), M:tm-327, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39981
in-theory        39981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and (((E and F) -> F) and (A -> ((B or (C -> (D or C))) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39981.        ((A -> ((B or (C -> (D or C))) and A)) and (((E and F) -> F) and (A -> ((B or (C -> (D or C))) and A)))), M:tm-326, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39982
in-theory        39982
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and (((E and F) -> E) and (A -> ((B or (C -> (D or C))) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39982.        ((A -> ((B or (C -> (D or C))) and A)) and (((E and F) -> E) and (A -> ((B or (C -> (D or C))) and A)))), M:tm-325, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39983
in-theory        39983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B or (C -> (D or C))) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39983.        ((A -> ((B or (C -> (D or C))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B or (C -> (D or C))) and A)))), M:tm-324, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39984
in-theory        39984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and ((E -> (F -> E)) and (A -> ((B or (C -> (D or C))) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39984.        ((A -> ((B or (C -> (D or C))) and A)) and ((E -> (F -> E)) and (A -> ((B or (C -> (D or C))) and A)))), M:tm-323, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39985
in-theory        39985
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39985.        ((A -> ((B or (C -> (D or C))) and A)) and ((E and F) -> F)), M:tm-322, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39986
in-theory        39986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39986.        ((A -> ((B or (C -> (D or C))) and A)) and ((E and F) -> E)), M:tm-320, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39987
in-theory        39987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39987.        ((A -> ((B or (C -> (D or C))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39988
in-theory        39988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39988.        ((A -> ((B or (C -> (D or C))) and A)) and (A -> A)), M:tm-316, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-39989
in-theory        39989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39989.        ((A -> ((B or (C -> (D or C))) and A)) and (E -> (F -> E))), M:tm-315, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39990
in-theory        39990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and ((A -> (not ((B or (C -> (D or C))) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39990.        ((A -> ((B or (C -> (D or C))) and A)) and ((A -> (not ((B or (C -> (D or C))) and A))) -> (not A))), M:tm-313, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-39991
in-theory        39991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and ((((B or (C -> (D or C))) and A) -> E) -> ((A or ((B or (C -> (D or C))) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39991.        ((A -> ((B or (C -> (D or C))) and A)) and ((((B or (C -> (D or C))) and A) -> E) -> ((A or ((B or (C -> (D or C))) and A)) -> E))), M:tm-312, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-39992
in-theory        39992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and (E or (A -> ((B or (C -> (D or C))) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39992.        ((A -> ((B or (C -> (D or C))) and A)) and (E or (A -> ((B or (C -> (D or C))) and A)))), M:tm-311, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39993
in-theory        39993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and ((A -> ((B or (C -> (D or C))) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39993.        ((A -> ((B or (C -> (D or C))) and A)) and ((A -> ((B or (C -> (D or C))) and A)) or E)), M:tm-310, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39994
in-theory        39994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and (E -> ((A -> ((B or (C -> (D or C))) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39994.        ((A -> ((B or (C -> (D or C))) and A)) and (E -> ((A -> ((B or (C -> (D or C))) and A)) and E))), M:tm-309, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39995
in-theory        39995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and (E -> (A -> ((B or (C -> (D or C))) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39995.        ((A -> ((B or (C -> (D or C))) and A)) and (E -> (A -> ((B or (C -> (D or C))) and A)))), M:tm-305, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39996
in-theory        39996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39996.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-303, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39997
in-theory        39997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D or (E -> (F or E))) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-540 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39997.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D or (E -> (F or E))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-540, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-39998
in-theory        39998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39998.        ((A -> (((B and C) -> C) and A)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-270, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-39999
in-theory        39999
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D or (E -> (F or E))) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-540 ((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-39999.        ((A or (((B and C) -> C) and A)) -> ((D or (E -> (F or E))) and (((B and C) -> C) and A))), M:tm-267, m:tm-540, u:((Am (and (-> (and A B) B) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-40000
in-theory        40000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40000.        ((A -> (((B and C) -> B) and A)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-239, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40001
in-theory        40001
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D or (E -> (F or E))) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-540 ((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40001.        ((A or (((B and C) -> B) and A)) -> ((D or (E -> (F or E))) and (((B and C) -> B) and A))), M:tm-236, m:tm-540, u:((Am (and (-> (and A B) A) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-40002
in-theory        40002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or (G -> (H or G))) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40002.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F or (G -> (H or G))) and E))), M:tm-210, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40003
in-theory        40003
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or (F -> (G or F))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-540 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (or Dm Cm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40003.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E or (F -> (G or F))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-540, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (or Dm Cm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-40004
in-theory        40004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40004.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-183, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40005
in-theory        40005
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D or (E -> (F or E))) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-540 ((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40005.        ((A or ((B -> (C -> B)) and A)) -> ((D or (E -> (F or E))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-540, u:((Am (and (-> A (-> B A)) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-40006
in-theory        40006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40006.        ((A -> ((B and C) -> C)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-157, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40007
in-theory        40007
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D or (E -> (F or E))) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-540 ((Am (-> (and A B) B)) (C (and (or Bm (-> Cm (or Dm Cm))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40007.        ((A or ((B and C) -> C)) -> ((D or (E -> (F or E))) and ((B and C) -> C))), M:tm-154, m:tm-540, u:((Am (-> (and A B) B)) (C (and (or Bm (-> Cm (or Dm Cm))) (-> (and A B) B))))
================================================================
tm-name          tm-40008
in-theory        40008
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40008.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-147, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40009
in-theory        40009
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or (E -> (F or E))) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-540 ((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40009.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D or (E -> (F or E))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-540, u:((Am (-> (and A (-> B C)) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-40010
in-theory        40010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40010.        ((A -> ((B and C) -> B)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-134, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40011
in-theory        40011
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D or (E -> (F or E))) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-540 ((Am (-> (and A B) A)) (C (and (or Bm (-> Cm (or Dm Cm))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40011.        ((A or ((B and C) -> B)) -> ((D or (E -> (F or E))) and ((B and C) -> B))), M:tm-131, m:tm-540, u:((Am (-> (and A B) A)) (C (and (or Bm (-> Cm (or Dm Cm))) (-> (and A B) A))))
================================================================
tm-name          tm-40012
in-theory        40012
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40012.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-125, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40013
in-theory        40013
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or (E -> (F or E))) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-540 ((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40013.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D or (E -> (F or E))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-540, u:((Am (-> (and (-> A B) C) B)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-40014
in-theory        40014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (H or G))) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40014.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F or (G -> (H or G))) and E))), M:tm-113, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40015
in-theory        40015
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or (F -> (G or F))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-540 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40015.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E or (F -> (G or F))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-540, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-40016
in-theory        40016
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40016.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E or (F -> (G or F))) and D))), M:tm-105, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40017
in-theory        40017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or (E -> (F or E))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-540 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40017.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D or (E -> (F or E))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-540, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-40018
in-theory        40018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D or (E -> (F or E))) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40018.        (((A -> B) -> (A -> A)) and (C -> ((D or (E -> (F or E))) and C))), M:tm-95, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40019
in-theory        40019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C or (D -> (E or D))) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-540 ((Am (-> A A)) (B (and (or Bm (-> Cm (or Dm Cm))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40019.        (((A -> B) or (A -> A)) -> ((C or (D -> (E or D))) and (A -> A))), M:tm-92, m:tm-540, u:((Am (-> A A)) (B (and (or Bm (-> Cm (or Dm Cm))) (-> A A))))
================================================================
tm-name          tm-40020
in-theory        40020
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C or (D -> (E or D))) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40020.        (A -> (B -> ((C or (D -> (E or D))) and A))), M:tm-84, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-40021
in-theory        40021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40021.        ((A -> (B -> (C -> B))) and (D -> ((E or (F -> (G or F))) and D))), M:tm-83, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40022
in-theory        40022
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D or (E -> (F or E))) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-540 ((Am (-> A (-> B A))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40022.        ((A or (B -> (C -> B))) -> ((D or (E -> (F or E))) and (B -> (C -> B)))), M:tm-80, m:tm-540, u:((Am (-> A (-> B A))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (-> B A)))))
================================================================
tm-name          tm-40023
in-theory        40023
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C or (D -> (E or D))) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40023.        (((not (not A)) -> A) and (B -> ((C or (D -> (E or D))) and B))), M:tm-76, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40024
in-theory        40024
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B or (C -> (D or C))) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40024.        (((not (not A)) or A) -> ((B or (C -> (D or C))) and A)), M:tm-73, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-40025
in-theory        40025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or (E -> (F or E))) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40025.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D or (E -> (F or E))) and C))), M:tm-69, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40026
in-theory        40026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or (D -> (E or D))) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-540 ((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40026.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C or (D -> (E or D))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-540, u:((Am (-> (-> A (not B)) (not A))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-40027
in-theory        40027
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40027.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E or (F -> (G or F))) and D))), M:tm-54, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40028
in-theory        40028
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or (E -> (F or E))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-540 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40028.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D or (E -> (F or E))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-540, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-40029
in-theory        40029
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C or (D -> (E or D))) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-540 ((Am (or A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40029.        ((A or (B or A)) -> ((C or (D -> (E or D))) and (B or A))), M:tm-50, m:tm-540, u:((Am (or A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (or A B))))
================================================================
tm-name          tm-40030
in-theory        40030
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C or (D -> (E or D))) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-540 ((Am (or A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40030.        ((A or (A or B)) -> ((C or (D -> (E or D))) and (A or B))), M:tm-49, m:tm-540, u:((Am (or A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (or A B))))
================================================================
tm-name          tm-40031
in-theory        40031
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C or (D -> (E or D))) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-540 ((Am (-> A (and B A))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40031.        ((A or (B -> (A and B))) -> ((C or (D -> (E or D))) and (B -> (A and B)))), M:tm-48, m:tm-540, u:((Am (-> A (and B A))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-40032
in-theory        40032
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C or (D -> (E or D))) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40032.        (((A and B) or B) -> ((C or (D -> (E or D))) and B)), M:tm-47, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-40033
in-theory        40033
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C or (D -> (E or D))) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40033.        (((A and B) or A) -> ((C or (D -> (E or D))) and A)), M:tm-46, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-40034
in-theory        40034
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (F or E))) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-540 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40034.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (F or E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-540, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-40035
in-theory        40035
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C or (D -> (E or D))) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-540 ((Am (-> A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40035.        ((A or (B -> A)) -> ((C or (D -> (E or D))) and (B -> A))), M:tm-44, m:tm-540, u:((Am (-> A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A B))))
================================================================
tm-name          tm-40036
in-theory        40036
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D or (E -> (F or E))) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40036.        ((A -> (B or A)) and (C -> ((D or (E -> (F or E))) and C))), M:tm-42, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40037
in-theory        40037
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D or (E -> (F or E))) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40037.        ((A -> (A or B)) and (C -> ((D or (E -> (F or E))) and C))), M:tm-32, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40038
in-theory        40038
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B or (C -> (D or C))) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40038.        (A -> (A and ((B or (C -> (D or C))) and A))), M:tm-24, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-40039
in-theory        40039
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D or (E -> (F or E))) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40039.        ((A -> (B -> (A and B))) and (C -> ((D or (E -> (F or E))) and C))), M:tm-23, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40040
in-theory        40040
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D or (E -> (F or E))) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40040.        (((A and B) -> B) and (C -> ((D or (E -> (F or E))) and C))), M:tm-22, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40041
in-theory        40041
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D or (E -> (F or E))) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40041.        (((A and B) -> A) and (C -> ((D or (E -> (F or E))) and C))), M:tm-21, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40042
in-theory        40042
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40042.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E or (F -> (G or F))) and D))), M:tm-20, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40043
in-theory        40043
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D or (E -> (F or E))) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40043.        ((A -> (B -> A)) and (C -> ((D or (E -> (F or E))) and C))), M:tm-19, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40044
in-theory        40044
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B or (C -> (D or C))) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-9 tm-5 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40044.        ((A -> (not ((B or (C -> (D or C))) and A))) -> (not A)), M:tm-9, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-40045
in-theory        40045
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (C or B))) and D) -> E) -> ((D or ((A or (B -> (C or B))) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40045.        ((((A or (B -> (C or B))) and D) -> E) -> ((D or ((A or (B -> (C or B))) and D)) -> E)), M:tm-8, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-40046
in-theory        40046
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C or (D -> (E or D))) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-7 tm-5)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40046.        (A or (B -> ((C or (D -> (E or D))) and B))), M:tm-7, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40047
in-theory        40047
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40047.        ((A -> ((B or (C -> (D or C))) and A)) or E), M:tm-6, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40048
in-theory        40048
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C or (D -> (E or D))) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40048.        (A -> ((B -> ((C or (D -> (E or D))) and B)) and A)), M:tm-5, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40049
in-theory        40049
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C or (D -> (E or D))) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40049.        (A -> (B -> ((C or (D -> (E or D))) and B))), M:tm-1, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-40050
in-theory        40050
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40050.        ((A or (B -> (C or B))) and (D -> (E or (F -> (G or F))))), M:tm-540, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40051
in-theory        40051
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40051.        ((A or (B -> (B or C))) and (D -> (E or (F -> (G or F))))), M:tm-530, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40052
in-theory        40052
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40052.        ((A or (B -> (C -> (B and C)))) and (D -> (E or (F -> (G or F))))), M:tm-520, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40053
in-theory        40053
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40053.        ((A or ((B and C) -> C)) and (D -> (E or (F -> (G or F))))), M:tm-510, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40054
in-theory        40054
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40054.        ((A or ((B and C) -> B)) and (D -> (E or (F -> (G or F))))), M:tm-500, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40055
in-theory        40055
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40055.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (H or G))))), M:tm-490, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40056
in-theory        40056
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40056.        ((A or (B -> (C -> B))) and (D -> (E or (F -> (G or F))))), M:tm-480, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40057
in-theory        40057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40057.        ((A -> (B -> (B or C))) and (D -> (E or (F -> (G or F))))), M:tm-469, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40058
in-theory        40058
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-466 tm-541 ((Am (-> A (or A B))) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40058.        ((A or (B -> (B or C))) -> (D or (E -> (F or E)))), M:tm-466, m:tm-541, u:((Am (-> A (or A B))) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40059
in-theory        40059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40059.        ((A -> (B or (C -> (D or C)))) and (E -> (E or F))), M:tm-456, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40060
in-theory        40060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40060.        ((A -> ((B -> (B or C)) and A)) and (D -> (E or (F -> (G or F))))), M:tm-453, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40061
in-theory        40061
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-450 tm-541 ((Am (and (-> A (or A B)) C)) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40061.        ((A or ((B -> (B or C)) and A)) -> (D or (E -> (F or E)))), M:tm-450, m:tm-541, u:((Am (and (-> A (or A B)) C)) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40062
in-theory        40062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and ((E -> (E or F)) and (A -> (B or (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40062.        ((A -> (B or (C -> (D or C)))) and ((E -> (E or F)) and (A -> (B or (C -> (D or C)))))), M:tm-443, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40063
in-theory        40063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40063.        (((A -> (A or B)) or C) and (D -> (E or (F -> (G or F))))), M:tm-409, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40064
in-theory        40064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40064.        (((A -> (B -> (A and B))) or C) and (D -> (E or (F -> (G or F))))), M:tm-400, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40065
in-theory        40065
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40065.        ((((A and B) -> B) or C) and (D -> (E or (F -> (G or F))))), M:tm-391, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40066
in-theory        40066
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40066.        ((((A and B) -> A) or C) and (D -> (E or (F -> (G or F))))), M:tm-382, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40067
in-theory        40067
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40067.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F or (G -> (H or G))))), M:tm-373, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40068
in-theory        40068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40068.        (((A -> (B -> A)) or C) and (D -> (E or (F -> (G or F))))), M:tm-364, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40069
in-theory        40069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40069.        ((A -> (B -> (C -> (B and C)))) and (D -> (E or (F -> (G or F))))), M:tm-354, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40070
in-theory        40070
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-351 tm-541 ((Am (-> A (-> B (and A B)))) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40070.        ((A or (B -> (C -> (B and C)))) -> (D or (E -> (F or E)))), M:tm-351, m:tm-541, u:((Am (-> A (-> B (and A B)))) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40071
in-theory        40071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40071.        ((A -> (B or (C -> (D or C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40072
in-theory        40072
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) -> D) -> ((A or (B -> (C or B))) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-541 ((Am (-> (or Bm (-> Cm (or Dm Cm))) B)) (A (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40072.        (((A or (B -> (C or B))) -> D) -> ((A or (B -> (C or B))) and D)), M:tm-339, m:tm-541, u:((Am (-> (or Bm (-> Cm (or Dm Cm))) B)) (A (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40073
in-theory        40073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D or (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40073.        (((A -> B) -> (A -> (A and B))) and (C -> (D or (E -> (F or E))))), M:tm-338, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40074
in-theory        40074
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C or (D -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-335 tm-541 ((Am (-> A (and A B))) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40074.        (((A -> B) or (A -> (A and B))) -> (C or (D -> (E or D)))), M:tm-335, m:tm-541, u:((Am (-> A (and A B))) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40075
in-theory        40075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (A -> (A and (B or (C -> (D or C))))))
theorem-size     21
proof            (modus-ponens tm-328 tm-541 ((A Am) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40075.        ((A -> (B or (C -> (D or C)))) and (A -> (A and (B or (C -> (D or C)))))), M:tm-328, m:tm-541, u:((A Am) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40076
in-theory        40076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and ((E -> (F -> (E and F))) and (A -> (B or (C -> (D or C))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40076.        ((A -> (B or (C -> (D or C)))) and ((E -> (F -> (E and F))) and (A -> (B or (C -> (D or C)))))), M:tm-327, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40077
in-theory        40077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (((E and F) -> F) and (A -> (B or (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40077.        ((A -> (B or (C -> (D or C)))) and (((E and F) -> F) and (A -> (B or (C -> (D or C)))))), M:tm-326, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40078
in-theory        40078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (((E and F) -> E) and (A -> (B or (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40078.        ((A -> (B or (C -> (D or C)))) and (((E and F) -> E) and (A -> (B or (C -> (D or C)))))), M:tm-325, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40079
in-theory        40079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B or (C -> (D or C))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40079.        ((A -> (B or (C -> (D or C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B or (C -> (D or C)))))), M:tm-324, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40080
in-theory        40080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and ((E -> (F -> E)) and (A -> (B or (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40080.        ((A -> (B or (C -> (D or C)))) and ((E -> (F -> E)) and (A -> (B or (C -> (D or C)))))), M:tm-323, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40081
in-theory        40081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40081.        ((A -> (B or (C -> (D or C)))) and ((E and F) -> F)), M:tm-322, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40082
in-theory        40082
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B or (C -> (D or C))) -> E)) -> (B or (C -> (D or C)))) and ((A and ((B or (C -> (D or C))) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-541 ((Am (and A (-> (or Bm (-> Cm (or Dm Cm))) C))) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40082.        (((A and ((B or (C -> (D or C))) -> E)) -> (B or (C -> (D or C)))) and ((A and ((B or (C -> (D or C))) -> E)) -> E)), M:tm-321, m:tm-541, u:((Am (and A (-> (or Bm (-> Cm (or Dm Cm))) C))) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40083
in-theory        40083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40083.        ((A -> (B or (C -> (D or C)))) and ((E and F) -> E)), M:tm-320, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40084
in-theory        40084
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> (C or B))) -> D) and E) -> (A or (B -> (C or B)))) and ((((A or (B -> (C or B))) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-541 ((Am (and (-> (or Bm (-> Cm (or Dm Cm))) B) C)) (A (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40084.        (((((A or (B -> (C or B))) -> D) and E) -> (A or (B -> (C or B)))) and ((((A or (B -> (C or B))) -> D) and E) -> D)), M:tm-319, m:tm-541, u:((Am (and (-> (or Bm (-> Cm (or Dm Cm))) B) C)) (A (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40085
in-theory        40085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40085.        ((A -> (B or (C -> (D or C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40086
in-theory        40086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-541 ((A Am) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40086.        ((A -> (B or (C -> (D or C)))) and (A -> A)), M:tm-316, m:tm-541, u:((A Am) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40087
in-theory        40087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40087.        ((A -> (B or (C -> (D or C)))) and (E -> (F -> E))), M:tm-315, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40088
in-theory        40088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and ((A -> (not (B or (C -> (D or C))))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-541 ((A Am) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40088.        ((A -> (B or (C -> (D or C)))) and ((A -> (not (B or (C -> (D or C))))) -> (not A))), M:tm-313, m:tm-541, u:((A Am) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40089
in-theory        40089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (((B or (C -> (D or C))) -> E) -> ((A or (B or (C -> (D or C)))) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-541 ((A Am) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40089.        ((A -> (B or (C -> (D or C)))) and (((B or (C -> (D or C))) -> E) -> ((A or (B or (C -> (D or C)))) -> E))), M:tm-312, m:tm-541, u:((A Am) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40090
in-theory        40090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (E or (A -> (B or (C -> (D or C))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40090.        ((A -> (B or (C -> (D or C)))) and (E or (A -> (B or (C -> (D or C)))))), M:tm-311, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40091
in-theory        40091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and ((A -> (B or (C -> (D or C)))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40091.        ((A -> (B or (C -> (D or C)))) and ((A -> (B or (C -> (D or C)))) or E)), M:tm-310, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40092
in-theory        40092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (E -> ((A -> (B or (C -> (D or C)))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40092.        ((A -> (B or (C -> (D or C)))) and (E -> ((A -> (B or (C -> (D or C)))) and E))), M:tm-309, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40093
in-theory        40093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (E -> (A -> (B or (C -> (D or C))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40093.        ((A -> (B or (C -> (D or C)))) and (E -> (A -> (B or (C -> (D or C)))))), M:tm-305, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40094
in-theory        40094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40094.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E or (F -> (G or F))))), M:tm-303, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40095
in-theory        40095
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D or (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-300 tm-541 ((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40095.        ((A or ((B -> (C -> (B and C))) and A)) -> (D or (E -> (F or E)))), M:tm-300, m:tm-541, u:((Am (and (-> A (-> B (and A B))) C)) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40096
in-theory        40096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40096.        ((A -> (((B and C) -> C) and A)) and (D -> (E or (F -> (G or F))))), M:tm-270, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40097
in-theory        40097
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-267 tm-541 ((Am (and (-> (and A B) B) C)) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40097.        ((A or (((B and C) -> C) and A)) -> (D or (E -> (F or E)))), M:tm-267, m:tm-541, u:((Am (and (-> (and A B) B) C)) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40098
in-theory        40098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40098.        ((A -> (((B and C) -> B) and A)) and (D -> (E or (F -> (G or F))))), M:tm-239, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40099
in-theory        40099
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-236 tm-541 ((Am (and (-> (and A B) A) C)) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40099.        ((A or (((B and C) -> B) and A)) -> (D or (E -> (F or E)))), M:tm-236, m:tm-541, u:((Am (and (-> (and A B) A) C)) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40100
in-theory        40100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40100.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F or (G -> (H or G))))), M:tm-210, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40101
in-theory        40101
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-207 tm-541 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40101.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E or (F -> (G or F)))), M:tm-207, m:tm-541, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40102
in-theory        40102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40102.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E or (F -> (G or F))))), M:tm-183, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40103
in-theory        40103
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-180 tm-541 ((Am (and (-> A (-> B A)) C)) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40103.        ((A or ((B -> (C -> B)) and A)) -> (D or (E -> (F or E)))), M:tm-180, m:tm-541, u:((Am (and (-> A (-> B A)) C)) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40104
in-theory        40104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40104.        ((A -> ((B and C) -> C)) and (D -> (E or (F -> (G or F))))), M:tm-157, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40105
in-theory        40105
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-154 tm-541 ((Am (-> (and A B) B)) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40105.        ((A or ((B and C) -> C)) -> (D or (E -> (F or E)))), M:tm-154, m:tm-541, u:((Am (-> (and A B) B)) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40106
in-theory        40106
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40106.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E or (F -> (G or F))))), M:tm-147, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40107
in-theory        40107
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-144 tm-541 ((Am (-> (and A (-> B C)) C)) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40107.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D or (E -> (F or E)))), M:tm-144, m:tm-541, u:((Am (-> (and A (-> B C)) C)) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40108
in-theory        40108
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B or (C -> (D or C))) -> E)) -> (B or (C -> (D or C))))
theorem-size     19
proof            (modus-ponens tm-142 tm-541 ((Am (and A (-> (or Bm (-> Cm (or Dm Cm))) C))) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40108.        ((A and ((B or (C -> (D or C))) -> E)) -> (B or (C -> (D or C)))), M:tm-142, m:tm-541, u:((Am (and A (-> (or Bm (-> Cm (or Dm Cm))) C))) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40109
in-theory        40109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40109.        ((A -> ((B and C) -> B)) and (D -> (E or (F -> (G or F))))), M:tm-134, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40110
in-theory        40110
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-131 tm-541 ((Am (-> (and A B) A)) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40110.        ((A or ((B and C) -> B)) -> (D or (E -> (F or E)))), M:tm-131, m:tm-541, u:((Am (-> (and A B) A)) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40111
in-theory        40111
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40111.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E or (F -> (G or F))))), M:tm-125, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40112
in-theory        40112
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-122 tm-541 ((Am (-> (and (-> A B) C) B)) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40112.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D or (E -> (F or E)))), M:tm-122, m:tm-541, u:((Am (-> (and (-> A B) C) B)) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40113
in-theory        40113
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> (C or B))) -> D) and E) -> (A or (B -> (C or B))))
theorem-size     19
proof            (modus-ponens tm-120 tm-541 ((Am (and (-> (or Bm (-> Cm (or Dm Cm))) B) C)) (A (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40113.        ((((A or (B -> (C or B))) -> D) and E) -> (A or (B -> (C or B)))), M:tm-120, m:tm-541, u:((Am (and (-> (or Bm (-> Cm (or Dm Cm))) B) C)) (A (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40114
in-theory        40114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40114.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F or (G -> (H or G))))), M:tm-113, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40115
in-theory        40115
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-110 tm-541 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40115.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or (F -> (G or F)))), M:tm-110, m:tm-541, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40116
in-theory        40116
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or (F -> (G or F)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40116.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or (F -> (G or F))))), M:tm-105, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40117
in-theory        40117
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or (E -> (F or E))))
theorem-size     27
proof            (modus-ponens tm-102 tm-541 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40117.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D or (E -> (F or E)))), M:tm-102, m:tm-541, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40118
in-theory        40118
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) -> D) -> (A or (B -> (C or B))))
theorem-size     17
proof            (modus-ponens tm-96 tm-541 ((Am (-> (or Bm (-> Cm (or Dm Cm))) B)) (A (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40118.        (((A or (B -> (C or B))) -> D) -> (A or (B -> (C or B)))), M:tm-96, m:tm-541, u:((Am (-> (or Bm (-> Cm (or Dm Cm))) B)) (A (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40119
in-theory        40119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D or (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40119.        (((A -> B) -> (A -> A)) and (C -> (D or (E -> (F or E))))), M:tm-95, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40120
in-theory        40120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C or (D -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-92 tm-541 ((Am (-> A A)) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40120.        (((A -> B) or (A -> A)) -> (C or (D -> (E or D)))), M:tm-92, m:tm-541, u:((Am (-> A A)) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40121
in-theory        40121
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C or (D -> (E or D)))))
theorem-size     11
proof            (modus-ponens tm-84 tm-541 ((A Am) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40121.        (A -> (B -> (C or (D -> (E or D))))), M:tm-84, m:tm-541, u:((A Am) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40122
in-theory        40122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40122.        ((A -> (B -> (C -> B))) and (D -> (E or (F -> (G or F))))), M:tm-83, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40123
in-theory        40123
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-80 tm-541 ((Am (-> A (-> B A))) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40123.        ((A or (B -> (C -> B))) -> (D or (E -> (F or E)))), M:tm-80, m:tm-541, u:((Am (-> A (-> B A))) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40124
in-theory        40124
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A or (B -> (C or B))) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-541 ((Am (not (not (-> (or Bm (-> Cm (or Dm Cm))) B)))) (A (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-10 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40124.        ((not (not ((A or (B -> (C or B))) -> D))) -> D), M:tm-77, m:tm-541, u:((Am (not (not (-> (or Bm (-> Cm (or Dm Cm))) B)))) (A (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40125
in-theory        40125
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C or (D -> (E or D)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40125.        (((not (not A)) -> A) and (B -> (C or (D -> (E or D))))), M:tm-76, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40126
in-theory        40126
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B or (C -> (D or C))))
theorem-size     13
proof            (modus-ponens tm-73 tm-541 ((A Am) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-10 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40126.        (((not (not A)) or A) -> (B or (C -> (D or C)))), M:tm-73, m:tm-541, u:((A Am) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40127
in-theory        40127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or (E -> (F or E)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40127.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D or (E -> (F or E))))), M:tm-69, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40128
in-theory        40128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or (D -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-66 tm-541 ((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-9 tm-1 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40128.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C or (D -> (E or D)))), M:tm-66, m:tm-541, u:((Am (-> (-> A (not B)) (not A))) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40129
in-theory        40129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40129.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E or (F -> (G or F))))), M:tm-54, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40130
in-theory        40130
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-51 tm-541 ((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40130.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D or (E -> (F or E)))), M:tm-51, m:tm-541, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40131
in-theory        40131
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C or (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-50 tm-541 ((Am (or A B)) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40131.        ((A or (B or A)) -> (C or (D -> (E or D)))), M:tm-50, m:tm-541, u:((Am (or A B)) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40132
in-theory        40132
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C or (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-49 tm-541 ((Am (or A B)) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40132.        ((A or (A or B)) -> (C or (D -> (E or D)))), M:tm-49, m:tm-541, u:((Am (or A B)) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40133
in-theory        40133
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C or (D -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-48 tm-541 ((Am (-> A (and B A))) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40133.        ((A or (B -> (A and B))) -> (C or (D -> (E or D)))), M:tm-48, m:tm-541, u:((Am (-> A (and B A))) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40134
in-theory        40134
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-47 tm-541 ((A Am) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40134.        (((A and B) or B) -> (C or (D -> (E or D)))), M:tm-47, m:tm-541, u:((A Am) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40135
in-theory        40135
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-46 tm-541 ((A Am) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40135.        (((A and B) or A) -> (C or (D -> (E or D)))), M:tm-46, m:tm-541, u:((A Am) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40136
in-theory        40136
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-45 tm-541 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40136.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (F or E)))), M:tm-45, m:tm-541, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40137
in-theory        40137
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-44 tm-541 ((Am (-> A B)) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40137.        ((A or (B -> A)) -> (C or (D -> (E or D)))), M:tm-44, m:tm-541, u:((Am (-> A B)) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40138
in-theory        40138
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40138.        ((A -> (B or A)) and (C -> (D or (E -> (F or E))))), M:tm-42, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40139
in-theory        40139
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40139.        ((A -> (A or B)) and (C -> (D or (E -> (F or E))))), M:tm-32, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40140
in-theory        40140
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B or (C -> (D or C)))))
theorem-size     11
proof            (modus-ponens tm-24 tm-541 ((A Am) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40140.        (A -> (A and (B or (C -> (D or C))))), M:tm-24, m:tm-541, u:((A Am) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40141
in-theory        40141
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D or (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40141.        ((A -> (B -> (A and B))) and (C -> (D or (E -> (F or E))))), M:tm-23, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40142
in-theory        40142
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40142.        (((A and B) -> B) and (C -> (D or (E -> (F or E))))), M:tm-22, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40143
in-theory        40143
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40143.        (((A and B) -> A) and (C -> (D or (E -> (F or E))))), M:tm-21, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40144
in-theory        40144
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40144.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or (F -> (G or F))))), M:tm-20, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40145
in-theory        40145
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40145.        ((A -> (B -> A)) and (C -> (D or (E -> (F or E))))), M:tm-19, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40146
in-theory        40146
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B or (C -> (D or C))) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-541 ((Am (and A (-> (or Bm (-> Cm (or Dm Cm))) C))) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-4 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40146.        ((A and ((B or (C -> (D or C))) -> E)) -> E), M:tm-17, m:tm-541, u:((Am (and A (-> (or Bm (-> Cm (or Dm Cm))) C))) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40147
in-theory        40147
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (C or B))) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-541 ((Am (and (-> (or Bm (-> Cm (or Dm Cm))) B) C)) (A (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-3 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40147.        ((((A or (B -> (C or B))) -> D) and E) -> D), M:tm-15, m:tm-541, u:((Am (and (-> (or Bm (-> Cm (or Dm Cm))) B) C)) (A (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40148
in-theory        40148
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B or (C -> (D or C))))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-541 ((A Am) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-9 tm-1 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40148.        ((A -> (not (B or (C -> (D or C))))) -> (not A)), M:tm-9, m:tm-541, u:((A Am) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40149
in-theory        40149
times-derived    2
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) -> D) -> ((E or (A or (B -> (C or B)))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-541 ((A Am) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40149.        (((A or (B -> (C or B))) -> D) -> ((E or (A or (B -> (C or B)))) -> D)), M:tm-8, m:tm-541, u:((A Am) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40150
in-theory        40150
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C or (D -> (E or D)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-7 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40150.        (A or (B -> (C or (D -> (E or D))))), M:tm-7, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40151
in-theory        40151
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-6 tm-1 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40151.        ((A -> (B or (C -> (D or C)))) or E), M:tm-6, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40152
in-theory        40152
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C or (D -> (E or D)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-40152.        (A -> ((B -> (C or (D -> (E or D)))) and A)), M:tm-5, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-40153
in-theory        40153
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40153.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-540, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40154
in-theory        40154
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40154.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-530, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40155
in-theory        40155
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40155.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-520, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40156
in-theory        40156
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40156.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-510, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40157
in-theory        40157
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40157.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-500, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40158
in-theory        40158
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40158.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H or G)) or I))), M:tm-490, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40159
in-theory        40159
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40159.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-480, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40160
in-theory        40160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40160.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-469, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40161
in-theory        40161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40161.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and (F -> (F or G))), M:tm-456, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40162
in-theory        40162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40162.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-453, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40163
in-theory        40163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40163.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> (D or C)) or E)))), M:tm-443, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40164
in-theory        40164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40164.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-409, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40165
in-theory        40165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40165.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-400, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40166
in-theory        40166
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40166.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-391, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40167
in-theory        40167
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40167.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-382, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40168
in-theory        40168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40168.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> (H or G)) or I))), M:tm-373, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40169
in-theory        40169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40169.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-364, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40170
in-theory        40170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40170.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-354, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40171
in-theory        40171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40171.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40172
in-theory        40172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40172.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> (F or E)) or G))), M:tm-338, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40173
in-theory        40173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> (D or C)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40173.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> (D or C)) or E)))), M:tm-327, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40174
in-theory        40174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40174.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> (D or C)) or E)))), M:tm-326, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40175
in-theory        40175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40175.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> (D or C)) or E)))), M:tm-325, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40176
in-theory        40176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> (D or C)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40176.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> (D or C)) or E)))), M:tm-324, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40177
in-theory        40177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40177.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> (D or C)) or E)))), M:tm-323, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40178
in-theory        40178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40178.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40179
in-theory        40179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40179.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40180
in-theory        40180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40180.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40181
in-theory        40181
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40181.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40182
in-theory        40182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and (F or ((A -> (A or B)) and ((C -> (D or C)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40182.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and (F or ((A -> (A or B)) and ((C -> (D or C)) or E)))), M:tm-311, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40183
in-theory        40183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and (((A -> (A or B)) and ((C -> (D or C)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40183.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and (((A -> (A or B)) and ((C -> (D or C)) or E)) or F)), M:tm-310, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40184
in-theory        40184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and (F -> (((A -> (A or B)) and ((C -> (D or C)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40184.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and (F -> (((A -> (A or B)) and ((C -> (D or C)) or E)) and F))), M:tm-309, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40185
in-theory        40185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((C -> (D or C)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-542 ((A (-> Am (or Am Bm))) (B (or (-> Cm (or Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40185.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((C -> (D or C)) or E)), M:tm-308, m:tm-542, u:((A (-> Am (or Am Bm))) (B (or (-> Cm (or Dm Cm)) Em)))
================================================================
tm-name          tm-40186
in-theory        40186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-542 ((A (-> Am (or Am Bm))) (B (or (-> Cm (or Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40186.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and (A -> (A or B))), M:tm-307, m:tm-542, u:((A (-> Am (or Am Bm))) (B (or (-> Cm (or Dm Cm)) Em)))
================================================================
tm-name          tm-40187
in-theory        40187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and (F -> ((A -> (A or B)) and ((C -> (D or C)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40187.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and (F -> ((A -> (A or B)) and ((C -> (D or C)) or E)))), M:tm-305, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40188
in-theory        40188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40188.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-303, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40189
in-theory        40189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40189.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-270, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40190
in-theory        40190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40190.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-239, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40191
in-theory        40191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40191.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> (H or G)) or I))), M:tm-210, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40192
in-theory        40192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40192.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-183, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40193
in-theory        40193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40193.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-157, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40194
in-theory        40194
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40194.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-147, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40195
in-theory        40195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40195.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-134, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40196
in-theory        40196
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40196.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-125, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40197
in-theory        40197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40197.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> (H or G)) or I))), M:tm-113, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40198
in-theory        40198
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40198.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-105, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40199
in-theory        40199
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40199.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> (F or E)) or G))), M:tm-95, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40200
in-theory        40200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40200.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-83, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40201
in-theory        40201
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> (E or D)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-10 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40201.        (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> (E or D)) or F))), M:tm-76, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40202
in-theory        40202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> (F or E)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-9 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40202.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> (F or E)) or G))), M:tm-69, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40203
in-theory        40203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40203.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-54, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40204
in-theory        40204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40204.        ((A -> (B or A)) and ((C -> (C or D)) and ((E -> (F or E)) or G))), M:tm-42, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40205
in-theory        40205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40205.        ((A -> (A or B)) and ((C -> (C or D)) and ((E -> (F or E)) or G))), M:tm-32, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40206
in-theory        40206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40206.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> (F or E)) or G))), M:tm-23, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40207
in-theory        40207
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40207.        (((A and B) -> B) and ((C -> (C or D)) and ((E -> (F or E)) or G))), M:tm-22, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40208
in-theory        40208
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40208.        (((A and B) -> A) and ((C -> (C or D)) and ((E -> (F or E)) or G))), M:tm-21, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40209
in-theory        40209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40209.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-20, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40210
in-theory        40210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40210.        ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> (F or E)) or G))), M:tm-19, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40211
in-theory        40211
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40211.        (A or ((B -> (B or C)) and ((D -> (E or D)) or F))), M:tm-7, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40212
in-theory        40212
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40212.        (((A -> (A or B)) and ((C -> (D or C)) or E)) or F), M:tm-6, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40213
in-theory        40213
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((D -> (E or D)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40213.        (A -> (((B -> (B or C)) and ((D -> (E or D)) or F)) and A)), M:tm-5, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40214
in-theory        40214
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-1 tm-5 tm-6 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40214.        (A -> ((B -> (B or C)) and ((D -> (E or D)) or F))), M:tm-1, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40215
in-theory        40215
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-540 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40215.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-540, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40216
in-theory        40216
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-530 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40216.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-530, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40217
in-theory        40217
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-520 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40217.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-520, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40218
in-theory        40218
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-510 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40218.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-510, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40219
in-theory        40219
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-500 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40219.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-500, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40220
in-theory        40220
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-490 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40220.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I))), M:tm-490, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40221
in-theory        40221
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-480 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40221.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-480, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40222
in-theory        40222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-469 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40222.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-469, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40223
in-theory        40223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40223.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (F -> (F or G))), M:tm-456, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40224
in-theory        40224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-453 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40224.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-453, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40225
in-theory        40225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> (D or C)) or E))))
theorem-size     37
proof            (modus-ponens tm-443 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40225.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)))), M:tm-443, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40226
in-theory        40226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-409 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40226.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-409, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40227
in-theory        40227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-400 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40227.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-400, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40228
in-theory        40228
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-391 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40228.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-391, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40229
in-theory        40229
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-382 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40229.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-382, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40230
in-theory        40230
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-373 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40230.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I))), M:tm-373, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40231
in-theory        40231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-364 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40231.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-364, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40232
in-theory        40232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-354 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40232.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-354, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40233
in-theory        40233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40233.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40234
in-theory        40234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G)))
theorem-size     25
proof            (modus-ponens tm-338 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40234.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G))), M:tm-338, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40235
in-theory        40235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> (D or C)) or E))))
theorem-size     39
proof            (modus-ponens tm-327 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40235.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)))), M:tm-327, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40236
in-theory        40236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> (D or C)) or E))))
theorem-size     37
proof            (modus-ponens tm-326 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40236.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)))), M:tm-326, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40237
in-theory        40237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> (D or C)) or E))))
theorem-size     37
proof            (modus-ponens tm-325 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40237.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)))), M:tm-325, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40238
in-theory        40238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> (D or C)) or E))))
theorem-size     45
proof            (modus-ponens tm-324 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40238.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)))), M:tm-324, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40239
in-theory        40239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> (D or C)) or E))))
theorem-size     37
proof            (modus-ponens tm-323 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40239.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)))), M:tm-323, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40240
in-theory        40240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40240.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40241
in-theory        40241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40241.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40242
in-theory        40242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40242.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40243
in-theory        40243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40243.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40244
in-theory        40244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (F or ((A -> (B -> (A and B))) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-311 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40244.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (F or ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)))), M:tm-311, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40245
in-theory        40245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40245.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) or F)), M:tm-310, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40246
in-theory        40246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (F -> (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40246.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (F -> (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and F))), M:tm-309, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40247
in-theory        40247
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((C -> (D or C)) or E))
theorem-size     23
proof            (modus-ponens tm-308 tm-543 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (or Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40247.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((C -> (D or C)) or E)), M:tm-308, m:tm-543, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (or Dm Cm)) Em)))
================================================================
tm-name          tm-40248
in-theory        40248
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-543 ((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (or Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40248.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (A -> (B -> (A and B)))), M:tm-307, m:tm-543, u:((A (-> Am (-> Bm (and Am Bm)))) (B (or (-> Cm (or Dm Cm)) Em)))
================================================================
tm-name          tm-40249
in-theory        40249
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (F -> ((A -> (B -> (A and B))) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-305 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40249.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (F -> ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)))), M:tm-305, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40250
in-theory        40250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-303 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40250.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-303, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40251
in-theory        40251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-270 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40251.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-270, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40252
in-theory        40252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-239 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40252.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-239, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40253
in-theory        40253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I)))
theorem-size     33
proof            (modus-ponens tm-210 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40253.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I))), M:tm-210, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40254
in-theory        40254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-183 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40254.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-183, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40255
in-theory        40255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-157 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40255.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-157, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40256
in-theory        40256
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     31
proof            (modus-ponens tm-147 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40256.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-147, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40257
in-theory        40257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-134 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40257.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-134, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40258
in-theory        40258
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     31
proof            (modus-ponens tm-125 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40258.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-125, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40259
in-theory        40259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-113 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40259.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I))), M:tm-113, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40260
in-theory        40260
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     35
proof            (modus-ponens tm-105 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40260.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-105, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40261
in-theory        40261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-95 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40261.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G))), M:tm-95, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40262
in-theory        40262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-83 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40262.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-83, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40263
in-theory        40263
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> (E or D)) or F)))
theorem-size     21
proof            (modus-ponens tm-76 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-10 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40263.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> (E or D)) or F))), M:tm-76, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40264
in-theory        40264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G)))
theorem-size     27
proof            (modus-ponens tm-69 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-9 tm-6 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40264.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G))), M:tm-69, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40265
in-theory        40265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-54 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40265.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-54, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40266
in-theory        40266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-42 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40266.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G))), M:tm-42, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40267
in-theory        40267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-32 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40267.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G))), M:tm-32, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40268
in-theory        40268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-23 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40268.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G))), M:tm-23, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40269
in-theory        40269
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-22 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40269.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G))), M:tm-22, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40270
in-theory        40270
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-21 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40270.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G))), M:tm-21, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40271
in-theory        40271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-20 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40271.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-20, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40272
in-theory        40272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-19 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40272.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> (F or E)) or G))), M:tm-19, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40273
in-theory        40273
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((D -> (E or D)) or F)))
theorem-size     17
proof            (modus-ponens tm-7 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40273.        (A or ((B -> (C -> (B and C))) and ((D -> (E or D)) or F))), M:tm-7, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40274
in-theory        40274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40274.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) or F), M:tm-6, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40275
in-theory        40275
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((D -> (E or D)) or F)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40275.        (A -> (((B -> (C -> (B and C))) and ((D -> (E or D)) or F)) and A)), M:tm-5, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40276
in-theory        40276
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((D -> (E or D)) or F)))
theorem-size     17
proof            (modus-ponens tm-1 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-1 tm-5 tm-6 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40276.        (A -> ((B -> (C -> (B and C))) and ((D -> (E or D)) or F))), M:tm-1, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40277
in-theory        40277
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40277.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-540, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40278
in-theory        40278
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40278.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-530, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40279
in-theory        40279
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40279.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-520, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40280
in-theory        40280
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40280.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-510, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40281
in-theory        40281
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40281.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-500, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40282
in-theory        40282
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40282.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H or G)) or I))), M:tm-490, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40283
in-theory        40283
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40283.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-480, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40284
in-theory        40284
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40284.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-469, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40285
in-theory        40285
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40285.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and (F -> (F or G))), M:tm-456, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40286
in-theory        40286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40286.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-453, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40287
in-theory        40287
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40287.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> (D or C)) or E)))), M:tm-443, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40288
in-theory        40288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40288.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-409, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40289
in-theory        40289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40289.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-400, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40290
in-theory        40290
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40290.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-391, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40291
in-theory        40291
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40291.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-382, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40292
in-theory        40292
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40292.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> (H or G)) or I))), M:tm-373, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40293
in-theory        40293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40293.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-364, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40294
in-theory        40294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40294.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-354, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40295
in-theory        40295
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40295.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40296
in-theory        40296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40296.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> (F or E)) or G))), M:tm-338, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40297
in-theory        40297
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> (D or C)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40297.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> (D or C)) or E)))), M:tm-327, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40298
in-theory        40298
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and (((F and G) -> G) and (((A and B) -> B) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40298.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and (((F and G) -> G) and (((A and B) -> B) and ((C -> (D or C)) or E)))), M:tm-326, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40299
in-theory        40299
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and (((F and G) -> F) and (((A and B) -> B) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40299.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and (((F and G) -> F) and (((A and B) -> B) and ((C -> (D or C)) or E)))), M:tm-325, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40300
in-theory        40300
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> (D or C)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40300.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> (D or C)) or E)))), M:tm-324, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40301
in-theory        40301
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40301.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> (D or C)) or E)))), M:tm-323, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40302
in-theory        40302
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40302.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40303
in-theory        40303
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40303.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40304
in-theory        40304
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40304.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40305
in-theory        40305
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40305.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40306
in-theory        40306
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and (F or (((A and B) -> B) and ((C -> (D or C)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40306.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and (F or (((A and B) -> B) and ((C -> (D or C)) or E)))), M:tm-311, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40307
in-theory        40307
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((((A and B) -> B) and ((C -> (D or C)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40307.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((((A and B) -> B) and ((C -> (D or C)) or E)) or F)), M:tm-310, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40308
in-theory        40308
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and (F -> ((((A and B) -> B) and ((C -> (D or C)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40308.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and (F -> ((((A and B) -> B) and ((C -> (D or C)) or E)) and F))), M:tm-309, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40309
in-theory        40309
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((C -> (D or C)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-544 ((A (-> (and Am Bm) Bm)) (B (or (-> Cm (or Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40309.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((C -> (D or C)) or E)), M:tm-308, m:tm-544, u:((A (-> (and Am Bm) Bm)) (B (or (-> Cm (or Dm Cm)) Em)))
================================================================
tm-name          tm-40310
in-theory        40310
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-544 ((A (-> (and Am Bm) Bm)) (B (or (-> Cm (or Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-6 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40310.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((A and B) -> B)), M:tm-307, m:tm-544, u:((A (-> (and Am Bm) Bm)) (B (or (-> Cm (or Dm Cm)) Em)))
================================================================
tm-name          tm-40311
in-theory        40311
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and (F -> (((A and B) -> B) and ((C -> (D or C)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40311.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and (F -> (((A and B) -> B) and ((C -> (D or C)) or E)))), M:tm-305, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40312
in-theory        40312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40312.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-303, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40313
in-theory        40313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40313.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-270, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40314
in-theory        40314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40314.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-239, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40315
in-theory        40315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40315.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> (H or G)) or I))), M:tm-210, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40316
in-theory        40316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40316.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-183, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40317
in-theory        40317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40317.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-157, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40318
in-theory        40318
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40318.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-147, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40319
in-theory        40319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40319.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-134, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40320
in-theory        40320
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40320.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-125, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40321
in-theory        40321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40321.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> (H or G)) or I))), M:tm-113, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40322
in-theory        40322
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40322.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-105, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40323
in-theory        40323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40323.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> (F or E)) or G))), M:tm-95, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40324
in-theory        40324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40324.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-83, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40325
in-theory        40325
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((D -> (E or D)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-10 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40325.        (((not (not A)) -> A) and (((B and C) -> C) and ((D -> (E or D)) or F))), M:tm-76, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40326
in-theory        40326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> (F or E)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-9 tm-4 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40326.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> (F or E)) or G))), M:tm-69, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40327
in-theory        40327
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40327.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-54, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40328
in-theory        40328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40328.        ((A -> (B or A)) and (((C and D) -> D) and ((E -> (F or E)) or G))), M:tm-42, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40329
in-theory        40329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40329.        ((A -> (A or B)) and (((C and D) -> D) and ((E -> (F or E)) or G))), M:tm-32, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40330
in-theory        40330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40330.        ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> (F or E)) or G))), M:tm-23, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40331
in-theory        40331
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40331.        (((A and B) -> B) and (((C and D) -> D) and ((E -> (F or E)) or G))), M:tm-22, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40332
in-theory        40332
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40332.        (((A and B) -> A) and (((C and D) -> D) and ((E -> (F or E)) or G))), M:tm-21, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40333
in-theory        40333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40333.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-20, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40334
in-theory        40334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40334.        ((A -> (B -> A)) and (((C and D) -> D) and ((E -> (F or E)) or G))), M:tm-19, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40335
in-theory        40335
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-7 tm-5 tm-4 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40335.        (A or (((B and C) -> C) and ((D -> (E or D)) or F))), M:tm-7, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40336
in-theory        40336
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-6 tm-5 tm-4 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40336.        ((((A and B) -> B) and ((C -> (D or C)) or E)) or F), M:tm-6, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40337
in-theory        40337
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((D -> (E or D)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40337.        (A -> ((((B and C) -> C) and ((D -> (E or D)) or F)) and A)), M:tm-5, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40338
in-theory        40338
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-1 tm-5 tm-4 tm-6 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40338.        (A -> (((B and C) -> C) and ((D -> (E or D)) or F))), M:tm-1, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40339
in-theory        40339
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40339.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-540, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40340
in-theory        40340
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40340.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-530, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40341
in-theory        40341
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40341.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-520, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40342
in-theory        40342
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40342.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-510, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40343
in-theory        40343
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40343.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-500, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40344
in-theory        40344
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40344.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H or G)) or I))), M:tm-490, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40345
in-theory        40345
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40345.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-480, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40346
in-theory        40346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40346.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-469, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40347
in-theory        40347
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40347.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and (F -> (F or G))), M:tm-456, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40348
in-theory        40348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40348.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-453, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40349
in-theory        40349
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40349.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> (D or C)) or E)))), M:tm-443, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40350
in-theory        40350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40350.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-409, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40351
in-theory        40351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40351.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-400, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40352
in-theory        40352
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40352.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-391, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40353
in-theory        40353
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40353.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-382, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40354
in-theory        40354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40354.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> (H or G)) or I))), M:tm-373, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40355
in-theory        40355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40355.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-364, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40356
in-theory        40356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40356.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-354, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40357
in-theory        40357
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40357.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40358
in-theory        40358
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40358.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> (F or E)) or G))), M:tm-338, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40359
in-theory        40359
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> (D or C)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40359.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> (D or C)) or E)))), M:tm-327, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40360
in-theory        40360
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and (((F and G) -> G) and (((A and B) -> A) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40360.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and (((F and G) -> G) and (((A and B) -> A) and ((C -> (D or C)) or E)))), M:tm-326, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40361
in-theory        40361
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and (((F and G) -> F) and (((A and B) -> A) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40361.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and (((F and G) -> F) and (((A and B) -> A) and ((C -> (D or C)) or E)))), M:tm-325, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40362
in-theory        40362
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> (D or C)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40362.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> (D or C)) or E)))), M:tm-324, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40363
in-theory        40363
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40363.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> (D or C)) or E)))), M:tm-323, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40364
in-theory        40364
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40364.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40365
in-theory        40365
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40365.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40366
in-theory        40366
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40366.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40367
in-theory        40367
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40367.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40368
in-theory        40368
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and (F or (((A and B) -> A) and ((C -> (D or C)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40368.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and (F or (((A and B) -> A) and ((C -> (D or C)) or E)))), M:tm-311, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40369
in-theory        40369
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((((A and B) -> A) and ((C -> (D or C)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40369.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((((A and B) -> A) and ((C -> (D or C)) or E)) or F)), M:tm-310, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40370
in-theory        40370
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and (F -> ((((A and B) -> A) and ((C -> (D or C)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40370.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and (F -> ((((A and B) -> A) and ((C -> (D or C)) or E)) and F))), M:tm-309, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40371
in-theory        40371
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((C -> (D or C)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-545 ((A (-> (and Am Bm) Am)) (B (or (-> Cm (or Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40371.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((C -> (D or C)) or E)), M:tm-308, m:tm-545, u:((A (-> (and Am Bm) Am)) (B (or (-> Cm (or Dm Cm)) Em)))
================================================================
tm-name          tm-40372
in-theory        40372
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-545 ((A (-> (and Am Bm) Am)) (B (or (-> Cm (or Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40372.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((A and B) -> A)), M:tm-307, m:tm-545, u:((A (-> (and Am Bm) Am)) (B (or (-> Cm (or Dm Cm)) Em)))
================================================================
tm-name          tm-40373
in-theory        40373
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and (F -> (((A and B) -> A) and ((C -> (D or C)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40373.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and (F -> (((A and B) -> A) and ((C -> (D or C)) or E)))), M:tm-305, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40374
in-theory        40374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40374.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-303, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40375
in-theory        40375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40375.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-270, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40376
in-theory        40376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40376.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-239, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40377
in-theory        40377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40377.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> (H or G)) or I))), M:tm-210, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40378
in-theory        40378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40378.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-183, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40379
in-theory        40379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40379.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-157, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40380
in-theory        40380
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40380.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-147, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40381
in-theory        40381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40381.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-134, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40382
in-theory        40382
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40382.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-125, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40383
in-theory        40383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40383.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> (H or G)) or I))), M:tm-113, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40384
in-theory        40384
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40384.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-105, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40385
in-theory        40385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40385.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> (F or E)) or G))), M:tm-95, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40386
in-theory        40386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40386.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-83, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40387
in-theory        40387
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((D -> (E or D)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-10 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40387.        (((not (not A)) -> A) and (((B and C) -> B) and ((D -> (E or D)) or F))), M:tm-76, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40388
in-theory        40388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> (F or E)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-9 tm-3 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40388.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> (F or E)) or G))), M:tm-69, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40389
in-theory        40389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40389.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-54, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40390
in-theory        40390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40390.        ((A -> (B or A)) and (((C and D) -> C) and ((E -> (F or E)) or G))), M:tm-42, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40391
in-theory        40391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40391.        ((A -> (A or B)) and (((C and D) -> C) and ((E -> (F or E)) or G))), M:tm-32, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40392
in-theory        40392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40392.        ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> (F or E)) or G))), M:tm-23, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40393
in-theory        40393
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40393.        (((A and B) -> B) and (((C and D) -> C) and ((E -> (F or E)) or G))), M:tm-22, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40394
in-theory        40394
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40394.        (((A and B) -> A) and (((C and D) -> C) and ((E -> (F or E)) or G))), M:tm-21, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40395
in-theory        40395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40395.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-20, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40396
in-theory        40396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40396.        ((A -> (B -> A)) and (((C and D) -> C) and ((E -> (F or E)) or G))), M:tm-19, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40397
in-theory        40397
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-7 tm-5 tm-3 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40397.        (A or (((B and C) -> B) and ((D -> (E or D)) or F))), M:tm-7, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40398
in-theory        40398
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-6 tm-5 tm-3 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40398.        ((((A and B) -> A) and ((C -> (D or C)) or E)) or F), M:tm-6, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40399
in-theory        40399
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((D -> (E or D)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40399.        (A -> ((((B and C) -> B) and ((D -> (E or D)) or F)) and A)), M:tm-5, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40400
in-theory        40400
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-1 tm-5 tm-3 tm-6 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40400.        (A -> (((B and C) -> B) and ((D -> (E or D)) or F))), M:tm-1, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40401
in-theory        40401
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40401.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-540, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40402
in-theory        40402
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40402.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-530, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40403
in-theory        40403
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40403.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-520, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40404
in-theory        40404
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40404.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-510, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40405
in-theory        40405
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40405.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-500, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40406
in-theory        40406
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I or H)) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40406.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I or H)) or J))), M:tm-490, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40407
in-theory        40407
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40407.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-480, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40408
in-theory        40408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40408.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-469, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40409
in-theory        40409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40409.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (G -> (G or H))), M:tm-456, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40410
in-theory        40410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40410.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-453, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40411
in-theory        40411
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40411.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)))), M:tm-443, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40412
in-theory        40412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40412.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-409, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40413
in-theory        40413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40413.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-400, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40414
in-theory        40414
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40414.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-391, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40415
in-theory        40415
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40415.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-382, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40416
in-theory        40416
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I or H)) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40416.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I or H)) or J))), M:tm-373, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40417
in-theory        40417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40417.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-364, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40418
in-theory        40418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40418.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-354, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40419
in-theory        40419
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40419.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40420
in-theory        40420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40420.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H))), M:tm-338, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40421
in-theory        40421
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40421.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)))), M:tm-327, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40422
in-theory        40422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40422.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)))), M:tm-326, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40423
in-theory        40423
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40423.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)))), M:tm-325, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40424
in-theory        40424
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40424.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)))), M:tm-324, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40425
in-theory        40425
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40425.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)))), M:tm-323, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40426
in-theory        40426
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40426.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((G and H) -> H)), M:tm-322, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40427
in-theory        40427
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40427.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((G and H) -> G)), M:tm-320, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40428
in-theory        40428
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40428.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40429
in-theory        40429
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40429.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (G -> (H -> G))), M:tm-315, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40430
in-theory        40430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40430.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)))), M:tm-311, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40431
in-theory        40431
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40431.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) or G)), M:tm-310, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40432
in-theory        40432
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40432.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and G))), M:tm-309, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40433
in-theory        40433
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((D -> (E or D)) or F))
theorem-size     29
proof            (modus-ponens tm-308 tm-546 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (or Em Dm)) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40433.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((D -> (E or D)) or F)), M:tm-308, m:tm-546, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (or Em Dm)) Fm)))
================================================================
tm-name          tm-40434
in-theory        40434
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-546 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (or Em Dm)) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40434.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-546, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> Dm (or Em Dm)) Fm)))
================================================================
tm-name          tm-40435
in-theory        40435
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40435.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)))), M:tm-305, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40436
in-theory        40436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40436.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-303, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40437
in-theory        40437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40437.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-270, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40438
in-theory        40438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40438.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-239, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40439
in-theory        40439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I or H)) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40439.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I or H)) or J))), M:tm-210, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40440
in-theory        40440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40440.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-183, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40441
in-theory        40441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40441.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-157, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40442
in-theory        40442
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40442.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-147, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40443
in-theory        40443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40443.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-134, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40444
in-theory        40444
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40444.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-125, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40445
in-theory        40445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I or H)) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40445.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I or H)) or J))), M:tm-113, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40446
in-theory        40446
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40446.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-105, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40447
in-theory        40447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40447.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H))), M:tm-95, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40448
in-theory        40448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40448.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-83, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40449
in-theory        40449
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F or E)) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40449.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F or E)) or G))), M:tm-76, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40450
in-theory        40450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-6 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40450.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H))), M:tm-69, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40451
in-theory        40451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40451.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-54, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40452
in-theory        40452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40452.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H))), M:tm-42, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40453
in-theory        40453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40453.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H))), M:tm-32, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40454
in-theory        40454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40454.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H))), M:tm-23, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40455
in-theory        40455
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40455.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H))), M:tm-22, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40456
in-theory        40456
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40456.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H))), M:tm-21, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40457
in-theory        40457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40457.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-20, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40458
in-theory        40458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40458.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> (G or F)) or H))), M:tm-19, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40459
in-theory        40459
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-7 tm-5 tm-2 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40459.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F or E)) or G))), M:tm-7, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40460
in-theory        40460
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-6 tm-5 tm-2 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40460.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) or G), M:tm-6, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40461
in-theory        40461
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F or E)) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40461.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F or E)) or G)) and A)), M:tm-5, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40462
in-theory        40462
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-1 tm-5 tm-2 tm-6 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40462.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F or E)) or G))), M:tm-1, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-40463
in-theory        40463
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40463.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-540, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40464
in-theory        40464
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40464.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-530, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40465
in-theory        40465
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40465.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-520, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40466
in-theory        40466
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40466.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-510, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40467
in-theory        40467
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40467.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-500, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40468
in-theory        40468
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40468.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H or G)) or I))), M:tm-490, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40469
in-theory        40469
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40469.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-480, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40470
in-theory        40470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40470.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-469, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40471
in-theory        40471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40471.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (F -> (F or G))), M:tm-456, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40472
in-theory        40472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40472.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-453, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40473
in-theory        40473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40473.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> (D or C)) or E)))), M:tm-443, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40474
in-theory        40474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40474.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-409, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40475
in-theory        40475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40475.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-400, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40476
in-theory        40476
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40476.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-391, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40477
in-theory        40477
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40477.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-382, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40478
in-theory        40478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40478.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> (H or G)) or I))), M:tm-373, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40479
in-theory        40479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40479.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-364, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40480
in-theory        40480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40480.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-354, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40481
in-theory        40481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40481.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40482
in-theory        40482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40482.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> (F or E)) or G))), M:tm-338, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40483
in-theory        40483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> (D or C)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40483.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> (D or C)) or E)))), M:tm-327, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40484
in-theory        40484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40484.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> (D or C)) or E)))), M:tm-326, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40485
in-theory        40485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40485.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> (D or C)) or E)))), M:tm-325, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40486
in-theory        40486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> (D or C)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40486.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> (D or C)) or E)))), M:tm-324, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40487
in-theory        40487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40487.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> (D or C)) or E)))), M:tm-323, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40488
in-theory        40488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40488.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40489
in-theory        40489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40489.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40490
in-theory        40490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40490.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40491
in-theory        40491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40491.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40492
in-theory        40492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (F or ((A -> (B -> A)) and ((C -> (D or C)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40492.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (F or ((A -> (B -> A)) and ((C -> (D or C)) or E)))), M:tm-311, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40493
in-theory        40493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (((A -> (B -> A)) and ((C -> (D or C)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40493.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (((A -> (B -> A)) and ((C -> (D or C)) or E)) or F)), M:tm-310, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40494
in-theory        40494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (F -> (((A -> (B -> A)) and ((C -> (D or C)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40494.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (F -> (((A -> (B -> A)) and ((C -> (D or C)) or E)) and F))), M:tm-309, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40495
in-theory        40495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((C -> (D or C)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-547 ((A (-> Am (-> Bm Am))) (B (or (-> Cm (or Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40495.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((C -> (D or C)) or E)), M:tm-308, m:tm-547, u:((A (-> Am (-> Bm Am))) (B (or (-> Cm (or Dm Cm)) Em)))
================================================================
tm-name          tm-40496
in-theory        40496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-547 ((A (-> Am (-> Bm Am))) (B (or (-> Cm (or Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40496.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (A -> (B -> A))), M:tm-307, m:tm-547, u:((A (-> Am (-> Bm Am))) (B (or (-> Cm (or Dm Cm)) Em)))
================================================================
tm-name          tm-40497
in-theory        40497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (F -> ((A -> (B -> A)) and ((C -> (D or C)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40497.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (F -> ((A -> (B -> A)) and ((C -> (D or C)) or E)))), M:tm-305, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40498
in-theory        40498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40498.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-303, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40499
in-theory        40499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40499.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-270, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40500
in-theory        40500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40500.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-239, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40501
in-theory        40501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40501.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> (H or G)) or I))), M:tm-210, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40502
in-theory        40502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40502.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-183, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40503
in-theory        40503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40503.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-157, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40504
in-theory        40504
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40504.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-147, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40505
in-theory        40505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40505.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-134, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40506
in-theory        40506
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40506.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-125, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40507
in-theory        40507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40507.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> (H or G)) or I))), M:tm-113, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40508
in-theory        40508
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40508.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-105, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40509
in-theory        40509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40509.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> (F or E)) or G))), M:tm-95, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40510
in-theory        40510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40510.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-83, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40511
in-theory        40511
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> (E or D)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40511.        (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> (E or D)) or F))), M:tm-76, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40512
in-theory        40512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> (F or E)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40512.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> (F or E)) or G))), M:tm-69, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40513
in-theory        40513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40513.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-54, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40514
in-theory        40514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40514.        ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> (F or E)) or G))), M:tm-42, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40515
in-theory        40515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40515.        ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> (F or E)) or G))), M:tm-32, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40516
in-theory        40516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40516.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> (F or E)) or G))), M:tm-23, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40517
in-theory        40517
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40517.        (((A and B) -> B) and ((C -> (D -> C)) and ((E -> (F or E)) or G))), M:tm-22, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40518
in-theory        40518
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40518.        (((A and B) -> A) and ((C -> (D -> C)) and ((E -> (F or E)) or G))), M:tm-21, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40519
in-theory        40519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40519.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-20, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40520
in-theory        40520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40520.        ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> (F or E)) or G))), M:tm-19, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40521
in-theory        40521
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-7 tm-5 tm-1 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40521.        (A or ((B -> (C -> B)) and ((D -> (E or D)) or F))), M:tm-7, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40522
in-theory        40522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-6 tm-5 tm-1 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40522.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) or F), M:tm-6, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40523
in-theory        40523
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((D -> (E or D)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40523.        (A -> (((B -> (C -> B)) and ((D -> (E or D)) or F)) and A)), M:tm-5, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40524
in-theory        40524
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-1 tm-5 tm-6 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40524.        (A -> ((B -> (C -> B)) and ((D -> (E or D)) or F))), M:tm-1, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-40525
in-theory        40525
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-540 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40525.        ((A or (B -> (C or B))) and (D or ((E -> (F or E)) or G))), M:tm-540, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40526
in-theory        40526
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-530 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40526.        ((A or (B -> (B or C))) and (D or ((E -> (F or E)) or G))), M:tm-530, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40527
in-theory        40527
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-520 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40527.        ((A or (B -> (C -> (B and C)))) and (D or ((E -> (F or E)) or G))), M:tm-520, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40528
in-theory        40528
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-510 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40528.        ((A or ((B and C) -> C)) and (D or ((E -> (F or E)) or G))), M:tm-510, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40529
in-theory        40529
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-500 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40529.        ((A or ((B and C) -> B)) and (D or ((E -> (F or E)) or G))), M:tm-500, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40530
in-theory        40530
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-490 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40530.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G or F)) or H))), M:tm-490, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40531
in-theory        40531
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-480 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40531.        ((A or (B -> (C -> B))) and (D or ((E -> (F or E)) or G))), M:tm-480, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40532
in-theory        40532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-469 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40532.        ((A -> (B -> (B or C))) and (D or ((E -> (F or E)) or G))), M:tm-469, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40533
in-theory        40533
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40533.        ((A or ((B -> (C or B)) or D)) and (E -> (E or F))), M:tm-456, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40534
in-theory        40534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-453 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40534.        ((A -> ((B -> (B or C)) and A)) and (D or ((E -> (F or E)) or G))), M:tm-453, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40535
in-theory        40535
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and ((E -> (E or F)) and (A or ((B -> (C or B)) or D))))
theorem-size     25
proof            (modus-ponens tm-443 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40535.        ((A or ((B -> (C or B)) or D)) and ((E -> (E or F)) and (A or ((B -> (C or B)) or D)))), M:tm-443, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40536
in-theory        40536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-409 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40536.        (((A -> (A or B)) or C) and (D or ((E -> (F or E)) or G))), M:tm-409, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40537
in-theory        40537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-400 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40537.        (((A -> (B -> (A and B))) or C) and (D or ((E -> (F or E)) or G))), M:tm-400, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40538
in-theory        40538
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-391 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40538.        ((((A and B) -> B) or C) and (D or ((E -> (F or E)) or G))), M:tm-391, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40539
in-theory        40539
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-382 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40539.        ((((A and B) -> A) or C) and (D or ((E -> (F or E)) or G))), M:tm-382, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40540
in-theory        40540
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-373 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40540.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> (G or F)) or H))), M:tm-373, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40541
in-theory        40541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-364 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40541.        (((A -> (B -> A)) or C) and (D or ((E -> (F or E)) or G))), M:tm-364, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40542
in-theory        40542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-354 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40542.        ((A -> (B -> (C -> (B and C)))) and (D or ((E -> (F or E)) or G))), M:tm-354, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40543
in-theory        40543
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40543.        ((A or ((B -> (C or B)) or D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40544
in-theory        40544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((D -> (E or D)) or F)))
theorem-size     19
proof            (modus-ponens tm-338 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40544.        (((A -> B) -> (A -> (A and B))) and (C or ((D -> (E or D)) or F))), M:tm-338, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40545
in-theory        40545
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and ((E -> (F -> (E and F))) and (A or ((B -> (C or B)) or D))))
theorem-size     27
proof            (modus-ponens tm-327 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40545.        ((A or ((B -> (C or B)) or D)) and ((E -> (F -> (E and F))) and (A or ((B -> (C or B)) or D)))), M:tm-327, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40546
in-theory        40546
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and (((E and F) -> F) and (A or ((B -> (C or B)) or D))))
theorem-size     25
proof            (modus-ponens tm-326 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40546.        ((A or ((B -> (C or B)) or D)) and (((E and F) -> F) and (A or ((B -> (C or B)) or D)))), M:tm-326, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40547
in-theory        40547
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and (((E and F) -> E) and (A or ((B -> (C or B)) or D))))
theorem-size     25
proof            (modus-ponens tm-325 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40547.        ((A or ((B -> (C or B)) or D)) and (((E and F) -> E) and (A or ((B -> (C or B)) or D)))), M:tm-325, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40548
in-theory        40548
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> (C or B)) or D))))
theorem-size     33
proof            (modus-ponens tm-324 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40548.        ((A or ((B -> (C or B)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> (C or B)) or D)))), M:tm-324, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40549
in-theory        40549
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and ((E -> (F -> E)) and (A or ((B -> (C or B)) or D))))
theorem-size     25
proof            (modus-ponens tm-323 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40549.        ((A or ((B -> (C or B)) or D)) and ((E -> (F -> E)) and (A or ((B -> (C or B)) or D)))), M:tm-323, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40550
in-theory        40550
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40550.        ((A or ((B -> (C or B)) or D)) and ((E and F) -> F)), M:tm-322, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40551
in-theory        40551
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40551.        ((A or ((B -> (C or B)) or D)) and ((E and F) -> E)), M:tm-320, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40552
in-theory        40552
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40552.        ((A or ((B -> (C or B)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40553
in-theory        40553
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40553.        ((A or ((B -> (C or B)) or D)) and (E -> (F -> E))), M:tm-315, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40554
in-theory        40554
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and (E or (A or ((B -> (C or B)) or D))))
theorem-size     21
proof            (modus-ponens tm-311 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40554.        ((A or ((B -> (C or B)) or D)) and (E or (A or ((B -> (C or B)) or D)))), M:tm-311, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40555
in-theory        40555
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and ((A or ((B -> (C or B)) or D)) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40555.        ((A or ((B -> (C or B)) or D)) and ((A or ((B -> (C or B)) or D)) or E)), M:tm-310, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40556
in-theory        40556
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and (E -> ((A or ((B -> (C or B)) or D)) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40556.        ((A or ((B -> (C or B)) or D)) and (E -> ((A or ((B -> (C or B)) or D)) and E))), M:tm-309, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40557
in-theory        40557
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and (E -> (A or ((B -> (C or B)) or D))))
theorem-size     21
proof            (modus-ponens tm-305 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40557.        ((A or ((B -> (C or B)) or D)) and (E -> (A or ((B -> (C or B)) or D)))), M:tm-305, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40558
in-theory        40558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-303 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40558.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> (F or E)) or G))), M:tm-303, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40559
in-theory        40559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-270 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40559.        ((A -> (((B and C) -> C) and A)) and (D or ((E -> (F or E)) or G))), M:tm-270, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40560
in-theory        40560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-239 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40560.        ((A -> (((B and C) -> B) and A)) and (D or ((E -> (F or E)) or G))), M:tm-239, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40561
in-theory        40561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-210 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40561.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> (G or F)) or H))), M:tm-210, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40562
in-theory        40562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-183 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40562.        ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> (F or E)) or G))), M:tm-183, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40563
in-theory        40563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-157 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40563.        ((A -> ((B and C) -> C)) and (D or ((E -> (F or E)) or G))), M:tm-157, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40564
in-theory        40564
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> (F or E)) or G)))
theorem-size     25
proof            (modus-ponens tm-147 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40564.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> (F or E)) or G))), M:tm-147, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40565
in-theory        40565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-134 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40565.        ((A -> ((B and C) -> B)) and (D or ((E -> (F or E)) or G))), M:tm-134, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40566
in-theory        40566
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> (F or E)) or G)))
theorem-size     25
proof            (modus-ponens tm-125 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40566.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> (F or E)) or G))), M:tm-125, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40567
in-theory        40567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-113 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40567.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> (G or F)) or H))), M:tm-113, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40568
in-theory        40568
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> (F or E)) or G)))
theorem-size     29
proof            (modus-ponens tm-105 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40568.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> (F or E)) or G))), M:tm-105, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40569
in-theory        40569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((D -> (E or D)) or F)))
theorem-size     17
proof            (modus-ponens tm-95 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40569.        (((A -> B) -> (A -> A)) and (C or ((D -> (E or D)) or F))), M:tm-95, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40570
in-theory        40570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-83 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40570.        ((A -> (B -> (C -> B))) and (D or ((E -> (F or E)) or G))), M:tm-83, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40571
in-theory        40571
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((C -> (D or C)) or E)))
theorem-size     15
proof            (modus-ponens tm-76 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40571.        (((not (not A)) -> A) and (B or ((C -> (D or C)) or E))), M:tm-76, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40572
in-theory        40572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> (E or D)) or F)))
theorem-size     21
proof            (modus-ponens tm-69 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40572.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> (E or D)) or F))), M:tm-69, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40573
in-theory        40573
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-54 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40573.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> (F or E)) or G))), M:tm-54, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40574
in-theory        40574
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-42 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40574.        ((A -> (B or A)) and (C or ((D -> (E or D)) or F))), M:tm-42, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40575
in-theory        40575
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-32 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40575.        ((A -> (A or B)) and (C or ((D -> (E or D)) or F))), M:tm-32, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40576
in-theory        40576
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((D -> (E or D)) or F)))
theorem-size     17
proof            (modus-ponens tm-23 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40576.        ((A -> (B -> (A and B))) and (C or ((D -> (E or D)) or F))), M:tm-23, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40577
in-theory        40577
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-22 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40577.        (((A and B) -> B) and (C or ((D -> (E or D)) or F))), M:tm-22, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40578
in-theory        40578
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-21 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40578.        (((A and B) -> A) and (C or ((D -> (E or D)) or F))), M:tm-21, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40579
in-theory        40579
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-20 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40579.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F or E)) or G))), M:tm-20, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40580
in-theory        40580
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-19 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40580.        ((A -> (B -> A)) and (C or ((D -> (E or D)) or F))), M:tm-19, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40581
in-theory        40581
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or ((C -> (D or C)) or E)))
theorem-size     11
proof            (modus-ponens tm-7 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-7 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40581.        (A or (B or ((C -> (D or C)) or E))), M:tm-7, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40582
in-theory        40582
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-6 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40582.        ((A or ((B -> (C or B)) or D)) or E), M:tm-6, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40583
in-theory        40583
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> (D or C)) or E)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40583.        (A -> ((B or ((C -> (D or C)) or E)) and A)), M:tm-5, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40584
in-theory        40584
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (D or C)) or E)))
theorem-size     11
proof            (modus-ponens tm-1 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-1 tm-7 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40584.        (A -> (B or ((C -> (D or C)) or E))), M:tm-1, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-40585
in-theory        40585
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40585.        ((A or (B -> (C or B))) and (((D -> (E or D)) or F) or G)), M:tm-540, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40586
in-theory        40586
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40586.        ((A or (B -> (B or C))) and (((D -> (E or D)) or F) or G)), M:tm-530, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40587
in-theory        40587
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E or D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40587.        ((A or (B -> (C -> (B and C)))) and (((D -> (E or D)) or F) or G)), M:tm-520, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40588
in-theory        40588
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40588.        ((A or ((B and C) -> C)) and (((D -> (E or D)) or F) or G)), M:tm-510, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40589
in-theory        40589
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40589.        ((A or ((B and C) -> B)) and (((D -> (E or D)) or F) or G)), M:tm-500, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40590
in-theory        40590
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F or E)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40590.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F or E)) or G) or H)), M:tm-490, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40591
in-theory        40591
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40591.        ((A or (B -> (C -> B))) and (((D -> (E or D)) or F) or G)), M:tm-480, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40592
in-theory        40592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40592.        ((A -> (B -> (B or C))) and (((D -> (E or D)) or F) or G)), M:tm-469, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40593
in-theory        40593
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40593.        ((((A -> (B or A)) or C) or D) and (E -> (E or F))), M:tm-456, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40594
in-theory        40594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E or D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40594.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E or D)) or F) or G)), M:tm-453, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40595
in-theory        40595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and ((E -> (E or F)) and (((A -> (B or A)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40595.        ((((A -> (B or A)) or C) or D) and ((E -> (E or F)) and (((A -> (B or A)) or C) or D))), M:tm-443, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40596
in-theory        40596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40596.        (((A -> (A or B)) or C) and (((D -> (E or D)) or F) or G)), M:tm-409, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40597
in-theory        40597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E or D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40597.        (((A -> (B -> (A and B))) or C) and (((D -> (E or D)) or F) or G)), M:tm-400, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40598
in-theory        40598
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40598.        ((((A and B) -> B) or C) and (((D -> (E or D)) or F) or G)), M:tm-391, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40599
in-theory        40599
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40599.        ((((A and B) -> A) or C) and (((D -> (E or D)) or F) or G)), M:tm-382, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40600
in-theory        40600
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F or E)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40600.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F or E)) or G) or H)), M:tm-373, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40601
in-theory        40601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40601.        (((A -> (B -> A)) or C) and (((D -> (E or D)) or F) or G)), M:tm-364, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40602
in-theory        40602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E or D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40602.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E or D)) or F) or G)), M:tm-354, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40603
in-theory        40603
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40603.        ((((A -> (B or A)) or C) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40604
in-theory        40604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D or C)) or E) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40604.        (((A -> B) -> (A -> (A and B))) and (((C -> (D or C)) or E) or F)), M:tm-338, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40605
in-theory        40605
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and ((E -> (F -> (E and F))) and (((A -> (B or A)) or C) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40605.        ((((A -> (B or A)) or C) or D) and ((E -> (F -> (E and F))) and (((A -> (B or A)) or C) or D))), M:tm-327, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40606
in-theory        40606
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and (((E and F) -> F) and (((A -> (B or A)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40606.        ((((A -> (B or A)) or C) or D) and (((E and F) -> F) and (((A -> (B or A)) or C) or D))), M:tm-326, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40607
in-theory        40607
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and (((E and F) -> E) and (((A -> (B or A)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40607.        ((((A -> (B or A)) or C) or D) and (((E and F) -> E) and (((A -> (B or A)) or C) or D))), M:tm-325, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40608
in-theory        40608
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B or A)) or C) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40608.        ((((A -> (B or A)) or C) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B or A)) or C) or D))), M:tm-324, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40609
in-theory        40609
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and ((E -> (F -> E)) and (((A -> (B or A)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40609.        ((((A -> (B or A)) or C) or D) and ((E -> (F -> E)) and (((A -> (B or A)) or C) or D))), M:tm-323, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40610
in-theory        40610
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40610.        ((((A -> (B or A)) or C) or D) and ((E and F) -> F)), M:tm-322, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40611
in-theory        40611
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40611.        ((((A -> (B or A)) or C) or D) and ((E and F) -> E)), M:tm-320, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40612
in-theory        40612
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40612.        ((((A -> (B or A)) or C) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40613
in-theory        40613
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40613.        ((((A -> (B or A)) or C) or D) and (E -> (F -> E))), M:tm-315, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40614
in-theory        40614
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and (E or (((A -> (B or A)) or C) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40614.        ((((A -> (B or A)) or C) or D) and (E or (((A -> (B or A)) or C) or D))), M:tm-311, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40615
in-theory        40615
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and ((((A -> (B or A)) or C) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40615.        ((((A -> (B or A)) or C) or D) and ((((A -> (B or A)) or C) or D) or E)), M:tm-310, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40616
in-theory        40616
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and (E -> ((((A -> (B or A)) or C) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40616.        ((((A -> (B or A)) or C) or D) and (E -> ((((A -> (B or A)) or C) or D) and E))), M:tm-309, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40617
in-theory        40617
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and (E -> (((A -> (B or A)) or C) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40617.        ((((A -> (B or A)) or C) or D) and (E -> (((A -> (B or A)) or C) or D))), M:tm-305, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40618
in-theory        40618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E or D)) or F) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40618.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E or D)) or F) or G)), M:tm-303, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40619
in-theory        40619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E or D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40619.        ((A -> (((B and C) -> C) and A)) and (((D -> (E or D)) or F) or G)), M:tm-270, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40620
in-theory        40620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E or D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40620.        ((A -> (((B and C) -> B) and A)) and (((D -> (E or D)) or F) or G)), M:tm-239, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40621
in-theory        40621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F or E)) or G) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40621.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F or E)) or G) or H)), M:tm-210, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40622
in-theory        40622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E or D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40622.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E or D)) or F) or G)), M:tm-183, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40623
in-theory        40623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40623.        ((A -> ((B and C) -> C)) and (((D -> (E or D)) or F) or G)), M:tm-157, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40624
in-theory        40624
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E or D)) or F) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40624.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E or D)) or F) or G)), M:tm-147, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40625
in-theory        40625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40625.        ((A -> ((B and C) -> B)) and (((D -> (E or D)) or F) or G)), M:tm-134, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40626
in-theory        40626
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E or D)) or F) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40626.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E or D)) or F) or G)), M:tm-125, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40627
in-theory        40627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F or E)) or G) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40627.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F or E)) or G) or H)), M:tm-113, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40628
in-theory        40628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E or D)) or F) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40628.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E or D)) or F) or G)), M:tm-105, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40629
in-theory        40629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D or C)) or E) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40629.        (((A -> B) -> (A -> A)) and (((C -> (D or C)) or E) or F)), M:tm-95, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40630
in-theory        40630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40630.        ((A -> (B -> (C -> B))) and (((D -> (E or D)) or F) or G)), M:tm-83, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40631
in-theory        40631
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C or B)) or D) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40631.        (((not (not A)) -> A) and (((B -> (C or B)) or D) or E)), M:tm-76, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40632
in-theory        40632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D or C)) or E) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40632.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D or C)) or E) or F)), M:tm-69, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40633
in-theory        40633
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E or D)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40633.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E or D)) or F) or G)), M:tm-54, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40634
in-theory        40634
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D or C)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40634.        ((A -> (B or A)) and (((C -> (D or C)) or E) or F)), M:tm-42, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40635
in-theory        40635
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D or C)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40635.        ((A -> (A or B)) and (((C -> (D or C)) or E) or F)), M:tm-32, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40636
in-theory        40636
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D or C)) or E) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40636.        ((A -> (B -> (A and B))) and (((C -> (D or C)) or E) or F)), M:tm-23, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40637
in-theory        40637
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D or C)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40637.        (((A and B) -> B) and (((C -> (D or C)) or E) or F)), M:tm-22, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40638
in-theory        40638
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D or C)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40638.        (((A and B) -> A) and (((C -> (D or C)) or E) or F)), M:tm-21, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40639
in-theory        40639
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E or D)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40639.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E or D)) or F) or G)), M:tm-20, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40640
in-theory        40640
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D or C)) or E) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40640.        ((A -> (B -> A)) and (((C -> (D or C)) or E) or F)), M:tm-19, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40641
in-theory        40641
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> (C or B)) or D) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-7 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40641.        (A or (((B -> (C or B)) or D) or E)), M:tm-7, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40642
in-theory        40642
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-6 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40642.        ((((A -> (B or A)) or C) or D) or E), M:tm-6, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40643
in-theory        40643
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (C or B)) or D) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40643.        (A -> ((((B -> (C or B)) or D) or E) and A)), M:tm-5, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40644
in-theory        40644
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) or D) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-1 tm-6 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40644.        (A -> (((B -> (C or B)) or D) or E)), M:tm-1, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-40645
in-theory        40645
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-550 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40645.        (((A -> (B or A)) or C) and (D -> (E or D))), M:tm-550, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-40646
in-theory        40646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-40646.        (((A -> (B or A)) or C) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-550, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-40647
in-theory        40647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-550 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-40647.        (((A -> (B or A)) or C) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-550, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-40648
in-theory        40648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-550 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-40648.        (((A -> (B or A)) or C) and ((not (not D)) -> D)), M:tm-550, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-40649
in-theory        40649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-550 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40649.        (((A -> (B or A)) or C) and (D -> (E -> (F -> E)))), M:tm-550, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-40650
in-theory        40650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-550 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-40650.        (((A -> (B or A)) or C) and ((D -> E) -> (D -> D))), M:tm-550, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-40651
in-theory        40651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-550 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-40651.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-550, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-40652
in-theory        40652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40652.        (((A -> (B or A)) or C) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-550, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-40653
in-theory        40653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-550 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-40653.        (((A -> (B or A)) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-550, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-40654
in-theory        40654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-550 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40654.        (((A -> (B or A)) or C) and (D -> ((E and F) -> E))), M:tm-550, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-40655
in-theory        40655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-550 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-40655.        (((A -> (B or A)) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-550, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-40656
in-theory        40656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-550 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40656.        (((A -> (B or A)) or C) and (D -> ((E and F) -> F))), M:tm-550, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-40657
in-theory        40657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-550 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40657.        (((A -> (B or A)) or C) and (D -> ((E -> (F -> E)) and D))), M:tm-550, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-40658
in-theory        40658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-550 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40658.        (((A -> (B or A)) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-550, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-40659
in-theory        40659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-550 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40659.        (((A -> (B or A)) or C) and (D -> (((E and F) -> E) and D))), M:tm-550, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-40660
in-theory        40660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-550 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40660.        (((A -> (B or A)) or C) and (D -> (((E and F) -> F) and D))), M:tm-550, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-40661
in-theory        40661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40661.        (((A -> (B or A)) or C) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-550, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-40662
in-theory        40662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-550 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-40662.        (((A -> (B or A)) or C) and ((D -> E) -> (D -> (D and E)))), M:tm-550, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-40663
in-theory        40663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40663.        (((A -> (B or A)) or C) and (D -> (E -> (F -> (E and F))))), M:tm-550, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-40664
in-theory        40664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-550 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40664.        (((A -> (B or A)) or C) and ((D -> (E -> D)) or F)), M:tm-550, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-40665
in-theory        40665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-550 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40665.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-550, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-40666
in-theory        40666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-550 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40666.        (((A -> (B or A)) or C) and (((D and E) -> D) or F)), M:tm-550, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-40667
in-theory        40667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-550 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40667.        (((A -> (B or A)) or C) and (((D and E) -> E) or F)), M:tm-550, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-40668
in-theory        40668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-550 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40668.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) or F)), M:tm-550, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-40669
in-theory        40669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-550 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40669.        (((A -> (B or A)) or C) and ((D -> (D or E)) or F)), M:tm-550, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-40670
in-theory        40670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-550 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40670.        (((A -> (B or A)) or C) and (D -> ((E -> (E or F)) and D))), M:tm-550, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-40671
in-theory        40671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-550 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40671.        (((A -> (B or A)) or C) and (D -> (E -> (E or F)))), M:tm-550, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-40672
in-theory        40672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-550 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40672.        (((A -> (B or A)) or C) and (D or (E -> (F -> E)))), M:tm-550, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-40673
in-theory        40673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40673.        (((A -> (B or A)) or C) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-550, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-40674
in-theory        40674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-550 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40674.        (((A -> (B or A)) or C) and (D or ((E and F) -> E))), M:tm-550, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-40675
in-theory        40675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-550 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40675.        (((A -> (B or A)) or C) and (D or ((E and F) -> F))), M:tm-550, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-40676
in-theory        40676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40676.        (((A -> (B or A)) or C) and (D or (E -> (F -> (E and F))))), M:tm-550, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-40677
in-theory        40677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-550 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40677.        (((A -> (B or A)) or C) and (D or (E -> (E or F)))), M:tm-550, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-40678
in-theory        40678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-550 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40678.        (((A -> (B or A)) or C) and (D or (E -> (F or E)))), M:tm-550, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-40679
in-theory        40679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-550 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40679.        (((A -> (B or A)) or C) and ((D -> (E or D)) or F)), M:tm-550, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-40680
in-theory        40680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-550 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40680.        (((A -> (B or A)) or C) and (D -> ((E -> (F or E)) and D))), M:tm-550, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-40681
in-theory        40681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-550 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40681.        (((A -> (B or A)) or C) and (D -> (E -> (F or E)))), M:tm-550, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-40682
in-theory        40682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-550 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-40682.        (((A -> (B or A)) or C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-550, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-40683
in-theory        40683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-550 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-40683.        (((A -> (B or A)) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-550, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-40684
in-theory        40684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-550 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-40684.        (((A -> (B or A)) or C) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-550, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-40685
in-theory        40685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-550 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-40685.        (((A -> (B or A)) or C) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-550, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-40686
in-theory        40686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-550 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-40686.        (((A -> (B or A)) or C) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-550, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-40687
in-theory        40687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-550 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-40687.        (((A -> (B or A)) or C) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-550, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-40688
in-theory        40688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-550 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-40688.        (((A -> (B or A)) or C) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-550, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-40689
in-theory        40689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-550 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-40689.        (((A -> (B or A)) or C) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-550, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-40690
in-theory        40690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-40690.        (((A -> (B or A)) or C) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-550, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-40691
in-theory        40691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-550 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-40691.        (((A -> (B or A)) or C) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-550, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-40692
in-theory        40692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-550 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-40692.        (((A -> (B or A)) or C) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-550, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-40693
in-theory        40693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-550 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-40693.        (((A -> (B or A)) or C) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-550, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-40694
in-theory        40694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-40694.        (((A -> (B or A)) or C) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-550, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-40695
in-theory        40695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-550 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-40695.        (((A -> (B or A)) or C) and ((D -> (not (E -> D))) -> (not D))), M:tm-550, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-40696
in-theory        40696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-40696.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-550, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-40697
in-theory        40697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-550 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-40697.        (((A -> (B or A)) or C) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-550, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-40698
in-theory        40698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-550 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-40698.        (((A -> (B or A)) or C) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-550, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-40699
in-theory        40699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-40699.        (((A -> (B or A)) or C) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-550, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-40700
in-theory        40700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-550 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-40700.        (((A -> (B or A)) or C) and ((D -> (not (D or E))) -> (not D))), M:tm-550, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-40701
in-theory        40701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-550 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-40701.        (((A -> (B or A)) or C) and ((D -> (not (E or D))) -> (not D))), M:tm-550, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-40702
in-theory        40702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-550 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-40702.        (((A -> (B or A)) or C) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-550, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-40703
in-theory        40703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-550 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-40703.        (((A -> (B or A)) or C) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-550, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-40704
in-theory        40704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-550 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-40704.        (((A -> (B or A)) or C) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-550, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-40705
in-theory        40705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-40705.        (((A -> (B or A)) or C) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-550, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-40706
in-theory        40706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-550 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-40706.        (((A -> (B or A)) or C) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-550, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-40707
in-theory        40707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-550 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-40707.        (((A -> (B or A)) or C) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-550, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-40708
in-theory        40708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-550 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-40708.        (((A -> (B or A)) or C) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-550, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-40709
in-theory        40709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-40709.        (((A -> (B or A)) or C) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-550, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-40710
in-theory        40710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-550 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-40710.        (((A -> (B or A)) or C) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-550, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-40711
in-theory        40711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-550 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-40711.        (((A -> (B or A)) or C) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-550, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-40712
in-theory        40712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-550 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-40712.        (((A -> (B or A)) or C) and (D or ((not (not E)) -> E))), M:tm-550, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-40713
in-theory        40713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-550 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-40713.        (((A -> (B or A)) or C) and (((not (not D)) -> D) or E)), M:tm-550, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-40714
in-theory        40714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-550 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-40714.        (((A -> (B or A)) or C) and (D -> (((not (not E)) -> E) and D))), M:tm-550, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-40715
in-theory        40715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-550 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-40715.        (((A -> (B or A)) or C) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-550, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-40716
in-theory        40716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-550 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-40716.        (((A -> (B or A)) or C) and (D -> ((not (not E)) -> E))), M:tm-550, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-40717
in-theory        40717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-40717.        (((A -> (B or A)) or C) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-550, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-40718
in-theory        40718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-550 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-40718.        (((A -> (B or A)) or C) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-550, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-40719
in-theory        40719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-40719.        (((A -> (B or A)) or C) and (D or (E -> (F -> (G -> F))))), M:tm-550, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-40720
in-theory        40720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-40720.        (((A -> (B or A)) or C) and ((D -> (E -> (F -> E))) or G)), M:tm-550, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-40721
in-theory        40721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-40721.        (((A -> (B or A)) or C) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-550, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-40722
in-theory        40722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-550 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-40722.        (((A -> (B or A)) or C) and ((D -> E) -> (D -> (F -> E)))), M:tm-550, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-40723
in-theory        40723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-40723.        (((A -> (B or A)) or C) and (D -> (E -> (F -> (G -> F))))), M:tm-550, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-40724
in-theory        40724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-550 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-40724.        (((A -> (B or A)) or C) and (D -> D)), M:tm-550, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-40725
in-theory        40725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-40725.        (((A -> (B or A)) or C) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-550, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-40726
in-theory        40726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-550 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-40726.        (((A -> (B or A)) or C) and ((D and E) -> (D and E))), M:tm-550, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-40727
in-theory        40727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-550 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-40727.        (((A -> (B or A)) or C) and ((D -> E) -> (D -> E))), M:tm-550, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-40728
in-theory        40728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-550 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-40728.        (((A -> (B or A)) or C) and ((not (not D)) -> (not (not D)))), M:tm-550, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-40729
in-theory        40729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-550 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-40729.        (((A -> (B or A)) or C) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-550, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-40730
in-theory        40730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-550 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-40730.        (((A -> (B or A)) or C) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-550, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-40731
in-theory        40731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-550 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-40731.        (((A -> (B or A)) or C) and (D or ((E -> F) -> (E -> E)))), M:tm-550, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-40732
in-theory        40732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-550 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-40732.        (((A -> (B or A)) or C) and (((D -> E) -> (D -> D)) or F)), M:tm-550, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-40733
in-theory        40733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-40733.        (((A -> (B or A)) or C) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-550, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-40734
in-theory        40734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-40734.        (((A -> (B or A)) or C) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-550, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-40735
in-theory        40735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-550 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-40735.        (((A -> (B or A)) or C) and (D -> ((E -> F) -> (E -> E)))), M:tm-550, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-40736
in-theory        40736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-40736.        (((A -> (B or A)) or C) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-550, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-40737
in-theory        40737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-550 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-40737.        (((A -> (B or A)) or C) and ((D -> (D -> E)) -> (D -> E))), M:tm-550, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-40738
in-theory        40738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-550 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-40738.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-550, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-40739
in-theory        40739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-550 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-40739.        (((A -> (B or A)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-550, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-40740
in-theory        40740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-550 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-40740.        (((A -> (B or A)) or C) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-550, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-40741
in-theory        40741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-40741.        (((A -> (B or A)) or C) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-550, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-40742
in-theory        40742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-550 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-40742.        (((A -> (B or A)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-550, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-40743
in-theory        40743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-550 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-40743.        (((A -> (B or A)) or C) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-550, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-40744
in-theory        40744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-550 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-40744.        (((A -> (B or A)) or C) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-550, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-40745
in-theory        40745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-40745.        (((A -> (B or A)) or C) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-550, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-40746
in-theory        40746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-550 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-40746.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-550, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-40747
in-theory        40747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-550 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-40747.        (((A -> (B or A)) or C) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-550, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-40748
in-theory        40748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-550 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-40748.        (((A -> (B or A)) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-550, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-40749
in-theory        40749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-550 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-40749.        (((A -> (B or A)) or C) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-550, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-40750
in-theory        40750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-550 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-40750.        (((A -> (B or A)) or C) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-550, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-40751
in-theory        40751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-550 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-40751.        (((A -> (B or A)) or C) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-550, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-40752
in-theory        40752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-550 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-40752.        (((A -> (B or A)) or C) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-550, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-40753
in-theory        40753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-550 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-40753.        (((A -> (B or A)) or C) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-550, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-40754
in-theory        40754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-550 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-40754.        (((A -> (B or A)) or C) and (((D -> E) and D) -> E)), M:tm-550, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-40755
in-theory        40755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-550 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-40755.        (((A -> (B or A)) or C) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-550, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-40756
in-theory        40756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-550 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-40756.        (((A -> (B or A)) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-550, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-40757
in-theory        40757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-550 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-40757.        (((A -> (B or A)) or C) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-550, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-40758
in-theory        40758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-550 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-40758.        (((A -> (B or A)) or C) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-550, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-40759
in-theory        40759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-550 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-40759.        (((A -> (B or A)) or C) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-550, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-40760
in-theory        40760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-550 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-40760.        (((A -> (B or A)) or C) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-550, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-40761
in-theory        40761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-550 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-40761.        (((A -> (B or A)) or C) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-550, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-40762
in-theory        40762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-550 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-40762.        (((A -> (B or A)) or C) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-550, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-40763
in-theory        40763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-550 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-40763.        (((A -> (B or A)) or C) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-550, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-40764
in-theory        40764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-550 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-40764.        (((A -> (B or A)) or C) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-550, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-40765
in-theory        40765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-550 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-40765.        (((A -> (B or A)) or C) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-550, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-40766
in-theory        40766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-550 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-40766.        (((A -> (B or A)) or C) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-550, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-40767
in-theory        40767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-550 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-40767.        (((A -> (B or A)) or C) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-550, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-40768
in-theory        40768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-1 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-40768.        (((A -> (B or A)) or C) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-550, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-40769
in-theory        40769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-550 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-40769.        (((A -> (B or A)) or C) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-550, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-40770
in-theory        40770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-550 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-40770.        (((A -> (B or A)) or C) and (D or (E -> ((F and G) -> F)))), M:tm-550, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-40771
in-theory        40771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-40771.        (((A -> (B or A)) or C) and ((D -> ((E and F) -> E)) or G)), M:tm-550, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-40772
in-theory        40772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-40772.        (((A -> (B or A)) or C) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-550, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-40773
in-theory        40773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-550 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-40773.        (((A -> (B or A)) or C) and ((D -> (E and F)) -> (D -> E))), M:tm-550, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-40774
in-theory        40774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-550 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-40774.        (((A -> (B or A)) or C) and (D -> (E -> ((F and G) -> F)))), M:tm-550, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-40775
in-theory        40775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-550 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-40775.        (((A -> (B or A)) or C) and ((D and (D -> E)) -> E)), M:tm-550, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-40776
in-theory        40776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-550 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-40776.        (((A -> (B or A)) or C) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-550, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-40777
in-theory        40777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-550 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-40777.        (((A -> (B or A)) or C) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-550, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-40778
in-theory        40778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-550 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-40778.        (((A -> (B or A)) or C) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-550, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-40779
in-theory        40779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-550 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-40779.        (((A -> (B or A)) or C) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-550, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-40780
in-theory        40780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-550 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-40780.        (((A -> (B or A)) or C) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-550, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-40781
in-theory        40781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-550 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-40781.        (((A -> (B or A)) or C) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-550, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-40782
in-theory        40782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-550 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-40782.        (((A -> (B or A)) or C) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-550, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-40783
in-theory        40783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-550 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-40783.        (((A -> (B or A)) or C) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-550, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-40784
in-theory        40784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-550 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-40784.        (((A -> (B or A)) or C) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-550, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-40785
in-theory        40785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-550 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-40785.        (((A -> (B or A)) or C) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-550, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-40786
in-theory        40786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-550 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-40786.        (((A -> (B or A)) or C) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-550, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-40787
in-theory        40787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-550 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-40787.        (((A -> (B or A)) or C) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-550, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-40788
in-theory        40788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-550 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-40788.        (((A -> (B or A)) or C) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-550, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-40789
in-theory        40789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-550 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-40789.        (((A -> (B or A)) or C) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-550, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-40790
in-theory        40790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-550 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-40790.        (((A -> (B or A)) or C) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-550, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-40791
in-theory        40791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-1 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-40791.        (((A -> (B or A)) or C) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-550, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-40792
in-theory        40792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-550 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-40792.        (((A -> (B or A)) or C) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-550, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-40793
in-theory        40793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-550 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-40793.        (((A -> (B or A)) or C) and (D or (E -> ((F and G) -> G)))), M:tm-550, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-40794
in-theory        40794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-40794.        (((A -> (B or A)) or C) and ((D -> ((E and F) -> F)) or G)), M:tm-550, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-40795
in-theory        40795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-40795.        (((A -> (B or A)) or C) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-550, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-40796
in-theory        40796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-550 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-40796.        (((A -> (B or A)) or C) and ((D -> (E and F)) -> (D -> F))), M:tm-550, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-40797
in-theory        40797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-550 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-40797.        (((A -> (B or A)) or C) and (D -> (E -> ((F and G) -> G)))), M:tm-550, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-40798
in-theory        40798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40798.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-550, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-40799
in-theory        40799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40799.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-550, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-40800
in-theory        40800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40800.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-550, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-40801
in-theory        40801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-550 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40801.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-550, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-40802
in-theory        40802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40802.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-550, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-40803
in-theory        40803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-550 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40803.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-550, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-40804
in-theory        40804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40804.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-550, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40805
in-theory        40805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-40805.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-550, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-40806
in-theory        40806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-550 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-40806.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-550, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-40807
in-theory        40807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-40807.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-550, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-40808
in-theory        40808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-40808.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-550, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-40809
in-theory        40809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-40809.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-550, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-40810
in-theory        40810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-550 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-40810.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-550, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-40811
in-theory        40811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-40811.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-550, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-40812
in-theory        40812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-550 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-40812.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-550, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-40813
in-theory        40813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-550 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-40813.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-550, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-40814
in-theory        40814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-550 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-40814.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-550, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-40815
in-theory        40815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-550 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-40815.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-550, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-40816
in-theory        40816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-40816.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-550, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-40817
in-theory        40817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-40817.        (((A -> (B or A)) or C) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-550, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-40818
in-theory        40818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-550 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-40818.        (((A -> (B or A)) or C) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-550, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-40819
in-theory        40819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-550 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-40819.        (((A -> (B or A)) or C) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-550, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-40820
in-theory        40820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-550 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-40820.        (((A -> (B or A)) or C) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-550, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-40821
in-theory        40821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-40821.        (((A -> (B or A)) or C) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-550, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-40822
in-theory        40822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-550 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-40822.        (((A -> (B or A)) or C) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-550, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-40823
in-theory        40823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-550 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40823.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-550, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-40824
in-theory        40824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40824.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-550, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-40825
in-theory        40825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-550 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40825.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-550, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-40826
in-theory        40826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-550 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40826.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-550, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-40827
in-theory        40827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40827.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-550, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-40828
in-theory        40828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40828.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-550, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-40829
in-theory        40829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-550 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40829.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-550, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-40830
in-theory        40830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-40830.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-550, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-40831
in-theory        40831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-550 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-40831.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-550, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-40832
in-theory        40832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-550 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-40832.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-550, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-40833
in-theory        40833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-40833.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-550, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-40834
in-theory        40834
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-550 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-40834.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-550, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-40835
in-theory        40835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-550 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-40835.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-550, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-40836
in-theory        40836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-550 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-40836.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-550, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-40837
in-theory        40837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-550 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-40837.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-550, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-40838
in-theory        40838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-550 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-40838.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-550, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-40839
in-theory        40839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-550 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-40839.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-550, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-40840
in-theory        40840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-550 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-40840.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-550, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-40841
in-theory        40841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-550 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-40841.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-550, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-40842
in-theory        40842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-550 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-40842.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-550, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-40843
in-theory        40843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-550 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-40843.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-550, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-40844
in-theory        40844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-550 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-40844.        (((A -> (B or A)) or C) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-550, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-40845
in-theory        40845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-550 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-40845.        (((A -> (B or A)) or C) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-550, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-40846
in-theory        40846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-550 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-40846.        (((A -> (B or A)) or C) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-550, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-40847
in-theory        40847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-550 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-40847.        (((A -> (B or A)) or C) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-550, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-40848
in-theory        40848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-550 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-40848.        (((A -> (B or A)) or C) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-550, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-40849
in-theory        40849
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-550 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-40849.        (((A -> (B or A)) or C) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-550, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-40850
in-theory        40850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40850.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-550, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-40851
in-theory        40851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40851.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-550, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-40852
in-theory        40852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40852.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((F and G) -> F))), M:tm-550, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-40853
in-theory        40853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-550 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40853.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((F and G) -> G))), M:tm-550, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-40854
in-theory        40854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40854.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-550, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-40855
in-theory        40855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-550 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40855.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (F or G)))), M:tm-550, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-40856
in-theory        40856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40856.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (G or F)))), M:tm-550, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40857
in-theory        40857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-40857.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-550, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-40858
in-theory        40858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-550 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-40858.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-550, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-40859
in-theory        40859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-40859.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-550, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-40860
in-theory        40860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-40860.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-550, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-40861
in-theory        40861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-40861.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-550, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-40862
in-theory        40862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-550 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-40862.        (((A -> (B or A)) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-550, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-40863
in-theory        40863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-40863.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-550, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-40864
in-theory        40864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-550 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-40864.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-550, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-40865
in-theory        40865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-550 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-40865.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-550, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-40866
in-theory        40866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-550 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-40866.        (((A -> (B or A)) or C) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-550, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-40867
in-theory        40867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-550 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-40867.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-550, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-40868
in-theory        40868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-40868.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-550, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-40869
in-theory        40869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-550 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-40869.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-550, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-40870
in-theory        40870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-40870.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-550, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-40871
in-theory        40871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-550 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-40871.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-550, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-40872
in-theory        40872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-40872.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-550, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-40873
in-theory        40873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-40873.        (((A -> (B or A)) or C) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-550, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-40874
in-theory        40874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-550 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-40874.        (((A -> (B or A)) or C) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-550, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-40875
in-theory        40875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-550 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-40875.        (((A -> (B or A)) or C) and (D or (E -> (((F and G) -> F) and E)))), M:tm-550, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-40876
in-theory        40876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-550 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-40876.        (((A -> (B or A)) or C) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-550, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-40877
in-theory        40877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-40877.        (((A -> (B or A)) or C) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-550, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-40878
in-theory        40878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-550 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-40878.        (((A -> (B or A)) or C) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-550, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-40879
in-theory        40879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40879.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-550, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-40880
in-theory        40880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40880.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-550, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-40881
in-theory        40881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40881.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((F and G) -> F))), M:tm-550, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-40882
in-theory        40882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-550 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40882.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((F and G) -> G))), M:tm-550, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-40883
in-theory        40883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40883.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-550, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-40884
in-theory        40884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-550 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40884.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (F or G)))), M:tm-550, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-40885
in-theory        40885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40885.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (G or F)))), M:tm-550, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40886
in-theory        40886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-40886.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-550, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-40887
in-theory        40887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-550 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-40887.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-550, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-40888
in-theory        40888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-40888.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-550, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-40889
in-theory        40889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-40889.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-550, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-40890
in-theory        40890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-40890.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-550, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-40891
in-theory        40891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-550 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-40891.        (((A -> (B or A)) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-550, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-40892
in-theory        40892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-40892.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-550, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-40893
in-theory        40893
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-550 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-40893.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-550, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-40894
in-theory        40894
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-550 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-40894.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-550, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-40895
in-theory        40895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-550 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-40895.        (((A -> (B or A)) or C) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-550, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-40896
in-theory        40896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-550 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-40896.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-550, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-40897
in-theory        40897
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-40897.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-550, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-40898
in-theory        40898
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-550 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-40898.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-550, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-40899
in-theory        40899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-40899.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-550, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-40900
in-theory        40900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-40900.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-550, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-40901
in-theory        40901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-40901.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-550, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-40902
in-theory        40902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-550 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-40902.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-550, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-40903
in-theory        40903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-40903.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-550, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-40904
in-theory        40904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-40904.        (((A -> (B or A)) or C) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-550, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-40905
in-theory        40905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-550 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-40905.        (((A -> (B or A)) or C) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-550, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-40906
in-theory        40906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-550 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-40906.        (((A -> (B or A)) or C) and (D or (E -> (((F and G) -> G) and E)))), M:tm-550, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-40907
in-theory        40907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-550 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-40907.        (((A -> (B or A)) or C) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-550, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-40908
in-theory        40908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-40908.        (((A -> (B or A)) or C) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-550, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-40909
in-theory        40909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-550 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-40909.        (((A -> (B or A)) or C) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-550, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-40910
in-theory        40910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40910.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-550, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-40911
in-theory        40911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40911.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-550, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-40912
in-theory        40912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-550 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40912.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-550, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-40913
in-theory        40913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-550 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40913.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-550, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-40914
in-theory        40914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40914.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-550, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-40915
in-theory        40915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-550 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40915.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-550, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-40916
in-theory        40916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40916.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-550, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-40917
in-theory        40917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-40917.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-550, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-40918
in-theory        40918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-40918.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-550, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-40919
in-theory        40919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-550 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-40919.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-550, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-40920
in-theory        40920
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-40920.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-550, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-40921
in-theory        40921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-40921.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-550, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-40922
in-theory        40922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-40922.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-550, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-40923
in-theory        40923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-550 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-40923.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-550, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-40924
in-theory        40924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-550 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-40924.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-550, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-40925
in-theory        40925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-550 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-40925.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-550, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-40926
in-theory        40926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-550 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-40926.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-550, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-40927
in-theory        40927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-550 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-40927.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-550, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-40928
in-theory        40928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-550 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-40928.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-550, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-40929
in-theory        40929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-550 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-40929.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-550, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-40930
in-theory        40930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-550 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-40930.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-550, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-40931
in-theory        40931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-550 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-40931.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-550, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-40932
in-theory        40932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-550 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-40932.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-550, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-40933
in-theory        40933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-550 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-40933.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-550, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-40934
in-theory        40934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-550 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-40934.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-550, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-40935
in-theory        40935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-550 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-40935.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-550, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-40936
in-theory        40936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-550 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-40936.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-550, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-40937
in-theory        40937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-550 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-40937.        (((A -> (B or A)) or C) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-550, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-40938
in-theory        40938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-550 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-40938.        (((A -> (B or A)) or C) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-550, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-40939
in-theory        40939
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-550 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-40939.        (((A -> (B or A)) or C) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-550, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-40940
in-theory        40940
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-550 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-40940.        (((A -> (B or A)) or C) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-550, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-40941
in-theory        40941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-550 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-40941.        (((A -> (B or A)) or C) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-550, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-40942
in-theory        40942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-550 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-40942.        (((A -> (B or A)) or C) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-550, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-40943
in-theory        40943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-550 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-40943.        (((A -> (B or A)) or C) and (D -> (D and (E -> D)))), M:tm-550, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-40944
in-theory        40944
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-40944.        (((A -> (B or A)) or C) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-550, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-40945
in-theory        40945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-550 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-40945.        (((A -> (B or A)) or C) and ((D and E) -> ((D and E) and D))), M:tm-550, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-40946
in-theory        40946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-550 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-40946.        (((A -> (B or A)) or C) and ((D and E) -> ((D and E) and E))), M:tm-550, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-40947
in-theory        40947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-40947.        (((A -> (B or A)) or C) and (D -> (D and (E -> (D and E))))), M:tm-550, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-40948
in-theory        40948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-550 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-40948.        (((A -> (B or A)) or C) and (D -> (D and (D or E)))), M:tm-550, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-40949
in-theory        40949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-550 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-40949.        (((A -> (B or A)) or C) and (D -> (D and (E or D)))), M:tm-550, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-40950
in-theory        40950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-550 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-40950.        (((A -> (B or A)) or C) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-550, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-40951
in-theory        40951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-40951.        (((A -> (B or A)) or C) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-550, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-40952
in-theory        40952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-550 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-40952.        (((A -> (B or A)) or C) and ((not (not D)) -> ((not (not D)) and D))), M:tm-550, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-40953
in-theory        40953
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-40953.        (((A -> (B or A)) or C) and (D -> (D and (E -> (F -> E))))), M:tm-550, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-40954
in-theory        40954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-550 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-40954.        (((A -> (B or A)) or C) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-550, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-40955
in-theory        40955
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-550 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-40955.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-550, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-40956
in-theory        40956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-550 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-40956.        (((A -> (B or A)) or C) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-550, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-40957
in-theory        40957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-550 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-40957.        (((A -> (B or A)) or C) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-550, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-40958
in-theory        40958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-550 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-40958.        (((A -> (B or A)) or C) and (D -> (D and ((E and F) -> E)))), M:tm-550, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-40959
in-theory        40959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-550 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-40959.        (((A -> (B or A)) or C) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-550, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-40960
in-theory        40960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-550 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-40960.        (((A -> (B or A)) or C) and (D -> (D and ((E and F) -> F)))), M:tm-550, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-40961
in-theory        40961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-550 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-40961.        (((A -> (B or A)) or C) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-550, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-40962
in-theory        40962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-550 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-40962.        (((A -> (B or A)) or C) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-550, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-40963
in-theory        40963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-550 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-40963.        (((A -> (B or A)) or C) and (D -> (D and (((E and F) -> E) and D)))), M:tm-550, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-40964
in-theory        40964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-550 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-40964.        (((A -> (B or A)) or C) and (D -> (D and (((E and F) -> F) and D)))), M:tm-550, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-40965
in-theory        40965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-550 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-40965.        (((A -> (B or A)) or C) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-550, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-40966
in-theory        40966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-40966.        (((A -> (B or A)) or C) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-550, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-40967
in-theory        40967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-550 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-40967.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-550, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-40968
in-theory        40968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-40968.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-550, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-40969
in-theory        40969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-40969.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-550, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-40970
in-theory        40970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-550 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-40970.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-550, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-40971
in-theory        40971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-40971.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-550, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-40972
in-theory        40972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-550 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-40972.        (((A -> (B or A)) or C) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-550, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-40973
in-theory        40973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-550 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-40973.        (((A -> (B or A)) or C) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-550, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-40974
in-theory        40974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-550 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-40974.        (((A -> (B or A)) or C) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-550, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-40975
in-theory        40975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-550 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-40975.        (((A -> (B or A)) or C) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-550, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-40976
in-theory        40976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-40976.        (((A -> (B or A)) or C) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-550, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-40977
in-theory        40977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-550 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-40977.        (((A -> (B or A)) or C) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-550, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-40978
in-theory        40978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-550 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-40978.        (((A -> (B or A)) or C) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-550, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-40979
in-theory        40979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-550 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-40979.        (((A -> (B or A)) or C) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-550, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-40980
in-theory        40980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-550 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-40980.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-550, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-40981
in-theory        40981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-550 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-40981.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-550, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-40982
in-theory        40982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-550 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-40982.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-550, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-40983
in-theory        40983
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-550 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-40983.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-550, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-40984
in-theory        40984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-550 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-40984.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-550, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-40985
in-theory        40985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-550 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-40985.        (((A -> (B or A)) or C) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-550, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-40986
in-theory        40986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-550 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-40986.        (((A -> (B or A)) or C) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-550, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-40987
in-theory        40987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-550 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-40987.        (((A -> (B or A)) or C) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-550, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-40988
in-theory        40988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-40988.        (((A -> (B or A)) or C) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-550, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-40989
in-theory        40989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-550 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-40989.        (((A -> (B or A)) or C) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-550, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-40990
in-theory        40990
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-550 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-40990.        (((A -> (B or A)) or C) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-550, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-40991
in-theory        40991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-550 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-40991.        (((A -> (B or A)) or C) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-550, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-40992
in-theory        40992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-40992.        (((A -> (B or A)) or C) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-550, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-40993
in-theory        40993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-550 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-40993.        (((A -> (B or A)) or C) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-550, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-40994
in-theory        40994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-550 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-40994.        (((A -> (B or A)) or C) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-550, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-40995
in-theory        40995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-550 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-40995.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-550, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-40996
in-theory        40996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-40996.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-550, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-40997
in-theory        40997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-40997.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-550, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-40998
in-theory        40998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-40998.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-550, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-40999
in-theory        40999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-40999.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-550, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-41000
in-theory        41000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-550 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-41000.        (((A -> (B or A)) or C) and (D or ((E -> (F -> E)) or G))), M:tm-550, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-41001
in-theory        41001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-41001.        (((A -> (B or A)) or C) and (((D -> (E -> D)) or F) or G)), M:tm-550, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-41002
in-theory        41002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-41002.        (((A -> (B or A)) or C) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-550, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41003
in-theory        41003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-550 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-41003.        (((A -> (B or A)) or C) and (D -> ((E -> (F -> E)) or G))), M:tm-550, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-41004
in-theory        41004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-550 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-41004.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-550, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-41005
in-theory        41005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-41005.        (((A -> (B or A)) or C) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-550, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-41006
in-theory        41006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-41006.        (((A -> (B or A)) or C) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-550, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-41007
in-theory        41007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-550 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-41007.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-550, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-41008
in-theory        41008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-41008.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-550, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-41009
in-theory        41009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-550 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-41009.        (((A -> (B or A)) or C) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-550, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-41010
in-theory        41010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-550 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-41010.        (((A -> (B or A)) or C) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-550, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-41011
in-theory        41011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-550 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-41011.        (((A -> (B or A)) or C) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-550, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-41012
in-theory        41012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-550 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-41012.        (((A -> (B or A)) or C) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-550, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-41013
in-theory        41013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-550 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-41013.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-550, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-41014
in-theory        41014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-41014.        (((A -> (B or A)) or C) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-550, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-41015
in-theory        41015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-41015.        (((A -> (B or A)) or C) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-550, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-41016
in-theory        41016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-41016.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-550, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-41017
in-theory        41017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-41017.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-550, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-41018
in-theory        41018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-550 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-41018.        (((A -> (B or A)) or C) and (D or (((E and F) -> E) or G))), M:tm-550, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-41019
in-theory        41019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-41019.        (((A -> (B or A)) or C) and ((((D and E) -> D) or F) or G)), M:tm-550, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-41020
in-theory        41020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-41020.        (((A -> (B or A)) or C) and (D -> ((((E and F) -> E) or G) and D))), M:tm-550, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-41021
in-theory        41021
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-550 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-41021.        (((A -> (B or A)) or C) and (D -> (((E and F) -> E) or G))), M:tm-550, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-41022
in-theory        41022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-550 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-41022.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-550, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-41023
in-theory        41023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-41023.        (((A -> (B or A)) or C) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-550, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-41024
in-theory        41024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-41024.        (((A -> (B or A)) or C) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-550, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-41025
in-theory        41025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-41025.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-550, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-41026
in-theory        41026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-41026.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-550, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-41027
in-theory        41027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-550 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-41027.        (((A -> (B or A)) or C) and (D or (((E and F) -> F) or G))), M:tm-550, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-41028
in-theory        41028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-41028.        (((A -> (B or A)) or C) and ((((D and E) -> E) or F) or G)), M:tm-550, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-41029
in-theory        41029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-41029.        (((A -> (B or A)) or C) and (D -> ((((E and F) -> F) or G) and D))), M:tm-550, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-41030
in-theory        41030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-550 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-41030.        (((A -> (B or A)) or C) and (D -> (((E and F) -> F) or G))), M:tm-550, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-41031
in-theory        41031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-550 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-41031.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-550, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-41032
in-theory        41032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-550 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-41032.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-550, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-41033
in-theory        41033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-550 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-41033.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-550, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-41034
in-theory        41034
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-550 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-41034.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-550, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-41035
in-theory        41035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-550 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-41035.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-550, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-41036
in-theory        41036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-550 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-41036.        (((A -> (B or A)) or C) and (D or ((E -> (F -> (E and F))) or G))), M:tm-550, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-41037
in-theory        41037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-550 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-41037.        (((A -> (B or A)) or C) and (((D -> (E -> (D and E))) or F) or G)), M:tm-550, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-41038
in-theory        41038
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-41038.        (((A -> (B or A)) or C) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-550, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-41039
in-theory        41039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-550 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-41039.        (((A -> (B or A)) or C) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-550, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-41040
in-theory        41040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-550 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-41040.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-550, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-41041
in-theory        41041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-41041.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-550, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-41042
in-theory        41042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-41042.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-550, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-41043
in-theory        41043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-41043.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-550, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-41044
in-theory        41044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-41044.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-550, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-41045
in-theory        41045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-550 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-41045.        (((A -> (B or A)) or C) and (D or ((E -> (E or F)) or G))), M:tm-550, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-41046
in-theory        41046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-41046.        (((A -> (B or A)) or C) and (((D -> (D or E)) or F) or G)), M:tm-550, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-41047
in-theory        41047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-41047.        (((A -> (B or A)) or C) and (D -> (((E -> (E or F)) or G) and D))), M:tm-550, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-41048
in-theory        41048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-550 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-41048.        (((A -> (B or A)) or C) and (D -> ((E -> (E or F)) or G))), M:tm-550, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-41049
in-theory        41049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41049.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-550, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41050
in-theory        41050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41050.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-550, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41051
in-theory        41051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41051.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-550, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41052
in-theory        41052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-550 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41052.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-550, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41053
in-theory        41053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41053.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-550, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41054
in-theory        41054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-550 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41054.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-550, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41055
in-theory        41055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41055.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-550, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41056
in-theory        41056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41056.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-550, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41057
in-theory        41057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-550 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41057.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-550, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41058
in-theory        41058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41058.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-550, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41059
in-theory        41059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-41059.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-550, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-41060
in-theory        41060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-41060.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-550, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-41061
in-theory        41061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-550 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-41061.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-550, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-41062
in-theory        41062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-41062.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-550, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-41063
in-theory        41063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-550 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-41063.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-550, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-41064
in-theory        41064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-550 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-41064.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-550, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-41065
in-theory        41065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-550 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-41065.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-550, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-41066
in-theory        41066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-550 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-41066.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-550, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-41067
in-theory        41067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-41067.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-550, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-41068
in-theory        41068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-550 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-41068.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-550, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-41069
in-theory        41069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-41069.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-550, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-41070
in-theory        41070
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-41070.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-550, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-41071
in-theory        41071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-550 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-41071.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-550, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-41072
in-theory        41072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-41072.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-550, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-41073
in-theory        41073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-550 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-41073.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-550, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-41074
in-theory        41074
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-41074.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-550, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-41075
in-theory        41075
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-41075.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-550, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-41076
in-theory        41076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-41076.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-550, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-41077
in-theory        41077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-41077.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-550, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-41078
in-theory        41078
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-550 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-41078.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-550, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-41079
in-theory        41079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-41079.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-550, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-41080
in-theory        41080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-41080.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-550, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-41081
in-theory        41081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-550 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-41081.        (((A -> (B or A)) or C) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-550, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-41082
in-theory        41082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-550 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-41082.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-550, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-41083
in-theory        41083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-41083.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-550, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-41084
in-theory        41084
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-41084.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-550, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-41085
in-theory        41085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-550 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-41085.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-550, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-41086
in-theory        41086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-41086.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-550, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-41087
in-theory        41087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-41087.        (((A -> (B or A)) or C) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-550, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-41088
in-theory        41088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-550 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-41088.        (((A -> (B or A)) or C) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-550, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-41089
in-theory        41089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-550 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-41089.        (((A -> (B or A)) or C) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-550, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-41090
in-theory        41090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-550 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-41090.        (((A -> (B or A)) or C) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-550, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-41091
in-theory        41091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-41091.        (((A -> (B or A)) or C) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-550, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-41092
in-theory        41092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-550 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-41092.        (((A -> (B or A)) or C) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-550, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-41093
in-theory        41093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-41093.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-550, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-41094
in-theory        41094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-41094.        (((A -> (B or A)) or C) and (D -> (D and (E -> (E or F))))), M:tm-550, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-41095
in-theory        41095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-41095.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-550, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-41096
in-theory        41096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-41096.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-550, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-41097
in-theory        41097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-41097.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-550, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-41098
in-theory        41098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-41098.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-550, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-41099
in-theory        41099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-41099.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-550, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-41100
in-theory        41100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-550 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-41100.        (((A -> (B or A)) or C) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-550, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-41101
in-theory        41101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-550 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-41101.        (((A -> (B or A)) or C) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-550, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-41102
in-theory        41102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-41102.        (((A -> (B or A)) or C) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-550, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-41103
in-theory        41103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-41103.        (((A -> (B or A)) or C) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-550, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-41104
in-theory        41104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-550 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-41104.        (((A -> (B or A)) or C) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-550, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-41105
in-theory        41105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-41105.        (((A -> (B or A)) or C) and (D or (E -> (F -> (F or G))))), M:tm-550, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-41106
in-theory        41106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-41106.        (((A -> (B or A)) or C) and ((D -> (E -> (E or F))) or G)), M:tm-550, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-41107
in-theory        41107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-41107.        (((A -> (B or A)) or C) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-550, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-41108
in-theory        41108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-550 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-41108.        (((A -> (B or A)) or C) and ((D -> E) -> (D -> (E or F)))), M:tm-550, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-41109
in-theory        41109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-41109.        (((A -> (B or A)) or C) and (D -> (E -> (F -> (F or G))))), M:tm-550, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-41110
in-theory        41110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-41110.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-550, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-41111
in-theory        41111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-41111.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-550, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-41112
in-theory        41112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-41112.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-550, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-41113
in-theory        41113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-41113.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-550, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-41114
in-theory        41114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-41114.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-550, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-41115
in-theory        41115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-41115.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-550, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-41116
in-theory        41116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-41116.        (((A -> (B or A)) or C) and (D or (E or (F -> (G -> F))))), M:tm-550, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-41117
in-theory        41117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-41117.        (((A -> (B or A)) or C) and ((D or (E -> (F -> E))) or G)), M:tm-550, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-41118
in-theory        41118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-41118.        (((A -> (B or A)) or C) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-550, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-41119
in-theory        41119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-41119.        (((A -> (B or A)) or C) and (D -> (E or (F -> (G -> F))))), M:tm-550, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-41120
in-theory        41120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-41120.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-550, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-41121
in-theory        41121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-550 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-41121.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-550, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-41122
in-theory        41122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-41122.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-550, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-41123
in-theory        41123
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-41123.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-550, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-41124
in-theory        41124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-550 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-41124.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-550, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-41125
in-theory        41125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-41125.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-550, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-41126
in-theory        41126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-550 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-41126.        (((A -> (B or A)) or C) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-550, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-41127
in-theory        41127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-550 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-41127.        (((A -> (B or A)) or C) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-550, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-41128
in-theory        41128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-550 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-41128.        (((A -> (B or A)) or C) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-550, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-41129
in-theory        41129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-550 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-41129.        (((A -> (B or A)) or C) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-550, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-41130
in-theory        41130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-550 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-41130.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-550, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-41131
in-theory        41131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-550 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-41131.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-550, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-41132
in-theory        41132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-550 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-41132.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-550, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-41133
in-theory        41133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-550 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-41133.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-550, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-41134
in-theory        41134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-550 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-41134.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-550, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-41135
in-theory        41135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-550 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-41135.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-550, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-41136
in-theory        41136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-550 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-41136.        (((A -> (B or A)) or C) and (D or (E or ((F and G) -> F)))), M:tm-550, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-41137
in-theory        41137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-41137.        (((A -> (B or A)) or C) and ((D or ((E and F) -> E)) or G)), M:tm-550, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-41138
in-theory        41138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-41138.        (((A -> (B or A)) or C) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-550, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-41139
in-theory        41139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-550 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-41139.        (((A -> (B or A)) or C) and (D -> (E or ((F and G) -> F)))), M:tm-550, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-41140
in-theory        41140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-550 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-41140.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-550, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-41141
in-theory        41141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-550 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-41141.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-550, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-41142
in-theory        41142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-550 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-41142.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-550, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-41143
in-theory        41143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-550 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-41143.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-550, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-41144
in-theory        41144
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-550 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-41144.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-550, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-41145
in-theory        41145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-550 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-41145.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-550, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-41146
in-theory        41146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-550 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-41146.        (((A -> (B or A)) or C) and (D or (E or ((F and G) -> G)))), M:tm-550, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-41147
in-theory        41147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-41147.        (((A -> (B or A)) or C) and ((D or ((E and F) -> F)) or G)), M:tm-550, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-41148
in-theory        41148
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-41148.        (((A -> (B or A)) or C) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-550, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-41149
in-theory        41149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-550 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-41149.        (((A -> (B or A)) or C) and (D -> (E or ((F and G) -> G)))), M:tm-550, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-41150
in-theory        41150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-550 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-41150.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-550, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-41151
in-theory        41151
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-550 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-41151.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-550, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-41152
in-theory        41152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-550 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-41152.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-550, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-41153
in-theory        41153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-550 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-41153.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-550, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-41154
in-theory        41154
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-550 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-41154.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-550, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-41155
in-theory        41155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-550 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-41155.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-550, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-41156
in-theory        41156
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-550 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-41156.        (((A -> (B or A)) or C) and (D or (E or (F -> (G -> (F and G)))))), M:tm-550, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-41157
in-theory        41157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-550 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-41157.        (((A -> (B or A)) or C) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-550, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-41158
in-theory        41158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-41158.        (((A -> (B or A)) or C) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-550, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-41159
in-theory        41159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-550 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-41159.        (((A -> (B or A)) or C) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-550, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-41160
in-theory        41160
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-41160.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-550, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-41161
in-theory        41161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-41161.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-550, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-41162
in-theory        41162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-41162.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-550, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-41163
in-theory        41163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-41163.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-550, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-41164
in-theory        41164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-41164.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-550, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-41165
in-theory        41165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-41165.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-550, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-41166
in-theory        41166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-41166.        (((A -> (B or A)) or C) and (D or (E or (F -> (F or G))))), M:tm-550, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-41167
in-theory        41167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-41167.        (((A -> (B or A)) or C) and ((D or (E -> (E or F))) or G)), M:tm-550, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-41168
in-theory        41168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-41168.        (((A -> (B or A)) or C) and (D -> ((E or (F -> (F or G))) and D))), M:tm-550, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-41169
in-theory        41169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-41169.        (((A -> (B or A)) or C) and (D -> (E or (F -> (F or G))))), M:tm-550, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-41170
in-theory        41170
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-41170.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-550, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-41171
in-theory        41171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-41171.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-550, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-41172
in-theory        41172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-41172.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-550, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-41173
in-theory        41173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-41173.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-550, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-41174
in-theory        41174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-41174.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-550, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-41175
in-theory        41175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-41175.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-550, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-41176
in-theory        41176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-41176.        (((A -> (B or A)) or C) and (D or (E or (F -> (G or F))))), M:tm-550, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-41177
in-theory        41177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-41177.        (((A -> (B or A)) or C) and ((D or (E -> (F or E))) or G)), M:tm-550, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-41178
in-theory        41178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-41178.        (((A -> (B or A)) or C) and (D -> ((E or (F -> (G or F))) and D))), M:tm-550, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-41179
in-theory        41179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-41179.        (((A -> (B or A)) or C) and (D -> (E or (F -> (G or F))))), M:tm-550, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-41180
in-theory        41180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41180.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-550, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-41181
in-theory        41181
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-550 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41181.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-550, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-41182
in-theory        41182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41182.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-550, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-41183
in-theory        41183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41183.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-550, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-41184
in-theory        41184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41184.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-550, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-41185
in-theory        41185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41185.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-550, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-41186
in-theory        41186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-550 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41186.        (((A -> (B or A)) or C) and (D or ((E -> (F or E)) or G))), M:tm-550, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41187
in-theory        41187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41187.        (((A -> (B or A)) or C) and (((D -> (E or D)) or F) or G)), M:tm-550, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-41188
in-theory        41188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41188.        (((A -> (B or A)) or C) and (D -> (((E -> (F or E)) or G) and D))), M:tm-550, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41189
in-theory        41189
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41189.        ((A or (B -> (C or B))) and (D -> (((E -> (F or E)) or G) and D))), M:tm-540, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41190
in-theory        41190
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41190.        ((A or (B -> (B or C))) and (D -> (((E -> (F or E)) or G) and D))), M:tm-530, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41191
in-theory        41191
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41191.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> (F or E)) or G) and D))), M:tm-520, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41192
in-theory        41192
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41192.        ((A or ((B and C) -> C)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-510, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41193
in-theory        41193
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41193.        ((A or ((B and C) -> B)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-500, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41194
in-theory        41194
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G or F)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41194.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G or F)) or H) and E))), M:tm-490, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41195
in-theory        41195
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41195.        ((A or (B -> (C -> B))) and (D -> (((E -> (F or E)) or G) and D))), M:tm-480, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41196
in-theory        41196
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C or B)) or D) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41196.        (A -> ((((B -> (C or B)) or D) and A) or E)), M:tm-470, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-41197
in-theory        41197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41197.        ((A -> (B -> (B or C))) and (D -> (((E -> (F or E)) or G) and D))), M:tm-469, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41198
in-theory        41198
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> (E or D)) or F) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-550 ((Am (-> A (or A B))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41198.        ((A or (B -> (B or C))) -> (((D -> (E or D)) or F) and (B -> (B or C)))), M:tm-466, m:tm-550, u:((Am (-> A (or A B))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (or A B)))))
================================================================
tm-name          tm-41199
in-theory        41199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41199.        ((A -> (((B -> (C or B)) or D) and A)) and (E -> (E or F))), M:tm-456, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41200
in-theory        41200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41200.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-453, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41201
in-theory        41201
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> (E or D)) or F) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-550 ((Am (and (-> A (or A B)) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41201.        ((A or ((B -> (B or C)) and A)) -> (((D -> (E or D)) or F) and ((B -> (B or C)) and A))), M:tm-450, m:tm-550, u:((Am (and (-> A (or A B)) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-41202
in-theory        41202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and ((E -> (E or F)) and (A -> (((B -> (C or B)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41202.        ((A -> (((B -> (C or B)) or D) and A)) and ((E -> (E or F)) and (A -> (((B -> (C or B)) or D) and A)))), M:tm-443, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41203
in-theory        41203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41203.        (((A -> (A or B)) or C) and (D -> (((E -> (F or E)) or G) and D))), M:tm-409, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41204
in-theory        41204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41204.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> (F or E)) or G) and D))), M:tm-400, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41205
in-theory        41205
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41205.        ((((A and B) -> B) or C) and (D -> (((E -> (F or E)) or G) and D))), M:tm-391, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41206
in-theory        41206
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41206.        ((((A and B) -> A) or C) and (D -> (((E -> (F or E)) or G) and D))), M:tm-382, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41207
in-theory        41207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (G or F)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41207.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> (G or F)) or H) and E))), M:tm-373, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41208
in-theory        41208
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41208.        (((A -> (B -> A)) or C) and (D -> (((E -> (F or E)) or G) and D))), M:tm-364, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41209
in-theory        41209
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> (D or C)) or E) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41209.        (A -> (B -> ((((C -> (D or C)) or E) and A) and B))), M:tm-355, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-41210
in-theory        41210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41210.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> (F or E)) or G) and D))), M:tm-354, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41211
in-theory        41211
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> (E or D)) or F) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-550 ((Am (-> A (-> B (and A B)))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41211.        ((A or (B -> (C -> (B and C)))) -> (((D -> (E or D)) or F) and (B -> (C -> (B and C))))), M:tm-351, m:tm-550, u:((Am (-> A (-> B (and A B)))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-41212
in-theory        41212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41212.        ((A -> (((B -> (C or B)) or D) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41213
in-theory        41213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (E or D)) or F) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41213.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> (E or D)) or F) and C))), M:tm-338, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41214
in-theory        41214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> (D or C)) or E) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-550 ((Am (-> A (and A B))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41214.        (((A -> B) or (A -> (A and B))) -> (((C -> (D or C)) or E) and (A -> (A and B)))), M:tm-335, m:tm-550, u:((Am (-> A (and A B))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (and A B)))))
================================================================
tm-name          tm-41215
in-theory        41215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (A -> (A and (((B -> (C or B)) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41215.        ((A -> (((B -> (C or B)) or D) and A)) and (A -> (A and (((B -> (C or B)) or D) and A)))), M:tm-328, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-41216
in-theory        41216
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> (C or B)) or D) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41216.        ((A -> (((B -> (C or B)) or D) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> (C or B)) or D) and A)))), M:tm-327, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41217
in-theory        41217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (((E and F) -> F) and (A -> (((B -> (C or B)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41217.        ((A -> (((B -> (C or B)) or D) and A)) and (((E and F) -> F) and (A -> (((B -> (C or B)) or D) and A)))), M:tm-326, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41218
in-theory        41218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (((E and F) -> E) and (A -> (((B -> (C or B)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41218.        ((A -> (((B -> (C or B)) or D) and A)) and (((E and F) -> E) and (A -> (((B -> (C or B)) or D) and A)))), M:tm-325, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41219
in-theory        41219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> (C or B)) or D) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41219.        ((A -> (((B -> (C or B)) or D) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> (C or B)) or D) and A)))), M:tm-324, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41220
in-theory        41220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and ((E -> (F -> E)) and (A -> (((B -> (C or B)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41220.        ((A -> (((B -> (C or B)) or D) and A)) and ((E -> (F -> E)) and (A -> (((B -> (C or B)) or D) and A)))), M:tm-323, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41221
in-theory        41221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41221.        ((A -> (((B -> (C or B)) or D) and A)) and ((E and F) -> F)), M:tm-322, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41222
in-theory        41222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41222.        ((A -> (((B -> (C or B)) or D) and A)) and ((E and F) -> E)), M:tm-320, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41223
in-theory        41223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41223.        ((A -> (((B -> (C or B)) or D) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41224
in-theory        41224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41224.        ((A -> (((B -> (C or B)) or D) and A)) and (A -> A)), M:tm-316, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-41225
in-theory        41225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41225.        ((A -> (((B -> (C or B)) or D) and A)) and (E -> (F -> E))), M:tm-315, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41226
in-theory        41226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and ((A -> (not (((B -> (C or B)) or D) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-6 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41226.        ((A -> (((B -> (C or B)) or D) and A)) and ((A -> (not (((B -> (C or B)) or D) and A))) -> (not A))), M:tm-313, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-41227
in-theory        41227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (((((B -> (C or B)) or D) and A) -> E) -> ((A or (((B -> (C or B)) or D) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41227.        ((A -> (((B -> (C or B)) or D) and A)) and (((((B -> (C or B)) or D) and A) -> E) -> ((A or (((B -> (C or B)) or D) and A)) -> E))), M:tm-312, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-41228
in-theory        41228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (E or (A -> (((B -> (C or B)) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41228.        ((A -> (((B -> (C or B)) or D) and A)) and (E or (A -> (((B -> (C or B)) or D) and A)))), M:tm-311, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41229
in-theory        41229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and ((A -> (((B -> (C or B)) or D) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41229.        ((A -> (((B -> (C or B)) or D) and A)) and ((A -> (((B -> (C or B)) or D) and A)) or E)), M:tm-310, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41230
in-theory        41230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (E -> ((A -> (((B -> (C or B)) or D) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41230.        ((A -> (((B -> (C or B)) or D) and A)) and (E -> ((A -> (((B -> (C or B)) or D) and A)) and E))), M:tm-309, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41231
in-theory        41231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (E -> (A -> (((B -> (C or B)) or D) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41231.        ((A -> (((B -> (C or B)) or D) and A)) and (E -> (A -> (((B -> (C or B)) or D) and A)))), M:tm-305, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41232
in-theory        41232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41232.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-303, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41233
in-theory        41233
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (E or D)) or F) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-550 ((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41233.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> (E or D)) or F) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-550, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-41234
in-theory        41234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41234.        ((A -> (((B and C) -> C) and A)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-270, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41235
in-theory        41235
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> (E or D)) or F) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-550 ((Am (and (-> (and A B) B) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41235.        ((A or (((B and C) -> C) and A)) -> (((D -> (E or D)) or F) and (((B and C) -> C) and A))), M:tm-267, m:tm-550, u:((Am (and (-> (and A B) B) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-41236
in-theory        41236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41236.        ((A -> (((B and C) -> B) and A)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-239, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41237
in-theory        41237
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> (E or D)) or F) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-550 ((Am (and (-> (and A B) A) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41237.        ((A or (((B and C) -> B) and A)) -> (((D -> (E or D)) or F) and (((B and C) -> B) and A))), M:tm-236, m:tm-550, u:((Am (and (-> (and A B) A) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-41238
in-theory        41238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (G or F)) or H) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41238.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> (G or F)) or H) and E))), M:tm-210, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41239
in-theory        41239
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (F or E)) or G) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-550 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (or Cm Bm)) Dm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-6 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41239.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> (F or E)) or G) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-550, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (or Cm Bm)) Dm) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-41240
in-theory        41240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41240.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-183, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41241
in-theory        41241
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> (E or D)) or F) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-550 ((Am (and (-> A (-> B A)) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41241.        ((A or ((B -> (C -> B)) and A)) -> (((D -> (E or D)) or F) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-550, u:((Am (and (-> A (-> B A)) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-41242
in-theory        41242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41242.        ((A -> ((B and C) -> C)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-157, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41243
in-theory        41243
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> (E or D)) or F) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-550 ((Am (-> (and A B) B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41243.        ((A or ((B and C) -> C)) -> (((D -> (E or D)) or F) and ((B and C) -> C))), M:tm-154, m:tm-550, u:((Am (-> (and A B) B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> (and A B) B))))
================================================================
tm-name          tm-41244
in-theory        41244
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41244.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-147, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41245
in-theory        41245
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (E or D)) or F) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-550 ((Am (-> (and A (-> B C)) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-6 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41245.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> (E or D)) or F) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-550, u:((Am (-> (and A (-> B C)) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-41246
in-theory        41246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41246.        ((A -> ((B and C) -> B)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-134, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41247
in-theory        41247
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> (E or D)) or F) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-550 ((Am (-> (and A B) A)) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41247.        ((A or ((B and C) -> B)) -> (((D -> (E or D)) or F) and ((B and C) -> B))), M:tm-131, m:tm-550, u:((Am (-> (and A B) A)) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> (and A B) A))))
================================================================
tm-name          tm-41248
in-theory        41248
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41248.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-125, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41249
in-theory        41249
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (E or D)) or F) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-550 ((Am (-> (and (-> A B) C) B)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-6 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41249.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> (E or D)) or F) and (((A -> B) and C) -> B))), M:tm-122, m:tm-550, u:((Am (-> (and (-> A B) C) B)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-41250
in-theory        41250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G or F)) or H) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41250.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> (G or F)) or H) and E))), M:tm-113, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41251
in-theory        41251
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (F or E)) or G) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-550 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41251.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> (F or E)) or G) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-550, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-41252
in-theory        41252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41252.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> (F or E)) or G) and D))), M:tm-105, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41253
in-theory        41253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (E or D)) or F) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-550 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41253.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> (E or D)) or F) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-550, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-41254
in-theory        41254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> (E or D)) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41254.        (((A -> B) -> (A -> A)) and (C -> (((D -> (E or D)) or F) and C))), M:tm-95, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41255
in-theory        41255
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> (D or C)) or E) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-550 ((Am (-> A A)) (B (and (or (-> Bm (or Cm Bm)) Dm) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41255.        (((A -> B) or (A -> A)) -> (((C -> (D or C)) or E) and (A -> A))), M:tm-92, m:tm-550, u:((Am (-> A A)) (B (and (or (-> Bm (or Cm Bm)) Dm) (-> A A))))
================================================================
tm-name          tm-41256
in-theory        41256
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D or C)) or E) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-6 tm-7)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41256.        (A -> (B -> (((C -> (D or C)) or E) and A))), M:tm-84, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-41257
in-theory        41257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41257.        ((A -> (B -> (C -> B))) and (D -> (((E -> (F or E)) or G) and D))), M:tm-83, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41258
in-theory        41258
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> (E or D)) or F) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-550 ((Am (-> A (-> B A))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41258.        ((A or (B -> (C -> B))) -> (((D -> (E or D)) or F) and (B -> (C -> B)))), M:tm-80, m:tm-550, u:((Am (-> A (-> B A))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (-> B A)))))
================================================================
tm-name          tm-41259
in-theory        41259
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> (D or C)) or E) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-10 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41259.        (((not (not A)) -> A) and (B -> (((C -> (D or C)) or E) and B))), M:tm-76, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41260
in-theory        41260
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> (C or B)) or D) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-6 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41260.        (((not (not A)) or A) -> (((B -> (C or B)) or D) and A)), M:tm-73, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-41261
in-theory        41261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (E or D)) or F) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-9 tm-6 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41261.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> (E or D)) or F) and C))), M:tm-69, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41262
in-theory        41262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (D or C)) or E) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-550 ((Am (-> (-> A (not B)) (not A))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-6 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41262.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> (D or C)) or E) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-550, u:((Am (-> (-> A (not B)) (not A))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-41263
in-theory        41263
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41263.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> (F or E)) or G) and D))), M:tm-54, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41264
in-theory        41264
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E or D)) or F) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-550 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41264.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> (E or D)) or F) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-550, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-41265
in-theory        41265
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> (D or C)) or E) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-550 ((Am (or A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41265.        ((A or (B or A)) -> (((C -> (D or C)) or E) and (B or A))), M:tm-50, m:tm-550, u:((Am (or A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (or A B))))
================================================================
tm-name          tm-41266
in-theory        41266
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> (D or C)) or E) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-550 ((Am (or A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41266.        ((A or (A or B)) -> (((C -> (D or C)) or E) and (A or B))), M:tm-49, m:tm-550, u:((Am (or A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (or A B))))
================================================================
tm-name          tm-41267
in-theory        41267
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> (D or C)) or E) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-550 ((Am (-> A (and B A))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41267.        ((A or (B -> (A and B))) -> (((C -> (D or C)) or E) and (B -> (A and B)))), M:tm-48, m:tm-550, u:((Am (-> A (and B A))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (and B A)))))
================================================================
tm-name          tm-41268
in-theory        41268
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> (D or C)) or E) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-6 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41268.        (((A and B) or B) -> (((C -> (D or C)) or E) and B)), M:tm-47, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-41269
in-theory        41269
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> (D or C)) or E) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-6 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41269.        (((A and B) or A) -> (((C -> (D or C)) or E) and A)), M:tm-46, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-41270
in-theory        41270
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E or D)) or F) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-550 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41270.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E or D)) or F) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-550, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-41271
in-theory        41271
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> (D or C)) or E) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-550 ((Am (-> A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41271.        ((A or (B -> A)) -> (((C -> (D or C)) or E) and (B -> A))), M:tm-44, m:tm-550, u:((Am (-> A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A B))))
================================================================
tm-name          tm-41272
in-theory        41272
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> (E or D)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41272.        ((A -> (B or A)) and (C -> (((D -> (E or D)) or F) and C))), M:tm-42, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41273
in-theory        41273
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> (E or D)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41273.        ((A -> (A or B)) and (C -> (((D -> (E or D)) or F) and C))), M:tm-32, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41274
in-theory        41274
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> (C or B)) or D) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41274.        (A -> (A and (((B -> (C or B)) or D) and A))), M:tm-24, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-41275
in-theory        41275
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> (E or D)) or F) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41275.        ((A -> (B -> (A and B))) and (C -> (((D -> (E or D)) or F) and C))), M:tm-23, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41276
in-theory        41276
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> (E or D)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41276.        (((A and B) -> B) and (C -> (((D -> (E or D)) or F) and C))), M:tm-22, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41277
in-theory        41277
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> (E or D)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41277.        (((A and B) -> A) and (C -> (((D -> (E or D)) or F) and C))), M:tm-21, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41278
in-theory        41278
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41278.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F or E)) or G) and D))), M:tm-20, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41279
in-theory        41279
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> (E or D)) or F) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41279.        ((A -> (B -> A)) and (C -> (((D -> (E or D)) or F) and C))), M:tm-19, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41280
in-theory        41280
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> (C or B)) or D) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-9 tm-5 tm-6 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41280.        ((A -> (not (((B -> (C or B)) or D) and A))) -> (not A)), M:tm-9, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-41281
in-theory        41281
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B or A)) or C) and D) -> E) -> ((D or (((A -> (B or A)) or C) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41281.        (((((A -> (B or A)) or C) and D) -> E) -> ((D or (((A -> (B or A)) or C) and D)) -> E)), M:tm-8, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-41282
in-theory        41282
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> (D or C)) or E) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41282.        (A or (B -> (((C -> (D or C)) or E) and B))), M:tm-7, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41283
in-theory        41283
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41283.        ((A -> (((B -> (C or B)) or D) and A)) or E), M:tm-6, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41284
in-theory        41284
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> (D or C)) or E) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41284.        (A -> ((B -> (((C -> (D or C)) or E) and B)) and A)), M:tm-5, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41285
in-theory        41285
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D or C)) or E) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-1 tm-5 tm-6 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41285.        (A -> (B -> (((C -> (D or C)) or E) and B))), M:tm-1, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-41286
in-theory        41286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-550 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41286.        (((A -> (B or A)) or C) and (D -> ((E -> (F or E)) or G))), M:tm-550, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41287
in-theory        41287
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-540 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41287.        ((A or (B -> (C or B))) and (D -> ((E -> (F or E)) or G))), M:tm-540, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41288
in-theory        41288
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-530 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41288.        ((A or (B -> (B or C))) and (D -> ((E -> (F or E)) or G))), M:tm-530, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41289
in-theory        41289
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-520 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41289.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F or E)) or G))), M:tm-520, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41290
in-theory        41290
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-510 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41290.        ((A or ((B and C) -> C)) and (D -> ((E -> (F or E)) or G))), M:tm-510, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41291
in-theory        41291
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-500 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41291.        ((A or ((B and C) -> B)) and (D -> ((E -> (F or E)) or G))), M:tm-500, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41292
in-theory        41292
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-490 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41292.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G or F)) or H))), M:tm-490, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41293
in-theory        41293
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-480 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41293.        ((A or (B -> (C -> B))) and (D -> ((E -> (F or E)) or G))), M:tm-480, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41294
in-theory        41294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-469 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41294.        ((A -> (B -> (B or C))) and (D -> ((E -> (F or E)) or G))), M:tm-469, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41295
in-theory        41295
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-466 tm-551 ((Am (-> A (or A B))) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41295.        ((A or (B -> (B or C))) -> ((D -> (E or D)) or F)), M:tm-466, m:tm-551, u:((Am (-> A (or A B))) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41296
in-theory        41296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41296.        ((A -> ((B -> (C or B)) or D)) and (E -> (E or F))), M:tm-456, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41297
in-theory        41297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-453 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41297.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F or E)) or G))), M:tm-453, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41298
in-theory        41298
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-450 tm-551 ((Am (and (-> A (or A B)) C)) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41298.        ((A or ((B -> (B or C)) and A)) -> ((D -> (E or D)) or F)), M:tm-450, m:tm-551, u:((Am (and (-> A (or A B)) C)) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41299
in-theory        41299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and ((E -> (E or F)) and (A -> ((B -> (C or B)) or D))))
theorem-size     25
proof            (modus-ponens tm-443 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41299.        ((A -> ((B -> (C or B)) or D)) and ((E -> (E or F)) and (A -> ((B -> (C or B)) or D)))), M:tm-443, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41300
in-theory        41300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-409 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41300.        (((A -> (A or B)) or C) and (D -> ((E -> (F or E)) or G))), M:tm-409, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41301
in-theory        41301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-400 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41301.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F or E)) or G))), M:tm-400, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41302
in-theory        41302
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-391 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41302.        ((((A and B) -> B) or C) and (D -> ((E -> (F or E)) or G))), M:tm-391, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41303
in-theory        41303
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-382 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41303.        ((((A and B) -> A) or C) and (D -> ((E -> (F or E)) or G))), M:tm-382, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41304
in-theory        41304
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-373 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41304.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G or F)) or H))), M:tm-373, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41305
in-theory        41305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-364 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41305.        (((A -> (B -> A)) or C) and (D -> ((E -> (F or E)) or G))), M:tm-364, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41306
in-theory        41306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-354 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41306.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F or E)) or G))), M:tm-354, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41307
in-theory        41307
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-351 tm-551 ((Am (-> A (-> B (and A B)))) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41307.        ((A or (B -> (C -> (B and C)))) -> ((D -> (E or D)) or F)), M:tm-351, m:tm-551, u:((Am (-> A (-> B (and A B)))) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41308
in-theory        41308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41308.        ((A -> ((B -> (C or B)) or D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41309
in-theory        41309
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) -> D) -> (((A -> (B or A)) or C) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-551 ((Am (-> (or (-> Bm (or Cm Bm)) Dm) B)) (A (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41309.        ((((A -> (B or A)) or C) -> D) -> (((A -> (B or A)) or C) and D)), M:tm-339, m:tm-551, u:((Am (-> (or (-> Bm (or Cm Bm)) Dm) B)) (A (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41310
in-theory        41310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E or D)) or F)))
theorem-size     19
proof            (modus-ponens tm-338 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41310.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E or D)) or F))), M:tm-338, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41311
in-theory        41311
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (D or C)) or E))
theorem-size     17
proof            (modus-ponens tm-335 tm-551 ((Am (-> A (and A B))) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41311.        (((A -> B) or (A -> (A and B))) -> ((C -> (D or C)) or E)), M:tm-335, m:tm-551, u:((Am (-> A (and A B))) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41312
in-theory        41312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and (A -> (A and ((B -> (C or B)) or D))))
theorem-size     21
proof            (modus-ponens tm-328 tm-551 ((A Am) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41312.        ((A -> ((B -> (C or B)) or D)) and (A -> (A and ((B -> (C or B)) or D)))), M:tm-328, m:tm-551, u:((A Am) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41313
in-theory        41313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and ((E -> (F -> (E and F))) and (A -> ((B -> (C or B)) or D))))
theorem-size     27
proof            (modus-ponens tm-327 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41313.        ((A -> ((B -> (C or B)) or D)) and ((E -> (F -> (E and F))) and (A -> ((B -> (C or B)) or D)))), M:tm-327, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41314
in-theory        41314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and (((E and F) -> F) and (A -> ((B -> (C or B)) or D))))
theorem-size     25
proof            (modus-ponens tm-326 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41314.        ((A -> ((B -> (C or B)) or D)) and (((E and F) -> F) and (A -> ((B -> (C or B)) or D)))), M:tm-326, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41315
in-theory        41315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and (((E and F) -> E) and (A -> ((B -> (C or B)) or D))))
theorem-size     25
proof            (modus-ponens tm-325 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41315.        ((A -> ((B -> (C or B)) or D)) and (((E and F) -> E) and (A -> ((B -> (C or B)) or D)))), M:tm-325, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41316
in-theory        41316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C or B)) or D))))
theorem-size     33
proof            (modus-ponens tm-324 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41316.        ((A -> ((B -> (C or B)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C or B)) or D)))), M:tm-324, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41317
in-theory        41317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and ((E -> (F -> E)) and (A -> ((B -> (C or B)) or D))))
theorem-size     25
proof            (modus-ponens tm-323 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41317.        ((A -> ((B -> (C or B)) or D)) and ((E -> (F -> E)) and (A -> ((B -> (C or B)) or D)))), M:tm-323, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41318
in-theory        41318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41318.        ((A -> ((B -> (C or B)) or D)) and ((E and F) -> F)), M:tm-322, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41319
in-theory        41319
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C or B)) or D) -> E)) -> ((B -> (C or B)) or D)) and ((A and (((B -> (C or B)) or D) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-551 ((Am (and A (-> (or (-> Bm (or Cm Bm)) Dm) C))) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-6 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41319.        (((A and (((B -> (C or B)) or D) -> E)) -> ((B -> (C or B)) or D)) and ((A and (((B -> (C or B)) or D) -> E)) -> E)), M:tm-321, m:tm-551, u:((Am (and A (-> (or (-> Bm (or Cm Bm)) Dm) C))) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41320
in-theory        41320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41320.        ((A -> ((B -> (C or B)) or D)) and ((E and F) -> E)), M:tm-320, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41321
in-theory        41321
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B or A)) or C) -> D) and E) -> ((A -> (B or A)) or C)) and (((((A -> (B or A)) or C) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-551 ((Am (and (-> (or (-> Bm (or Cm Bm)) Dm) B) C)) (A (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-6 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41321.        ((((((A -> (B or A)) or C) -> D) and E) -> ((A -> (B or A)) or C)) and (((((A -> (B or A)) or C) -> D) and E) -> D)), M:tm-319, m:tm-551, u:((Am (and (-> (or (-> Bm (or Cm Bm)) Dm) B) C)) (A (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41322
in-theory        41322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41322.        ((A -> ((B -> (C or B)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41323
in-theory        41323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-551 ((A Am) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41323.        ((A -> ((B -> (C or B)) or D)) and (A -> A)), M:tm-316, m:tm-551, u:((A Am) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41324
in-theory        41324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41324.        ((A -> ((B -> (C or B)) or D)) and (E -> (F -> E))), M:tm-315, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41325
in-theory        41325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and ((A -> (not ((B -> (C or B)) or D))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-551 ((A Am) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41325.        ((A -> ((B -> (C or B)) or D)) and ((A -> (not ((B -> (C or B)) or D))) -> (not A))), M:tm-313, m:tm-551, u:((A Am) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41326
in-theory        41326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and ((((B -> (C or B)) or D) -> E) -> ((A or ((B -> (C or B)) or D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-551 ((A Am) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41326.        ((A -> ((B -> (C or B)) or D)) and ((((B -> (C or B)) or D) -> E) -> ((A or ((B -> (C or B)) or D)) -> E))), M:tm-312, m:tm-551, u:((A Am) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41327
in-theory        41327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and (E or (A -> ((B -> (C or B)) or D))))
theorem-size     21
proof            (modus-ponens tm-311 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41327.        ((A -> ((B -> (C or B)) or D)) and (E or (A -> ((B -> (C or B)) or D)))), M:tm-311, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41328
in-theory        41328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and ((A -> ((B -> (C or B)) or D)) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41328.        ((A -> ((B -> (C or B)) or D)) and ((A -> ((B -> (C or B)) or D)) or E)), M:tm-310, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41329
in-theory        41329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and (E -> ((A -> ((B -> (C or B)) or D)) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41329.        ((A -> ((B -> (C or B)) or D)) and (E -> ((A -> ((B -> (C or B)) or D)) and E))), M:tm-309, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41330
in-theory        41330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and (E -> (A -> ((B -> (C or B)) or D))))
theorem-size     21
proof            (modus-ponens tm-305 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41330.        ((A -> ((B -> (C or B)) or D)) and (E -> (A -> ((B -> (C or B)) or D)))), M:tm-305, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41331
in-theory        41331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-303 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41331.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F or E)) or G))), M:tm-303, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41332
in-theory        41332
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E or D)) or F))
theorem-size     19
proof            (modus-ponens tm-300 tm-551 ((Am (and (-> A (-> B (and A B))) C)) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41332.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E or D)) or F)), M:tm-300, m:tm-551, u:((Am (and (-> A (-> B (and A B))) C)) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41333
in-theory        41333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-270 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41333.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F or E)) or G))), M:tm-270, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41334
in-theory        41334
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-267 tm-551 ((Am (and (-> (and A B) B) C)) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41334.        ((A or (((B and C) -> C) and A)) -> ((D -> (E or D)) or F)), M:tm-267, m:tm-551, u:((Am (and (-> (and A B) B) C)) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41335
in-theory        41335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-239 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41335.        ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F or E)) or G))), M:tm-239, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41336
in-theory        41336
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-236 tm-551 ((Am (and (-> (and A B) A) C)) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41336.        ((A or (((B and C) -> B) and A)) -> ((D -> (E or D)) or F)), M:tm-236, m:tm-551, u:((Am (and (-> (and A B) A) C)) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41337
in-theory        41337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-210 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41337.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G or F)) or H))), M:tm-210, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41338
in-theory        41338
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F or E)) or G))
theorem-size     25
proof            (modus-ponens tm-207 tm-551 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41338.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F or E)) or G)), M:tm-207, m:tm-551, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41339
in-theory        41339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-183 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41339.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F or E)) or G))), M:tm-183, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41340
in-theory        41340
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-180 tm-551 ((Am (and (-> A (-> B A)) C)) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41340.        ((A or ((B -> (C -> B)) and A)) -> ((D -> (E or D)) or F)), M:tm-180, m:tm-551, u:((Am (and (-> A (-> B A)) C)) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41341
in-theory        41341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-157 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41341.        ((A -> ((B and C) -> C)) and (D -> ((E -> (F or E)) or G))), M:tm-157, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41342
in-theory        41342
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-154 tm-551 ((Am (-> (and A B) B)) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-4 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41342.        ((A or ((B and C) -> C)) -> ((D -> (E or D)) or F)), M:tm-154, m:tm-551, u:((Am (-> (and A B) B)) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41343
in-theory        41343
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F or E)) or G)))
theorem-size     25
proof            (modus-ponens tm-147 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41343.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F or E)) or G))), M:tm-147, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41344
in-theory        41344
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E or D)) or F))
theorem-size     23
proof            (modus-ponens tm-144 tm-551 ((Am (-> (and A (-> B C)) C)) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-6 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41344.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E or D)) or F)), M:tm-144, m:tm-551, u:((Am (-> (and A (-> B C)) C)) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41345
in-theory        41345
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C or B)) or D) -> E)) -> ((B -> (C or B)) or D))
theorem-size     19
proof            (modus-ponens tm-142 tm-551 ((Am (and A (-> (or (-> Bm (or Cm Bm)) Dm) C))) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-4 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41345.        ((A and (((B -> (C or B)) or D) -> E)) -> ((B -> (C or B)) or D)), M:tm-142, m:tm-551, u:((Am (and A (-> (or (-> Bm (or Cm Bm)) Dm) C))) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41346
in-theory        41346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-134 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41346.        ((A -> ((B and C) -> B)) and (D -> ((E -> (F or E)) or G))), M:tm-134, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41347
in-theory        41347
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-131 tm-551 ((Am (-> (and A B) A)) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-3 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41347.        ((A or ((B and C) -> B)) -> ((D -> (E or D)) or F)), M:tm-131, m:tm-551, u:((Am (-> (and A B) A)) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41348
in-theory        41348
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F or E)) or G)))
theorem-size     25
proof            (modus-ponens tm-125 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41348.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F or E)) or G))), M:tm-125, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41349
in-theory        41349
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E or D)) or F))
theorem-size     23
proof            (modus-ponens tm-122 tm-551 ((Am (-> (and (-> A B) C) B)) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-6 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41349.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E or D)) or F)), M:tm-122, m:tm-551, u:((Am (-> (and (-> A B) C) B)) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41350
in-theory        41350
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) or C) -> D) and E) -> ((A -> (B or A)) or C))
theorem-size     19
proof            (modus-ponens tm-120 tm-551 ((Am (and (-> (or (-> Bm (or Cm Bm)) Dm) B) C)) (A (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-3 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41350.        (((((A -> (B or A)) or C) -> D) and E) -> ((A -> (B or A)) or C)), M:tm-120, m:tm-551, u:((Am (and (-> (or (-> Bm (or Cm Bm)) Dm) B) C)) (A (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41351
in-theory        41351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-113 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41351.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G or F)) or H))), M:tm-113, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41352
in-theory        41352
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F or E)) or G))
theorem-size     23
proof            (modus-ponens tm-110 tm-551 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41352.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F or E)) or G)), M:tm-110, m:tm-551, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41353
in-theory        41353
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F or E)) or G)))
theorem-size     29
proof            (modus-ponens tm-105 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41353.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F or E)) or G))), M:tm-105, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41354
in-theory        41354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E or D)) or F))
theorem-size     27
proof            (modus-ponens tm-102 tm-551 ((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41354.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E or D)) or F)), M:tm-102, m:tm-551, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41355
in-theory        41355
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) -> D) -> ((A -> (B or A)) or C))
theorem-size     17
proof            (modus-ponens tm-96 tm-551 ((Am (-> (or (-> Bm (or Cm Bm)) Dm) B)) (A (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41355.        ((((A -> (B or A)) or C) -> D) -> ((A -> (B or A)) or C)), M:tm-96, m:tm-551, u:((Am (-> (or (-> Bm (or Cm Bm)) Dm) B)) (A (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41356
in-theory        41356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (E or D)) or F)))
theorem-size     17
proof            (modus-ponens tm-95 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41356.        (((A -> B) -> (A -> A)) and (C -> ((D -> (E or D)) or F))), M:tm-95, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41357
in-theory        41357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (D or C)) or E))
theorem-size     15
proof            (modus-ponens tm-92 tm-551 ((Am (-> A A)) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41357.        (((A -> B) or (A -> A)) -> ((C -> (D or C)) or E)), M:tm-92, m:tm-551, u:((Am (-> A A)) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41358
in-theory        41358
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D or C)) or E)))
theorem-size     11
proof            (modus-ponens tm-84 tm-551 ((A Am) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-7)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41358.        (A -> (B -> ((C -> (D or C)) or E))), M:tm-84, m:tm-551, u:((A Am) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41359
in-theory        41359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-83 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41359.        ((A -> (B -> (C -> B))) and (D -> ((E -> (F or E)) or G))), M:tm-83, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41360
in-theory        41360
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-80 tm-551 ((Am (-> A (-> B A))) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41360.        ((A or (B -> (C -> B))) -> ((D -> (E or D)) or F)), M:tm-80, m:tm-551, u:((Am (-> A (-> B A))) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41361
in-theory        41361
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((A -> (B or A)) or C) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-551 ((Am (not (not (-> (or (-> Bm (or Cm Bm)) Dm) B)))) (A (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-10 tm-1 tm-6 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41361.        ((not (not (((A -> (B or A)) or C) -> D))) -> D), M:tm-77, m:tm-551, u:((Am (not (not (-> (or (-> Bm (or Cm Bm)) Dm) B)))) (A (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41362
in-theory        41362
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (D or C)) or E)))
theorem-size     15
proof            (modus-ponens tm-76 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41362.        (((not (not A)) -> A) and (B -> ((C -> (D or C)) or E))), M:tm-76, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41363
in-theory        41363
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (C or B)) or D))
theorem-size     13
proof            (modus-ponens tm-73 tm-551 ((A Am) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-10 tm-1 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41363.        (((not (not A)) or A) -> ((B -> (C or B)) or D)), M:tm-73, m:tm-551, u:((A Am) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41364
in-theory        41364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E or D)) or F)))
theorem-size     21
proof            (modus-ponens tm-69 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-1 tm-6 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41364.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E or D)) or F))), M:tm-69, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41365
in-theory        41365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D or C)) or E))
theorem-size     19
proof            (modus-ponens tm-66 tm-551 ((Am (-> (-> A (not B)) (not A))) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-9 tm-1 tm-6 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41365.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D or C)) or E)), M:tm-66, m:tm-551, u:((Am (-> (-> A (not B)) (not A))) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41366
in-theory        41366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-54 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41366.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F or E)) or G))), M:tm-54, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41367
in-theory        41367
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) or F))
theorem-size     21
proof            (modus-ponens tm-51 tm-551 ((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41367.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E or D)) or F)), M:tm-51, m:tm-551, u:((Am (-> (-> A B) (-> (or C A) B))) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41368
in-theory        41368
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (D or C)) or E))
theorem-size     13
proof            (modus-ponens tm-50 tm-551 ((Am (or A B)) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41368.        ((A or (B or A)) -> ((C -> (D or C)) or E)), M:tm-50, m:tm-551, u:((Am (or A B)) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41369
in-theory        41369
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (D or C)) or E))
theorem-size     13
proof            (modus-ponens tm-49 tm-551 ((Am (or A B)) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41369.        ((A or (A or B)) -> ((C -> (D or C)) or E)), M:tm-49, m:tm-551, u:((Am (or A B)) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41370
in-theory        41370
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (D or C)) or E))
theorem-size     15
proof            (modus-ponens tm-48 tm-551 ((Am (-> A (and B A))) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41370.        ((A or (B -> (A and B))) -> ((C -> (D or C)) or E)), M:tm-48, m:tm-551, u:((Am (-> A (and B A))) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41371
in-theory        41371
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (D or C)) or E))
theorem-size     13
proof            (modus-ponens tm-47 tm-551 ((A Am) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-4 tm-1 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41371.        (((A and B) or B) -> ((C -> (D or C)) or E)), M:tm-47, m:tm-551, u:((A Am) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41372
in-theory        41372
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (D or C)) or E))
theorem-size     13
proof            (modus-ponens tm-46 tm-551 ((A Am) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41372.        (((A and B) or A) -> ((C -> (D or C)) or E)), M:tm-46, m:tm-551, u:((A Am) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41373
in-theory        41373
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) or F))
theorem-size     21
proof            (modus-ponens tm-45 tm-551 ((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41373.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) or F)), M:tm-45, m:tm-551, u:((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41374
in-theory        41374
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (D or C)) or E))
theorem-size     13
proof            (modus-ponens tm-44 tm-551 ((Am (-> A B)) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41374.        ((A or (B -> A)) -> ((C -> (D or C)) or E)), M:tm-44, m:tm-551, u:((Am (-> A B)) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41375
in-theory        41375
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-42 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41375.        ((A -> (B or A)) and (C -> ((D -> (E or D)) or F))), M:tm-42, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41376
in-theory        41376
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-32 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41376.        ((A -> (A or B)) and (C -> ((D -> (E or D)) or F))), M:tm-32, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41377
in-theory        41377
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (C or B)) or D)))
theorem-size     11
proof            (modus-ponens tm-24 tm-551 ((A Am) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41377.        (A -> (A and ((B -> (C or B)) or D))), M:tm-24, m:tm-551, u:((A Am) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41378
in-theory        41378
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) or F)))
theorem-size     17
proof            (modus-ponens tm-23 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41378.        ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) or F))), M:tm-23, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41379
in-theory        41379
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-22 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41379.        (((A and B) -> B) and (C -> ((D -> (E or D)) or F))), M:tm-22, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41380
in-theory        41380
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-21 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41380.        (((A and B) -> A) and (C -> ((D -> (E or D)) or F))), M:tm-21, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41381
in-theory        41381
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-20 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41381.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) or G))), M:tm-20, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41382
in-theory        41382
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-19 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41382.        ((A -> (B -> A)) and (C -> ((D -> (E or D)) or F))), M:tm-19, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41383
in-theory        41383
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((B -> (C or B)) or D) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-551 ((Am (and A (-> (or (-> Bm (or Cm Bm)) Dm) C))) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-4 tm-1 tm-6 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41383.        ((A and (((B -> (C or B)) or D) -> E)) -> E), M:tm-17, m:tm-551, u:((Am (and A (-> (or (-> Bm (or Cm Bm)) Dm) C))) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41384
in-theory        41384
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B or A)) or C) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-551 ((Am (and (-> (or (-> Bm (or Cm Bm)) Dm) B) C)) (A (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-3 tm-1 tm-6 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41384.        (((((A -> (B or A)) or C) -> D) and E) -> D), M:tm-15, m:tm-551, u:((Am (and (-> (or (-> Bm (or Cm Bm)) Dm) B) C)) (A (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41385
in-theory        41385
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C or B)) or D))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-551 ((A Am) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-9 tm-1 tm-6 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41385.        ((A -> (not ((B -> (C or B)) or D))) -> (not A)), M:tm-9, m:tm-551, u:((A Am) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41386
in-theory        41386
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) -> D) -> ((E or ((A -> (B or A)) or C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-551 ((A Am) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41386.        ((((A -> (B or A)) or C) -> D) -> ((E or ((A -> (B or A)) or C)) -> D)), M:tm-8, m:tm-551, u:((A Am) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-41387
in-theory        41387
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (D or C)) or E)))
theorem-size     11
proof            (modus-ponens tm-7 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-7 tm-1 tm-6)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41387.        (A or (B -> ((C -> (D or C)) or E))), M:tm-7, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41388
in-theory        41388
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-6 tm-1 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41388.        ((A -> ((B -> (C or B)) or D)) or E), M:tm-6, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41389
in-theory        41389
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D or C)) or E)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-41389.        (A -> ((B -> ((C -> (D or C)) or E)) and A)), M:tm-5, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-41390
in-theory        41390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41390.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-550, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41391
in-theory        41391
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41391.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-540, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41392
in-theory        41392
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41392.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-530, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41393
in-theory        41393
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41393.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-520, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41394
in-theory        41394
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41394.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-510, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41395
in-theory        41395
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41395.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-500, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41396
in-theory        41396
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41396.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> G)))), M:tm-490, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41397
in-theory        41397
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41397.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-480, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41398
in-theory        41398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41398.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-469, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41399
in-theory        41399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41399.        (((A -> (B or A)) and (C -> (D -> C))) and (E -> (E or F))), M:tm-456, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41400
in-theory        41400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41400.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-453, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41401
in-theory        41401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and ((E -> (E or F)) and ((A -> (B or A)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41401.        (((A -> (B or A)) and (C -> (D -> C))) and ((E -> (E or F)) and ((A -> (B or A)) and (C -> (D -> C))))), M:tm-443, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41402
in-theory        41402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41402.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-409, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41403
in-theory        41403
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41403.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-400, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41404
in-theory        41404
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41404.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-391, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41405
in-theory        41405
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41405.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-382, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41406
in-theory        41406
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41406.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (H -> G)))), M:tm-373, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41407
in-theory        41407
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41407.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-364, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41408
in-theory        41408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41408.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-354, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41409
in-theory        41409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41409.        (((A -> (B or A)) and (C -> (D -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41410
in-theory        41410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41410.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (F -> E)))), M:tm-338, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41411
in-theory        41411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and (C -> (D -> C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41411.        (((A -> (B or A)) and (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and (C -> (D -> C))))), M:tm-327, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41412
in-theory        41412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and (((E and F) -> F) and ((A -> (B or A)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41412.        (((A -> (B or A)) and (C -> (D -> C))) and (((E and F) -> F) and ((A -> (B or A)) and (C -> (D -> C))))), M:tm-326, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41413
in-theory        41413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and (((E and F) -> E) and ((A -> (B or A)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41413.        (((A -> (B or A)) and (C -> (D -> C))) and (((E and F) -> E) and ((A -> (B or A)) and (C -> (D -> C))))), M:tm-325, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41414
in-theory        41414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and (C -> (D -> C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41414.        (((A -> (B or A)) and (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and (C -> (D -> C))))), M:tm-324, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41415
in-theory        41415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and ((E -> (F -> E)) and ((A -> (B or A)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41415.        (((A -> (B or A)) and (C -> (D -> C))) and ((E -> (F -> E)) and ((A -> (B or A)) and (C -> (D -> C))))), M:tm-323, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41416
in-theory        41416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41416.        (((A -> (B or A)) and (C -> (D -> C))) and ((E and F) -> F)), M:tm-322, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41417
in-theory        41417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41417.        (((A -> (B or A)) and (C -> (D -> C))) and ((E and F) -> E)), M:tm-320, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41418
in-theory        41418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41418.        (((A -> (B or A)) and (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41419
in-theory        41419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41419.        (((A -> (B or A)) and (C -> (D -> C))) and (E -> (F -> E))), M:tm-315, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41420
in-theory        41420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and (E or ((A -> (B or A)) and (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41420.        (((A -> (B or A)) and (C -> (D -> C))) and (E or ((A -> (B or A)) and (C -> (D -> C))))), M:tm-311, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41421
in-theory        41421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and (((A -> (B or A)) and (C -> (D -> C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41421.        (((A -> (B or A)) and (C -> (D -> C))) and (((A -> (B or A)) and (C -> (D -> C))) or E)), M:tm-310, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41422
in-theory        41422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and (E -> (((A -> (B or A)) and (C -> (D -> C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41422.        (((A -> (B or A)) and (C -> (D -> C))) and (E -> (((A -> (B or A)) and (C -> (D -> C))) and E))), M:tm-309, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41423
in-theory        41423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-308 tm-552 ((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41423.        (((A -> (B or A)) and (C -> (D -> C))) and (C -> (D -> C))), M:tm-308, m:tm-552, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-41424
in-theory        41424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and (A -> (B or A)))
theorem-size     17
proof            (modus-ponens tm-307 tm-552 ((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41424.        (((A -> (B or A)) and (C -> (D -> C))) and (A -> (B or A))), M:tm-307, m:tm-552, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-41425
in-theory        41425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and (E -> ((A -> (B or A)) and (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41425.        (((A -> (B or A)) and (C -> (D -> C))) and (E -> ((A -> (B or A)) and (C -> (D -> C))))), M:tm-305, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41426
in-theory        41426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41426.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-303, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41427
in-theory        41427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41427.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-270, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41428
in-theory        41428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41428.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-239, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41429
in-theory        41429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41429.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (H -> G)))), M:tm-210, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41430
in-theory        41430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41430.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-183, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41431
in-theory        41431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41431.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-157, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41432
in-theory        41432
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41432.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-147, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41433
in-theory        41433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41433.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-134, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41434
in-theory        41434
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41434.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-125, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41435
in-theory        41435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41435.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> G)))), M:tm-113, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41436
in-theory        41436
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41436.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-105, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41437
in-theory        41437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41437.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (F -> E)))), M:tm-95, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41438
in-theory        41438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41438.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-83, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41439
in-theory        41439
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41439.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (E -> D)))), M:tm-76, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41440
in-theory        41440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41440.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (F -> E)))), M:tm-69, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41441
in-theory        41441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41441.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-54, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41442
in-theory        41442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41442.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> (F -> E)))), M:tm-42, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41443
in-theory        41443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41443.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> (F -> E)))), M:tm-32, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41444
in-theory        41444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41444.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (F -> E)))), M:tm-23, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41445
in-theory        41445
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41445.        (((A and B) -> B) and ((C -> (D or C)) and (E -> (F -> E)))), M:tm-22, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41446
in-theory        41446
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41446.        (((A and B) -> A) and ((C -> (D or C)) and (E -> (F -> E)))), M:tm-21, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41447
in-theory        41447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41447.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-20, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41448
in-theory        41448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41448.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (F -> E)))), M:tm-19, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41449
in-theory        41449
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41449.        (A or ((B -> (C or B)) and (D -> (E -> D)))), M:tm-7, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41450
in-theory        41450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41450.        (((A -> (B or A)) and (C -> (D -> C))) or E), M:tm-6, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41451
in-theory        41451
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> (E -> D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41451.        (A -> (((B -> (C or B)) and (D -> (E -> D))) and A)), M:tm-5, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41452
in-theory        41452
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-41452.        (A -> ((B -> (C or B)) and (D -> (E -> D)))), M:tm-1, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-41453
in-theory        41453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41453.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-550, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41454
in-theory        41454
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41454.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-540, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41455
in-theory        41455
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41455.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-530, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41456
in-theory        41456
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41456.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-520, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41457
in-theory        41457
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41457.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-510, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41458
in-theory        41458
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41458.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-500, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41459
in-theory        41459
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41459.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-490, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41460
in-theory        41460
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41460.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-480, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41461
in-theory        41461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41461.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-469, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41462
in-theory        41462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41462.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41463
in-theory        41463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41463.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-453, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41464
in-theory        41464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41464.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-443, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41465
in-theory        41465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41465.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-409, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41466
in-theory        41466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41466.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-400, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41467
in-theory        41467
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41467.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-391, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41468
in-theory        41468
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41468.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-382, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41469
in-theory        41469
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41469.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-373, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41470
in-theory        41470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41470.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-364, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41471
in-theory        41471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41471.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-354, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41472
in-theory        41472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41472.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41473
in-theory        41473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41473.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-338, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41474
in-theory        41474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41474.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-327, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41475
in-theory        41475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41475.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-326, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41476
in-theory        41476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41476.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-325, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41477
in-theory        41477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41477.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-324, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41478
in-theory        41478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41478.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-323, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41479
in-theory        41479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41479.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41480
in-theory        41480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41480.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41481
in-theory        41481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41481.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41482
in-theory        41482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41482.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41483
in-theory        41483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41483.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-311, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41484
in-theory        41484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41484.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-310, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41485
in-theory        41485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41485.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F))), M:tm-309, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41486
in-theory        41486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-308 tm-553 ((A (-> Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41486.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-308, m:tm-553, u:((A (-> Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-41487
in-theory        41487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (A -> (B or A)))
theorem-size     25
proof            (modus-ponens tm-307 tm-553 ((A (-> Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41487.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (A -> (B or A))), M:tm-307, m:tm-553, u:((A (-> Am (or Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-41488
in-theory        41488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41488.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-305, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41489
in-theory        41489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41489.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-303, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41490
in-theory        41490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41490.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-270, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41491
in-theory        41491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41491.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-239, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41492
in-theory        41492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41492.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-210, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41493
in-theory        41493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41493.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-183, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41494
in-theory        41494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41494.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-157, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41495
in-theory        41495
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41495.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-147, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41496
in-theory        41496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41496.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-134, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41497
in-theory        41497
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41497.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-125, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41498
in-theory        41498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41498.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-113, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41499
in-theory        41499
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41499.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-105, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41500
in-theory        41500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41500.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-95, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41501
in-theory        41501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41501.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-83, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41502
in-theory        41502
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41502.        (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-76, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41503
in-theory        41503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41503.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-69, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41504
in-theory        41504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41504.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-54, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41505
in-theory        41505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41505.        ((A -> (B or A)) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-42, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41506
in-theory        41506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41506.        ((A -> (A or B)) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-32, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41507
in-theory        41507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41507.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-23, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41508
in-theory        41508
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41508.        (((A and B) -> B) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-22, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41509
in-theory        41509
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41509.        (((A and B) -> A) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-21, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41510
in-theory        41510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41510.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-20, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41511
in-theory        41511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41511.        ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-19, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41512
in-theory        41512
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41512.        (A or ((B -> (C or B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-7, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41513
in-theory        41513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-6 tm-5 tm-7 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41513.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F), M:tm-6, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41514
in-theory        41514
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41514.        (A -> (((B -> (C or B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)), M:tm-5, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41515
in-theory        41515
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-1 tm-5 tm-7 tm-2)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-41515.        (A -> ((B -> (C or B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-1, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-41516
in-theory        41516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41516.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-550, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41517
in-theory        41517
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41517.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-540, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41518
in-theory        41518
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41518.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-530, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41519
in-theory        41519
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41519.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-520, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41520
in-theory        41520
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41520.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-510, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41521
in-theory        41521
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41521.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-500, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41522
in-theory        41522
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41522.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G and H) -> G))), M:tm-490, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41523
in-theory        41523
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41523.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-480, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41524
in-theory        41524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41524.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-469, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41525
in-theory        41525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41525.        (((A -> (B or A)) and ((C and D) -> C)) and (E -> (E or F))), M:tm-456, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41526
in-theory        41526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41526.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-453, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41527
in-theory        41527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and ((E -> (E or F)) and ((A -> (B or A)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41527.        (((A -> (B or A)) and ((C and D) -> C)) and ((E -> (E or F)) and ((A -> (B or A)) and ((C and D) -> C)))), M:tm-443, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41528
in-theory        41528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41528.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-409, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41529
in-theory        41529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41529.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-400, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41530
in-theory        41530
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41530.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-391, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41531
in-theory        41531
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41531.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-382, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41532
in-theory        41532
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41532.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G and H) -> G))), M:tm-373, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41533
in-theory        41533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41533.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-364, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41534
in-theory        41534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41534.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-354, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41535
in-theory        41535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41535.        (((A -> (B or A)) and ((C and D) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41536
in-theory        41536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41536.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E and F) -> E))), M:tm-338, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41537
in-theory        41537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and ((C and D) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41537.        (((A -> (B or A)) and ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and ((C and D) -> C)))), M:tm-327, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41538
in-theory        41538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and (((E and F) -> F) and ((A -> (B or A)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41538.        (((A -> (B or A)) and ((C and D) -> C)) and (((E and F) -> F) and ((A -> (B or A)) and ((C and D) -> C)))), M:tm-326, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41539
in-theory        41539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and (((E and F) -> E) and ((A -> (B or A)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41539.        (((A -> (B or A)) and ((C and D) -> C)) and (((E and F) -> E) and ((A -> (B or A)) and ((C and D) -> C)))), M:tm-325, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41540
in-theory        41540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and ((C and D) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41540.        (((A -> (B or A)) and ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and ((C and D) -> C)))), M:tm-324, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41541
in-theory        41541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and ((E -> (F -> E)) and ((A -> (B or A)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41541.        (((A -> (B or A)) and ((C and D) -> C)) and ((E -> (F -> E)) and ((A -> (B or A)) and ((C and D) -> C)))), M:tm-323, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41542
in-theory        41542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41542.        (((A -> (B or A)) and ((C and D) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41543
in-theory        41543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41543.        (((A -> (B or A)) and ((C and D) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41544
in-theory        41544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41544.        (((A -> (B or A)) and ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41545
in-theory        41545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41545.        (((A -> (B or A)) and ((C and D) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41546
in-theory        41546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and (E or ((A -> (B or A)) and ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41546.        (((A -> (B or A)) and ((C and D) -> C)) and (E or ((A -> (B or A)) and ((C and D) -> C)))), M:tm-311, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41547
in-theory        41547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and (((A -> (B or A)) and ((C and D) -> C)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41547.        (((A -> (B or A)) and ((C and D) -> C)) and (((A -> (B or A)) and ((C and D) -> C)) or E)), M:tm-310, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41548
in-theory        41548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and (E -> (((A -> (B or A)) and ((C and D) -> C)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41548.        (((A -> (B or A)) and ((C and D) -> C)) and (E -> (((A -> (B or A)) and ((C and D) -> C)) and E))), M:tm-309, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41549
in-theory        41549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-308 tm-554 ((A (-> Am (or Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41549.        (((A -> (B or A)) and ((C and D) -> C)) and ((C and D) -> C)), M:tm-308, m:tm-554, u:((A (-> Am (or Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-41550
in-theory        41550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and (A -> (B or A)))
theorem-size     17
proof            (modus-ponens tm-307 tm-554 ((A (-> Am (or Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41550.        (((A -> (B or A)) and ((C and D) -> C)) and (A -> (B or A))), M:tm-307, m:tm-554, u:((A (-> Am (or Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-41551
in-theory        41551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and (E -> ((A -> (B or A)) and ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41551.        (((A -> (B or A)) and ((C and D) -> C)) and (E -> ((A -> (B or A)) and ((C and D) -> C)))), M:tm-305, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41552
in-theory        41552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41552.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-303, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41553
in-theory        41553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41553.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-270, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41554
in-theory        41554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41554.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-239, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41555
in-theory        41555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41555.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G and H) -> G))), M:tm-210, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41556
in-theory        41556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41556.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-183, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41557
in-theory        41557
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41557.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-157, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41558
in-theory        41558
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41558.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-147, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41559
in-theory        41559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41559.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-134, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41560
in-theory        41560
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41560.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-125, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41561
in-theory        41561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41561.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G and H) -> G))), M:tm-113, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41562
in-theory        41562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41562.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-105, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41563
in-theory        41563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41563.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E and F) -> E))), M:tm-95, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41564
in-theory        41564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41564.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-83, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41565
in-theory        41565
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((D and E) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-10 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41565.        (((not (not A)) -> A) and ((B -> (C or B)) and ((D and E) -> D))), M:tm-76, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41566
in-theory        41566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-9 tm-7 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41566.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E and F) -> E))), M:tm-69, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41567
in-theory        41567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41567.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-54, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41568
in-theory        41568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41568.        ((A -> (B or A)) and ((C -> (D or C)) and ((E and F) -> E))), M:tm-42, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41569
in-theory        41569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41569.        ((A -> (A or B)) and ((C -> (D or C)) and ((E and F) -> E))), M:tm-32, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41570
in-theory        41570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41570.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E and F) -> E))), M:tm-23, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41571
in-theory        41571
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41571.        (((A and B) -> B) and ((C -> (D or C)) and ((E and F) -> E))), M:tm-22, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41572
in-theory        41572
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41572.        (((A and B) -> A) and ((C -> (D or C)) and ((E and F) -> E))), M:tm-21, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41573
in-theory        41573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41573.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-20, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41574
in-theory        41574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41574.        ((A -> (B -> A)) and ((C -> (D or C)) and ((E and F) -> E))), M:tm-19, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41575
in-theory        41575
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41575.        (A or ((B -> (C or B)) and ((D and E) -> D))), M:tm-7, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41576
in-theory        41576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-6 tm-5 tm-7 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41576.        (((A -> (B or A)) and ((C and D) -> C)) or E), M:tm-6, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41577
in-theory        41577
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((D and E) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41577.        (A -> (((B -> (C or B)) and ((D and E) -> D)) and A)), M:tm-5, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41578
in-theory        41578
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-1 tm-5 tm-7 tm-3)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-41578.        (A -> ((B -> (C or B)) and ((D and E) -> D))), M:tm-1, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-41579
in-theory        41579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-550 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41579.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-550, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41580
in-theory        41580
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-540 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41580.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-540, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41581
in-theory        41581
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-530 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41581.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-530, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41582
in-theory        41582
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-520 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41582.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-520, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41583
in-theory        41583
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-510 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41583.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-510, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41584
in-theory        41584
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-500 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41584.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-500, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41585
in-theory        41585
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-490 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41585.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G and H) -> H))), M:tm-490, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41586
in-theory        41586
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-480 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41586.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-480, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41587
in-theory        41587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-469 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41587.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-469, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41588
in-theory        41588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41588.        (((A -> (B or A)) and ((C and D) -> D)) and (E -> (E or F))), M:tm-456, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41589
in-theory        41589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-453 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41589.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-453, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41590
in-theory        41590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and ((E -> (E or F)) and ((A -> (B or A)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-443 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41590.        (((A -> (B or A)) and ((C and D) -> D)) and ((E -> (E or F)) and ((A -> (B or A)) and ((C and D) -> D)))), M:tm-443, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41591
in-theory        41591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-409 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41591.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-409, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41592
in-theory        41592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-400 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41592.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-400, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41593
in-theory        41593
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-391 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41593.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-391, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41594
in-theory        41594
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-382 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41594.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-382, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41595
in-theory        41595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-373 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41595.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G and H) -> H))), M:tm-373, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41596
in-theory        41596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-364 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41596.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-364, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41597
in-theory        41597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-354 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41597.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-354, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41598
in-theory        41598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41598.        (((A -> (B or A)) and ((C and D) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41599
in-theory        41599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-338 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41599.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E and F) -> F))), M:tm-338, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41600
in-theory        41600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and ((C and D) -> D))))
theorem-size     31
proof            (modus-ponens tm-327 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41600.        (((A -> (B or A)) and ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and ((C and D) -> D)))), M:tm-327, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41601
in-theory        41601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and (((E and F) -> F) and ((A -> (B or A)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-326 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41601.        (((A -> (B or A)) and ((C and D) -> D)) and (((E and F) -> F) and ((A -> (B or A)) and ((C and D) -> D)))), M:tm-326, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41602
in-theory        41602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and (((E and F) -> E) and ((A -> (B or A)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-325 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41602.        (((A -> (B or A)) and ((C and D) -> D)) and (((E and F) -> E) and ((A -> (B or A)) and ((C and D) -> D)))), M:tm-325, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41603
in-theory        41603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and ((C and D) -> D))))
theorem-size     37
proof            (modus-ponens tm-324 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41603.        (((A -> (B or A)) and ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and ((C and D) -> D)))), M:tm-324, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41604
in-theory        41604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and ((E -> (F -> E)) and ((A -> (B or A)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-323 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41604.        (((A -> (B or A)) and ((C and D) -> D)) and ((E -> (F -> E)) and ((A -> (B or A)) and ((C and D) -> D)))), M:tm-323, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41605
in-theory        41605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41605.        (((A -> (B or A)) and ((C and D) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41606
in-theory        41606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41606.        (((A -> (B or A)) and ((C and D) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41607
in-theory        41607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41607.        (((A -> (B or A)) and ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41608
in-theory        41608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41608.        (((A -> (B or A)) and ((C and D) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41609
in-theory        41609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and (E or ((A -> (B or A)) and ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-311 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41609.        (((A -> (B or A)) and ((C and D) -> D)) and (E or ((A -> (B or A)) and ((C and D) -> D)))), M:tm-311, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41610
in-theory        41610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and (((A -> (B or A)) and ((C and D) -> D)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41610.        (((A -> (B or A)) and ((C and D) -> D)) and (((A -> (B or A)) and ((C and D) -> D)) or E)), M:tm-310, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41611
in-theory        41611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and (E -> (((A -> (B or A)) and ((C and D) -> D)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41611.        (((A -> (B or A)) and ((C and D) -> D)) and (E -> (((A -> (B or A)) and ((C and D) -> D)) and E))), M:tm-309, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41612
in-theory        41612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-308 tm-555 ((A (-> Am (or Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41612.        (((A -> (B or A)) and ((C and D) -> D)) and ((C and D) -> D)), M:tm-308, m:tm-555, u:((A (-> Am (or Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-41613
in-theory        41613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and (A -> (B or A)))
theorem-size     17
proof            (modus-ponens tm-307 tm-555 ((A (-> Am (or Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41613.        (((A -> (B or A)) and ((C and D) -> D)) and (A -> (B or A))), M:tm-307, m:tm-555, u:((A (-> Am (or Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-41614
in-theory        41614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and (E -> ((A -> (B or A)) and ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-305 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41614.        (((A -> (B or A)) and ((C and D) -> D)) and (E -> ((A -> (B or A)) and ((C and D) -> D)))), M:tm-305, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41615
in-theory        41615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-303 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41615.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-303, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41616
in-theory        41616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-270 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41616.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-270, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41617
in-theory        41617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-239 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41617.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-239, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41618
in-theory        41618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-210 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41618.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G and H) -> H))), M:tm-210, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41619
in-theory        41619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-183 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41619.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-183, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41620
in-theory        41620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-157 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41620.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-157, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41621
in-theory        41621
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-147 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41621.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-147, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41622
in-theory        41622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-134 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41622.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-134, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41623
in-theory        41623
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-125 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41623.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-125, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41624
in-theory        41624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-113 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41624.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G and H) -> H))), M:tm-113, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41625
in-theory        41625
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-105 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41625.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-105, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41626
in-theory        41626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-95 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41626.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E and F) -> F))), M:tm-95, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41627
in-theory        41627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-83 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41627.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-83, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41628
in-theory        41628
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((D and E) -> E)))
theorem-size     17
proof            (modus-ponens tm-76 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-10 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41628.        (((not (not A)) -> A) and ((B -> (C or B)) and ((D and E) -> E))), M:tm-76, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41629
in-theory        41629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-69 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-9 tm-7 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41629.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E and F) -> F))), M:tm-69, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41630
in-theory        41630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-54 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41630.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-54, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41631
in-theory        41631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-42 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41631.        ((A -> (B or A)) and ((C -> (D or C)) and ((E and F) -> F))), M:tm-42, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41632
in-theory        41632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-32 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41632.        ((A -> (A or B)) and ((C -> (D or C)) and ((E and F) -> F))), M:tm-32, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41633
in-theory        41633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-23 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41633.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E and F) -> F))), M:tm-23, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41634
in-theory        41634
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-22 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41634.        (((A and B) -> B) and ((C -> (D or C)) and ((E and F) -> F))), M:tm-22, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41635
in-theory        41635
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-21 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41635.        (((A and B) -> A) and ((C -> (D or C)) and ((E and F) -> F))), M:tm-21, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41636
in-theory        41636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-20 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41636.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-20, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41637
in-theory        41637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-19 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41637.        ((A -> (B -> A)) and ((C -> (D or C)) and ((E and F) -> F))), M:tm-19, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41638
in-theory        41638
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-7 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41638.        (A or ((B -> (C or B)) and ((D and E) -> E))), M:tm-7, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41639
in-theory        41639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-6 tm-5 tm-7 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41639.        (((A -> (B or A)) and ((C and D) -> D)) or E), M:tm-6, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41640
in-theory        41640
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((D and E) -> E)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41640.        (A -> (((B -> (C or B)) and ((D and E) -> E)) and A)), M:tm-5, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41641
in-theory        41641
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-1 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-1 tm-5 tm-7 tm-4)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-41641.        (A -> ((B -> (C or B)) and ((D and E) -> E))), M:tm-1, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-41642
in-theory        41642
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41642.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-550, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41643
in-theory        41643
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41643.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-540, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41644
in-theory        41644
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41644.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-530, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41645
in-theory        41645
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41645.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-520, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41646
in-theory        41646
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41646.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-510, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41647
in-theory        41647
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41647.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-500, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41648
in-theory        41648
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41648.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (G and H))))), M:tm-490, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41649
in-theory        41649
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41649.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-480, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41650
in-theory        41650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41650.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-469, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41651
in-theory        41651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41651.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41652
in-theory        41652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41652.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-453, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41653
in-theory        41653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A -> (B or A)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41653.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A -> (B or A)) and (C -> (D -> (C and D)))))), M:tm-443, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41654
in-theory        41654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41654.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-409, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41655
in-theory        41655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41655.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-400, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41656
in-theory        41656
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41656.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-391, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41657
in-theory        41657
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41657.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-382, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41658
in-theory        41658
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41658.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (G and H))))), M:tm-373, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41659
in-theory        41659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41659.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-364, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41660
in-theory        41660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41660.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-354, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41661
in-theory        41661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41661.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41662
in-theory        41662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41662.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (E and F))))), M:tm-338, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41663
in-theory        41663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and (C -> (D -> (C and D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41663.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and (C -> (D -> (C and D)))))), M:tm-327, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41664
in-theory        41664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A -> (B or A)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41664.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A -> (B or A)) and (C -> (D -> (C and D)))))), M:tm-326, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41665
in-theory        41665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A -> (B or A)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41665.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A -> (B or A)) and (C -> (D -> (C and D)))))), M:tm-325, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41666
in-theory        41666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and (C -> (D -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41666.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and (C -> (D -> (C and D)))))), M:tm-324, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41667
in-theory        41667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A -> (B or A)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41667.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A -> (B or A)) and (C -> (D -> (C and D)))))), M:tm-323, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41668
in-theory        41668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41668.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41669
in-theory        41669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41669.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41670
in-theory        41670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41670.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41671
in-theory        41671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41671.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41672
in-theory        41672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and (E or ((A -> (B or A)) and (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41672.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and (E or ((A -> (B or A)) and (C -> (D -> (C and D)))))), M:tm-311, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41673
in-theory        41673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and (((A -> (B or A)) and (C -> (D -> (C and D)))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41673.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and (((A -> (B or A)) and (C -> (D -> (C and D)))) or E)), M:tm-310, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41674
in-theory        41674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and (E -> (((A -> (B or A)) and (C -> (D -> (C and D)))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41674.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and (E -> (((A -> (B or A)) and (C -> (D -> (C and D)))) and E))), M:tm-309, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41675
in-theory        41675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-556 ((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41675.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and (C -> (D -> (C and D)))), M:tm-308, m:tm-556, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-41676
in-theory        41676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-556 ((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41676.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and (A -> (B or A))), M:tm-307, m:tm-556, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-41677
in-theory        41677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and (E -> ((A -> (B or A)) and (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41677.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and (E -> ((A -> (B or A)) and (C -> (D -> (C and D)))))), M:tm-305, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41678
in-theory        41678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41678.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-303, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41679
in-theory        41679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41679.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-270, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41680
in-theory        41680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41680.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-239, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41681
in-theory        41681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41681.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (H -> (G and H))))), M:tm-210, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41682
in-theory        41682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41682.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-183, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41683
in-theory        41683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41683.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-157, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41684
in-theory        41684
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41684.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-147, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41685
in-theory        41685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41685.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-134, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41686
in-theory        41686
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41686.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-125, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41687
in-theory        41687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41687.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (G and H))))), M:tm-113, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41688
in-theory        41688
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41688.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-105, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41689
in-theory        41689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41689.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (F -> (E and F))))), M:tm-95, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41690
in-theory        41690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41690.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-83, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41691
in-theory        41691
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41691.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (E -> (D and E))))), M:tm-76, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41692
in-theory        41692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41692.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (F -> (E and F))))), M:tm-69, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41693
in-theory        41693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41693.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-54, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41694
in-theory        41694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41694.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> (F -> (E and F))))), M:tm-42, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41695
in-theory        41695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41695.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> (F -> (E and F))))), M:tm-32, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41696
in-theory        41696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41696.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (E and F))))), M:tm-23, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41697
in-theory        41697
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41697.        (((A and B) -> B) and ((C -> (D or C)) and (E -> (F -> (E and F))))), M:tm-22, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41698
in-theory        41698
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41698.        (((A and B) -> A) and ((C -> (D or C)) and (E -> (F -> (E and F))))), M:tm-21, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41699
in-theory        41699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41699.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-20, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41700
in-theory        41700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41700.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (F -> (E and F))))), M:tm-19, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41701
in-theory        41701
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-7 tm-5)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41701.        (A or ((B -> (C or B)) and (D -> (E -> (D and E))))), M:tm-7, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41702
in-theory        41702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41702.        (((A -> (B or A)) and (C -> (D -> (C and D)))) or E), M:tm-6, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41703
in-theory        41703
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> (E -> (D and E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41703.        (A -> (((B -> (C or B)) and (D -> (E -> (D and E)))) and A)), M:tm-5, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41704
in-theory        41704
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-41704.        (A -> ((B -> (C or B)) and (D -> (E -> (D and E))))), M:tm-1, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-41705
in-theory        41705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-550 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41705.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-550, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41706
in-theory        41706
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-540 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41706.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-540, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41707
in-theory        41707
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-530 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41707.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-530, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41708
in-theory        41708
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-520 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41708.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-520, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41709
in-theory        41709
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-510 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41709.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-510, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41710
in-theory        41710
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-500 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41710.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-500, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41711
in-theory        41711
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-490 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41711.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (G or H)))), M:tm-490, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41712
in-theory        41712
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-480 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41712.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-480, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41713
in-theory        41713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-469 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41713.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-469, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41714
in-theory        41714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41714.        (((A -> (B or A)) and (C -> (C or D))) and (E -> (E or F))), M:tm-456, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41715
in-theory        41715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-453 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41715.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-453, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41716
in-theory        41716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and ((E -> (E or F)) and ((A -> (B or A)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41716.        (((A -> (B or A)) and (C -> (C or D))) and ((E -> (E or F)) and ((A -> (B or A)) and (C -> (C or D))))), M:tm-443, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41717
in-theory        41717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-409 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41717.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-409, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41718
in-theory        41718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-400 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41718.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-400, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41719
in-theory        41719
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-391 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41719.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-391, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41720
in-theory        41720
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-382 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41720.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-382, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41721
in-theory        41721
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-373 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41721.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (G or H)))), M:tm-373, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41722
in-theory        41722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-364 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41722.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-364, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41723
in-theory        41723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-354 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41723.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-354, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41724
in-theory        41724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41724.        (((A -> (B or A)) and (C -> (C or D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41725
in-theory        41725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-338 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41725.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (E or F)))), M:tm-338, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41726
in-theory        41726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and (C -> (C or D)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41726.        (((A -> (B or A)) and (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and (C -> (C or D))))), M:tm-327, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41727
in-theory        41727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and (((E and F) -> F) and ((A -> (B or A)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41727.        (((A -> (B or A)) and (C -> (C or D))) and (((E and F) -> F) and ((A -> (B or A)) and (C -> (C or D))))), M:tm-326, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41728
in-theory        41728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and (((E and F) -> E) and ((A -> (B or A)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41728.        (((A -> (B or A)) and (C -> (C or D))) and (((E and F) -> E) and ((A -> (B or A)) and (C -> (C or D))))), M:tm-325, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41729
in-theory        41729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and (C -> (C or D)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41729.        (((A -> (B or A)) and (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and (C -> (C or D))))), M:tm-324, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41730
in-theory        41730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and ((E -> (F -> E)) and ((A -> (B or A)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41730.        (((A -> (B or A)) and (C -> (C or D))) and ((E -> (F -> E)) and ((A -> (B or A)) and (C -> (C or D))))), M:tm-323, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41731
in-theory        41731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41731.        (((A -> (B or A)) and (C -> (C or D))) and ((E and F) -> F)), M:tm-322, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41732
in-theory        41732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41732.        (((A -> (B or A)) and (C -> (C or D))) and ((E and F) -> E)), M:tm-320, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41733
in-theory        41733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41733.        (((A -> (B or A)) and (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41734
in-theory        41734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41734.        (((A -> (B or A)) and (C -> (C or D))) and (E -> (F -> E))), M:tm-315, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41735
in-theory        41735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and (E or ((A -> (B or A)) and (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41735.        (((A -> (B or A)) and (C -> (C or D))) and (E or ((A -> (B or A)) and (C -> (C or D))))), M:tm-311, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41736
in-theory        41736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and (((A -> (B or A)) and (C -> (C or D))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41736.        (((A -> (B or A)) and (C -> (C or D))) and (((A -> (B or A)) and (C -> (C or D))) or E)), M:tm-310, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41737
in-theory        41737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and (E -> (((A -> (B or A)) and (C -> (C or D))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41737.        (((A -> (B or A)) and (C -> (C or D))) and (E -> (((A -> (B or A)) and (C -> (C or D))) and E))), M:tm-309, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41738
in-theory        41738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-308 tm-557 ((A (-> Am (or Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41738.        (((A -> (B or A)) and (C -> (C or D))) and (C -> (C or D))), M:tm-308, m:tm-557, u:((A (-> Am (or Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-41739
in-theory        41739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and (A -> (B or A)))
theorem-size     17
proof            (modus-ponens tm-307 tm-557 ((A (-> Am (or Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41739.        (((A -> (B or A)) and (C -> (C or D))) and (A -> (B or A))), M:tm-307, m:tm-557, u:((A (-> Am (or Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-41740
in-theory        41740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and (E -> ((A -> (B or A)) and (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41740.        (((A -> (B or A)) and (C -> (C or D))) and (E -> ((A -> (B or A)) and (C -> (C or D))))), M:tm-305, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41741
in-theory        41741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-303 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41741.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-303, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41742
in-theory        41742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-270 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41742.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-270, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41743
in-theory        41743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-239 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41743.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-239, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41744
in-theory        41744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-210 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41744.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (G or H)))), M:tm-210, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41745
in-theory        41745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-183 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41745.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-183, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41746
in-theory        41746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-157 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41746.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-157, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41747
in-theory        41747
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-147 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41747.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-147, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41748
in-theory        41748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-134 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41748.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-134, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41749
in-theory        41749
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-125 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41749.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-125, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41750
in-theory        41750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-113 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41750.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (G or H)))), M:tm-113, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41751
in-theory        41751
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-105 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41751.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-105, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41752
in-theory        41752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-95 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41752.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (E or F)))), M:tm-95, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41753
in-theory        41753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-83 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41753.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-83, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41754
in-theory        41754
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-76 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41754.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (D or E)))), M:tm-76, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41755
in-theory        41755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-69 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41755.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (E or F)))), M:tm-69, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41756
in-theory        41756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-54 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41756.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-54, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41757
in-theory        41757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-42 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41757.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> (E or F)))), M:tm-42, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41758
in-theory        41758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-32 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41758.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> (E or F)))), M:tm-32, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41759
in-theory        41759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-23 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41759.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (E or F)))), M:tm-23, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41760
in-theory        41760
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-22 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41760.        (((A and B) -> B) and ((C -> (D or C)) and (E -> (E or F)))), M:tm-22, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41761
in-theory        41761
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-21 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41761.        (((A and B) -> A) and ((C -> (D or C)) and (E -> (E or F)))), M:tm-21, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41762
in-theory        41762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-20 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41762.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-20, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41763
in-theory        41763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-19 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41763.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (E or F)))), M:tm-19, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41764
in-theory        41764
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-7 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41764.        (A or ((B -> (C or B)) and (D -> (D or E)))), M:tm-7, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41765
in-theory        41765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41765.        (((A -> (B or A)) and (C -> (C or D))) or E), M:tm-6, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41766
in-theory        41766
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> (D or E))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41766.        (A -> (((B -> (C or B)) and (D -> (D or E))) and A)), M:tm-5, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41767
in-theory        41767
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-1 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-6)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41767.        (A -> ((B -> (C or B)) and (D -> (D or E)))), M:tm-1, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-41768
in-theory        41768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41768.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-550, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41769
in-theory        41769
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41769.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-540, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41770
in-theory        41770
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41770.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-530, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41771
in-theory        41771
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41771.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-520, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41772
in-theory        41772
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41772.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-510, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41773
in-theory        41773
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41773.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-500, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41774
in-theory        41774
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41774.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H or G)))), M:tm-490, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41775
in-theory        41775
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41775.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-480, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41776
in-theory        41776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41776.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-469, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41777
in-theory        41777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41777.        (((A -> (B or A)) and (C -> (D or C))) and (E -> (E or F))), M:tm-456, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41778
in-theory        41778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41778.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-453, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41779
in-theory        41779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and ((E -> (E or F)) and ((A -> (B or A)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41779.        (((A -> (B or A)) and (C -> (D or C))) and ((E -> (E or F)) and ((A -> (B or A)) and (C -> (D or C))))), M:tm-443, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41780
in-theory        41780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41780.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-409, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41781
in-theory        41781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41781.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-400, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41782
in-theory        41782
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41782.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-391, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41783
in-theory        41783
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41783.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-382, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41784
in-theory        41784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41784.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (H or G)))), M:tm-373, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41785
in-theory        41785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41785.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-364, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41786
in-theory        41786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41786.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-354, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41787
in-theory        41787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41787.        (((A -> (B or A)) and (C -> (D or C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41788
in-theory        41788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41788.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (F or E)))), M:tm-338, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41789
in-theory        41789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and (C -> (D or C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41789.        (((A -> (B or A)) and (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and (C -> (D or C))))), M:tm-327, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41790
in-theory        41790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and (((E and F) -> F) and ((A -> (B or A)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41790.        (((A -> (B or A)) and (C -> (D or C))) and (((E and F) -> F) and ((A -> (B or A)) and (C -> (D or C))))), M:tm-326, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41791
in-theory        41791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and (((E and F) -> E) and ((A -> (B or A)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41791.        (((A -> (B or A)) and (C -> (D or C))) and (((E and F) -> E) and ((A -> (B or A)) and (C -> (D or C))))), M:tm-325, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41792
in-theory        41792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and (C -> (D or C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41792.        (((A -> (B or A)) and (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and (C -> (D or C))))), M:tm-324, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41793
in-theory        41793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and ((E -> (F -> E)) and ((A -> (B or A)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41793.        (((A -> (B or A)) and (C -> (D or C))) and ((E -> (F -> E)) and ((A -> (B or A)) and (C -> (D or C))))), M:tm-323, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41794
in-theory        41794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41794.        (((A -> (B or A)) and (C -> (D or C))) and ((E and F) -> F)), M:tm-322, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41795
in-theory        41795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41795.        (((A -> (B or A)) and (C -> (D or C))) and ((E and F) -> E)), M:tm-320, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41796
in-theory        41796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41796.        (((A -> (B or A)) and (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41797
in-theory        41797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41797.        (((A -> (B or A)) and (C -> (D or C))) and (E -> (F -> E))), M:tm-315, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41798
in-theory        41798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and (E or ((A -> (B or A)) and (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41798.        (((A -> (B or A)) and (C -> (D or C))) and (E or ((A -> (B or A)) and (C -> (D or C))))), M:tm-311, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41799
in-theory        41799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and (((A -> (B or A)) and (C -> (D or C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41799.        (((A -> (B or A)) and (C -> (D or C))) and (((A -> (B or A)) and (C -> (D or C))) or E)), M:tm-310, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41800
in-theory        41800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and (E -> (((A -> (B or A)) and (C -> (D or C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41800.        (((A -> (B or A)) and (C -> (D or C))) and (E -> (((A -> (B or A)) and (C -> (D or C))) and E))), M:tm-309, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41801
in-theory        41801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-308 tm-558 ((A (-> Am (or Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41801.        (((A -> (B or A)) and (C -> (D or C))) and (C -> (D or C))), M:tm-308, m:tm-558, u:((A (-> Am (or Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-41802
in-theory        41802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and (A -> (B or A)))
theorem-size     17
proof            (modus-ponens tm-307 tm-558 ((A (-> Am (or Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41802.        (((A -> (B or A)) and (C -> (D or C))) and (A -> (B or A))), M:tm-307, m:tm-558, u:((A (-> Am (or Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-41803
in-theory        41803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and (E -> ((A -> (B or A)) and (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41803.        (((A -> (B or A)) and (C -> (D or C))) and (E -> ((A -> (B or A)) and (C -> (D or C))))), M:tm-305, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41804
in-theory        41804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41804.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-303, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41805
in-theory        41805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41805.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-270, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41806
in-theory        41806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41806.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-239, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41807
in-theory        41807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41807.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (H or G)))), M:tm-210, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41808
in-theory        41808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41808.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-183, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41809
in-theory        41809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41809.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-157, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41810
in-theory        41810
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41810.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-147, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41811
in-theory        41811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41811.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-134, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41812
in-theory        41812
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41812.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-125, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41813
in-theory        41813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41813.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H or G)))), M:tm-113, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41814
in-theory        41814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41814.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-105, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41815
in-theory        41815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41815.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (F or E)))), M:tm-95, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41816
in-theory        41816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41816.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-83, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41817
in-theory        41817
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41817.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (E or D)))), M:tm-76, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41818
in-theory        41818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41818.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (F or E)))), M:tm-69, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41819
in-theory        41819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41819.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-54, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41820
in-theory        41820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41820.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> (F or E)))), M:tm-42, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41821
in-theory        41821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41821.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> (F or E)))), M:tm-32, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41822
in-theory        41822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41822.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (F or E)))), M:tm-23, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41823
in-theory        41823
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41823.        (((A and B) -> B) and ((C -> (D or C)) and (E -> (F or E)))), M:tm-22, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41824
in-theory        41824
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41824.        (((A and B) -> A) and ((C -> (D or C)) and (E -> (F or E)))), M:tm-21, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41825
in-theory        41825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41825.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-20, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41826
in-theory        41826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41826.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (F or E)))), M:tm-19, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41827
in-theory        41827
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-7 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41827.        (A or ((B -> (C or B)) and (D -> (E or D)))), M:tm-7, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41828
in-theory        41828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41828.        (((A -> (B or A)) and (C -> (D or C))) or E), M:tm-6, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41829
in-theory        41829
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> (E or D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41829.        (A -> (((B -> (C or B)) and (D -> (E or D))) and A)), M:tm-5, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41830
in-theory        41830
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41830.        (A -> ((B -> (C or B)) and (D -> (E or D)))), M:tm-1, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-41831
in-theory        41831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41831.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-550, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41832
in-theory        41832
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41832.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-540, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41833
in-theory        41833
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41833.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-530, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41834
in-theory        41834
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41834.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-520, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41835
in-theory        41835
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41835.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-510, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41836
in-theory        41836
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41836.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-500, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41837
in-theory        41837
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41837.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-490, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41838
in-theory        41838
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41838.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-480, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41839
in-theory        41839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41839.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-469, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41840
in-theory        41840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41840.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (F or G))), M:tm-456, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41841
in-theory        41841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41841.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-453, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41842
in-theory        41842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41842.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-443, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41843
in-theory        41843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41843.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-409, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41844
in-theory        41844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41844.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-400, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41845
in-theory        41845
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41845.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-391, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41846
in-theory        41846
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41846.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-382, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41847
in-theory        41847
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41847.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-373, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41848
in-theory        41848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41848.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-364, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41849
in-theory        41849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41849.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-354, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41850
in-theory        41850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41850.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41851
in-theory        41851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41851.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-338, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41852
in-theory        41852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41852.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-327, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41853
in-theory        41853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41853.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-326, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41854
in-theory        41854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41854.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-325, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41855
in-theory        41855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41855.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-324, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41856
in-theory        41856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41856.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-323, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41857
in-theory        41857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41857.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41858
in-theory        41858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41858.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41859
in-theory        41859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41859.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41860
in-theory        41860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41860.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41861
in-theory        41861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F or ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41861.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F or ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-311, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41862
in-theory        41862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41862.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)), M:tm-310, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41863
in-theory        41863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41863.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and F))), M:tm-309, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41864
in-theory        41864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     33
proof            (modus-ponens tm-308 tm-559 ((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41864.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-308, m:tm-559, u:((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))
================================================================
tm-name          tm-41865
in-theory        41865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (A -> (B or A)))
theorem-size     25
proof            (modus-ponens tm-307 tm-559 ((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41865.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (A -> (B or A))), M:tm-307, m:tm-559, u:((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))
================================================================
tm-name          tm-41866
in-theory        41866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41866.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-305, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41867
in-theory        41867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41867.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-303, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41868
in-theory        41868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41868.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-270, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41869
in-theory        41869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41869.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-239, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41870
in-theory        41870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41870.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-210, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41871
in-theory        41871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41871.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-183, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41872
in-theory        41872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41872.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-157, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41873
in-theory        41873
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41873.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-147, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41874
in-theory        41874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41874.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-134, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41875
in-theory        41875
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41875.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-125, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41876
in-theory        41876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41876.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-113, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41877
in-theory        41877
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41877.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-105, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41878
in-theory        41878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41878.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-95, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41879
in-theory        41879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41879.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-83, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41880
in-theory        41880
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41880.        (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-76, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41881
in-theory        41881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41881.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-69, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41882
in-theory        41882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41882.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-54, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41883
in-theory        41883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41883.        ((A -> (B or A)) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-42, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41884
in-theory        41884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41884.        ((A -> (A or B)) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-32, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41885
in-theory        41885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41885.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-23, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41886
in-theory        41886
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41886.        (((A and B) -> B) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-22, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41887
in-theory        41887
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41887.        (((A and B) -> A) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-21, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41888
in-theory        41888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41888.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-20, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41889
in-theory        41889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41889.        ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-19, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41890
in-theory        41890
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-7 tm-5 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41890.        (A or ((B -> (C or B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-7, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41891
in-theory        41891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-6 tm-5 tm-7 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41891.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) or F), M:tm-6, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41892
in-theory        41892
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41892.        (A -> (((B -> (C or B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and A)), M:tm-5, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41893
in-theory        41893
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-1 tm-5 tm-7 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-41893.        (A -> ((B -> (C or B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-1, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-41894
in-theory        41894
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-550 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41894.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-550, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41895
in-theory        41895
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-540 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41895.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-540, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41896
in-theory        41896
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-530 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41896.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-530, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41897
in-theory        41897
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-520 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41897.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-520, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41898
in-theory        41898
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-510 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41898.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-510, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41899
in-theory        41899
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-500 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41899.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-500, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41900
in-theory        41900
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-490 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41900.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-490, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41901
in-theory        41901
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-480 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41901.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-480, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41902
in-theory        41902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-469 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41902.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-469, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41903
in-theory        41903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41903.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (E or F))), M:tm-456, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41904
in-theory        41904
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-453 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41904.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-453, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41905
in-theory        41905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (E or F)) and ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-443 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41905.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (E or F)) and ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-443, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41906
in-theory        41906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-409 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41906.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-409, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41907
in-theory        41907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-400 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41907.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-400, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41908
in-theory        41908
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-391 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41908.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-391, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41909
in-theory        41909
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-382 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41909.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-382, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41910
in-theory        41910
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-373 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41910.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-373, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41911
in-theory        41911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-364 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41911.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-364, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41912
in-theory        41912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-354 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41912.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-354, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41913
in-theory        41913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41913.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41914
in-theory        41914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-338 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41914.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-338, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41915
in-theory        41915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     43
proof            (modus-ponens tm-327 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41915.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-327, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41916
in-theory        41916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> F) and ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-326 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41916.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> F) and ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-326, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41917
in-theory        41917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> E) and ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-325 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41917.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E and F) -> E) and ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-325, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41918
in-theory        41918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     49
proof            (modus-ponens tm-324 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41918.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-324, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41919
in-theory        41919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> E)) and ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-323 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41919.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> E)) and ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-323, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41920
in-theory        41920
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41920.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> F)), M:tm-322, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41921
in-theory        41921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41921.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E and F) -> E)), M:tm-320, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41922
in-theory        41922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41922.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41923
in-theory        41923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41923.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F -> E))), M:tm-315, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41924
in-theory        41924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E or ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     37
proof            (modus-ponens tm-311 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41924.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E or ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-311, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41925
in-theory        41925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41925.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E)), M:tm-310, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41926
in-theory        41926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41926.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and E))), M:tm-309, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41927
in-theory        41927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     29
proof            (modus-ponens tm-308 tm-560 ((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41927.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-308, m:tm-560, u:((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))
================================================================
tm-name          tm-41928
in-theory        41928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (A -> (B or A)))
theorem-size     23
proof            (modus-ponens tm-307 tm-560 ((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41928.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (A -> (B or A))), M:tm-307, m:tm-560, u:((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))
================================================================
tm-name          tm-41929
in-theory        41929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     37
proof            (modus-ponens tm-305 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41929.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-305, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41930
in-theory        41930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-303 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41930.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-303, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41931
in-theory        41931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-270 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41931.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-270, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41932
in-theory        41932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-239 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41932.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-239, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41933
in-theory        41933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-210 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41933.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-210, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41934
in-theory        41934
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-183 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41934.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-183, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41935
in-theory        41935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-157 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41935.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-157, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41936
in-theory        41936
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-147 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41936.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-147, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41937
in-theory        41937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-134 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41937.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-134, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41938
in-theory        41938
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-125 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41938.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-125, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41939
in-theory        41939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-113 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41939.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-113, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41940
in-theory        41940
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     37
proof            (modus-ponens tm-105 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41940.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-105, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41941
in-theory        41941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-95 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41941.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-95, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41942
in-theory        41942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-83 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41942.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-83, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41943
in-theory        41943
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-76 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41943.        (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-76, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41944
in-theory        41944
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     29
proof            (modus-ponens tm-69 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41944.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-69, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41945
in-theory        41945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-54 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41945.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-54, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41946
in-theory        41946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-42 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41946.        ((A -> (B or A)) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-42, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41947
in-theory        41947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-32 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41947.        ((A -> (A or B)) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-32, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41948
in-theory        41948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-23 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41948.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-23, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41949
in-theory        41949
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-22 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41949.        (((A and B) -> B) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-22, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41950
in-theory        41950
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-21 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41950.        (((A and B) -> A) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-21, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41951
in-theory        41951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-20 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41951.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-20, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41952
in-theory        41952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-19 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41952.        ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-19, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41953
in-theory        41953
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-7 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-7 tm-5 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41953.        (A or ((B -> (C or B)) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-7, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41954
in-theory        41954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-6 tm-5 tm-7 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41954.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) or E), M:tm-6, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41955
in-theory        41955
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41955.        (A -> (((B -> (C or B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and A)), M:tm-5, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41956
in-theory        41956
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     19
proof            (modus-ponens tm-1 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-1 tm-5 tm-7 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-41956.        (A -> ((B -> (C or B)) and ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-1, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-41957
in-theory        41957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41957.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-550, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41958
in-theory        41958
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41958.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-540, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41959
in-theory        41959
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41959.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-530, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41960
in-theory        41960
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41960.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-520, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41961
in-theory        41961
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41961.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-510, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41962
in-theory        41962
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41962.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-500, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41963
in-theory        41963
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41963.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((not (not G)) -> G))), M:tm-490, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41964
in-theory        41964
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41964.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-480, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41965
in-theory        41965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41965.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-469, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41966
in-theory        41966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41966.        (((A -> (B or A)) and ((not (not C)) -> C)) and (D -> (D or E))), M:tm-456, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41967
in-theory        41967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41967.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-453, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41968
in-theory        41968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and ((D -> (D or E)) and ((A -> (B or A)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41968.        (((A -> (B or A)) and ((not (not C)) -> C)) and ((D -> (D or E)) and ((A -> (B or A)) and ((not (not C)) -> C)))), M:tm-443, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41969
in-theory        41969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41969.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-409, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41970
in-theory        41970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41970.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-400, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41971
in-theory        41971
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41971.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-391, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41972
in-theory        41972
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41972.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-382, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41973
in-theory        41973
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41973.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((not (not G)) -> G))), M:tm-373, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41974
in-theory        41974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41974.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-364, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41975
in-theory        41975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41975.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-354, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41976
in-theory        41976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41976.        (((A -> (B or A)) and ((not (not C)) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41977
in-theory        41977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41977.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((not (not E)) -> E))), M:tm-338, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41978
in-theory        41978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and ((D -> (E -> (D and E))) and ((A -> (B or A)) and ((not (not C)) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41978.        (((A -> (B or A)) and ((not (not C)) -> C)) and ((D -> (E -> (D and E))) and ((A -> (B or A)) and ((not (not C)) -> C)))), M:tm-327, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41979
in-theory        41979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and (((D and E) -> E) and ((A -> (B or A)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41979.        (((A -> (B or A)) and ((not (not C)) -> C)) and (((D and E) -> E) and ((A -> (B or A)) and ((not (not C)) -> C)))), M:tm-326, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41980
in-theory        41980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and (((D and E) -> D) and ((A -> (B or A)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41980.        (((A -> (B or A)) and ((not (not C)) -> C)) and (((D and E) -> D) and ((A -> (B or A)) and ((not (not C)) -> C)))), M:tm-325, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41981
in-theory        41981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B or A)) and ((not (not C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41981.        (((A -> (B or A)) and ((not (not C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B or A)) and ((not (not C)) -> C)))), M:tm-324, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41982
in-theory        41982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and ((D -> (E -> D)) and ((A -> (B or A)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41982.        (((A -> (B or A)) and ((not (not C)) -> C)) and ((D -> (E -> D)) and ((A -> (B or A)) and ((not (not C)) -> C)))), M:tm-323, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41983
in-theory        41983
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41983.        (((A -> (B or A)) and ((not (not C)) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41984
in-theory        41984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41984.        (((A -> (B or A)) and ((not (not C)) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41985
in-theory        41985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41985.        (((A -> (B or A)) and ((not (not C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41986
in-theory        41986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41986.        (((A -> (B or A)) and ((not (not C)) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41987
in-theory        41987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and (D or ((A -> (B or A)) and ((not (not C)) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41987.        (((A -> (B or A)) and ((not (not C)) -> C)) and (D or ((A -> (B or A)) and ((not (not C)) -> C)))), M:tm-311, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41988
in-theory        41988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and (((A -> (B or A)) and ((not (not C)) -> C)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41988.        (((A -> (B or A)) and ((not (not C)) -> C)) and (((A -> (B or A)) and ((not (not C)) -> C)) or D)), M:tm-310, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41989
in-theory        41989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and (D -> (((A -> (B or A)) and ((not (not C)) -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41989.        (((A -> (B or A)) and ((not (not C)) -> C)) and (D -> (((A -> (B or A)) and ((not (not C)) -> C)) and D))), M:tm-309, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41990
in-theory        41990
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and ((not (not C)) -> C))
theorem-size     17
proof            (modus-ponens tm-308 tm-561 ((A (-> Am (or Bm Am))) (B (-> (not (not Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41990.        (((A -> (B or A)) and ((not (not C)) -> C)) and ((not (not C)) -> C)), M:tm-308, m:tm-561, u:((A (-> Am (or Bm Am))) (B (-> (not (not Cm)) Cm)))
================================================================
tm-name          tm-41991
in-theory        41991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and (A -> (B or A)))
theorem-size     17
proof            (modus-ponens tm-307 tm-561 ((A (-> Am (or Bm Am))) (B (-> (not (not Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41991.        (((A -> (B or A)) and ((not (not C)) -> C)) and (A -> (B or A))), M:tm-307, m:tm-561, u:((A (-> Am (or Bm Am))) (B (-> (not (not Cm)) Cm)))
================================================================
tm-name          tm-41992
in-theory        41992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and (D -> ((A -> (B or A)) and ((not (not C)) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41992.        (((A -> (B or A)) and ((not (not C)) -> C)) and (D -> ((A -> (B or A)) and ((not (not C)) -> C)))), M:tm-305, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41993
in-theory        41993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41993.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-303, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41994
in-theory        41994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41994.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-270, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41995
in-theory        41995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41995.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-239, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41996
in-theory        41996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41996.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((not (not G)) -> G))), M:tm-210, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41997
in-theory        41997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41997.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-183, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41998
in-theory        41998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41998.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-157, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-41999
in-theory        41999
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-41999.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-147, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42000
in-theory        42000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42000.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-134, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42001
in-theory        42001
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42001.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-125, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42002
in-theory        42002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42002.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((not (not G)) -> G))), M:tm-113, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42003
in-theory        42003
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-10)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42003.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-105, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42004
in-theory        42004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42004.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((not (not E)) -> E))), M:tm-95, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42005
in-theory        42005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42005.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-83, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42006
in-theory        42006
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((not (not D)) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42006.        (((not (not A)) -> A) and ((B -> (C or B)) and ((not (not D)) -> D))), M:tm-76, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42007
in-theory        42007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((not (not E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-7 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42007.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((not (not E)) -> E))), M:tm-69, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42008
in-theory        42008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42008.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-54, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42009
in-theory        42009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42009.        ((A -> (B or A)) and ((C -> (D or C)) and ((not (not E)) -> E))), M:tm-42, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42010
in-theory        42010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42010.        ((A -> (A or B)) and ((C -> (D or C)) and ((not (not E)) -> E))), M:tm-32, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42011
in-theory        42011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42011.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((not (not E)) -> E))), M:tm-23, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42012
in-theory        42012
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42012.        (((A and B) -> B) and ((C -> (D or C)) and ((not (not E)) -> E))), M:tm-22, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42013
in-theory        42013
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42013.        (((A and B) -> A) and ((C -> (D or C)) and ((not (not E)) -> E))), M:tm-21, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42014
in-theory        42014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42014.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-20, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42015
in-theory        42015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42015.        ((A -> (B -> A)) and ((C -> (D or C)) and ((not (not E)) -> E))), M:tm-19, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42016
in-theory        42016
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-7 tm-5 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42016.        (A or ((B -> (C or B)) and ((not (not D)) -> D))), M:tm-7, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42017
in-theory        42017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-6 tm-5 tm-7 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42017.        (((A -> (B or A)) and ((not (not C)) -> C)) or D), M:tm-6, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42018
in-theory        42018
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((not (not D)) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42018.        (A -> (((B -> (C or B)) and ((not (not D)) -> D)) and A)), M:tm-5, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42019
in-theory        42019
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((not (not D)) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-1 tm-5 tm-7 tm-10)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-42019.        (A -> ((B -> (C or B)) and ((not (not D)) -> D))), M:tm-1, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-42020
in-theory        42020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42020.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-550, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42021
in-theory        42021
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42021.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-540, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42022
in-theory        42022
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42022.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-530, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42023
in-theory        42023
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42023.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-520, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42024
in-theory        42024
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42024.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-510, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42025
in-theory        42025
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42025.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-500, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42026
in-theory        42026
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42026.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (I -> H))))), M:tm-490, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42027
in-theory        42027
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42027.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-480, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42028
in-theory        42028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42028.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-469, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42029
in-theory        42029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42029.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (F -> (F or G))), M:tm-456, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42030
in-theory        42030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42030.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-453, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42031
in-theory        42031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42031.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> (D -> (E -> D)))))), M:tm-443, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42032
in-theory        42032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42032.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-409, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42033
in-theory        42033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42033.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-400, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42034
in-theory        42034
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42034.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-391, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42035
in-theory        42035
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42035.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-382, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42036
in-theory        42036
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42036.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (I -> H))))), M:tm-373, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42037
in-theory        42037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42037.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-364, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42038
in-theory        42038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42038.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-354, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42039
in-theory        42039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42039.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42040
in-theory        42040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42040.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (G -> F))))), M:tm-338, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42041
in-theory        42041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> (D -> (E -> D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42041.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> (D -> (E -> D)))))), M:tm-327, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42042
in-theory        42042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42042.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> (D -> (E -> D)))))), M:tm-326, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42043
in-theory        42043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42043.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> (D -> (E -> D)))))), M:tm-325, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42044
in-theory        42044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> (D -> (E -> D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42044.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> (D -> (E -> D)))))), M:tm-324, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42045
in-theory        42045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42045.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> (D -> (E -> D)))))), M:tm-323, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42046
in-theory        42046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42046.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and ((F and G) -> G)), M:tm-322, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42047
in-theory        42047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42047.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and ((F and G) -> F)), M:tm-320, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42048
in-theory        42048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42048.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42049
in-theory        42049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42049.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (F -> (G -> F))), M:tm-315, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42050
in-theory        42050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (F or ((A -> (B or A)) and (C -> (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42050.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (F or ((A -> (B or A)) and (C -> (D -> (E -> D)))))), M:tm-311, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42051
in-theory        42051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (((A -> (B or A)) and (C -> (D -> (E -> D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42051.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (((A -> (B or A)) and (C -> (D -> (E -> D)))) or F)), M:tm-310, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42052
in-theory        42052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (F -> (((A -> (B or A)) and (C -> (D -> (E -> D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42052.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (F -> (((A -> (B or A)) and (C -> (D -> (E -> D)))) and F))), M:tm-309, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42053
in-theory        42053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (C -> (D -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-562 ((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42053.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (C -> (D -> (E -> D)))), M:tm-308, m:tm-562, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-42054
in-theory        42054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-562 ((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42054.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (A -> (B or A))), M:tm-307, m:tm-562, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-42055
in-theory        42055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (F -> ((A -> (B or A)) and (C -> (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42055.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (F -> ((A -> (B or A)) and (C -> (D -> (E -> D)))))), M:tm-305, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42056
in-theory        42056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42056.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-303, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42057
in-theory        42057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42057.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-270, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42058
in-theory        42058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42058.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-239, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42059
in-theory        42059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42059.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (H -> (I -> H))))), M:tm-210, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42060
in-theory        42060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42060.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-183, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42061
in-theory        42061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42061.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-157, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42062
in-theory        42062
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42062.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-147, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42063
in-theory        42063
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42063.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-134, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42064
in-theory        42064
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42064.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-125, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42065
in-theory        42065
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42065.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (I -> H))))), M:tm-113, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42066
in-theory        42066
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42066.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-105, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42067
in-theory        42067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42067.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (F -> (G -> F))))), M:tm-95, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42068
in-theory        42068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42068.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-83, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42069
in-theory        42069
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42069.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (E -> (F -> E))))), M:tm-76, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42070
in-theory        42070
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42070.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (F -> (G -> F))))), M:tm-69, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42071
in-theory        42071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42071.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-54, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42072
in-theory        42072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42072.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> (F -> (G -> F))))), M:tm-42, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42073
in-theory        42073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42073.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> (F -> (G -> F))))), M:tm-32, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42074
in-theory        42074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42074.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (G -> F))))), M:tm-23, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42075
in-theory        42075
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42075.        (((A and B) -> B) and ((C -> (D or C)) and (E -> (F -> (G -> F))))), M:tm-22, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42076
in-theory        42076
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42076.        (((A and B) -> A) and ((C -> (D or C)) and (E -> (F -> (G -> F))))), M:tm-21, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42077
in-theory        42077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42077.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-20, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42078
in-theory        42078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42078.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (F -> (G -> F))))), M:tm-19, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42079
in-theory        42079
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42079.        (A or ((B -> (C or B)) and (D -> (E -> (F -> E))))), M:tm-7, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42080
in-theory        42080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-7 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42080.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) or F), M:tm-6, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42081
in-theory        42081
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> (E -> (F -> E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42081.        (A -> (((B -> (C or B)) and (D -> (E -> (F -> E)))) and A)), M:tm-5, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42082
in-theory        42082
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-42082.        (A -> ((B -> (C or B)) and (D -> (E -> (F -> E))))), M:tm-1, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-42083
in-theory        42083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42083.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-550, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42084
in-theory        42084
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42084.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-540, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42085
in-theory        42085
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42085.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-530, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42086
in-theory        42086
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42086.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-520, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42087
in-theory        42087
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42087.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-510, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42088
in-theory        42088
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42088.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-500, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42089
in-theory        42089
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42089.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (G -> G)))), M:tm-490, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42090
in-theory        42090
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42090.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-480, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42091
in-theory        42091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42091.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-469, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42092
in-theory        42092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42092.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (E -> (E or F))), M:tm-456, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42093
in-theory        42093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42093.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-453, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42094
in-theory        42094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((E -> (E or F)) and ((A -> (B or A)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42094.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((E -> (E or F)) and ((A -> (B or A)) and ((C -> D) -> (C -> C))))), M:tm-443, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42095
in-theory        42095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42095.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-409, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42096
in-theory        42096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42096.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-400, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42097
in-theory        42097
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42097.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-391, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42098
in-theory        42098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42098.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-382, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42099
in-theory        42099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42099.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (G -> G)))), M:tm-373, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42100
in-theory        42100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42100.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-364, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42101
in-theory        42101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42101.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-354, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42102
in-theory        42102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42102.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42103
in-theory        42103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42103.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (E -> E)))), M:tm-338, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42104
in-theory        42104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and ((C -> D) -> (C -> C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42104.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and ((C -> D) -> (C -> C))))), M:tm-327, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42105
in-theory        42105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (((E and F) -> F) and ((A -> (B or A)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42105.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (((E and F) -> F) and ((A -> (B or A)) and ((C -> D) -> (C -> C))))), M:tm-326, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42106
in-theory        42106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (((E and F) -> E) and ((A -> (B or A)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42106.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (((E and F) -> E) and ((A -> (B or A)) and ((C -> D) -> (C -> C))))), M:tm-325, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42107
in-theory        42107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and ((C -> D) -> (C -> C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42107.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and ((C -> D) -> (C -> C))))), M:tm-324, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42108
in-theory        42108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((E -> (F -> E)) and ((A -> (B or A)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42108.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((E -> (F -> E)) and ((A -> (B or A)) and ((C -> D) -> (C -> C))))), M:tm-323, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42109
in-theory        42109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42109.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((E and F) -> F)), M:tm-322, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42110
in-theory        42110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42110.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((E and F) -> E)), M:tm-320, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42111
in-theory        42111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42111.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42112
in-theory        42112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42112.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (E -> (F -> E))), M:tm-315, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42113
in-theory        42113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (E or ((A -> (B or A)) and ((C -> D) -> (C -> C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42113.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (E or ((A -> (B or A)) and ((C -> D) -> (C -> C))))), M:tm-311, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42114
in-theory        42114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (((A -> (B or A)) and ((C -> D) -> (C -> C))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42114.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (((A -> (B or A)) and ((C -> D) -> (C -> C))) or E)), M:tm-310, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42115
in-theory        42115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (E -> (((A -> (B or A)) and ((C -> D) -> (C -> C))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42115.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (E -> (((A -> (B or A)) and ((C -> D) -> (C -> C))) and E))), M:tm-309, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42116
in-theory        42116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((C -> D) -> (C -> C)))
theorem-size     21
proof            (modus-ponens tm-308 tm-563 ((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> Cm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42116.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((C -> D) -> (C -> C))), M:tm-308, m:tm-563, u:((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> Cm Cm))))
================================================================
tm-name          tm-42117
in-theory        42117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-563 ((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> Cm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42117.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (A -> (B or A))), M:tm-307, m:tm-563, u:((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> Cm Cm))))
================================================================
tm-name          tm-42118
in-theory        42118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (E -> ((A -> (B or A)) and ((C -> D) -> (C -> C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42118.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (E -> ((A -> (B or A)) and ((C -> D) -> (C -> C))))), M:tm-305, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42119
in-theory        42119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42119.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-303, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42120
in-theory        42120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42120.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-270, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42121
in-theory        42121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42121.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-239, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42122
in-theory        42122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42122.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> H) -> (G -> G)))), M:tm-210, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42123
in-theory        42123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42123.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-183, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42124
in-theory        42124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42124.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-157, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42125
in-theory        42125
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42125.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-147, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42126
in-theory        42126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42126.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-134, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42127
in-theory        42127
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42127.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-125, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42128
in-theory        42128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42128.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (G -> G)))), M:tm-113, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42129
in-theory        42129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42129.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-105, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42130
in-theory        42130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42130.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> F) -> (E -> E)))), M:tm-95, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42131
in-theory        42131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42131.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-83, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42132
in-theory        42132
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> E) -> (D -> D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42132.        (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> E) -> (D -> D)))), M:tm-76, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42133
in-theory        42133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> F) -> (E -> E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42133.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> F) -> (E -> E)))), M:tm-69, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42134
in-theory        42134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42134.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-54, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42135
in-theory        42135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42135.        ((A -> (B or A)) and ((C -> (D or C)) and ((E -> F) -> (E -> E)))), M:tm-42, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42136
in-theory        42136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42136.        ((A -> (A or B)) and ((C -> (D or C)) and ((E -> F) -> (E -> E)))), M:tm-32, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42137
in-theory        42137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42137.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (E -> E)))), M:tm-23, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42138
in-theory        42138
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42138.        (((A and B) -> B) and ((C -> (D or C)) and ((E -> F) -> (E -> E)))), M:tm-22, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42139
in-theory        42139
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42139.        (((A and B) -> A) and ((C -> (D or C)) and ((E -> F) -> (E -> E)))), M:tm-21, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42140
in-theory        42140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42140.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-20, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42141
in-theory        42141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42141.        ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> F) -> (E -> E)))), M:tm-19, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42142
in-theory        42142
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42142.        (A or ((B -> (C or B)) and ((D -> E) -> (D -> D)))), M:tm-7, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42143
in-theory        42143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-2 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42143.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) or E), M:tm-6, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42144
in-theory        42144
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((D -> E) -> (D -> D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42144.        (A -> (((B -> (C or B)) and ((D -> E) -> (D -> D))) and A)), M:tm-5, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42145
in-theory        42145
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((D -> E) -> (D -> D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-2)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-42145.        (A -> ((B -> (C or B)) and ((D -> E) -> (D -> D)))), M:tm-1, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-42146
in-theory        42146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-550 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42146.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-550, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42147
in-theory        42147
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-540 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42147.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-540, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42148
in-theory        42148
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-530 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42148.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-530, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42149
in-theory        42149
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-520 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42149.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-520, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42150
in-theory        42150
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-510 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42150.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-510, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42151
in-theory        42151
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-500 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42151.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-500, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42152
in-theory        42152
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-490 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42152.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-490, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42153
in-theory        42153
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-480 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42153.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-480, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42154
in-theory        42154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-469 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42154.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-469, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42155
in-theory        42155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (F or G)))
theorem-size     31
proof            (modus-ponens tm-456 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42155.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42156
in-theory        42156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-453 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42156.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-453, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42157
in-theory        42157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-443 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42157.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (F or G)) and ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-443, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42158
in-theory        42158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-409 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42158.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-409, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42159
in-theory        42159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-400 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42159.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-400, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42160
in-theory        42160
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-391 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42160.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-391, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42161
in-theory        42161
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-382 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42161.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-382, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42162
in-theory        42162
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-373 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42162.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-373, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42163
in-theory        42163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-364 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42163.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-364, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42164
in-theory        42164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-354 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42164.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-354, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42165
in-theory        42165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     33
proof            (modus-ponens tm-341 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42165.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42166
in-theory        42166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-338 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42166.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-338, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42167
in-theory        42167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     59
proof            (modus-ponens tm-327 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42167.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-327, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42168
in-theory        42168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> G) and ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-326 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42168.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> G) and ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-326, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42169
in-theory        42169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> F) and ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-325 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42169.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F and G) -> F) and ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-325, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42170
in-theory        42170
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     65
proof            (modus-ponens tm-324 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42170.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-324, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42171
in-theory        42171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-323 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42171.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-323, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42172
in-theory        42172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> G))
theorem-size     31
proof            (modus-ponens tm-322 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42172.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42173
in-theory        42173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> F))
theorem-size     31
proof            (modus-ponens tm-320 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42173.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42174
in-theory        42174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     39
proof            (modus-ponens tm-318 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42174.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42175
in-theory        42175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     31
proof            (modus-ponens tm-315 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42175.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42176
in-theory        42176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F or ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-311 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42176.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F or ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-311, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42177
in-theory        42177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F))
theorem-size     53
proof            (modus-ponens tm-310 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42177.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F)), M:tm-310, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42178
in-theory        42178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and F)))
theorem-size     55
proof            (modus-ponens tm-309 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42178.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and F))), M:tm-309, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42179
in-theory        42179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     45
proof            (modus-ponens tm-308 tm-564 ((A (-> Am (or Bm Am))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42179.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-308, m:tm-564, u:((A (-> Am (or Bm Am))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))
================================================================
tm-name          tm-42180
in-theory        42180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (A -> (B or A)))
theorem-size     31
proof            (modus-ponens tm-307 tm-564 ((A (-> Am (or Bm Am))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42180.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (A -> (B or A))), M:tm-307, m:tm-564, u:((A (-> Am (or Bm Am))) (B (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))
================================================================
tm-name          tm-42181
in-theory        42181
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-305 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42181.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-305, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42182
in-theory        42182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-303 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42182.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-303, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42183
in-theory        42183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-270 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42183.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-270, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42184
in-theory        42184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-239 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42184.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-239, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42185
in-theory        42185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-210 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42185.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-210, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42186
in-theory        42186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-183 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42186.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-183, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42187
in-theory        42187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-157 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42187.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-157, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42188
in-theory        42188
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-147 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42188.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-147, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42189
in-theory        42189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-134 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42189.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-134, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42190
in-theory        42190
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-125 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42190.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-125, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42191
in-theory        42191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-113 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42191.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-113, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42192
in-theory        42192
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     45
proof            (modus-ponens tm-105 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42192.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-105, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42193
in-theory        42193
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-95 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42193.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-95, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42194
in-theory        42194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-83 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42194.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-83, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42195
in-theory        42195
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-76 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42195.        (((not (not A)) -> A) and ((B -> (C or B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-76, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42196
in-theory        42196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     37
proof            (modus-ponens tm-69 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42196.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-69, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42197
in-theory        42197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-54 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42197.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-54, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42198
in-theory        42198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-42 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42198.        ((A -> (B or A)) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-42, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42199
in-theory        42199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-32 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42199.        ((A -> (A or B)) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-32, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42200
in-theory        42200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-23 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42200.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-23, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42201
in-theory        42201
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-22 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42201.        (((A and B) -> B) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-22, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42202
in-theory        42202
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-21 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42202.        (((A and B) -> A) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-21, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42203
in-theory        42203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-20 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42203.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-20, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42204
in-theory        42204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-19 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42204.        ((A -> (B -> A)) and ((C -> (D or C)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-19, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42205
in-theory        42205
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-7 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42205.        (A or ((B -> (C or B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-7, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42206
in-theory        42206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F)
theorem-size     27
proof            (modus-ponens tm-6 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-6 tm-5 tm-7 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42206.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) or F), M:tm-6, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42207
in-theory        42207
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42207.        (A -> (((B -> (C or B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and A)), M:tm-5, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42208
in-theory        42208
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-1 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-1 tm-5 tm-7 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-42208.        (A -> ((B -> (C or B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-1, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-42209
in-theory        42209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42209.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-550, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42210
in-theory        42210
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42210.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-540, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42211
in-theory        42211
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42211.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-530, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42212
in-theory        42212
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42212.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-520, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42213
in-theory        42213
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42213.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-510, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42214
in-theory        42214
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42214.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-500, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42215
in-theory        42215
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42215.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-490, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42216
in-theory        42216
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42216.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-480, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42217
in-theory        42217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42217.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-469, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42218
in-theory        42218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42218.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H))), M:tm-456, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42219
in-theory        42219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42219.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-453, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42220
in-theory        42220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42220.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-443, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42221
in-theory        42221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42221.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-409, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42222
in-theory        42222
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42222.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-400, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42223
in-theory        42223
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42223.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-391, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42224
in-theory        42224
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42224.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-382, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42225
in-theory        42225
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42225.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-373, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42226
in-theory        42226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42226.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-364, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42227
in-theory        42227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42227.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-354, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42228
in-theory        42228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42228.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42229
in-theory        42229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42229.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-338, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42230
in-theory        42230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42230.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-327, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42231
in-theory        42231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42231.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-326, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42232
in-theory        42232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42232.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-325, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42233
in-theory        42233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42233.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-324, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42234
in-theory        42234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42234.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-323, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42235
in-theory        42235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42235.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42236
in-theory        42236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42236.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42237
in-theory        42237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42237.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42238
in-theory        42238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42238.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42239
in-theory        42239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42239.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-311, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42240
in-theory        42240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42240.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)), M:tm-310, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42241
in-theory        42241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42241.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G))), M:tm-309, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42242
in-theory        42242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-565 ((A (-> Am (or Bm Am))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42242.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-308, m:tm-565, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-42243
in-theory        42243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (B or A)))
theorem-size     27
proof            (modus-ponens tm-307 tm-565 ((A (-> Am (or Bm Am))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42243.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (B or A))), M:tm-307, m:tm-565, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-42244
in-theory        42244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42244.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-305, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42245
in-theory        42245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42245.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-303, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42246
in-theory        42246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42246.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-270, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42247
in-theory        42247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42247.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-239, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42248
in-theory        42248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42248.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-210, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42249
in-theory        42249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42249.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-183, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42250
in-theory        42250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42250.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-157, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42251
in-theory        42251
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42251.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-147, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42252
in-theory        42252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42252.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-134, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42253
in-theory        42253
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42253.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-125, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42254
in-theory        42254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42254.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-113, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42255
in-theory        42255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42255.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-105, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42256
in-theory        42256
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42256.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-95, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42257
in-theory        42257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42257.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-83, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42258
in-theory        42258
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42258.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-76, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42259
in-theory        42259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42259.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-69, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42260
in-theory        42260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42260.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-54, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42261
in-theory        42261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42261.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-42, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42262
in-theory        42262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42262.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-32, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42263
in-theory        42263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42263.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-23, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42264
in-theory        42264
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42264.        (((A and B) -> B) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-22, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42265
in-theory        42265
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42265.        (((A and B) -> A) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-21, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42266
in-theory        42266
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42266.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-20, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42267
in-theory        42267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42267.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-19, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42268
in-theory        42268
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-7 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-7 tm-5 tm-1 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42268.        (A or ((B -> (C or B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-7, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42269
in-theory        42269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-6 tm-5 tm-7 tm-1 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42269.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G), M:tm-6, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42270
in-theory        42270
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42270.        (A -> (((B -> (C or B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A)), M:tm-5, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42271
in-theory        42271
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-1 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-1 tm-5 tm-7 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42271.        (A -> ((B -> (C or B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-1, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-42272
in-theory        42272
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-550 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42272.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-550, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42273
in-theory        42273
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-540 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42273.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-540, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42274
in-theory        42274
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-530 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42274.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-530, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42275
in-theory        42275
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-520 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42275.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-520, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42276
in-theory        42276
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-510 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42276.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-510, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42277
in-theory        42277
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-500 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42277.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-500, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42278
in-theory        42278
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-490 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42278.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-490, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42279
in-theory        42279
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-480 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42279.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-480, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42280
in-theory        42280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-469 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42280.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-469, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42281
in-theory        42281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42281.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42282
in-theory        42282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-453 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42282.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-453, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42283
in-theory        42283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (F or G)) and ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42283.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (F or G)) and ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-443, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42284
in-theory        42284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-409 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42284.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-409, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42285
in-theory        42285
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-400 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42285.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-400, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42286
in-theory        42286
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-391 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42286.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-391, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42287
in-theory        42287
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-382 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42287.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-382, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42288
in-theory        42288
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-373 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42288.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-373, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42289
in-theory        42289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-364 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42289.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-364, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42290
in-theory        42290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-354 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42290.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-354, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42291
in-theory        42291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42291.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42292
in-theory        42292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-338 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42292.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-338, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42293
in-theory        42293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42293.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-327, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42294
in-theory        42294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> G) and ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42294.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> G) and ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-326, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42295
in-theory        42295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> F) and ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42295.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F and G) -> F) and ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-325, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42296
in-theory        42296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42296.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-324, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42297
in-theory        42297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> F)) and ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42297.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> F)) and ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-323, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42298
in-theory        42298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42298.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42299
in-theory        42299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42299.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42300
in-theory        42300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42300.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42301
in-theory        42301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42301.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42302
in-theory        42302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F or ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42302.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F or ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-311, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42303
in-theory        42303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42303.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F)), M:tm-310, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42304
in-theory        42304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42304.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and F))), M:tm-309, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42305
in-theory        42305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     37
proof            (modus-ponens tm-308 tm-566 ((A (-> Am (or Bm Am))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42305.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-308, m:tm-566, u:((A (-> Am (or Bm Am))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))
================================================================
tm-name          tm-42306
in-theory        42306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (A -> (B or A)))
theorem-size     27
proof            (modus-ponens tm-307 tm-566 ((A (-> Am (or Bm Am))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42306.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (A -> (B or A))), M:tm-307, m:tm-566, u:((A (-> Am (or Bm Am))) (B (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))
================================================================
tm-name          tm-42307
in-theory        42307
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42307.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-305, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42308
in-theory        42308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-303 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42308.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-303, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42309
in-theory        42309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-270 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42309.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-270, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42310
in-theory        42310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-239 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42310.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-239, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42311
in-theory        42311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-210 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42311.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-210, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42312
in-theory        42312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-183 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42312.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-183, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42313
in-theory        42313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-157 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42313.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-157, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42314
in-theory        42314
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-147 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42314.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-147, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42315
in-theory        42315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-134 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42315.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-134, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42316
in-theory        42316
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-125 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42316.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-125, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42317
in-theory        42317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-113 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42317.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-113, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42318
in-theory        42318
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     41
proof            (modus-ponens tm-105 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42318.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-105, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42319
in-theory        42319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-95 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42319.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-95, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42320
in-theory        42320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-83 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42320.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-83, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42321
in-theory        42321
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     27
proof            (modus-ponens tm-76 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42321.        (((not (not A)) -> A) and ((B -> (C or B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-76, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42322
in-theory        42322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     33
proof            (modus-ponens tm-69 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42322.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-69, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42323
in-theory        42323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-54 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42323.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-54, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42324
in-theory        42324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-42 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42324.        ((A -> (B or A)) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-42, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42325
in-theory        42325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-32 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42325.        ((A -> (A or B)) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-32, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42326
in-theory        42326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-23 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42326.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-23, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42327
in-theory        42327
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-22 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42327.        (((A and B) -> B) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-22, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42328
in-theory        42328
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-21 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42328.        (((A and B) -> A) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-21, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42329
in-theory        42329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-20 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42329.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-20, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42330
in-theory        42330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-19 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42330.        ((A -> (B -> A)) and ((C -> (D or C)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-19, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42331
in-theory        42331
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-7 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42331.        (A or ((B -> (C or B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-7, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42332
in-theory        42332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42332.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) or F), M:tm-6, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42333
in-theory        42333
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42333.        (A -> (((B -> (C or B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and A)), M:tm-5, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42334
in-theory        42334
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-1 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-2 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-42334.        (A -> ((B -> (C or B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-1, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-42335
in-theory        42335
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-550 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42335.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-550, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42336
in-theory        42336
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-540 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42336.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-540, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42337
in-theory        42337
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-530 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42337.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-530, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42338
in-theory        42338
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-520 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42338.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-520, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42339
in-theory        42339
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-510 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42339.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-510, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42340
in-theory        42340
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-500 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42340.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-500, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42341
in-theory        42341
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-490 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42341.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H and I) -> H)))), M:tm-490, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42342
in-theory        42342
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-480 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42342.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-480, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42343
in-theory        42343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-469 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42343.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-469, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42344
in-theory        42344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42344.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42345
in-theory        42345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-453 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42345.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-453, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42346
in-theory        42346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42346.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> ((D and E) -> D))))), M:tm-443, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42347
in-theory        42347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-409 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42347.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-409, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42348
in-theory        42348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-400 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42348.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-400, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42349
in-theory        42349
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-391 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42349.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-391, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42350
in-theory        42350
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-382 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42350.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-382, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42351
in-theory        42351
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-373 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42351.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> ((H and I) -> H)))), M:tm-373, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42352
in-theory        42352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-364 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42352.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-364, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42353
in-theory        42353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-354 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42353.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-354, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42354
in-theory        42354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42354.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42355
in-theory        42355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-338 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42355.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> ((F and G) -> F)))), M:tm-338, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42356
in-theory        42356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> ((D and E) -> D)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42356.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> ((D and E) -> D))))), M:tm-327, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42357
in-theory        42357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42357.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> ((D and E) -> D))))), M:tm-326, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42358
in-theory        42358
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42358.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> ((D and E) -> D))))), M:tm-325, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42359
in-theory        42359
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> ((D and E) -> D)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42359.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> ((D and E) -> D))))), M:tm-324, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42360
in-theory        42360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42360.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> ((D and E) -> D))))), M:tm-323, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42361
in-theory        42361
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42361.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42362
in-theory        42362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42362.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42363
in-theory        42363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42363.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42364
in-theory        42364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42364.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42365
in-theory        42365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and (F or ((A -> (B or A)) and (C -> ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42365.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and (F or ((A -> (B or A)) and (C -> ((D and E) -> D))))), M:tm-311, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42366
in-theory        42366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and (((A -> (B or A)) and (C -> ((D and E) -> D))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42366.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and (((A -> (B or A)) and (C -> ((D and E) -> D))) or F)), M:tm-310, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42367
in-theory        42367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and (F -> (((A -> (B or A)) and (C -> ((D and E) -> D))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42367.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and (F -> (((A -> (B or A)) and (C -> ((D and E) -> D))) and F))), M:tm-309, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42368
in-theory        42368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and (C -> ((D and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-308 tm-567 ((A (-> Am (or Bm Am))) (B (-> Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42368.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and (C -> ((D and E) -> D))), M:tm-308, m:tm-567, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-42369
in-theory        42369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-567 ((A (-> Am (or Bm Am))) (B (-> Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42369.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and (A -> (B or A))), M:tm-307, m:tm-567, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-42370
in-theory        42370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and (F -> ((A -> (B or A)) and (C -> ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42370.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and (F -> ((A -> (B or A)) and (C -> ((D and E) -> D))))), M:tm-305, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42371
in-theory        42371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-303 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42371.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-303, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42372
in-theory        42372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-270 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42372.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-270, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42373
in-theory        42373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-239 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42373.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-239, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42374
in-theory        42374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-210 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42374.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> ((H and I) -> H)))), M:tm-210, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42375
in-theory        42375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-183 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42375.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-183, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42376
in-theory        42376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-157 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42376.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-157, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42377
in-theory        42377
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-147 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42377.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-147, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42378
in-theory        42378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-134 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42378.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-134, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42379
in-theory        42379
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-125 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42379.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-125, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42380
in-theory        42380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-113 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42380.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H and I) -> H)))), M:tm-113, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42381
in-theory        42381
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-105 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42381.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-105, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42382
in-theory        42382
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-95 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42382.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> ((F and G) -> F)))), M:tm-95, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42383
in-theory        42383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-83 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42383.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-83, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42384
in-theory        42384
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-76 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42384.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> ((E and F) -> E)))), M:tm-76, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42385
in-theory        42385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-69 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42385.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> ((F and G) -> F)))), M:tm-69, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42386
in-theory        42386
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-54 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42386.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-54, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42387
in-theory        42387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-42 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42387.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> ((F and G) -> F)))), M:tm-42, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42388
in-theory        42388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-32 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42388.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> ((F and G) -> F)))), M:tm-32, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42389
in-theory        42389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-23 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42389.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> ((F and G) -> F)))), M:tm-23, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42390
in-theory        42390
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-22 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42390.        (((A and B) -> B) and ((C -> (D or C)) and (E -> ((F and G) -> F)))), M:tm-22, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42391
in-theory        42391
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-21 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42391.        (((A and B) -> A) and ((C -> (D or C)) and (E -> ((F and G) -> F)))), M:tm-21, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42392
in-theory        42392
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-20 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42392.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-20, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42393
in-theory        42393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-19 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42393.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> ((F and G) -> F)))), M:tm-19, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42394
in-theory        42394
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-7 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42394.        (A or ((B -> (C or B)) and (D -> ((E and F) -> E)))), M:tm-7, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42395
in-theory        42395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-1 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42395.        (((A -> (B or A)) and (C -> ((D and E) -> D))) or F), M:tm-6, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42396
in-theory        42396
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> ((E and F) -> E))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42396.        (A -> (((B -> (C or B)) and (D -> ((E and F) -> E))) and A)), M:tm-5, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42397
in-theory        42397
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-1 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-42397.        (A -> ((B -> (C or B)) and (D -> ((E and F) -> E)))), M:tm-1, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-42398
in-theory        42398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-550 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42398.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-550, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42399
in-theory        42399
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-540 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42399.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-540, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42400
in-theory        42400
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-530 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42400.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-530, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42401
in-theory        42401
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-520 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42401.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-520, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42402
in-theory        42402
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-510 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42402.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-510, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42403
in-theory        42403
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-500 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42403.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-500, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42404
in-theory        42404
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-490 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42404.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-490, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42405
in-theory        42405
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-480 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42405.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-480, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42406
in-theory        42406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-469 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42406.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-469, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42407
in-theory        42407
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42407.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42408
in-theory        42408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-453 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42408.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-453, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42409
in-theory        42409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (F or G)) and ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42409.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (F or G)) and ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-443, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42410
in-theory        42410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-409 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42410.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-409, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42411
in-theory        42411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-400 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42411.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-400, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42412
in-theory        42412
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-391 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42412.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-391, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42413
in-theory        42413
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-382 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42413.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-382, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42414
in-theory        42414
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-373 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42414.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-373, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42415
in-theory        42415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-364 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42415.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-364, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42416
in-theory        42416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-354 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42416.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-354, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42417
in-theory        42417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42417.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42418
in-theory        42418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-338 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42418.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-338, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42419
in-theory        42419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42419.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-327, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42420
in-theory        42420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> G) and ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42420.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> G) and ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-326, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42421
in-theory        42421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> F) and ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42421.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F and G) -> F) and ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-325, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42422
in-theory        42422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42422.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-324, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42423
in-theory        42423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42423.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-323, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42424
in-theory        42424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42424.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42425
in-theory        42425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42425.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42426
in-theory        42426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42426.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42427
in-theory        42427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42427.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42428
in-theory        42428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F or ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42428.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F or ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-311, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42429
in-theory        42429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42429.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F)), M:tm-310, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42430
in-theory        42430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42430.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and F))), M:tm-309, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42431
in-theory        42431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     37
proof            (modus-ponens tm-308 tm-568 ((A (-> Am (or Bm Am))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42431.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-308, m:tm-568, u:((A (-> Am (or Bm Am))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))
================================================================
tm-name          tm-42432
in-theory        42432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (A -> (B or A)))
theorem-size     27
proof            (modus-ponens tm-307 tm-568 ((A (-> Am (or Bm Am))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42432.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (A -> (B or A))), M:tm-307, m:tm-568, u:((A (-> Am (or Bm Am))) (B (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))
================================================================
tm-name          tm-42433
in-theory        42433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42433.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-305, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42434
in-theory        42434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-303 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42434.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-303, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42435
in-theory        42435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-270 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42435.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-270, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42436
in-theory        42436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-239 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42436.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-239, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42437
in-theory        42437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-210 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42437.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-210, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42438
in-theory        42438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-183 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42438.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-183, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42439
in-theory        42439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-157 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42439.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-157, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42440
in-theory        42440
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-147 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42440.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-147, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42441
in-theory        42441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-134 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42441.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-134, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42442
in-theory        42442
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-125 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42442.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-125, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42443
in-theory        42443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-113 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42443.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-113, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42444
in-theory        42444
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     41
proof            (modus-ponens tm-105 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42444.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-105, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42445
in-theory        42445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-95 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42445.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-95, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42446
in-theory        42446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-83 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42446.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-83, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42447
in-theory        42447
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     27
proof            (modus-ponens tm-76 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42447.        (((not (not A)) -> A) and ((B -> (C or B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-76, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42448
in-theory        42448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     33
proof            (modus-ponens tm-69 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42448.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-69, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42449
in-theory        42449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-54 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42449.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-54, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42450
in-theory        42450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-42 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42450.        ((A -> (B or A)) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-42, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42451
in-theory        42451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-32 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42451.        ((A -> (A or B)) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-32, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42452
in-theory        42452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-23 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42452.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-23, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42453
in-theory        42453
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-22 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42453.        (((A and B) -> B) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-22, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42454
in-theory        42454
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-21 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42454.        (((A and B) -> A) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-21, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42455
in-theory        42455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-20 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42455.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-20, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42456
in-theory        42456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-19 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42456.        ((A -> (B -> A)) and ((C -> (D or C)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-19, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42457
in-theory        42457
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-7 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-7 tm-5 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42457.        (A or ((B -> (C or B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-7, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42458
in-theory        42458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-6 tm-5 tm-7 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42458.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) or F), M:tm-6, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42459
in-theory        42459
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42459.        (A -> (((B -> (C or B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and A)), M:tm-5, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42460
in-theory        42460
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     23
proof            (modus-ponens tm-1 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-1 tm-5 tm-7 tm-2 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-42460.        (A -> ((B -> (C or B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-1, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-42461
in-theory        42461
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-550 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42461.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-550, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42462
in-theory        42462
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-540 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42462.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-540, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42463
in-theory        42463
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-530 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42463.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-530, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42464
in-theory        42464
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-520 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42464.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-520, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42465
in-theory        42465
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-510 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42465.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-510, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42466
in-theory        42466
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-500 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42466.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-500, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42467
in-theory        42467
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-490 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42467.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H and I) -> I)))), M:tm-490, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42468
in-theory        42468
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-480 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42468.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-480, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42469
in-theory        42469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-469 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42469.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-469, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42470
in-theory        42470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42470.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and (F -> (F or G))), M:tm-456, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42471
in-theory        42471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-453 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42471.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-453, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42472
in-theory        42472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42472.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> ((D and E) -> E))))), M:tm-443, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42473
in-theory        42473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-409 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42473.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-409, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42474
in-theory        42474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-400 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42474.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-400, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42475
in-theory        42475
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-391 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42475.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-391, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42476
in-theory        42476
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-382 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42476.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-382, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42477
in-theory        42477
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-373 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42477.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> ((H and I) -> I)))), M:tm-373, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42478
in-theory        42478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-364 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42478.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-364, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42479
in-theory        42479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-354 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42479.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-354, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42480
in-theory        42480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42480.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42481
in-theory        42481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-338 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42481.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> ((F and G) -> G)))), M:tm-338, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42482
in-theory        42482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> ((D and E) -> E)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42482.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> ((D and E) -> E))))), M:tm-327, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42483
in-theory        42483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42483.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> ((D and E) -> E))))), M:tm-326, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42484
in-theory        42484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42484.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> ((D and E) -> E))))), M:tm-325, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42485
in-theory        42485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> ((D and E) -> E)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42485.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> ((D and E) -> E))))), M:tm-324, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42486
in-theory        42486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42486.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> ((D and E) -> E))))), M:tm-323, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42487
in-theory        42487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42487.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42488
in-theory        42488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42488.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42489
in-theory        42489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42489.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42490
in-theory        42490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42490.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42491
in-theory        42491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and (F or ((A -> (B or A)) and (C -> ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42491.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and (F or ((A -> (B or A)) and (C -> ((D and E) -> E))))), M:tm-311, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42492
in-theory        42492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and (((A -> (B or A)) and (C -> ((D and E) -> E))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42492.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and (((A -> (B or A)) and (C -> ((D and E) -> E))) or F)), M:tm-310, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42493
in-theory        42493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and (F -> (((A -> (B or A)) and (C -> ((D and E) -> E))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42493.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and (F -> (((A -> (B or A)) and (C -> ((D and E) -> E))) and F))), M:tm-309, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42494
in-theory        42494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and (C -> ((D and E) -> E)))
theorem-size     21
proof            (modus-ponens tm-308 tm-569 ((A (-> Am (or Bm Am))) (B (-> Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42494.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and (C -> ((D and E) -> E))), M:tm-308, m:tm-569, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-42495
in-theory        42495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-569 ((A (-> Am (or Bm Am))) (B (-> Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42495.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and (A -> (B or A))), M:tm-307, m:tm-569, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-42496
in-theory        42496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and (F -> ((A -> (B or A)) and (C -> ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42496.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and (F -> ((A -> (B or A)) and (C -> ((D and E) -> E))))), M:tm-305, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42497
in-theory        42497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-303 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42497.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-303, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42498
in-theory        42498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-270 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42498.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-270, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42499
in-theory        42499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-239 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42499.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-239, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42500
in-theory        42500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-210 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42500.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> ((H and I) -> I)))), M:tm-210, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42501
in-theory        42501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-183 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42501.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-183, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42502
in-theory        42502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-157 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42502.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-157, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42503
in-theory        42503
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-147 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42503.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-147, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42504
in-theory        42504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-134 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42504.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-134, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42505
in-theory        42505
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-125 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42505.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-125, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42506
in-theory        42506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-113 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42506.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H and I) -> I)))), M:tm-113, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42507
in-theory        42507
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-105 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42507.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-105, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42508
in-theory        42508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-95 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42508.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> ((F and G) -> G)))), M:tm-95, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42509
in-theory        42509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-83 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42509.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-83, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42510
in-theory        42510
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-76 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42510.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> ((E and F) -> F)))), M:tm-76, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42511
in-theory        42511
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-69 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42511.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> ((F and G) -> G)))), M:tm-69, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42512
in-theory        42512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-54 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42512.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-54, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42513
in-theory        42513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-42 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42513.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> ((F and G) -> G)))), M:tm-42, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42514
in-theory        42514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-32 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42514.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> ((F and G) -> G)))), M:tm-32, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42515
in-theory        42515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-23 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42515.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> ((F and G) -> G)))), M:tm-23, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42516
in-theory        42516
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-22 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42516.        (((A and B) -> B) and ((C -> (D or C)) and (E -> ((F and G) -> G)))), M:tm-22, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42517
in-theory        42517
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-21 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42517.        (((A and B) -> A) and ((C -> (D or C)) and (E -> ((F and G) -> G)))), M:tm-21, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42518
in-theory        42518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-20 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42518.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-20, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42519
in-theory        42519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-19 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42519.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> ((F and G) -> G)))), M:tm-19, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42520
in-theory        42520
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-7 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-7 tm-5 tm-1 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42520.        (A or ((B -> (C or B)) and (D -> ((E and F) -> F)))), M:tm-7, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42521
in-theory        42521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-6 tm-5 tm-7 tm-1 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42521.        (((A -> (B or A)) and (C -> ((D and E) -> E))) or F), M:tm-6, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42522
in-theory        42522
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> ((E and F) -> F))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42522.        (A -> (((B -> (C or B)) and (D -> ((E and F) -> F))) and A)), M:tm-5, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42523
in-theory        42523
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-1 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-1 tm-5 tm-7 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-42523.        (A -> ((B -> (C or B)) and (D -> ((E and F) -> F)))), M:tm-1, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-42524
in-theory        42524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42524.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-550, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42525
in-theory        42525
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42525.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-540, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42526
in-theory        42526
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42526.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-530, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42527
in-theory        42527
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42527.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-520, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42528
in-theory        42528
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42528.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-510, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42529
in-theory        42529
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42529.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-500, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42530
in-theory        42530
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42530.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-490, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42531
in-theory        42531
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42531.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-480, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42532
in-theory        42532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42532.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-469, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42533
in-theory        42533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42533.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (F or G))), M:tm-456, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42534
in-theory        42534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42534.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-453, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42535
in-theory        42535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42535.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-443, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42536
in-theory        42536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42536.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-409, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42537
in-theory        42537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42537.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-400, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42538
in-theory        42538
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42538.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-391, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42539
in-theory        42539
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42539.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-382, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42540
in-theory        42540
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42540.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-373, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42541
in-theory        42541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42541.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-364, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42542
in-theory        42542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42542.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-354, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42543
in-theory        42543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42543.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42544
in-theory        42544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42544.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-338, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42545
in-theory        42545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42545.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-327, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42546
in-theory        42546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42546.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-326, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42547
in-theory        42547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42547.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-325, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42548
in-theory        42548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42548.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-324, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42549
in-theory        42549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42549.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-323, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42550
in-theory        42550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42550.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42551
in-theory        42551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42551.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42552
in-theory        42552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42552.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42553
in-theory        42553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42553.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42554
in-theory        42554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (F or ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42554.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (F or ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-311, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42555
in-theory        42555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42555.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) or F)), M:tm-310, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42556
in-theory        42556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42556.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and F))), M:tm-309, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42557
in-theory        42557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (C -> ((D -> (E -> D)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-570 ((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42557.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (C -> ((D -> (E -> D)) and C))), M:tm-308, m:tm-570, u:((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm))))
================================================================
tm-name          tm-42558
in-theory        42558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (A -> (B or A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-570 ((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42558.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (A -> (B or A))), M:tm-307, m:tm-570, u:((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (-> Em Dm)) Cm))))
================================================================
tm-name          tm-42559
in-theory        42559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (F -> ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42559.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (F -> ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-305, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42560
in-theory        42560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42560.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-303, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42561
in-theory        42561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42561.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-270, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42562
in-theory        42562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42562.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-239, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42563
in-theory        42563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42563.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-210, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42564
in-theory        42564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42564.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-183, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42565
in-theory        42565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42565.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-157, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42566
in-theory        42566
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42566.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-147, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42567
in-theory        42567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42567.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-134, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42568
in-theory        42568
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42568.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-125, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42569
in-theory        42569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42569.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-113, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42570
in-theory        42570
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42570.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-105, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42571
in-theory        42571
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42571.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-95, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42572
in-theory        42572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42572.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-83, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42573
in-theory        42573
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42573.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> ((E -> (F -> E)) and D)))), M:tm-76, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42574
in-theory        42574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42574.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-69, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42575
in-theory        42575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42575.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-54, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42576
in-theory        42576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42576.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-42, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42577
in-theory        42577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42577.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-32, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42578
in-theory        42578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42578.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-23, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42579
in-theory        42579
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42579.        (((A and B) -> B) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-22, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42580
in-theory        42580
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42580.        (((A and B) -> A) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-21, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42581
in-theory        42581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42581.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-20, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42582
in-theory        42582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42582.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> ((F -> (G -> F)) and E)))), M:tm-19, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42583
in-theory        42583
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42583.        (A or ((B -> (C or B)) and (D -> ((E -> (F -> E)) and D)))), M:tm-7, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42584
in-theory        42584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42584.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) or F), M:tm-6, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42585
in-theory        42585
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> ((E -> (F -> E)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42585.        (A -> (((B -> (C or B)) and (D -> ((E -> (F -> E)) and D))) and A)), M:tm-5, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42586
in-theory        42586
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> ((E -> (F -> E)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-42586.        (A -> ((B -> (C or B)) and (D -> ((E -> (F -> E)) and D)))), M:tm-1, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-42587
in-theory        42587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-550 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42587.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-550, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42588
in-theory        42588
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-540 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42588.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-540, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42589
in-theory        42589
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-530 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42589.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-530, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42590
in-theory        42590
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-520 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42590.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-520, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42591
in-theory        42591
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-510 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42591.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-510, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42592
in-theory        42592
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-500 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42592.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-500, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42593
in-theory        42593
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-490 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42593.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-490, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42594
in-theory        42594
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-480 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42594.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-480, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42595
in-theory        42595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-469 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42595.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-469, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42596
in-theory        42596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42596.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (G or H))), M:tm-456, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42597
in-theory        42597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-453 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42597.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-453, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42598
in-theory        42598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (G or H)) and ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42598.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (G or H)) and ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-443, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42599
in-theory        42599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-409 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42599.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-409, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42600
in-theory        42600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-400 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42600.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-400, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42601
in-theory        42601
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-391 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42601.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-391, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42602
in-theory        42602
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-382 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42602.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-382, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42603
in-theory        42603
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-373 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42603.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-373, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42604
in-theory        42604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-364 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42604.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-364, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42605
in-theory        42605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-354 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42605.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-354, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42606
in-theory        42606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42606.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42607
in-theory        42607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-338 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42607.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-338, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42608
in-theory        42608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42608.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-327, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42609
in-theory        42609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> H) and ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42609.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> H) and ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-326, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42610
in-theory        42610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> G) and ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42610.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G and H) -> G) and ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-325, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42611
in-theory        42611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42611.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-324, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42612
in-theory        42612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> G)) and ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42612.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> G)) and ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-323, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42613
in-theory        42613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42613.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> H)), M:tm-322, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42614
in-theory        42614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42614.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G and H) -> G)), M:tm-320, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42615
in-theory        42615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42615.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42616
in-theory        42616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42616.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H -> G))), M:tm-315, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42617
in-theory        42617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G or ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42617.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G or ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-311, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42618
in-theory        42618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42618.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G)), M:tm-310, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42619
in-theory        42619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42619.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and G))), M:tm-309, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42620
in-theory        42620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     41
proof            (modus-ponens tm-308 tm-571 ((A (-> Am (or Bm Am))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42620.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-308, m:tm-571, u:((A (-> Am (or Bm Am))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))
================================================================
tm-name          tm-42621
in-theory        42621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (A -> (B or A)))
theorem-size     29
proof            (modus-ponens tm-307 tm-571 ((A (-> Am (or Bm Am))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42621.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (A -> (B or A))), M:tm-307, m:tm-571, u:((A (-> Am (or Bm Am))) (B (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))
================================================================
tm-name          tm-42622
in-theory        42622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42622.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-305, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42623
in-theory        42623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-303 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42623.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-303, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42624
in-theory        42624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-270 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42624.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-270, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42625
in-theory        42625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-239 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42625.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-239, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42626
in-theory        42626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-210 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42626.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-210, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42627
in-theory        42627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-183 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42627.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-183, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42628
in-theory        42628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-157 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42628.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-157, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42629
in-theory        42629
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-147 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42629.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-147, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42630
in-theory        42630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-134 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42630.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-134, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42631
in-theory        42631
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-125 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42631.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-125, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42632
in-theory        42632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-113 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42632.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-113, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42633
in-theory        42633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     43
proof            (modus-ponens tm-105 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42633.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-105, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42634
in-theory        42634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-95 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42634.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-95, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42635
in-theory        42635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-83 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42635.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-83, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42636
in-theory        42636
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-76 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42636.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-76, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42637
in-theory        42637
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     35
proof            (modus-ponens tm-69 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42637.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-69, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42638
in-theory        42638
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-54 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42638.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-54, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42639
in-theory        42639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-42 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42639.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-42, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42640
in-theory        42640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-32 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42640.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-32, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42641
in-theory        42641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-23 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42641.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-23, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42642
in-theory        42642
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-22 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42642.        (((A and B) -> B) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-22, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42643
in-theory        42643
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-21 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42643.        (((A and B) -> A) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-21, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42644
in-theory        42644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-20 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42644.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-20, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42645
in-theory        42645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-19 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42645.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-19, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42646
in-theory        42646
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-7 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42646.        (A or ((B -> (C or B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-7, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42647
in-theory        42647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42647.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) or G), M:tm-6, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42648
in-theory        42648
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42648.        (A -> (((B -> (C or B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and A)), M:tm-5, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42649
in-theory        42649
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     25
proof            (modus-ponens tm-1 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-42649.        (A -> ((B -> (C or B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-1, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-42650
in-theory        42650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42650.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-550, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42651
in-theory        42651
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42651.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-540, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42652
in-theory        42652
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42652.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-530, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42653
in-theory        42653
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42653.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-520, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42654
in-theory        42654
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42654.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-510, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42655
in-theory        42655
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42655.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-500, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42656
in-theory        42656
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42656.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G)))), M:tm-490, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42657
in-theory        42657
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42657.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-480, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42658
in-theory        42658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42658.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-469, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42659
in-theory        42659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42659.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (F -> (F or G))), M:tm-456, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42660
in-theory        42660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42660.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-453, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42661
in-theory        42661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42661.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> (((D and E) -> D) and C))))), M:tm-443, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42662
in-theory        42662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42662.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-409, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42663
in-theory        42663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42663.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-400, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42664
in-theory        42664
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42664.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-391, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42665
in-theory        42665
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42665.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-382, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42666
in-theory        42666
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42666.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G)))), M:tm-373, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42667
in-theory        42667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42667.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-364, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42668
in-theory        42668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42668.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-354, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42669
in-theory        42669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42669.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42670
in-theory        42670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42670.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E)))), M:tm-338, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42671
in-theory        42671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42671.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> (((D and E) -> D) and C))))), M:tm-327, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42672
in-theory        42672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42672.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> (((D and E) -> D) and C))))), M:tm-326, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42673
in-theory        42673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42673.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> (((D and E) -> D) and C))))), M:tm-325, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42674
in-theory        42674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42674.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> (((D and E) -> D) and C))))), M:tm-324, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42675
in-theory        42675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42675.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> (((D and E) -> D) and C))))), M:tm-323, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42676
in-theory        42676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42676.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and ((F and G) -> G)), M:tm-322, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42677
in-theory        42677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42677.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and ((F and G) -> F)), M:tm-320, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42678
in-theory        42678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42678.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42679
in-theory        42679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42679.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (F -> (G -> F))), M:tm-315, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42680
in-theory        42680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (F or ((A -> (B or A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42680.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (F or ((A -> (B or A)) and (C -> (((D and E) -> D) and C))))), M:tm-311, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42681
in-theory        42681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42681.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) or F)), M:tm-310, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42682
in-theory        42682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (F -> (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42682.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (F -> (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and F))), M:tm-309, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42683
in-theory        42683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (C -> (((D and E) -> D) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-572 ((A (-> Am (or Bm Am))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42683.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (C -> (((D and E) -> D) and C))), M:tm-308, m:tm-572, u:((A (-> Am (or Bm Am))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm))))
================================================================
tm-name          tm-42684
in-theory        42684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (A -> (B or A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-572 ((A (-> Am (or Bm Am))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42684.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (A -> (B or A))), M:tm-307, m:tm-572, u:((A (-> Am (or Bm Am))) (B (-> Cm (and (-> (and Dm Em) Dm) Cm))))
================================================================
tm-name          tm-42685
in-theory        42685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (F -> ((A -> (B or A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42685.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (F -> ((A -> (B or A)) and (C -> (((D and E) -> D) and C))))), M:tm-305, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42686
in-theory        42686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42686.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-303, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42687
in-theory        42687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42687.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-270, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42688
in-theory        42688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42688.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-239, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42689
in-theory        42689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42689.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G)))), M:tm-210, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42690
in-theory        42690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42690.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-183, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42691
in-theory        42691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42691.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-157, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42692
in-theory        42692
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42692.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-147, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42693
in-theory        42693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42693.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-134, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42694
in-theory        42694
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42694.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-125, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42695
in-theory        42695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42695.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G)))), M:tm-113, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42696
in-theory        42696
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42696.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-105, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42697
in-theory        42697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42697.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E)))), M:tm-95, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42698
in-theory        42698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42698.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-83, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42699
in-theory        42699
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42699.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (((E and F) -> E) and D)))), M:tm-76, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42700
in-theory        42700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42700.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E)))), M:tm-69, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42701
in-theory        42701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42701.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-54, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42702
in-theory        42702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42702.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E)))), M:tm-42, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42703
in-theory        42703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42703.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E)))), M:tm-32, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42704
in-theory        42704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42704.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E)))), M:tm-23, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42705
in-theory        42705
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42705.        (((A and B) -> B) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E)))), M:tm-22, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42706
in-theory        42706
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42706.        (((A and B) -> A) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E)))), M:tm-21, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42707
in-theory        42707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42707.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-20, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42708
in-theory        42708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42708.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (((F and G) -> F) and E)))), M:tm-19, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42709
in-theory        42709
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42709.        (A or ((B -> (C or B)) and (D -> (((E and F) -> E) and D)))), M:tm-7, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42710
in-theory        42710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42710.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) or F), M:tm-6, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42711
in-theory        42711
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> (((E and F) -> E) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42711.        (A -> (((B -> (C or B)) and (D -> (((E and F) -> E) and D))) and A)), M:tm-5, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42712
in-theory        42712
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> (((E and F) -> E) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-42712.        (A -> ((B -> (C or B)) and (D -> (((E and F) -> E) and D)))), M:tm-1, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-42713
in-theory        42713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42713.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-550, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42714
in-theory        42714
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42714.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-540, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42715
in-theory        42715
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42715.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-530, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42716
in-theory        42716
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42716.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-520, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42717
in-theory        42717
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42717.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-510, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42718
in-theory        42718
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42718.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-500, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42719
in-theory        42719
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42719.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G)))), M:tm-490, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42720
in-theory        42720
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42720.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-480, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42721
in-theory        42721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42721.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-469, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42722
in-theory        42722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42722.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (F -> (F or G))), M:tm-456, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42723
in-theory        42723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42723.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-453, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42724
in-theory        42724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42724.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> (((D and E) -> E) and C))))), M:tm-443, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42725
in-theory        42725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42725.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-409, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42726
in-theory        42726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42726.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-400, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42727
in-theory        42727
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42727.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-391, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42728
in-theory        42728
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42728.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-382, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42729
in-theory        42729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42729.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G)))), M:tm-373, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42730
in-theory        42730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42730.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-364, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42731
in-theory        42731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42731.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-354, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42732
in-theory        42732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42732.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42733
in-theory        42733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42733.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E)))), M:tm-338, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42734
in-theory        42734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42734.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> (((D and E) -> E) and C))))), M:tm-327, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42735
in-theory        42735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42735.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> (((D and E) -> E) and C))))), M:tm-326, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42736
in-theory        42736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42736.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> (((D and E) -> E) and C))))), M:tm-325, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42737
in-theory        42737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42737.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> (((D and E) -> E) and C))))), M:tm-324, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42738
in-theory        42738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42738.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> (((D and E) -> E) and C))))), M:tm-323, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42739
in-theory        42739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42739.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and ((F and G) -> G)), M:tm-322, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42740
in-theory        42740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42740.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and ((F and G) -> F)), M:tm-320, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42741
in-theory        42741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42741.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42742
in-theory        42742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42742.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (F -> (G -> F))), M:tm-315, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42743
in-theory        42743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (F or ((A -> (B or A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42743.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (F or ((A -> (B or A)) and (C -> (((D and E) -> E) and C))))), M:tm-311, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42744
in-theory        42744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42744.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) or F)), M:tm-310, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42745
in-theory        42745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (F -> (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42745.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (F -> (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and F))), M:tm-309, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42746
in-theory        42746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (C -> (((D and E) -> E) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-573 ((A (-> Am (or Bm Am))) (B (-> Cm (and (-> (and Dm Em) Em) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42746.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (C -> (((D and E) -> E) and C))), M:tm-308, m:tm-573, u:((A (-> Am (or Bm Am))) (B (-> Cm (and (-> (and Dm Em) Em) Cm))))
================================================================
tm-name          tm-42747
in-theory        42747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (A -> (B or A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-573 ((A (-> Am (or Bm Am))) (B (-> Cm (and (-> (and Dm Em) Em) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42747.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (A -> (B or A))), M:tm-307, m:tm-573, u:((A (-> Am (or Bm Am))) (B (-> Cm (and (-> (and Dm Em) Em) Cm))))
================================================================
tm-name          tm-42748
in-theory        42748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (F -> ((A -> (B or A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42748.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (F -> ((A -> (B or A)) and (C -> (((D and E) -> E) and C))))), M:tm-305, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42749
in-theory        42749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42749.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-303, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42750
in-theory        42750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42750.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-270, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42751
in-theory        42751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42751.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-239, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42752
in-theory        42752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42752.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G)))), M:tm-210, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42753
in-theory        42753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42753.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-183, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42754
in-theory        42754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42754.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-157, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42755
in-theory        42755
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42755.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-147, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42756
in-theory        42756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42756.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-134, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42757
in-theory        42757
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42757.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-125, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42758
in-theory        42758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42758.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G)))), M:tm-113, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42759
in-theory        42759
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42759.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-105, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42760
in-theory        42760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42760.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E)))), M:tm-95, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42761
in-theory        42761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42761.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-83, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42762
in-theory        42762
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42762.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (((E and F) -> F) and D)))), M:tm-76, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42763
in-theory        42763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42763.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E)))), M:tm-69, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42764
in-theory        42764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42764.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-54, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42765
in-theory        42765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42765.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E)))), M:tm-42, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42766
in-theory        42766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42766.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E)))), M:tm-32, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42767
in-theory        42767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42767.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E)))), M:tm-23, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42768
in-theory        42768
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42768.        (((A and B) -> B) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E)))), M:tm-22, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42769
in-theory        42769
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42769.        (((A and B) -> A) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E)))), M:tm-21, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42770
in-theory        42770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42770.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-20, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42771
in-theory        42771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42771.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (((F and G) -> G) and E)))), M:tm-19, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42772
in-theory        42772
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42772.        (A or ((B -> (C or B)) and (D -> (((E and F) -> F) and D)))), M:tm-7, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42773
in-theory        42773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42773.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) or F), M:tm-6, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42774
in-theory        42774
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> (((E and F) -> F) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42774.        (A -> (((B -> (C or B)) and (D -> (((E and F) -> F) and D))) and A)), M:tm-5, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42775
in-theory        42775
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> (((E and F) -> F) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-42775.        (A -> ((B -> (C or B)) and (D -> (((E and F) -> F) and D)))), M:tm-1, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-42776
in-theory        42776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-550 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42776.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-550, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42777
in-theory        42777
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-540 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42777.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-540, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42778
in-theory        42778
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-530 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42778.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-530, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42779
in-theory        42779
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-520 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42779.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-520, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42780
in-theory        42780
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-510 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42780.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-510, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42781
in-theory        42781
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-500 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42781.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-500, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42782
in-theory        42782
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-490 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42782.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-490, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42783
in-theory        42783
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-480 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42783.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-480, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42784
in-theory        42784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-469 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42784.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-469, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42785
in-theory        42785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42785.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (F or G))), M:tm-456, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42786
in-theory        42786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-453 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42786.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-453, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42787
in-theory        42787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42787.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-443, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42788
in-theory        42788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-409 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42788.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-409, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42789
in-theory        42789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-400 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42789.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-400, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42790
in-theory        42790
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-391 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42790.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-391, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42791
in-theory        42791
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-382 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42791.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-382, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42792
in-theory        42792
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-373 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42792.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-373, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42793
in-theory        42793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-364 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42793.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-364, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42794
in-theory        42794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-354 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42794.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-354, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42795
in-theory        42795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42795.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42796
in-theory        42796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-338 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42796.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-338, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42797
in-theory        42797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42797.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-327, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42798
in-theory        42798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42798.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-326, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42799
in-theory        42799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42799.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-325, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42800
in-theory        42800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42800.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-324, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42801
in-theory        42801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42801.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-323, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42802
in-theory        42802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42802.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> G)), M:tm-322, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42803
in-theory        42803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42803.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F and G) -> F)), M:tm-320, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42804
in-theory        42804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42804.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42805
in-theory        42805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42805.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G -> F))), M:tm-315, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42806
in-theory        42806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F or ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42806.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F or ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-311, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42807
in-theory        42807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42807.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) or F)), M:tm-310, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42808
in-theory        42808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42808.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and F))), M:tm-309, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42809
in-theory        42809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     29
proof            (modus-ponens tm-308 tm-574 ((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42809.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-308, m:tm-574, u:((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))
================================================================
tm-name          tm-42810
in-theory        42810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (A -> (B or A)))
theorem-size     23
proof            (modus-ponens tm-307 tm-574 ((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42810.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (A -> (B or A))), M:tm-307, m:tm-574, u:((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))
================================================================
tm-name          tm-42811
in-theory        42811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42811.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-305, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42812
in-theory        42812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-303 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42812.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-303, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42813
in-theory        42813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-270 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42813.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-270, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42814
in-theory        42814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-239 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42814.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-239, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42815
in-theory        42815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-210 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42815.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-210, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42816
in-theory        42816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-183 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42816.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-183, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42817
in-theory        42817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-157 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42817.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-157, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42818
in-theory        42818
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-147 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42818.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-147, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42819
in-theory        42819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-134 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42819.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-134, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42820
in-theory        42820
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-125 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42820.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-125, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42821
in-theory        42821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-113 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42821.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-113, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42822
in-theory        42822
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     37
proof            (modus-ponens tm-105 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42822.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-105, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42823
in-theory        42823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-95 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42823.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-95, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42824
in-theory        42824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-83 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42824.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-83, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42825
in-theory        42825
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-76 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42825.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-76, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42826
in-theory        42826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     29
proof            (modus-ponens tm-69 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42826.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-69, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42827
in-theory        42827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-54 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42827.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-54, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42828
in-theory        42828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-42 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42828.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-42, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42829
in-theory        42829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-32 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42829.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-32, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42830
in-theory        42830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-23 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42830.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-23, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42831
in-theory        42831
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-22 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42831.        (((A and B) -> B) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-22, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42832
in-theory        42832
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-21 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42832.        (((A and B) -> A) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-21, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42833
in-theory        42833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-20 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42833.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-20, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42834
in-theory        42834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-19 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42834.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> ((F -> (G -> (F and G))) and E)))), M:tm-19, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42835
in-theory        42835
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-7 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-7 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42835.        (A or ((B -> (C or B)) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-7, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42836
in-theory        42836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42836.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) or F), M:tm-6, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42837
in-theory        42837
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> ((E -> (F -> (E and F))) and D))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42837.        (A -> (((B -> (C or B)) and (D -> ((E -> (F -> (E and F))) and D))) and A)), M:tm-5, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42838
in-theory        42838
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     19
proof            (modus-ponens tm-1 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-42838.        (A -> ((B -> (C or B)) and (D -> ((E -> (F -> (E and F))) and D)))), M:tm-1, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-42839
in-theory        42839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42839.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-550, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42840
in-theory        42840
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42840.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-540, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42841
in-theory        42841
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42841.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-530, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42842
in-theory        42842
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42842.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-520, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42843
in-theory        42843
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42843.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-510, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42844
in-theory        42844
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42844.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-500, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42845
in-theory        42845
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42845.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H))))), M:tm-490, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42846
in-theory        42846
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42846.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-480, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42847
in-theory        42847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42847.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-469, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42848
in-theory        42848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42848.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42849
in-theory        42849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42849.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-453, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42850
in-theory        42850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (E or F)) and ((A -> (B or A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42850.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (E or F)) and ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-443, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42851
in-theory        42851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42851.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-409, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42852
in-theory        42852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42852.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-400, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42853
in-theory        42853
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42853.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-391, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42854
in-theory        42854
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42854.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-382, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42855
in-theory        42855
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42855.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H))))), M:tm-373, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42856
in-theory        42856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42856.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-364, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42857
in-theory        42857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42857.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-354, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42858
in-theory        42858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42858.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42859
in-theory        42859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42859.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F))))), M:tm-338, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42860
in-theory        42860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42860.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> (E and F))) and ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-327, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42861
in-theory        42861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> F) and ((A -> (B or A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42861.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> F) and ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-326, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42862
in-theory        42862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> E) and ((A -> (B or A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42862.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (((E and F) -> E) and ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-325, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42863
in-theory        42863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42863.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-324, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42864
in-theory        42864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> E)) and ((A -> (B or A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42864.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> E)) and ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-323, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42865
in-theory        42865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42865.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42866
in-theory        42866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42866.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42867
in-theory        42867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42867.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42868
in-theory        42868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42868.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42869
in-theory        42869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (E or ((A -> (B or A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42869.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (E or ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-311, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42870
in-theory        42870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42870.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) or E)), M:tm-310, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42871
in-theory        42871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42871.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and E))), M:tm-309, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42872
in-theory        42872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((C -> D) -> (C -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-308 tm-575 ((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42872.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((C -> D) -> (C -> (C and D)))), M:tm-308, m:tm-575, u:((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))
================================================================
tm-name          tm-42873
in-theory        42873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (A -> (B or A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-575 ((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42873.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (A -> (B or A))), M:tm-307, m:tm-575, u:((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))
================================================================
tm-name          tm-42874
in-theory        42874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (E -> ((A -> (B or A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42874.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (E -> ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-305, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42875
in-theory        42875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42875.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-303, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42876
in-theory        42876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42876.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-270, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42877
in-theory        42877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42877.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-239, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42878
in-theory        42878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42878.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H))))), M:tm-210, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42879
in-theory        42879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42879.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-183, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42880
in-theory        42880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42880.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-157, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42881
in-theory        42881
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42881.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-147, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42882
in-theory        42882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42882.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-134, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42883
in-theory        42883
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42883.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-125, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42884
in-theory        42884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42884.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H))))), M:tm-113, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42885
in-theory        42885
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42885.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-105, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42886
in-theory        42886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42886.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F))))), M:tm-95, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42887
in-theory        42887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42887.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-83, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42888
in-theory        42888
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> E) -> (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42888.        (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> E) -> (D -> (D and E))))), M:tm-76, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42889
in-theory        42889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42889.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F))))), M:tm-69, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42890
in-theory        42890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42890.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-54, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42891
in-theory        42891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42891.        ((A -> (B or A)) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F))))), M:tm-42, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42892
in-theory        42892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42892.        ((A -> (A or B)) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F))))), M:tm-32, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42893
in-theory        42893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42893.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F))))), M:tm-23, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42894
in-theory        42894
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42894.        (((A and B) -> B) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F))))), M:tm-22, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42895
in-theory        42895
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42895.        (((A and B) -> A) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F))))), M:tm-21, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42896
in-theory        42896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42896.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-20, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42897
in-theory        42897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42897.        ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> F) -> (E -> (E and F))))), M:tm-19, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42898
in-theory        42898
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42898.        (A or ((B -> (C or B)) and ((D -> E) -> (D -> (D and E))))), M:tm-7, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42899
in-theory        42899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-6 tm-5 tm-7 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42899.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) or E), M:tm-6, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42900
in-theory        42900
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((D -> E) -> (D -> (D and E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42900.        (A -> (((B -> (C or B)) and ((D -> E) -> (D -> (D and E)))) and A)), M:tm-5, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42901
in-theory        42901
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((D -> E) -> (D -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-1 tm-5 tm-7 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-42901.        (A -> ((B -> (C or B)) and ((D -> E) -> (D -> (D and E))))), M:tm-1, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-42902
in-theory        42902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-550 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42902.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-550, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42903
in-theory        42903
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-540 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42903.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-540, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42904
in-theory        42904
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-530 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42904.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-530, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42905
in-theory        42905
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-520 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42905.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-520, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42906
in-theory        42906
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-510 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42906.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-510, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42907
in-theory        42907
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-500 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42907.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-500, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42908
in-theory        42908
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-490 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42908.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I)))))), M:tm-490, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42909
in-theory        42909
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-480 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42909.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-480, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42910
in-theory        42910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-469 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42910.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-469, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42911
in-theory        42911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42911.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (F -> (F or G))), M:tm-456, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42912
in-theory        42912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-453 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42912.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-453, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42913
in-theory        42913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42913.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))))), M:tm-443, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42914
in-theory        42914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-409 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42914.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-409, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42915
in-theory        42915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-400 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42915.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-400, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42916
in-theory        42916
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-391 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42916.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-391, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42917
in-theory        42917
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-382 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42917.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-382, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42918
in-theory        42918
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-373 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42918.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I)))))), M:tm-373, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42919
in-theory        42919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-364 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42919.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-364, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42920
in-theory        42920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-354 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42920.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-354, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42921
in-theory        42921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42921.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42922
in-theory        42922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-338 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42922.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G)))))), M:tm-338, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42923
in-theory        42923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42923.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))))), M:tm-327, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42924
in-theory        42924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42924.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))))), M:tm-326, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42925
in-theory        42925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42925.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))))), M:tm-325, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42926
in-theory        42926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42926.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))))), M:tm-324, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42927
in-theory        42927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42927.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))))), M:tm-323, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42928
in-theory        42928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42928.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> G)), M:tm-322, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42929
in-theory        42929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42929.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and ((F and G) -> F)), M:tm-320, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42930
in-theory        42930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42930.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42931
in-theory        42931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42931.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (F -> (G -> F))), M:tm-315, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42932
in-theory        42932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (F or ((A -> (B or A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42932.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (F or ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))))), M:tm-311, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42933
in-theory        42933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42933.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) or F)), M:tm-310, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42934
in-theory        42934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (F -> (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42934.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (F -> (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and F))), M:tm-309, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42935
in-theory        42935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (C -> (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-308 tm-576 ((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42935.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (C -> (D -> (E -> (D and E))))), M:tm-308, m:tm-576, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-42936
in-theory        42936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (A -> (B or A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-576 ((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42936.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (A -> (B or A))), M:tm-307, m:tm-576, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-42937
in-theory        42937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (F -> ((A -> (B or A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42937.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (F -> ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))))), M:tm-305, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42938
in-theory        42938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-303 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42938.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-303, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42939
in-theory        42939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-270 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42939.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-270, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42940
in-theory        42940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-239 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42940.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-239, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42941
in-theory        42941
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-210 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42941.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I)))))), M:tm-210, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42942
in-theory        42942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-183 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42942.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-183, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42943
in-theory        42943
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-157 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42943.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-157, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42944
in-theory        42944
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-147 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42944.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-147, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42945
in-theory        42945
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-134 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42945.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-134, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42946
in-theory        42946
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-125 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42946.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-125, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42947
in-theory        42947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-113 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42947.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I)))))), M:tm-113, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42948
in-theory        42948
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-105 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42948.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-105, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42949
in-theory        42949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-95 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42949.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G)))))), M:tm-95, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42950
in-theory        42950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-83 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42950.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-83, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42951
in-theory        42951
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-76 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42951.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (E -> (F -> (E and F)))))), M:tm-76, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42952
in-theory        42952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-69 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42952.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G)))))), M:tm-69, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42953
in-theory        42953
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-54 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42953.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-54, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42954
in-theory        42954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-42 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42954.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G)))))), M:tm-42, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42955
in-theory        42955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-32 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42955.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G)))))), M:tm-32, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42956
in-theory        42956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-23 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42956.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G)))))), M:tm-23, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42957
in-theory        42957
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-22 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42957.        (((A and B) -> B) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G)))))), M:tm-22, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42958
in-theory        42958
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-21 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42958.        (((A and B) -> A) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G)))))), M:tm-21, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42959
in-theory        42959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-20 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42959.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-20, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42960
in-theory        42960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-19 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42960.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (F -> (G -> (F and G)))))), M:tm-19, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42961
in-theory        42961
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-7 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42961.        (A or ((B -> (C or B)) and (D -> (E -> (F -> (E and F)))))), M:tm-7, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42962
in-theory        42962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-6 tm-5 tm-7 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42962.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) or F), M:tm-6, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42963
in-theory        42963
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> (E -> (F -> (E and F))))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42963.        (A -> (((B -> (C or B)) and (D -> (E -> (F -> (E and F))))) and A)), M:tm-5, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42964
in-theory        42964
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-1 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42964.        (A -> ((B -> (C or B)) and (D -> (E -> (F -> (E and F)))))), M:tm-1, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-42965
in-theory        42965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42965.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-550, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42966
in-theory        42966
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42966.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-540, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42967
in-theory        42967
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42967.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-530, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42968
in-theory        42968
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42968.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-520, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42969
in-theory        42969
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42969.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-510, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42970
in-theory        42970
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42970.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-500, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42971
in-theory        42971
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42971.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H -> G)) or I))), M:tm-490, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42972
in-theory        42972
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42972.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-480, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42973
in-theory        42973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42973.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-469, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42974
in-theory        42974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42974.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (F -> (F or G))), M:tm-456, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42975
in-theory        42975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42975.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-453, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42976
in-theory        42976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42976.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> (D -> C)) or E)))), M:tm-443, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42977
in-theory        42977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42977.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-409, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42978
in-theory        42978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42978.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-400, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42979
in-theory        42979
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42979.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-391, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42980
in-theory        42980
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42980.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-382, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42981
in-theory        42981
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42981.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> (H -> G)) or I))), M:tm-373, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42982
in-theory        42982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42982.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-364, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42983
in-theory        42983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42983.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-354, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42984
in-theory        42984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42984.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42985
in-theory        42985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42985.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> (F -> E)) or G))), M:tm-338, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42986
in-theory        42986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> (D -> C)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42986.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> (D -> C)) or E)))), M:tm-327, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42987
in-theory        42987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42987.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> (D -> C)) or E)))), M:tm-326, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42988
in-theory        42988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42988.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> (D -> C)) or E)))), M:tm-325, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42989
in-theory        42989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> (D -> C)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42989.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> (D -> C)) or E)))), M:tm-324, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42990
in-theory        42990
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42990.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> (D -> C)) or E)))), M:tm-323, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42991
in-theory        42991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42991.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42992
in-theory        42992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42992.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42993
in-theory        42993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42993.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42994
in-theory        42994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42994.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42995
in-theory        42995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (F or ((A -> (B or A)) and ((C -> (D -> C)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42995.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (F or ((A -> (B or A)) and ((C -> (D -> C)) or E)))), M:tm-311, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42996
in-theory        42996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (((A -> (B or A)) and ((C -> (D -> C)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42996.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (((A -> (B or A)) and ((C -> (D -> C)) or E)) or F)), M:tm-310, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42997
in-theory        42997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (F -> (((A -> (B or A)) and ((C -> (D -> C)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42997.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (F -> (((A -> (B or A)) and ((C -> (D -> C)) or E)) and F))), M:tm-309, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-42998
in-theory        42998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((C -> (D -> C)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-577 ((A (-> Am (or Bm Am))) (B (or (-> Cm (-> Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42998.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((C -> (D -> C)) or E)), M:tm-308, m:tm-577, u:((A (-> Am (or Bm Am))) (B (or (-> Cm (-> Dm Cm)) Em)))
================================================================
tm-name          tm-42999
in-theory        42999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-577 ((A (-> Am (or Bm Am))) (B (or (-> Cm (-> Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-42999.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (A -> (B or A))), M:tm-307, m:tm-577, u:((A (-> Am (or Bm Am))) (B (or (-> Cm (-> Dm Cm)) Em)))
================================================================
tm-name          tm-43000
in-theory        43000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (F -> ((A -> (B or A)) and ((C -> (D -> C)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43000.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (F -> ((A -> (B or A)) and ((C -> (D -> C)) or E)))), M:tm-305, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43001
in-theory        43001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43001.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-303, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43002
in-theory        43002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43002.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-270, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43003
in-theory        43003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43003.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-239, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43004
in-theory        43004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43004.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> (H -> G)) or I))), M:tm-210, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43005
in-theory        43005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43005.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-183, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43006
in-theory        43006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43006.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-157, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43007
in-theory        43007
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43007.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-147, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43008
in-theory        43008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43008.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-134, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43009
in-theory        43009
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43009.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-125, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43010
in-theory        43010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43010.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H -> G)) or I))), M:tm-113, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43011
in-theory        43011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43011.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-105, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43012
in-theory        43012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43012.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> (F -> E)) or G))), M:tm-95, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43013
in-theory        43013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43013.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-83, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43014
in-theory        43014
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> (E -> D)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43014.        (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> (E -> D)) or F))), M:tm-76, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43015
in-theory        43015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> (F -> E)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43015.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> (F -> E)) or G))), M:tm-69, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43016
in-theory        43016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43016.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-54, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43017
in-theory        43017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43017.        ((A -> (B or A)) and ((C -> (D or C)) and ((E -> (F -> E)) or G))), M:tm-42, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43018
in-theory        43018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43018.        ((A -> (A or B)) and ((C -> (D or C)) and ((E -> (F -> E)) or G))), M:tm-32, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43019
in-theory        43019
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43019.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> (F -> E)) or G))), M:tm-23, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43020
in-theory        43020
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43020.        (((A and B) -> B) and ((C -> (D or C)) and ((E -> (F -> E)) or G))), M:tm-22, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43021
in-theory        43021
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43021.        (((A and B) -> A) and ((C -> (D or C)) and ((E -> (F -> E)) or G))), M:tm-21, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43022
in-theory        43022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43022.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-20, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43023
in-theory        43023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43023.        ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> (F -> E)) or G))), M:tm-19, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43024
in-theory        43024
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-7 tm-5 tm-6 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43024.        (A or ((B -> (C or B)) and ((D -> (E -> D)) or F))), M:tm-7, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43025
in-theory        43025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-6 tm-5 tm-7 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43025.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) or F), M:tm-6, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43026
in-theory        43026
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((D -> (E -> D)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43026.        (A -> (((B -> (C or B)) and ((D -> (E -> D)) or F)) and A)), M:tm-5, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43027
in-theory        43027
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((D -> (E -> D)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-1 tm-5 tm-7 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-43027.        (A -> ((B -> (C or B)) and ((D -> (E -> D)) or F))), M:tm-1, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-43028
in-theory        43028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-550 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43028.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-550, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43029
in-theory        43029
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-540 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43029.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-540, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43030
in-theory        43030
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-530 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43030.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-530, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43031
in-theory        43031
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-520 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43031.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-520, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43032
in-theory        43032
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-510 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43032.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-510, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43033
in-theory        43033
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-500 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43033.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-500, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43034
in-theory        43034
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-490 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43034.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-490, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43035
in-theory        43035
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-480 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43035.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-480, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43036
in-theory        43036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-469 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43036.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-469, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43037
in-theory        43037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43037.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (G or H))), M:tm-456, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43038
in-theory        43038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-453 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43038.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-453, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43039
in-theory        43039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (G or H)) and ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-443 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43039.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (G or H)) and ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-443, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43040
in-theory        43040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-409 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43040.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-409, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43041
in-theory        43041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-400 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43041.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-400, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43042
in-theory        43042
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-391 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43042.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-391, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43043
in-theory        43043
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-382 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43043.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-382, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43044
in-theory        43044
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-373 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43044.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-373, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43045
in-theory        43045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-364 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43045.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-364, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43046
in-theory        43046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-354 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43046.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-354, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43047
in-theory        43047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43047.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> (G and H)))), M:tm-341, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43048
in-theory        43048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-338 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43048.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-338, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43049
in-theory        43049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     51
proof            (modus-ponens tm-327 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43049.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-327, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43050
in-theory        43050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> H) and ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-326 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43050.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> H) and ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-326, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43051
in-theory        43051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> G) and ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-325 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43051.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G and H) -> G) and ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-325, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43052
in-theory        43052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     57
proof            (modus-ponens tm-324 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43052.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-324, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43053
in-theory        43053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> G)) and ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-323 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43053.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> G)) and ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-323, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43054
in-theory        43054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43054.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> H)), M:tm-322, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43055
in-theory        43055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43055.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G and H) -> G)), M:tm-320, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43056
in-theory        43056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43056.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43057
in-theory        43057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43057.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H -> G))), M:tm-315, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43058
in-theory        43058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G or ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-311 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43058.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G or ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-311, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43059
in-theory        43059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43059.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G)), M:tm-310, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43060
in-theory        43060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43060.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and G))), M:tm-309, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43061
in-theory        43061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     37
proof            (modus-ponens tm-308 tm-578 ((A (-> Am (or Bm Am))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43061.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-308, m:tm-578, u:((A (-> Am (or Bm Am))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))
================================================================
tm-name          tm-43062
in-theory        43062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (A -> (B or A)))
theorem-size     27
proof            (modus-ponens tm-307 tm-578 ((A (-> Am (or Bm Am))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43062.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (A -> (B or A))), M:tm-307, m:tm-578, u:((A (-> Am (or Bm Am))) (B (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))
================================================================
tm-name          tm-43063
in-theory        43063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     45
proof            (modus-ponens tm-305 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43063.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-305, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43064
in-theory        43064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-303 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43064.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-303, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43065
in-theory        43065
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-270 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43065.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-270, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43066
in-theory        43066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-239 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43066.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-239, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43067
in-theory        43067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-210 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43067.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-210, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43068
in-theory        43068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-183 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43068.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-183, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43069
in-theory        43069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-157 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43069.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-157, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43070
in-theory        43070
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-147 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43070.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-147, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43071
in-theory        43071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-134 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43071.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-134, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43072
in-theory        43072
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-125 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43072.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-125, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43073
in-theory        43073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-113 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43073.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-113, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43074
in-theory        43074
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     41
proof            (modus-ponens tm-105 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43074.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-105, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43075
in-theory        43075
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-95 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43075.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-95, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43076
in-theory        43076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-83 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43076.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-83, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43077
in-theory        43077
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     27
proof            (modus-ponens tm-76 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43077.        (((not (not A)) -> A) and ((B -> (C or B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-76, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43078
in-theory        43078
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     33
proof            (modus-ponens tm-69 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43078.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-69, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43079
in-theory        43079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-54 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43079.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-54, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43080
in-theory        43080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-42 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43080.        ((A -> (B or A)) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-42, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43081
in-theory        43081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-32 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43081.        ((A -> (A or B)) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-32, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43082
in-theory        43082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-23 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43082.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-23, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43083
in-theory        43083
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-22 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43083.        (((A and B) -> B) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-22, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43084
in-theory        43084
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-21 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43084.        (((A and B) -> A) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-21, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43085
in-theory        43085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-20 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43085.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-20, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43086
in-theory        43086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-19 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43086.        ((A -> (B -> A)) and ((C -> (D or C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-19, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43087
in-theory        43087
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-7 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-7 tm-5 tm-6 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43087.        (A or ((B -> (C or B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-7, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43088
in-theory        43088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-6 tm-5 tm-7 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43088.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) or G), M:tm-6, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43089
in-theory        43089
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43089.        (A -> (((B -> (C or B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and A)), M:tm-5, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43090
in-theory        43090
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     23
proof            (modus-ponens tm-1 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-1 tm-5 tm-7 tm-6 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-43090.        (A -> ((B -> (C or B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-1, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-43091
in-theory        43091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43091.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-550, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43092
in-theory        43092
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43092.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-540, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43093
in-theory        43093
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43093.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-530, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43094
in-theory        43094
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43094.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-520, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43095
in-theory        43095
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43095.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-510, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43096
in-theory        43096
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43096.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-500, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43097
in-theory        43097
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43097.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G and H) -> G) or I))), M:tm-490, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43098
in-theory        43098
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43098.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-480, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43099
in-theory        43099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43099.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-469, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43100
in-theory        43100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43100.        (((A -> (B or A)) and (((C and D) -> C) or E)) and (F -> (F or G))), M:tm-456, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43101
in-theory        43101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43101.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-453, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43102
in-theory        43102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and ((F -> (F or G)) and ((A -> (B or A)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43102.        (((A -> (B or A)) and (((C and D) -> C) or E)) and ((F -> (F or G)) and ((A -> (B or A)) and (((C and D) -> C) or E)))), M:tm-443, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43103
in-theory        43103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43103.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-409, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43104
in-theory        43104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43104.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-400, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43105
in-theory        43105
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43105.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-391, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43106
in-theory        43106
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43106.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-382, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43107
in-theory        43107
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43107.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G and H) -> G) or I))), M:tm-373, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43108
in-theory        43108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43108.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-364, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43109
in-theory        43109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43109.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-354, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43110
in-theory        43110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43110.        (((A -> (B or A)) and (((C and D) -> C) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43111
in-theory        43111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43111.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E and F) -> E) or G))), M:tm-338, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43112
in-theory        43112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C and D) -> C) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43112.        (((A -> (B or A)) and (((C and D) -> C) or E)) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C and D) -> C) or E)))), M:tm-327, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43113
in-theory        43113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and (((F and G) -> G) and ((A -> (B or A)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43113.        (((A -> (B or A)) and (((C and D) -> C) or E)) and (((F and G) -> G) and ((A -> (B or A)) and (((C and D) -> C) or E)))), M:tm-326, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43114
in-theory        43114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and (((F and G) -> F) and ((A -> (B or A)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43114.        (((A -> (B or A)) and (((C and D) -> C) or E)) and (((F and G) -> F) and ((A -> (B or A)) and (((C and D) -> C) or E)))), M:tm-325, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43115
in-theory        43115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C and D) -> C) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43115.        (((A -> (B or A)) and (((C and D) -> C) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C and D) -> C) or E)))), M:tm-324, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43116
in-theory        43116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43116.        (((A -> (B or A)) and (((C and D) -> C) or E)) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C and D) -> C) or E)))), M:tm-323, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43117
in-theory        43117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43117.        (((A -> (B or A)) and (((C and D) -> C) or E)) and ((F and G) -> G)), M:tm-322, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43118
in-theory        43118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43118.        (((A -> (B or A)) and (((C and D) -> C) or E)) and ((F and G) -> F)), M:tm-320, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43119
in-theory        43119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43119.        (((A -> (B or A)) and (((C and D) -> C) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43120
in-theory        43120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43120.        (((A -> (B or A)) and (((C and D) -> C) or E)) and (F -> (G -> F))), M:tm-315, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43121
in-theory        43121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and (F or ((A -> (B or A)) and (((C and D) -> C) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43121.        (((A -> (B or A)) and (((C and D) -> C) or E)) and (F or ((A -> (B or A)) and (((C and D) -> C) or E)))), M:tm-311, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43122
in-theory        43122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and (((A -> (B or A)) and (((C and D) -> C) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43122.        (((A -> (B or A)) and (((C and D) -> C) or E)) and (((A -> (B or A)) and (((C and D) -> C) or E)) or F)), M:tm-310, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43123
in-theory        43123
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and (F -> (((A -> (B or A)) and (((C and D) -> C) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43123.        (((A -> (B or A)) and (((C and D) -> C) or E)) and (F -> (((A -> (B or A)) and (((C and D) -> C) or E)) and F))), M:tm-309, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43124
in-theory        43124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and (((C and D) -> C) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-579 ((A (-> Am (or Bm Am))) (B (or (-> (and Cm Dm) Cm) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43124.        (((A -> (B or A)) and (((C and D) -> C) or E)) and (((C and D) -> C) or E)), M:tm-308, m:tm-579, u:((A (-> Am (or Bm Am))) (B (or (-> (and Cm Dm) Cm) Em)))
================================================================
tm-name          tm-43125
in-theory        43125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-579 ((A (-> Am (or Bm Am))) (B (or (-> (and Cm Dm) Cm) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43125.        (((A -> (B or A)) and (((C and D) -> C) or E)) and (A -> (B or A))), M:tm-307, m:tm-579, u:((A (-> Am (or Bm Am))) (B (or (-> (and Cm Dm) Cm) Em)))
================================================================
tm-name          tm-43126
in-theory        43126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and (F -> ((A -> (B or A)) and (((C and D) -> C) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43126.        (((A -> (B or A)) and (((C and D) -> C) or E)) and (F -> ((A -> (B or A)) and (((C and D) -> C) or E)))), M:tm-305, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43127
in-theory        43127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43127.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-303, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43128
in-theory        43128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43128.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-270, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43129
in-theory        43129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43129.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-239, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43130
in-theory        43130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43130.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G and H) -> G) or I))), M:tm-210, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43131
in-theory        43131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43131.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-183, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43132
in-theory        43132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43132.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-157, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43133
in-theory        43133
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43133.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-147, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43134
in-theory        43134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43134.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-134, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43135
in-theory        43135
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43135.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-125, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43136
in-theory        43136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43136.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G and H) -> G) or I))), M:tm-113, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43137
in-theory        43137
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43137.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-105, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43138
in-theory        43138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43138.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E and F) -> E) or G))), M:tm-95, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43139
in-theory        43139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43139.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-83, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43140
in-theory        43140
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (((D and E) -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43140.        (((not (not A)) -> A) and ((B -> (C or B)) and (((D and E) -> D) or F))), M:tm-76, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43141
in-theory        43141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E and F) -> E) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43141.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E and F) -> E) or G))), M:tm-69, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43142
in-theory        43142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43142.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-54, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43143
in-theory        43143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43143.        ((A -> (B or A)) and ((C -> (D or C)) and (((E and F) -> E) or G))), M:tm-42, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43144
in-theory        43144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43144.        ((A -> (A or B)) and ((C -> (D or C)) and (((E and F) -> E) or G))), M:tm-32, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43145
in-theory        43145
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43145.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E and F) -> E) or G))), M:tm-23, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43146
in-theory        43146
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43146.        (((A and B) -> B) and ((C -> (D or C)) and (((E and F) -> E) or G))), M:tm-22, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43147
in-theory        43147
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43147.        (((A and B) -> A) and ((C -> (D or C)) and (((E and F) -> E) or G))), M:tm-21, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43148
in-theory        43148
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43148.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-20, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43149
in-theory        43149
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43149.        ((A -> (B -> A)) and ((C -> (D or C)) and (((E and F) -> E) or G))), M:tm-19, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43150
in-theory        43150
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-7 tm-5 tm-6 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43150.        (A or ((B -> (C or B)) and (((D and E) -> D) or F))), M:tm-7, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43151
in-theory        43151
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-6 tm-5 tm-7 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43151.        (((A -> (B or A)) and (((C and D) -> C) or E)) or F), M:tm-6, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43152
in-theory        43152
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (((D and E) -> D) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43152.        (A -> (((B -> (C or B)) and (((D and E) -> D) or F)) and A)), M:tm-5, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43153
in-theory        43153
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (((D and E) -> D) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-1 tm-5 tm-7 tm-6 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-43153.        (A -> ((B -> (C or B)) and (((D and E) -> D) or F))), M:tm-1, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-43154
in-theory        43154
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43154.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-550, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43155
in-theory        43155
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43155.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-540, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43156
in-theory        43156
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43156.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-530, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43157
in-theory        43157
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43157.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-520, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43158
in-theory        43158
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43158.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-510, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43159
in-theory        43159
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43159.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-500, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43160
in-theory        43160
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43160.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G and H) -> H) or I))), M:tm-490, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43161
in-theory        43161
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43161.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-480, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43162
in-theory        43162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43162.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-469, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43163
in-theory        43163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43163.        (((A -> (B or A)) and (((C and D) -> D) or E)) and (F -> (F or G))), M:tm-456, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43164
in-theory        43164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43164.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-453, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43165
in-theory        43165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and ((F -> (F or G)) and ((A -> (B or A)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43165.        (((A -> (B or A)) and (((C and D) -> D) or E)) and ((F -> (F or G)) and ((A -> (B or A)) and (((C and D) -> D) or E)))), M:tm-443, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43166
in-theory        43166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43166.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-409, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43167
in-theory        43167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43167.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-400, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43168
in-theory        43168
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43168.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-391, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43169
in-theory        43169
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43169.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-382, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43170
in-theory        43170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43170.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G and H) -> H) or I))), M:tm-373, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43171
in-theory        43171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43171.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-364, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43172
in-theory        43172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43172.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-354, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43173
in-theory        43173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43173.        (((A -> (B or A)) and (((C and D) -> D) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43174
in-theory        43174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43174.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E and F) -> F) or G))), M:tm-338, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43175
in-theory        43175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C and D) -> D) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43175.        (((A -> (B or A)) and (((C and D) -> D) or E)) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C and D) -> D) or E)))), M:tm-327, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43176
in-theory        43176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and (((F and G) -> G) and ((A -> (B or A)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43176.        (((A -> (B or A)) and (((C and D) -> D) or E)) and (((F and G) -> G) and ((A -> (B or A)) and (((C and D) -> D) or E)))), M:tm-326, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43177
in-theory        43177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and (((F and G) -> F) and ((A -> (B or A)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43177.        (((A -> (B or A)) and (((C and D) -> D) or E)) and (((F and G) -> F) and ((A -> (B or A)) and (((C and D) -> D) or E)))), M:tm-325, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43178
in-theory        43178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C and D) -> D) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43178.        (((A -> (B or A)) and (((C and D) -> D) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C and D) -> D) or E)))), M:tm-324, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43179
in-theory        43179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43179.        (((A -> (B or A)) and (((C and D) -> D) or E)) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C and D) -> D) or E)))), M:tm-323, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43180
in-theory        43180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43180.        (((A -> (B or A)) and (((C and D) -> D) or E)) and ((F and G) -> G)), M:tm-322, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43181
in-theory        43181
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43181.        (((A -> (B or A)) and (((C and D) -> D) or E)) and ((F and G) -> F)), M:tm-320, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43182
in-theory        43182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43182.        (((A -> (B or A)) and (((C and D) -> D) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43183
in-theory        43183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43183.        (((A -> (B or A)) and (((C and D) -> D) or E)) and (F -> (G -> F))), M:tm-315, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43184
in-theory        43184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and (F or ((A -> (B or A)) and (((C and D) -> D) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43184.        (((A -> (B or A)) and (((C and D) -> D) or E)) and (F or ((A -> (B or A)) and (((C and D) -> D) or E)))), M:tm-311, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43185
in-theory        43185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and (((A -> (B or A)) and (((C and D) -> D) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43185.        (((A -> (B or A)) and (((C and D) -> D) or E)) and (((A -> (B or A)) and (((C and D) -> D) or E)) or F)), M:tm-310, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43186
in-theory        43186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and (F -> (((A -> (B or A)) and (((C and D) -> D) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43186.        (((A -> (B or A)) and (((C and D) -> D) or E)) and (F -> (((A -> (B or A)) and (((C and D) -> D) or E)) and F))), M:tm-309, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43187
in-theory        43187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and (((C and D) -> D) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-580 ((A (-> Am (or Bm Am))) (B (or (-> (and Cm Dm) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43187.        (((A -> (B or A)) and (((C and D) -> D) or E)) and (((C and D) -> D) or E)), M:tm-308, m:tm-580, u:((A (-> Am (or Bm Am))) (B (or (-> (and Cm Dm) Dm) Em)))
================================================================
tm-name          tm-43188
in-theory        43188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-580 ((A (-> Am (or Bm Am))) (B (or (-> (and Cm Dm) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43188.        (((A -> (B or A)) and (((C and D) -> D) or E)) and (A -> (B or A))), M:tm-307, m:tm-580, u:((A (-> Am (or Bm Am))) (B (or (-> (and Cm Dm) Dm) Em)))
================================================================
tm-name          tm-43189
in-theory        43189
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and (F -> ((A -> (B or A)) and (((C and D) -> D) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43189.        (((A -> (B or A)) and (((C and D) -> D) or E)) and (F -> ((A -> (B or A)) and (((C and D) -> D) or E)))), M:tm-305, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43190
in-theory        43190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43190.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-303, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43191
in-theory        43191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43191.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-270, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43192
in-theory        43192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43192.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-239, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43193
in-theory        43193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43193.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G and H) -> H) or I))), M:tm-210, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43194
in-theory        43194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43194.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-183, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43195
in-theory        43195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43195.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-157, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43196
in-theory        43196
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43196.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-147, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43197
in-theory        43197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43197.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-134, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43198
in-theory        43198
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43198.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-125, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43199
in-theory        43199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43199.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G and H) -> H) or I))), M:tm-113, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43200
in-theory        43200
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43200.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-105, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43201
in-theory        43201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43201.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E and F) -> F) or G))), M:tm-95, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43202
in-theory        43202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43202.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-83, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43203
in-theory        43203
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (((D and E) -> E) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43203.        (((not (not A)) -> A) and ((B -> (C or B)) and (((D and E) -> E) or F))), M:tm-76, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43204
in-theory        43204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E and F) -> F) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43204.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E and F) -> F) or G))), M:tm-69, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43205
in-theory        43205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43205.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-54, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43206
in-theory        43206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43206.        ((A -> (B or A)) and ((C -> (D or C)) and (((E and F) -> F) or G))), M:tm-42, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43207
in-theory        43207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43207.        ((A -> (A or B)) and ((C -> (D or C)) and (((E and F) -> F) or G))), M:tm-32, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43208
in-theory        43208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43208.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E and F) -> F) or G))), M:tm-23, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43209
in-theory        43209
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43209.        (((A and B) -> B) and ((C -> (D or C)) and (((E and F) -> F) or G))), M:tm-22, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43210
in-theory        43210
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43210.        (((A and B) -> A) and ((C -> (D or C)) and (((E and F) -> F) or G))), M:tm-21, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43211
in-theory        43211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43211.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-20, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43212
in-theory        43212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43212.        ((A -> (B -> A)) and ((C -> (D or C)) and (((E and F) -> F) or G))), M:tm-19, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43213
in-theory        43213
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-7 tm-5 tm-6 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43213.        (A or ((B -> (C or B)) and (((D and E) -> E) or F))), M:tm-7, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43214
in-theory        43214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-6 tm-5 tm-7 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43214.        (((A -> (B or A)) and (((C and D) -> D) or E)) or F), M:tm-6, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43215
in-theory        43215
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (((D and E) -> E) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43215.        (A -> (((B -> (C or B)) and (((D and E) -> E) or F)) and A)), M:tm-5, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43216
in-theory        43216
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (((D and E) -> E) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-1 tm-5 tm-7 tm-6 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-43216.        (A -> ((B -> (C or B)) and (((D and E) -> E) or F))), M:tm-1, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-43217
in-theory        43217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-550 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43217.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-550, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43218
in-theory        43218
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-540 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43218.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-540, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43219
in-theory        43219
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-530 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43219.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-530, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43220
in-theory        43220
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-520 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43220.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-520, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43221
in-theory        43221
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-510 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43221.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-510, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43222
in-theory        43222
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-500 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43222.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-500, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43223
in-theory        43223
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-490 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43223.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I))), M:tm-490, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43224
in-theory        43224
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-480 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43224.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-480, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43225
in-theory        43225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-469 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43225.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-469, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43226
in-theory        43226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43226.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (F -> (F or G))), M:tm-456, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43227
in-theory        43227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-453 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43227.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-453, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43228
in-theory        43228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-443 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43228.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)))), M:tm-443, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43229
in-theory        43229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-409 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43229.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-409, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43230
in-theory        43230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-400 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43230.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-400, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43231
in-theory        43231
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-391 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43231.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-391, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43232
in-theory        43232
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-382 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43232.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-382, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43233
in-theory        43233
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-373 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43233.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I))), M:tm-373, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43234
in-theory        43234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-364 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43234.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-364, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43235
in-theory        43235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-354 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43235.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-354, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43236
in-theory        43236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43236.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43237
in-theory        43237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-338 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43237.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G))), M:tm-338, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43238
in-theory        43238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     39
proof            (modus-ponens tm-327 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43238.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)))), M:tm-327, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43239
in-theory        43239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-326 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43239.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)))), M:tm-326, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43240
in-theory        43240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-325 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43240.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)))), M:tm-325, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43241
in-theory        43241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     45
proof            (modus-ponens tm-324 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43241.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)))), M:tm-324, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43242
in-theory        43242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-323 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43242.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)))), M:tm-323, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43243
in-theory        43243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43243.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> G)), M:tm-322, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43244
in-theory        43244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43244.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((F and G) -> F)), M:tm-320, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43245
in-theory        43245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43245.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43246
in-theory        43246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43246.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (F -> (G -> F))), M:tm-315, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43247
in-theory        43247
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (F or ((A -> (B or A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     33
proof            (modus-ponens tm-311 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43247.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (F or ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)))), M:tm-311, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43248
in-theory        43248
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43248.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) or F)), M:tm-310, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43249
in-theory        43249
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (F -> (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43249.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (F -> (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and F))), M:tm-309, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43250
in-theory        43250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((C -> (D -> (C and D))) or E))
theorem-size     25
proof            (modus-ponens tm-308 tm-581 ((A (-> Am (or Bm Am))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43250.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((C -> (D -> (C and D))) or E)), M:tm-308, m:tm-581, u:((A (-> Am (or Bm Am))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em)))
================================================================
tm-name          tm-43251
in-theory        43251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (A -> (B or A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-581 ((A (-> Am (or Bm Am))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43251.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (A -> (B or A))), M:tm-307, m:tm-581, u:((A (-> Am (or Bm Am))) (B (or (-> Cm (-> Dm (and Cm Dm))) Em)))
================================================================
tm-name          tm-43252
in-theory        43252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (F -> ((A -> (B or A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     33
proof            (modus-ponens tm-305 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43252.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (F -> ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)))), M:tm-305, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43253
in-theory        43253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-303 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43253.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-303, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43254
in-theory        43254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-270 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43254.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-270, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43255
in-theory        43255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-239 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43255.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-239, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43256
in-theory        43256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-210 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43256.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I))), M:tm-210, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43257
in-theory        43257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-183 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43257.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-183, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43258
in-theory        43258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-157 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43258.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-157, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43259
in-theory        43259
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-147 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43259.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-147, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43260
in-theory        43260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-134 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43260.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-134, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43261
in-theory        43261
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-125 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43261.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-125, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43262
in-theory        43262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-113 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43262.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I))), M:tm-113, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43263
in-theory        43263
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     35
proof            (modus-ponens tm-105 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43263.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-105, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43264
in-theory        43264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-95 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43264.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G))), M:tm-95, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43265
in-theory        43265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-83 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43265.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-83, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43266
in-theory        43266
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> (E -> (D and E))) or F)))
theorem-size     21
proof            (modus-ponens tm-76 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43266.        (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> (E -> (D and E))) or F))), M:tm-76, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43267
in-theory        43267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     27
proof            (modus-ponens tm-69 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43267.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G))), M:tm-69, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43268
in-theory        43268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-54 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43268.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-54, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43269
in-theory        43269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-42 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43269.        ((A -> (B or A)) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G))), M:tm-42, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43270
in-theory        43270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-32 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43270.        ((A -> (A or B)) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G))), M:tm-32, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43271
in-theory        43271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-23 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43271.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G))), M:tm-23, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43272
in-theory        43272
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-22 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43272.        (((A and B) -> B) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G))), M:tm-22, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43273
in-theory        43273
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-21 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43273.        (((A and B) -> A) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G))), M:tm-21, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43274
in-theory        43274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-20 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43274.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-20, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43275
in-theory        43275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-19 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43275.        ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> (F -> (E and F))) or G))), M:tm-19, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43276
in-theory        43276
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-7 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43276.        (A or ((B -> (C or B)) and ((D -> (E -> (D and E))) or F))), M:tm-7, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43277
in-theory        43277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43277.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) or F), M:tm-6, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43278
in-theory        43278
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((D -> (E -> (D and E))) or F)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43278.        (A -> (((B -> (C or B)) and ((D -> (E -> (D and E))) or F)) and A)), M:tm-5, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43279
in-theory        43279
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((D -> (E -> (D and E))) or F)))
theorem-size     17
proof            (modus-ponens tm-1 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-1 tm-5 tm-7 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-43279.        (A -> ((B -> (C or B)) and ((D -> (E -> (D and E))) or F))), M:tm-1, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-43280
in-theory        43280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43280.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-550, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43281
in-theory        43281
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43281.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-540, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43282
in-theory        43282
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43282.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-530, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43283
in-theory        43283
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43283.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-520, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43284
in-theory        43284
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43284.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-510, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43285
in-theory        43285
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43285.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-500, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43286
in-theory        43286
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43286.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (G or H)) or I))), M:tm-490, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43287
in-theory        43287
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43287.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-480, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43288
in-theory        43288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43288.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-469, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43289
in-theory        43289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43289.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and (F -> (F or G))), M:tm-456, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43290
in-theory        43290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43290.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-453, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43291
in-theory        43291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43291.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> (C or D)) or E)))), M:tm-443, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43292
in-theory        43292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43292.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-409, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43293
in-theory        43293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43293.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-400, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43294
in-theory        43294
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43294.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-391, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43295
in-theory        43295
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43295.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-382, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43296
in-theory        43296
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43296.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> (G or H)) or I))), M:tm-373, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43297
in-theory        43297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43297.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-364, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43298
in-theory        43298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43298.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-354, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43299
in-theory        43299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43299.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43300
in-theory        43300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43300.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> (E or F)) or G))), M:tm-338, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43301
in-theory        43301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> (C or D)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43301.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> (C or D)) or E)))), M:tm-327, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43302
in-theory        43302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43302.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> (C or D)) or E)))), M:tm-326, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43303
in-theory        43303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43303.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> (C or D)) or E)))), M:tm-325, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43304
in-theory        43304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> (C or D)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43304.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> (C or D)) or E)))), M:tm-324, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43305
in-theory        43305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43305.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> (C or D)) or E)))), M:tm-323, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43306
in-theory        43306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43306.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43307
in-theory        43307
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43307.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43308
in-theory        43308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43308.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43309
in-theory        43309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43309.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43310
in-theory        43310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and (F or ((A -> (B or A)) and ((C -> (C or D)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43310.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and (F or ((A -> (B or A)) and ((C -> (C or D)) or E)))), M:tm-311, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43311
in-theory        43311
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and (((A -> (B or A)) and ((C -> (C or D)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43311.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and (((A -> (B or A)) and ((C -> (C or D)) or E)) or F)), M:tm-310, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43312
in-theory        43312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and (F -> (((A -> (B or A)) and ((C -> (C or D)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43312.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and (F -> (((A -> (B or A)) and ((C -> (C or D)) or E)) and F))), M:tm-309, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43313
in-theory        43313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((C -> (C or D)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-582 ((A (-> Am (or Bm Am))) (B (or (-> Cm (or Cm Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43313.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((C -> (C or D)) or E)), M:tm-308, m:tm-582, u:((A (-> Am (or Bm Am))) (B (or (-> Cm (or Cm Dm)) Em)))
================================================================
tm-name          tm-43314
in-theory        43314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-582 ((A (-> Am (or Bm Am))) (B (or (-> Cm (or Cm Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43314.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and (A -> (B or A))), M:tm-307, m:tm-582, u:((A (-> Am (or Bm Am))) (B (or (-> Cm (or Cm Dm)) Em)))
================================================================
tm-name          tm-43315
in-theory        43315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and (F -> ((A -> (B or A)) and ((C -> (C or D)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43315.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and (F -> ((A -> (B or A)) and ((C -> (C or D)) or E)))), M:tm-305, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43316
in-theory        43316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43316.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-303, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43317
in-theory        43317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43317.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-270, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43318
in-theory        43318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43318.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-239, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43319
in-theory        43319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43319.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> (G or H)) or I))), M:tm-210, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43320
in-theory        43320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43320.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-183, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43321
in-theory        43321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43321.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-157, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43322
in-theory        43322
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43322.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-147, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43323
in-theory        43323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43323.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-134, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43324
in-theory        43324
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43324.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-125, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43325
in-theory        43325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43325.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (G or H)) or I))), M:tm-113, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43326
in-theory        43326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43326.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-105, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43327
in-theory        43327
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43327.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> (E or F)) or G))), M:tm-95, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43328
in-theory        43328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43328.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-83, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43329
in-theory        43329
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> (D or E)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43329.        (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> (D or E)) or F))), M:tm-76, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43330
in-theory        43330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> (E or F)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43330.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> (E or F)) or G))), M:tm-69, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43331
in-theory        43331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43331.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-54, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43332
in-theory        43332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43332.        ((A -> (B or A)) and ((C -> (D or C)) and ((E -> (E or F)) or G))), M:tm-42, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43333
in-theory        43333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43333.        ((A -> (A or B)) and ((C -> (D or C)) and ((E -> (E or F)) or G))), M:tm-32, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43334
in-theory        43334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43334.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> (E or F)) or G))), M:tm-23, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43335
in-theory        43335
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43335.        (((A and B) -> B) and ((C -> (D or C)) and ((E -> (E or F)) or G))), M:tm-22, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43336
in-theory        43336
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43336.        (((A and B) -> A) and ((C -> (D or C)) and ((E -> (E or F)) or G))), M:tm-21, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43337
in-theory        43337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43337.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-20, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43338
in-theory        43338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43338.        ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> (E or F)) or G))), M:tm-19, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43339
in-theory        43339
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43339.        (A or ((B -> (C or B)) and ((D -> (D or E)) or F))), M:tm-7, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43340
in-theory        43340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43340.        (((A -> (B or A)) and ((C -> (C or D)) or E)) or F), M:tm-6, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43341
in-theory        43341
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((D -> (D or E)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43341.        (A -> (((B -> (C or B)) and ((D -> (D or E)) or F)) and A)), M:tm-5, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43342
in-theory        43342
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((D -> (D or E)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-1 tm-5 tm-7 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-43342.        (A -> ((B -> (C or B)) and ((D -> (D or E)) or F))), M:tm-1, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-43343
in-theory        43343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43343.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-550, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43344
in-theory        43344
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43344.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-540, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43345
in-theory        43345
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43345.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-530, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43346
in-theory        43346
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43346.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-520, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43347
in-theory        43347
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43347.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-510, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43348
in-theory        43348
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43348.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-500, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43349
in-theory        43349
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43349.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G)))), M:tm-490, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43350
in-theory        43350
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43350.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-480, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43351
in-theory        43351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43351.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-469, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43352
in-theory        43352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43352.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (F -> (F or G))), M:tm-456, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43353
in-theory        43353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43353.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-453, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43354
in-theory        43354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43354.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))))), M:tm-443, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43355
in-theory        43355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43355.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-409, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43356
in-theory        43356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43356.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-400, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43357
in-theory        43357
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43357.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-391, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43358
in-theory        43358
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43358.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-382, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43359
in-theory        43359
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43359.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G)))), M:tm-373, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43360
in-theory        43360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43360.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-364, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43361
in-theory        43361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43361.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-354, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43362
in-theory        43362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43362.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43363
in-theory        43363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43363.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E)))), M:tm-338, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43364
in-theory        43364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43364.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))))), M:tm-327, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43365
in-theory        43365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43365.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))))), M:tm-326, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43366
in-theory        43366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43366.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))))), M:tm-325, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43367
in-theory        43367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43367.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))))), M:tm-324, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43368
in-theory        43368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43368.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))))), M:tm-323, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43369
in-theory        43369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43369.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43370
in-theory        43370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43370.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43371
in-theory        43371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43371.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43372
in-theory        43372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43372.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43373
in-theory        43373
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (F or ((A -> (B or A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43373.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (F or ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))))), M:tm-311, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43374
in-theory        43374
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43374.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) or F)), M:tm-310, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43375
in-theory        43375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (F -> (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43375.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (F -> (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and F))), M:tm-309, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43376
in-theory        43376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (C -> ((D -> (D or E)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-583 ((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43376.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (C -> ((D -> (D or E)) and C))), M:tm-308, m:tm-583, u:((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm))))
================================================================
tm-name          tm-43377
in-theory        43377
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (A -> (B or A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-583 ((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43377.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (A -> (B or A))), M:tm-307, m:tm-583, u:((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (or Dm Em)) Cm))))
================================================================
tm-name          tm-43378
in-theory        43378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (F -> ((A -> (B or A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43378.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (F -> ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))))), M:tm-305, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43379
in-theory        43379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43379.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-303, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43380
in-theory        43380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43380.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-270, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43381
in-theory        43381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43381.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-239, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43382
in-theory        43382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43382.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G)))), M:tm-210, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43383
in-theory        43383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43383.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-183, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43384
in-theory        43384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43384.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-157, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43385
in-theory        43385
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43385.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-147, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43386
in-theory        43386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43386.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-134, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43387
in-theory        43387
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43387.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-125, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43388
in-theory        43388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43388.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G)))), M:tm-113, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43389
in-theory        43389
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43389.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-105, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43390
in-theory        43390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43390.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E)))), M:tm-95, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43391
in-theory        43391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43391.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-83, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43392
in-theory        43392
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43392.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> ((E -> (E or F)) and D)))), M:tm-76, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43393
in-theory        43393
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43393.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E)))), M:tm-69, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43394
in-theory        43394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43394.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-54, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43395
in-theory        43395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43395.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E)))), M:tm-42, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43396
in-theory        43396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43396.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E)))), M:tm-32, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43397
in-theory        43397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43397.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E)))), M:tm-23, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43398
in-theory        43398
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43398.        (((A and B) -> B) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E)))), M:tm-22, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43399
in-theory        43399
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43399.        (((A and B) -> A) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E)))), M:tm-21, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43400
in-theory        43400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43400.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-20, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43401
in-theory        43401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43401.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> ((F -> (F or G)) and E)))), M:tm-19, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43402
in-theory        43402
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43402.        (A or ((B -> (C or B)) and (D -> ((E -> (E or F)) and D)))), M:tm-7, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43403
in-theory        43403
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43403.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) or F), M:tm-6, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43404
in-theory        43404
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> ((E -> (E or F)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43404.        (A -> (((B -> (C or B)) and (D -> ((E -> (E or F)) and D))) and A)), M:tm-5, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43405
in-theory        43405
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> ((E -> (E or F)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-43405.        (A -> ((B -> (C or B)) and (D -> ((E -> (E or F)) and D)))), M:tm-1, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-43406
in-theory        43406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43406.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-550, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43407
in-theory        43407
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43407.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-540, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43408
in-theory        43408
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43408.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-530, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43409
in-theory        43409
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43409.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-520, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43410
in-theory        43410
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43410.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-510, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43411
in-theory        43411
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43411.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-500, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43412
in-theory        43412
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43412.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (H or I))))), M:tm-490, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43413
in-theory        43413
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43413.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-480, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43414
in-theory        43414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43414.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-469, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43415
in-theory        43415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43415.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and (F -> (F or G))), M:tm-456, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43416
in-theory        43416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43416.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-453, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43417
in-theory        43417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43417.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> (D -> (D or E)))))), M:tm-443, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43418
in-theory        43418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43418.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-409, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43419
in-theory        43419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43419.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-400, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43420
in-theory        43420
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43420.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-391, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43421
in-theory        43421
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43421.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-382, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43422
in-theory        43422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43422.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (H or I))))), M:tm-373, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43423
in-theory        43423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43423.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-364, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43424
in-theory        43424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43424.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-354, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43425
in-theory        43425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43425.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43426
in-theory        43426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43426.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (F or G))))), M:tm-338, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43427
in-theory        43427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> (D -> (D or E))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43427.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> (D -> (D or E)))))), M:tm-327, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43428
in-theory        43428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43428.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> (D -> (D or E)))))), M:tm-326, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43429
in-theory        43429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43429.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> (D -> (D or E)))))), M:tm-325, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43430
in-theory        43430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> (D -> (D or E))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43430.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> (D -> (D or E)))))), M:tm-324, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43431
in-theory        43431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43431.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> (D -> (D or E)))))), M:tm-323, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43432
in-theory        43432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43432.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and ((F and G) -> G)), M:tm-322, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43433
in-theory        43433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43433.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and ((F and G) -> F)), M:tm-320, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43434
in-theory        43434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43434.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43435
in-theory        43435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43435.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and (F -> (G -> F))), M:tm-315, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43436
in-theory        43436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and (F or ((A -> (B or A)) and (C -> (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43436.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and (F or ((A -> (B or A)) and (C -> (D -> (D or E)))))), M:tm-311, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43437
in-theory        43437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and (((A -> (B or A)) and (C -> (D -> (D or E)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43437.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and (((A -> (B or A)) and (C -> (D -> (D or E)))) or F)), M:tm-310, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43438
in-theory        43438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and (F -> (((A -> (B or A)) and (C -> (D -> (D or E)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43438.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and (F -> (((A -> (B or A)) and (C -> (D -> (D or E)))) and F))), M:tm-309, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43439
in-theory        43439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and (C -> (D -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-308 tm-584 ((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43439.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and (C -> (D -> (D or E)))), M:tm-308, m:tm-584, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-43440
in-theory        43440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-584 ((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43440.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and (A -> (B or A))), M:tm-307, m:tm-584, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-43441
in-theory        43441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and (F -> ((A -> (B or A)) and (C -> (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43441.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and (F -> ((A -> (B or A)) and (C -> (D -> (D or E)))))), M:tm-305, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43442
in-theory        43442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43442.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-303, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43443
in-theory        43443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43443.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-270, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43444
in-theory        43444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43444.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-239, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43445
in-theory        43445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43445.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (H -> (H or I))))), M:tm-210, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43446
in-theory        43446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43446.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-183, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43447
in-theory        43447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43447.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-157, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43448
in-theory        43448
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43448.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-147, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43449
in-theory        43449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43449.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-134, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43450
in-theory        43450
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43450.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-125, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43451
in-theory        43451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43451.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (H or I))))), M:tm-113, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43452
in-theory        43452
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43452.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-105, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43453
in-theory        43453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43453.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (F -> (F or G))))), M:tm-95, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43454
in-theory        43454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43454.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-83, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43455
in-theory        43455
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43455.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (E -> (E or F))))), M:tm-76, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43456
in-theory        43456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43456.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (F -> (F or G))))), M:tm-69, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43457
in-theory        43457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43457.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-54, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43458
in-theory        43458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43458.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> (F -> (F or G))))), M:tm-42, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43459
in-theory        43459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43459.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> (F -> (F or G))))), M:tm-32, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43460
in-theory        43460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43460.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (F or G))))), M:tm-23, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43461
in-theory        43461
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43461.        (((A and B) -> B) and ((C -> (D or C)) and (E -> (F -> (F or G))))), M:tm-22, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43462
in-theory        43462
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43462.        (((A and B) -> A) and ((C -> (D or C)) and (E -> (F -> (F or G))))), M:tm-21, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43463
in-theory        43463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43463.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-20, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43464
in-theory        43464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43464.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (F -> (F or G))))), M:tm-19, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43465
in-theory        43465
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-1 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43465.        (A or ((B -> (C or B)) and (D -> (E -> (E or F))))), M:tm-7, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43466
in-theory        43466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-7 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43466.        (((A -> (B or A)) and (C -> (D -> (D or E)))) or F), M:tm-6, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43467
in-theory        43467
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> (E -> (E or F)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43467.        (A -> (((B -> (C or B)) and (D -> (E -> (E or F)))) and A)), M:tm-5, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43468
in-theory        43468
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-7 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-43468.        (A -> ((B -> (C or B)) and (D -> (E -> (E or F))))), M:tm-1, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43469
in-theory        43469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43469.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-550, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43470
in-theory        43470
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43470.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-540, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43471
in-theory        43471
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43471.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-530, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43472
in-theory        43472
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43472.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-520, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43473
in-theory        43473
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43473.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-510, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43474
in-theory        43474
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43474.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-500, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43475
in-theory        43475
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43475.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (I -> H))))), M:tm-490, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43476
in-theory        43476
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43476.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-480, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43477
in-theory        43477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43477.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-469, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43478
in-theory        43478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43478.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and (F -> (F or G))), M:tm-456, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43479
in-theory        43479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43479.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-453, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43480
in-theory        43480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (B or A)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43480.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and ((F -> (F or G)) and ((A -> (B or A)) and (C or (D -> (E -> D)))))), M:tm-443, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43481
in-theory        43481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43481.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-409, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43482
in-theory        43482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43482.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-400, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43483
in-theory        43483
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43483.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-391, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43484
in-theory        43484
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43484.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-382, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43485
in-theory        43485
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43485.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or (H -> (I -> H))))), M:tm-373, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43486
in-theory        43486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43486.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-364, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43487
in-theory        43487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43487.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-354, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43488
in-theory        43488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43488.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43489
in-theory        43489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43489.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or (F -> (G -> F))))), M:tm-338, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43490
in-theory        43490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C or (D -> (E -> D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43490.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C or (D -> (E -> D)))))), M:tm-327, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43491
in-theory        43491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (B or A)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43491.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and (((F and G) -> G) and ((A -> (B or A)) and (C or (D -> (E -> D)))))), M:tm-326, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43492
in-theory        43492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (B or A)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43492.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and (((F and G) -> F) and ((A -> (B or A)) and (C or (D -> (E -> D)))))), M:tm-325, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43493
in-theory        43493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C or (D -> (E -> D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43493.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C or (D -> (E -> D)))))), M:tm-324, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43494
in-theory        43494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43494.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C or (D -> (E -> D)))))), M:tm-323, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43495
in-theory        43495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43495.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and ((F and G) -> G)), M:tm-322, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43496
in-theory        43496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43496.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and ((F and G) -> F)), M:tm-320, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43497
in-theory        43497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43497.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43498
in-theory        43498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43498.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and (F -> (G -> F))), M:tm-315, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43499
in-theory        43499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and (F or ((A -> (B or A)) and (C or (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43499.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and (F or ((A -> (B or A)) and (C or (D -> (E -> D)))))), M:tm-311, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43500
in-theory        43500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and (((A -> (B or A)) and (C or (D -> (E -> D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43500.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and (((A -> (B or A)) and (C or (D -> (E -> D)))) or F)), M:tm-310, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43501
in-theory        43501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and (F -> (((A -> (B or A)) and (C or (D -> (E -> D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43501.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and (F -> (((A -> (B or A)) and (C or (D -> (E -> D)))) and F))), M:tm-309, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43502
in-theory        43502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and (C or (D -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-585 ((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43502.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and (C or (D -> (E -> D)))), M:tm-308, m:tm-585, u:((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-43503
in-theory        43503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-585 ((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43503.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and (A -> (B or A))), M:tm-307, m:tm-585, u:((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-43504
in-theory        43504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and (F -> ((A -> (B or A)) and (C or (D -> (E -> D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43504.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and (F -> ((A -> (B or A)) and (C or (D -> (E -> D)))))), M:tm-305, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43505
in-theory        43505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43505.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-303, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43506
in-theory        43506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43506.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-270, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43507
in-theory        43507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43507.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-239, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43508
in-theory        43508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43508.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or (H -> (I -> H))))), M:tm-210, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43509
in-theory        43509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43509.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-183, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43510
in-theory        43510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43510.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-157, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43511
in-theory        43511
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43511.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-147, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43512
in-theory        43512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43512.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-134, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43513
in-theory        43513
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43513.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-125, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43514
in-theory        43514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43514.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (I -> H))))), M:tm-113, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43515
in-theory        43515
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43515.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-105, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43516
in-theory        43516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43516.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or (F -> (G -> F))))), M:tm-95, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43517
in-theory        43517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43517.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-83, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43518
in-theory        43518
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D or (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43518.        (((not (not A)) -> A) and ((B -> (C or B)) and (D or (E -> (F -> E))))), M:tm-76, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43519
in-theory        43519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or (F -> (G -> F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43519.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or (F -> (G -> F))))), M:tm-69, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43520
in-theory        43520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43520.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-54, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43521
in-theory        43521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43521.        ((A -> (B or A)) and ((C -> (D or C)) and (E or (F -> (G -> F))))), M:tm-42, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43522
in-theory        43522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43522.        ((A -> (A or B)) and ((C -> (D or C)) and (E or (F -> (G -> F))))), M:tm-32, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43523
in-theory        43523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43523.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or (F -> (G -> F))))), M:tm-23, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43524
in-theory        43524
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43524.        (((A and B) -> B) and ((C -> (D or C)) and (E or (F -> (G -> F))))), M:tm-22, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43525
in-theory        43525
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43525.        (((A and B) -> A) and ((C -> (D or C)) and (E or (F -> (G -> F))))), M:tm-21, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43526
in-theory        43526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43526.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-20, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43527
in-theory        43527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43527.        ((A -> (B -> A)) and ((C -> (D or C)) and (E or (F -> (G -> F))))), M:tm-19, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43528
in-theory        43528
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43528.        (A or ((B -> (C or B)) and (D or (E -> (F -> E))))), M:tm-7, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43529
in-theory        43529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-7 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43529.        (((A -> (B or A)) and (C or (D -> (E -> D)))) or F), M:tm-6, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43530
in-theory        43530
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D or (E -> (F -> E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43530.        (A -> (((B -> (C or B)) and (D or (E -> (F -> E)))) and A)), M:tm-5, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43531
in-theory        43531
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D or (E -> (F -> E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43531.        (A -> ((B -> (C or B)) and (D or (E -> (F -> E))))), M:tm-1, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-43532
in-theory        43532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-550 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43532.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-550, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43533
in-theory        43533
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-540 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43533.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-540, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43534
in-theory        43534
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-530 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43534.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-530, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43535
in-theory        43535
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-520 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43535.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-520, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43536
in-theory        43536
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-510 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43536.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-510, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43537
in-theory        43537
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-500 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43537.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-500, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43538
in-theory        43538
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-490 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43538.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-490, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43539
in-theory        43539
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-480 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43539.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-480, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43540
in-theory        43540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-469 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43540.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-469, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43541
in-theory        43541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43541.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (G or H))), M:tm-456, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43542
in-theory        43542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-453 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43542.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-453, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43543
in-theory        43543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43543.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (G or H)) and ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-443, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43544
in-theory        43544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-409 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43544.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-409, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43545
in-theory        43545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-400 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43545.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-400, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43546
in-theory        43546
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-391 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43546.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-391, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43547
in-theory        43547
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-382 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43547.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-382, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43548
in-theory        43548
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-373 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43548.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-373, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43549
in-theory        43549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-364 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43549.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-364, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43550
in-theory        43550
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-354 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43550.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-354, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43551
in-theory        43551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43551.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43552
in-theory        43552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-338 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43552.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-338, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43553
in-theory        43553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43553.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-327, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43554
in-theory        43554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43554.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> H) and ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-326, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43555
in-theory        43555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43555.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G and H) -> G) and ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-325, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43556
in-theory        43556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43556.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-324, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43557
in-theory        43557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43557.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> G)) and ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-323, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43558
in-theory        43558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43558.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> H)), M:tm-322, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43559
in-theory        43559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43559.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G and H) -> G)), M:tm-320, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43560
in-theory        43560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43560.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43561
in-theory        43561
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43561.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H -> G))), M:tm-315, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43562
in-theory        43562
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43562.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G or ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-311, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43563
in-theory        43563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43563.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)), M:tm-310, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43564
in-theory        43564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43564.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and G))), M:tm-309, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43565
in-theory        43565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-308 tm-586 ((A (-> Am (or Bm Am))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43565.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-308, m:tm-586, u:((A (-> Am (or Bm Am))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-43566
in-theory        43566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (B or A)))
theorem-size     27
proof            (modus-ponens tm-307 tm-586 ((A (-> Am (or Bm Am))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43566.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (A -> (B or A))), M:tm-307, m:tm-586, u:((A (-> Am (or Bm Am))) (B (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-43567
in-theory        43567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43567.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-305, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43568
in-theory        43568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-303 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43568.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-303, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43569
in-theory        43569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-270 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43569.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-270, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43570
in-theory        43570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-239 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43570.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-239, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43571
in-theory        43571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-210 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43571.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-210, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43572
in-theory        43572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-183 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43572.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-183, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43573
in-theory        43573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-157 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43573.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-157, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43574
in-theory        43574
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-147 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43574.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-147, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43575
in-theory        43575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-134 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43575.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-134, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43576
in-theory        43576
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-125 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43576.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-125, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43577
in-theory        43577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-113 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43577.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-113, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43578
in-theory        43578
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     41
proof            (modus-ponens tm-105 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43578.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-105, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43579
in-theory        43579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-95 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43579.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-95, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43580
in-theory        43580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-83 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43580.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-83, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43581
in-theory        43581
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-76 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-10 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43581.        (((not (not A)) -> A) and ((B -> (C or B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-76, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43582
in-theory        43582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     33
proof            (modus-ponens tm-69 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-9 tm-7 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43582.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-69, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43583
in-theory        43583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-54 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43583.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-54, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43584
in-theory        43584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-42 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43584.        ((A -> (B or A)) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-42, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43585
in-theory        43585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-32 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43585.        ((A -> (A or B)) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-32, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43586
in-theory        43586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-23 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43586.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-23, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43587
in-theory        43587
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-22 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-4 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43587.        (((A and B) -> B) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-22, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43588
in-theory        43588
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-21 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-3 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43588.        (((A and B) -> A) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-21, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43589
in-theory        43589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-20 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43589.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-20, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43590
in-theory        43590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-19 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43590.        ((A -> (B -> A)) and ((C -> (D or C)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-19, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43591
in-theory        43591
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-7 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43591.        (A or ((B -> (C or B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-7, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43592
in-theory        43592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-6 tm-5 tm-7 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43592.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or G), M:tm-6, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43593
in-theory        43593
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43593.        (A -> (((B -> (C or B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and A)), M:tm-5, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43594
in-theory        43594
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     23
proof            (modus-ponens tm-1 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-1 tm-5 tm-7 tm-2)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-43594.        (A -> ((B -> (C or B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-1, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-43595
in-theory        43595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-550 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43595.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-550, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43596
in-theory        43596
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-540 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43596.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-540, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43597
in-theory        43597
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-530 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43597.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-530, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43598
in-theory        43598
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-520 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43598.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-520, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43599
in-theory        43599
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-510 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43599.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-510, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43600
in-theory        43600
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-500 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43600.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-500, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43601
in-theory        43601
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-490 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43601.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H and I) -> H)))), M:tm-490, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43602
in-theory        43602
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-480 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43602.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-480, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43603
in-theory        43603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-469 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43603.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-469, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43604
in-theory        43604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43604.        (((A -> (B or A)) and (C or ((D and E) -> D))) and (F -> (F or G))), M:tm-456, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43605
in-theory        43605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-453 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43605.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-453, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43606
in-theory        43606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (B or A)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43606.        (((A -> (B or A)) and (C or ((D and E) -> D))) and ((F -> (F or G)) and ((A -> (B or A)) and (C or ((D and E) -> D))))), M:tm-443, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43607
in-theory        43607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-409 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43607.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-409, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43608
in-theory        43608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-400 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43608.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-400, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43609
in-theory        43609
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-391 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43609.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-391, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43610
in-theory        43610
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-382 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43610.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-382, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43611
in-theory        43611
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-373 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43611.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or ((H and I) -> H)))), M:tm-373, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43612
in-theory        43612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-364 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43612.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-364, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43613
in-theory        43613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-354 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43613.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-354, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43614
in-theory        43614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43614.        (((A -> (B or A)) and (C or ((D and E) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43615
in-theory        43615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-338 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43615.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or ((F and G) -> F)))), M:tm-338, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43616
in-theory        43616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C or ((D and E) -> D)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43616.        (((A -> (B or A)) and (C or ((D and E) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C or ((D and E) -> D))))), M:tm-327, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43617
in-theory        43617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and (((F and G) -> G) and ((A -> (B or A)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43617.        (((A -> (B or A)) and (C or ((D and E) -> D))) and (((F and G) -> G) and ((A -> (B or A)) and (C or ((D and E) -> D))))), M:tm-326, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43618
in-theory        43618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and (((F and G) -> F) and ((A -> (B or A)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43618.        (((A -> (B or A)) and (C or ((D and E) -> D))) and (((F and G) -> F) and ((A -> (B or A)) and (C or ((D and E) -> D))))), M:tm-325, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43619
in-theory        43619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C or ((D and E) -> D)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43619.        (((A -> (B or A)) and (C or ((D and E) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C or ((D and E) -> D))))), M:tm-324, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43620
in-theory        43620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43620.        (((A -> (B or A)) and (C or ((D and E) -> D))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C or ((D and E) -> D))))), M:tm-323, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43621
in-theory        43621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43621.        (((A -> (B or A)) and (C or ((D and E) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43622
in-theory        43622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43622.        (((A -> (B or A)) and (C or ((D and E) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43623
in-theory        43623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43623.        (((A -> (B or A)) and (C or ((D and E) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43624
in-theory        43624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43624.        (((A -> (B or A)) and (C or ((D and E) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43625
in-theory        43625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and (F or ((A -> (B or A)) and (C or ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43625.        (((A -> (B or A)) and (C or ((D and E) -> D))) and (F or ((A -> (B or A)) and (C or ((D and E) -> D))))), M:tm-311, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43626
in-theory        43626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and (((A -> (B or A)) and (C or ((D and E) -> D))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43626.        (((A -> (B or A)) and (C or ((D and E) -> D))) and (((A -> (B or A)) and (C or ((D and E) -> D))) or F)), M:tm-310, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43627
in-theory        43627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and (F -> (((A -> (B or A)) and (C or ((D and E) -> D))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43627.        (((A -> (B or A)) and (C or ((D and E) -> D))) and (F -> (((A -> (B or A)) and (C or ((D and E) -> D))) and F))), M:tm-309, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43628
in-theory        43628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and (C or ((D and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-308 tm-587 ((A (-> Am (or Bm Am))) (B (or Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43628.        (((A -> (B or A)) and (C or ((D and E) -> D))) and (C or ((D and E) -> D))), M:tm-308, m:tm-587, u:((A (-> Am (or Bm Am))) (B (or Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-43629
in-theory        43629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-587 ((A (-> Am (or Bm Am))) (B (or Cm (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43629.        (((A -> (B or A)) and (C or ((D and E) -> D))) and (A -> (B or A))), M:tm-307, m:tm-587, u:((A (-> Am (or Bm Am))) (B (or Cm (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-43630
in-theory        43630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and (F -> ((A -> (B or A)) and (C or ((D and E) -> D)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43630.        (((A -> (B or A)) and (C or ((D and E) -> D))) and (F -> ((A -> (B or A)) and (C or ((D and E) -> D))))), M:tm-305, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43631
in-theory        43631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-303 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43631.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-303, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43632
in-theory        43632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-270 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43632.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-270, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43633
in-theory        43633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-239 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43633.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-239, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43634
in-theory        43634
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-210 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43634.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or ((H and I) -> H)))), M:tm-210, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43635
in-theory        43635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-183 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43635.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-183, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43636
in-theory        43636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-157 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43636.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-157, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43637
in-theory        43637
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-147 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43637.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-147, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43638
in-theory        43638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-134 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43638.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-134, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43639
in-theory        43639
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-125 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43639.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-125, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43640
in-theory        43640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-113 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43640.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H and I) -> H)))), M:tm-113, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43641
in-theory        43641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-105 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43641.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-105, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43642
in-theory        43642
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-95 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43642.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or ((F and G) -> F)))), M:tm-95, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43643
in-theory        43643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-83 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43643.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-83, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43644
in-theory        43644
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D or ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-76 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43644.        (((not (not A)) -> A) and ((B -> (C or B)) and (D or ((E and F) -> E)))), M:tm-76, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43645
in-theory        43645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or ((F and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-69 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43645.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or ((F and G) -> F)))), M:tm-69, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43646
in-theory        43646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-54 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43646.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-54, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43647
in-theory        43647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-42 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43647.        ((A -> (B or A)) and ((C -> (D or C)) and (E or ((F and G) -> F)))), M:tm-42, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43648
in-theory        43648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-32 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43648.        ((A -> (A or B)) and ((C -> (D or C)) and (E or ((F and G) -> F)))), M:tm-32, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43649
in-theory        43649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-23 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43649.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or ((F and G) -> F)))), M:tm-23, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43650
in-theory        43650
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-22 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43650.        (((A and B) -> B) and ((C -> (D or C)) and (E or ((F and G) -> F)))), M:tm-22, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43651
in-theory        43651
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-21 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43651.        (((A and B) -> A) and ((C -> (D or C)) and (E or ((F and G) -> F)))), M:tm-21, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43652
in-theory        43652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-20 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43652.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-20, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43653
in-theory        43653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-19 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43653.        ((A -> (B -> A)) and ((C -> (D or C)) and (E or ((F and G) -> F)))), M:tm-19, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43654
in-theory        43654
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-7 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43654.        (A or ((B -> (C or B)) and (D or ((E and F) -> E)))), M:tm-7, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43655
in-theory        43655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43655.        (((A -> (B or A)) and (C or ((D and E) -> D))) or F), M:tm-6, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43656
in-theory        43656
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D or ((E and F) -> E))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43656.        (A -> (((B -> (C or B)) and (D or ((E and F) -> E))) and A)), M:tm-5, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43657
in-theory        43657
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D or ((E and F) -> E))))
theorem-size     15
proof            (modus-ponens tm-1 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-43657.        (A -> ((B -> (C or B)) and (D or ((E and F) -> E)))), M:tm-1, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-43658
in-theory        43658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-550 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43658.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-550, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43659
in-theory        43659
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-540 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43659.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-540, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43660
in-theory        43660
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-530 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43660.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-530, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43661
in-theory        43661
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-520 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43661.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-520, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43662
in-theory        43662
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-510 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43662.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-510, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43663
in-theory        43663
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-500 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43663.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-500, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43664
in-theory        43664
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-490 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43664.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H and I) -> I)))), M:tm-490, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43665
in-theory        43665
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-480 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43665.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-480, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43666
in-theory        43666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-469 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43666.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-469, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43667
in-theory        43667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43667.        (((A -> (B or A)) and (C or ((D and E) -> E))) and (F -> (F or G))), M:tm-456, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43668
in-theory        43668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-453 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43668.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-453, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43669
in-theory        43669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (B or A)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43669.        (((A -> (B or A)) and (C or ((D and E) -> E))) and ((F -> (F or G)) and ((A -> (B or A)) and (C or ((D and E) -> E))))), M:tm-443, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43670
in-theory        43670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-409 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43670.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-409, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43671
in-theory        43671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-400 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43671.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-400, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43672
in-theory        43672
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-391 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43672.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-391, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43673
in-theory        43673
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-382 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43673.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-382, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43674
in-theory        43674
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-373 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43674.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or ((H and I) -> I)))), M:tm-373, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43675
in-theory        43675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-364 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43675.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-364, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43676
in-theory        43676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-354 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43676.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-354, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43677
in-theory        43677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43677.        (((A -> (B or A)) and (C or ((D and E) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43678
in-theory        43678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-338 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43678.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or ((F and G) -> G)))), M:tm-338, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43679
in-theory        43679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C or ((D and E) -> E)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43679.        (((A -> (B or A)) and (C or ((D and E) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C or ((D and E) -> E))))), M:tm-327, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43680
in-theory        43680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and (((F and G) -> G) and ((A -> (B or A)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43680.        (((A -> (B or A)) and (C or ((D and E) -> E))) and (((F and G) -> G) and ((A -> (B or A)) and (C or ((D and E) -> E))))), M:tm-326, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43681
in-theory        43681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and (((F and G) -> F) and ((A -> (B or A)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43681.        (((A -> (B or A)) and (C or ((D and E) -> E))) and (((F and G) -> F) and ((A -> (B or A)) and (C or ((D and E) -> E))))), M:tm-325, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43682
in-theory        43682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C or ((D and E) -> E)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43682.        (((A -> (B or A)) and (C or ((D and E) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C or ((D and E) -> E))))), M:tm-324, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43683
in-theory        43683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43683.        (((A -> (B or A)) and (C or ((D and E) -> E))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C or ((D and E) -> E))))), M:tm-323, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43684
in-theory        43684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43684.        (((A -> (B or A)) and (C or ((D and E) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43685
in-theory        43685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43685.        (((A -> (B or A)) and (C or ((D and E) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43686
in-theory        43686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43686.        (((A -> (B or A)) and (C or ((D and E) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43687
in-theory        43687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43687.        (((A -> (B or A)) and (C or ((D and E) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43688
in-theory        43688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and (F or ((A -> (B or A)) and (C or ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43688.        (((A -> (B or A)) and (C or ((D and E) -> E))) and (F or ((A -> (B or A)) and (C or ((D and E) -> E))))), M:tm-311, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43689
in-theory        43689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and (((A -> (B or A)) and (C or ((D and E) -> E))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43689.        (((A -> (B or A)) and (C or ((D and E) -> E))) and (((A -> (B or A)) and (C or ((D and E) -> E))) or F)), M:tm-310, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43690
in-theory        43690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and (F -> (((A -> (B or A)) and (C or ((D and E) -> E))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43690.        (((A -> (B or A)) and (C or ((D and E) -> E))) and (F -> (((A -> (B or A)) and (C or ((D and E) -> E))) and F))), M:tm-309, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43691
in-theory        43691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and (C or ((D and E) -> E)))
theorem-size     21
proof            (modus-ponens tm-308 tm-588 ((A (-> Am (or Bm Am))) (B (or Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43691.        (((A -> (B or A)) and (C or ((D and E) -> E))) and (C or ((D and E) -> E))), M:tm-308, m:tm-588, u:((A (-> Am (or Bm Am))) (B (or Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-43692
in-theory        43692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-588 ((A (-> Am (or Bm Am))) (B (or Cm (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43692.        (((A -> (B or A)) and (C or ((D and E) -> E))) and (A -> (B or A))), M:tm-307, m:tm-588, u:((A (-> Am (or Bm Am))) (B (or Cm (-> (and Dm Em) Em))))
================================================================
tm-name          tm-43693
in-theory        43693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and (F -> ((A -> (B or A)) and (C or ((D and E) -> E)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43693.        (((A -> (B or A)) and (C or ((D and E) -> E))) and (F -> ((A -> (B or A)) and (C or ((D and E) -> E))))), M:tm-305, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43694
in-theory        43694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-303 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43694.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-303, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43695
in-theory        43695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-270 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43695.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-270, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43696
in-theory        43696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-239 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43696.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-239, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43697
in-theory        43697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-210 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43697.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or ((H and I) -> I)))), M:tm-210, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43698
in-theory        43698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-183 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43698.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-183, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43699
in-theory        43699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-157 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43699.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-157, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43700
in-theory        43700
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-147 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43700.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-147, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43701
in-theory        43701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-134 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43701.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-134, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43702
in-theory        43702
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-125 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43702.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-125, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43703
in-theory        43703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-113 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43703.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or ((H and I) -> I)))), M:tm-113, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43704
in-theory        43704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     33
proof            (modus-ponens tm-105 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43704.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-105, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43705
in-theory        43705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-95 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43705.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or ((F and G) -> G)))), M:tm-95, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43706
in-theory        43706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-83 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43706.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-83, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43707
in-theory        43707
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D or ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-76 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-10 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43707.        (((not (not A)) -> A) and ((B -> (C or B)) and (D or ((E and F) -> F)))), M:tm-76, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43708
in-theory        43708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or ((F and G) -> G))))
theorem-size     25
proof            (modus-ponens tm-69 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-9 tm-7 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43708.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or ((F and G) -> G)))), M:tm-69, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43709
in-theory        43709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-54 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43709.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-54, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43710
in-theory        43710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-42 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43710.        ((A -> (B or A)) and ((C -> (D or C)) and (E or ((F and G) -> G)))), M:tm-42, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43711
in-theory        43711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-32 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43711.        ((A -> (A or B)) and ((C -> (D or C)) and (E or ((F and G) -> G)))), M:tm-32, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43712
in-theory        43712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-23 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43712.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or ((F and G) -> G)))), M:tm-23, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43713
in-theory        43713
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-22 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43713.        (((A and B) -> B) and ((C -> (D or C)) and (E or ((F and G) -> G)))), M:tm-22, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43714
in-theory        43714
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-21 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43714.        (((A and B) -> A) and ((C -> (D or C)) and (E or ((F and G) -> G)))), M:tm-21, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43715
in-theory        43715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-20 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43715.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-20, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43716
in-theory        43716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-19 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43716.        ((A -> (B -> A)) and ((C -> (D or C)) and (E or ((F and G) -> G)))), M:tm-19, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43717
in-theory        43717
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-7 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43717.        (A or ((B -> (C or B)) and (D or ((E and F) -> F)))), M:tm-7, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43718
in-theory        43718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-6 tm-5 tm-7 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43718.        (((A -> (B or A)) and (C or ((D and E) -> E))) or F), M:tm-6, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43719
in-theory        43719
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D or ((E and F) -> F))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43719.        (A -> (((B -> (C or B)) and (D or ((E and F) -> F))) and A)), M:tm-5, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43720
in-theory        43720
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D or ((E and F) -> F))))
theorem-size     15
proof            (modus-ponens tm-1 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-1 tm-5 tm-7 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-43720.        (A -> ((B -> (C or B)) and (D or ((E and F) -> F)))), M:tm-1, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-43721
in-theory        43721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-550 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43721.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-550, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43722
in-theory        43722
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-540 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43722.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-540, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43723
in-theory        43723
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-530 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43723.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-530, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43724
in-theory        43724
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-520 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43724.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-520, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43725
in-theory        43725
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-510 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43725.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-510, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43726
in-theory        43726
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-500 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43726.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-500, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43727
in-theory        43727
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-490 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43727.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (I -> (H and I)))))), M:tm-490, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43728
in-theory        43728
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-480 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43728.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-480, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43729
in-theory        43729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-469 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43729.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-469, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43730
in-theory        43730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43730.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (F -> (F or G))), M:tm-456, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43731
in-theory        43731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-453 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43731.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-453, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43732
in-theory        43732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (B or A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43732.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and ((F -> (F or G)) and ((A -> (B or A)) and (C or (D -> (E -> (D and E))))))), M:tm-443, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43733
in-theory        43733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-409 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43733.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-409, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43734
in-theory        43734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-400 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43734.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-400, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43735
in-theory        43735
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-391 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43735.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-391, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43736
in-theory        43736
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-382 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43736.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-382, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43737
in-theory        43737
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-373 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43737.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or (H -> (I -> (H and I)))))), M:tm-373, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43738
in-theory        43738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-364 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43738.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-364, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43739
in-theory        43739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-354 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43739.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-354, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43740
in-theory        43740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43740.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43741
in-theory        43741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-338 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43741.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or (F -> (G -> (F and G)))))), M:tm-338, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43742
in-theory        43742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43742.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C or (D -> (E -> (D and E))))))), M:tm-327, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43743
in-theory        43743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (B or A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43743.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (((F and G) -> G) and ((A -> (B or A)) and (C or (D -> (E -> (D and E))))))), M:tm-326, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43744
in-theory        43744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (B or A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43744.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (((F and G) -> F) and ((A -> (B or A)) and (C or (D -> (E -> (D and E))))))), M:tm-325, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43745
in-theory        43745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43745.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C or (D -> (E -> (D and E))))))), M:tm-324, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43746
in-theory        43746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43746.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C or (D -> (E -> (D and E))))))), M:tm-323, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43747
in-theory        43747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43747.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and ((F and G) -> G)), M:tm-322, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43748
in-theory        43748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43748.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and ((F and G) -> F)), M:tm-320, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43749
in-theory        43749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43749.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43750
in-theory        43750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43750.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (F -> (G -> F))), M:tm-315, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43751
in-theory        43751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (F or ((A -> (B or A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43751.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (F or ((A -> (B or A)) and (C or (D -> (E -> (D and E))))))), M:tm-311, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43752
in-theory        43752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43752.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) or F)), M:tm-310, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43753
in-theory        43753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (F -> (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43753.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (F -> (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and F))), M:tm-309, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43754
in-theory        43754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (C or (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-308 tm-589 ((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43754.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (C or (D -> (E -> (D and E))))), M:tm-308, m:tm-589, u:((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-43755
in-theory        43755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (A -> (B or A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-589 ((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43755.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (A -> (B or A))), M:tm-307, m:tm-589, u:((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-43756
in-theory        43756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (F -> ((A -> (B or A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43756.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (F -> ((A -> (B or A)) and (C or (D -> (E -> (D and E))))))), M:tm-305, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43757
in-theory        43757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-303 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43757.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-303, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43758
in-theory        43758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-270 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43758.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-270, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43759
in-theory        43759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-239 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43759.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-239, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43760
in-theory        43760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-210 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43760.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or (H -> (I -> (H and I)))))), M:tm-210, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43761
in-theory        43761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-183 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43761.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-183, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43762
in-theory        43762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-157 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43762.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-157, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43763
in-theory        43763
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-147 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43763.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-147, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43764
in-theory        43764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-134 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43764.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-134, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43765
in-theory        43765
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-125 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43765.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-125, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43766
in-theory        43766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-113 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43766.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (I -> (H and I)))))), M:tm-113, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43767
in-theory        43767
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     35
proof            (modus-ponens tm-105 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43767.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-105, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43768
in-theory        43768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-95 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43768.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or (F -> (G -> (F and G)))))), M:tm-95, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43769
in-theory        43769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-83 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43769.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-83, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43770
in-theory        43770
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D or (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-76 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43770.        (((not (not A)) -> A) and ((B -> (C or B)) and (D or (E -> (F -> (E and F)))))), M:tm-76, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43771
in-theory        43771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or (F -> (G -> (F and G))))))
theorem-size     27
proof            (modus-ponens tm-69 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43771.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or (F -> (G -> (F and G)))))), M:tm-69, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43772
in-theory        43772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-54 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43772.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-54, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43773
in-theory        43773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-42 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43773.        ((A -> (B or A)) and ((C -> (D or C)) and (E or (F -> (G -> (F and G)))))), M:tm-42, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43774
in-theory        43774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-32 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43774.        ((A -> (A or B)) and ((C -> (D or C)) and (E or (F -> (G -> (F and G)))))), M:tm-32, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43775
in-theory        43775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-23 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43775.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or (F -> (G -> (F and G)))))), M:tm-23, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43776
in-theory        43776
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-22 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43776.        (((A and B) -> B) and ((C -> (D or C)) and (E or (F -> (G -> (F and G)))))), M:tm-22, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43777
in-theory        43777
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-21 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43777.        (((A and B) -> A) and ((C -> (D or C)) and (E or (F -> (G -> (F and G)))))), M:tm-21, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43778
in-theory        43778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-20 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43778.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-20, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43779
in-theory        43779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-19 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43779.        ((A -> (B -> A)) and ((C -> (D or C)) and (E or (F -> (G -> (F and G)))))), M:tm-19, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43780
in-theory        43780
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-7 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-7 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43780.        (A or ((B -> (C or B)) and (D or (E -> (F -> (E and F)))))), M:tm-7, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43781
in-theory        43781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43781.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) or F), M:tm-6, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43782
in-theory        43782
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D or (E -> (F -> (E and F))))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43782.        (A -> (((B -> (C or B)) and (D or (E -> (F -> (E and F))))) and A)), M:tm-5, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43783
in-theory        43783
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D or (E -> (F -> (E and F))))))
theorem-size     17
proof            (modus-ponens tm-1 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-43783.        (A -> ((B -> (C or B)) and (D or (E -> (F -> (E and F)))))), M:tm-1, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-43784
in-theory        43784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43784.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-550, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43785
in-theory        43785
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43785.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-540, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43786
in-theory        43786
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43786.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-530, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43787
in-theory        43787
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43787.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-520, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43788
in-theory        43788
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43788.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-510, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43789
in-theory        43789
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43789.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-500, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43790
in-theory        43790
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43790.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (H or I))))), M:tm-490, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43791
in-theory        43791
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43791.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-480, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43792
in-theory        43792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43792.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-469, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43793
in-theory        43793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43793.        (((A -> (B or A)) and (C or (D -> (D or E)))) and (F -> (F or G))), M:tm-456, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43794
in-theory        43794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43794.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-453, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43795
in-theory        43795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (B or A)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43795.        (((A -> (B or A)) and (C or (D -> (D or E)))) and ((F -> (F or G)) and ((A -> (B or A)) and (C or (D -> (D or E)))))), M:tm-443, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43796
in-theory        43796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43796.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-409, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43797
in-theory        43797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43797.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-400, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43798
in-theory        43798
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43798.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-391, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43799
in-theory        43799
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43799.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-382, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43800
in-theory        43800
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43800.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or (H -> (H or I))))), M:tm-373, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43801
in-theory        43801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43801.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-364, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43802
in-theory        43802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43802.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-354, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43803
in-theory        43803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43803.        (((A -> (B or A)) and (C or (D -> (D or E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43804
in-theory        43804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43804.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or (F -> (F or G))))), M:tm-338, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43805
in-theory        43805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C or (D -> (D or E))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43805.        (((A -> (B or A)) and (C or (D -> (D or E)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C or (D -> (D or E)))))), M:tm-327, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43806
in-theory        43806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and (((F and G) -> G) and ((A -> (B or A)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43806.        (((A -> (B or A)) and (C or (D -> (D or E)))) and (((F and G) -> G) and ((A -> (B or A)) and (C or (D -> (D or E)))))), M:tm-326, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43807
in-theory        43807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and (((F and G) -> F) and ((A -> (B or A)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43807.        (((A -> (B or A)) and (C or (D -> (D or E)))) and (((F and G) -> F) and ((A -> (B or A)) and (C or (D -> (D or E)))))), M:tm-325, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43808
in-theory        43808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C or (D -> (D or E))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43808.        (((A -> (B or A)) and (C or (D -> (D or E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C or (D -> (D or E)))))), M:tm-324, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43809
in-theory        43809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43809.        (((A -> (B or A)) and (C or (D -> (D or E)))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C or (D -> (D or E)))))), M:tm-323, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43810
in-theory        43810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43810.        (((A -> (B or A)) and (C or (D -> (D or E)))) and ((F and G) -> G)), M:tm-322, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43811
in-theory        43811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43811.        (((A -> (B or A)) and (C or (D -> (D or E)))) and ((F and G) -> F)), M:tm-320, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43812
in-theory        43812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43812.        (((A -> (B or A)) and (C or (D -> (D or E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43813
in-theory        43813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43813.        (((A -> (B or A)) and (C or (D -> (D or E)))) and (F -> (G -> F))), M:tm-315, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43814
in-theory        43814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and (F or ((A -> (B or A)) and (C or (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43814.        (((A -> (B or A)) and (C or (D -> (D or E)))) and (F or ((A -> (B or A)) and (C or (D -> (D or E)))))), M:tm-311, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43815
in-theory        43815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and (((A -> (B or A)) and (C or (D -> (D or E)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43815.        (((A -> (B or A)) and (C or (D -> (D or E)))) and (((A -> (B or A)) and (C or (D -> (D or E)))) or F)), M:tm-310, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43816
in-theory        43816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and (F -> (((A -> (B or A)) and (C or (D -> (D or E)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43816.        (((A -> (B or A)) and (C or (D -> (D or E)))) and (F -> (((A -> (B or A)) and (C or (D -> (D or E)))) and F))), M:tm-309, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43817
in-theory        43817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and (C or (D -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-308 tm-590 ((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43817.        (((A -> (B or A)) and (C or (D -> (D or E)))) and (C or (D -> (D or E)))), M:tm-308, m:tm-590, u:((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-43818
in-theory        43818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-590 ((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43818.        (((A -> (B or A)) and (C or (D -> (D or E)))) and (A -> (B or A))), M:tm-307, m:tm-590, u:((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-43819
in-theory        43819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and (F -> ((A -> (B or A)) and (C or (D -> (D or E))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43819.        (((A -> (B or A)) and (C or (D -> (D or E)))) and (F -> ((A -> (B or A)) and (C or (D -> (D or E)))))), M:tm-305, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43820
in-theory        43820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43820.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-303, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43821
in-theory        43821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43821.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-270, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43822
in-theory        43822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43822.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-239, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43823
in-theory        43823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43823.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or (H -> (H or I))))), M:tm-210, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43824
in-theory        43824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43824.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-183, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43825
in-theory        43825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43825.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-157, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43826
in-theory        43826
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43826.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-147, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43827
in-theory        43827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43827.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-134, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43828
in-theory        43828
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43828.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-125, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43829
in-theory        43829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43829.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (H or I))))), M:tm-113, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43830
in-theory        43830
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43830.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-105, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43831
in-theory        43831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43831.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or (F -> (F or G))))), M:tm-95, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43832
in-theory        43832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43832.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-83, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43833
in-theory        43833
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D or (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43833.        (((not (not A)) -> A) and ((B -> (C or B)) and (D or (E -> (E or F))))), M:tm-76, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43834
in-theory        43834
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or (F -> (F or G)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43834.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or (F -> (F or G))))), M:tm-69, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43835
in-theory        43835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43835.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-54, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43836
in-theory        43836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43836.        ((A -> (B or A)) and ((C -> (D or C)) and (E or (F -> (F or G))))), M:tm-42, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43837
in-theory        43837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43837.        ((A -> (A or B)) and ((C -> (D or C)) and (E or (F -> (F or G))))), M:tm-32, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43838
in-theory        43838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43838.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or (F -> (F or G))))), M:tm-23, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43839
in-theory        43839
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43839.        (((A and B) -> B) and ((C -> (D or C)) and (E or (F -> (F or G))))), M:tm-22, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43840
in-theory        43840
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43840.        (((A and B) -> A) and ((C -> (D or C)) and (E or (F -> (F or G))))), M:tm-21, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43841
in-theory        43841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43841.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-20, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43842
in-theory        43842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43842.        ((A -> (B -> A)) and ((C -> (D or C)) and (E or (F -> (F or G))))), M:tm-19, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43843
in-theory        43843
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43843.        (A or ((B -> (C or B)) and (D or (E -> (E or F))))), M:tm-7, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43844
in-theory        43844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43844.        (((A -> (B or A)) and (C or (D -> (D or E)))) or F), M:tm-6, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43845
in-theory        43845
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D or (E -> (E or F)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43845.        (A -> (((B -> (C or B)) and (D or (E -> (E or F)))) and A)), M:tm-5, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43846
in-theory        43846
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D or (E -> (E or F)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-1 tm-5 tm-7 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-43846.        (A -> ((B -> (C or B)) and (D or (E -> (E or F))))), M:tm-1, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-43847
in-theory        43847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43847.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-550, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43848
in-theory        43848
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43848.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-540, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43849
in-theory        43849
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43849.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-530, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43850
in-theory        43850
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43850.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-520, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43851
in-theory        43851
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43851.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-510, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43852
in-theory        43852
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43852.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-500, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43853
in-theory        43853
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43853.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (I or H))))), M:tm-490, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43854
in-theory        43854
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43854.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-480, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43855
in-theory        43855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43855.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-469, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43856
in-theory        43856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43856.        (((A -> (B or A)) and (C or (D -> (E or D)))) and (F -> (F or G))), M:tm-456, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43857
in-theory        43857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43857.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-453, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43858
in-theory        43858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (B or A)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43858.        (((A -> (B or A)) and (C or (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (B or A)) and (C or (D -> (E or D)))))), M:tm-443, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43859
in-theory        43859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43859.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-409, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43860
in-theory        43860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43860.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-400, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43861
in-theory        43861
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43861.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-391, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43862
in-theory        43862
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43862.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-382, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43863
in-theory        43863
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43863.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G or (H -> (I or H))))), M:tm-373, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43864
in-theory        43864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43864.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-364, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43865
in-theory        43865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43865.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-354, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43866
in-theory        43866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43866.        (((A -> (B or A)) and (C or (D -> (E or D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43867
in-theory        43867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43867.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E or (F -> (G or F))))), M:tm-338, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43868
in-theory        43868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C or (D -> (E or D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43868.        (((A -> (B or A)) and (C or (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C or (D -> (E or D)))))), M:tm-327, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43869
in-theory        43869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and (((F and G) -> G) and ((A -> (B or A)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43869.        (((A -> (B or A)) and (C or (D -> (E or D)))) and (((F and G) -> G) and ((A -> (B or A)) and (C or (D -> (E or D)))))), M:tm-326, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43870
in-theory        43870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and (((F and G) -> F) and ((A -> (B or A)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43870.        (((A -> (B or A)) and (C or (D -> (E or D)))) and (((F and G) -> F) and ((A -> (B or A)) and (C or (D -> (E or D)))))), M:tm-325, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43871
in-theory        43871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C or (D -> (E or D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43871.        (((A -> (B or A)) and (C or (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C or (D -> (E or D)))))), M:tm-324, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43872
in-theory        43872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43872.        (((A -> (B or A)) and (C or (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C or (D -> (E or D)))))), M:tm-323, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43873
in-theory        43873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43873.        (((A -> (B or A)) and (C or (D -> (E or D)))) and ((F and G) -> G)), M:tm-322, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43874
in-theory        43874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43874.        (((A -> (B or A)) and (C or (D -> (E or D)))) and ((F and G) -> F)), M:tm-320, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43875
in-theory        43875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43875.        (((A -> (B or A)) and (C or (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43876
in-theory        43876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43876.        (((A -> (B or A)) and (C or (D -> (E or D)))) and (F -> (G -> F))), M:tm-315, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43877
in-theory        43877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and (F or ((A -> (B or A)) and (C or (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43877.        (((A -> (B or A)) and (C or (D -> (E or D)))) and (F or ((A -> (B or A)) and (C or (D -> (E or D)))))), M:tm-311, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43878
in-theory        43878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and (((A -> (B or A)) and (C or (D -> (E or D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43878.        (((A -> (B or A)) and (C or (D -> (E or D)))) and (((A -> (B or A)) and (C or (D -> (E or D)))) or F)), M:tm-310, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43879
in-theory        43879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and (F -> (((A -> (B or A)) and (C or (D -> (E or D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43879.        (((A -> (B or A)) and (C or (D -> (E or D)))) and (F -> (((A -> (B or A)) and (C or (D -> (E or D)))) and F))), M:tm-309, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43880
in-theory        43880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and (C or (D -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-591 ((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43880.        (((A -> (B or A)) and (C or (D -> (E or D)))) and (C or (D -> (E or D)))), M:tm-308, m:tm-591, u:((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-43881
in-theory        43881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-591 ((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43881.        (((A -> (B or A)) and (C or (D -> (E or D)))) and (A -> (B or A))), M:tm-307, m:tm-591, u:((A (-> Am (or Bm Am))) (B (or Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-43882
in-theory        43882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and (F -> ((A -> (B or A)) and (C or (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43882.        (((A -> (B or A)) and (C or (D -> (E or D)))) and (F -> ((A -> (B or A)) and (C or (D -> (E or D)))))), M:tm-305, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43883
in-theory        43883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43883.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-303, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43884
in-theory        43884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43884.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-270, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43885
in-theory        43885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43885.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-239, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43886
in-theory        43886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43886.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G or (H -> (I or H))))), M:tm-210, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43887
in-theory        43887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43887.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-183, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43888
in-theory        43888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43888.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-157, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43889
in-theory        43889
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43889.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-147, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43890
in-theory        43890
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43890.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-134, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43891
in-theory        43891
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43891.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-125, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43892
in-theory        43892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43892.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G or (H -> (I or H))))), M:tm-113, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43893
in-theory        43893
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43893.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-105, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43894
in-theory        43894
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43894.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E or (F -> (G or F))))), M:tm-95, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43895
in-theory        43895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43895.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-83, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43896
in-theory        43896
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D or (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43896.        (((not (not A)) -> A) and ((B -> (C or B)) and (D or (E -> (F or E))))), M:tm-76, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43897
in-theory        43897
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43897.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E or (F -> (G or F))))), M:tm-69, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43898
in-theory        43898
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43898.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-54, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43899
in-theory        43899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43899.        ((A -> (B or A)) and ((C -> (D or C)) and (E or (F -> (G or F))))), M:tm-42, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43900
in-theory        43900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43900.        ((A -> (A or B)) and ((C -> (D or C)) and (E or (F -> (G or F))))), M:tm-32, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43901
in-theory        43901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43901.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E or (F -> (G or F))))), M:tm-23, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43902
in-theory        43902
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43902.        (((A and B) -> B) and ((C -> (D or C)) and (E or (F -> (G or F))))), M:tm-22, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43903
in-theory        43903
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43903.        (((A and B) -> A) and ((C -> (D or C)) and (E or (F -> (G or F))))), M:tm-21, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43904
in-theory        43904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43904.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-20, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43905
in-theory        43905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43905.        ((A -> (B -> A)) and ((C -> (D or C)) and (E or (F -> (G or F))))), M:tm-19, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43906
in-theory        43906
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-7 tm-5)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43906.        (A or ((B -> (C or B)) and (D or (E -> (F or E))))), M:tm-7, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43907
in-theory        43907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43907.        (((A -> (B or A)) and (C or (D -> (E or D)))) or F), M:tm-6, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43908
in-theory        43908
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D or (E -> (F or E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43908.        (A -> (((B -> (C or B)) and (D or (E -> (F or E)))) and A)), M:tm-5, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43909
in-theory        43909
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D or (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-43909.        (A -> ((B -> (C or B)) and (D or (E -> (F or E))))), M:tm-1, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-43910
in-theory        43910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-550 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43910.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-550, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43911
in-theory        43911
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-540 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43911.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-540, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43912
in-theory        43912
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-530 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43912.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-530, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43913
in-theory        43913
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-520 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43913.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-520, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43914
in-theory        43914
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-510 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43914.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-510, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43915
in-theory        43915
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-500 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43915.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-500, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43916
in-theory        43916
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-490 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43916.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H or G)) or I))), M:tm-490, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43917
in-theory        43917
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-480 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43917.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-480, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43918
in-theory        43918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-469 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43918.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-469, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43919
in-theory        43919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43919.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and (F -> (F or G))), M:tm-456, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43920
in-theory        43920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-453 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43920.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-453, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43921
in-theory        43921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-443 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43921.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> (D or C)) or E)))), M:tm-443, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43922
in-theory        43922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-409 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43922.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-409, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43923
in-theory        43923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-400 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43923.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-400, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43924
in-theory        43924
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-391 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43924.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-391, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43925
in-theory        43925
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-382 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43925.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-382, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43926
in-theory        43926
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-373 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43926.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> (H or G)) or I))), M:tm-373, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43927
in-theory        43927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-364 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43927.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-364, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43928
in-theory        43928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-354 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43928.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-354, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43929
in-theory        43929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43929.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43930
in-theory        43930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-338 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43930.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> (F or E)) or G))), M:tm-338, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43931
in-theory        43931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> (D or C)) or E))))
theorem-size     35
proof            (modus-ponens tm-327 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43931.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> (D or C)) or E)))), M:tm-327, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43932
in-theory        43932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-326 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43932.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> (D or C)) or E)))), M:tm-326, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43933
in-theory        43933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-325 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43933.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> (D or C)) or E)))), M:tm-325, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43934
in-theory        43934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> (D or C)) or E))))
theorem-size     41
proof            (modus-ponens tm-324 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43934.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> (D or C)) or E)))), M:tm-324, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43935
in-theory        43935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-323 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43935.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> (D or C)) or E)))), M:tm-323, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43936
in-theory        43936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43936.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((F and G) -> G)), M:tm-322, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43937
in-theory        43937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43937.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((F and G) -> F)), M:tm-320, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43938
in-theory        43938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43938.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43939
in-theory        43939
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43939.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and (F -> (G -> F))), M:tm-315, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43940
in-theory        43940
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and (F or ((A -> (B or A)) and ((C -> (D or C)) or E))))
theorem-size     29
proof            (modus-ponens tm-311 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43940.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and (F or ((A -> (B or A)) and ((C -> (D or C)) or E)))), M:tm-311, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43941
in-theory        43941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and (((A -> (B or A)) and ((C -> (D or C)) or E)) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43941.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and (((A -> (B or A)) and ((C -> (D or C)) or E)) or F)), M:tm-310, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43942
in-theory        43942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and (F -> (((A -> (B or A)) and ((C -> (D or C)) or E)) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43942.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and (F -> (((A -> (B or A)) and ((C -> (D or C)) or E)) and F))), M:tm-309, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43943
in-theory        43943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((C -> (D or C)) or E))
theorem-size     21
proof            (modus-ponens tm-308 tm-592 ((A (-> Am (or Bm Am))) (B (or (-> Cm (or Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43943.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((C -> (D or C)) or E)), M:tm-308, m:tm-592, u:((A (-> Am (or Bm Am))) (B (or (-> Cm (or Dm Cm)) Em)))
================================================================
tm-name          tm-43944
in-theory        43944
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-592 ((A (-> Am (or Bm Am))) (B (or (-> Cm (or Dm Cm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43944.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and (A -> (B or A))), M:tm-307, m:tm-592, u:((A (-> Am (or Bm Am))) (B (or (-> Cm (or Dm Cm)) Em)))
================================================================
tm-name          tm-43945
in-theory        43945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and (F -> ((A -> (B or A)) and ((C -> (D or C)) or E))))
theorem-size     29
proof            (modus-ponens tm-305 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43945.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and (F -> ((A -> (B or A)) and ((C -> (D or C)) or E)))), M:tm-305, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43946
in-theory        43946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-303 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43946.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-303, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43947
in-theory        43947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-270 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43947.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-270, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43948
in-theory        43948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-239 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43948.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-239, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43949
in-theory        43949
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-210 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43949.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> (H or G)) or I))), M:tm-210, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43950
in-theory        43950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-183 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43950.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-183, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43951
in-theory        43951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-157 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43951.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-157, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43952
in-theory        43952
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-147 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43952.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-147, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43953
in-theory        43953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-134 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43953.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-134, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43954
in-theory        43954
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-125 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43954.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-125, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43955
in-theory        43955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-113 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43955.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> (H or G)) or I))), M:tm-113, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43956
in-theory        43956
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     33
proof            (modus-ponens tm-105 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43956.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-105, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43957
in-theory        43957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-95 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43957.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> (F or E)) or G))), M:tm-95, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43958
in-theory        43958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-83 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43958.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-83, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43959
in-theory        43959
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> (E or D)) or F)))
theorem-size     19
proof            (modus-ponens tm-76 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-10 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43959.        (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> (E or D)) or F))), M:tm-76, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43960
in-theory        43960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> (F or E)) or G)))
theorem-size     25
proof            (modus-ponens tm-69 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-9 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43960.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> (F or E)) or G))), M:tm-69, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43961
in-theory        43961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-54 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43961.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-54, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43962
in-theory        43962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-42 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43962.        ((A -> (B or A)) and ((C -> (D or C)) and ((E -> (F or E)) or G))), M:tm-42, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43963
in-theory        43963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-32 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43963.        ((A -> (A or B)) and ((C -> (D or C)) and ((E -> (F or E)) or G))), M:tm-32, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43964
in-theory        43964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-23 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43964.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> (F or E)) or G))), M:tm-23, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43965
in-theory        43965
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-22 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-4 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43965.        (((A and B) -> B) and ((C -> (D or C)) and ((E -> (F or E)) or G))), M:tm-22, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43966
in-theory        43966
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-21 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-3 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43966.        (((A and B) -> A) and ((C -> (D or C)) and ((E -> (F or E)) or G))), M:tm-21, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43967
in-theory        43967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-20 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-2 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43967.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-20, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43968
in-theory        43968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-19 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43968.        ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> (F or E)) or G))), M:tm-19, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43969
in-theory        43969
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-7 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43969.        (A or ((B -> (C or B)) and ((D -> (E or D)) or F))), M:tm-7, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43970
in-theory        43970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43970.        (((A -> (B or A)) and ((C -> (D or C)) or E)) or F), M:tm-6, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43971
in-theory        43971
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((D -> (E or D)) or F)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43971.        (A -> (((B -> (C or B)) and ((D -> (E or D)) or F)) and A)), M:tm-5, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43972
in-theory        43972
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((D -> (E or D)) or F)))
theorem-size     15
proof            (modus-ponens tm-1 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-1 tm-5 tm-7 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-43972.        (A -> ((B -> (C or B)) and ((D -> (E or D)) or F))), M:tm-1, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-43973
in-theory        43973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43973.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-550, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43974
in-theory        43974
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43974.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-540, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43975
in-theory        43975
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43975.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-530, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43976
in-theory        43976
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43976.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-520, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43977
in-theory        43977
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43977.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-510, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43978
in-theory        43978
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43978.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-500, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43979
in-theory        43979
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43979.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G)))), M:tm-490, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43980
in-theory        43980
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43980.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-480, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43981
in-theory        43981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43981.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-469, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43982
in-theory        43982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43982.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (F -> (F or G))), M:tm-456, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43983
in-theory        43983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43983.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-453, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43984
in-theory        43984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43984.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))))), M:tm-443, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43985
in-theory        43985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43985.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-409, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43986
in-theory        43986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43986.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-400, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43987
in-theory        43987
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43987.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-391, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43988
in-theory        43988
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43988.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-382, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43989
in-theory        43989
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43989.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G)))), M:tm-373, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43990
in-theory        43990
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43990.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-364, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43991
in-theory        43991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43991.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-354, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43992
in-theory        43992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43992.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43993
in-theory        43993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43993.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E)))), M:tm-338, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43994
in-theory        43994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43994.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))))), M:tm-327, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43995
in-theory        43995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43995.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))))), M:tm-326, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43996
in-theory        43996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43996.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))))), M:tm-325, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43997
in-theory        43997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43997.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))))), M:tm-324, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43998
in-theory        43998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43998.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))))), M:tm-323, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-43999
in-theory        43999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-43999.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44000
in-theory        44000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44000.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44001
in-theory        44001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44001.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44002
in-theory        44002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44002.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44003
in-theory        44003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (F or ((A -> (B or A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44003.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (F or ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))))), M:tm-311, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44004
in-theory        44004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44004.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) or F)), M:tm-310, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44005
in-theory        44005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (F -> (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44005.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (F -> (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and F))), M:tm-309, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44006
in-theory        44006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (C -> ((D -> (E or D)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-593 ((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44006.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (C -> ((D -> (E or D)) and C))), M:tm-308, m:tm-593, u:((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm))))
================================================================
tm-name          tm-44007
in-theory        44007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (A -> (B or A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-593 ((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44007.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (A -> (B or A))), M:tm-307, m:tm-593, u:((A (-> Am (or Bm Am))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm))))
================================================================
tm-name          tm-44008
in-theory        44008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (F -> ((A -> (B or A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44008.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (F -> ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))))), M:tm-305, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44009
in-theory        44009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44009.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-303, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44010
in-theory        44010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44010.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-270, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44011
in-theory        44011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44011.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-239, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44012
in-theory        44012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44012.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G)))), M:tm-210, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44013
in-theory        44013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44013.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-183, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44014
in-theory        44014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44014.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-157, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44015
in-theory        44015
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44015.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-147, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44016
in-theory        44016
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44016.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-134, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44017
in-theory        44017
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44017.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-125, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44018
in-theory        44018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44018.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G)))), M:tm-113, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44019
in-theory        44019
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44019.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-105, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44020
in-theory        44020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44020.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E)))), M:tm-95, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44021
in-theory        44021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44021.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-83, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44022
in-theory        44022
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44022.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> ((E -> (F or E)) and D)))), M:tm-76, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44023
in-theory        44023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44023.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E)))), M:tm-69, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44024
in-theory        44024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44024.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-54, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44025
in-theory        44025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44025.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E)))), M:tm-42, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44026
in-theory        44026
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44026.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E)))), M:tm-32, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44027
in-theory        44027
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44027.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E)))), M:tm-23, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44028
in-theory        44028
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44028.        (((A and B) -> B) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E)))), M:tm-22, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44029
in-theory        44029
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44029.        (((A and B) -> A) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E)))), M:tm-21, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44030
in-theory        44030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44030.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-20, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44031
in-theory        44031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44031.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> ((F -> (G or F)) and E)))), M:tm-19, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44032
in-theory        44032
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-7 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44032.        (A or ((B -> (C or B)) and (D -> ((E -> (F or E)) and D)))), M:tm-7, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44033
in-theory        44033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44033.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) or F), M:tm-6, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44034
in-theory        44034
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> ((E -> (F or E)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44034.        (A -> (((B -> (C or B)) and (D -> ((E -> (F or E)) and D))) and A)), M:tm-5, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44035
in-theory        44035
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44035.        (A -> ((B -> (C or B)) and (D -> ((E -> (F or E)) and D)))), M:tm-1, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44036
in-theory        44036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44036.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-550, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44037
in-theory        44037
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44037.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-540, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44038
in-theory        44038
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44038.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-530, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44039
in-theory        44039
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44039.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-520, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44040
in-theory        44040
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44040.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-510, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44041
in-theory        44041
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44041.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-500, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44042
in-theory        44042
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44042.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G)))), M:tm-490, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44043
in-theory        44043
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44043.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-480, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44044
in-theory        44044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44044.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-469, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44045
in-theory        44045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44045.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (F -> (F or G))), M:tm-456, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44046
in-theory        44046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44046.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-453, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44047
in-theory        44047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44047.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))))), M:tm-443, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44048
in-theory        44048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44048.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-409, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44049
in-theory        44049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44049.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-400, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44050
in-theory        44050
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44050.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-391, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44051
in-theory        44051
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44051.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-382, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44052
in-theory        44052
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44052.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G)))), M:tm-373, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44053
in-theory        44053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44053.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-364, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44054
in-theory        44054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44054.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-354, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44055
in-theory        44055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44055.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44056
in-theory        44056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44056.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E)))), M:tm-338, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44057
in-theory        44057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44057.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))))), M:tm-327, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44058
in-theory        44058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44058.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))))), M:tm-326, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44059
in-theory        44059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44059.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))))), M:tm-325, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44060
in-theory        44060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44060.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))))), M:tm-324, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44061
in-theory        44061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44061.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))))), M:tm-323, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44062
in-theory        44062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44062.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44063
in-theory        44063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44063.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44064
in-theory        44064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44064.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44065
in-theory        44065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44065.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44066
in-theory        44066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (F or ((A -> (A or B)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44066.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (F or ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))))), M:tm-311, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44067
in-theory        44067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44067.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) or F)), M:tm-310, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44068
in-theory        44068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (F -> (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44068.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (F -> (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and F))), M:tm-309, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44069
in-theory        44069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (C -> ((D -> (E or D)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-594 ((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44069.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (C -> ((D -> (E or D)) and C))), M:tm-308, m:tm-594, u:((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm))))
================================================================
tm-name          tm-44070
in-theory        44070
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (A -> (A or B)))
theorem-size     21
proof            (modus-ponens tm-307 tm-594 ((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44070.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (A -> (A or B))), M:tm-307, m:tm-594, u:((A (-> Am (or Am Bm))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm))))
================================================================
tm-name          tm-44071
in-theory        44071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (F -> ((A -> (A or B)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44071.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (F -> ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))))), M:tm-305, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44072
in-theory        44072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44072.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-303, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44073
in-theory        44073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44073.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-270, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44074
in-theory        44074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44074.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-239, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44075
in-theory        44075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44075.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G)))), M:tm-210, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44076
in-theory        44076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44076.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-183, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44077
in-theory        44077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44077.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-157, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44078
in-theory        44078
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44078.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-147, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44079
in-theory        44079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44079.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-134, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44080
in-theory        44080
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44080.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-125, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44081
in-theory        44081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44081.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G)))), M:tm-113, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44082
in-theory        44082
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44082.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-105, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44083
in-theory        44083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44083.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E)))), M:tm-95, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44084
in-theory        44084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44084.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-83, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44085
in-theory        44085
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44085.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> ((E -> (F or E)) and D)))), M:tm-76, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44086
in-theory        44086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-6 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44086.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E)))), M:tm-69, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44087
in-theory        44087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44087.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-54, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44088
in-theory        44088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44088.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E)))), M:tm-42, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44089
in-theory        44089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44089.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E)))), M:tm-32, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44090
in-theory        44090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44090.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E)))), M:tm-23, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44091
in-theory        44091
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44091.        (((A and B) -> B) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E)))), M:tm-22, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44092
in-theory        44092
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44092.        (((A and B) -> A) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E)))), M:tm-21, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44093
in-theory        44093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44093.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-20, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44094
in-theory        44094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44094.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> ((F -> (G or F)) and E)))), M:tm-19, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44095
in-theory        44095
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-7 tm-5 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44095.        (A or ((B -> (B or C)) and (D -> ((E -> (F or E)) and D)))), M:tm-7, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44096
in-theory        44096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44096.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) or F), M:tm-6, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44097
in-theory        44097
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> ((E -> (F or E)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44097.        (A -> (((B -> (B or C)) and (D -> ((E -> (F or E)) and D))) and A)), M:tm-5, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44098
in-theory        44098
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-1 tm-5 tm-6 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44098.        (A -> ((B -> (B or C)) and (D -> ((E -> (F or E)) and D)))), M:tm-1, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44099
in-theory        44099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (A -> (B -> A))))
theorem-size     17
proof            (modus-ponens tm-595 tm-1 ((A (-> Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44099.        ((A -> (B -> A)) and ((C -> (D or C)) and (A -> (B -> A)))), M:tm-595, m:tm-1, u:((A (-> Am (-> Bm Am))))
================================================================
tm-name          tm-44100
in-theory        44100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-2 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44100.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))), M:tm-595, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-44101
in-theory        44101
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((A and B) -> A)))
theorem-size     17
proof            (modus-ponens tm-595 tm-3 ((A (-> (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-44101.        (((A and B) -> A) and ((C -> (D or C)) and ((A and B) -> A))), M:tm-595, m:tm-3, u:((A (-> (and Am Bm) Am)))
================================================================
tm-name          tm-44102
in-theory        44102
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((A and B) -> B)))
theorem-size     17
proof            (modus-ponens tm-595 tm-4 ((A (-> (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-44102.        (((A and B) -> B) and ((C -> (D or C)) and ((A and B) -> B))), M:tm-595, m:tm-4, u:((A (-> (and Am Bm) Bm)))
================================================================
tm-name          tm-44103
in-theory        44103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (A -> (B -> (A and B)))))
theorem-size     21
proof            (modus-ponens tm-595 tm-5 ((A (-> Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44103.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (A -> (B -> (A and B))))), M:tm-595, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-44104
in-theory        44104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (A -> (A or B))))
theorem-size     17
proof            (modus-ponens tm-595 tm-6 ((A (-> Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-44104.        ((A -> (A or B)) and ((C -> (D or C)) and (A -> (A or B)))), M:tm-595, m:tm-6, u:((A (-> Am (or Am Bm))))
================================================================
tm-name          tm-44105
in-theory        44105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (A -> (B or A))))
theorem-size     17
proof            (modus-ponens tm-595 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44105.        ((A -> (B or A)) and ((C -> (D or C)) and (A -> (B or A)))), M:tm-595, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-44106
in-theory        44106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44106.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((A -> B) -> ((B -> C) -> ((A or B) -> C))))), M:tm-595, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-44107
in-theory        44107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((A -> B) -> ((A -> (not B)) -> (not A)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-44107.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((A -> B) -> ((A -> (not B)) -> (not A))))), M:tm-595, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-44108
in-theory        44108
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((not (not A)) -> A)))
theorem-size     17
proof            (modus-ponens tm-595 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-44108.        (((not (not A)) -> A) and ((B -> (C or B)) and ((not (not A)) -> A))), M:tm-595, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-44109
in-theory        44109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (A -> (B -> (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-595 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-44109.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (A -> (B -> (C -> B))))), M:tm-595, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-44110
in-theory        44110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((A -> B) -> (A -> A))))
theorem-size     21
proof            (modus-ponens tm-595 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44110.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((A -> B) -> (A -> A)))), M:tm-595, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-44111
in-theory        44111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-44111.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-595, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-44112
in-theory        44112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-44112.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-595, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-44113
in-theory        44113
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B))))
theorem-size     37
proof            (modus-ponens tm-595 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-44113.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)))), M:tm-595, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-44114
in-theory        44114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (A -> ((B and C) -> B))))
theorem-size     21
proof            (modus-ponens tm-595 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-44114.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (A -> ((B and C) -> B)))), M:tm-595, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-44115
in-theory        44115
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-595 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-44115.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)))), M:tm-595, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-44116
in-theory        44116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (A -> ((B and C) -> C))))
theorem-size     21
proof            (modus-ponens tm-595 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-44116.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (A -> ((B and C) -> C)))), M:tm-595, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-44117
in-theory        44117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (A -> ((B -> (C -> B)) and A))))
theorem-size     25
proof            (modus-ponens tm-595 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-44117.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (A -> ((B -> (C -> B)) and A)))), M:tm-595, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-44118
in-theory        44118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     41
proof            (modus-ponens tm-595 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-44118.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-595, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-44119
in-theory        44119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (A -> (((B and C) -> B) and A))))
theorem-size     25
proof            (modus-ponens tm-595 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-44119.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (A -> (((B and C) -> B) and A)))), M:tm-595, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-44120
in-theory        44120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (A -> (((B and C) -> C) and A))))
theorem-size     25
proof            (modus-ponens tm-595 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-44120.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (A -> (((B and C) -> C) and A)))), M:tm-595, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-44121
in-theory        44121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (A -> ((B -> (C -> (B and C))) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-44121.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (A -> ((B -> (C -> (B and C))) and A)))), M:tm-595, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-44122
in-theory        44122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((A -> B) -> (A -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44122.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((A -> B) -> (A -> (A and B))))), M:tm-595, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-44123
in-theory        44123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (A -> (B -> (C -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-44123.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (A -> (B -> (C -> (B and C)))))), M:tm-595, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-44124
in-theory        44124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((A -> (B -> A)) or C)))
theorem-size     21
proof            (modus-ponens tm-595 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-44124.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((A -> (B -> A)) or C))), M:tm-595, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-44125
in-theory        44125
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D)))
theorem-size     37
proof            (modus-ponens tm-595 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-44125.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D))), M:tm-595, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-44126
in-theory        44126
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (((A and B) -> A) or C)))
theorem-size     21
proof            (modus-ponens tm-595 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-44126.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (((A and B) -> A) or C))), M:tm-595, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-44127
in-theory        44127
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (((A and B) -> B) or C)))
theorem-size     21
proof            (modus-ponens tm-595 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-44127.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (((A and B) -> B) or C))), M:tm-595, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-44128
in-theory        44128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((A -> (B -> (A and B))) or C)))
theorem-size     25
proof            (modus-ponens tm-595 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-44128.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((A -> (B -> (A and B))) or C))), M:tm-595, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-44129
in-theory        44129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((A -> (A or B)) or C)))
theorem-size     21
proof            (modus-ponens tm-595 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-44129.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((A -> (A or B)) or C))), M:tm-595, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-44130
in-theory        44130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (A -> ((B -> (B or C)) and A))))
theorem-size     25
proof            (modus-ponens tm-595 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-44130.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (A -> ((B -> (B or C)) and A)))), M:tm-595, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-44131
in-theory        44131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (A -> (B -> (B or C)))))
theorem-size     21
proof            (modus-ponens tm-595 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-44131.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (A -> (B -> (B or C))))), M:tm-595, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-44132
in-theory        44132
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (A or (B -> (C -> B)))))
theorem-size     21
proof            (modus-ponens tm-595 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-44132.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (A or (B -> (C -> B))))), M:tm-595, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-44133
in-theory        44133
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-44133.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-595, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-44134
in-theory        44134
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (A or ((B and C) -> B))))
theorem-size     21
proof            (modus-ponens tm-595 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-44134.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (A or ((B and C) -> B)))), M:tm-595, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-44135
in-theory        44135
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (A or ((B and C) -> C))))
theorem-size     21
proof            (modus-ponens tm-595 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-44135.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (A or ((B and C) -> C)))), M:tm-595, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-44136
in-theory        44136
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (A or (B -> (C -> (B and C))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-44136.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (A or (B -> (C -> (B and C)))))), M:tm-595, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-44137
in-theory        44137
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (A or (B -> (B or C)))))
theorem-size     21
proof            (modus-ponens tm-595 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-44137.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (A or (B -> (B or C))))), M:tm-595, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-44138
in-theory        44138
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (A or (B -> (C or B)))))
theorem-size     21
proof            (modus-ponens tm-595 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-44138.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (A or (B -> (C or B))))), M:tm-595, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-44139
in-theory        44139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((A -> (B or A)) or C)))
theorem-size     21
proof            (modus-ponens tm-595 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-44139.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((A -> (B or A)) or C))), M:tm-595, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-44140
in-theory        44140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (A -> ((B -> (C or B)) and A))))
theorem-size     25
proof            (modus-ponens tm-595 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44140.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (A -> ((B -> (C or B)) and A)))), M:tm-595, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-44141
in-theory        44141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (A -> (B -> (C or B)))))
theorem-size     21
proof            (modus-ponens tm-595 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-44141.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (A -> (B -> (C or B))))), M:tm-595, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-44142
in-theory        44142
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((A -> B) -> C) -> ((B or (A -> B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-595 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-44142.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((A -> B) -> C) -> ((B or (A -> B)) -> C)))), M:tm-595, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-44143
in-theory        44143
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     57
proof            (modus-ponens tm-595 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44143.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-595, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-44144
in-theory        44144
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((A -> B) -> (((A and C) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-595 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44144.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((A -> B) -> (((A and C) or A) -> B)))), M:tm-595, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-44145
in-theory        44145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((A -> B) -> (((C and A) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-595 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-44145.        (((A -> B) -> (((C and A) or A) -> B)) and ((D -> (E or D)) and ((A -> B) -> (((C and A) or A) -> B)))), M:tm-595, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-44146
in-theory        44146
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-595 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-44146.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((D -> (E or D)) and (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)))), M:tm-595, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-44147
in-theory        44147
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((A or B) -> C) -> ((A or (A or B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-595 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-44147.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((D -> (E or D)) and (((A or B) -> C) -> ((A or (A or B)) -> C)))), M:tm-595, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-44148
in-theory        44148
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((A or B) -> C) -> ((B or (A or B)) -> C))))
theorem-size     33
proof            (modus-ponens tm-595 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-44148.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((D -> (E or D)) and (((A or B) -> C) -> ((B or (A or B)) -> C)))), M:tm-595, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-44149
in-theory        44149
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))))
theorem-size     61
proof            (modus-ponens tm-595 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-44149.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((E -> (F or E)) and ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))), M:tm-595, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-44150
in-theory        44150
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-44150.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-595, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-44151
in-theory        44151
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D)))
theorem-size     37
proof            (modus-ponens tm-595 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-44151.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and ((E -> (F or E)) and (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D))), M:tm-595, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-44152
in-theory        44152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((E -> (F or E)) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))))
theorem-size     41
proof            (modus-ponens tm-595 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-44152.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and ((E -> (F or E)) and (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)))), M:tm-595, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-44153
in-theory        44153
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((D -> (E or D)) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-44153.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and ((D -> (E or D)) and (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))))), M:tm-595, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-44154
in-theory        44154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-44154.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and ((E -> (F or E)) and (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))), M:tm-595, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-44155
in-theory        44155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and ((C -> (D or C)) and ((A -> (not (B -> A))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-595 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-44155.        (((A -> (not (B -> A))) -> (not A)) and ((C -> (D or C)) and ((A -> (not (B -> A))) -> (not A)))), M:tm-595, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-44156
in-theory        44156
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((D -> (E or D)) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44156.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and ((D -> (E or D)) and (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))))), M:tm-595, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-44157
in-theory        44157
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and ((C -> (D or C)) and (((A and B) -> (not A)) -> (not (A and B)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44157.        ((((A and B) -> (not A)) -> (not (A and B))) and ((C -> (D or C)) and (((A and B) -> (not A)) -> (not (A and B))))), M:tm-595, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-44158
in-theory        44158
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and ((C -> (D or C)) and (((A and B) -> (not B)) -> (not (A and B)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-44158.        ((((A and B) -> (not B)) -> (not (A and B))) and ((C -> (D or C)) and (((A and B) -> (not B)) -> (not (A and B))))), M:tm-595, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-44159
in-theory        44159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and ((C -> (D or C)) and ((A -> (not (B -> (A and B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-44159.        (((A -> (not (B -> (A and B)))) -> (not A)) and ((C -> (D or C)) and ((A -> (not (B -> (A and B)))) -> (not A)))), M:tm-595, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-44160
in-theory        44160
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and ((C -> (D or C)) and ((A -> (not (A or B))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-595 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-44160.        (((A -> (not (A or B))) -> (not A)) and ((C -> (D or C)) and ((A -> (not (A or B))) -> (not A)))), M:tm-595, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-44161
in-theory        44161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and ((C -> (D or C)) and ((A -> (not (B or A))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-595 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-44161.        (((A -> (not (B or A))) -> (not A)) and ((C -> (D or C)) and ((A -> (not (B or A))) -> (not A)))), M:tm-595, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-44162
in-theory        44162
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((D -> (E or D)) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-8)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-44162.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and ((D -> (E or D)) and (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))))), M:tm-595, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-44163
in-theory        44163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((C -> (D or C)) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-44163.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and ((C -> (D or C)) and (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))))), M:tm-595, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-44164
in-theory        44164
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((D -> (E or D)) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))))
theorem-size     53
proof            (modus-ponens tm-595 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-44164.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((D -> (E or D)) and ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))), M:tm-595, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-44165
in-theory        44165
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E or D)) and (A or ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-44165.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E or D)) and (A or ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-595, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-44166
in-theory        44166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((D -> (E or D)) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C)))
theorem-size     33
proof            (modus-ponens tm-595 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-44166.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and ((D -> (E or D)) and (((A -> B) -> ((A -> (not B)) -> (not A))) or C))), M:tm-595, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-44167
in-theory        44167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((D -> (E or D)) and (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A))))
theorem-size     37
proof            (modus-ponens tm-595 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-44167.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and ((D -> (E or D)) and (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)))), M:tm-595, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-44168
in-theory        44168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((C -> (D or C)) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-44168.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and ((C -> (D or C)) and (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))))), M:tm-595, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-44169
in-theory        44169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E or D)) and (A -> ((B -> C) -> ((B -> (not C)) -> (not B))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-44169.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and ((D -> (E or D)) and (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))))), M:tm-595, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-44170
in-theory        44170
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((B -> (C or B)) and (((not (not A)) -> (not A)) -> (not (not (not A))))))
theorem-size     29
proof            (modus-ponens tm-595 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-44170.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and ((B -> (C or B)) and (((not (not A)) -> (not A)) -> (not (not (not A)))))), M:tm-595, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-44171
in-theory        44171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and ((C -> (D or C)) and ((A -> B) -> (((not (not A)) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-595 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-44171.        (((A -> B) -> (((not (not A)) or A) -> B)) and ((C -> (D or C)) and ((A -> B) -> (((not (not A)) or A) -> B)))), M:tm-595, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-44172
in-theory        44172
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and ((C -> (D or C)) and (A or ((not (not B)) -> B))))
theorem-size     21
proof            (modus-ponens tm-595 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-44172.        ((A or ((not (not B)) -> B)) and ((C -> (D or C)) and (A or ((not (not B)) -> B)))), M:tm-595, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-44173
in-theory        44173
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and ((C -> (D or C)) and (((not (not A)) -> A) or B)))
theorem-size     21
proof            (modus-ponens tm-595 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-44173.        ((((not (not A)) -> A) or B) and ((C -> (D or C)) and (((not (not A)) -> A) or B))), M:tm-595, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-44174
in-theory        44174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and ((C -> (D or C)) and (A -> (((not (not B)) -> B) and A))))
theorem-size     25
proof            (modus-ponens tm-595 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-44174.        ((A -> (((not (not B)) -> B) and A)) and ((C -> (D or C)) and (A -> (((not (not B)) -> B) and A)))), M:tm-595, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-44175
in-theory        44175
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((C -> (D or C)) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B))))
theorem-size     37
proof            (modus-ponens tm-595 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-44175.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((C -> (D or C)) and (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)))), M:tm-595, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-44176
in-theory        44176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and ((C -> (D or C)) and (A -> ((not (not B)) -> B))))
theorem-size     21
proof            (modus-ponens tm-595 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-44176.        ((A -> ((not (not B)) -> B)) and ((C -> (D or C)) and (A -> ((not (not B)) -> B)))), M:tm-595, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-44177
in-theory        44177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and ((D -> (E or D)) and ((A -> (not (B -> (C -> B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-44177.        (((A -> (not (B -> (C -> B)))) -> (not A)) and ((D -> (E or D)) and ((A -> (not (B -> (C -> B)))) -> (not A)))), M:tm-595, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-44178
in-theory        44178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((E -> (F or E)) and (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-595 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-44178.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((E -> (F or E)) and (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)))), M:tm-595, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-44179
in-theory        44179
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and ((E -> (F or E)) and (A or (B -> (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-44179.        ((A or (B -> (C -> (D -> C)))) and ((E -> (F or E)) and (A or (B -> (C -> (D -> C)))))), M:tm-595, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-44180
in-theory        44180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and ((E -> (F or E)) and ((A -> (B -> (C -> B))) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-44180.        (((A -> (B -> (C -> B))) or D) and ((E -> (F or E)) and ((A -> (B -> (C -> B))) or D))), M:tm-595, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-44181
in-theory        44181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and ((E -> (F or E)) and (A -> ((B -> (C -> (D -> C))) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-44181.        ((A -> ((B -> (C -> (D -> C))) and A)) and ((E -> (F or E)) and (A -> ((B -> (C -> (D -> C))) and A)))), M:tm-595, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-44182
in-theory        44182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and ((D -> (E or D)) and ((A -> B) -> (A -> (C -> B)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-44182.        (((A -> B) -> (A -> (C -> B))) and ((D -> (E or D)) and ((A -> B) -> (A -> (C -> B))))), M:tm-595, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-44183
in-theory        44183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and ((E -> (F or E)) and (A -> (B -> (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-44183.        ((A -> (B -> (C -> (D -> C)))) and ((E -> (F or E)) and (A -> (B -> (C -> (D -> C)))))), M:tm-595, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-44184
in-theory        44184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and ((B -> (C or B)) and (A -> A)))
theorem-size     13
proof            (modus-ponens tm-595 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-44184.        ((A -> A) and ((B -> (C or B)) and (A -> A))), M:tm-595, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-44185
in-theory        44185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and ((D -> (E or D)) and ((A -> (B -> C)) -> (A -> (B -> C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44185.        (((A -> (B -> C)) -> (A -> (B -> C))) and ((D -> (E or D)) and ((A -> (B -> C)) -> (A -> (B -> C))))), M:tm-595, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-44186
in-theory        44186
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and ((C -> (D or C)) and ((A and B) -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-595 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44186.        (((A and B) -> (A and B)) and ((C -> (D or C)) and ((A and B) -> (A and B)))), M:tm-595, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-44187
in-theory        44187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and ((C -> (D or C)) and ((A -> B) -> (A -> B))))
theorem-size     21
proof            (modus-ponens tm-595 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-44187.        (((A -> B) -> (A -> B)) and ((C -> (D or C)) and ((A -> B) -> (A -> B)))), M:tm-595, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-44188
in-theory        44188
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and ((B -> (C or B)) and ((not (not A)) -> (not (not A)))))
theorem-size     21
proof            (modus-ponens tm-595 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-10)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-44188.        (((not (not A)) -> (not (not A))) and ((B -> (C or B)) and ((not (not A)) -> (not (not A))))), M:tm-595, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-44189
in-theory        44189
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((C -> (D or C)) and (((A -> B) -> (not (A -> A))) -> (not (A -> B)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-44189.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and ((C -> (D or C)) and (((A -> B) -> (not (A -> A))) -> (not (A -> B))))), M:tm-595, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-44190
in-theory        44190
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((D -> (E or D)) and (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B))))
theorem-size     37
proof            (modus-ponens tm-595 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-44190.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((D -> (E or D)) and (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)))), M:tm-595, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-44191
in-theory        44191
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and ((D -> (E or D)) and (A or ((B -> C) -> (B -> B)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-44191.        ((A or ((B -> C) -> (B -> B))) and ((D -> (E or D)) and (A or ((B -> C) -> (B -> B))))), M:tm-595, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-44192
in-theory        44192
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and ((D -> (E or D)) and (((A -> B) -> (A -> A)) or C)))
theorem-size     25
proof            (modus-ponens tm-595 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-44192.        ((((A -> B) -> (A -> A)) or C) and ((D -> (E or D)) and (((A -> B) -> (A -> A)) or C))), M:tm-595, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-44193
in-theory        44193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and ((D -> (E or D)) and (A -> (((B -> C) -> (B -> B)) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-44193.        ((A -> (((B -> C) -> (B -> B)) and A)) and ((D -> (E or D)) and (A -> (((B -> C) -> (B -> B)) and A)))), M:tm-595, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-44194
in-theory        44194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and ((C -> (D or C)) and (((A -> B) -> A) -> ((A -> B) -> A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-44194.        ((((A -> B) -> A) -> ((A -> B) -> A)) and ((C -> (D or C)) and (((A -> B) -> A) -> ((A -> B) -> A)))), M:tm-595, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-44195
in-theory        44195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and ((D -> (E or D)) and (A -> ((B -> C) -> (B -> B)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-44195.        ((A -> ((B -> C) -> (B -> B))) and ((D -> (E or D)) and (A -> ((B -> C) -> (B -> B))))), M:tm-595, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-44196
in-theory        44196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and ((D -> (E or D)) and ((A -> ((B -> A) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-44196.        (((A -> ((B -> A) -> C)) -> (A -> C)) and ((D -> (E or D)) and ((A -> ((B -> A) -> C)) -> (A -> C)))), M:tm-595, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-44197
in-theory        44197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and ((C -> (D or C)) and ((A -> (A -> B)) -> (A -> B))))
theorem-size     25
proof            (modus-ponens tm-595 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-44197.        (((A -> (A -> B)) -> (A -> B)) and ((C -> (D or C)) and ((A -> (A -> B)) -> (A -> B)))), M:tm-595, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-44198
in-theory        44198
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((D -> (E or D)) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-44198.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and ((D -> (E or D)) and (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))))), M:tm-595, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-44199
in-theory        44199
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((D -> (E or D)) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B))))))
theorem-size     69
proof            (modus-ponens tm-595 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-44199.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((D -> (E or D)) and ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))))), M:tm-595, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-44200
in-theory        44200
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))))
theorem-size     73
proof            (modus-ponens tm-595 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-44200.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))), M:tm-595, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-44201
in-theory        44201
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F or E)) and (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-44201.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F or E)) and (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-595, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-44202
in-theory        44202
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and ((E -> (F or E)) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D)))
theorem-size     49
proof            (modus-ponens tm-595 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-44202.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and ((E -> (F or E)) and ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D))), M:tm-595, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-44203
in-theory        44203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((E -> (F or E)) and (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))))
theorem-size     53
proof            (modus-ponens tm-595 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-44203.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and ((E -> (F or E)) and (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)))), M:tm-595, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-44204
in-theory        44204
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((D -> (E or D)) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-595 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-44204.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((D -> (E or D)) and ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))), M:tm-595, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-44205
in-theory        44205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F or E)) and (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-44205.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and ((E -> (F or E)) and (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))), M:tm-595, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-44206
in-theory        44206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((E -> (F or E)) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-595 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-44206.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and ((E -> (F or E)) and (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)))), M:tm-595, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-44207
in-theory        44207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((E -> (F or E)) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A))))
theorem-size     45
proof            (modus-ponens tm-595 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-44207.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((E -> (F or E)) and ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)))), M:tm-595, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-44208
in-theory        44208
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((F -> (G or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))))
theorem-size     73
proof            (modus-ponens tm-595 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-44208.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((F -> (G or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))), M:tm-595, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-44209
in-theory        44209
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G or F)) and (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44209.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G or F)) and (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-595, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-44210
in-theory        44210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G or F)) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-595 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44210.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G or F)) and ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-595, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-44211
in-theory        44211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G or F)) and (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-595 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44211.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G or F)) and (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-595, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-44212
in-theory        44212
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-44212.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))))), M:tm-595, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-44213
in-theory        44213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G or F)) and (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44213.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G or F)) and (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-595, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-44214
in-theory        44214
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and ((C -> (D or C)) and (((A -> B) and A) -> B)))
theorem-size     21
proof            (modus-ponens tm-595 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-44214.        ((((A -> B) and A) -> B) and ((C -> (D or C)) and (((A -> B) and A) -> B))), M:tm-595, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-44215
in-theory        44215
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and ((E -> (F or E)) and ((((A -> (B -> A)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-595 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-44215.        (((((A -> (B -> A)) -> C) and D) -> C) and ((E -> (F or E)) and ((((A -> (B -> A)) -> C) and D) -> C))), M:tm-595, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-44216
in-theory        44216
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((F -> (G or F)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D)))
theorem-size     45
proof            (modus-ponens tm-595 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-44216.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and ((F -> (G or F)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D))), M:tm-595, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-44217
in-theory        44217
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((D -> (E or D)) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B))))
theorem-size     49
proof            (modus-ponens tm-595 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-44217.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and ((D -> (E or D)) and (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)))), M:tm-595, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-44218
in-theory        44218
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((D -> (E or D)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A))))
theorem-size     37
proof            (modus-ponens tm-595 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-44218.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((D -> (E or D)) and ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)))), M:tm-595, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-44219
in-theory        44219
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((D -> (E or D)) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A)))))
theorem-size     57
proof            (modus-ponens tm-595 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-44219.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and ((D -> (E or D)) and (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))))), M:tm-595, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-44220
in-theory        44220
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((E -> (F or E)) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))))
theorem-size     61
proof            (modus-ponens tm-595 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-44220.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((E -> (F or E)) and (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))), M:tm-595, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-44221
in-theory        44221
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F or E)) and (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-44221.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F or E)) and (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-595, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-44222
in-theory        44222
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((E -> (F or E)) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D)))
theorem-size     41
proof            (modus-ponens tm-595 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-44222.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and ((E -> (F or E)) and (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D))), M:tm-595, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-44223
in-theory        44223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((E -> (F or E)) and (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))))
theorem-size     45
proof            (modus-ponens tm-595 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-44223.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and ((E -> (F or E)) and (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)))), M:tm-595, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-44224
in-theory        44224
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((D -> (E or D)) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B))))
theorem-size     53
proof            (modus-ponens tm-595 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-44224.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((D -> (E or D)) and (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)))), M:tm-595, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-44225
in-theory        44225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F or E)) and (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-44225.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and ((E -> (F or E)) and (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))), M:tm-595, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-44226
in-theory        44226
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and ((E -> (F or E)) and (((((A and B) -> A) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-595 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-44226.        ((((((A and B) -> A) -> C) and D) -> C) and ((E -> (F or E)) and (((((A and B) -> A) -> C) and D) -> C))), M:tm-595, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-44227
in-theory        44227
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((D -> (E or D)) and (((A and B) -> (A -> C)) -> ((A and B) -> C))))
theorem-size     33
proof            (modus-ponens tm-595 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-44227.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and ((D -> (E or D)) and (((A and B) -> (A -> C)) -> ((A and B) -> C)))), M:tm-595, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-44228
in-theory        44228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and ((D -> (E or D)) and ((A -> (not ((B and C) -> B))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-44228.        (((A -> (not ((B and C) -> B))) -> (not A)) and ((D -> (E or D)) and ((A -> (not ((B and C) -> B))) -> (not A)))), M:tm-595, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-44229
in-theory        44229
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((E -> (F or E)) and ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C))))
theorem-size     41
proof            (modus-ponens tm-595 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-44229.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((E -> (F or E)) and ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)))), M:tm-595, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-44230
in-theory        44230
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and ((E -> (F or E)) and (A or (B -> ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-44230.        ((A or (B -> ((C and D) -> C))) and ((E -> (F or E)) and (A or (B -> ((C and D) -> C))))), M:tm-595, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-44231
in-theory        44231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and ((E -> (F or E)) and ((A -> ((B and C) -> B)) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-44231.        (((A -> ((B and C) -> B)) or D) and ((E -> (F or E)) and ((A -> ((B and C) -> B)) or D))), M:tm-595, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-44232
in-theory        44232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and ((E -> (F or E)) and (A -> ((B -> ((C and D) -> C)) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-44232.        ((A -> ((B -> ((C and D) -> C)) and A)) and ((E -> (F or E)) and (A -> ((B -> ((C and D) -> C)) and A)))), M:tm-595, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-44233
in-theory        44233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and ((D -> (E or D)) and ((A -> (B and C)) -> (A -> B))))
theorem-size     25
proof            (modus-ponens tm-595 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-44233.        (((A -> (B and C)) -> (A -> B)) and ((D -> (E or D)) and ((A -> (B and C)) -> (A -> B)))), M:tm-595, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-44234
in-theory        44234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and ((E -> (F or E)) and (A -> (B -> ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-44234.        ((A -> (B -> ((C and D) -> C))) and ((E -> (F or E)) and (A -> (B -> ((C and D) -> C))))), M:tm-595, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-44235
in-theory        44235
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and ((C -> (D or C)) and ((A and (A -> B)) -> B)))
theorem-size     21
proof            (modus-ponens tm-595 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-44235.        (((A and (A -> B)) -> B) and ((C -> (D or C)) and ((A and (A -> B)) -> B))), M:tm-595, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-44236
in-theory        44236
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and ((E -> (F or E)) and ((A and ((B -> (C -> B)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-595 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-44236.        (((A and ((B -> (C -> B)) -> D)) -> D) and ((E -> (F or E)) and ((A and ((B -> (C -> B)) -> D)) -> D))), M:tm-595, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-44237
in-theory        44237
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((F -> (G or F)) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E)))
theorem-size     45
proof            (modus-ponens tm-595 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-44237.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((F -> (G or F)) and ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E))), M:tm-595, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-44238
in-theory        44238
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and ((E -> (F or E)) and ((A and (((B and C) -> B) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-595 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-44238.        (((A and (((B and C) -> B) -> D)) -> D) and ((E -> (F or E)) and ((A and (((B and C) -> B) -> D)) -> D))), M:tm-595, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-44239
in-theory        44239
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((D -> (E or D)) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-595 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-44239.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and ((D -> (E or D)) and (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)))), M:tm-595, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-44240
in-theory        44240
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((D -> (E or D)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B))))
theorem-size     37
proof            (modus-ponens tm-595 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-44240.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((D -> (E or D)) and (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)))), M:tm-595, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-44241
in-theory        44241
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((D -> (E or D)) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B)))))
theorem-size     57
proof            (modus-ponens tm-595 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-44241.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((D -> (E or D)) and ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))))), M:tm-595, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-44242
in-theory        44242
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((E -> (F or E)) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))))
theorem-size     61
proof            (modus-ponens tm-595 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-44242.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((E -> (F or E)) and ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))), M:tm-595, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-44243
in-theory        44243
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F or E)) and (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-44243.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F or E)) and (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-595, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-44244
in-theory        44244
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and ((E -> (F or E)) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D)))
theorem-size     41
proof            (modus-ponens tm-595 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-44244.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and ((E -> (F or E)) and ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D))), M:tm-595, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-44245
in-theory        44245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((E -> (F or E)) and (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))))
theorem-size     45
proof            (modus-ponens tm-595 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-44245.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and ((E -> (F or E)) and (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)))), M:tm-595, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-44246
in-theory        44246
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((D -> (E or D)) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C))))
theorem-size     53
proof            (modus-ponens tm-595 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-44246.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((D -> (E or D)) and ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)))), M:tm-595, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-44247
in-theory        44247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F or E)) and (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-44247.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and ((E -> (F or E)) and (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))), M:tm-595, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-44248
in-theory        44248
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and ((E -> (F or E)) and ((A and (((B and C) -> C) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-595 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-44248.        (((A and (((B and C) -> C) -> D)) -> D) and ((E -> (F or E)) and ((A and (((B and C) -> C) -> D)) -> D))), M:tm-595, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-44249
in-theory        44249
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and ((E -> (F or E)) and (((((A and B) -> B) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-595 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-44249.        ((((((A and B) -> B) -> C) and D) -> C) and ((E -> (F or E)) and (((((A and B) -> B) -> C) and D) -> C))), M:tm-595, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-44250
in-theory        44250
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((D -> (E or D)) and (((A and B) -> (B -> C)) -> ((A and B) -> C))))
theorem-size     33
proof            (modus-ponens tm-595 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-44250.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and ((D -> (E or D)) and (((A and B) -> (B -> C)) -> ((A and B) -> C)))), M:tm-595, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-44251
in-theory        44251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and ((D -> (E or D)) and ((A -> (not ((B and C) -> C))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-44251.        (((A -> (not ((B and C) -> C))) -> (not A)) and ((D -> (E or D)) and ((A -> (not ((B and C) -> C))) -> (not A)))), M:tm-595, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-44252
in-theory        44252
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((E -> (F or E)) and ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C))))
theorem-size     41
proof            (modus-ponens tm-595 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-44252.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((E -> (F or E)) and ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)))), M:tm-595, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-44253
in-theory        44253
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and ((E -> (F or E)) and (A or (B -> ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-44253.        ((A or (B -> ((C and D) -> D))) and ((E -> (F or E)) and (A or (B -> ((C and D) -> D))))), M:tm-595, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-44254
in-theory        44254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and ((E -> (F or E)) and ((A -> ((B and C) -> C)) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-44254.        (((A -> ((B and C) -> C)) or D) and ((E -> (F or E)) and ((A -> ((B and C) -> C)) or D))), M:tm-595, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-44255
in-theory        44255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and ((E -> (F or E)) and (A -> ((B -> ((C and D) -> D)) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-44255.        ((A -> ((B -> ((C and D) -> D)) and A)) and ((E -> (F or E)) and (A -> ((B -> ((C and D) -> D)) and A)))), M:tm-595, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-44256
in-theory        44256
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and ((D -> (E or D)) and ((A -> (B and C)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-595 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-44256.        (((A -> (B and C)) -> (A -> C)) and ((D -> (E or D)) and ((A -> (B and C)) -> (A -> C)))), M:tm-595, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-44257
in-theory        44257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and ((E -> (F or E)) and (A -> (B -> ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-44257.        ((A -> (B -> ((C and D) -> D))) and ((E -> (F or E)) and (A -> (B -> ((C and D) -> D))))), M:tm-595, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-44258
in-theory        44258
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and ((E -> (F or E)) and ((A -> (B -> A)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-44258.        (((A -> (B -> A)) and (C -> (D -> C))) and ((E -> (F or E)) and ((A -> (B -> A)) and (C -> (D -> C))))), M:tm-595, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-44259
in-theory        44259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-44259.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-595, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-44260
in-theory        44260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and ((E -> (F or E)) and ((A -> (B -> A)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-44260.        (((A -> (B -> A)) and ((C and D) -> C)) and ((E -> (F or E)) and ((A -> (B -> A)) and ((C and D) -> C)))), M:tm-595, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-44261
in-theory        44261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and ((E -> (F or E)) and ((A -> (B -> A)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-595 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-44261.        (((A -> (B -> A)) and ((C and D) -> D)) and ((E -> (F or E)) and ((A -> (B -> A)) and ((C and D) -> D)))), M:tm-595, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-44262
in-theory        44262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A -> (B -> A)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-44262.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A -> (B -> A)) and (C -> (D -> (C and D)))))), M:tm-595, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-44263
in-theory        44263
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and ((E -> (F or E)) and ((A -> (B -> A)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-44263.        (((A -> (B -> A)) and (C -> (C or D))) and ((E -> (F or E)) and ((A -> (B -> A)) and (C -> (C or D))))), M:tm-595, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-44264
in-theory        44264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and ((E -> (F or E)) and ((A -> (B -> A)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-44264.        (((A -> (B -> A)) and (C -> (D or C))) and ((E -> (F or E)) and ((A -> (B -> A)) and (C -> (D or C))))), M:tm-595, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-44265
in-theory        44265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-44265.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-595, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-44266
in-theory        44266
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F or E)) and ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-44266.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F or E)) and ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-595, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-44267
in-theory        44267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and ((D -> (E or D)) and ((A -> (B -> A)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-44267.        (((A -> (B -> A)) and ((not (not C)) -> C)) and ((D -> (E or D)) and ((A -> (B -> A)) and ((not (not C)) -> C)))), M:tm-595, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-44268
in-theory        44268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-44268.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> (D -> (E -> D)))))), M:tm-595, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-44269
in-theory        44269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((E -> (F or E)) and ((A -> (B -> A)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-44269.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and ((E -> (F or E)) and ((A -> (B -> A)) and ((C -> D) -> (C -> C))))), M:tm-595, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-44270
in-theory        44270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-595 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-44270.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-595, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-44271
in-theory        44271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44271.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-595, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-44272
in-theory        44272
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G or F)) and ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-44272.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G or F)) and ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-595, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-44273
in-theory        44273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-44273.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> ((D and E) -> D))))), M:tm-595, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-44274
in-theory        44274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-44274.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-595, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-44275
in-theory        44275
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-44275.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> ((D and E) -> E))))), M:tm-595, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-44276
in-theory        44276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-44276.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-595, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-44277
in-theory        44277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((D -> (E or D)) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-44277.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((D -> (E or D)) and ((A -> (not ((B -> (C -> B)) and A))) -> (not A)))), M:tm-595, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-44278
in-theory        44278
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((E -> (F or E)) and ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-595 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-44278.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((E -> (F or E)) and ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)))), M:tm-595, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-44279
in-theory        44279
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and ((E -> (F or E)) and (A or (B -> ((C -> (D -> C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-44279.        ((A or (B -> ((C -> (D -> C)) and B))) and ((E -> (F or E)) and (A or (B -> ((C -> (D -> C)) and B))))), M:tm-595, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-44280
in-theory        44280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and ((E -> (F or E)) and ((A -> ((B -> (C -> B)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-595 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-44280.        (((A -> ((B -> (C -> B)) and A)) or D) and ((E -> (F or E)) and ((A -> ((B -> (C -> B)) and A)) or D))), M:tm-595, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-44281
in-theory        44281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((E -> (F or E)) and (A -> ((B -> ((C -> (D -> C)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-44281.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and ((E -> (F or E)) and (A -> ((B -> ((C -> (D -> C)) and B)) and A)))), M:tm-595, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-44282
in-theory        44282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and ((E -> (F or E)) and (A -> (B -> ((C -> (D -> C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-44282.        ((A -> (B -> ((C -> (D -> C)) and B))) and ((E -> (F or E)) and (A -> (B -> ((C -> (D -> C)) and B))))), M:tm-595, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-44283
in-theory        44283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-44283.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))))), M:tm-595, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-44284
in-theory        44284
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-44284.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-595, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-44285
in-theory        44285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-595 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-44285.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)))), M:tm-595, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-44286
in-theory        44286
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-595 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-44286.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)))), M:tm-595, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-44287
in-theory        44287
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-44287.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))))), M:tm-595, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-44288
in-theory        44288
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-44288.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))))), M:tm-595, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-44289
in-theory        44289
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-44289.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))))), M:tm-595, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-44290
in-theory        44290
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-44290.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))), M:tm-595, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-44291
in-theory        44291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D))))))
theorem-size     57
proof            (modus-ponens tm-595 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-44291.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))))), M:tm-595, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-44292
in-theory        44292
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((E -> (F or E)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D))))
theorem-size     45
proof            (modus-ponens tm-595 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-44292.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and ((E -> (F or E)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)))), M:tm-595, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-44293
in-theory        44293
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-44293.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))))), M:tm-595, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-44294
in-theory        44294
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-44294.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))))), M:tm-595, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-44295
in-theory        44295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))))
theorem-size     73
proof            (modus-ponens tm-595 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       249
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-44295.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))), M:tm-595, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-44296
in-theory        44296
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-595 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44296.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-595, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-44297
in-theory        44297
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))))
theorem-size     65
proof            (modus-ponens tm-595 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-44297.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))), M:tm-595, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-44298
in-theory        44298
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-44298.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))))), M:tm-595, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-44299
in-theory        44299
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))))
theorem-size     65
proof            (modus-ponens tm-595 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-44299.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))), M:tm-595, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-44300
in-theory        44300
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-44300.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))))), M:tm-595, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-44301
in-theory        44301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-44301.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))))), M:tm-595, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-44302
in-theory        44302
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (I or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))))
theorem-size     69
proof            (modus-ponens tm-595 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-44302.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and ((H -> (I or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))), M:tm-595, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-44303
in-theory        44303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H or G)) and ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-44303.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H or G)) and ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-595, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-44304
in-theory        44304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((E -> (F or E)) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A))))
theorem-size     49
proof            (modus-ponens tm-595 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-44304.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((E -> (F or E)) and ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)))), M:tm-595, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-44305
in-theory        44305
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((F -> (G or F)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))))
theorem-size     81
proof            (modus-ponens tm-595 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-44305.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((F -> (G or F)) and (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))), M:tm-595, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-44306
in-theory        44306
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G or F)) and (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-44306.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G or F)) and (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-595, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-44307
in-theory        44307
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and ((F -> (G or F)) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E)))
theorem-size     45
proof            (modus-ponens tm-595 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-44307.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and ((F -> (G or F)) and ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E))), M:tm-595, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-44308
in-theory        44308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((F -> (G or F)) and (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))))
theorem-size     49
proof            (modus-ponens tm-595 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-44308.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and ((F -> (G or F)) and (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)))), M:tm-595, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-44309
in-theory        44309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G or F)) and (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-44309.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and ((F -> (G or F)) and (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))), M:tm-595, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-44310
in-theory        44310
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and ((E -> (F or E)) and (((A and B) -> A) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-44310.        ((((A and B) -> A) and (C -> (D -> C))) and ((E -> (F or E)) and (((A and B) -> A) and (C -> (D -> C))))), M:tm-595, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-44311
in-theory        44311
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-44311.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-595, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-44312
in-theory        44312
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and ((E -> (F or E)) and (((A and B) -> A) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-44312.        ((((A and B) -> A) and ((C and D) -> C)) and ((E -> (F or E)) and (((A and B) -> A) and ((C and D) -> C)))), M:tm-595, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-44313
in-theory        44313
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and ((E -> (F or E)) and (((A and B) -> A) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-595 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-44313.        ((((A and B) -> A) and ((C and D) -> D)) and ((E -> (F or E)) and (((A and B) -> A) and ((C and D) -> D)))), M:tm-595, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-44314
in-theory        44314
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((E -> (F or E)) and (((A and B) -> A) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-44314.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and ((E -> (F or E)) and (((A and B) -> A) and (C -> (D -> (C and D)))))), M:tm-595, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-44315
in-theory        44315
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and ((E -> (F or E)) and (((A and B) -> A) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-44315.        ((((A and B) -> A) and (C -> (C or D))) and ((E -> (F or E)) and (((A and B) -> A) and (C -> (C or D))))), M:tm-595, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-44316
in-theory        44316
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and ((E -> (F or E)) and (((A and B) -> A) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-44316.        ((((A and B) -> A) and (C -> (D or C))) and ((E -> (F or E)) and (((A and B) -> A) and (C -> (D or C))))), M:tm-595, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-44317
in-theory        44317
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-44317.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-595, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-44318
in-theory        44318
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F or E)) and (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-44318.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F or E)) and (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-595, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-44319
in-theory        44319
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and ((D -> (E or D)) and (((A and B) -> A) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-44319.        ((((A and B) -> A) and ((not (not C)) -> C)) and ((D -> (E or D)) and (((A and B) -> A) and ((not (not C)) -> C)))), M:tm-595, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-44320
in-theory        44320
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-44320.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> (D -> (E -> D)))))), M:tm-595, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-44321
in-theory        44321
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((E -> (F or E)) and (((A and B) -> A) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-44321.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and ((E -> (F or E)) and (((A and B) -> A) and ((C -> D) -> (C -> C))))), M:tm-595, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-44322
in-theory        44322
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G or F)) and (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-595 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-44322.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G or F)) and (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-595, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-44323
in-theory        44323
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44323.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-595, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-44324
in-theory        44324
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G or F)) and (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-44324.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G or F)) and (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-595, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-44325
in-theory        44325
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-44325.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> ((D and E) -> D))))), M:tm-595, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-44326
in-theory        44326
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G or F)) and (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-44326.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G or F)) and (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-595, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-44327
in-theory        44327
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-44327.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> ((D and E) -> E))))), M:tm-595, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-44328
in-theory        44328
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-44328.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))))), M:tm-595, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-44329
in-theory        44329
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H or G)) and (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-44329.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H or G)) and (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-595, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-44330
in-theory        44330
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-44330.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> (((D and E) -> D) and C))))), M:tm-595, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-44331
in-theory        44331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-44331.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))))), M:tm-595, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-44332
in-theory        44332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-44332.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))))), M:tm-595, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-44333
in-theory        44333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((D -> (E or D)) and ((A -> (not (((B and C) -> B) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-44333.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((D -> (E or D)) and ((A -> (not (((B and C) -> B) and A))) -> (not A)))), M:tm-595, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-44334
in-theory        44334
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((E -> (F or E)) and (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-595 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-44334.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((E -> (F or E)) and (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)))), M:tm-595, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-44335
in-theory        44335
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and ((E -> (F or E)) and (A or (B -> (((C and D) -> C) and B)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-44335.        ((A or (B -> (((C and D) -> C) and B))) and ((E -> (F or E)) and (A or (B -> (((C and D) -> C) and B))))), M:tm-595, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-44336
in-theory        44336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and ((E -> (F or E)) and ((A -> (((B and C) -> B) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-595 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-44336.        (((A -> (((B and C) -> B) and A)) or D) and ((E -> (F or E)) and ((A -> (((B and C) -> B) and A)) or D))), M:tm-595, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-44337
in-theory        44337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((E -> (F or E)) and (A -> ((B -> (((C and D) -> C) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-44337.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and ((E -> (F or E)) and (A -> ((B -> (((C and D) -> C) and B)) and A)))), M:tm-595, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-44338
in-theory        44338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and ((E -> (F or E)) and (A -> (B -> (((C and D) -> C) and B)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-44338.        ((A -> (B -> (((C and D) -> C) and B))) and ((E -> (F or E)) and (A -> (B -> (((C and D) -> C) and B))))), M:tm-595, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-44339
in-theory        44339
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and ((E -> (F or E)) and (((A and B) -> B) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-44339.        ((((A and B) -> B) and (C -> (D -> C))) and ((E -> (F or E)) and (((A and B) -> B) and (C -> (D -> C))))), M:tm-595, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-44340
in-theory        44340
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-44340.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-595, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-44341
in-theory        44341
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and ((E -> (F or E)) and (((A and B) -> B) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-44341.        ((((A and B) -> B) and ((C and D) -> C)) and ((E -> (F or E)) and (((A and B) -> B) and ((C and D) -> C)))), M:tm-595, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-44342
in-theory        44342
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and ((E -> (F or E)) and (((A and B) -> B) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-595 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-44342.        ((((A and B) -> B) and ((C and D) -> D)) and ((E -> (F or E)) and (((A and B) -> B) and ((C and D) -> D)))), M:tm-595, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-44343
in-theory        44343
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((E -> (F or E)) and (((A and B) -> B) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-44343.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and ((E -> (F or E)) and (((A and B) -> B) and (C -> (D -> (C and D)))))), M:tm-595, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-44344
in-theory        44344
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and ((E -> (F or E)) and (((A and B) -> B) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-44344.        ((((A and B) -> B) and (C -> (C or D))) and ((E -> (F or E)) and (((A and B) -> B) and (C -> (C or D))))), M:tm-595, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-44345
in-theory        44345
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and ((E -> (F or E)) and (((A and B) -> B) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-44345.        ((((A and B) -> B) and (C -> (D or C))) and ((E -> (F or E)) and (((A and B) -> B) and (C -> (D or C))))), M:tm-595, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-44346
in-theory        44346
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-44346.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-595, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-44347
in-theory        44347
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F or E)) and (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-44347.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F or E)) and (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-595, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-44348
in-theory        44348
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and ((D -> (E or D)) and (((A and B) -> B) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-44348.        ((((A and B) -> B) and ((not (not C)) -> C)) and ((D -> (E or D)) and (((A and B) -> B) and ((not (not C)) -> C)))), M:tm-595, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-44349
in-theory        44349
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-44349.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> (D -> (E -> D)))))), M:tm-595, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-44350
in-theory        44350
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((E -> (F or E)) and (((A and B) -> B) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-44350.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and ((E -> (F or E)) and (((A and B) -> B) and ((C -> D) -> (C -> C))))), M:tm-595, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-44351
in-theory        44351
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G or F)) and (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-595 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-44351.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G or F)) and (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-595, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-44352
in-theory        44352
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44352.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-595, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-44353
in-theory        44353
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G or F)) and (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-44353.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G or F)) and (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-595, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-44354
in-theory        44354
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-44354.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> ((D and E) -> D))))), M:tm-595, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-44355
in-theory        44355
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G or F)) and (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-44355.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G or F)) and (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-595, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-44356
in-theory        44356
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-44356.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> ((D and E) -> E))))), M:tm-595, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-44357
in-theory        44357
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-44357.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))))), M:tm-595, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-44358
in-theory        44358
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H or G)) and (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-44358.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H or G)) and (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-595, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-44359
in-theory        44359
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-44359.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> (((D and E) -> D) and C))))), M:tm-595, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-44360
in-theory        44360
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-44360.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> (((D and E) -> E) and C))))), M:tm-595, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-44361
in-theory        44361
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-44361.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> (((D and E) -> E) and C))))), M:tm-595, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-44362
in-theory        44362
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-44362.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))))), M:tm-595, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-44363
in-theory        44363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-44363.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))))), M:tm-595, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-44364
in-theory        44364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((D -> (E or D)) and ((A -> (not (((B and C) -> C) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-44364.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((D -> (E or D)) and ((A -> (not (((B and C) -> C) and A))) -> (not A)))), M:tm-595, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-44365
in-theory        44365
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((E -> (F or E)) and (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-595 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-44365.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((E -> (F or E)) and (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)))), M:tm-595, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-44366
in-theory        44366
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and ((E -> (F or E)) and (A or (B -> (((C and D) -> D) and B)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-44366.        ((A or (B -> (((C and D) -> D) and B))) and ((E -> (F or E)) and (A or (B -> (((C and D) -> D) and B))))), M:tm-595, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-44367
in-theory        44367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and ((E -> (F or E)) and ((A -> (((B and C) -> C) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-595 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-44367.        (((A -> (((B and C) -> C) and A)) or D) and ((E -> (F or E)) and ((A -> (((B and C) -> C) and A)) or D))), M:tm-595, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-44368
in-theory        44368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((E -> (F or E)) and (A -> ((B -> (((C and D) -> D) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-44368.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and ((E -> (F or E)) and (A -> ((B -> (((C and D) -> D) and B)) and A)))), M:tm-595, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-44369
in-theory        44369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and ((E -> (F or E)) and (A -> (B -> (((C and D) -> D) and B)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-44369.        ((A -> (B -> (((C and D) -> D) and B))) and ((E -> (F or E)) and (A -> (B -> (((C and D) -> D) and B))))), M:tm-595, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-44370
in-theory        44370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and (C -> (D -> C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-44370.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and (C -> (D -> C))))), M:tm-595, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-44371
in-theory        44371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-44371.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-595, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-44372
in-theory        44372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and ((C and D) -> C))))
theorem-size     33
proof            (modus-ponens tm-595 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-44372.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and ((C and D) -> C)))), M:tm-595, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-44373
in-theory        44373
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and ((C and D) -> D))))
theorem-size     33
proof            (modus-ponens tm-595 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-44373.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and ((C and D) -> D)))), M:tm-595, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-44374
in-theory        44374
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and (C -> (D -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-44374.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))))), M:tm-595, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-44375
in-theory        44375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and (C -> (C or D)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-44375.        (((A -> (B -> (A and B))) and (C -> (C or D))) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and (C -> (C or D))))), M:tm-595, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-44376
in-theory        44376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and (C -> (D or C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-44376.        (((A -> (B -> (A and B))) and (C -> (D or C))) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and (C -> (D or C))))), M:tm-595, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-44377
in-theory        44377
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-44377.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-595, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-44378
in-theory        44378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-44378.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-595, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-44379
in-theory        44379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((D -> (E or D)) and ((A -> (B -> (A and B))) and ((not (not C)) -> C))))
theorem-size     33
proof            (modus-ponens tm-595 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-44379.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and ((D -> (E or D)) and ((A -> (B -> (A and B))) and ((not (not C)) -> C)))), M:tm-595, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-44380
in-theory        44380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-44380.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))))), M:tm-595, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-44381
in-theory        44381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-44381.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))))), M:tm-595, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-44382
in-theory        44382
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-44382.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-595, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-44383
in-theory        44383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     53
proof            (modus-ponens tm-595 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44383.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-595, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-44384
in-theory        44384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-44384.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-595, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-44385
in-theory        44385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> D)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-44385.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))))), M:tm-595, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-44386
in-theory        44386
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-44386.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-595, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-44387
in-theory        44387
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> E)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-44387.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))))), M:tm-595, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-44388
in-theory        44388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-44388.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))))), M:tm-595, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-44389
in-theory        44389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H or G)) and ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     57
proof            (modus-ponens tm-595 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-44389.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H or G)) and ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-595, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-44390
in-theory        44390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-44390.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))))), M:tm-595, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-44391
in-theory        44391
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-44391.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))))), M:tm-595, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-44392
in-theory        44392
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-44392.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-595, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-44393
in-theory        44393
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-44393.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-595, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-44394
in-theory        44394
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-44394.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-595, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-44395
in-theory        44395
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D)))))
theorem-size     57
proof            (modus-ponens tm-595 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-44395.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))))), M:tm-595, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-44396
in-theory        44396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-44396.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-595, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-44397
in-theory        44397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((D -> (E or D)) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A))))
theorem-size     37
proof            (modus-ponens tm-595 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-44397.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((D -> (E or D)) and ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)))), M:tm-595, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-44398
in-theory        44398
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((E -> (F or E)) and ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-595 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-44398.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((E -> (F or E)) and ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)))), M:tm-595, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-44399
in-theory        44399
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F or E)) and (A or (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-44399.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F or E)) and (A or (B -> ((C -> (D -> (C and D))) and B))))), M:tm-595, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-44400
in-theory        44400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and ((E -> (F or E)) and ((A -> ((B -> (C -> (B and C))) and A)) or D)))
theorem-size     33
proof            (modus-ponens tm-595 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-44400.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and ((E -> (F or E)) and ((A -> ((B -> (C -> (B and C))) and A)) or D))), M:tm-595, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-44401
in-theory        44401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((E -> (F or E)) and (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A))))
theorem-size     37
proof            (modus-ponens tm-595 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-44401.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and ((E -> (F or E)) and (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)))), M:tm-595, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-44402
in-theory        44402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F or E)) and (A -> (B -> ((C -> (D -> (C and D))) and B)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-44402.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and ((E -> (F or E)) and (A -> (B -> ((C -> (D -> (C and D))) and B))))), M:tm-595, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-44403
in-theory        44403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and ((C -> (D or C)) and (A -> (A and (B -> A)))))
theorem-size     21
proof            (modus-ponens tm-595 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-44403.        ((A -> (A and (B -> A))) and ((C -> (D or C)) and (A -> (A and (B -> A))))), M:tm-595, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-44404
in-theory        44404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((D -> (E or D)) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44404.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((D -> (E or D)) and ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))), M:tm-595, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-44405
in-theory        44405
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and ((C -> (D or C)) and ((A and B) -> ((A and B) and A))))
theorem-size     25
proof            (modus-ponens tm-595 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44405.        (((A and B) -> ((A and B) and A)) and ((C -> (D or C)) and ((A and B) -> ((A and B) and A)))), M:tm-595, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-44406
in-theory        44406
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and ((C -> (D or C)) and ((A and B) -> ((A and B) and B))))
theorem-size     25
proof            (modus-ponens tm-595 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-44406.        (((A and B) -> ((A and B) and B)) and ((C -> (D or C)) and ((A and B) -> ((A and B) and B)))), M:tm-595, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-44407
in-theory        44407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and ((C -> (D or C)) and (A -> (A and (B -> (A and B))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-44407.        ((A -> (A and (B -> (A and B)))) and ((C -> (D or C)) and (A -> (A and (B -> (A and B)))))), M:tm-595, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-44408
in-theory        44408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and ((C -> (D or C)) and (A -> (A and (A or B)))))
theorem-size     21
proof            (modus-ponens tm-595 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-44408.        ((A -> (A and (A or B))) and ((C -> (D or C)) and (A -> (A and (A or B))))), M:tm-595, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-44409
in-theory        44409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and ((C -> (D or C)) and (A -> (A and (B or A)))))
theorem-size     21
proof            (modus-ponens tm-595 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-44409.        ((A -> (A and (B or A))) and ((C -> (D or C)) and (A -> (A and (B or A))))), M:tm-595, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-44410
in-theory        44410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((D -> (E or D)) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-44410.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((D -> (E or D)) and ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))))), M:tm-595, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-44411
in-theory        44411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((C -> (D or C)) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-44411.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((C -> (D or C)) and ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))))), M:tm-595, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-44412
in-theory        44412
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and ((B -> (C or B)) and ((not (not A)) -> ((not (not A)) and A))))
theorem-size     25
proof            (modus-ponens tm-595 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-44412.        (((not (not A)) -> ((not (not A)) and A)) and ((B -> (C or B)) and ((not (not A)) -> ((not (not A)) and A)))), M:tm-595, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-44413
in-theory        44413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and ((D -> (E or D)) and (A -> (A and (B -> (C -> B))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-44413.        ((A -> (A and (B -> (C -> B)))) and ((D -> (E or D)) and (A -> (A and (B -> (C -> B)))))), M:tm-595, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-44414
in-theory        44414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and ((C -> (D or C)) and ((A -> B) -> ((A -> B) and (A -> A)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-44414.        (((A -> B) -> ((A -> B) and (A -> A))) and ((C -> (D or C)) and ((A -> B) -> ((A -> B) and (A -> A))))), M:tm-595, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-44415
in-theory        44415
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((D -> (E or D)) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-595 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-44415.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and ((D -> (E or D)) and (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))), M:tm-595, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-44416
in-theory        44416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((E -> (F or E)) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-44416.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and ((E -> (F or E)) and (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))), M:tm-595, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-44417
in-theory        44417
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((D -> (E or D)) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-44417.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((D -> (E or D)) and ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))), M:tm-595, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-44418
in-theory        44418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and ((D -> (E or D)) and (A -> (A and ((B and C) -> B)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-44418.        ((A -> (A and ((B and C) -> B))) and ((D -> (E or D)) and (A -> (A and ((B and C) -> B))))), M:tm-595, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-44419
in-theory        44419
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((D -> (E or D)) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-44419.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((D -> (E or D)) and (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))), M:tm-595, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-44420
in-theory        44420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and ((D -> (E or D)) and (A -> (A and ((B and C) -> C)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-44420.        ((A -> (A and ((B and C) -> C))) and ((D -> (E or D)) and (A -> (A and ((B and C) -> C))))), M:tm-595, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-44421
in-theory        44421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and ((D -> (E or D)) and (A -> (A and ((B -> (C -> B)) and A)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-44421.        ((A -> (A and ((B -> (C -> B)) and A))) and ((D -> (E or D)) and (A -> (A and ((B -> (C -> B)) and A))))), M:tm-595, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-44422
in-theory        44422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((E -> (F or E)) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-44422.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and ((E -> (F or E)) and (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))), M:tm-595, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-44423
in-theory        44423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and ((D -> (E or D)) and (A -> (A and (((B and C) -> B) and A)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-44423.        ((A -> (A and (((B and C) -> B) and A))) and ((D -> (E or D)) and (A -> (A and (((B and C) -> B) and A))))), M:tm-595, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-44424
in-theory        44424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and ((D -> (E or D)) and (A -> (A and (((B and C) -> C) and A)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-44424.        ((A -> (A and (((B and C) -> C) and A))) and ((D -> (E or D)) and (A -> (A and (((B and C) -> C) and A))))), M:tm-595, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-44425
in-theory        44425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((D -> (E or D)) and (A -> (A and ((B -> (C -> (B and C))) and A)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-44425.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and ((D -> (E or D)) and (A -> (A and ((B -> (C -> (B and C))) and A))))), M:tm-595, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-44426
in-theory        44426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((C -> (D or C)) and ((A -> B) -> ((A -> B) and (A -> (A and B))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-44426.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((C -> (D or C)) and ((A -> B) -> ((A -> B) and (A -> (A and B)))))), M:tm-595, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-44427
in-theory        44427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-44427.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F or E)) and ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))))), M:tm-595, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-44428
in-theory        44428
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F or E)) and (((A and B) -> B) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-44428.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F or E)) and (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))))), M:tm-595, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-44429
in-theory        44429
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F or E)) and (((A and B) -> A) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-44429.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F or E)) and (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))))), M:tm-595, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-44430
in-theory        44430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E))))))
theorem-size     53
proof            (modus-ponens tm-595 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-44430.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and ((F -> (G or F)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))))), M:tm-595, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-44431
in-theory        44431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F or E)) and ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-44431.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F or E)) and ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-595, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-44432
in-theory        44432
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((C -> (D or C)) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-44432.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and ((C -> (D or C)) and (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))))), M:tm-595, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-44433
in-theory        44433
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((D -> (E or D)) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C))))
theorem-size     45
proof            (modus-ponens tm-595 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-44433.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((D -> (E or D)) and (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)))), M:tm-595, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-44434
in-theory        44434
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and ((D -> (E or D)) and (A or ((B -> C) -> (B -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-595 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-44434.        ((A or ((B -> C) -> (B -> (B and C)))) and ((D -> (E or D)) and (A or ((B -> C) -> (B -> (B and C)))))), M:tm-595, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-44435
in-theory        44435
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and ((D -> (E or D)) and (((A -> B) -> (A -> (A and B))) or C)))
theorem-size     29
proof            (modus-ponens tm-595 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-44435.        ((((A -> B) -> (A -> (A and B))) or C) and ((D -> (E or D)) and (((A -> B) -> (A -> (A and B))) or C))), M:tm-595, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-44436
in-theory        44436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((D -> (E or D)) and (A -> (((B -> C) -> (B -> (B and C))) and A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-44436.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and ((D -> (E or D)) and (A -> (((B -> C) -> (B -> (B and C))) and A)))), M:tm-595, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-44437
in-theory        44437
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((C -> (D or C)) and (((A -> B) -> A) -> ((A -> B) -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-44437.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((C -> (D or C)) and (((A -> B) -> A) -> ((A -> B) -> (A and B))))), M:tm-595, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-44438
in-theory        44438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and ((D -> (E or D)) and (A -> ((B -> C) -> (B -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-595 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-44438.        ((A -> ((B -> C) -> (B -> (B and C)))) and ((D -> (E or D)) and (A -> ((B -> C) -> (B -> (B and C)))))), M:tm-595, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-44439
in-theory        44439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and ((D -> (E or D)) and (A -> (A and (B -> (C -> (B and C)))))))
theorem-size     29
proof            (modus-ponens tm-595 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-44439.        ((A -> (A and (B -> (C -> (B and C))))) and ((D -> (E or D)) and (A -> (A and (B -> (C -> (B and C))))))), M:tm-595, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-44440
in-theory        44440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E)))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44440.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))))), M:tm-595, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-44441
in-theory        44441
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44441.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> (D -> (E -> (D and E))))))), M:tm-595, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-44442
in-theory        44442
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44442.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> (D -> (E -> (D and E))))))), M:tm-595, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-44443
in-theory        44443
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-595 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44443.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))))), M:tm-595, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-44444
in-theory        44444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44444.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))))), M:tm-595, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-44445
in-theory        44445
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((E -> (F or E)) and ((A and ((B -> (C -> (B and C))) -> D)) -> D)))
theorem-size     33
proof            (modus-ponens tm-595 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-44445.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((E -> (F or E)) and ((A and ((B -> (C -> (B and C))) -> D)) -> D))), M:tm-595, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-44446
in-theory        44446
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((E -> (F or E)) and ((((A -> (B -> (A and B))) -> C) and D) -> C)))
theorem-size     33
proof            (modus-ponens tm-595 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-44446.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((E -> (F or E)) and ((((A -> (B -> (A and B))) -> C) and D) -> C))), M:tm-595, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-44447
in-theory        44447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((D -> (E or D)) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-595 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-44447.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((D -> (E or D)) and ((A -> ((B -> (A and B)) -> C)) -> (A -> C)))), M:tm-595, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-44448
in-theory        44448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((D -> (E or D)) and ((A -> (not (B -> (C -> (B and C))))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-44448.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((D -> (E or D)) and ((A -> (not (B -> (C -> (B and C))))) -> (not A)))), M:tm-595, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-44449
in-theory        44449
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((E -> (F or E)) and (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C))))
theorem-size     49
proof            (modus-ponens tm-595 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-44449.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((E -> (F or E)) and (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)))), M:tm-595, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-44450
in-theory        44450
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and ((E -> (F or E)) and (A or (B -> (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-595 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44450.        ((A or (B -> (C -> (D -> (C and D))))) and ((E -> (F or E)) and (A or (B -> (C -> (D -> (C and D))))))), M:tm-595, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-44451
in-theory        44451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and ((E -> (F or E)) and ((A -> (B -> (C -> (B and C)))) or D)))
theorem-size     29
proof            (modus-ponens tm-595 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44451.        (((A -> (B -> (C -> (B and C)))) or D) and ((E -> (F or E)) and ((A -> (B -> (C -> (B and C)))) or D))), M:tm-595, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-44452
in-theory        44452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((E -> (F or E)) and (A -> ((B -> (C -> (D -> (C and D)))) and A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44452.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and ((E -> (F or E)) and (A -> ((B -> (C -> (D -> (C and D)))) and A)))), M:tm-595, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-44453
in-theory        44453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and ((D -> (E or D)) and ((A -> B) -> (A -> (C -> (B and C))))))
theorem-size     29
proof            (modus-ponens tm-595 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-44453.        (((A -> B) -> (A -> (C -> (B and C)))) and ((D -> (E or D)) and ((A -> B) -> (A -> (C -> (B and C)))))), M:tm-595, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-44454
in-theory        44454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and ((E -> (F or E)) and (A -> (B -> (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-595 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44454.        ((A -> (B -> (C -> (D -> (C and D))))) and ((E -> (F or E)) and (A -> (B -> (C -> (D -> (C and D))))))), M:tm-595, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-44455
in-theory        44455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E))))
theorem-size     37
proof            (modus-ponens tm-595 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-44455.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)))), M:tm-595, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-44456
in-theory        44456
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-44456.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> (D -> C)) or E)))), M:tm-595, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-44457
in-theory        44457
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-44457.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> (D -> C)) or E)))), M:tm-595, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-44458
in-theory        44458
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-44458.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)))), M:tm-595, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-44459
in-theory        44459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-44459.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> (D -> C)) or E)))), M:tm-595, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-44460
in-theory        44460
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and ((E -> (F or E)) and (A or ((B -> (C -> B)) or D))))
theorem-size     25
proof            (modus-ponens tm-595 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-44460.        ((A or ((B -> (C -> B)) or D)) and ((E -> (F or E)) and (A or ((B -> (C -> B)) or D)))), M:tm-595, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-44461
in-theory        44461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and ((E -> (F or E)) and (((A -> (B -> A)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-44461.        ((((A -> (B -> A)) or C) or D) and ((E -> (F or E)) and (((A -> (B -> A)) or C) or D))), M:tm-595, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-44462
in-theory        44462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and ((E -> (F or E)) and (A -> (((B -> (C -> B)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-44462.        ((A -> (((B -> (C -> B)) or D) and A)) and ((E -> (F or E)) and (A -> (((B -> (C -> B)) or D) and A)))), M:tm-595, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-44463
in-theory        44463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and ((E -> (F or E)) and (A -> ((B -> (C -> B)) or D))))
theorem-size     25
proof            (modus-ponens tm-595 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-44463.        ((A -> ((B -> (C -> B)) or D)) and ((E -> (F or E)) and (A -> ((B -> (C -> B)) or D)))), M:tm-595, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-44464
in-theory        44464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H or G)) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     53
proof            (modus-ponens tm-595 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-44464.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H or G)) and ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-595, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-44465
in-theory        44465
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H or G)) and (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-44465.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H or G)) and (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-595, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-44466
in-theory        44466
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H or G)) and (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-44466.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H or G)) and (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-595, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-44467
in-theory        44467
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))))
theorem-size     65
proof            (modus-ponens tm-595 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-44467.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and ((H -> (I or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))), M:tm-595, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-44468
in-theory        44468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H or G)) and ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-44468.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H or G)) and ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-595, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-44469
in-theory        44469
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G or F)) and (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-595 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-44469.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G or F)) and (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-595, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-44470
in-theory        44470
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and ((F -> (G or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E)))
theorem-size     41
proof            (modus-ponens tm-595 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-44470.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and ((F -> (G or F)) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E))), M:tm-595, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-44471
in-theory        44471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((F -> (G or F)) and (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))))
theorem-size     45
proof            (modus-ponens tm-595 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-44471.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and ((F -> (G or F)) and (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)))), M:tm-595, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-44472
in-theory        44472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G or F)) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))))
theorem-size     41
proof            (modus-ponens tm-595 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-44472.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and ((F -> (G or F)) and (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))), M:tm-595, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-44473
in-theory        44473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C and D) -> C) or E))))
theorem-size     37
proof            (modus-ponens tm-595 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-44473.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C and D) -> C) or E)))), M:tm-595, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-44474
in-theory        44474
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and ((F -> (G or F)) and (((A and B) -> B) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-44474.        ((((A and B) -> B) and (((C and D) -> C) or E)) and ((F -> (G or F)) and (((A and B) -> B) and (((C and D) -> C) or E)))), M:tm-595, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-44475
in-theory        44475
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and ((F -> (G or F)) and (((A and B) -> A) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-44475.        ((((A and B) -> A) and (((C and D) -> C) or E)) and ((F -> (G or F)) and (((A and B) -> A) and (((C and D) -> C) or E)))), M:tm-595, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-44476
in-theory        44476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-44476.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)))), M:tm-595, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-44477
in-theory        44477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-44477.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C and D) -> C) or E)))), M:tm-595, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-44478
in-theory        44478
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and ((E -> (F or E)) and (A or (((B and C) -> B) or D))))
theorem-size     25
proof            (modus-ponens tm-595 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-44478.        ((A or (((B and C) -> B) or D)) and ((E -> (F or E)) and (A or (((B and C) -> B) or D)))), M:tm-595, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-44479
in-theory        44479
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and ((E -> (F or E)) and ((((A and B) -> A) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-44479.        (((((A and B) -> A) or C) or D) and ((E -> (F or E)) and ((((A and B) -> A) or C) or D))), M:tm-595, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-44480
in-theory        44480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and ((E -> (F or E)) and (A -> ((((B and C) -> B) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-44480.        ((A -> ((((B and C) -> B) or D) and A)) and ((E -> (F or E)) and (A -> ((((B and C) -> B) or D) and A)))), M:tm-595, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-44481
in-theory        44481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and ((E -> (F or E)) and (A -> (((B and C) -> B) or D))))
theorem-size     25
proof            (modus-ponens tm-595 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-44481.        ((A -> (((B and C) -> B) or D)) and ((E -> (F or E)) and (A -> (((B and C) -> B) or D)))), M:tm-595, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-44482
in-theory        44482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C and D) -> D) or E))))
theorem-size     37
proof            (modus-ponens tm-595 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-44482.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C and D) -> D) or E)))), M:tm-595, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-44483
in-theory        44483
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and ((F -> (G or F)) and (((A and B) -> B) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-44483.        ((((A and B) -> B) and (((C and D) -> D) or E)) and ((F -> (G or F)) and (((A and B) -> B) and (((C and D) -> D) or E)))), M:tm-595, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-44484
in-theory        44484
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and ((F -> (G or F)) and (((A and B) -> A) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-44484.        ((((A and B) -> A) and (((C and D) -> D) or E)) and ((F -> (G or F)) and (((A and B) -> A) and (((C and D) -> D) or E)))), M:tm-595, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-44485
in-theory        44485
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-44485.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)))), M:tm-595, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-44486
in-theory        44486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-44486.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C and D) -> D) or E)))), M:tm-595, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-44487
in-theory        44487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and ((E -> (F or E)) and (A or (((B and C) -> C) or D))))
theorem-size     25
proof            (modus-ponens tm-595 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-44487.        ((A or (((B and C) -> C) or D)) and ((E -> (F or E)) and (A or (((B and C) -> C) or D)))), M:tm-595, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-44488
in-theory        44488
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and ((E -> (F or E)) and ((((A and B) -> B) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-44488.        (((((A and B) -> B) or C) or D) and ((E -> (F or E)) and ((((A and B) -> B) or C) or D))), M:tm-595, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-44489
in-theory        44489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and ((E -> (F or E)) and (A -> ((((B and C) -> C) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-44489.        ((A -> ((((B and C) -> C) or D) and A)) and ((E -> (F or E)) and (A -> ((((B and C) -> C) or D) and A)))), M:tm-595, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-44490
in-theory        44490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and ((E -> (F or E)) and (A -> (((B and C) -> C) or D))))
theorem-size     25
proof            (modus-ponens tm-595 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-44490.        ((A -> (((B and C) -> C) or D)) and ((E -> (F or E)) and (A -> (((B and C) -> C) or D)))), M:tm-595, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-44491
in-theory        44491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E))))
theorem-size     41
proof            (modus-ponens tm-595 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-44491.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)))), M:tm-595, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-44492
in-theory        44492
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-595 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-44492.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> (D -> (C and D))) or E)))), M:tm-595, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-44493
in-theory        44493
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-595 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-44493.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> (D -> (C and D))) or E)))), M:tm-595, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-44494
in-theory        44494
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F))))
theorem-size     53
proof            (modus-ponens tm-595 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-44494.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)))), M:tm-595, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-44495
in-theory        44495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-595 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-44495.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)))), M:tm-595, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-44496
in-theory        44496
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and ((E -> (F or E)) and (A or ((B -> (C -> (B and C))) or D))))
theorem-size     29
proof            (modus-ponens tm-595 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-44496.        ((A or ((B -> (C -> (B and C))) or D)) and ((E -> (F or E)) and (A or ((B -> (C -> (B and C))) or D)))), M:tm-595, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-44497
in-theory        44497
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and ((E -> (F or E)) and (((A -> (B -> (A and B))) or C) or D)))
theorem-size     29
proof            (modus-ponens tm-595 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-44497.        ((((A -> (B -> (A and B))) or C) or D) and ((E -> (F or E)) and (((A -> (B -> (A and B))) or C) or D))), M:tm-595, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-44498
in-theory        44498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((E -> (F or E)) and (A -> (((B -> (C -> (B and C))) or D) and A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-44498.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and ((E -> (F or E)) and (A -> (((B -> (C -> (B and C))) or D) and A)))), M:tm-595, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-44499
in-theory        44499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and ((E -> (F or E)) and (A -> ((B -> (C -> (B and C))) or D))))
theorem-size     29
proof            (modus-ponens tm-595 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-44499.        ((A -> ((B -> (C -> (B and C))) or D)) and ((E -> (F or E)) and (A -> ((B -> (C -> (B and C))) or D)))), M:tm-595, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-44500
in-theory        44500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> (C or D)) or E))))
theorem-size     37
proof            (modus-ponens tm-595 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-44500.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)))), M:tm-595, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-44501
in-theory        44501
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-44501.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> (C or D)) or E)))), M:tm-595, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-44502
in-theory        44502
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-44502.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> (C or D)) or E)))), M:tm-595, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-44503
in-theory        44503
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-44503.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)))), M:tm-595, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-44504
in-theory        44504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-44504.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> (C or D)) or E)))), M:tm-595, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-44505
in-theory        44505
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and ((E -> (F or E)) and (A or ((B -> (B or C)) or D))))
theorem-size     25
proof            (modus-ponens tm-595 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-44505.        ((A or ((B -> (B or C)) or D)) and ((E -> (F or E)) and (A or ((B -> (B or C)) or D)))), M:tm-595, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-44506
in-theory        44506
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and ((E -> (F or E)) and (((A -> (A or B)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-44506.        ((((A -> (A or B)) or C) or D) and ((E -> (F or E)) and (((A -> (A or B)) or C) or D))), M:tm-595, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-44507
in-theory        44507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and ((E -> (F or E)) and (A -> (((B -> (B or C)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-44507.        ((A -> (((B -> (B or C)) or D) and A)) and ((E -> (F or E)) and (A -> (((B -> (B or C)) or D) and A)))), M:tm-595, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-44508
in-theory        44508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and ((E -> (F or E)) and (A -> ((B -> (B or C)) or D))))
theorem-size     25
proof            (modus-ponens tm-595 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-44508.        ((A -> ((B -> (B or C)) or D)) and ((E -> (F or E)) and (A -> ((B -> (B or C)) or D)))), M:tm-595, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-44509
in-theory        44509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and ((E -> (F or E)) and ((A -> (A or B)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-44509.        (((A -> (A or B)) and (C -> (D -> C))) and ((E -> (F or E)) and ((A -> (A or B)) and (C -> (D -> C))))), M:tm-595, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-44510
in-theory        44510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-44510.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-595, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-44511
in-theory        44511
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and ((E -> (F or E)) and ((A -> (A or B)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-44511.        (((A -> (A or B)) and ((C and D) -> C)) and ((E -> (F or E)) and ((A -> (A or B)) and ((C and D) -> C)))), M:tm-595, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-44512
in-theory        44512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and ((E -> (F or E)) and ((A -> (A or B)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-595 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-44512.        (((A -> (A or B)) and ((C and D) -> D)) and ((E -> (F or E)) and ((A -> (A or B)) and ((C and D) -> D)))), M:tm-595, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-44513
in-theory        44513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A -> (A or B)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-44513.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A -> (A or B)) and (C -> (D -> (C and D)))))), M:tm-595, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-44514
in-theory        44514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and ((E -> (F or E)) and ((A -> (A or B)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-44514.        (((A -> (A or B)) and (C -> (C or D))) and ((E -> (F or E)) and ((A -> (A or B)) and (C -> (C or D))))), M:tm-595, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-44515
in-theory        44515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and ((E -> (F or E)) and ((A -> (A or B)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-44515.        (((A -> (A or B)) and (C -> (D or C))) and ((E -> (F or E)) and ((A -> (A or B)) and (C -> (D or C))))), M:tm-595, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-44516
in-theory        44516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-44516.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-595, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-44517
in-theory        44517
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F or E)) and ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-44517.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F or E)) and ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-595, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-44518
in-theory        44518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and ((D -> (E or D)) and ((A -> (A or B)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-44518.        (((A -> (A or B)) and ((not (not C)) -> C)) and ((D -> (E or D)) and ((A -> (A or B)) and ((not (not C)) -> C)))), M:tm-595, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-44519
in-theory        44519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-44519.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> (D -> (E -> D)))))), M:tm-595, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-44520
in-theory        44520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((E -> (F or E)) and ((A -> (A or B)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-44520.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and ((E -> (F or E)) and ((A -> (A or B)) and ((C -> D) -> (C -> C))))), M:tm-595, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-44521
in-theory        44521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-595 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-44521.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-595, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-44522
in-theory        44522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44522.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-595, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-44523
in-theory        44523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G or F)) and ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-44523.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G or F)) and ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-595, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-44524
in-theory        44524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-44524.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> ((D and E) -> D))))), M:tm-595, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-44525
in-theory        44525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G or F)) and ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-44525.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G or F)) and ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-595, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-44526
in-theory        44526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-44526.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> ((D and E) -> E))))), M:tm-595, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-44527
in-theory        44527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-44527.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))))), M:tm-595, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-44528
in-theory        44528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H or G)) and ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-44528.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H or G)) and ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-595, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-44529
in-theory        44529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-44529.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> (((D and E) -> D) and C))))), M:tm-595, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-44530
in-theory        44530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-44530.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> (((D and E) -> E) and C))))), M:tm-595, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-44531
in-theory        44531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-44531.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-595, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-44532
in-theory        44532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F or E)) and ((A -> (A or B)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-44532.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F or E)) and ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))))), M:tm-595, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-44533
in-theory        44533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44533.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))))), M:tm-595, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-44534
in-theory        44534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-44534.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> (D -> C)) or E)))), M:tm-595, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-44535
in-theory        44535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H or G)) and ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-44535.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H or G)) and ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-595, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-44536
in-theory        44536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and ((F -> (G or F)) and ((A -> (A or B)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-44536.        (((A -> (A or B)) and (((C and D) -> C) or E)) and ((F -> (G or F)) and ((A -> (A or B)) and (((C and D) -> C) or E)))), M:tm-595, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-44537
in-theory        44537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and ((F -> (G or F)) and ((A -> (A or B)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-44537.        (((A -> (A or B)) and (((C and D) -> D) or E)) and ((F -> (G or F)) and ((A -> (A or B)) and (((C and D) -> D) or E)))), M:tm-595, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-44538
in-theory        44538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-595 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-44538.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)))), M:tm-595, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-44539
in-theory        44539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-44539.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> (C or D)) or E)))), M:tm-595, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-44540
in-theory        44540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-44540.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))))), M:tm-595, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-44541
in-theory        44541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and ((D -> (E or D)) and (A -> (A and ((B -> (B or C)) and A)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-44541.        ((A -> (A and ((B -> (B or C)) and A))) and ((D -> (E or D)) and (A -> (A and ((B -> (B or C)) and A))))), M:tm-595, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-44542
in-theory        44542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-44542.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))))), M:tm-595, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-44543
in-theory        44543
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-44543.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> ((D -> (D or E)) and C))))), M:tm-595, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-44544
in-theory        44544
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-44544.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> ((D -> (D or E)) and C))))), M:tm-595, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-44545
in-theory        44545
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-44545.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))))), M:tm-595, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-44546
in-theory        44546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-44546.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))))), M:tm-595, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-44547
in-theory        44547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((D -> (E or D)) and ((A -> (not ((B -> (B or C)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-44547.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((D -> (E or D)) and ((A -> (not ((B -> (B or C)) and A))) -> (not A)))), M:tm-595, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-44548
in-theory        44548
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((E -> (F or E)) and ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-595 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-44548.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((E -> (F or E)) and ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)))), M:tm-595, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-44549
in-theory        44549
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and ((E -> (F or E)) and (A or (B -> ((C -> (C or D)) and B)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-44549.        ((A or (B -> ((C -> (C or D)) and B))) and ((E -> (F or E)) and (A or (B -> ((C -> (C or D)) and B))))), M:tm-595, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-44550
in-theory        44550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and ((E -> (F or E)) and ((A -> ((B -> (B or C)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-595 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-44550.        (((A -> ((B -> (B or C)) and A)) or D) and ((E -> (F or E)) and ((A -> ((B -> (B or C)) and A)) or D))), M:tm-595, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-44551
in-theory        44551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((E -> (F or E)) and (A -> ((B -> ((C -> (C or D)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-44551.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and ((E -> (F or E)) and (A -> ((B -> ((C -> (C or D)) and B)) and A)))), M:tm-595, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-44552
in-theory        44552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and ((E -> (F or E)) and (A -> (B -> ((C -> (C or D)) and B)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-44552.        ((A -> (B -> ((C -> (C or D)) and B))) and ((E -> (F or E)) and (A -> (B -> ((C -> (C or D)) and B))))), M:tm-595, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-44553
in-theory        44553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-44553.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> (D -> (D or E)))))), M:tm-595, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-44554
in-theory        44554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and ((D -> (E or D)) and (A -> (A and (B -> (B or C))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-44554.        ((A -> (A and (B -> (B or C)))) and ((D -> (E or D)) and (A -> (A and (B -> (B or C)))))), M:tm-595, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-44555
in-theory        44555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> (D -> (D or E))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-44555.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))))), M:tm-595, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-44556
in-theory        44556
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-44556.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> (D -> (D or E)))))), M:tm-595, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-44557
in-theory        44557
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-44557.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> (D -> (D or E)))))), M:tm-595, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-44558
in-theory        44558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-44558.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))))), M:tm-595, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-44559
in-theory        44559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-44559.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> (D -> (D or E)))))), M:tm-595, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-44560
in-theory        44560
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and ((E -> (F or E)) and ((A and ((B -> (B or C)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-595 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-44560.        (((A and ((B -> (B or C)) -> D)) -> D) and ((E -> (F or E)) and ((A and ((B -> (B or C)) -> D)) -> D))), M:tm-595, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-44561
in-theory        44561
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and ((E -> (F or E)) and ((((A -> (A or B)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-595 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-44561.        (((((A -> (A or B)) -> C) and D) -> C) and ((E -> (F or E)) and ((((A -> (A or B)) -> C) and D) -> C))), M:tm-595, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-44562
in-theory        44562
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and ((D -> (E or D)) and ((A -> ((A or B) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-44562.        (((A -> ((A or B) -> C)) -> (A -> C)) and ((D -> (E or D)) and ((A -> ((A or B) -> C)) -> (A -> C)))), M:tm-595, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-44563
in-theory        44563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and ((D -> (E or D)) and ((A -> (not (B -> (B or C)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-44563.        (((A -> (not (B -> (B or C)))) -> (not A)) and ((D -> (E or D)) and ((A -> (not (B -> (B or C)))) -> (not A)))), M:tm-595, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-44564
in-theory        44564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((E -> (F or E)) and (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C))))
theorem-size     41
proof            (modus-ponens tm-595 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-44564.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((E -> (F or E)) and (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)))), M:tm-595, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-44565
in-theory        44565
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and ((E -> (F or E)) and (A or (B -> (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-44565.        ((A or (B -> (C -> (C or D)))) and ((E -> (F or E)) and (A or (B -> (C -> (C or D)))))), M:tm-595, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-44566
in-theory        44566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and ((E -> (F or E)) and ((A -> (B -> (B or C))) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-44566.        (((A -> (B -> (B or C))) or D) and ((E -> (F or E)) and ((A -> (B -> (B or C))) or D))), M:tm-595, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-44567
in-theory        44567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and ((E -> (F or E)) and (A -> ((B -> (C -> (C or D))) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-44567.        ((A -> ((B -> (C -> (C or D))) and A)) and ((E -> (F or E)) and (A -> ((B -> (C -> (C or D))) and A)))), M:tm-595, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-44568
in-theory        44568
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and ((D -> (E or D)) and ((A -> B) -> (A -> (B or C)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-44568.        (((A -> B) -> (A -> (B or C))) and ((D -> (E or D)) and ((A -> B) -> (A -> (B or C))))), M:tm-595, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-44569
in-theory        44569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and ((E -> (F or E)) and (A -> (B -> (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-44569.        ((A -> (B -> (C -> (C or D)))) and ((E -> (F or E)) and (A -> (B -> (C -> (C or D)))))), M:tm-595, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-44570
in-theory        44570
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (A or B)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-44570.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (A or B)) and (C or (D -> (E -> D)))))), M:tm-595, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-44571
in-theory        44571
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C or (D -> (E -> D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-44571.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))))), M:tm-595, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-44572
in-theory        44572
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((F -> (G or F)) and (((A and B) -> B) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-44572.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and ((F -> (G or F)) and (((A and B) -> B) and (C or (D -> (E -> D)))))), M:tm-595, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-44573
in-theory        44573
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((F -> (G or F)) and (((A and B) -> A) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-44573.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and ((F -> (G or F)) and (((A and B) -> A) and (C or (D -> (E -> D)))))), M:tm-595, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-44574
in-theory        44574
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-44574.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))))), M:tm-595, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-44575
in-theory        44575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-44575.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C or (D -> (E -> D)))))), M:tm-595, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-44576
in-theory        44576
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and ((E -> (F or E)) and (A or (B or (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-44576.        ((A or (B or (C -> (D -> C)))) and ((E -> (F or E)) and (A or (B or (C -> (D -> C)))))), M:tm-595, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-44577
in-theory        44577
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and ((E -> (F or E)) and ((A or (B -> (C -> B))) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-44577.        (((A or (B -> (C -> B))) or D) and ((E -> (F or E)) and ((A or (B -> (C -> B))) or D))), M:tm-595, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-44578
in-theory        44578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and ((E -> (F or E)) and (A -> ((B or (C -> (D -> C))) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-44578.        ((A -> ((B or (C -> (D -> C))) and A)) and ((E -> (F or E)) and (A -> ((B or (C -> (D -> C))) and A)))), M:tm-595, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-44579
in-theory        44579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and ((E -> (F or E)) and (A -> (B or (C -> (D -> C))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-44579.        ((A -> (B or (C -> (D -> C)))) and ((E -> (F or E)) and (A -> (B or (C -> (D -> C)))))), M:tm-595, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-44580
in-theory        44580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44580.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-595, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-44581
in-theory        44581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     53
proof            (modus-ponens tm-595 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44581.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-595, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-44582
in-theory        44582
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44582.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-595, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-44583
in-theory        44583
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44583.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-595, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-44584
in-theory        44584
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))))
theorem-size     65
proof            (modus-ponens tm-595 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44584.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and ((H -> (I or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))), M:tm-595, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-44585
in-theory        44585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44585.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-595, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-44586
in-theory        44586
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G or F)) and (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44586.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G or F)) and (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-595, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-44587
in-theory        44587
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G or F)) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E)))
theorem-size     41
proof            (modus-ponens tm-595 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44587.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and ((F -> (G or F)) and ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E))), M:tm-595, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-44588
in-theory        44588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G or F)) and (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))))
theorem-size     45
proof            (modus-ponens tm-595 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44588.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and ((F -> (G or F)) and (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))), M:tm-595, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-44589
in-theory        44589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G or F)) and (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44589.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((F -> (G or F)) and (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-595, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-44590
in-theory        44590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (A or B)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-44590.        (((A -> (A or B)) and (C or ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (A or B)) and (C or ((D and E) -> D))))), M:tm-595, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-44591
in-theory        44591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C or ((D and E) -> D)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-44591.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C or ((D and E) -> D))))), M:tm-595, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-44592
in-theory        44592
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and ((F -> (G or F)) and (((A and B) -> B) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-44592.        ((((A and B) -> B) and (C or ((D and E) -> D))) and ((F -> (G or F)) and (((A and B) -> B) and (C or ((D and E) -> D))))), M:tm-595, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-44593
in-theory        44593
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and ((F -> (G or F)) and (((A and B) -> A) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-44593.        ((((A and B) -> A) and (C or ((D and E) -> D))) and ((F -> (G or F)) and (((A and B) -> A) and (C or ((D and E) -> D))))), M:tm-595, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-44594
in-theory        44594
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-44594.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))))), M:tm-595, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-44595
in-theory        44595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-44595.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C or ((D and E) -> D))))), M:tm-595, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-44596
in-theory        44596
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and ((E -> (F or E)) and (A or (B or ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-44596.        ((A or (B or ((C and D) -> C))) and ((E -> (F or E)) and (A or (B or ((C and D) -> C))))), M:tm-595, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-44597
in-theory        44597
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and ((E -> (F or E)) and ((A or ((B and C) -> B)) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-44597.        (((A or ((B and C) -> B)) or D) and ((E -> (F or E)) and ((A or ((B and C) -> B)) or D))), M:tm-595, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-44598
in-theory        44598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and ((E -> (F or E)) and (A -> ((B or ((C and D) -> C)) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-44598.        ((A -> ((B or ((C and D) -> C)) and A)) and ((E -> (F or E)) and (A -> ((B or ((C and D) -> C)) and A)))), M:tm-595, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-44599
in-theory        44599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and ((E -> (F or E)) and (A -> (B or ((C and D) -> C)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-44599.        ((A -> (B or ((C and D) -> C))) and ((E -> (F or E)) and (A -> (B or ((C and D) -> C))))), M:tm-595, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-44600
in-theory        44600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (A or B)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-44600.        (((A -> (A or B)) and (C or ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (A or B)) and (C or ((D and E) -> E))))), M:tm-595, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-44601
in-theory        44601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C or ((D and E) -> E)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-44601.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C or ((D and E) -> E))))), M:tm-595, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-44602
in-theory        44602
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and ((F -> (G or F)) and (((A and B) -> B) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-44602.        ((((A and B) -> B) and (C or ((D and E) -> E))) and ((F -> (G or F)) and (((A and B) -> B) and (C or ((D and E) -> E))))), M:tm-595, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-44603
in-theory        44603
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and ((F -> (G or F)) and (((A and B) -> A) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-44603.        ((((A and B) -> A) and (C or ((D and E) -> E))) and ((F -> (G or F)) and (((A and B) -> A) and (C or ((D and E) -> E))))), M:tm-595, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-44604
in-theory        44604
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-44604.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))))), M:tm-595, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-44605
in-theory        44605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-44605.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C or ((D and E) -> E))))), M:tm-595, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-44606
in-theory        44606
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and ((E -> (F or E)) and (A or (B or ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-44606.        ((A or (B or ((C and D) -> D))) and ((E -> (F or E)) and (A or (B or ((C and D) -> D))))), M:tm-595, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-44607
in-theory        44607
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and ((E -> (F or E)) and ((A or ((B and C) -> C)) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-44607.        (((A or ((B and C) -> C)) or D) and ((E -> (F or E)) and ((A or ((B and C) -> C)) or D))), M:tm-595, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-44608
in-theory        44608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and ((E -> (F or E)) and (A -> ((B or ((C and D) -> D)) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-44608.        ((A -> ((B or ((C and D) -> D)) and A)) and ((E -> (F or E)) and (A -> ((B or ((C and D) -> D)) and A)))), M:tm-595, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-44609
in-theory        44609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and ((E -> (F or E)) and (A -> (B or ((C and D) -> D)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-44609.        ((A -> (B or ((C and D) -> D))) and ((E -> (F or E)) and (A -> (B or ((C and D) -> D))))), M:tm-595, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-44610
in-theory        44610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (A or B)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44610.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (A or B)) and (C or (D -> (E -> (D and E))))))), M:tm-595, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-44611
in-theory        44611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E)))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44611.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))))), M:tm-595, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-44612
in-theory        44612
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((F -> (G or F)) and (((A and B) -> B) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44612.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and ((F -> (G or F)) and (((A and B) -> B) and (C or (D -> (E -> (D and E))))))), M:tm-595, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-44613
in-theory        44613
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((F -> (G or F)) and (((A and B) -> A) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44613.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and ((F -> (G or F)) and (((A and B) -> A) and (C or (D -> (E -> (D and E))))))), M:tm-595, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-44614
in-theory        44614
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F)))))))
theorem-size     53
proof            (modus-ponens tm-595 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44614.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))))), M:tm-595, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-44615
in-theory        44615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44615.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))))), M:tm-595, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-44616
in-theory        44616
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and ((E -> (F or E)) and (A or (B or (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-595 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44616.        ((A or (B or (C -> (D -> (C and D))))) and ((E -> (F or E)) and (A or (B or (C -> (D -> (C and D))))))), M:tm-595, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-44617
in-theory        44617
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and ((E -> (F or E)) and ((A or (B -> (C -> (B and C)))) or D)))
theorem-size     29
proof            (modus-ponens tm-595 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44617.        (((A or (B -> (C -> (B and C)))) or D) and ((E -> (F or E)) and ((A or (B -> (C -> (B and C)))) or D))), M:tm-595, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-44618
in-theory        44618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((E -> (F or E)) and (A -> ((B or (C -> (D -> (C and D)))) and A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44618.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and ((E -> (F or E)) and (A -> ((B or (C -> (D -> (C and D)))) and A)))), M:tm-595, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-44619
in-theory        44619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and ((E -> (F or E)) and (A -> (B or (C -> (D -> (C and D)))))))
theorem-size     29
proof            (modus-ponens tm-595 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44619.        ((A -> (B or (C -> (D -> (C and D))))) and ((E -> (F or E)) and (A -> (B or (C -> (D -> (C and D))))))), M:tm-595, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-44620
in-theory        44620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (A or B)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-44620.        (((A -> (A or B)) and (C or (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (A or B)) and (C or (D -> (D or E)))))), M:tm-595, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-44621
in-theory        44621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C or (D -> (D or E))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-44621.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C or (D -> (D or E)))))), M:tm-595, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-44622
in-theory        44622
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and ((F -> (G or F)) and (((A and B) -> B) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-44622.        ((((A and B) -> B) and (C or (D -> (D or E)))) and ((F -> (G or F)) and (((A and B) -> B) and (C or (D -> (D or E)))))), M:tm-595, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-44623
in-theory        44623
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and ((F -> (G or F)) and (((A and B) -> A) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-44623.        ((((A and B) -> A) and (C or (D -> (D or E)))) and ((F -> (G or F)) and (((A and B) -> A) and (C or (D -> (D or E)))))), M:tm-595, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-44624
in-theory        44624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-44624.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))))), M:tm-595, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-44625
in-theory        44625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-44625.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C or (D -> (D or E)))))), M:tm-595, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-44626
in-theory        44626
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and ((E -> (F or E)) and (A or (B or (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-44626.        ((A or (B or (C -> (C or D)))) and ((E -> (F or E)) and (A or (B or (C -> (C or D)))))), M:tm-595, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-44627
in-theory        44627
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and ((E -> (F or E)) and ((A or (B -> (B or C))) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-44627.        (((A or (B -> (B or C))) or D) and ((E -> (F or E)) and ((A or (B -> (B or C))) or D))), M:tm-595, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-44628
in-theory        44628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and ((E -> (F or E)) and (A -> ((B or (C -> (C or D))) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-44628.        ((A -> ((B or (C -> (C or D))) and A)) and ((E -> (F or E)) and (A -> ((B or (C -> (C or D))) and A)))), M:tm-595, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-44629
in-theory        44629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and ((E -> (F or E)) and (A -> (B or (C -> (C or D))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-44629.        ((A -> (B or (C -> (C or D)))) and ((E -> (F or E)) and (A -> (B or (C -> (C or D)))))), M:tm-595, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-44630
in-theory        44630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (A or B)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-44630.        (((A -> (A or B)) and (C or (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (A or B)) and (C or (D -> (E or D)))))), M:tm-595, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-44631
in-theory        44631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C or (D -> (E or D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-44631.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C or (D -> (E or D)))))), M:tm-595, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-44632
in-theory        44632
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and ((F -> (G or F)) and (((A and B) -> B) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-44632.        ((((A and B) -> B) and (C or (D -> (E or D)))) and ((F -> (G or F)) and (((A and B) -> B) and (C or (D -> (E or D)))))), M:tm-595, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-44633
in-theory        44633
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and ((F -> (G or F)) and (((A and B) -> A) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-44633.        ((((A and B) -> A) and (C or (D -> (E or D)))) and ((F -> (G or F)) and (((A and B) -> A) and (C or (D -> (E or D)))))), M:tm-595, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-44634
in-theory        44634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-44634.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))))), M:tm-595, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-44635
in-theory        44635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-44635.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C or (D -> (E or D)))))), M:tm-595, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-44636
in-theory        44636
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and ((E -> (F or E)) and (A or (B or (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-44636.        ((A or (B or (C -> (D or C)))) and ((E -> (F or E)) and (A or (B or (C -> (D or C)))))), M:tm-595, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-44637
in-theory        44637
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and ((E -> (F or E)) and ((A or (B -> (C or B))) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-44637.        (((A or (B -> (C or B))) or D) and ((E -> (F or E)) and ((A or (B -> (C or B))) or D))), M:tm-595, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-44638
in-theory        44638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and ((E -> (F or E)) and (A -> ((B or (C -> (D or C))) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-44638.        ((A -> ((B or (C -> (D or C))) and A)) and ((E -> (F or E)) and (A -> ((B or (C -> (D or C))) and A)))), M:tm-595, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-44639
in-theory        44639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and ((E -> (F or E)) and (A -> (B or (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-44639.        ((A -> (B or (C -> (D or C)))) and ((E -> (F or E)) and (A -> (B or (C -> (D or C)))))), M:tm-595, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-44640
in-theory        44640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-44640.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> (D or C)) or E)))), M:tm-595, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-44641
in-theory        44641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> (D or C)) or E))))
theorem-size     37
proof            (modus-ponens tm-595 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-44641.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)))), M:tm-595, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-44642
in-theory        44642
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-44642.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> (D or C)) or E)))), M:tm-595, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-44643
in-theory        44643
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-44643.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> (D or C)) or E)))), M:tm-595, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-44644
in-theory        44644
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-44644.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)))), M:tm-595, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-44645
in-theory        44645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-44645.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> (D or C)) or E)))), M:tm-595, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-44646
in-theory        44646
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and ((E -> (F or E)) and (A or ((B -> (C or B)) or D))))
theorem-size     25
proof            (modus-ponens tm-595 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-44646.        ((A or ((B -> (C or B)) or D)) and ((E -> (F or E)) and (A or ((B -> (C or B)) or D)))), M:tm-595, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-44647
in-theory        44647
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and ((E -> (F or E)) and (((A -> (B or A)) or C) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-44647.        ((((A -> (B or A)) or C) or D) and ((E -> (F or E)) and (((A -> (B or A)) or C) or D))), M:tm-595, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-44648
in-theory        44648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and ((E -> (F or E)) and (A -> (((B -> (C or B)) or D) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-44648.        ((A -> (((B -> (C or B)) or D) and A)) and ((E -> (F or E)) and (A -> (((B -> (C or B)) or D) and A)))), M:tm-595, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-44649
in-theory        44649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and ((E -> (F or E)) and (A -> ((B -> (C or B)) or D))))
theorem-size     25
proof            (modus-ponens tm-595 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-44649.        ((A -> ((B -> (C or B)) or D)) and ((E -> (F or E)) and (A -> ((B -> (C or B)) or D)))), M:tm-595, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-44650
in-theory        44650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and ((E -> (F or E)) and ((A -> (B or A)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-44650.        (((A -> (B or A)) and (C -> (D -> C))) and ((E -> (F or E)) and ((A -> (B or A)) and (C -> (D -> C))))), M:tm-595, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-44651
in-theory        44651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-44651.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-595, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-44652
in-theory        44652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and ((E -> (F or E)) and ((A -> (B or A)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-44652.        (((A -> (B or A)) and ((C and D) -> C)) and ((E -> (F or E)) and ((A -> (B or A)) and ((C and D) -> C)))), M:tm-595, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-44653
in-theory        44653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and ((E -> (F or E)) and ((A -> (B or A)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-595 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-44653.        (((A -> (B or A)) and ((C and D) -> D)) and ((E -> (F or E)) and ((A -> (B or A)) and ((C and D) -> D)))), M:tm-595, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-44654
in-theory        44654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A -> (B or A)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-44654.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A -> (B or A)) and (C -> (D -> (C and D)))))), M:tm-595, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-44655
in-theory        44655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and ((E -> (F or E)) and ((A -> (B or A)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-44655.        (((A -> (B or A)) and (C -> (C or D))) and ((E -> (F or E)) and ((A -> (B or A)) and (C -> (C or D))))), M:tm-595, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-44656
in-theory        44656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and ((E -> (F or E)) and ((A -> (B or A)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-44656.        (((A -> (B or A)) and (C -> (D or C))) and ((E -> (F or E)) and ((A -> (B or A)) and (C -> (D or C))))), M:tm-595, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-44657
in-theory        44657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-44657.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))), M:tm-595, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-44658
in-theory        44658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F or E)) and ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C))))))
theorem-size     41
proof            (modus-ponens tm-595 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-44658.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((E -> (F or E)) and ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))))), M:tm-595, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-44659
in-theory        44659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and ((D -> (E or D)) and ((A -> (B or A)) and ((not (not C)) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-10)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-44659.        (((A -> (B or A)) and ((not (not C)) -> C)) and ((D -> (E or D)) and ((A -> (B or A)) and ((not (not C)) -> C)))), M:tm-595, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-44660
in-theory        44660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-44660.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> (D -> (E -> D)))))), M:tm-595, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-44661
in-theory        44661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((E -> (F or E)) and ((A -> (B or A)) and ((C -> D) -> (C -> C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-44661.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and ((E -> (F or E)) and ((A -> (B or A)) and ((C -> D) -> (C -> C))))), M:tm-595, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-44662
in-theory        44662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))))
theorem-size     57
proof            (modus-ponens tm-595 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-44662.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((F -> (G or F)) and ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))), M:tm-595, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-44663
in-theory        44663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44663.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-595, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-44664
in-theory        44664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G or F)) and ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-44664.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((F -> (G or F)) and ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))), M:tm-595, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-44665
in-theory        44665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-44665.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> ((D and E) -> D))))), M:tm-595, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-44666
in-theory        44666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G or F)) and ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-44666.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((F -> (G or F)) and ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))), M:tm-595, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-44667
in-theory        44667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-44667.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> ((D and E) -> E))))), M:tm-595, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-44668
in-theory        44668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-44668.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))))), M:tm-595, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-44669
in-theory        44669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H or G)) and ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-44669.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((G -> (H or G)) and ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))), M:tm-595, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-44670
in-theory        44670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> (((D and E) -> D) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-44670.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> (((D and E) -> D) and C))))), M:tm-595, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-44671
in-theory        44671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> (((D and E) -> E) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-44671.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> (((D and E) -> E) and C))))), M:tm-595, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-44672
in-theory        44672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-44672.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))))), M:tm-595, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-44673
in-theory        44673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F or E)) and ((A -> (B or A)) and ((C -> D) -> (C -> (C and D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-44673.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and ((E -> (F or E)) and ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))))), M:tm-595, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-44674
in-theory        44674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44674.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))))), M:tm-595, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-44675
in-theory        44675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> (D -> C)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-44675.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> (D -> C)) or E)))), M:tm-595, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-44676
in-theory        44676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H or G)) and ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))))
theorem-size     49
proof            (modus-ponens tm-595 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-44676.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((G -> (H or G)) and ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))), M:tm-595, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-44677
in-theory        44677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and ((F -> (G or F)) and ((A -> (B or A)) and (((C and D) -> C) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-44677.        (((A -> (B or A)) and (((C and D) -> C) or E)) and ((F -> (G or F)) and ((A -> (B or A)) and (((C and D) -> C) or E)))), M:tm-595, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-44678
in-theory        44678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and ((F -> (G or F)) and ((A -> (B or A)) and (((C and D) -> D) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-44678.        (((A -> (B or A)) and (((C and D) -> D) or E)) and ((F -> (G or F)) and ((A -> (B or A)) and (((C and D) -> D) or E)))), M:tm-595, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-44679
in-theory        44679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> (D -> (C and D))) or E))))
theorem-size     37
proof            (modus-ponens tm-595 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-44679.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)))), M:tm-595, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-44680
in-theory        44680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> (C or D)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-44680.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> (C or D)) or E)))), M:tm-595, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-44681
in-theory        44681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> ((D -> (D or E)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-44681.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))))), M:tm-595, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-44682
in-theory        44682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-44682.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> (D -> (D or E)))))), M:tm-595, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-44683
in-theory        44683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (B or A)) and (C or (D -> (E -> D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-44683.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and ((F -> (G or F)) and ((A -> (B or A)) and (C or (D -> (E -> D)))))), M:tm-595, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-44684
in-theory        44684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-44684.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((G -> (H or G)) and ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-595, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-44685
in-theory        44685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (B or A)) and (C or ((D and E) -> D)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-44685.        (((A -> (B or A)) and (C or ((D and E) -> D))) and ((F -> (G or F)) and ((A -> (B or A)) and (C or ((D and E) -> D))))), M:tm-595, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-44686
in-theory        44686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (B or A)) and (C or ((D and E) -> E)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-44686.        (((A -> (B or A)) and (C or ((D and E) -> E))) and ((F -> (G or F)) and ((A -> (B or A)) and (C or ((D and E) -> E))))), M:tm-595, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-44687
in-theory        44687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (B or A)) and (C or (D -> (E -> (D and E)))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-44687.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and ((F -> (G or F)) and ((A -> (B or A)) and (C or (D -> (E -> (D and E))))))), M:tm-595, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-44688
in-theory        44688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (B or A)) and (C or (D -> (D or E))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-44688.        (((A -> (B or A)) and (C or (D -> (D or E)))) and ((F -> (G or F)) and ((A -> (B or A)) and (C or (D -> (D or E)))))), M:tm-595, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-44689
in-theory        44689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (B or A)) and (C or (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-44689.        (((A -> (B or A)) and (C or (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (B or A)) and (C or (D -> (E or D)))))), M:tm-595, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-44690
in-theory        44690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> (D or C)) or E))))
theorem-size     33
proof            (modus-ponens tm-595 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-44690.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> (D or C)) or E)))), M:tm-595, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-44691
in-theory        44691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44691.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))))), M:tm-595, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44692
in-theory        44692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44692.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))))), M:tm-595, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44693
in-theory        44693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and ((D -> (E or D)) and (A -> (A and ((B -> (C or B)) and A)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44693.        ((A -> (A and ((B -> (C or B)) and A))) and ((D -> (E or D)) and (A -> (A and ((B -> (C or B)) and A))))), M:tm-595, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44694
in-theory        44694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-550 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44694.        (((A -> (B or A)) or C) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-550, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44695
in-theory        44695
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-540 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44695.        ((A or (B -> (C or B))) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-540, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44696
in-theory        44696
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-530 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44696.        ((A or (B -> (B or C))) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-530, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44697
in-theory        44697
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-520 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44697.        ((A or (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-520, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44698
in-theory        44698
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-510 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44698.        ((A or ((B and C) -> C)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-510, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44699
in-theory        44699
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-500 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44699.        ((A or ((B and C) -> B)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-500, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44700
in-theory        44700
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-490 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44700.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G or F)) and E)))), M:tm-490, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44701
in-theory        44701
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-480 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44701.        ((A or (B -> (C -> B))) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-480, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44702
in-theory        44702
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and ((B -> (C or B)) and A)) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44702.        (A -> ((A and ((B -> (C or B)) and A)) or D)), M:tm-470, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-44703
in-theory        44703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-469 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44703.        ((A -> (B -> (B or C))) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-469, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44704
in-theory        44704
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((D -> (E or D)) and (B -> (B or C)))))
theorem-size     25
proof            (modus-ponens tm-466 tm-595 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (and (-> Bm (or Cm Bm)) (-> A (or A B)))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44704.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and ((D -> (E or D)) and (B -> (B or C))))), M:tm-466, m:tm-595, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (and (-> Bm (or Cm Bm)) (-> A (or A B))))))
================================================================
tm-name          tm-44705
in-theory        44705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44705.        ((A -> (A and ((B -> (C or B)) and A))) and (D -> (D or E))), M:tm-456, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44706
in-theory        44706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-453 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44706.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-453, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44707
in-theory        44707
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and ((D -> (E or D)) and ((B -> (B or C)) and A))))
theorem-size     31
proof            (modus-ponens tm-450 tm-595 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (and (-> Bm (or Cm Bm)) (and (-> A (or A B)) C))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44707.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and ((D -> (E or D)) and ((B -> (B or C)) and A)))), M:tm-450, m:tm-595, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (and (-> Bm (or Cm Bm)) (and (-> A (or A B)) C)))))
================================================================
tm-name          tm-44708
in-theory        44708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and ((D -> (D or E)) and (A -> (A and ((B -> (C or B)) and A)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44708.        ((A -> (A and ((B -> (C or B)) and A))) and ((D -> (D or E)) and (A -> (A and ((B -> (C or B)) and A))))), M:tm-443, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44709
in-theory        44709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-409 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44709.        (((A -> (A or B)) or C) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-409, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44710
in-theory        44710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-400 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44710.        (((A -> (B -> (A and B))) or C) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-400, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44711
in-theory        44711
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-391 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44711.        ((((A and B) -> B) or C) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-391, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44712
in-theory        44712
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-382 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44712.        ((((A and B) -> A) or C) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-382, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44713
in-theory        44713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-373 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44713.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and ((F -> (G or F)) and E)))), M:tm-373, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44714
in-theory        44714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-364 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44714.        (((A -> (B -> A)) or C) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-364, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44715
in-theory        44715
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and ((C -> (D or C)) and A)) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44715.        (A -> (B -> ((A and ((C -> (D or C)) and A)) and B))), M:tm-355, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-44716
in-theory        44716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-354 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44716.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-354, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44717
in-theory        44717
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((D -> (E or D)) and (B -> (C -> (B and C))))))
theorem-size     31
proof            (modus-ponens tm-351 tm-595 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (and (-> Bm (or Cm Bm)) (-> A (-> B (and A B))))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44717.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and ((D -> (E or D)) and (B -> (C -> (B and C)))))), M:tm-351, m:tm-595, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (and (-> Bm (or Cm Bm)) (-> A (-> B (and A B)))))))
================================================================
tm-name          tm-44718
in-theory        44718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44718.        ((A -> (A and ((B -> (C or B)) and A))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44719
in-theory        44719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and ((D -> (E or D)) and C))))
theorem-size     21
proof            (modus-ponens tm-338 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44719.        (((A -> B) -> (A -> (A and B))) and (C -> (C and ((D -> (E or D)) and C)))), M:tm-338, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44720
in-theory        44720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((C -> (D or C)) and (A -> (A and B)))))
theorem-size     27
proof            (modus-ponens tm-335 tm-595 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (and (-> Bm (or Cm Bm)) (-> A (and A B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44720.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and ((C -> (D or C)) and (A -> (A and B))))), M:tm-335, m:tm-595, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (and (-> Bm (or Cm Bm)) (-> A (and A B))))))
================================================================
tm-name          tm-44721
in-theory        44721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (A -> (A and (A and ((B -> (C or B)) and A)))))
theorem-size     25
proof            (modus-ponens tm-328 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44721.        ((A -> (A and ((B -> (C or B)) and A))) and (A -> (A and (A and ((B -> (C or B)) and A))))), M:tm-328, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-44722
in-theory        44722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and ((D -> (E -> (D and E))) and (A -> (A and ((B -> (C or B)) and A)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44722.        ((A -> (A and ((B -> (C or B)) and A))) and ((D -> (E -> (D and E))) and (A -> (A and ((B -> (C or B)) and A))))), M:tm-327, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44723
in-theory        44723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (((D and E) -> E) and (A -> (A and ((B -> (C or B)) and A)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44723.        ((A -> (A and ((B -> (C or B)) and A))) and (((D and E) -> E) and (A -> (A and ((B -> (C or B)) and A))))), M:tm-326, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44724
in-theory        44724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (((D and E) -> D) and (A -> (A and ((B -> (C or B)) and A)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44724.        ((A -> (A and ((B -> (C or B)) and A))) and (((D and E) -> D) and (A -> (A and ((B -> (C or B)) and A))))), M:tm-325, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44725
in-theory        44725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and ((B -> (C or B)) and A)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44725.        ((A -> (A and ((B -> (C or B)) and A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and ((B -> (C or B)) and A))))), M:tm-324, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44726
in-theory        44726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and ((D -> (E -> D)) and (A -> (A and ((B -> (C or B)) and A)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44726.        ((A -> (A and ((B -> (C or B)) and A))) and ((D -> (E -> D)) and (A -> (A and ((B -> (C or B)) and A))))), M:tm-323, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44727
in-theory        44727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44727.        ((A -> (A and ((B -> (C or B)) and A))) and ((D and E) -> E)), M:tm-322, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44728
in-theory        44728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44728.        ((A -> (A and ((B -> (C or B)) and A))) and ((D and E) -> D)), M:tm-320, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44729
in-theory        44729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44729.        ((A -> (A and ((B -> (C or B)) and A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44730
in-theory        44730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44730.        ((A -> (A and ((B -> (C or B)) and A))) and (A -> A)), M:tm-316, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-44731
in-theory        44731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44731.        ((A -> (A and ((B -> (C or B)) and A))) and (D -> (E -> D))), M:tm-315, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44732
in-theory        44732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and ((A -> (not (A and ((B -> (C or B)) and A)))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44732.        ((A -> (A and ((B -> (C or B)) and A))) and ((A -> (not (A and ((B -> (C or B)) and A)))) -> (not A))), M:tm-313, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-44733
in-theory        44733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (((A and ((B -> (C or B)) and A)) -> D) -> ((A or (A and ((B -> (C or B)) and A))) -> D)))
theorem-size     37
proof            (modus-ponens tm-312 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44733.        ((A -> (A and ((B -> (C or B)) and A))) and (((A and ((B -> (C or B)) and A)) -> D) -> ((A or (A and ((B -> (C or B)) and A))) -> D))), M:tm-312, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-44734
in-theory        44734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (D or (A -> (A and ((B -> (C or B)) and A)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44734.        ((A -> (A and ((B -> (C or B)) and A))) and (D or (A -> (A and ((B -> (C or B)) and A))))), M:tm-311, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44735
in-theory        44735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and ((A -> (A and ((B -> (C or B)) and A))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44735.        ((A -> (A and ((B -> (C or B)) and A))) and ((A -> (A and ((B -> (C or B)) and A))) or D)), M:tm-310, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44736
in-theory        44736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (D -> ((A -> (A and ((B -> (C or B)) and A))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44736.        ((A -> (A and ((B -> (C or B)) and A))) and (D -> ((A -> (A and ((B -> (C or B)) and A))) and D))), M:tm-309, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44737
in-theory        44737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (D -> (A -> (A and ((B -> (C or B)) and A)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44737.        ((A -> (A and ((B -> (C or B)) and A))) and (D -> (A -> (A and ((B -> (C or B)) and A))))), M:tm-305, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44738
in-theory        44738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     23
proof            (modus-ponens tm-303 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44738.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-303, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44739
in-theory        44739
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and ((D -> (E or D)) and ((B -> (C -> (B and C))) and A))))
theorem-size     37
proof            (modus-ponens tm-300 tm-595 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (and (-> Bm (or Cm Bm)) (and (-> A (-> B (and A B))) C))))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44739.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and ((D -> (E or D)) and ((B -> (C -> (B and C))) and A)))), M:tm-300, m:tm-595, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (and (-> Bm (or Cm Bm)) (and (-> A (-> B (and A B))) C)))))
================================================================
tm-name          tm-44740
in-theory        44740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-270 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44740.        ((A -> (((B and C) -> C) and A)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-270, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44741
in-theory        44741
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((D -> (E or D)) and (((B and C) -> C) and A))))
theorem-size     31
proof            (modus-ponens tm-267 tm-595 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (and (-> Bm (or Cm Bm)) (and (-> (and A B) B) C))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44741.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and ((D -> (E or D)) and (((B and C) -> C) and A)))), M:tm-267, m:tm-595, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (and (-> Bm (or Cm Bm)) (and (-> (and A B) B) C)))))
================================================================
tm-name          tm-44742
in-theory        44742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-239 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44742.        ((A -> (((B and C) -> B) and A)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-239, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44743
in-theory        44743
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((D -> (E or D)) and (((B and C) -> B) and A))))
theorem-size     31
proof            (modus-ponens tm-236 tm-595 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (and (-> Bm (or Cm Bm)) (and (-> (and A B) A) C))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44743.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and ((D -> (E or D)) and (((B and C) -> B) and A)))), M:tm-236, m:tm-595, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (and (-> Bm (or Cm Bm)) (and (-> (and A B) A) C)))))
================================================================
tm-name          tm-44744
in-theory        44744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and ((F -> (G or F)) and E))))
theorem-size     29
proof            (modus-ponens tm-210 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44744.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and ((F -> (G or F)) and E)))), M:tm-210, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44745
in-theory        44745
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((E -> (F or E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     55
proof            (modus-ponens tm-207 tm-595 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (or Cm Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44745.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and ((E -> (F or E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-207, m:tm-595, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (or Cm Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-44746
in-theory        44746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-183 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44746.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-183, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44747
in-theory        44747
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and ((D -> (E or D)) and ((B -> (C -> B)) and A))))
theorem-size     31
proof            (modus-ponens tm-180 tm-595 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (and (-> Bm (or Cm Bm)) (and (-> A (-> B A)) C))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44747.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and ((D -> (E or D)) and ((B -> (C -> B)) and A)))), M:tm-180, m:tm-595, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (and (-> Bm (or Cm Bm)) (and (-> A (-> B A)) C)))))
================================================================
tm-name          tm-44748
in-theory        44748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-157 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44748.        ((A -> ((B and C) -> C)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-157, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44749
in-theory        44749
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((D -> (E or D)) and ((B and C) -> C))))
theorem-size     25
proof            (modus-ponens tm-154 tm-595 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (and (-> Bm (or Cm Bm)) (-> (and A B) B))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44749.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((D -> (E or D)) and ((B and C) -> C)))), M:tm-154, m:tm-595, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (and (-> Bm (or Cm Bm)) (-> (and A B) B)))))
================================================================
tm-name          tm-44750
in-theory        44750
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     27
proof            (modus-ponens tm-147 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44750.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-147, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44751
in-theory        44751
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((D -> (E or D)) and ((A and (B -> C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-144 tm-595 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (and (-> Bm (or Cm Bm)) (-> (and A (-> B C)) C))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44751.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((D -> (E or D)) and ((A and (B -> C)) -> C)))), M:tm-144, m:tm-595, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (and (-> Bm (or Cm Bm)) (-> (and A (-> B C)) C)))))
================================================================
tm-name          tm-44752
in-theory        44752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-134 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44752.        ((A -> ((B and C) -> B)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-134, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44753
in-theory        44753
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((D -> (E or D)) and ((B and C) -> B))))
theorem-size     25
proof            (modus-ponens tm-131 tm-595 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (and (-> Bm (or Cm Bm)) (-> (and A B) A))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44753.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((D -> (E or D)) and ((B and C) -> B)))), M:tm-131, m:tm-595, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (and (-> Bm (or Cm Bm)) (-> (and A B) A)))))
================================================================
tm-name          tm-44754
in-theory        44754
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     27
proof            (modus-ponens tm-125 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44754.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-125, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44755
in-theory        44755
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((D -> (E or D)) and (((A -> B) and C) -> B))))
theorem-size     37
proof            (modus-ponens tm-122 tm-595 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (and (-> Bm (or Cm Bm)) (-> (and (-> A B) C) B))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44755.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and ((D -> (E or D)) and (((A -> B) and C) -> B)))), M:tm-122, m:tm-595, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (and (-> Bm (or Cm Bm)) (-> (and (-> A B) C) B)))))
================================================================
tm-name          tm-44756
in-theory        44756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-113 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44756.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and ((F -> (G or F)) and E)))), M:tm-113, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44757
in-theory        44757
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F or E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     49
proof            (modus-ponens tm-110 tm-595 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (-> Bm (or Cm Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44757.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> (F or E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-110, m:tm-595, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (-> Bm (or Cm Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
================================================================
tm-name          tm-44758
in-theory        44758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     31
proof            (modus-ponens tm-105 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44758.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-105, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44759
in-theory        44759
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((D -> (E or D)) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-102 tm-595 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (and (-> Bm (or Cm Bm)) (-> (-> A (-> B C)) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44759.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((D -> (E or D)) and ((A -> (B -> C)) -> (A -> C))))), M:tm-102, m:tm-595, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (and (-> Bm (or Cm Bm)) (-> (-> A (-> B C)) (-> A C))))))
================================================================
tm-name          tm-44760
in-theory        44760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and ((D -> (E or D)) and C))))
theorem-size     19
proof            (modus-ponens tm-95 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44760.        (((A -> B) -> (A -> A)) and (C -> (C and ((D -> (E or D)) and C)))), M:tm-95, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44761
in-theory        44761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and ((C -> (D or C)) and (A -> A))))
theorem-size     21
proof            (modus-ponens tm-92 tm-595 ((Am (-> A A)) (B (and (-> A A) (and (-> Bm (or Cm Bm)) (-> A A))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44761.        (((A -> B) or (A -> A)) -> ((A -> A) and ((C -> (D or C)) and (A -> A)))), M:tm-92, m:tm-595, u:((Am (-> A A)) (B (and (-> A A) (and (-> Bm (or Cm Bm)) (-> A A)))))
================================================================
tm-name          tm-44762
in-theory        44762
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and ((C -> (D or C)) and A))))
theorem-size     13
proof            (modus-ponens tm-84 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44762.        (A -> (B -> (A and ((C -> (D or C)) and A)))), M:tm-84, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-44763
in-theory        44763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-83 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44763.        ((A -> (B -> (C -> B))) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-83, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44764
in-theory        44764
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((D -> (E or D)) and (B -> (C -> B)))))
theorem-size     25
proof            (modus-ponens tm-80 tm-595 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (and (-> Bm (or Cm Bm)) (-> A (-> B A)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44764.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and ((D -> (E or D)) and (B -> (C -> B))))), M:tm-80, m:tm-595, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (and (-> Bm (or Cm Bm)) (-> A (-> B A))))))
================================================================
tm-name          tm-44765
in-theory        44765
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and ((C -> (D or C)) and B))))
theorem-size     17
proof            (modus-ponens tm-76 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-10 tm-2 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44765.        (((not (not A)) -> A) and (B -> (B and ((C -> (D or C)) and B)))), M:tm-76, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44766
in-theory        44766
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and ((B -> (C or B)) and A)))
theorem-size     15
proof            (modus-ponens tm-73 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44766.        (((not (not A)) or A) -> (A and ((B -> (C or B)) and A))), M:tm-73, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-44767
in-theory        44767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and ((D -> (E or D)) and C))))
theorem-size     23
proof            (modus-ponens tm-69 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-9 tm-2 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44767.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and ((D -> (E or D)) and C)))), M:tm-69, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44768
in-theory        44768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((C -> (D or C)) and ((A -> (not B)) -> (not A)))))
theorem-size     33
proof            (modus-ponens tm-66 tm-595 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (and (-> Bm (or Cm Bm)) (-> (-> A (not B)) (not A)))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44768.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((C -> (D or C)) and ((A -> (not B)) -> (not A))))), M:tm-66, m:tm-595, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (and (-> Bm (or Cm Bm)) (-> (-> A (not B)) (not A))))))
================================================================
tm-name          tm-44769
in-theory        44769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     25
proof            (modus-ponens tm-54 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44769.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-54, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44770
in-theory        44770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     39
proof            (modus-ponens tm-51 tm-595 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> (or C A) B)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44770.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((D -> (E or D)) and ((B -> C) -> ((A or B) -> C))))), M:tm-51, m:tm-595, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> (or C A) B))))))
================================================================
tm-name          tm-44771
in-theory        44771
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and ((C -> (D or C)) and (B or A))))
theorem-size     19
proof            (modus-ponens tm-50 tm-595 ((Am (or A B)) (C (and (or A B) (and (-> Bm (or Cm Bm)) (or A B))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44771.        ((A or (B or A)) -> ((B or A) and ((C -> (D or C)) and (B or A)))), M:tm-50, m:tm-595, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (or Cm Bm)) (or A B)))))
================================================================
tm-name          tm-44772
in-theory        44772
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and ((C -> (D or C)) and (A or B))))
theorem-size     19
proof            (modus-ponens tm-49 tm-595 ((Am (or A B)) (C (and (or A B) (and (-> Bm (or Cm Bm)) (or A B))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44772.        ((A or (A or B)) -> ((A or B) and ((C -> (D or C)) and (A or B)))), M:tm-49, m:tm-595, u:((Am (or A B)) (C (and (or A B) (and (-> Bm (or Cm Bm)) (or A B)))))
================================================================
tm-name          tm-44773
in-theory        44773
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((C -> (D or C)) and (B -> (A and B)))))
theorem-size     25
proof            (modus-ponens tm-48 tm-595 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> Bm (or Cm Bm)) (-> A (and B A)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44773.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and ((C -> (D or C)) and (B -> (A and B))))), M:tm-48, m:tm-595, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (and (-> Bm (or Cm Bm)) (-> A (and B A))))))
================================================================
tm-name          tm-44774
in-theory        44774
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and ((C -> (D or C)) and B)))
theorem-size     15
proof            (modus-ponens tm-47 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44774.        (((A and B) or B) -> (B and ((C -> (D or C)) and B))), M:tm-47, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-44775
in-theory        44775
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and ((C -> (D or C)) and A)))
theorem-size     15
proof            (modus-ponens tm-46 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44775.        (((A and B) or A) -> (A and ((C -> (D or C)) and A))), M:tm-46, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-44776
in-theory        44776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E or D)) and ((A -> B) -> (A -> C)))))
theorem-size     35
proof            (modus-ponens tm-45 tm-595 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44776.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E or D)) and ((A -> B) -> (A -> C))))), M:tm-45, m:tm-595, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-44777
in-theory        44777
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and ((C -> (D or C)) and (B -> A))))
theorem-size     19
proof            (modus-ponens tm-44 tm-595 ((Am (-> A B)) (C (and (-> A B) (and (-> Bm (or Cm Bm)) (-> A B))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44777.        ((A or (B -> A)) -> ((B -> A) and ((C -> (D or C)) and (B -> A)))), M:tm-44, m:tm-595, u:((Am (-> A B)) (C (and (-> A B) (and (-> Bm (or Cm Bm)) (-> A B)))))
================================================================
tm-name          tm-44778
in-theory        44778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and ((D -> (E or D)) and C))))
theorem-size     17
proof            (modus-ponens tm-42 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44778.        ((A -> (B or A)) and (C -> (C and ((D -> (E or D)) and C)))), M:tm-42, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44779
in-theory        44779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and ((D -> (E or D)) and C))))
theorem-size     17
proof            (modus-ponens tm-32 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44779.        ((A -> (A or B)) and (C -> (C and ((D -> (E or D)) and C)))), M:tm-32, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44780
in-theory        44780
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and ((B -> (C or B)) and A))))
theorem-size     13
proof            (modus-ponens tm-24 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44780.        (A -> (A and (A and ((B -> (C or B)) and A)))), M:tm-24, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-44781
in-theory        44781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and ((D -> (E or D)) and C))))
theorem-size     19
proof            (modus-ponens tm-23 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44781.        ((A -> (B -> (A and B))) and (C -> (C and ((D -> (E or D)) and C)))), M:tm-23, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44782
in-theory        44782
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and ((D -> (E or D)) and C))))
theorem-size     17
proof            (modus-ponens tm-22 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44782.        (((A and B) -> B) and (C -> (C and ((D -> (E or D)) and C)))), M:tm-22, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44783
in-theory        44783
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and ((D -> (E or D)) and C))))
theorem-size     17
proof            (modus-ponens tm-21 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44783.        (((A and B) -> A) and (C -> (C and ((D -> (E or D)) and C)))), M:tm-21, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44784
in-theory        44784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     25
proof            (modus-ponens tm-20 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44784.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-20, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44785
in-theory        44785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and ((D -> (E or D)) and C))))
theorem-size     17
proof            (modus-ponens tm-19 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44785.        ((A -> (B -> A)) and (C -> (C and ((D -> (E or D)) and C)))), M:tm-19, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44786
in-theory        44786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and ((B -> (C or B)) and A)))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-9 tm-2 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44786.        ((A -> (not (A and ((B -> (C or B)) and A)))) -> (not A)), M:tm-9, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-44787
in-theory        44787
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) and A)) -> D) -> ((A or (A and ((B -> (C or B)) and A))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44787.        (((A and ((B -> (C or B)) and A)) -> D) -> ((A or (A and ((B -> (C or B)) and A))) -> D)), M:tm-8, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-44788
in-theory        44788
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and ((C -> (D or C)) and B))))
theorem-size     13
proof            (modus-ponens tm-7 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-7 tm-2 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44788.        (A or (B -> (B and ((C -> (D or C)) and B)))), M:tm-7, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44789
in-theory        44789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-6 tm-2 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44789.        ((A -> (A and ((B -> (C or B)) and A))) or D), M:tm-6, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44790
in-theory        44790
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and ((C -> (D or C)) and B))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44790.        (A -> ((B -> (B and ((C -> (D or C)) and B))) and A)), M:tm-5, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44791
in-theory        44791
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and ((C -> (D or C)) and B))))
theorem-size     13
proof            (modus-ponens tm-1 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-1 tm-2 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-44791.        (A -> (B -> (B and ((C -> (D or C)) and B)))), M:tm-1, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-44792
in-theory        44792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44792.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))))), M:tm-595, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44793
in-theory        44793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-550 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44793.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-550, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44794
in-theory        44794
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-540 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44794.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-540, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44795
in-theory        44795
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-530 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44795.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-530, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44796
in-theory        44796
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-520 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44796.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-520, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44797
in-theory        44797
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-510 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44797.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-510, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44798
in-theory        44798
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-500 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44798.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-500, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44799
in-theory        44799
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-490 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44799.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G)))), M:tm-490, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44800
in-theory        44800
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-480 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44800.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-480, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44801
in-theory        44801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-469 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44801.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-469, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44802
in-theory        44802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44802.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (F -> (F or G))), M:tm-456, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44803
in-theory        44803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-453 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44803.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-453, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44804
in-theory        44804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44804.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))))), M:tm-443, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44805
in-theory        44805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-409 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44805.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-409, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44806
in-theory        44806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-400 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44806.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-400, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44807
in-theory        44807
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-391 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44807.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-391, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44808
in-theory        44808
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-382 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44808.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-382, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44809
in-theory        44809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-373 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44809.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G)))), M:tm-373, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44810
in-theory        44810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-364 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44810.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-364, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44811
in-theory        44811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-354 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44811.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-354, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44812
in-theory        44812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44812.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44813
in-theory        44813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-338 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44813.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E)))), M:tm-338, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44814
in-theory        44814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44814.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))))), M:tm-327, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44815
in-theory        44815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44815.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))))), M:tm-326, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44816
in-theory        44816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44816.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))))), M:tm-325, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44817
in-theory        44817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44817.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))))), M:tm-324, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44818
in-theory        44818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44818.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))))), M:tm-323, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44819
in-theory        44819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44819.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44820
in-theory        44820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44820.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44821
in-theory        44821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44821.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44822
in-theory        44822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44822.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44823
in-theory        44823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (F or ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44823.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (F or ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))))), M:tm-311, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44824
in-theory        44824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44824.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) or F)), M:tm-310, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44825
in-theory        44825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (F -> (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44825.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (F -> (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and F))), M:tm-309, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44826
in-theory        44826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (C -> ((D -> (E or D)) and C)))
theorem-size     27
proof            (modus-ponens tm-308 tm-596 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44826.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (C -> ((D -> (E or D)) and C))), M:tm-308, m:tm-596, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm))))
================================================================
tm-name          tm-44827
in-theory        44827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (A -> (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-307 tm-596 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44827.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-596, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm))))
================================================================
tm-name          tm-44828
in-theory        44828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (F -> ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44828.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (F -> ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))))), M:tm-305, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44829
in-theory        44829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-303 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44829.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-303, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44830
in-theory        44830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-270 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44830.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-270, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44831
in-theory        44831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-239 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44831.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-239, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44832
in-theory        44832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     35
proof            (modus-ponens tm-210 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44832.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G)))), M:tm-210, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44833
in-theory        44833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-183 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44833.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-183, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44834
in-theory        44834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-157 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44834.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-157, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44835
in-theory        44835
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     33
proof            (modus-ponens tm-147 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44835.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-147, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44836
in-theory        44836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-134 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44836.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-134, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44837
in-theory        44837
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     33
proof            (modus-ponens tm-125 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44837.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-125, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44838
in-theory        44838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-113 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44838.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G)))), M:tm-113, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44839
in-theory        44839
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     37
proof            (modus-ponens tm-105 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44839.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-105, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44840
in-theory        44840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-95 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44840.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E)))), M:tm-95, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44841
in-theory        44841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-83 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44841.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-83, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44842
in-theory        44842
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> ((E -> (F or E)) and D))))
theorem-size     23
proof            (modus-ponens tm-76 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44842.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> ((E -> (F or E)) and D)))), M:tm-76, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44843
in-theory        44843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     29
proof            (modus-ponens tm-69 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44843.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E)))), M:tm-69, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44844
in-theory        44844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-54 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44844.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-54, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44845
in-theory        44845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-42 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44845.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E)))), M:tm-42, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44846
in-theory        44846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-32 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44846.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E)))), M:tm-32, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44847
in-theory        44847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-23 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44847.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E)))), M:tm-23, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44848
in-theory        44848
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-22 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44848.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E)))), M:tm-22, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44849
in-theory        44849
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-21 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44849.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E)))), M:tm-21, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44850
in-theory        44850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-20 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44850.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-20, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44851
in-theory        44851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-19 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44851.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> ((F -> (G or F)) and E)))), M:tm-19, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44852
in-theory        44852
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-7 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-7 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44852.        (A or ((B -> (C -> (B and C))) and (D -> ((E -> (F or E)) and D)))), M:tm-7, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44853
in-theory        44853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44853.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) or F), M:tm-6, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44854
in-theory        44854
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> ((E -> (F or E)) and D))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44854.        (A -> (((B -> (C -> (B and C))) and (D -> ((E -> (F or E)) and D))) and A)), M:tm-5, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44855
in-theory        44855
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-1 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44855.        (A -> ((B -> (C -> (B and C))) and (D -> ((E -> (F or E)) and D)))), M:tm-1, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44856
in-theory        44856
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44856.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> ((D -> (E or D)) and C))))), M:tm-595, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44857
in-theory        44857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44857.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-550, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44858
in-theory        44858
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44858.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-540, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44859
in-theory        44859
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44859.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-530, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44860
in-theory        44860
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44860.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-520, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44861
in-theory        44861
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44861.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-510, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44862
in-theory        44862
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44862.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-500, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44863
in-theory        44863
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44863.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G)))), M:tm-490, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44864
in-theory        44864
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44864.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-480, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44865
in-theory        44865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44865.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-469, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44866
in-theory        44866
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44866.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (F -> (F or G))), M:tm-456, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44867
in-theory        44867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44867.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-453, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44868
in-theory        44868
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44868.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> ((D -> (E or D)) and C))))), M:tm-443, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44869
in-theory        44869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44869.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-409, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44870
in-theory        44870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44870.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-400, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44871
in-theory        44871
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44871.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-391, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44872
in-theory        44872
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44872.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-382, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44873
in-theory        44873
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44873.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G)))), M:tm-373, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44874
in-theory        44874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44874.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-364, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44875
in-theory        44875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44875.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-354, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44876
in-theory        44876
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44876.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44877
in-theory        44877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44877.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E)))), M:tm-338, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44878
in-theory        44878
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> ((D -> (E or D)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44878.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> ((D -> (E or D)) and C))))), M:tm-327, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44879
in-theory        44879
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> G) and (((A and B) -> B) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44879.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> G) and (((A and B) -> B) and (C -> ((D -> (E or D)) and C))))), M:tm-326, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44880
in-theory        44880
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> F) and (((A and B) -> B) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44880.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> F) and (((A and B) -> B) and (C -> ((D -> (E or D)) and C))))), M:tm-325, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44881
in-theory        44881
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> ((D -> (E or D)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44881.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> ((D -> (E or D)) and C))))), M:tm-324, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44882
in-theory        44882
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44882.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> ((D -> (E or D)) and C))))), M:tm-323, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44883
in-theory        44883
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44883.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44884
in-theory        44884
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44884.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44885
in-theory        44885
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44885.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44886
in-theory        44886
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44886.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44887
in-theory        44887
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (F or (((A and B) -> B) and (C -> ((D -> (E or D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44887.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (F or (((A and B) -> B) and (C -> ((D -> (E or D)) and C))))), M:tm-311, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44888
in-theory        44888
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44888.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) or F)), M:tm-310, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44889
in-theory        44889
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (F -> ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44889.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (F -> ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and F))), M:tm-309, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44890
in-theory        44890
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (C -> ((D -> (E or D)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-597 ((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44890.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (C -> ((D -> (E or D)) and C))), M:tm-308, m:tm-597, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (or Em Dm)) Cm))))
================================================================
tm-name          tm-44891
in-theory        44891
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((A and B) -> B))
theorem-size     21
proof            (modus-ponens tm-307 tm-597 ((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44891.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and ((A and B) -> B)), M:tm-307, m:tm-597, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (and (-> Dm (or Em Dm)) Cm))))
================================================================
tm-name          tm-44892
in-theory        44892
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (F -> (((A and B) -> B) and (C -> ((D -> (E or D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44892.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (F -> (((A and B) -> B) and (C -> ((D -> (E or D)) and C))))), M:tm-305, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44893
in-theory        44893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44893.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-303, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44894
in-theory        44894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44894.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-270, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44895
in-theory        44895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44895.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-239, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44896
in-theory        44896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44896.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G)))), M:tm-210, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44897
in-theory        44897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44897.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-183, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44898
in-theory        44898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44898.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-157, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44899
in-theory        44899
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44899.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-147, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44900
in-theory        44900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44900.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-134, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44901
in-theory        44901
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44901.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-125, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44902
in-theory        44902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44902.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G)))), M:tm-113, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44903
in-theory        44903
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44903.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-105, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44904
in-theory        44904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44904.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E)))), M:tm-95, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44905
in-theory        44905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44905.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-83, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44906
in-theory        44906
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44906.        (((not (not A)) -> A) and (((B and C) -> C) and (D -> ((E -> (F or E)) and D)))), M:tm-76, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44907
in-theory        44907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44907.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E)))), M:tm-69, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44908
in-theory        44908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44908.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-54, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44909
in-theory        44909
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44909.        ((A -> (B or A)) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E)))), M:tm-42, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44910
in-theory        44910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44910.        ((A -> (A or B)) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E)))), M:tm-32, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44911
in-theory        44911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44911.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E)))), M:tm-23, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44912
in-theory        44912
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44912.        (((A and B) -> B) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E)))), M:tm-22, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44913
in-theory        44913
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44913.        (((A and B) -> A) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E)))), M:tm-21, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44914
in-theory        44914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44914.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-20, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44915
in-theory        44915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44915.        ((A -> (B -> A)) and (((C and D) -> D) and (E -> ((F -> (G or F)) and E)))), M:tm-19, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44916
in-theory        44916
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-7 tm-5 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44916.        (A or (((B and C) -> C) and (D -> ((E -> (F or E)) and D)))), M:tm-7, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44917
in-theory        44917
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-6 tm-5 tm-4 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44917.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) or F), M:tm-6, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44918
in-theory        44918
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> ((E -> (F or E)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44918.        (A -> ((((B and C) -> C) and (D -> ((E -> (F or E)) and D))) and A)), M:tm-5, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44919
in-theory        44919
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-1 tm-5 tm-4 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44919.        (A -> (((B and C) -> C) and (D -> ((E -> (F or E)) and D)))), M:tm-1, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44920
in-theory        44920
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44920.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> ((D -> (E or D)) and C))))), M:tm-595, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44921
in-theory        44921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44921.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-550, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44922
in-theory        44922
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44922.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-540, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44923
in-theory        44923
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44923.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-530, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44924
in-theory        44924
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44924.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-520, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44925
in-theory        44925
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44925.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-510, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44926
in-theory        44926
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44926.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-500, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44927
in-theory        44927
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44927.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G)))), M:tm-490, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44928
in-theory        44928
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44928.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-480, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44929
in-theory        44929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44929.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-469, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44930
in-theory        44930
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44930.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (F -> (F or G))), M:tm-456, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44931
in-theory        44931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44931.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-453, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44932
in-theory        44932
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44932.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> ((D -> (E or D)) and C))))), M:tm-443, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44933
in-theory        44933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44933.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-409, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44934
in-theory        44934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44934.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-400, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44935
in-theory        44935
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44935.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-391, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44936
in-theory        44936
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44936.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-382, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44937
in-theory        44937
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44937.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G)))), M:tm-373, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44938
in-theory        44938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44938.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-364, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44939
in-theory        44939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44939.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-354, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44940
in-theory        44940
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44940.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44941
in-theory        44941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44941.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E)))), M:tm-338, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44942
in-theory        44942
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> ((D -> (E or D)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44942.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> ((D -> (E or D)) and C))))), M:tm-327, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44943
in-theory        44943
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> G) and (((A and B) -> A) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44943.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> G) and (((A and B) -> A) and (C -> ((D -> (E or D)) and C))))), M:tm-326, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44944
in-theory        44944
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> F) and (((A and B) -> A) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44944.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> F) and (((A and B) -> A) and (C -> ((D -> (E or D)) and C))))), M:tm-325, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44945
in-theory        44945
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> ((D -> (E or D)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44945.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> ((D -> (E or D)) and C))))), M:tm-324, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44946
in-theory        44946
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44946.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> ((D -> (E or D)) and C))))), M:tm-323, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44947
in-theory        44947
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44947.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44948
in-theory        44948
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44948.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44949
in-theory        44949
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44949.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44950
in-theory        44950
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44950.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44951
in-theory        44951
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (F or (((A and B) -> A) and (C -> ((D -> (E or D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44951.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (F or (((A and B) -> A) and (C -> ((D -> (E or D)) and C))))), M:tm-311, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44952
in-theory        44952
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44952.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) or F)), M:tm-310, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44953
in-theory        44953
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (F -> ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44953.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (F -> ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and F))), M:tm-309, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44954
in-theory        44954
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (C -> ((D -> (E or D)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-598 ((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44954.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (C -> ((D -> (E or D)) and C))), M:tm-308, m:tm-598, u:((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (or Em Dm)) Cm))))
================================================================
tm-name          tm-44955
in-theory        44955
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((A and B) -> A))
theorem-size     21
proof            (modus-ponens tm-307 tm-598 ((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44955.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and ((A and B) -> A)), M:tm-307, m:tm-598, u:((A (-> (and Am Bm) Am)) (B (-> Cm (and (-> Dm (or Em Dm)) Cm))))
================================================================
tm-name          tm-44956
in-theory        44956
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (F -> (((A and B) -> A) and (C -> ((D -> (E or D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44956.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (F -> (((A and B) -> A) and (C -> ((D -> (E or D)) and C))))), M:tm-305, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44957
in-theory        44957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44957.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-303, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44958
in-theory        44958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44958.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-270, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44959
in-theory        44959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44959.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-239, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44960
in-theory        44960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44960.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G)))), M:tm-210, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44961
in-theory        44961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44961.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-183, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44962
in-theory        44962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44962.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-157, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44963
in-theory        44963
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44963.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-147, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44964
in-theory        44964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44964.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-134, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44965
in-theory        44965
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44965.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-125, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44966
in-theory        44966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44966.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G)))), M:tm-113, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44967
in-theory        44967
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44967.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-105, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44968
in-theory        44968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44968.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E)))), M:tm-95, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44969
in-theory        44969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44969.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-83, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44970
in-theory        44970
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44970.        (((not (not A)) -> A) and (((B and C) -> B) and (D -> ((E -> (F or E)) and D)))), M:tm-76, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44971
in-theory        44971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44971.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E)))), M:tm-69, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44972
in-theory        44972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44972.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-54, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44973
in-theory        44973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44973.        ((A -> (B or A)) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E)))), M:tm-42, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44974
in-theory        44974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44974.        ((A -> (A or B)) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E)))), M:tm-32, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44975
in-theory        44975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44975.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E)))), M:tm-23, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44976
in-theory        44976
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44976.        (((A and B) -> B) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E)))), M:tm-22, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44977
in-theory        44977
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44977.        (((A and B) -> A) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E)))), M:tm-21, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44978
in-theory        44978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44978.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-20, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44979
in-theory        44979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44979.        ((A -> (B -> A)) and (((C and D) -> C) and (E -> ((F -> (G or F)) and E)))), M:tm-19, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44980
in-theory        44980
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-7 tm-5 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44980.        (A or (((B and C) -> B) and (D -> ((E -> (F or E)) and D)))), M:tm-7, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44981
in-theory        44981
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-6 tm-5 tm-3 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44981.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) or F), M:tm-6, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44982
in-theory        44982
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> ((E -> (F or E)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44982.        (A -> ((((B and C) -> B) and (D -> ((E -> (F or E)) and D))) and A)), M:tm-5, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44983
in-theory        44983
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-1 tm-5 tm-3 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44983.        (A -> (((B and C) -> B) and (D -> ((E -> (F or E)) and D)))), M:tm-1, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-44984
in-theory        44984
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44984.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-595, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44985
in-theory        44985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-550 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44985.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-550, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44986
in-theory        44986
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-540 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44986.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-540, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44987
in-theory        44987
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-530 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44987.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-530, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44988
in-theory        44988
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-520 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44988.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-520, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44989
in-theory        44989
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-510 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44989.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-510, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44990
in-theory        44990
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-500 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44990.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-500, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44991
in-theory        44991
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J or I)) and H))))
theorem-size     39
proof            (modus-ponens tm-490 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44991.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-490, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44992
in-theory        44992
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-480 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44992.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-480, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44993
in-theory        44993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-469 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44993.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-469, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44994
in-theory        44994
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (G or H)))
theorem-size     29
proof            (modus-ponens tm-456 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44994.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (G or H))), M:tm-456, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44995
in-theory        44995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-453 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44995.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-453, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44996
in-theory        44996
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44996.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-443, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44997
in-theory        44997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-409 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44997.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-409, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44998
in-theory        44998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-400 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44998.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-400, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-44999
in-theory        44999
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-391 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-44999.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-391, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45000
in-theory        45000
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-382 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45000.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-382, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45001
in-theory        45001
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J or I)) and H))))
theorem-size     39
proof            (modus-ponens tm-373 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45001.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-373, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45002
in-theory        45002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-364 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45002.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-364, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45003
in-theory        45003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-354 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45003.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-354, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45004
in-theory        45004
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (H -> (G and H))))
theorem-size     31
proof            (modus-ponens tm-341 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45004.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45005
in-theory        45005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     33
proof            (modus-ponens tm-338 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45005.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-338, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45006
in-theory        45006
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45006.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-327, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45007
in-theory        45007
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45007.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-326, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45008
in-theory        45008
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45008.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-325, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45009
in-theory        45009
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45009.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-324, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45010
in-theory        45010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45010.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-323, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45011
in-theory        45011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((G and H) -> H))
theorem-size     29
proof            (modus-ponens tm-322 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45011.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((G and H) -> H)), M:tm-322, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45012
in-theory        45012
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((G and H) -> G))
theorem-size     29
proof            (modus-ponens tm-320 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45012.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((G and H) -> G)), M:tm-320, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45013
in-theory        45013
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     37
proof            (modus-ponens tm-318 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45013.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45014
in-theory        45014
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (H -> G)))
theorem-size     29
proof            (modus-ponens tm-315 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45014.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (H -> G))), M:tm-315, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45015
in-theory        45015
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45015.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-311, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45016
in-theory        45016
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) or G))
theorem-size     49
proof            (modus-ponens tm-310 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45016.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) or G)), M:tm-310, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45017
in-theory        45017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and G)))
theorem-size     51
proof            (modus-ponens tm-309 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45017.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and G))), M:tm-309, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45018
in-theory        45018
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (D -> ((E -> (F or E)) and D)))
theorem-size     33
proof            (modus-ponens tm-308 tm-599 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (or Fm Em)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45018.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (D -> ((E -> (F or E)) and D))), M:tm-308, m:tm-599, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (or Fm Em)) Dm))))
================================================================
tm-name          tm-45019
in-theory        45019
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-307 tm-599 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (or Fm Em)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45019.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-599, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> Em (or Fm Em)) Dm))))
================================================================
tm-name          tm-45020
in-theory        45020
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45020.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))))), M:tm-305, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45021
in-theory        45021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     35
proof            (modus-ponens tm-303 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45021.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-303, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45022
in-theory        45022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-270 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45022.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-270, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45023
in-theory        45023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-239 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45023.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-239, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45024
in-theory        45024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J or I)) and H))))
theorem-size     41
proof            (modus-ponens tm-210 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45024.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-210, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45025
in-theory        45025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-183 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45025.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-183, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45026
in-theory        45026
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-157 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45026.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-157, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45027
in-theory        45027
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     39
proof            (modus-ponens tm-147 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45027.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-147, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45028
in-theory        45028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-134 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45028.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-134, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45029
in-theory        45029
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     39
proof            (modus-ponens tm-125 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45029.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-125, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45030
in-theory        45030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J or I)) and H))))
theorem-size     39
proof            (modus-ponens tm-113 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45030.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-113, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45031
in-theory        45031
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     43
proof            (modus-ponens tm-105 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45031.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-105, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45032
in-theory        45032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-95 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45032.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-95, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45033
in-theory        45033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-83 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45033.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-83, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45034
in-theory        45034
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     29
proof            (modus-ponens tm-76 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45034.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G or F)) and E)))), M:tm-76, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45035
in-theory        45035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     35
proof            (modus-ponens tm-69 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45035.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-69, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45036
in-theory        45036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     37
proof            (modus-ponens tm-54 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45036.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-54, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45037
in-theory        45037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-42 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45037.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-42, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45038
in-theory        45038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-32 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45038.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-32, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45039
in-theory        45039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-23 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45039.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-23, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45040
in-theory        45040
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-22 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45040.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-22, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45041
in-theory        45041
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-21 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45041.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-21, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45042
in-theory        45042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     37
proof            (modus-ponens tm-20 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45042.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-20, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45043
in-theory        45043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-19 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45043.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> ((G -> (H or G)) and F)))), M:tm-19, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45044
in-theory        45044
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-7 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-7 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45044.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G or F)) and E)))), M:tm-7, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45045
in-theory        45045
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) or G)
theorem-size     25
proof            (modus-ponens tm-6 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45045.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) or G), M:tm-6, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45046
in-theory        45046
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G or F)) and E))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45046.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G or F)) and E))) and A)), M:tm-5, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45047
in-theory        45047
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-1 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45047.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> ((F -> (G or F)) and E)))), M:tm-1, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-45048
in-theory        45048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45048.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))))), M:tm-595, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45049
in-theory        45049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45049.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-550, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45050
in-theory        45050
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45050.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-540, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45051
in-theory        45051
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45051.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-530, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45052
in-theory        45052
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45052.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-520, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45053
in-theory        45053
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45053.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-510, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45054
in-theory        45054
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45054.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-500, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45055
in-theory        45055
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45055.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G)))), M:tm-490, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45056
in-theory        45056
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45056.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-480, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45057
in-theory        45057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45057.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-469, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45058
in-theory        45058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45058.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (F -> (F or G))), M:tm-456, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45059
in-theory        45059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45059.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-453, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45060
in-theory        45060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45060.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))))), M:tm-443, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45061
in-theory        45061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45061.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-409, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45062
in-theory        45062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45062.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-400, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45063
in-theory        45063
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45063.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-391, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45064
in-theory        45064
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45064.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-382, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45065
in-theory        45065
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45065.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G)))), M:tm-373, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45066
in-theory        45066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45066.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-364, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45067
in-theory        45067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45067.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-354, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45068
in-theory        45068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45068.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45069
in-theory        45069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45069.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E)))), M:tm-338, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45070
in-theory        45070
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45070.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))))), M:tm-327, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45071
in-theory        45071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45071.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))))), M:tm-326, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45072
in-theory        45072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45072.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))))), M:tm-325, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45073
in-theory        45073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45073.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))))), M:tm-324, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45074
in-theory        45074
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45074.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))))), M:tm-323, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45075
in-theory        45075
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45075.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> G)), M:tm-322, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45076
in-theory        45076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45076.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and ((F and G) -> F)), M:tm-320, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45077
in-theory        45077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45077.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45078
in-theory        45078
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45078.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (F -> (G -> F))), M:tm-315, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45079
in-theory        45079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (F or ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45079.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (F or ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))))), M:tm-311, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45080
in-theory        45080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45080.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) or F)), M:tm-310, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45081
in-theory        45081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (F -> (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45081.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (F -> (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and F))), M:tm-309, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45082
in-theory        45082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (C -> ((D -> (E or D)) and C)))
theorem-size     25
proof            (modus-ponens tm-308 tm-600 ((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45082.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (C -> ((D -> (E or D)) and C))), M:tm-308, m:tm-600, u:((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm))))
================================================================
tm-name          tm-45083
in-theory        45083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (A -> (B -> A)))
theorem-size     21
proof            (modus-ponens tm-307 tm-600 ((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45083.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (A -> (B -> A))), M:tm-307, m:tm-600, u:((A (-> Am (-> Bm Am))) (B (-> Cm (and (-> Dm (or Em Dm)) Cm))))
================================================================
tm-name          tm-45084
in-theory        45084
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (F -> ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45084.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (F -> ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))))), M:tm-305, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45085
in-theory        45085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45085.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-303, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45086
in-theory        45086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45086.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-270, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45087
in-theory        45087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45087.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-239, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45088
in-theory        45088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45088.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G)))), M:tm-210, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45089
in-theory        45089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45089.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-183, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45090
in-theory        45090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45090.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-157, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45091
in-theory        45091
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45091.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-147, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45092
in-theory        45092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45092.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-134, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45093
in-theory        45093
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45093.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-125, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45094
in-theory        45094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45094.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G)))), M:tm-113, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45095
in-theory        45095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45095.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-105, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45096
in-theory        45096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45096.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E)))), M:tm-95, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45097
in-theory        45097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45097.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-83, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45098
in-theory        45098
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45098.        (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> ((E -> (F or E)) and D)))), M:tm-76, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45099
in-theory        45099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45099.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E)))), M:tm-69, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45100
in-theory        45100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45100.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-54, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45101
in-theory        45101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45101.        ((A -> (B or A)) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E)))), M:tm-42, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45102
in-theory        45102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45102.        ((A -> (A or B)) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E)))), M:tm-32, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45103
in-theory        45103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45103.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E)))), M:tm-23, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45104
in-theory        45104
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45104.        (((A and B) -> B) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E)))), M:tm-22, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45105
in-theory        45105
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45105.        (((A and B) -> A) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E)))), M:tm-21, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45106
in-theory        45106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45106.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-20, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45107
in-theory        45107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45107.        ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> ((F -> (G or F)) and E)))), M:tm-19, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45108
in-theory        45108
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45108.        (A or ((B -> (C -> B)) and (D -> ((E -> (F or E)) and D)))), M:tm-7, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45109
in-theory        45109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45109.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) or F), M:tm-6, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45110
in-theory        45110
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> ((E -> (F or E)) and D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45110.        (A -> (((B -> (C -> B)) and (D -> ((E -> (F or E)) and D))) and A)), M:tm-5, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45111
in-theory        45111
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45111.        (A -> ((B -> (C -> B)) and (D -> ((E -> (F or E)) and D)))), M:tm-1, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-45112
in-theory        45112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((D -> (E or D)) and ((A -> (not ((B -> (C or B)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45112.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((D -> (E or D)) and ((A -> (not ((B -> (C or B)) and A))) -> (not A)))), M:tm-595, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45113
in-theory        45113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45113.        (((A -> (B or A)) or C) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-550, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45114
in-theory        45114
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45114.        ((A or (B -> (C or B))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-540, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45115
in-theory        45115
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45115.        ((A or (B -> (B or C))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-530, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45116
in-theory        45116
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45116.        ((A or (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-520, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45117
in-theory        45117
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45117.        ((A or ((B and C) -> C)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-510, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45118
in-theory        45118
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45118.        ((A or ((B and C) -> B)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-500, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45119
in-theory        45119
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G or F)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45119.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G or F)) and E))) -> (not E))), M:tm-490, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45120
in-theory        45120
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45120.        ((A or (B -> (C -> B))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-480, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45121
in-theory        45121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C or B)) and A))) -> ((not A) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45121.        ((A -> (not ((B -> (C or B)) and A))) -> ((not A) or D)), M:tm-470, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-45122
in-theory        45122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45122.        ((A -> (B -> (B or C))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-469, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45123
in-theory        45123
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not ((C -> (D or C)) and (A -> (A or B))))))
theorem-size     19
proof            (modus-ponens tm-465 tm-601 ((A (-> (-> B (or B C)) (not (and (-> Bm (or Cm Bm)) (-> B (or B C)))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45123.        (not ((A -> (A or B)) -> (not ((C -> (D or C)) and (A -> (A or B)))))), M:tm-465, m:tm-601, u:((A (-> (-> B (or B C)) (not (and (-> Bm (or Cm Bm)) (-> B (or B C)))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-45124
in-theory        45124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45124.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (D -> (D or E))), M:tm-456, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45125
in-theory        45125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45125.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-453, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45126
in-theory        45126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((D -> (D or E)) and ((A -> (not ((B -> (C or B)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45126.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((D -> (D or E)) and ((A -> (not ((B -> (C or B)) and A))) -> (not A)))), M:tm-443, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45127
in-theory        45127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45127.        (((A -> (A or B)) or C) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-409, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45128
in-theory        45128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45128.        (((A -> (B -> (A and B))) or C) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-400, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45129
in-theory        45129
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45129.        ((((A and B) -> B) or C) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-391, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45130
in-theory        45130
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45130.        ((((A and B) -> A) or C) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-382, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45131
in-theory        45131
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not ((F -> (G or F)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45131.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not ((F -> (G or F)) and E))) -> (not E))), M:tm-373, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45132
in-theory        45132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45132.        (((A -> (B -> A)) or C) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-364, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45133
in-theory        45133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C or B)) and A))) -> (D -> ((not A) and D)))
theorem-size     17
proof            (modus-ponens tm-355 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45133.        ((A -> (not ((B -> (C or B)) and A))) -> (D -> ((not A) and D))), M:tm-355, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-45134
in-theory        45134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45134.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-354, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45135
in-theory        45135
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not ((C -> (D or C)) and (A -> (B -> (A and B)))))))
theorem-size     23
proof            (modus-ponens tm-350 tm-601 ((A (-> (-> B (-> C (and B C))) (not (and (-> Bm (or Cm Bm)) (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45135.        (not ((A -> (B -> (A and B))) -> (not ((C -> (D or C)) and (A -> (B -> (A and B))))))), M:tm-350, m:tm-601, u:((A (-> (-> B (-> C (and B C))) (not (and (-> Bm (or Cm Bm)) (-> B (-> C (and B C))))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-45136
in-theory        45136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45136.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45137
in-theory        45137
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not ((D -> (E or D)) and C))) -> (not C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45137.        (((A -> B) -> (A -> (A and B))) and ((C -> (not ((D -> (E or D)) and C))) -> (not C))), M:tm-338, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45138
in-theory        45138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((A -> (not ((B -> (C or B)) and A))) -> ((A -> (not ((B -> (C or B)) and A))) and (not A))))
theorem-size     38
proof            (modus-ponens tm-328 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       154
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45138.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((A -> (not ((B -> (C or B)) and A))) -> ((A -> (not ((B -> (C or B)) and A))) and (not A)))), M:tm-328, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-45139
in-theory        45139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not ((B -> (C or B)) and A))) -> (not A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45139.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not ((B -> (C or B)) and A))) -> (not A)))), M:tm-327, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45140
in-theory        45140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((D and E) -> E) and ((A -> (not ((B -> (C or B)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45140.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((D and E) -> E) and ((A -> (not ((B -> (C or B)) and A))) -> (not A)))), M:tm-326, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45141
in-theory        45141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((D and E) -> D) and ((A -> (not ((B -> (C or B)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45141.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((D and E) -> D) and ((A -> (not ((B -> (C or B)) and A))) -> (not A)))), M:tm-325, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45142
in-theory        45142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not ((B -> (C or B)) and A))) -> (not A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45142.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not ((B -> (C or B)) and A))) -> (not A)))), M:tm-324, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45143
in-theory        45143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not ((B -> (C or B)) and A))) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45143.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not ((B -> (C or B)) and A))) -> (not A)))), M:tm-323, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45144
in-theory        45144
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45144.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((D and E) -> E)), M:tm-322, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45145
in-theory        45145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45145.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((D and E) -> D)), M:tm-320, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45146
in-theory        45146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45146.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45147
in-theory        45147
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((A -> (not ((B -> (C or B)) and A))) -> (A -> (not ((B -> (C or B)) and A)))))
theorem-size     35
proof            (modus-ponens tm-316 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45147.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((A -> (not ((B -> (C or B)) and A))) -> (A -> (not ((B -> (C or B)) and A))))), M:tm-316, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-45148
in-theory        45148
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45148.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (D -> (E -> D))), M:tm-315, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45149
in-theory        45149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((A -> (not ((B -> (C or B)) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (C or B)) and A))))))
theorem-size     40
proof            (modus-ponens tm-313 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       140
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45149.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((A -> (not ((B -> (C or B)) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (C or B)) and A)))))), M:tm-313, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-45150
in-theory        45150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((not A) -> D) -> (((A -> (not ((B -> (C or B)) and A))) or (not A)) -> D)))
theorem-size     34
proof            (modus-ponens tm-312 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-7)
proof-size       138
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45150.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((not A) -> D) -> (((A -> (not ((B -> (C or B)) and A))) or (not A)) -> D))), M:tm-312, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-45151
in-theory        45151
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (D or ((A -> (not ((B -> (C or B)) and A))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45151.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (D or ((A -> (not ((B -> (C or B)) and A))) -> (not A)))), M:tm-311, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45152
in-theory        45152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((A -> (not ((B -> (C or B)) and A))) -> (not A)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45152.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((A -> (not ((B -> (C or B)) and A))) -> (not A)) or D)), M:tm-310, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45153
in-theory        45153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (D -> (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45153.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (D -> (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and D))), M:tm-309, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45154
in-theory        45154
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (D -> ((A -> (not ((B -> (C or B)) and A))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45154.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (D -> ((A -> (not ((B -> (C or B)) and A))) -> (not A)))), M:tm-305, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45155
in-theory        45155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45155.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-303, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45156
in-theory        45156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45156.        ((A -> (((B and C) -> C) and A)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-270, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45157
in-theory        45157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45157.        ((A -> (((B and C) -> B) and A)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-239, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45158
in-theory        45158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not ((F -> (G or F)) and E))) -> (not E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45158.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not ((F -> (G or F)) and E))) -> (not E))), M:tm-210, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45159
in-theory        45159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45159.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-183, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45160
in-theory        45160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45160.        ((A -> ((B and C) -> C)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-157, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45161
in-theory        45161
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not ((C -> (D or C)) and ((A and B) -> B)))))
theorem-size     19
proof            (modus-ponens tm-153 tm-601 ((A (-> (-> (and B C) C) (not (and (-> Bm (or Cm Bm)) (-> (and B C) C))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45161.        (not (((A and B) -> B) -> (not ((C -> (D or C)) and ((A and B) -> B))))), M:tm-153, m:tm-601, u:((A (-> (-> (and B C) C) (not (and (-> Bm (or Cm Bm)) (-> (and B C) C))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-45162
in-theory        45162
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45162.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-147, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45163
in-theory        45163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45163.        ((A -> ((B and C) -> B)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-134, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45164
in-theory        45164
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not ((C -> (D or C)) and ((A and B) -> A)))))
theorem-size     19
proof            (modus-ponens tm-130 tm-601 ((A (-> (-> (and B C) B) (not (and (-> Bm (or Cm Bm)) (-> (and B C) B))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45164.        (not (((A and B) -> A) -> (not ((C -> (D or C)) and ((A and B) -> A))))), M:tm-130, m:tm-601, u:((A (-> (-> (and B C) B) (not (and (-> Bm (or Cm Bm)) (-> (and B C) B))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-45165
in-theory        45165
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45165.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-125, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45166
in-theory        45166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G or F)) and E))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45166.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not ((F -> (G or F)) and E))) -> (not E))), M:tm-113, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45167
in-theory        45167
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D -> (E or D)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))))
theorem-size     35
proof            (modus-ponens tm-109 tm-601 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (and (-> Bm (or Cm Bm)) (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-5 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45167.        (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((D -> (E or D)) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))), M:tm-109, m:tm-601, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (and (-> Bm (or Cm Bm)) (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-45168
in-theory        45168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45168.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-105, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45169
in-theory        45169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not ((D -> (E or D)) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45169.        (((A -> B) -> (A -> A)) and ((C -> (not ((D -> (E or D)) and C))) -> (not C))), M:tm-95, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45170
in-theory        45170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C or B)) and A))) -> (D -> (not A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45170.        ((A -> (not ((B -> (C or B)) and A))) -> (D -> (not A))), M:tm-84, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-45171
in-theory        45171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45171.        ((A -> (B -> (C -> B))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-83, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45172
in-theory        45172
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not ((C -> (D or C)) and (A -> (B -> A))))))
theorem-size     19
proof            (modus-ponens tm-79 tm-601 ((A (-> (-> B (-> C B)) (not (and (-> Bm (or Cm Bm)) (-> B (-> C B)))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45172.        (not ((A -> (B -> A)) -> (not ((C -> (D or C)) and (A -> (B -> A)))))), M:tm-79, m:tm-601, u:((A (-> (-> B (-> C B)) (not (and (-> Bm (or Cm Bm)) (-> B (-> C B)))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-45173
in-theory        45173
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not ((C -> (D or C)) and B))) -> (not B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45173.        (((not (not A)) -> A) and ((B -> (not ((C -> (D or C)) and B))) -> (not B))), M:tm-76, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45174
in-theory        45174
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not ((B -> (C or B)) and A))))) or (A -> (not ((B -> (C or B)) and A)))) -> (not A))
theorem-size     26
proof            (modus-ponens tm-73 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-5 tm-7)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45174.        (((not (not (A -> (not ((B -> (C or B)) and A))))) or (A -> (not ((B -> (C or B)) and A)))) -> (not A)), M:tm-73, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-45175
in-theory        45175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not ((D -> (E or D)) and C))) -> (not C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45175.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not ((D -> (E or D)) and C))) -> (not C))), M:tm-69, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45176
in-theory        45176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45176.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-54, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45177
in-theory        45177
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not ((C -> (D or C)) and B)))) or (B -> (not ((C -> (D or C)) and B)))) -> (not B))
theorem-size     26
proof            (modus-ponens tm-47 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-5 tm-7)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45177.        (((A and (B -> (not ((C -> (D or C)) and B)))) or (B -> (not ((C -> (D or C)) and B)))) -> (not B)), M:tm-47, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-45178
in-theory        45178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not ((B -> (C or B)) and A))) and D) or (A -> (not ((B -> (C or B)) and A)))) -> (not A))
theorem-size     26
proof            (modus-ponens tm-46 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-5 tm-7)
proof-size       100
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45178.        ((((A -> (not ((B -> (C or B)) and A))) and D) or (A -> (not ((B -> (C or B)) and A)))) -> (not A)), M:tm-46, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-45179
in-theory        45179
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A -> (B or A)) and C)) or (C -> (not ((A -> (B or A)) and C)))) -> (not C))
theorem-size     22
proof            (modus-ponens tm-44 tm-601 ((A Am) (B (not (and (-> Bm (or Cm Bm)) Am))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-5 tm-7)
proof-size       98
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45179.        (((not ((A -> (B or A)) and C)) or (C -> (not ((A -> (B or A)) and C)))) -> (not C)), M:tm-44, m:tm-601, u:((A Am) (B (not (and (-> Bm (or Cm Bm)) Am))) (C (not Am)))
================================================================
tm-name          tm-45180
in-theory        45180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not ((D -> (E or D)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45180.        ((A -> (B or A)) and ((C -> (not ((D -> (E or D)) and C))) -> (not C))), M:tm-42, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45181
in-theory        45181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not ((D -> (E or D)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45181.        ((A -> (A or B)) and ((C -> (not ((D -> (E or D)) and C))) -> (not C))), M:tm-32, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45182
in-theory        45182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C or B)) and A))) -> ((A -> (not ((B -> (C or B)) and A))) and (not A)))
theorem-size     24
proof            (modus-ponens tm-24 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       98
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45182.        ((A -> (not ((B -> (C or B)) and A))) -> ((A -> (not ((B -> (C or B)) and A))) and (not A))), M:tm-24, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-45183
in-theory        45183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not ((D -> (E or D)) and C))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45183.        ((A -> (B -> (A and B))) and ((C -> (not ((D -> (E or D)) and C))) -> (not C))), M:tm-23, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45184
in-theory        45184
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not ((D -> (E or D)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45184.        (((A and B) -> B) and ((C -> (not ((D -> (E or D)) and C))) -> (not C))), M:tm-22, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45185
in-theory        45185
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not ((D -> (E or D)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45185.        (((A and B) -> A) and ((C -> (not ((D -> (E or D)) and C))) -> (not C))), M:tm-21, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45186
in-theory        45186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45186.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-20, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45187
in-theory        45187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not ((D -> (E or D)) and C))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45187.        ((A -> (B -> A)) and ((C -> (not ((D -> (E or D)) and C))) -> (not C))), M:tm-19, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45188
in-theory        45188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C or B)) and A))) -> (A -> (not ((B -> (C or B)) and A))))
theorem-size     21
proof            (modus-ponens tm-12 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-5 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45188.        ((A -> (not ((B -> (C or B)) and A))) -> (A -> (not ((B -> (C or B)) and A)))), M:tm-12, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-45189
in-theory        45189
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (C or B)) and A)))))
theorem-size     26
proof            (modus-ponens tm-9 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-9 tm-5 tm-7)
proof-size       82
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45189.        (((A -> (not ((B -> (C or B)) and A))) -> (not (not A))) -> (not (A -> (not ((B -> (C or B)) and A))))), M:tm-9, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-45190
in-theory        45190
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not ((C -> (D or C)) and A))) or (not A)) -> B))
theorem-size     20
proof            (modus-ponens tm-8 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-5 tm-7)
proof-size       78
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45190.        (((not A) -> B) -> (((A -> (not ((C -> (D or C)) and A))) or (not A)) -> B)), M:tm-8, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-45191
in-theory        45191
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not ((C -> (D or C)) and B))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45191.        (A or ((B -> (not ((C -> (D or C)) and B))) -> (not B))), M:tm-7, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45192
in-theory        45192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-5 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45192.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) or D), M:tm-6, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45193
in-theory        45193
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not ((C -> (D or C)) and B))) -> (not B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45193.        (A -> (((B -> (not ((C -> (D or C)) and B))) -> (not B)) and A)), M:tm-5, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45194
in-theory        45194
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not ((C -> (D or C)) and B))) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-5 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45194.        (A -> ((B -> (not ((C -> (D or C)) and B))) -> (not B))), M:tm-1, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45195
in-theory        45195
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> ((B -> (C or B)) and A)))
theorem-size     19
proof            (modus-ponens tm-602 tm-1 ((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-45195.        ((A or ((B -> (C or B)) and A)) -> (D -> ((B -> (C or B)) and A))), M:tm-602, m:tm-1, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45196
in-theory        45196
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (B -> (C or B)))
theorem-size     15
proof            (modus-ponens tm-602 tm-3 ((Am (-> A (or B A))) (C Bm) (D (-> A (or B A)))))
axioms-used      (tm-8 tm-5 tm-7 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-45196.        ((A or ((B -> (C or B)) and A)) -> (B -> (C or B))), M:tm-602, m:tm-3, u:((Am (-> A (or B A))) (C Bm) (D (-> A (or B A))))
================================================================
tm-name          tm-45197
in-theory        45197
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> A)
theorem-size     11
proof            (modus-ponens tm-602 tm-4 ((Am (-> A (or B A))) (C Bm) (D Bm)))
axioms-used      (tm-8 tm-5 tm-7 tm-4)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-45197.        ((A or ((B -> (C or B)) and A)) -> A), M:tm-602, m:tm-4, u:((Am (-> A (or B A))) (C Bm) (D Bm))
================================================================
tm-name          tm-45198
in-theory        45198
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> (((B -> (C or B)) and A) and D)))
theorem-size     21
proof            (modus-ponens tm-602 tm-5 ((Am (and (-> A (or B A)) C)) (D (-> Bm (and (and (-> A (or B A)) C) Bm)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45198.        ((A or ((B -> (C or B)) and A)) -> (D -> (((B -> (C or B)) and A) and D))), M:tm-602, m:tm-5, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (and (and (-> A (or B A)) C) Bm))))
================================================================
tm-name          tm-45199
in-theory        45199
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) or D))
theorem-size     19
proof            (modus-ponens tm-602 tm-6 ((Am (and (-> A (or B A)) C)) (D (or (and (-> A (or B A)) C) Bm))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-45199.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) or D)), M:tm-602, m:tm-6, u:((Am (and (-> A (or B A)) C)) (D (or (and (-> A (or B A)) C) Bm)))
================================================================
tm-name          tm-45200
in-theory        45200
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D or ((B -> (C or B)) and A)))
theorem-size     19
proof            (modus-ponens tm-602 tm-7 ((Am (and (-> A (or B A)) C)) (D (or Bm (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45200.        ((A or ((B -> (C or B)) and A)) -> (D or ((B -> (C or B)) and A))), M:tm-602, m:tm-7, u:((Am (and (-> A (or B A)) C)) (D (or Bm (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45201
in-theory        45201
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-602 tm-11 ((Am (and (-> A (or B A)) C)) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-45201.        ((A or ((B -> (C or B)) and A)) -> (D -> (E -> D))), M:tm-602, m:tm-11, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-45202
in-theory        45202
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-602 tm-14 ((Am (and (-> A (or B A)) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45202.        ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-602, m:tm-14, u:((Am (and (-> A (or B A)) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-45203
in-theory        45203
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-602 tm-16 ((Am (and (-> A (or B A)) C)) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-45203.        ((A or ((B -> (C or B)) and A)) -> ((D and E) -> D)), M:tm-602, m:tm-16, u:((Am (and (-> A (or B A)) C)) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-45204
in-theory        45204
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-602 tm-18 ((Am (and (-> A (or B A)) C)) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-45204.        ((A or ((B -> (C or B)) and A)) -> ((D and E) -> E)), M:tm-602, m:tm-18, u:((Am (and (-> A (or B A)) C)) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-45205
in-theory        45205
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> D)) and ((B -> (C or B)) and A)))
theorem-size     23
proof            (modus-ponens tm-602 tm-19 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> Cm Bm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-45205.        ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> D)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-19, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> Cm Bm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45206
in-theory        45206
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (C or B)) and A)))
theorem-size     31
proof            (modus-ponens tm-602 tm-20 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45206.        ((A or ((B -> (C or B)) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-20, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45207
in-theory        45207
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D and E) -> D) and ((B -> (C or B)) and A)))
theorem-size     23
proof            (modus-ponens tm-602 tm-21 ((Am (and (-> A (or B A)) C)) (D (and (-> (and Bm Cm) Bm) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-45207.        ((A or ((B -> (C or B)) and A)) -> (((D and E) -> D) and ((B -> (C or B)) and A))), M:tm-602, m:tm-21, u:((Am (and (-> A (or B A)) C)) (D (and (-> (and Bm Cm) Bm) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45208
in-theory        45208
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D and E) -> E) and ((B -> (C or B)) and A)))
theorem-size     23
proof            (modus-ponens tm-602 tm-22 ((Am (and (-> A (or B A)) C)) (D (and (-> (and Bm Cm) Cm) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-45208.        ((A or ((B -> (C or B)) and A)) -> (((D and E) -> E) and ((B -> (C or B)) and A))), M:tm-602, m:tm-22, u:((Am (and (-> A (or B A)) C)) (D (and (-> (and Bm Cm) Cm) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45209
in-theory        45209
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> (D and E))) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-23 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-45209.        ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> (D and E))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-23, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45210
in-theory        45210
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-602 tm-25 ((Am (and (-> A (or B A)) C)) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-45210.        ((A or ((B -> (C or B)) and A)) -> (D -> (E -> (D and E)))), M:tm-602, m:tm-25, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-45211
in-theory        45211
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (D or E)) and ((B -> (C or B)) and A)))
theorem-size     23
proof            (modus-ponens tm-602 tm-32 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (or Bm Cm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-45211.        ((A or ((B -> (C or B)) and A)) -> ((D -> (D or E)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-32, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (or Bm Cm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45212
in-theory        45212
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-602 tm-33 ((Am (and (-> A (or B A)) C)) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-45212.        ((A or ((B -> (C or B)) and A)) -> (D -> (D or E))), M:tm-602, m:tm-33, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-45213
in-theory        45213
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (E or D)) and ((B -> (C or B)) and A)))
theorem-size     23
proof            (modus-ponens tm-602 tm-42 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (or Cm Bm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45213.        ((A or ((B -> (C or B)) and A)) -> ((D -> (E or D)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-42, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (or Cm Bm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45214
in-theory        45214
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-602 tm-43 ((Am (and (-> A (or B A)) C)) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-45214.        ((A or ((B -> (C or B)) and A)) -> (D -> (E or D))), M:tm-602, m:tm-43, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-45215
in-theory        45215
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> (C or B)) and A)))
theorem-size     31
proof            (modus-ponens tm-602 tm-54 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-45215.        ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-54, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45216
in-theory        45216
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-602 tm-56 ((Am (and (-> A (or B A)) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-45216.        ((A or ((B -> (C or B)) and A)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-602, m:tm-56, u:((Am (and (-> A (or B A)) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-45217
in-theory        45217
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B -> (C or B)) and A)))
theorem-size     29
proof            (modus-ponens tm-602 tm-69 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-45217.        ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-69, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45218
in-theory        45218
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-602 tm-71 ((Am (and (-> A (or B A)) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-45218.        ((A or ((B -> (C or B)) and A)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-602, m:tm-71, u:((Am (and (-> A (or B A)) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-45219
in-theory        45219
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((not (not D)) -> D) and ((B -> (C or B)) and A)))
theorem-size     23
proof            (modus-ponens tm-602 tm-76 ((Am (and (-> A (or B A)) C)) (D (and (-> (not (not Bm)) Bm) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-45219.        ((A or ((B -> (C or B)) and A)) -> (((not (not D)) -> D) and ((B -> (C or B)) and A))), M:tm-602, m:tm-76, u:((Am (and (-> A (or B A)) C)) (D (and (-> (not (not Bm)) Bm) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45220
in-theory        45220
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-602 tm-78 ((Am (and (-> A (or B A)) C)) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-45220.        ((A or ((B -> (C or B)) and A)) -> ((not (not D)) -> D)), M:tm-602, m:tm-78, u:((Am (and (-> A (or B A)) C)) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-45221
in-theory        45221
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> (F -> E))) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-83 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-45221.        ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> (F -> E))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-83, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45222
in-theory        45222
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-602 tm-85 ((Am (and (-> A (or B A)) C)) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-45222.        ((A or ((B -> (C or B)) and A)) -> (D -> (E -> (F -> E)))), M:tm-602, m:tm-85, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-45223
in-theory        45223
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((B -> (C or B)) and A))
theorem-size     17
proof            (modus-ponens tm-602 tm-86 ((Am (and (-> A (or B A)) C)) (D (and (-> A (or B A)) C))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45223.        ((A or ((B -> (C or B)) and A)) -> ((B -> (C or B)) and A)), M:tm-602, m:tm-86, u:((Am (and (-> A (or B A)) C)) (D (and (-> A (or B A)) C)))
================================================================
tm-name          tm-45224
in-theory        45224
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> (D -> D)) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-95 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-45224.        ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> (D -> D)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-95, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45225
in-theory        45225
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-602 tm-97 ((Am (and (-> A (or B A)) C)) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-45225.        ((A or ((B -> (C or B)) and A)) -> ((D -> E) -> (D -> D))), M:tm-602, m:tm-97, u:((Am (and (-> A (or B A)) C)) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-45226
in-theory        45226
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B -> (C or B)) and A)))
theorem-size     37
proof            (modus-ponens tm-602 tm-105 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-45226.        ((A or ((B -> (C or B)) and A)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-105, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45227
in-theory        45227
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-602 tm-107 ((Am (and (-> A (or B A)) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-45227.        ((A or ((B -> (C or B)) and A)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-602, m:tm-107, u:((Am (and (-> A (or B A)) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-45228
in-theory        45228
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (C or B)) and A)))
theorem-size     33
proof            (modus-ponens tm-602 tm-113 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-45228.        ((A or ((B -> (C or B)) and A)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-113, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45229
in-theory        45229
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-602 tm-115 ((Am (and (-> A (or B A)) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-45229.        ((A or ((B -> (C or B)) and A)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-602, m:tm-115, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-45230
in-theory        45230
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A -> (B or A)) and A)) -> (B or A))
theorem-size     13
proof            (modus-ponens tm-602 tm-116 ((A Am) (Bm (or B Am)) (C Am) (D (or B Am))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-3 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-45230.        ((A or ((A -> (B or A)) and A)) -> (B or A)), M:tm-602, m:tm-116, u:((A Am) (Bm (or B Am)) (C Am) (D (or B Am)))
================================================================
tm-name          tm-45231
in-theory        45231
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> B)) -> (D or (B -> (C -> B)))) and A)) -> (D or (B -> (C -> B))))
theorem-size     25
proof            (modus-ponens tm-602 tm-117 ((A (-> Am (-> Bm Am))) (Cm (or B (-> Am (-> Bm Am)))) (C Dm) (D (or B (-> Am (-> Bm Am))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-45231.        ((A or (((B -> (C -> B)) -> (D or (B -> (C -> B)))) and A)) -> (D or (B -> (C -> B)))), M:tm-602, m:tm-117, u:((A (-> Am (-> Bm Am))) (Cm (or B (-> Am (-> Bm Am)))) (C Dm) (D (or B (-> Am (-> Bm Am)))))
================================================================
tm-name          tm-45232
in-theory        45232
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and A)) -> (E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     49
proof            (modus-ponens tm-602 tm-118 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C Em) (D (or B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-45232.        ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and A)) -> (E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-602, m:tm-118, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C Em) (D (or B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-45233
in-theory        45233
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B -> (C or B)) and A)))
theorem-size     33
proof            (modus-ponens tm-602 tm-125 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-45233.        ((A or ((B -> (C or B)) and A)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-125, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45234
in-theory        45234
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-602 tm-127 ((Am (and (-> A (or B A)) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-45234.        ((A or ((B -> (C or B)) and A)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-602, m:tm-127, u:((Am (and (-> A (or B A)) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-45235
in-theory        45235
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> B) -> (D or ((B and C) -> B))) and A)) -> (D or ((B and C) -> B)))
theorem-size     25
proof            (modus-ponens tm-602 tm-128 ((A (-> (and Am Bm) Am)) (Cm (or B (-> (and Am Bm) Am))) (C Dm) (D (or B (-> (and Am Bm) Am)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-45235.        ((A or ((((B and C) -> B) -> (D or ((B and C) -> B))) and A)) -> (D or ((B and C) -> B))), M:tm-602, m:tm-128, u:((A (-> (and Am Bm) Am)) (Cm (or B (-> (and Am Bm) Am))) (C Dm) (D (or B (-> (and Am Bm) Am))))
================================================================
tm-name          tm-45236
in-theory        45236
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> ((E and F) -> E)) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-134 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-45236.        ((A or ((B -> (C or B)) and A)) -> ((D -> ((E and F) -> E)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-134, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45237
in-theory        45237
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-602 tm-136 ((Am (and (-> A (or B A)) C)) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-45237.        ((A or ((B -> (C or B)) and A)) -> (D -> ((E and F) -> E))), M:tm-602, m:tm-136, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-45238
in-theory        45238
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) or ((A -> (B or A)) and ((A -> (B or A)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-602 tm-137 ((Am (-> A (or B A))) (C (-> (-> A (or B A)) Bm)) (D Bm)))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-4 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-45238.        ((((A -> (B or A)) -> C) or ((A -> (B or A)) and ((A -> (B or A)) -> C))) -> C), M:tm-602, m:tm-137, u:((Am (-> A (or B A))) (C (-> (-> A (or B A)) Bm)) (D Bm))
================================================================
tm-name          tm-45239
in-theory        45239
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) or ((D -> (E or D)) and ((A -> (B -> A)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-602 tm-138 ((Am (-> A (or B A))) (C (-> (-> Bm (-> Cm Bm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-45239.        ((((A -> (B -> A)) -> C) or ((D -> (E or D)) and ((A -> (B -> A)) -> C))) -> C), M:tm-602, m:tm-138, u:((Am (-> A (or B A))) (C (-> (-> Bm (-> Cm Bm)) Dm)) (D Dm))
================================================================
tm-name          tm-45240
in-theory        45240
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or ((E -> (F or E)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D)
theorem-size     39
proof            (modus-ponens tm-602 tm-139 ((Am (-> A (or B A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (D Em)))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-45240.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) or ((E -> (F or E)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D))) -> D), M:tm-602, m:tm-139, u:((Am (-> A (or B A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (D Em))
================================================================
tm-name          tm-45241
in-theory        45241
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) or ((D -> (E or D)) and (((A and B) -> A) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-602 tm-140 ((Am (-> A (or B A))) (C (-> (-> (and Bm Cm) Bm) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-4 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-45241.        (((((A and B) -> A) -> C) or ((D -> (E or D)) and (((A and B) -> A) -> C))) -> C), M:tm-602, m:tm-140, u:((Am (-> A (or B A))) (C (-> (-> (and Bm Cm) Bm) Dm)) (D Dm))
================================================================
tm-name          tm-45242
in-theory        45242
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B -> (C or B)) and A)))
theorem-size     33
proof            (modus-ponens tm-602 tm-147 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-45242.        ((A or ((B -> (C or B)) and A)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-147, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45243
in-theory        45243
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-602 tm-149 ((Am (and (-> A (or B A)) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-45243.        ((A or ((B -> (C or B)) and A)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-602, m:tm-149, u:((Am (and (-> A (or B A)) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-45244
in-theory        45244
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) or ((D -> (E or D)) and (((A and B) -> B) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-602 tm-150 ((Am (-> A (or B A))) (C (-> (-> (and Bm Cm) Cm) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-45244.        (((((A and B) -> B) -> C) or ((D -> (E or D)) and (((A and B) -> B) -> C))) -> C), M:tm-602, m:tm-150, u:((Am (-> A (or B A))) (C (-> (-> (and Bm Cm) Cm) Dm)) (D Dm))
================================================================
tm-name          tm-45245
in-theory        45245
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> C) -> (D or ((B and C) -> C))) and A)) -> (D or ((B and C) -> C)))
theorem-size     25
proof            (modus-ponens tm-602 tm-151 ((A (-> (and Am Bm) Bm)) (Cm (or B (-> (and Am Bm) Bm))) (C Dm) (D (or B (-> (and Am Bm) Bm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-3 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-45245.        ((A or ((((B and C) -> C) -> (D or ((B and C) -> C))) and A)) -> (D or ((B and C) -> C))), M:tm-602, m:tm-151, u:((A (-> (and Am Bm) Bm)) (Cm (or B (-> (and Am Bm) Bm))) (C Dm) (D (or B (-> (and Am Bm) Bm))))
================================================================
tm-name          tm-45246
in-theory        45246
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> ((E and F) -> F)) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-157 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-45246.        ((A or ((B -> (C or B)) and A)) -> ((D -> ((E and F) -> F)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-157, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45247
in-theory        45247
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-602 tm-159 ((Am (and (-> A (or B A)) C)) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-45247.        ((A or ((B -> (C or B)) and A)) -> (D -> ((E and F) -> F))), M:tm-602, m:tm-159, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-45248
in-theory        45248
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> ((E -> (F -> E)) and D)) and ((B -> (C or B)) and A)))
theorem-size     27
proof            (modus-ponens tm-602 tm-183 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-45248.        ((A or ((B -> (C or B)) and A)) -> ((D -> ((E -> (F -> E)) and D)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-183, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45249
in-theory        45249
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-602 tm-184 ((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-45249.        ((A or ((B -> (C or B)) and A)) -> (D -> ((E -> (F -> E)) and D))), M:tm-602, m:tm-184, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-45250
in-theory        45250
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B -> (C or B)) and A)))
theorem-size     35
proof            (modus-ponens tm-602 tm-210 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-45250.        ((A or ((B -> (C or B)) and A)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-210, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45251
in-theory        45251
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-602 tm-211 ((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-45251.        ((A or ((B -> (C or B)) and A)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-602, m:tm-211, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-45252
in-theory        45252
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (((E and F) -> E) and D)) and ((B -> (C or B)) and A)))
theorem-size     27
proof            (modus-ponens tm-602 tm-239 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-45252.        ((A or ((B -> (C or B)) and A)) -> ((D -> (((E and F) -> E) and D)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-239, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45253
in-theory        45253
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-602 tm-240 ((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-45253.        ((A or ((B -> (C or B)) and A)) -> (D -> (((E and F) -> E) and D))), M:tm-602, m:tm-240, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-45254
in-theory        45254
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (((E and F) -> F) and D)) and ((B -> (C or B)) and A)))
theorem-size     27
proof            (modus-ponens tm-602 tm-270 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-45254.        ((A or ((B -> (C or B)) and A)) -> ((D -> (((E and F) -> F) and D)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-270, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45255
in-theory        45255
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-602 tm-271 ((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-45255.        ((A or ((B -> (C or B)) and A)) -> (D -> (((E and F) -> F) and D))), M:tm-602, m:tm-271, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-45256
in-theory        45256
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B -> (C or B)) and A)))
theorem-size     29
proof            (modus-ponens tm-602 tm-303 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-45256.        ((A or ((B -> (C or B)) and A)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-303, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45257
in-theory        45257
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-602 tm-304 ((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-45257.        ((A or ((B -> (C or B)) and A)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-602, m:tm-304, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-45258
in-theory        45258
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (D -> ((B -> (C or B)) and A))))
theorem-size     27
proof            (modus-ponens tm-602 tm-305 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> Bm (and (-> A (or B A)) C))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45258.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (D -> ((B -> (C or B)) and A)))), M:tm-602, m:tm-305, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> Bm (and (-> A (or B A)) C)))))
================================================================
tm-name          tm-45259
in-theory        45259
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (B -> (C or B))))
theorem-size     23
proof            (modus-ponens tm-602 tm-307 ((Am (-> A (or B A))) (C Bm) (D (and (and (-> A (or B A)) Bm) (-> A (or B A))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45259.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (B -> (C or B)))), M:tm-602, m:tm-307, u:((Am (-> A (or B A))) (C Bm) (D (and (and (-> A (or B A)) Bm) (-> A (or B A)))))
================================================================
tm-name          tm-45260
in-theory        45260
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and A))
theorem-size     19
proof            (modus-ponens tm-602 tm-308 ((Am (-> A (or B A))) (C Bm) (D (and (and (-> A (or B A)) Bm) Bm))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-45260.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and A)), M:tm-602, m:tm-308, u:((Am (-> A (or B A))) (C Bm) (D (and (and (-> A (or B A)) Bm) Bm)))
================================================================
tm-name          tm-45261
in-theory        45261
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (D -> (((B -> (C or B)) and A) and D))))
theorem-size     29
proof            (modus-ponens tm-602 tm-309 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> Bm (and (and (-> A (or B A)) C) Bm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-45261.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (D -> (((B -> (C or B)) and A) and D)))), M:tm-602, m:tm-309, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> Bm (and (and (-> A (or B A)) C) Bm)))))
================================================================
tm-name          tm-45262
in-theory        45262
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (((B -> (C or B)) and A) or D)))
theorem-size     27
proof            (modus-ponens tm-602 tm-310 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (or (and (-> A (or B A)) C) Bm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-45262.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (((B -> (C or B)) and A) or D))), M:tm-602, m:tm-310, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (or (and (-> A (or B A)) C) Bm))))
================================================================
tm-name          tm-45263
in-theory        45263
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (D or ((B -> (C or B)) and A))))
theorem-size     27
proof            (modus-ponens tm-602 tm-311 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (or Bm (and (-> A (or B A)) C))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-45263.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (D or ((B -> (C or B)) and A)))), M:tm-602, m:tm-311, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (or Bm (and (-> A (or B A)) C)))))
================================================================
tm-name          tm-45264
in-theory        45264
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (D -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-602 tm-315 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-45264.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (D -> (E -> D)))), M:tm-602, m:tm-315, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-45265
in-theory        45265
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-602 tm-318 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-45265.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-602, m:tm-318, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-45266
in-theory        45266
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and ((D and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-602 tm-320 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-45266.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and ((D and E) -> D))), M:tm-602, m:tm-320, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-45267
in-theory        45267
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and ((D and E) -> E)))
theorem-size     23
proof            (modus-ponens tm-602 tm-322 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-45267.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and ((D and E) -> E))), M:tm-602, m:tm-322, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-45268
in-theory        45268
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and ((D -> (E -> D)) and ((B -> (C or B)) and A))))
theorem-size     31
proof            (modus-ponens tm-602 tm-323 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (and (-> Bm (-> Cm Bm)) (and (-> A (or B A)) C))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-45268.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and ((D -> (E -> D)) and ((B -> (C or B)) and A)))), M:tm-602, m:tm-323, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (and (-> Bm (-> Cm Bm)) (and (-> A (or B A)) C)))))
================================================================
tm-name          tm-45269
in-theory        45269
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (C or B)) and A))))
theorem-size     39
proof            (modus-ponens tm-602 tm-324 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (or B A)) C))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-45269.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B -> (C or B)) and A)))), M:tm-602, m:tm-324, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and (-> A (or B A)) C)))))
================================================================
tm-name          tm-45270
in-theory        45270
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (((D and E) -> D) and ((B -> (C or B)) and A))))
theorem-size     31
proof            (modus-ponens tm-602 tm-325 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (and (-> (and Bm Cm) Bm) (and (-> A (or B A)) C))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-45270.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (((D and E) -> D) and ((B -> (C or B)) and A)))), M:tm-602, m:tm-325, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (and (-> (and Bm Cm) Bm) (and (-> A (or B A)) C)))))
================================================================
tm-name          tm-45271
in-theory        45271
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (((D and E) -> E) and ((B -> (C or B)) and A))))
theorem-size     31
proof            (modus-ponens tm-602 tm-326 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (and (-> (and Bm Cm) Cm) (and (-> A (or B A)) C))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-45271.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (((D and E) -> E) and ((B -> (C or B)) and A)))), M:tm-602, m:tm-326, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (and (-> (and Bm Cm) Cm) (and (-> A (or B A)) C)))))
================================================================
tm-name          tm-45272
in-theory        45272
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and ((D -> (E -> (D and E))) and ((B -> (C or B)) and A))))
theorem-size     33
proof            (modus-ponens tm-602 tm-327 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (or B A)) C))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-45272.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and ((D -> (E -> (D and E))) and ((B -> (C or B)) and A)))), M:tm-602, m:tm-327, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (and (-> Bm (-> Cm (and Bm Cm))) (and (-> A (or B A)) C)))))
================================================================
tm-name          tm-45273
in-theory        45273
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> (D -> (D and E))) and ((B -> (C or B)) and A)))
theorem-size     27
proof            (modus-ponens tm-602 tm-338 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-45273.        ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> (D -> (D and E))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-338, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45274
in-theory        45274
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-602 tm-340 ((Am (and (-> A (or B A)) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-45274.        ((A or ((B -> (C or B)) and A)) -> ((D -> E) -> (D -> (D and E)))), M:tm-602, m:tm-340, u:((Am (and (-> A (or B A)) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-45275
in-theory        45275
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (D -> (E -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-602 tm-341 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-45275.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (D -> (E -> (D and E))))), M:tm-602, m:tm-341, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-45276
in-theory        45276
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) or ((D -> (E or D)) and ((A -> (B -> (A and B))) -> C))) -> C)
theorem-size     27
proof            (modus-ponens tm-602 tm-347 ((Am (-> A (or B A))) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-45276.        ((((A -> (B -> (A and B))) -> C) or ((D -> (E or D)) and ((A -> (B -> (A and B))) -> C))) -> C), M:tm-602, m:tm-347, u:((Am (-> A (or B A))) (C (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) (D Dm))
================================================================
tm-name          tm-45277
in-theory        45277
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> (B and C))) -> (D or (B -> (C -> (B and C))))) and A)) -> (D or (B -> (C -> (B and C)))))
theorem-size     31
proof            (modus-ponens tm-602 tm-348 ((A (-> Am (-> Bm (and Am Bm)))) (Cm (or B (-> Am (-> Bm (and Am Bm))))) (C Dm) (D (or B (-> Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-45277.        ((A or (((B -> (C -> (B and C))) -> (D or (B -> (C -> (B and C))))) and A)) -> (D or (B -> (C -> (B and C))))), M:tm-602, m:tm-348, u:((A (-> Am (-> Bm (and Am Bm)))) (Cm (or B (-> Am (-> Bm (and Am Bm))))) (C Dm) (D (or B (-> Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-45278
in-theory        45278
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> (F -> (E and F)))) and ((B -> (C or B)) and A)))
theorem-size     27
proof            (modus-ponens tm-602 tm-354 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-45278.        ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> (F -> (E and F)))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-354, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45279
in-theory        45279
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-602 tm-356 ((Am (and (-> A (or B A)) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-45279.        ((A or ((B -> (C or B)) and A)) -> (D -> (E -> (F -> (E and F))))), M:tm-602, m:tm-356, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-45280
in-theory        45280
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> (E -> D)) or F) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-364 ((Am (and (-> A (or B A)) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-45280.        ((A or ((B -> (C or B)) and A)) -> (((D -> (E -> D)) or F) and ((B -> (C or B)) and A))), M:tm-602, m:tm-364, u:((Am (and (-> A (or B A)) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45281
in-theory        45281
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-602 tm-365 ((Am (and (-> A (or B A)) C)) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-45281.        ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> D)) or F)), M:tm-602, m:tm-365, u:((Am (and (-> A (or B A)) C)) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-45282
in-theory        45282
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B -> (C or B)) and A)))
theorem-size     33
proof            (modus-ponens tm-602 tm-373 ((Am (and (-> A (or B A)) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-45282.        ((A or ((B -> (C or B)) and A)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B -> (C or B)) and A))), M:tm-602, m:tm-373, u:((Am (and (-> A (or B A)) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45283
in-theory        45283
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-602 tm-374 ((Am (and (-> A (or B A)) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-45283.        ((A or ((B -> (C or B)) and A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-602, m:tm-374, u:((Am (and (-> A (or B A)) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-45284
in-theory        45284
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((((D and E) -> D) or F) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-382 ((Am (and (-> A (or B A)) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-45284.        ((A or ((B -> (C or B)) and A)) -> ((((D and E) -> D) or F) and ((B -> (C or B)) and A))), M:tm-602, m:tm-382, u:((Am (and (-> A (or B A)) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45285
in-theory        45285
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-602 tm-383 ((Am (and (-> A (or B A)) C)) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-45285.        ((A or ((B -> (C or B)) and A)) -> (((D and E) -> D) or F)), M:tm-602, m:tm-383, u:((Am (and (-> A (or B A)) C)) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-45286
in-theory        45286
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((((D and E) -> E) or F) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-391 ((Am (and (-> A (or B A)) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-45286.        ((A or ((B -> (C or B)) and A)) -> ((((D and E) -> E) or F) and ((B -> (C or B)) and A))), M:tm-602, m:tm-391, u:((Am (and (-> A (or B A)) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45287
in-theory        45287
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-602 tm-392 ((Am (and (-> A (or B A)) C)) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-45287.        ((A or ((B -> (C or B)) and A)) -> (((D and E) -> E) or F)), M:tm-602, m:tm-392, u:((Am (and (-> A (or B A)) C)) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-45288
in-theory        45288
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> (E -> (D and E))) or F) and ((B -> (C or B)) and A)))
theorem-size     27
proof            (modus-ponens tm-602 tm-400 ((Am (and (-> A (or B A)) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-45288.        ((A or ((B -> (C or B)) and A)) -> (((D -> (E -> (D and E))) or F) and ((B -> (C or B)) and A))), M:tm-602, m:tm-400, u:((Am (and (-> A (or B A)) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45289
in-theory        45289
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-602 tm-401 ((Am (and (-> A (or B A)) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-45289.        ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> (D and E))) or F)), M:tm-602, m:tm-401, u:((Am (and (-> A (or B A)) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-45290
in-theory        45290
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> (D or E)) or F) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-409 ((Am (and (-> A (or B A)) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-45290.        ((A or ((B -> (C or B)) and A)) -> (((D -> (D or E)) or F) and ((B -> (C or B)) and A))), M:tm-602, m:tm-409, u:((Am (and (-> A (or B A)) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45291
in-theory        45291
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-602 tm-410 ((Am (and (-> A (or B A)) C)) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-45291.        ((A or ((B -> (C or B)) and A)) -> ((D -> (D or E)) or F)), M:tm-602, m:tm-410, u:((Am (and (-> A (or B A)) C)) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-45292
in-theory        45292
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and ((D -> (D or E)) and ((B -> (C or B)) and A))))
theorem-size     31
proof            (modus-ponens tm-602 tm-443 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (and (-> Bm (or Bm Cm)) (and (-> A (or B A)) C))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-45292.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and ((D -> (D or E)) and ((B -> (C or B)) and A)))), M:tm-602, m:tm-443, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (and (-> Bm (or Bm Cm)) (and (-> A (or B A)) C)))))
================================================================
tm-name          tm-45293
in-theory        45293
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> ((E -> (E or F)) and D)) and ((B -> (C or B)) and A)))
theorem-size     27
proof            (modus-ponens tm-602 tm-453 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-45293.        ((A or ((B -> (C or B)) and A)) -> ((D -> ((E -> (E or F)) and D)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-453, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45294
in-theory        45294
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-602 tm-454 ((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-45294.        ((A or ((B -> (C or B)) and A)) -> (D -> ((E -> (E or F)) and D))), M:tm-602, m:tm-454, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-45295
in-theory        45295
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (D -> (D or E))))
theorem-size     23
proof            (modus-ponens tm-602 tm-456 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-45295.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (D -> (D or E)))), M:tm-602, m:tm-456, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-45296
in-theory        45296
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) or ((D -> (E or D)) and ((A -> (A or B)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-602 tm-462 ((Am (-> A (or B A))) (C (-> (-> Bm (or Bm Cm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-4 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-45296.        ((((A -> (A or B)) -> C) or ((D -> (E or D)) and ((A -> (A or B)) -> C))) -> C), M:tm-602, m:tm-462, u:((Am (-> A (or B A))) (C (-> (-> Bm (or Bm Cm)) Dm)) (D Dm))
================================================================
tm-name          tm-45297
in-theory        45297
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (B or C)) -> (D or (B -> (B or C)))) and A)) -> (D or (B -> (B or C))))
theorem-size     25
proof            (modus-ponens tm-602 tm-463 ((A (-> Am (or Am Bm))) (Cm (or B (-> Am (or Am Bm)))) (C Dm) (D (or B (-> Am (or Am Bm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-3 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-45297.        ((A or (((B -> (B or C)) -> (D or (B -> (B or C)))) and A)) -> (D or (B -> (B or C)))), M:tm-602, m:tm-463, u:((A (-> Am (or Am Bm))) (Cm (or B (-> Am (or Am Bm)))) (C Dm) (D (or B (-> Am (or Am Bm)))))
================================================================
tm-name          tm-45298
in-theory        45298
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> (E or F))) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-469 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-45298.        ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> (E or F))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-469, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45299
in-theory        45299
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-602 tm-471 ((Am (and (-> A (or B A)) C)) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-45299.        ((A or ((B -> (C or B)) and A)) -> (D -> (E -> (E or F)))), M:tm-602, m:tm-471, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-45300
in-theory        45300
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D or (E -> (F -> E))) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-480 ((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-45300.        ((A or ((B -> (C or B)) and A)) -> ((D or (E -> (F -> E))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-480, u:((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45301
in-theory        45301
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-602 tm-481 ((Am (and (-> A (or B A)) C)) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-45301.        ((A or ((B -> (C or B)) and A)) -> (D or (E -> (F -> E)))), M:tm-602, m:tm-481, u:((Am (and (-> A (or B A)) C)) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-45302
in-theory        45302
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (C or B)) and A)))
theorem-size     33
proof            (modus-ponens tm-602 tm-490 ((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-45302.        ((A or ((B -> (C or B)) and A)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-490, u:((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45303
in-theory        45303
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-602 tm-491 ((Am (and (-> A (or B A)) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-45303.        ((A or ((B -> (C or B)) and A)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-602, m:tm-491, u:((Am (and (-> A (or B A)) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-45304
in-theory        45304
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D or ((E and F) -> E)) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-500 ((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-45304.        ((A or ((B -> (C or B)) and A)) -> ((D or ((E and F) -> E)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-500, u:((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45305
in-theory        45305
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-602 tm-501 ((Am (and (-> A (or B A)) C)) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-45305.        ((A or ((B -> (C or B)) and A)) -> (D or ((E and F) -> E))), M:tm-602, m:tm-501, u:((Am (and (-> A (or B A)) C)) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-45306
in-theory        45306
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D or ((E and F) -> F)) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-510 ((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-45306.        ((A or ((B -> (C or B)) and A)) -> ((D or ((E and F) -> F)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-510, u:((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45307
in-theory        45307
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-602 tm-511 ((Am (and (-> A (or B A)) C)) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-45307.        ((A or ((B -> (C or B)) and A)) -> (D or ((E and F) -> F))), M:tm-602, m:tm-511, u:((Am (and (-> A (or B A)) C)) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-45308
in-theory        45308
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D or (E -> (F -> (E and F)))) and ((B -> (C or B)) and A)))
theorem-size     27
proof            (modus-ponens tm-602 tm-520 ((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-45308.        ((A or ((B -> (C or B)) and A)) -> ((D or (E -> (F -> (E and F)))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-520, u:((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45309
in-theory        45309
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-602 tm-521 ((Am (and (-> A (or B A)) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-45309.        ((A or ((B -> (C or B)) and A)) -> (D or (E -> (F -> (E and F))))), M:tm-602, m:tm-521, u:((Am (and (-> A (or B A)) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-45310
in-theory        45310
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D or (E -> (E or F))) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-530 ((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-45310.        ((A or ((B -> (C or B)) and A)) -> ((D or (E -> (E or F))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-530, u:((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45311
in-theory        45311
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-602 tm-531 ((Am (and (-> A (or B A)) C)) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-45311.        ((A or ((B -> (C or B)) and A)) -> (D or (E -> (E or F)))), M:tm-602, m:tm-531, u:((Am (and (-> A (or B A)) C)) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-45312
in-theory        45312
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D or (E -> (F or E))) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-540 ((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-45312.        ((A or ((B -> (C or B)) and A)) -> ((D or (E -> (F or E))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-540, u:((Am (and (-> A (or B A)) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45313
in-theory        45313
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-602 tm-541 ((Am (and (-> A (or B A)) C)) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-45313.        ((A or ((B -> (C or B)) and A)) -> (D or (E -> (F or E)))), M:tm-602, m:tm-541, u:((Am (and (-> A (or B A)) C)) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-45314
in-theory        45314
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> (E or D)) or F) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-550 ((Am (and (-> A (or B A)) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-45314.        ((A or ((B -> (C or B)) and A)) -> (((D -> (E or D)) or F) and ((B -> (C or B)) and A))), M:tm-602, m:tm-550, u:((Am (and (-> A (or B A)) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-45315
in-theory        45315
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-602 tm-551 ((Am (and (-> A (or B A)) C)) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-45315.        ((A or ((B -> (C or B)) and A)) -> ((D -> (E or D)) or F)), M:tm-602, m:tm-551, u:((Am (and (-> A (or B A)) C)) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-45316
in-theory        45316
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and ((D -> (E or D)) and ((B -> (C or B)) and A))))
theorem-size     31
proof            (modus-ponens tm-602 tm-595 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (and (-> Bm (or Cm Bm)) (and (-> A (or B A)) C))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45316.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and ((D -> (E or D)) and ((B -> (C or B)) and A)))), M:tm-602, m:tm-595, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (and (-> Bm (or Cm Bm)) (and (-> A (or B A)) C)))))
================================================================
tm-name          tm-45317
in-theory        45317
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((E -> (F or E)) and ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-595 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45317.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((E -> (F or E)) and ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)))), M:tm-595, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45318
in-theory        45318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-550 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45318.        (((A -> (B or A)) or C) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-550, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45319
in-theory        45319
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-540 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45319.        ((A or (B -> (C or B))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-540, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45320
in-theory        45320
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-530 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45320.        ((A or (B -> (B or C))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-530, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45321
in-theory        45321
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-520 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45321.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-520, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45322
in-theory        45322
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-510 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45322.        ((A or ((B and C) -> C)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-510, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45323
in-theory        45323
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-500 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45323.        ((A or ((B and C) -> B)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-500, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45324
in-theory        45324
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F or E)) and G) -> H) -> ((G or ((E -> (F or E)) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-490 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45324.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F or E)) and G) -> H) -> ((G or ((E -> (F or E)) and G)) -> H))), M:tm-490, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45325
in-theory        45325
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-480 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45325.        ((A or (B -> (C -> B))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-480, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45326
in-theory        45326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and C) -> D) -> (((C or ((A -> (B or A)) and C)) -> D) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45326.        ((((A -> (B or A)) and C) -> D) -> (((C or ((A -> (B or A)) and C)) -> D) or E)), M:tm-470, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45327
in-theory        45327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-469 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45327.        ((A -> (B -> (B or C))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-469, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45328
in-theory        45328
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C or B)) and D) -> (((B -> (C or B)) and D) or E))) -> ((D or ((B -> (C or B)) and D)) -> (((B -> (C or B)) and D) or E)))
theorem-size     39
proof            (modus-ponens tm-466 tm-602 ((A (and (-> Am (or Bm Am)) Cm)) (Dm (or (and (-> Am (or Bm Am)) Cm) B)) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (or (and (-> Am (or Bm Am)) Cm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45328.        ((A or (((B -> (C or B)) and D) -> (((B -> (C or B)) and D) or E))) -> ((D or ((B -> (C or B)) and D)) -> (((B -> (C or B)) and D) or E))), M:tm-466, m:tm-602, u:((A (and (-> Am (or Bm Am)) Cm)) (Dm (or (and (-> Am (or Bm Am)) Cm) B)) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (or (and (-> Am (or Bm Am)) Cm) B))))
================================================================
tm-name          tm-45329
in-theory        45329
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45329.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45330
in-theory        45330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-453 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45330.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-453, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45331
in-theory        45331
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((E -> (E or F)) and ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-443 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45331.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((E -> (E or F)) and ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)))), M:tm-443, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45332
in-theory        45332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-409 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45332.        (((A -> (A or B)) or C) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-409, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45333
in-theory        45333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-400 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45333.        (((A -> (B -> (A and B))) or C) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-400, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45334
in-theory        45334
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-391 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45334.        ((((A and B) -> B) or C) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-391, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45335
in-theory        45335
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-382 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45335.        ((((A and B) -> A) or C) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-382, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45336
in-theory        45336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F or E)) and G) -> H) -> ((G or ((E -> (F or E)) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-373 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45336.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F or E)) and G) -> H) -> ((G or ((E -> (F or E)) and G)) -> H))), M:tm-373, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45337
in-theory        45337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-364 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45337.        (((A -> (B -> A)) or C) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-364, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45338
in-theory        45338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and C) -> D) -> (E -> (((C or ((A -> (B or A)) and C)) -> D) and E)))
theorem-size     25
proof            (modus-ponens tm-355 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45338.        ((((A -> (B or A)) and C) -> D) -> (E -> (((C or ((A -> (B or A)) and C)) -> D) and E))), M:tm-355, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45339
in-theory        45339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-354 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45339.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-354, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45340
in-theory        45340
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C or B)) and D) -> (E -> (((B -> (C or B)) and D) and E)))) -> ((D or ((B -> (C or B)) and D)) -> (E -> (((B -> (C or B)) and D) and E))))
theorem-size     43
proof            (modus-ponens tm-351 tm-602 ((A (and (-> Am (or Bm Am)) Cm)) (Dm (-> B (and (and (-> Am (or Bm Am)) Cm) B))) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (-> B (and (and (-> Am (or Bm Am)) Cm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45340.        ((A or (((B -> (C or B)) and D) -> (E -> (((B -> (C or B)) and D) and E)))) -> ((D or ((B -> (C or B)) and D)) -> (E -> (((B -> (C or B)) and D) and E)))), M:tm-351, m:tm-602, u:((A (and (-> Am (or Bm Am)) Cm)) (Dm (-> B (and (and (-> Am (or Bm Am)) Cm) B))) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (-> B (and (and (-> Am (or Bm Am)) Cm) B)))))
================================================================
tm-name          tm-45341
in-theory        45341
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45341.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45342
in-theory        45342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-338 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45342.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F))), M:tm-338, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45343
in-theory        45343
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) or (((A -> (B or A)) and C) -> (((A -> (B or A)) and C) and D))) -> ((C or ((A -> (B or A)) and C)) -> (((A -> (B or A)) and C) and D)))
theorem-size     47
proof            (modus-ponens tm-335 tm-602 ((A (and (-> Am (or Bm Am)) Cm)) (Dm (and (and (-> Am (or Bm Am)) Cm) B)) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (and (and (-> Am (or Bm Am)) Cm) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45343.        (((((A -> (B or A)) and C) -> D) or (((A -> (B or A)) and C) -> (((A -> (B or A)) and C) and D))) -> ((C or ((A -> (B or A)) and C)) -> (((A -> (B or A)) and C) and D))), M:tm-335, m:tm-602, u:((A (and (-> Am (or Bm Am)) Cm)) (Dm (and (and (-> Am (or Bm Am)) Cm) B)) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (and (and (-> Am (or Bm Am)) Cm) B))))
================================================================
tm-name          tm-45344
in-theory        45344
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((((A -> (B or A)) and C) -> D) -> ((((A -> (B or A)) and C) -> D) and ((C or ((A -> (B or A)) and C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-328 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45344.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((((A -> (B or A)) and C) -> D) -> ((((A -> (B or A)) and C) -> D) and ((C or ((A -> (B or A)) and C)) -> D)))), M:tm-328, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45345
in-theory        45345
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((E -> (F -> (E and F))) and ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D))))
theorem-size     51
proof            (modus-ponens tm-327 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45345.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((E -> (F -> (E and F))) and ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)))), M:tm-327, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45346
in-theory        45346
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (((E and F) -> F) and ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-326 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45346.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (((E and F) -> F) and ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)))), M:tm-326, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45347
in-theory        45347
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (((E and F) -> E) and ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-325 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45347.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (((E and F) -> E) and ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)))), M:tm-325, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45348
in-theory        45348
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-324 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45348.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)))), M:tm-324, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45349
in-theory        45349
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((E -> (F -> E)) and ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-323 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45349.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((E -> (F -> E)) and ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)))), M:tm-323, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45350
in-theory        45350
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45350.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45351
in-theory        45351
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45351.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45352
in-theory        45352
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45352.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45353
in-theory        45353
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((((A -> (B or A)) and C) -> D) -> (((A -> (B or A)) and C) -> D)))
theorem-size     41
proof            (modus-ponens tm-316 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45353.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((((A -> (B or A)) and C) -> D) -> (((A -> (B or A)) and C) -> D))), M:tm-316, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45354
in-theory        45354
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45354.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45355
in-theory        45355
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (((((A -> (B or A)) and C) -> D) -> (not ((C or ((A -> (B or A)) and C)) -> D))) -> (not (((A -> (B or A)) and C) -> D))))
theorem-size     55
proof            (modus-ponens tm-313 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-7)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45355.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (((((A -> (B or A)) and C) -> D) -> (not ((C or ((A -> (B or A)) and C)) -> D))) -> (not (((A -> (B or A)) and C) -> D)))), M:tm-313, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45356
in-theory        45356
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((((C or ((A -> (B or A)) and C)) -> D) -> E) -> (((((A -> (B or A)) and C) -> D) or ((C or ((A -> (B or A)) and C)) -> D)) -> E)))
theorem-size     59
proof            (modus-ponens tm-312 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45356.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((((C or ((A -> (B or A)) and C)) -> D) -> E) -> (((((A -> (B or A)) and C) -> D) or ((C or ((A -> (B or A)) and C)) -> D)) -> E))), M:tm-312, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45357
in-theory        45357
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (E or ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-311 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45357.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (E or ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)))), M:tm-311, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45358
in-theory        45358
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45358.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) or E)), M:tm-310, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45359
in-theory        45359
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (E -> (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45359.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (E -> (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and E))), M:tm-309, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45360
in-theory        45360
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (((((A -> (B or A)) and C) -> D) -> (C or ((A -> (B or A)) and C))) -> ((((A -> (B or A)) and C) -> D) -> D)))
theorem-size     53
proof            (modus-ponens tm-306 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (or Cm (and (-> Am (or Bm Am)) Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45360.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (((((A -> (B or A)) and C) -> D) -> (C or ((A -> (B or A)) and C))) -> ((((A -> (B or A)) and C) -> D) -> D))), M:tm-306, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (or Cm (and (-> Am (or Bm Am)) Cm))) (C Dm))
================================================================
tm-name          tm-45361
in-theory        45361
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (E -> ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-305 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45361.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (E -> ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)))), M:tm-305, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45362
in-theory        45362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-303 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45362.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-303, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45363
in-theory        45363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-270 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45363.        ((A -> (((B and C) -> C) and A)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-270, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45364
in-theory        45364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-239 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45364.        ((A -> (((B and C) -> B) and A)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-239, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45365
in-theory        45365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F or E)) and G) -> H) -> ((G or ((E -> (F or E)) and G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-210 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45365.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F or E)) and G) -> H) -> ((G or ((E -> (F or E)) and G)) -> H))), M:tm-210, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45366
in-theory        45366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-183 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45366.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-183, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45367
in-theory        45367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-157 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45367.        ((A -> ((B and C) -> C)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-157, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45368
in-theory        45368
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C or B)) and D) -> D)) -> ((D or ((B -> (C or B)) and D)) -> D))
theorem-size     23
proof            (modus-ponens tm-154 tm-602 ((A (-> Am (or Bm Am))) (Dm Cm) (B Cm) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Cm))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45368.        ((A or (((B -> (C or B)) and D) -> D)) -> ((D or ((B -> (C or B)) and D)) -> D)), M:tm-154, m:tm-602, u:((A (-> Am (or Bm Am))) (Dm Cm) (B Cm) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Cm)))
================================================================
tm-name          tm-45369
in-theory        45369
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-147 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45369.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-147, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45370
in-theory        45370
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and (C -> D)) -> C) or (((A -> (B or A)) and (C -> D)) -> D)) -> (((C -> D) or ((A -> (B or A)) and (C -> D))) -> D))
theorem-size     39
proof            (modus-ponens tm-144 tm-602 ((A (-> Am (or Bm Am))) (Cm (-> B Dm)) (C Dm) (D (-> (or (-> B Dm) (and (-> Am (or Bm Am)) (-> B Dm))) Dm))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-7)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45370.        (((((A -> (B or A)) and (C -> D)) -> C) or (((A -> (B or A)) and (C -> D)) -> D)) -> (((C -> D) or ((A -> (B or A)) and (C -> D))) -> D)), M:tm-144, m:tm-602, u:((A (-> Am (or Bm Am))) (Cm (-> B Dm)) (C Dm) (D (-> (or (-> B Dm) (and (-> Am (or Bm Am)) (-> B Dm))) Dm)))
================================================================
tm-name          tm-45371
in-theory        45371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-134 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45371.        ((A -> ((B and C) -> B)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-134, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45372
in-theory        45372
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C or B)) and D) -> (B -> (C or B)))) -> ((D or ((B -> (C or B)) and D)) -> (B -> (C or B))))
theorem-size     31
proof            (modus-ponens tm-131 tm-602 ((Dm (-> Am (or Bm Am))) (B Cm) (A (-> Am (or Bm Am))) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (-> Am (or Bm Am))))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45372.        ((A or (((B -> (C or B)) and D) -> (B -> (C or B)))) -> ((D or ((B -> (C or B)) and D)) -> (B -> (C or B)))), M:tm-131, m:tm-602, u:((Dm (-> Am (or Bm Am))) (B Cm) (A (-> Am (or Bm Am))) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (-> Am (or Bm Am)))))
================================================================
tm-name          tm-45373
in-theory        45373
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-125 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45373.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-125, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45374
in-theory        45374
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> A) or (((A -> (B or A)) and C) -> (B or A))) -> ((C or ((A -> (B or A)) and C)) -> (B or A)))
theorem-size     35
proof            (modus-ponens tm-122 tm-602 ((A Am) (Dm (or Bm Am)) (C Cm) (B (or Bm Am)) (D (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (or Bm Am)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45374.        (((((A -> (B or A)) and C) -> A) or (((A -> (B or A)) and C) -> (B or A))) -> ((C or ((A -> (B or A)) and C)) -> (B or A))), M:tm-122, m:tm-602, u:((A Am) (Dm (or Bm Am)) (C Cm) (B (or Bm Am)) (D (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (or Bm Am))))
================================================================
tm-name          tm-45375
in-theory        45375
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and C) -> (D -> E)) -> (((C or ((A -> (B or A)) and C)) -> D) -> ((C or ((A -> (B or A)) and C)) -> E)))
theorem-size     35
proof            (modus-ponens tm-114 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) (-> C D))) (B (or Cm (and (-> Am (or Bm Am)) Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45375.        ((((A -> (B or A)) and C) -> (D -> E)) -> (((C or ((A -> (B or A)) and C)) -> D) -> ((C or ((A -> (B or A)) and C)) -> E))), M:tm-114, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) (-> C D))) (B (or Cm (and (-> Am (or Bm Am)) Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-45376
in-theory        45376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F or E)) and G) -> H) -> ((G or ((E -> (F or E)) and G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-113 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45376.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F or E)) and G) -> H) -> ((G or ((E -> (F or E)) and G)) -> H))), M:tm-113, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45377
in-theory        45377
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-105 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45377.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-105, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45378
in-theory        45378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-95 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45378.        (((A -> B) -> (A -> A)) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F))), M:tm-95, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45379
in-theory        45379
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) or (((A -> (B or A)) and C) -> ((A -> (B or A)) and C))) -> ((C or ((A -> (B or A)) and C)) -> ((A -> (B or A)) and C)))
theorem-size     43
proof            (modus-ponens tm-92 tm-602 ((Dm (and (-> Am (or Bm Am)) Cm)) (A (and (-> Am (or Bm Am)) Cm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (and (-> Am (or Bm Am)) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45379.        (((((A -> (B or A)) and C) -> D) or (((A -> (B or A)) and C) -> ((A -> (B or A)) and C))) -> ((C or ((A -> (B or A)) and C)) -> ((A -> (B or A)) and C))), M:tm-92, m:tm-602, u:((Dm (and (-> Am (or Bm Am)) Cm)) (A (and (-> Am (or Bm Am)) Cm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (and (-> Am (or Bm Am)) Cm))))
================================================================
tm-name          tm-45380
in-theory        45380
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and C) -> D) -> (E -> ((C or ((A -> (B or A)) and C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-84 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45380.        ((((A -> (B or A)) and C) -> D) -> (E -> ((C or ((A -> (B or A)) and C)) -> D))), M:tm-84, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45381
in-theory        45381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-83 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45381.        ((A -> (B -> (C -> B))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-83, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45382
in-theory        45382
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C or B)) and D) -> (E -> ((B -> (C or B)) and D)))) -> ((D or ((B -> (C or B)) and D)) -> (E -> ((B -> (C or B)) and D))))
theorem-size     39
proof            (modus-ponens tm-80 tm-602 ((A (and (-> Am (or Bm Am)) Cm)) (Dm (-> B (and (-> Am (or Bm Am)) Cm))) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (-> B (and (-> Am (or Bm Am)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45382.        ((A or (((B -> (C or B)) and D) -> (E -> ((B -> (C or B)) and D)))) -> ((D or ((B -> (C or B)) and D)) -> (E -> ((B -> (C or B)) and D)))), M:tm-80, m:tm-602, u:((A (and (-> Am (or Bm Am)) Cm)) (Dm (-> B (and (-> Am (or Bm Am)) Cm))) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (-> B (and (-> Am (or Bm Am)) Cm)))))
================================================================
tm-name          tm-45383
in-theory        45383
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C or B)) and D) -> E) -> ((D or ((B -> (C or B)) and D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-76 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45383.        (((not (not A)) -> A) and ((((B -> (C or B)) and D) -> E) -> ((D or ((B -> (C or B)) and D)) -> E))), M:tm-76, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45384
in-theory        45384
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (B or A)) and C) -> D))) or (((A -> (B or A)) and C) -> D)) -> ((C or ((A -> (B or A)) and C)) -> D))
theorem-size     33
proof            (modus-ponens tm-73 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-5 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45384.        (((not (not (((A -> (B or A)) and C) -> D))) or (((A -> (B or A)) and C) -> D)) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-73, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45385
in-theory        45385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-69 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-7)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45385.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F))), M:tm-69, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45386
in-theory        45386
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and C) -> (C or ((A -> (B or A)) and C))) -> ((((A -> (B or A)) and C) or (C or ((A -> (B or A)) and C))) -> (C or ((A -> (B or A)) and C))))
theorem-size     45
proof            (modus-ponens tm-55 tm-602 ((A (and (-> Am (or Bm Am)) Cm)) (Dm (or Cm (and (-> Am (or Bm Am)) Cm))) (B (or Cm (and (-> Am (or Bm Am)) Cm))) (C (or Cm (and (-> Am (or Bm Am)) Cm)))))
axioms-used      (tm-2 tm-8 tm-5 tm-7)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45386.        ((((A -> (B or A)) and C) -> (C or ((A -> (B or A)) and C))) -> ((((A -> (B or A)) and C) or (C or ((A -> (B or A)) and C))) -> (C or ((A -> (B or A)) and C)))), M:tm-55, m:tm-602, u:((A (and (-> Am (or Bm Am)) Cm)) (Dm (or Cm (and (-> Am (or Bm Am)) Cm))) (B (or Cm (and (-> Am (or Bm Am)) Cm))) (C (or Cm (and (-> Am (or Bm Am)) Cm))))
================================================================
tm-name          tm-45387
in-theory        45387
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-54 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45387.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-54, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45388
in-theory        45388
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (C or B)) and D) -> (A and ((B -> (C or B)) and D)))) -> ((D or ((B -> (C or B)) and D)) -> (A and ((B -> (C or B)) and D))))
theorem-size     39
proof            (modus-ponens tm-48 tm-602 ((A (and (-> Am (or Bm Am)) Cm)) (Dm (and B (and (-> Am (or Bm Am)) Cm))) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (and B (and (-> Am (or Bm Am)) Cm))))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45388.        ((A or (((B -> (C or B)) and D) -> (A and ((B -> (C or B)) and D)))) -> ((D or ((B -> (C or B)) and D)) -> (A and ((B -> (C or B)) and D)))), M:tm-48, m:tm-602, u:((A (and (-> Am (or Bm Am)) Cm)) (Dm (and B (and (-> Am (or Bm Am)) Cm))) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (and B (and (-> Am (or Bm Am)) Cm)))))
================================================================
tm-name          tm-45389
in-theory        45389
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B -> (C or B)) and D) -> E)) or (((B -> (C or B)) and D) -> E)) -> ((D or ((B -> (C or B)) and D)) -> E))
theorem-size     33
proof            (modus-ponens tm-47 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45389.        (((A and (((B -> (C or B)) and D) -> E)) or (((B -> (C or B)) and D) -> E)) -> ((D or ((B -> (C or B)) and D)) -> E)), M:tm-47, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45390
in-theory        45390
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B or A)) and C) -> D) and E) or (((A -> (B or A)) and C) -> D)) -> ((C or ((A -> (B or A)) and C)) -> D))
theorem-size     33
proof            (modus-ponens tm-46 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45390.        ((((((A -> (B or A)) and C) -> D) and E) or (((A -> (B or A)) and C) -> D)) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-46, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45391
in-theory        45391
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> (C or B)) and D) -> A)) -> ((D or ((B -> (C or B)) and D)) -> A))
theorem-size     23
proof            (modus-ponens tm-44 tm-602 ((A (and (-> Am (or Bm Am)) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45391.        ((A or (((B -> (C or B)) and D) -> A)) -> ((D or ((B -> (C or B)) and D)) -> A)), M:tm-44, m:tm-602, u:((A (and (-> Am (or Bm Am)) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45392
in-theory        45392
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-42 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45392.        ((A -> (B or A)) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F))), M:tm-42, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45393
in-theory        45393
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-32 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45393.        ((A -> (A or B)) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F))), M:tm-32, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45394
in-theory        45394
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and C) -> D) -> ((((A -> (B or A)) and C) -> D) and ((C or ((A -> (B or A)) and C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-24 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45394.        ((((A -> (B or A)) and C) -> D) -> ((((A -> (B or A)) and C) -> D) and ((C or ((A -> (B or A)) and C)) -> D))), M:tm-24, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45395
in-theory        45395
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-23 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45395.        ((A -> (B -> (A and B))) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F))), M:tm-23, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45396
in-theory        45396
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-22 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45396.        (((A and B) -> B) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F))), M:tm-22, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45397
in-theory        45397
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-21 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45397.        (((A and B) -> A) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F))), M:tm-21, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45398
in-theory        45398
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-20 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45398.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-20, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45399
in-theory        45399
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-19 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45399.        ((A -> (B -> A)) and ((((C -> (D or C)) and E) -> F) -> ((E or ((C -> (D or C)) and E)) -> F))), M:tm-19, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45400
in-theory        45400
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and C) -> D) -> (((A -> (B or A)) and C) -> D))
theorem-size     19
proof            (modus-ponens tm-12 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45400.        ((((A -> (B or A)) and C) -> D) -> (((A -> (B or A)) and C) -> D)), M:tm-12, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45401
in-theory        45401
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> (not ((C or ((A -> (B or A)) and C)) -> D))) -> (not (((A -> (B or A)) and C) -> D)))
theorem-size     33
proof            (modus-ponens tm-9 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-5 tm-7)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45401.        (((((A -> (B or A)) and C) -> D) -> (not ((C or ((A -> (B or A)) and C)) -> D))) -> (not (((A -> (B or A)) and C) -> D))), M:tm-9, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45402
in-theory        45402
times-derived    2
----------------------------------------------------------------
theorem          ((((A or ((B -> (C or B)) and A)) -> D) -> E) -> (((((B -> (C or B)) and A) -> D) or ((A or ((B -> (C or B)) and A)) -> D)) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45402.        ((((A or ((B -> (C or B)) and A)) -> D) -> E) -> (((((B -> (C or B)) and A) -> D) or ((A or ((B -> (C or B)) and A)) -> D)) -> E)), M:tm-8, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-45403
in-theory        45403
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> (C or B)) and D) -> E) -> ((D or ((B -> (C or B)) and D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-7 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-5)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45403.        (A or ((((B -> (C or B)) and D) -> E) -> ((D or ((B -> (C or B)) and D)) -> E))), M:tm-7, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45404
in-theory        45404
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-5 tm-7)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45404.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) or E), M:tm-6, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45405
in-theory        45405
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> (C or B)) and D) -> E) -> ((D or ((B -> (C or B)) and D)) -> E)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45405.        (A -> (((((B -> (C or B)) and D) -> E) -> ((D or ((B -> (C or B)) and D)) -> E)) and A)), M:tm-5, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45406
in-theory        45406
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> (C or ((A -> (B or A)) and C))) -> ((((A -> (B or A)) and C) -> D) -> D))
theorem-size     31
proof            (modus-ponens tm-2 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (or Cm (and (-> Am (or Bm Am)) Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-5 tm-7)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45406.        (((((A -> (B or A)) and C) -> D) -> (C or ((A -> (B or A)) and C))) -> ((((A -> (B or A)) and C) -> D) -> D)), M:tm-2, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (or Cm (and (-> Am (or Bm Am)) Cm))) (C Dm))
================================================================
tm-name          tm-45407
in-theory        45407
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (C or B)) and D) -> E) -> ((D or ((B -> (C or B)) and D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-1 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-5 tm-7)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-45407.        (A -> ((((B -> (C or B)) and D) -> E) -> ((D or ((B -> (C or B)) and D)) -> E))), M:tm-1, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45408
in-theory        45408
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and ((E -> (F or E)) and (A or (B -> ((C -> (D or C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45408.        ((A or (B -> ((C -> (D or C)) and B))) and ((E -> (F or E)) and (A or (B -> ((C -> (D or C)) and B))))), M:tm-595, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45409
in-theory        45409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-550 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45409.        (((A -> (B or A)) or C) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-550, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45410
in-theory        45410
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-540 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45410.        ((A or (B -> (C or B))) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-540, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45411
in-theory        45411
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-530 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45411.        ((A or (B -> (B or C))) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-530, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45412
in-theory        45412
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-520 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45412.        ((A or (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-520, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45413
in-theory        45413
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-510 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45413.        ((A or ((B and C) -> C)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-510, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45414
in-theory        45414
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-500 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45414.        ((A or ((B and C) -> B)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-500, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45415
in-theory        45415
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-490 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45415.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H or G)) and F)))), M:tm-490, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45416
in-theory        45416
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-480 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45416.        ((A or (B -> (C -> B))) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-480, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45417
in-theory        45417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-469 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45417.        ((A -> (B -> (B or C))) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-469, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45418
in-theory        45418
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45418.        ((A or (B -> ((C -> (D or C)) and B))) and (E -> (E or F))), M:tm-456, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45419
in-theory        45419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-453 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45419.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-453, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45420
in-theory        45420
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and ((E -> (E or F)) and (A or (B -> ((C -> (D or C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45420.        ((A or (B -> ((C -> (D or C)) and B))) and ((E -> (E or F)) and (A or (B -> ((C -> (D or C)) and B))))), M:tm-443, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45421
in-theory        45421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-409 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45421.        (((A -> (A or B)) or C) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-409, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45422
in-theory        45422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-400 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45422.        (((A -> (B -> (A and B))) or C) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-400, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45423
in-theory        45423
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-391 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45423.        ((((A and B) -> B) or C) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-391, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45424
in-theory        45424
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-382 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45424.        ((((A and B) -> A) or C) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-382, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45425
in-theory        45425
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-373 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45425.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> ((G -> (H or G)) and F)))), M:tm-373, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45426
in-theory        45426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-364 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45426.        (((A -> (B -> A)) or C) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-364, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45427
in-theory        45427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-354 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45427.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-354, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45428
in-theory        45428
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45428.        ((A or (B -> ((C -> (D or C)) and B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45429
in-theory        45429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-338 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45429.        (((A -> B) -> (A -> (A and B))) and (C or (D -> ((E -> (F or E)) and D)))), M:tm-338, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45430
in-theory        45430
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and ((E -> (F -> (E and F))) and (A or (B -> ((C -> (D or C)) and B)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45430.        ((A or (B -> ((C -> (D or C)) and B))) and ((E -> (F -> (E and F))) and (A or (B -> ((C -> (D or C)) and B))))), M:tm-327, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45431
in-theory        45431
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and (((E and F) -> F) and (A or (B -> ((C -> (D or C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45431.        ((A or (B -> ((C -> (D or C)) and B))) and (((E and F) -> F) and (A or (B -> ((C -> (D or C)) and B))))), M:tm-326, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45432
in-theory        45432
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and (((E and F) -> E) and (A or (B -> ((C -> (D or C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45432.        ((A or (B -> ((C -> (D or C)) and B))) and (((E and F) -> E) and (A or (B -> ((C -> (D or C)) and B))))), M:tm-325, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45433
in-theory        45433
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> ((C -> (D or C)) and B)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45433.        ((A or (B -> ((C -> (D or C)) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> ((C -> (D or C)) and B))))), M:tm-324, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45434
in-theory        45434
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and ((E -> (F -> E)) and (A or (B -> ((C -> (D or C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45434.        ((A or (B -> ((C -> (D or C)) and B))) and ((E -> (F -> E)) and (A or (B -> ((C -> (D or C)) and B))))), M:tm-323, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45435
in-theory        45435
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45435.        ((A or (B -> ((C -> (D or C)) and B))) and ((E and F) -> F)), M:tm-322, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45436
in-theory        45436
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45436.        ((A or (B -> ((C -> (D or C)) and B))) and ((E and F) -> E)), M:tm-320, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45437
in-theory        45437
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45437.        ((A or (B -> ((C -> (D or C)) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45438
in-theory        45438
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45438.        ((A or (B -> ((C -> (D or C)) and B))) and (E -> (F -> E))), M:tm-315, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45439
in-theory        45439
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and (E or (A or (B -> ((C -> (D or C)) and B)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45439.        ((A or (B -> ((C -> (D or C)) and B))) and (E or (A or (B -> ((C -> (D or C)) and B))))), M:tm-311, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45440
in-theory        45440
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and ((A or (B -> ((C -> (D or C)) and B))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45440.        ((A or (B -> ((C -> (D or C)) and B))) and ((A or (B -> ((C -> (D or C)) and B))) or E)), M:tm-310, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45441
in-theory        45441
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and (E -> ((A or (B -> ((C -> (D or C)) and B))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45441.        ((A or (B -> ((C -> (D or C)) and B))) and (E -> ((A or (B -> ((C -> (D or C)) and B))) and E))), M:tm-309, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45442
in-theory        45442
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and (E -> (A or (B -> ((C -> (D or C)) and B)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45442.        ((A or (B -> ((C -> (D or C)) and B))) and (E -> (A or (B -> ((C -> (D or C)) and B))))), M:tm-305, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45443
in-theory        45443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-303 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45443.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-303, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45444
in-theory        45444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-270 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45444.        ((A -> (((B and C) -> C) and A)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-270, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45445
in-theory        45445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-239 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45445.        ((A -> (((B and C) -> B) and A)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-239, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45446
in-theory        45446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-210 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45446.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> ((G -> (H or G)) and F)))), M:tm-210, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45447
in-theory        45447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-183 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45447.        ((A -> ((B -> (C -> B)) and A)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-183, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45448
in-theory        45448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-157 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45448.        ((A -> ((B and C) -> C)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-157, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45449
in-theory        45449
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-147 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45449.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-147, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45450
in-theory        45450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-134 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45450.        ((A -> ((B and C) -> B)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-134, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45451
in-theory        45451
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-125 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45451.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-125, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45452
in-theory        45452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-113 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45452.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> ((G -> (H or G)) and F)))), M:tm-113, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45453
in-theory        45453
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     31
proof            (modus-ponens tm-105 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45453.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-105, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45454
in-theory        45454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-95 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45454.        (((A -> B) -> (A -> A)) and (C or (D -> ((E -> (F or E)) and D)))), M:tm-95, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45455
in-theory        45455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-83 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45455.        ((A -> (B -> (C -> B))) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-83, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45456
in-theory        45456
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> ((D -> (E or D)) and C))))
theorem-size     17
proof            (modus-ponens tm-76 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45456.        (((not (not A)) -> A) and (B or (C -> ((D -> (E or D)) and C)))), M:tm-76, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45457
in-theory        45457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> ((E -> (F or E)) and D))))
theorem-size     23
proof            (modus-ponens tm-69 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45457.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> ((E -> (F or E)) and D)))), M:tm-69, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45458
in-theory        45458
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-54 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45458.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-54, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45459
in-theory        45459
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-42 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45459.        ((A -> (B or A)) and (C or (D -> ((E -> (F or E)) and D)))), M:tm-42, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45460
in-theory        45460
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-32 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45460.        ((A -> (A or B)) and (C or (D -> ((E -> (F or E)) and D)))), M:tm-32, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45461
in-theory        45461
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-23 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45461.        ((A -> (B -> (A and B))) and (C or (D -> ((E -> (F or E)) and D)))), M:tm-23, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45462
in-theory        45462
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-22 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45462.        (((A and B) -> B) and (C or (D -> ((E -> (F or E)) and D)))), M:tm-22, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45463
in-theory        45463
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-21 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45463.        (((A and B) -> A) and (C or (D -> ((E -> (F or E)) and D)))), M:tm-21, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45464
in-theory        45464
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-20 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45464.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-20, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45465
in-theory        45465
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-19 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45465.        ((A -> (B -> A)) and (C or (D -> ((E -> (F or E)) and D)))), M:tm-19, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45466
in-theory        45466
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C -> ((D -> (E or D)) and C))))
theorem-size     13
proof            (modus-ponens tm-7 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-7 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45466.        (A or (B or (C -> ((D -> (E or D)) and C)))), M:tm-7, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45467
in-theory        45467
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-6 tm-7 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45467.        ((A or (B -> ((C -> (D or C)) and B))) or E), M:tm-6, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45468
in-theory        45468
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C -> ((D -> (E or D)) and C))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45468.        (A -> ((B or (C -> ((D -> (E or D)) and C))) and A)), M:tm-5, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45469
in-theory        45469
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C -> ((D -> (E or D)) and C))))
theorem-size     13
proof            (modus-ponens tm-1 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-1 tm-7 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45469.        (A -> (B or (C -> ((D -> (E or D)) and C)))), M:tm-1, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-45470
in-theory        45470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and ((E -> (F or E)) and ((A -> ((B -> (C or B)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-595 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45470.        (((A -> ((B -> (C or B)) and A)) or D) and ((E -> (F or E)) and ((A -> ((B -> (C or B)) and A)) or D))), M:tm-595, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45471
in-theory        45471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-550 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45471.        (((A -> (B or A)) or C) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-550, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45472
in-theory        45472
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-540 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45472.        ((A or (B -> (C or B))) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-540, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45473
in-theory        45473
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-530 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45473.        ((A or (B -> (B or C))) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-530, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45474
in-theory        45474
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-520 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45474.        ((A or (B -> (C -> (B and C)))) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-520, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45475
in-theory        45475
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-510 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45475.        ((A or ((B and C) -> C)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-510, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45476
in-theory        45476
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-500 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45476.        ((A or ((B and C) -> B)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-500, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45477
in-theory        45477
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G or F)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-490 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45477.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G or F)) and E)) or H)), M:tm-490, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45478
in-theory        45478
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-480 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45478.        ((A or (B -> (C -> B))) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-480, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45479
in-theory        45479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-469 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45479.        ((A -> (B -> (B or C))) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-469, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45480
in-theory        45480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45480.        (((A -> ((B -> (C or B)) and A)) or D) and (E -> (E or F))), M:tm-456, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45481
in-theory        45481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-453 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45481.        ((A -> ((B -> (B or C)) and A)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-453, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45482
in-theory        45482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and ((E -> (E or F)) and ((A -> ((B -> (C or B)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-443 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45482.        (((A -> ((B -> (C or B)) and A)) or D) and ((E -> (E or F)) and ((A -> ((B -> (C or B)) and A)) or D))), M:tm-443, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45483
in-theory        45483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-409 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45483.        (((A -> (A or B)) or C) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-409, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45484
in-theory        45484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-400 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45484.        (((A -> (B -> (A and B))) or C) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-400, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45485
in-theory        45485
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-391 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45485.        ((((A and B) -> B) or C) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-391, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45486
in-theory        45486
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-382 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45486.        ((((A and B) -> A) or C) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-382, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45487
in-theory        45487
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F -> (G or F)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-373 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45487.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F -> (G or F)) and E)) or H)), M:tm-373, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45488
in-theory        45488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-364 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45488.        (((A -> (B -> A)) or C) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-364, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45489
in-theory        45489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-354 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45489.        ((A -> (B -> (C -> (B and C)))) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-354, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45490
in-theory        45490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45490.        (((A -> ((B -> (C or B)) and A)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45491
in-theory        45491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> ((D -> (E or D)) and C)) or F))
theorem-size     21
proof            (modus-ponens tm-338 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45491.        (((A -> B) -> (A -> (A and B))) and ((C -> ((D -> (E or D)) and C)) or F)), M:tm-338, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45492
in-theory        45492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and ((E -> (F -> (E and F))) and ((A -> ((B -> (C or B)) and A)) or D)))
theorem-size     31
proof            (modus-ponens tm-327 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45492.        (((A -> ((B -> (C or B)) and A)) or D) and ((E -> (F -> (E and F))) and ((A -> ((B -> (C or B)) and A)) or D))), M:tm-327, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45493
in-theory        45493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and (((E and F) -> F) and ((A -> ((B -> (C or B)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-326 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45493.        (((A -> ((B -> (C or B)) and A)) or D) and (((E and F) -> F) and ((A -> ((B -> (C or B)) and A)) or D))), M:tm-326, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45494
in-theory        45494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and (((E and F) -> E) and ((A -> ((B -> (C or B)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-325 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45494.        (((A -> ((B -> (C or B)) and A)) or D) and (((E and F) -> E) and ((A -> ((B -> (C or B)) and A)) or D))), M:tm-325, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45495
in-theory        45495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> ((B -> (C or B)) and A)) or D)))
theorem-size     37
proof            (modus-ponens tm-324 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45495.        (((A -> ((B -> (C or B)) and A)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> ((B -> (C or B)) and A)) or D))), M:tm-324, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45496
in-theory        45496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and ((E -> (F -> E)) and ((A -> ((B -> (C or B)) and A)) or D)))
theorem-size     29
proof            (modus-ponens tm-323 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45496.        (((A -> ((B -> (C or B)) and A)) or D) and ((E -> (F -> E)) and ((A -> ((B -> (C or B)) and A)) or D))), M:tm-323, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45497
in-theory        45497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45497.        (((A -> ((B -> (C or B)) and A)) or D) and ((E and F) -> F)), M:tm-322, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45498
in-theory        45498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45498.        (((A -> ((B -> (C or B)) and A)) or D) and ((E and F) -> E)), M:tm-320, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45499
in-theory        45499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45499.        (((A -> ((B -> (C or B)) and A)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45500
in-theory        45500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45500.        (((A -> ((B -> (C or B)) and A)) or D) and (E -> (F -> E))), M:tm-315, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45501
in-theory        45501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and (E or ((A -> ((B -> (C or B)) and A)) or D)))
theorem-size     25
proof            (modus-ponens tm-311 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45501.        (((A -> ((B -> (C or B)) and A)) or D) and (E or ((A -> ((B -> (C or B)) and A)) or D))), M:tm-311, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45502
in-theory        45502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and (((A -> ((B -> (C or B)) and A)) or D) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45502.        (((A -> ((B -> (C or B)) and A)) or D) and (((A -> ((B -> (C or B)) and A)) or D) or E)), M:tm-310, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45503
in-theory        45503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and (E -> (((A -> ((B -> (C or B)) and A)) or D) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45503.        (((A -> ((B -> (C or B)) and A)) or D) and (E -> (((A -> ((B -> (C or B)) and A)) or D) and E))), M:tm-309, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45504
in-theory        45504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and (E -> ((A -> ((B -> (C or B)) and A)) or D)))
theorem-size     25
proof            (modus-ponens tm-305 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45504.        (((A -> ((B -> (C or B)) and A)) or D) and (E -> ((A -> ((B -> (C or B)) and A)) or D))), M:tm-305, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45505
in-theory        45505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-303 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45505.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-303, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45506
in-theory        45506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-270 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45506.        ((A -> (((B and C) -> C) and A)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-270, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45507
in-theory        45507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-239 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45507.        ((A -> (((B and C) -> B) and A)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-239, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45508
in-theory        45508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F -> (G or F)) and E)) or H))
theorem-size     29
proof            (modus-ponens tm-210 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45508.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F -> (G or F)) and E)) or H)), M:tm-210, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45509
in-theory        45509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-183 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45509.        ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-183, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45510
in-theory        45510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-157 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45510.        ((A -> ((B and C) -> C)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-157, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45511
in-theory        45511
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-147 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45511.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-147, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45512
in-theory        45512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-134 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45512.        ((A -> ((B and C) -> B)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-134, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45513
in-theory        45513
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-125 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45513.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-125, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45514
in-theory        45514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G or F)) and E)) or H))
theorem-size     27
proof            (modus-ponens tm-113 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45514.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F -> (G or F)) and E)) or H)), M:tm-113, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45515
in-theory        45515
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     31
proof            (modus-ponens tm-105 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45515.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-105, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45516
in-theory        45516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> ((D -> (E or D)) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-95 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45516.        (((A -> B) -> (A -> A)) and ((C -> ((D -> (E or D)) and C)) or F)), M:tm-95, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45517
in-theory        45517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-83 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45517.        ((A -> (B -> (C -> B))) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-83, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45518
in-theory        45518
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> ((C -> (D or C)) and B)) or E))
theorem-size     17
proof            (modus-ponens tm-76 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45518.        (((not (not A)) -> A) and ((B -> ((C -> (D or C)) and B)) or E)), M:tm-76, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45519
in-theory        45519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D -> (E or D)) and C)) or F))
theorem-size     23
proof            (modus-ponens tm-69 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45519.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D -> (E or D)) and C)) or F)), M:tm-69, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45520
in-theory        45520
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-54 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45520.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-54, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45521
in-theory        45521
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> ((D -> (E or D)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-42 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45521.        ((A -> (B or A)) and ((C -> ((D -> (E or D)) and C)) or F)), M:tm-42, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45522
in-theory        45522
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> ((D -> (E or D)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-32 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45522.        ((A -> (A or B)) and ((C -> ((D -> (E or D)) and C)) or F)), M:tm-32, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45523
in-theory        45523
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> ((D -> (E or D)) and C)) or F))
theorem-size     19
proof            (modus-ponens tm-23 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45523.        ((A -> (B -> (A and B))) and ((C -> ((D -> (E or D)) and C)) or F)), M:tm-23, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45524
in-theory        45524
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> ((D -> (E or D)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-22 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45524.        (((A and B) -> B) and ((C -> ((D -> (E or D)) and C)) or F)), M:tm-22, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45525
in-theory        45525
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> ((D -> (E or D)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-21 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45525.        (((A and B) -> A) and ((C -> ((D -> (E or D)) and C)) or F)), M:tm-21, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45526
in-theory        45526
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-20 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45526.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-20, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45527
in-theory        45527
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> ((D -> (E or D)) and C)) or F))
theorem-size     17
proof            (modus-ponens tm-19 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45527.        ((A -> (B -> A)) and ((C -> ((D -> (E or D)) and C)) or F)), M:tm-19, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45528
in-theory        45528
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> ((C -> (D or C)) and B)) or E))
theorem-size     13
proof            (modus-ponens tm-7 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-7 tm-6 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45528.        (A or ((B -> ((C -> (D or C)) and B)) or E)), M:tm-7, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45529
in-theory        45529
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45529.        (((A -> ((B -> (C or B)) and A)) or D) or E), M:tm-6, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45530
in-theory        45530
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> ((C -> (D or C)) and B)) or E) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45530.        (A -> (((B -> ((C -> (D or C)) and B)) or E) and A)), M:tm-5, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45531
in-theory        45531
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D or C)) and B)) or E))
theorem-size     13
proof            (modus-ponens tm-1 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-1 tm-6 tm-5 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45531.        (A -> ((B -> ((C -> (D or C)) and B)) or E)), M:tm-1, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45532
in-theory        45532
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-605 tm-7 ((A (-> Am (or Bm Am)))))
axioms-used      (tm-5 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45532.        ((A -> ((B -> (C or B)) and A)) and (D -> (E or D))), M:tm-605, m:tm-7, u:((A (-> Am (or Bm Am))))
================================================================
tm-name          tm-45533
in-theory        45533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45533.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-605, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-45534
in-theory        45534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-605 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-45534.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-605, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-45535
in-theory        45535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((not (not D)) -> D))
theorem-size     15
proof            (modus-ponens tm-605 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-45535.        ((A -> ((B -> (C or B)) and A)) and ((not (not D)) -> D)), M:tm-605, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-45536
in-theory        45536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-605 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-45536.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (F -> E)))), M:tm-605, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-45537
in-theory        45537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-605 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45537.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (D -> D))), M:tm-605, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-45538
in-theory        45538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-605 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-45538.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-605, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-45539
in-theory        45539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45539.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-605, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-45540
in-theory        45540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-605 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-45540.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-605, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-45541
in-theory        45541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-605 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-45541.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E and F) -> E))), M:tm-605, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-45542
in-theory        45542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-605 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-45542.        ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-605, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-45543
in-theory        45543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-605 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-45543.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E and F) -> F))), M:tm-605, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-45544
in-theory        45544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-605 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-45544.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> E)) and D))), M:tm-605, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-45545
in-theory        45545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-605 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45545.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-605, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-45546
in-theory        45546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-605 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-45546.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E and F) -> E) and D))), M:tm-605, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-45547
in-theory        45547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-605 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-45547.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E and F) -> F) and D))), M:tm-605, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-45548
in-theory        45548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-45548.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-605, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-45549
in-theory        45549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (D -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-605 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45549.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (D -> (D and E)))), M:tm-605, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-45550
in-theory        45550
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-45550.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (F -> (E and F))))), M:tm-605, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-45551
in-theory        45551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-605 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-45551.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) or F)), M:tm-605, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-45552
in-theory        45552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-605 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45552.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-605, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-45553
in-theory        45553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) or F))
theorem-size     17
proof            (modus-ponens tm-605 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-45553.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) or F)), M:tm-605, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-45554
in-theory        45554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) or F))
theorem-size     17
proof            (modus-ponens tm-605 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-45554.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) or F)), M:tm-605, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-45555
in-theory        45555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-605 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-45555.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) or F)), M:tm-605, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-45556
in-theory        45556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) or F))
theorem-size     17
proof            (modus-ponens tm-605 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-45556.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) or F)), M:tm-605, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-45557
in-theory        45557
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (E or F)) and D)))
theorem-size     19
proof            (modus-ponens tm-605 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-45557.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (E or F)) and D))), M:tm-605, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-45558
in-theory        45558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-605 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-45558.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (E or F)))), M:tm-605, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-45559
in-theory        45559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-605 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-45559.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> (F -> E)))), M:tm-605, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-45560
in-theory        45560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45560.        ((A -> ((B -> (C or B)) and A)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-605, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-45561
in-theory        45561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-605 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-45561.        ((A -> ((B -> (C or B)) and A)) and (D or ((E and F) -> E))), M:tm-605, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-45562
in-theory        45562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-605 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-45562.        ((A -> ((B -> (C or B)) and A)) and (D or ((E and F) -> F))), M:tm-605, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-45563
in-theory        45563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-45563.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> (F -> (E and F))))), M:tm-605, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-45564
in-theory        45564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-605 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-45564.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> (E or F)))), M:tm-605, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-45565
in-theory        45565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-605 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-45565.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> (F or E)))), M:tm-605, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-45566
in-theory        45566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) or F))
theorem-size     17
proof            (modus-ponens tm-605 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-45566.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) or F)), M:tm-605, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-45567
in-theory        45567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-605 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-45567.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F or E)) and D))), M:tm-605, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-45568
in-theory        45568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-605 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-45568.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (F or E)))), M:tm-605, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-45569
in-theory        45569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-605 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45569.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-605, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-45570
in-theory        45570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-605 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-45570.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-605, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-45571
in-theory        45571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-605 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45571.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-605, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-45572
in-theory        45572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-605 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-45572.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-605, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-45573
in-theory        45573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-605 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-45573.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-605, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-45574
in-theory        45574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-605 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-45574.        ((A -> ((B -> (C or B)) and A)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-605, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-45575
in-theory        45575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-605 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-45575.        ((A -> ((B -> (C or B)) and A)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-605, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-45576
in-theory        45576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     37
proof            (modus-ponens tm-605 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45576.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-605, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-45577
in-theory        45577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-45577.        ((A -> ((B -> (C or B)) and A)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-605, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-45578
in-theory        45578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     25
proof            (modus-ponens tm-605 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-45578.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-605, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-45579
in-theory        45579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-605 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-45579.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-605, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-45580
in-theory        45580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-605 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-45580.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-605, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-45581
in-theory        45581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-45581.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-605, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-45582
in-theory        45582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-605 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45582.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not (E -> D))) -> (not D))), M:tm-605, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-45583
in-theory        45583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-45583.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-605, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-45584
in-theory        45584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-605 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45584.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-605, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-45585
in-theory        45585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     21
proof            (modus-ponens tm-605 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-45585.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-605, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-45586
in-theory        45586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-45586.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-605, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-45587
in-theory        45587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-605 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-45587.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not (D or E))) -> (not D))), M:tm-605, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-45588
in-theory        45588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-605 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-45588.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not (E or D))) -> (not D))), M:tm-605, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-45589
in-theory        45589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-605 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45589.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-605, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-45590
in-theory        45590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-605 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-45590.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-605, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-45591
in-theory        45591
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-605 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-9)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-45591.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-605, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-45592
in-theory        45592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-45592.        ((A -> ((B -> (C or B)) and A)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-605, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-45593
in-theory        45593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     23
proof            (modus-ponens tm-605 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-45593.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-605, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-45594
in-theory        45594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     25
proof            (modus-ponens tm-605 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-45594.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-605, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-45595
in-theory        45595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-605 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-45595.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-605, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-45596
in-theory        45596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-45596.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-605, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-45597
in-theory        45597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     21
proof            (modus-ponens tm-605 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-7 tm-9 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-45597.        ((A -> ((B -> (C or B)) and A)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-605, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-45598
in-theory        45598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-605 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-45598.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-605, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-45599
in-theory        45599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-605 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-45599.        ((A -> ((B -> (C or B)) and A)) and (D or ((not (not E)) -> E))), M:tm-605, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-45600
in-theory        45600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((not (not D)) -> D) or E))
theorem-size     17
proof            (modus-ponens tm-605 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-45600.        ((A -> ((B -> (C or B)) and A)) and (((not (not D)) -> D) or E)), M:tm-605, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-45601
in-theory        45601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-605 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-45601.        ((A -> ((B -> (C or B)) and A)) and (D -> (((not (not E)) -> E) and D))), M:tm-605, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-45602
in-theory        45602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     25
proof            (modus-ponens tm-605 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-45602.        ((A -> ((B -> (C or B)) and A)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-605, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-45603
in-theory        45603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((not (not E)) -> E)))
theorem-size     17
proof            (modus-ponens tm-605 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-45603.        ((A -> ((B -> (C or B)) and A)) and (D -> ((not (not E)) -> E))), M:tm-605, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-45604
in-theory        45604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-45604.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-605, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-45605
in-theory        45605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-605 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-45605.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-605, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-45606
in-theory        45606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-45606.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> (F -> (G -> F))))), M:tm-605, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-45607
in-theory        45607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-45607.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (F -> E))) or G)), M:tm-605, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-45608
in-theory        45608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-45608.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-605, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-45609
in-theory        45609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-605 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-45609.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (D -> (F -> E)))), M:tm-605, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-45610
in-theory        45610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-45610.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (F -> (G -> F))))), M:tm-605, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-45611
in-theory        45611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> D))
theorem-size     13
proof            (modus-ponens tm-605 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45611.        ((A -> ((B -> (C or B)) and A)) and (D -> D)), M:tm-605, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-45612
in-theory        45612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-45612.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-605, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-45613
in-theory        45613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D and E) -> (D and E)))
theorem-size     17
proof            (modus-ponens tm-605 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45613.        ((A -> ((B -> (C or B)) and A)) and ((D and E) -> (D and E))), M:tm-605, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-45614
in-theory        45614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-605 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45614.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (D -> E))), M:tm-605, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-45615
in-theory        45615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((not (not D)) -> (not (not D))))
theorem-size     17
proof            (modus-ponens tm-605 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-45615.        ((A -> ((B -> (C or B)) and A)) and ((not (not D)) -> (not (not D)))), M:tm-605, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-45616
in-theory        45616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-605 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-45616.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-605, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-45617
in-theory        45617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-605 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-45617.        ((A -> ((B -> (C or B)) and A)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-605, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-45618
in-theory        45618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-605 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-45618.        ((A -> ((B -> (C or B)) and A)) and (D or ((E -> F) -> (E -> E)))), M:tm-605, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-45619
in-theory        45619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (D -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-605 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-45619.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (D -> D)) or F)), M:tm-605, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-45620
in-theory        45620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-45620.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-605, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-45621
in-theory        45621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-45621.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-605, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-45622
in-theory        45622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     19
proof            (modus-ponens tm-605 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-45622.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> F) -> (E -> E)))), M:tm-605, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-45623
in-theory        45623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-45623.        ((A -> ((B -> (C or B)) and A)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-605, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-45624
in-theory        45624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-605 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-45624.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D -> E)) -> (D -> E))), M:tm-605, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-45625
in-theory        45625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-605 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-45625.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-605, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-45626
in-theory        45626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     41
proof            (modus-ponens tm-605 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-45626.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-605, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-45627
in-theory        45627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-605 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-45627.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-605, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-45628
in-theory        45628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-45628.        ((A -> ((B -> (C or B)) and A)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-605, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-45629
in-theory        45629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     31
proof            (modus-ponens tm-605 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-45629.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-605, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-45630
in-theory        45630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-605 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-45630.        ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-605, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-45631
in-theory        45631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-605 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-45631.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-605, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-45632
in-theory        45632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-45632.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-605, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-45633
in-theory        45633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-605 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-45633.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-605, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-45634
in-theory        45634
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-605 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-45634.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-605, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-45635
in-theory        45635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     43
proof            (modus-ponens tm-605 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-45635.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-605, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-45636
in-theory        45636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-605 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-45636.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-605, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-45637
in-theory        45637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-605 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-45637.        ((A -> ((B -> (C or B)) and A)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-605, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-45638
in-theory        45638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-605 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-45638.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-605, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-45639
in-theory        45639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-605 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-45639.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-605, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-45640
in-theory        45640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-605 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-45640.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-605, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-45641
in-theory        45641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) and D) -> E))
theorem-size     17
proof            (modus-ponens tm-605 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-45641.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) and D) -> E)), M:tm-605, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-45642
in-theory        45642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-605 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-45642.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-605, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-45643
in-theory        45643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-605 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-45643.        ((A -> ((B -> (C or B)) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-605, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-45644
in-theory        45644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-605 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-45644.        ((A -> ((B -> (C or B)) and A)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-605, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-45645
in-theory        45645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     25
proof            (modus-ponens tm-605 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-45645.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-605, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-45646
in-theory        45646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     35
proof            (modus-ponens tm-605 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-45646.        ((A -> ((B -> (C or B)) and A)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-605, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-45647
in-theory        45647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     37
proof            (modus-ponens tm-605 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-45647.        ((A -> ((B -> (C or B)) and A)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-605, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-45648
in-theory        45648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-605 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-45648.        ((A -> ((B -> (C or B)) and A)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-605, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-45649
in-theory        45649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-605 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-45649.        ((A -> ((B -> (C or B)) and A)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-605, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-45650
in-theory        45650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-605 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-45650.        ((A -> ((B -> (C or B)) and A)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-605, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-45651
in-theory        45651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     33
proof            (modus-ponens tm-605 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-45651.        ((A -> ((B -> (C or B)) and A)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-605, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-45652
in-theory        45652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     27
proof            (modus-ponens tm-605 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-45652.        ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-605, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-45653
in-theory        45653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-605 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-45653.        ((A -> ((B -> (C or B)) and A)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-605, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-45654
in-theory        45654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-605 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-45654.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-605, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-45655
in-theory        45655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-45655.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-605, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-45656
in-theory        45656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     27
proof            (modus-ponens tm-605 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-45656.        ((A -> ((B -> (C or B)) and A)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-605, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-45657
in-theory        45657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-605 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-45657.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> ((F and G) -> F)))), M:tm-605, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-45658
in-theory        45658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-45658.        ((A -> ((B -> (C or B)) and A)) and ((D -> ((E and F) -> E)) or G)), M:tm-605, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-45659
in-theory        45659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-45659.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-605, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-45660
in-theory        45660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-605 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-45660.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E and F)) -> (D -> E))), M:tm-605, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-45661
in-theory        45661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-605 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-45661.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> ((F and G) -> F)))), M:tm-605, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-45662
in-theory        45662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D and (D -> E)) -> E))
theorem-size     17
proof            (modus-ponens tm-605 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-45662.        ((A -> ((B -> (C or B)) and A)) and ((D and (D -> E)) -> E)), M:tm-605, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-45663
in-theory        45663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-605 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-45663.        ((A -> ((B -> (C or B)) and A)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-605, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-45664
in-theory        45664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-605 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-45664.        ((A -> ((B -> (C or B)) and A)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-605, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-45665
in-theory        45665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-605 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-45665.        ((A -> ((B -> (C or B)) and A)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-605, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-45666
in-theory        45666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-605 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-45666.        ((A -> ((B -> (C or B)) and A)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-605, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-45667
in-theory        45667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     25
proof            (modus-ponens tm-605 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-45667.        ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-605, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-45668
in-theory        45668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     35
proof            (modus-ponens tm-605 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-45668.        ((A -> ((B -> (C or B)) and A)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-605, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-45669
in-theory        45669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-605 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-45669.        ((A -> ((B -> (C or B)) and A)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-605, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-45670
in-theory        45670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-605 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-45670.        ((A -> ((B -> (C or B)) and A)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-605, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-45671
in-theory        45671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-605 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-45671.        ((A -> ((B -> (C or B)) and A)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-605, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-45672
in-theory        45672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-605 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-45672.        ((A -> ((B -> (C or B)) and A)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-605, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-45673
in-theory        45673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     33
proof            (modus-ponens tm-605 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-45673.        ((A -> ((B -> (C or B)) and A)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-605, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-45674
in-theory        45674
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     27
proof            (modus-ponens tm-605 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-45674.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-605, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-45675
in-theory        45675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-605 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-45675.        ((A -> ((B -> (C or B)) and A)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-605, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-45676
in-theory        45676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-605 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-45676.        ((A -> ((B -> (C or B)) and A)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-605, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-45677
in-theory        45677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     23
proof            (modus-ponens tm-605 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-45677.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-605, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-45678
in-theory        45678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-45678.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-605, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-45679
in-theory        45679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-605 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-45679.        ((A -> ((B -> (C or B)) and A)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-605, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-45680
in-theory        45680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-605 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-45680.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> ((F and G) -> G)))), M:tm-605, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-45681
in-theory        45681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-45681.        ((A -> ((B -> (C or B)) and A)) and ((D -> ((E and F) -> F)) or G)), M:tm-605, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-45682
in-theory        45682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-45682.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-605, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-45683
in-theory        45683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-605 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-45683.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E and F)) -> (D -> F))), M:tm-605, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-45684
in-theory        45684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-605 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-45684.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> ((F and G) -> G)))), M:tm-605, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-45685
in-theory        45685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-45685.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-605, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-45686
in-theory        45686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45686.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-605, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-45687
in-theory        45687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-45687.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-605, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-45688
in-theory        45688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-605 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-45688.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-605, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-45689
in-theory        45689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-45689.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-605, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-45690
in-theory        45690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-605 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-45690.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-605, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-45691
in-theory        45691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-45691.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-605, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-45692
in-theory        45692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-45692.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-605, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-45693
in-theory        45693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-605 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-45693.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-605, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-45694
in-theory        45694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-45694.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-605, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-45695
in-theory        45695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-45695.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-605, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-45696
in-theory        45696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-45696.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-605, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-45697
in-theory        45697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-605 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-45697.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-605, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-45698
in-theory        45698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-45698.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-605, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-45699
in-theory        45699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-605 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-45699.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-605, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-45700
in-theory        45700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-605 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-45700.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-605, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-45701
in-theory        45701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-605 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-45701.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-605, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-45702
in-theory        45702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-605 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-45702.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-605, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-45703
in-theory        45703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-45703.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-605, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-45704
in-theory        45704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-45704.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-605, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-45705
in-theory        45705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-605 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-45705.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-605, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-45706
in-theory        45706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-605 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-45706.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-605, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-45707
in-theory        45707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-605 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-45707.        ((A -> ((B -> (C or B)) and A)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-605, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-45708
in-theory        45708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-45708.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-605, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-45709
in-theory        45709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     21
proof            (modus-ponens tm-605 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-45709.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-605, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-45710
in-theory        45710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-605 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-45710.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-605, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-45711
in-theory        45711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45711.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-605, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-45712
in-theory        45712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-605 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-45712.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-605, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-45713
in-theory        45713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-605 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-45713.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-605, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-45714
in-theory        45714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-45714.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-605, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-45715
in-theory        45715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-45715.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-605, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-45716
in-theory        45716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-605 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-45716.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-605, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-45717
in-theory        45717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-45717.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-605, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-45718
in-theory        45718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     35
proof            (modus-ponens tm-605 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-45718.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-605, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-45719
in-theory        45719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     29
proof            (modus-ponens tm-605 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-45719.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-605, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-45720
in-theory        45720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-45720.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-605, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-45721
in-theory        45721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     31
proof            (modus-ponens tm-605 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-45721.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-605, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-45722
in-theory        45722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-605 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-45722.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-605, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-45723
in-theory        45723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-605 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-45723.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-605, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-45724
in-theory        45724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-605 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-45724.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-605, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-45725
in-theory        45725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-605 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-45725.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-605, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-45726
in-theory        45726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     39
proof            (modus-ponens tm-605 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-45726.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-605, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-45727
in-theory        45727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-605 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-45727.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-605, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-45728
in-theory        45728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     33
proof            (modus-ponens tm-605 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-45728.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-605, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-45729
in-theory        45729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     41
proof            (modus-ponens tm-605 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-45729.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-605, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-45730
in-theory        45730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-605 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-45730.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-605, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-45731
in-theory        45731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-605 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-45731.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-605, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-45732
in-theory        45732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-605 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-45732.        ((A -> ((B -> (C or B)) and A)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-605, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-45733
in-theory        45733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-605 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-45733.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-605, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-45734
in-theory        45734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     29
proof            (modus-ponens tm-605 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-45734.        ((A -> ((B -> (C or B)) and A)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-605, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-45735
in-theory        45735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     31
proof            (modus-ponens tm-605 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-45735.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-605, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-45736
in-theory        45736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     29
proof            (modus-ponens tm-605 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-45736.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-605, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-45737
in-theory        45737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-45737.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-605, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-45738
in-theory        45738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45738.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-605, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-45739
in-theory        45739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-45739.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-605, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-45740
in-theory        45740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-605 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-45740.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-605, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-45741
in-theory        45741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-45741.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-605, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-45742
in-theory        45742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-605 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-45742.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-605, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-45743
in-theory        45743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-45743.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-605, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-45744
in-theory        45744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-45744.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-605, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-45745
in-theory        45745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-605 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-45745.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-605, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-45746
in-theory        45746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-45746.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-605, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-45747
in-theory        45747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-45747.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-605, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-45748
in-theory        45748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-45748.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-605, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-45749
in-theory        45749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-605 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-45749.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-605, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-45750
in-theory        45750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-45750.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-605, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-45751
in-theory        45751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-605 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-45751.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-605, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-45752
in-theory        45752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-605 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-45752.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-605, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-45753
in-theory        45753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-605 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-45753.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-605, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-45754
in-theory        45754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-605 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-45754.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-605, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-45755
in-theory        45755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-45755.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-605, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-45756
in-theory        45756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-605 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-45756.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-605, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-45757
in-theory        45757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-45757.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-605, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-45758
in-theory        45758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     33
proof            (modus-ponens tm-605 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-45758.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-605, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-45759
in-theory        45759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-45759.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-605, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-45760
in-theory        45760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-45760.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-605, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-45761
in-theory        45761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-605 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-45761.        ((A -> ((B -> (C or B)) and A)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-605, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-45762
in-theory        45762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-605 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-45762.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-605, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-45763
in-theory        45763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-605 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-45763.        ((A -> ((B -> (C or B)) and A)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-605, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-45764
in-theory        45764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-45764.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-605, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-45765
in-theory        45765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     21
proof            (modus-ponens tm-605 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-45765.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-605, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-45766
in-theory        45766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-45766.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-605, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-45767
in-theory        45767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45767.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-605, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-45768
in-theory        45768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-45768.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-605, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-45769
in-theory        45769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-605 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-45769.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-605, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-45770
in-theory        45770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-45770.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-605, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-45771
in-theory        45771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-605 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-45771.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-605, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-45772
in-theory        45772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-45772.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-605, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-45773
in-theory        45773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-45773.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-605, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-45774
in-theory        45774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-605 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-45774.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-605, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-45775
in-theory        45775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-45775.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-605, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-45776
in-theory        45776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-45776.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-605, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-45777
in-theory        45777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-45777.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-605, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-45778
in-theory        45778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-605 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-45778.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-605, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-45779
in-theory        45779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-45779.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-605, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-45780
in-theory        45780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-605 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-45780.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-605, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-45781
in-theory        45781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-605 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-45781.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-605, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-45782
in-theory        45782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-605 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-45782.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-605, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-45783
in-theory        45783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-605 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-45783.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-605, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-45784
in-theory        45784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-45784.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-605, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-45785
in-theory        45785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-605 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-45785.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-605, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-45786
in-theory        45786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-45786.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-605, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-45787
in-theory        45787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-45787.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-605, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-45788
in-theory        45788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-45788.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-605, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-45789
in-theory        45789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     33
proof            (modus-ponens tm-605 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-45789.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-605, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-45790
in-theory        45790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-45790.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-605, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-45791
in-theory        45791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-45791.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-605, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-45792
in-theory        45792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-605 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-45792.        ((A -> ((B -> (C or B)) and A)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-605, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-45793
in-theory        45793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-605 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-45793.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-605, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-45794
in-theory        45794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-605 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-45794.        ((A -> ((B -> (C or B)) and A)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-605, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-45795
in-theory        45795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-45795.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-605, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-45796
in-theory        45796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     21
proof            (modus-ponens tm-605 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-45796.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-605, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-45797
in-theory        45797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-45797.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-605, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-45798
in-theory        45798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45798.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-605, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-45799
in-theory        45799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-605 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-45799.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-605, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-45800
in-theory        45800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-605 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-45800.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-605, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-45801
in-theory        45801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-45801.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-605, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-45802
in-theory        45802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-605 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-45802.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-605, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-45803
in-theory        45803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-45803.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-605, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-45804
in-theory        45804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-45804.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-605, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-45805
in-theory        45805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-45805.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-605, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-45806
in-theory        45806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-605 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-45806.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-605, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-45807
in-theory        45807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-45807.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-605, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-45808
in-theory        45808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-45808.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-605, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-45809
in-theory        45809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-45809.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-605, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-45810
in-theory        45810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-605 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-45810.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-605, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-45811
in-theory        45811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-605 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-45811.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-605, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-45812
in-theory        45812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-605 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-45812.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-605, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-45813
in-theory        45813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-605 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-45813.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-605, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-45814
in-theory        45814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-605 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-45814.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-605, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-45815
in-theory        45815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-605 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-45815.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-605, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-45816
in-theory        45816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-605 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-45816.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-605, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-45817
in-theory        45817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-605 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-45817.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-605, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-45818
in-theory        45818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-605 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-45818.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-605, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-45819
in-theory        45819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-605 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-45819.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-605, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-45820
in-theory        45820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-605 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-45820.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-605, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-45821
in-theory        45821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-605 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-45821.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-605, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-45822
in-theory        45822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     35
proof            (modus-ponens tm-605 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-45822.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-605, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-45823
in-theory        45823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-605 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-45823.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-605, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-45824
in-theory        45824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-605 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-45824.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-605, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-45825
in-theory        45825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-605 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-45825.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-605, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-45826
in-theory        45826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-605 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-45826.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-605, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-45827
in-theory        45827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-605 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-45827.        ((A -> ((B -> (C or B)) and A)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-605, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-45828
in-theory        45828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-605 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-45828.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-605, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-45829
in-theory        45829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     23
proof            (modus-ponens tm-605 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-45829.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-605, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-45830
in-theory        45830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and (E -> D))))
theorem-size     17
proof            (modus-ponens tm-605 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45830.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and (E -> D)))), M:tm-605, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-45831
in-theory        45831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-45831.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-605, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-45832
in-theory        45832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D and E) -> ((D and E) and D)))
theorem-size     19
proof            (modus-ponens tm-605 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45832.        ((A -> ((B -> (C or B)) and A)) and ((D and E) -> ((D and E) and D))), M:tm-605, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-45833
in-theory        45833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D and E) -> ((D and E) and E)))
theorem-size     19
proof            (modus-ponens tm-605 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-45833.        ((A -> ((B -> (C or B)) and A)) and ((D and E) -> ((D and E) and E))), M:tm-605, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-45834
in-theory        45834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-45834.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and (E -> (D and E))))), M:tm-605, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-45835
in-theory        45835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and (D or E))))
theorem-size     17
proof            (modus-ponens tm-605 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-45835.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and (D or E)))), M:tm-605, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-45836
in-theory        45836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and (E or D))))
theorem-size     17
proof            (modus-ponens tm-605 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-45836.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and (E or D)))), M:tm-605, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-45837
in-theory        45837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     27
proof            (modus-ponens tm-605 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45837.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-605, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-45838
in-theory        45838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-45838.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-605, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-45839
in-theory        45839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     19
proof            (modus-ponens tm-605 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-10)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-45839.        ((A -> ((B -> (C or B)) and A)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-605, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-45840
in-theory        45840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and (E -> (F -> E)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-45840.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and (E -> (F -> E))))), M:tm-605, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-45841
in-theory        45841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     21
proof            (modus-ponens tm-605 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-45841.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-605, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-45842
in-theory        45842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-605 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-45842.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-605, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-45843
in-theory        45843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     27
proof            (modus-ponens tm-605 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-45843.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-605, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-45844
in-theory        45844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     33
proof            (modus-ponens tm-605 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-45844.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-605, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-45845
in-theory        45845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and ((E and F) -> E))))
theorem-size     19
proof            (modus-ponens tm-605 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-45845.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and ((E and F) -> E)))), M:tm-605, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-45846
in-theory        45846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     33
proof            (modus-ponens tm-605 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-45846.        ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-605, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-45847
in-theory        45847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and ((E and F) -> F))))
theorem-size     19
proof            (modus-ponens tm-605 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-45847.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and ((E and F) -> F)))), M:tm-605, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-45848
in-theory        45848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     21
proof            (modus-ponens tm-605 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-45848.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-605, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-45849
in-theory        45849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     29
proof            (modus-ponens tm-605 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-45849.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-605, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-45850
in-theory        45850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     21
proof            (modus-ponens tm-605 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-45850.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-605, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-45851
in-theory        45851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     21
proof            (modus-ponens tm-605 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-45851.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-605, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-45852
in-theory        45852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     23
proof            (modus-ponens tm-605 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-45852.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-605, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-45853
in-theory        45853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-45853.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-605, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-45854
in-theory        45854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-605 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-45854.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-605, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-45855
in-theory        45855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-45855.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-605, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-45856
in-theory        45856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-45856.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-605, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-45857
in-theory        45857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-605 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-45857.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-605, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-45858
in-theory        45858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-45858.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-605, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-45859
in-theory        45859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-605 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-45859.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-605, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-45860
in-theory        45860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     29
proof            (modus-ponens tm-605 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-45860.        ((A -> ((B -> (C or B)) and A)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-605, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-45861
in-theory        45861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-605 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-45861.        ((A -> ((B -> (C or B)) and A)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-605, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-45862
in-theory        45862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     21
proof            (modus-ponens tm-605 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-45862.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-605, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-45863
in-theory        45863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-45863.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-605, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-45864
in-theory        45864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-605 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-45864.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-605, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-45865
in-theory        45865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-605 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-45865.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-605, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-45866
in-theory        45866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     21
proof            (modus-ponens tm-605 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-45866.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-605, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-45867
in-theory        45867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-605 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-45867.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-605, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-45868
in-theory        45868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-605 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-45868.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-605, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-45869
in-theory        45869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-605 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-45869.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-605, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-45870
in-theory        45870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-605 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-45870.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-605, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-45871
in-theory        45871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-605 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-45871.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-605, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-45872
in-theory        45872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-605 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-45872.        ((A -> ((B -> (C or B)) and A)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-605, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-45873
in-theory        45873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-605 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-45873.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-605, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-45874
in-theory        45874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-605 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-45874.        ((A -> ((B -> (C or B)) and A)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-605, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-45875
in-theory        45875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-45875.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-605, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-45876
in-theory        45876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     31
proof            (modus-ponens tm-605 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-45876.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-605, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-45877
in-theory        45877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-605 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-45877.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-605, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-45878
in-theory        45878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-605 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-45878.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-605, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-45879
in-theory        45879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-45879.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-605, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-45880
in-theory        45880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-605 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-45880.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-605, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-45881
in-theory        45881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-605 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-45881.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-605, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-45882
in-theory        45882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-605 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-45882.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-605, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-45883
in-theory        45883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-45883.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-605, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-45884
in-theory        45884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-45884.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-605, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-45885
in-theory        45885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-45885.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-605, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-45886
in-theory        45886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-45886.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-605, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-45887
in-theory        45887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-605 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-45887.        ((A -> ((B -> (C or B)) and A)) and (D or ((E -> (F -> E)) or G))), M:tm-605, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-45888
in-theory        45888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-45888.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> D)) or F) or G)), M:tm-605, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-45889
in-theory        45889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-45889.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-605, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-45890
in-theory        45890
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     19
proof            (modus-ponens tm-605 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-45890.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> E)) or G))), M:tm-605, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-45891
in-theory        45891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-605 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-45891.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-605, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-45892
in-theory        45892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-45892.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-605, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-45893
in-theory        45893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-45893.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-605, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-45894
in-theory        45894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     39
proof            (modus-ponens tm-605 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-45894.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-605, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-45895
in-theory        45895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-45895.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-605, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-45896
in-theory        45896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-605 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-45896.        ((A -> ((B -> (C or B)) and A)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-605, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-45897
in-theory        45897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     27
proof            (modus-ponens tm-605 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-45897.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-605, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-45898
in-theory        45898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     29
proof            (modus-ponens tm-605 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-45898.        ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-605, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-45899
in-theory        45899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     27
proof            (modus-ponens tm-605 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-45899.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-605, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-45900
in-theory        45900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-605 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-45900.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-605, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-45901
in-theory        45901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-45901.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-605, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-45902
in-theory        45902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-45902.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-605, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-45903
in-theory        45903
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-45903.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-605, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-45904
in-theory        45904
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-45904.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-605, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-45905
in-theory        45905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-605 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-45905.        ((A -> ((B -> (C or B)) and A)) and (D or (((E and F) -> E) or G))), M:tm-605, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-45906
in-theory        45906
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D and E) -> D) or F) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-45906.        ((A -> ((B -> (C or B)) and A)) and ((((D and E) -> D) or F) or G)), M:tm-605, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-45907
in-theory        45907
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-45907.        ((A -> ((B -> (C or B)) and A)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-605, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-45908
in-theory        45908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E and F) -> E) or G)))
theorem-size     19
proof            (modus-ponens tm-605 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-45908.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E and F) -> E) or G))), M:tm-605, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-45909
in-theory        45909
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-605 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-45909.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-605, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-45910
in-theory        45910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-45910.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-605, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-45911
in-theory        45911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-45911.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-605, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-45912
in-theory        45912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-45912.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-605, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-45913
in-theory        45913
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-45913.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-605, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-45914
in-theory        45914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-605 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-45914.        ((A -> ((B -> (C or B)) and A)) and (D or (((E and F) -> F) or G))), M:tm-605, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-45915
in-theory        45915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D and E) -> E) or F) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-45915.        ((A -> ((B -> (C or B)) and A)) and ((((D and E) -> E) or F) or G)), M:tm-605, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-45916
in-theory        45916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-45916.        ((A -> ((B -> (C or B)) and A)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-605, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-45917
in-theory        45917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E and F) -> F) or G)))
theorem-size     19
proof            (modus-ponens tm-605 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-45917.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E and F) -> F) or G))), M:tm-605, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-45918
in-theory        45918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-605 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-45918.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-605, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-45919
in-theory        45919
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-605 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-45919.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-605, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-45920
in-theory        45920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-605 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-45920.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-605, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-45921
in-theory        45921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     33
proof            (modus-ponens tm-605 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-45921.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-605, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-45922
in-theory        45922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-605 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-45922.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-605, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-45923
in-theory        45923
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-605 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-45923.        ((A -> ((B -> (C or B)) and A)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-605, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-45924
in-theory        45924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     21
proof            (modus-ponens tm-605 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-45924.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-605, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-45925
in-theory        45925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-45925.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-605, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-45926
in-theory        45926
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     21
proof            (modus-ponens tm-605 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-45926.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-605, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-45927
in-theory        45927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-605 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-45927.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-605, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-45928
in-theory        45928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-45928.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-605, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-45929
in-theory        45929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-45929.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-605, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-45930
in-theory        45930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-45930.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-605, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-45931
in-theory        45931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-45931.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-605, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-45932
in-theory        45932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-605 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-45932.        ((A -> ((B -> (C or B)) and A)) and (D or ((E -> (E or F)) or G))), M:tm-605, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-45933
in-theory        45933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (D or E)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-45933.        ((A -> ((B -> (C or B)) and A)) and (((D -> (D or E)) or F) or G)), M:tm-605, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-45934
in-theory        45934
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-45934.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-605, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-45935
in-theory        45935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (E or F)) or G)))
theorem-size     19
proof            (modus-ponens tm-605 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-45935.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (E or F)) or G))), M:tm-605, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-45936
in-theory        45936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-45936.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-605, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-45937
in-theory        45937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45937.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-605, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-45938
in-theory        45938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-45938.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-605, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-45939
in-theory        45939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-605 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-45939.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-605, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-45940
in-theory        45940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-45940.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-605, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-45941
in-theory        45941
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-605 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-45941.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-605, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-45942
in-theory        45942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-45942.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-605, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-45943
in-theory        45943
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-45943.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-605, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-45944
in-theory        45944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-605 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-45944.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-605, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-45945
in-theory        45945
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-45945.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-605, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-45946
in-theory        45946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-45946.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-605, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-45947
in-theory        45947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-45947.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-605, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-45948
in-theory        45948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-605 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-45948.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-605, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-45949
in-theory        45949
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-45949.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-605, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-45950
in-theory        45950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-605 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-45950.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-605, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-45951
in-theory        45951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-605 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-45951.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-605, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-45952
in-theory        45952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-605 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-45952.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-605, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-45953
in-theory        45953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-605 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-45953.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-605, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-45954
in-theory        45954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-45954.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-605, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-45955
in-theory        45955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-605 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-45955.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-605, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-45956
in-theory        45956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-45956.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-605, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-45957
in-theory        45957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-45957.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-605, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-45958
in-theory        45958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-605 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-45958.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-605, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-45959
in-theory        45959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-45959.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-605, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-45960
in-theory        45960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-605 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-45960.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-605, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-45961
in-theory        45961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-45961.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-605, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-45962
in-theory        45962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-45962.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-605, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-45963
in-theory        45963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-45963.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-605, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-45964
in-theory        45964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-45964.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-605, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-45965
in-theory        45965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-605 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-45965.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-605, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-45966
in-theory        45966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-45966.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-605, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-45967
in-theory        45967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-45967.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-605, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-45968
in-theory        45968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     21
proof            (modus-ponens tm-605 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-45968.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-605, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-45969
in-theory        45969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-605 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-45969.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-605, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-45970
in-theory        45970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-45970.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-605, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-45971
in-theory        45971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-45971.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-605, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-45972
in-theory        45972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     33
proof            (modus-ponens tm-605 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-45972.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-605, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-45973
in-theory        45973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-45973.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-605, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-45974
in-theory        45974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-45974.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-605, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-45975
in-theory        45975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-605 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-45975.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-605, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-45976
in-theory        45976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-605 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-45976.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-605, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-45977
in-theory        45977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-605 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-45977.        ((A -> ((B -> (C or B)) and A)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-605, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-45978
in-theory        45978
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-45978.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-605, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-45979
in-theory        45979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     21
proof            (modus-ponens tm-605 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-45979.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-605, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-45980
in-theory        45980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-45980.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-605, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-45981
in-theory        45981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and (E -> (E or F)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-45981.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and (E -> (E or F))))), M:tm-605, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-45982
in-theory        45982
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-45982.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-605, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-45983
in-theory        45983
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-45983.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-605, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-45984
in-theory        45984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-45984.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-605, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-45985
in-theory        45985
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-45985.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-605, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-45986
in-theory        45986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-45986.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-605, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-45987
in-theory        45987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-605 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-45987.        ((A -> ((B -> (C or B)) and A)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-605, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-45988
in-theory        45988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-605 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-45988.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-605, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-45989
in-theory        45989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-45989.        ((A -> ((B -> (C or B)) and A)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-605, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-45990
in-theory        45990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-45990.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-605, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-45991
in-theory        45991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-605 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-45991.        ((A -> ((B -> (C or B)) and A)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-605, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-45992
in-theory        45992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-45992.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> (F -> (F or G))))), M:tm-605, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-45993
in-theory        45993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-45993.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (E or F))) or G)), M:tm-605, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-45994
in-theory        45994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-45994.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-605, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-45995
in-theory        45995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (D -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-605 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-45995.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (D -> (E or F)))), M:tm-605, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-45996
in-theory        45996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-45996.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (F -> (F or G))))), M:tm-605, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-45997
in-theory        45997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-45997.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-605, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-45998
in-theory        45998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-45998.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-605, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-45999
in-theory        45999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-45999.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-605, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46000
in-theory        46000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46000.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-605, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46001
in-theory        46001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46001.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-605, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-46002
in-theory        46002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46002.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-605, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46003
in-theory        46003
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46003.        ((A -> ((B -> (C or B)) and A)) and (D or (E or (F -> (G -> F))))), M:tm-605, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-46004
in-theory        46004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (F -> E))) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46004.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (F -> E))) or G)), M:tm-605, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-46005
in-theory        46005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46005.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-605, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-46006
in-theory        46006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E or (F -> (G -> F)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46006.        ((A -> ((B -> (C or B)) and A)) and (D -> (E or (F -> (G -> F))))), M:tm-605, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-46007
in-theory        46007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46007.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-605, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46008
in-theory        46008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-605 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46008.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-605, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46009
in-theory        46009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46009.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-605, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46010
in-theory        46010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46010.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-605, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46011
in-theory        46011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     39
proof            (modus-ponens tm-605 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46011.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-605, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-46012
in-theory        46012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46012.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-605, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46013
in-theory        46013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-605 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46013.        ((A -> ((B -> (C or B)) and A)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-605, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-46014
in-theory        46014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     27
proof            (modus-ponens tm-605 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46014.        ((A -> ((B -> (C or B)) and A)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-605, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-46015
in-theory        46015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     29
proof            (modus-ponens tm-605 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46015.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-605, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-46016
in-theory        46016
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     27
proof            (modus-ponens tm-605 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46016.        ((A -> ((B -> (C or B)) and A)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-605, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-46017
in-theory        46017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-605 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46017.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-605, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46018
in-theory        46018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-605 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46018.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-605, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46019
in-theory        46019
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-605 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46019.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-605, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46020
in-theory        46020
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-605 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46020.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-605, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46021
in-theory        46021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     31
proof            (modus-ponens tm-605 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46021.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-605, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-46022
in-theory        46022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-605 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46022.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-605, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46023
in-theory        46023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-605 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46023.        ((A -> ((B -> (C or B)) and A)) and (D or (E or ((F and G) -> F)))), M:tm-605, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-46024
in-theory        46024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or ((E and F) -> E)) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46024.        ((A -> ((B -> (C or B)) and A)) and ((D or ((E and F) -> E)) or G)), M:tm-605, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-46025
in-theory        46025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46025.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-605, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-46026
in-theory        46026
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E or ((F and G) -> F))))
theorem-size     19
proof            (modus-ponens tm-605 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46026.        ((A -> ((B -> (C or B)) and A)) and (D -> (E or ((F and G) -> F)))), M:tm-605, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-46027
in-theory        46027
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-605 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46027.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-605, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46028
in-theory        46028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-605 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46028.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-605, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46029
in-theory        46029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-605 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46029.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-605, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46030
in-theory        46030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-605 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46030.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-605, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46031
in-theory        46031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     31
proof            (modus-ponens tm-605 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46031.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-605, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-46032
in-theory        46032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-605 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46032.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-605, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46033
in-theory        46033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-605 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46033.        ((A -> ((B -> (C or B)) and A)) and (D or (E or ((F and G) -> G)))), M:tm-605, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-46034
in-theory        46034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or ((E and F) -> F)) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46034.        ((A -> ((B -> (C or B)) and A)) and ((D or ((E and F) -> F)) or G)), M:tm-605, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-46035
in-theory        46035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46035.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-605, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-46036
in-theory        46036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E or ((F and G) -> G))))
theorem-size     19
proof            (modus-ponens tm-605 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46036.        ((A -> ((B -> (C or B)) and A)) and (D -> (E or ((F and G) -> G)))), M:tm-605, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-46037
in-theory        46037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-605 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46037.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-605, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46038
in-theory        46038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-605 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46038.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-605, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46039
in-theory        46039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-605 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46039.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-605, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46040
in-theory        46040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-605 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46040.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-605, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46041
in-theory        46041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     33
proof            (modus-ponens tm-605 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46041.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-605, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-46042
in-theory        46042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-605 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46042.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-605, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46043
in-theory        46043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-605 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46043.        ((A -> ((B -> (C or B)) and A)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-605, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-46044
in-theory        46044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     21
proof            (modus-ponens tm-605 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46044.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-605, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-46045
in-theory        46045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46045.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-605, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-46046
in-theory        46046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     21
proof            (modus-ponens tm-605 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46046.        ((A -> ((B -> (C or B)) and A)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-605, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-46047
in-theory        46047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46047.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-605, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46048
in-theory        46048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46048.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-605, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46049
in-theory        46049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46049.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-605, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46050
in-theory        46050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46050.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-605, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46051
in-theory        46051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46051.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-605, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-46052
in-theory        46052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46052.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-605, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46053
in-theory        46053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46053.        ((A -> ((B -> (C or B)) and A)) and (D or (E or (F -> (F or G))))), M:tm-605, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-46054
in-theory        46054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (E or F))) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46054.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (E or F))) or G)), M:tm-605, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-46055
in-theory        46055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46055.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-605, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-46056
in-theory        46056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E or (F -> (F or G)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46056.        ((A -> ((B -> (C or B)) and A)) and (D -> (E or (F -> (F or G))))), M:tm-605, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-46057
in-theory        46057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46057.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-605, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46058
in-theory        46058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46058.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-605, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46059
in-theory        46059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46059.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-605, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46060
in-theory        46060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46060.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-605, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46061
in-theory        46061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46061.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-605, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-46062
in-theory        46062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46062.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-605, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46063
in-theory        46063
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46063.        ((A -> ((B -> (C or B)) and A)) and (D or (E or (F -> (G or F))))), M:tm-605, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-46064
in-theory        46064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46064.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> (F or E))) or G)), M:tm-605, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-46065
in-theory        46065
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46065.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-605, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-46066
in-theory        46066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E or (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46066.        ((A -> ((B -> (C or B)) and A)) and (D -> (E or (F -> (G or F))))), M:tm-605, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-46067
in-theory        46067
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46067.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-605, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-46068
in-theory        46068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-605 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46068.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-605, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-46069
in-theory        46069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46069.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-605, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-46070
in-theory        46070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46070.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-605, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-46071
in-theory        46071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46071.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-605, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-46072
in-theory        46072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46072.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-605, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-46073
in-theory        46073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-605 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46073.        ((A -> ((B -> (C or B)) and A)) and (D or ((E -> (F or E)) or G))), M:tm-605, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-46074
in-theory        46074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E or D)) or F) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46074.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E or D)) or F) or G)), M:tm-605, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-46075
in-theory        46075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46075.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-605, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-46076
in-theory        46076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F or E)) or G)))
theorem-size     19
proof            (modus-ponens tm-605 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46076.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F or E)) or G))), M:tm-605, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-46077
in-theory        46077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-46077.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-605, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-46078
in-theory        46078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-46078.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-605, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-46079
in-theory        46079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-46079.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-605, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-46080
in-theory        46080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-605 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-46080.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-605, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-46081
in-theory        46081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-46081.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-605, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-46082
in-theory        46082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-605 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-46082.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-605, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-46083
in-theory        46083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-46083.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-605, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-46084
in-theory        46084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-46084.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-605, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-46085
in-theory        46085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-605 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-46085.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-605, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-46086
in-theory        46086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-46086.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-605, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-46087
in-theory        46087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-46087.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-605, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46088
in-theory        46088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-46088.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-605, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-46089
in-theory        46089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-605 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-46089.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-605, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-46090
in-theory        46090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46090.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-605, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46091
in-theory        46091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-605 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-46091.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-605, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-46092
in-theory        46092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-605 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-46092.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-605, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46093
in-theory        46093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-605 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-46093.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-605, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-46094
in-theory        46094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-605 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-46094.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-605, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46095
in-theory        46095
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-46095.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-605, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-46096
in-theory        46096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-605 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-46096.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-605, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-46097
in-theory        46097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-46097.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-605, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-46098
in-theory        46098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-46098.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-605, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-46099
in-theory        46099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-605 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-46099.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-605, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-46100
in-theory        46100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-46100.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-605, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-46101
in-theory        46101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-605 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46101.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-605, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46102
in-theory        46102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-46102.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-605, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-46103
in-theory        46103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-605 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-46103.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-605, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-46104
in-theory        46104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-46104.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-605, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-46105
in-theory        46105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-46105.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-605, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-46106
in-theory        46106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-605 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-46106.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-605, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-46107
in-theory        46107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-46107.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-605, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-46108
in-theory        46108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-46108.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-605, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-46109
in-theory        46109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-46109.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-605, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46110
in-theory        46110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46110.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-605, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46111
in-theory        46111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-605 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46111.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-605, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46112
in-theory        46112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-605 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46112.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-605, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46113
in-theory        46113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-605 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46113.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-605, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46114
in-theory        46114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-605 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46114.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-605, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46115
in-theory        46115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46115.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-605, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46116
in-theory        46116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46116.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-605, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46117
in-theory        46117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-605 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46117.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-605, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-46118
in-theory        46118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46118.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-605, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-46119
in-theory        46119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46119.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-605, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-46120
in-theory        46120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-605 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-46120.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-605, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-46121
in-theory        46121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-605 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46121.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-605, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-46122
in-theory        46122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46122.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-605, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-46123
in-theory        46123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46123.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-605, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-46124
in-theory        46124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     33
proof            (modus-ponens tm-605 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46124.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-605, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-46125
in-theory        46125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46125.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-605, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-46126
in-theory        46126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-46126.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-605, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-46127
in-theory        46127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-605 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-46127.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-605, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-46128
in-theory        46128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-605 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46128.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-605, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46129
in-theory        46129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-605 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46129.        ((A -> ((B -> (C or B)) and A)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-605, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-46130
in-theory        46130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46130.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-605, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46131
in-theory        46131
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> ((E -> (F or E)) and D)) and ((B -> (C or B)) and A)))
theorem-size     27
proof            (modus-ponens tm-602 tm-605 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46131.        ((A or ((B -> (C or B)) and A)) -> ((D -> ((E -> (F or E)) and D)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-605, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-46132
in-theory        46132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((E -> (F or E)) and (A -> ((B -> ((C -> (D or C)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46132.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((E -> (F or E)) and (A -> ((B -> ((C -> (D or C)) and B)) and A)))), M:tm-595, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46133
in-theory        46133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46133.        (((A -> (B or A)) or C) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-550, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46134
in-theory        46134
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46134.        ((A or (B -> (C or B))) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-540, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46135
in-theory        46135
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46135.        ((A or (B -> (B or C))) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-530, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46136
in-theory        46136
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46136.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-520, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46137
in-theory        46137
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46137.        ((A or ((B and C) -> C)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-510, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46138
in-theory        46138
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46138.        ((A or ((B and C) -> B)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-500, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46139
in-theory        46139
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H or G)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46139.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H or G)) and F)) and E))), M:tm-490, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46140
in-theory        46140
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46140.        ((A or (B -> (C -> B))) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-480, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46141
in-theory        46141
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> ((C -> (D or C)) and B)) and A) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46141.        (A -> (((B -> ((C -> (D or C)) and B)) and A) or E)), M:tm-470, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-46142
in-theory        46142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46142.        ((A -> (B -> (B or C))) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-469, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46143
in-theory        46143
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> ((E -> (F or E)) and D)) and (B -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-466 tm-605 ((Am (-> A (or A B))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46143.        ((A or (B -> (B or C))) -> ((D -> ((E -> (F or E)) and D)) and (B -> (B or C)))), M:tm-466, m:tm-605, u:((Am (-> A (or A B))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A (or A B)))))
================================================================
tm-name          tm-46144
in-theory        46144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46144.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (E -> (E or F))), M:tm-456, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46145
in-theory        46145
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46145.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-453, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46146
in-theory        46146
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> ((E -> (F or E)) and D)) and ((B -> (B or C)) and A)))
theorem-size     27
proof            (modus-ponens tm-450 tm-605 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46146.        ((A or ((B -> (B or C)) and A)) -> ((D -> ((E -> (F or E)) and D)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-605, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-46147
in-theory        46147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((E -> (E or F)) and (A -> ((B -> ((C -> (D or C)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46147.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((E -> (E or F)) and (A -> ((B -> ((C -> (D or C)) and B)) and A)))), M:tm-443, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46148
in-theory        46148
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46148.        (((A -> (A or B)) or C) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-409, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46149
in-theory        46149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46149.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-400, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46150
in-theory        46150
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46150.        ((((A and B) -> B) or C) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-391, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46151
in-theory        46151
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46151.        ((((A and B) -> A) or C) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-382, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46152
in-theory        46152
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> ((G -> (H or G)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46152.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> ((G -> (H or G)) and F)) and E))), M:tm-373, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46153
in-theory        46153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46153.        (((A -> (B -> A)) or C) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-364, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46154
in-theory        46154
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> ((D -> (E or D)) and C)) and A) and B)))
theorem-size     17
proof            (modus-ponens tm-355 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46154.        (A -> (B -> (((C -> ((D -> (E or D)) and C)) and A) and B))), M:tm-355, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-46155
in-theory        46155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46155.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-354, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46156
in-theory        46156
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> ((E -> (F or E)) and D)) and (B -> (C -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-351 tm-605 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46156.        ((A or (B -> (C -> (B and C)))) -> ((D -> ((E -> (F or E)) and D)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-605, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-46157
in-theory        46157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46157.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46158
in-theory        46158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> ((E -> (F or E)) and D)) and C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46158.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> ((E -> (F or E)) and D)) and C))), M:tm-338, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46159
in-theory        46159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> ((D -> (E or D)) and C)) and (A -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-335 tm-605 ((Am (-> A (and A B))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46159.        (((A -> B) or (A -> (A and B))) -> ((C -> ((D -> (E or D)) and C)) and (A -> (A and B)))), M:tm-335, m:tm-605, u:((Am (-> A (and A B))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A (and A B)))))
================================================================
tm-name          tm-46160
in-theory        46160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (A -> (A and ((B -> ((C -> (D or C)) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-328 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46160.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (A -> (A and ((B -> ((C -> (D or C)) and B)) and A)))), M:tm-328, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-46161
in-theory        46161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> ((C -> (D or C)) and B)) and A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46161.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> ((C -> (D or C)) and B)) and A)))), M:tm-327, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46162
in-theory        46162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (((E and F) -> F) and (A -> ((B -> ((C -> (D or C)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46162.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (((E and F) -> F) and (A -> ((B -> ((C -> (D or C)) and B)) and A)))), M:tm-326, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46163
in-theory        46163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (((E and F) -> E) and (A -> ((B -> ((C -> (D or C)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46163.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (((E and F) -> E) and (A -> ((B -> ((C -> (D or C)) and B)) and A)))), M:tm-325, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46164
in-theory        46164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> ((C -> (D or C)) and B)) and A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46164.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> ((C -> (D or C)) and B)) and A)))), M:tm-324, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46165
in-theory        46165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((E -> (F -> E)) and (A -> ((B -> ((C -> (D or C)) and B)) and A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46165.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((E -> (F -> E)) and (A -> ((B -> ((C -> (D or C)) and B)) and A)))), M:tm-323, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46166
in-theory        46166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46166.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46167
in-theory        46167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46167.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46168
in-theory        46168
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46168.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46169
in-theory        46169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (A -> A))
theorem-size     17
proof            (modus-ponens tm-316 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46169.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (A -> A)), M:tm-316, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-46170
in-theory        46170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46170.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46171
in-theory        46171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((A -> (not ((B -> ((C -> (D or C)) and B)) and A))) -> (not A)))
theorem-size     31
proof            (modus-ponens tm-313 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46171.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((A -> (not ((B -> ((C -> (D or C)) and B)) and A))) -> (not A))), M:tm-313, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-46172
in-theory        46172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((((B -> ((C -> (D or C)) and B)) and A) -> E) -> ((A or ((B -> ((C -> (D or C)) and B)) and A)) -> E)))
theorem-size     43
proof            (modus-ponens tm-312 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46172.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((((B -> ((C -> (D or C)) and B)) and A) -> E) -> ((A or ((B -> ((C -> (D or C)) and B)) and A)) -> E))), M:tm-312, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-46173
in-theory        46173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (E or (A -> ((B -> ((C -> (D or C)) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46173.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (E or (A -> ((B -> ((C -> (D or C)) and B)) and A)))), M:tm-311, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46174
in-theory        46174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((A -> ((B -> ((C -> (D or C)) and B)) and A)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46174.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and ((A -> ((B -> ((C -> (D or C)) and B)) and A)) or E)), M:tm-310, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46175
in-theory        46175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (E -> ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46175.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (E -> ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and E))), M:tm-309, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46176
in-theory        46176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (E -> (A -> ((B -> ((C -> (D or C)) and B)) and A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46176.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (E -> (A -> ((B -> ((C -> (D or C)) and B)) and A)))), M:tm-305, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46177
in-theory        46177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46177.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-303, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46178
in-theory        46178
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> ((E -> (F or E)) and D)) and ((B -> (C -> (B and C))) and A)))
theorem-size     31
proof            (modus-ponens tm-300 tm-605 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46178.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> ((E -> (F or E)) and D)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-605, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-46179
in-theory        46179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46179.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-270, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46180
in-theory        46180
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> ((E -> (F or E)) and D)) and (((B and C) -> C) and A)))
theorem-size     27
proof            (modus-ponens tm-267 tm-605 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46180.        ((A or (((B and C) -> C) and A)) -> ((D -> ((E -> (F or E)) and D)) and (((B and C) -> C) and A))), M:tm-267, m:tm-605, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-46181
in-theory        46181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46181.        ((A -> (((B and C) -> B) and A)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-239, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46182
in-theory        46182
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> ((E -> (F or E)) and D)) and (((B and C) -> B) and A)))
theorem-size     27
proof            (modus-ponens tm-236 tm-605 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46182.        ((A or (((B and C) -> B) and A)) -> ((D -> ((E -> (F or E)) and D)) and (((B and C) -> B) and A))), M:tm-236, m:tm-605, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-46183
in-theory        46183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> ((G -> (H or G)) and F)) and E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46183.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> ((G -> (H or G)) and F)) and E))), M:tm-210, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46184
in-theory        46184
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> ((F -> (G or F)) and E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     43
proof            (modus-ponens tm-207 tm-605 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-7)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46184.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> ((F -> (G or F)) and E)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-605, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-46185
in-theory        46185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46185.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-183, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46186
in-theory        46186
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> ((E -> (F or E)) and D)) and ((B -> (C -> B)) and A)))
theorem-size     27
proof            (modus-ponens tm-180 tm-605 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46186.        ((A or ((B -> (C -> B)) and A)) -> ((D -> ((E -> (F or E)) and D)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-605, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-46187
in-theory        46187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46187.        ((A -> ((B and C) -> C)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-157, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46188
in-theory        46188
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((B and C) -> C)))
theorem-size     23
proof            (modus-ponens tm-154 tm-605 ((Am (-> (and A B) B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46188.        ((A or ((B and C) -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((B and C) -> C))), M:tm-154, m:tm-605, u:((Am (-> (and A B) B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (and A B) B))))
================================================================
tm-name          tm-46189
in-theory        46189
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46189.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-147, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46190
in-theory        46190
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((A and (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-144 tm-605 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46190.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-605, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-46191
in-theory        46191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46191.        ((A -> ((B and C) -> B)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-134, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46192
in-theory        46192
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> ((E -> (F or E)) and D)) and ((B and C) -> B)))
theorem-size     23
proof            (modus-ponens tm-131 tm-605 ((Am (-> (and A B) A)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46192.        ((A or ((B and C) -> B)) -> ((D -> ((E -> (F or E)) and D)) and ((B and C) -> B))), M:tm-131, m:tm-605, u:((Am (-> (and A B) A)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (and A B) A))))
================================================================
tm-name          tm-46193
in-theory        46193
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46193.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-125, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46194
in-theory        46194
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> ((E -> (F or E)) and D)) and (((A -> B) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-122 tm-605 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46194.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> ((E -> (F or E)) and D)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-605, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-46195
in-theory        46195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H or G)) and F)) and E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46195.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> ((G -> (H or G)) and F)) and E))), M:tm-113, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46196
in-theory        46196
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> ((F -> (G or F)) and E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     39
proof            (modus-ponens tm-110 tm-605 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46196.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> ((F -> (G or F)) and E)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-605, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-46197
in-theory        46197
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46197.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-105, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46198
in-theory        46198
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> ((E -> (F or E)) and D)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-102 tm-605 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46198.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> ((E -> (F or E)) and D)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-605, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-46199
in-theory        46199
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> ((E -> (F or E)) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46199.        (((A -> B) -> (A -> A)) and (C -> ((D -> ((E -> (F or E)) and D)) and C))), M:tm-95, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46200
in-theory        46200
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> ((D -> (E or D)) and C)) and (A -> A)))
theorem-size     21
proof            (modus-ponens tm-92 tm-605 ((Am (-> A A)) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46200.        (((A -> B) or (A -> A)) -> ((C -> ((D -> (E or D)) and C)) and (A -> A))), M:tm-92, m:tm-605, u:((Am (-> A A)) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A A))))
================================================================
tm-name          tm-46201
in-theory        46201
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> ((D -> (E or D)) and C)) and A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46201.        (A -> (B -> ((C -> ((D -> (E or D)) and C)) and A))), M:tm-84, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-46202
in-theory        46202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46202.        ((A -> (B -> (C -> B))) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-83, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46203
in-theory        46203
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> ((E -> (F or E)) and D)) and (B -> (C -> B))))
theorem-size     23
proof            (modus-ponens tm-80 tm-605 ((Am (-> A (-> B A))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46203.        ((A or (B -> (C -> B))) -> ((D -> ((E -> (F or E)) and D)) and (B -> (C -> B)))), M:tm-80, m:tm-605, u:((Am (-> A (-> B A))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A (-> B A)))))
================================================================
tm-name          tm-46204
in-theory        46204
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> ((D -> (E or D)) and C)) and B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-10 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46204.        (((not (not A)) -> A) and (B -> ((C -> ((D -> (E or D)) and C)) and B))), M:tm-76, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46205
in-theory        46205
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> ((C -> (D or C)) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-73 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46205.        (((not (not A)) or A) -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-73, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-46206
in-theory        46206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> ((E -> (F or E)) and D)) and C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-9 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46206.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> ((E -> (F or E)) and D)) and C))), M:tm-69, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46207
in-theory        46207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> ((D -> (E or D)) and C)) and ((A -> (not B)) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-66 tm-605 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46207.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> ((D -> (E or D)) and C)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-605, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-46208
in-theory        46208
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46208.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-54, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46209
in-theory        46209
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((E -> (F or E)) and D)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-51 tm-605 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46209.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> ((E -> (F or E)) and D)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-605, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-46210
in-theory        46210
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> ((D -> (E or D)) and C)) and (B or A)))
theorem-size     19
proof            (modus-ponens tm-50 tm-605 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46210.        ((A or (B or A)) -> ((C -> ((D -> (E or D)) and C)) and (B or A))), M:tm-50, m:tm-605, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (or A B))))
================================================================
tm-name          tm-46211
in-theory        46211
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> ((D -> (E or D)) and C)) and (A or B)))
theorem-size     19
proof            (modus-ponens tm-49 tm-605 ((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46211.        ((A or (A or B)) -> ((C -> ((D -> (E or D)) and C)) and (A or B))), M:tm-49, m:tm-605, u:((Am (or A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (or A B))))
================================================================
tm-name          tm-46212
in-theory        46212
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> ((D -> (E or D)) and C)) and (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-48 tm-605 ((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46212.        ((A or (B -> (A and B))) -> ((C -> ((D -> (E or D)) and C)) and (B -> (A and B)))), M:tm-48, m:tm-605, u:((Am (-> A (and B A))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A (and B A)))))
================================================================
tm-name          tm-46213
in-theory        46213
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> ((D -> (E or D)) and C)) and B))
theorem-size     17
proof            (modus-ponens tm-47 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46213.        (((A and B) or B) -> ((C -> ((D -> (E or D)) and C)) and B)), M:tm-47, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-46214
in-theory        46214
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> ((D -> (E or D)) and C)) and A))
theorem-size     17
proof            (modus-ponens tm-46 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46214.        (((A and B) or A) -> ((C -> ((D -> (E or D)) and C)) and A)), M:tm-46, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-46215
in-theory        46215
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F or E)) and D)) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-45 tm-605 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46215.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F or E)) and D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-605, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-46216
in-theory        46216
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> ((D -> (E or D)) and C)) and (B -> A)))
theorem-size     19
proof            (modus-ponens tm-44 tm-605 ((Am (-> A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46216.        ((A or (B -> A)) -> ((C -> ((D -> (E or D)) and C)) and (B -> A))), M:tm-44, m:tm-605, u:((Am (-> A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A B))))
================================================================
tm-name          tm-46217
in-theory        46217
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> ((E -> (F or E)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46217.        ((A -> (B or A)) and (C -> ((D -> ((E -> (F or E)) and D)) and C))), M:tm-42, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46218
in-theory        46218
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> ((E -> (F or E)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46218.        ((A -> (A or B)) and (C -> ((D -> ((E -> (F or E)) and D)) and C))), M:tm-32, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46219
in-theory        46219
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> ((C -> (D or C)) and B)) and A)))
theorem-size     15
proof            (modus-ponens tm-24 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46219.        (A -> (A and ((B -> ((C -> (D or C)) and B)) and A))), M:tm-24, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-46220
in-theory        46220
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> ((E -> (F or E)) and D)) and C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46220.        ((A -> (B -> (A and B))) and (C -> ((D -> ((E -> (F or E)) and D)) and C))), M:tm-23, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46221
in-theory        46221
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> ((E -> (F or E)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-4 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46221.        (((A and B) -> B) and (C -> ((D -> ((E -> (F or E)) and D)) and C))), M:tm-22, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46222
in-theory        46222
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> ((E -> (F or E)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-3 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46222.        (((A and B) -> A) and (C -> ((D -> ((E -> (F or E)) and D)) and C))), M:tm-21, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46223
in-theory        46223
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-2 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46223.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-20, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46224
in-theory        46224
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> ((E -> (F or E)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46224.        ((A -> (B -> A)) and (C -> ((D -> ((E -> (F or E)) and D)) and C))), M:tm-19, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46225
in-theory        46225
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> ((C -> (D or C)) and B)) and A))) -> (not A))
theorem-size     17
proof            (modus-ponens tm-9 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-9 tm-5 tm-7)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46225.        ((A -> (not ((B -> ((C -> (D or C)) and B)) and A))) -> (not A)), M:tm-9, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-46226
in-theory        46226
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C or B)) and A)) and D) -> E) -> ((D or ((A -> ((B -> (C or B)) and A)) and D)) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-8 tm-5 tm-7)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46226.        ((((A -> ((B -> (C or B)) and A)) and D) -> E) -> ((D or ((A -> ((B -> (C or B)) and A)) and D)) -> E)), M:tm-8, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-46227
in-theory        46227
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> ((D -> (E or D)) and C)) and B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-7 tm-5)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46227.        (A or (B -> ((C -> ((D -> (E or D)) and C)) and B))), M:tm-7, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46228
in-theory        46228
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-6 tm-5 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46228.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) or E), M:tm-6, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46229
in-theory        46229
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> ((D -> (E or D)) and C)) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46229.        (A -> ((B -> ((C -> ((D -> (E or D)) and C)) and B)) and A)), M:tm-5, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46230
in-theory        46230
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> ((D -> (E or D)) and C)) and B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46230.        (A -> (B -> ((C -> ((D -> (E or D)) and C)) and B))), M:tm-1, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46231
in-theory        46231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-605 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46231.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-605, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46232
in-theory        46232
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-602 tm-606 ((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46232.        ((A or ((B -> (C or B)) and A)) -> (D -> ((E -> (F or E)) and D))), M:tm-602, m:tm-606, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46233
in-theory        46233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and ((E -> (F or E)) and (A -> (B -> ((C -> (D or C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46233.        ((A -> (B -> ((C -> (D or C)) and B))) and ((E -> (F or E)) and (A -> (B -> ((C -> (D or C)) and B))))), M:tm-595, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46234
in-theory        46234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-550 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46234.        (((A -> (B or A)) or C) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-550, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46235
in-theory        46235
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-540 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46235.        ((A or (B -> (C or B))) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-540, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46236
in-theory        46236
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-530 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46236.        ((A or (B -> (B or C))) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-530, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46237
in-theory        46237
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-520 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46237.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-520, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46238
in-theory        46238
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-510 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46238.        ((A or ((B and C) -> C)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-510, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46239
in-theory        46239
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-500 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46239.        ((A or ((B and C) -> B)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-500, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46240
in-theory        46240
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-490 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46240.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H or G)) and F)))), M:tm-490, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46241
in-theory        46241
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-480 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46241.        ((A or (B -> (C -> B))) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-480, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46242
in-theory        46242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-469 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46242.        ((A -> (B -> (B or C))) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-469, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46243
in-theory        46243
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-466 tm-606 ((Am (-> A (or A B))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46243.        ((A or (B -> (B or C))) -> (D -> ((E -> (F or E)) and D))), M:tm-466, m:tm-606, u:((Am (-> A (or A B))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46244
in-theory        46244
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (A or D)))
theorem-size     11
proof            (modus-ponens tm-464 tm-606 ((A Am) (Bm (or Am B)) (C (and (-> Cm (or Dm Cm)) (or Am B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46244.        (A -> ((B -> (C or B)) and (A or D))), M:tm-464, m:tm-606, u:((A Am) (Bm (or Am B)) (C (and (-> Cm (or Dm Cm)) (or Am B))))
================================================================
tm-name          tm-46245
in-theory        46245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46245.        ((A -> (B -> ((C -> (D or C)) and B))) and (E -> (E or F))), M:tm-456, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46246
in-theory        46246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-453 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46246.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-453, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46247
in-theory        46247
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-450 tm-606 ((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46247.        ((A or ((B -> (B or C)) and A)) -> (D -> ((E -> (F or E)) and D))), M:tm-450, m:tm-606, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46248
in-theory        46248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and ((E -> (E or F)) and (A -> (B -> ((C -> (D or C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46248.        ((A -> (B -> ((C -> (D or C)) and B))) and ((E -> (E or F)) and (A -> (B -> ((C -> (D or C)) and B))))), M:tm-443, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46249
in-theory        46249
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-409 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46249.        (((A -> (A or B)) or C) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-409, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46250
in-theory        46250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-400 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46250.        (((A -> (B -> (A and B))) or C) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-400, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46251
in-theory        46251
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-391 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46251.        ((((A and B) -> B) or C) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-391, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46252
in-theory        46252
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-382 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46252.        ((((A and B) -> A) or C) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-382, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46253
in-theory        46253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-373 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46253.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> ((G -> (H or G)) and F)))), M:tm-373, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46254
in-theory        46254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-364 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46254.        (((A -> (B -> A)) or C) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-364, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46255
in-theory        46255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-354 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46255.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-354, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46256
in-theory        46256
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-351 tm-606 ((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46256.        ((A or (B -> (C -> (B and C)))) -> (D -> ((E -> (F or E)) and D))), M:tm-351, m:tm-606, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46257
in-theory        46257
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> (A and D))))
theorem-size     13
proof            (modus-ponens tm-349 tm-606 ((A Am) (Bm (-> B (and Am B))) (C (and (-> Cm (or Dm Cm)) (-> B (and Am B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46257.        (A -> ((B -> (C or B)) and (D -> (A and D)))), M:tm-349, m:tm-606, u:((A Am) (Bm (-> B (and Am B))) (C (and (-> Cm (or Dm Cm)) (-> B (and Am B)))))
================================================================
tm-name          tm-46258
in-theory        46258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46258.        ((A -> (B -> ((C -> (D or C)) and B))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46259
in-theory        46259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) -> D) -> ((A -> ((B -> (C or B)) and A)) and D))
theorem-size     23
proof            (modus-ponens tm-339 tm-606 ((Am (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) B)) (A (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46259.        (((A -> ((B -> (C or B)) and A)) -> D) -> ((A -> ((B -> (C or B)) and A)) and D)), M:tm-339, m:tm-606, u:((Am (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) B)) (A (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46260
in-theory        46260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> ((E -> (F or E)) and D))))
theorem-size     21
proof            (modus-ponens tm-338 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46260.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> ((E -> (F or E)) and D)))), M:tm-338, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46261
in-theory        46261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> ((D -> (E or D)) and C)))
theorem-size     19
proof            (modus-ponens tm-335 tm-606 ((Am (-> A (and A B))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46261.        (((A -> B) or (A -> (A and B))) -> (C -> ((D -> (E or D)) and C))), M:tm-335, m:tm-606, u:((Am (-> A (and A B))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46262
in-theory        46262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (A -> (A and (B -> ((C -> (D or C)) and B)))))
theorem-size     25
proof            (modus-ponens tm-328 tm-606 ((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46262.        ((A -> (B -> ((C -> (D or C)) and B))) and (A -> (A and (B -> ((C -> (D or C)) and B))))), M:tm-328, m:tm-606, u:((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46263
in-theory        46263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and ((E -> (F -> (E and F))) and (A -> (B -> ((C -> (D or C)) and B)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46263.        ((A -> (B -> ((C -> (D or C)) and B))) and ((E -> (F -> (E and F))) and (A -> (B -> ((C -> (D or C)) and B))))), M:tm-327, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46264
in-theory        46264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (((E and F) -> F) and (A -> (B -> ((C -> (D or C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46264.        ((A -> (B -> ((C -> (D or C)) and B))) and (((E and F) -> F) and (A -> (B -> ((C -> (D or C)) and B))))), M:tm-326, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46265
in-theory        46265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (((E and F) -> E) and (A -> (B -> ((C -> (D or C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46265.        ((A -> (B -> ((C -> (D or C)) and B))) and (((E and F) -> E) and (A -> (B -> ((C -> (D or C)) and B))))), M:tm-325, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46266
in-theory        46266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> ((C -> (D or C)) and B)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46266.        ((A -> (B -> ((C -> (D or C)) and B))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> ((C -> (D or C)) and B))))), M:tm-324, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46267
in-theory        46267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and ((E -> (F -> E)) and (A -> (B -> ((C -> (D or C)) and B)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46267.        ((A -> (B -> ((C -> (D or C)) and B))) and ((E -> (F -> E)) and (A -> (B -> ((C -> (D or C)) and B))))), M:tm-323, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46268
in-theory        46268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46268.        ((A -> (B -> ((C -> (D or C)) and B))) and ((E and F) -> F)), M:tm-322, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46269
in-theory        46269
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> ((C -> (D or C)) and B)) -> E)) -> (B -> ((C -> (D or C)) and B))) and ((A and ((B -> ((C -> (D or C)) and B)) -> E)) -> E))
theorem-size     39
proof            (modus-ponens tm-321 tm-606 ((Am (and A (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) C))) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46269.        (((A and ((B -> ((C -> (D or C)) and B)) -> E)) -> (B -> ((C -> (D or C)) and B))) and ((A and ((B -> ((C -> (D or C)) and B)) -> E)) -> E)), M:tm-321, m:tm-606, u:((Am (and A (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) C))) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46270
in-theory        46270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46270.        ((A -> (B -> ((C -> (D or C)) and B))) and ((E and F) -> E)), M:tm-320, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46271
in-theory        46271
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> ((B -> (C or B)) and A)) -> D) and E) -> (A -> ((B -> (C or B)) and A))) and ((((A -> ((B -> (C or B)) and A)) -> D) and E) -> D))
theorem-size     39
proof            (modus-ponens tm-319 tm-606 ((Am (and (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46271.        (((((A -> ((B -> (C or B)) and A)) -> D) and E) -> (A -> ((B -> (C or B)) and A))) and ((((A -> ((B -> (C or B)) and A)) -> D) and E) -> D)), M:tm-319, m:tm-606, u:((Am (and (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46272
in-theory        46272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46272.        ((A -> (B -> ((C -> (D or C)) and B))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46273
in-theory        46273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C or B)) and A) -> D)) -> (A -> ((B -> (C or B)) and A))) and ((A -> (((B -> (C or B)) and A) -> D)) -> (A -> D)))
theorem-size     37
proof            (modus-ponens tm-317 tm-606 ((Am (-> Bm (-> (and (-> Cm (or Dm Cm)) Bm) C))) (A Bm) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46273.        (((A -> (((B -> (C or B)) and A) -> D)) -> (A -> ((B -> (C or B)) and A))) and ((A -> (((B -> (C or B)) and A) -> D)) -> (A -> D))), M:tm-317, m:tm-606, u:((Am (-> Bm (-> (and (-> Cm (or Dm Cm)) Bm) C))) (A Bm) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-46274
in-theory        46274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-606 ((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46274.        ((A -> (B -> ((C -> (D or C)) and B))) and (A -> A)), M:tm-316, m:tm-606, u:((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46275
in-theory        46275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46275.        ((A -> (B -> ((C -> (D or C)) and B))) and (E -> (F -> E))), M:tm-315, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46276
in-theory        46276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and ((A -> (not (B -> ((C -> (D or C)) and B)))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-606 ((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46276.        ((A -> (B -> ((C -> (D or C)) and B))) and ((A -> (not (B -> ((C -> (D or C)) and B)))) -> (not A))), M:tm-313, m:tm-606, u:((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46277
in-theory        46277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (((B -> ((C -> (D or C)) and B)) -> E) -> ((A or (B -> ((C -> (D or C)) and B))) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-606 ((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46277.        ((A -> (B -> ((C -> (D or C)) and B))) and (((B -> ((C -> (D or C)) and B)) -> E) -> ((A or (B -> ((C -> (D or C)) and B))) -> E))), M:tm-312, m:tm-606, u:((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46278
in-theory        46278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (E or (A -> (B -> ((C -> (D or C)) and B)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46278.        ((A -> (B -> ((C -> (D or C)) and B))) and (E or (A -> (B -> ((C -> (D or C)) and B))))), M:tm-311, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46279
in-theory        46279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and ((A -> (B -> ((C -> (D or C)) and B))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46279.        ((A -> (B -> ((C -> (D or C)) and B))) and ((A -> (B -> ((C -> (D or C)) and B))) or E)), M:tm-310, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46280
in-theory        46280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (E -> ((A -> (B -> ((C -> (D or C)) and B))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46280.        ((A -> (B -> ((C -> (D or C)) and B))) and (E -> ((A -> (B -> ((C -> (D or C)) and B))) and E))), M:tm-309, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46281
in-theory        46281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and ((A -> B) -> (A -> ((C -> (D or C)) and B))))
theorem-size     25
proof            (modus-ponens tm-306 tm-606 ((A Am) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46281.        ((A -> (B -> ((C -> (D or C)) and B))) and ((A -> B) -> (A -> ((C -> (D or C)) and B)))), M:tm-306, m:tm-606, u:((A Am) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-46282
in-theory        46282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (E -> (A -> (B -> ((C -> (D or C)) and B)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46282.        ((A -> (B -> ((C -> (D or C)) and B))) and (E -> (A -> (B -> ((C -> (D or C)) and B))))), M:tm-305, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46283
in-theory        46283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-303 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46283.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-303, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46284
in-theory        46284
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     21
proof            (modus-ponens tm-300 tm-606 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46284.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> ((E -> (F or E)) and D))), M:tm-300, m:tm-606, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46285
in-theory        46285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-270 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46285.        ((A -> (((B and C) -> C) and A)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-270, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46286
in-theory        46286
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-267 tm-606 ((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46286.        ((A or (((B and C) -> C) and A)) -> (D -> ((E -> (F or E)) and D))), M:tm-267, m:tm-606, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46287
in-theory        46287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-239 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46287.        ((A -> (((B and C) -> B) and A)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-239, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46288
in-theory        46288
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-236 tm-606 ((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46288.        ((A or (((B and C) -> B) and A)) -> (D -> ((E -> (F or E)) and D))), M:tm-236, m:tm-606, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46289
in-theory        46289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-210 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46289.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> ((G -> (H or G)) and F)))), M:tm-210, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46290
in-theory        46290
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((F -> (G or F)) and E)))
theorem-size     27
proof            (modus-ponens tm-207 tm-606 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46290.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> ((F -> (G or F)) and E))), M:tm-207, m:tm-606, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46291
in-theory        46291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     21
proof            (modus-ponens tm-183 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46291.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-183, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46292
in-theory        46292
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     19
proof            (modus-ponens tm-180 tm-606 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46292.        ((A or ((B -> (C -> B)) and A)) -> (D -> ((E -> (F or E)) and D))), M:tm-180, m:tm-606, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46293
in-theory        46293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-157 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46293.        ((A -> ((B and C) -> C)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-157, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46294
in-theory        46294
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-154 tm-606 ((Am (-> (and A B) B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46294.        ((A or ((B and C) -> C)) -> (D -> ((E -> (F or E)) and D))), M:tm-154, m:tm-606, u:((Am (-> (and A B) B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46295
in-theory        46295
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> ((C -> (D or C)) and B))
theorem-size     11
proof            (modus-ponens tm-152 tm-606 ((Am (and A Bm)) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-4 tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46295.        ((A and B) -> ((C -> (D or C)) and B)), M:tm-152, m:tm-606, u:((Am (and A Bm)) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-46296
in-theory        46296
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-147 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46296.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-147, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46297
in-theory        46297
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     25
proof            (modus-ponens tm-144 tm-606 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-5 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46297.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> ((E -> (F or E)) and D))), M:tm-144, m:tm-606, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46298
in-theory        46298
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (D or C)) and B)) -> E)) -> (B -> ((C -> (D or C)) and B)))
theorem-size     23
proof            (modus-ponens tm-142 tm-606 ((Am (and A (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) C))) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-5 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46298.        ((A and ((B -> ((C -> (D or C)) and B)) -> E)) -> (B -> ((C -> (D or C)) and B))), M:tm-142, m:tm-606, u:((Am (and A (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) C))) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46299
in-theory        46299
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (D or C)) and B)) -> B)) -> ((C -> (D or C)) and B))
theorem-size     21
proof            (modus-ponens tm-141 tm-606 ((Am (and A (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Bm))) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-4 tm-1 tm-5 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46299.        ((A and ((B -> ((C -> (D or C)) and B)) -> B)) -> ((C -> (D or C)) and B)), M:tm-141, m:tm-606, u:((Am (and A (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Bm))) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-46300
in-theory        46300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-134 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46300.        ((A -> ((B and C) -> B)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-134, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46301
in-theory        46301
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-131 tm-606 ((Am (-> (and A B) A)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46301.        ((A or ((B and C) -> B)) -> (D -> ((E -> (F or E)) and D))), M:tm-131, m:tm-606, u:((Am (-> (and A B) A)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46302
in-theory        46302
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> ((C -> (D or C)) and A))
theorem-size     11
proof            (modus-ponens tm-129 tm-606 ((Am (and Bm B)) (A Bm) (C (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-3 tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46302.        ((A and B) -> ((C -> (D or C)) and A)), M:tm-129, m:tm-606, u:((Am (and Bm B)) (A Bm) (C (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-46303
in-theory        46303
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     27
proof            (modus-ponens tm-125 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46303.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-125, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46304
in-theory        46304
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     25
proof            (modus-ponens tm-122 tm-606 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-5 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46304.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> ((E -> (F or E)) and D))), M:tm-122, m:tm-606, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46305
in-theory        46305
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C or B)) and A)) -> D) and E) -> (A -> ((B -> (C or B)) and A)))
theorem-size     23
proof            (modus-ponens tm-120 tm-606 ((Am (and (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-5 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46305.        ((((A -> ((B -> (C or B)) and A)) -> D) and E) -> (A -> ((B -> (C or B)) and A))), M:tm-120, m:tm-606, u:((Am (and (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46306
in-theory        46306
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C or B)) and A)) -> A) and D) -> ((B -> (C or B)) and A))
theorem-size     21
proof            (modus-ponens tm-119 tm-606 ((Am (and (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Bm) C)) (A Bm) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-3 tm-1 tm-5 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46306.        ((((A -> ((B -> (C or B)) and A)) -> A) and D) -> ((B -> (C or B)) and A)), M:tm-119, m:tm-606, u:((Am (and (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Bm) C)) (A Bm) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-46307
in-theory        46307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-113 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46307.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> ((G -> (H or G)) and F)))), M:tm-113, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46308
in-theory        46308
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((F -> (G or F)) and E)))
theorem-size     25
proof            (modus-ponens tm-110 tm-606 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46308.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> ((F -> (G or F)) and E))), M:tm-110, m:tm-606, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46309
in-theory        46309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))
theorem-size     19
proof            (modus-ponens tm-108 tm-606 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> Cm (or Dm Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46309.        ((A -> (B -> C)) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-108, m:tm-606, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> Cm (or Dm Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-46310
in-theory        46310
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     31
proof            (modus-ponens tm-105 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46310.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-105, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46311
in-theory        46311
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((E -> (F or E)) and D)))
theorem-size     29
proof            (modus-ponens tm-102 tm-606 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46311.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> ((E -> (F or E)) and D))), M:tm-102, m:tm-606, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46312
in-theory        46312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) and A) -> D)) -> (A -> ((B -> (C or B)) and A)))
theorem-size     21
proof            (modus-ponens tm-100 tm-606 ((Am (-> Bm (-> (and (-> Cm (or Dm Cm)) Bm) C))) (A Bm) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46312.        ((A -> (((B -> (C or B)) and A) -> D)) -> (A -> ((B -> (C or B)) and A))), M:tm-100, m:tm-606, u:((Am (-> Bm (-> (and (-> Cm (or Dm Cm)) Bm) C))) (A Bm) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-46313
in-theory        46313
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> A)))
theorem-size     11
proof            (modus-ponens tm-98 tm-606 ((A Am) (Bm (-> B Am)) (C (and (-> Cm (or Dm Cm)) (-> B Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46313.        (A -> ((B -> (C or B)) and (D -> A))), M:tm-98, m:tm-606, u:((A Am) (Bm (-> B Am)) (C (and (-> Cm (or Dm Cm)) (-> B Am))))
================================================================
tm-name          tm-46314
in-theory        46314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) -> D) -> (A -> ((B -> (C or B)) and A)))
theorem-size     21
proof            (modus-ponens tm-96 tm-606 ((Am (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) B)) (A (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46314.        (((A -> ((B -> (C or B)) and A)) -> D) -> (A -> ((B -> (C or B)) and A))), M:tm-96, m:tm-606, u:((Am (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) B)) (A (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46315
in-theory        46315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-95 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46315.        (((A -> B) -> (A -> A)) and (C -> (D -> ((E -> (F or E)) and D)))), M:tm-95, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46316
in-theory        46316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> ((D -> (E or D)) and C)))
theorem-size     17
proof            (modus-ponens tm-92 tm-606 ((Am (-> A A)) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46316.        (((A -> B) or (A -> A)) -> (C -> ((D -> (E or D)) and C))), M:tm-92, m:tm-606, u:((Am (-> A A)) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46317
in-theory        46317
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C -> ((D -> (E or D)) and C))))
theorem-size     13
proof            (modus-ponens tm-84 tm-606 ((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46317.        (A -> (B -> (C -> ((D -> (E or D)) and C)))), M:tm-84, m:tm-606, u:((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46318
in-theory        46318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-83 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46318.        ((A -> (B -> (C -> B))) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-83, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46319
in-theory        46319
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-80 tm-606 ((Am (-> A (-> B A))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46319.        ((A or (B -> (C -> B))) -> (D -> ((E -> (F or E)) and D))), M:tm-80, m:tm-606, u:((Am (-> A (-> B A))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46320
in-theory        46320
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> ((B -> (C or B)) and A)) -> D))) -> D)
theorem-size     15
proof            (modus-ponens tm-77 tm-606 ((Am (not (not (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) B)))) (A (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-5 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46320.        ((not (not ((A -> ((B -> (C or B)) and A)) -> D))) -> D), M:tm-77, m:tm-606, u:((Am (not (not (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) B)))) (A (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46321
in-theory        46321
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> ((D -> (E or D)) and C))))
theorem-size     17
proof            (modus-ponens tm-76 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46321.        (((not (not A)) -> A) and (B -> (C -> ((D -> (E or D)) and C)))), M:tm-76, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46322
in-theory        46322
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> ((C -> (D or C)) and B)))
theorem-size     15
proof            (modus-ponens tm-73 tm-606 ((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46322.        (((not (not A)) or A) -> (B -> ((C -> (D or C)) and B))), M:tm-73, m:tm-606, u:((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46323
in-theory        46323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> ((E -> (F or E)) and D))))
theorem-size     23
proof            (modus-ponens tm-69 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46323.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> ((E -> (F or E)) and D)))), M:tm-69, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46324
in-theory        46324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((D -> (E or D)) and C)))
theorem-size     21
proof            (modus-ponens tm-66 tm-606 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-5 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46324.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> ((D -> (E or D)) and C))), M:tm-66, m:tm-606, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46325
in-theory        46325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> ((C -> (D or C)) and B)))
theorem-size     15
proof            (modus-ponens tm-55 tm-606 ((Am (-> A Bm)) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-8 tm-1 tm-5 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46325.        ((A -> B) -> ((A or B) -> ((C -> (D or C)) and B))), M:tm-55, m:tm-606, u:((Am (-> A Bm)) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-46326
in-theory        46326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-54 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46326.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-54, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46327
in-theory        46327
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (F or E)) and D)))
theorem-size     23
proof            (modus-ponens tm-51 tm-606 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46327.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> ((E -> (F or E)) and D))), M:tm-51, m:tm-606, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46328
in-theory        46328
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> ((D -> (E or D)) and C)))
theorem-size     15
proof            (modus-ponens tm-50 tm-606 ((Am (or A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46328.        ((A or (B or A)) -> (C -> ((D -> (E or D)) and C))), M:tm-50, m:tm-606, u:((Am (or A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46329
in-theory        46329
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> ((D -> (E or D)) and C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-606 ((Am (or A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46329.        ((A or (A or B)) -> (C -> ((D -> (E or D)) and C))), M:tm-49, m:tm-606, u:((Am (or A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46330
in-theory        46330
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> ((D -> (E or D)) and C)))
theorem-size     17
proof            (modus-ponens tm-48 tm-606 ((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46330.        ((A or (B -> (A and B))) -> (C -> ((D -> (E or D)) and C))), M:tm-48, m:tm-606, u:((Am (-> A (and B A))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46331
in-theory        46331
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D -> (E or D)) and C)))
theorem-size     15
proof            (modus-ponens tm-47 tm-606 ((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46331.        (((A and B) or B) -> (C -> ((D -> (E or D)) and C))), M:tm-47, m:tm-606, u:((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46332
in-theory        46332
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D -> (E or D)) and C)))
theorem-size     15
proof            (modus-ponens tm-46 tm-606 ((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46332.        (((A and B) or A) -> (C -> ((D -> (E or D)) and C))), M:tm-46, m:tm-606, u:((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46333
in-theory        46333
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F or E)) and D)))
theorem-size     23
proof            (modus-ponens tm-45 tm-606 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46333.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F or E)) and D))), M:tm-45, m:tm-606, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46334
in-theory        46334
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D -> (E or D)) and C)))
theorem-size     15
proof            (modus-ponens tm-44 tm-606 ((Am (-> A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46334.        ((A or (B -> A)) -> (C -> ((D -> (E or D)) and C))), M:tm-44, m:tm-606, u:((Am (-> A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46335
in-theory        46335
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-42 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46335.        ((A -> (B or A)) and (C -> (D -> ((E -> (F or E)) and D)))), M:tm-42, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46336
in-theory        46336
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-32 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46336.        ((A -> (A or B)) and (C -> (D -> ((E -> (F or E)) and D)))), M:tm-32, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46337
in-theory        46337
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B -> ((C -> (D or C)) and B))))
theorem-size     13
proof            (modus-ponens tm-24 tm-606 ((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46337.        (A -> (A and (B -> ((C -> (D or C)) and B)))), M:tm-24, m:tm-606, u:((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46338
in-theory        46338
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-23 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46338.        ((A -> (B -> (A and B))) and (C -> (D -> ((E -> (F or E)) and D)))), M:tm-23, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46339
in-theory        46339
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-22 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46339.        (((A and B) -> B) and (C -> (D -> ((E -> (F or E)) and D)))), M:tm-22, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46340
in-theory        46340
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-21 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46340.        (((A and B) -> A) and (C -> (D -> ((E -> (F or E)) and D)))), M:tm-21, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46341
in-theory        46341
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-20 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46341.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-20, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46342
in-theory        46342
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> ((E -> (F or E)) and D))))
theorem-size     17
proof            (modus-ponens tm-19 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46342.        ((A -> (B -> A)) and (C -> (D -> ((E -> (F or E)) and D)))), M:tm-19, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46343
in-theory        46343
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> ((C -> (D or C)) and B)) -> E)) -> E)
theorem-size     15
proof            (modus-ponens tm-17 tm-606 ((Am (and A (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) C))) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-5 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46343.        ((A and ((B -> ((C -> (D or C)) and B)) -> E)) -> E), M:tm-17, m:tm-606, u:((Am (and A (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) C))) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46344
in-theory        46344
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> ((B -> (C or B)) and A)) -> D) and E) -> D)
theorem-size     15
proof            (modus-ponens tm-15 tm-606 ((Am (and (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-5 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46344.        ((((A -> ((B -> (C or B)) and A)) -> D) and E) -> D), M:tm-15, m:tm-606, u:((Am (and (-> (-> Bm (and (-> Cm (or Dm Cm)) Bm)) B) C)) (A (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46345
in-theory        46345
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) and A) -> D)) -> (A -> D))
theorem-size     15
proof            (modus-ponens tm-13 tm-606 ((Am (-> Bm (-> (and (-> Cm (or Dm Cm)) Bm) C))) (A Bm) (B (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46345.        ((A -> (((B -> (C or B)) and A) -> D)) -> (A -> D)), M:tm-13, m:tm-606, u:((Am (-> Bm (-> (and (-> Cm (or Dm Cm)) Bm) C))) (A Bm) (B (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-46346
in-theory        46346
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B -> ((C -> (D or C)) and B)))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-606 ((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-9 tm-1 tm-5 tm-7)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46346.        ((A -> (not (B -> ((C -> (D or C)) and B)))) -> (not A)), M:tm-9, m:tm-606, u:((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46347
in-theory        46347
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) -> D) -> ((E or (A -> ((B -> (C or B)) and A))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-606 ((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46347.        (((A -> ((B -> (C or B)) and A)) -> D) -> ((E or (A -> ((B -> (C or B)) and A))) -> D)), M:tm-8, m:tm-606, u:((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-46348
in-theory        46348
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C -> ((D -> (E or D)) and C))))
theorem-size     13
proof            (modus-ponens tm-7 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-7 tm-1 tm-5)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46348.        (A or (B -> (C -> ((D -> (E or D)) and C)))), M:tm-7, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46349
in-theory        46349
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-6 tm-1 tm-5 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46349.        ((A -> (B -> ((C -> (D or C)) and B))) or E), M:tm-6, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46350
in-theory        46350
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> ((D -> (E or D)) and C))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46350.        (A -> ((B -> (C -> ((D -> (E or D)) and C))) and A)), M:tm-5, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-46351
in-theory        46351
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> ((C -> (D or C)) and B)))
theorem-size     13
proof            (modus-ponens tm-2 tm-606 ((A Am) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-46351.        ((A -> B) -> (A -> ((C -> (D or C)) and B))), M:tm-2, m:tm-606, u:((A Am) (B Bm) (C (and (-> Cm (or Dm Cm)) Bm)))
================================================================
tm-name          tm-46352
in-theory        46352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46352.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-605, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46353
in-theory        46353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46353.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (B or A)) and (C -> (D -> (E or D)))))), M:tm-595, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46354
in-theory        46354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46354.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-550, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46355
in-theory        46355
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46355.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-540, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46356
in-theory        46356
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46356.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-530, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46357
in-theory        46357
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46357.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-520, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46358
in-theory        46358
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46358.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-510, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46359
in-theory        46359
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46359.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-500, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46360
in-theory        46360
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46360.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (I or H))))), M:tm-490, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46361
in-theory        46361
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46361.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-480, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46362
in-theory        46362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46362.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-469, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46363
in-theory        46363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46363.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and (F -> (F or G))), M:tm-456, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46364
in-theory        46364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46364.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-453, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46365
in-theory        46365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46365.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (B or A)) and (C -> (D -> (E or D)))))), M:tm-443, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46366
in-theory        46366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46366.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-409, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46367
in-theory        46367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46367.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-400, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46368
in-theory        46368
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46368.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-391, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46369
in-theory        46369
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46369.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-382, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46370
in-theory        46370
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46370.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (G -> (H -> (I or H))))), M:tm-373, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46371
in-theory        46371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46371.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-364, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46372
in-theory        46372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46372.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-354, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46373
in-theory        46373
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46373.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46374
in-theory        46374
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46374.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (G or F))))), M:tm-338, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46375
in-theory        46375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> (D -> (E or D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46375.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (C -> (D -> (E or D)))))), M:tm-327, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46376
in-theory        46376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46376.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and (((F and G) -> G) and ((A -> (B or A)) and (C -> (D -> (E or D)))))), M:tm-326, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46377
in-theory        46377
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46377.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and (((F and G) -> F) and ((A -> (B or A)) and (C -> (D -> (E or D)))))), M:tm-325, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46378
in-theory        46378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> (D -> (E or D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46378.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (C -> (D -> (E or D)))))), M:tm-324, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46379
in-theory        46379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46379.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (B or A)) and (C -> (D -> (E or D)))))), M:tm-323, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46380
in-theory        46380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46380.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and ((F and G) -> G)), M:tm-322, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46381
in-theory        46381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46381.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and ((F and G) -> F)), M:tm-320, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46382
in-theory        46382
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46382.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46383
in-theory        46383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46383.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and (F -> (G -> F))), M:tm-315, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46384
in-theory        46384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and (F or ((A -> (B or A)) and (C -> (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46384.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and (F or ((A -> (B or A)) and (C -> (D -> (E or D)))))), M:tm-311, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46385
in-theory        46385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and (((A -> (B or A)) and (C -> (D -> (E or D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46385.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and (((A -> (B or A)) and (C -> (D -> (E or D)))) or F)), M:tm-310, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46386
in-theory        46386
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and (F -> (((A -> (B or A)) and (C -> (D -> (E or D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46386.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and (F -> (((A -> (B or A)) and (C -> (D -> (E or D)))) and F))), M:tm-309, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46387
in-theory        46387
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and (C -> (D -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-607 ((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46387.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and (C -> (D -> (E or D)))), M:tm-308, m:tm-607, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-46388
in-theory        46388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-607 ((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46388.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and (A -> (B or A))), M:tm-307, m:tm-607, u:((A (-> Am (or Bm Am))) (B (-> Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-46389
in-theory        46389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and (F -> ((A -> (B or A)) and (C -> (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46389.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and (F -> ((A -> (B or A)) and (C -> (D -> (E or D)))))), M:tm-305, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46390
in-theory        46390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46390.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-303, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46391
in-theory        46391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46391.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-270, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46392
in-theory        46392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46392.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-239, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46393
in-theory        46393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46393.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (G -> (H -> (I or H))))), M:tm-210, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46394
in-theory        46394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46394.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-183, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46395
in-theory        46395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46395.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-157, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46396
in-theory        46396
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46396.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-147, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46397
in-theory        46397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46397.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-134, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46398
in-theory        46398
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46398.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-125, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46399
in-theory        46399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46399.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (G -> (H -> (I or H))))), M:tm-113, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46400
in-theory        46400
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46400.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-105, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46401
in-theory        46401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46401.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (E -> (F -> (G or F))))), M:tm-95, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46402
in-theory        46402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46402.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-83, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46403
in-theory        46403
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46403.        (((not (not A)) -> A) and ((B -> (C or B)) and (D -> (E -> (F or E))))), M:tm-76, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46404
in-theory        46404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46404.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (E -> (F -> (G or F))))), M:tm-69, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46405
in-theory        46405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46405.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-54, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46406
in-theory        46406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46406.        ((A -> (B or A)) and ((C -> (D or C)) and (E -> (F -> (G or F))))), M:tm-42, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46407
in-theory        46407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46407.        ((A -> (A or B)) and ((C -> (D or C)) and (E -> (F -> (G or F))))), M:tm-32, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46408
in-theory        46408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46408.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (E -> (F -> (G or F))))), M:tm-23, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46409
in-theory        46409
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46409.        (((A and B) -> B) and ((C -> (D or C)) and (E -> (F -> (G or F))))), M:tm-22, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46410
in-theory        46410
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46410.        (((A and B) -> A) and ((C -> (D or C)) and (E -> (F -> (G or F))))), M:tm-21, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46411
in-theory        46411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46411.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-20, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46412
in-theory        46412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46412.        ((A -> (B -> A)) and ((C -> (D or C)) and (E -> (F -> (G or F))))), M:tm-19, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46413
in-theory        46413
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46413.        (A or ((B -> (C or B)) and (D -> (E -> (F or E))))), M:tm-7, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46414
in-theory        46414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-7 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46414.        (((A -> (B or A)) and (C -> (D -> (E or D)))) or F), M:tm-6, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46415
in-theory        46415
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (D -> (E -> (F or E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46415.        (A -> (((B -> (C or B)) and (D -> (E -> (F or E)))) and A)), M:tm-5, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46416
in-theory        46416
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46416.        (A -> ((B -> (C or B)) and (D -> (E -> (F or E))))), M:tm-1, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46417
in-theory        46417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46417.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-605, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46418
in-theory        46418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46418.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (A or B)) and (C -> (D -> (E or D)))))), M:tm-595, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46419
in-theory        46419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46419.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-550, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46420
in-theory        46420
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46420.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-540, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46421
in-theory        46421
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46421.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-530, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46422
in-theory        46422
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46422.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-520, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46423
in-theory        46423
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46423.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-510, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46424
in-theory        46424
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46424.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-500, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46425
in-theory        46425
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46425.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (I or H))))), M:tm-490, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46426
in-theory        46426
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46426.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-480, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46427
in-theory        46427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46427.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-469, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46428
in-theory        46428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46428.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and (F -> (F or G))), M:tm-456, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46429
in-theory        46429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46429.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-453, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46430
in-theory        46430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46430.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (A or B)) and (C -> (D -> (E or D)))))), M:tm-443, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46431
in-theory        46431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46431.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-409, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46432
in-theory        46432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46432.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-400, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46433
in-theory        46433
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46433.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-391, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46434
in-theory        46434
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46434.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-382, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46435
in-theory        46435
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46435.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (G -> (H -> (I or H))))), M:tm-373, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46436
in-theory        46436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46436.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-364, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46437
in-theory        46437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46437.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-354, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46438
in-theory        46438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46438.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46439
in-theory        46439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46439.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (G or F))))), M:tm-338, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46440
in-theory        46440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> (D -> (E or D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46440.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (C -> (D -> (E or D)))))), M:tm-327, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46441
in-theory        46441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46441.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and (((F and G) -> G) and ((A -> (A or B)) and (C -> (D -> (E or D)))))), M:tm-326, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46442
in-theory        46442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46442.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and (((F and G) -> F) and ((A -> (A or B)) and (C -> (D -> (E or D)))))), M:tm-325, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46443
in-theory        46443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> (D -> (E or D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46443.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (C -> (D -> (E or D)))))), M:tm-324, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46444
in-theory        46444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46444.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (A or B)) and (C -> (D -> (E or D)))))), M:tm-323, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46445
in-theory        46445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46445.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and ((F and G) -> G)), M:tm-322, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46446
in-theory        46446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46446.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and ((F and G) -> F)), M:tm-320, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46447
in-theory        46447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46447.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46448
in-theory        46448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46448.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and (F -> (G -> F))), M:tm-315, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46449
in-theory        46449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and (F or ((A -> (A or B)) and (C -> (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46449.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and (F or ((A -> (A or B)) and (C -> (D -> (E or D)))))), M:tm-311, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46450
in-theory        46450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and (((A -> (A or B)) and (C -> (D -> (E or D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46450.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and (((A -> (A or B)) and (C -> (D -> (E or D)))) or F)), M:tm-310, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46451
in-theory        46451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and (F -> (((A -> (A or B)) and (C -> (D -> (E or D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46451.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and (F -> (((A -> (A or B)) and (C -> (D -> (E or D)))) and F))), M:tm-309, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46452
in-theory        46452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and (C -> (D -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-608 ((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46452.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and (C -> (D -> (E or D)))), M:tm-308, m:tm-608, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-46453
in-theory        46453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and (A -> (A or B)))
theorem-size     19
proof            (modus-ponens tm-307 tm-608 ((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46453.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and (A -> (A or B))), M:tm-307, m:tm-608, u:((A (-> Am (or Am Bm))) (B (-> Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-46454
in-theory        46454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and (F -> ((A -> (A or B)) and (C -> (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46454.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and (F -> ((A -> (A or B)) and (C -> (D -> (E or D)))))), M:tm-305, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46455
in-theory        46455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46455.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-303, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46456
in-theory        46456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46456.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-270, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46457
in-theory        46457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46457.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-239, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46458
in-theory        46458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46458.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (G -> (H -> (I or H))))), M:tm-210, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46459
in-theory        46459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46459.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-183, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46460
in-theory        46460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46460.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-157, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46461
in-theory        46461
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46461.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-147, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46462
in-theory        46462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46462.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-134, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46463
in-theory        46463
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46463.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-125, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46464
in-theory        46464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46464.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (G -> (H -> (I or H))))), M:tm-113, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46465
in-theory        46465
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46465.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-105, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46466
in-theory        46466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46466.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (E -> (F -> (G or F))))), M:tm-95, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46467
in-theory        46467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46467.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-83, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46468
in-theory        46468
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46468.        (((not (not A)) -> A) and ((B -> (B or C)) and (D -> (E -> (F or E))))), M:tm-76, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46469
in-theory        46469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-6 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46469.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (E -> (F -> (G or F))))), M:tm-69, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46470
in-theory        46470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46470.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-54, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46471
in-theory        46471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46471.        ((A -> (B or A)) and ((C -> (C or D)) and (E -> (F -> (G or F))))), M:tm-42, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46472
in-theory        46472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46472.        ((A -> (A or B)) and ((C -> (C or D)) and (E -> (F -> (G or F))))), M:tm-32, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46473
in-theory        46473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46473.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (E -> (F -> (G or F))))), M:tm-23, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46474
in-theory        46474
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46474.        (((A and B) -> B) and ((C -> (C or D)) and (E -> (F -> (G or F))))), M:tm-22, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46475
in-theory        46475
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46475.        (((A and B) -> A) and ((C -> (C or D)) and (E -> (F -> (G or F))))), M:tm-21, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46476
in-theory        46476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46476.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-20, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46477
in-theory        46477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46477.        ((A -> (B -> A)) and ((C -> (C or D)) and (E -> (F -> (G or F))))), M:tm-19, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46478
in-theory        46478
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-6 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46478.        (A or ((B -> (B or C)) and (D -> (E -> (F or E))))), M:tm-7, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46479
in-theory        46479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-1 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46479.        (((A -> (A or B)) and (C -> (D -> (E or D)))) or F), M:tm-6, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46480
in-theory        46480
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (D -> (E -> (F or E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46480.        (A -> (((B -> (B or C)) and (D -> (E -> (F or E)))) and A)), M:tm-5, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46481
in-theory        46481
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-6 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-46481.        (A -> ((B -> (B or C)) and (D -> (E -> (F or E))))), M:tm-1, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46482
in-theory        46482
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-609 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-46482.        ((A -> (B -> (C or B))) and (D -> (E or D))), M:tm-609, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-46483
in-theory        46483
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-46483.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or D))), M:tm-609, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-46484
in-theory        46484
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or E)))
theorem-size     31
proof            (modus-ponens tm-609 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-46484.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or E))), M:tm-609, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-46485
in-theory        46485
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-46485.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or D))), M:tm-609, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-46486
in-theory        46486
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-46486.        (((A -> B) -> (((C and A) or A) -> B)) and (D -> (E or D))), M:tm-609, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-46487
in-theory        46487
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-609 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-46487.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (D -> (E or D))), M:tm-609, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-46488
in-theory        46488
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-46488.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (D -> (E or D))), M:tm-609, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-46489
in-theory        46489
times-derived    2
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-46489.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (D -> (E or D))), M:tm-609, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-46490
in-theory        46490
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F or E)))
theorem-size     33
proof            (modus-ponens tm-609 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-46490.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and (E -> (F or E))), M:tm-609, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-46491
in-theory        46491
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-46491.        ((A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or E))), M:tm-609, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-46492
in-theory        46492
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-46492.        ((((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D) and (E -> (F or E))), M:tm-609, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-46493
in-theory        46493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-46493.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (E -> (F or E))), M:tm-609, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-46494
in-theory        46494
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-609 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-46494.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (D -> (E or D))), M:tm-609, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-46495
in-theory        46495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-46495.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (E -> (F or E))), M:tm-609, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-46496
in-theory        46496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-609 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-46496.        (((A -> (not (B -> A))) -> (not A)) and (C -> (D or C))), M:tm-609, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-46497
in-theory        46497
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (D -> (E or D)))
theorem-size     27
proof            (modus-ponens tm-609 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-46497.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (D -> (E or D))), M:tm-609, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-46498
in-theory        46498
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-609 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-46498.        ((((A and B) -> (not A)) -> (not (A and B))) and (C -> (D or C))), M:tm-609, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-46499
in-theory        46499
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-609 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-46499.        ((((A and B) -> (not B)) -> (not (A and B))) and (C -> (D or C))), M:tm-609, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-46500
in-theory        46500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-609 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-46500.        (((A -> (not (B -> (A and B)))) -> (not A)) and (C -> (D or C))), M:tm-609, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-46501
in-theory        46501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-609 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-46501.        (((A -> (not (A or B))) -> (not A)) and (C -> (D or C))), M:tm-609, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-46502
in-theory        46502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-609 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-46502.        (((A -> (not (B or A))) -> (not A)) and (C -> (D or C))), M:tm-609, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-46503
in-theory        46503
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-609 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-46503.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (D -> (E or D))), M:tm-609, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-46504
in-theory        46504
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (C -> (D or C)))
theorem-size     23
proof            (modus-ponens tm-609 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-46504.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (C -> (D or C))), M:tm-609, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-46505
in-theory        46505
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (D -> (E or D)))
theorem-size     29
proof            (modus-ponens tm-609 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-46505.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and (D -> (E or D))), M:tm-609, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-46506
in-theory        46506
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-46506.        ((A or ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (E or D))), M:tm-609, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-46507
in-theory        46507
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-46507.        ((((A -> B) -> ((A -> (not B)) -> (not A))) or C) and (D -> (E or D))), M:tm-609, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-46508
in-theory        46508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-46508.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (D -> (E or D))), M:tm-609, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-46509
in-theory        46509
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (C -> (D or C)))
theorem-size     21
proof            (modus-ponens tm-609 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-46509.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (C -> (D or C))), M:tm-609, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-46510
in-theory        46510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-46510.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (D -> (E or D))), M:tm-609, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-46511
in-theory        46511
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (B -> (C or B)))
theorem-size     17
proof            (modus-ponens tm-609 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-46511.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (B -> (C or B))), M:tm-609, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-46512
in-theory        46512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-609 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-10)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-46512.        (((A -> B) -> (((not (not A)) or A) -> B)) and (C -> (D or C))), M:tm-609, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-46513
in-theory        46513
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((not (not B)) -> B)) and (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-609 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-46513.        ((A or ((not (not B)) -> B)) and (C -> (D or C))), M:tm-609, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-46514
in-theory        46514
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> A) or B) and (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-609 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-46514.        ((((not (not A)) -> A) or B) and (C -> (D or C))), M:tm-609, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-46515
in-theory        46515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-609 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-46515.        ((A -> (((not (not B)) -> B) and A)) and (C -> (D or C))), M:tm-609, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-46516
in-theory        46516
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (C -> (D or C)))
theorem-size     21
proof            (modus-ponens tm-609 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-46516.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (C -> (D or C))), M:tm-609, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-46517
in-theory        46517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-609 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-46517.        ((A -> ((not (not B)) -> B)) and (C -> (D or C))), M:tm-609, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-46518
in-theory        46518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-46518.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (D -> (E or D))), M:tm-609, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-46519
in-theory        46519
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-46519.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (E -> (F or E))), M:tm-609, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-46520
in-theory        46520
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> C)))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-46520.        ((A or (B -> (C -> (D -> C)))) and (E -> (F or E))), M:tm-609, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-46521
in-theory        46521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-46521.        (((A -> (B -> (C -> B))) or D) and (E -> (F or E))), M:tm-609, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-46522
in-theory        46522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-46522.        ((A -> ((B -> (C -> (D -> C))) and A)) and (E -> (F or E))), M:tm-609, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-46523
in-theory        46523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-46523.        (((A -> B) -> (A -> (C -> B))) and (D -> (E or D))), M:tm-609, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-46524
in-theory        46524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-46524.        ((A -> (B -> (C -> (D -> C)))) and (E -> (F or E))), M:tm-609, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-46525
in-theory        46525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and (B -> (C or B)))
theorem-size     9
proof            (modus-ponens tm-609 tm-86 ((A (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       97
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-46525.        ((A -> A) and (B -> (C or B))), M:tm-609, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-46526
in-theory        46526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-46526.        (((A -> (B -> C)) -> (A -> (B -> C))) and (D -> (E or D))), M:tm-609, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-46527
in-theory        46527
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-609 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-46527.        (((A and B) -> (A and B)) and (C -> (D or C))), M:tm-609, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-46528
in-theory        46528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-609 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-46528.        (((A -> B) -> (A -> B)) and (C -> (D or C))), M:tm-609, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-46529
in-theory        46529
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and (B -> (C or B)))
theorem-size     13
proof            (modus-ponens tm-609 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-46529.        (((not (not A)) -> (not (not A))) and (B -> (C or B))), M:tm-609, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-46530
in-theory        46530
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (C -> (D or C)))
theorem-size     19
proof            (modus-ponens tm-609 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-46530.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (C -> (D or C))), M:tm-609, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-46531
in-theory        46531
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-46531.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (D -> (E or D))), M:tm-609, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-46532
in-theory        46532
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> B))) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-46532.        ((A or ((B -> C) -> (B -> B))) and (D -> (E or D))), M:tm-609, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-46533
in-theory        46533
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) or C) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-46533.        ((((A -> B) -> (A -> A)) or C) and (D -> (E or D))), M:tm-609, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-46534
in-theory        46534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-46534.        ((A -> (((B -> C) -> (B -> B)) and A)) and (D -> (E or D))), M:tm-609, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-46535
in-theory        46535
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-609 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-46535.        ((((A -> B) -> A) -> ((A -> B) -> A)) and (C -> (D or C))), M:tm-609, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-46536
in-theory        46536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-46536.        ((A -> ((B -> C) -> (B -> B))) and (D -> (E or D))), M:tm-609, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-46537
in-theory        46537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-46537.        (((A -> ((B -> A) -> C)) -> (A -> C)) and (D -> (E or D))), M:tm-609, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-46538
in-theory        46538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-609 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-46538.        (((A -> (A -> B)) -> (A -> B)) and (C -> (D or C))), M:tm-609, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-46539
in-theory        46539
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-609 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-46539.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (D -> (E or D))), M:tm-609, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-46540
in-theory        46540
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (D -> (E or D)))
theorem-size     37
proof            (modus-ponens tm-609 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-46540.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (D -> (E or D))), M:tm-609, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-46541
in-theory        46541
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (E -> (F or E)))
theorem-size     39
proof            (modus-ponens tm-609 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-46541.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and (E -> (F or E))), M:tm-609, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-46542
in-theory        46542
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-46542.        ((A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (F or E))), M:tm-609, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-46543
in-theory        46543
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-46543.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D) and (E -> (F or E))), M:tm-609, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-46544
in-theory        46544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (E -> (F or E)))
theorem-size     29
proof            (modus-ponens tm-609 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-46544.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (E -> (F or E))), M:tm-609, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-46545
in-theory        46545
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (D -> (E or D)))
theorem-size     35
proof            (modus-ponens tm-609 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-46545.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (D -> (E or D))), M:tm-609, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-46546
in-theory        46546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-46546.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (E -> (F or E))), M:tm-609, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-46547
in-theory        46547
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (E -> (F or E)))
theorem-size     29
proof            (modus-ponens tm-609 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-46547.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-46548
in-theory        46548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-46548.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (E -> (F or E))), M:tm-609, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-46549
in-theory        46549
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (F -> (G or F)))
theorem-size     39
proof            (modus-ponens tm-609 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-46549.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and (F -> (G or F))), M:tm-609, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-46550
in-theory        46550
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46550.        ((A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G or F))), M:tm-609, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-46551
in-theory        46551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46551.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (G or F))), M:tm-609, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-46552
in-theory        46552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46552.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (G or F))), M:tm-609, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-46553
in-theory        46553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-46553.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (E -> (F or E))), M:tm-609, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-46554
in-theory        46554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46554.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G or F))), M:tm-609, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-46555
in-theory        46555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-609 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-46555.        ((((A -> B) and A) -> B) and (C -> (D or C))), M:tm-609, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-46556
in-theory        46556
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-46556.        (((((A -> (B -> A)) -> C) and D) -> C) and (E -> (F or E))), M:tm-609, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-46557
in-theory        46557
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-46557.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (F -> (G or F))), M:tm-609, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-46558
in-theory        46558
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (D -> (E or D)))
theorem-size     27
proof            (modus-ponens tm-609 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-46558.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (D -> (E or D))), M:tm-609, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-46559
in-theory        46559
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-46559.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and (D -> (E or D))), M:tm-609, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-46560
in-theory        46560
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (D -> (E or D)))
theorem-size     31
proof            (modus-ponens tm-609 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-46560.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (D -> (E or D))), M:tm-609, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-46561
in-theory        46561
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (E -> (F or E)))
theorem-size     33
proof            (modus-ponens tm-609 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-46561.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-46562
in-theory        46562
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-46562.        ((A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (F or E))), M:tm-609, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-46563
in-theory        46563
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-46563.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D) and (E -> (F or E))), M:tm-609, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-46564
in-theory        46564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-46564.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (E -> (F or E))), M:tm-609, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-46565
in-theory        46565
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (D -> (E or D)))
theorem-size     29
proof            (modus-ponens tm-609 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-46565.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (D -> (E or D))), M:tm-609, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-46566
in-theory        46566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-46566.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (E -> (F or E))), M:tm-609, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-46567
in-theory        46567
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-46567.        ((((((A and B) -> A) -> C) and D) -> C) and (E -> (F or E))), M:tm-609, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-46568
in-theory        46568
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-46568.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (D -> (E or D))), M:tm-609, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-46569
in-theory        46569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-46569.        (((A -> (not ((B and C) -> B))) -> (not A)) and (D -> (E or D))), M:tm-609, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-46570
in-theory        46570
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-46570.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and (E -> (F or E))), M:tm-609, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-46571
in-theory        46571
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> C))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-46571.        ((A or (B -> ((C and D) -> C))) and (E -> (F or E))), M:tm-609, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-46572
in-theory        46572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-46572.        (((A -> ((B and C) -> B)) or D) and (E -> (F or E))), M:tm-609, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-46573
in-theory        46573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-46573.        ((A -> ((B -> ((C and D) -> C)) and A)) and (E -> (F or E))), M:tm-609, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-46574
in-theory        46574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-46574.        (((A -> (B and C)) -> (A -> B)) and (D -> (E or D))), M:tm-609, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-46575
in-theory        46575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-46575.        ((A -> (B -> ((C and D) -> C))) and (E -> (F or E))), M:tm-609, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-46576
in-theory        46576
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-609 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-46576.        (((A and (A -> B)) -> B) and (C -> (D or C))), M:tm-609, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-46577
in-theory        46577
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-46577.        (((A and ((B -> (C -> B)) -> D)) -> D) and (E -> (F or E))), M:tm-609, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-46578
in-theory        46578
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-46578.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and (F -> (G or F))), M:tm-609, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-46579
in-theory        46579
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-46579.        (((A and (((B and C) -> B) -> D)) -> D) and (E -> (F or E))), M:tm-609, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-46580
in-theory        46580
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (D -> (E or D)))
theorem-size     27
proof            (modus-ponens tm-609 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-46580.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (D -> (E or D))), M:tm-609, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-46581
in-theory        46581
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-46581.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (D -> (E or D))), M:tm-609, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-46582
in-theory        46582
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (D -> (E or D)))
theorem-size     31
proof            (modus-ponens tm-609 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-46582.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (D -> (E or D))), M:tm-609, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-46583
in-theory        46583
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (E -> (F or E)))
theorem-size     33
proof            (modus-ponens tm-609 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-46583.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-46584
in-theory        46584
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-46584.        ((A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (F or E))), M:tm-609, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-46585
in-theory        46585
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-46585.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D) and (E -> (F or E))), M:tm-609, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-46586
in-theory        46586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-46586.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (E -> (F or E))), M:tm-609, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-46587
in-theory        46587
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (D -> (E or D)))
theorem-size     29
proof            (modus-ponens tm-609 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-46587.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (D -> (E or D))), M:tm-609, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-46588
in-theory        46588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-46588.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (E -> (F or E))), M:tm-609, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-46589
in-theory        46589
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-46589.        (((A and (((B and C) -> C) -> D)) -> D) and (E -> (F or E))), M:tm-609, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-46590
in-theory        46590
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-46590.        ((((((A and B) -> B) -> C) and D) -> C) and (E -> (F or E))), M:tm-609, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-46591
in-theory        46591
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-46591.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (D -> (E or D))), M:tm-609, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-46592
in-theory        46592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-46592.        (((A -> (not ((B and C) -> C))) -> (not A)) and (D -> (E or D))), M:tm-609, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-46593
in-theory        46593
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-46593.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and (E -> (F or E))), M:tm-609, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-46594
in-theory        46594
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C and D) -> D))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-46594.        ((A or (B -> ((C and D) -> D))) and (E -> (F or E))), M:tm-609, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-46595
in-theory        46595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-46595.        (((A -> ((B and C) -> C)) or D) and (E -> (F or E))), M:tm-609, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-46596
in-theory        46596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-46596.        ((A -> ((B -> ((C and D) -> D)) and A)) and (E -> (F or E))), M:tm-609, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-46597
in-theory        46597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-46597.        (((A -> (B and C)) -> (A -> C)) and (D -> (E or D))), M:tm-609, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-46598
in-theory        46598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-46598.        ((A -> (B -> ((C and D) -> D))) and (E -> (F or E))), M:tm-609, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-46599
in-theory        46599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-46599.        (((A -> (B -> A)) and (C -> (D -> C))) and (E -> (F or E))), M:tm-609, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-46600
in-theory        46600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-46600.        (((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-46601
in-theory        46601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> C)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-46601.        (((A -> (B -> A)) and ((C and D) -> C)) and (E -> (F or E))), M:tm-609, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-46602
in-theory        46602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C and D) -> D)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-46602.        (((A -> (B -> A)) and ((C and D) -> D)) and (E -> (F or E))), M:tm-609, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-46603
in-theory        46603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-46603.        (((A -> (B -> A)) and (C -> (D -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-46604
in-theory        46604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (C or D))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-46604.        (((A -> (B -> A)) and (C -> (C or D))) and (E -> (F or E))), M:tm-609, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-46605
in-theory        46605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D or C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-46605.        (((A -> (B -> A)) and (C -> (D or C))) and (E -> (F or E))), M:tm-609, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-46606
in-theory        46606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-46606.        (((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G or F))), M:tm-609, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-46607
in-theory        46607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-46607.        (((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F or E))), M:tm-609, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-46608
in-theory        46608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((not (not C)) -> C)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-46608.        (((A -> (B -> A)) and ((not (not C)) -> C)) and (D -> (E or D))), M:tm-609, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-46609
in-theory        46609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-46609.        (((A -> (B -> A)) and (C -> (D -> (E -> D)))) and (F -> (G or F))), M:tm-609, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46610
in-theory        46610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-46610.        (((A -> (B -> A)) and ((C -> D) -> (C -> C))) and (E -> (F or E))), M:tm-609, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-46611
in-theory        46611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G or F)))
theorem-size     31
proof            (modus-ponens tm-609 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-46611.        (((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-46612
in-theory        46612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46612.        (((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G))), M:tm-609, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46613
in-theory        46613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-46613.        (((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-46614
in-theory        46614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-46614.        (((A -> (B -> A)) and (C -> ((D and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46615
in-theory        46615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-46615.        (((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-46616
in-theory        46616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-46616.        (((A -> (B -> A)) and (C -> ((D and E) -> E))) and (F -> (G or F))), M:tm-609, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46617
in-theory        46617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-46617.        (((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G or F))), M:tm-609, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-46618
in-theory        46618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-46618.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (D -> (E or D))), M:tm-609, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-46619
in-theory        46619
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-46619.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-46620
in-theory        46620
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> C)) and B))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-46620.        ((A or (B -> ((C -> (D -> C)) and B))) and (E -> (F or E))), M:tm-609, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-46621
in-theory        46621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> B)) and A)) or D) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-46621.        (((A -> ((B -> (C -> B)) and A)) or D) and (E -> (F or E))), M:tm-609, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-46622
in-theory        46622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-46622.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (E -> (F or E))), M:tm-609, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-46623
in-theory        46623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-46623.        ((A -> (B -> ((C -> (D -> C)) and B))) and (E -> (F or E))), M:tm-609, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-46624
in-theory        46624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-46624.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))) and (F -> (G or F))), M:tm-609, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-46625
in-theory        46625
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H or G)))
theorem-size     33
proof            (modus-ponens tm-609 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-46625.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H or G))), M:tm-609, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-46626
in-theory        46626
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-46626.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)) and (F -> (G or F))), M:tm-609, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-46627
in-theory        46627
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-46627.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)) and (F -> (G or F))), M:tm-609, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-46628
in-theory        46628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-46628.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))) and (F -> (G or F))), M:tm-609, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-46629
in-theory        46629
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-46629.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))) and (F -> (G or F))), M:tm-609, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-46630
in-theory        46630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-46630.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))) and (F -> (G or F))), M:tm-609, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-46631
in-theory        46631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (H or G)))
theorem-size     33
proof            (modus-ponens tm-609 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-46631.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (G -> (H or G))), M:tm-609, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-46632
in-theory        46632
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (G or F)))
theorem-size     31
proof            (modus-ponens tm-609 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-46632.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))) and (F -> (G or F))), M:tm-609, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-46633
in-theory        46633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-46633.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-46634
in-theory        46634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-46634.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))) and (G -> (H or G))), M:tm-609, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-46635
in-theory        46635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-46635.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))) and (F -> (G or F))), M:tm-609, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-46636
in-theory        46636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (H or G)))
theorem-size     39
proof            (modus-ponens tm-609 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-46636.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (G -> (H or G))), M:tm-609, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-46637
in-theory        46637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I or H)))
theorem-size     35
proof            (modus-ponens tm-609 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46637.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I or H))), M:tm-609, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-46638
in-theory        46638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (H or G)))
theorem-size     35
proof            (modus-ponens tm-609 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-46638.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (G -> (H or G))), M:tm-609, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-46639
in-theory        46639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-46639.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))) and (G -> (H or G))), M:tm-609, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-46640
in-theory        46640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (H or G)))
theorem-size     35
proof            (modus-ponens tm-609 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-46640.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (G -> (H or G))), M:tm-609, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-46641
in-theory        46641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-46641.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))) and (G -> (H or G))), M:tm-609, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-46642
in-theory        46642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-46642.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))) and (G -> (H or G))), M:tm-609, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-46643
in-theory        46643
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (I or H)))
theorem-size     37
proof            (modus-ponens tm-609 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-46643.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (H -> (I or H))), M:tm-609, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-46644
in-theory        46644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-46644.        (((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H or G))), M:tm-609, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-46645
in-theory        46645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-46645.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (E -> (F or E))), M:tm-609, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-46646
in-theory        46646
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (F -> (G or F)))
theorem-size     43
proof            (modus-ponens tm-609 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-46646.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (F -> (G or F))), M:tm-609, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-46647
in-theory        46647
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-46647.        ((A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (G or F))), M:tm-609, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-46648
in-theory        46648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-46648.        (((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E) and (F -> (G or F))), M:tm-609, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-46649
in-theory        46649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-46649.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (F -> (G or F))), M:tm-609, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-46650
in-theory        46650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-46650.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (F -> (G or F))), M:tm-609, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-46651
in-theory        46651
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-46651.        ((((A and B) -> A) and (C -> (D -> C))) and (E -> (F or E))), M:tm-609, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-46652
in-theory        46652
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-46652.        ((((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-46653
in-theory        46653
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> C)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-46653.        ((((A and B) -> A) and ((C and D) -> C)) and (E -> (F or E))), M:tm-609, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-46654
in-theory        46654
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C and D) -> D)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-46654.        ((((A and B) -> A) and ((C and D) -> D)) and (E -> (F or E))), M:tm-609, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-46655
in-theory        46655
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (C and D)))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-46655.        ((((A and B) -> A) and (C -> (D -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-46656
in-theory        46656
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (C or D))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-46656.        ((((A and B) -> A) and (C -> (C or D))) and (E -> (F or E))), M:tm-609, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-46657
in-theory        46657
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D or C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-46657.        ((((A and B) -> A) and (C -> (D or C))) and (E -> (F or E))), M:tm-609, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-46658
in-theory        46658
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-46658.        ((((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G or F))), M:tm-609, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-46659
in-theory        46659
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-46659.        ((((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F or E))), M:tm-609, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-46660
in-theory        46660
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((not (not C)) -> C)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-46660.        ((((A and B) -> A) and ((not (not C)) -> C)) and (D -> (E or D))), M:tm-609, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-46661
in-theory        46661
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-46661.        ((((A and B) -> A) and (C -> (D -> (E -> D)))) and (F -> (G or F))), M:tm-609, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46662
in-theory        46662
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-46662.        ((((A and B) -> A) and ((C -> D) -> (C -> C))) and (E -> (F or E))), M:tm-609, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-46663
in-theory        46663
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G or F)))
theorem-size     31
proof            (modus-ponens tm-609 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-46663.        ((((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-46664
in-theory        46664
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46664.        ((((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G))), M:tm-609, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46665
in-theory        46665
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-46665.        ((((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-46666
in-theory        46666
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> D))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-46666.        ((((A and B) -> A) and (C -> ((D and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46667
in-theory        46667
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-46667.        ((((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-46668
in-theory        46668
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D and E) -> E))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-46668.        ((((A and B) -> A) and (C -> ((D and E) -> E))) and (F -> (G or F))), M:tm-609, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46669
in-theory        46669
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-46669.        ((((A and B) -> A) and (C -> ((D -> (E -> D)) and C))) and (F -> (G or F))), M:tm-609, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-46670
in-theory        46670
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-46670.        ((((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H or G))), M:tm-609, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-46671
in-theory        46671
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-46671.        ((((A and B) -> A) and (C -> (((D and E) -> D) and C))) and (F -> (G or F))), M:tm-609, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-46672
in-theory        46672
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-46672.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))) and (G -> (H or G))), M:tm-609, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-46673
in-theory        46673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-46673.        (((A -> (B -> A)) and (C -> (((D and E) -> D) and C))) and (F -> (G or F))), M:tm-609, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-46674
in-theory        46674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-46674.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (D -> (E or D))), M:tm-609, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-46675
in-theory        46675
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-46675.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-46676
in-theory        46676
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> C) and B))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-46676.        ((A or (B -> (((C and D) -> C) and B))) and (E -> (F or E))), M:tm-609, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-46677
in-theory        46677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> B) and A)) or D) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-46677.        (((A -> (((B and C) -> B) and A)) or D) and (E -> (F or E))), M:tm-609, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-46678
in-theory        46678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-46678.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (E -> (F or E))), M:tm-609, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-46679
in-theory        46679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-46679.        ((A -> (B -> (((C and D) -> C) and B))) and (E -> (F or E))), M:tm-609, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-46680
in-theory        46680
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-46680.        ((((A and B) -> B) and (C -> (D -> C))) and (E -> (F or E))), M:tm-609, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-46681
in-theory        46681
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-46681.        ((((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-46682
in-theory        46682
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> C)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-46682.        ((((A and B) -> B) and ((C and D) -> C)) and (E -> (F or E))), M:tm-609, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-46683
in-theory        46683
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C and D) -> D)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-46683.        ((((A and B) -> B) and ((C and D) -> D)) and (E -> (F or E))), M:tm-609, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-46684
in-theory        46684
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (C and D)))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-46684.        ((((A and B) -> B) and (C -> (D -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-46685
in-theory        46685
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (C or D))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-46685.        ((((A and B) -> B) and (C -> (C or D))) and (E -> (F or E))), M:tm-609, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-46686
in-theory        46686
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D or C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-46686.        ((((A and B) -> B) and (C -> (D or C))) and (E -> (F or E))), M:tm-609, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-46687
in-theory        46687
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-46687.        ((((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G or F))), M:tm-609, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-46688
in-theory        46688
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-46688.        ((((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F or E))), M:tm-609, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-46689
in-theory        46689
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((not (not C)) -> C)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-46689.        ((((A and B) -> B) and ((not (not C)) -> C)) and (D -> (E or D))), M:tm-609, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-46690
in-theory        46690
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-46690.        ((((A and B) -> B) and (C -> (D -> (E -> D)))) and (F -> (G or F))), M:tm-609, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46691
in-theory        46691
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-46691.        ((((A and B) -> B) and ((C -> D) -> (C -> C))) and (E -> (F or E))), M:tm-609, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-46692
in-theory        46692
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G or F)))
theorem-size     31
proof            (modus-ponens tm-609 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-46692.        ((((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-46693
in-theory        46693
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46693.        ((((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G))), M:tm-609, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46694
in-theory        46694
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-46694.        ((((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-46695
in-theory        46695
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> D))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-46695.        ((((A and B) -> B) and (C -> ((D and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46696
in-theory        46696
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-46696.        ((((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-46697
in-theory        46697
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D and E) -> E))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-46697.        ((((A and B) -> B) and (C -> ((D and E) -> E))) and (F -> (G or F))), M:tm-609, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46698
in-theory        46698
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-46698.        ((((A and B) -> B) and (C -> ((D -> (E -> D)) and C))) and (F -> (G or F))), M:tm-609, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-46699
in-theory        46699
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-46699.        ((((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H or G))), M:tm-609, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-46700
in-theory        46700
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-46700.        ((((A and B) -> B) and (C -> (((D and E) -> D) and C))) and (F -> (G or F))), M:tm-609, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-46701
in-theory        46701
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-46701.        ((((A and B) -> B) and (C -> (((D and E) -> E) and C))) and (F -> (G or F))), M:tm-609, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-46702
in-theory        46702
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-46702.        ((((A and B) -> A) and (C -> (((D and E) -> E) and C))) and (F -> (G or F))), M:tm-609, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-46703
in-theory        46703
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-46703.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))) and (G -> (H or G))), M:tm-609, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-46704
in-theory        46704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-46704.        (((A -> (B -> A)) and (C -> (((D and E) -> E) and C))) and (F -> (G or F))), M:tm-609, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-46705
in-theory        46705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-46705.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (D -> (E or D))), M:tm-609, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-46706
in-theory        46706
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-46706.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-46707
in-theory        46707
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (((C and D) -> D) and B))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-46707.        ((A or (B -> (((C and D) -> D) and B))) and (E -> (F or E))), M:tm-609, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-46708
in-theory        46708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B and C) -> C) and A)) or D) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-46708.        (((A -> (((B and C) -> C) and A)) or D) and (E -> (F or E))), M:tm-609, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-46709
in-theory        46709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-46709.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (E -> (F or E))), M:tm-609, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-46710
in-theory        46710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-46710.        ((A -> (B -> (((C and D) -> D) and B))) and (E -> (F or E))), M:tm-609, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-46711
in-theory        46711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> C))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-46711.        (((A -> (B -> (A and B))) and (C -> (D -> C))) and (E -> (F or E))), M:tm-609, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-46712
in-theory        46712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-46712.        (((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-46713
in-theory        46713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> C)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-46713.        (((A -> (B -> (A and B))) and ((C and D) -> C)) and (E -> (F or E))), M:tm-609, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-46714
in-theory        46714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C and D) -> D)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-46714.        (((A -> (B -> (A and B))) and ((C and D) -> D)) and (E -> (F or E))), M:tm-609, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-46715
in-theory        46715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-46715.        (((A -> (B -> (A and B))) and (C -> (D -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-46716
in-theory        46716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (C or D))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-46716.        (((A -> (B -> (A and B))) and (C -> (C or D))) and (E -> (F or E))), M:tm-609, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-46717
in-theory        46717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D or C))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-46717.        (((A -> (B -> (A and B))) and (C -> (D or C))) and (E -> (F or E))), M:tm-609, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-46718
in-theory        46718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-46718.        (((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G or F))), M:tm-609, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-46719
in-theory        46719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-46719.        (((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F or E))), M:tm-609, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-46720
in-theory        46720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-46720.        (((A -> (B -> (A and B))) and ((not (not C)) -> C)) and (D -> (E or D))), M:tm-609, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-46721
in-theory        46721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-46721.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))) and (F -> (G or F))), M:tm-609, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46722
in-theory        46722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-46722.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))) and (E -> (F or E))), M:tm-609, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-46723
in-theory        46723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G or F)))
theorem-size     33
proof            (modus-ponens tm-609 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-46723.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-46724
in-theory        46724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46724.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G))), M:tm-609, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46725
in-theory        46725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G or F)))
theorem-size     29
proof            (modus-ponens tm-609 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-46725.        (((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-46726
in-theory        46726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-46726.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46727
in-theory        46727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G or F)))
theorem-size     29
proof            (modus-ponens tm-609 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-46727.        (((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-46728
in-theory        46728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-46728.        (((A -> (B -> (A and B))) and (C -> ((D and E) -> E))) and (F -> (G or F))), M:tm-609, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46729
in-theory        46729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-46729.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))) and (F -> (G or F))), M:tm-609, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-46730
in-theory        46730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H or G)))
theorem-size     31
proof            (modus-ponens tm-609 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-46730.        (((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H or G))), M:tm-609, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-46731
in-theory        46731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-46731.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))) and (F -> (G or F))), M:tm-609, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-46732
in-theory        46732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-46732.        (((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))) and (F -> (G or F))), M:tm-609, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-46733
in-theory        46733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-46733.        (((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G or F))), M:tm-609, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-46734
in-theory        46734
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-46734.        ((((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G or F))), M:tm-609, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-46735
in-theory        46735
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-46735.        ((((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G or F))), M:tm-609, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-46736
in-theory        46736
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (H or G)))
theorem-size     31
proof            (modus-ponens tm-609 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-46736.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))) and (G -> (H or G))), M:tm-609, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-46737
in-theory        46737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-46737.        (((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G or F))), M:tm-609, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-46738
in-theory        46738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-46738.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (D -> (E or D))), M:tm-609, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-46739
in-theory        46739
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (E -> (F or E)))
theorem-size     31
proof            (modus-ponens tm-609 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-46739.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-46740
in-theory        46740
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D -> (C and D))) and B))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-46740.        ((A or (B -> ((C -> (D -> (C and D))) and B))) and (E -> (F or E))), M:tm-609, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-46741
in-theory        46741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> (B and C))) and A)) or D) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-46741.        (((A -> ((B -> (C -> (B and C))) and A)) or D) and (E -> (F or E))), M:tm-609, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-46742
in-theory        46742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-46742.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (E -> (F or E))), M:tm-609, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-46743
in-theory        46743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-46743.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (E -> (F or E))), M:tm-609, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-46744
in-theory        46744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-609 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-46744.        ((A -> (A and (B -> A))) and (C -> (D or C))), M:tm-609, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-46745
in-theory        46745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-609 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-46745.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (D -> (E or D))), M:tm-609, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-46746
in-theory        46746
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-609 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-46746.        (((A and B) -> ((A and B) and A)) and (C -> (D or C))), M:tm-609, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-46747
in-theory        46747
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-609 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-46747.        (((A and B) -> ((A and B) and B)) and (C -> (D or C))), M:tm-609, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-46748
in-theory        46748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-609 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-46748.        ((A -> (A and (B -> (A and B)))) and (C -> (D or C))), M:tm-609, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-46749
in-theory        46749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-609 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-46749.        ((A -> (A and (A or B))) and (C -> (D or C))), M:tm-609, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-46750
in-theory        46750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-609 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-46750.        ((A -> (A and (B or A))) and (C -> (D or C))), M:tm-609, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-46751
in-theory        46751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-609 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-46751.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and (D -> (E or D))), M:tm-609, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-46752
in-theory        46752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (C -> (D or C)))
theorem-size     21
proof            (modus-ponens tm-609 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-46752.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and (C -> (D or C))), M:tm-609, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-46753
in-theory        46753
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and (B -> (C or B)))
theorem-size     15
proof            (modus-ponens tm-609 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-46753.        (((not (not A)) -> ((not (not A)) and A)) and (B -> (C or B))), M:tm-609, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-46754
in-theory        46754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-46754.        ((A -> (A and (B -> (C -> B)))) and (D -> (E or D))), M:tm-609, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-46755
in-theory        46755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-609 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-46755.        (((A -> B) -> ((A -> B) and (A -> A))) and (C -> (D or C))), M:tm-609, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-46756
in-theory        46756
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (D -> (E or D)))
theorem-size     35
proof            (modus-ponens tm-609 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-46756.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (D -> (E or D))), M:tm-609, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-46757
in-theory        46757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-46757.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (E -> (F or E))), M:tm-609, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-46758
in-theory        46758
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (D -> (E or D)))
theorem-size     29
proof            (modus-ponens tm-609 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-46758.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and (D -> (E or D))), M:tm-609, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-46759
in-theory        46759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-46759.        ((A -> (A and ((B and C) -> B))) and (D -> (E or D))), M:tm-609, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-46760
in-theory        46760
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (D -> (E or D)))
theorem-size     29
proof            (modus-ponens tm-609 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-46760.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (D -> (E or D))), M:tm-609, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-46761
in-theory        46761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-46761.        ((A -> (A and ((B and C) -> C))) and (D -> (E or D))), M:tm-609, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-46762
in-theory        46762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-46762.        ((A -> (A and ((B -> (C -> B)) and A))) and (D -> (E or D))), M:tm-609, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-46763
in-theory        46763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-46763.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (E -> (F or E))), M:tm-609, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-46764
in-theory        46764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-46764.        ((A -> (A and (((B and C) -> B) and A))) and (D -> (E or D))), M:tm-609, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-46765
in-theory        46765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-46765.        ((A -> (A and (((B and C) -> C) and A))) and (D -> (E or D))), M:tm-609, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-46766
in-theory        46766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-46766.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (D -> (E or D))), M:tm-609, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-46767
in-theory        46767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (C -> (D or C)))
theorem-size     19
proof            (modus-ponens tm-609 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-46767.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and (C -> (D or C))), M:tm-609, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-46768
in-theory        46768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-46768.        (((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-46769
in-theory        46769
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-46769.        ((((A and B) -> B) and ((C -> D) -> (C -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-46770
in-theory        46770
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-46770.        ((((A and B) -> A) and ((C -> D) -> (C -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-46771
in-theory        46771
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (G or F)))
theorem-size     29
proof            (modus-ponens tm-609 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-46771.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))) and (F -> (G or F))), M:tm-609, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-46772
in-theory        46772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-46772.        (((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-46773
in-theory        46773
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (C -> (D or C)))
theorem-size     21
proof            (modus-ponens tm-609 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-46773.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (C -> (D or C))), M:tm-609, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-46774
in-theory        46774
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-609 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-46774.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (D -> (E or D))), M:tm-609, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-46775
in-theory        46775
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (B -> (B and C)))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-46775.        ((A or ((B -> C) -> (B -> (B and C)))) and (D -> (E or D))), M:tm-609, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-46776
in-theory        46776
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) or C) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-46776.        ((((A -> B) -> (A -> (A and B))) or C) and (D -> (E or D))), M:tm-609, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-46777
in-theory        46777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-46777.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (D -> (E or D))), M:tm-609, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-46778
in-theory        46778
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (C -> (D or C)))
theorem-size     19
proof            (modus-ponens tm-609 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-46778.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (C -> (D or C))), M:tm-609, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-46779
in-theory        46779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-46779.        ((A -> ((B -> C) -> (B -> (B and C)))) and (D -> (E or D))), M:tm-609, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-46780
in-theory        46780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-46780.        ((A -> (A and (B -> (C -> (B and C))))) and (D -> (E or D))), M:tm-609, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-46781
in-theory        46781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46781.        (((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))) and (F -> (G or F))), M:tm-609, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46782
in-theory        46782
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46782.        ((((A and B) -> B) and (C -> (D -> (E -> (D and E))))) and (F -> (G or F))), M:tm-609, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46783
in-theory        46783
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46783.        ((((A and B) -> A) and (C -> (D -> (E -> (D and E))))) and (F -> (G or F))), M:tm-609, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46784
in-theory        46784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46784.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))) and (G -> (H or G))), M:tm-609, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-46785
in-theory        46785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46785.        (((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))) and (F -> (G or F))), M:tm-609, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46786
in-theory        46786
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-46786.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and (E -> (F or E))), M:tm-609, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-46787
in-theory        46787
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-46787.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and (E -> (F or E))), M:tm-609, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-46788
in-theory        46788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-46788.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and (D -> (E or D))), M:tm-609, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-46789
in-theory        46789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-46789.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (D -> (E or D))), M:tm-609, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-46790
in-theory        46790
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-46790.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (E -> (F or E))), M:tm-609, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-46791
in-theory        46791
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D -> (C and D))))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46791.        ((A or (B -> (C -> (D -> (C and D))))) and (E -> (F or E))), M:tm-609, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-46792
in-theory        46792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) or D) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46792.        (((A -> (B -> (C -> (B and C)))) or D) and (E -> (F or E))), M:tm-609, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-46793
in-theory        46793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46793.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (E -> (F or E))), M:tm-609, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-46794
in-theory        46794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-46794.        (((A -> B) -> (A -> (C -> (B and C)))) and (D -> (E or D))), M:tm-609, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-46795
in-theory        46795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46795.        ((A -> (B -> (C -> (D -> (C and D))))) and (E -> (F or E))), M:tm-609, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-46796
in-theory        46796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-46796.        (((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)) and (F -> (G or F))), M:tm-609, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-46797
in-theory        46797
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-46797.        ((((A and B) -> B) and ((C -> (D -> C)) or E)) and (F -> (G or F))), M:tm-609, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-46798
in-theory        46798
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-46798.        ((((A and B) -> A) and ((C -> (D -> C)) or E)) and (F -> (G or F))), M:tm-609, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-46799
in-theory        46799
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-46799.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)) and (G -> (H or G))), M:tm-609, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-46800
in-theory        46800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-46800.        (((A -> (B -> A)) and ((C -> (D -> C)) or E)) and (F -> (G or F))), M:tm-609, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-46801
in-theory        46801
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) or D)) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-46801.        ((A or ((B -> (C -> B)) or D)) and (E -> (F or E))), M:tm-609, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-46802
in-theory        46802
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) or C) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-46802.        ((((A -> (B -> A)) or C) or D) and (E -> (F or E))), M:tm-609, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-46803
in-theory        46803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-46803.        ((A -> (((B -> (C -> B)) or D) and A)) and (E -> (F or E))), M:tm-609, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-46804
in-theory        46804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-46804.        ((A -> ((B -> (C -> B)) or D)) and (E -> (F or E))), M:tm-609, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-46805
in-theory        46805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-46805.        (((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H or G))), M:tm-609, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-46806
in-theory        46806
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-46806.        ((((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H or G))), M:tm-609, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-46807
in-theory        46807
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-46807.        ((((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H or G))), M:tm-609, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-46808
in-theory        46808
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (I or H)))
theorem-size     35
proof            (modus-ponens tm-609 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-46808.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (H -> (I or H))), M:tm-609, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-46809
in-theory        46809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-46809.        (((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H or G))), M:tm-609, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-46810
in-theory        46810
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-46810.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (G or F))), M:tm-609, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-46811
in-theory        46811
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-46811.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E) and (F -> (G or F))), M:tm-609, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-46812
in-theory        46812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-46812.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (F -> (G or F))), M:tm-609, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-46813
in-theory        46813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-46813.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (F -> (G or F))), M:tm-609, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-46814
in-theory        46814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-46814.        (((A -> (B -> (A and B))) and (((C and D) -> C) or E)) and (F -> (G or F))), M:tm-609, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-46815
in-theory        46815
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> C) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-46815.        ((((A and B) -> B) and (((C and D) -> C) or E)) and (F -> (G or F))), M:tm-609, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-46816
in-theory        46816
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> C) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-46816.        ((((A and B) -> A) and (((C and D) -> C) or E)) and (F -> (G or F))), M:tm-609, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-46817
in-theory        46817
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-46817.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)) and (G -> (H or G))), M:tm-609, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-46818
in-theory        46818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> C) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-46818.        (((A -> (B -> A)) and (((C and D) -> C) or E)) and (F -> (G or F))), M:tm-609, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-46819
in-theory        46819
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) or D)) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-46819.        ((A or (((B and C) -> B) or D)) and (E -> (F or E))), M:tm-609, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-46820
in-theory        46820
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) or C) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-46820.        (((((A and B) -> A) or C) or D) and (E -> (F or E))), M:tm-609, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-46821
in-theory        46821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-46821.        ((A -> ((((B and C) -> B) or D) and A)) and (E -> (F or E))), M:tm-609, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-46822
in-theory        46822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-46822.        ((A -> (((B and C) -> B) or D)) and (E -> (F or E))), M:tm-609, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-46823
in-theory        46823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-46823.        (((A -> (B -> (A and B))) and (((C and D) -> D) or E)) and (F -> (G or F))), M:tm-609, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-46824
in-theory        46824
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C and D) -> D) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-46824.        ((((A and B) -> B) and (((C and D) -> D) or E)) and (F -> (G or F))), M:tm-609, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-46825
in-theory        46825
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C and D) -> D) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-46825.        ((((A and B) -> A) and (((C and D) -> D) or E)) and (F -> (G or F))), M:tm-609, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-46826
in-theory        46826
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-46826.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)) and (G -> (H or G))), M:tm-609, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-46827
in-theory        46827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C and D) -> D) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-46827.        (((A -> (B -> A)) and (((C and D) -> D) or E)) and (F -> (G or F))), M:tm-609, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-46828
in-theory        46828
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) or D)) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-46828.        ((A or (((B and C) -> C) or D)) and (E -> (F or E))), M:tm-609, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-46829
in-theory        46829
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) or C) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-46829.        (((((A and B) -> B) or C) or D) and (E -> (F or E))), M:tm-609, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-46830
in-theory        46830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-46830.        ((A -> ((((B and C) -> C) or D) and A)) and (E -> (F or E))), M:tm-609, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-46831
in-theory        46831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-46831.        ((A -> (((B and C) -> C) or D)) and (E -> (F or E))), M:tm-609, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-46832
in-theory        46832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-46832.        (((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)) and (F -> (G or F))), M:tm-609, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-46833
in-theory        46833
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-46833.        ((((A and B) -> B) and ((C -> (D -> (C and D))) or E)) and (F -> (G or F))), M:tm-609, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-46834
in-theory        46834
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-46834.        ((((A and B) -> A) and ((C -> (D -> (C and D))) or E)) and (F -> (G or F))), M:tm-609, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-46835
in-theory        46835
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-46835.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)) and (G -> (H or G))), M:tm-609, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-46836
in-theory        46836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-46836.        (((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)) and (F -> (G or F))), M:tm-609, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-46837
in-theory        46837
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) or D)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-46837.        ((A or ((B -> (C -> (B and C))) or D)) and (E -> (F or E))), M:tm-609, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-46838
in-theory        46838
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) or C) or D) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-46838.        ((((A -> (B -> (A and B))) or C) or D) and (E -> (F or E))), M:tm-609, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-46839
in-theory        46839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-46839.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (E -> (F or E))), M:tm-609, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-46840
in-theory        46840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-46840.        ((A -> ((B -> (C -> (B and C))) or D)) and (E -> (F or E))), M:tm-609, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-46841
in-theory        46841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-46841.        (((A -> (B -> (A and B))) and ((C -> (C or D)) or E)) and (F -> (G or F))), M:tm-609, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-46842
in-theory        46842
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (C or D)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-46842.        ((((A and B) -> B) and ((C -> (C or D)) or E)) and (F -> (G or F))), M:tm-609, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-46843
in-theory        46843
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (C or D)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-46843.        ((((A and B) -> A) and ((C -> (C or D)) or E)) and (F -> (G or F))), M:tm-609, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-46844
in-theory        46844
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-46844.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)) and (G -> (H or G))), M:tm-609, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-46845
in-theory        46845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-46845.        (((A -> (B -> A)) and ((C -> (C or D)) or E)) and (F -> (G or F))), M:tm-609, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-46846
in-theory        46846
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) or D)) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-46846.        ((A or ((B -> (B or C)) or D)) and (E -> (F or E))), M:tm-609, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-46847
in-theory        46847
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) or C) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-46847.        ((((A -> (A or B)) or C) or D) and (E -> (F or E))), M:tm-609, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-46848
in-theory        46848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-46848.        ((A -> (((B -> (B or C)) or D) and A)) and (E -> (F or E))), M:tm-609, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-46849
in-theory        46849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-46849.        ((A -> ((B -> (B or C)) or D)) and (E -> (F or E))), M:tm-609, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-46850
in-theory        46850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-46850.        (((A -> (A or B)) and (C -> (D -> C))) and (E -> (F or E))), M:tm-609, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-46851
in-theory        46851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-46851.        (((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-46852
in-theory        46852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> C)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-46852.        (((A -> (A or B)) and ((C and D) -> C)) and (E -> (F or E))), M:tm-609, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-46853
in-theory        46853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C and D) -> D)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-46853.        (((A -> (A or B)) and ((C and D) -> D)) and (E -> (F or E))), M:tm-609, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-46854
in-theory        46854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (C and D)))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-46854.        (((A -> (A or B)) and (C -> (D -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-46855
in-theory        46855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (C or D))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-46855.        (((A -> (A or B)) and (C -> (C or D))) and (E -> (F or E))), M:tm-609, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-46856
in-theory        46856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D or C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-46856.        (((A -> (A or B)) and (C -> (D or C))) and (E -> (F or E))), M:tm-609, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-46857
in-theory        46857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-46857.        (((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G or F))), M:tm-609, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-46858
in-theory        46858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-46858.        (((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F or E))), M:tm-609, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-46859
in-theory        46859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((not (not C)) -> C)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-46859.        (((A -> (A or B)) and ((not (not C)) -> C)) and (D -> (E or D))), M:tm-609, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-46860
in-theory        46860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-46860.        (((A -> (A or B)) and (C -> (D -> (E -> D)))) and (F -> (G or F))), M:tm-609, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46861
in-theory        46861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-46861.        (((A -> (A or B)) and ((C -> D) -> (C -> C))) and (E -> (F or E))), M:tm-609, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-46862
in-theory        46862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G or F)))
theorem-size     31
proof            (modus-ponens tm-609 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-46862.        (((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-46863
in-theory        46863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46863.        (((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G))), M:tm-609, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46864
in-theory        46864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-46864.        (((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-46865
in-theory        46865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> D))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-46865.        (((A -> (A or B)) and (C -> ((D and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46866
in-theory        46866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-46866.        (((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-46867
in-theory        46867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D and E) -> E))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-46867.        (((A -> (A or B)) and (C -> ((D and E) -> E))) and (F -> (G or F))), M:tm-609, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46868
in-theory        46868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-46868.        (((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G or F))), M:tm-609, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-46869
in-theory        46869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-46869.        (((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H or G))), M:tm-609, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-46870
in-theory        46870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-46870.        (((A -> (A or B)) and (C -> (((D and E) -> D) and C))) and (F -> (G or F))), M:tm-609, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-46871
in-theory        46871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-46871.        (((A -> (A or B)) and (C -> (((D and E) -> E) and C))) and (F -> (G or F))), M:tm-609, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-46872
in-theory        46872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-46872.        (((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G or F))), M:tm-609, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-46873
in-theory        46873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-46873.        (((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-46874
in-theory        46874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46874.        (((A -> (A or B)) and (C -> (D -> (E -> (D and E))))) and (F -> (G or F))), M:tm-609, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46875
in-theory        46875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-46875.        (((A -> (A or B)) and ((C -> (D -> C)) or E)) and (F -> (G or F))), M:tm-609, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-46876
in-theory        46876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-46876.        (((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H or G))), M:tm-609, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-46877
in-theory        46877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> C) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-46877.        (((A -> (A or B)) and (((C and D) -> C) or E)) and (F -> (G or F))), M:tm-609, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-46878
in-theory        46878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C and D) -> D) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-46878.        (((A -> (A or B)) and (((C and D) -> D) or E)) and (F -> (G or F))), M:tm-609, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-46879
in-theory        46879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-46879.        (((A -> (A or B)) and ((C -> (D -> (C and D))) or E)) and (F -> (G or F))), M:tm-609, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-46880
in-theory        46880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (C or D)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-46880.        (((A -> (A or B)) and ((C -> (C or D)) or E)) and (F -> (G or F))), M:tm-609, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-46881
in-theory        46881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-46881.        (((A -> (A or B)) and (C -> ((D -> (D or E)) and C))) and (F -> (G or F))), M:tm-609, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-46882
in-theory        46882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-46882.        ((A -> (A and ((B -> (B or C)) and A))) and (D -> (E or D))), M:tm-609, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-46883
in-theory        46883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-46883.        (((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))) and (F -> (G or F))), M:tm-609, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-46884
in-theory        46884
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-46884.        ((((A and B) -> B) and (C -> ((D -> (D or E)) and C))) and (F -> (G or F))), M:tm-609, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-46885
in-theory        46885
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-46885.        ((((A and B) -> A) and (C -> ((D -> (D or E)) and C))) and (F -> (G or F))), M:tm-609, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-46886
in-theory        46886
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-46886.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))) and (G -> (H or G))), M:tm-609, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-46887
in-theory        46887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-46887.        (((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))) and (F -> (G or F))), M:tm-609, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-46888
in-theory        46888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-46888.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (D -> (E or D))), M:tm-609, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-46889
in-theory        46889
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-46889.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-46890
in-theory        46890
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (C or D)) and B))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-46890.        ((A or (B -> ((C -> (C or D)) and B))) and (E -> (F or E))), M:tm-609, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-46891
in-theory        46891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (B or C)) and A)) or D) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-46891.        (((A -> ((B -> (B or C)) and A)) or D) and (E -> (F or E))), M:tm-609, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-46892
in-theory        46892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-46892.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (E -> (F or E))), M:tm-609, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-46893
in-theory        46893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-46893.        ((A -> (B -> ((C -> (C or D)) and B))) and (E -> (F or E))), M:tm-609, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-46894
in-theory        46894
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (D or E)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-46894.        (((A -> (A or B)) and (C -> (D -> (D or E)))) and (F -> (G or F))), M:tm-609, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46895
in-theory        46895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-46895.        ((A -> (A and (B -> (B or C)))) and (D -> (E or D))), M:tm-609, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-46896
in-theory        46896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-46896.        (((A -> (B -> (A and B))) and (C -> (D -> (D or E)))) and (F -> (G or F))), M:tm-609, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46897
in-theory        46897
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (D or E)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-46897.        ((((A and B) -> B) and (C -> (D -> (D or E)))) and (F -> (G or F))), M:tm-609, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46898
in-theory        46898
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (D or E)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-46898.        ((((A and B) -> A) and (C -> (D -> (D or E)))) and (F -> (G or F))), M:tm-609, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46899
in-theory        46899
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-46899.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))) and (G -> (H or G))), M:tm-609, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-46900
in-theory        46900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-46900.        (((A -> (B -> A)) and (C -> (D -> (D or E)))) and (F -> (G or F))), M:tm-609, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46901
in-theory        46901
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-46901.        (((A and ((B -> (B or C)) -> D)) -> D) and (E -> (F or E))), M:tm-609, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-46902
in-theory        46902
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-46902.        (((((A -> (A or B)) -> C) and D) -> C) and (E -> (F or E))), M:tm-609, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-46903
in-theory        46903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-46903.        (((A -> ((A or B) -> C)) -> (A -> C)) and (D -> (E or D))), M:tm-609, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-46904
in-theory        46904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-6)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-46904.        (((A -> (not (B -> (B or C)))) -> (not A)) and (D -> (E or D))), M:tm-609, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-46905
in-theory        46905
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-46905.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (E -> (F or E))), M:tm-609, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-46906
in-theory        46906
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (C or D)))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-46906.        ((A or (B -> (C -> (C or D)))) and (E -> (F or E))), M:tm-609, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-46907
in-theory        46907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-46907.        (((A -> (B -> (B or C))) or D) and (E -> (F or E))), M:tm-609, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-46908
in-theory        46908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-46908.        ((A -> ((B -> (C -> (C or D))) and A)) and (E -> (F or E))), M:tm-609, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-46909
in-theory        46909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-46909.        (((A -> B) -> (A -> (B or C))) and (D -> (E or D))), M:tm-609, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-46910
in-theory        46910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-46910.        ((A -> (B -> (C -> (C or D)))) and (E -> (F or E))), M:tm-609, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-46911
in-theory        46911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46911.        (((A -> (A or B)) and (C or (D -> (E -> D)))) and (F -> (G or F))), M:tm-609, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46912
in-theory        46912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46912.        (((A -> (B -> (A and B))) and (C or (D -> (E -> D)))) and (F -> (G or F))), M:tm-609, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46913
in-theory        46913
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46913.        ((((A and B) -> B) and (C or (D -> (E -> D)))) and (F -> (G or F))), M:tm-609, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46914
in-theory        46914
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46914.        ((((A and B) -> A) and (C or (D -> (E -> D)))) and (F -> (G or F))), M:tm-609, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46915
in-theory        46915
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46915.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))) and (G -> (H or G))), M:tm-609, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-46916
in-theory        46916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46916.        (((A -> (B -> A)) and (C or (D -> (E -> D)))) and (F -> (G or F))), M:tm-609, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-46917
in-theory        46917
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> C)))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46917.        ((A or (B or (C -> (D -> C)))) and (E -> (F or E))), M:tm-609, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-46918
in-theory        46918
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> B))) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46918.        (((A or (B -> (C -> B))) or D) and (E -> (F or E))), M:tm-609, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-46919
in-theory        46919
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46919.        ((A -> ((B or (C -> (D -> C))) and A)) and (E -> (F or E))), M:tm-609, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-46920
in-theory        46920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-46920.        ((A -> (B or (C -> (D -> C)))) and (E -> (F or E))), M:tm-609, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-46921
in-theory        46921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46921.        (((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G))), M:tm-609, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46922
in-theory        46922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46922.        (((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G))), M:tm-609, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46923
in-theory        46923
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46923.        ((((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G))), M:tm-609, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46924
in-theory        46924
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46924.        ((((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G))), M:tm-609, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46925
in-theory        46925
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I or H)))
theorem-size     35
proof            (modus-ponens tm-609 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46925.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (H -> (I or H))), M:tm-609, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-46926
in-theory        46926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46926.        (((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G))), M:tm-609, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-46927
in-theory        46927
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46927.        ((A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G or F))), M:tm-609, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-46928
in-theory        46928
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46928.        (((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E) and (F -> (G or F))), M:tm-609, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-46929
in-theory        46929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46929.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (F -> (G or F))), M:tm-609, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-46930
in-theory        46930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-46930.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (F -> (G or F))), M:tm-609, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-46931
in-theory        46931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> D))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46931.        (((A -> (A or B)) and (C or ((D and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46932
in-theory        46932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46932.        (((A -> (B -> (A and B))) and (C or ((D and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46933
in-theory        46933
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> D))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46933.        ((((A and B) -> B) and (C or ((D and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46934
in-theory        46934
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> D))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46934.        ((((A and B) -> A) and (C or ((D and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46935
in-theory        46935
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46935.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))) and (G -> (H or G))), M:tm-609, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-46936
in-theory        46936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> D))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46936.        (((A -> (B -> A)) and (C or ((D and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-46937
in-theory        46937
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> C))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46937.        ((A or (B or ((C and D) -> C))) and (E -> (F or E))), M:tm-609, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-46938
in-theory        46938
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> B)) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46938.        (((A or ((B and C) -> B)) or D) and (E -> (F or E))), M:tm-609, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-46939
in-theory        46939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46939.        ((A -> ((B or ((C and D) -> C)) and A)) and (E -> (F or E))), M:tm-609, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-46940
in-theory        46940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-46940.        ((A -> (B or ((C and D) -> C))) and (E -> (F or E))), M:tm-609, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-46941
in-theory        46941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or ((D and E) -> E))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46941.        (((A -> (A or B)) and (C or ((D and E) -> E))) and (F -> (G or F))), M:tm-609, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46942
in-theory        46942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46942.        (((A -> (B -> (A and B))) and (C or ((D and E) -> E))) and (F -> (G or F))), M:tm-609, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46943
in-theory        46943
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or ((D and E) -> E))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46943.        ((((A and B) -> B) and (C or ((D and E) -> E))) and (F -> (G or F))), M:tm-609, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46944
in-theory        46944
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or ((D and E) -> E))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46944.        ((((A and B) -> A) and (C or ((D and E) -> E))) and (F -> (G or F))), M:tm-609, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46945
in-theory        46945
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46945.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))) and (G -> (H or G))), M:tm-609, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-46946
in-theory        46946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or ((D and E) -> E))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46946.        (((A -> (B -> A)) and (C or ((D and E) -> E))) and (F -> (G or F))), M:tm-609, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-46947
in-theory        46947
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or ((C and D) -> D))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46947.        ((A or (B or ((C and D) -> D))) and (E -> (F or E))), M:tm-609, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-46948
in-theory        46948
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and C) -> C)) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46948.        (((A or ((B and C) -> C)) or D) and (E -> (F or E))), M:tm-609, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-46949
in-theory        46949
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46949.        ((A -> ((B or ((C and D) -> D)) and A)) and (E -> (F or E))), M:tm-609, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-46950
in-theory        46950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-46950.        ((A -> (B or ((C and D) -> D))) and (E -> (F or E))), M:tm-609, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-46951
in-theory        46951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46951.        (((A -> (A or B)) and (C or (D -> (E -> (D and E))))) and (F -> (G or F))), M:tm-609, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46952
in-theory        46952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46952.        (((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))) and (F -> (G or F))), M:tm-609, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46953
in-theory        46953
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46953.        ((((A and B) -> B) and (C or (D -> (E -> (D and E))))) and (F -> (G or F))), M:tm-609, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46954
in-theory        46954
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46954.        ((((A and B) -> A) and (C or (D -> (E -> (D and E))))) and (F -> (G or F))), M:tm-609, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46955
in-theory        46955
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46955.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))) and (G -> (H or G))), M:tm-609, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-46956
in-theory        46956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46956.        (((A -> (B -> A)) and (C or (D -> (E -> (D and E))))) and (F -> (G or F))), M:tm-609, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-46957
in-theory        46957
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D -> (C and D))))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46957.        ((A or (B or (C -> (D -> (C and D))))) and (E -> (F or E))), M:tm-609, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-46958
in-theory        46958
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C -> (B and C)))) or D) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46958.        (((A or (B -> (C -> (B and C)))) or D) and (E -> (F or E))), M:tm-609, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-46959
in-theory        46959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46959.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (E -> (F or E))), M:tm-609, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-46960
in-theory        46960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-46960.        ((A -> (B or (C -> (D -> (C and D))))) and (E -> (F or E))), M:tm-609, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-46961
in-theory        46961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (D or E)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46961.        (((A -> (A or B)) and (C or (D -> (D or E)))) and (F -> (G or F))), M:tm-609, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46962
in-theory        46962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46962.        (((A -> (B -> (A and B))) and (C or (D -> (D or E)))) and (F -> (G or F))), M:tm-609, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46963
in-theory        46963
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (D or E)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46963.        ((((A and B) -> B) and (C or (D -> (D or E)))) and (F -> (G or F))), M:tm-609, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46964
in-theory        46964
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (D or E)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46964.        ((((A and B) -> A) and (C or (D -> (D or E)))) and (F -> (G or F))), M:tm-609, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46965
in-theory        46965
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46965.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))) and (G -> (H or G))), M:tm-609, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-46966
in-theory        46966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (D or E)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46966.        (((A -> (B -> A)) and (C or (D -> (D or E)))) and (F -> (G or F))), M:tm-609, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-46967
in-theory        46967
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (C or D)))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46967.        ((A or (B or (C -> (C or D)))) and (E -> (F or E))), M:tm-609, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-46968
in-theory        46968
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (B or C))) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46968.        (((A or (B -> (B or C))) or D) and (E -> (F or E))), M:tm-609, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-46969
in-theory        46969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46969.        ((A -> ((B or (C -> (C or D))) and A)) and (E -> (F or E))), M:tm-609, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-46970
in-theory        46970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-46970.        ((A -> (B or (C -> (C or D)))) and (E -> (F or E))), M:tm-609, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-46971
in-theory        46971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C or (D -> (E or D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46971.        (((A -> (A or B)) and (C or (D -> (E or D)))) and (F -> (G or F))), M:tm-609, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46972
in-theory        46972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46972.        (((A -> (B -> (A and B))) and (C or (D -> (E or D)))) and (F -> (G or F))), M:tm-609, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46973
in-theory        46973
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C or (D -> (E or D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46973.        ((((A and B) -> B) and (C or (D -> (E or D)))) and (F -> (G or F))), M:tm-609, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46974
in-theory        46974
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C or (D -> (E or D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46974.        ((((A and B) -> A) and (C or (D -> (E or D)))) and (F -> (G or F))), M:tm-609, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46975
in-theory        46975
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46975.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))) and (G -> (H or G))), M:tm-609, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-46976
in-theory        46976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C or (D -> (E or D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46976.        (((A -> (B -> A)) and (C or (D -> (E or D)))) and (F -> (G or F))), M:tm-609, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-46977
in-theory        46977
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or (C -> (D or C)))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46977.        ((A or (B or (C -> (D or C)))) and (E -> (F or E))), M:tm-609, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-46978
in-theory        46978
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> (C or B))) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46978.        (((A or (B -> (C or B))) or D) and (E -> (F or E))), M:tm-609, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-46979
in-theory        46979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46979.        ((A -> ((B or (C -> (D or C))) and A)) and (E -> (F or E))), M:tm-609, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-46980
in-theory        46980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-46980.        ((A -> (B or (C -> (D or C)))) and (E -> (F or E))), M:tm-609, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-46981
in-theory        46981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> (D or C)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46981.        (((A -> (A or B)) and ((C -> (D or C)) or E)) and (F -> (G or F))), M:tm-609, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-46982
in-theory        46982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46982.        (((A -> (B -> (A and B))) and ((C -> (D or C)) or E)) and (F -> (G or F))), M:tm-609, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-46983
in-theory        46983
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> (D or C)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46983.        ((((A and B) -> B) and ((C -> (D or C)) or E)) and (F -> (G or F))), M:tm-609, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-46984
in-theory        46984
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> (D or C)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46984.        ((((A and B) -> A) and ((C -> (D or C)) or E)) and (F -> (G or F))), M:tm-609, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-46985
in-theory        46985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46985.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)) and (G -> (H or G))), M:tm-609, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-46986
in-theory        46986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46986.        (((A -> (B -> A)) and ((C -> (D or C)) or E)) and (F -> (G or F))), M:tm-609, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-46987
in-theory        46987
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) or D)) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46987.        ((A or ((B -> (C or B)) or D)) and (E -> (F or E))), M:tm-609, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-46988
in-theory        46988
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) or C) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46988.        ((((A -> (B or A)) or C) or D) and (E -> (F or E))), M:tm-609, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-46989
in-theory        46989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46989.        ((A -> (((B -> (C or B)) or D) and A)) and (E -> (F or E))), M:tm-609, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-46990
in-theory        46990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-46990.        ((A -> ((B -> (C or B)) or D)) and (E -> (F or E))), M:tm-609, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-46991
in-theory        46991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-46991.        (((A -> (B or A)) and (C -> (D -> C))) and (E -> (F or E))), M:tm-609, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-46992
in-theory        46992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-46992.        (((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-46993
in-theory        46993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> C)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-46993.        (((A -> (B or A)) and ((C and D) -> C)) and (E -> (F or E))), M:tm-609, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-46994
in-theory        46994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C and D) -> D)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-46994.        (((A -> (B or A)) and ((C and D) -> D)) and (E -> (F or E))), M:tm-609, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-46995
in-theory        46995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (C and D)))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-46995.        (((A -> (B or A)) and (C -> (D -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-46996
in-theory        46996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (C or D))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-46996.        (((A -> (B or A)) and (C -> (C or D))) and (E -> (F or E))), M:tm-609, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-46997
in-theory        46997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D or C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-46997.        (((A -> (B or A)) and (C -> (D or C))) and (E -> (F or E))), M:tm-609, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-46998
in-theory        46998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-46998.        (((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and (F -> (G or F))), M:tm-609, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-46999
in-theory        46999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-46999.        (((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))) and (E -> (F or E))), M:tm-609, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-47000
in-theory        47000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((not (not C)) -> C)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-10)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-47000.        (((A -> (B or A)) and ((not (not C)) -> C)) and (D -> (E or D))), M:tm-609, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-47001
in-theory        47001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-47001.        (((A -> (B or A)) and (C -> (D -> (E -> D)))) and (F -> (G or F))), M:tm-609, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-47002
in-theory        47002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-47002.        (((A -> (B or A)) and ((C -> D) -> (C -> C))) and (E -> (F or E))), M:tm-609, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-47003
in-theory        47003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G or F)))
theorem-size     31
proof            (modus-ponens tm-609 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-47003.        (((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-47004
in-theory        47004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-47004.        (((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G))), M:tm-609, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-47005
in-theory        47005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-47005.        (((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-47006
in-theory        47006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> D))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-47006.        (((A -> (B or A)) and (C -> ((D and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-47007
in-theory        47007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-47007.        (((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-47008
in-theory        47008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D and E) -> E))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-47008.        (((A -> (B or A)) and (C -> ((D and E) -> E))) and (F -> (G or F))), M:tm-609, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-47009
in-theory        47009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-47009.        (((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))) and (F -> (G or F))), M:tm-609, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-47010
in-theory        47010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-47010.        (((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and (G -> (H or G))), M:tm-609, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-47011
in-theory        47011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-47011.        (((A -> (B or A)) and (C -> (((D and E) -> D) and C))) and (F -> (G or F))), M:tm-609, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-47012
in-theory        47012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-47012.        (((A -> (B or A)) and (C -> (((D and E) -> E) and C))) and (F -> (G or F))), M:tm-609, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-47013
in-theory        47013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-47013.        (((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))) and (F -> (G or F))), M:tm-609, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-47014
in-theory        47014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-47014.        (((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-47015
in-theory        47015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-47015.        (((A -> (B or A)) and (C -> (D -> (E -> (D and E))))) and (F -> (G or F))), M:tm-609, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-47016
in-theory        47016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-47016.        (((A -> (B or A)) and ((C -> (D -> C)) or E)) and (F -> (G or F))), M:tm-609, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-47017
in-theory        47017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-47017.        (((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and (G -> (H or G))), M:tm-609, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-47018
in-theory        47018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> C) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-47018.        (((A -> (B or A)) and (((C and D) -> C) or E)) and (F -> (G or F))), M:tm-609, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-47019
in-theory        47019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C and D) -> D) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-47019.        (((A -> (B or A)) and (((C and D) -> D) or E)) and (F -> (G or F))), M:tm-609, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-47020
in-theory        47020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-47020.        (((A -> (B or A)) and ((C -> (D -> (C and D))) or E)) and (F -> (G or F))), M:tm-609, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-47021
in-theory        47021
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (C or D)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-47021.        (((A -> (B or A)) and ((C -> (C or D)) or E)) and (F -> (G or F))), M:tm-609, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-47022
in-theory        47022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-47022.        (((A -> (B or A)) and (C -> ((D -> (D or E)) and C))) and (F -> (G or F))), M:tm-609, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-47023
in-theory        47023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (D or E)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-47023.        (((A -> (B or A)) and (C -> (D -> (D or E)))) and (F -> (G or F))), M:tm-609, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-47024
in-theory        47024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-47024.        (((A -> (B or A)) and (C or (D -> (E -> D)))) and (F -> (G or F))), M:tm-609, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-47025
in-theory        47025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-47025.        (((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (G -> (H or G))), M:tm-609, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-47026
in-theory        47026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> D))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-47026.        (((A -> (B or A)) and (C or ((D and E) -> D))) and (F -> (G or F))), M:tm-609, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-47027
in-theory        47027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or ((D and E) -> E))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-47027.        (((A -> (B or A)) and (C or ((D and E) -> E))) and (F -> (G or F))), M:tm-609, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-47028
in-theory        47028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-47028.        (((A -> (B or A)) and (C or (D -> (E -> (D and E))))) and (F -> (G or F))), M:tm-609, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-47029
in-theory        47029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (D or E)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-47029.        (((A -> (B or A)) and (C or (D -> (D or E)))) and (F -> (G or F))), M:tm-609, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-47030
in-theory        47030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C or (D -> (E or D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-47030.        (((A -> (B or A)) and (C or (D -> (E or D)))) and (F -> (G or F))), M:tm-609, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47031
in-theory        47031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> (D or C)) or E)) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-47031.        (((A -> (B or A)) and ((C -> (D or C)) or E)) and (F -> (G or F))), M:tm-609, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-47032
in-theory        47032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-47032.        (((A -> (B or A)) and (C -> ((D -> (E or D)) and C))) and (F -> (G or F))), M:tm-609, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-47033
in-theory        47033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-47033.        (((A -> (A or B)) and (C -> ((D -> (E or D)) and C))) and (F -> (G or F))), M:tm-609, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-47034
in-theory        47034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-47034.        ((A -> (A and ((B -> (C or B)) and A))) and (D -> (E or D))), M:tm-609, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-47035
in-theory        47035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-47035.        (((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))) and (F -> (G or F))), M:tm-609, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-47036
in-theory        47036
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-47036.        ((((A and B) -> B) and (C -> ((D -> (E or D)) and C))) and (F -> (G or F))), M:tm-609, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-47037
in-theory        47037
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-47037.        ((((A and B) -> A) and (C -> ((D -> (E or D)) and C))) and (F -> (G or F))), M:tm-609, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-47038
in-theory        47038
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (H or G)))
theorem-size     29
proof            (modus-ponens tm-609 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-47038.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))) and (G -> (H or G))), M:tm-609, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-47039
in-theory        47039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-47039.        (((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))) and (F -> (G or F))), M:tm-609, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-47040
in-theory        47040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-47040.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (D -> (E or D))), M:tm-609, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-47041
in-theory        47041
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-47041.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-47042
in-theory        47042
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C -> (D or C)) and B))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-47042.        ((A or (B -> ((C -> (D or C)) and B))) and (E -> (F or E))), M:tm-609, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-47043
in-theory        47043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) and A)) or D) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-47043.        (((A -> ((B -> (C or B)) and A)) or D) and (E -> (F or E))), M:tm-609, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-47044
in-theory        47044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-47044.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (E -> (F or E))), M:tm-609, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-47045
in-theory        47045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-47045.        ((A -> (B -> ((C -> (D or C)) and B))) and (E -> (F or E))), M:tm-609, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-47046
in-theory        47046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (C -> (D -> (E or D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47046.        (((A -> (B or A)) and (C -> (D -> (E or D)))) and (F -> (G or F))), M:tm-609, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47047
in-theory        47047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (C -> (D -> (E or D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47047.        (((A -> (A or B)) and (C -> (D -> (E or D)))) and (F -> (G or F))), M:tm-609, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47048
in-theory        47048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47048.        ((A -> (A and (B -> (C or B)))) and (D -> (E or D))), M:tm-609, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47049
in-theory        47049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (D and (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47049.        ((A -> ((B -> (C or B)) and A)) and (D -> (D and (E -> (F or E))))), M:tm-605, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47050
in-theory        47050
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (D -> (E or D))))
theorem-size     23
proof            (modus-ponens tm-602 tm-609 ((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47050.        ((A or ((B -> (C or B)) and A)) -> (((B -> (C or B)) and A) and (D -> (E or D)))), M:tm-602, m:tm-609, u:((Am (and (-> A (or B A)) C)) (D (and (and (-> A (or B A)) C) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47051
in-theory        47051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and ((D -> (E or D)) and (A -> (A and (B -> (C or B))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47051.        ((A -> (A and (B -> (C or B)))) and ((D -> (E or D)) and (A -> (A and (B -> (C or B)))))), M:tm-595, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47052
in-theory        47052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47052.        (((A -> (B or A)) or C) and (D -> (D and (E -> (F or E))))), M:tm-550, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47053
in-theory        47053
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47053.        ((A or (B -> (C or B))) and (D -> (D and (E -> (F or E))))), M:tm-540, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47054
in-theory        47054
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47054.        ((A or (B -> (B or C))) and (D -> (D and (E -> (F or E))))), M:tm-530, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47055
in-theory        47055
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (D and (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47055.        ((A or (B -> (C -> (B and C)))) and (D -> (D and (E -> (F or E))))), M:tm-520, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47056
in-theory        47056
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47056.        ((A or ((B and C) -> C)) and (D -> (D and (E -> (F or E))))), M:tm-510, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47057
in-theory        47057
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47057.        ((A or ((B and C) -> B)) and (D -> (D and (E -> (F or E))))), M:tm-500, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47058
in-theory        47058
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47058.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (G or F))))), M:tm-490, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47059
in-theory        47059
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47059.        ((A or (B -> (C -> B))) and (D -> (D and (E -> (F or E))))), M:tm-480, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47060
in-theory        47060
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((A and (B -> (C or B))) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47060.        (A -> ((A and (B -> (C or B))) or D)), M:tm-470, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47061
in-theory        47061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47061.        ((A -> (B -> (B or C))) and (D -> (D and (E -> (F or E))))), M:tm-469, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47062
in-theory        47062
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (D -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-466 tm-609 ((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47062.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (D -> (E or D)))), M:tm-466, m:tm-609, u:((Am (-> A (or A B))) (C (and (-> A (or A B)) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47063
in-theory        47063
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47063.        ((A -> (A and (B -> (C or B)))) and (D -> (D or E))), M:tm-456, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47064
in-theory        47064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (D and (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47064.        ((A -> ((B -> (B or C)) and A)) and (D -> (D and (E -> (F or E))))), M:tm-453, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47065
in-theory        47065
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (D -> (E or D))))
theorem-size     23
proof            (modus-ponens tm-450 tm-609 ((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47065.        ((A or ((B -> (B or C)) and A)) -> (((B -> (B or C)) and A) and (D -> (E or D)))), M:tm-450, m:tm-609, u:((Am (and (-> A (or A B)) C)) (D (and (and (-> A (or A B)) C) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47066
in-theory        47066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and ((D -> (D or E)) and (A -> (A and (B -> (C or B))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47066.        ((A -> (A and (B -> (C or B)))) and ((D -> (D or E)) and (A -> (A and (B -> (C or B)))))), M:tm-443, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47067
in-theory        47067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47067.        (((A -> (A or B)) or C) and (D -> (D and (E -> (F or E))))), M:tm-409, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47068
in-theory        47068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (D and (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47068.        (((A -> (B -> (A and B))) or C) and (D -> (D and (E -> (F or E))))), M:tm-400, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47069
in-theory        47069
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47069.        ((((A and B) -> B) or C) and (D -> (D and (E -> (F or E))))), M:tm-391, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47070
in-theory        47070
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47070.        ((((A and B) -> A) or C) and (D -> (D and (E -> (F or E))))), M:tm-382, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47071
in-theory        47071
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47071.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (E and (F -> (G or F))))), M:tm-373, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47072
in-theory        47072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47072.        (((A -> (B -> A)) or C) and (D -> (D and (E -> (F or E))))), M:tm-364, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47073
in-theory        47073
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((A and (C -> (D or C))) and B)))
theorem-size     13
proof            (modus-ponens tm-355 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47073.        (A -> (B -> ((A and (C -> (D or C))) and B))), M:tm-355, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47074
in-theory        47074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (D and (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47074.        ((A -> (B -> (C -> (B and C)))) and (D -> (D and (E -> (F or E))))), M:tm-354, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47075
in-theory        47075
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (D -> (E or D))))
theorem-size     23
proof            (modus-ponens tm-351 tm-609 ((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47075.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (D -> (E or D)))), M:tm-351, m:tm-609, u:((Am (-> A (-> B (and A B)))) (C (and (-> A (-> B (and A B))) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47076
in-theory        47076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47076.        ((A -> (A and (B -> (C or B)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47077
in-theory        47077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (C and (D -> (E or D)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47077.        (((A -> B) -> (A -> (A and B))) and (C -> (C and (D -> (E or D))))), M:tm-338, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47078
in-theory        47078
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (C -> (D or C))))
theorem-size     21
proof            (modus-ponens tm-335 tm-609 ((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47078.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (C -> (D or C)))), M:tm-335, m:tm-609, u:((Am (-> A (and A B))) (C (and (-> A (and A B)) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47079
in-theory        47079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (A -> (A and (A and (B -> (C or B))))))
theorem-size     21
proof            (modus-ponens tm-328 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47079.        ((A -> (A and (B -> (C or B)))) and (A -> (A and (A and (B -> (C or B)))))), M:tm-328, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47080
in-theory        47080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and ((D -> (E -> (D and E))) and (A -> (A and (B -> (C or B))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47080.        ((A -> (A and (B -> (C or B)))) and ((D -> (E -> (D and E))) and (A -> (A and (B -> (C or B)))))), M:tm-327, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47081
in-theory        47081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (((D and E) -> E) and (A -> (A and (B -> (C or B))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47081.        ((A -> (A and (B -> (C or B)))) and (((D and E) -> E) and (A -> (A and (B -> (C or B)))))), M:tm-326, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47082
in-theory        47082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (((D and E) -> D) and (A -> (A and (B -> (C or B))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47082.        ((A -> (A and (B -> (C or B)))) and (((D and E) -> D) and (A -> (A and (B -> (C or B)))))), M:tm-325, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47083
in-theory        47083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and (B -> (C or B))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47083.        ((A -> (A and (B -> (C or B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (A -> (A and (B -> (C or B)))))), M:tm-324, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47084
in-theory        47084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and ((D -> (E -> D)) and (A -> (A and (B -> (C or B))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47084.        ((A -> (A and (B -> (C or B)))) and ((D -> (E -> D)) and (A -> (A and (B -> (C or B)))))), M:tm-323, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47085
in-theory        47085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47085.        ((A -> (A and (B -> (C or B)))) and ((D and E) -> E)), M:tm-322, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47086
in-theory        47086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47086.        ((A -> (A and (B -> (C or B)))) and ((D and E) -> D)), M:tm-320, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47087
in-theory        47087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47087.        ((A -> (A and (B -> (C or B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47088
in-theory        47088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47088.        ((A -> (A and (B -> (C or B)))) and (A -> A)), M:tm-316, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47089
in-theory        47089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47089.        ((A -> (A and (B -> (C or B)))) and (D -> (E -> D))), M:tm-315, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47090
in-theory        47090
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and ((A -> (not (A and (B -> (C or B))))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47090.        ((A -> (A and (B -> (C or B)))) and ((A -> (not (A and (B -> (C or B))))) -> (not A))), M:tm-313, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47091
in-theory        47091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (((A and (B -> (C or B))) -> D) -> ((A or (A and (B -> (C or B)))) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47091.        ((A -> (A and (B -> (C or B)))) and (((A and (B -> (C or B))) -> D) -> ((A or (A and (B -> (C or B)))) -> D))), M:tm-312, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47092
in-theory        47092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (D or (A -> (A and (B -> (C or B))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47092.        ((A -> (A and (B -> (C or B)))) and (D or (A -> (A and (B -> (C or B)))))), M:tm-311, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47093
in-theory        47093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and ((A -> (A and (B -> (C or B)))) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47093.        ((A -> (A and (B -> (C or B)))) and ((A -> (A and (B -> (C or B)))) or D)), M:tm-310, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47094
in-theory        47094
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (D -> ((A -> (A and (B -> (C or B)))) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47094.        ((A -> (A and (B -> (C or B)))) and (D -> ((A -> (A and (B -> (C or B)))) and D))), M:tm-309, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47095
in-theory        47095
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (D -> (A -> (A and (B -> (C or B))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47095.        ((A -> (A and (B -> (C or B)))) and (D -> (A -> (A and (B -> (C or B)))))), M:tm-305, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47096
in-theory        47096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (E -> (F or E)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47096.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (D and (E -> (F or E))))), M:tm-303, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47097
in-theory        47097
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (D -> (E or D))))
theorem-size     27
proof            (modus-ponens tm-300 tm-609 ((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47097.        ((A or ((B -> (C -> (B and C))) and A)) -> (((B -> (C -> (B and C))) and A) and (D -> (E or D)))), M:tm-300, m:tm-609, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (and (-> A (-> B (and A B))) C) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47098
in-theory        47098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (D and (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47098.        ((A -> (((B and C) -> C) and A)) and (D -> (D and (E -> (F or E))))), M:tm-270, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47099
in-theory        47099
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (D -> (E or D))))
theorem-size     23
proof            (modus-ponens tm-267 tm-609 ((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47099.        ((A or (((B and C) -> C) and A)) -> ((((B and C) -> C) and A) and (D -> (E or D)))), M:tm-267, m:tm-609, u:((Am (and (-> (and A B) B) C)) (D (and (and (-> (and A B) B) C) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47100
in-theory        47100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (D and (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47100.        ((A -> (((B and C) -> B) and A)) and (D -> (D and (E -> (F or E))))), M:tm-239, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47101
in-theory        47101
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (D -> (E or D))))
theorem-size     23
proof            (modus-ponens tm-236 tm-609 ((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47101.        ((A or (((B and C) -> B) and A)) -> ((((B and C) -> B) and A) and (D -> (E or D)))), M:tm-236, m:tm-609, u:((Am (and (-> (and A B) A) C)) (D (and (and (-> (and A B) A) C) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47102
in-theory        47102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (F -> (G or F)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47102.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (E and (F -> (G or F))))), M:tm-210, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47103
in-theory        47103
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (E -> (F or E))))
theorem-size     39
proof            (modus-ponens tm-207 tm-609 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47103.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A) and (E -> (F or E)))), M:tm-207, m:tm-609, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47104
in-theory        47104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47104.        ((A -> ((B -> (C -> B)) and A)) and (D -> (D and (E -> (F or E))))), M:tm-183, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47105
in-theory        47105
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (D -> (E or D))))
theorem-size     23
proof            (modus-ponens tm-180 tm-609 ((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47105.        ((A or ((B -> (C -> B)) and A)) -> (((B -> (C -> B)) and A) and (D -> (E or D)))), M:tm-180, m:tm-609, u:((Am (and (-> A (-> B A)) C)) (D (and (and (-> A (-> B A)) C) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47106
in-theory        47106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47106.        ((A -> ((B and C) -> C)) and (D -> (D and (E -> (F or E))))), M:tm-157, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47107
in-theory        47107
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and (D -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-154 tm-609 ((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47107.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and (D -> (E or D)))), M:tm-154, m:tm-609, u:((Am (-> (and A B) B)) (C (and (-> (and A B) B) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47108
in-theory        47108
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (E -> (F or E)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47108.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (D and (E -> (F or E))))), M:tm-147, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47109
in-theory        47109
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (D -> (E or D))))
theorem-size     29
proof            (modus-ponens tm-144 tm-609 ((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47109.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and (D -> (E or D)))), M:tm-144, m:tm-609, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (and A (-> B C)) C) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47110
in-theory        47110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47110.        ((A -> ((B and C) -> B)) and (D -> (D and (E -> (F or E))))), M:tm-134, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47111
in-theory        47111
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and (D -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-131 tm-609 ((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47111.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and (D -> (E or D)))), M:tm-131, m:tm-609, u:((Am (-> (and A B) A)) (C (and (-> (and A B) A) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47112
in-theory        47112
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (E -> (F or E)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47112.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (D and (E -> (F or E))))), M:tm-125, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47113
in-theory        47113
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (D -> (E or D))))
theorem-size     29
proof            (modus-ponens tm-122 tm-609 ((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47113.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (D -> (E or D)))), M:tm-122, m:tm-609, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (and (-> A B) C) B) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47114
in-theory        47114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47114.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (E and (F -> (G or F))))), M:tm-113, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47115
in-theory        47115
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F or E))))
theorem-size     35
proof            (modus-ponens tm-110 tm-609 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47115.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F or E)))), M:tm-110, m:tm-609, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47116
in-theory        47116
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (E -> (F or E)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47116.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D and (E -> (F or E))))), M:tm-105, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47117
in-theory        47117
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (D -> (E or D))))
theorem-size     35
proof            (modus-ponens tm-102 tm-609 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47117.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (D -> (E or D)))), M:tm-102, m:tm-609, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> A (-> B C)) (-> A C)) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47118
in-theory        47118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (C and (D -> (E or D)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47118.        (((A -> B) -> (A -> A)) and (C -> (C and (D -> (E or D))))), M:tm-95, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47119
in-theory        47119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and (C -> (D or C))))
theorem-size     17
proof            (modus-ponens tm-92 tm-609 ((Am (-> A A)) (B (and (-> A A) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47119.        (((A -> B) or (A -> A)) -> ((A -> A) and (C -> (D or C)))), M:tm-92, m:tm-609, u:((Am (-> A A)) (B (and (-> A A) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47120
in-theory        47120
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (A and (C -> (D or C)))))
theorem-size     11
proof            (modus-ponens tm-84 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47120.        (A -> (B -> (A and (C -> (D or C))))), M:tm-84, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47121
in-theory        47121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47121.        ((A -> (B -> (C -> B))) and (D -> (D and (E -> (F or E))))), M:tm-83, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47122
in-theory        47122
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (D -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-80 tm-609 ((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47122.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (D -> (E or D)))), M:tm-80, m:tm-609, u:((Am (-> A (-> B A))) (C (and (-> A (-> B A)) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47123
in-theory        47123
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (B and (C -> (D or C)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47123.        (((not (not A)) -> A) and (B -> (B and (C -> (D or C))))), M:tm-76, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47124
in-theory        47124
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (A and (B -> (C or B))))
theorem-size     13
proof            (modus-ponens tm-73 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47124.        (((not (not A)) or A) -> (A and (B -> (C or B)))), M:tm-73, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47125
in-theory        47125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (D -> (E or D)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47125.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (C and (D -> (E or D))))), M:tm-69, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47126
in-theory        47126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (C -> (D or C))))
theorem-size     25
proof            (modus-ponens tm-66 tm-609 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47126.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (C -> (D or C)))), M:tm-66, m:tm-609, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> A (not B)) (not A)) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47127
in-theory        47127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (E -> (F or E)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47127.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (D and (E -> (F or E))))), M:tm-54, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47128
in-theory        47128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> (E or D))))
theorem-size     29
proof            (modus-ponens tm-51 tm-609 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47128.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and (D -> (E or D)))), M:tm-51, m:tm-609, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> A B) (-> (or C A) B)) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47129
in-theory        47129
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((B or A) and (C -> (D or C))))
theorem-size     15
proof            (modus-ponens tm-50 tm-609 ((Am (or A B)) (C (and (or A B) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47129.        ((A or (B or A)) -> ((B or A) and (C -> (D or C)))), M:tm-50, m:tm-609, u:((Am (or A B)) (C (and (or A B) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47130
in-theory        47130
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((A or B) and (C -> (D or C))))
theorem-size     15
proof            (modus-ponens tm-49 tm-609 ((Am (or A B)) (C (and (or A B) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47130.        ((A or (A or B)) -> ((A or B) and (C -> (D or C)))), M:tm-49, m:tm-609, u:((Am (or A B)) (C (and (or A B) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47131
in-theory        47131
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> (D or C))))
theorem-size     19
proof            (modus-ponens tm-48 tm-609 ((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47131.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (C -> (D or C)))), M:tm-48, m:tm-609, u:((Am (-> A (and B A))) (C (and (-> A (and B A)) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47132
in-theory        47132
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (C -> (D or C))))
theorem-size     13
proof            (modus-ponens tm-47 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47132.        (((A and B) or B) -> (B and (C -> (D or C)))), M:tm-47, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47133
in-theory        47133
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (C -> (D or C))))
theorem-size     13
proof            (modus-ponens tm-46 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47133.        (((A and B) or A) -> (A and (C -> (D or C)))), M:tm-46, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47134
in-theory        47134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (E or D))))
theorem-size     27
proof            (modus-ponens tm-45 tm-609 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47134.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (E or D)))), M:tm-45, m:tm-609, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47135
in-theory        47135
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (C -> (D or C))))
theorem-size     15
proof            (modus-ponens tm-44 tm-609 ((Am (-> A B)) (C (and (-> A B) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47135.        ((A or (B -> A)) -> ((B -> A) and (C -> (D or C)))), M:tm-44, m:tm-609, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47136
in-theory        47136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (C and (D -> (E or D)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47136.        ((A -> (B or A)) and (C -> (C and (D -> (E or D))))), M:tm-42, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47137
in-theory        47137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (C and (D -> (E or D)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47137.        ((A -> (A or B)) and (C -> (C and (D -> (E or D))))), M:tm-32, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47138
in-theory        47138
times-derived    1
----------------------------------------------------------------
theorem          (A -> (A and (A and (B -> (C or B)))))
theorem-size     11
proof            (modus-ponens tm-24 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47138.        (A -> (A and (A and (B -> (C or B))))), M:tm-24, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47139
in-theory        47139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (C and (D -> (E or D)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47139.        ((A -> (B -> (A and B))) and (C -> (C and (D -> (E or D))))), M:tm-23, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47140
in-theory        47140
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (C and (D -> (E or D)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47140.        (((A and B) -> B) and (C -> (C and (D -> (E or D))))), M:tm-22, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47141
in-theory        47141
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (C and (D -> (E or D)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47141.        (((A and B) -> A) and (C -> (C and (D -> (E or D))))), M:tm-21, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47142
in-theory        47142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (E -> (F or E)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47142.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D and (E -> (F or E))))), M:tm-20, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47143
in-theory        47143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (C and (D -> (E or D)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47143.        ((A -> (B -> A)) and (C -> (C and (D -> (E or D))))), M:tm-19, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47144
in-theory        47144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A and (B -> (C or B))))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-9 tm-2 tm-5 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47144.        ((A -> (not (A and (B -> (C or B))))) -> (not A)), M:tm-9, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47145
in-theory        47145
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C or B))) -> D) -> ((A or (A and (B -> (C or B)))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47145.        (((A and (B -> (C or B))) -> D) -> ((A or (A and (B -> (C or B)))) -> D)), M:tm-8, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-47146
in-theory        47146
times-derived    1
----------------------------------------------------------------
theorem          (A or (B -> (B and (C -> (D or C)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-7 tm-2 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47146.        (A or (B -> (B and (C -> (D or C))))), M:tm-7, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47147
in-theory        47147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-6 tm-2 tm-5 tm-1 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47147.        ((A -> (A and (B -> (C or B)))) or D), M:tm-6, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47148
in-theory        47148
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B and (C -> (D or C)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47148.        (A -> ((B -> (B and (C -> (D or C)))) and A)), M:tm-5, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47149
in-theory        47149
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (B and (C -> (D or C)))))
theorem-size     11
proof            (modus-ponens tm-1 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-1 tm-2 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47149.        (A -> (B -> (B and (C -> (D or C))))), M:tm-1, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47150
in-theory        47150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (F -> (G or F)))
theorem-size     21
proof            (modus-ponens tm-609 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47150.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (F -> (G or F))), M:tm-609, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47151
in-theory        47151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-605 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47151.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-605, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47152
in-theory        47152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> (D -> (E or D))))))
theorem-size     37
proof            (modus-ponens tm-595 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47152.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))))), M:tm-595, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47153
in-theory        47153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-550 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47153.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-550, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47154
in-theory        47154
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-540 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47154.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-540, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47155
in-theory        47155
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-530 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47155.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-530, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47156
in-theory        47156
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-520 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47156.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-520, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47157
in-theory        47157
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-510 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47157.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-510, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47158
in-theory        47158
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-500 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47158.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-500, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47159
in-theory        47159
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-490 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47159.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H))))), M:tm-490, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47160
in-theory        47160
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-480 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47160.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-480, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47161
in-theory        47161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-469 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47161.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-469, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47162
in-theory        47162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (F -> (F or G)))
theorem-size     21
proof            (modus-ponens tm-456 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47162.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (F -> (F or G))), M:tm-456, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47163
in-theory        47163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-453 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47163.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-453, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47164
in-theory        47164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> (D -> (E or D))))))
theorem-size     37
proof            (modus-ponens tm-443 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47164.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))))), M:tm-443, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47165
in-theory        47165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-409 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47165.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-409, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47166
in-theory        47166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-400 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47166.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-400, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47167
in-theory        47167
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-391 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47167.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-391, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47168
in-theory        47168
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-382 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47168.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-382, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47169
in-theory        47169
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-373 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47169.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H))))), M:tm-373, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47170
in-theory        47170
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-364 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47170.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-364, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47171
in-theory        47171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-354 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47171.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-354, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47172
in-theory        47172
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (F -> (G -> (F and G))))
theorem-size     23
proof            (modus-ponens tm-341 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47172.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47173
in-theory        47173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-338 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47173.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F))))), M:tm-338, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47174
in-theory        47174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> (D -> (E or D))))))
theorem-size     39
proof            (modus-ponens tm-327 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47174.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))))), M:tm-327, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47175
in-theory        47175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> (D -> (E or D))))))
theorem-size     37
proof            (modus-ponens tm-326 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47175.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))))), M:tm-326, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47176
in-theory        47176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> (D -> (E or D))))))
theorem-size     37
proof            (modus-ponens tm-325 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47176.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))))), M:tm-325, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47177
in-theory        47177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> (D -> (E or D))))))
theorem-size     45
proof            (modus-ponens tm-324 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47177.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))))), M:tm-324, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47178
in-theory        47178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> (D -> (E or D))))))
theorem-size     37
proof            (modus-ponens tm-323 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47178.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))))), M:tm-323, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47179
in-theory        47179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and ((F and G) -> G))
theorem-size     21
proof            (modus-ponens tm-322 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47179.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and ((F and G) -> G)), M:tm-322, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47180
in-theory        47180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and ((F and G) -> F))
theorem-size     21
proof            (modus-ponens tm-320 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47180.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and ((F and G) -> F)), M:tm-320, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47181
in-theory        47181
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     29
proof            (modus-ponens tm-318 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47181.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47182
in-theory        47182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (F -> (G -> F)))
theorem-size     21
proof            (modus-ponens tm-315 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47182.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (F -> (G -> F))), M:tm-315, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47183
in-theory        47183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (F or ((A -> (B -> (A and B))) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-311 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47183.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (F or ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))))), M:tm-311, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47184
in-theory        47184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) or F))
theorem-size     33
proof            (modus-ponens tm-310 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47184.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) or F)), M:tm-310, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47185
in-theory        47185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (F -> (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and F)))
theorem-size     35
proof            (modus-ponens tm-309 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47185.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (F -> (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and F))), M:tm-309, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47186
in-theory        47186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (C -> (D -> (E or D))))
theorem-size     23
proof            (modus-ponens tm-308 tm-610 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47186.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (C -> (D -> (E or D)))), M:tm-308, m:tm-610, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-47187
in-theory        47187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (A -> (B -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-307 tm-610 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47187.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-610, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-47188
in-theory        47188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (F -> ((A -> (B -> (A and B))) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-305 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47188.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) and (F -> ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))))), M:tm-305, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47189
in-theory        47189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-303 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47189.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-303, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47190
in-theory        47190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-270 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47190.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-270, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47191
in-theory        47191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-239 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47191.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-239, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47192
in-theory        47192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H)))))
theorem-size     33
proof            (modus-ponens tm-210 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47192.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H))))), M:tm-210, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47193
in-theory        47193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-183 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47193.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-183, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47194
in-theory        47194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-157 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47194.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-157, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47195
in-theory        47195
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-147 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47195.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-147, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47196
in-theory        47196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-134 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47196.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-134, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47197
in-theory        47197
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-125 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47197.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-125, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47198
in-theory        47198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-113 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47198.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H))))), M:tm-113, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47199
in-theory        47199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     35
proof            (modus-ponens tm-105 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47199.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-105, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47200
in-theory        47200
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-95 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47200.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F))))), M:tm-95, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47201
in-theory        47201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-83 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47201.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-83, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47202
in-theory        47202
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (E -> (F or E)))))
theorem-size     21
proof            (modus-ponens tm-76 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47202.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (D -> (E -> (F or E))))), M:tm-76, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47203
in-theory        47203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F)))))
theorem-size     27
proof            (modus-ponens tm-69 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47203.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F))))), M:tm-69, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47204
in-theory        47204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-54 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47204.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-54, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47205
in-theory        47205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-42 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47205.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F))))), M:tm-42, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47206
in-theory        47206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-32 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47206.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F))))), M:tm-32, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47207
in-theory        47207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-23 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47207.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F))))), M:tm-23, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47208
in-theory        47208
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-22 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47208.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F))))), M:tm-22, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47209
in-theory        47209
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-21 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47209.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F))))), M:tm-21, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47210
in-theory        47210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-20 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47210.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-20, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47211
in-theory        47211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-19 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47211.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (E -> (F -> (G or F))))), M:tm-19, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47212
in-theory        47212
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (D -> (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-7 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47212.        (A or ((B -> (C -> (B and C))) and (D -> (E -> (F or E))))), M:tm-7, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47213
in-theory        47213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) or F)
theorem-size     17
proof            (modus-ponens tm-6 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47213.        (((A -> (B -> (A and B))) and (C -> (D -> (E or D)))) or F), M:tm-6, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47214
in-theory        47214
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (D -> (E -> (F or E)))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47214.        (A -> (((B -> (C -> (B and C))) and (D -> (E -> (F or E)))) and A)), M:tm-5, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47215
in-theory        47215
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D -> (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-1 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47215.        (A -> ((B -> (C -> (B and C))) and (D -> (E -> (F or E))))), M:tm-1, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47216
in-theory        47216
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47216.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and (F -> (G or F))), M:tm-609, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47217
in-theory        47217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47217.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-605, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47218
in-theory        47218
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47218.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((F -> (G or F)) and (((A and B) -> B) and (C -> (D -> (E or D)))))), M:tm-595, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47219
in-theory        47219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47219.        (((A -> (B or A)) or C) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-550, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47220
in-theory        47220
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47220.        ((A or (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-540, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47221
in-theory        47221
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47221.        ((A or (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-530, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47222
in-theory        47222
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47222.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-520, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47223
in-theory        47223
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47223.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-510, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47224
in-theory        47224
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47224.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-500, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47225
in-theory        47225
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47225.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (I or H))))), M:tm-490, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47226
in-theory        47226
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47226.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-480, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47227
in-theory        47227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47227.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-469, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47228
in-theory        47228
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47228.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and (F -> (F or G))), M:tm-456, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47229
in-theory        47229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47229.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-453, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47230
in-theory        47230
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47230.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((F -> (F or G)) and (((A and B) -> B) and (C -> (D -> (E or D)))))), M:tm-443, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47231
in-theory        47231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47231.        (((A -> (A or B)) or C) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-409, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47232
in-theory        47232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47232.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-400, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47233
in-theory        47233
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47233.        ((((A and B) -> B) or C) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-391, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47234
in-theory        47234
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47234.        ((((A and B) -> A) or C) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-382, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47235
in-theory        47235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47235.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (G -> (H -> (I or H))))), M:tm-373, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47236
in-theory        47236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47236.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-364, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47237
in-theory        47237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47237.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-354, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47238
in-theory        47238
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47238.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47239
in-theory        47239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47239.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (E -> (F -> (G or F))))), M:tm-338, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47240
in-theory        47240
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> (D -> (E or D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47240.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (C -> (D -> (E or D)))))), M:tm-327, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47241
in-theory        47241
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and (((F and G) -> G) and (((A and B) -> B) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47241.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and (((F and G) -> G) and (((A and B) -> B) and (C -> (D -> (E or D)))))), M:tm-326, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47242
in-theory        47242
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and (((F and G) -> F) and (((A and B) -> B) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47242.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and (((F and G) -> F) and (((A and B) -> B) and (C -> (D -> (E or D)))))), M:tm-325, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47243
in-theory        47243
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> (D -> (E or D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47243.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (C -> (D -> (E or D)))))), M:tm-324, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47244
in-theory        47244
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47244.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((F -> (G -> F)) and (((A and B) -> B) and (C -> (D -> (E or D)))))), M:tm-323, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47245
in-theory        47245
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47245.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((F and G) -> G)), M:tm-322, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47246
in-theory        47246
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47246.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((F and G) -> F)), M:tm-320, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47247
in-theory        47247
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47247.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47248
in-theory        47248
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47248.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and (F -> (G -> F))), M:tm-315, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47249
in-theory        47249
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and (F or (((A and B) -> B) and (C -> (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47249.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and (F or (((A and B) -> B) and (C -> (D -> (E or D)))))), M:tm-311, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47250
in-theory        47250
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((((A and B) -> B) and (C -> (D -> (E or D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47250.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((((A and B) -> B) and (C -> (D -> (E or D)))) or F)), M:tm-310, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47251
in-theory        47251
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and (F -> ((((A and B) -> B) and (C -> (D -> (E or D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47251.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and (F -> ((((A and B) -> B) and (C -> (D -> (E or D)))) and F))), M:tm-309, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47252
in-theory        47252
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and (C -> (D -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-611 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47252.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and (C -> (D -> (E or D)))), M:tm-308, m:tm-611, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-47253
in-theory        47253
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-307 tm-611 ((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47253.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and ((A and B) -> B)), M:tm-307, m:tm-611, u:((A (-> (and Am Bm) Bm)) (B (-> Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-47254
in-theory        47254
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) and (F -> (((A and B) -> B) and (C -> (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47254.        ((((A and B) -> B) and (C -> (D -> (E or D)))) and (F -> (((A and B) -> B) and (C -> (D -> (E or D)))))), M:tm-305, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47255
in-theory        47255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47255.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-303, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47256
in-theory        47256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47256.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-270, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47257
in-theory        47257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47257.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-239, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47258
in-theory        47258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47258.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (G -> (H -> (I or H))))), M:tm-210, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47259
in-theory        47259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47259.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-183, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47260
in-theory        47260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47260.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-157, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47261
in-theory        47261
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47261.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-147, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47262
in-theory        47262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47262.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-134, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47263
in-theory        47263
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47263.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-125, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47264
in-theory        47264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47264.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (G -> (H -> (I or H))))), M:tm-113, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47265
in-theory        47265
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47265.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-105, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47266
in-theory        47266
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47266.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (E -> (F -> (G or F))))), M:tm-95, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47267
in-theory        47267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47267.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-83, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47268
in-theory        47268
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (D -> (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47268.        (((not (not A)) -> A) and (((B and C) -> C) and (D -> (E -> (F or E))))), M:tm-76, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47269
in-theory        47269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-4 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47269.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (E -> (F -> (G or F))))), M:tm-69, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47270
in-theory        47270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47270.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-54, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47271
in-theory        47271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47271.        ((A -> (B or A)) and (((C and D) -> D) and (E -> (F -> (G or F))))), M:tm-42, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47272
in-theory        47272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47272.        ((A -> (A or B)) and (((C and D) -> D) and (E -> (F -> (G or F))))), M:tm-32, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47273
in-theory        47273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47273.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (E -> (F -> (G or F))))), M:tm-23, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47274
in-theory        47274
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47274.        (((A and B) -> B) and (((C and D) -> D) and (E -> (F -> (G or F))))), M:tm-22, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47275
in-theory        47275
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47275.        (((A and B) -> A) and (((C and D) -> D) and (E -> (F -> (G or F))))), M:tm-21, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47276
in-theory        47276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47276.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-20, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47277
in-theory        47277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47277.        ((A -> (B -> A)) and (((C and D) -> D) and (E -> (F -> (G or F))))), M:tm-19, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47278
in-theory        47278
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-4 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47278.        (A or (((B and C) -> C) and (D -> (E -> (F or E))))), M:tm-7, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47279
in-theory        47279
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (C -> (D -> (E or D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-4 tm-1 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47279.        ((((A and B) -> B) and (C -> (D -> (E or D)))) or F), M:tm-6, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47280
in-theory        47280
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (D -> (E -> (F or E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47280.        (A -> ((((B and C) -> C) and (D -> (E -> (F or E)))) and A)), M:tm-5, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47281
in-theory        47281
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-4 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47281.        (A -> (((B and C) -> C) and (D -> (E -> (F or E))))), M:tm-1, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47282
in-theory        47282
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47282.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and (F -> (G or F))), M:tm-609, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47283
in-theory        47283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47283.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-605, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47284
in-theory        47284
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47284.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((F -> (G or F)) and (((A and B) -> A) and (C -> (D -> (E or D)))))), M:tm-595, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47285
in-theory        47285
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47285.        (((A -> (B or A)) or C) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-550, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47286
in-theory        47286
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47286.        ((A or (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-540, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47287
in-theory        47287
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47287.        ((A or (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-530, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47288
in-theory        47288
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47288.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-520, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47289
in-theory        47289
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47289.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-510, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47290
in-theory        47290
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47290.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-500, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47291
in-theory        47291
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47291.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (I or H))))), M:tm-490, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47292
in-theory        47292
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47292.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-480, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47293
in-theory        47293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47293.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-469, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47294
in-theory        47294
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47294.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and (F -> (F or G))), M:tm-456, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47295
in-theory        47295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47295.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-453, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47296
in-theory        47296
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47296.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((F -> (F or G)) and (((A and B) -> A) and (C -> (D -> (E or D)))))), M:tm-443, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47297
in-theory        47297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47297.        (((A -> (A or B)) or C) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-409, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47298
in-theory        47298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47298.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-400, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47299
in-theory        47299
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47299.        ((((A and B) -> B) or C) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-391, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47300
in-theory        47300
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47300.        ((((A and B) -> A) or C) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-382, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47301
in-theory        47301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47301.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (G -> (H -> (I or H))))), M:tm-373, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47302
in-theory        47302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47302.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-364, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47303
in-theory        47303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47303.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-354, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47304
in-theory        47304
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47304.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47305
in-theory        47305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47305.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (E -> (F -> (G or F))))), M:tm-338, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47306
in-theory        47306
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> (D -> (E or D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47306.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (C -> (D -> (E or D)))))), M:tm-327, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47307
in-theory        47307
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and (((F and G) -> G) and (((A and B) -> A) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47307.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and (((F and G) -> G) and (((A and B) -> A) and (C -> (D -> (E or D)))))), M:tm-326, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47308
in-theory        47308
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and (((F and G) -> F) and (((A and B) -> A) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47308.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and (((F and G) -> F) and (((A and B) -> A) and (C -> (D -> (E or D)))))), M:tm-325, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47309
in-theory        47309
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> (D -> (E or D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47309.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (C -> (D -> (E or D)))))), M:tm-324, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47310
in-theory        47310
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47310.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((F -> (G -> F)) and (((A and B) -> A) and (C -> (D -> (E or D)))))), M:tm-323, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47311
in-theory        47311
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47311.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((F and G) -> G)), M:tm-322, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47312
in-theory        47312
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47312.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((F and G) -> F)), M:tm-320, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47313
in-theory        47313
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47313.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47314
in-theory        47314
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47314.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and (F -> (G -> F))), M:tm-315, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47315
in-theory        47315
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and (F or (((A and B) -> A) and (C -> (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47315.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and (F or (((A and B) -> A) and (C -> (D -> (E or D)))))), M:tm-311, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47316
in-theory        47316
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((((A and B) -> A) and (C -> (D -> (E or D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47316.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((((A and B) -> A) and (C -> (D -> (E or D)))) or F)), M:tm-310, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47317
in-theory        47317
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and (F -> ((((A and B) -> A) and (C -> (D -> (E or D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47317.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and (F -> ((((A and B) -> A) and (C -> (D -> (E or D)))) and F))), M:tm-309, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47318
in-theory        47318
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and (C -> (D -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-612 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47318.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and (C -> (D -> (E or D)))), M:tm-308, m:tm-612, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-47319
in-theory        47319
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-307 tm-612 ((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47319.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and ((A and B) -> A)), M:tm-307, m:tm-612, u:((A (-> (and Am Bm) Am)) (B (-> Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-47320
in-theory        47320
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) and (F -> (((A and B) -> A) and (C -> (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47320.        ((((A and B) -> A) and (C -> (D -> (E or D)))) and (F -> (((A and B) -> A) and (C -> (D -> (E or D)))))), M:tm-305, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47321
in-theory        47321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47321.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-303, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47322
in-theory        47322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47322.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-270, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47323
in-theory        47323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47323.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-239, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47324
in-theory        47324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47324.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (G -> (H -> (I or H))))), M:tm-210, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47325
in-theory        47325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47325.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-183, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47326
in-theory        47326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47326.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-157, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47327
in-theory        47327
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47327.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-147, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47328
in-theory        47328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47328.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-134, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47329
in-theory        47329
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47329.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-125, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47330
in-theory        47330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47330.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (G -> (H -> (I or H))))), M:tm-113, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47331
in-theory        47331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47331.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-105, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47332
in-theory        47332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47332.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (E -> (F -> (G or F))))), M:tm-95, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47333
in-theory        47333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47333.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-83, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47334
in-theory        47334
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (D -> (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47334.        (((not (not A)) -> A) and (((B and C) -> B) and (D -> (E -> (F or E))))), M:tm-76, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47335
in-theory        47335
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-3 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47335.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (E -> (F -> (G or F))))), M:tm-69, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47336
in-theory        47336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47336.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-54, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47337
in-theory        47337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47337.        ((A -> (B or A)) and (((C and D) -> C) and (E -> (F -> (G or F))))), M:tm-42, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47338
in-theory        47338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47338.        ((A -> (A or B)) and (((C and D) -> C) and (E -> (F -> (G or F))))), M:tm-32, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47339
in-theory        47339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47339.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (E -> (F -> (G or F))))), M:tm-23, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47340
in-theory        47340
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47340.        (((A and B) -> B) and (((C and D) -> C) and (E -> (F -> (G or F))))), M:tm-22, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47341
in-theory        47341
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47341.        (((A and B) -> A) and (((C and D) -> C) and (E -> (F -> (G or F))))), M:tm-21, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47342
in-theory        47342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47342.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-20, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47343
in-theory        47343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47343.        ((A -> (B -> A)) and (((C and D) -> C) and (E -> (F -> (G or F))))), M:tm-19, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47344
in-theory        47344
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-3 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47344.        (A or (((B and C) -> B) and (D -> (E -> (F or E))))), M:tm-7, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47345
in-theory        47345
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (C -> (D -> (E or D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-3 tm-1 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47345.        ((((A and B) -> A) and (C -> (D -> (E or D)))) or F), M:tm-6, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47346
in-theory        47346
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (D -> (E -> (F or E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47346.        (A -> ((((B and C) -> B) and (D -> (E -> (F or E)))) and A)), M:tm-5, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47347
in-theory        47347
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-3 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47347.        (A -> (((B and C) -> B) and (D -> (E -> (F or E))))), M:tm-1, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47348
in-theory        47348
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (G -> (H or G)))
theorem-size     27
proof            (modus-ponens tm-609 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47348.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (G -> (H or G))), M:tm-609, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47349
in-theory        47349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47349.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-605, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47350
in-theory        47350
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47350.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))))), M:tm-595, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47351
in-theory        47351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47351.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-550, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47352
in-theory        47352
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47352.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-540, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47353
in-theory        47353
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47353.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-530, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47354
in-theory        47354
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47354.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-520, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47355
in-theory        47355
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47355.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-510, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47356
in-theory        47356
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47356.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-500, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47357
in-theory        47357
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47357.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J or I))))), M:tm-490, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47358
in-theory        47358
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47358.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-480, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47359
in-theory        47359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47359.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-469, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47360
in-theory        47360
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (G -> (G or H)))
theorem-size     27
proof            (modus-ponens tm-456 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47360.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (G -> (G or H))), M:tm-456, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47361
in-theory        47361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47361.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-453, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47362
in-theory        47362
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47362.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))))), M:tm-443, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47363
in-theory        47363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47363.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-409, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47364
in-theory        47364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47364.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-400, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47365
in-theory        47365
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47365.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-391, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47366
in-theory        47366
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47366.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-382, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47367
in-theory        47367
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47367.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J or I))))), M:tm-373, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47368
in-theory        47368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47368.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-364, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47369
in-theory        47369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47369.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-354, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47370
in-theory        47370
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (G -> (H -> (G and H))))
theorem-size     29
proof            (modus-ponens tm-341 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47370.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47371
in-theory        47371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47371.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G))))), M:tm-338, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47372
in-theory        47372
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47372.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))))), M:tm-327, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47373
in-theory        47373
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47373.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))))), M:tm-326, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47374
in-theory        47374
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47374.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))))), M:tm-325, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47375
in-theory        47375
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47375.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))))), M:tm-324, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47376
in-theory        47376
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47376.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))))), M:tm-323, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47377
in-theory        47377
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((G and H) -> H))
theorem-size     27
proof            (modus-ponens tm-322 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47377.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((G and H) -> H)), M:tm-322, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47378
in-theory        47378
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((G and H) -> G))
theorem-size     27
proof            (modus-ponens tm-320 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47378.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((G and H) -> G)), M:tm-320, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47379
in-theory        47379
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     35
proof            (modus-ponens tm-318 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47379.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47380
in-theory        47380
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (G -> (H -> G)))
theorem-size     27
proof            (modus-ponens tm-315 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47380.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (G -> (H -> G))), M:tm-315, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47381
in-theory        47381
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47381.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))))), M:tm-311, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47382
in-theory        47382
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) or G))
theorem-size     45
proof            (modus-ponens tm-310 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47382.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) or G)), M:tm-310, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47383
in-theory        47383
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and G)))
theorem-size     47
proof            (modus-ponens tm-309 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47383.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and G))), M:tm-309, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47384
in-theory        47384
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (D -> (E -> (F or E))))
theorem-size     29
proof            (modus-ponens tm-308 tm-613 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (or Fm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47384.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (D -> (E -> (F or E)))), M:tm-308, m:tm-613, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (or Fm Em)))))
================================================================
tm-name          tm-47385
in-theory        47385
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-307 tm-613 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (or Fm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47385.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-613, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (or Fm Em)))))
================================================================
tm-name          tm-47386
in-theory        47386
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47386.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))))), M:tm-305, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47387
in-theory        47387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47387.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-303, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47388
in-theory        47388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47388.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-270, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47389
in-theory        47389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47389.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-239, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47390
in-theory        47390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J or I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47390.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J or I))))), M:tm-210, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47391
in-theory        47391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47391.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-183, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47392
in-theory        47392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47392.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-157, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47393
in-theory        47393
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47393.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-147, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47394
in-theory        47394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47394.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-134, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47395
in-theory        47395
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47395.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-125, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47396
in-theory        47396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J or I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47396.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J or I))))), M:tm-113, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47397
in-theory        47397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47397.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-105, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47398
in-theory        47398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47398.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G))))), M:tm-95, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47399
in-theory        47399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47399.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-83, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47400
in-theory        47400
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G or F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47400.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G or F))))), M:tm-76, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47401
in-theory        47401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47401.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G))))), M:tm-69, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47402
in-theory        47402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47402.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-54, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47403
in-theory        47403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47403.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G))))), M:tm-42, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47404
in-theory        47404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47404.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G))))), M:tm-32, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47405
in-theory        47405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47405.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G))))), M:tm-23, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47406
in-theory        47406
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47406.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G))))), M:tm-22, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47407
in-theory        47407
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47407.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G))))), M:tm-21, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47408
in-theory        47408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47408.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-20, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47409
in-theory        47409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47409.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (F -> (G -> (H or G))))), M:tm-19, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47410
in-theory        47410
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-7 tm-5 tm-2 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47410.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G or F))))), M:tm-7, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47411
in-theory        47411
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) or G)
theorem-size     23
proof            (modus-ponens tm-6 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-6 tm-5 tm-2 tm-1 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47411.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))) or G), M:tm-6, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47412
in-theory        47412
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G or F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47412.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G or F)))) and A)), M:tm-5, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47413
in-theory        47413
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-1 tm-5 tm-2 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47413.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E -> (F -> (G or F))))), M:tm-1, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-47414
in-theory        47414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (F -> (G or F)))
theorem-size     19
proof            (modus-ponens tm-609 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47414.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (F -> (G or F))), M:tm-609, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47415
in-theory        47415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47415.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-605, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47416
in-theory        47416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47416.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and ((F -> (G or F)) and ((A -> (B -> A)) and (C -> (D -> (E or D)))))), M:tm-595, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47417
in-theory        47417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47417.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-550, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47418
in-theory        47418
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47418.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-540, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47419
in-theory        47419
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47419.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-530, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47420
in-theory        47420
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47420.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-520, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47421
in-theory        47421
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47421.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-510, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47422
in-theory        47422
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47422.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-500, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47423
in-theory        47423
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47423.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I or H))))), M:tm-490, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47424
in-theory        47424
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47424.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-480, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47425
in-theory        47425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47425.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-469, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47426
in-theory        47426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (F -> (F or G)))
theorem-size     19
proof            (modus-ponens tm-456 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47426.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (F -> (F or G))), M:tm-456, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47427
in-theory        47427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47427.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-453, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47428
in-theory        47428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47428.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and ((F -> (F or G)) and ((A -> (B -> A)) and (C -> (D -> (E or D)))))), M:tm-443, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47429
in-theory        47429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47429.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-409, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47430
in-theory        47430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47430.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-400, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47431
in-theory        47431
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47431.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-391, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47432
in-theory        47432
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47432.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-382, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47433
in-theory        47433
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47433.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (G -> (H -> (I or H))))), M:tm-373, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47434
in-theory        47434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47434.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-364, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47435
in-theory        47435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47435.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-354, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47436
in-theory        47436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (F -> (G -> (F and G))))
theorem-size     21
proof            (modus-ponens tm-341 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47436.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47437
in-theory        47437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47437.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (G or F))))), M:tm-338, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47438
in-theory        47438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> (D -> (E or D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47438.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (C -> (D -> (E or D)))))), M:tm-327, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47439
in-theory        47439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47439.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (((F and G) -> G) and ((A -> (B -> A)) and (C -> (D -> (E or D)))))), M:tm-326, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47440
in-theory        47440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47440.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (((F and G) -> F) and ((A -> (B -> A)) and (C -> (D -> (E or D)))))), M:tm-325, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47441
in-theory        47441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> (D -> (E or D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47441.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (C -> (D -> (E or D)))))), M:tm-324, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47442
in-theory        47442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> (D -> (E or D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47442.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (C -> (D -> (E or D)))))), M:tm-323, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47443
in-theory        47443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and ((F and G) -> G))
theorem-size     19
proof            (modus-ponens tm-322 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47443.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and ((F and G) -> G)), M:tm-322, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47444
in-theory        47444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and ((F and G) -> F))
theorem-size     19
proof            (modus-ponens tm-320 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47444.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and ((F and G) -> F)), M:tm-320, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47445
in-theory        47445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     27
proof            (modus-ponens tm-318 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47445.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47446
in-theory        47446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (F -> (G -> F)))
theorem-size     19
proof            (modus-ponens tm-315 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47446.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (F -> (G -> F))), M:tm-315, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47447
in-theory        47447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (F or ((A -> (B -> A)) and (C -> (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47447.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (F or ((A -> (B -> A)) and (C -> (D -> (E or D)))))), M:tm-311, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47448
in-theory        47448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (((A -> (B -> A)) and (C -> (D -> (E or D)))) or F))
theorem-size     29
proof            (modus-ponens tm-310 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47448.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (((A -> (B -> A)) and (C -> (D -> (E or D)))) or F)), M:tm-310, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47449
in-theory        47449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (F -> (((A -> (B -> A)) and (C -> (D -> (E or D)))) and F)))
theorem-size     31
proof            (modus-ponens tm-309 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47449.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (F -> (((A -> (B -> A)) and (C -> (D -> (E or D)))) and F))), M:tm-309, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47450
in-theory        47450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (C -> (D -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-308 tm-614 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47450.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (C -> (D -> (E or D)))), M:tm-308, m:tm-614, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-47451
in-theory        47451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (A -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-307 tm-614 ((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47451.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (A -> (B -> A))), M:tm-307, m:tm-614, u:((A (-> Am (-> Bm Am))) (B (-> Cm (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-47452
in-theory        47452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (F -> ((A -> (B -> A)) and (C -> (D -> (E or D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47452.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) and (F -> ((A -> (B -> A)) and (C -> (D -> (E or D)))))), M:tm-305, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47453
in-theory        47453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47453.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-303, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47454
in-theory        47454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47454.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-270, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47455
in-theory        47455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47455.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-239, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47456
in-theory        47456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (H -> (I or H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47456.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (G -> (H -> (I or H))))), M:tm-210, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47457
in-theory        47457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47457.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-183, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47458
in-theory        47458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47458.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-157, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47459
in-theory        47459
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47459.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-147, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47460
in-theory        47460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47460.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-134, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47461
in-theory        47461
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47461.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-125, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47462
in-theory        47462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47462.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (G -> (H -> (I or H))))), M:tm-113, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47463
in-theory        47463
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47463.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-105, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47464
in-theory        47464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47464.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (E -> (F -> (G or F))))), M:tm-95, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47465
in-theory        47465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47465.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-83, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47466
in-theory        47466
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47466.        (((not (not A)) -> A) and ((B -> (C -> B)) and (D -> (E -> (F or E))))), M:tm-76, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47467
in-theory        47467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47467.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (E -> (F -> (G or F))))), M:tm-69, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47468
in-theory        47468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47468.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-54, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47469
in-theory        47469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47469.        ((A -> (B or A)) and ((C -> (D -> C)) and (E -> (F -> (G or F))))), M:tm-42, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47470
in-theory        47470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47470.        ((A -> (A or B)) and ((C -> (D -> C)) and (E -> (F -> (G or F))))), M:tm-32, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47471
in-theory        47471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47471.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (E -> (F -> (G or F))))), M:tm-23, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47472
in-theory        47472
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47472.        (((A and B) -> B) and ((C -> (D -> C)) and (E -> (F -> (G or F))))), M:tm-22, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47473
in-theory        47473
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47473.        (((A and B) -> A) and ((C -> (D -> C)) and (E -> (F -> (G or F))))), M:tm-21, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47474
in-theory        47474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47474.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-20, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47475
in-theory        47475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47475.        ((A -> (B -> A)) and ((C -> (D -> C)) and (E -> (F -> (G or F))))), M:tm-19, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47476
in-theory        47476
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47476.        (A or ((B -> (C -> B)) and (D -> (E -> (F or E))))), M:tm-7, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47477
in-theory        47477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (C -> (D -> (E or D)))) or F)
theorem-size     15
proof            (modus-ponens tm-6 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-6 tm-5 tm-1 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47477.        (((A -> (B -> A)) and (C -> (D -> (E or D)))) or F), M:tm-6, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47478
in-theory        47478
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (D -> (E -> (F or E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47478.        (A -> (((B -> (C -> B)) and (D -> (E -> (F or E)))) and A)), M:tm-5, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47479
in-theory        47479
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-47479.        (A -> ((B -> (C -> B)) and (D -> (E -> (F or E))))), M:tm-1, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-47480
in-theory        47480
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47480.        (((A and ((B -> (C or B)) -> D)) -> D) and (E -> (F or E))), M:tm-609, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47481
in-theory        47481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-605 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47481.        ((A -> ((B -> (C or B)) and A)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-605, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47482
in-theory        47482
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) or ((D -> (E or D)) and ((A -> (B or A)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-602 tm-615 ((Am (-> A (or B A))) (C (-> (-> Bm (or Cm Bm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47482.        ((((A -> (B or A)) -> C) or ((D -> (E or D)) and ((A -> (B or A)) -> C))) -> C), M:tm-602, m:tm-615, u:((Am (-> A (or B A))) (C (-> (-> Bm (or Cm Bm)) Dm)) (D Dm))
================================================================
tm-name          tm-47483
in-theory        47483
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and ((E -> (F or E)) and ((A and ((B -> (C or B)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-595 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47483.        (((A and ((B -> (C or B)) -> D)) -> D) and ((E -> (F or E)) and ((A and ((B -> (C or B)) -> D)) -> D))), M:tm-595, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47484
in-theory        47484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-550 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47484.        (((A -> (B or A)) or C) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-550, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47485
in-theory        47485
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-540 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47485.        ((A or (B -> (C or B))) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-540, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47486
in-theory        47486
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-530 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47486.        ((A or (B -> (B or C))) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-530, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47487
in-theory        47487
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-520 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47487.        ((A or (B -> (C -> (B and C)))) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-520, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47488
in-theory        47488
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-510 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47488.        ((A or ((B and C) -> C)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-510, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47489
in-theory        47489
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-500 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-4 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47489.        ((A or ((B and C) -> B)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-500, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47490
in-theory        47490
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (G or F)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-490 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47490.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (G or F)) -> H)) -> H)), M:tm-490, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47491
in-theory        47491
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-480 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47491.        ((A or (B -> (C -> B))) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-480, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47492
in-theory        47492
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> D)) -> (D or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-6 tm-4 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47492.        ((A and ((B -> (C or B)) -> D)) -> (D or E)), M:tm-470, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-47493
in-theory        47493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-469 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47493.        ((A -> (B -> (B or C))) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-469, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47494
in-theory        47494
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C or B)) -> (not (D -> (D or E))))))
theorem-size     15
proof            (modus-ponens tm-465 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) (not (-> B (or B C)))))) (Dm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47494.        (not (A and ((B -> (C or B)) -> (not (D -> (D or E)))))), M:tm-465, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) (not (-> B (or B C)))))) (Dm (not (-> B (or B C)))))
================================================================
tm-name          tm-47495
in-theory        47495
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47495.        (((A and ((B -> (C or B)) -> D)) -> D) and (E -> (E or F))), M:tm-456, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47496
in-theory        47496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-453 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47496.        ((A -> ((B -> (B or C)) and A)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-453, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47497
in-theory        47497
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) or ((D -> (D or E)) and ((A -> (B or A)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-450 tm-615 ((Am (-> A (or A B))) (C (-> (-> Bm (or Cm Bm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-4 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47497.        ((((A -> (B or A)) -> C) or ((D -> (D or E)) and ((A -> (B or A)) -> C))) -> C), M:tm-450, m:tm-615, u:((Am (-> A (or A B))) (C (-> (-> Bm (or Cm Bm)) Dm)) (D Dm))
================================================================
tm-name          tm-47498
in-theory        47498
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and ((E -> (E or F)) and ((A and ((B -> (C or B)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-443 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47498.        (((A and ((B -> (C or B)) -> D)) -> D) and ((E -> (E or F)) and ((A and ((B -> (C or B)) -> D)) -> D))), M:tm-443, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47499
in-theory        47499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-409 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47499.        (((A -> (A or B)) or C) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-409, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47500
in-theory        47500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-400 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47500.        (((A -> (B -> (A and B))) or C) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-400, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47501
in-theory        47501
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-391 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47501.        ((((A and B) -> B) or C) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-391, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47502
in-theory        47502
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-382 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47502.        ((((A and B) -> A) or C) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-382, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47503
in-theory        47503
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and ((F -> (G or F)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-373 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47503.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E and ((F -> (G or F)) -> H)) -> H)), M:tm-373, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47504
in-theory        47504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-364 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47504.        (((A -> (B -> A)) or C) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-364, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47505
in-theory        47505
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> D)) -> (E -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-355 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-5 tm-4 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47505.        ((A and ((B -> (C or B)) -> D)) -> (E -> (D and E))), M:tm-355, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-47506
in-theory        47506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-354 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47506.        ((A -> (B -> (C -> (B and C)))) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-354, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47507
in-theory        47507
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C or B)) -> (not (D -> (E -> (D and E)))))))
theorem-size     17
proof            (modus-ponens tm-350 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) (not (-> B (-> C (and B C))))))) (Dm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47507.        (not (A and ((B -> (C or B)) -> (not (D -> (E -> (D and E))))))), M:tm-350, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) (not (-> B (-> C (and B C))))))) (Dm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-47508
in-theory        47508
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47508.        (((A and ((B -> (C or B)) -> D)) -> D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47509
in-theory        47509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C and ((D -> (E or D)) -> F)) -> F))
theorem-size     21
proof            (modus-ponens tm-338 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47509.        (((A -> B) -> (A -> (A and B))) and ((C and ((D -> (E or D)) -> F)) -> F)), M:tm-338, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47510
in-theory        47510
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and ((A and ((B -> (C or B)) -> D)) -> ((A and ((B -> (C or B)) -> D)) and D)))
theorem-size     33
proof            (modus-ponens tm-328 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47510.        (((A and ((B -> (C or B)) -> D)) -> D) and ((A and ((B -> (C or B)) -> D)) -> ((A and ((B -> (C or B)) -> D)) and D))), M:tm-328, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-47511
in-theory        47511
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and ((E -> (F -> (E and F))) and ((A and ((B -> (C or B)) -> D)) -> D)))
theorem-size     31
proof            (modus-ponens tm-327 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47511.        (((A and ((B -> (C or B)) -> D)) -> D) and ((E -> (F -> (E and F))) and ((A and ((B -> (C or B)) -> D)) -> D))), M:tm-327, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47512
in-theory        47512
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and (((E and F) -> F) and ((A and ((B -> (C or B)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-326 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47512.        (((A and ((B -> (C or B)) -> D)) -> D) and (((E and F) -> F) and ((A and ((B -> (C or B)) -> D)) -> D))), M:tm-326, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47513
in-theory        47513
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and (((E and F) -> E) and ((A and ((B -> (C or B)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-325 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47513.        (((A and ((B -> (C or B)) -> D)) -> D) and (((E and F) -> E) and ((A and ((B -> (C or B)) -> D)) -> D))), M:tm-325, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47514
in-theory        47514
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A and ((B -> (C or B)) -> D)) -> D)))
theorem-size     37
proof            (modus-ponens tm-324 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47514.        (((A and ((B -> (C or B)) -> D)) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A and ((B -> (C or B)) -> D)) -> D))), M:tm-324, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47515
in-theory        47515
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and ((E -> (F -> E)) and ((A and ((B -> (C or B)) -> D)) -> D)))
theorem-size     29
proof            (modus-ponens tm-323 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47515.        (((A and ((B -> (C or B)) -> D)) -> D) and ((E -> (F -> E)) and ((A and ((B -> (C or B)) -> D)) -> D))), M:tm-323, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47516
in-theory        47516
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47516.        (((A and ((B -> (C or B)) -> D)) -> D) and ((E and F) -> F)), M:tm-322, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47517
in-theory        47517
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> (B -> (C or B)))) -> (B -> (C or B))) and ((A and ((B -> (C or B)) -> (B -> (C or B)))) -> (B -> (C or B))))
theorem-size     39
proof            (modus-ponens tm-321 tm-615 ((A Am) (Dm (-> Bm (or Cm Bm))) (C (-> Bm (or Cm Bm))) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47517.        (((A and ((B -> (C or B)) -> (B -> (C or B)))) -> (B -> (C or B))) and ((A and ((B -> (C or B)) -> (B -> (C or B)))) -> (B -> (C or B)))), M:tm-321, m:tm-615, u:((A Am) (Dm (-> Bm (or Cm Bm))) (C (-> Bm (or Cm Bm))) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-47518
in-theory        47518
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47518.        (((A and ((B -> (C or B)) -> D)) -> D) and ((E and F) -> E)), M:tm-320, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47519
in-theory        47519
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and ((C -> (D or C)) -> A)) -> A) and (((A -> B) and ((C -> (D or C)) -> A)) -> B))
theorem-size     27
proof            (modus-ponens tm-319 tm-615 ((Am (-> Dm B)) (C (-> (-> Bm (or Cm Bm)) Dm)) (A Dm)))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47519.        ((((A -> B) and ((C -> (D or C)) -> A)) -> A) and (((A -> B) and ((C -> (D or C)) -> A)) -> B)), M:tm-319, m:tm-615, u:((Am (-> Dm B)) (C (-> (-> Bm (or Cm Bm)) Dm)) (A Dm))
================================================================
tm-name          tm-47520
in-theory        47520
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47520.        (((A and ((B -> (C or B)) -> D)) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47521
in-theory        47521
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and ((A and ((B -> (C or B)) -> D)) -> (A and ((B -> (C or B)) -> D))))
theorem-size     31
proof            (modus-ponens tm-316 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47521.        (((A and ((B -> (C or B)) -> D)) -> D) and ((A and ((B -> (C or B)) -> D)) -> (A and ((B -> (C or B)) -> D)))), M:tm-316, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-47522
in-theory        47522
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47522.        (((A and ((B -> (C or B)) -> D)) -> D) and (E -> (F -> E))), M:tm-315, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47523
in-theory        47523
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and (((A and ((B -> (C or B)) -> D)) -> (not D)) -> (not (A and ((B -> (C or B)) -> D)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-9 tm-4 tm-1 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47523.        (((A and ((B -> (C or B)) -> D)) -> D) and (((A and ((B -> (C or B)) -> D)) -> (not D)) -> (not (A and ((B -> (C or B)) -> D))))), M:tm-313, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-47524
in-theory        47524
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and ((D -> E) -> (((A and ((B -> (C or B)) -> D)) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-312 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47524.        (((A and ((B -> (C or B)) -> D)) -> D) and ((D -> E) -> (((A and ((B -> (C or B)) -> D)) or D) -> E))), M:tm-312, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-47525
in-theory        47525
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and (E or ((A and ((B -> (C or B)) -> D)) -> D)))
theorem-size     25
proof            (modus-ponens tm-311 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47525.        (((A and ((B -> (C or B)) -> D)) -> D) and (E or ((A and ((B -> (C or B)) -> D)) -> D))), M:tm-311, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47526
in-theory        47526
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and (((A and ((B -> (C or B)) -> D)) -> D) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47526.        (((A and ((B -> (C or B)) -> D)) -> D) and (((A and ((B -> (C or B)) -> D)) -> D) or E)), M:tm-310, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47527
in-theory        47527
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and (E -> (((A and ((B -> (C or B)) -> D)) -> D) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47527.        (((A and ((B -> (C or B)) -> D)) -> D) and (E -> (((A and ((B -> (C or B)) -> D)) -> D) and E))), M:tm-309, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47528
in-theory        47528
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> (D -> E))) -> (D -> E)) and (((A and ((B -> (C or B)) -> (D -> E))) -> D) -> ((A and ((B -> (C or B)) -> (D -> E))) -> E)))
theorem-size     43
proof            (modus-ponens tm-306 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47528.        (((A and ((B -> (C or B)) -> (D -> E))) -> (D -> E)) and (((A and ((B -> (C or B)) -> (D -> E))) -> D) -> ((A and ((B -> (C or B)) -> (D -> E))) -> E))), M:tm-306, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-47529
in-theory        47529
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and (E -> ((A and ((B -> (C or B)) -> D)) -> D)))
theorem-size     25
proof            (modus-ponens tm-305 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47529.        (((A and ((B -> (C or B)) -> D)) -> D) and (E -> ((A and ((B -> (C or B)) -> D)) -> D))), M:tm-305, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47530
in-theory        47530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-303 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47530.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-303, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47531
in-theory        47531
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) or ((D -> (E -> (D and E))) and ((A -> (B or A)) -> C))) -> C)
theorem-size     25
proof            (modus-ponens tm-300 tm-615 ((Am (-> A (-> B (and A B)))) (C (-> (-> Bm (or Cm Bm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47531.        ((((A -> (B or A)) -> C) or ((D -> (E -> (D and E))) and ((A -> (B or A)) -> C))) -> C), M:tm-300, m:tm-615, u:((Am (-> A (-> B (and A B)))) (C (-> (-> Bm (or Cm Bm)) Dm)) (D Dm))
================================================================
tm-name          tm-47532
in-theory        47532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-270 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47532.        ((A -> (((B and C) -> C) and A)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-270, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47533
in-theory        47533
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) or (((D and E) -> E) and ((A -> (B or A)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-267 tm-615 ((Am (-> (and A B) B)) (C (-> (-> Bm (or Cm Bm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-4 tm-2 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47533.        ((((A -> (B or A)) -> C) or (((D and E) -> E) and ((A -> (B or A)) -> C))) -> C), M:tm-267, m:tm-615, u:((Am (-> (and A B) B)) (C (-> (-> Bm (or Cm Bm)) Dm)) (D Dm))
================================================================
tm-name          tm-47534
in-theory        47534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-239 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47534.        ((A -> (((B and C) -> B) and A)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-239, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47535
in-theory        47535
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) or (((D and E) -> D) and ((A -> (B or A)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-236 tm-615 ((Am (-> (and A B) A)) (C (-> (-> Bm (or Cm Bm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-3 tm-2 tm-4 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47535.        ((((A -> (B or A)) -> C) or (((D and E) -> D) and ((A -> (B or A)) -> C))) -> C), M:tm-236, m:tm-615, u:((Am (-> (and A B) A)) (C (-> (-> Bm (or Cm Bm)) Dm)) (D Dm))
================================================================
tm-name          tm-47536
in-theory        47536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and ((F -> (G or F)) -> H)) -> H))
theorem-size     29
proof            (modus-ponens tm-210 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47536.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E and ((F -> (G or F)) -> H)) -> H)), M:tm-210, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47537
in-theory        47537
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B or A)) -> C))) -> C)
theorem-size     31
proof            (modus-ponens tm-207 tm-615 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm (or Cm Bm)) Dm)) (E Dm)))
axioms-used      (tm-8 tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47537.        ((((A -> (B or A)) -> C) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B or A)) -> C))) -> C), M:tm-207, m:tm-615, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm (or Cm Bm)) Dm)) (E Dm))
================================================================
tm-name          tm-47538
in-theory        47538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-183 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47538.        ((A -> ((B -> (C -> B)) and A)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-183, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47539
in-theory        47539
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) or ((D -> (E -> D)) and ((A -> (B or A)) -> C))) -> C)
theorem-size     23
proof            (modus-ponens tm-180 tm-615 ((Am (-> A (-> B A))) (C (-> (-> Bm (or Cm Bm)) Dm)) (D Dm)))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47539.        ((((A -> (B or A)) -> C) or ((D -> (E -> D)) and ((A -> (B or A)) -> C))) -> C), M:tm-180, m:tm-615, u:((Am (-> A (-> B A))) (C (-> (-> Bm (or Cm Bm)) Dm)) (D Dm))
================================================================
tm-name          tm-47540
in-theory        47540
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> (D and E))) -> E)
theorem-size     13
proof            (modus-ponens tm-158 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) (and B C)))) (Dm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47540.        ((A and ((B -> (C or B)) -> (D and E))) -> E), M:tm-158, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) (and B C)))) (Dm (and B C)))
================================================================
tm-name          tm-47541
in-theory        47541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-157 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47541.        ((A -> ((B and C) -> C)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-157, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47542
in-theory        47542
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C or B)) -> (not ((D and E) -> E)))))
theorem-size     15
proof            (modus-ponens tm-153 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) (not (-> (and B C) C))))) (Dm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47542.        (not (A and ((B -> (C or B)) -> (not ((D and E) -> E))))), M:tm-153, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) (not (-> (and B C) C))))) (Dm (not (-> (and B C) C))))
================================================================
tm-name          tm-47543
in-theory        47543
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-147 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47543.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-147, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47544
in-theory        47544
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> (B -> (C or B)))) -> (B -> (C or B)))
theorem-size     19
proof            (modus-ponens tm-142 tm-615 ((A Am) (Dm (-> Bm (or Cm Bm))) (C (-> Bm (or Cm Bm))) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47544.        ((A and ((B -> (C or B)) -> (B -> (C or B)))) -> (B -> (C or B))), M:tm-142, m:tm-615, u:((A Am) (Dm (-> Bm (or Cm Bm))) (C (-> Bm (or Cm Bm))) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-47545
in-theory        47545
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> (D and E))) -> D)
theorem-size     13
proof            (modus-ponens tm-135 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) (and B C)))) (Dm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47545.        ((A and ((B -> (C or B)) -> (D and E))) -> D), M:tm-135, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) (and B C)))) (Dm (and B C)))
================================================================
tm-name          tm-47546
in-theory        47546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-134 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47546.        ((A -> ((B and C) -> B)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-134, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47547
in-theory        47547
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C or B)) -> (not ((D and E) -> D)))))
theorem-size     15
proof            (modus-ponens tm-130 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) (not (-> (and B C) B))))) (Dm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47547.        (not (A and ((B -> (C or B)) -> (not ((D and E) -> D))))), M:tm-130, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) (not (-> (and B C) B))))) (Dm (not (-> (and B C) B))))
================================================================
tm-name          tm-47548
in-theory        47548
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> (A -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-129 tm-615 ((A Am) (B (-> (-> Bm (or Cm Bm)) (-> Am C))) (Dm (-> Am C))))
axioms-used      (tm-2 tm-1 tm-3 tm-4 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47548.        ((A and ((B -> (C or B)) -> (A -> D))) -> D), M:tm-129, m:tm-615, u:((A Am) (B (-> (-> Bm (or Cm Bm)) (-> Am C))) (Dm (-> Am C)))
================================================================
tm-name          tm-47549
in-theory        47549
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-125 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47549.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-125, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47550
in-theory        47550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and ((C -> (D or C)) -> A)) -> A)
theorem-size     13
proof            (modus-ponens tm-120 tm-615 ((Am (-> Dm B)) (C (-> (-> Bm (or Cm Bm)) Dm)) (A Dm)))
axioms-used      (tm-2 tm-1 tm-3 tm-4 tm-7)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47550.        (((A -> B) and ((C -> (D or C)) -> A)) -> A), M:tm-120, m:tm-615, u:((Am (-> Dm B)) (C (-> (-> Bm (or Cm Bm)) Dm)) (A Dm))
================================================================
tm-name          tm-47551
in-theory        47551
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) and ((C -> (D or C)) -> (A -> B))) -> B)
theorem-size     17
proof            (modus-ponens tm-119 tm-615 ((Am (-> (-> A B) A)) (C (-> (-> Bm (or Cm Bm)) (-> A B))) (Dm (-> A B))))
axioms-used      (tm-2 tm-3 tm-4 tm-1 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47551.        ((((A -> B) -> A) and ((C -> (D or C)) -> (A -> B))) -> B), M:tm-119, m:tm-615, u:((Am (-> (-> A B) A)) (C (-> (-> Bm (or Cm Bm)) (-> A B))) (Dm (-> A B)))
================================================================
tm-name          tm-47552
in-theory        47552
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> (D -> (E -> F)))) -> ((D -> E) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-114 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) (-> B (-> C D))))) (Dm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-4 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47552.        ((A and ((B -> (C or B)) -> (D -> (E -> F)))) -> ((D -> E) -> (D -> F))), M:tm-114, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) (-> B (-> C D))))) (Dm (-> B (-> C D))))
================================================================
tm-name          tm-47553
in-theory        47553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (G or F)) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-113 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47553.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E and ((F -> (G or F)) -> H)) -> H)), M:tm-113, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47554
in-theory        47554
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C or B)) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))))
theorem-size     23
proof            (modus-ponens tm-109 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Dm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47554.        (not (A and ((B -> (C or B)) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))), M:tm-109, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Dm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-47555
in-theory        47555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     31
proof            (modus-ponens tm-105 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47555.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-105, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47556
in-theory        47556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C and ((D -> (E or D)) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-95 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47556.        (((A -> B) -> (A -> A)) and ((C and ((D -> (E or D)) -> F)) -> F)), M:tm-95, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47557
in-theory        47557
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> (D -> E))) -> (D -> E))
theorem-size     15
proof            (modus-ponens tm-87 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47557.        ((A and ((B -> (C or B)) -> (D -> E))) -> (D -> E)), M:tm-87, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-47558
in-theory        47558
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> D)) -> (E -> D))
theorem-size     13
proof            (modus-ponens tm-84 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-4 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47558.        ((A and ((B -> (C or B)) -> D)) -> (E -> D)), M:tm-84, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-47559
in-theory        47559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-83 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47559.        ((A -> (B -> (C -> B))) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-83, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47560
in-theory        47560
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C or B)) -> (not (D -> (E -> D))))))
theorem-size     15
proof            (modus-ponens tm-79 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) (not (-> B (-> C B)))))) (Dm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47560.        (not (A and ((B -> (C or B)) -> (not (D -> (E -> D)))))), M:tm-79, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) (not (-> B (-> C B)))))) (Dm (not (-> B (-> C B)))))
================================================================
tm-name          tm-47561
in-theory        47561
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B and ((C -> (D or C)) -> E)) -> E))
theorem-size     17
proof            (modus-ponens tm-76 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-10 tm-2 tm-4 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47561.        (((not (not A)) -> A) and ((B and ((C -> (D or C)) -> E)) -> E)), M:tm-76, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47562
in-theory        47562
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A and ((B -> (C or B)) -> D)))) or (A and ((B -> (C or B)) -> D))) -> D)
theorem-size     23
proof            (modus-ponens tm-73 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-8 tm-10 tm-2 tm-4 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47562.        (((not (not (A and ((B -> (C or B)) -> D)))) or (A and ((B -> (C or B)) -> D))) -> D), M:tm-73, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-47563
in-theory        47563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and ((D -> (E or D)) -> F)) -> F))
theorem-size     23
proof            (modus-ponens tm-69 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-9 tm-2 tm-4 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47563.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C and ((D -> (E or D)) -> F)) -> F)), M:tm-69, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47564
in-theory        47564
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C or B)) -> (not A))))
theorem-size     11
proof            (modus-ponens tm-59 tm-615 ((A Am) (B (-> (-> Bm (or Cm Bm)) (not Am))) (Dm (not Am))))
axioms-used      (tm-9 tm-3 tm-2 tm-4 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47564.        (not (A and ((B -> (C or B)) -> (not A)))), M:tm-59, m:tm-615, u:((A Am) (B (-> (-> Bm (or Cm Bm)) (not Am))) (Dm (not Am)))
================================================================
tm-name          tm-47565
in-theory        47565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-54 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47565.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-54, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47566
in-theory        47566
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and ((C -> (D or C)) -> E))) or (B and ((C -> (D or C)) -> E))) -> E)
theorem-size     23
proof            (modus-ponens tm-47 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47566.        (((A and (B and ((C -> (D or C)) -> E))) or (B and ((C -> (D or C)) -> E))) -> E), M:tm-47, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-47567
in-theory        47567
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C or B)) -> D)) and E) or (A and ((B -> (C or B)) -> D))) -> D)
theorem-size     23
proof            (modus-ponens tm-46 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-8 tm-3 tm-2 tm-4 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47567.        ((((A and ((B -> (C or B)) -> D)) and E) or (A and ((B -> (C or B)) -> D))) -> D), M:tm-46, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-47568
in-theory        47568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C and ((D -> (E or D)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-42 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47568.        ((A -> (B or A)) and ((C and ((D -> (E or D)) -> F)) -> F)), M:tm-42, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47569
in-theory        47569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C and ((D -> (E or D)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-32 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47569.        ((A -> (A or B)) and ((C and ((D -> (E or D)) -> F)) -> F)), M:tm-32, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47570
in-theory        47570
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> D)) -> ((A and ((B -> (C or B)) -> D)) and D))
theorem-size     21
proof            (modus-ponens tm-24 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47570.        ((A and ((B -> (C or B)) -> D)) -> ((A and ((B -> (C or B)) -> D)) and D)), M:tm-24, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-47571
in-theory        47571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C and ((D -> (E or D)) -> F)) -> F))
theorem-size     19
proof            (modus-ponens tm-23 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47571.        ((A -> (B -> (A and B))) and ((C and ((D -> (E or D)) -> F)) -> F)), M:tm-23, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47572
in-theory        47572
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C and ((D -> (E or D)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-22 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47572.        (((A and B) -> B) and ((C and ((D -> (E or D)) -> F)) -> F)), M:tm-22, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47573
in-theory        47573
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C and ((D -> (E or D)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-21 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-3 tm-2 tm-4 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47573.        (((A and B) -> A) and ((C and ((D -> (E or D)) -> F)) -> F)), M:tm-21, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47574
in-theory        47574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-20 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47574.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-20, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47575
in-theory        47575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C and ((D -> (E or D)) -> F)) -> F))
theorem-size     17
proof            (modus-ponens tm-19 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47575.        ((A -> (B -> A)) and ((C and ((D -> (E or D)) -> F)) -> F)), M:tm-19, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47576
in-theory        47576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and ((C -> (D or C)) -> A)) -> B)
theorem-size     13
proof            (modus-ponens tm-15 tm-615 ((Am (-> Dm B)) (C (-> (-> Bm (or Cm Bm)) Dm)) (A Dm)))
axioms-used      (tm-2 tm-3 tm-4 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47576.        (((A -> B) and ((C -> (D or C)) -> A)) -> B), M:tm-15, m:tm-615, u:((Am (-> Dm B)) (C (-> (-> Bm (or Cm Bm)) Dm)) (A Dm))
================================================================
tm-name          tm-47577
in-theory        47577
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> D)) -> (A and ((B -> (C or B)) -> D)))
theorem-size     19
proof            (modus-ponens tm-12 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-4 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47577.        ((A and ((B -> (C or B)) -> D)) -> (A and ((B -> (C or B)) -> D))), M:tm-12, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-47578
in-theory        47578
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> (not D)) -> (not (A and ((B -> (C or B)) -> D))))
theorem-size     23
proof            (modus-ponens tm-9 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-9 tm-2 tm-4 tm-1 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47578.        (((A and ((B -> (C or B)) -> D)) -> (not D)) -> (not (A and ((B -> (C or B)) -> D)))), M:tm-9, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-47579
in-theory        47579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C and ((D -> (E or D)) -> A)) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47579.        ((A -> B) -> (((C and ((D -> (E or D)) -> A)) or A) -> B)), M:tm-8, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-47580
in-theory        47580
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B and ((C -> (D or C)) -> E)) -> E))
theorem-size     13
proof            (modus-ponens tm-7 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-7 tm-2 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47580.        (A or ((B and ((C -> (D or C)) -> E)) -> E)), M:tm-7, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47581
in-theory        47581
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-6 tm-2 tm-4 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47581.        (((A and ((B -> (C or B)) -> D)) -> D) or E), M:tm-6, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47582
in-theory        47582
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and ((C -> (D or C)) -> E)) -> E) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47582.        (A -> (((B and ((C -> (D or C)) -> E)) -> E) and A)), M:tm-5, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47583
in-theory        47583
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> (D -> E))) -> D) -> ((A and ((B -> (C or B)) -> (D -> E))) -> E))
theorem-size     27
proof            (modus-ponens tm-2 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) (-> B C)))) (Dm (-> B C))))
axioms-used      (tm-2 tm-4 tm-1 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47583.        (((A and ((B -> (C or B)) -> (D -> E))) -> D) -> ((A and ((B -> (C or B)) -> (D -> E))) -> E)), M:tm-2, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) (-> B C)))) (Dm (-> B C)))
================================================================
tm-name          tm-47584
in-theory        47584
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B and ((C -> (D or C)) -> E)) -> E))
theorem-size     13
proof            (modus-ponens tm-1 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-1 tm-2 tm-4 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47584.        (A -> ((B and ((C -> (D or C)) -> E)) -> E)), M:tm-1, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-47585
in-theory        47585
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47585.        (((((A -> (B or A)) -> C) and D) -> C) and (E -> (F or E))), M:tm-609, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47586
in-theory        47586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-605 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47586.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-605, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47587
in-theory        47587
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C or B)) -> (D or (B -> (C or B)))) and A)) -> (D or (B -> (C or B))))
theorem-size     25
proof            (modus-ponens tm-602 tm-616 ((A (-> Am (or Bm Am))) (Cm (or B (-> Am (or Bm Am)))) (C Dm) (D (or B (-> Am (or Bm Am))))))
axioms-used      (tm-8 tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47587.        ((A or (((B -> (C or B)) -> (D or (B -> (C or B)))) and A)) -> (D or (B -> (C or B)))), M:tm-602, m:tm-616, u:((A (-> Am (or Bm Am))) (Cm (or B (-> Am (or Bm Am)))) (C Dm) (D (or B (-> Am (or Bm Am)))))
================================================================
tm-name          tm-47588
in-theory        47588
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and ((E -> (F or E)) and ((((A -> (B or A)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-595 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47588.        (((((A -> (B or A)) -> C) and D) -> C) and ((E -> (F or E)) and ((((A -> (B or A)) -> C) and D) -> C))), M:tm-595, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47589
in-theory        47589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-550 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47589.        (((A -> (B or A)) or C) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-550, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47590
in-theory        47590
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-540 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47590.        ((A or (B -> (C or B))) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-540, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47591
in-theory        47591
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-530 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47591.        ((A or (B -> (B or C))) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-530, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47592
in-theory        47592
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-520 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47592.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-520, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47593
in-theory        47593
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-510 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-3 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47593.        ((A or ((B and C) -> C)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-510, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47594
in-theory        47594
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-500 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47594.        ((A or ((B and C) -> B)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-500, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47595
in-theory        47595
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F or E)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-490 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47595.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F or E)) -> G) and H) -> G)), M:tm-490, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47596
in-theory        47596
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-480 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47596.        ((A or (B -> (C -> B))) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-480, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47597
in-theory        47597
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) and D) -> (C or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-6 tm-3 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47597.        ((((A -> (B or A)) -> C) and D) -> (C or E)), M:tm-470, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-47598
in-theory        47598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-469 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47598.        ((A -> (B -> (B or C))) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-469, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47599
in-theory        47599
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B or A)) -> (not (C -> (C or D)))) and E))
theorem-size     15
proof            (modus-ponens tm-465 tm-616 ((A (and (-> (-> Am (or Bm Am)) (not (-> B (or B C)))) Dm)) (Cm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-2 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47599.        (not (((A -> (B or A)) -> (not (C -> (C or D)))) and E)), M:tm-465, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) (not (-> B (or B C)))) Dm)) (Cm (not (-> B (or B C)))))
================================================================
tm-name          tm-47600
in-theory        47600
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47600.        (((((A -> (B or A)) -> C) and D) -> C) and (E -> (E or F))), M:tm-456, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47601
in-theory        47601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-453 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47601.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-453, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47602
in-theory        47602
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C or B)) -> ((B -> (C or B)) or D)) and A)) -> ((B -> (C or B)) or D))
theorem-size     25
proof            (modus-ponens tm-450 tm-616 ((A (-> Am (or Bm Am))) (Cm (or (-> Am (or Bm Am)) B)) (C Dm) (D (or (-> Am (or Bm Am)) B))))
axioms-used      (tm-8 tm-5 tm-6 tm-2 tm-3 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47602.        ((A or (((B -> (C or B)) -> ((B -> (C or B)) or D)) and A)) -> ((B -> (C or B)) or D)), M:tm-450, m:tm-616, u:((A (-> Am (or Bm Am))) (Cm (or (-> Am (or Bm Am)) B)) (C Dm) (D (or (-> Am (or Bm Am)) B)))
================================================================
tm-name          tm-47603
in-theory        47603
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and ((E -> (E or F)) and ((((A -> (B or A)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-443 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47603.        (((((A -> (B or A)) -> C) and D) -> C) and ((E -> (E or F)) and ((((A -> (B or A)) -> C) and D) -> C))), M:tm-443, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47604
in-theory        47604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-409 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47604.        (((A -> (A or B)) or C) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-409, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47605
in-theory        47605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-400 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47605.        (((A -> (B -> (A and B))) or C) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-400, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47606
in-theory        47606
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-391 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47606.        ((((A and B) -> B) or C) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-391, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47607
in-theory        47607
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-382 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47607.        ((((A and B) -> A) or C) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-382, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47608
in-theory        47608
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F or E)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-373 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47608.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F or E)) -> G) and H) -> G)), M:tm-373, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47609
in-theory        47609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-364 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47609.        (((A -> (B -> A)) or C) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-364, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47610
in-theory        47610
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) and D) -> (E -> (C and E)))
theorem-size     15
proof            (modus-ponens tm-355 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-5 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47610.        ((((A -> (B or A)) -> C) and D) -> (E -> (C and E))), M:tm-355, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-47611
in-theory        47611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-354 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47611.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-354, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47612
in-theory        47612
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B or A)) -> (not (C -> (D -> (C and D))))) and E))
theorem-size     17
proof            (modus-ponens tm-350 tm-616 ((A (and (-> (-> Am (or Bm Am)) (not (-> B (-> C (and B C))))) Dm)) (Cm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47612.        (not (((A -> (B or A)) -> (not (C -> (D -> (C and D))))) and E)), M:tm-350, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) (not (-> B (-> C (and B C))))) Dm)) (Cm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-47613
in-theory        47613
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47613.        (((((A -> (B or A)) -> C) and D) -> C) and (E -> (F -> (E and F)))), M:tm-341, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47614
in-theory        47614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D or C)) -> E) and F) -> E))
theorem-size     21
proof            (modus-ponens tm-338 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47614.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D or C)) -> E) and F) -> E)), M:tm-338, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47615
in-theory        47615
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and ((((A -> (B or A)) -> C) and D) -> ((((A -> (B or A)) -> C) and D) and C)))
theorem-size     33
proof            (modus-ponens tm-328 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47615.        (((((A -> (B or A)) -> C) and D) -> C) and ((((A -> (B or A)) -> C) and D) -> ((((A -> (B or A)) -> C) and D) and C))), M:tm-328, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-47616
in-theory        47616
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and ((E -> (F -> (E and F))) and ((((A -> (B or A)) -> C) and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-327 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47616.        (((((A -> (B or A)) -> C) and D) -> C) and ((E -> (F -> (E and F))) and ((((A -> (B or A)) -> C) and D) -> C))), M:tm-327, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47617
in-theory        47617
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and (((E and F) -> F) and ((((A -> (B or A)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-326 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47617.        (((((A -> (B or A)) -> C) and D) -> C) and (((E and F) -> F) and ((((A -> (B or A)) -> C) and D) -> C))), M:tm-326, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47618
in-theory        47618
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and (((E and F) -> E) and ((((A -> (B or A)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-325 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47618.        (((((A -> (B or A)) -> C) and D) -> C) and (((E and F) -> E) and ((((A -> (B or A)) -> C) and D) -> C))), M:tm-325, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47619
in-theory        47619
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B or A)) -> C) and D) -> C)))
theorem-size     37
proof            (modus-ponens tm-324 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47619.        (((((A -> (B or A)) -> C) and D) -> C) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B or A)) -> C) and D) -> C))), M:tm-324, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47620
in-theory        47620
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and ((E -> (F -> E)) and ((((A -> (B or A)) -> C) and D) -> C)))
theorem-size     29
proof            (modus-ponens tm-323 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47620.        (((((A -> (B or A)) -> C) and D) -> C) and ((E -> (F -> E)) and ((((A -> (B or A)) -> C) and D) -> C))), M:tm-323, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47621
in-theory        47621
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47621.        (((((A -> (B or A)) -> C) and D) -> C) and ((E and F) -> F)), M:tm-322, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47622
in-theory        47622
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and (C -> D)) -> C) and ((((A -> (B or A)) -> C) and (C -> D)) -> D))
theorem-size     27
proof            (modus-ponens tm-321 tm-616 ((A (-> (-> Am (or Bm Am)) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47622.        (((((A -> (B or A)) -> C) and (C -> D)) -> C) and ((((A -> (B or A)) -> C) and (C -> D)) -> D)), M:tm-321, m:tm-616, u:((A (-> (-> Am (or Bm Am)) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-47623
in-theory        47623
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47623.        (((((A -> (B or A)) -> C) and D) -> C) and ((E and F) -> E)), M:tm-320, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47624
in-theory        47624
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> (A -> (B or A))) and C) -> (A -> (B or A))) and ((((A -> (B or A)) -> (A -> (B or A))) and C) -> (A -> (B or A))))
theorem-size     39
proof            (modus-ponens tm-319 tm-616 ((Cm (-> Am (or Bm Am))) (B (-> Am (or Bm Am))) (C Dm) (A (-> Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47624.        (((((A -> (B or A)) -> (A -> (B or A))) and C) -> (A -> (B or A))) and ((((A -> (B or A)) -> (A -> (B or A))) and C) -> (A -> (B or A)))), M:tm-319, m:tm-616, u:((Cm (-> Am (or Bm Am))) (B (-> Am (or Bm Am))) (C Dm) (A (-> Am (or Bm Am))))
================================================================
tm-name          tm-47625
in-theory        47625
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47625.        (((((A -> (B or A)) -> C) and D) -> C) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47626
in-theory        47626
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and ((((A -> (B or A)) -> C) and D) -> (((A -> (B or A)) -> C) and D)))
theorem-size     31
proof            (modus-ponens tm-316 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47626.        (((((A -> (B or A)) -> C) and D) -> C) and ((((A -> (B or A)) -> C) and D) -> (((A -> (B or A)) -> C) and D))), M:tm-316, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-47627
in-theory        47627
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47627.        (((((A -> (B or A)) -> C) and D) -> C) and (E -> (F -> E))), M:tm-315, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47628
in-theory        47628
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and (((((A -> (B or A)) -> C) and D) -> (not C)) -> (not (((A -> (B or A)) -> C) and D))))
theorem-size     35
proof            (modus-ponens tm-313 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-9 tm-3 tm-1 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47628.        (((((A -> (B or A)) -> C) and D) -> C) and (((((A -> (B or A)) -> C) and D) -> (not C)) -> (not (((A -> (B or A)) -> C) and D)))), M:tm-313, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-47629
in-theory        47629
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and ((C -> E) -> (((((A -> (B or A)) -> C) and D) or C) -> E)))
theorem-size     29
proof            (modus-ponens tm-312 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47629.        (((((A -> (B or A)) -> C) and D) -> C) and ((C -> E) -> (((((A -> (B or A)) -> C) and D) or C) -> E))), M:tm-312, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-47630
in-theory        47630
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and (E or ((((A -> (B or A)) -> C) and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-311 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47630.        (((((A -> (B or A)) -> C) and D) -> C) and (E or ((((A -> (B or A)) -> C) and D) -> C))), M:tm-311, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47631
in-theory        47631
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and (((((A -> (B or A)) -> C) and D) -> C) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47631.        (((((A -> (B or A)) -> C) and D) -> C) and (((((A -> (B or A)) -> C) and D) -> C) or E)), M:tm-310, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47632
in-theory        47632
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and (E -> (((((A -> (B or A)) -> C) and D) -> C) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47632.        (((((A -> (B or A)) -> C) and D) -> C) and (E -> (((((A -> (B or A)) -> C) and D) -> C) and E))), M:tm-309, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47633
in-theory        47633
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> (C -> D)) and E) -> (C -> D)) and (((((A -> (B or A)) -> (C -> D)) and E) -> C) -> ((((A -> (B or A)) -> (C -> D)) and E) -> D)))
theorem-size     43
proof            (modus-ponens tm-306 tm-616 ((A (and (-> (-> Am (or Bm Am)) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47633.        (((((A -> (B or A)) -> (C -> D)) and E) -> (C -> D)) and (((((A -> (B or A)) -> (C -> D)) and E) -> C) -> ((((A -> (B or A)) -> (C -> D)) and E) -> D))), M:tm-306, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-47634
in-theory        47634
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and (E -> ((((A -> (B or A)) -> C) and D) -> C)))
theorem-size     25
proof            (modus-ponens tm-305 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47634.        (((((A -> (B or A)) -> C) and D) -> C) and (E -> ((((A -> (B or A)) -> C) and D) -> C))), M:tm-305, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47635
in-theory        47635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-303 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47635.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-303, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47636
in-theory        47636
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C or B)) -> (D -> ((B -> (C or B)) and D))) and A)) -> (D -> ((B -> (C or B)) and D)))
theorem-size     29
proof            (modus-ponens tm-300 tm-616 ((A (-> Am (or Bm Am))) (Cm (-> B (and (-> Am (or Bm Am)) B))) (C Dm) (D (-> B (and (-> Am (or Bm Am)) B)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47636.        ((A or (((B -> (C or B)) -> (D -> ((B -> (C or B)) and D))) and A)) -> (D -> ((B -> (C or B)) and D))), M:tm-300, m:tm-616, u:((A (-> Am (or Bm Am))) (Cm (-> B (and (-> Am (or Bm Am)) B))) (C Dm) (D (-> B (and (-> Am (or Bm Am)) B))))
================================================================
tm-name          tm-47637
in-theory        47637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-270 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47637.        ((A -> (((B and C) -> C) and A)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-270, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47638
in-theory        47638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-239 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47638.        ((A -> (((B and C) -> B) and A)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-239, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47639
in-theory        47639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F or E)) -> G) and H) -> G))
theorem-size     29
proof            (modus-ponens tm-210 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47639.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F or E)) -> G) and H) -> G)), M:tm-210, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47640
in-theory        47640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-183 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47640.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-183, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47641
in-theory        47641
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C or B)) -> (D -> (B -> (C or B)))) and A)) -> (D -> (B -> (C or B))))
theorem-size     25
proof            (modus-ponens tm-180 tm-616 ((A (-> Am (or Bm Am))) (Cm (-> B (-> Am (or Bm Am)))) (C Dm) (D (-> B (-> Am (or Bm Am))))))
axioms-used      (tm-8 tm-5 tm-1 tm-2 tm-3 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47641.        ((A or (((B -> (C or B)) -> (D -> (B -> (C or B)))) and A)) -> (D -> (B -> (C or B)))), M:tm-180, m:tm-616, u:((A (-> Am (or Bm Am))) (Cm (-> B (-> Am (or Bm Am)))) (C Dm) (D (-> B (-> Am (or Bm Am)))))
================================================================
tm-name          tm-47642
in-theory        47642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> (C and D)) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-158 tm-616 ((A (and (-> (-> Am (or Bm Am)) (and B C)) Dm)) (Cm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47642.        ((((A -> (B or A)) -> (C and D)) and E) -> D), M:tm-158, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) (and B C)) Dm)) (Cm (and B C)))
================================================================
tm-name          tm-47643
in-theory        47643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-157 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47643.        ((A -> ((B and C) -> C)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-157, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47644
in-theory        47644
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B or A)) -> (not ((C and D) -> D))) and E))
theorem-size     15
proof            (modus-ponens tm-153 tm-616 ((A (and (-> (-> Am (or Bm Am)) (not (-> (and B C) C))) Dm)) (Cm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-2 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47644.        (not (((A -> (B or A)) -> (not ((C and D) -> D))) and E)), M:tm-153, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) (not (-> (and B C) C))) Dm)) (Cm (not (-> (and B C) C))))
================================================================
tm-name          tm-47645
in-theory        47645
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> (C -> D)) and C) -> D)
theorem-size     13
proof            (modus-ponens tm-152 tm-616 ((A (-> (-> Am (or Bm Am)) (-> Dm C))) (B Dm) (Cm (-> Dm C))))
axioms-used      (tm-2 tm-1 tm-4 tm-3 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47645.        ((((A -> (B or A)) -> (C -> D)) and C) -> D), M:tm-152, m:tm-616, u:((A (-> (-> Am (or Bm Am)) (-> Dm C))) (B Dm) (Cm (-> Dm C)))
================================================================
tm-name          tm-47646
in-theory        47646
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-147 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47646.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-147, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47647
in-theory        47647
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) and (C -> D)) -> C)
theorem-size     13
proof            (modus-ponens tm-142 tm-616 ((A (-> (-> Am (or Bm Am)) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-4 tm-3 tm-7)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47647.        ((((A -> (B or A)) -> C) and (C -> D)) -> C), M:tm-142, m:tm-616, u:((A (-> (-> Am (or Bm Am)) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-47648
in-theory        47648
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> (C -> D)) and ((C -> D) -> C)) -> D)
theorem-size     17
proof            (modus-ponens tm-141 tm-616 ((A (-> (-> Am (or Bm Am)) (-> B C))) (Dm (-> (-> B C) B)) (Cm (-> B C))))
axioms-used      (tm-2 tm-4 tm-3 tm-1 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47648.        ((((A -> (B or A)) -> (C -> D)) and ((C -> D) -> C)) -> D), M:tm-141, m:tm-616, u:((A (-> (-> Am (or Bm Am)) (-> B C))) (Dm (-> (-> B C) B)) (Cm (-> B C)))
================================================================
tm-name          tm-47649
in-theory        47649
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> (C and D)) and E) -> C)
theorem-size     13
proof            (modus-ponens tm-135 tm-616 ((A (and (-> (-> Am (or Bm Am)) (and B C)) Dm)) (Cm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47649.        ((((A -> (B or A)) -> (C and D)) and E) -> C), M:tm-135, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) (and B C)) Dm)) (Cm (and B C)))
================================================================
tm-name          tm-47650
in-theory        47650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-134 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47650.        ((A -> ((B and C) -> B)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-134, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47651
in-theory        47651
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B or A)) -> (not ((C and D) -> C))) and E))
theorem-size     15
proof            (modus-ponens tm-130 tm-616 ((A (and (-> (-> Am (or Bm Am)) (not (-> (and B C) B))) Dm)) (Cm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-2 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47651.        (not (((A -> (B or A)) -> (not ((C and D) -> C))) and E)), M:tm-130, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) (not (-> (and B C) B))) Dm)) (Cm (not (-> (and B C) B))))
================================================================
tm-name          tm-47652
in-theory        47652
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-125 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47652.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-125, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47653
in-theory        47653
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> (A -> (B or A))) and C) -> (A -> (B or A)))
theorem-size     19
proof            (modus-ponens tm-120 tm-616 ((Cm (-> Am (or Bm Am))) (B (-> Am (or Bm Am))) (C Dm) (A (-> Am (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-3 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47653.        ((((A -> (B or A)) -> (A -> (B or A))) and C) -> (A -> (B or A))), M:tm-120, m:tm-616, u:((Cm (-> Am (or Bm Am))) (B (-> Am (or Bm Am))) (C Dm) (A (-> Am (or Bm Am))))
================================================================
tm-name          tm-47654
in-theory        47654
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> (C -> (D -> E))) and F) -> ((C -> D) -> (C -> E)))
theorem-size     21
proof            (modus-ponens tm-114 tm-616 ((A (and (-> (-> Am (or Bm Am)) (-> B (-> C D))) Dm)) (Cm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-3 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47654.        ((((A -> (B or A)) -> (C -> (D -> E))) and F) -> ((C -> D) -> (C -> E))), M:tm-114, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) (-> B (-> C D))) Dm)) (Cm (-> B (-> C D))))
================================================================
tm-name          tm-47655
in-theory        47655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F or E)) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-113 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47655.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F or E)) -> G) and H) -> G)), M:tm-113, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47656
in-theory        47656
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B or A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F))
theorem-size     23
proof            (modus-ponens tm-109 tm-616 ((A (and (-> (-> Am (or Bm Am)) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Dm)) (Cm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47656.        (not (((A -> (B or A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and F)), M:tm-109, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Dm)) (Cm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-47657
in-theory        47657
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     31
proof            (modus-ponens tm-105 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47657.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-105, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47658
in-theory        47658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D or C)) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-95 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47658.        (((A -> B) -> (A -> A)) and ((((C -> (D or C)) -> E) and F) -> E)), M:tm-95, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47659
in-theory        47659
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> (C -> D)) and E) -> (C -> D))
theorem-size     15
proof            (modus-ponens tm-87 tm-616 ((A (and (-> (-> Am (or Bm Am)) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47659.        ((((A -> (B or A)) -> (C -> D)) and E) -> (C -> D)), M:tm-87, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-47660
in-theory        47660
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) and D) -> (E -> C))
theorem-size     13
proof            (modus-ponens tm-84 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-3 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47660.        ((((A -> (B or A)) -> C) and D) -> (E -> C)), M:tm-84, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-47661
in-theory        47661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-83 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47661.        ((A -> (B -> (C -> B))) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-83, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47662
in-theory        47662
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B or A)) -> (not (C -> (D -> C)))) and E))
theorem-size     15
proof            (modus-ponens tm-79 tm-616 ((A (and (-> (-> Am (or Bm Am)) (not (-> B (-> C B)))) Dm)) (Cm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-2 tm-3 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47662.        (not (((A -> (B or A)) -> (not (C -> (D -> C)))) and E)), M:tm-79, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) (not (-> B (-> C B)))) Dm)) (Cm (not (-> B (-> C B)))))
================================================================
tm-name          tm-47663
in-theory        47663
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C or B)) -> D) and E) -> D))
theorem-size     17
proof            (modus-ponens tm-76 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-10 tm-2 tm-3 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47663.        (((not (not A)) -> A) and ((((B -> (C or B)) -> D) and E) -> D)), M:tm-76, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47664
in-theory        47664
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (B or A)) -> C) and D))) or (((A -> (B or A)) -> C) and D)) -> C)
theorem-size     23
proof            (modus-ponens tm-73 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-10 tm-2 tm-3 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47664.        (((not (not (((A -> (B or A)) -> C) and D))) or (((A -> (B or A)) -> C) and D)) -> C), M:tm-73, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-47665
in-theory        47665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D or C)) -> E) and F) -> E))
theorem-size     23
proof            (modus-ponens tm-69 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-9 tm-2 tm-3 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47665.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D or C)) -> E) and F) -> E)), M:tm-69, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47666
in-theory        47666
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B or A)) -> (not C)) and C))
theorem-size     11
proof            (modus-ponens tm-60 tm-616 ((A (-> (-> Am (or Bm Am)) (not Dm))) (B Dm) (Cm (not Dm))))
axioms-used      (tm-9 tm-4 tm-2 tm-3 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47666.        (not (((A -> (B or A)) -> (not C)) and C)), M:tm-60, m:tm-616, u:((A (-> (-> Am (or Bm Am)) (not Dm))) (B Dm) (Cm (not Dm)))
================================================================
tm-name          tm-47667
in-theory        47667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-54 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47667.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-54, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47668
in-theory        47668
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C or B)) -> D) and E)) or (((B -> (C or B)) -> D) and E)) -> D)
theorem-size     23
proof            (modus-ponens tm-47 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-4 tm-2 tm-3 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47668.        (((A and (((B -> (C or B)) -> D) and E)) or (((B -> (C or B)) -> D) and E)) -> D), M:tm-47, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-47669
in-theory        47669
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B or A)) -> C) and D) and E) or (((A -> (B or A)) -> C) and D)) -> C)
theorem-size     23
proof            (modus-ponens tm-46 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47669.        ((((((A -> (B or A)) -> C) and D) and E) or (((A -> (B or A)) -> C) and D)) -> C), M:tm-46, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-47670
in-theory        47670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D or C)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-42 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47670.        ((A -> (B or A)) and ((((C -> (D or C)) -> E) and F) -> E)), M:tm-42, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47671
in-theory        47671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D or C)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-32 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47671.        ((A -> (A or B)) and ((((C -> (D or C)) -> E) and F) -> E)), M:tm-32, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47672
in-theory        47672
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) and D) -> ((((A -> (B or A)) -> C) and D) and C))
theorem-size     21
proof            (modus-ponens tm-24 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47672.        ((((A -> (B or A)) -> C) and D) -> ((((A -> (B or A)) -> C) and D) and C)), M:tm-24, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-47673
in-theory        47673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D or C)) -> E) and F) -> E))
theorem-size     19
proof            (modus-ponens tm-23 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47673.        ((A -> (B -> (A and B))) and ((((C -> (D or C)) -> E) and F) -> E)), M:tm-23, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47674
in-theory        47674
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D or C)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-22 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-4 tm-2 tm-3 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47674.        (((A and B) -> B) and ((((C -> (D or C)) -> E) and F) -> E)), M:tm-22, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47675
in-theory        47675
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D or C)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-21 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47675.        (((A and B) -> A) and ((((C -> (D or C)) -> E) and F) -> E)), M:tm-21, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47676
in-theory        47676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-20 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47676.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-20, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47677
in-theory        47677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D or C)) -> E) and F) -> E))
theorem-size     17
proof            (modus-ponens tm-19 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47677.        ((A -> (B -> A)) and ((((C -> (D or C)) -> E) and F) -> E)), M:tm-19, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47678
in-theory        47678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) and (C -> D)) -> D)
theorem-size     13
proof            (modus-ponens tm-17 tm-616 ((A (-> (-> Am (or Bm Am)) Cm)) (Dm (-> Cm C)) (B Cm)))
axioms-used      (tm-2 tm-4 tm-3 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47678.        ((((A -> (B or A)) -> C) and (C -> D)) -> D), M:tm-17, m:tm-616, u:((A (-> (-> Am (or Bm Am)) Cm)) (Dm (-> Cm C)) (B Cm))
================================================================
tm-name          tm-47679
in-theory        47679
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) and D) -> (((A -> (B or A)) -> C) and D))
theorem-size     19
proof            (modus-ponens tm-12 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-3 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47679.        ((((A -> (B or A)) -> C) and D) -> (((A -> (B or A)) -> C) and D)), M:tm-12, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-47680
in-theory        47680
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> (not C)) -> (not (((A -> (B or A)) -> C) and D)))
theorem-size     23
proof            (modus-ponens tm-9 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-9 tm-2 tm-3 tm-1 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47680.        (((((A -> (B or A)) -> C) and D) -> (not C)) -> (not (((A -> (B or A)) -> C) and D))), M:tm-9, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-47681
in-theory        47681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((((C -> (D or C)) -> A) and E) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47681.        ((A -> B) -> (((((C -> (D or C)) -> A) and E) or A) -> B)), M:tm-8, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-47682
in-theory        47682
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> (C or B)) -> D) and E) -> D))
theorem-size     13
proof            (modus-ponens tm-7 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-7 tm-2 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47682.        (A or ((((B -> (C or B)) -> D) and E) -> D)), M:tm-7, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47683
in-theory        47683
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-6 tm-2 tm-3 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47683.        (((((A -> (B or A)) -> C) and D) -> C) or E), M:tm-6, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47684
in-theory        47684
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> (C or B)) -> D) and E) -> D) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47684.        (A -> (((((B -> (C or B)) -> D) and E) -> D) and A)), M:tm-5, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47685
in-theory        47685
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> (C -> D)) and E) -> C) -> ((((A -> (B or A)) -> (C -> D)) and E) -> D))
theorem-size     27
proof            (modus-ponens tm-2 tm-616 ((A (and (-> (-> Am (or Bm Am)) (-> B C)) Dm)) (Cm (-> B C))))
axioms-used      (tm-2 tm-3 tm-1 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47685.        (((((A -> (B or A)) -> (C -> D)) and E) -> C) -> ((((A -> (B or A)) -> (C -> D)) and E) -> D)), M:tm-2, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) (-> B C)) Dm)) (Cm (-> B C)))
================================================================
tm-name          tm-47686
in-theory        47686
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C or B)) -> D) and E) -> D))
theorem-size     13
proof            (modus-ponens tm-1 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-1 tm-2 tm-3 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47686.        (A -> ((((B -> (C or B)) -> D) and E) -> D)), M:tm-1, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-47687
in-theory        47687
times-derived    2
----------------------------------------------------------------
theorem          (A -> (B or (C or A)))
theorem-size     7
proof            (modus-ponens tm-617 tm-43 ((A Am) (Bm (or B Am)) (C (or Cm (or B Am)))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47687.        (A -> (B or (C or A))), M:tm-617, m:tm-43, u:((A Am) (Bm (or B Am)) (C (or Cm (or B Am))))
================================================================
tm-name          tm-47688
in-theory        47688
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (D or A)))
theorem-size     11
proof            (modus-ponens tm-617 tm-184 ((A Am) (Bm (or B Am)) (C (and (-> Cm (-> Dm Cm)) (or B Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-47688.        (A -> ((B -> (C -> B)) and (D or A))), M:tm-617, m:tm-184, u:((A Am) (Bm (or B Am)) (C (and (-> Cm (-> Dm Cm)) (or B Am))))
================================================================
tm-name          tm-47689
in-theory        47689
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or A)))
theorem-size     19
proof            (modus-ponens tm-617 tm-211 ((A Am) (Bm (or B Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or B Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-47689.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (E or A))), M:tm-617, m:tm-211, u:((A Am) (Bm (or B Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (or B Am))))
================================================================
tm-name          tm-47690
in-theory        47690
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (D or A)))
theorem-size     11
proof            (modus-ponens tm-617 tm-240 ((A Am) (Bm (or B Am)) (C (and (-> (and Cm Dm) Cm) (or B Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-47690.        (A -> (((B and C) -> B) and (D or A))), M:tm-617, m:tm-240, u:((A Am) (Bm (or B Am)) (C (and (-> (and Cm Dm) Cm) (or B Am))))
================================================================
tm-name          tm-47691
in-theory        47691
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (D or A)))
theorem-size     11
proof            (modus-ponens tm-617 tm-271 ((A Am) (Bm (or B Am)) (C (and (-> (and Cm Dm) Dm) (or B Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-47691.        (A -> (((B and C) -> C) and (D or A))), M:tm-617, m:tm-271, u:((A Am) (Bm (or B Am)) (C (and (-> (and Cm Dm) Dm) (or B Am))))
================================================================
tm-name          tm-47692
in-theory        47692
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (D or A)))
theorem-size     13
proof            (modus-ponens tm-617 tm-304 ((A Am) (Bm (or B Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or B Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-47692.        (A -> ((B -> (C -> (B and C))) and (D or A))), M:tm-617, m:tm-304, u:((A Am) (Bm (or B Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (or B Am))))
================================================================
tm-name          tm-47693
in-theory        47693
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (D or A)))
theorem-size     11
proof            (modus-ponens tm-617 tm-454 ((A Am) (Bm (or B Am)) (C (and (-> Cm (or Cm Dm)) (or B Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-47693.        (A -> ((B -> (B or C)) and (D or A))), M:tm-617, m:tm-454, u:((A Am) (Bm (or B Am)) (C (and (-> Cm (or Cm Dm)) (or B Am))))
================================================================
tm-name          tm-47694
in-theory        47694
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (D or A)))
theorem-size     11
proof            (modus-ponens tm-617 tm-606 ((A Am) (Bm (or B Am)) (C (and (-> Cm (or Dm Cm)) (or B Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-47694.        (A -> ((B -> (C or B)) and (D or A))), M:tm-617, m:tm-606, u:((A Am) (Bm (or B Am)) (C (and (-> Cm (or Dm Cm)) (or B Am))))
================================================================
tm-name          tm-47695
in-theory        47695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47695.        (((A -> ((B or A) -> C)) -> (A -> C)) and (D -> (E or D))), M:tm-609, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47696
in-theory        47696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47696.        ((A -> ((B -> (C or B)) and A)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-605, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47697
in-theory        47697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and ((D -> (E or D)) and ((A -> ((B or A) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47697.        (((A -> ((B or A) -> C)) -> (A -> C)) and ((D -> (E or D)) and ((A -> ((B or A) -> C)) -> (A -> C)))), M:tm-595, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47698
in-theory        47698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47698.        (((A -> (B or A)) or C) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-550, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47699
in-theory        47699
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47699.        ((A or (B -> (C or B))) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-540, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47700
in-theory        47700
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47700.        ((A or (B -> (B or C))) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-530, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47701
in-theory        47701
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47701.        ((A or (B -> (C -> (B and C)))) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-520, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47702
in-theory        47702
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47702.        ((A or ((B and C) -> C)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-510, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47703
in-theory        47703
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47703.        ((A or ((B and C) -> B)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-500, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47704
in-theory        47704
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F or E) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47704.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F or E) -> G)) -> (E -> G))), M:tm-490, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47705
in-theory        47705
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47705.        ((A or (B -> (C -> B))) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-480, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47706
in-theory        47706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or A) -> C)) -> ((A -> C) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47706.        ((A -> ((B or A) -> C)) -> ((A -> C) or D)), M:tm-470, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-47707
in-theory        47707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47707.        ((A -> (B -> (B or C))) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-469, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47708
in-theory        47708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47708.        (((A -> ((B or A) -> C)) -> (A -> C)) and (D -> (D or E))), M:tm-456, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47709
in-theory        47709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47709.        ((A -> ((B -> (B or C)) and A)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-453, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47710
in-theory        47710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and ((D -> (D or E)) and ((A -> ((B or A) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47710.        (((A -> ((B or A) -> C)) -> (A -> C)) and ((D -> (D or E)) and ((A -> ((B or A) -> C)) -> (A -> C)))), M:tm-443, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47711
in-theory        47711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47711.        (((A -> (A or B)) or C) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-409, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47712
in-theory        47712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47712.        (((A -> (B -> (A and B))) or C) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-400, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47713
in-theory        47713
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47713.        ((((A and B) -> B) or C) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-391, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47714
in-theory        47714
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47714.        ((((A and B) -> A) or C) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-382, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47715
in-theory        47715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F or E) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47715.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> ((F or E) -> G)) -> (E -> G))), M:tm-373, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47716
in-theory        47716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47716.        (((A -> (B -> A)) or C) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-364, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47717
in-theory        47717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or A) -> C)) -> (D -> ((A -> C) and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47717.        ((A -> ((B or A) -> C)) -> (D -> ((A -> C) and D))), M:tm-355, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-47718
in-theory        47718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47718.        ((A -> (B -> (C -> (B and C)))) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-354, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47719
in-theory        47719
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C or B) -> (B and (C or B))))) -> (B -> (B and (C or B))))
theorem-size     21
proof            (modus-ponens tm-351 tm-617 ((A Am) (B (or Bm Am)) (Cm (and Am (or Bm Am))) (C (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47719.        ((A or (B -> ((C or B) -> (B and (C or B))))) -> (B -> (B and (C or B)))), M:tm-351, m:tm-617, u:((A Am) (B (or Bm Am)) (Cm (and Am (or Bm Am))) (C (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-47720
in-theory        47720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47720.        (((A -> ((B or A) -> C)) -> (A -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47721
in-theory        47721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> ((D or C) -> E)) -> (C -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47721.        (((A -> B) -> (A -> (A and B))) and ((C -> ((D or C) -> E)) -> (C -> E))), M:tm-338, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47722
in-theory        47722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and ((A -> ((B or A) -> C)) -> ((A -> ((B or A) -> C)) and (A -> C))))
theorem-size     31
proof            (modus-ponens tm-328 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47722.        (((A -> ((B or A) -> C)) -> (A -> C)) and ((A -> ((B or A) -> C)) -> ((A -> ((B or A) -> C)) and (A -> C)))), M:tm-328, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-47723
in-theory        47723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> ((B or A) -> C)) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47723.        (((A -> ((B or A) -> C)) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> ((B or A) -> C)) -> (A -> C)))), M:tm-327, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47724
in-theory        47724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (((D and E) -> E) and ((A -> ((B or A) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47724.        (((A -> ((B or A) -> C)) -> (A -> C)) and (((D and E) -> E) and ((A -> ((B or A) -> C)) -> (A -> C)))), M:tm-326, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47725
in-theory        47725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (((D and E) -> D) and ((A -> ((B or A) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47725.        (((A -> ((B or A) -> C)) -> (A -> C)) and (((D and E) -> D) and ((A -> ((B or A) -> C)) -> (A -> C)))), M:tm-325, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47726
in-theory        47726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> ((B or A) -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47726.        (((A -> ((B or A) -> C)) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> ((B or A) -> C)) -> (A -> C)))), M:tm-324, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47727
in-theory        47727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and ((D -> (E -> D)) and ((A -> ((B or A) -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47727.        (((A -> ((B or A) -> C)) -> (A -> C)) and ((D -> (E -> D)) and ((A -> ((B or A) -> C)) -> (A -> C)))), M:tm-323, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47728
in-theory        47728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47728.        (((A -> ((B or A) -> C)) -> (A -> C)) and ((D and E) -> E)), M:tm-322, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47729
in-theory        47729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47729.        (((A -> ((B or A) -> C)) -> (A -> C)) and ((D and E) -> D)), M:tm-320, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47730
in-theory        47730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47730.        (((A -> ((B or A) -> C)) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47731
in-theory        47731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> (B or A))) -> (A -> (B or A))) and ((A -> ((B or A) -> (B or A))) -> (A -> (B or A))))
theorem-size     31
proof            (modus-ponens tm-317 tm-617 ((Cm (or Bm Am)) (C (or Bm Am)) (A Am) (B (or Bm Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47731.        (((A -> ((B or A) -> (B or A))) -> (A -> (B or A))) and ((A -> ((B or A) -> (B or A))) -> (A -> (B or A)))), M:tm-317, m:tm-617, u:((Cm (or Bm Am)) (C (or Bm Am)) (A Am) (B (or Bm Am)))
================================================================
tm-name          tm-47732
in-theory        47732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and ((A -> ((B or A) -> C)) -> (A -> ((B or A) -> C))))
theorem-size     27
proof            (modus-ponens tm-316 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47732.        (((A -> ((B or A) -> C)) -> (A -> C)) and ((A -> ((B or A) -> C)) -> (A -> ((B or A) -> C)))), M:tm-316, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-47733
in-theory        47733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47733.        (((A -> ((B or A) -> C)) -> (A -> C)) and (D -> (E -> D))), M:tm-315, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47734
in-theory        47734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (((A -> ((B or A) -> C)) -> (not (A -> C))) -> (not (A -> ((B or A) -> C)))))
theorem-size     33
proof            (modus-ponens tm-313 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47734.        (((A -> ((B or A) -> C)) -> (A -> C)) and (((A -> ((B or A) -> C)) -> (not (A -> C))) -> (not (A -> ((B or A) -> C))))), M:tm-313, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-47735
in-theory        47735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (((A -> C) -> D) -> (((A -> ((B or A) -> C)) or (A -> C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-312 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47735.        (((A -> ((B or A) -> C)) -> (A -> C)) and (((A -> C) -> D) -> (((A -> ((B or A) -> C)) or (A -> C)) -> D))), M:tm-312, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-47736
in-theory        47736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (D or ((A -> ((B or A) -> C)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47736.        (((A -> ((B or A) -> C)) -> (A -> C)) and (D or ((A -> ((B or A) -> C)) -> (A -> C)))), M:tm-311, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47737
in-theory        47737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (((A -> ((B or A) -> C)) -> (A -> C)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47737.        (((A -> ((B or A) -> C)) -> (A -> C)) and (((A -> ((B or A) -> C)) -> (A -> C)) or D)), M:tm-310, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47738
in-theory        47738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (D -> (((A -> ((B or A) -> C)) -> (A -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47738.        (((A -> ((B or A) -> C)) -> (A -> C)) and (D -> (((A -> ((B or A) -> C)) -> (A -> C)) and D))), M:tm-309, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47739
in-theory        47739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (((A -> ((B or A) -> C)) -> A) -> ((A -> ((B or A) -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-306 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B Am) (C Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47739.        (((A -> ((B or A) -> C)) -> (A -> C)) and (((A -> ((B or A) -> C)) -> A) -> ((A -> ((B or A) -> C)) -> C))), M:tm-306, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B Am) (C Cm))
================================================================
tm-name          tm-47740
in-theory        47740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and (D -> ((A -> ((B or A) -> C)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47740.        (((A -> ((B or A) -> C)) -> (A -> C)) and (D -> ((A -> ((B or A) -> C)) -> (A -> C)))), M:tm-305, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47741
in-theory        47741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47741.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-303, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47742
in-theory        47742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47742.        ((A -> (((B and C) -> C) and A)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-270, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47743
in-theory        47743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47743.        ((A -> (((B and C) -> B) and A)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-239, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47744
in-theory        47744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F or E) -> G)) -> (E -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47744.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> ((F or E) -> G)) -> (E -> G))), M:tm-210, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47745
in-theory        47745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47745.        ((A -> ((B -> (C -> B)) and A)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-183, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47746
in-theory        47746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47746.        ((A -> ((B and C) -> C)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-157, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47747
in-theory        47747
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47747.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-147, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47748
in-theory        47748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47748.        ((A -> ((B and C) -> B)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-134, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47749
in-theory        47749
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47749.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-125, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47750
in-theory        47750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or A) -> (C -> D))) -> ((A -> C) -> (A -> D)))
theorem-size     17
proof            (modus-ponens tm-114 tm-617 ((A (-> Am (-> (or Bm Am) (-> C D)))) (B Am) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47750.        ((A -> ((B or A) -> (C -> D))) -> ((A -> C) -> (A -> D))), M:tm-114, m:tm-617, u:((A (-> Am (-> (or Bm Am) (-> C D)))) (B Am) (Cm (-> C D)))
================================================================
tm-name          tm-47751
in-theory        47751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F or E) -> G)) -> (E -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47751.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> ((F or E) -> G)) -> (E -> G))), M:tm-113, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47752
in-theory        47752
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47752.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-105, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47753
in-theory        47753
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B or A) -> (B or A))) -> (A -> (B or A)))
theorem-size     15
proof            (modus-ponens tm-100 tm-617 ((Cm (or Bm Am)) (C (or Bm Am)) (A Am) (B (or Bm Am))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47753.        ((A -> ((B or A) -> (B or A))) -> (A -> (B or A))), M:tm-100, m:tm-617, u:((Cm (or Bm Am)) (C (or Bm Am)) (A Am) (B (or Bm Am)))
================================================================
tm-name          tm-47754
in-theory        47754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> ((D or C) -> E)) -> (C -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47754.        (((A -> B) -> (A -> A)) and ((C -> ((D or C) -> E)) -> (C -> E))), M:tm-95, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47755
in-theory        47755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or A) -> C)) -> (D -> (A -> C)))
theorem-size     13
proof            (modus-ponens tm-84 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47755.        ((A -> ((B or A) -> C)) -> (D -> (A -> C))), M:tm-84, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-47756
in-theory        47756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47756.        ((A -> (B -> (C -> B))) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-83, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47757
in-theory        47757
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> ((C or B) -> B))) -> (B -> B))
theorem-size     13
proof            (modus-ponens tm-80 tm-617 ((Cm Am) (B (or Bm Am)) (A Am) (C (-> Am Am))))
axioms-used      (tm-8 tm-1 tm-2 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47757.        ((A or (B -> ((C or B) -> B))) -> (B -> B)), M:tm-80, m:tm-617, u:((Cm Am) (B (or Bm Am)) (A Am) (C (-> Am Am)))
================================================================
tm-name          tm-47758
in-theory        47758
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> ((C or B) -> D)) -> (B -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47758.        (((not (not A)) -> A) and ((B -> ((C or B) -> D)) -> (B -> D))), M:tm-76, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47759
in-theory        47759
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> ((B or A) -> C)))) or (A -> ((B or A) -> C))) -> (A -> C))
theorem-size     21
proof            (modus-ponens tm-73 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47759.        (((not (not (A -> ((B or A) -> C)))) or (A -> ((B or A) -> C))) -> (A -> C)), M:tm-73, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-47760
in-theory        47760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D or C) -> E)) -> (C -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47760.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> ((D or C) -> E)) -> (C -> E))), M:tm-69, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47761
in-theory        47761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47761.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-54, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47762
in-theory        47762
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> ((C or B) -> D))) or (B -> ((C or B) -> D))) -> (B -> D))
theorem-size     21
proof            (modus-ponens tm-47 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47762.        (((A and (B -> ((C or B) -> D))) or (B -> ((C or B) -> D))) -> (B -> D)), M:tm-47, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-47763
in-theory        47763
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B or A) -> C)) and D) or (A -> ((B or A) -> C))) -> (A -> C))
theorem-size     21
proof            (modus-ponens tm-46 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47763.        ((((A -> ((B or A) -> C)) and D) or (A -> ((B or A) -> C))) -> (A -> C)), M:tm-46, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-47764
in-theory        47764
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) or (B -> ((A or B) -> C))) -> (B -> C))
theorem-size     17
proof            (modus-ponens tm-44 tm-617 ((A Am) (B (-> (or Bm Am) Cm)) (C (-> Am Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47764.        ((((A or B) -> C) or (B -> ((A or B) -> C))) -> (B -> C)), M:tm-44, m:tm-617, u:((A Am) (B (-> (or Bm Am) Cm)) (C (-> Am Cm)))
================================================================
tm-name          tm-47765
in-theory        47765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> ((D or C) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47765.        ((A -> (B or A)) and ((C -> ((D or C) -> E)) -> (C -> E))), M:tm-42, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47766
in-theory        47766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> ((D or C) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47766.        ((A -> (A or B)) and ((C -> ((D or C) -> E)) -> (C -> E))), M:tm-32, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47767
in-theory        47767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or A) -> C)) -> ((A -> ((B or A) -> C)) and (A -> C)))
theorem-size     19
proof            (modus-ponens tm-24 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47767.        ((A -> ((B or A) -> C)) -> ((A -> ((B or A) -> C)) and (A -> C))), M:tm-24, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-47768
in-theory        47768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> ((D or C) -> E)) -> (C -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47768.        ((A -> (B -> (A and B))) and ((C -> ((D or C) -> E)) -> (C -> E))), M:tm-23, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47769
in-theory        47769
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> ((D or C) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47769.        (((A and B) -> B) and ((C -> ((D or C) -> E)) -> (C -> E))), M:tm-22, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47770
in-theory        47770
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> ((D or C) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47770.        (((A and B) -> A) and ((C -> ((D or C) -> E)) -> (C -> E))), M:tm-21, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47771
in-theory        47771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47771.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-20, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47772
in-theory        47772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> ((D or C) -> E)) -> (C -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47772.        ((A -> (B -> A)) and ((C -> ((D or C) -> E)) -> (C -> E))), M:tm-19, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47773
in-theory        47773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or A) -> C)) -> (A -> ((B or A) -> C)))
theorem-size     15
proof            (modus-ponens tm-12 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47773.        ((A -> ((B or A) -> C)) -> (A -> ((B or A) -> C))), M:tm-12, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-47774
in-theory        47774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (not (A -> C))) -> (not (A -> ((B or A) -> C))))
theorem-size     21
proof            (modus-ponens tm-9 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-9 tm-2 tm-1 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47774.        (((A -> ((B or A) -> C)) -> (not (A -> C))) -> (not (A -> ((B or A) -> C)))), M:tm-9, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-47775
in-theory        47775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (((A -> ((D or A) -> B)) or (A -> B)) -> C))
theorem-size     19
proof            (modus-ponens tm-8 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47775.        (((A -> B) -> C) -> (((A -> ((D or A) -> B)) or (A -> B)) -> C)), M:tm-8, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-47776
in-theory        47776
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> ((C or B) -> D)) -> (B -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-7 tm-2 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47776.        (A or ((B -> ((C or B) -> D)) -> (B -> D))), M:tm-7, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47777
in-theory        47777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-6 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47777.        (((A -> ((B or A) -> C)) -> (A -> C)) or D), M:tm-6, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47778
in-theory        47778
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> ((C or B) -> D)) -> (B -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47778.        (A -> (((B -> ((C or B) -> D)) -> (B -> D)) and A)), M:tm-5, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47779
in-theory        47779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> A) -> ((A -> ((B or A) -> C)) -> C))
theorem-size     19
proof            (modus-ponens tm-2 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B Am) (C Cm)))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47779.        (((A -> ((B or A) -> C)) -> A) -> ((A -> ((B or A) -> C)) -> C)), M:tm-2, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B Am) (C Cm))
================================================================
tm-name          tm-47780
in-theory        47780
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> ((C or B) -> D)) -> (B -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-1 tm-2 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-47780.        (A -> ((B -> ((C or B) -> D)) -> (B -> D))), M:tm-1, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-47781
in-theory        47781
times-derived    1
----------------------------------------------------------------
theorem          (not ((not (A -> (B or A))) and C))
theorem-size     9
proof            (modus-ponens tm-618 tm-3 ((A (and (not (-> B (or C B))) Bm)) (Am (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-3)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-47781.        (not ((not (A -> (B or A))) and C)), M:tm-618, m:tm-3, u:((A (and (not (-> B (or C B))) Bm)) (Am (not (-> B (or C B)))))
================================================================
tm-name          tm-47782
in-theory        47782
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (not (B -> (C or B)))))
theorem-size     9
proof            (modus-ponens tm-618 tm-4 ((A (and Am (not (-> B (or C B))))) (Bm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-4)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47782.        (not (A and (not (B -> (C or B))))), M:tm-618, m:tm-4, u:((A (and Am (not (-> B (or C B))))) (Bm (not (-> B (or C B)))))
================================================================
tm-name          tm-47783
in-theory        47783
times-derived    1
----------------------------------------------------------------
theorem          (not (not (not (not (A -> (B or A))))))
theorem-size     9
proof            (modus-ponens tm-618 tm-10 ((A (not (not (not (-> B (or C B)))))) (Am (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-47783.        (not (not (not (not (A -> (B or A)))))), M:tm-618, m:tm-10, u:((A (not (not (not (-> B (or C B)))))) (Am (not (-> B (or C B)))))
================================================================
tm-name          tm-47784
in-theory        47784
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (C -> (A -> (B or A))))))
theorem-size     15
proof            (modus-ponens tm-618 tm-57 ((A (-> (-> B (or C B)) (not (-> Bm (-> B (or C B)))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-47784.        (not ((A -> (B or A)) -> (not (C -> (A -> (B or A)))))), M:tm-618, m:tm-57, u:((A (-> (-> B (or C B)) (not (-> Bm (-> B (or C B)))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47785
in-theory        47785
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (C -> ((A -> (B or A)) and C)))))
theorem-size     17
proof            (modus-ponens tm-618 tm-61 ((A (-> (-> B (or C B)) (not (-> Bm (and (-> B (or C B)) Bm))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-47785.        (not ((A -> (B or A)) -> (not (C -> ((A -> (B or A)) and C))))), M:tm-618, m:tm-61, u:((A (-> (-> B (or C B)) (not (-> Bm (and (-> B (or C B)) Bm))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47786
in-theory        47786
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not ((A -> (B or A)) or C))))
theorem-size     15
proof            (modus-ponens tm-618 tm-62 ((A (-> (-> B (or C B)) (not (or (-> B (or C B)) Bm)))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-47786.        (not ((A -> (B or A)) -> (not ((A -> (B or A)) or C)))), M:tm-618, m:tm-62, u:((A (-> (-> B (or C B)) (not (or (-> B (or C B)) Bm)))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47787
in-theory        47787
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (C or (A -> (B or A))))))
theorem-size     15
proof            (modus-ponens tm-618 tm-63 ((A (-> (-> B (or C B)) (not (or Bm (-> B (or C B)))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-47787.        (not ((A -> (B or A)) -> (not (C or (A -> (B or A)))))), M:tm-618, m:tm-63, u:((A (-> (-> B (or C B)) (not (or Bm (-> B (or C B)))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47788
in-theory        47788
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (((B or A) -> C) -> ((A or (B or A)) -> C)))))
theorem-size     21
proof            (modus-ponens tm-618 tm-64 ((A (-> (-> Am (or C Am)) (not (-> (-> (or C Am) Cm) (-> (or Am (or C Am)) Cm))))) (B Am) (Bm (or C Am))))
axioms-used      (tm-9 tm-1 tm-7 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-47788.        (not ((A -> (B or A)) -> (not (((B or A) -> C) -> ((A or (B or A)) -> C))))), M:tm-618, m:tm-64, u:((A (-> (-> Am (or C Am)) (not (-> (-> (or C Am) Cm) (-> (or Am (or C Am)) Cm))))) (B Am) (Bm (or C Am)))
================================================================
tm-name          tm-47789
in-theory        47789
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not ((A -> (not (B or A))) -> (not A)))))
theorem-size     17
proof            (modus-ponens tm-618 tm-65 ((A (-> (-> Am (or C Am)) (not (-> (-> Am (not (or C Am))) (not Am))))) (B Am) (Bm (or C Am))))
axioms-used      (tm-9 tm-1 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-47789.        (not ((A -> (B or A)) -> (not ((A -> (not (B or A))) -> (not A))))), M:tm-618, m:tm-65, u:((A (-> (-> Am (or C Am)) (not (-> (-> Am (not (or C Am))) (not Am))))) (B Am) (Bm (or C Am)))
================================================================
tm-name          tm-47790
in-theory        47790
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (C -> (D -> C)))))
theorem-size     13
proof            (modus-ponens tm-618 tm-79 ((A (-> (-> B (or C B)) (not (-> Bm (-> Cm Bm))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-47790.        (not ((A -> (B or A)) -> (not (C -> (D -> C))))), M:tm-618, m:tm-79, u:((A (-> (-> B (or C B)) (not (-> Bm (-> Cm Bm))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47791
in-theory        47791
times-derived    1
----------------------------------------------------------------
theorem          (not (not (A -> (B or A))))
theorem-size     7
proof            (modus-ponens tm-618 tm-86 ((A (not (-> B (or C B)))) (Am (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-47791.        (not (not (A -> (B or A)))), M:tm-618, m:tm-86, u:((A (not (-> B (or C B)))) (Am (not (-> B (or C B)))))
================================================================
tm-name          tm-47792
in-theory        47792
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (A -> A))))
theorem-size     11
proof            (modus-ponens tm-618 tm-91 ((A (-> (-> Am (or C Am)) (not (-> Am Am)))) (B Am) (Bm (or C Am))))
axioms-used      (tm-9 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-47792.        (not ((A -> (B or A)) -> (not (A -> A)))), M:tm-618, m:tm-91, u:((A (-> (-> Am (or C Am)) (not (-> Am Am)))) (B Am) (Bm (or C Am)))
================================================================
tm-name          tm-47793
in-theory        47793
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     21
proof            (modus-ponens tm-618 tm-109 ((A (-> (-> B (or C B)) (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-47793.        (not ((A -> (B or A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-618, m:tm-109, u:((A (-> (-> B (or C B)) (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47794
in-theory        47794
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (not (B -> (C or B)))) and A))
theorem-size     11
proof            (modus-ponens tm-618 tm-116 ((A (and (-> Am (not (-> B (or C B)))) Am)) (Bm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-3 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-47794.        (not ((A -> (not (B -> (C or B)))) and A)), M:tm-618, m:tm-116, u:((A (and (-> Am (not (-> B (or C B)))) Am)) (Bm (not (-> B (or C B)))))
================================================================
tm-name          tm-47795
in-theory        47795
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> A)) -> (not (C -> (D or C)))) and E))
theorem-size     15
proof            (modus-ponens tm-618 tm-117 ((A (and (-> (-> Am (-> Bm Am)) (not (-> B (or C B)))) Dm)) (Cm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-47795.        (not (((A -> (B -> A)) -> (not (C -> (D or C)))) and E)), M:tm-618, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) (not (-> B (or C B)))) Dm)) (Cm (not (-> B (or C B)))))
================================================================
tm-name          tm-47796
in-theory        47796
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (E or D)))) and F))
theorem-size     23
proof            (modus-ponens tm-618 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not (-> B (or C B)))) Em)) (Dm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-47796.        (not ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (E or D)))) and F)), M:tm-618, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not (-> B (or C B)))) Em)) (Dm (not (-> B (or C B)))))
================================================================
tm-name          tm-47797
in-theory        47797
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> A) -> (not (C -> (D or C)))) and E))
theorem-size     15
proof            (modus-ponens tm-618 tm-128 ((A (and (-> (-> (and Am Bm) Am) (not (-> B (or C B)))) Dm)) (Cm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-47797.        (not ((((A and B) -> A) -> (not (C -> (D or C)))) and E)), M:tm-618, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) (not (-> B (or C B)))) Dm)) (Cm (not (-> B (or C B)))))
================================================================
tm-name          tm-47798
in-theory        47798
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not ((C and D) -> C))))
theorem-size     13
proof            (modus-ponens tm-618 tm-130 ((A (-> (-> B (or C B)) (not (-> (and Bm Cm) Bm)))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-47798.        (not ((A -> (B or A)) -> (not ((C and D) -> C)))), M:tm-618, m:tm-130, u:((A (-> (-> B (or C B)) (not (-> (and Bm Cm) Bm)))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47799
in-theory        47799
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (A -> (not (B -> (C or B))))))
theorem-size     11
proof            (modus-ponens tm-618 tm-137 ((A (and Am (-> Am (not (-> B (or C B)))))) (Bm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-4 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-47799.        (not (A and (A -> (not (B -> (C or B)))))), M:tm-618, m:tm-137, u:((A (and Am (-> Am (not (-> B (or C B)))))) (Bm (not (-> B (or C B)))))
================================================================
tm-name          tm-47800
in-theory        47800
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> B)) -> (not (D -> (E or D))))))
theorem-size     15
proof            (modus-ponens tm-618 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) (not (-> B (or C B)))))) (Dm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-47800.        (not (A and ((B -> (C -> B)) -> (not (D -> (E or D)))))), M:tm-618, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) (not (-> B (or C B)))))) (Dm (not (-> B (or C B)))))
================================================================
tm-name          tm-47801
in-theory        47801
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not (E -> (F or E))))))
theorem-size     23
proof            (modus-ponens tm-618 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not (-> B (or C B)))))) (Em (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-47801.        (not (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (not (E -> (F or E)))))), M:tm-618, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (not (-> B (or C B)))))) (Em (not (-> B (or C B)))))
================================================================
tm-name          tm-47802
in-theory        47802
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> B) -> (not (D -> (E or D))))))
theorem-size     15
proof            (modus-ponens tm-618 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) (not (-> B (or C B)))))) (Dm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-47802.        (not (A and (((B and C) -> B) -> (not (D -> (E or D)))))), M:tm-618, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) (not (-> B (or C B)))))) (Dm (not (-> B (or C B)))))
================================================================
tm-name          tm-47803
in-theory        47803
times-derived    1
----------------------------------------------------------------
theorem          (not (A and (((B and C) -> C) -> (not (D -> (E or D))))))
theorem-size     15
proof            (modus-ponens tm-618 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) (not (-> B (or C B)))))) (Dm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-47803.        (not (A and (((B and C) -> C) -> (not (D -> (E or D)))))), M:tm-618, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) (not (-> B (or C B)))))) (Dm (not (-> B (or C B)))))
================================================================
tm-name          tm-47804
in-theory        47804
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A and B) -> B) -> (not (C -> (D or C)))) and E))
theorem-size     15
proof            (modus-ponens tm-618 tm-151 ((A (and (-> (-> (and Am Bm) Bm) (not (-> B (or C B)))) Dm)) (Cm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-47804.        (not ((((A and B) -> B) -> (not (C -> (D or C)))) and E)), M:tm-618, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) (not (-> B (or C B)))) Dm)) (Cm (not (-> B (or C B)))))
================================================================
tm-name          tm-47805
in-theory        47805
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not ((C and D) -> D))))
theorem-size     13
proof            (modus-ponens tm-618 tm-153 ((A (-> (-> B (or C B)) (not (-> (and Bm Cm) Cm)))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-47805.        (not ((A -> (B or A)) -> (not ((C and D) -> D)))), M:tm-618, m:tm-153, u:((A (-> (-> B (or C B)) (not (-> (and Bm Cm) Cm)))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47806
in-theory        47806
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not ((C -> (D -> C)) and (A -> (B or A))))))
theorem-size     19
proof            (modus-ponens tm-618 tm-179 ((A (-> (-> B (or C B)) (not (and (-> Bm (-> Cm Bm)) (-> B (or C B)))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-47806.        (not ((A -> (B or A)) -> (not ((C -> (D -> C)) and (A -> (B or A)))))), M:tm-618, m:tm-179, u:((A (-> (-> B (or C B)) (not (and (-> Bm (-> Cm Bm)) (-> B (or C B)))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47807
in-theory        47807
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B or A))))))
theorem-size     27
proof            (modus-ponens tm-618 tm-206 ((A (-> (-> B (or C B)) (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B (or C B)))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-47807.        (not ((A -> (B or A)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> (B or A)))))), M:tm-618, m:tm-206, u:((A (-> (-> B (or C B)) (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> B (or C B)))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47808
in-theory        47808
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (((C and D) -> C) and (A -> (B or A))))))
theorem-size     19
proof            (modus-ponens tm-618 tm-235 ((A (-> (-> B (or C B)) (not (and (-> (and Bm Cm) Bm) (-> B (or C B)))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7 tm-5 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-47808.        (not ((A -> (B or A)) -> (not (((C and D) -> C) and (A -> (B or A)))))), M:tm-618, m:tm-235, u:((A (-> (-> B (or C B)) (not (and (-> (and Bm Cm) Bm) (-> B (or C B)))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47809
in-theory        47809
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (((C and D) -> D) and (A -> (B or A))))))
theorem-size     19
proof            (modus-ponens tm-618 tm-266 ((A (-> (-> B (or C B)) (not (and (-> (and Bm Cm) Cm) (-> B (or C B)))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7 tm-5 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-47809.        (not ((A -> (B or A)) -> (not (((C and D) -> D) and (A -> (B or A)))))), M:tm-618, m:tm-266, u:((A (-> (-> B (or C B)) (not (and (-> (and Bm Cm) Cm) (-> B (or C B)))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47810
in-theory        47810
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not ((C -> (D -> (C and D))) and (A -> (B or A))))))
theorem-size     21
proof            (modus-ponens tm-618 tm-299 ((A (-> (-> B (or C B)) (not (and (-> Bm (-> Cm (and Bm Cm))) (-> B (or C B)))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-47810.        (not ((A -> (B or A)) -> (not ((C -> (D -> (C and D))) and (A -> (B or A)))))), M:tm-618, m:tm-299, u:((A (-> (-> B (or C B)) (not (and (-> Bm (-> Cm (and Bm Cm))) (-> B (or C B)))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47811
in-theory        47811
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (A -> (A and (B or A))))))
theorem-size     15
proof            (modus-ponens tm-618 tm-334 ((A (-> (-> Am (or C Am)) (not (-> Am (and Am (or C Am)))))) (B Am) (Bm (or C Am))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-47811.        (not ((A -> (B or A)) -> (not (A -> (A and (B or A)))))), M:tm-618, m:tm-334, u:((A (-> (-> Am (or C Am)) (not (-> Am (and Am (or C Am)))))) (B Am) (Bm (or C Am)))
================================================================
tm-name          tm-47812
in-theory        47812
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C -> (B and C))) -> (not (D -> (E or D))))))
theorem-size     17
proof            (modus-ponens tm-618 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (not (-> B (or C B)))))) (Dm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-4 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-47812.        (not (A and ((B -> (C -> (B and C))) -> (not (D -> (E or D)))))), M:tm-618, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) (not (-> B (or C B)))))) (Dm (not (-> B (or C B)))))
================================================================
tm-name          tm-47813
in-theory        47813
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> (A and B))) -> (not (C -> (D or C)))) and E))
theorem-size     17
proof            (modus-ponens tm-618 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) (not (-> B (or C B)))) Dm)) (Cm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-3 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-47813.        (not (((A -> (B -> (A and B))) -> (not (C -> (D or C)))) and E)), M:tm-618, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) (not (-> B (or C B)))) Dm)) (Cm (not (-> B (or C B)))))
================================================================
tm-name          tm-47814
in-theory        47814
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (C -> (D -> (C and D))))))
theorem-size     15
proof            (modus-ponens tm-618 tm-350 ((A (-> (-> B (or C B)) (not (-> Bm (-> Cm (and Bm Cm)))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-47814.        (not ((A -> (B or A)) -> (not (C -> (D -> (C and D)))))), M:tm-618, m:tm-350, u:((A (-> (-> B (or C B)) (not (-> Bm (-> Cm (and Bm Cm)))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47815
in-theory        47815
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not ((C -> (C or D)) and (A -> (B or A))))))
theorem-size     19
proof            (modus-ponens tm-618 tm-449 ((A (-> (-> B (or C B)) (not (and (-> Bm (or Bm Cm)) (-> B (or C B)))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-47815.        (not ((A -> (B or A)) -> (not ((C -> (C or D)) and (A -> (B or A)))))), M:tm-618, m:tm-449, u:((A (-> (-> B (or C B)) (not (and (-> Bm (or Bm Cm)) (-> B (or C B)))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47816
in-theory        47816
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (B or C)) -> (not (D -> (E or D))))))
theorem-size     15
proof            (modus-ponens tm-618 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) (not (-> B (or C B)))))) (Dm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-47816.        (not (A and ((B -> (B or C)) -> (not (D -> (E or D)))))), M:tm-618, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) (not (-> B (or C B)))))) (Dm (not (-> B (or C B)))))
================================================================
tm-name          tm-47817
in-theory        47817
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (A or B)) -> (not (C -> (D or C)))) and E))
theorem-size     15
proof            (modus-ponens tm-618 tm-463 ((A (and (-> (-> Am (or Am Bm)) (not (-> B (or C B)))) Dm)) (Cm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-47817.        (not (((A -> (A or B)) -> (not (C -> (D or C)))) and E)), M:tm-618, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) (not (-> B (or C B)))) Dm)) (Cm (not (-> B (or C B)))))
================================================================
tm-name          tm-47818
in-theory        47818
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (C -> (C or D)))))
theorem-size     13
proof            (modus-ponens tm-618 tm-465 ((A (-> (-> B (or C B)) (not (-> Bm (or Bm Cm))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-47818.        (not ((A -> (B or A)) -> (not (C -> (C or D))))), M:tm-618, m:tm-465, u:((A (-> (-> B (or C B)) (not (-> Bm (or Bm Cm))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47819
in-theory        47819
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not ((C -> (D or C)) and (A -> (B or A))))))
theorem-size     19
proof            (modus-ponens tm-618 tm-601 ((A (-> (-> B (or C B)) (not (and (-> Bm (or Cm Bm)) (-> B (or C B)))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-47819.        (not ((A -> (B or A)) -> (not ((C -> (D or C)) and (A -> (B or A)))))), M:tm-618, m:tm-601, u:((A (-> (-> B (or C B)) (not (and (-> Bm (or Cm Bm)) (-> B (or C B)))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47820
in-theory        47820
times-derived    1
----------------------------------------------------------------
theorem          (not (A and ((B -> (C or B)) -> (not (D -> (E or D))))))
theorem-size     15
proof            (modus-ponens tm-618 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) (not (-> B (or C B)))))) (Dm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-47820.        (not (A and ((B -> (C or B)) -> (not (D -> (E or D)))))), M:tm-618, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) (not (-> B (or C B)))))) (Dm (not (-> B (or C B)))))
================================================================
tm-name          tm-47821
in-theory        47821
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B or A)) -> (not (C -> (D or C)))) and E))
theorem-size     15
proof            (modus-ponens tm-618 tm-616 ((A (and (-> (-> Am (or Bm Am)) (not (-> B (or C B)))) Dm)) (Cm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-47821.        (not (((A -> (B or A)) -> (not (C -> (D or C)))) and E)), M:tm-618, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) (not (-> B (or C B)))) Dm)) (Cm (not (-> B (or C B)))))
================================================================
tm-name          tm-47822
in-theory        47822
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (C -> (D or C)))))
theorem-size     13
proof            (modus-ponens tm-618 tm-618 ((A (-> (-> B (or C B)) (not (-> Bm (or Cm Bm))))) (Am (-> B (or C B)))))
axioms-used      (tm-9 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47822.        (not ((A -> (B or A)) -> (not (C -> (D or C))))), M:tm-618, m:tm-618, u:((A (-> (-> B (or C B)) (not (-> Bm (or Cm Bm))))) (Am (-> B (or C B))))
================================================================
tm-name          tm-47823
in-theory        47823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47823.        (((A -> (not (B -> (C or B)))) -> (not A)) and (D -> (E or D))), M:tm-609, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47824
in-theory        47824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47824.        ((A -> ((B -> (C or B)) and A)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-605, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47825
in-theory        47825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and ((D -> (E or D)) and ((A -> (not (B -> (C or B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47825.        (((A -> (not (B -> (C or B)))) -> (not A)) and ((D -> (E or D)) and ((A -> (not (B -> (C or B)))) -> (not A)))), M:tm-595, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47826
in-theory        47826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47826.        (((A -> (B or A)) or C) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-550, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47827
in-theory        47827
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47827.        ((A or (B -> (C or B))) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-540, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47828
in-theory        47828
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47828.        ((A or (B -> (B or C))) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-530, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47829
in-theory        47829
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47829.        ((A or (B -> (C -> (B and C)))) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-520, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47830
in-theory        47830
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47830.        ((A or ((B and C) -> C)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-510, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47831
in-theory        47831
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47831.        ((A or ((B and C) -> B)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-500, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47832
in-theory        47832
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (G or F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47832.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (G or F)))) -> (not E))), M:tm-490, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47833
in-theory        47833
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-9)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47833.        ((A or (B -> (C -> B))) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-480, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47834
in-theory        47834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C or B)))) -> ((not A) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47834.        ((A -> (not (B -> (C or B)))) -> ((not A) or D)), M:tm-470, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-47835
in-theory        47835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47835.        ((A -> (B -> (B or C))) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-469, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47836
in-theory        47836
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (C -> (D or C)))))
theorem-size     13
proof            (modus-ponens tm-465 tm-618 ((A (-> (-> B (or B C)) (not (-> Bm (or Cm Bm))))) (Am (-> B (or B C)))))
axioms-used      (tm-9 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47836.        (not ((A -> (A or B)) -> (not (C -> (D or C))))), M:tm-465, m:tm-618, u:((A (-> (-> B (or B C)) (not (-> Bm (or Cm Bm))))) (Am (-> B (or B C))))
================================================================
tm-name          tm-47837
in-theory        47837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-7)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47837.        (((A -> (not (B -> (C or B)))) -> (not A)) and (D -> (D or E))), M:tm-456, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47838
in-theory        47838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47838.        ((A -> ((B -> (B or C)) and A)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-453, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47839
in-theory        47839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and ((D -> (D or E)) and ((A -> (not (B -> (C or B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47839.        (((A -> (not (B -> (C or B)))) -> (not A)) and ((D -> (D or E)) and ((A -> (not (B -> (C or B)))) -> (not A)))), M:tm-443, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47840
in-theory        47840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47840.        (((A -> (A or B)) or C) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-409, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47841
in-theory        47841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47841.        (((A -> (B -> (A and B))) or C) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-400, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47842
in-theory        47842
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47842.        ((((A and B) -> B) or C) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-391, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47843
in-theory        47843
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47843.        ((((A and B) -> A) or C) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-382, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47844
in-theory        47844
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (F -> (G or F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-1 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47844.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (not (F -> (G or F)))) -> (not E))), M:tm-373, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47845
in-theory        47845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47845.        (((A -> (B -> A)) or C) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-364, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47846
in-theory        47846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C or B)))) -> (D -> ((not A) and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47846.        ((A -> (not (B -> (C or B)))) -> (D -> ((not A) and D))), M:tm-355, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-47847
in-theory        47847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47847.        ((A -> (B -> (C -> (B and C)))) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-354, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47848
in-theory        47848
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (C -> (D or C)))))
theorem-size     15
proof            (modus-ponens tm-350 tm-618 ((A (-> (-> B (-> C (and B C))) (not (-> Bm (or Cm Bm))))) (Am (-> B (-> C (and B C))))))
axioms-used      (tm-9 tm-1 tm-5 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47848.        (not ((A -> (B -> (A and B))) -> (not (C -> (D or C))))), M:tm-350, m:tm-618, u:((A (-> (-> B (-> C (and B C))) (not (-> Bm (or Cm Bm))))) (Am (-> B (-> C (and B C)))))
================================================================
tm-name          tm-47849
in-theory        47849
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47849.        (((A -> (not (B -> (C or B)))) -> (not A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47850
in-theory        47850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (not (D -> (E or D)))) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47850.        (((A -> B) -> (A -> (A and B))) and ((C -> (not (D -> (E or D)))) -> (not C))), M:tm-338, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47851
in-theory        47851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and ((A -> (not (B -> (C or B)))) -> ((A -> (not (B -> (C or B)))) and (not A))))
theorem-size     32
proof            (modus-ponens tm-328 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       142
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47851.        (((A -> (not (B -> (C or B)))) -> (not A)) and ((A -> (not (B -> (C or B)))) -> ((A -> (not (B -> (C or B)))) and (not A)))), M:tm-328, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-47852
in-theory        47852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not (B -> (C or B)))) -> (not A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47852.        (((A -> (not (B -> (C or B)))) -> (not A)) and ((D -> (E -> (D and E))) and ((A -> (not (B -> (C or B)))) -> (not A)))), M:tm-327, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47853
in-theory        47853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (((D and E) -> E) and ((A -> (not (B -> (C or B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-1 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47853.        (((A -> (not (B -> (C or B)))) -> (not A)) and (((D and E) -> E) and ((A -> (not (B -> (C or B)))) -> (not A)))), M:tm-326, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47854
in-theory        47854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (((D and E) -> D) and ((A -> (not (B -> (C or B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-1 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47854.        (((A -> (not (B -> (C or B)))) -> (not A)) and (((D and E) -> D) and ((A -> (not (B -> (C or B)))) -> (not A)))), M:tm-325, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47855
in-theory        47855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not (B -> (C or B)))) -> (not A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47855.        (((A -> (not (B -> (C or B)))) -> (not A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (not (B -> (C or B)))) -> (not A)))), M:tm-324, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47856
in-theory        47856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not (B -> (C or B)))) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47856.        (((A -> (not (B -> (C or B)))) -> (not A)) and ((D -> (E -> D)) and ((A -> (not (B -> (C or B)))) -> (not A)))), M:tm-323, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47857
in-theory        47857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-7)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47857.        (((A -> (not (B -> (C or B)))) -> (not A)) and ((D and E) -> E)), M:tm-322, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47858
in-theory        47858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-7)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47858.        (((A -> (not (B -> (C or B)))) -> (not A)) and ((D and E) -> D)), M:tm-320, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47859
in-theory        47859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47859.        (((A -> (not (B -> (C or B)))) -> (not A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47860
in-theory        47860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and ((A -> (not (B -> (C or B)))) -> (A -> (not (B -> (C or B))))))
theorem-size     29
proof            (modus-ponens tm-316 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47860.        (((A -> (not (B -> (C or B)))) -> (not A)) and ((A -> (not (B -> (C or B)))) -> (A -> (not (B -> (C or B)))))), M:tm-316, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-47861
in-theory        47861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47861.        (((A -> (not (B -> (C or B)))) -> (not A)) and (D -> (E -> D))), M:tm-315, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47862
in-theory        47862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (((A -> (not (B -> (C or B)))) -> (not (not A))) -> (not (A -> (not (B -> (C or B)))))))
theorem-size     34
proof            (modus-ponens tm-313 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47862.        (((A -> (not (B -> (C or B)))) -> (not A)) and (((A -> (not (B -> (C or B)))) -> (not (not A))) -> (not (A -> (not (B -> (C or B))))))), M:tm-313, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-47863
in-theory        47863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (((not A) -> D) -> (((A -> (not (B -> (C or B)))) or (not A)) -> D)))
theorem-size     30
proof            (modus-ponens tm-312 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-1 tm-7)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47863.        (((A -> (not (B -> (C or B)))) -> (not A)) and (((not A) -> D) -> (((A -> (not (B -> (C or B)))) or (not A)) -> D))), M:tm-312, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-47864
in-theory        47864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (D or ((A -> (not (B -> (C or B)))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47864.        (((A -> (not (B -> (C or B)))) -> (not A)) and (D or ((A -> (not (B -> (C or B)))) -> (not A)))), M:tm-311, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47865
in-theory        47865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (((A -> (not (B -> (C or B)))) -> (not A)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47865.        (((A -> (not (B -> (C or B)))) -> (not A)) and (((A -> (not (B -> (C or B)))) -> (not A)) or D)), M:tm-310, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47866
in-theory        47866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (D -> (((A -> (not (B -> (C or B)))) -> (not A)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47866.        (((A -> (not (B -> (C or B)))) -> (not A)) and (D -> (((A -> (not (B -> (C or B)))) -> (not A)) and D))), M:tm-309, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47867
in-theory        47867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (D -> ((A -> (not (B -> (C or B)))) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47867.        (((A -> (not (B -> (C or B)))) -> (not A)) and (D -> ((A -> (not (B -> (C or B)))) -> (not A)))), M:tm-305, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47868
in-theory        47868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47868.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-303, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47869
in-theory        47869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47869.        ((A -> (((B and C) -> C) and A)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-270, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47870
in-theory        47870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47870.        ((A -> (((B and C) -> B) and A)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-239, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47871
in-theory        47871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (F -> (G or F)))) -> (not E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47871.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (not (F -> (G or F)))) -> (not E))), M:tm-210, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47872
in-theory        47872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47872.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-183, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47873
in-theory        47873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47873.        ((A -> ((B and C) -> C)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-157, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47874
in-theory        47874
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (not (C -> (D or C)))) -> (not (C -> (D or C))))) -> (not (B and (not (C -> (D or C))))))
theorem-size     27
proof            (modus-ponens tm-154 tm-618 ((Am (and A (not (-> Bm (or Cm Bm))))) (B (not (-> Bm (or Cm Bm)))) (C (not (and A (not (-> Bm (or Cm Bm))))))))
axioms-used      (tm-8 tm-1 tm-4 tm-9 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47874.        ((A or ((B and (not (C -> (D or C)))) -> (not (C -> (D or C))))) -> (not (B and (not (C -> (D or C)))))), M:tm-154, m:tm-618, u:((Am (and A (not (-> Bm (or Cm Bm))))) (B (not (-> Bm (or Cm Bm)))) (C (not (and A (not (-> Bm (or Cm Bm)))))))
================================================================
tm-name          tm-47875
in-theory        47875
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not (C -> (D or C)))))
theorem-size     13
proof            (modus-ponens tm-153 tm-618 ((A (-> (-> (and B C) C) (not (-> Bm (or Cm Bm))))) (Am (-> (and B C) C))))
axioms-used      (tm-9 tm-1 tm-4 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47875.        (not (((A and B) -> B) -> (not (C -> (D or C))))), M:tm-153, m:tm-618, u:((A (-> (-> (and B C) C) (not (-> Bm (or Cm Bm))))) (Am (-> (and B C) C)))
================================================================
tm-name          tm-47876
in-theory        47876
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-1 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47876.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-147, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47877
in-theory        47877
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (not (C -> (D or C))))) -> B) or ((A and (B -> (not (C -> (D or C))))) -> (not (C -> (D or C))))) -> (not (A and (B -> (not (C -> (D or C)))))))
theorem-size     42
proof            (modus-ponens tm-144 tm-618 ((Am (and A (-> B (not (-> Bm (or Cm Bm)))))) (C (not (-> Bm (or Cm Bm)))) (D (not (and A (-> B (not (-> Bm (or Cm Bm)))))))))
axioms-used      (tm-8 tm-2 tm-4 tm-9 tm-1 tm-7)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47877.        ((((A and (B -> (not (C -> (D or C))))) -> B) or ((A and (B -> (not (C -> (D or C))))) -> (not (C -> (D or C))))) -> (not (A and (B -> (not (C -> (D or C))))))), M:tm-144, m:tm-618, u:((Am (and A (-> B (not (-> Bm (or Cm Bm)))))) (C (not (-> Bm (or Cm Bm)))) (D (not (and A (-> B (not (-> Bm (or Cm Bm))))))))
================================================================
tm-name          tm-47878
in-theory        47878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47878.        ((A -> ((B and C) -> B)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-134, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47879
in-theory        47879
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((not (B -> (C or B))) and D) -> (not (B -> (C or B))))) -> (not ((not (B -> (C or B))) and D)))
theorem-size     27
proof            (modus-ponens tm-131 tm-618 ((Am (and (not (-> Bm (or Cm Bm))) B)) (A (not (-> Bm (or Cm Bm)))) (C (not (and (not (-> Bm (or Cm Bm))) B)))))
axioms-used      (tm-8 tm-1 tm-3 tm-9 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47879.        ((A or (((not (B -> (C or B))) and D) -> (not (B -> (C or B))))) -> (not ((not (B -> (C or B))) and D))), M:tm-131, m:tm-618, u:((Am (and (not (-> Bm (or Cm Bm))) B)) (A (not (-> Bm (or Cm Bm)))) (C (not (and (not (-> Bm (or Cm Bm))) B))))
================================================================
tm-name          tm-47880
in-theory        47880
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not (C -> (D or C)))))
theorem-size     13
proof            (modus-ponens tm-130 tm-618 ((A (-> (-> (and B C) B) (not (-> Bm (or Cm Bm))))) (Am (-> (and B C) B))))
axioms-used      (tm-9 tm-1 tm-3 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47880.        (not (((A and B) -> A) -> (not (C -> (D or C))))), M:tm-130, m:tm-618, u:((A (-> (-> (and B C) B) (not (-> Bm (or Cm Bm))))) (Am (-> (and B C) B)))
================================================================
tm-name          tm-47881
in-theory        47881
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-1 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47881.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-125, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47882
in-theory        47882
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not (B -> (C or B)))) and D) -> A) or (((A -> (not (B -> (C or B)))) and D) -> (not (B -> (C or B))))) -> (not ((A -> (not (B -> (C or B)))) and D)))
theorem-size     42
proof            (modus-ponens tm-122 tm-618 ((Am (and (-> A (not (-> Bm (or Cm Bm)))) C)) (B (not (-> Bm (or Cm Bm)))) (D (not (and (-> A (not (-> Bm (or Cm Bm)))) C)))))
axioms-used      (tm-8 tm-2 tm-3 tm-9 tm-1 tm-7)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47882.        (((((A -> (not (B -> (C or B)))) and D) -> A) or (((A -> (not (B -> (C or B)))) and D) -> (not (B -> (C or B))))) -> (not ((A -> (not (B -> (C or B)))) and D))), M:tm-122, m:tm-618, u:((Am (and (-> A (not (-> Bm (or Cm Bm)))) C)) (B (not (-> Bm (or Cm Bm)))) (D (not (and (-> A (not (-> Bm (or Cm Bm)))) C))))
================================================================
tm-name          tm-47883
in-theory        47883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (G or F)))) -> (not E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47883.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (not (F -> (G or F)))) -> (not E))), M:tm-113, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47884
in-theory        47884
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (E or D)))))
theorem-size     21
proof            (modus-ponens tm-109 tm-618 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> Bm (or Cm Bm))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
axioms-used      (tm-9 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47884.        (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (D -> (E or D))))), M:tm-109, m:tm-618, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> Bm (or Cm Bm))))) (Am (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))
================================================================
tm-name          tm-47885
in-theory        47885
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47885.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-105, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47886
in-theory        47886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (not (D -> (E or D)))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47886.        (((A -> B) -> (A -> A)) and ((C -> (not (D -> (E or D)))) -> (not C))), M:tm-95, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47887
in-theory        47887
times-derived    1
----------------------------------------------------------------
theorem          ((((not (A -> (B or A))) -> C) or ((not (A -> (B or A))) -> (not (A -> (B or A))))) -> (not (not (A -> (B or A)))))
theorem-size     30
proof            (modus-ponens tm-92 tm-618 ((Am (not (-> Bm (or Cm Bm)))) (A (not (-> Bm (or Cm Bm)))) (B (not (not (-> Bm (or Cm Bm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-9 tm-7)
proof-size       122
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47887.        ((((not (A -> (B or A))) -> C) or ((not (A -> (B or A))) -> (not (A -> (B or A))))) -> (not (not (A -> (B or A))))), M:tm-92, m:tm-618, u:((Am (not (-> Bm (or Cm Bm)))) (A (not (-> Bm (or Cm Bm)))) (B (not (not (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-47888
in-theory        47888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C or B)))) -> (D -> (not A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47888.        ((A -> (not (B -> (C or B)))) -> (D -> (not A))), M:tm-84, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-47889
in-theory        47889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47889.        ((A -> (B -> (C -> B))) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-83, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47890
in-theory        47890
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (C -> (D or C)))))
theorem-size     13
proof            (modus-ponens tm-79 tm-618 ((A (-> (-> B (-> C B)) (not (-> Bm (or Cm Bm))))) (Am (-> B (-> C B)))))
axioms-used      (tm-9 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47890.        (not ((A -> (B -> A)) -> (not (C -> (D or C))))), M:tm-79, m:tm-618, u:((A (-> (-> B (-> C B)) (not (-> Bm (or Cm Bm))))) (Am (-> B (-> C B))))
================================================================
tm-name          tm-47891
in-theory        47891
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (not (C -> (D or C)))) -> (not B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-10 tm-9 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47891.        (((not (not A)) -> A) and ((B -> (not (C -> (D or C)))) -> (not B))), M:tm-76, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47892
in-theory        47892
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> (not (B -> (C or B)))))) or (A -> (not (B -> (C or B))))) -> (not A))
theorem-size     22
proof            (modus-ponens tm-73 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-8 tm-10 tm-9 tm-1 tm-7)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47892.        (((not (not (A -> (not (B -> (C or B)))))) or (A -> (not (B -> (C or B))))) -> (not A)), M:tm-73, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-47893
in-theory        47893
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (D -> (E or D)))) -> (not C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47893.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (not (D -> (E or D)))) -> (not C))), M:tm-69, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47894
in-theory        47894
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) or (((A -> (B or A)) -> (not C)) -> (not (A -> (B or A))))) -> (not ((A -> (B or A)) -> (not C))))
theorem-size     33
proof            (modus-ponens tm-66 tm-618 ((Am (-> (-> Bm (or Cm Bm)) (not B))) (A (-> Bm (or Cm Bm))) (C (not (-> (-> Bm (or Cm Bm)) (not B))))))
axioms-used      (tm-8 tm-9 tm-1 tm-7)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47894.        ((((A -> (B or A)) -> C) or (((A -> (B or A)) -> (not C)) -> (not (A -> (B or A))))) -> (not ((A -> (B or A)) -> (not C)))), M:tm-66, m:tm-618, u:((Am (-> (-> Bm (or Cm Bm)) (not B))) (A (-> Bm (or Cm Bm))) (C (not (-> (-> Bm (or Cm Bm)) (not B)))))
================================================================
tm-name          tm-47895
in-theory        47895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-9 tm-1 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47895.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-54, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47896
in-theory        47896
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (not (C -> (D or C))))) or (B -> (not (C -> (D or C))))) -> (not B))
theorem-size     22
proof            (modus-ponens tm-47 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-8 tm-4 tm-9 tm-1 tm-7)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47896.        (((A and (B -> (not (C -> (D or C))))) or (B -> (not (C -> (D or C))))) -> (not B)), M:tm-47, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-47897
in-theory        47897
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not (B -> (C or B)))) and D) or (A -> (not (B -> (C or B))))) -> (not A))
theorem-size     22
proof            (modus-ponens tm-46 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-8 tm-3 tm-9 tm-1 tm-7)
proof-size       90
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47897.        ((((A -> (not (B -> (C or B)))) and D) or (A -> (not (B -> (C or B))))) -> (not A)), M:tm-46, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-47898
in-theory        47898
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> (B or A))) or (C -> (not (A -> (B or A))))) -> (not C))
theorem-size     18
proof            (modus-ponens tm-44 tm-618 ((A Am) (B (not (-> Bm (or Cm Bm)))) (C (not Am))))
axioms-used      (tm-8 tm-1 tm-9 tm-7)
proof-size       88
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47898.        (((not (A -> (B or A))) or (C -> (not (A -> (B or A))))) -> (not C)), M:tm-44, m:tm-618, u:((A Am) (B (not (-> Bm (or Cm Bm)))) (C (not Am)))
================================================================
tm-name          tm-47899
in-theory        47899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (not (D -> (E or D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-7 tm-9 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47899.        ((A -> (B or A)) and ((C -> (not (D -> (E or D)))) -> (not C))), M:tm-42, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47900
in-theory        47900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (not (D -> (E or D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-6 tm-9 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47900.        ((A -> (A or B)) and ((C -> (not (D -> (E or D)))) -> (not C))), M:tm-32, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47901
in-theory        47901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C or B)))) -> ((A -> (not (B -> (C or B)))) and (not A)))
theorem-size     20
proof            (modus-ponens tm-24 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       88
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47901.        ((A -> (not (B -> (C or B)))) -> ((A -> (not (B -> (C or B)))) and (not A))), M:tm-24, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-47902
in-theory        47902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (not (D -> (E or D)))) -> (not C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47902.        ((A -> (B -> (A and B))) and ((C -> (not (D -> (E or D)))) -> (not C))), M:tm-23, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47903
in-theory        47903
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (not (D -> (E or D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-4 tm-9 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47903.        (((A and B) -> B) and ((C -> (not (D -> (E or D)))) -> (not C))), M:tm-22, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47904
in-theory        47904
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (not (D -> (E or D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-3 tm-9 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47904.        (((A and B) -> A) and ((C -> (not (D -> (E or D)))) -> (not C))), M:tm-21, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47905
in-theory        47905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-2 tm-9 tm-1 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47905.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-20, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47906
in-theory        47906
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (not (D -> (E or D)))) -> (not C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-9 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47906.        ((A -> (B -> A)) and ((C -> (not (D -> (E or D)))) -> (not C))), M:tm-19, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47907
in-theory        47907
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C or B)))) -> (A -> (not (B -> (C or B)))))
theorem-size     17
proof            (modus-ponens tm-12 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-9 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47907.        ((A -> (not (B -> (C or B)))) -> (A -> (not (B -> (C or B))))), M:tm-12, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-47908
in-theory        47908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not (not A))) -> (not (A -> (not (B -> (C or B))))))
theorem-size     22
proof            (modus-ponens tm-9 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-9 tm-1 tm-7)
proof-size       72
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47908.        (((A -> (not (B -> (C or B)))) -> (not (not A))) -> (not (A -> (not (B -> (C or B)))))), M:tm-9, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-47909
in-theory        47909
times-derived    1
----------------------------------------------------------------
theorem          (((not A) -> B) -> (((A -> (not (C -> (D or C)))) or (not A)) -> B))
theorem-size     18
proof            (modus-ponens tm-8 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-8 tm-9 tm-1 tm-7)
proof-size       70
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47909.        (((not A) -> B) -> (((A -> (not (C -> (D or C)))) or (not A)) -> B)), M:tm-8, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-47910
in-theory        47910
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (not (C -> (D or C)))) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-7 tm-9 tm-1)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47910.        (A or ((B -> (not (C -> (D or C)))) -> (not B))), M:tm-7, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47911
in-theory        47911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-6 tm-9 tm-1 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47911.        (((A -> (not (B -> (C or B)))) -> (not A)) or D), M:tm-6, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47912
in-theory        47912
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (not (C -> (D or C)))) -> (not B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47912.        (A -> (((B -> (not (C -> (D or C)))) -> (not B)) and A)), M:tm-5, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47913
in-theory        47913
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (not (C -> (D or C)))) -> (not B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-1 tm-9 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47913.        (A -> ((B -> (not (C -> (D or C)))) -> (not B))), M:tm-1, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-47914
in-theory        47914
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> (B -> (C or B))))
theorem-size     15
proof            (modus-ponens tm-619 tm-1 ((Am (-> A (or B A))) (C (-> Bm (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47914.        ((A or (B -> (C or B))) -> (D -> (B -> (C or B)))), M:tm-619, m:tm-1, u:((Am (-> A (or B A))) (C (-> Bm (-> A (or B A)))))
================================================================
tm-name          tm-47915
in-theory        47915
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> ((B -> (C or B)) and D)))
theorem-size     17
proof            (modus-ponens tm-619 tm-5 ((Am (-> A (or B A))) (C (-> Bm (and (-> A (or B A)) Bm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-47915.        ((A or (B -> (C or B))) -> (D -> ((B -> (C or B)) and D))), M:tm-619, m:tm-5, u:((Am (-> A (or B A))) (C (-> Bm (and (-> A (or B A)) Bm))))
================================================================
tm-name          tm-47916
in-theory        47916
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) or D))
theorem-size     15
proof            (modus-ponens tm-619 tm-6 ((Am (-> A (or B A))) (C (or (-> A (or B A)) Bm))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-47916.        ((A or (B -> (C or B))) -> ((B -> (C or B)) or D)), M:tm-619, m:tm-6, u:((Am (-> A (or B A))) (C (or (-> A (or B A)) Bm)))
================================================================
tm-name          tm-47917
in-theory        47917
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D or (B -> (C or B))))
theorem-size     15
proof            (modus-ponens tm-619 tm-7 ((Am (-> A (or B A))) (C (or Bm (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47917.        ((A or (B -> (C or B))) -> (D or (B -> (C or B)))), M:tm-619, m:tm-7, u:((Am (-> A (or B A))) (C (or Bm (-> A (or B A)))))
================================================================
tm-name          tm-47918
in-theory        47918
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((C or B) -> D) -> ((B or (C or B)) -> D)))
theorem-size     21
proof            (modus-ponens tm-619 tm-8 ((A Am) (Bm (or B Am)) (C (-> (-> (or B Am) Cm) (-> (or Am (or B Am)) Cm)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47918.        ((A or (B -> (C or B))) -> (((C or B) -> D) -> ((B or (C or B)) -> D))), M:tm-619, m:tm-8, u:((A Am) (Bm (or B Am)) (C (-> (-> (or B Am) Cm) (-> (or Am (or B Am)) Cm))))
================================================================
tm-name          tm-47919
in-theory        47919
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (not (C or B))) -> (not B)))
theorem-size     17
proof            (modus-ponens tm-619 tm-9 ((A Am) (Bm (or B Am)) (C (-> (-> Am (not (or B Am))) (not Am)))))
axioms-used      (tm-8 tm-1 tm-7 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-47919.        ((A or (B -> (C or B))) -> ((B -> (not (C or B))) -> (not B))), M:tm-619, m:tm-9, u:((A Am) (Bm (or B Am)) (C (-> (-> Am (not (or B Am))) (not Am))))
================================================================
tm-name          tm-47920
in-theory        47920
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-619 tm-11 ((Am (-> A (or B A))) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-47920.        ((A or (B -> (C or B))) -> (D -> (E -> D))), M:tm-619, m:tm-11, u:((Am (-> A (or B A))) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-47921
in-theory        47921
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (B -> B))
theorem-size     11
proof            (modus-ponens tm-619 tm-12 ((A Am) (Bm (or B Am)) (C (-> Am Am))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-47921.        ((A or (B -> (C or B))) -> (B -> B)), M:tm-619, m:tm-12, u:((A Am) (Bm (or B Am)) (C (-> Am Am)))
================================================================
tm-name          tm-47922
in-theory        47922
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-619 tm-14 ((Am (-> A (or B A))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-47922.        ((A or (B -> (C or B))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-619, m:tm-14, u:((Am (-> A (or B A))) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-47923
in-theory        47923
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-619 tm-16 ((Am (-> A (or B A))) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-7 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-47923.        ((A or (B -> (C or B))) -> ((D and E) -> D)), M:tm-619, m:tm-16, u:((Am (-> A (or B A))) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-47924
in-theory        47924
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-619 tm-18 ((Am (-> A (or B A))) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-1 tm-7 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-47924.        ((A or (B -> (C or B))) -> ((D and E) -> E)), M:tm-619, m:tm-18, u:((Am (-> A (or B A))) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-47925
in-theory        47925
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (E -> D)) and (B -> (C or B))))
theorem-size     19
proof            (modus-ponens tm-619 tm-19 ((Am (-> A (or B A))) (C (and (-> Bm (-> Cm Bm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-47925.        ((A or (B -> (C or B))) -> ((D -> (E -> D)) and (B -> (C or B)))), M:tm-619, m:tm-19, u:((Am (-> A (or B A))) (C (and (-> Bm (-> Cm Bm)) (-> A (or B A)))))
================================================================
tm-name          tm-47926
in-theory        47926
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (C or B))))
theorem-size     27
proof            (modus-ponens tm-619 tm-20 ((Am (-> A (or B A))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-47926.        ((A or (B -> (C or B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (C or B)))), M:tm-619, m:tm-20, u:((Am (-> A (or B A))) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (or B A)))))
================================================================
tm-name          tm-47927
in-theory        47927
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D and E) -> D) and (B -> (C or B))))
theorem-size     19
proof            (modus-ponens tm-619 tm-21 ((Am (-> A (or B A))) (C (and (-> (and Bm Cm) Bm) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-47927.        ((A or (B -> (C or B))) -> (((D and E) -> D) and (B -> (C or B)))), M:tm-619, m:tm-21, u:((Am (-> A (or B A))) (C (and (-> (and Bm Cm) Bm) (-> A (or B A)))))
================================================================
tm-name          tm-47928
in-theory        47928
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D and E) -> E) and (B -> (C or B))))
theorem-size     19
proof            (modus-ponens tm-619 tm-22 ((Am (-> A (or B A))) (C (and (-> (and Bm Cm) Cm) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-47928.        ((A or (B -> (C or B))) -> (((D and E) -> E) and (B -> (C or B)))), M:tm-619, m:tm-22, u:((Am (-> A (or B A))) (C (and (-> (and Bm Cm) Cm) (-> A (or B A)))))
================================================================
tm-name          tm-47929
in-theory        47929
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (E -> (D and E))) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-23 ((Am (-> A (or B A))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-47929.        ((A or (B -> (C or B))) -> ((D -> (E -> (D and E))) and (B -> (C or B)))), M:tm-619, m:tm-23, u:((Am (-> A (or B A))) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A (or B A)))))
================================================================
tm-name          tm-47930
in-theory        47930
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (B -> (B and (C or B))))
theorem-size     15
proof            (modus-ponens tm-619 tm-24 ((A Am) (Bm (or B Am)) (C (-> Am (and Am (or B Am))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-47930.        ((A or (B -> (C or B))) -> (B -> (B and (C or B)))), M:tm-619, m:tm-24, u:((A Am) (Bm (or B Am)) (C (-> Am (and Am (or B Am)))))
================================================================
tm-name          tm-47931
in-theory        47931
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-619 tm-25 ((Am (-> A (or B A))) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-47931.        ((A or (B -> (C or B))) -> (D -> (E -> (D and E)))), M:tm-619, m:tm-25, u:((Am (-> A (or B A))) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-47932
in-theory        47932
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (D or E)) and (B -> (C or B))))
theorem-size     19
proof            (modus-ponens tm-619 tm-32 ((Am (-> A (or B A))) (C (and (-> Bm (or Bm Cm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-47932.        ((A or (B -> (C or B))) -> ((D -> (D or E)) and (B -> (C or B)))), M:tm-619, m:tm-32, u:((Am (-> A (or B A))) (C (and (-> Bm (or Bm Cm)) (-> A (or B A)))))
================================================================
tm-name          tm-47933
in-theory        47933
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-619 tm-33 ((Am (-> A (or B A))) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-47933.        ((A or (B -> (C or B))) -> (D -> (D or E))), M:tm-619, m:tm-33, u:((Am (-> A (or B A))) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-47934
in-theory        47934
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (E or D)) and (B -> (C or B))))
theorem-size     19
proof            (modus-ponens tm-619 tm-42 ((Am (-> A (or B A))) (C (and (-> Bm (or Cm Bm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-47934.        ((A or (B -> (C or B))) -> ((D -> (E or D)) and (B -> (C or B)))), M:tm-619, m:tm-42, u:((Am (-> A (or B A))) (C (and (-> Bm (or Cm Bm)) (-> A (or B A)))))
================================================================
tm-name          tm-47935
in-theory        47935
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-619 tm-43 ((Am (-> A (or B A))) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-47935.        ((A or (B -> (C or B))) -> (D -> (E or D))), M:tm-619, m:tm-43, u:((Am (-> A (or B A))) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-47936
in-theory        47936
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (D or (B -> C)))) -> ((C or (B -> C)) -> (D or (B -> C))))
theorem-size     23
proof            (modus-ponens tm-619 tm-44 ((A (-> Am Bm)) (Cm (or B (-> Am Bm))) (C (-> (or Bm (-> Am Bm)) (or B (-> Am Bm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-47936.        ((A or ((B -> C) -> (D or (B -> C)))) -> ((C or (B -> C)) -> (D or (B -> C)))), M:tm-619, m:tm-44, u:((A (-> Am Bm)) (Cm (or B (-> Am Bm))) (C (-> (or Bm (-> Am Bm)) (or B (-> Am Bm)))))
================================================================
tm-name          tm-47937
in-theory        47937
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (E or ((B -> C) -> (B -> D))))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E or ((B -> C) -> (B -> D)))))
theorem-size     43
proof            (modus-ponens tm-619 tm-45 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (or B (-> (-> Am Bm) (-> Am Cm)))) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or B (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-47937.        ((A or (((B -> C) -> (B -> D)) -> (E or ((B -> C) -> (B -> D))))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E or ((B -> C) -> (B -> D))))), M:tm-619, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (or B (-> (-> Am Bm) (-> Am Cm)))) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or B (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-47938
in-theory        47938
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((B and D) or B) -> (C or B)))
theorem-size     17
proof            (modus-ponens tm-619 tm-46 ((A Am) (Bm (or B Am)) (C (-> (or (and Am Cm) Am) (or B Am)))))
axioms-used      (tm-8 tm-1 tm-7 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-47938.        ((A or (B -> (C or B))) -> (((B and D) or B) -> (C or B))), M:tm-619, m:tm-46, u:((A Am) (Bm (or B Am)) (C (-> (or (and Am Cm) Am) (or B Am))))
================================================================
tm-name          tm-47939
in-theory        47939
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D and B) or B) -> (C or B)))
theorem-size     17
proof            (modus-ponens tm-619 tm-47 ((A Am) (Bm (or B Am)) (C (-> (or (and Cm Am) Am) (or B Am)))))
axioms-used      (tm-8 tm-1 tm-7 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-47939.        ((A or (B -> (C or B))) -> (((D and B) or B) -> (C or B))), M:tm-619, m:tm-47, u:((A Am) (Bm (or B Am)) (C (-> (or (and Cm Am) Am) (or B Am))))
================================================================
tm-name          tm-47940
in-theory        47940
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C and B)) -> (D or (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (D or (B -> (C and B)))))
theorem-size     31
proof            (modus-ponens tm-619 tm-48 ((A (-> Am (and Bm Am))) (Cm (or B (-> Am (and Bm Am)))) (C (-> (or Bm (-> Am (and Bm Am))) (or B (-> Am (and Bm Am)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-47940.        ((A or ((B -> (C and B)) -> (D or (B -> (C and B))))) -> ((C or (B -> (C and B))) -> (D or (B -> (C and B))))), M:tm-619, m:tm-48, u:((A (-> Am (and Bm Am))) (Cm (or B (-> Am (and Bm Am)))) (C (-> (or Bm (-> Am (and Bm Am))) (or B (-> Am (and Bm Am))))))
================================================================
tm-name          tm-47941
in-theory        47941
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D or (B or C)))) -> ((B or (B or C)) -> (D or (B or C))))
theorem-size     23
proof            (modus-ponens tm-619 tm-49 ((A (or Am Bm)) (Cm (or B (or Am Bm))) (C (-> (or Am (or Am Bm)) (or B (or Am Bm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-47941.        ((A or ((B or C) -> (D or (B or C)))) -> ((B or (B or C)) -> (D or (B or C)))), M:tm-619, m:tm-49, u:((A (or Am Bm)) (Cm (or B (or Am Bm))) (C (-> (or Am (or Am Bm)) (or B (or Am Bm)))))
================================================================
tm-name          tm-47942
in-theory        47942
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B or C) -> (D or (B or C)))) -> ((C or (B or C)) -> (D or (B or C))))
theorem-size     23
proof            (modus-ponens tm-619 tm-50 ((A (or Am Bm)) (Cm (or B (or Am Bm))) (C (-> (or Bm (or Am Bm)) (or B (or Am Bm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-47942.        ((A or ((B or C) -> (D or (B or C)))) -> ((C or (B or C)) -> (D or (B or C)))), M:tm-619, m:tm-50, u:((A (or Am Bm)) (Cm (or B (or Am Bm))) (C (-> (or Bm (or Am Bm)) (or B (or Am Bm)))))
================================================================
tm-name          tm-47943
in-theory        47943
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> ((D or B) -> C)) -> (E or ((B -> C) -> ((D or B) -> C))))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (E or ((B -> C) -> ((D or B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-619 tm-51 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (or B (-> (-> Am Bm) (-> (or Cm Am) Bm)))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-47943.        ((A or (((B -> C) -> ((D or B) -> C)) -> (E or ((B -> C) -> ((D or B) -> C))))) -> (((D -> B) or ((B -> C) -> ((D or B) -> C))) -> (E or ((B -> C) -> ((D or B) -> C))))), M:tm-619, m:tm-51, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (Dm (or B (-> (-> Am Bm) (-> (or Cm Am) Bm)))) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (or B (-> (-> Am Bm) (-> (or Cm Am) Bm))))))
================================================================
tm-name          tm-47944
in-theory        47944
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B -> (C or B))))
theorem-size     27
proof            (modus-ponens tm-619 tm-54 ((Am (-> A (or B A))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-47944.        ((A or (B -> (C or B))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (B -> (C or B)))), M:tm-619, m:tm-54, u:((Am (-> A (or B A))) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A (or B A)))))
================================================================
tm-name          tm-47945
in-theory        47945
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-619 tm-56 ((Am (-> A (or B A))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-47945.        ((A or (B -> (C or B))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-619, m:tm-56, u:((Am (-> A (or B A))) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-47946
in-theory        47946
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (not C)) -> (not B)) -> (D or ((B -> (not C)) -> (not B))))) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> (D or ((B -> (not C)) -> (not B)))))
theorem-size     41
proof            (modus-ponens tm-619 tm-66 ((A (-> (-> Am (not Bm)) (not Am))) (Cm (or B (-> (-> Am (not Bm)) (not Am)))) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (or B (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-9)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-47946.        ((A or (((B -> (not C)) -> (not B)) -> (D or ((B -> (not C)) -> (not B))))) -> (((B -> C) or ((B -> (not C)) -> (not B))) -> (D or ((B -> (not C)) -> (not B))))), M:tm-619, m:tm-66, u:((A (-> (-> Am (not Bm)) (not Am))) (Cm (or B (-> (-> Am (not Bm)) (not Am)))) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (or B (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-47947
in-theory        47947
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (B -> (C or B))))
theorem-size     25
proof            (modus-ponens tm-619 tm-69 ((Am (-> A (or B A))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-47947.        ((A or (B -> (C or B))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (B -> (C or B)))), M:tm-619, m:tm-69, u:((Am (-> A (or B A))) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A (or B A)))))
================================================================
tm-name          tm-47948
in-theory        47948
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-619 tm-71 ((Am (-> A (or B A))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-47948.        ((A or (B -> (C or B))) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-619, m:tm-71, u:((Am (-> A (or B A))) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-47949
in-theory        47949
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((not (not B)) or B) -> (C or B)))
theorem-size     17
proof            (modus-ponens tm-619 tm-73 ((A Am) (Bm (or B Am)) (C (-> (or (not (not Am)) Am) (or B Am)))))
axioms-used      (tm-8 tm-1 tm-7 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-47949.        ((A or (B -> (C or B))) -> (((not (not B)) or B) -> (C or B))), M:tm-619, m:tm-73, u:((A Am) (Bm (or B Am)) (C (-> (or (not (not Am)) Am) (or B Am))))
================================================================
tm-name          tm-47950
in-theory        47950
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((not (not D)) -> D) and (B -> (C or B))))
theorem-size     19
proof            (modus-ponens tm-619 tm-76 ((Am (-> A (or B A))) (C (and (-> (not (not Bm)) Bm) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-47950.        ((A or (B -> (C or B))) -> (((not (not D)) -> D) and (B -> (C or B)))), M:tm-619, m:tm-76, u:((Am (-> A (or B A))) (C (and (-> (not (not Bm)) Bm) (-> A (or B A)))))
================================================================
tm-name          tm-47951
in-theory        47951
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-619 tm-78 ((Am (-> A (or B A))) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-7 tm-10)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-47951.        ((A or (B -> (C or B))) -> ((not (not D)) -> D)), M:tm-619, m:tm-78, u:((Am (-> A (or B A))) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-47952
in-theory        47952
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) -> (D or (B -> (C -> B))))) -> ((E or (B -> (C -> B))) -> (D or (B -> (C -> B)))))
theorem-size     31
proof            (modus-ponens tm-619 tm-80 ((A (-> Am (-> Bm Am))) (Cm (or B (-> Am (-> Bm Am)))) (C (-> (or Dm (-> Am (-> Bm Am))) (or B (-> Am (-> Bm Am)))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-47952.        ((A or ((B -> (C -> B)) -> (D or (B -> (C -> B))))) -> ((E or (B -> (C -> B))) -> (D or (B -> (C -> B))))), M:tm-619, m:tm-80, u:((A (-> Am (-> Bm Am))) (Cm (or B (-> Am (-> Bm Am)))) (C (-> (or Dm (-> Am (-> Bm Am))) (or B (-> Am (-> Bm Am))))))
================================================================
tm-name          tm-47953
in-theory        47953
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (E -> (F -> E))) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-83 ((Am (-> A (or B A))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-47953.        ((A or (B -> (C or B))) -> ((D -> (E -> (F -> E))) and (B -> (C or B)))), M:tm-619, m:tm-83, u:((Am (-> A (or B A))) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A (or B A)))))
================================================================
tm-name          tm-47954
in-theory        47954
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (B -> (D -> (C or B))))
theorem-size     15
proof            (modus-ponens tm-619 tm-84 ((A Am) (Bm (or B Am)) (C (-> Am (-> Cm (or B Am))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-47954.        ((A or (B -> (C or B))) -> (B -> (D -> (C or B)))), M:tm-619, m:tm-84, u:((A Am) (Bm (or B Am)) (C (-> Am (-> Cm (or B Am)))))
================================================================
tm-name          tm-47955
in-theory        47955
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-619 tm-85 ((Am (-> A (or B A))) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-47955.        ((A or (B -> (C or B))) -> (D -> (E -> (F -> E)))), M:tm-619, m:tm-85, u:((Am (-> A (or B A))) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-47956
in-theory        47956
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (B -> (C or B)))
theorem-size     13
proof            (modus-ponens tm-619 tm-86 ((Am (-> A (or B A))) (C (-> A (or B A)))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-47956.        ((A or (B -> (C or B))) -> (B -> (C or B))), M:tm-619, m:tm-86, u:((Am (-> A (or B A))) (C (-> A (or B A))))
================================================================
tm-name          tm-47957
in-theory        47957
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> B) -> (C or (B -> B)))) -> (((B -> D) or (B -> B)) -> (C or (B -> B))))
theorem-size     25
proof            (modus-ponens tm-619 tm-92 ((A (-> Am Am)) (Bm (or B (-> Am Am))) (C (-> (or (-> Am Cm) (-> Am Am)) (or B (-> Am Am))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-47957.        ((A or ((B -> B) -> (C or (B -> B)))) -> (((B -> D) or (B -> B)) -> (C or (B -> B)))), M:tm-619, m:tm-92, u:((A (-> Am Am)) (Bm (or B (-> Am Am))) (C (-> (or (-> Am Cm) (-> Am Am)) (or B (-> Am Am)))))
================================================================
tm-name          tm-47958
in-theory        47958
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> E) -> (D -> D)) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-95 ((Am (-> A (or B A))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-47958.        ((A or (B -> (C or B))) -> (((D -> E) -> (D -> D)) and (B -> (C or B)))), M:tm-619, m:tm-95, u:((Am (-> A (or B A))) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A (or B A)))))
================================================================
tm-name          tm-47959
in-theory        47959
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-619 tm-97 ((Am (-> A (or B A))) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-47959.        ((A or (B -> (C or B))) -> ((D -> E) -> (D -> D))), M:tm-619, m:tm-97, u:((Am (-> A (or B A))) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-47960
in-theory        47960
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> (B -> D)) -> (E or ((B -> (C -> D)) -> (B -> D))))) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> (E or ((B -> (C -> D)) -> (B -> D)))))
theorem-size     55
proof            (modus-ponens tm-619 tm-102 ((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (Dm (or B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (or B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-47960.        ((A or (((B -> (C -> D)) -> (B -> D)) -> (E or ((B -> (C -> D)) -> (B -> D))))) -> ((((B -> (C -> D)) -> (B -> C)) or ((B -> (C -> D)) -> (B -> D))) -> (E or ((B -> (C -> D)) -> (B -> D))))), M:tm-619, m:tm-102, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (Dm (or B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (or B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-47961
in-theory        47961
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (B -> (C or B))))
theorem-size     33
proof            (modus-ponens tm-619 tm-105 ((Am (-> A (or B A))) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-47961.        ((A or (B -> (C or B))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (B -> (C or B)))), M:tm-619, m:tm-105, u:((Am (-> A (or B A))) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A (or B A)))))
================================================================
tm-name          tm-47962
in-theory        47962
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-619 tm-107 ((Am (-> A (or B A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-47962.        ((A or (B -> (C or B))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-619, m:tm-107, u:((Am (-> A (or B A))) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-47963
in-theory        47963
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     63
proof            (modus-ponens tm-619 tm-110 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (or B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-47963.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> (E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> ((F or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-619, m:tm-110, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (or B (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
================================================================
tm-name          tm-47964
in-theory        47964
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (C or B))))
theorem-size     29
proof            (modus-ponens tm-619 tm-113 ((Am (-> A (or B A))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-47964.        ((A or (B -> (C or B))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (C or B)))), M:tm-619, m:tm-113, u:((Am (-> A (or B A))) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (or B A)))))
================================================================
tm-name          tm-47965
in-theory        47965
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-619 tm-115 ((Am (-> A (or B A))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-47965.        ((A or (B -> (C or B))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-619, m:tm-115, u:((Am (-> A (or B A))) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-47966
in-theory        47966
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) and D) -> C) -> (E or (((B -> C) and D) -> C)))) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> (E or (((B -> C) and D) -> C))))
theorem-size     45
proof            (modus-ponens tm-619 tm-122 ((A (-> (and (-> Am Bm) Cm) Bm)) (Dm (or B (-> (and (-> Am Bm) Cm) Bm))) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (or B (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-47966.        ((A or ((((B -> C) and D) -> C) -> (E or (((B -> C) and D) -> C)))) -> (((((B -> C) and D) -> B) or (((B -> C) and D) -> C)) -> (E or (((B -> C) and D) -> C)))), M:tm-619, m:tm-122, u:((A (-> (and (-> Am Bm) Cm) Bm)) (Dm (or B (-> (and (-> Am Bm) Cm) Bm))) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (or B (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-47967
in-theory        47967
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (B -> (C or B))))
theorem-size     29
proof            (modus-ponens tm-619 tm-125 ((Am (-> A (or B A))) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-47967.        ((A or (B -> (C or B))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (B -> (C or B)))), M:tm-619, m:tm-125, u:((Am (-> A (or B A))) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A (or B A)))))
================================================================
tm-name          tm-47968
in-theory        47968
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-619 tm-127 ((Am (-> A (or B A))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-47968.        ((A or (B -> (C or B))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-619, m:tm-127, u:((Am (-> A (or B A))) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-47969
in-theory        47969
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) -> (D or ((B and C) -> B)))) -> ((E or ((B and C) -> B)) -> (D or ((B and C) -> B))))
theorem-size     31
proof            (modus-ponens tm-619 tm-131 ((A (-> (and Am Bm) Am)) (Cm (or B (-> (and Am Bm) Am))) (C (-> (or Dm (-> (and Am Bm) Am)) (or B (-> (and Am Bm) Am))))))
axioms-used      (tm-8 tm-1 tm-7 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-47969.        ((A or (((B and C) -> B) -> (D or ((B and C) -> B)))) -> ((E or ((B and C) -> B)) -> (D or ((B and C) -> B)))), M:tm-619, m:tm-131, u:((A (-> (and Am Bm) Am)) (Cm (or B (-> (and Am Bm) Am))) (C (-> (or Dm (-> (and Am Bm) Am)) (or B (-> (and Am Bm) Am)))))
================================================================
tm-name          tm-47970
in-theory        47970
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> ((E and F) -> E)) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-134 ((Am (-> A (or B A))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-47970.        ((A or (B -> (C or B))) -> ((D -> ((E and F) -> E)) and (B -> (C or B)))), M:tm-619, m:tm-134, u:((Am (-> A (or B A))) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A (or B A)))))
================================================================
tm-name          tm-47971
in-theory        47971
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-619 tm-136 ((Am (-> A (or B A))) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-47971.        ((A or (B -> (C or B))) -> (D -> ((E and F) -> E))), M:tm-619, m:tm-136, u:((Am (-> A (or B A))) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-47972
in-theory        47972
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and (C -> D)) -> D) -> (E or ((B and (C -> D)) -> D)))) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> (E or ((B and (C -> D)) -> D))))
theorem-size     45
proof            (modus-ponens tm-619 tm-144 ((A (-> (and Am (-> Bm Cm)) Cm)) (Dm (or B (-> (and Am (-> Bm Cm)) Cm))) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (or B (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-4)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-47972.        ((A or (((B and (C -> D)) -> D) -> (E or ((B and (C -> D)) -> D)))) -> ((((B and (C -> D)) -> C) or ((B and (C -> D)) -> D)) -> (E or ((B and (C -> D)) -> D)))), M:tm-619, m:tm-144, u:((A (-> (and Am (-> Bm Cm)) Cm)) (Dm (or B (-> (and Am (-> Bm Cm)) Cm))) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (or B (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-47973
in-theory        47973
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (B -> (C or B))))
theorem-size     29
proof            (modus-ponens tm-619 tm-147 ((Am (-> A (or B A))) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-47973.        ((A or (B -> (C or B))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (B -> (C or B)))), M:tm-619, m:tm-147, u:((Am (-> A (or B A))) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A (or B A)))))
================================================================
tm-name          tm-47974
in-theory        47974
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-619 tm-149 ((Am (-> A (or B A))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-47974.        ((A or (B -> (C or B))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-619, m:tm-149, u:((Am (-> A (or B A))) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-47975
in-theory        47975
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) -> (D or ((B and C) -> C)))) -> ((E or ((B and C) -> C)) -> (D or ((B and C) -> C))))
theorem-size     31
proof            (modus-ponens tm-619 tm-154 ((A (-> (and Am Bm) Bm)) (Cm (or B (-> (and Am Bm) Bm))) (C (-> (or Dm (-> (and Am Bm) Bm)) (or B (-> (and Am Bm) Bm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-47975.        ((A or (((B and C) -> C) -> (D or ((B and C) -> C)))) -> ((E or ((B and C) -> C)) -> (D or ((B and C) -> C)))), M:tm-619, m:tm-154, u:((A (-> (and Am Bm) Bm)) (Cm (or B (-> (and Am Bm) Bm))) (C (-> (or Dm (-> (and Am Bm) Bm)) (or B (-> (and Am Bm) Bm)))))
================================================================
tm-name          tm-47976
in-theory        47976
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> ((E and F) -> F)) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-157 ((Am (-> A (or B A))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-47976.        ((A or (B -> (C or B))) -> ((D -> ((E and F) -> F)) and (B -> (C or B)))), M:tm-619, m:tm-157, u:((Am (-> A (or B A))) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A (or B A)))))
================================================================
tm-name          tm-47977
in-theory        47977
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-619 tm-159 ((Am (-> A (or B A))) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-47977.        ((A or (B -> (C or B))) -> (D -> ((E and F) -> F))), M:tm-619, m:tm-159, u:((Am (-> A (or B A))) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-47978
in-theory        47978
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> B)) and D) -> (E or ((B -> (C -> B)) and D)))) -> ((D or ((B -> (C -> B)) and D)) -> (E or ((B -> (C -> B)) and D))))
theorem-size     39
proof            (modus-ponens tm-619 tm-180 ((A (and (-> Am (-> Bm Am)) Cm)) (Dm (or B (and (-> Am (-> Bm Am)) Cm))) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (or B (and (-> Am (-> Bm Am)) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-47978.        ((A or (((B -> (C -> B)) and D) -> (E or ((B -> (C -> B)) and D)))) -> ((D or ((B -> (C -> B)) and D)) -> (E or ((B -> (C -> B)) and D)))), M:tm-619, m:tm-180, u:((A (and (-> Am (-> Bm Am)) Cm)) (Dm (or B (and (-> Am (-> Bm Am)) Cm))) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) (or B (and (-> Am (-> Bm Am)) Cm)))))
================================================================
tm-name          tm-47979
in-theory        47979
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> ((E -> (F -> E)) and D)) and (B -> (C or B))))
theorem-size     23
proof            (modus-ponens tm-619 tm-183 ((Am (-> A (or B A))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-47979.        ((A or (B -> (C or B))) -> ((D -> ((E -> (F -> E)) and D)) and (B -> (C or B)))), M:tm-619, m:tm-183, u:((Am (-> A (or B A))) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A (or B A)))))
================================================================
tm-name          tm-47980
in-theory        47980
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-619 tm-184 ((Am (-> A (or B A))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-47980.        ((A or (B -> (C or B))) -> (D -> ((E -> (F -> E)) and D))), M:tm-619, m:tm-184, u:((Am (-> A (or B A))) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-47981
in-theory        47981
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> (F or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> (F or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E))))
theorem-size     71
proof            (modus-ponens tm-619 tm-207 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (or B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (or B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-2)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-47981.        ((A or ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E) -> (F or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))) -> ((E or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)) -> (F or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and E)))), M:tm-619, m:tm-207, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (or B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (or B (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-47982
in-theory        47982
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (B -> (C or B))))
theorem-size     31
proof            (modus-ponens tm-619 tm-210 ((Am (-> A (or B A))) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-47982.        ((A or (B -> (C or B))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (B -> (C or B)))), M:tm-619, m:tm-210, u:((Am (-> A (or B A))) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A (or B A)))))
================================================================
tm-name          tm-47983
in-theory        47983
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-619 tm-211 ((Am (-> A (or B A))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-47983.        ((A or (B -> (C or B))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-619, m:tm-211, u:((Am (-> A (or B A))) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-47984
in-theory        47984
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> B) and D) -> (E or (((B and C) -> B) and D)))) -> ((D or (((B and C) -> B) and D)) -> (E or (((B and C) -> B) and D))))
theorem-size     39
proof            (modus-ponens tm-619 tm-236 ((A (and (-> (and Am Bm) Am) Cm)) (Dm (or B (and (-> (and Am Bm) Am) Cm))) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (or B (and (-> (and Am Bm) Am) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-47984.        ((A or ((((B and C) -> B) and D) -> (E or (((B and C) -> B) and D)))) -> ((D or (((B and C) -> B) and D)) -> (E or (((B and C) -> B) and D)))), M:tm-619, m:tm-236, u:((A (and (-> (and Am Bm) Am) Cm)) (Dm (or B (and (-> (and Am Bm) Am) Cm))) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) (or B (and (-> (and Am Bm) Am) Cm)))))
================================================================
tm-name          tm-47985
in-theory        47985
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (((E and F) -> E) and D)) and (B -> (C or B))))
theorem-size     23
proof            (modus-ponens tm-619 tm-239 ((Am (-> A (or B A))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-47985.        ((A or (B -> (C or B))) -> ((D -> (((E and F) -> E) and D)) and (B -> (C or B)))), M:tm-619, m:tm-239, u:((Am (-> A (or B A))) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A (or B A)))))
================================================================
tm-name          tm-47986
in-theory        47986
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-619 tm-240 ((Am (-> A (or B A))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-47986.        ((A or (B -> (C or B))) -> (D -> (((E and F) -> E) and D))), M:tm-619, m:tm-240, u:((Am (-> A (or B A))) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-47987
in-theory        47987
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) -> C) and D) -> (E or (((B and C) -> C) and D)))) -> ((D or (((B and C) -> C) and D)) -> (E or (((B and C) -> C) and D))))
theorem-size     39
proof            (modus-ponens tm-619 tm-267 ((A (and (-> (and Am Bm) Bm) Cm)) (Dm (or B (and (-> (and Am Bm) Bm) Cm))) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (or B (and (-> (and Am Bm) Bm) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-47987.        ((A or ((((B and C) -> C) and D) -> (E or (((B and C) -> C) and D)))) -> ((D or (((B and C) -> C) and D)) -> (E or (((B and C) -> C) and D)))), M:tm-619, m:tm-267, u:((A (and (-> (and Am Bm) Bm) Cm)) (Dm (or B (and (-> (and Am Bm) Bm) Cm))) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) (or B (and (-> (and Am Bm) Bm) Cm)))))
================================================================
tm-name          tm-47988
in-theory        47988
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (((E and F) -> F) and D)) and (B -> (C or B))))
theorem-size     23
proof            (modus-ponens tm-619 tm-270 ((Am (-> A (or B A))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-47988.        ((A or (B -> (C or B))) -> ((D -> (((E and F) -> F) and D)) and (B -> (C or B)))), M:tm-619, m:tm-270, u:((Am (-> A (or B A))) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A (or B A)))))
================================================================
tm-name          tm-47989
in-theory        47989
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-619 tm-271 ((Am (-> A (or B A))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-47989.        ((A or (B -> (C or B))) -> (D -> (((E and F) -> F) and D))), M:tm-619, m:tm-271, u:((Am (-> A (or B A))) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-47990
in-theory        47990
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> (B and C))) and D) -> (E or ((B -> (C -> (B and C))) and D)))) -> ((D or ((B -> (C -> (B and C))) and D)) -> (E or ((B -> (C -> (B and C))) and D))))
theorem-size     47
proof            (modus-ponens tm-619 tm-300 ((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (or B (and (-> Am (-> Bm (and Am Bm))) Cm))) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (or B (and (-> Am (-> Bm (and Am Bm))) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-47990.        ((A or (((B -> (C -> (B and C))) and D) -> (E or ((B -> (C -> (B and C))) and D)))) -> ((D or ((B -> (C -> (B and C))) and D)) -> (E or ((B -> (C -> (B and C))) and D)))), M:tm-619, m:tm-300, u:((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (Dm (or B (and (-> Am (-> Bm (and Am Bm))) Cm))) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) (or B (and (-> Am (-> Bm (and Am Bm))) Cm)))))
================================================================
tm-name          tm-47991
in-theory        47991
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> ((E -> (F -> (E and F))) and D)) and (B -> (C or B))))
theorem-size     25
proof            (modus-ponens tm-619 tm-303 ((Am (-> A (or B A))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-47991.        ((A or (B -> (C or B))) -> ((D -> ((E -> (F -> (E and F))) and D)) and (B -> (C or B)))), M:tm-619, m:tm-303, u:((Am (-> A (or B A))) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A (or B A)))))
================================================================
tm-name          tm-47992
in-theory        47992
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-619 tm-304 ((Am (-> A (or B A))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-47992.        ((A or (B -> (C or B))) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-619, m:tm-304, u:((Am (-> A (or B A))) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-47993
in-theory        47993
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (D -> (B -> (C or B)))))
theorem-size     21
proof            (modus-ponens tm-619 tm-305 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> Bm (-> A (or B A)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-47993.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (D -> (B -> (C or B))))), M:tm-619, m:tm-305, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> Bm (-> A (or B A))))))
================================================================
tm-name          tm-47994
in-theory        47994
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (D -> ((B -> (C or B)) and D))))
theorem-size     23
proof            (modus-ponens tm-619 tm-309 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> Bm (and (-> A (or B A)) Bm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-47994.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (D -> ((B -> (C or B)) and D)))), M:tm-619, m:tm-309, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> Bm (and (-> A (or B A)) Bm)))))
================================================================
tm-name          tm-47995
in-theory        47995
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((B -> (C or B)) or D)))
theorem-size     21
proof            (modus-ponens tm-619 tm-310 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (or (-> A (or B A)) Bm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-47995.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((B -> (C or B)) or D))), M:tm-619, m:tm-310, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (or (-> A (or B A)) Bm))))
================================================================
tm-name          tm-47996
in-theory        47996
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (D or (B -> (C or B)))))
theorem-size     21
proof            (modus-ponens tm-619 tm-311 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (or Bm (-> A (or B A)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-47996.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (D or (B -> (C or B))))), M:tm-619, m:tm-311, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (or Bm (-> A (or B A))))))
================================================================
tm-name          tm-47997
in-theory        47997
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (((C or B) -> D) -> ((B or (C or B)) -> D))))
theorem-size     27
proof            (modus-ponens tm-619 tm-312 ((A Am) (Bm (or B Am)) (C (and (-> Am (or B Am)) (-> (-> (or B Am) Cm) (-> (or Am (or B Am)) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-47997.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (((C or B) -> D) -> ((B or (C or B)) -> D)))), M:tm-619, m:tm-312, u:((A Am) (Bm (or B Am)) (C (and (-> Am (or B Am)) (-> (-> (or B Am) Cm) (-> (or Am (or B Am)) Cm)))))
================================================================
tm-name          tm-47998
in-theory        47998
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((B -> (not (C or B))) -> (not B))))
theorem-size     23
proof            (modus-ponens tm-619 tm-313 ((A Am) (Bm (or B Am)) (C (and (-> Am (or B Am)) (-> (-> Am (not (or B Am))) (not Am))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-47998.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((B -> (not (C or B))) -> (not B)))), M:tm-619, m:tm-313, u:((A Am) (Bm (or B Am)) (C (and (-> Am (or B Am)) (-> (-> Am (not (or B Am))) (not Am)))))
================================================================
tm-name          tm-47999
in-theory        47999
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (D -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-619 tm-315 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-47999.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (D -> (E -> D)))), M:tm-619, m:tm-315, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-48000
in-theory        48000
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (B -> B)))
theorem-size     17
proof            (modus-ponens tm-619 tm-316 ((A Am) (Bm (or B Am)) (C (and (-> Am (or B Am)) (-> Am Am)))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-48000.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (B -> B))), M:tm-619, m:tm-316, u:((A Am) (Bm (or B Am)) (C (and (-> Am (or B Am)) (-> Am Am))))
================================================================
tm-name          tm-48001
in-theory        48001
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-619 tm-318 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-48001.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-619, m:tm-318, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-48002
in-theory        48002
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((D and E) -> D)))
theorem-size     19
proof            (modus-ponens tm-619 tm-320 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-48002.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((D and E) -> D))), M:tm-619, m:tm-320, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-48003
in-theory        48003
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((D and E) -> E)))
theorem-size     19
proof            (modus-ponens tm-619 tm-322 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-48003.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((D and E) -> E))), M:tm-619, m:tm-322, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-48004
in-theory        48004
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((D -> (E -> D)) and (B -> (C or B)))))
theorem-size     25
proof            (modus-ponens tm-619 tm-323 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (and (-> Bm (-> Cm Bm)) (-> A (or B A)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-48004.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((D -> (E -> D)) and (B -> (C or B))))), M:tm-619, m:tm-323, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (and (-> Bm (-> Cm Bm)) (-> A (or B A))))))
================================================================
tm-name          tm-48005
in-theory        48005
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (C or B)))))
theorem-size     33
proof            (modus-ponens tm-619 tm-324 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (or B A)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-48005.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> (C or B))))), M:tm-619, m:tm-324, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A (or B A))))))
================================================================
tm-name          tm-48006
in-theory        48006
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (((D and E) -> D) and (B -> (C or B)))))
theorem-size     25
proof            (modus-ponens tm-619 tm-325 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (and (-> (and Bm Cm) Bm) (-> A (or B A)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-48006.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (((D and E) -> D) and (B -> (C or B))))), M:tm-619, m:tm-325, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (and (-> (and Bm Cm) Bm) (-> A (or B A))))))
================================================================
tm-name          tm-48007
in-theory        48007
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (((D and E) -> E) and (B -> (C or B)))))
theorem-size     25
proof            (modus-ponens tm-619 tm-326 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (and (-> (and Bm Cm) Cm) (-> A (or B A)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-48007.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (((D and E) -> E) and (B -> (C or B))))), M:tm-619, m:tm-326, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (and (-> (and Bm Cm) Cm) (-> A (or B A))))))
================================================================
tm-name          tm-48008
in-theory        48008
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((D -> (E -> (D and E))) and (B -> (C or B)))))
theorem-size     27
proof            (modus-ponens tm-619 tm-327 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (and (-> Bm (-> Cm (and Bm Cm))) (-> A (or B A)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-48008.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((D -> (E -> (D and E))) and (B -> (C or B))))), M:tm-619, m:tm-327, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (and (-> Bm (-> Cm (and Bm Cm))) (-> A (or B A))))))
================================================================
tm-name          tm-48009
in-theory        48009
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (B -> (B and (C or B)))))
theorem-size     21
proof            (modus-ponens tm-619 tm-328 ((A Am) (Bm (or B Am)) (C (and (-> Am (or B Am)) (-> Am (and Am (or B Am)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-48009.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (B -> (B and (C or B))))), M:tm-619, m:tm-328, u:((A Am) (Bm (or B Am)) (C (and (-> Am (or B Am)) (-> Am (and Am (or B Am))))))
================================================================
tm-name          tm-48010
in-theory        48010
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B and C)) -> (D or (B -> (B and C))))) -> (((B -> C) or (B -> (B and C))) -> (D or (B -> (B and C)))))
theorem-size     33
proof            (modus-ponens tm-619 tm-335 ((A (-> Am (and Am Bm))) (Cm (or B (-> Am (and Am Bm)))) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) (or B (-> Am (and Am Bm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-48010.        ((A or ((B -> (B and C)) -> (D or (B -> (B and C))))) -> (((B -> C) or (B -> (B and C))) -> (D or (B -> (B and C))))), M:tm-619, m:tm-335, u:((A (-> Am (and Am Bm))) (Cm (or B (-> Am (and Am Bm)))) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) (or B (-> Am (and Am Bm))))))
================================================================
tm-name          tm-48011
in-theory        48011
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> E) -> (D -> (D and E))) and (B -> (C or B))))
theorem-size     23
proof            (modus-ponens tm-619 tm-338 ((Am (-> A (or B A))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-48011.        ((A or (B -> (C or B))) -> (((D -> E) -> (D -> (D and E))) and (B -> (C or B)))), M:tm-619, m:tm-338, u:((Am (-> A (or B A))) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A (or B A)))))
================================================================
tm-name          tm-48012
in-theory        48012
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-619 tm-340 ((Am (-> A (or B A))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-48012.        ((A or (B -> (C or B))) -> ((D -> E) -> (D -> (D and E)))), M:tm-619, m:tm-340, u:((Am (-> A (or B A))) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-48013
in-theory        48013
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (D -> (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-619 tm-341 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-48013.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (D -> (E -> (D and E))))), M:tm-619, m:tm-341, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-48014
in-theory        48014
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) -> (D or (B -> (C -> (B and C)))))) -> ((E or (B -> (C -> (B and C)))) -> (D or (B -> (C -> (B and C))))))
theorem-size     39
proof            (modus-ponens tm-619 tm-351 ((A (-> Am (-> Bm (and Am Bm)))) (Cm (or B (-> Am (-> Bm (and Am Bm))))) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (or B (-> Am (-> Bm (and Am Bm))))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-48014.        ((A or ((B -> (C -> (B and C))) -> (D or (B -> (C -> (B and C)))))) -> ((E or (B -> (C -> (B and C)))) -> (D or (B -> (C -> (B and C)))))), M:tm-619, m:tm-351, u:((A (-> Am (-> Bm (and Am Bm)))) (Cm (or B (-> Am (-> Bm (and Am Bm))))) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (or B (-> Am (-> Bm (and Am Bm)))))))
================================================================
tm-name          tm-48015
in-theory        48015
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (E -> (F -> (E and F)))) and (B -> (C or B))))
theorem-size     23
proof            (modus-ponens tm-619 tm-354 ((Am (-> A (or B A))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48015.        ((A or (B -> (C or B))) -> ((D -> (E -> (F -> (E and F)))) and (B -> (C or B)))), M:tm-619, m:tm-354, u:((Am (-> A (or B A))) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (or B A)))))
================================================================
tm-name          tm-48016
in-theory        48016
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (B -> (D -> ((C or B) and D))))
theorem-size     17
proof            (modus-ponens tm-619 tm-355 ((A Am) (Bm (or B Am)) (C (-> Am (-> Cm (and (or B Am) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-48016.        ((A or (B -> (C or B))) -> (B -> (D -> ((C or B) and D)))), M:tm-619, m:tm-355, u:((A Am) (Bm (or B Am)) (C (-> Am (-> Cm (and (or B Am) Cm)))))
================================================================
tm-name          tm-48017
in-theory        48017
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-619 tm-356 ((Am (-> A (or B A))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48017.        ((A or (B -> (C or B))) -> (D -> (E -> (F -> (E and F))))), M:tm-619, m:tm-356, u:((Am (-> A (or B A))) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-48018
in-theory        48018
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> (E -> D)) or F) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-364 ((Am (-> A (or B A))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-48018.        ((A or (B -> (C or B))) -> (((D -> (E -> D)) or F) and (B -> (C or B)))), M:tm-619, m:tm-364, u:((Am (-> A (or B A))) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A (or B A)))))
================================================================
tm-name          tm-48019
in-theory        48019
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-619 tm-365 ((Am (-> A (or B A))) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-48019.        ((A or (B -> (C or B))) -> ((D -> (E -> D)) or F)), M:tm-619, m:tm-365, u:((Am (-> A (or B A))) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-48020
in-theory        48020
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (B -> (C or B))))
theorem-size     29
proof            (modus-ponens tm-619 tm-373 ((Am (-> A (or B A))) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-48020.        ((A or (B -> (C or B))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (B -> (C or B)))), M:tm-619, m:tm-373, u:((Am (-> A (or B A))) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A (or B A)))))
================================================================
tm-name          tm-48021
in-theory        48021
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-619 tm-374 ((Am (-> A (or B A))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-7 tm-6 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-48021.        ((A or (B -> (C or B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-619, m:tm-374, u:((Am (-> A (or B A))) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-48022
in-theory        48022
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((((D and E) -> D) or F) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-382 ((Am (-> A (or B A))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-6 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-48022.        ((A or (B -> (C or B))) -> ((((D and E) -> D) or F) and (B -> (C or B)))), M:tm-619, m:tm-382, u:((Am (-> A (or B A))) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A (or B A)))))
================================================================
tm-name          tm-48023
in-theory        48023
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-619 tm-383 ((Am (-> A (or B A))) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-1 tm-7 tm-6 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-48023.        ((A or (B -> (C or B))) -> (((D and E) -> D) or F)), M:tm-619, m:tm-383, u:((Am (-> A (or B A))) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-48024
in-theory        48024
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((((D and E) -> E) or F) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-391 ((Am (-> A (or B A))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-48024.        ((A or (B -> (C or B))) -> ((((D and E) -> E) or F) and (B -> (C or B)))), M:tm-619, m:tm-391, u:((Am (-> A (or B A))) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A (or B A)))))
================================================================
tm-name          tm-48025
in-theory        48025
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-619 tm-392 ((Am (-> A (or B A))) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-1 tm-7 tm-6 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-48025.        ((A or (B -> (C or B))) -> (((D and E) -> E) or F)), M:tm-619, m:tm-392, u:((Am (-> A (or B A))) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-48026
in-theory        48026
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> (E -> (D and E))) or F) and (B -> (C or B))))
theorem-size     23
proof            (modus-ponens tm-619 tm-400 ((Am (-> A (or B A))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-48026.        ((A or (B -> (C or B))) -> (((D -> (E -> (D and E))) or F) and (B -> (C or B)))), M:tm-619, m:tm-400, u:((Am (-> A (or B A))) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A (or B A)))))
================================================================
tm-name          tm-48027
in-theory        48027
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-619 tm-401 ((Am (-> A (or B A))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-1 tm-7 tm-6 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-48027.        ((A or (B -> (C or B))) -> ((D -> (E -> (D and E))) or F)), M:tm-619, m:tm-401, u:((Am (-> A (or B A))) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-48028
in-theory        48028
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> (D or E)) or F) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-409 ((Am (-> A (or B A))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-48028.        ((A or (B -> (C or B))) -> (((D -> (D or E)) or F) and (B -> (C or B)))), M:tm-619, m:tm-409, u:((Am (-> A (or B A))) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A (or B A)))))
================================================================
tm-name          tm-48029
in-theory        48029
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-619 tm-410 ((Am (-> A (or B A))) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-48029.        ((A or (B -> (C or B))) -> ((D -> (D or E)) or F)), M:tm-619, m:tm-410, u:((Am (-> A (or B A))) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-48030
in-theory        48030
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((D -> (D or E)) and (B -> (C or B)))))
theorem-size     25
proof            (modus-ponens tm-619 tm-443 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (and (-> Bm (or Bm Cm)) (-> A (or B A)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-48030.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((D -> (D or E)) and (B -> (C or B))))), M:tm-619, m:tm-443, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (and (-> Bm (or Bm Cm)) (-> A (or B A))))))
================================================================
tm-name          tm-48031
in-theory        48031
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (B or C)) and D) -> (E or ((B -> (B or C)) and D)))) -> ((D or ((B -> (B or C)) and D)) -> (E or ((B -> (B or C)) and D))))
theorem-size     39
proof            (modus-ponens tm-619 tm-450 ((A (and (-> Am (or Am Bm)) Cm)) (Dm (or B (and (-> Am (or Am Bm)) Cm))) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (or B (and (-> Am (or Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-48031.        ((A or (((B -> (B or C)) and D) -> (E or ((B -> (B or C)) and D)))) -> ((D or ((B -> (B or C)) and D)) -> (E or ((B -> (B or C)) and D)))), M:tm-619, m:tm-450, u:((A (and (-> Am (or Am Bm)) Cm)) (Dm (or B (and (-> Am (or Am Bm)) Cm))) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) (or B (and (-> Am (or Am Bm)) Cm)))))
================================================================
tm-name          tm-48032
in-theory        48032
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> ((E -> (E or F)) and D)) and (B -> (C or B))))
theorem-size     23
proof            (modus-ponens tm-619 tm-453 ((Am (-> A (or B A))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-48032.        ((A or (B -> (C or B))) -> ((D -> ((E -> (E or F)) and D)) and (B -> (C or B)))), M:tm-619, m:tm-453, u:((Am (-> A (or B A))) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A (or B A)))))
================================================================
tm-name          tm-48033
in-theory        48033
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-619 tm-454 ((Am (-> A (or B A))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-48033.        ((A or (B -> (C or B))) -> (D -> ((E -> (E or F)) and D))), M:tm-619, m:tm-454, u:((Am (-> A (or B A))) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-48034
in-theory        48034
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (D -> (D or E))))
theorem-size     19
proof            (modus-ponens tm-619 tm-456 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-48034.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (D -> (D or E)))), M:tm-619, m:tm-456, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-48035
in-theory        48035
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) -> (D or (B -> (B or C))))) -> ((E or (B -> (B or C))) -> (D or (B -> (B or C)))))
theorem-size     31
proof            (modus-ponens tm-619 tm-466 ((A (-> Am (or Am Bm))) (Cm (or B (-> Am (or Am Bm)))) (C (-> (or Dm (-> Am (or Am Bm))) (or B (-> Am (or Am Bm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-48035.        ((A or ((B -> (B or C)) -> (D or (B -> (B or C))))) -> ((E or (B -> (B or C))) -> (D or (B -> (B or C))))), M:tm-619, m:tm-466, u:((A (-> Am (or Am Bm))) (Cm (or B (-> Am (or Am Bm)))) (C (-> (or Dm (-> Am (or Am Bm))) (or B (-> Am (or Am Bm))))))
================================================================
tm-name          tm-48036
in-theory        48036
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (E -> (E or F))) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-469 ((Am (-> A (or B A))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-48036.        ((A or (B -> (C or B))) -> ((D -> (E -> (E or F))) and (B -> (C or B)))), M:tm-619, m:tm-469, u:((Am (-> A (or B A))) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A (or B A)))))
================================================================
tm-name          tm-48037
in-theory        48037
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (B -> ((C or B) or D)))
theorem-size     15
proof            (modus-ponens tm-619 tm-470 ((A Am) (Bm (or B Am)) (C (-> Am (or (or B Am) Cm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-48037.        ((A or (B -> (C or B))) -> (B -> ((C or B) or D))), M:tm-619, m:tm-470, u:((A Am) (Bm (or B Am)) (C (-> Am (or (or B Am) Cm))))
================================================================
tm-name          tm-48038
in-theory        48038
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-619 tm-471 ((Am (-> A (or B A))) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-48038.        ((A or (B -> (C or B))) -> (D -> (E -> (E or F)))), M:tm-619, m:tm-471, u:((Am (-> A (or B A))) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-48039
in-theory        48039
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D or (E -> (F -> E))) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-480 ((Am (-> A (or B A))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-48039.        ((A or (B -> (C or B))) -> ((D or (E -> (F -> E))) and (B -> (C or B)))), M:tm-619, m:tm-480, u:((Am (-> A (or B A))) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A (or B A)))))
================================================================
tm-name          tm-48040
in-theory        48040
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-619 tm-481 ((Am (-> A (or B A))) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-48040.        ((A or (B -> (C or B))) -> (D or (E -> (F -> E)))), M:tm-619, m:tm-481, u:((Am (-> A (or B A))) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-48041
in-theory        48041
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (C or B))))
theorem-size     29
proof            (modus-ponens tm-619 tm-490 ((Am (-> A (or B A))) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48041.        ((A or (B -> (C or B))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (B -> (C or B)))), M:tm-619, m:tm-490, u:((Am (-> A (or B A))) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A (or B A)))))
================================================================
tm-name          tm-48042
in-theory        48042
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-619 tm-491 ((Am (-> A (or B A))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48042.        ((A or (B -> (C or B))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-619, m:tm-491, u:((Am (-> A (or B A))) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-48043
in-theory        48043
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D or ((E and F) -> E)) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-500 ((Am (-> A (or B A))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-48043.        ((A or (B -> (C or B))) -> ((D or ((E and F) -> E)) and (B -> (C or B)))), M:tm-619, m:tm-500, u:((Am (-> A (or B A))) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A (or B A)))))
================================================================
tm-name          tm-48044
in-theory        48044
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-619 tm-501 ((Am (-> A (or B A))) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-48044.        ((A or (B -> (C or B))) -> (D or ((E and F) -> E))), M:tm-619, m:tm-501, u:((Am (-> A (or B A))) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-48045
in-theory        48045
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D or ((E and F) -> F)) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-510 ((Am (-> A (or B A))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-48045.        ((A or (B -> (C or B))) -> ((D or ((E and F) -> F)) and (B -> (C or B)))), M:tm-619, m:tm-510, u:((Am (-> A (or B A))) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A (or B A)))))
================================================================
tm-name          tm-48046
in-theory        48046
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-619 tm-511 ((Am (-> A (or B A))) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-48046.        ((A or (B -> (C or B))) -> (D or ((E and F) -> F))), M:tm-619, m:tm-511, u:((Am (-> A (or B A))) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-48047
in-theory        48047
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D or (E -> (F -> (E and F)))) and (B -> (C or B))))
theorem-size     23
proof            (modus-ponens tm-619 tm-520 ((Am (-> A (or B A))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48047.        ((A or (B -> (C or B))) -> ((D or (E -> (F -> (E and F)))) and (B -> (C or B)))), M:tm-619, m:tm-520, u:((Am (-> A (or B A))) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A (or B A)))))
================================================================
tm-name          tm-48048
in-theory        48048
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-619 tm-521 ((Am (-> A (or B A))) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48048.        ((A or (B -> (C or B))) -> (D or (E -> (F -> (E and F))))), M:tm-619, m:tm-521, u:((Am (-> A (or B A))) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-48049
in-theory        48049
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D or (E -> (E or F))) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-530 ((Am (-> A (or B A))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-48049.        ((A or (B -> (C or B))) -> ((D or (E -> (E or F))) and (B -> (C or B)))), M:tm-619, m:tm-530, u:((Am (-> A (or B A))) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A (or B A)))))
================================================================
tm-name          tm-48050
in-theory        48050
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-619 tm-531 ((Am (-> A (or B A))) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-48050.        ((A or (B -> (C or B))) -> (D or (E -> (E or F)))), M:tm-619, m:tm-531, u:((Am (-> A (or B A))) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-48051
in-theory        48051
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D or (E -> (F or E))) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-540 ((Am (-> A (or B A))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-48051.        ((A or (B -> (C or B))) -> ((D or (E -> (F or E))) and (B -> (C or B)))), M:tm-619, m:tm-540, u:((Am (-> A (or B A))) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A (or B A)))))
================================================================
tm-name          tm-48052
in-theory        48052
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-619 tm-541 ((Am (-> A (or B A))) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-48052.        ((A or (B -> (C or B))) -> (D or (E -> (F or E)))), M:tm-619, m:tm-541, u:((Am (-> A (or B A))) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-48053
in-theory        48053
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> (E or D)) or F) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-550 ((Am (-> A (or B A))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-48053.        ((A or (B -> (C or B))) -> (((D -> (E or D)) or F) and (B -> (C or B)))), M:tm-619, m:tm-550, u:((Am (-> A (or B A))) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A (or B A)))))
================================================================
tm-name          tm-48054
in-theory        48054
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-619 tm-551 ((Am (-> A (or B A))) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-48054.        ((A or (B -> (C or B))) -> ((D -> (E or D)) or F)), M:tm-619, m:tm-551, u:((Am (-> A (or B A))) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-48055
in-theory        48055
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((D -> (E or D)) and (B -> (C or B)))))
theorem-size     25
proof            (modus-ponens tm-619 tm-595 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (and (-> Bm (or Cm Bm)) (-> A (or B A)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-48055.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and ((D -> (E or D)) and (B -> (C or B))))), M:tm-619, m:tm-595, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (and (-> Bm (or Cm Bm)) (-> A (or B A))))))
================================================================
tm-name          tm-48056
in-theory        48056
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C or B)) and D) -> (E or ((B -> (C or B)) and D)))) -> ((D or ((B -> (C or B)) and D)) -> (E or ((B -> (C or B)) and D))))
theorem-size     39
proof            (modus-ponens tm-619 tm-602 ((A (and (-> Am (or Bm Am)) Cm)) (Dm (or B (and (-> Am (or Bm Am)) Cm))) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (or B (and (-> Am (or Bm Am)) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-48056.        ((A or (((B -> (C or B)) and D) -> (E or ((B -> (C or B)) and D)))) -> ((D or ((B -> (C or B)) and D)) -> (E or ((B -> (C or B)) and D)))), M:tm-619, m:tm-602, u:((A (and (-> Am (or Bm Am)) Cm)) (Dm (or B (and (-> Am (or Bm Am)) Cm))) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) (or B (and (-> Am (or Bm Am)) Cm)))))
================================================================
tm-name          tm-48057
in-theory        48057
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> ((E -> (F or E)) and D)) and (B -> (C or B))))
theorem-size     23
proof            (modus-ponens tm-619 tm-605 ((Am (-> A (or B A))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-48057.        ((A or (B -> (C or B))) -> ((D -> ((E -> (F or E)) and D)) and (B -> (C or B)))), M:tm-619, m:tm-605, u:((Am (-> A (or B A))) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A (or B A)))))
================================================================
tm-name          tm-48058
in-theory        48058
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-619 tm-606 ((Am (-> A (or B A))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-48058.        ((A or (B -> (C or B))) -> (D -> ((E -> (F or E)) and D))), M:tm-619, m:tm-606, u:((Am (-> A (or B A))) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-48059
in-theory        48059
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (D -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-619 tm-609 ((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48059.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (D -> (E or D)))), M:tm-619, m:tm-609, u:((Am (-> A (or B A))) (C (and (-> A (or B A)) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-48060
in-theory        48060
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) -> (D or (B -> (C or B))))) -> ((E or (B -> (C or B))) -> (D or (B -> (C or B)))))
theorem-size     31
proof            (modus-ponens tm-619 tm-619 ((A (-> Am (or Bm Am))) (Cm (or B (-> Am (or Bm Am)))) (C (-> (or Dm (-> Am (or Bm Am))) (or B (-> Am (or Bm Am)))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48060.        ((A or ((B -> (C or B)) -> (D or (B -> (C or B))))) -> ((E or (B -> (C or B))) -> (D or (B -> (C or B))))), M:tm-619, m:tm-619, u:((A (-> Am (or Bm Am))) (Cm (or B (-> Am (or Bm Am)))) (C (-> (or Dm (-> Am (or Bm Am))) (or B (-> Am (or Bm Am))))))
================================================================
tm-name          tm-48061
in-theory        48061
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48061.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (E -> (F or E))), M:tm-609, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48062
in-theory        48062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-605 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48062.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-605, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48063
in-theory        48063
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((E -> (F or E)) and (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-595 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48063.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((E -> (F or E)) and (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)))), M:tm-595, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48064
in-theory        48064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-550 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48064.        (((A -> (B or A)) or C) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-550, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48065
in-theory        48065
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-540 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48065.        ((A or (B -> (C or B))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-540, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48066
in-theory        48066
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-530 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48066.        ((A or (B -> (B or C))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-530, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48067
in-theory        48067
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-520 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48067.        ((A or (B -> (C -> (B and C)))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-520, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48068
in-theory        48068
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-510 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48068.        ((A or ((B and C) -> C)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-510, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48069
in-theory        48069
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-500 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48069.        ((A or ((B and C) -> B)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-500, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48070
in-theory        48070
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-490 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48070.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G))), M:tm-490, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48071
in-theory        48071
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-480 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48071.        ((A or (B -> (C -> B))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-480, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48072
in-theory        48072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> (((D or (A -> (B or A))) -> C) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48072.        (((A -> (B or A)) -> C) -> (((D or (A -> (B or A))) -> C) or E)), M:tm-470, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48073
in-theory        48073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-469 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48073.        ((A -> (B -> (B or C))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-469, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48074
in-theory        48074
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) -> ((B -> (C or B)) or D))) -> ((E or (B -> (C or B))) -> ((B -> (C or B)) or D)))
theorem-size     31
proof            (modus-ponens tm-466 tm-619 ((A (-> Am (or Bm Am))) (Cm (or (-> Am (or Bm Am)) B)) (C (-> (or Dm (-> Am (or Bm Am))) (or (-> Am (or Bm Am)) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48074.        ((A or ((B -> (C or B)) -> ((B -> (C or B)) or D))) -> ((E or (B -> (C or B))) -> ((B -> (C or B)) or D))), M:tm-466, m:tm-619, u:((A (-> Am (or Bm Am))) (Cm (or (-> Am (or Bm Am)) B)) (C (-> (or Dm (-> Am (or Bm Am))) (or (-> Am (or Bm Am)) B))))
================================================================
tm-name          tm-48075
in-theory        48075
times-derived    4
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> C)
theorem-size     9
proof            (modus-ponens tm-464 tm-619 ((Dm (-> (-> Am (or Bm Am)) Cm)) (A (-> (-> Am (or Bm Am)) Cm)) (B (-> Am (or Bm Am))) (C Cm)))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48075.        (((A -> (B or A)) -> C) -> C), M:tm-464, m:tm-619, u:((Dm (-> (-> Am (or Bm Am)) Cm)) (A (-> (-> Am (or Bm Am)) Cm)) (B (-> Am (or Bm Am))) (C Cm))
================================================================
tm-name          tm-48076
in-theory        48076
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48076.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (E -> (E or F))), M:tm-456, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48077
in-theory        48077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-453 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48077.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-453, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48078
in-theory        48078
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((E -> (E or F)) and (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-443 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48078.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((E -> (E or F)) and (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)))), M:tm-443, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48079
in-theory        48079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-409 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48079.        (((A -> (A or B)) or C) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-409, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48080
in-theory        48080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-400 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48080.        (((A -> (B -> (A and B))) or C) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-400, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48081
in-theory        48081
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-391 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48081.        ((((A and B) -> B) or C) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-391, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48082
in-theory        48082
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-382 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48082.        ((((A and B) -> A) or C) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-382, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48083
in-theory        48083
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-373 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48083.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G))), M:tm-373, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48084
in-theory        48084
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-364 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48084.        (((A -> (B -> A)) or C) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-364, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48085
in-theory        48085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> (D -> (((E or (A -> (B or A))) -> C) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48085.        (((A -> (B or A)) -> C) -> (D -> (((E or (A -> (B or A))) -> C) and D))), M:tm-355, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48086
in-theory        48086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-354 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48086.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-354, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48087
in-theory        48087
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) -> (D -> ((B -> (C or B)) and D)))) -> ((E or (B -> (C or B))) -> (D -> ((B -> (C or B)) and D))))
theorem-size     35
proof            (modus-ponens tm-351 tm-619 ((A (-> Am (or Bm Am))) (Cm (-> B (and (-> Am (or Bm Am)) B))) (C (-> (or Dm (-> Am (or Bm Am))) (-> B (and (-> Am (or Bm Am)) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48087.        ((A or ((B -> (C or B)) -> (D -> ((B -> (C or B)) and D)))) -> ((E or (B -> (C or B))) -> (D -> ((B -> (C or B)) and D)))), M:tm-351, m:tm-619, u:((A (-> Am (or Bm Am))) (Cm (-> B (and (-> Am (or Bm Am)) B))) (C (-> (or Dm (-> Am (or Bm Am))) (-> B (and (-> Am (or Bm Am)) B)))))
================================================================
tm-name          tm-48088
in-theory        48088
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48088.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48089
in-theory        48089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E)))
theorem-size     27
proof            (modus-ponens tm-338 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48089.        (((A -> B) -> (A -> (A and B))) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E))), M:tm-338, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48090
in-theory        48090
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) or ((A -> (B or A)) -> ((A -> (B or A)) and C))) -> ((D or (A -> (B or A))) -> ((A -> (B or A)) and C)))
theorem-size     37
proof            (modus-ponens tm-335 tm-619 ((A (-> Am (or Bm Am))) (Cm (and (-> Am (or Bm Am)) B)) (C (-> (or Dm (-> Am (or Bm Am))) (and (-> Am (or Bm Am)) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48090.        ((((A -> (B or A)) -> C) or ((A -> (B or A)) -> ((A -> (B or A)) and C))) -> ((D or (A -> (B or A))) -> ((A -> (B or A)) and C))), M:tm-335, m:tm-619, u:((A (-> Am (or Bm Am))) (Cm (and (-> Am (or Bm Am)) B)) (C (-> (or Dm (-> Am (or Bm Am))) (and (-> Am (or Bm Am)) B))))
================================================================
tm-name          tm-48091
in-theory        48091
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (((A -> (B or A)) -> C) -> (((A -> (B or A)) -> C) and ((D or (A -> (B or A))) -> C))))
theorem-size     43
proof            (modus-ponens tm-328 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48091.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (((A -> (B or A)) -> C) -> (((A -> (B or A)) -> C) and ((D or (A -> (B or A))) -> C)))), M:tm-328, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48092
in-theory        48092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((E -> (F -> (E and F))) and (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C))))
theorem-size     43
proof            (modus-ponens tm-327 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48092.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((E -> (F -> (E and F))) and (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)))), M:tm-327, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48093
in-theory        48093
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (((E and F) -> F) and (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-326 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48093.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (((E and F) -> F) and (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)))), M:tm-326, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48094
in-theory        48094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (((E and F) -> E) and (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-325 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48094.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (((E and F) -> E) and (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)))), M:tm-325, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48095
in-theory        48095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C))))
theorem-size     49
proof            (modus-ponens tm-324 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48095.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)))), M:tm-324, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48096
in-theory        48096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((E -> (F -> E)) and (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C))))
theorem-size     41
proof            (modus-ponens tm-323 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48096.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((E -> (F -> E)) and (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)))), M:tm-323, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48097
in-theory        48097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48097.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48098
in-theory        48098
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48098.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48099
in-theory        48099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48099.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48100
in-theory        48100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (((A -> (B or A)) -> C) -> ((A -> (B or A)) -> C)))
theorem-size     33
proof            (modus-ponens tm-316 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48100.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (((A -> (B or A)) -> C) -> ((A -> (B or A)) -> C))), M:tm-316, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48101
in-theory        48101
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48101.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48102
in-theory        48102
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((((A -> (B or A)) -> C) -> (not ((D or (A -> (B or A))) -> C))) -> (not ((A -> (B or A)) -> C))))
theorem-size     45
proof            (modus-ponens tm-313 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48102.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((((A -> (B or A)) -> C) -> (not ((D or (A -> (B or A))) -> C))) -> (not ((A -> (B or A)) -> C)))), M:tm-313, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48103
in-theory        48103
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((((D or (A -> (B or A))) -> C) -> E) -> ((((A -> (B or A)) -> C) or ((D or (A -> (B or A))) -> C)) -> E)))
theorem-size     49
proof            (modus-ponens tm-312 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48103.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((((D or (A -> (B or A))) -> C) -> E) -> ((((A -> (B or A)) -> C) or ((D or (A -> (B or A))) -> C)) -> E))), M:tm-312, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48104
in-theory        48104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (E or (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C))))
theorem-size     37
proof            (modus-ponens tm-311 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48104.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (E or (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)))), M:tm-311, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48105
in-theory        48105
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48105.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) or E)), M:tm-310, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48106
in-theory        48106
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (E -> ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48106.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (E -> ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and E))), M:tm-309, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48107
in-theory        48107
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((((A -> (B or A)) -> C) -> (D or (A -> (B or A)))) -> (((A -> (B or A)) -> C) -> C)))
theorem-size     43
proof            (modus-ponens tm-306 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (or Dm (-> Am (or Bm Am)))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48107.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((((A -> (B or A)) -> C) -> (D or (A -> (B or A)))) -> (((A -> (B or A)) -> C) -> C))), M:tm-306, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (or Dm (-> Am (or Bm Am)))) (C Cm))
================================================================
tm-name          tm-48108
in-theory        48108
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (E -> (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C))))
theorem-size     37
proof            (modus-ponens tm-305 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48108.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (E -> (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)))), M:tm-305, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48109
in-theory        48109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     29
proof            (modus-ponens tm-303 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48109.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-303, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48110
in-theory        48110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-270 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48110.        ((A -> (((B and C) -> C) and A)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-270, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48111
in-theory        48111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-239 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48111.        ((A -> (((B and C) -> B) and A)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-239, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48112
in-theory        48112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-210 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48112.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G))), M:tm-210, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48113
in-theory        48113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     27
proof            (modus-ponens tm-183 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48113.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-183, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48114
in-theory        48114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-157 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48114.        ((A -> ((B and C) -> C)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-157, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48115
in-theory        48115
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-147 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48115.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-147, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48116
in-theory        48116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-134 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48116.        ((A -> ((B and C) -> B)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-134, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48117
in-theory        48117
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     33
proof            (modus-ponens tm-125 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48117.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-125, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48118
in-theory        48118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> (C -> D)) -> (((E or (A -> (B or A))) -> C) -> ((E or (A -> (B or A))) -> D)))
theorem-size     29
proof            (modus-ponens tm-114 tm-619 ((A (-> (-> Am (or Bm Am)) (-> C D))) (B (or Dm (-> Am (or Bm Am)))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48118.        (((A -> (B or A)) -> (C -> D)) -> (((E or (A -> (B or A))) -> C) -> ((E or (A -> (B or A))) -> D))), M:tm-114, m:tm-619, u:((A (-> (-> Am (or Bm Am)) (-> C D))) (B (or Dm (-> Am (or Bm Am)))) (Cm (-> C D)))
================================================================
tm-name          tm-48119
in-theory        48119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G)))
theorem-size     33
proof            (modus-ponens tm-113 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48119.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G))), M:tm-113, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48120
in-theory        48120
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-105 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48120.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-105, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48121
in-theory        48121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E)))
theorem-size     25
proof            (modus-ponens tm-95 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48121.        (((A -> B) -> (A -> A)) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E))), M:tm-95, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48122
in-theory        48122
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) or ((A -> (B or A)) -> (A -> (B or A)))) -> ((D or (A -> (B or A))) -> (A -> (B or A))))
theorem-size     33
proof            (modus-ponens tm-92 tm-619 ((Cm (-> Am (or Bm Am))) (A (-> Am (or Bm Am))) (B (-> (or Dm (-> Am (or Bm Am))) (-> Am (or Bm Am))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48122.        ((((A -> (B or A)) -> C) or ((A -> (B or A)) -> (A -> (B or A)))) -> ((D or (A -> (B or A))) -> (A -> (B or A)))), M:tm-92, m:tm-619, u:((Cm (-> Am (or Bm Am))) (A (-> Am (or Bm Am))) (B (-> (or Dm (-> Am (or Bm Am))) (-> Am (or Bm Am)))))
================================================================
tm-name          tm-48123
in-theory        48123
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> (D -> ((E or (A -> (B or A))) -> C)))
theorem-size     19
proof            (modus-ponens tm-84 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48123.        (((A -> (B or A)) -> C) -> (D -> ((E or (A -> (B or A))) -> C))), M:tm-84, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48124
in-theory        48124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-83 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48124.        ((A -> (B -> (C -> B))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-83, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48125
in-theory        48125
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) -> (D -> (B -> (C or B))))) -> ((E or (B -> (C or B))) -> (D -> (B -> (C or B)))))
theorem-size     31
proof            (modus-ponens tm-80 tm-619 ((A (-> Am (or Bm Am))) (Cm (-> B (-> Am (or Bm Am)))) (C (-> (or Dm (-> Am (or Bm Am))) (-> B (-> Am (or Bm Am)))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48125.        ((A or ((B -> (C or B)) -> (D -> (B -> (C or B))))) -> ((E or (B -> (C or B))) -> (D -> (B -> (C or B))))), M:tm-80, m:tm-619, u:((A (-> Am (or Bm Am))) (Cm (-> B (-> Am (or Bm Am)))) (C (-> (or Dm (-> Am (or Bm Am))) (-> B (-> Am (or Bm Am))))))
================================================================
tm-name          tm-48126
in-theory        48126
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C or B)) -> D) -> ((E or (B -> (C or B))) -> D)))
theorem-size     23
proof            (modus-ponens tm-76 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48126.        (((not (not A)) -> A) and (((B -> (C or B)) -> D) -> ((E or (B -> (C or B))) -> D))), M:tm-76, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48127
in-theory        48127
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B or A)) -> C))) or ((A -> (B or A)) -> C)) -> ((D or (A -> (B or A))) -> C))
theorem-size     27
proof            (modus-ponens tm-73 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-8 tm-10 tm-1 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48127.        (((not (not ((A -> (B or A)) -> C))) or ((A -> (B or A)) -> C)) -> ((D or (A -> (B or A))) -> C)), M:tm-73, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48128
in-theory        48128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E)))
theorem-size     29
proof            (modus-ponens tm-69 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48128.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E))), M:tm-69, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48129
in-theory        48129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> (C or (A -> (B or A)))) -> (((A -> (B or A)) or (C or (A -> (B or A)))) -> (C or (A -> (B or A)))))
theorem-size     35
proof            (modus-ponens tm-55 tm-619 ((A (-> Am (or Bm Am))) (Cm (or Dm (-> Am (or Bm Am)))) (B (or Dm (-> Am (or Bm Am)))) (C (or Dm (-> Am (or Bm Am))))))
axioms-used      (tm-2 tm-8 tm-1 tm-7)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48129.        (((A -> (B or A)) -> (C or (A -> (B or A)))) -> (((A -> (B or A)) or (C or (A -> (B or A)))) -> (C or (A -> (B or A))))), M:tm-55, m:tm-619, u:((A (-> Am (or Bm Am))) (Cm (or Dm (-> Am (or Bm Am)))) (B (or Dm (-> Am (or Bm Am)))) (C (or Dm (-> Am (or Bm Am)))))
================================================================
tm-name          tm-48130
in-theory        48130
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-54 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48130.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-54, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48131
in-theory        48131
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> (C or B)) -> ((A or B) -> (C or B)))) -> ((D or (B -> (C or B))) -> ((A or B) -> (C or B))))
theorem-size     33
proof            (modus-ponens tm-51 tm-619 ((A Am) (B (or Bm Am)) (Cm (-> (or C Am) (or Bm Am))) (D (-> (or Dm (-> Am (or Bm Am))) (-> (or C Am) (or Bm Am))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48131.        (((A -> B) or ((B -> (C or B)) -> ((A or B) -> (C or B)))) -> ((D or (B -> (C or B))) -> ((A or B) -> (C or B)))), M:tm-51, m:tm-619, u:((A Am) (B (or Bm Am)) (Cm (-> (or C Am) (or Bm Am))) (D (-> (or Dm (-> Am (or Bm Am))) (-> (or C Am) (or Bm Am)))))
================================================================
tm-name          tm-48132
in-theory        48132
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) -> (A and (B -> (C or B))))) -> ((D or (B -> (C or B))) -> (A and (B -> (C or B)))))
theorem-size     31
proof            (modus-ponens tm-48 tm-619 ((A (-> Am (or Bm Am))) (Cm (and B (-> Am (or Bm Am)))) (C (-> (or Dm (-> Am (or Bm Am))) (and B (-> Am (or Bm Am)))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48132.        ((A or ((B -> (C or B)) -> (A and (B -> (C or B))))) -> ((D or (B -> (C or B))) -> (A and (B -> (C or B))))), M:tm-48, m:tm-619, u:((A (-> Am (or Bm Am))) (Cm (and B (-> Am (or Bm Am)))) (C (-> (or Dm (-> Am (or Bm Am))) (and B (-> Am (or Bm Am))))))
================================================================
tm-name          tm-48133
in-theory        48133
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) or ((B -> (C or B)) -> D)) -> ((E or (B -> (C or B))) -> D))
theorem-size     27
proof            (modus-ponens tm-47 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48133.        (((A and ((B -> (C or B)) -> D)) or ((B -> (C or B)) -> D)) -> ((E or (B -> (C or B))) -> D)), M:tm-47, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48134
in-theory        48134
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) or ((A -> (B or A)) -> C)) -> ((E or (A -> (B or A))) -> C))
theorem-size     27
proof            (modus-ponens tm-46 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48134.        (((((A -> (B or A)) -> C) and D) or ((A -> (B or A)) -> C)) -> ((E or (A -> (B or A))) -> C)), M:tm-46, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48135
in-theory        48135
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) or ((A -> (B or A)) -> (A -> C))) -> ((D or (A -> (B or A))) -> (A -> C)))
theorem-size     29
proof            (modus-ponens tm-45 tm-619 ((A Am) (B (or Bm Am)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (or Bm Am))) (-> Am C)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48135.        (((A -> ((B or A) -> C)) or ((A -> (B or A)) -> (A -> C))) -> ((D or (A -> (B or A))) -> (A -> C))), M:tm-45, m:tm-619, u:((A Am) (B (or Bm Am)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (or Bm Am))) (-> Am C))))
================================================================
tm-name          tm-48136
in-theory        48136
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) -> A)) -> ((D or (B -> (C or B))) -> A))
theorem-size     19
proof            (modus-ponens tm-44 tm-619 ((A (-> Am (or Bm Am))) (B Cm) (C (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48136.        ((A or ((B -> (C or B)) -> A)) -> ((D or (B -> (C or B))) -> A)), M:tm-44, m:tm-619, u:((A (-> Am (or Bm Am))) (B Cm) (C (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48137
in-theory        48137
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-42 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48137.        ((A -> (B or A)) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E))), M:tm-42, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48138
in-theory        48138
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-32 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48138.        ((A -> (A or B)) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E))), M:tm-32, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48139
in-theory        48139
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> (((A -> (B or A)) -> C) and ((D or (A -> (B or A))) -> C)))
theorem-size     25
proof            (modus-ponens tm-24 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48139.        (((A -> (B or A)) -> C) -> (((A -> (B or A)) -> C) and ((D or (A -> (B or A))) -> C))), M:tm-24, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48140
in-theory        48140
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E)))
theorem-size     25
proof            (modus-ponens tm-23 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48140.        ((A -> (B -> (A and B))) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E))), M:tm-23, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48141
in-theory        48141
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-22 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48141.        (((A and B) -> B) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E))), M:tm-22, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48142
in-theory        48142
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-21 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48142.        (((A and B) -> A) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E))), M:tm-21, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48143
in-theory        48143
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-20 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48143.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-20, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48144
in-theory        48144
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E)))
theorem-size     23
proof            (modus-ponens tm-19 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48144.        ((A -> (B -> A)) and (((C -> (D or C)) -> E) -> ((F or (C -> (D or C))) -> E))), M:tm-19, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48145
in-theory        48145
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> ((A -> (B or A)) -> C))
theorem-size     15
proof            (modus-ponens tm-12 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48145.        (((A -> (B or A)) -> C) -> ((A -> (B or A)) -> C)), M:tm-12, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48146
in-theory        48146
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> (not ((D or (A -> (B or A))) -> C))) -> (not ((A -> (B or A)) -> C)))
theorem-size     27
proof            (modus-ponens tm-9 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-9 tm-8 tm-1 tm-7)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48146.        ((((A -> (B or A)) -> C) -> (not ((D or (A -> (B or A))) -> C))) -> (not ((A -> (B or A)) -> C))), M:tm-9, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48147
in-theory        48147
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> (C or B))) -> D) -> E) -> ((((B -> (C or B)) -> D) or ((A or (B -> (C or B))) -> D)) -> E))
theorem-size     31
proof            (modus-ponens tm-8 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48147.        ((((A or (B -> (C or B))) -> D) -> E) -> ((((B -> (C or B)) -> D) or ((A or (B -> (C or B))) -> D)) -> E)), M:tm-8, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-48148
in-theory        48148
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> (C or B)) -> D) -> ((E or (B -> (C or B))) -> D)))
theorem-size     19
proof            (modus-ponens tm-7 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-7 tm-8 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48148.        (A or (((B -> (C or B)) -> D) -> ((E or (B -> (C or B))) -> D))), M:tm-7, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48149
in-theory        48149
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-6 tm-8 tm-1 tm-7)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48149.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) or E), M:tm-6, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48150
in-theory        48150
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> (C or B)) -> D) -> ((E or (B -> (C or B))) -> D)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48150.        (A -> ((((B -> (C or B)) -> D) -> ((E or (B -> (C or B))) -> D)) and A)), M:tm-5, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48151
in-theory        48151
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> (D or (A -> (B or A)))) -> (((A -> (B or A)) -> C) -> C))
theorem-size     25
proof            (modus-ponens tm-2 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (or Dm (-> Am (or Bm Am)))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-1 tm-7)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48151.        ((((A -> (B or A)) -> C) -> (D or (A -> (B or A)))) -> (((A -> (B or A)) -> C) -> C)), M:tm-2, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (or Dm (-> Am (or Bm Am)))) (C Cm))
================================================================
tm-name          tm-48152
in-theory        48152
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) -> D) -> ((E or (B -> (C or B))) -> D)))
theorem-size     19
proof            (modus-ponens tm-1 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-1 tm-8 tm-7)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48152.        (A -> (((B -> (C or B)) -> D) -> ((E or (B -> (C or B))) -> D))), M:tm-1, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48153
in-theory        48153
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48153.        ((A or (B -> (C -> (D or C)))) and (E -> (F or E))), M:tm-609, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48154
in-theory        48154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48154.        ((A -> ((B -> (C or B)) and A)) and (D or (E -> (F -> (G or F))))), M:tm-605, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48155
in-theory        48155
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and ((E -> (F or E)) and (A or (B -> (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48155.        ((A or (B -> (C -> (D or C)))) and ((E -> (F or E)) and (A or (B -> (C -> (D or C)))))), M:tm-595, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48156
in-theory        48156
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48156.        (((A -> (B or A)) or C) and (D or (E -> (F -> (G or F))))), M:tm-550, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48157
in-theory        48157
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48157.        ((A or (B -> (C or B))) and (D or (E -> (F -> (G or F))))), M:tm-540, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48158
in-theory        48158
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48158.        ((A or (B -> (B or C))) and (D or (E -> (F -> (G or F))))), M:tm-530, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48159
in-theory        48159
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48159.        ((A or (B -> (C -> (B and C)))) and (D or (E -> (F -> (G or F))))), M:tm-520, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48160
in-theory        48160
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48160.        ((A or ((B and C) -> C)) and (D or (E -> (F -> (G or F))))), M:tm-510, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48161
in-theory        48161
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48161.        ((A or ((B and C) -> B)) and (D or (E -> (F -> (G or F))))), M:tm-500, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48162
in-theory        48162
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48162.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (H or G))))), M:tm-490, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48163
in-theory        48163
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48163.        ((A or (B -> (C -> B))) and (D or (E -> (F -> (G or F))))), M:tm-480, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48164
in-theory        48164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48164.        ((A -> (B -> (B or C))) and (D or (E -> (F -> (G or F))))), M:tm-469, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48165
in-theory        48165
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48165.        ((A or (B -> (C -> (D or C)))) and (E -> (E or F))), M:tm-456, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48166
in-theory        48166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48166.        ((A -> ((B -> (B or C)) and A)) and (D or (E -> (F -> (G or F))))), M:tm-453, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48167
in-theory        48167
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and ((E -> (E or F)) and (A or (B -> (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48167.        ((A or (B -> (C -> (D or C)))) and ((E -> (E or F)) and (A or (B -> (C -> (D or C)))))), M:tm-443, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48168
in-theory        48168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48168.        (((A -> (A or B)) or C) and (D or (E -> (F -> (G or F))))), M:tm-409, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48169
in-theory        48169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48169.        (((A -> (B -> (A and B))) or C) and (D or (E -> (F -> (G or F))))), M:tm-400, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48170
in-theory        48170
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48170.        ((((A and B) -> B) or C) and (D or (E -> (F -> (G or F))))), M:tm-391, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48171
in-theory        48171
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48171.        ((((A and B) -> A) or C) and (D or (E -> (F -> (G or F))))), M:tm-382, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48172
in-theory        48172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48172.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (F -> (G -> (H or G))))), M:tm-373, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48173
in-theory        48173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48173.        (((A -> (B -> A)) or C) and (D or (E -> (F -> (G or F))))), M:tm-364, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48174
in-theory        48174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48174.        ((A -> (B -> (C -> (B and C)))) and (D or (E -> (F -> (G or F))))), M:tm-354, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48175
in-theory        48175
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48175.        ((A or (B -> (C -> (D or C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48176
in-theory        48176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (D -> (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48176.        (((A -> B) -> (A -> (A and B))) and (C or (D -> (E -> (F or E))))), M:tm-338, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48177
in-theory        48177
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and ((E -> (F -> (E and F))) and (A or (B -> (C -> (D or C))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48177.        ((A or (B -> (C -> (D or C)))) and ((E -> (F -> (E and F))) and (A or (B -> (C -> (D or C)))))), M:tm-327, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48178
in-theory        48178
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and (((E and F) -> F) and (A or (B -> (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48178.        ((A or (B -> (C -> (D or C)))) and (((E and F) -> F) and (A or (B -> (C -> (D or C)))))), M:tm-326, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48179
in-theory        48179
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and (((E and F) -> E) and (A or (B -> (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48179.        ((A or (B -> (C -> (D or C)))) and (((E and F) -> E) and (A or (B -> (C -> (D or C)))))), M:tm-325, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48180
in-theory        48180
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> (C -> (D or C))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48180.        ((A or (B -> (C -> (D or C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (B -> (C -> (D or C)))))), M:tm-324, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48181
in-theory        48181
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and ((E -> (F -> E)) and (A or (B -> (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48181.        ((A or (B -> (C -> (D or C)))) and ((E -> (F -> E)) and (A or (B -> (C -> (D or C)))))), M:tm-323, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48182
in-theory        48182
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48182.        ((A or (B -> (C -> (D or C)))) and ((E and F) -> F)), M:tm-322, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48183
in-theory        48183
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48183.        ((A or (B -> (C -> (D or C)))) and ((E and F) -> E)), M:tm-320, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48184
in-theory        48184
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48184.        ((A or (B -> (C -> (D or C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48185
in-theory        48185
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48185.        ((A or (B -> (C -> (D or C)))) and (E -> (F -> E))), M:tm-315, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48186
in-theory        48186
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and (E or (A or (B -> (C -> (D or C))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48186.        ((A or (B -> (C -> (D or C)))) and (E or (A or (B -> (C -> (D or C)))))), M:tm-311, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48187
in-theory        48187
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and ((A or (B -> (C -> (D or C)))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48187.        ((A or (B -> (C -> (D or C)))) and ((A or (B -> (C -> (D or C)))) or E)), M:tm-310, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48188
in-theory        48188
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and (E -> ((A or (B -> (C -> (D or C)))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48188.        ((A or (B -> (C -> (D or C)))) and (E -> ((A or (B -> (C -> (D or C)))) and E))), M:tm-309, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48189
in-theory        48189
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) and (E -> (A or (B -> (C -> (D or C))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48189.        ((A or (B -> (C -> (D or C)))) and (E -> (A or (B -> (C -> (D or C)))))), M:tm-305, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48190
in-theory        48190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48190.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (E -> (F -> (G or F))))), M:tm-303, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48191
in-theory        48191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48191.        ((A -> (((B and C) -> C) and A)) and (D or (E -> (F -> (G or F))))), M:tm-270, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48192
in-theory        48192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48192.        ((A -> (((B and C) -> B) and A)) and (D or (E -> (F -> (G or F))))), M:tm-239, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48193
in-theory        48193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48193.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (F -> (G -> (H or G))))), M:tm-210, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48194
in-theory        48194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48194.        ((A -> ((B -> (C -> B)) and A)) and (D or (E -> (F -> (G or F))))), M:tm-183, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48195
in-theory        48195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48195.        ((A -> ((B and C) -> C)) and (D or (E -> (F -> (G or F))))), M:tm-157, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48196
in-theory        48196
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48196.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (E -> (F -> (G or F))))), M:tm-147, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48197
in-theory        48197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48197.        ((A -> ((B and C) -> B)) and (D or (E -> (F -> (G or F))))), M:tm-134, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48198
in-theory        48198
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48198.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (E -> (F -> (G or F))))), M:tm-125, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48199
in-theory        48199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48199.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (F -> (G -> (H or G))))), M:tm-113, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48200
in-theory        48200
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (F -> (G or F)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48200.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (E -> (F -> (G or F))))), M:tm-105, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48201
in-theory        48201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (D -> (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48201.        (((A -> B) -> (A -> A)) and (C or (D -> (E -> (F or E))))), M:tm-95, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48202
in-theory        48202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48202.        ((A -> (B -> (C -> B))) and (D or (E -> (F -> (G or F))))), M:tm-83, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48203
in-theory        48203
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (C -> (D -> (E or D)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-10 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48203.        (((not (not A)) -> A) and (B or (C -> (D -> (E or D))))), M:tm-76, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48204
in-theory        48204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (E -> (F or E)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-9 tm-7 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48204.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (D -> (E -> (F or E))))), M:tm-69, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48205
in-theory        48205
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48205.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (E -> (F -> (G or F))))), M:tm-54, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48206
in-theory        48206
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48206.        ((A -> (B or A)) and (C or (D -> (E -> (F or E))))), M:tm-42, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48207
in-theory        48207
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48207.        ((A -> (A or B)) and (C or (D -> (E -> (F or E))))), M:tm-32, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48208
in-theory        48208
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (D -> (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48208.        ((A -> (B -> (A and B))) and (C or (D -> (E -> (F or E))))), M:tm-23, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48209
in-theory        48209
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48209.        (((A and B) -> B) and (C or (D -> (E -> (F or E))))), M:tm-22, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48210
in-theory        48210
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48210.        (((A and B) -> A) and (C or (D -> (E -> (F or E))))), M:tm-21, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48211
in-theory        48211
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-7 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48211.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (G or F))))), M:tm-20, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48212
in-theory        48212
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48212.        ((A -> (B -> A)) and (C or (D -> (E -> (F or E))))), M:tm-19, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48213
in-theory        48213
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (C -> (D -> (E or D)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-7 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48213.        (A or (B or (C -> (D -> (E or D))))), M:tm-7, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48214
in-theory        48214
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (D or C)))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-6 tm-7 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48214.        ((A or (B -> (C -> (D or C)))) or E), M:tm-6, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48215
in-theory        48215
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (C -> (D -> (E or D)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48215.        (A -> ((B or (C -> (D -> (E or D)))) and A)), M:tm-5, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48216
in-theory        48216
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (C -> (D -> (E or D)))))
theorem-size     11
proof            (modus-ponens tm-1 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-1 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48216.        (A -> (B or (C -> (D -> (E or D))))), M:tm-1, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48217
in-theory        48217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48217.        (((A -> (B -> (C or B))) or D) and (E -> (F or E))), M:tm-609, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48218
in-theory        48218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-605 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48218.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (F or E))) or G)), M:tm-605, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48219
in-theory        48219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and ((E -> (F or E)) and ((A -> (B -> (C or B))) or D)))
theorem-size     25
proof            (modus-ponens tm-595 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48219.        (((A -> (B -> (C or B))) or D) and ((E -> (F or E)) and ((A -> (B -> (C or B))) or D))), M:tm-595, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48220
in-theory        48220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-550 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48220.        (((A -> (B or A)) or C) and ((D -> (E -> (F or E))) or G)), M:tm-550, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48221
in-theory        48221
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-540 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48221.        ((A or (B -> (C or B))) and ((D -> (E -> (F or E))) or G)), M:tm-540, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48222
in-theory        48222
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-530 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48222.        ((A or (B -> (B or C))) and ((D -> (E -> (F or E))) or G)), M:tm-530, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48223
in-theory        48223
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-520 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48223.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (F or E))) or G)), M:tm-520, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48224
in-theory        48224
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-510 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48224.        ((A or ((B and C) -> C)) and ((D -> (E -> (F or E))) or G)), M:tm-510, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48225
in-theory        48225
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-500 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48225.        ((A or ((B and C) -> B)) and ((D -> (E -> (F or E))) or G)), M:tm-500, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48226
in-theory        48226
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G or F))) or H))
theorem-size     25
proof            (modus-ponens tm-490 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48226.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G or F))) or H)), M:tm-490, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48227
in-theory        48227
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-480 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48227.        ((A or (B -> (C -> B))) and ((D -> (E -> (F or E))) or G)), M:tm-480, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48228
in-theory        48228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-469 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48228.        ((A -> (B -> (B or C))) and ((D -> (E -> (F or E))) or G)), M:tm-469, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48229
in-theory        48229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48229.        (((A -> (B -> (C or B))) or D) and (E -> (E or F))), M:tm-456, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48230
in-theory        48230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-453 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48230.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (F or E))) or G)), M:tm-453, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48231
in-theory        48231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and ((E -> (E or F)) and ((A -> (B -> (C or B))) or D)))
theorem-size     25
proof            (modus-ponens tm-443 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48231.        (((A -> (B -> (C or B))) or D) and ((E -> (E or F)) and ((A -> (B -> (C or B))) or D))), M:tm-443, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48232
in-theory        48232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-409 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48232.        (((A -> (A or B)) or C) and ((D -> (E -> (F or E))) or G)), M:tm-409, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48233
in-theory        48233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-400 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48233.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (F or E))) or G)), M:tm-400, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48234
in-theory        48234
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-391 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48234.        ((((A and B) -> B) or C) and ((D -> (E -> (F or E))) or G)), M:tm-391, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48235
in-theory        48235
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-382 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48235.        ((((A and B) -> A) or C) and ((D -> (E -> (F or E))) or G)), M:tm-382, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48236
in-theory        48236
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (G or F))) or H))
theorem-size     25
proof            (modus-ponens tm-373 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48236.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (G or F))) or H)), M:tm-373, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48237
in-theory        48237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-364 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48237.        (((A -> (B -> A)) or C) and ((D -> (E -> (F or E))) or G)), M:tm-364, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48238
in-theory        48238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-354 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48238.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (F or E))) or G)), M:tm-354, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48239
in-theory        48239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48239.        (((A -> (B -> (C or B))) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48240
in-theory        48240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (E or D))) or F))
theorem-size     19
proof            (modus-ponens tm-338 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48240.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (E or D))) or F)), M:tm-338, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48241
in-theory        48241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and ((E -> (F -> (E and F))) and ((A -> (B -> (C or B))) or D)))
theorem-size     27
proof            (modus-ponens tm-327 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48241.        (((A -> (B -> (C or B))) or D) and ((E -> (F -> (E and F))) and ((A -> (B -> (C or B))) or D))), M:tm-327, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48242
in-theory        48242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and (((E and F) -> F) and ((A -> (B -> (C or B))) or D)))
theorem-size     25
proof            (modus-ponens tm-326 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48242.        (((A -> (B -> (C or B))) or D) and (((E and F) -> F) and ((A -> (B -> (C or B))) or D))), M:tm-326, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48243
in-theory        48243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and (((E and F) -> E) and ((A -> (B -> (C or B))) or D)))
theorem-size     25
proof            (modus-ponens tm-325 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48243.        (((A -> (B -> (C or B))) or D) and (((E and F) -> E) and ((A -> (B -> (C or B))) or D))), M:tm-325, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48244
in-theory        48244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (C or B))) or D)))
theorem-size     33
proof            (modus-ponens tm-324 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48244.        (((A -> (B -> (C or B))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> (B -> (C or B))) or D))), M:tm-324, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48245
in-theory        48245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and ((E -> (F -> E)) and ((A -> (B -> (C or B))) or D)))
theorem-size     25
proof            (modus-ponens tm-323 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48245.        (((A -> (B -> (C or B))) or D) and ((E -> (F -> E)) and ((A -> (B -> (C or B))) or D))), M:tm-323, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48246
in-theory        48246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48246.        (((A -> (B -> (C or B))) or D) and ((E and F) -> F)), M:tm-322, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48247
in-theory        48247
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48247.        (((A -> (B -> (C or B))) or D) and ((E and F) -> E)), M:tm-320, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48248
in-theory        48248
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48248.        (((A -> (B -> (C or B))) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48249
in-theory        48249
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48249.        (((A -> (B -> (C or B))) or D) and (E -> (F -> E))), M:tm-315, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48250
in-theory        48250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and (E or ((A -> (B -> (C or B))) or D)))
theorem-size     21
proof            (modus-ponens tm-311 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48250.        (((A -> (B -> (C or B))) or D) and (E or ((A -> (B -> (C or B))) or D))), M:tm-311, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48251
in-theory        48251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and (((A -> (B -> (C or B))) or D) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48251.        (((A -> (B -> (C or B))) or D) and (((A -> (B -> (C or B))) or D) or E)), M:tm-310, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48252
in-theory        48252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and (E -> (((A -> (B -> (C or B))) or D) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48252.        (((A -> (B -> (C or B))) or D) and (E -> (((A -> (B -> (C or B))) or D) and E))), M:tm-309, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48253
in-theory        48253
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) and (E -> ((A -> (B -> (C or B))) or D)))
theorem-size     21
proof            (modus-ponens tm-305 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48253.        (((A -> (B -> (C or B))) or D) and (E -> ((A -> (B -> (C or B))) or D))), M:tm-305, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48254
in-theory        48254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (F or E))) or G))
theorem-size     21
proof            (modus-ponens tm-303 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48254.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (F or E))) or G)), M:tm-303, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48255
in-theory        48255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-270 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48255.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (F or E))) or G)), M:tm-270, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48256
in-theory        48256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-239 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48256.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (F or E))) or G)), M:tm-239, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48257
in-theory        48257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (G or F))) or H))
theorem-size     27
proof            (modus-ponens tm-210 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48257.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (G or F))) or H)), M:tm-210, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48258
in-theory        48258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (F or E))) or G))
theorem-size     19
proof            (modus-ponens tm-183 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48258.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (F or E))) or G)), M:tm-183, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48259
in-theory        48259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-157 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48259.        ((A -> ((B and C) -> C)) and ((D -> (E -> (F or E))) or G)), M:tm-157, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48260
in-theory        48260
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (F or E))) or G))
theorem-size     25
proof            (modus-ponens tm-147 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48260.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (F or E))) or G)), M:tm-147, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48261
in-theory        48261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-134 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48261.        ((A -> ((B and C) -> B)) and ((D -> (E -> (F or E))) or G)), M:tm-134, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48262
in-theory        48262
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (F or E))) or G))
theorem-size     25
proof            (modus-ponens tm-125 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48262.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (F or E))) or G)), M:tm-125, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48263
in-theory        48263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G or F))) or H))
theorem-size     25
proof            (modus-ponens tm-113 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48263.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (G or F))) or H)), M:tm-113, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48264
in-theory        48264
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (F or E))) or G))
theorem-size     29
proof            (modus-ponens tm-105 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48264.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (F or E))) or G)), M:tm-105, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48265
in-theory        48265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (E or D))) or F))
theorem-size     17
proof            (modus-ponens tm-95 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48265.        (((A -> B) -> (A -> A)) and ((C -> (D -> (E or D))) or F)), M:tm-95, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48266
in-theory        48266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-83 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48266.        ((A -> (B -> (C -> B))) and ((D -> (E -> (F or E))) or G)), M:tm-83, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48267
in-theory        48267
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (D or C))) or E))
theorem-size     15
proof            (modus-ponens tm-76 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48267.        (((not (not A)) -> A) and ((B -> (C -> (D or C))) or E)), M:tm-76, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48268
in-theory        48268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (E or D))) or F))
theorem-size     21
proof            (modus-ponens tm-69 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-1 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48268.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (E or D))) or F)), M:tm-69, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48269
in-theory        48269
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (F or E))) or G))
theorem-size     23
proof            (modus-ponens tm-54 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48269.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (F or E))) or G)), M:tm-54, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48270
in-theory        48270
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (E or D))) or F))
theorem-size     15
proof            (modus-ponens tm-42 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48270.        ((A -> (B or A)) and ((C -> (D -> (E or D))) or F)), M:tm-42, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48271
in-theory        48271
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (E or D))) or F))
theorem-size     15
proof            (modus-ponens tm-32 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48271.        ((A -> (A or B)) and ((C -> (D -> (E or D))) or F)), M:tm-32, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48272
in-theory        48272
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (E or D))) or F))
theorem-size     17
proof            (modus-ponens tm-23 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48272.        ((A -> (B -> (A and B))) and ((C -> (D -> (E or D))) or F)), M:tm-23, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48273
in-theory        48273
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (E or D))) or F))
theorem-size     15
proof            (modus-ponens tm-22 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48273.        (((A and B) -> B) and ((C -> (D -> (E or D))) or F)), M:tm-22, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48274
in-theory        48274
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (E or D))) or F))
theorem-size     15
proof            (modus-ponens tm-21 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48274.        (((A and B) -> A) and ((C -> (D -> (E or D))) or F)), M:tm-21, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48275
in-theory        48275
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (F or E))) or G))
theorem-size     23
proof            (modus-ponens tm-20 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48275.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (F or E))) or G)), M:tm-20, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48276
in-theory        48276
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (E or D))) or F))
theorem-size     15
proof            (modus-ponens tm-19 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48276.        ((A -> (B -> A)) and ((C -> (D -> (E or D))) or F)), M:tm-19, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48277
in-theory        48277
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (D or C))) or E))
theorem-size     11
proof            (modus-ponens tm-7 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-7 tm-6 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48277.        (A or ((B -> (C -> (D or C))) or E)), M:tm-7, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48278
in-theory        48278
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) or D) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-6 tm-1 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48278.        (((A -> (B -> (C or B))) or D) or E), M:tm-6, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48279
in-theory        48279
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (D or C))) or E) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48279.        (A -> (((B -> (C -> (D or C))) or E) and A)), M:tm-5, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48280
in-theory        48280
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (D or C))) or E))
theorem-size     11
proof            (modus-ponens tm-1 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-1 tm-6 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48280.        (A -> ((B -> (C -> (D or C))) or E)), M:tm-1, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48281
in-theory        48281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48281.        ((A -> (B -> (C or B))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-622, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-48282
in-theory        48282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-622 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-48282.        ((A -> (B -> (C or B))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-622, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-48283
in-theory        48283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-622 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-48283.        ((A -> (B -> (C or B))) and ((not (not D)) -> D)), M:tm-622, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-48284
in-theory        48284
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-622 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48284.        ((A -> (B -> (C or B))) and (D -> (E -> (F -> E)))), M:tm-622, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-48285
in-theory        48285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-622 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-48285.        ((A -> (B -> (C or B))) and ((D -> E) -> (D -> D))), M:tm-622, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-48286
in-theory        48286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-622 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-48286.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-622, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-48287
in-theory        48287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-48287.        ((A -> (B -> (C or B))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-622, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-48288
in-theory        48288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-622 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-48288.        ((A -> (B -> (C or B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-622, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-48289
in-theory        48289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-622 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48289.        ((A -> (B -> (C or B))) and (D -> ((E and F) -> E))), M:tm-622, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-48290
in-theory        48290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-622 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-48290.        ((A -> (B -> (C or B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-622, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-48291
in-theory        48291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-622 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-48291.        ((A -> (B -> (C or B))) and (D -> ((E and F) -> F))), M:tm-622, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-48292
in-theory        48292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-622 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48292.        ((A -> (B -> (C or B))) and (D -> ((E -> (F -> E)) and D))), M:tm-622, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-48293
in-theory        48293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-622 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-48293.        ((A -> (B -> (C or B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-622, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-48294
in-theory        48294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-622 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48294.        ((A -> (B -> (C or B))) and (D -> (((E and F) -> E) and D))), M:tm-622, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-48295
in-theory        48295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-622 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-48295.        ((A -> (B -> (C or B))) and (D -> (((E and F) -> F) and D))), M:tm-622, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-48296
in-theory        48296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-48296.        ((A -> (B -> (C or B))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-622, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-48297
in-theory        48297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-622 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-48297.        ((A -> (B -> (C or B))) and ((D -> E) -> (D -> (D and E)))), M:tm-622, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-48298
in-theory        48298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-48298.        ((A -> (B -> (C or B))) and (D -> (E -> (F -> (E and F))))), M:tm-622, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-48299
in-theory        48299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-622 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48299.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) or F)), M:tm-622, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-48300
in-theory        48300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-622 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-48300.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-622, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-48301
in-theory        48301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-622 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48301.        ((A -> (B -> (C or B))) and (((D and E) -> D) or F)), M:tm-622, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-48302
in-theory        48302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-622 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-48302.        ((A -> (B -> (C or B))) and (((D and E) -> E) or F)), M:tm-622, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-48303
in-theory        48303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-622 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-48303.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) or F)), M:tm-622, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-48304
in-theory        48304
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-622 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-48304.        ((A -> (B -> (C or B))) and ((D -> (D or E)) or F)), M:tm-622, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-48305
in-theory        48305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-622 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-48305.        ((A -> (B -> (C or B))) and (D -> ((E -> (E or F)) and D))), M:tm-622, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-48306
in-theory        48306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-622 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-48306.        ((A -> (B -> (C or B))) and (D -> (E -> (E or F)))), M:tm-622, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-48307
in-theory        48307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-622 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48307.        ((A -> (B -> (C or B))) and (D or (E -> (F -> E)))), M:tm-622, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-48308
in-theory        48308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-48308.        ((A -> (B -> (C or B))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-622, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-48309
in-theory        48309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-622 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48309.        ((A -> (B -> (C or B))) and (D or ((E and F) -> E))), M:tm-622, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-48310
in-theory        48310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-622 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-48310.        ((A -> (B -> (C or B))) and (D or ((E and F) -> F))), M:tm-622, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-48311
in-theory        48311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-48311.        ((A -> (B -> (C or B))) and (D or (E -> (F -> (E and F))))), M:tm-622, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-48312
in-theory        48312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-622 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-48312.        ((A -> (B -> (C or B))) and (D or (E -> (E or F)))), M:tm-622, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-48313
in-theory        48313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-622 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48313.        ((A -> (B -> (C or B))) and (D or (E -> (F or E)))), M:tm-622, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-48314
in-theory        48314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-622 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48314.        ((A -> (B -> (C or B))) and ((D -> (E or D)) or F)), M:tm-622, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-48315
in-theory        48315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-622 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48315.        ((A -> (B -> (C or B))) and (D -> ((E -> (F or E)) and D))), M:tm-622, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-48316
in-theory        48316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-622 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48316.        ((A -> (B -> (C or B))) and (D -> (E -> (F or E)))), M:tm-622, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-48317
in-theory        48317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-622 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48317.        ((A -> (B -> (C or B))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-622, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-48318
in-theory        48318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-622 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-48318.        ((A -> (B -> (C or B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-622, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-48319
in-theory        48319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-622 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48319.        ((A -> (B -> (C or B))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-622, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-48320
in-theory        48320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-622 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-48320.        ((A -> (B -> (C or B))) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-622, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-48321
in-theory        48321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-622 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-48321.        ((A -> (B -> (C or B))) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-622, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-48322
in-theory        48322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-622 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-48322.        ((A -> (B -> (C or B))) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-622, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-48323
in-theory        48323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-622 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-48323.        ((A -> (B -> (C or B))) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-622, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-48324
in-theory        48324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     35
proof            (modus-ponens tm-622 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-48324.        ((A -> (B -> (C or B))) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-622, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-48325
in-theory        48325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-48325.        ((A -> (B -> (C or B))) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-622, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-48326
in-theory        48326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-622 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-48326.        ((A -> (B -> (C or B))) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-622, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-48327
in-theory        48327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-622 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-48327.        ((A -> (B -> (C or B))) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-622, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-48328
in-theory        48328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-622 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-48328.        ((A -> (B -> (C or B))) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-622, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-48329
in-theory        48329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-48329.        ((A -> (B -> (C or B))) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-622, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-48330
in-theory        48330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-622 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48330.        ((A -> (B -> (C or B))) and ((D -> (not (E -> D))) -> (not D))), M:tm-622, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-48331
in-theory        48331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-48331.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-622, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-48332
in-theory        48332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-622 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48332.        ((A -> (B -> (C or B))) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-622, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-48333
in-theory        48333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     19
proof            (modus-ponens tm-622 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-48333.        ((A -> (B -> (C or B))) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-622, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-48334
in-theory        48334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-48334.        ((A -> (B -> (C or B))) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-622, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-48335
in-theory        48335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not (D or E))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-622 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-48335.        ((A -> (B -> (C or B))) and ((D -> (not (D or E))) -> (not D))), M:tm-622, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-48336
in-theory        48336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not (E or D))) -> (not D)))
theorem-size     17
proof            (modus-ponens tm-622 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-48336.        ((A -> (B -> (C or B))) and ((D -> (not (E or D))) -> (not D))), M:tm-622, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-48337
in-theory        48337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-622 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-48337.        ((A -> (B -> (C or B))) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-622, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-48338
in-theory        48338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-622 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-48338.        ((A -> (B -> (C or B))) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-622, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-48339
in-theory        48339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-622 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-48339.        ((A -> (B -> (C or B))) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-622, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-48340
in-theory        48340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-48340.        ((A -> (B -> (C or B))) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-622, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-48341
in-theory        48341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     21
proof            (modus-ponens tm-622 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-48341.        ((A -> (B -> (C or B))) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-622, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-48342
in-theory        48342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     23
proof            (modus-ponens tm-622 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-48342.        ((A -> (B -> (C or B))) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-622, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-48343
in-theory        48343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-622 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-48343.        ((A -> (B -> (C or B))) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-622, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-48344
in-theory        48344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-48344.        ((A -> (B -> (C or B))) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-622, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-48345
in-theory        48345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     19
proof            (modus-ponens tm-622 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-48345.        ((A -> (B -> (C or B))) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-622, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-48346
in-theory        48346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-622 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-48346.        ((A -> (B -> (C or B))) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-622, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-48347
in-theory        48347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-622 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-48347.        ((A -> (B -> (C or B))) and (D or ((not (not E)) -> E))), M:tm-622, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-48348
in-theory        48348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((not (not D)) -> D) or E))
theorem-size     15
proof            (modus-ponens tm-622 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-48348.        ((A -> (B -> (C or B))) and (((not (not D)) -> D) or E)), M:tm-622, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-48349
in-theory        48349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((not (not E)) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-622 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-48349.        ((A -> (B -> (C or B))) and (D -> (((not (not E)) -> E) and D))), M:tm-622, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-48350
in-theory        48350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     23
proof            (modus-ponens tm-622 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-48350.        ((A -> (B -> (C or B))) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-622, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-48351
in-theory        48351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((not (not E)) -> E)))
theorem-size     15
proof            (modus-ponens tm-622 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-48351.        ((A -> (B -> (C or B))) and (D -> ((not (not E)) -> E))), M:tm-622, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-48352
in-theory        48352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-48352.        ((A -> (B -> (C or B))) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-622, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-48353
in-theory        48353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-622 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-48353.        ((A -> (B -> (C or B))) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-622, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-48354
in-theory        48354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-48354.        ((A -> (B -> (C or B))) and (D or (E -> (F -> (G -> F))))), M:tm-622, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-48355
in-theory        48355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-48355.        ((A -> (B -> (C or B))) and ((D -> (E -> (F -> E))) or G)), M:tm-622, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-48356
in-theory        48356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-48356.        ((A -> (B -> (C or B))) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-622, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-48357
in-theory        48357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> (D -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-622 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-48357.        ((A -> (B -> (C or B))) and ((D -> E) -> (D -> (F -> E)))), M:tm-622, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-48358
in-theory        48358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-48358.        ((A -> (B -> (C or B))) and (D -> (E -> (F -> (G -> F))))), M:tm-622, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-48359
in-theory        48359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> D))
theorem-size     11
proof            (modus-ponens tm-622 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       79
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48359.        ((A -> (B -> (C or B))) and (D -> D)), M:tm-622, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-48360
in-theory        48360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-48360.        ((A -> (B -> (C or B))) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-622, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-48361
in-theory        48361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D and E) -> (D and E)))
theorem-size     15
proof            (modus-ponens tm-622 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48361.        ((A -> (B -> (C or B))) and ((D and E) -> (D and E))), M:tm-622, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-48362
in-theory        48362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> (D -> E)))
theorem-size     15
proof            (modus-ponens tm-622 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-48362.        ((A -> (B -> (C or B))) and ((D -> E) -> (D -> E))), M:tm-622, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-48363
in-theory        48363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((not (not D)) -> (not (not D))))
theorem-size     15
proof            (modus-ponens tm-622 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-10)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-48363.        ((A -> (B -> (C or B))) and ((not (not D)) -> (not (not D)))), M:tm-622, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-48364
in-theory        48364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     21
proof            (modus-ponens tm-622 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-48364.        ((A -> (B -> (C or B))) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-622, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-48365
in-theory        48365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-622 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-48365.        ((A -> (B -> (C or B))) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-622, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-48366
in-theory        48366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-622 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-48366.        ((A -> (B -> (C or B))) and (D or ((E -> F) -> (E -> E)))), M:tm-622, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-48367
in-theory        48367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> (D -> D)) or F))
theorem-size     17
proof            (modus-ponens tm-622 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-48367.        ((A -> (B -> (C or B))) and (((D -> E) -> (D -> D)) or F)), M:tm-622, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-48368
in-theory        48368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-48368.        ((A -> (B -> (C or B))) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-622, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-48369
in-theory        48369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-48369.        ((A -> (B -> (C or B))) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-622, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-48370
in-theory        48370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> F) -> (E -> E))))
theorem-size     17
proof            (modus-ponens tm-622 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-48370.        ((A -> (B -> (C or B))) and (D -> ((E -> F) -> (E -> E)))), M:tm-622, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-48371
in-theory        48371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-48371.        ((A -> (B -> (C or B))) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-622, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-48372
in-theory        48372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-622 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-48372.        ((A -> (B -> (C or B))) and ((D -> (D -> E)) -> (D -> E))), M:tm-622, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-48373
in-theory        48373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     27
proof            (modus-ponens tm-622 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-48373.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-622, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-48374
in-theory        48374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-622 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-48374.        ((A -> (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-622, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-48375
in-theory        48375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-622 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-48375.        ((A -> (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-622, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-48376
in-theory        48376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-48376.        ((A -> (B -> (C or B))) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-622, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-48377
in-theory        48377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-622 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-48377.        ((A -> (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-622, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-48378
in-theory        48378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-622 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-48378.        ((A -> (B -> (C or B))) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-622, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-48379
in-theory        48379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-622 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-48379.        ((A -> (B -> (C or B))) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-622, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-48380
in-theory        48380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-48380.        ((A -> (B -> (C or B))) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-622, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-48381
in-theory        48381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-622 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-48381.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-622, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-48382
in-theory        48382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-622 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-48382.        ((A -> (B -> (C or B))) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-622, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-48383
in-theory        48383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     41
proof            (modus-ponens tm-622 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-48383.        ((A -> (B -> (C or B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-622, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-48384
in-theory        48384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-622 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48384.        ((A -> (B -> (C or B))) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-622, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-48385
in-theory        48385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-622 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48385.        ((A -> (B -> (C or B))) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-622, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-48386
in-theory        48386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-622 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48386.        ((A -> (B -> (C or B))) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-622, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-48387
in-theory        48387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-622 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-48387.        ((A -> (B -> (C or B))) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-622, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-48388
in-theory        48388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-622 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48388.        ((A -> (B -> (C or B))) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-622, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-48389
in-theory        48389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) and D) -> E))
theorem-size     15
proof            (modus-ponens tm-622 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-48389.        ((A -> (B -> (C or B))) and (((D -> E) and D) -> E)), M:tm-622, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-48390
in-theory        48390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-622 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-48390.        ((A -> (B -> (C or B))) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-622, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-48391
in-theory        48391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     27
proof            (modus-ponens tm-622 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-48391.        ((A -> (B -> (C or B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-622, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-48392
in-theory        48392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-622 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-48392.        ((A -> (B -> (C or B))) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-622, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-48393
in-theory        48393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     23
proof            (modus-ponens tm-622 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-48393.        ((A -> (B -> (C or B))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-622, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-48394
in-theory        48394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     33
proof            (modus-ponens tm-622 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-48394.        ((A -> (B -> (C or B))) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-622, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-48395
in-theory        48395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     35
proof            (modus-ponens tm-622 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-48395.        ((A -> (B -> (C or B))) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-622, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-48396
in-theory        48396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-622 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-48396.        ((A -> (B -> (C or B))) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-622, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-48397
in-theory        48397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-622 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-48397.        ((A -> (B -> (C or B))) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-622, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-48398
in-theory        48398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-622 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-48398.        ((A -> (B -> (C or B))) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-622, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-48399
in-theory        48399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     31
proof            (modus-ponens tm-622 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-48399.        ((A -> (B -> (C or B))) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-622, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-48400
in-theory        48400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     25
proof            (modus-ponens tm-622 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-48400.        ((A -> (B -> (C or B))) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-622, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-48401
in-theory        48401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-622 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-48401.        ((A -> (B -> (C or B))) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-622, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-48402
in-theory        48402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-622 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-48402.        ((A -> (B -> (C or B))) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-622, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-48403
in-theory        48403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-48403.        ((A -> (B -> (C or B))) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-622, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-48404
in-theory        48404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     25
proof            (modus-ponens tm-622 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-48404.        ((A -> (B -> (C or B))) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-622, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-48405
in-theory        48405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-622 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-48405.        ((A -> (B -> (C or B))) and (D or (E -> ((F and G) -> F)))), M:tm-622, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-48406
in-theory        48406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-48406.        ((A -> (B -> (C or B))) and ((D -> ((E and F) -> E)) or G)), M:tm-622, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-48407
in-theory        48407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-48407.        ((A -> (B -> (C or B))) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-622, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-48408
in-theory        48408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E and F)) -> (D -> E)))
theorem-size     17
proof            (modus-ponens tm-622 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-48408.        ((A -> (B -> (C or B))) and ((D -> (E and F)) -> (D -> E))), M:tm-622, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-48409
in-theory        48409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-622 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-48409.        ((A -> (B -> (C or B))) and (D -> (E -> ((F and G) -> F)))), M:tm-622, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-48410
in-theory        48410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D and (D -> E)) -> E))
theorem-size     15
proof            (modus-ponens tm-622 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-48410.        ((A -> (B -> (C or B))) and ((D and (D -> E)) -> E)), M:tm-622, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-48411
in-theory        48411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-622 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-48411.        ((A -> (B -> (C or B))) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-622, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-48412
in-theory        48412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     27
proof            (modus-ponens tm-622 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-48412.        ((A -> (B -> (C or B))) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-622, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-48413
in-theory        48413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-622 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-48413.        ((A -> (B -> (C or B))) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-622, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-48414
in-theory        48414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-622 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-48414.        ((A -> (B -> (C or B))) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-622, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-48415
in-theory        48415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     23
proof            (modus-ponens tm-622 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-48415.        ((A -> (B -> (C or B))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-622, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-48416
in-theory        48416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     33
proof            (modus-ponens tm-622 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-48416.        ((A -> (B -> (C or B))) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-622, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-48417
in-theory        48417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-622 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-48417.        ((A -> (B -> (C or B))) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-622, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-48418
in-theory        48418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-622 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-48418.        ((A -> (B -> (C or B))) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-622, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-48419
in-theory        48419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-622 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-48419.        ((A -> (B -> (C or B))) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-622, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-48420
in-theory        48420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-622 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-48420.        ((A -> (B -> (C or B))) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-622, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-48421
in-theory        48421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-622 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-48421.        ((A -> (B -> (C or B))) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-622, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-48422
in-theory        48422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     25
proof            (modus-ponens tm-622 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-48422.        ((A -> (B -> (C or B))) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-622, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-48423
in-theory        48423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-622 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-48423.        ((A -> (B -> (C or B))) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-622, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-48424
in-theory        48424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-622 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-48424.        ((A -> (B -> (C or B))) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-622, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-48425
in-theory        48425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     21
proof            (modus-ponens tm-622 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-48425.        ((A -> (B -> (C or B))) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-622, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-48426
in-theory        48426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-48426.        ((A -> (B -> (C or B))) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-622, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-48427
in-theory        48427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-622 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-48427.        ((A -> (B -> (C or B))) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-622, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-48428
in-theory        48428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-622 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-48428.        ((A -> (B -> (C or B))) and (D or (E -> ((F and G) -> G)))), M:tm-622, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-48429
in-theory        48429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-48429.        ((A -> (B -> (C or B))) and ((D -> ((E and F) -> F)) or G)), M:tm-622, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-48430
in-theory        48430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-48430.        ((A -> (B -> (C or B))) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-622, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-48431
in-theory        48431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E and F)) -> (D -> F)))
theorem-size     17
proof            (modus-ponens tm-622 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-48431.        ((A -> (B -> (C or B))) and ((D -> (E and F)) -> (D -> F))), M:tm-622, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-48432
in-theory        48432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-622 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-48432.        ((A -> (B -> (C or B))) and (D -> (E -> ((F and G) -> G)))), M:tm-622, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-48433
in-theory        48433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48433.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-622, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-48434
in-theory        48434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-48434.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-622, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-48435
in-theory        48435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48435.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-622, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-48436
in-theory        48436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-622 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-48436.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-622, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-48437
in-theory        48437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-48437.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-622, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-48438
in-theory        48438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-622 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-48438.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-622, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-48439
in-theory        48439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48439.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-622, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-48440
in-theory        48440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-48440.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-622, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-48441
in-theory        48441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-622 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-48441.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-622, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-48442
in-theory        48442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-48442.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-622, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-48443
in-theory        48443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-48443.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-622, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-48444
in-theory        48444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-48444.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-622, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-48445
in-theory        48445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-622 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-48445.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-622, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-48446
in-theory        48446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48446.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-622, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-48447
in-theory        48447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-622 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-48447.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-622, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-48448
in-theory        48448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-622 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-48448.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-622, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-48449
in-theory        48449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-622 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-48449.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-622, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-48450
in-theory        48450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-622 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-48450.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-622, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-48451
in-theory        48451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-48451.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-622, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-48452
in-theory        48452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-48452.        ((A -> (B -> (C or B))) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-622, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-48453
in-theory        48453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-622 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-48453.        ((A -> (B -> (C or B))) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-622, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-48454
in-theory        48454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-622 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-48454.        ((A -> (B -> (C or B))) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-622, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-48455
in-theory        48455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-622 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-48455.        ((A -> (B -> (C or B))) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-622, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-48456
in-theory        48456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-48456.        ((A -> (B -> (C or B))) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-622, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-48457
in-theory        48457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     19
proof            (modus-ponens tm-622 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-48457.        ((A -> (B -> (C or B))) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-622, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-48458
in-theory        48458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-622 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48458.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-622, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-48459
in-theory        48459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-48459.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-622, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-48460
in-theory        48460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-622 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48460.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-622, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-48461
in-theory        48461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-622 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-48461.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-622, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-48462
in-theory        48462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-48462.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-622, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-48463
in-theory        48463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-48463.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-622, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-48464
in-theory        48464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-622 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48464.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-622, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-48465
in-theory        48465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-48465.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-622, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-48466
in-theory        48466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     33
proof            (modus-ponens tm-622 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-48466.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-622, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-48467
in-theory        48467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     27
proof            (modus-ponens tm-622 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-10)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-48467.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-622, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-48468
in-theory        48468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-48468.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-622, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-48469
in-theory        48469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     29
proof            (modus-ponens tm-622 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-48469.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-622, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-48470
in-theory        48470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-622 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-48470.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-622, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-48471
in-theory        48471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-622 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48471.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-622, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-48472
in-theory        48472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     37
proof            (modus-ponens tm-622 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-48472.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-622, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-48473
in-theory        48473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-622 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-48473.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-622, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-48474
in-theory        48474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     37
proof            (modus-ponens tm-622 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-48474.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-622, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-48475
in-theory        48475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-622 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-48475.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-622, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-48476
in-theory        48476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     31
proof            (modus-ponens tm-622 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-48476.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-622, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-48477
in-theory        48477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     39
proof            (modus-ponens tm-622 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-48477.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-622, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-48478
in-theory        48478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-622 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-48478.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-622, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-48479
in-theory        48479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-622 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-48479.        ((A -> (B -> (C or B))) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-622, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-48480
in-theory        48480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-622 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-48480.        ((A -> (B -> (C or B))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-622, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-48481
in-theory        48481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-622 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-48481.        ((A -> (B -> (C or B))) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-622, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-48482
in-theory        48482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     27
proof            (modus-ponens tm-622 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-48482.        ((A -> (B -> (C or B))) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-622, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-48483
in-theory        48483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-622 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-48483.        ((A -> (B -> (C or B))) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-622, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-48484
in-theory        48484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     27
proof            (modus-ponens tm-622 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-48484.        ((A -> (B -> (C or B))) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-622, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-48485
in-theory        48485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48485.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-622, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-48486
in-theory        48486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-48486.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-622, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-48487
in-theory        48487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48487.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F and G) -> F))), M:tm-622, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-48488
in-theory        48488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-622 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-48488.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F and G) -> G))), M:tm-622, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-48489
in-theory        48489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-48489.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-622, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-48490
in-theory        48490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-622 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-48490.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (F or G)))), M:tm-622, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-48491
in-theory        48491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48491.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (G or F)))), M:tm-622, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-48492
in-theory        48492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-48492.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-622, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-48493
in-theory        48493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-622 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-48493.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-622, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-48494
in-theory        48494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-48494.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-622, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-48495
in-theory        48495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-48495.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-622, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-48496
in-theory        48496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-48496.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-622, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-48497
in-theory        48497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-622 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-48497.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-622, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-48498
in-theory        48498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48498.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-622, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-48499
in-theory        48499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-622 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-48499.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-622, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-48500
in-theory        48500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-622 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-48500.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-622, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-48501
in-theory        48501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-622 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-48501.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-622, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-48502
in-theory        48502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-622 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-48502.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-622, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-48503
in-theory        48503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-48503.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-622, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-48504
in-theory        48504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-622 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-48504.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-622, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-48505
in-theory        48505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-48505.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-622, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-48506
in-theory        48506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     31
proof            (modus-ponens tm-622 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-48506.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-622, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-48507
in-theory        48507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-48507.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-622, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-48508
in-theory        48508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-48508.        ((A -> (B -> (C or B))) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-622, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-48509
in-theory        48509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-622 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-48509.        ((A -> (B -> (C or B))) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-622, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-48510
in-theory        48510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-622 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-48510.        ((A -> (B -> (C or B))) and (D or (E -> (((F and G) -> F) and E)))), M:tm-622, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-48511
in-theory        48511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-622 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-48511.        ((A -> (B -> (C or B))) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-622, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-48512
in-theory        48512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-48512.        ((A -> (B -> (C or B))) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-622, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-48513
in-theory        48513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     19
proof            (modus-ponens tm-622 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-48513.        ((A -> (B -> (C or B))) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-622, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-48514
in-theory        48514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48514.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-622, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-48515
in-theory        48515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-48515.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-622, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-48516
in-theory        48516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48516.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F and G) -> F))), M:tm-622, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-48517
in-theory        48517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-622 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-48517.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F and G) -> G))), M:tm-622, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-48518
in-theory        48518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-48518.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-622, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-48519
in-theory        48519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-622 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-48519.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (F or G)))), M:tm-622, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-48520
in-theory        48520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48520.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (G or F)))), M:tm-622, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-48521
in-theory        48521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-48521.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-622, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-48522
in-theory        48522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-622 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-48522.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-622, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-48523
in-theory        48523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-48523.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-622, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-48524
in-theory        48524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-48524.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-622, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-48525
in-theory        48525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-48525.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-622, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-48526
in-theory        48526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-622 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-48526.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-622, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-48527
in-theory        48527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48527.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-622, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-48528
in-theory        48528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-622 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-48528.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-622, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-48529
in-theory        48529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-622 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-48529.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-622, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-48530
in-theory        48530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-622 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-48530.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-622, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-48531
in-theory        48531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-622 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-48531.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-622, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-48532
in-theory        48532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-48532.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-622, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-48533
in-theory        48533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-622 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-48533.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-622, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-48534
in-theory        48534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-48534.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-622, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-48535
in-theory        48535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-48535.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-622, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-48536
in-theory        48536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-48536.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-622, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-48537
in-theory        48537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     31
proof            (modus-ponens tm-622 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-48537.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-622, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-48538
in-theory        48538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-48538.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-622, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-48539
in-theory        48539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-48539.        ((A -> (B -> (C or B))) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-622, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-48540
in-theory        48540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-622 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-48540.        ((A -> (B -> (C or B))) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-622, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-48541
in-theory        48541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-622 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-48541.        ((A -> (B -> (C or B))) and (D or (E -> (((F and G) -> G) and E)))), M:tm-622, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-48542
in-theory        48542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-622 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-48542.        ((A -> (B -> (C or B))) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-622, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-48543
in-theory        48543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-48543.        ((A -> (B -> (C or B))) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-622, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-48544
in-theory        48544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     19
proof            (modus-ponens tm-622 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-48544.        ((A -> (B -> (C or B))) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-622, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-48545
in-theory        48545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48545.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-622, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-48546
in-theory        48546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-48546.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-622, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-48547
in-theory        48547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-622 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48547.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-622, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-48548
in-theory        48548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-622 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-48548.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-622, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-48549
in-theory        48549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-48549.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-622, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-48550
in-theory        48550
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-622 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-48550.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-622, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-48551
in-theory        48551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48551.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-622, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-48552
in-theory        48552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-48552.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-622, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-48553
in-theory        48553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-48553.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-622, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-48554
in-theory        48554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     21
proof            (modus-ponens tm-622 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-48554.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-622, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-48555
in-theory        48555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-48555.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-622, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-48556
in-theory        48556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-48556.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-622, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-48557
in-theory        48557
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-48557.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-622, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-48558
in-theory        48558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-622 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48558.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-622, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-48559
in-theory        48559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     31
proof            (modus-ponens tm-622 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-48559.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-622, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-48560
in-theory        48560
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-622 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-48560.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-622, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-48561
in-theory        48561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     31
proof            (modus-ponens tm-622 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-48561.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-622, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-48562
in-theory        48562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-622 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-48562.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-622, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-48563
in-theory        48563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     25
proof            (modus-ponens tm-622 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-48563.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-622, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-48564
in-theory        48564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     33
proof            (modus-ponens tm-622 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-48564.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-622, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-48565
in-theory        48565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     25
proof            (modus-ponens tm-622 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-48565.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-622, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-48566
in-theory        48566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     25
proof            (modus-ponens tm-622 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-48566.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-622, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-48567
in-theory        48567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     27
proof            (modus-ponens tm-622 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-48567.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-622, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-48568
in-theory        48568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-622 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-48568.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-622, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-48569
in-theory        48569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-622 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-48569.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-622, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-48570
in-theory        48570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     33
proof            (modus-ponens tm-622 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-48570.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-622, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-48571
in-theory        48571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-622 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-48571.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-622, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-48572
in-theory        48572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-622 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-48572.        ((A -> (B -> (C or B))) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-622, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-48573
in-theory        48573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-622 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-48573.        ((A -> (B -> (C or B))) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-622, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-48574
in-theory        48574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-622 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-48574.        ((A -> (B -> (C or B))) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-622, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-48575
in-theory        48575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     21
proof            (modus-ponens tm-622 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-48575.        ((A -> (B -> (C or B))) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-622, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-48576
in-theory        48576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     23
proof            (modus-ponens tm-622 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-48576.        ((A -> (B -> (C or B))) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-622, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-48577
in-theory        48577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     21
proof            (modus-ponens tm-622 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-48577.        ((A -> (B -> (C or B))) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-622, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-48578
in-theory        48578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and (E -> D))))
theorem-size     15
proof            (modus-ponens tm-622 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-48578.        ((A -> (B -> (C or B))) and (D -> (D and (E -> D)))), M:tm-622, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-48579
in-theory        48579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-48579.        ((A -> (B -> (C or B))) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-622, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-48580
in-theory        48580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D and E) -> ((D and E) and D)))
theorem-size     17
proof            (modus-ponens tm-622 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-48580.        ((A -> (B -> (C or B))) and ((D and E) -> ((D and E) and D))), M:tm-622, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-48581
in-theory        48581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D and E) -> ((D and E) and E)))
theorem-size     17
proof            (modus-ponens tm-622 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-48581.        ((A -> (B -> (C or B))) and ((D and E) -> ((D and E) and E))), M:tm-622, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-48582
in-theory        48582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and (E -> (D and E)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-48582.        ((A -> (B -> (C or B))) and (D -> (D and (E -> (D and E))))), M:tm-622, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-48583
in-theory        48583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and (D or E))))
theorem-size     15
proof            (modus-ponens tm-622 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-48583.        ((A -> (B -> (C or B))) and (D -> (D and (D or E)))), M:tm-622, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-48584
in-theory        48584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and (E or D))))
theorem-size     15
proof            (modus-ponens tm-622 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-48584.        ((A -> (B -> (C or B))) and (D -> (D and (E or D)))), M:tm-622, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-48585
in-theory        48585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     25
proof            (modus-ponens tm-622 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-48585.        ((A -> (B -> (C or B))) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-622, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-48586
in-theory        48586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-9)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-48586.        ((A -> (B -> (C or B))) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-622, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-48587
in-theory        48587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     17
proof            (modus-ponens tm-622 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-10)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-48587.        ((A -> (B -> (C or B))) and ((not (not D)) -> ((not (not D)) and D))), M:tm-622, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-48588
in-theory        48588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and (E -> (F -> E)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-48588.        ((A -> (B -> (C or B))) and (D -> (D and (E -> (F -> E))))), M:tm-622, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-48589
in-theory        48589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     19
proof            (modus-ponens tm-622 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-48589.        ((A -> (B -> (C or B))) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-622, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-48590
in-theory        48590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-622 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-48590.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-622, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-48591
in-theory        48591
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     25
proof            (modus-ponens tm-622 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-48591.        ((A -> (B -> (C or B))) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-622, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-48592
in-theory        48592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     31
proof            (modus-ponens tm-622 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-48592.        ((A -> (B -> (C or B))) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-622, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-48593
in-theory        48593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and ((E and F) -> E))))
theorem-size     17
proof            (modus-ponens tm-622 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-48593.        ((A -> (B -> (C or B))) and (D -> (D and ((E and F) -> E)))), M:tm-622, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-48594
in-theory        48594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     31
proof            (modus-ponens tm-622 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-48594.        ((A -> (B -> (C or B))) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-622, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-48595
in-theory        48595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and ((E and F) -> F))))
theorem-size     17
proof            (modus-ponens tm-622 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-48595.        ((A -> (B -> (C or B))) and (D -> (D and ((E and F) -> F)))), M:tm-622, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-48596
in-theory        48596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     19
proof            (modus-ponens tm-622 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-48596.        ((A -> (B -> (C or B))) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-622, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-48597
in-theory        48597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     27
proof            (modus-ponens tm-622 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-48597.        ((A -> (B -> (C or B))) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-622, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-48598
in-theory        48598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     19
proof            (modus-ponens tm-622 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-48598.        ((A -> (B -> (C or B))) and (D -> (D and (((E and F) -> E) and D)))), M:tm-622, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-48599
in-theory        48599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     19
proof            (modus-ponens tm-622 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-48599.        ((A -> (B -> (C or B))) and (D -> (D and (((E and F) -> F) and D)))), M:tm-622, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-48600
in-theory        48600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     21
proof            (modus-ponens tm-622 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-48600.        ((A -> (B -> (C or B))) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-622, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-48601
in-theory        48601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-48601.        ((A -> (B -> (C or B))) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-622, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-48602
in-theory        48602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-622 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-48602.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-622, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-48603
in-theory        48603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-48603.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-622, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-48604
in-theory        48604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-48604.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-622, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-48605
in-theory        48605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-622 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-48605.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-622, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-48606
in-theory        48606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-48606.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-622, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-48607
in-theory        48607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     23
proof            (modus-ponens tm-622 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-2)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-48607.        ((A -> (B -> (C or B))) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-622, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-48608
in-theory        48608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     27
proof            (modus-ponens tm-622 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-48608.        ((A -> (B -> (C or B))) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-622, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-48609
in-theory        48609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-622 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-48609.        ((A -> (B -> (C or B))) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-622, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-48610
in-theory        48610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     19
proof            (modus-ponens tm-622 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-48610.        ((A -> (B -> (C or B))) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-622, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-48611
in-theory        48611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-48611.        ((A -> (B -> (C or B))) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-622, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-48612
in-theory        48612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-622 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-48612.        ((A -> (B -> (C or B))) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-622, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-48613
in-theory        48613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-622 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-48613.        ((A -> (B -> (C or B))) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-622, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-48614
in-theory        48614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     19
proof            (modus-ponens tm-622 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-48614.        ((A -> (B -> (C or B))) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-622, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-48615
in-theory        48615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-622 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48615.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-622, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-48616
in-theory        48616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-622 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48616.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-622, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-48617
in-theory        48617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-622 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48617.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-622, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-48618
in-theory        48618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-622 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48618.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-622, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-48619
in-theory        48619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-622 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48619.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-622, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-48620
in-theory        48620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     21
proof            (modus-ponens tm-622 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-48620.        ((A -> (B -> (C or B))) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-622, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-48621
in-theory        48621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     21
proof            (modus-ponens tm-622 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-48621.        ((A -> (B -> (C or B))) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-622, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-48622
in-theory        48622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-622 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-48622.        ((A -> (B -> (C or B))) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-622, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-48623
in-theory        48623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-48623.        ((A -> (B -> (C or B))) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-622, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-48624
in-theory        48624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     29
proof            (modus-ponens tm-622 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-48624.        ((A -> (B -> (C or B))) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-622, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-48625
in-theory        48625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-622 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48625.        ((A -> (B -> (C or B))) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-622, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-48626
in-theory        48626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-622 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48626.        ((A -> (B -> (C or B))) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-622, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-48627
in-theory        48627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48627.        ((A -> (B -> (C or B))) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-622, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-48628
in-theory        48628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-622 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-48628.        ((A -> (B -> (C or B))) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-622, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-48629
in-theory        48629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-622 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48629.        ((A -> (B -> (C or B))) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-622, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-48630
in-theory        48630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     23
proof            (modus-ponens tm-622 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-48630.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-622, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-48631
in-theory        48631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-48631.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-622, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-48632
in-theory        48632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-48632.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-622, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-48633
in-theory        48633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-48633.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-622, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-48634
in-theory        48634
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-48634.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-622, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-48635
in-theory        48635
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-622 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-48635.        ((A -> (B -> (C or B))) and (D or ((E -> (F -> E)) or G))), M:tm-622, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-48636
in-theory        48636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-48636.        ((A -> (B -> (C or B))) and (((D -> (E -> D)) or F) or G)), M:tm-622, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-48637
in-theory        48637
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-48637.        ((A -> (B -> (C or B))) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-622, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-48638
in-theory        48638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (F -> E)) or G)))
theorem-size     17
proof            (modus-ponens tm-622 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-48638.        ((A -> (B -> (C or B))) and (D -> ((E -> (F -> E)) or G))), M:tm-622, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-48639
in-theory        48639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     31
proof            (modus-ponens tm-622 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-48639.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-622, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-48640
in-theory        48640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-48640.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-622, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-48641
in-theory        48641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-48641.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-622, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-48642
in-theory        48642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     37
proof            (modus-ponens tm-622 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-48642.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-622, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-48643
in-theory        48643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-48643.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-622, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-48644
in-theory        48644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-622 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-48644.        ((A -> (B -> (C or B))) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-622, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-48645
in-theory        48645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     25
proof            (modus-ponens tm-622 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-48645.        ((A -> (B -> (C or B))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-622, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-48646
in-theory        48646
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     27
proof            (modus-ponens tm-622 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-48646.        ((A -> (B -> (C or B))) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-622, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-48647
in-theory        48647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     25
proof            (modus-ponens tm-622 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-48647.        ((A -> (B -> (C or B))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-622, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-48648
in-theory        48648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     23
proof            (modus-ponens tm-622 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-48648.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-622, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-48649
in-theory        48649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-48649.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-622, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-48650
in-theory        48650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-48650.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-622, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-48651
in-theory        48651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-48651.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-622, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-48652
in-theory        48652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-48652.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-622, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-48653
in-theory        48653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-622 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-48653.        ((A -> (B -> (C or B))) and (D or (((E and F) -> E) or G))), M:tm-622, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-48654
in-theory        48654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D and E) -> D) or F) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-48654.        ((A -> (B -> (C or B))) and ((((D and E) -> D) or F) or G)), M:tm-622, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-48655
in-theory        48655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-48655.        ((A -> (B -> (C or B))) and (D -> ((((E and F) -> E) or G) and D))), M:tm-622, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-48656
in-theory        48656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E and F) -> E) or G)))
theorem-size     17
proof            (modus-ponens tm-622 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-48656.        ((A -> (B -> (C or B))) and (D -> (((E and F) -> E) or G))), M:tm-622, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-48657
in-theory        48657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     23
proof            (modus-ponens tm-622 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-48657.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-622, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-48658
in-theory        48658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-48658.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-622, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-48659
in-theory        48659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-48659.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-622, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-48660
in-theory        48660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-48660.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-622, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-48661
in-theory        48661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-48661.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-622, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-48662
in-theory        48662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-622 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-48662.        ((A -> (B -> (C or B))) and (D or (((E and F) -> F) or G))), M:tm-622, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-48663
in-theory        48663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D and E) -> E) or F) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-48663.        ((A -> (B -> (C or B))) and ((((D and E) -> E) or F) or G)), M:tm-622, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-48664
in-theory        48664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-48664.        ((A -> (B -> (C or B))) and (D -> ((((E and F) -> F) or G) and D))), M:tm-622, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-48665
in-theory        48665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E and F) -> F) or G)))
theorem-size     17
proof            (modus-ponens tm-622 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-48665.        ((A -> (B -> (C or B))) and (D -> (((E and F) -> F) or G))), M:tm-622, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-48666
in-theory        48666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     25
proof            (modus-ponens tm-622 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-48666.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-622, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-48667
in-theory        48667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-622 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-48667.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-622, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-48668
in-theory        48668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-622 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-48668.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-622, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-48669
in-theory        48669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     31
proof            (modus-ponens tm-622 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-48669.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-622, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-48670
in-theory        48670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-622 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-48670.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-622, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-48671
in-theory        48671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-622 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-48671.        ((A -> (B -> (C or B))) and (D or ((E -> (F -> (E and F))) or G))), M:tm-622, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-48672
in-theory        48672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     19
proof            (modus-ponens tm-622 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-48672.        ((A -> (B -> (C or B))) and (((D -> (E -> (D and E))) or F) or G)), M:tm-622, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-48673
in-theory        48673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-48673.        ((A -> (B -> (C or B))) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-622, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-48674
in-theory        48674
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     19
proof            (modus-ponens tm-622 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-48674.        ((A -> (B -> (C or B))) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-622, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-48675
in-theory        48675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     23
proof            (modus-ponens tm-622 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-48675.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-622, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-48676
in-theory        48676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-48676.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-622, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-48677
in-theory        48677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-48677.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-622, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-48678
in-theory        48678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-48678.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-622, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-48679
in-theory        48679
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-48679.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-622, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-48680
in-theory        48680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-622 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-48680.        ((A -> (B -> (C or B))) and (D or ((E -> (E or F)) or G))), M:tm-622, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-48681
in-theory        48681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (D or E)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-48681.        ((A -> (B -> (C or B))) and (((D -> (D or E)) or F) or G)), M:tm-622, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-48682
in-theory        48682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-48682.        ((A -> (B -> (C or B))) and (D -> (((E -> (E or F)) or G) and D))), M:tm-622, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-48683
in-theory        48683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (E or F)) or G)))
theorem-size     17
proof            (modus-ponens tm-622 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-48683.        ((A -> (B -> (C or B))) and (D -> ((E -> (E or F)) or G))), M:tm-622, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-48684
in-theory        48684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48684.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-622, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-48685
in-theory        48685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-48685.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-622, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-48686
in-theory        48686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48686.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-622, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-48687
in-theory        48687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-622 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-48687.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-622, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-48688
in-theory        48688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-48688.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-622, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-48689
in-theory        48689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-622 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-48689.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-622, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-48690
in-theory        48690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48690.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-622, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-48691
in-theory        48691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-48691.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-622, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-48692
in-theory        48692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-622 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-48692.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-622, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-48693
in-theory        48693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-48693.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-622, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-48694
in-theory        48694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-48694.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-622, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-48695
in-theory        48695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-48695.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-622, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-48696
in-theory        48696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-622 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-48696.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-622, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-48697
in-theory        48697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48697.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-622, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-48698
in-theory        48698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-622 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-48698.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-622, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-48699
in-theory        48699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-622 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-48699.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-622, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-48700
in-theory        48700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-622 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-48700.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-622, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-48701
in-theory        48701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-622 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-48701.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-622, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-48702
in-theory        48702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-48702.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-622, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-48703
in-theory        48703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-622 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-48703.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-622, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-48704
in-theory        48704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-48704.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-622, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-48705
in-theory        48705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-48705.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-622, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-48706
in-theory        48706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-622 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-48706.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-622, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-48707
in-theory        48707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-48707.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-622, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-48708
in-theory        48708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-622 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48708.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-622, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-48709
in-theory        48709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-48709.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-622, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-48710
in-theory        48710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-48710.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-622, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-48711
in-theory        48711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-48711.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-622, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-48712
in-theory        48712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-48712.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-622, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-48713
in-theory        48713
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-622 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-48713.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-622, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-48714
in-theory        48714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-48714.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-622, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-48715
in-theory        48715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-48715.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-622, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-48716
in-theory        48716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     19
proof            (modus-ponens tm-622 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-48716.        ((A -> (B -> (C or B))) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-622, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-48717
in-theory        48717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     25
proof            (modus-ponens tm-622 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-48717.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-622, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-48718
in-theory        48718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-48718.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-622, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-48719
in-theory        48719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-48719.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-622, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-48720
in-theory        48720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     31
proof            (modus-ponens tm-622 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-48720.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-622, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-48721
in-theory        48721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-48721.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-622, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-48722
in-theory        48722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-48722.        ((A -> (B -> (C or B))) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-622, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-48723
in-theory        48723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-622 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-48723.        ((A -> (B -> (C or B))) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-622, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-48724
in-theory        48724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-622 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-48724.        ((A -> (B -> (C or B))) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-622, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-48725
in-theory        48725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-622 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-48725.        ((A -> (B -> (C or B))) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-622, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-48726
in-theory        48726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-48726.        ((A -> (B -> (C or B))) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-622, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-48727
in-theory        48727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     19
proof            (modus-ponens tm-622 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-48727.        ((A -> (B -> (C or B))) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-622, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-48728
in-theory        48728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-48728.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-622, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-48729
in-theory        48729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and (E -> (E or F)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-48729.        ((A -> (B -> (C or B))) and (D -> (D and (E -> (E or F))))), M:tm-622, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-48730
in-theory        48730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-48730.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-622, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-48731
in-theory        48731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-48731.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-622, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-48732
in-theory        48732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-48732.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-622, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-48733
in-theory        48733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-48733.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-622, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-48734
in-theory        48734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-48734.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-622, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-48735
in-theory        48735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-622 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-48735.        ((A -> (B -> (C or B))) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-622, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-48736
in-theory        48736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-622 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-48736.        ((A -> (B -> (C or B))) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-622, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-48737
in-theory        48737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-48737.        ((A -> (B -> (C or B))) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-622, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-48738
in-theory        48738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-48738.        ((A -> (B -> (C or B))) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-622, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-48739
in-theory        48739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     25
proof            (modus-ponens tm-622 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-48739.        ((A -> (B -> (C or B))) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-622, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-48740
in-theory        48740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-48740.        ((A -> (B -> (C or B))) and (D or (E -> (F -> (F or G))))), M:tm-622, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-48741
in-theory        48741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-48741.        ((A -> (B -> (C or B))) and ((D -> (E -> (E or F))) or G)), M:tm-622, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-48742
in-theory        48742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-48742.        ((A -> (B -> (C or B))) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-622, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-48743
in-theory        48743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> (D -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-622 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-48743.        ((A -> (B -> (C or B))) and ((D -> E) -> (D -> (E or F)))), M:tm-622, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-48744
in-theory        48744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-48744.        ((A -> (B -> (C or B))) and (D -> (E -> (F -> (F or G))))), M:tm-622, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-48745
in-theory        48745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-48745.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-622, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-48746
in-theory        48746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-48746.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-622, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-48747
in-theory        48747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-48747.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-622, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-48748
in-theory        48748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-48748.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-622, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-48749
in-theory        48749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-48749.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-622, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-48750
in-theory        48750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-48750.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-622, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-48751
in-theory        48751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-48751.        ((A -> (B -> (C or B))) and (D or (E or (F -> (G -> F))))), M:tm-622, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-48752
in-theory        48752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (F -> E))) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-48752.        ((A -> (B -> (C or B))) and ((D or (E -> (F -> E))) or G)), M:tm-622, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-48753
in-theory        48753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-48753.        ((A -> (B -> (C or B))) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-622, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-48754
in-theory        48754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E or (F -> (G -> F)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-48754.        ((A -> (B -> (C or B))) and (D -> (E or (F -> (G -> F))))), M:tm-622, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-48755
in-theory        48755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48755.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-622, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-48756
in-theory        48756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     31
proof            (modus-ponens tm-622 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48756.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-622, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-48757
in-theory        48757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48757.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-622, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-48758
in-theory        48758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48758.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-622, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-48759
in-theory        48759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     37
proof            (modus-ponens tm-622 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48759.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-622, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-48760
in-theory        48760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48760.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-622, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-48761
in-theory        48761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-622 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48761.        ((A -> (B -> (C or B))) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-622, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-48762
in-theory        48762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     25
proof            (modus-ponens tm-622 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48762.        ((A -> (B -> (C or B))) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-622, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-48763
in-theory        48763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     27
proof            (modus-ponens tm-622 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48763.        ((A -> (B -> (C or B))) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-622, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-48764
in-theory        48764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     25
proof            (modus-ponens tm-622 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48764.        ((A -> (B -> (C or B))) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-622, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-48765
in-theory        48765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-622 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-48765.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-622, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-48766
in-theory        48766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     23
proof            (modus-ponens tm-622 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-48766.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-622, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-48767
in-theory        48767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-622 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-48767.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-622, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-48768
in-theory        48768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-622 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-48768.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-622, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-48769
in-theory        48769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     29
proof            (modus-ponens tm-622 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-48769.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-622, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-48770
in-theory        48770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-622 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-48770.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-622, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-48771
in-theory        48771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-622 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-48771.        ((A -> (B -> (C or B))) and (D or (E or ((F and G) -> F)))), M:tm-622, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-48772
in-theory        48772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or ((E and F) -> E)) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-48772.        ((A -> (B -> (C or B))) and ((D or ((E and F) -> E)) or G)), M:tm-622, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-48773
in-theory        48773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-48773.        ((A -> (B -> (C or B))) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-622, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-48774
in-theory        48774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E or ((F and G) -> F))))
theorem-size     17
proof            (modus-ponens tm-622 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-48774.        ((A -> (B -> (C or B))) and (D -> (E or ((F and G) -> F)))), M:tm-622, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-48775
in-theory        48775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-622 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-48775.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-622, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-48776
in-theory        48776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     23
proof            (modus-ponens tm-622 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-48776.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-622, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-48777
in-theory        48777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-622 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-48777.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-622, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-48778
in-theory        48778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-622 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-48778.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-622, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-48779
in-theory        48779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     29
proof            (modus-ponens tm-622 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-48779.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-622, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-48780
in-theory        48780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-622 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-48780.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-622, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-48781
in-theory        48781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-622 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-48781.        ((A -> (B -> (C or B))) and (D or (E or ((F and G) -> G)))), M:tm-622, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-48782
in-theory        48782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or ((E and F) -> F)) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-48782.        ((A -> (B -> (C or B))) and ((D or ((E and F) -> F)) or G)), M:tm-622, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-48783
in-theory        48783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-48783.        ((A -> (B -> (C or B))) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-622, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-48784
in-theory        48784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E or ((F and G) -> G))))
theorem-size     17
proof            (modus-ponens tm-622 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-48784.        ((A -> (B -> (C or B))) and (D -> (E or ((F and G) -> G)))), M:tm-622, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-48785
in-theory        48785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-622 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48785.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-622, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-48786
in-theory        48786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     25
proof            (modus-ponens tm-622 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48786.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-622, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-48787
in-theory        48787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-622 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48787.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-622, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-48788
in-theory        48788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-622 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48788.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-622, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-48789
in-theory        48789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     31
proof            (modus-ponens tm-622 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48789.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-622, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-48790
in-theory        48790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-622 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48790.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-622, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-48791
in-theory        48791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-622 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48791.        ((A -> (B -> (C or B))) and (D or (E or (F -> (G -> (F and G)))))), M:tm-622, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-48792
in-theory        48792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     19
proof            (modus-ponens tm-622 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48792.        ((A -> (B -> (C or B))) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-622, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-48793
in-theory        48793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48793.        ((A -> (B -> (C or B))) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-622, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-48794
in-theory        48794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     19
proof            (modus-ponens tm-622 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48794.        ((A -> (B -> (C or B))) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-622, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-48795
in-theory        48795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-48795.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-622, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-48796
in-theory        48796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-48796.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-622, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-48797
in-theory        48797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-48797.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-622, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-48798
in-theory        48798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-48798.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-622, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-48799
in-theory        48799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-48799.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-622, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-48800
in-theory        48800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-48800.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-622, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-48801
in-theory        48801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-48801.        ((A -> (B -> (C or B))) and (D or (E or (F -> (F or G))))), M:tm-622, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-48802
in-theory        48802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (E or F))) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-48802.        ((A -> (B -> (C or B))) and ((D or (E -> (E or F))) or G)), M:tm-622, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-48803
in-theory        48803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-48803.        ((A -> (B -> (C or B))) and (D -> ((E or (F -> (F or G))) and D))), M:tm-622, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-48804
in-theory        48804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E or (F -> (F or G)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-48804.        ((A -> (B -> (C or B))) and (D -> (E or (F -> (F or G))))), M:tm-622, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-48805
in-theory        48805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-48805.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-622, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-48806
in-theory        48806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-48806.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-622, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-48807
in-theory        48807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-48807.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-622, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-48808
in-theory        48808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-48808.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-622, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-48809
in-theory        48809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-48809.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-622, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-48810
in-theory        48810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-48810.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-622, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-48811
in-theory        48811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-48811.        ((A -> (B -> (C or B))) and (D or (E or (F -> (G or F))))), M:tm-622, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48812
in-theory        48812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-48812.        ((A -> (B -> (C or B))) and ((D or (E -> (F or E))) or G)), M:tm-622, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48813
in-theory        48813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-48813.        ((A -> (B -> (C or B))) and (D -> ((E or (F -> (G or F))) and D))), M:tm-622, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48814
in-theory        48814
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E or (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-48814.        ((A -> (B -> (C or B))) and (D -> (E or (F -> (G or F))))), M:tm-622, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48815
in-theory        48815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-48815.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-622, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-48816
in-theory        48816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     23
proof            (modus-ponens tm-622 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-48816.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-622, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-48817
in-theory        48817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-48817.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-622, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-48818
in-theory        48818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-48818.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-622, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-48819
in-theory        48819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-48819.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-622, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-48820
in-theory        48820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-48820.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-622, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-48821
in-theory        48821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-622 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-48821.        ((A -> (B -> (C or B))) and (D or ((E -> (F or E)) or G))), M:tm-622, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-48822
in-theory        48822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E or D)) or F) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-48822.        ((A -> (B -> (C or B))) and (((D -> (E or D)) or F) or G)), M:tm-622, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-48823
in-theory        48823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-48823.        ((A -> (B -> (C or B))) and (D -> (((E -> (F or E)) or G) and D))), M:tm-622, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-48824
in-theory        48824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (F or E)) or G)))
theorem-size     17
proof            (modus-ponens tm-622 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-48824.        ((A -> (B -> (C or B))) and (D -> ((E -> (F or E)) or G))), M:tm-622, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-48825
in-theory        48825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-48825.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-622, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-48826
in-theory        48826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-48826.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-622, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-48827
in-theory        48827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-48827.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-622, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-48828
in-theory        48828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-622 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-48828.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-622, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-48829
in-theory        48829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-48829.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-622, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-48830
in-theory        48830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-622 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-48830.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-622, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-48831
in-theory        48831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-48831.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-622, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-48832
in-theory        48832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-48832.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-622, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-48833
in-theory        48833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     25
proof            (modus-ponens tm-622 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-48833.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-622, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-48834
in-theory        48834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-10)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-48834.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-622, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-48835
in-theory        48835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-48835.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-622, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-48836
in-theory        48836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-48836.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-622, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-48837
in-theory        48837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-622 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-48837.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-622, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-48838
in-theory        48838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48838.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-622, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-48839
in-theory        48839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-622 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-48839.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-622, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-48840
in-theory        48840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-622 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-48840.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-622, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-48841
in-theory        48841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     29
proof            (modus-ponens tm-622 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-48841.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-622, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-48842
in-theory        48842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-622 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-48842.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-622, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-48843
in-theory        48843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-48843.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-622, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-48844
in-theory        48844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     31
proof            (modus-ponens tm-622 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-48844.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-622, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-48845
in-theory        48845
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-48845.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-622, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-48846
in-theory        48846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-48846.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-622, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-48847
in-theory        48847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     25
proof            (modus-ponens tm-622 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-48847.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-622, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-48848
in-theory        48848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-48848.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-622, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-48849
in-theory        48849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-622 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48849.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-622, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-48850
in-theory        48850
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-48850.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-622, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-48851
in-theory        48851
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     29
proof            (modus-ponens tm-622 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-48851.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-622, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-48852
in-theory        48852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-48852.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-622, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-48853
in-theory        48853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-48853.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-622, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-48854
in-theory        48854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     23
proof            (modus-ponens tm-622 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-48854.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-622, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-48855
in-theory        48855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-48855.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-622, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-48856
in-theory        48856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-48856.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-622, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-48857
in-theory        48857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-48857.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-622, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-48858
in-theory        48858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-48858.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-622, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-48859
in-theory        48859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     29
proof            (modus-ponens tm-622 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-48859.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-622, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-48860
in-theory        48860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     21
proof            (modus-ponens tm-622 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-48860.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-622, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-48861
in-theory        48861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     21
proof            (modus-ponens tm-622 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-48861.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-622, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-48862
in-theory        48862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     23
proof            (modus-ponens tm-622 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-48862.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-622, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-48863
in-theory        48863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-48863.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-622, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-48864
in-theory        48864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-48864.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-622, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-48865
in-theory        48865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     21
proof            (modus-ponens tm-622 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-48865.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-622, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-48866
in-theory        48866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-48866.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-622, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-48867
in-theory        48867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-48867.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-622, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-48868
in-theory        48868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     19
proof            (modus-ponens tm-622 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-48868.        ((A -> (B -> (C or B))) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-622, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-48869
in-theory        48869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     25
proof            (modus-ponens tm-622 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-48869.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-622, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-48870
in-theory        48870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-48870.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-622, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-48871
in-theory        48871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-48871.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-622, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-48872
in-theory        48872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     31
proof            (modus-ponens tm-622 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-48872.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-622, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-48873
in-theory        48873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-48873.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-622, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-48874
in-theory        48874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-48874.        ((A -> (B -> (C or B))) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-622, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-48875
in-theory        48875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-622 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-48875.        ((A -> (B -> (C or B))) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-622, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-48876
in-theory        48876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-622 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-48876.        ((A -> (B -> (C or B))) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-622, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-48877
in-theory        48877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     19
proof            (modus-ponens tm-622 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-48877.        ((A -> (B -> (C or B))) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-622, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-48878
in-theory        48878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-48878.        ((A -> (B -> (C or B))) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-622, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-48879
in-theory        48879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     19
proof            (modus-ponens tm-622 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-48879.        ((A -> (B -> (C or B))) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-622, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-48880
in-theory        48880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48880.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-622, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-48881
in-theory        48881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48881.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-622, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-48882
in-theory        48882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (D and (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48882.        ((A -> (B -> (C or B))) and (D -> (D and (E -> (F or E))))), M:tm-622, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-48883
in-theory        48883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     23
proof            (modus-ponens tm-622 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48883.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-622, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-48884
in-theory        48884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48884.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-622, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-48885
in-theory        48885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48885.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-622, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-48886
in-theory        48886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48886.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-622, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-48887
in-theory        48887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48887.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-622, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-48888
in-theory        48888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     19
proof            (modus-ponens tm-622 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-4)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-48888.        ((A -> (B -> (C or B))) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-622, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-48889
in-theory        48889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     19
proof            (modus-ponens tm-622 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-3)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-48889.        ((A -> (B -> (C or B))) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-622, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-48890
in-theory        48890
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-48890.        ((A -> (B -> (C or B))) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-622, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-48891
in-theory        48891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-9)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48891.        ((A -> (B -> (C or B))) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-622, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-48892
in-theory        48892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     25
proof            (modus-ponens tm-622 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-48892.        ((A -> (B -> (C or B))) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-622, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-48893
in-theory        48893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48893.        ((A -> (B -> (C or B))) and (D or (E -> (F -> (G or F))))), M:tm-622, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-48894
in-theory        48894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (F or E))) or G))
theorem-size     17
proof            (modus-ponens tm-622 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48894.        ((A -> (B -> (C or B))) and ((D -> (E -> (F or E))) or G)), M:tm-622, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-48895
in-theory        48895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-622 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48895.        ((A -> (B -> (C or B))) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-622, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48896
in-theory        48896
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> (E -> (F or E))) and (B -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-619 tm-622 ((Am (-> A (or B A))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48896.        ((A or (B -> (C or B))) -> ((D -> (E -> (F or E))) and (B -> (C or B)))), M:tm-619, m:tm-622, u:((Am (-> A (or B A))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (or B A)))))
================================================================
tm-name          tm-48897
in-theory        48897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48897.        ((A -> ((B -> (C -> (D or C))) and A)) and (E -> (F or E))), M:tm-609, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48898
in-theory        48898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-605 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48898.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-605, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48899
in-theory        48899
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> (F or E))) and ((B -> (C or B)) and A)))
theorem-size     25
proof            (modus-ponens tm-602 tm-622 ((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48899.        ((A or ((B -> (C or B)) and A)) -> ((D -> (E -> (F or E))) and ((B -> (C or B)) and A))), M:tm-602, m:tm-622, u:((Am (and (-> A (or B A)) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-48900
in-theory        48900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and ((E -> (F or E)) and (A -> ((B -> (C -> (D or C))) and A))))
theorem-size     29
proof            (modus-ponens tm-595 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48900.        ((A -> ((B -> (C -> (D or C))) and A)) and ((E -> (F or E)) and (A -> ((B -> (C -> (D or C))) and A)))), M:tm-595, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48901
in-theory        48901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-550 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48901.        (((A -> (B or A)) or C) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-550, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48902
in-theory        48902
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-540 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48902.        ((A or (B -> (C or B))) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-540, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48903
in-theory        48903
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-530 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48903.        ((A or (B -> (B or C))) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-530, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48904
in-theory        48904
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-520 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48904.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-520, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48905
in-theory        48905
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-510 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48905.        ((A or ((B and C) -> C)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-510, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48906
in-theory        48906
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-500 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48906.        ((A or ((B and C) -> B)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-500, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48907
in-theory        48907
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (H or G))) and E)))
theorem-size     27
proof            (modus-ponens tm-490 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48907.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (H or G))) and E))), M:tm-490, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48908
in-theory        48908
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-480 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48908.        ((A or (B -> (C -> B))) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-480, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48909
in-theory        48909
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (D or C))) and A) or E))
theorem-size     13
proof            (modus-ponens tm-470 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-7)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48909.        (A -> (((B -> (C -> (D or C))) and A) or E)), M:tm-470, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-48910
in-theory        48910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-469 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48910.        ((A -> (B -> (B or C))) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-469, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48911
in-theory        48911
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> (E -> (F or E))) and (B -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-466 tm-622 ((Am (-> A (or A B))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48911.        ((A or (B -> (B or C))) -> ((D -> (E -> (F or E))) and (B -> (B or C)))), M:tm-466, m:tm-622, u:((Am (-> A (or A B))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (or A B)))))
================================================================
tm-name          tm-48912
in-theory        48912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48912.        ((A -> ((B -> (C -> (D or C))) and A)) and (E -> (E or F))), M:tm-456, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48913
in-theory        48913
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-453 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48913.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-453, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48914
in-theory        48914
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> (F or E))) and ((B -> (B or C)) and A)))
theorem-size     25
proof            (modus-ponens tm-450 tm-622 ((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48914.        ((A or ((B -> (B or C)) and A)) -> ((D -> (E -> (F or E))) and ((B -> (B or C)) and A))), M:tm-450, m:tm-622, u:((Am (and (-> A (or A B)) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-48915
in-theory        48915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and ((E -> (E or F)) and (A -> ((B -> (C -> (D or C))) and A))))
theorem-size     29
proof            (modus-ponens tm-443 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48915.        ((A -> ((B -> (C -> (D or C))) and A)) and ((E -> (E or F)) and (A -> ((B -> (C -> (D or C))) and A)))), M:tm-443, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48916
in-theory        48916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-409 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48916.        (((A -> (A or B)) or C) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-409, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48917
in-theory        48917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-400 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48917.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-400, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48918
in-theory        48918
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-391 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48918.        ((((A and B) -> B) or C) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-391, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48919
in-theory        48919
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-382 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48919.        ((((A and B) -> A) or C) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-382, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48920
in-theory        48920
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> (H or G))) and E)))
theorem-size     27
proof            (modus-ponens tm-373 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48920.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> (G -> (H or G))) and E))), M:tm-373, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48921
in-theory        48921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-364 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48921.        (((A -> (B -> A)) or C) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-364, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48922
in-theory        48922
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> (D -> (E or D))) and A) and B)))
theorem-size     15
proof            (modus-ponens tm-355 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48922.        (A -> (B -> (((C -> (D -> (E or D))) and A) and B))), M:tm-355, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-48923
in-theory        48923
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-354 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48923.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-354, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48924
in-theory        48924
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> (F or E))) and (B -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-351 tm-622 ((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48924.        ((A or (B -> (C -> (B and C)))) -> ((D -> (E -> (F or E))) and (B -> (C -> (B and C))))), M:tm-351, m:tm-622, u:((Am (-> A (-> B (and A B)))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-48925
in-theory        48925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48925.        ((A -> ((B -> (C -> (D or C))) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48926
in-theory        48926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> (F or E))) and C)))
theorem-size     21
proof            (modus-ponens tm-338 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48926.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> (E -> (F or E))) and C))), M:tm-338, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48927
in-theory        48927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> (D -> (E or D))) and (A -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-335 tm-622 ((Am (-> A (and A B))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48927.        (((A -> B) or (A -> (A and B))) -> ((C -> (D -> (E or D))) and (A -> (A and B)))), M:tm-335, m:tm-622, u:((Am (-> A (and A B))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (and A B)))))
================================================================
tm-name          tm-48928
in-theory        48928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and (A -> (A and ((B -> (C -> (D or C))) and A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48928.        ((A -> ((B -> (C -> (D or C))) and A)) and (A -> (A and ((B -> (C -> (D or C))) and A)))), M:tm-328, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-48929
in-theory        48929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> (C -> (D or C))) and A))))
theorem-size     31
proof            (modus-ponens tm-327 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48929.        ((A -> ((B -> (C -> (D or C))) and A)) and ((E -> (F -> (E and F))) and (A -> ((B -> (C -> (D or C))) and A)))), M:tm-327, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48930
in-theory        48930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and (((E and F) -> F) and (A -> ((B -> (C -> (D or C))) and A))))
theorem-size     29
proof            (modus-ponens tm-326 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48930.        ((A -> ((B -> (C -> (D or C))) and A)) and (((E and F) -> F) and (A -> ((B -> (C -> (D or C))) and A)))), M:tm-326, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48931
in-theory        48931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and (((E and F) -> E) and (A -> ((B -> (C -> (D or C))) and A))))
theorem-size     29
proof            (modus-ponens tm-325 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48931.        ((A -> ((B -> (C -> (D or C))) and A)) and (((E and F) -> E) and (A -> ((B -> (C -> (D or C))) and A)))), M:tm-325, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48932
in-theory        48932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C -> (D or C))) and A))))
theorem-size     37
proof            (modus-ponens tm-324 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48932.        ((A -> ((B -> (C -> (D or C))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> (C -> (D or C))) and A)))), M:tm-324, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48933
in-theory        48933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and ((E -> (F -> E)) and (A -> ((B -> (C -> (D or C))) and A))))
theorem-size     29
proof            (modus-ponens tm-323 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48933.        ((A -> ((B -> (C -> (D or C))) and A)) and ((E -> (F -> E)) and (A -> ((B -> (C -> (D or C))) and A)))), M:tm-323, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48934
in-theory        48934
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48934.        ((A -> ((B -> (C -> (D or C))) and A)) and ((E and F) -> F)), M:tm-322, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48935
in-theory        48935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48935.        ((A -> ((B -> (C -> (D or C))) and A)) and ((E and F) -> E)), M:tm-320, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48936
in-theory        48936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48936.        ((A -> ((B -> (C -> (D or C))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48937
in-theory        48937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and (A -> A))
theorem-size     15
proof            (modus-ponens tm-316 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48937.        ((A -> ((B -> (C -> (D or C))) and A)) and (A -> A)), M:tm-316, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-48938
in-theory        48938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       107
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48938.        ((A -> ((B -> (C -> (D or C))) and A)) and (E -> (F -> E))), M:tm-315, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48939
in-theory        48939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and ((A -> (not ((B -> (C -> (D or C))) and A))) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-313 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48939.        ((A -> ((B -> (C -> (D or C))) and A)) and ((A -> (not ((B -> (C -> (D or C))) and A))) -> (not A))), M:tm-313, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-48940
in-theory        48940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and ((((B -> (C -> (D or C))) and A) -> E) -> ((A or ((B -> (C -> (D or C))) and A)) -> E)))
theorem-size     37
proof            (modus-ponens tm-312 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48940.        ((A -> ((B -> (C -> (D or C))) and A)) and ((((B -> (C -> (D or C))) and A) -> E) -> ((A or ((B -> (C -> (D or C))) and A)) -> E))), M:tm-312, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-48941
in-theory        48941
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and (E or (A -> ((B -> (C -> (D or C))) and A))))
theorem-size     25
proof            (modus-ponens tm-311 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48941.        ((A -> ((B -> (C -> (D or C))) and A)) and (E or (A -> ((B -> (C -> (D or C))) and A)))), M:tm-311, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48942
in-theory        48942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and ((A -> ((B -> (C -> (D or C))) and A)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48942.        ((A -> ((B -> (C -> (D or C))) and A)) and ((A -> ((B -> (C -> (D or C))) and A)) or E)), M:tm-310, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48943
in-theory        48943
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and (E -> ((A -> ((B -> (C -> (D or C))) and A)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48943.        ((A -> ((B -> (C -> (D or C))) and A)) and (E -> ((A -> ((B -> (C -> (D or C))) and A)) and E))), M:tm-309, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48944
in-theory        48944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and (E -> (A -> ((B -> (C -> (D or C))) and A))))
theorem-size     25
proof            (modus-ponens tm-305 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48944.        ((A -> ((B -> (C -> (D or C))) and A)) and (E -> (A -> ((B -> (C -> (D or C))) and A)))), M:tm-305, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48945
in-theory        48945
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     23
proof            (modus-ponens tm-303 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48945.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-303, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48946
in-theory        48946
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> (F or E))) and ((B -> (C -> (B and C))) and A)))
theorem-size     29
proof            (modus-ponens tm-300 tm-622 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48946.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> (E -> (F or E))) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-622, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-48947
in-theory        48947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-270 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48947.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-270, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48948
in-theory        48948
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> (E -> (F or E))) and (((B and C) -> C) and A)))
theorem-size     25
proof            (modus-ponens tm-267 tm-622 ((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48948.        ((A or (((B and C) -> C) and A)) -> ((D -> (E -> (F or E))) and (((B and C) -> C) and A))), M:tm-267, m:tm-622, u:((Am (and (-> (and A B) B) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-48949
in-theory        48949
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-239 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48949.        ((A -> (((B and C) -> B) and A)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-239, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48950
in-theory        48950
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> (E -> (F or E))) and (((B and C) -> B) and A)))
theorem-size     25
proof            (modus-ponens tm-236 tm-622 ((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48950.        ((A or (((B and C) -> B) and A)) -> ((D -> (E -> (F or E))) and (((B and C) -> B) and A))), M:tm-236, m:tm-622, u:((Am (and (-> (and A B) A) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-48951
in-theory        48951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> (H or G))) and E)))
theorem-size     29
proof            (modus-ponens tm-210 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48951.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> (G -> (H or G))) and E))), M:tm-210, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48952
in-theory        48952
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> (G or F))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     41
proof            (modus-ponens tm-207 tm-622 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (or Dm Cm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48952.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> (F -> (G or F))) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-622, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (or Dm Cm))) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-48953
in-theory        48953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     21
proof            (modus-ponens tm-183 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48953.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-183, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48954
in-theory        48954
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> (F or E))) and ((B -> (C -> B)) and A)))
theorem-size     25
proof            (modus-ponens tm-180 tm-622 ((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48954.        ((A or ((B -> (C -> B)) and A)) -> ((D -> (E -> (F or E))) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-622, u:((Am (and (-> A (-> B A)) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-48955
in-theory        48955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-157 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48955.        ((A -> ((B and C) -> C)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-157, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48956
in-theory        48956
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> (E -> (F or E))) and ((B and C) -> C)))
theorem-size     21
proof            (modus-ponens tm-154 tm-622 ((Am (-> (and A B) B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48956.        ((A or ((B and C) -> C)) -> ((D -> (E -> (F or E))) and ((B and C) -> C))), M:tm-154, m:tm-622, u:((Am (-> (and A B) B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> (and A B) B))))
================================================================
tm-name          tm-48957
in-theory        48957
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     27
proof            (modus-ponens tm-147 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48957.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-147, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48958
in-theory        48958
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> (F or E))) and ((A and (B -> C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-144 tm-622 ((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48958.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> (E -> (F or E))) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-622, u:((Am (-> (and A (-> B C)) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-48959
in-theory        48959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-134 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48959.        ((A -> ((B and C) -> B)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-134, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48960
in-theory        48960
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> (E -> (F or E))) and ((B and C) -> B)))
theorem-size     21
proof            (modus-ponens tm-131 tm-622 ((Am (-> (and A B) A)) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48960.        ((A or ((B and C) -> B)) -> ((D -> (E -> (F or E))) and ((B and C) -> B))), M:tm-131, m:tm-622, u:((Am (-> (and A B) A)) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> (and A B) A))))
================================================================
tm-name          tm-48961
in-theory        48961
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     27
proof            (modus-ponens tm-125 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48961.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-125, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48962
in-theory        48962
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> (F or E))) and (((A -> B) and C) -> B)))
theorem-size     31
proof            (modus-ponens tm-122 tm-622 ((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48962.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> (E -> (F or E))) and (((A -> B) and C) -> B))), M:tm-122, m:tm-622, u:((Am (-> (and (-> A B) C) B)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-48963
in-theory        48963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (H or G))) and E)))
theorem-size     27
proof            (modus-ponens tm-113 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48963.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> (G -> (H or G))) and E))), M:tm-113, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48964
in-theory        48964
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> (G or F))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-110 tm-622 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48964.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> (F -> (G or F))) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-622, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-48965
in-theory        48965
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     31
proof            (modus-ponens tm-105 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48965.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-105, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48966
in-theory        48966
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> (F or E))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-102 tm-622 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48966.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> (E -> (F or E))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-622, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-48967
in-theory        48967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> (F or E))) and C)))
theorem-size     19
proof            (modus-ponens tm-95 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48967.        (((A -> B) -> (A -> A)) and (C -> ((D -> (E -> (F or E))) and C))), M:tm-95, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48968
in-theory        48968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> (D -> (E or D))) and (A -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-622 ((Am (-> A A)) (B (and (-> Bm (-> Cm (or Dm Cm))) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48968.        (((A -> B) or (A -> A)) -> ((C -> (D -> (E or D))) and (A -> A))), M:tm-92, m:tm-622, u:((Am (-> A A)) (B (and (-> Bm (-> Cm (or Dm Cm))) (-> A A))))
================================================================
tm-name          tm-48969
in-theory        48969
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> (E or D))) and A)))
theorem-size     13
proof            (modus-ponens tm-84 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48969.        (A -> (B -> ((C -> (D -> (E or D))) and A))), M:tm-84, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-48970
in-theory        48970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     19
proof            (modus-ponens tm-83 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48970.        ((A -> (B -> (C -> B))) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-83, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48971
in-theory        48971
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> (E -> (F or E))) and (B -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-80 tm-622 ((Am (-> A (-> B A))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48971.        ((A or (B -> (C -> B))) -> ((D -> (E -> (F or E))) and (B -> (C -> B)))), M:tm-80, m:tm-622, u:((Am (-> A (-> B A))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (-> B A)))))
================================================================
tm-name          tm-48972
in-theory        48972
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> (D -> (E or D))) and B)))
theorem-size     17
proof            (modus-ponens tm-76 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-10 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48972.        (((not (not A)) -> A) and (B -> ((C -> (D -> (E or D))) and B))), M:tm-76, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48973
in-theory        48973
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> (C -> (D or C))) and A))
theorem-size     15
proof            (modus-ponens tm-73 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48973.        (((not (not A)) or A) -> ((B -> (C -> (D or C))) and A)), M:tm-73, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-48974
in-theory        48974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> (F or E))) and C)))
theorem-size     23
proof            (modus-ponens tm-69 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48974.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> (E -> (F or E))) and C))), M:tm-69, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48975
in-theory        48975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> (E or D))) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-66 tm-622 ((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48975.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> (D -> (E or D))) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-622, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-48976
in-theory        48976
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     25
proof            (modus-ponens tm-54 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48976.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-54, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48977
in-theory        48977
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (F or E))) and ((B -> C) -> ((A or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-51 tm-622 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48977.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> (E -> (F or E))) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-622, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-48978
in-theory        48978
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> (D -> (E or D))) and (B or A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-622 ((Am (or A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48978.        ((A or (B or A)) -> ((C -> (D -> (E or D))) and (B or A))), M:tm-50, m:tm-622, u:((Am (or A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (or A B))))
================================================================
tm-name          tm-48979
in-theory        48979
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> (D -> (E or D))) and (A or B)))
theorem-size     17
proof            (modus-ponens tm-49 tm-622 ((Am (or A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48979.        ((A or (A or B)) -> ((C -> (D -> (E or D))) and (A or B))), M:tm-49, m:tm-622, u:((Am (or A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (or A B))))
================================================================
tm-name          tm-48980
in-theory        48980
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> (D -> (E or D))) and (B -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-48 tm-622 ((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48980.        ((A or (B -> (A and B))) -> ((C -> (D -> (E or D))) and (B -> (A and B)))), M:tm-48, m:tm-622, u:((Am (-> A (and B A))) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A (and B A)))))
================================================================
tm-name          tm-48981
in-theory        48981
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (D -> (E or D))) and B))
theorem-size     15
proof            (modus-ponens tm-47 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48981.        (((A and B) or B) -> ((C -> (D -> (E or D))) and B)), M:tm-47, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-48982
in-theory        48982
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (D -> (E or D))) and A))
theorem-size     15
proof            (modus-ponens tm-46 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48982.        (((A and B) or A) -> ((C -> (D -> (E or D))) and A)), M:tm-46, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-48983
in-theory        48983
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (F or E))) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-45 tm-622 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48983.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (F or E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-622, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-48984
in-theory        48984
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (D -> (E or D))) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-622 ((Am (-> A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48984.        ((A or (B -> A)) -> ((C -> (D -> (E or D))) and (B -> A))), M:tm-44, m:tm-622, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A B))))
================================================================
tm-name          tm-48985
in-theory        48985
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> (E -> (F or E))) and C)))
theorem-size     17
proof            (modus-ponens tm-42 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48985.        ((A -> (B or A)) and (C -> ((D -> (E -> (F or E))) and C))), M:tm-42, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48986
in-theory        48986
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> (E -> (F or E))) and C)))
theorem-size     17
proof            (modus-ponens tm-32 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48986.        ((A -> (A or B)) and (C -> ((D -> (E -> (F or E))) and C))), M:tm-32, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48987
in-theory        48987
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> (C -> (D or C))) and A)))
theorem-size     13
proof            (modus-ponens tm-24 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48987.        (A -> (A and ((B -> (C -> (D or C))) and A))), M:tm-24, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-48988
in-theory        48988
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (F or E))) and C)))
theorem-size     19
proof            (modus-ponens tm-23 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48988.        ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (F or E))) and C))), M:tm-23, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48989
in-theory        48989
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> (E -> (F or E))) and C)))
theorem-size     17
proof            (modus-ponens tm-22 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48989.        (((A and B) -> B) and (C -> ((D -> (E -> (F or E))) and C))), M:tm-22, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48990
in-theory        48990
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> (E -> (F or E))) and C)))
theorem-size     17
proof            (modus-ponens tm-21 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48990.        (((A and B) -> A) and (C -> ((D -> (E -> (F or E))) and C))), M:tm-21, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48991
in-theory        48991
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     25
proof            (modus-ponens tm-20 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48991.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-20, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48992
in-theory        48992
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> (E -> (F or E))) and C)))
theorem-size     17
proof            (modus-ponens tm-19 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48992.        ((A -> (B -> A)) and (C -> ((D -> (E -> (F or E))) and C))), M:tm-19, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48993
in-theory        48993
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> (D or C))) and A))) -> (not A))
theorem-size     15
proof            (modus-ponens tm-9 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-9 tm-5 tm-1 tm-7)
proof-size       61
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48993.        ((A -> (not ((B -> (C -> (D or C))) and A))) -> (not A)), M:tm-9, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-48994
in-theory        48994
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (C or B))) and D) -> E) -> ((D or ((A -> (B -> (C or B))) and D)) -> E))
theorem-size     25
proof            (modus-ponens tm-8 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48994.        ((((A -> (B -> (C or B))) and D) -> E) -> ((D or ((A -> (B -> (C or B))) and D)) -> E)), M:tm-8, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-48995
in-theory        48995
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> (D -> (E or D))) and B)))
theorem-size     13
proof            (modus-ponens tm-7 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-7 tm-5 tm-1)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48995.        (A or (B -> ((C -> (D -> (E or D))) and B))), M:tm-7, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48996
in-theory        48996
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-6 tm-5 tm-1 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48996.        ((A -> ((B -> (C -> (D or C))) and A)) or E), M:tm-6, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48997
in-theory        48997
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> (D -> (E or D))) and B)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       57
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48997.        (A -> ((B -> ((C -> (D -> (E or D))) and B)) and A)), M:tm-5, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48998
in-theory        48998
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> (D -> (E or D))) and B)))
theorem-size     13
proof            (modus-ponens tm-1 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-1 tm-5 tm-7)
proof-size       53
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-48998.        (A -> (B -> ((C -> (D -> (E or D))) and B))), M:tm-1, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-48999
in-theory        48999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or ((B -> D) -> ((A or B) -> D))))
theorem-size     15
proof            (modus-ponens tm-623 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-48999.        ((A -> B) -> (C or ((B -> D) -> ((A or B) -> D)))), M:tm-623, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-49000
in-theory        49000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or ((A -> (not B)) -> (not A))))
theorem-size     13
proof            (modus-ponens tm-623 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-49000.        ((A -> B) -> (C or ((A -> (not B)) -> (not A)))), M:tm-623, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-49001
in-theory        49001
times-derived    1
----------------------------------------------------------------
theorem          ((not (not A)) -> (B or A))
theorem-size     7
proof            (modus-ponens tm-623 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-2 tm-1 tm-7 tm-10)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-49001.        ((not (not A)) -> (B or A)), M:tm-623, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-49002
in-theory        49002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or (A -> A)))
theorem-size     9
proof            (modus-ponens tm-623 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-49002.        ((A -> B) -> (C or (A -> A))), M:tm-623, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-49003
in-theory        49003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (D or ((A -> (B -> C)) -> (A -> C))))
theorem-size     21
proof            (modus-ponens tm-623 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-49003.        (((A -> (B -> C)) -> (A -> B)) -> (D or ((A -> (B -> C)) -> (A -> C)))), M:tm-623, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-49004
in-theory        49004
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> (D or (((A -> B) and C) -> B)))
theorem-size     17
proof            (modus-ponens tm-623 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-49004.        ((((A -> B) and C) -> A) -> (D or (((A -> B) and C) -> B))), M:tm-623, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-49005
in-theory        49005
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> (D or ((A and (B -> C)) -> C)))
theorem-size     17
proof            (modus-ponens tm-623 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-49005.        (((A and (B -> C)) -> B) -> (D or ((A and (B -> C)) -> C))), M:tm-623, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-49006
in-theory        49006
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (D -> C)) and A)))
theorem-size     11
proof            (modus-ponens tm-623 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-49006.        (A -> (B or ((C -> (D -> C)) and A))), M:tm-623, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-49007
in-theory        49007
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))
theorem-size     19
proof            (modus-ponens tm-623 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-49007.        (A -> (B or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))), M:tm-623, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-49008
in-theory        49008
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((C and D) -> C) and A)))
theorem-size     11
proof            (modus-ponens tm-623 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-3)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-49008.        (A -> (B or (((C and D) -> C) and A))), M:tm-623, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-49009
in-theory        49009
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((C and D) -> D) and A)))
theorem-size     11
proof            (modus-ponens tm-623 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-4)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-49009.        (A -> (B or (((C and D) -> D) and A))), M:tm-623, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-49010
in-theory        49010
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (D -> (C and D))) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-49010.        (A -> (B or ((C -> (D -> (C and D))) and A))), M:tm-623, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-49011
in-theory        49011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or (A -> (A and B))))
theorem-size     11
proof            (modus-ponens tm-623 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-49011.        ((A -> B) -> (C or (A -> (A and B)))), M:tm-623, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-49012
in-theory        49012
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (C or D)) and A)))
theorem-size     11
proof            (modus-ponens tm-623 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-49012.        (A -> (B or ((C -> (C or D)) and A))), M:tm-623, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-49013
in-theory        49013
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (D or C)) and A)))
theorem-size     11
proof            (modus-ponens tm-623 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-49013.        (A -> (B or ((C -> (D or C)) and A))), M:tm-623, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-49014
in-theory        49014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (D or ((B or (A -> B)) -> C)))
theorem-size     15
proof            (modus-ponens tm-623 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-49014.        (((A -> B) -> C) -> (D or ((B or (A -> B)) -> C))), M:tm-623, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-49015
in-theory        49015
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     27
proof            (modus-ponens tm-623 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-49015.        ((((A -> B) -> (A -> C)) -> D) -> (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-623, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-49016
in-theory        49016
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or (((A and D) or A) -> B)))
theorem-size     13
proof            (modus-ponens tm-623 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-49016.        ((A -> B) -> (C or (((A and D) or A) -> B))), M:tm-623, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-49017
in-theory        49017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or (((D and A) or A) -> B)))
theorem-size     13
proof            (modus-ponens tm-623 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49017.        ((A -> B) -> (C or (((D and A) or A) -> B))), M:tm-623, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-49018
in-theory        49018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> (D or ((B or (A -> (B and A))) -> C)))
theorem-size     19
proof            (modus-ponens tm-623 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-49018.        (((A -> (B and A)) -> C) -> (D or ((B or (A -> (B and A))) -> C))), M:tm-623, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-49019
in-theory        49019
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D or ((A or (A or B)) -> C)))
theorem-size     15
proof            (modus-ponens tm-623 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-49019.        (((A or B) -> C) -> (D or ((A or (A or B)) -> C))), M:tm-623, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-49020
in-theory        49020
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> (D or ((B or (A or B)) -> C)))
theorem-size     15
proof            (modus-ponens tm-623 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-49020.        (((A or B) -> C) -> (D or ((B or (A or B)) -> C))), M:tm-623, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-49021
in-theory        49021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> (E or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     29
proof            (modus-ponens tm-623 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49021.        ((((A -> B) -> ((C or A) -> B)) -> D) -> (E or (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-623, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-49022
in-theory        49022
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and A)))
theorem-size     19
proof            (modus-ponens tm-623 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-8)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-49022.        (A -> (B or (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and A))), M:tm-623, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-49023
in-theory        49023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (B -> C)) -> (D or ((A -> B) -> ((A or B) -> C))))
theorem-size     19
proof            (modus-ponens tm-623 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-49023.        (((A -> B) -> (B -> C)) -> (D or ((A -> B) -> ((A or B) -> C)))), M:tm-623, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-49024
in-theory        49024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> A))) -> (C or (not A)))
theorem-size     11
proof            (modus-ponens tm-623 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-49024.        ((A -> (not (B -> A))) -> (C or (not A))), M:tm-623, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-49025
in-theory        49025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (D or (not (A -> (B -> C)))))
theorem-size     23
proof            (modus-ponens tm-623 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-49025.        (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (D or (not (A -> (B -> C))))), M:tm-623, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-49026
in-theory        49026
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not A)) -> (C or (not (A and B))))
theorem-size     13
proof            (modus-ponens tm-623 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-49026.        (((A and B) -> (not A)) -> (C or (not (A and B)))), M:tm-623, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-49027
in-theory        49027
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (not B)) -> (C or (not (A and B))))
theorem-size     13
proof            (modus-ponens tm-623 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49027.        (((A and B) -> (not B)) -> (C or (not (A and B)))), M:tm-623, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-49028
in-theory        49028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (A and B)))) -> (C or (not A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-5)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-49028.        ((A -> (not (B -> (A and B)))) -> (C or (not A))), M:tm-623, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-49029
in-theory        49029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (A or B))) -> (C or (not A)))
theorem-size     11
proof            (modus-ponens tm-623 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-49029.        ((A -> (not (A or B))) -> (C or (not A))), M:tm-623, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-49030
in-theory        49030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B or A))) -> (C or (not A)))
theorem-size     11
proof            (modus-ponens tm-623 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-49030.        ((A -> (not (B or A))) -> (C or (not A))), M:tm-623, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-49031
in-theory        49031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (D or (not (A -> B))))
theorem-size     21
proof            (modus-ponens tm-623 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49031.        (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (D or (not (A -> B)))), M:tm-623, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-49032
in-theory        49032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (C or (not (A -> B))))
theorem-size     19
proof            (modus-ponens tm-623 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-49032.        (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (C or (not (A -> B)))), M:tm-623, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-49033
in-theory        49033
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> C) -> (D or (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))
theorem-size     25
proof            (modus-ponens tm-623 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-9)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-49033.        ((((A -> (not B)) -> (not A)) -> C) -> (D or (((A -> B) or ((A -> (not B)) -> (not A))) -> C))), M:tm-623, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-49034
in-theory        49034
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((C -> D) -> ((C -> (not D)) -> (not C))) and A)))
theorem-size     17
proof            (modus-ponens tm-623 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-9)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-49034.        (A -> (B or (((C -> D) -> ((C -> (not D)) -> (not C))) and A))), M:tm-623, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-49035
in-theory        49035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (not B))) -> (C or ((A -> B) -> (not A))))
theorem-size     17
proof            (modus-ponens tm-623 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-49035.        (((A -> B) -> (A -> (not B))) -> (C or ((A -> B) -> (not A)))), M:tm-623, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-49036
in-theory        49036
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not A)) -> (B or (not (not (not A)))))
theorem-size     13
proof            (modus-ponens tm-623 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-10)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-49036.        (((not (not A)) -> (not A)) -> (B or (not (not (not A))))), M:tm-623, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-49037
in-theory        49037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or (((not (not A)) or A) -> B)))
theorem-size     13
proof            (modus-ponens tm-623 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-10)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-49037.        ((A -> B) -> (C or (((not (not A)) or A) -> B))), M:tm-623, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-49038
in-theory        49038
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((not (not C)) -> C) and A)))
theorem-size     11
proof            (modus-ponens tm-623 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-10)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-49038.        (A -> (B or (((not (not C)) -> C) and A))), M:tm-623, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-49039
in-theory        49039
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) -> A) -> (C or ((not (not (A -> B))) -> B)))
theorem-size     17
proof            (modus-ponens tm-623 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-49039.        (((not (not (A -> B))) -> A) -> (C or ((not (not (A -> B))) -> B))), M:tm-623, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-49040
in-theory        49040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> B)))) -> (D or (not A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-49040.        ((A -> (not (B -> (C -> B)))) -> (D or (not A))), M:tm-623, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-49041
in-theory        49041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> (D or ((E or (A -> (B -> A))) -> C)))
theorem-size     19
proof            (modus-ponens tm-623 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-49041.        (((A -> (B -> A)) -> C) -> (D or ((E or (A -> (B -> A))) -> C))), M:tm-623, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-49042
in-theory        49042
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (D -> (E -> D))) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-49042.        (A -> (B or ((C -> (D -> (E -> D))) and A))), M:tm-623, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-49043
in-theory        49043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or (A -> (D -> B))))
theorem-size     11
proof            (modus-ponens tm-623 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-49043.        ((A -> B) -> (C or (A -> (D -> B)))), M:tm-623, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-49044
in-theory        49044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (D or (A -> (B -> C))))
theorem-size     13
proof            (modus-ponens tm-623 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-49044.        ((A -> (B -> C)) -> (D or (A -> (B -> C)))), M:tm-623, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-49045
in-theory        49045
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (C or (A and B)))
theorem-size     9
proof            (modus-ponens tm-623 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-3)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-49045.        ((A and B) -> (C or (A and B))), M:tm-623, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-49046
in-theory        49046
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (C or (A -> B)))
theorem-size     9
proof            (modus-ponens tm-623 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49046.        ((A -> B) -> (C or (A -> B))), M:tm-623, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-49047
in-theory        49047
times-derived    1
----------------------------------------------------------------
theorem          ((not (not A)) -> (B or (not (not A))))
theorem-size     9
proof            (modus-ponens tm-623 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-10)
proof-size       85
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-49047.        ((not (not A)) -> (B or (not (not A)))), M:tm-623, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-49048
in-theory        49048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> A))) -> (C or (not (A -> B))))
theorem-size     15
proof            (modus-ponens tm-623 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-49048.        (((A -> B) -> (not (A -> A))) -> (C or (not (A -> B)))), M:tm-623, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-49049
in-theory        49049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> B) -> (C or (((A -> D) or (A -> A)) -> B)))
theorem-size     17
proof            (modus-ponens tm-623 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-49049.        (((A -> A) -> B) -> (C or (((A -> D) or (A -> A)) -> B))), M:tm-623, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-49050
in-theory        49050
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((C -> D) -> (C -> C)) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-49050.        (A -> (B or (((C -> D) -> (C -> C)) and A))), M:tm-623, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-49051
in-theory        49051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> (C or ((A -> B) -> A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-49051.        (((A -> B) -> A) -> (C or ((A -> B) -> A))), M:tm-623, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-49052
in-theory        49052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> A) -> C)) -> (D or (A -> C)))
theorem-size     13
proof            (modus-ponens tm-623 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-49052.        ((A -> ((B -> A) -> C)) -> (D or (A -> C))), M:tm-623, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-49053
in-theory        49053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A -> B)) -> (C or (A -> B)))
theorem-size     11
proof            (modus-ponens tm-623 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-49053.        ((A -> (A -> B)) -> (C or (A -> B))), M:tm-623, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-49054
in-theory        49054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (D or ((A -> (B -> C)) -> (A -> B))))
theorem-size     21
proof            (modus-ponens tm-623 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-49054.        (((A -> (B -> C)) -> (A -> B)) -> (D or ((A -> (B -> C)) -> (A -> B)))), M:tm-623, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-49055
in-theory        49055
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (D or (not ((A -> (B -> C)) -> (A -> B)))))
theorem-size     33
proof            (modus-ponens tm-623 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-49055.        ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (D or (not ((A -> (B -> C)) -> (A -> B))))), M:tm-623, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-49056
in-theory        49056
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> D) -> (E or ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))
theorem-size     35
proof            (modus-ponens tm-623 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-49056.        ((((A -> (B -> C)) -> (A -> C)) -> D) -> (E or ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))), M:tm-623, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-49057
in-theory        49057
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and A)))
theorem-size     25
proof            (modus-ponens tm-623 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-49057.        (A -> (B or ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and A))), M:tm-623, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-49058
in-theory        49058
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (D or (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-623 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-49058.        ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (D or (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))), M:tm-623, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-49059
in-theory        49059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (E or ((A -> (B -> C)) -> D)))
theorem-size     25
proof            (modus-ponens tm-623 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-49059.        (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> (E or ((A -> (B -> C)) -> D))), M:tm-623, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-49060
in-theory        49060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (E or (not A)))
theorem-size     21
proof            (modus-ponens tm-623 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-49060.        ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (E or (not A))), M:tm-623, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-49061
in-theory        49061
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (E or ((F or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))
theorem-size     35
proof            (modus-ponens tm-623 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-49061.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (E or ((F or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))), M:tm-623, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-49062
in-theory        49062
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)))
theorem-size     21
proof            (modus-ponens tm-623 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-49062.        (A -> (B or ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))), M:tm-623, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-49063
in-theory        49063
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> D))) -> (E or (A -> ((B -> C) -> (B -> D)))))
theorem-size     19
proof            (modus-ponens tm-623 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-49063.        ((A -> (B -> (C -> D))) -> (E or (A -> ((B -> C) -> (B -> D))))), M:tm-623, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-49064
in-theory        49064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and A) -> (C or B))
theorem-size     9
proof            (modus-ponens tm-623 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-2 tm-1 tm-7 tm-3 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-49064.        (((A -> B) and A) -> (C or B)), M:tm-623, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-49065
in-theory        49065
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) and D) -> (E or C))
theorem-size     13
proof            (modus-ponens tm-623 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-7 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-49065.        ((((A -> (B -> A)) -> C) and D) -> (E or C)), M:tm-623, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-49066
in-theory        49066
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (F or D))
theorem-size     21
proof            (modus-ponens tm-623 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-2 tm-1 tm-7 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-49066.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> (F or D)), M:tm-623, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-49067
in-theory        49067
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> A) and C) -> (A -> B)) -> (D or ((((A -> B) -> A) and C) -> B)))
theorem-size     23
proof            (modus-ponens tm-623 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-49067.        (((((A -> B) -> A) and C) -> (A -> B)) -> (D or ((((A -> B) -> A) and C) -> B))), M:tm-623, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-49068
in-theory        49068
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> (D or (((A -> B) and C) -> A)))
theorem-size     17
proof            (modus-ponens tm-623 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-49068.        ((((A -> B) and C) -> A) -> (D or (((A -> B) and C) -> A))), M:tm-623, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-49069
in-theory        49069
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (D or (not (((A -> B) and C) -> A))))
theorem-size     27
proof            (modus-ponens tm-623 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-49069.        (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (D or (not (((A -> B) and C) -> A)))), M:tm-623, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-49070
in-theory        49070
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> D) -> (E or (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))
theorem-size     29
proof            (modus-ponens tm-623 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-49070.        (((((A -> B) and C) -> B) -> D) -> (E or (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))), M:tm-623, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-49071
in-theory        49071
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and A)))
theorem-size     21
proof            (modus-ponens tm-623 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-49071.        (A -> (B or (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and A))), M:tm-623, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-49072
in-theory        49072
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (D or ((((A -> B) and C) -> A) -> B)))
theorem-size     25
proof            (modus-ponens tm-623 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-49072.        (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> (D or ((((A -> B) and C) -> A) -> B))), M:tm-623, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-49073
in-theory        49073
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) and D) -> (E or C))
theorem-size     13
proof            (modus-ponens tm-623 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-7 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-49073.        (((((A and B) -> A) -> C) and D) -> (E or C)), M:tm-623, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-49074
in-theory        49074
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A -> C)) -> (D or ((A and B) -> C)))
theorem-size     15
proof            (modus-ponens tm-623 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-49074.        (((A and B) -> (A -> C)) -> (D or ((A and B) -> C))), M:tm-623, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-49075
in-theory        49075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B and C) -> B))) -> (D or (not A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-3)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-49075.        ((A -> (not ((B and C) -> B))) -> (D or (not A))), M:tm-623, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-49076
in-theory        49076
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> (D or ((E or ((A and B) -> A)) -> C)))
theorem-size     19
proof            (modus-ponens tm-623 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-49076.        ((((A and B) -> A) -> C) -> (D or ((E or ((A and B) -> A)) -> C))), M:tm-623, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-49077
in-theory        49077
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> ((D and E) -> D)) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-49077.        (A -> (B or ((C -> ((D and E) -> D)) and A))), M:tm-623, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-49078
in-theory        49078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> (D or (A -> B)))
theorem-size     11
proof            (modus-ponens tm-623 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-3)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-49078.        ((A -> (B and C)) -> (D or (A -> B))), M:tm-623, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-49079
in-theory        49079
times-derived    1
----------------------------------------------------------------
theorem          ((A and (A -> B)) -> (C or B))
theorem-size     9
proof            (modus-ponens tm-623 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-7 tm-4 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-49079.        ((A and (A -> B)) -> (C or B)), M:tm-623, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-49080
in-theory        49080
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> B)) -> D)) -> (E or D))
theorem-size     13
proof            (modus-ponens tm-623 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-7 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-49080.        ((A and ((B -> (C -> B)) -> D)) -> (E or D)), M:tm-623, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-49081
in-theory        49081
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (F or E))
theorem-size     21
proof            (modus-ponens tm-623 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-2 tm-1 tm-7 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-49081.        ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> (F or E)), M:tm-623, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-49082
in-theory        49082
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> B) -> D)) -> (E or D))
theorem-size     13
proof            (modus-ponens tm-623 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-7 tm-4 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-49082.        ((A and (((B and C) -> B) -> D)) -> (E or D)), M:tm-623, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-49083
in-theory        49083
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> B)) -> (B -> C)) -> (D or ((A and ((B -> C) -> B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-623 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-49083.        (((A and ((B -> C) -> B)) -> (B -> C)) -> (D or ((A and ((B -> C) -> B)) -> C))), M:tm-623, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-49084
in-theory        49084
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> (D or ((A and (B -> C)) -> B)))
theorem-size     17
proof            (modus-ponens tm-623 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-49084.        (((A and (B -> C)) -> B) -> (D or ((A and (B -> C)) -> B))), M:tm-623, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-49085
in-theory        49085
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (D or (not ((A and (B -> C)) -> B))))
theorem-size     27
proof            (modus-ponens tm-623 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-49085.        ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (D or (not ((A and (B -> C)) -> B)))), M:tm-623, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-49086
in-theory        49086
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> D) -> (E or ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))
theorem-size     29
proof            (modus-ponens tm-623 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-49086.        ((((A and (B -> C)) -> C) -> D) -> (E or ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))), M:tm-623, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-49087
in-theory        49087
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and A)))
theorem-size     21
proof            (modus-ponens tm-623 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-49087.        (A -> (B or ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and A))), M:tm-623, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-49088
in-theory        49088
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (D or (((A and (B -> C)) -> B) -> C)))
theorem-size     25
proof            (modus-ponens tm-623 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-49088.        ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (D or (((A and (B -> C)) -> B) -> C))), M:tm-623, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-49089
in-theory        49089
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B and C) -> C) -> D)) -> (E or D))
theorem-size     13
proof            (modus-ponens tm-623 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-7 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-49089.        ((A and (((B and C) -> C) -> D)) -> (E or D)), M:tm-623, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-49090
in-theory        49090
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) and D) -> (E or C))
theorem-size     13
proof            (modus-ponens tm-623 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-7 tm-3 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-49090.        (((((A and B) -> B) -> C) and D) -> (E or C)), M:tm-623, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-49091
in-theory        49091
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (B -> C)) -> (D or ((A and B) -> C)))
theorem-size     15
proof            (modus-ponens tm-623 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-49091.        (((A and B) -> (B -> C)) -> (D or ((A and B) -> C))), M:tm-623, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-49092
in-theory        49092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B and C) -> C))) -> (D or (not A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-4)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-49092.        ((A -> (not ((B and C) -> C))) -> (D or (not A))), M:tm-623, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-49093
in-theory        49093
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> (D or ((E or ((A and B) -> B)) -> C)))
theorem-size     19
proof            (modus-ponens tm-623 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-49093.        ((((A and B) -> B) -> C) -> (D or ((E or ((A and B) -> B)) -> C))), M:tm-623, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-49094
in-theory        49094
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> ((D and E) -> E)) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-4)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-49094.        (A -> (B or ((C -> ((D and E) -> E)) and A))), M:tm-623, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-49095
in-theory        49095
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B and C)) -> (D or (A -> C)))
theorem-size     11
proof            (modus-ponens tm-623 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-4)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-49095.        ((A -> (B and C)) -> (D or (A -> C))), M:tm-623, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-49096
in-theory        49096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> B)) and A))) -> (D or (not A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-49096.        ((A -> (not ((B -> (C -> B)) and A))) -> (D or (not A))), M:tm-623, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-49097
in-theory        49097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and C) -> D) -> (E or ((C or ((A -> (B -> A)) and C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-623 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-49097.        ((((A -> (B -> A)) and C) -> D) -> (E or ((C or ((A -> (B -> A)) and C)) -> D))), M:tm-623, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-49098
in-theory        49098
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> ((D -> (E -> D)) and C)) and A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-49098.        (A -> (B or ((C -> ((D -> (E -> D)) and C)) and A))), M:tm-623, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-49099
in-theory        49099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (E or (not A)))
theorem-size     23
proof            (modus-ponens tm-623 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-5)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-49099.        ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (E or (not A))), M:tm-623, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-49100
in-theory        49100
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (F or ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))
theorem-size     39
proof            (modus-ponens tm-623 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-49100.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> (F or ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))), M:tm-623, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-49101
in-theory        49101
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and A)))
theorem-size     23
proof            (modus-ponens tm-623 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-49101.        (A -> (B or ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and A))), M:tm-623, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-49102
in-theory        49102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> B) and A))) -> (D or (not A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-5 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-49102.        ((A -> (not (((B and C) -> B) and A))) -> (D or (not A))), M:tm-623, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-49103
in-theory        49103
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and C) -> D) -> (E or ((C or (((A and B) -> A) and C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-623 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-49103.        (((((A and B) -> A) and C) -> D) -> (E or ((C or (((A and B) -> A) and C)) -> D))), M:tm-623, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-49104
in-theory        49104
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (((D and E) -> D) and C)) and A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-49104.        (A -> (B or ((C -> (((D and E) -> D) and C)) and A))), M:tm-623, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-49105
in-theory        49105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (((B and C) -> C) and A))) -> (D or (not A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-5 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-49105.        ((A -> (not (((B and C) -> C) and A))) -> (D or (not A))), M:tm-623, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-49106
in-theory        49106
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and C) -> D) -> (E or ((C or (((A and B) -> B) and C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-623 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-49106.        (((((A and B) -> B) and C) -> D) -> (E or ((C or (((A and B) -> B) and C)) -> D))), M:tm-623, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-49107
in-theory        49107
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (((D and E) -> E) and C)) and A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-49107.        (A -> (B or ((C -> (((D and E) -> E) and C)) and A))), M:tm-623, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-49108
in-theory        49108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (D or (not A)))
theorem-size     17
proof            (modus-ponens tm-623 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-49108.        ((A -> (not ((B -> (C -> (B and C))) and A))) -> (D or (not A))), M:tm-623, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-49109
in-theory        49109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and C) -> D) -> (E or ((C or ((A -> (B -> (A and B))) and C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-623 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-49109.        ((((A -> (B -> (A and B))) and C) -> D) -> (E or ((C or ((A -> (B -> (A and B))) and C)) -> D))), M:tm-623, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-49110
in-theory        49110
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> ((D -> (E -> (D and E))) and C)) and A)))
theorem-size     17
proof            (modus-ponens tm-623 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-49110.        (A -> (B or ((C -> ((D -> (E -> (D and E))) and C)) and A))), M:tm-623, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-49111
in-theory        49111
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and (C -> A))))
theorem-size     9
proof            (modus-ponens tm-623 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-49111.        (A -> (B or (A and (C -> A)))), M:tm-623, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-49112
in-theory        49112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (D or ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))
theorem-size     21
proof            (modus-ponens tm-623 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-49112.        ((A -> (B -> C)) -> (D or ((A -> (B -> C)) and ((A -> B) -> (A -> C))))), M:tm-623, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-49113
in-theory        49113
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (C or ((A and B) and A)))
theorem-size     11
proof            (modus-ponens tm-623 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-49113.        ((A and B) -> (C or ((A and B) and A))), M:tm-623, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-49114
in-theory        49114
times-derived    1
----------------------------------------------------------------
theorem          ((A and B) -> (C or ((A and B) and B)))
theorem-size     11
proof            (modus-ponens tm-623 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-49114.        ((A and B) -> (C or ((A and B) and B))), M:tm-623, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-49115
in-theory        49115
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and (C -> (A and C)))))
theorem-size     11
proof            (modus-ponens tm-623 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-49115.        (A -> (B or (A and (C -> (A and C))))), M:tm-623, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-49116
in-theory        49116
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and (A or C))))
theorem-size     9
proof            (modus-ponens tm-623 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-49116.        (A -> (B or (A and (A or C)))), M:tm-623, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-49117
in-theory        49117
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and (C or A))))
theorem-size     9
proof            (modus-ponens tm-623 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-49117.        (A -> (B or (A and (C or A)))), M:tm-623, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-49118
in-theory        49118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or ((A -> B) and ((B -> D) -> ((A or B) -> D)))))
theorem-size     19
proof            (modus-ponens tm-623 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49118.        ((A -> B) -> (C or ((A -> B) and ((B -> D) -> ((A or B) -> D))))), M:tm-623, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-49119
in-theory        49119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or ((A -> B) and ((A -> (not B)) -> (not A)))))
theorem-size     17
proof            (modus-ponens tm-623 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-49119.        ((A -> B) -> (C or ((A -> B) and ((A -> (not B)) -> (not A))))), M:tm-623, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-49120
in-theory        49120
times-derived    1
----------------------------------------------------------------
theorem          ((not (not A)) -> (B or ((not (not A)) and A)))
theorem-size     11
proof            (modus-ponens tm-623 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-10)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-49120.        ((not (not A)) -> (B or ((not (not A)) and A))), M:tm-623, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-49121
in-theory        49121
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and (C -> (D -> C)))))
theorem-size     11
proof            (modus-ponens tm-623 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-49121.        (A -> (B or (A and (C -> (D -> C))))), M:tm-623, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-49122
in-theory        49122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or ((A -> B) and (A -> A))))
theorem-size     13
proof            (modus-ponens tm-623 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-49122.        ((A -> B) -> (C or ((A -> B) and (A -> A)))), M:tm-623, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-49123
in-theory        49123
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> B)) -> (D or (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     31
proof            (modus-ponens tm-623 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-49123.        (((A -> (B -> C)) -> (A -> B)) -> (D or (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))), M:tm-623, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-49124
in-theory        49124
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     19
proof            (modus-ponens tm-623 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-49124.        (A -> (B or (A and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-623, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-49125
in-theory        49125
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) -> A) -> (D or ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))
theorem-size     25
proof            (modus-ponens tm-623 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-49125.        ((((A -> B) and C) -> A) -> (D or ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))), M:tm-623, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-49126
in-theory        49126
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and ((C and D) -> C))))
theorem-size     11
proof            (modus-ponens tm-623 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-3)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-49126.        (A -> (B or (A and ((C and D) -> C)))), M:tm-623, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-49127
in-theory        49127
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) -> B) -> (D or (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))
theorem-size     25
proof            (modus-ponens tm-623 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-49127.        (((A and (B -> C)) -> B) -> (D or (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))), M:tm-623, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-49128
in-theory        49128
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and ((C and D) -> D))))
theorem-size     11
proof            (modus-ponens tm-623 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-4)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-49128.        (A -> (B or (A and ((C and D) -> D)))), M:tm-623, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-49129
in-theory        49129
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and ((C -> (D -> C)) and A))))
theorem-size     13
proof            (modus-ponens tm-623 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-49129.        (A -> (B or (A and ((C -> (D -> C)) and A)))), M:tm-623, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-49130
in-theory        49130
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))))
theorem-size     21
proof            (modus-ponens tm-623 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-49130.        (A -> (B or (A and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))), M:tm-623, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-49131
in-theory        49131
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and (((C and D) -> C) and A))))
theorem-size     13
proof            (modus-ponens tm-623 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-49131.        (A -> (B or (A and (((C and D) -> C) and A)))), M:tm-623, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-49132
in-theory        49132
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and (((C and D) -> D) and A))))
theorem-size     13
proof            (modus-ponens tm-623 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-49132.        (A -> (B or (A and (((C and D) -> D) and A)))), M:tm-623, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-49133
in-theory        49133
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and ((C -> (D -> (C and D))) and A))))
theorem-size     15
proof            (modus-ponens tm-623 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-49133.        (A -> (B or (A and ((C -> (D -> (C and D))) and A)))), M:tm-623, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-49134
in-theory        49134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or ((A -> B) and (A -> (A and B)))))
theorem-size     15
proof            (modus-ponens tm-623 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-49134.        ((A -> B) -> (C or ((A -> B) and (A -> (A and B))))), M:tm-623, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-49135
in-theory        49135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (A and B)))) -> (C or (not (A -> B))))
theorem-size     17
proof            (modus-ponens tm-623 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-49135.        (((A -> B) -> (not (A -> (A and B)))) -> (C or (not (A -> B)))), M:tm-623, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-49136
in-theory        49136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> C) -> (D or (((A -> B) or (A -> (A and B))) -> C)))
theorem-size     21
proof            (modus-ponens tm-623 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-49136.        (((A -> (A and B)) -> C) -> (D or (((A -> B) or (A -> (A and B))) -> C))), M:tm-623, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-49137
in-theory        49137
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((C -> D) -> (C -> (C and D))) and A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-49137.        (A -> (B or (((C -> D) -> (C -> (C and D))) and A))), M:tm-623, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-49138
in-theory        49138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> (C or ((A -> B) -> (A and B))))
theorem-size     15
proof            (modus-ponens tm-623 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-49138.        (((A -> B) -> A) -> (C or ((A -> B) -> (A and B)))), M:tm-623, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-49139
in-theory        49139
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and (C -> (D -> (C and D))))))
theorem-size     13
proof            (modus-ponens tm-623 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-49139.        (A -> (B or (A and (C -> (D -> (C and D)))))), M:tm-623, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-49140
in-theory        49140
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (B and C))) -> D)) -> (E or D))
theorem-size     15
proof            (modus-ponens tm-623 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-7 tm-4 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-49140.        ((A and ((B -> (C -> (B and C))) -> D)) -> (E or D)), M:tm-623, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-49141
in-theory        49141
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) and D) -> (E or C))
theorem-size     15
proof            (modus-ponens tm-623 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-7 tm-3 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-49141.        ((((A -> (B -> (A and B))) -> C) and D) -> (E or C)), M:tm-623, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-49142
in-theory        49142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (A and B)) -> C)) -> (D or (A -> C)))
theorem-size     15
proof            (modus-ponens tm-623 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-49142.        ((A -> ((B -> (A and B)) -> C)) -> (D or (A -> C))), M:tm-623, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-49143
in-theory        49143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> (B and C))))) -> (D or (not A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-49143.        ((A -> (not (B -> (C -> (B and C))))) -> (D or (not A))), M:tm-623, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-49144
in-theory        49144
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> (D or ((E or (A -> (B -> (A and B)))) -> C)))
theorem-size     23
proof            (modus-ponens tm-623 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-49144.        (((A -> (B -> (A and B))) -> C) -> (D or ((E or (A -> (B -> (A and B)))) -> C))), M:tm-623, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-49145
in-theory        49145
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (D -> (E -> (D and E)))) and A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-49145.        (A -> (B or ((C -> (D -> (E -> (D and E)))) and A))), M:tm-623, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-49146
in-theory        49146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or (A -> (D -> (B and D)))))
theorem-size     13
proof            (modus-ponens tm-623 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-49146.        ((A -> B) -> (C or (A -> (D -> (B and D))))), M:tm-623, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-49147
in-theory        49147
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((C -> (D -> C)) or E) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-49147.        (A -> (B or (((C -> (D -> C)) or E) and A))), M:tm-623, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-49148
in-theory        49148
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and A)))
theorem-size     21
proof            (modus-ponens tm-623 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-49148.        (A -> (B or ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and A))), M:tm-623, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-49149
in-theory        49149
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((((C and D) -> C) or E) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-49149.        (A -> (B or ((((C and D) -> C) or E) and A))), M:tm-623, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-49150
in-theory        49150
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((((C and D) -> D) or E) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6 tm-4)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-49150.        (A -> (B or ((((C and D) -> D) or E) and A))), M:tm-623, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-49151
in-theory        49151
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((C -> (D -> (C and D))) or E) and A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-49151.        (A -> (B or (((C -> (D -> (C and D))) or E) and A))), M:tm-623, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-49152
in-theory        49152
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((C -> (C or D)) or E) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-49152.        (A -> (B or (((C -> (C or D)) or E) and A))), M:tm-623, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-49153
in-theory        49153
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and ((C -> (C or D)) and A))))
theorem-size     13
proof            (modus-ponens tm-623 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-49153.        (A -> (B or (A and ((C -> (C or D)) and A)))), M:tm-623, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-49154
in-theory        49154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (B or C)) and A))) -> (D or (not A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-5 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-49154.        ((A -> (not ((B -> (B or C)) and A))) -> (D or (not A))), M:tm-623, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-49155
in-theory        49155
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and C) -> D) -> (E or ((C or ((A -> (A or B)) and C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-623 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-49155.        ((((A -> (A or B)) and C) -> D) -> (E or ((C or ((A -> (A or B)) and C)) -> D))), M:tm-623, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-49156
in-theory        49156
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> ((D -> (D or E)) and C)) and A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-49156.        (A -> (B or ((C -> ((D -> (D or E)) and C)) and A))), M:tm-623, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-49157
in-theory        49157
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and (C -> (C or D)))))
theorem-size     11
proof            (modus-ponens tm-623 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-49157.        (A -> (B or (A and (C -> (C or D))))), M:tm-623, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-49158
in-theory        49158
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (B or C)) -> D)) -> (E or D))
theorem-size     13
proof            (modus-ponens tm-623 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-7 tm-4 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-49158.        ((A and ((B -> (B or C)) -> D)) -> (E or D)), M:tm-623, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-49159
in-theory        49159
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) and D) -> (E or C))
theorem-size     13
proof            (modus-ponens tm-623 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-7 tm-3 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-49159.        ((((A -> (A or B)) -> C) and D) -> (E or C)), M:tm-623, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-49160
in-theory        49160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((A or B) -> C)) -> (D or (A -> C)))
theorem-size     13
proof            (modus-ponens tm-623 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-49160.        ((A -> ((A or B) -> C)) -> (D or (A -> C))), M:tm-623, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-49161
in-theory        49161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (B or C)))) -> (D or (not A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-6)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-49161.        ((A -> (not (B -> (B or C)))) -> (D or (not A))), M:tm-623, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-49162
in-theory        49162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> (D or ((E or (A -> (A or B))) -> C)))
theorem-size     19
proof            (modus-ponens tm-623 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-49162.        (((A -> (A or B)) -> C) -> (D or ((E or (A -> (A or B))) -> C))), M:tm-623, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-49163
in-theory        49163
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (D -> (D or E))) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-49163.        (A -> (B or ((C -> (D -> (D or E))) and A))), M:tm-623, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-49164
in-theory        49164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or (A -> (B or D))))
theorem-size     11
proof            (modus-ponens tm-623 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-6)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-49164.        ((A -> B) -> (C or (A -> (B or D)))), M:tm-623, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-49165
in-theory        49165
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C or (D -> (E -> D))) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-49165.        (A -> (B or ((C or (D -> (E -> D))) and A))), M:tm-623, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-49166
in-theory        49166
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)))
theorem-size     21
proof            (modus-ponens tm-623 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-49166.        (A -> (B or ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))), M:tm-623, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-49167
in-theory        49167
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C or ((D and E) -> D)) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-3)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-49167.        (A -> (B or ((C or ((D and E) -> D)) and A))), M:tm-623, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-49168
in-theory        49168
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C or ((D and E) -> E)) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-4)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-49168.        (A -> (B or ((C or ((D and E) -> E)) and A))), M:tm-623, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-49169
in-theory        49169
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C or (D -> (E -> (D and E)))) and A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-49169.        (A -> (B or ((C or (D -> (E -> (D and E)))) and A))), M:tm-623, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-49170
in-theory        49170
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C or (D -> (D or E))) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-49170.        (A -> (B or ((C or (D -> (D or E))) and A))), M:tm-623, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-49171
in-theory        49171
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C or (D -> (E or D))) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-49171.        (A -> (B or ((C or (D -> (E or D))) and A))), M:tm-623, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-49172
in-theory        49172
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((C -> (D or C)) or E) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-6)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-49172.        (A -> (B or (((C -> (D or C)) or E) and A))), M:tm-623, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-49173
in-theory        49173
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and ((C -> (D or C)) and A))))
theorem-size     13
proof            (modus-ponens tm-623 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-49173.        (A -> (B or (A and ((C -> (D or C)) and A)))), M:tm-623, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-49174
in-theory        49174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not ((B -> (C or B)) and A))) -> (D or (not A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-49174.        ((A -> (not ((B -> (C or B)) and A))) -> (D or (not A))), M:tm-623, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-49175
in-theory        49175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and C) -> D) -> (E or ((C or ((A -> (B or A)) and C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-623 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-49175.        ((((A -> (B or A)) and C) -> D) -> (E or ((C or ((A -> (B or A)) and C)) -> D))), M:tm-623, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-49176
in-theory        49176
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> ((D -> (E or D)) and C)) and A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-49176.        (A -> (B or ((C -> ((D -> (E or D)) and C)) and A))), M:tm-623, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-49177
in-theory        49177
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (A and (C -> (D or C)))))
theorem-size     11
proof            (modus-ponens tm-623 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       105
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-49177.        (A -> (B or (A and (C -> (D or C))))), M:tm-623, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-49178
in-theory        49178
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C or B)) -> D)) -> (E or D))
theorem-size     13
proof            (modus-ponens tm-623 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-1 tm-7 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-49178.        ((A and ((B -> (C or B)) -> D)) -> (E or D)), M:tm-623, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-49179
in-theory        49179
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) and D) -> (E or C))
theorem-size     13
proof            (modus-ponens tm-623 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-1 tm-7 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-49179.        ((((A -> (B or A)) -> C) and D) -> (E or C)), M:tm-623, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-49180
in-theory        49180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or A) -> C)) -> (D or (A -> C)))
theorem-size     13
proof            (modus-ponens tm-623 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-49180.        ((A -> ((B or A) -> C)) -> (D or (A -> C))), M:tm-623, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-49181
in-theory        49181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C or B)))) -> (D or (not A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-9)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-49181.        ((A -> (not (B -> (C or B)))) -> (D or (not A))), M:tm-623, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-49182
in-theory        49182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> (D or ((E or (A -> (B or A))) -> C)))
theorem-size     19
proof            (modus-ponens tm-623 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-49182.        (((A -> (B or A)) -> C) -> (D or ((E or (A -> (B or A))) -> C))), M:tm-623, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-49183
in-theory        49183
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((C -> (D -> (E or D))) and A)))
theorem-size     13
proof            (modus-ponens tm-623 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5)
proof-size       87
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49183.        (A -> (B or ((C -> (D -> (E or D))) and A))), M:tm-623, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-49184
in-theory        49184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or (A -> (D or B))))
theorem-size     11
proof            (modus-ponens tm-623 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49184.        ((A -> B) -> (C or (A -> (D or B)))), M:tm-623, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49185
in-theory        49185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-622 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49185.        ((A -> (B -> (C or B))) and ((D -> E) -> (D -> (F or E)))), M:tm-622, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49186
in-theory        49186
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (B -> (D or (C or B))))
theorem-size     15
proof            (modus-ponens tm-619 tm-623 ((A Am) (Bm (or B Am)) (C (-> Am (or Cm (or B Am))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49186.        ((A or (B -> (C or B))) -> (B -> (D or (C or B)))), M:tm-619, m:tm-623, u:((A Am) (Bm (or B Am)) (C (-> Am (or Cm (or B Am)))))
================================================================
tm-name          tm-49187
in-theory        49187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49187.        (((A -> B) -> (A -> (C or B))) and (D -> (E or D))), M:tm-609, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49188
in-theory        49188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (D -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-605 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49188.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> (D -> (F or E)))), M:tm-605, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49189
in-theory        49189
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and ((D -> (E or D)) and ((A -> B) -> (A -> (C or B)))))
theorem-size     25
proof            (modus-ponens tm-595 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49189.        (((A -> B) -> (A -> (C or B))) and ((D -> (E or D)) and ((A -> B) -> (A -> (C or B))))), M:tm-595, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49190
in-theory        49190
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-550 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49190.        (((A -> (B or A)) or C) and ((D -> E) -> (D -> (F or E)))), M:tm-550, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49191
in-theory        49191
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-540 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49191.        ((A or (B -> (C or B))) and ((D -> E) -> (D -> (F or E)))), M:tm-540, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49192
in-theory        49192
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-530 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49192.        ((A or (B -> (B or C))) and ((D -> E) -> (D -> (F or E)))), M:tm-530, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49193
in-theory        49193
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-520 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49193.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (F or E)))), M:tm-520, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49194
in-theory        49194
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-510 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49194.        ((A or ((B and C) -> C)) and ((D -> E) -> (D -> (F or E)))), M:tm-510, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49195
in-theory        49195
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-500 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49195.        ((A or ((B and C) -> B)) and ((D -> E) -> (D -> (F or E)))), M:tm-500, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49196
in-theory        49196
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-490 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49196.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (G or F)))), M:tm-490, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49197
in-theory        49197
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-480 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49197.        ((A or (B -> (C -> B))) and ((D -> E) -> (D -> (F or E)))), M:tm-480, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49198
in-theory        49198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> (C or B)) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49198.        ((A -> B) -> ((A -> (C or B)) or D)), M:tm-470, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49199
in-theory        49199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-469 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49199.        ((A -> (B -> (B or C))) and ((D -> E) -> (D -> (F or E)))), M:tm-469, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49200
in-theory        49200
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (B -> (D or (B or C))))
theorem-size     15
proof            (modus-ponens tm-466 tm-623 ((A Am) (Bm (or Am B)) (C (-> Am (or Cm (or Am B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49200.        ((A or (B -> (B or C))) -> (B -> (D or (B or C)))), M:tm-466, m:tm-623, u:((A Am) (Bm (or Am B)) (C (-> Am (or Cm (or Am B)))))
================================================================
tm-name          tm-49201
in-theory        49201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49201.        (((A -> B) -> (A -> (C or B))) and (D -> (D or E))), M:tm-456, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49202
in-theory        49202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (D -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-453 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49202.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> (D -> (F or E)))), M:tm-453, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49203
in-theory        49203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and ((D -> (D or E)) and ((A -> B) -> (A -> (C or B)))))
theorem-size     25
proof            (modus-ponens tm-443 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49203.        (((A -> B) -> (A -> (C or B))) and ((D -> (D or E)) and ((A -> B) -> (A -> (C or B))))), M:tm-443, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49204
in-theory        49204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-409 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49204.        (((A -> (A or B)) or C) and ((D -> E) -> (D -> (F or E)))), M:tm-409, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49205
in-theory        49205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> (D -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-400 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49205.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> (D -> (F or E)))), M:tm-400, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49206
in-theory        49206
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-391 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49206.        ((((A and B) -> B) or C) and ((D -> E) -> (D -> (F or E)))), M:tm-391, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49207
in-theory        49207
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-382 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49207.        ((((A and B) -> A) or C) and ((D -> E) -> (D -> (F or E)))), M:tm-382, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49208
in-theory        49208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (E -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-373 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49208.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> (E -> (G or F)))), M:tm-373, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49209
in-theory        49209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-364 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49209.        (((A -> (B -> A)) or C) and ((D -> E) -> (D -> (F or E)))), M:tm-364, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49210
in-theory        49210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((A -> (D or B)) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49210.        ((A -> B) -> (C -> ((A -> (D or B)) and C))), M:tm-355, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49211
in-theory        49211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-354 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49211.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> (D -> (F or E)))), M:tm-354, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49212
in-theory        49212
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (B -> (D or (C -> (B and C)))))
theorem-size     19
proof            (modus-ponens tm-351 tm-623 ((A Am) (Bm (-> B (and Am B))) (C (-> Am (or Cm (-> B (and Am B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49212.        ((A or (B -> (C -> (B and C)))) -> (B -> (D or (C -> (B and C))))), M:tm-351, m:tm-623, u:((A Am) (Bm (-> B (and Am B))) (C (-> Am (or Cm (-> B (and Am B))))))
================================================================
tm-name          tm-49213
in-theory        49213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49213.        (((A -> B) -> (A -> (C or B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49214
in-theory        49214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (C -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-338 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49214.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> (C -> (E or D)))), M:tm-338, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49215
in-theory        49215
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (A -> (C or (A and B))))
theorem-size     17
proof            (modus-ponens tm-335 tm-623 ((A Am) (Bm (and Am B)) (C (-> Am (or Cm (and Am B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49215.        (((A -> B) or (A -> (A and B))) -> (A -> (C or (A and B)))), M:tm-335, m:tm-623, u:((A Am) (Bm (and Am B)) (C (-> Am (or Cm (and Am B)))))
================================================================
tm-name          tm-49216
in-theory        49216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and ((A -> B) -> ((A -> B) and (A -> (C or B)))))
theorem-size     23
proof            (modus-ponens tm-328 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49216.        (((A -> B) -> (A -> (C or B))) and ((A -> B) -> ((A -> B) and (A -> (C or B))))), M:tm-328, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49217
in-theory        49217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> (C or B)))))
theorem-size     27
proof            (modus-ponens tm-327 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49217.        (((A -> B) -> (A -> (C or B))) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> (C or B))))), M:tm-327, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49218
in-theory        49218
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (((D and E) -> E) and ((A -> B) -> (A -> (C or B)))))
theorem-size     25
proof            (modus-ponens tm-326 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49218.        (((A -> B) -> (A -> (C or B))) and (((D and E) -> E) and ((A -> B) -> (A -> (C or B))))), M:tm-326, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49219
in-theory        49219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (((D and E) -> D) and ((A -> B) -> (A -> (C or B)))))
theorem-size     25
proof            (modus-ponens tm-325 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49219.        (((A -> B) -> (A -> (C or B))) and (((D and E) -> D) and ((A -> B) -> (A -> (C or B))))), M:tm-325, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49220
in-theory        49220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> (C or B)))))
theorem-size     33
proof            (modus-ponens tm-324 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49220.        (((A -> B) -> (A -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> (C or B))))), M:tm-324, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49221
in-theory        49221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and ((D -> (E -> D)) and ((A -> B) -> (A -> (C or B)))))
theorem-size     25
proof            (modus-ponens tm-323 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49221.        (((A -> B) -> (A -> (C or B))) and ((D -> (E -> D)) and ((A -> B) -> (A -> (C or B))))), M:tm-323, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49222
in-theory        49222
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49222.        (((A -> B) -> (A -> (C or B))) and ((D and E) -> E)), M:tm-322, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49223
in-theory        49223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49223.        (((A -> B) -> (A -> (C or B))) and ((D and E) -> D)), M:tm-320, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49224
in-theory        49224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49224.        (((A -> B) -> (A -> (C or B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49225
in-theory        49225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and ((A -> B) -> (A -> B)))
theorem-size     17
proof            (modus-ponens tm-316 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49225.        (((A -> B) -> (A -> (C or B))) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49226
in-theory        49226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49226.        (((A -> B) -> (A -> (C or B))) and (D -> (E -> D))), M:tm-315, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49227
in-theory        49227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (((A -> B) -> (not (A -> (C or B)))) -> (not (A -> B))))
theorem-size     25
proof            (modus-ponens tm-313 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49227.        (((A -> B) -> (A -> (C or B))) and (((A -> B) -> (not (A -> (C or B)))) -> (not (A -> B)))), M:tm-313, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49228
in-theory        49228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (((A -> (C or B)) -> D) -> (((A -> B) or (A -> (C or B))) -> D)))
theorem-size     29
proof            (modus-ponens tm-312 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49228.        (((A -> B) -> (A -> (C or B))) and (((A -> (C or B)) -> D) -> (((A -> B) or (A -> (C or B))) -> D))), M:tm-312, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49229
in-theory        49229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (D or ((A -> B) -> (A -> (C or B)))))
theorem-size     21
proof            (modus-ponens tm-311 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49229.        (((A -> B) -> (A -> (C or B))) and (D or ((A -> B) -> (A -> (C or B))))), M:tm-311, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49230
in-theory        49230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (((A -> B) -> (A -> (C or B))) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49230.        (((A -> B) -> (A -> (C or B))) and (((A -> B) -> (A -> (C or B))) or D)), M:tm-310, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49231
in-theory        49231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (D -> (((A -> B) -> (A -> (C or B))) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49231.        (((A -> B) -> (A -> (C or B))) and (D -> (((A -> B) -> (A -> (C or B))) and D))), M:tm-309, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49232
in-theory        49232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (((A -> B) -> A) -> ((A -> B) -> (C or B))))
theorem-size     23
proof            (modus-ponens tm-306 tm-623 ((A (-> Am Bm)) (B Am) (C (or Cm Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49232.        (((A -> B) -> (A -> (C or B))) and (((A -> B) -> A) -> ((A -> B) -> (C or B)))), M:tm-306, m:tm-623, u:((A (-> Am Bm)) (B Am) (C (or Cm Bm)))
================================================================
tm-name          tm-49233
in-theory        49233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and (D -> ((A -> B) -> (A -> (C or B)))))
theorem-size     21
proof            (modus-ponens tm-305 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49233.        (((A -> B) -> (A -> (C or B))) and (D -> ((A -> B) -> (A -> (C or B))))), M:tm-305, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49234
in-theory        49234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (D -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-303 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49234.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> (D -> (F or E)))), M:tm-303, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49235
in-theory        49235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (D -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-270 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49235.        ((A -> (((B and C) -> C) and A)) and ((D -> E) -> (D -> (F or E)))), M:tm-270, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49236
in-theory        49236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (D -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-239 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49236.        ((A -> (((B and C) -> B) and A)) and ((D -> E) -> (D -> (F or E)))), M:tm-239, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49237
in-theory        49237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (E -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-210 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49237.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> (E -> (G or F)))), M:tm-210, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49238
in-theory        49238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (D -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-183 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49238.        ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> (D -> (F or E)))), M:tm-183, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49239
in-theory        49239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-157 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49239.        ((A -> ((B and C) -> C)) and ((D -> E) -> (D -> (F or E)))), M:tm-157, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49240
in-theory        49240
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((B and C) -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-154 tm-623 ((Am (and A Bm)) (B Bm) (C (-> (and A Bm) (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49240.        ((A or ((B and C) -> C)) -> ((B and C) -> (D or C))), M:tm-154, m:tm-623, u:((Am (and A Bm)) (B Bm) (C (-> (and A Bm) (or Cm Bm))))
================================================================
tm-name          tm-49241
in-theory        49241
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (D -> (F or E))))
theorem-size     25
proof            (modus-ponens tm-147 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49241.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> (D -> (F or E)))), M:tm-147, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49242
in-theory        49242
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> (D or C)))
theorem-size     25
proof            (modus-ponens tm-144 tm-623 ((Am (and A (-> B Bm))) (C Bm) (D (-> (and A (-> B Bm)) (or Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49242.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> (D or C))), M:tm-144, m:tm-623, u:((Am (and A (-> B Bm))) (C Bm) (D (-> (and A (-> B Bm)) (or Cm Bm))))
================================================================
tm-name          tm-49243
in-theory        49243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-134 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49243.        ((A -> ((B and C) -> B)) and ((D -> E) -> (D -> (F or E)))), M:tm-134, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49244
in-theory        49244
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((B and C) -> (D or B)))
theorem-size     15
proof            (modus-ponens tm-131 tm-623 ((Am (and Bm B)) (A Bm) (C (-> (and Bm B) (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49244.        ((A or ((B and C) -> B)) -> ((B and C) -> (D or B))), M:tm-131, m:tm-623, u:((Am (and Bm B)) (A Bm) (C (-> (and Bm B) (or Cm Bm))))
================================================================
tm-name          tm-49245
in-theory        49245
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (D -> (F or E))))
theorem-size     25
proof            (modus-ponens tm-125 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49245.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> (D -> (F or E)))), M:tm-125, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49246
in-theory        49246
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> (D or B)))
theorem-size     25
proof            (modus-ponens tm-122 tm-623 ((Am (and (-> A Bm) C)) (B Bm) (D (-> (and (-> A Bm) C) (or Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49246.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> (D or B))), M:tm-122, m:tm-623, u:((Am (and (-> A Bm) C)) (B Bm) (D (-> (and (-> A Bm) C) (or Cm Bm))))
================================================================
tm-name          tm-49247
in-theory        49247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-113 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49247.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> (E -> (G or F)))), M:tm-113, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49248
in-theory        49248
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> (E or ((B -> C) -> (B -> D)))))
theorem-size     31
proof            (modus-ponens tm-110 tm-623 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> A (-> B C)) (or Cm (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49248.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((B -> (C -> D)) -> (E or ((B -> C) -> (B -> D))))), M:tm-110, m:tm-623, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> (-> A (-> B C)) (or Cm (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-49249
in-theory        49249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (D -> (F or E))))
theorem-size     29
proof            (modus-ponens tm-105 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49249.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> (D -> (F or E)))), M:tm-105, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49250
in-theory        49250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> (D or (A -> C))))
theorem-size     31
proof            (modus-ponens tm-102 tm-623 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> A (-> B C)) (or Cm (-> A C))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49250.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> (D or (A -> C)))), M:tm-102, m:tm-623, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (-> (-> A (-> B C)) (or Cm (-> A C)))))
================================================================
tm-name          tm-49251
in-theory        49251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> (C -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-95 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49251.        (((A -> B) -> (A -> A)) and ((C -> D) -> (C -> (E or D)))), M:tm-95, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49252
in-theory        49252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (A -> (C or A)))
theorem-size     13
proof            (modus-ponens tm-92 tm-623 ((Bm Am) (A Am) (B (-> Am (or Cm Am)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49252.        (((A -> B) or (A -> A)) -> (A -> (C or A))), M:tm-92, m:tm-623, u:((Bm Am) (A Am) (B (-> Am (or Cm Am))))
================================================================
tm-name          tm-49253
in-theory        49253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (A -> (D or B))))
theorem-size     11
proof            (modus-ponens tm-84 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       89
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49253.        ((A -> B) -> (C -> (A -> (D or B)))), M:tm-84, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49254
in-theory        49254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> (D -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-83 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49254.        ((A -> (B -> (C -> B))) and ((D -> E) -> (D -> (F or E)))), M:tm-83, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49255
in-theory        49255
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (B -> (D or (C -> B))))
theorem-size     15
proof            (modus-ponens tm-80 tm-623 ((A Am) (Bm (-> B Am)) (C (-> Am (or Cm (-> B Am))))))
axioms-used      (tm-8 tm-1 tm-2 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49255.        ((A or (B -> (C -> B))) -> (B -> (D or (C -> B)))), M:tm-80, m:tm-623, u:((A Am) (Bm (-> B Am)) (C (-> Am (or Cm (-> B Am)))))
================================================================
tm-name          tm-49256
in-theory        49256
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> (B -> (D or C))))
theorem-size     15
proof            (modus-ponens tm-76 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49256.        (((not (not A)) -> A) and ((B -> C) -> (B -> (D or C)))), M:tm-76, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49257
in-theory        49257
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> (A -> (C or B)))
theorem-size     15
proof            (modus-ponens tm-73 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49257.        (((not (not (A -> B))) or (A -> B)) -> (A -> (C or B))), M:tm-73, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49258
in-theory        49258
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (C -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-69 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49258.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> (C -> (E or D)))), M:tm-69, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49259
in-theory        49259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> (C or (not A))))
theorem-size     21
proof            (modus-ponens tm-66 tm-623 ((Am (-> A (not B))) (Bm (not A)) (C (-> (-> A (not B)) (or Cm (not A))))))
axioms-used      (tm-8 tm-9 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49259.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> (C or (not A)))), M:tm-66, m:tm-623, u:((Am (-> A (not B))) (Bm (not A)) (C (-> (-> A (not B)) (or Cm (not A)))))
================================================================
tm-name          tm-49260
in-theory        49260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) -> ((A or A) -> (B or A)))
theorem-size     11
proof            (modus-ponens tm-55 tm-623 ((A Bm) (Am Bm) (B Bm) (C (or Cm Bm))))
axioms-used      (tm-2 tm-8 tm-1 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49260.        ((A -> A) -> ((A or A) -> (B or A))), M:tm-55, m:tm-623, u:((A Bm) (Am Bm) (B Bm) (C (or Cm Bm)))
================================================================
tm-name          tm-49261
in-theory        49261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-54 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49261.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> (D -> (F or E)))), M:tm-54, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49262
in-theory        49262
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (D or ((A or B) -> C))))
theorem-size     25
proof            (modus-ponens tm-51 tm-623 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (or Cm (-> (or C A) B))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49262.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((B -> C) -> (D or ((A or B) -> C)))), M:tm-51, m:tm-623, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (-> (-> A B) (or Cm (-> (or C A) B)))))
================================================================
tm-name          tm-49263
in-theory        49263
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (B -> (C or (A and B))))
theorem-size     15
proof            (modus-ponens tm-48 tm-623 ((A Am) (Bm (and B Am)) (C (-> Am (or Cm (and B Am))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49263.        ((A or (B -> (A and B))) -> (B -> (C or (A and B)))), M:tm-48, m:tm-623, u:((A Am) (Bm (and B Am)) (C (-> Am (or Cm (and B Am)))))
================================================================
tm-name          tm-49264
in-theory        49264
times-derived    2
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (B -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-47 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49264.        (((A and (B -> C)) or (B -> C)) -> (B -> (D or C))), M:tm-47, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49265
in-theory        49265
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (A -> (D or B)))
theorem-size     15
proof            (modus-ponens tm-46 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49265.        ((((A -> B) and C) or (A -> B)) -> (A -> (D or B))), M:tm-46, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49266
in-theory        49266
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D or (A -> C))))
theorem-size     23
proof            (modus-ponens tm-45 tm-623 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (or Cm (-> A C))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49266.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D or (A -> C)))), M:tm-45, m:tm-623, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (or Cm (-> A C)))))
================================================================
tm-name          tm-49267
in-theory        49267
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (B -> (C or A)))
theorem-size     11
proof            (modus-ponens tm-44 tm-623 ((A Am) (B Bm) (C (-> Am (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49267.        ((A or (B -> A)) -> (B -> (C or A))), M:tm-44, m:tm-623, u:((A Am) (B Bm) (C (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49268
in-theory        49268
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (C -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-42 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49268.        ((A -> (B or A)) and ((C -> D) -> (C -> (E or D)))), M:tm-42, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49269
in-theory        49269
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (C -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-32 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49269.        ((A -> (A or B)) and ((C -> D) -> (C -> (E or D)))), M:tm-32, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49270
in-theory        49270
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (A -> (C or B))))
theorem-size     13
proof            (modus-ponens tm-24 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49270.        ((A -> B) -> ((A -> B) and (A -> (C or B)))), M:tm-24, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49271
in-theory        49271
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-23 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49271.        ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (E or D)))), M:tm-23, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49272
in-theory        49272
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (C -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-22 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49272.        (((A and B) -> B) and ((C -> D) -> (C -> (E or D)))), M:tm-22, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49273
in-theory        49273
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (C -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-21 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49273.        (((A and B) -> A) and ((C -> D) -> (C -> (E or D)))), M:tm-21, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49274
in-theory        49274
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-20 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49274.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (F or E)))), M:tm-20, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49275
in-theory        49275
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (C -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-19 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49275.        ((A -> (B -> A)) and ((C -> D) -> (C -> (E or D)))), M:tm-19, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49276
in-theory        49276
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (C or B)))) -> (not (A -> B)))
theorem-size     15
proof            (modus-ponens tm-9 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-9 tm-2 tm-1 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49276.        (((A -> B) -> (not (A -> (C or B)))) -> (not (A -> B))), M:tm-9, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49277
in-theory        49277
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or C)) -> D) -> (((A -> C) or (A -> (B or C))) -> D))
theorem-size     19
proof            (modus-ponens tm-8 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49277.        (((A -> (B or C)) -> D) -> (((A -> C) or (A -> (B or C))) -> D)), M:tm-8, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-49278
in-theory        49278
times-derived    2
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (B -> (D or C))))
theorem-size     11
proof            (modus-ponens tm-7 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-7 tm-2 tm-1)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49278.        (A or ((B -> C) -> (B -> (D or C)))), M:tm-7, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49279
in-theory        49279
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-6 tm-2 tm-1 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49279.        (((A -> B) -> (A -> (C or B))) or D), M:tm-6, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49280
in-theory        49280
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> (D or C))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49280.        (A -> (((B -> C) -> (B -> (D or C))) and A)), M:tm-5, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49281
in-theory        49281
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> ((A -> B) -> (C or B)))
theorem-size     13
proof            (modus-ponens tm-2 tm-623 ((A (-> Am Bm)) (B Am) (C (or Cm Bm))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49281.        (((A -> B) -> A) -> ((A -> B) -> (C or B))), M:tm-2, m:tm-623, u:((A (-> Am Bm)) (B Am) (C (or Cm Bm)))
================================================================
tm-name          tm-49282
in-theory        49282
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (B -> (D or C))))
theorem-size     11
proof            (modus-ponens tm-1 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-1 tm-2 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-49282.        (A -> ((B -> C) -> (B -> (D or C)))), M:tm-1, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-49283
in-theory        49283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-622 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49283.        ((A -> (B -> (C or B))) and (D -> (E -> (F -> (G or F))))), M:tm-622, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49284
in-theory        49284
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-619 tm-624 ((Am (-> A (or B A))) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49284.        ((A or (B -> (C or B))) -> (D -> (E -> (F or E)))), M:tm-619, m:tm-624, u:((Am (-> A (or B A))) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49285
in-theory        49285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (E -> (F or E)))
theorem-size     15
proof            (modus-ponens tm-609 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49285.        ((A -> (B -> (C -> (D or C)))) and (E -> (F or E))), M:tm-609, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49286
in-theory        49286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-605 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49286.        ((A -> ((B -> (C or B)) and A)) and (D -> (E -> (F -> (G or F))))), M:tm-605, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49287
in-theory        49287
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-602 tm-624 ((Am (and (-> A (or B A)) C)) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49287.        ((A or ((B -> (C or B)) and A)) -> (D -> (E -> (F or E)))), M:tm-602, m:tm-624, u:((Am (and (-> A (or B A)) C)) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49288
in-theory        49288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and ((E -> (F or E)) and (A -> (B -> (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-595 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49288.        ((A -> (B -> (C -> (D or C)))) and ((E -> (F or E)) and (A -> (B -> (C -> (D or C)))))), M:tm-595, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49289
in-theory        49289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-550 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49289.        (((A -> (B or A)) or C) and (D -> (E -> (F -> (G or F))))), M:tm-550, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49290
in-theory        49290
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-540 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49290.        ((A or (B -> (C or B))) and (D -> (E -> (F -> (G or F))))), M:tm-540, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49291
in-theory        49291
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-530 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49291.        ((A or (B -> (B or C))) and (D -> (E -> (F -> (G or F))))), M:tm-530, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49292
in-theory        49292
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-520 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49292.        ((A or (B -> (C -> (B and C)))) and (D -> (E -> (F -> (G or F))))), M:tm-520, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49293
in-theory        49293
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-510 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49293.        ((A or ((B and C) -> C)) and (D -> (E -> (F -> (G or F))))), M:tm-510, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49294
in-theory        49294
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-500 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49294.        ((A or ((B and C) -> B)) and (D -> (E -> (F -> (G or F))))), M:tm-500, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49295
in-theory        49295
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-490 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49295.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (H or G))))), M:tm-490, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49296
in-theory        49296
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-480 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49296.        ((A or (B -> (C -> B))) and (D -> (E -> (F -> (G or F))))), M:tm-480, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49297
in-theory        49297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-469 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49297.        ((A -> (B -> (B or C))) and (D -> (E -> (F -> (G or F))))), M:tm-469, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49298
in-theory        49298
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-466 tm-624 ((Am (-> A (or A B))) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49298.        ((A or (B -> (B or C))) -> (D -> (E -> (F or E)))), M:tm-466, m:tm-624, u:((Am (-> A (or A B))) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49299
in-theory        49299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (E -> (E or F)))
theorem-size     15
proof            (modus-ponens tm-456 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49299.        ((A -> (B -> (C -> (D or C)))) and (E -> (E or F))), M:tm-456, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49300
in-theory        49300
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-453 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49300.        ((A -> ((B -> (B or C)) and A)) and (D -> (E -> (F -> (G or F))))), M:tm-453, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49301
in-theory        49301
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-450 tm-624 ((Am (and (-> A (or A B)) C)) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49301.        ((A or ((B -> (B or C)) and A)) -> (D -> (E -> (F or E)))), M:tm-450, m:tm-624, u:((Am (and (-> A (or A B)) C)) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49302
in-theory        49302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and ((E -> (E or F)) and (A -> (B -> (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-443 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49302.        ((A -> (B -> (C -> (D or C)))) and ((E -> (E or F)) and (A -> (B -> (C -> (D or C)))))), M:tm-443, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49303
in-theory        49303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-409 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49303.        (((A -> (A or B)) or C) and (D -> (E -> (F -> (G or F))))), M:tm-409, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49304
in-theory        49304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-400 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49304.        (((A -> (B -> (A and B))) or C) and (D -> (E -> (F -> (G or F))))), M:tm-400, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49305
in-theory        49305
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-391 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49305.        ((((A and B) -> B) or C) and (D -> (E -> (F -> (G or F))))), M:tm-391, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49306
in-theory        49306
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-382 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49306.        ((((A and B) -> A) or C) and (D -> (E -> (F -> (G or F))))), M:tm-382, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49307
in-theory        49307
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-373 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49307.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (F -> (G -> (H or G))))), M:tm-373, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49308
in-theory        49308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-364 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49308.        (((A -> (B -> A)) or C) and (D -> (E -> (F -> (G or F))))), M:tm-364, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49309
in-theory        49309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-354 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49309.        ((A -> (B -> (C -> (B and C)))) and (D -> (E -> (F -> (G or F))))), M:tm-354, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49310
in-theory        49310
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-351 tm-624 ((Am (-> A (-> B (and A B)))) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49310.        ((A or (B -> (C -> (B and C)))) -> (D -> (E -> (F or E)))), M:tm-351, m:tm-624, u:((Am (-> A (-> B (and A B)))) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49311
in-theory        49311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (E -> (F -> (E and F))))
theorem-size     17
proof            (modus-ponens tm-341 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49311.        ((A -> (B -> (C -> (D or C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49312
in-theory        49312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) -> D) -> ((A -> (B -> (C or B))) and D))
theorem-size     19
proof            (modus-ponens tm-339 tm-624 ((Am (-> (-> Bm (-> Cm (or Dm Cm))) B)) (A (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49312.        (((A -> (B -> (C or B))) -> D) -> ((A -> (B -> (C or B))) and D)), M:tm-339, m:tm-624, u:((Am (-> (-> Bm (-> Cm (or Dm Cm))) B)) (A (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49313
in-theory        49313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (D -> (E -> (F or E)))))
theorem-size     19
proof            (modus-ponens tm-338 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49313.        (((A -> B) -> (A -> (A and B))) and (C -> (D -> (E -> (F or E))))), M:tm-338, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49314
in-theory        49314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (C -> (D -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-335 tm-624 ((Am (-> A (and A B))) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49314.        (((A -> B) or (A -> (A and B))) -> (C -> (D -> (E or D)))), M:tm-335, m:tm-624, u:((Am (-> A (and A B))) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49315
in-theory        49315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (A -> (A and (B -> (C -> (D or C))))))
theorem-size     21
proof            (modus-ponens tm-328 tm-624 ((A Am) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49315.        ((A -> (B -> (C -> (D or C)))) and (A -> (A and (B -> (C -> (D or C)))))), M:tm-328, m:tm-624, u:((A Am) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49316
in-theory        49316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and ((E -> (F -> (E and F))) and (A -> (B -> (C -> (D or C))))))
theorem-size     27
proof            (modus-ponens tm-327 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49316.        ((A -> (B -> (C -> (D or C)))) and ((E -> (F -> (E and F))) and (A -> (B -> (C -> (D or C)))))), M:tm-327, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49317
in-theory        49317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (((E and F) -> F) and (A -> (B -> (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-326 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49317.        ((A -> (B -> (C -> (D or C)))) and (((E and F) -> F) and (A -> (B -> (C -> (D or C)))))), M:tm-326, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49318
in-theory        49318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (((E and F) -> E) and (A -> (B -> (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-325 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49318.        ((A -> (B -> (C -> (D or C)))) and (((E and F) -> E) and (A -> (B -> (C -> (D or C)))))), M:tm-325, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49319
in-theory        49319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> (C -> (D or C))))))
theorem-size     33
proof            (modus-ponens tm-324 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49319.        ((A -> (B -> (C -> (D or C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (B -> (C -> (D or C)))))), M:tm-324, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49320
in-theory        49320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and ((E -> (F -> E)) and (A -> (B -> (C -> (D or C))))))
theorem-size     25
proof            (modus-ponens tm-323 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49320.        ((A -> (B -> (C -> (D or C)))) and ((E -> (F -> E)) and (A -> (B -> (C -> (D or C)))))), M:tm-323, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49321
in-theory        49321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and ((E and F) -> F))
theorem-size     15
proof            (modus-ponens tm-322 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49321.        ((A -> (B -> (C -> (D or C)))) and ((E and F) -> F)), M:tm-322, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49322
in-theory        49322
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (D or C))) -> E)) -> (B -> (C -> (D or C)))) and ((A and ((B -> (C -> (D or C))) -> E)) -> E))
theorem-size     33
proof            (modus-ponens tm-321 tm-624 ((Am (and A (-> (-> Bm (-> Cm (or Dm Cm))) C))) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49322.        (((A and ((B -> (C -> (D or C))) -> E)) -> (B -> (C -> (D or C)))) and ((A and ((B -> (C -> (D or C))) -> E)) -> E)), M:tm-321, m:tm-624, u:((Am (and A (-> (-> Bm (-> Cm (or Dm Cm))) C))) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49323
in-theory        49323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and ((E and F) -> E))
theorem-size     15
proof            (modus-ponens tm-320 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49323.        ((A -> (B -> (C -> (D or C)))) and ((E and F) -> E)), M:tm-320, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49324
in-theory        49324
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (C or B))) -> D) and E) -> (A -> (B -> (C or B)))) and ((((A -> (B -> (C or B))) -> D) and E) -> D))
theorem-size     33
proof            (modus-ponens tm-319 tm-624 ((Am (and (-> (-> Bm (-> Cm (or Dm Cm))) B) C)) (A (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49324.        (((((A -> (B -> (C or B))) -> D) and E) -> (A -> (B -> (C or B)))) and ((((A -> (B -> (C or B))) -> D) and E) -> D)), M:tm-319, m:tm-624, u:((Am (and (-> (-> Bm (-> Cm (or Dm Cm))) B) C)) (A (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49325
in-theory        49325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     23
proof            (modus-ponens tm-318 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49325.        ((A -> (B -> (C -> (D or C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49326
in-theory        49326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C or B)) -> D)) -> (A -> (B -> (C or B)))) and ((A -> ((B -> (C or B)) -> D)) -> (A -> D)))
theorem-size     31
proof            (modus-ponens tm-317 tm-624 ((Am (-> Bm (-> (-> Cm (or Dm Cm)) C))) (A Bm) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49326.        (((A -> ((B -> (C or B)) -> D)) -> (A -> (B -> (C or B)))) and ((A -> ((B -> (C or B)) -> D)) -> (A -> D))), M:tm-317, m:tm-624, u:((Am (-> Bm (-> (-> Cm (or Dm Cm)) C))) (A Bm) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-49327
in-theory        49327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (A -> A))
theorem-size     13
proof            (modus-ponens tm-316 tm-624 ((A Am) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49327.        ((A -> (B -> (C -> (D or C)))) and (A -> A)), M:tm-316, m:tm-624, u:((A Am) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49328
in-theory        49328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (E -> (F -> E)))
theorem-size     15
proof            (modus-ponens tm-315 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       101
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49328.        ((A -> (B -> (C -> (D or C)))) and (E -> (F -> E))), M:tm-315, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49329
in-theory        49329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and ((A -> (not (B -> (C -> (D or C))))) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-313 tm-624 ((A Am) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49329.        ((A -> (B -> (C -> (D or C)))) and ((A -> (not (B -> (C -> (D or C))))) -> (not A))), M:tm-313, m:tm-624, u:((A Am) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49330
in-theory        49330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (((B -> (C -> (D or C))) -> E) -> ((A or (B -> (C -> (D or C)))) -> E)))
theorem-size     31
proof            (modus-ponens tm-312 tm-624 ((A Am) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49330.        ((A -> (B -> (C -> (D or C)))) and (((B -> (C -> (D or C))) -> E) -> ((A or (B -> (C -> (D or C)))) -> E))), M:tm-312, m:tm-624, u:((A Am) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49331
in-theory        49331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (E or (A -> (B -> (C -> (D or C))))))
theorem-size     21
proof            (modus-ponens tm-311 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49331.        ((A -> (B -> (C -> (D or C)))) and (E or (A -> (B -> (C -> (D or C)))))), M:tm-311, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49332
in-theory        49332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and ((A -> (B -> (C -> (D or C)))) or E))
theorem-size     21
proof            (modus-ponens tm-310 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49332.        ((A -> (B -> (C -> (D or C)))) and ((A -> (B -> (C -> (D or C)))) or E)), M:tm-310, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49333
in-theory        49333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (E -> ((A -> (B -> (C -> (D or C)))) and E)))
theorem-size     23
proof            (modus-ponens tm-309 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49333.        ((A -> (B -> (C -> (D or C)))) and (E -> ((A -> (B -> (C -> (D or C)))) and E))), M:tm-309, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49334
in-theory        49334
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and ((A -> B) -> (A -> (C -> (D or C)))))
theorem-size     21
proof            (modus-ponens tm-306 tm-624 ((A Am) (B Bm) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49334.        ((A -> (B -> (C -> (D or C)))) and ((A -> B) -> (A -> (C -> (D or C))))), M:tm-306, m:tm-624, u:((A Am) (B Bm) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-49335
in-theory        49335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (E -> (A -> (B -> (C -> (D or C))))))
theorem-size     21
proof            (modus-ponens tm-305 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49335.        ((A -> (B -> (C -> (D or C)))) and (E -> (A -> (B -> (C -> (D or C)))))), M:tm-305, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49336
in-theory        49336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-303 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49336.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (E -> (F -> (G or F))))), M:tm-303, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49337
in-theory        49337
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-300 tm-624 ((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49337.        ((A or ((B -> (C -> (B and C))) and A)) -> (D -> (E -> (F or E)))), M:tm-300, m:tm-624, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49338
in-theory        49338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-270 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49338.        ((A -> (((B and C) -> C) and A)) and (D -> (E -> (F -> (G or F))))), M:tm-270, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49339
in-theory        49339
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-267 tm-624 ((Am (and (-> (and A B) B) C)) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49339.        ((A or (((B and C) -> C) and A)) -> (D -> (E -> (F or E)))), M:tm-267, m:tm-624, u:((Am (and (-> (and A B) B) C)) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49340
in-theory        49340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-239 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49340.        ((A -> (((B and C) -> B) and A)) and (D -> (E -> (F -> (G or F))))), M:tm-239, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49341
in-theory        49341
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-236 tm-624 ((Am (and (-> (and A B) A) C)) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49341.        ((A or (((B and C) -> B) and A)) -> (D -> (E -> (F or E)))), M:tm-236, m:tm-624, u:((Am (and (-> (and A B) A) C)) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49342
in-theory        49342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-210 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49342.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (F -> (G -> (H or G))))), M:tm-210, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49343
in-theory        49343
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-207 tm-624 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49343.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (E -> (F -> (G or F)))), M:tm-207, m:tm-624, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49344
in-theory        49344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (F -> (G or F)))))
theorem-size     19
proof            (modus-ponens tm-183 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49344.        ((A -> ((B -> (C -> B)) and A)) and (D -> (E -> (F -> (G or F))))), M:tm-183, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49345
in-theory        49345
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (D -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-180 tm-624 ((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49345.        ((A or ((B -> (C -> B)) and A)) -> (D -> (E -> (F or E)))), M:tm-180, m:tm-624, u:((Am (and (-> A (-> B A)) C)) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49346
in-theory        49346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-157 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49346.        ((A -> ((B and C) -> C)) and (D -> (E -> (F -> (G or F))))), M:tm-157, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49347
in-theory        49347
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-154 tm-624 ((Am (-> (and A B) B)) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-4 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49347.        ((A or ((B and C) -> C)) -> (D -> (E -> (F or E)))), M:tm-154, m:tm-624, u:((Am (-> (and A B) B)) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49348
in-theory        49348
times-derived    2
----------------------------------------------------------------
theorem          ((A and B) -> (C -> (D or C)))
theorem-size     9
proof            (modus-ponens tm-152 tm-624 ((Am (and A Bm)) (B Bm) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-7)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49348.        ((A and B) -> (C -> (D or C))), M:tm-152, m:tm-624, u:((Am (and A Bm)) (B Bm) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-49349
in-theory        49349
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-147 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49349.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (E -> (F -> (G or F))))), M:tm-147, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49350
in-theory        49350
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-144 tm-624 ((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49350.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (D -> (E -> (F or E)))), M:tm-144, m:tm-624, u:((Am (-> (and A (-> B C)) C)) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49351
in-theory        49351
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (D or C))) -> E)) -> (B -> (C -> (D or C))))
theorem-size     19
proof            (modus-ponens tm-142 tm-624 ((Am (and A (-> (-> Bm (-> Cm (or Dm Cm))) C))) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-4 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49351.        ((A and ((B -> (C -> (D or C))) -> E)) -> (B -> (C -> (D or C)))), M:tm-142, m:tm-624, u:((Am (and A (-> (-> Bm (-> Cm (or Dm Cm))) C))) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49352
in-theory        49352
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (D or C))) -> B)) -> (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-141 tm-624 ((Am (and A (-> (-> Bm (-> Cm (or Dm Cm))) Bm))) (B Bm) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-4 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49352.        ((A and ((B -> (C -> (D or C))) -> B)) -> (C -> (D or C))), M:tm-141, m:tm-624, u:((Am (and A (-> (-> Bm (-> Cm (or Dm Cm))) Bm))) (B Bm) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-49353
in-theory        49353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-134 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49353.        ((A -> ((B and C) -> B)) and (D -> (E -> (F -> (G or F))))), M:tm-134, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49354
in-theory        49354
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-131 tm-624 ((Am (-> (and A B) A)) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49354.        ((A or ((B and C) -> B)) -> (D -> (E -> (F or E)))), M:tm-131, m:tm-624, u:((Am (-> (and A B) A)) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49355
in-theory        49355
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (F -> (G or F)))))
theorem-size     25
proof            (modus-ponens tm-125 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49355.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (E -> (F -> (G or F))))), M:tm-125, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49356
in-theory        49356
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-122 tm-624 ((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49356.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (D -> (E -> (F or E)))), M:tm-122, m:tm-624, u:((Am (-> (and (-> A B) C) B)) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49357
in-theory        49357
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (C or B))) -> D) and E) -> (A -> (B -> (C or B))))
theorem-size     19
proof            (modus-ponens tm-120 tm-624 ((Am (and (-> (-> Bm (-> Cm (or Dm Cm))) B) C)) (A (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49357.        ((((A -> (B -> (C or B))) -> D) and E) -> (A -> (B -> (C or B)))), M:tm-120, m:tm-624, u:((Am (and (-> (-> Bm (-> Cm (or Dm Cm))) B) C)) (A (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49358
in-theory        49358
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (C or B))) -> A) and D) -> (B -> (C or B)))
theorem-size     17
proof            (modus-ponens tm-119 tm-624 ((Am (and (-> (-> Bm (-> Cm (or Dm Cm))) Bm) C)) (A Bm) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-3 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49358.        ((((A -> (B -> (C or B))) -> A) and D) -> (B -> (C or B))), M:tm-119, m:tm-624, u:((Am (and (-> (-> Bm (-> Cm (or Dm Cm))) Bm) C)) (A Bm) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-49359
in-theory        49359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-113 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49359.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (F -> (G -> (H or G))))), M:tm-113, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49360
in-theory        49360
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-110 tm-624 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49360.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (E -> (F -> (G or F)))), M:tm-110, m:tm-624, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49361
in-theory        49361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (D -> (E or D)))
theorem-size     11
proof            (modus-ponens tm-108 tm-624 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49361.        ((A -> (B -> C)) -> (D -> (E or D))), M:tm-108, m:tm-624, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-49362
in-theory        49362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) -> (A -> B)) -> (A -> (C or B)))
theorem-size     17
proof            (modus-ponens tm-106 tm-624 ((Am (-> (-> Bm (-> Cm (or Dm Cm))) (-> Bm Cm))) (A Bm) (B Cm) (C (or Dm Cm))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49362.        (((A -> (B -> (C or B))) -> (A -> B)) -> (A -> (C or B))), M:tm-106, m:tm-624, u:((Am (-> (-> Bm (-> Cm (or Dm Cm))) (-> Bm Cm))) (A Bm) (B Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-49363
in-theory        49363
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (F -> (G or F)))))
theorem-size     29
proof            (modus-ponens tm-105 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49363.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (F -> (G or F))))), M:tm-105, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49364
in-theory        49364
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (E -> (F or E))))
theorem-size     27
proof            (modus-ponens tm-102 tm-624 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49364.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (D -> (E -> (F or E)))), M:tm-102, m:tm-624, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49365
in-theory        49365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) -> D)) -> (A -> (B -> (C or B))))
theorem-size     17
proof            (modus-ponens tm-100 tm-624 ((Am (-> Bm (-> (-> Cm (or Dm Cm)) C))) (A Bm) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49365.        ((A -> ((B -> (C or B)) -> D)) -> (A -> (B -> (C or B)))), M:tm-100, m:tm-624, u:((Am (-> Bm (-> (-> Cm (or Dm Cm)) C))) (A Bm) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-49366
in-theory        49366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) -> D) -> (A -> (B -> (C or B))))
theorem-size     17
proof            (modus-ponens tm-96 tm-624 ((Am (-> (-> Bm (-> Cm (or Dm Cm))) B)) (A (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49366.        (((A -> (B -> (C or B))) -> D) -> (A -> (B -> (C or B)))), M:tm-96, m:tm-624, u:((Am (-> (-> Bm (-> Cm (or Dm Cm))) B)) (A (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49367
in-theory        49367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (D -> (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-95 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49367.        (((A -> B) -> (A -> A)) and (C -> (D -> (E -> (F or E))))), M:tm-95, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49368
in-theory        49368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (C -> (D -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-92 tm-624 ((Am (-> A A)) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49368.        (((A -> B) or (A -> A)) -> (C -> (D -> (E or D)))), M:tm-92, m:tm-624, u:((Am (-> A A)) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49369
in-theory        49369
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (C -> (D -> (E or D)))))
theorem-size     11
proof            (modus-ponens tm-84 tm-624 ((A Am) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       81
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49369.        (A -> (B -> (C -> (D -> (E or D))))), M:tm-84, m:tm-624, u:((A Am) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49370
in-theory        49370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (E -> (F -> (G or F)))))
theorem-size     17
proof            (modus-ponens tm-83 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       83
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49370.        ((A -> (B -> (C -> B))) and (D -> (E -> (F -> (G or F))))), M:tm-83, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49371
in-theory        49371
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-80 tm-624 ((Am (-> A (-> B A))) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49371.        ((A or (B -> (C -> B))) -> (D -> (E -> (F or E)))), M:tm-80, m:tm-624, u:((Am (-> A (-> B A))) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49372
in-theory        49372
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((A -> (B -> (C or B))) -> D))) -> D)
theorem-size     13
proof            (modus-ponens tm-77 tm-624 ((Am (not (not (-> (-> Bm (-> Cm (or Dm Cm))) B)))) (A (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-10 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49372.        ((not (not ((A -> (B -> (C or B))) -> D))) -> D), M:tm-77, m:tm-624, u:((Am (not (not (-> (-> Bm (-> Cm (or Dm Cm))) B)))) (A (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49373
in-theory        49373
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (C -> (D -> (E or D)))))
theorem-size     15
proof            (modus-ponens tm-76 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-10 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49373.        (((not (not A)) -> A) and (B -> (C -> (D -> (E or D))))), M:tm-76, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49374
in-theory        49374
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (B -> (C -> (D or C))))
theorem-size     13
proof            (modus-ponens tm-73 tm-624 ((A Am) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-10 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49374.        (((not (not A)) or A) -> (B -> (C -> (D or C)))), M:tm-73, m:tm-624, u:((A Am) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49375
in-theory        49375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (E -> (F or E)))))
theorem-size     21
proof            (modus-ponens tm-69 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-9 tm-1 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49375.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (D -> (E -> (F or E))))), M:tm-69, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49376
in-theory        49376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (D -> (E or D))))
theorem-size     19
proof            (modus-ponens tm-66 tm-624 ((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-9 tm-1 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49376.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (C -> (D -> (E or D)))), M:tm-66, m:tm-624, u:((Am (-> (-> A (not B)) (not A))) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49377
in-theory        49377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A or B) -> (C -> (D or C))))
theorem-size     13
proof            (modus-ponens tm-55 tm-624 ((Am (-> A Bm)) (B Bm) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-8 tm-1 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49377.        ((A -> B) -> ((A or B) -> (C -> (D or C)))), M:tm-55, m:tm-624, u:((Am (-> A Bm)) (B Bm) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-49378
in-theory        49378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-54 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49378.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (E -> (F -> (G or F))))), M:tm-54, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49379
in-theory        49379
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-51 tm-624 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49379.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (D -> (E -> (F or E)))), M:tm-51, m:tm-624, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49380
in-theory        49380
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (C -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-50 tm-624 ((Am (or A B)) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49380.        ((A or (B or A)) -> (C -> (D -> (E or D)))), M:tm-50, m:tm-624, u:((Am (or A B)) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49381
in-theory        49381
times-derived    3
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (C -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-49 tm-624 ((Am (or A B)) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49381.        ((A or (A or B)) -> (C -> (D -> (E or D)))), M:tm-49, m:tm-624, u:((Am (or A B)) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49382
in-theory        49382
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (C -> (D -> (E or D))))
theorem-size     15
proof            (modus-ponens tm-48 tm-624 ((Am (-> A (and B A))) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-5 tm-1 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49382.        ((A or (B -> (A and B))) -> (C -> (D -> (E or D)))), M:tm-48, m:tm-624, u:((Am (-> A (and B A))) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49383
in-theory        49383
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-47 tm-624 ((A Am) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49383.        (((A and B) or B) -> (C -> (D -> (E or D)))), M:tm-47, m:tm-624, u:((A Am) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49384
in-theory        49384
times-derived    3
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-46 tm-624 ((A Am) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49384.        (((A and B) or A) -> (C -> (D -> (E or D)))), M:tm-46, m:tm-624, u:((A Am) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49385
in-theory        49385
times-derived    3
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-45 tm-624 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49385.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (F or E)))), M:tm-45, m:tm-624, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49386
in-theory        49386
times-derived    3
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-44 tm-624 ((Am (-> A B)) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49386.        ((A or (B -> A)) -> (C -> (D -> (E or D)))), M:tm-44, m:tm-624, u:((Am (-> A B)) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49387
in-theory        49387
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-42 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-7 tm-1)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49387.        ((A -> (B or A)) and (C -> (D -> (E -> (F or E))))), M:tm-42, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49388
in-theory        49388
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-32 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49388.        ((A -> (A or B)) and (C -> (D -> (E -> (F or E))))), M:tm-32, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49389
in-theory        49389
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (B -> (C -> (D or C)))))
theorem-size     11
proof            (modus-ponens tm-24 tm-624 ((A Am) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7)
proof-size       71
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49389.        (A -> (A and (B -> (C -> (D or C))))), M:tm-24, m:tm-624, u:((A Am) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49390
in-theory        49390
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (F or E)))))
theorem-size     17
proof            (modus-ponens tm-23 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       73
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49390.        ((A -> (B -> (A and B))) and (C -> (D -> (E -> (F or E))))), M:tm-23, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49391
in-theory        49391
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-22 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-4 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49391.        (((A and B) -> B) and (C -> (D -> (E -> (F or E))))), M:tm-22, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49392
in-theory        49392
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-21 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-3 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49392.        (((A and B) -> A) and (C -> (D -> (E -> (F or E))))), M:tm-21, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49393
in-theory        49393
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-20 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49393.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (G or F))))), M:tm-20, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49394
in-theory        49394
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (D -> (E -> (F or E)))))
theorem-size     15
proof            (modus-ponens tm-19 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       67
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49394.        ((A -> (B -> A)) and (C -> (D -> (E -> (F or E))))), M:tm-19, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49395
in-theory        49395
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((B -> (C -> (D or C))) -> E)) -> E)
theorem-size     13
proof            (modus-ponens tm-17 tm-624 ((Am (and A (-> (-> Bm (-> Cm (or Dm Cm))) C))) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-4 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49395.        ((A and ((B -> (C -> (D or C))) -> E)) -> E), M:tm-17, m:tm-624, u:((Am (and A (-> (-> Bm (-> Cm (or Dm Cm))) C))) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49396
in-theory        49396
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> (C or B))) -> D) and E) -> D)
theorem-size     13
proof            (modus-ponens tm-15 tm-624 ((Am (and (-> (-> Bm (-> Cm (or Dm Cm))) B) C)) (A (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-3 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49396.        ((((A -> (B -> (C or B))) -> D) and E) -> D), M:tm-15, m:tm-624, u:((Am (and (-> (-> Bm (-> Cm (or Dm Cm))) B) C)) (A (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49397
in-theory        49397
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) -> D)) -> (A -> D))
theorem-size     13
proof            (modus-ponens tm-13 tm-624 ((Am (-> Bm (-> (-> Cm (or Dm Cm)) C))) (A Bm) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49397.        ((A -> ((B -> (C or B)) -> D)) -> (A -> D)), M:tm-13, m:tm-624, u:((Am (-> Bm (-> (-> Cm (or Dm Cm)) C))) (A Bm) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-49398
in-theory        49398
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (B -> (C -> (D or C))))) -> (not A))
theorem-size     13
proof            (modus-ponens tm-9 tm-624 ((A Am) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-9 tm-1 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49398.        ((A -> (not (B -> (C -> (D or C))))) -> (not A)), M:tm-9, m:tm-624, u:((A Am) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49399
in-theory        49399
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) -> D) -> ((E or (A -> (B -> (C or B)))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-624 ((A Am) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49399.        (((A -> (B -> (C or B))) -> D) -> ((E or (A -> (B -> (C or B)))) -> D)), M:tm-8, m:tm-624, u:((A Am) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-49400
in-theory        49400
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (C -> (D -> (E or D)))))
theorem-size     11
proof            (modus-ponens tm-7 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-7 tm-1)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49400.        (A or (B -> (C -> (D -> (E or D))))), M:tm-7, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49401
in-theory        49401
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) or E)
theorem-size     11
proof            (modus-ponens tm-6 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-6 tm-1 tm-7)
proof-size       47
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49401.        ((A -> (B -> (C -> (D or C)))) or E), M:tm-6, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49402
in-theory        49402
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (D -> (E or D)))) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-1 tm-7)
proof-size       51
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49402.        (A -> ((B -> (C -> (D -> (E or D)))) and A)), M:tm-5, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-49403
in-theory        49403
times-derived    2
----------------------------------------------------------------
theorem          ((A -> B) -> (A -> (C -> (D or C))))
theorem-size     11
proof            (modus-ponens tm-2 tm-624 ((A Am) (B Bm) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-1 tm-7)
proof-size       55
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-49403.        ((A -> B) -> (A -> (C -> (D or C)))), M:tm-2, m:tm-624, u:((A Am) (B Bm) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-49404
in-theory        49404
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (D -> (B -> A))))
theorem-size     13
proof            (modus-ponens tm-623 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49404.        ((A or (B -> A)) -> (C or (D -> (B -> A)))), M:tm-623, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49405
in-theory        49405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-622 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49405.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-622, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49406
in-theory        49406
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49406.        (((A or (B -> A)) -> (C -> (B -> A))) and (D -> (E or D))), M:tm-609, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49407
in-theory        49407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-605 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49407.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-605, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49408
in-theory        49408
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and ((D -> (E or D)) and ((A or (B -> A)) -> (C -> (B -> A)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49408.        (((A or (B -> A)) -> (C -> (B -> A))) and ((D -> (E or D)) and ((A or (B -> A)) -> (C -> (B -> A))))), M:tm-595, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49409
in-theory        49409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-550 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49409.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-550, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49410
in-theory        49410
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-540 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49410.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-540, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49411
in-theory        49411
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-530 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49411.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-530, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49412
in-theory        49412
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-520 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49412.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-520, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49413
in-theory        49413
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-510 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49413.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-510, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49414
in-theory        49414
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-500 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49414.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-500, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49415
in-theory        49415
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-490 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49415.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (F -> E)))), M:tm-490, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49416
in-theory        49416
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-480 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49416.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-480, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49417
in-theory        49417
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (B -> A)) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49417.        ((A or (B -> A)) -> ((C -> (B -> A)) or D)), M:tm-470, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49418
in-theory        49418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-469 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49418.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-469, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49419
in-theory        49419
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49419.        (((A or (B -> A)) -> (C -> (B -> A))) and (D -> (D or E))), M:tm-456, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49420
in-theory        49420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-453 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49420.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-453, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49421
in-theory        49421
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and ((D -> (D or E)) and ((A or (B -> A)) -> (C -> (B -> A)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49421.        (((A or (B -> A)) -> (C -> (B -> A))) and ((D -> (D or E)) and ((A or (B -> A)) -> (C -> (B -> A))))), M:tm-443, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49422
in-theory        49422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-409 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49422.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-409, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49423
in-theory        49423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-400 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49423.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-400, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49424
in-theory        49424
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-391 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49424.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-391, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49425
in-theory        49425
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-382 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49425.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-382, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49426
in-theory        49426
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (G -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-373 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49426.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (G -> (F -> E)))), M:tm-373, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49427
in-theory        49427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-364 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49427.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-364, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49428
in-theory        49428
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D -> (B -> A)) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49428.        ((A or (B -> A)) -> (C -> ((D -> (B -> A)) and C))), M:tm-355, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49429
in-theory        49429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-354 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49429.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-354, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49430
in-theory        49430
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49430.        (((A or (B -> A)) -> (C -> (B -> A))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49431
in-theory        49431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (E -> (D -> C))))
theorem-size     21
proof            (modus-ponens tm-338 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49431.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (E -> (D -> C)))), M:tm-338, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49432
in-theory        49432
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (B -> A)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49432.        (((A or (B -> A)) -> (C -> (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (B -> A))))), M:tm-328, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49433
in-theory        49433
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and ((D -> (E -> (D and E))) and ((A or (B -> A)) -> (C -> (B -> A)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49433.        (((A or (B -> A)) -> (C -> (B -> A))) and ((D -> (E -> (D and E))) and ((A or (B -> A)) -> (C -> (B -> A))))), M:tm-327, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49434
in-theory        49434
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (((D and E) -> E) and ((A or (B -> A)) -> (C -> (B -> A)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49434.        (((A or (B -> A)) -> (C -> (B -> A))) and (((D and E) -> E) and ((A or (B -> A)) -> (C -> (B -> A))))), M:tm-326, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49435
in-theory        49435
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (((D and E) -> D) and ((A or (B -> A)) -> (C -> (B -> A)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49435.        (((A or (B -> A)) -> (C -> (B -> A))) and (((D and E) -> D) and ((A or (B -> A)) -> (C -> (B -> A))))), M:tm-325, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49436
in-theory        49436
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> A)) -> (C -> (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49436.        (((A or (B -> A)) -> (C -> (B -> A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> A)) -> (C -> (B -> A))))), M:tm-324, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49437
in-theory        49437
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and ((D -> (E -> D)) and ((A or (B -> A)) -> (C -> (B -> A)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49437.        (((A or (B -> A)) -> (C -> (B -> A))) and ((D -> (E -> D)) and ((A or (B -> A)) -> (C -> (B -> A))))), M:tm-323, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49438
in-theory        49438
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49438.        (((A or (B -> A)) -> (C -> (B -> A))) and ((D and E) -> E)), M:tm-322, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49439
in-theory        49439
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49439.        (((A or (B -> A)) -> (C -> (B -> A))) and ((D and E) -> D)), M:tm-320, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49440
in-theory        49440
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49440.        (((A or (B -> A)) -> (C -> (B -> A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49441
in-theory        49441
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49441.        (((A or (B -> A)) -> (C -> (B -> A))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49442
in-theory        49442
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49442.        (((A or (B -> A)) -> (C -> (B -> A))) and (D -> (E -> D))), M:tm-315, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49443
in-theory        49443
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (((A or (B -> A)) -> (not (C -> (B -> A)))) -> (not (A or (B -> A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49443.        (((A or (B -> A)) -> (C -> (B -> A))) and (((A or (B -> A)) -> (not (C -> (B -> A)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49444
in-theory        49444
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (((C -> (B -> A)) -> D) -> (((A or (B -> A)) or (C -> (B -> A))) -> D)))
theorem-size     33
proof            (modus-ponens tm-312 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49444.        (((A or (B -> A)) -> (C -> (B -> A))) and (((C -> (B -> A)) -> D) -> (((A or (B -> A)) or (C -> (B -> A))) -> D))), M:tm-312, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49445
in-theory        49445
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (D or ((A or (B -> A)) -> (C -> (B -> A)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49445.        (((A or (B -> A)) -> (C -> (B -> A))) and (D or ((A or (B -> A)) -> (C -> (B -> A))))), M:tm-311, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49446
in-theory        49446
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (((A or (B -> A)) -> (C -> (B -> A))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49446.        (((A or (B -> A)) -> (C -> (B -> A))) and (((A or (B -> A)) -> (C -> (B -> A))) or D)), M:tm-310, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49447
in-theory        49447
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (D -> (((A or (B -> A)) -> (C -> (B -> A))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49447.        (((A or (B -> A)) -> (C -> (B -> A))) and (D -> (((A or (B -> A)) -> (C -> (B -> A))) and D))), M:tm-309, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49448
in-theory        49448
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (B -> A))))
theorem-size     29
proof            (modus-ponens tm-306 tm-625 ((A (or Am (-> Bm Am))) (B Cm) (C (-> Bm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49448.        (((A or (B -> A)) -> (C -> (B -> A))) and (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (B -> A)))), M:tm-306, m:tm-625, u:((A (or Am (-> Bm Am))) (B Cm) (C (-> Bm Am)))
================================================================
tm-name          tm-49449
in-theory        49449
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and (D -> ((A or (B -> A)) -> (C -> (B -> A)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49449.        (((A or (B -> A)) -> (C -> (B -> A))) and (D -> ((A or (B -> A)) -> (C -> (B -> A))))), M:tm-305, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49450
in-theory        49450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-303 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49450.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-303, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49451
in-theory        49451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-270 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49451.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-270, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49452
in-theory        49452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-239 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49452.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-239, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49453
in-theory        49453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (G -> (F -> E))))
theorem-size     29
proof            (modus-ponens tm-210 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49453.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (G -> (F -> E)))), M:tm-210, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49454
in-theory        49454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-183 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49454.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-183, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49455
in-theory        49455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-157 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49455.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-157, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49456
in-theory        49456
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     27
proof            (modus-ponens tm-147 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49456.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-147, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49457
in-theory        49457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-134 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49457.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-134, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49458
in-theory        49458
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     27
proof            (modus-ponens tm-125 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49458.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-125, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49459
in-theory        49459
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> B) -> (C -> A)))
theorem-size     13
proof            (modus-ponens tm-114 tm-625 ((A (or Am (-> Bm Am))) (B Cm) (C Bm) (D Am)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49459.        ((A or (B -> A)) -> ((C -> B) -> (C -> A))), M:tm-114, m:tm-625, u:((A (or Am (-> Bm Am))) (B Cm) (C Bm) (D Am))
================================================================
tm-name          tm-49460
in-theory        49460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-113 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49460.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (F -> E)))), M:tm-113, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49461
in-theory        49461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     31
proof            (modus-ponens tm-105 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49461.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-105, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49462
in-theory        49462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (E -> (D -> C))))
theorem-size     19
proof            (modus-ponens tm-95 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49462.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (E -> (D -> C)))), M:tm-95, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49463
in-theory        49463
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (D -> (B -> A))))
theorem-size     13
proof            (modus-ponens tm-84 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49463.        ((A or (B -> A)) -> (C -> (D -> (B -> A)))), M:tm-84, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49464
in-theory        49464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     19
proof            (modus-ponens tm-83 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49464.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-83, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49465
in-theory        49465
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> (D -> (C -> B))))
theorem-size     17
proof            (modus-ponens tm-76 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49465.        (((not (not A)) -> A) and ((B or (C -> B)) -> (D -> (C -> B)))), M:tm-76, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49466
in-theory        49466
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (C -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-73 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-8 tm-10 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49466.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (C -> (B -> A))), M:tm-73, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49467
in-theory        49467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (E -> (D -> C))))
theorem-size     23
proof            (modus-ponens tm-69 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49467.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (E -> (D -> C)))), M:tm-69, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49468
in-theory        49468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     25
proof            (modus-ponens tm-54 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49468.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-54, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49469
in-theory        49469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> (C -> (A -> B)))
theorem-size     15
proof            (modus-ponens tm-50 tm-625 ((A Am) (B (-> Bm Am)) (C (-> Cm (-> Bm Am)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49469.        (((A -> B) or (B or (A -> B))) -> (C -> (A -> B))), M:tm-50, m:tm-625, u:((A Am) (B (-> Bm Am)) (C (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49470
in-theory        49470
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> (C -> (B -> A)))
theorem-size     13
proof            (modus-ponens tm-49 tm-625 ((A Am) (B (-> Bm Am)) (C (-> Cm (-> Bm Am)))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49470.        ((A or (A or (B -> A))) -> (C -> (B -> A))), M:tm-49, m:tm-625, u:((A Am) (B (-> Bm Am)) (C (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49471
in-theory        49471
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> (D -> (C -> B)))
theorem-size     19
proof            (modus-ponens tm-47 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49471.        (((A and (B or (C -> B))) or (B or (C -> B))) -> (D -> (C -> B))), M:tm-47, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49472
in-theory        49472
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> (D -> (B -> A)))
theorem-size     19
proof            (modus-ponens tm-46 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49472.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> (D -> (B -> A))), M:tm-46, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49473
in-theory        49473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> (E -> (D -> C))))
theorem-size     17
proof            (modus-ponens tm-42 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49473.        ((A -> (B or A)) and ((C or (D -> C)) -> (E -> (D -> C)))), M:tm-42, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49474
in-theory        49474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> (E -> (D -> C))))
theorem-size     17
proof            (modus-ponens tm-32 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49474.        ((A -> (A or B)) and ((C or (D -> C)) -> (E -> (D -> C)))), M:tm-32, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49475
in-theory        49475
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (B -> A))))
theorem-size     17
proof            (modus-ponens tm-24 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49475.        ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (B -> A)))), M:tm-24, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49476
in-theory        49476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (E -> (D -> C))))
theorem-size     19
proof            (modus-ponens tm-23 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49476.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (E -> (D -> C)))), M:tm-23, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49477
in-theory        49477
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> (E -> (D -> C))))
theorem-size     17
proof            (modus-ponens tm-22 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49477.        (((A and B) -> B) and ((C or (D -> C)) -> (E -> (D -> C)))), M:tm-22, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49478
in-theory        49478
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> (E -> (D -> C))))
theorem-size     17
proof            (modus-ponens tm-21 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49478.        (((A and B) -> A) and ((C or (D -> C)) -> (E -> (D -> C)))), M:tm-21, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49479
in-theory        49479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     25
proof            (modus-ponens tm-20 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49479.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-20, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49480
in-theory        49480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> (E -> (D -> C))))
theorem-size     17
proof            (modus-ponens tm-19 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49480.        ((A -> (B -> A)) and ((C or (D -> C)) -> (E -> (D -> C)))), M:tm-19, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49481
in-theory        49481
times-derived    24
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (A or (B -> A)))
theorem-size     11
proof            (modus-ponens tm-12 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49481.        ((A or (B -> A)) -> (A or (B -> A))), M:tm-12, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49482
in-theory        49482
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not (C -> (B -> A)))) -> (not (A or (B -> A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-9 tm-8 tm-1)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49482.        (((A or (B -> A)) -> (not (C -> (B -> A)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49483
in-theory        49483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> D) -> (((C or (B -> C)) or (A -> (B -> C))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-8 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49483.        (((A -> (B -> C)) -> D) -> (((C or (B -> C)) or (A -> (B -> C))) -> D)), M:tm-8, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-49484
in-theory        49484
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> (D -> (C -> B))))
theorem-size     13
proof            (modus-ponens tm-7 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-7 tm-8 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49484.        (A or ((B or (C -> B)) -> (D -> (C -> B)))), M:tm-7, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49485
in-theory        49485
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-6 tm-8 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49485.        (((A or (B -> A)) -> (C -> (B -> A))) or D), M:tm-6, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49486
in-theory        49486
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> (D -> (C -> B))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49486.        (A -> (((B or (C -> B)) -> (D -> (C -> B))) and A)), M:tm-5, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49487
in-theory        49487
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (B -> A)))
theorem-size     17
proof            (modus-ponens tm-2 tm-625 ((A (or Am (-> Bm Am))) (B Cm) (C (-> Bm Am))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49487.        (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (B -> A))), M:tm-2, m:tm-625, u:((A (or Am (-> Bm Am))) (B Cm) (C (-> Bm Am)))
================================================================
tm-name          tm-49488
in-theory        49488
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (D -> (C -> B))))
theorem-size     13
proof            (modus-ponens tm-1 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-1 tm-8)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-49488.        (A -> ((B or (C -> B)) -> (D -> (C -> B)))), M:tm-1, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-49489
in-theory        49489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (C -> (A -> B))) -> (D or ((C -> A) -> (C -> B))))
theorem-size     19
proof            (modus-ponens tm-623 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49489.        (((A -> B) or (C -> (A -> B))) -> (D or ((C -> A) -> (C -> B)))), M:tm-623, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49490
in-theory        49490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-622 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49490.        ((A -> (B -> (C or B))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-622, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49491
in-theory        49491
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-609 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49491.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (D -> (E or D))), M:tm-609, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49492
in-theory        49492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-605 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49492.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-605, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49493
in-theory        49493
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((D -> (E or D)) and (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49493.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((D -> (E or D)) and (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))))), M:tm-595, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49494
in-theory        49494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-550 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49494.        (((A -> (B or A)) or C) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-550, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49495
in-theory        49495
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-540 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49495.        ((A or (B -> (C or B))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-540, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49496
in-theory        49496
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-530 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49496.        ((A or (B -> (B or C))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-530, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49497
in-theory        49497
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-520 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49497.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-520, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49498
in-theory        49498
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-510 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49498.        ((A or ((B and C) -> C)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-510, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49499
in-theory        49499
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-500 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49499.        ((A or ((B and C) -> B)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-500, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49500
in-theory        49500
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F))))
theorem-size     33
proof            (modus-ponens tm-490 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49500.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F)))), M:tm-490, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49501
in-theory        49501
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-480 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49501.        ((A or (B -> (C -> B))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-480, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49502
in-theory        49502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (C -> (A -> B))) -> (((C -> A) -> (C -> B)) or D))
theorem-size     19
proof            (modus-ponens tm-470 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49502.        (((A -> B) or (C -> (A -> B))) -> (((C -> A) -> (C -> B)) or D)), M:tm-470, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49503
in-theory        49503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-469 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49503.        ((A -> (B -> (B or C))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-469, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49504
in-theory        49504
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-456 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49504.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (D -> (D or E))), M:tm-456, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49505
in-theory        49505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-453 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49505.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-453, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49506
in-theory        49506
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((D -> (D or E)) and (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49506.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((D -> (D or E)) and (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))))), M:tm-443, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49507
in-theory        49507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-409 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49507.        (((A -> (A or B)) or C) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-409, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49508
in-theory        49508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-400 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49508.        (((A -> (B -> (A and B))) or C) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-400, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49509
in-theory        49509
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-391 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49509.        ((((A and B) -> B) or C) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-391, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49510
in-theory        49510
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-382 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49510.        ((((A and B) -> A) or C) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-382, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49511
in-theory        49511
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F))))
theorem-size     33
proof            (modus-ponens tm-373 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49511.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F)))), M:tm-373, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49512
in-theory        49512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-364 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49512.        (((A -> (B -> A)) or C) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-364, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49513
in-theory        49513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (C -> (A -> B))) -> (D -> (((C -> A) -> (C -> B)) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49513.        (((A -> B) or (C -> (A -> B))) -> (D -> (((C -> A) -> (C -> B)) and D))), M:tm-355, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49514
in-theory        49514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-354 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49514.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-354, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49515
in-theory        49515
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-341 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49515.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49516
in-theory        49516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D))))
theorem-size     27
proof            (modus-ponens tm-338 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49516.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D)))), M:tm-338, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49517
in-theory        49517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((A -> B) or (C -> (A -> B))) -> (((A -> B) or (C -> (A -> B))) and ((C -> A) -> (C -> B)))))
theorem-size     45
proof            (modus-ponens tm-328 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49517.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((A -> B) or (C -> (A -> B))) -> (((A -> B) or (C -> (A -> B))) and ((C -> A) -> (C -> B))))), M:tm-328, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49518
in-theory        49518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((D -> (E -> (D and E))) and (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49518.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((D -> (E -> (D and E))) and (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))))), M:tm-327, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49519
in-theory        49519
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((D and E) -> E) and (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49519.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((D and E) -> E) and (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))))), M:tm-326, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49520
in-theory        49520
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((D and E) -> D) and (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49520.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((D and E) -> D) and (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))))), M:tm-325, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49521
in-theory        49521
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49521.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))))), M:tm-324, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49522
in-theory        49522
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((D -> (E -> D)) and (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49522.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((D -> (E -> D)) and (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))))), M:tm-323, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49523
in-theory        49523
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-322 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49523.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((D and E) -> E)), M:tm-322, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49524
in-theory        49524
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-320 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49524.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((D and E) -> D)), M:tm-320, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49525
in-theory        49525
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-318 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49525.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49526
in-theory        49526
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((A -> B) or (C -> (A -> B))) -> ((A -> B) or (C -> (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-316 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49526.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((A -> B) or (C -> (A -> B))) -> ((A -> B) or (C -> (A -> B))))), M:tm-316, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49527
in-theory        49527
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-315 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49527.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (D -> (E -> D))), M:tm-315, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49528
in-theory        49528
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((((A -> B) or (C -> (A -> B))) -> (not ((C -> A) -> (C -> B)))) -> (not ((A -> B) or (C -> (A -> B))))))
theorem-size     47
proof            (modus-ponens tm-313 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49528.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((((A -> B) or (C -> (A -> B))) -> (not ((C -> A) -> (C -> B)))) -> (not ((A -> B) or (C -> (A -> B)))))), M:tm-313, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49529
in-theory        49529
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((((C -> A) -> (C -> B)) -> D) -> ((((A -> B) or (C -> (A -> B))) or ((C -> A) -> (C -> B))) -> D)))
theorem-size     47
proof            (modus-ponens tm-312 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49529.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((((C -> A) -> (C -> B)) -> D) -> ((((A -> B) or (C -> (A -> B))) or ((C -> A) -> (C -> B))) -> D))), M:tm-312, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49530
in-theory        49530
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (D or (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49530.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (D or (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))))), M:tm-311, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49531
in-theory        49531
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) or D))
theorem-size     37
proof            (modus-ponens tm-310 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49531.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) or D)), M:tm-310, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49532
in-theory        49532
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (D -> ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and D)))
theorem-size     39
proof            (modus-ponens tm-309 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49532.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (D -> ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and D))), M:tm-309, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49533
in-theory        49533
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((((A -> B) or (C -> (A -> B))) -> (C -> A)) -> (((A -> B) or (C -> (A -> B))) -> (C -> B))))
theorem-size     45
proof            (modus-ponens tm-306 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> Cm Am)) (C (-> Cm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49533.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and ((((A -> B) or (C -> (A -> B))) -> (C -> A)) -> (((A -> B) or (C -> (A -> B))) -> (C -> B)))), M:tm-306, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> Cm Am)) (C (-> Cm Bm)))
================================================================
tm-name          tm-49534
in-theory        49534
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (D -> (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49534.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (D -> (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))))), M:tm-305, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49535
in-theory        49535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     29
proof            (modus-ponens tm-303 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49535.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-303, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49536
in-theory        49536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-270 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49536.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-270, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49537
in-theory        49537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-239 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49537.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-239, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49538
in-theory        49538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F))))
theorem-size     35
proof            (modus-ponens tm-210 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49538.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F)))), M:tm-210, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49539
in-theory        49539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     27
proof            (modus-ponens tm-183 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49539.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-183, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49540
in-theory        49540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-157 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49540.        ((A -> ((B and C) -> C)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-157, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49541
in-theory        49541
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     33
proof            (modus-ponens tm-147 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49541.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-147, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49542
in-theory        49542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-134 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49542.        ((A -> ((B and C) -> B)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-134, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49543
in-theory        49543
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     33
proof            (modus-ponens tm-125 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49543.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-125, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49544
in-theory        49544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (C -> (A -> B))) -> (((C -> A) -> C) -> ((C -> A) -> B)))
theorem-size     21
proof            (modus-ponens tm-114 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> Cm Am)) (C Cm) (D Bm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49544.        (((A -> B) or (C -> (A -> B))) -> (((C -> A) -> C) -> ((C -> A) -> B))), M:tm-114, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> Cm Am)) (C Cm) (D Bm))
================================================================
tm-name          tm-49545
in-theory        49545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F))))
theorem-size     33
proof            (modus-ponens tm-113 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49545.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F)))), M:tm-113, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49546
in-theory        49546
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     37
proof            (modus-ponens tm-105 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49546.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-105, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49547
in-theory        49547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D))))
theorem-size     25
proof            (modus-ponens tm-95 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49547.        (((A -> B) -> (A -> A)) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D)))), M:tm-95, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49548
in-theory        49548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (C -> (A -> B))) -> (D -> ((C -> A) -> (C -> B))))
theorem-size     19
proof            (modus-ponens tm-84 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49548.        (((A -> B) or (C -> (A -> B))) -> (D -> ((C -> A) -> (C -> B)))), M:tm-84, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49549
in-theory        49549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-83 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49549.        ((A -> (B -> (C -> B))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-83, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49550
in-theory        49550
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or (D -> (B -> C))) -> ((D -> B) -> (D -> C))))
theorem-size     23
proof            (modus-ponens tm-76 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49550.        (((not (not A)) -> A) and (((B -> C) or (D -> (B -> C))) -> ((D -> B) -> (D -> C)))), M:tm-76, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49551
in-theory        49551
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or (C -> (A -> B))))) or ((A -> B) or (C -> (A -> B)))) -> ((C -> A) -> (C -> B)))
theorem-size     29
proof            (modus-ponens tm-73 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49551.        (((not (not ((A -> B) or (C -> (A -> B))))) or ((A -> B) or (C -> (A -> B)))) -> ((C -> A) -> (C -> B))), M:tm-73, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49552
in-theory        49552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D))))
theorem-size     29
proof            (modus-ponens tm-69 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49552.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D)))), M:tm-69, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49553
in-theory        49553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     31
proof            (modus-ponens tm-54 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49553.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-54, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49554
in-theory        49554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((B -> C) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C)))
theorem-size     23
proof            (modus-ponens tm-50 tm-626 ((A (-> Am Bm)) (B (-> Cm (-> Am Bm))) (C (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49554.        (((A -> (B -> C)) or ((B -> C) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C))), M:tm-50, m:tm-626, u:((A (-> Am Bm)) (B (-> Cm (-> Am Bm))) (C (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49555
in-theory        49555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or (C -> (A -> B)))) -> ((C -> A) -> (C -> B)))
theorem-size     21
proof            (modus-ponens tm-49 tm-626 ((A (-> Am Bm)) (B (-> Cm (-> Am Bm))) (C (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49555.        (((A -> B) or ((A -> B) or (C -> (A -> B)))) -> ((C -> A) -> (C -> B))), M:tm-49, m:tm-626, u:((A (-> Am Bm)) (B (-> Cm (-> Am Bm))) (C (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49556
in-theory        49556
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or (D -> (B -> C)))) or ((B -> C) or (D -> (B -> C)))) -> ((D -> B) -> (D -> C)))
theorem-size     29
proof            (modus-ponens tm-47 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49556.        (((A and ((B -> C) or (D -> (B -> C)))) or ((B -> C) or (D -> (B -> C)))) -> ((D -> B) -> (D -> C))), M:tm-47, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49557
in-theory        49557
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or (C -> (A -> B))) and D) or ((A -> B) or (C -> (A -> B)))) -> ((C -> A) -> (C -> B)))
theorem-size     29
proof            (modus-ponens tm-46 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49557.        (((((A -> B) or (C -> (A -> B))) and D) or ((A -> B) or (C -> (A -> B)))) -> ((C -> A) -> (C -> B))), M:tm-46, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49558
in-theory        49558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-42 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49558.        ((A -> (B or A)) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D)))), M:tm-42, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49559
in-theory        49559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-32 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49559.        ((A -> (A or B)) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D)))), M:tm-32, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49560
in-theory        49560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (C -> (A -> B))) -> (((A -> B) or (C -> (A -> B))) and ((C -> A) -> (C -> B))))
theorem-size     27
proof            (modus-ponens tm-24 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49560.        (((A -> B) or (C -> (A -> B))) -> (((A -> B) or (C -> (A -> B))) and ((C -> A) -> (C -> B)))), M:tm-24, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49561
in-theory        49561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D))))
theorem-size     25
proof            (modus-ponens tm-23 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49561.        ((A -> (B -> (A and B))) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D)))), M:tm-23, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49562
in-theory        49562
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-22 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49562.        (((A and B) -> B) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D)))), M:tm-22, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49563
in-theory        49563
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-21 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49563.        (((A and B) -> A) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D)))), M:tm-21, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49564
in-theory        49564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     31
proof            (modus-ponens tm-20 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49564.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-20, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49565
in-theory        49565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-19 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49565.        ((A -> (B -> A)) and (((C -> D) or (E -> (C -> D))) -> ((E -> C) -> (E -> D)))), M:tm-19, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49566
in-theory        49566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (C -> (A -> B))) -> ((A -> B) or (C -> (A -> B))))
theorem-size     19
proof            (modus-ponens tm-12 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49566.        (((A -> B) or (C -> (A -> B))) -> ((A -> B) or (C -> (A -> B)))), M:tm-12, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49567
in-theory        49567
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> (not ((C -> A) -> (C -> B)))) -> (not ((A -> B) or (C -> (A -> B)))))
theorem-size     29
proof            (modus-ponens tm-9 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-9 tm-8 tm-1 tm-2)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49567.        ((((A -> B) or (C -> (A -> B))) -> (not ((C -> A) -> (C -> B)))) -> (not ((A -> B) or (C -> (A -> B))))), M:tm-9, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49568
in-theory        49568
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> ((((B -> C) or (A -> (B -> C))) or ((A -> B) -> (A -> C))) -> D))
theorem-size     29
proof            (modus-ponens tm-8 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49568.        ((((A -> B) -> (A -> C)) -> D) -> ((((B -> C) or (A -> (B -> C))) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-49569
in-theory        49569
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or (D -> (B -> C))) -> ((D -> B) -> (D -> C))))
theorem-size     19
proof            (modus-ponens tm-7 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-7 tm-8 tm-1 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49569.        (A or (((B -> C) or (D -> (B -> C))) -> ((D -> B) -> (D -> C)))), M:tm-7, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49570
in-theory        49570
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) or D)
theorem-size     19
proof            (modus-ponens tm-6 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-6 tm-8 tm-1 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49570.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) or D), M:tm-6, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49571
in-theory        49571
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or (D -> (B -> C))) -> ((D -> B) -> (D -> C))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49571.        (A -> ((((B -> C) or (D -> (B -> C))) -> ((D -> B) -> (D -> C))) and A)), M:tm-5, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49572
in-theory        49572
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> (C -> A)) -> (((A -> B) or (C -> (A -> B))) -> (C -> B)))
theorem-size     27
proof            (modus-ponens tm-2 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> Cm Am)) (C (-> Cm Bm))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49572.        ((((A -> B) or (C -> (A -> B))) -> (C -> A)) -> (((A -> B) or (C -> (A -> B))) -> (C -> B))), M:tm-2, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> Cm Am)) (C (-> Cm Bm)))
================================================================
tm-name          tm-49573
in-theory        49573
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or (D -> (B -> C))) -> ((D -> B) -> (D -> C))))
theorem-size     19
proof            (modus-ponens tm-1 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-49573.        (A -> (((B -> C) or (D -> (B -> C))) -> ((D -> B) -> (D -> C)))), M:tm-1, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-49574
in-theory        49574
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (D -> ((B -> A) and D))))
theorem-size     15
proof            (modus-ponens tm-623 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49574.        ((A or (B -> A)) -> (C or (D -> ((B -> A) and D)))), M:tm-623, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49575
in-theory        49575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49575.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-622, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49576
in-theory        49576
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (C or (A or (B -> A)))))
theorem-size     17
proof            (modus-ponens tm-617 tm-627 ((A (or Am (-> Bm Am))) (Cm (or B (or Am (-> Bm Am)))) (C (and (-> Bm Am) (or B (or Am (-> Bm Am)))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49576.        ((A or (B -> A)) -> ((B -> A) and (C or (A or (B -> A))))), M:tm-617, m:tm-627, u:((A (or Am (-> Bm Am))) (Cm (or B (or Am (-> Bm Am)))) (C (and (-> Bm Am) (or B (or Am (-> Bm Am))))))
================================================================
tm-name          tm-49577
in-theory        49577
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49577.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (D -> (E or D))), M:tm-609, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49578
in-theory        49578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49578.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-605, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49579
in-theory        49579
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((D -> (E or D)) and ((A or (B -> A)) -> (C -> ((B -> A) and C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49579.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((D -> (E or D)) and ((A or (B -> A)) -> (C -> ((B -> A) and C))))), M:tm-595, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49580
in-theory        49580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49580.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-550, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49581
in-theory        49581
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49581.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-540, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49582
in-theory        49582
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49582.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-530, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49583
in-theory        49583
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49583.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-520, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49584
in-theory        49584
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49584.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-510, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49585
in-theory        49585
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49585.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-500, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49586
in-theory        49586
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> ((F -> E) and G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49586.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> ((F -> E) and G)))), M:tm-490, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49587
in-theory        49587
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49587.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-480, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49588
in-theory        49588
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> ((B -> A) and C)) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49588.        ((A or (B -> A)) -> ((C -> ((B -> A) and C)) or D)), M:tm-470, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49589
in-theory        49589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49589.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-469, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49590
in-theory        49590
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and ((A or (B -> A)) or C)))
theorem-size     17
proof            (modus-ponens tm-464 tm-627 ((A (or Am (-> Bm Am))) (Cm (or (or Am (-> Bm Am)) B)) (C (and (-> Bm Am) (or (or Am (-> Bm Am)) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49590.        ((A or (B -> A)) -> ((B -> A) and ((A or (B -> A)) or C))), M:tm-464, m:tm-627, u:((A (or Am (-> Bm Am))) (Cm (or (or Am (-> Bm Am)) B)) (C (and (-> Bm Am) (or (or Am (-> Bm Am)) B))))
================================================================
tm-name          tm-49591
in-theory        49591
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49591.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (D -> (D or E))), M:tm-456, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49592
in-theory        49592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49592.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-453, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49593
in-theory        49593
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((D -> (D or E)) and ((A or (B -> A)) -> (C -> ((B -> A) and C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49593.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((D -> (D or E)) and ((A or (B -> A)) -> (C -> ((B -> A) and C))))), M:tm-443, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49594
in-theory        49594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49594.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-409, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49595
in-theory        49595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49595.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-400, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49596
in-theory        49596
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49596.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-391, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49597
in-theory        49597
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49597.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-382, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49598
in-theory        49598
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (G -> ((F -> E) and G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49598.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (G -> ((F -> E) and G)))), M:tm-373, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49599
in-theory        49599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49599.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-364, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49600
in-theory        49600
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D -> ((B -> A) and D)) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49600.        ((A or (B -> A)) -> (C -> ((D -> ((B -> A) and D)) and C))), M:tm-355, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49601
in-theory        49601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49601.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-354, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49602
in-theory        49602
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (C -> ((A or (B -> A)) and C))))
theorem-size     19
proof            (modus-ponens tm-349 tm-627 ((A (or Am (-> Bm Am))) (Cm (-> B (and (or Am (-> Bm Am)) B))) (C (and (-> Bm Am) (-> B (and (or Am (-> Bm Am)) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49602.        ((A or (B -> A)) -> ((B -> A) and (C -> ((A or (B -> A)) and C)))), M:tm-349, m:tm-627, u:((A (or Am (-> Bm Am))) (Cm (-> B (and (or Am (-> Bm Am)) B))) (C (and (-> Bm Am) (-> B (and (or Am (-> Bm Am)) B)))))
================================================================
tm-name          tm-49603
in-theory        49603
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49603.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49604
in-theory        49604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (E -> ((D -> C) and E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49604.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (E -> ((D -> C) and E)))), M:tm-338, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49605
in-theory        49605
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((A or (B -> A)) -> ((A or (B -> A)) and (C -> ((B -> A) and C)))))
theorem-size     33
proof            (modus-ponens tm-328 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49605.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((A or (B -> A)) -> ((A or (B -> A)) and (C -> ((B -> A) and C))))), M:tm-328, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49606
in-theory        49606
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((D -> (E -> (D and E))) and ((A or (B -> A)) -> (C -> ((B -> A) and C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49606.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((D -> (E -> (D and E))) and ((A or (B -> A)) -> (C -> ((B -> A) and C))))), M:tm-327, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49607
in-theory        49607
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((D and E) -> E) and ((A or (B -> A)) -> (C -> ((B -> A) and C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49607.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((D and E) -> E) and ((A or (B -> A)) -> (C -> ((B -> A) and C))))), M:tm-326, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49608
in-theory        49608
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((D and E) -> D) and ((A or (B -> A)) -> (C -> ((B -> A) and C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49608.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((D and E) -> D) and ((A or (B -> A)) -> (C -> ((B -> A) and C))))), M:tm-325, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49609
in-theory        49609
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> A)) -> (C -> ((B -> A) and C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49609.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> A)) -> (C -> ((B -> A) and C))))), M:tm-324, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49610
in-theory        49610
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((D -> (E -> D)) and ((A or (B -> A)) -> (C -> ((B -> A) and C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49610.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((D -> (E -> D)) and ((A or (B -> A)) -> (C -> ((B -> A) and C))))), M:tm-323, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49611
in-theory        49611
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49611.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((D and E) -> E)), M:tm-322, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49612
in-theory        49612
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49612.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((D and E) -> D)), M:tm-320, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49613
in-theory        49613
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49613.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49614
in-theory        49614
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     25
proof            (modus-ponens tm-316 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49614.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49615
in-theory        49615
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49615.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (D -> (E -> D))), M:tm-315, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49616
in-theory        49616
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((A or (B -> A)) -> (not (C -> ((B -> A) and C)))) -> (not (A or (B -> A)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49616.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((A or (B -> A)) -> (not (C -> ((B -> A) and C)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49617
in-theory        49617
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((C -> ((B -> A) and C)) -> D) -> (((A or (B -> A)) or (C -> ((B -> A) and C))) -> D)))
theorem-size     39
proof            (modus-ponens tm-312 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49617.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((C -> ((B -> A) and C)) -> D) -> (((A or (B -> A)) or (C -> ((B -> A) and C))) -> D))), M:tm-312, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49618
in-theory        49618
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (D or ((A or (B -> A)) -> (C -> ((B -> A) and C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49618.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (D or ((A or (B -> A)) -> (C -> ((B -> A) and C))))), M:tm-311, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49619
in-theory        49619
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((A or (B -> A)) -> (C -> ((B -> A) and C))) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49619.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((A or (B -> A)) -> (C -> ((B -> A) and C))) or D)), M:tm-310, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49620
in-theory        49620
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (D -> (((A or (B -> A)) -> (C -> ((B -> A) and C))) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49620.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (D -> (((A or (B -> A)) -> (C -> ((B -> A) and C))) and D))), M:tm-309, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49621
in-theory        49621
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> ((B -> A) and C))))
theorem-size     33
proof            (modus-ponens tm-306 tm-627 ((A (or Am (-> Bm Am))) (B Cm) (C (and (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49621.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> ((B -> A) and C)))), M:tm-306, m:tm-627, u:((A (or Am (-> Bm Am))) (B Cm) (C (and (-> Bm Am) Cm)))
================================================================
tm-name          tm-49622
in-theory        49622
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (D -> ((A or (B -> A)) -> (C -> ((B -> A) and C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49622.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and (D -> ((A or (B -> A)) -> (C -> ((B -> A) and C))))), M:tm-305, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49623
in-theory        49623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49623.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-303, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49624
in-theory        49624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49624.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-270, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49625
in-theory        49625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49625.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-239, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49626
in-theory        49626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (G -> ((F -> E) and G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49626.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (G -> ((F -> E) and G)))), M:tm-210, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49627
in-theory        49627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49627.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-183, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49628
in-theory        49628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49628.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-157, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49629
in-theory        49629
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49629.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-147, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49630
in-theory        49630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49630.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-134, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49631
in-theory        49631
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49631.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-125, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49632
in-theory        49632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> ((F -> E) and G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49632.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> ((F -> E) and G)))), M:tm-113, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49633
in-theory        49633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49633.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-105, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49634
in-theory        49634
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (A or (B -> A))))
theorem-size     15
proof            (modus-ponens tm-99 tm-627 ((Cm (or Am (-> Bm Am))) (A (or Am (-> Bm Am))) (B (and (-> Bm Am) (or Am (-> Bm Am))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49634.        ((A or (B -> A)) -> ((B -> A) and (A or (B -> A)))), M:tm-99, m:tm-627, u:((Cm (or Am (-> Bm Am))) (A (or Am (-> Bm Am))) (B (and (-> Bm Am) (or Am (-> Bm Am)))))
================================================================
tm-name          tm-49635
in-theory        49635
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (C -> (A or (B -> A)))))
theorem-size     17
proof            (modus-ponens tm-98 tm-627 ((A (or Am (-> Bm Am))) (Cm (-> B (or Am (-> Bm Am)))) (C (and (-> Bm Am) (-> B (or Am (-> Bm Am)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49635.        ((A or (B -> A)) -> ((B -> A) and (C -> (A or (B -> A))))), M:tm-98, m:tm-627, u:((A (or Am (-> Bm Am))) (Cm (-> B (or Am (-> Bm Am)))) (C (and (-> Bm Am) (-> B (or Am (-> Bm Am))))))
================================================================
tm-name          tm-49636
in-theory        49636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (E -> ((D -> C) and E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49636.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (E -> ((D -> C) and E)))), M:tm-95, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49637
in-theory        49637
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (D -> ((B -> A) and D))))
theorem-size     15
proof            (modus-ponens tm-84 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49637.        ((A or (B -> A)) -> (C -> (D -> ((B -> A) and D)))), M:tm-84, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49638
in-theory        49638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49638.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-83, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49639
in-theory        49639
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> (D -> ((C -> B) and D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49639.        (((not (not A)) -> A) and ((B or (C -> B)) -> (D -> ((C -> B) and D)))), M:tm-76, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49640
in-theory        49640
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (C -> ((B -> A) and C)))
theorem-size     21
proof            (modus-ponens tm-73 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49640.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (C -> ((B -> A) and C))), M:tm-73, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49641
in-theory        49641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (E -> ((D -> C) and E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49641.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (E -> ((D -> C) and E)))), M:tm-69, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49642
in-theory        49642
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49642.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-54, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49643
in-theory        49643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> (C -> ((A -> B) and C)))
theorem-size     17
proof            (modus-ponens tm-50 tm-627 ((A Am) (B (-> Bm Am)) (C (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49643.        (((A -> B) or (B or (A -> B))) -> (C -> ((A -> B) and C))), M:tm-50, m:tm-627, u:((A Am) (B (-> Bm Am)) (C (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49644
in-theory        49644
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> (C -> ((B -> A) and C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-627 ((A Am) (B (-> Bm Am)) (C (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49644.        ((A or (A or (B -> A))) -> (C -> ((B -> A) and C))), M:tm-49, m:tm-627, u:((A Am) (B (-> Bm Am)) (C (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49645
in-theory        49645
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> (D -> ((C -> B) and D)))
theorem-size     21
proof            (modus-ponens tm-47 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49645.        (((A and (B or (C -> B))) or (B or (C -> B))) -> (D -> ((C -> B) and D))), M:tm-47, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49646
in-theory        49646
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> (D -> ((B -> A) and D)))
theorem-size     21
proof            (modus-ponens tm-46 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49646.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> (D -> ((B -> A) and D))), M:tm-46, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49647
in-theory        49647
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> (E -> ((D -> C) and E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49647.        ((A -> (B or A)) and ((C or (D -> C)) -> (E -> ((D -> C) and E)))), M:tm-42, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49648
in-theory        49648
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> (E -> ((D -> C) and E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49648.        ((A -> (A or B)) and ((C or (D -> C)) -> (E -> ((D -> C) and E)))), M:tm-32, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49649
in-theory        49649
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and (C -> ((B -> A) and C))))
theorem-size     19
proof            (modus-ponens tm-24 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49649.        ((A or (B -> A)) -> ((A or (B -> A)) and (C -> ((B -> A) and C)))), M:tm-24, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49650
in-theory        49650
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (E -> ((D -> C) and E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49650.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (E -> ((D -> C) and E)))), M:tm-23, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49651
in-theory        49651
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> (E -> ((D -> C) and E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49651.        (((A and B) -> B) and ((C or (D -> C)) -> (E -> ((D -> C) and E)))), M:tm-22, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49652
in-theory        49652
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> (E -> ((D -> C) and E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49652.        (((A and B) -> A) and ((C or (D -> C)) -> (E -> ((D -> C) and E)))), M:tm-21, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49653
in-theory        49653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49653.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-20, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49654
in-theory        49654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> (E -> ((D -> C) and E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49654.        ((A -> (B -> A)) and ((C or (D -> C)) -> (E -> ((D -> C) and E)))), M:tm-19, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49655
in-theory        49655
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not (C -> ((B -> A) and C)))) -> (not (A or (B -> A))))
theorem-size     21
proof            (modus-ponens tm-9 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-9 tm-8 tm-1 tm-5)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49655.        (((A or (B -> A)) -> (not (C -> ((B -> A) and C)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49656
in-theory        49656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) and A)) -> D) -> (((C or (B -> C)) or (A -> ((B -> C) and A))) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49656.        (((A -> ((B -> C) and A)) -> D) -> (((C or (B -> C)) or (A -> ((B -> C) and A))) -> D)), M:tm-8, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-49657
in-theory        49657
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> (D -> ((C -> B) and D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-7 tm-8 tm-1 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49657.        (A or ((B or (C -> B)) -> (D -> ((C -> B) and D)))), M:tm-7, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49658
in-theory        49658
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-6 tm-8 tm-1 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49658.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) or D), M:tm-6, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49659
in-theory        49659
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> (D -> ((C -> B) and D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49659.        (A -> (((B or (C -> B)) -> (D -> ((C -> B) and D))) and A)), M:tm-5, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49660
in-theory        49660
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> ((B -> A) and C)))
theorem-size     19
proof            (modus-ponens tm-2 tm-627 ((A (or Am (-> Bm Am))) (B Cm) (C (and (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49660.        (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> ((B -> A) and C))), M:tm-2, m:tm-627, u:((A (or Am (-> Bm Am))) (B Cm) (C (and (-> Bm Am) Cm)))
================================================================
tm-name          tm-49661
in-theory        49661
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (D -> ((C -> B) and D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-49661.        (A -> ((B or (C -> B)) -> (D -> ((C -> B) and D)))), M:tm-1, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-49662
in-theory        49662
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or ((B -> A) or D)))
theorem-size     13
proof            (modus-ponens tm-623 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49662.        ((A or (B -> A)) -> (C or ((B -> A) or D))), M:tm-623, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49663
in-theory        49663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49663.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-622, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49664
in-theory        49664
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49664.        (((A or (B -> A)) -> ((B -> A) or C)) and (D -> (E or D))), M:tm-609, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49665
in-theory        49665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49665.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-605, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49666
in-theory        49666
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and ((D -> (E or D)) and ((A or (B -> A)) -> ((B -> A) or C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49666.        (((A or (B -> A)) -> ((B -> A) or C)) and ((D -> (E or D)) and ((A or (B -> A)) -> ((B -> A) or C)))), M:tm-595, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49667
in-theory        49667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49667.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-550, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49668
in-theory        49668
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49668.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-540, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49669
in-theory        49669
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49669.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-530, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49670
in-theory        49670
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49670.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-520, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49671
in-theory        49671
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49671.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-510, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49672
in-theory        49672
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49672.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-500, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49673
in-theory        49673
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((F -> E) or G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49673.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((F -> E) or G))), M:tm-490, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49674
in-theory        49674
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49674.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-480, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49675
in-theory        49675
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((B -> A) or C) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49675.        ((A or (B -> A)) -> (((B -> A) or C) or D)), M:tm-470, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49676
in-theory        49676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49676.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-469, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49677
in-theory        49677
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49677.        (((A or (B -> A)) -> ((B -> A) or C)) and (D -> (D or E))), M:tm-456, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49678
in-theory        49678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49678.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-453, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49679
in-theory        49679
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and ((D -> (D or E)) and ((A or (B -> A)) -> ((B -> A) or C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49679.        (((A or (B -> A)) -> ((B -> A) or C)) and ((D -> (D or E)) and ((A or (B -> A)) -> ((B -> A) or C)))), M:tm-443, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49680
in-theory        49680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49680.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-409, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49681
in-theory        49681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49681.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-400, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49682
in-theory        49682
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49682.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-391, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49683
in-theory        49683
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49683.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-382, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49684
in-theory        49684
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((F -> E) or G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49684.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((F -> E) or G))), M:tm-373, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49685
in-theory        49685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49685.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-364, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49686
in-theory        49686
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((B -> A) or D) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49686.        ((A or (B -> A)) -> (C -> (((B -> A) or D) and C))), M:tm-355, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49687
in-theory        49687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49687.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-354, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49688
in-theory        49688
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49688.        (((A or (B -> A)) -> ((B -> A) or C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49689
in-theory        49689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((D -> C) or E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49689.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((D -> C) or E))), M:tm-338, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49690
in-theory        49690
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and ((A or (B -> A)) -> ((A or (B -> A)) and ((B -> A) or C))))
theorem-size     29
proof            (modus-ponens tm-328 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49690.        (((A or (B -> A)) -> ((B -> A) or C)) and ((A or (B -> A)) -> ((A or (B -> A)) and ((B -> A) or C)))), M:tm-328, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49691
in-theory        49691
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and ((D -> (E -> (D and E))) and ((A or (B -> A)) -> ((B -> A) or C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49691.        (((A or (B -> A)) -> ((B -> A) or C)) and ((D -> (E -> (D and E))) and ((A or (B -> A)) -> ((B -> A) or C)))), M:tm-327, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49692
in-theory        49692
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and (((D and E) -> E) and ((A or (B -> A)) -> ((B -> A) or C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49692.        (((A or (B -> A)) -> ((B -> A) or C)) and (((D and E) -> E) and ((A or (B -> A)) -> ((B -> A) or C)))), M:tm-326, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49693
in-theory        49693
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and (((D and E) -> D) and ((A or (B -> A)) -> ((B -> A) or C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49693.        (((A or (B -> A)) -> ((B -> A) or C)) and (((D and E) -> D) and ((A or (B -> A)) -> ((B -> A) or C)))), M:tm-325, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49694
in-theory        49694
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> A)) -> ((B -> A) or C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49694.        (((A or (B -> A)) -> ((B -> A) or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> A)) -> ((B -> A) or C)))), M:tm-324, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49695
in-theory        49695
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and ((D -> (E -> D)) and ((A or (B -> A)) -> ((B -> A) or C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49695.        (((A or (B -> A)) -> ((B -> A) or C)) and ((D -> (E -> D)) and ((A or (B -> A)) -> ((B -> A) or C)))), M:tm-323, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49696
in-theory        49696
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49696.        (((A or (B -> A)) -> ((B -> A) or C)) and ((D and E) -> E)), M:tm-322, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49697
in-theory        49697
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49697.        (((A or (B -> A)) -> ((B -> A) or C)) and ((D and E) -> D)), M:tm-320, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49698
in-theory        49698
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49698.        (((A or (B -> A)) -> ((B -> A) or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49699
in-theory        49699
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49699.        (((A or (B -> A)) -> ((B -> A) or C)) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49700
in-theory        49700
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49700.        (((A or (B -> A)) -> ((B -> A) or C)) and (D -> (E -> D))), M:tm-315, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49701
in-theory        49701
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and (((A or (B -> A)) -> (not ((B -> A) or C))) -> (not (A or (B -> A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49701.        (((A or (B -> A)) -> ((B -> A) or C)) and (((A or (B -> A)) -> (not ((B -> A) or C))) -> (not (A or (B -> A))))), M:tm-313, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49702
in-theory        49702
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and ((((B -> A) or C) -> D) -> (((A or (B -> A)) or ((B -> A) or C)) -> D)))
theorem-size     33
proof            (modus-ponens tm-312 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49702.        (((A or (B -> A)) -> ((B -> A) or C)) and ((((B -> A) or C) -> D) -> (((A or (B -> A)) or ((B -> A) or C)) -> D))), M:tm-312, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49703
in-theory        49703
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and (D or ((A or (B -> A)) -> ((B -> A) or C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49703.        (((A or (B -> A)) -> ((B -> A) or C)) and (D or ((A or (B -> A)) -> ((B -> A) or C)))), M:tm-311, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49704
in-theory        49704
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and (((A or (B -> A)) -> ((B -> A) or C)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49704.        (((A or (B -> A)) -> ((B -> A) or C)) and (((A or (B -> A)) -> ((B -> A) or C)) or D)), M:tm-310, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49705
in-theory        49705
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and (D -> (((A or (B -> A)) -> ((B -> A) or C)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49705.        (((A or (B -> A)) -> ((B -> A) or C)) and (D -> (((A or (B -> A)) -> ((B -> A) or C)) and D))), M:tm-309, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49706
in-theory        49706
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and (D -> ((A or (B -> A)) -> ((B -> A) or C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49706.        (((A or (B -> A)) -> ((B -> A) or C)) and (D -> ((A or (B -> A)) -> ((B -> A) or C)))), M:tm-305, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49707
in-theory        49707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49707.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-303, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49708
in-theory        49708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49708.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-270, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49709
in-theory        49709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49709.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-239, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49710
in-theory        49710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((F -> E) or G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49710.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((F -> E) or G))), M:tm-210, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49711
in-theory        49711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49711.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-183, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49712
in-theory        49712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49712.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-157, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49713
in-theory        49713
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49713.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-147, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49714
in-theory        49714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49714.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-134, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49715
in-theory        49715
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49715.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-125, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49716
in-theory        49716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((F -> E) or G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49716.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((F -> E) or G))), M:tm-113, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49717
in-theory        49717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49717.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-105, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49718
in-theory        49718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((D -> C) or E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49718.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((D -> C) or E))), M:tm-95, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49719
in-theory        49719
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((B -> A) or D)))
theorem-size     13
proof            (modus-ponens tm-84 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49719.        ((A or (B -> A)) -> (C -> ((B -> A) or D))), M:tm-84, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49720
in-theory        49720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49720.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-83, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49721
in-theory        49721
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> ((C -> B) or D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49721.        (((not (not A)) -> A) and ((B or (C -> B)) -> ((C -> B) or D))), M:tm-76, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49722
in-theory        49722
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((B -> A) or C))
theorem-size     19
proof            (modus-ponens tm-73 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-8 tm-10 tm-1 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49722.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((B -> A) or C)), M:tm-73, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49723
in-theory        49723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((D -> C) or E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49723.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((D -> C) or E))), M:tm-69, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49724
in-theory        49724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49724.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-54, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49725
in-theory        49725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> ((A -> B) or C))
theorem-size     15
proof            (modus-ponens tm-50 tm-628 ((A Am) (B (-> Bm Am)) (C (or (-> Bm Am) Cm))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49725.        (((A -> B) or (B or (A -> B))) -> ((A -> B) or C)), M:tm-50, m:tm-628, u:((A Am) (B (-> Bm Am)) (C (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49726
in-theory        49726
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> ((B -> A) or C))
theorem-size     13
proof            (modus-ponens tm-49 tm-628 ((A Am) (B (-> Bm Am)) (C (or (-> Bm Am) Cm))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49726.        ((A or (A or (B -> A))) -> ((B -> A) or C)), M:tm-49, m:tm-628, u:((A Am) (B (-> Bm Am)) (C (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49727
in-theory        49727
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> ((C -> B) or D))
theorem-size     19
proof            (modus-ponens tm-47 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49727.        (((A and (B or (C -> B))) or (B or (C -> B))) -> ((C -> B) or D)), M:tm-47, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49728
in-theory        49728
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((B -> A) or D))
theorem-size     19
proof            (modus-ponens tm-46 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49728.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((B -> A) or D)), M:tm-46, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49729
in-theory        49729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> ((D -> C) or E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49729.        ((A -> (B or A)) and ((C or (D -> C)) -> ((D -> C) or E))), M:tm-42, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49730
in-theory        49730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> ((D -> C) or E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49730.        ((A -> (A or B)) and ((C or (D -> C)) -> ((D -> C) or E))), M:tm-32, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49731
in-theory        49731
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and ((B -> A) or C)))
theorem-size     17
proof            (modus-ponens tm-24 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49731.        ((A or (B -> A)) -> ((A or (B -> A)) and ((B -> A) or C))), M:tm-24, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49732
in-theory        49732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((D -> C) or E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49732.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((D -> C) or E))), M:tm-23, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49733
in-theory        49733
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> ((D -> C) or E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49733.        (((A and B) -> B) and ((C or (D -> C)) -> ((D -> C) or E))), M:tm-22, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49734
in-theory        49734
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> ((D -> C) or E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49734.        (((A and B) -> A) and ((C or (D -> C)) -> ((D -> C) or E))), M:tm-21, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49735
in-theory        49735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49735.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-20, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49736
in-theory        49736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> ((D -> C) or E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49736.        ((A -> (B -> A)) and ((C or (D -> C)) -> ((D -> C) or E))), M:tm-19, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49737
in-theory        49737
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not ((B -> A) or C))) -> (not (A or (B -> A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-9 tm-8 tm-1 tm-6)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49737.        (((A or (B -> A)) -> (not ((B -> A) or C))) -> (not (A or (B -> A)))), M:tm-9, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49738
in-theory        49738
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or C) -> D) -> (((B or (A -> B)) or ((A -> B) or C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49738.        ((((A -> B) or C) -> D) -> (((B or (A -> B)) or ((A -> B) or C)) -> D)), M:tm-8, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-49739
in-theory        49739
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> ((C -> B) or D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-7 tm-8 tm-1 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49739.        (A or ((B or (C -> B)) -> ((C -> B) or D))), M:tm-7, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49740
in-theory        49740
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-6 tm-8 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49740.        (((A or (B -> A)) -> ((B -> A) or C)) or D), M:tm-6, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49741
in-theory        49741
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> ((C -> B) or D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49741.        (A -> (((B or (C -> B)) -> ((C -> B) or D)) and A)), M:tm-5, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49742
in-theory        49742
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> ((C -> B) or D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-1 tm-8 tm-6)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-49742.        (A -> ((B or (C -> B)) -> ((C -> B) or D))), M:tm-1, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-49743
in-theory        49743
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (D or (B -> A))))
theorem-size     13
proof            (modus-ponens tm-623 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49743.        ((A or (B -> A)) -> (C or (D or (B -> A)))), M:tm-623, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49744
in-theory        49744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-622 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49744.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-622, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49745
in-theory        49745
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49745.        (((A or (B -> A)) -> (C or (B -> A))) and (D -> (E or D))), M:tm-609, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49746
in-theory        49746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     21
proof            (modus-ponens tm-605 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49746.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-605, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49747
in-theory        49747
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and ((D -> (E or D)) and ((A or (B -> A)) -> (C or (B -> A)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49747.        (((A or (B -> A)) -> (C or (B -> A))) and ((D -> (E or D)) and ((A or (B -> A)) -> (C or (B -> A))))), M:tm-595, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49748
in-theory        49748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-550 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49748.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-550, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49749
in-theory        49749
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-540 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49749.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-540, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49750
in-theory        49750
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-530 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49750.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-530, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49751
in-theory        49751
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     21
proof            (modus-ponens tm-520 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49751.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-520, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49752
in-theory        49752
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-510 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49752.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-510, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49753
in-theory        49753
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-500 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49753.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-500, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49754
in-theory        49754
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G or (F -> E))))
theorem-size     27
proof            (modus-ponens tm-490 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49754.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G or (F -> E)))), M:tm-490, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49755
in-theory        49755
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-480 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49755.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-480, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49756
in-theory        49756
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C or (B -> A)) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49756.        ((A or (B -> A)) -> ((C or (B -> A)) or D)), M:tm-470, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49757
in-theory        49757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-469 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49757.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-469, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49758
in-theory        49758
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49758.        (((A or (B -> A)) -> (C or (B -> A))) and (D -> (D or E))), M:tm-456, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49759
in-theory        49759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     21
proof            (modus-ponens tm-453 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49759.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-453, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49760
in-theory        49760
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and ((D -> (D or E)) and ((A or (B -> A)) -> (C or (B -> A)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49760.        (((A or (B -> A)) -> (C or (B -> A))) and ((D -> (D or E)) and ((A or (B -> A)) -> (C or (B -> A))))), M:tm-443, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49761
in-theory        49761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-409 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49761.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-409, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49762
in-theory        49762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     21
proof            (modus-ponens tm-400 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49762.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-400, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49763
in-theory        49763
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-391 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49763.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-391, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49764
in-theory        49764
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-382 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49764.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-382, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49765
in-theory        49765
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (G or (F -> E))))
theorem-size     27
proof            (modus-ponens tm-373 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49765.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (G or (F -> E)))), M:tm-373, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49766
in-theory        49766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-364 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49766.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-364, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49767
in-theory        49767
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D or (B -> A)) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49767.        ((A or (B -> A)) -> (C -> ((D or (B -> A)) and C))), M:tm-355, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49768
in-theory        49768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     21
proof            (modus-ponens tm-354 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49768.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-354, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49769
in-theory        49769
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49769.        (((A or (B -> A)) -> (C or (B -> A))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49770
in-theory        49770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (E or (D -> C))))
theorem-size     21
proof            (modus-ponens tm-338 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49770.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (E or (D -> C)))), M:tm-338, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49771
in-theory        49771
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and (C or (B -> A)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49771.        (((A or (B -> A)) -> (C or (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and (C or (B -> A))))), M:tm-328, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49772
in-theory        49772
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and ((D -> (E -> (D and E))) and ((A or (B -> A)) -> (C or (B -> A)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49772.        (((A or (B -> A)) -> (C or (B -> A))) and ((D -> (E -> (D and E))) and ((A or (B -> A)) -> (C or (B -> A))))), M:tm-327, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49773
in-theory        49773
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (((D and E) -> E) and ((A or (B -> A)) -> (C or (B -> A)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49773.        (((A or (B -> A)) -> (C or (B -> A))) and (((D and E) -> E) and ((A or (B -> A)) -> (C or (B -> A))))), M:tm-326, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49774
in-theory        49774
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (((D and E) -> D) and ((A or (B -> A)) -> (C or (B -> A)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49774.        (((A or (B -> A)) -> (C or (B -> A))) and (((D and E) -> D) and ((A or (B -> A)) -> (C or (B -> A))))), M:tm-325, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49775
in-theory        49775
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> A)) -> (C or (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49775.        (((A or (B -> A)) -> (C or (B -> A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> A)) -> (C or (B -> A))))), M:tm-324, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49776
in-theory        49776
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and ((D -> (E -> D)) and ((A or (B -> A)) -> (C or (B -> A)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49776.        (((A or (B -> A)) -> (C or (B -> A))) and ((D -> (E -> D)) and ((A or (B -> A)) -> (C or (B -> A))))), M:tm-323, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49777
in-theory        49777
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49777.        (((A or (B -> A)) -> (C or (B -> A))) and ((D and E) -> E)), M:tm-322, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49778
in-theory        49778
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49778.        (((A or (B -> A)) -> (C or (B -> A))) and ((D and E) -> D)), M:tm-320, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49779
in-theory        49779
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49779.        (((A or (B -> A)) -> (C or (B -> A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49780
in-theory        49780
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49780.        (((A or (B -> A)) -> (C or (B -> A))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49781
in-theory        49781
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49781.        (((A or (B -> A)) -> (C or (B -> A))) and (D -> (E -> D))), M:tm-315, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49782
in-theory        49782
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (((A or (B -> A)) -> (not (C or (B -> A)))) -> (not (A or (B -> A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49782.        (((A or (B -> A)) -> (C or (B -> A))) and (((A or (B -> A)) -> (not (C or (B -> A)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49783
in-theory        49783
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (((C or (B -> A)) -> D) -> (((A or (B -> A)) or (C or (B -> A))) -> D)))
theorem-size     33
proof            (modus-ponens tm-312 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49783.        (((A or (B -> A)) -> (C or (B -> A))) and (((C or (B -> A)) -> D) -> (((A or (B -> A)) or (C or (B -> A))) -> D))), M:tm-312, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49784
in-theory        49784
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (D or ((A or (B -> A)) -> (C or (B -> A)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49784.        (((A or (B -> A)) -> (C or (B -> A))) and (D or ((A or (B -> A)) -> (C or (B -> A))))), M:tm-311, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49785
in-theory        49785
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (((A or (B -> A)) -> (C or (B -> A))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49785.        (((A or (B -> A)) -> (C or (B -> A))) and (((A or (B -> A)) -> (C or (B -> A))) or D)), M:tm-310, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49786
in-theory        49786
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (D -> (((A or (B -> A)) -> (C or (B -> A))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49786.        (((A or (B -> A)) -> (C or (B -> A))) and (D -> (((A or (B -> A)) -> (C or (B -> A))) and D))), M:tm-309, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49787
in-theory        49787
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and (D -> ((A or (B -> A)) -> (C or (B -> A)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49787.        (((A or (B -> A)) -> (C or (B -> A))) and (D -> ((A or (B -> A)) -> (C or (B -> A))))), M:tm-305, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49788
in-theory        49788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     23
proof            (modus-ponens tm-303 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49788.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-303, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49789
in-theory        49789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     21
proof            (modus-ponens tm-270 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49789.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-270, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49790
in-theory        49790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     21
proof            (modus-ponens tm-239 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49790.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-239, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49791
in-theory        49791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (G or (F -> E))))
theorem-size     29
proof            (modus-ponens tm-210 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49791.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (G or (F -> E)))), M:tm-210, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49792
in-theory        49792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     21
proof            (modus-ponens tm-183 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49792.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-183, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49793
in-theory        49793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-157 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49793.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-157, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49794
in-theory        49794
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     27
proof            (modus-ponens tm-147 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49794.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-147, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49795
in-theory        49795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-134 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49795.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-134, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49796
in-theory        49796
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     27
proof            (modus-ponens tm-125 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49796.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-125, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49797
in-theory        49797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G or (F -> E))))
theorem-size     27
proof            (modus-ponens tm-113 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49797.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G or (F -> E)))), M:tm-113, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49798
in-theory        49798
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     31
proof            (modus-ponens tm-105 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49798.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-105, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49799
in-theory        49799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (E or (D -> C))))
theorem-size     19
proof            (modus-ponens tm-95 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49799.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (E or (D -> C)))), M:tm-95, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49800
in-theory        49800
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (D or (B -> A))))
theorem-size     13
proof            (modus-ponens tm-84 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49800.        ((A or (B -> A)) -> (C -> (D or (B -> A)))), M:tm-84, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49801
in-theory        49801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     19
proof            (modus-ponens tm-83 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49801.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-83, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49802
in-theory        49802
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> (D or (C -> B))))
theorem-size     17
proof            (modus-ponens tm-76 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49802.        (((not (not A)) -> A) and ((B or (C -> B)) -> (D or (C -> B)))), M:tm-76, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49803
in-theory        49803
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (C or (B -> A)))
theorem-size     19
proof            (modus-ponens tm-73 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-8 tm-10 tm-1 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49803.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (C or (B -> A))), M:tm-73, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49804
in-theory        49804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (E or (D -> C))))
theorem-size     23
proof            (modus-ponens tm-69 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49804.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (E or (D -> C)))), M:tm-69, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49805
in-theory        49805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     25
proof            (modus-ponens tm-54 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49805.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-54, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49806
in-theory        49806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> (C or (A -> B)))
theorem-size     15
proof            (modus-ponens tm-50 tm-629 ((A Am) (B (-> Bm Am)) (C (or Cm (-> Bm Am)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49806.        (((A -> B) or (B or (A -> B))) -> (C or (A -> B))), M:tm-50, m:tm-629, u:((A Am) (B (-> Bm Am)) (C (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49807
in-theory        49807
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> (C or (B -> A)))
theorem-size     13
proof            (modus-ponens tm-49 tm-629 ((A Am) (B (-> Bm Am)) (C (or Cm (-> Bm Am)))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49807.        ((A or (A or (B -> A))) -> (C or (B -> A))), M:tm-49, m:tm-629, u:((A Am) (B (-> Bm Am)) (C (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49808
in-theory        49808
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> (D or (C -> B)))
theorem-size     19
proof            (modus-ponens tm-47 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49808.        (((A and (B or (C -> B))) or (B or (C -> B))) -> (D or (C -> B))), M:tm-47, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49809
in-theory        49809
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> (D or (B -> A)))
theorem-size     19
proof            (modus-ponens tm-46 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49809.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> (D or (B -> A))), M:tm-46, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49810
in-theory        49810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> (E or (D -> C))))
theorem-size     17
proof            (modus-ponens tm-42 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49810.        ((A -> (B or A)) and ((C or (D -> C)) -> (E or (D -> C)))), M:tm-42, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49811
in-theory        49811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> (E or (D -> C))))
theorem-size     17
proof            (modus-ponens tm-32 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49811.        ((A -> (A or B)) and ((C or (D -> C)) -> (E or (D -> C)))), M:tm-32, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49812
in-theory        49812
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and (C or (B -> A))))
theorem-size     17
proof            (modus-ponens tm-24 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49812.        ((A or (B -> A)) -> ((A or (B -> A)) and (C or (B -> A)))), M:tm-24, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49813
in-theory        49813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (E or (D -> C))))
theorem-size     19
proof            (modus-ponens tm-23 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49813.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (E or (D -> C)))), M:tm-23, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49814
in-theory        49814
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> (E or (D -> C))))
theorem-size     17
proof            (modus-ponens tm-22 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49814.        (((A and B) -> B) and ((C or (D -> C)) -> (E or (D -> C)))), M:tm-22, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49815
in-theory        49815
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> (E or (D -> C))))
theorem-size     17
proof            (modus-ponens tm-21 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49815.        (((A and B) -> A) and ((C or (D -> C)) -> (E or (D -> C)))), M:tm-21, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49816
in-theory        49816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     25
proof            (modus-ponens tm-20 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49816.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-20, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49817
in-theory        49817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> (E or (D -> C))))
theorem-size     17
proof            (modus-ponens tm-19 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49817.        ((A -> (B -> A)) and ((C or (D -> C)) -> (E or (D -> C)))), M:tm-19, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49818
in-theory        49818
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not (C or (B -> A)))) -> (not (A or (B -> A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-9 tm-8 tm-1 tm-7)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49818.        (((A or (B -> A)) -> (not (C or (B -> A)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49819
in-theory        49819
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> C)) -> D) -> (((C or (B -> C)) or (A or (B -> C))) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49819.        (((A or (B -> C)) -> D) -> (((C or (B -> C)) or (A or (B -> C))) -> D)), M:tm-8, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-49820
in-theory        49820
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> (D or (C -> B))))
theorem-size     13
proof            (modus-ponens tm-7 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-7 tm-8 tm-1)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49820.        (A or ((B or (C -> B)) -> (D or (C -> B)))), M:tm-7, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49821
in-theory        49821
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-6 tm-8 tm-1 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49821.        (((A or (B -> A)) -> (C or (B -> A))) or D), M:tm-6, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49822
in-theory        49822
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> (D or (C -> B))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49822.        (A -> (((B or (C -> B)) -> (D or (C -> B))) and A)), M:tm-5, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49823
in-theory        49823
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (D or (C -> B))))
theorem-size     13
proof            (modus-ponens tm-1 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-1 tm-8 tm-7)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-49823.        (A -> ((B or (C -> B)) -> (D or (C -> B)))), M:tm-1, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-49824
in-theory        49824
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or ((A -> D) -> ((B or A) -> D))))
theorem-size     17
proof            (modus-ponens tm-623 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49824.        ((A or (B -> A)) -> (C or ((A -> D) -> ((B or A) -> D)))), M:tm-623, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49825
in-theory        49825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49825.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-622, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49826
in-theory        49826
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49826.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (D -> (E or D))), M:tm-609, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49827
in-theory        49827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49827.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-605, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49828
in-theory        49828
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((D -> (E or D)) and ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49828.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((D -> (E or D)) and ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))))), M:tm-595, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49829
in-theory        49829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49829.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-550, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49830
in-theory        49830
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49830.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-540, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49831
in-theory        49831
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49831.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-530, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49832
in-theory        49832
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49832.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-520, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49833
in-theory        49833
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49833.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-510, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49834
in-theory        49834
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49834.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-500, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49835
in-theory        49835
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49835.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G)))), M:tm-490, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49836
in-theory        49836
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49836.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-480, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49837
in-theory        49837
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((A -> C) -> ((B or A) -> C)) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49837.        ((A or (B -> A)) -> (((A -> C) -> ((B or A) -> C)) or D)), M:tm-470, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49838
in-theory        49838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49838.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-469, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49839
in-theory        49839
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49839.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (D -> (D or E))), M:tm-456, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49840
in-theory        49840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49840.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-453, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49841
in-theory        49841
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((D -> (D or E)) and ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49841.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((D -> (D or E)) and ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))))), M:tm-443, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49842
in-theory        49842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49842.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-409, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49843
in-theory        49843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49843.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-400, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49844
in-theory        49844
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49844.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-391, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49845
in-theory        49845
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49845.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-382, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49846
in-theory        49846
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49846.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G)))), M:tm-373, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49847
in-theory        49847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49847.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-364, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49848
in-theory        49848
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((A -> D) -> ((B or A) -> D)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49848.        ((A or (B -> A)) -> (C -> (((A -> D) -> ((B or A) -> D)) and C))), M:tm-355, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49849
in-theory        49849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49849.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-354, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49850
in-theory        49850
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B or A) -> ((A or (B -> A)) and A)))
theorem-size     17
proof            (modus-ponens tm-349 tm-630 ((A (or Am (-> Bm Am))) (B Am) (Cm (and (or Am (-> Bm Am)) Am)) (C (-> (or Bm Am) (and (or Am (-> Bm Am)) Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49850.        ((A or (B -> A)) -> ((B or A) -> ((A or (B -> A)) and A))), M:tm-349, m:tm-630, u:((A (or Am (-> Bm Am))) (B Am) (Cm (and (or Am (-> Bm Am)) Am)) (C (-> (or Bm Am) (and (or Am (-> Bm Am)) Am))))
================================================================
tm-name          tm-49851
in-theory        49851
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49851.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49852
in-theory        49852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49852.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E)))), M:tm-338, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49853
in-theory        49853
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((A or (B -> A)) -> ((A or (B -> A)) and ((A -> C) -> ((B or A) -> C)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49853.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((A or (B -> A)) -> ((A or (B -> A)) and ((A -> C) -> ((B or A) -> C))))), M:tm-328, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49854
in-theory        49854
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((D -> (E -> (D and E))) and ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49854.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((D -> (E -> (D and E))) and ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))))), M:tm-327, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49855
in-theory        49855
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((D and E) -> E) and ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49855.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((D and E) -> E) and ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))))), M:tm-326, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49856
in-theory        49856
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((D and E) -> D) and ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49856.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((D and E) -> D) and ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))))), M:tm-325, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49857
in-theory        49857
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49857.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))))), M:tm-324, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49858
in-theory        49858
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((D -> (E -> D)) and ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49858.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((D -> (E -> D)) and ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))))), M:tm-323, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49859
in-theory        49859
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49859.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49860
in-theory        49860
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49860.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49861
in-theory        49861
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49861.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49862
in-theory        49862
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     27
proof            (modus-ponens tm-316 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49862.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49863
in-theory        49863
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49863.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49864
in-theory        49864
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((A or (B -> A)) -> (not ((A -> C) -> ((B or A) -> C)))) -> (not (A or (B -> A)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49864.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((A or (B -> A)) -> (not ((A -> C) -> ((B or A) -> C)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49865
in-theory        49865
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((((A -> C) -> ((B or A) -> C)) -> D) -> (((A or (B -> A)) or ((A -> C) -> ((B or A) -> C))) -> D)))
theorem-size     45
proof            (modus-ponens tm-312 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49865.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((((A -> C) -> ((B or A) -> C)) -> D) -> (((A or (B -> A)) or ((A -> C) -> ((B or A) -> C))) -> D))), M:tm-312, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49866
in-theory        49866
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (D or ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49866.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (D or ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))))), M:tm-311, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49867
in-theory        49867
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49867.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) or D)), M:tm-310, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49868
in-theory        49868
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (D -> (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49868.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (D -> (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and D))), M:tm-309, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49869
in-theory        49869
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((A or (B -> A)) -> (A -> C)) -> ((A or (B -> A)) -> ((B or A) -> C))))
theorem-size     37
proof            (modus-ponens tm-306 tm-630 ((A (or Am (-> Bm Am))) (B (-> Am Cm)) (C (-> (or Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49869.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (((A or (B -> A)) -> (A -> C)) -> ((A or (B -> A)) -> ((B or A) -> C)))), M:tm-306, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> Am Cm)) (C (-> (or Bm Am) Cm)))
================================================================
tm-name          tm-49870
in-theory        49870
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (D -> ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49870.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and (D -> ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))))), M:tm-305, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49871
in-theory        49871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49871.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-303, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49872
in-theory        49872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49872.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-270, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49873
in-theory        49873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49873.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-239, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49874
in-theory        49874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49874.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G)))), M:tm-210, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49875
in-theory        49875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49875.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-183, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49876
in-theory        49876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49876.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-157, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49877
in-theory        49877
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49877.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-147, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49878
in-theory        49878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49878.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-134, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49879
in-theory        49879
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49879.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-125, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49880
in-theory        49880
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((A -> C) -> (B or A)) -> ((A -> C) -> C)))
theorem-size     19
proof            (modus-ponens tm-114 tm-630 ((A (or Am (-> Bm Am))) (B (-> Am Cm)) (C (or Bm Am)) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49880.        ((A or (B -> A)) -> (((A -> C) -> (B or A)) -> ((A -> C) -> C))), M:tm-114, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> Am Cm)) (C (or Bm Am)) (D Cm))
================================================================
tm-name          tm-49881
in-theory        49881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49881.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G)))), M:tm-113, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49882
in-theory        49882
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49882.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-105, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49883
in-theory        49883
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B or A) -> (A or (B -> A))))
theorem-size     15
proof            (modus-ponens tm-98 tm-630 ((Cm (or Am (-> Bm Am))) (B Am) (A (or Am (-> Bm Am))) (C (-> (or Bm Am) (or Am (-> Bm Am))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49883.        ((A or (B -> A)) -> ((B or A) -> (A or (B -> A)))), M:tm-98, m:tm-630, u:((Cm (or Am (-> Bm Am))) (B Am) (A (or Am (-> Bm Am))) (C (-> (or Bm Am) (or Am (-> Bm Am)))))
================================================================
tm-name          tm-49884
in-theory        49884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49884.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E)))), M:tm-95, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49885
in-theory        49885
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((A -> D) -> ((B or A) -> D))))
theorem-size     17
proof            (modus-ponens tm-84 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49885.        ((A or (B -> A)) -> (C -> ((A -> D) -> ((B or A) -> D)))), M:tm-84, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49886
in-theory        49886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49886.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-83, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49887
in-theory        49887
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> ((B -> D) -> ((C or B) -> D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49887.        (((not (not A)) -> A) and ((B or (C -> B)) -> ((B -> D) -> ((C or B) -> D)))), M:tm-76, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49888
in-theory        49888
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((A -> C) -> ((B or A) -> C)))
theorem-size     23
proof            (modus-ponens tm-73 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-8 tm-10 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49888.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((A -> C) -> ((B or A) -> C))), M:tm-73, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49889
in-theory        49889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49889.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E)))), M:tm-69, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49890
in-theory        49890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49890.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-54, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49891
in-theory        49891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> ((B -> C) -> ((A or B) -> C)))
theorem-size     19
proof            (modus-ponens tm-50 tm-630 ((A Am) (B (-> Bm Am)) (C (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49891.        (((A -> B) or (B or (A -> B))) -> ((B -> C) -> ((A or B) -> C))), M:tm-50, m:tm-630, u:((A Am) (B (-> Bm Am)) (C (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49892
in-theory        49892
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> ((A -> C) -> ((B or A) -> C)))
theorem-size     17
proof            (modus-ponens tm-49 tm-630 ((A Am) (B (-> Bm Am)) (C (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49892.        ((A or (A or (B -> A))) -> ((A -> C) -> ((B or A) -> C))), M:tm-49, m:tm-630, u:((A Am) (B (-> Bm Am)) (C (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49893
in-theory        49893
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> ((B -> D) -> ((C or B) -> D)))
theorem-size     23
proof            (modus-ponens tm-47 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49893.        (((A and (B or (C -> B))) or (B or (C -> B))) -> ((B -> D) -> ((C or B) -> D))), M:tm-47, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49894
in-theory        49894
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((A -> D) -> ((B or A) -> D)))
theorem-size     23
proof            (modus-ponens tm-46 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49894.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((A -> D) -> ((B or A) -> D))), M:tm-46, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49895
in-theory        49895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49895.        ((A -> (B or A)) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E)))), M:tm-42, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49896
in-theory        49896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E))))
theorem-size     21
proof            (modus-ponens tm-32 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49896.        ((A -> (A or B)) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E)))), M:tm-32, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49897
in-theory        49897
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and ((A -> C) -> ((B or A) -> C))))
theorem-size     21
proof            (modus-ponens tm-24 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49897.        ((A or (B -> A)) -> ((A or (B -> A)) and ((A -> C) -> ((B or A) -> C)))), M:tm-24, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49898
in-theory        49898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E))))
theorem-size     23
proof            (modus-ponens tm-23 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49898.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E)))), M:tm-23, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49899
in-theory        49899
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E))))
theorem-size     21
proof            (modus-ponens tm-22 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49899.        (((A and B) -> B) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E)))), M:tm-22, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49900
in-theory        49900
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E))))
theorem-size     21
proof            (modus-ponens tm-21 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49900.        (((A and B) -> A) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E)))), M:tm-21, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49901
in-theory        49901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     29
proof            (modus-ponens tm-20 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49901.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-20, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49902
in-theory        49902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E))))
theorem-size     21
proof            (modus-ponens tm-19 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49902.        ((A -> (B -> A)) and ((C or (D -> C)) -> ((C -> E) -> ((D or C) -> E)))), M:tm-19, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49903
in-theory        49903
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not ((A -> C) -> ((B or A) -> C)))) -> (not (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-9 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-9 tm-8 tm-1)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49903.        (((A or (B -> A)) -> (not ((A -> C) -> ((B or A) -> C)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49904
in-theory        49904
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A or (C -> A)) or ((A -> B) -> ((C or A) -> B))) -> D))
theorem-size     29
proof            (modus-ponens tm-8 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-8 tm-1)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49904.        ((((A -> B) -> ((C or A) -> B)) -> D) -> (((A or (C -> A)) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-49905
in-theory        49905
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> ((B -> D) -> ((C or B) -> D))))
theorem-size     17
proof            (modus-ponens tm-7 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-7 tm-8 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49905.        (A or ((B or (C -> B)) -> ((B -> D) -> ((C or B) -> D)))), M:tm-7, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49906
in-theory        49906
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-6 tm-8 tm-1)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49906.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) or D), M:tm-6, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49907
in-theory        49907
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> ((B -> D) -> ((C or B) -> D))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49907.        (A -> (((B or (C -> B)) -> ((B -> D) -> ((C or B) -> D))) and A)), M:tm-5, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49908
in-theory        49908
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (A -> C)) -> ((A or (B -> A)) -> ((B or A) -> C)))
theorem-size     21
proof            (modus-ponens tm-2 tm-630 ((A (or Am (-> Bm Am))) (B (-> Am Cm)) (C (-> (or Bm Am) Cm))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49908.        (((A or (B -> A)) -> (A -> C)) -> ((A or (B -> A)) -> ((B or A) -> C))), M:tm-2, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> Am Cm)) (C (-> (or Bm Am) Cm)))
================================================================
tm-name          tm-49909
in-theory        49909
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> ((B -> D) -> ((C or B) -> D))))
theorem-size     17
proof            (modus-ponens tm-1 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-1 tm-8)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-49909.        (A -> ((B or (C -> B)) -> ((B -> D) -> ((C or B) -> D)))), M:tm-1, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-49910
in-theory        49910
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or ((B -> (not A)) -> (not B))))
theorem-size     15
proof            (modus-ponens tm-623 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49910.        ((A or (B -> A)) -> (C or ((B -> (not A)) -> (not B)))), M:tm-623, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49911
in-theory        49911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-622 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49911.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-622, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49912
in-theory        49912
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (C -> (D or C)))
theorem-size     19
proof            (modus-ponens tm-609 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-9)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49912.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (C -> (D or C))), M:tm-609, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49913
in-theory        49913
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     23
proof            (modus-ponens tm-605 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49913.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-605, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49914
in-theory        49914
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((C -> (D or C)) and ((A or (B -> A)) -> ((B -> (not A)) -> (not B)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-9)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49914.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((C -> (D or C)) and ((A or (B -> A)) -> ((B -> (not A)) -> (not B))))), M:tm-595, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49915
in-theory        49915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-550 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49915.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-550, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49916
in-theory        49916
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-540 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49916.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-540, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49917
in-theory        49917
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-530 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49917.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-530, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49918
in-theory        49918
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     23
proof            (modus-ponens tm-520 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49918.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-520, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49919
in-theory        49919
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-510 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49919.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-510, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49920
in-theory        49920
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-500 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49920.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-500, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49921
in-theory        49921
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F))))
theorem-size     29
proof            (modus-ponens tm-490 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-9)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49921.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F)))), M:tm-490, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49922
in-theory        49922
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-480 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49922.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-480, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49923
in-theory        49923
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((B -> (not A)) -> (not B)) or C))
theorem-size     15
proof            (modus-ponens tm-470 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49923.        ((A or (B -> A)) -> (((B -> (not A)) -> (not B)) or C)), M:tm-470, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49924
in-theory        49924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-469 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49924.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-469, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49925
in-theory        49925
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (C -> (C or D)))
theorem-size     19
proof            (modus-ponens tm-456 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-9)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49925.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (C -> (C or D))), M:tm-456, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49926
in-theory        49926
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     23
proof            (modus-ponens tm-453 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49926.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-453, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49927
in-theory        49927
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((C -> (C or D)) and ((A or (B -> A)) -> ((B -> (not A)) -> (not B)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-9)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49927.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((C -> (C or D)) and ((A or (B -> A)) -> ((B -> (not A)) -> (not B))))), M:tm-443, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49928
in-theory        49928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-409 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49928.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-409, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49929
in-theory        49929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     23
proof            (modus-ponens tm-400 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49929.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-400, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49930
in-theory        49930
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-391 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49930.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-391, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49931
in-theory        49931
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-382 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49931.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-382, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49932
in-theory        49932
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F))))
theorem-size     29
proof            (modus-ponens tm-373 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-9)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49932.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F)))), M:tm-373, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49933
in-theory        49933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-364 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49933.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-364, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49934
in-theory        49934
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((B -> (not A)) -> (not B)) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49934.        ((A or (B -> A)) -> (C -> (((B -> (not A)) -> (not B)) and C))), M:tm-355, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49935
in-theory        49935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     23
proof            (modus-ponens tm-354 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49935.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-354, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49936
in-theory        49936
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-341 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49936.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49937
in-theory        49937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-338 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49937.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D)))), M:tm-338, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49938
in-theory        49938
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((A or (B -> A)) -> ((A or (B -> A)) and ((B -> (not A)) -> (not B)))))
theorem-size     33
proof            (modus-ponens tm-328 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49938.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((A or (B -> A)) -> ((A or (B -> A)) and ((B -> (not A)) -> (not B))))), M:tm-328, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49939
in-theory        49939
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((C -> (D -> (C and D))) and ((A or (B -> A)) -> ((B -> (not A)) -> (not B)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49939.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((C -> (D -> (C and D))) and ((A or (B -> A)) -> ((B -> (not A)) -> (not B))))), M:tm-327, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49940
in-theory        49940
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((C and D) -> D) and ((A or (B -> A)) -> ((B -> (not A)) -> (not B)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-9)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49940.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((C and D) -> D) and ((A or (B -> A)) -> ((B -> (not A)) -> (not B))))), M:tm-326, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49941
in-theory        49941
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((C and D) -> C) and ((A or (B -> A)) -> ((B -> (not A)) -> (not B)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-9)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49941.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((C and D) -> C) and ((A or (B -> A)) -> ((B -> (not A)) -> (not B))))), M:tm-325, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49942
in-theory        49942
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A or (B -> A)) -> ((B -> (not A)) -> (not B)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49942.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A or (B -> A)) -> ((B -> (not A)) -> (not B))))), M:tm-324, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49943
in-theory        49943
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((C -> (D -> C)) and ((A or (B -> A)) -> ((B -> (not A)) -> (not B)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49943.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((C -> (D -> C)) and ((A or (B -> A)) -> ((B -> (not A)) -> (not B))))), M:tm-323, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49944
in-theory        49944
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((C and D) -> D))
theorem-size     19
proof            (modus-ponens tm-322 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-9)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49944.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((C and D) -> D)), M:tm-322, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49945
in-theory        49945
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((C and D) -> C))
theorem-size     19
proof            (modus-ponens tm-320 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-9)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49945.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((C and D) -> C)), M:tm-320, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49946
in-theory        49946
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-318 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49946.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49947
in-theory        49947
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     25
proof            (modus-ponens tm-316 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49947.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49948
in-theory        49948
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (C -> (D -> C)))
theorem-size     19
proof            (modus-ponens tm-315 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49948.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (C -> (D -> C))), M:tm-315, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49949
in-theory        49949
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((A or (B -> A)) -> (not ((B -> (not A)) -> (not B)))) -> (not (A or (B -> A)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49949.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((A or (B -> A)) -> (not ((B -> (not A)) -> (not B)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49950
in-theory        49950
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((((B -> (not A)) -> (not B)) -> C) -> (((A or (B -> A)) or ((B -> (not A)) -> (not B))) -> C)))
theorem-size     39
proof            (modus-ponens tm-312 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49950.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((((B -> (not A)) -> (not B)) -> C) -> (((A or (B -> A)) or ((B -> (not A)) -> (not B))) -> C))), M:tm-312, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49951
in-theory        49951
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (C or ((A or (B -> A)) -> ((B -> (not A)) -> (not B)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49951.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (C or ((A or (B -> A)) -> ((B -> (not A)) -> (not B))))), M:tm-311, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49952
in-theory        49952
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) or C))
theorem-size     29
proof            (modus-ponens tm-310 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49952.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) or C)), M:tm-310, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49953
in-theory        49953
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (C -> (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and C)))
theorem-size     31
proof            (modus-ponens tm-309 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49953.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (C -> (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and C))), M:tm-309, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49954
in-theory        49954
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((A or (B -> A)) -> (B -> (not A))) -> ((A or (B -> A)) -> (not B))))
theorem-size     33
proof            (modus-ponens tm-306 tm-631 ((A (or Am (-> Bm Am))) (B (-> Bm (not Am))) (C (not Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49954.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (((A or (B -> A)) -> (B -> (not A))) -> ((A or (B -> A)) -> (not B)))), M:tm-306, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> Bm (not Am))) (C (not Bm)))
================================================================
tm-name          tm-49955
in-theory        49955
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (C -> ((A or (B -> A)) -> ((B -> (not A)) -> (not B)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49955.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and (C -> ((A or (B -> A)) -> ((B -> (not A)) -> (not B))))), M:tm-305, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49956
in-theory        49956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-303 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49956.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-303, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49957
in-theory        49957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     23
proof            (modus-ponens tm-270 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49957.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-270, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49958
in-theory        49958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     23
proof            (modus-ponens tm-239 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49958.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-239, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49959
in-theory        49959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F))))
theorem-size     31
proof            (modus-ponens tm-210 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-9)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49959.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F)))), M:tm-210, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49960
in-theory        49960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     23
proof            (modus-ponens tm-183 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49960.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-183, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49961
in-theory        49961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-157 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49961.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-157, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49962
in-theory        49962
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     29
proof            (modus-ponens tm-147 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-9)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49962.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-147, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49963
in-theory        49963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-134 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49963.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-134, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49964
in-theory        49964
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     29
proof            (modus-ponens tm-125 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-9)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49964.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-125, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49965
in-theory        49965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F))))
theorem-size     29
proof            (modus-ponens tm-113 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-9)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49965.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F)))), M:tm-113, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49966
in-theory        49966
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     33
proof            (modus-ponens tm-105 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-9)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49966.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-105, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49967
in-theory        49967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-95 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49967.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D)))), M:tm-95, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49968
in-theory        49968
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((B -> (not A)) -> (not B))))
theorem-size     15
proof            (modus-ponens tm-84 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-9)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49968.        ((A or (B -> A)) -> (C -> ((B -> (not A)) -> (not B)))), M:tm-84, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49969
in-theory        49969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     21
proof            (modus-ponens tm-83 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49969.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-83, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49970
in-theory        49970
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> ((C -> (not B)) -> (not C))))
theorem-size     19
proof            (modus-ponens tm-76 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49970.        (((not (not A)) -> A) and ((B or (C -> B)) -> ((C -> (not B)) -> (not C)))), M:tm-76, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49971
in-theory        49971
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((B -> (not A)) -> (not B)))
theorem-size     21
proof            (modus-ponens tm-73 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49971.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((B -> (not A)) -> (not B))), M:tm-73, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49972
in-theory        49972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-69 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49972.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D)))), M:tm-69, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49973
in-theory        49973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-54 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49973.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-54, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49974
in-theory        49974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> ((A -> (not B)) -> (not A)))
theorem-size     17
proof            (modus-ponens tm-50 tm-631 ((A Am) (B (-> Bm Am)) (C (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-9)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49974.        (((A -> B) or (B or (A -> B))) -> ((A -> (not B)) -> (not A))), M:tm-50, m:tm-631, u:((A Am) (B (-> Bm Am)) (C (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49975
in-theory        49975
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> ((B -> (not A)) -> (not B)))
theorem-size     15
proof            (modus-ponens tm-49 tm-631 ((A Am) (B (-> Bm Am)) (C (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49975.        ((A or (A or (B -> A))) -> ((B -> (not A)) -> (not B))), M:tm-49, m:tm-631, u:((A Am) (B (-> Bm Am)) (C (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49976
in-theory        49976
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> ((C -> (not B)) -> (not C)))
theorem-size     21
proof            (modus-ponens tm-47 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49976.        (((A and (B or (C -> B))) or (B or (C -> B))) -> ((C -> (not B)) -> (not C))), M:tm-47, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49977
in-theory        49977
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((B -> (not A)) -> (not B)))
theorem-size     21
proof            (modus-ponens tm-46 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49977.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((B -> (not A)) -> (not B))), M:tm-46, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49978
in-theory        49978
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-42 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49978.        ((A -> (B or A)) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D)))), M:tm-42, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49979
in-theory        49979
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-32 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49979.        ((A -> (A or B)) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D)))), M:tm-32, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49980
in-theory        49980
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and ((B -> (not A)) -> (not B))))
theorem-size     19
proof            (modus-ponens tm-24 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49980.        ((A or (B -> A)) -> ((A or (B -> A)) and ((B -> (not A)) -> (not B)))), M:tm-24, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49981
in-theory        49981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D))))
theorem-size     21
proof            (modus-ponens tm-23 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49981.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D)))), M:tm-23, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49982
in-theory        49982
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-22 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49982.        (((A and B) -> B) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D)))), M:tm-22, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49983
in-theory        49983
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-21 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49983.        (((A and B) -> A) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D)))), M:tm-21, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49984
in-theory        49984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-20 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-9)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49984.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-20, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49985
in-theory        49985
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-19 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-9)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49985.        ((A -> (B -> A)) and ((C or (D -> C)) -> ((D -> (not C)) -> (not D)))), M:tm-19, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49986
in-theory        49986
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not ((B -> (not A)) -> (not B)))) -> (not (A or (B -> A))))
theorem-size     21
proof            (modus-ponens tm-9 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-9 tm-8 tm-1)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49986.        (((A or (B -> A)) -> (not ((B -> (not A)) -> (not B)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49987
in-theory        49987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> C) -> (((B or (A -> B)) or ((A -> (not B)) -> (not A))) -> C))
theorem-size     25
proof            (modus-ponens tm-8 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49987.        ((((A -> (not B)) -> (not A)) -> C) -> (((B or (A -> B)) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-49988
in-theory        49988
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> ((C -> (not B)) -> (not C))))
theorem-size     15
proof            (modus-ponens tm-7 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-7 tm-8 tm-1 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49988.        (A or ((B or (C -> B)) -> ((C -> (not B)) -> (not C)))), M:tm-7, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49989
in-theory        49989
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) or C)
theorem-size     15
proof            (modus-ponens tm-6 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-6 tm-8 tm-1 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49989.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) or C), M:tm-6, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49990
in-theory        49990
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> ((C -> (not B)) -> (not C))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49990.        (A -> (((B or (C -> B)) -> ((C -> (not B)) -> (not C))) and A)), M:tm-5, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49991
in-theory        49991
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (not A))) -> ((A or (B -> A)) -> (not B)))
theorem-size     19
proof            (modus-ponens tm-2 tm-631 ((A (or Am (-> Bm Am))) (B (-> Bm (not Am))) (C (not Bm))))
axioms-used      (tm-2 tm-8 tm-1 tm-9)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49991.        (((A or (B -> A)) -> (B -> (not A))) -> ((A or (B -> A)) -> (not B))), M:tm-2, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> Bm (not Am))) (C (not Bm)))
================================================================
tm-name          tm-49992
in-theory        49992
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> ((C -> (not B)) -> (not C))))
theorem-size     15
proof            (modus-ponens tm-1 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-1 tm-8 tm-9)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-49992.        (A -> ((B or (C -> B)) -> ((C -> (not B)) -> (not C)))), M:tm-1, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-49993
in-theory        49993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-49993.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-622, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-49994
in-theory        49994
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (D or (A or (B -> A)))))
theorem-size     15
proof            (modus-ponens tm-617 tm-632 ((A (or Am (-> Bm Am))) (Cm (or B (or Am (-> Bm Am)))) (C (-> Dm (or B (or Am (-> Bm Am)))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-49994.        ((A or (B -> A)) -> (C -> (D or (A or (B -> A))))), M:tm-617, m:tm-632, u:((A (or Am (-> Bm Am))) (Cm (or B (or Am (-> Bm Am)))) (C (-> Dm (or B (or Am (-> Bm Am))))))
================================================================
tm-name          tm-49995
in-theory        49995
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-49995.        (((A or (B -> A)) -> (C -> (D -> C))) and (E -> (F or E))), M:tm-609, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-49996
in-theory        49996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-49996.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-605, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-49997
in-theory        49997
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and ((E -> (F or E)) and ((A or (B -> A)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-49997.        (((A or (B -> A)) -> (C -> (D -> C))) and ((E -> (F or E)) and ((A or (B -> A)) -> (C -> (D -> C))))), M:tm-595, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-49998
in-theory        49998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-49998.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-550, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-49999
in-theory        49999
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-49999.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-540, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50000
in-theory        50000
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50000.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-530, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50001
in-theory        50001
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50001.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-520, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50002
in-theory        50002
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50002.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-510, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50003
in-theory        50003
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50003.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-500, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50004
in-theory        50004
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50004.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (H -> G)))), M:tm-490, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50005
in-theory        50005
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50005.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-480, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50006
in-theory        50006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50006.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-469, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50007
in-theory        50007
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((A or (B -> A)) or D)))
theorem-size     15
proof            (modus-ponens tm-464 tm-632 ((A (or Am (-> Bm Am))) (Cm (or (or Am (-> Bm Am)) B)) (C (-> Dm (or (or Am (-> Bm Am)) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50007.        ((A or (B -> A)) -> (C -> ((A or (B -> A)) or D))), M:tm-464, m:tm-632, u:((A (or Am (-> Bm Am))) (Cm (or (or Am (-> Bm Am)) B)) (C (-> Dm (or (or Am (-> Bm Am)) B))))
================================================================
tm-name          tm-50008
in-theory        50008
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50008.        (((A or (B -> A)) -> (C -> (D -> C))) and (E -> (E or F))), M:tm-456, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50009
in-theory        50009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50009.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-453, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50010
in-theory        50010
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and ((E -> (E or F)) and ((A or (B -> A)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50010.        (((A or (B -> A)) -> (C -> (D -> C))) and ((E -> (E or F)) and ((A or (B -> A)) -> (C -> (D -> C))))), M:tm-443, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50011
in-theory        50011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50011.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-409, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50012
in-theory        50012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50012.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-400, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50013
in-theory        50013
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50013.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-391, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50014
in-theory        50014
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50014.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-382, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50015
in-theory        50015
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50015.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (G -> (H -> G)))), M:tm-373, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50016
in-theory        50016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50016.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-364, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50017
in-theory        50017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50017.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-354, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50018
in-theory        50018
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (D -> ((A or (B -> A)) and D))))
theorem-size     17
proof            (modus-ponens tm-349 tm-632 ((A (or Am (-> Bm Am))) (Cm (-> B (and (or Am (-> Bm Am)) B))) (C (-> Dm (-> B (and (or Am (-> Bm Am)) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50018.        ((A or (B -> A)) -> (C -> (D -> ((A or (B -> A)) and D)))), M:tm-349, m:tm-632, u:((A (or Am (-> Bm Am))) (Cm (-> B (and (or Am (-> Bm Am)) B))) (C (-> Dm (-> B (and (or Am (-> Bm Am)) B)))))
================================================================
tm-name          tm-50019
in-theory        50019
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50019.        (((A or (B -> A)) -> (C -> (D -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50020
in-theory        50020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50020.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (E -> (F -> E)))), M:tm-338, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50021
in-theory        50021
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-632 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50021.        (((A or (B -> A)) -> (C -> (D -> C))) and ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (D -> C))))), M:tm-328, m:tm-632, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-50022
in-theory        50022
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> (C -> (D -> C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50022.        (((A or (B -> A)) -> (C -> (D -> C))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> (C -> (D -> C))))), M:tm-327, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50023
in-theory        50023
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (((E and F) -> F) and ((A or (B -> A)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50023.        (((A or (B -> A)) -> (C -> (D -> C))) and (((E and F) -> F) and ((A or (B -> A)) -> (C -> (D -> C))))), M:tm-326, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50024
in-theory        50024
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (((E and F) -> E) and ((A or (B -> A)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50024.        (((A or (B -> A)) -> (C -> (D -> C))) and (((E and F) -> E) and ((A or (B -> A)) -> (C -> (D -> C))))), M:tm-325, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50025
in-theory        50025
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> (C -> (D -> C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50025.        (((A or (B -> A)) -> (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> (C -> (D -> C))))), M:tm-324, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50026
in-theory        50026
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and ((E -> (F -> E)) and ((A or (B -> A)) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50026.        (((A or (B -> A)) -> (C -> (D -> C))) and ((E -> (F -> E)) and ((A or (B -> A)) -> (C -> (D -> C))))), M:tm-323, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50027
in-theory        50027
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50027.        (((A or (B -> A)) -> (C -> (D -> C))) and ((E and F) -> F)), M:tm-322, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50028
in-theory        50028
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50028.        (((A or (B -> A)) -> (C -> (D -> C))) and ((E and F) -> E)), M:tm-320, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50029
in-theory        50029
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50029.        (((A or (B -> A)) -> (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50030
in-theory        50030
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-632 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50030.        (((A or (B -> A)) -> (C -> (D -> C))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-632, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-50031
in-theory        50031
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50031.        (((A or (B -> A)) -> (C -> (D -> C))) and (E -> (F -> E))), M:tm-315, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50032
in-theory        50032
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (((A or (B -> A)) -> (not (C -> (D -> C)))) -> (not (A or (B -> A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-632 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50032.        (((A or (B -> A)) -> (C -> (D -> C))) and (((A or (B -> A)) -> (not (C -> (D -> C)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-632, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-50033
in-theory        50033
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (((C -> (D -> C)) -> E) -> (((A or (B -> A)) or (C -> (D -> C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-632 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50033.        (((A or (B -> A)) -> (C -> (D -> C))) and (((C -> (D -> C)) -> E) -> (((A or (B -> A)) or (C -> (D -> C))) -> E))), M:tm-312, m:tm-632, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-50034
in-theory        50034
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (E or ((A or (B -> A)) -> (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50034.        (((A or (B -> A)) -> (C -> (D -> C))) and (E or ((A or (B -> A)) -> (C -> (D -> C))))), M:tm-311, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50035
in-theory        50035
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (((A or (B -> A)) -> (C -> (D -> C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50035.        (((A or (B -> A)) -> (C -> (D -> C))) and (((A or (B -> A)) -> (C -> (D -> C))) or E)), M:tm-310, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50036
in-theory        50036
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (E -> (((A or (B -> A)) -> (C -> (D -> C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50036.        (((A or (B -> A)) -> (C -> (D -> C))) and (E -> (((A or (B -> A)) -> (C -> (D -> C))) and E))), M:tm-309, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50037
in-theory        50037
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (D -> C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-632 ((A (or Am (-> Bm Am))) (B Cm) (C (-> Dm Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50037.        (((A or (B -> A)) -> (C -> (D -> C))) and (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (D -> C)))), M:tm-306, m:tm-632, u:((A (or Am (-> Bm Am))) (B Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-50038
in-theory        50038
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and (E -> ((A or (B -> A)) -> (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50038.        (((A or (B -> A)) -> (C -> (D -> C))) and (E -> ((A or (B -> A)) -> (C -> (D -> C))))), M:tm-305, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50039
in-theory        50039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50039.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-303, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50040
in-theory        50040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50040.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-270, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50041
in-theory        50041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50041.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-239, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50042
in-theory        50042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50042.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (G -> (H -> G)))), M:tm-210, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50043
in-theory        50043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50043.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-183, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50044
in-theory        50044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50044.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-157, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50045
in-theory        50045
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50045.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-147, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50046
in-theory        50046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50046.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-134, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50047
in-theory        50047
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50047.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-125, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50048
in-theory        50048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50048.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (H -> G)))), M:tm-113, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50049
in-theory        50049
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50049.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-105, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50050
in-theory        50050
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (A or (B -> A))))
theorem-size     13
proof            (modus-ponens tm-99 tm-632 ((Cm (or Am (-> Bm Am))) (A (or Am (-> Bm Am))) (B (-> Dm (or Am (-> Bm Am))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50050.        ((A or (B -> A)) -> (C -> (A or (B -> A)))), M:tm-99, m:tm-632, u:((Cm (or Am (-> Bm Am))) (A (or Am (-> Bm Am))) (B (-> Dm (or Am (-> Bm Am)))))
================================================================
tm-name          tm-50051
in-theory        50051
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (D -> (A or (B -> A)))))
theorem-size     15
proof            (modus-ponens tm-98 tm-632 ((A (or Am (-> Bm Am))) (Cm (-> B (or Am (-> Bm Am)))) (C (-> Dm (-> B (or Am (-> Bm Am)))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50051.        ((A or (B -> A)) -> (C -> (D -> (A or (B -> A))))), M:tm-98, m:tm-632, u:((A (or Am (-> Bm Am))) (Cm (-> B (or Am (-> Bm Am)))) (C (-> Dm (-> B (or Am (-> Bm Am))))))
================================================================
tm-name          tm-50052
in-theory        50052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50052.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (E -> (F -> E)))), M:tm-95, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50053
in-theory        50053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50053.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-83, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50054
in-theory        50054
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> (D -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50054.        (((not (not A)) -> A) and ((B or (C -> B)) -> (D -> (E -> D)))), M:tm-76, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50055
in-theory        50055
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (C -> (D -> C)))
theorem-size     19
proof            (modus-ponens tm-73 tm-632 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-10 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50055.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (C -> (D -> C))), M:tm-73, m:tm-632, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-50056
in-theory        50056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50056.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (E -> (F -> E)))), M:tm-69, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50057
in-theory        50057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50057.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-54, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50058
in-theory        50058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-50 tm-632 ((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50058.        (((A -> B) or (B or (A -> B))) -> (C -> (D -> C))), M:tm-50, m:tm-632, u:((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-50059
in-theory        50059
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-49 tm-632 ((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50059.        ((A or (A or (B -> A))) -> (C -> (D -> C))), M:tm-49, m:tm-632, u:((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-50060
in-theory        50060
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-47 tm-632 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50060.        (((A and (B or (C -> B))) or (B or (C -> B))) -> (D -> (E -> D))), M:tm-47, m:tm-632, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-50061
in-theory        50061
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-46 tm-632 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50061.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> (D -> (E -> D))), M:tm-46, m:tm-632, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-50062
in-theory        50062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50062.        ((A -> (B or A)) and ((C or (D -> C)) -> (E -> (F -> E)))), M:tm-42, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50063
in-theory        50063
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50063.        ((A -> (A or B)) and ((C or (D -> C)) -> (E -> (F -> E)))), M:tm-32, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50064
in-theory        50064
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (D -> C))))
theorem-size     17
proof            (modus-ponens tm-24 tm-632 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50064.        ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (D -> C)))), M:tm-24, m:tm-632, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-50065
in-theory        50065
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50065.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (E -> (F -> E)))), M:tm-23, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50066
in-theory        50066
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50066.        (((A and B) -> B) and ((C or (D -> C)) -> (E -> (F -> E)))), M:tm-22, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50067
in-theory        50067
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50067.        (((A and B) -> A) and ((C or (D -> C)) -> (E -> (F -> E)))), M:tm-21, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50068
in-theory        50068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50068.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-20, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50069
in-theory        50069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50069.        ((A -> (B -> A)) and ((C or (D -> C)) -> (E -> (F -> E)))), M:tm-19, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50070
in-theory        50070
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not (C -> (D -> C)))) -> (not (A or (B -> A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-632 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-9 tm-8 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50070.        (((A or (B -> A)) -> (not (C -> (D -> C)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-632, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-50071
in-theory        50071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> (((D or (E -> D)) or (A -> (B -> A))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-632 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50071.        (((A -> (B -> A)) -> C) -> (((D or (E -> D)) or (A -> (B -> A))) -> C)), M:tm-8, m:tm-632, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-50072
in-theory        50072
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-7 tm-8 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50072.        (A or ((B or (C -> B)) -> (D -> (E -> D)))), M:tm-7, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50073
in-theory        50073
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-6 tm-8 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50073.        (((A or (B -> A)) -> (C -> (D -> C))) or E), M:tm-6, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50074
in-theory        50074
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> (D -> (E -> D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50074.        (A -> (((B or (C -> B)) -> (D -> (E -> D))) and A)), M:tm-5, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50075
in-theory        50075
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-2 tm-632 ((A (or Am (-> Bm Am))) (B Cm) (C (-> Dm Cm))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50075.        (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (D -> C))), M:tm-2, m:tm-632, u:((A (or Am (-> Bm Am))) (B Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-50076
in-theory        50076
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-1 tm-8)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-50076.        (A -> ((B or (C -> B)) -> (D -> (E -> D)))), M:tm-1, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-50077
in-theory        50077
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (B -> B)))
theorem-size     11
proof            (modus-ponens tm-623 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50077.        ((A or (B -> A)) -> (C or (B -> B))), M:tm-623, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-50078
in-theory        50078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-622 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50078.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (E -> E))), M:tm-622, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50079
in-theory        50079
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-609 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       135
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50079.        (((A or (B -> A)) -> (B -> B)) and (C -> (D or C))), M:tm-609, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50080
in-theory        50080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-605 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50080.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (E -> E))), M:tm-605, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50081
in-theory        50081
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and ((C -> (D or C)) and ((A or (B -> A)) -> (B -> B))))
theorem-size     25
proof            (modus-ponens tm-595 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50081.        (((A or (B -> A)) -> (B -> B)) and ((C -> (D or C)) and ((A or (B -> A)) -> (B -> B)))), M:tm-595, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50082
in-theory        50082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-550 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50082.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> (E -> E))), M:tm-550, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50083
in-theory        50083
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-540 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50083.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> (E -> E))), M:tm-540, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50084
in-theory        50084
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-530 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50084.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> (E -> E))), M:tm-530, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50085
in-theory        50085
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-520 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50085.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (E -> E))), M:tm-520, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50086
in-theory        50086
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-510 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50086.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (E -> E))), M:tm-510, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50087
in-theory        50087
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-500 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50087.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (E -> E))), M:tm-500, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50088
in-theory        50088
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (F -> F)))
theorem-size     25
proof            (modus-ponens tm-490 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50088.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (F -> F))), M:tm-490, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50089
in-theory        50089
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-480 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50089.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (E -> E))), M:tm-480, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50090
in-theory        50090
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> B) or C))
theorem-size     11
proof            (modus-ponens tm-470 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50090.        ((A or (B -> A)) -> ((B -> B) or C)), M:tm-470, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-50091
in-theory        50091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-469 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50091.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (E -> E))), M:tm-469, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50092
in-theory        50092
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-456 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       135
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50092.        (((A or (B -> A)) -> (B -> B)) and (C -> (C or D))), M:tm-456, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50093
in-theory        50093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-453 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50093.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (E -> E))), M:tm-453, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50094
in-theory        50094
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and ((C -> (C or D)) and ((A or (B -> A)) -> (B -> B))))
theorem-size     25
proof            (modus-ponens tm-443 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50094.        (((A or (B -> A)) -> (B -> B)) and ((C -> (C or D)) and ((A or (B -> A)) -> (B -> B)))), M:tm-443, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50095
in-theory        50095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-409 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50095.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> (E -> E))), M:tm-409, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50096
in-theory        50096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-400 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50096.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (E -> E))), M:tm-400, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50097
in-theory        50097
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-391 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50097.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> (E -> E))), M:tm-391, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50098
in-theory        50098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-382 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50098.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> (E -> E))), M:tm-382, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50099
in-theory        50099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (F -> F)))
theorem-size     25
proof            (modus-ponens tm-373 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50099.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (F -> F))), M:tm-373, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50100
in-theory        50100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-364 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50100.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (E -> E))), M:tm-364, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50101
in-theory        50101
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((B -> B) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50101.        ((A or (B -> A)) -> (C -> ((B -> B) and C))), M:tm-355, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-50102
in-theory        50102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-354 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50102.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (E -> E))), M:tm-354, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50103
in-theory        50103
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-341 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50103.        (((A or (B -> A)) -> (B -> B)) and (C -> (D -> (C and D)))), M:tm-341, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50104
in-theory        50104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (D -> D)))
theorem-size     19
proof            (modus-ponens tm-338 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50104.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (D -> D))), M:tm-338, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50105
in-theory        50105
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and ((A or (B -> A)) -> ((A or (B -> A)) and (B -> B))))
theorem-size     25
proof            (modus-ponens tm-328 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50105.        (((A or (B -> A)) -> (B -> B)) and ((A or (B -> A)) -> ((A or (B -> A)) and (B -> B)))), M:tm-328, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-50106
in-theory        50106
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and ((C -> (D -> (C and D))) and ((A or (B -> A)) -> (B -> B))))
theorem-size     27
proof            (modus-ponens tm-327 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50106.        (((A or (B -> A)) -> (B -> B)) and ((C -> (D -> (C and D))) and ((A or (B -> A)) -> (B -> B)))), M:tm-327, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50107
in-theory        50107
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (((C and D) -> D) and ((A or (B -> A)) -> (B -> B))))
theorem-size     25
proof            (modus-ponens tm-326 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50107.        (((A or (B -> A)) -> (B -> B)) and (((C and D) -> D) and ((A or (B -> A)) -> (B -> B)))), M:tm-326, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50108
in-theory        50108
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (((C and D) -> C) and ((A or (B -> A)) -> (B -> B))))
theorem-size     25
proof            (modus-ponens tm-325 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50108.        (((A or (B -> A)) -> (B -> B)) and (((C and D) -> C) and ((A or (B -> A)) -> (B -> B)))), M:tm-325, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50109
in-theory        50109
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A or (B -> A)) -> (B -> B))))
theorem-size     33
proof            (modus-ponens tm-324 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50109.        (((A or (B -> A)) -> (B -> B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A or (B -> A)) -> (B -> B)))), M:tm-324, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50110
in-theory        50110
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and ((C -> (D -> C)) and ((A or (B -> A)) -> (B -> B))))
theorem-size     25
proof            (modus-ponens tm-323 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50110.        (((A or (B -> A)) -> (B -> B)) and ((C -> (D -> C)) and ((A or (B -> A)) -> (B -> B)))), M:tm-323, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50111
in-theory        50111
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-322 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       135
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50111.        (((A or (B -> A)) -> (B -> B)) and ((C and D) -> D)), M:tm-322, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50112
in-theory        50112
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-320 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       135
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50112.        (((A or (B -> A)) -> (B -> B)) and ((C and D) -> C)), M:tm-320, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50113
in-theory        50113
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-318 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50113.        (((A or (B -> A)) -> (B -> B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50114
in-theory        50114
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     21
proof            (modus-ponens tm-316 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50114.        (((A or (B -> A)) -> (B -> B)) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-50115
in-theory        50115
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-315 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       135
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50115.        (((A or (B -> A)) -> (B -> B)) and (C -> (D -> C))), M:tm-315, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50116
in-theory        50116
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (((A or (B -> A)) -> (not (B -> B))) -> (not (A or (B -> A)))))
theorem-size     27
proof            (modus-ponens tm-313 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50116.        (((A or (B -> A)) -> (B -> B)) and (((A or (B -> A)) -> (not (B -> B))) -> (not (A or (B -> A))))), M:tm-313, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-50117
in-theory        50117
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (((B -> B) -> C) -> (((A or (B -> A)) or (B -> B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-312 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50117.        (((A or (B -> A)) -> (B -> B)) and (((B -> B) -> C) -> (((A or (B -> A)) or (B -> B)) -> C))), M:tm-312, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-50118
in-theory        50118
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (C or ((A or (B -> A)) -> (B -> B))))
theorem-size     21
proof            (modus-ponens tm-311 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50118.        (((A or (B -> A)) -> (B -> B)) and (C or ((A or (B -> A)) -> (B -> B)))), M:tm-311, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50119
in-theory        50119
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (((A or (B -> A)) -> (B -> B)) or C))
theorem-size     21
proof            (modus-ponens tm-310 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50119.        (((A or (B -> A)) -> (B -> B)) and (((A or (B -> A)) -> (B -> B)) or C)), M:tm-310, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50120
in-theory        50120
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (C -> (((A or (B -> A)) -> (B -> B)) and C)))
theorem-size     23
proof            (modus-ponens tm-309 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50120.        (((A or (B -> A)) -> (B -> B)) and (C -> (((A or (B -> A)) -> (B -> B)) and C))), M:tm-309, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50121
in-theory        50121
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (((A or (B -> A)) -> B) -> ((A or (B -> A)) -> B)))
theorem-size     25
proof            (modus-ponens tm-306 tm-633 ((A (or Am (-> Bm Am))) (B Bm) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50121.        (((A or (B -> A)) -> (B -> B)) and (((A or (B -> A)) -> B) -> ((A or (B -> A)) -> B))), M:tm-306, m:tm-633, u:((A (or Am (-> Bm Am))) (B Bm) (C Bm))
================================================================
tm-name          tm-50122
in-theory        50122
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and (C -> ((A or (B -> A)) -> (B -> B))))
theorem-size     21
proof            (modus-ponens tm-305 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50122.        (((A or (B -> A)) -> (B -> B)) and (C -> ((A or (B -> A)) -> (B -> B)))), M:tm-305, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50123
in-theory        50123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-303 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50123.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (E -> E))), M:tm-303, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50124
in-theory        50124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-270 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50124.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (E -> E))), M:tm-270, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50125
in-theory        50125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-239 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50125.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (E -> E))), M:tm-239, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50126
in-theory        50126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (F -> F)))
theorem-size     27
proof            (modus-ponens tm-210 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50126.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (F -> F))), M:tm-210, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50127
in-theory        50127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     19
proof            (modus-ponens tm-183 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50127.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (E -> E))), M:tm-183, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50128
in-theory        50128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-157 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50128.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (E -> E))), M:tm-157, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50129
in-theory        50129
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     25
proof            (modus-ponens tm-147 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50129.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (E -> E))), M:tm-147, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50130
in-theory        50130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-134 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50130.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (E -> E))), M:tm-134, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50131
in-theory        50131
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     25
proof            (modus-ponens tm-125 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50131.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (E -> E))), M:tm-125, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50132
in-theory        50132
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> A)) -> (((B -> C) -> B) -> ((B -> C) -> C)))
theorem-size     19
proof            (modus-ponens tm-114 tm-633 ((A (or Am (-> (-> C D) Am))) (B (-> C D)) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50132.        ((A or ((B -> C) -> A)) -> (((B -> C) -> B) -> ((B -> C) -> C))), M:tm-114, m:tm-633, u:((A (or Am (-> (-> C D) Am))) (B (-> C D)) (Bm (-> C D)))
================================================================
tm-name          tm-50133
in-theory        50133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (F -> F)))
theorem-size     25
proof            (modus-ponens tm-113 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50133.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (F -> F))), M:tm-113, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50134
in-theory        50134
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (E -> E)))
theorem-size     29
proof            (modus-ponens tm-105 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50134.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (E -> E))), M:tm-105, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50135
in-theory        50135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-95 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50135.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (D -> D))), M:tm-95, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50136
in-theory        50136
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (B -> B)))
theorem-size     11
proof            (modus-ponens tm-84 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       115
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50136.        ((A or (B -> A)) -> (C -> (B -> B))), M:tm-84, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-50137
in-theory        50137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (E -> E)))
theorem-size     17
proof            (modus-ponens tm-83 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50137.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (E -> E))), M:tm-83, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50138
in-theory        50138
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> (C -> C)))
theorem-size     15
proof            (modus-ponens tm-76 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50138.        (((not (not A)) -> A) and ((B or (C -> B)) -> (C -> C))), M:tm-76, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50139
in-theory        50139
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (B -> B))
theorem-size     17
proof            (modus-ponens tm-73 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-8 tm-10 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50139.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (B -> B)), M:tm-73, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-50140
in-theory        50140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-69 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50140.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (D -> D))), M:tm-69, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50141
in-theory        50141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-54 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50141.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (E -> E))), M:tm-54, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50142
in-theory        50142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> (A -> A))
theorem-size     13
proof            (modus-ponens tm-50 tm-633 ((A Am) (B (-> Bm Am)) (C (-> Bm Bm))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50142.        (((A -> B) or (B or (A -> B))) -> (A -> A)), M:tm-50, m:tm-633, u:((A Am) (B (-> Bm Am)) (C (-> Bm Bm)))
================================================================
tm-name          tm-50143
in-theory        50143
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> (B -> B))
theorem-size     11
proof            (modus-ponens tm-49 tm-633 ((A Am) (B (-> Bm Am)) (C (-> Bm Bm))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50143.        ((A or (A or (B -> A))) -> (B -> B)), M:tm-49, m:tm-633, u:((A Am) (B (-> Bm Am)) (C (-> Bm Bm)))
================================================================
tm-name          tm-50144
in-theory        50144
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> (C -> C))
theorem-size     17
proof            (modus-ponens tm-47 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50144.        (((A and (B or (C -> B))) or (B or (C -> B))) -> (C -> C)), M:tm-47, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-50145
in-theory        50145
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> (B -> B))
theorem-size     17
proof            (modus-ponens tm-46 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50145.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> (B -> B)), M:tm-46, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-50146
in-theory        50146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-42 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50146.        ((A -> (B or A)) and ((C or (D -> C)) -> (D -> D))), M:tm-42, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50147
in-theory        50147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-32 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50147.        ((A -> (A or B)) and ((C or (D -> C)) -> (D -> D))), M:tm-32, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50148
in-theory        50148
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and (B -> B)))
theorem-size     15
proof            (modus-ponens tm-24 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50148.        ((A or (B -> A)) -> ((A or (B -> A)) and (B -> B))), M:tm-24, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-50149
in-theory        50149
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (D -> D)))
theorem-size     17
proof            (modus-ponens tm-23 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50149.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (D -> D))), M:tm-23, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50150
in-theory        50150
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-22 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50150.        (((A and B) -> B) and ((C or (D -> C)) -> (D -> D))), M:tm-22, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50151
in-theory        50151
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-21 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50151.        (((A and B) -> A) and ((C or (D -> C)) -> (D -> D))), M:tm-21, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50152
in-theory        50152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-20 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50152.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (E -> E))), M:tm-20, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50153
in-theory        50153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-19 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50153.        ((A -> (B -> A)) and ((C or (D -> C)) -> (D -> D))), M:tm-19, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50154
in-theory        50154
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not (B -> B))) -> (not (A or (B -> A))))
theorem-size     17
proof            (modus-ponens tm-9 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-9 tm-8 tm-1 tm-2)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50154.        (((A or (B -> A)) -> (not (B -> B))) -> (not (A or (B -> A)))), M:tm-9, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-50155
in-theory        50155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> B) -> (((C or (A -> C)) or (A -> A)) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50155.        (((A -> A) -> B) -> (((C or (A -> C)) or (A -> A)) -> B)), M:tm-8, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-50156
in-theory        50156
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> (C -> C)))
theorem-size     11
proof            (modus-ponens tm-7 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-7 tm-8 tm-1 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50156.        (A or ((B or (C -> B)) -> (C -> C))), M:tm-7, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50157
in-theory        50157
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) or C)
theorem-size     11
proof            (modus-ponens tm-6 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-6 tm-8 tm-1 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50157.        (((A or (B -> A)) -> (B -> B)) or C), M:tm-6, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50158
in-theory        50158
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> (C -> C)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50158.        (A -> (((B or (C -> B)) -> (C -> C)) and A)), M:tm-5, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50159
in-theory        50159
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> B) -> ((A or (B -> A)) -> B))
theorem-size     15
proof            (modus-ponens tm-2 tm-633 ((A (or Am (-> Bm Am))) (B Bm) (C Bm)))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50159.        (((A or (B -> A)) -> B) -> ((A or (B -> A)) -> B)), M:tm-2, m:tm-633, u:((A (or Am (-> Bm Am))) (B Bm) (C Bm))
================================================================
tm-name          tm-50160
in-theory        50160
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (C -> C)))
theorem-size     11
proof            (modus-ponens tm-1 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-50160.        (A -> ((B or (C -> B)) -> (C -> C))), M:tm-1, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-50161
in-theory        50161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (D or ((A -> (B -> C)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-623 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50161.        (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (D or ((A -> (B -> C)) -> (A -> C)))), M:tm-623, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50162
in-theory        50162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-622 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50162.        ((A -> (B -> (C or B))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-622, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50163
in-theory        50163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or D)))
theorem-size     29
proof            (modus-ponens tm-609 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50163.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or D))), M:tm-609, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50164
in-theory        50164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-605 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50164.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-605, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50165
in-theory        50165
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50165.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-595, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50166
in-theory        50166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-550 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50166.        (((A -> (B or A)) or C) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-550, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50167
in-theory        50167
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-540 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50167.        ((A or (B -> (C or B))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-540, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50168
in-theory        50168
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-530 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50168.        ((A or (B -> (B or C))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-530, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50169
in-theory        50169
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-520 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50169.        ((A or (B -> (C -> (B and C)))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-520, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50170
in-theory        50170
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-510 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50170.        ((A or ((B and C) -> C)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-510, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50171
in-theory        50171
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-500 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50171.        ((A or ((B and C) -> B)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-500, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50172
in-theory        50172
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-490 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50172.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-490, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50173
in-theory        50173
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-480 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50173.        ((A or (B -> (C -> B))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-480, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50174
in-theory        50174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> C)) or D))
theorem-size     25
proof            (modus-ponens tm-470 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50174.        (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> C)) or D)), M:tm-470, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50175
in-theory        50175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-469 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50175.        ((A -> (B -> (B or C))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-469, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50176
in-theory        50176
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D or E)))
theorem-size     29
proof            (modus-ponens tm-456 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50176.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D or E))), M:tm-456, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50177
in-theory        50177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-453 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50177.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-453, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50178
in-theory        50178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50178.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-443, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50179
in-theory        50179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-409 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50179.        (((A -> (A or B)) or C) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-409, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50180
in-theory        50180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-400 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50180.        (((A -> (B -> (A and B))) or C) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-400, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50181
in-theory        50181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-391 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50181.        ((((A and B) -> B) or C) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-391, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50182
in-theory        50182
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-382 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50182.        ((((A and B) -> A) or C) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-382, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50183
in-theory        50183
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-373 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50183.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-373, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50184
in-theory        50184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-364 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50184.        (((A -> (B -> A)) or C) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-364, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50185
in-theory        50185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (D -> (((A -> (B -> C)) -> (A -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-355 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50185.        (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (D -> (((A -> (B -> C)) -> (A -> C)) and D))), M:tm-355, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50186
in-theory        50186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-354 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50186.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-354, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50187
in-theory        50187
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-341 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50187.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50188
in-theory        50188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-338 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50188.        (((A -> B) -> (A -> (A and B))) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-338, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50189
in-theory        50189
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> B) or ((A -> (B -> C)) -> (A -> B))) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-328 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50189.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> B) or ((A -> (B -> C)) -> (A -> B))) and ((A -> (B -> C)) -> (A -> C))))), M:tm-328, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50190
in-theory        50190
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50190.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-327, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50191
in-theory        50191
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50191.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-326, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50192
in-theory        50192
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50192.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-325, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50193
in-theory        50193
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       245
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50193.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-324, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50194
in-theory        50194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50194.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-323, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50195
in-theory        50195
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> E))
theorem-size     29
proof            (modus-ponens tm-322 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50195.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> E)), M:tm-322, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50196
in-theory        50196
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> D))
theorem-size     29
proof            (modus-ponens tm-320 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50196.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> D)), M:tm-320, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50197
in-theory        50197
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-318 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50197.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50198
in-theory        50198
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> B) or ((A -> (B -> C)) -> (A -> B)))))
theorem-size     51
proof            (modus-ponens tm-316 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50198.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> B) or ((A -> (B -> C)) -> (A -> B))))), M:tm-316, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50199
in-theory        50199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> D)))
theorem-size     29
proof            (modus-ponens tm-315 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50199.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> D))), M:tm-315, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50200
in-theory        50200
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> B) or ((A -> (B -> C)) -> (A -> B))))))
theorem-size     63
proof            (modus-ponens tm-313 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50200.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> B) or ((A -> (B -> C)) -> (A -> B)))))), M:tm-313, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50201
in-theory        50201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> C))) -> D)))
theorem-size     61
proof            (modus-ponens tm-312 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50201.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> C))) -> D))), M:tm-312, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50202
in-theory        50202
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50202.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-311, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50203
in-theory        50203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) or D))
theorem-size     49
proof            (modus-ponens tm-310 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50203.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) or D)), M:tm-310, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50204
in-theory        50204
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and D)))
theorem-size     51
proof            (modus-ponens tm-309 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50204.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and D))), M:tm-309, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50205
in-theory        50205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (A -> (B -> C))) -> (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (A -> C))))
theorem-size     61
proof            (modus-ponens tm-306 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50205.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (A -> (B -> C))) -> (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (A -> C)))), M:tm-306, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
================================================================
tm-name          tm-50206
in-theory        50206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50206.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-305, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50207
in-theory        50207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-303 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50207.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-303, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50208
in-theory        50208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-270 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50208.        ((A -> (((B and C) -> C) and A)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-270, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50209
in-theory        50209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-239 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50209.        ((A -> (((B and C) -> B) and A)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-239, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50210
in-theory        50210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-210 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50210.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-210, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50211
in-theory        50211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-183 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50211.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-183, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50212
in-theory        50212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-157 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50212.        ((A -> ((B and C) -> C)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-157, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50213
in-theory        50213
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-147 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50213.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-147, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50214
in-theory        50214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-134 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50214.        ((A -> ((B and C) -> B)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-134, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50215
in-theory        50215
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-125 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50215.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-125, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50216
in-theory        50216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> C)))
theorem-size     29
proof            (modus-ponens tm-114 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C Am) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50216.        (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> C))), M:tm-114, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C Am) (D Cm))
================================================================
tm-name          tm-50217
in-theory        50217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-113 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50217.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-113, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50218
in-theory        50218
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-105 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50218.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-105, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50219
in-theory        50219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     31
proof            (modus-ponens tm-95 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50219.        (((A -> B) -> (A -> A)) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-95, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50220
in-theory        50220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (D -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-84 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50220.        (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (D -> ((A -> (B -> C)) -> (A -> C)))), M:tm-84, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50221
in-theory        50221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-83 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50221.        ((A -> (B -> (C -> B))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-83, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50222
in-theory        50222
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     29
proof            (modus-ponens tm-76 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50222.        (((not (not A)) -> A) and (((B -> C) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-76, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50223
in-theory        50223
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) or ((A -> (B -> C)) -> (A -> B))))) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     39
proof            (modus-ponens tm-73 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50223.        (((not (not ((A -> B) or ((A -> (B -> C)) -> (A -> B))))) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-73, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50224
in-theory        50224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-69 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50224.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-69, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50225
in-theory        50225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-54 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50225.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-54, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50226
in-theory        50226
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     33
proof            (modus-ponens tm-50 tm-634 ((A (-> Am Bm)) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50226.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-50, m:tm-634, u:((A (-> Am Bm)) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50227
in-theory        50227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     27
proof            (modus-ponens tm-49 tm-634 ((A (-> Am Bm)) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50227.        (((A -> B) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-49, m:tm-634, u:((A (-> Am Bm)) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50228
in-theory        50228
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) or ((B -> (C -> D)) -> (B -> C)))) or ((B -> C) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D)))
theorem-size     39
proof            (modus-ponens tm-47 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50228.        (((A and ((B -> C) or ((B -> (C -> D)) -> (B -> C)))) or ((B -> C) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50229
in-theory        50229
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) or ((A -> (B -> C)) -> (A -> B))) and D) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     39
proof            (modus-ponens tm-46 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50229.        (((((A -> B) or ((A -> (B -> C)) -> (A -> B))) and D) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50230
in-theory        50230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-42 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50230.        ((A -> (B or A)) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50231
in-theory        50231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-32 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50231.        ((A -> (A or B)) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50232
in-theory        50232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> B) or ((A -> (B -> C)) -> (A -> B))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-24 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50232.        (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> B) or ((A -> (B -> C)) -> (A -> B))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50233
in-theory        50233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     31
proof            (modus-ponens tm-23 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50233.        ((A -> (B -> (A and B))) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50234
in-theory        50234
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-22 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50234.        (((A and B) -> B) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50235
in-theory        50235
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-21 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50235.        (((A and B) -> A) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50236
in-theory        50236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-20 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50236.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50237
in-theory        50237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-19 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50237.        ((A -> (B -> A)) and (((C -> D) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50238
in-theory        50238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> B) or ((A -> (B -> C)) -> (A -> B))))
theorem-size     27
proof            (modus-ponens tm-12 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50238.        (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> B) or ((A -> (B -> C)) -> (A -> B)))), M:tm-12, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50239
in-theory        50239
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> B) or ((A -> (B -> C)) -> (A -> B)))))
theorem-size     39
proof            (modus-ponens tm-9 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-9 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50239.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> B) or ((A -> (B -> C)) -> (A -> B))))), M:tm-9, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50240
in-theory        50240
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> C))) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50240.        ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-50241
in-theory        50241
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     25
proof            (modus-ponens tm-7 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-7 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50241.        (A or (((B -> C) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50242
in-theory        50242
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) or D)
theorem-size     25
proof            (modus-ponens tm-6 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-6 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50242.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50243
in-theory        50243
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50243.        (A -> ((((B -> C) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50244
in-theory        50244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (A -> (B -> C))) -> (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (A -> C)))
theorem-size     37
proof            (modus-ponens tm-2 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50244.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (A -> (B -> C))) -> (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (A -> C))), M:tm-2, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
================================================================
tm-name          tm-50245
in-theory        50245
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     25
proof            (modus-ponens tm-1 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-50245.        (A -> (((B -> C) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-50246
in-theory        50246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50246.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-622, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50247
in-theory        50247
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50247.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50248
in-theory        50248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50248.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-605, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50249
in-theory        50249
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50249.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-595, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50250
in-theory        50250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50250.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-550, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50251
in-theory        50251
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50251.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-540, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50252
in-theory        50252
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50252.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-530, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50253
in-theory        50253
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50253.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-520, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50254
in-theory        50254
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50254.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-510, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50255
in-theory        50255
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50255.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-500, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50256
in-theory        50256
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50256.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-490, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50257
in-theory        50257
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50257.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-480, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50258
in-theory        50258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50258.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-469, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50259
in-theory        50259
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50259.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50260
in-theory        50260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50260.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-453, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50261
in-theory        50261
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50261.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-443, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50262
in-theory        50262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50262.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-409, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50263
in-theory        50263
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50263.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-400, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50264
in-theory        50264
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50264.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-391, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50265
in-theory        50265
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50265.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-382, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50266
in-theory        50266
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50266.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-373, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50267
in-theory        50267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50267.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-364, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50268
in-theory        50268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50268.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-354, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50269
in-theory        50269
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50269.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50270
in-theory        50270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50270.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-338, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50271
in-theory        50271
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-328 tm-635 ((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50271.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-328, m:tm-635, u:((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-50272
in-theory        50272
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50272.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-327, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50273
in-theory        50273
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50273.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-326, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50274
in-theory        50274
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50274.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-325, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50275
in-theory        50275
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50275.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-324, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50276
in-theory        50276
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50276.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-323, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50277
in-theory        50277
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50277.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50278
in-theory        50278
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50278.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50279
in-theory        50279
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50279.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50280
in-theory        50280
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     31
proof            (modus-ponens tm-316 tm-635 ((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50280.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-635, u:((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-50281
in-theory        50281
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50281.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50282
in-theory        50282
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B -> A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (B -> A)))))
theorem-size     47
proof            (modus-ponens tm-313 tm-635 ((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50282.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B -> A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (B -> A))))), M:tm-313, m:tm-635, u:((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-50283
in-theory        50283
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> (((A or (B -> A)) or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     57
proof            (modus-ponens tm-312 tm-635 ((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50283.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> (((A or (B -> A)) or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-312, m:tm-635, u:((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-50284
in-theory        50284
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50284.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-311, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50285
in-theory        50285
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50285.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-310, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50286
in-theory        50286
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50286.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F))), M:tm-309, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50287
in-theory        50287
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B -> A)) -> (C -> (D -> E))) -> ((A or (B -> A)) -> ((C -> D) -> (C -> E)))))
theorem-size     45
proof            (modus-ponens tm-306 tm-635 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50287.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A or (B -> A)) -> (C -> (D -> E))) -> ((A or (B -> A)) -> ((C -> D) -> (C -> E))))), M:tm-306, m:tm-635, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-50288
in-theory        50288
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50288.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-305, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50289
in-theory        50289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50289.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-303, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50290
in-theory        50290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50290.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-270, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50291
in-theory        50291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50291.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-239, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50292
in-theory        50292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50292.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-210, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50293
in-theory        50293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50293.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-183, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50294
in-theory        50294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50294.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-157, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50295
in-theory        50295
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50295.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-147, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50296
in-theory        50296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50296.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-134, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50297
in-theory        50297
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50297.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-125, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50298
in-theory        50298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50298.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-113, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50299
in-theory        50299
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50299.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-105, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50300
in-theory        50300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50300.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-95, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50301
in-theory        50301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50301.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-83, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50302
in-theory        50302
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50302.        (((not (not A)) -> A) and ((B or (C -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-76, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50303
in-theory        50303
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-73 tm-635 ((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-10 tm-1 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50303.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-73, m:tm-635, u:((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-50304
in-theory        50304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50304.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-69, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50305
in-theory        50305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50305.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-54, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50306
in-theory        50306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-50 tm-635 ((A Am) (B (-> Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50306.        (((A -> B) or (B or (A -> B))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-50, m:tm-635, u:((A Am) (B (-> Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-50307
in-theory        50307
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-49 tm-635 ((A Am) (B (-> Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50307.        ((A or (A or (B -> A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-49, m:tm-635, u:((A Am) (B (-> Bm Am)) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-50308
in-theory        50308
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-47 tm-635 ((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50308.        (((A and (B or (C -> B))) or (B or (C -> B))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-47, m:tm-635, u:((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-50309
in-theory        50309
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-46 tm-635 ((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50309.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-46, m:tm-635, u:((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-50310
in-theory        50310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50310.        ((A -> (B or A)) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-42, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50311
in-theory        50311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50311.        ((A -> (A or B)) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-32, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50312
in-theory        50312
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     25
proof            (modus-ponens tm-24 tm-635 ((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50312.        ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-24, m:tm-635, u:((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-50313
in-theory        50313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50313.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-23, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50314
in-theory        50314
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50314.        (((A and B) -> B) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-22, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50315
in-theory        50315
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50315.        (((A and B) -> A) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-21, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50316
in-theory        50316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50316.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-20, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50317
in-theory        50317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50317.        ((A -> (B -> A)) and ((C or (D -> C)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-19, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50318
in-theory        50318
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (B -> A))))
theorem-size     27
proof            (modus-ponens tm-9 tm-635 ((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-9 tm-8 tm-1 tm-2)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50318.        (((A or (B -> A)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not (A or (B -> A)))), M:tm-9, m:tm-635, u:((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-50319
in-theory        50319
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((E or (F -> E)) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-635 ((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50319.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> (((E or (F -> E)) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-635, u:((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-50320
in-theory        50320
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-7 tm-8 tm-1 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50320.        (A or ((B or (C -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-7, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50321
in-theory        50321
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-6 tm-8 tm-1 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50321.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F), M:tm-6, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50322
in-theory        50322
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50322.        (A -> (((B or (C -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)), M:tm-5, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50323
in-theory        50323
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> E))) -> ((A or (B -> A)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-2 tm-635 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50323.        (((A or (B -> A)) -> (C -> (D -> E))) -> ((A or (B -> A)) -> ((C -> D) -> (C -> E)))), M:tm-2, m:tm-635, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-50324
in-theory        50324
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-50324.        (A -> ((B or (C -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-1, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-50325
in-theory        50325
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((A -> B) and C) -> A)) -> (D or (((A -> B) and C) -> B)))
theorem-size     19
proof            (modus-ponens tm-623 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50325.        ((A or (((A -> B) and C) -> A)) -> (D or (((A -> B) and C) -> B))), M:tm-623, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50326
in-theory        50326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-622 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50326.        ((A -> (B -> (C or B))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-622, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50327
in-theory        50327
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-609 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50327.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (D -> (E or D))), M:tm-609, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50328
in-theory        50328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-605 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50328.        ((A -> ((B -> (C or B)) and A)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-605, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50329
in-theory        50329
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     41
proof            (modus-ponens tm-595 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50329.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-595, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50330
in-theory        50330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-550 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50330.        (((A -> (B or A)) or C) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-550, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50331
in-theory        50331
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-540 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50331.        ((A or (B -> (C or B))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-540, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50332
in-theory        50332
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-530 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50332.        ((A or (B -> (B or C))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-530, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50333
in-theory        50333
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-520 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50333.        ((A or (B -> (C -> (B and C)))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-520, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50334
in-theory        50334
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-510 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50334.        ((A or ((B and C) -> C)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-510, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50335
in-theory        50335
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-500 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50335.        ((A or ((B and C) -> B)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-500, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50336
in-theory        50336
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-490 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50336.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-490, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50337
in-theory        50337
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-480 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50337.        ((A or (B -> (C -> B))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-480, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50338
in-theory        50338
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> B) or D))
theorem-size     19
proof            (modus-ponens tm-470 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50338.        ((A or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> B) or D)), M:tm-470, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50339
in-theory        50339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-469 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50339.        ((A -> (B -> (B or C))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-469, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50340
in-theory        50340
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-456 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50340.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (D -> (D or E))), M:tm-456, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50341
in-theory        50341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-453 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50341.        ((A -> ((B -> (B or C)) and A)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-453, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50342
in-theory        50342
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     41
proof            (modus-ponens tm-443 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50342.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-443, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50343
in-theory        50343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-409 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50343.        (((A -> (A or B)) or C) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-409, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50344
in-theory        50344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-400 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50344.        (((A -> (B -> (A and B))) or C) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-400, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50345
in-theory        50345
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-391 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50345.        ((((A and B) -> B) or C) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-391, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50346
in-theory        50346
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-382 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50346.        ((((A and B) -> A) or C) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-382, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50347
in-theory        50347
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-373 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50347.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-373, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50348
in-theory        50348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-364 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50348.        (((A -> (B -> A)) or C) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-364, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50349
in-theory        50349
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((A -> B) and C) -> A)) -> (D -> ((((A -> B) and C) -> B) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50349.        ((A or (((A -> B) and C) -> A)) -> (D -> ((((A -> B) and C) -> B) and D))), M:tm-355, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50350
in-theory        50350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-354 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50350.        ((A -> (B -> (C -> (B and C)))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-354, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50351
in-theory        50351
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-341 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50351.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50352
in-theory        50352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-338 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50352.        (((A -> B) -> (A -> (A and B))) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-338, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50353
in-theory        50353
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((A or (((A -> B) and C) -> A)) -> ((A or (((A -> B) and C) -> A)) and (((A -> B) and C) -> B))))
theorem-size     45
proof            (modus-ponens tm-328 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50353.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((A or (((A -> B) and C) -> A)) -> ((A or (((A -> B) and C) -> A)) and (((A -> B) and C) -> B)))), M:tm-328, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50354
in-theory        50354
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     43
proof            (modus-ponens tm-327 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50354.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-327, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50355
in-theory        50355
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     41
proof            (modus-ponens tm-326 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50355.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-326, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50356
in-theory        50356
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     41
proof            (modus-ponens tm-325 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50356.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-325, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50357
in-theory        50357
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     49
proof            (modus-ponens tm-324 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50357.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-324, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50358
in-theory        50358
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     41
proof            (modus-ponens tm-323 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50358.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-323, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50359
in-theory        50359
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-322 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50359.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((D and E) -> E)), M:tm-322, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50360
in-theory        50360
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-320 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50360.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((D and E) -> D)), M:tm-320, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50361
in-theory        50361
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-318 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50361.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50362
in-theory        50362
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((A or (((A -> B) and C) -> A)) -> (A or (((A -> B) and C) -> A))))
theorem-size     37
proof            (modus-ponens tm-316 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50362.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((A or (((A -> B) and C) -> A)) -> (A or (((A -> B) and C) -> A)))), M:tm-316, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50363
in-theory        50363
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-315 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50363.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (D -> (E -> D))), M:tm-315, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50364
in-theory        50364
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((A or (((A -> B) and C) -> A)) -> (not (((A -> B) and C) -> B))) -> (not (A or (((A -> B) and C) -> A)))))
theorem-size     47
proof            (modus-ponens tm-313 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50364.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((A or (((A -> B) and C) -> A)) -> (not (((A -> B) and C) -> B))) -> (not (A or (((A -> B) and C) -> A))))), M:tm-313, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50365
in-theory        50365
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((((A -> B) and C) -> B) -> D) -> (((A or (((A -> B) and C) -> A)) or (((A -> B) and C) -> B)) -> D)))
theorem-size     47
proof            (modus-ponens tm-312 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50365.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((((A -> B) and C) -> B) -> D) -> (((A or (((A -> B) and C) -> A)) or (((A -> B) and C) -> B)) -> D))), M:tm-312, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50366
in-theory        50366
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (D or ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     37
proof            (modus-ponens tm-311 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50366.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (D or ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-311, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50367
in-theory        50367
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) or D))
theorem-size     37
proof            (modus-ponens tm-310 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50367.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) or D)), M:tm-310, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50368
in-theory        50368
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (D -> (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and D)))
theorem-size     39
proof            (modus-ponens tm-309 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50368.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (D -> (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and D))), M:tm-309, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50369
in-theory        50369
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((A or (((A -> B) and C) -> A)) -> ((A -> B) and C)) -> ((A or (((A -> B) and C) -> A)) -> B)))
theorem-size     45
proof            (modus-ponens tm-306 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (and (-> Am Bm) Cm)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50369.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((A or (((A -> B) and C) -> A)) -> ((A -> B) and C)) -> ((A or (((A -> B) and C) -> A)) -> B))), M:tm-306, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (and (-> Am Bm) Cm)) (C Bm))
================================================================
tm-name          tm-50370
in-theory        50370
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (D -> ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     37
proof            (modus-ponens tm-305 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50370.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (D -> ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-305, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50371
in-theory        50371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-303 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50371.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-303, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50372
in-theory        50372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-270 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50372.        ((A -> (((B and C) -> C) and A)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-270, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50373
in-theory        50373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-239 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50373.        ((A -> (((B and C) -> B) and A)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-239, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50374
in-theory        50374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     35
proof            (modus-ponens tm-210 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50374.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-210, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50375
in-theory        50375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-183 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50375.        ((A -> ((B -> (C -> B)) and A)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-183, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50376
in-theory        50376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-157 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50376.        ((A -> ((B and C) -> C)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-157, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50377
in-theory        50377
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-147 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50377.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-147, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50378
in-theory        50378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-134 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50378.        ((A -> ((B and C) -> B)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-134, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50379
in-theory        50379
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-125 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50379.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-125, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50380
in-theory        50380
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((A -> (B -> C)) and D) -> A)) -> ((((A -> (B -> C)) and D) -> B) -> (((A -> (B -> C)) and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-114 tm-636 ((A (or Am (-> (and (-> Am (-> C D)) Cm) Am))) (B (and (-> Am (-> C D)) Cm)) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50380.        ((A or (((A -> (B -> C)) and D) -> A)) -> ((((A -> (B -> C)) and D) -> B) -> (((A -> (B -> C)) and D) -> C))), M:tm-114, m:tm-636, u:((A (or Am (-> (and (-> Am (-> C D)) Cm) Am))) (B (and (-> Am (-> C D)) Cm)) (Bm (-> C D)))
================================================================
tm-name          tm-50381
in-theory        50381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-113 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50381.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-113, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50382
in-theory        50382
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     37
proof            (modus-ponens tm-105 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50382.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-105, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50383
in-theory        50383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     25
proof            (modus-ponens tm-95 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50383.        (((A -> B) -> (A -> A)) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-95, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50384
in-theory        50384
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((A -> B) and C) -> A)) -> (D -> (((A -> B) and C) -> B)))
theorem-size     19
proof            (modus-ponens tm-84 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50384.        ((A or (((A -> B) and C) -> A)) -> (D -> (((A -> B) and C) -> B))), M:tm-84, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50385
in-theory        50385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-83 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50385.        ((A -> (B -> (C -> B))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-83, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50386
in-theory        50386
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))
theorem-size     23
proof            (modus-ponens tm-76 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-2 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50386.        (((not (not A)) -> A) and ((B or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))), M:tm-76, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50387
in-theory        50387
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (((A -> B) and C) -> A)))) or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))
theorem-size     29
proof            (modus-ponens tm-73 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-10 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50387.        (((not (not (A or (((A -> B) and C) -> A)))) or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)), M:tm-73, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50388
in-theory        50388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     29
proof            (modus-ponens tm-69 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-2 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50388.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-69, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50389
in-theory        50389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-54 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50389.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-54, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50390
in-theory        50390
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))
theorem-size     25
proof            (modus-ponens tm-50 tm-636 ((A Am) (B (-> (and (-> Am Bm) Cm) Am)) (C (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-7 tm-1 tm-2 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50390.        (((((A -> B) and C) -> A) or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)), M:tm-50, m:tm-636, u:((A Am) (B (-> (and (-> Am Bm) Cm) Am)) (C (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50391
in-theory        50391
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))
theorem-size     19
proof            (modus-ponens tm-49 tm-636 ((A Am) (B (-> (and (-> Am Bm) Cm) Am)) (C (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-6 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50391.        ((A or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)), M:tm-49, m:tm-636, u:((A Am) (B (-> (and (-> Am Bm) Cm) Am)) (C (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50392
in-theory        50392
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (((B -> C) and D) -> B))) or (B or (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C))
theorem-size     29
proof            (modus-ponens tm-47 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-4 tm-1 tm-2 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50392.        (((A and (B or (((B -> C) and D) -> B))) or (B or (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50393
in-theory        50393
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (((A -> B) and C) -> A)) and D) or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))
theorem-size     29
proof            (modus-ponens tm-46 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50393.        ((((A or (((A -> B) and C) -> A)) and D) or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50394
in-theory        50394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-42 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50394.        ((A -> (B or A)) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50395
in-theory        50395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-32 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50395.        ((A -> (A or B)) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50396
in-theory        50396
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((A -> B) and C) -> A)) -> ((A or (((A -> B) and C) -> A)) and (((A -> B) and C) -> B)))
theorem-size     27
proof            (modus-ponens tm-24 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50396.        ((A or (((A -> B) and C) -> A)) -> ((A or (((A -> B) and C) -> A)) and (((A -> B) and C) -> B))), M:tm-24, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50397
in-theory        50397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     25
proof            (modus-ponens tm-23 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50397.        ((A -> (B -> (A and B))) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50398
in-theory        50398
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-22 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50398.        (((A and B) -> B) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50399
in-theory        50399
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-21 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50399.        (((A and B) -> A) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50400
in-theory        50400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-20 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50400.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50401
in-theory        50401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     23
proof            (modus-ponens tm-19 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50401.        ((A -> (B -> A)) and ((C or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50402
in-theory        50402
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((A -> B) and C) -> A)) -> (A or (((A -> B) and C) -> A)))
theorem-size     19
proof            (modus-ponens tm-12 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50402.        ((A or (((A -> B) and C) -> A)) -> (A or (((A -> B) and C) -> A))), M:tm-12, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50403
in-theory        50403
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (not (((A -> B) and C) -> B))) -> (not (A or (((A -> B) and C) -> A))))
theorem-size     29
proof            (modus-ponens tm-9 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-9 tm-8 tm-1 tm-2 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50403.        (((A or (((A -> B) and C) -> A)) -> (not (((A -> B) and C) -> B))) -> (not (A or (((A -> B) and C) -> A)))), M:tm-9, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50404
in-theory        50404
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> D) -> (((A or (((A -> B) and C) -> A)) or (((A -> B) and C) -> B)) -> D))
theorem-size     29
proof            (modus-ponens tm-8 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50404.        (((((A -> B) and C) -> B) -> D) -> (((A or (((A -> B) and C) -> A)) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-50405
in-theory        50405
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))
theorem-size     19
proof            (modus-ponens tm-7 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-7 tm-8 tm-1 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50405.        (A or ((B or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50406
in-theory        50406
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) or D)
theorem-size     19
proof            (modus-ponens tm-6 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-6 tm-8 tm-1 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50406.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50407
in-theory        50407
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50407.        (A -> (((B or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50408
in-theory        50408
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> ((A -> B) and C)) -> ((A or (((A -> B) and C) -> A)) -> B))
theorem-size     27
proof            (modus-ponens tm-2 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (and (-> Am Bm) Cm)) (C Bm)))
axioms-used      (tm-2 tm-8 tm-1 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50408.        (((A or (((A -> B) and C) -> A)) -> ((A -> B) and C)) -> ((A or (((A -> B) and C) -> A)) -> B)), M:tm-2, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (and (-> Am Bm) Cm)) (C Bm))
================================================================
tm-name          tm-50409
in-theory        50409
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))
theorem-size     19
proof            (modus-ponens tm-1 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-1 tm-8 tm-2 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-50409.        (A -> ((B or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-50410
in-theory        50410
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50410.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-622, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50411
in-theory        50411
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50411.        (((A or (B -> A)) -> ((C and D) -> C)) and (E -> (F or E))), M:tm-609, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50412
in-theory        50412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50412.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-605, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50413
in-theory        50413
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and ((E -> (F or E)) and ((A or (B -> A)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50413.        (((A or (B -> A)) -> ((C and D) -> C)) and ((E -> (F or E)) and ((A or (B -> A)) -> ((C and D) -> C)))), M:tm-595, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50414
in-theory        50414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50414.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-550, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50415
in-theory        50415
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50415.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-540, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50416
in-theory        50416
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50416.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-530, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50417
in-theory        50417
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50417.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-520, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50418
in-theory        50418
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50418.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-510, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50419
in-theory        50419
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50419.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-500, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50420
in-theory        50420
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50420.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G and H) -> G))), M:tm-490, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50421
in-theory        50421
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50421.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-480, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50422
in-theory        50422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50422.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-469, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50423
in-theory        50423
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50423.        (((A or (B -> A)) -> ((C and D) -> C)) and (E -> (E or F))), M:tm-456, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50424
in-theory        50424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50424.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-453, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50425
in-theory        50425
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and ((E -> (E or F)) and ((A or (B -> A)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50425.        (((A or (B -> A)) -> ((C and D) -> C)) and ((E -> (E or F)) and ((A or (B -> A)) -> ((C and D) -> C)))), M:tm-443, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50426
in-theory        50426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50426.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-409, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50427
in-theory        50427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50427.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-400, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50428
in-theory        50428
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50428.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-391, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50429
in-theory        50429
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50429.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-382, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50430
in-theory        50430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50430.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((G and H) -> G))), M:tm-373, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50431
in-theory        50431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50431.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-364, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50432
in-theory        50432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50432.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-354, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50433
in-theory        50433
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50433.        (((A or (B -> A)) -> ((C and D) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50434
in-theory        50434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50434.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((E and F) -> E))), M:tm-338, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50435
in-theory        50435
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and ((A or (B -> A)) -> ((A or (B -> A)) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-328 tm-637 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50435.        (((A or (B -> A)) -> ((C and D) -> C)) and ((A or (B -> A)) -> ((A or (B -> A)) and ((C and D) -> C)))), M:tm-328, m:tm-637, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-50436
in-theory        50436
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> ((C and D) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50436.        (((A or (B -> A)) -> ((C and D) -> C)) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> ((C and D) -> C)))), M:tm-327, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50437
in-theory        50437
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (((E and F) -> F) and ((A or (B -> A)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50437.        (((A or (B -> A)) -> ((C and D) -> C)) and (((E and F) -> F) and ((A or (B -> A)) -> ((C and D) -> C)))), M:tm-326, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50438
in-theory        50438
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (((E and F) -> E) and ((A or (B -> A)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50438.        (((A or (B -> A)) -> ((C and D) -> C)) and (((E and F) -> E) and ((A or (B -> A)) -> ((C and D) -> C)))), M:tm-325, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50439
in-theory        50439
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> ((C and D) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50439.        (((A or (B -> A)) -> ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> ((C and D) -> C)))), M:tm-324, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50440
in-theory        50440
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and ((E -> (F -> E)) and ((A or (B -> A)) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50440.        (((A or (B -> A)) -> ((C and D) -> C)) and ((E -> (F -> E)) and ((A or (B -> A)) -> ((C and D) -> C)))), M:tm-323, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50441
in-theory        50441
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50441.        (((A or (B -> A)) -> ((C and D) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50442
in-theory        50442
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50442.        (((A or (B -> A)) -> ((C and D) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50443
in-theory        50443
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50443.        (((A or (B -> A)) -> ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50444
in-theory        50444
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-637 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50444.        (((A or (B -> A)) -> ((C and D) -> C)) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-637, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-50445
in-theory        50445
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50445.        (((A or (B -> A)) -> ((C and D) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50446
in-theory        50446
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (((A or (B -> A)) -> (not ((C and D) -> C))) -> (not (A or (B -> A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-637 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50446.        (((A or (B -> A)) -> ((C and D) -> C)) and (((A or (B -> A)) -> (not ((C and D) -> C))) -> (not (A or (B -> A))))), M:tm-313, m:tm-637, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-50447
in-theory        50447
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and ((((C and D) -> C) -> E) -> (((A or (B -> A)) or ((C and D) -> C)) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-637 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50447.        (((A or (B -> A)) -> ((C and D) -> C)) and ((((C and D) -> C) -> E) -> (((A or (B -> A)) or ((C and D) -> C)) -> E))), M:tm-312, m:tm-637, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-50448
in-theory        50448
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (E or ((A or (B -> A)) -> ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50448.        (((A or (B -> A)) -> ((C and D) -> C)) and (E or ((A or (B -> A)) -> ((C and D) -> C)))), M:tm-311, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50449
in-theory        50449
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (((A or (B -> A)) -> ((C and D) -> C)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50449.        (((A or (B -> A)) -> ((C and D) -> C)) and (((A or (B -> A)) -> ((C and D) -> C)) or E)), M:tm-310, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50450
in-theory        50450
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (E -> (((A or (B -> A)) -> ((C and D) -> C)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50450.        (((A or (B -> A)) -> ((C and D) -> C)) and (E -> (((A or (B -> A)) -> ((C and D) -> C)) and E))), M:tm-309, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50451
in-theory        50451
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (((A or (B -> A)) -> (C and D)) -> ((A or (B -> A)) -> C)))
theorem-size     29
proof            (modus-ponens tm-306 tm-637 ((A (or Am (-> Bm Am))) (B (and Cm Dm)) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50451.        (((A or (B -> A)) -> ((C and D) -> C)) and (((A or (B -> A)) -> (C and D)) -> ((A or (B -> A)) -> C))), M:tm-306, m:tm-637, u:((A (or Am (-> Bm Am))) (B (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-50452
in-theory        50452
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and (E -> ((A or (B -> A)) -> ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50452.        (((A or (B -> A)) -> ((C and D) -> C)) and (E -> ((A or (B -> A)) -> ((C and D) -> C)))), M:tm-305, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50453
in-theory        50453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50453.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-303, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50454
in-theory        50454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50454.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-270, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50455
in-theory        50455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50455.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-239, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50456
in-theory        50456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50456.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((G and H) -> G))), M:tm-210, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50457
in-theory        50457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50457.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-183, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50458
in-theory        50458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50458.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-157, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50459
in-theory        50459
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50459.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-147, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50460
in-theory        50460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50460.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-134, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50461
in-theory        50461
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50461.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-125, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50462
in-theory        50462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50462.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G and H) -> G))), M:tm-113, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50463
in-theory        50463
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50463.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-105, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50464
in-theory        50464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50464.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((E and F) -> E))), M:tm-95, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50465
in-theory        50465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50465.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-83, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50466
in-theory        50466
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> ((D and E) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50466.        (((not (not A)) -> A) and ((B or (C -> B)) -> ((D and E) -> D))), M:tm-76, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50467
in-theory        50467
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((C and D) -> C))
theorem-size     19
proof            (modus-ponens tm-73 tm-637 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-10 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50467.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((C and D) -> C)), M:tm-73, m:tm-637, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-50468
in-theory        50468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50468.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((E and F) -> E))), M:tm-69, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50469
in-theory        50469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50469.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-54, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50470
in-theory        50470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-50 tm-637 ((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-7 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50470.        (((A -> B) or (B or (A -> B))) -> ((C and D) -> C)), M:tm-50, m:tm-637, u:((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-50471
in-theory        50471
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-49 tm-637 ((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-6 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50471.        ((A or (A or (B -> A))) -> ((C and D) -> C)), M:tm-49, m:tm-637, u:((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-50472
in-theory        50472
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-47 tm-637 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-4 tm-1 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50472.        (((A and (B or (C -> B))) or (B or (C -> B))) -> ((D and E) -> D)), M:tm-47, m:tm-637, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-50473
in-theory        50473
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-46 tm-637 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50473.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((D and E) -> D)), M:tm-46, m:tm-637, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-50474
in-theory        50474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50474.        ((A -> (B or A)) and ((C or (D -> C)) -> ((E and F) -> E))), M:tm-42, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50475
in-theory        50475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50475.        ((A -> (A or B)) and ((C or (D -> C)) -> ((E and F) -> E))), M:tm-32, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50476
in-theory        50476
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and ((C and D) -> C)))
theorem-size     17
proof            (modus-ponens tm-24 tm-637 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50476.        ((A or (B -> A)) -> ((A or (B -> A)) and ((C and D) -> C))), M:tm-24, m:tm-637, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-50477
in-theory        50477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50477.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((E and F) -> E))), M:tm-23, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50478
in-theory        50478
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50478.        (((A and B) -> B) and ((C or (D -> C)) -> ((E and F) -> E))), M:tm-22, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50479
in-theory        50479
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50479.        (((A and B) -> A) and ((C or (D -> C)) -> ((E and F) -> E))), M:tm-21, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50480
in-theory        50480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50480.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-20, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50481
in-theory        50481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50481.        ((A -> (B -> A)) and ((C or (D -> C)) -> ((E and F) -> E))), M:tm-19, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50482
in-theory        50482
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not ((C and D) -> C))) -> (not (A or (B -> A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-637 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-9 tm-8 tm-1 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50482.        (((A or (B -> A)) -> (not ((C and D) -> C))) -> (not (A or (B -> A)))), M:tm-9, m:tm-637, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-50483
in-theory        50483
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> (((D or (E -> D)) or ((A and B) -> A)) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-637 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50483.        ((((A and B) -> A) -> C) -> (((D or (E -> D)) or ((A and B) -> A)) -> C)), M:tm-8, m:tm-637, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-50484
in-theory        50484
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-7 tm-8 tm-1 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50484.        (A or ((B or (C -> B)) -> ((D and E) -> D))), M:tm-7, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50485
in-theory        50485
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-6 tm-8 tm-1 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50485.        (((A or (B -> A)) -> ((C and D) -> C)) or E), M:tm-6, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50486
in-theory        50486
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> ((D and E) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50486.        (A -> (((B or (C -> B)) -> ((D and E) -> D)) and A)), M:tm-5, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50487
in-theory        50487
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C and D)) -> ((A or (B -> A)) -> C))
theorem-size     17
proof            (modus-ponens tm-2 tm-637 ((A (or Am (-> Bm Am))) (B (and Cm Dm)) (C Cm)))
axioms-used      (tm-2 tm-8 tm-1 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50487.        (((A or (B -> A)) -> (C and D)) -> ((A or (B -> A)) -> C)), M:tm-2, m:tm-637, u:((A (or Am (-> Bm Am))) (B (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-50488
in-theory        50488
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-50488.        (A -> ((B or (C -> B)) -> ((D and E) -> D))), M:tm-1, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-50489
in-theory        50489
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (A -> C)) -> A)) -> (D or ((B and (A -> C)) -> C)))
theorem-size     19
proof            (modus-ponens tm-623 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50489.        ((A or ((B and (A -> C)) -> A)) -> (D or ((B and (A -> C)) -> C))), M:tm-623, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50490
in-theory        50490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-622 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50490.        ((A -> (B -> (C or B))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-622, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50491
in-theory        50491
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-609 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50491.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (D -> (E or D))), M:tm-609, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50492
in-theory        50492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-605 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50492.        ((A -> ((B -> (C or B)) and A)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-605, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50493
in-theory        50493
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((D -> (E or D)) and ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C))))
theorem-size     41
proof            (modus-ponens tm-595 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50493.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((D -> (E or D)) and ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)))), M:tm-595, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50494
in-theory        50494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-550 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50494.        (((A -> (B or A)) or C) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-550, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50495
in-theory        50495
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-540 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50495.        ((A or (B -> (C or B))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-540, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50496
in-theory        50496
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-530 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50496.        ((A or (B -> (B or C))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-530, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50497
in-theory        50497
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-520 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50497.        ((A or (B -> (C -> (B and C)))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-520, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50498
in-theory        50498
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-510 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50498.        ((A or ((B and C) -> C)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-510, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50499
in-theory        50499
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-500 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50499.        ((A or ((B and C) -> B)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-500, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50500
in-theory        50500
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-490 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50500.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G))), M:tm-490, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50501
in-theory        50501
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-480 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50501.        ((A or (B -> (C -> B))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-480, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50502
in-theory        50502
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (A -> C)) -> A)) -> (((B and (A -> C)) -> C) or D))
theorem-size     19
proof            (modus-ponens tm-470 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50502.        ((A or ((B and (A -> C)) -> A)) -> (((B and (A -> C)) -> C) or D)), M:tm-470, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50503
in-theory        50503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-469 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50503.        ((A -> (B -> (B or C))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-469, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50504
in-theory        50504
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-456 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50504.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (D -> (D or E))), M:tm-456, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50505
in-theory        50505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-453 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50505.        ((A -> ((B -> (B or C)) and A)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-453, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50506
in-theory        50506
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((D -> (D or E)) and ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C))))
theorem-size     41
proof            (modus-ponens tm-443 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50506.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((D -> (D or E)) and ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)))), M:tm-443, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50507
in-theory        50507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-409 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50507.        (((A -> (A or B)) or C) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-409, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50508
in-theory        50508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-400 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50508.        (((A -> (B -> (A and B))) or C) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-400, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50509
in-theory        50509
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-391 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50509.        ((((A and B) -> B) or C) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-391, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50510
in-theory        50510
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-382 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50510.        ((((A and B) -> A) or C) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-382, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50511
in-theory        50511
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-373 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50511.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G))), M:tm-373, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50512
in-theory        50512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-364 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50512.        (((A -> (B -> A)) or C) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-364, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50513
in-theory        50513
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (A -> C)) -> A)) -> (D -> (((B and (A -> C)) -> C) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50513.        ((A or ((B and (A -> C)) -> A)) -> (D -> (((B and (A -> C)) -> C) and D))), M:tm-355, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50514
in-theory        50514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-354 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50514.        ((A -> (B -> (C -> (B and C)))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-354, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50515
in-theory        50515
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-341 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50515.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50516
in-theory        50516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E)))
theorem-size     27
proof            (modus-ponens tm-338 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50516.        (((A -> B) -> (A -> (A and B))) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E))), M:tm-338, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50517
in-theory        50517
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((A or ((B and (A -> C)) -> A)) -> ((A or ((B and (A -> C)) -> A)) and ((B and (A -> C)) -> C))))
theorem-size     45
proof            (modus-ponens tm-328 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50517.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((A or ((B and (A -> C)) -> A)) -> ((A or ((B and (A -> C)) -> A)) and ((B and (A -> C)) -> C)))), M:tm-328, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50518
in-theory        50518
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((D -> (E -> (D and E))) and ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C))))
theorem-size     43
proof            (modus-ponens tm-327 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50518.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((D -> (E -> (D and E))) and ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)))), M:tm-327, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50519
in-theory        50519
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (((D and E) -> E) and ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C))))
theorem-size     41
proof            (modus-ponens tm-326 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50519.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (((D and E) -> E) and ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)))), M:tm-326, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50520
in-theory        50520
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (((D and E) -> D) and ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C))))
theorem-size     41
proof            (modus-ponens tm-325 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-4)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50520.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (((D and E) -> D) and ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)))), M:tm-325, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50521
in-theory        50521
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C))))
theorem-size     49
proof            (modus-ponens tm-324 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50521.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)))), M:tm-324, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50522
in-theory        50522
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((D -> (E -> D)) and ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C))))
theorem-size     41
proof            (modus-ponens tm-323 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50522.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((D -> (E -> D)) and ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)))), M:tm-323, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50523
in-theory        50523
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-322 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50523.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50524
in-theory        50524
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-320 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50524.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50525
in-theory        50525
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-318 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50525.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50526
in-theory        50526
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((A or ((B and (A -> C)) -> A)) -> (A or ((B and (A -> C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-316 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50526.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((A or ((B and (A -> C)) -> A)) -> (A or ((B and (A -> C)) -> A)))), M:tm-316, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50527
in-theory        50527
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-315 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50527.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50528
in-theory        50528
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (((A or ((B and (A -> C)) -> A)) -> (not ((B and (A -> C)) -> C))) -> (not (A or ((B and (A -> C)) -> A)))))
theorem-size     47
proof            (modus-ponens tm-313 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50528.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (((A or ((B and (A -> C)) -> A)) -> (not ((B and (A -> C)) -> C))) -> (not (A or ((B and (A -> C)) -> A))))), M:tm-313, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50529
in-theory        50529
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((((B and (A -> C)) -> C) -> D) -> (((A or ((B and (A -> C)) -> A)) or ((B and (A -> C)) -> C)) -> D)))
theorem-size     47
proof            (modus-ponens tm-312 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50529.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((((B and (A -> C)) -> C) -> D) -> (((A or ((B and (A -> C)) -> A)) or ((B and (A -> C)) -> C)) -> D))), M:tm-312, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50530
in-theory        50530
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (D or ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-311 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50530.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (D or ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)))), M:tm-311, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50531
in-theory        50531
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) or D))
theorem-size     37
proof            (modus-ponens tm-310 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50531.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) or D)), M:tm-310, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50532
in-theory        50532
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (D -> (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and D)))
theorem-size     39
proof            (modus-ponens tm-309 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50532.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (D -> (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and D))), M:tm-309, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50533
in-theory        50533
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (((A or ((B and (A -> C)) -> A)) -> (B and (A -> C))) -> ((A or ((B and (A -> C)) -> A)) -> C)))
theorem-size     45
proof            (modus-ponens tm-306 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (and Bm (-> Am Cm))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50533.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (((A or ((B and (A -> C)) -> A)) -> (B and (A -> C))) -> ((A or ((B and (A -> C)) -> A)) -> C))), M:tm-306, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (and Bm (-> Am Cm))) (C Cm))
================================================================
tm-name          tm-50534
in-theory        50534
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (D -> ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C))))
theorem-size     37
proof            (modus-ponens tm-305 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50534.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and (D -> ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)))), M:tm-305, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50535
in-theory        50535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-303 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50535.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-303, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50536
in-theory        50536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-270 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50536.        ((A -> (((B and C) -> C) and A)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-270, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50537
in-theory        50537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-239 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50537.        ((A -> (((B and C) -> B) and A)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-239, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50538
in-theory        50538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G)))
theorem-size     35
proof            (modus-ponens tm-210 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50538.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G))), M:tm-210, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50539
in-theory        50539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-183 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50539.        ((A -> ((B -> (C -> B)) and A)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-183, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50540
in-theory        50540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-157 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50540.        ((A -> ((B and C) -> C)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-157, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50541
in-theory        50541
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-147 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50541.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-147, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50542
in-theory        50542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-134 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50542.        ((A -> ((B and C) -> B)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-134, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50543
in-theory        50543
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-125 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50543.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-125, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50544
in-theory        50544
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (A -> (C -> D))) -> A)) -> (((B and (A -> (C -> D))) -> C) -> ((B and (A -> (C -> D))) -> D)))
theorem-size     31
proof            (modus-ponens tm-114 tm-638 ((A (or Am (-> (and Bm (-> Am (-> C D))) Am))) (B (and Bm (-> Am (-> C D)))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50544.        ((A or ((B and (A -> (C -> D))) -> A)) -> (((B and (A -> (C -> D))) -> C) -> ((B and (A -> (C -> D))) -> D))), M:tm-114, m:tm-638, u:((A (or Am (-> (and Bm (-> Am (-> C D))) Am))) (B (and Bm (-> Am (-> C D)))) (Cm (-> C D)))
================================================================
tm-name          tm-50545
in-theory        50545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-113 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50545.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G))), M:tm-113, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50546
in-theory        50546
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     37
proof            (modus-ponens tm-105 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50546.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-105, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50547
in-theory        50547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E)))
theorem-size     25
proof            (modus-ponens tm-95 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50547.        (((A -> B) -> (A -> A)) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E))), M:tm-95, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50548
in-theory        50548
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (A -> C)) -> A)) -> (D -> ((B and (A -> C)) -> C)))
theorem-size     19
proof            (modus-ponens tm-84 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50548.        ((A or ((B and (A -> C)) -> A)) -> (D -> ((B and (A -> C)) -> C))), M:tm-84, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50549
in-theory        50549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-83 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50549.        ((A -> (B -> (C -> B))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-83, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50550
in-theory        50550
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or ((C and (B -> D)) -> B)) -> ((C and (B -> D)) -> D)))
theorem-size     23
proof            (modus-ponens tm-76 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-2 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50550.        (((not (not A)) -> A) and ((B or ((C and (B -> D)) -> B)) -> ((C and (B -> D)) -> D))), M:tm-76, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50551
in-theory        50551
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or ((B and (A -> C)) -> A)))) or (A or ((B and (A -> C)) -> A))) -> ((B and (A -> C)) -> C))
theorem-size     29
proof            (modus-ponens tm-73 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-8 tm-10 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50551.        (((not (not (A or ((B and (A -> C)) -> A)))) or (A or ((B and (A -> C)) -> A))) -> ((B and (A -> C)) -> C)), M:tm-73, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50552
in-theory        50552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E)))
theorem-size     29
proof            (modus-ponens tm-69 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50552.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E))), M:tm-69, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50553
in-theory        50553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-54 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50553.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-54, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50554
in-theory        50554
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or (B or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C))
theorem-size     25
proof            (modus-ponens tm-50 tm-638 ((A Am) (B (-> (and Bm (-> Am Cm)) Am)) (C (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-8 tm-7 tm-1 tm-2 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50554.        ((((A and (B -> C)) -> B) or (B or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C)), M:tm-50, m:tm-638, u:((A Am) (B (-> (and Bm (-> Am Cm)) Am)) (C (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50555
in-theory        50555
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or ((B and (A -> C)) -> A))) -> ((B and (A -> C)) -> C))
theorem-size     19
proof            (modus-ponens tm-49 tm-638 ((A Am) (B (-> (and Bm (-> Am Cm)) Am)) (C (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-8 tm-6 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50555.        ((A or (A or ((B and (A -> C)) -> A))) -> ((B and (A -> C)) -> C)), M:tm-49, m:tm-638, u:((A Am) (B (-> (and Bm (-> Am Cm)) Am)) (C (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50556
in-theory        50556
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or ((C and (B -> D)) -> B))) or (B or ((C and (B -> D)) -> B))) -> ((C and (B -> D)) -> D))
theorem-size     29
proof            (modus-ponens tm-47 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50556.        (((A and (B or ((C and (B -> D)) -> B))) or (B or ((C and (B -> D)) -> B))) -> ((C and (B -> D)) -> D)), M:tm-47, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50557
in-theory        50557
times-derived    1
----------------------------------------------------------------
theorem          ((((A or ((B and (A -> C)) -> A)) and D) or (A or ((B and (A -> C)) -> A))) -> ((B and (A -> C)) -> C))
theorem-size     29
proof            (modus-ponens tm-46 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-8 tm-3 tm-1 tm-2 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50557.        ((((A or ((B and (A -> C)) -> A)) and D) or (A or ((B and (A -> C)) -> A))) -> ((B and (A -> C)) -> C)), M:tm-46, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50558
in-theory        50558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-42 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50558.        ((A -> (B or A)) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E))), M:tm-42, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50559
in-theory        50559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-32 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50559.        ((A -> (A or B)) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E))), M:tm-32, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50560
in-theory        50560
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (A -> C)) -> A)) -> ((A or ((B and (A -> C)) -> A)) and ((B and (A -> C)) -> C)))
theorem-size     27
proof            (modus-ponens tm-24 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50560.        ((A or ((B and (A -> C)) -> A)) -> ((A or ((B and (A -> C)) -> A)) and ((B and (A -> C)) -> C))), M:tm-24, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50561
in-theory        50561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E)))
theorem-size     25
proof            (modus-ponens tm-23 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50561.        ((A -> (B -> (A and B))) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E))), M:tm-23, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50562
in-theory        50562
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-22 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50562.        (((A and B) -> B) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E))), M:tm-22, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50563
in-theory        50563
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-21 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50563.        (((A and B) -> A) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E))), M:tm-21, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50564
in-theory        50564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-20 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50564.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-20, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50565
in-theory        50565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E)))
theorem-size     23
proof            (modus-ponens tm-19 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50565.        ((A -> (B -> A)) and ((C or ((D and (C -> E)) -> C)) -> ((D and (C -> E)) -> E))), M:tm-19, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50566
in-theory        50566
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and (A -> C)) -> A)) -> (A or ((B and (A -> C)) -> A)))
theorem-size     19
proof            (modus-ponens tm-12 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50566.        ((A or ((B and (A -> C)) -> A)) -> (A or ((B and (A -> C)) -> A))), M:tm-12, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50567
in-theory        50567
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> (not ((B and (A -> C)) -> C))) -> (not (A or ((B and (A -> C)) -> A))))
theorem-size     29
proof            (modus-ponens tm-9 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-9 tm-8 tm-1 tm-2 tm-4)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50567.        (((A or ((B and (A -> C)) -> A)) -> (not ((B and (A -> C)) -> C))) -> (not (A or ((B and (A -> C)) -> A)))), M:tm-9, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50568
in-theory        50568
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> D) -> (((B or ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> C)) -> D))
theorem-size     29
proof            (modus-ponens tm-8 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50568.        ((((A and (B -> C)) -> C) -> D) -> (((B or ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-50569
in-theory        50569
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or ((C and (B -> D)) -> B)) -> ((C and (B -> D)) -> D)))
theorem-size     19
proof            (modus-ponens tm-7 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-7 tm-8 tm-1 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50569.        (A or ((B or ((C and (B -> D)) -> B)) -> ((C and (B -> D)) -> D))), M:tm-7, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50570
in-theory        50570
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) or D)
theorem-size     19
proof            (modus-ponens tm-6 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-6 tm-8 tm-1 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50570.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) or D), M:tm-6, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50571
in-theory        50571
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or ((C and (B -> D)) -> B)) -> ((C and (B -> D)) -> D)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50571.        (A -> (((B or ((C and (B -> D)) -> B)) -> ((C and (B -> D)) -> D)) and A)), M:tm-5, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50572
in-theory        50572
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> (B and (A -> C))) -> ((A or ((B and (A -> C)) -> A)) -> C))
theorem-size     27
proof            (modus-ponens tm-2 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (and Bm (-> Am Cm))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-1 tm-4)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50572.        (((A or ((B and (A -> C)) -> A)) -> (B and (A -> C))) -> ((A or ((B and (A -> C)) -> A)) -> C)), M:tm-2, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (and Bm (-> Am Cm))) (C Cm))
================================================================
tm-name          tm-50573
in-theory        50573
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or ((C and (B -> D)) -> B)) -> ((C and (B -> D)) -> D)))
theorem-size     19
proof            (modus-ponens tm-1 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-1 tm-8 tm-2 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-50573.        (A -> ((B or ((C and (B -> D)) -> B)) -> ((C and (B -> D)) -> D))), M:tm-1, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-50574
in-theory        50574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-622 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50574.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-622, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50575
in-theory        50575
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50575.        (((A or (B -> A)) -> ((C and D) -> D)) and (E -> (F or E))), M:tm-609, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50576
in-theory        50576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-605 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50576.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-605, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50577
in-theory        50577
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and ((E -> (F or E)) and ((A or (B -> A)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-595 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50577.        (((A or (B -> A)) -> ((C and D) -> D)) and ((E -> (F or E)) and ((A or (B -> A)) -> ((C and D) -> D)))), M:tm-595, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50578
in-theory        50578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-550 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50578.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-550, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50579
in-theory        50579
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-540 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50579.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-540, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50580
in-theory        50580
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-530 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50580.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-530, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50581
in-theory        50581
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-520 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50581.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-520, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50582
in-theory        50582
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-510 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50582.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-510, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50583
in-theory        50583
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-500 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50583.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-500, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50584
in-theory        50584
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-490 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50584.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G and H) -> H))), M:tm-490, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50585
in-theory        50585
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-480 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50585.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-480, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50586
in-theory        50586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-469 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50586.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-469, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50587
in-theory        50587
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50587.        (((A or (B -> A)) -> ((C and D) -> D)) and (E -> (E or F))), M:tm-456, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50588
in-theory        50588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-453 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50588.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-453, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50589
in-theory        50589
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and ((E -> (E or F)) and ((A or (B -> A)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-443 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50589.        (((A or (B -> A)) -> ((C and D) -> D)) and ((E -> (E or F)) and ((A or (B -> A)) -> ((C and D) -> D)))), M:tm-443, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50590
in-theory        50590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-409 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50590.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-409, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50591
in-theory        50591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-400 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50591.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-400, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50592
in-theory        50592
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-391 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50592.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-391, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50593
in-theory        50593
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-382 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50593.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-382, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50594
in-theory        50594
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-373 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50594.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((G and H) -> H))), M:tm-373, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50595
in-theory        50595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-364 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50595.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-364, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50596
in-theory        50596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-354 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50596.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-354, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50597
in-theory        50597
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50597.        (((A or (B -> A)) -> ((C and D) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50598
in-theory        50598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-338 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50598.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((E and F) -> F))), M:tm-338, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50599
in-theory        50599
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and ((A or (B -> A)) -> ((A or (B -> A)) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-328 tm-639 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50599.        (((A or (B -> A)) -> ((C and D) -> D)) and ((A or (B -> A)) -> ((A or (B -> A)) and ((C and D) -> D)))), M:tm-328, m:tm-639, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-50600
in-theory        50600
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> ((C and D) -> D))))
theorem-size     31
proof            (modus-ponens tm-327 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50600.        (((A or (B -> A)) -> ((C and D) -> D)) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> ((C and D) -> D)))), M:tm-327, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50601
in-theory        50601
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (((E and F) -> F) and ((A or (B -> A)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-326 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50601.        (((A or (B -> A)) -> ((C and D) -> D)) and (((E and F) -> F) and ((A or (B -> A)) -> ((C and D) -> D)))), M:tm-326, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50602
in-theory        50602
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (((E and F) -> E) and ((A or (B -> A)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-325 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50602.        (((A or (B -> A)) -> ((C and D) -> D)) and (((E and F) -> E) and ((A or (B -> A)) -> ((C and D) -> D)))), M:tm-325, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50603
in-theory        50603
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> ((C and D) -> D))))
theorem-size     37
proof            (modus-ponens tm-324 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50603.        (((A or (B -> A)) -> ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> ((C and D) -> D)))), M:tm-324, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50604
in-theory        50604
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and ((E -> (F -> E)) and ((A or (B -> A)) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-323 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50604.        (((A or (B -> A)) -> ((C and D) -> D)) and ((E -> (F -> E)) and ((A or (B -> A)) -> ((C and D) -> D)))), M:tm-323, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50605
in-theory        50605
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50605.        (((A or (B -> A)) -> ((C and D) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50606
in-theory        50606
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50606.        (((A or (B -> A)) -> ((C and D) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50607
in-theory        50607
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50607.        (((A or (B -> A)) -> ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50608
in-theory        50608
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-639 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50608.        (((A or (B -> A)) -> ((C and D) -> D)) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-639, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-50609
in-theory        50609
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50609.        (((A or (B -> A)) -> ((C and D) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50610
in-theory        50610
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (((A or (B -> A)) -> (not ((C and D) -> D))) -> (not (A or (B -> A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-639 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50610.        (((A or (B -> A)) -> ((C and D) -> D)) and (((A or (B -> A)) -> (not ((C and D) -> D))) -> (not (A or (B -> A))))), M:tm-313, m:tm-639, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-50611
in-theory        50611
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and ((((C and D) -> D) -> E) -> (((A or (B -> A)) or ((C and D) -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-639 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50611.        (((A or (B -> A)) -> ((C and D) -> D)) and ((((C and D) -> D) -> E) -> (((A or (B -> A)) or ((C and D) -> D)) -> E))), M:tm-312, m:tm-639, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-50612
in-theory        50612
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (E or ((A or (B -> A)) -> ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-311 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50612.        (((A or (B -> A)) -> ((C and D) -> D)) and (E or ((A or (B -> A)) -> ((C and D) -> D)))), M:tm-311, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50613
in-theory        50613
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (((A or (B -> A)) -> ((C and D) -> D)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50613.        (((A or (B -> A)) -> ((C and D) -> D)) and (((A or (B -> A)) -> ((C and D) -> D)) or E)), M:tm-310, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50614
in-theory        50614
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (E -> (((A or (B -> A)) -> ((C and D) -> D)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50614.        (((A or (B -> A)) -> ((C and D) -> D)) and (E -> (((A or (B -> A)) -> ((C and D) -> D)) and E))), M:tm-309, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50615
in-theory        50615
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (((A or (B -> A)) -> (C and D)) -> ((A or (B -> A)) -> D)))
theorem-size     29
proof            (modus-ponens tm-306 tm-639 ((A (or Am (-> Bm Am))) (B (and Cm Dm)) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50615.        (((A or (B -> A)) -> ((C and D) -> D)) and (((A or (B -> A)) -> (C and D)) -> ((A or (B -> A)) -> D))), M:tm-306, m:tm-639, u:((A (or Am (-> Bm Am))) (B (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-50616
in-theory        50616
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and (E -> ((A or (B -> A)) -> ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-305 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50616.        (((A or (B -> A)) -> ((C and D) -> D)) and (E -> ((A or (B -> A)) -> ((C and D) -> D)))), M:tm-305, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50617
in-theory        50617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-303 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50617.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-303, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50618
in-theory        50618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-270 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50618.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-270, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50619
in-theory        50619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-239 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50619.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-239, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50620
in-theory        50620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-210 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50620.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((G and H) -> H))), M:tm-210, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50621
in-theory        50621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-183 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50621.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-183, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50622
in-theory        50622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-157 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50622.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-157, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50623
in-theory        50623
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-147 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50623.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-147, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50624
in-theory        50624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-134 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50624.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-134, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50625
in-theory        50625
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-125 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50625.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-125, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50626
in-theory        50626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-113 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50626.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G and H) -> H))), M:tm-113, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50627
in-theory        50627
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-105 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50627.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-105, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50628
in-theory        50628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-95 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50628.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((E and F) -> F))), M:tm-95, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50629
in-theory        50629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-83 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50629.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-83, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50630
in-theory        50630
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> ((D and E) -> E)))
theorem-size     17
proof            (modus-ponens tm-76 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50630.        (((not (not A)) -> A) and ((B or (C -> B)) -> ((D and E) -> E))), M:tm-76, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50631
in-theory        50631
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((C and D) -> D))
theorem-size     19
proof            (modus-ponens tm-73 tm-639 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-10 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50631.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((C and D) -> D)), M:tm-73, m:tm-639, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-50632
in-theory        50632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-69 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50632.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((E and F) -> F))), M:tm-69, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50633
in-theory        50633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-54 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50633.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-54, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50634
in-theory        50634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-50 tm-639 ((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-7 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50634.        (((A -> B) or (B or (A -> B))) -> ((C and D) -> D)), M:tm-50, m:tm-639, u:((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-50635
in-theory        50635
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-49 tm-639 ((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-6 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50635.        ((A or (A or (B -> A))) -> ((C and D) -> D)), M:tm-49, m:tm-639, u:((A Am) (B (-> Bm Am)) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-50636
in-theory        50636
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-47 tm-639 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50636.        (((A and (B or (C -> B))) or (B or (C -> B))) -> ((D and E) -> E)), M:tm-47, m:tm-639, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-50637
in-theory        50637
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-46 tm-639 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50637.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((D and E) -> E)), M:tm-46, m:tm-639, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-50638
in-theory        50638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-42 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50638.        ((A -> (B or A)) and ((C or (D -> C)) -> ((E and F) -> F))), M:tm-42, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50639
in-theory        50639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-32 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50639.        ((A -> (A or B)) and ((C or (D -> C)) -> ((E and F) -> F))), M:tm-32, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50640
in-theory        50640
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and ((C and D) -> D)))
theorem-size     17
proof            (modus-ponens tm-24 tm-639 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50640.        ((A or (B -> A)) -> ((A or (B -> A)) and ((C and D) -> D))), M:tm-24, m:tm-639, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-50641
in-theory        50641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-23 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50641.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((E and F) -> F))), M:tm-23, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50642
in-theory        50642
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-22 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50642.        (((A and B) -> B) and ((C or (D -> C)) -> ((E and F) -> F))), M:tm-22, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50643
in-theory        50643
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-21 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50643.        (((A and B) -> A) and ((C or (D -> C)) -> ((E and F) -> F))), M:tm-21, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50644
in-theory        50644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-20 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50644.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-20, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50645
in-theory        50645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-19 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50645.        ((A -> (B -> A)) and ((C or (D -> C)) -> ((E and F) -> F))), M:tm-19, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50646
in-theory        50646
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not ((C and D) -> D))) -> (not (A or (B -> A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-639 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-9 tm-8 tm-1 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50646.        (((A or (B -> A)) -> (not ((C and D) -> D))) -> (not (A or (B -> A)))), M:tm-9, m:tm-639, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-50647
in-theory        50647
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> (((D or (E -> D)) or ((A and B) -> B)) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-639 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50647.        ((((A and B) -> B) -> C) -> (((D or (E -> D)) or ((A and B) -> B)) -> C)), M:tm-8, m:tm-639, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-50648
in-theory        50648
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-7 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-7 tm-8 tm-1 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50648.        (A or ((B or (C -> B)) -> ((D and E) -> E))), M:tm-7, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50649
in-theory        50649
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-6 tm-8 tm-1 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50649.        (((A or (B -> A)) -> ((C and D) -> D)) or E), M:tm-6, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50650
in-theory        50650
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> ((D and E) -> E)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50650.        (A -> (((B or (C -> B)) -> ((D and E) -> E)) and A)), M:tm-5, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50651
in-theory        50651
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C and D)) -> ((A or (B -> A)) -> D))
theorem-size     17
proof            (modus-ponens tm-2 tm-639 ((A (or Am (-> Bm Am))) (B (and Cm Dm)) (C Dm)))
axioms-used      (tm-2 tm-8 tm-1 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50651.        (((A or (B -> A)) -> (C and D)) -> ((A or (B -> A)) -> D)), M:tm-2, m:tm-639, u:((A (or Am (-> Bm Am))) (B (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-50652
in-theory        50652
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-1 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-1 tm-8 tm-4)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-50652.        (A -> ((B or (C -> B)) -> ((D and E) -> E))), M:tm-1, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-50653
in-theory        50653
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or ((D -> (E -> D)) and (B -> A))))
theorem-size     17
proof            (modus-ponens tm-623 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50653.        ((A or (B -> A)) -> (C or ((D -> (E -> D)) and (B -> A)))), M:tm-623, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50654
in-theory        50654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-622 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50654.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-622, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50655
in-theory        50655
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50655.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (E -> (F or E))), M:tm-609, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50656
in-theory        50656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-605 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50656.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-605, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50657
in-theory        50657
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((E -> (F or E)) and ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50657.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((E -> (F or E)) and ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))))), M:tm-595, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50658
in-theory        50658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-550 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50658.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-550, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50659
in-theory        50659
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-540 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50659.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-540, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50660
in-theory        50660
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-530 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50660.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-530, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50661
in-theory        50661
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-520 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50661.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-520, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50662
in-theory        50662
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-510 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50662.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-510, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50663
in-theory        50663
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-500 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50663.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-500, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50664
in-theory        50664
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-490 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50664.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E)))), M:tm-490, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50665
in-theory        50665
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-480 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50665.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-480, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50666
in-theory        50666
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> (D -> C)) and (B -> A)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50666.        ((A or (B -> A)) -> (((C -> (D -> C)) and (B -> A)) or E)), M:tm-470, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50667
in-theory        50667
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-469 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50667.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-469, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50668
in-theory        50668
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50668.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (E -> (E or F))), M:tm-456, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50669
in-theory        50669
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-453 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50669.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-453, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50670
in-theory        50670
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((E -> (E or F)) and ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50670.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((E -> (E or F)) and ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))))), M:tm-443, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50671
in-theory        50671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-409 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50671.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-409, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50672
in-theory        50672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-400 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50672.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-400, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50673
in-theory        50673
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-391 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50673.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-391, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50674
in-theory        50674
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-382 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50674.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-382, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50675
in-theory        50675
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-373 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50675.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E)))), M:tm-373, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50676
in-theory        50676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-364 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50676.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-364, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50677
in-theory        50677
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((D -> (E -> D)) and (B -> A)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50677.        ((A or (B -> A)) -> (C -> (((D -> (E -> D)) and (B -> A)) and C))), M:tm-355, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50678
in-theory        50678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-354 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50678.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-354, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50679
in-theory        50679
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50679.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50680
in-theory        50680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C))))
theorem-size     25
proof            (modus-ponens tm-338 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50680.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C)))), M:tm-338, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50681
in-theory        50681
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D -> C)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50681.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D -> C)) and (B -> A))))), M:tm-328, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50682
in-theory        50682
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50682.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))))), M:tm-327, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50683
in-theory        50683
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (((E and F) -> F) and ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50683.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (((E and F) -> F) and ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))))), M:tm-326, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50684
in-theory        50684
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (((E and F) -> E) and ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50684.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (((E and F) -> E) and ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))))), M:tm-325, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50685
in-theory        50685
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50685.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))))), M:tm-324, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50686
in-theory        50686
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((E -> (F -> E)) and ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50686.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((E -> (F -> E)) and ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))))), M:tm-323, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50687
in-theory        50687
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50687.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((E and F) -> F)), M:tm-322, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50688
in-theory        50688
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50688.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((E and F) -> E)), M:tm-320, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50689
in-theory        50689
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50689.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50690
in-theory        50690
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     27
proof            (modus-ponens tm-316 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50690.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50691
in-theory        50691
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50691.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (E -> (F -> E))), M:tm-315, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50692
in-theory        50692
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (((A or (B -> A)) -> (not ((C -> (D -> C)) and (B -> A)))) -> (not (A or (B -> A)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50692.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (((A or (B -> A)) -> (not ((C -> (D -> C)) and (B -> A)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50693
in-theory        50693
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((((C -> (D -> C)) and (B -> A)) -> E) -> (((A or (B -> A)) or ((C -> (D -> C)) and (B -> A))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50693.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((((C -> (D -> C)) and (B -> A)) -> E) -> (((A or (B -> A)) or ((C -> (D -> C)) and (B -> A))) -> E))), M:tm-312, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50694
in-theory        50694
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (E or ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50694.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (E or ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))))), M:tm-311, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50695
in-theory        50695
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50695.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) or E)), M:tm-310, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50696
in-theory        50696
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (E -> (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50696.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (E -> (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and E))), M:tm-309, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50697
in-theory        50697
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (E -> ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50697.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and (E -> ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))))), M:tm-305, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50698
in-theory        50698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-303 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50698.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-303, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50699
in-theory        50699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-270 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50699.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-270, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50700
in-theory        50700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-239 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50700.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-239, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50701
in-theory        50701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E))))
theorem-size     33
proof            (modus-ponens tm-210 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50701.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E)))), M:tm-210, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50702
in-theory        50702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-183 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50702.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-183, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50703
in-theory        50703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-157 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50703.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-157, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50704
in-theory        50704
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-147 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50704.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-147, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50705
in-theory        50705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-134 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50705.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-134, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50706
in-theory        50706
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-125 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50706.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-125, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50707
in-theory        50707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-113 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50707.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E)))), M:tm-113, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50708
in-theory        50708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     35
proof            (modus-ponens tm-105 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50708.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-105, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50709
in-theory        50709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-95 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50709.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C)))), M:tm-95, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50710
in-theory        50710
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D -> (E -> D)) and (B -> A))))
theorem-size     17
proof            (modus-ponens tm-84 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50710.        ((A or (B -> A)) -> (C -> ((D -> (E -> D)) and (B -> A)))), M:tm-84, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50711
in-theory        50711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-83 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50711.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-83, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50712
in-theory        50712
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> ((D -> (E -> D)) and (C -> B))))
theorem-size     21
proof            (modus-ponens tm-76 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50712.        (((not (not A)) -> A) and ((B or (C -> B)) -> ((D -> (E -> D)) and (C -> B)))), M:tm-76, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50713
in-theory        50713
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((C -> (D -> C)) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-73 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50713.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((C -> (D -> C)) and (B -> A))), M:tm-73, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50714
in-theory        50714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C))))
theorem-size     27
proof            (modus-ponens tm-69 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50714.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C)))), M:tm-69, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50715
in-theory        50715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-54 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50715.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-54, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50716
in-theory        50716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> ((C -> (D -> C)) and (A -> B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-640 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50716.        (((A -> B) or (B or (A -> B))) -> ((C -> (D -> C)) and (A -> B))), M:tm-50, m:tm-640, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50717
in-theory        50717
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> ((C -> (D -> C)) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-49 tm-640 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50717.        ((A or (A or (B -> A))) -> ((C -> (D -> C)) and (B -> A))), M:tm-49, m:tm-640, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50718
in-theory        50718
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> ((D -> (E -> D)) and (C -> B)))
theorem-size     23
proof            (modus-ponens tm-47 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50718.        (((A and (B or (C -> B))) or (B or (C -> B))) -> ((D -> (E -> D)) and (C -> B))), M:tm-47, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50719
in-theory        50719
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((D -> (E -> D)) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-46 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50719.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((D -> (E -> D)) and (B -> A))), M:tm-46, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50720
in-theory        50720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-42 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50720.        ((A -> (B or A)) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C)))), M:tm-42, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50721
in-theory        50721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-32 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50721.        ((A -> (A or B)) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C)))), M:tm-32, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50722
in-theory        50722
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D -> C)) and (B -> A))))
theorem-size     21
proof            (modus-ponens tm-24 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50722.        ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D -> C)) and (B -> A)))), M:tm-24, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50723
in-theory        50723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-23 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50723.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C)))), M:tm-23, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50724
in-theory        50724
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-22 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50724.        (((A and B) -> B) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C)))), M:tm-22, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50725
in-theory        50725
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-21 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50725.        (((A and B) -> A) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C)))), M:tm-21, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50726
in-theory        50726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-20 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50726.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-20, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50727
in-theory        50727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-19 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50727.        ((A -> (B -> A)) and ((C or (D -> C)) -> ((E -> (F -> E)) and (D -> C)))), M:tm-19, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50728
in-theory        50728
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not ((C -> (D -> C)) and (B -> A)))) -> (not (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-9 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-9 tm-8 tm-1 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50728.        (((A or (B -> A)) -> (not ((C -> (D -> C)) and (B -> A)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50729
in-theory        50729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and (C -> D)) -> E) -> (((D or (C -> D)) or ((A -> (B -> A)) and (C -> D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50729.        ((((A -> (B -> A)) and (C -> D)) -> E) -> (((D or (C -> D)) or ((A -> (B -> A)) and (C -> D))) -> E)), M:tm-8, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-50730
in-theory        50730
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> ((D -> (E -> D)) and (C -> B))))
theorem-size     17
proof            (modus-ponens tm-7 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-7 tm-8 tm-1 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50730.        (A or ((B or (C -> B)) -> ((D -> (E -> D)) and (C -> B)))), M:tm-7, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50731
in-theory        50731
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-6 tm-8 tm-1 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50731.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) or E), M:tm-6, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50732
in-theory        50732
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> ((D -> (E -> D)) and (C -> B))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50732.        (A -> (((B or (C -> B)) -> ((D -> (E -> D)) and (C -> B))) and A)), M:tm-5, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50733
in-theory        50733
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> ((D -> (E -> D)) and (C -> B))))
theorem-size     17
proof            (modus-ponens tm-1 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-50733.        (A -> ((B or (C -> B)) -> ((D -> (E -> D)) and (C -> B)))), M:tm-1, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-50734
in-theory        50734
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> A))))
theorem-size     25
proof            (modus-ponens tm-623 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50734.        ((A or (B -> A)) -> (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> A)))), M:tm-623, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50735
in-theory        50735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-622 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50735.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-622, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50736
in-theory        50736
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (F -> (G or F)))
theorem-size     29
proof            (modus-ponens tm-609 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50736.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (F -> (G or F))), M:tm-609, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50737
in-theory        50737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-605 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50737.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-605, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50738
in-theory        50738
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((F -> (G or F)) and ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50738.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((F -> (G or F)) and ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))), M:tm-595, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50739
in-theory        50739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-550 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50739.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-550, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50740
in-theory        50740
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-540 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50740.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-540, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50741
in-theory        50741
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-530 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50741.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-530, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50742
in-theory        50742
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-520 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50742.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-520, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50743
in-theory        50743
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-510 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50743.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-510, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50744
in-theory        50744
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-500 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50744.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-500, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50745
in-theory        50745
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E))))
theorem-size     39
proof            (modus-ponens tm-490 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50745.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E)))), M:tm-490, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50746
in-theory        50746
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-480 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50746.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-480, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50747
in-theory        50747
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)) or F))
theorem-size     25
proof            (modus-ponens tm-470 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50747.        ((A or (B -> A)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)) or F)), M:tm-470, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50748
in-theory        50748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-469 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50748.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-469, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50749
in-theory        50749
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (F -> (F or G)))
theorem-size     29
proof            (modus-ponens tm-456 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50749.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (F -> (F or G))), M:tm-456, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50750
in-theory        50750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-453 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50750.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-453, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50751
in-theory        50751
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((F -> (F or G)) and ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50751.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((F -> (F or G)) and ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))), M:tm-443, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50752
in-theory        50752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-409 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50752.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-409, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50753
in-theory        50753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-400 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50753.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-400, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50754
in-theory        50754
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-391 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50754.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-391, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50755
in-theory        50755
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-382 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50755.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-382, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50756
in-theory        50756
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E))))
theorem-size     39
proof            (modus-ponens tm-373 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50756.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E)))), M:tm-373, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50757
in-theory        50757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-364 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50757.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-364, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50758
in-theory        50758
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> A)) and C)))
theorem-size     27
proof            (modus-ponens tm-355 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50758.        ((A or (B -> A)) -> (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> A)) and C))), M:tm-355, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50759
in-theory        50759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-354 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50759.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-354, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50760
in-theory        50760
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (F -> (G -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-341 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50760.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50761
in-theory        50761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C))))
theorem-size     33
proof            (modus-ponens tm-338 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50761.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C)))), M:tm-338, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50762
in-theory        50762
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))))
theorem-size     53
proof            (modus-ponens tm-328 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50762.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))), M:tm-328, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50763
in-theory        50763
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((F -> (G -> (F and G))) and ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50763.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((F -> (G -> (F and G))) and ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))), M:tm-327, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50764
in-theory        50764
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((F and G) -> G) and ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50764.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((F and G) -> G) and ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))), M:tm-326, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50765
in-theory        50765
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((F and G) -> F) and ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50765.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((F and G) -> F) and ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))), M:tm-325, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50766
in-theory        50766
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       237
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50766.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))), M:tm-324, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50767
in-theory        50767
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((F -> (G -> F)) and ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50767.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((F -> (G -> F)) and ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))), M:tm-323, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50768
in-theory        50768
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((F and G) -> G))
theorem-size     29
proof            (modus-ponens tm-322 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50768.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((F and G) -> G)), M:tm-322, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50769
in-theory        50769
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((F and G) -> F))
theorem-size     29
proof            (modus-ponens tm-320 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50769.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((F and G) -> F)), M:tm-320, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50770
in-theory        50770
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-318 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50770.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50771
in-theory        50771
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     35
proof            (modus-ponens tm-316 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50771.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50772
in-theory        50772
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (F -> (G -> F)))
theorem-size     29
proof            (modus-ponens tm-315 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50772.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (F -> (G -> F))), M:tm-315, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50773
in-theory        50773
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((A or (B -> A)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))) -> (not (A or (B -> A)))))
theorem-size     55
proof            (modus-ponens tm-313 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50773.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((A or (B -> A)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50774
in-theory        50774
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)) -> F) -> (((A or (B -> A)) or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) -> F)))
theorem-size     69
proof            (modus-ponens tm-312 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50774.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)) -> F) -> (((A or (B -> A)) or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) -> F))), M:tm-312, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50775
in-theory        50775
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (F or ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50775.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (F or ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))), M:tm-311, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50776
in-theory        50776
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) or F))
theorem-size     49
proof            (modus-ponens tm-310 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50776.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) or F)), M:tm-310, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50777
in-theory        50777
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (F -> (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and F)))
theorem-size     51
proof            (modus-ponens tm-309 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50777.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (F -> (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and F))), M:tm-309, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50778
in-theory        50778
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (F -> ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50778.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and (F -> ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))), M:tm-305, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50779
in-theory        50779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     35
proof            (modus-ponens tm-303 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50779.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-303, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50780
in-theory        50780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-270 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50780.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-270, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50781
in-theory        50781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-239 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50781.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-239, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50782
in-theory        50782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E))))
theorem-size     41
proof            (modus-ponens tm-210 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50782.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E)))), M:tm-210, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50783
in-theory        50783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-183 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50783.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-183, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50784
in-theory        50784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-157 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50784.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-157, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50785
in-theory        50785
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     39
proof            (modus-ponens tm-147 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50785.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-147, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50786
in-theory        50786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-134 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50786.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-134, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50787
in-theory        50787
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     39
proof            (modus-ponens tm-125 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50787.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-125, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50788
in-theory        50788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E))))
theorem-size     39
proof            (modus-ponens tm-113 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50788.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E)))), M:tm-113, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50789
in-theory        50789
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     43
proof            (modus-ponens tm-105 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50789.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-105, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50790
in-theory        50790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C))))
theorem-size     31
proof            (modus-ponens tm-95 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50790.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C)))), M:tm-95, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50791
in-theory        50791
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> A))))
theorem-size     25
proof            (modus-ponens tm-84 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50791.        ((A or (B -> A)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> A)))), M:tm-84, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50792
in-theory        50792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-83 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50792.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-83, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50793
in-theory        50793
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> B))))
theorem-size     29
proof            (modus-ponens tm-76 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50793.        (((not (not A)) -> A) and ((B or (C -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> B)))), M:tm-76, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50794
in-theory        50794
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))
theorem-size     31
proof            (modus-ponens tm-73 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50794.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-73, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50795
in-theory        50795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C))))
theorem-size     35
proof            (modus-ponens tm-69 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50795.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C)))), M:tm-69, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50796
in-theory        50796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     37
proof            (modus-ponens tm-54 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50796.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-54, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50797
in-theory        50797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> B)))
theorem-size     27
proof            (modus-ponens tm-50 tm-641 ((A Am) (B (-> Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50797.        (((A -> B) or (B or (A -> B))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> B))), M:tm-50, m:tm-641, u:((A Am) (B (-> Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50798
in-theory        50798
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))
theorem-size     25
proof            (modus-ponens tm-49 tm-641 ((A Am) (B (-> Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50798.        ((A or (A or (B -> A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-49, m:tm-641, u:((A Am) (B (-> Bm Am)) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50799
in-theory        50799
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> B)))
theorem-size     31
proof            (modus-ponens tm-47 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50799.        (((A and (B or (C -> B))) or (B or (C -> B))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> B))), M:tm-47, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50800
in-theory        50800
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> A)))
theorem-size     31
proof            (modus-ponens tm-46 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50800.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (B -> A))), M:tm-46, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50801
in-theory        50801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C))))
theorem-size     29
proof            (modus-ponens tm-42 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50801.        ((A -> (B or A)) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C)))), M:tm-42, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50802
in-theory        50802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C))))
theorem-size     29
proof            (modus-ponens tm-32 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50802.        ((A -> (A or B)) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C)))), M:tm-32, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50803
in-theory        50803
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))
theorem-size     29
proof            (modus-ponens tm-24 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50803.        ((A or (B -> A)) -> ((A or (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))), M:tm-24, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50804
in-theory        50804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C))))
theorem-size     31
proof            (modus-ponens tm-23 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50804.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C)))), M:tm-23, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50805
in-theory        50805
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C))))
theorem-size     29
proof            (modus-ponens tm-22 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50805.        (((A and B) -> B) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C)))), M:tm-22, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50806
in-theory        50806
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C))))
theorem-size     29
proof            (modus-ponens tm-21 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50806.        (((A and B) -> A) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C)))), M:tm-21, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50807
in-theory        50807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     37
proof            (modus-ponens tm-20 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50807.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-20, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50808
in-theory        50808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C))))
theorem-size     29
proof            (modus-ponens tm-19 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50808.        ((A -> (B -> A)) and ((C or (D -> C)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (D -> C)))), M:tm-19, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50809
in-theory        50809
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))) -> (not (A or (B -> A))))
theorem-size     31
proof            (modus-ponens tm-9 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-9 tm-8 tm-1 tm-5 tm-2)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50809.        (((A or (B -> A)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50810
in-theory        50810
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> E)) -> F) -> (((E or (D -> E)) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> E))) -> F))
theorem-size     45
proof            (modus-ponens tm-8 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50810.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> E)) -> F) -> (((E or (D -> E)) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> E))) -> F)), M:tm-8, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-50811
in-theory        50811
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> B))))
theorem-size     25
proof            (modus-ponens tm-7 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-7 tm-8 tm-1 tm-5 tm-2)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50811.        (A or ((B or (C -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> B)))), M:tm-7, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50812
in-theory        50812
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) or F)
theorem-size     25
proof            (modus-ponens tm-6 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-6 tm-8 tm-1 tm-5 tm-2)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50812.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) or F), M:tm-6, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50813
in-theory        50813
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> B))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50813.        (A -> (((B or (C -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> B))) and A)), M:tm-5, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50814
in-theory        50814
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> B))))
theorem-size     25
proof            (modus-ponens tm-1 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-1 tm-8 tm-5 tm-2)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-50814.        (A -> ((B or (C -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (C -> B)))), M:tm-1, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-50815
in-theory        50815
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (((D and E) -> D) and (B -> A))))
theorem-size     17
proof            (modus-ponens tm-623 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50815.        ((A or (B -> A)) -> (C or (((D and E) -> D) and (B -> A)))), M:tm-623, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50816
in-theory        50816
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-622 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50816.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-622, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50817
in-theory        50817
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50817.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (E -> (F or E))), M:tm-609, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50818
in-theory        50818
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-605 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50818.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-605, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50819
in-theory        50819
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((E -> (F or E)) and ((A or (B -> A)) -> (((C and D) -> C) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50819.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((E -> (F or E)) and ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))))), M:tm-595, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50820
in-theory        50820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-550 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50820.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-550, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50821
in-theory        50821
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-540 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50821.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-540, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50822
in-theory        50822
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-530 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50822.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-530, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50823
in-theory        50823
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-520 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50823.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-520, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50824
in-theory        50824
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-510 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50824.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-510, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50825
in-theory        50825
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-500 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50825.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-500, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50826
in-theory        50826
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-490 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50826.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E)))), M:tm-490, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50827
in-theory        50827
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-480 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50827.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-480, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50828
in-theory        50828
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C and D) -> C) and (B -> A)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50828.        ((A or (B -> A)) -> ((((C and D) -> C) and (B -> A)) or E)), M:tm-470, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50829
in-theory        50829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-469 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50829.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-469, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50830
in-theory        50830
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50830.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (E -> (E or F))), M:tm-456, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50831
in-theory        50831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-453 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50831.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-453, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50832
in-theory        50832
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((E -> (E or F)) and ((A or (B -> A)) -> (((C and D) -> C) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50832.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((E -> (E or F)) and ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))))), M:tm-443, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50833
in-theory        50833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-409 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50833.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-409, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50834
in-theory        50834
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-400 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50834.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-400, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50835
in-theory        50835
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-391 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50835.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-391, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50836
in-theory        50836
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-382 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50836.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-382, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50837
in-theory        50837
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-373 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50837.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E)))), M:tm-373, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50838
in-theory        50838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-364 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50838.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-364, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50839
in-theory        50839
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((((D and E) -> D) and (B -> A)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50839.        ((A or (B -> A)) -> (C -> ((((D and E) -> D) and (B -> A)) and C))), M:tm-355, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50840
in-theory        50840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-354 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50840.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-354, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50841
in-theory        50841
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50841.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50842
in-theory        50842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C))))
theorem-size     25
proof            (modus-ponens tm-338 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50842.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C)))), M:tm-338, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50843
in-theory        50843
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and (((C and D) -> C) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50843.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and (((C and D) -> C) and (B -> A))))), M:tm-328, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50844
in-theory        50844
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> (((C and D) -> C) and (B -> A)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50844.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))))), M:tm-327, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50845
in-theory        50845
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((E and F) -> F) and ((A or (B -> A)) -> (((C and D) -> C) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50845.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((E and F) -> F) and ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))))), M:tm-326, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50846
in-theory        50846
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((E and F) -> E) and ((A or (B -> A)) -> (((C and D) -> C) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50846.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((E and F) -> E) and ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))))), M:tm-325, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50847
in-theory        50847
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> (((C and D) -> C) and (B -> A)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50847.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))))), M:tm-324, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50848
in-theory        50848
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((E -> (F -> E)) and ((A or (B -> A)) -> (((C and D) -> C) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50848.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((E -> (F -> E)) and ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))))), M:tm-323, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50849
in-theory        50849
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50849.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((E and F) -> F)), M:tm-322, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50850
in-theory        50850
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50850.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((E and F) -> E)), M:tm-320, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50851
in-theory        50851
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50851.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50852
in-theory        50852
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     27
proof            (modus-ponens tm-316 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50852.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50853
in-theory        50853
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50853.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (E -> (F -> E))), M:tm-315, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50854
in-theory        50854
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((A or (B -> A)) -> (not (((C and D) -> C) and (B -> A)))) -> (not (A or (B -> A)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50854.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((A or (B -> A)) -> (not (((C and D) -> C) and (B -> A)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50855
in-theory        50855
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((((C and D) -> C) and (B -> A)) -> E) -> (((A or (B -> A)) or (((C and D) -> C) and (B -> A))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50855.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((((C and D) -> C) and (B -> A)) -> E) -> (((A or (B -> A)) or (((C and D) -> C) and (B -> A))) -> E))), M:tm-312, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50856
in-theory        50856
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (E or ((A or (B -> A)) -> (((C and D) -> C) and (B -> A)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50856.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (E or ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))))), M:tm-311, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50857
in-theory        50857
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50857.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) or E)), M:tm-310, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50858
in-theory        50858
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (E -> (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50858.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (E -> (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and E))), M:tm-309, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50859
in-theory        50859
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (E -> ((A or (B -> A)) -> (((C and D) -> C) and (B -> A)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50859.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and (E -> ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))))), M:tm-305, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50860
in-theory        50860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-303 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50860.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-303, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50861
in-theory        50861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-270 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50861.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-270, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50862
in-theory        50862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-239 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50862.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-239, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50863
in-theory        50863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E))))
theorem-size     33
proof            (modus-ponens tm-210 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50863.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E)))), M:tm-210, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50864
in-theory        50864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-183 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50864.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-183, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50865
in-theory        50865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-157 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50865.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-157, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50866
in-theory        50866
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-147 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50866.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-147, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50867
in-theory        50867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-134 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50867.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-134, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50868
in-theory        50868
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-125 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50868.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-125, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50869
in-theory        50869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-113 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50869.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E)))), M:tm-113, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50870
in-theory        50870
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     35
proof            (modus-ponens tm-105 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50870.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-105, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50871
in-theory        50871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-95 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50871.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C)))), M:tm-95, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50872
in-theory        50872
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((D and E) -> D) and (B -> A))))
theorem-size     17
proof            (modus-ponens tm-84 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50872.        ((A or (B -> A)) -> (C -> (((D and E) -> D) and (B -> A)))), M:tm-84, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50873
in-theory        50873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-83 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50873.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-83, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50874
in-theory        50874
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> (((D and E) -> D) and (C -> B))))
theorem-size     21
proof            (modus-ponens tm-76 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50874.        (((not (not A)) -> A) and ((B or (C -> B)) -> (((D and E) -> D) and (C -> B)))), M:tm-76, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50875
in-theory        50875
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (((C and D) -> C) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-73 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50875.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (((C and D) -> C) and (B -> A))), M:tm-73, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50876
in-theory        50876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C))))
theorem-size     27
proof            (modus-ponens tm-69 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50876.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C)))), M:tm-69, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50877
in-theory        50877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-54 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50877.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-54, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50878
in-theory        50878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> (((C and D) -> C) and (A -> B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-642 ((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50878.        (((A -> B) or (B or (A -> B))) -> (((C and D) -> C) and (A -> B))), M:tm-50, m:tm-642, u:((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50879
in-theory        50879
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> (((C and D) -> C) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-49 tm-642 ((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50879.        ((A or (A or (B -> A))) -> (((C and D) -> C) and (B -> A))), M:tm-49, m:tm-642, u:((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50880
in-theory        50880
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> (((D and E) -> D) and (C -> B)))
theorem-size     23
proof            (modus-ponens tm-47 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50880.        (((A and (B or (C -> B))) or (B or (C -> B))) -> (((D and E) -> D) and (C -> B))), M:tm-47, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50881
in-theory        50881
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> (((D and E) -> D) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-46 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50881.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> (((D and E) -> D) and (B -> A))), M:tm-46, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50882
in-theory        50882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-42 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50882.        ((A -> (B or A)) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C)))), M:tm-42, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50883
in-theory        50883
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-32 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50883.        ((A -> (A or B)) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C)))), M:tm-32, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50884
in-theory        50884
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and (((C and D) -> C) and (B -> A))))
theorem-size     21
proof            (modus-ponens tm-24 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50884.        ((A or (B -> A)) -> ((A or (B -> A)) and (((C and D) -> C) and (B -> A)))), M:tm-24, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50885
in-theory        50885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-23 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50885.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C)))), M:tm-23, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50886
in-theory        50886
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-22 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50886.        (((A and B) -> B) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C)))), M:tm-22, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50887
in-theory        50887
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-21 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50887.        (((A and B) -> A) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C)))), M:tm-21, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50888
in-theory        50888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-20 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50888.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-20, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50889
in-theory        50889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-19 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50889.        ((A -> (B -> A)) and ((C or (D -> C)) -> (((E and F) -> E) and (D -> C)))), M:tm-19, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50890
in-theory        50890
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not (((C and D) -> C) and (B -> A)))) -> (not (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-9 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-9 tm-8 tm-1 tm-5 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50890.        (((A or (B -> A)) -> (not (((C and D) -> C) and (B -> A)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50891
in-theory        50891
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and (C -> D)) -> E) -> (((D or (C -> D)) or (((A and B) -> A) and (C -> D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50891.        (((((A and B) -> A) and (C -> D)) -> E) -> (((D or (C -> D)) or (((A and B) -> A) and (C -> D))) -> E)), M:tm-8, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-50892
in-theory        50892
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> (((D and E) -> D) and (C -> B))))
theorem-size     17
proof            (modus-ponens tm-7 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-7 tm-8 tm-1 tm-5 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50892.        (A or ((B or (C -> B)) -> (((D and E) -> D) and (C -> B)))), M:tm-7, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50893
in-theory        50893
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-6 tm-8 tm-1 tm-5 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50893.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) or E), M:tm-6, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50894
in-theory        50894
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> (((D and E) -> D) and (C -> B))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50894.        (A -> (((B or (C -> B)) -> (((D and E) -> D) and (C -> B))) and A)), M:tm-5, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50895
in-theory        50895
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (((D and E) -> D) and (C -> B))))
theorem-size     17
proof            (modus-ponens tm-1 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-1 tm-8 tm-5 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-50895.        (A -> ((B or (C -> B)) -> (((D and E) -> D) and (C -> B)))), M:tm-1, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-50896
in-theory        50896
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (((D and E) -> E) and (B -> A))))
theorem-size     17
proof            (modus-ponens tm-623 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50896.        ((A or (B -> A)) -> (C or (((D and E) -> E) and (B -> A)))), M:tm-623, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50897
in-theory        50897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-622 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50897.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-622, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50898
in-theory        50898
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50898.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (E -> (F or E))), M:tm-609, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50899
in-theory        50899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-605 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50899.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-605, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50900
in-theory        50900
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((E -> (F or E)) and ((A or (B -> A)) -> (((C and D) -> D) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50900.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((E -> (F or E)) and ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))))), M:tm-595, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50901
in-theory        50901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-550 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50901.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-550, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50902
in-theory        50902
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-540 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50902.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-540, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50903
in-theory        50903
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-530 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50903.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-530, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50904
in-theory        50904
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-520 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50904.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-520, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50905
in-theory        50905
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-510 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50905.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-510, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50906
in-theory        50906
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-500 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50906.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-500, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50907
in-theory        50907
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-490 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50907.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E)))), M:tm-490, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50908
in-theory        50908
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-480 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50908.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-480, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50909
in-theory        50909
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C and D) -> D) and (B -> A)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50909.        ((A or (B -> A)) -> ((((C and D) -> D) and (B -> A)) or E)), M:tm-470, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50910
in-theory        50910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-469 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50910.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-469, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50911
in-theory        50911
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50911.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (E -> (E or F))), M:tm-456, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50912
in-theory        50912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-453 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50912.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-453, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50913
in-theory        50913
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((E -> (E or F)) and ((A or (B -> A)) -> (((C and D) -> D) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50913.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((E -> (E or F)) and ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))))), M:tm-443, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50914
in-theory        50914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-409 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50914.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-409, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50915
in-theory        50915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-400 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50915.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-400, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50916
in-theory        50916
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-391 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50916.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-391, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50917
in-theory        50917
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-382 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50917.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-382, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50918
in-theory        50918
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-373 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50918.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E)))), M:tm-373, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50919
in-theory        50919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-364 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50919.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-364, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50920
in-theory        50920
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((((D and E) -> E) and (B -> A)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50920.        ((A or (B -> A)) -> (C -> ((((D and E) -> E) and (B -> A)) and C))), M:tm-355, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50921
in-theory        50921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-354 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50921.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-354, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50922
in-theory        50922
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50922.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50923
in-theory        50923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C))))
theorem-size     25
proof            (modus-ponens tm-338 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50923.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C)))), M:tm-338, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50924
in-theory        50924
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and (((C and D) -> D) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50924.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and (((C and D) -> D) and (B -> A))))), M:tm-328, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50925
in-theory        50925
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> (((C and D) -> D) and (B -> A)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50925.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))))), M:tm-327, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50926
in-theory        50926
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((E and F) -> F) and ((A or (B -> A)) -> (((C and D) -> D) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50926.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((E and F) -> F) and ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))))), M:tm-326, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50927
in-theory        50927
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((E and F) -> E) and ((A or (B -> A)) -> (((C and D) -> D) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50927.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((E and F) -> E) and ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))))), M:tm-325, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50928
in-theory        50928
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> (((C and D) -> D) and (B -> A)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50928.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))))), M:tm-324, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50929
in-theory        50929
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((E -> (F -> E)) and ((A or (B -> A)) -> (((C and D) -> D) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50929.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((E -> (F -> E)) and ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))))), M:tm-323, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50930
in-theory        50930
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50930.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((E and F) -> F)), M:tm-322, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50931
in-theory        50931
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50931.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((E and F) -> E)), M:tm-320, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50932
in-theory        50932
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50932.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50933
in-theory        50933
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     27
proof            (modus-ponens tm-316 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50933.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50934
in-theory        50934
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50934.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (E -> (F -> E))), M:tm-315, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50935
in-theory        50935
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((A or (B -> A)) -> (not (((C and D) -> D) and (B -> A)))) -> (not (A or (B -> A)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50935.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((A or (B -> A)) -> (not (((C and D) -> D) and (B -> A)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50936
in-theory        50936
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((((C and D) -> D) and (B -> A)) -> E) -> (((A or (B -> A)) or (((C and D) -> D) and (B -> A))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50936.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((((C and D) -> D) and (B -> A)) -> E) -> (((A or (B -> A)) or (((C and D) -> D) and (B -> A))) -> E))), M:tm-312, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50937
in-theory        50937
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (E or ((A or (B -> A)) -> (((C and D) -> D) and (B -> A)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50937.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (E or ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))))), M:tm-311, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50938
in-theory        50938
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50938.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) or E)), M:tm-310, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50939
in-theory        50939
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (E -> (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50939.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (E -> (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and E))), M:tm-309, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50940
in-theory        50940
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (E -> ((A or (B -> A)) -> (((C and D) -> D) and (B -> A)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50940.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and (E -> ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))))), M:tm-305, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50941
in-theory        50941
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-303 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50941.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-303, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50942
in-theory        50942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-270 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50942.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-270, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50943
in-theory        50943
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-239 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50943.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-239, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50944
in-theory        50944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E))))
theorem-size     33
proof            (modus-ponens tm-210 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50944.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E)))), M:tm-210, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50945
in-theory        50945
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-183 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50945.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-183, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50946
in-theory        50946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-157 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50946.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-157, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50947
in-theory        50947
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-147 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50947.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-147, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50948
in-theory        50948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-134 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50948.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-134, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50949
in-theory        50949
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-125 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50949.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-125, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50950
in-theory        50950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-113 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50950.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E)))), M:tm-113, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50951
in-theory        50951
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     35
proof            (modus-ponens tm-105 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50951.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-105, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50952
in-theory        50952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-95 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50952.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C)))), M:tm-95, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50953
in-theory        50953
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((D and E) -> E) and (B -> A))))
theorem-size     17
proof            (modus-ponens tm-84 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50953.        ((A or (B -> A)) -> (C -> (((D and E) -> E) and (B -> A)))), M:tm-84, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50954
in-theory        50954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-83 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50954.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-83, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50955
in-theory        50955
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> (((D and E) -> E) and (C -> B))))
theorem-size     21
proof            (modus-ponens tm-76 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50955.        (((not (not A)) -> A) and ((B or (C -> B)) -> (((D and E) -> E) and (C -> B)))), M:tm-76, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50956
in-theory        50956
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (((C and D) -> D) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-73 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50956.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (((C and D) -> D) and (B -> A))), M:tm-73, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50957
in-theory        50957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C))))
theorem-size     27
proof            (modus-ponens tm-69 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50957.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C)))), M:tm-69, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50958
in-theory        50958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-54 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50958.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-54, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50959
in-theory        50959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> (((C and D) -> D) and (A -> B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-643 ((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50959.        (((A -> B) or (B or (A -> B))) -> (((C and D) -> D) and (A -> B))), M:tm-50, m:tm-643, u:((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50960
in-theory        50960
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> (((C and D) -> D) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-49 tm-643 ((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50960.        ((A or (A or (B -> A))) -> (((C and D) -> D) and (B -> A))), M:tm-49, m:tm-643, u:((A Am) (B (-> Bm Am)) (C (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50961
in-theory        50961
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> (((D and E) -> E) and (C -> B)))
theorem-size     23
proof            (modus-ponens tm-47 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50961.        (((A and (B or (C -> B))) or (B or (C -> B))) -> (((D and E) -> E) and (C -> B))), M:tm-47, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50962
in-theory        50962
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> (((D and E) -> E) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-46 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50962.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> (((D and E) -> E) and (B -> A))), M:tm-46, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50963
in-theory        50963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-42 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50963.        ((A -> (B or A)) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C)))), M:tm-42, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50964
in-theory        50964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-32 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50964.        ((A -> (A or B)) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C)))), M:tm-32, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50965
in-theory        50965
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and (((C and D) -> D) and (B -> A))))
theorem-size     21
proof            (modus-ponens tm-24 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50965.        ((A or (B -> A)) -> ((A or (B -> A)) and (((C and D) -> D) and (B -> A)))), M:tm-24, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50966
in-theory        50966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-23 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50966.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C)))), M:tm-23, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50967
in-theory        50967
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-22 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50967.        (((A and B) -> B) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C)))), M:tm-22, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50968
in-theory        50968
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-21 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50968.        (((A and B) -> A) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C)))), M:tm-21, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50969
in-theory        50969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-20 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50969.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-20, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50970
in-theory        50970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-19 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50970.        ((A -> (B -> A)) and ((C or (D -> C)) -> (((E and F) -> F) and (D -> C)))), M:tm-19, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50971
in-theory        50971
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not (((C and D) -> D) and (B -> A)))) -> (not (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-9 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-9 tm-8 tm-1 tm-5 tm-4)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50971.        (((A or (B -> A)) -> (not (((C and D) -> D) and (B -> A)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50972
in-theory        50972
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and (C -> D)) -> E) -> (((D or (C -> D)) or (((A and B) -> B) and (C -> D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50972.        (((((A and B) -> B) and (C -> D)) -> E) -> (((D or (C -> D)) or (((A and B) -> B) and (C -> D))) -> E)), M:tm-8, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-50973
in-theory        50973
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> (((D and E) -> E) and (C -> B))))
theorem-size     17
proof            (modus-ponens tm-7 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-7 tm-8 tm-1 tm-5 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50973.        (A or ((B or (C -> B)) -> (((D and E) -> E) and (C -> B)))), M:tm-7, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50974
in-theory        50974
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-6 tm-8 tm-1 tm-5 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50974.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) or E), M:tm-6, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50975
in-theory        50975
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> (((D and E) -> E) and (C -> B))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50975.        (A -> (((B or (C -> B)) -> (((D and E) -> E) and (C -> B))) and A)), M:tm-5, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50976
in-theory        50976
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (((D and E) -> E) and (C -> B))))
theorem-size     17
proof            (modus-ponens tm-1 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-1 tm-8 tm-5 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-50976.        (A -> ((B or (C -> B)) -> (((D and E) -> E) and (C -> B)))), M:tm-1, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-50977
in-theory        50977
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or ((D -> (E -> (D and E))) and (B -> A))))
theorem-size     19
proof            (modus-ponens tm-623 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50977.        ((A or (B -> A)) -> (C or ((D -> (E -> (D and E))) and (B -> A)))), M:tm-623, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-50978
in-theory        50978
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-622 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50978.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-622, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50979
in-theory        50979
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50979.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (E -> (F or E))), M:tm-609, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50980
in-theory        50980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-605 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50980.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-605, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50981
in-theory        50981
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((E -> (F or E)) and ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50981.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((E -> (F or E)) and ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))))), M:tm-595, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50982
in-theory        50982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-550 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50982.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-550, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50983
in-theory        50983
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-540 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50983.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-540, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50984
in-theory        50984
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-530 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50984.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-530, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50985
in-theory        50985
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-520 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50985.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-520, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50986
in-theory        50986
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-510 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50986.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-510, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50987
in-theory        50987
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-500 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50987.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-500, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50988
in-theory        50988
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E))))
theorem-size     33
proof            (modus-ponens tm-490 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50988.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E)))), M:tm-490, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50989
in-theory        50989
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-480 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50989.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-480, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50990
in-theory        50990
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> (D -> (C and D))) and (B -> A)) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50990.        ((A or (B -> A)) -> (((C -> (D -> (C and D))) and (B -> A)) or E)), M:tm-470, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-50991
in-theory        50991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-469 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50991.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-469, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50992
in-theory        50992
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50992.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (E -> (E or F))), M:tm-456, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50993
in-theory        50993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-453 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50993.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-453, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50994
in-theory        50994
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((E -> (E or F)) and ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50994.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((E -> (E or F)) and ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))))), M:tm-443, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50995
in-theory        50995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-409 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50995.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-409, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50996
in-theory        50996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-400 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50996.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-400, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50997
in-theory        50997
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-391 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50997.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-391, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50998
in-theory        50998
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-382 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50998.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-382, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-50999
in-theory        50999
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E))))
theorem-size     33
proof            (modus-ponens tm-373 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-50999.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E)))), M:tm-373, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51000
in-theory        51000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-364 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51000.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-364, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51001
in-theory        51001
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((D -> (E -> (D and E))) and (B -> A)) and C)))
theorem-size     21
proof            (modus-ponens tm-355 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51001.        ((A or (B -> A)) -> (C -> (((D -> (E -> (D and E))) and (B -> A)) and C))), M:tm-355, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-51002
in-theory        51002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-354 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51002.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-354, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51003
in-theory        51003
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51003.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51004
in-theory        51004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C))))
theorem-size     27
proof            (modus-ponens tm-338 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51004.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C)))), M:tm-338, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51005
in-theory        51005
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D -> (C and D))) and (B -> A)))))
theorem-size     41
proof            (modus-ponens tm-328 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51005.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D -> (C and D))) and (B -> A))))), M:tm-328, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-51006
in-theory        51006
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51006.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))))), M:tm-327, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51007
in-theory        51007
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (((E and F) -> F) and ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51007.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (((E and F) -> F) and ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))))), M:tm-326, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51008
in-theory        51008
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (((E and F) -> E) and ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51008.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (((E and F) -> E) and ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))))), M:tm-325, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51009
in-theory        51009
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51009.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))))), M:tm-324, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51010
in-theory        51010
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((E -> (F -> E)) and ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51010.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((E -> (F -> E)) and ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))))), M:tm-323, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51011
in-theory        51011
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51011.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((E and F) -> F)), M:tm-322, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51012
in-theory        51012
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51012.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((E and F) -> E)), M:tm-320, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51013
in-theory        51013
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51013.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51014
in-theory        51014
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     29
proof            (modus-ponens tm-316 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51014.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-51015
in-theory        51015
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51015.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (E -> (F -> E))), M:tm-315, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51016
in-theory        51016
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (((A or (B -> A)) -> (not ((C -> (D -> (C and D))) and (B -> A)))) -> (not (A or (B -> A)))))
theorem-size     43
proof            (modus-ponens tm-313 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51016.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (((A or (B -> A)) -> (not ((C -> (D -> (C and D))) and (B -> A)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-51017
in-theory        51017
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((((C -> (D -> (C and D))) and (B -> A)) -> E) -> (((A or (B -> A)) or ((C -> (D -> (C and D))) and (B -> A))) -> E)))
theorem-size     51
proof            (modus-ponens tm-312 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51017.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((((C -> (D -> (C and D))) and (B -> A)) -> E) -> (((A or (B -> A)) or ((C -> (D -> (C and D))) and (B -> A))) -> E))), M:tm-312, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-51018
in-theory        51018
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (E or ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51018.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (E or ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))))), M:tm-311, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51019
in-theory        51019
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51019.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) or E)), M:tm-310, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51020
in-theory        51020
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (E -> (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51020.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (E -> (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and E))), M:tm-309, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51021
in-theory        51021
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (E -> ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51021.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and (E -> ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))))), M:tm-305, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51022
in-theory        51022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-303 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51022.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-303, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51023
in-theory        51023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-270 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51023.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-270, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51024
in-theory        51024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-239 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51024.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-239, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51025
in-theory        51025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E))))
theorem-size     35
proof            (modus-ponens tm-210 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51025.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E)))), M:tm-210, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51026
in-theory        51026
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-183 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51026.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-183, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51027
in-theory        51027
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-157 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51027.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-157, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51028
in-theory        51028
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-147 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51028.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-147, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51029
in-theory        51029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-134 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51029.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-134, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51030
in-theory        51030
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     33
proof            (modus-ponens tm-125 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51030.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-125, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51031
in-theory        51031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E))))
theorem-size     33
proof            (modus-ponens tm-113 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51031.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E)))), M:tm-113, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51032
in-theory        51032
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     37
proof            (modus-ponens tm-105 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51032.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-105, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51033
in-theory        51033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C))))
theorem-size     25
proof            (modus-ponens tm-95 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51033.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C)))), M:tm-95, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51034
in-theory        51034
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D -> (E -> (D and E))) and (B -> A))))
theorem-size     19
proof            (modus-ponens tm-84 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51034.        ((A or (B -> A)) -> (C -> ((D -> (E -> (D and E))) and (B -> A)))), M:tm-84, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-51035
in-theory        51035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-83 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51035.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-83, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51036
in-theory        51036
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> ((D -> (E -> (D and E))) and (C -> B))))
theorem-size     23
proof            (modus-ponens tm-76 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51036.        (((not (not A)) -> A) and ((B or (C -> B)) -> ((D -> (E -> (D and E))) and (C -> B)))), M:tm-76, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51037
in-theory        51037
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((C -> (D -> (C and D))) and (B -> A)))
theorem-size     25
proof            (modus-ponens tm-73 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51037.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-73, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-51038
in-theory        51038
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C))))
theorem-size     29
proof            (modus-ponens tm-69 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51038.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C)))), M:tm-69, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51039
in-theory        51039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-54 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51039.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-54, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51040
in-theory        51040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> ((C -> (D -> (C and D))) and (A -> B)))
theorem-size     21
proof            (modus-ponens tm-50 tm-644 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51040.        (((A -> B) or (B or (A -> B))) -> ((C -> (D -> (C and D))) and (A -> B))), M:tm-50, m:tm-644, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-51041
in-theory        51041
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> ((C -> (D -> (C and D))) and (B -> A)))
theorem-size     19
proof            (modus-ponens tm-49 tm-644 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51041.        ((A or (A or (B -> A))) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-49, m:tm-644, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-51042
in-theory        51042
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> ((D -> (E -> (D and E))) and (C -> B)))
theorem-size     25
proof            (modus-ponens tm-47 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51042.        (((A and (B or (C -> B))) or (B or (C -> B))) -> ((D -> (E -> (D and E))) and (C -> B))), M:tm-47, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-51043
in-theory        51043
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((D -> (E -> (D and E))) and (B -> A)))
theorem-size     25
proof            (modus-ponens tm-46 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51043.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((D -> (E -> (D and E))) and (B -> A))), M:tm-46, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-51044
in-theory        51044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-42 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51044.        ((A -> (B or A)) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C)))), M:tm-42, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51045
in-theory        51045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-32 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51045.        ((A -> (A or B)) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C)))), M:tm-32, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51046
in-theory        51046
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D -> (C and D))) and (B -> A))))
theorem-size     23
proof            (modus-ponens tm-24 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51046.        ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D -> (C and D))) and (B -> A)))), M:tm-24, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-51047
in-theory        51047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C))))
theorem-size     25
proof            (modus-ponens tm-23 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51047.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C)))), M:tm-23, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51048
in-theory        51048
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-22 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51048.        (((A and B) -> B) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C)))), M:tm-22, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51049
in-theory        51049
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-21 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51049.        (((A and B) -> A) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C)))), M:tm-21, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51050
in-theory        51050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-20 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51050.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-20, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51051
in-theory        51051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-19 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51051.        ((A -> (B -> A)) and ((C or (D -> C)) -> ((E -> (F -> (E and F))) and (D -> C)))), M:tm-19, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51052
in-theory        51052
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not ((C -> (D -> (C and D))) and (B -> A)))) -> (not (A or (B -> A))))
theorem-size     25
proof            (modus-ponens tm-9 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-9 tm-8 tm-1 tm-5)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51052.        (((A or (B -> A)) -> (not ((C -> (D -> (C and D))) and (B -> A)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-51053
in-theory        51053
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and (C -> D)) -> E) -> (((D or (C -> D)) or ((A -> (B -> (A and B))) and (C -> D))) -> E))
theorem-size     33
proof            (modus-ponens tm-8 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51053.        ((((A -> (B -> (A and B))) and (C -> D)) -> E) -> (((D or (C -> D)) or ((A -> (B -> (A and B))) and (C -> D))) -> E)), M:tm-8, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-51054
in-theory        51054
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> ((D -> (E -> (D and E))) and (C -> B))))
theorem-size     19
proof            (modus-ponens tm-7 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-7 tm-8 tm-1 tm-5)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51054.        (A or ((B or (C -> B)) -> ((D -> (E -> (D and E))) and (C -> B)))), M:tm-7, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51055
in-theory        51055
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-6 tm-8 tm-1 tm-5)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51055.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) or E), M:tm-6, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51056
in-theory        51056
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> ((D -> (E -> (D and E))) and (C -> B))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51056.        (A -> (((B or (C -> B)) -> ((D -> (E -> (D and E))) and (C -> B))) and A)), M:tm-5, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51057
in-theory        51057
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> ((D -> (E -> (D and E))) and (C -> B))))
theorem-size     19
proof            (modus-ponens tm-1 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-51057.        (A -> ((B or (C -> B)) -> ((D -> (E -> (D and E))) and (C -> B)))), M:tm-1, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-51058
in-theory        51058
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (B -> (B and A))))
theorem-size     13
proof            (modus-ponens tm-623 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51058.        ((A or (B -> A)) -> (C or (B -> (B and A)))), M:tm-623, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51059
in-theory        51059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-622 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51059.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-622, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51060
in-theory        51060
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-609 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51060.        (((A or (B -> A)) -> (B -> (B and A))) and (C -> (D or C))), M:tm-609, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51061
in-theory        51061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     21
proof            (modus-ponens tm-605 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51061.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-605, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51062
in-theory        51062
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and ((C -> (D or C)) and ((A or (B -> A)) -> (B -> (B and A)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51062.        (((A or (B -> A)) -> (B -> (B and A))) and ((C -> (D or C)) and ((A or (B -> A)) -> (B -> (B and A))))), M:tm-595, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51063
in-theory        51063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-550 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51063.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-550, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51064
in-theory        51064
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-540 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51064.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-540, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51065
in-theory        51065
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-530 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51065.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-530, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51066
in-theory        51066
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     21
proof            (modus-ponens tm-520 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51066.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-520, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51067
in-theory        51067
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-510 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51067.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-510, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51068
in-theory        51068
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-500 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51068.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-500, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51069
in-theory        51069
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (F -> (F and E))))
theorem-size     27
proof            (modus-ponens tm-490 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51069.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (F -> (F and E)))), M:tm-490, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51070
in-theory        51070
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-480 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51070.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-480, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51071
in-theory        51071
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> (B and A)) or C))
theorem-size     13
proof            (modus-ponens tm-470 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51071.        ((A or (B -> A)) -> ((B -> (B and A)) or C)), M:tm-470, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51072
in-theory        51072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-469 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51072.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-469, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51073
in-theory        51073
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-456 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51073.        (((A or (B -> A)) -> (B -> (B and A))) and (C -> (C or D))), M:tm-456, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51074
in-theory        51074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     21
proof            (modus-ponens tm-453 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51074.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-453, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51075
in-theory        51075
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and ((C -> (C or D)) and ((A or (B -> A)) -> (B -> (B and A)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51075.        (((A or (B -> A)) -> (B -> (B and A))) and ((C -> (C or D)) and ((A or (B -> A)) -> (B -> (B and A))))), M:tm-443, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51076
in-theory        51076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-409 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51076.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-409, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51077
in-theory        51077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     21
proof            (modus-ponens tm-400 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51077.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-400, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51078
in-theory        51078
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-391 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51078.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-391, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51079
in-theory        51079
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-382 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51079.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-382, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51080
in-theory        51080
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (F -> (F and E))))
theorem-size     27
proof            (modus-ponens tm-373 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51080.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (F -> (F and E)))), M:tm-373, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51081
in-theory        51081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-364 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51081.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-364, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51082
in-theory        51082
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((B -> (B and A)) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51082.        ((A or (B -> A)) -> (C -> ((B -> (B and A)) and C))), M:tm-355, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51083
in-theory        51083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     21
proof            (modus-ponens tm-354 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51083.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-354, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51084
in-theory        51084
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (C -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-341 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51084.        (((A or (B -> A)) -> (B -> (B and A))) and (C -> (D -> (C and D)))), M:tm-341, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51085
in-theory        51085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (D -> (D and C))))
theorem-size     21
proof            (modus-ponens tm-338 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51085.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (D -> (D and C)))), M:tm-338, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51086
in-theory        51086
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and ((A or (B -> A)) -> ((A or (B -> A)) and (B -> (B and A)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51086.        (((A or (B -> A)) -> (B -> (B and A))) and ((A or (B -> A)) -> ((A or (B -> A)) and (B -> (B and A))))), M:tm-328, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51087
in-theory        51087
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and ((C -> (D -> (C and D))) and ((A or (B -> A)) -> (B -> (B and A)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51087.        (((A or (B -> A)) -> (B -> (B and A))) and ((C -> (D -> (C and D))) and ((A or (B -> A)) -> (B -> (B and A))))), M:tm-327, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51088
in-theory        51088
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (((C and D) -> D) and ((A or (B -> A)) -> (B -> (B and A)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51088.        (((A or (B -> A)) -> (B -> (B and A))) and (((C and D) -> D) and ((A or (B -> A)) -> (B -> (B and A))))), M:tm-326, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51089
in-theory        51089
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (((C and D) -> C) and ((A or (B -> A)) -> (B -> (B and A)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51089.        (((A or (B -> A)) -> (B -> (B and A))) and (((C and D) -> C) and ((A or (B -> A)) -> (B -> (B and A))))), M:tm-325, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51090
in-theory        51090
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A or (B -> A)) -> (B -> (B and A)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51090.        (((A or (B -> A)) -> (B -> (B and A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((A or (B -> A)) -> (B -> (B and A))))), M:tm-324, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51091
in-theory        51091
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and ((C -> (D -> C)) and ((A or (B -> A)) -> (B -> (B and A)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51091.        (((A or (B -> A)) -> (B -> (B and A))) and ((C -> (D -> C)) and ((A or (B -> A)) -> (B -> (B and A))))), M:tm-323, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51092
in-theory        51092
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-322 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51092.        (((A or (B -> A)) -> (B -> (B and A))) and ((C and D) -> D)), M:tm-322, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51093
in-theory        51093
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-320 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51093.        (((A or (B -> A)) -> (B -> (B and A))) and ((C and D) -> C)), M:tm-320, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51094
in-theory        51094
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-318 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51094.        (((A or (B -> A)) -> (B -> (B and A))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51095
in-theory        51095
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51095.        (((A or (B -> A)) -> (B -> (B and A))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51096
in-theory        51096
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-315 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51096.        (((A or (B -> A)) -> (B -> (B and A))) and (C -> (D -> C))), M:tm-315, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51097
in-theory        51097
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (((A or (B -> A)) -> (not (B -> (B and A)))) -> (not (A or (B -> A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51097.        (((A or (B -> A)) -> (B -> (B and A))) and (((A or (B -> A)) -> (not (B -> (B and A)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51098
in-theory        51098
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (((B -> (B and A)) -> C) -> (((A or (B -> A)) or (B -> (B and A))) -> C)))
theorem-size     33
proof            (modus-ponens tm-312 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51098.        (((A or (B -> A)) -> (B -> (B and A))) and (((B -> (B and A)) -> C) -> (((A or (B -> A)) or (B -> (B and A))) -> C))), M:tm-312, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51099
in-theory        51099
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (C or ((A or (B -> A)) -> (B -> (B and A)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51099.        (((A or (B -> A)) -> (B -> (B and A))) and (C or ((A or (B -> A)) -> (B -> (B and A))))), M:tm-311, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51100
in-theory        51100
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (((A or (B -> A)) -> (B -> (B and A))) or C))
theorem-size     25
proof            (modus-ponens tm-310 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51100.        (((A or (B -> A)) -> (B -> (B and A))) and (((A or (B -> A)) -> (B -> (B and A))) or C)), M:tm-310, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51101
in-theory        51101
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (C -> (((A or (B -> A)) -> (B -> (B and A))) and C)))
theorem-size     27
proof            (modus-ponens tm-309 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51101.        (((A or (B -> A)) -> (B -> (B and A))) and (C -> (((A or (B -> A)) -> (B -> (B and A))) and C))), M:tm-309, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51102
in-theory        51102
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (((A or (B -> A)) -> B) -> ((A or (B -> A)) -> (B and A))))
theorem-size     29
proof            (modus-ponens tm-306 tm-645 ((A (or Am (-> Bm Am))) (B Bm) (C (and Bm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51102.        (((A or (B -> A)) -> (B -> (B and A))) and (((A or (B -> A)) -> B) -> ((A or (B -> A)) -> (B and A)))), M:tm-306, m:tm-645, u:((A (or Am (-> Bm Am))) (B Bm) (C (and Bm Am)))
================================================================
tm-name          tm-51103
in-theory        51103
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and (C -> ((A or (B -> A)) -> (B -> (B and A)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51103.        (((A or (B -> A)) -> (B -> (B and A))) and (C -> ((A or (B -> A)) -> (B -> (B and A))))), M:tm-305, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51104
in-theory        51104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     23
proof            (modus-ponens tm-303 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51104.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-303, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51105
in-theory        51105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     21
proof            (modus-ponens tm-270 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51105.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-270, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51106
in-theory        51106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     21
proof            (modus-ponens tm-239 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51106.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-239, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51107
in-theory        51107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (F -> (F and E))))
theorem-size     29
proof            (modus-ponens tm-210 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51107.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (F -> (F and E)))), M:tm-210, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51108
in-theory        51108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     21
proof            (modus-ponens tm-183 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51108.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-183, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51109
in-theory        51109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-157 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51109.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-157, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51110
in-theory        51110
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     27
proof            (modus-ponens tm-147 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51110.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-147, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51111
in-theory        51111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-134 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51111.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-134, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51112
in-theory        51112
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     27
proof            (modus-ponens tm-125 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51112.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-125, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51113
in-theory        51113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (F -> (F and E))))
theorem-size     27
proof            (modus-ponens tm-113 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51113.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (F -> (F and E)))), M:tm-113, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51114
in-theory        51114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     31
proof            (modus-ponens tm-105 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51114.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-105, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51115
in-theory        51115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (D -> (D and C))))
theorem-size     19
proof            (modus-ponens tm-95 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51115.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (D -> (D and C)))), M:tm-95, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51116
in-theory        51116
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (B -> (B and A))))
theorem-size     13
proof            (modus-ponens tm-84 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51116.        ((A or (B -> A)) -> (C -> (B -> (B and A)))), M:tm-84, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51117
in-theory        51117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     19
proof            (modus-ponens tm-83 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51117.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-83, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51118
in-theory        51118
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> (C -> (C and B))))
theorem-size     17
proof            (modus-ponens tm-76 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-2)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51118.        (((not (not A)) -> A) and ((B or (C -> B)) -> (C -> (C and B)))), M:tm-76, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51119
in-theory        51119
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (B -> (B and A)))
theorem-size     19
proof            (modus-ponens tm-73 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-8 tm-10 tm-1 tm-2 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51119.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (B -> (B and A))), M:tm-73, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51120
in-theory        51120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (D -> (D and C))))
theorem-size     23
proof            (modus-ponens tm-69 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51120.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (D -> (D and C)))), M:tm-69, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51121
in-theory        51121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     25
proof            (modus-ponens tm-54 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51121.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-54, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51122
in-theory        51122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> (A -> (A and B)))
theorem-size     15
proof            (modus-ponens tm-50 tm-645 ((A Am) (B (-> Bm Am)) (C (-> Bm (and Bm Am)))))
axioms-used      (tm-8 tm-7 tm-1 tm-2 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51122.        (((A -> B) or (B or (A -> B))) -> (A -> (A and B))), M:tm-50, m:tm-645, u:((A Am) (B (-> Bm Am)) (C (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51123
in-theory        51123
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> (B -> (B and A)))
theorem-size     13
proof            (modus-ponens tm-49 tm-645 ((A Am) (B (-> Bm Am)) (C (-> Bm (and Bm Am)))))
axioms-used      (tm-8 tm-6 tm-1 tm-2 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51123.        ((A or (A or (B -> A))) -> (B -> (B and A))), M:tm-49, m:tm-645, u:((A Am) (B (-> Bm Am)) (C (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51124
in-theory        51124
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> (C -> (C and B)))
theorem-size     19
proof            (modus-ponens tm-47 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-8 tm-4 tm-1 tm-2 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51124.        (((A and (B or (C -> B))) or (B or (C -> B))) -> (C -> (C and B))), M:tm-47, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51125
in-theory        51125
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> (B -> (B and A)))
theorem-size     19
proof            (modus-ponens tm-46 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-8 tm-3 tm-1 tm-2 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51125.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> (B -> (B and A))), M:tm-46, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51126
in-theory        51126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> (D -> (D and C))))
theorem-size     17
proof            (modus-ponens tm-42 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51126.        ((A -> (B or A)) and ((C or (D -> C)) -> (D -> (D and C)))), M:tm-42, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51127
in-theory        51127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> (D -> (D and C))))
theorem-size     17
proof            (modus-ponens tm-32 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51127.        ((A -> (A or B)) and ((C or (D -> C)) -> (D -> (D and C)))), M:tm-32, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51128
in-theory        51128
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and (B -> (B and A))))
theorem-size     17
proof            (modus-ponens tm-24 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51128.        ((A or (B -> A)) -> ((A or (B -> A)) and (B -> (B and A)))), M:tm-24, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51129
in-theory        51129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (D -> (D and C))))
theorem-size     19
proof            (modus-ponens tm-23 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51129.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (D -> (D and C)))), M:tm-23, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51130
in-theory        51130
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> (D -> (D and C))))
theorem-size     17
proof            (modus-ponens tm-22 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51130.        (((A and B) -> B) and ((C or (D -> C)) -> (D -> (D and C)))), M:tm-22, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51131
in-theory        51131
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> (D -> (D and C))))
theorem-size     17
proof            (modus-ponens tm-21 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51131.        (((A and B) -> A) and ((C or (D -> C)) -> (D -> (D and C)))), M:tm-21, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51132
in-theory        51132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     25
proof            (modus-ponens tm-20 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51132.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-20, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51133
in-theory        51133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> (D -> (D and C))))
theorem-size     17
proof            (modus-ponens tm-19 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51133.        ((A -> (B -> A)) and ((C or (D -> C)) -> (D -> (D and C)))), M:tm-19, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51134
in-theory        51134
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not (B -> (B and A)))) -> (not (A or (B -> A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-9 tm-8 tm-1 tm-2 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51134.        (((A or (B -> A)) -> (not (B -> (B and A)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51135
in-theory        51135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> C) -> (((B or (A -> B)) or (A -> (A and B))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51135.        (((A -> (A and B)) -> C) -> (((B or (A -> B)) or (A -> (A and B))) -> C)), M:tm-8, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-51136
in-theory        51136
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> (C -> (C and B))))
theorem-size     13
proof            (modus-ponens tm-7 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-7 tm-8 tm-1 tm-2 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51136.        (A or ((B or (C -> B)) -> (C -> (C and B)))), M:tm-7, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51137
in-theory        51137
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) or C)
theorem-size     13
proof            (modus-ponens tm-6 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-6 tm-8 tm-1 tm-2 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51137.        (((A or (B -> A)) -> (B -> (B and A))) or C), M:tm-6, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51138
in-theory        51138
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> (C -> (C and B))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51138.        (A -> (((B or (C -> B)) -> (C -> (C and B))) and A)), M:tm-5, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51139
in-theory        51139
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> B) -> ((A or (B -> A)) -> (B and A)))
theorem-size     17
proof            (modus-ponens tm-2 tm-645 ((A (or Am (-> Bm Am))) (B Bm) (C (and Bm Am))))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51139.        (((A or (B -> A)) -> B) -> ((A or (B -> A)) -> (B and A))), M:tm-2, m:tm-645, u:((A (or Am (-> Bm Am))) (B Bm) (C (and Bm Am)))
================================================================
tm-name          tm-51140
in-theory        51140
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (C -> (C and B))))
theorem-size     13
proof            (modus-ponens tm-1 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-1 tm-8 tm-2 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-51140.        (A -> ((B or (C -> B)) -> (C -> (C and B)))), M:tm-1, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-51141
in-theory        51141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51141.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-622, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51142
in-theory        51142
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D or (A or (B -> A))) and C)))
theorem-size     17
proof            (modus-ponens tm-617 tm-646 ((A (or Am (-> Bm Am))) (Cm (or B (or Am (-> Bm Am)))) (C (-> Dm (and (or B (or Am (-> Bm Am))) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51142.        ((A or (B -> A)) -> (C -> ((D or (A or (B -> A))) and C))), M:tm-617, m:tm-646, u:((A (or Am (-> Bm Am))) (Cm (or B (or Am (-> Bm Am)))) (C (-> Dm (and (or B (or Am (-> Bm Am))) Dm))))
================================================================
tm-name          tm-51143
in-theory        51143
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51143.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51144
in-theory        51144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51144.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-605, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51145
in-theory        51145
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A or (B -> A)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51145.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((E -> (F or E)) and ((A or (B -> A)) -> (C -> (D -> (C and D)))))), M:tm-595, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51146
in-theory        51146
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51146.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-550, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51147
in-theory        51147
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51147.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-540, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51148
in-theory        51148
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51148.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-530, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51149
in-theory        51149
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51149.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-520, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51150
in-theory        51150
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51150.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-510, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51151
in-theory        51151
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51151.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-500, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51152
in-theory        51152
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51152.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (H -> (G and H))))), M:tm-490, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51153
in-theory        51153
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51153.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-480, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51154
in-theory        51154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51154.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-469, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51155
in-theory        51155
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((A or (B -> A)) or D) and C)))
theorem-size     17
proof            (modus-ponens tm-464 tm-646 ((A (or Am (-> Bm Am))) (Cm (or (or Am (-> Bm Am)) B)) (C (-> Dm (and (or (or Am (-> Bm Am)) B) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51155.        ((A or (B -> A)) -> (C -> (((A or (B -> A)) or D) and C))), M:tm-464, m:tm-646, u:((A (or Am (-> Bm Am))) (Cm (or (or Am (-> Bm Am)) B)) (C (-> Dm (and (or (or Am (-> Bm Am)) B) Dm))))
================================================================
tm-name          tm-51156
in-theory        51156
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51156.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51157
in-theory        51157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51157.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-453, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51158
in-theory        51158
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A or (B -> A)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51158.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((E -> (E or F)) and ((A or (B -> A)) -> (C -> (D -> (C and D)))))), M:tm-443, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51159
in-theory        51159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51159.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-409, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51160
in-theory        51160
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51160.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-400, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51161
in-theory        51161
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51161.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-391, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51162
in-theory        51162
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51162.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-382, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51163
in-theory        51163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51163.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (G -> (H -> (G and H))))), M:tm-373, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51164
in-theory        51164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51164.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-364, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51165
in-theory        51165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51165.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-354, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51166
in-theory        51166
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D -> ((A or (B -> A)) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-349 tm-646 ((A (or Am (-> Bm Am))) (Cm (-> B (and (or Am (-> Bm Am)) B))) (C (-> Dm (and (-> B (and (or Am (-> Bm Am)) B)) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51166.        ((A or (B -> A)) -> (C -> ((D -> ((A or (B -> A)) and D)) and C))), M:tm-349, m:tm-646, u:((A (or Am (-> Bm Am))) (Cm (-> B (and (or Am (-> Bm Am)) B))) (C (-> Dm (and (-> B (and (or Am (-> Bm Am)) B)) Dm))))
================================================================
tm-name          tm-51167
in-theory        51167
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51167.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51168
in-theory        51168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51168.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (E -> (F -> (E and F))))), M:tm-338, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51169
in-theory        51169
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-328 tm-646 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51169.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (D -> (C and D)))))), M:tm-328, m:tm-646, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-51170
in-theory        51170
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> (C -> (D -> (C and D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51170.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> (C -> (D -> (C and D)))))), M:tm-327, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51171
in-theory        51171
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A or (B -> A)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51171.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((E and F) -> F) and ((A or (B -> A)) -> (C -> (D -> (C and D)))))), M:tm-326, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51172
in-theory        51172
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A or (B -> A)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51172.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((E and F) -> E) and ((A or (B -> A)) -> (C -> (D -> (C and D)))))), M:tm-325, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51173
in-theory        51173
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> (C -> (D -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51173.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> (C -> (D -> (C and D)))))), M:tm-324, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51174
in-theory        51174
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A or (B -> A)) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51174.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((E -> (F -> E)) and ((A or (B -> A)) -> (C -> (D -> (C and D)))))), M:tm-323, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51175
in-theory        51175
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51175.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51176
in-theory        51176
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51176.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51177
in-theory        51177
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51177.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51178
in-theory        51178
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     25
proof            (modus-ponens tm-316 tm-646 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51178.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-646, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-51179
in-theory        51179
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51179.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51180
in-theory        51180
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((A or (B -> A)) -> (not (C -> (D -> (C and D))))) -> (not (A or (B -> A)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-646 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51180.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((A or (B -> A)) -> (not (C -> (D -> (C and D))))) -> (not (A or (B -> A))))), M:tm-313, m:tm-646, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-51181
in-theory        51181
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((C -> (D -> (C and D))) -> E) -> (((A or (B -> A)) or (C -> (D -> (C and D)))) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-646 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51181.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((C -> (D -> (C and D))) -> E) -> (((A or (B -> A)) or (C -> (D -> (C and D)))) -> E))), M:tm-312, m:tm-646, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-51182
in-theory        51182
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (E or ((A or (B -> A)) -> (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51182.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (E or ((A or (B -> A)) -> (C -> (D -> (C and D)))))), M:tm-311, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51183
in-theory        51183
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((A or (B -> A)) -> (C -> (D -> (C and D)))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51183.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((A or (B -> A)) -> (C -> (D -> (C and D)))) or E)), M:tm-310, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51184
in-theory        51184
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (E -> (((A or (B -> A)) -> (C -> (D -> (C and D)))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51184.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (E -> (((A or (B -> A)) -> (C -> (D -> (C and D)))) and E))), M:tm-309, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51185
in-theory        51185
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (D -> (C and D)))))
theorem-size     33
proof            (modus-ponens tm-306 tm-646 ((A (or Am (-> Bm Am))) (B Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51185.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (D -> (C and D))))), M:tm-306, m:tm-646, u:((A (or Am (-> Bm Am))) (B Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-51186
in-theory        51186
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (E -> ((A or (B -> A)) -> (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51186.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and (E -> ((A or (B -> A)) -> (C -> (D -> (C and D)))))), M:tm-305, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51187
in-theory        51187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51187.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-303, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51188
in-theory        51188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51188.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-270, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51189
in-theory        51189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51189.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-239, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51190
in-theory        51190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51190.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (G -> (H -> (G and H))))), M:tm-210, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51191
in-theory        51191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51191.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-183, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51192
in-theory        51192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51192.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-157, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51193
in-theory        51193
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51193.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-147, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51194
in-theory        51194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51194.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-134, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51195
in-theory        51195
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51195.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-125, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51196
in-theory        51196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51196.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (H -> (G and H))))), M:tm-113, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51197
in-theory        51197
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51197.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-105, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51198
in-theory        51198
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((A or (B -> A)) and C)))
theorem-size     15
proof            (modus-ponens tm-99 tm-646 ((Cm (or Am (-> Bm Am))) (A (or Am (-> Bm Am))) (B (-> Dm (and (or Am (-> Bm Am)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51198.        ((A or (B -> A)) -> (C -> ((A or (B -> A)) and C))), M:tm-99, m:tm-646, u:((Cm (or Am (-> Bm Am))) (A (or Am (-> Bm Am))) (B (-> Dm (and (or Am (-> Bm Am)) Dm))))
================================================================
tm-name          tm-51199
in-theory        51199
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D -> (A or (B -> A))) and C)))
theorem-size     17
proof            (modus-ponens tm-98 tm-646 ((A (or Am (-> Bm Am))) (Cm (-> B (or Am (-> Bm Am)))) (C (-> Dm (and (-> B (or Am (-> Bm Am))) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51199.        ((A or (B -> A)) -> (C -> ((D -> (A or (B -> A))) and C))), M:tm-98, m:tm-646, u:((A (or Am (-> Bm Am))) (Cm (-> B (or Am (-> Bm Am)))) (C (-> Dm (and (-> B (or Am (-> Bm Am))) Dm))))
================================================================
tm-name          tm-51200
in-theory        51200
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51200.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (E -> (F -> (E and F))))), M:tm-95, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51201
in-theory        51201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51201.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-83, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51202
in-theory        51202
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> (D -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51202.        (((not (not A)) -> A) and ((B or (C -> B)) -> (D -> (E -> (D and E))))), M:tm-76, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51203
in-theory        51203
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-73 tm-646 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-10 tm-1 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51203.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (C -> (D -> (C and D)))), M:tm-73, m:tm-646, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-51204
in-theory        51204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51204.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (E -> (F -> (E and F))))), M:tm-69, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51205
in-theory        51205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51205.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-54, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51206
in-theory        51206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-50 tm-646 ((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51206.        (((A -> B) or (B or (A -> B))) -> (C -> (D -> (C and D)))), M:tm-50, m:tm-646, u:((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-51207
in-theory        51207
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-49 tm-646 ((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51207.        ((A or (A or (B -> A))) -> (C -> (D -> (C and D)))), M:tm-49, m:tm-646, u:((A Am) (B (-> Bm Am)) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-51208
in-theory        51208
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-47 tm-646 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-4 tm-1 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51208.        (((A and (B or (C -> B))) or (B or (C -> B))) -> (D -> (E -> (D and E)))), M:tm-47, m:tm-646, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-51209
in-theory        51209
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-46 tm-646 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51209.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> (D -> (E -> (D and E)))), M:tm-46, m:tm-646, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-51210
in-theory        51210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51210.        ((A -> (B or A)) and ((C or (D -> C)) -> (E -> (F -> (E and F))))), M:tm-42, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51211
in-theory        51211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51211.        ((A -> (A or B)) and ((C or (D -> C)) -> (E -> (F -> (E and F))))), M:tm-32, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51212
in-theory        51212
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (D -> (C and D)))))
theorem-size     19
proof            (modus-ponens tm-24 tm-646 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51212.        ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (D -> (C and D))))), M:tm-24, m:tm-646, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-51213
in-theory        51213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51213.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (E -> (F -> (E and F))))), M:tm-23, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51214
in-theory        51214
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51214.        (((A and B) -> B) and ((C or (D -> C)) -> (E -> (F -> (E and F))))), M:tm-22, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51215
in-theory        51215
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51215.        (((A and B) -> A) and ((C or (D -> C)) -> (E -> (F -> (E and F))))), M:tm-21, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51216
in-theory        51216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51216.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-20, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51217
in-theory        51217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51217.        ((A -> (B -> A)) and ((C or (D -> C)) -> (E -> (F -> (E and F))))), M:tm-19, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51218
in-theory        51218
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not (C -> (D -> (C and D))))) -> (not (A or (B -> A))))
theorem-size     21
proof            (modus-ponens tm-9 tm-646 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-9 tm-8 tm-1 tm-5)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51218.        (((A or (B -> A)) -> (not (C -> (D -> (C and D))))) -> (not (A or (B -> A)))), M:tm-9, m:tm-646, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-51219
in-theory        51219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> (((D or (E -> D)) or (A -> (B -> (A and B)))) -> C))
theorem-size     25
proof            (modus-ponens tm-8 tm-646 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51219.        (((A -> (B -> (A and B))) -> C) -> (((D or (E -> D)) or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-646, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-51220
in-theory        51220
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-7 tm-8 tm-1 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51220.        (A or ((B or (C -> B)) -> (D -> (E -> (D and E))))), M:tm-7, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51221
in-theory        51221
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-6 tm-8 tm-1 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51221.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) or E), M:tm-6, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51222
in-theory        51222
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> (D -> (E -> (D and E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51222.        (A -> (((B or (C -> B)) -> (D -> (E -> (D and E)))) and A)), M:tm-5, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51223
in-theory        51223
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-2 tm-646 ((A (or Am (-> Bm Am))) (B Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51223.        (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (D -> (C and D)))), M:tm-2, m:tm-646, u:((A (or Am (-> Bm Am))) (B Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-51224
in-theory        51224
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-1 tm-8 tm-5)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-51224.        (A -> ((B or (C -> B)) -> (D -> (E -> (D and E))))), M:tm-1, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51225
in-theory        51225
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or ((D -> (D or E)) and (B -> A))))
theorem-size     17
proof            (modus-ponens tm-623 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51225.        ((A or (B -> A)) -> (C or ((D -> (D or E)) and (B -> A)))), M:tm-623, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51226
in-theory        51226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-622 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51226.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-622, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51227
in-theory        51227
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51227.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (E -> (F or E))), M:tm-609, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51228
in-theory        51228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-605 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51228.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-605, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51229
in-theory        51229
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((E -> (F or E)) and ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51229.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((E -> (F or E)) and ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))))), M:tm-595, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51230
in-theory        51230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-550 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51230.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-550, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51231
in-theory        51231
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-540 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51231.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-540, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51232
in-theory        51232
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-530 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51232.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-530, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51233
in-theory        51233
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-520 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51233.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-520, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51234
in-theory        51234
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-510 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51234.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-510, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51235
in-theory        51235
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-500 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51235.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-500, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51236
in-theory        51236
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-490 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51236.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E)))), M:tm-490, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51237
in-theory        51237
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-480 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51237.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-480, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51238
in-theory        51238
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> (C or D)) and (B -> A)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51238.        ((A or (B -> A)) -> (((C -> (C or D)) and (B -> A)) or E)), M:tm-470, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51239
in-theory        51239
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-469 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51239.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-469, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51240
in-theory        51240
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51240.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (E -> (E or F))), M:tm-456, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51241
in-theory        51241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-453 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51241.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-453, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51242
in-theory        51242
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((E -> (E or F)) and ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51242.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((E -> (E or F)) and ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))))), M:tm-443, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51243
in-theory        51243
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-409 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51243.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-409, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51244
in-theory        51244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-400 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51244.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-400, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51245
in-theory        51245
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-391 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51245.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-391, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51246
in-theory        51246
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-382 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51246.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-382, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51247
in-theory        51247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-373 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51247.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E)))), M:tm-373, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51248
in-theory        51248
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-364 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51248.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-364, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51249
in-theory        51249
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((D -> (D or E)) and (B -> A)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51249.        ((A or (B -> A)) -> (C -> (((D -> (D or E)) and (B -> A)) and C))), M:tm-355, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51250
in-theory        51250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-354 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51250.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-354, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51251
in-theory        51251
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51251.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51252
in-theory        51252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C))))
theorem-size     25
proof            (modus-ponens tm-338 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51252.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C)))), M:tm-338, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51253
in-theory        51253
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (C or D)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51253.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (C or D)) and (B -> A))))), M:tm-328, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51254
in-theory        51254
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51254.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))))), M:tm-327, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51255
in-theory        51255
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (((E and F) -> F) and ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51255.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (((E and F) -> F) and ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))))), M:tm-326, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51256
in-theory        51256
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (((E and F) -> E) and ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51256.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (((E and F) -> E) and ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))))), M:tm-325, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51257
in-theory        51257
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51257.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))))), M:tm-324, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51258
in-theory        51258
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((E -> (F -> E)) and ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51258.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((E -> (F -> E)) and ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))))), M:tm-323, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51259
in-theory        51259
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51259.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((E and F) -> F)), M:tm-322, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51260
in-theory        51260
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51260.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((E and F) -> E)), M:tm-320, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51261
in-theory        51261
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51261.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51262
in-theory        51262
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     27
proof            (modus-ponens tm-316 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51262.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51263
in-theory        51263
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51263.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (E -> (F -> E))), M:tm-315, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51264
in-theory        51264
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (((A or (B -> A)) -> (not ((C -> (C or D)) and (B -> A)))) -> (not (A or (B -> A)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51264.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (((A or (B -> A)) -> (not ((C -> (C or D)) and (B -> A)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51265
in-theory        51265
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((((C -> (C or D)) and (B -> A)) -> E) -> (((A or (B -> A)) or ((C -> (C or D)) and (B -> A))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51265.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((((C -> (C or D)) and (B -> A)) -> E) -> (((A or (B -> A)) or ((C -> (C or D)) and (B -> A))) -> E))), M:tm-312, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51266
in-theory        51266
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (E or ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51266.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (E or ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))))), M:tm-311, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51267
in-theory        51267
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51267.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) or E)), M:tm-310, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51268
in-theory        51268
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (E -> (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51268.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (E -> (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and E))), M:tm-309, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51269
in-theory        51269
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (E -> ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51269.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and (E -> ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))))), M:tm-305, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51270
in-theory        51270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-303 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51270.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-303, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51271
in-theory        51271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-270 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51271.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-270, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51272
in-theory        51272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-239 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51272.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-239, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51273
in-theory        51273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E))))
theorem-size     33
proof            (modus-ponens tm-210 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51273.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E)))), M:tm-210, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51274
in-theory        51274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-183 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51274.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-183, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51275
in-theory        51275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-157 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51275.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-157, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51276
in-theory        51276
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-147 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51276.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-147, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51277
in-theory        51277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-134 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51277.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-134, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51278
in-theory        51278
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-125 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51278.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-125, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51279
in-theory        51279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-113 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51279.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E)))), M:tm-113, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51280
in-theory        51280
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     35
proof            (modus-ponens tm-105 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51280.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-105, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51281
in-theory        51281
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-95 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51281.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C)))), M:tm-95, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51282
in-theory        51282
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D -> (D or E)) and (B -> A))))
theorem-size     17
proof            (modus-ponens tm-84 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51282.        ((A or (B -> A)) -> (C -> ((D -> (D or E)) and (B -> A)))), M:tm-84, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51283
in-theory        51283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-83 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51283.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-83, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51284
in-theory        51284
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> ((D -> (D or E)) and (C -> B))))
theorem-size     21
proof            (modus-ponens tm-76 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51284.        (((not (not A)) -> A) and ((B or (C -> B)) -> ((D -> (D or E)) and (C -> B)))), M:tm-76, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51285
in-theory        51285
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((C -> (C or D)) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-73 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51285.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((C -> (C or D)) and (B -> A))), M:tm-73, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51286
in-theory        51286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C))))
theorem-size     27
proof            (modus-ponens tm-69 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51286.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C)))), M:tm-69, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51287
in-theory        51287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-54 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51287.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-54, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51288
in-theory        51288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> ((C -> (C or D)) and (A -> B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-647 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51288.        (((A -> B) or (B or (A -> B))) -> ((C -> (C or D)) and (A -> B))), M:tm-50, m:tm-647, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51289
in-theory        51289
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> ((C -> (C or D)) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-49 tm-647 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51289.        ((A or (A or (B -> A))) -> ((C -> (C or D)) and (B -> A))), M:tm-49, m:tm-647, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51290
in-theory        51290
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> ((D -> (D or E)) and (C -> B)))
theorem-size     23
proof            (modus-ponens tm-47 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51290.        (((A and (B or (C -> B))) or (B or (C -> B))) -> ((D -> (D or E)) and (C -> B))), M:tm-47, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51291
in-theory        51291
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((D -> (D or E)) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-46 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51291.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((D -> (D or E)) and (B -> A))), M:tm-46, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51292
in-theory        51292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-42 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51292.        ((A -> (B or A)) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C)))), M:tm-42, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51293
in-theory        51293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-32 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51293.        ((A -> (A or B)) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C)))), M:tm-32, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51294
in-theory        51294
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (C or D)) and (B -> A))))
theorem-size     21
proof            (modus-ponens tm-24 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51294.        ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (C or D)) and (B -> A)))), M:tm-24, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51295
in-theory        51295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-23 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51295.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C)))), M:tm-23, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51296
in-theory        51296
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-22 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51296.        (((A and B) -> B) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C)))), M:tm-22, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51297
in-theory        51297
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-21 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51297.        (((A and B) -> A) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C)))), M:tm-21, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51298
in-theory        51298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-20 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51298.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-20, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51299
in-theory        51299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-19 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51299.        ((A -> (B -> A)) and ((C or (D -> C)) -> ((E -> (E or F)) and (D -> C)))), M:tm-19, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51300
in-theory        51300
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not ((C -> (C or D)) and (B -> A)))) -> (not (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-9 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-9 tm-8 tm-1 tm-5 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51300.        (((A or (B -> A)) -> (not ((C -> (C or D)) and (B -> A)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51301
in-theory        51301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and (C -> D)) -> E) -> (((D or (C -> D)) or ((A -> (A or B)) and (C -> D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51301.        ((((A -> (A or B)) and (C -> D)) -> E) -> (((D or (C -> D)) or ((A -> (A or B)) and (C -> D))) -> E)), M:tm-8, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-51302
in-theory        51302
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> ((D -> (D or E)) and (C -> B))))
theorem-size     17
proof            (modus-ponens tm-7 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-7 tm-8 tm-1 tm-5 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51302.        (A or ((B or (C -> B)) -> ((D -> (D or E)) and (C -> B)))), M:tm-7, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51303
in-theory        51303
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-6 tm-8 tm-1 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51303.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) or E), M:tm-6, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51304
in-theory        51304
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> ((D -> (D or E)) and (C -> B))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51304.        (A -> (((B or (C -> B)) -> ((D -> (D or E)) and (C -> B))) and A)), M:tm-5, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51305
in-theory        51305
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> ((D -> (D or E)) and (C -> B))))
theorem-size     17
proof            (modus-ponens tm-1 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-1 tm-8 tm-5 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-51305.        (A -> ((B or (C -> B)) -> ((D -> (D or E)) and (C -> B)))), M:tm-1, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-51306
in-theory        51306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-622 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51306.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-622, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51307
in-theory        51307
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C or (A or (B -> A))) or D))
theorem-size     15
proof            (modus-ponens tm-617 tm-648 ((A (or Am (-> Bm Am))) (Cm (or B (or Am (-> Bm Am)))) (C (or (or B (or Am (-> Bm Am))) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51307.        ((A or (B -> A)) -> ((C or (A or (B -> A))) or D)), M:tm-617, m:tm-648, u:((A (or Am (-> Bm Am))) (Cm (or B (or Am (-> Bm Am)))) (C (or (or B (or Am (-> Bm Am))) Dm)))
================================================================
tm-name          tm-51308
in-theory        51308
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51308.        (((A or (B -> A)) -> (C -> (C or D))) and (E -> (F or E))), M:tm-609, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51309
in-theory        51309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-605 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51309.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-605, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51310
in-theory        51310
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and ((E -> (F or E)) and ((A or (B -> A)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51310.        (((A or (B -> A)) -> (C -> (C or D))) and ((E -> (F or E)) and ((A or (B -> A)) -> (C -> (C or D))))), M:tm-595, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51311
in-theory        51311
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-550 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51311.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-550, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51312
in-theory        51312
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-540 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51312.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-540, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51313
in-theory        51313
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-530 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51313.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-530, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51314
in-theory        51314
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-520 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51314.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-520, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51315
in-theory        51315
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-510 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51315.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-510, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51316
in-theory        51316
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-500 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51316.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-500, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51317
in-theory        51317
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-490 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51317.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (G or H)))), M:tm-490, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51318
in-theory        51318
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-480 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51318.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-480, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51319
in-theory        51319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-469 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51319.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-469, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51320
in-theory        51320
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((A or (B -> A)) or C) or D))
theorem-size     15
proof            (modus-ponens tm-464 tm-648 ((A (or Am (-> Bm Am))) (Cm (or (or Am (-> Bm Am)) B)) (C (or (or (or Am (-> Bm Am)) B) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51320.        ((A or (B -> A)) -> (((A or (B -> A)) or C) or D)), M:tm-464, m:tm-648, u:((A (or Am (-> Bm Am))) (Cm (or (or Am (-> Bm Am)) B)) (C (or (or (or Am (-> Bm Am)) B) Dm)))
================================================================
tm-name          tm-51321
in-theory        51321
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51321.        (((A or (B -> A)) -> (C -> (C or D))) and (E -> (E or F))), M:tm-456, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51322
in-theory        51322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-453 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51322.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-453, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51323
in-theory        51323
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and ((E -> (E or F)) and ((A or (B -> A)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51323.        (((A or (B -> A)) -> (C -> (C or D))) and ((E -> (E or F)) and ((A or (B -> A)) -> (C -> (C or D))))), M:tm-443, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51324
in-theory        51324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-409 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51324.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-409, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51325
in-theory        51325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-400 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51325.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-400, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51326
in-theory        51326
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-391 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51326.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-391, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51327
in-theory        51327
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-382 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51327.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-382, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51328
in-theory        51328
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-373 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51328.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (G -> (G or H)))), M:tm-373, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51329
in-theory        51329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-364 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51329.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-364, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51330
in-theory        51330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-354 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51330.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-354, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51331
in-theory        51331
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> ((A or (B -> A)) and C)) or D))
theorem-size     17
proof            (modus-ponens tm-349 tm-648 ((A (or Am (-> Bm Am))) (Cm (-> B (and (or Am (-> Bm Am)) B))) (C (or (-> B (and (or Am (-> Bm Am)) B)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51331.        ((A or (B -> A)) -> ((C -> ((A or (B -> A)) and C)) or D)), M:tm-349, m:tm-648, u:((A (or Am (-> Bm Am))) (Cm (-> B (and (or Am (-> Bm Am)) B))) (C (or (-> B (and (or Am (-> Bm Am)) B)) Dm)))
================================================================
tm-name          tm-51332
in-theory        51332
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51332.        (((A or (B -> A)) -> (C -> (C or D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51333
in-theory        51333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-338 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51333.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (E -> (E or F)))), M:tm-338, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51334
in-theory        51334
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-648 ((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51334.        (((A or (B -> A)) -> (C -> (C or D))) and ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (C or D))))), M:tm-328, m:tm-648, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-51335
in-theory        51335
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> (C -> (C or D)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51335.        (((A or (B -> A)) -> (C -> (C or D))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> (C -> (C or D))))), M:tm-327, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51336
in-theory        51336
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (((E and F) -> F) and ((A or (B -> A)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51336.        (((A or (B -> A)) -> (C -> (C or D))) and (((E and F) -> F) and ((A or (B -> A)) -> (C -> (C or D))))), M:tm-326, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51337
in-theory        51337
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (((E and F) -> E) and ((A or (B -> A)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51337.        (((A or (B -> A)) -> (C -> (C or D))) and (((E and F) -> E) and ((A or (B -> A)) -> (C -> (C or D))))), M:tm-325, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51338
in-theory        51338
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> (C -> (C or D)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51338.        (((A or (B -> A)) -> (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> (C -> (C or D))))), M:tm-324, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51339
in-theory        51339
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and ((E -> (F -> E)) and ((A or (B -> A)) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51339.        (((A or (B -> A)) -> (C -> (C or D))) and ((E -> (F -> E)) and ((A or (B -> A)) -> (C -> (C or D))))), M:tm-323, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51340
in-theory        51340
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51340.        (((A or (B -> A)) -> (C -> (C or D))) and ((E and F) -> F)), M:tm-322, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51341
in-theory        51341
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51341.        (((A or (B -> A)) -> (C -> (C or D))) and ((E and F) -> E)), M:tm-320, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51342
in-theory        51342
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51342.        (((A or (B -> A)) -> (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51343
in-theory        51343
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-648 ((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51343.        (((A or (B -> A)) -> (C -> (C or D))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-648, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-51344
in-theory        51344
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51344.        (((A or (B -> A)) -> (C -> (C or D))) and (E -> (F -> E))), M:tm-315, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51345
in-theory        51345
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (((A or (B -> A)) -> (not (C -> (C or D)))) -> (not (A or (B -> A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-648 ((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51345.        (((A or (B -> A)) -> (C -> (C or D))) and (((A or (B -> A)) -> (not (C -> (C or D)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-648, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-51346
in-theory        51346
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (((C -> (C or D)) -> E) -> (((A or (B -> A)) or (C -> (C or D))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-648 ((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51346.        (((A or (B -> A)) -> (C -> (C or D))) and (((C -> (C or D)) -> E) -> (((A or (B -> A)) or (C -> (C or D))) -> E))), M:tm-312, m:tm-648, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-51347
in-theory        51347
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (E or ((A or (B -> A)) -> (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51347.        (((A or (B -> A)) -> (C -> (C or D))) and (E or ((A or (B -> A)) -> (C -> (C or D))))), M:tm-311, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51348
in-theory        51348
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (((A or (B -> A)) -> (C -> (C or D))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51348.        (((A or (B -> A)) -> (C -> (C or D))) and (((A or (B -> A)) -> (C -> (C or D))) or E)), M:tm-310, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51349
in-theory        51349
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (E -> (((A or (B -> A)) -> (C -> (C or D))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51349.        (((A or (B -> A)) -> (C -> (C or D))) and (E -> (((A or (B -> A)) -> (C -> (C or D))) and E))), M:tm-309, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51350
in-theory        51350
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (C or D))))
theorem-size     29
proof            (modus-ponens tm-306 tm-648 ((A (or Am (-> Bm Am))) (B Cm) (C (or Cm Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51350.        (((A or (B -> A)) -> (C -> (C or D))) and (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (C or D)))), M:tm-306, m:tm-648, u:((A (or Am (-> Bm Am))) (B Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-51351
in-theory        51351
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and (E -> ((A or (B -> A)) -> (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51351.        (((A or (B -> A)) -> (C -> (C or D))) and (E -> ((A or (B -> A)) -> (C -> (C or D))))), M:tm-305, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51352
in-theory        51352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-303 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51352.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-303, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51353
in-theory        51353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-270 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51353.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-270, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51354
in-theory        51354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-239 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51354.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-239, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51355
in-theory        51355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-210 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51355.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (G -> (G or H)))), M:tm-210, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51356
in-theory        51356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-183 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51356.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-183, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51357
in-theory        51357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-157 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51357.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-157, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51358
in-theory        51358
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-147 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51358.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-147, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51359
in-theory        51359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-134 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51359.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-134, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51360
in-theory        51360
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-125 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51360.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-125, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51361
in-theory        51361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-113 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51361.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (G or H)))), M:tm-113, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51362
in-theory        51362
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-105 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51362.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-105, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51363
in-theory        51363
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) or C))
theorem-size     13
proof            (modus-ponens tm-99 tm-648 ((Cm (or Am (-> Bm Am))) (A (or Am (-> Bm Am))) (B (or (or Am (-> Bm Am)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51363.        ((A or (B -> A)) -> ((A or (B -> A)) or C)), M:tm-99, m:tm-648, u:((Cm (or Am (-> Bm Am))) (A (or Am (-> Bm Am))) (B (or (or Am (-> Bm Am)) Dm)))
================================================================
tm-name          tm-51364
in-theory        51364
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> (A or (B -> A))) or D))
theorem-size     15
proof            (modus-ponens tm-98 tm-648 ((A (or Am (-> Bm Am))) (Cm (-> B (or Am (-> Bm Am)))) (C (or (-> B (or Am (-> Bm Am))) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51364.        ((A or (B -> A)) -> ((C -> (A or (B -> A))) or D)), M:tm-98, m:tm-648, u:((A (or Am (-> Bm Am))) (Cm (-> B (or Am (-> Bm Am)))) (C (or (-> B (or Am (-> Bm Am))) Dm)))
================================================================
tm-name          tm-51365
in-theory        51365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-95 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51365.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (E -> (E or F)))), M:tm-95, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51366
in-theory        51366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-83 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51366.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-83, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51367
in-theory        51367
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> (D -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-76 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51367.        (((not (not A)) -> A) and ((B or (C -> B)) -> (D -> (D or E)))), M:tm-76, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51368
in-theory        51368
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (C -> (C or D)))
theorem-size     19
proof            (modus-ponens tm-73 tm-648 ((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51368.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (C -> (C or D))), M:tm-73, m:tm-648, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-51369
in-theory        51369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-69 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51369.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (E -> (E or F)))), M:tm-69, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51370
in-theory        51370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-54 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51370.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-54, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51371
in-theory        51371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-50 tm-648 ((A Am) (B (-> Bm Am)) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51371.        (((A -> B) or (B or (A -> B))) -> (C -> (C or D))), M:tm-50, m:tm-648, u:((A Am) (B (-> Bm Am)) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-51372
in-theory        51372
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-49 tm-648 ((A Am) (B (-> Bm Am)) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51372.        ((A or (A or (B -> A))) -> (C -> (C or D))), M:tm-49, m:tm-648, u:((A Am) (B (-> Bm Am)) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-51373
in-theory        51373
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-47 tm-648 ((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51373.        (((A and (B or (C -> B))) or (B or (C -> B))) -> (D -> (D or E))), M:tm-47, m:tm-648, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-51374
in-theory        51374
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-46 tm-648 ((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51374.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> (D -> (D or E))), M:tm-46, m:tm-648, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-51375
in-theory        51375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-42 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51375.        ((A -> (B or A)) and ((C or (D -> C)) -> (E -> (E or F)))), M:tm-42, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51376
in-theory        51376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-32 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51376.        ((A -> (A or B)) and ((C or (D -> C)) -> (E -> (E or F)))), M:tm-32, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51377
in-theory        51377
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (C or D))))
theorem-size     17
proof            (modus-ponens tm-24 tm-648 ((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51377.        ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (C or D)))), M:tm-24, m:tm-648, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-51378
in-theory        51378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-23 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51378.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (E -> (E or F)))), M:tm-23, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51379
in-theory        51379
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-22 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51379.        (((A and B) -> B) and ((C or (D -> C)) -> (E -> (E or F)))), M:tm-22, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51380
in-theory        51380
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-21 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51380.        (((A and B) -> A) and ((C or (D -> C)) -> (E -> (E or F)))), M:tm-21, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51381
in-theory        51381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-20 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51381.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-20, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51382
in-theory        51382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-19 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-6)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51382.        ((A -> (B -> A)) and ((C or (D -> C)) -> (E -> (E or F)))), M:tm-19, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51383
in-theory        51383
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not (C -> (C or D)))) -> (not (A or (B -> A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-648 ((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-9 tm-8 tm-1 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51383.        (((A or (B -> A)) -> (not (C -> (C or D)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-648, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-51384
in-theory        51384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> (((D or (E -> D)) or (A -> (A or B))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-648 ((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51384.        (((A -> (A or B)) -> C) -> (((D or (E -> D)) or (A -> (A or B))) -> C)), M:tm-8, m:tm-648, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-51385
in-theory        51385
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-7 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-7 tm-8 tm-1 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51385.        (A or ((B or (C -> B)) -> (D -> (D or E)))), M:tm-7, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51386
in-theory        51386
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-6 tm-8 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51386.        (((A or (B -> A)) -> (C -> (C or D))) or E), M:tm-6, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51387
in-theory        51387
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> (D -> (D or E))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51387.        (A -> (((B or (C -> B)) -> (D -> (D or E))) and A)), M:tm-5, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51388
in-theory        51388
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-2 tm-648 ((A (or Am (-> Bm Am))) (B Cm) (C (or Cm Dm))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51388.        (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (C or D))), M:tm-2, m:tm-648, u:((A (or Am (-> Bm Am))) (B Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-51389
in-theory        51389
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-1 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-1 tm-8 tm-6)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-51389.        (A -> ((B or (C -> B)) -> (D -> (D or E)))), M:tm-1, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51390
in-theory        51390
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or ((D -> (E or D)) and (B -> A))))
theorem-size     17
proof            (modus-ponens tm-623 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51390.        ((A or (B -> A)) -> (C or ((D -> (E or D)) and (B -> A)))), M:tm-623, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51391
in-theory        51391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-622 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51391.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-622, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51392
in-theory        51392
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51392.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (E -> (F or E))), M:tm-609, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51393
in-theory        51393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-605 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51393.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-605, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51394
in-theory        51394
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((E -> (F or E)) and ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51394.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((E -> (F or E)) and ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))))), M:tm-595, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51395
in-theory        51395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-550 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51395.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-550, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51396
in-theory        51396
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-540 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51396.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-540, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51397
in-theory        51397
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-530 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51397.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-530, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51398
in-theory        51398
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-520 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51398.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-520, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51399
in-theory        51399
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-510 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51399.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-510, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51400
in-theory        51400
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-500 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51400.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-500, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51401
in-theory        51401
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-490 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51401.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E)))), M:tm-490, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51402
in-theory        51402
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-480 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51402.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-480, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51403
in-theory        51403
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> (D or C)) and (B -> A)) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51403.        ((A or (B -> A)) -> (((C -> (D or C)) and (B -> A)) or E)), M:tm-470, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51404
in-theory        51404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-469 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51404.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-469, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51405
in-theory        51405
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51405.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (E -> (E or F))), M:tm-456, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51406
in-theory        51406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-453 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51406.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-453, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51407
in-theory        51407
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((E -> (E or F)) and ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51407.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((E -> (E or F)) and ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))))), M:tm-443, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51408
in-theory        51408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-409 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51408.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-409, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51409
in-theory        51409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-400 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51409.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-400, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51410
in-theory        51410
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-391 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51410.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-391, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51411
in-theory        51411
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-382 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51411.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-382, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51412
in-theory        51412
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-373 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51412.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E)))), M:tm-373, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51413
in-theory        51413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-364 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51413.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-364, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51414
in-theory        51414
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((D -> (E or D)) and (B -> A)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51414.        ((A or (B -> A)) -> (C -> (((D -> (E or D)) and (B -> A)) and C))), M:tm-355, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51415
in-theory        51415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-354 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51415.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-354, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51416
in-theory        51416
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51416.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51417
in-theory        51417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C))))
theorem-size     25
proof            (modus-ponens tm-338 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51417.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C)))), M:tm-338, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51418
in-theory        51418
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D or C)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-328 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51418.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D or C)) and (B -> A))))), M:tm-328, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51419
in-theory        51419
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51419.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))))), M:tm-327, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51420
in-theory        51420
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (((E and F) -> F) and ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51420.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (((E and F) -> F) and ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))))), M:tm-326, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51421
in-theory        51421
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (((E and F) -> E) and ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51421.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (((E and F) -> E) and ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))))), M:tm-325, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51422
in-theory        51422
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51422.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))))), M:tm-324, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51423
in-theory        51423
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((E -> (F -> E)) and ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51423.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((E -> (F -> E)) and ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))))), M:tm-323, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51424
in-theory        51424
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51424.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((E and F) -> F)), M:tm-322, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51425
in-theory        51425
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51425.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((E and F) -> E)), M:tm-320, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51426
in-theory        51426
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51426.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51427
in-theory        51427
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     27
proof            (modus-ponens tm-316 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51427.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51428
in-theory        51428
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51428.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (E -> (F -> E))), M:tm-315, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51429
in-theory        51429
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (((A or (B -> A)) -> (not ((C -> (D or C)) and (B -> A)))) -> (not (A or (B -> A)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51429.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (((A or (B -> A)) -> (not ((C -> (D or C)) and (B -> A)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51430
in-theory        51430
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((((C -> (D or C)) and (B -> A)) -> E) -> (((A or (B -> A)) or ((C -> (D or C)) and (B -> A))) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51430.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((((C -> (D or C)) and (B -> A)) -> E) -> (((A or (B -> A)) or ((C -> (D or C)) and (B -> A))) -> E))), M:tm-312, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51431
in-theory        51431
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (E or ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51431.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (E or ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))))), M:tm-311, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51432
in-theory        51432
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51432.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) or E)), M:tm-310, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51433
in-theory        51433
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (E -> (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51433.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (E -> (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and E))), M:tm-309, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51434
in-theory        51434
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (E -> ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51434.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and (E -> ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))))), M:tm-305, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51435
in-theory        51435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-303 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51435.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-303, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51436
in-theory        51436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-270 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51436.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-270, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51437
in-theory        51437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-239 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51437.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-239, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51438
in-theory        51438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E))))
theorem-size     33
proof            (modus-ponens tm-210 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51438.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E)))), M:tm-210, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51439
in-theory        51439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     25
proof            (modus-ponens tm-183 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51439.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-183, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51440
in-theory        51440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-157 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51440.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-157, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51441
in-theory        51441
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-147 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51441.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-147, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51442
in-theory        51442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-134 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51442.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-134, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51443
in-theory        51443
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-125 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51443.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-125, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51444
in-theory        51444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E))))
theorem-size     31
proof            (modus-ponens tm-113 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51444.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E)))), M:tm-113, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51445
in-theory        51445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     35
proof            (modus-ponens tm-105 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51445.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-105, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51446
in-theory        51446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-95 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51446.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C)))), M:tm-95, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51447
in-theory        51447
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((D -> (E or D)) and (B -> A))))
theorem-size     17
proof            (modus-ponens tm-84 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51447.        ((A or (B -> A)) -> (C -> ((D -> (E or D)) and (B -> A)))), M:tm-84, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51448
in-theory        51448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     23
proof            (modus-ponens tm-83 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51448.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-83, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51449
in-theory        51449
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> ((D -> (E or D)) and (C -> B))))
theorem-size     21
proof            (modus-ponens tm-76 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51449.        (((not (not A)) -> A) and ((B or (C -> B)) -> ((D -> (E or D)) and (C -> B)))), M:tm-76, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51450
in-theory        51450
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((C -> (D or C)) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-73 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-10 tm-1 tm-5 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51450.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> ((C -> (D or C)) and (B -> A))), M:tm-73, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51451
in-theory        51451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C))))
theorem-size     27
proof            (modus-ponens tm-69 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51451.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C)))), M:tm-69, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51452
in-theory        51452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-54 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51452.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-54, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51453
in-theory        51453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> ((C -> (D or C)) and (A -> B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-649 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-7 tm-1 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51453.        (((A -> B) or (B or (A -> B))) -> ((C -> (D or C)) and (A -> B))), M:tm-50, m:tm-649, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51454
in-theory        51454
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> ((C -> (D or C)) and (B -> A)))
theorem-size     17
proof            (modus-ponens tm-49 tm-649 ((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-6 tm-1 tm-5 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51454.        ((A or (A or (B -> A))) -> ((C -> (D or C)) and (B -> A))), M:tm-49, m:tm-649, u:((A Am) (B (-> Bm Am)) (C (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51455
in-theory        51455
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> ((D -> (E or D)) and (C -> B)))
theorem-size     23
proof            (modus-ponens tm-47 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-4 tm-1 tm-5 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51455.        (((A and (B or (C -> B))) or (B or (C -> B))) -> ((D -> (E or D)) and (C -> B))), M:tm-47, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51456
in-theory        51456
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((D -> (E or D)) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-46 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51456.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((D -> (E or D)) and (B -> A))), M:tm-46, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51457
in-theory        51457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-42 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51457.        ((A -> (B or A)) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C)))), M:tm-42, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51458
in-theory        51458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-32 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51458.        ((A -> (A or B)) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C)))), M:tm-32, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51459
in-theory        51459
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D or C)) and (B -> A))))
theorem-size     21
proof            (modus-ponens tm-24 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51459.        ((A or (B -> A)) -> ((A or (B -> A)) and ((C -> (D or C)) and (B -> A)))), M:tm-24, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51460
in-theory        51460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C))))
theorem-size     23
proof            (modus-ponens tm-23 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51460.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C)))), M:tm-23, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51461
in-theory        51461
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-22 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51461.        (((A and B) -> B) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C)))), M:tm-22, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51462
in-theory        51462
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-21 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51462.        (((A and B) -> A) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C)))), M:tm-21, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51463
in-theory        51463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-20 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51463.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-20, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51464
in-theory        51464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C))))
theorem-size     21
proof            (modus-ponens tm-19 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51464.        ((A -> (B -> A)) and ((C or (D -> C)) -> ((E -> (F or E)) and (D -> C)))), M:tm-19, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51465
in-theory        51465
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not ((C -> (D or C)) and (B -> A)))) -> (not (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-9 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-9 tm-8 tm-1 tm-5 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51465.        (((A or (B -> A)) -> (not ((C -> (D or C)) and (B -> A)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51466
in-theory        51466
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and (C -> D)) -> E) -> (((D or (C -> D)) or ((A -> (B or A)) and (C -> D))) -> E))
theorem-size     29
proof            (modus-ponens tm-8 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51466.        ((((A -> (B or A)) and (C -> D)) -> E) -> (((D or (C -> D)) or ((A -> (B or A)) and (C -> D))) -> E)), M:tm-8, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-51467
in-theory        51467
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> ((D -> (E or D)) and (C -> B))))
theorem-size     17
proof            (modus-ponens tm-7 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-7 tm-8 tm-1 tm-5)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51467.        (A or ((B or (C -> B)) -> ((D -> (E or D)) and (C -> B)))), M:tm-7, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51468
in-theory        51468
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-6 tm-8 tm-1 tm-5 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51468.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) or E), M:tm-6, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51469
in-theory        51469
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> ((D -> (E or D)) and (C -> B))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51469.        (A -> (((B or (C -> B)) -> ((D -> (E or D)) and (C -> B))) and A)), M:tm-5, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51470
in-theory        51470
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> ((D -> (E or D)) and (C -> B))))
theorem-size     17
proof            (modus-ponens tm-1 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-1 tm-8 tm-5 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-51470.        (A -> ((B or (C -> B)) -> ((D -> (E or D)) and (C -> B)))), M:tm-1, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-51471
in-theory        51471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51471.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-622, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51472
in-theory        51472
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (D or (A or (B -> A)))))
theorem-size     15
proof            (modus-ponens tm-617 tm-650 ((A (or Am (-> Bm Am))) (Cm (or B (or Am (-> Bm Am)))) (C (or Dm (or B (or Am (-> Bm Am)))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51472.        ((A or (B -> A)) -> (C or (D or (A or (B -> A))))), M:tm-617, m:tm-650, u:((A (or Am (-> Bm Am))) (Cm (or B (or Am (-> Bm Am)))) (C (or Dm (or B (or Am (-> Bm Am))))))
================================================================
tm-name          tm-51473
in-theory        51473
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51473.        (((A or (B -> A)) -> (C -> (D or C))) and (E -> (F or E))), M:tm-609, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51474
in-theory        51474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51474.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-605, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51475
in-theory        51475
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and ((E -> (F or E)) and ((A or (B -> A)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51475.        (((A or (B -> A)) -> (C -> (D or C))) and ((E -> (F or E)) and ((A or (B -> A)) -> (C -> (D or C))))), M:tm-595, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51476
in-theory        51476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51476.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-550, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51477
in-theory        51477
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51477.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-540, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51478
in-theory        51478
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51478.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-530, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51479
in-theory        51479
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51479.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-520, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51480
in-theory        51480
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51480.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-510, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51481
in-theory        51481
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51481.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-500, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51482
in-theory        51482
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51482.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (H or G)))), M:tm-490, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51483
in-theory        51483
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51483.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-480, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51484
in-theory        51484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51484.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-469, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51485
in-theory        51485
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or ((A or (B -> A)) or D)))
theorem-size     15
proof            (modus-ponens tm-464 tm-650 ((A (or Am (-> Bm Am))) (Cm (or (or Am (-> Bm Am)) B)) (C (or Dm (or (or Am (-> Bm Am)) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51485.        ((A or (B -> A)) -> (C or ((A or (B -> A)) or D))), M:tm-464, m:tm-650, u:((A (or Am (-> Bm Am))) (Cm (or (or Am (-> Bm Am)) B)) (C (or Dm (or (or Am (-> Bm Am)) B))))
================================================================
tm-name          tm-51486
in-theory        51486
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51486.        (((A or (B -> A)) -> (C -> (D or C))) and (E -> (E or F))), M:tm-456, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51487
in-theory        51487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51487.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-453, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51488
in-theory        51488
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and ((E -> (E or F)) and ((A or (B -> A)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51488.        (((A or (B -> A)) -> (C -> (D or C))) and ((E -> (E or F)) and ((A or (B -> A)) -> (C -> (D or C))))), M:tm-443, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51489
in-theory        51489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51489.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-409, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51490
in-theory        51490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51490.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-400, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51491
in-theory        51491
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51491.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-391, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51492
in-theory        51492
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51492.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-382, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51493
in-theory        51493
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51493.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (G -> (H or G)))), M:tm-373, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51494
in-theory        51494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51494.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-364, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51495
in-theory        51495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51495.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-354, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51496
in-theory        51496
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (D -> ((A or (B -> A)) and D))))
theorem-size     17
proof            (modus-ponens tm-349 tm-650 ((A (or Am (-> Bm Am))) (Cm (-> B (and (or Am (-> Bm Am)) B))) (C (or Dm (-> B (and (or Am (-> Bm Am)) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51496.        ((A or (B -> A)) -> (C or (D -> ((A or (B -> A)) and D)))), M:tm-349, m:tm-650, u:((A (or Am (-> Bm Am))) (Cm (-> B (and (or Am (-> Bm Am)) B))) (C (or Dm (-> B (and (or Am (-> Bm Am)) B)))))
================================================================
tm-name          tm-51497
in-theory        51497
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51497.        (((A or (B -> A)) -> (C -> (D or C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51498
in-theory        51498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51498.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (E -> (F or E)))), M:tm-338, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51499
in-theory        51499
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-650 ((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51499.        (((A or (B -> A)) -> (C -> (D or C))) and ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (D or C))))), M:tm-328, m:tm-650, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-51500
in-theory        51500
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> (C -> (D or C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51500.        (((A or (B -> A)) -> (C -> (D or C))) and ((E -> (F -> (E and F))) and ((A or (B -> A)) -> (C -> (D or C))))), M:tm-327, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51501
in-theory        51501
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (((E and F) -> F) and ((A or (B -> A)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51501.        (((A or (B -> A)) -> (C -> (D or C))) and (((E and F) -> F) and ((A or (B -> A)) -> (C -> (D or C))))), M:tm-326, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51502
in-theory        51502
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (((E and F) -> E) and ((A or (B -> A)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51502.        (((A or (B -> A)) -> (C -> (D or C))) and (((E and F) -> E) and ((A or (B -> A)) -> (C -> (D or C))))), M:tm-325, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51503
in-theory        51503
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> (C -> (D or C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51503.        (((A or (B -> A)) -> (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (B -> A)) -> (C -> (D or C))))), M:tm-324, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51504
in-theory        51504
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and ((E -> (F -> E)) and ((A or (B -> A)) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51504.        (((A or (B -> A)) -> (C -> (D or C))) and ((E -> (F -> E)) and ((A or (B -> A)) -> (C -> (D or C))))), M:tm-323, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51505
in-theory        51505
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51505.        (((A or (B -> A)) -> (C -> (D or C))) and ((E and F) -> F)), M:tm-322, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51506
in-theory        51506
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51506.        (((A or (B -> A)) -> (C -> (D or C))) and ((E and F) -> E)), M:tm-320, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51507
in-theory        51507
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51507.        (((A or (B -> A)) -> (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51508
in-theory        51508
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     23
proof            (modus-ponens tm-316 tm-650 ((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51508.        (((A or (B -> A)) -> (C -> (D or C))) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-650, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-51509
in-theory        51509
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       131
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51509.        (((A or (B -> A)) -> (C -> (D or C))) and (E -> (F -> E))), M:tm-315, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51510
in-theory        51510
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (((A or (B -> A)) -> (not (C -> (D or C)))) -> (not (A or (B -> A)))))
theorem-size     31
proof            (modus-ponens tm-313 tm-650 ((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51510.        (((A or (B -> A)) -> (C -> (D or C))) and (((A or (B -> A)) -> (not (C -> (D or C)))) -> (not (A or (B -> A))))), M:tm-313, m:tm-650, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-51511
in-theory        51511
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (((C -> (D or C)) -> E) -> (((A or (B -> A)) or (C -> (D or C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-650 ((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51511.        (((A or (B -> A)) -> (C -> (D or C))) and (((C -> (D or C)) -> E) -> (((A or (B -> A)) or (C -> (D or C))) -> E))), M:tm-312, m:tm-650, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-51512
in-theory        51512
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (E or ((A or (B -> A)) -> (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51512.        (((A or (B -> A)) -> (C -> (D or C))) and (E or ((A or (B -> A)) -> (C -> (D or C))))), M:tm-311, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51513
in-theory        51513
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (((A or (B -> A)) -> (C -> (D or C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51513.        (((A or (B -> A)) -> (C -> (D or C))) and (((A or (B -> A)) -> (C -> (D or C))) or E)), M:tm-310, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51514
in-theory        51514
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (E -> (((A or (B -> A)) -> (C -> (D or C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51514.        (((A or (B -> A)) -> (C -> (D or C))) and (E -> (((A or (B -> A)) -> (C -> (D or C))) and E))), M:tm-309, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51515
in-theory        51515
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (D or C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-650 ((A (or Am (-> Bm Am))) (B Cm) (C (or Dm Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51515.        (((A or (B -> A)) -> (C -> (D or C))) and (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (D or C)))), M:tm-306, m:tm-650, u:((A (or Am (-> Bm Am))) (B Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-51516
in-theory        51516
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and (E -> ((A or (B -> A)) -> (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51516.        (((A or (B -> A)) -> (C -> (D or C))) and (E -> ((A or (B -> A)) -> (C -> (D or C))))), M:tm-305, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51517
in-theory        51517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51517.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-303, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51518
in-theory        51518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51518.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-270, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51519
in-theory        51519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51519.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-239, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51520
in-theory        51520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51520.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (G -> (H or G)))), M:tm-210, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51521
in-theory        51521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51521.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-183, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51522
in-theory        51522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51522.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-157, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51523
in-theory        51523
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51523.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-147, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51524
in-theory        51524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51524.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-134, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51525
in-theory        51525
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51525.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-125, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51526
in-theory        51526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51526.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (G -> (H or G)))), M:tm-113, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51527
in-theory        51527
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51527.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-105, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51528
in-theory        51528
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (A or (B -> A))))
theorem-size     13
proof            (modus-ponens tm-99 tm-650 ((Cm (or Am (-> Bm Am))) (A (or Am (-> Bm Am))) (B (or Dm (or Am (-> Bm Am))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51528.        ((A or (B -> A)) -> (C or (A or (B -> A)))), M:tm-99, m:tm-650, u:((Cm (or Am (-> Bm Am))) (A (or Am (-> Bm Am))) (B (or Dm (or Am (-> Bm Am)))))
================================================================
tm-name          tm-51529
in-theory        51529
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (D -> (A or (B -> A)))))
theorem-size     15
proof            (modus-ponens tm-98 tm-650 ((A (or Am (-> Bm Am))) (Cm (-> B (or Am (-> Bm Am)))) (C (or Dm (-> B (or Am (-> Bm Am)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51529.        ((A or (B -> A)) -> (C or (D -> (A or (B -> A))))), M:tm-98, m:tm-650, u:((A (or Am (-> Bm Am))) (Cm (-> B (or Am (-> Bm Am)))) (C (or Dm (-> B (or Am (-> Bm Am))))))
================================================================
tm-name          tm-51530
in-theory        51530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51530.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (E -> (F or E)))), M:tm-95, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51531
in-theory        51531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51531.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-83, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51532
in-theory        51532
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> (D -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51532.        (((not (not A)) -> A) and ((B or (C -> B)) -> (D -> (E or D)))), M:tm-76, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51533
in-theory        51533
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (C -> (D or C)))
theorem-size     19
proof            (modus-ponens tm-73 tm-650 ((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51533.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (C -> (D or C))), M:tm-73, m:tm-650, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-51534
in-theory        51534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51534.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (E -> (F or E)))), M:tm-69, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51535
in-theory        51535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51535.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-54, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51536
in-theory        51536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-50 tm-650 ((A Am) (B (-> Bm Am)) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51536.        (((A -> B) or (B or (A -> B))) -> (C -> (D or C))), M:tm-50, m:tm-650, u:((A Am) (B (-> Bm Am)) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-51537
in-theory        51537
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-49 tm-650 ((A Am) (B (-> Bm Am)) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51537.        ((A or (A or (B -> A))) -> (C -> (D or C))), M:tm-49, m:tm-650, u:((A Am) (B (-> Bm Am)) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-51538
in-theory        51538
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-47 tm-650 ((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51538.        (((A and (B or (C -> B))) or (B or (C -> B))) -> (D -> (E or D))), M:tm-47, m:tm-650, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-51539
in-theory        51539
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-46 tm-650 ((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51539.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> (D -> (E or D))), M:tm-46, m:tm-650, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-51540
in-theory        51540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51540.        ((A -> (B or A)) and ((C or (D -> C)) -> (E -> (F or E)))), M:tm-42, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51541
in-theory        51541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51541.        ((A -> (A or B)) and ((C or (D -> C)) -> (E -> (F or E)))), M:tm-32, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51542
in-theory        51542
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (D or C))))
theorem-size     17
proof            (modus-ponens tm-24 tm-650 ((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51542.        ((A or (B -> A)) -> ((A or (B -> A)) and (C -> (D or C)))), M:tm-24, m:tm-650, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-51543
in-theory        51543
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51543.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (E -> (F or E)))), M:tm-23, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51544
in-theory        51544
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51544.        (((A and B) -> B) and ((C or (D -> C)) -> (E -> (F or E)))), M:tm-22, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51545
in-theory        51545
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51545.        (((A and B) -> A) and ((C or (D -> C)) -> (E -> (F or E)))), M:tm-21, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51546
in-theory        51546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51546.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-20, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51547
in-theory        51547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-7)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51547.        ((A -> (B -> A)) and ((C or (D -> C)) -> (E -> (F or E)))), M:tm-19, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51548
in-theory        51548
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not (C -> (D or C)))) -> (not (A or (B -> A))))
theorem-size     19
proof            (modus-ponens tm-9 tm-650 ((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-9 tm-8 tm-1 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51548.        (((A or (B -> A)) -> (not (C -> (D or C)))) -> (not (A or (B -> A)))), M:tm-9, m:tm-650, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-51549
in-theory        51549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> (((D or (E -> D)) or (A -> (B or A))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-650 ((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51549.        (((A -> (B or A)) -> C) -> (((D or (E -> D)) or (A -> (B or A))) -> C)), M:tm-8, m:tm-650, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-51550
in-theory        51550
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-7 tm-8 tm-1)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51550.        (A or ((B or (C -> B)) -> (D -> (E or D)))), M:tm-7, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51551
in-theory        51551
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-6 tm-8 tm-1 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51551.        (((A or (B -> A)) -> (C -> (D or C))) or E), M:tm-6, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51552
in-theory        51552
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> (D -> (E or D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       81
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51552.        (A -> (((B or (C -> B)) -> (D -> (E or D))) and A)), M:tm-5, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51553
in-theory        51553
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-2 tm-650 ((A (or Am (-> Bm Am))) (B Cm) (C (or Dm Cm))))
axioms-used      (tm-2 tm-8 tm-1 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51553.        (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> (D or C))), M:tm-2, m:tm-650, u:((A (or Am (-> Bm Am))) (B Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-51554
in-theory        51554
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-1 tm-8 tm-7)
proof-size       77
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-51554.        (A -> ((B or (C -> B)) -> (D -> (E or D)))), M:tm-1, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51555
in-theory        51555
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> A)) -> (D or ((C or (B -> C)) -> A)))
theorem-size     17
proof            (modus-ponens tm-623 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51555.        ((A or ((B -> C) -> A)) -> (D or ((C or (B -> C)) -> A))), M:tm-623, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51556
in-theory        51556
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-622 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51556.        ((A -> (B -> (C or B))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-622, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51557
in-theory        51557
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51557.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (D -> (E or D))), M:tm-609, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51558
in-theory        51558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-605 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51558.        ((A -> ((B -> (C or B)) and A)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-605, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51559
in-theory        51559
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((D -> (E or D)) and ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-595 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51559.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((D -> (E or D)) and ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)))), M:tm-595, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51560
in-theory        51560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-550 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51560.        (((A -> (B or A)) or C) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-550, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51561
in-theory        51561
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-540 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51561.        ((A or (B -> (C or B))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-540, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51562
in-theory        51562
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-530 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51562.        ((A or (B -> (B or C))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-530, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51563
in-theory        51563
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-520 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51563.        ((A or (B -> (C -> (B and C)))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-520, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51564
in-theory        51564
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-510 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51564.        ((A or ((B and C) -> C)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-510, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51565
in-theory        51565
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-500 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51565.        ((A or ((B and C) -> B)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-500, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51566
in-theory        51566
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-490 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51566.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E))), M:tm-490, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51567
in-theory        51567
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-480 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51567.        ((A or (B -> (C -> B))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-480, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51568
in-theory        51568
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> A)) -> (((C or (B -> C)) -> A) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51568.        ((A or ((B -> C) -> A)) -> (((C or (B -> C)) -> A) or D)), M:tm-470, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51569
in-theory        51569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-469 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51569.        ((A -> (B -> (B or C))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-469, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51570
in-theory        51570
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51570.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (D -> (D or E))), M:tm-456, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51571
in-theory        51571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-453 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51571.        ((A -> ((B -> (B or C)) and A)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-453, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51572
in-theory        51572
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((D -> (D or E)) and ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-443 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51572.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((D -> (D or E)) and ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)))), M:tm-443, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51573
in-theory        51573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-409 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51573.        (((A -> (A or B)) or C) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-409, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51574
in-theory        51574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-400 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51574.        (((A -> (B -> (A and B))) or C) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-400, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51575
in-theory        51575
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-391 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51575.        ((((A and B) -> B) or C) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-391, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51576
in-theory        51576
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-382 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51576.        ((((A and B) -> A) or C) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-382, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51577
in-theory        51577
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-373 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51577.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E))), M:tm-373, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51578
in-theory        51578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-364 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51578.        (((A -> (B -> A)) or C) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-364, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51579
in-theory        51579
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> A)) -> (D -> (((C or (B -> C)) -> A) and D)))
theorem-size     19
proof            (modus-ponens tm-355 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51579.        ((A or ((B -> C) -> A)) -> (D -> (((C or (B -> C)) -> A) and D))), M:tm-355, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51580
in-theory        51580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-354 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51580.        ((A -> (B -> (C -> (B and C)))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-354, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51581
in-theory        51581
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51581.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51582
in-theory        51582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C)))
theorem-size     25
proof            (modus-ponens tm-338 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51582.        (((A -> B) -> (A -> (A and B))) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C))), M:tm-338, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51583
in-theory        51583
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((A or ((B -> C) -> A)) -> ((A or ((B -> C) -> A)) and ((C or (B -> C)) -> A))))
theorem-size     39
proof            (modus-ponens tm-328 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51583.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((A or ((B -> C) -> A)) -> ((A or ((B -> C) -> A)) and ((C or (B -> C)) -> A)))), M:tm-328, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51584
in-theory        51584
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((D -> (E -> (D and E))) and ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A))))
theorem-size     39
proof            (modus-ponens tm-327 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51584.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((D -> (E -> (D and E))) and ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)))), M:tm-327, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51585
in-theory        51585
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (((D and E) -> E) and ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-326 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51585.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (((D and E) -> E) and ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)))), M:tm-326, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51586
in-theory        51586
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (((D and E) -> D) and ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-325 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51586.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (((D and E) -> D) and ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)))), M:tm-325, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51587
in-theory        51587
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A))))
theorem-size     45
proof            (modus-ponens tm-324 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51587.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)))), M:tm-324, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51588
in-theory        51588
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((D -> (E -> D)) and ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A))))
theorem-size     37
proof            (modus-ponens tm-323 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51588.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((D -> (E -> D)) and ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)))), M:tm-323, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51589
in-theory        51589
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51589.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((D and E) -> E)), M:tm-322, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51590
in-theory        51590
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51590.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((D and E) -> D)), M:tm-320, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51591
in-theory        51591
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51591.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51592
in-theory        51592
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((A or ((B -> C) -> A)) -> (A or ((B -> C) -> A))))
theorem-size     31
proof            (modus-ponens tm-316 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51592.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((A or ((B -> C) -> A)) -> (A or ((B -> C) -> A)))), M:tm-316, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51593
in-theory        51593
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51593.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (D -> (E -> D))), M:tm-315, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51594
in-theory        51594
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (((A or ((B -> C) -> A)) -> (not ((C or (B -> C)) -> A))) -> (not (A or ((B -> C) -> A)))))
theorem-size     41
proof            (modus-ponens tm-313 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51594.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (((A or ((B -> C) -> A)) -> (not ((C or (B -> C)) -> A))) -> (not (A or ((B -> C) -> A))))), M:tm-313, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51595
in-theory        51595
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((((C or (B -> C)) -> A) -> D) -> (((A or ((B -> C) -> A)) or ((C or (B -> C)) -> A)) -> D)))
theorem-size     43
proof            (modus-ponens tm-312 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51595.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((((C or (B -> C)) -> A) -> D) -> (((A or ((B -> C) -> A)) or ((C or (B -> C)) -> A)) -> D))), M:tm-312, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51596
in-theory        51596
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (D or ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A))))
theorem-size     33
proof            (modus-ponens tm-311 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51596.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (D or ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)))), M:tm-311, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51597
in-theory        51597
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51597.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) or D)), M:tm-310, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51598
in-theory        51598
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (D -> (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51598.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (D -> (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and D))), M:tm-309, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51599
in-theory        51599
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (((A or ((B -> C) -> A)) -> (C or (B -> C))) -> ((A or ((B -> C) -> A)) -> A)))
theorem-size     39
proof            (modus-ponens tm-306 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (or Cm (-> Bm Cm))) (C Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51599.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (((A or ((B -> C) -> A)) -> (C or (B -> C))) -> ((A or ((B -> C) -> A)) -> A))), M:tm-306, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (or Cm (-> Bm Cm))) (C Am))
================================================================
tm-name          tm-51600
in-theory        51600
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (D -> ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A))))
theorem-size     33
proof            (modus-ponens tm-305 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51600.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and (D -> ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)))), M:tm-305, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51601
in-theory        51601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     27
proof            (modus-ponens tm-303 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51601.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-303, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51602
in-theory        51602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-270 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51602.        ((A -> (((B and C) -> C) and A)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-270, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51603
in-theory        51603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-239 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51603.        ((A -> (((B and C) -> B) and A)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-239, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51604
in-theory        51604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E)))
theorem-size     33
proof            (modus-ponens tm-210 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51604.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E))), M:tm-210, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51605
in-theory        51605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     25
proof            (modus-ponens tm-183 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51605.        ((A -> ((B -> (C -> B)) and A)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-183, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51606
in-theory        51606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-157 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51606.        ((A -> ((B and C) -> C)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-157, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51607
in-theory        51607
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     31
proof            (modus-ponens tm-147 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51607.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-147, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51608
in-theory        51608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-134 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51608.        ((A -> ((B and C) -> B)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-134, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51609
in-theory        51609
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     31
proof            (modus-ponens tm-125 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51609.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-125, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51610
in-theory        51610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((C -> D) -> (A -> B))) -> (((D or (C -> D)) -> A) -> ((D or (C -> D)) -> B)))
theorem-size     27
proof            (modus-ponens tm-114 tm-651 ((A (or (-> C D) (-> (-> Bm Cm) (-> C D)))) (B (or Cm (-> Bm Cm))) (Am (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51610.        (((A -> B) or ((C -> D) -> (A -> B))) -> (((D or (C -> D)) -> A) -> ((D or (C -> D)) -> B))), M:tm-114, m:tm-651, u:((A (or (-> C D) (-> (-> Bm Cm) (-> C D)))) (B (or Cm (-> Bm Cm))) (Am (-> C D)))
================================================================
tm-name          tm-51611
in-theory        51611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E)))
theorem-size     31
proof            (modus-ponens tm-113 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51611.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E))), M:tm-113, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51612
in-theory        51612
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     35
proof            (modus-ponens tm-105 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51612.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-105, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51613
in-theory        51613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C)))
theorem-size     23
proof            (modus-ponens tm-95 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51613.        (((A -> B) -> (A -> A)) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C))), M:tm-95, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51614
in-theory        51614
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> A)) -> (D -> ((C or (B -> C)) -> A)))
theorem-size     17
proof            (modus-ponens tm-84 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51614.        ((A or ((B -> C) -> A)) -> (D -> ((C or (B -> C)) -> A))), M:tm-84, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51615
in-theory        51615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     23
proof            (modus-ponens tm-83 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51615.        ((A -> (B -> (C -> B))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-83, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51616
in-theory        51616
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or ((C -> D) -> B)) -> ((D or (C -> D)) -> B)))
theorem-size     21
proof            (modus-ponens tm-76 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51616.        (((not (not A)) -> A) and ((B or ((C -> D) -> B)) -> ((D or (C -> D)) -> B))), M:tm-76, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51617
in-theory        51617
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or ((B -> C) -> A)))) or (A or ((B -> C) -> A))) -> ((C or (B -> C)) -> A))
theorem-size     25
proof            (modus-ponens tm-73 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-8 tm-10 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51617.        (((not (not (A or ((B -> C) -> A)))) or (A or ((B -> C) -> A))) -> ((C or (B -> C)) -> A)), M:tm-73, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51618
in-theory        51618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C)))
theorem-size     27
proof            (modus-ponens tm-69 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51618.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C))), M:tm-69, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51619
in-theory        51619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-54 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51619.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-54, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51620
in-theory        51620
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or (C or ((A -> B) -> C))) -> ((B or (A -> B)) -> C))
theorem-size     21
proof            (modus-ponens tm-50 tm-651 ((A Am) (B (-> (-> Bm Cm) Am)) (C (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51620.        ((((A -> B) -> C) or (C or ((A -> B) -> C))) -> ((B or (A -> B)) -> C)), M:tm-50, m:tm-651, u:((A Am) (B (-> (-> Bm Cm) Am)) (C (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51621
in-theory        51621
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or ((B -> C) -> A))) -> ((C or (B -> C)) -> A))
theorem-size     17
proof            (modus-ponens tm-49 tm-651 ((A Am) (B (-> (-> Bm Cm) Am)) (C (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51621.        ((A or (A or ((B -> C) -> A))) -> ((C or (B -> C)) -> A)), M:tm-49, m:tm-651, u:((A Am) (B (-> (-> Bm Cm) Am)) (C (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51622
in-theory        51622
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or ((C -> D) -> B))) or (B or ((C -> D) -> B))) -> ((D or (C -> D)) -> B))
theorem-size     25
proof            (modus-ponens tm-47 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51622.        (((A and (B or ((C -> D) -> B))) or (B or ((C -> D) -> B))) -> ((D or (C -> D)) -> B)), M:tm-47, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51623
in-theory        51623
times-derived    1
----------------------------------------------------------------
theorem          ((((A or ((B -> C) -> A)) and D) or (A or ((B -> C) -> A))) -> ((C or (B -> C)) -> A))
theorem-size     25
proof            (modus-ponens tm-46 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51623.        ((((A or ((B -> C) -> A)) and D) or (A or ((B -> C) -> A))) -> ((C or (B -> C)) -> A)), M:tm-46, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51624
in-theory        51624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-42 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51624.        ((A -> (B or A)) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C))), M:tm-42, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51625
in-theory        51625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-32 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51625.        ((A -> (A or B)) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C))), M:tm-32, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51626
in-theory        51626
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> A)) -> ((A or ((B -> C) -> A)) and ((C or (B -> C)) -> A)))
theorem-size     23
proof            (modus-ponens tm-24 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51626.        ((A or ((B -> C) -> A)) -> ((A or ((B -> C) -> A)) and ((C or (B -> C)) -> A))), M:tm-24, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51627
in-theory        51627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C)))
theorem-size     23
proof            (modus-ponens tm-23 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51627.        ((A -> (B -> (A and B))) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C))), M:tm-23, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51628
in-theory        51628
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-22 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51628.        (((A and B) -> B) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C))), M:tm-22, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51629
in-theory        51629
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-21 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51629.        (((A and B) -> A) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C))), M:tm-21, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51630
in-theory        51630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-20 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51630.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-20, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51631
in-theory        51631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C)))
theorem-size     21
proof            (modus-ponens tm-19 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51631.        ((A -> (B -> A)) and ((C or ((D -> E) -> C)) -> ((E or (D -> E)) -> C))), M:tm-19, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51632
in-theory        51632
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> A)) -> (A or ((B -> C) -> A)))
theorem-size     15
proof            (modus-ponens tm-12 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51632.        ((A or ((B -> C) -> A)) -> (A or ((B -> C) -> A))), M:tm-12, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51633
in-theory        51633
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> (not ((C or (B -> C)) -> A))) -> (not (A or ((B -> C) -> A))))
theorem-size     25
proof            (modus-ponens tm-9 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-9 tm-8 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51633.        (((A or ((B -> C) -> A)) -> (not ((C or (B -> C)) -> A))) -> (not (A or ((B -> C) -> A)))), M:tm-9, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51634
in-theory        51634
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> D) -> (((C or ((B -> A) -> C)) or ((A or (B -> A)) -> C)) -> D))
theorem-size     27
proof            (modus-ponens tm-8 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-8 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51634.        ((((A or (B -> A)) -> C) -> D) -> (((C or ((B -> A) -> C)) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-51635
in-theory        51635
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or ((C -> D) -> B)) -> ((D or (C -> D)) -> B)))
theorem-size     17
proof            (modus-ponens tm-7 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-7 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51635.        (A or ((B or ((C -> D) -> B)) -> ((D or (C -> D)) -> B))), M:tm-7, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51636
in-theory        51636
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-6 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51636.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) or D), M:tm-6, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51637
in-theory        51637
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or ((C -> D) -> B)) -> ((D or (C -> D)) -> B)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51637.        (A -> (((B or ((C -> D) -> B)) -> ((D or (C -> D)) -> B)) and A)), M:tm-5, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51638
in-theory        51638
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> (C or (B -> C))) -> ((A or ((B -> C) -> A)) -> A))
theorem-size     23
proof            (modus-ponens tm-2 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (or Cm (-> Bm Cm))) (C Am)))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51638.        (((A or ((B -> C) -> A)) -> (C or (B -> C))) -> ((A or ((B -> C) -> A)) -> A)), M:tm-2, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (or Cm (-> Bm Cm))) (C Am))
================================================================
tm-name          tm-51639
in-theory        51639
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> D) -> B)) -> ((D or (C -> D)) -> B)))
theorem-size     17
proof            (modus-ponens tm-1 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-51639.        (A -> ((B or ((C -> D) -> B)) -> ((D or (C -> D)) -> B))), M:tm-1, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-51640
in-theory        51640
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51640.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-622, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51641
in-theory        51641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51641.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51642
in-theory        51642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51642.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-605, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51643
in-theory        51643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G or F)) and ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51643.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G or F)) and ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-595, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51644
in-theory        51644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51644.        (((A -> (B or A)) or C) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-550, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51645
in-theory        51645
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51645.        ((A or (B -> (C or B))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-540, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51646
in-theory        51646
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51646.        ((A or (B -> (B or C))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-530, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51647
in-theory        51647
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51647.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-520, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51648
in-theory        51648
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51648.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-510, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51649
in-theory        51649
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51649.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-500, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51650
in-theory        51650
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51650.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-490, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51651
in-theory        51651
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51651.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-480, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51652
in-theory        51652
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51652.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-469, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51653
in-theory        51653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51653.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51654
in-theory        51654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51654.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-453, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51655
in-theory        51655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (F or G)) and ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51655.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (F or G)) and ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-443, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51656
in-theory        51656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51656.        (((A -> (A or B)) or C) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-409, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51657
in-theory        51657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51657.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-400, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51658
in-theory        51658
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51658.        ((((A and B) -> B) or C) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-391, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51659
in-theory        51659
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51659.        ((((A and B) -> A) or C) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-382, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51660
in-theory        51660
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51660.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-373, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51661
in-theory        51661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51661.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-364, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51662
in-theory        51662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51662.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-354, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51663
in-theory        51663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51663.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51664
in-theory        51664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51664.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-338, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51665
in-theory        51665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51665.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-327, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51666
in-theory        51666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> G) and ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51666.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> G) and ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-326, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51667
in-theory        51667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> F) and ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51667.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> F) and ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-325, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51668
in-theory        51668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51668.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-324, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51669
in-theory        51669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51669.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> F)) and ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-323, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51670
in-theory        51670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51670.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51671
in-theory        51671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51671.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51672
in-theory        51672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51672.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51673
in-theory        51673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51673.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51674
in-theory        51674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F or ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51674.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F or ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-311, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51675
in-theory        51675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51675.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F)), M:tm-310, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51676
in-theory        51676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51676.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and F))), M:tm-309, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51677
in-theory        51677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-652 ((A (-> Am (or Bm Am))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51677.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-308, m:tm-652, u:((A (-> Am (or Bm Am))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))
================================================================
tm-name          tm-51678
in-theory        51678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (A -> (B or A)))
theorem-size     25
proof            (modus-ponens tm-307 tm-652 ((A (-> Am (or Bm Am))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51678.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (A -> (B or A))), M:tm-307, m:tm-652, u:((A (-> Am (or Bm Am))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))
================================================================
tm-name          tm-51679
in-theory        51679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51679.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-305, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51680
in-theory        51680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51680.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-303, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51681
in-theory        51681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51681.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-270, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51682
in-theory        51682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51682.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-239, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51683
in-theory        51683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51683.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-210, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51684
in-theory        51684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51684.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-183, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51685
in-theory        51685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51685.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-157, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51686
in-theory        51686
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51686.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-147, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51687
in-theory        51687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51687.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-134, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51688
in-theory        51688
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51688.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-125, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51689
in-theory        51689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51689.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-113, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51690
in-theory        51690
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51690.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-105, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51691
in-theory        51691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51691.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-95, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51692
in-theory        51692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51692.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-83, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51693
in-theory        51693
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51693.        (((not (not A)) -> A) and ((B -> (C or B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-76, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51694
in-theory        51694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51694.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-69, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51695
in-theory        51695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51695.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-54, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51696
in-theory        51696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51696.        ((A -> (B or A)) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-42, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51697
in-theory        51697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51697.        ((A -> (A or B)) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-32, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51698
in-theory        51698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51698.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-23, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51699
in-theory        51699
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51699.        (((A and B) -> B) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-22, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51700
in-theory        51700
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51700.        (((A and B) -> A) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-21, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51701
in-theory        51701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51701.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-20, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51702
in-theory        51702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51702.        ((A -> (B -> A)) and ((C -> (D or C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-19, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51703
in-theory        51703
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-7 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-8 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51703.        (A or ((B -> (C or B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-7, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51704
in-theory        51704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-7 tm-8 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51704.        (((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F), M:tm-6, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51705
in-theory        51705
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51705.        (A -> (((B -> (C or B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and A)), M:tm-5, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51706
in-theory        51706
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-1 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-7 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51706.        (A -> ((B -> (C or B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-1, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51707
in-theory        51707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51707.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-622, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51708
in-theory        51708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51708.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51709
in-theory        51709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51709.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-605, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51710
in-theory        51710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G or F)) and ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51710.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G or F)) and ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-595, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51711
in-theory        51711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51711.        (((A -> (B or A)) or C) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-550, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51712
in-theory        51712
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51712.        ((A or (B -> (C or B))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-540, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51713
in-theory        51713
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51713.        ((A or (B -> (B or C))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-530, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51714
in-theory        51714
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51714.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-520, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51715
in-theory        51715
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51715.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-510, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51716
in-theory        51716
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51716.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-500, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51717
in-theory        51717
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51717.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-490, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51718
in-theory        51718
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51718.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-480, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51719
in-theory        51719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51719.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-469, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51720
in-theory        51720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51720.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51721
in-theory        51721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51721.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-453, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51722
in-theory        51722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (F or G)) and ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51722.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (F or G)) and ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-443, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51723
in-theory        51723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51723.        (((A -> (A or B)) or C) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-409, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51724
in-theory        51724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51724.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-400, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51725
in-theory        51725
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51725.        ((((A and B) -> B) or C) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-391, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51726
in-theory        51726
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51726.        ((((A and B) -> A) or C) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-382, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51727
in-theory        51727
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51727.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-373, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51728
in-theory        51728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51728.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-364, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51729
in-theory        51729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51729.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-354, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51730
in-theory        51730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51730.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51731
in-theory        51731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51731.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-338, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51732
in-theory        51732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51732.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-327, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51733
in-theory        51733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> G) and ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51733.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> G) and ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-326, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51734
in-theory        51734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> F) and ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51734.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> F) and ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-325, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51735
in-theory        51735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51735.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-324, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51736
in-theory        51736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51736.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> F)) and ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-323, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51737
in-theory        51737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51737.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51738
in-theory        51738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51738.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51739
in-theory        51739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51739.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51740
in-theory        51740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51740.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51741
in-theory        51741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F or ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51741.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F or ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-311, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51742
in-theory        51742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51742.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F)), M:tm-310, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51743
in-theory        51743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51743.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and F))), M:tm-309, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51744
in-theory        51744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-653 ((A (-> Am (or Am Bm))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51744.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-308, m:tm-653, u:((A (-> Am (or Am Bm))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))
================================================================
tm-name          tm-51745
in-theory        51745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (A -> (A or B)))
theorem-size     25
proof            (modus-ponens tm-307 tm-653 ((A (-> Am (or Am Bm))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51745.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (A -> (A or B))), M:tm-307, m:tm-653, u:((A (-> Am (or Am Bm))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))
================================================================
tm-name          tm-51746
in-theory        51746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51746.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-305, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51747
in-theory        51747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51747.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-303, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51748
in-theory        51748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51748.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-270, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51749
in-theory        51749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51749.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-239, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51750
in-theory        51750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51750.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-210, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51751
in-theory        51751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51751.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-183, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51752
in-theory        51752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51752.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-157, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51753
in-theory        51753
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51753.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-147, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51754
in-theory        51754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51754.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-134, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51755
in-theory        51755
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51755.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-125, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51756
in-theory        51756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51756.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-113, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51757
in-theory        51757
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51757.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-105, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51758
in-theory        51758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51758.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-95, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51759
in-theory        51759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51759.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-83, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51760
in-theory        51760
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51760.        (((not (not A)) -> A) and ((B -> (B or C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-76, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51761
in-theory        51761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-6 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51761.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-69, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51762
in-theory        51762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51762.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-54, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51763
in-theory        51763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51763.        ((A -> (B or A)) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-42, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51764
in-theory        51764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51764.        ((A -> (A or B)) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-32, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51765
in-theory        51765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51765.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-23, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51766
in-theory        51766
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51766.        (((A and B) -> B) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-22, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51767
in-theory        51767
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51767.        (((A and B) -> A) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-21, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51768
in-theory        51768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51768.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-20, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51769
in-theory        51769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51769.        ((A -> (B -> A)) and ((C -> (C or D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-19, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51770
in-theory        51770
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-7 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-6 tm-8 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51770.        (A or ((B -> (B or C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-7, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51771
in-theory        51771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-8 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51771.        (((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F), M:tm-6, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51772
in-theory        51772
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51772.        (A -> (((B -> (B or C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and A)), M:tm-5, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51773
in-theory        51773
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-1 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-6 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51773.        (A -> ((B -> (B or C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-1, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-51774
in-theory        51774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> (A -> B))) and ((B or (A -> B)) -> (C -> (A -> B))))
theorem-size     21
proof            (modus-ponens tm-654 tm-1 ((Am (-> A B)) (C (-> Bm (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51774.        (((A -> B) -> (C -> (A -> B))) and ((B or (A -> B)) -> (C -> (A -> B)))), M:tm-654, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
================================================================
tm-name          tm-51775
in-theory        51775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((B -> C) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-654 tm-2 ((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51775.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((B -> C) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))), M:tm-654, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-51776
in-theory        51776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> ((A -> B) and C))) and ((B or (A -> B)) -> (C -> ((A -> B) and C))))
theorem-size     25
proof            (modus-ponens tm-654 tm-5 ((Am (-> A B)) (C (-> Bm (and (-> A B) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51776.        (((A -> B) -> (C -> ((A -> B) and C))) and ((B or (A -> B)) -> (C -> ((A -> B) and C)))), M:tm-654, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
================================================================
tm-name          tm-51777
in-theory        51777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) or C)) and ((B or (A -> B)) -> ((A -> B) or C)))
theorem-size     21
proof            (modus-ponens tm-654 tm-6 ((Am (-> A B)) (C (or (-> A B) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-51777.        (((A -> B) -> ((A -> B) or C)) and ((B or (A -> B)) -> ((A -> B) or C))), M:tm-654, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
================================================================
tm-name          tm-51778
in-theory        51778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C or (A -> B))) and ((B or (A -> B)) -> (C or (A -> B))))
theorem-size     21
proof            (modus-ponens tm-654 tm-7 ((Am (-> A B)) (C (or Bm (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-51778.        (((A -> B) -> (C or (A -> B))) and ((B or (A -> B)) -> (C or (A -> B)))), M:tm-654, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
================================================================
tm-name          tm-51779
in-theory        51779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((B or (A -> B)) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-654 tm-8 ((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51779.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((B or (A -> B)) -> ((B -> C) -> ((A or B) -> C)))), M:tm-654, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-51780
in-theory        51780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((B or (A -> B)) -> ((A -> (not B)) -> (not A))))
theorem-size     25
proof            (modus-ponens tm-654 tm-9 ((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-51780.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((B or (A -> B)) -> ((A -> (not B)) -> (not A)))), M:tm-654, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-51781
in-theory        51781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> (D -> C))) and ((B or (A -> B)) -> (C -> (D -> C))))
theorem-size     21
proof            (modus-ponens tm-654 tm-11 ((Am (-> A B)) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-51781.        (((A -> B) -> (C -> (D -> C))) and ((B or (A -> B)) -> (C -> (D -> C)))), M:tm-654, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-51782
in-theory        51782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((B or (A -> B)) -> (A -> A)))
theorem-size     17
proof            (modus-ponens tm-654 tm-12 ((A Am) (B Bm) (C (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-51782.        (((A -> B) -> (A -> A)) and ((B or (A -> B)) -> (A -> A))), M:tm-654, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
================================================================
tm-name          tm-51783
in-theory        51783
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-654 tm-13 ((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-51783.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-654, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-51784
in-theory        51784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((B or (A -> B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     37
proof            (modus-ponens tm-654 tm-14 ((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-51784.        (((A -> B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((B or (A -> B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-654, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-51785
in-theory        51785
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))
theorem-size     33
proof            (modus-ponens tm-654 tm-15 ((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-51785.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))), M:tm-654, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-51786
in-theory        51786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C and D) -> C)) and ((B or (A -> B)) -> ((C and D) -> C)))
theorem-size     21
proof            (modus-ponens tm-654 tm-16 ((Am (-> A B)) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-51786.        (((A -> B) -> ((C and D) -> C)) and ((B or (A -> B)) -> ((C and D) -> C))), M:tm-654, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-51787
in-theory        51787
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((B or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-654 tm-17 ((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-51787.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((B or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))), M:tm-654, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-51788
in-theory        51788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C and D) -> D)) and ((B or (A -> B)) -> ((C and D) -> D)))
theorem-size     21
proof            (modus-ponens tm-654 tm-18 ((Am (-> A B)) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-51788.        (((A -> B) -> ((C and D) -> D)) and ((B or (A -> B)) -> ((C and D) -> D))), M:tm-654, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-51789
in-theory        51789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (D -> C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> (D -> C)) and (A -> B))))
theorem-size     29
proof            (modus-ponens tm-654 tm-19 ((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-51789.        (((A -> B) -> ((C -> (D -> C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> (D -> C)) and (A -> B)))), M:tm-654, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
================================================================
tm-name          tm-51790
in-theory        51790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> B))) and ((B or (A -> B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> B))))
theorem-size     45
proof            (modus-ponens tm-654 tm-20 ((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-51790.        (((A -> B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> B))) and ((B or (A -> B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> B)))), M:tm-654, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
================================================================
tm-name          tm-51791
in-theory        51791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and D) -> C) and (A -> B))) and ((B or (A -> B)) -> (((C and D) -> C) and (A -> B))))
theorem-size     29
proof            (modus-ponens tm-654 tm-21 ((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-51791.        (((A -> B) -> (((C and D) -> C) and (A -> B))) and ((B or (A -> B)) -> (((C and D) -> C) and (A -> B)))), M:tm-654, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
================================================================
tm-name          tm-51792
in-theory        51792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and D) -> D) and (A -> B))) and ((B or (A -> B)) -> (((C and D) -> D) and (A -> B))))
theorem-size     29
proof            (modus-ponens tm-654 tm-22 ((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-51792.        (((A -> B) -> (((C and D) -> D) and (A -> B))) and ((B or (A -> B)) -> (((C and D) -> D) and (A -> B)))), M:tm-654, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
================================================================
tm-name          tm-51793
in-theory        51793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (D -> (C and D))) and (A -> B))) and ((B or (A -> B)) -> ((C -> (D -> (C and D))) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-23 ((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-51793.        (((A -> B) -> ((C -> (D -> (C and D))) and (A -> B))) and ((B or (A -> B)) -> ((C -> (D -> (C and D))) and (A -> B)))), M:tm-654, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
================================================================
tm-name          tm-51794
in-theory        51794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((B or (A -> B)) -> (A -> (A and B))))
theorem-size     21
proof            (modus-ponens tm-654 tm-24 ((A Am) (B Bm) (C (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51794.        (((A -> B) -> (A -> (A and B))) and ((B or (A -> B)) -> (A -> (A and B)))), M:tm-654, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
================================================================
tm-name          tm-51795
in-theory        51795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> (D -> (C and D)))) and ((B or (A -> B)) -> (C -> (D -> (C and D)))))
theorem-size     25
proof            (modus-ponens tm-654 tm-25 ((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-51795.        (((A -> B) -> (C -> (D -> (C and D)))) and ((B or (A -> B)) -> (C -> (D -> (C and D))))), M:tm-654, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-51796
in-theory        51796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (C or D)) and (A -> B))) and ((B or (A -> B)) -> ((C -> (C or D)) and (A -> B))))
theorem-size     29
proof            (modus-ponens tm-654 tm-32 ((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-51796.        (((A -> B) -> ((C -> (C or D)) and (A -> B))) and ((B or (A -> B)) -> ((C -> (C or D)) and (A -> B)))), M:tm-654, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
================================================================
tm-name          tm-51797
in-theory        51797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> (C or D))) and ((B or (A -> B)) -> (C -> (C or D))))
theorem-size     21
proof            (modus-ponens tm-654 tm-33 ((Am (-> A B)) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-51797.        (((A -> B) -> (C -> (C or D))) and ((B or (A -> B)) -> (C -> (C or D)))), M:tm-654, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-51798
in-theory        51798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (D or C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> (D or C)) and (A -> B))))
theorem-size     29
proof            (modus-ponens tm-654 tm-42 ((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-51798.        (((A -> B) -> ((C -> (D or C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> (D or C)) and (A -> B)))), M:tm-654, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
================================================================
tm-name          tm-51799
in-theory        51799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> (D or C))) and ((B or (A -> B)) -> (C -> (D or C))))
theorem-size     21
proof            (modus-ponens tm-654 tm-43 ((Am (-> A B)) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-51799.        (((A -> B) -> (C -> (D or C))) and ((B or (A -> B)) -> (C -> (D or C)))), M:tm-654, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-51800
in-theory        51800
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((C or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-654 tm-44 ((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51800.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((C or ((A -> B) -> C)) -> ((B or (A -> B)) -> C))), M:tm-654, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-51801
in-theory        51801
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((D or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     53
proof            (modus-ponens tm-654 tm-45 ((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-51801.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((D or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-654, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-51802
in-theory        51802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((B or (A -> B)) -> (((A and C) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-654 tm-46 ((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-51802.        (((A -> B) -> (((A and C) or A) -> B)) and ((B or (A -> B)) -> (((A and C) or A) -> B))), M:tm-654, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-51803
in-theory        51803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((B or (A -> B)) -> (((C and A) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-654 tm-47 ((A Am) (B Bm) (C (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-51803.        (((A -> B) -> (((C and A) or A) -> B)) and ((B or (A -> B)) -> (((C and A) or A) -> B))), M:tm-654, m:tm-47, u:((A Am) (B Bm) (C (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-51804
in-theory        51804
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((C or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-654 tm-48 ((A (-> Am (and Bm Am))) (B Cm) (C (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-51804.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and ((C or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C))), M:tm-654, m:tm-48, u:((A (-> Am (and Bm Am))) (B Cm) (C (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-51805
in-theory        51805
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((C or ((A or B) -> C)) -> ((A or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-654 tm-49 ((A (or Am Bm)) (B Cm) (C (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-51805.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and ((C or ((A or B) -> C)) -> ((A or (A or B)) -> C))), M:tm-654, m:tm-49, u:((A (or Am Bm)) (B Cm) (C (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-51806
in-theory        51806
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((C or ((A or B) -> C)) -> ((B or (A or B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-654 tm-50 ((A (or Am Bm)) (B Cm) (C (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-51806.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and ((C or ((A or B) -> C)) -> ((B or (A or B)) -> C))), M:tm-654, m:tm-50, u:((A (or Am Bm)) (B Cm) (C (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-51807
in-theory        51807
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((D or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     57
proof            (modus-ponens tm-654 tm-51 ((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B Dm) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-51807.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((D or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-654, m:tm-51, u:((A (-> (-> Am Bm) (-> (or Cm Am) Bm))) (B Dm) (C (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-51808
in-theory        51808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> B))) and ((B or (A -> B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> B))))
theorem-size     45
proof            (modus-ponens tm-654 tm-54 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-51808.        (((A -> B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> B))) and ((B or (A -> B)) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> B)))), M:tm-654, m:tm-54, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A B))))
================================================================
tm-name          tm-51809
in-theory        51809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((B -> C) or ((A -> B) -> (B -> C))) -> ((A -> B) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-654 tm-55 ((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-51809.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((B -> C) or ((A -> B) -> (B -> C))) -> ((A -> B) -> ((A or B) -> C)))), M:tm-654, m:tm-55, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-51810
in-theory        51810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((B or (A -> B)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))))
theorem-size     37
proof            (modus-ponens tm-654 tm-56 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-51810.        (((A -> B) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))) and ((B or (A -> B)) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))), M:tm-654, m:tm-56, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-51811
in-theory        51811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and (((not (B -> A)) or (A -> (not (B -> A)))) -> (not A)))
theorem-size     24
proof            (modus-ponens tm-654 tm-57 ((A Am) (B (not (-> Bm Am))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-51811.        (((A -> (not (B -> A))) -> (not A)) and (((not (B -> A)) or (A -> (not (B -> A)))) -> (not A))), M:tm-654, m:tm-57, u:((A Am) (B (not (-> Bm Am))) (C (not Am)))
================================================================
tm-name          tm-51812
in-theory        51812
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((not ((A -> B) -> (A -> C))) or ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C)))))
theorem-size     52
proof            (modus-ponens tm-654 tm-58 ((A (-> Am (-> Bm Cm))) (B (not (-> (-> Am Bm) (-> Am Cm)))) (C (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       176
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-51812.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((not ((A -> B) -> (A -> C))) or ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C))))), M:tm-654, m:tm-58, u:((A (-> Am (-> Bm Cm))) (B (not (-> (-> Am Bm) (-> Am Cm)))) (C (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-51813
in-theory        51813
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (((not A) or ((A and B) -> (not A))) -> (not (A and B))))
theorem-size     26
proof            (modus-ponens tm-654 tm-59 ((A (and Am Bm)) (B (not Am)) (C (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-3)
proof-size       132
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-51813.        ((((A and B) -> (not A)) -> (not (A and B))) and (((not A) or ((A and B) -> (not A))) -> (not (A and B)))), M:tm-654, m:tm-59, u:((A (and Am Bm)) (B (not Am)) (C (not (and Am Bm))))
================================================================
tm-name          tm-51814
in-theory        51814
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (((not B) or ((A and B) -> (not B))) -> (not (A and B))))
theorem-size     26
proof            (modus-ponens tm-654 tm-60 ((A (and Am Bm)) (B (not Bm)) (C (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-4)
proof-size       132
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-51814.        ((((A and B) -> (not B)) -> (not (A and B))) and (((not B) or ((A and B) -> (not B))) -> (not (A and B)))), M:tm-654, m:tm-60, u:((A (and Am Bm)) (B (not Bm)) (C (not (and Am Bm))))
================================================================
tm-name          tm-51815
in-theory        51815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and (((not (B -> (A and B))) or (A -> (not (B -> (A and B))))) -> (not A)))
theorem-size     30
proof            (modus-ponens tm-654 tm-61 ((A Am) (B (not (-> Bm (and Am Bm)))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       138
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-51815.        (((A -> (not (B -> (A and B)))) -> (not A)) and (((not (B -> (A and B))) or (A -> (not (B -> (A and B))))) -> (not A))), M:tm-654, m:tm-61, u:((A Am) (B (not (-> Bm (and Am Bm)))) (C (not Am)))
================================================================
tm-name          tm-51816
in-theory        51816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and (((not (A or B)) or (A -> (not (A or B)))) -> (not A)))
theorem-size     24
proof            (modus-ponens tm-654 tm-62 ((A Am) (B (not (or Am Bm))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-6)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-51816.        (((A -> (not (A or B))) -> (not A)) and (((not (A or B)) or (A -> (not (A or B)))) -> (not A))), M:tm-654, m:tm-62, u:((A Am) (B (not (or Am Bm))) (C (not Am)))
================================================================
tm-name          tm-51817
in-theory        51817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and (((not (B or A)) or (A -> (not (B or A)))) -> (not A)))
theorem-size     24
proof            (modus-ponens tm-654 tm-63 ((A Am) (B (not (or Bm Am))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-7)
proof-size       128
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-51817.        (((A -> (not (B or A))) -> (not A)) and (((not (B or A)) or (A -> (not (B or A)))) -> (not A))), M:tm-654, m:tm-63, u:((A Am) (B (not (or Bm Am))) (C (not Am)))
================================================================
tm-name          tm-51818
in-theory        51818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((not ((B -> C) -> ((A or B) -> C))) or ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))) -> (not (A -> B))))
theorem-size     50
proof            (modus-ponens tm-654 tm-64 ((A (-> Am Bm)) (B (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (C (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       172
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-51818.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((not ((B -> C) -> ((A or B) -> C))) or ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))) -> (not (A -> B)))), M:tm-654, m:tm-64, u:((A (-> Am Bm)) (B (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (C (not (-> Am Bm))))
================================================================
tm-name          tm-51819
in-theory        51819
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((not ((A -> (not B)) -> (not A))) or ((A -> B) -> (not ((A -> (not B)) -> (not A))))) -> (not (A -> B))))
theorem-size     44
proof            (modus-ponens tm-654 tm-65 ((A (-> Am Bm)) (B (not (-> (-> Am (not Bm)) (not Am)))) (C (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       162
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-51819.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((not ((A -> (not B)) -> (not A))) or ((A -> B) -> (not ((A -> (not B)) -> (not A))))) -> (not (A -> B)))), M:tm-654, m:tm-65, u:((A (-> Am Bm)) (B (not (-> (-> Am (not Bm)) (not Am)))) (C (not (-> Am Bm))))
================================================================
tm-name          tm-51820
in-theory        51820
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((C or (((A -> (not B)) -> (not A)) -> C)) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))
theorem-size     49
proof            (modus-ponens tm-654 tm-66 ((A (-> (-> Am (not Bm)) (not Am))) (B Cm) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-51820.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((C or (((A -> (not B)) -> (not A)) -> C)) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))), M:tm-654, m:tm-66, u:((A (-> (-> Am (not Bm)) (not Am))) (B Cm) (C (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-51821
in-theory        51821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> B))) and ((B or (A -> B)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> B))))
theorem-size     41
proof            (modus-ponens tm-654 tm-69 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-51821.        (((A -> B) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> B))) and ((B or (A -> B)) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> B)))), M:tm-654, m:tm-69, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A B))))
================================================================
tm-name          tm-51822
in-theory        51822
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((A -> (not B)) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A))))
theorem-size     36
proof            (modus-ponens tm-654 tm-70 ((A (-> Am Bm)) (B (-> Am (not Bm))) (C (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-51822.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((A -> (not B)) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A)))), M:tm-654, m:tm-70, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-51823
in-theory        51823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((B or (A -> B)) -> ((C -> D) -> ((C -> (not D)) -> (not C)))))
theorem-size     33
proof            (modus-ponens tm-654 tm-71 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-51823.        (((A -> B) -> ((C -> D) -> ((C -> (not D)) -> (not C)))) and ((B or (A -> B)) -> ((C -> D) -> ((C -> (not D)) -> (not C))))), M:tm-654, m:tm-71, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-51824
in-theory        51824
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((not A) or ((not (not A)) -> (not A))) -> (not (not (not A)))))
theorem-size     26
proof            (modus-ponens tm-654 tm-72 ((A (not (not Am))) (B (not Am)) (C (not (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-10)
proof-size       132
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-51824.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((not A) or ((not (not A)) -> (not A))) -> (not (not (not A))))), M:tm-654, m:tm-72, u:((A (not (not Am))) (B (not Am)) (C (not (not (not Am)))))
================================================================
tm-name          tm-51825
in-theory        51825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and ((B or (A -> B)) -> (((not (not A)) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-654 tm-73 ((A Am) (B Bm) (C (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-10)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-51825.        (((A -> B) -> (((not (not A)) or A) -> B)) and ((B or (A -> B)) -> (((not (not A)) or A) -> B))), M:tm-654, m:tm-73, u:((A Am) (B Bm) (C (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-51826
in-theory        51826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not C)) -> C) and (A -> B))) and ((B or (A -> B)) -> (((not (not C)) -> C) and (A -> B))))
theorem-size     29
proof            (modus-ponens tm-654 tm-76 ((Am (-> A B)) (C (and (-> (not (not Bm)) Bm) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-10)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-51826.        (((A -> B) -> (((not (not C)) -> C) and (A -> B))) and ((B or (A -> B)) -> (((not (not C)) -> C) and (A -> B)))), M:tm-654, m:tm-76, u:((Am (-> A B)) (C (and (-> (not (not Bm)) Bm) (-> A B))))
================================================================
tm-name          tm-51827
in-theory        51827
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((A or ((not (not (A -> B))) -> A)) -> ((not (not (A -> B))) -> B)))
theorem-size     33
proof            (modus-ponens tm-654 tm-77 ((A (not (not (-> Am Bm)))) (B Am) (C (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-10)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-51827.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and ((A or ((not (not (A -> B))) -> A)) -> ((not (not (A -> B))) -> B))), M:tm-654, m:tm-77, u:((A (not (not (-> Am Bm)))) (B Am) (C (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-51828
in-theory        51828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((not (not C)) -> C)) and ((B or (A -> B)) -> ((not (not C)) -> C)))
theorem-size     21
proof            (modus-ponens tm-654 tm-78 ((Am (-> A B)) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-51828.        (((A -> B) -> ((not (not C)) -> C)) and ((B or (A -> B)) -> ((not (not C)) -> C))), M:tm-654, m:tm-78, u:((Am (-> A B)) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-51829
in-theory        51829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and (((not (B -> (C -> B))) or (A -> (not (B -> (C -> B))))) -> (not A)))
theorem-size     30
proof            (modus-ponens tm-654 tm-79 ((A Am) (B (not (-> Bm (-> Cm Bm)))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       148
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-51829.        (((A -> (not (B -> (C -> B)))) -> (not A)) and (((not (B -> (C -> B))) or (A -> (not (B -> (C -> B))))) -> (not A))), M:tm-654, m:tm-79, u:((A Am) (B (not (-> Bm (-> Cm Bm)))) (C (not Am)))
================================================================
tm-name          tm-51830
in-theory        51830
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((C or ((A -> (B -> A)) -> C)) -> ((D or (A -> (B -> A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-654 tm-80 ((A (-> Am (-> Bm Am))) (B Cm) (C (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-51830.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and ((C or ((A -> (B -> A)) -> C)) -> ((D or (A -> (B -> A))) -> C))), M:tm-654, m:tm-80, u:((A (-> Am (-> Bm Am))) (B Cm) (C (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-51831
in-theory        51831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (D -> (E -> D))) and (A -> B))) and ((B or (A -> B)) -> ((C -> (D -> (E -> D))) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-83 ((Am (-> A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-51831.        (((A -> B) -> ((C -> (D -> (E -> D))) and (A -> B))) and ((B or (A -> B)) -> ((C -> (D -> (E -> D))) and (A -> B)))), M:tm-654, m:tm-83, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A B))))
================================================================
tm-name          tm-51832
in-theory        51832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and ((B or (A -> B)) -> (A -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-654 tm-84 ((A Am) (B Bm) (C (-> Am (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-51832.        (((A -> B) -> (A -> (C -> B))) and ((B or (A -> B)) -> (A -> (C -> B)))), M:tm-654, m:tm-84, u:((A Am) (B Bm) (C (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-51833
in-theory        51833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> (D -> (E -> D)))) and ((B or (A -> B)) -> (C -> (D -> (E -> D)))))
theorem-size     25
proof            (modus-ponens tm-654 tm-85 ((Am (-> A B)) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-51833.        (((A -> B) -> (C -> (D -> (E -> D)))) and ((B or (A -> B)) -> (C -> (D -> (E -> D))))), M:tm-654, m:tm-85, u:((Am (-> A B)) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-51834
in-theory        51834
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and ((B or (A -> B)) -> (A -> B)))
theorem-size     17
proof            (modus-ponens tm-654 tm-86 ((Am (-> A B)) (C (-> A B))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-51834.        (((A -> B) -> (A -> B)) and ((B or (A -> B)) -> (A -> B))), M:tm-654, m:tm-86, u:((Am (-> A B)) (C (-> A B)))
================================================================
tm-name          tm-51835
in-theory        51835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and (((B -> C) or (A -> (B -> C))) -> (A -> (B -> C))))
theorem-size     27
proof            (modus-ponens tm-654 tm-87 ((A Am) (B (-> Bm Cm)) (C (-> Am (-> Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-51835.        (((A -> (B -> C)) -> (A -> (B -> C))) and (((B -> C) or (A -> (B -> C))) -> (A -> (B -> C)))), M:tm-654, m:tm-87, u:((A Am) (B (-> Bm Cm)) (C (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-51836
in-theory        51836
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((not (A -> A)) or ((A -> B) -> (not (A -> A)))) -> (not (A -> B))))
theorem-size     32
proof            (modus-ponens tm-654 tm-91 ((A (-> Am Bm)) (B (not (-> Am Am))) (C (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       160
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-51836.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((not (A -> A)) or ((A -> B) -> (not (A -> A)))) -> (not (A -> B)))), M:tm-654, m:tm-91, u:((A (-> Am Bm)) (B (not (-> Am Am))) (C (not (-> Am Bm))))
================================================================
tm-name          tm-51837
in-theory        51837
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((B or ((A -> A) -> B)) -> (((A -> C) or (A -> A)) -> B)))
theorem-size     33
proof            (modus-ponens tm-654 tm-92 ((A (-> Am Am)) (B Bm) (C (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-51837.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and ((B or ((A -> A) -> B)) -> (((A -> C) or (A -> A)) -> B))), M:tm-654, m:tm-92, u:((A (-> Am Am)) (B Bm) (C (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-51838
in-theory        51838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> D) -> (C -> C)) and (A -> B))) and ((B or (A -> B)) -> (((C -> D) -> (C -> C)) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-95 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-51838.        (((A -> B) -> (((C -> D) -> (C -> C)) and (A -> B))) and ((B or (A -> B)) -> (((C -> D) -> (C -> C)) and (A -> B)))), M:tm-654, m:tm-95, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A B))))
================================================================
tm-name          tm-51839
in-theory        51839
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and ((A or ((A -> B) -> A)) -> ((A -> B) -> A)))
theorem-size     25
proof            (modus-ponens tm-654 tm-96 ((A (-> Am Bm)) (B Am) (C (-> (-> Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-51839.        ((((A -> B) -> A) -> ((A -> B) -> A)) and ((A or ((A -> B) -> A)) -> ((A -> B) -> A))), M:tm-654, m:tm-96, u:((A (-> Am Bm)) (B Am) (C (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-51840
in-theory        51840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> D) -> (C -> C))) and ((B or (A -> B)) -> ((C -> D) -> (C -> C))))
theorem-size     25
proof            (modus-ponens tm-654 tm-97 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-51840.        (((A -> B) -> ((C -> D) -> (C -> C))) and ((B or (A -> B)) -> ((C -> D) -> (C -> C)))), M:tm-654, m:tm-97, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-51841
in-theory        51841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and ((((B -> A) -> C) or (A -> ((B -> A) -> C))) -> (A -> C)))
theorem-size     29
proof            (modus-ponens tm-654 tm-98 ((A Am) (B (-> (-> Bm Am) Cm)) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-51841.        (((A -> ((B -> A) -> C)) -> (A -> C)) and ((((B -> A) -> C) or (A -> ((B -> A) -> C))) -> (A -> C))), M:tm-654, m:tm-98, u:((A Am) (B (-> (-> Bm Am) Cm)) (C (-> Am Cm)))
================================================================
tm-name          tm-51842
in-theory        51842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and (((A -> B) or (A -> (A -> B))) -> (A -> B)))
theorem-size     23
proof            (modus-ponens tm-654 tm-99 ((A Am) (B (-> Am Bm)) (C (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-51842.        (((A -> (A -> B)) -> (A -> B)) and (((A -> B) or (A -> (A -> B))) -> (A -> B))), M:tm-654, m:tm-99, u:((A Am) (B (-> Am Bm)) (C (-> Am Bm)))
================================================================
tm-name          tm-51843
in-theory        51843
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B))))
theorem-size     43
proof            (modus-ponens tm-654 tm-100 ((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-51843.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B)))), M:tm-654, m:tm-100, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-51844
in-theory        51844
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((not ((A -> (B -> C)) -> (A -> C))) or (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C))))) -> (not ((A -> (B -> C)) -> (A -> B)))))
theorem-size     74
proof            (modus-ponens tm-654 tm-101 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       240
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-51844.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and (((not ((A -> (B -> C)) -> (A -> C))) or (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C))))) -> (not ((A -> (B -> C)) -> (A -> B))))), M:tm-654, m:tm-101, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (C (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-51845
in-theory        51845
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((D or (((A -> (B -> C)) -> (A -> C)) -> D)) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))
theorem-size     69
proof            (modus-ponens tm-654 tm-102 ((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (B Dm) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-51845.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((D or (((A -> (B -> C)) -> (A -> C)) -> D)) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))), M:tm-654, m:tm-102, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (B Dm) (C (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-51846
in-theory        51846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> B))) and ((B or (A -> B)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> B))))
theorem-size     57
proof            (modus-ponens tm-654 tm-105 ((Am (-> A B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-51846.        (((A -> B) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> B))) and ((B or (A -> B)) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> B)))), M:tm-654, m:tm-105, u:((Am (-> A B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A B))))
================================================================
tm-name          tm-51847
in-theory        51847
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))
theorem-size     65
proof            (modus-ponens tm-654 tm-106 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-51847.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))), M:tm-654, m:tm-106, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-51848
in-theory        51848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((B or (A -> B)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))))
theorem-size     49
proof            (modus-ponens tm-654 tm-107 ((Am (-> A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-51848.        (((A -> B) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))) and ((B or (A -> B)) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))), M:tm-654, m:tm-107, u:((Am (-> A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-51849
in-theory        51849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((((A -> B) -> (A -> C)) -> D) or ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))) -> ((A -> (B -> C)) -> D)))
theorem-size     57
proof            (modus-ponens tm-654 tm-108 ((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (C (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       237
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-51849.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((((A -> B) -> (A -> C)) -> D) or ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))) -> ((A -> (B -> C)) -> D))), M:tm-654, m:tm-108, u:((A (-> Am (-> Bm Cm))) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (C (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-51850
in-theory        51850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not A)))
theorem-size     54
proof            (modus-ponens tm-654 tm-109 ((A Am) (B (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       196
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-51850.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and (((not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not A))), M:tm-654, m:tm-109, u:((A Am) (B (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (C (not Am)))
================================================================
tm-name          tm-51851
in-theory        51851
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D)) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))
theorem-size     69
proof            (modus-ponens tm-654 tm-110 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-51851.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D)) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))), M:tm-654, m:tm-110, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-51852
in-theory        51852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> B))) and ((B or (A -> B)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> B))))
theorem-size     49
proof            (modus-ponens tm-654 tm-113 ((Am (-> A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-51852.        (((A -> B) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> B))) and ((B or (A -> B)) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> B)))), M:tm-654, m:tm-113, u:((Am (-> A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A B))))
================================================================
tm-name          tm-51853
in-theory        51853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((B -> (C -> D)) or (A -> (B -> (C -> D)))) -> (A -> ((B -> C) -> (B -> D)))))
theorem-size     41
proof            (modus-ponens tm-654 tm-114 ((A Am) (B (-> Bm (-> Cm Dm))) (C (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-51853.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and (((B -> (C -> D)) or (A -> (B -> (C -> D)))) -> (A -> ((B -> C) -> (B -> D))))), M:tm-654, m:tm-114, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-51854
in-theory        51854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((B or (A -> B)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     41
proof            (modus-ponens tm-654 tm-115 ((Am (-> A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-51854.        (((A -> B) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((B or (A -> B)) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-654, m:tm-115, u:((Am (-> A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-51855
in-theory        51855
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((A -> B) or ((((A -> B) -> A) and C) -> (A -> B))) -> ((((A -> B) -> A) and C) -> B)))
theorem-size     47
proof            (modus-ponens tm-654 tm-119 ((A (and (-> (-> Am Bm) Am) Cm)) (B (-> Am Bm)) (C (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-51855.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((A -> B) or ((((A -> B) -> A) and C) -> (A -> B))) -> ((((A -> B) -> A) and C) -> B))), M:tm-654, m:tm-119, u:((A (and (-> (-> Am Bm) Am) Cm)) (B (-> Am Bm)) (C (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-51856
in-theory        51856
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> A)))
theorem-size     33
proof            (modus-ponens tm-654 tm-120 ((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-51856.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> A))), M:tm-654, m:tm-120, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-51857
in-theory        51857
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((not (((A -> B) and C) -> B)) or ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B)))) -> (not (((A -> B) and C) -> A))))
theorem-size     60
proof            (modus-ponens tm-654 tm-121 ((A (-> (and (-> Am Bm) Cm) Am)) (B (not (-> (and (-> Am Bm) Cm) Bm))) (C (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-3)
proof-size       208
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-51857.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((not (((A -> B) and C) -> B)) or ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B)))) -> (not (((A -> B) and C) -> A)))), M:tm-654, m:tm-121, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (not (-> (and (-> Am Bm) Cm) Bm))) (C (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-51858
in-theory        51858
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((D or ((((A -> B) and C) -> B) -> D)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))
theorem-size     57
proof            (modus-ponens tm-654 tm-122 ((A (-> (and (-> Am Bm) Cm) Bm)) (B Dm) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-51858.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and ((D or ((((A -> B) and C) -> B) -> D)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))), M:tm-654, m:tm-122, u:((A (-> (and (-> Am Bm) Cm) Bm)) (B Dm) (C (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-51859
in-theory        51859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> B))) and ((B or (A -> B)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> B))))
theorem-size     49
proof            (modus-ponens tm-654 tm-125 ((Am (-> A B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-51859.        (((A -> B) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> B))) and ((B or (A -> B)) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> B)))), M:tm-654, m:tm-125, u:((Am (-> A B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A B))))
================================================================
tm-name          tm-51860
in-theory        51860
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((((A -> B) and C) or ((((A -> B) and C) -> A) -> ((A -> B) and C))) -> ((((A -> B) and C) -> A) -> B)))
theorem-size     53
proof            (modus-ponens tm-654 tm-126 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-51860.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and ((((A -> B) and C) or ((((A -> B) and C) -> A) -> ((A -> B) and C))) -> ((((A -> B) and C) -> A) -> B))), M:tm-654, m:tm-126, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-51861
in-theory        51861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((B or (A -> B)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))))
theorem-size     41
proof            (modus-ponens tm-654 tm-127 ((Am (-> A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-51861.        (((A -> B) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))) and ((B or (A -> B)) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))), M:tm-654, m:tm-127, u:((Am (-> A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-51862
in-theory        51862
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((A -> C) or ((A and B) -> (A -> C))) -> ((A and B) -> C)))
theorem-size     31
proof            (modus-ponens tm-654 tm-129 ((A (and Am Bm)) (B (-> Am Cm)) (C (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-51862.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((A -> C) or ((A and B) -> (A -> C))) -> ((A and B) -> C))), M:tm-654, m:tm-129, u:((A (and Am Bm)) (B (-> Am Cm)) (C (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-51863
in-theory        51863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and (((not ((B and C) -> B)) or (A -> (not ((B and C) -> B)))) -> (not A)))
theorem-size     30
proof            (modus-ponens tm-654 tm-130 ((A Am) (B (not (-> (and Bm Cm) Bm))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-3)
proof-size       148
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-51863.        (((A -> (not ((B and C) -> B))) -> (not A)) and (((not ((B and C) -> B)) or (A -> (not ((B and C) -> B)))) -> (not A))), M:tm-654, m:tm-130, u:((A Am) (B (not (-> (and Bm Cm) Bm))) (C (not Am)))
================================================================
tm-name          tm-51864
in-theory        51864
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((C or (((A and B) -> A) -> C)) -> ((D or ((A and B) -> A)) -> C)))
theorem-size     37
proof            (modus-ponens tm-654 tm-131 ((A (-> (and Am Bm) Am)) (B Cm) (C (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-51864.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((C or (((A and B) -> A) -> C)) -> ((D or ((A and B) -> A)) -> C))), M:tm-654, m:tm-131, u:((A (-> (and Am Bm) Am)) (B Cm) (C (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-51865
in-theory        51865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> ((D and E) -> D)) and (A -> B))) and ((B or (A -> B)) -> ((C -> ((D and E) -> D)) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-134 ((Am (-> A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-51865.        (((A -> B) -> ((C -> ((D and E) -> D)) and (A -> B))) and ((B or (A -> B)) -> ((C -> ((D and E) -> D)) and (A -> B)))), M:tm-654, m:tm-134, u:((Am (-> A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A B))))
================================================================
tm-name          tm-51866
in-theory        51866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and (((B and C) or (A -> (B and C))) -> (A -> B)))
theorem-size     23
proof            (modus-ponens tm-654 tm-135 ((A Am) (B (and Bm Cm)) (C (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-51866.        (((A -> (B and C)) -> (A -> B)) and (((B and C) or (A -> (B and C))) -> (A -> B))), M:tm-654, m:tm-135, u:((A Am) (B (and Bm Cm)) (C (-> Am Bm)))
================================================================
tm-name          tm-51867
in-theory        51867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> ((D and E) -> D))) and ((B or (A -> B)) -> (C -> ((D and E) -> D))))
theorem-size     25
proof            (modus-ponens tm-654 tm-136 ((Am (-> A B)) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-51867.        (((A -> B) -> (C -> ((D and E) -> D))) and ((B or (A -> B)) -> (C -> ((D and E) -> D)))), M:tm-654, m:tm-136, u:((Am (-> A B)) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-51868
in-theory        51868
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((B -> C) or ((A and ((B -> C) -> B)) -> (B -> C))) -> ((A and ((B -> C) -> B)) -> C)))
theorem-size     47
proof            (modus-ponens tm-654 tm-141 ((A (and Am (-> (-> Bm Cm) Bm))) (B (-> Bm Cm)) (C (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-51868.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((B -> C) or ((A and ((B -> C) -> B)) -> (B -> C))) -> ((A and ((B -> C) -> B)) -> C))), M:tm-654, m:tm-141, u:((A (and Am (-> (-> Bm Cm) Bm))) (B (-> Bm Cm)) (C (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-51869
in-theory        51869
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((B or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> B)))
theorem-size     33
proof            (modus-ponens tm-654 tm-142 ((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-51869.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and ((B or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> B))), M:tm-654, m:tm-142, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-51870
in-theory        51870
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((not ((A and (B -> C)) -> C)) or (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C)))) -> (not ((A and (B -> C)) -> B))))
theorem-size     60
proof            (modus-ponens tm-654 tm-143 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (not (-> (and Am (-> Bm Cm)) Cm))) (C (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-4)
proof-size       208
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-51870.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and (((not ((A and (B -> C)) -> C)) or (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C)))) -> (not ((A and (B -> C)) -> B)))), M:tm-654, m:tm-143, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (not (-> (and Am (-> Bm Cm)) Cm))) (C (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-51871
in-theory        51871
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((D or (((A and (B -> C)) -> C) -> D)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))
theorem-size     57
proof            (modus-ponens tm-654 tm-144 ((A (-> (and Am (-> Bm Cm)) Cm)) (B Dm) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-51871.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((D or (((A and (B -> C)) -> C) -> D)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))), M:tm-654, m:tm-144, u:((A (-> (and Am (-> Bm Cm)) Cm)) (B Dm) (C (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-51872
in-theory        51872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> B))) and ((B or (A -> B)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> B))))
theorem-size     49
proof            (modus-ponens tm-654 tm-147 ((Am (-> A B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-51872.        (((A -> B) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> B))) and ((B or (A -> B)) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> B)))), M:tm-654, m:tm-147, u:((Am (-> A B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A B))))
================================================================
tm-name          tm-51873
in-theory        51873
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((A and (B -> C)) or (((A and (B -> C)) -> B) -> (A and (B -> C)))) -> (((A and (B -> C)) -> B) -> C)))
theorem-size     53
proof            (modus-ponens tm-654 tm-148 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-51873.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and (((A and (B -> C)) or (((A and (B -> C)) -> B) -> (A and (B -> C)))) -> (((A and (B -> C)) -> B) -> C))), M:tm-654, m:tm-148, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-51874
in-theory        51874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((B or (A -> B)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))))
theorem-size     41
proof            (modus-ponens tm-654 tm-149 ((Am (-> A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-51874.        (((A -> B) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))) and ((B or (A -> B)) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))), M:tm-654, m:tm-149, u:((Am (-> A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-51875
in-theory        51875
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((B -> C) or ((A and B) -> (B -> C))) -> ((A and B) -> C)))
theorem-size     31
proof            (modus-ponens tm-654 tm-152 ((A (and Am Bm)) (B (-> Bm Cm)) (C (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-51875.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((B -> C) or ((A and B) -> (B -> C))) -> ((A and B) -> C))), M:tm-654, m:tm-152, u:((A (and Am Bm)) (B (-> Bm Cm)) (C (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-51876
in-theory        51876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and (((not ((B and C) -> C)) or (A -> (not ((B and C) -> C)))) -> (not A)))
theorem-size     30
proof            (modus-ponens tm-654 tm-153 ((A Am) (B (not (-> (and Bm Cm) Cm))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-4)
proof-size       148
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-51876.        (((A -> (not ((B and C) -> C))) -> (not A)) and (((not ((B and C) -> C)) or (A -> (not ((B and C) -> C)))) -> (not A))), M:tm-654, m:tm-153, u:((A Am) (B (not (-> (and Bm Cm) Cm))) (C (not Am)))
================================================================
tm-name          tm-51877
in-theory        51877
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((C or (((A and B) -> B) -> C)) -> ((D or ((A and B) -> B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-654 tm-154 ((A (-> (and Am Bm) Bm)) (B Cm) (C (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-51877.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((C or (((A and B) -> B) -> C)) -> ((D or ((A and B) -> B)) -> C))), M:tm-654, m:tm-154, u:((A (-> (and Am Bm) Bm)) (B Cm) (C (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-51878
in-theory        51878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> ((D and E) -> E)) and (A -> B))) and ((B or (A -> B)) -> ((C -> ((D and E) -> E)) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-157 ((Am (-> A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-51878.        (((A -> B) -> ((C -> ((D and E) -> E)) and (A -> B))) and ((B or (A -> B)) -> ((C -> ((D and E) -> E)) and (A -> B)))), M:tm-654, m:tm-157, u:((Am (-> A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A B))))
================================================================
tm-name          tm-51879
in-theory        51879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and (((B and C) or (A -> (B and C))) -> (A -> C)))
theorem-size     23
proof            (modus-ponens tm-654 tm-158 ((A Am) (B (and Bm Cm)) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-51879.        (((A -> (B and C)) -> (A -> C)) and (((B and C) or (A -> (B and C))) -> (A -> C))), M:tm-654, m:tm-158, u:((A Am) (B (and Bm Cm)) (C (-> Am Cm)))
================================================================
tm-name          tm-51880
in-theory        51880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> ((D and E) -> E))) and ((B or (A -> B)) -> (C -> ((D and E) -> E))))
theorem-size     25
proof            (modus-ponens tm-654 tm-159 ((Am (-> A B)) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-51880.        (((A -> B) -> (C -> ((D and E) -> E))) and ((B or (A -> B)) -> (C -> ((D and E) -> E)))), M:tm-654, m:tm-159, u:((Am (-> A B)) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-51881
in-theory        51881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((not ((B -> (C -> B)) and A)) or (A -> (not ((B -> (C -> B)) and A)))) -> (not A)))
theorem-size     36
proof            (modus-ponens tm-654 tm-179 ((A Am) (B (not (and (-> Bm (-> Cm Bm)) Am))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       160
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-51881.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and (((not ((B -> (C -> B)) and A)) or (A -> (not ((B -> (C -> B)) and A)))) -> (not A))), M:tm-654, m:tm-179, u:((A Am) (B (not (and (-> Bm (-> Cm Bm)) Am))) (C (not Am)))
================================================================
tm-name          tm-51882
in-theory        51882
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((D or (((A -> (B -> A)) and C) -> D)) -> ((C or ((A -> (B -> A)) and C)) -> D)))
theorem-size     45
proof            (modus-ponens tm-654 tm-180 ((A (and (-> Am (-> Bm Am)) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-51882.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((D or (((A -> (B -> A)) and C) -> D)) -> ((C or ((A -> (B -> A)) and C)) -> D))), M:tm-654, m:tm-180, u:((A (and (-> Am (-> Bm Am)) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-51883
in-theory        51883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> ((D -> (E -> D)) and C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> ((D -> (E -> D)) and C)) and (A -> B))))
theorem-size     37
proof            (modus-ponens tm-654 tm-183 ((Am (-> A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-51883.        (((A -> B) -> ((C -> ((D -> (E -> D)) and C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> ((D -> (E -> D)) and C)) and (A -> B)))), M:tm-654, m:tm-183, u:((Am (-> A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A B))))
================================================================
tm-name          tm-51884
in-theory        51884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> ((D -> (E -> D)) and C))) and ((B or (A -> B)) -> (C -> ((D -> (E -> D)) and C))))
theorem-size     29
proof            (modus-ponens tm-654 tm-184 ((Am (-> A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-51884.        (((A -> B) -> (C -> ((D -> (E -> D)) and C))) and ((B or (A -> B)) -> (C -> ((D -> (E -> D)) and C)))), M:tm-654, m:tm-184, u:((Am (-> A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-51885
in-theory        51885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))) -> (not A)))
theorem-size     60
proof            (modus-ponens tm-654 tm-206 ((A Am) (B (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       208
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-51885.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and (((not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))) -> (not A))), M:tm-654, m:tm-206, u:((A Am) (B (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (C (not Am)))
================================================================
tm-name          tm-51886
in-theory        51886
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((E or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E)) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))
theorem-size     77
proof            (modus-ponens tm-654 tm-207 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B Em) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-51886.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and ((E or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E)) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))), M:tm-654, m:tm-207, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B Em) (C (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-51887
in-theory        51887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> B))))
theorem-size     53
proof            (modus-ponens tm-654 tm-210 ((Am (-> A B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-51887.        (((A -> B) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> B)))), M:tm-654, m:tm-210, u:((Am (-> A B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A B))))
================================================================
tm-name          tm-51888
in-theory        51888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((B or (A -> B)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))))
theorem-size     45
proof            (modus-ponens tm-654 tm-211 ((Am (-> A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-51888.        (((A -> B) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))) and ((B or (A -> B)) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))), M:tm-654, m:tm-211, u:((Am (-> A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-51889
in-theory        51889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((not (((B and C) -> B) and A)) or (A -> (not (((B and C) -> B) and A)))) -> (not A)))
theorem-size     36
proof            (modus-ponens tm-654 tm-235 ((A Am) (B (not (and (-> (and Bm Cm) Bm) Am))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-3)
proof-size       160
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-51889.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and (((not (((B and C) -> B) and A)) or (A -> (not (((B and C) -> B) and A)))) -> (not A))), M:tm-654, m:tm-235, u:((A Am) (B (not (and (-> (and Bm Cm) Bm) Am))) (C (not Am)))
================================================================
tm-name          tm-51890
in-theory        51890
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((D or ((((A and B) -> A) and C) -> D)) -> ((C or (((A and B) -> A) and C)) -> D)))
theorem-size     45
proof            (modus-ponens tm-654 tm-236 ((A (and (-> (and Am Bm) Am) Cm)) (B Dm) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-51890.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and ((D or ((((A and B) -> A) and C) -> D)) -> ((C or (((A and B) -> A) and C)) -> D))), M:tm-654, m:tm-236, u:((A (and (-> (and Am Bm) Am) Cm)) (B Dm) (C (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-51891
in-theory        51891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (((D and E) -> D) and C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> (((D and E) -> D) and C)) and (A -> B))))
theorem-size     37
proof            (modus-ponens tm-654 tm-239 ((Am (-> A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-51891.        (((A -> B) -> ((C -> (((D and E) -> D) and C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> (((D and E) -> D) and C)) and (A -> B)))), M:tm-654, m:tm-239, u:((Am (-> A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A B))))
================================================================
tm-name          tm-51892
in-theory        51892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> (((D and E) -> D) and C))) and ((B or (A -> B)) -> (C -> (((D and E) -> D) and C))))
theorem-size     29
proof            (modus-ponens tm-654 tm-240 ((Am (-> A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-51892.        (((A -> B) -> (C -> (((D and E) -> D) and C))) and ((B or (A -> B)) -> (C -> (((D and E) -> D) and C)))), M:tm-654, m:tm-240, u:((Am (-> A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-51893
in-theory        51893
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((not (((B and C) -> C) and A)) or (A -> (not (((B and C) -> C) and A)))) -> (not A)))
theorem-size     36
proof            (modus-ponens tm-654 tm-266 ((A Am) (B (not (and (-> (and Bm Cm) Cm) Am))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-4)
proof-size       160
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-51893.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and (((not (((B and C) -> C) and A)) or (A -> (not (((B and C) -> C) and A)))) -> (not A))), M:tm-654, m:tm-266, u:((A Am) (B (not (and (-> (and Bm Cm) Cm) Am))) (C (not Am)))
================================================================
tm-name          tm-51894
in-theory        51894
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((D or ((((A and B) -> B) and C) -> D)) -> ((C or (((A and B) -> B) and C)) -> D)))
theorem-size     45
proof            (modus-ponens tm-654 tm-267 ((A (and (-> (and Am Bm) Bm) Cm)) (B Dm) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-51894.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and ((D or ((((A and B) -> B) and C) -> D)) -> ((C or (((A and B) -> B) and C)) -> D))), M:tm-654, m:tm-267, u:((A (and (-> (and Am Bm) Bm) Cm)) (B Dm) (C (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-51895
in-theory        51895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (((D and E) -> E) and C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> (((D and E) -> E) and C)) and (A -> B))))
theorem-size     37
proof            (modus-ponens tm-654 tm-270 ((Am (-> A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-51895.        (((A -> B) -> ((C -> (((D and E) -> E) and C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> (((D and E) -> E) and C)) and (A -> B)))), M:tm-654, m:tm-270, u:((Am (-> A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A B))))
================================================================
tm-name          tm-51896
in-theory        51896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> (((D and E) -> E) and C))) and ((B or (A -> B)) -> (C -> (((D and E) -> E) and C))))
theorem-size     29
proof            (modus-ponens tm-654 tm-271 ((Am (-> A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-51896.        (((A -> B) -> (C -> (((D and E) -> E) and C))) and ((B or (A -> B)) -> (C -> (((D and E) -> E) and C)))), M:tm-654, m:tm-271, u:((Am (-> A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-51897
in-theory        51897
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((not ((B -> (C -> (B and C))) and A)) or (A -> (not ((B -> (C -> (B and C))) and A)))) -> (not A)))
theorem-size     42
proof            (modus-ponens tm-654 tm-299 ((A Am) (B (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       172
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-51897.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and (((not ((B -> (C -> (B and C))) and A)) or (A -> (not ((B -> (C -> (B and C))) and A)))) -> (not A))), M:tm-654, m:tm-299, u:((A Am) (B (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (C (not Am)))
================================================================
tm-name          tm-51898
in-theory        51898
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((D or (((A -> (B -> (A and B))) and C) -> D)) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)))
theorem-size     53
proof            (modus-ponens tm-654 tm-300 ((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-51898.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((D or (((A -> (B -> (A and B))) and C) -> D)) -> ((C or ((A -> (B -> (A and B))) and C)) -> D))), M:tm-654, m:tm-300, u:((A (and (-> Am (-> Bm (and Am Bm))) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-51899
in-theory        51899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> B))))
theorem-size     41
proof            (modus-ponens tm-654 tm-303 ((Am (-> A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-51899.        (((A -> B) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> B)))), M:tm-654, m:tm-303, u:((Am (-> A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A B))))
================================================================
tm-name          tm-51900
in-theory        51900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> ((D -> (E -> (D and E))) and C))) and ((B or (A -> B)) -> (C -> ((D -> (E -> (D and E))) and C))))
theorem-size     33
proof            (modus-ponens tm-654 tm-304 ((Am (-> A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-51900.        (((A -> B) -> (C -> ((D -> (E -> (D and E))) and C))) and ((B or (A -> B)) -> (C -> ((D -> (E -> (D and E))) and C)))), M:tm-654, m:tm-304, u:((Am (-> A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-51901
in-theory        51901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (C -> (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and (C -> (A -> B)))))
theorem-size     29
proof            (modus-ponens tm-654 tm-305 ((Am (-> A B)) (C (and (-> A B) (-> Bm (-> A B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-51901.        (((A -> B) -> ((A -> B) and (C -> (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and (C -> (A -> B))))), M:tm-654, m:tm-305, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (-> A B)))))
================================================================
tm-name          tm-51902
in-theory        51902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (((B -> C) or (A -> (B -> C))) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))
theorem-size     43
proof            (modus-ponens tm-654 tm-306 ((A Am) (B (-> Bm Cm)) (C (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-51902.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and (((B -> C) or (A -> (B -> C))) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))), M:tm-654, m:tm-306, u:((A Am) (B (-> Bm Cm)) (C (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-51903
in-theory        51903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (C -> ((A -> B) and C)))) and ((B or (A -> B)) -> ((A -> B) and (C -> ((A -> B) and C)))))
theorem-size     33
proof            (modus-ponens tm-654 tm-309 ((Am (-> A B)) (C (and (-> A B) (-> Bm (and (-> A B) Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-51903.        (((A -> B) -> ((A -> B) and (C -> ((A -> B) and C)))) and ((B or (A -> B)) -> ((A -> B) and (C -> ((A -> B) and C))))), M:tm-654, m:tm-309, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (and (-> A B) Bm)))))
================================================================
tm-name          tm-51904
in-theory        51904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> B) or C))) and ((B or (A -> B)) -> ((A -> B) and ((A -> B) or C))))
theorem-size     29
proof            (modus-ponens tm-654 tm-310 ((Am (-> A B)) (C (and (-> A B) (or (-> A B) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-51904.        (((A -> B) -> ((A -> B) and ((A -> B) or C))) and ((B or (A -> B)) -> ((A -> B) and ((A -> B) or C)))), M:tm-654, m:tm-310, u:((Am (-> A B)) (C (and (-> A B) (or (-> A B) Bm))))
================================================================
tm-name          tm-51905
in-theory        51905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (C or (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and (C or (A -> B)))))
theorem-size     29
proof            (modus-ponens tm-654 tm-311 ((Am (-> A B)) (C (and (-> A B) (or Bm (-> A B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-51905.        (((A -> B) -> ((A -> B) and (C or (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and (C or (A -> B))))), M:tm-654, m:tm-311, u:((Am (-> A B)) (C (and (-> A B) (or Bm (-> A B)))))
================================================================
tm-name          tm-51906
in-theory        51906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((B or (A -> B)) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     37
proof            (modus-ponens tm-654 tm-312 ((A Am) (B Bm) (C (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-51906.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((B or (A -> B)) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))), M:tm-654, m:tm-312, u:((A Am) (B Bm) (C (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-51907
in-theory        51907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((B or (A -> B)) -> ((A -> B) and ((A -> (not B)) -> (not A)))))
theorem-size     33
proof            (modus-ponens tm-654 tm-313 ((A Am) (B Bm) (C (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-51907.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((B or (A -> B)) -> ((A -> B) and ((A -> (not B)) -> (not A))))), M:tm-654, m:tm-313, u:((A Am) (B Bm) (C (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-51908
in-theory        51908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (C -> (D -> C)))) and ((B or (A -> B)) -> ((A -> B) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-654 tm-315 ((Am (-> A B)) (C (and (-> A B) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-51908.        (((A -> B) -> ((A -> B) and (C -> (D -> C)))) and ((B or (A -> B)) -> ((A -> B) and (C -> (D -> C))))), M:tm-654, m:tm-315, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-51909
in-theory        51909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and ((B or (A -> B)) -> ((A -> B) and (A -> A))))
theorem-size     25
proof            (modus-ponens tm-654 tm-316 ((A Am) (B Bm) (C (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-51909.        (((A -> B) -> ((A -> B) and (A -> A))) and ((B or (A -> B)) -> ((A -> B) and (A -> A)))), M:tm-654, m:tm-316, u:((A Am) (B Bm) (C (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-51910
in-theory        51910
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     63
proof            (modus-ponens tm-654 tm-317 ((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       245
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-51910.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))), M:tm-654, m:tm-317, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-51911
in-theory        51911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((B or (A -> B)) -> ((A -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-654 tm-318 ((Am (-> A B)) (C (and (-> A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-51911.        (((A -> B) -> ((A -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and ((B or (A -> B)) -> ((A -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-654, m:tm-318, u:((Am (-> A B)) (C (and (-> A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-51912
in-theory        51912
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((A or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))
theorem-size     49
proof            (modus-ponens tm-654 tm-319 ((A (and (-> Am Bm) Cm)) (B Am) (C (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-51912.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((A or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))), M:tm-654, m:tm-319, u:((A (and (-> Am Bm) Cm)) (B Am) (C (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-51913
in-theory        51913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((C and D) -> C))) and ((B or (A -> B)) -> ((A -> B) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-654 tm-320 ((Am (-> A B)) (C (and (-> A B) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-51913.        (((A -> B) -> ((A -> B) and ((C and D) -> C))) and ((B or (A -> B)) -> ((A -> B) and ((C and D) -> C)))), M:tm-654, m:tm-320, u:((Am (-> A B)) (C (and (-> A B) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-51914
in-theory        51914
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((B or ((A and (B -> C)) -> B)) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))
theorem-size     49
proof            (modus-ponens tm-654 tm-321 ((A (and Am (-> Bm Cm))) (B Bm) (C (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-51914.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and ((B or ((A and (B -> C)) -> B)) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))), M:tm-654, m:tm-321, u:((A (and Am (-> Bm Cm))) (B Bm) (C (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-51915
in-theory        51915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((C and D) -> D))) and ((B or (A -> B)) -> ((A -> B) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-654 tm-322 ((Am (-> A B)) (C (and (-> A B) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-51915.        (((A -> B) -> ((A -> B) and ((C and D) -> D))) and ((B or (A -> B)) -> ((A -> B) and ((C and D) -> D)))), M:tm-654, m:tm-322, u:((Am (-> A B)) (C (and (-> A B) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-51916
in-theory        51916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((C -> (D -> C)) and (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and ((C -> (D -> C)) and (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-654 tm-323 ((Am (-> A B)) (C (and (-> A B) (and (-> Bm (-> Cm Bm)) (-> A B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-51916.        (((A -> B) -> ((A -> B) and ((C -> (D -> C)) and (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and ((C -> (D -> C)) and (A -> B))))), M:tm-654, m:tm-323, u:((Am (-> A B)) (C (and (-> A B) (and (-> Bm (-> Cm Bm)) (-> A B)))))
================================================================
tm-name          tm-51917
in-theory        51917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> B)))))
theorem-size     53
proof            (modus-ponens tm-654 tm-324 ((Am (-> A B)) (C (and (-> A B) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-51917.        (((A -> B) -> ((A -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> B))))), M:tm-654, m:tm-324, u:((Am (-> A B)) (C (and (-> A B) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B)))))
================================================================
tm-name          tm-51918
in-theory        51918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and D) -> C) and (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and (((C and D) -> C) and (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-654 tm-325 ((Am (-> A B)) (C (and (-> A B) (and (-> (and Bm Cm) Bm) (-> A B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-51918.        (((A -> B) -> ((A -> B) and (((C and D) -> C) and (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and (((C and D) -> C) and (A -> B))))), M:tm-654, m:tm-325, u:((Am (-> A B)) (C (and (-> A B) (and (-> (and Bm Cm) Bm) (-> A B)))))
================================================================
tm-name          tm-51919
in-theory        51919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((C and D) -> D) and (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and (((C and D) -> D) and (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-654 tm-326 ((Am (-> A B)) (C (and (-> A B) (and (-> (and Bm Cm) Cm) (-> A B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-51919.        (((A -> B) -> ((A -> B) and (((C and D) -> D) and (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and (((C and D) -> D) and (A -> B))))), M:tm-654, m:tm-326, u:((Am (-> A B)) (C (and (-> A B) (and (-> (and Bm Cm) Cm) (-> A B)))))
================================================================
tm-name          tm-51920
in-theory        51920
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((C -> (D -> (C and D))) and (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and ((C -> (D -> (C and D))) and (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-654 tm-327 ((Am (-> A B)) (C (and (-> A B) (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-51920.        (((A -> B) -> ((A -> B) and ((C -> (D -> (C and D))) and (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and ((C -> (D -> (C and D))) and (A -> B))))), M:tm-654, m:tm-327, u:((Am (-> A B)) (C (and (-> A B) (and (-> Bm (-> Cm (and Bm Cm))) (-> A B)))))
================================================================
tm-name          tm-51921
in-theory        51921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((B or (A -> B)) -> ((A -> B) and (A -> (A and B)))))
theorem-size     29
proof            (modus-ponens tm-654 tm-328 ((A Am) (B Bm) (C (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-51921.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((B or (A -> B)) -> ((A -> B) and (A -> (A and B))))), M:tm-654, m:tm-328, u:((A Am) (B Bm) (C (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-51922
in-theory        51922
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((not (A -> (A and B))) or ((A -> B) -> (not (A -> (A and B))))) -> (not (A -> B))))
theorem-size     38
proof            (modus-ponens tm-654 tm-334 ((A (-> Am Bm)) (B (not (-> Am (and Am Bm)))) (C (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       172
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-51922.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((not (A -> (A and B))) or ((A -> B) -> (not (A -> (A and B))))) -> (not (A -> B)))), M:tm-654, m:tm-334, u:((A (-> Am Bm)) (B (not (-> Am (and Am Bm)))) (C (not (-> Am Bm))))
================================================================
tm-name          tm-51923
in-theory        51923
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((C or ((A -> (A and B)) -> C)) -> (((A -> B) or (A -> (A and B))) -> C)))
theorem-size     41
proof            (modus-ponens tm-654 tm-335 ((A (-> Am (and Am Bm))) (B Cm) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-51923.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and ((C or ((A -> (A and B)) -> C)) -> (((A -> B) or (A -> (A and B))) -> C))), M:tm-654, m:tm-335, u:((A (-> Am (and Am Bm))) (B Cm) (C (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-51924
in-theory        51924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> D) -> (C -> (C and D))) and (A -> B))) and ((B or (A -> B)) -> (((C -> D) -> (C -> (C and D))) and (A -> B))))
theorem-size     37
proof            (modus-ponens tm-654 tm-338 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-51924.        (((A -> B) -> (((C -> D) -> (C -> (C and D))) and (A -> B))) and ((B or (A -> B)) -> (((C -> D) -> (C -> (C and D))) and (A -> B)))), M:tm-654, m:tm-338, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A B))))
================================================================
tm-name          tm-51925
in-theory        51925
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((A or ((A -> B) -> A)) -> ((A -> B) -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-654 tm-339 ((A (-> Am Bm)) (B Am) (C (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-51925.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and ((A or ((A -> B) -> A)) -> ((A -> B) -> (A and B)))), M:tm-654, m:tm-339, u:((A (-> Am Bm)) (B Am) (C (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-51926
in-theory        51926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> D) -> (C -> (C and D)))) and ((B or (A -> B)) -> ((C -> D) -> (C -> (C and D)))))
theorem-size     29
proof            (modus-ponens tm-654 tm-340 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-51926.        (((A -> B) -> ((C -> D) -> (C -> (C and D)))) and ((B or (A -> B)) -> ((C -> D) -> (C -> (C and D))))), M:tm-654, m:tm-340, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-51927
in-theory        51927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (C -> (D -> (C and D))))) and ((B or (A -> B)) -> ((A -> B) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-654 tm-341 ((Am (-> A B)) (C (and (-> A B) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-51927.        (((A -> B) -> ((A -> B) and (C -> (D -> (C and D))))) and ((B or (A -> B)) -> ((A -> B) and (C -> (D -> (C and D)))))), M:tm-654, m:tm-341, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-51928
in-theory        51928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((((B -> (A and B)) -> C) or (A -> ((B -> (A and B)) -> C))) -> (A -> C)))
theorem-size     35
proof            (modus-ponens tm-654 tm-349 ((A Am) (B (-> (-> Bm (and Am Bm)) Cm)) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-51928.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((((B -> (A and B)) -> C) or (A -> ((B -> (A and B)) -> C))) -> (A -> C))), M:tm-654, m:tm-349, u:((A Am) (B (-> (-> Bm (and Am Bm)) Cm)) (C (-> Am Cm)))
================================================================
tm-name          tm-51929
in-theory        51929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((not (B -> (C -> (B and C)))) or (A -> (not (B -> (C -> (B and C)))))) -> (not A)))
theorem-size     36
proof            (modus-ponens tm-654 tm-350 ((A Am) (B (not (-> Bm (-> Cm (and Bm Cm))))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       160
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-51929.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and (((not (B -> (C -> (B and C)))) or (A -> (not (B -> (C -> (B and C)))))) -> (not A))), M:tm-654, m:tm-350, u:((A Am) (B (not (-> Bm (-> Cm (and Bm Cm))))) (C (not Am)))
================================================================
tm-name          tm-51930
in-theory        51930
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((C or ((A -> (B -> (A and B))) -> C)) -> ((D or (A -> (B -> (A and B)))) -> C)))
theorem-size     45
proof            (modus-ponens tm-654 tm-351 ((A (-> Am (-> Bm (and Am Bm)))) (B Cm) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-51930.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and ((C or ((A -> (B -> (A and B))) -> C)) -> ((D or (A -> (B -> (A and B)))) -> C))), M:tm-654, m:tm-351, u:((A (-> Am (-> Bm (and Am Bm)))) (B Cm) (C (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-51931
in-theory        51931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (D -> (E -> (D and E)))) and (A -> B))) and ((B or (A -> B)) -> ((C -> (D -> (E -> (D and E)))) and (A -> B))))
theorem-size     37
proof            (modus-ponens tm-654 tm-354 ((Am (-> A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-51931.        (((A -> B) -> ((C -> (D -> (E -> (D and E)))) and (A -> B))) and ((B or (A -> B)) -> ((C -> (D -> (E -> (D and E)))) and (A -> B)))), M:tm-654, m:tm-354, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A B))))
================================================================
tm-name          tm-51932
in-theory        51932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and ((B or (A -> B)) -> (A -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-654 tm-355 ((A Am) (B Bm) (C (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-51932.        (((A -> B) -> (A -> (C -> (B and C)))) and ((B or (A -> B)) -> (A -> (C -> (B and C))))), M:tm-654, m:tm-355, u:((A Am) (B Bm) (C (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-51933
in-theory        51933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> (D -> (E -> (D and E))))) and ((B or (A -> B)) -> (C -> (D -> (E -> (D and E))))))
theorem-size     29
proof            (modus-ponens tm-654 tm-356 ((Am (-> A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-51933.        (((A -> B) -> (C -> (D -> (E -> (D and E))))) and ((B or (A -> B)) -> (C -> (D -> (E -> (D and E)))))), M:tm-654, m:tm-356, u:((Am (-> A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51934
in-theory        51934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> (D -> C)) or E) and (A -> B))) and ((B or (A -> B)) -> (((C -> (D -> C)) or E) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-364 ((Am (-> A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-51934.        (((A -> B) -> (((C -> (D -> C)) or E) and (A -> B))) and ((B or (A -> B)) -> (((C -> (D -> C)) or E) and (A -> B)))), M:tm-654, m:tm-364, u:((Am (-> A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A B))))
================================================================
tm-name          tm-51935
in-theory        51935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (D -> C)) or E)) and ((B or (A -> B)) -> ((C -> (D -> C)) or E)))
theorem-size     25
proof            (modus-ponens tm-654 tm-365 ((Am (-> A B)) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-51935.        (((A -> B) -> ((C -> (D -> C)) or E)) and ((B or (A -> B)) -> ((C -> (D -> C)) or E))), M:tm-654, m:tm-365, u:((Am (-> A B)) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-51936
in-theory        51936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> B))) and ((B or (A -> B)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> B))))
theorem-size     49
proof            (modus-ponens tm-654 tm-373 ((Am (-> A B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-51936.        (((A -> B) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> B))) and ((B or (A -> B)) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> B)))), M:tm-654, m:tm-373, u:((Am (-> A B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A B))))
================================================================
tm-name          tm-51937
in-theory        51937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((B or (A -> B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)))
theorem-size     41
proof            (modus-ponens tm-654 tm-374 ((Am (-> A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-51937.        (((A -> B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)) and ((B or (A -> B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))), M:tm-654, m:tm-374, u:((Am (-> A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-51938
in-theory        51938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C and D) -> C) or E) and (A -> B))) and ((B or (A -> B)) -> ((((C and D) -> C) or E) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-382 ((Am (-> A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-51938.        (((A -> B) -> ((((C and D) -> C) or E) and (A -> B))) and ((B or (A -> B)) -> ((((C and D) -> C) or E) and (A -> B)))), M:tm-654, m:tm-382, u:((Am (-> A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A B))))
================================================================
tm-name          tm-51939
in-theory        51939
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and D) -> C) or E)) and ((B or (A -> B)) -> (((C and D) -> C) or E)))
theorem-size     25
proof            (modus-ponens tm-654 tm-383 ((Am (-> A B)) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-51939.        (((A -> B) -> (((C and D) -> C) or E)) and ((B or (A -> B)) -> (((C and D) -> C) or E))), M:tm-654, m:tm-383, u:((Am (-> A B)) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-51940
in-theory        51940
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C and D) -> D) or E) and (A -> B))) and ((B or (A -> B)) -> ((((C and D) -> D) or E) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-391 ((Am (-> A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-51940.        (((A -> B) -> ((((C and D) -> D) or E) and (A -> B))) and ((B or (A -> B)) -> ((((C and D) -> D) or E) and (A -> B)))), M:tm-654, m:tm-391, u:((Am (-> A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A B))))
================================================================
tm-name          tm-51941
in-theory        51941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and D) -> D) or E)) and ((B or (A -> B)) -> (((C and D) -> D) or E)))
theorem-size     25
proof            (modus-ponens tm-654 tm-392 ((Am (-> A B)) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-51941.        (((A -> B) -> (((C and D) -> D) or E)) and ((B or (A -> B)) -> (((C and D) -> D) or E))), M:tm-654, m:tm-392, u:((Am (-> A B)) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-51942
in-theory        51942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> (D -> (C and D))) or E) and (A -> B))) and ((B or (A -> B)) -> (((C -> (D -> (C and D))) or E) and (A -> B))))
theorem-size     37
proof            (modus-ponens tm-654 tm-400 ((Am (-> A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-51942.        (((A -> B) -> (((C -> (D -> (C and D))) or E) and (A -> B))) and ((B or (A -> B)) -> (((C -> (D -> (C and D))) or E) and (A -> B)))), M:tm-654, m:tm-400, u:((Am (-> A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A B))))
================================================================
tm-name          tm-51943
in-theory        51943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (D -> (C and D))) or E)) and ((B or (A -> B)) -> ((C -> (D -> (C and D))) or E)))
theorem-size     29
proof            (modus-ponens tm-654 tm-401 ((Am (-> A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-51943.        (((A -> B) -> ((C -> (D -> (C and D))) or E)) and ((B or (A -> B)) -> ((C -> (D -> (C and D))) or E))), M:tm-654, m:tm-401, u:((Am (-> A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-51944
in-theory        51944
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> (C or D)) or E) and (A -> B))) and ((B or (A -> B)) -> (((C -> (C or D)) or E) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-409 ((Am (-> A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-51944.        (((A -> B) -> (((C -> (C or D)) or E) and (A -> B))) and ((B or (A -> B)) -> (((C -> (C or D)) or E) and (A -> B)))), M:tm-654, m:tm-409, u:((Am (-> A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A B))))
================================================================
tm-name          tm-51945
in-theory        51945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (C or D)) or E)) and ((B or (A -> B)) -> ((C -> (C or D)) or E)))
theorem-size     25
proof            (modus-ponens tm-654 tm-410 ((Am (-> A B)) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-51945.        (((A -> B) -> ((C -> (C or D)) or E)) and ((B or (A -> B)) -> ((C -> (C or D)) or E))), M:tm-654, m:tm-410, u:((Am (-> A B)) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-51946
in-theory        51946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((C -> (C or D)) and (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and ((C -> (C or D)) and (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-654 tm-443 ((Am (-> A B)) (C (and (-> A B) (and (-> Bm (or Bm Cm)) (-> A B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-51946.        (((A -> B) -> ((A -> B) and ((C -> (C or D)) and (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and ((C -> (C or D)) and (A -> B))))), M:tm-654, m:tm-443, u:((Am (-> A B)) (C (and (-> A B) (and (-> Bm (or Bm Cm)) (-> A B)))))
================================================================
tm-name          tm-51947
in-theory        51947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((not ((B -> (B or C)) and A)) or (A -> (not ((B -> (B or C)) and A)))) -> (not A)))
theorem-size     36
proof            (modus-ponens tm-654 tm-449 ((A Am) (B (not (and (-> Bm (or Bm Cm)) Am))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-6)
proof-size       160
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-51947.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and (((not ((B -> (B or C)) and A)) or (A -> (not ((B -> (B or C)) and A)))) -> (not A))), M:tm-654, m:tm-449, u:((A Am) (B (not (and (-> Bm (or Bm Cm)) Am))) (C (not Am)))
================================================================
tm-name          tm-51948
in-theory        51948
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((D or (((A -> (A or B)) and C) -> D)) -> ((C or ((A -> (A or B)) and C)) -> D)))
theorem-size     45
proof            (modus-ponens tm-654 tm-450 ((A (and (-> Am (or Am Bm)) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-51948.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((D or (((A -> (A or B)) and C) -> D)) -> ((C or ((A -> (A or B)) and C)) -> D))), M:tm-654, m:tm-450, u:((A (and (-> Am (or Am Bm)) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-51949
in-theory        51949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> ((D -> (D or E)) and C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> ((D -> (D or E)) and C)) and (A -> B))))
theorem-size     37
proof            (modus-ponens tm-654 tm-453 ((Am (-> A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-51949.        (((A -> B) -> ((C -> ((D -> (D or E)) and C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> ((D -> (D or E)) and C)) and (A -> B)))), M:tm-654, m:tm-453, u:((Am (-> A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A B))))
================================================================
tm-name          tm-51950
in-theory        51950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> ((D -> (D or E)) and C))) and ((B or (A -> B)) -> (C -> ((D -> (D or E)) and C))))
theorem-size     29
proof            (modus-ponens tm-654 tm-454 ((Am (-> A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-51950.        (((A -> B) -> (C -> ((D -> (D or E)) and C))) and ((B or (A -> B)) -> (C -> ((D -> (D or E)) and C)))), M:tm-654, m:tm-454, u:((Am (-> A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-51951
in-theory        51951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (C -> (C or D)))) and ((B or (A -> B)) -> ((A -> B) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-654 tm-456 ((Am (-> A B)) (C (and (-> A B) (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-51951.        (((A -> B) -> ((A -> B) and (C -> (C or D)))) and ((B or (A -> B)) -> ((A -> B) and (C -> (C or D))))), M:tm-654, m:tm-456, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-51952
in-theory        51952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and ((((A or B) -> C) or (A -> ((A or B) -> C))) -> (A -> C)))
theorem-size     29
proof            (modus-ponens tm-654 tm-464 ((A Am) (B (-> (or Am Bm) Cm)) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-51952.        (((A -> ((A or B) -> C)) -> (A -> C)) and ((((A or B) -> C) or (A -> ((A or B) -> C))) -> (A -> C))), M:tm-654, m:tm-464, u:((A Am) (B (-> (or Am Bm) Cm)) (C (-> Am Cm)))
================================================================
tm-name          tm-51953
in-theory        51953
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and (((not (B -> (B or C))) or (A -> (not (B -> (B or C))))) -> (not A)))
theorem-size     30
proof            (modus-ponens tm-654 tm-465 ((A Am) (B (not (-> Bm (or Bm Cm)))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-6)
proof-size       148
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-51953.        (((A -> (not (B -> (B or C)))) -> (not A)) and (((not (B -> (B or C))) or (A -> (not (B -> (B or C))))) -> (not A))), M:tm-654, m:tm-465, u:((A Am) (B (not (-> Bm (or Bm Cm)))) (C (not Am)))
================================================================
tm-name          tm-51954
in-theory        51954
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((C or ((A -> (A or B)) -> C)) -> ((D or (A -> (A or B))) -> C)))
theorem-size     37
proof            (modus-ponens tm-654 tm-466 ((A (-> Am (or Am Bm))) (B Cm) (C (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-51954.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and ((C or ((A -> (A or B)) -> C)) -> ((D or (A -> (A or B))) -> C))), M:tm-654, m:tm-466, u:((A (-> Am (or Am Bm))) (B Cm) (C (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-51955
in-theory        51955
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (D -> (D or E))) and (A -> B))) and ((B or (A -> B)) -> ((C -> (D -> (D or E))) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-469 ((Am (-> A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-51955.        (((A -> B) -> ((C -> (D -> (D or E))) and (A -> B))) and ((B or (A -> B)) -> ((C -> (D -> (D or E))) and (A -> B)))), M:tm-654, m:tm-469, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A B))))
================================================================
tm-name          tm-51956
in-theory        51956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and ((B or (A -> B)) -> (A -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-654 tm-470 ((A Am) (B Bm) (C (-> Am (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-51956.        (((A -> B) -> (A -> (B or C))) and ((B or (A -> B)) -> (A -> (B or C)))), M:tm-654, m:tm-470, u:((A Am) (B Bm) (C (-> Am (or Bm Cm))))
================================================================
tm-name          tm-51957
in-theory        51957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> (D -> (D or E)))) and ((B or (A -> B)) -> (C -> (D -> (D or E)))))
theorem-size     25
proof            (modus-ponens tm-654 tm-471 ((Am (-> A B)) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-51957.        (((A -> B) -> (C -> (D -> (D or E)))) and ((B or (A -> B)) -> (C -> (D -> (D or E))))), M:tm-654, m:tm-471, u:((Am (-> A B)) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51958
in-theory        51958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or (D -> (E -> D))) and (A -> B))) and ((B or (A -> B)) -> ((C or (D -> (E -> D))) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-480 ((Am (-> A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-51958.        (((A -> B) -> ((C or (D -> (E -> D))) and (A -> B))) and ((B or (A -> B)) -> ((C or (D -> (E -> D))) and (A -> B)))), M:tm-654, m:tm-480, u:((Am (-> A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A B))))
================================================================
tm-name          tm-51959
in-theory        51959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C or (D -> (E -> D)))) and ((B or (A -> B)) -> (C or (D -> (E -> D)))))
theorem-size     25
proof            (modus-ponens tm-654 tm-481 ((Am (-> A B)) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-51959.        (((A -> B) -> (C or (D -> (E -> D)))) and ((B or (A -> B)) -> (C or (D -> (E -> D))))), M:tm-654, m:tm-481, u:((Am (-> A B)) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-51960
in-theory        51960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> B))) and ((B or (A -> B)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> B))))
theorem-size     49
proof            (modus-ponens tm-654 tm-490 ((Am (-> A B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-51960.        (((A -> B) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> B))) and ((B or (A -> B)) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> B)))), M:tm-654, m:tm-490, u:((Am (-> A B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A B))))
================================================================
tm-name          tm-51961
in-theory        51961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((B or (A -> B)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     41
proof            (modus-ponens tm-654 tm-491 ((Am (-> A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-51961.        (((A -> B) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and ((B or (A -> B)) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-654, m:tm-491, u:((Am (-> A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-51962
in-theory        51962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or ((D and E) -> D)) and (A -> B))) and ((B or (A -> B)) -> ((C or ((D and E) -> D)) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-500 ((Am (-> A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-51962.        (((A -> B) -> ((C or ((D and E) -> D)) and (A -> B))) and ((B or (A -> B)) -> ((C or ((D and E) -> D)) and (A -> B)))), M:tm-654, m:tm-500, u:((Am (-> A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A B))))
================================================================
tm-name          tm-51963
in-theory        51963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C or ((D and E) -> D))) and ((B or (A -> B)) -> (C or ((D and E) -> D))))
theorem-size     25
proof            (modus-ponens tm-654 tm-501 ((Am (-> A B)) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-51963.        (((A -> B) -> (C or ((D and E) -> D))) and ((B or (A -> B)) -> (C or ((D and E) -> D)))), M:tm-654, m:tm-501, u:((Am (-> A B)) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-51964
in-theory        51964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or ((D and E) -> E)) and (A -> B))) and ((B or (A -> B)) -> ((C or ((D and E) -> E)) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-510 ((Am (-> A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-51964.        (((A -> B) -> ((C or ((D and E) -> E)) and (A -> B))) and ((B or (A -> B)) -> ((C or ((D and E) -> E)) and (A -> B)))), M:tm-654, m:tm-510, u:((Am (-> A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A B))))
================================================================
tm-name          tm-51965
in-theory        51965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C or ((D and E) -> E))) and ((B or (A -> B)) -> (C or ((D and E) -> E))))
theorem-size     25
proof            (modus-ponens tm-654 tm-511 ((Am (-> A B)) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-51965.        (((A -> B) -> (C or ((D and E) -> E))) and ((B or (A -> B)) -> (C or ((D and E) -> E)))), M:tm-654, m:tm-511, u:((Am (-> A B)) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-51966
in-theory        51966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or (D -> (E -> (D and E)))) and (A -> B))) and ((B or (A -> B)) -> ((C or (D -> (E -> (D and E)))) and (A -> B))))
theorem-size     37
proof            (modus-ponens tm-654 tm-520 ((Am (-> A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-51966.        (((A -> B) -> ((C or (D -> (E -> (D and E)))) and (A -> B))) and ((B or (A -> B)) -> ((C or (D -> (E -> (D and E)))) and (A -> B)))), M:tm-654, m:tm-520, u:((Am (-> A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A B))))
================================================================
tm-name          tm-51967
in-theory        51967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C or (D -> (E -> (D and E))))) and ((B or (A -> B)) -> (C or (D -> (E -> (D and E))))))
theorem-size     29
proof            (modus-ponens tm-654 tm-521 ((Am (-> A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-51967.        (((A -> B) -> (C or (D -> (E -> (D and E))))) and ((B or (A -> B)) -> (C or (D -> (E -> (D and E)))))), M:tm-654, m:tm-521, u:((Am (-> A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-51968
in-theory        51968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or (D -> (D or E))) and (A -> B))) and ((B or (A -> B)) -> ((C or (D -> (D or E))) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-530 ((Am (-> A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-51968.        (((A -> B) -> ((C or (D -> (D or E))) and (A -> B))) and ((B or (A -> B)) -> ((C or (D -> (D or E))) and (A -> B)))), M:tm-654, m:tm-530, u:((Am (-> A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A B))))
================================================================
tm-name          tm-51969
in-theory        51969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C or (D -> (D or E)))) and ((B or (A -> B)) -> (C or (D -> (D or E)))))
theorem-size     25
proof            (modus-ponens tm-654 tm-531 ((Am (-> A B)) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-51969.        (((A -> B) -> (C or (D -> (D or E)))) and ((B or (A -> B)) -> (C or (D -> (D or E))))), M:tm-654, m:tm-531, u:((Am (-> A B)) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-51970
in-theory        51970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C or (D -> (E or D))) and (A -> B))) and ((B or (A -> B)) -> ((C or (D -> (E or D))) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-540 ((Am (-> A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-51970.        (((A -> B) -> ((C or (D -> (E or D))) and (A -> B))) and ((B or (A -> B)) -> ((C or (D -> (E or D))) and (A -> B)))), M:tm-654, m:tm-540, u:((Am (-> A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A B))))
================================================================
tm-name          tm-51971
in-theory        51971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C or (D -> (E or D)))) and ((B or (A -> B)) -> (C or (D -> (E or D)))))
theorem-size     25
proof            (modus-ponens tm-654 tm-541 ((Am (-> A B)) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-51971.        (((A -> B) -> (C or (D -> (E or D)))) and ((B or (A -> B)) -> (C or (D -> (E or D))))), M:tm-654, m:tm-541, u:((Am (-> A B)) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51972
in-theory        51972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> (D or C)) or E) and (A -> B))) and ((B or (A -> B)) -> (((C -> (D or C)) or E) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-550 ((Am (-> A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-51972.        (((A -> B) -> (((C -> (D or C)) or E) and (A -> B))) and ((B or (A -> B)) -> (((C -> (D or C)) or E) and (A -> B)))), M:tm-654, m:tm-550, u:((Am (-> A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A B))))
================================================================
tm-name          tm-51973
in-theory        51973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (D or C)) or E)) and ((B or (A -> B)) -> ((C -> (D or C)) or E)))
theorem-size     25
proof            (modus-ponens tm-654 tm-551 ((Am (-> A B)) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-51973.        (((A -> B) -> ((C -> (D or C)) or E)) and ((B or (A -> B)) -> ((C -> (D or C)) or E))), M:tm-654, m:tm-551, u:((Am (-> A B)) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-51974
in-theory        51974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((C -> (D or C)) and (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and ((C -> (D or C)) and (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-654 tm-595 ((Am (-> A B)) (C (and (-> A B) (and (-> Bm (or Cm Bm)) (-> A B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-51974.        (((A -> B) -> ((A -> B) and ((C -> (D or C)) and (A -> B)))) and ((B or (A -> B)) -> ((A -> B) and ((C -> (D or C)) and (A -> B))))), M:tm-654, m:tm-595, u:((Am (-> A B)) (C (and (-> A B) (and (-> Bm (or Cm Bm)) (-> A B)))))
================================================================
tm-name          tm-51975
in-theory        51975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((not ((B -> (C or B)) and A)) or (A -> (not ((B -> (C or B)) and A)))) -> (not A)))
theorem-size     36
proof            (modus-ponens tm-654 tm-601 ((A Am) (B (not (and (-> Bm (or Cm Bm)) Am))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-7)
proof-size       160
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-51975.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and (((not ((B -> (C or B)) and A)) or (A -> (not ((B -> (C or B)) and A)))) -> (not A))), M:tm-654, m:tm-601, u:((A Am) (B (not (and (-> Bm (or Cm Bm)) Am))) (C (not Am)))
================================================================
tm-name          tm-51976
in-theory        51976
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((D or (((A -> (B or A)) and C) -> D)) -> ((C or ((A -> (B or A)) and C)) -> D)))
theorem-size     45
proof            (modus-ponens tm-654 tm-602 ((A (and (-> Am (or Bm Am)) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-51976.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((D or (((A -> (B or A)) and C) -> D)) -> ((C or ((A -> (B or A)) and C)) -> D))), M:tm-654, m:tm-602, u:((A (and (-> Am (or Bm Am)) Cm)) (B Dm) (C (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-51977
in-theory        51977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> ((D -> (E or D)) and C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> ((D -> (E or D)) and C)) and (A -> B))))
theorem-size     37
proof            (modus-ponens tm-654 tm-605 ((Am (-> A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-51977.        (((A -> B) -> ((C -> ((D -> (E or D)) and C)) and (A -> B))) and ((B or (A -> B)) -> ((C -> ((D -> (E or D)) and C)) and (A -> B)))), M:tm-654, m:tm-605, u:((Am (-> A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A B))))
================================================================
tm-name          tm-51978
in-theory        51978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> ((D -> (E or D)) and C))) and ((B or (A -> B)) -> (C -> ((D -> (E or D)) and C))))
theorem-size     29
proof            (modus-ponens tm-654 tm-606 ((Am (-> A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-51978.        (((A -> B) -> (C -> ((D -> (E or D)) and C))) and ((B or (A -> B)) -> (C -> ((D -> (E or D)) and C)))), M:tm-654, m:tm-606, u:((Am (-> A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-51979
in-theory        51979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (C -> (D or C)))) and ((B or (A -> B)) -> ((A -> B) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-654 tm-609 ((Am (-> A B)) (C (and (-> A B) (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-51979.        (((A -> B) -> ((A -> B) and (C -> (D or C)))) and ((B or (A -> B)) -> ((A -> B) and (C -> (D or C))))), M:tm-654, m:tm-609, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-51980
in-theory        51980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and ((((B or A) -> C) or (A -> ((B or A) -> C))) -> (A -> C)))
theorem-size     29
proof            (modus-ponens tm-654 tm-617 ((A Am) (B (-> (or Bm Am) Cm)) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-51980.        (((A -> ((B or A) -> C)) -> (A -> C)) and ((((B or A) -> C) or (A -> ((B or A) -> C))) -> (A -> C))), M:tm-654, m:tm-617, u:((A Am) (B (-> (or Bm Am) Cm)) (C (-> Am Cm)))
================================================================
tm-name          tm-51981
in-theory        51981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and (((not (B -> (C or B))) or (A -> (not (B -> (C or B))))) -> (not A)))
theorem-size     30
proof            (modus-ponens tm-654 tm-618 ((A Am) (B (not (-> Bm (or Cm Bm)))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-7)
proof-size       148
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-51981.        (((A -> (not (B -> (C or B)))) -> (not A)) and (((not (B -> (C or B))) or (A -> (not (B -> (C or B))))) -> (not A))), M:tm-654, m:tm-618, u:((A Am) (B (not (-> Bm (or Cm Bm)))) (C (not Am)))
================================================================
tm-name          tm-51982
in-theory        51982
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((C or ((A -> (B or A)) -> C)) -> ((D or (A -> (B or A))) -> C)))
theorem-size     37
proof            (modus-ponens tm-654 tm-619 ((A (-> Am (or Bm Am))) (B Cm) (C (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-51982.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and ((C or ((A -> (B or A)) -> C)) -> ((D or (A -> (B or A))) -> C))), M:tm-654, m:tm-619, u:((A (-> Am (or Bm Am))) (B Cm) (C (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-51983
in-theory        51983
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> (D -> (E or D))) and (A -> B))) and ((B or (A -> B)) -> ((C -> (D -> (E or D))) and (A -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-622 ((Am (-> A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-51983.        (((A -> B) -> ((C -> (D -> (E or D))) and (A -> B))) and ((B or (A -> B)) -> ((C -> (D -> (E or D))) and (A -> B)))), M:tm-654, m:tm-622, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A B))))
================================================================
tm-name          tm-51984
in-theory        51984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and ((B or (A -> B)) -> (A -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-654 tm-623 ((A Am) (B Bm) (C (-> Am (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-51984.        (((A -> B) -> (A -> (C or B))) and ((B or (A -> B)) -> (A -> (C or B)))), M:tm-654, m:tm-623, u:((A Am) (B Bm) (C (-> Am (or Cm Bm))))
================================================================
tm-name          tm-51985
in-theory        51985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> (D -> (E or D)))) and ((B or (A -> B)) -> (C -> (D -> (E or D)))))
theorem-size     25
proof            (modus-ponens tm-654 tm-624 ((Am (-> A B)) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-51985.        (((A -> B) -> (C -> (D -> (E or D)))) and ((B or (A -> B)) -> (C -> (D -> (E or D))))), M:tm-654, m:tm-624, u:((Am (-> A B)) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-51986
in-theory        51986
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((C or ((A -> B) -> C)) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))))
theorem-size     41
proof            (modus-ponens tm-654 tm-654 ((A (-> Am Bm)) (B Cm) (C (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51986.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((C or ((A -> B) -> C)) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))), M:tm-654, m:tm-654, u:((A (-> Am Bm)) (B Cm) (C (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-51987
in-theory        51987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (D or (((A -> B) -> C) and ((B or (A -> B)) -> C))))
theorem-size     21
proof            (modus-ponens tm-623 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51987.        (((A -> B) -> C) -> (D or (((A -> B) -> C) and ((B or (A -> B)) -> C)))), M:tm-623, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-51988
in-theory        51988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-622 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51988.        ((A -> (B -> (C or B))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-622, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-51989
in-theory        51989
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (D or (B -> C)))) -> (((B -> C) -> (D or (B -> C))) and ((C or (B -> C)) -> (D or (B -> C)))))
theorem-size     33
proof            (modus-ponens tm-619 tm-654 ((A (-> Am Bm)) (Cm (or B (-> Am Bm))) (C (and (-> (-> Am Bm) (or B (-> Am Bm))) (-> (or Bm (-> Am Bm)) (or B (-> Am Bm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51989.        ((A or ((B -> C) -> (D or (B -> C)))) -> (((B -> C) -> (D or (B -> C))) and ((C or (B -> C)) -> (D or (B -> C))))), M:tm-619, m:tm-654, u:((A (-> Am Bm)) (Cm (or B (-> Am Bm))) (C (and (-> (-> Am Bm) (or B (-> Am Bm))) (-> (or Bm (-> Am Bm)) (or B (-> Am Bm))))))
================================================================
tm-name          tm-51990
in-theory        51990
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-609 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51990.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (D -> (E or D))), M:tm-609, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-51991
in-theory        51991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-605 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51991.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-605, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-51992
in-theory        51992
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((D -> (E or D)) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51992.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((D -> (E or D)) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))))), M:tm-595, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-51993
in-theory        51993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-550 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51993.        (((A -> (B or A)) or C) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-550, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-51994
in-theory        51994
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-540 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51994.        ((A or (B -> (C or B))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-540, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-51995
in-theory        51995
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-530 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51995.        ((A or (B -> (B or C))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-530, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-51996
in-theory        51996
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-520 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51996.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-520, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-51997
in-theory        51997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-510 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51997.        ((A or ((B and C) -> C)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-510, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-51998
in-theory        51998
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-500 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51998.        ((A or ((B and C) -> B)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-500, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-51999
in-theory        51999
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-490 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-51999.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G)))), M:tm-490, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52000
in-theory        52000
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-480 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52000.        ((A or (B -> (C -> B))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-480, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52001
in-theory        52001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> ((((A -> B) -> C) and ((B or (A -> B)) -> C)) or D))
theorem-size     21
proof            (modus-ponens tm-470 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52001.        (((A -> B) -> C) -> ((((A -> B) -> C) and ((B or (A -> B)) -> C)) or D)), M:tm-470, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-52002
in-theory        52002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-469 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52002.        ((A -> (B -> (B or C))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-469, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52003
in-theory        52003
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> C) or D))) -> (((B -> C) -> ((B -> C) or D)) and ((C or (B -> C)) -> ((B -> C) or D))))
theorem-size     33
proof            (modus-ponens tm-466 tm-654 ((A (-> Am Bm)) (Cm (or (-> Am Bm) B)) (C (and (-> (-> Am Bm) (or (-> Am Bm) B)) (-> (or Bm (-> Am Bm)) (or (-> Am Bm) B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52003.        ((A or ((B -> C) -> ((B -> C) or D))) -> (((B -> C) -> ((B -> C) or D)) and ((C or (B -> C)) -> ((B -> C) or D)))), M:tm-466, m:tm-654, u:((A (-> Am Bm)) (Cm (or (-> Am Bm) B)) (C (and (-> (-> Am Bm) (or (-> Am Bm) B)) (-> (or Bm (-> Am Bm)) (or (-> Am Bm) B)))))
================================================================
tm-name          tm-52004
in-theory        52004
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-456 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52004.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (D -> (D or E))), M:tm-456, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52005
in-theory        52005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-453 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52005.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-453, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52006
in-theory        52006
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((D -> (D or E)) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52006.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((D -> (D or E)) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))))), M:tm-443, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52007
in-theory        52007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-409 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52007.        (((A -> (A or B)) or C) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-409, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52008
in-theory        52008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-400 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52008.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-400, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52009
in-theory        52009
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-391 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52009.        ((((A and B) -> B) or C) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-391, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52010
in-theory        52010
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-382 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52010.        ((((A and B) -> A) or C) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-382, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52011
in-theory        52011
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-373 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52011.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G)))), M:tm-373, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52012
in-theory        52012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-364 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52012.        (((A -> (B -> A)) or C) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-364, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52013
in-theory        52013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (D -> ((((A -> B) -> C) and ((B or (A -> B)) -> C)) and D)))
theorem-size     23
proof            (modus-ponens tm-355 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52013.        (((A -> B) -> C) -> (D -> ((((A -> B) -> C) and ((B or (A -> B)) -> C)) and D))), M:tm-355, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-52014
in-theory        52014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-354 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52014.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-354, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52015
in-theory        52015
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (D -> ((B -> C) and D)))) -> (((B -> C) -> (D -> ((B -> C) and D))) and ((C or (B -> C)) -> (D -> ((B -> C) and D)))))
theorem-size     39
proof            (modus-ponens tm-351 tm-654 ((A (-> Am Bm)) (Cm (-> B (and (-> Am Bm) B))) (C (and (-> (-> Am Bm) (-> B (and (-> Am Bm) B))) (-> (or Bm (-> Am Bm)) (-> B (and (-> Am Bm) B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52015.        ((A or ((B -> C) -> (D -> ((B -> C) and D)))) -> (((B -> C) -> (D -> ((B -> C) and D))) and ((C or (B -> C)) -> (D -> ((B -> C) and D))))), M:tm-351, m:tm-654, u:((A (-> Am Bm)) (Cm (-> B (and (-> Am Bm) B))) (C (and (-> (-> Am Bm) (-> B (and (-> Am Bm) B))) (-> (or Bm (-> Am Bm)) (-> B (and (-> Am Bm) B))))))
================================================================
tm-name          tm-52016
in-theory        52016
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (D -> (E -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-341 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52016.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52017
in-theory        52017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E))))
theorem-size     29
proof            (modus-ponens tm-338 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52017.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E)))), M:tm-338, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52018
in-theory        52018
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((A -> B) -> ((A -> B) and C))) -> (((A -> B) -> ((A -> B) and C)) and ((B or (A -> B)) -> ((A -> B) and C))))
theorem-size     37
proof            (modus-ponens tm-335 tm-654 ((A (-> Am Bm)) (Cm (and (-> Am Bm) B)) (C (and (-> (-> Am Bm) (and (-> Am Bm) B)) (-> (or Bm (-> Am Bm)) (and (-> Am Bm) B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52018.        ((((A -> B) -> C) or ((A -> B) -> ((A -> B) and C))) -> (((A -> B) -> ((A -> B) and C)) and ((B or (A -> B)) -> ((A -> B) and C)))), M:tm-335, m:tm-654, u:((A (-> Am Bm)) (Cm (and (-> Am Bm) B)) (C (and (-> (-> Am Bm) (and (-> Am Bm) B)) (-> (or Bm (-> Am Bm)) (and (-> Am Bm) B)))))
================================================================
tm-name          tm-52019
in-theory        52019
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((A -> B) -> C) -> (((A -> B) -> C) and (((A -> B) -> C) and ((B or (A -> B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-328 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52019.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((A -> B) -> C) -> (((A -> B) -> C) and (((A -> B) -> C) and ((B or (A -> B)) -> C))))), M:tm-328, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-52020
in-theory        52020
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((D -> (E -> (D and E))) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52020.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((D -> (E -> (D and E))) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))))), M:tm-327, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52021
in-theory        52021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((D and E) -> E) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52021.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((D and E) -> E) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))))), M:tm-326, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52022
in-theory        52022
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((D and E) -> D) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52022.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((D and E) -> D) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))))), M:tm-325, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52023
in-theory        52023
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52023.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))))), M:tm-324, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52024
in-theory        52024
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((D -> (E -> D)) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52024.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((D -> (E -> D)) and (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))))), M:tm-323, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52025
in-theory        52025
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-322 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52025.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52026
in-theory        52026
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-320 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52026.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52027
in-theory        52027
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-318 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52027.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52028
in-theory        52028
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((A -> B) -> C) -> ((A -> B) -> C)))
theorem-size     31
proof            (modus-ponens tm-316 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52028.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((A -> B) -> C) -> ((A -> B) -> C))), M:tm-316, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-52029
in-theory        52029
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-315 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52029.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52030
in-theory        52030
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((((A -> B) -> C) -> (not (((A -> B) -> C) and ((B or (A -> B)) -> C)))) -> (not ((A -> B) -> C))))
theorem-size     47
proof            (modus-ponens tm-313 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52030.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((((A -> B) -> C) -> (not (((A -> B) -> C) and ((B or (A -> B)) -> C)))) -> (not ((A -> B) -> C)))), M:tm-313, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-52031
in-theory        52031
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((((A -> B) -> C) and ((B or (A -> B)) -> C)) -> D) -> ((((A -> B) -> C) or (((A -> B) -> C) and ((B or (A -> B)) -> C))) -> D)))
theorem-size     57
proof            (modus-ponens tm-312 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52031.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((((A -> B) -> C) and ((B or (A -> B)) -> C)) -> D) -> ((((A -> B) -> C) or (((A -> B) -> C) and ((B or (A -> B)) -> C))) -> D))), M:tm-312, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-52032
in-theory        52032
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (D or (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52032.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (D or (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))))), M:tm-311, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52033
in-theory        52033
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) or D))
theorem-size     41
proof            (modus-ponens tm-310 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52033.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) or D)), M:tm-310, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52034
in-theory        52034
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (D -> ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and D)))
theorem-size     43
proof            (modus-ponens tm-309 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52034.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (D -> ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and D))), M:tm-309, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52035
in-theory        52035
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (D -> (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52035.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (D -> (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))))), M:tm-305, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52036
in-theory        52036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-303 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52036.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-303, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52037
in-theory        52037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-270 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52037.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-270, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52038
in-theory        52038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-239 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52038.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-239, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52039
in-theory        52039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-210 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52039.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G)))), M:tm-210, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52040
in-theory        52040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     29
proof            (modus-ponens tm-183 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52040.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-183, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52041
in-theory        52041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-157 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52041.        ((A -> ((B and C) -> C)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-157, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52042
in-theory        52042
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-147 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52042.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-147, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52043
in-theory        52043
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-134 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52043.        ((A -> ((B and C) -> B)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-134, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52044
in-theory        52044
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-125 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52044.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-125, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52045
in-theory        52045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-113 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52045.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G)))), M:tm-113, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52046
in-theory        52046
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((C -> D) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))))
theorem-size     47
proof            (modus-ponens tm-110 tm-654 ((A Am) (Bm (-> B C)) (Cm (-> (-> Am B) (-> Am C))) (D (and (-> (-> Am (-> B C)) (-> (-> Am B) (-> Am C))) (-> (or (-> B C) (-> Am (-> B C))) (-> (-> Am B) (-> Am C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52046.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((C -> D) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-654, u:((A Am) (Bm (-> B C)) (Cm (-> (-> Am B) (-> Am C))) (D (and (-> (-> Am (-> B C)) (-> (-> Am B) (-> Am C))) (-> (or (-> B C) (-> Am (-> B C))) (-> (-> Am B) (-> Am C))))))
================================================================
tm-name          tm-52047
in-theory        52047
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     39
proof            (modus-ponens tm-105 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52047.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-105, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52048
in-theory        52048
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((B -> C) or (A -> (B -> C))) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-102 tm-654 ((A Am) (Bm (-> B C)) (Cm (-> Am C)) (D (and (-> (-> Am (-> B C)) (-> Am C)) (-> (or (-> B C) (-> Am (-> B C))) (-> Am C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52048.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and (((B -> C) or (A -> (B -> C))) -> (A -> C)))), M:tm-102, m:tm-654, u:((A Am) (Bm (-> B C)) (Cm (-> Am C)) (D (and (-> (-> Am (-> B C)) (-> Am C)) (-> (or (-> B C) (-> Am (-> B C))) (-> Am C)))))
================================================================
tm-name          tm-52049
in-theory        52049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E))))
theorem-size     27
proof            (modus-ponens tm-95 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52049.        (((A -> B) -> (A -> A)) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E)))), M:tm-95, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52050
in-theory        52050
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((A -> B) -> (A -> B))) -> (((A -> B) -> (A -> B)) and ((B or (A -> B)) -> (A -> B))))
theorem-size     31
proof            (modus-ponens tm-92 tm-654 ((Cm (-> Am Bm)) (A (-> Am Bm)) (B (and (-> (-> Am Bm) (-> Am Bm)) (-> (or Bm (-> Am Bm)) (-> Am Bm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52050.        ((((A -> B) -> C) or ((A -> B) -> (A -> B))) -> (((A -> B) -> (A -> B)) and ((B or (A -> B)) -> (A -> B)))), M:tm-92, m:tm-654, u:((Cm (-> Am Bm)) (A (-> Am Bm)) (B (and (-> (-> Am Bm) (-> Am Bm)) (-> (or Bm (-> Am Bm)) (-> Am Bm)))))
================================================================
tm-name          tm-52051
in-theory        52051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (D -> (((A -> B) -> C) and ((B or (A -> B)) -> C))))
theorem-size     21
proof            (modus-ponens tm-84 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52051.        (((A -> B) -> C) -> (D -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))), M:tm-84, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-52052
in-theory        52052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-83 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52052.        ((A -> (B -> (C -> B))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-83, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52053
in-theory        52053
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (D -> (B -> C)))) -> (((B -> C) -> (D -> (B -> C))) and ((C or (B -> C)) -> (D -> (B -> C)))))
theorem-size     33
proof            (modus-ponens tm-80 tm-654 ((A (-> Am Bm)) (Cm (-> B (-> Am Bm))) (C (and (-> (-> Am Bm) (-> B (-> Am Bm))) (-> (or Bm (-> Am Bm)) (-> B (-> Am Bm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52053.        ((A or ((B -> C) -> (D -> (B -> C)))) -> (((B -> C) -> (D -> (B -> C))) and ((C or (B -> C)) -> (D -> (B -> C))))), M:tm-80, m:tm-654, u:((A (-> Am Bm)) (Cm (-> B (-> Am Bm))) (C (and (-> (-> Am Bm) (-> B (-> Am Bm))) (-> (or Bm (-> Am Bm)) (-> B (-> Am Bm))))))
================================================================
tm-name          tm-52054
in-theory        52054
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> D) -> (((B -> C) -> D) and ((C or (B -> C)) -> D))))
theorem-size     25
proof            (modus-ponens tm-76 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52054.        (((not (not A)) -> A) and (((B -> C) -> D) -> (((B -> C) -> D) and ((C or (B -> C)) -> D)))), M:tm-76, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52055
in-theory        52055
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> C))) or ((A -> B) -> C)) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-73 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52055.        (((not (not ((A -> B) -> C))) or ((A -> B) -> C)) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-73, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-52056
in-theory        52056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E))))
theorem-size     31
proof            (modus-ponens tm-69 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52056.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E)))), M:tm-69, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52057
in-theory        52057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((not B) or (A -> (not B))) -> (not A))))
theorem-size     30
proof            (modus-ponens tm-66 tm-654 ((A Am) (Bm (not B)) (Cm (not Am)) (C (and (-> (-> Am (not B)) (not Am)) (-> (or (not B) (-> Am (not B))) (not Am))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-1)
proof-size       156
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52057.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and (((not B) or (A -> (not B))) -> (not A)))), M:tm-66, m:tm-654, u:((A Am) (Bm (not B)) (Cm (not Am)) (C (and (-> (-> Am (not B)) (not Am)) (-> (or (not B) (-> Am (not B))) (not Am)))))
================================================================
tm-name          tm-52058
in-theory        52058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-54 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52058.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-54, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52059
in-theory        52059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((C or (B -> C)) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-51 tm-654 ((A Am) (B Bm) (Cm (-> (or C Am) Bm)) (D (and (-> (-> Am Bm) (-> (or C Am) Bm)) (-> (or Bm (-> Am Bm)) (-> (or C Am) Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52059.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((C or (B -> C)) -> ((A or B) -> C)))), M:tm-51, m:tm-654, u:((A Am) (B Bm) (Cm (-> (or C Am) Bm)) (D (and (-> (-> Am Bm) (-> (or C Am) Bm)) (-> (or Bm (-> Am Bm)) (-> (or C Am) Bm)))))
================================================================
tm-name          tm-52060
in-theory        52060
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (A and (B -> C)))) -> (((B -> C) -> (A and (B -> C))) and ((C or (B -> C)) -> (A and (B -> C)))))
theorem-size     33
proof            (modus-ponens tm-48 tm-654 ((A (-> Am Bm)) (Cm (and B (-> Am Bm))) (C (and (-> (-> Am Bm) (and B (-> Am Bm))) (-> (or Bm (-> Am Bm)) (and B (-> Am Bm)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52060.        ((A or ((B -> C) -> (A and (B -> C)))) -> (((B -> C) -> (A and (B -> C))) and ((C or (B -> C)) -> (A and (B -> C))))), M:tm-48, m:tm-654, u:((A (-> Am Bm)) (Cm (and B (-> Am Bm))) (C (and (-> (-> Am Bm) (and B (-> Am Bm))) (-> (or Bm (-> Am Bm)) (and B (-> Am Bm))))))
================================================================
tm-name          tm-52061
in-theory        52061
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (((B -> C) -> D) and ((C or (B -> C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-47 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52061.        (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (((B -> C) -> D) and ((C or (B -> C)) -> D))), M:tm-47, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-52062
in-theory        52062
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-46 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52062.        (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-46, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-52063
in-theory        52063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((B or (A -> B)) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-45 tm-654 ((A Am) (B Bm) (Cm (-> Am C)) (D (and (-> (-> Am Bm) (-> Am C)) (-> (or Bm (-> Am Bm)) (-> Am C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52063.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((B or (A -> B)) -> (A -> C)))), M:tm-45, m:tm-654, u:((A Am) (B Bm) (Cm (-> Am C)) (D (and (-> (-> Am Bm) (-> Am C)) (-> (or Bm (-> Am Bm)) (-> Am C)))))
================================================================
tm-name          tm-52064
in-theory        52064
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> A)) -> (((B -> C) -> A) and ((C or (B -> C)) -> A)))
theorem-size     21
proof            (modus-ponens tm-44 tm-654 ((A (-> Am Bm)) (B Cm) (C (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52064.        ((A or ((B -> C) -> A)) -> (((B -> C) -> A) and ((C or (B -> C)) -> A))), M:tm-44, m:tm-654, u:((A (-> Am Bm)) (B Cm) (C (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-52065
in-theory        52065
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-42 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52065.        ((A -> (B or A)) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E)))), M:tm-42, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52066
in-theory        52066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-32 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52066.        ((A -> (A or B)) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E)))), M:tm-32, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52067
in-theory        52067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (((A -> B) -> C) and (((A -> B) -> C) and ((B or (A -> B)) -> C))))
theorem-size     25
proof            (modus-ponens tm-24 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52067.        (((A -> B) -> C) -> (((A -> B) -> C) and (((A -> B) -> C) and ((B or (A -> B)) -> C)))), M:tm-24, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-52068
in-theory        52068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E))))
theorem-size     27
proof            (modus-ponens tm-23 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52068.        ((A -> (B -> (A and B))) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E)))), M:tm-23, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52069
in-theory        52069
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-22 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52069.        (((A and B) -> B) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E)))), M:tm-22, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52070
in-theory        52070
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-21 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52070.        (((A and B) -> A) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E)))), M:tm-21, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52071
in-theory        52071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-20 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52071.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-20, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52072
in-theory        52072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E))))
theorem-size     25
proof            (modus-ponens tm-19 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52072.        ((A -> (B -> A)) and (((C -> D) -> E) -> (((C -> D) -> E) and ((D or (C -> D)) -> E)))), M:tm-19, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52073
in-theory        52073
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (not (((A -> B) -> C) and ((B or (A -> B)) -> C)))) -> (not ((A -> B) -> C)))
theorem-size     27
proof            (modus-ponens tm-9 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-9 tm-2 tm-5 tm-8 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52073.        ((((A -> B) -> C) -> (not (((A -> B) -> C) and ((B or (A -> B)) -> C)))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-52074
in-theory        52074
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) and ((B or (A -> B)) -> C)) -> D) -> ((((A -> B) -> C) or (((A -> B) -> C) and ((B or (A -> B)) -> C))) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52074.        (((((A -> B) -> C) and ((B or (A -> B)) -> C)) -> D) -> ((((A -> B) -> C) or (((A -> B) -> C) and ((B or (A -> B)) -> C))) -> D)), M:tm-8, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-52075
in-theory        52075
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> D) -> (((B -> C) -> D) and ((C or (B -> C)) -> D))))
theorem-size     21
proof            (modus-ponens tm-7 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-7 tm-2 tm-5 tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52075.        (A or (((B -> C) -> D) -> (((B -> C) -> D) and ((C or (B -> C)) -> D)))), M:tm-7, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52076
in-theory        52076
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) or D)
theorem-size     21
proof            (modus-ponens tm-6 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-6 tm-2 tm-5 tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52076.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) or D), M:tm-6, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52077
in-theory        52077
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> D) -> (((B -> C) -> D) and ((C or (B -> C)) -> D))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52077.        (A -> ((((B -> C) -> D) -> (((B -> C) -> D) and ((C or (B -> C)) -> D))) and A)), M:tm-5, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52078
in-theory        52078
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> D) -> (((B -> C) -> D) and ((C or (B -> C)) -> D))))
theorem-size     21
proof            (modus-ponens tm-1 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-1 tm-2 tm-5 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52078.        (A -> (((B -> C) -> D) -> (((B -> C) -> D) and ((C or (B -> C)) -> D)))), M:tm-1, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-52079
in-theory        52079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-622 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52079.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-622, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52080
in-theory        52080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52080.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52081
in-theory        52081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-605 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52081.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-605, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52082
in-theory        52082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52082.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-595, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52083
in-theory        52083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-550 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52083.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-550, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52084
in-theory        52084
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-540 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52084.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-540, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52085
in-theory        52085
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-530 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52085.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-530, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52086
in-theory        52086
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-520 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52086.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-520, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52087
in-theory        52087
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-510 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52087.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-510, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52088
in-theory        52088
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-500 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52088.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-500, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52089
in-theory        52089
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-490 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52089.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-490, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52090
in-theory        52090
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-480 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52090.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-480, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52091
in-theory        52091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-469 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52091.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-469, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52092
in-theory        52092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52092.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52093
in-theory        52093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-453 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52093.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-453, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52094
in-theory        52094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52094.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-443, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52095
in-theory        52095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-409 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52095.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-409, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52096
in-theory        52096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-400 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52096.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-400, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52097
in-theory        52097
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-391 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52097.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-391, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52098
in-theory        52098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-382 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52098.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-382, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52099
in-theory        52099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-373 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52099.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-373, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52100
in-theory        52100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-364 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52100.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-364, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52101
in-theory        52101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-354 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52101.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-354, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52102
in-theory        52102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52102.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52103
in-theory        52103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-338 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52103.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-338, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52104
in-theory        52104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52104.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-327, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52105
in-theory        52105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52105.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-326, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52106
in-theory        52106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52106.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-325, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52107
in-theory        52107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52107.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-324, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52108
in-theory        52108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52108.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-323, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52109
in-theory        52109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52109.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52110
in-theory        52110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52110.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52111
in-theory        52111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52111.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52112
in-theory        52112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52112.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52113
in-theory        52113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F or ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52113.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F or ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-311, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52114
in-theory        52114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52114.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F)), M:tm-310, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52115
in-theory        52115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52115.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and F))), M:tm-309, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52116
in-theory        52116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     35
proof            (modus-ponens tm-308 tm-655 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52116.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-308, m:tm-655, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))
================================================================
tm-name          tm-52117
in-theory        52117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (A -> (B -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-307 tm-655 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52117.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-655, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))
================================================================
tm-name          tm-52118
in-theory        52118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52118.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-305, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52119
in-theory        52119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-303 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52119.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-303, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52120
in-theory        52120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-270 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52120.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-270, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52121
in-theory        52121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-239 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52121.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-239, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52122
in-theory        52122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-210 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52122.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-210, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52123
in-theory        52123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-183 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52123.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-183, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52124
in-theory        52124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-157 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52124.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-157, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52125
in-theory        52125
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-147 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52125.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-147, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52126
in-theory        52126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-134 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52126.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-134, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52127
in-theory        52127
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-125 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52127.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-125, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52128
in-theory        52128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-113 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52128.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-113, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52129
in-theory        52129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     41
proof            (modus-ponens tm-105 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52129.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-105, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52130
in-theory        52130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-95 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52130.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-95, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52131
in-theory        52131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-83 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52131.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-83, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52132
in-theory        52132
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-76 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52132.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-76, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52133
in-theory        52133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-69 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52133.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-69, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52134
in-theory        52134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-54 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52134.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-54, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52135
in-theory        52135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-42 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52135.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-42, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52136
in-theory        52136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-32 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52136.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-32, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52137
in-theory        52137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-23 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52137.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-23, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52138
in-theory        52138
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-22 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52138.        (((A and B) -> B) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-22, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52139
in-theory        52139
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-21 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52139.        (((A and B) -> A) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-21, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52140
in-theory        52140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-20 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52140.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-20, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52141
in-theory        52141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-19 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52141.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-19, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52142
in-theory        52142
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     23
proof            (modus-ponens tm-7 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52142.        (A or ((B -> (C -> (B and C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-7, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52143
in-theory        52143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52143.        (((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F), M:tm-6, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52144
in-theory        52144
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52144.        (A -> (((B -> (C -> (B and C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and A)), M:tm-5, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52145
in-theory        52145
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     23
proof            (modus-ponens tm-1 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52145.        (A -> ((B -> (C -> (B and C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-1, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52146
in-theory        52146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52146.        ((A -> (B -> (C or B))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-622, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52147
in-theory        52147
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52147.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52148
in-theory        52148
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52148.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-605, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52149
in-theory        52149
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G or F)) and (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52149.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G or F)) and (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-595, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52150
in-theory        52150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52150.        (((A -> (B or A)) or C) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-550, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52151
in-theory        52151
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52151.        ((A or (B -> (C or B))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-540, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52152
in-theory        52152
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52152.        ((A or (B -> (B or C))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-530, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52153
in-theory        52153
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52153.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-520, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52154
in-theory        52154
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52154.        ((A or ((B and C) -> C)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-510, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52155
in-theory        52155
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52155.        ((A or ((B and C) -> B)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-500, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52156
in-theory        52156
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52156.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-490, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52157
in-theory        52157
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52157.        ((A or (B -> (C -> B))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-480, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52158
in-theory        52158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52158.        ((A -> (B -> (B or C))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-469, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52159
in-theory        52159
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52159.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52160
in-theory        52160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52160.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-453, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52161
in-theory        52161
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (F or G)) and (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52161.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (F or G)) and (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-443, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52162
in-theory        52162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52162.        (((A -> (A or B)) or C) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-409, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52163
in-theory        52163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52163.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-400, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52164
in-theory        52164
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52164.        ((((A and B) -> B) or C) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-391, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52165
in-theory        52165
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52165.        ((((A and B) -> A) or C) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-382, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52166
in-theory        52166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52166.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-373, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52167
in-theory        52167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52167.        (((A -> (B -> A)) or C) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-364, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52168
in-theory        52168
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52168.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-354, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52169
in-theory        52169
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52169.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52170
in-theory        52170
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52170.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-338, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52171
in-theory        52171
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52171.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-327, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52172
in-theory        52172
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> G) and (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52172.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> G) and (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-326, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52173
in-theory        52173
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> F) and (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52173.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> F) and (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-325, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52174
in-theory        52174
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52174.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-324, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52175
in-theory        52175
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> F)) and (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52175.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> F)) and (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-323, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52176
in-theory        52176
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52176.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52177
in-theory        52177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52177.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52178
in-theory        52178
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52178.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52179
in-theory        52179
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52179.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52180
in-theory        52180
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F or (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52180.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F or (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-311, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52181
in-theory        52181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52181.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F)), M:tm-310, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52182
in-theory        52182
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52182.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and F))), M:tm-309, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52183
in-theory        52183
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-656 ((A (-> (and Am Bm) Bm)) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52183.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-308, m:tm-656, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))
================================================================
tm-name          tm-52184
in-theory        52184
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((A and B) -> B))
theorem-size     25
proof            (modus-ponens tm-307 tm-656 ((A (-> (and Am Bm) Bm)) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52184.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((A and B) -> B)), M:tm-307, m:tm-656, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))
================================================================
tm-name          tm-52185
in-theory        52185
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52185.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-305, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52186
in-theory        52186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52186.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-303, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52187
in-theory        52187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52187.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-270, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52188
in-theory        52188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52188.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-239, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52189
in-theory        52189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52189.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-210, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52190
in-theory        52190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52190.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-183, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52191
in-theory        52191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52191.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-157, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52192
in-theory        52192
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52192.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-147, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52193
in-theory        52193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52193.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-134, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52194
in-theory        52194
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52194.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-125, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52195
in-theory        52195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52195.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-113, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52196
in-theory        52196
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52196.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-105, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52197
in-theory        52197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52197.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-95, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52198
in-theory        52198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52198.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-83, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52199
in-theory        52199
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-4 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52199.        (((not (not A)) -> A) and (((B and C) -> C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-76, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52200
in-theory        52200
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-4 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52200.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-69, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52201
in-theory        52201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52201.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-54, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52202
in-theory        52202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52202.        ((A -> (B or A)) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-42, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52203
in-theory        52203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52203.        ((A -> (A or B)) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-32, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52204
in-theory        52204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52204.        ((A -> (B -> (A and B))) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-23, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52205
in-theory        52205
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52205.        (((A and B) -> B) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-22, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52206
in-theory        52206
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52206.        (((A and B) -> A) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-21, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52207
in-theory        52207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52207.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-20, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52208
in-theory        52208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52208.        ((A -> (B -> A)) and (((C and D) -> D) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-19, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52209
in-theory        52209
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-7 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-4 tm-8 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52209.        (A or (((B and C) -> C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-7, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52210
in-theory        52210
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-4 tm-8 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52210.        ((((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F), M:tm-6, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52211
in-theory        52211
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52211.        (A -> ((((B and C) -> C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and A)), M:tm-5, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52212
in-theory        52212
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-1 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-4 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52212.        (A -> (((B and C) -> C) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-1, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52213
in-theory        52213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52213.        ((A -> (B -> (C or B))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-622, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52214
in-theory        52214
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52214.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52215
in-theory        52215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52215.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-605, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52216
in-theory        52216
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G or F)) and (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52216.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G or F)) and (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-595, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52217
in-theory        52217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52217.        (((A -> (B or A)) or C) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-550, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52218
in-theory        52218
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52218.        ((A or (B -> (C or B))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-540, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52219
in-theory        52219
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52219.        ((A or (B -> (B or C))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-530, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52220
in-theory        52220
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52220.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-520, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52221
in-theory        52221
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52221.        ((A or ((B and C) -> C)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-510, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52222
in-theory        52222
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52222.        ((A or ((B and C) -> B)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-500, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52223
in-theory        52223
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52223.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-490, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52224
in-theory        52224
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52224.        ((A or (B -> (C -> B))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-480, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52225
in-theory        52225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52225.        ((A -> (B -> (B or C))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-469, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52226
in-theory        52226
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52226.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52227
in-theory        52227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52227.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-453, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52228
in-theory        52228
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (F or G)) and (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52228.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (F or G)) and (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-443, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52229
in-theory        52229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52229.        (((A -> (A or B)) or C) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-409, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52230
in-theory        52230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52230.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-400, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52231
in-theory        52231
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52231.        ((((A and B) -> B) or C) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-391, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52232
in-theory        52232
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52232.        ((((A and B) -> A) or C) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-382, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52233
in-theory        52233
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52233.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-373, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52234
in-theory        52234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52234.        (((A -> (B -> A)) or C) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-364, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52235
in-theory        52235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52235.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-354, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52236
in-theory        52236
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52236.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52237
in-theory        52237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52237.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-338, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52238
in-theory        52238
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52238.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-327, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52239
in-theory        52239
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> G) and (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52239.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> G) and (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-326, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52240
in-theory        52240
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> F) and (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52240.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> F) and (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-325, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52241
in-theory        52241
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52241.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-324, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52242
in-theory        52242
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> F)) and (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52242.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> F)) and (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-323, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52243
in-theory        52243
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52243.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52244
in-theory        52244
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52244.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52245
in-theory        52245
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52245.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52246
in-theory        52246
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52246.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52247
in-theory        52247
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F or (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52247.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F or (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-311, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52248
in-theory        52248
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52248.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F)), M:tm-310, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52249
in-theory        52249
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52249.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and F))), M:tm-309, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52250
in-theory        52250
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-657 ((A (-> (and Am Bm) Am)) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52250.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-308, m:tm-657, u:((A (-> (and Am Bm) Am)) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))
================================================================
tm-name          tm-52251
in-theory        52251
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((A and B) -> A))
theorem-size     25
proof            (modus-ponens tm-307 tm-657 ((A (-> (and Am Bm) Am)) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52251.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((A and B) -> A)), M:tm-307, m:tm-657, u:((A (-> (and Am Bm) Am)) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))
================================================================
tm-name          tm-52252
in-theory        52252
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52252.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-305, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52253
in-theory        52253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52253.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-303, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52254
in-theory        52254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52254.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-270, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52255
in-theory        52255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52255.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-239, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52256
in-theory        52256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52256.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-210, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52257
in-theory        52257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52257.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-183, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52258
in-theory        52258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52258.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-157, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52259
in-theory        52259
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52259.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-147, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52260
in-theory        52260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52260.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-134, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52261
in-theory        52261
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52261.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-125, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52262
in-theory        52262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52262.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-113, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52263
in-theory        52263
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52263.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-105, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52264
in-theory        52264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52264.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-95, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52265
in-theory        52265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52265.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-83, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52266
in-theory        52266
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-3 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52266.        (((not (not A)) -> A) and (((B and C) -> B) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-76, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52267
in-theory        52267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-3 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52267.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-69, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52268
in-theory        52268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52268.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-54, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52269
in-theory        52269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52269.        ((A -> (B or A)) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-42, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52270
in-theory        52270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52270.        ((A -> (A or B)) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-32, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52271
in-theory        52271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52271.        ((A -> (B -> (A and B))) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-23, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52272
in-theory        52272
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52272.        (((A and B) -> B) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-22, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52273
in-theory        52273
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52273.        (((A and B) -> A) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-21, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52274
in-theory        52274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52274.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-20, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52275
in-theory        52275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52275.        ((A -> (B -> A)) and (((C and D) -> C) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-19, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52276
in-theory        52276
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-7 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-3 tm-8 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52276.        (A or (((B and C) -> B) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-7, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52277
in-theory        52277
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-3 tm-8 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52277.        ((((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F), M:tm-6, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52278
in-theory        52278
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52278.        (A -> ((((B and C) -> B) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and A)), M:tm-5, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52279
in-theory        52279
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-1 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-3 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52279.        (A -> (((B and C) -> B) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-1, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52280
in-theory        52280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-622 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52280.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-622, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52281
in-theory        52281
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (H or G)))
theorem-size     33
proof            (modus-ponens tm-609 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52281.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (H or G))), M:tm-609, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52282
in-theory        52282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-605 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52282.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-605, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52283
in-theory        52283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-595 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52283.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-595, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52284
in-theory        52284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-550 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52284.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-550, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52285
in-theory        52285
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-540 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52285.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-540, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52286
in-theory        52286
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-530 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52286.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-530, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52287
in-theory        52287
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-520 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52287.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-520, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52288
in-theory        52288
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-510 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52288.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-510, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52289
in-theory        52289
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-500 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52289.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-500, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52290
in-theory        52290
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-490 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52290.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-490, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52291
in-theory        52291
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-480 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52291.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-480, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52292
in-theory        52292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-469 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52292.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-469, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52293
in-theory        52293
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (G or H)))
theorem-size     33
proof            (modus-ponens tm-456 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52293.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (G or H))), M:tm-456, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52294
in-theory        52294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-453 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52294.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-453, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52295
in-theory        52295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-443 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52295.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-443, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52296
in-theory        52296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-409 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52296.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-409, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52297
in-theory        52297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-400 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52297.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-400, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52298
in-theory        52298
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-391 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52298.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-391, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52299
in-theory        52299
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-382 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52299.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-382, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52300
in-theory        52300
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-373 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52300.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-373, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52301
in-theory        52301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-364 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52301.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-364, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52302
in-theory        52302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-354 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52302.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-354, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52303
in-theory        52303
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (H -> (G and H))))
theorem-size     35
proof            (modus-ponens tm-341 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52303.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52304
in-theory        52304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     37
proof            (modus-ponens tm-338 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52304.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-338, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52305
in-theory        52305
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     63
proof            (modus-ponens tm-327 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52305.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-327, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52306
in-theory        52306
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-326 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52306.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-326, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52307
in-theory        52307
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-325 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52307.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-325, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52308
in-theory        52308
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     69
proof            (modus-ponens tm-324 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       249
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52308.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-324, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52309
in-theory        52309
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     61
proof            (modus-ponens tm-323 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52309.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-323, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52310
in-theory        52310
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G and H) -> H))
theorem-size     33
proof            (modus-ponens tm-322 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52310.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52311
in-theory        52311
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G and H) -> G))
theorem-size     33
proof            (modus-ponens tm-320 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52311.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52312
in-theory        52312
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     41
proof            (modus-ponens tm-318 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52312.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52313
in-theory        52313
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (H -> G)))
theorem-size     33
proof            (modus-ponens tm-315 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52313.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52314
in-theory        52314
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     57
proof            (modus-ponens tm-311 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52314.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-311, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52315
in-theory        52315
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) or G))
theorem-size     57
proof            (modus-ponens tm-310 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52315.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) or G)), M:tm-310, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52316
in-theory        52316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and G)))
theorem-size     59
proof            (modus-ponens tm-309 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52316.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and G))), M:tm-309, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52317
in-theory        52317
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     41
proof            (modus-ponens tm-308 tm-658 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52317.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-308, m:tm-658, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))
================================================================
tm-name          tm-52318
in-theory        52318
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-307 tm-658 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52318.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-658, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))
================================================================
tm-name          tm-52319
in-theory        52319
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))))
theorem-size     57
proof            (modus-ponens tm-305 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52319.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))), M:tm-305, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52320
in-theory        52320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-303 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52320.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-303, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52321
in-theory        52321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-270 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52321.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-270, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52322
in-theory        52322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-239 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52322.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-239, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52323
in-theory        52323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J))))
theorem-size     45
proof            (modus-ponens tm-210 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52323.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-210, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52324
in-theory        52324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-183 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52324.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-183, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52325
in-theory        52325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-157 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52325.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-157, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52326
in-theory        52326
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     43
proof            (modus-ponens tm-147 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52326.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-147, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52327
in-theory        52327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-134 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52327.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-134, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52328
in-theory        52328
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     43
proof            (modus-ponens tm-125 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52328.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-125, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52329
in-theory        52329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J))))
theorem-size     43
proof            (modus-ponens tm-113 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52329.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-113, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52330
in-theory        52330
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-105 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52330.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-105, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52331
in-theory        52331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-95 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52331.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-95, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52332
in-theory        52332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-83 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52332.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-83, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52333
in-theory        52333
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     33
proof            (modus-ponens tm-76 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52333.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-76, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52334
in-theory        52334
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-69 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52334.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-69, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52335
in-theory        52335
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-54 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52335.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-54, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52336
in-theory        52336
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-42 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52336.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-42, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52337
in-theory        52337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-32 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52337.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-32, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52338
in-theory        52338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-23 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52338.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-23, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52339
in-theory        52339
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-22 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52339.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-22, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52340
in-theory        52340
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-21 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52340.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-21, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52341
in-theory        52341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-20 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52341.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-20, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52342
in-theory        52342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-19 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52342.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-19, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52343
in-theory        52343
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-7 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-8 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52343.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-7, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52344
in-theory        52344
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) or G)
theorem-size     29
proof            (modus-ponens tm-6 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-8 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52344.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) or G), M:tm-6, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52345
in-theory        52345
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52345.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))) and A)), M:tm-5, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52346
in-theory        52346
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-1 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-8)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52346.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-1, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-52347
in-theory        52347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52347.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-622, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52348
in-theory        52348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52348.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G or F))), M:tm-609, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52349
in-theory        52349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52349.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-605, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52350
in-theory        52350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52350.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G or F)) and ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-595, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52351
in-theory        52351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52351.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-550, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52352
in-theory        52352
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52352.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-540, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52353
in-theory        52353
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52353.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-530, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52354
in-theory        52354
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52354.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-520, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52355
in-theory        52355
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52355.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-510, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52356
in-theory        52356
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52356.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-500, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52357
in-theory        52357
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52357.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-490, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52358
in-theory        52358
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52358.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-480, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52359
in-theory        52359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52359.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-469, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52360
in-theory        52360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52360.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (F or G))), M:tm-456, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52361
in-theory        52361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52361.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-453, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52362
in-theory        52362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52362.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (F or G)) and ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-443, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52363
in-theory        52363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52363.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-409, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52364
in-theory        52364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52364.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-400, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52365
in-theory        52365
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52365.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-391, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52366
in-theory        52366
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52366.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-382, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52367
in-theory        52367
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52367.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-373, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52368
in-theory        52368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52368.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-364, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52369
in-theory        52369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52369.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-354, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52370
in-theory        52370
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       159
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52370.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52371
in-theory        52371
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52371.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-338, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52372
in-theory        52372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52372.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-327, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52373
in-theory        52373
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> G) and ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52373.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> G) and ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-326, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52374
in-theory        52374
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> F) and ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52374.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F and G) -> F) and ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-325, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52375
in-theory        52375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52375.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-324, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52376
in-theory        52376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52376.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> F)) and ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-323, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52377
in-theory        52377
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52377.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52378
in-theory        52378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52378.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52379
in-theory        52379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52379.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52380
in-theory        52380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52380.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52381
in-theory        52381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F or ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52381.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F or ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-311, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52382
in-theory        52382
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52382.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F)), M:tm-310, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52383
in-theory        52383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52383.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and F))), M:tm-309, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52384
in-theory        52384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-308 tm-659 ((A (-> Am (-> Bm Am))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52384.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-308, m:tm-659, u:((A (-> Am (-> Bm Am))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))
================================================================
tm-name          tm-52385
in-theory        52385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (A -> (B -> A)))
theorem-size     25
proof            (modus-ponens tm-307 tm-659 ((A (-> Am (-> Bm Am))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52385.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (A -> (B -> A))), M:tm-307, m:tm-659, u:((A (-> Am (-> Bm Am))) (B (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))
================================================================
tm-name          tm-52386
in-theory        52386
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52386.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and (F -> ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))))), M:tm-305, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52387
in-theory        52387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52387.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-303, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52388
in-theory        52388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52388.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-270, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52389
in-theory        52389
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52389.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-239, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52390
in-theory        52390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52390.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-210, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52391
in-theory        52391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52391.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-183, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52392
in-theory        52392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52392.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-157, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52393
in-theory        52393
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52393.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-147, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52394
in-theory        52394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52394.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-134, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52395
in-theory        52395
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52395.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-125, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52396
in-theory        52396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52396.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-113, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52397
in-theory        52397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52397.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-105, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52398
in-theory        52398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52398.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-95, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52399
in-theory        52399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52399.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-83, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52400
in-theory        52400
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52400.        (((not (not A)) -> A) and ((B -> (C -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-76, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52401
in-theory        52401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52401.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-69, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52402
in-theory        52402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52402.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-54, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52403
in-theory        52403
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52403.        ((A -> (B or A)) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-42, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52404
in-theory        52404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52404.        ((A -> (A or B)) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-32, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52405
in-theory        52405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52405.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-23, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52406
in-theory        52406
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52406.        (((A and B) -> B) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-22, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52407
in-theory        52407
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52407.        (((A and B) -> A) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-21, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52408
in-theory        52408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52408.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-20, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52409
in-theory        52409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52409.        ((A -> (B -> A)) and ((C -> (D -> C)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-19, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52410
in-theory        52410
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-7 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-7 tm-5 tm-1 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52410.        (A or ((B -> (C -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-7, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52411
in-theory        52411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-6 tm-5 tm-1 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52411.        (((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))) or F), M:tm-6, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52412
in-theory        52412
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52412.        (A -> (((B -> (C -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and A)), M:tm-5, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52413
in-theory        52413
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-1 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52413.        (A -> ((B -> (C -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-1, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-52414
in-theory        52414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (D -> C)))
theorem-size     9
proof            (modus-ponens tm-660 tm-11 ((Am (-> A B)) (C (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-52414.        ((A -> B) -> (C -> (D -> C))), M:tm-660, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-52415
in-theory        52415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     17
proof            (modus-ponens tm-660 tm-14 ((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-52415.        ((A -> B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-660, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-52416
in-theory        52416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C and D) -> C))
theorem-size     9
proof            (modus-ponens tm-660 tm-16 ((Am (-> A B)) (C (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-52416.        ((A -> B) -> ((C and D) -> C)), M:tm-660, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-52417
in-theory        52417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C and D) -> D))
theorem-size     9
proof            (modus-ponens tm-660 tm-18 ((Am (-> A B)) (C (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-52417.        ((A -> B) -> ((C and D) -> D)), M:tm-660, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-52418
in-theory        52418
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (D -> C)) and (A -> B)))
theorem-size     13
proof            (modus-ponens tm-660 tm-19 ((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-52418.        ((A -> B) -> ((C -> (D -> C)) and (A -> B))), M:tm-660, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
================================================================
tm-name          tm-52419
in-theory        52419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> B)))
theorem-size     21
proof            (modus-ponens tm-660 tm-20 ((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-52419.        ((A -> B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> B))), M:tm-660, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
================================================================
tm-name          tm-52420
in-theory        52420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C and D) -> C) and (A -> B)))
theorem-size     13
proof            (modus-ponens tm-660 tm-21 ((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-52420.        ((A -> B) -> (((C and D) -> C) and (A -> B))), M:tm-660, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
================================================================
tm-name          tm-52421
in-theory        52421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C and D) -> D) and (A -> B)))
theorem-size     13
proof            (modus-ponens tm-660 tm-22 ((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-52421.        ((A -> B) -> (((C and D) -> D) and (A -> B))), M:tm-660, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
================================================================
tm-name          tm-52422
in-theory        52422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (D -> (C and D))) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-23 ((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-52422.        ((A -> B) -> ((C -> (D -> (C and D))) and (A -> B))), M:tm-660, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
================================================================
tm-name          tm-52423
in-theory        52423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (D -> (C and D))))
theorem-size     11
proof            (modus-ponens tm-660 tm-25 ((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-52423.        ((A -> B) -> (C -> (D -> (C and D)))), M:tm-660, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-52424
in-theory        52424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (C or D)) and (A -> B)))
theorem-size     13
proof            (modus-ponens tm-660 tm-32 ((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-52424.        ((A -> B) -> ((C -> (C or D)) and (A -> B))), M:tm-660, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
================================================================
tm-name          tm-52425
in-theory        52425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (C or D)))
theorem-size     9
proof            (modus-ponens tm-660 tm-33 ((Am (-> A B)) (C (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-52425.        ((A -> B) -> (C -> (C or D))), M:tm-660, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-52426
in-theory        52426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (D or C)) and (A -> B)))
theorem-size     13
proof            (modus-ponens tm-660 tm-42 ((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-52426.        ((A -> B) -> ((C -> (D or C)) and (A -> B))), M:tm-660, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
================================================================
tm-name          tm-52427
in-theory        52427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (D or C)))
theorem-size     9
proof            (modus-ponens tm-660 tm-43 ((Am (-> A B)) (C (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-52427.        ((A -> B) -> (C -> (D or C))), M:tm-660, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-52428
in-theory        52428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> B)))
theorem-size     21
proof            (modus-ponens tm-660 tm-54 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-52428.        ((A -> B) -> (((C -> D) -> ((D -> E) -> ((C or D) -> E))) and (A -> B))), M:tm-660, m:tm-54, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> A B))))
================================================================
tm-name          tm-52429
in-theory        52429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     17
proof            (modus-ponens tm-660 tm-56 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-52429.        ((A -> B) -> ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-660, m:tm-56, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-52430
in-theory        52430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> B)))
theorem-size     19
proof            (modus-ponens tm-660 tm-69 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-52430.        ((A -> B) -> (((C -> D) -> ((C -> (not D)) -> (not C))) and (A -> B))), M:tm-660, m:tm-69, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> A B))))
================================================================
tm-name          tm-52431
in-theory        52431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> D) -> ((C -> (not D)) -> (not C))))
theorem-size     15
proof            (modus-ponens tm-660 tm-71 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-9)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-52431.        ((A -> B) -> ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-660, m:tm-71, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-52432
in-theory        52432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((not (not C)) -> C) and (A -> B)))
theorem-size     13
proof            (modus-ponens tm-660 tm-76 ((Am (-> A B)) (C (and (-> (not (not Bm)) Bm) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-10)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-52432.        ((A -> B) -> (((not (not C)) -> C) and (A -> B))), M:tm-660, m:tm-76, u:((Am (-> A B)) (C (and (-> (not (not Bm)) Bm) (-> A B))))
================================================================
tm-name          tm-52433
in-theory        52433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((not (not C)) -> C))
theorem-size     9
proof            (modus-ponens tm-660 tm-78 ((Am (-> A B)) (C (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-10)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-52433.        ((A -> B) -> ((not (not C)) -> C)), M:tm-660, m:tm-78, u:((Am (-> A B)) (C (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-52434
in-theory        52434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (D -> (E -> D))) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-83 ((Am (-> A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-52434.        ((A -> B) -> ((C -> (D -> (E -> D))) and (A -> B))), M:tm-660, m:tm-83, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (-> Dm Cm))) (-> A B))))
================================================================
tm-name          tm-52435
in-theory        52435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (D -> (E -> D))))
theorem-size     11
proof            (modus-ponens tm-660 tm-85 ((Am (-> A B)) (C (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-52435.        ((A -> B) -> (C -> (D -> (E -> D)))), M:tm-660, m:tm-85, u:((Am (-> A B)) (C (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-52436
in-theory        52436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> D) -> (C -> C)) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-95 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-52436.        ((A -> B) -> (((C -> D) -> (C -> C)) and (A -> B))), M:tm-660, m:tm-95, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> Bm Bm)) (-> A B))))
================================================================
tm-name          tm-52437
in-theory        52437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> D) -> (C -> C)))
theorem-size     11
proof            (modus-ponens tm-660 tm-97 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-52437.        ((A -> B) -> ((C -> D) -> (C -> C))), M:tm-660, m:tm-97, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-52438
in-theory        52438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> B)))
theorem-size     27
proof            (modus-ponens tm-660 tm-105 ((Am (-> A B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-52438.        ((A -> B) -> ((((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))) and (A -> B))), M:tm-660, m:tm-105, u:((Am (-> A B)) (C (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> A B))))
================================================================
tm-name          tm-52439
in-theory        52439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-660 tm-107 ((Am (-> A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-52439.        ((A -> B) -> (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-660, m:tm-107, u:((Am (-> A B)) (C (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-52440
in-theory        52440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> B)))
theorem-size     23
proof            (modus-ponens tm-660 tm-113 ((Am (-> A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-52440.        ((A -> B) -> ((C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> B))), M:tm-660, m:tm-113, u:((Am (-> A B)) (C (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A B))))
================================================================
tm-name          tm-52441
in-theory        52441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     19
proof            (modus-ponens tm-660 tm-115 ((Am (-> A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-52441.        ((A -> B) -> (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-660, m:tm-115, u:((Am (-> A B)) (C (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-52442
in-theory        52442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> B)))
theorem-size     23
proof            (modus-ponens tm-660 tm-125 ((Am (-> A B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-52442.        ((A -> B) -> (((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)) and (A -> B))), M:tm-660, m:tm-125, u:((Am (-> A B)) (C (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> A B))))
================================================================
tm-name          tm-52443
in-theory        52443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D)))
theorem-size     19
proof            (modus-ponens tm-660 tm-127 ((Am (-> A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-52443.        ((A -> B) -> ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-660, m:tm-127, u:((Am (-> A B)) (C (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-52444
in-theory        52444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> ((D and E) -> D)) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-134 ((Am (-> A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-52444.        ((A -> B) -> ((C -> ((D and E) -> D)) and (A -> B))), M:tm-660, m:tm-134, u:((Am (-> A B)) (C (and (-> Bm (-> (and Cm Dm) Cm)) (-> A B))))
================================================================
tm-name          tm-52445
in-theory        52445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((D and E) -> D)))
theorem-size     11
proof            (modus-ponens tm-660 tm-136 ((Am (-> A B)) (C (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-52445.        ((A -> B) -> (C -> ((D and E) -> D))), M:tm-660, m:tm-136, u:((Am (-> A B)) (C (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-52446
in-theory        52446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> B)))
theorem-size     23
proof            (modus-ponens tm-660 tm-147 ((Am (-> A B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-52446.        ((A -> B) -> ((((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)) and (A -> B))), M:tm-660, m:tm-147, u:((Am (-> A B)) (C (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> A B))))
================================================================
tm-name          tm-52447
in-theory        52447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-660 tm-149 ((Am (-> A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-52447.        ((A -> B) -> (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-660, m:tm-149, u:((Am (-> A B)) (C (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-52448
in-theory        52448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> ((D and E) -> E)) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-157 ((Am (-> A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-52448.        ((A -> B) -> ((C -> ((D and E) -> E)) and (A -> B))), M:tm-660, m:tm-157, u:((Am (-> A B)) (C (and (-> Bm (-> (and Cm Dm) Dm)) (-> A B))))
================================================================
tm-name          tm-52449
in-theory        52449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((D and E) -> E)))
theorem-size     11
proof            (modus-ponens tm-660 tm-159 ((Am (-> A B)) (C (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-52449.        ((A -> B) -> (C -> ((D and E) -> E))), M:tm-660, m:tm-159, u:((Am (-> A B)) (C (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-52450
in-theory        52450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> ((D -> (E -> D)) and C)) and (A -> B)))
theorem-size     17
proof            (modus-ponens tm-660 tm-183 ((Am (-> A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-52450.        ((A -> B) -> ((C -> ((D -> (E -> D)) and C)) and (A -> B))), M:tm-660, m:tm-183, u:((Am (-> A B)) (C (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> A B))))
================================================================
tm-name          tm-52451
in-theory        52451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((D -> (E -> D)) and C)))
theorem-size     13
proof            (modus-ponens tm-660 tm-184 ((Am (-> A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-52451.        ((A -> B) -> (C -> ((D -> (E -> D)) and C))), M:tm-660, m:tm-184, u:((Am (-> A B)) (C (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-52452
in-theory        52452
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> B)))
theorem-size     25
proof            (modus-ponens tm-660 tm-210 ((Am (-> A B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-52452.        ((A -> B) -> ((C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and (A -> B))), M:tm-660, m:tm-210, u:((Am (-> A B)) (C (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> A B))))
================================================================
tm-name          tm-52453
in-theory        52453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     21
proof            (modus-ponens tm-660 tm-211 ((Am (-> A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-52453.        ((A -> B) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-660, m:tm-211, u:((Am (-> A B)) (C (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-52454
in-theory        52454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (((D and E) -> D) and C)) and (A -> B)))
theorem-size     17
proof            (modus-ponens tm-660 tm-239 ((Am (-> A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-52454.        ((A -> B) -> ((C -> (((D and E) -> D) and C)) and (A -> B))), M:tm-660, m:tm-239, u:((Am (-> A B)) (C (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> A B))))
================================================================
tm-name          tm-52455
in-theory        52455
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (((D and E) -> D) and C)))
theorem-size     13
proof            (modus-ponens tm-660 tm-240 ((Am (-> A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-52455.        ((A -> B) -> (C -> (((D and E) -> D) and C))), M:tm-660, m:tm-240, u:((Am (-> A B)) (C (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-52456
in-theory        52456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (((D and E) -> E) and C)) and (A -> B)))
theorem-size     17
proof            (modus-ponens tm-660 tm-270 ((Am (-> A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-52456.        ((A -> B) -> ((C -> (((D and E) -> E) and C)) and (A -> B))), M:tm-660, m:tm-270, u:((Am (-> A B)) (C (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> A B))))
================================================================
tm-name          tm-52457
in-theory        52457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (((D and E) -> E) and C)))
theorem-size     13
proof            (modus-ponens tm-660 tm-271 ((Am (-> A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-52457.        ((A -> B) -> (C -> (((D and E) -> E) and C))), M:tm-660, m:tm-271, u:((Am (-> A B)) (C (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-52458
in-theory        52458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> B)))
theorem-size     19
proof            (modus-ponens tm-660 tm-303 ((Am (-> A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-52458.        ((A -> B) -> ((C -> ((D -> (E -> (D and E))) and C)) and (A -> B))), M:tm-660, m:tm-303, u:((Am (-> A B)) (C (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> A B))))
================================================================
tm-name          tm-52459
in-theory        52459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((D -> (E -> (D and E))) and C)))
theorem-size     15
proof            (modus-ponens tm-660 tm-304 ((Am (-> A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-52459.        ((A -> B) -> (C -> ((D -> (E -> (D and E))) and C))), M:tm-660, m:tm-304, u:((Am (-> A B)) (C (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-52460
in-theory        52460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (C -> (A -> B))))
theorem-size     13
proof            (modus-ponens tm-660 tm-305 ((Am (-> A B)) (C (and (-> A B) (-> Bm (-> A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-52460.        ((A -> B) -> ((A -> B) and (C -> (A -> B)))), M:tm-660, m:tm-305, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (-> A B)))))
================================================================
tm-name          tm-52461
in-theory        52461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (C -> ((A -> B) and C))))
theorem-size     15
proof            (modus-ponens tm-660 tm-309 ((Am (-> A B)) (C (and (-> A B) (-> Bm (and (-> A B) Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-52461.        ((A -> B) -> ((A -> B) and (C -> ((A -> B) and C)))), M:tm-660, m:tm-309, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (and (-> A B) Bm)))))
================================================================
tm-name          tm-52462
in-theory        52462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((A -> B) or C)))
theorem-size     13
proof            (modus-ponens tm-660 tm-310 ((Am (-> A B)) (C (and (-> A B) (or (-> A B) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-52462.        ((A -> B) -> ((A -> B) and ((A -> B) or C))), M:tm-660, m:tm-310, u:((Am (-> A B)) (C (and (-> A B) (or (-> A B) Bm))))
================================================================
tm-name          tm-52463
in-theory        52463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (C or (A -> B))))
theorem-size     13
proof            (modus-ponens tm-660 tm-311 ((Am (-> A B)) (C (and (-> A B) (or Bm (-> A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-52463.        ((A -> B) -> ((A -> B) and (C or (A -> B)))), M:tm-660, m:tm-311, u:((Am (-> A B)) (C (and (-> A B) (or Bm (-> A B)))))
================================================================
tm-name          tm-52464
in-theory        52464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (C -> (D -> C))))
theorem-size     13
proof            (modus-ponens tm-660 tm-315 ((Am (-> A B)) (C (and (-> A B) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       135
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-52464.        ((A -> B) -> ((A -> B) and (C -> (D -> C)))), M:tm-660, m:tm-315, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-52465
in-theory        52465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     21
proof            (modus-ponens tm-660 tm-318 ((Am (-> A B)) (C (and (-> A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-52465.        ((A -> B) -> ((A -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-660, m:tm-318, u:((Am (-> A B)) (C (and (-> A B) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-52466
in-theory        52466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((C and D) -> C)))
theorem-size     13
proof            (modus-ponens tm-660 tm-320 ((Am (-> A B)) (C (and (-> A B) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       135
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-52466.        ((A -> B) -> ((A -> B) and ((C and D) -> C))), M:tm-660, m:tm-320, u:((Am (-> A B)) (C (and (-> A B) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-52467
in-theory        52467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((C and D) -> D)))
theorem-size     13
proof            (modus-ponens tm-660 tm-322 ((Am (-> A B)) (C (and (-> A B) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       135
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-52467.        ((A -> B) -> ((A -> B) and ((C and D) -> D))), M:tm-660, m:tm-322, u:((Am (-> A B)) (C (and (-> A B) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-52468
in-theory        52468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((C -> (D -> C)) and (A -> B))))
theorem-size     17
proof            (modus-ponens tm-660 tm-323 ((Am (-> A B)) (C (and (-> A B) (and (-> Bm (-> Cm Bm)) (-> A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-52468.        ((A -> B) -> ((A -> B) and ((C -> (D -> C)) and (A -> B)))), M:tm-660, m:tm-323, u:((Am (-> A B)) (C (and (-> A B) (and (-> Bm (-> Cm Bm)) (-> A B)))))
================================================================
tm-name          tm-52469
in-theory        52469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> B))))
theorem-size     25
proof            (modus-ponens tm-660 tm-324 ((Am (-> A B)) (C (and (-> A B) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-52469.        ((A -> B) -> ((A -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (A -> B)))), M:tm-660, m:tm-324, u:((Am (-> A B)) (C (and (-> A B) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B)))))
================================================================
tm-name          tm-52470
in-theory        52470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (((C and D) -> C) and (A -> B))))
theorem-size     17
proof            (modus-ponens tm-660 tm-325 ((Am (-> A B)) (C (and (-> A B) (and (-> (and Bm Cm) Bm) (-> A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-52470.        ((A -> B) -> ((A -> B) and (((C and D) -> C) and (A -> B)))), M:tm-660, m:tm-325, u:((Am (-> A B)) (C (and (-> A B) (and (-> (and Bm Cm) Bm) (-> A B)))))
================================================================
tm-name          tm-52471
in-theory        52471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (((C and D) -> D) and (A -> B))))
theorem-size     17
proof            (modus-ponens tm-660 tm-326 ((Am (-> A B)) (C (and (-> A B) (and (-> (and Bm Cm) Cm) (-> A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-52471.        ((A -> B) -> ((A -> B) and (((C and D) -> D) and (A -> B)))), M:tm-660, m:tm-326, u:((Am (-> A B)) (C (and (-> A B) (and (-> (and Bm Cm) Cm) (-> A B)))))
================================================================
tm-name          tm-52472
in-theory        52472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((C -> (D -> (C and D))) and (A -> B))))
theorem-size     19
proof            (modus-ponens tm-660 tm-327 ((Am (-> A B)) (C (and (-> A B) (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-52472.        ((A -> B) -> ((A -> B) and ((C -> (D -> (C and D))) and (A -> B)))), M:tm-660, m:tm-327, u:((Am (-> A B)) (C (and (-> A B) (and (-> Bm (-> Cm (and Bm Cm))) (-> A B)))))
================================================================
tm-name          tm-52473
in-theory        52473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> D) -> (C -> (C and D))) and (A -> B)))
theorem-size     17
proof            (modus-ponens tm-660 tm-338 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-52473.        ((A -> B) -> (((C -> D) -> (C -> (C and D))) and (A -> B))), M:tm-660, m:tm-338, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> A B))))
================================================================
tm-name          tm-52474
in-theory        52474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> D) -> (C -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-660 tm-340 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-52474.        ((A -> B) -> ((C -> D) -> (C -> (C and D)))), M:tm-660, m:tm-340, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-52475
in-theory        52475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (C -> (D -> (C and D)))))
theorem-size     15
proof            (modus-ponens tm-660 tm-341 ((Am (-> A B)) (C (and (-> A B) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       143
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-52475.        ((A -> B) -> ((A -> B) and (C -> (D -> (C and D))))), M:tm-660, m:tm-341, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-52476
in-theory        52476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (D -> (E -> (D and E)))) and (A -> B)))
theorem-size     17
proof            (modus-ponens tm-660 tm-354 ((Am (-> A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-52476.        ((A -> B) -> ((C -> (D -> (E -> (D and E)))) and (A -> B))), M:tm-660, m:tm-354, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A B))))
================================================================
tm-name          tm-52477
in-theory        52477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (D -> (E -> (D and E)))))
theorem-size     13
proof            (modus-ponens tm-660 tm-356 ((Am (-> A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-52477.        ((A -> B) -> (C -> (D -> (E -> (D and E))))), M:tm-660, m:tm-356, u:((Am (-> A B)) (C (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-52478
in-theory        52478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> (D -> C)) or E) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-364 ((Am (-> A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-52478.        ((A -> B) -> (((C -> (D -> C)) or E) and (A -> B))), M:tm-660, m:tm-364, u:((Am (-> A B)) (C (and (or (-> Bm (-> Cm Bm)) Dm) (-> A B))))
================================================================
tm-name          tm-52479
in-theory        52479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (D -> C)) or E))
theorem-size     11
proof            (modus-ponens tm-660 tm-365 ((Am (-> A B)) (C (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-52479.        ((A -> B) -> ((C -> (D -> C)) or E)), M:tm-660, m:tm-365, u:((Am (-> A B)) (C (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-52480
in-theory        52480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> B)))
theorem-size     23
proof            (modus-ponens tm-660 tm-373 ((Am (-> A B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-52480.        ((A -> B) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F) and (A -> B))), M:tm-660, m:tm-373, u:((Am (-> A B)) (C (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> A B))))
================================================================
tm-name          tm-52481
in-theory        52481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F))
theorem-size     19
proof            (modus-ponens tm-660 tm-374 ((Am (-> A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-52481.        ((A -> B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-660, m:tm-374, u:((Am (-> A B)) (C (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-52482
in-theory        52482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C and D) -> C) or E) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-382 ((Am (-> A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-52482.        ((A -> B) -> ((((C and D) -> C) or E) and (A -> B))), M:tm-660, m:tm-382, u:((Am (-> A B)) (C (and (or (-> (and Bm Cm) Bm) Dm) (-> A B))))
================================================================
tm-name          tm-52483
in-theory        52483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C and D) -> C) or E))
theorem-size     11
proof            (modus-ponens tm-660 tm-383 ((Am (-> A B)) (C (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-52483.        ((A -> B) -> (((C and D) -> C) or E)), M:tm-660, m:tm-383, u:((Am (-> A B)) (C (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-52484
in-theory        52484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C and D) -> D) or E) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-391 ((Am (-> A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-52484.        ((A -> B) -> ((((C and D) -> D) or E) and (A -> B))), M:tm-660, m:tm-391, u:((Am (-> A B)) (C (and (or (-> (and Bm Cm) Cm) Dm) (-> A B))))
================================================================
tm-name          tm-52485
in-theory        52485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C and D) -> D) or E))
theorem-size     11
proof            (modus-ponens tm-660 tm-392 ((Am (-> A B)) (C (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-52485.        ((A -> B) -> (((C and D) -> D) or E)), M:tm-660, m:tm-392, u:((Am (-> A B)) (C (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-52486
in-theory        52486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> (D -> (C and D))) or E) and (A -> B)))
theorem-size     17
proof            (modus-ponens tm-660 tm-400 ((Am (-> A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-52486.        ((A -> B) -> (((C -> (D -> (C and D))) or E) and (A -> B))), M:tm-660, m:tm-400, u:((Am (-> A B)) (C (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> A B))))
================================================================
tm-name          tm-52487
in-theory        52487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (D -> (C and D))) or E))
theorem-size     13
proof            (modus-ponens tm-660 tm-401 ((Am (-> A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-52487.        ((A -> B) -> ((C -> (D -> (C and D))) or E)), M:tm-660, m:tm-401, u:((Am (-> A B)) (C (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-52488
in-theory        52488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> (C or D)) or E) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-409 ((Am (-> A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-52488.        ((A -> B) -> (((C -> (C or D)) or E) and (A -> B))), M:tm-660, m:tm-409, u:((Am (-> A B)) (C (and (or (-> Bm (or Bm Cm)) Dm) (-> A B))))
================================================================
tm-name          tm-52489
in-theory        52489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (C or D)) or E))
theorem-size     11
proof            (modus-ponens tm-660 tm-410 ((Am (-> A B)) (C (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-52489.        ((A -> B) -> ((C -> (C or D)) or E)), M:tm-660, m:tm-410, u:((Am (-> A B)) (C (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-52490
in-theory        52490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((C -> (C or D)) and (A -> B))))
theorem-size     17
proof            (modus-ponens tm-660 tm-443 ((Am (-> A B)) (C (and (-> A B) (and (-> Bm (or Bm Cm)) (-> A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-52490.        ((A -> B) -> ((A -> B) and ((C -> (C or D)) and (A -> B)))), M:tm-660, m:tm-443, u:((Am (-> A B)) (C (and (-> A B) (and (-> Bm (or Bm Cm)) (-> A B)))))
================================================================
tm-name          tm-52491
in-theory        52491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> ((D -> (D or E)) and C)) and (A -> B)))
theorem-size     17
proof            (modus-ponens tm-660 tm-453 ((Am (-> A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-52491.        ((A -> B) -> ((C -> ((D -> (D or E)) and C)) and (A -> B))), M:tm-660, m:tm-453, u:((Am (-> A B)) (C (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> A B))))
================================================================
tm-name          tm-52492
in-theory        52492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((D -> (D or E)) and C)))
theorem-size     13
proof            (modus-ponens tm-660 tm-454 ((Am (-> A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-52492.        ((A -> B) -> (C -> ((D -> (D or E)) and C))), M:tm-660, m:tm-454, u:((Am (-> A B)) (C (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-52493
in-theory        52493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (C -> (C or D))))
theorem-size     13
proof            (modus-ponens tm-660 tm-456 ((Am (-> A B)) (C (and (-> A B) (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       135
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-52493.        ((A -> B) -> ((A -> B) and (C -> (C or D)))), M:tm-660, m:tm-456, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-52494
in-theory        52494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (D -> (D or E))) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-469 ((Am (-> A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-52494.        ((A -> B) -> ((C -> (D -> (D or E))) and (A -> B))), M:tm-660, m:tm-469, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (or Cm Dm))) (-> A B))))
================================================================
tm-name          tm-52495
in-theory        52495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (D -> (D or E))))
theorem-size     11
proof            (modus-ponens tm-660 tm-471 ((Am (-> A B)) (C (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-52495.        ((A -> B) -> (C -> (D -> (D or E)))), M:tm-660, m:tm-471, u:((Am (-> A B)) (C (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-52496
in-theory        52496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C or (D -> (E -> D))) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-480 ((Am (-> A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-52496.        ((A -> B) -> ((C or (D -> (E -> D))) and (A -> B))), M:tm-660, m:tm-480, u:((Am (-> A B)) (C (and (or Bm (-> Cm (-> Dm Cm))) (-> A B))))
================================================================
tm-name          tm-52497
in-theory        52497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or (D -> (E -> D))))
theorem-size     11
proof            (modus-ponens tm-660 tm-481 ((Am (-> A B)) (C (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-52497.        ((A -> B) -> (C or (D -> (E -> D)))), M:tm-660, m:tm-481, u:((Am (-> A B)) (C (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-52498
in-theory        52498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> B)))
theorem-size     23
proof            (modus-ponens tm-660 tm-490 ((Am (-> A B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-52498.        ((A -> B) -> ((C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (A -> B))), M:tm-660, m:tm-490, u:((Am (-> A B)) (C (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> A B))))
================================================================
tm-name          tm-52499
in-theory        52499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     19
proof            (modus-ponens tm-660 tm-491 ((Am (-> A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-52499.        ((A -> B) -> (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-660, m:tm-491, u:((Am (-> A B)) (C (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-52500
in-theory        52500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C or ((D and E) -> D)) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-500 ((Am (-> A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-52500.        ((A -> B) -> ((C or ((D and E) -> D)) and (A -> B))), M:tm-660, m:tm-500, u:((Am (-> A B)) (C (and (or Bm (-> (and Cm Dm) Cm)) (-> A B))))
================================================================
tm-name          tm-52501
in-theory        52501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or ((D and E) -> D)))
theorem-size     11
proof            (modus-ponens tm-660 tm-501 ((Am (-> A B)) (C (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 tm-3)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-52501.        ((A -> B) -> (C or ((D and E) -> D))), M:tm-660, m:tm-501, u:((Am (-> A B)) (C (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-52502
in-theory        52502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C or ((D and E) -> E)) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-510 ((Am (-> A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-52502.        ((A -> B) -> ((C or ((D and E) -> E)) and (A -> B))), M:tm-660, m:tm-510, u:((Am (-> A B)) (C (and (or Bm (-> (and Cm Dm) Dm)) (-> A B))))
================================================================
tm-name          tm-52503
in-theory        52503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or ((D and E) -> E)))
theorem-size     11
proof            (modus-ponens tm-660 tm-511 ((Am (-> A B)) (C (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 tm-4)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-52503.        ((A -> B) -> (C or ((D and E) -> E))), M:tm-660, m:tm-511, u:((Am (-> A B)) (C (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-52504
in-theory        52504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C or (D -> (E -> (D and E)))) and (A -> B)))
theorem-size     17
proof            (modus-ponens tm-660 tm-520 ((Am (-> A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-52504.        ((A -> B) -> ((C or (D -> (E -> (D and E)))) and (A -> B))), M:tm-660, m:tm-520, u:((Am (-> A B)) (C (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> A B))))
================================================================
tm-name          tm-52505
in-theory        52505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or (D -> (E -> (D and E)))))
theorem-size     13
proof            (modus-ponens tm-660 tm-521 ((Am (-> A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-52505.        ((A -> B) -> (C or (D -> (E -> (D and E))))), M:tm-660, m:tm-521, u:((Am (-> A B)) (C (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-52506
in-theory        52506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C or (D -> (D or E))) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-530 ((Am (-> A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-52506.        ((A -> B) -> ((C or (D -> (D or E))) and (A -> B))), M:tm-660, m:tm-530, u:((Am (-> A B)) (C (and (or Bm (-> Cm (or Cm Dm))) (-> A B))))
================================================================
tm-name          tm-52507
in-theory        52507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or (D -> (D or E))))
theorem-size     11
proof            (modus-ponens tm-660 tm-531 ((Am (-> A B)) (C (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 tm-6)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-52507.        ((A -> B) -> (C or (D -> (D or E)))), M:tm-660, m:tm-531, u:((Am (-> A B)) (C (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-52508
in-theory        52508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C or (D -> (E or D))) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-540 ((Am (-> A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-52508.        ((A -> B) -> ((C or (D -> (E or D))) and (A -> B))), M:tm-660, m:tm-540, u:((Am (-> A B)) (C (and (or Bm (-> Cm (or Dm Cm))) (-> A B))))
================================================================
tm-name          tm-52509
in-theory        52509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or (D -> (E or D))))
theorem-size     11
proof            (modus-ponens tm-660 tm-541 ((Am (-> A B)) (C (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-52509.        ((A -> B) -> (C or (D -> (E or D)))), M:tm-660, m:tm-541, u:((Am (-> A B)) (C (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-52510
in-theory        52510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> (D or C)) or E) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-550 ((Am (-> A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-52510.        ((A -> B) -> (((C -> (D or C)) or E) and (A -> B))), M:tm-660, m:tm-550, u:((Am (-> A B)) (C (and (or (-> Bm (or Cm Bm)) Dm) (-> A B))))
================================================================
tm-name          tm-52511
in-theory        52511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (D or C)) or E))
theorem-size     11
proof            (modus-ponens tm-660 tm-551 ((Am (-> A B)) (C (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-52511.        ((A -> B) -> ((C -> (D or C)) or E)), M:tm-660, m:tm-551, u:((Am (-> A B)) (C (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-52512
in-theory        52512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((C -> (D or C)) and (A -> B))))
theorem-size     17
proof            (modus-ponens tm-660 tm-595 ((Am (-> A B)) (C (and (-> A B) (and (-> Bm (or Cm Bm)) (-> A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-52512.        ((A -> B) -> ((A -> B) and ((C -> (D or C)) and (A -> B)))), M:tm-660, m:tm-595, u:((Am (-> A B)) (C (and (-> A B) (and (-> Bm (or Cm Bm)) (-> A B)))))
================================================================
tm-name          tm-52513
in-theory        52513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> ((D -> (E or D)) and C)) and (A -> B)))
theorem-size     17
proof            (modus-ponens tm-660 tm-605 ((Am (-> A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-52513.        ((A -> B) -> ((C -> ((D -> (E or D)) and C)) and (A -> B))), M:tm-660, m:tm-605, u:((Am (-> A B)) (C (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> A B))))
================================================================
tm-name          tm-52514
in-theory        52514
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((D -> (E or D)) and C)))
theorem-size     13
proof            (modus-ponens tm-660 tm-606 ((Am (-> A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-52514.        ((A -> B) -> (C -> ((D -> (E or D)) and C))), M:tm-660, m:tm-606, u:((Am (-> A B)) (C (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-52515
in-theory        52515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (C -> (D or C))))
theorem-size     13
proof            (modus-ponens tm-660 tm-609 ((Am (-> A B)) (C (and (-> A B) (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       135
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-52515.        ((A -> B) -> ((A -> B) and (C -> (D or C)))), M:tm-660, m:tm-609, u:((Am (-> A B)) (C (and (-> A B) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-52516
in-theory        52516
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> (D -> (E or D))) and (A -> B)))
theorem-size     15
proof            (modus-ponens tm-660 tm-622 ((Am (-> A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-52516.        ((A -> B) -> ((C -> (D -> (E or D))) and (A -> B))), M:tm-660, m:tm-622, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (or Dm Cm))) (-> A B))))
================================================================
tm-name          tm-52517
in-theory        52517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (D -> (E or D))))
theorem-size     11
proof            (modus-ponens tm-660 tm-624 ((Am (-> A B)) (C (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       109
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-52517.        ((A -> B) -> (C -> (D -> (E or D)))), M:tm-660, m:tm-624, u:((Am (-> A B)) (C (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-52518
in-theory        52518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and ((C or ((A -> B) -> C)) -> ((A -> B) -> C)))
theorem-size     25
proof            (modus-ponens tm-654 tm-660 ((A (-> Am Bm)) (B Cm) (C (-> (-> Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52518.        ((((A -> B) -> C) -> ((A -> B) -> C)) and ((C or ((A -> B) -> C)) -> ((A -> B) -> C))), M:tm-654, m:tm-660, u:((A (-> Am Bm)) (B Cm) (C (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52519
in-theory        52519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (D or ((A -> B) -> C)))
theorem-size     13
proof            (modus-ponens tm-623 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52519.        (((A -> B) -> C) -> (D or ((A -> B) -> C))), M:tm-623, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52520
in-theory        52520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52520.        ((A -> (B -> (C or B))) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-622, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52521
in-theory        52521
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (D or (B -> C)))) -> ((B -> C) -> (D or (B -> C))))
theorem-size     21
proof            (modus-ponens tm-619 tm-660 ((A (-> Am Bm)) (Cm (or B (-> Am Bm))) (C (-> (-> Am Bm) (or B (-> Am Bm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52521.        ((A or ((B -> C) -> (D or (B -> C)))) -> ((B -> C) -> (D or (B -> C)))), M:tm-619, m:tm-660, u:((A (-> Am Bm)) (Cm (or B (-> Am Bm))) (C (-> (-> Am Bm) (or B (-> Am Bm)))))
================================================================
tm-name          tm-52522
in-theory        52522
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52522.        ((((A -> B) -> C) -> ((A -> B) -> C)) and (D -> (E or D))), M:tm-609, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52523
in-theory        52523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52523.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-605, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52524
in-theory        52524
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and ((D -> (E or D)) and (((A -> B) -> C) -> ((A -> B) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52524.        ((((A -> B) -> C) -> ((A -> B) -> C)) and ((D -> (E or D)) and (((A -> B) -> C) -> ((A -> B) -> C)))), M:tm-595, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52525
in-theory        52525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52525.        (((A -> (B or A)) or C) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-550, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52526
in-theory        52526
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52526.        ((A or (B -> (C or B))) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-540, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52527
in-theory        52527
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52527.        ((A or (B -> (B or C))) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-530, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52528
in-theory        52528
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52528.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-520, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52529
in-theory        52529
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52529.        ((A or ((B and C) -> C)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-510, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52530
in-theory        52530
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52530.        ((A or ((B and C) -> B)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-500, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52531
in-theory        52531
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> G) -> ((E -> F) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52531.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> G) -> ((E -> F) -> G))), M:tm-490, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52532
in-theory        52532
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52532.        ((A or (B -> (C -> B))) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-480, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52533
in-theory        52533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (((A -> B) -> C) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52533.        (((A -> B) -> C) -> (((A -> B) -> C) or D)), M:tm-470, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52534
in-theory        52534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52534.        ((A -> (B -> (B or C))) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-469, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52535
in-theory        52535
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> ((B -> C) or D))) -> ((B -> C) -> ((B -> C) or D)))
theorem-size     21
proof            (modus-ponens tm-466 tm-660 ((A (-> Am Bm)) (Cm (or (-> Am Bm) B)) (C (-> (-> Am Bm) (or (-> Am Bm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52535.        ((A or ((B -> C) -> ((B -> C) or D))) -> ((B -> C) -> ((B -> C) or D))), M:tm-466, m:tm-660, u:((A (-> Am Bm)) (Cm (or (-> Am Bm) B)) (C (-> (-> Am Bm) (or (-> Am Bm) B))))
================================================================
tm-name          tm-52536
in-theory        52536
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52536.        ((((A -> B) -> C) -> ((A -> B) -> C)) and (D -> (D or E))), M:tm-456, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52537
in-theory        52537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52537.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-453, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52538
in-theory        52538
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and ((D -> (D or E)) and (((A -> B) -> C) -> ((A -> B) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52538.        ((((A -> B) -> C) -> ((A -> B) -> C)) and ((D -> (D or E)) and (((A -> B) -> C) -> ((A -> B) -> C)))), M:tm-443, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52539
in-theory        52539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52539.        (((A -> (A or B)) or C) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-409, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52540
in-theory        52540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52540.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-400, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52541
in-theory        52541
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52541.        ((((A and B) -> B) or C) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-391, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52542
in-theory        52542
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52542.        ((((A and B) -> A) or C) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-382, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52543
in-theory        52543
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> G) -> ((E -> F) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52543.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> G) -> ((E -> F) -> G))), M:tm-373, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52544
in-theory        52544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52544.        (((A -> (B -> A)) or C) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-364, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52545
in-theory        52545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (D -> (((A -> B) -> C) and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52545.        (((A -> B) -> C) -> (D -> (((A -> B) -> C) and D))), M:tm-355, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52546
in-theory        52546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52546.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-354, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52547
in-theory        52547
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (D -> ((B -> C) and D)))) -> ((B -> C) -> (D -> ((B -> C) and D))))
theorem-size     25
proof            (modus-ponens tm-351 tm-660 ((A (-> Am Bm)) (Cm (-> B (and (-> Am Bm) B))) (C (-> (-> Am Bm) (-> B (and (-> Am Bm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52547.        ((A or ((B -> C) -> (D -> ((B -> C) and D)))) -> ((B -> C) -> (D -> ((B -> C) and D)))), M:tm-351, m:tm-660, u:((A (-> Am Bm)) (Cm (-> B (and (-> Am Bm) B))) (C (-> (-> Am Bm) (-> B (and (-> Am Bm) B)))))
================================================================
tm-name          tm-52548
in-theory        52548
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52548.        ((((A -> B) -> C) -> ((A -> B) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52549
in-theory        52549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> E) -> ((C -> D) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52549.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> E) -> ((C -> D) -> E))), M:tm-338, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52550
in-theory        52550
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((A -> B) -> ((A -> B) and C))) -> ((A -> B) -> ((A -> B) and C)))
theorem-size     25
proof            (modus-ponens tm-335 tm-660 ((A (-> Am Bm)) (Cm (and (-> Am Bm) B)) (C (-> (-> Am Bm) (and (-> Am Bm) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52550.        ((((A -> B) -> C) or ((A -> B) -> ((A -> B) and C))) -> ((A -> B) -> ((A -> B) and C))), M:tm-335, m:tm-660, u:((A (-> Am Bm)) (Cm (and (-> Am Bm) B)) (C (-> (-> Am Bm) (and (-> Am Bm) B))))
================================================================
tm-name          tm-52551
in-theory        52551
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and (((A -> B) -> C) -> (((A -> B) -> C) and ((A -> B) -> C))))
theorem-size     29
proof            (modus-ponens tm-328 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52551.        ((((A -> B) -> C) -> ((A -> B) -> C)) and (((A -> B) -> C) -> (((A -> B) -> C) and ((A -> B) -> C)))), M:tm-328, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52552
in-theory        52552
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and ((D -> (E -> (D and E))) and (((A -> B) -> C) -> ((A -> B) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52552.        ((((A -> B) -> C) -> ((A -> B) -> C)) and ((D -> (E -> (D and E))) and (((A -> B) -> C) -> ((A -> B) -> C)))), M:tm-327, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52553
in-theory        52553
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and (((D and E) -> E) and (((A -> B) -> C) -> ((A -> B) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52553.        ((((A -> B) -> C) -> ((A -> B) -> C)) and (((D and E) -> E) and (((A -> B) -> C) -> ((A -> B) -> C)))), M:tm-326, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52554
in-theory        52554
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and (((D and E) -> D) and (((A -> B) -> C) -> ((A -> B) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52554.        ((((A -> B) -> C) -> ((A -> B) -> C)) and (((D and E) -> D) and (((A -> B) -> C) -> ((A -> B) -> C)))), M:tm-325, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52555
in-theory        52555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> C) -> ((A -> B) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52555.        ((((A -> B) -> C) -> ((A -> B) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> C) -> ((A -> B) -> C)))), M:tm-324, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52556
in-theory        52556
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and ((D -> (E -> D)) and (((A -> B) -> C) -> ((A -> B) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52556.        ((((A -> B) -> C) -> ((A -> B) -> C)) and ((D -> (E -> D)) and (((A -> B) -> C) -> ((A -> B) -> C)))), M:tm-323, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52557
in-theory        52557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52557.        ((((A -> B) -> C) -> ((A -> B) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52558
in-theory        52558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52558.        ((((A -> B) -> C) -> ((A -> B) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52559
in-theory        52559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52559.        ((((A -> B) -> C) -> ((A -> B) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52560
in-theory        52560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and (((A -> B) -> C) -> ((A -> B) -> C)))
theorem-size     23
proof            (modus-ponens tm-316 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52560.        ((((A -> B) -> C) -> ((A -> B) -> C)) and (((A -> B) -> C) -> ((A -> B) -> C))), M:tm-316, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52561
in-theory        52561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       139
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52561.        ((((A -> B) -> C) -> ((A -> B) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52562
in-theory        52562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and ((((A -> B) -> C) -> (not ((A -> B) -> C))) -> (not ((A -> B) -> C))))
theorem-size     31
proof            (modus-ponens tm-313 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52562.        ((((A -> B) -> C) -> ((A -> B) -> C)) and ((((A -> B) -> C) -> (not ((A -> B) -> C))) -> (not ((A -> B) -> C)))), M:tm-313, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52563
in-theory        52563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and ((((A -> B) -> C) -> D) -> ((((A -> B) -> C) or ((A -> B) -> C)) -> D)))
theorem-size     33
proof            (modus-ponens tm-312 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52563.        ((((A -> B) -> C) -> ((A -> B) -> C)) and ((((A -> B) -> C) -> D) -> ((((A -> B) -> C) or ((A -> B) -> C)) -> D))), M:tm-312, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52564
in-theory        52564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and (D or (((A -> B) -> C) -> ((A -> B) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52564.        ((((A -> B) -> C) -> ((A -> B) -> C)) and (D or (((A -> B) -> C) -> ((A -> B) -> C)))), M:tm-311, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52565
in-theory        52565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and ((((A -> B) -> C) -> ((A -> B) -> C)) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52565.        ((((A -> B) -> C) -> ((A -> B) -> C)) and ((((A -> B) -> C) -> ((A -> B) -> C)) or D)), M:tm-310, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52566
in-theory        52566
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and (D -> ((((A -> B) -> C) -> ((A -> B) -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52566.        ((((A -> B) -> C) -> ((A -> B) -> C)) and (D -> ((((A -> B) -> C) -> ((A -> B) -> C)) and D))), M:tm-309, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52567
in-theory        52567
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and ((((A -> B) -> C) -> (A -> B)) -> (((A -> B) -> C) -> C)))
theorem-size     29
proof            (modus-ponens tm-306 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> Am Bm)) (C Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52567.        ((((A -> B) -> C) -> ((A -> B) -> C)) and ((((A -> B) -> C) -> (A -> B)) -> (((A -> B) -> C) -> C))), M:tm-306, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> Am Bm)) (C Cm))
================================================================
tm-name          tm-52568
in-theory        52568
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and (D -> (((A -> B) -> C) -> ((A -> B) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52568.        ((((A -> B) -> C) -> ((A -> B) -> C)) and (D -> (((A -> B) -> C) -> ((A -> B) -> C)))), M:tm-305, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52569
in-theory        52569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52569.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-303, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52570
in-theory        52570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52570.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-270, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52571
in-theory        52571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52571.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-239, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52572
in-theory        52572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> G) -> ((E -> F) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52572.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> G) -> ((E -> F) -> G))), M:tm-210, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52573
in-theory        52573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52573.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-183, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52574
in-theory        52574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52574.        ((A -> ((B and C) -> C)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-157, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52575
in-theory        52575
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52575.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-147, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52576
in-theory        52576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52576.        ((A -> ((B and C) -> B)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-134, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52577
in-theory        52577
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52577.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-125, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52578
in-theory        52578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (C -> D)) -> (((A -> B) -> C) -> ((A -> B) -> D)))
theorem-size     19
proof            (modus-ponens tm-114 tm-660 ((A (-> (-> Am Bm) (-> C D))) (B (-> Am Bm)) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52578.        (((A -> B) -> (C -> D)) -> (((A -> B) -> C) -> ((A -> B) -> D))), M:tm-114, m:tm-660, u:((A (-> (-> Am Bm) (-> C D))) (B (-> Am Bm)) (Cm (-> C D)))
================================================================
tm-name          tm-52579
in-theory        52579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> G) -> ((E -> F) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52579.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> G) -> ((E -> F) -> G))), M:tm-113, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52580
in-theory        52580
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52580.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-105, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52581
in-theory        52581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> E) -> ((C -> D) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52581.        (((A -> B) -> (A -> A)) and (((C -> D) -> E) -> ((C -> D) -> E))), M:tm-95, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52582
in-theory        52582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (D -> ((A -> B) -> C)))
theorem-size     13
proof            (modus-ponens tm-84 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52582.        (((A -> B) -> C) -> (D -> ((A -> B) -> C))), M:tm-84, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52583
in-theory        52583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52583.        ((A -> (B -> (C -> B))) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-83, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52584
in-theory        52584
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (D -> (B -> C)))) -> ((B -> C) -> (D -> (B -> C))))
theorem-size     21
proof            (modus-ponens tm-80 tm-660 ((A (-> Am Bm)) (Cm (-> B (-> Am Bm))) (C (-> (-> Am Bm) (-> B (-> Am Bm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52584.        ((A or ((B -> C) -> (D -> (B -> C)))) -> ((B -> C) -> (D -> (B -> C)))), M:tm-80, m:tm-660, u:((A (-> Am Bm)) (Cm (-> B (-> Am Bm))) (C (-> (-> Am Bm) (-> B (-> Am Bm)))))
================================================================
tm-name          tm-52585
in-theory        52585
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> D) -> ((B -> C) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52585.        (((not (not A)) -> A) and (((B -> C) -> D) -> ((B -> C) -> D))), M:tm-76, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52586
in-theory        52586
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> C))) or ((A -> B) -> C)) -> ((A -> B) -> C))
theorem-size     19
proof            (modus-ponens tm-73 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52586.        (((not (not ((A -> B) -> C))) or ((A -> B) -> C)) -> ((A -> B) -> C)), M:tm-73, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52587
in-theory        52587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> E) -> ((C -> D) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52587.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> E) -> ((C -> D) -> E))), M:tm-69, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52588
in-theory        52588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52588.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-54, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52589
in-theory        52589
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (A and (B -> C)))) -> ((B -> C) -> (A and (B -> C))))
theorem-size     21
proof            (modus-ponens tm-48 tm-660 ((A (-> Am Bm)) (Cm (and B (-> Am Bm))) (C (-> (-> Am Bm) (and B (-> Am Bm))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52589.        ((A or ((B -> C) -> (A and (B -> C)))) -> ((B -> C) -> (A and (B -> C)))), M:tm-48, m:tm-660, u:((A (-> Am Bm)) (Cm (and B (-> Am Bm))) (C (-> (-> Am Bm) (and B (-> Am Bm)))))
================================================================
tm-name          tm-52590
in-theory        52590
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((B -> C) -> D))
theorem-size     19
proof            (modus-ponens tm-47 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52590.        (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> ((B -> C) -> D)), M:tm-47, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52591
in-theory        52591
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((A -> B) -> C))
theorem-size     19
proof            (modus-ponens tm-46 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52591.        (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((A -> B) -> C)), M:tm-46, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52592
in-theory        52592
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> A)) -> ((B -> C) -> A))
theorem-size     13
proof            (modus-ponens tm-44 tm-660 ((A (-> Am Bm)) (B Cm) (C (-> (-> Am Bm) Cm))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52592.        ((A or ((B -> C) -> A)) -> ((B -> C) -> A)), M:tm-44, m:tm-660, u:((A (-> Am Bm)) (B Cm) (C (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52593
in-theory        52593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> E) -> ((C -> D) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52593.        ((A -> (B or A)) and (((C -> D) -> E) -> ((C -> D) -> E))), M:tm-42, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52594
in-theory        52594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> E) -> ((C -> D) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52594.        ((A -> (A or B)) and (((C -> D) -> E) -> ((C -> D) -> E))), M:tm-32, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52595
in-theory        52595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> (((A -> B) -> C) and ((A -> B) -> C)))
theorem-size     17
proof            (modus-ponens tm-24 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52595.        (((A -> B) -> C) -> (((A -> B) -> C) and ((A -> B) -> C))), M:tm-24, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52596
in-theory        52596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((C -> D) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52596.        ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((C -> D) -> E))), M:tm-23, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52597
in-theory        52597
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> E) -> ((C -> D) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52597.        (((A and B) -> B) and (((C -> D) -> E) -> ((C -> D) -> E))), M:tm-22, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52598
in-theory        52598
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> E) -> ((C -> D) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52598.        (((A and B) -> A) and (((C -> D) -> E) -> ((C -> D) -> E))), M:tm-21, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52599
in-theory        52599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52599.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-20, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52600
in-theory        52600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> E) -> ((C -> D) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52600.        ((A -> (B -> A)) and (((C -> D) -> E) -> ((C -> D) -> E))), M:tm-19, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52601
in-theory        52601
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (not ((A -> B) -> C))) -> (not ((A -> B) -> C)))
theorem-size     19
proof            (modus-ponens tm-9 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-9 tm-2 tm-1 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52601.        ((((A -> B) -> C) -> (not ((A -> B) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52602
in-theory        52602
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> D) -> ((((A -> B) -> C) or ((A -> B) -> C)) -> D))
theorem-size     21
proof            (modus-ponens tm-8 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52602.        ((((A -> B) -> C) -> D) -> ((((A -> B) -> C) or ((A -> B) -> C)) -> D)), M:tm-8, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-52603
in-theory        52603
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> D) -> ((B -> C) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-7 tm-2 tm-1 tm-8)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52603.        (A or (((B -> C) -> D) -> ((B -> C) -> D))), M:tm-7, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52604
in-theory        52604
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-6 tm-2 tm-1 tm-8)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52604.        ((((A -> B) -> C) -> ((A -> B) -> C)) or D), M:tm-6, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52605
in-theory        52605
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> D) -> ((B -> C) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52605.        (A -> ((((B -> C) -> D) -> ((B -> C) -> D)) and A)), M:tm-5, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52606
in-theory        52606
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (A -> B)) -> (((A -> B) -> C) -> C))
theorem-size     17
proof            (modus-ponens tm-2 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> Am Bm)) (C Cm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52606.        ((((A -> B) -> C) -> (A -> B)) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> Am Bm)) (C Cm))
================================================================
tm-name          tm-52607
in-theory        52607
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> D) -> ((B -> C) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-1 tm-2 tm-8)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52607.        (A -> (((B -> C) -> D) -> ((B -> C) -> D))), M:tm-1, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52608
in-theory        52608
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((not ((B or (A -> B)) -> C)) or (((A -> B) -> C) -> (not ((B or (A -> B)) -> C)))) -> (not ((A -> B) -> C))))
theorem-size     52
proof            (modus-ponens tm-654 tm-661 ((A (-> (-> Am Bm) Cm)) (B (not (-> (or Bm (-> Am Bm)) Cm))) (C (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       194
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52608.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((not ((B or (A -> B)) -> C)) or (((A -> B) -> C) -> (not ((B or (A -> B)) -> C)))) -> (not ((A -> B) -> C)))), M:tm-654, m:tm-661, u:((A (-> (-> Am Bm) Cm)) (B (not (-> (or Bm (-> Am Bm)) Cm))) (C (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52609
in-theory        52609
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (D or (not ((A -> B) -> C))))
theorem-size     23
proof            (modus-ponens tm-623 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52609.        ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (D or (not ((A -> B) -> C)))), M:tm-623, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52610
in-theory        52610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-622 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52610.        ((A -> (B -> (C or B))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-622, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52611
in-theory        52611
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> B) -> (C or (A -> B))) -> (not ((B or (A -> B)) -> (C or (A -> B))))))
theorem-size     23
proof            (modus-ponens tm-618 tm-661 ((A (-> (-> (-> Am Bm) (or C (-> Am Bm))) (not (-> (or Bm (-> Am Bm)) (or C (-> Am Bm)))))) (B (-> Am Bm)) (Cm (or C (-> Am Bm)))))
axioms-used      (tm-9 tm-1 tm-7 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52611.        (not (((A -> B) -> (C or (A -> B))) -> (not ((B or (A -> B)) -> (C or (A -> B)))))), M:tm-618, m:tm-661, u:((A (-> (-> (-> Am Bm) (or C (-> Am Bm))) (not (-> (or Bm (-> Am Bm)) (or C (-> Am Bm)))))) (B (-> Am Bm)) (Cm (or C (-> Am Bm))))
================================================================
tm-name          tm-52612
in-theory        52612
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (D -> (E or D)))
theorem-size     27
proof            (modus-ponens tm-609 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52612.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (D -> (E or D))), M:tm-609, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52613
in-theory        52613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     31
proof            (modus-ponens tm-605 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52613.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-605, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52614
in-theory        52614
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((D -> (E or D)) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52614.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((D -> (E or D)) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))))), M:tm-595, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52615
in-theory        52615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-550 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52615.        (((A -> (B or A)) or C) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-550, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52616
in-theory        52616
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-540 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52616.        ((A or (B -> (C or B))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-540, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52617
in-theory        52617
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-530 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52617.        ((A or (B -> (B or C))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-530, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52618
in-theory        52618
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     31
proof            (modus-ponens tm-520 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52618.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-520, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52619
in-theory        52619
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-510 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52619.        ((A or ((B and C) -> C)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-510, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52620
in-theory        52620
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-500 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52620.        ((A or ((B and C) -> B)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-500, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52621
in-theory        52621
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G))))
theorem-size     37
proof            (modus-ponens tm-490 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-8 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52621.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G)))), M:tm-490, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52622
in-theory        52622
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-480 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52622.        ((A or (B -> (C -> B))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-480, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52623
in-theory        52623
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> ((not ((A -> B) -> C)) or D))
theorem-size     23
proof            (modus-ponens tm-470 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52623.        ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> ((not ((A -> B) -> C)) or D)), M:tm-470, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52624
in-theory        52624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-469 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52624.        ((A -> (B -> (B or C))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-469, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52625
in-theory        52625
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> B) -> ((A -> B) or C)) -> (not ((B or (A -> B)) -> ((A -> B) or C)))))
theorem-size     23
proof            (modus-ponens tm-465 tm-661 ((A (-> (-> (-> Am Bm) (or (-> Am Bm) C)) (not (-> (or Bm (-> Am Bm)) (or (-> Am Bm) C))))) (B (-> Am Bm)) (Cm (or (-> Am Bm) C))))
axioms-used      (tm-9 tm-1 tm-6 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52625.        (not (((A -> B) -> ((A -> B) or C)) -> (not ((B or (A -> B)) -> ((A -> B) or C))))), M:tm-465, m:tm-661, u:((A (-> (-> (-> Am Bm) (or (-> Am Bm) C)) (not (-> (or Bm (-> Am Bm)) (or (-> Am Bm) C))))) (B (-> Am Bm)) (Cm (or (-> Am Bm) C)))
================================================================
tm-name          tm-52626
in-theory        52626
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (D -> (D or E)))
theorem-size     27
proof            (modus-ponens tm-456 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52626.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (D -> (D or E))), M:tm-456, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52627
in-theory        52627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     31
proof            (modus-ponens tm-453 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52627.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-453, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52628
in-theory        52628
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((D -> (D or E)) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52628.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((D -> (D or E)) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))))), M:tm-443, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52629
in-theory        52629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-409 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52629.        (((A -> (A or B)) or C) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-409, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52630
in-theory        52630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     31
proof            (modus-ponens tm-400 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52630.        (((A -> (B -> (A and B))) or C) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-400, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52631
in-theory        52631
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-391 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52631.        ((((A and B) -> B) or C) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-391, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52632
in-theory        52632
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-382 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52632.        ((((A and B) -> A) or C) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-382, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52633
in-theory        52633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G))))
theorem-size     37
proof            (modus-ponens tm-373 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-8 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52633.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G)))), M:tm-373, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52634
in-theory        52634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-364 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52634.        (((A -> (B -> A)) or C) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-364, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52635
in-theory        52635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (D -> ((not ((A -> B) -> C)) and D)))
theorem-size     25
proof            (modus-ponens tm-355 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-8)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52635.        ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (D -> ((not ((A -> B) -> C)) and D))), M:tm-355, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52636
in-theory        52636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     31
proof            (modus-ponens tm-354 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52636.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-354, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52637
in-theory        52637
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> B) -> (C -> ((A -> B) and C))) -> (not ((B or (A -> B)) -> (C -> ((A -> B) and C))))))
theorem-size     27
proof            (modus-ponens tm-350 tm-661 ((A (-> (-> (-> Am Bm) (-> C (and (-> Am Bm) C))) (not (-> (or Bm (-> Am Bm)) (-> C (and (-> Am Bm) C)))))) (B (-> Am Bm)) (Cm (-> C (and (-> Am Bm) C)))))
axioms-used      (tm-9 tm-1 tm-5 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52637.        (not (((A -> B) -> (C -> ((A -> B) and C))) -> (not ((B or (A -> B)) -> (C -> ((A -> B) and C)))))), M:tm-350, m:tm-661, u:((A (-> (-> (-> Am Bm) (-> C (and (-> Am Bm) C))) (not (-> (or Bm (-> Am Bm)) (-> C (and (-> Am Bm) C)))))) (B (-> Am Bm)) (Cm (-> C (and (-> Am Bm) C))))
================================================================
tm-name          tm-52638
in-theory        52638
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (D -> (E -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-341 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52638.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52639
in-theory        52639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E))))
theorem-size     31
proof            (modus-ponens tm-338 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52639.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E)))), M:tm-338, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52640
in-theory        52640
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) and (not ((A -> B) -> C)))))
theorem-size     58
proof            (modus-ponens tm-328 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       192
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52640.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) and (not ((A -> B) -> C))))), M:tm-328, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52641
in-theory        52641
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((D -> (E -> (D and E))) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52641.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((D -> (E -> (D and E))) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))))), M:tm-327, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52642
in-theory        52642
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((D and E) -> E) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52642.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((D and E) -> E) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))))), M:tm-326, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52643
in-theory        52643
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((D and E) -> D) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52643.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((D and E) -> D) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))))), M:tm-325, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52644
in-theory        52644
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52644.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))))), M:tm-324, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52645
in-theory        52645
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((D -> (E -> D)) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52645.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((D -> (E -> D)) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))))), M:tm-323, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52646
in-theory        52646
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((D and E) -> E))
theorem-size     27
proof            (modus-ponens tm-322 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52646.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52647
in-theory        52647
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((D and E) -> D))
theorem-size     27
proof            (modus-ponens tm-320 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52647.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52648
in-theory        52648
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-318 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52648.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52649
in-theory        52649
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (((A -> B) -> C) -> (not ((B or (A -> B)) -> C)))))
theorem-size     51
proof            (modus-ponens tm-316 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52649.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (((A -> B) -> C) -> (not ((B or (A -> B)) -> C))))), M:tm-316, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52650
in-theory        52650
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (D -> (E -> D)))
theorem-size     27
proof            (modus-ponens tm-315 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52650.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52651
in-theory        52651
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not (not ((A -> B) -> C)))) -> (not (((A -> B) -> C) -> (not ((B or (A -> B)) -> C))))))
theorem-size     60
proof            (modus-ponens tm-313 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       178
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52651.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not (not ((A -> B) -> C)))) -> (not (((A -> B) -> C) -> (not ((B or (A -> B)) -> C)))))), M:tm-313, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52652
in-theory        52652
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((not ((A -> B) -> C)) -> D) -> (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) or (not ((A -> B) -> C))) -> D)))
theorem-size     54
proof            (modus-ponens tm-312 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-1)
proof-size       176
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52652.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((not ((A -> B) -> C)) -> D) -> (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) or (not ((A -> B) -> C))) -> D))), M:tm-312, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52653
in-theory        52653
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (D or ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52653.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (D or ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))))), M:tm-311, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52654
in-theory        52654
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) or D))
theorem-size     45
proof            (modus-ponens tm-310 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52654.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) or D)), M:tm-310, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52655
in-theory        52655
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (D -> (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and D)))
theorem-size     47
proof            (modus-ponens tm-309 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52655.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (D -> (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and D))), M:tm-309, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52656
in-theory        52656
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (D -> ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52656.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and (D -> ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))))), M:tm-305, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52657
in-theory        52657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-303 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52657.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-303, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52658
in-theory        52658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     31
proof            (modus-ponens tm-270 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52658.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-270, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52659
in-theory        52659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     31
proof            (modus-ponens tm-239 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52659.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-239, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52660
in-theory        52660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G))))
theorem-size     39
proof            (modus-ponens tm-210 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52660.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G)))), M:tm-210, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52661
in-theory        52661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     31
proof            (modus-ponens tm-183 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52661.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-183, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52662
in-theory        52662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-157 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52662.        ((A -> ((B and C) -> C)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-157, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52663
in-theory        52663
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     37
proof            (modus-ponens tm-147 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-8 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52663.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-147, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52664
in-theory        52664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-134 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52664.        ((A -> ((B and C) -> B)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-134, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52665
in-theory        52665
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     37
proof            (modus-ponens tm-125 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-8 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52665.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-125, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52666
in-theory        52666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G))))
theorem-size     37
proof            (modus-ponens tm-113 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-8)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52666.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G)))), M:tm-113, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52667
in-theory        52667
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((B -> C) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))))
theorem-size     33
proof            (modus-ponens tm-109 tm-661 ((A (-> (-> (-> Am (-> C D)) (-> (-> Am C) (-> Am D))) (not (-> (or (-> C D) (-> Am (-> C D))) (-> (-> Am C) (-> Am D)))))) (B Am) (Bm (-> C D)) (Cm (-> (-> Am C) (-> Am D)))))
axioms-used      (tm-9 tm-1 tm-2 tm-8)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52667.        (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not (((B -> C) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))))), M:tm-109, m:tm-661, u:((A (-> (-> (-> Am (-> C D)) (-> (-> Am C) (-> Am D))) (not (-> (or (-> C D) (-> Am (-> C D))) (-> (-> Am C) (-> Am D)))))) (B Am) (Bm (-> C D)) (Cm (-> (-> Am C) (-> Am D))))
================================================================
tm-name          tm-52668
in-theory        52668
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     41
proof            (modus-ponens tm-105 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 tm-1)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52668.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-105, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52669
in-theory        52669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E))))
theorem-size     29
proof            (modus-ponens tm-95 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52669.        (((A -> B) -> (A -> A)) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E)))), M:tm-95, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52670
in-theory        52670
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (D -> (not ((A -> B) -> C))))
theorem-size     23
proof            (modus-ponens tm-84 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52670.        ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (D -> (not ((A -> B) -> C)))), M:tm-84, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52671
in-theory        52671
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     29
proof            (modus-ponens tm-83 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52671.        ((A -> (B -> (C -> B))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-83, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52672
in-theory        52672
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> B) -> (C -> (A -> B))) -> (not ((B or (A -> B)) -> (C -> (A -> B))))))
theorem-size     23
proof            (modus-ponens tm-79 tm-661 ((A (-> (-> (-> Am Bm) (-> C (-> Am Bm))) (not (-> (or Bm (-> Am Bm)) (-> C (-> Am Bm)))))) (B (-> Am Bm)) (Cm (-> C (-> Am Bm)))))
axioms-used      (tm-9 tm-1 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52672.        (not (((A -> B) -> (C -> (A -> B))) -> (not ((B or (A -> B)) -> (C -> (A -> B)))))), M:tm-79, m:tm-661, u:((A (-> (-> (-> Am Bm) (-> C (-> Am Bm))) (not (-> (or Bm (-> Am Bm)) (-> C (-> Am Bm)))))) (B (-> Am Bm)) (Cm (-> C (-> Am Bm))))
================================================================
tm-name          tm-52673
in-theory        52673
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) -> D) -> (not ((C or (B -> C)) -> D))) -> (not ((B -> C) -> D))))
theorem-size     27
proof            (modus-ponens tm-76 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-10 tm-9 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52673.        (((not (not A)) -> A) and ((((B -> C) -> D) -> (not ((C or (B -> C)) -> D))) -> (not ((B -> C) -> D)))), M:tm-76, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52674
in-theory        52674
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) -> C) -> (not ((B or (A -> B)) -> C))))) or (((A -> B) -> C) -> (not ((B or (A -> B)) -> C)))) -> (not ((A -> B) -> C)))
theorem-size     38
proof            (modus-ponens tm-73 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-8 tm-10 tm-9 tm-1)
proof-size       130
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52674.        (((not (not (((A -> B) -> C) -> (not ((B or (A -> B)) -> C))))) or (((A -> B) -> C) -> (not ((B or (A -> B)) -> C)))) -> (not ((A -> B) -> C))), M:tm-73, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52675
in-theory        52675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E))))
theorem-size     33
proof            (modus-ponens tm-69 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52675.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E)))), M:tm-69, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52676
in-theory        52676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     35
proof            (modus-ponens tm-54 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52676.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-54, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52677
in-theory        52677
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> D) -> (not ((C or (B -> C)) -> D)))) or (((B -> C) -> D) -> (not ((C or (B -> C)) -> D)))) -> (not ((B -> C) -> D)))
theorem-size     38
proof            (modus-ponens tm-47 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-8 tm-4 tm-9 tm-1)
proof-size       130
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52677.        (((A and (((B -> C) -> D) -> (not ((C or (B -> C)) -> D)))) or (((B -> C) -> D) -> (not ((C or (B -> C)) -> D)))) -> (not ((B -> C) -> D))), M:tm-47, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52678
in-theory        52678
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) and D) or (((A -> B) -> C) -> (not ((B or (A -> B)) -> C)))) -> (not ((A -> B) -> C)))
theorem-size     38
proof            (modus-ponens tm-46 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-8 tm-3 tm-9 tm-1)
proof-size       130
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52678.        ((((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) and D) or (((A -> B) -> C) -> (not ((B or (A -> B)) -> C)))) -> (not ((A -> B) -> C))), M:tm-46, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52679
in-theory        52679
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A or (B -> A)) -> C)) or (((B -> A) -> C) -> (not ((A or (B -> A)) -> C)))) -> (not ((B -> A) -> C)))
theorem-size     30
proof            (modus-ponens tm-44 tm-661 ((A (-> (-> Am Bm) Cm)) (B (not (-> (or Bm (-> Am Bm)) Cm))) (C (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       124
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52679.        (((not ((A or (B -> A)) -> C)) or (((B -> A) -> C) -> (not ((A or (B -> A)) -> C)))) -> (not ((B -> A) -> C))), M:tm-44, m:tm-661, u:((A (-> (-> Am Bm) Cm)) (B (not (-> (or Bm (-> Am Bm)) Cm))) (C (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52680
in-theory        52680
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E))))
theorem-size     27
proof            (modus-ponens tm-42 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52680.        ((A -> (B or A)) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E)))), M:tm-42, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52681
in-theory        52681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E))))
theorem-size     27
proof            (modus-ponens tm-32 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52681.        ((A -> (A or B)) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E)))), M:tm-32, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52682
in-theory        52682
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) and (not ((A -> B) -> C))))
theorem-size     36
proof            (modus-ponens tm-24 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       128
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52682.        ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) and (not ((A -> B) -> C)))), M:tm-24, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52683
in-theory        52683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E))))
theorem-size     29
proof            (modus-ponens tm-23 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52683.        ((A -> (B -> (A and B))) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E)))), M:tm-23, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52684
in-theory        52684
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E))))
theorem-size     27
proof            (modus-ponens tm-22 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52684.        (((A and B) -> B) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E)))), M:tm-22, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52685
in-theory        52685
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E))))
theorem-size     27
proof            (modus-ponens tm-21 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52685.        (((A and B) -> A) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E)))), M:tm-21, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52686
in-theory        52686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     35
proof            (modus-ponens tm-20 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52686.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-20, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52687
in-theory        52687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E))))
theorem-size     27
proof            (modus-ponens tm-19 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52687.        ((A -> (B -> A)) and ((((C -> D) -> E) -> (not ((D or (C -> D)) -> E))) -> (not ((C -> D) -> E)))), M:tm-19, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52688
in-theory        52688
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (((A -> B) -> C) -> (not ((B or (A -> B)) -> C))))
theorem-size     29
proof            (modus-ponens tm-12 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-8)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52688.        ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (((A -> B) -> C) -> (not ((B or (A -> B)) -> C)))), M:tm-12, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52689
in-theory        52689
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not (not ((A -> B) -> C)))) -> (not (((A -> B) -> C) -> (not ((B or (A -> B)) -> C)))))
theorem-size     38
proof            (modus-ponens tm-9 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-9 tm-8 tm-1)
proof-size       112
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52689.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not (not ((A -> B) -> C)))) -> (not (((A -> B) -> C) -> (not ((B or (A -> B)) -> C))))), M:tm-9, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52690
in-theory        52690
times-derived    1
----------------------------------------------------------------
theorem          (((not ((A -> B) -> C)) -> D) -> (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) or (not ((A -> B) -> C))) -> D))
theorem-size     32
proof            (modus-ponens tm-8 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-8 tm-9 tm-1)
proof-size       108
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52690.        (((not ((A -> B) -> C)) -> D) -> (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) or (not ((A -> B) -> C))) -> D)), M:tm-8, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-52691
in-theory        52691
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) -> D) -> (not ((C or (B -> C)) -> D))) -> (not ((B -> C) -> D))))
theorem-size     23
proof            (modus-ponens tm-7 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-7 tm-9 tm-8 tm-1)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52691.        (A or ((((B -> C) -> D) -> (not ((C or (B -> C)) -> D))) -> (not ((B -> C) -> D)))), M:tm-7, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52692
in-theory        52692
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) or D)
theorem-size     23
proof            (modus-ponens tm-6 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-6 tm-9 tm-8 tm-1)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52692.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) or D), M:tm-6, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52693
in-theory        52693
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> D) -> (not ((C or (B -> C)) -> D))) -> (not ((B -> C) -> D))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52693.        (A -> (((((B -> C) -> D) -> (not ((C or (B -> C)) -> D))) -> (not ((B -> C) -> D))) and A)), M:tm-5, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52694
in-theory        52694
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> D) -> (not ((C or (B -> C)) -> D))) -> (not ((B -> C) -> D))))
theorem-size     23
proof            (modus-ponens tm-1 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-1 tm-9 tm-8)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52694.        (A -> ((((B -> C) -> D) -> (not ((C or (B -> C)) -> D))) -> (not ((B -> C) -> D)))), M:tm-1, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-52695
in-theory        52695
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((B or (A -> B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-662 tm-1 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52695.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((B or (A -> B)) -> C))), M:tm-662, m:tm-1, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52696
in-theory        52696
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (C -> D)) or ((B or (A -> B)) -> (C -> D))) -> (((B or (A -> B)) -> C) -> ((B or (A -> B)) -> D)))
theorem-size     33
proof            (modus-ponens tm-662 tm-2 ((Am (or A (-> B A))) (C (-> Bm Cm)) (D (-> (-> (or A (-> B A)) Bm) (-> (or A (-> B A)) Cm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-52696.        ((((A -> B) -> (C -> D)) or ((B or (A -> B)) -> (C -> D))) -> (((B or (A -> B)) -> C) -> ((B or (A -> B)) -> D))), M:tm-662, m:tm-2, u:((Am (or A (-> B A))) (C (-> Bm Cm)) (D (-> (-> (or A (-> B A)) Bm) (-> (or A (-> B A)) Cm))))
================================================================
tm-name          tm-52697
in-theory        52697
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (((B or (A -> B)) -> C) and D)))
theorem-size     25
proof            (modus-ponens tm-662 tm-5 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> (or A (-> B A)) C) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-52697.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (((B or (A -> B)) -> C) and D))), M:tm-662, m:tm-5, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> (or A (-> B A)) C) Bm))))
================================================================
tm-name          tm-52698
in-theory        52698
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) or D))
theorem-size     23
proof            (modus-ponens tm-662 tm-6 ((Am (-> (or A (-> B A)) C)) (D (or (-> (or A (-> B A)) C) Bm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-52698.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) or D)), M:tm-662, m:tm-6, u:((Am (-> (or A (-> B A)) C)) (D (or (-> (or A (-> B A)) C) Bm)))
================================================================
tm-name          tm-52699
in-theory        52699
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or ((B or (A -> B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-662 tm-7 ((Am (-> (or A (-> B A)) C)) (D (or Bm (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-52699.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or ((B or (A -> B)) -> C))), M:tm-662, m:tm-7, u:((Am (-> (or A (-> B A)) C)) (D (or Bm (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52700
in-theory        52700
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((C -> D) -> (((B or (A -> B)) or C) -> D)))
theorem-size     27
proof            (modus-ponens tm-662 tm-8 ((Am (or A (-> B A))) (C Bm) (D (-> (-> Bm Cm) (-> (or (or A (-> B A)) Bm) Cm)))))
axioms-used      (tm-8 tm-1)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52700.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((C -> D) -> (((B or (A -> B)) or C) -> D))), M:tm-662, m:tm-8, u:((Am (or A (-> B A))) (C Bm) (D (-> (-> Bm Cm) (-> (or (or A (-> B A)) Bm) Cm))))
================================================================
tm-name          tm-52701
in-theory        52701
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> (not C)) -> (not (B or (A -> B)))))
theorem-size     29
proof            (modus-ponens tm-662 tm-9 ((Am (or A (-> B A))) (C Bm) (D (-> (-> (or A (-> B A)) (not Bm)) (not (or A (-> B A)))))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-52701.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> (not C)) -> (not (B or (A -> B))))), M:tm-662, m:tm-9, u:((Am (or A (-> B A))) (C Bm) (D (-> (-> (or A (-> B A)) (not Bm)) (not (or A (-> B A))))))
================================================================
tm-name          tm-52702
in-theory        52702
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-662 tm-11 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-52702.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (E -> D))), M:tm-662, m:tm-11, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-52703
in-theory        52703
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (A -> B)) -> (B or (A -> B))))
theorem-size     25
proof            (modus-ponens tm-662 tm-12 ((Am (or A (-> B A))) (C Bm) (D (-> (or A (-> B A)) (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-52703.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (A -> B)) -> (B or (A -> B)))), M:tm-662, m:tm-12, u:((Am (or A (-> B A))) (C Bm) (D (-> (or A (-> B A)) (or A (-> B A)))))
================================================================
tm-name          tm-52704
in-theory        52704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-662 tm-14 ((Am (-> (or A (-> B A)) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-52704.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-662, m:tm-14, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-52705
in-theory        52705
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-662 tm-16 ((Am (-> (or A (-> B A)) C)) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-52705.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D and E) -> D)), M:tm-662, m:tm-16, u:((Am (-> (or A (-> B A)) C)) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-52706
in-theory        52706
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-662 tm-18 ((Am (-> (or A (-> B A)) C)) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-52706.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D and E) -> E)), M:tm-662, m:tm-18, u:((Am (-> (or A (-> B A)) C)) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-52707
in-theory        52707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> D)) and ((B or (A -> B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-662 tm-19 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> Cm Bm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-52707.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> D)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-19, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> Cm Bm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52708
in-theory        52708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B or (A -> B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-662 tm-20 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-52708.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-20, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52709
in-theory        52709
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D and E) -> D) and ((B or (A -> B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-662 tm-21 ((Am (-> (or A (-> B A)) C)) (D (and (-> (and Bm Cm) Bm) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-52709.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D and E) -> D) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-21, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (and Bm Cm) Bm) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52710
in-theory        52710
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D and E) -> E) and ((B or (A -> B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-662 tm-22 ((Am (-> (or A (-> B A)) C)) (D (and (-> (and Bm Cm) Cm) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-52710.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D and E) -> E) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-22, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (and Bm Cm) Cm) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52711
in-theory        52711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> (D and E))) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-23 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-52711.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> (D and E))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-23, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52712
in-theory        52712
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (A -> B)) -> ((B or (A -> B)) and C)))
theorem-size     27
proof            (modus-ponens tm-662 tm-24 ((Am (or A (-> B A))) (C Bm) (D (-> (or A (-> B A)) (and (or A (-> B A)) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-52712.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (A -> B)) -> ((B or (A -> B)) and C))), M:tm-662, m:tm-24, u:((Am (or A (-> B A))) (C Bm) (D (-> (or A (-> B A)) (and (or A (-> B A)) Bm))))
================================================================
tm-name          tm-52713
in-theory        52713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-662 tm-25 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-52713.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (E -> (D and E)))), M:tm-662, m:tm-25, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-52714
in-theory        52714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (D or E)) and ((B or (A -> B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-662 tm-32 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (or Bm Cm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-52714.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (D or E)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-32, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (or Bm Cm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52715
in-theory        52715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-662 tm-33 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-52715.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (D or E))), M:tm-662, m:tm-33, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-52716
in-theory        52716
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E or D)) and ((B or (A -> B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-662 tm-42 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (or Cm Bm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-52716.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E or D)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-42, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (or Cm Bm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52717
in-theory        52717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-662 tm-43 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-52717.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (E or D))), M:tm-662, m:tm-43, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-52718
in-theory        52718
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((B or (A -> B)) and D) or (B or (A -> B))) -> C))
theorem-size     29
proof            (modus-ponens tm-662 tm-46 ((Am (or A (-> B A))) (C Bm) (D (-> (or (and (or A (-> B A)) Cm) (or A (-> B A))) Bm))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-52718.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((B or (A -> B)) and D) or (B or (A -> B))) -> C)), M:tm-662, m:tm-46, u:((Am (or A (-> B A))) (C Bm) (D (-> (or (and (or A (-> B A)) Cm) (or A (-> B A))) Bm)))
================================================================
tm-name          tm-52719
in-theory        52719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D and (B or (A -> B))) or (B or (A -> B))) -> C))
theorem-size     29
proof            (modus-ponens tm-662 tm-47 ((Am (or A (-> B A))) (C Bm) (D (-> (or (and Cm (or A (-> B A))) (or A (-> B A))) Bm))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-52719.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D and (B or (A -> B))) or (B or (A -> B))) -> C)), M:tm-662, m:tm-47, u:((Am (or A (-> B A))) (C Bm) (D (-> (or (and Cm (or A (-> B A))) (or A (-> B A))) Bm)))
================================================================
tm-name          tm-52720
in-theory        52720
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (B or (A -> B))) -> C))
theorem-size     23
proof            (modus-ponens tm-662 tm-49 ((A Am) (Bm (-> B Am)) (C Cm) (D (-> (or Am (or Am (-> B Am))) Cm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-52720.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (B or (A -> B))) -> C)), M:tm-662, m:tm-49, u:((A Am) (Bm (-> B Am)) (C Cm) (D (-> (or Am (or Am (-> B Am))) Cm)))
================================================================
tm-name          tm-52721
in-theory        52721
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((A -> B) or (B or (A -> B))) -> C))
theorem-size     25
proof            (modus-ponens tm-662 tm-50 ((A Am) (Bm (-> B Am)) (C Cm) (D (-> (or (-> B Am) (or Am (-> B Am))) Cm))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-52721.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((A -> B) or (B or (A -> B))) -> C)), M:tm-662, m:tm-50, u:((A Am) (Bm (-> B Am)) (C Cm) (D (-> (or (-> B Am) (or Am (-> B Am))) Cm)))
================================================================
tm-name          tm-52722
in-theory        52722
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B or (A -> B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-662 tm-54 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-52722.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-54, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52723
in-theory        52723
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-662 tm-56 ((Am (-> (or A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-52723.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-662, m:tm-56, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-52724
in-theory        52724
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (C -> (B or (A -> B))))) or ((B or (A -> B)) -> (not (C -> (B or (A -> B)))))) -> (not (B or (A -> B))))
theorem-size     34
proof            (modus-ponens tm-662 tm-57 ((Am (or A (-> B A))) (C (not (-> Bm (or A (-> B A))))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       128
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-52724.        ((((A -> B) -> (not (C -> (B or (A -> B))))) or ((B or (A -> B)) -> (not (C -> (B or (A -> B)))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-57, u:((Am (or A (-> B A))) (C (not (-> Bm (or A (-> B A))))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52725
in-theory        52725
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (C -> ((B or (A -> B)) and C)))) or ((B or (A -> B)) -> (not (C -> ((B or (A -> B)) and C))))) -> (not (B or (A -> B))))
theorem-size     38
proof            (modus-ponens tm-662 tm-61 ((Am (or A (-> B A))) (C (not (-> Bm (and (or A (-> B A)) Bm)))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-5)
proof-size       136
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-52725.        ((((A -> B) -> (not (C -> ((B or (A -> B)) and C)))) or ((B or (A -> B)) -> (not (C -> ((B or (A -> B)) and C))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-61, u:((Am (or A (-> B A))) (C (not (-> Bm (and (or A (-> B A)) Bm)))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52726
in-theory        52726
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B or (A -> B)) or C))) or ((B or (A -> B)) -> (not ((B or (A -> B)) or C)))) -> (not (B or (A -> B))))
theorem-size     34
proof            (modus-ponens tm-662 tm-62 ((Am (or A (-> B A))) (C (not (or (or A (-> B A)) Bm))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-6)
proof-size       128
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-52726.        ((((A -> B) -> (not ((B or (A -> B)) or C))) or ((B or (A -> B)) -> (not ((B or (A -> B)) or C)))) -> (not (B or (A -> B)))), M:tm-662, m:tm-62, u:((Am (or A (-> B A))) (C (not (or (or A (-> B A)) Bm))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52727
in-theory        52727
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (C or (B or (A -> B))))) or ((B or (A -> B)) -> (not (C or (B or (A -> B)))))) -> (not (B or (A -> B))))
theorem-size     34
proof            (modus-ponens tm-662 tm-63 ((Am (or A (-> B A))) (C (not (or Bm (or A (-> B A))))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-7)
proof-size       128
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-52727.        ((((A -> B) -> (not (C or (B or (A -> B))))) or ((B or (A -> B)) -> (not (C or (B or (A -> B)))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-63, u:((Am (or A (-> B A))) (C (not (or Bm (or A (-> B A))))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52728
in-theory        52728
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B or (A -> B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-662 tm-69 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-9)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-52728.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-69, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52729
in-theory        52729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-662 tm-71 ((Am (-> (or A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-52729.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-662, m:tm-71, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-52730
in-theory        52730
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((not (not (B or (A -> B)))) or (B or (A -> B))) -> C))
theorem-size     29
proof            (modus-ponens tm-662 tm-73 ((Am (or A (-> B A))) (C Bm) (D (-> (or (not (not (or A (-> B A)))) (or A (-> B A))) Bm))))
axioms-used      (tm-8 tm-1 tm-10)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-52730.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((not (not (B or (A -> B)))) or (B or (A -> B))) -> C)), M:tm-662, m:tm-73, u:((Am (or A (-> B A))) (C Bm) (D (-> (or (not (not (or A (-> B A)))) (or A (-> B A))) Bm)))
================================================================
tm-name          tm-52731
in-theory        52731
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((not (not D)) -> D) and ((B or (A -> B)) -> C)))
theorem-size     27
proof            (modus-ponens tm-662 tm-76 ((Am (-> (or A (-> B A)) C)) (D (and (-> (not (not Bm)) Bm) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-10)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-52731.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((not (not D)) -> D) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-76, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (not (not Bm)) Bm) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52732
in-theory        52732
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((not (not D)) -> D))
theorem-size     19
proof            (modus-ponens tm-662 tm-78 ((Am (-> (or A (-> B A)) C)) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-1 tm-10)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-52732.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((not (not D)) -> D)), M:tm-662, m:tm-78, u:((Am (-> (or A (-> B A)) C)) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-52733
in-theory        52733
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (C -> (D -> C)))) or ((B or (A -> B)) -> (not (C -> (D -> C))))) -> (not (B or (A -> B))))
theorem-size     30
proof            (modus-ponens tm-662 tm-79 ((Am (or A (-> B A))) (C (not (-> Bm (-> Cm Bm)))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9)
proof-size       138
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-52733.        ((((A -> B) -> (not (C -> (D -> C)))) or ((B or (A -> B)) -> (not (C -> (D -> C))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-79, u:((Am (or A (-> B A))) (C (not (-> Bm (-> Cm Bm)))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52734
in-theory        52734
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> (F -> E))) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-83 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-52734.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> (F -> E))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-83, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52735
in-theory        52735
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (A -> B)) -> (D -> C)))
theorem-size     23
proof            (modus-ponens tm-662 tm-84 ((Am (or A (-> B A))) (C Bm) (D (-> (or A (-> B A)) (-> Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-52735.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (A -> B)) -> (D -> C))), M:tm-662, m:tm-84, u:((Am (or A (-> B A))) (C Bm) (D (-> (or A (-> B A)) (-> Cm Bm))))
================================================================
tm-name          tm-52736
in-theory        52736
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-662 tm-85 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-52736.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (E -> (F -> E)))), M:tm-662, m:tm-85, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-52737
in-theory        52737
times-derived    3
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (A -> B)) -> C))
theorem-size     21
proof            (modus-ponens tm-662 tm-86 ((Am (-> (or A (-> B A)) C)) (D (-> (or A (-> B A)) C))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-52737.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (A -> B)) -> C)), M:tm-662, m:tm-86, u:((Am (-> (or A (-> B A)) C)) (D (-> (or A (-> B A)) C)))
================================================================
tm-name          tm-52738
in-theory        52738
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (C -> D)) or ((B or (A -> B)) -> (C -> D))) -> ((B or (A -> B)) -> (C -> D)))
theorem-size     27
proof            (modus-ponens tm-662 tm-87 ((Am (or A (-> B A))) (C (-> Bm Cm)) (D (-> (or A (-> B A)) (-> Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-52738.        ((((A -> B) -> (C -> D)) or ((B or (A -> B)) -> (C -> D))) -> ((B or (A -> B)) -> (C -> D))), M:tm-662, m:tm-87, u:((Am (or A (-> B A))) (C (-> Bm Cm)) (D (-> (or A (-> B A)) (-> Bm Cm))))
================================================================
tm-name          tm-52739
in-theory        52739
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> (D -> D)) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-95 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-52739.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> (D -> D)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-95, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52740
in-theory        52740
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> E) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-662 tm-97 ((Am (-> (or A (-> B A)) C)) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-52740.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> E) -> (D -> D))), M:tm-662, m:tm-97, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-52741
in-theory        52741
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C -> (B or (A -> B))) -> D)) or ((B or (A -> B)) -> ((C -> (B or (A -> B))) -> D))) -> ((B or (A -> B)) -> D))
theorem-size     37
proof            (modus-ponens tm-662 tm-98 ((Am (or A (-> B A))) (C (-> (-> Bm (or A (-> B A))) Cm)) (D (-> (or A (-> B A)) Cm))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-52741.        ((((A -> B) -> ((C -> (B or (A -> B))) -> D)) or ((B or (A -> B)) -> ((C -> (B or (A -> B))) -> D))) -> ((B or (A -> B)) -> D)), M:tm-662, m:tm-98, u:((Am (or A (-> B A))) (C (-> (-> Bm (or A (-> B A))) Cm)) (D (-> (or A (-> B A)) Cm)))
================================================================
tm-name          tm-52742
in-theory        52742
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((B or (A -> B)) -> C)) or ((B or (A -> B)) -> ((B or (A -> B)) -> C))) -> ((B or (A -> B)) -> C))
theorem-size     33
proof            (modus-ponens tm-662 tm-99 ((Am (or A (-> B A))) (C (-> (or A (-> B A)) Bm)) (D (-> (or A (-> B A)) Bm))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-52742.        ((((A -> B) -> ((B or (A -> B)) -> C)) or ((B or (A -> B)) -> ((B or (A -> B)) -> C))) -> ((B or (A -> B)) -> C)), M:tm-662, m:tm-99, u:((Am (or A (-> B A))) (C (-> (or A (-> B A)) Bm)) (D (-> (or A (-> B A)) Bm)))
================================================================
tm-name          tm-52743
in-theory        52743
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B or (A -> B)) -> C)))
theorem-size     41
proof            (modus-ponens tm-662 tm-105 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-52743.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-105, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52744
in-theory        52744
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-662 tm-107 ((Am (-> (or A (-> B A)) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-52744.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-662, m:tm-107, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-52745
in-theory        52745
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or ((B or (A -> B)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not (B or (A -> B))))
theorem-size     46
proof            (modus-ponens tm-662 tm-109 ((Am (or A (-> B A))) (C (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-2)
proof-size       178
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-52745.        ((((A -> B) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) or ((B or (A -> B)) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-109, u:((Am (or A (-> B A))) (C (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52746
in-theory        52746
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B or (A -> B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-662 tm-113 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-52746.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-113, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52747
in-theory        52747
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (C -> (D -> E))) or ((B or (A -> B)) -> (C -> (D -> E)))) -> ((B or (A -> B)) -> ((C -> D) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-662 tm-114 ((Am (or A (-> B A))) (C (-> Bm (-> Cm Dm))) (D (-> (or A (-> B A)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-52747.        ((((A -> B) -> (C -> (D -> E))) or ((B or (A -> B)) -> (C -> (D -> E)))) -> ((B or (A -> B)) -> ((C -> D) -> (C -> E)))), M:tm-662, m:tm-114, u:((Am (or A (-> B A))) (C (-> Bm (-> Cm Dm))) (D (-> (or A (-> B A)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-52748
in-theory        52748
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-662 tm-115 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-52748.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-662, m:tm-115, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-52749
in-theory        52749
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B or (A -> B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-662 tm-125 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-52749.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-125, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52750
in-theory        52750
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-662 tm-127 ((Am (-> (or A (-> B A)) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-52750.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-662, m:tm-127, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-52751
in-theory        52751
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((C and D) -> C))) or ((B or (A -> B)) -> (not ((C and D) -> C)))) -> (not (B or (A -> B))))
theorem-size     30
proof            (modus-ponens tm-662 tm-130 ((Am (or A (-> B A))) (C (not (-> (and Bm Cm) Bm))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-3)
proof-size       138
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-52751.        ((((A -> B) -> (not ((C and D) -> C))) or ((B or (A -> B)) -> (not ((C and D) -> C)))) -> (not (B or (A -> B)))), M:tm-662, m:tm-130, u:((Am (or A (-> B A))) (C (not (-> (and Bm Cm) Bm))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52752
in-theory        52752
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> ((E and F) -> E)) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-134 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-52752.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> ((E and F) -> E)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-134, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52753
in-theory        52753
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (C and D)) or ((B or (A -> B)) -> (C and D))) -> ((B or (A -> B)) -> C))
theorem-size     25
proof            (modus-ponens tm-662 tm-135 ((Am (or A (-> B A))) (C (and Bm Cm)) (D (-> (or A (-> B A)) Bm))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-52753.        ((((A -> B) -> (C and D)) or ((B or (A -> B)) -> (C and D))) -> ((B or (A -> B)) -> C)), M:tm-662, m:tm-135, u:((Am (or A (-> B A))) (C (and Bm Cm)) (D (-> (or A (-> B A)) Bm)))
================================================================
tm-name          tm-52754
in-theory        52754
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-662 tm-136 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-52754.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((E and F) -> E))), M:tm-662, m:tm-136, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-52755
in-theory        52755
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B or (A -> B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-662 tm-147 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-4)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-52755.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-147, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52756
in-theory        52756
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-662 tm-149 ((Am (-> (or A (-> B A)) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-52756.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-662, m:tm-149, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-52757
in-theory        52757
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((C and D) -> D))) or ((B or (A -> B)) -> (not ((C and D) -> D)))) -> (not (B or (A -> B))))
theorem-size     30
proof            (modus-ponens tm-662 tm-153 ((Am (or A (-> B A))) (C (not (-> (and Bm Cm) Cm))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-4)
proof-size       138
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-52757.        ((((A -> B) -> (not ((C and D) -> D))) or ((B or (A -> B)) -> (not ((C and D) -> D)))) -> (not (B or (A -> B)))), M:tm-662, m:tm-153, u:((Am (or A (-> B A))) (C (not (-> (and Bm Cm) Cm))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52758
in-theory        52758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> ((E and F) -> F)) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-157 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-52758.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> ((E and F) -> F)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-157, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52759
in-theory        52759
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (C and D)) or ((B or (A -> B)) -> (C and D))) -> ((B or (A -> B)) -> D))
theorem-size     25
proof            (modus-ponens tm-662 tm-158 ((Am (or A (-> B A))) (C (and Bm Cm)) (D (-> (or A (-> B A)) Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-52759.        ((((A -> B) -> (C and D)) or ((B or (A -> B)) -> (C and D))) -> ((B or (A -> B)) -> D)), M:tm-662, m:tm-158, u:((Am (or A (-> B A))) (C (and Bm Cm)) (D (-> (or A (-> B A)) Cm)))
================================================================
tm-name          tm-52760
in-theory        52760
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-662 tm-159 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-52760.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((E and F) -> F))), M:tm-662, m:tm-159, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-52761
in-theory        52761
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((C -> (D -> C)) and (B or (A -> B))))) or ((B or (A -> B)) -> (not ((C -> (D -> C)) and (B or (A -> B)))))) -> (not (B or (A -> B))))
theorem-size     42
proof            (modus-ponens tm-662 tm-179 ((Am (or A (-> B A))) (C (not (and (-> Bm (-> Cm Bm)) (or A (-> B A))))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-5)
proof-size       156
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-52761.        ((((A -> B) -> (not ((C -> (D -> C)) and (B or (A -> B))))) or ((B or (A -> B)) -> (not ((C -> (D -> C)) and (B or (A -> B)))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-179, u:((Am (or A (-> B A))) (C (not (and (-> Bm (-> Cm Bm)) (or A (-> B A))))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52762
in-theory        52762
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((B or (A -> B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-662 tm-183 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-52762.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-183, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52763
in-theory        52763
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-662 tm-184 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-52763.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((E -> (F -> E)) and D))), M:tm-662, m:tm-184, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-52764
in-theory        52764
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or (A -> B))))) or ((B or (A -> B)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or (A -> B)))))) -> (not (B or (A -> B))))
theorem-size     58
proof            (modus-ponens tm-662 tm-206 ((Am (or A (-> B A))) (C (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A (-> B A))))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-5 tm-2)
proof-size       196
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-52764.        ((((A -> B) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or (A -> B))))) or ((B or (A -> B)) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B or (A -> B)))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-206, u:((Am (or A (-> B A))) (C (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or A (-> B A))))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52765
in-theory        52765
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B or (A -> B)) -> C)))
theorem-size     39
proof            (modus-ponens tm-662 tm-210 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-52765.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-210, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52766
in-theory        52766
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-662 tm-211 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-52766.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-662, m:tm-211, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-52767
in-theory        52767
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and D) -> C) and (B or (A -> B))))) or ((B or (A -> B)) -> (not (((C and D) -> C) and (B or (A -> B)))))) -> (not (B or (A -> B))))
theorem-size     42
proof            (modus-ponens tm-662 tm-235 ((Am (or A (-> B A))) (C (not (and (-> (and Bm Cm) Bm) (or A (-> B A))))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-5 tm-3)
proof-size       156
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-52767.        ((((A -> B) -> (not (((C and D) -> C) and (B or (A -> B))))) or ((B or (A -> B)) -> (not (((C and D) -> C) and (B or (A -> B)))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-235, u:((Am (or A (-> B A))) (C (not (and (-> (and Bm Cm) Bm) (or A (-> B A))))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52768
in-theory        52768
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (((E and F) -> E) and D)) and ((B or (A -> B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-662 tm-239 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-52768.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (((E and F) -> E) and D)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-239, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52769
in-theory        52769
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (((E and F) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-662 tm-240 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-52769.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (((E and F) -> E) and D))), M:tm-662, m:tm-240, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-52770
in-theory        52770
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((C and D) -> D) and (B or (A -> B))))) or ((B or (A -> B)) -> (not (((C and D) -> D) and (B or (A -> B)))))) -> (not (B or (A -> B))))
theorem-size     42
proof            (modus-ponens tm-662 tm-266 ((Am (or A (-> B A))) (C (not (and (-> (and Bm Cm) Cm) (or A (-> B A))))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-5 tm-4)
proof-size       156
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-52770.        ((((A -> B) -> (not (((C and D) -> D) and (B or (A -> B))))) or ((B or (A -> B)) -> (not (((C and D) -> D) and (B or (A -> B)))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-266, u:((Am (or A (-> B A))) (C (not (and (-> (and Bm Cm) Cm) (or A (-> B A))))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52771
in-theory        52771
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (((E and F) -> F) and D)) and ((B or (A -> B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-662 tm-270 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-52771.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (((E and F) -> F) and D)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-270, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52772
in-theory        52772
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (((E and F) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-662 tm-271 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-52772.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (((E and F) -> F) and D))), M:tm-662, m:tm-271, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-52773
in-theory        52773
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((C -> (D -> (C and D))) and (B or (A -> B))))) or ((B or (A -> B)) -> (not ((C -> (D -> (C and D))) and (B or (A -> B)))))) -> (not (B or (A -> B))))
theorem-size     46
proof            (modus-ponens tm-662 tm-299 ((Am (or A (-> B A))) (C (not (and (-> Bm (-> Cm (and Bm Cm))) (or A (-> B A))))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-5)
proof-size       166
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-52773.        ((((A -> B) -> (not ((C -> (D -> (C and D))) and (B or (A -> B))))) or ((B or (A -> B)) -> (not ((C -> (D -> (C and D))) and (B or (A -> B)))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-299, u:((Am (or A (-> B A))) (C (not (and (-> Bm (-> Cm (and Bm Cm))) (or A (-> B A))))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52774
in-theory        52774
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B or (A -> B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-662 tm-303 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-52774.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-303, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52775
in-theory        52775
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     25
proof            (modus-ponens tm-662 tm-304 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-52775.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-662, m:tm-304, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-52776
in-theory        52776
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (D -> ((B or (A -> B)) -> C))))
theorem-size     31
proof            (modus-ponens tm-662 tm-305 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> Bm (-> (or A (-> B A)) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-52776.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (D -> ((B or (A -> B)) -> C)))), M:tm-662, m:tm-305, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> Bm (-> (or A (-> B A)) C)))))
================================================================
tm-name          tm-52777
in-theory        52777
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (C -> D)) or ((B or (A -> B)) -> (C -> D))) -> (((B or (A -> B)) -> (C -> D)) and (((B or (A -> B)) -> C) -> ((B or (A -> B)) -> D))))
theorem-size     43
proof            (modus-ponens tm-662 tm-306 ((Am (or A (-> B A))) (C (-> Bm Cm)) (D (and (-> (or A (-> B A)) (-> Bm Cm)) (-> (-> (or A (-> B A)) Bm) (-> (or A (-> B A)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-52777.        ((((A -> B) -> (C -> D)) or ((B or (A -> B)) -> (C -> D))) -> (((B or (A -> B)) -> (C -> D)) and (((B or (A -> B)) -> C) -> ((B or (A -> B)) -> D)))), M:tm-662, m:tm-306, u:((Am (or A (-> B A))) (C (-> Bm Cm)) (D (and (-> (or A (-> B A)) (-> Bm Cm)) (-> (-> (or A (-> B A)) Bm) (-> (or A (-> B A)) Cm)))))
================================================================
tm-name          tm-52778
in-theory        52778
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (D -> (((B or (A -> B)) -> C) and D))))
theorem-size     33
proof            (modus-ponens tm-662 tm-309 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> Bm (and (-> (or A (-> B A)) C) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-52778.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (D -> (((B or (A -> B)) -> C) and D)))), M:tm-662, m:tm-309, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> Bm (and (-> (or A (-> B A)) C) Bm)))))
================================================================
tm-name          tm-52779
in-theory        52779
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (((B or (A -> B)) -> C) or D)))
theorem-size     31
proof            (modus-ponens tm-662 tm-310 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (or (-> (or A (-> B A)) C) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-52779.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (((B or (A -> B)) -> C) or D))), M:tm-662, m:tm-310, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (or (-> (or A (-> B A)) C) Bm))))
================================================================
tm-name          tm-52780
in-theory        52780
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (D or ((B or (A -> B)) -> C))))
theorem-size     31
proof            (modus-ponens tm-662 tm-311 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (or Bm (-> (or A (-> B A)) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-52780.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (D or ((B or (A -> B)) -> C)))), M:tm-662, m:tm-311, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (or Bm (-> (or A (-> B A)) C)))))
================================================================
tm-name          tm-52781
in-theory        52781
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((C -> D) -> (((B or (A -> B)) or C) -> D))))
theorem-size     35
proof            (modus-ponens tm-662 tm-312 ((Am (or A (-> B A))) (C Bm) (D (and (-> (or A (-> B A)) Bm) (-> (-> Bm Cm) (-> (or (or A (-> B A)) Bm) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-52781.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((C -> D) -> (((B or (A -> B)) or C) -> D)))), M:tm-662, m:tm-312, u:((Am (or A (-> B A))) (C Bm) (D (and (-> (or A (-> B A)) Bm) (-> (-> Bm Cm) (-> (or (or A (-> B A)) Bm) Cm)))))
================================================================
tm-name          tm-52782
in-theory        52782
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (((B or (A -> B)) -> (not C)) -> (not (B or (A -> B))))))
theorem-size     37
proof            (modus-ponens tm-662 tm-313 ((Am (or A (-> B A))) (C Bm) (D (and (-> (or A (-> B A)) Bm) (-> (-> (or A (-> B A)) (not Bm)) (not (or A (-> B A))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-52782.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (((B or (A -> B)) -> (not C)) -> (not (B or (A -> B)))))), M:tm-662, m:tm-313, u:((Am (or A (-> B A))) (C Bm) (D (and (-> (or A (-> B A)) Bm) (-> (-> (or A (-> B A)) (not Bm)) (not (or A (-> B A)))))))
================================================================
tm-name          tm-52783
in-theory        52783
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (D -> (E -> D))))
theorem-size     27
proof            (modus-ponens tm-662 tm-315 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-52783.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (D -> (E -> D)))), M:tm-662, m:tm-315, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-52784
in-theory        52784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((B or (A -> B)) -> (B or (A -> B)))))
theorem-size     33
proof            (modus-ponens tm-662 tm-316 ((Am (or A (-> B A))) (C Bm) (D (and (-> (or A (-> B A)) Bm) (-> (or A (-> B A)) (or A (-> B A)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-52784.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((B or (A -> B)) -> (B or (A -> B))))), M:tm-662, m:tm-316, u:((Am (or A (-> B A))) (C Bm) (D (and (-> (or A (-> B A)) Bm) (-> (or A (-> B A)) (or A (-> B A))))))
================================================================
tm-name          tm-52785
in-theory        52785
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-662 tm-318 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-52785.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-662, m:tm-318, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-52786
in-theory        52786
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((D and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-662 tm-320 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-52786.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((D and E) -> D))), M:tm-662, m:tm-320, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-52787
in-theory        52787
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((D and E) -> E)))
theorem-size     27
proof            (modus-ponens tm-662 tm-322 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-52787.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((D and E) -> E))), M:tm-662, m:tm-322, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-52788
in-theory        52788
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((D -> (E -> D)) and ((B or (A -> B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-662 tm-323 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (and (-> Bm (-> Cm Bm)) (-> (or A (-> B A)) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-52788.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((D -> (E -> D)) and ((B or (A -> B)) -> C)))), M:tm-662, m:tm-323, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (and (-> Bm (-> Cm Bm)) (-> (or A (-> B A)) C)))))
================================================================
tm-name          tm-52789
in-theory        52789
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B or (A -> B)) -> C))))
theorem-size     43
proof            (modus-ponens tm-662 tm-324 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (-> B A)) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-52789.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((B or (A -> B)) -> C)))), M:tm-662, m:tm-324, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or A (-> B A)) C)))))
================================================================
tm-name          tm-52790
in-theory        52790
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (((D and E) -> D) and ((B or (A -> B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-662 tm-325 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (and (-> (and Bm Cm) Bm) (-> (or A (-> B A)) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-52790.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (((D and E) -> D) and ((B or (A -> B)) -> C)))), M:tm-662, m:tm-325, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (and (-> (and Bm Cm) Bm) (-> (or A (-> B A)) C)))))
================================================================
tm-name          tm-52791
in-theory        52791
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (((D and E) -> E) and ((B or (A -> B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-662 tm-326 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (and (-> (and Bm Cm) Cm) (-> (or A (-> B A)) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-52791.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (((D and E) -> E) and ((B or (A -> B)) -> C)))), M:tm-662, m:tm-326, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (and (-> (and Bm Cm) Cm) (-> (or A (-> B A)) C)))))
================================================================
tm-name          tm-52792
in-theory        52792
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((D -> (E -> (D and E))) and ((B or (A -> B)) -> C))))
theorem-size     37
proof            (modus-ponens tm-662 tm-327 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (-> B A)) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-52792.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((D -> (E -> (D and E))) and ((B or (A -> B)) -> C)))), M:tm-662, m:tm-327, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or A (-> B A)) C)))))
================================================================
tm-name          tm-52793
in-theory        52793
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((B or (A -> B)) -> ((B or (A -> B)) and C))))
theorem-size     35
proof            (modus-ponens tm-662 tm-328 ((Am (or A (-> B A))) (C Bm) (D (and (-> (or A (-> B A)) Bm) (-> (or A (-> B A)) (and (or A (-> B A)) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-52793.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((B or (A -> B)) -> ((B or (A -> B)) and C)))), M:tm-662, m:tm-328, u:((Am (or A (-> B A))) (C Bm) (D (and (-> (or A (-> B A)) Bm) (-> (or A (-> B A)) (and (or A (-> B A)) Bm)))))
================================================================
tm-name          tm-52794
in-theory        52794
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> (D -> (D and E))) and ((B or (A -> B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-662 tm-338 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-52794.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> (D -> (D and E))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-338, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52795
in-theory        52795
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-662 tm-340 ((Am (-> (or A (-> B A)) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-52795.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> E) -> (D -> (D and E)))), M:tm-662, m:tm-340, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-52796
in-theory        52796
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (D -> (E -> (D and E)))))
theorem-size     29
proof            (modus-ponens tm-662 tm-341 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-52796.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (D -> (E -> (D and E))))), M:tm-662, m:tm-341, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-52797
in-theory        52797
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C -> ((B or (A -> B)) and C)) -> D)) or ((B or (A -> B)) -> ((C -> ((B or (A -> B)) and C)) -> D))) -> ((B or (A -> B)) -> D))
theorem-size     41
proof            (modus-ponens tm-662 tm-349 ((Am (or A (-> B A))) (C (-> (-> Bm (and (or A (-> B A)) Bm)) Cm)) (D (-> (or A (-> B A)) Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-52797.        ((((A -> B) -> ((C -> ((B or (A -> B)) and C)) -> D)) or ((B or (A -> B)) -> ((C -> ((B or (A -> B)) and C)) -> D))) -> ((B or (A -> B)) -> D)), M:tm-662, m:tm-349, u:((Am (or A (-> B A))) (C (-> (-> Bm (and (or A (-> B A)) Bm)) Cm)) (D (-> (or A (-> B A)) Cm)))
================================================================
tm-name          tm-52798
in-theory        52798
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (C -> (D -> (C and D))))) or ((B or (A -> B)) -> (not (C -> (D -> (C and D)))))) -> (not (B or (A -> B))))
theorem-size     34
proof            (modus-ponens tm-662 tm-350 ((Am (or A (-> B A))) (C (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-5)
proof-size       148
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-52798.        ((((A -> B) -> (not (C -> (D -> (C and D))))) or ((B or (A -> B)) -> (not (C -> (D -> (C and D)))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-350, u:((Am (or A (-> B A))) (C (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52799
in-theory        52799
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((B or (A -> B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-662 tm-354 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-52799.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-354, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52800
in-theory        52800
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (A -> B)) -> (D -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-662 tm-355 ((Am (or A (-> B A))) (C Bm) (D (-> (or A (-> B A)) (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-52800.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (A -> B)) -> (D -> (C and D)))), M:tm-662, m:tm-355, u:((Am (or A (-> B A))) (C Bm) (D (-> (or A (-> B A)) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-52801
in-theory        52801
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-662 tm-356 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-52801.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (E -> (F -> (E and F))))), M:tm-662, m:tm-356, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-52802
in-theory        52802
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (E -> D)) or F) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-364 ((Am (-> (or A (-> B A)) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-52802.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (E -> D)) or F) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-364, u:((Am (-> (or A (-> B A)) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52803
in-theory        52803
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-662 tm-365 ((Am (-> (or A (-> B A)) C)) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-52803.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> D)) or F)), M:tm-662, m:tm-365, u:((Am (-> (or A (-> B A)) C)) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-52804
in-theory        52804
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B or (A -> B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-662 tm-373 ((Am (-> (or A (-> B A)) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-52804.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-373, u:((Am (-> (or A (-> B A)) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52805
in-theory        52805
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-662 tm-374 ((Am (-> (or A (-> B A)) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-52805.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-662, m:tm-374, u:((Am (-> (or A (-> B A)) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-52806
in-theory        52806
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D and E) -> D) or F) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-382 ((Am (-> (or A (-> B A)) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-52806.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D and E) -> D) or F) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-382, u:((Am (-> (or A (-> B A)) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52807
in-theory        52807
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D and E) -> D) or F))
theorem-size     21
proof            (modus-ponens tm-662 tm-383 ((Am (-> (or A (-> B A)) C)) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-52807.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D and E) -> D) or F)), M:tm-662, m:tm-383, u:((Am (-> (or A (-> B A)) C)) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-52808
in-theory        52808
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D and E) -> E) or F) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-391 ((Am (-> (or A (-> B A)) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-52808.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D and E) -> E) or F) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-391, u:((Am (-> (or A (-> B A)) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52809
in-theory        52809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D and E) -> E) or F))
theorem-size     21
proof            (modus-ponens tm-662 tm-392 ((Am (-> (or A (-> B A)) C)) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-52809.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D and E) -> E) or F)), M:tm-662, m:tm-392, u:((Am (-> (or A (-> B A)) C)) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-52810
in-theory        52810
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (E -> (D and E))) or F) and ((B or (A -> B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-662 tm-400 ((Am (-> (or A (-> B A)) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-52810.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (E -> (D and E))) or F) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-400, u:((Am (-> (or A (-> B A)) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52811
in-theory        52811
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> (D and E))) or F))
theorem-size     23
proof            (modus-ponens tm-662 tm-401 ((Am (-> (or A (-> B A)) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-52811.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> (D and E))) or F)), M:tm-662, m:tm-401, u:((Am (-> (or A (-> B A)) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-52812
in-theory        52812
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (D or E)) or F) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-409 ((Am (-> (or A (-> B A)) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-52812.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (D or E)) or F) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-409, u:((Am (-> (or A (-> B A)) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52813
in-theory        52813
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (D or E)) or F))
theorem-size     21
proof            (modus-ponens tm-662 tm-410 ((Am (-> (or A (-> B A)) C)) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-52813.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (D or E)) or F)), M:tm-662, m:tm-410, u:((Am (-> (or A (-> B A)) C)) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-52814
in-theory        52814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((D -> (D or E)) and ((B or (A -> B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-662 tm-443 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (and (-> Bm (or Bm Cm)) (-> (or A (-> B A)) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-52814.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((D -> (D or E)) and ((B or (A -> B)) -> C)))), M:tm-662, m:tm-443, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (and (-> Bm (or Bm Cm)) (-> (or A (-> B A)) C)))))
================================================================
tm-name          tm-52815
in-theory        52815
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((C -> (C or D)) and (B or (A -> B))))) or ((B or (A -> B)) -> (not ((C -> (C or D)) and (B or (A -> B)))))) -> (not (B or (A -> B))))
theorem-size     42
proof            (modus-ponens tm-662 tm-449 ((Am (or A (-> B A))) (C (not (and (-> Bm (or Bm Cm)) (or A (-> B A))))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-5 tm-6)
proof-size       156
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-52815.        ((((A -> B) -> (not ((C -> (C or D)) and (B or (A -> B))))) or ((B or (A -> B)) -> (not ((C -> (C or D)) and (B or (A -> B)))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-449, u:((Am (or A (-> B A))) (C (not (and (-> Bm (or Bm Cm)) (or A (-> B A))))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52816
in-theory        52816
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((B or (A -> B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-662 tm-453 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-52816.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-453, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52817
in-theory        52817
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-662 tm-454 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-52817.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((E -> (E or F)) and D))), M:tm-662, m:tm-454, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-52818
in-theory        52818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (D -> (D or E))))
theorem-size     27
proof            (modus-ponens tm-662 tm-456 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-52818.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (D -> (D or E)))), M:tm-662, m:tm-456, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-52819
in-theory        52819
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((B or (A -> B)) or C) -> D)) or ((B or (A -> B)) -> (((B or (A -> B)) or C) -> D))) -> ((B or (A -> B)) -> D))
theorem-size     37
proof            (modus-ponens tm-662 tm-464 ((Am (or A (-> B A))) (C (-> (or (or A (-> B A)) Bm) Cm)) (D (-> (or A (-> B A)) Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-52819.        ((((A -> B) -> (((B or (A -> B)) or C) -> D)) or ((B or (A -> B)) -> (((B or (A -> B)) or C) -> D))) -> ((B or (A -> B)) -> D)), M:tm-662, m:tm-464, u:((Am (or A (-> B A))) (C (-> (or (or A (-> B A)) Bm) Cm)) (D (-> (or A (-> B A)) Cm)))
================================================================
tm-name          tm-52820
in-theory        52820
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (C -> (C or D)))) or ((B or (A -> B)) -> (not (C -> (C or D))))) -> (not (B or (A -> B))))
theorem-size     30
proof            (modus-ponens tm-662 tm-465 ((Am (or A (-> B A))) (C (not (-> Bm (or Bm Cm)))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-6)
proof-size       138
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-52820.        ((((A -> B) -> (not (C -> (C or D)))) or ((B or (A -> B)) -> (not (C -> (C or D))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-465, u:((Am (or A (-> B A))) (C (not (-> Bm (or Bm Cm)))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52821
in-theory        52821
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> (E or F))) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-469 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-52821.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> (E or F))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-469, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52822
in-theory        52822
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (A -> B)) -> (C or D)))
theorem-size     23
proof            (modus-ponens tm-662 tm-470 ((Am (or A (-> B A))) (C Bm) (D (-> (or A (-> B A)) (or Bm Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-52822.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (A -> B)) -> (C or D))), M:tm-662, m:tm-470, u:((Am (or A (-> B A))) (C Bm) (D (-> (or A (-> B A)) (or Bm Cm))))
================================================================
tm-name          tm-52823
in-theory        52823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-662 tm-471 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-52823.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (E -> (E or F)))), M:tm-662, m:tm-471, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-52824
in-theory        52824
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or (E -> (F -> E))) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-480 ((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-52824.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or (E -> (F -> E))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-480, u:((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52825
in-theory        52825
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-662 tm-481 ((Am (-> (or A (-> B A)) C)) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-52825.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or (E -> (F -> E)))), M:tm-662, m:tm-481, u:((Am (-> (or A (-> B A)) C)) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-52826
in-theory        52826
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B or (A -> B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-662 tm-490 ((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-52826.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-490, u:((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52827
in-theory        52827
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-662 tm-491 ((Am (-> (or A (-> B A)) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-52827.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-662, m:tm-491, u:((Am (-> (or A (-> B A)) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-52828
in-theory        52828
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or ((E and F) -> E)) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-500 ((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-52828.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or ((E and F) -> E)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-500, u:((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52829
in-theory        52829
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-662 tm-501 ((Am (-> (or A (-> B A)) C)) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-52829.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or ((E and F) -> E))), M:tm-662, m:tm-501, u:((Am (-> (or A (-> B A)) C)) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-52830
in-theory        52830
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or ((E and F) -> F)) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-510 ((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-52830.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or ((E and F) -> F)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-510, u:((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52831
in-theory        52831
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-662 tm-511 ((Am (-> (or A (-> B A)) C)) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-52831.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or ((E and F) -> F))), M:tm-662, m:tm-511, u:((Am (-> (or A (-> B A)) C)) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-52832
in-theory        52832
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or (E -> (F -> (E and F)))) and ((B or (A -> B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-662 tm-520 ((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-52832.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or (E -> (F -> (E and F)))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-520, u:((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52833
in-theory        52833
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-662 tm-521 ((Am (-> (or A (-> B A)) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-52833.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or (E -> (F -> (E and F))))), M:tm-662, m:tm-521, u:((Am (-> (or A (-> B A)) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-52834
in-theory        52834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or (E -> (E or F))) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-530 ((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-52834.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or (E -> (E or F))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-530, u:((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52835
in-theory        52835
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-662 tm-531 ((Am (-> (or A (-> B A)) C)) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-52835.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or (E -> (E or F)))), M:tm-662, m:tm-531, u:((Am (-> (or A (-> B A)) C)) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-52836
in-theory        52836
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or (E -> (F or E))) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-540 ((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-52836.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D or (E -> (F or E))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-540, u:((Am (-> (or A (-> B A)) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52837
in-theory        52837
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-662 tm-541 ((Am (-> (or A (-> B A)) C)) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-52837.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D or (E -> (F or E)))), M:tm-662, m:tm-541, u:((Am (-> (or A (-> B A)) C)) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-52838
in-theory        52838
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (E or D)) or F) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-550 ((Am (-> (or A (-> B A)) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-52838.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> (E or D)) or F) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-550, u:((Am (-> (or A (-> B A)) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52839
in-theory        52839
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E or D)) or F))
theorem-size     21
proof            (modus-ponens tm-662 tm-551 ((Am (-> (or A (-> B A)) C)) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-1 tm-6 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-52839.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E or D)) or F)), M:tm-662, m:tm-551, u:((Am (-> (or A (-> B A)) C)) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-52840
in-theory        52840
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((D -> (E or D)) and ((B or (A -> B)) -> C))))
theorem-size     35
proof            (modus-ponens tm-662 tm-595 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (and (-> Bm (or Cm Bm)) (-> (or A (-> B A)) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-52840.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((D -> (E or D)) and ((B or (A -> B)) -> C)))), M:tm-662, m:tm-595, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (and (-> Bm (or Cm Bm)) (-> (or A (-> B A)) C)))))
================================================================
tm-name          tm-52841
in-theory        52841
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((C -> (D or C)) and (B or (A -> B))))) or ((B or (A -> B)) -> (not ((C -> (D or C)) and (B or (A -> B)))))) -> (not (B or (A -> B))))
theorem-size     42
proof            (modus-ponens tm-662 tm-601 ((Am (or A (-> B A))) (C (not (and (-> Bm (or Cm Bm)) (or A (-> B A))))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-5 tm-7)
proof-size       156
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-52841.        ((((A -> B) -> (not ((C -> (D or C)) and (B or (A -> B))))) or ((B or (A -> B)) -> (not ((C -> (D or C)) and (B or (A -> B)))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-601, u:((Am (or A (-> B A))) (C (not (and (-> Bm (or Cm Bm)) (or A (-> B A))))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52842
in-theory        52842
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((B or (A -> B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-662 tm-605 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-52842.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-605, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52843
in-theory        52843
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     23
proof            (modus-ponens tm-662 tm-606 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-52843.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> ((E -> (F or E)) and D))), M:tm-662, m:tm-606, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-52844
in-theory        52844
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (D -> (E or D))))
theorem-size     27
proof            (modus-ponens tm-662 tm-609 ((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-52844.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and (D -> (E or D)))), M:tm-662, m:tm-609, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (or A (-> B A)) C) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-52845
in-theory        52845
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or (B or (A -> B))) -> D)) or ((B or (A -> B)) -> ((C or (B or (A -> B))) -> D))) -> ((B or (A -> B)) -> D))
theorem-size     37
proof            (modus-ponens tm-662 tm-617 ((Am (or A (-> B A))) (C (-> (or Bm (or A (-> B A))) Cm)) (D (-> (or A (-> B A)) Cm))))
axioms-used      (tm-8 tm-1 tm-2 tm-7)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-52845.        ((((A -> B) -> ((C or (B or (A -> B))) -> D)) or ((B or (A -> B)) -> ((C or (B or (A -> B))) -> D))) -> ((B or (A -> B)) -> D)), M:tm-662, m:tm-617, u:((Am (or A (-> B A))) (C (-> (or Bm (or A (-> B A))) Cm)) (D (-> (or A (-> B A)) Cm)))
================================================================
tm-name          tm-52846
in-theory        52846
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (C -> (D or C)))) or ((B or (A -> B)) -> (not (C -> (D or C))))) -> (not (B or (A -> B))))
theorem-size     30
proof            (modus-ponens tm-662 tm-618 ((Am (or A (-> B A))) (C (not (-> Bm (or Cm Bm)))) (D (not (or A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-9 tm-7)
proof-size       138
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-52846.        ((((A -> B) -> (not (C -> (D or C)))) or ((B or (A -> B)) -> (not (C -> (D or C))))) -> (not (B or (A -> B)))), M:tm-662, m:tm-618, u:((Am (or A (-> B A))) (C (not (-> Bm (or Cm Bm)))) (D (not (or A (-> B A)))))
================================================================
tm-name          tm-52847
in-theory        52847
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> (F or E))) and ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-662 tm-622 ((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-52847.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> (E -> (F or E))) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-622, u:((Am (-> (or A (-> B A)) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-52848
in-theory        52848
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (A -> B)) -> (D or C)))
theorem-size     23
proof            (modus-ponens tm-662 tm-623 ((Am (or A (-> B A))) (C Bm) (D (-> (or A (-> B A)) (or Cm Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-52848.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((B or (A -> B)) -> (D or C))), M:tm-662, m:tm-623, u:((Am (or A (-> B A))) (C Bm) (D (-> (or A (-> B A)) (or Cm Bm))))
================================================================
tm-name          tm-52849
in-theory        52849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-662 tm-624 ((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-52849.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (D -> (E -> (F or E)))), M:tm-662, m:tm-624, u:((Am (-> (or A (-> B A)) C)) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-52850
in-theory        52850
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((D or (((A or (B -> A)) -> C) -> D)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))
theorem-size     53
proof            (modus-ponens tm-654 tm-662 ((A (-> (or Am (-> Bm Am)) Cm)) (B Dm) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52850.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((D or (((A or (B -> A)) -> C) -> D)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))), M:tm-654, m:tm-662, u:((A (-> (or Am (-> Bm Am)) Cm)) (B Dm) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52851
in-theory        52851
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> D) -> (E or ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-623 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52851.        ((((A or (B -> A)) -> C) -> D) -> (E or ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))), M:tm-623, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52852
in-theory        52852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-622 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52852.        ((A -> (B -> (C or B))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-622, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52853
in-theory        52853
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C -> B)) -> D) -> (E or ((B or (C -> B)) -> D)))) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> (E or ((B or (C -> B)) -> D))))
theorem-size     43
proof            (modus-ponens tm-619 tm-662 ((A (-> (or Am (-> Bm Am)) Cm)) (Dm (or B (-> (or Am (-> Bm Am)) Cm))) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (or B (-> (or Am (-> Bm Am)) Cm))))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52853.        ((A or (((B or (C -> B)) -> D) -> (E or ((B or (C -> B)) -> D)))) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> (E or ((B or (C -> B)) -> D)))), M:tm-619, m:tm-662, u:((A (-> (or Am (-> Bm Am)) Cm)) (Dm (or B (-> (or Am (-> Bm Am)) Cm))) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (or B (-> (or Am (-> Bm Am)) Cm)))))
================================================================
tm-name          tm-52854
in-theory        52854
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (E -> (F or E)))
theorem-size     31
proof            (modus-ponens tm-609 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52854.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52855
in-theory        52855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-605 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52855.        ((A -> ((B -> (C or B)) and A)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-605, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52856
in-theory        52856
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((E -> (F or E)) and ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-595 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52856.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((E -> (F or E)) and ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))), M:tm-595, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52857
in-theory        52857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-550 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52857.        (((A -> (B or A)) or C) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-550, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52858
in-theory        52858
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-540 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52858.        ((A or (B -> (C or B))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-540, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52859
in-theory        52859
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-530 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52859.        ((A or (B -> (B or C))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-530, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52860
in-theory        52860
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-520 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52860.        ((A or (B -> (C -> (B and C)))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-520, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52861
in-theory        52861
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-510 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52861.        ((A or ((B and C) -> C)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-510, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52862
in-theory        52862
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-500 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52862.        ((A or ((B and C) -> B)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-500, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52863
in-theory        52863
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (F -> E)) -> G) -> H) -> ((((F -> E) -> G) or ((E or (F -> E)) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-490 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52863.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (F -> E)) -> G) -> H) -> ((((F -> E) -> G) or ((E or (F -> E)) -> G)) -> H))), M:tm-490, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52864
in-theory        52864
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-480 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52864.        ((A or (B -> (C -> B))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-480, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52865
in-theory        52865
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> D) -> (((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D) or E))
theorem-size     27
proof            (modus-ponens tm-470 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52865.        ((((A or (B -> A)) -> C) -> D) -> (((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D) or E)), M:tm-470, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52866
in-theory        52866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-469 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52866.        ((A -> (B -> (B or C))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-469, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52867
in-theory        52867
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C -> B)) -> D) -> (((B or (C -> B)) -> D) or E))) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> (((B or (C -> B)) -> D) or E)))
theorem-size     43
proof            (modus-ponens tm-466 tm-662 ((A (-> (or Am (-> Bm Am)) Cm)) (Dm (or (-> (or Am (-> Bm Am)) Cm) B)) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (or (-> (or Am (-> Bm Am)) Cm) B)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52867.        ((A or (((B or (C -> B)) -> D) -> (((B or (C -> B)) -> D) or E))) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> (((B or (C -> B)) -> D) or E))), M:tm-466, m:tm-662, u:((A (-> (or Am (-> Bm Am)) Cm)) (Dm (or (-> (or Am (-> Bm Am)) Cm) B)) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (or (-> (or Am (-> Bm Am)) Cm) B))))
================================================================
tm-name          tm-52868
in-theory        52868
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (E -> (E or F)))
theorem-size     31
proof            (modus-ponens tm-456 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52868.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52869
in-theory        52869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-453 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52869.        ((A -> ((B -> (B or C)) and A)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-453, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52870
in-theory        52870
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((E -> (E or F)) and ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-443 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52870.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((E -> (E or F)) and ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))), M:tm-443, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52871
in-theory        52871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-409 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52871.        (((A -> (A or B)) or C) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-409, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52872
in-theory        52872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-400 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52872.        (((A -> (B -> (A and B))) or C) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-400, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52873
in-theory        52873
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-391 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52873.        ((((A and B) -> B) or C) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-391, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52874
in-theory        52874
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-382 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52874.        ((((A and B) -> A) or C) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-382, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52875
in-theory        52875
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or (F -> E)) -> G) -> H) -> ((((F -> E) -> G) or ((E or (F -> E)) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-373 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52875.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E or (F -> E)) -> G) -> H) -> ((((F -> E) -> G) or ((E or (F -> E)) -> G)) -> H))), M:tm-373, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52876
in-theory        52876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-364 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52876.        (((A -> (B -> A)) or C) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-364, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52877
in-theory        52877
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> D) -> (E -> (((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D) and E)))
theorem-size     29
proof            (modus-ponens tm-355 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52877.        ((((A or (B -> A)) -> C) -> D) -> (E -> (((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D) and E))), M:tm-355, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52878
in-theory        52878
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-354 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52878.        ((A -> (B -> (C -> (B and C)))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-354, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52879
in-theory        52879
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C -> B)) -> D) -> (E -> (((B or (C -> B)) -> D) and E)))) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> (E -> (((B or (C -> B)) -> D) and E))))
theorem-size     47
proof            (modus-ponens tm-351 tm-662 ((A (-> (or Am (-> Bm Am)) Cm)) (Dm (-> B (and (-> (or Am (-> Bm Am)) Cm) B))) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (-> B (and (-> (or Am (-> Bm Am)) Cm) B))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52879.        ((A or (((B or (C -> B)) -> D) -> (E -> (((B or (C -> B)) -> D) and E)))) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> (E -> (((B or (C -> B)) -> D) and E)))), M:tm-351, m:tm-662, u:((A (-> (or Am (-> Bm Am)) Cm)) (Dm (-> B (and (-> (or Am (-> Bm Am)) Cm) B))) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (-> B (and (-> (or Am (-> Bm Am)) Cm) B)))))
================================================================
tm-name          tm-52880
in-theory        52880
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-341 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52880.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52881
in-theory        52881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-338 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52881.        (((A -> B) -> (A -> (A and B))) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F))), M:tm-338, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52882
in-theory        52882
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) or (((A or (B -> A)) -> C) -> (((A or (B -> A)) -> C) and D))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> (((A or (B -> A)) -> C) and D)))
theorem-size     51
proof            (modus-ponens tm-335 tm-662 ((A (-> (or Am (-> Bm Am)) Cm)) (Dm (and (-> (or Am (-> Bm Am)) Cm) B)) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (and (-> (or Am (-> Bm Am)) Cm) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52882.        (((((A or (B -> A)) -> C) -> D) or (((A or (B -> A)) -> C) -> (((A or (B -> A)) -> C) and D))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> (((A or (B -> A)) -> C) and D))), M:tm-335, m:tm-662, u:((A (-> (or Am (-> Bm Am)) Cm)) (Dm (and (-> (or Am (-> Bm Am)) Cm) B)) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (and (-> (or Am (-> Bm Am)) Cm) B))))
================================================================
tm-name          tm-52883
in-theory        52883
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((((A or (B -> A)) -> C) -> D) -> ((((A or (B -> A)) -> C) -> D) and ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))))
theorem-size     61
proof            (modus-ponens tm-328 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52883.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((((A or (B -> A)) -> C) -> D) -> ((((A or (B -> A)) -> C) -> D) and ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))), M:tm-328, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52884
in-theory        52884
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((E -> (F -> (E and F))) and ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))))
theorem-size     59
proof            (modus-ponens tm-327 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52884.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((E -> (F -> (E and F))) and ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))), M:tm-327, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52885
in-theory        52885
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (((E and F) -> F) and ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-326 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52885.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (((E and F) -> F) and ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))), M:tm-326, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52886
in-theory        52886
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (((E and F) -> E) and ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-325 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52886.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (((E and F) -> E) and ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))), M:tm-325, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52887
in-theory        52887
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))))
theorem-size     65
proof            (modus-ponens tm-324 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52887.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))), M:tm-324, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52888
in-theory        52888
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((E -> (F -> E)) and ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-323 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52888.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((E -> (F -> E)) and ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))), M:tm-323, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52889
in-theory        52889
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((E and F) -> F))
theorem-size     31
proof            (modus-ponens tm-322 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52889.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52890
in-theory        52890
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((E and F) -> E))
theorem-size     31
proof            (modus-ponens tm-320 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52890.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52891
in-theory        52891
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-318 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52891.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52892
in-theory        52892
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((((A or (B -> A)) -> C) -> D) -> (((A or (B -> A)) -> C) -> D)))
theorem-size     45
proof            (modus-ponens tm-316 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52892.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((((A or (B -> A)) -> C) -> D) -> (((A or (B -> A)) -> C) -> D))), M:tm-316, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52893
in-theory        52893
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (E -> (F -> E)))
theorem-size     31
proof            (modus-ponens tm-315 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52893.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52894
in-theory        52894
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (((((A or (B -> A)) -> C) -> D) -> (not ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))) -> (not (((A or (B -> A)) -> C) -> D))))
theorem-size     63
proof            (modus-ponens tm-313 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52894.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (((((A or (B -> A)) -> C) -> D) -> (not ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))) -> (not (((A or (B -> A)) -> C) -> D)))), M:tm-313, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52895
in-theory        52895
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D) -> E) -> (((((A or (B -> A)) -> C) -> D) or ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) -> E)))
theorem-size     71
proof            (modus-ponens tm-312 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52895.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D) -> E) -> (((((A or (B -> A)) -> C) -> D) or ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) -> E))), M:tm-312, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52896
in-theory        52896
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (E or ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-311 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52896.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (E or ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))), M:tm-311, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52897
in-theory        52897
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) or E))
theorem-size     53
proof            (modus-ponens tm-310 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52897.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) or E)), M:tm-310, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52898
in-theory        52898
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (E -> (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and E)))
theorem-size     55
proof            (modus-ponens tm-309 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52898.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (E -> (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and E))), M:tm-309, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52899
in-theory        52899
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (((((A or (B -> A)) -> C) -> D) -> (((B -> A) -> C) or ((A or (B -> A)) -> C))) -> ((((A or (B -> A)) -> C) -> D) -> D)))
theorem-size     61
proof            (modus-ponens tm-306 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52899.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (((((A or (B -> A)) -> C) -> D) -> (((B -> A) -> C) or ((A or (B -> A)) -> C))) -> ((((A or (B -> A)) -> C) -> D) -> D))), M:tm-306, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm))) (C Dm))
================================================================
tm-name          tm-52900
in-theory        52900
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (E -> ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-305 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52900.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and (E -> ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))), M:tm-305, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52901
in-theory        52901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-303 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52901.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-303, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52902
in-theory        52902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-270 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52902.        ((A -> (((B and C) -> C) and A)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-270, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52903
in-theory        52903
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-239 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52903.        ((A -> (((B and C) -> B) and A)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-239, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52904
in-theory        52904
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or (F -> E)) -> G) -> H) -> ((((F -> E) -> G) or ((E or (F -> E)) -> G)) -> H)))
theorem-size     43
proof            (modus-ponens tm-210 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52904.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E or (F -> E)) -> G) -> H) -> ((((F -> E) -> G) or ((E or (F -> E)) -> G)) -> H))), M:tm-210, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52905
in-theory        52905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-183 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52905.        ((A -> ((B -> (C -> B)) and A)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-183, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52906
in-theory        52906
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-157 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52906.        ((A -> ((B and C) -> C)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-157, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52907
in-theory        52907
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-147 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52907.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-147, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52908
in-theory        52908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-134 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52908.        ((A -> ((B and C) -> B)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-134, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52909
in-theory        52909
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-125 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52909.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-125, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52910
in-theory        52910
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> (D -> E)) -> (((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> E)))
theorem-size     43
proof            (modus-ponens tm-114 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) (-> C D))) (B (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52910.        ((((A or (B -> A)) -> C) -> (D -> E)) -> (((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> E))), M:tm-114, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) (-> C D))) (B (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-52911
in-theory        52911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (F -> E)) -> G) -> H) -> ((((F -> E) -> G) or ((E or (F -> E)) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-113 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52911.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E or (F -> E)) -> G) -> H) -> ((((F -> E) -> G) or ((E or (F -> E)) -> G)) -> H))), M:tm-113, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52912
in-theory        52912
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C -> B)) -> (D -> E)) -> (((B or (C -> B)) -> D) -> ((B or (C -> B)) -> E)))) -> ((((C -> B) -> (D -> E)) or ((B or (C -> B)) -> (D -> E))) -> (((B or (C -> B)) -> D) -> ((B or (C -> B)) -> E))))
theorem-size     61
proof            (modus-ponens tm-110 tm-662 ((A (or Am (-> Bm Am))) (Cm (-> B C)) (Dm (-> (-> (or Am (-> Bm Am)) B) (-> (or Am (-> Bm Am)) C))) (D (-> (or (-> (-> Bm Am) (-> B C)) (-> (or Am (-> Bm Am)) (-> B C))) (-> (-> (or Am (-> Bm Am)) B) (-> (or Am (-> Bm Am)) C))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52912.        ((A or (((B or (C -> B)) -> (D -> E)) -> (((B or (C -> B)) -> D) -> ((B or (C -> B)) -> E)))) -> ((((C -> B) -> (D -> E)) or ((B or (C -> B)) -> (D -> E))) -> (((B or (C -> B)) -> D) -> ((B or (C -> B)) -> E)))), M:tm-110, m:tm-662, u:((A (or Am (-> Bm Am))) (Cm (-> B C)) (Dm (-> (-> (or Am (-> Bm Am)) B) (-> (or Am (-> Bm Am)) C))) (D (-> (or (-> (-> Bm Am) (-> B C)) (-> (or Am (-> Bm Am)) (-> B C))) (-> (-> (or Am (-> Bm Am)) B) (-> (or Am (-> Bm Am)) C)))))
================================================================
tm-name          tm-52913
in-theory        52913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     45
proof            (modus-ponens tm-105 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52913.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-105, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52914
in-theory        52914
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> (C -> D)) -> ((A or (B -> A)) -> C)) or (((A or (B -> A)) -> (C -> D)) -> ((A or (B -> A)) -> D))) -> ((((B -> A) -> (C -> D)) or ((A or (B -> A)) -> (C -> D))) -> ((A or (B -> A)) -> D)))
theorem-size     61
proof            (modus-ponens tm-102 tm-662 ((A (or Am (-> Bm Am))) (Cm (-> B C)) (Dm (-> (or Am (-> Bm Am)) C)) (D (-> (or (-> (-> Bm Am) (-> B C)) (-> (or Am (-> Bm Am)) (-> B C))) (-> (or Am (-> Bm Am)) C)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       221
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52914.        (((((A or (B -> A)) -> (C -> D)) -> ((A or (B -> A)) -> C)) or (((A or (B -> A)) -> (C -> D)) -> ((A or (B -> A)) -> D))) -> ((((B -> A) -> (C -> D)) or ((A or (B -> A)) -> (C -> D))) -> ((A or (B -> A)) -> D))), M:tm-102, m:tm-662, u:((A (or Am (-> Bm Am))) (Cm (-> B C)) (Dm (-> (or Am (-> Bm Am)) C)) (D (-> (or (-> (-> Bm Am) (-> B C)) (-> (or Am (-> Bm Am)) (-> B C))) (-> (or Am (-> Bm Am)) C))))
================================================================
tm-name          tm-52915
in-theory        52915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-95 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52915.        (((A -> B) -> (A -> A)) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F))), M:tm-95, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52916
in-theory        52916
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) or (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> C))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((A or (B -> A)) -> C)))
theorem-size     47
proof            (modus-ponens tm-92 tm-662 ((Dm (-> (or Am (-> Bm Am)) Cm)) (A (-> (or Am (-> Bm Am)) Cm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (-> (or Am (-> Bm Am)) Cm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52916.        (((((A or (B -> A)) -> C) -> D) or (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> C))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((A or (B -> A)) -> C))), M:tm-92, m:tm-662, u:((Dm (-> (or Am (-> Bm Am)) Cm)) (A (-> (or Am (-> Bm Am)) Cm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (-> (or Am (-> Bm Am)) Cm))))
================================================================
tm-name          tm-52917
in-theory        52917
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> D) -> (E -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-84 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52917.        ((((A or (B -> A)) -> C) -> D) -> (E -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))), M:tm-84, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52918
in-theory        52918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-83 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52918.        ((A -> (B -> (C -> B))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-83, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52919
in-theory        52919
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B or (C -> B)) -> D) -> (E -> ((B or (C -> B)) -> D)))) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> (E -> ((B or (C -> B)) -> D))))
theorem-size     43
proof            (modus-ponens tm-80 tm-662 ((A (-> (or Am (-> Bm Am)) Cm)) (Dm (-> B (-> (or Am (-> Bm Am)) Cm))) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (-> B (-> (or Am (-> Bm Am)) Cm))))))
axioms-used      (tm-8 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52919.        ((A or (((B or (C -> B)) -> D) -> (E -> ((B or (C -> B)) -> D)))) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> (E -> ((B or (C -> B)) -> D)))), M:tm-80, m:tm-662, u:((A (-> (or Am (-> Bm Am)) Cm)) (Dm (-> B (-> (or Am (-> Bm Am)) Cm))) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (-> B (-> (or Am (-> Bm Am)) Cm)))))
================================================================
tm-name          tm-52920
in-theory        52920
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B or (C -> B)) -> D) -> E) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-76 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52920.        (((not (not A)) -> A) and ((((B or (C -> B)) -> D) -> E) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> E))), M:tm-76, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52921
in-theory        52921
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A or (B -> A)) -> C) -> D))) or (((A or (B -> A)) -> C) -> D)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))
theorem-size     37
proof            (modus-ponens tm-73 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52921.        (((not (not (((A or (B -> A)) -> C) -> D))) or (((A or (B -> A)) -> C) -> D)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-73, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52922
in-theory        52922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-69 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52922.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F))), M:tm-69, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52923
in-theory        52923
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) or (((A or (B -> A)) -> (not C)) -> (not (A or (B -> A))))) -> ((((B -> A) -> (not C)) or ((A or (B -> A)) -> (not C))) -> (not (A or (B -> A)))))
theorem-size     46
proof            (modus-ponens tm-66 tm-662 ((A (or Am (-> Bm Am))) (Cm (not B)) (Dm (not (or Am (-> Bm Am)))) (C (-> (or (-> (-> Bm Am) (not B)) (-> (or Am (-> Bm Am)) (not B))) (not (or Am (-> Bm Am)))))))
axioms-used      (tm-8 tm-9 tm-1)
proof-size       162
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52923.        ((((A or (B -> A)) -> C) or (((A or (B -> A)) -> (not C)) -> (not (A or (B -> A))))) -> ((((B -> A) -> (not C)) or ((A or (B -> A)) -> (not C))) -> (not (A or (B -> A))))), M:tm-66, m:tm-662, u:((A (or Am (-> Bm Am))) (Cm (not B)) (Dm (not (or Am (-> Bm Am)))) (C (-> (or (-> (-> Bm Am) (not B)) (-> (or Am (-> Bm Am)) (not B))) (not (or Am (-> Bm Am))))))
================================================================
tm-name          tm-52924
in-theory        52924
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> (((B -> A) -> C) or ((A or (B -> A)) -> C))) -> ((((A or (B -> A)) -> C) or (((B -> A) -> C) or ((A or (B -> A)) -> C))) -> (((B -> A) -> C) or ((A or (B -> A)) -> C))))
theorem-size     57
proof            (modus-ponens tm-55 tm-662 ((A (-> (or Am (-> Bm Am)) Cm)) (Dm (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm))) (B (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm))) (C (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       169
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52924.        ((((A or (B -> A)) -> C) -> (((B -> A) -> C) or ((A or (B -> A)) -> C))) -> ((((A or (B -> A)) -> C) or (((B -> A) -> C) or ((A or (B -> A)) -> C))) -> (((B -> A) -> C) or ((A or (B -> A)) -> C)))), M:tm-55, m:tm-662, u:((A (-> (or Am (-> Bm Am)) Cm)) (Dm (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm))) (B (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm))) (C (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm))))
================================================================
tm-name          tm-52925
in-theory        52925
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-54 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52925.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-54, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52926
in-theory        52926
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B or (C -> B))) or (((B or (C -> B)) -> D) -> ((A or (B or (C -> B))) -> D))) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> ((A or (B or (C -> B))) -> D)))
theorem-size     49
proof            (modus-ponens tm-51 tm-662 ((A (or Am (-> Bm Am))) (B Cm) (Dm (-> (or C (or Am (-> Bm Am))) Cm)) (D (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (-> (or C (or Am (-> Bm Am))) Cm)))))
axioms-used      (tm-8 tm-1)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52926.        (((A -> (B or (C -> B))) or (((B or (C -> B)) -> D) -> ((A or (B or (C -> B))) -> D))) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> ((A or (B or (C -> B))) -> D))), M:tm-51, m:tm-662, u:((A (or Am (-> Bm Am))) (B Cm) (Dm (-> (or C (or Am (-> Bm Am))) Cm)) (D (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (-> (or C (or Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-52927
in-theory        52927
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B or (C -> B)) -> D) -> (A and ((B or (C -> B)) -> D)))) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> (A and ((B or (C -> B)) -> D))))
theorem-size     43
proof            (modus-ponens tm-48 tm-662 ((A (-> (or Am (-> Bm Am)) Cm)) (Dm (and B (-> (or Am (-> Bm Am)) Cm))) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (and B (-> (or Am (-> Bm Am)) Cm))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52927.        ((A or (((B or (C -> B)) -> D) -> (A and ((B or (C -> B)) -> D)))) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> (A and ((B or (C -> B)) -> D)))), M:tm-48, m:tm-662, u:((A (-> (or Am (-> Bm Am)) Cm)) (Dm (and B (-> (or Am (-> Bm Am)) Cm))) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (and B (-> (or Am (-> Bm Am)) Cm)))))
================================================================
tm-name          tm-52928
in-theory        52928
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B or (C -> B)) -> D) -> E)) or (((B or (C -> B)) -> D) -> E)) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> E))
theorem-size     37
proof            (modus-ponens tm-47 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52928.        (((A and (((B or (C -> B)) -> D) -> E)) or (((B or (C -> B)) -> D) -> E)) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> E)), M:tm-47, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52929
in-theory        52929
times-derived    2
----------------------------------------------------------------
theorem          ((((((A or (B -> A)) -> C) -> D) and E) or (((A or (B -> A)) -> C) -> D)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))
theorem-size     37
proof            (modus-ponens tm-46 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52929.        ((((((A or (B -> A)) -> C) -> D) and E) or (((A or (B -> A)) -> C) -> D)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-46, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52930
in-theory        52930
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> (C -> D)) or (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> D))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((A or (B -> A)) -> D)))
theorem-size     47
proof            (modus-ponens tm-45 tm-662 ((A (or Am (-> Bm Am))) (B Cm) (Dm (-> (or Am (-> Bm Am)) C)) (D (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (-> (or Am (-> Bm Am)) C)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52930.        ((((A or (B -> A)) -> (C -> D)) or (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> D))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((A or (B -> A)) -> D))), M:tm-45, m:tm-662, u:((A (or Am (-> Bm Am))) (B Cm) (Dm (-> (or Am (-> Bm Am)) C)) (D (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (-> (or Am (-> Bm Am)) C))))
================================================================
tm-name          tm-52931
in-theory        52931
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B or (C -> B)) -> D) -> A)) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> A))
theorem-size     27
proof            (modus-ponens tm-44 tm-662 ((A (-> (or Am (-> Bm Am)) Cm)) (B Dm) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52931.        ((A or (((B or (C -> B)) -> D) -> A)) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> A)), M:tm-44, m:tm-662, u:((A (-> (or Am (-> Bm Am)) Cm)) (B Dm) (C (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52932
in-theory        52932
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-42 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52932.        ((A -> (B or A)) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F))), M:tm-42, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52933
in-theory        52933
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-32 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52933.        ((A -> (A or B)) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F))), M:tm-32, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52934
in-theory        52934
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> D) -> ((((A or (B -> A)) -> C) -> D) and ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))
theorem-size     35
proof            (modus-ponens tm-24 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52934.        ((((A or (B -> A)) -> C) -> D) -> ((((A or (B -> A)) -> C) -> D) and ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))), M:tm-24, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52935
in-theory        52935
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-23 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52935.        ((A -> (B -> (A and B))) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F))), M:tm-23, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52936
in-theory        52936
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-22 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52936.        (((A and B) -> B) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F))), M:tm-22, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52937
in-theory        52937
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-21 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52937.        (((A and B) -> A) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F))), M:tm-21, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52938
in-theory        52938
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-20 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52938.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-20, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52939
in-theory        52939
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-19 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52939.        ((A -> (B -> A)) and ((((C or (D -> C)) -> E) -> F) -> ((((D -> C) -> E) or ((C or (D -> C)) -> E)) -> F))), M:tm-19, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52940
in-theory        52940
times-derived    2
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> D) -> (((A or (B -> A)) -> C) -> D))
theorem-size     19
proof            (modus-ponens tm-12 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52940.        ((((A or (B -> A)) -> C) -> D) -> (((A or (B -> A)) -> C) -> D)), M:tm-12, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52941
in-theory        52941
times-derived    2
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> (not ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))) -> (not (((A or (B -> A)) -> C) -> D)))
theorem-size     37
proof            (modus-ponens tm-9 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-1)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52941.        (((((A or (B -> A)) -> C) -> D) -> (not ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))) -> (not (((A or (B -> A)) -> C) -> D))), M:tm-9, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52942
in-theory        52942
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> D) -> E) -> (((((B or (A -> B)) -> C) -> D) or ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> D)) -> E))
theorem-size     45
proof            (modus-ponens tm-8 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-8 tm-1)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52942.        ((((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> D) -> E) -> (((((B or (A -> B)) -> C) -> D) or ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> D)) -> E)), M:tm-8, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-52943
in-theory        52943
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B or (C -> B)) -> D) -> E) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-7 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-1)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52943.        (A or ((((B or (C -> B)) -> D) -> E) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> E))), M:tm-7, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52944
in-theory        52944
times-derived    2
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) or E)
theorem-size     27
proof            (modus-ponens tm-6 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-1)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52944.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) or E), M:tm-6, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52945
in-theory        52945
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B or (C -> B)) -> D) -> E) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> E)) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52945.        (A -> (((((B or (C -> B)) -> D) -> E) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> E)) and A)), M:tm-5, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52946
in-theory        52946
times-derived    2
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> (((B -> A) -> C) or ((A or (B -> A)) -> C))) -> ((((A or (B -> A)) -> C) -> D) -> D))
theorem-size     35
proof            (modus-ponens tm-2 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52946.        (((((A or (B -> A)) -> C) -> D) -> (((B -> A) -> C) or ((A or (B -> A)) -> C))) -> ((((A or (B -> A)) -> C) -> D) -> D)), M:tm-2, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm))) (C Dm))
================================================================
tm-name          tm-52947
in-theory        52947
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B or (C -> B)) -> D) -> E) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-1 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-1 tm-8)
proof-size       101
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-52947.        (A -> ((((B or (C -> B)) -> D) -> E) -> ((((C -> B) -> D) or ((B or (C -> B)) -> D)) -> E))), M:tm-1, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-52948
in-theory        52948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-622 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52948.        ((A -> (B -> (C or B))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-622, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52949
in-theory        52949
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52949.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (F or E))), M:tm-609, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52950
in-theory        52950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-605 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52950.        ((A -> ((B -> (C or B)) and A)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-605, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52951
in-theory        52951
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F or E)) and (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52951.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F or E)) and (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-595, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52952
in-theory        52952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-550 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52952.        (((A -> (B or A)) or C) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-550, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52953
in-theory        52953
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-540 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52953.        ((A or (B -> (C or B))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-540, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52954
in-theory        52954
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-530 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52954.        ((A or (B -> (B or C))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-530, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52955
in-theory        52955
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-520 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52955.        ((A or (B -> (C -> (B and C)))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-520, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52956
in-theory        52956
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-510 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52956.        ((A or ((B and C) -> C)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-510, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52957
in-theory        52957
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-500 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52957.        ((A or ((B and C) -> B)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-500, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52958
in-theory        52958
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-490 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52958.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-490, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52959
in-theory        52959
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-480 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52959.        ((A or (B -> (C -> B))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-480, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52960
in-theory        52960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-469 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52960.        ((A -> (B -> (B or C))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-469, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52961
in-theory        52961
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52961.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (E or F))), M:tm-456, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52962
in-theory        52962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-453 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52962.        ((A -> ((B -> (B or C)) and A)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-453, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52963
in-theory        52963
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (E or F)) and (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52963.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (E or F)) and (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-443, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52964
in-theory        52964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-409 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52964.        (((A -> (A or B)) or C) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-409, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52965
in-theory        52965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-400 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52965.        (((A -> (B -> (A and B))) or C) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-400, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52966
in-theory        52966
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-391 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52966.        ((((A and B) -> B) or C) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-391, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52967
in-theory        52967
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-382 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52967.        ((((A and B) -> A) or C) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-382, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52968
in-theory        52968
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-373 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52968.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-373, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52969
in-theory        52969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-364 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52969.        (((A -> (B -> A)) or C) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-364, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52970
in-theory        52970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-354 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52970.        ((A -> (B -> (C -> (B and C)))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-354, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52971
in-theory        52971
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52971.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52972
in-theory        52972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-338 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52972.        (((A -> B) -> (A -> (A and B))) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-338, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52973
in-theory        52973
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F -> (E and F))) and (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52973.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F -> (E and F))) and (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-327, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52974
in-theory        52974
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((E and F) -> F) and (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52974.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((E and F) -> F) and (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-326, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52975
in-theory        52975
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((E and F) -> E) and (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52975.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((E and F) -> E) and (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-325, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52976
in-theory        52976
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52976.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-324, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52977
in-theory        52977
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F -> E)) and (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52977.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F -> E)) and (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-323, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52978
in-theory        52978
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52978.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52979
in-theory        52979
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52979.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52980
in-theory        52980
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52980.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52981
in-theory        52981
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52981.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52982
in-theory        52982
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E or (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52982.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E or (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-311, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52983
in-theory        52983
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52983.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) or E)), M:tm-310, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52984
in-theory        52984
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52984.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and E))), M:tm-309, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52985
in-theory        52985
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52985.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-305, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52986
in-theory        52986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-303 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52986.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-303, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52987
in-theory        52987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-270 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52987.        ((A -> (((B and C) -> C) and A)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-270, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52988
in-theory        52988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-239 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52988.        ((A -> (((B and C) -> B) and A)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-239, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52989
in-theory        52989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-210 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52989.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-210, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52990
in-theory        52990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-183 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52990.        ((A -> ((B -> (C -> B)) and A)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-183, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52991
in-theory        52991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-157 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52991.        ((A -> ((B and C) -> C)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-157, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52992
in-theory        52992
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-147 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52992.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-147, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52993
in-theory        52993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-134 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52993.        ((A -> ((B and C) -> B)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-134, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52994
in-theory        52994
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-125 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52994.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-125, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52995
in-theory        52995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-113 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52995.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-113, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52996
in-theory        52996
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-105 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52996.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-105, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52997
in-theory        52997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     23
proof            (modus-ponens tm-95 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52997.        (((A -> B) -> (A -> A)) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-95, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52998
in-theory        52998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-83 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52998.        ((A -> (B -> (C -> B))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-83, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-52999
in-theory        52999
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or (((C -> D) -> E) -> ((D or (C -> D)) -> E))))
theorem-size     21
proof            (modus-ponens tm-76 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-52999.        (((not (not A)) -> A) and (B or (((C -> D) -> E) -> ((D or (C -> D)) -> E)))), M:tm-76, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53000
in-theory        53000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-69 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53000.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-69, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53001
in-theory        53001
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-54 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53001.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-54, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53002
in-theory        53002
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-42 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53002.        ((A -> (B or A)) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-42, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53003
in-theory        53003
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-32 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53003.        ((A -> (A or B)) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-32, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53004
in-theory        53004
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     23
proof            (modus-ponens tm-23 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53004.        ((A -> (B -> (A and B))) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-23, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53005
in-theory        53005
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-22 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53005.        (((A and B) -> B) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-22, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53006
in-theory        53006
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-21 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53006.        (((A and B) -> A) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-21, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53007
in-theory        53007
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-20 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53007.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-20, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53008
in-theory        53008
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-19 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53008.        ((A -> (B -> A)) and (C or (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-19, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53009
in-theory        53009
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or (((C -> D) -> E) -> ((D or (C -> D)) -> E))))
theorem-size     17
proof            (modus-ponens tm-7 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-7 tm-8 tm-1)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53009.        (A or (B or (((C -> D) -> E) -> ((D or (C -> D)) -> E)))), M:tm-7, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53010
in-theory        53010
times-derived    2
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-6 tm-7 tm-8 tm-1)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53010.        ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) or E), M:tm-6, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53011
in-theory        53011
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53011.        (A -> ((B or (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and A)), M:tm-5, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53012
in-theory        53012
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or (((C -> D) -> E) -> ((D or (C -> D)) -> E))))
theorem-size     17
proof            (modus-ponens tm-1 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-1 tm-7 tm-8)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53012.        (A -> (B or (((C -> D) -> E) -> ((D or (C -> D)) -> E)))), M:tm-1, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53013
in-theory        53013
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-651 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> (-> B C) (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53013.        ((A or (B -> A)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-651, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> (-> B C) (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53014
in-theory        53014
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-649 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53014.        ((A -> (B or A)) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-649, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53015
in-theory        53015
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-647 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53015.        ((A -> (A or B)) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-647, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53016
in-theory        53016
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> C) -> D) -> ((C or (B -> C)) -> D))))
theorem-size     17
proof            (modus-ponens tm-645 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53016.        (A -> (A and (((B -> C) -> D) -> ((C or (B -> C)) -> D)))), M:tm-645, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53017
in-theory        53017
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     23
proof            (modus-ponens tm-644 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53017.        ((A -> (B -> (A and B))) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-644, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53018
in-theory        53018
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-643 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53018.        (((A and B) -> B) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-643, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53019
in-theory        53019
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-642 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53019.        (((A and B) -> A) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-642, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53020
in-theory        53020
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-641 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53020.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-641, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53021
in-theory        53021
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     21
proof            (modus-ponens tm-640 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53021.        ((A -> (B -> A)) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-640, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53022
in-theory        53022
times-derived    2
----------------------------------------------------------------
theorem          ((A and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) -> E)) -> E)
theorem-size     19
proof            (modus-ponens tm-638 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> (and B (-> (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) C)) (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-4 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53022.        ((A and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) -> E)) -> E), M:tm-638, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> (and B (-> (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) C)) (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53023
in-theory        53023
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) and E) -> D)
theorem-size     19
proof            (modus-ponens tm-636 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> (and (-> (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) B) C) (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-3 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53023.        ((((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) and E) -> D), M:tm-636, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> (and (-> (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) B) C) (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53024
in-theory        53024
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((B or (A -> B)) -> C) -> D)) -> (((A -> B) -> C) -> D))
theorem-size     23
proof            (modus-ponens tm-634 tm-664 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)) (Dm (-> (-> (-> (-> Am Bm) Cm) (-> (-> (or Bm (-> Am Bm)) Cm) C)) (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53024.        ((((A -> B) -> C) -> (((B or (A -> B)) -> C) -> D)) -> (((A -> B) -> C) -> D)), M:tm-634, m:tm-664, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)) (Dm (-> (-> (-> (-> Am Bm) Cm) (-> (-> (or Bm (-> Am Bm)) Cm) C)) (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53025
in-theory        53025
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> C) -> D) -> ((C or (B -> C)) -> D)))) -> (not A))
theorem-size     19
proof            (modus-ponens tm-631 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-9 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53025.        ((A -> (not (((B -> C) -> D) -> ((C or (B -> C)) -> D)))) -> (not A)), M:tm-631, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53026
in-theory        53026
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) -> ((E or (((A -> B) -> C) -> ((B or (A -> B)) -> C))) -> D))
theorem-size     33
proof            (modus-ponens tm-630 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53026.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) -> ((E or (((A -> B) -> C) -> ((B or (A -> B)) -> C))) -> D)), M:tm-630, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53027
in-theory        53027
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))))
theorem-size     17
proof            (modus-ponens tm-629 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53027.        (A or (B -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))), M:tm-629, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53028
in-theory        53028
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) or E)
theorem-size     17
proof            (modus-ponens tm-628 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53028.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) or E), M:tm-628, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53029
in-theory        53029
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and A))
theorem-size     19
proof            (modus-ponens tm-627 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53029.        (A -> ((B -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and A)), M:tm-627, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53030
in-theory        53030
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> D)) -> (A -> ((C or (B -> C)) -> D)))
theorem-size     17
proof            (modus-ponens tm-626 tm-664 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)) (Dm (-> C (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53030.        ((A -> ((B -> C) -> D)) -> (A -> ((C or (B -> C)) -> D))), M:tm-626, m:tm-664, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)) (Dm (-> C (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53031
in-theory        53031
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))))
theorem-size     17
proof            (modus-ponens tm-625 tm-664 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53031.        (A -> (B -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))), M:tm-625, m:tm-664, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))) (Dm (-> B (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53032
in-theory        53032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-622 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53032.        ((A -> (B -> (C or B))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-622, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53033
in-theory        53033
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53033.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (E -> (F or E))), M:tm-609, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53034
in-theory        53034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-605 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53034.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-605, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53035
in-theory        53035
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and ((E -> (F or E)) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-595 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53035.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and ((E -> (F or E)) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D))), M:tm-595, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53036
in-theory        53036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-550 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53036.        (((A -> (B or A)) or C) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-550, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53037
in-theory        53037
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-540 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53037.        ((A or (B -> (C or B))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-540, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53038
in-theory        53038
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-530 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53038.        ((A or (B -> (B or C))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-530, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53039
in-theory        53039
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-520 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53039.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-520, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53040
in-theory        53040
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-510 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53040.        ((A or ((B and C) -> C)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-510, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53041
in-theory        53041
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-500 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53041.        ((A or ((B and C) -> B)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-500, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53042
in-theory        53042
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-490 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53042.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H)), M:tm-490, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53043
in-theory        53043
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-480 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53043.        ((A or (B -> (C -> B))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-480, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53044
in-theory        53044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-469 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53044.        ((A -> (B -> (B or C))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-469, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53045
in-theory        53045
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53045.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (E -> (E or F))), M:tm-456, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53046
in-theory        53046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-453 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53046.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-453, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53047
in-theory        53047
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and ((E -> (E or F)) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-443 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53047.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and ((E -> (E or F)) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D))), M:tm-443, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53048
in-theory        53048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-409 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53048.        (((A -> (A or B)) or C) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-409, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53049
in-theory        53049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-400 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53049.        (((A -> (B -> (A and B))) or C) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-400, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53050
in-theory        53050
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-391 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53050.        ((((A and B) -> B) or C) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-391, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53051
in-theory        53051
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-382 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53051.        ((((A and B) -> A) or C) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-382, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53052
in-theory        53052
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-373 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53052.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H)), M:tm-373, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53053
in-theory        53053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-364 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53053.        (((A -> (B -> A)) or C) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-364, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53054
in-theory        53054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-354 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53054.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-354, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53055
in-theory        53055
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53055.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53056
in-theory        53056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F))
theorem-size     25
proof            (modus-ponens tm-338 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53056.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F)), M:tm-338, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53057
in-theory        53057
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and ((E -> (F -> (E and F))) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D)))
theorem-size     39
proof            (modus-ponens tm-327 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53057.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and ((E -> (F -> (E and F))) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D))), M:tm-327, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53058
in-theory        53058
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (((E and F) -> F) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-326 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53058.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (((E and F) -> F) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D))), M:tm-326, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53059
in-theory        53059
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (((E and F) -> E) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-325 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53059.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (((E and F) -> E) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D))), M:tm-325, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53060
in-theory        53060
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D)))
theorem-size     45
proof            (modus-ponens tm-324 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53060.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D))), M:tm-324, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53061
in-theory        53061
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and ((E -> (F -> E)) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-323 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53061.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and ((E -> (F -> E)) and ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D))), M:tm-323, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53062
in-theory        53062
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53062.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and ((E and F) -> F)), M:tm-322, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53063
in-theory        53063
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53063.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and ((E and F) -> E)), M:tm-320, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53064
in-theory        53064
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53064.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53065
in-theory        53065
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53065.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (E -> (F -> E))), M:tm-315, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53066
in-theory        53066
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (E or ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D)))
theorem-size     33
proof            (modus-ponens tm-311 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53066.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (E or ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D))), M:tm-311, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53067
in-theory        53067
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53067.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) or E)), M:tm-310, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53068
in-theory        53068
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (E -> (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53068.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (E -> (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and E))), M:tm-309, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53069
in-theory        53069
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (E -> ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D)))
theorem-size     33
proof            (modus-ponens tm-305 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53069.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) and (E -> ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D))), M:tm-305, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53070
in-theory        53070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-303 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53070.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-303, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53071
in-theory        53071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-270 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53071.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-270, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53072
in-theory        53072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-239 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53072.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-239, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53073
in-theory        53073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H))
theorem-size     33
proof            (modus-ponens tm-210 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53073.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H)), M:tm-210, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53074
in-theory        53074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     25
proof            (modus-ponens tm-183 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53074.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-183, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53075
in-theory        53075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-157 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53075.        ((A -> ((B and C) -> C)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-157, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53076
in-theory        53076
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     31
proof            (modus-ponens tm-147 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53076.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-147, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53077
in-theory        53077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-134 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53077.        ((A -> ((B and C) -> B)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-134, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53078
in-theory        53078
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     31
proof            (modus-ponens tm-125 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53078.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-125, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53079
in-theory        53079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H))
theorem-size     31
proof            (modus-ponens tm-113 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53079.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H)), M:tm-113, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53080
in-theory        53080
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     35
proof            (modus-ponens tm-105 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53080.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-105, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53081
in-theory        53081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F))
theorem-size     23
proof            (modus-ponens tm-95 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53081.        (((A -> B) -> (A -> A)) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F)), M:tm-95, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53082
in-theory        53082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-83 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53082.        ((A -> (B -> (C -> B))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-83, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53083
in-theory        53083
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) or E))
theorem-size     21
proof            (modus-ponens tm-76 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53083.        (((not (not A)) -> A) and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) or E)), M:tm-76, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53084
in-theory        53084
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F))
theorem-size     27
proof            (modus-ponens tm-69 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-8 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53084.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F)), M:tm-69, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53085
in-theory        53085
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-54 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53085.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-54, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53086
in-theory        53086
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-42 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53086.        ((A -> (B or A)) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F)), M:tm-42, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53087
in-theory        53087
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-32 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53087.        ((A -> (A or B)) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F)), M:tm-32, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53088
in-theory        53088
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F))
theorem-size     23
proof            (modus-ponens tm-23 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53088.        ((A -> (B -> (A and B))) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F)), M:tm-23, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53089
in-theory        53089
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-22 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53089.        (((A and B) -> B) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F)), M:tm-22, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53090
in-theory        53090
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-21 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53090.        (((A and B) -> A) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F)), M:tm-21, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53091
in-theory        53091
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-20 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53091.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-20, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53092
in-theory        53092
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F))
theorem-size     21
proof            (modus-ponens tm-19 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53092.        ((A -> (B -> A)) and ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) or F)), M:tm-19, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53093
in-theory        53093
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) or E))
theorem-size     17
proof            (modus-ponens tm-7 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-7 tm-6 tm-8 tm-1)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53093.        (A or ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) or E)), M:tm-7, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53094
in-theory        53094
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-6 tm-8 tm-1)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53094.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D) or E), M:tm-6, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53095
in-theory        53095
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> D) -> ((C or (B -> C)) -> D)) or E) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53095.        (A -> (((((B -> C) -> D) -> ((C or (B -> C)) -> D)) or E) and A)), M:tm-5, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53096
in-theory        53096
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) or E))
theorem-size     17
proof            (modus-ponens tm-1 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-1 tm-6 tm-8)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53096.        (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) or E)), M:tm-1, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53097
in-theory        53097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53097.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-665, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-53098
in-theory        53098
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-665 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-53098.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-665, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-53099
in-theory        53099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((not (not D)) -> D))
theorem-size     19
proof            (modus-ponens tm-665 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-8 tm-1 tm-10)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-53099.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((not (not D)) -> D)), M:tm-665, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-53100
in-theory        53100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-665 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-53100.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (F -> E)))), M:tm-665, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-53101
in-theory        53101
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-665 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-53101.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (D -> D))), M:tm-665, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-53102
in-theory        53102
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-665 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-53102.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-665, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-53103
in-theory        53103
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-53103.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-665, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-53104
in-theory        53104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-665 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-53104.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-665, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-53105
in-theory        53105
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-665 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-53105.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E and F) -> E))), M:tm-665, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-53106
in-theory        53106
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-665 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-53106.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-665, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-53107
in-theory        53107
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-665 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-53107.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E and F) -> F))), M:tm-665, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-53108
in-theory        53108
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-665 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-53108.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> E)) and D))), M:tm-665, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-53109
in-theory        53109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-665 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-53109.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-665, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-53110
in-theory        53110
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E and F) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-665 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-53110.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E and F) -> E) and D))), M:tm-665, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-53111
in-theory        53111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E and F) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-665 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-53111.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E and F) -> F) and D))), M:tm-665, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-53112
in-theory        53112
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-53112.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-665, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-53113
in-theory        53113
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-665 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-53113.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (D -> (D and E)))), M:tm-665, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-53114
in-theory        53114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-53114.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (F -> (E and F))))), M:tm-665, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-53115
in-theory        53115
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-665 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-53115.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) or F)), M:tm-665, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-53116
in-theory        53116
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-665 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-53116.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-665, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-53117
in-theory        53117
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) or F))
theorem-size     21
proof            (modus-ponens tm-665 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-53117.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) or F)), M:tm-665, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-53118
in-theory        53118
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) or F))
theorem-size     21
proof            (modus-ponens tm-665 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-53118.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) or F)), M:tm-665, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-53119
in-theory        53119
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) or F))
theorem-size     23
proof            (modus-ponens tm-665 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-53119.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) or F)), M:tm-665, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-53120
in-theory        53120
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) or F))
theorem-size     21
proof            (modus-ponens tm-665 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-53120.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) or F)), M:tm-665, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-53121
in-theory        53121
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (E or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-665 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-53121.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (E or F)) and D))), M:tm-665, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-53122
in-theory        53122
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-665 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-53122.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (E or F)))), M:tm-665, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-53123
in-theory        53123
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-665 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-53123.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (F -> E)))), M:tm-665, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-53124
in-theory        53124
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-53124.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-665, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-53125
in-theory        53125
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-665 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-53125.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E and F) -> E))), M:tm-665, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-53126
in-theory        53126
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-665 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-53126.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E and F) -> F))), M:tm-665, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-53127
in-theory        53127
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-53127.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (F -> (E and F))))), M:tm-665, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-53128
in-theory        53128
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-665 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-53128.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (E or F)))), M:tm-665, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-53129
in-theory        53129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-665 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-53129.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (F or E)))), M:tm-665, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-53130
in-theory        53130
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) or F))
theorem-size     21
proof            (modus-ponens tm-665 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-53130.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) or F)), M:tm-665, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-53131
in-theory        53131
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F or E)) and D)))
theorem-size     23
proof            (modus-ponens tm-665 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-53131.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F or E)) and D))), M:tm-665, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-53132
in-theory        53132
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-665 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-53132.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (F or E)))), M:tm-665, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-53133
in-theory        53133
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-665 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53133.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-665, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-53134
in-theory        53134
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     39
proof            (modus-ponens tm-665 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-53134.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-665, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-53135
in-theory        53135
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-665 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-53135.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-665, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-53136
in-theory        53136
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-665 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-53136.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-665, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-53137
in-theory        53137
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-665 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-53137.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-665, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-53138
in-theory        53138
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-665 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-53138.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-665, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-53139
in-theory        53139
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-665 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-53139.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-665, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-53140
in-theory        53140
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     41
proof            (modus-ponens tm-665 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-53140.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-665, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-53141
in-theory        53141
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-53141.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-665, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-53142
in-theory        53142
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     29
proof            (modus-ponens tm-665 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-53142.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-665, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-53143
in-theory        53143
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-665 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-53143.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-665, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-53144
in-theory        53144
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-665 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-53144.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-665, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-53145
in-theory        53145
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-53145.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-665, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-53146
in-theory        53146
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-665 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-53146.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (E -> D))) -> (not D))), M:tm-665, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-53147
in-theory        53147
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-53147.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-665, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-53148
in-theory        53148
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     25
proof            (modus-ponens tm-665 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-53148.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-665, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-53149
in-theory        53149
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     25
proof            (modus-ponens tm-665 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-53149.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-665, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-53150
in-theory        53150
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-53150.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-665, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-53151
in-theory        53151
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-665 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-53151.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (D or E))) -> (not D))), M:tm-665, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-53152
in-theory        53152
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-665 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-53152.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (E or D))) -> (not D))), M:tm-665, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-53153
in-theory        53153
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     33
proof            (modus-ponens tm-665 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-53153.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-665, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-53154
in-theory        53154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-665 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-53154.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-665, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-53155
in-theory        53155
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     37
proof            (modus-ponens tm-665 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-53155.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-665, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-53156
in-theory        53156
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-9)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-53156.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-665, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-53157
in-theory        53157
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     27
proof            (modus-ponens tm-665 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-9)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-53157.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-665, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-53158
in-theory        53158
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     29
proof            (modus-ponens tm-665 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-53158.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-665, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-53159
in-theory        53159
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     29
proof            (modus-ponens tm-665 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-9)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-53159.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-665, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-53160
in-theory        53160
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-53160.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-665, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-53161
in-theory        53161
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     25
proof            (modus-ponens tm-665 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-53161.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-665, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-53162
in-theory        53162
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-665 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-10)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-53162.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-665, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-53163
in-theory        53163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-665 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-53163.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((not (not E)) -> E))), M:tm-665, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-53164
in-theory        53164
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((not (not D)) -> D) or E))
theorem-size     21
proof            (modus-ponens tm-665 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-53164.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((not (not D)) -> D) or E)), M:tm-665, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-53165
in-theory        53165
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-665 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-53165.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((not (not E)) -> E) and D))), M:tm-665, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-53166
in-theory        53166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     29
proof            (modus-ponens tm-665 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-10)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-53166.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-665, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-53167
in-theory        53167
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((not (not E)) -> E)))
theorem-size     21
proof            (modus-ponens tm-665 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-53167.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((not (not E)) -> E))), M:tm-665, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-53168
in-theory        53168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-53168.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-665, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-53169
in-theory        53169
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-665 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-53169.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-665, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-53170
in-theory        53170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-53170.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (F -> (G -> F))))), M:tm-665, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-53171
in-theory        53171
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (F -> E))) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-53171.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (F -> E))) or G)), M:tm-665, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-53172
in-theory        53172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-53172.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-665, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-53173
in-theory        53173
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-665 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-53173.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (D -> (F -> E)))), M:tm-665, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-53174
in-theory        53174
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-53174.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (F -> (G -> F))))), M:tm-665, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-53175
in-theory        53175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> D))
theorem-size     17
proof            (modus-ponens tm-665 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-53175.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> D)), M:tm-665, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-53176
in-theory        53176
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-53176.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-665, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-53177
in-theory        53177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and E) -> (D and E)))
theorem-size     21
proof            (modus-ponens tm-665 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-53177.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and E) -> (D and E))), M:tm-665, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-53178
in-theory        53178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (D -> E)))
theorem-size     21
proof            (modus-ponens tm-665 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-53178.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (D -> E))), M:tm-665, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-53179
in-theory        53179
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((not (not D)) -> (not (not D))))
theorem-size     21
proof            (modus-ponens tm-665 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-10)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-53179.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((not (not D)) -> (not (not D)))), M:tm-665, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-53180
in-theory        53180
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-665 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-53180.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-665, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-53181
in-theory        53181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-665 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-53181.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-665, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-53182
in-theory        53182
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-665 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-53182.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> F) -> (E -> E)))), M:tm-665, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-53183
in-theory        53183
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (D -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-665 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-53183.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (D -> D)) or F)), M:tm-665, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-53184
in-theory        53184
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-53184.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-665, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-53185
in-theory        53185
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-53185.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-665, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-53186
in-theory        53186
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     23
proof            (modus-ponens tm-665 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-53186.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> F) -> (E -> E)))), M:tm-665, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-53187
in-theory        53187
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-53187.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-665, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-53188
in-theory        53188
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     23
proof            (modus-ponens tm-665 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-53188.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D -> E)) -> (D -> E))), M:tm-665, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-53189
in-theory        53189
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     33
proof            (modus-ponens tm-665 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-53189.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-665, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-53190
in-theory        53190
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     45
proof            (modus-ponens tm-665 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-53190.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-665, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-53191
in-theory        53191
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     47
proof            (modus-ponens tm-665 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-53191.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-665, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-53192
in-theory        53192
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-53192.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-665, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-53193
in-theory        53193
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     35
proof            (modus-ponens tm-665 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-53193.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-665, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-53194
in-theory        53194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     37
proof            (modus-ponens tm-665 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-53194.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-665, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-53195
in-theory        53195
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-665 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-53195.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-665, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-53196
in-theory        53196
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-53196.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-665, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-53197
in-theory        53197
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-665 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-53197.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-665, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-53198
in-theory        53198
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-665 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-53198.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-665, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-53199
in-theory        53199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     47
proof            (modus-ponens tm-665 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-53199.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-665, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-53200
in-theory        53200
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-665 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53200.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-665, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-53201
in-theory        53201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-665 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53201.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-665, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-53202
in-theory        53202
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-665 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53202.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-665, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-53203
in-theory        53203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-665 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-53203.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-665, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-53204
in-theory        53204
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-665 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53204.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-665, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-53205
in-theory        53205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) and D) -> E))
theorem-size     21
proof            (modus-ponens tm-665 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-53205.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) and D) -> E)), M:tm-665, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-53206
in-theory        53206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-665 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-53206.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-665, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-53207
in-theory        53207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     33
proof            (modus-ponens tm-665 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-53207.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-665, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-53208
in-theory        53208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-665 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-53208.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-665, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-53209
in-theory        53209
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     29
proof            (modus-ponens tm-665 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-53209.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-665, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-53210
in-theory        53210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     39
proof            (modus-ponens tm-665 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-2 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-53210.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-665, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-53211
in-theory        53211
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     41
proof            (modus-ponens tm-665 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-53211.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-665, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-53212
in-theory        53212
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-665 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-53212.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-665, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-53213
in-theory        53213
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     31
proof            (modus-ponens tm-665 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-53213.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-665, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-53214
in-theory        53214
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     33
proof            (modus-ponens tm-665 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-53214.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-665, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-53215
in-theory        53215
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     37
proof            (modus-ponens tm-665 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-53215.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-665, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-53216
in-theory        53216
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     31
proof            (modus-ponens tm-665 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-53216.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-665, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-53217
in-theory        53217
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-665 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-53217.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-665, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-53218
in-theory        53218
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     27
proof            (modus-ponens tm-665 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-53218.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-665, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-53219
in-theory        53219
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-53219.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-665, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-53220
in-theory        53220
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     31
proof            (modus-ponens tm-665 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-53220.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-665, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-53221
in-theory        53221
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-665 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-53221.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> ((F and G) -> F)))), M:tm-665, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-53222
in-theory        53222
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E and F) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-53222.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E and F) -> E)) or G)), M:tm-665, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-53223
in-theory        53223
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-53223.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-665, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-53224
in-theory        53224
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     23
proof            (modus-ponens tm-665 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-53224.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E and F)) -> (D -> E))), M:tm-665, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-53225
in-theory        53225
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-665 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-53225.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> ((F and G) -> F)))), M:tm-665, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-53226
in-theory        53226
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and (D -> E)) -> E))
theorem-size     21
proof            (modus-ponens tm-665 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-53226.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and (D -> E)) -> E)), M:tm-665, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-53227
in-theory        53227
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-665 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-53227.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-665, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-53228
in-theory        53228
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     33
proof            (modus-ponens tm-665 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-53228.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-665, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-53229
in-theory        53229
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-665 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-53229.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-665, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-53230
in-theory        53230
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-665 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-53230.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-665, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-53231
in-theory        53231
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     29
proof            (modus-ponens tm-665 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-53231.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-665, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-53232
in-theory        53232
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     39
proof            (modus-ponens tm-665 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-2 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-53232.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-665, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-53233
in-theory        53233
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     41
proof            (modus-ponens tm-665 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-53233.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-665, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-53234
in-theory        53234
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-665 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-53234.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-665, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-53235
in-theory        53235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     31
proof            (modus-ponens tm-665 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-53235.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-665, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-53236
in-theory        53236
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     33
proof            (modus-ponens tm-665 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-53236.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-665, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-53237
in-theory        53237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     37
proof            (modus-ponens tm-665 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-53237.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-665, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-53238
in-theory        53238
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     31
proof            (modus-ponens tm-665 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-53238.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-665, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-53239
in-theory        53239
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-665 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-53239.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-665, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-53240
in-theory        53240
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-665 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-53240.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-665, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-53241
in-theory        53241
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     27
proof            (modus-ponens tm-665 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-53241.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-665, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-53242
in-theory        53242
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-53242.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-665, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-53243
in-theory        53243
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-665 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-53243.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-665, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-53244
in-theory        53244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-665 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-53244.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> ((F and G) -> G)))), M:tm-665, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-53245
in-theory        53245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E and F) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-53245.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E and F) -> F)) or G)), M:tm-665, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-53246
in-theory        53246
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-53246.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-665, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-53247
in-theory        53247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-665 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-53247.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E and F)) -> (D -> F))), M:tm-665, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-53248
in-theory        53248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-665 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-53248.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> ((F and G) -> G)))), M:tm-665, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-53249
in-theory        53249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-53249.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-665, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-53250
in-theory        53250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-53250.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-665, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-53251
in-theory        53251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-53251.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-665, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-53252
in-theory        53252
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-665 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-53252.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-665, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-53253
in-theory        53253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-53253.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-665, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-53254
in-theory        53254
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-665 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-53254.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-665, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-53255
in-theory        53255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-53255.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-665, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-53256
in-theory        53256
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-53256.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-665, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-53257
in-theory        53257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-665 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-53257.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-665, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-53258
in-theory        53258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-53258.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-665, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-53259
in-theory        53259
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-53259.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-665, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-53260
in-theory        53260
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-53260.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-665, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-53261
in-theory        53261
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-665 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-53261.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-665, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-53262
in-theory        53262
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53262.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-665, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-53263
in-theory        53263
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-665 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-53263.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-665, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-53264
in-theory        53264
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-665 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-53264.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-665, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-53265
in-theory        53265
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-665 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-53265.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-665, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-53266
in-theory        53266
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-665 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-53266.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-665, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-53267
in-theory        53267
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-53267.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-665, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-53268
in-theory        53268
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-53268.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-665, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-53269
in-theory        53269
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-665 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-53269.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-665, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-53270
in-theory        53270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-665 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-53270.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-665, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-53271
in-theory        53271
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-665 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-53271.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-665, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-53272
in-theory        53272
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-53272.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-665, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-53273
in-theory        53273
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     25
proof            (modus-ponens tm-665 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-53273.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-665, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-53274
in-theory        53274
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-665 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-53274.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-665, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-53275
in-theory        53275
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-53275.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-665, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-53276
in-theory        53276
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-665 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-53276.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-665, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-53277
in-theory        53277
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-665 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-53277.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-665, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-53278
in-theory        53278
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-53278.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-665, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-53279
in-theory        53279
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-53279.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-665, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-53280
in-theory        53280
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-665 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-53280.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-665, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-53281
in-theory        53281
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-53281.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-665, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-53282
in-theory        53282
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     39
proof            (modus-ponens tm-665 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-53282.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-665, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-53283
in-theory        53283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-665 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-10)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-53283.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-665, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-53284
in-theory        53284
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-53284.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-665, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-53285
in-theory        53285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     35
proof            (modus-ponens tm-665 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-53285.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-665, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-53286
in-theory        53286
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-665 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-53286.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-665, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-53287
in-theory        53287
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-665 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53287.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-665, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-53288
in-theory        53288
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     43
proof            (modus-ponens tm-665 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-53288.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-665, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-53289
in-theory        53289
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-665 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-53289.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-665, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-53290
in-theory        53290
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     43
proof            (modus-ponens tm-665 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-53290.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-665, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-53291
in-theory        53291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-665 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-53291.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-665, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-53292
in-theory        53292
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     37
proof            (modus-ponens tm-665 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-53292.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-665, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-53293
in-theory        53293
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     45
proof            (modus-ponens tm-665 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-53293.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-665, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-53294
in-theory        53294
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-665 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-53294.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-665, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-53295
in-theory        53295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     35
proof            (modus-ponens tm-665 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-53295.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-665, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-53296
in-theory        53296
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     51
proof            (modus-ponens tm-665 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-53296.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-665, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-53297
in-theory        53297
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-665 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-53297.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-665, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-53298
in-theory        53298
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     33
proof            (modus-ponens tm-665 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-53298.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-665, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-53299
in-theory        53299
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     35
proof            (modus-ponens tm-665 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-53299.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-665, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-53300
in-theory        53300
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     33
proof            (modus-ponens tm-665 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-53300.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-665, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-53301
in-theory        53301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-53301.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-665, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-53302
in-theory        53302
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-53302.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-665, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-53303
in-theory        53303
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-53303.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-665, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-53304
in-theory        53304
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-665 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-53304.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-665, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-53305
in-theory        53305
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-53305.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-665, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-53306
in-theory        53306
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-665 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-53306.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-665, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-53307
in-theory        53307
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-53307.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-665, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-53308
in-theory        53308
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-53308.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-665, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-53309
in-theory        53309
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-665 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-53309.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-665, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-53310
in-theory        53310
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-53310.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-665, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-53311
in-theory        53311
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-53311.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-665, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-53312
in-theory        53312
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-53312.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-665, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-53313
in-theory        53313
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-665 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-53313.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-665, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-53314
in-theory        53314
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53314.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-665, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-53315
in-theory        53315
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-665 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-53315.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-665, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-53316
in-theory        53316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-665 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-53316.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-665, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-53317
in-theory        53317
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-665 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-53317.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-665, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-53318
in-theory        53318
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-665 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-53318.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-665, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-53319
in-theory        53319
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-53319.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-665, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-53320
in-theory        53320
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-665 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-53320.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-665, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-53321
in-theory        53321
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-53321.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-665, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-53322
in-theory        53322
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     37
proof            (modus-ponens tm-665 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-53322.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-665, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-53323
in-theory        53323
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-53323.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-665, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-53324
in-theory        53324
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-53324.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-665, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-53325
in-theory        53325
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-665 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-53325.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-665, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-53326
in-theory        53326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-665 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-53326.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-665, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-53327
in-theory        53327
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-665 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-53327.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-665, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-53328
in-theory        53328
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-53328.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-665, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-53329
in-theory        53329
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     25
proof            (modus-ponens tm-665 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-53329.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-665, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-53330
in-theory        53330
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-53330.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-665, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-53331
in-theory        53331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-53331.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-665, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-53332
in-theory        53332
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-53332.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-665, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-53333
in-theory        53333
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-665 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-53333.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-665, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-53334
in-theory        53334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-53334.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-665, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-53335
in-theory        53335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-665 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-53335.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-665, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-53336
in-theory        53336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-53336.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-665, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-53337
in-theory        53337
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-53337.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-665, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-53338
in-theory        53338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-665 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-53338.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-665, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-53339
in-theory        53339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-53339.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-665, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-53340
in-theory        53340
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-53340.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-665, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-53341
in-theory        53341
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-53341.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-665, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-53342
in-theory        53342
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-665 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-53342.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-665, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-53343
in-theory        53343
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53343.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-665, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-53344
in-theory        53344
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-665 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-53344.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-665, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-53345
in-theory        53345
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-665 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-53345.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-665, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-53346
in-theory        53346
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-665 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-53346.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-665, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-53347
in-theory        53347
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-665 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-53347.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-665, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-53348
in-theory        53348
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-53348.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-665, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-53349
in-theory        53349
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-665 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-53349.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-665, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-53350
in-theory        53350
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-53350.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-665, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-53351
in-theory        53351
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-53351.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-665, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-53352
in-theory        53352
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-53352.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-665, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-53353
in-theory        53353
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     37
proof            (modus-ponens tm-665 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-53353.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-665, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-53354
in-theory        53354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-53354.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-665, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-53355
in-theory        53355
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-53355.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-665, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-53356
in-theory        53356
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-665 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-53356.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-665, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-53357
in-theory        53357
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-665 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-53357.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-665, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-53358
in-theory        53358
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-665 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-53358.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-665, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-53359
in-theory        53359
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-53359.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-665, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-53360
in-theory        53360
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     25
proof            (modus-ponens tm-665 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-53360.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-665, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-53361
in-theory        53361
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-53361.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-665, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-53362
in-theory        53362
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-53362.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-665, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-53363
in-theory        53363
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-665 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-53363.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-665, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-53364
in-theory        53364
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-665 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-53364.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-665, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-53365
in-theory        53365
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-53365.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-665, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-53366
in-theory        53366
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-665 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-53366.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-665, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-53367
in-theory        53367
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-53367.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-665, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-53368
in-theory        53368
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-53368.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-665, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-53369
in-theory        53369
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-53369.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-665, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-53370
in-theory        53370
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-665 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-10)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-53370.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-665, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-53371
in-theory        53371
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-53371.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-665, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-53372
in-theory        53372
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-53372.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-665, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-53373
in-theory        53373
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-53373.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-665, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-53374
in-theory        53374
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-665 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53374.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-665, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-53375
in-theory        53375
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     37
proof            (modus-ponens tm-665 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-53375.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-665, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-53376
in-theory        53376
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-665 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-53376.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-665, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-53377
in-theory        53377
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     37
proof            (modus-ponens tm-665 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-53377.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-665, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-53378
in-theory        53378
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-665 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-53378.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-665, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-53379
in-theory        53379
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     31
proof            (modus-ponens tm-665 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-53379.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-665, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-53380
in-theory        53380
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     39
proof            (modus-ponens tm-665 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-53380.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-665, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-53381
in-theory        53381
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     31
proof            (modus-ponens tm-665 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-53381.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-665, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-53382
in-theory        53382
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     31
proof            (modus-ponens tm-665 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-53382.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-665, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-53383
in-theory        53383
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     33
proof            (modus-ponens tm-665 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-53383.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-665, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-53384
in-theory        53384
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-665 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-53384.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-665, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-53385
in-theory        53385
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-665 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-53385.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-665, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-53386
in-theory        53386
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     39
proof            (modus-ponens tm-665 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-53386.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-665, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-53387
in-theory        53387
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-665 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-53387.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-665, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-53388
in-theory        53388
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     29
proof            (modus-ponens tm-665 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-53388.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-665, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-53389
in-theory        53389
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-665 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-53389.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-665, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-53390
in-theory        53390
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-665 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-53390.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-665, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-53391
in-theory        53391
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     27
proof            (modus-ponens tm-665 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-53391.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-665, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-53392
in-theory        53392
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-665 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-53392.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-665, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-53393
in-theory        53393
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     27
proof            (modus-ponens tm-665 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-53393.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-665, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-53394
in-theory        53394
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (E -> D))))
theorem-size     21
proof            (modus-ponens tm-665 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-53394.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (E -> D)))), M:tm-665, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-53395
in-theory        53395
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-53395.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-665, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-53396
in-theory        53396
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and E) -> ((D and E) and D)))
theorem-size     23
proof            (modus-ponens tm-665 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-53396.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and E) -> ((D and E) and D))), M:tm-665, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-53397
in-theory        53397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and E) -> ((D and E) and E)))
theorem-size     23
proof            (modus-ponens tm-665 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-53397.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and E) -> ((D and E) and E))), M:tm-665, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-53398
in-theory        53398
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-53398.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (E -> (D and E))))), M:tm-665, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-53399
in-theory        53399
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (D or E))))
theorem-size     21
proof            (modus-ponens tm-665 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-53399.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (D or E)))), M:tm-665, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-53400
in-theory        53400
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (E or D))))
theorem-size     21
proof            (modus-ponens tm-665 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-53400.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (E or D)))), M:tm-665, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-53401
in-theory        53401
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     31
proof            (modus-ponens tm-665 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-53401.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-665, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-53402
in-theory        53402
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-9)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-53402.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-665, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-53403
in-theory        53403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     23
proof            (modus-ponens tm-665 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-10)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-53403.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-665, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-53404
in-theory        53404
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (E -> (F -> E)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-53404.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (E -> (F -> E))))), M:tm-665, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-53405
in-theory        53405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     25
proof            (modus-ponens tm-665 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-53405.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-665, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-53406
in-theory        53406
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-665 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-53406.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-665, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-53407
in-theory        53407
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     31
proof            (modus-ponens tm-665 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-53407.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-665, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-53408
in-theory        53408
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     37
proof            (modus-ponens tm-665 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-53408.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-665, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-53409
in-theory        53409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and ((E and F) -> E))))
theorem-size     23
proof            (modus-ponens tm-665 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-53409.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and ((E and F) -> E)))), M:tm-665, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-53410
in-theory        53410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     37
proof            (modus-ponens tm-665 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-53410.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-665, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-53411
in-theory        53411
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and ((E and F) -> F))))
theorem-size     23
proof            (modus-ponens tm-665 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-53411.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and ((E and F) -> F)))), M:tm-665, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-53412
in-theory        53412
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     25
proof            (modus-ponens tm-665 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-53412.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-665, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-53413
in-theory        53413
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     33
proof            (modus-ponens tm-665 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-53413.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-665, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-53414
in-theory        53414
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     25
proof            (modus-ponens tm-665 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-53414.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-665, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-53415
in-theory        53415
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     25
proof            (modus-ponens tm-665 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-53415.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-665, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-53416
in-theory        53416
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     27
proof            (modus-ponens tm-665 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-53416.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-665, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-53417
in-theory        53417
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-53417.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-665, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-53418
in-theory        53418
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-665 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-53418.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-665, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-53419
in-theory        53419
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-53419.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-665, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-53420
in-theory        53420
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-53420.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-665, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-53421
in-theory        53421
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-665 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-53421.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-665, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-53422
in-theory        53422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-53422.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-665, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-53423
in-theory        53423
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-665 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-53423.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-665, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-53424
in-theory        53424
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     33
proof            (modus-ponens tm-665 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-53424.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-665, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-53425
in-theory        53425
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-665 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-53425.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-665, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-53426
in-theory        53426
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     25
proof            (modus-ponens tm-665 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-53426.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-665, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-53427
in-theory        53427
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-53427.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-665, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-53428
in-theory        53428
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-665 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-53428.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-665, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-53429
in-theory        53429
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-665 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-53429.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-665, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-53430
in-theory        53430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     25
proof            (modus-ponens tm-665 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-53430.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-665, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-53431
in-theory        53431
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-665 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53431.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-665, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-53432
in-theory        53432
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-665 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53432.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-665, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-53433
in-theory        53433
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-665 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53433.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-665, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-53434
in-theory        53434
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-665 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53434.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-665, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-53435
in-theory        53435
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-665 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53435.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-665, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-53436
in-theory        53436
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     27
proof            (modus-ponens tm-665 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-53436.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-665, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-53437
in-theory        53437
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     27
proof            (modus-ponens tm-665 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-53437.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-665, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-53438
in-theory        53438
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     27
proof            (modus-ponens tm-665 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-53438.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-665, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-53439
in-theory        53439
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-53439.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-665, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-53440
in-theory        53440
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     35
proof            (modus-ponens tm-665 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-53440.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-665, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-53441
in-theory        53441
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-665 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53441.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-665, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-53442
in-theory        53442
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     25
proof            (modus-ponens tm-665 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53442.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-665, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-53443
in-theory        53443
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53443.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-665, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-53444
in-theory        53444
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-665 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-53444.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-665, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-53445
in-theory        53445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-665 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53445.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-665, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-53446
in-theory        53446
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     29
proof            (modus-ponens tm-665 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-53446.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-665, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-53447
in-theory        53447
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-53447.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-665, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-53448
in-theory        53448
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-53448.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-665, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-53449
in-theory        53449
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-53449.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-665, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-53450
in-theory        53450
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-53450.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-665, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-53451
in-theory        53451
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-665 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-53451.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> (F -> E)) or G))), M:tm-665, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-53452
in-theory        53452
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> D)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-53452.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> D)) or F) or G)), M:tm-665, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-53453
in-theory        53453
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-53453.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-665, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-53454
in-theory        53454
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     23
proof            (modus-ponens tm-665 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-53454.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> E)) or G))), M:tm-665, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-53455
in-theory        53455
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     37
proof            (modus-ponens tm-665 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-53455.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-665, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-53456
in-theory        53456
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-6 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-53456.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-665, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-53457
in-theory        53457
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-6 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-53457.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-665, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-53458
in-theory        53458
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     43
proof            (modus-ponens tm-665 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-53458.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-665, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-53459
in-theory        53459
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-53459.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-665, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-53460
in-theory        53460
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-665 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-53460.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-665, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-53461
in-theory        53461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     31
proof            (modus-ponens tm-665 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-53461.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-665, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-53462
in-theory        53462
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     33
proof            (modus-ponens tm-665 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-53462.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-665, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-53463
in-theory        53463
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     31
proof            (modus-ponens tm-665 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-53463.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-665, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-53464
in-theory        53464
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     29
proof            (modus-ponens tm-665 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-53464.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-665, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-53465
in-theory        53465
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-53465.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-665, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-53466
in-theory        53466
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-53466.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-665, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-53467
in-theory        53467
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-53467.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-665, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-53468
in-theory        53468
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-53468.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-665, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-53469
in-theory        53469
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-665 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-53469.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E and F) -> E) or G))), M:tm-665, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-53470
in-theory        53470
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and E) -> D) or F) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-53470.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and E) -> D) or F) or G)), M:tm-665, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-53471
in-theory        53471
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-53471.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-665, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-53472
in-theory        53472
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E and F) -> E) or G)))
theorem-size     23
proof            (modus-ponens tm-665 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-53472.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E and F) -> E) or G))), M:tm-665, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-53473
in-theory        53473
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     29
proof            (modus-ponens tm-665 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-53473.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-665, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-53474
in-theory        53474
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-53474.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-665, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-53475
in-theory        53475
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-53475.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-665, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-53476
in-theory        53476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-53476.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-665, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-53477
in-theory        53477
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-53477.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-665, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-53478
in-theory        53478
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-665 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-53478.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E and F) -> F) or G))), M:tm-665, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-53479
in-theory        53479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and E) -> E) or F) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-53479.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and E) -> E) or F) or G)), M:tm-665, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-53480
in-theory        53480
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-53480.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-665, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-53481
in-theory        53481
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E and F) -> F) or G)))
theorem-size     23
proof            (modus-ponens tm-665 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-53481.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E and F) -> F) or G))), M:tm-665, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-53482
in-theory        53482
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     31
proof            (modus-ponens tm-665 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-53482.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-665, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-53483
in-theory        53483
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-665 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-53483.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-665, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-53484
in-theory        53484
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-665 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-53484.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-665, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-53485
in-theory        53485
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     37
proof            (modus-ponens tm-665 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-53485.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-665, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-53486
in-theory        53486
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-665 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-53486.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-665, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-53487
in-theory        53487
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-665 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-53487.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-665, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-53488
in-theory        53488
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     25
proof            (modus-ponens tm-665 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-53488.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-665, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-53489
in-theory        53489
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-53489.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-665, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-53490
in-theory        53490
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     25
proof            (modus-ponens tm-665 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-53490.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-665, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-53491
in-theory        53491
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     29
proof            (modus-ponens tm-665 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-53491.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-665, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-53492
in-theory        53492
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-53492.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-665, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-53493
in-theory        53493
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-53493.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-665, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-53494
in-theory        53494
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-53494.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-665, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-53495
in-theory        53495
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-53495.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-665, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-53496
in-theory        53496
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-665 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-53496.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> (E or F)) or G))), M:tm-665, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-53497
in-theory        53497
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (D or E)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-53497.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (D or E)) or F) or G)), M:tm-665, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-53498
in-theory        53498
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-53498.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-665, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-53499
in-theory        53499
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (E or F)) or G)))
theorem-size     23
proof            (modus-ponens tm-665 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-53499.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (E or F)) or G))), M:tm-665, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-53500
in-theory        53500
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-53500.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-665, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-53501
in-theory        53501
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-53501.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-665, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-53502
in-theory        53502
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-53502.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-665, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-53503
in-theory        53503
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-665 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-53503.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-665, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-53504
in-theory        53504
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-53504.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-665, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-53505
in-theory        53505
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-665 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-53505.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-665, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-53506
in-theory        53506
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-53506.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-665, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-53507
in-theory        53507
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-53507.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-665, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-53508
in-theory        53508
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-665 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-53508.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-665, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-53509
in-theory        53509
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-53509.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-665, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-53510
in-theory        53510
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-53510.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-665, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-53511
in-theory        53511
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-53511.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-665, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-53512
in-theory        53512
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-665 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-53512.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-665, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-53513
in-theory        53513
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53513.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-665, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-53514
in-theory        53514
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-665 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-53514.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-665, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-53515
in-theory        53515
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-665 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-53515.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-665, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-53516
in-theory        53516
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-665 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-53516.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-665, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-53517
in-theory        53517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-665 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-53517.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-665, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-53518
in-theory        53518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-53518.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-665, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-53519
in-theory        53519
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-665 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-53519.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-665, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-53520
in-theory        53520
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-53520.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-665, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-53521
in-theory        53521
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-53521.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-665, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-53522
in-theory        53522
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-665 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-53522.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-665, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-53523
in-theory        53523
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-53523.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-665, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-53524
in-theory        53524
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-665 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53524.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-665, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-53525
in-theory        53525
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-53525.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-665, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-53526
in-theory        53526
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-53526.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-665, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-53527
in-theory        53527
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-53527.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-665, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-53528
in-theory        53528
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-53528.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-665, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-53529
in-theory        53529
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-665 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-53529.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-665, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-53530
in-theory        53530
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-53530.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-665, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-53531
in-theory        53531
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-53531.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-665, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-53532
in-theory        53532
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     25
proof            (modus-ponens tm-665 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-53532.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-665, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-53533
in-theory        53533
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     31
proof            (modus-ponens tm-665 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-53533.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-665, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-53534
in-theory        53534
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-53534.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-665, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-53535
in-theory        53535
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-53535.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-665, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-53536
in-theory        53536
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     37
proof            (modus-ponens tm-665 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-53536.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-665, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-53537
in-theory        53537
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-53537.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-665, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-53538
in-theory        53538
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-53538.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-665, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-53539
in-theory        53539
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-665 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-53539.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-665, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-53540
in-theory        53540
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-665 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-53540.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-665, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-53541
in-theory        53541
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-665 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-53541.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-665, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-53542
in-theory        53542
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-53542.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-665, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-53543
in-theory        53543
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     25
proof            (modus-ponens tm-665 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-53543.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-665, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-53544
in-theory        53544
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-53544.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-665, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-53545
in-theory        53545
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (E -> (E or F)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-53545.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (E -> (E or F))))), M:tm-665, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-53546
in-theory        53546
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-53546.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-665, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-53547
in-theory        53547
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-53547.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-665, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-53548
in-theory        53548
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-53548.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-665, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-53549
in-theory        53549
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-53549.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-665, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-53550
in-theory        53550
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-53550.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-665, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-53551
in-theory        53551
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-665 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-53551.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-665, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-53552
in-theory        53552
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-665 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-53552.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-665, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-53553
in-theory        53553
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-53553.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-665, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-53554
in-theory        53554
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-53554.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-665, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-53555
in-theory        53555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-665 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-53555.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-665, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-53556
in-theory        53556
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-53556.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (F -> (F or G))))), M:tm-665, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-53557
in-theory        53557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (E or F))) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-53557.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (E or F))) or G)), M:tm-665, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-53558
in-theory        53558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-53558.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-665, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-53559
in-theory        53559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (D -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-665 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-53559.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (D -> (E or F)))), M:tm-665, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-53560
in-theory        53560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-53560.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (F -> (F or G))))), M:tm-665, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-53561
in-theory        53561
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-53561.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-665, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-53562
in-theory        53562
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-53562.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-665, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-53563
in-theory        53563
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-53563.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-665, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-53564
in-theory        53564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-53564.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-665, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-53565
in-theory        53565
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-53565.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-665, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-53566
in-theory        53566
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-53566.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-665, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-53567
in-theory        53567
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-53567.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or (F -> (G -> F))))), M:tm-665, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-53568
in-theory        53568
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (F -> E))) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-53568.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (F -> E))) or G)), M:tm-665, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-53569
in-theory        53569
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-53569.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-665, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-53570
in-theory        53570
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or (F -> (G -> F)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-53570.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or (F -> (G -> F))))), M:tm-665, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-53571
in-theory        53571
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53571.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-665, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-53572
in-theory        53572
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     37
proof            (modus-ponens tm-665 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53572.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-665, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-53573
in-theory        53573
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-7 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53573.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-665, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-53574
in-theory        53574
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-7 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53574.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-665, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-53575
in-theory        53575
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     43
proof            (modus-ponens tm-665 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53575.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-665, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-53576
in-theory        53576
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53576.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-665, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-53577
in-theory        53577
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-665 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53577.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-665, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-53578
in-theory        53578
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     31
proof            (modus-ponens tm-665 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53578.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-665, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-53579
in-theory        53579
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     33
proof            (modus-ponens tm-665 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53579.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-665, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-53580
in-theory        53580
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     31
proof            (modus-ponens tm-665 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53580.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-665, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-53581
in-theory        53581
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-665 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-53581.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-665, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-53582
in-theory        53582
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     29
proof            (modus-ponens tm-665 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-53582.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-665, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-53583
in-theory        53583
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-665 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-53583.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-665, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-53584
in-theory        53584
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-665 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-53584.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-665, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-53585
in-theory        53585
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     35
proof            (modus-ponens tm-665 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-53585.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-665, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-53586
in-theory        53586
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-665 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-53586.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-665, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-53587
in-theory        53587
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-665 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-53587.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or ((F and G) -> F)))), M:tm-665, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-53588
in-theory        53588
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E and F) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-53588.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E and F) -> E)) or G)), M:tm-665, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-53589
in-theory        53589
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-53589.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-665, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-53590
in-theory        53590
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or ((F and G) -> F))))
theorem-size     23
proof            (modus-ponens tm-665 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-53590.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or ((F and G) -> F)))), M:tm-665, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-53591
in-theory        53591
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-665 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-53591.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-665, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-53592
in-theory        53592
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     29
proof            (modus-ponens tm-665 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-53592.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-665, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-53593
in-theory        53593
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-665 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-53593.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-665, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-53594
in-theory        53594
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-665 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-53594.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-665, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-53595
in-theory        53595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     35
proof            (modus-ponens tm-665 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-53595.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-665, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-53596
in-theory        53596
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-665 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-53596.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-665, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-53597
in-theory        53597
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-665 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-53597.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or ((F and G) -> G)))), M:tm-665, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-53598
in-theory        53598
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E and F) -> F)) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-53598.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E and F) -> F)) or G)), M:tm-665, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-53599
in-theory        53599
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-53599.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-665, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-53600
in-theory        53600
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or ((F and G) -> G))))
theorem-size     23
proof            (modus-ponens tm-665 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-53600.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or ((F and G) -> G)))), M:tm-665, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-53601
in-theory        53601
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-665 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53601.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-665, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-53602
in-theory        53602
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     31
proof            (modus-ponens tm-665 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53602.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-665, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-53603
in-theory        53603
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-665 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53603.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-665, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-53604
in-theory        53604
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-665 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53604.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-665, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-53605
in-theory        53605
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     37
proof            (modus-ponens tm-665 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53605.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-665, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-53606
in-theory        53606
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-665 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53606.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-665, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-53607
in-theory        53607
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-665 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53607.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-665, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-53608
in-theory        53608
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     25
proof            (modus-ponens tm-665 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53608.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-665, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-53609
in-theory        53609
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53609.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-665, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-53610
in-theory        53610
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     25
proof            (modus-ponens tm-665 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53610.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-665, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-53611
in-theory        53611
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-53611.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-665, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-53612
in-theory        53612
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-53612.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-665, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-53613
in-theory        53613
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-53613.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-665, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-53614
in-theory        53614
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-53614.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-665, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-53615
in-theory        53615
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-53615.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-665, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-53616
in-theory        53616
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-53616.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-665, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-53617
in-theory        53617
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-53617.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or (F -> (F or G))))), M:tm-665, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-53618
in-theory        53618
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (E or F))) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-53618.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (E or F))) or G)), M:tm-665, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-53619
in-theory        53619
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-53619.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-665, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-53620
in-theory        53620
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or (F -> (F or G)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-53620.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or (F -> (F or G))))), M:tm-665, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-53621
in-theory        53621
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-53621.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-665, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-53622
in-theory        53622
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-53622.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-665, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-53623
in-theory        53623
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-53623.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-665, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-53624
in-theory        53624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-53624.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-665, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-53625
in-theory        53625
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-53625.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-665, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-53626
in-theory        53626
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-53626.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-665, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-53627
in-theory        53627
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-53627.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E or (F -> (G or F))))), M:tm-665, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-53628
in-theory        53628
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (F or E))) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-53628.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> (F or E))) or G)), M:tm-665, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-53629
in-theory        53629
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-53629.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-665, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-53630
in-theory        53630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-53630.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E or (F -> (G or F))))), M:tm-665, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-53631
in-theory        53631
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-53631.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-665, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-53632
in-theory        53632
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     29
proof            (modus-ponens tm-665 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-53632.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-665, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-53633
in-theory        53633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-53633.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-665, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-53634
in-theory        53634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-53634.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-665, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-53635
in-theory        53635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-53635.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-665, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-53636
in-theory        53636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-53636.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-665, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-53637
in-theory        53637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-665 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-53637.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> (F or E)) or G))), M:tm-665, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-53638
in-theory        53638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E or D)) or F) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-53638.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E or D)) or F) or G)), M:tm-665, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-53639
in-theory        53639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-53639.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-665, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-53640
in-theory        53640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F or E)) or G)))
theorem-size     23
proof            (modus-ponens tm-665 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-53640.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F or E)) or G))), M:tm-665, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-53641
in-theory        53641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-53641.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-665, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-53642
in-theory        53642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-53642.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-665, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-53643
in-theory        53643
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-53643.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-665, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-53644
in-theory        53644
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-665 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-53644.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-665, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-53645
in-theory        53645
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-53645.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-665, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-53646
in-theory        53646
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-665 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-53646.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-665, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-53647
in-theory        53647
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-53647.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-665, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-53648
in-theory        53648
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-53648.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-665, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-53649
in-theory        53649
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-665 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-53649.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-665, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-53650
in-theory        53650
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-53650.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-665, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-53651
in-theory        53651
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-53651.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-665, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-53652
in-theory        53652
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-53652.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-665, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-53653
in-theory        53653
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-665 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-53653.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-665, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-53654
in-theory        53654
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53654.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-665, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-53655
in-theory        53655
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-665 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-53655.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-665, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-53656
in-theory        53656
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-665 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-53656.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-665, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-53657
in-theory        53657
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-665 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-53657.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-665, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-53658
in-theory        53658
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-665 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-53658.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-665, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-53659
in-theory        53659
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-53659.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-665, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-53660
in-theory        53660
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-665 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-53660.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-665, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-53661
in-theory        53661
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-53661.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-665, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-53662
in-theory        53662
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-53662.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-665, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-53663
in-theory        53663
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-665 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-53663.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-665, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-53664
in-theory        53664
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-53664.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-665, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-53665
in-theory        53665
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-665 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53665.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-665, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-53666
in-theory        53666
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-53666.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-665, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-53667
in-theory        53667
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-665 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-53667.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-665, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-53668
in-theory        53668
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-53668.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-665, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-53669
in-theory        53669
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-53669.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-665, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-53670
in-theory        53670
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-665 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-53670.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-665, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-53671
in-theory        53671
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-53671.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-665, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-53672
in-theory        53672
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-53672.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-665, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-53673
in-theory        53673
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-53673.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-665, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-53674
in-theory        53674
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-53674.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-665, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-53675
in-theory        53675
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-665 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-53675.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-665, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-53676
in-theory        53676
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-665 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-53676.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-665, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-53677
in-theory        53677
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-665 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-53677.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-665, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-53678
in-theory        53678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-665 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-53678.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-665, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-53679
in-theory        53679
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-53679.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-665, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-53680
in-theory        53680
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-53680.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-665, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-53681
in-theory        53681
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-665 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-53681.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-665, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-53682
in-theory        53682
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-53682.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-665, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-53683
in-theory        53683
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-53683.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-665, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-53684
in-theory        53684
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     25
proof            (modus-ponens tm-665 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-53684.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-665, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-53685
in-theory        53685
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     31
proof            (modus-ponens tm-665 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-53685.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-665, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-53686
in-theory        53686
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-53686.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-665, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-53687
in-theory        53687
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-53687.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-665, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-53688
in-theory        53688
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     37
proof            (modus-ponens tm-665 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-53688.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-665, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-53689
in-theory        53689
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-53689.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-665, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-53690
in-theory        53690
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-53690.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-665, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-53691
in-theory        53691
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-665 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-53691.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-665, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-53692
in-theory        53692
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-665 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-53692.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-665, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-53693
in-theory        53693
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-665 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-53693.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-665, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-53694
in-theory        53694
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-53694.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-665, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-53695
in-theory        53695
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     25
proof            (modus-ponens tm-665 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-53695.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-665, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-53696
in-theory        53696
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-53696.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-665, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-53697
in-theory        53697
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-53697.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-665, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-53698
in-theory        53698
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (E -> (F or E)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-53698.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (D and (E -> (F or E))))), M:tm-665, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-53699
in-theory        53699
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     29
proof            (modus-ponens tm-665 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-53699.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-665, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-53700
in-theory        53700
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-53700.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-665, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-53701
in-theory        53701
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-53701.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-665, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-53702
in-theory        53702
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-53702.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-665, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-53703
in-theory        53703
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-53703.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-665, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-53704
in-theory        53704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-665 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-53704.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-665, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-53705
in-theory        53705
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-665 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-53705.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-665, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-53706
in-theory        53706
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-53706.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-665, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-53707
in-theory        53707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-53707.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-665, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-53708
in-theory        53708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     31
proof            (modus-ponens tm-665 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-53708.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-665, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-53709
in-theory        53709
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-53709.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (E -> (F -> (G or F))))), M:tm-665, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-53710
in-theory        53710
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (F or E))) or G))
theorem-size     23
proof            (modus-ponens tm-665 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-53710.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (F or E))) or G)), M:tm-665, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-53711
in-theory        53711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     25
proof            (modus-ponens tm-665 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-53711.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-665, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-53712
in-theory        53712
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (D -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-665 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-53712.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> (D -> (F or E)))), M:tm-665, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-53713
in-theory        53713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (F -> (G or F)))))
theorem-size     23
proof            (modus-ponens tm-665 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-53713.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (E -> (F -> (G or F))))), M:tm-665, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-53714
in-theory        53714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     25
proof            (modus-ponens tm-665 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-53714.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-665, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-53715
in-theory        53715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     31
proof            (modus-ponens tm-665 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-53715.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-665, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-53716
in-theory        53716
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-53716.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-665, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-53717
in-theory        53717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-53717.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-665, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-53718
in-theory        53718
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     25
proof            (modus-ponens tm-665 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-53718.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-665, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-53719
in-theory        53719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-53719.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-665, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-53720
in-theory        53720
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-665 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-53720.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-665, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-53721
in-theory        53721
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-53721.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-665, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-53722
in-theory        53722
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-665 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-53722.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (E -> E))), M:tm-665, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-53723
in-theory        53723
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-665 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-53723.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-665, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-53724
in-theory        53724
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-53724.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-665, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-53725
in-theory        53725
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-665 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-53725.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-665, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-53726
in-theory        53726
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-53726.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-665, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-53727
in-theory        53727
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-665 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-53727.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-665, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-53728
in-theory        53728
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-665 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-53728.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-665, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-53729
in-theory        53729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-665 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-53729.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-665, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-53730
in-theory        53730
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     37
proof            (modus-ponens tm-665 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-53730.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-665, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-53731
in-theory        53731
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-665 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-53731.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-665, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-53732
in-theory        53732
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-665 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-53732.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-665, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-53733
in-theory        53733
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     31
proof            (modus-ponens tm-665 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-53733.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-665, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-53734
in-theory        53734
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     25
proof            (modus-ponens tm-665 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-53734.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-665, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-53735
in-theory        53735
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-53735.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-665, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-53736
in-theory        53736
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-665 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-53736.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-665, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-53737
in-theory        53737
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-665 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-53737.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-665, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-53738
in-theory        53738
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-665 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-53738.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-665, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-53739
in-theory        53739
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-53739.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-665, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-53740
in-theory        53740
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     29
proof            (modus-ponens tm-665 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-53740.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-665, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-53741
in-theory        53741
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53741.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-665, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-53742
in-theory        53742
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53742.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-665, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-53743
in-theory        53743
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     33
proof            (modus-ponens tm-665 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-53743.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-665, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-53744
in-theory        53744
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     35
proof            (modus-ponens tm-665 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53744.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-665, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-53745
in-theory        53745
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53745.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-665, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-53746
in-theory        53746
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53746.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-665, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-53747
in-theory        53747
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     41
proof            (modus-ponens tm-665 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53747.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-665, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-53748
in-theory        53748
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53748.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-665, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-53749
in-theory        53749
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-53749.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-665, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-53750
in-theory        53750
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     35
proof            (modus-ponens tm-665 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-53750.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-665, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-53751
in-theory        53751
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-665 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-53751.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-665, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-53752
in-theory        53752
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-665 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53752.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-665, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53753
in-theory        53753
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-665 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53753.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-665, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-53754
in-theory        53754
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-665 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53754.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-665, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53755
in-theory        53755
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B or (A -> B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-662 tm-665 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53755.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-665, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-53756
in-theory        53756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> B)))
theorem-size     21
proof            (modus-ponens tm-660 tm-665 ((Am (-> A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53756.        ((A -> B) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> B))), M:tm-660, m:tm-665, u:((Am (-> A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A B))))
================================================================
tm-name          tm-53757
in-theory        53757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> B))) and ((B or (A -> B)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> B))))
theorem-size     45
proof            (modus-ponens tm-654 tm-665 ((Am (-> A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53757.        (((A -> B) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> B))) and ((B or (A -> B)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> B)))), M:tm-654, m:tm-665, u:((Am (-> A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A B))))
================================================================
tm-name          tm-53758
in-theory        53758
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and A)))
theorem-size     19
proof            (modus-ponens tm-623 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-8)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53758.        (A -> (B or ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and A))), M:tm-623, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-53759
in-theory        53759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-622 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53759.        ((A -> (B -> (C or B))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-622, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53760
in-theory        53760
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (B -> (C or B))))
theorem-size     27
proof            (modus-ponens tm-619 tm-665 ((Am (-> A (or B A))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53760.        ((A or (B -> (C or B))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (B -> (C or B)))), M:tm-619, m:tm-665, u:((Am (-> A (or B A))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A (or B A)))))
================================================================
tm-name          tm-53761
in-theory        53761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53761.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (E -> (F or E))), M:tm-609, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53762
in-theory        53762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-605 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53762.        ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-605, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53763
in-theory        53763
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B -> (C or B)) and A)))
theorem-size     31
proof            (modus-ponens tm-602 tm-665 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53763.        ((A or ((B -> (C or B)) and A)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-665, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-53764
in-theory        53764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((E -> (F or E)) and (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-595 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53764.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((E -> (F or E)) and (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)))), M:tm-595, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53765
in-theory        53765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-550 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53765.        (((A -> (B or A)) or C) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-550, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53766
in-theory        53766
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-540 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53766.        ((A or (B -> (C or B))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-540, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53767
in-theory        53767
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-530 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53767.        ((A or (B -> (B or C))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-530, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53768
in-theory        53768
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-520 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53768.        ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-520, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53769
in-theory        53769
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-510 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53769.        ((A or ((B and C) -> C)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-510, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53770
in-theory        53770
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-500 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53770.        ((A or ((B and C) -> B)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-500, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53771
in-theory        53771
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-490 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53771.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E))), M:tm-490, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53772
in-theory        53772
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-480 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53772.        ((A or (B -> (C -> B))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-480, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53773
in-theory        53773
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-8)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53773.        (A -> (((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A) or E)), M:tm-470, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-53774
in-theory        53774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-469 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53774.        ((A -> (B -> (B or C))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-469, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53775
in-theory        53775
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (B -> (B or C))))
theorem-size     27
proof            (modus-ponens tm-466 tm-665 ((Am (-> A (or A B))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53775.        ((A or (B -> (B or C))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (B -> (B or C)))), M:tm-466, m:tm-665, u:((Am (-> A (or A B))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A (or A B)))))
================================================================
tm-name          tm-53776
in-theory        53776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53776.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (E -> (E or F))), M:tm-456, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53777
in-theory        53777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-453 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53777.        ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-453, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53778
in-theory        53778
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B -> (B or C)) and A)))
theorem-size     31
proof            (modus-ponens tm-450 tm-665 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53778.        ((A or ((B -> (B or C)) and A)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-665, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-53779
in-theory        53779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((E -> (E or F)) and (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-443 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53779.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((E -> (E or F)) and (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)))), M:tm-443, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53780
in-theory        53780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-409 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53780.        (((A -> (A or B)) or C) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-409, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53781
in-theory        53781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-400 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53781.        (((A -> (B -> (A and B))) or C) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-400, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53782
in-theory        53782
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-391 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53782.        ((((A and B) -> B) or C) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-391, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53783
in-theory        53783
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-382 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53783.        ((((A and B) -> A) or C) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-382, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53784
in-theory        53784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-373 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53784.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E))), M:tm-373, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53785
in-theory        53785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-364 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53785.        (((A -> (B -> A)) or C) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-364, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53786
in-theory        53786
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and A) and B)))
theorem-size     21
proof            (modus-ponens tm-355 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53786.        (A -> (B -> (((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and A) and B))), M:tm-355, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-53787
in-theory        53787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-354 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53787.        ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-354, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53788
in-theory        53788
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (B -> (C -> (B and C)))))
theorem-size     31
proof            (modus-ponens tm-351 tm-665 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53788.        ((A or (B -> (C -> (B and C)))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-665, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-53789
in-theory        53789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53789.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53790
in-theory        53790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C)))
theorem-size     27
proof            (modus-ponens tm-338 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53790.        (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C))), M:tm-338, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53791
in-theory        53791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> (A and B))))
theorem-size     29
proof            (modus-ponens tm-335 tm-665 ((Am (-> A (and A B))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53791.        (((A -> B) or (A -> (A and B))) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> (A and B)))), M:tm-335, m:tm-665, u:((Am (-> A (and A B))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A (and A B)))))
================================================================
tm-name          tm-53792
in-theory        53792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (A -> (A and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))))
theorem-size     37
proof            (modus-ponens tm-328 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53792.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (A -> (A and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)))), M:tm-328, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-53793
in-theory        53793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))))
theorem-size     43
proof            (modus-ponens tm-327 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53793.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((E -> (F -> (E and F))) and (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)))), M:tm-327, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53794
in-theory        53794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (((E and F) -> F) and (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-326 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53794.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (((E and F) -> F) and (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)))), M:tm-326, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53795
in-theory        53795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (((E and F) -> E) and (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-325 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53795.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (((E and F) -> E) and (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)))), M:tm-325, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53796
in-theory        53796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))))
theorem-size     49
proof            (modus-ponens tm-324 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53796.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)))), M:tm-324, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53797
in-theory        53797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((E -> (F -> E)) and (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))))
theorem-size     41
proof            (modus-ponens tm-323 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53797.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((E -> (F -> E)) and (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)))), M:tm-323, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53798
in-theory        53798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53798.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53799
in-theory        53799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53799.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53800
in-theory        53800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53800.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53801
in-theory        53801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (A -> A))
theorem-size     21
proof            (modus-ponens tm-316 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53801.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (A -> A)), M:tm-316, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-53802
in-theory        53802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53802.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53803
in-theory        53803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((A -> (not ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))) -> (not A)))
theorem-size     39
proof            (modus-ponens tm-313 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53803.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((A -> (not ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))) -> (not A))), M:tm-313, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-53804
in-theory        53804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A) -> E) -> ((A or ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53804.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A) -> E) -> ((A or ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) -> E))), M:tm-312, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-53805
in-theory        53805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (E or (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))))
theorem-size     37
proof            (modus-ponens tm-311 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53805.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (E or (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)))), M:tm-311, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53806
in-theory        53806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53806.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) or E)), M:tm-310, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53807
in-theory        53807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (E -> ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53807.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (E -> ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and E))), M:tm-309, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53808
in-theory        53808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (E -> (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))))
theorem-size     37
proof            (modus-ponens tm-305 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53808.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (E -> (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)))), M:tm-305, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53809
in-theory        53809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-303 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53809.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-303, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53810
in-theory        53810
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B -> (C -> (B and C))) and A)))
theorem-size     35
proof            (modus-ponens tm-300 tm-665 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53810.        ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-665, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-53811
in-theory        53811
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-270 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53811.        ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-270, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53812
in-theory        53812
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (((B and C) -> C) and A)))
theorem-size     31
proof            (modus-ponens tm-267 tm-665 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53812.        ((A or (((B and C) -> C) and A)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (((B and C) -> C) and A))), M:tm-267, m:tm-665, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-53813
in-theory        53813
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-239 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53813.        ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-239, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53814
in-theory        53814
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (((B and C) -> B) and A)))
theorem-size     31
proof            (modus-ponens tm-236 tm-665 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53814.        ((A or (((B and C) -> B) and A)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (((B and C) -> B) and A))), M:tm-236, m:tm-665, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-53815
in-theory        53815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E)))
theorem-size     35
proof            (modus-ponens tm-210 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53815.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E))), M:tm-210, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53816
in-theory        53816
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     47
proof            (modus-ponens tm-207 tm-665 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53816.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-665, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-53817
in-theory        53817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     27
proof            (modus-ponens tm-183 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53817.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-183, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53818
in-theory        53818
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B -> (C -> B)) and A)))
theorem-size     31
proof            (modus-ponens tm-180 tm-665 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53818.        ((A or ((B -> (C -> B)) and A)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-665, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-53819
in-theory        53819
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-157 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53819.        ((A -> ((B and C) -> C)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-157, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53820
in-theory        53820
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B and C) -> C)))
theorem-size     27
proof            (modus-ponens tm-154 tm-665 ((Am (-> (and A B) B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53820.        ((A or ((B and C) -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B and C) -> C))), M:tm-154, m:tm-665, u:((Am (-> (and A B) B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (and A B) B))))
================================================================
tm-name          tm-53821
in-theory        53821
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     33
proof            (modus-ponens tm-147 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53821.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-147, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53822
in-theory        53822
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A and (B -> C)) -> C)))
theorem-size     37
proof            (modus-ponens tm-144 tm-665 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53822.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-665, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-53823
in-theory        53823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-134 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53823.        ((A -> ((B and C) -> B)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-134, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53824
in-theory        53824
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B and C) -> B)))
theorem-size     27
proof            (modus-ponens tm-131 tm-665 ((Am (-> (and A B) A)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53824.        ((A or ((B and C) -> B)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B and C) -> B))), M:tm-131, m:tm-665, u:((Am (-> (and A B) A)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (and A B) A))))
================================================================
tm-name          tm-53825
in-theory        53825
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     33
proof            (modus-ponens tm-125 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53825.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-125, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53826
in-theory        53826
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (((A -> B) and C) -> B)))
theorem-size     37
proof            (modus-ponens tm-122 tm-665 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53826.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-665, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-53827
in-theory        53827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E)))
theorem-size     33
proof            (modus-ponens tm-113 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53827.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E))), M:tm-113, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53828
in-theory        53828
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     43
proof            (modus-ponens tm-110 tm-665 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53828.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-665, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-53829
in-theory        53829
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     37
proof            (modus-ponens tm-105 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53829.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-105, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53830
in-theory        53830
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-102 tm-665 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53830.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-665, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-53831
in-theory        53831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C)))
theorem-size     25
proof            (modus-ponens tm-95 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53831.        (((A -> B) -> (A -> A)) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C))), M:tm-95, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53832
in-theory        53832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> A)))
theorem-size     25
proof            (modus-ponens tm-92 tm-665 ((Am (-> A A)) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53832.        (((A -> B) or (A -> A)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A -> A))), M:tm-92, m:tm-665, u:((Am (-> A A)) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A A))))
================================================================
tm-name          tm-53833
in-theory        53833
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and A)))
theorem-size     19
proof            (modus-ponens tm-84 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53833.        (A -> (B -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and A))), M:tm-84, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-53834
in-theory        53834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     25
proof            (modus-ponens tm-83 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53834.        ((A -> (B -> (C -> B))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-83, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53835
in-theory        53835
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (B -> (C -> B))))
theorem-size     27
proof            (modus-ponens tm-80 tm-665 ((Am (-> A (-> B A))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53835.        ((A or (B -> (C -> B))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (B -> (C -> B)))), M:tm-80, m:tm-665, u:((Am (-> A (-> B A))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A (-> B A)))))
================================================================
tm-name          tm-53836
in-theory        53836
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and B)))
theorem-size     23
proof            (modus-ponens tm-76 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53836.        (((not (not A)) -> A) and (B -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and B))), M:tm-76, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53837
in-theory        53837
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))
theorem-size     21
proof            (modus-ponens tm-73 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53837.        (((not (not A)) or A) -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-73, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-53838
in-theory        53838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C)))
theorem-size     29
proof            (modus-ponens tm-69 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53838.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C))), M:tm-69, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53839
in-theory        53839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and ((A -> (not B)) -> (not A))))
theorem-size     33
proof            (modus-ponens tm-66 tm-665 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53839.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-665, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-53840
in-theory        53840
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-54 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53840.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-54, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53841
in-theory        53841
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     37
proof            (modus-ponens tm-51 tm-665 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53841.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-665, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-53842
in-theory        53842
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (B or A)))
theorem-size     23
proof            (modus-ponens tm-50 tm-665 ((Am (or A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53842.        ((A or (B or A)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (B or A))), M:tm-50, m:tm-665, u:((Am (or A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (or A B))))
================================================================
tm-name          tm-53843
in-theory        53843
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A or B)))
theorem-size     23
proof            (modus-ponens tm-49 tm-665 ((Am (or A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53843.        ((A or (A or B)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (A or B))), M:tm-49, m:tm-665, u:((Am (or A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (or A B))))
================================================================
tm-name          tm-53844
in-theory        53844
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (B -> (A and B))))
theorem-size     27
proof            (modus-ponens tm-48 tm-665 ((Am (-> A (and B A))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53844.        ((A or (B -> (A and B))) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (B -> (A and B)))), M:tm-48, m:tm-665, u:((Am (-> A (and B A))) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A (and B A)))))
================================================================
tm-name          tm-53845
in-theory        53845
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and B))
theorem-size     21
proof            (modus-ponens tm-47 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53845.        (((A and B) or B) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and B)), M:tm-47, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-53846
in-theory        53846
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and A))
theorem-size     21
proof            (modus-ponens tm-46 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53846.        (((A and B) or A) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and A)), M:tm-46, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-53847
in-theory        53847
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-45 tm-665 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53847.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-665, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-53848
in-theory        53848
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (B -> A)))
theorem-size     23
proof            (modus-ponens tm-44 tm-665 ((Am (-> A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53848.        ((A or (B -> A)) -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and (B -> A))), M:tm-44, m:tm-665, u:((Am (-> A B)) (C (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> A B))))
================================================================
tm-name          tm-53849
in-theory        53849
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-42 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53849.        ((A -> (B or A)) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C))), M:tm-42, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53850
in-theory        53850
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-32 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53850.        ((A -> (A or B)) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C))), M:tm-32, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53851
in-theory        53851
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)))
theorem-size     19
proof            (modus-ponens tm-24 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53851.        (A -> (A and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))), M:tm-24, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-53852
in-theory        53852
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C)))
theorem-size     25
proof            (modus-ponens tm-23 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53852.        ((A -> (B -> (A and B))) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C))), M:tm-23, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53853
in-theory        53853
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-22 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53853.        (((A and B) -> B) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C))), M:tm-22, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53854
in-theory        53854
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-21 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53854.        (((A and B) -> A) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C))), M:tm-21, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53855
in-theory        53855
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-20 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53855.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-20, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53856
in-theory        53856
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C)))
theorem-size     23
proof            (modus-ponens tm-19 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53856.        ((A -> (B -> A)) and (C -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and C))), M:tm-19, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53857
in-theory        53857
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))) -> (not A))
theorem-size     21
proof            (modus-ponens tm-9 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-9 tm-5 tm-8 tm-1)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53857.        ((A -> (not ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))) -> (not A)), M:tm-9, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-53858
in-theory        53858
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and D) -> E) -> ((D or ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and D)) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       105
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53858.        ((((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and D) -> E) -> ((D or ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and D)) -> E)), M:tm-8, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-53859
in-theory        53859
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and B)))
theorem-size     19
proof            (modus-ponens tm-7 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-7 tm-5 tm-8 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53859.        (A or (B -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and B))), M:tm-7, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53860
in-theory        53860
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-6 tm-5 tm-8 tm-1)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53860.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) or E), M:tm-6, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53861
in-theory        53861
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and B)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       83
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53861.        (A -> ((B -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and B)) and A)), M:tm-5, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53862
in-theory        53862
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and B)))
theorem-size     19
proof            (modus-ponens tm-1 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-1 tm-5 tm-8)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53862.        (A -> (B -> ((((C -> D) -> E) -> ((D or (C -> D)) -> E)) and B))), M:tm-1, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-53863
in-theory        53863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> B))) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-666 tm-365 ((Am (-> (-> A (-> Bm (-> Cm Bm))) C)) (B (-> Bm (-> Cm Bm))) (Dm (-> A (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-53863.        (((A -> (B -> (C -> B))) -> D) -> D), M:tm-666, m:tm-365, u:((Am (-> (-> A (-> Bm (-> Cm Bm))) C)) (B (-> Bm (-> Cm Bm))) (Dm (-> A (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-53864
in-theory        53864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> E)
theorem-size     19
proof            (modus-ponens tm-666 tm-374 ((Am (-> (-> A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) C)) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (Em (-> A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-53864.        (((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> E) -> E), M:tm-666, m:tm-374, u:((Am (-> (-> A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) C)) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (Em (-> A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-53865
in-theory        53865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> B)) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-666 tm-383 ((Am (-> (-> A (-> (and Bm Cm) Bm)) C)) (B (-> (and Bm Cm) Bm)) (Dm (-> A (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-8 tm-1 tm-6 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-53865.        (((A -> ((B and C) -> B)) -> D) -> D), M:tm-666, m:tm-383, u:((Am (-> (-> A (-> (and Bm Cm) Bm)) C)) (B (-> (and Bm Cm) Bm)) (Dm (-> A (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-53866
in-theory        53866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B and C) -> C)) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-666 tm-392 ((Am (-> (-> A (-> (and Bm Cm) Cm)) C)) (B (-> (and Bm Cm) Cm)) (Dm (-> A (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-8 tm-1 tm-6 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-53866.        (((A -> ((B and C) -> C)) -> D) -> D), M:tm-666, m:tm-392, u:((Am (-> (-> A (-> (and Bm Cm) Cm)) C)) (B (-> (and Bm Cm) Cm)) (Dm (-> A (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-53867
in-theory        53867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> (B and C)))) -> D) -> D)
theorem-size     13
proof            (modus-ponens tm-666 tm-401 ((Am (-> (-> A (-> Bm (-> Cm (and Bm Cm)))) C)) (B (-> Bm (-> Cm (and Bm Cm)))) (Dm (-> A (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-8 tm-1 tm-6 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-53867.        (((A -> (B -> (C -> (B and C)))) -> D) -> D), M:tm-666, m:tm-401, u:((Am (-> (-> A (-> Bm (-> Cm (and Bm Cm)))) C)) (B (-> Bm (-> Cm (and Bm Cm)))) (Dm (-> A (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-53868
in-theory        53868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (B or C))) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-666 tm-410 ((Am (-> (-> A (-> Bm (or Bm Cm))) C)) (B (-> Bm (or Bm Cm))) (Dm (-> A (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-53868.        (((A -> (B -> (B or C))) -> D) -> D), M:tm-666, m:tm-410, u:((Am (-> (-> A (-> Bm (or Bm Cm))) C)) (B (-> Bm (or Bm Cm))) (Dm (-> A (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-53869
in-theory        53869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C or B))) -> D) -> D)
theorem-size     11
proof            (modus-ponens tm-666 tm-551 ((Am (-> (-> A (-> Bm (or Cm Bm))) C)) (B (-> Bm (or Cm Bm))) (Dm (-> A (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-8 tm-1 tm-6 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-53869.        (((A -> (B -> (C or B))) -> D) -> D), M:tm-666, m:tm-551, u:((Am (-> (-> A (-> Bm (or Cm Bm))) C)) (B (-> Bm (or Cm Bm))) (Dm (-> A (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-53870
in-theory        53870
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-665 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53870.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-665, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53871
in-theory        53871
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((B or (A -> B)) or (((A -> B) -> C) -> (B or (A -> B)))) -> (((A -> B) -> C) -> C)))
theorem-size     45
proof            (modus-ponens tm-654 tm-666 ((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53871.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((B or (A -> B)) or (((A -> B) -> C) -> (B or (A -> B)))) -> (((A -> B) -> C) -> C))), M:tm-654, m:tm-666, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53872
in-theory        53872
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (B or (A -> B))) -> (D or (((A -> B) -> C) -> C)))
theorem-size     21
proof            (modus-ponens tm-623 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53872.        ((((A -> B) -> C) -> (B or (A -> B))) -> (D or (((A -> B) -> C) -> C))), M:tm-623, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53873
in-theory        53873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-622 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53873.        ((A -> (B -> (C or B))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-622, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53874
in-theory        53874
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-609 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53874.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (D -> (E or D))), M:tm-609, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53875
in-theory        53875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-605 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53875.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-605, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53876
in-theory        53876
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((D -> (E or D)) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-595 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53876.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((D -> (E or D)) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)))), M:tm-595, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53877
in-theory        53877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-550 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53877.        (((A -> (B or A)) or C) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-550, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53878
in-theory        53878
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-540 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53878.        ((A or (B -> (C or B))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-540, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53879
in-theory        53879
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-530 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53879.        ((A or (B -> (B or C))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-530, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53880
in-theory        53880
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-520 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53880.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-520, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53881
in-theory        53881
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-510 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53881.        ((A or ((B and C) -> C)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-510, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53882
in-theory        53882
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-500 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53882.        ((A or ((B and C) -> B)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-500, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53883
in-theory        53883
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-490 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53883.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G))), M:tm-490, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53884
in-theory        53884
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-480 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53884.        ((A or (B -> (C -> B))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-480, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53885
in-theory        53885
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (B or (A -> B))) -> ((((A -> B) -> C) -> C) or D))
theorem-size     21
proof            (modus-ponens tm-470 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53885.        ((((A -> B) -> C) -> (B or (A -> B))) -> ((((A -> B) -> C) -> C) or D)), M:tm-470, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53886
in-theory        53886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-469 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53886.        ((A -> (B -> (B or C))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-469, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53887
in-theory        53887
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-456 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53887.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (D -> (D or E))), M:tm-456, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53888
in-theory        53888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-453 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53888.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-453, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53889
in-theory        53889
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((D -> (D or E)) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-443 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53889.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((D -> (D or E)) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)))), M:tm-443, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53890
in-theory        53890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-409 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53890.        (((A -> (A or B)) or C) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-409, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53891
in-theory        53891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-400 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53891.        (((A -> (B -> (A and B))) or C) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-400, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53892
in-theory        53892
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-391 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53892.        ((((A and B) -> B) or C) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-391, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53893
in-theory        53893
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-382 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53893.        ((((A and B) -> A) or C) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-382, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53894
in-theory        53894
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-373 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53894.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G))), M:tm-373, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53895
in-theory        53895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-364 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53895.        (((A -> (B -> A)) or C) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-364, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53896
in-theory        53896
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (B or (A -> B))) -> (D -> ((((A -> B) -> C) -> C) and D)))
theorem-size     23
proof            (modus-ponens tm-355 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53896.        ((((A -> B) -> C) -> (B or (A -> B))) -> (D -> ((((A -> B) -> C) -> C) and D))), M:tm-355, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53897
in-theory        53897
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-354 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53897.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-354, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53898
in-theory        53898
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (D -> (E -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-341 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53898.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53899
in-theory        53899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E)))
theorem-size     29
proof            (modus-ponens tm-338 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53899.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E))), M:tm-338, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53900
in-theory        53900
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((((A -> B) -> C) -> (B or (A -> B))) -> ((((A -> B) -> C) -> (B or (A -> B))) and (((A -> B) -> C) -> C))))
theorem-size     51
proof            (modus-ponens tm-328 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53900.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((((A -> B) -> C) -> (B or (A -> B))) -> ((((A -> B) -> C) -> (B or (A -> B))) and (((A -> B) -> C) -> C)))), M:tm-328, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53901
in-theory        53901
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((D -> (E -> (D and E))) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C))))
theorem-size     47
proof            (modus-ponens tm-327 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53901.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((D -> (E -> (D and E))) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)))), M:tm-327, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53902
in-theory        53902
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((D and E) -> E) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-326 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53902.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((D and E) -> E) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)))), M:tm-326, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53903
in-theory        53903
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((D and E) -> D) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-325 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53903.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((D and E) -> D) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)))), M:tm-325, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53904
in-theory        53904
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C))))
theorem-size     53
proof            (modus-ponens tm-324 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53904.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)))), M:tm-324, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53905
in-theory        53905
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((D -> (E -> D)) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C))))
theorem-size     45
proof            (modus-ponens tm-323 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53905.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((D -> (E -> D)) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)))), M:tm-323, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53906
in-theory        53906
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-322 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53906.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((D and E) -> E)), M:tm-322, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53907
in-theory        53907
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-320 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53907.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((D and E) -> D)), M:tm-320, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53908
in-theory        53908
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-318 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53908.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53909
in-theory        53909
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> (B or (A -> B)))))
theorem-size     43
proof            (modus-ponens tm-316 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53909.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> (B or (A -> B))))), M:tm-316, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53910
in-theory        53910
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-315 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53910.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (D -> (E -> D))), M:tm-315, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53911
in-theory        53911
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((((A -> B) -> C) -> (B or (A -> B))) -> (not (((A -> B) -> C) -> C))) -> (not (((A -> B) -> C) -> (B or (A -> B))))))
theorem-size     53
proof            (modus-ponens tm-313 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53911.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((((A -> B) -> C) -> (B or (A -> B))) -> (not (((A -> B) -> C) -> C))) -> (not (((A -> B) -> C) -> (B or (A -> B)))))), M:tm-313, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53912
in-theory        53912
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((((A -> B) -> C) -> C) -> D) -> (((((A -> B) -> C) -> (B or (A -> B))) or (((A -> B) -> C) -> C)) -> D)))
theorem-size     51
proof            (modus-ponens tm-312 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53912.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((((A -> B) -> C) -> C) -> D) -> (((((A -> B) -> C) -> (B or (A -> B))) or (((A -> B) -> C) -> C)) -> D))), M:tm-312, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53913
in-theory        53913
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (D or ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C))))
theorem-size     41
proof            (modus-ponens tm-311 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53913.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (D or ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)))), M:tm-311, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53914
in-theory        53914
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) or D))
theorem-size     41
proof            (modus-ponens tm-310 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53914.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) or D)), M:tm-310, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53915
in-theory        53915
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (D -> (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and D)))
theorem-size     43
proof            (modus-ponens tm-309 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53915.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (D -> (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and D))), M:tm-309, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53916
in-theory        53916
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((((A -> B) -> C) -> (B or (A -> B))) -> ((A -> B) -> C)) -> ((((A -> B) -> C) -> (B or (A -> B))) -> C)))
theorem-size     51
proof            (modus-ponens tm-306 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> Am Bm) Cm)) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53916.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (((((A -> B) -> C) -> (B or (A -> B))) -> ((A -> B) -> C)) -> ((((A -> B) -> C) -> (B or (A -> B))) -> C))), M:tm-306, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> Am Bm) Cm)) (C Cm))
================================================================
tm-name          tm-53917
in-theory        53917
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (D -> ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C))))
theorem-size     41
proof            (modus-ponens tm-305 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53917.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and (D -> ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)))), M:tm-305, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53918
in-theory        53918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-303 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53918.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-303, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53919
in-theory        53919
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-270 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53919.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-270, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53920
in-theory        53920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-239 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53920.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-239, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53921
in-theory        53921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G)))
theorem-size     37
proof            (modus-ponens tm-210 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53921.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G))), M:tm-210, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53922
in-theory        53922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     29
proof            (modus-ponens tm-183 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53922.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-183, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53923
in-theory        53923
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-157 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53923.        ((A -> ((B and C) -> C)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-157, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53924
in-theory        53924
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     35
proof            (modus-ponens tm-147 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53924.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-147, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53925
in-theory        53925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-134 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53925.        ((A -> ((B and C) -> B)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-134, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53926
in-theory        53926
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     35
proof            (modus-ponens tm-125 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53926.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-125, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53927
in-theory        53927
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (C -> D)) -> (B or (A -> B))) -> ((((A -> B) -> (C -> D)) -> C) -> (((A -> B) -> (C -> D)) -> D)))
theorem-size     33
proof            (modus-ponens tm-114 tm-666 ((A (-> (-> (-> Am Bm) (-> C D)) (or Bm (-> Am Bm)))) (B (-> (-> Am Bm) (-> C D))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53927.        ((((A -> B) -> (C -> D)) -> (B or (A -> B))) -> ((((A -> B) -> (C -> D)) -> C) -> (((A -> B) -> (C -> D)) -> D))), M:tm-114, m:tm-666, u:((A (-> (-> (-> Am Bm) (-> C D)) (or Bm (-> Am Bm)))) (B (-> (-> Am Bm) (-> C D))) (Cm (-> C D)))
================================================================
tm-name          tm-53928
in-theory        53928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G)))
theorem-size     35
proof            (modus-ponens tm-113 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53928.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G))), M:tm-113, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53929
in-theory        53929
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     39
proof            (modus-ponens tm-105 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53929.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-105, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53930
in-theory        53930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E)))
theorem-size     27
proof            (modus-ponens tm-95 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53930.        (((A -> B) -> (A -> A)) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E))), M:tm-95, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53931
in-theory        53931
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (B or (A -> B))) -> (D -> (((A -> B) -> C) -> C)))
theorem-size     21
proof            (modus-ponens tm-84 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53931.        ((((A -> B) -> C) -> (B or (A -> B))) -> (D -> (((A -> B) -> C) -> C))), M:tm-84, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53932
in-theory        53932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     27
proof            (modus-ponens tm-83 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53932.        ((A -> (B -> (C -> B))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-83, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53933
in-theory        53933
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) -> D) -> (C or (B -> C))) -> (((B -> C) -> D) -> D)))
theorem-size     25
proof            (modus-ponens tm-76 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53933.        (((not (not A)) -> A) and ((((B -> C) -> D) -> (C or (B -> C))) -> (((B -> C) -> D) -> D))), M:tm-76, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53934
in-theory        53934
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) -> C) -> (B or (A -> B))))) or (((A -> B) -> C) -> (B or (A -> B)))) -> (((A -> B) -> C) -> C))
theorem-size     33
proof            (modus-ponens tm-73 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53934.        (((not (not (((A -> B) -> C) -> (B or (A -> B))))) or (((A -> B) -> C) -> (B or (A -> B)))) -> (((A -> B) -> C) -> C)), M:tm-73, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53935
in-theory        53935
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (B or (A -> B)))) -> (B or (A -> B))) -> (not ((A -> B) -> (not (B or (A -> B))))))
theorem-size     28
proof            (modus-ponens tm-70 tm-666 ((B (or Bm (-> Am Bm))) (A (-> (-> Am Bm) (not (or Bm (-> Am Bm))))) (Cm (not (or Bm (-> Am Bm))))))
axioms-used      (tm-2 tm-9 tm-8 tm-1)
proof-size       130
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53935.        ((((A -> B) -> (not (B or (A -> B)))) -> (B or (A -> B))) -> (not ((A -> B) -> (not (B or (A -> B)))))), M:tm-70, m:tm-666, u:((B (or Bm (-> Am Bm))) (A (-> (-> Am Bm) (not (or Bm (-> Am Bm))))) (Cm (not (or Bm (-> Am Bm)))))
================================================================
tm-name          tm-53936
in-theory        53936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E)))
theorem-size     31
proof            (modus-ponens tm-69 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53936.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E))), M:tm-69, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53937
in-theory        53937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-54 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53937.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-54, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53938
in-theory        53938
times-derived    2
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> D) -> (C or (B -> C)))) or (((B -> C) -> D) -> (C or (B -> C)))) -> (((B -> C) -> D) -> D))
theorem-size     33
proof            (modus-ponens tm-47 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53938.        (((A and (((B -> C) -> D) -> (C or (B -> C)))) or (((B -> C) -> D) -> (C or (B -> C)))) -> (((B -> C) -> D) -> D)), M:tm-47, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53939
in-theory        53939
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) -> (B or (A -> B))) and D) or (((A -> B) -> C) -> (B or (A -> B)))) -> (((A -> B) -> C) -> C))
theorem-size     33
proof            (modus-ponens tm-46 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53939.        ((((((A -> B) -> C) -> (B or (A -> B))) and D) or (((A -> B) -> C) -> (B or (A -> B)))) -> (((A -> B) -> C) -> C)), M:tm-46, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53940
in-theory        53940
times-derived    2
----------------------------------------------------------------
theorem          (((A or (B -> A)) or (((B -> A) -> C) -> (A or (B -> A)))) -> (((B -> A) -> C) -> C))
theorem-size     25
proof            (modus-ponens tm-44 tm-666 ((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53940.        (((A or (B -> A)) or (((B -> A) -> C) -> (A or (B -> A)))) -> (((B -> A) -> C) -> C)), M:tm-44, m:tm-666, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53941
in-theory        53941
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-42 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53941.        ((A -> (B or A)) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E))), M:tm-42, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53942
in-theory        53942
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-32 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53942.        ((A -> (A or B)) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E))), M:tm-32, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53943
in-theory        53943
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (B or (A -> B))) -> ((((A -> B) -> C) -> (B or (A -> B))) and (((A -> B) -> C) -> C)))
theorem-size     31
proof            (modus-ponens tm-24 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53943.        ((((A -> B) -> C) -> (B or (A -> B))) -> ((((A -> B) -> C) -> (B or (A -> B))) and (((A -> B) -> C) -> C))), M:tm-24, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53944
in-theory        53944
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E)))
theorem-size     27
proof            (modus-ponens tm-23 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53944.        ((A -> (B -> (A and B))) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E))), M:tm-23, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53945
in-theory        53945
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-22 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53945.        (((A and B) -> B) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E))), M:tm-22, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53946
in-theory        53946
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-21 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-8 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53946.        (((A and B) -> A) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E))), M:tm-21, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53947
in-theory        53947
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-20 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53947.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-20, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53948
in-theory        53948
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-19 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53948.        ((A -> (B -> A)) and ((((C -> D) -> E) -> (D or (C -> D))) -> (((C -> D) -> E) -> E))), M:tm-19, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53949
in-theory        53949
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> (B or (A -> B))))
theorem-size     23
proof            (modus-ponens tm-12 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53949.        ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> (B or (A -> B)))), M:tm-12, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53950
in-theory        53950
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (not (((A -> B) -> C) -> C))) -> (not (((A -> B) -> C) -> (B or (A -> B)))))
theorem-size     33
proof            (modus-ponens tm-9 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-9 tm-2 tm-8 tm-1)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53950.        (((((A -> B) -> C) -> (B or (A -> B))) -> (not (((A -> B) -> C) -> C))) -> (not (((A -> B) -> C) -> (B or (A -> B))))), M:tm-9, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53951
in-theory        53951
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> C) -> D) -> (((((A -> B) -> C) -> (B or (A -> B))) or (((A -> B) -> C) -> C)) -> D))
theorem-size     31
proof            (modus-ponens tm-8 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53951.        (((((A -> B) -> C) -> C) -> D) -> (((((A -> B) -> C) -> (B or (A -> B))) or (((A -> B) -> C) -> C)) -> D)), M:tm-8, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-53952
in-theory        53952
times-derived    2
----------------------------------------------------------------
theorem          (A or ((((B -> C) -> D) -> (C or (B -> C))) -> (((B -> C) -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-7 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-7 tm-2 tm-8 tm-1)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53952.        (A or ((((B -> C) -> D) -> (C or (B -> C))) -> (((B -> C) -> D) -> D))), M:tm-7, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53953
in-theory        53953
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) or D)
theorem-size     21
proof            (modus-ponens tm-6 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-6 tm-2 tm-8 tm-1)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53953.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) or D), M:tm-6, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53954
in-theory        53954
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> D) -> (C or (B -> C))) -> (((B -> C) -> D) -> D)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       93
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53954.        (A -> (((((B -> C) -> D) -> (C or (B -> C))) -> (((B -> C) -> D) -> D)) and A)), M:tm-5, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53955
in-theory        53955
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> ((A -> B) -> C)) -> ((((A -> B) -> C) -> (B or (A -> B))) -> C))
theorem-size     31
proof            (modus-ponens tm-2 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> Am Bm) Cm)) (C Cm)))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53955.        (((((A -> B) -> C) -> (B or (A -> B))) -> ((A -> B) -> C)) -> ((((A -> B) -> C) -> (B or (A -> B))) -> C)), M:tm-2, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> Am Bm) Cm)) (C Cm))
================================================================
tm-name          tm-53956
in-theory        53956
times-derived    3
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> D) -> (C or (B -> C))) -> (((B -> C) -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-1 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-1 tm-2 tm-8)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-53956.        (A -> ((((B -> C) -> D) -> (C or (B -> C))) -> (((B -> C) -> D) -> D))), M:tm-1, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-53957
in-theory        53957
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-665 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53957.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-665, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53958
in-theory        53958
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-662 tm-667 ((Am (-> (or A (-> B A)) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53958.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-662, m:tm-667, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-53959
in-theory        53959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     17
proof            (modus-ponens tm-660 tm-667 ((Am (-> A B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53959.        ((A -> B) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-660, m:tm-667, u:((Am (-> A B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-53960
in-theory        53960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((B or (A -> B)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))))
theorem-size     37
proof            (modus-ponens tm-654 tm-667 ((Am (-> A B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53960.        (((A -> B) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))) and ((B or (A -> B)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))), M:tm-654, m:tm-667, u:((Am (-> A B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-53961
in-theory        53961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-622 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53961.        ((A -> (B -> (C or B))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-622, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53962
in-theory        53962
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-619 tm-667 ((Am (-> A (or B A))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53962.        ((A or (B -> (C or B))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-619, m:tm-667, u:((Am (-> A (or B A))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-53963
in-theory        53963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53963.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (F or E))), M:tm-609, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53964
in-theory        53964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-605 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53964.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-605, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53965
in-theory        53965
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-602 tm-667 ((Am (and (-> A (or B A)) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53965.        ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-602, m:tm-667, u:((Am (and (-> A (or B A)) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-53966
in-theory        53966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F or E)) and (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53966.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F or E)) and (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-595, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53967
in-theory        53967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-550 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53967.        (((A -> (B or A)) or C) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-550, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53968
in-theory        53968
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-540 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53968.        ((A or (B -> (C or B))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-540, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53969
in-theory        53969
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-530 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53969.        ((A or (B -> (B or C))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-530, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53970
in-theory        53970
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-520 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53970.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-520, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53971
in-theory        53971
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-510 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53971.        ((A or ((B and C) -> C)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-510, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53972
in-theory        53972
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-500 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53972.        ((A or ((B and C) -> B)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-500, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53973
in-theory        53973
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-490 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53973.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-490, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53974
in-theory        53974
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-480 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53974.        ((A or (B -> (C -> B))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-480, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53975
in-theory        53975
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-469 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53975.        ((A -> (B -> (B or C))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-469, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53976
in-theory        53976
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-466 tm-667 ((Am (-> A (or A B))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53976.        ((A or (B -> (B or C))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-466, m:tm-667, u:((Am (-> A (or A B))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-53977
in-theory        53977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53977.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (E or F))), M:tm-456, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53978
in-theory        53978
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-453 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53978.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-453, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53979
in-theory        53979
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-450 tm-667 ((Am (and (-> A (or A B)) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53979.        ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-450, m:tm-667, u:((Am (and (-> A (or A B)) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-53980
in-theory        53980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (E or F)) and (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53980.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (E or F)) and (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-443, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53981
in-theory        53981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-409 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53981.        (((A -> (A or B)) or C) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-409, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53982
in-theory        53982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-400 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53982.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-400, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53983
in-theory        53983
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-391 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53983.        ((((A and B) -> B) or C) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-391, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53984
in-theory        53984
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-382 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53984.        ((((A and B) -> A) or C) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-382, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53985
in-theory        53985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-373 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53985.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-373, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53986
in-theory        53986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-364 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53986.        (((A -> (B -> A)) or C) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-364, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53987
in-theory        53987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-354 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53987.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-354, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53988
in-theory        53988
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-351 tm-667 ((Am (-> A (-> B (and A B)))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53988.        ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-351, m:tm-667, u:((Am (-> A (-> B (and A B)))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-53989
in-theory        53989
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (A and (C -> B))))
theorem-size     13
proof            (modus-ponens tm-349 tm-667 ((A Am) (B (-> Bm Cm)) (Dm (and Am (-> Bm Cm))) (C (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53989.        (A -> ((B or (C -> B)) -> (A and (C -> B)))), M:tm-349, m:tm-667, u:((A Am) (B (-> Bm Cm)) (Dm (and Am (-> Bm Cm))) (C (-> (or Cm (-> Bm Cm)) (and Am (-> Bm Cm)))))
================================================================
tm-name          tm-53990
in-theory        53990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53990.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53991
in-theory        53991
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) -> ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and D))
theorem-size     31
proof            (modus-ponens tm-339 tm-667 ((Am (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) B)) (A (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53991.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) -> ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and D)), M:tm-339, m:tm-667, u:((Am (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) B)) (A (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-53992
in-theory        53992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     25
proof            (modus-ponens tm-338 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53992.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-338, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53993
in-theory        53993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     23
proof            (modus-ponens tm-335 tm-667 ((Am (-> A (and A B))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53993.        (((A -> B) or (A -> (A and B))) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-335, m:tm-667, u:((Am (-> A (and A B))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-53994
in-theory        53994
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (A -> (A and (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-328 tm-667 ((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53994.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (A -> (A and (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-328, m:tm-667, u:((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-53995
in-theory        53995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F -> (E and F))) and (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53995.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F -> (E and F))) and (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-327, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53996
in-theory        53996
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((E and F) -> F) and (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53996.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((E and F) -> F) and (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-326, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53997
in-theory        53997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((E and F) -> E) and (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53997.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((E and F) -> E) and (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-325, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53998
in-theory        53998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53998.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-324, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-53999
in-theory        53999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F -> E)) and (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-53999.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F -> E)) and (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-323, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54000
in-theory        54000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54000.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54001
in-theory        54001
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) -> E)) -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((A and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) -> E)) -> E))
theorem-size     51
proof            (modus-ponens tm-321 tm-667 ((Am (and A (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) C))) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54001.        (((A and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) -> E)) -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((A and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) -> E)) -> E)), M:tm-321, m:tm-667, u:((Am (and A (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) C))) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54002
in-theory        54002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54002.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54003
in-theory        54003
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) and E) -> (((A -> B) -> C) -> ((B or (A -> B)) -> C))) and ((((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) and E) -> D))
theorem-size     51
proof            (modus-ponens tm-319 tm-667 ((Am (and (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) B) C)) (A (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54003.        (((((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) and E) -> (((A -> B) -> C) -> ((B or (A -> B)) -> C))) and ((((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) and E) -> D)), M:tm-319, m:tm-667, u:((Am (and (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) B) C)) (A (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54004
in-theory        54004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54004.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54005
in-theory        54005
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (((B or (A -> B)) -> C) -> D)) -> (((A -> B) -> C) -> ((B or (A -> B)) -> C))) and ((((A -> B) -> C) -> (((B or (A -> B)) -> C) -> D)) -> (((A -> B) -> C) -> D)))
theorem-size     53
proof            (modus-ponens tm-317 tm-667 ((Am (-> (-> (-> Bm Cm) Dm) (-> (-> (or Cm (-> Bm Cm)) Dm) C))) (A (-> (-> Bm Cm) Dm)) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54005.        (((((A -> B) -> C) -> (((B or (A -> B)) -> C) -> D)) -> (((A -> B) -> C) -> ((B or (A -> B)) -> C))) and ((((A -> B) -> C) -> (((B or (A -> B)) -> C) -> D)) -> (((A -> B) -> C) -> D))), M:tm-317, m:tm-667, u:((Am (-> (-> (-> Bm Cm) Dm) (-> (-> (or Cm (-> Bm Cm)) Dm) C))) (A (-> (-> Bm Cm) Dm)) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-54006
in-theory        54006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (A -> A))
theorem-size     19
proof            (modus-ponens tm-316 tm-667 ((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54006.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (A -> A)), M:tm-316, m:tm-667, u:((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54007
in-theory        54007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54007.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54008
in-theory        54008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((A -> (not (((B -> C) -> D) -> ((C or (B -> C)) -> D)))) -> (not A)))
theorem-size     35
proof            (modus-ponens tm-313 tm-667 ((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54008.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((A -> (not (((B -> C) -> D) -> ((C or (B -> C)) -> D)))) -> (not A))), M:tm-313, m:tm-667, u:((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54009
in-theory        54009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((((B -> C) -> D) -> ((C or (B -> C)) -> D)) -> E) -> ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) -> E)))
theorem-size     49
proof            (modus-ponens tm-312 tm-667 ((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54009.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((((B -> C) -> D) -> ((C or (B -> C)) -> D)) -> E) -> ((A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))) -> E))), M:tm-312, m:tm-667, u:((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54010
in-theory        54010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E or (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54010.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E or (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-311, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54011
in-theory        54011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54011.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) or E)), M:tm-310, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54012
in-theory        54012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54012.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and E))), M:tm-309, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54013
in-theory        54013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((A -> ((B -> C) -> D)) -> (A -> ((C or (B -> C)) -> D))))
theorem-size     33
proof            (modus-ponens tm-306 tm-667 ((A Am) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54013.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and ((A -> ((B -> C) -> D)) -> (A -> ((C or (B -> C)) -> D)))), M:tm-306, m:tm-667, u:((A Am) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-54014
in-theory        54014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54014.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (E -> (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))))), M:tm-305, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54015
in-theory        54015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-303 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54015.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-303, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54016
in-theory        54016
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-300 tm-667 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54016.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-300, m:tm-667, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54017
in-theory        54017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-270 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54017.        ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-270, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54018
in-theory        54018
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-267 tm-667 ((Am (and (-> (and A B) B) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54018.        ((A or (((B and C) -> C) and A)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-267, m:tm-667, u:((Am (and (-> (and A B) B) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54019
in-theory        54019
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-239 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54019.        ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-239, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54020
in-theory        54020
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-236 tm-667 ((Am (and (-> (and A B) A) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54020.        ((A or (((B and C) -> B) and A)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-236, m:tm-667, u:((Am (and (-> (and A B) A) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54021
in-theory        54021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-210 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54021.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-210, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54022
in-theory        54022
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-207 tm-667 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54022.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))), M:tm-207, m:tm-667, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54023
in-theory        54023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     25
proof            (modus-ponens tm-183 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54023.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-183, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54024
in-theory        54024
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     23
proof            (modus-ponens tm-180 tm-667 ((Am (and (-> A (-> B A)) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54024.        ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-180, m:tm-667, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54025
in-theory        54025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-157 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54025.        ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-157, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54026
in-theory        54026
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-154 tm-667 ((Am (-> (and A B) B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54026.        ((A or ((B and C) -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-154, m:tm-667, u:((Am (-> (and A B) B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54027
in-theory        54027
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((B -> C) -> D)) -> ((C or (B -> C)) -> D))
theorem-size     15
proof            (modus-ponens tm-152 tm-667 ((Am (and A (-> (-> Bm Cm) Dm))) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-4 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54027.        ((A and ((B -> C) -> D)) -> ((C or (B -> C)) -> D)), M:tm-152, m:tm-667, u:((Am (and A (-> (-> Bm Cm) Dm))) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-54028
in-theory        54028
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-147 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54028.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-147, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54029
in-theory        54029
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-144 tm-667 ((Am (-> (and A (-> B C)) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54029.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-144, m:tm-667, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54030
in-theory        54030
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) -> E)) -> (((B -> C) -> D) -> ((C or (B -> C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-142 tm-667 ((Am (and A (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) C))) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54030.        ((A and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) -> E)) -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-142, m:tm-667, u:((Am (and A (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) C))) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54031
in-theory        54031
times-derived    1
----------------------------------------------------------------
theorem          ((A and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) -> ((B -> C) -> D))) -> ((C or (B -> C)) -> D))
theorem-size     29
proof            (modus-ponens tm-141 tm-667 ((Am (and A (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> Bm Cm) Dm)))) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-4 tm-1 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54031.        ((A and ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) -> ((B -> C) -> D))) -> ((C or (B -> C)) -> D)), M:tm-141, m:tm-667, u:((Am (and A (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> Bm Cm) Dm)))) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-54032
in-theory        54032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-134 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54032.        ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-134, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54033
in-theory        54033
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-131 tm-667 ((Am (-> (and A B) A)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54033.        ((A or ((B and C) -> B)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-131, m:tm-667, u:((Am (-> (and A B) A)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54034
in-theory        54034
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) and D) -> ((B or (A -> B)) -> C))
theorem-size     15
proof            (modus-ponens tm-129 tm-667 ((Am (and (-> (-> Bm Cm) Dm) B)) (A (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-3 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54034.        ((((A -> B) -> C) and D) -> ((B or (A -> B)) -> C)), M:tm-129, m:tm-667, u:((Am (and (-> (-> Bm Cm) Dm) B)) (A (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-54035
in-theory        54035
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     31
proof            (modus-ponens tm-125 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54035.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-125, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54036
in-theory        54036
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-122 tm-667 ((Am (-> (and (-> A B) C) B)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54036.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-122, m:tm-667, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54037
in-theory        54037
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) and E) -> (((A -> B) -> C) -> ((B or (A -> B)) -> C)))
theorem-size     31
proof            (modus-ponens tm-120 tm-667 ((Am (and (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) B) C)) (A (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54037.        ((((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) and E) -> (((A -> B) -> C) -> ((B or (A -> B)) -> C))), M:tm-120, m:tm-667, u:((Am (and (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) B) C)) (A (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54038
in-theory        54038
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> ((A -> B) -> C)) and D) -> ((B or (A -> B)) -> C))
theorem-size     29
proof            (modus-ponens tm-119 tm-667 ((Am (and (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> Bm Cm) Dm)) C)) (A (-> (-> Bm Cm) Dm)) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-3 tm-1 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54038.        ((((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> ((A -> B) -> C)) and D) -> ((B or (A -> B)) -> C)), M:tm-119, m:tm-667, u:((Am (and (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> Bm Cm) Dm)) C)) (A (-> (-> Bm Cm) Dm)) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-54039
in-theory        54039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-113 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54039.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-113, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54040
in-theory        54040
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-110 tm-667 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54040.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))), M:tm-110, m:tm-667, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54041
in-theory        54041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((B or (A -> B)) -> (A -> C)))
theorem-size     15
proof            (modus-ponens tm-108 tm-667 ((Am (-> Bm (-> Cm C))) (A Bm) (B Cm) (Dm (-> Bm C)) (D (-> (or Cm (-> Bm Cm)) (-> Bm C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54041.        ((A -> (B -> C)) -> ((B or (A -> B)) -> (A -> C))), M:tm-108, m:tm-667, u:((Am (-> Bm (-> Cm C))) (A Bm) (B Cm) (Dm (-> Bm C)) (D (-> (or Cm (-> Bm Cm)) (-> Bm C))))
================================================================
tm-name          tm-54042
in-theory        54042
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> (((A -> B) -> C) -> (B or (A -> B)))) -> (((A -> B) -> C) -> C))
theorem-size     33
proof            (modus-ponens tm-106 tm-667 ((Am (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> (-> Bm Cm) Dm) (or Cm (-> Bm Cm))))) (A (-> (-> Bm Cm) Dm)) (B (or Cm (-> Bm Cm))) (C Dm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54042.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> (((A -> B) -> C) -> (B or (A -> B)))) -> (((A -> B) -> C) -> C)), M:tm-106, m:tm-667, u:((Am (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> (-> Bm Cm) Dm) (or Cm (-> Bm Cm))))) (A (-> (-> Bm Cm) Dm)) (B (or Cm (-> Bm Cm))) (C Dm))
================================================================
tm-name          tm-54043
in-theory        54043
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     35
proof            (modus-ponens tm-105 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54043.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-105, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54044
in-theory        54044
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-102 tm-667 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54044.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-102, m:tm-667, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54045
in-theory        54045
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((B or (A -> B)) -> C) -> D)) -> (((A -> B) -> C) -> ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-100 tm-667 ((Am (-> (-> (-> Bm Cm) Dm) (-> (-> (or Cm (-> Bm Cm)) Dm) C))) (A (-> (-> Bm Cm) Dm)) (B (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54045.        ((((A -> B) -> C) -> (((B or (A -> B)) -> C) -> D)) -> (((A -> B) -> C) -> ((B or (A -> B)) -> C))), M:tm-100, m:tm-667, u:((Am (-> (-> (-> Bm Cm) Dm) (-> (-> (or Cm (-> Bm Cm)) Dm) C))) (A (-> (-> Bm Cm) Dm)) (B (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-54046
in-theory        54046
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> A))
theorem-size     9
proof            (modus-ponens tm-98 tm-667 ((Dm Am) (B (-> Bm Cm)) (A Am) (C (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54046.        (A -> ((B or (C -> B)) -> A)), M:tm-98, m:tm-667, u:((Dm Am) (B (-> Bm Cm)) (A Am) (C (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-54047
in-theory        54047
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) -> (((A -> B) -> C) -> ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-96 tm-667 ((Am (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) B)) (A (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54047.        (((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D) -> (((A -> B) -> C) -> ((B or (A -> B)) -> C))), M:tm-96, m:tm-667, u:((Am (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) B)) (A (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54048
in-theory        54048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     23
proof            (modus-ponens tm-95 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54048.        (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-95, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54049
in-theory        54049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     21
proof            (modus-ponens tm-92 tm-667 ((Am (-> A A)) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54049.        (((A -> B) or (A -> A)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-92, m:tm-667, u:((Am (-> A A)) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54050
in-theory        54050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     23
proof            (modus-ponens tm-83 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54050.        ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-83, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54051
in-theory        54051
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-80 tm-667 ((Am (-> A (-> B A))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54051.        ((A or (B -> (C -> B))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-80, m:tm-667, u:((Am (-> A (-> B A))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54052
in-theory        54052
times-derived    1
----------------------------------------------------------------
theorem          ((not (not ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D))) -> D)
theorem-size     19
proof            (modus-ponens tm-77 tm-667 ((Am (not (not (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) B)))) (A (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-8)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54052.        ((not (not ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) -> D))) -> D), M:tm-77, m:tm-667, u:((Am (not (not (-> (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) B)))) (A (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54053
in-theory        54053
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))))
theorem-size     21
proof            (modus-ponens tm-76 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54053.        (((not (not A)) -> A) and (B -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))), M:tm-76, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54054
in-theory        54054
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> C) -> D) -> ((C or (B -> C)) -> D)))
theorem-size     19
proof            (modus-ponens tm-73 tm-667 ((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-10 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54054.        (((not (not A)) or A) -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-73, m:tm-667, u:((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54055
in-theory        54055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     27
proof            (modus-ponens tm-69 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54055.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-69, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54056
in-theory        54056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-66 tm-667 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-9 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54056.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-66, m:tm-667, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54057
in-theory        54057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> D)) -> ((A or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-55 tm-667 ((Am (-> A (-> (-> Bm Cm) Dm))) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54057.        ((A -> ((B -> C) -> D)) -> ((A or ((B -> C) -> D)) -> ((C or (B -> C)) -> D))), M:tm-55, m:tm-667, u:((Am (-> A (-> (-> Bm Cm) Dm))) (B (-> (-> Bm Cm) Dm)) (C (-> (or Cm (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-54058
in-theory        54058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     29
proof            (modus-ponens tm-54 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54058.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-54, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-54059
in-theory        54059
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-51 tm-667 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-1)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54059.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-51, m:tm-667, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54060
in-theory        54060
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-50 tm-667 ((Am (or A B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-7 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54060.        ((A or (B or A)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-50, m:tm-667, u:((Am (or A B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54061
in-theory        54061
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-49 tm-667 ((Am (or A B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-6 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54061.        ((A or (A or B)) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-49, m:tm-667, u:((Am (or A B)) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54062
in-theory        54062
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     21
proof            (modus-ponens tm-48 tm-667 ((Am (-> A (and B A))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-5 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54062.        ((A or (B -> (A and B))) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-48, m:tm-667, u:((Am (-> A (and B A))) (C (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54063
in-theory        54063
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-47 tm-667 ((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54063.        (((A and B) or B) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-47, m:tm-667, u:((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54064
in-theory        54064
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E)))
theorem-size     19
proof            (modus-ponens tm-46 tm-667 ((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54064.        (((A and B) or A) -> (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-46, m:tm-667, u:((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54065
in-theory        54065
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-45 tm-667 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-54065.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-45, m:tm-667, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-54066
in-theory        54066
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (B -> (B -> C))))
theorem-size     11
proof            (modus-ponens tm-668 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-54066.        (A -> ((B -> C) -> (B -> (B -> C)))), M:tm-668, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-54067
in-theory        54067
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (B -> ((B -> C) and B))))
theorem-size     13
proof            (modus-ponens tm-668 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-5)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-54067.        (A -> ((B -> C) -> (B -> ((B -> C) and B)))), M:tm-668, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-54068
in-theory        54068
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> B) -> ((B -> C) -> (((B -> C) or B) -> C))))
theorem-size     19
proof            (modus-ponens tm-668 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-54068.        (A -> (((B -> C) -> B) -> ((B -> C) -> (((B -> C) or B) -> C)))), M:tm-668, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-54069
in-theory        54069
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (B -> (D -> B))))
theorem-size     11
proof            (modus-ponens tm-668 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-54069.        (A -> ((B -> C) -> (B -> (D -> B)))), M:tm-668, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-54070
in-theory        54070
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> E) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     23
proof            (modus-ponens tm-668 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-54070.        (A -> (((B -> (C -> D)) -> E) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-668, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-54071
in-theory        54071
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> D) -> ((B and C) -> B)))
theorem-size     13
proof            (modus-ponens tm-668 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-54071.        (A -> (((B and C) -> D) -> ((B and C) -> B))), M:tm-668, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-54072
in-theory        54072
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> D) -> ((B and C) -> C)))
theorem-size     13
proof            (modus-ponens tm-668 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-54072.        (A -> (((B and C) -> D) -> ((B and C) -> C))), M:tm-668, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-54073
in-theory        54073
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (B -> (D -> (B and D)))))
theorem-size     13
proof            (modus-ponens tm-668 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-54073.        (A -> ((B -> C) -> (B -> (D -> (B and D))))), M:tm-668, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-54074
in-theory        54074
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (B -> (B or D))))
theorem-size     11
proof            (modus-ponens tm-668 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-54074.        (A -> ((B -> C) -> (B -> (B or D)))), M:tm-668, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-54075
in-theory        54075
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> (B -> (D or B))))
theorem-size     11
proof            (modus-ponens tm-668 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-54075.        (A -> ((B -> C) -> (B -> (D or B)))), M:tm-668, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-54076
in-theory        54076
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-665 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54076.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-665, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54077
in-theory        54077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> ((A -> B) -> (A -> C)))))
theorem-size     25
proof            (modus-ponens tm-623 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54077.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> ((A -> B) -> (A -> C))))), M:tm-623, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54078
in-theory        54078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-622 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54078.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-622, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54079
in-theory        54079
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (E -> (F or E)))
theorem-size     29
proof            (modus-ponens tm-609 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54079.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (E -> (F or E))), M:tm-609, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54080
in-theory        54080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-605 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54080.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-605, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54081
in-theory        54081
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C))))))
theorem-size     53
proof            (modus-ponens tm-595 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54081.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))))), M:tm-595, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54082
in-theory        54082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-550 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54082.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-550, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54083
in-theory        54083
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-540 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54083.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-540, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54084
in-theory        54084
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-530 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54084.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-530, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54085
in-theory        54085
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-520 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54085.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-520, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54086
in-theory        54086
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-510 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54086.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-510, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54087
in-theory        54087
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-500 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54087.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-500, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54088
in-theory        54088
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G)))))
theorem-size     39
proof            (modus-ponens tm-490 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54088.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G))))), M:tm-490, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54089
in-theory        54089
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-480 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54089.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-480, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54090
in-theory        54090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((A -> B) -> (A -> C))) or E))
theorem-size     25
proof            (modus-ponens tm-470 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54090.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((A -> B) -> (A -> C))) or E)), M:tm-470, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54091
in-theory        54091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-469 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54091.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-469, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54092
in-theory        54092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (E -> (E or F)))
theorem-size     29
proof            (modus-ponens tm-456 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54092.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (E -> (E or F))), M:tm-456, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54093
in-theory        54093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-453 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54093.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-453, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54094
in-theory        54094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C))))))
theorem-size     53
proof            (modus-ponens tm-443 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54094.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))))), M:tm-443, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54095
in-theory        54095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-409 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54095.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-409, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54096
in-theory        54096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-400 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54096.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-400, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54097
in-theory        54097
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-391 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54097.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-391, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54098
in-theory        54098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-382 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54098.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-382, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54099
in-theory        54099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G)))))
theorem-size     39
proof            (modus-ponens tm-373 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54099.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G))))), M:tm-373, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54100
in-theory        54100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-364 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54100.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-364, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54101
in-theory        54101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> ((A -> B) -> (A -> C))) and D)))
theorem-size     27
proof            (modus-ponens tm-355 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54101.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> ((A -> B) -> (A -> C))) and D))), M:tm-355, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54102
in-theory        54102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-354 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54102.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-354, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54103
in-theory        54103
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (E -> (F -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-341 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54103.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54104
in-theory        54104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-338 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54104.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E))))), M:tm-338, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54105
in-theory        54105
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-328 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54105.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> ((A -> B) -> (A -> C)))))), M:tm-328, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54106
in-theory        54106
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C))))))
theorem-size     55
proof            (modus-ponens tm-327 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54106.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))))), M:tm-327, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54107
in-theory        54107
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C))))))
theorem-size     53
proof            (modus-ponens tm-326 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54107.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))))), M:tm-326, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54108
in-theory        54108
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C))))))
theorem-size     53
proof            (modus-ponens tm-325 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54108.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))))), M:tm-325, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54109
in-theory        54109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-324 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54109.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))))), M:tm-324, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54110
in-theory        54110
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C))))))
theorem-size     53
proof            (modus-ponens tm-323 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54110.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))))), M:tm-323, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54111
in-theory        54111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((E and F) -> F))
theorem-size     29
proof            (modus-ponens tm-322 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54111.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((E and F) -> F)), M:tm-322, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54112
in-theory        54112
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((E and F) -> E))
theorem-size     29
proof            (modus-ponens tm-320 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54112.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((E and F) -> E)), M:tm-320, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54113
in-theory        54113
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-318 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54113.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54114
in-theory        54114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     51
proof            (modus-ponens tm-316 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54114.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54115
in-theory        54115
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (E -> (F -> E)))
theorem-size     29
proof            (modus-ponens tm-315 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54115.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (E -> (F -> E))), M:tm-315, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54116
in-theory        54116
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     63
proof            (modus-ponens tm-313 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54116.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54117
in-theory        54117
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((D -> ((A -> B) -> (A -> C))) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (D -> ((A -> B) -> (A -> C)))) -> E)))
theorem-size     61
proof            (modus-ponens tm-312 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54117.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((D -> ((A -> B) -> (A -> C))) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (D -> ((A -> B) -> (A -> C)))) -> E))), M:tm-312, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54118
in-theory        54118
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C))))))
theorem-size     49
proof            (modus-ponens tm-311 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54118.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))))), M:tm-311, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54119
in-theory        54119
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) or E))
theorem-size     49
proof            (modus-ponens tm-310 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54119.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) or E)), M:tm-310, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54120
in-theory        54120
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and E)))
theorem-size     51
proof            (modus-ponens tm-309 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54120.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and E))), M:tm-309, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54121
in-theory        54121
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-306 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54121.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> C))))), M:tm-306, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-54122
in-theory        54122
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C))))))
theorem-size     49
proof            (modus-ponens tm-305 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54122.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))))), M:tm-305, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54123
in-theory        54123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-303 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54123.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-303, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54124
in-theory        54124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-270 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54124.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-270, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54125
in-theory        54125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-239 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54125.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-239, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54126
in-theory        54126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G)))))
theorem-size     41
proof            (modus-ponens tm-210 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54126.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G))))), M:tm-210, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54127
in-theory        54127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-183 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54127.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-183, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54128
in-theory        54128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-157 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54128.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-157, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54129
in-theory        54129
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-147 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54129.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-147, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54130
in-theory        54130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-134 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54130.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-134, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54131
in-theory        54131
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-125 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54131.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-125, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54132
in-theory        54132
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (A -> B)) -> (D -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-114 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> Am Bm)) (D (-> Am Cm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54132.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (A -> B)) -> (D -> (A -> C)))), M:tm-114, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> Am Bm)) (D (-> Am Cm)))
================================================================
tm-name          tm-54133
in-theory        54133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G)))))
theorem-size     39
proof            (modus-ponens tm-113 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54133.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G))))), M:tm-113, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54134
in-theory        54134
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-105 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54134.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-105, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54135
in-theory        54135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E)))))
theorem-size     31
proof            (modus-ponens tm-95 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54135.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E))))), M:tm-95, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54136
in-theory        54136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> ((A -> B) -> (A -> C)))))
theorem-size     25
proof            (modus-ponens tm-84 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54136.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> ((A -> B) -> (A -> C))))), M:tm-84, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54137
in-theory        54137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-83 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54137.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-83, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54138
in-theory        54138
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> ((B -> C) -> (B -> D)))))
theorem-size     29
proof            (modus-ponens tm-76 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54138.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> ((B -> C) -> (B -> D))))), M:tm-76, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54139
in-theory        54139
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> ((A -> B) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-73 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54139.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-73, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54140
in-theory        54140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-69 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-1)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54140.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E))))), M:tm-69, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54141
in-theory        54141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-54 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54141.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-54, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54142
in-theory        54142
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-50 tm-668 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54142.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-50, m:tm-668, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54143
in-theory        54143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-49 tm-668 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54143.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-49, m:tm-668, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54144
in-theory        54144
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (E -> ((B -> C) -> (B -> D))))
theorem-size     39
proof            (modus-ponens tm-47 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54144.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (E -> ((B -> C) -> (B -> D)))), M:tm-47, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54145
in-theory        54145
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> ((A -> B) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-46 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54145.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> ((A -> B) -> (A -> C)))), M:tm-46, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54146
in-theory        54146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E)))))
theorem-size     29
proof            (modus-ponens tm-42 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54146.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E))))), M:tm-42, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54147
in-theory        54147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E)))))
theorem-size     29
proof            (modus-ponens tm-32 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54147.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E))))), M:tm-32, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54148
in-theory        54148
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> ((A -> B) -> (A -> C)))))
theorem-size     37
proof            (modus-ponens tm-24 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54148.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> ((A -> B) -> (A -> C))))), M:tm-24, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54149
in-theory        54149
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E)))))
theorem-size     31
proof            (modus-ponens tm-23 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54149.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E))))), M:tm-23, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54150
in-theory        54150
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E)))))
theorem-size     29
proof            (modus-ponens tm-22 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54150.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E))))), M:tm-22, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54151
in-theory        54151
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E)))))
theorem-size     29
proof            (modus-ponens tm-21 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54151.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E))))), M:tm-21, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54152
in-theory        54152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-20 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54152.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-20, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54153
in-theory        54153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E)))))
theorem-size     29
proof            (modus-ponens tm-19 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54153.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> ((C -> D) -> (C -> E))))), M:tm-19, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54154
in-theory        54154
times-derived    26
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-12 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54154.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))), M:tm-12, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54155
in-theory        54155
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     39
proof            (modus-ponens tm-9 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-9 tm-8 tm-2 tm-1)
proof-size       129
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54155.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54156
in-theory        54156
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> (B -> D))) -> E) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) or (A -> ((B -> C) -> (B -> D)))) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       129
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54156.        (((A -> ((B -> C) -> (B -> D))) -> E) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) or (A -> ((B -> C) -> (B -> D)))) -> E)), M:tm-8, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54157
in-theory        54157
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> ((B -> C) -> (B -> D)))))
theorem-size     25
proof            (modus-ponens tm-7 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-7 tm-8 tm-2 tm-1)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54157.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> ((B -> C) -> (B -> D))))), M:tm-7, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54158
in-theory        54158
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) or E)
theorem-size     25
proof            (modus-ponens tm-6 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-6 tm-8 tm-2 tm-1)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54158.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) or E), M:tm-6, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54159
in-theory        54159
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> ((B -> C) -> (B -> D)))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54159.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> ((B -> C) -> (B -> D)))) and A)), M:tm-5, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54160
in-theory        54160
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-2 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       129
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54160.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> C)))), M:tm-2, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-54161
in-theory        54161
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> ((B -> C) -> (B -> D)))))
theorem-size     25
proof            (modus-ponens tm-1 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-54161.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> ((B -> C) -> (B -> D))))), M:tm-1, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54162
in-theory        54162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> ((A -> B) -> (A -> B)))
theorem-size     13
proof            (modus-ponens tm-669 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-54162.        (((A -> B) -> A) -> ((A -> B) -> (A -> B))), M:tm-669, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-54163
in-theory        54163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> ((A -> B) -> ((A -> B) and A)))
theorem-size     15
proof            (modus-ponens tm-669 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-7 tm-5)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-54163.        (((A -> B) -> A) -> ((A -> B) -> ((A -> B) and A))), M:tm-669, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-54164
in-theory        54164
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> (A -> B)) -> (((A -> B) -> A) -> (((A -> B) or A) -> B)))
theorem-size     23
proof            (modus-ponens tm-669 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-7)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-54164.        ((((A -> B) -> A) -> (A -> B)) -> (((A -> B) -> A) -> (((A -> B) or A) -> B))), M:tm-669, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-54165
in-theory        54165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> ((A -> B) -> (C -> A)))
theorem-size     13
proof            (modus-ponens tm-669 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-54165.        (((A -> B) -> A) -> ((A -> B) -> (C -> A))), M:tm-669, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-54166
in-theory        54166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> D) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> D) -> ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-669 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-54166.        ((((A -> (B -> C)) -> D) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> D) -> ((A -> B) -> (A -> C)))), M:tm-669, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-54167
in-theory        54167
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> C) -> (A and B)) -> (((A and B) -> C) -> A))
theorem-size     17
proof            (modus-ponens tm-669 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-54167.        ((((A and B) -> C) -> (A and B)) -> (((A and B) -> C) -> A)), M:tm-669, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-54168
in-theory        54168
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> C) -> (A and B)) -> (((A and B) -> C) -> B))
theorem-size     17
proof            (modus-ponens tm-669 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-54168.        ((((A and B) -> C) -> (A and B)) -> (((A and B) -> C) -> B)), M:tm-669, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-54169
in-theory        54169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> ((A -> B) -> (C -> (A and C))))
theorem-size     15
proof            (modus-ponens tm-669 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-54169.        (((A -> B) -> A) -> ((A -> B) -> (C -> (A and C)))), M:tm-669, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-54170
in-theory        54170
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> ((A -> B) -> (A or C)))
theorem-size     13
proof            (modus-ponens tm-669 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-54170.        (((A -> B) -> A) -> ((A -> B) -> (A or C))), M:tm-669, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-54171
in-theory        54171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> ((A -> B) -> (C or A)))
theorem-size     13
proof            (modus-ponens tm-669 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-54171.        (((A -> B) -> A) -> ((A -> B) -> (C or A))), M:tm-669, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-54172
in-theory        54172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     39
proof            (modus-ponens tm-665 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54172.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-665, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54173
in-theory        54173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((A -> B) -> A) -> ((A -> B) -> C))))
theorem-size     27
proof            (modus-ponens tm-623 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54173.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((A -> B) -> A) -> ((A -> B) -> C)))), M:tm-623, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54174
in-theory        54174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-622 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54174.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-622, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54175
in-theory        54175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (D -> (E or D)))
theorem-size     31
proof            (modus-ponens tm-609 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54175.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (D -> (E or D))), M:tm-609, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54176
in-theory        54176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     35
proof            (modus-ponens tm-605 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54176.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-605, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54177
in-theory        54177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((D -> (E or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-595 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54177.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((D -> (E or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))))), M:tm-595, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54178
in-theory        54178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-550 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54178.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-550, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54179
in-theory        54179
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-540 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54179.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-540, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54180
in-theory        54180
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-530 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54180.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-530, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54181
in-theory        54181
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     35
proof            (modus-ponens tm-520 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54181.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-520, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54182
in-theory        54182
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-510 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54182.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-510, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54183
in-theory        54183
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-500 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54183.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-500, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54184
in-theory        54184
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G))))
theorem-size     41
proof            (modus-ponens tm-490 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54184.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G)))), M:tm-490, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54185
in-theory        54185
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-480 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54185.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-480, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54186
in-theory        54186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) -> A) -> ((A -> B) -> C)) or D))
theorem-size     27
proof            (modus-ponens tm-470 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54186.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) -> A) -> ((A -> B) -> C)) or D)), M:tm-470, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54187
in-theory        54187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-469 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54187.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-469, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54188
in-theory        54188
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (D -> (D or E)))
theorem-size     31
proof            (modus-ponens tm-456 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54188.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (D -> (D or E))), M:tm-456, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54189
in-theory        54189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     35
proof            (modus-ponens tm-453 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54189.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-453, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54190
in-theory        54190
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((D -> (D or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-443 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54190.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((D -> (D or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))))), M:tm-443, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54191
in-theory        54191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-409 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54191.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-409, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54192
in-theory        54192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     35
proof            (modus-ponens tm-400 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54192.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-400, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54193
in-theory        54193
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-391 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54193.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-391, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54194
in-theory        54194
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-382 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54194.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-382, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54195
in-theory        54195
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G))))
theorem-size     41
proof            (modus-ponens tm-373 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54195.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G)))), M:tm-373, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54196
in-theory        54196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-364 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54196.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-364, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54197
in-theory        54197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((A -> B) -> A) -> ((A -> B) -> C)) and D)))
theorem-size     29
proof            (modus-ponens tm-355 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54197.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((A -> B) -> A) -> ((A -> B) -> C)) and D))), M:tm-355, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54198
in-theory        54198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     35
proof            (modus-ponens tm-354 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54198.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-354, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54199
in-theory        54199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (D -> (E -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-341 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54199.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54200
in-theory        54200
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E))))
theorem-size     35
proof            (modus-ponens tm-338 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54200.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E)))), M:tm-338, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54201
in-theory        54201
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> B) -> A) -> ((A -> B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-328 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54201.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> B) -> A) -> ((A -> B) -> C))))), M:tm-328, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54202
in-theory        54202
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C)))))
theorem-size     59
proof            (modus-ponens tm-327 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54202.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))))), M:tm-327, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54203
in-theory        54203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((D and E) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-326 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54203.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((D and E) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))))), M:tm-326, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54204
in-theory        54204
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((D and E) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-325 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54204.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((D and E) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))))), M:tm-325, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54205
in-theory        54205
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C)))))
theorem-size     65
proof            (modus-ponens tm-324 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54205.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))))), M:tm-324, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54206
in-theory        54206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((D -> (E -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C)))))
theorem-size     57
proof            (modus-ponens tm-323 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54206.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((D -> (E -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))))), M:tm-323, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54207
in-theory        54207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((D and E) -> E))
theorem-size     31
proof            (modus-ponens tm-322 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54207.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((D and E) -> E)), M:tm-322, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54208
in-theory        54208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((D and E) -> D))
theorem-size     31
proof            (modus-ponens tm-320 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54208.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((D and E) -> D)), M:tm-320, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54209
in-theory        54209
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-318 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54209.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54210
in-theory        54210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-316 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54210.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54211
in-theory        54211
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (D -> (E -> D)))
theorem-size     31
proof            (modus-ponens tm-315 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54211.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (D -> (E -> D))), M:tm-315, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54212
in-theory        54212
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> B) -> A) -> ((A -> B) -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     67
proof            (modus-ponens tm-313 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54212.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> B) -> A) -> ((A -> B) -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54213
in-theory        54213
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((((A -> B) -> A) -> ((A -> B) -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((A -> B) -> A) -> ((A -> B) -> C))) -> D)))
theorem-size     67
proof            (modus-ponens tm-312 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54213.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((((A -> B) -> A) -> ((A -> B) -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((A -> B) -> A) -> ((A -> B) -> C))) -> D))), M:tm-312, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54214
in-theory        54214
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (D or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C)))))
theorem-size     53
proof            (modus-ponens tm-311 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54214.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (D or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))))), M:tm-311, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54215
in-theory        54215
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) or D))
theorem-size     53
proof            (modus-ponens tm-310 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54215.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) or D)), M:tm-310, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54216
in-theory        54216
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (D -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and D)))
theorem-size     55
proof            (modus-ponens tm-309 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54216.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (D -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and D))), M:tm-309, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54217
in-theory        54217
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> A)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> C))))
theorem-size     65
proof            (modus-ponens tm-306 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) Am)) (C (-> (-> Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54217.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> A)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> C)))), M:tm-306, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) Am)) (C (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-54218
in-theory        54218
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C)))))
theorem-size     53
proof            (modus-ponens tm-305 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54218.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))))), M:tm-305, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54219
in-theory        54219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     37
proof            (modus-ponens tm-303 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54219.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-303, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54220
in-theory        54220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     35
proof            (modus-ponens tm-270 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54220.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-270, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54221
in-theory        54221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     35
proof            (modus-ponens tm-239 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54221.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-239, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54222
in-theory        54222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G))))
theorem-size     43
proof            (modus-ponens tm-210 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54222.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G)))), M:tm-210, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54223
in-theory        54223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     35
proof            (modus-ponens tm-183 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54223.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-183, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54224
in-theory        54224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-157 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54224.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-157, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54225
in-theory        54225
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     41
proof            (modus-ponens tm-147 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54225.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-147, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54226
in-theory        54226
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-134 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54226.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-134, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54227
in-theory        54227
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     41
proof            (modus-ponens tm-125 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54227.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-125, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54228
in-theory        54228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) -> A) -> (A -> B)) -> (((A -> B) -> A) -> C)))
theorem-size     31
proof            (modus-ponens tm-114 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) Am)) (C (-> Am Bm)) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54228.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) -> A) -> (A -> B)) -> (((A -> B) -> A) -> C))), M:tm-114, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) Am)) (C (-> Am Bm)) (D Cm))
================================================================
tm-name          tm-54229
in-theory        54229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G))))
theorem-size     41
proof            (modus-ponens tm-113 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54229.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G)))), M:tm-113, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54230
in-theory        54230
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     45
proof            (modus-ponens tm-105 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54230.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-105, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54231
in-theory        54231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E))))
theorem-size     33
proof            (modus-ponens tm-95 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54231.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E)))), M:tm-95, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54232
in-theory        54232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> A) -> ((A -> B) -> C))))
theorem-size     27
proof            (modus-ponens tm-84 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54232.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> A) -> ((A -> B) -> C)))), M:tm-84, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54233
in-theory        54233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-83 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54233.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-83, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54234
in-theory        54234
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> B) -> ((B -> C) -> D))))
theorem-size     31
proof            (modus-ponens tm-76 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54234.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> B) -> ((B -> C) -> D)))), M:tm-76, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54235
in-theory        54235
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> A) -> ((A -> B) -> C)))
theorem-size     41
proof            (modus-ponens tm-73 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54235.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-73, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54236
in-theory        54236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E))))
theorem-size     37
proof            (modus-ponens tm-69 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54236.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E)))), M:tm-69, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54237
in-theory        54237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     39
proof            (modus-ponens tm-54 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54237.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-54, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54238
in-theory        54238
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> A) -> ((A -> B) -> C)))
theorem-size     33
proof            (modus-ponens tm-50 tm-669 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-8 tm-7 tm-2)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54238.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-50, m:tm-669, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54239
in-theory        54239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> A) -> ((A -> B) -> C)))
theorem-size     31
proof            (modus-ponens tm-49 tm-669 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-8 tm-6 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54239.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-49, m:tm-669, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54240
in-theory        54240
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((B -> C) -> B) -> ((B -> C) -> D)))
theorem-size     41
proof            (modus-ponens tm-47 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54240.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((B -> C) -> B) -> ((B -> C) -> D))), M:tm-47, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54241
in-theory        54241
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> A) -> ((A -> B) -> C)))
theorem-size     41
proof            (modus-ponens tm-46 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54241.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-46, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54242
in-theory        54242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E))))
theorem-size     31
proof            (modus-ponens tm-42 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54242.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E)))), M:tm-42, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54243
in-theory        54243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E))))
theorem-size     31
proof            (modus-ponens tm-32 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54243.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E)))), M:tm-32, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54244
in-theory        54244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> B) -> A) -> ((A -> B) -> C))))
theorem-size     39
proof            (modus-ponens tm-24 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54244.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> B) -> A) -> ((A -> B) -> C)))), M:tm-24, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54245
in-theory        54245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E))))
theorem-size     33
proof            (modus-ponens tm-23 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54245.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E)))), M:tm-23, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54246
in-theory        54246
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E))))
theorem-size     31
proof            (modus-ponens tm-22 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54246.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E)))), M:tm-22, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54247
in-theory        54247
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E))))
theorem-size     31
proof            (modus-ponens tm-21 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54247.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E)))), M:tm-21, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54248
in-theory        54248
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     39
proof            (modus-ponens tm-20 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54248.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-20, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54249
in-theory        54249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E))))
theorem-size     31
proof            (modus-ponens tm-19 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54249.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> C) -> ((C -> D) -> E)))), M:tm-19, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54250
in-theory        54250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> B) -> A) -> ((A -> B) -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-9 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-9 tm-8 tm-2)
proof-size       141
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54250.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> B) -> A) -> ((A -> B) -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54251
in-theory        54251
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> A) -> ((A -> B) -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((A -> B) -> A) -> ((A -> B) -> C))) -> D))
theorem-size     41
proof            (modus-ponens tm-8 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       143
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54251.        (((((A -> B) -> A) -> ((A -> B) -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((A -> B) -> A) -> ((A -> B) -> C))) -> D)), M:tm-8, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-54252
in-theory        54252
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> B) -> ((B -> C) -> D))))
theorem-size     27
proof            (modus-ponens tm-7 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-7 tm-8 tm-2)
proof-size       121
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54252.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> B) -> ((B -> C) -> D)))), M:tm-7, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54253
in-theory        54253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) or D)
theorem-size     27
proof            (modus-ponens tm-6 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-6 tm-8 tm-2)
proof-size       121
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54253.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) or D), M:tm-6, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54254
in-theory        54254
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> B) -> ((B -> C) -> D))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       125
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54254.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> B) -> ((B -> C) -> D))) and A)), M:tm-5, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54255
in-theory        54255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> A)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> C)))
theorem-size     39
proof            (modus-ponens tm-2 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) Am)) (C (-> (-> Am Bm) Cm))))
axioms-used      (tm-2 tm-8)
proof-size       141
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54255.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> A)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> C))), M:tm-2, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) Am)) (C (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-54256
in-theory        54256
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> B) -> ((B -> C) -> D))))
theorem-size     27
proof            (modus-ponens tm-1 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       121
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-54256.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> B) -> ((B -> C) -> D)))), M:tm-1, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-54257
in-theory        54257
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> (B -> C))) and A))
theorem-size     13
proof            (modus-ponens tm-670 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-54257.        (A -> (((B -> C) -> (B -> (B -> C))) and A)), M:tm-670, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-54258
in-theory        54258
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> ((B -> C) and B))) and A))
theorem-size     15
proof            (modus-ponens tm-670 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-54258.        (A -> (((B -> C) -> (B -> ((B -> C) and B))) and A)), M:tm-670, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-54259
in-theory        54259
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> B) -> ((B -> C) -> (((B -> C) or B) -> C))) and A))
theorem-size     21
proof            (modus-ponens tm-670 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-54259.        (A -> ((((B -> C) -> B) -> ((B -> C) -> (((B -> C) or B) -> C))) and A)), M:tm-670, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-54260
in-theory        54260
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> (D -> B))) and A))
theorem-size     13
proof            (modus-ponens tm-670 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-54260.        (A -> (((B -> C) -> (B -> (D -> B))) and A)), M:tm-670, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-54261
in-theory        54261
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> E) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and A))
theorem-size     25
proof            (modus-ponens tm-670 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-54261.        (A -> ((((B -> (C -> D)) -> E) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and A)), M:tm-670, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-54262
in-theory        54262
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> D) -> ((B and C) -> B)) and A))
theorem-size     15
proof            (modus-ponens tm-670 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-54262.        (A -> ((((B and C) -> D) -> ((B and C) -> B)) and A)), M:tm-670, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-54263
in-theory        54263
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> D) -> ((B and C) -> C)) and A))
theorem-size     15
proof            (modus-ponens tm-670 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-54263.        (A -> ((((B and C) -> D) -> ((B and C) -> C)) and A)), M:tm-670, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-54264
in-theory        54264
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> (D -> (B and D)))) and A))
theorem-size     15
proof            (modus-ponens tm-670 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-54264.        (A -> (((B -> C) -> (B -> (D -> (B and D)))) and A)), M:tm-670, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-54265
in-theory        54265
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> (B or D))) and A))
theorem-size     13
proof            (modus-ponens tm-670 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-54265.        (A -> (((B -> C) -> (B -> (B or D))) and A)), M:tm-670, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-54266
in-theory        54266
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (B -> (D or B))) and A))
theorem-size     13
proof            (modus-ponens tm-670 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-54266.        (A -> (((B -> C) -> (B -> (D or B))) and A)), M:tm-670, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-54267
in-theory        54267
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     39
proof            (modus-ponens tm-665 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54267.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-665, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54268
in-theory        54268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (((A -> B) -> (A -> C)) and E))))
theorem-size     27
proof            (modus-ponens tm-623 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54268.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (((A -> B) -> (A -> C)) and E)))), M:tm-623, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54269
in-theory        54269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-622 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54269.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-622, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54270
in-theory        54270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D or ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     37
proof            (modus-ponens tm-617 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (and (-> (-> Am Bm) (-> Am Cm)) (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54270.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-617, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (and (-> (-> Am Bm) (-> Am Cm)) (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
================================================================
tm-name          tm-54271
in-theory        54271
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (E -> (F or E)))
theorem-size     31
proof            (modus-ponens tm-609 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54271.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (E -> (F or E))), M:tm-609, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54272
in-theory        54272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-605 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54272.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-605, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54273
in-theory        54273
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D)))))
theorem-size     57
proof            (modus-ponens tm-595 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54273.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))))), M:tm-595, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54274
in-theory        54274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-550 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54274.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-550, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54275
in-theory        54275
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-540 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54275.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-540, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54276
in-theory        54276
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-530 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54276.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-530, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54277
in-theory        54277
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-520 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54277.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-520, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54278
in-theory        54278
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-510 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54278.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-510, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54279
in-theory        54279
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-500 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54279.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-500, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54280
in-theory        54280
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H))))
theorem-size     41
proof            (modus-ponens tm-490 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54280.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H)))), M:tm-490, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54281
in-theory        54281
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-480 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54281.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-480, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54282
in-theory        54282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((A -> B) -> (A -> C)) and D)) or E))
theorem-size     27
proof            (modus-ponens tm-470 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54282.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((A -> B) -> (A -> C)) and D)) or E)), M:tm-470, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54283
in-theory        54283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-469 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54283.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-469, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54284
in-theory        54284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D)))
theorem-size     37
proof            (modus-ponens tm-464 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C (and (-> (-> Am Bm) (-> Am Cm)) (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54284.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D))), M:tm-464, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C (and (-> (-> Am Bm) (-> Am Cm)) (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))))
================================================================
tm-name          tm-54285
in-theory        54285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (E -> (E or F)))
theorem-size     31
proof            (modus-ponens tm-456 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54285.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (E -> (E or F))), M:tm-456, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54286
in-theory        54286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-453 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54286.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-453, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54287
in-theory        54287
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D)))))
theorem-size     57
proof            (modus-ponens tm-443 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54287.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))))), M:tm-443, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54288
in-theory        54288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-409 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54288.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-409, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54289
in-theory        54289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-400 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54289.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-400, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54290
in-theory        54290
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-391 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54290.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-391, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54291
in-theory        54291
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-382 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54291.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-382, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54292
in-theory        54292
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H))))
theorem-size     41
proof            (modus-ponens tm-373 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54292.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H)))), M:tm-373, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54293
in-theory        54293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-364 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54293.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-364, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54294
in-theory        54294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (((A -> B) -> (A -> C)) and E)) and D)))
theorem-size     29
proof            (modus-ponens tm-355 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54294.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (((A -> B) -> (A -> C)) and E)) and D))), M:tm-355, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54295
in-theory        54295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-354 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54295.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-354, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54296
in-theory        54296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D))))
theorem-size     39
proof            (modus-ponens tm-349 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))) (C (and (-> (-> Am Bm) (-> Am Cm)) (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54296.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D)))), M:tm-349, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))) (C (and (-> (-> Am Bm) (-> Am Cm)) (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)))))
================================================================
tm-name          tm-54297
in-theory        54297
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (E -> (F -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-341 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54297.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54298
in-theory        54298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F))))
theorem-size     35
proof            (modus-ponens tm-338 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54298.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F)))), M:tm-338, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54299
in-theory        54299
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (((A -> B) -> (A -> C)) and D)))))
theorem-size     65
proof            (modus-ponens tm-328 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54299.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (((A -> B) -> (A -> C)) and D))))), M:tm-328, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54300
in-theory        54300
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D)))))
theorem-size     59
proof            (modus-ponens tm-327 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54300.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))))), M:tm-327, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54301
in-theory        54301
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D)))))
theorem-size     57
proof            (modus-ponens tm-326 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54301.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))))), M:tm-326, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54302
in-theory        54302
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D)))))
theorem-size     57
proof            (modus-ponens tm-325 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54302.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))))), M:tm-325, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54303
in-theory        54303
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D)))))
theorem-size     65
proof            (modus-ponens tm-324 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54303.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))))), M:tm-324, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54304
in-theory        54304
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D)))))
theorem-size     57
proof            (modus-ponens tm-323 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54304.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))))), M:tm-323, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54305
in-theory        54305
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((E and F) -> F))
theorem-size     31
proof            (modus-ponens tm-322 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54305.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((E and F) -> F)), M:tm-322, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54306
in-theory        54306
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((E and F) -> E))
theorem-size     31
proof            (modus-ponens tm-320 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54306.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((E and F) -> E)), M:tm-320, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54307
in-theory        54307
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-318 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54307.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54308
in-theory        54308
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-316 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54308.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54309
in-theory        54309
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (E -> (F -> E)))
theorem-size     31
proof            (modus-ponens tm-315 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54309.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (E -> (F -> E))), M:tm-315, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54310
in-theory        54310
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (((A -> B) -> (A -> C)) and D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     67
proof            (modus-ponens tm-313 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54310.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (((A -> B) -> (A -> C)) and D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54311
in-theory        54311
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((D -> (((A -> B) -> (A -> C)) and D)) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (D -> (((A -> B) -> (A -> C)) and D))) -> E)))
theorem-size     67
proof            (modus-ponens tm-312 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54311.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((D -> (((A -> B) -> (A -> C)) and D)) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (D -> (((A -> B) -> (A -> C)) and D))) -> E))), M:tm-312, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54312
in-theory        54312
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D)))))
theorem-size     53
proof            (modus-ponens tm-311 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54312.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))))), M:tm-311, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54313
in-theory        54313
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) or E))
theorem-size     53
proof            (modus-ponens tm-310 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54313.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) or E)), M:tm-310, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54314
in-theory        54314
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and E)))
theorem-size     55
proof            (modus-ponens tm-309 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54314.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and E))), M:tm-309, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54315
in-theory        54315
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and D))))
theorem-size     65
proof            (modus-ponens tm-306 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54315.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and D)))), M:tm-306, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (and (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54316
in-theory        54316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D)))))
theorem-size     53
proof            (modus-ponens tm-305 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54316.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))))), M:tm-305, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54317
in-theory        54317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     37
proof            (modus-ponens tm-303 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54317.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-303, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54318
in-theory        54318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-270 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54318.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-270, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54319
in-theory        54319
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-239 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54319.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-239, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54320
in-theory        54320
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H))))
theorem-size     43
proof            (modus-ponens tm-210 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54320.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H)))), M:tm-210, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54321
in-theory        54321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     35
proof            (modus-ponens tm-183 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54321.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-183, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54322
in-theory        54322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-157 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54322.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-157, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54323
in-theory        54323
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     41
proof            (modus-ponens tm-147 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54323.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-147, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54324
in-theory        54324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-134 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54324.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-134, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54325
in-theory        54325
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     41
proof            (modus-ponens tm-125 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54325.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-125, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54326
in-theory        54326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H))))
theorem-size     41
proof            (modus-ponens tm-113 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54326.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H)))), M:tm-113, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54327
in-theory        54327
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     45
proof            (modus-ponens tm-105 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54327.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-105, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54328
in-theory        54328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     35
proof            (modus-ponens tm-99 tm-670 ((Dm (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Am Bm) (-> Am Cm)) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54328.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-99, m:tm-670, u:((Dm (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Am Bm) (-> Am Cm)) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54329
in-theory        54329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     37
proof            (modus-ponens tm-98 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (and (-> (-> Am Bm) (-> Am Cm)) (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54329.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-98, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (and (-> (-> Am Bm) (-> Am Cm)) (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
================================================================
tm-name          tm-54330
in-theory        54330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F))))
theorem-size     33
proof            (modus-ponens tm-95 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54330.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F)))), M:tm-95, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54331
in-theory        54331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (((A -> B) -> (A -> C)) and E))))
theorem-size     27
proof            (modus-ponens tm-84 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54331.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (((A -> B) -> (A -> C)) and E)))), M:tm-84, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54332
in-theory        54332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     33
proof            (modus-ponens tm-83 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54332.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-83, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54333
in-theory        54333
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (((B -> C) -> (B -> D)) and E))))
theorem-size     31
proof            (modus-ponens tm-76 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54333.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (((B -> C) -> (B -> D)) and E)))), M:tm-76, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54334
in-theory        54334
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (((A -> B) -> (A -> C)) and D)))
theorem-size     41
proof            (modus-ponens tm-73 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54334.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-73, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54335
in-theory        54335
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F))))
theorem-size     37
proof            (modus-ponens tm-69 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54335.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F)))), M:tm-69, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54336
in-theory        54336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     39
proof            (modus-ponens tm-54 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54336.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-54, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54337
in-theory        54337
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (((A -> B) -> (A -> C)) and D)))
theorem-size     33
proof            (modus-ponens tm-50 tm-670 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54337.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-50, m:tm-670, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54338
in-theory        54338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (((A -> B) -> (A -> C)) and D)))
theorem-size     31
proof            (modus-ponens tm-49 tm-670 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54338.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-49, m:tm-670, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54339
in-theory        54339
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (E -> (((B -> C) -> (B -> D)) and E)))
theorem-size     41
proof            (modus-ponens tm-47 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54339.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (E -> (((B -> C) -> (B -> D)) and E))), M:tm-47, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54340
in-theory        54340
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> (((A -> B) -> (A -> C)) and E)))
theorem-size     41
proof            (modus-ponens tm-46 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54340.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> (((A -> B) -> (A -> C)) and E))), M:tm-46, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54341
in-theory        54341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F))))
theorem-size     31
proof            (modus-ponens tm-42 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54341.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F)))), M:tm-42, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54342
in-theory        54342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F))))
theorem-size     31
proof            (modus-ponens tm-32 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54342.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F)))), M:tm-32, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54343
in-theory        54343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (((A -> B) -> (A -> C)) and D))))
theorem-size     39
proof            (modus-ponens tm-24 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54343.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (((A -> B) -> (A -> C)) and D)))), M:tm-24, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54344
in-theory        54344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F))))
theorem-size     33
proof            (modus-ponens tm-23 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54344.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F)))), M:tm-23, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54345
in-theory        54345
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F))))
theorem-size     31
proof            (modus-ponens tm-22 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54345.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F)))), M:tm-22, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54346
in-theory        54346
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F))))
theorem-size     31
proof            (modus-ponens tm-21 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54346.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F)))), M:tm-21, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54347
in-theory        54347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     39
proof            (modus-ponens tm-20 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54347.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-20, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54348
in-theory        54348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F))))
theorem-size     31
proof            (modus-ponens tm-19 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54348.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (((C -> D) -> (C -> E)) and F)))), M:tm-19, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54349
in-theory        54349
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (((A -> B) -> (A -> C)) and D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-9 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-9 tm-8 tm-2 tm-5)
proof-size       135
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54349.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (((A -> B) -> (A -> C)) and D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54350
in-theory        54350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((B -> C) -> (B -> D)) and A)) -> E) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) or (A -> (((B -> C) -> (B -> D)) and A))) -> E))
theorem-size     41
proof            (modus-ponens tm-8 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       137
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54350.        (((A -> (((B -> C) -> (B -> D)) and A)) -> E) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) or (A -> (((B -> C) -> (B -> D)) and A))) -> E)), M:tm-8, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54351
in-theory        54351
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (((B -> C) -> (B -> D)) and E))))
theorem-size     27
proof            (modus-ponens tm-7 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-7 tm-8 tm-2 tm-5)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54351.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (((B -> C) -> (B -> D)) and E)))), M:tm-7, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54352
in-theory        54352
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) or E)
theorem-size     27
proof            (modus-ponens tm-6 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-6 tm-8 tm-2 tm-5)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54352.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) or E), M:tm-6, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54353
in-theory        54353
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (((B -> C) -> (B -> D)) and E))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       119
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54353.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (((B -> C) -> (B -> D)) and E))) and A)), M:tm-5, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54354
in-theory        54354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and D)))
theorem-size     39
proof            (modus-ponens tm-2 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       135
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54354.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and D))), M:tm-2, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (and (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54355
in-theory        54355
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (((B -> C) -> (B -> D)) and E))))
theorem-size     27
proof            (modus-ponens tm-1 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-1 tm-8 tm-2 tm-5)
proof-size       115
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-54355.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (((B -> C) -> (B -> D)) and E)))), M:tm-1, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54356
in-theory        54356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A -> B))) or C)
theorem-size     11
proof            (modus-ponens tm-671 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-6 tm-7 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-54356.        (((A -> B) -> (A -> (A -> B))) or C), M:tm-671, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-54357
in-theory        54357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> ((A -> B) and A))) or C)
theorem-size     13
proof            (modus-ponens tm-671 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-6 tm-7 tm-5)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-54357.        (((A -> B) -> (A -> ((A -> B) and A))) or C), M:tm-671, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-54358
in-theory        54358
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (((A -> B) or A) -> B))) or C)
theorem-size     19
proof            (modus-ponens tm-671 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-6 tm-7)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-54358.        ((((A -> B) -> A) -> ((A -> B) -> (((A -> B) or A) -> B))) or C), M:tm-671, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-54359
in-theory        54359
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> A))) or D)
theorem-size     11
proof            (modus-ponens tm-671 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-6 tm-7 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-54359.        (((A -> B) -> (A -> (C -> A))) or D), M:tm-671, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-54360
in-theory        54360
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> D) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) or E)
theorem-size     23
proof            (modus-ponens tm-671 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-6 tm-7 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-54360.        ((((A -> (B -> C)) -> D) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) or E), M:tm-671, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-54361
in-theory        54361
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> C) -> ((A and B) -> A)) or D)
theorem-size     13
proof            (modus-ponens tm-671 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-6 tm-7 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-54361.        ((((A and B) -> C) -> ((A and B) -> A)) or D), M:tm-671, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-54362
in-theory        54362
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> C) -> ((A and B) -> B)) or D)
theorem-size     13
proof            (modus-ponens tm-671 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-6 tm-7 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-54362.        ((((A and B) -> C) -> ((A and B) -> B)) or D), M:tm-671, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-54363
in-theory        54363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (A and C)))) or D)
theorem-size     13
proof            (modus-ponens tm-671 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-6 tm-7 tm-1 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-54363.        (((A -> B) -> (A -> (C -> (A and C)))) or D), M:tm-671, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-54364
in-theory        54364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A or C))) or D)
theorem-size     11
proof            (modus-ponens tm-671 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-6 tm-7 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-54364.        (((A -> B) -> (A -> (A or C))) or D), M:tm-671, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-54365
in-theory        54365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or A))) or D)
theorem-size     11
proof            (modus-ponens tm-671 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-6 tm-7 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-54365.        (((A -> B) -> (A -> (C or A))) or D), M:tm-671, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-54366
in-theory        54366
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     37
proof            (modus-ponens tm-665 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54366.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-665, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54367
in-theory        54367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((A -> B) -> (A -> C)) or E)))
theorem-size     25
proof            (modus-ponens tm-623 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54367.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((A -> B) -> (A -> C)) or E))), M:tm-623, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54368
in-theory        54368
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-622 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54368.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-622, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54369
in-theory        54369
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (E -> (F or E)))
theorem-size     29
proof            (modus-ponens tm-609 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54369.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (E -> (F or E))), M:tm-609, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54370
in-theory        54370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-605 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54370.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-605, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54371
in-theory        54371
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D))))
theorem-size     53
proof            (modus-ponens tm-595 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54371.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)))), M:tm-595, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54372
in-theory        54372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-550 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54372.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-550, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54373
in-theory        54373
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-540 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54373.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-540, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54374
in-theory        54374
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-530 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54374.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-530, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54375
in-theory        54375
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-520 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54375.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-520, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54376
in-theory        54376
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-510 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54376.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-510, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54377
in-theory        54377
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-500 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54377.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-500, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54378
in-theory        54378
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H)))
theorem-size     39
proof            (modus-ponens tm-490 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54378.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H))), M:tm-490, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54379
in-theory        54379
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-480 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54379.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-480, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54380
in-theory        54380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) -> (A -> C)) or D) or E))
theorem-size     25
proof            (modus-ponens tm-470 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54380.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) -> (A -> C)) or D) or E)), M:tm-470, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54381
in-theory        54381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-469 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54381.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-469, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54382
in-theory        54382
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (E -> (E or F)))
theorem-size     29
proof            (modus-ponens tm-456 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54382.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (E -> (E or F))), M:tm-456, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54383
in-theory        54383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-453 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54383.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-453, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54384
in-theory        54384
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D))))
theorem-size     53
proof            (modus-ponens tm-443 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54384.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)))), M:tm-443, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54385
in-theory        54385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-409 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54385.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-409, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54386
in-theory        54386
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-400 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54386.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-400, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54387
in-theory        54387
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-391 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54387.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-391, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54388
in-theory        54388
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-382 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54388.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-382, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54389
in-theory        54389
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H)))
theorem-size     39
proof            (modus-ponens tm-373 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54389.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H))), M:tm-373, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54390
in-theory        54390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-364 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54390.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-364, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54391
in-theory        54391
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((A -> B) -> (A -> C)) or E) and D)))
theorem-size     27
proof            (modus-ponens tm-355 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54391.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((A -> B) -> (A -> C)) or E) and D))), M:tm-355, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54392
in-theory        54392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-354 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54392.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-354, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54393
in-theory        54393
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (E -> (F -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-341 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54393.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54394
in-theory        54394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F)))
theorem-size     33
proof            (modus-ponens tm-338 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54394.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F))), M:tm-338, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54395
in-theory        54395
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> B) -> (A -> C)) or D))))
theorem-size     61
proof            (modus-ponens tm-328 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54395.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> B) -> (A -> C)) or D)))), M:tm-328, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54396
in-theory        54396
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D))))
theorem-size     55
proof            (modus-ponens tm-327 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54396.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)))), M:tm-327, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54397
in-theory        54397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D))))
theorem-size     53
proof            (modus-ponens tm-326 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-6)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54397.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)))), M:tm-326, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54398
in-theory        54398
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D))))
theorem-size     53
proof            (modus-ponens tm-325 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-6)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54398.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)))), M:tm-325, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54399
in-theory        54399
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D))))
theorem-size     61
proof            (modus-ponens tm-324 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54399.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)))), M:tm-324, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54400
in-theory        54400
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D))))
theorem-size     53
proof            (modus-ponens tm-323 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54400.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)))), M:tm-323, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54401
in-theory        54401
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((E and F) -> F))
theorem-size     29
proof            (modus-ponens tm-322 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54401.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((E and F) -> F)), M:tm-322, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54402
in-theory        54402
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((E and F) -> E))
theorem-size     29
proof            (modus-ponens tm-320 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54402.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((E and F) -> E)), M:tm-320, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54403
in-theory        54403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-318 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54403.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54404
in-theory        54404
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     51
proof            (modus-ponens tm-316 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54404.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54405
in-theory        54405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (E -> (F -> E)))
theorem-size     29
proof            (modus-ponens tm-315 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54405.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (E -> (F -> E))), M:tm-315, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54406
in-theory        54406
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> B) -> (A -> C)) or D))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     63
proof            (modus-ponens tm-313 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-6)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54406.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> B) -> (A -> C)) or D))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54407
in-theory        54407
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((((A -> B) -> (A -> C)) or D) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((A -> B) -> (A -> C)) or D)) -> E)))
theorem-size     61
proof            (modus-ponens tm-312 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54407.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((((A -> B) -> (A -> C)) or D) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((A -> B) -> (A -> C)) or D)) -> E))), M:tm-312, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54408
in-theory        54408
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D))))
theorem-size     49
proof            (modus-ponens tm-311 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54408.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)))), M:tm-311, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54409
in-theory        54409
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) or E))
theorem-size     49
proof            (modus-ponens tm-310 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54409.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) or E)), M:tm-310, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54410
in-theory        54410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and E)))
theorem-size     51
proof            (modus-ponens tm-309 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54410.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and E))), M:tm-309, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54411
in-theory        54411
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D))))
theorem-size     49
proof            (modus-ponens tm-305 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54411.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)))), M:tm-305, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54412
in-theory        54412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     35
proof            (modus-ponens tm-303 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54412.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-303, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54413
in-theory        54413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-270 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54413.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-270, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54414
in-theory        54414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-239 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54414.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-239, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54415
in-theory        54415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H)))
theorem-size     41
proof            (modus-ponens tm-210 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54415.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H))), M:tm-210, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54416
in-theory        54416
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     33
proof            (modus-ponens tm-183 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54416.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-183, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54417
in-theory        54417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-157 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54417.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-157, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54418
in-theory        54418
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     39
proof            (modus-ponens tm-147 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54418.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-147, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54419
in-theory        54419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-134 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54419.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-134, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54420
in-theory        54420
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     39
proof            (modus-ponens tm-125 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54420.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-125, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54421
in-theory        54421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H)))
theorem-size     39
proof            (modus-ponens tm-113 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54421.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H))), M:tm-113, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54422
in-theory        54422
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     43
proof            (modus-ponens tm-105 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54422.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-105, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54423
in-theory        54423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F)))
theorem-size     31
proof            (modus-ponens tm-95 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54423.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F))), M:tm-95, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54424
in-theory        54424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) or E)))
theorem-size     25
proof            (modus-ponens tm-84 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54424.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) or E))), M:tm-84, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54425
in-theory        54425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     31
proof            (modus-ponens tm-83 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54425.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-83, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54426
in-theory        54426
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (B -> D)) or E)))
theorem-size     29
proof            (modus-ponens tm-76 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-6)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54426.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (B -> D)) or E))), M:tm-76, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54427
in-theory        54427
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) or D))
theorem-size     39
proof            (modus-ponens tm-73 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-2 tm-6)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54427.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) or D)), M:tm-73, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54428
in-theory        54428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F)))
theorem-size     35
proof            (modus-ponens tm-69 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-6)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54428.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F))), M:tm-69, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54429
in-theory        54429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     37
proof            (modus-ponens tm-54 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54429.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-54, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54430
in-theory        54430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) or D))
theorem-size     31
proof            (modus-ponens tm-50 tm-671 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-8 tm-7 tm-2 tm-6)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54430.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) or D)), M:tm-50, m:tm-671, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54431
in-theory        54431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) or D))
theorem-size     29
proof            (modus-ponens tm-49 tm-671 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-8 tm-6 tm-2)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54431.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) or D)), M:tm-49, m:tm-671, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54432
in-theory        54432
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((B -> C) -> (B -> D)) or E))
theorem-size     39
proof            (modus-ponens tm-47 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-2 tm-6)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54432.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((B -> C) -> (B -> D)) or E)), M:tm-47, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54433
in-theory        54433
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) or E))
theorem-size     39
proof            (modus-ponens tm-46 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-2 tm-6)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54433.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) or E)), M:tm-46, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54434
in-theory        54434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F)))
theorem-size     29
proof            (modus-ponens tm-42 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-6)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54434.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F))), M:tm-42, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54435
in-theory        54435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F)))
theorem-size     29
proof            (modus-ponens tm-32 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54435.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F))), M:tm-32, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54436
in-theory        54436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> B) -> (A -> C)) or D)))
theorem-size     37
proof            (modus-ponens tm-24 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54436.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> B) -> (A -> C)) or D))), M:tm-24, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54437
in-theory        54437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F)))
theorem-size     31
proof            (modus-ponens tm-23 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54437.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F))), M:tm-23, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54438
in-theory        54438
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F)))
theorem-size     29
proof            (modus-ponens tm-22 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-6)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54438.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F))), M:tm-22, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54439
in-theory        54439
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F)))
theorem-size     29
proof            (modus-ponens tm-21 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-6)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54439.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F))), M:tm-21, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54440
in-theory        54440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     37
proof            (modus-ponens tm-20 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54440.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-20, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54441
in-theory        54441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F)))
theorem-size     29
proof            (modus-ponens tm-19 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-6)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54441.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (C -> E)) or F))), M:tm-19, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54442
in-theory        54442
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> B) -> (A -> C)) or D))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     39
proof            (modus-ponens tm-9 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-2 tm-6)
proof-size       129
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54442.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> B) -> (A -> C)) or D))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54443
in-theory        54443
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) or D) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((A -> B) -> (A -> C)) or D)) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-8 tm-2 tm-6)
proof-size       129
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54443.        (((((A -> B) -> (A -> C)) or D) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((A -> B) -> (A -> C)) or D)) -> E)), M:tm-8, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54444
in-theory        54444
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (B -> D)) or E)))
theorem-size     25
proof            (modus-ponens tm-7 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-2 tm-6)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54444.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (B -> D)) or E))), M:tm-7, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54445
in-theory        54445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) or E)
theorem-size     25
proof            (modus-ponens tm-6 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-2)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54445.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) or E), M:tm-6, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54446
in-theory        54446
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (B -> D)) or E)) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54446.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (B -> D)) or E)) and A)), M:tm-5, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54447
in-theory        54447
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (B -> D)) or E)))
theorem-size     25
proof            (modus-ponens tm-1 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-2 tm-6)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-54447.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (B -> D)) or E))), M:tm-1, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54448
in-theory        54448
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (B -> (B -> C))))
theorem-size     11
proof            (modus-ponens tm-672 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-54448.        (A or ((B -> C) -> (B -> (B -> C)))), M:tm-672, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-54449
in-theory        54449
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (B -> ((B -> C) and B))))
theorem-size     13
proof            (modus-ponens tm-672 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-7 tm-5)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-54449.        (A or ((B -> C) -> (B -> ((B -> C) and B)))), M:tm-672, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-54450
in-theory        54450
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> B) -> ((B -> C) -> (((B -> C) or B) -> C))))
theorem-size     19
proof            (modus-ponens tm-672 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-7)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-54450.        (A or (((B -> C) -> B) -> ((B -> C) -> (((B -> C) or B) -> C)))), M:tm-672, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-54451
in-theory        54451
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (B -> (D -> B))))
theorem-size     11
proof            (modus-ponens tm-672 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-54451.        (A or ((B -> C) -> (B -> (D -> B)))), M:tm-672, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-54452
in-theory        54452
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> E) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     23
proof            (modus-ponens tm-672 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-54452.        (A or (((B -> (C -> D)) -> E) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-672, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-54453
in-theory        54453
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> D) -> ((B and C) -> B)))
theorem-size     13
proof            (modus-ponens tm-672 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-54453.        (A or (((B and C) -> D) -> ((B and C) -> B))), M:tm-672, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-54454
in-theory        54454
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> D) -> ((B and C) -> C)))
theorem-size     13
proof            (modus-ponens tm-672 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-54454.        (A or (((B and C) -> D) -> ((B and C) -> C))), M:tm-672, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-54455
in-theory        54455
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (B -> (D -> (B and D)))))
theorem-size     13
proof            (modus-ponens tm-672 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-54455.        (A or ((B -> C) -> (B -> (D -> (B and D))))), M:tm-672, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-54456
in-theory        54456
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (B -> (B or D))))
theorem-size     11
proof            (modus-ponens tm-672 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-54456.        (A or ((B -> C) -> (B -> (B or D)))), M:tm-672, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-54457
in-theory        54457
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> C) -> (B -> (D or B))))
theorem-size     11
proof            (modus-ponens tm-672 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-54457.        (A or ((B -> C) -> (B -> (D or B)))), M:tm-672, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-54458
in-theory        54458
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-665 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54458.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-665, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54459
in-theory        54459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E or ((A -> B) -> (A -> C)))))
theorem-size     25
proof            (modus-ponens tm-623 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54459.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E or ((A -> B) -> (A -> C))))), M:tm-623, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54460
in-theory        54460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-622 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54460.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-622, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54461
in-theory        54461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (E -> (F or E)))
theorem-size     29
proof            (modus-ponens tm-609 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54461.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (E -> (F or E))), M:tm-609, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54462
in-theory        54462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-605 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54462.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-605, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54463
in-theory        54463
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C))))))
theorem-size     53
proof            (modus-ponens tm-595 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54463.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))))), M:tm-595, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54464
in-theory        54464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-550 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54464.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-550, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54465
in-theory        54465
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-540 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54465.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-540, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54466
in-theory        54466
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-530 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54466.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-530, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54467
in-theory        54467
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-520 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54467.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-520, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54468
in-theory        54468
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-510 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54468.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-510, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54469
in-theory        54469
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-500 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54469.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-500, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54470
in-theory        54470
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G)))))
theorem-size     39
proof            (modus-ponens tm-490 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54470.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G))))), M:tm-490, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54471
in-theory        54471
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-480 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54471.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-480, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54472
in-theory        54472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((A -> B) -> (A -> C))) or E))
theorem-size     25
proof            (modus-ponens tm-470 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54472.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((A -> B) -> (A -> C))) or E)), M:tm-470, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54473
in-theory        54473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-469 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54473.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-469, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54474
in-theory        54474
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (E -> (E or F)))
theorem-size     29
proof            (modus-ponens tm-456 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54474.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (E -> (E or F))), M:tm-456, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54475
in-theory        54475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-453 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54475.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-453, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54476
in-theory        54476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C))))))
theorem-size     53
proof            (modus-ponens tm-443 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54476.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))))), M:tm-443, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54477
in-theory        54477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-409 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54477.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-409, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54478
in-theory        54478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-400 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54478.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-400, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54479
in-theory        54479
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-391 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54479.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-391, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54480
in-theory        54480
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-382 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54480.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-382, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54481
in-theory        54481
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G)))))
theorem-size     39
proof            (modus-ponens tm-373 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54481.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G))))), M:tm-373, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54482
in-theory        54482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-364 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54482.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-364, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54483
in-theory        54483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E or ((A -> B) -> (A -> C))) and D)))
theorem-size     27
proof            (modus-ponens tm-355 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54483.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E or ((A -> B) -> (A -> C))) and D))), M:tm-355, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54484
in-theory        54484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-354 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54484.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-354, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54485
in-theory        54485
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (E -> (F -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-341 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54485.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54486
in-theory        54486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-338 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54486.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E))))), M:tm-338, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54487
in-theory        54487
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D or ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-328 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54487.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D or ((A -> B) -> (A -> C)))))), M:tm-328, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54488
in-theory        54488
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C))))))
theorem-size     55
proof            (modus-ponens tm-327 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54488.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))))), M:tm-327, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54489
in-theory        54489
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C))))))
theorem-size     53
proof            (modus-ponens tm-326 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-7)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54489.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))))), M:tm-326, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54490
in-theory        54490
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C))))))
theorem-size     53
proof            (modus-ponens tm-325 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-7)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54490.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))))), M:tm-325, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54491
in-theory        54491
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-324 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54491.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))))), M:tm-324, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54492
in-theory        54492
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C))))))
theorem-size     53
proof            (modus-ponens tm-323 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54492.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))))), M:tm-323, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54493
in-theory        54493
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((E and F) -> F))
theorem-size     29
proof            (modus-ponens tm-322 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54493.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((E and F) -> F)), M:tm-322, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54494
in-theory        54494
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((E and F) -> E))
theorem-size     29
proof            (modus-ponens tm-320 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54494.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((E and F) -> E)), M:tm-320, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54495
in-theory        54495
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-318 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54495.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54496
in-theory        54496
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     51
proof            (modus-ponens tm-316 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54496.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54497
in-theory        54497
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (E -> (F -> E)))
theorem-size     29
proof            (modus-ponens tm-315 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54497.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (E -> (F -> E))), M:tm-315, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54498
in-theory        54498
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D or ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     63
proof            (modus-ponens tm-313 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-7)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54498.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D or ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54499
in-theory        54499
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((D or ((A -> B) -> (A -> C))) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (D or ((A -> B) -> (A -> C)))) -> E)))
theorem-size     61
proof            (modus-ponens tm-312 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54499.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((D or ((A -> B) -> (A -> C))) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (D or ((A -> B) -> (A -> C)))) -> E))), M:tm-312, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54500
in-theory        54500
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C))))))
theorem-size     49
proof            (modus-ponens tm-311 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54500.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))))), M:tm-311, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54501
in-theory        54501
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) or E))
theorem-size     49
proof            (modus-ponens tm-310 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54501.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) or E)), M:tm-310, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54502
in-theory        54502
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and E)))
theorem-size     51
proof            (modus-ponens tm-309 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54502.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and E))), M:tm-309, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54503
in-theory        54503
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C))))))
theorem-size     49
proof            (modus-ponens tm-305 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54503.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))))), M:tm-305, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54504
in-theory        54504
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-303 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54504.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-303, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54505
in-theory        54505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-270 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54505.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-270, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54506
in-theory        54506
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-239 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54506.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-239, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54507
in-theory        54507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G)))))
theorem-size     41
proof            (modus-ponens tm-210 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54507.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G))))), M:tm-210, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54508
in-theory        54508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-183 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54508.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-183, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54509
in-theory        54509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-157 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54509.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-157, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54510
in-theory        54510
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-147 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54510.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-147, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54511
in-theory        54511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-134 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54511.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-134, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54512
in-theory        54512
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-125 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54512.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-125, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54513
in-theory        54513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G)))))
theorem-size     39
proof            (modus-ponens tm-113 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54513.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G))))), M:tm-113, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54514
in-theory        54514
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-105 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54514.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-105, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54515
in-theory        54515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E)))))
theorem-size     31
proof            (modus-ponens tm-95 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54515.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E))))), M:tm-95, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54516
in-theory        54516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or ((A -> B) -> (A -> C)))))
theorem-size     25
proof            (modus-ponens tm-84 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54516.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or ((A -> B) -> (A -> C))))), M:tm-84, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54517
in-theory        54517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-83 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54517.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-83, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54518
in-theory        54518
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E or ((B -> C) -> (B -> D)))))
theorem-size     29
proof            (modus-ponens tm-76 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-7)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54518.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E or ((B -> C) -> (B -> D))))), M:tm-76, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54519
in-theory        54519
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D or ((A -> B) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-73 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-7)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54519.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D or ((A -> B) -> (A -> C)))), M:tm-73, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54520
in-theory        54520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-69 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-7)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54520.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E))))), M:tm-69, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54521
in-theory        54521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-54 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54521.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-54, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54522
in-theory        54522
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D or ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-50 tm-672 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-7 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54522.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D or ((A -> B) -> (A -> C)))), M:tm-50, m:tm-672, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54523
in-theory        54523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D or ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-49 tm-672 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-7)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54523.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D or ((A -> B) -> (A -> C)))), M:tm-49, m:tm-672, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54524
in-theory        54524
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (E or ((B -> C) -> (B -> D))))
theorem-size     39
proof            (modus-ponens tm-47 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-7)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54524.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (E or ((B -> C) -> (B -> D)))), M:tm-47, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54525
in-theory        54525
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E or ((A -> B) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-46 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-7)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54525.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E or ((A -> B) -> (A -> C)))), M:tm-46, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54526
in-theory        54526
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E)))))
theorem-size     29
proof            (modus-ponens tm-42 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54526.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E))))), M:tm-42, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54527
in-theory        54527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E)))))
theorem-size     29
proof            (modus-ponens tm-32 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-7)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54527.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E))))), M:tm-32, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54528
in-theory        54528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D or ((A -> B) -> (A -> C)))))
theorem-size     37
proof            (modus-ponens tm-24 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54528.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D or ((A -> B) -> (A -> C))))), M:tm-24, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54529
in-theory        54529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E)))))
theorem-size     31
proof            (modus-ponens tm-23 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54529.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E))))), M:tm-23, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54530
in-theory        54530
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E)))))
theorem-size     29
proof            (modus-ponens tm-22 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-7)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54530.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E))))), M:tm-22, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54531
in-theory        54531
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E)))))
theorem-size     29
proof            (modus-ponens tm-21 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-7)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54531.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E))))), M:tm-21, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54532
in-theory        54532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-20 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54532.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-20, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54533
in-theory        54533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E)))))
theorem-size     29
proof            (modus-ponens tm-19 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-7)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54533.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F or ((C -> D) -> (C -> E))))), M:tm-19, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54534
in-theory        54534
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D or ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     39
proof            (modus-ponens tm-9 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-9 tm-8 tm-2 tm-7)
proof-size       129
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54534.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D or ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54535
in-theory        54535
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> (B -> D))) -> E) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) or (A or ((B -> C) -> (B -> D)))) -> E))
theorem-size     37
proof            (modus-ponens tm-8 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-7)
proof-size       129
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54535.        (((A or ((B -> C) -> (B -> D))) -> E) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) or (A or ((B -> C) -> (B -> D)))) -> E)), M:tm-8, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-54536
in-theory        54536
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E or ((B -> C) -> (B -> D)))))
theorem-size     25
proof            (modus-ponens tm-7 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-7 tm-8 tm-2)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54536.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E or ((B -> C) -> (B -> D))))), M:tm-7, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54537
in-theory        54537
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) or E)
theorem-size     25
proof            (modus-ponens tm-6 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-6 tm-8 tm-2 tm-7)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54537.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) or E), M:tm-6, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54538
in-theory        54538
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E or ((B -> C) -> (B -> D)))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       113
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54538.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E or ((B -> C) -> (B -> D)))) and A)), M:tm-5, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54539
in-theory        54539
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E or ((B -> C) -> (B -> D)))))
theorem-size     25
proof            (modus-ponens tm-1 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-1 tm-8 tm-2 tm-7)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-54539.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E or ((B -> C) -> (B -> D))))), M:tm-1, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54540
in-theory        54540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> C) -> (((A -> B) or (A -> (A -> B))) -> C))
theorem-size     19
proof            (modus-ponens tm-673 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-54540.        (((A -> (A -> B)) -> C) -> (((A -> B) or (A -> (A -> B))) -> C)), M:tm-673, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-54541
in-theory        54541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A -> B) and A)) -> C) -> (((A -> B) or (A -> ((A -> B) and A))) -> C))
theorem-size     23
proof            (modus-ponens tm-673 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-7 tm-5)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-54541.        (((A -> ((A -> B) and A)) -> C) -> (((A -> B) or (A -> ((A -> B) and A))) -> C)), M:tm-673, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-54542
in-theory        54542
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A -> B) or A) -> B)) -> C) -> ((((A -> B) -> A) or ((A -> B) -> (((A -> B) or A) -> B))) -> C))
theorem-size     33
proof            (modus-ponens tm-673 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-7)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-54542.        ((((A -> B) -> (((A -> B) or A) -> B)) -> C) -> ((((A -> B) -> A) or ((A -> B) -> (((A -> B) or A) -> B))) -> C)), M:tm-673, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-54543
in-theory        54543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> (((A -> D) or (A -> (B -> A))) -> C))
theorem-size     19
proof            (modus-ponens tm-673 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-54543.        (((A -> (B -> A)) -> C) -> (((A -> D) or (A -> (B -> A))) -> C)), M:tm-673, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-54544
in-theory        54544
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((((A -> (B -> C)) -> E) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))
theorem-size     39
proof            (modus-ponens tm-673 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-54544.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((((A -> (B -> C)) -> E) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-673, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-54545
in-theory        54545
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> ((((A and B) -> D) or ((A and B) -> A)) -> C))
theorem-size     21
proof            (modus-ponens tm-673 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-54545.        ((((A and B) -> A) -> C) -> ((((A and B) -> D) or ((A and B) -> A)) -> C)), M:tm-673, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-54546
in-theory        54546
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> ((((A and B) -> D) or ((A and B) -> B)) -> C))
theorem-size     21
proof            (modus-ponens tm-673 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-54546.        ((((A and B) -> B) -> C) -> ((((A and B) -> D) or ((A and B) -> B)) -> C)), M:tm-673, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-54547
in-theory        54547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> (((A -> D) or (A -> (B -> (A and B)))) -> C))
theorem-size     23
proof            (modus-ponens tm-673 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-5)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-54547.        (((A -> (B -> (A and B))) -> C) -> (((A -> D) or (A -> (B -> (A and B)))) -> C)), M:tm-673, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-54548
in-theory        54548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> (((A -> D) or (A -> (A or B))) -> C))
theorem-size     19
proof            (modus-ponens tm-673 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-54548.        (((A -> (A or B)) -> C) -> (((A -> D) or (A -> (A or B))) -> C)), M:tm-673, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-54549
in-theory        54549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> (((A -> D) or (A -> (B or A))) -> C))
theorem-size     19
proof            (modus-ponens tm-673 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-54549.        (((A -> (B or A)) -> C) -> (((A -> D) or (A -> (B or A))) -> C)), M:tm-673, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-54550
in-theory        54550
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     43
proof            (modus-ponens tm-665 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54550.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-665, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54551
in-theory        54551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((A -> C) -> E) -> (((A -> B) or (A -> C)) -> E))))
theorem-size     31
proof            (modus-ponens tm-623 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54551.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((A -> C) -> E) -> (((A -> B) or (A -> C)) -> E)))), M:tm-623, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54552
in-theory        54552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-622 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54552.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-622, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54553
in-theory        54553
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (E -> (F or E)))
theorem-size     35
proof            (modus-ponens tm-609 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54553.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (E -> (F or E))), M:tm-609, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54554
in-theory        54554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     39
proof            (modus-ponens tm-605 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54554.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-605, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54555
in-theory        54555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))))
theorem-size     65
proof            (modus-ponens tm-595 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54555.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))), M:tm-595, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54556
in-theory        54556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-550 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54556.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-550, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54557
in-theory        54557
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-540 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54557.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-540, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54558
in-theory        54558
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-530 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54558.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-530, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54559
in-theory        54559
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     39
proof            (modus-ponens tm-520 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54559.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-520, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54560
in-theory        54560
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-510 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54560.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-510, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54561
in-theory        54561
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-500 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54561.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-500, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54562
in-theory        54562
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> G) -> H) -> (((E -> F) or (E -> G)) -> H))))
theorem-size     45
proof            (modus-ponens tm-490 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54562.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> G) -> H) -> (((E -> F) or (E -> G)) -> H)))), M:tm-490, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54563
in-theory        54563
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-480 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54563.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-480, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54564
in-theory        54564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)) or E))
theorem-size     31
proof            (modus-ponens tm-470 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54564.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)) or E)), M:tm-470, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54565
in-theory        54565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-469 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54565.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-469, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54566
in-theory        54566
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (E -> (E or F)))
theorem-size     35
proof            (modus-ponens tm-456 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54566.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (E -> (E or F))), M:tm-456, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54567
in-theory        54567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     39
proof            (modus-ponens tm-453 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54567.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-453, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54568
in-theory        54568
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))))
theorem-size     65
proof            (modus-ponens tm-443 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54568.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))), M:tm-443, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54569
in-theory        54569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-409 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54569.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-409, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54570
in-theory        54570
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     39
proof            (modus-ponens tm-400 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54570.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-400, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54571
in-theory        54571
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-391 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54571.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-391, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54572
in-theory        54572
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-382 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54572.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-382, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54573
in-theory        54573
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> G) -> H) -> (((E -> F) or (E -> G)) -> H))))
theorem-size     45
proof            (modus-ponens tm-373 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54573.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> G) -> H) -> (((E -> F) or (E -> G)) -> H)))), M:tm-373, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54574
in-theory        54574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-364 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54574.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-364, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54575
in-theory        54575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((A -> C) -> E) -> (((A -> B) or (A -> C)) -> E)) and D)))
theorem-size     33
proof            (modus-ponens tm-355 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54575.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((A -> C) -> E) -> (((A -> B) or (A -> C)) -> E)) and D))), M:tm-355, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54576
in-theory        54576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     39
proof            (modus-ponens tm-354 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54576.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-354, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54577
in-theory        54577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) or (A -> C)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (A -> C))))
theorem-size     39
proof            (modus-ponens tm-349 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Am Cm)) (Dm (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Am Cm))) (C (-> (or (-> Am Bm) (-> Am Cm)) (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54577.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) or (A -> C)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (A -> C)))), M:tm-349, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Am Cm)) (Dm (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Am Cm))) (C (-> (or (-> Am Bm) (-> Am Cm)) (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Am Cm)))))
================================================================
tm-name          tm-54578
in-theory        54578
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (E -> (F -> (E and F))))
theorem-size     37
proof            (modus-ponens tm-341 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54578.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54579
in-theory        54579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F))))
theorem-size     39
proof            (modus-ponens tm-338 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54579.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F)))), M:tm-338, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54580
in-theory        54580
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))))
theorem-size     73
proof            (modus-ponens tm-328 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54580.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))), M:tm-328, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54581
in-theory        54581
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))))
theorem-size     67
proof            (modus-ponens tm-327 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54581.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))), M:tm-327, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54582
in-theory        54582
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))))
theorem-size     65
proof            (modus-ponens tm-326 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54582.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))), M:tm-326, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54583
in-theory        54583
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))))
theorem-size     65
proof            (modus-ponens tm-325 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54583.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))), M:tm-325, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54584
in-theory        54584
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))))
theorem-size     73
proof            (modus-ponens tm-324 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       251
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54584.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))), M:tm-324, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54585
in-theory        54585
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))))
theorem-size     65
proof            (modus-ponens tm-323 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54585.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))), M:tm-323, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54586
in-theory        54586
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((E and F) -> F))
theorem-size     35
proof            (modus-ponens tm-322 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54586.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54587
in-theory        54587
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((E and F) -> E))
theorem-size     35
proof            (modus-ponens tm-320 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54587.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54588
in-theory        54588
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-318 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54588.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54589
in-theory        54589
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-316 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54589.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54590
in-theory        54590
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (E -> (F -> E)))
theorem-size     35
proof            (modus-ponens tm-315 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54590.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54591
in-theory        54591
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     75
proof            (modus-ponens tm-313 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       223
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54591.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54592
in-theory        54592
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) -> E)))
theorem-size     79
proof            (modus-ponens tm-312 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       231
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54592.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) -> E))), M:tm-312, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54593
in-theory        54593
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))))
theorem-size     61
proof            (modus-ponens tm-311 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54593.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))), M:tm-311, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54594
in-theory        54594
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) or E))
theorem-size     61
proof            (modus-ponens tm-310 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54594.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) or E)), M:tm-310, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54595
in-theory        54595
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and E)))
theorem-size     63
proof            (modus-ponens tm-309 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54595.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and E))), M:tm-309, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54596
in-theory        54596
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> C) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) or (A -> C)) -> D))))
theorem-size     73
proof            (modus-ponens tm-306 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Cm) Dm)) (C (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       227
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54596.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> C) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) or (A -> C)) -> D)))), M:tm-306, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Cm) Dm)) (C (-> (or (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54597
in-theory        54597
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))))
theorem-size     61
proof            (modus-ponens tm-305 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54597.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))), M:tm-305, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54598
in-theory        54598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-303 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54598.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-303, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54599
in-theory        54599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     39
proof            (modus-ponens tm-270 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54599.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-270, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54600
in-theory        54600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     39
proof            (modus-ponens tm-239 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54600.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-239, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54601
in-theory        54601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> G) -> H) -> (((E -> F) or (E -> G)) -> H))))
theorem-size     47
proof            (modus-ponens tm-210 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54601.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> G) -> H) -> (((E -> F) or (E -> G)) -> H)))), M:tm-210, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54602
in-theory        54602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     39
proof            (modus-ponens tm-183 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54602.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-183, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54603
in-theory        54603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-157 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54603.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-157, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54604
in-theory        54604
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-147 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54604.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-147, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54605
in-theory        54605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-134 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54605.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-134, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54606
in-theory        54606
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-125 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54606.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-125, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54607
in-theory        54607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> C) -> D) -> ((A -> B) or (A -> C))) -> (((A -> C) -> D) -> D)))
theorem-size     35
proof            (modus-ponens tm-114 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Cm) Dm)) (C (or (-> Am Bm) (-> Am Cm))) (D Dm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54607.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> C) -> D) -> ((A -> B) or (A -> C))) -> (((A -> C) -> D) -> D))), M:tm-114, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Cm) Dm)) (C (or (-> Am Bm) (-> Am Cm))) (D Dm))
================================================================
tm-name          tm-54608
in-theory        54608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> G) -> H) -> (((E -> F) or (E -> G)) -> H))))
theorem-size     45
proof            (modus-ponens tm-113 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54608.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> G) -> H) -> (((E -> F) or (E -> G)) -> H)))), M:tm-113, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54609
in-theory        54609
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     49
proof            (modus-ponens tm-105 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54609.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-105, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54610
in-theory        54610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) or (A -> C)) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     35
proof            (modus-ponens tm-98 tm-673 ((Dm (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Am Cm)) (A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (-> (or (-> Am Bm) (-> Am Cm)) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54610.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) or (A -> C)) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-98, m:tm-673, u:((Dm (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Am Cm)) (A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (-> (or (-> Am Bm) (-> Am Cm)) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54611
in-theory        54611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F))))
theorem-size     37
proof            (modus-ponens tm-95 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54611.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F)))), M:tm-95, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54612
in-theory        54612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> C) -> E) -> (((A -> B) or (A -> C)) -> E))))
theorem-size     31
proof            (modus-ponens tm-84 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54612.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> C) -> E) -> (((A -> B) or (A -> C)) -> E)))), M:tm-84, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54613
in-theory        54613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     37
proof            (modus-ponens tm-83 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54613.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-83, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54614
in-theory        54614
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> D) -> E) -> (((B -> C) or (B -> D)) -> E))))
theorem-size     35
proof            (modus-ponens tm-76 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54614.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> D) -> E) -> (((B -> C) or (B -> D)) -> E)))), M:tm-76, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54615
in-theory        54615
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))
theorem-size     45
proof            (modus-ponens tm-73 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54615.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-73, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54616
in-theory        54616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F))))
theorem-size     41
proof            (modus-ponens tm-69 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54616.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F)))), M:tm-69, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54617
in-theory        54617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     43
proof            (modus-ponens tm-54 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54617.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-54, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54618
in-theory        54618
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))
theorem-size     37
proof            (modus-ponens tm-50 tm-673 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-7 tm-2)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54618.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-50, m:tm-673, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54619
in-theory        54619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))
theorem-size     35
proof            (modus-ponens tm-49 tm-673 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-6 tm-2)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54619.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-49, m:tm-673, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54620
in-theory        54620
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((B -> D) -> E) -> (((B -> C) or (B -> D)) -> E)))
theorem-size     45
proof            (modus-ponens tm-47 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54620.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((B -> D) -> E) -> (((B -> C) or (B -> D)) -> E))), M:tm-47, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54621
in-theory        54621
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> C) -> E) -> (((A -> B) or (A -> C)) -> E)))
theorem-size     45
proof            (modus-ponens tm-46 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54621.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> C) -> E) -> (((A -> B) or (A -> C)) -> E))), M:tm-46, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54622
in-theory        54622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-42 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54622.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F)))), M:tm-42, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54623
in-theory        54623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-32 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54623.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F)))), M:tm-32, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54624
in-theory        54624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))
theorem-size     43
proof            (modus-ponens tm-24 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54624.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))), M:tm-24, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54625
in-theory        54625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F))))
theorem-size     37
proof            (modus-ponens tm-23 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54625.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F)))), M:tm-23, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54626
in-theory        54626
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-22 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54626.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F)))), M:tm-22, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54627
in-theory        54627
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-21 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54627.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F)))), M:tm-21, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54628
in-theory        54628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     43
proof            (modus-ponens tm-20 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54628.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-20, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54629
in-theory        54629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F))))
theorem-size     35
proof            (modus-ponens tm-19 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54629.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> E) -> F) -> (((C -> D) or (C -> E)) -> F)))), M:tm-19, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54630
in-theory        54630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-9 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-9 tm-8 tm-2)
proof-size       149
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54630.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54631
in-theory        54631
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (((A -> D) or (A -> B)) -> C)) -> E) -> ((((A -> (D -> B)) or ((A -> D) -> (A -> B))) or (((A -> B) -> C) -> (((A -> D) or (A -> B)) -> C))) -> E))
theorem-size     49
proof            (modus-ponens tm-8 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-2)
proof-size       155
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54631.        (((((A -> B) -> C) -> (((A -> D) or (A -> B)) -> C)) -> E) -> ((((A -> (D -> B)) or ((A -> D) -> (A -> B))) or (((A -> B) -> C) -> (((A -> D) or (A -> B)) -> C))) -> E)), M:tm-8, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-54632
in-theory        54632
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> D) -> E) -> (((B -> C) or (B -> D)) -> E))))
theorem-size     31
proof            (modus-ponens tm-7 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-7 tm-8 tm-2)
proof-size       129
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54632.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> D) -> E) -> (((B -> C) or (B -> D)) -> E)))), M:tm-7, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54633
in-theory        54633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) or E)
theorem-size     31
proof            (modus-ponens tm-6 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-6 tm-8 tm-2)
proof-size       129
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54633.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) or E), M:tm-6, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54634
in-theory        54634
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> D) -> E) -> (((B -> C) or (B -> D)) -> E))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       133
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54634.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> D) -> E) -> (((B -> C) or (B -> D)) -> E))) and A)), M:tm-5, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54635
in-theory        54635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> C) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) or (A -> C)) -> D)))
theorem-size     43
proof            (modus-ponens tm-2 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Cm) Dm)) (C (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-8)
proof-size       149
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54635.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> C) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) or (A -> C)) -> D))), M:tm-2, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Cm) Dm)) (C (-> (or (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-54636
in-theory        54636
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> D) -> E) -> (((B -> C) or (B -> D)) -> E))))
theorem-size     31
proof            (modus-ponens tm-1 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       129
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-54636.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> D) -> E) -> (((B -> C) or (B -> D)) -> E)))), M:tm-1, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-54637
in-theory        54637
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (A -> B)))) -> (not (A -> B)))
theorem-size     15
proof            (modus-ponens tm-674 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-9 tm-7 tm-1)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-54637.        (((A -> B) -> (not (A -> (A -> B)))) -> (not (A -> B))), M:tm-674, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-54638
in-theory        54638
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> ((A -> B) and A)))) -> (not (A -> B)))
theorem-size     17
proof            (modus-ponens tm-674 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-9 tm-7 tm-5)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-54638.        (((A -> B) -> (not (A -> ((A -> B) and A)))) -> (not (A -> B))), M:tm-674, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-54639
in-theory        54639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> (not ((A -> B) -> (((A -> B) or A) -> B)))) -> (not ((A -> B) -> A)))
theorem-size     25
proof            (modus-ponens tm-674 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-9 tm-7)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-54639.        ((((A -> B) -> A) -> (not ((A -> B) -> (((A -> B) or A) -> B)))) -> (not ((A -> B) -> A))), M:tm-674, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-54640
in-theory        54640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (C -> A)))) -> (not (A -> B)))
theorem-size     15
proof            (modus-ponens tm-674 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-9 tm-7 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-54640.        (((A -> B) -> (not (A -> (C -> A)))) -> (not (A -> B))), M:tm-674, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-54641
in-theory        54641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> D) -> (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-674 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-9 tm-7 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-54641.        ((((A -> (B -> C)) -> D) -> (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) -> D))), M:tm-674, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-54642
in-theory        54642
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> C) -> (not ((A and B) -> A))) -> (not ((A and B) -> C)))
theorem-size     19
proof            (modus-ponens tm-674 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-9 tm-7 tm-1 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-54642.        ((((A and B) -> C) -> (not ((A and B) -> A))) -> (not ((A and B) -> C))), M:tm-674, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-54643
in-theory        54643
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> C) -> (not ((A and B) -> B))) -> (not ((A and B) -> C)))
theorem-size     19
proof            (modus-ponens tm-674 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-9 tm-7 tm-1 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-54643.        ((((A and B) -> C) -> (not ((A and B) -> B))) -> (not ((A and B) -> C))), M:tm-674, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-54644
in-theory        54644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (C -> (A and C))))) -> (not (A -> B)))
theorem-size     17
proof            (modus-ponens tm-674 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-9 tm-7 tm-1 tm-5)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-54644.        (((A -> B) -> (not (A -> (C -> (A and C))))) -> (not (A -> B))), M:tm-674, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-54645
in-theory        54645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (A or C)))) -> (not (A -> B)))
theorem-size     15
proof            (modus-ponens tm-674 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-9 tm-7 tm-1 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-54645.        (((A -> B) -> (not (A -> (A or C)))) -> (not (A -> B))), M:tm-674, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-54646
in-theory        54646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (A -> (C or A)))) -> (not (A -> B)))
theorem-size     15
proof            (modus-ponens tm-674 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-9 tm-7 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-54646.        (((A -> B) -> (not (A -> (C or A)))) -> (not (A -> B))), M:tm-674, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-54647
in-theory        54647
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-9)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54647.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-665, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54648
in-theory        54648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))
theorem-size     29
proof            (modus-ponens tm-623 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-9)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54648.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((A -> B) -> (not (A -> C))) -> (not (A -> B))))), M:tm-623, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54649
in-theory        54649
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54649.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-622, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54650
in-theory        54650
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (D -> (E or D)))
theorem-size     33
proof            (modus-ponens tm-609 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-9)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54650.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (D -> (E or D))), M:tm-609, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54651
in-theory        54651
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54651.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-605, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54652
in-theory        54652
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((D -> (E or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-9)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54652.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((D -> (E or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))), M:tm-595, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54653
in-theory        54653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54653.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-550, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54654
in-theory        54654
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54654.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-540, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54655
in-theory        54655
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54655.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-530, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54656
in-theory        54656
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54656.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-520, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54657
in-theory        54657
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54657.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-510, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54658
in-theory        54658
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54658.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-500, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54659
in-theory        54659
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (not (E -> G))) -> (not (E -> F)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-9)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54659.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (not (E -> G))) -> (not (E -> F))))), M:tm-490, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54660
in-theory        54660
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54660.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-480, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54661
in-theory        54661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) -> (not (A -> C))) -> (not (A -> B))) or D))
theorem-size     29
proof            (modus-ponens tm-470 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-9)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54661.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) -> (not (A -> C))) -> (not (A -> B))) or D)), M:tm-470, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54662
in-theory        54662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54662.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-469, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54663
in-theory        54663
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (D -> (D or E)))
theorem-size     33
proof            (modus-ponens tm-456 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-9)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54663.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (D -> (D or E))), M:tm-456, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54664
in-theory        54664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54664.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-453, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54665
in-theory        54665
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((D -> (D or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-9)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54665.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((D -> (D or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))), M:tm-443, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54666
in-theory        54666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54666.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-409, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54667
in-theory        54667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54667.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-400, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54668
in-theory        54668
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54668.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-391, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54669
in-theory        54669
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54669.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-382, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54670
in-theory        54670
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (not (E -> G))) -> (not (E -> F)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-9)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54670.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (not (E -> G))) -> (not (E -> F))))), M:tm-373, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54671
in-theory        54671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54671.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-364, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54672
in-theory        54672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((A -> B) -> (not (A -> C))) -> (not (A -> B))) and D)))
theorem-size     31
proof            (modus-ponens tm-355 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-9)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54672.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((A -> B) -> (not (A -> C))) -> (not (A -> B))) and D))), M:tm-355, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54673
in-theory        54673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54673.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-354, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54674
in-theory        54674
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (D -> (E -> (D and E))))
theorem-size     35
proof            (modus-ponens tm-341 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54674.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54675
in-theory        54675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-9)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54675.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D))))), M:tm-338, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54676
in-theory        54676
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> B) -> (not (A -> C))) -> (not (A -> B))))))
theorem-size     69
proof            (modus-ponens tm-328 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54676.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))), M:tm-328, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54677
in-theory        54677
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54677.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))), M:tm-327, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54678
in-theory        54678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((D and E) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-9)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54678.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((D and E) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))), M:tm-326, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54679
in-theory        54679
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((D and E) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-9)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54679.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((D and E) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))), M:tm-325, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54680
in-theory        54680
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54680.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))), M:tm-324, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54681
in-theory        54681
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((D -> (E -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54681.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((D -> (E -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))), M:tm-323, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54682
in-theory        54682
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((D and E) -> E))
theorem-size     33
proof            (modus-ponens tm-322 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-9)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54682.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((D and E) -> E)), M:tm-322, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54683
in-theory        54683
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((D and E) -> D))
theorem-size     33
proof            (modus-ponens tm-320 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-9)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54683.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((D and E) -> D)), M:tm-320, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54684
in-theory        54684
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-318 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54684.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54685
in-theory        54685
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     55
proof            (modus-ponens tm-316 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54685.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54686
in-theory        54686
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (D -> (E -> D)))
theorem-size     33
proof            (modus-ponens tm-315 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54686.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (D -> (E -> D))), M:tm-315, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54687
in-theory        54687
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> B) -> (not (A -> C))) -> (not (A -> B))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     71
proof            (modus-ponens tm-313 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54687.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> B) -> (not (A -> C))) -> (not (A -> B))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54688
in-theory        54688
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((((A -> B) -> (not (A -> C))) -> (not (A -> B))) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) -> D)))
theorem-size     73
proof            (modus-ponens tm-312 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       221
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54688.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((((A -> B) -> (not (A -> C))) -> (not (A -> B))) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) -> D))), M:tm-312, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54689
in-theory        54689
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (D or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-9)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54689.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (D or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))), M:tm-311, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54690
in-theory        54690
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) or D))
theorem-size     57
proof            (modus-ponens tm-310 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-9)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54690.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) or D)), M:tm-310, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54691
in-theory        54691
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (D -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and D)))
theorem-size     59
proof            (modus-ponens tm-309 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54691.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (D -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and D))), M:tm-309, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54692
in-theory        54692
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (not (A -> C)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (A -> B)))))
theorem-size     69
proof            (modus-ponens tm-306 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (not (-> Am Cm)))) (C (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       219
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54692.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (not (A -> C)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (A -> B))))), M:tm-306, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (not (-> Am Cm)))) (C (not (-> Am Bm))))
================================================================
tm-name          tm-54693
in-theory        54693
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-9)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54693.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))), M:tm-305, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54694
in-theory        54694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54694.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-303, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54695
in-theory        54695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54695.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-270, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54696
in-theory        54696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54696.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-239, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54697
in-theory        54697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (not (E -> G))) -> (not (E -> F)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-9)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54697.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (not (E -> G))) -> (not (E -> F))))), M:tm-210, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54698
in-theory        54698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54698.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-183, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54699
in-theory        54699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54699.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-157, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54700
in-theory        54700
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-9)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54700.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-147, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54701
in-theory        54701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54701.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-134, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54702
in-theory        54702
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-9)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54702.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-125, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54703
in-theory        54703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (not (E -> G))) -> (not (E -> F)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-9)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54703.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (not (E -> G))) -> (not (E -> F))))), M:tm-113, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54704
in-theory        54704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-9)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54704.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-105, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54705
in-theory        54705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-9)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54705.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D))))), M:tm-95, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54706
in-theory        54706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))
theorem-size     29
proof            (modus-ponens tm-84 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-9)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54706.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))), M:tm-84, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54707
in-theory        54707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-9)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54707.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-83, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54708
in-theory        54708
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (not (B -> D))) -> (not (B -> C)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-9)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54708.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (not (B -> D))) -> (not (B -> C))))), M:tm-76, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54709
in-theory        54709
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))
theorem-size     43
proof            (modus-ponens tm-73 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-9)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54709.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-73, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54710
in-theory        54710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54710.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D))))), M:tm-69, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54711
in-theory        54711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     41
proof            (modus-ponens tm-54 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54711.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-54, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54712
in-theory        54712
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))
theorem-size     35
proof            (modus-ponens tm-50 tm-674 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-9)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54712.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-50, m:tm-674, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54713
in-theory        54713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))
theorem-size     33
proof            (modus-ponens tm-49 tm-674 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-9)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54713.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-49, m:tm-674, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54714
in-theory        54714
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((B -> C) -> (not (B -> D))) -> (not (B -> C))))
theorem-size     43
proof            (modus-ponens tm-47 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-9)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54714.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((B -> C) -> (not (B -> D))) -> (not (B -> C)))), M:tm-47, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54715
in-theory        54715
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))
theorem-size     43
proof            (modus-ponens tm-46 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-9)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54715.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-46, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54716
in-theory        54716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D)))))
theorem-size     33
proof            (modus-ponens tm-42 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-9)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54716.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D))))), M:tm-42, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54717
in-theory        54717
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D)))))
theorem-size     33
proof            (modus-ponens tm-32 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-9)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54717.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D))))), M:tm-32, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54718
in-theory        54718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-24 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54718.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((A -> B) -> (not (A -> C))) -> (not (A -> B))))), M:tm-24, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54719
in-theory        54719
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D)))))
theorem-size     35
proof            (modus-ponens tm-23 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54719.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D))))), M:tm-23, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54720
in-theory        54720
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D)))))
theorem-size     33
proof            (modus-ponens tm-22 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-9)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54720.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D))))), M:tm-22, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54721
in-theory        54721
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D)))))
theorem-size     33
proof            (modus-ponens tm-21 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-9)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54721.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D))))), M:tm-21, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54722
in-theory        54722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     41
proof            (modus-ponens tm-20 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-9)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54722.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-20, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54723
in-theory        54723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D)))))
theorem-size     33
proof            (modus-ponens tm-19 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-9)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54723.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((C -> D) -> (not (C -> E))) -> (not (C -> D))))), M:tm-19, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54724
in-theory        54724
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> B) -> (not (A -> C))) -> (not (A -> B))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     43
proof            (modus-ponens tm-9 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-9 tm-8 tm-2)
proof-size       143
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54724.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> B) -> (not (A -> C))) -> (not (A -> B))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54725
in-theory        54725
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (not (A -> C))) -> (not (A -> B))) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) -> D))
theorem-size     45
proof            (modus-ponens tm-8 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-8 tm-2 tm-9)
proof-size       147
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54725.        (((((A -> B) -> (not (A -> C))) -> (not (A -> B))) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) -> D)), M:tm-8, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-54726
in-theory        54726
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (not (B -> D))) -> (not (B -> C)))))
theorem-size     29
proof            (modus-ponens tm-7 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-7 tm-8 tm-2 tm-9)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54726.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (not (B -> D))) -> (not (B -> C))))), M:tm-7, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54727
in-theory        54727
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) or D)
theorem-size     29
proof            (modus-ponens tm-6 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-6 tm-8 tm-2 tm-9)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54727.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) or D), M:tm-6, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54728
in-theory        54728
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (not (B -> D))) -> (not (B -> C)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54728.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (not (B -> D))) -> (not (B -> C)))) and A)), M:tm-5, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54729
in-theory        54729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (not (A -> C)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (A -> B))))
theorem-size     41
proof            (modus-ponens tm-2 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (not (-> Am Cm)))) (C (not (-> Am Bm)))))
axioms-used      (tm-2 tm-8 tm-9)
proof-size       143
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54729.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (not (A -> C)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (A -> B)))), M:tm-2, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (not (-> Am Cm)))) (C (not (-> Am Bm))))
================================================================
tm-name          tm-54730
in-theory        54730
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (not (B -> D))) -> (not (B -> C)))))
theorem-size     29
proof            (modus-ponens tm-1 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-1 tm-8 tm-2 tm-9)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-54730.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (not (B -> D))) -> (not (B -> C))))), M:tm-1, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-54731
in-theory        54731
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-665 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54731.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-665, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54732
in-theory        54732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-622 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54732.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-622, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54733
in-theory        54733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     31
proof            (modus-ponens tm-617 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> Em (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54733.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-617, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> Em (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
================================================================
tm-name          tm-54734
in-theory        54734
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54734.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (F -> (G or F))), M:tm-609, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54735
in-theory        54735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-605 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54735.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-605, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54736
in-theory        54736
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54736.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))))), M:tm-595, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54737
in-theory        54737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-550 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54737.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-550, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54738
in-theory        54738
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-540 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54738.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-540, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54739
in-theory        54739
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-530 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54739.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-530, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54740
in-theory        54740
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-520 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54740.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-520, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54741
in-theory        54741
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-510 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54741.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-510, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54742
in-theory        54742
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-500 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54742.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-500, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54743
in-theory        54743
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-490 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54743.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H)))), M:tm-490, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54744
in-theory        54744
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-480 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54744.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-480, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54745
in-theory        54745
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-469 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54745.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-469, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54746
in-theory        54746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) or E)))
theorem-size     31
proof            (modus-ponens tm-464 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C (-> Em (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54746.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) or E))), M:tm-464, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C (-> Em (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))))
================================================================
tm-name          tm-54747
in-theory        54747
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54747.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (F -> (F or G))), M:tm-456, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54748
in-theory        54748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-453 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54748.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-453, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54749
in-theory        54749
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54749.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))))), M:tm-443, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54750
in-theory        54750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-409 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54750.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-409, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54751
in-theory        54751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-400 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54751.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-400, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54752
in-theory        54752
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-391 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54752.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-391, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54753
in-theory        54753
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-382 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54753.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-382, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54754
in-theory        54754
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-373 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54754.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H)))), M:tm-373, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54755
in-theory        54755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-364 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54755.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-364, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54756
in-theory        54756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-354 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54756.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-354, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54757
in-theory        54757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E))))
theorem-size     33
proof            (modus-ponens tm-349 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))) (C (-> Em (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54757.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E)))), M:tm-349, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))) (C (-> Em (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)))))
================================================================
tm-name          tm-54758
in-theory        54758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54758.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54759
in-theory        54759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F))))
theorem-size     29
proof            (modus-ponens tm-338 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54759.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F)))), M:tm-338, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54760
in-theory        54760
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (E -> D)))))
theorem-size     53
proof            (modus-ponens tm-328 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54760.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (E -> D))))), M:tm-328, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-54761
in-theory        54761
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54761.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))))), M:tm-327, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54762
in-theory        54762
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54762.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))))), M:tm-326, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54763
in-theory        54763
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54763.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))))), M:tm-325, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54764
in-theory        54764
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54764.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))))), M:tm-324, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54765
in-theory        54765
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54765.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))))), M:tm-323, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54766
in-theory        54766
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54766.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((F and G) -> G)), M:tm-322, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54767
in-theory        54767
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54767.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((F and G) -> F)), M:tm-320, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54768
in-theory        54768
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54768.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54769
in-theory        54769
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     47
proof            (modus-ponens tm-316 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54769.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-54770
in-theory        54770
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54770.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (F -> (G -> F))), M:tm-315, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54771
in-theory        54771
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E -> D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     55
proof            (modus-ponens tm-313 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54771.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E -> D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-54772
in-theory        54772
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((D -> (E -> D)) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (D -> (E -> D))) -> F)))
theorem-size     49
proof            (modus-ponens tm-312 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54772.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((D -> (E -> D)) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (D -> (E -> D))) -> F))), M:tm-312, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-54773
in-theory        54773
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54773.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))))), M:tm-311, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54774
in-theory        54774
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54774.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) or F)), M:tm-310, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54775
in-theory        54775
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54775.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and F))), M:tm-309, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54776
in-theory        54776
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E -> D))))
theorem-size     53
proof            (modus-ponens tm-306 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> Em Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54776.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E -> D)))), M:tm-306, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> Em Dm)))
================================================================
tm-name          tm-54777
in-theory        54777
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54777.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))))), M:tm-305, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54778
in-theory        54778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     31
proof            (modus-ponens tm-303 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54778.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-303, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54779
in-theory        54779
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-270 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54779.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-270, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54780
in-theory        54780
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-239 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54780.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-239, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54781
in-theory        54781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H))))
theorem-size     37
proof            (modus-ponens tm-210 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54781.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H)))), M:tm-210, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54782
in-theory        54782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-183 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54782.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-183, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54783
in-theory        54783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-157 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54783.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-157, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54784
in-theory        54784
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     35
proof            (modus-ponens tm-147 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54784.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-147, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54785
in-theory        54785
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-134 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54785.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-134, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54786
in-theory        54786
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     35
proof            (modus-ponens tm-125 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54786.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-125, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54787
in-theory        54787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H))))
theorem-size     35
proof            (modus-ponens tm-113 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54787.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H)))), M:tm-113, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54788
in-theory        54788
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-105 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54788.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-105, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54789
in-theory        54789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-99 tm-675 ((Dm (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Em (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54789.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-99, m:tm-675, u:((Dm (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Em (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-54790
in-theory        54790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     31
proof            (modus-ponens tm-98 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> Em (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54790.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-98, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> Em (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
================================================================
tm-name          tm-54791
in-theory        54791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-95 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54791.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F)))), M:tm-95, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54792
in-theory        54792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-83 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54792.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-83, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54793
in-theory        54793
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> E))))
theorem-size     25
proof            (modus-ponens tm-76 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54793.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> E)))), M:tm-76, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54794
in-theory        54794
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> D)))
theorem-size     35
proof            (modus-ponens tm-73 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54794.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> D))), M:tm-73, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-54795
in-theory        54795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-69 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54795.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F)))), M:tm-69, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54796
in-theory        54796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-54 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54796.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-54, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54797
in-theory        54797
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> D)))
theorem-size     27
proof            (modus-ponens tm-50 tm-675 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em Dm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54797.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> D))), M:tm-50, m:tm-675, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-54798
in-theory        54798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> D)))
theorem-size     25
proof            (modus-ponens tm-49 tm-675 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em Dm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54798.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> D))), M:tm-49, m:tm-675, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-54799
in-theory        54799
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (E -> (F -> E)))
theorem-size     35
proof            (modus-ponens tm-47 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54799.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (E -> (F -> E))), M:tm-47, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-54800
in-theory        54800
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> (F -> E)))
theorem-size     35
proof            (modus-ponens tm-46 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54800.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> (F -> E))), M:tm-46, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-54801
in-theory        54801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-42 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54801.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F)))), M:tm-42, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54802
in-theory        54802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-32 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54802.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F)))), M:tm-32, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54803
in-theory        54803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (E -> D))))
theorem-size     33
proof            (modus-ponens tm-24 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54803.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (E -> D)))), M:tm-24, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-54804
in-theory        54804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-23 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54804.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F)))), M:tm-23, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54805
in-theory        54805
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-22 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54805.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F)))), M:tm-22, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54806
in-theory        54806
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-21 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54806.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F)))), M:tm-21, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54807
in-theory        54807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     33
proof            (modus-ponens tm-20 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54807.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-20, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54808
in-theory        54808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-19 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54808.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> F)))), M:tm-19, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54809
in-theory        54809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E -> D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     35
proof            (modus-ponens tm-9 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-9 tm-8 tm-2 tm-1)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54809.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E -> D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-54810
in-theory        54810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> ((((D -> (E -> F)) or ((D -> E) -> (D -> F))) or (A -> (B -> A))) -> C))
theorem-size     29
proof            (modus-ponens tm-8 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54810.        (((A -> (B -> A)) -> C) -> ((((D -> (E -> F)) or ((D -> E) -> (D -> F))) or (A -> (B -> A))) -> C)), M:tm-8, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-54811
in-theory        54811
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-7 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-7 tm-8 tm-2 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54811.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> E)))), M:tm-7, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54812
in-theory        54812
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-6 tm-8 tm-2 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54812.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) or F), M:tm-6, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54813
in-theory        54813
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> E))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54813.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> E))) and A)), M:tm-5, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54814
in-theory        54814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E -> D)))
theorem-size     33
proof            (modus-ponens tm-2 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> Em Dm))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54814.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E -> D))), M:tm-2, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> Em Dm)))
================================================================
tm-name          tm-54815
in-theory        54815
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-1 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-54815.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> E)))), M:tm-1, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-54816
in-theory        54816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> D) -> ((A -> (B -> C)) -> D))
theorem-size     15
proof            (modus-ponens tm-676 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-7.            (A -> (B or A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-54816.        (((A -> (B -> C)) -> D) -> ((A -> (B -> C)) -> D)), M:tm-676, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-54817
in-theory        54817
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> C) -> ((A and B) -> C))
theorem-size     11
proof            (modus-ponens tm-676 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-54817.        (((A and B) -> C) -> ((A and B) -> C)), M:tm-676, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-54818
in-theory        54818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     35
proof            (modus-ponens tm-665 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54818.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-665, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54819
in-theory        54819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> B))))
theorem-size     23
proof            (modus-ponens tm-623 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54819.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> B)))), M:tm-623, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54820
in-theory        54820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-622 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54820.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-622, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54821
in-theory        54821
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (D -> (E or D)))
theorem-size     27
proof            (modus-ponens tm-609 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54821.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (D -> (E or D))), M:tm-609, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54822
in-theory        54822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     31
proof            (modus-ponens tm-605 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54822.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-605, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54823
in-theory        54823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((D -> (E or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54823.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((D -> (E or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))))), M:tm-595, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54824
in-theory        54824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-550 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54824.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-550, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54825
in-theory        54825
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-540 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54825.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-540, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54826
in-theory        54826
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-530 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54826.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-530, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54827
in-theory        54827
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     31
proof            (modus-ponens tm-520 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54827.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-520, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54828
in-theory        54828
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-510 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54828.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-510, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54829
in-theory        54829
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-500 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54829.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-500, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54830
in-theory        54830
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F))))
theorem-size     37
proof            (modus-ponens tm-490 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54830.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F)))), M:tm-490, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54831
in-theory        54831
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-480 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54831.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-480, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54832
in-theory        54832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> B)) or D))
theorem-size     23
proof            (modus-ponens tm-470 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54832.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> B)) or D)), M:tm-470, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54833
in-theory        54833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-469 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54833.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-469, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54834
in-theory        54834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (D -> (D or E)))
theorem-size     27
proof            (modus-ponens tm-456 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54834.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (D -> (D or E))), M:tm-456, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54835
in-theory        54835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     31
proof            (modus-ponens tm-453 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54835.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-453, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54836
in-theory        54836
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((D -> (D or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54836.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((D -> (D or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))))), M:tm-443, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54837
in-theory        54837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-409 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54837.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-409, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54838
in-theory        54838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     31
proof            (modus-ponens tm-400 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54838.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-400, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54839
in-theory        54839
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-391 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54839.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-391, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54840
in-theory        54840
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-382 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54840.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-382, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54841
in-theory        54841
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F))))
theorem-size     37
proof            (modus-ponens tm-373 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54841.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F)))), M:tm-373, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54842
in-theory        54842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-364 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54842.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-364, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54843
in-theory        54843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> B)) and D)))
theorem-size     25
proof            (modus-ponens tm-355 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54843.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> B)) and D))), M:tm-355, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54844
in-theory        54844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     31
proof            (modus-ponens tm-354 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54844.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-354, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54845
in-theory        54845
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (D -> (E -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-341 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54845.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54846
in-theory        54846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D))))
theorem-size     31
proof            (modus-ponens tm-338 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54846.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D)))), M:tm-338, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54847
in-theory        54847
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((A -> B) -> (A -> B)))))
theorem-size     57
proof            (modus-ponens tm-328 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54847.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((A -> B) -> (A -> B))))), M:tm-328, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54848
in-theory        54848
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54848.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))))), M:tm-327, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54849
in-theory        54849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((D and E) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54849.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((D and E) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))))), M:tm-326, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54850
in-theory        54850
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((D and E) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54850.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((D and E) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))))), M:tm-325, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54851
in-theory        54851
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       239
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54851.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))))), M:tm-324, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54852
in-theory        54852
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((D -> (E -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54852.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((D -> (E -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))))), M:tm-323, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54853
in-theory        54853
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((D and E) -> E))
theorem-size     27
proof            (modus-ponens tm-322 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54853.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((D and E) -> E)), M:tm-322, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54854
in-theory        54854
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((D and E) -> D))
theorem-size     27
proof            (modus-ponens tm-320 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54854.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((D and E) -> D)), M:tm-320, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54855
in-theory        54855
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-318 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54855.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54856
in-theory        54856
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-316 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54856.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54857
in-theory        54857
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (D -> (E -> D)))
theorem-size     27
proof            (modus-ponens tm-315 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54857.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (D -> (E -> D))), M:tm-315, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54858
in-theory        54858
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((A -> B) -> (A -> B)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     59
proof            (modus-ponens tm-313 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54858.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((A -> B) -> (A -> B)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54859
in-theory        54859
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((((A -> B) -> (A -> B)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((A -> B) -> (A -> B))) -> D)))
theorem-size     55
proof            (modus-ponens tm-312 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54859.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((((A -> B) -> (A -> B)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((A -> B) -> (A -> B))) -> D))), M:tm-312, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54860
in-theory        54860
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (D or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54860.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (D or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))))), M:tm-311, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54861
in-theory        54861
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) or D))
theorem-size     45
proof            (modus-ponens tm-310 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54861.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) or D)), M:tm-310, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54862
in-theory        54862
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (D -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and D)))
theorem-size     47
proof            (modus-ponens tm-309 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54862.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (D -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and D))), M:tm-309, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54863
in-theory        54863
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> B)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> B))))
theorem-size     57
proof            (modus-ponens tm-306 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Am Bm)) (C (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54863.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> B)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> B)))), M:tm-306, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Am Bm)) (C (-> Am Bm)))
================================================================
tm-name          tm-54864
in-theory        54864
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54864.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))))), M:tm-305, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54865
in-theory        54865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     33
proof            (modus-ponens tm-303 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54865.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-303, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54866
in-theory        54866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     31
proof            (modus-ponens tm-270 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54866.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-270, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54867
in-theory        54867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     31
proof            (modus-ponens tm-239 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54867.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-239, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54868
in-theory        54868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F))))
theorem-size     39
proof            (modus-ponens tm-210 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54868.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F)))), M:tm-210, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54869
in-theory        54869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     31
proof            (modus-ponens tm-183 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54869.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-183, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54870
in-theory        54870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-157 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54870.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-157, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54871
in-theory        54871
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     37
proof            (modus-ponens tm-147 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54871.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-147, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54872
in-theory        54872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-134 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54872.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-134, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54873
in-theory        54873
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     37
proof            (modus-ponens tm-125 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54873.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-125, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54874
in-theory        54874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> B)))
theorem-size     25
proof            (modus-ponens tm-114 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Am Bm)) (C Am) (D Bm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54874.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> B))), M:tm-114, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Am Bm)) (C Am) (D Bm))
================================================================
tm-name          tm-54875
in-theory        54875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F))))
theorem-size     37
proof            (modus-ponens tm-113 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54875.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F)))), M:tm-113, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54876
in-theory        54876
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     41
proof            (modus-ponens tm-105 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54876.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-105, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54877
in-theory        54877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D))))
theorem-size     29
proof            (modus-ponens tm-95 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54877.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D)))), M:tm-95, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54878
in-theory        54878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> B))))
theorem-size     23
proof            (modus-ponens tm-84 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54878.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> B)))), M:tm-84, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54879
in-theory        54879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     29
proof            (modus-ponens tm-83 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54879.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-83, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54880
in-theory        54880
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> (B -> C))))
theorem-size     27
proof            (modus-ponens tm-76 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54880.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> (B -> C)))), M:tm-76, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54881
in-theory        54881
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B)))
theorem-size     37
proof            (modus-ponens tm-73 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54881.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B))), M:tm-73, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54882
in-theory        54882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D))))
theorem-size     33
proof            (modus-ponens tm-69 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54882.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D)))), M:tm-69, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54883
in-theory        54883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     35
proof            (modus-ponens tm-54 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54883.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-54, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54884
in-theory        54884
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B)))
theorem-size     29
proof            (modus-ponens tm-50 tm-676 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54884.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B))), M:tm-50, m:tm-676, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54885
in-theory        54885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B)))
theorem-size     27
proof            (modus-ponens tm-49 tm-676 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54885.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B))), M:tm-49, m:tm-676, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54886
in-theory        54886
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((B -> C) -> (B -> C)))
theorem-size     37
proof            (modus-ponens tm-47 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54886.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((B -> C) -> (B -> C))), M:tm-47, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54887
in-theory        54887
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B)))
theorem-size     37
proof            (modus-ponens tm-46 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54887.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B))), M:tm-46, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54888
in-theory        54888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D))))
theorem-size     27
proof            (modus-ponens tm-42 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54888.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D)))), M:tm-42, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54889
in-theory        54889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D))))
theorem-size     27
proof            (modus-ponens tm-32 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54889.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D)))), M:tm-32, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54890
in-theory        54890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((A -> B) -> (A -> B))))
theorem-size     35
proof            (modus-ponens tm-24 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54890.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((A -> B) -> (A -> B)))), M:tm-24, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54891
in-theory        54891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D))))
theorem-size     29
proof            (modus-ponens tm-23 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54891.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D)))), M:tm-23, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54892
in-theory        54892
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D))))
theorem-size     27
proof            (modus-ponens tm-22 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54892.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D)))), M:tm-22, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54893
in-theory        54893
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D))))
theorem-size     27
proof            (modus-ponens tm-21 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54893.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D)))), M:tm-21, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54894
in-theory        54894
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     35
proof            (modus-ponens tm-20 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54894.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-20, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54895
in-theory        54895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D))))
theorem-size     27
proof            (modus-ponens tm-19 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54895.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> (C -> D)))), M:tm-19, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54896
in-theory        54896
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((A -> B) -> (A -> B)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     37
proof            (modus-ponens tm-9 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-9 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54896.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((A -> B) -> (A -> B)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54897
in-theory        54897
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> B)) -> C) -> ((((A -> (B -> D)) or ((A -> B) -> (A -> D))) or ((A -> B) -> (A -> B))) -> C))
theorem-size     33
proof            (modus-ponens tm-8 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54897.        ((((A -> B) -> (A -> B)) -> C) -> ((((A -> (B -> D)) or ((A -> B) -> (A -> D))) or ((A -> B) -> (A -> B))) -> C)), M:tm-8, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-54898
in-theory        54898
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> (B -> C))))
theorem-size     23
proof            (modus-ponens tm-7 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-7 tm-8 tm-2 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54898.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> (B -> C)))), M:tm-7, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54899
in-theory        54899
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) or D)
theorem-size     23
proof            (modus-ponens tm-6 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-6 tm-8 tm-2 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54899.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) or D), M:tm-6, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54900
in-theory        54900
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> (B -> C))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54900.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> (B -> C))) and A)), M:tm-5, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54901
in-theory        54901
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> B)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> B)))
theorem-size     35
proof            (modus-ponens tm-2 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Am Bm)) (C (-> Am Bm))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54901.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> B)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> B))), M:tm-2, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Am Bm)) (C (-> Am Bm)))
================================================================
tm-name          tm-54902
in-theory        54902
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> (B -> C))))
theorem-size     23
proof            (modus-ponens tm-1 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-54902.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> (B -> C)))), M:tm-1, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-54903
in-theory        54903
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-665 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54903.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-665, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54904
in-theory        54904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (D or ((A -> (B -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-623 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54904.        (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (D or ((A -> (B -> C)) -> (A -> C)))), M:tm-623, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54905
in-theory        54905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-622 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54905.        ((A -> (B -> (C or B))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-622, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54906
in-theory        54906
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or D)))
theorem-size     33
proof            (modus-ponens tm-609 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54906.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E or D))), M:tm-609, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54907
in-theory        54907
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-605 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54907.        ((A -> ((B -> (C or B)) and A)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-605, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54908
in-theory        54908
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-595 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       245
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54908.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-595, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54909
in-theory        54909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-550 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54909.        (((A -> (B or A)) or C) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-550, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54910
in-theory        54910
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-540 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54910.        ((A or (B -> (C or B))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-540, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54911
in-theory        54911
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-530 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54911.        ((A or (B -> (B or C))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-530, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54912
in-theory        54912
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-520 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54912.        ((A or (B -> (C -> (B and C)))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-520, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54913
in-theory        54913
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-510 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54913.        ((A or ((B and C) -> C)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-510, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54914
in-theory        54914
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-500 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54914.        ((A or ((B and C) -> B)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-500, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54915
in-theory        54915
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> ((F -> G) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-490 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54915.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> ((F -> G) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-490, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54916
in-theory        54916
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-480 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54916.        ((A or (B -> (C -> B))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-480, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54917
in-theory        54917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> C)) or D))
theorem-size     29
proof            (modus-ponens tm-470 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54917.        (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> C)) or D)), M:tm-470, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54918
in-theory        54918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-469 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54918.        ((A -> (B -> (B or C))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-469, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54919
in-theory        54919
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D or E)))
theorem-size     33
proof            (modus-ponens tm-456 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54919.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (D or E))), M:tm-456, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54920
in-theory        54920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-453 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54920.        ((A -> ((B -> (B or C)) and A)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-453, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54921
in-theory        54921
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-443 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       245
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54921.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-443, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54922
in-theory        54922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-409 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54922.        (((A -> (A or B)) or C) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-409, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54923
in-theory        54923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-400 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54923.        (((A -> (B -> (A and B))) or C) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-400, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54924
in-theory        54924
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-391 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54924.        ((((A and B) -> B) or C) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-391, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54925
in-theory        54925
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-382 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54925.        ((((A and B) -> A) or C) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-382, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54926
in-theory        54926
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> ((F -> G) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-373 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54926.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> ((F -> G) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-373, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54927
in-theory        54927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-364 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54927.        (((A -> (B -> A)) or C) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-364, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54928
in-theory        54928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (D -> (((A -> (B -> C)) -> (A -> C)) and D)))
theorem-size     31
proof            (modus-ponens tm-355 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54928.        (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (D -> (((A -> (B -> C)) -> (A -> C)) and D))), M:tm-355, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54929
in-theory        54929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-354 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54929.        ((A -> (B -> (C -> (B and C)))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-354, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54930
in-theory        54930
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (D and E))))
theorem-size     35
proof            (modus-ponens tm-341 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54930.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54931
in-theory        54931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     37
proof            (modus-ponens tm-338 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54931.        (((A -> B) -> (A -> (A and B))) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-338, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54932
in-theory        54932
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     73
proof            (modus-ponens tm-328 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       267
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54932.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) and ((A -> (B -> C)) -> (A -> C))))), M:tm-328, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54933
in-theory        54933
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     63
proof            (modus-ponens tm-327 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       253
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54933.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-327, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54934
in-theory        54934
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-326 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       245
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54934.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-326, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54935
in-theory        54935
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-325 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       245
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54935.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-325, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54936
in-theory        54936
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-324 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       277
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54936.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-324, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54937
in-theory        54937
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-323 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       245
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54937.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-323, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54938
in-theory        54938
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> E))
theorem-size     33
proof            (modus-ponens tm-322 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54938.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> E)), M:tm-322, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54939
in-theory        54939
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> D))
theorem-size     33
proof            (modus-ponens tm-320 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54939.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D and E) -> D)), M:tm-320, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54940
in-theory        54940
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-318 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54940.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54941
in-theory        54941
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))))
theorem-size     63
proof            (modus-ponens tm-316 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       251
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54941.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))))), M:tm-316, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54942
in-theory        54942
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> D)))
theorem-size     33
proof            (modus-ponens tm-315 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54942.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (E -> D))), M:tm-315, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54943
in-theory        54943
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))))))
theorem-size     75
proof            (modus-ponens tm-313 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       253
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54943.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))))), M:tm-313, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54944
in-theory        54944
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> C))) -> D)))
theorem-size     69
proof            (modus-ponens tm-312 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       251
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54944.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> C))) -> D))), M:tm-312, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54945
in-theory        54945
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-311 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54945.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D or (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-311, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54946
in-theory        54946
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) or D))
theorem-size     57
proof            (modus-ponens tm-310 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54946.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) or D)), M:tm-310, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54947
in-theory        54947
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and D)))
theorem-size     59
proof            (modus-ponens tm-309 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54947.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and D))), M:tm-309, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54948
in-theory        54948
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (A -> (B -> C))) -> (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (A -> C))))
theorem-size     73
proof            (modus-ponens tm-306 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       257
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54948.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (A -> (B -> C))) -> (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (A -> C)))), M:tm-306, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
================================================================
tm-name          tm-54949
in-theory        54949
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-305 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54949.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-305, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54950
in-theory        54950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-303 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54950.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-303, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54951
in-theory        54951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-270 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54951.        ((A -> (((B and C) -> C) and A)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-270, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54952
in-theory        54952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-239 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54952.        ((A -> (((B and C) -> B) and A)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-239, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54953
in-theory        54953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> ((F -> G) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-210 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54953.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> ((F -> G) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-210, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54954
in-theory        54954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-183 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54954.        ((A -> ((B -> (C -> B)) and A)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-183, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54955
in-theory        54955
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-157 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54955.        ((A -> ((B and C) -> C)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-157, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54956
in-theory        54956
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-147 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54956.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-147, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54957
in-theory        54957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-134 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54957.        ((A -> ((B and C) -> B)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-134, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54958
in-theory        54958
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-125 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54958.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-125, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54959
in-theory        54959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> C)))
theorem-size     33
proof            (modus-ponens tm-114 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C Am) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54959.        (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> C))), M:tm-114, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C Am) (D Cm))
================================================================
tm-name          tm-54960
in-theory        54960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> ((F -> G) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-113 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54960.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> ((F -> G) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-113, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54961
in-theory        54961
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     47
proof            (modus-ponens tm-105 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       245
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54961.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-105, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54962
in-theory        54962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-95 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54962.        (((A -> B) -> (A -> A)) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-95, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54963
in-theory        54963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (D -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-84 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54963.        (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (D -> ((A -> (B -> C)) -> (A -> C)))), M:tm-84, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54964
in-theory        54964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-83 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54964.        ((A -> (B -> (C -> B))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-83, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54965
in-theory        54965
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> ((C -> D) -> C)) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     33
proof            (modus-ponens tm-76 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54965.        (((not (not A)) -> A) and (((B -> ((C -> D) -> C)) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-76, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54966
in-theory        54966
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))))) or ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     47
proof            (modus-ponens tm-73 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54966.        (((not (not ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))))) or ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-73, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54967
in-theory        54967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     39
proof            (modus-ponens tm-69 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54967.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-69, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54968
in-theory        54968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-54 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54968.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-54, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54969
in-theory        54969
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     37
proof            (modus-ponens tm-50 tm-677 ((A (-> Am (-> (-> Bm Cm) Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-7 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54969.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-50, m:tm-677, u:((A (-> Am (-> (-> Bm Cm) Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54970
in-theory        54970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> B)) or ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     35
proof            (modus-ponens tm-49 tm-677 ((A (-> Am (-> (-> Bm Cm) Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-6 tm-2)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54970.        (((A -> ((B -> C) -> B)) or ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-49, m:tm-677, u:((A (-> Am (-> (-> Bm Cm) Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54971
in-theory        54971
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> ((C -> D) -> C)) or ((B -> (C -> D)) -> (B -> C)))) or ((B -> ((C -> D) -> C)) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D)))
theorem-size     47
proof            (modus-ponens tm-47 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54971.        (((A and ((B -> ((C -> D) -> C)) or ((B -> (C -> D)) -> (B -> C)))) or ((B -> ((C -> D) -> C)) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54972
in-theory        54972
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) and D) or ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     47
proof            (modus-ponens tm-46 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54972.        (((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) and D) or ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54973
in-theory        54973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-42 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54973.        ((A -> (B or A)) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54974
in-theory        54974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-32 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54974.        ((A -> (A or B)) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54975
in-theory        54975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     45
proof            (modus-ponens tm-24 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54975.        (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54976
in-theory        54976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-23 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54976.        ((A -> (B -> (A and B))) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54977
in-theory        54977
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-22 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54977.        (((A and B) -> B) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54978
in-theory        54978
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-21 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54978.        (((A and B) -> A) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54979
in-theory        54979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-20 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54979.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54980
in-theory        54980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-19 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54980.        ((A -> (B -> A)) and (((C -> ((D -> E) -> D)) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54981
in-theory        54981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))))
theorem-size     35
proof            (modus-ponens tm-12 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54981.        (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))), M:tm-12, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54982
in-theory        54982
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))))
theorem-size     47
proof            (modus-ponens tm-9 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-9 tm-8 tm-2)
proof-size       181
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54982.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))))), M:tm-9, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54983
in-theory        54983
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> C))) -> D))
theorem-size     41
proof            (modus-ponens tm-8 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54983.        ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-54984
in-theory        54984
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> ((C -> D) -> C)) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     29
proof            (modus-ponens tm-7 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-7 tm-8 tm-2)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54984.        (A or (((B -> ((C -> D) -> C)) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54985
in-theory        54985
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) or D)
theorem-size     29
proof            (modus-ponens tm-6 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-6 tm-8 tm-2)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54985.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54986
in-theory        54986
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> ((C -> D) -> C)) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54986.        (A -> ((((B -> ((C -> D) -> C)) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54987
in-theory        54987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (A -> (B -> C))) -> (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (A -> C)))
theorem-size     45
proof            (modus-ponens tm-2 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-8)
proof-size       181
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54987.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (A -> (B -> C))) -> (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (A -> C))), M:tm-2, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
================================================================
tm-name          tm-54988
in-theory        54988
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> ((C -> D) -> C)) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     29
proof            (modus-ponens tm-1 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-54988.        (A -> (((B -> ((C -> D) -> C)) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-54989
in-theory        54989
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-54989.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-665, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-54990
in-theory        54990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-54990.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-622, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-54991
in-theory        54991
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H or G)))
theorem-size     33
proof            (modus-ponens tm-609 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-54991.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H or G))), M:tm-609, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-54992
in-theory        54992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-54992.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-605, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-54993
in-theory        54993
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-54993.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-595, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-54994
in-theory        54994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-54994.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-550, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-54995
in-theory        54995
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-54995.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-540, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-54996
in-theory        54996
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-54996.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-530, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-54997
in-theory        54997
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-54997.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-520, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-54998
in-theory        54998
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-54998.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-510, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-54999
in-theory        54999
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-54999.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-500, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55000
in-theory        55000
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55000.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-490, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55001
in-theory        55001
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55001.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-480, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55002
in-theory        55002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55002.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-469, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55003
in-theory        55003
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (G or H)))
theorem-size     33
proof            (modus-ponens tm-456 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55003.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (G or H))), M:tm-456, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55004
in-theory        55004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55004.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-453, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55005
in-theory        55005
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (G or H)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55005.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (G or H)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-443, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55006
in-theory        55006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55006.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-409, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55007
in-theory        55007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55007.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-400, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55008
in-theory        55008
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55008.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-391, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55009
in-theory        55009
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55009.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-382, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55010
in-theory        55010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55010.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-373, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55011
in-theory        55011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55011.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-364, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55012
in-theory        55012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55012.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-354, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55013
in-theory        55013
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H -> (G and H))))
theorem-size     35
proof            (modus-ponens tm-341 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55013.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55014
in-theory        55014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55014.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-338, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55015
in-theory        55015
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     69
proof            (modus-ponens tm-328 tm-678 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       251
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55015.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-328, m:tm-678, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-55016
in-theory        55016
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55016.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-327, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55017
in-theory        55017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and H) -> H) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55017.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and H) -> H) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-326, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55018
in-theory        55018
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and H) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55018.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G and H) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-325, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55019
in-theory        55019
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       265
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55019.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-324, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55020
in-theory        55020
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55020.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-323, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55021
in-theory        55021
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G and H) -> H))
theorem-size     33
proof            (modus-ponens tm-322 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55021.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G and H) -> H)), M:tm-322, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55022
in-theory        55022
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G and H) -> G))
theorem-size     33
proof            (modus-ponens tm-320 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55022.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G and H) -> G)), M:tm-320, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55023
in-theory        55023
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     41
proof            (modus-ponens tm-318 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55023.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55024
in-theory        55024
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     55
proof            (modus-ponens tm-316 tm-678 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55024.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-678, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-55025
in-theory        55025
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H -> G)))
theorem-size     33
proof            (modus-ponens tm-315 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55025.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (H -> G))), M:tm-315, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55026
in-theory        55026
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     71
proof            (modus-ponens tm-313 tm-678 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55026.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-678, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-55027
in-theory        55027
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     73
proof            (modus-ponens tm-312 tm-678 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55027.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-312, m:tm-678, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-55028
in-theory        55028
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55028.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-311, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55029
in-theory        55029
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G))
theorem-size     57
proof            (modus-ponens tm-310 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55029.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)), M:tm-310, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55030
in-theory        55030
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and G)))
theorem-size     59
proof            (modus-ponens tm-309 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55030.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and G))), M:tm-309, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55031
in-theory        55031
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> F))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (D -> F)))))
theorem-size     69
proof            (modus-ponens tm-306 tm-678 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Fm))) (C (-> (-> Dm Em) (-> Dm Fm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55031.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> F))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (D -> F))))), M:tm-306, m:tm-678, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Fm))) (C (-> (-> Dm Em) (-> Dm Fm))))
================================================================
tm-name          tm-55032
in-theory        55032
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55032.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (G -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-305, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55033
in-theory        55033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55033.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-303, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55034
in-theory        55034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55034.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-270, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55035
in-theory        55035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55035.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-239, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55036
in-theory        55036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55036.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-210, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55037
in-theory        55037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55037.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-183, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55038
in-theory        55038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55038.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-157, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55039
in-theory        55039
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55039.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-147, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55040
in-theory        55040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55040.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-134, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55041
in-theory        55041
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55041.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-125, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55042
in-theory        55042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55042.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-113, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55043
in-theory        55043
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55043.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-105, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55044
in-theory        55044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55044.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-95, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55045
in-theory        55045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55045.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-83, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55046
in-theory        55046
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55046.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-76, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55047
in-theory        55047
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-73 tm-678 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55047.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-73, m:tm-678, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-55048
in-theory        55048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-1)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55048.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-69, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55049
in-theory        55049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-54 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55049.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-54, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55050
in-theory        55050
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-50 tm-678 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55050.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-50, m:tm-678, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-55051
in-theory        55051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-49 tm-678 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55051.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-49, m:tm-678, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-55052
in-theory        55052
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-47 tm-678 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55052.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-47, m:tm-678, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-55053
in-theory        55053
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-46 tm-678 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55053.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-46, m:tm-678, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-55054
in-theory        55054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-42 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55054.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-42, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55055
in-theory        55055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-32 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55055.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-32, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55056
in-theory        55056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-24 tm-678 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55056.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-24, m:tm-678, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-55057
in-theory        55057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-23 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55057.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-23, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55058
in-theory        55058
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-22 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55058.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-22, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55059
in-theory        55059
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-21 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55059.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-21, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55060
in-theory        55060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     41
proof            (modus-ponens tm-20 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55060.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-20, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55061
in-theory        55061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-19 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55061.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-19, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55062
in-theory        55062
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     43
proof            (modus-ponens tm-9 tm-678 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-9 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55062.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-678, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-55063
in-theory        55063
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((((E -> (F -> G)) or ((E -> F) -> (E -> G))) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))
theorem-size     45
proof            (modus-ponens tm-8 tm-678 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       169
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55063.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((((E -> (F -> G)) or ((E -> F) -> (E -> G))) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-678, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-55064
in-theory        55064
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-7 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-7 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55064.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-7, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55065
in-theory        55065
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G)
theorem-size     29
proof            (modus-ponens tm-6 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-6 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55065.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) or G), M:tm-6, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55066
in-theory        55066
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55066.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and A)), M:tm-5, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55067
in-theory        55067
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> F))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-2 tm-678 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Fm))) (C (-> (-> Dm Em) (-> Dm Fm)))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55067.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> F))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (D -> F)))), M:tm-2, m:tm-678, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Fm))) (C (-> (-> Dm Em) (-> Dm Fm))))
================================================================
tm-name          tm-55068
in-theory        55068
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-1 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-55068.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-1, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-55069
in-theory        55069
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-665 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55069.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-665, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55070
in-theory        55070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-622 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55070.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-622, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55071
in-theory        55071
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55071.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (F -> (G or F))), M:tm-609, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55072
in-theory        55072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-605 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55072.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-605, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55073
in-theory        55073
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-595 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55073.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)))), M:tm-595, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55074
in-theory        55074
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-550 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55074.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-550, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55075
in-theory        55075
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-540 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55075.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-540, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55076
in-theory        55076
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-530 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55076.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-530, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55077
in-theory        55077
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-520 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55077.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-520, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55078
in-theory        55078
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-510 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55078.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-510, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55079
in-theory        55079
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-500 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55079.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-500, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55080
in-theory        55080
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-490 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55080.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H))), M:tm-490, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55081
in-theory        55081
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-480 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55081.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-480, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55082
in-theory        55082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-469 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55082.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-469, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55083
in-theory        55083
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55083.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (F -> (F or G))), M:tm-456, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55084
in-theory        55084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-453 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55084.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-453, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55085
in-theory        55085
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-443 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55085.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)))), M:tm-443, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55086
in-theory        55086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-409 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55086.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-409, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55087
in-theory        55087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-400 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55087.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-400, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55088
in-theory        55088
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-391 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55088.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-391, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55089
in-theory        55089
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-382 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55089.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-382, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55090
in-theory        55090
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-373 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55090.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H))), M:tm-373, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55091
in-theory        55091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-364 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55091.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-364, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55092
in-theory        55092
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-354 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55092.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-354, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55093
in-theory        55093
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55093.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55094
in-theory        55094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F)))
theorem-size     29
proof            (modus-ponens tm-338 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55094.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F))), M:tm-338, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55095
in-theory        55095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D and E) -> D))))
theorem-size     53
proof            (modus-ponens tm-328 tm-679 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55095.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D and E) -> D)))), M:tm-328, m:tm-679, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-55096
in-theory        55096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D))))
theorem-size     47
proof            (modus-ponens tm-327 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55096.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)))), M:tm-327, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55097
in-theory        55097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-326 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55097.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)))), M:tm-326, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55098
in-theory        55098
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-325 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55098.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)))), M:tm-325, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55099
in-theory        55099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D))))
theorem-size     53
proof            (modus-ponens tm-324 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55099.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)))), M:tm-324, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55100
in-theory        55100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D))))
theorem-size     45
proof            (modus-ponens tm-323 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55100.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)))), M:tm-323, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55101
in-theory        55101
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55101.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((F and G) -> G)), M:tm-322, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55102
in-theory        55102
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55102.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((F and G) -> F)), M:tm-320, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55103
in-theory        55103
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55103.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55104
in-theory        55104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     47
proof            (modus-ponens tm-316 tm-679 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55104.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-679, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-55105
in-theory        55105
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55105.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (F -> (G -> F))), M:tm-315, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55106
in-theory        55106
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D and E) -> D))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     55
proof            (modus-ponens tm-313 tm-679 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55106.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D and E) -> D))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-679, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-55107
in-theory        55107
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((((D and E) -> D) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((D and E) -> D)) -> F)))
theorem-size     49
proof            (modus-ponens tm-312 tm-679 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55107.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((((D and E) -> D) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((D and E) -> D)) -> F))), M:tm-312, m:tm-679, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-55108
in-theory        55108
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D))))
theorem-size     41
proof            (modus-ponens tm-311 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55108.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)))), M:tm-311, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55109
in-theory        55109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55109.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) or F)), M:tm-310, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55110
in-theory        55110
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55110.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and F))), M:tm-309, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55111
in-theory        55111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and E)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     53
proof            (modus-ponens tm-306 tm-679 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and Dm Em)) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55111.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and E)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-306, m:tm-679, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and Dm Em)) (C Dm))
================================================================
tm-name          tm-55112
in-theory        55112
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D))))
theorem-size     41
proof            (modus-ponens tm-305 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55112.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)))), M:tm-305, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55113
in-theory        55113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     31
proof            (modus-ponens tm-303 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55113.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-303, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55114
in-theory        55114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-270 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55114.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-270, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55115
in-theory        55115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-239 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55115.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-239, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55116
in-theory        55116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H)))
theorem-size     37
proof            (modus-ponens tm-210 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55116.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H))), M:tm-210, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55117
in-theory        55117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-183 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55117.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-183, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55118
in-theory        55118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-157 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55118.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-157, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55119
in-theory        55119
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     35
proof            (modus-ponens tm-147 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55119.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-147, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55120
in-theory        55120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-134 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55120.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-134, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55121
in-theory        55121
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     35
proof            (modus-ponens tm-125 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55121.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-125, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55122
in-theory        55122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H)))
theorem-size     35
proof            (modus-ponens tm-113 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55122.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H))), M:tm-113, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55123
in-theory        55123
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-105 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55123.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-105, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55124
in-theory        55124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-95 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55124.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F))), M:tm-95, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55125
in-theory        55125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-83 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55125.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-83, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55126
in-theory        55126
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> E)))
theorem-size     25
proof            (modus-ponens tm-76 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55126.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> E))), M:tm-76, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55127
in-theory        55127
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> D))
theorem-size     35
proof            (modus-ponens tm-73 tm-679 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55127.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> D)), M:tm-73, m:tm-679, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-55128
in-theory        55128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-69 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-1 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55128.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F))), M:tm-69, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55129
in-theory        55129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-54 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55129.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-54, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55130
in-theory        55130
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> D))
theorem-size     27
proof            (modus-ponens tm-50 tm-679 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Dm))))
axioms-used      (tm-8 tm-7 tm-2 tm-1 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55130.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> D)), M:tm-50, m:tm-679, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-55131
in-theory        55131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> D))
theorem-size     25
proof            (modus-ponens tm-49 tm-679 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Dm))))
axioms-used      (tm-8 tm-6 tm-2 tm-1 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55131.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> D)), M:tm-49, m:tm-679, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-55132
in-theory        55132
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((E and F) -> E))
theorem-size     35
proof            (modus-ponens tm-47 tm-679 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55132.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((E and F) -> E)), M:tm-47, m:tm-679, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-55133
in-theory        55133
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((E and F) -> E))
theorem-size     35
proof            (modus-ponens tm-46 tm-679 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55133.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((E and F) -> E)), M:tm-46, m:tm-679, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-55134
in-theory        55134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-42 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55134.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F))), M:tm-42, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55135
in-theory        55135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-32 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55135.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F))), M:tm-32, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55136
in-theory        55136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D and E) -> D)))
theorem-size     33
proof            (modus-ponens tm-24 tm-679 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55136.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D and E) -> D))), M:tm-24, m:tm-679, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-55137
in-theory        55137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-23 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55137.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F))), M:tm-23, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55138
in-theory        55138
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-22 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55138.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F))), M:tm-22, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55139
in-theory        55139
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-21 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55139.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F))), M:tm-21, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55140
in-theory        55140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     33
proof            (modus-ponens tm-20 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55140.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-20, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55141
in-theory        55141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-19 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55141.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> F))), M:tm-19, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55142
in-theory        55142
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D and E) -> D))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     35
proof            (modus-ponens tm-9 tm-679 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-9 tm-8 tm-2 tm-1 tm-3)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55142.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D and E) -> D))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-679, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-55143
in-theory        55143
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> ((((D -> (E -> F)) or ((D -> E) -> (D -> F))) or ((A and B) -> A)) -> C))
theorem-size     29
proof            (modus-ponens tm-8 tm-679 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55143.        ((((A and B) -> A) -> C) -> ((((D -> (E -> F)) or ((D -> E) -> (D -> F))) or ((A and B) -> A)) -> C)), M:tm-8, m:tm-679, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-55144
in-theory        55144
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-7 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-7 tm-8 tm-2 tm-1 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55144.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> E))), M:tm-7, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55145
in-theory        55145
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-6 tm-8 tm-2 tm-1 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55145.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) or F), M:tm-6, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55146
in-theory        55146
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> E)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55146.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> E)) and A)), M:tm-5, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55147
in-theory        55147
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and E)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     33
proof            (modus-ponens tm-2 tm-679 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and Dm Em)) (C Dm)))
axioms-used      (tm-2 tm-8 tm-1 tm-3)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55147.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and E)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-2, m:tm-679, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and Dm Em)) (C Dm))
================================================================
tm-name          tm-55148
in-theory        55148
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-1 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-1 tm-8 tm-2 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-55148.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> E))), M:tm-1, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-55149
in-theory        55149
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-665 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55149.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-665, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55150
in-theory        55150
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-622 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55150.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-622, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55151
in-theory        55151
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55151.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (F -> (G or F))), M:tm-609, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55152
in-theory        55152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-605 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55152.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-605, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55153
in-theory        55153
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-595 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55153.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)))), M:tm-595, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55154
in-theory        55154
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-550 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55154.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-550, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55155
in-theory        55155
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-540 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55155.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-540, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55156
in-theory        55156
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-530 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55156.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-530, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55157
in-theory        55157
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-520 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55157.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-520, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55158
in-theory        55158
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-510 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55158.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-510, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55159
in-theory        55159
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-500 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55159.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-500, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55160
in-theory        55160
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-490 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55160.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I))), M:tm-490, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55161
in-theory        55161
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-480 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55161.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-480, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55162
in-theory        55162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-469 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55162.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-469, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55163
in-theory        55163
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55163.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (F -> (F or G))), M:tm-456, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55164
in-theory        55164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-453 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55164.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-453, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55165
in-theory        55165
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-443 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55165.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)))), M:tm-443, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55166
in-theory        55166
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-409 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55166.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-409, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55167
in-theory        55167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-400 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55167.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-400, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55168
in-theory        55168
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-391 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55168.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-391, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55169
in-theory        55169
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-382 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55169.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-382, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55170
in-theory        55170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-373 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55170.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I))), M:tm-373, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55171
in-theory        55171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-364 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55171.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-364, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55172
in-theory        55172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-354 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55172.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-354, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55173
in-theory        55173
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55173.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55174
in-theory        55174
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G)))
theorem-size     29
proof            (modus-ponens tm-338 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55174.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G))), M:tm-338, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55175
in-theory        55175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D and E) -> E))))
theorem-size     53
proof            (modus-ponens tm-328 tm-680 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55175.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D and E) -> E)))), M:tm-328, m:tm-680, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-55176
in-theory        55176
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E))))
theorem-size     47
proof            (modus-ponens tm-327 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55176.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)))), M:tm-327, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55177
in-theory        55177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-326 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55177.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)))), M:tm-326, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55178
in-theory        55178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-325 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-4)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55178.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)))), M:tm-325, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55179
in-theory        55179
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E))))
theorem-size     53
proof            (modus-ponens tm-324 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55179.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)))), M:tm-324, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55180
in-theory        55180
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E))))
theorem-size     45
proof            (modus-ponens tm-323 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55180.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)))), M:tm-323, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55181
in-theory        55181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55181.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((F and G) -> G)), M:tm-322, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55182
in-theory        55182
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55182.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((F and G) -> F)), M:tm-320, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55183
in-theory        55183
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55183.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55184
in-theory        55184
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     47
proof            (modus-ponens tm-316 tm-680 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55184.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-680, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-55185
in-theory        55185
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55185.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (F -> (G -> F))), M:tm-315, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55186
in-theory        55186
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D and E) -> E))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     55
proof            (modus-ponens tm-313 tm-680 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-4)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55186.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D and E) -> E))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-680, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-55187
in-theory        55187
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((((D and E) -> E) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((D and E) -> E)) -> F)))
theorem-size     49
proof            (modus-ponens tm-312 tm-680 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55187.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((((D and E) -> E) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((D and E) -> E)) -> F))), M:tm-312, m:tm-680, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-55188
in-theory        55188
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E))))
theorem-size     41
proof            (modus-ponens tm-311 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55188.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)))), M:tm-311, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55189
in-theory        55189
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55189.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) or F)), M:tm-310, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55190
in-theory        55190
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55190.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and F))), M:tm-309, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55191
in-theory        55191
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and E)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)))
theorem-size     53
proof            (modus-ponens tm-306 tm-680 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and Dm Em)) (C Em)))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55191.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and E)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))), M:tm-306, m:tm-680, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and Dm Em)) (C Em))
================================================================
tm-name          tm-55192
in-theory        55192
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E))))
theorem-size     41
proof            (modus-ponens tm-305 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55192.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)))), M:tm-305, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55193
in-theory        55193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     31
proof            (modus-ponens tm-303 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55193.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-303, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55194
in-theory        55194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-270 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55194.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-270, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55195
in-theory        55195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-239 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55195.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-239, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55196
in-theory        55196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I)))
theorem-size     37
proof            (modus-ponens tm-210 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55196.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I))), M:tm-210, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55197
in-theory        55197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-183 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55197.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-183, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55198
in-theory        55198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-157 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55198.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-157, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55199
in-theory        55199
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     35
proof            (modus-ponens tm-147 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55199.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-147, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55200
in-theory        55200
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-134 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55200.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-134, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55201
in-theory        55201
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     35
proof            (modus-ponens tm-125 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55201.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-125, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55202
in-theory        55202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I)))
theorem-size     35
proof            (modus-ponens tm-113 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55202.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I))), M:tm-113, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55203
in-theory        55203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-105 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55203.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-105, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55204
in-theory        55204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-95 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55204.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G))), M:tm-95, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55205
in-theory        55205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-83 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55205.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-83, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55206
in-theory        55206
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> F)))
theorem-size     25
proof            (modus-ponens tm-76 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55206.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> F))), M:tm-76, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55207
in-theory        55207
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> E))
theorem-size     35
proof            (modus-ponens tm-73 tm-680 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55207.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> E)), M:tm-73, m:tm-680, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-55208
in-theory        55208
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-69 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-1 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55208.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G))), M:tm-69, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55209
in-theory        55209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-54 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55209.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-54, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55210
in-theory        55210
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> E))
theorem-size     27
proof            (modus-ponens tm-50 tm-680 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Em))))
axioms-used      (tm-8 tm-7 tm-2 tm-1 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55210.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> E)), M:tm-50, m:tm-680, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Em)))
================================================================
tm-name          tm-55211
in-theory        55211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> E))
theorem-size     25
proof            (modus-ponens tm-49 tm-680 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Em))))
axioms-used      (tm-8 tm-6 tm-2 tm-1 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55211.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> E)), M:tm-49, m:tm-680, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (and Dm Em) Em)))
================================================================
tm-name          tm-55212
in-theory        55212
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((E and F) -> F))
theorem-size     35
proof            (modus-ponens tm-47 tm-680 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55212.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((E and F) -> F)), M:tm-47, m:tm-680, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-55213
in-theory        55213
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((E and F) -> F))
theorem-size     35
proof            (modus-ponens tm-46 tm-680 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55213.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((E and F) -> F)), M:tm-46, m:tm-680, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-55214
in-theory        55214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-42 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55214.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G))), M:tm-42, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55215
in-theory        55215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-32 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55215.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G))), M:tm-32, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55216
in-theory        55216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D and E) -> E)))
theorem-size     33
proof            (modus-ponens tm-24 tm-680 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55216.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D and E) -> E))), M:tm-24, m:tm-680, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-55217
in-theory        55217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-23 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55217.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G))), M:tm-23, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55218
in-theory        55218
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-22 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55218.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G))), M:tm-22, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55219
in-theory        55219
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-21 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55219.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G))), M:tm-21, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55220
in-theory        55220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     33
proof            (modus-ponens tm-20 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-4)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55220.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-20, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55221
in-theory        55221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-19 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55221.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F and G) -> G))), M:tm-19, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55222
in-theory        55222
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D and E) -> E))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     35
proof            (modus-ponens tm-9 tm-680 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-9 tm-8 tm-2 tm-1 tm-4)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55222.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D and E) -> E))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-680, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-55223
in-theory        55223
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> ((((D -> (E -> F)) or ((D -> E) -> (D -> F))) or ((A and B) -> B)) -> C))
theorem-size     29
proof            (modus-ponens tm-8 tm-680 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55223.        ((((A and B) -> B) -> C) -> ((((D -> (E -> F)) or ((D -> E) -> (D -> F))) or ((A and B) -> B)) -> C)), M:tm-8, m:tm-680, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-55224
in-theory        55224
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-7 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-7 tm-8 tm-2 tm-1 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55224.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> F))), M:tm-7, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55225
in-theory        55225
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-6 tm-8 tm-2 tm-1 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55225.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) or F), M:tm-6, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55226
in-theory        55226
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> F)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55226.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> F)) and A)), M:tm-5, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55227
in-theory        55227
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and E)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))
theorem-size     33
proof            (modus-ponens tm-2 tm-680 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and Dm Em)) (C Em)))
axioms-used      (tm-2 tm-8 tm-1 tm-4)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55227.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and E)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)), M:tm-2, m:tm-680, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and Dm Em)) (C Em))
================================================================
tm-name          tm-55228
in-theory        55228
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-1 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-1 tm-8 tm-2 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-55228.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E and F) -> F))), M:tm-1, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-55229
in-theory        55229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (C -> (C -> D))))
theorem-size     15
proof            (modus-ponens tm-681 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-55229.        ((A -> (B -> A)) and ((C -> D) -> (C -> (C -> D)))), M:tm-681, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-55230
in-theory        55230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (C -> ((C -> D) and C))))
theorem-size     17
proof            (modus-ponens tm-681 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-55230.        ((A -> (B -> A)) and ((C -> D) -> (C -> ((C -> D) and C)))), M:tm-681, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-55231
in-theory        55231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> C) -> ((C -> D) -> (((C -> D) or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-681 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-55231.        ((A -> (B -> A)) and (((C -> D) -> C) -> ((C -> D) -> (((C -> D) or C) -> D)))), M:tm-681, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-55232
in-theory        55232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (C -> (E -> C))))
theorem-size     15
proof            (modus-ponens tm-681 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-55232.        ((A -> (B -> A)) and ((C -> D) -> (C -> (E -> C)))), M:tm-681, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-55233
in-theory        55233
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> F) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     27
proof            (modus-ponens tm-681 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-55233.        ((A -> (B -> A)) and (((C -> (D -> E)) -> F) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-681, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-55234
in-theory        55234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> E) -> ((C and D) -> C)))
theorem-size     17
proof            (modus-ponens tm-681 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-55234.        ((A -> (B -> A)) and (((C and D) -> E) -> ((C and D) -> C))), M:tm-681, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-55235
in-theory        55235
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> E) -> ((C and D) -> D)))
theorem-size     17
proof            (modus-ponens tm-681 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-55235.        ((A -> (B -> A)) and (((C and D) -> E) -> ((C and D) -> D))), M:tm-681, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-55236
in-theory        55236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (C -> (E -> (C and E)))))
theorem-size     17
proof            (modus-ponens tm-681 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-55236.        ((A -> (B -> A)) and ((C -> D) -> (C -> (E -> (C and E))))), M:tm-681, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-55237
in-theory        55237
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (C -> (C or E))))
theorem-size     15
proof            (modus-ponens tm-681 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-55237.        ((A -> (B -> A)) and ((C -> D) -> (C -> (C or E)))), M:tm-681, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-55238
in-theory        55238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> (C -> (E or C))))
theorem-size     15
proof            (modus-ponens tm-681 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-55238.        ((A -> (B -> A)) and ((C -> D) -> (C -> (E or C)))), M:tm-681, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-55239
in-theory        55239
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55239.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-665, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55240
in-theory        55240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> (F -> E)) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-623 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55240.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> (F -> E)) and ((A -> B) -> (A -> C))))), M:tm-623, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55241
in-theory        55241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55241.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-622, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55242
in-theory        55242
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (F -> (G or F)))
theorem-size     33
proof            (modus-ponens tm-609 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55242.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (F -> (G or F))), M:tm-609, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55243
in-theory        55243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55243.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-605, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55244
in-theory        55244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55244.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))), M:tm-595, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55245
in-theory        55245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55245.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-550, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55246
in-theory        55246
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55246.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-540, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55247
in-theory        55247
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55247.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-530, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55248
in-theory        55248
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55248.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-520, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55249
in-theory        55249
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55249.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-510, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55250
in-theory        55250
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55250.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-500, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55251
in-theory        55251
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> H)) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55251.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> H)) and ((E -> F) -> (E -> G))))), M:tm-490, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55252
in-theory        55252
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55252.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-480, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55253
in-theory        55253
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> D)) and ((A -> B) -> (A -> C))) or F))
theorem-size     29
proof            (modus-ponens tm-470 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55253.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> D)) and ((A -> B) -> (A -> C))) or F)), M:tm-470, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55254
in-theory        55254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55254.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-469, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55255
in-theory        55255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (F -> (F or G)))
theorem-size     33
proof            (modus-ponens tm-456 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55255.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (F -> (F or G))), M:tm-456, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55256
in-theory        55256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55256.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-453, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55257
in-theory        55257
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55257.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))), M:tm-443, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55258
in-theory        55258
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55258.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-409, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55259
in-theory        55259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55259.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-400, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55260
in-theory        55260
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55260.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-391, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55261
in-theory        55261
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55261.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-382, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55262
in-theory        55262
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> H)) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55262.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> H)) and ((E -> F) -> (E -> G))))), M:tm-373, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55263
in-theory        55263
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55263.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-364, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55264
in-theory        55264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E -> (F -> E)) and ((A -> B) -> (A -> C))) and D)))
theorem-size     31
proof            (modus-ponens tm-355 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55264.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E -> (F -> E)) and ((A -> B) -> (A -> C))) and D))), M:tm-355, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55265
in-theory        55265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55265.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-354, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55266
in-theory        55266
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (F -> (G -> (F and G))))
theorem-size     35
proof            (modus-ponens tm-341 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55266.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55267
in-theory        55267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55267.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E))))), M:tm-338, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55268
in-theory        55268
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((A -> B) -> (A -> C))))))
theorem-size     69
proof            (modus-ponens tm-328 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       239
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55268.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))), M:tm-328, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55269
in-theory        55269
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55269.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))), M:tm-327, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55270
in-theory        55270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55270.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))), M:tm-326, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55271
in-theory        55271
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55271.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))), M:tm-325, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55272
in-theory        55272
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       253
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55272.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))), M:tm-324, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55273
in-theory        55273
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55273.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))), M:tm-323, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55274
in-theory        55274
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((F and G) -> G))
theorem-size     33
proof            (modus-ponens tm-322 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55274.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((F and G) -> G)), M:tm-322, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55275
in-theory        55275
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((F and G) -> F))
theorem-size     33
proof            (modus-ponens tm-320 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55275.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((F and G) -> F)), M:tm-320, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55276
in-theory        55276
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     41
proof            (modus-ponens tm-318 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55276.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55277
in-theory        55277
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     55
proof            (modus-ponens tm-316 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55277.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55278
in-theory        55278
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (F -> (G -> F)))
theorem-size     33
proof            (modus-ponens tm-315 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55278.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (F -> (G -> F))), M:tm-315, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55279
in-theory        55279
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> D)) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     71
proof            (modus-ponens tm-313 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55279.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> D)) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55280
in-theory        55280
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((((D -> (E -> D)) and ((A -> B) -> (A -> C))) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) -> F)))
theorem-size     73
proof            (modus-ponens tm-312 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55280.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((((D -> (E -> D)) and ((A -> B) -> (A -> C))) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) -> F))), M:tm-312, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55281
in-theory        55281
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55281.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))), M:tm-311, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55282
in-theory        55282
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) or F))
theorem-size     57
proof            (modus-ponens tm-310 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55282.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) or F)), M:tm-310, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55283
in-theory        55283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and F)))
theorem-size     59
proof            (modus-ponens tm-309 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55283.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and F))), M:tm-309, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55284
in-theory        55284
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55284.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))), M:tm-305, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55285
in-theory        55285
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55285.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-303, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55286
in-theory        55286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55286.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-270, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55287
in-theory        55287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55287.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-239, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55288
in-theory        55288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> H)) and ((E -> F) -> (E -> G)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55288.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> H)) and ((E -> F) -> (E -> G))))), M:tm-210, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55289
in-theory        55289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55289.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-183, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55290
in-theory        55290
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55290.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-157, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55291
in-theory        55291
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55291.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-147, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55292
in-theory        55292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55292.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-134, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55293
in-theory        55293
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55293.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-125, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55294
in-theory        55294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> H)) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55294.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> H)) and ((E -> F) -> (E -> G))))), M:tm-113, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55295
in-theory        55295
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55295.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-105, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55296
in-theory        55296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55296.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E))))), M:tm-95, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55297
in-theory        55297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> E)) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-84 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55297.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> E)) and ((A -> B) -> (A -> C))))), M:tm-84, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55298
in-theory        55298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55298.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-83, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55299
in-theory        55299
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> E)) and ((B -> C) -> (B -> D)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55299.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> E)) and ((B -> C) -> (B -> D))))), M:tm-76, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55300
in-theory        55300
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-73 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55300.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-73, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55301
in-theory        55301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55301.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E))))), M:tm-69, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55302
in-theory        55302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-54 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55302.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-54, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55303
in-theory        55303
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-50 tm-681 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55303.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-50, m:tm-681, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55304
in-theory        55304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-49 tm-681 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55304.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-49, m:tm-681, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55305
in-theory        55305
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((E -> (F -> E)) and ((B -> C) -> (B -> D))))
theorem-size     43
proof            (modus-ponens tm-47 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55305.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((E -> (F -> E)) and ((B -> C) -> (B -> D)))), M:tm-47, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55306
in-theory        55306
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((E -> (F -> E)) and ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-46 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55306.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((E -> (F -> E)) and ((A -> B) -> (A -> C)))), M:tm-46, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55307
in-theory        55307
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-42 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55307.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E))))), M:tm-42, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55308
in-theory        55308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-32 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55308.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E))))), M:tm-32, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55309
in-theory        55309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-24 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55309.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((A -> B) -> (A -> C))))), M:tm-24, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55310
in-theory        55310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-23 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55310.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E))))), M:tm-23, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55311
in-theory        55311
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-22 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55311.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E))))), M:tm-22, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55312
in-theory        55312
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-21 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55312.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E))))), M:tm-21, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55313
in-theory        55313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-20 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55313.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-20, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55314
in-theory        55314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-19 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55314.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> F)) and ((C -> D) -> (C -> E))))), M:tm-19, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55315
in-theory        55315
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> D)) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     43
proof            (modus-ponens tm-9 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-9 tm-8 tm-2 tm-5 tm-1)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55315.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> D)) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55316
in-theory        55316
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and ((C -> D) -> (C -> E))) -> F) -> ((((C -> (D -> E)) or ((C -> D) -> (C -> E))) or ((A -> (B -> A)) and ((C -> D) -> (C -> E)))) -> F))
theorem-size     45
proof            (modus-ponens tm-8 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55316.        ((((A -> (B -> A)) and ((C -> D) -> (C -> E))) -> F) -> ((((C -> (D -> E)) or ((C -> D) -> (C -> E))) or ((A -> (B -> A)) and ((C -> D) -> (C -> E)))) -> F)), M:tm-8, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55317
in-theory        55317
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> E)) and ((B -> C) -> (B -> D)))))
theorem-size     29
proof            (modus-ponens tm-7 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-7 tm-8 tm-2 tm-5 tm-1)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55317.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> E)) and ((B -> C) -> (B -> D))))), M:tm-7, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55318
in-theory        55318
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) or F)
theorem-size     29
proof            (modus-ponens tm-6 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-6 tm-8 tm-2 tm-5 tm-1)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55318.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) or F), M:tm-6, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55319
in-theory        55319
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> E)) and ((B -> C) -> (B -> D)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55319.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> E)) and ((B -> C) -> (B -> D)))) and A)), M:tm-5, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55320
in-theory        55320
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> E)) and ((B -> C) -> (B -> D)))))
theorem-size     29
proof            (modus-ponens tm-1 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-1 tm-8 tm-2 tm-5)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-55320.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> E)) and ((B -> C) -> (B -> D))))), M:tm-1, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55321
in-theory        55321
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D -> E))))
theorem-size     23
proof            (modus-ponens tm-682 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-55321.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D -> E)))), M:tm-682, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-55322
in-theory        55322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> ((D -> E) and D))))
theorem-size     25
proof            (modus-ponens tm-682 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-55322.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> ((D -> E) and D)))), M:tm-682, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-55323
in-theory        55323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> D) -> ((D -> E) -> (((D -> E) or D) -> E))))
theorem-size     31
proof            (modus-ponens tm-682 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-55323.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> D) -> ((D -> E) -> (((D -> E) or D) -> E)))), M:tm-682, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-55324
in-theory        55324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (F -> D))))
theorem-size     23
proof            (modus-ponens tm-682 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-55324.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (F -> D)))), M:tm-682, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-55325
in-theory        55325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> G) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-682 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-55325.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> G) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-682, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-55326
in-theory        55326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> F) -> ((D and E) -> D)))
theorem-size     25
proof            (modus-ponens tm-682 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-55326.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> F) -> ((D and E) -> D))), M:tm-682, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-55327
in-theory        55327
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> F) -> ((D and E) -> E)))
theorem-size     25
proof            (modus-ponens tm-682 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-55327.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> F) -> ((D and E) -> E))), M:tm-682, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-55328
in-theory        55328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (F -> (D and F)))))
theorem-size     25
proof            (modus-ponens tm-682 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-55328.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (F -> (D and F))))), M:tm-682, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-55329
in-theory        55329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D or F))))
theorem-size     23
proof            (modus-ponens tm-682 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-55329.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D or F)))), M:tm-682, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-55330
in-theory        55330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (F or D))))
theorem-size     23
proof            (modus-ponens tm-682 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-55330.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (F or D)))), M:tm-682, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-55331
in-theory        55331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     49
proof            (modus-ponens tm-665 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55331.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-665, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55332
in-theory        55332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> B) -> (A -> C)))))
theorem-size     37
proof            (modus-ponens tm-623 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55332.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> B) -> (A -> C))))), M:tm-623, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55333
in-theory        55333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-622 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55333.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-622, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55334
in-theory        55334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (G -> (H or G)))
theorem-size     41
proof            (modus-ponens tm-609 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55334.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (G -> (H or G))), M:tm-609, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55335
in-theory        55335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-605 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55335.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-605, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55336
in-theory        55336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((G -> (H or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))))
theorem-size     77
proof            (modus-ponens tm-595 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       261
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55336.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((G -> (H or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))), M:tm-595, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55337
in-theory        55337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-550 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55337.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-550, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55338
in-theory        55338
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-540 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55338.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-540, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55339
in-theory        55339
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-530 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55339.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-530, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55340
in-theory        55340
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-520 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55340.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-520, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55341
in-theory        55341
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-510 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55341.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-510, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55342
in-theory        55342
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-500 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55342.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-500, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55343
in-theory        55343
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((E -> F) -> (E -> G)))))
theorem-size     51
proof            (modus-ponens tm-490 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55343.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((E -> F) -> (E -> G))))), M:tm-490, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55344
in-theory        55344
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-480 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55344.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-480, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55345
in-theory        55345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))) or G))
theorem-size     37
proof            (modus-ponens tm-470 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55345.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))) or G)), M:tm-470, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55346
in-theory        55346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-469 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55346.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-469, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55347
in-theory        55347
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (G -> (G or H)))
theorem-size     41
proof            (modus-ponens tm-456 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55347.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (G -> (G or H))), M:tm-456, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55348
in-theory        55348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-453 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55348.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-453, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55349
in-theory        55349
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((G -> (G or H)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))))
theorem-size     77
proof            (modus-ponens tm-443 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       261
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55349.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((G -> (G or H)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))), M:tm-443, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55350
in-theory        55350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-409 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55350.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-409, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55351
in-theory        55351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-400 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55351.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-400, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55352
in-theory        55352
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-391 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55352.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-391, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55353
in-theory        55353
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-382 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55353.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-382, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55354
in-theory        55354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((E -> F) -> (E -> G)))))
theorem-size     51
proof            (modus-ponens tm-373 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55354.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((E -> F) -> (E -> G))))), M:tm-373, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55355
in-theory        55355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-364 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55355.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-364, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55356
in-theory        55356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> B) -> (A -> C))) and D)))
theorem-size     39
proof            (modus-ponens tm-355 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55356.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> B) -> (A -> C))) and D))), M:tm-355, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55357
in-theory        55357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-354 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55357.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-354, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55358
in-theory        55358
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (G -> (H -> (G and H))))
theorem-size     43
proof            (modus-ponens tm-341 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55358.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55359
in-theory        55359
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E)))))
theorem-size     45
proof            (modus-ponens tm-338 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55359.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E))))), M:tm-338, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55360
in-theory        55360
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))))
theorem-size     85
proof            (modus-ponens tm-328 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       279
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55360.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))), M:tm-328, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55361
in-theory        55361
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))))
theorem-size     79
proof            (modus-ponens tm-327 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       269
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55361.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))), M:tm-327, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55362
in-theory        55362
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((G and H) -> H) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))))
theorem-size     77
proof            (modus-ponens tm-326 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       261
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55362.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((G and H) -> H) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))), M:tm-326, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55363
in-theory        55363
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((G and H) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))))
theorem-size     77
proof            (modus-ponens tm-325 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       261
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55363.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((G and H) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))), M:tm-325, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55364
in-theory        55364
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))))
theorem-size     85
proof            (modus-ponens tm-324 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       293
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55364.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))), M:tm-324, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55365
in-theory        55365
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((G -> (H -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))))
theorem-size     77
proof            (modus-ponens tm-323 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       261
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55365.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((G -> (H -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))), M:tm-323, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55366
in-theory        55366
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((G and H) -> H))
theorem-size     41
proof            (modus-ponens tm-322 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55366.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((G and H) -> H)), M:tm-322, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55367
in-theory        55367
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((G and H) -> G))
theorem-size     41
proof            (modus-ponens tm-320 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55367.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((G and H) -> G)), M:tm-320, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55368
in-theory        55368
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     49
proof            (modus-ponens tm-318 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       251
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55368.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55369
in-theory        55369
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     63
proof            (modus-ponens tm-316 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       251
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55369.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55370
in-theory        55370
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (G -> (H -> G)))
theorem-size     41
proof            (modus-ponens tm-315 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55370.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (G -> (H -> G))), M:tm-315, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55371
in-theory        55371
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     87
proof            (modus-ponens tm-313 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       265
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55371.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55372
in-theory        55372
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))) -> G) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) -> G)))
theorem-size     97
proof            (modus-ponens tm-312 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       279
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55372.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))) -> G) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) -> G))), M:tm-312, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55373
in-theory        55373
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (G or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))))
theorem-size     73
proof            (modus-ponens tm-311 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55373.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (G or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))), M:tm-311, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55374
in-theory        55374
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) or G))
theorem-size     73
proof            (modus-ponens tm-310 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55374.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) or G)), M:tm-310, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55375
in-theory        55375
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (G -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and G)))
theorem-size     75
proof            (modus-ponens tm-309 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55375.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (G -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and G))), M:tm-309, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55376
in-theory        55376
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (G -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))))
theorem-size     73
proof            (modus-ponens tm-305 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55376.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (G -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))), M:tm-305, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55377
in-theory        55377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     47
proof            (modus-ponens tm-303 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55377.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-303, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55378
in-theory        55378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-270 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55378.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-270, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55379
in-theory        55379
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-239 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55379.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-239, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55380
in-theory        55380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((E -> F) -> (E -> G)))))
theorem-size     53
proof            (modus-ponens tm-210 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55380.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((E -> F) -> (E -> G))))), M:tm-210, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55381
in-theory        55381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-183 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55381.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-183, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55382
in-theory        55382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-157 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55382.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-157, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55383
in-theory        55383
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     51
proof            (modus-ponens tm-147 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55383.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-147, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55384
in-theory        55384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-134 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55384.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-134, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55385
in-theory        55385
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     51
proof            (modus-ponens tm-125 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55385.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-125, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55386
in-theory        55386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((E -> F) -> (E -> G)))))
theorem-size     51
proof            (modus-ponens tm-113 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55386.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((E -> F) -> (E -> G))))), M:tm-113, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55387
in-theory        55387
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     55
proof            (modus-ponens tm-105 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       253
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55387.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-105, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55388
in-theory        55388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E)))))
theorem-size     43
proof            (modus-ponens tm-95 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55388.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E))))), M:tm-95, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55389
in-theory        55389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> B) -> (A -> C)))))
theorem-size     37
proof            (modus-ponens tm-84 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55389.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> B) -> (A -> C))))), M:tm-84, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55390
in-theory        55390
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-83 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55390.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-83, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55391
in-theory        55391
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> C) -> (B -> D)))))
theorem-size     41
proof            (modus-ponens tm-76 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55391.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> C) -> (B -> D))))), M:tm-76, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55392
in-theory        55392
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))
theorem-size     51
proof            (modus-ponens tm-73 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55392.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-73, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55393
in-theory        55393
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E)))))
theorem-size     47
proof            (modus-ponens tm-69 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55393.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E))))), M:tm-69, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55394
in-theory        55394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     49
proof            (modus-ponens tm-54 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55394.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-54, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55395
in-theory        55395
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-50 tm-682 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55395.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-50, m:tm-682, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55396
in-theory        55396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-49 tm-682 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55396.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-49, m:tm-682, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55397
in-theory        55397
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> C) -> (B -> D))))
theorem-size     51
proof            (modus-ponens tm-47 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55397.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> C) -> (B -> D)))), M:tm-47, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55398
in-theory        55398
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> B) -> (A -> C))))
theorem-size     51
proof            (modus-ponens tm-46 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55398.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A -> B) -> (A -> C)))), M:tm-46, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55399
in-theory        55399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E)))))
theorem-size     41
proof            (modus-ponens tm-42 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55399.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E))))), M:tm-42, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55400
in-theory        55400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E)))))
theorem-size     41
proof            (modus-ponens tm-32 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55400.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E))))), M:tm-32, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55401
in-theory        55401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-24 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55401.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))), M:tm-24, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55402
in-theory        55402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E)))))
theorem-size     43
proof            (modus-ponens tm-23 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55402.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E))))), M:tm-23, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55403
in-theory        55403
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E)))))
theorem-size     41
proof            (modus-ponens tm-22 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55403.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E))))), M:tm-22, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55404
in-theory        55404
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E)))))
theorem-size     41
proof            (modus-ponens tm-21 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55404.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E))))), M:tm-21, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55405
in-theory        55405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     49
proof            (modus-ponens tm-20 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55405.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-20, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55406
in-theory        55406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E)))))
theorem-size     41
proof            (modus-ponens tm-19 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55406.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((C -> D) -> (C -> E))))), M:tm-19, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55407
in-theory        55407
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     51
proof            (modus-ponens tm-9 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-9 tm-8 tm-2 tm-5)
proof-size       185
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55407.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55408
in-theory        55408
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> F))) -> G) -> ((((D -> (E -> F)) or ((D -> E) -> (D -> F))) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> F)))) -> G))
theorem-size     61
proof            (modus-ponens tm-8 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       197
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55408.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> F))) -> G) -> ((((D -> (E -> F)) or ((D -> E) -> (D -> F))) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> F)))) -> G)), M:tm-8, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55409
in-theory        55409
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-7 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-7 tm-8 tm-2 tm-5)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55409.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> C) -> (B -> D))))), M:tm-7, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55410
in-theory        55410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) or G)
theorem-size     37
proof            (modus-ponens tm-6 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-6 tm-8 tm-2 tm-5)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55410.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) or G), M:tm-6, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55411
in-theory        55411
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> C) -> (B -> D)))) and A))
theorem-size     39
proof            (modus-ponens tm-5 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       169
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55411.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> C) -> (B -> D)))) and A)), M:tm-5, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55412
in-theory        55412
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-1 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-1 tm-8 tm-2 tm-5)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-55412.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((B -> C) -> (B -> D))))), M:tm-1, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55413
in-theory        55413
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (C -> (C -> D))))
theorem-size     15
proof            (modus-ponens tm-683 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-55413.        (((A and B) -> A) and ((C -> D) -> (C -> (C -> D)))), M:tm-683, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-55414
in-theory        55414
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (C -> ((C -> D) and C))))
theorem-size     17
proof            (modus-ponens tm-683 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-55414.        (((A and B) -> A) and ((C -> D) -> (C -> ((C -> D) and C)))), M:tm-683, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-55415
in-theory        55415
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> C) -> ((C -> D) -> (((C -> D) or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-683 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-55415.        (((A and B) -> A) and (((C -> D) -> C) -> ((C -> D) -> (((C -> D) or C) -> D)))), M:tm-683, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-55416
in-theory        55416
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (C -> (E -> C))))
theorem-size     15
proof            (modus-ponens tm-683 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-55416.        (((A and B) -> A) and ((C -> D) -> (C -> (E -> C)))), M:tm-683, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-55417
in-theory        55417
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> F) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     27
proof            (modus-ponens tm-683 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-55417.        (((A and B) -> A) and (((C -> (D -> E)) -> F) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-683, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-55418
in-theory        55418
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> E) -> ((C and D) -> C)))
theorem-size     17
proof            (modus-ponens tm-683 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-55418.        (((A and B) -> A) and (((C and D) -> E) -> ((C and D) -> C))), M:tm-683, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-55419
in-theory        55419
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> E) -> ((C and D) -> D)))
theorem-size     17
proof            (modus-ponens tm-683 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-7 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-55419.        (((A and B) -> A) and (((C and D) -> E) -> ((C and D) -> D))), M:tm-683, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-55420
in-theory        55420
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (C -> (E -> (C and E)))))
theorem-size     17
proof            (modus-ponens tm-683 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-55420.        (((A and B) -> A) and ((C -> D) -> (C -> (E -> (C and E))))), M:tm-683, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-55421
in-theory        55421
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (C -> (C or E))))
theorem-size     15
proof            (modus-ponens tm-683 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-7 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-55421.        (((A and B) -> A) and ((C -> D) -> (C -> (C or E)))), M:tm-683, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-55422
in-theory        55422
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> (C -> (E or C))))
theorem-size     15
proof            (modus-ponens tm-683 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-7 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-55422.        (((A and B) -> A) and ((C -> D) -> (C -> (E or C)))), M:tm-683, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-55423
in-theory        55423
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55423.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-665, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55424
in-theory        55424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((E and F) -> E) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-623 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55424.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((E and F) -> E) and ((A -> B) -> (A -> C))))), M:tm-623, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55425
in-theory        55425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55425.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-622, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55426
in-theory        55426
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (F -> (G or F)))
theorem-size     33
proof            (modus-ponens tm-609 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55426.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (F -> (G or F))), M:tm-609, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55427
in-theory        55427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55427.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-605, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55428
in-theory        55428
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55428.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))))), M:tm-595, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55429
in-theory        55429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55429.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-550, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55430
in-theory        55430
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55430.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-540, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55431
in-theory        55431
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55431.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-530, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55432
in-theory        55432
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55432.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-520, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55433
in-theory        55433
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55433.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-510, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55434
in-theory        55434
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55434.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-500, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55435
in-theory        55435
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> H) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55435.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> H) and ((E -> F) -> (E -> G))))), M:tm-490, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55436
in-theory        55436
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55436.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-480, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55437
in-theory        55437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and E) -> D) and ((A -> B) -> (A -> C))) or F))
theorem-size     29
proof            (modus-ponens tm-470 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55437.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and E) -> D) and ((A -> B) -> (A -> C))) or F)), M:tm-470, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55438
in-theory        55438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55438.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-469, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55439
in-theory        55439
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (F -> (F or G)))
theorem-size     33
proof            (modus-ponens tm-456 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55439.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (F -> (F or G))), M:tm-456, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55440
in-theory        55440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55440.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-453, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55441
in-theory        55441
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55441.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))))), M:tm-443, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55442
in-theory        55442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55442.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-409, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55443
in-theory        55443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55443.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-400, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55444
in-theory        55444
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55444.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-391, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55445
in-theory        55445
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55445.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-382, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55446
in-theory        55446
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> H) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55446.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> H) and ((E -> F) -> (E -> G))))), M:tm-373, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55447
in-theory        55447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55447.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-364, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55448
in-theory        55448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((E and F) -> E) and ((A -> B) -> (A -> C))) and D)))
theorem-size     31
proof            (modus-ponens tm-355 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55448.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((E and F) -> E) and ((A -> B) -> (A -> C))) and D))), M:tm-355, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55449
in-theory        55449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55449.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-354, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55450
in-theory        55450
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (F -> (G -> (F and G))))
theorem-size     35
proof            (modus-ponens tm-341 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55450.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55451
in-theory        55451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55451.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E))))), M:tm-338, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55452
in-theory        55452
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((A -> B) -> (A -> C))))))
theorem-size     69
proof            (modus-ponens tm-328 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       239
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55452.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((A -> B) -> (A -> C)))))), M:tm-328, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55453
in-theory        55453
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55453.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))))), M:tm-327, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55454
in-theory        55454
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55454.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))))), M:tm-326, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55455
in-theory        55455
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55455.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))))), M:tm-325, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55456
in-theory        55456
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       253
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55456.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))))), M:tm-324, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55457
in-theory        55457
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55457.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))))), M:tm-323, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55458
in-theory        55458
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((F and G) -> G))
theorem-size     33
proof            (modus-ponens tm-322 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55458.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((F and G) -> G)), M:tm-322, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55459
in-theory        55459
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((F and G) -> F))
theorem-size     33
proof            (modus-ponens tm-320 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55459.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((F and G) -> F)), M:tm-320, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55460
in-theory        55460
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     41
proof            (modus-ponens tm-318 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55460.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55461
in-theory        55461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     55
proof            (modus-ponens tm-316 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55461.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55462
in-theory        55462
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (F -> (G -> F)))
theorem-size     33
proof            (modus-ponens tm-315 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55462.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (F -> (G -> F))), M:tm-315, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55463
in-theory        55463
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and E) -> D) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     71
proof            (modus-ponens tm-313 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55463.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and E) -> D) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55464
in-theory        55464
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((((D and E) -> D) and ((A -> B) -> (A -> C))) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((D and E) -> D) and ((A -> B) -> (A -> C)))) -> F)))
theorem-size     73
proof            (modus-ponens tm-312 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55464.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((((D and E) -> D) and ((A -> B) -> (A -> C))) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((D and E) -> D) and ((A -> B) -> (A -> C)))) -> F))), M:tm-312, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55465
in-theory        55465
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55465.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))))), M:tm-311, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55466
in-theory        55466
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) or F))
theorem-size     57
proof            (modus-ponens tm-310 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55466.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) or F)), M:tm-310, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55467
in-theory        55467
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and F)))
theorem-size     59
proof            (modus-ponens tm-309 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55467.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and F))), M:tm-309, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55468
in-theory        55468
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55468.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))))), M:tm-305, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55469
in-theory        55469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55469.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-303, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55470
in-theory        55470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55470.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-270, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55471
in-theory        55471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55471.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-239, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55472
in-theory        55472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> H) and ((E -> F) -> (E -> G)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55472.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> H) and ((E -> F) -> (E -> G))))), M:tm-210, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55473
in-theory        55473
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55473.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-183, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55474
in-theory        55474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55474.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-157, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55475
in-theory        55475
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55475.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-147, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55476
in-theory        55476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55476.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-134, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55477
in-theory        55477
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55477.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-125, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55478
in-theory        55478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> H) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55478.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> H) and ((E -> F) -> (E -> G))))), M:tm-113, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55479
in-theory        55479
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55479.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-105, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55480
in-theory        55480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55480.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E))))), M:tm-95, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55481
in-theory        55481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E and F) -> E) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-84 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55481.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E and F) -> E) and ((A -> B) -> (A -> C))))), M:tm-84, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55482
in-theory        55482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55482.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-83, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55483
in-theory        55483
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> E) and ((B -> C) -> (B -> D)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55483.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> E) and ((B -> C) -> (B -> D))))), M:tm-76, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55484
in-theory        55484
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-73 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55484.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-73, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55485
in-theory        55485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55485.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E))))), M:tm-69, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55486
in-theory        55486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-54 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55486.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-54, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55487
in-theory        55487
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-50 tm-683 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55487.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-50, m:tm-683, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55488
in-theory        55488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-49 tm-683 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55488.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-49, m:tm-683, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55489
in-theory        55489
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((E and F) -> E) and ((B -> C) -> (B -> D))))
theorem-size     43
proof            (modus-ponens tm-47 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55489.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((E and F) -> E) and ((B -> C) -> (B -> D)))), M:tm-47, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55490
in-theory        55490
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((E and F) -> E) and ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-46 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55490.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((E and F) -> E) and ((A -> B) -> (A -> C)))), M:tm-46, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55491
in-theory        55491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-42 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55491.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E))))), M:tm-42, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55492
in-theory        55492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-32 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55492.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E))))), M:tm-32, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55493
in-theory        55493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((A -> B) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-24 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55493.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((A -> B) -> (A -> C))))), M:tm-24, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55494
in-theory        55494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-23 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55494.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E))))), M:tm-23, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55495
in-theory        55495
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-22 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55495.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E))))), M:tm-22, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55496
in-theory        55496
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-21 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55496.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E))))), M:tm-21, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55497
in-theory        55497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-20 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55497.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-20, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55498
in-theory        55498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-19 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55498.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> F) and ((C -> D) -> (C -> E))))), M:tm-19, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55499
in-theory        55499
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and E) -> D) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     43
proof            (modus-ponens tm-9 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-9 tm-8 tm-2 tm-5 tm-3)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55499.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and E) -> D) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55500
in-theory        55500
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and ((C -> D) -> (C -> E))) -> F) -> ((((C -> (D -> E)) or ((C -> D) -> (C -> E))) or (((A and B) -> A) and ((C -> D) -> (C -> E)))) -> F))
theorem-size     45
proof            (modus-ponens tm-8 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55500.        (((((A and B) -> A) and ((C -> D) -> (C -> E))) -> F) -> ((((C -> (D -> E)) or ((C -> D) -> (C -> E))) or (((A and B) -> A) and ((C -> D) -> (C -> E)))) -> F)), M:tm-8, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55501
in-theory        55501
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> E) and ((B -> C) -> (B -> D)))))
theorem-size     29
proof            (modus-ponens tm-7 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-7 tm-8 tm-2 tm-5 tm-3)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55501.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> E) and ((B -> C) -> (B -> D))))), M:tm-7, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55502
in-theory        55502
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) or F)
theorem-size     29
proof            (modus-ponens tm-6 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-6 tm-8 tm-2 tm-5 tm-3)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55502.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) or F), M:tm-6, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55503
in-theory        55503
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> E) and ((B -> C) -> (B -> D)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55503.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> E) and ((B -> C) -> (B -> D)))) and A)), M:tm-5, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55504
in-theory        55504
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> E) and ((B -> C) -> (B -> D)))))
theorem-size     29
proof            (modus-ponens tm-1 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-1 tm-8 tm-2 tm-5 tm-3)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-55504.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> E) and ((B -> C) -> (B -> D))))), M:tm-1, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55505
in-theory        55505
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (C -> (C -> D))))
theorem-size     15
proof            (modus-ponens tm-684 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-55505.        (((A and B) -> B) and ((C -> D) -> (C -> (C -> D)))), M:tm-684, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-55506
in-theory        55506
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (C -> ((C -> D) and C))))
theorem-size     17
proof            (modus-ponens tm-684 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-55506.        (((A and B) -> B) and ((C -> D) -> (C -> ((C -> D) and C)))), M:tm-684, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-55507
in-theory        55507
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> C) -> ((C -> D) -> (((C -> D) or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-684 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-55507.        (((A and B) -> B) and (((C -> D) -> C) -> ((C -> D) -> (((C -> D) or C) -> D)))), M:tm-684, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-55508
in-theory        55508
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (C -> (E -> C))))
theorem-size     15
proof            (modus-ponens tm-684 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-55508.        (((A and B) -> B) and ((C -> D) -> (C -> (E -> C)))), M:tm-684, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-55509
in-theory        55509
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> F) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     27
proof            (modus-ponens tm-684 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-55509.        (((A and B) -> B) and (((C -> (D -> E)) -> F) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-684, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-55510
in-theory        55510
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> E) -> ((C and D) -> C)))
theorem-size     17
proof            (modus-ponens tm-684 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-7 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-55510.        (((A and B) -> B) and (((C and D) -> E) -> ((C and D) -> C))), M:tm-684, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-55511
in-theory        55511
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> E) -> ((C and D) -> D)))
theorem-size     17
proof            (modus-ponens tm-684 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-55511.        (((A and B) -> B) and (((C and D) -> E) -> ((C and D) -> D))), M:tm-684, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-55512
in-theory        55512
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (C -> (E -> (C and E)))))
theorem-size     17
proof            (modus-ponens tm-684 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-55512.        (((A and B) -> B) and ((C -> D) -> (C -> (E -> (C and E))))), M:tm-684, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-55513
in-theory        55513
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (C -> (C or E))))
theorem-size     15
proof            (modus-ponens tm-684 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-7 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-55513.        (((A and B) -> B) and ((C -> D) -> (C -> (C or E)))), M:tm-684, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-55514
in-theory        55514
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> (C -> (E or C))))
theorem-size     15
proof            (modus-ponens tm-684 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-7 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-55514.        (((A and B) -> B) and ((C -> D) -> (C -> (E or C)))), M:tm-684, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-55515
in-theory        55515
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55515.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-665, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55516
in-theory        55516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((E and F) -> F) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-623 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55516.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((E and F) -> F) and ((A -> B) -> (A -> C))))), M:tm-623, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55517
in-theory        55517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55517.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-622, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55518
in-theory        55518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (F -> (G or F)))
theorem-size     33
proof            (modus-ponens tm-609 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55518.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (F -> (G or F))), M:tm-609, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55519
in-theory        55519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55519.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-605, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55520
in-theory        55520
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55520.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))))), M:tm-595, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55521
in-theory        55521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55521.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-550, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55522
in-theory        55522
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55522.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-540, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55523
in-theory        55523
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55523.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-530, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55524
in-theory        55524
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55524.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-520, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55525
in-theory        55525
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55525.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-510, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55526
in-theory        55526
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55526.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-500, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55527
in-theory        55527
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> I) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55527.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> I) and ((E -> F) -> (E -> G))))), M:tm-490, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55528
in-theory        55528
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55528.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-480, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55529
in-theory        55529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and E) -> E) and ((A -> B) -> (A -> C))) or F))
theorem-size     29
proof            (modus-ponens tm-470 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55529.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and E) -> E) and ((A -> B) -> (A -> C))) or F)), M:tm-470, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55530
in-theory        55530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55530.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-469, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55531
in-theory        55531
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (F -> (F or G)))
theorem-size     33
proof            (modus-ponens tm-456 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55531.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (F -> (F or G))), M:tm-456, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55532
in-theory        55532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55532.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-453, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55533
in-theory        55533
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55533.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))))), M:tm-443, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55534
in-theory        55534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55534.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-409, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55535
in-theory        55535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55535.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-400, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55536
in-theory        55536
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55536.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-391, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55537
in-theory        55537
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55537.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-382, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55538
in-theory        55538
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> I) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55538.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> I) and ((E -> F) -> (E -> G))))), M:tm-373, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55539
in-theory        55539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55539.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-364, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55540
in-theory        55540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((E and F) -> F) and ((A -> B) -> (A -> C))) and D)))
theorem-size     31
proof            (modus-ponens tm-355 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55540.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((E and F) -> F) and ((A -> B) -> (A -> C))) and D))), M:tm-355, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55541
in-theory        55541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55541.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-354, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55542
in-theory        55542
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (F -> (G -> (F and G))))
theorem-size     35
proof            (modus-ponens tm-341 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55542.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55543
in-theory        55543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55543.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E))))), M:tm-338, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55544
in-theory        55544
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((A -> B) -> (A -> C))))))
theorem-size     69
proof            (modus-ponens tm-328 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       239
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55544.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((A -> B) -> (A -> C)))))), M:tm-328, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55545
in-theory        55545
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55545.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))))), M:tm-327, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55546
in-theory        55546
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55546.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))))), M:tm-326, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55547
in-theory        55547
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55547.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))))), M:tm-325, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55548
in-theory        55548
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       253
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55548.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))))), M:tm-324, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55549
in-theory        55549
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55549.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))))), M:tm-323, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55550
in-theory        55550
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((F and G) -> G))
theorem-size     33
proof            (modus-ponens tm-322 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55550.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((F and G) -> G)), M:tm-322, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55551
in-theory        55551
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((F and G) -> F))
theorem-size     33
proof            (modus-ponens tm-320 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55551.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((F and G) -> F)), M:tm-320, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55552
in-theory        55552
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     41
proof            (modus-ponens tm-318 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55552.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55553
in-theory        55553
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     55
proof            (modus-ponens tm-316 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55553.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55554
in-theory        55554
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (F -> (G -> F)))
theorem-size     33
proof            (modus-ponens tm-315 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55554.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (F -> (G -> F))), M:tm-315, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55555
in-theory        55555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and E) -> E) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     71
proof            (modus-ponens tm-313 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55555.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and E) -> E) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55556
in-theory        55556
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((((D and E) -> E) and ((A -> B) -> (A -> C))) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((D and E) -> E) and ((A -> B) -> (A -> C)))) -> F)))
theorem-size     73
proof            (modus-ponens tm-312 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55556.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((((D and E) -> E) and ((A -> B) -> (A -> C))) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (((D and E) -> E) and ((A -> B) -> (A -> C)))) -> F))), M:tm-312, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55557
in-theory        55557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55557.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))))), M:tm-311, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55558
in-theory        55558
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) or F))
theorem-size     57
proof            (modus-ponens tm-310 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55558.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) or F)), M:tm-310, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55559
in-theory        55559
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and F)))
theorem-size     59
proof            (modus-ponens tm-309 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55559.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and F))), M:tm-309, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55560
in-theory        55560
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55560.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))))), M:tm-305, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55561
in-theory        55561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55561.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-303, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55562
in-theory        55562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55562.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-270, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55563
in-theory        55563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55563.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-239, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55564
in-theory        55564
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> I) and ((E -> F) -> (E -> G)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55564.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> I) and ((E -> F) -> (E -> G))))), M:tm-210, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55565
in-theory        55565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55565.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-183, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55566
in-theory        55566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55566.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-157, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55567
in-theory        55567
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55567.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-147, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55568
in-theory        55568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55568.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-134, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55569
in-theory        55569
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55569.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-125, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55570
in-theory        55570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> I) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55570.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> I) and ((E -> F) -> (E -> G))))), M:tm-113, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55571
in-theory        55571
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55571.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-105, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55572
in-theory        55572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55572.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E))))), M:tm-95, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55573
in-theory        55573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E and F) -> F) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-84 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55573.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E and F) -> F) and ((A -> B) -> (A -> C))))), M:tm-84, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55574
in-theory        55574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55574.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-83, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55575
in-theory        55575
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> F) and ((B -> C) -> (B -> D)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55575.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> F) and ((B -> C) -> (B -> D))))), M:tm-76, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55576
in-theory        55576
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-73 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55576.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-73, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55577
in-theory        55577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55577.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E))))), M:tm-69, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55578
in-theory        55578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-54 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55578.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-54, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55579
in-theory        55579
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-50 tm-684 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-4)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55579.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-50, m:tm-684, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55580
in-theory        55580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-49 tm-684 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55580.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-49, m:tm-684, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55581
in-theory        55581
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((E and F) -> F) and ((B -> C) -> (B -> D))))
theorem-size     43
proof            (modus-ponens tm-47 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55581.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (((E and F) -> F) and ((B -> C) -> (B -> D)))), M:tm-47, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55582
in-theory        55582
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((E and F) -> F) and ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-46 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55582.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((E and F) -> F) and ((A -> B) -> (A -> C)))), M:tm-46, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55583
in-theory        55583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-42 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55583.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E))))), M:tm-42, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55584
in-theory        55584
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-32 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55584.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E))))), M:tm-32, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55585
in-theory        55585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((A -> B) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-24 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55585.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((A -> B) -> (A -> C))))), M:tm-24, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55586
in-theory        55586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-23 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55586.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E))))), M:tm-23, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55587
in-theory        55587
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-22 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55587.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E))))), M:tm-22, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55588
in-theory        55588
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-21 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55588.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E))))), M:tm-21, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55589
in-theory        55589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-20 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55589.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-20, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55590
in-theory        55590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-19 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55590.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (((F and G) -> G) and ((C -> D) -> (C -> E))))), M:tm-19, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55591
in-theory        55591
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and E) -> E) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     43
proof            (modus-ponens tm-9 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-9 tm-8 tm-2 tm-5 tm-4)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55591.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and E) -> E) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55592
in-theory        55592
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and ((C -> D) -> (C -> E))) -> F) -> ((((C -> (D -> E)) or ((C -> D) -> (C -> E))) or (((A and B) -> B) and ((C -> D) -> (C -> E)))) -> F))
theorem-size     45
proof            (modus-ponens tm-8 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55592.        (((((A and B) -> B) and ((C -> D) -> (C -> E))) -> F) -> ((((C -> (D -> E)) or ((C -> D) -> (C -> E))) or (((A and B) -> B) and ((C -> D) -> (C -> E)))) -> F)), M:tm-8, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55593
in-theory        55593
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> F) and ((B -> C) -> (B -> D)))))
theorem-size     29
proof            (modus-ponens tm-7 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-7 tm-8 tm-2 tm-5 tm-4)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55593.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> F) and ((B -> C) -> (B -> D))))), M:tm-7, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55594
in-theory        55594
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) or F)
theorem-size     29
proof            (modus-ponens tm-6 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-6 tm-8 tm-2 tm-5 tm-4)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55594.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) or F), M:tm-6, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55595
in-theory        55595
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> F) and ((B -> C) -> (B -> D)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55595.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> F) and ((B -> C) -> (B -> D)))) and A)), M:tm-5, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55596
in-theory        55596
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> F) and ((B -> C) -> (B -> D)))))
theorem-size     29
proof            (modus-ponens tm-1 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-1 tm-8 tm-2 tm-5 tm-4)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-55596.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((E and F) -> F) and ((B -> C) -> (B -> D))))), M:tm-1, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55597
in-theory        55597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C -> D))))
theorem-size     17
proof            (modus-ponens tm-685 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-55597.        ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C -> D)))), M:tm-685, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-55598
in-theory        55598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> ((C -> D) and C))))
theorem-size     19
proof            (modus-ponens tm-685 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-55598.        ((A -> (B -> (A and B))) and ((C -> D) -> (C -> ((C -> D) and C)))), M:tm-685, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-55599
in-theory        55599
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> C) -> ((C -> D) -> (((C -> D) or C) -> D))))
theorem-size     25
proof            (modus-ponens tm-685 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-55599.        ((A -> (B -> (A and B))) and (((C -> D) -> C) -> ((C -> D) -> (((C -> D) or C) -> D)))), M:tm-685, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-55600
in-theory        55600
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (E -> C))))
theorem-size     17
proof            (modus-ponens tm-685 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-55600.        ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (E -> C)))), M:tm-685, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-55601
in-theory        55601
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> F) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     29
proof            (modus-ponens tm-685 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-55601.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> F) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-685, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-55602
in-theory        55602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> E) -> ((C and D) -> C)))
theorem-size     19
proof            (modus-ponens tm-685 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-55602.        ((A -> (B -> (A and B))) and (((C and D) -> E) -> ((C and D) -> C))), M:tm-685, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-55603
in-theory        55603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> E) -> ((C and D) -> D)))
theorem-size     19
proof            (modus-ponens tm-685 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-55603.        ((A -> (B -> (A and B))) and (((C and D) -> E) -> ((C and D) -> D))), M:tm-685, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-55604
in-theory        55604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (E -> (C and E)))))
theorem-size     19
proof            (modus-ponens tm-685 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-55604.        ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (E -> (C and E))))), M:tm-685, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-55605
in-theory        55605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C or E))))
theorem-size     17
proof            (modus-ponens tm-685 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-55605.        ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C or E)))), M:tm-685, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-55606
in-theory        55606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (E or C))))
theorem-size     17
proof            (modus-ponens tm-685 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-55606.        ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (E or C)))), M:tm-685, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-55607
in-theory        55607
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-665 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55607.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-665, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55608
in-theory        55608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> (F -> (E and F))) and ((A -> B) -> (A -> C)))))
theorem-size     31
proof            (modus-ponens tm-623 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55608.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> (F -> (E and F))) and ((A -> B) -> (A -> C))))), M:tm-623, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55609
in-theory        55609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-622 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55609.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-622, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55610
in-theory        55610
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (F -> (G or F)))
theorem-size     35
proof            (modus-ponens tm-609 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55610.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (F -> (G or F))), M:tm-609, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55611
in-theory        55611
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-605 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55611.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-605, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55612
in-theory        55612
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-595 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55612.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))), M:tm-595, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55613
in-theory        55613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-550 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55613.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-550, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55614
in-theory        55614
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-540 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55614.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-540, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55615
in-theory        55615
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-530 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55615.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-530, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55616
in-theory        55616
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-520 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55616.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-520, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55617
in-theory        55617
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-510 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55617.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-510, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55618
in-theory        55618
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-500 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55618.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-500, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55619
in-theory        55619
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> (H and I))) and ((E -> F) -> (E -> G)))))
theorem-size     45
proof            (modus-ponens tm-490 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55619.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> (H and I))) and ((E -> F) -> (E -> G))))), M:tm-490, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55620
in-theory        55620
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-480 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55620.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-480, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55621
in-theory        55621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))) or F))
theorem-size     31
proof            (modus-ponens tm-470 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55621.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))) or F)), M:tm-470, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55622
in-theory        55622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-469 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55622.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-469, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55623
in-theory        55623
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (F -> (F or G)))
theorem-size     35
proof            (modus-ponens tm-456 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55623.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (F -> (F or G))), M:tm-456, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55624
in-theory        55624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-453 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55624.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-453, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55625
in-theory        55625
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-443 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55625.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))), M:tm-443, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55626
in-theory        55626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-409 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55626.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-409, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55627
in-theory        55627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-400 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55627.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-400, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55628
in-theory        55628
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-391 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55628.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-391, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55629
in-theory        55629
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-382 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55629.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-382, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55630
in-theory        55630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> (H and I))) and ((E -> F) -> (E -> G)))))
theorem-size     45
proof            (modus-ponens tm-373 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55630.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> (H and I))) and ((E -> F) -> (E -> G))))), M:tm-373, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55631
in-theory        55631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-364 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55631.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-364, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55632
in-theory        55632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E -> (F -> (E and F))) and ((A -> B) -> (A -> C))) and D)))
theorem-size     33
proof            (modus-ponens tm-355 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55632.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E -> (F -> (E and F))) and ((A -> B) -> (A -> C))) and D))), M:tm-355, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55633
in-theory        55633
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-354 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55633.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-354, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55634
in-theory        55634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (F -> (G -> (F and G))))
theorem-size     37
proof            (modus-ponens tm-341 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55634.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55635
in-theory        55635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E)))))
theorem-size     39
proof            (modus-ponens tm-338 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55635.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E))))), M:tm-338, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55636
in-theory        55636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))))
theorem-size     73
proof            (modus-ponens tm-328 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       249
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55636.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))), M:tm-328, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55637
in-theory        55637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))))
theorem-size     67
proof            (modus-ponens tm-327 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       239
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55637.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))), M:tm-327, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55638
in-theory        55638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-326 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55638.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))), M:tm-326, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55639
in-theory        55639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-325 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55639.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))), M:tm-325, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55640
in-theory        55640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))))
theorem-size     73
proof            (modus-ponens tm-324 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       263
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55640.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))), M:tm-324, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55641
in-theory        55641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-323 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55641.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))), M:tm-323, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55642
in-theory        55642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((F and G) -> G))
theorem-size     35
proof            (modus-ponens tm-322 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55642.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((F and G) -> G)), M:tm-322, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55643
in-theory        55643
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((F and G) -> F))
theorem-size     35
proof            (modus-ponens tm-320 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55643.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((F and G) -> F)), M:tm-320, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55644
in-theory        55644
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     43
proof            (modus-ponens tm-318 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55644.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55645
in-theory        55645
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-316 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55645.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55646
in-theory        55646
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (F -> (G -> F)))
theorem-size     35
proof            (modus-ponens tm-315 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55646.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (F -> (G -> F))), M:tm-315, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55647
in-theory        55647
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     75
proof            (modus-ponens tm-313 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55647.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55648
in-theory        55648
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) -> F)))
theorem-size     79
proof            (modus-ponens tm-312 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55648.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) -> F))), M:tm-312, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55649
in-theory        55649
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-311 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55649.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))), M:tm-311, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55650
in-theory        55650
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) or F))
theorem-size     61
proof            (modus-ponens tm-310 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55650.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) or F)), M:tm-310, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55651
in-theory        55651
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and F)))
theorem-size     63
proof            (modus-ponens tm-309 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55651.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and F))), M:tm-309, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55652
in-theory        55652
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-305 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55652.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))), M:tm-305, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55653
in-theory        55653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-303 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55653.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-303, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55654
in-theory        55654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-270 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55654.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-270, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55655
in-theory        55655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-239 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55655.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-239, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55656
in-theory        55656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> (H and I))) and ((E -> F) -> (E -> G)))))
theorem-size     47
proof            (modus-ponens tm-210 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55656.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> (H and I))) and ((E -> F) -> (E -> G))))), M:tm-210, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55657
in-theory        55657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-183 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55657.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-183, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55658
in-theory        55658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-157 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55658.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-157, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55659
in-theory        55659
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-147 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55659.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-147, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55660
in-theory        55660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-134 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55660.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-134, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55661
in-theory        55661
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-125 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55661.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-125, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55662
in-theory        55662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> (H and I))) and ((E -> F) -> (E -> G)))))
theorem-size     45
proof            (modus-ponens tm-113 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55662.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> (H and I))) and ((E -> F) -> (E -> G))))), M:tm-113, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55663
in-theory        55663
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     49
proof            (modus-ponens tm-105 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55663.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-105, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55664
in-theory        55664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E)))))
theorem-size     37
proof            (modus-ponens tm-95 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55664.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E))))), M:tm-95, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55665
in-theory        55665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> (E and F))) and ((A -> B) -> (A -> C)))))
theorem-size     31
proof            (modus-ponens tm-84 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55665.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> (E and F))) and ((A -> B) -> (A -> C))))), M:tm-84, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55666
in-theory        55666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-83 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55666.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-83, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55667
in-theory        55667
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> (E and F))) and ((B -> C) -> (B -> D)))))
theorem-size     35
proof            (modus-ponens tm-76 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55667.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> (E and F))) and ((B -> C) -> (B -> D))))), M:tm-76, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55668
in-theory        55668
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))
theorem-size     45
proof            (modus-ponens tm-73 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55668.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-73, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55669
in-theory        55669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E)))))
theorem-size     41
proof            (modus-ponens tm-69 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55669.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E))))), M:tm-69, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55670
in-theory        55670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-54 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55670.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-54, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55671
in-theory        55671
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-50 tm-685 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55671.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-50, m:tm-685, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55672
in-theory        55672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-49 tm-685 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55672.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-49, m:tm-685, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55673
in-theory        55673
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((E -> (F -> (E and F))) and ((B -> C) -> (B -> D))))
theorem-size     45
proof            (modus-ponens tm-47 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55673.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((E -> (F -> (E and F))) and ((B -> C) -> (B -> D)))), M:tm-47, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55674
in-theory        55674
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((E -> (F -> (E and F))) and ((A -> B) -> (A -> C))))
theorem-size     45
proof            (modus-ponens tm-46 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55674.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((E -> (F -> (E and F))) and ((A -> B) -> (A -> C)))), M:tm-46, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55675
in-theory        55675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-42 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55675.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E))))), M:tm-42, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55676
in-theory        55676
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-32 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55676.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E))))), M:tm-32, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55677
in-theory        55677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))
theorem-size     43
proof            (modus-ponens tm-24 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55677.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))), M:tm-24, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55678
in-theory        55678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E)))))
theorem-size     37
proof            (modus-ponens tm-23 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55678.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E))))), M:tm-23, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55679
in-theory        55679
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-22 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55679.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E))))), M:tm-22, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55680
in-theory        55680
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-21 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55680.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E))))), M:tm-21, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55681
in-theory        55681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-20 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55681.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-20, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55682
in-theory        55682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-19 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55682.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G -> (F and G))) and ((C -> D) -> (C -> E))))), M:tm-19, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55683
in-theory        55683
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-9 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-9 tm-8 tm-2 tm-5)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55683.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55684
in-theory        55684
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and ((C -> D) -> (C -> E))) -> F) -> ((((C -> (D -> E)) or ((C -> D) -> (C -> E))) or ((A -> (B -> (A and B))) and ((C -> D) -> (C -> E)))) -> F))
theorem-size     49
proof            (modus-ponens tm-8 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55684.        ((((A -> (B -> (A and B))) and ((C -> D) -> (C -> E))) -> F) -> ((((C -> (D -> E)) or ((C -> D) -> (C -> E))) or ((A -> (B -> (A and B))) and ((C -> D) -> (C -> E)))) -> F)), M:tm-8, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55685
in-theory        55685
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> (E and F))) and ((B -> C) -> (B -> D)))))
theorem-size     31
proof            (modus-ponens tm-7 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-7 tm-8 tm-2 tm-5)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55685.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> (E and F))) and ((B -> C) -> (B -> D))))), M:tm-7, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55686
in-theory        55686
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) or F)
theorem-size     31
proof            (modus-ponens tm-6 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-6 tm-8 tm-2 tm-5)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55686.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) or F), M:tm-6, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55687
in-theory        55687
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> (E and F))) and ((B -> C) -> (B -> D)))) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55687.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> (E and F))) and ((B -> C) -> (B -> D)))) and A)), M:tm-5, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55688
in-theory        55688
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> (E and F))) and ((B -> C) -> (B -> D)))))
theorem-size     31
proof            (modus-ponens tm-1 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-1 tm-8 tm-2 tm-5)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-55688.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F -> (E and F))) and ((B -> C) -> (B -> D))))), M:tm-1, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55689
in-theory        55689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (A -> (A -> B))))
theorem-size     13
proof            (modus-ponens tm-686 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-55689.        ((A -> B) -> ((A -> B) and (A -> (A -> B)))), M:tm-686, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-55690
in-theory        55690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (A -> ((A -> B) and A))))
theorem-size     15
proof            (modus-ponens tm-686 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-55690.        ((A -> B) -> ((A -> B) and (A -> ((A -> B) and A)))), M:tm-686, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-55691
in-theory        55691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> A) -> (((A -> B) -> A) and ((A -> B) -> (((A -> B) or A) -> B))))
theorem-size     23
proof            (modus-ponens tm-686 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-55691.        (((A -> B) -> A) -> (((A -> B) -> A) and ((A -> B) -> (((A -> B) or A) -> B)))), M:tm-686, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-55692
in-theory        55692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (A -> (C -> A))))
theorem-size     13
proof            (modus-ponens tm-686 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-55692.        ((A -> B) -> ((A -> B) and (A -> (C -> A)))), M:tm-686, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-55693
in-theory        55693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> D) -> (((A -> (B -> C)) -> D) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-686 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-55693.        (((A -> (B -> C)) -> D) -> (((A -> (B -> C)) -> D) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))), M:tm-686, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-55694
in-theory        55694
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> C) -> (((A and B) -> C) and ((A and B) -> A)))
theorem-size     17
proof            (modus-ponens tm-686 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-55694.        (((A and B) -> C) -> (((A and B) -> C) and ((A and B) -> A))), M:tm-686, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-55695
in-theory        55695
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> C) -> (((A and B) -> C) and ((A and B) -> B)))
theorem-size     17
proof            (modus-ponens tm-686 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-55695.        (((A and B) -> C) -> (((A and B) -> C) and ((A and B) -> B))), M:tm-686, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-55696
in-theory        55696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (A -> (C -> (A and C)))))
theorem-size     15
proof            (modus-ponens tm-686 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-55696.        ((A -> B) -> ((A -> B) and (A -> (C -> (A and C))))), M:tm-686, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-55697
in-theory        55697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (A -> (A or C))))
theorem-size     13
proof            (modus-ponens tm-686 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-55697.        ((A -> B) -> ((A -> B) and (A -> (A or C)))), M:tm-686, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-55698
in-theory        55698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and (A -> (C or A))))
theorem-size     13
proof            (modus-ponens tm-686 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-55698.        ((A -> B) -> ((A -> B) and (A -> (C or A)))), M:tm-686, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-55699
in-theory        55699
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-665 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55699.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-665, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55700
in-theory        55700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> ((A -> B) and (A -> C)))))
theorem-size     27
proof            (modus-ponens tm-623 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55700.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> ((A -> B) and (A -> C))))), M:tm-623, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55701
in-theory        55701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-622 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55701.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-622, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55702
in-theory        55702
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (D -> (E or D)))
theorem-size     31
proof            (modus-ponens tm-609 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55702.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (D -> (E or D))), M:tm-609, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55703
in-theory        55703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-605 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55703.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-605, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55704
in-theory        55704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((D -> (E or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-595 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       223
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55704.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((D -> (E or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))))), M:tm-595, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55705
in-theory        55705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-550 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55705.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-550, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55706
in-theory        55706
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-540 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55706.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-540, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55707
in-theory        55707
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-530 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55707.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-530, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55708
in-theory        55708
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-520 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55708.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-520, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55709
in-theory        55709
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-510 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55709.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-510, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55710
in-theory        55710
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-500 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55710.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-500, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55711
in-theory        55711
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G)))))
theorem-size     41
proof            (modus-ponens tm-490 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55711.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G))))), M:tm-490, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55712
in-theory        55712
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-480 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55712.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-480, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55713
in-theory        55713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> ((A -> B) and (A -> C))) or D))
theorem-size     27
proof            (modus-ponens tm-470 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55713.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> ((A -> B) and (A -> C))) or D)), M:tm-470, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55714
in-theory        55714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-469 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55714.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-469, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55715
in-theory        55715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (D -> (D or E)))
theorem-size     31
proof            (modus-ponens tm-456 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55715.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (D -> (D or E))), M:tm-456, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55716
in-theory        55716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-453 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55716.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-453, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55717
in-theory        55717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((D -> (D or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-443 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       223
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55717.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((D -> (D or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))))), M:tm-443, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55718
in-theory        55718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-409 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55718.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-409, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55719
in-theory        55719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-400 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55719.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-400, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55720
in-theory        55720
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-391 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55720.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-391, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55721
in-theory        55721
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-382 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55721.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-382, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55722
in-theory        55722
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G)))))
theorem-size     41
proof            (modus-ponens tm-373 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55722.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G))))), M:tm-373, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55723
in-theory        55723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-364 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55723.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-364, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55724
in-theory        55724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> ((A -> B) and (A -> C))) and D)))
theorem-size     29
proof            (modus-ponens tm-355 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55724.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> ((A -> B) and (A -> C))) and D))), M:tm-355, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55725
in-theory        55725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-354 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55725.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-354, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55726
in-theory        55726
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (D -> (E -> (D and E))))
theorem-size     33
proof            (modus-ponens tm-341 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55726.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55727
in-theory        55727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-338 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55727.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E))))), M:tm-338, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55728
in-theory        55728
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((A -> B) -> ((A -> B) and (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-328 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55728.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((A -> B) -> ((A -> B) and (A -> C)))))), M:tm-328, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55729
in-theory        55729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C))))))
theorem-size     59
proof            (modus-ponens tm-327 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55729.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))))), M:tm-327, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55730
in-theory        55730
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((D and E) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-326 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       223
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55730.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((D and E) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))))), M:tm-326, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55731
in-theory        55731
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((D and E) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-325 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       223
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55731.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((D and E) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))))), M:tm-325, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55732
in-theory        55732
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-324 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       255
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55732.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))))), M:tm-324, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55733
in-theory        55733
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((D -> (E -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-323 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       223
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55733.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((D -> (E -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))))), M:tm-323, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55734
in-theory        55734
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((D and E) -> E))
theorem-size     31
proof            (modus-ponens tm-322 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55734.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((D and E) -> E)), M:tm-322, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55735
in-theory        55735
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((D and E) -> D))
theorem-size     31
proof            (modus-ponens tm-320 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55735.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((D and E) -> D)), M:tm-320, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55736
in-theory        55736
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-318 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       223
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55736.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55737
in-theory        55737
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-316 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       223
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55737.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55738
in-theory        55738
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (D -> (E -> D)))
theorem-size     31
proof            (modus-ponens tm-315 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55738.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (D -> (E -> D))), M:tm-315, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55739
in-theory        55739
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((A -> B) -> ((A -> B) and (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     67
proof            (modus-ponens tm-313 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55739.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((A -> B) -> ((A -> B) and (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55740
in-theory        55740
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((((A -> B) -> ((A -> B) and (A -> C))) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((A -> B) -> ((A -> B) and (A -> C)))) -> D)))
theorem-size     67
proof            (modus-ponens tm-312 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55740.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((((A -> B) -> ((A -> B) and (A -> C))) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((A -> B) -> ((A -> B) and (A -> C)))) -> D))), M:tm-312, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55741
in-theory        55741
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (D or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C))))))
theorem-size     53
proof            (modus-ponens tm-311 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55741.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (D or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))))), M:tm-311, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55742
in-theory        55742
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) or D))
theorem-size     53
proof            (modus-ponens tm-310 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55742.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) or D)), M:tm-310, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55743
in-theory        55743
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (D -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and D)))
theorem-size     55
proof            (modus-ponens tm-309 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55743.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (D -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and D))), M:tm-309, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55744
in-theory        55744
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> B)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) and (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-306 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Am Bm)) (C (and (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55744.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> B)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) and (A -> C))))), M:tm-306, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Am Bm)) (C (and (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-55745
in-theory        55745
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C))))))
theorem-size     53
proof            (modus-ponens tm-305 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55745.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))))), M:tm-305, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55746
in-theory        55746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-303 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55746.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-303, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55747
in-theory        55747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-270 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55747.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-270, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55748
in-theory        55748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-239 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55748.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-239, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55749
in-theory        55749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-210 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55749.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G))))), M:tm-210, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55750
in-theory        55750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-183 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55750.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-183, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55751
in-theory        55751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-157 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55751.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-157, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55752
in-theory        55752
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-147 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55752.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-147, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55753
in-theory        55753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-134 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55753.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-134, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55754
in-theory        55754
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-125 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55754.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-125, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55755
in-theory        55755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G)))))
theorem-size     41
proof            (modus-ponens tm-113 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55755.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G))))), M:tm-113, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55756
in-theory        55756
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     45
proof            (modus-ponens tm-105 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55756.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-105, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55757
in-theory        55757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-95 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55757.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E))))), M:tm-95, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55758
in-theory        55758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> ((A -> B) and (A -> C)))))
theorem-size     27
proof            (modus-ponens tm-84 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55758.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> ((A -> B) and (A -> C))))), M:tm-84, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55759
in-theory        55759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-83 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55759.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-83, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55760
in-theory        55760
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> ((B -> C) and (B -> D)))))
theorem-size     31
proof            (modus-ponens tm-76 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55760.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> ((B -> C) and (B -> D))))), M:tm-76, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55761
in-theory        55761
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> ((A -> B) and (A -> C))))
theorem-size     41
proof            (modus-ponens tm-73 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55761.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-73, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55762
in-theory        55762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E)))))
theorem-size     37
proof            (modus-ponens tm-69 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55762.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E))))), M:tm-69, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55763
in-theory        55763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-54 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55763.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-54, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55764
in-theory        55764
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> ((A -> B) and (A -> C))))
theorem-size     33
proof            (modus-ponens tm-50 tm-686 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55764.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-50, m:tm-686, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55765
in-theory        55765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> ((A -> B) and (A -> C))))
theorem-size     31
proof            (modus-ponens tm-49 tm-686 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55765.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-49, m:tm-686, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55766
in-theory        55766
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((B -> C) -> ((B -> C) and (B -> D))))
theorem-size     41
proof            (modus-ponens tm-47 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55766.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((B -> C) -> ((B -> C) and (B -> D)))), M:tm-47, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55767
in-theory        55767
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> ((A -> B) and (A -> C))))
theorem-size     41
proof            (modus-ponens tm-46 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55767.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-46, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55768
in-theory        55768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E)))))
theorem-size     31
proof            (modus-ponens tm-42 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55768.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E))))), M:tm-42, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55769
in-theory        55769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E)))))
theorem-size     31
proof            (modus-ponens tm-32 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55769.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E))))), M:tm-32, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55770
in-theory        55770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((A -> B) -> ((A -> B) and (A -> C)))))
theorem-size     39
proof            (modus-ponens tm-24 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55770.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((A -> B) -> ((A -> B) and (A -> C))))), M:tm-24, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55771
in-theory        55771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-23 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55771.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E))))), M:tm-23, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55772
in-theory        55772
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E)))))
theorem-size     31
proof            (modus-ponens tm-22 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55772.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E))))), M:tm-22, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55773
in-theory        55773
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E)))))
theorem-size     31
proof            (modus-ponens tm-21 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55773.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E))))), M:tm-21, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55774
in-theory        55774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-20 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55774.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-20, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55775
in-theory        55775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E)))))
theorem-size     31
proof            (modus-ponens tm-19 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55775.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> ((C -> D) and (C -> E))))), M:tm-19, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55776
in-theory        55776
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((A -> B) -> ((A -> B) and (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-9 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-9 tm-8 tm-2 tm-5)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55776.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((A -> B) -> ((A -> B) and (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55777
in-theory        55777
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> B) and (A -> C))) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((A -> B) -> ((A -> B) and (A -> C)))) -> D))
theorem-size     41
proof            (modus-ponens tm-8 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55777.        ((((A -> B) -> ((A -> B) and (A -> C))) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((A -> B) -> ((A -> B) and (A -> C)))) -> D)), M:tm-8, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55778
in-theory        55778
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> ((B -> C) and (B -> D)))))
theorem-size     27
proof            (modus-ponens tm-7 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-7 tm-8 tm-2 tm-5)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55778.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> ((B -> C) and (B -> D))))), M:tm-7, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55779
in-theory        55779
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) or D)
theorem-size     27
proof            (modus-ponens tm-6 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-6 tm-8 tm-2 tm-5)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55779.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) or D), M:tm-6, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55780
in-theory        55780
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> ((B -> C) and (B -> D)))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55780.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> ((B -> C) and (B -> D)))) and A)), M:tm-5, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55781
in-theory        55781
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> B)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) and (A -> C))))
theorem-size     39
proof            (modus-ponens tm-2 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Am Bm)) (C (and (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-8 tm-5)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55781.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> B)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) and (A -> C)))), M:tm-2, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Am Bm)) (C (and (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-55782
in-theory        55782
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> ((B -> C) and (B -> D)))))
theorem-size     27
proof            (modus-ponens tm-1 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-1 tm-8 tm-2 tm-5)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-55782.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> ((B -> C) and (B -> D))))), M:tm-1, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55783
in-theory        55783
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-665 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55783.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-665, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55784
in-theory        55784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-622 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55784.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-622, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55785
in-theory        55785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) and D)))
theorem-size     33
proof            (modus-ponens tm-617 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> Em (and (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Em)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55785.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) and D))), M:tm-617, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> Em (and (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Em))))
================================================================
tm-name          tm-55786
in-theory        55786
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55786.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (F -> (G or F))), M:tm-609, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55787
in-theory        55787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-605 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55787.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-605, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55788
in-theory        55788
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-595 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55788.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))))), M:tm-595, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55789
in-theory        55789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-550 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55789.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-550, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55790
in-theory        55790
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-540 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55790.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-540, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55791
in-theory        55791
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-530 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55791.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-530, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55792
in-theory        55792
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-520 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55792.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-520, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55793
in-theory        55793
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-510 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55793.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-510, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55794
in-theory        55794
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-500 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55794.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-500, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55795
in-theory        55795
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-490 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55795.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I))))), M:tm-490, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55796
in-theory        55796
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-480 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55796.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-480, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55797
in-theory        55797
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-469 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55797.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-469, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55798
in-theory        55798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or E) and D)))
theorem-size     33
proof            (modus-ponens tm-464 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C (-> Em (and (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B) Em)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55798.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or E) and D))), M:tm-464, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C (-> Em (and (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B) Em))))
================================================================
tm-name          tm-55799
in-theory        55799
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55799.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (F -> (F or G))), M:tm-456, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55800
in-theory        55800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-453 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55800.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-453, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55801
in-theory        55801
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-443 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55801.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))))), M:tm-443, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55802
in-theory        55802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-409 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55802.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-409, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55803
in-theory        55803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-400 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55803.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-400, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55804
in-theory        55804
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-391 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55804.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-391, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55805
in-theory        55805
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-382 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55805.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-382, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55806
in-theory        55806
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-373 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55806.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I))))), M:tm-373, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55807
in-theory        55807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-364 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55807.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-364, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55808
in-theory        55808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-354 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55808.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-354, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55809
in-theory        55809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E)) and D)))
theorem-size     35
proof            (modus-ponens tm-349 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))) (C (-> Em (and (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) Em)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55809.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E)) and D))), M:tm-349, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))) (C (-> Em (and (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) Em))))
================================================================
tm-name          tm-55810
in-theory        55810
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55810.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55811
in-theory        55811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G)))))
theorem-size     31
proof            (modus-ponens tm-338 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55811.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G))))), M:tm-338, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55812
in-theory        55812
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (E -> (D and E))))))
theorem-size     57
proof            (modus-ponens tm-328 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55812.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))))), M:tm-328, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-55813
in-theory        55813
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E))))))
theorem-size     51
proof            (modus-ponens tm-327 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55813.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))))), M:tm-327, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55814
in-theory        55814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-326 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55814.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))))), M:tm-326, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55815
in-theory        55815
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-325 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55815.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))))), M:tm-325, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55816
in-theory        55816
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E))))))
theorem-size     57
proof            (modus-ponens tm-324 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55816.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))))), M:tm-324, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55817
in-theory        55817
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E))))))
theorem-size     49
proof            (modus-ponens tm-323 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55817.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))))), M:tm-323, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55818
in-theory        55818
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55818.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((F and G) -> G)), M:tm-322, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55819
in-theory        55819
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55819.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((F and G) -> F)), M:tm-320, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55820
in-theory        55820
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55820.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55821
in-theory        55821
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-316 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55821.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-55822
in-theory        55822
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55822.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (F -> (G -> F))), M:tm-315, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55823
in-theory        55823
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E -> (D and E))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     59
proof            (modus-ponens tm-313 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55823.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E -> (D and E))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-55824
in-theory        55824
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((D -> (E -> (D and E))) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (D -> (E -> (D and E)))) -> F)))
theorem-size     55
proof            (modus-ponens tm-312 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55824.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((D -> (E -> (D and E))) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (D -> (E -> (D and E)))) -> F))), M:tm-312, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-55825
in-theory        55825
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E))))))
theorem-size     45
proof            (modus-ponens tm-311 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55825.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))))), M:tm-311, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55826
in-theory        55826
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55826.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) or F)), M:tm-310, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55827
in-theory        55827
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55827.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and F))), M:tm-309, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55828
in-theory        55828
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E -> (D and E)))))
theorem-size     57
proof            (modus-ponens tm-306 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> Em (and Dm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55828.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E -> (D and E))))), M:tm-306, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> Em (and Dm Em))))
================================================================
tm-name          tm-55829
in-theory        55829
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E))))))
theorem-size     45
proof            (modus-ponens tm-305 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55829.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))))), M:tm-305, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55830
in-theory        55830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-303 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55830.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-303, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55831
in-theory        55831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-270 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55831.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-270, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55832
in-theory        55832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-239 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55832.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-239, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55833
in-theory        55833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I)))))
theorem-size     39
proof            (modus-ponens tm-210 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55833.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I))))), M:tm-210, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55834
in-theory        55834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-183 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55834.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-183, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55835
in-theory        55835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-157 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55835.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-157, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55836
in-theory        55836
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-147 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55836.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-147, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55837
in-theory        55837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-134 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55837.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-134, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55838
in-theory        55838
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     37
proof            (modus-ponens tm-125 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55838.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-125, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55839
in-theory        55839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I)))))
theorem-size     37
proof            (modus-ponens tm-113 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55839.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I))))), M:tm-113, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55840
in-theory        55840
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-105 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55840.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-105, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55841
in-theory        55841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D)))
theorem-size     31
proof            (modus-ponens tm-99 tm-687 ((Dm (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Em (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Em)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55841.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D))), M:tm-99, m:tm-687, u:((Dm (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Em (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Em))))
================================================================
tm-name          tm-55842
in-theory        55842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) and D)))
theorem-size     33
proof            (modus-ponens tm-98 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> Em (and (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Em)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55842.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) and D))), M:tm-98, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> Em (and (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Em))))
================================================================
tm-name          tm-55843
in-theory        55843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-95 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55843.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G))))), M:tm-95, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55844
in-theory        55844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-83 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55844.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-83, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55845
in-theory        55845
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> (E and F)))))
theorem-size     27
proof            (modus-ponens tm-76 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55845.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> (E and F))))), M:tm-76, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55846
in-theory        55846
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> (D and E))))
theorem-size     37
proof            (modus-ponens tm-73 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-5)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55846.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> (D and E)))), M:tm-73, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-55847
in-theory        55847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-69 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55847.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G))))), M:tm-69, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55848
in-theory        55848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-54 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55848.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-54, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55849
in-theory        55849
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-50 tm-687 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-8 tm-7 tm-2 tm-1 tm-5)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55849.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> (D and E)))), M:tm-50, m:tm-687, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-55850
in-theory        55850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-49 tm-687 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-8 tm-6 tm-2 tm-1 tm-5)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55850.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> (D and E)))), M:tm-49, m:tm-687, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-55851
in-theory        55851
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (E -> (F -> (E and F))))
theorem-size     37
proof            (modus-ponens tm-47 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-5)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55851.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (E -> (F -> (E and F)))), M:tm-47, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-55852
in-theory        55852
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> (F -> (E and F))))
theorem-size     37
proof            (modus-ponens tm-46 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-5)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55852.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> (F -> (E and F)))), M:tm-46, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-55853
in-theory        55853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-42 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55853.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G))))), M:tm-42, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55854
in-theory        55854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-32 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55854.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G))))), M:tm-32, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55855
in-theory        55855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))))
theorem-size     35
proof            (modus-ponens tm-24 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55855.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (E -> (D and E))))), M:tm-24, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-55856
in-theory        55856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-23 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55856.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G))))), M:tm-23, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55857
in-theory        55857
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-22 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55857.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G))))), M:tm-22, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55858
in-theory        55858
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-21 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55858.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G))))), M:tm-21, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55859
in-theory        55859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-20 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55859.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-20, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55860
in-theory        55860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-19 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55860.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G -> (F and G))))), M:tm-19, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55861
in-theory        55861
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E -> (D and E))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     37
proof            (modus-ponens tm-9 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-9 tm-8 tm-2 tm-1 tm-5)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55861.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E -> (D and E))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-55862
in-theory        55862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> ((((D -> (E -> F)) or ((D -> E) -> (D -> F))) or (A -> (B -> (A and B)))) -> C))
theorem-size     33
proof            (modus-ponens tm-8 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55862.        (((A -> (B -> (A and B))) -> C) -> ((((D -> (E -> F)) or ((D -> E) -> (D -> F))) or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-55863
in-theory        55863
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-7 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-7 tm-8 tm-2 tm-1 tm-5)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55863.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> (E and F))))), M:tm-7, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55864
in-theory        55864
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-6 tm-8 tm-2 tm-1 tm-5)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55864.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) or F), M:tm-6, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55865
in-theory        55865
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> (E and F)))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55865.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> (E and F)))) and A)), M:tm-5, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55866
in-theory        55866
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E -> (D and E))))
theorem-size     35
proof            (modus-ponens tm-2 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> Em (and Dm Em)))))
axioms-used      (tm-2 tm-8 tm-1 tm-5)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55866.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E -> (D and E)))), M:tm-2, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (-> Em (and Dm Em))))
================================================================
tm-name          tm-55867
in-theory        55867
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-1 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-1 tm-8 tm-2 tm-5)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-55867.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F -> (E and F))))), M:tm-1, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-55868
in-theory        55868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (C -> (C -> D))))
theorem-size     15
proof            (modus-ponens tm-688 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-55868.        ((A -> (A or B)) and ((C -> D) -> (C -> (C -> D)))), M:tm-688, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-55869
in-theory        55869
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (C -> ((C -> D) and C))))
theorem-size     17
proof            (modus-ponens tm-688 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-55869.        ((A -> (A or B)) and ((C -> D) -> (C -> ((C -> D) and C)))), M:tm-688, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-55870
in-theory        55870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> C) -> ((C -> D) -> (((C -> D) or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-688 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-55870.        ((A -> (A or B)) and (((C -> D) -> C) -> ((C -> D) -> (((C -> D) or C) -> D)))), M:tm-688, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-55871
in-theory        55871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (C -> (E -> C))))
theorem-size     15
proof            (modus-ponens tm-688 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-55871.        ((A -> (A or B)) and ((C -> D) -> (C -> (E -> C)))), M:tm-688, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-55872
in-theory        55872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> F) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     27
proof            (modus-ponens tm-688 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-55872.        ((A -> (A or B)) and (((C -> (D -> E)) -> F) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-688, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-55873
in-theory        55873
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> E) -> ((C and D) -> C)))
theorem-size     17
proof            (modus-ponens tm-688 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-55873.        ((A -> (A or B)) and (((C and D) -> E) -> ((C and D) -> C))), M:tm-688, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-55874
in-theory        55874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> E) -> ((C and D) -> D)))
theorem-size     17
proof            (modus-ponens tm-688 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-55874.        ((A -> (A or B)) and (((C and D) -> E) -> ((C and D) -> D))), M:tm-688, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-55875
in-theory        55875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (C -> (E -> (C and E)))))
theorem-size     17
proof            (modus-ponens tm-688 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-55875.        ((A -> (A or B)) and ((C -> D) -> (C -> (E -> (C and E))))), M:tm-688, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-55876
in-theory        55876
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (C -> (C or E))))
theorem-size     15
proof            (modus-ponens tm-688 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-55876.        ((A -> (A or B)) and ((C -> D) -> (C -> (C or E)))), M:tm-688, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-55877
in-theory        55877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> (C -> (E or C))))
theorem-size     15
proof            (modus-ponens tm-688 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-55877.        ((A -> (A or B)) and ((C -> D) -> (C -> (E or C)))), M:tm-688, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-55878
in-theory        55878
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55878.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-665, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55879
in-theory        55879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> (E or F)) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-623 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55879.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> (E or F)) and ((A -> B) -> (A -> C))))), M:tm-623, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55880
in-theory        55880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55880.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-622, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55881
in-theory        55881
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (F -> (G or F)))
theorem-size     33
proof            (modus-ponens tm-609 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55881.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (F -> (G or F))), M:tm-609, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55882
in-theory        55882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55882.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-605, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55883
in-theory        55883
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55883.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))))), M:tm-595, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55884
in-theory        55884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55884.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-550, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55885
in-theory        55885
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55885.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-540, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55886
in-theory        55886
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55886.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-530, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55887
in-theory        55887
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55887.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-520, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55888
in-theory        55888
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55888.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-510, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55889
in-theory        55889
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55889.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-500, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55890
in-theory        55890
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (H or I)) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-6)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55890.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (H or I)) and ((E -> F) -> (E -> G))))), M:tm-490, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55891
in-theory        55891
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55891.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-480, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55892
in-theory        55892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (D or E)) and ((A -> B) -> (A -> C))) or F))
theorem-size     29
proof            (modus-ponens tm-470 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55892.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (D or E)) and ((A -> B) -> (A -> C))) or F)), M:tm-470, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55893
in-theory        55893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55893.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-469, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55894
in-theory        55894
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (F -> (F or G)))
theorem-size     33
proof            (modus-ponens tm-456 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55894.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (F -> (F or G))), M:tm-456, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55895
in-theory        55895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55895.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-453, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55896
in-theory        55896
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55896.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))))), M:tm-443, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55897
in-theory        55897
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55897.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-409, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55898
in-theory        55898
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55898.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-400, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55899
in-theory        55899
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55899.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-391, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55900
in-theory        55900
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55900.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-382, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55901
in-theory        55901
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (H or I)) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55901.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (H or I)) and ((E -> F) -> (E -> G))))), M:tm-373, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55902
in-theory        55902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55902.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-364, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55903
in-theory        55903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E -> (E or F)) and ((A -> B) -> (A -> C))) and D)))
theorem-size     31
proof            (modus-ponens tm-355 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55903.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E -> (E or F)) and ((A -> B) -> (A -> C))) and D))), M:tm-355, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55904
in-theory        55904
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55904.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-354, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55905
in-theory        55905
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (F -> (G -> (F and G))))
theorem-size     35
proof            (modus-ponens tm-341 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55905.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55906
in-theory        55906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55906.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E))))), M:tm-338, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55907
in-theory        55907
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((A -> B) -> (A -> C))))))
theorem-size     69
proof            (modus-ponens tm-328 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       239
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55907.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((A -> B) -> (A -> C)))))), M:tm-328, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55908
in-theory        55908
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55908.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))))), M:tm-327, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55909
in-theory        55909
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-6)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55909.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))))), M:tm-326, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55910
in-theory        55910
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-6)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55910.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))))), M:tm-325, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55911
in-theory        55911
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       253
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55911.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))))), M:tm-324, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55912
in-theory        55912
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55912.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))))), M:tm-323, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55913
in-theory        55913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((F and G) -> G))
theorem-size     33
proof            (modus-ponens tm-322 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55913.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((F and G) -> G)), M:tm-322, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55914
in-theory        55914
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((F and G) -> F))
theorem-size     33
proof            (modus-ponens tm-320 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55914.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((F and G) -> F)), M:tm-320, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55915
in-theory        55915
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     41
proof            (modus-ponens tm-318 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55915.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55916
in-theory        55916
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     55
proof            (modus-ponens tm-316 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55916.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55917
in-theory        55917
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (F -> (G -> F)))
theorem-size     33
proof            (modus-ponens tm-315 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55917.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (F -> (G -> F))), M:tm-315, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55918
in-theory        55918
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (D or E)) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     71
proof            (modus-ponens tm-313 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-6)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55918.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (D or E)) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55919
in-theory        55919
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((((D -> (D or E)) and ((A -> B) -> (A -> C))) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((D -> (D or E)) and ((A -> B) -> (A -> C)))) -> F)))
theorem-size     73
proof            (modus-ponens tm-312 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55919.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((((D -> (D or E)) and ((A -> B) -> (A -> C))) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((D -> (D or E)) and ((A -> B) -> (A -> C)))) -> F))), M:tm-312, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55920
in-theory        55920
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-6)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55920.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))))), M:tm-311, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55921
in-theory        55921
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) or F))
theorem-size     57
proof            (modus-ponens tm-310 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55921.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) or F)), M:tm-310, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55922
in-theory        55922
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and F)))
theorem-size     59
proof            (modus-ponens tm-309 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55922.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and F))), M:tm-309, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55923
in-theory        55923
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55923.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))))), M:tm-305, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55924
in-theory        55924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55924.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-303, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55925
in-theory        55925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55925.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-270, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55926
in-theory        55926
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55926.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-239, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55927
in-theory        55927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (H or I)) and ((E -> F) -> (E -> G)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55927.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (H or I)) and ((E -> F) -> (E -> G))))), M:tm-210, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55928
in-theory        55928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55928.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-183, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55929
in-theory        55929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55929.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-157, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55930
in-theory        55930
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55930.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-147, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55931
in-theory        55931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55931.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-134, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55932
in-theory        55932
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55932.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-125, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55933
in-theory        55933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (H or I)) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55933.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (H or I)) and ((E -> F) -> (E -> G))))), M:tm-113, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55934
in-theory        55934
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55934.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-105, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55935
in-theory        55935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55935.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E))))), M:tm-95, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55936
in-theory        55936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (E or F)) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-84 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55936.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (E or F)) and ((A -> B) -> (A -> C))))), M:tm-84, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55937
in-theory        55937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55937.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-83, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55938
in-theory        55938
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (E or F)) and ((B -> C) -> (B -> D)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55938.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (E or F)) and ((B -> C) -> (B -> D))))), M:tm-76, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55939
in-theory        55939
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-73 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-6)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55939.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-73, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55940
in-theory        55940
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-6)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55940.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E))))), M:tm-69, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55941
in-theory        55941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-54 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55941.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-54, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55942
in-theory        55942
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-50 tm-688 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5 tm-6)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55942.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-50, m:tm-688, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55943
in-theory        55943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-49 tm-688 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55943.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-49, m:tm-688, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55944
in-theory        55944
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((E -> (E or F)) and ((B -> C) -> (B -> D))))
theorem-size     43
proof            (modus-ponens tm-47 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-6)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55944.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((E -> (E or F)) and ((B -> C) -> (B -> D)))), M:tm-47, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55945
in-theory        55945
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((E -> (E or F)) and ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-46 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-6)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55945.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((E -> (E or F)) and ((A -> B) -> (A -> C)))), M:tm-46, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55946
in-theory        55946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-42 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55946.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E))))), M:tm-42, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55947
in-theory        55947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-32 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55947.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E))))), M:tm-32, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55948
in-theory        55948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((A -> B) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-24 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55948.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((A -> B) -> (A -> C))))), M:tm-24, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55949
in-theory        55949
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-23 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55949.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E))))), M:tm-23, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55950
in-theory        55950
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-22 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55950.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E))))), M:tm-22, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55951
in-theory        55951
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-21 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55951.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E))))), M:tm-21, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55952
in-theory        55952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-20 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-6)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55952.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-20, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55953
in-theory        55953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-19 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55953.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (F or G)) and ((C -> D) -> (C -> E))))), M:tm-19, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55954
in-theory        55954
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (D or E)) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     43
proof            (modus-ponens tm-9 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-9 tm-8 tm-2 tm-5 tm-6)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55954.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (D or E)) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55955
in-theory        55955
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and ((C -> D) -> (C -> E))) -> F) -> ((((C -> (D -> E)) or ((C -> D) -> (C -> E))) or ((A -> (A or B)) and ((C -> D) -> (C -> E)))) -> F))
theorem-size     45
proof            (modus-ponens tm-8 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55955.        ((((A -> (A or B)) and ((C -> D) -> (C -> E))) -> F) -> ((((C -> (D -> E)) or ((C -> D) -> (C -> E))) or ((A -> (A or B)) and ((C -> D) -> (C -> E)))) -> F)), M:tm-8, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-55956
in-theory        55956
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (E or F)) and ((B -> C) -> (B -> D)))))
theorem-size     29
proof            (modus-ponens tm-7 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-7 tm-8 tm-2 tm-5 tm-6)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55956.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (E or F)) and ((B -> C) -> (B -> D))))), M:tm-7, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55957
in-theory        55957
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) or F)
theorem-size     29
proof            (modus-ponens tm-6 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-6 tm-8 tm-2 tm-5)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55957.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) or F), M:tm-6, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55958
in-theory        55958
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (E or F)) and ((B -> C) -> (B -> D)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55958.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (E or F)) and ((B -> C) -> (B -> D)))) and A)), M:tm-5, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55959
in-theory        55959
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (E or F)) and ((B -> C) -> (B -> D)))))
theorem-size     29
proof            (modus-ponens tm-1 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-1 tm-8 tm-2 tm-5 tm-6)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-55959.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (E or F)) and ((B -> C) -> (B -> D))))), M:tm-1, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-55960
in-theory        55960
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-665 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55960.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-665, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55961
in-theory        55961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-622 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55961.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-622, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55962
in-theory        55962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or E))
theorem-size     31
proof            (modus-ponens tm-617 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (or (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Em))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-6)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55962.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or E)), M:tm-617, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (or (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Em)))
================================================================
tm-name          tm-55963
in-theory        55963
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-6)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55963.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (F -> (G or F))), M:tm-609, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55964
in-theory        55964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-605 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55964.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-605, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55965
in-theory        55965
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55965.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))))), M:tm-595, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55966
in-theory        55966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-550 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55966.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-550, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55967
in-theory        55967
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-540 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55967.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-540, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55968
in-theory        55968
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-530 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55968.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-530, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55969
in-theory        55969
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-520 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55969.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-520, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55970
in-theory        55970
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-510 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55970.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-510, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55971
in-theory        55971
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-500 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55971.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-500, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55972
in-theory        55972
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-490 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55972.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I)))), M:tm-490, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55973
in-theory        55973
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-480 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55973.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-480, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55974
in-theory        55974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-469 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55974.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-469, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55975
in-theory        55975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D) or E))
theorem-size     31
proof            (modus-ponens tm-464 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C (or (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B) Em))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55975.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D) or E)), M:tm-464, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C (or (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B) Em)))
================================================================
tm-name          tm-55976
in-theory        55976
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55976.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (F -> (F or G))), M:tm-456, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55977
in-theory        55977
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-453 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55977.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-453, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55978
in-theory        55978
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55978.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))))), M:tm-443, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55979
in-theory        55979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-409 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55979.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-409, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55980
in-theory        55980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-400 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55980.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-400, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55981
in-theory        55981
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-391 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55981.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-391, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55982
in-theory        55982
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-382 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55982.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-382, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55983
in-theory        55983
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-373 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55983.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I)))), M:tm-373, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55984
in-theory        55984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-364 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55984.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-364, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55985
in-theory        55985
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-354 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55985.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-354, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55986
in-theory        55986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D)) or E))
theorem-size     33
proof            (modus-ponens tm-349 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))) (C (or (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) Em))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-6)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55986.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D)) or E)), M:tm-349, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))) (C (or (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) Em)))
================================================================
tm-name          tm-55987
in-theory        55987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55987.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55988
in-theory        55988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G))))
theorem-size     29
proof            (modus-ponens tm-338 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55988.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G)))), M:tm-338, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55989
in-theory        55989
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (D or E)))))
theorem-size     53
proof            (modus-ponens tm-328 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55989.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (D or E))))), M:tm-328, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-55990
in-theory        55990
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55990.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))))), M:tm-327, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55991
in-theory        55991
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-6)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55991.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))))), M:tm-326, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55992
in-theory        55992
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55992.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))))), M:tm-325, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55993
in-theory        55993
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55993.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))))), M:tm-324, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55994
in-theory        55994
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55994.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))))), M:tm-323, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55995
in-theory        55995
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55995.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((F and G) -> G)), M:tm-322, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55996
in-theory        55996
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55996.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((F and G) -> F)), M:tm-320, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55997
in-theory        55997
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55997.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-55998
in-theory        55998
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     47
proof            (modus-ponens tm-316 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55998.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-55999
in-theory        55999
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-55999.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (F -> (G -> F))), M:tm-315, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56000
in-theory        56000
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (D or E)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     55
proof            (modus-ponens tm-313 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-6)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56000.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (D or E)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-56001
in-theory        56001
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((D -> (D or E)) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (D -> (D or E))) -> F)))
theorem-size     49
proof            (modus-ponens tm-312 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56001.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((D -> (D or E)) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (D -> (D or E))) -> F))), M:tm-312, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-56002
in-theory        56002
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56002.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))))), M:tm-311, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56003
in-theory        56003
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56003.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) or F)), M:tm-310, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56004
in-theory        56004
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56004.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and F))), M:tm-309, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56005
in-theory        56005
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or E))))
theorem-size     53
proof            (modus-ponens tm-306 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (or Dm Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56005.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or E)))), M:tm-306, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (or Dm Em)))
================================================================
tm-name          tm-56006
in-theory        56006
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56006.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))))), M:tm-305, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56007
in-theory        56007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     31
proof            (modus-ponens tm-303 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56007.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-303, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56008
in-theory        56008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-270 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56008.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-270, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56009
in-theory        56009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-239 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56009.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-239, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56010
in-theory        56010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I))))
theorem-size     37
proof            (modus-ponens tm-210 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56010.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I)))), M:tm-210, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56011
in-theory        56011
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-183 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56011.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-183, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56012
in-theory        56012
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-157 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56012.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-157, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56013
in-theory        56013
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     35
proof            (modus-ponens tm-147 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56013.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-147, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56014
in-theory        56014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-134 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56014.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-134, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56015
in-theory        56015
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     35
proof            (modus-ponens tm-125 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56015.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-125, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56016
in-theory        56016
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I))))
theorem-size     35
proof            (modus-ponens tm-113 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56016.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I)))), M:tm-113, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56017
in-theory        56017
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-105 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56017.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-105, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56018
in-theory        56018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D))
theorem-size     29
proof            (modus-ponens tm-99 tm-689 ((Dm (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Em))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56018.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D)), M:tm-99, m:tm-689, u:((Dm (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Em)))
================================================================
tm-name          tm-56019
in-theory        56019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or E))
theorem-size     31
proof            (modus-ponens tm-98 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (or (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Em))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56019.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or E)), M:tm-98, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (or (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Em)))
================================================================
tm-name          tm-56020
in-theory        56020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-95 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-6)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56020.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G)))), M:tm-95, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56021
in-theory        56021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-83 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56021.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-83, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56022
in-theory        56022
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (E or F))))
theorem-size     25
proof            (modus-ponens tm-76 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56022.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (E or F)))), M:tm-76, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56023
in-theory        56023
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (D or E)))
theorem-size     35
proof            (modus-ponens tm-73 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56023.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (D or E))), M:tm-73, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-56024
in-theory        56024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-69 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-1 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56024.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G)))), M:tm-69, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56025
in-theory        56025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-54 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56025.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-54, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56026
in-theory        56026
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (D or E)))
theorem-size     27
proof            (modus-ponens tm-50 tm-689 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Dm Em)))))
axioms-used      (tm-8 tm-7 tm-2 tm-1 tm-6)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56026.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (D or E))), M:tm-50, m:tm-689, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Dm Em))))
================================================================
tm-name          tm-56027
in-theory        56027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (D or E)))
theorem-size     25
proof            (modus-ponens tm-49 tm-689 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Dm Em)))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56027.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (D or E))), M:tm-49, m:tm-689, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Dm Em))))
================================================================
tm-name          tm-56028
in-theory        56028
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (E -> (E or F)))
theorem-size     35
proof            (modus-ponens tm-47 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56028.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (E -> (E or F))), M:tm-47, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-56029
in-theory        56029
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> (E or F)))
theorem-size     35
proof            (modus-ponens tm-46 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-6)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56029.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> (E or F))), M:tm-46, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-56030
in-theory        56030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-42 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56030.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G)))), M:tm-42, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56031
in-theory        56031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-32 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56031.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G)))), M:tm-32, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56032
in-theory        56032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (D or E))))
theorem-size     33
proof            (modus-ponens tm-24 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56032.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (D or E)))), M:tm-24, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-56033
in-theory        56033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-23 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56033.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G)))), M:tm-23, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56034
in-theory        56034
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-22 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56034.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G)))), M:tm-22, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56035
in-theory        56035
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-21 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56035.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G)))), M:tm-21, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56036
in-theory        56036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     33
proof            (modus-ponens tm-20 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-6)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56036.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-20, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56037
in-theory        56037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-19 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-6)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56037.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (F or G)))), M:tm-19, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56038
in-theory        56038
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (D or E)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     35
proof            (modus-ponens tm-9 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-9 tm-8 tm-2 tm-1 tm-6)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56038.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (D or E)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-56039
in-theory        56039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> ((((D -> (E -> F)) or ((D -> E) -> (D -> F))) or (A -> (A or B))) -> C))
theorem-size     29
proof            (modus-ponens tm-8 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56039.        (((A -> (A or B)) -> C) -> ((((D -> (E -> F)) or ((D -> E) -> (D -> F))) or (A -> (A or B))) -> C)), M:tm-8, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-56040
in-theory        56040
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-7 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-7 tm-8 tm-2 tm-1 tm-6)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56040.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (E or F)))), M:tm-7, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56041
in-theory        56041
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-6 tm-8 tm-2 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56041.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) or F), M:tm-6, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56042
in-theory        56042
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (E or F))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56042.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (E or F))) and A)), M:tm-5, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56043
in-theory        56043
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or E)))
theorem-size     33
proof            (modus-ponens tm-2 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (or Dm Em))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56043.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or E))), M:tm-2, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (or Dm Em)))
================================================================
tm-name          tm-56044
in-theory        56044
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-1 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-1 tm-8 tm-2 tm-6)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-56044.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (E or F)))), M:tm-1, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-56045
in-theory        56045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (C -> (C -> D))))
theorem-size     15
proof            (modus-ponens tm-690 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-56045.        ((A -> (B or A)) and ((C -> D) -> (C -> (C -> D)))), M:tm-690, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-56046
in-theory        56046
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (C -> ((C -> D) and C))))
theorem-size     17
proof            (modus-ponens tm-690 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-56046.        ((A -> (B or A)) and ((C -> D) -> (C -> ((C -> D) and C)))), M:tm-690, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-56047
in-theory        56047
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> C) -> ((C -> D) -> (((C -> D) or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-690 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-56047.        ((A -> (B or A)) and (((C -> D) -> C) -> ((C -> D) -> (((C -> D) or C) -> D)))), M:tm-690, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-56048
in-theory        56048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (C -> (E -> C))))
theorem-size     15
proof            (modus-ponens tm-690 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-56048.        ((A -> (B or A)) and ((C -> D) -> (C -> (E -> C)))), M:tm-690, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-56049
in-theory        56049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> F) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     27
proof            (modus-ponens tm-690 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-56049.        ((A -> (B or A)) and (((C -> (D -> E)) -> F) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-690, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-56050
in-theory        56050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> E) -> ((C and D) -> C)))
theorem-size     17
proof            (modus-ponens tm-690 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-56050.        ((A -> (B or A)) and (((C and D) -> E) -> ((C and D) -> C))), M:tm-690, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-56051
in-theory        56051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> E) -> ((C and D) -> D)))
theorem-size     17
proof            (modus-ponens tm-690 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-56051.        ((A -> (B or A)) and (((C and D) -> E) -> ((C and D) -> D))), M:tm-690, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-56052
in-theory        56052
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (C -> (E -> (C and E)))))
theorem-size     17
proof            (modus-ponens tm-690 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-56052.        ((A -> (B or A)) and ((C -> D) -> (C -> (E -> (C and E))))), M:tm-690, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-56053
in-theory        56053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (C -> (C or E))))
theorem-size     15
proof            (modus-ponens tm-690 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-56053.        ((A -> (B or A)) and ((C -> D) -> (C -> (C or E)))), M:tm-690, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-56054
in-theory        56054
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> (C -> (E or C))))
theorem-size     15
proof            (modus-ponens tm-690 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-56054.        ((A -> (B or A)) and ((C -> D) -> (C -> (E or C)))), M:tm-690, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-56055
in-theory        56055
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-665 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56055.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-665, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56056
in-theory        56056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> (F or E)) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-623 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-5)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56056.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> (F or E)) and ((A -> B) -> (A -> C))))), M:tm-623, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56057
in-theory        56057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-622 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56057.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-622, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56058
in-theory        56058
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (F -> (G or F)))
theorem-size     33
proof            (modus-ponens tm-609 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56058.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (F -> (G or F))), M:tm-609, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56059
in-theory        56059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-605 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56059.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-605, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56060
in-theory        56060
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-595 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56060.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))))), M:tm-595, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56061
in-theory        56061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-550 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56061.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-550, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56062
in-theory        56062
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-540 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56062.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-540, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56063
in-theory        56063
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-530 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56063.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-530, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56064
in-theory        56064
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-520 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56064.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-520, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56065
in-theory        56065
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-510 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56065.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-510, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56066
in-theory        56066
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-500 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56066.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-500, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56067
in-theory        56067
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I or H)) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-490 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56067.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I or H)) and ((E -> F) -> (E -> G))))), M:tm-490, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56068
in-theory        56068
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-480 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56068.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-480, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56069
in-theory        56069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E or D)) and ((A -> B) -> (A -> C))) or F))
theorem-size     29
proof            (modus-ponens tm-470 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-5 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56069.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E or D)) and ((A -> B) -> (A -> C))) or F)), M:tm-470, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56070
in-theory        56070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-469 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56070.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-469, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56071
in-theory        56071
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (F -> (F or G)))
theorem-size     33
proof            (modus-ponens tm-456 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56071.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (F -> (F or G))), M:tm-456, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56072
in-theory        56072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-453 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56072.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-453, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56073
in-theory        56073
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-443 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56073.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))))), M:tm-443, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56074
in-theory        56074
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-409 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56074.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-409, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56075
in-theory        56075
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-400 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56075.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-400, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56076
in-theory        56076
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-391 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56076.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-391, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56077
in-theory        56077
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-382 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56077.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-382, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56078
in-theory        56078
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I or H)) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-373 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-7)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56078.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I or H)) and ((E -> F) -> (E -> G))))), M:tm-373, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56079
in-theory        56079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-364 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56079.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-364, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56080
in-theory        56080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E -> (F or E)) and ((A -> B) -> (A -> C))) and D)))
theorem-size     31
proof            (modus-ponens tm-355 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56080.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E -> (F or E)) and ((A -> B) -> (A -> C))) and D))), M:tm-355, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56081
in-theory        56081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-354 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56081.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-354, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56082
in-theory        56082
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (F -> (G -> (F and G))))
theorem-size     35
proof            (modus-ponens tm-341 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56082.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56083
in-theory        56083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E)))))
theorem-size     37
proof            (modus-ponens tm-338 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56083.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E))))), M:tm-338, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56084
in-theory        56084
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((A -> B) -> (A -> C))))))
theorem-size     69
proof            (modus-ponens tm-328 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       239
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56084.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((A -> B) -> (A -> C)))))), M:tm-328, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56085
in-theory        56085
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))))
theorem-size     63
proof            (modus-ponens tm-327 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56085.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))))), M:tm-327, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56086
in-theory        56086
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-326 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-7)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56086.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))))), M:tm-326, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56087
in-theory        56087
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-325 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-7)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56087.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))))), M:tm-325, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56088
in-theory        56088
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))))
theorem-size     69
proof            (modus-ponens tm-324 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       253
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56088.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))))), M:tm-324, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56089
in-theory        56089
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-323 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56089.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))))), M:tm-323, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56090
in-theory        56090
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((F and G) -> G))
theorem-size     33
proof            (modus-ponens tm-322 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56090.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((F and G) -> G)), M:tm-322, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56091
in-theory        56091
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((F and G) -> F))
theorem-size     33
proof            (modus-ponens tm-320 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56091.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((F and G) -> F)), M:tm-320, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56092
in-theory        56092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     41
proof            (modus-ponens tm-318 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56092.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56093
in-theory        56093
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     55
proof            (modus-ponens tm-316 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56093.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56094
in-theory        56094
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (F -> (G -> F)))
theorem-size     33
proof            (modus-ponens tm-315 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56094.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (F -> (G -> F))), M:tm-315, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56095
in-theory        56095
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E or D)) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     71
proof            (modus-ponens tm-313 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-7)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56095.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E or D)) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56096
in-theory        56096
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((((D -> (E or D)) and ((A -> B) -> (A -> C))) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((D -> (E or D)) and ((A -> B) -> (A -> C)))) -> F)))
theorem-size     73
proof            (modus-ponens tm-312 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56096.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((((D -> (E or D)) and ((A -> B) -> (A -> C))) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((D -> (E or D)) and ((A -> B) -> (A -> C)))) -> F))), M:tm-312, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56097
in-theory        56097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-311 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56097.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))))), M:tm-311, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56098
in-theory        56098
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) or F))
theorem-size     57
proof            (modus-ponens tm-310 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-7)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56098.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) or F)), M:tm-310, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56099
in-theory        56099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and F)))
theorem-size     59
proof            (modus-ponens tm-309 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56099.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and F))), M:tm-309, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56100
in-theory        56100
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-305 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56100.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))))), M:tm-305, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56101
in-theory        56101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-303 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56101.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-303, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56102
in-theory        56102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-270 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56102.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-270, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56103
in-theory        56103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-239 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56103.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-239, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56104
in-theory        56104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I or H)) and ((E -> F) -> (E -> G)))))
theorem-size     45
proof            (modus-ponens tm-210 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56104.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I or H)) and ((E -> F) -> (E -> G))))), M:tm-210, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56105
in-theory        56105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-183 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56105.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-183, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56106
in-theory        56106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-157 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56106.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-157, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56107
in-theory        56107
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-147 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56107.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-147, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56108
in-theory        56108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-134 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56108.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-134, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56109
in-theory        56109
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     43
proof            (modus-ponens tm-125 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56109.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-125, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56110
in-theory        56110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I or H)) and ((E -> F) -> (E -> G)))))
theorem-size     43
proof            (modus-ponens tm-113 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56110.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I or H)) and ((E -> F) -> (E -> G))))), M:tm-113, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56111
in-theory        56111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     47
proof            (modus-ponens tm-105 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56111.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-105, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56112
in-theory        56112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-95 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56112.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E))))), M:tm-95, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56113
in-theory        56113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F or E)) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-84 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56113.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F or E)) and ((A -> B) -> (A -> C))))), M:tm-84, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56114
in-theory        56114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-83 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56114.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-83, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56115
in-theory        56115
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F or E)) and ((B -> C) -> (B -> D)))))
theorem-size     33
proof            (modus-ponens tm-76 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56115.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F or E)) and ((B -> C) -> (B -> D))))), M:tm-76, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56116
in-theory        56116
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-73 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-7)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56116.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-73, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56117
in-theory        56117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E)))))
theorem-size     39
proof            (modus-ponens tm-69 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-7)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56117.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E))))), M:tm-69, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56118
in-theory        56118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-54 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56118.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-54, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56119
in-theory        56119
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-50 tm-690 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-7 tm-2 tm-5)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56119.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-50, m:tm-690, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56120
in-theory        56120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-49 tm-690 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-6 tm-2 tm-5 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56120.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-49, m:tm-690, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56121
in-theory        56121
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((E -> (F or E)) and ((B -> C) -> (B -> D))))
theorem-size     43
proof            (modus-ponens tm-47 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-7)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56121.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((E -> (F or E)) and ((B -> C) -> (B -> D)))), M:tm-47, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56122
in-theory        56122
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((E -> (F or E)) and ((A -> B) -> (A -> C))))
theorem-size     43
proof            (modus-ponens tm-46 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-7)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56122.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((E -> (F or E)) and ((A -> B) -> (A -> C)))), M:tm-46, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56123
in-theory        56123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-42 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56123.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E))))), M:tm-42, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56124
in-theory        56124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-32 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56124.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E))))), M:tm-32, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56125
in-theory        56125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((A -> B) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-24 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56125.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((A -> B) -> (A -> C))))), M:tm-24, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56126
in-theory        56126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E)))))
theorem-size     35
proof            (modus-ponens tm-23 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56126.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E))))), M:tm-23, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56127
in-theory        56127
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-22 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56127.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E))))), M:tm-22, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56128
in-theory        56128
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-21 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56128.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E))))), M:tm-21, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56129
in-theory        56129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-20 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-7)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56129.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-20, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56130
in-theory        56130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E)))))
theorem-size     33
proof            (modus-ponens tm-19 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56130.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((F -> (G or F)) and ((C -> D) -> (C -> E))))), M:tm-19, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56131
in-theory        56131
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E or D)) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     43
proof            (modus-ponens tm-9 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-9 tm-8 tm-2 tm-5 tm-7)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56131.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E or D)) and ((A -> B) -> (A -> C))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56132
in-theory        56132
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and ((C -> D) -> (C -> E))) -> F) -> ((((C -> (D -> E)) or ((C -> D) -> (C -> E))) or ((A -> (B or A)) and ((C -> D) -> (C -> E)))) -> F))
theorem-size     45
proof            (modus-ponens tm-8 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56132.        ((((A -> (B or A)) and ((C -> D) -> (C -> E))) -> F) -> ((((C -> (D -> E)) or ((C -> D) -> (C -> E))) or ((A -> (B or A)) and ((C -> D) -> (C -> E)))) -> F)), M:tm-8, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-56133
in-theory        56133
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F or E)) and ((B -> C) -> (B -> D)))))
theorem-size     29
proof            (modus-ponens tm-7 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-7 tm-8 tm-2 tm-5)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56133.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F or E)) and ((B -> C) -> (B -> D))))), M:tm-7, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56134
in-theory        56134
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) or F)
theorem-size     29
proof            (modus-ponens tm-6 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-6 tm-8 tm-2 tm-5 tm-7)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56134.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) or F), M:tm-6, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56135
in-theory        56135
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F or E)) and ((B -> C) -> (B -> D)))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56135.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F or E)) and ((B -> C) -> (B -> D)))) and A)), M:tm-5, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56136
in-theory        56136
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F or E)) and ((B -> C) -> (B -> D)))))
theorem-size     29
proof            (modus-ponens tm-1 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-1 tm-8 tm-2 tm-5 tm-7)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-56136.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((E -> (F or E)) and ((B -> C) -> (B -> D))))), M:tm-1, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56137
in-theory        56137
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-665 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-7)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56137.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-665, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56138
in-theory        56138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-622 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56138.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-622, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56139
in-theory        56139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E or ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     31
proof            (modus-ponens tm-617 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (or Em (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56139.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-617, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (or Em (or B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
================================================================
tm-name          tm-56140
in-theory        56140
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56140.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (F -> (G or F))), M:tm-609, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56141
in-theory        56141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-605 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56141.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-605, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56142
in-theory        56142
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56142.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((F -> (G or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))))), M:tm-595, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56143
in-theory        56143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-550 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56143.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-550, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56144
in-theory        56144
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-540 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56144.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-540, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56145
in-theory        56145
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-530 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56145.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-530, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56146
in-theory        56146
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-520 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56146.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-520, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56147
in-theory        56147
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-510 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56147.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-510, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56148
in-theory        56148
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-500 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56148.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-500, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56149
in-theory        56149
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-490 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56149.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H)))), M:tm-490, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56150
in-theory        56150
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-480 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56150.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-480, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56151
in-theory        56151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-469 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56151.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-469, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56152
in-theory        56152
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) or E)))
theorem-size     31
proof            (modus-ponens tm-464 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C (or Em (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-7)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56152.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) or E))), M:tm-464, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)) (C (or Em (or (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))))
================================================================
tm-name          tm-56153
in-theory        56153
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-7)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56153.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (F -> (F or G))), M:tm-456, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56154
in-theory        56154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-453 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56154.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-453, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56155
in-theory        56155
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56155.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((F -> (F or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))))), M:tm-443, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56156
in-theory        56156
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-409 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56156.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-409, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56157
in-theory        56157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-400 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56157.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-400, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56158
in-theory        56158
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-391 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56158.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-391, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56159
in-theory        56159
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-382 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56159.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-382, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56160
in-theory        56160
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-373 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56160.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H)))), M:tm-373, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56161
in-theory        56161
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-364 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56161.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-364, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56162
in-theory        56162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-354 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56162.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-354, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56163
in-theory        56163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E))))
theorem-size     33
proof            (modus-ponens tm-349 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))) (C (or Em (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-7)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56163.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E)))), M:tm-349, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B))) (C (or Em (-> B (and (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B)))))
================================================================
tm-name          tm-56164
in-theory        56164
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56164.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56165
in-theory        56165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F))))
theorem-size     29
proof            (modus-ponens tm-338 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56165.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F)))), M:tm-338, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56166
in-theory        56166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (E or D)))))
theorem-size     53
proof            (modus-ponens tm-328 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56166.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (E or D))))), M:tm-328, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-56167
in-theory        56167
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56167.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((F -> (G -> (F and G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))))), M:tm-327, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56168
in-theory        56168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-7)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56168.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((F and G) -> G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))))), M:tm-326, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56169
in-theory        56169
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56169.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((F and G) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))))), M:tm-325, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56170
in-theory        56170
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56170.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))))), M:tm-324, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56171
in-theory        56171
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56171.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((F -> (G -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))))), M:tm-323, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56172
in-theory        56172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56172.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((F and G) -> G)), M:tm-322, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56173
in-theory        56173
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56173.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((F and G) -> F)), M:tm-320, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56174
in-theory        56174
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56174.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56175
in-theory        56175
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     47
proof            (modus-ponens tm-316 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56175.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-56176
in-theory        56176
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56176.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (F -> (G -> F))), M:tm-315, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56177
in-theory        56177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E or D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     55
proof            (modus-ponens tm-313 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-7)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56177.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E or D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-56178
in-theory        56178
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((D -> (E or D)) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (D -> (E or D))) -> F)))
theorem-size     49
proof            (modus-ponens tm-312 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56178.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((D -> (E or D)) -> F) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or (D -> (E or D))) -> F))), M:tm-312, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-56179
in-theory        56179
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56179.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))))), M:tm-311, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56180
in-theory        56180
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56180.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) or F)), M:tm-310, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56181
in-theory        56181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56181.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and F))), M:tm-309, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56182
in-theory        56182
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E or D))))
theorem-size     53
proof            (modus-ponens tm-306 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (or Em Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56182.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E or D)))), M:tm-306, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (or Em Dm)))
================================================================
tm-name          tm-56183
in-theory        56183
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56183.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))))), M:tm-305, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56184
in-theory        56184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     31
proof            (modus-ponens tm-303 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56184.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-303, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56185
in-theory        56185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-270 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56185.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-270, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56186
in-theory        56186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-239 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56186.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-239, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56187
in-theory        56187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H))))
theorem-size     37
proof            (modus-ponens tm-210 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56187.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H)))), M:tm-210, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56188
in-theory        56188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-183 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56188.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-183, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56189
in-theory        56189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-157 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56189.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-157, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56190
in-theory        56190
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     35
proof            (modus-ponens tm-147 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56190.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-147, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56191
in-theory        56191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-134 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56191.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-134, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56192
in-theory        56192
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     35
proof            (modus-ponens tm-125 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56192.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-125, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56193
in-theory        56193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H))))
theorem-size     35
proof            (modus-ponens tm-113 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56193.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H)))), M:tm-113, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56194
in-theory        56194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-105 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56194.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-105, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56195
in-theory        56195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-99 tm-691 ((Dm (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Em (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56195.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-99, m:tm-691, u:((Dm (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Em (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56196
in-theory        56196
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     31
proof            (modus-ponens tm-98 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (or Em (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56196.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-98, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (or Em (-> B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
================================================================
tm-name          tm-56197
in-theory        56197
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-95 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-7)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56197.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F)))), M:tm-95, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56198
in-theory        56198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-83 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56198.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-83, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56199
in-theory        56199
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F or E))))
theorem-size     25
proof            (modus-ponens tm-76 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56199.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F or E)))), M:tm-76, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56200
in-theory        56200
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E or D)))
theorem-size     35
proof            (modus-ponens tm-73 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-1 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56200.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E or D))), M:tm-73, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-56201
in-theory        56201
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-69 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-1 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56201.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F)))), M:tm-69, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56202
in-theory        56202
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-54 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56202.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-54, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56203
in-theory        56203
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E or D)))
theorem-size     27
proof            (modus-ponens tm-50 tm-691 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Em Dm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56203.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E or D))), M:tm-50, m:tm-691, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Em Dm))))
================================================================
tm-name          tm-56204
in-theory        56204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E or D)))
theorem-size     25
proof            (modus-ponens tm-49 tm-691 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Em Dm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-1 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56204.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E or D))), M:tm-49, m:tm-691, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> Dm (or Em Dm))))
================================================================
tm-name          tm-56205
in-theory        56205
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (E -> (F or E)))
theorem-size     35
proof            (modus-ponens tm-47 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56205.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> (E -> (F or E))), M:tm-47, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-56206
in-theory        56206
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> (F or E)))
theorem-size     35
proof            (modus-ponens tm-46 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-7)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56206.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> (F or E))), M:tm-46, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-56207
in-theory        56207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-42 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56207.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F)))), M:tm-42, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56208
in-theory        56208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-32 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56208.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F)))), M:tm-32, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56209
in-theory        56209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (E or D))))
theorem-size     33
proof            (modus-ponens tm-24 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56209.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and (D -> (E or D)))), M:tm-24, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-56210
in-theory        56210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-23 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56210.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F)))), M:tm-23, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56211
in-theory        56211
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-22 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56211.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F)))), M:tm-22, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56212
in-theory        56212
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-21 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56212.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F)))), M:tm-21, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56213
in-theory        56213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     33
proof            (modus-ponens tm-20 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-7)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56213.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-20, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56214
in-theory        56214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-19 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56214.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> (F -> (G or F)))), M:tm-19, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56215
in-theory        56215
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E or D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     35
proof            (modus-ponens tm-9 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-9 tm-8 tm-2 tm-1 tm-7)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56215.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E or D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-56216
in-theory        56216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> ((((D -> (E -> F)) or ((D -> E) -> (D -> F))) or (A -> (B or A))) -> C))
theorem-size     29
proof            (modus-ponens tm-8 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56216.        (((A -> (B or A)) -> C) -> ((((D -> (E -> F)) or ((D -> E) -> (D -> F))) or (A -> (B or A))) -> C)), M:tm-8, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-56217
in-theory        56217
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-7 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-7 tm-8 tm-2 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56217.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F or E)))), M:tm-7, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56218
in-theory        56218
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-6 tm-8 tm-2 tm-1 tm-7)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56218.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) or F), M:tm-6, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56219
in-theory        56219
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F or E))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56219.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F or E))) and A)), M:tm-5, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56220
in-theory        56220
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E or D)))
theorem-size     33
proof            (modus-ponens tm-2 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (or Em Dm))))
axioms-used      (tm-2 tm-8 tm-1 tm-7)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56220.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E or D))), M:tm-2, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (C (or Em Dm)))
================================================================
tm-name          tm-56221
in-theory        56221
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-1 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-1 tm-8 tm-2 tm-7)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-56221.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (F or E)))), M:tm-1, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-56222
in-theory        56222
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (B -> (B -> A)))
theorem-size     11
proof            (modus-ponens tm-692 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-56222.        ((A or (B -> A)) -> (B -> (B -> A))), M:tm-692, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-56223
in-theory        56223
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (B -> ((B -> A) and B)))
theorem-size     13
proof            (modus-ponens tm-692 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-5)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-56223.        ((A or (B -> A)) -> (B -> ((B -> A) and B))), M:tm-692, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-56224
in-theory        56224
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A -> B) -> A)) -> ((A -> B) -> (((A -> B) or A) -> B)))
theorem-size     19
proof            (modus-ponens tm-692 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-56224.        ((A or ((A -> B) -> A)) -> ((A -> B) -> (((A -> B) or A) -> B))), M:tm-692, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-56225
in-theory        56225
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (B -> (C -> B)))
theorem-size     11
proof            (modus-ponens tm-692 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-7.            (A -> (B or A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-56225.        ((A or (B -> A)) -> (B -> (C -> B))), M:tm-692, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-56226
in-theory        56226
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> A)) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))
theorem-size     23
proof            (modus-ponens tm-692 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-7.            (A -> (B or A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-56226.        ((A or ((B -> (C -> D)) -> A)) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-692, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-56227
in-theory        56227
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> A)) -> ((B and C) -> B))
theorem-size     13
proof            (modus-ponens tm-692 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-56227.        ((A or ((B and C) -> A)) -> ((B and C) -> B)), M:tm-692, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-56228
in-theory        56228
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> A)) -> ((B and C) -> C))
theorem-size     13
proof            (modus-ponens tm-692 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-56228.        ((A or ((B and C) -> A)) -> ((B and C) -> C)), M:tm-692, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-56229
in-theory        56229
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (B -> (C -> (B and C))))
theorem-size     13
proof            (modus-ponens tm-692 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-5)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-56229.        ((A or (B -> A)) -> (B -> (C -> (B and C)))), M:tm-692, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-56230
in-theory        56230
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (B -> (B or C)))
theorem-size     11
proof            (modus-ponens tm-692 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-56230.        ((A or (B -> A)) -> (B -> (B or C))), M:tm-692, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-56231
in-theory        56231
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (B -> (C or B)))
theorem-size     11
proof            (modus-ponens tm-692 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-56231.        ((A or (B -> A)) -> (B -> (C or B))), M:tm-692, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-56232
in-theory        56232
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-665 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56232.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-665, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56233
in-theory        56233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((B or (A -> B)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-623 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56233.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((B or (A -> B)) -> (A -> C)))), M:tm-623, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56234
in-theory        56234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-622 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56234.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-622, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56235
in-theory        56235
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (D -> (E or D)))
theorem-size     29
proof            (modus-ponens tm-609 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56235.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (D -> (E or D))), M:tm-609, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56236
in-theory        56236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-605 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56236.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-605, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56237
in-theory        56237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((D -> (E or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-595 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56237.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((D -> (E or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))))), M:tm-595, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56238
in-theory        56238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-550 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56238.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-550, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56239
in-theory        56239
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-540 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56239.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-540, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56240
in-theory        56240
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-530 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56240.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-530, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56241
in-theory        56241
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-520 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56241.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-520, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56242
in-theory        56242
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-510 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56242.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-510, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56243
in-theory        56243
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-500 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56243.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-500, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56244
in-theory        56244
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-490 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56244.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G)))), M:tm-490, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56245
in-theory        56245
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-480 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56245.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-480, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56246
in-theory        56246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((B or (A -> B)) -> (A -> C)) or D))
theorem-size     25
proof            (modus-ponens tm-470 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56246.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((B or (A -> B)) -> (A -> C)) or D)), M:tm-470, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56247
in-theory        56247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-469 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56247.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-469, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56248
in-theory        56248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (D -> (D or E)))
theorem-size     29
proof            (modus-ponens tm-456 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56248.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (D -> (D or E))), M:tm-456, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56249
in-theory        56249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-453 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56249.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-453, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56250
in-theory        56250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((D -> (D or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-443 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56250.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((D -> (D or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))))), M:tm-443, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56251
in-theory        56251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-409 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56251.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-409, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56252
in-theory        56252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-400 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56252.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-400, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56253
in-theory        56253
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-391 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56253.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-391, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56254
in-theory        56254
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-382 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56254.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-382, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56255
in-theory        56255
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-373 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56255.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G)))), M:tm-373, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56256
in-theory        56256
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-364 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56256.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-364, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56257
in-theory        56257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((B or (A -> B)) -> (A -> C)) and D)))
theorem-size     27
proof            (modus-ponens tm-355 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56257.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((B or (A -> B)) -> (A -> C)) and D))), M:tm-355, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56258
in-theory        56258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-354 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56258.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-354, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56259
in-theory        56259
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (D -> (E -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-341 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56259.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56260
in-theory        56260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-338 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56260.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E)))), M:tm-338, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56261
in-theory        56261
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((B or (A -> B)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-328 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       237
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56261.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((B or (A -> B)) -> (A -> C))))), M:tm-328, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56262
in-theory        56262
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C)))))
theorem-size     55
proof            (modus-ponens tm-327 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56262.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((D -> (E -> (D and E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))))), M:tm-327, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56263
in-theory        56263
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((D and E) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-326 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56263.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((D and E) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))))), M:tm-326, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56264
in-theory        56264
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((D and E) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-325 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56264.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((D and E) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))))), M:tm-325, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56265
in-theory        56265
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-324 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       251
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56265.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))))), M:tm-324, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56266
in-theory        56266
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((D -> (E -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-323 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56266.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((D -> (E -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))))), M:tm-323, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56267
in-theory        56267
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((D and E) -> E))
theorem-size     29
proof            (modus-ponens tm-322 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56267.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((D and E) -> E)), M:tm-322, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56268
in-theory        56268
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((D and E) -> D))
theorem-size     29
proof            (modus-ponens tm-320 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56268.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((D and E) -> D)), M:tm-320, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56269
in-theory        56269
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-318 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56269.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56270
in-theory        56270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     51
proof            (modus-ponens tm-316 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       221
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56270.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56271
in-theory        56271
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (D -> (E -> D)))
theorem-size     29
proof            (modus-ponens tm-315 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56271.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (D -> (E -> D))), M:tm-315, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56272
in-theory        56272
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((B or (A -> B)) -> (A -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     63
proof            (modus-ponens tm-313 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56272.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((B or (A -> B)) -> (A -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56273
in-theory        56273
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((((B or (A -> B)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((B or (A -> B)) -> (A -> C))) -> D)))
theorem-size     61
proof            (modus-ponens tm-312 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56273.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((((B or (A -> B)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((B or (A -> B)) -> (A -> C))) -> D))), M:tm-312, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56274
in-theory        56274
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (D or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-311 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56274.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (D or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))))), M:tm-311, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56275
in-theory        56275
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) or D))
theorem-size     49
proof            (modus-ponens tm-310 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56275.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) or D)), M:tm-310, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56276
in-theory        56276
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (D -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and D)))
theorem-size     51
proof            (modus-ponens tm-309 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56276.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (D -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and D))), M:tm-309, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56277
in-theory        56277
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (B or (A -> B))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> C))))
theorem-size     61
proof            (modus-ponens tm-306 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Bm (-> Am Bm))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56277.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (B or (A -> B))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> C)))), M:tm-306, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Bm (-> Am Bm))) (C (-> Am Cm)))
================================================================
tm-name          tm-56278
in-theory        56278
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-305 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56278.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))))), M:tm-305, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56279
in-theory        56279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-303 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56279.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-303, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56280
in-theory        56280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-270 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56280.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-270, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56281
in-theory        56281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-239 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56281.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-239, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56282
in-theory        56282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-210 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56282.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G)))), M:tm-210, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56283
in-theory        56283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-183 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56283.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-183, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56284
in-theory        56284
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-157 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56284.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-157, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56285
in-theory        56285
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-147 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56285.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-147, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56286
in-theory        56286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-134 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56286.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-134, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56287
in-theory        56287
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-125 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56287.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-125, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56288
in-theory        56288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((B or (A -> B)) -> A) -> ((B or (A -> B)) -> C)))
theorem-size     29
proof            (modus-ponens tm-114 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Bm (-> Am Bm))) (C Am) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56288.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((B or (A -> B)) -> A) -> ((B or (A -> B)) -> C))), M:tm-114, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Bm (-> Am Bm))) (C Am) (D Cm))
================================================================
tm-name          tm-56289
in-theory        56289
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-113 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56289.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G)))), M:tm-113, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56290
in-theory        56290
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-105 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56290.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-105, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56291
in-theory        56291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E))))
theorem-size     31
proof            (modus-ponens tm-95 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56291.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E)))), M:tm-95, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56292
in-theory        56292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((B or (A -> B)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-84 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56292.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((B or (A -> B)) -> (A -> C)))), M:tm-84, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56293
in-theory        56293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-83 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56293.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-83, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56294
in-theory        56294
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((C or (B -> C)) -> (B -> D))))
theorem-size     29
proof            (modus-ponens tm-76 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56294.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((C or (B -> C)) -> (B -> D)))), M:tm-76, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56295
in-theory        56295
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((B or (A -> B)) -> (A -> C)))
theorem-size     39
proof            (modus-ponens tm-73 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56295.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((B or (A -> B)) -> (A -> C))), M:tm-73, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56296
in-theory        56296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-69 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56296.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E)))), M:tm-69, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56297
in-theory        56297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-54 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56297.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-54, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56298
in-theory        56298
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((B or (A -> B)) -> (A -> C)))
theorem-size     31
proof            (modus-ponens tm-50 tm-692 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56298.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((B or (A -> B)) -> (A -> C))), M:tm-50, m:tm-692, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56299
in-theory        56299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((B or (A -> B)) -> (A -> C)))
theorem-size     29
proof            (modus-ponens tm-49 tm-692 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56299.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((B or (A -> B)) -> (A -> C))), M:tm-49, m:tm-692, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56300
in-theory        56300
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((C or (B -> C)) -> (B -> D)))
theorem-size     39
proof            (modus-ponens tm-47 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56300.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((C or (B -> C)) -> (B -> D))), M:tm-47, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56301
in-theory        56301
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((B or (A -> B)) -> (A -> C)))
theorem-size     39
proof            (modus-ponens tm-46 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56301.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((B or (A -> B)) -> (A -> C))), M:tm-46, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56302
in-theory        56302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-42 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56302.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E)))), M:tm-42, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56303
in-theory        56303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-32 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56303.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E)))), M:tm-32, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56304
in-theory        56304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((B or (A -> B)) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-24 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56304.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((B or (A -> B)) -> (A -> C)))), M:tm-24, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56305
in-theory        56305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E))))
theorem-size     31
proof            (modus-ponens tm-23 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56305.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E)))), M:tm-23, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56306
in-theory        56306
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-22 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56306.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E)))), M:tm-22, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56307
in-theory        56307
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-21 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56307.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E)))), M:tm-21, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56308
in-theory        56308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-20 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56308.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-20, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56309
in-theory        56309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-19 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56309.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((D or (C -> D)) -> (C -> E)))), M:tm-19, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56310
in-theory        56310
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((B or (A -> B)) -> (A -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     39
proof            (modus-ponens tm-9 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-9 tm-8 tm-2 tm-1)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56310.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((B or (A -> B)) -> (A -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56311
in-theory        56311
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> (B -> C)) -> D) -> ((((B -> (A -> C)) or ((B -> A) -> (B -> C))) or ((A or (B -> A)) -> (B -> C))) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56311.        ((((A or (B -> A)) -> (B -> C)) -> D) -> ((((B -> (A -> C)) or ((B -> A) -> (B -> C))) or ((A or (B -> A)) -> (B -> C))) -> D)), M:tm-8, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-56312
in-theory        56312
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((C or (B -> C)) -> (B -> D))))
theorem-size     25
proof            (modus-ponens tm-7 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-7 tm-8 tm-2 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56312.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((C or (B -> C)) -> (B -> D)))), M:tm-7, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56313
in-theory        56313
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) or D)
theorem-size     25
proof            (modus-ponens tm-6 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-6 tm-8 tm-2 tm-1)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56313.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) or D), M:tm-6, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56314
in-theory        56314
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((C or (B -> C)) -> (B -> D))) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56314.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((C or (B -> C)) -> (B -> D))) and A)), M:tm-5, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56315
in-theory        56315
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (B or (A -> B))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> C)))
theorem-size     37
proof            (modus-ponens tm-2 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Bm (-> Am Bm))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56315.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (B or (A -> B))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> C))), M:tm-2, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Bm (-> Am Bm))) (C (-> Am Cm)))
================================================================
tm-name          tm-56316
in-theory        56316
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((C or (B -> C)) -> (B -> D))))
theorem-size     25
proof            (modus-ponens tm-1 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-56316.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((C or (B -> C)) -> (B -> D)))), M:tm-1, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-56317
in-theory        56317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-693 tm-34 ((Am (-> (-> A B) (-> (-> A C) (-> (-> A B) (-> A C))))) (Bm (-> (-> A B) (-> A C))) (Cm (-> A B)) (D (-> (-> A B) (-> A C)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-56317.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) -> (A -> C)))), M:tm-693, m:tm-34, u:((Am (-> (-> A B) (-> (-> A C) (-> (-> A B) (-> A C))))) (Bm (-> (-> A B) (-> A C))) (Cm (-> A B)) (D (-> (-> A B) (-> A C))))
================================================================
tm-name          tm-56318
in-theory        56318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (((A -> B) -> (A -> C)) and (A -> B))))
theorem-size     29
proof            (modus-ponens tm-693 tm-38 ((Am (-> (-> A B) (-> (-> A C) (and (-> (-> A B) (-> A C)) (-> A B))))) (Bm (-> (-> A B) (-> A C))) (Cm (-> A B)) (D (and (-> (-> A B) (-> A C)) (-> A B)))))
axioms-used      (tm-8 tm-2 tm-7 tm-5)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-56318.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (((A -> B) -> (A -> C)) and (A -> B)))), M:tm-693, m:tm-38, u:((Am (-> (-> A B) (-> (-> A C) (and (-> (-> A B) (-> A C)) (-> A B))))) (Bm (-> (-> A B) (-> A C))) (Cm (-> A B)) (D (and (-> (-> A B) (-> A C)) (-> A B))))
================================================================
tm-name          tm-56319
in-theory        56319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D -> (A -> B))))
theorem-size     23
proof            (modus-ponens tm-693 tm-81 ((Am (-> (-> A B) (-> (-> A C) (-> Dm (-> A B))))) (Bm (-> (-> A B) (-> A C))) (Cm (-> A B)) (D (-> Dm (-> A B)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-56319.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D -> (A -> B)))), M:tm-693, m:tm-81, u:((Am (-> (-> A B) (-> (-> A C) (-> Dm (-> A B))))) (Bm (-> (-> A B) (-> A C))) (Cm (-> A B)) (D (-> Dm (-> A B))))
================================================================
tm-name          tm-56320
in-theory        56320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> C) -> D)) or ((A -> (B -> C)) -> (A -> D))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-693 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> (-> Cm C) (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) (-> Cm C))) (A Cm) (B (-> Dm Em)) (D (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-56320.        (((A -> ((B -> C) -> D)) or ((A -> (B -> C)) -> (A -> D))) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-693, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> (-> Cm C) (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) (-> Cm C))) (A Cm) (B (-> Dm Em)) (D (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-56321
in-theory        56321
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D -> ((A -> B) and D))))
theorem-size     25
proof            (modus-ponens tm-693 tm-352 ((Am (-> (-> A B) (-> (-> A C) (-> Dm (and (-> A B) Dm))))) (Bm (-> (-> A B) (-> A C))) (Cm (-> A B)) (D (-> Dm (and (-> A B) Dm)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-5)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-56321.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D -> ((A -> B) and D)))), M:tm-693, m:tm-352, u:((Am (-> (-> A B) (-> (-> A C) (-> Dm (and (-> A B) Dm))))) (Bm (-> (-> A B) (-> A C))) (Cm (-> A B)) (D (-> Dm (and (-> A B) Dm))))
================================================================
tm-name          tm-56322
in-theory        56322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) or D)))
theorem-size     23
proof            (modus-ponens tm-693 tm-467 ((Am (-> (-> A B) (-> (-> A C) (or (-> A B) Dm)))) (Bm (-> (-> A B) (-> A C))) (Cm (-> A B)) (D (or (-> A B) Dm))))
axioms-used      (tm-8 tm-2 tm-7 tm-1 tm-6)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-56322.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) or D))), M:tm-693, m:tm-467, u:((Am (-> (-> A B) (-> (-> A C) (or (-> A B) Dm)))) (Bm (-> (-> A B) (-> A C))) (Cm (-> A B)) (D (or (-> A B) Dm)))
================================================================
tm-name          tm-56323
in-theory        56323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D or (A -> B))))
theorem-size     23
proof            (modus-ponens tm-693 tm-620 ((Am (-> (-> A B) (-> (-> A C) (or Dm (-> A B))))) (Bm (-> (-> A B) (-> A C))) (Cm (-> A B)) (D (or Dm (-> A B)))))
axioms-used      (tm-8 tm-2 tm-7 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-56323.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D or (A -> B)))), M:tm-693, m:tm-620, u:((Am (-> (-> A B) (-> (-> A C) (or Dm (-> A B))))) (Bm (-> (-> A B) (-> A C))) (Cm (-> A B)) (D (or Dm (-> A B))))
================================================================
tm-name          tm-56324
in-theory        56324
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     57
proof            (modus-ponens tm-665 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       257
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56324.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-665, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56325
in-theory        56325
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))
theorem-size     45
proof            (modus-ponens tm-623 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56325.        ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))), M:tm-623, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56326
in-theory        56326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-622 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56326.        ((A -> (B -> (C or B))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-622, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56327
in-theory        56327
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (E -> (F or E)))
theorem-size     49
proof            (modus-ponens tm-609 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       249
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56327.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (E -> (F or E))), M:tm-609, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56328
in-theory        56328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     53
proof            (modus-ponens tm-605 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56328.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-605, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56329
in-theory        56329
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((E -> (F or E)) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))))
theorem-size     93
proof            (modus-ponens tm-595 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       299
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56329.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((E -> (F or E)) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))), M:tm-595, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56330
in-theory        56330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-550 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56330.        (((A -> (B or A)) or C) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-550, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56331
in-theory        56331
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-540 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56331.        ((A or (B -> (C or B))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-540, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56332
in-theory        56332
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-530 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56332.        ((A or (B -> (B or C))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-530, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56333
in-theory        56333
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     53
proof            (modus-ponens tm-520 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56333.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-520, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56334
in-theory        56334
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-510 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56334.        ((A or ((B and C) -> C)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-510, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56335
in-theory        56335
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-500 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56335.        ((A or ((B and C) -> B)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-500, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56336
in-theory        56336
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((E -> G) -> H)) or (((E -> F) -> (E -> G)) -> ((E -> F) -> H))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> H))))
theorem-size     59
proof            (modus-ponens tm-490 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56336.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((E -> G) -> H)) or (((E -> F) -> (E -> G)) -> ((E -> F) -> H))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> H)))), M:tm-490, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56337
in-theory        56337
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-480 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56337.        ((A or (B -> (C -> B))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-480, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56338
in-theory        56338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)) or E))
theorem-size     45
proof            (modus-ponens tm-470 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56338.        ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)) or E)), M:tm-470, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56339
in-theory        56339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-469 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56339.        ((A -> (B -> (B or C))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-469, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56340
in-theory        56340
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (E -> (E or F)))
theorem-size     49
proof            (modus-ponens tm-456 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       249
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56340.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (E -> (E or F))), M:tm-456, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56341
in-theory        56341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     53
proof            (modus-ponens tm-453 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56341.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-453, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56342
in-theory        56342
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((E -> (E or F)) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))))
theorem-size     93
proof            (modus-ponens tm-443 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       299
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56342.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((E -> (E or F)) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))), M:tm-443, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56343
in-theory        56343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-409 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56343.        (((A -> (A or B)) or C) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-409, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56344
in-theory        56344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     53
proof            (modus-ponens tm-400 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56344.        (((A -> (B -> (A and B))) or C) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-400, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56345
in-theory        56345
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-391 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56345.        ((((A and B) -> B) or C) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-391, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56346
in-theory        56346
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-382 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56346.        ((((A and B) -> A) or C) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-382, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56347
in-theory        56347
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> ((E -> G) -> H)) or (((E -> F) -> (E -> G)) -> ((E -> F) -> H))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> H))))
theorem-size     59
proof            (modus-ponens tm-373 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56347.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> ((E -> G) -> H)) or (((E -> F) -> (E -> G)) -> ((E -> F) -> H))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> H)))), M:tm-373, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56348
in-theory        56348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-364 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56348.        (((A -> (B -> A)) or C) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-364, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56349
in-theory        56349
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)) and E)))
theorem-size     47
proof            (modus-ponens tm-355 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56349.        ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)) and E))), M:tm-355, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56350
in-theory        56350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     53
proof            (modus-ponens tm-354 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56350.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-354, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56351
in-theory        56351
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (E -> (F -> (E and F))))
theorem-size     51
proof            (modus-ponens tm-341 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       257
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56351.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56352
in-theory        56352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F))))
theorem-size     53
proof            (modus-ponens tm-338 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56352.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F)))), M:tm-338, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56353
in-theory        56353
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))))
theorem-size     111
proof            (modus-ponens tm-328 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       327
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56353.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))), M:tm-328, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56354
in-theory        56354
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((E -> (F -> (E and F))) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))))
theorem-size     95
proof            (modus-ponens tm-327 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       307
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56354.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((E -> (F -> (E and F))) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))), M:tm-327, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56355
in-theory        56355
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (((E and F) -> F) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))))
theorem-size     93
proof            (modus-ponens tm-326 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       299
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56355.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (((E and F) -> F) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))), M:tm-326, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56356
in-theory        56356
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (((E and F) -> E) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))))
theorem-size     93
proof            (modus-ponens tm-325 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       299
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56356.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (((E and F) -> E) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))), M:tm-325, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56357
in-theory        56357
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))))
theorem-size     101
proof            (modus-ponens tm-324 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       331
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56357.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))), M:tm-324, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56358
in-theory        56358
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((E -> (F -> E)) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))))
theorem-size     93
proof            (modus-ponens tm-323 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       299
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56358.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((E -> (F -> E)) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))), M:tm-323, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56359
in-theory        56359
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((E and F) -> F))
theorem-size     49
proof            (modus-ponens tm-322 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       249
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56359.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56360
in-theory        56360
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((E and F) -> E))
theorem-size     49
proof            (modus-ponens tm-320 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       249
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56360.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56361
in-theory        56361
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     57
proof            (modus-ponens tm-318 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       281
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56361.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56362
in-theory        56362
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))))
theorem-size     91
proof            (modus-ponens tm-316 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       301
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56362.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))))), M:tm-316, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56363
in-theory        56363
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (E -> (F -> E)))
theorem-size     49
proof            (modus-ponens tm-315 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       249
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56363.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56364
in-theory        56364
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))) -> (not (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))))))
theorem-size     113
proof            (modus-ponens tm-313 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       313
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56364.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))) -> (not (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))))), M:tm-313, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56365
in-theory        56365
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)) -> E) -> (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) -> E)))
theorem-size     111
proof            (modus-ponens tm-312 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       315
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56365.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)) -> E) -> (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) -> E))), M:tm-312, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56366
in-theory        56366
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (E or ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))))
theorem-size     89
proof            (modus-ponens tm-311 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       275
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56366.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (E or ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))), M:tm-311, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56367
in-theory        56367
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) or E))
theorem-size     89
proof            (modus-ponens tm-310 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       275
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56367.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) or E)), M:tm-310, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56368
in-theory        56368
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (E -> (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and E)))
theorem-size     91
proof            (modus-ponens tm-309 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       281
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56368.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (E -> (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and E))), M:tm-309, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56369
in-theory        56369
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((A -> B) -> D))))
theorem-size     111
proof            (modus-ponens tm-306 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (-> (-> Am Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       317
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56369.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((A -> B) -> D)))), M:tm-306, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (-> (-> Am Bm) Dm)))
================================================================
tm-name          tm-56370
in-theory        56370
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (E -> ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))))
theorem-size     89
proof            (modus-ponens tm-305 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       275
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56370.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and (E -> ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))), M:tm-305, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56371
in-theory        56371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-303 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56371.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-303, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56372
in-theory        56372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     53
proof            (modus-ponens tm-270 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56372.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-270, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56373
in-theory        56373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     53
proof            (modus-ponens tm-239 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56373.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-239, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56374
in-theory        56374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> ((E -> G) -> H)) or (((E -> F) -> (E -> G)) -> ((E -> F) -> H))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> H))))
theorem-size     61
proof            (modus-ponens tm-210 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       271
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56374.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> ((E -> G) -> H)) or (((E -> F) -> (E -> G)) -> ((E -> F) -> H))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> H)))), M:tm-210, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56375
in-theory        56375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     53
proof            (modus-ponens tm-183 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56375.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-183, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56376
in-theory        56376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-157 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56376.        ((A -> ((B and C) -> C)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-157, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56377
in-theory        56377
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     59
proof            (modus-ponens tm-147 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56377.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-147, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56378
in-theory        56378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-134 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56378.        ((A -> ((B and C) -> B)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-134, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56379
in-theory        56379
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     59
proof            (modus-ponens tm-125 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56379.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-125, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56380
in-theory        56380
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> B)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     57
proof            (modus-ponens tm-114 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (-> Am Bm)) (D Dm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       265
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56380.        ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> B)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-114, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (-> Am Bm)) (D Dm))
================================================================
tm-name          tm-56381
in-theory        56381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((E -> G) -> H)) or (((E -> F) -> (E -> G)) -> ((E -> F) -> H))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> H))))
theorem-size     59
proof            (modus-ponens tm-113 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56381.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> ((E -> G) -> H)) or (((E -> F) -> (E -> G)) -> ((E -> F) -> H))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> H)))), M:tm-113, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56382
in-theory        56382
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     63
proof            (modus-ponens tm-105 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       283
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56382.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-105, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56383
in-theory        56383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F))))
theorem-size     51
proof            (modus-ponens tm-95 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56383.        (((A -> B) -> (A -> A)) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F)))), M:tm-95, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56384
in-theory        56384
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))
theorem-size     45
proof            (modus-ponens tm-84 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56384.        ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))), M:tm-84, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56385
in-theory        56385
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     51
proof            (modus-ponens tm-83 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56385.        ((A -> (B -> (C -> B))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-83, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56386
in-theory        56386
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) -> ((B -> D) -> E)) or (((B -> C) -> (B -> D)) -> ((B -> C) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> E))))
theorem-size     49
proof            (modus-ponens tm-76 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56386.        (((not (not A)) -> A) and ((((B -> C) -> ((B -> D) -> E)) or (((B -> C) -> (B -> D)) -> ((B -> C) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> E)))), M:tm-76, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56387
in-theory        56387
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))))) or (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))
theorem-size     69
proof            (modus-ponens tm-73 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       243
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56387.        (((not (not (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))))) or (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-73, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56388
in-theory        56388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F))))
theorem-size     55
proof            (modus-ponens tm-69 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       233
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56388.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F)))), M:tm-69, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56389
in-theory        56389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     57
proof            (modus-ponens tm-54 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       239
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56389.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-54, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56390
in-theory        56390
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) or (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))
theorem-size     57
proof            (modus-ponens tm-50 tm-693 ((A (-> (-> Am Bm) (-> (-> Am Cm) Dm))) (B (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-8 tm-7 tm-2)
proof-size       233
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56390.        (((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) or (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-50, m:tm-693, u:((A (-> (-> Am Bm) (-> (-> Am Cm) Dm))) (B (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56391
in-theory        56391
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))
theorem-size     53
proof            (modus-ponens tm-49 tm-693 ((A (-> (-> Am Bm) (-> (-> Am Cm) Dm))) (B (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-8 tm-6 tm-2)
proof-size       229
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56391.        ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-49, m:tm-693, u:((A (-> (-> Am Bm) (-> (-> Am Cm) Dm))) (B (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56392
in-theory        56392
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> ((B -> D) -> E)) or (((B -> C) -> (B -> D)) -> ((B -> C) -> E)))) or (((B -> C) -> ((B -> D) -> E)) or (((B -> C) -> (B -> D)) -> ((B -> C) -> E)))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> E)))
theorem-size     69
proof            (modus-ponens tm-47 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       243
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56392.        (((A and (((B -> C) -> ((B -> D) -> E)) or (((B -> C) -> (B -> D)) -> ((B -> C) -> E)))) or (((B -> C) -> ((B -> D) -> E)) or (((B -> C) -> (B -> D)) -> ((B -> C) -> E)))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> E))), M:tm-47, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56393
in-theory        56393
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) and E) or (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))
theorem-size     69
proof            (modus-ponens tm-46 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       243
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56393.        ((((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) and E) or (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-46, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56394
in-theory        56394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F))))
theorem-size     49
proof            (modus-ponens tm-42 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56394.        ((A -> (B or A)) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F)))), M:tm-42, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56395
in-theory        56395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F))))
theorem-size     49
proof            (modus-ponens tm-32 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56395.        ((A -> (A or B)) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F)))), M:tm-32, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56396
in-theory        56396
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))
theorem-size     67
proof            (modus-ponens tm-24 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       241
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56396.        ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))), M:tm-24, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56397
in-theory        56397
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F))))
theorem-size     51
proof            (modus-ponens tm-23 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       221
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56397.        ((A -> (B -> (A and B))) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F)))), M:tm-23, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56398
in-theory        56398
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F))))
theorem-size     49
proof            (modus-ponens tm-22 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56398.        (((A and B) -> B) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F)))), M:tm-22, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56399
in-theory        56399
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F))))
theorem-size     49
proof            (modus-ponens tm-21 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56399.        (((A and B) -> A) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F)))), M:tm-21, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56400
in-theory        56400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     57
proof            (modus-ponens tm-20 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       239
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56400.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-20, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56401
in-theory        56401
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F))))
theorem-size     49
proof            (modus-ponens tm-19 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56401.        ((A -> (B -> A)) and ((((C -> D) -> ((C -> E) -> F)) or (((C -> D) -> (C -> E)) -> ((C -> D) -> F))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((C -> D) -> F)))), M:tm-19, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56402
in-theory        56402
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))))
theorem-size     47
proof            (modus-ponens tm-12 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56402.        ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))), M:tm-12, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56403
in-theory        56403
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))) -> (not (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))))
theorem-size     69
proof            (modus-ponens tm-9 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-9 tm-8 tm-2)
proof-size       225
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56403.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))) -> (not (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))))), M:tm-9, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56404
in-theory        56404
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)) -> E) -> (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) -> E))
theorem-size     67
proof            (modus-ponens tm-8 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-8 tm-2)
proof-size       225
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56404.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)) -> E) -> (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) -> E)), M:tm-8, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-56405
in-theory        56405
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) -> ((B -> D) -> E)) or (((B -> C) -> (B -> D)) -> ((B -> C) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> E))))
theorem-size     45
proof            (modus-ponens tm-7 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-7 tm-8 tm-2)
proof-size       195
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56405.        (A or ((((B -> C) -> ((B -> D) -> E)) or (((B -> C) -> (B -> D)) -> ((B -> C) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> E)))), M:tm-7, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56406
in-theory        56406
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) or E)
theorem-size     45
proof            (modus-ponens tm-6 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-6 tm-8 tm-2)
proof-size       195
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56406.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) or E), M:tm-6, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56407
in-theory        56407
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> ((B -> D) -> E)) or (((B -> C) -> (B -> D)) -> ((B -> C) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> E))) and A))
theorem-size     47
proof            (modus-ponens tm-5 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       199
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56407.        (A -> (((((B -> C) -> ((B -> D) -> E)) or (((B -> C) -> (B -> D)) -> ((B -> C) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> E))) and A)), M:tm-5, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56408
in-theory        56408
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((A -> B) -> D)))
theorem-size     67
proof            (modus-ponens tm-2 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (-> (-> Am Bm) Dm))))
axioms-used      (tm-2 tm-8)
proof-size       225
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56408.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((A -> B) -> D))), M:tm-2, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (-> (-> Am Bm) Dm)))
================================================================
tm-name          tm-56409
in-theory        56409
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((B -> D) -> E)) or (((B -> C) -> (B -> D)) -> ((B -> C) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> E))))
theorem-size     45
proof            (modus-ponens tm-1 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       195
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-56409.        (A -> ((((B -> C) -> ((B -> D) -> E)) or (((B -> C) -> (B -> D)) -> ((B -> C) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((B -> C) -> E)))), M:tm-1, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-56410
in-theory        56410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     41
proof            (modus-ponens tm-665 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56410.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-665, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56411
in-theory        56411
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> A)) -> (E or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))
theorem-size     29
proof            (modus-ponens tm-623 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56411.        ((A or (((B -> C) -> (B -> D)) -> A)) -> (E or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))), M:tm-623, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56412
in-theory        56412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-622 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56412.        ((A -> (B -> (C or B))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-622, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56413
in-theory        56413
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (E -> (F or E)))
theorem-size     33
proof            (modus-ponens tm-609 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56413.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (E -> (F or E))), M:tm-609, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56414
in-theory        56414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     37
proof            (modus-ponens tm-605 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56414.        ((A -> ((B -> (C or B)) and A)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-605, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56415
in-theory        56415
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((E -> (F or E)) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))))
theorem-size     61
proof            (modus-ponens tm-595 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56415.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((E -> (F or E)) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))), M:tm-595, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56416
in-theory        56416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-550 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56416.        (((A -> (B or A)) or C) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-550, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56417
in-theory        56417
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-540 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56417.        ((A or (B -> (C or B))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-540, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56418
in-theory        56418
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-530 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56418.        ((A or (B -> (B or C))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-530, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56419
in-theory        56419
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     37
proof            (modus-ponens tm-520 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56419.        ((A or (B -> (C -> (B and C)))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-520, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56420
in-theory        56420
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-510 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56420.        ((A or ((B and C) -> C)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-510, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56421
in-theory        56421
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-500 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56421.        ((A or ((B and C) -> B)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-500, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56422
in-theory        56422
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> (F -> H)) -> E)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> E)))
theorem-size     43
proof            (modus-ponens tm-490 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56422.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> (F -> H)) -> E)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> E))), M:tm-490, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56423
in-theory        56423
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-480 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56423.        ((A or (B -> (C -> B))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-480, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56424
in-theory        56424
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> A)) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A) or E))
theorem-size     29
proof            (modus-ponens tm-470 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56424.        ((A or (((B -> C) -> (B -> D)) -> A)) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A) or E)), M:tm-470, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56425
in-theory        56425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-469 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56425.        ((A -> (B -> (B or C))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-469, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56426
in-theory        56426
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (E -> (E or F)))
theorem-size     33
proof            (modus-ponens tm-456 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56426.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (E -> (E or F))), M:tm-456, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56427
in-theory        56427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     37
proof            (modus-ponens tm-453 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56427.        ((A -> ((B -> (B or C)) and A)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-453, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56428
in-theory        56428
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((E -> (E or F)) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))))
theorem-size     61
proof            (modus-ponens tm-443 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56428.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((E -> (E or F)) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))), M:tm-443, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56429
in-theory        56429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-409 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56429.        (((A -> (A or B)) or C) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-409, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56430
in-theory        56430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     37
proof            (modus-ponens tm-400 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56430.        (((A -> (B -> (A and B))) or C) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-400, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56431
in-theory        56431
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-391 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56431.        ((((A and B) -> B) or C) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-391, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56432
in-theory        56432
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-382 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56432.        ((((A and B) -> A) or C) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-382, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56433
in-theory        56433
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (((F -> G) -> (F -> H)) -> E)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> E)))
theorem-size     43
proof            (modus-ponens tm-373 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56433.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (((F -> G) -> (F -> H)) -> E)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> E))), M:tm-373, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56434
in-theory        56434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-364 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56434.        (((A -> (B -> A)) or C) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-364, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56435
in-theory        56435
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> A)) -> (E -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A) and E)))
theorem-size     31
proof            (modus-ponens tm-355 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56435.        ((A or (((B -> C) -> (B -> D)) -> A)) -> (E -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A) and E))), M:tm-355, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56436
in-theory        56436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     37
proof            (modus-ponens tm-354 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56436.        ((A -> (B -> (C -> (B and C)))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-354, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56437
in-theory        56437
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (E -> (F -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-341 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56437.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56438
in-theory        56438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C)))
theorem-size     37
proof            (modus-ponens tm-338 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56438.        (((A -> B) -> (A -> (A and B))) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C))), M:tm-338, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56439
in-theory        56439
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((A or (((B -> C) -> (B -> D)) -> A)) -> ((A or (((B -> C) -> (B -> D)) -> A)) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))))
theorem-size     67
proof            (modus-ponens tm-328 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       247
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56439.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((A or (((B -> C) -> (B -> D)) -> A)) -> ((A or (((B -> C) -> (B -> D)) -> A)) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))), M:tm-328, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56440
in-theory        56440
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((E -> (F -> (E and F))) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))))
theorem-size     63
proof            (modus-ponens tm-327 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       239
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56440.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((E -> (F -> (E and F))) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))), M:tm-327, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56441
in-theory        56441
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((E and F) -> F) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))))
theorem-size     61
proof            (modus-ponens tm-326 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56441.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((E and F) -> F) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))), M:tm-326, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56442
in-theory        56442
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((E and F) -> E) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))))
theorem-size     61
proof            (modus-ponens tm-325 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56442.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((E and F) -> E) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))), M:tm-325, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56443
in-theory        56443
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))))
theorem-size     69
proof            (modus-ponens tm-324 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       263
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56443.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))), M:tm-324, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56444
in-theory        56444
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((E -> (F -> E)) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))))
theorem-size     61
proof            (modus-ponens tm-323 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56444.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((E -> (F -> E)) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))), M:tm-323, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56445
in-theory        56445
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((E and F) -> F))
theorem-size     33
proof            (modus-ponens tm-322 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56445.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((E and F) -> F)), M:tm-322, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56446
in-theory        56446
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((E and F) -> E))
theorem-size     33
proof            (modus-ponens tm-320 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56446.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((E and F) -> E)), M:tm-320, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56447
in-theory        56447
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-318 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56447.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56448
in-theory        56448
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (A or (((B -> C) -> (B -> D)) -> A))))
theorem-size     51
proof            (modus-ponens tm-316 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56448.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((A or (((B -> C) -> (B -> D)) -> A)) -> (A or (((B -> C) -> (B -> D)) -> A)))), M:tm-316, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56449
in-theory        56449
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (E -> (F -> E)))
theorem-size     33
proof            (modus-ponens tm-315 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56449.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (E -> (F -> E))), M:tm-315, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56450
in-theory        56450
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((A or (((B -> C) -> (B -> D)) -> A)) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))) -> (not (A or (((B -> C) -> (B -> D)) -> A)))))
theorem-size     69
proof            (modus-ponens tm-313 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56450.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((A or (((B -> C) -> (B -> D)) -> A)) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))) -> (not (A or (((B -> C) -> (B -> D)) -> A))))), M:tm-313, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56451
in-theory        56451
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A) -> E) -> (((A or (((B -> C) -> (B -> D)) -> A)) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) -> E)))
theorem-size     75
proof            (modus-ponens tm-312 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56451.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A) -> E) -> (((A or (((B -> C) -> (B -> D)) -> A)) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) -> E))), M:tm-312, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56452
in-theory        56452
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (E or ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))))
theorem-size     57
proof            (modus-ponens tm-311 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56452.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (E or ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))), M:tm-311, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56453
in-theory        56453
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) or E))
theorem-size     57
proof            (modus-ponens tm-310 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56453.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) or E)), M:tm-310, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56454
in-theory        56454
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (E -> (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and E)))
theorem-size     59
proof            (modus-ponens tm-309 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56454.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (E -> (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and E))), M:tm-309, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56455
in-theory        56455
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((A or (((B -> C) -> (B -> D)) -> A)) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((A or (((B -> C) -> (B -> D)) -> A)) -> A)))
theorem-size     67
proof            (modus-ponens tm-306 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56455.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (((A or (((B -> C) -> (B -> D)) -> A)) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((A or (((B -> C) -> (B -> D)) -> A)) -> A))), M:tm-306, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C Am))
================================================================
tm-name          tm-56456
in-theory        56456
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (E -> ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))))
theorem-size     57
proof            (modus-ponens tm-305 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56456.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and (E -> ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))), M:tm-305, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56457
in-theory        56457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     39
proof            (modus-ponens tm-303 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56457.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-303, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56458
in-theory        56458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     37
proof            (modus-ponens tm-270 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56458.        ((A -> (((B and C) -> C) and A)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-270, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56459
in-theory        56459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     37
proof            (modus-ponens tm-239 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56459.        ((A -> (((B and C) -> B) and A)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-239, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56460
in-theory        56460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (((F -> G) -> (F -> H)) -> E)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> E)))
theorem-size     45
proof            (modus-ponens tm-210 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56460.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (((F -> G) -> (F -> H)) -> E)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> E))), M:tm-210, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56461
in-theory        56461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     37
proof            (modus-ponens tm-183 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56461.        ((A -> ((B -> (C -> B)) and A)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-183, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56462
in-theory        56462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-157 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56462.        ((A -> ((B and C) -> C)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-157, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56463
in-theory        56463
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     43
proof            (modus-ponens tm-147 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56463.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-147, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56464
in-theory        56464
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-134 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56464.        ((A -> ((B and C) -> B)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-134, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56465
in-theory        56465
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     43
proof            (modus-ponens tm-125 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56465.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-125, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56466
in-theory        56466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((C -> D) -> (C -> E)) -> (A -> B))) -> ((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> A) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> B)))
theorem-size     47
proof            (modus-ponens tm-114 tm-694 ((A (or (-> C D) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> C D)))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (Am (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56466.        (((A -> B) or (((C -> D) -> (C -> E)) -> (A -> B))) -> ((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> A) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> B))), M:tm-114, m:tm-694, u:((A (or (-> C D) (-> (-> (-> Bm Cm) (-> Bm Dm)) (-> C D)))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (Am (-> C D)))
================================================================
tm-name          tm-56467
in-theory        56467
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> (F -> H)) -> E)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> E)))
theorem-size     43
proof            (modus-ponens tm-113 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56467.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (((F -> G) -> (F -> H)) -> E)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> E))), M:tm-113, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56468
in-theory        56468
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     47
proof            (modus-ponens tm-105 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56468.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-105, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56469
in-theory        56469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C)))
theorem-size     35
proof            (modus-ponens tm-95 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56469.        (((A -> B) -> (A -> A)) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C))), M:tm-95, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56470
in-theory        56470
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> A)) -> (E -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))
theorem-size     29
proof            (modus-ponens tm-84 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56470.        ((A or (((B -> C) -> (B -> D)) -> A)) -> (E -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))), M:tm-84, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56471
in-theory        56471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     35
proof            (modus-ponens tm-83 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56471.        ((A -> (B -> (C -> B))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-83, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56472
in-theory        56472
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (((C -> D) -> (C -> E)) -> B)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> B)))
theorem-size     33
proof            (modus-ponens tm-76 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56472.        (((not (not A)) -> A) and ((B or (((C -> D) -> (C -> E)) -> B)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> B))), M:tm-76, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56473
in-theory        56473
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (((B -> C) -> (B -> D)) -> A)))) or (A or (((B -> C) -> (B -> D)) -> A))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))
theorem-size     41
proof            (modus-ponens tm-73 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-8 tm-10 tm-1 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56473.        (((not (not (A or (((B -> C) -> (B -> D)) -> A)))) or (A or (((B -> C) -> (B -> D)) -> A))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-73, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56474
in-theory        56474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C)))
theorem-size     39
proof            (modus-ponens tm-69 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56474.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C))), M:tm-69, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56475
in-theory        56475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     41
proof            (modus-ponens tm-54 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56475.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-54, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56476
in-theory        56476
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (D or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     37
proof            (modus-ponens tm-50 tm-694 ((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56476.        (((((A -> B) -> (A -> C)) -> D) or (D or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-50, m:tm-694, u:((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56477
in-theory        56477
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (((B -> C) -> (B -> D)) -> A))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))
theorem-size     29
proof            (modus-ponens tm-49 tm-694 ((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56477.        ((A or (A or (((B -> C) -> (B -> D)) -> A))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-49, m:tm-694, u:((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56478
in-theory        56478
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (((C -> D) -> (C -> E)) -> B))) or (B or (((C -> D) -> (C -> E)) -> B))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> B))
theorem-size     41
proof            (modus-ponens tm-47 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56478.        (((A and (B or (((C -> D) -> (C -> E)) -> B))) or (B or (((C -> D) -> (C -> E)) -> B))) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> B)), M:tm-47, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56479
in-theory        56479
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (((B -> C) -> (B -> D)) -> A)) and E) or (A or (((B -> C) -> (B -> D)) -> A))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))
theorem-size     41
proof            (modus-ponens tm-46 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56479.        ((((A or (((B -> C) -> (B -> D)) -> A)) and E) or (A or (((B -> C) -> (B -> D)) -> A))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-46, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56480
in-theory        56480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C)))
theorem-size     33
proof            (modus-ponens tm-42 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56480.        ((A -> (B or A)) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C))), M:tm-42, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56481
in-theory        56481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C)))
theorem-size     33
proof            (modus-ponens tm-32 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56481.        ((A -> (A or B)) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C))), M:tm-32, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56482
in-theory        56482
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> A)) -> ((A or (((B -> C) -> (B -> D)) -> A)) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))
theorem-size     39
proof            (modus-ponens tm-24 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56482.        ((A or (((B -> C) -> (B -> D)) -> A)) -> ((A or (((B -> C) -> (B -> D)) -> A)) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))), M:tm-24, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56483
in-theory        56483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C)))
theorem-size     35
proof            (modus-ponens tm-23 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56483.        ((A -> (B -> (A and B))) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C))), M:tm-23, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56484
in-theory        56484
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C)))
theorem-size     33
proof            (modus-ponens tm-22 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56484.        (((A and B) -> B) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C))), M:tm-22, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56485
in-theory        56485
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C)))
theorem-size     33
proof            (modus-ponens tm-21 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56485.        (((A and B) -> A) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C))), M:tm-21, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56486
in-theory        56486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     41
proof            (modus-ponens tm-20 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56486.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-20, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56487
in-theory        56487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C)))
theorem-size     33
proof            (modus-ponens tm-19 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56487.        ((A -> (B -> A)) and ((C or (((D -> E) -> (D -> F)) -> C)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> C))), M:tm-19, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56488
in-theory        56488
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> A)) -> (A or (((B -> C) -> (B -> D)) -> A)))
theorem-size     23
proof            (modus-ponens tm-12 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56488.        ((A or (((B -> C) -> (B -> D)) -> A)) -> (A or (((B -> C) -> (B -> D)) -> A))), M:tm-12, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56489
in-theory        56489
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))) -> (not (A or (((B -> C) -> (B -> D)) -> A))))
theorem-size     41
proof            (modus-ponens tm-9 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-9 tm-8 tm-1 tm-2)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56489.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))) -> (not (A or (((B -> C) -> (B -> D)) -> A)))), M:tm-9, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56490
in-theory        56490
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((D or (((A -> B) -> (A -> C)) -> D)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))
theorem-size     47
proof            (modus-ponens tm-8 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       169
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56490.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((D or (((A -> B) -> (A -> C)) -> D)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-56491
in-theory        56491
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (((C -> D) -> (C -> E)) -> B)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> B)))
theorem-size     29
proof            (modus-ponens tm-7 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-7 tm-8 tm-1 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56491.        (A or ((B or (((C -> D) -> (C -> E)) -> B)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> B))), M:tm-7, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56492
in-theory        56492
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) or E)
theorem-size     29
proof            (modus-ponens tm-6 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-6 tm-8 tm-1 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56492.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) or E), M:tm-6, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56493
in-theory        56493
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (((C -> D) -> (C -> E)) -> B)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> B)) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56493.        (A -> (((B or (((C -> D) -> (C -> E)) -> B)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> B)) and A)), M:tm-5, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56494
in-theory        56494
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((A or (((B -> C) -> (B -> D)) -> A)) -> A))
theorem-size     39
proof            (modus-ponens tm-2 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C Am)))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56494.        (((A or (((B -> C) -> (B -> D)) -> A)) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((A or (((B -> C) -> (B -> D)) -> A)) -> A)), M:tm-2, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C Am))
================================================================
tm-name          tm-56495
in-theory        56495
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (((C -> D) -> (C -> E)) -> B)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> B)))
theorem-size     29
proof            (modus-ponens tm-1 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56495.        (A -> ((B or (((C -> D) -> (C -> E)) -> B)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> B))), M:tm-1, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-56496
in-theory        56496
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-665 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56496.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-665, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56497
in-theory        56497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-622 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56497.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-622, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56498
in-theory        56498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H or G)))
theorem-size     37
proof            (modus-ponens tm-609 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56498.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H or G))), M:tm-609, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56499
in-theory        56499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-605 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56499.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-605, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56500
in-theory        56500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H or G)) and ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-595 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56500.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H or G)) and ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-595, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56501
in-theory        56501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-550 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56501.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-550, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56502
in-theory        56502
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-540 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56502.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-540, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56503
in-theory        56503
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-530 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56503.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-530, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56504
in-theory        56504
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-520 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56504.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-520, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56505
in-theory        56505
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-510 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56505.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-510, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56506
in-theory        56506
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-500 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56506.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-500, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56507
in-theory        56507
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-490 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56507.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-490, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56508
in-theory        56508
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-480 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56508.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-480, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56509
in-theory        56509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-469 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56509.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-469, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56510
in-theory        56510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (G or H)))
theorem-size     37
proof            (modus-ponens tm-456 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56510.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (G or H))), M:tm-456, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56511
in-theory        56511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-453 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56511.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-453, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56512
in-theory        56512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (G or H)) and ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-443 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56512.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (G or H)) and ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-443, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56513
in-theory        56513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-409 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56513.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-409, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56514
in-theory        56514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-400 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56514.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-400, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56515
in-theory        56515
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-391 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56515.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-391, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56516
in-theory        56516
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-382 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56516.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-382, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56517
in-theory        56517
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-373 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56517.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-373, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56518
in-theory        56518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-364 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56518.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-364, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56519
in-theory        56519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-354 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56519.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-354, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56520
in-theory        56520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> (G and H))))
theorem-size     39
proof            (modus-ponens tm-341 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56520.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56521
in-theory        56521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-338 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56521.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-338, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56522
in-theory        56522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     71
proof            (modus-ponens tm-327 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56522.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> (G and H))) and ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-327, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56523
in-theory        56523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> H) and ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-326 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56523.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> H) and ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-326, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56524
in-theory        56524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> G) and ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-325 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56524.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> G) and ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-325, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56525
in-theory        56525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     77
proof            (modus-ponens tm-324 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       265
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56525.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-324, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56526
in-theory        56526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> G)) and ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-323 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56526.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> G)) and ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-323, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56527
in-theory        56527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> H))
theorem-size     37
proof            (modus-ponens tm-322 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56527.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56528
in-theory        56528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> G))
theorem-size     37
proof            (modus-ponens tm-320 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56528.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56529
in-theory        56529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     45
proof            (modus-ponens tm-318 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56529.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56530
in-theory        56530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> G)))
theorem-size     37
proof            (modus-ponens tm-315 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56530.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56531
in-theory        56531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G or ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     65
proof            (modus-ponens tm-311 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56531.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G or ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-311, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56532
in-theory        56532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G))
theorem-size     65
proof            (modus-ponens tm-310 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56532.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G)), M:tm-310, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56533
in-theory        56533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and G)))
theorem-size     67
proof            (modus-ponens tm-309 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56533.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and G))), M:tm-309, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56534
in-theory        56534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     57
proof            (modus-ponens tm-308 tm-695 ((A (-> Am (or Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56534.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-308, m:tm-695, u:((A (-> Am (or Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-56535
in-theory        56535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (A -> (B or A)))
theorem-size     37
proof            (modus-ponens tm-307 tm-695 ((A (-> Am (or Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56535.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (A -> (B or A))), M:tm-307, m:tm-695, u:((A (-> Am (or Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-56536
in-theory        56536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     65
proof            (modus-ponens tm-305 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56536.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-305, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56537
in-theory        56537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-303 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56537.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-303, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56538
in-theory        56538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-270 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56538.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-270, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56539
in-theory        56539
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-239 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56539.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-239, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56540
in-theory        56540
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-210 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56540.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-210, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56541
in-theory        56541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-183 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56541.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-183, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56542
in-theory        56542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-157 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56542.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-157, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56543
in-theory        56543
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-147 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56543.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-147, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56544
in-theory        56544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-134 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56544.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-134, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56545
in-theory        56545
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-125 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56545.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-125, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56546
in-theory        56546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-113 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56546.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-113, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56547
in-theory        56547
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     51
proof            (modus-ponens tm-105 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56547.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-105, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56548
in-theory        56548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-95 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56548.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-95, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56549
in-theory        56549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-83 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56549.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-83, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56550
in-theory        56550
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     37
proof            (modus-ponens tm-76 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56550.        (((not (not A)) -> A) and ((B -> (C or B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-76, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56551
in-theory        56551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     43
proof            (modus-ponens tm-69 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56551.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-69, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56552
in-theory        56552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-54 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56552.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-54, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56553
in-theory        56553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-42 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56553.        ((A -> (B or A)) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-42, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56554
in-theory        56554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-32 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56554.        ((A -> (A or B)) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-32, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56555
in-theory        56555
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-23 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56555.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-23, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56556
in-theory        56556
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-22 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56556.        (((A and B) -> B) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-22, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56557
in-theory        56557
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-21 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56557.        (((A and B) -> A) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-21, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56558
in-theory        56558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-20 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56558.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-20, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56559
in-theory        56559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-19 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56559.        ((A -> (B -> A)) and ((C -> (D or C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-19, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56560
in-theory        56560
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-7 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56560.        (A or ((B -> (C or B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-7, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56561
in-theory        56561
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G)
theorem-size     33
proof            (modus-ponens tm-6 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56561.        (((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G), M:tm-6, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56562
in-theory        56562
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56562.        (A -> (((B -> (C or B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and A)), M:tm-5, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56563
in-theory        56563
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-1 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56563.        (A -> ((B -> (C or B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-1, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56564
in-theory        56564
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-665 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56564.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-665, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56565
in-theory        56565
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-622 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56565.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-622, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56566
in-theory        56566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H or G)))
theorem-size     37
proof            (modus-ponens tm-609 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56566.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H or G))), M:tm-609, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56567
in-theory        56567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-605 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56567.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-605, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56568
in-theory        56568
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H or G)) and ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-595 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56568.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H or G)) and ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-595, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56569
in-theory        56569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-550 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56569.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-550, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56570
in-theory        56570
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-540 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56570.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-540, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56571
in-theory        56571
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-530 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56571.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-530, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56572
in-theory        56572
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-520 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56572.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-520, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56573
in-theory        56573
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-510 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56573.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-510, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56574
in-theory        56574
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-500 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56574.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-500, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56575
in-theory        56575
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-490 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56575.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-490, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56576
in-theory        56576
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-480 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56576.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-480, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56577
in-theory        56577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-469 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56577.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-469, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56578
in-theory        56578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (G or H)))
theorem-size     37
proof            (modus-ponens tm-456 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56578.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (G or H))), M:tm-456, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56579
in-theory        56579
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-453 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56579.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-453, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56580
in-theory        56580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (G or H)) and ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-443 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56580.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (G or H)) and ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-443, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56581
in-theory        56581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-409 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56581.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-409, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56582
in-theory        56582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-400 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56582.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-400, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56583
in-theory        56583
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-391 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56583.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-391, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56584
in-theory        56584
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-382 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56584.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-382, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56585
in-theory        56585
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-373 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56585.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-373, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56586
in-theory        56586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-364 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56586.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-364, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56587
in-theory        56587
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-354 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56587.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-354, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56588
in-theory        56588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> (G and H))))
theorem-size     39
proof            (modus-ponens tm-341 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56588.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56589
in-theory        56589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-338 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56589.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-338, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56590
in-theory        56590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     71
proof            (modus-ponens tm-327 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56590.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> (G and H))) and ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-327, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56591
in-theory        56591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> H) and ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-326 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56591.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> H) and ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-326, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56592
in-theory        56592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> G) and ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-325 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56592.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> G) and ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-325, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56593
in-theory        56593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     77
proof            (modus-ponens tm-324 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       265
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56593.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-324, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56594
in-theory        56594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> G)) and ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-323 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56594.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> G)) and ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-323, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56595
in-theory        56595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> H))
theorem-size     37
proof            (modus-ponens tm-322 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56595.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56596
in-theory        56596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> G))
theorem-size     37
proof            (modus-ponens tm-320 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56596.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56597
in-theory        56597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     45
proof            (modus-ponens tm-318 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56597.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56598
in-theory        56598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> G)))
theorem-size     37
proof            (modus-ponens tm-315 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56598.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56599
in-theory        56599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G or ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     65
proof            (modus-ponens tm-311 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56599.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G or ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-311, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56600
in-theory        56600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G))
theorem-size     65
proof            (modus-ponens tm-310 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56600.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G)), M:tm-310, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56601
in-theory        56601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and G)))
theorem-size     67
proof            (modus-ponens tm-309 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56601.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and G))), M:tm-309, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56602
in-theory        56602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     57
proof            (modus-ponens tm-308 tm-696 ((A (-> Am (or Am Bm))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56602.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-308, m:tm-696, u:((A (-> Am (or Am Bm))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-56603
in-theory        56603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (A -> (A or B)))
theorem-size     37
proof            (modus-ponens tm-307 tm-696 ((A (-> Am (or Am Bm))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56603.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (A -> (A or B))), M:tm-307, m:tm-696, u:((A (-> Am (or Am Bm))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-56604
in-theory        56604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     65
proof            (modus-ponens tm-305 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56604.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-305, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56605
in-theory        56605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-303 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56605.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-303, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56606
in-theory        56606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-270 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56606.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-270, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56607
in-theory        56607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-239 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56607.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-239, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56608
in-theory        56608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-210 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56608.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-210, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56609
in-theory        56609
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-183 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56609.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-183, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56610
in-theory        56610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-157 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56610.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-157, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56611
in-theory        56611
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-147 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56611.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-147, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56612
in-theory        56612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-134 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56612.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-134, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56613
in-theory        56613
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-125 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56613.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-125, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56614
in-theory        56614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-113 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56614.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-113, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56615
in-theory        56615
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     51
proof            (modus-ponens tm-105 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56615.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-105, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56616
in-theory        56616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-95 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56616.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-95, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56617
in-theory        56617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-83 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56617.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-83, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56618
in-theory        56618
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     37
proof            (modus-ponens tm-76 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-10 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56618.        (((not (not A)) -> A) and ((B -> (B or C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-76, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56619
in-theory        56619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     43
proof            (modus-ponens tm-69 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-9 tm-6 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56619.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-69, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56620
in-theory        56620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-54 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56620.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-54, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56621
in-theory        56621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-42 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56621.        ((A -> (B or A)) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-42, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56622
in-theory        56622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-32 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56622.        ((A -> (A or B)) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-32, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56623
in-theory        56623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-23 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56623.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-23, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56624
in-theory        56624
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-22 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56624.        (((A and B) -> B) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-22, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56625
in-theory        56625
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-21 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56625.        (((A and B) -> A) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-21, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56626
in-theory        56626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-20 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56626.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-20, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56627
in-theory        56627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-19 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56627.        ((A -> (B -> A)) and ((C -> (C or D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-19, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56628
in-theory        56628
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-7 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-7 tm-5 tm-6 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56628.        (A or ((B -> (B or C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-7, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56629
in-theory        56629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G)
theorem-size     33
proof            (modus-ponens tm-6 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56629.        (((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G), M:tm-6, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56630
in-theory        56630
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56630.        (A -> (((B -> (B or C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and A)), M:tm-5, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56631
in-theory        56631
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-1 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-1 tm-5 tm-6 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56631.        (A -> ((B -> (B or C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-1, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56632
in-theory        56632
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-697 tm-1 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-56632.        ((((A -> B) -> (A -> C)) -> (D -> ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C))))), M:tm-697, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56633
in-theory        56633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))))
theorem-size     45
proof            (modus-ponens tm-697 tm-2 ((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56633.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C)))), M:tm-697, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
================================================================
tm-name          tm-56634
in-theory        56634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))))
theorem-size     45
proof            (modus-ponens tm-697 tm-5 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56634.        ((((A -> B) -> (A -> C)) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D)))), M:tm-697, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
================================================================
tm-name          tm-56635
in-theory        56635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)))
theorem-size     41
proof            (modus-ponens tm-697 tm-6 ((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-56635.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) or D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D))), M:tm-697, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
================================================================
tm-name          tm-56636
in-theory        56636
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D or ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-697 tm-7 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-56636.        ((((A -> B) -> (A -> C)) -> (D or ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C))))), M:tm-697, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56637
in-theory        56637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-697 tm-8 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       181
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56637.        ((((A -> B) -> (A -> C)) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))), M:tm-697, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
================================================================
tm-name          tm-56638
in-theory        56638
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))
theorem-size     49
proof            (modus-ponens tm-697 tm-9 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       175
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-56638.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))), M:tm-697, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
================================================================
tm-name          tm-56639
in-theory        56639
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> (E -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))))
theorem-size     33
proof            (modus-ponens tm-697 tm-11 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-56639.        ((((A -> B) -> (A -> C)) -> (D -> (E -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D)))), M:tm-697, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-56640
in-theory        56640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> B))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))))
theorem-size     37
proof            (modus-ponens tm-697 tm-12 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-56640.        ((((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> B))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B)))), M:tm-697, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
================================================================
tm-name          tm-56641
in-theory        56641
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     47
proof            (modus-ponens tm-697 tm-13 ((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-56641.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-697, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-56642
in-theory        56642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     49
proof            (modus-ponens tm-697 tm-14 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-56642.        ((((A -> B) -> (A -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-697, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-56643
in-theory        56643
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D and E) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)))
theorem-size     33
proof            (modus-ponens tm-697 tm-16 ((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-56643.        ((((A -> B) -> (A -> C)) -> ((D and E) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D))), M:tm-697, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-56644
in-theory        56644
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D and E) -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)))
theorem-size     33
proof            (modus-ponens tm-697 tm-18 ((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-56644.        ((((A -> B) -> (A -> C)) -> ((D and E) -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E))), M:tm-697, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-56645
in-theory        56645
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-697 tm-19 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-56645.        ((((A -> B) -> (A -> C)) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56646
in-theory        56646
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-697 tm-20 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-56646.        ((((A -> B) -> (A -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56647
in-theory        56647
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-697 tm-21 ((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-56647.        ((((A -> B) -> (A -> C)) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56648
in-theory        56648
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-697 tm-22 ((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-56648.        ((((A -> B) -> (A -> C)) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56649
in-theory        56649
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-23 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-56649.        ((((A -> B) -> (A -> C)) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56650
in-theory        56650
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-697 tm-24 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56650.        ((((A -> B) -> (A -> C)) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C))))), M:tm-697, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
================================================================
tm-name          tm-56651
in-theory        56651
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> (E -> (D and E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))))
theorem-size     37
proof            (modus-ponens tm-697 tm-25 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-56651.        ((((A -> B) -> (A -> C)) -> (D -> (E -> (D and E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E))))), M:tm-697, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-56652
in-theory        56652
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-697 tm-32 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-56652.        ((((A -> B) -> (A -> C)) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56653
in-theory        56653
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> (D or E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))))
theorem-size     33
proof            (modus-ponens tm-697 tm-33 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-56653.        ((((A -> B) -> (A -> C)) -> (D -> (D or E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E)))), M:tm-697, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-56654
in-theory        56654
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-697 tm-42 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-56654.        ((((A -> B) -> (A -> C)) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56655
in-theory        56655
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> (E or D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))))
theorem-size     33
proof            (modus-ponens tm-697 tm-43 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-56655.        ((((A -> B) -> (A -> C)) -> (D -> (E or D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D)))), M:tm-697, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-56656
in-theory        56656
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((B or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-697 tm-44 ((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-56656.        ((((A -> B) -> (A -> C)) -> ((B or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C)))), M:tm-697, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
================================================================
tm-name          tm-56657
in-theory        56657
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))
theorem-size     77
proof            (modus-ponens tm-697 tm-45 ((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       243
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56657.        (((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))), M:tm-697, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
================================================================
tm-name          tm-56658
in-theory        56658
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))))
theorem-size     49
proof            (modus-ponens tm-697 tm-46 ((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-56658.        ((((A -> B) -> (A -> C)) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))), M:tm-697, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
================================================================
tm-name          tm-56659
in-theory        56659
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))))
theorem-size     49
proof            (modus-ponens tm-697 tm-47 ((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and Cm (-> A B)) (-> A B)) (-> A C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-56659.        ((((A -> B) -> (A -> C)) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))), M:tm-697, m:tm-47, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and Cm (-> A B)) (-> A B)) (-> A C))))
================================================================
tm-name          tm-56660
in-theory        56660
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> (A -> C)) -> ((B or (A -> (B and A))) -> (A -> C))) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C))))
theorem-size     51
proof            (modus-ponens tm-697 tm-48 ((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (-> (or Bm (-> Am (and Bm Am))) (-> Am C)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-56660.        ((((A -> (B and A)) -> (A -> C)) -> ((B or (A -> (B and A))) -> (A -> C))) and (((A -> ((B and A) -> C)) or ((A -> (B and A)) -> (A -> C))) -> ((B or (A -> (B and A))) -> (A -> C)))), M:tm-697, m:tm-48, u:((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (-> (or Bm (-> Am (and Bm Am))) (-> Am C))))
================================================================
tm-name          tm-56661
in-theory        56661
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))) and ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))))
theorem-size     83
proof            (modus-ponens tm-697 tm-51 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) C)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       251
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-56661.        (((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))) and ((((A -> B) -> (((C or A) -> B) -> D)) or (((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D))) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))), M:tm-697, m:tm-51, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) C))))
================================================================
tm-name          tm-56662
in-theory        56662
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-697 tm-54 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-56662.        ((((A -> B) -> (A -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-54, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56663
in-theory        56663
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> (A -> B)) -> ((A -> A) -> ((A or A) -> B))) and (((A -> (A -> B)) or ((A -> A) -> (A -> B))) -> ((A -> A) -> ((A or A) -> B))))
theorem-size     41
proof            (modus-ponens tm-697 tm-55 ((Bm Am) (B Am) (A Am) (C Cm) (D (-> (-> Am Am) (-> (or Am Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-56663.        ((((A -> A) -> (A -> B)) -> ((A -> A) -> ((A or A) -> B))) and (((A -> (A -> B)) or ((A -> A) -> (A -> B))) -> ((A -> A) -> ((A or A) -> B)))), M:tm-697, m:tm-55, u:((Bm Am) (B Am) (A Am) (C Cm) (D (-> (-> Am Am) (-> (or Am Am) Cm))))
================================================================
tm-name          tm-56664
in-theory        56664
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))))
theorem-size     49
proof            (modus-ponens tm-697 tm-56 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-56664.        ((((A -> B) -> (A -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))), M:tm-697, m:tm-56, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-56665
in-theory        56665
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> ((A -> (not B)) -> C)) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> C))) and ((((A -> (not B)) -> ((not A) -> C)) or (((A -> (not B)) -> (not A)) -> ((A -> (not B)) -> C))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> C))))
theorem-size     77
proof            (modus-ponens tm-697 tm-66 ((A (-> Am (not Bm))) (B (not Am)) (Cm (-> (-> Am (not Bm)) C)) (D (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (-> (-> Am (not Bm)) C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       239
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-56665.        (((((A -> (not B)) -> (not A)) -> ((A -> (not B)) -> C)) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> C))) and ((((A -> (not B)) -> ((not A) -> C)) or (((A -> (not B)) -> (not A)) -> ((A -> (not B)) -> C))) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> C)))), M:tm-697, m:tm-66, u:((A (-> Am (not Bm))) (B (not Am)) (Cm (-> (-> Am (not Bm)) C)) (D (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (-> (-> Am (not Bm)) C))))
================================================================
tm-name          tm-56666
in-theory        56666
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> B) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-697 tm-69 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-56666.        ((((A -> B) -> (A -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-69, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56667
in-theory        56667
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((A -> (B -> (not B))) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A))))
theorem-size     38
proof            (modus-ponens tm-697 tm-70 ((B Bm) (A Am) (C (not Bm)) (D (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       192
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-56667.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((A -> (B -> (not B))) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A)))), M:tm-697, m:tm-70, u:((B Bm) (A Am) (C (not Bm)) (D (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-56668
in-theory        56668
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> ((D -> (not E)) -> (not D)))))
theorem-size     45
proof            (modus-ponens tm-697 tm-71 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-56668.        ((((A -> B) -> (A -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> ((D -> (not E)) -> (not D))))), M:tm-697, m:tm-71, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-56669
in-theory        56669
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((not (not (A -> B))) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((not (not (A -> B))) or (A -> B)) -> (A -> C))))
theorem-size     49
proof            (modus-ponens tm-697 tm-73 ((Am (-> A B)) (Bm (-> A C)) (D (-> (or (not (not (-> A B))) (-> A B)) (-> A C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-56669.        ((((A -> B) -> (A -> C)) -> (((not (not (A -> B))) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((not (not (A -> B))) or (A -> B)) -> (A -> C)))), M:tm-697, m:tm-73, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (not (not (-> A B))) (-> A B)) (-> A C))))
================================================================
tm-name          tm-56670
in-theory        56670
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((not (not D)) -> D) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((not (not D)) -> D) and ((A -> B) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-697 tm-76 ((Am (-> (-> A B) (-> A C))) (D (and (-> (not (not Bm)) Bm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-10)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-56670.        ((((A -> B) -> (A -> C)) -> (((not (not D)) -> D) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((not (not D)) -> D) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-76, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (not (not Bm)) Bm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56671
in-theory        56671
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((not (not D)) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((not (not D)) -> D)))
theorem-size     33
proof            (modus-ponens tm-697 tm-78 ((Am (-> (-> A B) (-> A C))) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-10)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-56671.        ((((A -> B) -> (A -> C)) -> ((not (not D)) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((not (not D)) -> D))), M:tm-697, m:tm-78, u:((Am (-> (-> A B) (-> A C))) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-56672
in-theory        56672
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> (A -> C)) -> ((D or (A -> (B -> A))) -> (A -> C))) and (((A -> ((B -> A) -> C)) or ((A -> (B -> A)) -> (A -> C))) -> ((D or (A -> (B -> A))) -> (A -> C))))
theorem-size     51
proof            (modus-ponens tm-697 tm-80 ((A Am) (B (-> Bm Am)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (-> Bm Am))) (-> Am C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-56672.        ((((A -> (B -> A)) -> (A -> C)) -> ((D or (A -> (B -> A))) -> (A -> C))) and (((A -> ((B -> A) -> C)) or ((A -> (B -> A)) -> (A -> C))) -> ((D or (A -> (B -> A))) -> (A -> C)))), M:tm-697, m:tm-80, u:((A Am) (B (-> Bm Am)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (-> Bm Am))) (-> Am C))))
================================================================
tm-name          tm-56673
in-theory        56673
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (E -> (F -> E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (F -> E))) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-83 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-56673.        ((((A -> B) -> (A -> C)) -> ((D -> (E -> (F -> E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (F -> E))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-83, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56674
in-theory        56674
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((A -> B) -> (D -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D -> (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-697 tm-84 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> Cm (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-56674.        ((((A -> B) -> (A -> C)) -> ((A -> B) -> (D -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D -> (A -> C))))), M:tm-697, m:tm-84, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> Cm (-> A C)))))
================================================================
tm-name          tm-56675
in-theory        56675
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> (E -> (F -> E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (F -> E)))))
theorem-size     37
proof            (modus-ponens tm-697 tm-85 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-56675.        ((((A -> B) -> (A -> C)) -> (D -> (E -> (F -> E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (F -> E))))), M:tm-697, m:tm-85, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-56676
in-theory        56676
times-derived    4
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> C))))
theorem-size     37
proof            (modus-ponens tm-697 tm-86 ((Am (-> (-> A B) (-> A C))) (D (-> (-> A B) (-> A C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-56676.        ((((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> C)))), M:tm-697, m:tm-86, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> A B) (-> A C))))
================================================================
tm-name          tm-56677
in-theory        56677
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> (A -> B)) -> (((A -> C) or (A -> A)) -> (A -> B))) and (((A -> (A -> B)) or ((A -> A) -> (A -> B))) -> (((A -> C) or (A -> A)) -> (A -> B))))
theorem-size     45
proof            (modus-ponens tm-697 tm-92 ((A Am) (B Am) (Bm (-> Am C)) (D (-> (or (-> Am Cm) (-> Am Am)) (-> Am C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-56677.        ((((A -> A) -> (A -> B)) -> (((A -> C) or (A -> A)) -> (A -> B))) and (((A -> (A -> B)) or ((A -> A) -> (A -> B))) -> (((A -> C) or (A -> A)) -> (A -> B)))), M:tm-697, m:tm-92, u:((A Am) (B Am) (Bm (-> Am C)) (D (-> (or (-> Am Cm) (-> Am Am)) (-> Am C))))
================================================================
tm-name          tm-56678
in-theory        56678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> E) -> (D -> D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (D -> D)) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-95 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-56678.        ((((A -> B) -> (A -> C)) -> (((D -> E) -> (D -> D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (D -> D)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-95, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56679
in-theory        56679
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> E) -> (D -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (D -> D))))
theorem-size     37
proof            (modus-ponens tm-697 tm-97 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-56679.        ((((A -> B) -> (A -> C)) -> ((D -> E) -> (D -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (D -> D)))), M:tm-697, m:tm-97, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-56680
in-theory        56680
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B))))
theorem-size     47
proof            (modus-ponens tm-697 tm-100 ((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       251
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-56680.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B)))), M:tm-697, m:tm-100, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-56681
in-theory        56681
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> ((A -> (B -> C)) -> D)) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> D))) and ((((A -> (B -> C)) -> ((A -> C) -> D)) or (((A -> (B -> C)) -> (A -> C)) -> ((A -> (B -> C)) -> D))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> D))))
theorem-size     103
proof            (modus-ponens tm-697 tm-102 ((A (-> Am (-> Bm Cm))) (B (-> Am Cm)) (Dm (-> (-> Am (-> Bm Cm)) C)) (D (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> (-> Am (-> Bm Cm)) C)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       309
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-56681.        (((((A -> (B -> C)) -> (A -> C)) -> ((A -> (B -> C)) -> D)) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> D))) and ((((A -> (B -> C)) -> ((A -> C) -> D)) or (((A -> (B -> C)) -> (A -> C)) -> ((A -> (B -> C)) -> D))) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> D)))), M:tm-697, m:tm-102, u:((A (-> Am (-> Bm Cm))) (B (-> Am Cm)) (Dm (-> (-> Am (-> Bm Cm)) C)) (D (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> (-> Am (-> Bm Cm)) C))))
================================================================
tm-name          tm-56682
in-theory        56682
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> B) -> (A -> C)))))
theorem-size     77
proof            (modus-ponens tm-697 tm-105 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       267
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-56682.        ((((A -> B) -> (A -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-105, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56683
in-theory        56683
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))))
theorem-size     61
proof            (modus-ponens tm-697 tm-107 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-56683.        ((((A -> B) -> (A -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))), M:tm-697, m:tm-107, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-56684
in-theory        56684
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> D)) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> D))) and ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> D))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> D))))
theorem-size     107
proof            (modus-ponens tm-697 tm-110 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (-> (-> Am (-> Bm Cm)) C)) (D (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> Am (-> Bm Cm)) C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       301
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-56684.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> D)) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> D))) and ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> D))) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> D)))), M:tm-697, m:tm-110, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (-> (-> Am (-> Bm Cm)) C)) (D (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> Am (-> Bm Cm)) C))))
================================================================
tm-name          tm-56685
in-theory        56685
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-697 tm-113 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-56685.        ((((A -> B) -> (A -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-113, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56686
in-theory        56686
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (C -> D))) -> ((A -> B) -> ((A -> C) -> (A -> D)))) and (((A -> (B -> (C -> D))) or ((A -> B) -> (A -> (C -> D)))) -> ((A -> B) -> ((A -> C) -> (A -> D)))))
theorem-size     51
proof            (modus-ponens tm-697 tm-114 ((Am (-> Bm B)) (A Bm) (C (-> Cm Dm)) (D (-> (-> Bm B) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-56686.        ((((A -> B) -> (A -> (C -> D))) -> ((A -> B) -> ((A -> C) -> (A -> D)))) and (((A -> (B -> (C -> D))) or ((A -> B) -> (A -> (C -> D)))) -> ((A -> B) -> ((A -> C) -> (A -> D))))), M:tm-697, m:tm-114, u:((Am (-> Bm B)) (A Bm) (C (-> Cm Dm)) (D (-> (-> Bm B) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-56687
in-theory        56687
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     53
proof            (modus-ponens tm-697 tm-115 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-56687.        ((((A -> B) -> (A -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-697, m:tm-115, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-56688
in-theory        56688
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> (((A -> B) and C) -> D)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> D))) and (((((A -> B) and C) -> (B -> D)) or ((((A -> B) and C) -> B) -> (((A -> B) and C) -> D))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> D))))
theorem-size     89
proof            (modus-ponens tm-697 tm-122 ((A (and (-> Am Bm) Cm)) (B Bm) (Dm (-> (and (-> Am Bm) Cm) C)) (D (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (-> (and (-> Am Bm) Cm) C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       277
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-56688.        ((((((A -> B) and C) -> B) -> (((A -> B) and C) -> D)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> D))) and (((((A -> B) and C) -> (B -> D)) or ((((A -> B) and C) -> B) -> (((A -> B) and C) -> D))) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> D)))), M:tm-697, m:tm-122, u:((A (and (-> Am Bm) Cm)) (B Bm) (Dm (-> (and (-> Am Bm) Cm) C)) (D (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (-> (and (-> Am Bm) Cm) C))))
================================================================
tm-name          tm-56689
in-theory        56689
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> B) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-697 tm-125 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-56689.        ((((A -> B) -> (A -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-125, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56690
in-theory        56690
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))))
theorem-size     53
proof            (modus-ponens tm-697 tm-127 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-56690.        ((((A -> B) -> (A -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))), M:tm-697, m:tm-127, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-56691
in-theory        56691
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> ((A and B) -> C)) -> ((D or ((A and B) -> A)) -> ((A and B) -> C))) and ((((A and B) -> (A -> C)) or (((A and B) -> A) -> ((A and B) -> C))) -> ((D or ((A and B) -> A)) -> ((A and B) -> C))))
theorem-size     59
proof            (modus-ponens tm-697 tm-131 ((A (and Am Bm)) (B Am) (Cm (-> (and Am Bm) C)) (D (-> (or Dm (-> (and Am Bm) Am)) (-> (and Am Bm) C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-56691.        (((((A and B) -> A) -> ((A and B) -> C)) -> ((D or ((A and B) -> A)) -> ((A and B) -> C))) and ((((A and B) -> (A -> C)) or (((A and B) -> A) -> ((A and B) -> C))) -> ((D or ((A and B) -> A)) -> ((A and B) -> C)))), M:tm-697, m:tm-131, u:((A (and Am Bm)) (B Am) (Cm (-> (and Am Bm) C)) (D (-> (or Dm (-> (and Am Bm) Am)) (-> (and Am Bm) C))))
================================================================
tm-name          tm-56692
in-theory        56692
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> ((E and F) -> E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E and F) -> E)) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-134 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-56692.        ((((A -> B) -> (A -> C)) -> ((D -> ((E and F) -> E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E and F) -> E)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-134, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56693
in-theory        56693
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> ((E and F) -> E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E and F) -> E))))
theorem-size     37
proof            (modus-ponens tm-697 tm-136 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-56693.        ((((A -> B) -> (A -> C)) -> (D -> ((E and F) -> E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E and F) -> E)))), M:tm-697, m:tm-136, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-56694
in-theory        56694
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> ((A and (B -> C)) -> D)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> D))) and ((((A and (B -> C)) -> (C -> D)) or (((A and (B -> C)) -> C) -> ((A and (B -> C)) -> D))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> D))))
theorem-size     89
proof            (modus-ponens tm-697 tm-144 ((A (and Am (-> Bm Cm))) (B Cm) (Dm (-> (and Am (-> Bm Cm)) C)) (D (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (-> (and Am (-> Bm Cm)) C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       277
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-56694.        (((((A and (B -> C)) -> C) -> ((A and (B -> C)) -> D)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> D))) and ((((A and (B -> C)) -> (C -> D)) or (((A and (B -> C)) -> C) -> ((A and (B -> C)) -> D))) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> D)))), M:tm-697, m:tm-144, u:((A (and Am (-> Bm Cm))) (B Cm) (Dm (-> (and Am (-> Bm Cm)) C)) (D (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (-> (and Am (-> Bm Cm)) C))))
================================================================
tm-name          tm-56695
in-theory        56695
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> B) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-697 tm-147 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-56695.        ((((A -> B) -> (A -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-147, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56696
in-theory        56696
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))))
theorem-size     53
proof            (modus-ponens tm-697 tm-149 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-56696.        ((((A -> B) -> (A -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))), M:tm-697, m:tm-149, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-56697
in-theory        56697
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> ((A and B) -> C)) -> ((D or ((A and B) -> B)) -> ((A and B) -> C))) and ((((A and B) -> (B -> C)) or (((A and B) -> B) -> ((A and B) -> C))) -> ((D or ((A and B) -> B)) -> ((A and B) -> C))))
theorem-size     59
proof            (modus-ponens tm-697 tm-154 ((A (and Am Bm)) (B Bm) (Cm (-> (and Am Bm) C)) (D (-> (or Dm (-> (and Am Bm) Bm)) (-> (and Am Bm) C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-56697.        (((((A and B) -> B) -> ((A and B) -> C)) -> ((D or ((A and B) -> B)) -> ((A and B) -> C))) and ((((A and B) -> (B -> C)) or (((A and B) -> B) -> ((A and B) -> C))) -> ((D or ((A and B) -> B)) -> ((A and B) -> C)))), M:tm-697, m:tm-154, u:((A (and Am Bm)) (B Bm) (Cm (-> (and Am Bm) C)) (D (-> (or Dm (-> (and Am Bm) Bm)) (-> (and Am Bm) C))))
================================================================
tm-name          tm-56698
in-theory        56698
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> ((E and F) -> F)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E and F) -> F)) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-157 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-56698.        ((((A -> B) -> (A -> C)) -> ((D -> ((E and F) -> F)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E and F) -> F)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-157, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56699
in-theory        56699
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> ((E and F) -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E and F) -> F))))
theorem-size     37
proof            (modus-ponens tm-697 tm-159 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-56699.        ((((A -> B) -> (A -> C)) -> (D -> ((E and F) -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E and F) -> F)))), M:tm-697, m:tm-159, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-56700
in-theory        56700
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> B) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-697 tm-183 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-56700.        ((((A -> B) -> (A -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-183, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56701
in-theory        56701
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> ((E -> (F -> E)) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> E)) and D))))
theorem-size     41
proof            (modus-ponens tm-697 tm-184 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-56701.        ((((A -> B) -> (A -> C)) -> (D -> ((E -> (F -> E)) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> E)) and D)))), M:tm-697, m:tm-184, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-56702
in-theory        56702
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> B) -> (A -> C)))))
theorem-size     73
proof            (modus-ponens tm-697 tm-210 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       253
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-56702.        ((((A -> B) -> (A -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-210, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56703
in-theory        56703
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     57
proof            (modus-ponens tm-697 tm-211 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-56703.        ((((A -> B) -> (A -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-697, m:tm-211, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-56704
in-theory        56704
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (((E and F) -> E) and D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((E and F) -> E) and D)) and ((A -> B) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-697 tm-239 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-56704.        ((((A -> B) -> (A -> C)) -> ((D -> (((E and F) -> E) and D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((E and F) -> E) and D)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-239, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56705
in-theory        56705
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> (((E and F) -> E) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E and F) -> E) and D))))
theorem-size     41
proof            (modus-ponens tm-697 tm-240 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-56705.        ((((A -> B) -> (A -> C)) -> (D -> (((E and F) -> E) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E and F) -> E) and D)))), M:tm-697, m:tm-240, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-56706
in-theory        56706
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (((E and F) -> F) and D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((E and F) -> F) and D)) and ((A -> B) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-697 tm-270 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-56706.        ((((A -> B) -> (A -> C)) -> ((D -> (((E and F) -> F) and D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((E and F) -> F) and D)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-270, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56707
in-theory        56707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> (((E and F) -> F) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E and F) -> F) and D))))
theorem-size     41
proof            (modus-ponens tm-697 tm-271 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-56707.        ((((A -> B) -> (A -> C)) -> (D -> (((E and F) -> F) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((E and F) -> F) and D)))), M:tm-697, m:tm-271, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-56708
in-theory        56708
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> B) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-697 tm-303 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-56708.        ((((A -> B) -> (A -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-303, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56709
in-theory        56709
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> ((E -> (F -> (E and F))) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> (E and F))) and D))))
theorem-size     45
proof            (modus-ponens tm-697 tm-304 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-56709.        ((((A -> B) -> (A -> C)) -> (D -> ((E -> (F -> (E and F))) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F -> (E and F))) and D)))), M:tm-697, m:tm-304, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-56710
in-theory        56710
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> ((A -> B) -> (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-697 tm-305 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-56710.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> ((A -> B) -> (A -> C)))))), M:tm-697, m:tm-305, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-56711
in-theory        56711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> B) -> A) -> ((A -> B) -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> B) -> A) -> ((A -> B) -> C)))))
theorem-size     61
proof            (modus-ponens tm-697 tm-306 ((Am (-> Bm B)) (A Bm) (C Cm) (D (and (-> (-> Bm B) (-> Bm Cm)) (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-56711.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> B) -> A) -> ((A -> B) -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> B) -> A) -> ((A -> B) -> C))))), M:tm-697, m:tm-306, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (and (-> (-> Bm B) (-> Bm Cm)) (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm)))))
================================================================
tm-name          tm-56712
in-theory        56712
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (((A -> B) -> (A -> C)) and D)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (((A -> B) -> (A -> C)) and D)))))
theorem-size     61
proof            (modus-ponens tm-697 tm-309 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (and (-> (-> A B) (-> A C)) Bm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-56712.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (((A -> B) -> (A -> C)) and D)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (((A -> B) -> (A -> C)) and D))))), M:tm-697, m:tm-309, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (and (-> (-> A B) (-> A C)) Bm)))))
================================================================
tm-name          tm-56713
in-theory        56713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (A -> C)) or D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (A -> C)) or D))))
theorem-size     57
proof            (modus-ponens tm-697 tm-310 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (or (-> (-> A B) (-> A C)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-56713.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (A -> C)) or D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (A -> C)) or D)))), M:tm-697, m:tm-310, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (or (-> (-> A B) (-> A C)) Bm))))
================================================================
tm-name          tm-56714
in-theory        56714
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D or ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D or ((A -> B) -> (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-697 tm-311 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (or Bm (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-56714.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D or ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D or ((A -> B) -> (A -> C)))))), M:tm-697, m:tm-311, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (or Bm (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-56715
in-theory        56715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))))
theorem-size     69
proof            (modus-ponens tm-697 tm-312 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-56715.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))), M:tm-697, m:tm-312, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm)))))
================================================================
tm-name          tm-56716
in-theory        56716
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (not (A -> C))) -> (not (A -> B))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (not (A -> C))) -> (not (A -> B))))))
theorem-size     65
proof            (modus-ponens tm-697 tm-313 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-56716.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (not (A -> C))) -> (not (A -> B))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))), M:tm-697, m:tm-313, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> (-> A B) (not (-> A C))) (not (-> A B))))))
================================================================
tm-name          tm-56717
in-theory        56717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (E -> D)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (E -> D)))))
theorem-size     49
proof            (modus-ponens tm-697 tm-315 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-56717.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (E -> D)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (E -> D))))), M:tm-697, m:tm-315, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-56718
in-theory        56718
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((A -> B) -> (A -> B)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((A -> B) -> (A -> B)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-316 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> A B) (-> A B))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-56718.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((A -> B) -> (A -> B)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((A -> B) -> (A -> B))))), M:tm-697, m:tm-316, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> A B) (-> A B)))))
================================================================
tm-name          tm-56719
in-theory        56719
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     67
proof            (modus-ponens tm-697 tm-317 ((B (-> Bm Cm)) (A Am) (C Bm) (D (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       285
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-56719.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))), M:tm-697, m:tm-317, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-56720
in-theory        56720
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))))
theorem-size     65
proof            (modus-ponens tm-697 tm-318 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       259
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-56720.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))), M:tm-697, m:tm-318, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-56721
in-theory        56721
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D and E) -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D and E) -> D))))
theorem-size     49
proof            (modus-ponens tm-697 tm-320 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-56721.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D and E) -> D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D and E) -> D)))), M:tm-697, m:tm-320, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-56722
in-theory        56722
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D and E) -> E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D and E) -> E))))
theorem-size     49
proof            (modus-ponens tm-697 tm-322 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-4)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-56722.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D and E) -> E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D and E) -> E)))), M:tm-697, m:tm-322, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-56723
in-theory        56723
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E -> D)) and ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E -> D)) and ((A -> B) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-697 tm-323 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-56723.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E -> D)) and ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))), M:tm-697, m:tm-323, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-56724
in-theory        56724
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))))
theorem-size     81
proof            (modus-ponens tm-697 tm-324 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       281
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-56724.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))), M:tm-697, m:tm-324, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-56725
in-theory        56725
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D and E) -> D) and ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D and E) -> D) and ((A -> B) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-697 tm-325 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-56725.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D and E) -> D) and ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D and E) -> D) and ((A -> B) -> (A -> C)))))), M:tm-697, m:tm-325, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-56726
in-theory        56726
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D and E) -> E) and ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D and E) -> E) and ((A -> B) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-697 tm-326 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-56726.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D and E) -> E) and ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (((D and E) -> E) and ((A -> B) -> (A -> C)))))), M:tm-697, m:tm-326, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-56727
in-theory        56727
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))))
theorem-size     69
proof            (modus-ponens tm-697 tm-327 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       251
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-56727.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))), M:tm-697, m:tm-327, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-56728
in-theory        56728
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((A -> B) -> ((A -> B) and (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((A -> B) -> ((A -> B) and (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-697 tm-328 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> A B) (and (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       247
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-56728.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((A -> B) -> ((A -> B) and (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((A -> B) -> ((A -> B) and (A -> C)))))), M:tm-697, m:tm-328, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> A B) (and (-> A B) (-> A C))))))
================================================================
tm-name          tm-56729
in-theory        56729
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> (A -> C)) -> (((A -> B) or (A -> (A and B))) -> (A -> C))) and (((A -> ((A and B) -> C)) or ((A -> (A and B)) -> (A -> C))) -> (((A -> B) or (A -> (A and B))) -> (A -> C))))
theorem-size     55
proof            (modus-ponens tm-697 tm-335 ((A Am) (B (and Am Bm)) (Cm (-> Am C)) (D (-> (or (-> Am Bm) (-> Am (and Am Bm))) (-> Am C)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-56729.        ((((A -> (A and B)) -> (A -> C)) -> (((A -> B) or (A -> (A and B))) -> (A -> C))) and (((A -> ((A and B) -> C)) or ((A -> (A and B)) -> (A -> C))) -> (((A -> B) or (A -> (A and B))) -> (A -> C)))), M:tm-697, m:tm-335, u:((A Am) (B (and Am Bm)) (Cm (-> Am C)) (D (-> (or (-> Am Bm) (-> Am (and Am Bm))) (-> Am C))))
================================================================
tm-name          tm-56730
in-theory        56730
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> E) -> (D -> (D and E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (D -> (D and E))) and ((A -> B) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-697 tm-338 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-56730.        ((((A -> B) -> (A -> C)) -> (((D -> E) -> (D -> (D and E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (D -> (D and E))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-338, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56731
in-theory        56731
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> E) -> (D -> (D and E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (D -> (D and E)))))
theorem-size     41
proof            (modus-ponens tm-697 tm-340 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-56731.        ((((A -> B) -> (A -> C)) -> ((D -> E) -> (D -> (D and E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (D -> (D and E))))), M:tm-697, m:tm-340, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-56732
in-theory        56732
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (E -> (D and E))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (E -> (D and E))))))
theorem-size     53
proof            (modus-ponens tm-697 tm-341 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-56732.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (E -> (D and E))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (E -> (D and E)))))), M:tm-697, m:tm-341, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-56733
in-theory        56733
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> (A -> C)) -> ((D or (A -> (B -> (A and B)))) -> (A -> C))) and (((A -> ((B -> (A and B)) -> C)) or ((A -> (B -> (A and B))) -> (A -> C))) -> ((D or (A -> (B -> (A and B)))) -> (A -> C))))
theorem-size     61
proof            (modus-ponens tm-697 tm-351 ((A Am) (B (-> Bm (and Am Bm))) (Cm (-> Am C)) (D (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> Am C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-56733.        ((((A -> (B -> (A and B))) -> (A -> C)) -> ((D or (A -> (B -> (A and B)))) -> (A -> C))) and (((A -> ((B -> (A and B)) -> C)) or ((A -> (B -> (A and B))) -> (A -> C))) -> ((D or (A -> (B -> (A and B)))) -> (A -> C)))), M:tm-697, m:tm-351, u:((A Am) (B (-> Bm (and Am Bm))) (Cm (-> Am C)) (D (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> Am C))))
================================================================
tm-name          tm-56734
in-theory        56734
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-697 tm-354 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-56734.        ((((A -> B) -> (A -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-354, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56735
in-theory        56735
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((A -> B) -> (D -> ((A -> C) and D)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D -> ((A -> C) and D)))))
theorem-size     45
proof            (modus-ponens tm-697 tm-355 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> Cm (and (-> A C) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-56735.        ((((A -> B) -> (A -> C)) -> ((A -> B) -> (D -> ((A -> C) and D)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D -> ((A -> C) and D))))), M:tm-697, m:tm-355, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> Cm (and (-> A C) Cm)))))
================================================================
tm-name          tm-56736
in-theory        56736
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> (E -> (F -> (E and F))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (F -> (E and F))))))
theorem-size     41
proof            (modus-ponens tm-697 tm-356 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-56736.        ((((A -> B) -> (A -> C)) -> (D -> (E -> (F -> (E and F))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (F -> (E and F)))))), M:tm-697, m:tm-356, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-56737
in-theory        56737
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> (E -> D)) or F) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> D)) or F) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-364 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-56737.        ((((A -> B) -> (A -> C)) -> (((D -> (E -> D)) or F) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> D)) or F) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-364, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56738
in-theory        56738
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (E -> D)) or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) or F)))
theorem-size     37
proof            (modus-ponens tm-697 tm-365 ((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-56738.        ((((A -> B) -> (A -> C)) -> ((D -> (E -> D)) or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) or F))), M:tm-697, m:tm-365, u:((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-56739
in-theory        56739
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> B) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-697 tm-373 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56739.        ((((A -> B) -> (A -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-373, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56740
in-theory        56740
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)))
theorem-size     53
proof            (modus-ponens tm-697 tm-374 ((Am (-> (-> A B) (-> A C))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56740.        ((((A -> B) -> (A -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))), M:tm-697, m:tm-374, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-56741
in-theory        56741
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((((D and E) -> D) or F) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and E) -> D) or F) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-382 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-56741.        ((((A -> B) -> (A -> C)) -> ((((D and E) -> D) or F) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and E) -> D) or F) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-382, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56742
in-theory        56742
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D and E) -> D) or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) or F)))
theorem-size     37
proof            (modus-ponens tm-697 tm-383 ((Am (-> (-> A B) (-> A C))) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-56742.        ((((A -> B) -> (A -> C)) -> (((D and E) -> D) or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) or F))), M:tm-697, m:tm-383, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-56743
in-theory        56743
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((((D and E) -> E) or F) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and E) -> E) or F) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-391 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-4)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-56743.        ((((A -> B) -> (A -> C)) -> ((((D and E) -> E) or F) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D and E) -> E) or F) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-391, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56744
in-theory        56744
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D and E) -> E) or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) or F)))
theorem-size     37
proof            (modus-ponens tm-697 tm-392 ((Am (-> (-> A B) (-> A C))) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-56744.        ((((A -> B) -> (A -> C)) -> (((D and E) -> E) or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) or F))), M:tm-697, m:tm-392, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-56745
in-theory        56745
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> (E -> (D and E))) or F) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> (D and E))) or F) and ((A -> B) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-697 tm-400 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-56745.        ((((A -> B) -> (A -> C)) -> (((D -> (E -> (D and E))) or F) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> (D and E))) or F) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-400, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56746
in-theory        56746
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (E -> (D and E))) or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) or F)))
theorem-size     41
proof            (modus-ponens tm-697 tm-401 ((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-56746.        ((((A -> B) -> (A -> C)) -> ((D -> (E -> (D and E))) or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) or F))), M:tm-697, m:tm-401, u:((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-56747
in-theory        56747
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> (D or E)) or F) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (D or E)) or F) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-409 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-56747.        ((((A -> B) -> (A -> C)) -> (((D -> (D or E)) or F) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (D or E)) or F) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-409, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56748
in-theory        56748
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (D or E)) or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) or F)))
theorem-size     37
proof            (modus-ponens tm-697 tm-410 ((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-56748.        ((((A -> B) -> (A -> C)) -> ((D -> (D or E)) or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) or F))), M:tm-697, m:tm-410, u:((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-56749
in-theory        56749
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (D or E)) and ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (D or E)) and ((A -> B) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-697 tm-443 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-56749.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (D or E)) and ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (D or E)) and ((A -> B) -> (A -> C)))))), M:tm-697, m:tm-443, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-56750
in-theory        56750
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (E or F)) and D)) and ((A -> B) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-697 tm-453 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-56750.        ((((A -> B) -> (A -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (E or F)) and D)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-453, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56751
in-theory        56751
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> ((E -> (E or F)) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (E or F)) and D))))
theorem-size     41
proof            (modus-ponens tm-697 tm-454 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-56751.        ((((A -> B) -> (A -> C)) -> (D -> ((E -> (E or F)) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (E or F)) and D)))), M:tm-697, m:tm-454, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-56752
in-theory        56752
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (D or E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (D or E)))))
theorem-size     49
proof            (modus-ponens tm-697 tm-456 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-56752.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (D or E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (D or E))))), M:tm-697, m:tm-456, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-56753
in-theory        56753
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> (A -> C)) -> ((D or (A -> (A or B))) -> (A -> C))) and (((A -> ((A or B) -> C)) or ((A -> (A or B)) -> (A -> C))) -> ((D or (A -> (A or B))) -> (A -> C))))
theorem-size     51
proof            (modus-ponens tm-697 tm-466 ((A Am) (B (or Am Bm)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (or Am Bm))) (-> Am C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-56753.        ((((A -> (A or B)) -> (A -> C)) -> ((D or (A -> (A or B))) -> (A -> C))) and (((A -> ((A or B) -> C)) or ((A -> (A or B)) -> (A -> C))) -> ((D or (A -> (A or B))) -> (A -> C)))), M:tm-697, m:tm-466, u:((A Am) (B (or Am Bm)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (or Am Bm))) (-> Am C))))
================================================================
tm-name          tm-56754
in-theory        56754
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (E -> (E or F))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (E or F))) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-469 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-56754.        ((((A -> B) -> (A -> C)) -> ((D -> (E -> (E or F))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (E or F))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-469, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56755
in-theory        56755
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((A -> B) -> ((A -> C) or D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> C) or D))))
theorem-size     41
proof            (modus-ponens tm-697 tm-470 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (or (-> A C) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-56755.        ((((A -> B) -> (A -> C)) -> ((A -> B) -> ((A -> C) or D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> C) or D)))), M:tm-697, m:tm-470, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (or (-> A C) Cm))))
================================================================
tm-name          tm-56756
in-theory        56756
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> (E -> (E or F)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (E or F)))))
theorem-size     37
proof            (modus-ponens tm-697 tm-471 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-56756.        ((((A -> B) -> (A -> C)) -> (D -> (E -> (E or F)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (E or F))))), M:tm-697, m:tm-471, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-56757
in-theory        56757
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D or (E -> (F -> E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (F -> E))) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-480 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-56757.        ((((A -> B) -> (A -> C)) -> ((D or (E -> (F -> E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (F -> E))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-480, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56758
in-theory        56758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D or (E -> (F -> E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (F -> E)))))
theorem-size     37
proof            (modus-ponens tm-697 tm-481 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-56758.        ((((A -> B) -> (A -> C)) -> (D or (E -> (F -> E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (F -> E))))), M:tm-697, m:tm-481, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-56759
in-theory        56759
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-697 tm-490 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-56759.        ((((A -> B) -> (A -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-490, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56760
in-theory        56760
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     53
proof            (modus-ponens tm-697 tm-491 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-56760.        ((((A -> B) -> (A -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-697, m:tm-491, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-56761
in-theory        56761
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D or ((E and F) -> E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E and F) -> E)) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-500 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-56761.        ((((A -> B) -> (A -> C)) -> ((D or ((E and F) -> E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E and F) -> E)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-500, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56762
in-theory        56762
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D or ((E and F) -> E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E and F) -> E))))
theorem-size     37
proof            (modus-ponens tm-697 tm-501 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-56762.        ((((A -> B) -> (A -> C)) -> (D or ((E and F) -> E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E and F) -> E)))), M:tm-697, m:tm-501, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-56763
in-theory        56763
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D or ((E and F) -> F)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E and F) -> F)) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-510 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-4)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-56763.        ((((A -> B) -> (A -> C)) -> ((D or ((E and F) -> F)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((E and F) -> F)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-510, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56764
in-theory        56764
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D or ((E and F) -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E and F) -> F))))
theorem-size     37
proof            (modus-ponens tm-697 tm-511 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-56764.        ((((A -> B) -> (A -> C)) -> (D or ((E and F) -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((E and F) -> F)))), M:tm-697, m:tm-511, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-56765
in-theory        56765
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D or (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-697 tm-520 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-56765.        ((((A -> B) -> (A -> C)) -> ((D or (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-520, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56766
in-theory        56766
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D or (E -> (F -> (E and F))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (F -> (E and F))))))
theorem-size     41
proof            (modus-ponens tm-697 tm-521 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-56766.        ((((A -> B) -> (A -> C)) -> (D or (E -> (F -> (E and F))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (F -> (E and F)))))), M:tm-697, m:tm-521, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-56767
in-theory        56767
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D or (E -> (E or F))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (E or F))) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-530 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7 tm-6)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-56767.        ((((A -> B) -> (A -> C)) -> ((D or (E -> (E or F))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (E or F))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-530, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56768
in-theory        56768
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D or (E -> (E or F)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (E or F)))))
theorem-size     37
proof            (modus-ponens tm-697 tm-531 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7 tm-6)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-56768.        ((((A -> B) -> (A -> C)) -> (D or (E -> (E or F)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (E or F))))), M:tm-697, m:tm-531, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-56769
in-theory        56769
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D or (E -> (F or E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (F or E))) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-540 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-56769.        ((((A -> B) -> (A -> C)) -> ((D or (E -> (F or E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or (E -> (F or E))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-540, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56770
in-theory        56770
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D or (E -> (F or E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (F or E)))))
theorem-size     37
proof            (modus-ponens tm-697 tm-541 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-56770.        ((((A -> B) -> (A -> C)) -> (D or (E -> (F or E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or (E -> (F or E))))), M:tm-697, m:tm-541, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-56771
in-theory        56771
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> (E or D)) or F) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E or D)) or F) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-550 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-6 tm-7)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-56771.        ((((A -> B) -> (A -> C)) -> (((D -> (E or D)) or F) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E or D)) or F) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-550, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56772
in-theory        56772
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (E or D)) or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) or F)))
theorem-size     37
proof            (modus-ponens tm-697 tm-551 ((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-6 tm-7)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-56772.        ((((A -> B) -> (A -> C)) -> ((D -> (E or D)) or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) or F))), M:tm-697, m:tm-551, u:((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-56773
in-theory        56773
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E or D)) and ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E or D)) and ((A -> B) -> (A -> C))))))
theorem-size     65
proof            (modus-ponens tm-697 tm-595 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-56773.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E or D)) and ((A -> B) -> (A -> C))))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((D -> (E or D)) and ((A -> B) -> (A -> C)))))), M:tm-697, m:tm-595, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-56774
in-theory        56774
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F or E)) and D)) and ((A -> B) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-697 tm-605 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-7)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-56774.        ((((A -> B) -> (A -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((E -> (F or E)) and D)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-605, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56775
in-theory        56775
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> ((E -> (F or E)) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F or E)) and D))))
theorem-size     41
proof            (modus-ponens tm-697 tm-606 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-56775.        ((((A -> B) -> (A -> C)) -> (D -> ((E -> (F or E)) and D))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((E -> (F or E)) and D)))), M:tm-697, m:tm-606, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-56776
in-theory        56776
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (E or D)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (E or D)))))
theorem-size     49
proof            (modus-ponens tm-697 tm-609 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-56776.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (E or D)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and (D -> (E or D))))), M:tm-697, m:tm-609, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-56777
in-theory        56777
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> (A -> C)) -> ((D or (A -> (B or A))) -> (A -> C))) and (((A -> ((B or A) -> C)) or ((A -> (B or A)) -> (A -> C))) -> ((D or (A -> (B or A))) -> (A -> C))))
theorem-size     51
proof            (modus-ponens tm-697 tm-619 ((A Am) (B (or Bm Am)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (or Bm Am))) (-> Am C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-56777.        ((((A -> (B or A)) -> (A -> C)) -> ((D or (A -> (B or A))) -> (A -> C))) and (((A -> ((B or A) -> C)) or ((A -> (B or A)) -> (A -> C))) -> ((D or (A -> (B or A))) -> (A -> C)))), M:tm-697, m:tm-619, u:((A Am) (B (or Bm Am)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (or Bm Am))) (-> Am C))))
================================================================
tm-name          tm-56778
in-theory        56778
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> (E -> (F or E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (F or E))) and ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-697 tm-622 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-56778.        ((((A -> B) -> (A -> C)) -> ((D -> (E -> (F or E))) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (F or E))) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-622, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56779
in-theory        56779
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((A -> B) -> (D or (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D or (A -> C)))))
theorem-size     41
proof            (modus-ponens tm-697 tm-623 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (or Cm (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-56779.        ((((A -> B) -> (A -> C)) -> ((A -> B) -> (D or (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (D or (A -> C))))), M:tm-697, m:tm-623, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (or Cm (-> A C)))))
================================================================
tm-name          tm-56780
in-theory        56780
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> (E -> (F or E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (F or E)))))
theorem-size     37
proof            (modus-ponens tm-697 tm-624 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-7)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-56780.        ((((A -> B) -> (A -> C)) -> (D -> (E -> (F or E)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (F or E))))), M:tm-697, m:tm-624, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-56781
in-theory        56781
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((B or (A -> B)) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((B or (A -> B)) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-697 tm-654 ((A Am) (B Bm) (Cm (-> Am C)) (D (and (-> (-> Am Bm) (-> Am C)) (-> (or Bm (-> Am Bm)) (-> Am C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       251
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-56781.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((B or (A -> B)) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((B or (A -> B)) -> (A -> C))))), M:tm-697, m:tm-654, u:((A Am) (B Bm) (Cm (-> Am C)) (D (and (-> (-> Am Bm) (-> Am C)) (-> (or Bm (-> Am Bm)) (-> Am C)))))
================================================================
tm-name          tm-56782
in-theory        56782
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> ((A or (B -> A)) -> D)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((A or (B -> A)) -> D))) and ((((A or (B -> A)) -> (C -> D)) or (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> D))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((A or (B -> A)) -> D))))
theorem-size     85
proof            (modus-ponens tm-697 tm-662 ((A (or Am (-> Bm Am))) (B Cm) (Dm (-> (or Am (-> Bm Am)) C)) (D (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (-> (or Am (-> Bm Am)) C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       269
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-56782.        (((((A or (B -> A)) -> C) -> ((A or (B -> A)) -> D)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((A or (B -> A)) -> D))) and ((((A or (B -> A)) -> (C -> D)) or (((A or (B -> A)) -> C) -> ((A or (B -> A)) -> D))) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((A or (B -> A)) -> D)))), M:tm-697, m:tm-662, u:((A (or Am (-> Bm Am))) (B Cm) (Dm (-> (or Am (-> Bm Am)) C)) (D (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (-> (or Am (-> Bm Am)) C))))
================================================================
tm-name          tm-56783
in-theory        56783
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> B) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-697 tm-665 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-56783.        ((((A -> B) -> (A -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-665, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-56784
in-theory        56784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))))
theorem-size     49
proof            (modus-ponens tm-697 tm-667 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-56784.        ((((A -> B) -> (A -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))), M:tm-697, m:tm-667, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-56785
in-theory        56785
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) -> ((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))))
theorem-size     105
proof            (modus-ponens tm-697 tm-697 ((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) C)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       335
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56785.        (((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) -> ((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))), M:tm-697, m:tm-697, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) C)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C)))))
================================================================
tm-name          tm-56786
in-theory        56786
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     49
proof            (modus-ponens tm-665 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56786.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-665, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56787
in-theory        56787
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((D or (((A -> B) -> (A -> C)) -> D)) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     73
proof            (modus-ponens tm-654 tm-697 ((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       267
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56787.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((D or (((A -> B) -> (A -> C)) -> D)) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-654, m:tm-697, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56788
in-theory        56788
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> (E or ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     37
proof            (modus-ponens tm-623 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56788.        ((((A -> B) -> (A -> C)) -> D) -> (E or ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-623, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56789
in-theory        56789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-622 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56789.        ((A -> (B -> (C or B))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-622, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56790
in-theory        56790
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (E or ((B -> C) -> (B -> D))))) -> ((((B -> C) -> (B -> D)) -> (E or ((B -> C) -> (B -> D)))) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E or ((B -> C) -> (B -> D))))))
theorem-size     61
proof            (modus-ponens tm-619 tm-697 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (or B (-> (-> Am Bm) (-> Am Cm)))) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) (or B (-> (-> Am Bm) (-> Am Cm)))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or B (-> (-> Am Bm) (-> Am Cm))))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56790.        ((A or (((B -> C) -> (B -> D)) -> (E or ((B -> C) -> (B -> D))))) -> ((((B -> C) -> (B -> D)) -> (E or ((B -> C) -> (B -> D)))) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E or ((B -> C) -> (B -> D)))))), M:tm-619, m:tm-697, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (or B (-> (-> Am Bm) (-> Am Cm)))) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) (or B (-> (-> Am Bm) (-> Am Cm)))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or B (-> (-> Am Bm) (-> Am Cm)))))))
================================================================
tm-name          tm-56791
in-theory        56791
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (E -> (F or E)))
theorem-size     41
proof            (modus-ponens tm-609 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56791.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (E -> (F or E))), M:tm-609, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56792
in-theory        56792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     45
proof            (modus-ponens tm-605 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56792.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-605, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56793
in-theory        56793
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((E -> (F or E)) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))))
theorem-size     77
proof            (modus-ponens tm-595 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       253
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56793.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((E -> (F or E)) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))), M:tm-595, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56794
in-theory        56794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-550 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56794.        (((A -> (B or A)) or C) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-550, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56795
in-theory        56795
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-540 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56795.        ((A or (B -> (C or B))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-540, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56796
in-theory        56796
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-530 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56796.        ((A or (B -> (B or C))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-530, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56797
in-theory        56797
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     45
proof            (modus-ponens tm-520 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56797.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-520, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56798
in-theory        56798
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-510 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56798.        ((A or ((B and C) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-510, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56799
in-theory        56799
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-500 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56799.        ((A or ((B and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-500, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56800
in-theory        56800
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> ((((E -> F) -> (E -> G)) -> H) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     51
proof            (modus-ponens tm-490 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56800.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> ((((E -> F) -> (E -> G)) -> H) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-490, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56801
in-theory        56801
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-480 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56801.        ((A or (B -> (C -> B))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-480, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56802
in-theory        56802
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> (((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E))
theorem-size     37
proof            (modus-ponens tm-470 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56802.        ((((A -> B) -> (A -> C)) -> D) -> (((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E)), M:tm-470, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56803
in-theory        56803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-469 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56803.        ((A -> (B -> (B or C))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-469, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56804
in-theory        56804
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (((B -> C) -> (B -> D)) or E))) -> ((((B -> C) -> (B -> D)) -> (((B -> C) -> (B -> D)) or E)) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (B -> D)) or E))))
theorem-size     61
proof            (modus-ponens tm-466 tm-697 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (or (-> (-> Am Bm) (-> Am Cm)) B)) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) (or (-> (-> Am Bm) (-> Am Cm)) B)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56804.        ((A or (((B -> C) -> (B -> D)) -> (((B -> C) -> (B -> D)) or E))) -> ((((B -> C) -> (B -> D)) -> (((B -> C) -> (B -> D)) or E)) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> (B -> D)) or E)))), M:tm-466, m:tm-697, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (or (-> (-> Am Bm) (-> Am Cm)) B)) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) (or (-> (-> Am Bm) (-> Am Cm)) B)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) B)))))
================================================================
tm-name          tm-56805
in-theory        56805
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (E -> (E or F)))
theorem-size     41
proof            (modus-ponens tm-456 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56805.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (E -> (E or F))), M:tm-456, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56806
in-theory        56806
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     45
proof            (modus-ponens tm-453 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56806.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-453, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56807
in-theory        56807
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((E -> (E or F)) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))))
theorem-size     77
proof            (modus-ponens tm-443 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       253
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56807.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((E -> (E or F)) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))), M:tm-443, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56808
in-theory        56808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-409 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56808.        (((A -> (A or B)) or C) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-409, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56809
in-theory        56809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     45
proof            (modus-ponens tm-400 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56809.        (((A -> (B -> (A and B))) or C) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-400, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56810
in-theory        56810
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-391 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56810.        ((((A and B) -> B) or C) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-391, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56811
in-theory        56811
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-382 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56811.        ((((A and B) -> A) or C) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-382, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56812
in-theory        56812
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> (E -> G)) -> H) -> ((((E -> F) -> (E -> G)) -> H) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     51
proof            (modus-ponens tm-373 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56812.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> (E -> G)) -> H) -> ((((E -> F) -> (E -> G)) -> H) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-373, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56813
in-theory        56813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-364 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56813.        (((A -> (B -> A)) or C) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-364, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56814
in-theory        56814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> (E -> (((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and E)))
theorem-size     39
proof            (modus-ponens tm-355 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56814.        ((((A -> B) -> (A -> C)) -> D) -> (E -> (((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and E))), M:tm-355, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56815
in-theory        56815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     45
proof            (modus-ponens tm-354 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56815.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-354, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56816
in-theory        56816
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (E -> (((B -> C) -> (B -> D)) and E)))) -> ((((B -> C) -> (B -> D)) -> (E -> (((B -> C) -> (B -> D)) and E))) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (((B -> C) -> (B -> D)) and E)))))
theorem-size     67
proof            (modus-ponens tm-351 tm-697 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (-> B (and (-> (-> Am Bm) (-> Am Cm)) B))) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> B (and (-> (-> Am Bm) (-> Am Cm)) B))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B (and (-> (-> Am Bm) (-> Am Cm)) B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56816.        ((A or (((B -> C) -> (B -> D)) -> (E -> (((B -> C) -> (B -> D)) and E)))) -> ((((B -> C) -> (B -> D)) -> (E -> (((B -> C) -> (B -> D)) and E))) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> (((B -> C) -> (B -> D)) and E))))), M:tm-351, m:tm-697, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (-> B (and (-> (-> Am Bm) (-> Am Cm)) B))) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> B (and (-> (-> Am Bm) (-> Am Cm)) B))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B (and (-> (-> Am Bm) (-> Am Cm)) B))))))
================================================================
tm-name          tm-56817
in-theory        56817
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (E -> (F -> (E and F))))
theorem-size     43
proof            (modus-ponens tm-341 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56817.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56818
in-theory        56818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     45
proof            (modus-ponens tm-338 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56818.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-338, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56819
in-theory        56819
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and D))) -> ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and D))))
theorem-size     69
proof            (modus-ponens tm-335 tm-697 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (and (-> (-> Am Bm) (-> Am Cm)) B)) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) (and (-> (-> Am Bm) (-> Am Cm)) B)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Am Bm) (-> Am Cm)) B))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       245
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56819.        (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and D))) -> ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and D)))), M:tm-335, m:tm-697, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (and (-> (-> Am Bm) (-> Am Cm)) B)) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) (and (-> (-> Am Bm) (-> Am Cm)) B)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Am Bm) (-> Am Cm)) B)))))
================================================================
tm-name          tm-56820
in-theory        56820
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))))
theorem-size     81
proof            (modus-ponens tm-328 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       267
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56820.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))), M:tm-328, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56821
in-theory        56821
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((E -> (F -> (E and F))) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))))
theorem-size     79
proof            (modus-ponens tm-327 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       261
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56821.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((E -> (F -> (E and F))) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))), M:tm-327, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56822
in-theory        56822
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((E and F) -> F) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))))
theorem-size     77
proof            (modus-ponens tm-326 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       253
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56822.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((E and F) -> F) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))), M:tm-326, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56823
in-theory        56823
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((E and F) -> E) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))))
theorem-size     77
proof            (modus-ponens tm-325 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       253
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56823.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((E and F) -> E) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))), M:tm-325, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56824
in-theory        56824
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))))
theorem-size     85
proof            (modus-ponens tm-324 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       285
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56824.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))), M:tm-324, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56825
in-theory        56825
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((E -> (F -> E)) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))))
theorem-size     77
proof            (modus-ponens tm-323 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       253
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56825.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((E -> (F -> E)) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))), M:tm-323, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56826
in-theory        56826
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((E and F) -> F))
theorem-size     41
proof            (modus-ponens tm-322 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56826.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56827
in-theory        56827
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((E and F) -> E))
theorem-size     41
proof            (modus-ponens tm-320 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56827.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56828
in-theory        56828
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     49
proof            (modus-ponens tm-318 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56828.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56829
in-theory        56829
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)))
theorem-size     55
proof            (modus-ponens tm-316 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56829.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D))), M:tm-316, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56830
in-theory        56830
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (E -> (F -> E)))
theorem-size     41
proof            (modus-ponens tm-315 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56830.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56831
in-theory        56831
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((((A -> B) -> (A -> C)) -> D) -> (not ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (not (((A -> B) -> (A -> C)) -> D))))
theorem-size     83
proof            (modus-ponens tm-313 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       253
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56831.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((((A -> B) -> (A -> C)) -> D) -> (not ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (not (((A -> B) -> (A -> C)) -> D)))), M:tm-313, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56832
in-theory        56832
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> (((((A -> B) -> (A -> C)) -> D) or ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> E)))
theorem-size     101
proof            (modus-ponens tm-312 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       275
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56832.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> (((((A -> B) -> (A -> C)) -> D) or ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> E))), M:tm-312, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56833
in-theory        56833
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (E or ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))))
theorem-size     73
proof            (modus-ponens tm-311 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56833.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (E or ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))), M:tm-311, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56834
in-theory        56834
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) or E))
theorem-size     73
proof            (modus-ponens tm-310 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56834.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) or E)), M:tm-310, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56835
in-theory        56835
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (E -> (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and E)))
theorem-size     75
proof            (modus-ponens tm-309 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56835.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (E -> (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and E))), M:tm-309, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56836
in-theory        56836
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (E -> ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))))
theorem-size     73
proof            (modus-ponens tm-305 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56836.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (E -> ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))), M:tm-305, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56837
in-theory        56837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     47
proof            (modus-ponens tm-303 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56837.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-303, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56838
in-theory        56838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     45
proof            (modus-ponens tm-270 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56838.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-270, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56839
in-theory        56839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     45
proof            (modus-ponens tm-239 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56839.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-239, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56840
in-theory        56840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> (E -> G)) -> H) -> ((((E -> F) -> (E -> G)) -> H) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     53
proof            (modus-ponens tm-210 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56840.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> (E -> G)) -> H) -> ((((E -> F) -> (E -> G)) -> H) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-210, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56841
in-theory        56841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     45
proof            (modus-ponens tm-183 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56841.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-183, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56842
in-theory        56842
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-157 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56842.        ((A -> ((B and C) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-157, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56843
in-theory        56843
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     51
proof            (modus-ponens tm-147 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56843.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-147, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56844
in-theory        56844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-134 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56844.        ((A -> ((B and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-134, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56845
in-theory        56845
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     51
proof            (modus-ponens tm-125 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56845.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-125, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56846
in-theory        56846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> ((((E -> F) -> (E -> G)) -> H) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     51
proof            (modus-ponens tm-113 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56846.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> ((((E -> F) -> (E -> G)) -> H) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-113, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56847
in-theory        56847
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (((B -> C) -> B) -> ((B -> C) -> D)))) -> ((((B -> C) -> (B -> D)) -> (((B -> C) -> B) -> ((B -> C) -> D))) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> B) -> ((B -> C) -> D)))))
theorem-size     67
proof            (modus-ponens tm-110 tm-697 ((A (-> Am Bm)) (B Am) (C Cm) (Dm (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))) (D (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       261
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56847.        ((A or (((B -> C) -> (B -> D)) -> (((B -> C) -> B) -> ((B -> C) -> D)))) -> ((((B -> C) -> (B -> D)) -> (((B -> C) -> B) -> ((B -> C) -> D))) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (((B -> C) -> B) -> ((B -> C) -> D))))), M:tm-110, m:tm-697, u:((A (-> Am Bm)) (B Am) (C Cm) (Dm (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))) (D (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
================================================================
tm-name          tm-56848
in-theory        56848
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     55
proof            (modus-ponens tm-105 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       245
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56848.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-105, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56849
in-theory        56849
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((A -> B) -> A)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> C))) -> ((((A -> B) -> (A -> C)) -> ((A -> B) -> C)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> C))))
theorem-size     61
proof            (modus-ponens tm-102 tm-697 ((A (-> Am Bm)) (B Am) (C Cm) (Dm (-> (-> Am Bm) Cm)) (D (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Cm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       267
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56849.        (((((A -> B) -> (A -> C)) -> ((A -> B) -> A)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> C))) -> ((((A -> B) -> (A -> C)) -> ((A -> B) -> C)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> C)))), M:tm-102, m:tm-697, u:((A (-> Am Bm)) (B Am) (C Cm) (Dm (-> (-> Am Bm) Cm)) (D (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Cm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-56850
in-theory        56850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     43
proof            (modus-ponens tm-95 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56850.        (((A -> B) -> (A -> A)) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-95, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56851
in-theory        56851
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> C)))))
theorem-size     63
proof            (modus-ponens tm-92 tm-697 ((Dm (-> (-> Am Bm) (-> Am Cm))) (A (-> (-> Am Bm) (-> Am Cm))) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56851.        (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> C))))), M:tm-92, m:tm-697, u:((Dm (-> (-> Am Bm) (-> Am Cm))) (A (-> (-> Am Bm) (-> Am Cm))) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-56852
in-theory        56852
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> (E -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     37
proof            (modus-ponens tm-84 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56852.        ((((A -> B) -> (A -> C)) -> D) -> (E -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-84, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56853
in-theory        56853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     43
proof            (modus-ponens tm-83 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56853.        ((A -> (B -> (C -> B))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-83, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56854
in-theory        56854
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (E -> ((B -> C) -> (B -> D))))) -> ((((B -> C) -> (B -> D)) -> (E -> ((B -> C) -> (B -> D)))) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> ((B -> C) -> (B -> D))))))
theorem-size     61
proof            (modus-ponens tm-80 tm-697 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (-> B (-> (-> Am Bm) (-> Am Cm)))) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> B (-> (-> Am Bm) (-> Am Cm)))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B (-> (-> Am Bm) (-> Am Cm))))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56854.        ((A or (((B -> C) -> (B -> D)) -> (E -> ((B -> C) -> (B -> D))))) -> ((((B -> C) -> (B -> D)) -> (E -> ((B -> C) -> (B -> D)))) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> ((B -> C) -> (B -> D)))))), M:tm-80, m:tm-697, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (-> B (-> (-> Am Bm) (-> Am Cm)))) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> B (-> (-> Am Bm) (-> Am Cm)))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B (-> (-> Am Bm) (-> Am Cm)))))))
================================================================
tm-name          tm-56855
in-theory        56855
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) -> (B -> D)) -> E) -> ((((B -> C) -> (B -> D)) -> E) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     41
proof            (modus-ponens tm-76 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56855.        (((not (not A)) -> A) and ((((B -> C) -> (B -> D)) -> E) -> ((((B -> C) -> (B -> D)) -> E) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-76, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56856
in-theory        56856
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) -> (A -> C)) -> D))) or (((A -> B) -> (A -> C)) -> D)) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     47
proof            (modus-ponens tm-73 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56856.        (((not (not (((A -> B) -> (A -> C)) -> D))) or (((A -> B) -> (A -> C)) -> D)) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-73, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56857
in-theory        56857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     47
proof            (modus-ponens tm-69 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56857.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-69, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56858
in-theory        56858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     49
proof            (modus-ponens tm-54 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56858.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-54, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56859
in-theory        56859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> ((((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D))) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D)))))
theorem-size     65
proof            (modus-ponens tm-51 tm-697 ((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (or C (-> Am Bm)) (-> Am Cm))) (D (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> (or C (-> Am Bm)) (-> Am Cm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or C (-> Am Bm)) (-> Am Cm)))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       233
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56859.        (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> ((((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D))) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((A or (B -> C)) -> (B -> D))))), M:tm-51, m:tm-697, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (or C (-> Am Bm)) (-> Am Cm))) (D (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> (or C (-> Am Bm)) (-> Am Cm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or C (-> Am Bm)) (-> Am Cm))))))
================================================================
tm-name          tm-56860
in-theory        56860
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> ((((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D)))) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D))))))
theorem-size     61
proof            (modus-ponens tm-48 tm-697 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (and B (-> (-> Am Bm) (-> Am Cm)))) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) (and B (-> (-> Am Bm) (-> Am Cm)))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and B (-> (-> Am Bm) (-> Am Cm))))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       213
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56860.        ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> ((((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D)))) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D)))))), M:tm-48, m:tm-697, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (and B (-> (-> Am Bm) (-> Am Cm)))) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) (and B (-> (-> Am Bm) (-> Am Cm)))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and B (-> (-> Am Bm) (-> Am Cm)))))))
================================================================
tm-name          tm-56861
in-theory        56861
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> ((((B -> C) -> (B -> D)) -> E) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     47
proof            (modus-ponens tm-47 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56861.        (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> ((((B -> C) -> (B -> D)) -> E) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-47, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56862
in-theory        56862
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     47
proof            (modus-ponens tm-46 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56862.        ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-46, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56863
in-theory        56863
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))
theorem-size     57
proof            (modus-ponens tm-45 tm-697 ((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) C)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       223
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56863.        ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> ((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))), M:tm-45, m:tm-697, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) C)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C)))))
================================================================
tm-name          tm-56864
in-theory        56864
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> A)) -> ((((B -> C) -> (B -> D)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))
theorem-size     37
proof            (modus-ponens tm-44 tm-697 ((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56864.        ((A or (((B -> C) -> (B -> D)) -> A)) -> ((((B -> C) -> (B -> D)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))), M:tm-44, m:tm-697, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56865
in-theory        56865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     41
proof            (modus-ponens tm-42 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56865.        ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-42, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56866
in-theory        56866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     41
proof            (modus-ponens tm-32 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56866.        ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-32, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56867
in-theory        56867
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     45
proof            (modus-ponens tm-24 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56867.        ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-24, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56868
in-theory        56868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     43
proof            (modus-ponens tm-23 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56868.        ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-23, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56869
in-theory        56869
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     41
proof            (modus-ponens tm-22 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56869.        (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-22, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56870
in-theory        56870
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     41
proof            (modus-ponens tm-21 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56870.        (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-21, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56871
in-theory        56871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     49
proof            (modus-ponens tm-20 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56871.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-20, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56872
in-theory        56872
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     41
proof            (modus-ponens tm-19 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56872.        ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> ((((C -> D) -> (C -> E)) -> F) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-19, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56873
in-theory        56873
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (not ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (not (((A -> B) -> (A -> C)) -> D)))
theorem-size     47
proof            (modus-ponens tm-9 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-9 tm-2 tm-5 tm-8)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56873.        (((((A -> B) -> (A -> C)) -> D) -> (not ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56874
in-theory        56874
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> (((((A -> B) -> (A -> C)) -> D) or ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> E))
theorem-size     65
proof            (modus-ponens tm-8 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       193
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56874.        ((((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> (((((A -> B) -> (A -> C)) -> D) or ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> E)), M:tm-8, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-56875
in-theory        56875
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) -> (B -> D)) -> E) -> ((((B -> C) -> (B -> D)) -> E) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     37
proof            (modus-ponens tm-7 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-7 tm-2 tm-5 tm-8)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56875.        (A or ((((B -> C) -> (B -> D)) -> E) -> ((((B -> C) -> (B -> D)) -> E) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-7, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56876
in-theory        56876
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) or E)
theorem-size     37
proof            (modus-ponens tm-6 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-6 tm-2 tm-5 tm-8)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56876.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) or E), M:tm-6, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56877
in-theory        56877
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> (B -> D)) -> E) -> ((((B -> C) -> (B -> D)) -> E) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and A))
theorem-size     39
proof            (modus-ponens tm-5 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56877.        (A -> (((((B -> C) -> (B -> D)) -> E) -> ((((B -> C) -> (B -> D)) -> E) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and A)), M:tm-5, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56878
in-theory        56878
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (B -> D)) -> E) -> ((((B -> C) -> (B -> D)) -> E) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     37
proof            (modus-ponens tm-1 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-1 tm-2 tm-5 tm-8)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56878.        (A -> ((((B -> C) -> (B -> D)) -> E) -> ((((B -> C) -> (B -> D)) -> E) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-1, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-56879
in-theory        56879
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-665 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56879.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-665, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56880
in-theory        56880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-622 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56880.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-622, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56881
in-theory        56881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H or G)))
theorem-size     39
proof            (modus-ponens tm-609 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56881.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H or G))), M:tm-609, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56882
in-theory        56882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-605 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56882.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-605, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56883
in-theory        56883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H or G)) and ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-595 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56883.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H or G)) and ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-595, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56884
in-theory        56884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-550 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56884.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-550, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56885
in-theory        56885
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-540 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56885.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-540, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56886
in-theory        56886
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-530 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56886.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-530, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56887
in-theory        56887
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-520 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56887.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-520, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56888
in-theory        56888
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-510 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56888.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-510, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56889
in-theory        56889
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-500 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56889.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-500, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56890
in-theory        56890
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-490 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56890.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-490, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56891
in-theory        56891
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-480 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56891.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-480, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56892
in-theory        56892
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-469 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56892.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-469, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56893
in-theory        56893
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (G or H)))
theorem-size     39
proof            (modus-ponens tm-456 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56893.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (G or H))), M:tm-456, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56894
in-theory        56894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-453 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56894.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-453, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56895
in-theory        56895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (G or H)) and ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-443 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56895.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (G or H)) and ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-443, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56896
in-theory        56896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-409 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56896.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-409, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56897
in-theory        56897
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-400 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56897.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-400, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56898
in-theory        56898
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-391 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56898.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-391, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56899
in-theory        56899
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-382 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56899.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-382, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56900
in-theory        56900
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-373 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56900.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-373, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56901
in-theory        56901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-364 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56901.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-364, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56902
in-theory        56902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-354 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56902.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-354, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56903
in-theory        56903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> (G and H))))
theorem-size     41
proof            (modus-ponens tm-341 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56903.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56904
in-theory        56904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     43
proof            (modus-ponens tm-338 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56904.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-338, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56905
in-theory        56905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> (G and H))) and ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     75
proof            (modus-ponens tm-327 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       251
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56905.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> (G and H))) and ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-327, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56906
in-theory        56906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> H) and ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-326 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56906.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> H) and ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-326, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56907
in-theory        56907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> G) and ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-325 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56907.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> G) and ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-325, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56908
in-theory        56908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     81
proof            (modus-ponens tm-324 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       275
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56908.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-324, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56909
in-theory        56909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> G)) and ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     73
proof            (modus-ponens tm-323 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56909.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> G)) and ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-323, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56910
in-theory        56910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> H))
theorem-size     39
proof            (modus-ponens tm-322 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56910.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56911
in-theory        56911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> G))
theorem-size     39
proof            (modus-ponens tm-320 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56911.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56912
in-theory        56912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     47
proof            (modus-ponens tm-318 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56912.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56913
in-theory        56913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> G)))
theorem-size     39
proof            (modus-ponens tm-315 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56913.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56914
in-theory        56914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G or ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-311 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56914.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G or ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-311, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56915
in-theory        56915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G))
theorem-size     69
proof            (modus-ponens tm-310 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56915.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G)), M:tm-310, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56916
in-theory        56916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and G)))
theorem-size     71
proof            (modus-ponens tm-309 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56916.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and G))), M:tm-309, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56917
in-theory        56917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     59
proof            (modus-ponens tm-308 tm-698 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56917.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-308, m:tm-698, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-56918
in-theory        56918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (A -> (B -> (A and B))))
theorem-size     41
proof            (modus-ponens tm-307 tm-698 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56918.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-698, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-56919
in-theory        56919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-305 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56919.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-305, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56920
in-theory        56920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-303 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56920.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-303, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56921
in-theory        56921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-270 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56921.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-270, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56922
in-theory        56922
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-239 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56922.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-239, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56923
in-theory        56923
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     51
proof            (modus-ponens tm-210 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56923.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-210, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56924
in-theory        56924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-183 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56924.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-183, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56925
in-theory        56925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-157 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56925.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-157, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56926
in-theory        56926
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     49
proof            (modus-ponens tm-147 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56926.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-147, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56927
in-theory        56927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-134 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56927.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-134, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56928
in-theory        56928
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     49
proof            (modus-ponens tm-125 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56928.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-125, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56929
in-theory        56929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-113 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56929.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-113, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56930
in-theory        56930
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     53
proof            (modus-ponens tm-105 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56930.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-105, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56931
in-theory        56931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-95 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56931.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-95, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56932
in-theory        56932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-83 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56932.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-83, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56933
in-theory        56933
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     39
proof            (modus-ponens tm-76 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56933.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-76, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56934
in-theory        56934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     45
proof            (modus-ponens tm-69 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56934.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-69, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56935
in-theory        56935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-54 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56935.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-54, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56936
in-theory        56936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-42 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56936.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-42, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56937
in-theory        56937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-32 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56937.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-32, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56938
in-theory        56938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-23 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56938.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-23, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56939
in-theory        56939
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-22 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56939.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-22, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56940
in-theory        56940
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-21 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56940.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-21, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56941
in-theory        56941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-20 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56941.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-20, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56942
in-theory        56942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-19 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56942.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-19, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56943
in-theory        56943
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     35
proof            (modus-ponens tm-7 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56943.        (A or ((B -> (C -> (B and C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-7, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56944
in-theory        56944
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G)
theorem-size     35
proof            (modus-ponens tm-6 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56944.        (((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G), M:tm-6, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56945
in-theory        56945
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and A))
theorem-size     37
proof            (modus-ponens tm-5 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56945.        (A -> (((B -> (C -> (B and C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and A)), M:tm-5, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56946
in-theory        56946
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     35
proof            (modus-ponens tm-1 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56946.        (A -> ((B -> (C -> (B and C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-1, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56947
in-theory        56947
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-665 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56947.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-665, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56948
in-theory        56948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-622 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56948.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-622, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56949
in-theory        56949
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H or G)))
theorem-size     37
proof            (modus-ponens tm-609 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56949.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H or G))), M:tm-609, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56950
in-theory        56950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-605 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56950.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-605, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56951
in-theory        56951
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H or G)) and (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-595 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56951.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H or G)) and (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-595, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56952
in-theory        56952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-550 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56952.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-550, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56953
in-theory        56953
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-540 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56953.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-540, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56954
in-theory        56954
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-530 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56954.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-530, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56955
in-theory        56955
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-520 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56955.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-520, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56956
in-theory        56956
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-510 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56956.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-510, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56957
in-theory        56957
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-500 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56957.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-500, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56958
in-theory        56958
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-490 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56958.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-490, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56959
in-theory        56959
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-480 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56959.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-480, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56960
in-theory        56960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-469 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56960.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-469, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56961
in-theory        56961
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (G or H)))
theorem-size     37
proof            (modus-ponens tm-456 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56961.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (G or H))), M:tm-456, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56962
in-theory        56962
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-453 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56962.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-453, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56963
in-theory        56963
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (G or H)) and (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-443 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56963.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (G or H)) and (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-443, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56964
in-theory        56964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-409 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56964.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-409, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56965
in-theory        56965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-400 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56965.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-400, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56966
in-theory        56966
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-391 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56966.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-391, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56967
in-theory        56967
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-382 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56967.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-382, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56968
in-theory        56968
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-373 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56968.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-373, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56969
in-theory        56969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-364 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56969.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-364, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56970
in-theory        56970
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-354 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56970.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-354, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56971
in-theory        56971
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> (G and H))))
theorem-size     39
proof            (modus-ponens tm-341 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56971.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56972
in-theory        56972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-338 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56972.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-338, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56973
in-theory        56973
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> (G and H))) and (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     71
proof            (modus-ponens tm-327 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56973.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> (G and H))) and (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-327, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56974
in-theory        56974
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> H) and (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-326 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56974.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> H) and (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-326, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56975
in-theory        56975
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> G) and (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-325 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56975.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> G) and (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-325, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56976
in-theory        56976
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     77
proof            (modus-ponens tm-324 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       265
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56976.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-324, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56977
in-theory        56977
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> G)) and (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-323 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56977.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> G)) and (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-323, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56978
in-theory        56978
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> H))
theorem-size     37
proof            (modus-ponens tm-322 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56978.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56979
in-theory        56979
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> G))
theorem-size     37
proof            (modus-ponens tm-320 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56979.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56980
in-theory        56980
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     45
proof            (modus-ponens tm-318 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56980.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56981
in-theory        56981
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> G)))
theorem-size     37
proof            (modus-ponens tm-315 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56981.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56982
in-theory        56982
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G or (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     65
proof            (modus-ponens tm-311 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56982.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G or (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-311, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56983
in-theory        56983
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G))
theorem-size     65
proof            (modus-ponens tm-310 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56983.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G)), M:tm-310, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56984
in-theory        56984
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and G)))
theorem-size     67
proof            (modus-ponens tm-309 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56984.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and G))), M:tm-309, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56985
in-theory        56985
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     57
proof            (modus-ponens tm-308 tm-699 ((A (-> (and Am Bm) Bm)) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56985.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-308, m:tm-699, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-56986
in-theory        56986
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((A and B) -> B))
theorem-size     37
proof            (modus-ponens tm-307 tm-699 ((A (-> (and Am Bm) Bm)) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56986.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((A and B) -> B)), M:tm-307, m:tm-699, u:((A (-> (and Am Bm) Bm)) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-56987
in-theory        56987
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     65
proof            (modus-ponens tm-305 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56987.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-305, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56988
in-theory        56988
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-303 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56988.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-303, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56989
in-theory        56989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-270 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56989.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-270, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56990
in-theory        56990
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-239 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56990.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-239, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56991
in-theory        56991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-210 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56991.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-210, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56992
in-theory        56992
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-183 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56992.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-183, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56993
in-theory        56993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-157 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56993.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-157, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56994
in-theory        56994
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-147 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56994.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-147, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56995
in-theory        56995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-134 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56995.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-134, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56996
in-theory        56996
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-125 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56996.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-125, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56997
in-theory        56997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-113 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56997.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-113, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56998
in-theory        56998
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     51
proof            (modus-ponens tm-105 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56998.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-105, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-56999
in-theory        56999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-95 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-56999.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-95, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57000
in-theory        57000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-83 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57000.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-83, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57001
in-theory        57001
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     37
proof            (modus-ponens tm-76 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57001.        (((not (not A)) -> A) and (((B and C) -> C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-76, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57002
in-theory        57002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     43
proof            (modus-ponens tm-69 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57002.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-69, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57003
in-theory        57003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-54 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57003.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-54, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57004
in-theory        57004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-42 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57004.        ((A -> (B or A)) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-42, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57005
in-theory        57005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-32 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57005.        ((A -> (A or B)) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-32, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57006
in-theory        57006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-23 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57006.        ((A -> (B -> (A and B))) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-23, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57007
in-theory        57007
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-22 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57007.        (((A and B) -> B) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-22, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57008
in-theory        57008
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-21 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57008.        (((A and B) -> A) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-21, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57009
in-theory        57009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-20 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57009.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-20, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57010
in-theory        57010
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-19 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57010.        ((A -> (B -> A)) and (((C and D) -> D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-19, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57011
in-theory        57011
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-7 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-7 tm-5 tm-4 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57011.        (A or (((B and C) -> C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-7, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57012
in-theory        57012
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G)
theorem-size     33
proof            (modus-ponens tm-6 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-6 tm-5 tm-4 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57012.        ((((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G), M:tm-6, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57013
in-theory        57013
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57013.        (A -> ((((B and C) -> C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and A)), M:tm-5, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57014
in-theory        57014
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-1 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-1 tm-5 tm-4 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57014.        (A -> (((B and C) -> C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-1, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57015
in-theory        57015
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-665 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57015.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-665, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57016
in-theory        57016
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-622 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57016.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-622, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57017
in-theory        57017
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H or G)))
theorem-size     37
proof            (modus-ponens tm-609 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57017.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H or G))), M:tm-609, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57018
in-theory        57018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-605 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57018.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-605, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57019
in-theory        57019
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H or G)) and (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-595 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57019.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H or G)) and (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-595, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57020
in-theory        57020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-550 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57020.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-550, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57021
in-theory        57021
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-540 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57021.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-540, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57022
in-theory        57022
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-530 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57022.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-530, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57023
in-theory        57023
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-520 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57023.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-520, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57024
in-theory        57024
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-510 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57024.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-510, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57025
in-theory        57025
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-500 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57025.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-500, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57026
in-theory        57026
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-490 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57026.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-490, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57027
in-theory        57027
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-480 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57027.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-480, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57028
in-theory        57028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-469 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57028.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-469, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57029
in-theory        57029
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (G or H)))
theorem-size     37
proof            (modus-ponens tm-456 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57029.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (G or H))), M:tm-456, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57030
in-theory        57030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-453 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57030.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-453, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57031
in-theory        57031
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (G or H)) and (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-443 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57031.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (G or H)) and (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-443, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57032
in-theory        57032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-409 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57032.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-409, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57033
in-theory        57033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-400 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57033.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-400, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57034
in-theory        57034
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-391 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57034.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-391, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57035
in-theory        57035
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-382 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57035.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-382, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57036
in-theory        57036
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-373 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57036.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-373, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57037
in-theory        57037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-364 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57037.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-364, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57038
in-theory        57038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-354 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57038.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-354, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57039
in-theory        57039
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> (G and H))))
theorem-size     39
proof            (modus-ponens tm-341 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57039.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57040
in-theory        57040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-338 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57040.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-338, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57041
in-theory        57041
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> (G and H))) and (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     71
proof            (modus-ponens tm-327 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57041.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> (G and H))) and (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-327, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57042
in-theory        57042
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> H) and (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-326 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57042.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> H) and (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-326, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57043
in-theory        57043
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> G) and (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-325 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57043.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> G) and (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-325, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57044
in-theory        57044
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     77
proof            (modus-ponens tm-324 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       265
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57044.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-324, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57045
in-theory        57045
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> G)) and (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-323 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57045.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> G)) and (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-323, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57046
in-theory        57046
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> H))
theorem-size     37
proof            (modus-ponens tm-322 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57046.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57047
in-theory        57047
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> G))
theorem-size     37
proof            (modus-ponens tm-320 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57047.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57048
in-theory        57048
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     45
proof            (modus-ponens tm-318 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57048.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57049
in-theory        57049
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> G)))
theorem-size     37
proof            (modus-ponens tm-315 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57049.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57050
in-theory        57050
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G or (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     65
proof            (modus-ponens tm-311 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57050.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G or (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-311, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57051
in-theory        57051
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G))
theorem-size     65
proof            (modus-ponens tm-310 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57051.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G)), M:tm-310, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57052
in-theory        57052
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and G)))
theorem-size     67
proof            (modus-ponens tm-309 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57052.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and G))), M:tm-309, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57053
in-theory        57053
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     57
proof            (modus-ponens tm-308 tm-700 ((A (-> (and Am Bm) Am)) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57053.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-308, m:tm-700, u:((A (-> (and Am Bm) Am)) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-57054
in-theory        57054
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((A and B) -> A))
theorem-size     37
proof            (modus-ponens tm-307 tm-700 ((A (-> (and Am Bm) Am)) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57054.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((A and B) -> A)), M:tm-307, m:tm-700, u:((A (-> (and Am Bm) Am)) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-57055
in-theory        57055
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     65
proof            (modus-ponens tm-305 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57055.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-305, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57056
in-theory        57056
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-303 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57056.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-303, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57057
in-theory        57057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-270 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57057.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-270, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57058
in-theory        57058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-239 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57058.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-239, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57059
in-theory        57059
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-210 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57059.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-210, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57060
in-theory        57060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-183 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57060.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-183, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57061
in-theory        57061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-157 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57061.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-157, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57062
in-theory        57062
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-147 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57062.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-147, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57063
in-theory        57063
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-134 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57063.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-134, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57064
in-theory        57064
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-125 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57064.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-125, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57065
in-theory        57065
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-113 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57065.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-113, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57066
in-theory        57066
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     51
proof            (modus-ponens tm-105 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57066.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-105, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57067
in-theory        57067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-95 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57067.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-95, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57068
in-theory        57068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-83 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57068.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-83, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57069
in-theory        57069
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     37
proof            (modus-ponens tm-76 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57069.        (((not (not A)) -> A) and (((B and C) -> B) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-76, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57070
in-theory        57070
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     43
proof            (modus-ponens tm-69 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57070.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-69, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57071
in-theory        57071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-54 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57071.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-54, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57072
in-theory        57072
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-42 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57072.        ((A -> (B or A)) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-42, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57073
in-theory        57073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-32 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57073.        ((A -> (A or B)) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-32, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57074
in-theory        57074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-23 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57074.        ((A -> (B -> (A and B))) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-23, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57075
in-theory        57075
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-22 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57075.        (((A and B) -> B) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-22, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57076
in-theory        57076
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-21 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57076.        (((A and B) -> A) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-21, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57077
in-theory        57077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-20 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57077.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-20, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57078
in-theory        57078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-19 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57078.        ((A -> (B -> A)) and (((C and D) -> C) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-19, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57079
in-theory        57079
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-7 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-7 tm-5 tm-3 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57079.        (A or (((B and C) -> B) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-7, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57080
in-theory        57080
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G)
theorem-size     33
proof            (modus-ponens tm-6 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-6 tm-5 tm-3 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57080.        ((((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G), M:tm-6, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57081
in-theory        57081
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57081.        (A -> ((((B and C) -> B) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and A)), M:tm-5, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57082
in-theory        57082
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-1 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-1 tm-5 tm-3 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57082.        (A -> (((B and C) -> B) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-1, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57083
in-theory        57083
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     53
proof            (modus-ponens tm-665 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57083.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-665, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57084
in-theory        57084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-622 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57084.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-622, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57085
in-theory        57085
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H -> (I or H)))
theorem-size     45
proof            (modus-ponens tm-609 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57085.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H -> (I or H))), M:tm-609, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57086
in-theory        57086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-605 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57086.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-605, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57087
in-theory        57087
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H -> (I or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))))
theorem-size     85
proof            (modus-ponens tm-595 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       273
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57087.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H -> (I or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))), M:tm-595, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57088
in-theory        57088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-550 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57088.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-550, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57089
in-theory        57089
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-540 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57089.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-540, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57090
in-theory        57090
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-530 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57090.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-530, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57091
in-theory        57091
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-520 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57091.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-520, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57092
in-theory        57092
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-510 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57092.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-510, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57093
in-theory        57093
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-500 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57093.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-500, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57094
in-theory        57094
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K))))
theorem-size     55
proof            (modus-ponens tm-490 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57094.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K)))), M:tm-490, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57095
in-theory        57095
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-480 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57095.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-480, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57096
in-theory        57096
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-469 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57096.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-469, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57097
in-theory        57097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H -> (H or I)))
theorem-size     45
proof            (modus-ponens tm-456 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57097.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H -> (H or I))), M:tm-456, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57098
in-theory        57098
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-453 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57098.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-453, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57099
in-theory        57099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H -> (H or I)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))))
theorem-size     85
proof            (modus-ponens tm-443 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       273
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57099.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H -> (H or I)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))), M:tm-443, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57100
in-theory        57100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-409 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57100.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-409, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57101
in-theory        57101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-400 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57101.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-400, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57102
in-theory        57102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-391 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57102.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-391, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57103
in-theory        57103
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-382 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57103.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-382, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57104
in-theory        57104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K))))
theorem-size     55
proof            (modus-ponens tm-373 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57104.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K)))), M:tm-373, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57105
in-theory        57105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-364 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57105.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-364, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57106
in-theory        57106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-354 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57106.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-354, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57107
in-theory        57107
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H -> (I -> (H and I))))
theorem-size     47
proof            (modus-ponens tm-341 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57107.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H -> (I -> (H and I)))), M:tm-341, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57108
in-theory        57108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     49
proof            (modus-ponens tm-338 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57108.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-338, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57109
in-theory        57109
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H -> (I -> (H and I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))))
theorem-size     87
proof            (modus-ponens tm-327 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       281
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57109.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H -> (I -> (H and I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))), M:tm-327, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57110
in-theory        57110
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (((H and I) -> I) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))))
theorem-size     85
proof            (modus-ponens tm-326 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       273
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57110.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (((H and I) -> I) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))), M:tm-326, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57111
in-theory        57111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (((H and I) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))))
theorem-size     85
proof            (modus-ponens tm-325 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       273
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57111.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (((H and I) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))), M:tm-325, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57112
in-theory        57112
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))))
theorem-size     93
proof            (modus-ponens tm-324 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       305
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57112.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))), M:tm-324, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57113
in-theory        57113
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H -> (I -> H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))))
theorem-size     85
proof            (modus-ponens tm-323 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       273
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57113.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H -> (I -> H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))), M:tm-323, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57114
in-theory        57114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H and I) -> I))
theorem-size     45
proof            (modus-ponens tm-322 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57114.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H and I) -> I)), M:tm-322, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57115
in-theory        57115
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H and I) -> H))
theorem-size     45
proof            (modus-ponens tm-320 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57115.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H and I) -> H)), M:tm-320, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57116
in-theory        57116
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))
theorem-size     53
proof            (modus-ponens tm-318 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       259
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57116.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))), M:tm-318, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57117
in-theory        57117
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H -> (I -> H)))
theorem-size     45
proof            (modus-ponens tm-315 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57117.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H -> (I -> H))), M:tm-315, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57118
in-theory        57118
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))))
theorem-size     81
proof            (modus-ponens tm-311 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57118.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))), M:tm-311, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57119
in-theory        57119
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) or H))
theorem-size     81
proof            (modus-ponens tm-310 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57119.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) or H)), M:tm-310, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57120
in-theory        57120
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and H)))
theorem-size     83
proof            (modus-ponens tm-309 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57120.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and H))), M:tm-309, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57121
in-theory        57121
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     65
proof            (modus-ponens tm-308 tm-701 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57121.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-308, m:tm-701, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-57122
in-theory        57122
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     53
proof            (modus-ponens tm-307 tm-701 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57122.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-701, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-57123
in-theory        57123
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))))
theorem-size     81
proof            (modus-ponens tm-305 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57123.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (H -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))), M:tm-305, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57124
in-theory        57124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     51
proof            (modus-ponens tm-303 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57124.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-303, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57125
in-theory        57125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-270 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57125.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-270, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57126
in-theory        57126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-239 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57126.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-239, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57127
in-theory        57127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K))))
theorem-size     57
proof            (modus-ponens tm-210 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57127.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K)))), M:tm-210, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57128
in-theory        57128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-183 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57128.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-183, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57129
in-theory        57129
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-157 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57129.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-157, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57130
in-theory        57130
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     55
proof            (modus-ponens tm-147 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57130.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-147, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57131
in-theory        57131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-134 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57131.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-134, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57132
in-theory        57132
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     55
proof            (modus-ponens tm-125 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57132.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-125, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57133
in-theory        57133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K))))
theorem-size     55
proof            (modus-ponens tm-113 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57133.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K)))), M:tm-113, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57134
in-theory        57134
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     59
proof            (modus-ponens tm-105 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       261
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57134.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-105, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57135
in-theory        57135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-95 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57135.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-95, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57136
in-theory        57136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-83 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57136.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-83, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57137
in-theory        57137
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     45
proof            (modus-ponens tm-76 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57137.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-76, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57138
in-theory        57138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     51
proof            (modus-ponens tm-69 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57138.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-69, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57139
in-theory        57139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     53
proof            (modus-ponens tm-54 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57139.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-54, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57140
in-theory        57140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-42 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57140.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-42, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57141
in-theory        57141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-32 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57141.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-32, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57142
in-theory        57142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-23 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57142.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-23, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57143
in-theory        57143
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-22 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57143.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-22, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57144
in-theory        57144
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-21 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57144.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-21, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57145
in-theory        57145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     53
proof            (modus-ponens tm-20 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57145.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-20, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57146
in-theory        57146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-19 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57146.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-19, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57147
in-theory        57147
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-7 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-7 tm-5 tm-2 tm-8)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57147.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-7, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57148
in-theory        57148
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) or H)
theorem-size     41
proof            (modus-ponens tm-6 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-6 tm-5 tm-2 tm-8)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57148.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) or H), M:tm-6, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57149
in-theory        57149
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))) and A))
theorem-size     43
proof            (modus-ponens tm-5 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57149.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))) and A)), M:tm-5, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57150
in-theory        57150
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-1 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-1 tm-5 tm-2 tm-8)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57150.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-1, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-57151
in-theory        57151
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-665 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57151.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-665, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57152
in-theory        57152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-622 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57152.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-622, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57153
in-theory        57153
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H or G)))
theorem-size     37
proof            (modus-ponens tm-609 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57153.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H or G))), M:tm-609, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57154
in-theory        57154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-605 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57154.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-605, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57155
in-theory        57155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H or G)) and ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-595 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57155.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H or G)) and ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-595, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57156
in-theory        57156
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-550 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57156.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-550, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57157
in-theory        57157
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-540 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57157.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-540, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57158
in-theory        57158
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-530 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57158.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-530, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57159
in-theory        57159
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-520 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57159.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-520, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57160
in-theory        57160
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-510 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57160.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-510, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57161
in-theory        57161
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-500 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57161.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-500, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57162
in-theory        57162
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-490 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57162.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-490, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57163
in-theory        57163
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-480 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57163.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-480, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57164
in-theory        57164
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-469 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57164.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-469, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57165
in-theory        57165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (G or H)))
theorem-size     37
proof            (modus-ponens tm-456 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57165.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (G or H))), M:tm-456, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57166
in-theory        57166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-453 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57166.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-453, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57167
in-theory        57167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (G or H)) and ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-443 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57167.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (G or H)) and ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-443, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57168
in-theory        57168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-409 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57168.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-409, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57169
in-theory        57169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-400 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57169.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-400, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57170
in-theory        57170
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-391 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57170.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-391, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57171
in-theory        57171
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-382 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57171.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-382, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57172
in-theory        57172
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-373 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57172.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-373, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57173
in-theory        57173
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-364 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57173.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-364, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57174
in-theory        57174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-354 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57174.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-354, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57175
in-theory        57175
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> (G and H))))
theorem-size     39
proof            (modus-ponens tm-341 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57175.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57176
in-theory        57176
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-338 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57176.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-338, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57177
in-theory        57177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     71
proof            (modus-ponens tm-327 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57177.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> (G and H))) and ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-327, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57178
in-theory        57178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> H) and ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-326 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57178.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> H) and ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-326, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57179
in-theory        57179
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> G) and ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-325 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57179.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G and H) -> G) and ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-325, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57180
in-theory        57180
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     77
proof            (modus-ponens tm-324 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       265
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57180.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-324, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57181
in-theory        57181
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> G)) and ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     69
proof            (modus-ponens tm-323 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57181.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> G)) and ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-323, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57182
in-theory        57182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> H))
theorem-size     37
proof            (modus-ponens tm-322 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57182.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> H)), M:tm-322, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57183
in-theory        57183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> G))
theorem-size     37
proof            (modus-ponens tm-320 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57183.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G and H) -> G)), M:tm-320, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57184
in-theory        57184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     45
proof            (modus-ponens tm-318 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57184.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57185
in-theory        57185
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> G)))
theorem-size     37
proof            (modus-ponens tm-315 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57185.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (H -> G))), M:tm-315, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57186
in-theory        57186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G or ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     65
proof            (modus-ponens tm-311 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57186.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G or ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-311, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57187
in-theory        57187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G))
theorem-size     65
proof            (modus-ponens tm-310 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57187.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G)), M:tm-310, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57188
in-theory        57188
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and G)))
theorem-size     67
proof            (modus-ponens tm-309 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57188.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and G))), M:tm-309, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57189
in-theory        57189
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     57
proof            (modus-ponens tm-308 tm-702 ((A (-> Am (-> Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57189.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-308, m:tm-702, u:((A (-> Am (-> Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-57190
in-theory        57190
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (A -> (B -> A)))
theorem-size     37
proof            (modus-ponens tm-307 tm-702 ((A (-> Am (-> Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57190.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (A -> (B -> A))), M:tm-307, m:tm-702, u:((A (-> Am (-> Bm Am))) (B (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-57191
in-theory        57191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))))
theorem-size     65
proof            (modus-ponens tm-305 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57191.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and (G -> ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))), M:tm-305, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57192
in-theory        57192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-303 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57192.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-303, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57193
in-theory        57193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-270 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57193.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-270, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57194
in-theory        57194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-239 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57194.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-239, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57195
in-theory        57195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     49
proof            (modus-ponens tm-210 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57195.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-210, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57196
in-theory        57196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     41
proof            (modus-ponens tm-183 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57196.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-183, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57197
in-theory        57197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-157 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57197.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-157, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57198
in-theory        57198
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-147 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57198.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-147, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57199
in-theory        57199
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-134 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57199.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-134, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57200
in-theory        57200
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     47
proof            (modus-ponens tm-125 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57200.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-125, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57201
in-theory        57201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     47
proof            (modus-ponens tm-113 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57201.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-113, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57202
in-theory        57202
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     51
proof            (modus-ponens tm-105 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57202.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-105, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57203
in-theory        57203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-95 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57203.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-95, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57204
in-theory        57204
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     39
proof            (modus-ponens tm-83 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57204.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-83, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57205
in-theory        57205
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     37
proof            (modus-ponens tm-76 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57205.        (((not (not A)) -> A) and ((B -> (C -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-76, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57206
in-theory        57206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     43
proof            (modus-ponens tm-69 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57206.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-69, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57207
in-theory        57207
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-54 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57207.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-54, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57208
in-theory        57208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-42 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57208.        ((A -> (B or A)) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-42, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57209
in-theory        57209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-32 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57209.        ((A -> (A or B)) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-32, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57210
in-theory        57210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-23 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57210.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-23, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57211
in-theory        57211
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-22 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57211.        (((A and B) -> B) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-22, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57212
in-theory        57212
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-21 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57212.        (((A and B) -> A) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-21, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57213
in-theory        57213
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-20 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57213.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-20, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57214
in-theory        57214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-19 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57214.        ((A -> (B -> A)) and ((C -> (D -> C)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-19, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57215
in-theory        57215
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-7 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57215.        (A or ((B -> (C -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-7, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57216
in-theory        57216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G)
theorem-size     33
proof            (modus-ponens tm-6 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57216.        (((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) or G), M:tm-6, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57217
in-theory        57217
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57217.        (A -> (((B -> (C -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and A)), M:tm-5, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57218
in-theory        57218
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-1 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57218.        (A -> ((B -> (C -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-1, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-57219
in-theory        57219
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> ((A -> B) -> (A -> C))))
theorem-size     17
proof            (modus-ponens tm-703 tm-1 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57219.        (((A -> B) -> (A -> C)) -> (D -> ((A -> B) -> (A -> C)))), M:tm-703, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57220
in-theory        57220
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> A) -> ((A -> B) -> C)))
theorem-size     19
proof            (modus-ponens tm-703 tm-2 ((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57220.        (((A -> B) -> (A -> C)) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-703, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
================================================================
tm-name          tm-57221
in-theory        57221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> (((A -> B) -> (A -> C)) and D)))
theorem-size     19
proof            (modus-ponens tm-703 tm-5 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-57221.        (((A -> B) -> (A -> C)) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-703, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
================================================================
tm-name          tm-57222
in-theory        57222
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) or D))
theorem-size     17
proof            (modus-ponens tm-703 tm-6 ((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-57222.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) or D)), M:tm-703, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
================================================================
tm-name          tm-57223
in-theory        57223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D or ((A -> B) -> (A -> C))))
theorem-size     17
proof            (modus-ponens tm-703 tm-7 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-57223.        (((A -> B) -> (A -> C)) -> (D or ((A -> B) -> (A -> C)))), M:tm-703, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57224
in-theory        57224
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-703 tm-8 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57224.        (((A -> B) -> (A -> C)) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-703, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
================================================================
tm-name          tm-57225
in-theory        57225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))
theorem-size     21
proof            (modus-ponens tm-703 tm-9 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-9)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57225.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-703, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
================================================================
tm-name          tm-57226
in-theory        57226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> (E -> D)))
theorem-size     13
proof            (modus-ponens tm-703 tm-11 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-57226.        (((A -> B) -> (A -> C)) -> (D -> (E -> D))), M:tm-703, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-57227
in-theory        57227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> B)))
theorem-size     15
proof            (modus-ponens tm-703 tm-12 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57227.        (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> B))), M:tm-703, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
================================================================
tm-name          tm-57228
in-theory        57228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     21
proof            (modus-ponens tm-703 tm-14 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-57228.        (((A -> B) -> (A -> C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-703, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-57229
in-theory        57229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D and E) -> D))
theorem-size     13
proof            (modus-ponens tm-703 tm-16 ((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-57229.        (((A -> B) -> (A -> C)) -> ((D and E) -> D)), M:tm-703, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-57230
in-theory        57230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D and E) -> E))
theorem-size     13
proof            (modus-ponens tm-703 tm-18 ((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-57230.        (((A -> B) -> (A -> C)) -> ((D and E) -> E)), M:tm-703, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-57231
in-theory        57231
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))
theorem-size     21
proof            (modus-ponens tm-703 tm-19 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-57231.        (((A -> B) -> (A -> C)) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57232
in-theory        57232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-703 tm-20 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-57232.        (((A -> B) -> (A -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57233
in-theory        57233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))
theorem-size     21
proof            (modus-ponens tm-703 tm-21 ((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-57233.        (((A -> B) -> (A -> C)) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57234
in-theory        57234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))
theorem-size     21
proof            (modus-ponens tm-703 tm-22 ((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-57234.        (((A -> B) -> (A -> C)) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57235
in-theory        57235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-23 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-57235.        (((A -> B) -> (A -> C)) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57236
in-theory        57236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((A -> B) -> ((A -> B) and (A -> C))))
theorem-size     19
proof            (modus-ponens tm-703 tm-24 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-57236.        (((A -> B) -> (A -> C)) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-703, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
================================================================
tm-name          tm-57237
in-theory        57237
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> (E -> (D and E))))
theorem-size     15
proof            (modus-ponens tm-703 tm-25 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-57237.        (((A -> B) -> (A -> C)) -> (D -> (E -> (D and E)))), M:tm-703, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-57238
in-theory        57238
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))
theorem-size     21
proof            (modus-ponens tm-703 tm-32 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-57238.        (((A -> B) -> (A -> C)) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57239
in-theory        57239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> (D or E)))
theorem-size     13
proof            (modus-ponens tm-703 tm-33 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-57239.        (((A -> B) -> (A -> C)) -> (D -> (D or E))), M:tm-703, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-57240
in-theory        57240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))
theorem-size     21
proof            (modus-ponens tm-703 tm-42 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-57240.        (((A -> B) -> (A -> C)) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57241
in-theory        57241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> (E or D)))
theorem-size     13
proof            (modus-ponens tm-703 tm-43 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-57241.        (((A -> B) -> (A -> C)) -> (D -> (E or D))), M:tm-703, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-57242
in-theory        57242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((B or (A -> B)) -> (A -> C)))
theorem-size     17
proof            (modus-ponens tm-703 tm-44 ((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-57242.        (((A -> B) -> (A -> C)) -> ((B or (A -> B)) -> (A -> C))), M:tm-703, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
================================================================
tm-name          tm-57243
in-theory        57243
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))
theorem-size     33
proof            (modus-ponens tm-703 tm-45 ((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57243.        ((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-703, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
================================================================
tm-name          tm-57244
in-theory        57244
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))
theorem-size     21
proof            (modus-ponens tm-703 tm-46 ((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-57244.        (((A -> B) -> (A -> C)) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-703, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
================================================================
tm-name          tm-57245
in-theory        57245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D and (A -> B)) or (A -> B)) -> (A -> C)))
theorem-size     21
proof            (modus-ponens tm-703 tm-47 ((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and Cm (-> A B)) (-> A B)) (-> A C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-57245.        (((A -> B) -> (A -> C)) -> (((D and (A -> B)) or (A -> B)) -> (A -> C))), M:tm-703, m:tm-47, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and Cm (-> A B)) (-> A B)) (-> A C))))
================================================================
tm-name          tm-57246
in-theory        57246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> (A -> C)) -> ((B or (A -> (B and A))) -> (A -> C)))
theorem-size     21
proof            (modus-ponens tm-703 tm-48 ((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (-> (or Bm (-> Am (and Bm Am))) (-> Am C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-57246.        (((A -> (B and A)) -> (A -> C)) -> ((B or (A -> (B and A))) -> (A -> C))), M:tm-703, m:tm-48, u:((A Am) (B (and Bm Am)) (Cm (-> Am C)) (D (-> (or Bm (-> Am (and Bm Am))) (-> Am C))))
================================================================
tm-name          tm-57247
in-theory        57247
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D)))
theorem-size     35
proof            (modus-ponens tm-703 tm-51 ((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-57247.        ((((A -> B) -> ((C or A) -> B)) -> ((A -> B) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> ((A -> B) -> D))), M:tm-703, m:tm-51, u:((A (-> Am Bm)) (B (-> (or Cm Am) Bm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) (-> (-> Am Bm) C))))
================================================================
tm-name          tm-57248
in-theory        57248
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-703 tm-54 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-57248.        (((A -> B) -> (A -> C)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-54, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57249
in-theory        57249
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> (A -> B)) -> ((A -> A) -> ((A or A) -> B)))
theorem-size     17
proof            (modus-ponens tm-703 tm-55 ((Bm Am) (B Am) (A Am) (C Cm) (D (-> (-> Am Am) (-> (or Am Am) Cm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-57249.        (((A -> A) -> (A -> B)) -> ((A -> A) -> ((A or A) -> B))), M:tm-703, m:tm-55, u:((Bm Am) (B Am) (A Am) (C Cm) (D (-> (-> Am Am) (-> (or Am Am) Cm))))
================================================================
tm-name          tm-57250
in-theory        57250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-703 tm-56 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-57250.        (((A -> B) -> (A -> C)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-703, m:tm-56, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-57251
in-theory        57251
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> ((A -> (not B)) -> C)) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-703 tm-66 ((A (-> Am (not Bm))) (B (not Am)) (Cm (-> (-> Am (not Bm)) C)) (D (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (-> (-> Am (not Bm)) C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-9)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-57251.        ((((A -> (not B)) -> (not A)) -> ((A -> (not B)) -> C)) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> ((A -> (not B)) -> C))), M:tm-703, m:tm-66, u:((A (-> Am (not Bm))) (B (not Am)) (Cm (-> (-> Am (not Bm)) C)) (D (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) (-> (-> Am (not Bm)) C))))
================================================================
tm-name          tm-57252
in-theory        57252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> B) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-703 tm-69 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-57252.        (((A -> B) -> (A -> C)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-69, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57253
in-theory        57253
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     19
proof            (modus-ponens tm-703 tm-71 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-9)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-57253.        (((A -> B) -> (A -> C)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-703, m:tm-71, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-57254
in-theory        57254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((not (not (A -> B))) or (A -> B)) -> (A -> C)))
theorem-size     21
proof            (modus-ponens tm-703 tm-73 ((Am (-> A B)) (Bm (-> A C)) (D (-> (or (not (not (-> A B))) (-> A B)) (-> A C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-10)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-57254.        (((A -> B) -> (A -> C)) -> (((not (not (A -> B))) or (A -> B)) -> (A -> C))), M:tm-703, m:tm-73, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (not (not (-> A B))) (-> A B)) (-> A C))))
================================================================
tm-name          tm-57255
in-theory        57255
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((not (not D)) -> D) and ((A -> B) -> (A -> C))))
theorem-size     21
proof            (modus-ponens tm-703 tm-76 ((Am (-> (-> A B) (-> A C))) (D (and (-> (not (not Bm)) Bm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-10)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-57255.        (((A -> B) -> (A -> C)) -> (((not (not D)) -> D) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-76, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (not (not Bm)) Bm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57256
in-theory        57256
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((not (not D)) -> D))
theorem-size     13
proof            (modus-ponens tm-703 tm-78 ((Am (-> (-> A B) (-> A C))) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-10)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-57256.        (((A -> B) -> (A -> C)) -> ((not (not D)) -> D)), M:tm-703, m:tm-78, u:((Am (-> (-> A B) (-> A C))) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-57257
in-theory        57257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> (A -> C)) -> ((D or (A -> (B -> A))) -> (A -> C)))
theorem-size     21
proof            (modus-ponens tm-703 tm-80 ((A Am) (B (-> Bm Am)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (-> Bm Am))) (-> Am C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-57257.        (((A -> (B -> A)) -> (A -> C)) -> ((D or (A -> (B -> A))) -> (A -> C))), M:tm-703, m:tm-80, u:((A Am) (B (-> Bm Am)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (-> Bm Am))) (-> Am C))))
================================================================
tm-name          tm-57258
in-theory        57258
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (E -> (F -> E))) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-83 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-57258.        (((A -> B) -> (A -> C)) -> ((D -> (E -> (F -> E))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-83, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57259
in-theory        57259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((A -> B) -> (D -> (A -> C))))
theorem-size     17
proof            (modus-ponens tm-703 tm-84 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> Cm (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-57259.        (((A -> B) -> (A -> C)) -> ((A -> B) -> (D -> (A -> C)))), M:tm-703, m:tm-84, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> Cm (-> A C)))))
================================================================
tm-name          tm-57260
in-theory        57260
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-703 tm-85 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-57260.        (((A -> B) -> (A -> C)) -> (D -> (E -> (F -> E)))), M:tm-703, m:tm-85, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-57261
in-theory        57261
times-derived    4
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C)))
theorem-size     15
proof            (modus-ponens tm-703 tm-86 ((Am (-> (-> A B) (-> A C))) (D (-> (-> A B) (-> A C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-57261.        (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C))), M:tm-703, m:tm-86, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> A B) (-> A C))))
================================================================
tm-name          tm-57262
in-theory        57262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> (A -> B)) -> (((A -> C) or (A -> A)) -> (A -> B)))
theorem-size     19
proof            (modus-ponens tm-703 tm-92 ((A Am) (B Am) (Bm (-> Am C)) (D (-> (or (-> Am Cm) (-> Am Am)) (-> Am C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-57262.        (((A -> A) -> (A -> B)) -> (((A -> C) or (A -> A)) -> (A -> B))), M:tm-703, m:tm-92, u:((A Am) (B Am) (Bm (-> Am C)) (D (-> (or (-> Am Cm) (-> Am Am)) (-> Am C))))
================================================================
tm-name          tm-57263
in-theory        57263
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> E) -> (D -> D)) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-95 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-57263.        (((A -> B) -> (A -> C)) -> (((D -> E) -> (D -> D)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-95, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57264
in-theory        57264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> E) -> (D -> D)))
theorem-size     15
proof            (modus-ponens tm-703 tm-97 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-57264.        (((A -> B) -> (A -> C)) -> ((D -> E) -> (D -> D))), M:tm-703, m:tm-97, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-57265
in-theory        57265
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> ((A -> (B -> C)) -> D)) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> D)))
theorem-size     45
proof            (modus-ponens tm-703 tm-102 ((A (-> Am (-> Bm Cm))) (B (-> Am Cm)) (Dm (-> (-> Am (-> Bm Cm)) C)) (D (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> (-> Am (-> Bm Cm)) C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-57265.        ((((A -> (B -> C)) -> (A -> C)) -> ((A -> (B -> C)) -> D)) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((A -> (B -> C)) -> D))), M:tm-703, m:tm-102, u:((A (-> Am (-> Bm Cm))) (B (-> Am Cm)) (Dm (-> (-> Am (-> Bm Cm)) C)) (D (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) (-> (-> Am (-> Bm Cm)) C))))
================================================================
tm-name          tm-57266
in-theory        57266
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-703 tm-105 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-57266.        (((A -> B) -> (A -> C)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-105, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57267
in-theory        57267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-703 tm-107 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-57267.        (((A -> B) -> (A -> C)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-703, m:tm-107, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-57268
in-theory        57268
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> D)) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> D)))
theorem-size     45
proof            (modus-ponens tm-703 tm-110 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (-> (-> Am (-> Bm Cm)) C)) (D (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> Am (-> Bm Cm)) C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-57268.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) -> D)) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> ((A -> (B -> C)) -> D))), M:tm-703, m:tm-110, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (-> (-> Am (-> Bm Cm)) C)) (D (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> Am (-> Bm Cm)) C))))
================================================================
tm-name          tm-57269
in-theory        57269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-703 tm-113 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-57269.        (((A -> B) -> (A -> C)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-113, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57270
in-theory        57270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> D))) -> ((A -> B) -> ((A -> C) -> (A -> D))))
theorem-size     21
proof            (modus-ponens tm-703 tm-114 ((Am (-> Bm B)) (A Bm) (C (-> Cm Dm)) (D (-> (-> Bm B) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-57270.        (((A -> B) -> (A -> (C -> D))) -> ((A -> B) -> ((A -> C) -> (A -> D)))), M:tm-703, m:tm-114, u:((Am (-> Bm B)) (A Bm) (C (-> Cm Dm)) (D (-> (-> Bm B) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-57271
in-theory        57271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-703 tm-115 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-57271.        (((A -> B) -> (A -> C)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-703, m:tm-115, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-57272
in-theory        57272
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> (((A -> B) and C) -> D)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> D)))
theorem-size     39
proof            (modus-ponens tm-703 tm-122 ((A (and (-> Am Bm) Cm)) (B Bm) (Dm (-> (and (-> Am Bm) Cm) C)) (D (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (-> (and (-> Am Bm) Cm) C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-57272.        (((((A -> B) and C) -> B) -> (((A -> B) and C) -> D)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((A -> B) and C) -> D))), M:tm-703, m:tm-122, u:((A (and (-> Am Bm) Cm)) (B Bm) (Dm (-> (and (-> Am Bm) Cm) C)) (D (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) (-> (and (-> Am Bm) Cm) C))))
================================================================
tm-name          tm-57273
in-theory        57273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-703 tm-125 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-57273.        (((A -> B) -> (A -> C)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-125, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57274
in-theory        57274
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-703 tm-127 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-57274.        (((A -> B) -> (A -> C)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-703, m:tm-127, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-57275
in-theory        57275
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> ((A and B) -> C)) -> ((D or ((A and B) -> A)) -> ((A and B) -> C)))
theorem-size     25
proof            (modus-ponens tm-703 tm-131 ((A (and Am Bm)) (B Am) (Cm (-> (and Am Bm) C)) (D (-> (or Dm (-> (and Am Bm) Am)) (-> (and Am Bm) C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-57275.        ((((A and B) -> A) -> ((A and B) -> C)) -> ((D or ((A and B) -> A)) -> ((A and B) -> C))), M:tm-703, m:tm-131, u:((A (and Am Bm)) (B Am) (Cm (-> (and Am Bm) C)) (D (-> (or Dm (-> (and Am Bm) Am)) (-> (and Am Bm) C))))
================================================================
tm-name          tm-57276
in-theory        57276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> ((E and F) -> E)) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-134 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-57276.        (((A -> B) -> (A -> C)) -> ((D -> ((E and F) -> E)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-134, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57277
in-theory        57277
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-703 tm-136 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-57277.        (((A -> B) -> (A -> C)) -> (D -> ((E and F) -> E))), M:tm-703, m:tm-136, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-57278
in-theory        57278
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> ((A and (B -> C)) -> D)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> D)))
theorem-size     39
proof            (modus-ponens tm-703 tm-144 ((A (and Am (-> Bm Cm))) (B Cm) (Dm (-> (and Am (-> Bm Cm)) C)) (D (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (-> (and Am (-> Bm Cm)) C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-57278.        ((((A and (B -> C)) -> C) -> ((A and (B -> C)) -> D)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((A and (B -> C)) -> D))), M:tm-703, m:tm-144, u:((A (and Am (-> Bm Cm))) (B Cm) (Dm (-> (and Am (-> Bm Cm)) C)) (D (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) (-> (and Am (-> Bm Cm)) C))))
================================================================
tm-name          tm-57279
in-theory        57279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-703 tm-147 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-57279.        (((A -> B) -> (A -> C)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-147, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57280
in-theory        57280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-703 tm-149 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-57280.        (((A -> B) -> (A -> C)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-703, m:tm-149, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-57281
in-theory        57281
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> ((A and B) -> C)) -> ((D or ((A and B) -> B)) -> ((A and B) -> C)))
theorem-size     25
proof            (modus-ponens tm-703 tm-154 ((A (and Am Bm)) (B Bm) (Cm (-> (and Am Bm) C)) (D (-> (or Dm (-> (and Am Bm) Bm)) (-> (and Am Bm) C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-57281.        ((((A and B) -> B) -> ((A and B) -> C)) -> ((D or ((A and B) -> B)) -> ((A and B) -> C))), M:tm-703, m:tm-154, u:((A (and Am Bm)) (B Bm) (Cm (-> (and Am Bm) C)) (D (-> (or Dm (-> (and Am Bm) Bm)) (-> (and Am Bm) C))))
================================================================
tm-name          tm-57282
in-theory        57282
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> ((E and F) -> F)) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-157 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-57282.        (((A -> B) -> (A -> C)) -> ((D -> ((E and F) -> F)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-157, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57283
in-theory        57283
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-703 tm-159 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-57283.        (((A -> B) -> (A -> C)) -> (D -> ((E and F) -> F))), M:tm-703, m:tm-159, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-57284
in-theory        57284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> B) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-703 tm-183 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-57284.        (((A -> B) -> (A -> C)) -> ((D -> ((E -> (F -> E)) and D)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-183, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57285
in-theory        57285
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     17
proof            (modus-ponens tm-703 tm-184 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-57285.        (((A -> B) -> (A -> C)) -> (D -> ((E -> (F -> E)) and D))), M:tm-703, m:tm-184, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-57286
in-theory        57286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-703 tm-210 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-57286.        (((A -> B) -> (A -> C)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-210, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57287
in-theory        57287
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     25
proof            (modus-ponens tm-703 tm-211 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-57287.        (((A -> B) -> (A -> C)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-703, m:tm-211, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-57288
in-theory        57288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (((E and F) -> E) and D)) and ((A -> B) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-703 tm-239 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-57288.        (((A -> B) -> (A -> C)) -> ((D -> (((E and F) -> E) and D)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-239, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57289
in-theory        57289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> (((E and F) -> E) and D)))
theorem-size     17
proof            (modus-ponens tm-703 tm-240 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-57289.        (((A -> B) -> (A -> C)) -> (D -> (((E and F) -> E) and D))), M:tm-703, m:tm-240, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-57290
in-theory        57290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (((E and F) -> F) and D)) and ((A -> B) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-703 tm-270 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-57290.        (((A -> B) -> (A -> C)) -> ((D -> (((E and F) -> F) and D)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-270, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57291
in-theory        57291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> (((E and F) -> F) and D)))
theorem-size     17
proof            (modus-ponens tm-703 tm-271 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-57291.        (((A -> B) -> (A -> C)) -> (D -> (((E and F) -> F) and D))), M:tm-703, m:tm-271, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-57292
in-theory        57292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> B) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-703 tm-303 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-57292.        (((A -> B) -> (A -> C)) -> ((D -> ((E -> (F -> (E and F))) and D)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-303, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57293
in-theory        57293
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     19
proof            (modus-ponens tm-703 tm-304 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-57293.        (((A -> B) -> (A -> C)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-703, m:tm-304, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-57294
in-theory        57294
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> ((A -> B) -> (A -> C)))))
theorem-size     25
proof            (modus-ponens tm-703 tm-305 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-57294.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> ((A -> B) -> (A -> C))))), M:tm-703, m:tm-305, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57295
in-theory        57295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> B) -> A) -> ((A -> B) -> C))))
theorem-size     27
proof            (modus-ponens tm-703 tm-306 ((Am (-> Bm B)) (A Bm) (C Cm) (D (and (-> (-> Bm B) (-> Bm Cm)) (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-57295.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> B) -> A) -> ((A -> B) -> C)))), M:tm-703, m:tm-306, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (and (-> (-> Bm B) (-> Bm Cm)) (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm)))))
================================================================
tm-name          tm-57296
in-theory        57296
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (((A -> B) -> (A -> C)) and D))))
theorem-size     27
proof            (modus-ponens tm-703 tm-309 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (and (-> (-> A B) (-> A C)) Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-57296.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (((A -> B) -> (A -> C)) and D)))), M:tm-703, m:tm-309, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (and (-> (-> A B) (-> A C)) Bm)))))
================================================================
tm-name          tm-57297
in-theory        57297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (A -> C)) or D)))
theorem-size     25
proof            (modus-ponens tm-703 tm-310 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (or (-> (-> A B) (-> A C)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-57297.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (A -> C)) or D))), M:tm-703, m:tm-310, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (or (-> (-> A B) (-> A C)) Bm))))
================================================================
tm-name          tm-57298
in-theory        57298
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D or ((A -> B) -> (A -> C)))))
theorem-size     25
proof            (modus-ponens tm-703 tm-311 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (or Bm (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-57298.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D or ((A -> B) -> (A -> C))))), M:tm-703, m:tm-311, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (or Bm (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57299
in-theory        57299
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))
theorem-size     31
proof            (modus-ponens tm-703 tm-312 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-57299.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))), M:tm-703, m:tm-312, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm)))))
================================================================
tm-name          tm-57300
in-theory        57300
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))
theorem-size     29
proof            (modus-ponens tm-703 tm-313 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-9)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-57300.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((A -> B) -> (not (A -> C))) -> (not (A -> B))))), M:tm-703, m:tm-313, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> (-> A B) (not (-> A C))) (not (-> A B))))))
================================================================
tm-name          tm-57301
in-theory        57301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (E -> D))))
theorem-size     21
proof            (modus-ponens tm-703 tm-315 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-57301.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (E -> D)))), M:tm-703, m:tm-315, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-57302
in-theory        57302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((A -> B) -> (A -> B))))
theorem-size     23
proof            (modus-ponens tm-703 tm-316 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> A B) (-> A B))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-57302.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((A -> B) -> (A -> B)))), M:tm-703, m:tm-316, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> A B) (-> A B)))))
================================================================
tm-name          tm-57303
in-theory        57303
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     29
proof            (modus-ponens tm-703 tm-318 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-57303.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-703, m:tm-318, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-57304
in-theory        57304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D and E) -> D)))
theorem-size     21
proof            (modus-ponens tm-703 tm-320 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-57304.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D and E) -> D))), M:tm-703, m:tm-320, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-57305
in-theory        57305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D and E) -> E)))
theorem-size     21
proof            (modus-ponens tm-703 tm-322 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-57305.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D and E) -> E))), M:tm-703, m:tm-322, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-57306
in-theory        57306
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-703 tm-323 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-57306.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E -> D)) and ((A -> B) -> (A -> C))))), M:tm-703, m:tm-323, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57307
in-theory        57307
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))
theorem-size     37
proof            (modus-ponens tm-703 tm-324 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-57307.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))), M:tm-703, m:tm-324, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57308
in-theory        57308
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D and E) -> D) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-703 tm-325 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-57308.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D and E) -> D) and ((A -> B) -> (A -> C))))), M:tm-703, m:tm-325, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57309
in-theory        57309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D and E) -> E) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-703 tm-326 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-57309.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (((D and E) -> E) and ((A -> B) -> (A -> C))))), M:tm-703, m:tm-326, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57310
in-theory        57310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))
theorem-size     31
proof            (modus-ponens tm-703 tm-327 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-57310.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))), M:tm-703, m:tm-327, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57311
in-theory        57311
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((A -> B) -> ((A -> B) and (A -> C)))))
theorem-size     27
proof            (modus-ponens tm-703 tm-328 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> A B) (and (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-57311.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((A -> B) -> ((A -> B) and (A -> C))))), M:tm-703, m:tm-328, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (-> A B) (and (-> A B) (-> A C))))))
================================================================
tm-name          tm-57312
in-theory        57312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> (A -> C)) -> (((A -> B) or (A -> (A and B))) -> (A -> C)))
theorem-size     23
proof            (modus-ponens tm-703 tm-335 ((A Am) (B (and Am Bm)) (Cm (-> Am C)) (D (-> (or (-> Am Bm) (-> Am (and Am Bm))) (-> Am C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-57312.        (((A -> (A and B)) -> (A -> C)) -> (((A -> B) or (A -> (A and B))) -> (A -> C))), M:tm-703, m:tm-335, u:((A Am) (B (and Am Bm)) (Cm (-> Am C)) (D (-> (or (-> Am Bm) (-> Am (and Am Bm))) (-> Am C))))
================================================================
tm-name          tm-57313
in-theory        57313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> E) -> (D -> (D and E))) and ((A -> B) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-703 tm-338 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-57313.        (((A -> B) -> (A -> C)) -> (((D -> E) -> (D -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-338, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57314
in-theory        57314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-703 tm-340 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-57314.        (((A -> B) -> (A -> C)) -> ((D -> E) -> (D -> (D and E)))), M:tm-703, m:tm-340, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-57315
in-theory        57315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (E -> (D and E)))))
theorem-size     23
proof            (modus-ponens tm-703 tm-341 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-57315.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (E -> (D and E))))), M:tm-703, m:tm-341, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-57316
in-theory        57316
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> (A -> C)) -> ((D or (A -> (B -> (A and B)))) -> (A -> C)))
theorem-size     25
proof            (modus-ponens tm-703 tm-351 ((A Am) (B (-> Bm (and Am Bm))) (Cm (-> Am C)) (D (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> Am C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-57316.        (((A -> (B -> (A and B))) -> (A -> C)) -> ((D or (A -> (B -> (A and B)))) -> (A -> C))), M:tm-703, m:tm-351, u:((A Am) (B (-> Bm (and Am Bm))) (Cm (-> Am C)) (D (-> (or Dm (-> Am (-> Bm (and Am Bm)))) (-> Am C))))
================================================================
tm-name          tm-57317
in-theory        57317
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-703 tm-354 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-57317.        (((A -> B) -> (A -> C)) -> ((D -> (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-354, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57318
in-theory        57318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((A -> B) -> (D -> ((A -> C) and D))))
theorem-size     19
proof            (modus-ponens tm-703 tm-355 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> Cm (and (-> A C) Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-57318.        (((A -> B) -> (A -> C)) -> ((A -> B) -> (D -> ((A -> C) and D)))), M:tm-703, m:tm-355, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> Cm (and (-> A C) Cm)))))
================================================================
tm-name          tm-57319
in-theory        57319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-703 tm-356 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-57319.        (((A -> B) -> (A -> C)) -> (D -> (E -> (F -> (E and F))))), M:tm-703, m:tm-356, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-57320
in-theory        57320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> (E -> D)) or F) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-364 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-57320.        (((A -> B) -> (A -> C)) -> (((D -> (E -> D)) or F) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-364, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57321
in-theory        57321
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (E -> D)) or F))
theorem-size     15
proof            (modus-ponens tm-703 tm-365 ((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-57321.        (((A -> B) -> (A -> C)) -> ((D -> (E -> D)) or F)), M:tm-703, m:tm-365, u:((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-57322
in-theory        57322
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-703 tm-373 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57322.        (((A -> B) -> (A -> C)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-373, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57323
in-theory        57323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     23
proof            (modus-ponens tm-703 tm-374 ((Am (-> (-> A B) (-> A C))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57323.        (((A -> B) -> (A -> C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-703, m:tm-374, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-57324
in-theory        57324
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((((D and E) -> D) or F) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-382 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-57324.        (((A -> B) -> (A -> C)) -> ((((D and E) -> D) or F) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-382, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57325
in-theory        57325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D and E) -> D) or F))
theorem-size     15
proof            (modus-ponens tm-703 tm-383 ((Am (-> (-> A B) (-> A C))) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-57325.        (((A -> B) -> (A -> C)) -> (((D and E) -> D) or F)), M:tm-703, m:tm-383, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-57326
in-theory        57326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((((D and E) -> E) or F) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-391 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-57326.        (((A -> B) -> (A -> C)) -> ((((D and E) -> E) or F) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-391, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57327
in-theory        57327
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D and E) -> E) or F))
theorem-size     15
proof            (modus-ponens tm-703 tm-392 ((Am (-> (-> A B) (-> A C))) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-57327.        (((A -> B) -> (A -> C)) -> (((D and E) -> E) or F)), M:tm-703, m:tm-392, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-57328
in-theory        57328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> (E -> (D and E))) or F) and ((A -> B) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-703 tm-400 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-57328.        (((A -> B) -> (A -> C)) -> (((D -> (E -> (D and E))) or F) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-400, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57329
in-theory        57329
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (E -> (D and E))) or F))
theorem-size     17
proof            (modus-ponens tm-703 tm-401 ((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 tm-5)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-57329.        (((A -> B) -> (A -> C)) -> ((D -> (E -> (D and E))) or F)), M:tm-703, m:tm-401, u:((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-57330
in-theory        57330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> (D or E)) or F) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-409 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-57330.        (((A -> B) -> (A -> C)) -> (((D -> (D or E)) or F) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-409, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57331
in-theory        57331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (D or E)) or F))
theorem-size     15
proof            (modus-ponens tm-703 tm-410 ((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-57331.        (((A -> B) -> (A -> C)) -> ((D -> (D or E)) or F)), M:tm-703, m:tm-410, u:((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-57332
in-theory        57332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (D or E)) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-703 tm-443 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-57332.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (D or E)) and ((A -> B) -> (A -> C))))), M:tm-703, m:tm-443, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57333
in-theory        57333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((A -> B) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-703 tm-453 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-57333.        (((A -> B) -> (A -> C)) -> ((D -> ((E -> (E or F)) and D)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-453, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57334
in-theory        57334
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     17
proof            (modus-ponens tm-703 tm-454 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-57334.        (((A -> B) -> (A -> C)) -> (D -> ((E -> (E or F)) and D))), M:tm-703, m:tm-454, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-57335
in-theory        57335
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (D or E))))
theorem-size     21
proof            (modus-ponens tm-703 tm-456 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-57335.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (D or E)))), M:tm-703, m:tm-456, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-57336
in-theory        57336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> (A -> C)) -> ((D or (A -> (A or B))) -> (A -> C)))
theorem-size     21
proof            (modus-ponens tm-703 tm-466 ((A Am) (B (or Am Bm)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (or Am Bm))) (-> Am C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-57336.        (((A -> (A or B)) -> (A -> C)) -> ((D or (A -> (A or B))) -> (A -> C))), M:tm-703, m:tm-466, u:((A Am) (B (or Am Bm)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (or Am Bm))) (-> Am C))))
================================================================
tm-name          tm-57337
in-theory        57337
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (E -> (E or F))) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-469 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-57337.        (((A -> B) -> (A -> C)) -> ((D -> (E -> (E or F))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-469, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57338
in-theory        57338
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((A -> B) -> ((A -> C) or D)))
theorem-size     17
proof            (modus-ponens tm-703 tm-470 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (or (-> A C) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-57338.        (((A -> B) -> (A -> C)) -> ((A -> B) -> ((A -> C) or D))), M:tm-703, m:tm-470, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (or (-> A C) Cm))))
================================================================
tm-name          tm-57339
in-theory        57339
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-703 tm-471 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-57339.        (((A -> B) -> (A -> C)) -> (D -> (E -> (E or F)))), M:tm-703, m:tm-471, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-57340
in-theory        57340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D or (E -> (F -> E))) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-480 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-57340.        (((A -> B) -> (A -> C)) -> ((D or (E -> (F -> E))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-480, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57341
in-theory        57341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D or (E -> (F -> E))))
theorem-size     15
proof            (modus-ponens tm-703 tm-481 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-57341.        (((A -> B) -> (A -> C)) -> (D or (E -> (F -> E)))), M:tm-703, m:tm-481, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-57342
in-theory        57342
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-703 tm-490 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-57342.        (((A -> B) -> (A -> C)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-490, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57343
in-theory        57343
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     23
proof            (modus-ponens tm-703 tm-491 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-57343.        (((A -> B) -> (A -> C)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-703, m:tm-491, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-57344
in-theory        57344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D or ((E and F) -> E)) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-500 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-57344.        (((A -> B) -> (A -> C)) -> ((D or ((E and F) -> E)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-500, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57345
in-theory        57345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D or ((E and F) -> E)))
theorem-size     15
proof            (modus-ponens tm-703 tm-501 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-57345.        (((A -> B) -> (A -> C)) -> (D or ((E and F) -> E))), M:tm-703, m:tm-501, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-57346
in-theory        57346
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D or ((E and F) -> F)) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-510 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-57346.        (((A -> B) -> (A -> C)) -> ((D or ((E and F) -> F)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-510, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57347
in-theory        57347
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D or ((E and F) -> F)))
theorem-size     15
proof            (modus-ponens tm-703 tm-511 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-57347.        (((A -> B) -> (A -> C)) -> (D or ((E and F) -> F))), M:tm-703, m:tm-511, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-57348
in-theory        57348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D or (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-703 tm-520 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-57348.        (((A -> B) -> (A -> C)) -> ((D or (E -> (F -> (E and F)))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-520, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57349
in-theory        57349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D or (E -> (F -> (E and F)))))
theorem-size     17
proof            (modus-ponens tm-703 tm-521 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 tm-5)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-57349.        (((A -> B) -> (A -> C)) -> (D or (E -> (F -> (E and F))))), M:tm-703, m:tm-521, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-57350
in-theory        57350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D or (E -> (E or F))) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-530 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-57350.        (((A -> B) -> (A -> C)) -> ((D or (E -> (E or F))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-530, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57351
in-theory        57351
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D or (E -> (E or F))))
theorem-size     15
proof            (modus-ponens tm-703 tm-531 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7 tm-6)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-57351.        (((A -> B) -> (A -> C)) -> (D or (E -> (E or F)))), M:tm-703, m:tm-531, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-57352
in-theory        57352
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D or (E -> (F or E))) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-540 ((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-57352.        (((A -> B) -> (A -> C)) -> ((D or (E -> (F or E))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-540, u:((Am (-> (-> A B) (-> A C))) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57353
in-theory        57353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D or (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-703 tm-541 ((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-57353.        (((A -> B) -> (A -> C)) -> (D or (E -> (F or E)))), M:tm-703, m:tm-541, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-57354
in-theory        57354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> (E or D)) or F) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-550 ((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-6 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-57354.        (((A -> B) -> (A -> C)) -> (((D -> (E or D)) or F) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-550, u:((Am (-> (-> A B) (-> A C))) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57355
in-theory        57355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (E or D)) or F))
theorem-size     15
proof            (modus-ponens tm-703 tm-551 ((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-6 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-57355.        (((A -> B) -> (A -> C)) -> ((D -> (E or D)) or F)), M:tm-703, m:tm-551, u:((Am (-> (-> A B) (-> A C))) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-57356
in-theory        57356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E or D)) and ((A -> B) -> (A -> C)))))
theorem-size     29
proof            (modus-ponens tm-703 tm-595 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-57356.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((D -> (E or D)) and ((A -> B) -> (A -> C))))), M:tm-703, m:tm-595, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57357
in-theory        57357
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((A -> B) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-703 tm-605 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-57357.        (((A -> B) -> (A -> C)) -> ((D -> ((E -> (F or E)) and D)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-605, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57358
in-theory        57358
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     17
proof            (modus-ponens tm-703 tm-606 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-57358.        (((A -> B) -> (A -> C)) -> (D -> ((E -> (F or E)) and D))), M:tm-703, m:tm-606, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-57359
in-theory        57359
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (E or D))))
theorem-size     21
proof            (modus-ponens tm-703 tm-609 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-57359.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and (D -> (E or D)))), M:tm-703, m:tm-609, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> A B) (-> A C)) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-57360
in-theory        57360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> (A -> C)) -> ((D or (A -> (B or A))) -> (A -> C)))
theorem-size     21
proof            (modus-ponens tm-703 tm-619 ((A Am) (B (or Bm Am)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (or Bm Am))) (-> Am C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-57360.        (((A -> (B or A)) -> (A -> C)) -> ((D or (A -> (B or A))) -> (A -> C))), M:tm-703, m:tm-619, u:((A Am) (B (or Bm Am)) (Cm (-> Am C)) (D (-> (or Dm (-> Am (or Bm Am))) (-> Am C))))
================================================================
tm-name          tm-57361
in-theory        57361
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> (E -> (F or E))) and ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-703 tm-622 ((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-57361.        (((A -> B) -> (A -> C)) -> ((D -> (E -> (F or E))) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-622, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57362
in-theory        57362
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((A -> B) -> (D or (A -> C))))
theorem-size     17
proof            (modus-ponens tm-703 tm-623 ((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (or Cm (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-57362.        (((A -> B) -> (A -> C)) -> ((A -> B) -> (D or (A -> C)))), M:tm-703, m:tm-623, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (or Cm (-> A C)))))
================================================================
tm-name          tm-57363
in-theory        57363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (D -> (E -> (F or E))))
theorem-size     15
proof            (modus-ponens tm-703 tm-624 ((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-7)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-57363.        (((A -> B) -> (A -> C)) -> (D -> (E -> (F or E)))), M:tm-703, m:tm-624, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-57364
in-theory        57364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((B or (A -> B)) -> (A -> C))))
theorem-size     25
proof            (modus-ponens tm-703 tm-654 ((A Am) (B Bm) (Cm (-> Am C)) (D (and (-> (-> Am Bm) (-> Am C)) (-> (or Bm (-> Am Bm)) (-> Am C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-57364.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((B or (A -> B)) -> (A -> C)))), M:tm-703, m:tm-654, u:((A Am) (B Bm) (Cm (-> Am C)) (D (and (-> (-> Am Bm) (-> Am C)) (-> (or Bm (-> Am Bm)) (-> Am C)))))
================================================================
tm-name          tm-57365
in-theory        57365
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> ((A or (B -> A)) -> D)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((A or (B -> A)) -> D)))
theorem-size     37
proof            (modus-ponens tm-703 tm-662 ((A (or Am (-> Bm Am))) (B Cm) (Dm (-> (or Am (-> Bm Am)) C)) (D (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (-> (or Am (-> Bm Am)) C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-57365.        ((((A or (B -> A)) -> C) -> ((A or (B -> A)) -> D)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> ((A or (B -> A)) -> D))), M:tm-703, m:tm-662, u:((A (or Am (-> Bm Am))) (B Cm) (Dm (-> (or Am (-> Bm Am)) C)) (D (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) (-> (or Am (-> Bm Am)) C))))
================================================================
tm-name          tm-57366
in-theory        57366
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> B) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-703 tm-665 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-57366.        (((A -> B) -> (A -> C)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-665, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-57367
in-theory        57367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     21
proof            (modus-ponens tm-703 tm-667 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-57367.        (((A -> B) -> (A -> C)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-703, m:tm-667, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-57368
in-theory        57368
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) -> ((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))
theorem-size     47
proof            (modus-ponens tm-703 tm-697 ((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) C)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       257
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57368.        ((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) -> ((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))), M:tm-703, m:tm-697, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) C)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C)))))
================================================================
tm-name          tm-57369
in-theory        57369
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))
theorem-size     27
proof            (modus-ponens tm-703 tm-703 ((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57369.        ((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> D))), M:tm-703, m:tm-703, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) C))))
================================================================
tm-name          tm-57370
in-theory        57370
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> D))))
theorem-size     65
proof            (modus-ponens tm-697 tm-703 ((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       275
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57370.        (((((A -> B) -> (A -> C)) -> ((A -> B) -> D)) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) and ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))), M:tm-697, m:tm-703, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) C))))
================================================================
tm-name          tm-57371
in-theory        57371
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-665 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57371.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-665, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57372
in-theory        57372
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((D or (((A -> B) -> (A -> C)) -> D)) -> (((A -> B) -> (A -> C)) -> D)))
theorem-size     41
proof            (modus-ponens tm-654 tm-703 ((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57372.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((D or (((A -> B) -> (A -> C)) -> D)) -> (((A -> B) -> (A -> C)) -> D))), M:tm-654, m:tm-703, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57373
in-theory        57373
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> (E or (((A -> B) -> (A -> C)) -> D)))
theorem-size     21
proof            (modus-ponens tm-623 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57373.        ((((A -> B) -> (A -> C)) -> D) -> (E or (((A -> B) -> (A -> C)) -> D))), M:tm-623, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57374
in-theory        57374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-622 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57374.        ((A -> (B -> (C or B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-622, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57375
in-theory        57375
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (E or ((B -> C) -> (B -> D))))) -> (((B -> C) -> (B -> D)) -> (E or ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-619 tm-703 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (or B (-> (-> Am Bm) (-> Am Cm)))) (C (-> (-> (-> Am Bm) (-> Am Cm)) (or B (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57375.        ((A or (((B -> C) -> (B -> D)) -> (E or ((B -> C) -> (B -> D))))) -> (((B -> C) -> (B -> D)) -> (E or ((B -> C) -> (B -> D))))), M:tm-619, m:tm-703, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (or B (-> (-> Am Bm) (-> Am Cm)))) (C (-> (-> (-> Am Bm) (-> Am Cm)) (or B (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-57376
in-theory        57376
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57376.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57377
in-theory        57377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-605 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57377.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-605, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57378
in-theory        57378
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((E -> (F or E)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-595 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57378.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((E -> (F or E)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)))), M:tm-595, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57379
in-theory        57379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-550 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57379.        (((A -> (B or A)) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-550, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57380
in-theory        57380
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-540 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57380.        ((A or (B -> (C or B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-540, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57381
in-theory        57381
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-530 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57381.        ((A or (B -> (B or C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-530, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57382
in-theory        57382
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-520 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57382.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-520, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57383
in-theory        57383
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-510 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57383.        ((A or ((B and C) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-510, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57384
in-theory        57384
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-500 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57384.        ((A or ((B and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-500, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57385
in-theory        57385
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H)))
theorem-size     35
proof            (modus-ponens tm-490 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57385.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H))), M:tm-490, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57386
in-theory        57386
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-480 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57386.        ((A or (B -> (C -> B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-480, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57387
in-theory        57387
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) or E))
theorem-size     21
proof            (modus-ponens tm-470 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57387.        ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) or E)), M:tm-470, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57388
in-theory        57388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-469 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57388.        ((A -> (B -> (B or C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-469, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57389
in-theory        57389
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (((B -> C) -> (B -> D)) or E))) -> (((B -> C) -> (B -> D)) -> (((B -> C) -> (B -> D)) or E)))
theorem-size     37
proof            (modus-ponens tm-466 tm-703 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (or (-> (-> Am Bm) (-> Am Cm)) B)) (C (-> (-> (-> Am Bm) (-> Am Cm)) (or (-> (-> Am Bm) (-> Am Cm)) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57389.        ((A or (((B -> C) -> (B -> D)) -> (((B -> C) -> (B -> D)) or E))) -> (((B -> C) -> (B -> D)) -> (((B -> C) -> (B -> D)) or E))), M:tm-466, m:tm-703, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (or (-> (-> Am Bm) (-> Am Cm)) B)) (C (-> (-> (-> Am Bm) (-> Am Cm)) (or (-> (-> Am Bm) (-> Am Cm)) B))))
================================================================
tm-name          tm-57390
in-theory        57390
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57390.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57391
in-theory        57391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-453 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57391.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-453, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57392
in-theory        57392
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((E -> (E or F)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-443 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57392.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((E -> (E or F)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)))), M:tm-443, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57393
in-theory        57393
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-409 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57393.        (((A -> (A or B)) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-409, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57394
in-theory        57394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-400 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57394.        (((A -> (B -> (A and B))) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-400, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57395
in-theory        57395
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-391 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57395.        ((((A and B) -> B) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-391, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57396
in-theory        57396
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-382 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-1 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57396.        ((((A and B) -> A) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-382, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57397
in-theory        57397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H)))
theorem-size     35
proof            (modus-ponens tm-373 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57397.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H))), M:tm-373, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57398
in-theory        57398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-364 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57398.        (((A -> (B -> A)) or C) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-364, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57399
in-theory        57399
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> (E -> ((((A -> B) -> (A -> C)) -> D) and E)))
theorem-size     23
proof            (modus-ponens tm-355 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57399.        ((((A -> B) -> (A -> C)) -> D) -> (E -> ((((A -> B) -> (A -> C)) -> D) and E))), M:tm-355, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57400
in-theory        57400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-354 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57400.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-354, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57401
in-theory        57401
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (E -> (((B -> C) -> (B -> D)) and E)))) -> (((B -> C) -> (B -> D)) -> (E -> (((B -> C) -> (B -> D)) and E))))
theorem-size     41
proof            (modus-ponens tm-351 tm-703 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (-> B (and (-> (-> Am Bm) (-> Am Cm)) B))) (C (-> (-> (-> Am Bm) (-> Am Cm)) (-> B (and (-> (-> Am Bm) (-> Am Cm)) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57401.        ((A or (((B -> C) -> (B -> D)) -> (E -> (((B -> C) -> (B -> D)) and E)))) -> (((B -> C) -> (B -> D)) -> (E -> (((B -> C) -> (B -> D)) and E)))), M:tm-351, m:tm-703, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (-> B (and (-> (-> Am Bm) (-> Am Cm)) B))) (C (-> (-> (-> Am Bm) (-> Am Cm)) (-> B (and (-> (-> Am Bm) (-> Am Cm)) B)))))
================================================================
tm-name          tm-57402
in-theory        57402
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57402.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57403
in-theory        57403
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-338 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57403.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F))), M:tm-338, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57404
in-theory        57404
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and D))) -> (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and D)))
theorem-size     45
proof            (modus-ponens tm-335 tm-703 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (and (-> (-> Am Bm) (-> Am Cm)) B)) (C (-> (-> (-> Am Bm) (-> Am Cm)) (and (-> (-> Am Bm) (-> Am Cm)) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57404.        (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and D))) -> (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and D))), M:tm-335, m:tm-703, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (and (-> (-> Am Bm) (-> Am Cm)) B)) (C (-> (-> (-> Am Bm) (-> Am Cm)) (and (-> (-> Am Bm) (-> Am Cm)) B))))
================================================================
tm-name          tm-57405
in-theory        57405
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> B) -> (A -> C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-328 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57405.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> B) -> (A -> C)) -> D)))), M:tm-328, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57406
in-theory        57406
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((E -> (F -> (E and F))) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D))))
theorem-size     47
proof            (modus-ponens tm-327 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57406.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((E -> (F -> (E and F))) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)))), M:tm-327, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57407
in-theory        57407
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((E and F) -> F) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-326 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57407.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((E and F) -> F) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)))), M:tm-326, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57408
in-theory        57408
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((E and F) -> E) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-325 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57408.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((E and F) -> E) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)))), M:tm-325, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57409
in-theory        57409
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-324 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       233
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57409.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)))), M:tm-324, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57410
in-theory        57410
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((E -> (F -> E)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D))))
theorem-size     45
proof            (modus-ponens tm-323 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57410.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((E -> (F -> E)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)))), M:tm-323, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57411
in-theory        57411
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57411.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57412
in-theory        57412
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57412.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57413
in-theory        57413
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57413.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57414
in-theory        57414
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)))
theorem-size     39
proof            (modus-ponens tm-316 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57414.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D))), M:tm-316, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57415
in-theory        57415
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57415.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57416
in-theory        57416
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> B) -> (A -> C)) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))))
theorem-size     51
proof            (modus-ponens tm-313 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-8)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57416.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> B) -> (A -> C)) -> D))) -> (not (((A -> B) -> (A -> C)) -> D)))), M:tm-313, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57417
in-theory        57417
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> D)) -> E)))
theorem-size     53
proof            (modus-ponens tm-312 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57417.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> D)) -> E))), M:tm-312, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57418
in-theory        57418
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (E or ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D))))
theorem-size     41
proof            (modus-ponens tm-311 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57418.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (E or ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)))), M:tm-311, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57419
in-theory        57419
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57419.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) or E)), M:tm-310, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57420
in-theory        57420
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (E -> (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57420.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (E -> (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and E))), M:tm-309, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57421
in-theory        57421
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> B) -> (A -> C))) -> ((((A -> B) -> (A -> C)) -> D) -> D)))
theorem-size     49
proof            (modus-ponens tm-306 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> Am Bm) (-> Am Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57421.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> B) -> (A -> C))) -> ((((A -> B) -> (A -> C)) -> D) -> D))), M:tm-306, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> Am Bm) (-> Am Cm))) (C Dm))
================================================================
tm-name          tm-57422
in-theory        57422
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (E -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D))))
theorem-size     41
proof            (modus-ponens tm-305 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57422.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and (E -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)))), M:tm-305, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57423
in-theory        57423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-303 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57423.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-303, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57424
in-theory        57424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-270 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57424.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-270, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57425
in-theory        57425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-239 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57425.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-239, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57426
in-theory        57426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H)))
theorem-size     37
proof            (modus-ponens tm-210 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57426.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H))), M:tm-210, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57427
in-theory        57427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     29
proof            (modus-ponens tm-183 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57427.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-183, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57428
in-theory        57428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-157 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57428.        ((A -> ((B and C) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-157, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57429
in-theory        57429
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-147 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57429.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-147, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57430
in-theory        57430
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-134 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57430.        ((A -> ((B and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-134, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57431
in-theory        57431
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-125 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57431.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-125, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57432
in-theory        57432
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (D -> E)) -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> E)))
theorem-size     31
proof            (modus-ponens tm-114 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) (-> C D))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57432.        ((((A -> B) -> (A -> C)) -> (D -> E)) -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> E))), M:tm-114, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) (-> C D))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-57433
in-theory        57433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H)))
theorem-size     35
proof            (modus-ponens tm-113 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57433.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H))), M:tm-113, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57434
in-theory        57434
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (((B -> C) -> B) -> ((B -> C) -> D)))) -> (((B -> C) -> (B -> D)) -> (((B -> C) -> B) -> ((B -> C) -> D))))
theorem-size     41
proof            (modus-ponens tm-110 tm-703 ((A (-> Am Bm)) (B Am) (C Cm) (Dm (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))) (D (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57434.        ((A or (((B -> C) -> (B -> D)) -> (((B -> C) -> B) -> ((B -> C) -> D)))) -> (((B -> C) -> (B -> D)) -> (((B -> C) -> B) -> ((B -> C) -> D)))), M:tm-110, m:tm-703, u:((A (-> Am Bm)) (B Am) (C Cm) (Dm (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))) (D (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-57435
in-theory        57435
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-105 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57435.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-105, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57436
in-theory        57436
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((A -> B) -> A)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> C))) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> C)))
theorem-size     41
proof            (modus-ponens tm-102 tm-703 ((A (-> Am Bm)) (B Am) (C Cm) (Dm (-> (-> Am Bm) Cm)) (D (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57436.        (((((A -> B) -> (A -> C)) -> ((A -> B) -> A)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> C))) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> C))), M:tm-102, m:tm-703, u:((A (-> Am Bm)) (B Am) (C Cm) (Dm (-> (-> Am Bm) Cm)) (D (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-57437
in-theory        57437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-95 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57437.        (((A -> B) -> (A -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F))), M:tm-95, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57438
in-theory        57438
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-92 tm-703 ((Dm (-> (-> Am Bm) (-> Am Cm))) (A (-> (-> Am Bm) (-> Am Cm))) (B (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57438.        (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C)))), M:tm-92, m:tm-703, u:((Dm (-> (-> Am Bm) (-> Am Cm))) (A (-> (-> Am Bm) (-> Am Cm))) (B (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-57439
in-theory        57439
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> (E -> (((A -> B) -> (A -> C)) -> D)))
theorem-size     21
proof            (modus-ponens tm-84 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57439.        ((((A -> B) -> (A -> C)) -> D) -> (E -> (((A -> B) -> (A -> C)) -> D))), M:tm-84, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57440
in-theory        57440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     27
proof            (modus-ponens tm-83 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57440.        ((A -> (B -> (C -> B))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-83, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57441
in-theory        57441
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (E -> ((B -> C) -> (B -> D))))) -> (((B -> C) -> (B -> D)) -> (E -> ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-80 tm-703 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (-> B (-> (-> Am Bm) (-> Am Cm)))) (C (-> (-> (-> Am Bm) (-> Am Cm)) (-> B (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57441.        ((A or (((B -> C) -> (B -> D)) -> (E -> ((B -> C) -> (B -> D))))) -> (((B -> C) -> (B -> D)) -> (E -> ((B -> C) -> (B -> D))))), M:tm-80, m:tm-703, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (-> B (-> (-> Am Bm) (-> Am Cm)))) (C (-> (-> (-> Am Bm) (-> Am Cm)) (-> B (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-57442
in-theory        57442
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) -> (B -> D)) -> E) -> (((B -> C) -> (B -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-76 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57442.        (((not (not A)) -> A) and ((((B -> C) -> (B -> D)) -> E) -> (((B -> C) -> (B -> D)) -> E))), M:tm-76, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57443
in-theory        57443
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) -> (A -> C)) -> D))) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> B) -> (A -> C)) -> D))
theorem-size     31
proof            (modus-ponens tm-73 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57443.        (((not (not (((A -> B) -> (A -> C)) -> D))) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> B) -> (A -> C)) -> D)), M:tm-73, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57444
in-theory        57444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-69 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-1 tm-8)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57444.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F))), M:tm-69, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57445
in-theory        57445
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C))) -> ((((A -> B) -> (A -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-55 tm-703 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (-> (-> Am Bm) (-> Am Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57445.        ((((A -> B) -> (A -> C)) -> ((A -> B) -> (A -> C))) -> ((((A -> B) -> (A -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> C)))), M:tm-55, m:tm-703, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (-> (-> Am Bm) (-> Am Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-57446
in-theory        57446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-54 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57446.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-54, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57447
in-theory        57447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D))))
theorem-size     41
proof            (modus-ponens tm-51 tm-703 ((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (or C (-> Am Bm)) (-> Am Cm))) (D (-> (-> (-> Am Bm) (-> Am Cm)) (-> (or C (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57447.        (((A -> (B -> C)) or (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))) -> (((B -> C) -> (B -> D)) -> ((A or (B -> C)) -> (B -> D)))), M:tm-51, m:tm-703, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (or C (-> Am Bm)) (-> Am Cm))) (D (-> (-> (-> Am Bm) (-> Am Cm)) (-> (or C (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-57448
in-theory        57448
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D)))))
theorem-size     37
proof            (modus-ponens tm-48 tm-703 ((A (-> (-> Am Bm) (-> Am Cm))) (Dm (and B (-> (-> Am Bm) (-> Am Cm)))) (C (-> (-> (-> Am Bm) (-> Am Cm)) (and B (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57448.        ((A or (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))) -> (((B -> C) -> (B -> D)) -> (A and ((B -> C) -> (B -> D))))), M:tm-48, m:tm-703, u:((A (-> (-> Am Bm) (-> Am Cm))) (Dm (and B (-> (-> Am Bm) (-> Am Cm)))) (C (-> (-> (-> Am Bm) (-> Am Cm)) (and B (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-57449
in-theory        57449
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> C) -> (B -> D)) -> E))
theorem-size     31
proof            (modus-ponens tm-47 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57449.        (((A and (((B -> C) -> (B -> D)) -> E)) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> C) -> (B -> D)) -> E)), M:tm-47, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57450
in-theory        57450
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> B) -> (A -> C)) -> D))
theorem-size     31
proof            (modus-ponens tm-46 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57450.        ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> B) -> (A -> C)) -> D)), M:tm-46, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57451
in-theory        57451
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))
theorem-size     37
proof            (modus-ponens tm-45 tm-703 ((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) C)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57451.        ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> B) -> (A -> C)) -> ((A -> B) -> D))), M:tm-45, m:tm-703, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) C))))
================================================================
tm-name          tm-57452
in-theory        57452
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> C) -> (B -> D)) -> A))
theorem-size     21
proof            (modus-ponens tm-44 tm-703 ((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57452.        ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> C) -> (B -> D)) -> A)), M:tm-44, m:tm-703, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57453
in-theory        57453
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-42 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57453.        ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F))), M:tm-42, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57454
in-theory        57454
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-32 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57454.        ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F))), M:tm-32, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57455
in-theory        57455
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> B) -> (A -> C)) -> D)))
theorem-size     29
proof            (modus-ponens tm-24 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57455.        ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> B) -> (A -> C)) -> D))), M:tm-24, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57456
in-theory        57456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F)))
theorem-size     27
proof            (modus-ponens tm-23 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57456.        ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F))), M:tm-23, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57457
in-theory        57457
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-22 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57457.        (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F))), M:tm-22, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57458
in-theory        57458
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-21 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-1 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57458.        (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F))), M:tm-21, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57459
in-theory        57459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-20 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57459.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-20, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57460
in-theory        57460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-19 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57460.        ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> D) -> (C -> E)) -> F))), M:tm-19, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57461
in-theory        57461
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> B) -> (A -> C)) -> D))) -> (not (((A -> B) -> (A -> C)) -> D)))
theorem-size     31
proof            (modus-ponens tm-9 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-9 tm-2 tm-1 tm-8)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57461.        (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> B) -> (A -> C)) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57462
in-theory        57462
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> D)) -> E))
theorem-size     33
proof            (modus-ponens tm-8 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57462.        (((((A -> B) -> (A -> C)) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> B) -> (A -> C)) -> D)) -> E)), M:tm-8, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-57463
in-theory        57463
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> C) -> (B -> D)) -> E)))
theorem-size     21
proof            (modus-ponens tm-7 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-7 tm-2 tm-1 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57463.        (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> C) -> (B -> D)) -> E))), M:tm-7, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57464
in-theory        57464
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-6 tm-2 tm-1 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57464.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) or E), M:tm-6, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57465
in-theory        57465
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> C) -> (B -> D)) -> E)) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57465.        (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> C) -> (B -> D)) -> E)) and A)), M:tm-5, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57466
in-theory        57466
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((A -> B) -> (A -> C))) -> ((((A -> B) -> (A -> C)) -> D) -> D))
theorem-size     29
proof            (modus-ponens tm-2 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> Am Bm) (-> Am Cm))) (C Dm)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57466.        (((((A -> B) -> (A -> C)) -> D) -> ((A -> B) -> (A -> C))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> Am Bm) (-> Am Cm))) (C Dm))
================================================================
tm-name          tm-57467
in-theory        57467
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> C) -> (B -> D)) -> E)))
theorem-size     21
proof            (modus-ponens tm-1 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-1 tm-2 tm-8)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57467.        (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> C) -> (B -> D)) -> E))), M:tm-1, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57468
in-theory        57468
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     51
proof            (modus-ponens tm-665 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-2)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57468.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-665, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57469
in-theory        57469
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (not (((A -> B) -> (A -> C)) -> D))))
theorem-size     92
proof            (modus-ponens tm-654 tm-704 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9)
proof-size       270
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57469.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (not (((A -> B) -> (A -> C)) -> D)))), M:tm-654, m:tm-704, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57470
in-theory        57470
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (E or (not (((A -> B) -> (A -> C)) -> D))))
theorem-size     39
proof            (modus-ponens tm-623 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57470.        (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (E or (not (((A -> B) -> (A -> C)) -> D)))), M:tm-623, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57471
in-theory        57471
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-622 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57471.        ((A -> (B -> (C or B))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-622, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57472
in-theory        57472
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> B) -> (A -> C)) -> (D or ((A -> B) -> (A -> C)))) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))))))
theorem-size     43
proof            (modus-ponens tm-618 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) (or C (-> (-> Am Bm) (-> Am Cm)))) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or C (-> (-> Am Bm) (-> Am Cm))))))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (or C (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-9 tm-1 tm-7 tm-8 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57472.        (not ((((A -> B) -> (A -> C)) -> (D or ((A -> B) -> (A -> C)))) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C))))))), M:tm-618, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) (or C (-> (-> Am Bm) (-> Am Cm)))) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or C (-> (-> Am Bm) (-> Am Cm))))))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (or C (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-57473
in-theory        57473
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (E -> (F or E)))
theorem-size     43
proof            (modus-ponens tm-609 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57473.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (E -> (F or E))), M:tm-609, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57474
in-theory        57474
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-605 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57474.        ((A -> ((B -> (C or B)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-605, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57475
in-theory        57475
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((E -> (F or E)) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D)))))
theorem-size     81
proof            (modus-ponens tm-595 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-8)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57475.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((E -> (F or E)) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))))), M:tm-595, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57476
in-theory        57476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-550 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57476.        (((A -> (B or A)) or C) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-550, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57477
in-theory        57477
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-540 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57477.        ((A or (B -> (C or B))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-540, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57478
in-theory        57478
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-530 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57478.        ((A or (B -> (B or C))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-530, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57479
in-theory        57479
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-520 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57479.        ((A or (B -> (C -> (B and C)))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-520, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57480
in-theory        57480
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-510 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57480.        ((A or ((B and C) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-510, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57481
in-theory        57481
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-500 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57481.        ((A or ((B and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-500, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57482
in-theory        57482
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> (E -> G)) -> H) -> (not (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))) -> (not (((E -> F) -> (E -> G)) -> H))))
theorem-size     53
proof            (modus-ponens tm-490 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57482.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> (E -> G)) -> H) -> (not (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))) -> (not (((E -> F) -> (E -> G)) -> H)))), M:tm-490, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57483
in-theory        57483
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-480 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57483.        ((A or (B -> (C -> B))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-480, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57484
in-theory        57484
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> ((not (((A -> B) -> (A -> C)) -> D)) or E))
theorem-size     39
proof            (modus-ponens tm-470 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57484.        (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> ((not (((A -> B) -> (A -> C)) -> D)) or E)), M:tm-470, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57485
in-theory        57485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-469 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57485.        ((A -> (B -> (B or C))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-469, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57486
in-theory        57486
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) or D)) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)))))
theorem-size     43
proof            (modus-ponens tm-465 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) (or (-> (-> Am Bm) (-> Am Cm)) C)) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) C))))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (or (-> (-> Am Bm) (-> Am Cm)) C))))
axioms-used      (tm-9 tm-1 tm-6 tm-8 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57486.        (not ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) or D)) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D))))), M:tm-465, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) (or (-> (-> Am Bm) (-> Am Cm)) C)) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) C))))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (or (-> (-> Am Bm) (-> Am Cm)) C)))
================================================================
tm-name          tm-57487
in-theory        57487
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (E -> (E or F)))
theorem-size     43
proof            (modus-ponens tm-456 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57487.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (E -> (E or F))), M:tm-456, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57488
in-theory        57488
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-453 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57488.        ((A -> ((B -> (B or C)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-453, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57489
in-theory        57489
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((E -> (E or F)) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D)))))
theorem-size     81
proof            (modus-ponens tm-443 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-8)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57489.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((E -> (E or F)) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))))), M:tm-443, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57490
in-theory        57490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-409 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57490.        (((A -> (A or B)) or C) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-409, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57491
in-theory        57491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-400 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57491.        (((A -> (B -> (A and B))) or C) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-400, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57492
in-theory        57492
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-391 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57492.        ((((A and B) -> B) or C) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-391, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57493
in-theory        57493
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-382 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57493.        ((((A and B) -> A) or C) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-382, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57494
in-theory        57494
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) -> (E -> G)) -> H) -> (not (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))) -> (not (((E -> F) -> (E -> G)) -> H))))
theorem-size     53
proof            (modus-ponens tm-373 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57494.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) -> (E -> G)) -> H) -> (not (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))) -> (not (((E -> F) -> (E -> G)) -> H)))), M:tm-373, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57495
in-theory        57495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-364 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57495.        (((A -> (B -> A)) or C) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-364, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57496
in-theory        57496
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (E -> ((not (((A -> B) -> (A -> C)) -> D)) and E)))
theorem-size     41
proof            (modus-ponens tm-355 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57496.        (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (E -> ((not (((A -> B) -> (A -> C)) -> D)) and E))), M:tm-355, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57497
in-theory        57497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-354 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57497.        ((A -> (B -> (C -> (B and C)))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-354, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57498
in-theory        57498
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> B) -> (A -> C)) -> (D -> (((A -> B) -> (A -> C)) and D))) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))))))
theorem-size     47
proof            (modus-ponens tm-350 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) (-> C (and (-> (-> Am Bm) (-> Am Cm)) C))) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> C (and (-> (-> Am Bm) (-> Am Cm)) C)))))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (-> C (and (-> (-> Am Bm) (-> Am Cm)) C)))))
axioms-used      (tm-9 tm-1 tm-5 tm-8 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57498.        (not ((((A -> B) -> (A -> C)) -> (D -> (((A -> B) -> (A -> C)) and D))) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D)))))), M:tm-350, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) (-> C (and (-> (-> Am Bm) (-> Am Cm)) C))) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> C (and (-> (-> Am Bm) (-> Am Cm)) C)))))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (-> C (and (-> (-> Am Bm) (-> Am Cm)) C))))
================================================================
tm-name          tm-57499
in-theory        57499
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (E -> (F -> (E and F))))
theorem-size     45
proof            (modus-ponens tm-341 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57499.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57500
in-theory        57500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F))))
theorem-size     47
proof            (modus-ponens tm-338 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57500.        (((A -> B) -> (A -> (A and B))) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F)))), M:tm-338, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57501
in-theory        57501
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (not (((A -> B) -> (A -> C)) -> D)))))
theorem-size     102
proof            (modus-ponens tm-328 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       272
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57501.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (not (((A -> B) -> (A -> C)) -> D))))), M:tm-328, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57502
in-theory        57502
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((E -> (F -> (E and F))) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D)))))
theorem-size     83
proof            (modus-ponens tm-327 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57502.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((E -> (F -> (E and F))) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))))), M:tm-327, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57503
in-theory        57503
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((E and F) -> F) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D)))))
theorem-size     81
proof            (modus-ponens tm-326 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-8)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57503.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((E and F) -> F) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))))), M:tm-326, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57504
in-theory        57504
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((E and F) -> E) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D)))))
theorem-size     81
proof            (modus-ponens tm-325 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-8)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57504.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((E and F) -> E) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))))), M:tm-325, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57505
in-theory        57505
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D)))))
theorem-size     89
proof            (modus-ponens tm-324 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       273
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57505.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))))), M:tm-324, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57506
in-theory        57506
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((E -> (F -> E)) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D)))))
theorem-size     81
proof            (modus-ponens tm-323 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57506.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((E -> (F -> E)) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))))), M:tm-323, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57507
in-theory        57507
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((E and F) -> F))
theorem-size     43
proof            (modus-ponens tm-322 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57507.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57508
in-theory        57508
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((E and F) -> E))
theorem-size     43
proof            (modus-ponens tm-320 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57508.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57509
in-theory        57509
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     51
proof            (modus-ponens tm-318 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57509.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57510
in-theory        57510
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))))
theorem-size     91
proof            (modus-ponens tm-316 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57510.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))), M:tm-316, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57511
in-theory        57511
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (E -> (F -> E)))
theorem-size     43
proof            (modus-ponens tm-315 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57511.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57512
in-theory        57512
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (not (((A -> B) -> (A -> C)) -> D)))) -> (not ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))))
theorem-size     104
proof            (modus-ponens tm-313 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       258
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57512.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (not (((A -> B) -> (A -> C)) -> D)))) -> (not ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))))), M:tm-313, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57513
in-theory        57513
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((not (((A -> B) -> (A -> C)) -> D)) -> E) -> ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) or (not (((A -> B) -> (A -> C)) -> D))) -> E)))
theorem-size     90
proof            (modus-ponens tm-312 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9)
proof-size       248
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57513.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((not (((A -> B) -> (A -> C)) -> D)) -> E) -> ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) or (not (((A -> B) -> (A -> C)) -> D))) -> E))), M:tm-312, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57514
in-theory        57514
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (E or (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D)))))
theorem-size     77
proof            (modus-ponens tm-311 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-8)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57514.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (E or (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))))), M:tm-311, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57515
in-theory        57515
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) or E))
theorem-size     77
proof            (modus-ponens tm-310 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-8)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57515.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) or E)), M:tm-310, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57516
in-theory        57516
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (E -> ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and E)))
theorem-size     79
proof            (modus-ponens tm-309 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       223
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57516.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (E -> ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and E))), M:tm-309, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57517
in-theory        57517
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (E -> (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D)))))
theorem-size     77
proof            (modus-ponens tm-305 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57517.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (E -> (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))))), M:tm-305, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57518
in-theory        57518
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     49
proof            (modus-ponens tm-303 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57518.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-303, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57519
in-theory        57519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-270 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57519.        ((A -> (((B and C) -> C) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-270, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57520
in-theory        57520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-239 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57520.        ((A -> (((B and C) -> B) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-239, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57521
in-theory        57521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) -> (E -> G)) -> H) -> (not (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))) -> (not (((E -> F) -> (E -> G)) -> H))))
theorem-size     55
proof            (modus-ponens tm-210 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8)
proof-size       219
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57521.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) -> (E -> G)) -> H) -> (not (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))) -> (not (((E -> F) -> (E -> G)) -> H)))), M:tm-210, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57522
in-theory        57522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     47
proof            (modus-ponens tm-183 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57522.        ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-183, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57523
in-theory        57523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-157 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57523.        ((A -> ((B and C) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-157, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57524
in-theory        57524
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     53
proof            (modus-ponens tm-147 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57524.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-147, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57525
in-theory        57525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-134 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57525.        ((A -> ((B and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-134, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57526
in-theory        57526
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     53
proof            (modus-ponens tm-125 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57526.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-125, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57527
in-theory        57527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> (E -> G)) -> H) -> (not (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))) -> (not (((E -> F) -> (E -> G)) -> H))))
theorem-size     53
proof            (modus-ponens tm-113 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57527.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> (E -> G)) -> H) -> (not (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))) -> (not (((E -> F) -> (E -> G)) -> H)))), M:tm-113, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57528
in-theory        57528
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> B) -> (A -> C)) -> (((A -> B) -> A) -> ((A -> B) -> C))) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))))))
theorem-size     47
proof            (modus-ponens tm-109 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))) (B (-> Am Bm)) (C Am) (D Cm) (Dm (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-9 tm-1 tm-2 tm-8)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57528.        (not ((((A -> B) -> (A -> C)) -> (((A -> B) -> A) -> ((A -> B) -> C))) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C)))))), M:tm-109, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))) (B (-> Am Bm)) (C Am) (D Cm) (Dm (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-57529
in-theory        57529
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     57
proof            (modus-ponens tm-105 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8)
proof-size       231
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57529.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-105, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57530
in-theory        57530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F))))
theorem-size     45
proof            (modus-ponens tm-95 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57530.        (((A -> B) -> (A -> A)) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F)))), M:tm-95, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57531
in-theory        57531
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (E -> (not (((A -> B) -> (A -> C)) -> D))))
theorem-size     39
proof            (modus-ponens tm-84 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57531.        (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (E -> (not (((A -> B) -> (A -> C)) -> D)))), M:tm-84, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57532
in-theory        57532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-83 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57532.        ((A -> (B -> (C -> B))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-83, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57533
in-theory        57533
times-derived    1
----------------------------------------------------------------
theorem          (not ((((A -> B) -> (A -> C)) -> (D -> ((A -> B) -> (A -> C)))) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))))))
theorem-size     43
proof            (modus-ponens tm-79 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) (-> C (-> (-> Am Bm) (-> Am Cm)))) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> C (-> (-> Am Bm) (-> Am Cm))))))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (-> C (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-9 tm-1 tm-8 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57533.        (not ((((A -> B) -> (A -> C)) -> (D -> ((A -> B) -> (A -> C)))) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C))))))), M:tm-79, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) (-> C (-> (-> Am Bm) (-> Am Cm)))) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> C (-> (-> Am Bm) (-> Am Cm))))))) (B (-> (-> Am Bm) (-> Am Cm))) (Dm (-> C (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-57534
in-theory        57534
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> C) -> (B -> D)) -> E) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) -> (not (((B -> C) -> (B -> D)) -> E))))
theorem-size     43
proof            (modus-ponens tm-76 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-10 tm-9 tm-8 tm-2)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57534.        (((not (not A)) -> A) and (((((B -> C) -> (B -> D)) -> E) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) -> (not (((B -> C) -> (B -> D)) -> E)))), M:tm-76, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57535
in-theory        57535
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))) or ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (not (((A -> B) -> (A -> C)) -> D)))
theorem-size     66
proof            (modus-ponens tm-73 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-10 tm-9 tm-2)
proof-size       194
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57535.        (((not (not ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))) or ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-73, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57536
in-theory        57536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F))))
theorem-size     49
proof            (modus-ponens tm-69 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       181
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57536.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F)))), M:tm-69, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57537
in-theory        57537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     51
proof            (modus-ponens tm-54 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-2)
proof-size       187
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57537.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-54, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57538
in-theory        57538
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B -> C) -> (B -> D)) -> E) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))) or ((((B -> C) -> (B -> D)) -> E) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))) -> (not (((B -> C) -> (B -> D)) -> E)))
theorem-size     66
proof            (modus-ponens tm-47 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-4 tm-9 tm-2)
proof-size       194
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57538.        (((A and ((((B -> C) -> (B -> D)) -> E) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))) or ((((B -> C) -> (B -> D)) -> E) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))) -> (not (((B -> C) -> (B -> D)) -> E))), M:tm-47, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57539
in-theory        57539
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and E) or ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (not (((A -> B) -> (A -> C)) -> D)))
theorem-size     66
proof            (modus-ponens tm-46 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-3 tm-9 tm-2)
proof-size       194
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57539.        (((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and E) or ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-46, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57540
in-theory        57540
times-derived    1
----------------------------------------------------------------
theorem          (((not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (not (((A -> B) -> (A -> C)) -> D)))
theorem-size     54
proof            (modus-ponens tm-44 tm-704 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-1 tm-9 tm-2)
proof-size       184
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57540.        (((not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-44, m:tm-704, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57541
in-theory        57541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F))))
theorem-size     43
proof            (modus-ponens tm-42 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-2)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57541.        ((A -> (B or A)) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F)))), M:tm-42, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57542
in-theory        57542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F))))
theorem-size     43
proof            (modus-ponens tm-32 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-2)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57542.        ((A -> (A or B)) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F)))), M:tm-32, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57543
in-theory        57543
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (not (((A -> B) -> (A -> C)) -> D))))
theorem-size     64
proof            (modus-ponens tm-24 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       192
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57543.        (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (not (((A -> B) -> (A -> C)) -> D)))), M:tm-24, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57544
in-theory        57544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F))))
theorem-size     45
proof            (modus-ponens tm-23 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       169
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57544.        ((A -> (B -> (A and B))) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F)))), M:tm-23, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57545
in-theory        57545
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F))))
theorem-size     43
proof            (modus-ponens tm-22 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8 tm-2)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57545.        (((A and B) -> B) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F)))), M:tm-22, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57546
in-theory        57546
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F))))
theorem-size     43
proof            (modus-ponens tm-21 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8 tm-2)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57546.        (((A and B) -> A) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F)))), M:tm-21, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57547
in-theory        57547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     51
proof            (modus-ponens tm-20 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8)
proof-size       187
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57547.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-20, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57548
in-theory        57548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F))))
theorem-size     43
proof            (modus-ponens tm-19 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-2)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57548.        ((A -> (B -> A)) and (((((C -> D) -> (C -> E)) -> F) -> (not (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) -> (not (((C -> D) -> (C -> E)) -> F)))), M:tm-19, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57549
in-theory        57549
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     53
proof            (modus-ponens tm-12 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-8)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57549.        (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-12, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57550
in-theory        57550
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (not (((A -> B) -> (A -> C)) -> D)))) -> (not ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))))
theorem-size     66
proof            (modus-ponens tm-9 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-9 tm-8 tm-2)
proof-size       176
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57550.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (not (((A -> B) -> (A -> C)) -> D)))) -> (not ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))), M:tm-9, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57551
in-theory        57551
times-derived    1
----------------------------------------------------------------
theorem          (((not (((A -> B) -> (A -> C)) -> D)) -> E) -> ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) or (not (((A -> B) -> (A -> C)) -> D))) -> E))
theorem-size     52
proof            (modus-ponens tm-8 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-8 tm-9 tm-2)
proof-size       164
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57551.        (((not (((A -> B) -> (A -> C)) -> D)) -> E) -> ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) or (not (((A -> B) -> (A -> C)) -> D))) -> E)), M:tm-8, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-57552
in-theory        57552
times-derived    1
----------------------------------------------------------------
theorem          (A or (((((B -> C) -> (B -> D)) -> E) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) -> (not (((B -> C) -> (B -> D)) -> E))))
theorem-size     39
proof            (modus-ponens tm-7 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-7 tm-9 tm-8 tm-2)
proof-size       143
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57552.        (A or (((((B -> C) -> (B -> D)) -> E) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) -> (not (((B -> C) -> (B -> D)) -> E)))), M:tm-7, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57553
in-theory        57553
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) or E)
theorem-size     39
proof            (modus-ponens tm-6 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-6 tm-9 tm-8 tm-2)
proof-size       143
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57553.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) or E), M:tm-6, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57554
in-theory        57554
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) -> (B -> D)) -> E) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) -> (not (((B -> C) -> (B -> D)) -> E))) and A))
theorem-size     41
proof            (modus-ponens tm-5 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       147
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57554.        (A -> ((((((B -> C) -> (B -> D)) -> E) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) -> (not (((B -> C) -> (B -> D)) -> E))) and A)), M:tm-5, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57555
in-theory        57555
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> (B -> D)) -> E) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) -> (not (((B -> C) -> (B -> D)) -> E))))
theorem-size     39
proof            (modus-ponens tm-1 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-1 tm-9 tm-8 tm-2)
proof-size       143
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57555.        (A -> (((((B -> C) -> (B -> D)) -> E) -> (not (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) -> (not (((B -> C) -> (B -> D)) -> E)))), M:tm-1, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-57556
in-theory        57556
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     43
proof            (modus-ponens tm-705 tm-1 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       157
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-57556.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-1, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57557
in-theory        57557
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (D -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E))) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)))
theorem-size     61
proof            (modus-ponens tm-705 tm-2 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm Cm)) (E (-> (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       183
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57557.        (((((A -> B) -> (A -> C)) -> (D -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E))) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))), M:tm-705, m:tm-2, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm Cm)) (E (-> (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm))))
================================================================
tm-name          tm-57558
in-theory        57558
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and E)))
theorem-size     45
proof            (modus-ponens tm-705 tm-5 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       161
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-57558.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and E))), M:tm-705, m:tm-5, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm))))
================================================================
tm-name          tm-57559
in-theory        57559
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) or E))
theorem-size     43
proof            (modus-ponens tm-705 tm-6 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm))))
axioms-used      (tm-8 tm-2 tm-6)
proof-size       157
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-57559.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) or E)), M:tm-705, m:tm-6, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm)))
================================================================
tm-name          tm-57560
in-theory        57560
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     43
proof            (modus-ponens tm-705 tm-7 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-7)
proof-size       157
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-57560.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-7, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57561
in-theory        57561
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((D -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D) -> E)))
theorem-size     47
proof            (modus-ponens tm-705 tm-8 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (-> Bm Cm) (-> (or (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) Cm)))))
axioms-used      (tm-8 tm-2)
proof-size       169
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57561.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((D -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D) -> E))), M:tm-705, m:tm-8, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (-> Bm Cm) (-> (or (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) Cm))))
================================================================
tm-name          tm-57562
in-theory        57562
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not D)) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     57
proof            (modus-ponens tm-705 tm-9 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (not Bm)) (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))))
axioms-used      (tm-8 tm-2 tm-9)
proof-size       177
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57562.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not D)) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-705, m:tm-9, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (not Bm)) (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
================================================================
tm-name          tm-57563
in-theory        57563
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (F -> E)))
theorem-size     31
proof            (modus-ponens tm-705 tm-11 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-57563.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (F -> E))), M:tm-705, m:tm-11, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-57564
in-theory        57564
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     53
proof            (modus-ponens tm-705 tm-12 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       187
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-57564.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-12, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57565
in-theory        57565
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-705 tm-14 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       181
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-57565.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-705, m:tm-14, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-57566
in-theory        57566
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E and F) -> E))
theorem-size     31
proof            (modus-ponens tm-705 tm-16 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-57566.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E and F) -> E)), M:tm-705, m:tm-16, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-57567
in-theory        57567
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E and F) -> F))
theorem-size     31
proof            (modus-ponens tm-705 tm-18 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-57567.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E and F) -> F)), M:tm-705, m:tm-18, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-57568
in-theory        57568
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     47
proof            (modus-ponens tm-705 tm-19 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-57568.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-19, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57569
in-theory        57569
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     55
proof            (modus-ponens tm-705 tm-20 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       201
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-57569.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-20, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57570
in-theory        57570
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     47
proof            (modus-ponens tm-705 tm-21 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (and Bm Cm) Bm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-57570.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-21, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (and Bm Cm) Bm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57571
in-theory        57571
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     47
proof            (modus-ponens tm-705 tm-22 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (and Bm Cm) Cm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-57571.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-22, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (and Bm Cm) Cm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57572
in-theory        57572
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-23 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       183
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-57572.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-23, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57573
in-theory        57573
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D)))
theorem-size     55
proof            (modus-ponens tm-705 tm-24 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       193
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-57573.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D))), M:tm-705, m:tm-24, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm))))
================================================================
tm-name          tm-57574
in-theory        57574
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (F -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-705 tm-25 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-57574.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (F -> (E and F)))), M:tm-705, m:tm-25, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-57575
in-theory        57575
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     47
proof            (modus-ponens tm-705 tm-32 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (or Bm Cm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-57575.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-32, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (or Bm Cm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57576
in-theory        57576
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (E or F)))
theorem-size     31
proof            (modus-ponens tm-705 tm-33 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-57576.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (E or F))), M:tm-705, m:tm-33, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-57577
in-theory        57577
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     47
proof            (modus-ponens tm-705 tm-42 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (or Cm Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-57577.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-42, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (or Cm Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57578
in-theory        57578
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (F or E)))
theorem-size     31
proof            (modus-ponens tm-705 tm-43 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-57578.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (F or E))), M:tm-705, m:tm-43, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-57579
in-theory        57579
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D))
theorem-size     57
proof            (modus-ponens tm-705 tm-46 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (and (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Bm))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       195
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-57579.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D)), M:tm-705, m:tm-46, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (and (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Bm)))
================================================================
tm-name          tm-57580
in-theory        57580
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D))
theorem-size     57
proof            (modus-ponens tm-705 tm-47 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (and Cm (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Bm))))
axioms-used      (tm-8 tm-2 tm-4)
proof-size       195
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-57580.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D)), M:tm-705, m:tm-47, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (and Cm (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Bm)))
================================================================
tm-name          tm-57581
in-theory        57581
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D))
theorem-size     47
proof            (modus-ponens tm-705 tm-49 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D Cm) (E (-> (or (-> A (-> B C)) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Cm))))
axioms-used      (tm-8 tm-2 tm-6)
proof-size       187
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-57581.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D)), M:tm-705, m:tm-49, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D Cm) (E (-> (or (-> A (-> B C)) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Cm)))
================================================================
tm-name          tm-57582
in-theory        57582
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D))
theorem-size     49
proof            (modus-ponens tm-705 tm-50 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D Cm) (E (-> (or (-> (-> A B) (-> A C)) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Cm))))
axioms-used      (tm-8 tm-2 tm-7)
proof-size       189
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-57582.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D)), M:tm-705, m:tm-50, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D Cm) (E (-> (or (-> (-> A B) (-> A C)) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Cm)))
================================================================
tm-name          tm-57583
in-theory        57583
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     55
proof            (modus-ponens tm-705 tm-54 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       201
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-57583.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-54, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57584
in-theory        57584
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     39
proof            (modus-ponens tm-705 tm-56 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       181
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-57584.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))), M:tm-705, m:tm-56, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-57585
in-theory        57585
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not (D -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     70
proof            (modus-ponens tm-705 tm-57 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> Bm (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-1)
proof-size       204
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-57585.        (((((A -> B) -> (A -> C)) -> (not (D -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-57, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> Bm (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57586
in-theory        57586
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D)))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     74
proof            (modus-ponens tm-705 tm-61 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> Bm (and (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-5)
proof-size       212
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-57586.        (((((A -> B) -> (A -> C)) -> (not (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D)))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-61, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> Bm (and (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57587
in-theory        57587
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     70
proof            (modus-ponens tm-705 tm-62 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (or (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-6)
proof-size       204
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-57587.        (((((A -> B) -> (A -> C)) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-62, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (or (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57588
in-theory        57588
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not (D or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D or ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     70
proof            (modus-ponens tm-705 tm-63 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (or Bm (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-7)
proof-size       204
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-57588.        (((((A -> B) -> (A -> C)) -> (not (D or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D or ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-63, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (or Bm (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57589
in-theory        57589
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> ((E -> (not F)) -> (not E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     53
proof            (modus-ponens tm-705 tm-69 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-9)
proof-size       195
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-57589.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> ((E -> (not F)) -> (not E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-69, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57590
in-theory        57590
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> F) -> ((E -> (not F)) -> (not E))))
theorem-size     37
proof            (modus-ponens tm-705 tm-71 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-9)
proof-size       175
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-57590.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> F) -> ((E -> (not F)) -> (not E)))), M:tm-705, m:tm-71, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-57591
in-theory        57591
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D))
theorem-size     57
proof            (modus-ponens tm-705 tm-73 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (not (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Bm))))
axioms-used      (tm-8 tm-2 tm-10)
proof-size       195
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-57591.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D)), M:tm-705, m:tm-73, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (not (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Bm)))
================================================================
tm-name          tm-57592
in-theory        57592
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((not (not E)) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     47
proof            (modus-ponens tm-705 tm-76 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (not (not Bm)) Bm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-10)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-57592.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((not (not E)) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-76, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (not (not Bm)) Bm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57593
in-theory        57593
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((not (not E)) -> E))
theorem-size     31
proof            (modus-ponens tm-705 tm-78 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-10)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-57593.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((not (not E)) -> E)), M:tm-705, m:tm-78, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-57594
in-theory        57594
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not (D -> (E -> D)))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E -> D))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     50
proof            (modus-ponens tm-705 tm-79 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> Bm (-> Cm Bm)))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-1)
proof-size       198
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-57594.        (((((A -> B) -> (A -> C)) -> (not (D -> (E -> D)))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E -> D))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-79, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> Bm (-> Cm Bm)))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57595
in-theory        57595
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> (G -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-83 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-57595.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> (G -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-83, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57596
in-theory        57596
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E -> D)))
theorem-size     43
proof            (modus-ponens tm-705 tm-84 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-57596.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E -> D))), M:tm-705, m:tm-84, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Cm Bm))))
================================================================
tm-name          tm-57597
in-theory        57597
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (F -> (G -> F))))
theorem-size     33
proof            (modus-ponens tm-705 tm-85 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-57597.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (F -> (G -> F)))), M:tm-705, m:tm-85, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-57598
in-theory        57598
times-derived    3
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     41
proof            (modus-ponens tm-705 tm-86 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-57598.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-705, m:tm-86, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))
================================================================
tm-name          tm-57599
in-theory        57599
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (D -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E)))
theorem-size     47
proof            (modus-ponens tm-705 tm-87 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm Cm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-57599.        (((((A -> B) -> (A -> C)) -> (D -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E))), M:tm-705, m:tm-87, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm Cm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm Cm))))
================================================================
tm-name          tm-57600
in-theory        57600
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> (E -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-95 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-57600.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> (E -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-95, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57601
in-theory        57601
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> F) -> (E -> E)))
theorem-size     33
proof            (modus-ponens tm-705 tm-97 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-57601.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> F) -> (E -> E))), M:tm-705, m:tm-97, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-57602
in-theory        57602
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((D -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))
theorem-size     73
proof            (modus-ponens tm-705 tm-98 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Cm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-57602.        (((((A -> B) -> (A -> C)) -> ((D -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)), M:tm-705, m:tm-98, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Cm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm)))
================================================================
tm-name          tm-57603
in-theory        57603
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     69
proof            (modus-ponens tm-705 tm-99 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       257
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-57603.        (((((A -> B) -> (A -> C)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-705, m:tm-99, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)))
================================================================
tm-name          tm-57604
in-theory        57604
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     61
proof            (modus-ponens tm-705 tm-105 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       245
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-57604.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-105, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57605
in-theory        57605
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-705 tm-107 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-57605.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-705, m:tm-107, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-57606
in-theory        57606
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     66
proof            (modus-ponens tm-705 tm-109 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-1)
proof-size       238
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-57606.        (((((A -> B) -> (A -> C)) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-109, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57607
in-theory        57607
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     57
proof            (modus-ponens tm-705 tm-113 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-57607.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-113, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57608
in-theory        57608
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (D -> (E -> F))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> F)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (D -> F))))
theorem-size     55
proof            (modus-ponens tm-705 tm-114 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> Cm Dm))) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       227
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-57608.        (((((A -> B) -> (A -> C)) -> (D -> (E -> F))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> F)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (D -> F)))), M:tm-705, m:tm-114, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm (-> Cm Dm))) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-57609
in-theory        57609
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-705 tm-115 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-57609.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-705, m:tm-115, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-57610
in-theory        57610
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     57
proof            (modus-ponens tm-705 tm-125 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-57610.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-125, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57611
in-theory        57611
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))
theorem-size     41
proof            (modus-ponens tm-705 tm-127 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-57611.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))), M:tm-705, m:tm-127, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-57612
in-theory        57612
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not ((D and E) -> D))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D and E) -> D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     50
proof            (modus-ponens tm-705 tm-130 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> (and Bm Cm) Bm))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-1 tm-3)
proof-size       198
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-57612.        (((((A -> B) -> (A -> C)) -> (not ((D and E) -> D))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D and E) -> D)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-130, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> (and Bm Cm) Bm))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57613
in-theory        57613
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> ((F and G) -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-134 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-57613.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> ((F and G) -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-134, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57614
in-theory        57614
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (D and E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     45
proof            (modus-ponens tm-705 tm-135 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and Bm Cm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-57614.        (((((A -> B) -> (A -> C)) -> (D and E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-705, m:tm-135, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and Bm Cm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)))
================================================================
tm-name          tm-57615
in-theory        57615
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((F and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-705 tm-136 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-57615.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((F and G) -> F))), M:tm-705, m:tm-136, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-57616
in-theory        57616
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     57
proof            (modus-ponens tm-705 tm-147 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-57616.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-147, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57617
in-theory        57617
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))
theorem-size     41
proof            (modus-ponens tm-705 tm-149 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-57617.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))), M:tm-705, m:tm-149, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-57618
in-theory        57618
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not ((D and E) -> E))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D and E) -> E)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     50
proof            (modus-ponens tm-705 tm-153 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> (and Bm Cm) Cm))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-1 tm-4)
proof-size       198
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-57618.        (((((A -> B) -> (A -> C)) -> (not ((D and E) -> E))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D and E) -> E)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-153, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> (and Bm Cm) Cm))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57619
in-theory        57619
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> ((F and G) -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-157 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-57619.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> ((F and G) -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-157, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57620
in-theory        57620
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (D and E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))
theorem-size     45
proof            (modus-ponens tm-705 tm-158 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and Bm Cm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-57620.        (((((A -> B) -> (A -> C)) -> (D and E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D and E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)), M:tm-705, m:tm-158, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and Bm Cm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm)))
================================================================
tm-name          tm-57621
in-theory        57621
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((F and G) -> G)))
theorem-size     33
proof            (modus-ponens tm-705 tm-159 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-4)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-57621.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((F and G) -> G))), M:tm-705, m:tm-159, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-57622
in-theory        57622
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not ((D -> (E -> D)) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> D)) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     78
proof            (modus-ponens tm-705 tm-179 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (and (-> Bm (-> Cm Bm)) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-5 tm-1)
proof-size       232
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-57622.        (((((A -> B) -> (A -> C)) -> (not ((D -> (E -> D)) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> D)) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-179, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (and (-> Bm (-> Cm Bm)) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57623
in-theory        57623
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> ((F -> (G -> F)) and E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     51
proof            (modus-ponens tm-705 tm-183 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-57623.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> ((F -> (G -> F)) and E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-183, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57624
in-theory        57624
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((F -> (G -> F)) and E)))
theorem-size     35
proof            (modus-ponens tm-705 tm-184 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-57624.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((F -> (G -> F)) and E))), M:tm-705, m:tm-184, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-57625
in-theory        57625
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     94
proof            (modus-ponens tm-705 tm-206 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-5)
proof-size       272
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-57625.        (((((A -> B) -> (A -> C)) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-206, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57626
in-theory        57626
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     59
proof            (modus-ponens tm-705 tm-210 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       233
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-57626.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-210, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57627
in-theory        57627
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     43
proof            (modus-ponens tm-705 tm-211 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       213
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-57627.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-705, m:tm-211, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-57628
in-theory        57628
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not (((D and E) -> D) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and E) -> D) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     78
proof            (modus-ponens tm-705 tm-235 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (and (-> (and Bm Cm) Bm) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-5 tm-3)
proof-size       232
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-57628.        (((((A -> B) -> (A -> C)) -> (not (((D and E) -> D) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and E) -> D) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-235, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (and (-> (and Bm Cm) Bm) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57629
in-theory        57629
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (((F and G) -> F) and E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     51
proof            (modus-ponens tm-705 tm-239 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-57629.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (((F and G) -> F) and E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-239, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57630
in-theory        57630
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (((F and G) -> F) and E)))
theorem-size     35
proof            (modus-ponens tm-705 tm-240 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-3)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-57630.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (((F and G) -> F) and E))), M:tm-705, m:tm-240, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-57631
in-theory        57631
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not (((D and E) -> E) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and E) -> E) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     78
proof            (modus-ponens tm-705 tm-266 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (and (-> (and Bm Cm) Cm) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-5 tm-4)
proof-size       232
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-57631.        (((((A -> B) -> (A -> C)) -> (not (((D and E) -> E) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (((D and E) -> E) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-266, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (and (-> (and Bm Cm) Cm) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57632
in-theory        57632
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (((F and G) -> G) and E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     51
proof            (modus-ponens tm-705 tm-270 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-57632.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (((F and G) -> G) and E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-270, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57633
in-theory        57633
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (((F and G) -> G) and E)))
theorem-size     35
proof            (modus-ponens tm-705 tm-271 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-4)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-57633.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (((F and G) -> G) and E))), M:tm-705, m:tm-271, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-57634
in-theory        57634
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not ((D -> (E -> (D and E))) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> (D and E))) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     82
proof            (modus-ponens tm-705 tm-299 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (and (-> Bm (-> Cm (and Bm Cm))) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-5)
proof-size       242
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-57634.        (((((A -> B) -> (A -> C)) -> (not ((D -> (E -> (D and E))) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E -> (D and E))) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-299, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (and (-> Bm (-> Cm (and Bm Cm))) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57635
in-theory        57635
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> ((F -> (G -> (F and G))) and E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     53
proof            (modus-ponens tm-705 tm-303 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-57635.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> ((F -> (G -> (F and G))) and E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-303, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57636
in-theory        57636
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((F -> (G -> (F and G))) and E)))
theorem-size     37
proof            (modus-ponens tm-705 tm-304 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-57636.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((F -> (G -> (F and G))) and E))), M:tm-705, m:tm-304, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-57637
in-theory        57637
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     59
proof            (modus-ponens tm-705 tm-305 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-57637.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-705, m:tm-305, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-57638
in-theory        57638
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (D -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E))) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))))
theorem-size     79
proof            (modus-ponens tm-705 tm-306 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm Cm)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm Cm)) (-> (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       249
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-57638.        (((((A -> B) -> (A -> C)) -> (D -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E))) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)))), M:tm-705, m:tm-306, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> Bm Cm)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Bm Cm)) (-> (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm)))))
================================================================
tm-name          tm-57639
in-theory        57639
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and E))))
theorem-size     61
proof            (modus-ponens tm-705 tm-309 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-57639.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and E)))), M:tm-705, m:tm-309, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm)))))
================================================================
tm-name          tm-57640
in-theory        57640
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) or E)))
theorem-size     59
proof            (modus-ponens tm-705 tm-310 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (or (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-57640.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) or E))), M:tm-705, m:tm-310, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (or (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) Bm))))
================================================================
tm-name          tm-57641
in-theory        57641
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     59
proof            (modus-ponens tm-705 tm-311 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (or Bm (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-57641.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-705, m:tm-311, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (or Bm (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-57642
in-theory        57642
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((D -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D) -> E))))
theorem-size     63
proof            (modus-ponens tm-705 tm-312 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (-> Bm Cm) (-> (or (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) Cm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       231
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-57642.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((D -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D) -> E)))), M:tm-705, m:tm-312, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (-> Bm Cm) (-> (or (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) Cm)))))
================================================================
tm-name          tm-57643
in-theory        57643
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not D)) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))))
theorem-size     73
proof            (modus-ponens tm-705 tm-313 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (not Bm)) (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))))
axioms-used      (tm-8 tm-2 tm-5 tm-9)
proof-size       237
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-57643.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not D)) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))), M:tm-705, m:tm-313, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (not Bm)) (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))))
================================================================
tm-name          tm-57644
in-theory        57644
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (E -> (F -> E))))
theorem-size     47
proof            (modus-ponens tm-705 tm-315 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-57644.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (E -> (F -> E)))), M:tm-705, m:tm-315, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-57645
in-theory        57645
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     69
proof            (modus-ponens tm-705 tm-316 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-57645.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-705, m:tm-316, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
================================================================
tm-name          tm-57646
in-theory        57646
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-705 tm-318 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-57646.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-705, m:tm-318, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-57647
in-theory        57647
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((E and F) -> E)))
theorem-size     47
proof            (modus-ponens tm-705 tm-320 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-57647.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((E and F) -> E))), M:tm-705, m:tm-320, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-57648
in-theory        57648
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((E and F) -> F)))
theorem-size     47
proof            (modus-ponens tm-705 tm-322 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-57648.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((E and F) -> F))), M:tm-705, m:tm-322, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-57649
in-theory        57649
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     63
proof            (modus-ponens tm-705 tm-323 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (-> Cm Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-57649.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-705, m:tm-323, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (-> Cm Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-57650
in-theory        57650
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     71
proof            (modus-ponens tm-705 tm-324 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       265
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-57650.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-705, m:tm-324, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-57651
in-theory        57651
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     63
proof            (modus-ponens tm-705 tm-325 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> (and Bm Cm) Bm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-57651.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-705, m:tm-325, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> (and Bm Cm) Bm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-57652
in-theory        57652
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     63
proof            (modus-ponens tm-705 tm-326 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> (and Bm Cm) Cm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-2 tm-5 tm-4)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-57652.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-705, m:tm-326, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> (and Bm Cm) Cm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-57653
in-theory        57653
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     65
proof            (modus-ponens tm-705 tm-327 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-57653.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-705, m:tm-327, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-57654
in-theory        57654
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D))))
theorem-size     71
proof            (modus-ponens tm-705 tm-328 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       251
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-57654.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D)))), M:tm-705, m:tm-328, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (and (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)))))
================================================================
tm-name          tm-57655
in-theory        57655
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> (E -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     51
proof            (modus-ponens tm-705 tm-338 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-57655.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> (E -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-338, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57656
in-theory        57656
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> F) -> (E -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-705 tm-340 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-57656.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> F) -> (E -> (E and F)))), M:tm-705, m:tm-340, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-57657
in-theory        57657
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (E -> (F -> (E and F)))))
theorem-size     49
proof            (modus-ponens tm-705 tm-341 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-57657.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (E -> (F -> (E and F))))), M:tm-705, m:tm-341, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-57658
in-theory        57658
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D)) -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D)) -> E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))
theorem-size     77
proof            (modus-ponens tm-705 tm-349 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm (and (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)) Cm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       265
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-57658.        (((((A -> B) -> (A -> C)) -> ((D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D)) -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D)) -> E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)), M:tm-705, m:tm-349, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm (and (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm)) Cm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm)))
================================================================
tm-name          tm-57659
in-theory        57659
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not (D -> (E -> (D and E))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E -> (D and E)))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     54
proof            (modus-ponens tm-705 tm-350 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> Bm (-> Cm (and Bm Cm))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-1 tm-5)
proof-size       208
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-57659.        (((((A -> B) -> (A -> C)) -> (not (D -> (E -> (D and E))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E -> (D and E)))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-350, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> Bm (-> Cm (and Bm Cm))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57660
in-theory        57660
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> (G -> (F and G)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     51
proof            (modus-ponens tm-705 tm-354 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-57660.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> (G -> (F and G)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-354, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57661
in-theory        57661
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E -> (D and E))))
theorem-size     45
proof            (modus-ponens tm-705 tm-355 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-57661.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E -> (D and E)))), M:tm-705, m:tm-355, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-57662
in-theory        57662
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (F -> (G -> (F and G)))))
theorem-size     35
proof            (modus-ponens tm-705 tm-356 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-57662.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (F -> (G -> (F and G))))), M:tm-705, m:tm-356, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-57663
in-theory        57663
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (F -> E)) or G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-364 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-1)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-57663.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (F -> E)) or G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-364, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57664
in-theory        57664
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> E)) or G))
theorem-size     33
proof            (modus-ponens tm-705 tm-365 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-57664.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> E)) or G)), M:tm-705, m:tm-365, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-57665
in-theory        57665
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     57
proof            (modus-ponens tm-705 tm-373 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57665.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-373, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57666
in-theory        57666
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))
theorem-size     41
proof            (modus-ponens tm-705 tm-374 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57666.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)), M:tm-705, m:tm-374, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-57667
in-theory        57667
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E and F) -> E) or G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-382 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (and Bm Cm) Bm) Dm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-3)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-57667.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E and F) -> E) or G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-382, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (and Bm Cm) Bm) Dm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57668
in-theory        57668
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E and F) -> E) or G))
theorem-size     33
proof            (modus-ponens tm-705 tm-383 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-3)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-57668.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E and F) -> E) or G)), M:tm-705, m:tm-383, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-57669
in-theory        57669
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E and F) -> F) or G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-391 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (and Bm Cm) Cm) Dm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-4)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-57669.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E and F) -> F) or G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-391, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> (and Bm Cm) Cm) Dm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57670
in-theory        57670
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E and F) -> F) or G))
theorem-size     33
proof            (modus-ponens tm-705 tm-392 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-4)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-57670.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E and F) -> F) or G)), M:tm-705, m:tm-392, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-57671
in-theory        57671
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (F -> (E and F))) or G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     51
proof            (modus-ponens tm-705 tm-400 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-57671.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (F -> (E and F))) or G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-400, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57672
in-theory        57672
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> (E and F))) or G))
theorem-size     35
proof            (modus-ponens tm-705 tm-401 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-5)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-57672.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> (E and F))) or G)), M:tm-705, m:tm-401, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-57673
in-theory        57673
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (E or F)) or G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-409 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (or Bm Cm)) Dm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-57673.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (E or F)) or G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-409, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (or Bm Cm)) Dm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57674
in-theory        57674
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (E or F)) or G))
theorem-size     33
proof            (modus-ponens tm-705 tm-410 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-57674.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (E or F)) or G)), M:tm-705, m:tm-410, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-57675
in-theory        57675
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     63
proof            (modus-ponens tm-705 tm-443 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (or Bm Cm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-57675.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-705, m:tm-443, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (or Bm Cm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-57676
in-theory        57676
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not ((D -> (D or E)) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (D or E)) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     78
proof            (modus-ponens tm-705 tm-449 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (and (-> Bm (or Bm Cm)) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-5 tm-6)
proof-size       232
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-57676.        (((((A -> B) -> (A -> C)) -> (not ((D -> (D or E)) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (D or E)) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-449, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (and (-> Bm (or Bm Cm)) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57677
in-theory        57677
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> ((F -> (F or G)) and E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     51
proof            (modus-ponens tm-705 tm-453 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-57677.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> ((F -> (F or G)) and E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-453, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57678
in-theory        57678
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((F -> (F or G)) and E)))
theorem-size     35
proof            (modus-ponens tm-705 tm-454 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-6)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-57678.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((F -> (F or G)) and E))), M:tm-705, m:tm-454, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-57679
in-theory        57679
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (E -> (E or F))))
theorem-size     47
proof            (modus-ponens tm-705 tm-456 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-57679.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (E -> (E or F)))), M:tm-705, m:tm-456, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-57680
in-theory        57680
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D) -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D) -> E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))
theorem-size     73
proof            (modus-ponens tm-705 tm-464 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (or (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) Cm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-57680.        (((((A -> B) -> (A -> C)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D) -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or D) -> E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)), M:tm-705, m:tm-464, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (or (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) Cm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm)))
================================================================
tm-name          tm-57681
in-theory        57681
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not (D -> (D or E)))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (D or E))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     50
proof            (modus-ponens tm-705 tm-465 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> Bm (or Bm Cm)))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-1 tm-6)
proof-size       198
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-57681.        (((((A -> B) -> (A -> C)) -> (not (D -> (D or E)))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (D or E))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-465, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> Bm (or Bm Cm)))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57682
in-theory        57682
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> (F or G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-469 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (or Cm Dm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-57682.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> (F or G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-469, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (or Cm Dm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57683
in-theory        57683
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or E)))
theorem-size     43
proof            (modus-ponens tm-705 tm-470 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (or Bm Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-57683.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or E))), M:tm-705, m:tm-470, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (or Bm Cm))))
================================================================
tm-name          tm-57684
in-theory        57684
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (F -> (F or G))))
theorem-size     33
proof            (modus-ponens tm-705 tm-471 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-57684.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (F -> (F or G)))), M:tm-705, m:tm-471, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-57685
in-theory        57685
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or (F -> (G -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-480 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (-> Dm Cm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-1)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-57685.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or (F -> (G -> F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-480, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (-> Dm Cm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57686
in-theory        57686
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or (F -> (G -> F))))
theorem-size     33
proof            (modus-ponens tm-705 tm-481 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-57686.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or (F -> (G -> F)))), M:tm-705, m:tm-481, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-57687
in-theory        57687
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     57
proof            (modus-ponens tm-705 tm-490 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-57687.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-490, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57688
in-theory        57688
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-705 tm-491 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-57688.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-705, m:tm-491, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-57689
in-theory        57689
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or ((F and G) -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-500 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (and Cm Dm) Cm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-3)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-57689.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or ((F and G) -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-500, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (and Cm Dm) Cm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57690
in-theory        57690
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or ((F and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-705 tm-501 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-3)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-57690.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or ((F and G) -> F))), M:tm-705, m:tm-501, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-57691
in-theory        57691
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or ((F and G) -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-510 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (and Cm Dm) Dm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-4)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-57691.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or ((F and G) -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-510, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> (and Cm Dm) Dm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57692
in-theory        57692
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or ((F and G) -> G)))
theorem-size     33
proof            (modus-ponens tm-705 tm-511 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-4)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-57692.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or ((F and G) -> G))), M:tm-705, m:tm-511, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-57693
in-theory        57693
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or (F -> (G -> (F and G)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     51
proof            (modus-ponens tm-705 tm-520 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-57693.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or (F -> (G -> (F and G)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-520, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57694
in-theory        57694
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or (F -> (G -> (F and G)))))
theorem-size     35
proof            (modus-ponens tm-705 tm-521 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-5)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-57694.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or (F -> (G -> (F and G))))), M:tm-705, m:tm-521, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-57695
in-theory        57695
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or (F -> (F or G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-530 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (or Cm Dm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-6)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-57695.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or (F -> (F or G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-530, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (or Cm Dm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57696
in-theory        57696
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or (F -> (F or G))))
theorem-size     33
proof            (modus-ponens tm-705 tm-531 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7 tm-6)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-57696.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or (F -> (F or G)))), M:tm-705, m:tm-531, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-57697
in-theory        57697
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or (F -> (G or F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-540 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (or Dm Cm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-57697.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E or (F -> (G or F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-540, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or Bm (-> Cm (or Dm Cm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57698
in-theory        57698
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or (F -> (G or F))))
theorem-size     33
proof            (modus-ponens tm-705 tm-541 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-57698.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E or (F -> (G or F)))), M:tm-705, m:tm-541, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-57699
in-theory        57699
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (F or E)) or G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-550 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (or Cm Bm)) Dm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-7)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-57699.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> (F or E)) or G) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-550, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (or (-> Bm (or Cm Bm)) Dm) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57700
in-theory        57700
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F or E)) or G))
theorem-size     33
proof            (modus-ponens tm-705 tm-551 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-7)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-57700.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F or E)) or G)), M:tm-705, m:tm-551, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-57701
in-theory        57701
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     63
proof            (modus-ponens tm-705 tm-595 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (or Cm Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-57701.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-705, m:tm-595, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (and (-> Bm (or Cm Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
================================================================
tm-name          tm-57702
in-theory        57702
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not ((D -> (E or D)) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E or D)) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     78
proof            (modus-ponens tm-705 tm-601 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (and (-> Bm (or Cm Bm)) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-5 tm-7)
proof-size       232
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-57702.        (((((A -> B) -> (A -> C)) -> (not ((D -> (E or D)) and ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((D -> (E or D)) and ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-601, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (and (-> Bm (or Cm Bm)) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57703
in-theory        57703
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> ((F -> (G or F)) and E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     51
proof            (modus-ponens tm-705 tm-605 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-57703.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> ((F -> (G or F)) and E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-605, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57704
in-theory        57704
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((F -> (G or F)) and E)))
theorem-size     35
proof            (modus-ponens tm-705 tm-606 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-7)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-57704.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> ((F -> (G or F)) and E))), M:tm-705, m:tm-606, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-57705
in-theory        57705
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (E -> (F or E))))
theorem-size     47
proof            (modus-ponens tm-705 tm-609 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-57705.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (E -> (F or E)))), M:tm-705, m:tm-609, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-57706
in-theory        57706
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> ((D or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))
theorem-size     73
proof            (modus-ponens tm-705 tm-617 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (or Bm (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Cm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-57706.        (((((A -> B) -> (A -> C)) -> ((D or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)), M:tm-705, m:tm-617, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (or Bm (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Cm)) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm)))
================================================================
tm-name          tm-57707
in-theory        57707
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not (D -> (E or D)))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E or D))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     50
proof            (modus-ponens tm-705 tm-618 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> Bm (or Cm Bm)))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-2 tm-9 tm-1 tm-7)
proof-size       198
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-57707.        (((((A -> B) -> (A -> C)) -> (not (D -> (E or D)))) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not (D -> (E or D))))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-705, m:tm-618, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (not (-> Bm (or Cm Bm)))) (E (not (or (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-57708
in-theory        57708
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> (G or F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     49
proof            (modus-ponens tm-705 tm-622 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (or Dm Cm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-7)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-57708.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> (F -> (G or F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-622, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> Bm (-> Cm (or Dm Cm))) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57709
in-theory        57709
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E or D)))
theorem-size     43
proof            (modus-ponens tm-705 tm-623 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (or Cm Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-57709.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (E or D))), M:tm-705, m:tm-623, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) (or Cm Bm))))
================================================================
tm-name          tm-57710
in-theory        57710
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (F -> (G or F))))
theorem-size     33
proof            (modus-ponens tm-705 tm-624 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-2 tm-1 tm-7)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-57710.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (E -> (F -> (G or F)))), M:tm-705, m:tm-624, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-57711
in-theory        57711
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     55
proof            (modus-ponens tm-705 tm-665 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       219
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-57711.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-665, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-57712
in-theory        57712
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-705 tm-667 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-57712.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))), M:tm-705, m:tm-667, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-57713
in-theory        57713
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)))
theorem-size     73
proof            (modus-ponens tm-703 tm-705 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (Em (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C)) (D (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       277
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57713.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))), M:tm-703, m:tm-705, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (Em (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C)) (D (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C))))
================================================================
tm-name          tm-57714
in-theory        57714
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E)) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))))
theorem-size     165
proof            (modus-ponens tm-697 tm-705 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (Em (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C)) (D (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       389
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57714.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E)) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)))), M:tm-697, m:tm-705, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (Em (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C)) (D (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C))))
================================================================
tm-name          tm-57715
in-theory        57715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     59
proof            (modus-ponens tm-665 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       223
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57715.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-665, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57716
in-theory        57716
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((E or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))
theorem-size     93
proof            (modus-ponens tm-654 tm-705 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B Em) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       281
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57716.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((E or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))), M:tm-654, m:tm-705, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B Em) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57717
in-theory        57717
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (F or (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))
theorem-size     47
proof            (modus-ponens tm-623 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57717.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (F or (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))), M:tm-623, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57718
in-theory        57718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-622 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57718.        ((A -> (B -> (C or B))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-622, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57719
in-theory        57719
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> (F or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> (F or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     79
proof            (modus-ponens tm-619 tm-705 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (or B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (or B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       235
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57719.        ((A or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> (F or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> (F or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-619, m:tm-705, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (or B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (or B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57720
in-theory        57720
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (F -> (G or F)))
theorem-size     51
proof            (modus-ponens tm-609 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57720.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (F -> (G or F))), M:tm-609, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57721
in-theory        57721
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-605 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57721.        ((A -> ((B -> (C or B)) and A)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-605, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57722
in-theory        57722
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((F -> (G or F)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))))
theorem-size     97
proof            (modus-ponens tm-595 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       267
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57722.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((F -> (G or F)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))), M:tm-595, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57723
in-theory        57723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-550 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57723.        (((A -> (B or A)) or C) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-550, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57724
in-theory        57724
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-540 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57724.        ((A or (B -> (C or B))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-540, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57725
in-theory        57725
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-530 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57725.        ((A or (B -> (B or C))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-530, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57726
in-theory        57726
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-520 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57726.        ((A or (B -> (C -> (B and C)))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-520, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57727
in-theory        57727
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-510 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57727.        ((A or ((B and C) -> C)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-510, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57728
in-theory        57728
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-500 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57728.        ((A or ((B and C) -> B)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-500, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57729
in-theory        57729
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H) -> I) -> (((((E -> F) -> (E -> G)) -> H) or (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) -> I)))
theorem-size     61
proof            (modus-ponens tm-490 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       229
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57729.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H) -> I) -> (((((E -> F) -> (E -> G)) -> H) or (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) -> I))), M:tm-490, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57730
in-theory        57730
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-480 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57730.        ((A or (B -> (C -> B))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-480, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57731
in-theory        57731
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> ((((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) or F))
theorem-size     47
proof            (modus-ponens tm-470 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57731.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> ((((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) or F)), M:tm-470, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57732
in-theory        57732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-469 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57732.        ((A -> (B -> (B or C))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-469, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57733
in-theory        57733
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) or F))) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) or F)))
theorem-size     79
proof            (modus-ponens tm-466 tm-705 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (or (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B)) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (or (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       235
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57733.        ((A or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) or F))) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) or F))), M:tm-466, m:tm-705, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (or (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B)) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (or (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B))))
================================================================
tm-name          tm-57734
in-theory        57734
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (F -> (F or G)))
theorem-size     51
proof            (modus-ponens tm-456 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57734.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (F -> (F or G))), M:tm-456, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57735
in-theory        57735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-453 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57735.        ((A -> ((B -> (B or C)) and A)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-453, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57736
in-theory        57736
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((F -> (F or G)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))))
theorem-size     97
proof            (modus-ponens tm-443 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       267
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57736.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((F -> (F or G)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))), M:tm-443, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57737
in-theory        57737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-409 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57737.        (((A -> (A or B)) or C) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-409, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57738
in-theory        57738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-400 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57738.        (((A -> (B -> (A and B))) or C) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-400, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57739
in-theory        57739
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-391 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57739.        ((((A and B) -> B) or C) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-391, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57740
in-theory        57740
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-382 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57740.        ((((A and B) -> A) or C) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-382, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57741
in-theory        57741
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H) -> I) -> (((((E -> F) -> (E -> G)) -> H) or (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) -> I)))
theorem-size     61
proof            (modus-ponens tm-373 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       229
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57741.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H) -> I) -> (((((E -> F) -> (E -> G)) -> H) or (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) -> I))), M:tm-373, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57742
in-theory        57742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-364 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57742.        (((A -> (B -> A)) or C) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-364, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57743
in-theory        57743
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (F -> ((((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) and F)))
theorem-size     49
proof            (modus-ponens tm-355 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57743.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (F -> ((((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) and F))), M:tm-355, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57744
in-theory        57744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-354 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57744.        ((A -> (B -> (C -> (B and C)))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-354, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57745
in-theory        57745
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> (F -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) and F)))) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> (F -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) and F))))
theorem-size     83
proof            (modus-ponens tm-351 tm-705 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> B (and (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B))) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> B (and (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       247
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57745.        ((A or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> (F -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) and F)))) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> (F -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) and F)))), M:tm-351, m:tm-705, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> B (and (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B))) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> B (and (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B)))))
================================================================
tm-name          tm-57746
in-theory        57746
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (F -> (G -> (F and G))))
theorem-size     53
proof            (modus-ponens tm-341 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57746.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57747
in-theory        57747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G)))
theorem-size     55
proof            (modus-ponens tm-338 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       213
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57747.        (((A -> B) -> (A -> (A and B))) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G))), M:tm-338, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57748
in-theory        57748
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and E))) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and E)))
theorem-size     95
proof            (modus-ponens tm-335 tm-705 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (and (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B)) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (and (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       265
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57748.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and E))) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and E))), M:tm-335, m:tm-705, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (and (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B)) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (and (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) B))))
================================================================
tm-name          tm-57749
in-theory        57749
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) and (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))))
theorem-size     109
proof            (modus-ponens tm-328 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       289
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57749.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) and (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))), M:tm-328, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57750
in-theory        57750
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((F -> (G -> (F and G))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))))
theorem-size     99
proof            (modus-ponens tm-327 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       275
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57750.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((F -> (G -> (F and G))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))), M:tm-327, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57751
in-theory        57751
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (((F and G) -> G) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))))
theorem-size     97
proof            (modus-ponens tm-326 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       267
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57751.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (((F and G) -> G) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))), M:tm-326, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57752
in-theory        57752
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (((F and G) -> F) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))))
theorem-size     97
proof            (modus-ponens tm-325 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       267
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57752.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (((F and G) -> F) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))), M:tm-325, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57753
in-theory        57753
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))))
theorem-size     105
proof            (modus-ponens tm-324 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       299
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57753.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))), M:tm-324, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57754
in-theory        57754
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((F -> (G -> F)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))))
theorem-size     97
proof            (modus-ponens tm-323 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       267
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57754.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((F -> (G -> F)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))), M:tm-323, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57755
in-theory        57755
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((F and G) -> G))
theorem-size     51
proof            (modus-ponens tm-322 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57755.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((F and G) -> G)), M:tm-322, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57756
in-theory        57756
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((F and G) -> F))
theorem-size     51
proof            (modus-ponens tm-320 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57756.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((F and G) -> F)), M:tm-320, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57757
in-theory        57757
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     59
proof            (modus-ponens tm-318 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57757.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57758
in-theory        57758
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)))
theorem-size     81
proof            (modus-ponens tm-316 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57758.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E))), M:tm-316, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57759
in-theory        57759
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (F -> (G -> F)))
theorem-size     51
proof            (modus-ponens tm-315 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57759.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (F -> (G -> F))), M:tm-315, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57760
in-theory        57760
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (not (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))) -> (not ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E))))
theorem-size     111
proof            (modus-ponens tm-313 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       275
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57760.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (not (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))) -> (not ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)))), M:tm-313, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57761
in-theory        57761
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (((((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> F) -> ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) or (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) -> F)))
theorem-size     123
proof            (modus-ponens tm-312 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       291
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57761.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (((((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> F) -> ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) or (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) -> F))), M:tm-312, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57762
in-theory        57762
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (F or (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))))
theorem-size     93
proof            (modus-ponens tm-311 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       243
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57762.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (F or (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))), M:tm-311, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57763
in-theory        57763
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) or F))
theorem-size     93
proof            (modus-ponens tm-310 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       243
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57763.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) or F)), M:tm-310, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57764
in-theory        57764
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (F -> ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and F)))
theorem-size     95
proof            (modus-ponens tm-309 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       249
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57764.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (F -> ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and F))), M:tm-309, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57765
in-theory        57765
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> ((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> E)))
theorem-size     109
proof            (modus-ponens tm-306 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C Em)))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       279
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57765.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> ((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> E))), M:tm-306, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C Em))
================================================================
tm-name          tm-57766
in-theory        57766
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (F -> (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))))
theorem-size     93
proof            (modus-ponens tm-305 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       243
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57766.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (F -> (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))), M:tm-305, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57767
in-theory        57767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     57
proof            (modus-ponens tm-303 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       213
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57767.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-303, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57768
in-theory        57768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-270 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57768.        ((A -> (((B and C) -> C) and A)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-270, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57769
in-theory        57769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-239 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57769.        ((A -> (((B and C) -> B) and A)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-239, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57770
in-theory        57770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H) -> I) -> (((((E -> F) -> (E -> G)) -> H) or (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) -> I)))
theorem-size     63
proof            (modus-ponens tm-210 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       237
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57770.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H) -> I) -> (((((E -> F) -> (E -> G)) -> H) or (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) -> I))), M:tm-210, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57771
in-theory        57771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     55
proof            (modus-ponens tm-183 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57771.        ((A -> ((B -> (C -> B)) and A)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-183, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57772
in-theory        57772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-157 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57772.        ((A -> ((B and C) -> C)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-157, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57773
in-theory        57773
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     61
proof            (modus-ponens tm-147 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       229
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57773.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-147, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57774
in-theory        57774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-134 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57774.        ((A -> ((B and C) -> B)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-134, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57775
in-theory        57775
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     61
proof            (modus-ponens tm-125 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       229
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57775.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-125, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57776
in-theory        57776
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (E -> F)) -> ((((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> F)))
theorem-size     75
proof            (modus-ponens tm-114 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> C D))) (B (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       247
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57776.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (E -> F)) -> ((((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> F))), M:tm-114, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> C D))) (B (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> C D)))
================================================================
tm-name          tm-57777
in-theory        57777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H) -> I) -> (((((E -> F) -> (E -> G)) -> H) or (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) -> I)))
theorem-size     61
proof            (modus-ponens tm-113 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       229
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57777.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H) -> I) -> (((((E -> F) -> (E -> G)) -> H) or (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) -> I))), M:tm-113, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57778
in-theory        57778
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> F)) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> F)))) -> (((((B -> C) -> (B -> D)) -> (E -> F)) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> F))) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> F))))
theorem-size     113
proof            (modus-ponens tm-110 tm-705 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B C)) (Em (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C))) (D (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) (-> B C)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B C))) (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       301
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57778.        ((A or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> F)) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> F)))) -> (((((B -> C) -> (B -> D)) -> (E -> F)) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (E -> F))) -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> F)))), M:tm-110, m:tm-705, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B C)) (Em (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C))) (D (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) (-> B C)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B C))) (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) B) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C)))))
================================================================
tm-name          tm-57779
in-theory        57779
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     65
proof            (modus-ponens tm-105 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       249
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57779.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-105, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57780
in-theory        57780
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))) -> (((((A -> B) -> (A -> C)) -> (D -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)))
theorem-size     113
proof            (modus-ponens tm-102 tm-705 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B C)) (Em (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C)) (D (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) (-> B C)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B C))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C)))))
axioms-used      (tm-8 tm-2)
proof-size       313
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57780.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))) -> (((((A -> B) -> (A -> C)) -> (D -> E)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))), M:tm-102, m:tm-705, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> B C)) (Em (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C)) (D (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) (-> B C)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> B C))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C))))
================================================================
tm-name          tm-57781
in-theory        57781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G)))
theorem-size     53
proof            (modus-ponens tm-95 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57781.        (((A -> B) -> (A -> A)) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G))), M:tm-95, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57782
in-theory        57782
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     91
proof            (modus-ponens tm-92 tm-705 ((Em (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       253
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57782.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-92, m:tm-705, u:((Em (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-57783
in-theory        57783
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (F -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))
theorem-size     47
proof            (modus-ponens tm-84 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57783.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (F -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))), M:tm-84, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57784
in-theory        57784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-83 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57784.        ((A -> (B -> (C -> B))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-83, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57785
in-theory        57785
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> (F -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> (F -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     79
proof            (modus-ponens tm-80 tm-705 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       235
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57785.        ((A or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> (F -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> (F -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-80, m:tm-705, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57786
in-theory        57786
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> F) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)))
theorem-size     51
proof            (modus-ponens tm-76 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       181
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57786.        (((not (not A)) -> A) and (((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> F) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F))), M:tm-76, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57787
in-theory        57787
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E))) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))
theorem-size     65
proof            (modus-ponens tm-73 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       203
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57787.        (((not (not ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E))) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-73, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57788
in-theory        57788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G)))
theorem-size     57
proof            (modus-ponens tm-69 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       199
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57788.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G))), M:tm-69, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57789
in-theory        57789
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not D)) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) -> (((((A -> B) -> (A -> C)) -> (not D)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not D))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     90
proof            (modus-ponens tm-66 tm-705 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (not B)) (Em (not (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) (not B)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not B))) (not (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))))
axioms-used      (tm-8 tm-9 tm-2)
proof-size       246
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57789.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not D)) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) -> (((((A -> B) -> (A -> C)) -> (not D)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not D))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-66, m:tm-705, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (not B)) (Em (not (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) (not B)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (not B))) (not (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
================================================================
tm-name          tm-57790
in-theory        57790
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> ((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) or ((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> ((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     109
proof            (modus-ponens tm-55 tm-705 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (B (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-8)
proof-size       261
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57790.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> ((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) or ((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> ((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-55, m:tm-705, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (B (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-57791
in-theory        57791
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     59
proof            (modus-ponens tm-54 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       205
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57791.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-54, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57792
in-theory        57792
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> ((A or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> E))) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> ((A or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> E)))
theorem-size     93
proof            (modus-ponens tm-51 tm-705 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (Em (-> (or C (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)) (D (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> (or C (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-8 tm-2)
proof-size       255
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57792.        (((A -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> ((A or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> E))) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> ((A or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> E))), M:tm-51, m:tm-705, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (Em (-> (or C (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)) (D (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> (or C (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-57793
in-theory        57793
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> (A and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> (A and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     79
proof            (modus-ponens tm-48 tm-705 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (and B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (and B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       225
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57793.        ((A or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> (A and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> (A and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-48, m:tm-705, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (and B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (and B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57794
in-theory        57794
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> F)) or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> F)) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F))
theorem-size     65
proof            (modus-ponens tm-47 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       203
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57794.        (((A and ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> F)) or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> F)) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)), M:tm-47, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57795
in-theory        57795
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) and F) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))
theorem-size     65
proof            (modus-ponens tm-46 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       203
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57795.        (((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) and F) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-46, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57796
in-theory        57796
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E)) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)))
theorem-size     91
proof            (modus-ponens tm-45 tm-705 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (Em (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C)) (D (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C)))))
axioms-used      (tm-8 tm-2)
proof-size       251
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57796.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> E)) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))), M:tm-45, m:tm-705, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B Dm) (Em (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C)) (D (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) C))))
================================================================
tm-name          tm-57797
in-theory        57797
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> A)) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> A))
theorem-size     47
proof            (modus-ponens tm-44 tm-705 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B Em) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       187
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57797.        ((A or ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> A)) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> A)), M:tm-44, m:tm-705, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B Em) (C (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57798
in-theory        57798
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G)))
theorem-size     51
proof            (modus-ponens tm-42 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       181
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57798.        ((A -> (B or A)) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G))), M:tm-42, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57799
in-theory        57799
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G)))
theorem-size     51
proof            (modus-ponens tm-32 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       181
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57799.        ((A -> (A or B)) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G))), M:tm-32, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57800
in-theory        57800
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) and (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))
theorem-size     63
proof            (modus-ponens tm-24 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       201
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57800.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) and (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))), M:tm-24, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57801
in-theory        57801
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G)))
theorem-size     53
proof            (modus-ponens tm-23 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       187
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57801.        ((A -> (B -> (A and B))) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G))), M:tm-23, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57802
in-theory        57802
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G)))
theorem-size     51
proof            (modus-ponens tm-22 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       181
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57802.        (((A and B) -> B) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G))), M:tm-22, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57803
in-theory        57803
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G)))
theorem-size     51
proof            (modus-ponens tm-21 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       181
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57803.        (((A and B) -> A) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G))), M:tm-21, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57804
in-theory        57804
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     59
proof            (modus-ponens tm-20 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       205
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57804.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-20, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57805
in-theory        57805
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G)))
theorem-size     51
proof            (modus-ponens tm-19 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       181
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57805.        ((A -> (B -> A)) and (((((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F) -> G) -> (((((C -> D) -> (C -> E)) -> F) or (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) -> G))), M:tm-19, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57806
in-theory        57806
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E))
theorem-size     35
proof            (modus-ponens tm-12 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       169
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57806.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)), M:tm-12, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57807
in-theory        57807
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (not (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))) -> (not ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)))
theorem-size     65
proof            (modus-ponens tm-9 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-9 tm-8 tm-2)
proof-size       185
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57807.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (not (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))) -> (not ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E))), M:tm-9, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57808
in-theory        57808
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> F) -> ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) or (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) -> F))
theorem-size     77
proof            (modus-ponens tm-8 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-8 tm-2)
proof-size       199
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57808.        (((((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> F) -> ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) or (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) -> F)), M:tm-8, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57809
in-theory        57809
times-derived    2
----------------------------------------------------------------
theorem          (A or (((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> F) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)))
theorem-size     47
proof            (modus-ponens tm-7 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-7 tm-8 tm-2)
proof-size       161
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57809.        (A or (((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> F) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F))), M:tm-7, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57810
in-theory        57810
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) or F)
theorem-size     47
proof            (modus-ponens tm-6 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-6 tm-8 tm-2)
proof-size       161
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57810.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) or F), M:tm-6, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57811
in-theory        57811
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> F) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)) and A))
theorem-size     49
proof            (modus-ponens tm-5 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       165
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57811.        (A -> ((((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> F) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)) and A)), M:tm-5, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57812
in-theory        57812
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> ((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> E))
theorem-size     63
proof            (modus-ponens tm-2 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C Em)))
axioms-used      (tm-2 tm-8)
proof-size       185
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57812.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> ((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> E)), M:tm-2, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (C Em))
================================================================
tm-name          tm-57813
in-theory        57813
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> F) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)))
theorem-size     47
proof            (modus-ponens tm-1 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-1 tm-8 tm-2)
proof-size       161
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-57813.        (A -> (((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E) -> F) -> (((((B -> C) -> (B -> D)) -> E) or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F))), M:tm-1, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-57814
in-theory        57814
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-665 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57814.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-665, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57815
in-theory        57815
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-622 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57815.        ((A -> (B -> (C or B))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-622, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57816
in-theory        57816
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (G or F)))
theorem-size     33
proof            (modus-ponens tm-609 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57816.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (G or F))), M:tm-609, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57817
in-theory        57817
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-605 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57817.        ((A -> ((B -> (C or B)) and A)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-605, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57818
in-theory        57818
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G or F)) and (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-595 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57818.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G or F)) and (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-595, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57819
in-theory        57819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-550 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57819.        (((A -> (B or A)) or C) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-550, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57820
in-theory        57820
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-540 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57820.        ((A or (B -> (C or B))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-540, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57821
in-theory        57821
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-530 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57821.        ((A or (B -> (B or C))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-530, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57822
in-theory        57822
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-520 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57822.        ((A or (B -> (C -> (B and C)))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-520, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57823
in-theory        57823
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-510 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57823.        ((A or ((B and C) -> C)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-510, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57824
in-theory        57824
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-500 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57824.        ((A or ((B and C) -> B)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-500, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57825
in-theory        57825
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-490 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57825.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-490, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57826
in-theory        57826
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-480 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57826.        ((A or (B -> (C -> B))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-480, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57827
in-theory        57827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-469 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57827.        ((A -> (B -> (B or C))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-469, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57828
in-theory        57828
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (F or G)))
theorem-size     33
proof            (modus-ponens tm-456 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57828.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (F or G))), M:tm-456, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57829
in-theory        57829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-453 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57829.        ((A -> ((B -> (B or C)) and A)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-453, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57830
in-theory        57830
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (F or G)) and (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-443 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57830.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (F or G)) and (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-443, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57831
in-theory        57831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-409 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57831.        (((A -> (A or B)) or C) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-409, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57832
in-theory        57832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-400 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57832.        (((A -> (B -> (A and B))) or C) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-400, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57833
in-theory        57833
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-391 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57833.        ((((A and B) -> B) or C) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-391, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57834
in-theory        57834
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-382 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57834.        ((((A and B) -> A) or C) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-382, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57835
in-theory        57835
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-373 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57835.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-373, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57836
in-theory        57836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-364 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57836.        (((A -> (B -> A)) or C) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-364, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57837
in-theory        57837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-354 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57837.        ((A -> (B -> (C -> (B and C)))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-354, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57838
in-theory        57838
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (G -> (F and G))))
theorem-size     35
proof            (modus-ponens tm-341 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57838.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57839
in-theory        57839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     37
proof            (modus-ponens tm-338 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57839.        (((A -> B) -> (A -> (A and B))) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-338, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57840
in-theory        57840
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G -> (F and G))) and (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     63
proof            (modus-ponens tm-327 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57840.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G -> (F and G))) and (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-327, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57841
in-theory        57841
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((F and G) -> G) and (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-326 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57841.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((F and G) -> G) and (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-326, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57842
in-theory        57842
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((F and G) -> F) and (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-325 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57842.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((F and G) -> F) and (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-325, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57843
in-theory        57843
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     69
proof            (modus-ponens tm-324 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57843.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-324, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57844
in-theory        57844
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G -> F)) and (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-323 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57844.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G -> F)) and (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-323, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57845
in-theory        57845
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F and G) -> G))
theorem-size     33
proof            (modus-ponens tm-322 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57845.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57846
in-theory        57846
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F and G) -> F))
theorem-size     33
proof            (modus-ponens tm-320 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57846.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57847
in-theory        57847
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     41
proof            (modus-ponens tm-318 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57847.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57848
in-theory        57848
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (G -> F)))
theorem-size     33
proof            (modus-ponens tm-315 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57848.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57849
in-theory        57849
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F or (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     57
proof            (modus-ponens tm-311 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57849.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F or (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-311, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57850
in-theory        57850
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) or F))
theorem-size     57
proof            (modus-ponens tm-310 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57850.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) or F)), M:tm-310, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57851
in-theory        57851
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and F)))
theorem-size     59
proof            (modus-ponens tm-309 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57851.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and F))), M:tm-309, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57852
in-theory        57852
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     57
proof            (modus-ponens tm-305 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57852.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-305, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57853
in-theory        57853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-303 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57853.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-303, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57854
in-theory        57854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-270 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57854.        ((A -> (((B and C) -> C) and A)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-270, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57855
in-theory        57855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-239 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57855.        ((A -> (((B and C) -> B) and A)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-239, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57856
in-theory        57856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-210 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57856.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-210, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57857
in-theory        57857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-183 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57857.        ((A -> ((B -> (C -> B)) and A)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-183, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57858
in-theory        57858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-157 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57858.        ((A -> ((B and C) -> C)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-157, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57859
in-theory        57859
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     43
proof            (modus-ponens tm-147 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57859.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-147, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57860
in-theory        57860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-134 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57860.        ((A -> ((B and C) -> B)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-134, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57861
in-theory        57861
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     43
proof            (modus-ponens tm-125 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57861.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-125, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57862
in-theory        57862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-113 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57862.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-113, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57863
in-theory        57863
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     47
proof            (modus-ponens tm-105 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57863.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-105, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57864
in-theory        57864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     35
proof            (modus-ponens tm-95 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57864.        (((A -> B) -> (A -> A)) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-95, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57865
in-theory        57865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-83 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57865.        ((A -> (B -> (C -> B))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-83, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57866
in-theory        57866
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     33
proof            (modus-ponens tm-76 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57866.        (((not (not A)) -> A) and (B or ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-76, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57867
in-theory        57867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     39
proof            (modus-ponens tm-69 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8 tm-2)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57867.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-69, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57868
in-theory        57868
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-54 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-8 tm-7 tm-2)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57868.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-54, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57869
in-theory        57869
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-42 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57869.        ((A -> (B or A)) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-42, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57870
in-theory        57870
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-32 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57870.        ((A -> (A or B)) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-32, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57871
in-theory        57871
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     35
proof            (modus-ponens tm-23 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57871.        ((A -> (B -> (A and B))) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-23, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57872
in-theory        57872
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-22 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57872.        (((A and B) -> B) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-22, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57873
in-theory        57873
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-21 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57873.        (((A and B) -> A) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-21, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57874
in-theory        57874
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-20 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57874.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-20, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57875
in-theory        57875
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-19 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57875.        ((A -> (B -> A)) and (C or ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-19, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57876
in-theory        57876
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     29
proof            (modus-ponens tm-7 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-7 tm-8 tm-2)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57876.        (A or (B or ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-7, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57877
in-theory        57877
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) or F)
theorem-size     29
proof            (modus-ponens tm-6 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-6 tm-7 tm-8 tm-2)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57877.        ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) or F), M:tm-6, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57878
in-theory        57878
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       121
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57878.        (A -> ((B or ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and A)), M:tm-5, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57879
in-theory        57879
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     29
proof            (modus-ponens tm-1 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-1 tm-7 tm-8 tm-2)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57879.        (A -> (B or ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-1, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-57880
in-theory        57880
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     39
proof            (modus-ponens tm-694 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> (-> (-> B C) (-> B D)) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57880.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-694, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> (-> (-> B C) (-> B D)) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57881
in-theory        57881
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) -> ((((A -> B) -> (A -> C)) -> D) -> D))
theorem-size     49
proof            (modus-ponens tm-692 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57881.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-692, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57882
in-theory        57882
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F)))
theorem-size     41
proof            (modus-ponens tm-690 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-6)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57882.        ((A -> (B or A)) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F))), M:tm-690, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57883
in-theory        57883
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F)))
theorem-size     41
proof            (modus-ponens tm-688 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57883.        ((A -> (A or B)) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F))), M:tm-688, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57884
in-theory        57884
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) -> D) -> D)))
theorem-size     59
proof            (modus-ponens tm-686 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57884.        (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) -> D) -> D))), M:tm-686, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57885
in-theory        57885
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F)))
theorem-size     43
proof            (modus-ponens tm-685 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57885.        ((A -> (B -> (A and B))) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F))), M:tm-685, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57886
in-theory        57886
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F)))
theorem-size     41
proof            (modus-ponens tm-684 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-6)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57886.        (((A and B) -> B) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F))), M:tm-684, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57887
in-theory        57887
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F)))
theorem-size     41
proof            (modus-ponens tm-683 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-6)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57887.        (((A and B) -> A) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F))), M:tm-683, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57888
in-theory        57888
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     49
proof            (modus-ponens tm-682 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57888.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-682, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57889
in-theory        57889
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F)))
theorem-size     41
proof            (modus-ponens tm-681 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57889.        ((A -> (B -> A)) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F))), M:tm-681, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57890
in-theory        57890
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     47
proof            (modus-ponens tm-676 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57890.        (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-676, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57891
in-theory        57891
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (not ((((A -> B) -> (A -> C)) -> D) -> D))) -> (not ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     61
proof            (modus-ponens tm-674 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-9 tm-6)
proof-size       233
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57891.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (not ((((A -> B) -> (A -> C)) -> D) -> D))) -> (not ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-674, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57892
in-theory        57892
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> D) -> E) -> ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((((A -> B) -> (A -> C)) -> D) -> D)) -> E))
theorem-size     51
proof            (modus-ponens tm-673 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-6)
proof-size       227
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57892.        ((((((A -> B) -> (A -> C)) -> D) -> D) -> E) -> ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((((A -> B) -> (A -> C)) -> D) -> D)) -> E)), M:tm-673, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57893
in-theory        57893
times-derived    2
----------------------------------------------------------------
theorem          (A or (((((B -> C) -> (B -> D)) -> E) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((((B -> C) -> (B -> D)) -> E) -> E)))
theorem-size     37
proof            (modus-ponens tm-672 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-7 tm-6)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57893.        (A or (((((B -> C) -> (B -> D)) -> E) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((((B -> C) -> (B -> D)) -> E) -> E))), M:tm-672, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57894
in-theory        57894
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) or E)
theorem-size     37
proof            (modus-ponens tm-671 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-6)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57894.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) or E), M:tm-671, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57895
in-theory        57895
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) -> (B -> D)) -> E) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((((B -> C) -> (B -> D)) -> E) -> E)) and A))
theorem-size     39
proof            (modus-ponens tm-670 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57895.        (A -> ((((((B -> C) -> (B -> D)) -> E) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((((B -> C) -> (B -> D)) -> E) -> E)) and A)), M:tm-670, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57896
in-theory        57896
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) -> D)) -> (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D))
theorem-size     59
proof            (modus-ponens tm-669 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-6)
proof-size       231
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57896.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) -> D)) -> (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D)), M:tm-669, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57897
in-theory        57897
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> (B -> D)) -> E) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((((B -> C) -> (B -> D)) -> E) -> E)))
theorem-size     37
proof            (modus-ponens tm-668 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57897.        (A -> (((((B -> C) -> (B -> D)) -> E) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((((B -> C) -> (B -> D)) -> E) -> E))), M:tm-668, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-57898
in-theory        57898
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     41
proof            (modus-ponens tm-665 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57898.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-665, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57899
in-theory        57899
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-651 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> (-> B C) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57899.        ((A or (B -> A)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-651, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> (-> B C) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57900
in-theory        57900
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-649 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-6 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57900.        ((A -> (B or A)) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-649, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57901
in-theory        57901
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-647 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57901.        ((A -> (A or B)) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-647, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57902
in-theory        57902
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     29
proof            (modus-ponens tm-645 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57902.        (A -> (A and ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-645, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57903
in-theory        57903
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     35
proof            (modus-ponens tm-644 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57903.        ((A -> (B -> (A and B))) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-644, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57904
in-theory        57904
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-643 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4 tm-6 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57904.        (((A and B) -> B) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-643, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57905
in-theory        57905
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-642 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3 tm-6 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57905.        (((A and B) -> A) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-642, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57906
in-theory        57906
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-641 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-6)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57906.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-641, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57907
in-theory        57907
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     33
proof            (modus-ponens tm-640 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57907.        ((A -> (B -> A)) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-640, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57908
in-theory        57908
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)) -> F)
theorem-size     31
proof            (modus-ponens tm-638 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> (and B (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) C)) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-4 tm-6)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57908.        ((A and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)) -> F), M:tm-638, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> (and B (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) C)) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57909
in-theory        57909
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) and F) -> E)
theorem-size     31
proof            (modus-ponens tm-636 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> (and (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) B) C) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-3 tm-6)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57909.        (((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) and F) -> E), M:tm-636, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> (and (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) B) C) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57910
in-theory        57910
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> ((((A -> B) -> (A -> C)) -> D) -> E))
theorem-size     39
proof            (modus-ponens tm-634 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) C)) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57910.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> ((((A -> B) -> (A -> C)) -> D) -> E)), M:tm-634, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) C)) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57911
in-theory        57911
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))) -> (not A))
theorem-size     31
proof            (modus-ponens tm-631 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-9 tm-6 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57911.        ((A -> (not ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))) -> (not A)), M:tm-631, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57912
in-theory        57912
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> ((F or ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> E))
theorem-size     57
proof            (modus-ponens tm-630 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57912.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> ((F or ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> E)), M:tm-630, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57913
in-theory        57913
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     29
proof            (modus-ponens tm-629 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57913.        (A or (B -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-629, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57914
in-theory        57914
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) or F)
theorem-size     29
proof            (modus-ponens tm-628 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57914.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) or F), M:tm-628, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57915
in-theory        57915
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and A))
theorem-size     31
proof            (modus-ponens tm-627 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-2)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57915.        (A -> ((B -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and A)), M:tm-627, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57916
in-theory        57916
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> D)) -> E)) -> (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     29
proof            (modus-ponens tm-626 tm-707 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> C (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57916.        ((A -> (((B -> C) -> (B -> D)) -> E)) -> (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-626, m:tm-707, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (Em (-> C (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57917
in-theory        57917
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     29
proof            (modus-ponens tm-625 tm-707 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57917.        (A -> (B -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-625, m:tm-707, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (Em (-> B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-57918
in-theory        57918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-622 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57918.        ((A -> (B -> (C or B))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-622, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57919
in-theory        57919
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (F -> (G or F)))
theorem-size     33
proof            (modus-ponens tm-609 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57919.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (F -> (G or F))), M:tm-609, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57920
in-theory        57920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     37
proof            (modus-ponens tm-605 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57920.        ((A -> ((B -> (C or B)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-605, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57921
in-theory        57921
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((F -> (G or F)) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E)))
theorem-size     61
proof            (modus-ponens tm-595 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57921.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((F -> (G or F)) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E))), M:tm-595, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57922
in-theory        57922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-550 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57922.        (((A -> (B or A)) or C) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-550, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57923
in-theory        57923
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-540 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57923.        ((A or (B -> (C or B))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-540, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57924
in-theory        57924
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-530 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57924.        ((A or (B -> (B or C))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-530, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57925
in-theory        57925
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     37
proof            (modus-ponens tm-520 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57925.        ((A or (B -> (C -> (B and C)))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-520, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57926
in-theory        57926
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-510 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57926.        ((A or ((B and C) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-510, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57927
in-theory        57927
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-500 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57927.        ((A or ((B and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-500, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57928
in-theory        57928
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) or I))
theorem-size     43
proof            (modus-ponens tm-490 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57928.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) or I)), M:tm-490, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57929
in-theory        57929
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-480 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57929.        ((A or (B -> (C -> B))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-480, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57930
in-theory        57930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-469 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57930.        ((A -> (B -> (B or C))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-469, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57931
in-theory        57931
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (F -> (F or G)))
theorem-size     33
proof            (modus-ponens tm-456 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57931.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (F -> (F or G))), M:tm-456, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57932
in-theory        57932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     37
proof            (modus-ponens tm-453 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57932.        ((A -> ((B -> (B or C)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-453, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57933
in-theory        57933
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((F -> (F or G)) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E)))
theorem-size     61
proof            (modus-ponens tm-443 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57933.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((F -> (F or G)) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E))), M:tm-443, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57934
in-theory        57934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-409 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57934.        (((A -> (A or B)) or C) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-409, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57935
in-theory        57935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     37
proof            (modus-ponens tm-400 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57935.        (((A -> (B -> (A and B))) or C) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-400, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57936
in-theory        57936
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-391 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57936.        ((((A and B) -> B) or C) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-391, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57937
in-theory        57937
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-382 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57937.        ((((A and B) -> A) or C) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-382, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57938
in-theory        57938
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) or I))
theorem-size     43
proof            (modus-ponens tm-373 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57938.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) or I)), M:tm-373, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57939
in-theory        57939
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-364 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57939.        (((A -> (B -> A)) or C) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-364, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57940
in-theory        57940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     37
proof            (modus-ponens tm-354 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57940.        ((A -> (B -> (C -> (B and C)))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-354, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57941
in-theory        57941
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (F -> (G -> (F and G))))
theorem-size     35
proof            (modus-ponens tm-341 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57941.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (F -> (G -> (F and G)))), M:tm-341, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57942
in-theory        57942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G))
theorem-size     37
proof            (modus-ponens tm-338 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57942.        (((A -> B) -> (A -> (A and B))) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G)), M:tm-338, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57943
in-theory        57943
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((F -> (G -> (F and G))) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E)))
theorem-size     63
proof            (modus-ponens tm-327 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57943.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((F -> (G -> (F and G))) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E))), M:tm-327, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57944
in-theory        57944
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (((F and G) -> G) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E)))
theorem-size     61
proof            (modus-ponens tm-326 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57944.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (((F and G) -> G) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E))), M:tm-326, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57945
in-theory        57945
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (((F and G) -> F) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E)))
theorem-size     61
proof            (modus-ponens tm-325 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57945.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (((F and G) -> F) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E))), M:tm-325, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57946
in-theory        57946
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E)))
theorem-size     69
proof            (modus-ponens tm-324 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57946.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E))), M:tm-324, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57947
in-theory        57947
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((F -> (G -> F)) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E)))
theorem-size     61
proof            (modus-ponens tm-323 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57947.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((F -> (G -> F)) and (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E))), M:tm-323, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57948
in-theory        57948
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((F and G) -> G))
theorem-size     33
proof            (modus-ponens tm-322 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57948.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((F and G) -> G)), M:tm-322, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57949
in-theory        57949
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((F and G) -> F))
theorem-size     33
proof            (modus-ponens tm-320 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57949.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((F and G) -> F)), M:tm-320, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57950
in-theory        57950
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     41
proof            (modus-ponens tm-318 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57950.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57951
in-theory        57951
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (F -> (G -> F)))
theorem-size     33
proof            (modus-ponens tm-315 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57951.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (F -> (G -> F))), M:tm-315, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57952
in-theory        57952
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (F or (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E)))
theorem-size     57
proof            (modus-ponens tm-311 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57952.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (F or (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E))), M:tm-311, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57953
in-theory        57953
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) or F))
theorem-size     57
proof            (modus-ponens tm-310 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57953.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) or F)), M:tm-310, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57954
in-theory        57954
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (F -> ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and F)))
theorem-size     59
proof            (modus-ponens tm-309 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57954.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (F -> ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and F))), M:tm-309, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57955
in-theory        57955
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (F -> (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E)))
theorem-size     57
proof            (modus-ponens tm-305 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57955.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) and (F -> (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E))), M:tm-305, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57956
in-theory        57956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     39
proof            (modus-ponens tm-303 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57956.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-303, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57957
in-theory        57957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     37
proof            (modus-ponens tm-270 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57957.        ((A -> (((B and C) -> C) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-270, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57958
in-theory        57958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     37
proof            (modus-ponens tm-239 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-3 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57958.        ((A -> (((B and C) -> B) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-239, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57959
in-theory        57959
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) or I))
theorem-size     45
proof            (modus-ponens tm-210 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57959.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) or I)), M:tm-210, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57960
in-theory        57960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     37
proof            (modus-ponens tm-183 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57960.        ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-183, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57961
in-theory        57961
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-157 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57961.        ((A -> ((B and C) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-157, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57962
in-theory        57962
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     43
proof            (modus-ponens tm-147 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57962.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-147, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57963
in-theory        57963
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-134 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57963.        ((A -> ((B and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-134, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57964
in-theory        57964
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     43
proof            (modus-ponens tm-125 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57964.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-125, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57965
in-theory        57965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) or I))
theorem-size     43
proof            (modus-ponens tm-113 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57965.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) or I)), M:tm-113, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57966
in-theory        57966
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     47
proof            (modus-ponens tm-105 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57966.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-105, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57967
in-theory        57967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G))
theorem-size     35
proof            (modus-ponens tm-95 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57967.        (((A -> B) -> (A -> A)) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G)), M:tm-95, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57968
in-theory        57968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-83 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57968.        ((A -> (B -> (C -> B))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-83, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57969
in-theory        57969
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) or F))
theorem-size     33
proof            (modus-ponens tm-76 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-10 tm-6 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57969.        (((not (not A)) -> A) and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) or F)), M:tm-76, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57970
in-theory        57970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G))
theorem-size     39
proof            (modus-ponens tm-69 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-9 tm-6 tm-8 tm-2)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57970.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G)), M:tm-69, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57971
in-theory        57971
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     41
proof            (modus-ponens tm-54 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-8 tm-6 tm-2)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57971.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-54, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57972
in-theory        57972
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G))
theorem-size     33
proof            (modus-ponens tm-42 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57972.        ((A -> (B or A)) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G)), M:tm-42, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57973
in-theory        57973
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G))
theorem-size     33
proof            (modus-ponens tm-32 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57973.        ((A -> (A or B)) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G)), M:tm-32, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57974
in-theory        57974
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G))
theorem-size     35
proof            (modus-ponens tm-23 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57974.        ((A -> (B -> (A and B))) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G)), M:tm-23, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57975
in-theory        57975
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G))
theorem-size     33
proof            (modus-ponens tm-22 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57975.        (((A and B) -> B) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G)), M:tm-22, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57976
in-theory        57976
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G))
theorem-size     33
proof            (modus-ponens tm-21 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-3 tm-6 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57976.        (((A and B) -> A) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G)), M:tm-21, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57977
in-theory        57977
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     41
proof            (modus-ponens tm-20 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-2 tm-6 tm-8)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57977.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-20, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57978
in-theory        57978
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G))
theorem-size     33
proof            (modus-ponens tm-19 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57978.        ((A -> (B -> A)) and (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) or G)), M:tm-19, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57979
in-theory        57979
times-derived    2
----------------------------------------------------------------
theorem          (A or (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) or F))
theorem-size     29
proof            (modus-ponens tm-7 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-7 tm-6 tm-8 tm-2)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57979.        (A or (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) or F)), M:tm-7, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57980
in-theory        57980
times-derived    2
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) or F)
theorem-size     29
proof            (modus-ponens tm-6 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-6 tm-8 tm-2)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57980.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E) or F), M:tm-6, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57981
in-theory        57981
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) or F) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       121
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57981.        (A -> ((((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) or F) and A)), M:tm-5, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57982
in-theory        57982
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) or F))
theorem-size     29
proof            (modus-ponens tm-1 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-1 tm-6 tm-8 tm-2)
proof-size       117
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57982.        (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) or F)), M:tm-1, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-57983
in-theory        57983
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       139
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-57983.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((F -> G) -> ((E or F) -> G)))), M:tm-708, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-57984
in-theory        57984
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((E -> (not F)) -> (not E))))
theorem-size     37
proof            (modus-ponens tm-708 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       135
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-57984.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((E -> (not F)) -> (not E)))), M:tm-708, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-57985
in-theory        57985
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((not (not E)) -> E))
theorem-size     31
proof            (modus-ponens tm-708 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-8 tm-2 tm-10)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-10.           ((not (not A)) -> A), axiom
tm-57985.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((not (not E)) -> E)), M:tm-708, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-57986
in-theory        57986
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (G -> F))))
theorem-size     33
proof            (modus-ponens tm-708 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-57986.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (G -> F)))), M:tm-708, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-57987
in-theory        57987
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (E -> E)))
theorem-size     33
proof            (modus-ponens tm-708 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-57987.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (E -> E))), M:tm-708, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-57988
in-theory        57988
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-708 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       177
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-57988.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-708, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-57989
in-theory        57989
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-57989.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-708, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-57990
in-theory        57990
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))
theorem-size     41
proof            (modus-ponens tm-708 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-57990.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))), M:tm-708, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-57991
in-theory        57991
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-708 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-57991.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F and G) -> F))), M:tm-708, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-57992
in-theory        57992
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))
theorem-size     41
proof            (modus-ponens tm-708 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-57992.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))), M:tm-708, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-57993
in-theory        57993
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F and G) -> G)))
theorem-size     33
proof            (modus-ponens tm-708 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-57993.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F and G) -> G))), M:tm-708, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-57994
in-theory        57994
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> F)) and E)))
theorem-size     35
proof            (modus-ponens tm-708 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-57994.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> F)) and E))), M:tm-708, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-57995
in-theory        57995
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     43
proof            (modus-ponens tm-708 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-57995.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-708, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-57996
in-theory        57996
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F and G) -> F) and E)))
theorem-size     35
proof            (modus-ponens tm-708 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-57996.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F and G) -> F) and E))), M:tm-708, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-57997
in-theory        57997
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F and G) -> G) and E)))
theorem-size     35
proof            (modus-ponens tm-708 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-57997.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F and G) -> G) and E))), M:tm-708, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-57998
in-theory        57998
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> (F and G))) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-57998.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> (F and G))) and E))), M:tm-708, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-57999
in-theory        57999
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (E -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-708 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-57999.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (E -> (E and F)))), M:tm-708, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-58000
in-theory        58000
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (G -> (F and G)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-58000.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (G -> (F and G))))), M:tm-708, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-58001
in-theory        58001
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) or G))
theorem-size     33
proof            (modus-ponens tm-708 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-58001.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) or G)), M:tm-708, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-58002
in-theory        58002
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))
theorem-size     41
proof            (modus-ponens tm-708 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-58002.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)), M:tm-708, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-58003
in-theory        58003
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) or G))
theorem-size     33
proof            (modus-ponens tm-708 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-3)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-58003.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) or G)), M:tm-708, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-58004
in-theory        58004
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) or G))
theorem-size     33
proof            (modus-ponens tm-708 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-4)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-58004.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) or G)), M:tm-708, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-58005
in-theory        58005
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) or G))
theorem-size     35
proof            (modus-ponens tm-708 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-58005.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) or G)), M:tm-708, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-58006
in-theory        58006
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) or G))
theorem-size     33
proof            (modus-ponens tm-708 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-58006.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) or G)), M:tm-708, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-58007
in-theory        58007
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (F or G)) and E)))
theorem-size     35
proof            (modus-ponens tm-708 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-58007.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (F or G)) and E))), M:tm-708, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-58008
in-theory        58008
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (F or G))))
theorem-size     33
proof            (modus-ponens tm-708 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-58008.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (F or G)))), M:tm-708, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-58009
in-theory        58009
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (G -> F))))
theorem-size     33
proof            (modus-ponens tm-708 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-58009.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (G -> F)))), M:tm-708, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-58010
in-theory        58010
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-58010.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-708, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-58011
in-theory        58011
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-708 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-3)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-58011.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F and G) -> F))), M:tm-708, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-58012
in-theory        58012
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F and G) -> G)))
theorem-size     33
proof            (modus-ponens tm-708 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-4)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-58012.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F and G) -> G))), M:tm-708, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-58013
in-theory        58013
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (G -> (F and G)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-58013.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (G -> (F and G))))), M:tm-708, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-58014
in-theory        58014
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (F or G))))
theorem-size     33
proof            (modus-ponens tm-708 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-58014.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (F or G)))), M:tm-708, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-58015
in-theory        58015
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (G or F))))
theorem-size     33
proof            (modus-ponens tm-708 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-58015.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (G or F)))), M:tm-708, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-58016
in-theory        58016
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) or G))
theorem-size     33
proof            (modus-ponens tm-708 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-58016.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) or G)), M:tm-708, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-58017
in-theory        58017
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G or F)) and E)))
theorem-size     35
proof            (modus-ponens tm-708 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-58017.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G or F)) and E))), M:tm-708, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-58018
in-theory        58018
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (G or F))))
theorem-size     33
proof            (modus-ponens tm-708 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-58018.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (G or F)))), M:tm-708, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-58019
in-theory        58019
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-708 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58019.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> G) -> ((F or (E -> F)) -> G))), M:tm-708, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-58020
in-theory        58020
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     51
proof            (modus-ponens tm-708 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       189
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58020.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-708, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-58021
in-theory        58021
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (((E and G) or E) -> F)))
theorem-size     37
proof            (modus-ponens tm-708 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-58021.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (((E and G) or E) -> F))), M:tm-708, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-58022
in-theory        58022
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (((G and E) or E) -> F)))
theorem-size     37
proof            (modus-ponens tm-708 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-58022.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (((G and E) or E) -> F))), M:tm-708, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-58023
in-theory        58023
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-708 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-58023.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F and E)) -> G) -> ((F or (E -> (F and E))) -> G))), M:tm-708, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-58024
in-theory        58024
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E or F) -> G) -> ((E or (E or F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-708 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-58024.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E or F) -> G) -> ((E or (E or F)) -> G))), M:tm-708, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-58025
in-theory        58025
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E or F) -> G) -> ((F or (E or F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-708 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       157
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-58025.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E or F) -> G) -> ((F or (E or F)) -> G))), M:tm-708, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-58026
in-theory        58026
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H)))
theorem-size     53
proof            (modus-ponens tm-708 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       193
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-58026.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> ((G or E) -> F)) -> H) -> (((G -> E) or ((E -> F) -> ((G or E) -> F))) -> H))), M:tm-708, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-58027
in-theory        58027
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-58027.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-708, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-58028
in-theory        58028
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H))
theorem-size     41
proof            (modus-ponens tm-708 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-58028.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((F -> G) -> ((E or F) -> G))) or H)), M:tm-708, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-58029
in-theory        58029
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E)))
theorem-size     43
proof            (modus-ponens tm-708 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-58029.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> ((G -> H) -> ((F or G) -> H))) and E))), M:tm-708, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-58030
in-theory        58030
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G))))
theorem-size     43
proof            (modus-ponens tm-708 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       173
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-58030.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (F -> G)) -> ((E -> F) -> ((E or F) -> G)))), M:tm-708, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-58031
in-theory        58031
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-58031.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-708, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-58032
in-theory        58032
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (F -> E))) -> (not E)))
theorem-size     35
proof            (modus-ponens tm-708 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-1)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58032.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (F -> E))) -> (not E))), M:tm-708, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-58033
in-theory        58033
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       179
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-58033.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> (not ((E -> F) -> (E -> G)))) -> (not (E -> (F -> G))))), M:tm-708, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-58034
in-theory        58034
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> (not E)) -> (not (E and F))))
theorem-size     37
proof            (modus-ponens tm-708 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-3)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-58034.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> (not E)) -> (not (E and F)))), M:tm-708, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-58035
in-theory        58035
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> (not F)) -> (not (E and F))))
theorem-size     37
proof            (modus-ponens tm-708 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-4)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-58035.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> (not F)) -> (not (E and F)))), M:tm-708, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-58036
in-theory        58036
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (F -> (E and F)))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-58036.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (F -> (E and F)))) -> (not E))), M:tm-708, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-58037
in-theory        58037
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (E or F))) -> (not E)))
theorem-size     35
proof            (modus-ponens tm-708 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-6)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-58037.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (E or F))) -> (not E))), M:tm-708, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-58038
in-theory        58038
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (F or E))) -> (not E)))
theorem-size     35
proof            (modus-ponens tm-708 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-7)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-58038.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (F or E))) -> (not E))), M:tm-708, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-58039
in-theory        58039
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F))))
theorem-size     45
proof            (modus-ponens tm-708 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       175
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-58039.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (not ((F -> G) -> ((E or F) -> G)))) -> (not (E -> F)))), M:tm-708, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-58040
in-theory        58040
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F))))
theorem-size     43
proof            (modus-ponens tm-708 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       169
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-58040.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (not ((E -> (not F)) -> (not E)))) -> (not (E -> F)))), M:tm-708, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-58041
in-theory        58041
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G)))
theorem-size     49
proof            (modus-ponens tm-708 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       183
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-58041.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (not F)) -> (not E)) -> G) -> (((E -> F) or ((E -> (not F)) -> (not E))) -> G))), M:tm-708, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-58042
in-theory        58042
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-9)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-58042.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-708, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-58043
in-theory        58043
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G))
theorem-size     39
proof            (modus-ponens tm-708 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-9)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-58043.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((E -> (not F)) -> (not E))) or G)), M:tm-708, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-58044
in-theory        58044
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E)))
theorem-size     41
proof            (modus-ponens tm-708 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-58044.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> ((F -> (not G)) -> (not F))) and E))), M:tm-708, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-58045
in-theory        58045
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E))))
theorem-size     41
proof            (modus-ponens tm-708 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-58045.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (E -> (not F))) -> ((E -> F) -> (not E)))), M:tm-708, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-58046
in-theory        58046
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-9)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-58046.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-708, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-58047
in-theory        58047
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((not (not E)) -> (not E)) -> (not (not (not E)))))
theorem-size     37
proof            (modus-ponens tm-708 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-10)
proof-size       151
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-58047.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((not (not E)) -> (not E)) -> (not (not (not E))))), M:tm-708, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-58048
in-theory        58048
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (((not (not E)) or E) -> F)))
theorem-size     37
proof            (modus-ponens tm-708 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-10)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-58048.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (((not (not E)) or E) -> F))), M:tm-708, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-58049
in-theory        58049
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((not (not F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-708 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-10)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-58049.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((not (not F)) -> F))), M:tm-708, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-58050
in-theory        58050
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((not (not E)) -> E) or F))
theorem-size     33
proof            (modus-ponens tm-708 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-10)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-58050.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((not (not E)) -> E) or F)), M:tm-708, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-58051
in-theory        58051
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((not (not F)) -> F) and E)))
theorem-size     35
proof            (modus-ponens tm-708 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-10)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-58051.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((not (not F)) -> F) and E))), M:tm-708, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-58052
in-theory        58052
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F)))
theorem-size     41
proof            (modus-ponens tm-708 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-10)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-58052.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((not (not (E -> F))) -> E) -> ((not (not (E -> F))) -> F))), M:tm-708, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-58053
in-theory        58053
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((not (not F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-708 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-10)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-58053.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((not (not F)) -> F))), M:tm-708, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-58054
in-theory        58054
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (F -> (G -> F)))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-1)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-58054.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (F -> (G -> F)))) -> (not E))), M:tm-708, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-58055
in-theory        58055
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-708 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-58055.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> E)) -> G) -> ((H or (E -> (F -> E))) -> G))), M:tm-708, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-58056
in-theory        58056
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (G -> (H -> G)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-58056.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (G -> (H -> G))))), M:tm-708, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-58057
in-theory        58057
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (G -> F))) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-58057.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (G -> F))) or H)), M:tm-708, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-58058
in-theory        58058
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> (H -> G))) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-58058.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> (H -> G))) and E))), M:tm-708, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-58059
in-theory        58059
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (E -> (G -> F))))
theorem-size     35
proof            (modus-ponens tm-708 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-58059.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (E -> (G -> F)))), M:tm-708, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-58060
in-theory        58060
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (G -> (H -> G)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-58060.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (G -> (H -> G))))), M:tm-708, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-58061
in-theory        58061
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> E))
theorem-size     29
proof            (modus-ponens tm-708 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58061.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> E)), M:tm-708, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-58062
in-theory        58062
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> G)) -> (E -> (F -> G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-58062.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> G)) -> (E -> (F -> G)))), M:tm-708, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-58063
in-theory        58063
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and F) -> (E and F)))
theorem-size     33
proof            (modus-ponens tm-708 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-58063.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and F) -> (E and F))), M:tm-708, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-58064
in-theory        58064
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (E -> F)))
theorem-size     33
proof            (modus-ponens tm-708 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-58064.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (E -> F))), M:tm-708, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-58065
in-theory        58065
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((not (not E)) -> (not (not E))))
theorem-size     33
proof            (modus-ponens tm-708 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-10)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-58065.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((not (not E)) -> (not (not E)))), M:tm-708, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-58066
in-theory        58066
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (not (E -> E))) -> (not (E -> F))))
theorem-size     39
proof            (modus-ponens tm-708 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-1)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-58066.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (not (E -> E))) -> (not (E -> F)))), M:tm-708, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-58067
in-theory        58067
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F)))
theorem-size     41
proof            (modus-ponens tm-708 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-58067.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> E) -> F) -> (((E -> G) or (E -> E)) -> F))), M:tm-708, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-58068
in-theory        58068
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> G) -> (F -> F))))
theorem-size     35
proof            (modus-ponens tm-708 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-58068.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> G) -> (F -> F)))), M:tm-708, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-58069
in-theory        58069
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (E -> E)) or G))
theorem-size     35
proof            (modus-ponens tm-708 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-58069.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (E -> E)) or G)), M:tm-708, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-58070
in-theory        58070
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> (F -> F)) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-58070.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> (F -> F)) and E))), M:tm-708, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-58071
in-theory        58071
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> E) -> ((E -> F) -> E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-58071.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> E) -> ((E -> F) -> E))), M:tm-708, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-58072
in-theory        58072
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> G) -> (F -> F))))
theorem-size     35
proof            (modus-ponens tm-708 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-58072.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> G) -> (F -> F)))), M:tm-708, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-58073
in-theory        58073
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F -> E) -> G)) -> (E -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-58073.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F -> E) -> G)) -> (E -> G))), M:tm-708, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-58074
in-theory        58074
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E -> F)) -> (E -> F)))
theorem-size     35
proof            (modus-ponens tm-708 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-58074.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E -> F)) -> (E -> F))), M:tm-708, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-58075
in-theory        58075
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F))))
theorem-size     45
proof            (modus-ponens tm-708 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-58075.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> F)))), M:tm-708, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-58076
in-theory        58076
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> G)) -> (E -> F)) -> (not ((E -> (F -> G)) -> (E -> G)))) -> (not ((E -> (F -> G)) -> (E -> F)))))
theorem-size     57
proof            (modus-ponens tm-708 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       231
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-58076.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> G)) -> (E -> F)) -> (not ((E -> (F -> G)) -> (E -> G)))) -> (not ((E -> (F -> G)) -> (E -> F))))), M:tm-708, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-58077
in-theory        58077
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> G)) -> (E -> G)) -> H) -> ((((E -> (F -> G)) -> (E -> F)) or ((E -> (F -> G)) -> (E -> G))) -> H)))
theorem-size     59
proof            (modus-ponens tm-708 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       237
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-58077.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> G)) -> (E -> G)) -> H) -> ((((E -> (F -> G)) -> (E -> F)) or ((E -> (F -> G)) -> (E -> G))) -> H))), M:tm-708, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-58078
in-theory        58078
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-58078.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-708, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-58079
in-theory        58079
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H))
theorem-size     47
proof            (modus-ponens tm-708 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-58079.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) or H)), M:tm-708, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-58080
in-theory        58080
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E)))
theorem-size     49
proof            (modus-ponens tm-708 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-58080.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))) and E))), M:tm-708, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-58081
in-theory        58081
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> G)) -> (E -> F)) -> (E -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G))))
theorem-size     55
proof            (modus-ponens tm-708 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       229
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-58081.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> G)) -> (E -> F)) -> (E -> (F -> G))) -> (((E -> (F -> G)) -> (E -> F)) -> (E -> G)))), M:tm-708, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-58082
in-theory        58082
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-58082.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-708, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-58083
in-theory        58083
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> (((E -> F) -> (E -> G)) -> H)) -> ((E -> (F -> G)) -> H)))
theorem-size     49
proof            (modus-ponens tm-708 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-58083.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> (((E -> F) -> (E -> G)) -> H)) -> ((E -> (F -> G)) -> H))), M:tm-708, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-58084
in-theory        58084
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E)))
theorem-size     45
proof            (modus-ponens tm-708 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-1)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-58084.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))) -> (not E))), M:tm-708, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-58085
in-theory        58085
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) -> ((I or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) -> H)))
theorem-size     59
proof            (modus-ponens tm-708 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       225
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-58085.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) -> ((I or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) -> H))), M:tm-708, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-58086
in-theory        58086
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     43
proof            (modus-ponens tm-708 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58086.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-708, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-58087
in-theory        58087
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     43
proof            (modus-ponens tm-708 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58087.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-708, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-58088
in-theory        58088
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     45
proof            (modus-ponens tm-708 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58088.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-708, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-58089
in-theory        58089
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H)))))
theorem-size     43
proof            (modus-ponens tm-708 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-58089.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (G -> H))) -> (E -> ((F -> G) -> (F -> H))))), M:tm-708, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-58090
in-theory        58090
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     43
proof            (modus-ponens tm-708 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58090.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-708, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-58091
in-theory        58091
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) and E) -> F))
theorem-size     33
proof            (modus-ponens tm-708 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-4)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-58091.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) and E) -> F)), M:tm-708, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-58092
in-theory        58092
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> E)) -> G) and H) -> G))
theorem-size     37
proof            (modus-ponens tm-708 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-58092.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> E)) -> G) and H) -> G)), M:tm-708, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-58093
in-theory        58093
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) and I) -> H))
theorem-size     45
proof            (modus-ponens tm-708 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-58093.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H) and I) -> H)), M:tm-708, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-58094
in-theory        58094
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F)))
theorem-size     47
proof            (modus-ponens tm-708 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-58094.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) -> E) and G) -> (E -> F)) -> ((((E -> F) -> E) and G) -> F))), M:tm-708, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-58095
in-theory        58095
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E)))
theorem-size     41
proof            (modus-ponens tm-708 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-58095.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) -> E) -> (((E -> F) and G) -> E))), M:tm-708, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-58096
in-theory        58096
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) and G) -> E) -> (not (((E -> F) and G) -> F))) -> (not (((E -> F) and G) -> E))))
theorem-size     51
proof            (modus-ponens tm-708 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-3)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-58096.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) and G) -> E) -> (not (((E -> F) and G) -> F))) -> (not (((E -> F) and G) -> E)))), M:tm-708, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-58097
in-theory        58097
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) and G) -> F) -> H) -> (((((E -> F) and G) -> E) or (((E -> F) and G) -> F)) -> H)))
theorem-size     53
proof            (modus-ponens tm-708 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       213
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-58097.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) and G) -> F) -> H) -> (((((E -> F) and G) -> E) or (((E -> F) and G) -> F)) -> H))), M:tm-708, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-58098
in-theory        58098
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     43
proof            (modus-ponens tm-708 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-3)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-58098.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-708, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-58099
in-theory        58099
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H))
theorem-size     43
proof            (modus-ponens tm-708 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-3)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-58099.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) or H)), M:tm-708, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-58100
in-theory        58100
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E)))
theorem-size     45
proof            (modus-ponens tm-708 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-58100.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)) and E))), M:tm-708, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-58101
in-theory        58101
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F)))
theorem-size     49
proof            (modus-ponens tm-708 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-58101.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) and G) -> E) -> ((E -> F) and G)) -> ((((E -> F) and G) -> E) -> F))), M:tm-708, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-58102
in-theory        58102
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     43
proof            (modus-ponens tm-708 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-58102.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-708, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-58103
in-theory        58103
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E and F) -> E) -> G) and H) -> G))
theorem-size     37
proof            (modus-ponens tm-708 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-58103.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E and F) -> E) -> G) and H) -> G)), M:tm-708, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-58104
in-theory        58104
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> (E -> G)) -> ((E and F) -> G)))
theorem-size     39
proof            (modus-ponens tm-708 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-58104.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> (E -> G)) -> ((E and F) -> G))), M:tm-708, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-58105
in-theory        58105
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not ((F and G) -> F))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-1 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-58105.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not ((F and G) -> F))) -> (not E))), M:tm-708, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-58106
in-theory        58106
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G)))
theorem-size     43
proof            (modus-ponens tm-708 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-58106.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and F) -> E) -> G) -> ((H or ((E and F) -> E)) -> G))), M:tm-708, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-58107
in-theory        58107
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> ((G and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-708 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-58107.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> ((G and H) -> G)))), M:tm-708, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-58108
in-theory        58108
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F and G) -> F)) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-58108.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F and G) -> F)) or H)), M:tm-708, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-58109
in-theory        58109
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> ((G and H) -> G)) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-58109.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> ((G and H) -> G)) and E))), M:tm-708, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-58110
in-theory        58110
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F and G)) -> (E -> F)))
theorem-size     35
proof            (modus-ponens tm-708 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-58110.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F and G)) -> (E -> F))), M:tm-708, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-58111
in-theory        58111
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> ((G and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-708 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-58111.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> ((G and H) -> G)))), M:tm-708, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-58112
in-theory        58112
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and (E -> F)) -> F))
theorem-size     33
proof            (modus-ponens tm-708 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-3.            ((A and B) -> A), axiom
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-58112.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and (E -> F)) -> F)), M:tm-708, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-58113
in-theory        58113
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and ((F -> (G -> F)) -> H)) -> H))
theorem-size     37
proof            (modus-ponens tm-708 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-58113.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and ((F -> (G -> F)) -> H)) -> H)), M:tm-708, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-58114
in-theory        58114
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I))
theorem-size     45
proof            (modus-ponens tm-708 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-58114.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) -> I)) -> I)), M:tm-708, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-58115
in-theory        58115
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and (((F and G) -> F) -> H)) -> H))
theorem-size     37
proof            (modus-ponens tm-708 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-58115.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and (((F and G) -> F) -> H)) -> H)), M:tm-708, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-58116
in-theory        58116
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G)))
theorem-size     47
proof            (modus-ponens tm-708 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-58116.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and ((F -> G) -> F)) -> (F -> G)) -> ((E and ((F -> G) -> F)) -> G))), M:tm-708, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-58117
in-theory        58117
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F)))
theorem-size     41
proof            (modus-ponens tm-708 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-58117.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> F))), M:tm-708, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-58118
in-theory        58118
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and (F -> G)) -> F) -> (not ((E and (F -> G)) -> G))) -> (not ((E and (F -> G)) -> F))))
theorem-size     51
proof            (modus-ponens tm-708 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-4)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-58118.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and (F -> G)) -> F) -> (not ((E and (F -> G)) -> G))) -> (not ((E and (F -> G)) -> F)))), M:tm-708, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-58119
in-theory        58119
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and (F -> G)) -> G) -> H) -> ((((E and (F -> G)) -> F) or ((E and (F -> G)) -> G)) -> H)))
theorem-size     53
proof            (modus-ponens tm-708 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       213
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-58119.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and (F -> G)) -> G) -> H) -> ((((E and (F -> G)) -> F) or ((E and (F -> G)) -> G)) -> H))), M:tm-708, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-58120
in-theory        58120
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     43
proof            (modus-ponens tm-708 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-4)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-58120.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-708, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-58121
in-theory        58121
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H))
theorem-size     43
proof            (modus-ponens tm-708 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-4)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-58121.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) or H)), M:tm-708, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-58122
in-theory        58122
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E)))
theorem-size     45
proof            (modus-ponens tm-708 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-58122.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)) and E))), M:tm-708, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-58123
in-theory        58123
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and (F -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G)))
theorem-size     49
proof            (modus-ponens tm-708 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-58123.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and (F -> G)) -> F) -> (E and (F -> G))) -> (((E and (F -> G)) -> F) -> G))), M:tm-708, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-58124
in-theory        58124
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     43
proof            (modus-ponens tm-708 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-58124.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-708, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-58125
in-theory        58125
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and (((F and G) -> G) -> H)) -> H))
theorem-size     37
proof            (modus-ponens tm-708 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-58125.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and (((F and G) -> G) -> H)) -> H)), M:tm-708, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-58126
in-theory        58126
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E and F) -> F) -> G) and H) -> G))
theorem-size     37
proof            (modus-ponens tm-708 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-58126.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E and F) -> F) -> G) and H) -> G)), M:tm-708, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-58127
in-theory        58127
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> (F -> G)) -> ((E and F) -> G)))
theorem-size     39
proof            (modus-ponens tm-708 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-58127.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> (F -> G)) -> ((E and F) -> G))), M:tm-708, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-58128
in-theory        58128
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not ((F and G) -> G))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-1 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-58128.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not ((F and G) -> G))) -> (not E))), M:tm-708, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-58129
in-theory        58129
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-708 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-58129.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and F) -> F) -> G) -> ((H or ((E and F) -> F)) -> G))), M:tm-708, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-58130
in-theory        58130
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> ((G and H) -> H))))
theorem-size     35
proof            (modus-ponens tm-708 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-58130.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> ((G and H) -> H)))), M:tm-708, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-58131
in-theory        58131
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F and G) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-58131.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F and G) -> G)) or H)), M:tm-708, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-58132
in-theory        58132
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> ((G and H) -> H)) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-58132.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> ((G and H) -> H)) and E))), M:tm-708, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-58133
in-theory        58133
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F and G)) -> (E -> G)))
theorem-size     35
proof            (modus-ponens tm-708 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-58133.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F and G)) -> (E -> G))), M:tm-708, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-58134
in-theory        58134
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> ((G and H) -> H))))
theorem-size     35
proof            (modus-ponens tm-708 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-58134.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> ((G and H) -> H)))), M:tm-708, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-58135
in-theory        58135
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (H -> G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-58135.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (H -> G)))), M:tm-708, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-58136
in-theory        58136
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-58136.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-708, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-58137
in-theory        58137
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G and H) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-58137.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G and H) -> G))), M:tm-708, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-58138
in-theory        58138
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G and H) -> H)))
theorem-size     37
proof            (modus-ponens tm-708 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-58138.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G and H) -> H))), M:tm-708, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-58139
in-theory        58139
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-58139.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (G and H))))), M:tm-708, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-58140
in-theory        58140
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (G or H))))
theorem-size     37
proof            (modus-ponens tm-708 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-58140.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (G or H)))), M:tm-708, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-58141
in-theory        58141
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (H or G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-58141.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (H or G)))), M:tm-708, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-58142
in-theory        58142
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-58142.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-708, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-58143
in-theory        58143
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     43
proof            (modus-ponens tm-708 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-9)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-58143.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-708, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-58144
in-theory        58144
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((not (not G)) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-10)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-58144.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((not (not G)) -> G))), M:tm-708, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-58145
in-theory        58145
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (I -> H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-58145.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (I -> H))))), M:tm-708, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-58146
in-theory        58146
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> (G -> G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-58146.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> (G -> G)))), M:tm-708, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-58147
in-theory        58147
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     51
proof            (modus-ponens tm-708 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-58147.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-708, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-58148
in-theory        58148
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58148.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-708, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-58149
in-theory        58149
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     47
proof            (modus-ponens tm-708 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-58149.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-708, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-58150
in-theory        58150
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> ((H and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-708 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-58150.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> ((H and I) -> H)))), M:tm-708, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-58151
in-theory        58151
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     47
proof            (modus-ponens tm-708 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-58151.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-708, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-58152
in-theory        58152
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> ((H and I) -> I))))
theorem-size     39
proof            (modus-ponens tm-708 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-58152.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> ((H and I) -> I)))), M:tm-708, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-58153
in-theory        58153
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-58153.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-708, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-58154
in-theory        58154
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-58154.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not ((F -> (G -> F)) and E))) -> (not E))), M:tm-708, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-58155
in-theory        58155
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> E)) and G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-708 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-58155.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> E)) and G) -> H) -> ((G or ((E -> (F -> E)) and G)) -> H))), M:tm-708, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-58156
in-theory        58156
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> ((G -> (H -> G)) and F))))
theorem-size     37
proof            (modus-ponens tm-708 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-58156.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> ((G -> (H -> G)) and F)))), M:tm-708, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-58157
in-theory        58157
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F -> (G -> F)) and E)) or H))
theorem-size     37
proof            (modus-ponens tm-708 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-58157.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F -> (G -> F)) and E)) or H)), M:tm-708, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-58158
in-theory        58158
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> ((G -> (H -> G)) and F)) and E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-58158.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> ((G -> (H -> G)) and F)) and E))), M:tm-708, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-58159
in-theory        58159
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> ((G -> (H -> G)) and F))))
theorem-size     37
proof            (modus-ponens tm-708 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-58159.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> ((G -> (H -> G)) and F)))), M:tm-708, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-58160
in-theory        58160
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> H))))
theorem-size     45
proof            (modus-ponens tm-708 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-58160.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> H)))), M:tm-708, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-58161
in-theory        58161
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-58161.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-708, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-58162
in-theory        58162
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> H)))
theorem-size     45
proof            (modus-ponens tm-708 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-58162.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> H))), M:tm-708, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-58163
in-theory        58163
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> I)))
theorem-size     45
proof            (modus-ponens tm-708 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-58163.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H and I) -> I))), M:tm-708, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-58164
in-theory        58164
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (H and I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-58164.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (H and I))))), M:tm-708, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-58165
in-theory        58165
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (H or I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-58165.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (H or I)))), M:tm-708, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-58166
in-theory        58166
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I or H))))
theorem-size     45
proof            (modus-ponens tm-708 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-58166.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I or H)))), M:tm-708, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-58167
in-theory        58167
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-58167.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((I -> J) -> ((H or I) -> J))))), M:tm-708, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-58168
in-theory        58168
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H)))))
theorem-size     51
proof            (modus-ponens tm-708 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-58168.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> ((H -> (not I)) -> (not H))))), M:tm-708, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-58169
in-theory        58169
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((not (not H)) -> H)))
theorem-size     45
proof            (modus-ponens tm-708 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-10)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-58169.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((not (not H)) -> H))), M:tm-708, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-58170
in-theory        58170
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-58170.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> I))))), M:tm-708, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-58171
in-theory        58171
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> H))))
theorem-size     47
proof            (modus-ponens tm-708 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-58171.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> H)))), M:tm-708, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-58172
in-theory        58172
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J)))))
theorem-size     59
proof            (modus-ponens tm-708 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       261
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-58172.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> (H -> I)) -> ((H -> (I -> J)) -> (H -> J))))), M:tm-708, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-58173
in-theory        58173
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     55
proof            (modus-ponens tm-708 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58173.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-708, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-58174
in-theory        58174
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I))))
theorem-size     55
proof            (modus-ponens tm-708 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-58174.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) and J) -> H) -> (((H -> I) and J) -> I)))), M:tm-708, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-58175
in-theory        58175
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> I))))
theorem-size     47
proof            (modus-ponens tm-708 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-58175.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> I)))), M:tm-708, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-58176
in-theory        58176
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J))))
theorem-size     55
proof            (modus-ponens tm-708 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-58176.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and (I -> J)) -> I) -> ((H and (I -> J)) -> J)))), M:tm-708, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-58177
in-theory        58177
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> J))))
theorem-size     47
proof            (modus-ponens tm-708 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-58177.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I and J) -> J)))), M:tm-708, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-58178
in-theory        58178
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> I)) and H))))
theorem-size     49
proof            (modus-ponens tm-708 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-58178.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> I)) and H)))), M:tm-708, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-58179
in-theory        58179
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H))))
theorem-size     57
proof            (modus-ponens tm-708 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-58179.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I -> (J -> K)) -> ((I -> J) -> (I -> K))) and H)))), M:tm-708, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-58180
in-theory        58180
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     49
proof            (modus-ponens tm-708 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-58180.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-708, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-58181
in-theory        58181
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E)))
theorem-size     47
proof            (modus-ponens tm-708 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-58181.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))) -> (not E))), M:tm-708, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-58182
in-theory        58182
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H) -> I) -> ((H or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H)) -> I)))
theorem-size     63
proof            (modus-ponens tm-708 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       237
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-58182.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H) -> I) -> ((H or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and H)) -> I))), M:tm-708, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-58183
in-theory        58183
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     45
proof            (modus-ponens tm-708 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-58183.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-708, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-58184
in-theory        58184
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I))
theorem-size     45
proof            (modus-ponens tm-708 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-58184.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) or I)), M:tm-708, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-58185
in-theory        58185
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E)))
theorem-size     47
proof            (modus-ponens tm-708 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-58185.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)) and E))), M:tm-708, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-58186
in-theory        58186
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     45
proof            (modus-ponens tm-708 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-58186.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-708, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-58187
in-theory        58187
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (H -> G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-58187.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (H -> G)))), M:tm-708, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-58188
in-theory        58188
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-58188.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-708, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-58189
in-theory        58189
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G and H) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-58189.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G and H) -> G))), M:tm-708, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-58190
in-theory        58190
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G and H) -> H)))
theorem-size     37
proof            (modus-ponens tm-708 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-58190.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G and H) -> H))), M:tm-708, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-58191
in-theory        58191
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (H -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-58191.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (H -> (G and H))))), M:tm-708, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-58192
in-theory        58192
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (G or H))))
theorem-size     37
proof            (modus-ponens tm-708 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-58192.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (G or H)))), M:tm-708, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-58193
in-theory        58193
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (H or G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-58193.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (H or G)))), M:tm-708, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-58194
in-theory        58194
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-58194.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-708, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-58195
in-theory        58195
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     43
proof            (modus-ponens tm-708 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-9)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-58195.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-708, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-58196
in-theory        58196
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((not (not G)) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-10)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-58196.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((not (not G)) -> G))), M:tm-708, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-58197
in-theory        58197
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (H -> (I -> H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-58197.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (H -> (I -> H))))), M:tm-708, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-58198
in-theory        58198
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> H) -> (G -> G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-58198.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> H) -> (G -> G)))), M:tm-708, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-58199
in-theory        58199
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     51
proof            (modus-ponens tm-708 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-58199.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-708, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-58200
in-theory        58200
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58200.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-708, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-58201
in-theory        58201
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     47
proof            (modus-ponens tm-708 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-58201.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-708, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-58202
in-theory        58202
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> ((H and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-708 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-58202.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> ((H and I) -> H)))), M:tm-708, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-58203
in-theory        58203
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     47
proof            (modus-ponens tm-708 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-58203.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-708, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-58204
in-theory        58204
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> ((H and I) -> I))))
theorem-size     39
proof            (modus-ponens tm-708 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-58204.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> ((H and I) -> I)))), M:tm-708, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-58205
in-theory        58205
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-58205.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> ((H -> (I -> H)) and G)))), M:tm-708, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-58206
in-theory        58206
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     49
proof            (modus-ponens tm-708 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-58206.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-708, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-58207
in-theory        58207
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (((H and I) -> H) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-58207.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (((H and I) -> H) and G)))), M:tm-708, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-58208
in-theory        58208
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> I) and H))))
theorem-size     49
proof            (modus-ponens tm-708 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-58208.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> I) and H)))), M:tm-708, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-58209
in-theory        58209
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-58209.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (((H and I) -> H) and G)))), M:tm-708, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-58210
in-theory        58210
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (((F and G) -> F) and E))) -> (not E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-58210.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (((F and G) -> F) and E))) -> (not E))), M:tm-708, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-58211
in-theory        58211
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E and F) -> E) and G) -> H) -> ((G or (((E and F) -> E) and G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-708 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-58211.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E and F) -> E) and G) -> H) -> ((G or (((E and F) -> E) and G)) -> H))), M:tm-708, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-58212
in-theory        58212
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (((G and H) -> G) and F))))
theorem-size     37
proof            (modus-ponens tm-708 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-58212.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (((G and H) -> G) and F)))), M:tm-708, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-58213
in-theory        58213
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (((F and G) -> F) and E)) or H))
theorem-size     37
proof            (modus-ponens tm-708 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-58213.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (((F and G) -> F) and E)) or H)), M:tm-708, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-58214
in-theory        58214
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (((G and H) -> G) and F)) and E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-58214.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (((G and H) -> G) and F)) and E))), M:tm-708, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-58215
in-theory        58215
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (((G and H) -> G) and F))))
theorem-size     37
proof            (modus-ponens tm-708 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-58215.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (((G and H) -> G) and F)))), M:tm-708, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-58216
in-theory        58216
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (H -> G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-58216.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (H -> G)))), M:tm-708, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-58217
in-theory        58217
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-58217.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-708, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-58218
in-theory        58218
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G and H) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-58218.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G and H) -> G))), M:tm-708, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-58219
in-theory        58219
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G and H) -> H)))
theorem-size     37
proof            (modus-ponens tm-708 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-58219.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G and H) -> H))), M:tm-708, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-58220
in-theory        58220
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (H -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-58220.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (H -> (G and H))))), M:tm-708, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-58221
in-theory        58221
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (G or H))))
theorem-size     37
proof            (modus-ponens tm-708 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-58221.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (G or H)))), M:tm-708, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-58222
in-theory        58222
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (H or G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-58222.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (H or G)))), M:tm-708, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-58223
in-theory        58223
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-58223.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-708, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-58224
in-theory        58224
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     43
proof            (modus-ponens tm-708 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-9)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-58224.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-708, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-58225
in-theory        58225
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((not (not G)) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-10)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-58225.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((not (not G)) -> G))), M:tm-708, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-58226
in-theory        58226
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (H -> (I -> H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-58226.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (H -> (I -> H))))), M:tm-708, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-58227
in-theory        58227
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> H) -> (G -> G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-58227.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> H) -> (G -> G)))), M:tm-708, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-58228
in-theory        58228
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     51
proof            (modus-ponens tm-708 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-58228.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-708, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-58229
in-theory        58229
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58229.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-708, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-58230
in-theory        58230
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     47
proof            (modus-ponens tm-708 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-58230.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-708, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-58231
in-theory        58231
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> ((H and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-708 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-58231.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> ((H and I) -> H)))), M:tm-708, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-58232
in-theory        58232
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     47
proof            (modus-ponens tm-708 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-58232.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-708, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-58233
in-theory        58233
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> ((H and I) -> I))))
theorem-size     39
proof            (modus-ponens tm-708 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-58233.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> ((H and I) -> I)))), M:tm-708, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-58234
in-theory        58234
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-58234.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> ((H -> (I -> H)) and G)))), M:tm-708, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-58235
in-theory        58235
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     49
proof            (modus-ponens tm-708 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-58235.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-708, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-58236
in-theory        58236
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (((H and I) -> H) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-58236.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (((H and I) -> H) and G)))), M:tm-708, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-58237
in-theory        58237
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (((H and I) -> I) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-58237.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (((H and I) -> I) and G)))), M:tm-708, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-58238
in-theory        58238
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (((H and I) -> I) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-58238.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (((H and I) -> I) and G)))), M:tm-708, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-58239
in-theory        58239
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> J) and H))))
theorem-size     49
proof            (modus-ponens tm-708 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-58239.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (((I and J) -> J) and H)))), M:tm-708, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-58240
in-theory        58240
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-58240.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (((H and I) -> I) and G)))), M:tm-708, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-58241
in-theory        58241
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (((F and G) -> G) and E))) -> (not E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-58241.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (((F and G) -> G) and E))) -> (not E))), M:tm-708, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-58242
in-theory        58242
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E and F) -> F) and G) -> H) -> ((G or (((E and F) -> F) and G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-708 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-58242.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E and F) -> F) and G) -> H) -> ((G or (((E and F) -> F) and G)) -> H))), M:tm-708, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-58243
in-theory        58243
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (((G and H) -> H) and F))))
theorem-size     37
proof            (modus-ponens tm-708 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-58243.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (((G and H) -> H) and F)))), M:tm-708, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-58244
in-theory        58244
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (((F and G) -> G) and E)) or H))
theorem-size     37
proof            (modus-ponens tm-708 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-58244.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (((F and G) -> G) and E)) or H)), M:tm-708, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-58245
in-theory        58245
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (((G and H) -> H) and F)) and E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-58245.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (((G and H) -> H) and F)) and E))), M:tm-708, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-58246
in-theory        58246
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (((G and H) -> H) and F))))
theorem-size     37
proof            (modus-ponens tm-708 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-58246.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (((G and H) -> H) and F)))), M:tm-708, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-58247
in-theory        58247
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-58247.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> G)))), M:tm-708, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-58248
in-theory        58248
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-58248.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-708, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-58249
in-theory        58249
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G and H) -> G)))
theorem-size     39
proof            (modus-ponens tm-708 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-58249.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G and H) -> G))), M:tm-708, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-58250
in-theory        58250
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G and H) -> H)))
theorem-size     39
proof            (modus-ponens tm-708 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-58250.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G and H) -> H))), M:tm-708, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-58251
in-theory        58251
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-58251.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (G and H))))), M:tm-708, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-58252
in-theory        58252
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (G or H))))
theorem-size     39
proof            (modus-ponens tm-708 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-58252.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (G or H)))), M:tm-708, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-58253
in-theory        58253
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H or G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-58253.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H or G)))), M:tm-708, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-58254
in-theory        58254
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-58254.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-708, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-58255
in-theory        58255
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-58255.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-708, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-58256
in-theory        58256
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((not (not G)) -> G)))
theorem-size     39
proof            (modus-ponens tm-708 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-10)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-58256.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((not (not G)) -> G))), M:tm-708, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-58257
in-theory        58257
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-58257.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> H))))), M:tm-708, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-58258
in-theory        58258
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-58258.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> G)))), M:tm-708, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-58259
in-theory        58259
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-58259.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-708, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-58260
in-theory        58260
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-708 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58260.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-708, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-58261
in-theory        58261
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     49
proof            (modus-ponens tm-708 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-58261.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-708, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-58262
in-theory        58262
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-708 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-58262.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> H)))), M:tm-708, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-58263
in-theory        58263
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     49
proof            (modus-ponens tm-708 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-58263.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-708, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-58264
in-theory        58264
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-708 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-58264.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H and I) -> I)))), M:tm-708, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-58265
in-theory        58265
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     43
proof            (modus-ponens tm-708 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-58265.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-708, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-58266
in-theory        58266
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     51
proof            (modus-ponens tm-708 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-58266.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-708, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-58267
in-theory        58267
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G))))
theorem-size     43
proof            (modus-ponens tm-708 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-58267.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> H) and G)))), M:tm-708, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-58268
in-theory        58268
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G))))
theorem-size     43
proof            (modus-ponens tm-708 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-58268.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (((H and I) -> I) and G)))), M:tm-708, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-58269
in-theory        58269
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     45
proof            (modus-ponens tm-708 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-58269.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-708, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-58270
in-theory        58270
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     43
proof            (modus-ponens tm-708 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-58270.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-708, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-58271
in-theory        58271
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     43
proof            (modus-ponens tm-708 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-58271.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-708, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-58272
in-theory        58272
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> (I and J))) and H))))
theorem-size     51
proof            (modus-ponens tm-708 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-58272.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J -> (I and J))) and H)))), M:tm-708, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-58273
in-theory        58273
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     43
proof            (modus-ponens tm-708 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-58273.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-708, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-58274
in-theory        58274
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E)))
theorem-size     41
proof            (modus-ponens tm-708 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-58274.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not ((F -> (G -> (F and G))) and E))) -> (not E))), M:tm-708, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-58275
in-theory        58275
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> (E and F))) and G) -> H) -> ((G or ((E -> (F -> (E and F))) and G)) -> H)))
theorem-size     51
proof            (modus-ponens tm-708 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-58275.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> (E and F))) and G) -> H) -> ((G or ((E -> (F -> (E and F))) and G)) -> H))), M:tm-708, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-58276
in-theory        58276
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     39
proof            (modus-ponens tm-708 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-58276.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> ((G -> (H -> (G and H))) and F)))), M:tm-708, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-58277
in-theory        58277
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F -> (G -> (F and G))) and E)) or H))
theorem-size     39
proof            (modus-ponens tm-708 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-58277.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F -> (G -> (F and G))) and E)) or H)), M:tm-708, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-58278
in-theory        58278
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E)))
theorem-size     41
proof            (modus-ponens tm-708 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-58278.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> ((G -> (H -> (G and H))) and F)) and E))), M:tm-708, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-58279
in-theory        58279
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     39
proof            (modus-ponens tm-708 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-58279.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> ((G -> (H -> (G and H))) and F)))), M:tm-708, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-58280
in-theory        58280
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (F -> E))))
theorem-size     33
proof            (modus-ponens tm-708 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58280.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (F -> E)))), M:tm-708, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-58281
in-theory        58281
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-58281.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> G)) -> ((E -> (F -> G)) and ((E -> F) -> (E -> G))))), M:tm-708, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-58282
in-theory        58282
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and F) -> ((E and F) and E)))
theorem-size     35
proof            (modus-ponens tm-708 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-58282.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and F) -> ((E and F) and E))), M:tm-708, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-58283
in-theory        58283
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and F) -> ((E and F) and F)))
theorem-size     35
proof            (modus-ponens tm-708 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-58283.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and F) -> ((E and F) and F))), M:tm-708, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-58284
in-theory        58284
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (F -> (E and F)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-58284.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (F -> (E and F))))), M:tm-708, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-58285
in-theory        58285
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (E or F))))
theorem-size     33
proof            (modus-ponens tm-708 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-58285.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (E or F)))), M:tm-708, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-58286
in-theory        58286
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (F or E))))
theorem-size     33
proof            (modus-ponens tm-708 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-58286.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (F or E)))), M:tm-708, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-58287
in-theory        58287
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G)))))
theorem-size     43
proof            (modus-ponens tm-708 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-58287.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((E -> F) and ((F -> G) -> ((E or F) -> G))))), M:tm-708, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-58288
in-theory        58288
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-58288.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((E -> F) and ((E -> (not F)) -> (not E))))), M:tm-708, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-58289
in-theory        58289
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((not (not E)) -> ((not (not E)) and E)))
theorem-size     35
proof            (modus-ponens tm-708 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-10)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-58289.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((not (not E)) -> ((not (not E)) and E))), M:tm-708, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-58290
in-theory        58290
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (F -> (G -> F)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-58290.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (F -> (G -> F))))), M:tm-708, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-58291
in-theory        58291
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((E -> F) and (E -> E))))
theorem-size     37
proof            (modus-ponens tm-708 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-58291.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((E -> F) and (E -> E)))), M:tm-708, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-58292
in-theory        58292
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> (E -> F)) -> (((E -> (F -> G)) -> (E -> F)) and ((E -> (F -> G)) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-708 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       245
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-58292.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> (E -> F)) -> (((E -> (F -> G)) -> (E -> F)) and ((E -> (F -> G)) -> (E -> G))))), M:tm-708, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-58293
in-theory        58293
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     43
proof            (modus-ponens tm-708 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-58293.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-708, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-58294
in-theory        58294
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) -> E) -> ((((E -> F) and G) -> E) and (((E -> F) and G) -> F))))
theorem-size     49
proof            (modus-ponens tm-708 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-58294.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) -> E) -> ((((E -> F) and G) -> E) and (((E -> F) and G) -> F)))), M:tm-708, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-58295
in-theory        58295
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and ((F and G) -> F))))
theorem-size     35
proof            (modus-ponens tm-708 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-58295.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and ((F and G) -> F)))), M:tm-708, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-58296
in-theory        58296
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) -> F) -> (((E and (F -> G)) -> F) and ((E and (F -> G)) -> G))))
theorem-size     49
proof            (modus-ponens tm-708 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-58296.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) -> F) -> (((E and (F -> G)) -> F) and ((E and (F -> G)) -> G)))), M:tm-708, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-58297
in-theory        58297
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and ((F and G) -> G))))
theorem-size     35
proof            (modus-ponens tm-708 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-58297.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and ((F and G) -> G)))), M:tm-708, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-58298
in-theory        58298
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and ((F -> (G -> F)) and E))))
theorem-size     37
proof            (modus-ponens tm-708 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-58298.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and ((F -> (G -> F)) and E)))), M:tm-708, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-58299
in-theory        58299
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     45
proof            (modus-ponens tm-708 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-58299.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-708, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-58300
in-theory        58300
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (((F and G) -> F) and E))))
theorem-size     37
proof            (modus-ponens tm-708 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-58300.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (((F and G) -> F) and E)))), M:tm-708, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-58301
in-theory        58301
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (((F and G) -> G) and E))))
theorem-size     37
proof            (modus-ponens tm-708 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-58301.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (((F and G) -> G) and E)))), M:tm-708, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-58302
in-theory        58302
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and ((F -> (G -> (F and G))) and E))))
theorem-size     39
proof            (modus-ponens tm-708 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-58302.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and ((F -> (G -> (F and G))) and E)))), M:tm-708, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-58303
in-theory        58303
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((E -> F) and (E -> (E and F)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-58303.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((E -> F) and (E -> (E and F))))), M:tm-708, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-58304
in-theory        58304
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     43
proof            (modus-ponens tm-708 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-58304.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> (G -> (G and H))))), M:tm-708, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-58305
in-theory        58305
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-58305.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> H) -> (G -> (G and H))))), M:tm-708, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-58306
in-theory        58306
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-58306.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> H) -> (G -> (G and H))))), M:tm-708, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-58307
in-theory        58307
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> (H and I)))))
theorem-size     49
proof            (modus-ponens tm-708 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-58307.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (H -> (H and I))))), M:tm-708, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-58308
in-theory        58308
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-58308.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> (G -> (G and H))))), M:tm-708, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-58309
in-theory        58309
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F))))
theorem-size     41
proof            (modus-ponens tm-708 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-58309.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (not (E -> (E and F)))) -> (not (E -> F)))), M:tm-708, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-58310
in-theory        58310
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-708 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-58310.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (E and F)) -> G) -> (((E -> F) or (E -> (E and F))) -> G))), M:tm-708, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-58311
in-theory        58311
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> G) -> (F -> (F and G)))))
theorem-size     37
proof            (modus-ponens tm-708 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-58311.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> G) -> (F -> (F and G))))), M:tm-708, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-58312
in-theory        58312
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (E -> (E and F))) or G))
theorem-size     37
proof            (modus-ponens tm-708 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-58312.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (E -> (E and F))) or G)), M:tm-708, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-58313
in-theory        58313
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> (F -> (F and G))) and E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-58313.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> (F -> (F and G))) and E))), M:tm-708, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-58314
in-theory        58314
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> E) -> ((E -> F) -> (E and F))))
theorem-size     39
proof            (modus-ponens tm-708 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-58314.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> E) -> ((E -> F) -> (E and F)))), M:tm-708, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-58315
in-theory        58315
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> G) -> (F -> (F and G)))))
theorem-size     37
proof            (modus-ponens tm-708 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-58315.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> G) -> (F -> (F and G))))), M:tm-708, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-58316
in-theory        58316
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (F -> (G -> (F and G))))))
theorem-size     37
proof            (modus-ponens tm-708 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-58316.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (F -> (G -> (F and G)))))), M:tm-708, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-58317
in-theory        58317
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-708 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58317.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (I -> (H and I)))))), M:tm-708, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-58318
in-theory        58318
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (H -> (I -> (H and I))))))
theorem-size     41
proof            (modus-ponens tm-708 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58318.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (H -> (I -> (H and I)))))), M:tm-708, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-58319
in-theory        58319
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (H -> (I -> (H and I))))))
theorem-size     41
proof            (modus-ponens tm-708 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58319.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (H -> (I -> (H and I)))))), M:tm-708, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-58320
in-theory        58320
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> (I and J))))))
theorem-size     49
proof            (modus-ponens tm-708 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58320.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J -> (I and J)))))), M:tm-708, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-58321
in-theory        58321
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I))))))
theorem-size     41
proof            (modus-ponens tm-708 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58321.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (I -> (H and I)))))), M:tm-708, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-58322
in-theory        58322
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and ((F -> (G -> (F and G))) -> H)) -> H))
theorem-size     39
proof            (modus-ponens tm-708 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-58322.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and ((F -> (G -> (F and G))) -> H)) -> H)), M:tm-708, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-58323
in-theory        58323
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> (E and F))) -> G) and H) -> G))
theorem-size     39
proof            (modus-ponens tm-708 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-58323.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> (E and F))) -> G) and H) -> G)), M:tm-708, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-58324
in-theory        58324
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G)))
theorem-size     39
proof            (modus-ponens tm-708 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-58324.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F -> (E and F)) -> G)) -> (E -> G))), M:tm-708, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-58325
in-theory        58325
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (F -> (G -> (F and G))))) -> (not E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-58325.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (F -> (G -> (F and G))))) -> (not E))), M:tm-708, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-58326
in-theory        58326
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> (E and F))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G)))
theorem-size     47
proof            (modus-ponens tm-708 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-58326.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> (E and F))) -> G) -> ((H or (E -> (F -> (E and F)))) -> G))), M:tm-708, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-58327
in-theory        58327
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (G -> (H -> (G and H))))))
theorem-size     37
proof            (modus-ponens tm-708 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58327.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (G -> (H -> (G and H)))))), M:tm-708, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-58328
in-theory        58328
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (G -> (F and G)))) or H))
theorem-size     37
proof            (modus-ponens tm-708 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58328.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (G -> (F and G)))) or H)), M:tm-708, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-58329
in-theory        58329
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> (H -> (G and H)))) and E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58329.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> (H -> (G and H)))) and E))), M:tm-708, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-58330
in-theory        58330
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (E -> (G -> (F and G)))))
theorem-size     37
proof            (modus-ponens tm-708 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-58330.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (E -> (G -> (F and G))))), M:tm-708, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-58331
in-theory        58331
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (G -> (H -> (G and H))))))
theorem-size     37
proof            (modus-ponens tm-708 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58331.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (G -> (H -> (G and H)))))), M:tm-708, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-58332
in-theory        58332
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I)))
theorem-size     41
proof            (modus-ponens tm-708 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-58332.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (H -> G)) or I))), M:tm-708, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-58333
in-theory        58333
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> (H -> G)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-6 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-58333.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> (H -> G)) or I))), M:tm-708, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-58334
in-theory        58334
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> (H -> G)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-6 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-58334.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> (H -> G)) or I))), M:tm-708, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-58335
in-theory        58335
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> H)) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-58335.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> H)) or J))), M:tm-708, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-58336
in-theory        58336
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> (H -> G)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-58336.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> (H -> G)) or I))), M:tm-708, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-58337
in-theory        58337
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> (G -> F)) or H)))
theorem-size     35
proof            (modus-ponens tm-708 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-58337.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> (G -> F)) or H))), M:tm-708, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-58338
in-theory        58338
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> E)) or G) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-58338.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> E)) or G) or H)), M:tm-708, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-58339
in-theory        58339
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (G -> F)) or H) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-58339.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (G -> F)) or H) and E))), M:tm-708, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-58340
in-theory        58340
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> F)) or H)))
theorem-size     35
proof            (modus-ponens tm-708 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-58340.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> F)) or H))), M:tm-708, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-58341
in-theory        58341
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     49
proof            (modus-ponens tm-708 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58341.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-708, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-58342
in-theory        58342
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-6)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58342.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-708, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-58343
in-theory        58343
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-6)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58343.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-708, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-58344
in-theory        58344
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K)))
theorem-size     55
proof            (modus-ponens tm-708 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58344.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) or K))), M:tm-708, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-58345
in-theory        58345
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58345.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-708, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-58346
in-theory        58346
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     43
proof            (modus-ponens tm-708 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58346.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-708, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58347
in-theory        58347
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) or I))
theorem-size     43
proof            (modus-ponens tm-708 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58347.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) or I)), M:tm-708, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-58348
in-theory        58348
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E)))
theorem-size     45
proof            (modus-ponens tm-708 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58348.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I) and E))), M:tm-708, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-58349
in-theory        58349
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     43
proof            (modus-ponens tm-708 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58349.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-708, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58350
in-theory        58350
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I)))
theorem-size     41
proof            (modus-ponens tm-708 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-58350.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (((G and H) -> G) or I))), M:tm-708, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-58351
in-theory        58351
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (((G and H) -> G) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-6 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-58351.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (((G and H) -> G) or I))), M:tm-708, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-58352
in-theory        58352
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (((G and H) -> G) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-58352.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (((G and H) -> G) or I))), M:tm-708, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-58353
in-theory        58353
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> H) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-58353.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> H) or J))), M:tm-708, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-58354
in-theory        58354
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G and H) -> G) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-58354.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G and H) -> G) or I))), M:tm-708, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-58355
in-theory        58355
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F and G) -> F) or H)))
theorem-size     35
proof            (modus-ponens tm-708 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-58355.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F and G) -> F) or H))), M:tm-708, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-58356
in-theory        58356
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and F) -> E) or G) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-58356.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and F) -> E) or G) or H)), M:tm-708, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-58357
in-theory        58357
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F and G) -> F) or H) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-58357.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F and G) -> F) or H) and E))), M:tm-708, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-58358
in-theory        58358
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F and G) -> F) or H)))
theorem-size     35
proof            (modus-ponens tm-708 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-58358.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F and G) -> F) or H))), M:tm-708, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-58359
in-theory        58359
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I)))
theorem-size     41
proof            (modus-ponens tm-708 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-58359.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (((G and H) -> H) or I))), M:tm-708, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-58360
in-theory        58360
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (((G and H) -> H) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-58360.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (((G and H) -> H) or I))), M:tm-708, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-58361
in-theory        58361
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (((G and H) -> H) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-6 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-58361.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (((G and H) -> H) or I))), M:tm-708, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-58362
in-theory        58362
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> I) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-58362.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H and I) -> I) or J))), M:tm-708, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-58363
in-theory        58363
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G and H) -> H) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-58363.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G and H) -> H) or I))), M:tm-708, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-58364
in-theory        58364
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F and G) -> G) or H)))
theorem-size     35
proof            (modus-ponens tm-708 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-58364.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F and G) -> G) or H))), M:tm-708, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-58365
in-theory        58365
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and F) -> F) or G) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-58365.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and F) -> F) or G) or H)), M:tm-708, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-58366
in-theory        58366
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F and G) -> G) or H) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-58366.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F and G) -> G) or H) and E))), M:tm-708, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-58367
in-theory        58367
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F and G) -> G) or H)))
theorem-size     35
proof            (modus-ponens tm-708 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-58367.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F and G) -> G) or H))), M:tm-708, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-58368
in-theory        58368
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     43
proof            (modus-ponens tm-708 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-58368.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (H -> (G and H))) or I))), M:tm-708, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-58369
in-theory        58369
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I)))
theorem-size     41
proof            (modus-ponens tm-708 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-58369.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> (H -> (G and H))) or I))), M:tm-708, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-58370
in-theory        58370
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I)))
theorem-size     41
proof            (modus-ponens tm-708 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-58370.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> (H -> (G and H))) or I))), M:tm-708, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-58371
in-theory        58371
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> (H and I))) or J)))
theorem-size     49
proof            (modus-ponens tm-708 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-58371.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I -> (H and I))) or J))), M:tm-708, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-58372
in-theory        58372
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I)))
theorem-size     41
proof            (modus-ponens tm-708 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-58372.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> (H -> (G and H))) or I))), M:tm-708, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-58373
in-theory        58373
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> (G -> (F and G))) or H)))
theorem-size     37
proof            (modus-ponens tm-708 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-58373.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> (G -> (F and G))) or H))), M:tm-708, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-58374
in-theory        58374
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> (E and F))) or G) or H))
theorem-size     37
proof            (modus-ponens tm-708 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-58374.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> (E and F))) or G) or H)), M:tm-708, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-58375
in-theory        58375
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (G -> (F and G))) or H) and E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-58375.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (G -> (F and G))) or H) and E))), M:tm-708, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-58376
in-theory        58376
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> (F and G))) or H)))
theorem-size     37
proof            (modus-ponens tm-708 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-58376.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> (F and G))) or H))), M:tm-708, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-58377
in-theory        58377
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I)))
theorem-size     41
proof            (modus-ponens tm-708 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-58377.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (G or H)) or I))), M:tm-708, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-58378
in-theory        58378
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> (G or H)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-58378.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> (G or H)) or I))), M:tm-708, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-58379
in-theory        58379
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> (G or H)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-58379.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> (G or H)) or I))), M:tm-708, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-58380
in-theory        58380
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (H or I)) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-58380.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (H or I)) or J))), M:tm-708, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-58381
in-theory        58381
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> (G or H)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-58381.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> (G or H)) or I))), M:tm-708, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-58382
in-theory        58382
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> (F or G)) or H)))
theorem-size     35
proof            (modus-ponens tm-708 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-58382.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> (F or G)) or H))), M:tm-708, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-58383
in-theory        58383
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (E or F)) or G) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-58383.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (E or F)) or G) or H)), M:tm-708, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-58384
in-theory        58384
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (F or G)) or H) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-58384.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (F or G)) or H) and E))), M:tm-708, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-58385
in-theory        58385
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (F or G)) or H)))
theorem-size     35
proof            (modus-ponens tm-708 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-58385.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (F or G)) or H))), M:tm-708, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-58386
in-theory        58386
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (H -> G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-58386.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (H -> G)))), M:tm-708, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-58387
in-theory        58387
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-58387.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-708, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-58388
in-theory        58388
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G and H) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-58388.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G and H) -> G))), M:tm-708, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-58389
in-theory        58389
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G and H) -> H)))
theorem-size     37
proof            (modus-ponens tm-708 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-58389.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G and H) -> H))), M:tm-708, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-58390
in-theory        58390
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (H -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-58390.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (H -> (G and H))))), M:tm-708, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-58391
in-theory        58391
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (G or H))))
theorem-size     37
proof            (modus-ponens tm-708 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-58391.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (G or H)))), M:tm-708, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-58392
in-theory        58392
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (H or G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-58392.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (H or G)))), M:tm-708, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-58393
in-theory        58393
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-58393.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-708, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-58394
in-theory        58394
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     43
proof            (modus-ponens tm-708 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-9)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-58394.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-708, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-58395
in-theory        58395
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((not (not G)) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-10)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-58395.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((not (not G)) -> G))), M:tm-708, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-58396
in-theory        58396
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (H -> (I -> H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-58396.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (H -> (I -> H))))), M:tm-708, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-58397
in-theory        58397
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> H) -> (G -> G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-58397.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> H) -> (G -> G)))), M:tm-708, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-58398
in-theory        58398
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     51
proof            (modus-ponens tm-708 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-58398.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-708, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-58399
in-theory        58399
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58399.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-708, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-58400
in-theory        58400
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     47
proof            (modus-ponens tm-708 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-58400.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-708, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-58401
in-theory        58401
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> ((H and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-708 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-58401.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> ((H and I) -> H)))), M:tm-708, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-58402
in-theory        58402
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     47
proof            (modus-ponens tm-708 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-58402.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-708, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-58403
in-theory        58403
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> ((H and I) -> I))))
theorem-size     39
proof            (modus-ponens tm-708 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-58403.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> ((H and I) -> I)))), M:tm-708, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-58404
in-theory        58404
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-58404.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (I -> H)) and G)))), M:tm-708, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-58405
in-theory        58405
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     49
proof            (modus-ponens tm-708 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-58405.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-708, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-58406
in-theory        58406
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-58406.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (((H and I) -> H) and G)))), M:tm-708, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-58407
in-theory        58407
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-58407.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (((H and I) -> I) and G)))), M:tm-708, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-58408
in-theory        58408
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     43
proof            (modus-ponens tm-708 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-58408.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-708, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-58409
in-theory        58409
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-58409.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> H) -> (G -> (G and H))))), M:tm-708, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-58410
in-theory        58410
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I))))))
theorem-size     41
proof            (modus-ponens tm-708 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58410.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (H -> (I -> (H and I)))))), M:tm-708, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-58411
in-theory        58411
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> (H -> G)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-58411.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> (H -> G)) or I))), M:tm-708, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-58412
in-theory        58412
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58412.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-708, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-58413
in-theory        58413
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (((G and H) -> G) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-58413.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (((G and H) -> G) or I))), M:tm-708, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-58414
in-theory        58414
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (((G and H) -> H) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-58414.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (((G and H) -> H) or I))), M:tm-708, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-58415
in-theory        58415
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I)))
theorem-size     41
proof            (modus-ponens tm-708 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-58415.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> (H -> (G and H))) or I))), M:tm-708, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-58416
in-theory        58416
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> (G or H)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-58416.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> (G or H)) or I))), M:tm-708, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-58417
in-theory        58417
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-58417.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (H or I)) and G)))), M:tm-708, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-58418
in-theory        58418
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and ((F -> (F or G)) and E))))
theorem-size     37
proof            (modus-ponens tm-708 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-58418.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and ((F -> (F or G)) and E)))), M:tm-708, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-58419
in-theory        58419
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     43
proof            (modus-ponens tm-708 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-58419.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (H or I)) and G)))), M:tm-708, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-58420
in-theory        58420
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-58420.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> ((H -> (H or I)) and G)))), M:tm-708, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-58421
in-theory        58421
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-58421.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> ((H -> (H or I)) and G)))), M:tm-708, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-58422
in-theory        58422
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (I or J)) and H))))
theorem-size     49
proof            (modus-ponens tm-708 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-58422.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (I or J)) and H)))), M:tm-708, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-58423
in-theory        58423
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-58423.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (H or I)) and G)))), M:tm-708, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-58424
in-theory        58424
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not ((F -> (F or G)) and E))) -> (not E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-6)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-58424.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not ((F -> (F or G)) and E))) -> (not E))), M:tm-708, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-58425
in-theory        58425
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (E or F)) and G) -> H) -> ((G or ((E -> (E or F)) and G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-708 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-58425.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (E or F)) and G) -> H) -> ((G or ((E -> (E or F)) and G)) -> H))), M:tm-708, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-58426
in-theory        58426
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> ((G -> (G or H)) and F))))
theorem-size     37
proof            (modus-ponens tm-708 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-58426.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> ((G -> (G or H)) and F)))), M:tm-708, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-58427
in-theory        58427
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F -> (F or G)) and E)) or H))
theorem-size     37
proof            (modus-ponens tm-708 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-58427.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F -> (F or G)) and E)) or H)), M:tm-708, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-58428
in-theory        58428
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> ((G -> (G or H)) and F)) and E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-58428.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> ((G -> (G or H)) and F)) and E))), M:tm-708, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-58429
in-theory        58429
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> ((G -> (G or H)) and F))))
theorem-size     37
proof            (modus-ponens tm-708 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-58429.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> ((G -> (G or H)) and F)))), M:tm-708, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-58430
in-theory        58430
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (H -> (H or I)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-58430.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (H -> (H or I))))), M:tm-708, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-58431
in-theory        58431
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (F -> (F or G)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-58431.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (F -> (F or G))))), M:tm-708, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-58432
in-theory        58432
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-58432.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (H or I))))), M:tm-708, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-58433
in-theory        58433
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (H -> (H or I)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-58433.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (H -> (H or I))))), M:tm-708, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-58434
in-theory        58434
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (H -> (H or I)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-58434.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (H -> (H or I))))), M:tm-708, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-58435
in-theory        58435
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (I or J)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-58435.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (I or J))))), M:tm-708, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-58436
in-theory        58436
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (H or I)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-58436.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (H or I))))), M:tm-708, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-58437
in-theory        58437
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and ((F -> (F or G)) -> H)) -> H))
theorem-size     37
proof            (modus-ponens tm-708 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-58437.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and ((F -> (F or G)) -> H)) -> H)), M:tm-708, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-58438
in-theory        58438
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (E or F)) -> G) and H) -> G))
theorem-size     37
proof            (modus-ponens tm-708 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-58438.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (E or F)) -> G) and H) -> G)), M:tm-708, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-58439
in-theory        58439
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((E or F) -> G)) -> (E -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-58439.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((E or F) -> G)) -> (E -> G))), M:tm-708, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-58440
in-theory        58440
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (F -> (F or G)))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-1 tm-6)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-58440.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (F -> (F or G)))) -> (not E))), M:tm-708, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-58441
in-theory        58441
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G)))
theorem-size     43
proof            (modus-ponens tm-708 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-58441.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (E or F)) -> G) -> ((H or (E -> (E or F))) -> G))), M:tm-708, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-58442
in-theory        58442
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (G -> (G or H)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-58442.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (G -> (G or H))))), M:tm-708, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-58443
in-theory        58443
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (F or G))) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-58443.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (F or G))) or H)), M:tm-708, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-58444
in-theory        58444
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> (G or H))) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-58444.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> (G or H))) and E))), M:tm-708, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-58445
in-theory        58445
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (E -> (F or G))))
theorem-size     35
proof            (modus-ponens tm-708 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-58445.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (E -> (F or G)))), M:tm-708, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-58446
in-theory        58446
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (G -> (G or H)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-58446.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (G -> (G or H))))), M:tm-708, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-58447
in-theory        58447
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or (H -> (I -> H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-58447.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or (H -> (I -> H))))), M:tm-708, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-58448
in-theory        58448
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-58448.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G or (H -> (I -> H))))), M:tm-708, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-58449
in-theory        58449
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or (H -> (I -> H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-7 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-58449.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or (H -> (I -> H))))), M:tm-708, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-58450
in-theory        58450
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or (H -> (I -> H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-7 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-58450.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or (H -> (I -> H))))), M:tm-708, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-58451
in-theory        58451
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-58451.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> I))))), M:tm-708, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-58452
in-theory        58452
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or (H -> (I -> H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-58452.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or (H -> (I -> H))))), M:tm-708, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-58453
in-theory        58453
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or (G -> (H -> G)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-58453.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or (G -> (H -> G))))), M:tm-708, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-58454
in-theory        58454
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (G -> F))) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-58454.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (G -> F))) or H)), M:tm-708, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-58455
in-theory        58455
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or (G -> (H -> G))) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-58455.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or (G -> (H -> G))) and E))), M:tm-708, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-58456
in-theory        58456
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or (G -> (H -> G)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-58456.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or (G -> (H -> G))))), M:tm-708, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-58457
in-theory        58457
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58457.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-708, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-58458
in-theory        58458
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     49
proof            (modus-ponens tm-708 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58458.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-708, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-58459
in-theory        58459
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-7)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58459.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-708, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-58460
in-theory        58460
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-7)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58460.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-708, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-58461
in-theory        58461
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K))))))
theorem-size     55
proof            (modus-ponens tm-708 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58461.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I -> (J -> K)) -> ((I -> J) -> (I -> K)))))), M:tm-708, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-58462
in-theory        58462
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58462.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-708, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-58463
in-theory        58463
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     43
proof            (modus-ponens tm-708 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58463.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-708, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-58464
in-theory        58464
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I))
theorem-size     43
proof            (modus-ponens tm-708 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58464.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) or I)), M:tm-708, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-58465
in-theory        58465
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E)))
theorem-size     45
proof            (modus-ponens tm-708 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58465.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))) and E))), M:tm-708, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-58466
in-theory        58466
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     43
proof            (modus-ponens tm-708 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58466.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-708, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-58467
in-theory        58467
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or ((H and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-708 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-58467.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or ((H and I) -> H)))), M:tm-708, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-58468
in-theory        58468
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-708 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-58468.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G or ((H and I) -> H)))), M:tm-708, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-58469
in-theory        58469
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or ((H and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-708 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-7 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-58469.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or ((H and I) -> H)))), M:tm-708, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-58470
in-theory        58470
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or ((H and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-708 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-58470.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or ((H and I) -> H)))), M:tm-708, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-58471
in-theory        58471
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> I))))
theorem-size     47
proof            (modus-ponens tm-708 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-58471.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> I)))), M:tm-708, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-58472
in-theory        58472
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or ((H and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-708 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-58472.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or ((H and I) -> H)))), M:tm-708, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-58473
in-theory        58473
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or ((G and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-708 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-58473.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or ((G and H) -> G)))), M:tm-708, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-58474
in-theory        58474
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F and G) -> F)) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-58474.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F and G) -> F)) or H)), M:tm-708, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-58475
in-theory        58475
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or ((G and H) -> G)) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-58475.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or ((G and H) -> G)) and E))), M:tm-708, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-58476
in-theory        58476
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or ((G and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-708 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-58476.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or ((G and H) -> G)))), M:tm-708, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-58477
in-theory        58477
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or ((H and I) -> I))))
theorem-size     39
proof            (modus-ponens tm-708 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-58477.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or ((H and I) -> I)))), M:tm-708, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-58478
in-theory        58478
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I))))
theorem-size     41
proof            (modus-ponens tm-708 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-58478.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G or ((H and I) -> I)))), M:tm-708, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-58479
in-theory        58479
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or ((H and I) -> I))))
theorem-size     39
proof            (modus-ponens tm-708 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-58479.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or ((H and I) -> I)))), M:tm-708, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-58480
in-theory        58480
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or ((H and I) -> I))))
theorem-size     39
proof            (modus-ponens tm-708 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-7 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-58480.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or ((H and I) -> I)))), M:tm-708, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-58481
in-theory        58481
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> J))))
theorem-size     47
proof            (modus-ponens tm-708 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-58481.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or ((I and J) -> J)))), M:tm-708, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-58482
in-theory        58482
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or ((H and I) -> I))))
theorem-size     39
proof            (modus-ponens tm-708 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-58482.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or ((H and I) -> I)))), M:tm-708, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-58483
in-theory        58483
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or ((G and H) -> H))))
theorem-size     35
proof            (modus-ponens tm-708 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-58483.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or ((G and H) -> H)))), M:tm-708, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-58484
in-theory        58484
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F and G) -> G)) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-58484.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F and G) -> G)) or H)), M:tm-708, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-58485
in-theory        58485
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or ((G and H) -> H)) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-58485.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or ((G and H) -> H)) and E))), M:tm-708, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-58486
in-theory        58486
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or ((G and H) -> H))))
theorem-size     35
proof            (modus-ponens tm-708 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-58486.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or ((G and H) -> H)))), M:tm-708, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-58487
in-theory        58487
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or (H -> (I -> (H and I))))))
theorem-size     41
proof            (modus-ponens tm-708 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58487.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or (H -> (I -> (H and I)))))), M:tm-708, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-58488
in-theory        58488
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I))))))
theorem-size     43
proof            (modus-ponens tm-708 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58488.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G or (H -> (I -> (H and I)))))), M:tm-708, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-58489
in-theory        58489
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or (H -> (I -> (H and I))))))
theorem-size     41
proof            (modus-ponens tm-708 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58489.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or (H -> (I -> (H and I)))))), M:tm-708, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-58490
in-theory        58490
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or (H -> (I -> (H and I))))))
theorem-size     41
proof            (modus-ponens tm-708 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58490.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or (H -> (I -> (H and I)))))), M:tm-708, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-58491
in-theory        58491
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> (I and J))))))
theorem-size     49
proof            (modus-ponens tm-708 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58491.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J -> (I and J)))))), M:tm-708, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-58492
in-theory        58492
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I))))))
theorem-size     41
proof            (modus-ponens tm-708 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58492.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or (H -> (I -> (H and I)))))), M:tm-708, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-58493
in-theory        58493
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or (G -> (H -> (G and H))))))
theorem-size     37
proof            (modus-ponens tm-708 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58493.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or (G -> (H -> (G and H)))))), M:tm-708, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-58494
in-theory        58494
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (G -> (F and G)))) or H))
theorem-size     37
proof            (modus-ponens tm-708 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58494.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (G -> (F and G)))) or H)), M:tm-708, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-58495
in-theory        58495
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or (G -> (H -> (G and H)))) and E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58495.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or (G -> (H -> (G and H)))) and E))), M:tm-708, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-58496
in-theory        58496
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or (G -> (H -> (G and H))))))
theorem-size     37
proof            (modus-ponens tm-708 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58496.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or (G -> (H -> (G and H)))))), M:tm-708, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-58497
in-theory        58497
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or (H -> (H or I)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-58497.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or (H -> (H or I))))), M:tm-708, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-58498
in-theory        58498
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G or (H -> (H or I)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-58498.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G or (H -> (H or I))))), M:tm-708, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-58499
in-theory        58499
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or (H -> (H or I)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-7 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-58499.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or (H -> (H or I))))), M:tm-708, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-58500
in-theory        58500
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or (H -> (H or I)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-7 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-58500.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or (H -> (H or I))))), M:tm-708, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-58501
in-theory        58501
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (I or J)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-58501.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (I or J))))), M:tm-708, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-58502
in-theory        58502
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or (H -> (H or I)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-58502.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or (H -> (H or I))))), M:tm-708, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-58503
in-theory        58503
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or (G -> (G or H)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-58503.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or (G -> (G or H))))), M:tm-708, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-58504
in-theory        58504
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (F or G))) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-58504.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (F or G))) or H)), M:tm-708, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-58505
in-theory        58505
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or (G -> (G or H))) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-58505.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or (G -> (G or H))) and E))), M:tm-708, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-58506
in-theory        58506
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or (G -> (G or H)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-58506.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or (G -> (G or H))))), M:tm-708, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-58507
in-theory        58507
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or (H -> (I or H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-58507.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G or (H -> (I or H))))), M:tm-708, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-58508
in-theory        58508
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G or (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-58508.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G or (H -> (I or H))))), M:tm-708, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-58509
in-theory        58509
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or (H -> (I or H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-58509.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G or (H -> (I or H))))), M:tm-708, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-58510
in-theory        58510
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or (H -> (I or H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-58510.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G or (H -> (I or H))))), M:tm-708, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-58511
in-theory        58511
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J or I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-58511.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H or (I -> (J or I))))), M:tm-708, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-58512
in-theory        58512
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or (H -> (I or H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-58512.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G or (H -> (I or H))))), M:tm-708, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-58513
in-theory        58513
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or (G -> (H or G)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-58513.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F or (G -> (H or G))))), M:tm-708, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-58514
in-theory        58514
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (G or F))) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-58514.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> (G or F))) or H)), M:tm-708, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-58515
in-theory        58515
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or (G -> (H or G))) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-58515.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F or (G -> (H or G))) and E))), M:tm-708, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-58516
in-theory        58516
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or (G -> (H or G)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-58516.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F or (G -> (H or G))))), M:tm-708, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-58517
in-theory        58517
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> (H or G)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-58517.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> (H or G)) or I))), M:tm-708, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-58518
in-theory        58518
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I)))
theorem-size     41
proof            (modus-ponens tm-708 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-58518.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> (H or G)) or I))), M:tm-708, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-58519
in-theory        58519
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> (H or G)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-6 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-58519.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> (H or G)) or I))), M:tm-708, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-58520
in-theory        58520
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> (H or G)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-6 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-58520.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> (H or G)) or I))), M:tm-708, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-58521
in-theory        58521
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I or H)) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-58521.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> (I or H)) or J))), M:tm-708, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-58522
in-theory        58522
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> (H or G)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-58522.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> (H or G)) or I))), M:tm-708, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-58523
in-theory        58523
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> (G or F)) or H)))
theorem-size     35
proof            (modus-ponens tm-708 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-58523.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> (G or F)) or H))), M:tm-708, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-58524
in-theory        58524
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F or E)) or G) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-58524.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F or E)) or G) or H)), M:tm-708, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-58525
in-theory        58525
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (G or F)) or H) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-58525.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> (G or F)) or H) and E))), M:tm-708, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-58526
in-theory        58526
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G or F)) or H)))
theorem-size     35
proof            (modus-ponens tm-708 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-58526.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G or F)) or H))), M:tm-708, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-58527
in-theory        58527
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (H -> G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-58527.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (H -> G)))), M:tm-708, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-58528
in-theory        58528
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-58528.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-708, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-58529
in-theory        58529
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G and H) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-58529.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G and H) -> G))), M:tm-708, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-58530
in-theory        58530
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G and H) -> H)))
theorem-size     37
proof            (modus-ponens tm-708 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-58530.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G and H) -> H))), M:tm-708, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-58531
in-theory        58531
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (H -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-58531.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (H -> (G and H))))), M:tm-708, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-58532
in-theory        58532
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (G or H))))
theorem-size     37
proof            (modus-ponens tm-708 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-58532.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (G or H)))), M:tm-708, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-58533
in-theory        58533
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (H or G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-58533.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (H or G)))), M:tm-708, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-58534
in-theory        58534
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-58534.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-708, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-58535
in-theory        58535
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     43
proof            (modus-ponens tm-708 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-9)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-58535.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-708, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-58536
in-theory        58536
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((not (not G)) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-10)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-58536.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((not (not G)) -> G))), M:tm-708, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-58537
in-theory        58537
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (H -> (I -> H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-58537.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (H -> (I -> H))))), M:tm-708, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-58538
in-theory        58538
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> H) -> (G -> G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-58538.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> H) -> (G -> G)))), M:tm-708, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-58539
in-theory        58539
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     51
proof            (modus-ponens tm-708 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-58539.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-708, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-58540
in-theory        58540
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58540.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-708, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-58541
in-theory        58541
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     47
proof            (modus-ponens tm-708 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-58541.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-708, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-58542
in-theory        58542
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> ((H and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-708 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-58542.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> ((H and I) -> H)))), M:tm-708, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-58543
in-theory        58543
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     47
proof            (modus-ponens tm-708 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-58543.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-708, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-58544
in-theory        58544
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> ((H and I) -> I))))
theorem-size     39
proof            (modus-ponens tm-708 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-58544.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> ((H and I) -> I)))), M:tm-708, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-58545
in-theory        58545
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-58545.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (I -> H)) and G)))), M:tm-708, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-58546
in-theory        58546
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     49
proof            (modus-ponens tm-708 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-58546.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-708, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-58547
in-theory        58547
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-58547.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (((H and I) -> H) and G)))), M:tm-708, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-58548
in-theory        58548
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-58548.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (((H and I) -> I) and G)))), M:tm-708, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-58549
in-theory        58549
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     43
proof            (modus-ponens tm-708 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-58549.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-708, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-58550
in-theory        58550
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-58550.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> H) -> (G -> (G and H))))), M:tm-708, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-58551
in-theory        58551
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I))))))
theorem-size     41
proof            (modus-ponens tm-708 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58551.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (H -> (I -> (H and I)))))), M:tm-708, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-58552
in-theory        58552
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> (H -> G)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-58552.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> (H -> G)) or I))), M:tm-708, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-58553
in-theory        58553
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     47
proof            (modus-ponens tm-708 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58553.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-708, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-58554
in-theory        58554
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (((G and H) -> G) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-58554.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (((G and H) -> G) or I))), M:tm-708, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-58555
in-theory        58555
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (((G and H) -> H) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-58555.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (((G and H) -> H) or I))), M:tm-708, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-58556
in-theory        58556
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I)))
theorem-size     41
proof            (modus-ponens tm-708 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-58556.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> (H -> (G and H))) or I))), M:tm-708, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-58557
in-theory        58557
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> (G or H)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-58557.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> (G or H)) or I))), M:tm-708, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-58558
in-theory        58558
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-58558.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (H or I)) and G)))), M:tm-708, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-58559
in-theory        58559
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (H -> (H or I)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-58559.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (H -> (H or I))))), M:tm-708, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-58560
in-theory        58560
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or (H -> (I -> H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-58560.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or (H -> (I -> H))))), M:tm-708, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-58561
in-theory        58561
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     47
proof            (modus-ponens tm-708 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-58561.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-708, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-58562
in-theory        58562
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or ((H and I) -> H))))
theorem-size     39
proof            (modus-ponens tm-708 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-58562.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or ((H and I) -> H)))), M:tm-708, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-58563
in-theory        58563
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or ((H and I) -> I))))
theorem-size     39
proof            (modus-ponens tm-708 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-58563.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or ((H and I) -> I)))), M:tm-708, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-58564
in-theory        58564
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or (H -> (I -> (H and I))))))
theorem-size     41
proof            (modus-ponens tm-708 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58564.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or (H -> (I -> (H and I)))))), M:tm-708, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-58565
in-theory        58565
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or (H -> (H or I)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-58565.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or (H -> (H or I))))), M:tm-708, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-58566
in-theory        58566
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or (H -> (I or H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-58566.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G or (H -> (I or H))))), M:tm-708, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-58567
in-theory        58567
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> (H or G)) or I)))
theorem-size     39
proof            (modus-ponens tm-708 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-6)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-58567.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> (H or G)) or I))), M:tm-708, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-58568
in-theory        58568
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-58568.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> ((H -> (I or H)) and G)))), M:tm-708, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-58569
in-theory        58569
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-58569.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> ((H -> (I or H)) and G)))), M:tm-708, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-58570
in-theory        58570
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and ((F -> (G or F)) and E))))
theorem-size     37
proof            (modus-ponens tm-708 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-58570.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and ((F -> (G or F)) and E)))), M:tm-708, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-58571
in-theory        58571
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     43
proof            (modus-ponens tm-708 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-58571.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> ((H -> (I or H)) and G)))), M:tm-708, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-58572
in-theory        58572
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-58572.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> ((H -> (I or H)) and G)))), M:tm-708, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-58573
in-theory        58573
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-58573.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> ((H -> (I or H)) and G)))), M:tm-708, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-58574
in-theory        58574
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J or I)) and H))))
theorem-size     49
proof            (modus-ponens tm-708 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-58574.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> ((I -> (J or I)) and H)))), M:tm-708, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-58575
in-theory        58575
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-58575.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> ((H -> (I or H)) and G)))), M:tm-708, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-58576
in-theory        58576
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not ((F -> (G or F)) and E))) -> (not E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-7)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-58576.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not ((F -> (G or F)) and E))) -> (not E))), M:tm-708, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-58577
in-theory        58577
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F or E)) and G) -> H) -> ((G or ((E -> (F or E)) and G)) -> H)))
theorem-size     47
proof            (modus-ponens tm-708 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-58577.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F or E)) and G) -> H) -> ((G or ((E -> (F or E)) and G)) -> H))), M:tm-708, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-58578
in-theory        58578
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> ((G -> (H or G)) and F))))
theorem-size     37
proof            (modus-ponens tm-708 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-58578.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> ((G -> (H or G)) and F)))), M:tm-708, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-58579
in-theory        58579
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F -> (G or F)) and E)) or H))
theorem-size     37
proof            (modus-ponens tm-708 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-58579.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F -> (G or F)) and E)) or H)), M:tm-708, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-58580
in-theory        58580
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> ((G -> (H or G)) and F)) and E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-58580.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> ((G -> (H or G)) and F)) and E))), M:tm-708, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-58581
in-theory        58581
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> ((G -> (H or G)) and F))))
theorem-size     37
proof            (modus-ponens tm-708 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-58581.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> ((G -> (H or G)) and F)))), M:tm-708, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-58582
in-theory        58582
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (H -> (I or H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-58582.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (G -> (H -> (I or H))))), M:tm-708, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-58583
in-theory        58583
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (H -> (I or H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-58583.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (G -> (H -> (I or H))))), M:tm-708, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-58584
in-theory        58584
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (F -> (G or F)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-58584.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (E and (F -> (G or F))))), M:tm-708, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-58585
in-theory        58585
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H)))))
theorem-size     41
proof            (modus-ponens tm-708 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-58585.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (G -> (H -> (I or H))))), M:tm-708, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-58586
in-theory        58586
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (H -> (I or H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-58586.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (G -> (H -> (I or H))))), M:tm-708, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-58587
in-theory        58587
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (H -> (I or H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-58587.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (G -> (H -> (I or H))))), M:tm-708, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-58588
in-theory        58588
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J or I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-58588.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (H -> (I -> (J or I))))), M:tm-708, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-58589
in-theory        58589
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (I or H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-58589.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (G -> (H -> (I or H))))), M:tm-708, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-58590
in-theory        58590
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and ((F -> (G or F)) -> H)) -> H))
theorem-size     37
proof            (modus-ponens tm-708 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-58590.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E and ((F -> (G or F)) -> H)) -> H)), M:tm-708, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-58591
in-theory        58591
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F or E)) -> G) and H) -> G))
theorem-size     37
proof            (modus-ponens tm-708 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1 tm-7)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-58591.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F or E)) -> G) and H) -> G)), M:tm-708, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-58592
in-theory        58592
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F or E) -> G)) -> (E -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-58592.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> ((F or E) -> G)) -> (E -> G))), M:tm-708, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-58593
in-theory        58593
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (F -> (G or F)))) -> (not E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-1 tm-7)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-58593.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (not (F -> (G or F)))) -> (not E))), M:tm-708, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-58594
in-theory        58594
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G)))
theorem-size     43
proof            (modus-ponens tm-708 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-58594.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F or E)) -> G) -> ((H or (E -> (F or E))) -> G))), M:tm-708, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-58595
in-theory        58595
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (G -> (H or G)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-58595.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (F -> (G -> (H or G))))), M:tm-708, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-58596
in-theory        58596
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (G or F))) or H))
theorem-size     35
proof            (modus-ponens tm-708 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-58596.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (G or F))) or H)), M:tm-708, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-58597
in-theory        58597
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> (H or G))) and E)))
theorem-size     37
proof            (modus-ponens tm-708 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-58597.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> (G -> (H or G))) and E))), M:tm-708, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-58598
in-theory        58598
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (E -> (G or F))))
theorem-size     35
proof            (modus-ponens tm-708 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-58598.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> (E -> (G or F)))), M:tm-708, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-58599
in-theory        58599
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (G -> (H or G)))))
theorem-size     35
proof            (modus-ponens tm-708 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-58599.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (F -> (G -> (H or G))))), M:tm-708, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-58600
in-theory        58600
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (G -> (F -> E))))
theorem-size     37
proof            (modus-ponens tm-708 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-58600.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (G -> (F -> E)))), M:tm-708, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-58601
in-theory        58601
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F))))
theorem-size     43
proof            (modus-ponens tm-708 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-58601.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or (G -> (E -> F))) -> ((G -> E) -> (G -> F)))), M:tm-708, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-58602
in-theory        58602
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (G -> ((F -> E) and G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-58602.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (G -> ((F -> E) and G)))), M:tm-708, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-58603
in-theory        58603
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((F -> E) or G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-58603.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((F -> E) or G))), M:tm-708, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-58604
in-theory        58604
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (G or (F -> E))))
theorem-size     37
proof            (modus-ponens tm-708 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-58604.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (G or (F -> E)))), M:tm-708, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-58605
in-theory        58605
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-58605.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((E -> G) -> ((F or E) -> G)))), M:tm-708, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-58606
in-theory        58606
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F))))
theorem-size     39
proof            (modus-ponens tm-708 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-9)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-58606.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((F -> (not E)) -> (not F)))), M:tm-708, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-58607
in-theory        58607
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (G -> (H -> G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-58607.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (G -> (H -> G)))), M:tm-708, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-58608
in-theory        58608
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (F -> F)))
theorem-size     35
proof            (modus-ponens tm-708 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-58608.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (F -> F))), M:tm-708, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-58609
in-theory        58609
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     49
proof            (modus-ponens tm-708 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-58609.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-708, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-58610
in-theory        58610
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-58610.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-708, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-58611
in-theory        58611
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     43
proof            (modus-ponens tm-708 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-58611.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-708, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-58612
in-theory        58612
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((G and H) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-58612.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((G and H) -> G))), M:tm-708, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-58613
in-theory        58613
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G)))
theorem-size     43
proof            (modus-ponens tm-708 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-58613.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F and (E -> G)) -> E)) -> ((F and (E -> G)) -> G))), M:tm-708, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-58614
in-theory        58614
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((G and H) -> H)))
theorem-size     37
proof            (modus-ponens tm-708 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-58614.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((G and H) -> H))), M:tm-708, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-58615
in-theory        58615
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E))))
theorem-size     41
proof            (modus-ponens tm-708 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-58615.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((G -> (H -> G)) and (F -> E)))), M:tm-708, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-58616
in-theory        58616
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E))))
theorem-size     49
proof            (modus-ponens tm-708 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-58616.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (F -> E)))), M:tm-708, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-58617
in-theory        58617
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E))))
theorem-size     41
proof            (modus-ponens tm-708 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-58617.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (((G and H) -> G) and (F -> E)))), M:tm-708, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-58618
in-theory        58618
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E))))
theorem-size     41
proof            (modus-ponens tm-708 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-58618.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (((G and H) -> H) and (F -> E)))), M:tm-708, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-58619
in-theory        58619
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E))))
theorem-size     43
proof            (modus-ponens tm-708 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-58619.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((G -> (H -> (G and H))) and (F -> E)))), M:tm-708, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-58620
in-theory        58620
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (F -> (F and E))))
theorem-size     37
proof            (modus-ponens tm-708 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-58620.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (F -> (F and E)))), M:tm-708, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-58621
in-theory        58621
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (G -> (H -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-58621.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (G -> (H -> (G and H))))), M:tm-708, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-58622
in-theory        58622
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E))))
theorem-size     41
proof            (modus-ponens tm-708 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-58622.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((G -> (G or H)) and (F -> E)))), M:tm-708, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-58623
in-theory        58623
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (G -> (G or H))))
theorem-size     37
proof            (modus-ponens tm-708 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-58623.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (G -> (G or H)))), M:tm-708, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-58624
in-theory        58624
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E))))
theorem-size     41
proof            (modus-ponens tm-708 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-58624.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> ((G -> (H or G)) and (F -> E)))), M:tm-708, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-58625
in-theory        58625
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (G -> (H or G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-58625.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (G -> (H or G)))), M:tm-708, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-58626
in-theory        58626
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E)))
theorem-size     41
proof            (modus-ponens tm-708 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-58626.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or ((F -> G) -> E)) -> ((G or (F -> G)) -> E))), M:tm-708, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-58627
in-theory        58627
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-58627.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-708, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-58628
in-theory        58628
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-58628.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-708, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-58629
in-theory        58629
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G))))
theorem-size     45
proof            (modus-ponens tm-708 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-58629.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> G) -> (((E -> F) -> G) and ((F or (E -> F)) -> G)))), M:tm-708, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-58630
in-theory        58630
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     47
proof            (modus-ponens tm-708 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-58630.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-708, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-58631
in-theory        58631
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-58631.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-708, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-58632
in-theory        58632
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-58632.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-708, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-58633
in-theory        58633
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J))))
theorem-size     53
proof            (modus-ponens tm-708 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-58633.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((H -> I) -> J) -> ((I or (H -> I)) -> J)))), M:tm-708, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-58634
in-theory        58634
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-58634.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-708, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-58635
in-theory        58635
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> G) -> ((E -> F) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-58635.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> G) -> ((E -> F) -> G))), M:tm-708, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-58636
in-theory        58636
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G))))
theorem-size     47
proof            (modus-ponens tm-708 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-1)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-58636.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> G) -> (not ((F or (E -> F)) -> G))) -> (not ((E -> F) -> G)))), M:tm-708, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-58637
in-theory        58637
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E or (F -> E)) -> G) -> H) -> ((((F -> E) -> G) or ((E or (F -> E)) -> G)) -> H)))
theorem-size     51
proof            (modus-ponens tm-708 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-58637.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E or (F -> E)) -> G) -> H) -> ((((F -> E) -> G) or ((E or (F -> E)) -> G)) -> H))), M:tm-708, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-58638
in-theory        58638
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     41
proof            (modus-ponens tm-708 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-1)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-58638.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-708, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-58639
in-theory        58639
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H))
theorem-size     41
proof            (modus-ponens tm-708 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-1)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-58639.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) or H)), M:tm-708, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-58640
in-theory        58640
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E)))
theorem-size     43
proof            (modus-ponens tm-708 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-58640.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> G) -> H) -> ((G or (F -> G)) -> H)) and E))), M:tm-708, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-58641
in-theory        58641
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G)))
theorem-size     45
proof            (modus-ponens tm-708 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-58641.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> G) -> (F or (E -> F))) -> (((E -> F) -> G) -> G))), M:tm-708, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-58642
in-theory        58642
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     41
proof            (modus-ponens tm-708 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-58642.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-708, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-58643
in-theory        58643
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G)))))
theorem-size     49
proof            (modus-ponens tm-708 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-58643.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> ((E -> F) -> (E -> G))))), M:tm-708, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-58644
in-theory        58644
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G))))
theorem-size     51
proof            (modus-ponens tm-708 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       227
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-58644.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> E) -> ((E -> F) -> G)))), M:tm-708, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-58645
in-theory        58645
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H))))
theorem-size     51
proof            (modus-ponens tm-708 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       221
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-58645.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (((E -> F) -> (E -> G)) and H)))), M:tm-708, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-58646
in-theory        58646
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H)))
theorem-size     49
proof            (modus-ponens tm-708 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-58646.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (E -> G)) or H))), M:tm-708, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-58647
in-theory        58647
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G)))))
theorem-size     49
proof            (modus-ponens tm-708 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-58647.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H or ((E -> F) -> (E -> G))))), M:tm-708, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-58648
in-theory        58648
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> G) -> H) -> (((E -> F) or (E -> G)) -> H))))
theorem-size     55
proof            (modus-ponens tm-708 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       235
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-58648.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> G) -> H) -> (((E -> F) or (E -> G)) -> H)))), M:tm-708, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-58649
in-theory        58649
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (not (E -> G))) -> (not (E -> F)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       229
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-58649.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((E -> F) -> (not (E -> G))) -> (not (E -> F))))), M:tm-708, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-58650
in-theory        58650
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H))))
theorem-size     45
proof            (modus-ponens tm-708 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-58650.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> H)))), M:tm-708, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-58651
in-theory        58651
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F))))
theorem-size     47
proof            (modus-ponens tm-708 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-58651.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> (E -> F)))), M:tm-708, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-58652
in-theory        58652
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> ((F -> G) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     53
proof            (modus-ponens tm-708 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-58652.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> ((F -> G) -> F)) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-708, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-58653
in-theory        58653
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       251
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-58653.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))), M:tm-708, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-58654
in-theory        58654
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H)))
theorem-size     45
proof            (modus-ponens tm-708 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-58654.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> H))), M:tm-708, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-58655
in-theory        58655
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I)))
theorem-size     45
proof            (modus-ponens tm-708 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-4)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-58655.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H and I) -> I))), M:tm-708, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-58656
in-theory        58656
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> H)) and ((E -> F) -> (E -> G)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-58656.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> H)) and ((E -> F) -> (E -> G))))), M:tm-708, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-58657
in-theory        58657
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((E -> F) -> (E -> G)))))
theorem-size     61
proof            (modus-ponens tm-708 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       271
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-58657.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and ((E -> F) -> (E -> G))))), M:tm-708, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-58658
in-theory        58658
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> H) and ((E -> F) -> (E -> G)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-58658.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> H) and ((E -> F) -> (E -> G))))), M:tm-708, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-58659
in-theory        58659
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> I) and ((E -> F) -> (E -> G)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-58659.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (((H and I) -> I) and ((E -> F) -> (E -> G))))), M:tm-708, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-58660
in-theory        58660
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> (H and I))) and ((E -> F) -> (E -> G)))))
theorem-size     55
proof            (modus-ponens tm-708 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-58660.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I -> (H and I))) and ((E -> F) -> (E -> G))))), M:tm-708, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-58661
in-theory        58661
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G)))))
theorem-size     51
proof            (modus-ponens tm-708 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       243
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-58661.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> ((E -> F) and (E -> G))))), M:tm-708, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-58662
in-theory        58662
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I)))))
theorem-size     47
proof            (modus-ponens tm-708 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-58662.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I -> (H and I))))), M:tm-708, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-58663
in-theory        58663
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (H or I)) and ((E -> F) -> (E -> G)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-58663.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (H or I)) and ((E -> F) -> (E -> G))))), M:tm-708, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-58664
in-theory        58664
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I))))
theorem-size     45
proof            (modus-ponens tm-708 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-6)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-58664.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (H or I)))), M:tm-708, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-58665
in-theory        58665
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I or H)) and ((E -> F) -> (E -> G)))))
theorem-size     53
proof            (modus-ponens tm-708 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-58665.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((H -> (I or H)) and ((E -> F) -> (E -> G))))), M:tm-708, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-58666
in-theory        58666
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H))))
theorem-size     45
proof            (modus-ponens tm-708 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-7)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-58666.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> (H -> (I or H)))), M:tm-708, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-58667
in-theory        58667
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G))))
theorem-size     49
proof            (modus-ponens tm-708 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-58667.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((F or (E -> F)) -> (E -> G)))), M:tm-708, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-58668
in-theory        58668
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> ((E -> G) -> H)) or (((E -> F) -> (E -> G)) -> ((E -> F) -> H))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> H))))
theorem-size     69
proof            (modus-ponens tm-708 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       301
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-58668.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> ((E -> G) -> H)) or (((E -> F) -> (E -> G)) -> ((E -> F) -> H))) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((E -> F) -> H)))), M:tm-708, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-58669
in-theory        58669
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (((F -> G) -> (F -> H)) -> E)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> E)))
theorem-size     53
proof            (modus-ponens tm-708 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58669.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (((F -> G) -> (F -> H)) -> E)) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> E))), M:tm-708, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-58670
in-theory        58670
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     57
proof            (modus-ponens tm-708 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58670.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-708, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-58671
in-theory        58671
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     57
proof            (modus-ponens tm-708 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58671.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-708, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-58672
in-theory        58672
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> (E -> G)) -> H) -> ((((E -> F) -> (E -> G)) -> H) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     61
proof            (modus-ponens tm-708 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58672.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> (E -> G)) -> H) -> ((((E -> F) -> (E -> G)) -> H) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-708, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-58673
in-theory        58673
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     59
proof            (modus-ponens tm-708 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58673.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-708, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-58674
in-theory        58674
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     57
proof            (modus-ponens tm-708 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58674.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-708, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-58675
in-theory        58675
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     57
proof            (modus-ponens tm-708 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58675.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-708, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-58676
in-theory        58676
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K))))
theorem-size     65
proof            (modus-ponens tm-708 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       279
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58676.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((H -> I) -> (H -> J)) -> K) -> (((H -> (I -> J)) or ((H -> I) -> (H -> J))) -> K)))), M:tm-708, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-58677
in-theory        58677
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     57
proof            (modus-ponens tm-708 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58677.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-708, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-58678
in-theory        58678
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H)))
theorem-size     45
proof            (modus-ponens tm-708 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58678.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) -> (E -> G)) -> H) -> (((E -> F) -> (E -> G)) -> H))), M:tm-708, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-58679
in-theory        58679
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) -> (E -> G)) -> H) -> (not (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))) -> (not (((E -> F) -> (E -> G)) -> H))))
theorem-size     63
proof            (modus-ponens tm-708 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9)
proof-size       249
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58679.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) -> (E -> G)) -> H) -> (not (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))) -> (not (((E -> F) -> (E -> G)) -> H)))), M:tm-708, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-58680
in-theory        58680
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H) -> I) -> (((((E -> F) -> (E -> G)) -> H) or (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) -> I)))
theorem-size     71
proof            (modus-ponens tm-708 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       267
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58680.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H) -> I) -> (((((E -> F) -> (E -> G)) -> H) or (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) -> I))), M:tm-708, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-58681
in-theory        58681
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     53
proof            (modus-ponens tm-708 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7)
proof-size       223
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58681.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-708, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58682
in-theory        58682
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) or I))
theorem-size     53
proof            (modus-ponens tm-708 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-8 tm-2 tm-6)
proof-size       223
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58682.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) or I)), M:tm-708, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-58683
in-theory        58683
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)) and E)))
theorem-size     55
proof            (modus-ponens tm-708 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       229
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58683.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)) and E))), M:tm-708, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58684
in-theory        58684
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     67
proof            (modus-ponens tm-705 tm-708 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       263
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58684.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-708, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-58685
in-theory        58685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> B) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-703 tm-708 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58685.        (((A -> B) -> (A -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-708, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-58686
in-theory        58686
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> B) -> (A -> C)))))
theorem-size     89
proof            (modus-ponens tm-697 tm-708 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       291
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58686.        ((((A -> B) -> (A -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-708, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-58687
in-theory        58687
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     43
proof            (modus-ponens tm-665 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58687.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-665, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58688
in-theory        58688
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B or (A -> B)) -> C)))
theorem-size     47
proof            (modus-ponens tm-662 tm-708 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58688.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-708, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-58689
in-theory        58689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> B)))
theorem-size     33
proof            (modus-ponens tm-660 tm-708 ((Am (-> A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58689.        ((A -> B) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> B))), M:tm-660, m:tm-708, u:((Am (-> A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A B))))
================================================================
tm-name          tm-58690
in-theory        58690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> B))) and ((B or (A -> B)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> B))))
theorem-size     69
proof            (modus-ponens tm-654 tm-708 ((Am (-> A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58690.        (((A -> B) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> B))) and ((B or (A -> B)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> B)))), M:tm-654, m:tm-708, u:((Am (-> A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A B))))
================================================================
tm-name          tm-58691
in-theory        58691
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and A)))
theorem-size     31
proof            (modus-ponens tm-623 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-8)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58691.        (A -> (B or (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and A))), M:tm-623, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-58692
in-theory        58692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-622 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58692.        ((A -> (B -> (C or B))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-622, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58693
in-theory        58693
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (B -> (C or B))))
theorem-size     39
proof            (modus-ponens tm-619 tm-708 ((Am (-> A (or B A))) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58693.        ((A or (B -> (C or B))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (B -> (C or B)))), M:tm-619, m:tm-708, u:((Am (-> A (or B A))) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A (or B A)))))
================================================================
tm-name          tm-58694
in-theory        58694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (F -> (G or F)))
theorem-size     35
proof            (modus-ponens tm-609 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58694.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (F -> (G or F))), M:tm-609, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58695
in-theory        58695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-605 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58695.        ((A -> ((B -> (C or B)) and A)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-605, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58696
in-theory        58696
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B -> (C or B)) and A)))
theorem-size     43
proof            (modus-ponens tm-602 tm-708 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58696.        ((A or ((B -> (C or B)) and A)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-708, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-58697
in-theory        58697
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((F -> (G or F)) and (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))))
theorem-size     65
proof            (modus-ponens tm-595 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58697.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((F -> (G or F)) and (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)))), M:tm-595, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58698
in-theory        58698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-550 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58698.        (((A -> (B or A)) or C) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-550, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58699
in-theory        58699
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-540 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58699.        ((A or (B -> (C or B))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-540, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58700
in-theory        58700
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-530 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58700.        ((A or (B -> (B or C))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-530, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58701
in-theory        58701
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-520 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58701.        ((A or (B -> (C -> (B and C)))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-520, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58702
in-theory        58702
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-510 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58702.        ((A or ((B and C) -> C)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-510, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58703
in-theory        58703
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-500 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58703.        ((A or ((B and C) -> B)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-500, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58704
in-theory        58704
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)) and E)))
theorem-size     45
proof            (modus-ponens tm-490 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58704.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)) and E))), M:tm-490, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58705
in-theory        58705
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-480 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58705.        ((A or (B -> (C -> B))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-480, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58706
in-theory        58706
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A) or F))
theorem-size     31
proof            (modus-ponens tm-470 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-8)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58706.        (A -> ((((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A) or F)), M:tm-470, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-58707
in-theory        58707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-469 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58707.        ((A -> (B -> (B or C))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-469, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58708
in-theory        58708
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (B -> (B or C))))
theorem-size     39
proof            (modus-ponens tm-466 tm-708 ((Am (-> A (or A B))) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58708.        ((A or (B -> (B or C))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (B -> (B or C)))), M:tm-466, m:tm-708, u:((Am (-> A (or A B))) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A (or A B)))))
================================================================
tm-name          tm-58709
in-theory        58709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (F -> (F or G)))
theorem-size     35
proof            (modus-ponens tm-456 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58709.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (F -> (F or G))), M:tm-456, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58710
in-theory        58710
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-453 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58710.        ((A -> ((B -> (B or C)) and A)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-453, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58711
in-theory        58711
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B -> (B or C)) and A)))
theorem-size     43
proof            (modus-ponens tm-450 tm-708 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58711.        ((A or ((B -> (B or C)) and A)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-708, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-58712
in-theory        58712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((F -> (F or G)) and (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))))
theorem-size     65
proof            (modus-ponens tm-443 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58712.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((F -> (F or G)) and (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)))), M:tm-443, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58713
in-theory        58713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-409 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58713.        (((A -> (A or B)) or C) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-409, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58714
in-theory        58714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-400 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58714.        (((A -> (B -> (A and B))) or C) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-400, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58715
in-theory        58715
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-391 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58715.        ((((A and B) -> B) or C) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-391, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58716
in-theory        58716
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-382 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58716.        ((((A and B) -> A) or C) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-382, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58717
in-theory        58717
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)) and E)))
theorem-size     45
proof            (modus-ponens tm-373 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58717.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)) and E))), M:tm-373, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58718
in-theory        58718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-364 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58718.        (((A -> (B -> A)) or C) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-364, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58719
in-theory        58719
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and A) and B)))
theorem-size     33
proof            (modus-ponens tm-355 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58719.        (A -> (B -> ((((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and A) and B))), M:tm-355, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-58720
in-theory        58720
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-354 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58720.        ((A -> (B -> (C -> (B and C)))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-354, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58721
in-theory        58721
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (B -> (C -> (B and C)))))
theorem-size     43
proof            (modus-ponens tm-351 tm-708 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58721.        ((A or (B -> (C -> (B and C)))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-708, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-58722
in-theory        58722
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (F -> (G -> (F and G))))
theorem-size     37
proof            (modus-ponens tm-341 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58722.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58723
in-theory        58723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C)))
theorem-size     39
proof            (modus-ponens tm-338 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58723.        (((A -> B) -> (A -> (A and B))) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C))), M:tm-338, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58724
in-theory        58724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> (A and B))))
theorem-size     41
proof            (modus-ponens tm-335 tm-708 ((Am (-> A (and A B))) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58724.        (((A -> B) or (A -> (A and B))) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> (A and B)))), M:tm-335, m:tm-708, u:((Am (-> A (and A B))) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A (and A B)))))
================================================================
tm-name          tm-58725
in-theory        58725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (A -> (A and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))))
theorem-size     61
proof            (modus-ponens tm-328 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58725.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (A -> (A and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)))), M:tm-328, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-58726
in-theory        58726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((F -> (G -> (F and G))) and (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))))
theorem-size     67
proof            (modus-ponens tm-327 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58726.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((F -> (G -> (F and G))) and (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)))), M:tm-327, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58727
in-theory        58727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (((F and G) -> G) and (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))))
theorem-size     65
proof            (modus-ponens tm-326 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58727.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (((F and G) -> G) and (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)))), M:tm-326, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58728
in-theory        58728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (((F and G) -> F) and (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))))
theorem-size     65
proof            (modus-ponens tm-325 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58728.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (((F and G) -> F) and (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)))), M:tm-325, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58729
in-theory        58729
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))))
theorem-size     73
proof            (modus-ponens tm-324 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       245
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58729.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)))), M:tm-324, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58730
in-theory        58730
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((F -> (G -> F)) and (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))))
theorem-size     65
proof            (modus-ponens tm-323 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58730.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((F -> (G -> F)) and (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)))), M:tm-323, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58731
in-theory        58731
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((F and G) -> G))
theorem-size     35
proof            (modus-ponens tm-322 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58731.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((F and G) -> G)), M:tm-322, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58732
in-theory        58732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((F and G) -> F))
theorem-size     35
proof            (modus-ponens tm-320 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58732.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((F and G) -> F)), M:tm-320, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58733
in-theory        58733
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     43
proof            (modus-ponens tm-318 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58733.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58734
in-theory        58734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (A -> A))
theorem-size     33
proof            (modus-ponens tm-316 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58734.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (A -> A)), M:tm-316, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-58735
in-theory        58735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (F -> (G -> F)))
theorem-size     35
proof            (modus-ponens tm-315 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58735.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (F -> (G -> F))), M:tm-315, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58736
in-theory        58736
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((A -> (not (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))) -> (not A)))
theorem-size     63
proof            (modus-ponens tm-313 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58736.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((A -> (not (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))) -> (not A))), M:tm-313, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-58737
in-theory        58737
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (((((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A) -> F) -> ((A or (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) -> F)))
theorem-size     91
proof            (modus-ponens tm-312 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       237
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58737.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (((((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A) -> F) -> ((A or (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) -> F))), M:tm-312, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-58738
in-theory        58738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (F or (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))))
theorem-size     61
proof            (modus-ponens tm-311 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58738.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (F or (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)))), M:tm-311, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58739
in-theory        58739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) or F))
theorem-size     61
proof            (modus-ponens tm-310 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58739.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) or F)), M:tm-310, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58740
in-theory        58740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (F -> ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and F)))
theorem-size     63
proof            (modus-ponens tm-309 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58740.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (F -> ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and F))), M:tm-309, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58741
in-theory        58741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (F -> (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))))
theorem-size     61
proof            (modus-ponens tm-305 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58741.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (F -> (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)))), M:tm-305, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58742
in-theory        58742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     41
proof            (modus-ponens tm-303 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58742.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-303, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58743
in-theory        58743
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B -> (C -> (B and C))) and A)))
theorem-size     47
proof            (modus-ponens tm-300 tm-708 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58743.        ((A or ((B -> (C -> (B and C))) and A)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-708, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-58744
in-theory        58744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-270 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58744.        ((A -> (((B and C) -> C) and A)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-270, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58745
in-theory        58745
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (((B and C) -> C) and A)))
theorem-size     43
proof            (modus-ponens tm-267 tm-708 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58745.        ((A or (((B and C) -> C) and A)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (((B and C) -> C) and A))), M:tm-267, m:tm-708, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-58746
in-theory        58746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-239 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58746.        ((A -> (((B and C) -> B) and A)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-239, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58747
in-theory        58747
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (((B and C) -> B) and A)))
theorem-size     43
proof            (modus-ponens tm-236 tm-708 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58747.        ((A or (((B and C) -> B) and A)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (((B and C) -> B) and A))), M:tm-236, m:tm-708, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-58748
in-theory        58748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)) and E)))
theorem-size     47
proof            (modus-ponens tm-210 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58748.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)) and E))), M:tm-210, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58749
in-theory        58749
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     59
proof            (modus-ponens tm-207 tm-708 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       233
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58749.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-708, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-58750
in-theory        58750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     39
proof            (modus-ponens tm-183 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58750.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-183, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58751
in-theory        58751
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B -> (C -> B)) and A)))
theorem-size     43
proof            (modus-ponens tm-180 tm-708 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58751.        ((A or ((B -> (C -> B)) and A)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-708, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-58752
in-theory        58752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-157 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58752.        ((A -> ((B and C) -> C)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-157, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58753
in-theory        58753
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B and C) -> C)))
theorem-size     39
proof            (modus-ponens tm-154 tm-708 ((Am (-> (and A B) B)) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58753.        ((A or ((B and C) -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B and C) -> C))), M:tm-154, m:tm-708, u:((Am (-> (and A B) B)) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (and A B) B))))
================================================================
tm-name          tm-58754
in-theory        58754
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     45
proof            (modus-ponens tm-147 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58754.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-147, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58755
in-theory        58755
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A and (B -> C)) -> C)))
theorem-size     49
proof            (modus-ponens tm-144 tm-708 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58755.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-708, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-58756
in-theory        58756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-134 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58756.        ((A -> ((B and C) -> B)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-134, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58757
in-theory        58757
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B and C) -> B)))
theorem-size     39
proof            (modus-ponens tm-131 tm-708 ((Am (-> (and A B) A)) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58757.        ((A or ((B and C) -> B)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B and C) -> B))), M:tm-131, m:tm-708, u:((Am (-> (and A B) A)) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (and A B) A))))
================================================================
tm-name          tm-58758
in-theory        58758
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     45
proof            (modus-ponens tm-125 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58758.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-125, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58759
in-theory        58759
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (((A -> B) and C) -> B)))
theorem-size     49
proof            (modus-ponens tm-122 tm-708 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58759.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-708, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-58760
in-theory        58760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)) and E)))
theorem-size     45
proof            (modus-ponens tm-113 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58760.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)) and E))), M:tm-113, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58761
in-theory        58761
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     55
proof            (modus-ponens tm-110 tm-708 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5)
proof-size       221
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58761.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-708, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-58762
in-theory        58762
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     49
proof            (modus-ponens tm-105 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       211
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58762.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-105, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58763
in-theory        58763
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     55
proof            (modus-ponens tm-102 tm-708 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       233
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58763.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-708, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-58764
in-theory        58764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C)))
theorem-size     37
proof            (modus-ponens tm-95 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58764.        (((A -> B) -> (A -> A)) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C))), M:tm-95, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58765
in-theory        58765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> A)))
theorem-size     37
proof            (modus-ponens tm-92 tm-708 ((Am (-> A A)) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58765.        (((A -> B) or (A -> A)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A -> A))), M:tm-92, m:tm-708, u:((Am (-> A A)) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A A))))
================================================================
tm-name          tm-58766
in-theory        58766
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and A)))
theorem-size     31
proof            (modus-ponens tm-84 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58766.        (A -> (B -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and A))), M:tm-84, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-58767
in-theory        58767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     37
proof            (modus-ponens tm-83 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58767.        ((A -> (B -> (C -> B))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-83, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58768
in-theory        58768
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (B -> (C -> B))))
theorem-size     39
proof            (modus-ponens tm-80 tm-708 ((Am (-> A (-> B A))) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58768.        ((A or (B -> (C -> B))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (B -> (C -> B)))), M:tm-80, m:tm-708, u:((Am (-> A (-> B A))) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A (-> B A)))))
================================================================
tm-name          tm-58769
in-theory        58769
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and B)))
theorem-size     35
proof            (modus-ponens tm-76 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58769.        (((not (not A)) -> A) and (B -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and B))), M:tm-76, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58770
in-theory        58770
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))
theorem-size     33
proof            (modus-ponens tm-73 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58770.        (((not (not A)) or A) -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-73, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-58771
in-theory        58771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C)))
theorem-size     41
proof            (modus-ponens tm-69 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-2)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58771.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C))), M:tm-69, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58772
in-theory        58772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and ((A -> (not B)) -> (not A))))
theorem-size     45
proof            (modus-ponens tm-66 tm-708 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-2)
proof-size       179
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58772.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-708, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-58773
in-theory        58773
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     43
proof            (modus-ponens tm-54 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58773.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-54, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58774
in-theory        58774
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     49
proof            (modus-ponens tm-51 tm-708 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       189
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58774.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-708, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-58775
in-theory        58775
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (B or A)))
theorem-size     35
proof            (modus-ponens tm-50 tm-708 ((Am (or A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-2)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58775.        ((A or (B or A)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (B or A))), M:tm-50, m:tm-708, u:((Am (or A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (or A B))))
================================================================
tm-name          tm-58776
in-theory        58776
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A or B)))
theorem-size     35
proof            (modus-ponens tm-49 tm-708 ((Am (or A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-2)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58776.        ((A or (A or B)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (A or B))), M:tm-49, m:tm-708, u:((Am (or A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (or A B))))
================================================================
tm-name          tm-58777
in-theory        58777
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (B -> (A and B))))
theorem-size     39
proof            (modus-ponens tm-48 tm-708 ((Am (-> A (and B A))) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58777.        ((A or (B -> (A and B))) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (B -> (A and B)))), M:tm-48, m:tm-708, u:((Am (-> A (and B A))) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A (and B A)))))
================================================================
tm-name          tm-58778
in-theory        58778
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and B))
theorem-size     33
proof            (modus-ponens tm-47 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58778.        (((A and B) or B) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and B)), M:tm-47, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-58779
in-theory        58779
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and A))
theorem-size     33
proof            (modus-ponens tm-46 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58779.        (((A and B) or A) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and A)), M:tm-46, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-58780
in-theory        58780
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> B) -> (A -> C))))
theorem-size     47
proof            (modus-ponens tm-45 tm-708 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5)
proof-size       185
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58780.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-708, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-58781
in-theory        58781
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (B -> A)))
theorem-size     35
proof            (modus-ponens tm-44 tm-708 ((Am (-> A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58781.        ((A or (B -> A)) -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and (B -> A))), M:tm-44, m:tm-708, u:((Am (-> A B)) (C (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> A B))))
================================================================
tm-name          tm-58782
in-theory        58782
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C)))
theorem-size     35
proof            (modus-ponens tm-42 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58782.        ((A -> (B or A)) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C))), M:tm-42, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58783
in-theory        58783
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C)))
theorem-size     35
proof            (modus-ponens tm-32 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58783.        ((A -> (A or B)) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C))), M:tm-32, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58784
in-theory        58784
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)))
theorem-size     31
proof            (modus-ponens tm-24 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58784.        (A -> (A and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))), M:tm-24, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-58785
in-theory        58785
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C)))
theorem-size     37
proof            (modus-ponens tm-23 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       149
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58785.        ((A -> (B -> (A and B))) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C))), M:tm-23, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58786
in-theory        58786
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C)))
theorem-size     35
proof            (modus-ponens tm-22 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58786.        (((A and B) -> B) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C))), M:tm-22, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58787
in-theory        58787
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C)))
theorem-size     35
proof            (modus-ponens tm-21 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58787.        (((A and B) -> A) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C))), M:tm-21, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58788
in-theory        58788
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     43
proof            (modus-ponens tm-20 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58788.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-20, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58789
in-theory        58789
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C)))
theorem-size     35
proof            (modus-ponens tm-19 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58789.        ((A -> (B -> A)) and (C -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and C))), M:tm-19, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58790
in-theory        58790
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))) -> (not A))
theorem-size     33
proof            (modus-ponens tm-9 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-9 tm-5 tm-8 tm-2)
proof-size       131
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58790.        ((A -> (not (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))) -> (not A)), M:tm-9, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-58791
in-theory        58791
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and E) -> F) -> ((E or (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and E)) -> F))
theorem-size     61
proof            (modus-ponens tm-8 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-8 tm-5 tm-2)
proof-size       161
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58791.        (((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and E) -> F) -> ((E or (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and E)) -> F)), M:tm-8, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-58792
in-theory        58792
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and B)))
theorem-size     31
proof            (modus-ponens tm-7 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-7 tm-5 tm-8 tm-2)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58792.        (A or (B -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and B))), M:tm-7, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58793
in-theory        58793
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) or F)
theorem-size     31
proof            (modus-ponens tm-6 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-6 tm-5 tm-8 tm-2)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58793.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) or F), M:tm-6, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58794
in-theory        58794
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and B)) and A))
theorem-size     33
proof            (modus-ponens tm-5 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       127
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58794.        (A -> ((B -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and B)) and A)), M:tm-5, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58795
in-theory        58795
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and B)))
theorem-size     31
proof            (modus-ponens tm-1 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-1 tm-5 tm-8 tm-2)
proof-size       123
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58795.        (A -> (B -> (((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)) and B))), M:tm-1, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-58796
in-theory        58796
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> A)) -> C) -> C)
theorem-size     11
proof            (modus-ponens tm-709 tm-365 ((Am (-> (-> (-> Bm Cm) (-> Bm Bm)) D)) (A Bm) (B Cm) (C Bm) (Dm (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-58796.        ((((A -> B) -> (A -> A)) -> C) -> C), M:tm-709, m:tm-365, u:((Am (-> (-> (-> Bm Cm) (-> Bm Bm)) D)) (A Bm) (B Cm) (C Bm) (Dm (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-58797
in-theory        58797
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) -> D)
theorem-size     23
proof            (modus-ponens tm-709 tm-374 ((Am (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) D)) (A (-> Bm (-> Cm Dm))) (B (-> Bm Cm)) (C (-> Bm Dm)) (Em (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-8 tm-1 tm-6)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-58797.        (((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) -> D) -> D), M:tm-709, m:tm-374, u:((Am (-> (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) D)) (A (-> Bm (-> Cm Dm))) (B (-> Bm Cm)) (C (-> Bm Dm)) (Em (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-58798
in-theory        58798
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) -> D)
theorem-size     19
proof            (modus-ponens tm-709 tm-383 ((Am (-> (-> (-> (and (-> B C) Cm) B) (-> (and (-> B C) Cm) C)) D)) (A (and (-> B C) Cm)) (Bm (-> B C)) (Dm (-> (-> (and (-> B C) Cm) B) (-> (and (-> B C) Cm) C)))))
axioms-used      (tm-2 tm-8 tm-1 tm-6 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-58798.        ((((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) -> D) -> D), M:tm-709, m:tm-383, u:((Am (-> (-> (-> (and (-> B C) Cm) B) (-> (and (-> B C) Cm) C)) D)) (A (and (-> B C) Cm)) (Bm (-> B C)) (Dm (-> (-> (and (-> B C) Cm) B) (-> (and (-> B C) Cm) C))))
================================================================
tm-name          tm-58799
in-theory        58799
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) -> D)
theorem-size     19
proof            (modus-ponens tm-709 tm-392 ((Am (-> (-> (-> (and Bm (-> B C)) B) (-> (and Bm (-> B C)) C)) D)) (A (and Bm (-> B C))) (Cm (-> B C)) (Dm (-> (-> (and Bm (-> B C)) B) (-> (and Bm (-> B C)) C)))))
axioms-used      (tm-2 tm-8 tm-1 tm-6 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-58799.        (((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) -> D) -> D), M:tm-709, m:tm-392, u:((Am (-> (-> (-> (and Bm (-> B C)) B) (-> (and Bm (-> B C)) C)) D)) (A (and Bm (-> B C))) (Cm (-> B C)) (Dm (-> (-> (and Bm (-> B C)) B) (-> (and Bm (-> B C)) C))))
================================================================
tm-name          tm-58800
in-theory        58800
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A and B))) -> C) -> C)
theorem-size     13
proof            (modus-ponens tm-709 tm-401 ((Am (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) D)) (A Bm) (B Cm) (C (and Bm Cm)) (Dm (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-8 tm-1 tm-6 tm-5)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-58800.        ((((A -> B) -> (A -> (A and B))) -> C) -> C), M:tm-709, m:tm-401, u:((Am (-> (-> (-> Bm Cm) (-> Bm (and Bm Cm))) D)) (A Bm) (B Cm) (C (and Bm Cm)) (Dm (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-58801
in-theory        58801
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (A -> B))) -> C) -> C)
theorem-size     13
proof            (modus-ponens tm-709 tm-481 ((Am (-> (-> (-> Dm B) (-> Dm (-> Dm B))) D)) (Bm (-> Dm (-> B (-> Dm B)))) (Cm (-> Dm B)) (A Dm) (C (-> Dm B))))
axioms-used      (tm-2 tm-8 tm-1 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-58801.        ((((A -> B) -> (A -> (A -> B))) -> C) -> C), M:tm-709, m:tm-481, u:((Am (-> (-> (-> Dm B) (-> Dm (-> Dm B))) D)) (Bm (-> Dm (-> B (-> Dm B)))) (Cm (-> Dm B)) (A Dm) (C (-> Dm B)))
================================================================
tm-name          tm-58802
in-theory        58802
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> ((A -> B) and A))) -> C) -> C)
theorem-size     15
proof            (modus-ponens tm-709 tm-521 ((Am (-> (-> (-> Dm B) (-> Dm (and (-> Dm B) Dm))) D)) (Bm (-> Dm (-> B (and (-> Dm B) Dm)))) (Cm (-> Dm B)) (A Dm) (C (and (-> Dm B) Dm))))
axioms-used      (tm-2 tm-8 tm-1 tm-7 tm-5)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-58802.        ((((A -> B) -> (A -> ((A -> B) and A))) -> C) -> C), M:tm-709, m:tm-521, u:((Am (-> (-> (-> Dm B) (-> Dm (and (-> Dm B) Dm))) D)) (Bm (-> Dm (-> B (and (-> Dm B) Dm)))) (Cm (-> Dm B)) (A Dm) (C (and (-> Dm B) Dm)))
================================================================
tm-name          tm-58803
in-theory        58803
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) -> (E -> G)) -> H) -> ((E -> (F -> G)) or ((E -> F) -> (E -> G)))) -> ((((E -> F) -> (E -> G)) -> H) -> H)))
theorem-size     61
proof            (modus-ponens tm-708 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       247
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58803.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) -> (E -> G)) -> H) -> ((E -> (F -> G)) or ((E -> F) -> (E -> G)))) -> ((((E -> F) -> (E -> G)) -> H) -> H))), M:tm-708, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58804
in-theory        58804
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     49
proof            (modus-ponens tm-665 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58804.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-665, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58805
in-theory        58805
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) -> ((((A -> B) -> (A -> C)) -> D) -> D)))
theorem-size     85
proof            (modus-ponens tm-654 tm-709 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       263
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58805.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) -> ((((A -> B) -> (A -> C)) -> D) -> D))), M:tm-654, m:tm-709, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))
================================================================
tm-name          tm-58806
in-theory        58806
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E or ((((A -> B) -> (A -> C)) -> D) -> D)))
theorem-size     37
proof            (modus-ponens tm-623 tm-709 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58806.        (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E or ((((A -> B) -> (A -> C)) -> D) -> D))), M:tm-623, m:tm-709, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))
================================================================
tm-name          tm-58807
in-theory        58807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-622 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58807.        ((A -> (B -> (C or B))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-622, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58808
in-theory        58808
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (E -> (F or E)))
theorem-size     41
proof            (modus-ponens tm-609 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58808.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (E -> (F or E))), M:tm-609, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58809
in-theory        58809
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     45
proof            (modus-ponens tm-605 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58809.        ((A -> ((B -> (C or B)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-605, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58810
in-theory        58810
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((E -> (F or E)) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D))))
theorem-size     77
proof            (modus-ponens tm-595 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58810.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((E -> (F or E)) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)))), M:tm-595, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58811
in-theory        58811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-550 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58811.        (((A -> (B or A)) or C) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-550, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58812
in-theory        58812
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-540 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58812.        ((A or (B -> (C or B))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-540, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58813
in-theory        58813
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-530 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58813.        ((A or (B -> (B or C))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-530, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58814
in-theory        58814
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     45
proof            (modus-ponens tm-520 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58814.        ((A or (B -> (C -> (B and C)))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-520, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58815
in-theory        58815
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-510 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58815.        ((A or ((B and C) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-510, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58816
in-theory        58816
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-500 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58816.        ((A or ((B and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-500, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58817
in-theory        58817
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> (E -> G)) -> H) -> ((E -> (F -> G)) or ((E -> F) -> (E -> G)))) -> ((((E -> F) -> (E -> G)) -> H) -> H)))
theorem-size     51
proof            (modus-ponens tm-490 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58817.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> (E -> G)) -> H) -> ((E -> (F -> G)) or ((E -> F) -> (E -> G)))) -> ((((E -> F) -> (E -> G)) -> H) -> H))), M:tm-490, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58818
in-theory        58818
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-480 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58818.        ((A or (B -> (C -> B))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-480, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58819
in-theory        58819
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((((A -> B) -> (A -> C)) -> D) -> D) or E))
theorem-size     37
proof            (modus-ponens tm-470 tm-709 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58819.        (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((((A -> B) -> (A -> C)) -> D) -> D) or E)), M:tm-470, m:tm-709, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))
================================================================
tm-name          tm-58820
in-theory        58820
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-469 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58820.        ((A -> (B -> (B or C))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-469, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58821
in-theory        58821
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (E -> (E or F)))
theorem-size     41
proof            (modus-ponens tm-456 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58821.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (E -> (E or F))), M:tm-456, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58822
in-theory        58822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     45
proof            (modus-ponens tm-453 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58822.        ((A -> ((B -> (B or C)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-453, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58823
in-theory        58823
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((E -> (E or F)) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D))))
theorem-size     77
proof            (modus-ponens tm-443 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58823.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((E -> (E or F)) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)))), M:tm-443, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58824
in-theory        58824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-409 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58824.        (((A -> (A or B)) or C) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-409, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58825
in-theory        58825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     45
proof            (modus-ponens tm-400 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58825.        (((A -> (B -> (A and B))) or C) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-400, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58826
in-theory        58826
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-391 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58826.        ((((A and B) -> B) or C) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-391, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58827
in-theory        58827
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-382 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58827.        ((((A and B) -> A) or C) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-382, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58828
in-theory        58828
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) -> (E -> G)) -> H) -> ((E -> (F -> G)) or ((E -> F) -> (E -> G)))) -> ((((E -> F) -> (E -> G)) -> H) -> H)))
theorem-size     51
proof            (modus-ponens tm-373 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58828.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) -> (E -> G)) -> H) -> ((E -> (F -> G)) or ((E -> F) -> (E -> G)))) -> ((((E -> F) -> (E -> G)) -> H) -> H))), M:tm-373, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58829
in-theory        58829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-364 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58829.        (((A -> (B -> A)) or C) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-364, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58830
in-theory        58830
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> (((((A -> B) -> (A -> C)) -> D) -> D) and E)))
theorem-size     39
proof            (modus-ponens tm-355 tm-709 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58830.        (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> (((((A -> B) -> (A -> C)) -> D) -> D) and E))), M:tm-355, m:tm-709, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))
================================================================
tm-name          tm-58831
in-theory        58831
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     45
proof            (modus-ponens tm-354 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58831.        ((A -> (B -> (C -> (B and C)))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-354, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58832
in-theory        58832
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (E -> (F -> (E and F))))
theorem-size     43
proof            (modus-ponens tm-341 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58832.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58833
in-theory        58833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F)))
theorem-size     45
proof            (modus-ponens tm-338 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58833.        (((A -> B) -> (A -> (A and B))) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F))), M:tm-338, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58834
in-theory        58834
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) -> D) -> D))))
theorem-size     95
proof            (modus-ponens tm-328 tm-709 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       265
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58834.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) and ((((A -> B) -> (A -> C)) -> D) -> D)))), M:tm-328, m:tm-709, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))
================================================================
tm-name          tm-58835
in-theory        58835
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((E -> (F -> (E and F))) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D))))
theorem-size     79
proof            (modus-ponens tm-327 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       245
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58835.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((E -> (F -> (E and F))) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)))), M:tm-327, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58836
in-theory        58836
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (((E and F) -> F) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D))))
theorem-size     77
proof            (modus-ponens tm-326 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58836.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (((E and F) -> F) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)))), M:tm-326, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58837
in-theory        58837
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (((E and F) -> E) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D))))
theorem-size     77
proof            (modus-ponens tm-325 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58837.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (((E and F) -> E) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)))), M:tm-325, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58838
in-theory        58838
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D))))
theorem-size     85
proof            (modus-ponens tm-324 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       269
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58838.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)))), M:tm-324, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58839
in-theory        58839
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((E -> (F -> E)) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D))))
theorem-size     77
proof            (modus-ponens tm-323 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58839.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((E -> (F -> E)) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)))), M:tm-323, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58840
in-theory        58840
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((E and F) -> F))
theorem-size     41
proof            (modus-ponens tm-322 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58840.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58841
in-theory        58841
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((E and F) -> E))
theorem-size     41
proof            (modus-ponens tm-320 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58841.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58842
in-theory        58842
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     49
proof            (modus-ponens tm-318 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58842.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58843
in-theory        58843
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     83
proof            (modus-ponens tm-316 tm-709 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58843.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-316, m:tm-709, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))
================================================================
tm-name          tm-58844
in-theory        58844
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (E -> (F -> E)))
theorem-size     41
proof            (modus-ponens tm-315 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58844.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58845
in-theory        58845
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (not ((((A -> B) -> (A -> C)) -> D) -> D))) -> (not ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))))
theorem-size     97
proof            (modus-ponens tm-313 tm-709 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8)
proof-size       251
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58845.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (not ((((A -> B) -> (A -> C)) -> D) -> D))) -> (not ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))), M:tm-313, m:tm-709, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))
================================================================
tm-name          tm-58846
in-theory        58846
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((((((A -> B) -> (A -> C)) -> D) -> D) -> E) -> ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((((A -> B) -> (A -> C)) -> D) -> D)) -> E)))
theorem-size     87
proof            (modus-ponens tm-312 tm-709 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       245
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58846.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((((((A -> B) -> (A -> C)) -> D) -> D) -> E) -> ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) or ((((A -> B) -> (A -> C)) -> D) -> D)) -> E))), M:tm-312, m:tm-709, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))
================================================================
tm-name          tm-58847
in-theory        58847
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (E or (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D))))
theorem-size     73
proof            (modus-ponens tm-311 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8)
proof-size       213
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58847.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (E or (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)))), M:tm-311, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58848
in-theory        58848
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) or E))
theorem-size     73
proof            (modus-ponens tm-310 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8)
proof-size       213
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58848.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) or E)), M:tm-310, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58849
in-theory        58849
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (E -> ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and E)))
theorem-size     75
proof            (modus-ponens tm-309 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       219
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58849.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (E -> ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and E))), M:tm-309, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58850
in-theory        58850
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) -> D)) -> (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D)))
theorem-size     95
proof            (modus-ponens tm-306 tm-709 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8)
proof-size       255
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58850.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) -> D)) -> (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D))), M:tm-306, m:tm-709, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (C Dm))
================================================================
tm-name          tm-58851
in-theory        58851
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (E -> (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D))))
theorem-size     73
proof            (modus-ponens tm-305 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       213
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58851.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (E -> (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)))), M:tm-305, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58852
in-theory        58852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-303 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58852.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-303, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58853
in-theory        58853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     45
proof            (modus-ponens tm-270 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58853.        ((A -> (((B and C) -> C) and A)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-270, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58854
in-theory        58854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     45
proof            (modus-ponens tm-239 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58854.        ((A -> (((B and C) -> B) and A)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-239, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58855
in-theory        58855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) -> (E -> G)) -> H) -> ((E -> (F -> G)) or ((E -> F) -> (E -> G)))) -> ((((E -> F) -> (E -> G)) -> H) -> H)))
theorem-size     53
proof            (modus-ponens tm-210 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58855.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) -> (E -> G)) -> H) -> ((E -> (F -> G)) or ((E -> F) -> (E -> G)))) -> ((((E -> F) -> (E -> G)) -> H) -> H))), M:tm-210, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58856
in-theory        58856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     45
proof            (modus-ponens tm-183 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58856.        ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-183, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58857
in-theory        58857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-157 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58857.        ((A -> ((B and C) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-157, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58858
in-theory        58858
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     51
proof            (modus-ponens tm-147 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58858.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-147, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58859
in-theory        58859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-134 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58859.        ((A -> ((B and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-134, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58860
in-theory        58860
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     51
proof            (modus-ponens tm-125 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58860.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-125, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58861
in-theory        58861
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (D -> E)) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((((A -> B) -> (A -> C)) -> (D -> E)) -> D) -> ((((A -> B) -> (A -> C)) -> (D -> E)) -> E)))
theorem-size     53
proof            (modus-ponens tm-114 tm-709 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) (-> C D)) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> Am Bm) (-> Am Cm)) (-> C D))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58861.        (((((A -> B) -> (A -> C)) -> (D -> E)) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((((A -> B) -> (A -> C)) -> (D -> E)) -> D) -> ((((A -> B) -> (A -> C)) -> (D -> E)) -> E))), M:tm-114, m:tm-709, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) (-> C D)) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> Am Bm) (-> Am Cm)) (-> C D))) (Dm (-> C D)))
================================================================
tm-name          tm-58862
in-theory        58862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> (E -> G)) -> H) -> ((E -> (F -> G)) or ((E -> F) -> (E -> G)))) -> ((((E -> F) -> (E -> G)) -> H) -> H)))
theorem-size     51
proof            (modus-ponens tm-113 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       209
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58862.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> (E -> G)) -> H) -> ((E -> (F -> G)) or ((E -> F) -> (E -> G)))) -> ((((E -> F) -> (E -> G)) -> H) -> H))), M:tm-113, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58863
in-theory        58863
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     55
proof            (modus-ponens tm-105 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8)
proof-size       229
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58863.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-105, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58864
in-theory        58864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F)))
theorem-size     43
proof            (modus-ponens tm-95 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58864.        (((A -> B) -> (A -> A)) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F))), M:tm-95, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58865
in-theory        58865
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> ((((A -> B) -> (A -> C)) -> D) -> D)))
theorem-size     37
proof            (modus-ponens tm-84 tm-709 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58865.        (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (E -> ((((A -> B) -> (A -> C)) -> D) -> D))), M:tm-84, m:tm-709, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))
================================================================
tm-name          tm-58866
in-theory        58866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     43
proof            (modus-ponens tm-83 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58866.        ((A -> (B -> (C -> B))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-83, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58867
in-theory        58867
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> C) -> (B -> D)) -> E) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((((B -> C) -> (B -> D)) -> E) -> E)))
theorem-size     41
proof            (modus-ponens tm-76 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-8)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58867.        (((not (not A)) -> A) and (((((B -> C) -> (B -> D)) -> E) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((((B -> C) -> (B -> D)) -> E) -> E))), M:tm-76, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58868
in-theory        58868
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) -> ((((A -> B) -> (A -> C)) -> D) -> D))
theorem-size     61
proof            (modus-ponens tm-73 tm-709 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
axioms-used      (tm-8 tm-10 tm-2)
proof-size       189
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58868.        (((not (not ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))) or ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-73, m:tm-709, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))
================================================================
tm-name          tm-58869
in-theory        58869
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (not (((A -> B) -> (A -> C)) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))))
theorem-size     60
proof            (modus-ponens tm-70 tm-709 ((B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (A (-> (-> (-> Am Bm) (-> Am Cm)) (not (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))) (Dm (not (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-2 tm-9 tm-8)
proof-size       198
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58869.        (((((A -> B) -> (A -> C)) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (not (((A -> B) -> (A -> C)) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))), M:tm-70, m:tm-709, u:((B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (A (-> (-> (-> Am Bm) (-> Am Cm)) (not (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))) (Dm (not (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-58870
in-theory        58870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F)))
theorem-size     47
proof            (modus-ponens tm-69 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-8)
proof-size       179
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58870.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) -> (C -> E)) -> F) -> ((C -> (D -> E)) or ((C -> D) -> (C -> E)))) -> ((((C -> D) -> (C -> E)) -> F) -> F))), M:tm-69, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58871
in-theory        58871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     49
proof            (modus-ponens tm-54 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2)
proof-size       185
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58871.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-54, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-58872
in-theory        58872
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((((B -> C) -> (B -> D)) -> E) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D))))) or ((((B -> C) -> (B -> D)) -> E) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D))))) -> ((((B -> C) -> (B -> D)) -> E) -> E))
theorem-size     61
proof            (modus-ponens tm-47 tm-709 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       189
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58872.        (((A and ((((B -> C) -> (B -> D)) -> E) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D))))) or ((((B -> C) -> (B -> D)) -> E) -> ((B -> (C -> D)) or ((B -> C) -> (B -> D))))) -> ((((B -> C) -> (B -> D)) -> E) -> E)), M:tm-47, m:tm-709, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))
================================================================
tm-name          tm-58873
in-theory        58873
times-derived    2
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) and E) or ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) -> ((((A -> B) -> (A -> C)) -> D) -> D))
theorem-size     61
proof            (modus-ponens tm-46 tm-709 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       189
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-58873.        (((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) and E) or ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-46, m:tm-709, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))
================================================================
tm-name          tm-58874
in-theory        58874
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     53
proof            (modus-ponens tm-708 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1)
proof-size       223
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58874.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-708, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58875
in-theory        58875
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     51
proof            (modus-ponens tm-705 tm-710 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       243
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58875.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-705, m:tm-710, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58876
in-theory        58876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-703 tm-710 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58876.        (((A -> B) -> (A -> C)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-703, m:tm-710, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58877
in-theory        58877
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     73
proof            (modus-ponens tm-697 tm-710 ((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       271
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58877.        ((((A -> B) -> (A -> C)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-697, m:tm-710, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58878
in-theory        58878
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-665 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58878.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-665, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58879
in-theory        58879
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     39
proof            (modus-ponens tm-662 tm-710 ((Am (-> (or A (-> B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       191
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58879.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-662, m:tm-710, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58880
in-theory        58880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     29
proof            (modus-ponens tm-660 tm-710 ((Am (-> A B)) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58880.        ((A -> B) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-660, m:tm-710, u:((Am (-> A B)) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58881
in-theory        58881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((B or (A -> B)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     61
proof            (modus-ponens tm-654 tm-710 ((Am (-> A B)) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58881.        (((A -> B) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))) and ((B or (A -> B)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-654, m:tm-710, u:((Am (-> A B)) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58882
in-theory        58882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-622 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58882.        ((A -> (B -> (C or B))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-622, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58883
in-theory        58883
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-619 tm-710 ((Am (-> A (or B A))) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-1 tm-7 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58883.        ((A or (B -> (C or B))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-619, m:tm-710, u:((Am (-> A (or B A))) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58884
in-theory        58884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (G or F)))
theorem-size     33
proof            (modus-ponens tm-609 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58884.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (G or F))), M:tm-609, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58885
in-theory        58885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-605 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58885.        ((A -> ((B -> (C or B)) and A)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-605, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58886
in-theory        58886
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-602 tm-710 ((Am (and (-> A (or B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58886.        ((A or ((B -> (C or B)) and A)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-602, m:tm-710, u:((Am (and (-> A (or B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58887
in-theory        58887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G or F)) and (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-595 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58887.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G or F)) and (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-595, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58888
in-theory        58888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-550 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58888.        (((A -> (B or A)) or C) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-550, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58889
in-theory        58889
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-540 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58889.        ((A or (B -> (C or B))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-540, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58890
in-theory        58890
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-530 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58890.        ((A or (B -> (B or C))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-530, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58891
in-theory        58891
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-520 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58891.        ((A or (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-520, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58892
in-theory        58892
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-510 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58892.        ((A or ((B and C) -> C)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-510, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58893
in-theory        58893
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-500 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58893.        ((A or ((B and C) -> B)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-500, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58894
in-theory        58894
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-490 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58894.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-490, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58895
in-theory        58895
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-480 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58895.        ((A or (B -> (C -> B))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-480, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58896
in-theory        58896
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-469 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58896.        ((A -> (B -> (B or C))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-469, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58897
in-theory        58897
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-466 tm-710 ((Am (-> A (or A B))) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-1 tm-6 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58897.        ((A or (B -> (B or C))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-466, m:tm-710, u:((Am (-> A (or A B))) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58898
in-theory        58898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (F or G)))
theorem-size     33
proof            (modus-ponens tm-456 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58898.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (F or G))), M:tm-456, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58899
in-theory        58899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-453 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58899.        ((A -> ((B -> (B or C)) and A)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-453, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58900
in-theory        58900
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-450 tm-710 ((Am (and (-> A (or A B)) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58900.        ((A or ((B -> (B or C)) and A)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-450, m:tm-710, u:((Am (and (-> A (or A B)) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58901
in-theory        58901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (F or G)) and (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-443 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58901.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (F or G)) and (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-443, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58902
in-theory        58902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-409 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58902.        (((A -> (A or B)) or C) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-409, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58903
in-theory        58903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-400 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58903.        (((A -> (B -> (A and B))) or C) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-400, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58904
in-theory        58904
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-391 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58904.        ((((A and B) -> B) or C) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-391, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58905
in-theory        58905
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-382 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58905.        ((((A and B) -> A) or C) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-382, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58906
in-theory        58906
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-373 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58906.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-373, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58907
in-theory        58907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-364 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58907.        (((A -> (B -> A)) or C) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-364, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58908
in-theory        58908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-354 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58908.        ((A -> (B -> (C -> (B and C)))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-354, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58909
in-theory        58909
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-351 tm-710 ((Am (-> A (-> B (and A B)))) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-1 tm-5 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58909.        ((A or (B -> (C -> (B and C)))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-351, m:tm-710, u:((Am (-> A (-> B (and A B)))) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58910
in-theory        58910
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D)))))
theorem-size     25
proof            (modus-ponens tm-349 tm-710 ((A Am) (B (-> (-> Bm Cm) (-> Bm Dm))) (Em (and Am (-> (-> Bm Cm) (-> Bm Dm)))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58910.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> (A and ((B -> C) -> (B -> D))))), M:tm-349, m:tm-710, u:((A Am) (B (-> (-> Bm Cm) (-> Bm Dm))) (Em (and Am (-> (-> Bm Cm) (-> Bm Dm)))) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (and Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-58911
in-theory        58911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (G -> (F and G))))
theorem-size     35
proof            (modus-ponens tm-341 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58911.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58912
in-theory        58912
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and E))
theorem-size     55
proof            (modus-ponens tm-339 tm-710 ((Am (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) B)) (A (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58912.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and E)), M:tm-339, m:tm-710, u:((Am (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) B)) (A (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58913
in-theory        58913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     37
proof            (modus-ponens tm-338 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58913.        (((A -> B) -> (A -> (A and B))) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-338, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58914
in-theory        58914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     35
proof            (modus-ponens tm-335 tm-710 ((Am (-> A (and A B))) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58914.        (((A -> B) or (A -> (A and B))) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-335, m:tm-710, u:((Am (-> A (and A B))) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58915
in-theory        58915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (A -> (A and ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     57
proof            (modus-ponens tm-328 tm-710 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58915.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (A -> (A and ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-328, m:tm-710, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58916
in-theory        58916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G -> (F and G))) and (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     63
proof            (modus-ponens tm-327 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58916.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G -> (F and G))) and (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-327, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58917
in-theory        58917
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((F and G) -> G) and (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-326 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58917.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((F and G) -> G) and (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-326, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58918
in-theory        58918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((F and G) -> F) and (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-325 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58918.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((F and G) -> F) and (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-325, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58919
in-theory        58919
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     69
proof            (modus-ponens tm-324 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58919.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-324, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58920
in-theory        58920
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G -> F)) and (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     61
proof            (modus-ponens tm-323 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58920.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G -> F)) and (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-323, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58921
in-theory        58921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F and G) -> G))
theorem-size     33
proof            (modus-ponens tm-322 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58921.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F and G) -> G)), M:tm-322, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58922
in-theory        58922
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)) -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((A and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)) -> F))
theorem-size     87
proof            (modus-ponens tm-321 tm-710 ((Am (and A (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) C))) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58922.        (((A and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)) -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((A and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)) -> F)), M:tm-321, m:tm-710, u:((Am (and A (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) C))) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58923
in-theory        58923
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F and G) -> F))
theorem-size     33
proof            (modus-ponens tm-320 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58923.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F and G) -> F)), M:tm-320, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58924
in-theory        58924
times-derived    1
----------------------------------------------------------------
theorem          ((((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) and F) -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) and F) -> E))
theorem-size     87
proof            (modus-ponens tm-319 tm-710 ((Am (and (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) B) C)) (A (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58924.        ((((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) and F) -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) and F) -> E)), M:tm-319, m:tm-710, u:((Am (and (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) B) C)) (A (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58925
in-theory        58925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     41
proof            (modus-ponens tm-318 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58925.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58926
in-theory        58926
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((((A -> B) -> (A -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> ((((A -> B) -> (A -> C)) -> D) -> E)))
theorem-size     93
proof            (modus-ponens tm-317 tm-710 ((Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) C))) (A (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       279
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58926.        ((((((A -> B) -> (A -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and (((((A -> B) -> (A -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> ((((A -> B) -> (A -> C)) -> D) -> E))), M:tm-317, m:tm-710, u:((Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) C))) (A (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-58927
in-theory        58927
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (A -> A))
theorem-size     31
proof            (modus-ponens tm-316 tm-710 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58927.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (A -> A)), M:tm-316, m:tm-710, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58928
in-theory        58928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (G -> F)))
theorem-size     33
proof            (modus-ponens tm-315 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58928.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (G -> F))), M:tm-315, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58929
in-theory        58929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((A -> (not ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))) -> (not A)))
theorem-size     59
proof            (modus-ponens tm-313 tm-710 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-8)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58929.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((A -> (not ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))) -> (not A))), M:tm-313, m:tm-710, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58930
in-theory        58930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F) -> ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) -> F)))
theorem-size     85
proof            (modus-ponens tm-312 tm-710 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1)
proof-size       227
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58930.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F) -> ((A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) -> F))), M:tm-312, m:tm-710, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58931
in-theory        58931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F or (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     57
proof            (modus-ponens tm-311 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58931.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F or (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-311, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58932
in-theory        58932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) or F))
theorem-size     57
proof            (modus-ponens tm-310 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58932.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) or F)), M:tm-310, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58933
in-theory        58933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and F)))
theorem-size     59
proof            (modus-ponens tm-309 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58933.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and F))), M:tm-309, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58934
in-theory        58934
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((A -> (((B -> C) -> (B -> D)) -> E)) -> (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     57
proof            (modus-ponens tm-306 tm-710 ((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58934.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and ((A -> (((B -> C) -> (B -> D)) -> E)) -> (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-306, m:tm-710, u:((A Am) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-58935
in-theory        58935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))))
theorem-size     57
proof            (modus-ponens tm-305 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58935.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (F -> (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))), M:tm-305, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58936
in-theory        58936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-303 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58936.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-303, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58937
in-theory        58937
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     37
proof            (modus-ponens tm-300 tm-710 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58937.        ((A or ((B -> (C -> (B and C))) and A)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-300, m:tm-710, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58938
in-theory        58938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-270 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58938.        ((A -> (((B and C) -> C) and A)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-270, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58939
in-theory        58939
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-267 tm-710 ((Am (and (-> (and A B) B) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58939.        ((A or (((B and C) -> C) and A)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-267, m:tm-710, u:((Am (and (-> (and A B) B) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58940
in-theory        58940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-239 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58940.        ((A -> (((B and C) -> B) and A)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-239, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58941
in-theory        58941
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-236 tm-710 ((Am (and (-> (and A B) A) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58941.        ((A or (((B and C) -> B) and A)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-236, m:tm-710, u:((Am (and (-> (and A B) A) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58942
in-theory        58942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-210 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58942.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-210, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58943
in-theory        58943
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     43
proof            (modus-ponens tm-207 tm-710 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1)
proof-size       213
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58943.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-207, m:tm-710, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58944
in-theory        58944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     37
proof            (modus-ponens tm-183 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58944.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-183, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58945
in-theory        58945
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     35
proof            (modus-ponens tm-180 tm-710 ((Am (and (-> A (-> B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58945.        ((A or ((B -> (C -> B)) and A)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-180, m:tm-710, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58946
in-theory        58946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-157 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58946.        ((A -> ((B and C) -> C)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-157, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58947
in-theory        58947
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-154 tm-710 ((Am (-> (and A B) B)) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58947.        ((A or ((B and C) -> C)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-154, m:tm-710, u:((Am (-> (and A B) B)) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58948
in-theory        58948
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))
theorem-size     27
proof            (modus-ponens tm-152 tm-710 ((Am (and A (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-4 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58948.        ((A and (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)), M:tm-152, m:tm-710, u:((Am (and A (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-58949
in-theory        58949
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     43
proof            (modus-ponens tm-147 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58949.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-147, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58950
in-theory        58950
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-144 tm-710 ((Am (-> (and A (-> B C)) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58950.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-144, m:tm-710, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58951
in-theory        58951
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)) -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     55
proof            (modus-ponens tm-142 tm-710 ((Am (and A (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) C))) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-1 tm-4 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58951.        ((A and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> F)) -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-142, m:tm-710, u:((Am (and A (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) C))) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58952
in-theory        58952
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))
theorem-size     53
proof            (modus-ponens tm-141 tm-710 ((Am (and A (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-4 tm-1 tm-8)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58952.        ((A and (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) -> (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)), M:tm-141, m:tm-710, u:((Am (and A (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-58953
in-theory        58953
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-134 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58953.        ((A -> ((B and C) -> B)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-134, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58954
in-theory        58954
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-131 tm-710 ((Am (-> (and A B) A)) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58954.        ((A or ((B and C) -> B)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-131, m:tm-710, u:((Am (-> (and A B) A)) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58955
in-theory        58955
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) and E) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     27
proof            (modus-ponens tm-129 tm-710 ((Am (and (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) B)) (A (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-3 tm-8)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58955.        (((((A -> B) -> (A -> C)) -> D) and E) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-129, m:tm-710, u:((Am (and (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) B)) (A (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-58956
in-theory        58956
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     43
proof            (modus-ponens tm-125 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58956.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-125, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58957
in-theory        58957
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     41
proof            (modus-ponens tm-122 tm-710 ((Am (-> (and (-> A B) C) B)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58957.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-122, m:tm-710, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58958
in-theory        58958
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) and F) -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     55
proof            (modus-ponens tm-120 tm-710 ((Am (and (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) B) C)) (A (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-1 tm-3 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58958.        (((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) and F) -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-120, m:tm-710, u:((Am (and (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) B) C)) (A (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58959
in-theory        58959
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> B) -> (A -> C)) -> D)) and E) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     53
proof            (modus-ponens tm-119 tm-710 ((Am (and (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) C)) (A (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-3 tm-1 tm-8)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58959.        (((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((A -> B) -> (A -> C)) -> D)) and E) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-119, m:tm-710, u:((Am (and (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) C)) (A (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-58960
in-theory        58960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-113 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58960.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-113, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58961
in-theory        58961
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     41
proof            (modus-ponens tm-110 tm-710 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58961.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-110, m:tm-710, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58962
in-theory        58962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> C) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))
theorem-size     29
proof            (modus-ponens tm-108 tm-710 ((Am (-> (-> Bm Cm) (-> (-> Bm Dm) C))) (A (-> Bm Cm)) (B (-> Bm Dm)) (Em (-> (-> Bm Cm) C)) (D (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> Bm Cm) C)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58962.        (((A -> B) -> ((A -> C) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-108, m:tm-710, u:((Am (-> (-> Bm Cm) (-> (-> Bm Dm) C))) (A (-> Bm Cm)) (B (-> Bm Dm)) (Em (-> (-> Bm Cm) C)) (D (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> Bm Cm) C))))
================================================================
tm-name          tm-58963
in-theory        58963
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) -> ((((A -> B) -> (A -> C)) -> D) -> D))
theorem-size     61
proof            (modus-ponens tm-106 tm-710 ((Am (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (A (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C Em)))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       231
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58963.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-106, m:tm-710, u:((Am (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (A (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (B (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) (C Em))
================================================================
tm-name          tm-58964
in-theory        58964
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     47
proof            (modus-ponens tm-105 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58964.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-105, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58965
in-theory        58965
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-102 tm-710 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       219
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58965.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-102, m:tm-710, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58966
in-theory        58966
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     53
proof            (modus-ponens tm-100 tm-710 ((Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) C))) (A (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58966.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-100, m:tm-710, u:((Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) C))) (A (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-58967
in-theory        58967
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))
theorem-size     17
proof            (modus-ponens tm-98 tm-710 ((Em Am) (B (-> (-> Bm Cm) (-> Bm Dm))) (A Am) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58967.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-98, m:tm-710, u:((Em Am) (B (-> (-> Bm Cm) (-> Bm Dm))) (A Am) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-58968
in-theory        58968
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     53
proof            (modus-ponens tm-96 tm-710 ((Am (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) B)) (A (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-1 tm-8)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58968.        ((((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E) -> ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-96, m:tm-710, u:((Am (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) B)) (A (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58969
in-theory        58969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     35
proof            (modus-ponens tm-95 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58969.        (((A -> B) -> (A -> A)) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-95, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58970
in-theory        58970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     33
proof            (modus-ponens tm-92 tm-710 ((Am (-> A A)) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-2 tm-1)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58970.        (((A -> B) or (A -> A)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-92, m:tm-710, u:((Am (-> A A)) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58971
in-theory        58971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     35
proof            (modus-ponens tm-83 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58971.        ((A -> (B -> (C -> B))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-83, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58972
in-theory        58972
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     33
proof            (modus-ponens tm-80 tm-710 ((Am (-> A (-> B A))) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58972.        ((A or (B -> (C -> B))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-80, m:tm-710, u:((Am (-> A (-> B A))) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58973
in-theory        58973
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))) -> E)
theorem-size     31
proof            (modus-ponens tm-77 tm-710 ((Am (not (not (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) B)))) (A (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-10 tm-1 tm-8)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58973.        ((not (not (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))) -> E), M:tm-77, m:tm-710, u:((Am (not (not (-> (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) B)))) (A (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58974
in-theory        58974
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))))
theorem-size     33
proof            (modus-ponens tm-76 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58974.        (((not (not A)) -> A) and (B -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))), M:tm-76, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58975
in-theory        58975
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     31
proof            (modus-ponens tm-73 tm-710 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-10 tm-1 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58975.        (((not (not A)) or A) -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-73, m:tm-710, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58976
in-theory        58976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     39
proof            (modus-ponens tm-69 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8 tm-2)
proof-size       155
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58976.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-69, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58977
in-theory        58977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     37
proof            (modus-ponens tm-66 tm-710 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-9 tm-1 tm-2)
proof-size       167
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58977.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-66, m:tm-710, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58978
in-theory        58978
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> D)) -> E)) -> ((A or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     39
proof            (modus-ponens tm-55 tm-710 ((Am (-> A (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-8 tm-1)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58978.        ((A -> (((B -> C) -> (B -> D)) -> E)) -> ((A or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-55, m:tm-710, u:((Am (-> A (-> (-> (-> Bm Cm) (-> Bm Dm)) Em))) (B (-> (-> (-> Bm Cm) (-> Bm Dm)) Em)) (C (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-58979
in-theory        58979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     41
proof            (modus-ponens tm-54 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58979.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-54, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-58980
in-theory        58980
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     39
proof            (modus-ponens tm-51 tm-710 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-1 tm-2)
proof-size       175
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58980.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-51, m:tm-710, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58981
in-theory        58981
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-50 tm-710 ((Am (or A B)) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-7 tm-1 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58981.        ((A or (B or A)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-50, m:tm-710, u:((Am (or A B)) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58982
in-theory        58982
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-49 tm-710 ((Am (or A B)) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-6 tm-1 tm-2)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58982.        ((A or (A or B)) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-49, m:tm-710, u:((Am (or A B)) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58983
in-theory        58983
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     33
proof            (modus-ponens tm-48 tm-710 ((Am (-> A (and B A))) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-5 tm-1 tm-2)
proof-size       153
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58983.        ((A or (B -> (A and B))) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-48, m:tm-710, u:((Am (-> A (and B A))) (C (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58984
in-theory        58984
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-47 tm-710 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58984.        (((A and B) or B) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-47, m:tm-710, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58985
in-theory        58985
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-46 tm-710 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-58985.        (((A and B) or A) -> ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-46, m:tm-710, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-58986
in-theory        58986
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (G -> E)))
theorem-size     35
proof            (modus-ponens tm-708 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58986.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (G -> E))), M:tm-708, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-58987
in-theory        58987
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (F -> D)))
theorem-size     23
proof            (modus-ponens tm-665 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58987.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (F -> D))), M:tm-665, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-58988
in-theory        58988
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (D -> A)))
theorem-size     11
proof            (modus-ponens tm-623 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58988.        (((A and B) or A) -> (C or (D -> A))), M:tm-623, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-58989
in-theory        58989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-622 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58989.        ((A -> (B -> (C or B))) and (((D and E) or D) -> (F -> D))), M:tm-622, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-58990
in-theory        58990
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58990.        ((((A and B) or A) -> (C -> A)) and (D -> (E or D))), M:tm-609, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-58991
in-theory        58991
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (F -> D)))
theorem-size     19
proof            (modus-ponens tm-605 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58991.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (F -> D))), M:tm-605, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-58992
in-theory        58992
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and ((D -> (E or D)) and (((A and B) or A) -> (C -> A))))
theorem-size     25
proof            (modus-ponens tm-595 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58992.        ((((A and B) or A) -> (C -> A)) and ((D -> (E or D)) and (((A and B) or A) -> (C -> A)))), M:tm-595, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-58993
in-theory        58993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-550 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58993.        (((A -> (B or A)) or C) and (((D and E) or D) -> (F -> D))), M:tm-550, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-58994
in-theory        58994
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-540 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58994.        ((A or (B -> (C or B))) and (((D and E) or D) -> (F -> D))), M:tm-540, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-58995
in-theory        58995
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-530 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58995.        ((A or (B -> (B or C))) and (((D and E) or D) -> (F -> D))), M:tm-530, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-58996
in-theory        58996
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> D)))
theorem-size     19
proof            (modus-ponens tm-520 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58996.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> D))), M:tm-520, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-58997
in-theory        58997
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-510 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58997.        ((A or ((B and C) -> C)) and (((D and E) or D) -> (F -> D))), M:tm-510, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-58998
in-theory        58998
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-500 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58998.        ((A or ((B and C) -> B)) and (((D and E) or D) -> (F -> D))), M:tm-500, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-58999
in-theory        58999
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> E)))
theorem-size     25
proof            (modus-ponens tm-490 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-58999.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> E))), M:tm-490, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59000
in-theory        59000
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-480 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59000.        ((A or (B -> (C -> B))) and (((D and E) or D) -> (F -> D))), M:tm-480, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59001
in-theory        59001
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> A) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59001.        (((A and B) or A) -> ((C -> A) or D)), M:tm-470, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-59002
in-theory        59002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-469 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59002.        ((A -> (B -> (B or C))) and (((D and E) or D) -> (F -> D))), M:tm-469, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59003
in-theory        59003
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59003.        ((((A and B) or A) -> (C -> A)) and (D -> (D or E))), M:tm-456, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59004
in-theory        59004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (F -> D)))
theorem-size     19
proof            (modus-ponens tm-453 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59004.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (F -> D))), M:tm-453, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59005
in-theory        59005
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and ((D -> (D or E)) and (((A and B) or A) -> (C -> A))))
theorem-size     25
proof            (modus-ponens tm-443 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59005.        ((((A and B) or A) -> (C -> A)) and ((D -> (D or E)) and (((A and B) or A) -> (C -> A)))), M:tm-443, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59006
in-theory        59006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-409 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59006.        (((A -> (A or B)) or C) and (((D and E) or D) -> (F -> D))), M:tm-409, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59007
in-theory        59007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (F -> D)))
theorem-size     19
proof            (modus-ponens tm-400 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59007.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (F -> D))), M:tm-400, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59008
in-theory        59008
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-391 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59008.        ((((A and B) -> B) or C) and (((D and E) or D) -> (F -> D))), M:tm-391, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59009
in-theory        59009
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-382 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59009.        ((((A and B) -> A) or C) and (((D and E) or D) -> (F -> D))), M:tm-382, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59010
in-theory        59010
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (G -> E)))
theorem-size     25
proof            (modus-ponens tm-373 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59010.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (G -> E))), M:tm-373, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59011
in-theory        59011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-364 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59011.        (((A -> (B -> A)) or C) and (((D and E) or D) -> (F -> D))), M:tm-364, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59012
in-theory        59012
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D -> A) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59012.        (((A and B) or A) -> (C -> ((D -> A) and C))), M:tm-355, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-59013
in-theory        59013
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> D)))
theorem-size     19
proof            (modus-ponens tm-354 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59013.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> D))), M:tm-354, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59014
in-theory        59014
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59014.        ((((A and B) or A) -> (C -> A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59015
in-theory        59015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (E -> C)))
theorem-size     19
proof            (modus-ponens tm-338 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59015.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (E -> C))), M:tm-338, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59016
in-theory        59016
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (((A and B) or A) -> (((A and B) or A) and (C -> A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59016.        ((((A and B) or A) -> (C -> A)) and (((A and B) or A) -> (((A and B) or A) and (C -> A)))), M:tm-328, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-59017
in-theory        59017
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and ((D -> (E -> (D and E))) and (((A and B) or A) -> (C -> A))))
theorem-size     27
proof            (modus-ponens tm-327 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59017.        ((((A and B) or A) -> (C -> A)) and ((D -> (E -> (D and E))) and (((A and B) or A) -> (C -> A)))), M:tm-327, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59018
in-theory        59018
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (((D and E) -> E) and (((A and B) or A) -> (C -> A))))
theorem-size     25
proof            (modus-ponens tm-326 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59018.        ((((A and B) or A) -> (C -> A)) and (((D and E) -> E) and (((A and B) or A) -> (C -> A)))), M:tm-326, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59019
in-theory        59019
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (((D and E) -> D) and (((A and B) or A) -> (C -> A))))
theorem-size     25
proof            (modus-ponens tm-325 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59019.        ((((A and B) or A) -> (C -> A)) and (((D and E) -> D) and (((A and B) or A) -> (C -> A)))), M:tm-325, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59020
in-theory        59020
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or A) -> (C -> A))))
theorem-size     33
proof            (modus-ponens tm-324 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59020.        ((((A and B) or A) -> (C -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or A) -> (C -> A)))), M:tm-324, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59021
in-theory        59021
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and ((D -> (E -> D)) and (((A and B) or A) -> (C -> A))))
theorem-size     25
proof            (modus-ponens tm-323 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59021.        ((((A and B) or A) -> (C -> A)) and ((D -> (E -> D)) and (((A and B) or A) -> (C -> A)))), M:tm-323, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59022
in-theory        59022
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59022.        ((((A and B) or A) -> (C -> A)) and ((D and E) -> E)), M:tm-322, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59023
in-theory        59023
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59023.        ((((A and B) or A) -> (C -> A)) and ((D and E) -> D)), M:tm-320, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59024
in-theory        59024
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59024.        ((((A and B) or A) -> (C -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59025
in-theory        59025
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     21
proof            (modus-ponens tm-316 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59025.        ((((A and B) or A) -> (C -> A)) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-59026
in-theory        59026
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59026.        ((((A and B) or A) -> (C -> A)) and (D -> (E -> D))), M:tm-315, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59027
in-theory        59027
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and ((((A and B) or A) -> (not (C -> A))) -> (not ((A and B) or A))))
theorem-size     27
proof            (modus-ponens tm-313 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59027.        ((((A and B) or A) -> (C -> A)) and ((((A and B) or A) -> (not (C -> A))) -> (not ((A and B) or A)))), M:tm-313, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-59028
in-theory        59028
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (((C -> A) -> D) -> ((((A and B) or A) or (C -> A)) -> D)))
theorem-size     27
proof            (modus-ponens tm-312 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59028.        ((((A and B) or A) -> (C -> A)) and (((C -> A) -> D) -> ((((A and B) or A) or (C -> A)) -> D))), M:tm-312, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-59029
in-theory        59029
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (D or (((A and B) or A) -> (C -> A))))
theorem-size     21
proof            (modus-ponens tm-311 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59029.        ((((A and B) or A) -> (C -> A)) and (D or (((A and B) or A) -> (C -> A)))), M:tm-311, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59030
in-theory        59030
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and ((((A and B) or A) -> (C -> A)) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59030.        ((((A and B) or A) -> (C -> A)) and ((((A and B) or A) -> (C -> A)) or D)), M:tm-310, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59031
in-theory        59031
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (D -> ((((A and B) or A) -> (C -> A)) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59031.        ((((A and B) or A) -> (C -> A)) and (D -> ((((A and B) or A) -> (C -> A)) and D))), M:tm-309, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59032
in-theory        59032
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and ((((A and B) or A) -> C) -> (((A and B) or A) -> A)))
theorem-size     25
proof            (modus-ponens tm-306 tm-711 ((A (or (and Am Bm) Am)) (B Cm) (C Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59032.        ((((A and B) or A) -> (C -> A)) and ((((A and B) or A) -> C) -> (((A and B) or A) -> A))), M:tm-306, m:tm-711, u:((A (or (and Am Bm) Am)) (B Cm) (C Am))
================================================================
tm-name          tm-59033
in-theory        59033
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (D -> (((A and B) or A) -> (C -> A))))
theorem-size     21
proof            (modus-ponens tm-305 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59033.        ((((A and B) or A) -> (C -> A)) and (D -> (((A and B) or A) -> (C -> A)))), M:tm-305, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59034
in-theory        59034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (F -> D)))
theorem-size     21
proof            (modus-ponens tm-303 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59034.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (F -> D))), M:tm-303, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59035
in-theory        59035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (F -> D)))
theorem-size     19
proof            (modus-ponens tm-270 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59035.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (F -> D))), M:tm-270, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59036
in-theory        59036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (F -> D)))
theorem-size     19
proof            (modus-ponens tm-239 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59036.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (F -> D))), M:tm-239, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59037
in-theory        59037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (G -> E)))
theorem-size     27
proof            (modus-ponens tm-210 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59037.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (G -> E))), M:tm-210, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59038
in-theory        59038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (F -> D)))
theorem-size     19
proof            (modus-ponens tm-183 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59038.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (F -> D))), M:tm-183, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59039
in-theory        59039
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-157 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59039.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> (F -> D))), M:tm-157, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59040
in-theory        59040
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (F -> D)))
theorem-size     25
proof            (modus-ponens tm-147 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59040.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (F -> D))), M:tm-147, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59041
in-theory        59041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-134 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59041.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> (F -> D))), M:tm-134, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59042
in-theory        59042
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (F -> D)))
theorem-size     25
proof            (modus-ponens tm-125 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59042.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (F -> D))), M:tm-125, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59043
in-theory        59043
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((D -> A) -> (D -> B)))
theorem-size     17
proof            (modus-ponens tm-114 tm-711 ((A (or (and (-> C D) Bm) (-> C D))) (B Cm) (Am (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59043.        ((((A -> B) and C) or (A -> B)) -> ((D -> A) -> (D -> B))), M:tm-114, m:tm-711, u:((A (or (and (-> C D) Bm) (-> C D))) (B Cm) (Am (-> C D)))
================================================================
tm-name          tm-59044
in-theory        59044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> E)))
theorem-size     25
proof            (modus-ponens tm-113 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59044.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> E))), M:tm-113, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59045
in-theory        59045
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (F -> D)))
theorem-size     29
proof            (modus-ponens tm-105 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59045.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (F -> D))), M:tm-105, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59046
in-theory        59046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> (E -> C)))
theorem-size     17
proof            (modus-ponens tm-95 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59046.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> (E -> C))), M:tm-95, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59047
in-theory        59047
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (D -> A)))
theorem-size     11
proof            (modus-ponens tm-84 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59047.        (((A and B) or A) -> (C -> (D -> A))), M:tm-84, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-59048
in-theory        59048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> (F -> D)))
theorem-size     17
proof            (modus-ponens tm-83 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59048.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> (F -> D))), M:tm-83, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59049
in-theory        59049
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> (D -> B)))
theorem-size     15
proof            (modus-ponens tm-76 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59049.        (((not (not A)) -> A) and (((B and C) or B) -> (D -> B))), M:tm-76, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59050
in-theory        59050
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> (C -> A))
theorem-size     17
proof            (modus-ponens tm-73 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-8 tm-10 tm-3 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59050.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> (C -> A)), M:tm-73, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-59051
in-theory        59051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (E -> C)))
theorem-size     21
proof            (modus-ponens tm-69 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59051.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (E -> C))), M:tm-69, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59052
in-theory        59052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (F -> D)))
theorem-size     23
proof            (modus-ponens tm-54 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59052.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (F -> D))), M:tm-54, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59053
in-theory        59053
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> (C -> A))
theorem-size     11
proof            (modus-ponens tm-50 tm-711 ((A (and Am Bm)) (B Am) (C (-> Cm Am))))
axioms-used      (tm-8 tm-7 tm-3 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59053.        ((A or ((A and B) or A)) -> (C -> A)), M:tm-50, m:tm-711, u:((A (and Am Bm)) (B Am) (C (-> Cm Am)))
================================================================
tm-name          tm-59054
in-theory        59054
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> (C -> A))
theorem-size     13
proof            (modus-ponens tm-49 tm-711 ((A (and Am Bm)) (B Am) (C (-> Cm Am))))
axioms-used      (tm-8 tm-6 tm-3 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59054.        (((A and B) or ((A and B) or A)) -> (C -> A)), M:tm-49, m:tm-711, u:((A (and Am Bm)) (B Am) (C (-> Cm Am)))
================================================================
tm-name          tm-59055
in-theory        59055
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> (D -> B))
theorem-size     17
proof            (modus-ponens tm-47 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-8 tm-4 tm-3 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59055.        (((A and ((B and C) or B)) or ((B and C) or B)) -> (D -> B)), M:tm-47, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-59056
in-theory        59056
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> (D -> A))
theorem-size     17
proof            (modus-ponens tm-46 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59056.        (((((A and B) or A) and C) or ((A and B) or A)) -> (D -> A)), M:tm-46, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-59057
in-theory        59057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> (E -> C)))
theorem-size     15
proof            (modus-ponens tm-42 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59057.        ((A -> (B or A)) and (((C and D) or C) -> (E -> C))), M:tm-42, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59058
in-theory        59058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> (E -> C)))
theorem-size     15
proof            (modus-ponens tm-32 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59058.        ((A -> (A or B)) and (((C and D) or C) -> (E -> C))), M:tm-32, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59059
in-theory        59059
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and (C -> A)))
theorem-size     15
proof            (modus-ponens tm-24 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59059.        (((A and B) or A) -> (((A and B) or A) and (C -> A))), M:tm-24, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-59060
in-theory        59060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> (E -> C)))
theorem-size     17
proof            (modus-ponens tm-23 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59060.        ((A -> (B -> (A and B))) and (((C and D) or C) -> (E -> C))), M:tm-23, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59061
in-theory        59061
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> (E -> C)))
theorem-size     15
proof            (modus-ponens tm-22 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59061.        (((A and B) -> B) and (((C and D) or C) -> (E -> C))), M:tm-22, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59062
in-theory        59062
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> (E -> C)))
theorem-size     15
proof            (modus-ponens tm-21 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59062.        (((A and B) -> A) and (((C and D) or C) -> (E -> C))), M:tm-21, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59063
in-theory        59063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (F -> D)))
theorem-size     23
proof            (modus-ponens tm-20 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59063.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (F -> D))), M:tm-20, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59064
in-theory        59064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> (E -> C)))
theorem-size     15
proof            (modus-ponens tm-19 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59064.        ((A -> (B -> A)) and (((C and D) or C) -> (E -> C))), M:tm-19, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59065
in-theory        59065
times-derived    18
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((A and B) or A))
theorem-size     11
proof            (modus-ponens tm-12 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59065.        (((A and B) or A) -> ((A and B) or A)), M:tm-12, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-59066
in-theory        59066
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not (C -> A))) -> (not ((A and B) or A)))
theorem-size     17
proof            (modus-ponens tm-9 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-9 tm-8 tm-3 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59066.        ((((A and B) or A) -> (not (C -> A))) -> (not ((A and B) or A))), M:tm-9, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-59067
in-theory        59067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> ((((B and D) or B) or (A -> B)) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59067.        (((A -> B) -> C) -> ((((B and D) or B) or (A -> B)) -> C)), M:tm-8, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-59068
in-theory        59068
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> (D -> B)))
theorem-size     11
proof            (modus-ponens tm-7 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-7 tm-8 tm-3 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59068.        (A or (((B and C) or B) -> (D -> B))), M:tm-7, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59069
in-theory        59069
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-6 tm-8 tm-3 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59069.        ((((A and B) or A) -> (C -> A)) or D), M:tm-6, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59070
in-theory        59070
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> (D -> B)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59070.        (A -> ((((B and C) or B) -> (D -> B)) and A)), M:tm-5, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59071
in-theory        59071
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> C) -> (((A and B) or A) -> A))
theorem-size     15
proof            (modus-ponens tm-2 tm-711 ((A (or (and Am Bm) Am)) (B Cm) (C Am)))
axioms-used      (tm-2 tm-8 tm-3 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59071.        ((((A and B) or A) -> C) -> (((A and B) or A) -> A)), M:tm-2, m:tm-711, u:((A (or (and Am Bm) Am)) (B Cm) (C Am))
================================================================
tm-name          tm-59072
in-theory        59072
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> (D -> B)))
theorem-size     11
proof            (modus-ponens tm-1 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-59072.        (A -> (((B and C) or B) -> (D -> B))), M:tm-1, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-59073
in-theory        59073
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     47
proof            (modus-ponens tm-708 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59073.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-708, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59074
in-theory        59074
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-665 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59074.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-665, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59075
in-theory        59075
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (E or ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-623 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59075.        ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (E or ((A -> B) -> (A -> C)))), M:tm-623, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59076
in-theory        59076
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-622 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59076.        ((A -> (B -> (C or B))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-622, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59077
in-theory        59077
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59077.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (E -> (F or E))), M:tm-609, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59078
in-theory        59078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-605 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59078.        ((A -> ((B -> (C or B)) and A)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-605, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59079
in-theory        59079
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((E -> (F or E)) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59079.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((E -> (F or E)) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))), M:tm-595, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59080
in-theory        59080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-550 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59080.        (((A -> (B or A)) or C) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-550, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59081
in-theory        59081
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-540 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59081.        ((A or (B -> (C or B))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-540, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59082
in-theory        59082
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-530 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59082.        ((A or (B -> (B or C))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-530, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59083
in-theory        59083
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-520 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59083.        ((A or (B -> (C -> (B and C)))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-520, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59084
in-theory        59084
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-510 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59084.        ((A or ((B and C) -> C)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-510, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59085
in-theory        59085
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-500 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59085.        ((A or ((B and C) -> B)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-500, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59086
in-theory        59086
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-490 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59086.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-490, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59087
in-theory        59087
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-480 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59087.        ((A or (B -> (C -> B))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-480, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59088
in-theory        59088
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (((A -> B) -> (A -> C)) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59088.        ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (((A -> B) -> (A -> C)) or E)), M:tm-470, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59089
in-theory        59089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-469 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59089.        ((A -> (B -> (B or C))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-469, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59090
in-theory        59090
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59090.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (E -> (E or F))), M:tm-456, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59091
in-theory        59091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-453 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59091.        ((A -> ((B -> (B or C)) and A)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-453, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59092
in-theory        59092
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((E -> (E or F)) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59092.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((E -> (E or F)) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))), M:tm-443, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59093
in-theory        59093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-409 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59093.        (((A -> (A or B)) or C) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-409, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59094
in-theory        59094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-400 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59094.        (((A -> (B -> (A and B))) or C) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-400, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59095
in-theory        59095
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-391 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59095.        ((((A and B) -> B) or C) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-391, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59096
in-theory        59096
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-382 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59096.        ((((A and B) -> A) or C) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-382, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59097
in-theory        59097
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-373 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59097.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-373, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59098
in-theory        59098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-364 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59098.        (((A -> (B -> A)) or C) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-364, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59099
in-theory        59099
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (E -> (((A -> B) -> (A -> C)) and E)))
theorem-size     25
proof            (modus-ponens tm-355 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59099.        ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (E -> (((A -> B) -> (A -> C)) and E))), M:tm-355, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59100
in-theory        59100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-354 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59100.        ((A -> (B -> (C -> (B and C)))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-354, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59101
in-theory        59101
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59101.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59102
in-theory        59102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E))))
theorem-size     31
proof            (modus-ponens tm-338 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59102.        (((A -> B) -> (A -> (A and B))) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E)))), M:tm-338, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59103
in-theory        59103
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((((A -> (B -> C)) and D) or (A -> (B -> C))) and ((A -> B) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-328 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59103.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((((A -> (B -> C)) and D) or (A -> (B -> C))) and ((A -> B) -> (A -> C))))), M:tm-328, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59104
in-theory        59104
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((E -> (F -> (E and F))) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59104.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((E -> (F -> (E and F))) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))), M:tm-327, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59105
in-theory        59105
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((E and F) -> F) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59105.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((E and F) -> F) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))), M:tm-326, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59106
in-theory        59106
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((E and F) -> E) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59106.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((E and F) -> E) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))), M:tm-325, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59107
in-theory        59107
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59107.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))), M:tm-324, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59108
in-theory        59108
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((E -> (F -> E)) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59108.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((E -> (F -> E)) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))), M:tm-323, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59109
in-theory        59109
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59109.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((E and F) -> F)), M:tm-322, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59110
in-theory        59110
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59110.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((E and F) -> E)), M:tm-320, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59111
in-theory        59111
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59111.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59112
in-theory        59112
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (((A -> (B -> C)) and D) or (A -> (B -> C)))))
theorem-size     49
proof            (modus-ponens tm-316 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59112.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (((A -> (B -> C)) and D) or (A -> (B -> C))))), M:tm-316, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59113
in-theory        59113
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59113.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (E -> (F -> E))), M:tm-315, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59114
in-theory        59114
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (not ((A -> B) -> (A -> C)))) -> (not (((A -> (B -> C)) and D) or (A -> (B -> C))))))
theorem-size     59
proof            (modus-ponens tm-313 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59114.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (not ((A -> B) -> (A -> C)))) -> (not (((A -> (B -> C)) and D) or (A -> (B -> C)))))), M:tm-313, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59115
in-theory        59115
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((((A -> B) -> (A -> C)) -> E) -> (((((A -> (B -> C)) and D) or (A -> (B -> C))) or ((A -> B) -> (A -> C))) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59115.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((((A -> B) -> (A -> C)) -> E) -> (((((A -> (B -> C)) and D) or (A -> (B -> C))) or ((A -> B) -> (A -> C))) -> E))), M:tm-312, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59116
in-theory        59116
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (E or ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59116.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (E or ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))), M:tm-311, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59117
in-theory        59117
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59117.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) or E)), M:tm-310, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59118
in-theory        59118
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (E -> (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59118.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (E -> (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and E))), M:tm-309, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59119
in-theory        59119
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> B)) -> ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> C))))
theorem-size     57
proof            (modus-ponens tm-306 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> Am Bm)) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59119.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> B)) -> ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> C)))), M:tm-306, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> Am Bm)) (C (-> Am Cm)))
================================================================
tm-name          tm-59120
in-theory        59120
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (E -> ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59120.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and (E -> ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))), M:tm-305, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59121
in-theory        59121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-303 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59121.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-303, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59122
in-theory        59122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-270 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59122.        ((A -> (((B and C) -> C) and A)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-270, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59123
in-theory        59123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-239 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59123.        ((A -> (((B and C) -> B) and A)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-239, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59124
in-theory        59124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-210 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59124.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-210, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59125
in-theory        59125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-183 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59125.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-183, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59126
in-theory        59126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-157 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59126.        ((A -> ((B and C) -> C)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-157, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59127
in-theory        59127
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-147 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59127.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-147, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59128
in-theory        59128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-134 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59128.        ((A -> ((B and C) -> B)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-134, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59129
in-theory        59129
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-125 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59129.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-125, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59130
in-theory        59130
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C)))
theorem-size     25
proof            (modus-ponens tm-114 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> Am Bm)) (C Am) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59130.        ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-114, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> Am Bm)) (C Am) (D Cm))
================================================================
tm-name          tm-59131
in-theory        59131
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-113 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59131.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> (F -> G)) and H) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-113, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59132
in-theory        59132
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-105 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59132.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-105, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59133
in-theory        59133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-95 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59133.        (((A -> B) -> (A -> A)) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E)))), M:tm-95, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59134
in-theory        59134
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (E -> ((A -> B) -> (A -> C))))
theorem-size     23
proof            (modus-ponens tm-84 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59134.        ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (E -> ((A -> B) -> (A -> C)))), M:tm-84, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59135
in-theory        59135
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-83 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59135.        ((A -> (B -> (C -> B))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-83, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59136
in-theory        59136
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> (C -> D)) and E) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))
theorem-size     27
proof            (modus-ponens tm-76 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59136.        (((not (not A)) -> A) and ((((B -> (C -> D)) and E) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))), M:tm-76, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59137
in-theory        59137
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> (B -> C)) and D) or (A -> (B -> C))))) or (((A -> (B -> C)) and D) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C)))
theorem-size     37
proof            (modus-ponens tm-73 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-8 tm-10 tm-3 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59137.        (((not (not (((A -> (B -> C)) and D) or (A -> (B -> C))))) or (((A -> (B -> C)) and D) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C))), M:tm-73, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59138
in-theory        59138
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-69 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59138.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E)))), M:tm-69, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59139
in-theory        59139
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-54 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59139.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-54, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59140
in-theory        59140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((A -> (B -> C)) and D) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C)))
theorem-size     27
proof            (modus-ponens tm-50 tm-712 ((A (and (-> Am (-> Bm Cm)) Dm)) (B (-> Am (-> Bm Cm))) (C (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-8 tm-7 tm-3 tm-2)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59140.        (((A -> (B -> C)) or (((A -> (B -> C)) and D) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C))), M:tm-50, m:tm-712, u:((A (and (-> Am (-> Bm Cm)) Dm)) (B (-> Am (-> Bm Cm))) (C (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59141
in-theory        59141
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and D) or (((A -> (B -> C)) and D) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C)))
theorem-size     29
proof            (modus-ponens tm-49 tm-712 ((A (and (-> Am (-> Bm Cm)) Dm)) (B (-> Am (-> Bm Cm))) (C (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-8 tm-6 tm-3 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59141.        ((((A -> (B -> C)) and D) or (((A -> (B -> C)) and D) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C))), M:tm-49, m:tm-712, u:((A (and (-> Am (-> Bm Cm)) Dm)) (B (-> Am (-> Bm Cm))) (C (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59142
in-theory        59142
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) and E) or (B -> (C -> D)))) or (((B -> (C -> D)) and E) or (B -> (C -> D)))) -> ((B -> C) -> (B -> D)))
theorem-size     37
proof            (modus-ponens tm-47 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-8 tm-4 tm-3 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59142.        (((A and (((B -> (C -> D)) and E) or (B -> (C -> D)))) or (((B -> (C -> D)) and E) or (B -> (C -> D)))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59143
in-theory        59143
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) and D) or (A -> (B -> C))) and E) or (((A -> (B -> C)) and D) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C)))
theorem-size     37
proof            (modus-ponens tm-46 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59143.        ((((((A -> (B -> C)) and D) or (A -> (B -> C))) and E) or (((A -> (B -> C)) and D) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59144
in-theory        59144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-42 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59144.        ((A -> (B or A)) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59145
in-theory        59145
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-32 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59145.        ((A -> (A or B)) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59146
in-theory        59146
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((((A -> (B -> C)) and D) or (A -> (B -> C))) and ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-24 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59146.        ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((((A -> (B -> C)) and D) or (A -> (B -> C))) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59147
in-theory        59147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E))))
theorem-size     29
proof            (modus-ponens tm-23 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59147.        ((A -> (B -> (A and B))) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59148
in-theory        59148
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-22 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59148.        (((A and B) -> B) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59149
in-theory        59149
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-21 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59149.        (((A and B) -> A) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59150
in-theory        59150
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-20 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59150.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59151
in-theory        59151
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-19 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59151.        ((A -> (B -> A)) and ((((C -> (D -> E)) and F) or (C -> (D -> E))) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59152
in-theory        59152
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (((A -> (B -> C)) and D) or (A -> (B -> C))))
theorem-size     27
proof            (modus-ponens tm-12 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59152.        ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (((A -> (B -> C)) and D) or (A -> (B -> C)))), M:tm-12, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59153
in-theory        59153
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (not ((A -> B) -> (A -> C)))) -> (not (((A -> (B -> C)) and D) or (A -> (B -> C)))))
theorem-size     37
proof            (modus-ponens tm-9 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-9 tm-8 tm-3 tm-2)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59153.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (not ((A -> B) -> (A -> C)))) -> (not (((A -> (B -> C)) and D) or (A -> (B -> C))))), M:tm-9, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59154
in-theory        59154
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> (((((A -> (B -> C)) and E) or (A -> (B -> C))) or ((A -> B) -> (A -> C))) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59154.        ((((A -> B) -> (A -> C)) -> D) -> (((((A -> (B -> C)) and E) or (A -> (B -> C))) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-59155
in-theory        59155
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> (C -> D)) and E) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))
theorem-size     23
proof            (modus-ponens tm-7 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-7 tm-8 tm-3 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59155.        (A or ((((B -> (C -> D)) and E) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59156
in-theory        59156
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-6 tm-8 tm-3 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59156.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) or E), M:tm-6, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59157
in-theory        59157
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> D)) and E) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59157.        (A -> (((((B -> (C -> D)) and E) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59158
in-theory        59158
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> B)) -> ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> C)))
theorem-size     35
proof            (modus-ponens tm-2 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> Am Bm)) (C (-> Am Cm))))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59158.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> B)) -> ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> C))), M:tm-2, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> Am Bm)) (C (-> Am Cm)))
================================================================
tm-name          tm-59159
in-theory        59159
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) and E) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))
theorem-size     23
proof            (modus-ponens tm-1 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-1 tm-8 tm-3 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-59159.        (A -> ((((B -> (C -> D)) and E) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-59160
in-theory        59160
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and F) and G) or (E and F)) -> E))
theorem-size     37
proof            (modus-ponens tm-708 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59160.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and F) and G) or (E and F)) -> E)), M:tm-708, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59161
in-theory        59161
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     25
proof            (modus-ponens tm-665 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59161.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-665, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59162
in-theory        59162
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> (D or A))
theorem-size     13
proof            (modus-ponens tm-623 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59162.        ((((A and B) and C) or (A and B)) -> (D or A)), M:tm-623, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59163
in-theory        59163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-622 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59163.        ((A -> (B -> (C or B))) and ((((D and E) and F) or (D and E)) -> D)), M:tm-622, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59164
in-theory        59164
times-derived    1
----------------------------------------------------------------
theorem          (not ((((not (A -> (B or A))) and C) and D) or ((not (A -> (B or A))) and C)))
theorem-size     20
proof            (modus-ponens tm-618 tm-713 ((A (or (and (and (not (-> B (or C B))) Bm) Cm) (and (not (-> B (or C B))) Bm))) (Am (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-8 tm-3)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59164.        (not ((((not (A -> (B or A))) and C) and D) or ((not (A -> (B or A))) and C))), M:tm-618, m:tm-713, u:((A (or (and (and (not (-> B (or C B))) Bm) Cm) (and (not (-> B (or C B))) Bm))) (Am (not (-> B (or C B)))))
================================================================
tm-name          tm-59165
in-theory        59165
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59165.        (((((A and B) and C) or (A and B)) -> A) and (D -> (E or D))), M:tm-609, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59166
in-theory        59166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     21
proof            (modus-ponens tm-605 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59166.        ((A -> ((B -> (C or B)) and A)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-605, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59167
in-theory        59167
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and ((D -> (E or D)) and ((((A and B) and C) or (A and B)) -> A)))
theorem-size     29
proof            (modus-ponens tm-595 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59167.        (((((A and B) and C) or (A and B)) -> A) and ((D -> (E or D)) and ((((A and B) and C) or (A and B)) -> A))), M:tm-595, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59168
in-theory        59168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-550 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59168.        (((A -> (B or A)) or C) and ((((D and E) and F) or (D and E)) -> D)), M:tm-550, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59169
in-theory        59169
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-540 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59169.        ((A or (B -> (C or B))) and ((((D and E) and F) or (D and E)) -> D)), M:tm-540, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59170
in-theory        59170
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-530 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59170.        ((A or (B -> (B or C))) and ((((D and E) and F) or (D and E)) -> D)), M:tm-530, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59171
in-theory        59171
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     21
proof            (modus-ponens tm-520 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59171.        ((A or (B -> (C -> (B and C)))) and ((((D and E) and F) or (D and E)) -> D)), M:tm-520, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59172
in-theory        59172
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-510 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59172.        ((A or ((B and C) -> C)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-510, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59173
in-theory        59173
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-500 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59173.        ((A or ((B and C) -> B)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-500, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59174
in-theory        59174
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) and G) or (E and F)) -> E))
theorem-size     27
proof            (modus-ponens tm-490 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59174.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) and G) or (E and F)) -> E)), M:tm-490, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59175
in-theory        59175
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-480 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59175.        ((A or (B -> (C -> B))) and ((((D and E) and F) or (D and E)) -> D)), M:tm-480, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59176
in-theory        59176
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> (A or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59176.        ((((A and B) and C) or (A and B)) -> (A or D)), M:tm-470, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59177
in-theory        59177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-469 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59177.        ((A -> (B -> (B or C))) and ((((D and E) and F) or (D and E)) -> D)), M:tm-469, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59178
in-theory        59178
times-derived    1
----------------------------------------------------------------
theorem          (not ((((not (A -> (A or B))) and C) and D) or ((not (A -> (A or B))) and C)))
theorem-size     20
proof            (modus-ponens tm-465 tm-713 ((A (or (and (and (not (-> B (or B C))) Bm) Cm) (and (not (-> B (or B C))) Bm))) (Am (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-8 tm-3)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59178.        (not ((((not (A -> (A or B))) and C) and D) or ((not (A -> (A or B))) and C))), M:tm-465, m:tm-713, u:((A (or (and (and (not (-> B (or B C))) Bm) Cm) (and (not (-> B (or B C))) Bm))) (Am (not (-> B (or B C)))))
================================================================
tm-name          tm-59179
in-theory        59179
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59179.        (((((A and B) and C) or (A and B)) -> A) and (D -> (D or E))), M:tm-456, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59180
in-theory        59180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     21
proof            (modus-ponens tm-453 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59180.        ((A -> ((B -> (B or C)) and A)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-453, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59181
in-theory        59181
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and ((D -> (D or E)) and ((((A and B) and C) or (A and B)) -> A)))
theorem-size     29
proof            (modus-ponens tm-443 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59181.        (((((A and B) and C) or (A and B)) -> A) and ((D -> (D or E)) and ((((A and B) and C) or (A and B)) -> A))), M:tm-443, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59182
in-theory        59182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-409 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59182.        (((A -> (A or B)) or C) and ((((D and E) and F) or (D and E)) -> D)), M:tm-409, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59183
in-theory        59183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     21
proof            (modus-ponens tm-400 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59183.        (((A -> (B -> (A and B))) or C) and ((((D and E) and F) or (D and E)) -> D)), M:tm-400, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59184
in-theory        59184
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-391 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59184.        ((((A and B) -> B) or C) and ((((D and E) and F) or (D and E)) -> D)), M:tm-391, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59185
in-theory        59185
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-382 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59185.        ((((A and B) -> A) or C) and ((((D and E) and F) or (D and E)) -> D)), M:tm-382, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59186
in-theory        59186
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and F) and G) or (E and F)) -> E))
theorem-size     27
proof            (modus-ponens tm-373 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59186.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and F) and G) or (E and F)) -> E)), M:tm-373, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59187
in-theory        59187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-364 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59187.        (((A -> (B -> A)) or C) and ((((D and E) and F) or (D and E)) -> D)), M:tm-364, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59188
in-theory        59188
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> (D -> (A and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59188.        ((((A and B) and C) or (A and B)) -> (D -> (A and D))), M:tm-355, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59189
in-theory        59189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     21
proof            (modus-ponens tm-354 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59189.        ((A -> (B -> (C -> (B and C)))) and ((((D and E) and F) or (D and E)) -> D)), M:tm-354, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59190
in-theory        59190
times-derived    1
----------------------------------------------------------------
theorem          (not ((((not (A -> (B -> (A and B)))) and C) and D) or ((not (A -> (B -> (A and B)))) and C)))
theorem-size     24
proof            (modus-ponens tm-350 tm-713 ((A (or (and (and (not (-> B (-> C (and B C)))) Bm) Cm) (and (not (-> B (-> C (and B C)))) Bm))) (Am (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-8 tm-3)
proof-size       114
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59190.        (not ((((not (A -> (B -> (A and B)))) and C) and D) or ((not (A -> (B -> (A and B)))) and C))), M:tm-350, m:tm-713, u:((A (or (and (and (not (-> B (-> C (and B C)))) Bm) Cm) (and (not (-> B (-> C (and B C)))) Bm))) (Am (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-59191
in-theory        59191
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59191.        (((((A and B) and C) or (A and B)) -> A) and (D -> (E -> (D and E)))), M:tm-341, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59192
in-theory        59192
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C and D) and E) or (C and D)) -> C))
theorem-size     21
proof            (modus-ponens tm-338 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59192.        (((A -> B) -> (A -> (A and B))) and ((((C and D) and E) or (C and D)) -> C)), M:tm-338, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59193
in-theory        59193
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and ((((A and B) and C) or (A and B)) -> ((((A and B) and C) or (A and B)) and A)))
theorem-size     33
proof            (modus-ponens tm-328 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59193.        (((((A and B) and C) or (A and B)) -> A) and ((((A and B) and C) or (A and B)) -> ((((A and B) and C) or (A and B)) and A))), M:tm-328, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59194
in-theory        59194
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and ((D -> (E -> (D and E))) and ((((A and B) and C) or (A and B)) -> A)))
theorem-size     31
proof            (modus-ponens tm-327 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59194.        (((((A and B) and C) or (A and B)) -> A) and ((D -> (E -> (D and E))) and ((((A and B) and C) or (A and B)) -> A))), M:tm-327, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59195
in-theory        59195
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and (((D and E) -> E) and ((((A and B) and C) or (A and B)) -> A)))
theorem-size     29
proof            (modus-ponens tm-326 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59195.        (((((A and B) and C) or (A and B)) -> A) and (((D and E) -> E) and ((((A and B) and C) or (A and B)) -> A))), M:tm-326, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59196
in-theory        59196
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and (((D and E) -> D) and ((((A and B) and C) or (A and B)) -> A)))
theorem-size     29
proof            (modus-ponens tm-325 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59196.        (((((A and B) and C) or (A and B)) -> A) and (((D and E) -> D) and ((((A and B) and C) or (A and B)) -> A))), M:tm-325, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59197
in-theory        59197
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A and B) and C) or (A and B)) -> A)))
theorem-size     37
proof            (modus-ponens tm-324 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59197.        (((((A and B) and C) or (A and B)) -> A) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A and B) and C) or (A and B)) -> A))), M:tm-324, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59198
in-theory        59198
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and ((D -> (E -> D)) and ((((A and B) and C) or (A and B)) -> A)))
theorem-size     29
proof            (modus-ponens tm-323 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59198.        (((((A and B) and C) or (A and B)) -> A) and ((D -> (E -> D)) and ((((A and B) and C) or (A and B)) -> A))), M:tm-323, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59199
in-theory        59199
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59199.        (((((A and B) and C) or (A and B)) -> A) and ((D and E) -> E)), M:tm-322, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59200
in-theory        59200
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59200.        (((((A and B) and C) or (A and B)) -> A) and ((D and E) -> D)), M:tm-320, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59201
in-theory        59201
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59201.        (((((A and B) and C) or (A and B)) -> A) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59202
in-theory        59202
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and ((((A and B) and C) or (A and B)) -> (((A and B) and C) or (A and B))))
theorem-size     31
proof            (modus-ponens tm-316 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59202.        (((((A and B) and C) or (A and B)) -> A) and ((((A and B) and C) or (A and B)) -> (((A and B) and C) or (A and B)))), M:tm-316, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59203
in-theory        59203
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59203.        (((((A and B) and C) or (A and B)) -> A) and (D -> (E -> D))), M:tm-315, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59204
in-theory        59204
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and (((((A and B) and C) or (A and B)) -> (not A)) -> (not (((A and B) and C) or (A and B)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59204.        (((((A and B) and C) or (A and B)) -> A) and (((((A and B) and C) or (A and B)) -> (not A)) -> (not (((A and B) and C) or (A and B))))), M:tm-313, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59205
in-theory        59205
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and ((A -> D) -> (((((A and B) and C) or (A and B)) or A) -> D)))
theorem-size     29
proof            (modus-ponens tm-312 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59205.        (((((A and B) and C) or (A and B)) -> A) and ((A -> D) -> (((((A and B) and C) or (A and B)) or A) -> D))), M:tm-312, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59206
in-theory        59206
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and (D or ((((A and B) and C) or (A and B)) -> A)))
theorem-size     25
proof            (modus-ponens tm-311 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59206.        (((((A and B) and C) or (A and B)) -> A) and (D or ((((A and B) and C) or (A and B)) -> A))), M:tm-311, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59207
in-theory        59207
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and (((((A and B) and C) or (A and B)) -> A) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59207.        (((((A and B) and C) or (A and B)) -> A) and (((((A and B) and C) or (A and B)) -> A) or D)), M:tm-310, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59208
in-theory        59208
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and (D -> (((((A and B) and C) or (A and B)) -> A) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59208.        (((((A and B) and C) or (A and B)) -> A) and (D -> (((((A and B) and C) or (A and B)) -> A) and D))), M:tm-309, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59209
in-theory        59209
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) and D) or ((A -> B) and C)) -> (A -> B)) and ((((((A -> B) and C) and D) or ((A -> B) and C)) -> A) -> (((((A -> B) and C) and D) or ((A -> B) and C)) -> B)))
theorem-size     49
proof            (modus-ponens tm-306 tm-713 ((A (or (and (and (-> B C) Bm) Cm) (and (-> B C) Bm))) (Am (-> B C))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59209.        ((((((A -> B) and C) and D) or ((A -> B) and C)) -> (A -> B)) and ((((((A -> B) and C) and D) or ((A -> B) and C)) -> A) -> (((((A -> B) and C) and D) or ((A -> B) and C)) -> B))), M:tm-306, m:tm-713, u:((A (or (and (and (-> B C) Bm) Cm) (and (-> B C) Bm))) (Am (-> B C)))
================================================================
tm-name          tm-59210
in-theory        59210
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and (D -> ((((A and B) and C) or (A and B)) -> A)))
theorem-size     25
proof            (modus-ponens tm-305 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59210.        (((((A and B) and C) or (A and B)) -> A) and (D -> ((((A and B) and C) or (A and B)) -> A))), M:tm-305, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59211
in-theory        59211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     23
proof            (modus-ponens tm-303 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59211.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-303, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59212
in-theory        59212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     21
proof            (modus-ponens tm-270 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59212.        ((A -> (((B and C) -> C) and A)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-270, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59213
in-theory        59213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     21
proof            (modus-ponens tm-239 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59213.        ((A -> (((B and C) -> B) and A)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-239, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59214
in-theory        59214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and F) and G) or (E and F)) -> E))
theorem-size     29
proof            (modus-ponens tm-210 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59214.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and F) and G) or (E and F)) -> E)), M:tm-210, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59215
in-theory        59215
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     21
proof            (modus-ponens tm-183 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59215.        ((A -> ((B -> (C -> B)) and A)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-183, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59216
in-theory        59216
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) and D) or ((A and B) and C)) -> B)
theorem-size     15
proof            (modus-ponens tm-158 tm-713 ((A (or (and (and (and B C) Bm) Cm) (and (and B C) Bm))) (Am (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59216.        (((((A and B) and C) and D) or ((A and B) and C)) -> B), M:tm-158, m:tm-713, u:((A (or (and (and (and B C) Bm) Cm) (and (and B C) Bm))) (Am (and B C)))
================================================================
tm-name          tm-59217
in-theory        59217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-157 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59217.        ((A -> ((B and C) -> C)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-157, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59218
in-theory        59218
times-derived    1
----------------------------------------------------------------
theorem          (not ((((not ((A and B) -> B)) and C) and D) or ((not ((A and B) -> B)) and C)))
theorem-size     20
proof            (modus-ponens tm-153 tm-713 ((A (or (and (and (not (-> (and B C) C)) Bm) Cm) (and (not (-> (and B C) C)) Bm))) (Am (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-8 tm-3)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59218.        (not ((((not ((A and B) -> B)) and C) and D) or ((not ((A and B) -> B)) and C))), M:tm-153, m:tm-713, u:((A (or (and (and (not (-> (and B C) C)) Bm) Cm) (and (not (-> (and B C) C)) Bm))) (Am (not (-> (and B C) C))))
================================================================
tm-name          tm-59219
in-theory        59219
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     27
proof            (modus-ponens tm-147 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59219.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-147, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59220
in-theory        59220
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) and D) or ((A and B) and C)) -> A)
theorem-size     15
proof            (modus-ponens tm-135 tm-713 ((A (or (and (and (and B C) Bm) Cm) (and (and B C) Bm))) (Am (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-8)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59220.        (((((A and B) and C) and D) or ((A and B) and C)) -> A), M:tm-135, m:tm-713, u:((A (or (and (and (and B C) Bm) Cm) (and (and B C) Bm))) (Am (and B C)))
================================================================
tm-name          tm-59221
in-theory        59221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-134 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59221.        ((A -> ((B and C) -> B)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-134, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59222
in-theory        59222
times-derived    1
----------------------------------------------------------------
theorem          (not ((((not ((A and B) -> A)) and C) and D) or ((not ((A and B) -> A)) and C)))
theorem-size     20
proof            (modus-ponens tm-130 tm-713 ((A (or (and (and (not (-> (and B C) B)) Bm) Cm) (and (not (-> (and B C) B)) Bm))) (Am (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-8)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59222.        (not ((((not ((A and B) -> A)) and C) and D) or ((not ((A and B) -> A)) and C))), M:tm-130, m:tm-713, u:((A (or (and (and (not (-> (and B C) B)) Bm) Cm) (and (not (-> (and B C) B)) Bm))) (Am (not (-> (and B C) B))))
================================================================
tm-name          tm-59223
in-theory        59223
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     27
proof            (modus-ponens tm-125 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59223.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-125, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59224
in-theory        59224
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) and E) or ((A -> (B -> C)) and D)) -> ((A -> B) -> (A -> C)))
theorem-size     25
proof            (modus-ponens tm-114 tm-713 ((A (or (and (and (-> B (-> C D)) Bm) Cm) (and (-> B (-> C D)) Bm))) (Am (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59224.        (((((A -> (B -> C)) and D) and E) or ((A -> (B -> C)) and D)) -> ((A -> B) -> (A -> C))), M:tm-114, m:tm-713, u:((A (or (and (and (-> B (-> C D)) Bm) Cm) (and (-> B (-> C D)) Bm))) (Am (-> B (-> C D))))
================================================================
tm-name          tm-59225
in-theory        59225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) and G) or (E and F)) -> E))
theorem-size     27
proof            (modus-ponens tm-113 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59225.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) and G) or (E and F)) -> E)), M:tm-113, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59226
in-theory        59226
times-derived    1
----------------------------------------------------------------
theorem          (not ((((not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and D) and E) or ((not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and D)))
theorem-size     36
proof            (modus-ponens tm-109 tm-713 ((A (or (and (and (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))) Bm) Cm) (and (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))) Bm))) (Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-8 tm-3)
proof-size       144
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59226.        (not ((((not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and D) and E) or ((not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) and D))), M:tm-109, m:tm-713, u:((A (or (and (and (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))) Bm) Cm) (and (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))) Bm))) (Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-59227
in-theory        59227
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     31
proof            (modus-ponens tm-105 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59227.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and E) and F) or (D and E)) -> D)), M:tm-105, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59228
in-theory        59228
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C and D) and E) or (C and D)) -> C))
theorem-size     19
proof            (modus-ponens tm-95 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59228.        (((A -> B) -> (A -> A)) and ((((C and D) and E) or (C and D)) -> C)), M:tm-95, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59229
in-theory        59229
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) and D) or ((A -> B) and C)) -> (A -> B))
theorem-size     17
proof            (modus-ponens tm-87 tm-713 ((A (or (and (and (-> B C) Bm) Cm) (and (-> B C) Bm))) (Am (-> B C))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59229.        (((((A -> B) and C) and D) or ((A -> B) and C)) -> (A -> B)), M:tm-87, m:tm-713, u:((A (or (and (and (-> B C) Bm) Cm) (and (-> B C) Bm))) (Am (-> B C)))
================================================================
tm-name          tm-59230
in-theory        59230
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> (D -> A))
theorem-size     13
proof            (modus-ponens tm-84 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59230.        ((((A and B) and C) or (A and B)) -> (D -> A)), M:tm-84, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59231
in-theory        59231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-83 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59231.        ((A -> (B -> (C -> B))) and ((((D and E) and F) or (D and E)) -> D)), M:tm-83, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59232
in-theory        59232
times-derived    1
----------------------------------------------------------------
theorem          (not ((((not (A -> (B -> A))) and C) and D) or ((not (A -> (B -> A))) and C)))
theorem-size     20
proof            (modus-ponens tm-79 tm-713 ((A (or (and (and (not (-> B (-> C B))) Bm) Cm) (and (not (-> B (-> C B))) Bm))) (Am (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-8 tm-3)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59232.        (not ((((not (A -> (B -> A))) and C) and D) or ((not (A -> (B -> A))) and C))), M:tm-79, m:tm-713, u:((A (or (and (and (not (-> B (-> C B))) Bm) Cm) (and (not (-> B (-> C B))) Bm))) (Am (not (-> B (-> C B)))))
================================================================
tm-name          tm-59233
in-theory        59233
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B and C) and D) or (B and C)) -> B))
theorem-size     17
proof            (modus-ponens tm-76 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59233.        (((not (not A)) -> A) and ((((B and C) and D) or (B and C)) -> B)), M:tm-76, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59234
in-theory        59234
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A and B) and C) or (A and B)))) or (((A and B) and C) or (A and B))) -> A)
theorem-size     23
proof            (modus-ponens tm-73 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-8 tm-10 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59234.        (((not (not (((A and B) and C) or (A and B)))) or (((A and B) and C) or (A and B))) -> A), M:tm-73, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59235
in-theory        59235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and D) and E) or (C and D)) -> C))
theorem-size     23
proof            (modus-ponens tm-69 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59235.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and D) and E) or (C and D)) -> C)), M:tm-69, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59236
in-theory        59236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     25
proof            (modus-ponens tm-54 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59236.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and E) and F) or (D and E)) -> D)), M:tm-54, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59237
in-theory        59237
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or (((A and B) and C) or (A and B))) -> A)
theorem-size     15
proof            (modus-ponens tm-50 tm-713 ((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Am)))
axioms-used      (tm-8 tm-7 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59237.        (((A and B) or (((A and B) and C) or (A and B))) -> A), M:tm-50, m:tm-713, u:((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Am))
================================================================
tm-name          tm-59238
in-theory        59238
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (((A and B) and C) or (A and B))) -> A)
theorem-size     17
proof            (modus-ponens tm-49 tm-713 ((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Am)))
axioms-used      (tm-8 tm-6 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59238.        ((((A and B) and C) or (((A and B) and C) or (A and B))) -> A), M:tm-49, m:tm-713, u:((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Am))
================================================================
tm-name          tm-59239
in-theory        59239
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) and D) or (B and C))) or (((B and C) and D) or (B and C))) -> B)
theorem-size     23
proof            (modus-ponens tm-47 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-8 tm-4 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59239.        (((A and (((B and C) and D) or (B and C))) or (((B and C) and D) or (B and C))) -> B), M:tm-47, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59240
in-theory        59240
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) and C) or (A and B)) and D) or (((A and B) and C) or (A and B))) -> A)
theorem-size     23
proof            (modus-ponens tm-46 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-8 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59240.        ((((((A and B) and C) or (A and B)) and D) or (((A and B) and C) or (A and B))) -> A), M:tm-46, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59241
in-theory        59241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C and D) and E) or (C and D)) -> C))
theorem-size     17
proof            (modus-ponens tm-42 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59241.        ((A -> (B or A)) and ((((C and D) and E) or (C and D)) -> C)), M:tm-42, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59242
in-theory        59242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C and D) and E) or (C and D)) -> C))
theorem-size     17
proof            (modus-ponens tm-32 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59242.        ((A -> (A or B)) and ((((C and D) and E) or (C and D)) -> C)), M:tm-32, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59243
in-theory        59243
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> ((((A and B) and C) or (A and B)) and A))
theorem-size     21
proof            (modus-ponens tm-24 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59243.        ((((A and B) and C) or (A and B)) -> ((((A and B) and C) or (A and B)) and A)), M:tm-24, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59244
in-theory        59244
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C and D) and E) or (C and D)) -> C))
theorem-size     19
proof            (modus-ponens tm-23 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59244.        ((A -> (B -> (A and B))) and ((((C and D) and E) or (C and D)) -> C)), M:tm-23, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59245
in-theory        59245
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C and D) and E) or (C and D)) -> C))
theorem-size     17
proof            (modus-ponens tm-22 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59245.        (((A and B) -> B) and ((((C and D) and E) or (C and D)) -> C)), M:tm-22, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59246
in-theory        59246
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C and D) and E) or (C and D)) -> C))
theorem-size     17
proof            (modus-ponens tm-21 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59246.        (((A and B) -> A) and ((((C and D) and E) or (C and D)) -> C)), M:tm-21, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59247
in-theory        59247
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     25
proof            (modus-ponens tm-20 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59247.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and E) and F) or (D and E)) -> D)), M:tm-20, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59248
in-theory        59248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C and D) and E) or (C and D)) -> C))
theorem-size     17
proof            (modus-ponens tm-19 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59248.        ((A -> (B -> A)) and ((((C and D) and E) or (C and D)) -> C)), M:tm-19, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59249
in-theory        59249
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> (((A and B) and C) or (A and B)))
theorem-size     19
proof            (modus-ponens tm-12 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59249.        ((((A and B) and C) or (A and B)) -> (((A and B) and C) or (A and B))), M:tm-12, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59250
in-theory        59250
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> (not A)) -> (not (((A and B) and C) or (A and B))))
theorem-size     23
proof            (modus-ponens tm-9 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-9 tm-8 tm-3)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59250.        (((((A and B) and C) or (A and B)) -> (not A)) -> (not (((A and B) and C) or (A and B)))), M:tm-9, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59251
in-theory        59251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((((A and C) and D) or (A and C)) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-8 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59251.        ((A -> B) -> (((((A and C) and D) or (A and C)) or A) -> B)), M:tm-8, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-59252
in-theory        59252
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B and C) and D) or (B and C)) -> B))
theorem-size     13
proof            (modus-ponens tm-7 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-7 tm-8 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59252.        (A or ((((B and C) and D) or (B and C)) -> B)), M:tm-7, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59253
in-theory        59253
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-6 tm-8 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59253.        (((((A and B) and C) or (A and B)) -> A) or D), M:tm-6, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59254
in-theory        59254
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B and C) and D) or (B and C)) -> B) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59254.        (A -> (((((B and C) and D) or (B and C)) -> B) and A)), M:tm-5, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59255
in-theory        59255
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) and D) or ((A -> B) and C)) -> A) -> (((((A -> B) and C) and D) or ((A -> B) and C)) -> B))
theorem-size     31
proof            (modus-ponens tm-2 tm-713 ((A (or (and (and (-> B C) Bm) Cm) (and (-> B C) Bm))) (Am (-> B C))))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59255.        ((((((A -> B) and C) and D) or ((A -> B) and C)) -> A) -> (((((A -> B) and C) and D) or ((A -> B) and C)) -> B)), M:tm-2, m:tm-713, u:((A (or (and (and (-> B C) Bm) Cm) (and (-> B C) Bm))) (Am (-> B C)))
================================================================
tm-name          tm-59256
in-theory        59256
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) and D) or (B and C)) -> B))
theorem-size     13
proof            (modus-ponens tm-1 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-59256.        (A -> ((((B and C) and D) or (B and C)) -> B)), M:tm-1, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-59257
in-theory        59257
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and F) and G) or (E and F)) -> F))
theorem-size     37
proof            (modus-ponens tm-708 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-4)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59257.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E and F) and G) or (E and F)) -> F)), M:tm-708, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59258
in-theory        59258
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     25
proof            (modus-ponens tm-665 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59258.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-665, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59259
in-theory        59259
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> (D or B))
theorem-size     13
proof            (modus-ponens tm-623 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59259.        ((((A and B) and C) or (A and B)) -> (D or B)), M:tm-623, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-59260
in-theory        59260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-622 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59260.        ((A -> (B -> (C or B))) and ((((D and E) and F) or (D and E)) -> E)), M:tm-622, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59261
in-theory        59261
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and (not (B -> (C or B)))) and D) or (A and (not (B -> (C or B))))))
theorem-size     20
proof            (modus-ponens tm-618 tm-714 ((A (or (and (and Am (not (-> B (or C B)))) Cm) (and Am (not (-> B (or C B)))))) (Bm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-8 tm-3 tm-4)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59261.        (not (((A and (not (B -> (C or B)))) and D) or (A and (not (B -> (C or B)))))), M:tm-618, m:tm-714, u:((A (or (and (and Am (not (-> B (or C B)))) Cm) (and Am (not (-> B (or C B)))))) (Bm (not (-> B (or C B)))))
================================================================
tm-name          tm-59262
in-theory        59262
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59262.        (((((A and B) and C) or (A and B)) -> B) and (D -> (E or D))), M:tm-609, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59263
in-theory        59263
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     21
proof            (modus-ponens tm-605 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59263.        ((A -> ((B -> (C or B)) and A)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-605, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59264
in-theory        59264
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and ((D -> (E or D)) and ((((A and B) and C) or (A and B)) -> B)))
theorem-size     29
proof            (modus-ponens tm-595 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59264.        (((((A and B) and C) or (A and B)) -> B) and ((D -> (E or D)) and ((((A and B) and C) or (A and B)) -> B))), M:tm-595, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59265
in-theory        59265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-550 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59265.        (((A -> (B or A)) or C) and ((((D and E) and F) or (D and E)) -> E)), M:tm-550, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59266
in-theory        59266
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-540 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59266.        ((A or (B -> (C or B))) and ((((D and E) and F) or (D and E)) -> E)), M:tm-540, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59267
in-theory        59267
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-530 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59267.        ((A or (B -> (B or C))) and ((((D and E) and F) or (D and E)) -> E)), M:tm-530, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59268
in-theory        59268
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     21
proof            (modus-ponens tm-520 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59268.        ((A or (B -> (C -> (B and C)))) and ((((D and E) and F) or (D and E)) -> E)), M:tm-520, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59269
in-theory        59269
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-510 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59269.        ((A or ((B and C) -> C)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-510, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59270
in-theory        59270
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-500 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59270.        ((A or ((B and C) -> B)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-500, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59271
in-theory        59271
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) and G) or (E and F)) -> F))
theorem-size     27
proof            (modus-ponens tm-490 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59271.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) and G) or (E and F)) -> F)), M:tm-490, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59272
in-theory        59272
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-480 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59272.        ((A or (B -> (C -> B))) and ((((D and E) and F) or (D and E)) -> E)), M:tm-480, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59273
in-theory        59273
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> (B or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59273.        ((((A and B) and C) or (A and B)) -> (B or D)), M:tm-470, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-59274
in-theory        59274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-469 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59274.        ((A -> (B -> (B or C))) and ((((D and E) and F) or (D and E)) -> E)), M:tm-469, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59275
in-theory        59275
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and (not (B -> (B or C)))) and D) or (A and (not (B -> (B or C))))))
theorem-size     20
proof            (modus-ponens tm-465 tm-714 ((A (or (and (and Am (not (-> B (or B C)))) Cm) (and Am (not (-> B (or B C)))))) (Bm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-8 tm-3 tm-4)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59275.        (not (((A and (not (B -> (B or C)))) and D) or (A and (not (B -> (B or C)))))), M:tm-465, m:tm-714, u:((A (or (and (and Am (not (-> B (or B C)))) Cm) (and Am (not (-> B (or B C)))))) (Bm (not (-> B (or B C)))))
================================================================
tm-name          tm-59276
in-theory        59276
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59276.        (((((A and B) and C) or (A and B)) -> B) and (D -> (D or E))), M:tm-456, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59277
in-theory        59277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     21
proof            (modus-ponens tm-453 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59277.        ((A -> ((B -> (B or C)) and A)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-453, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59278
in-theory        59278
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and ((D -> (D or E)) and ((((A and B) and C) or (A and B)) -> B)))
theorem-size     29
proof            (modus-ponens tm-443 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59278.        (((((A and B) and C) or (A and B)) -> B) and ((D -> (D or E)) and ((((A and B) and C) or (A and B)) -> B))), M:tm-443, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59279
in-theory        59279
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-409 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59279.        (((A -> (A or B)) or C) and ((((D and E) and F) or (D and E)) -> E)), M:tm-409, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59280
in-theory        59280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     21
proof            (modus-ponens tm-400 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59280.        (((A -> (B -> (A and B))) or C) and ((((D and E) and F) or (D and E)) -> E)), M:tm-400, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59281
in-theory        59281
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-391 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59281.        ((((A and B) -> B) or C) and ((((D and E) and F) or (D and E)) -> E)), M:tm-391, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59282
in-theory        59282
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-382 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59282.        ((((A and B) -> A) or C) and ((((D and E) and F) or (D and E)) -> E)), M:tm-382, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59283
in-theory        59283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and F) and G) or (E and F)) -> F))
theorem-size     27
proof            (modus-ponens tm-373 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59283.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E and F) and G) or (E and F)) -> F)), M:tm-373, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59284
in-theory        59284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-364 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59284.        (((A -> (B -> A)) or C) and ((((D and E) and F) or (D and E)) -> E)), M:tm-364, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59285
in-theory        59285
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> (D -> (B and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59285.        ((((A and B) and C) or (A and B)) -> (D -> (B and D))), M:tm-355, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-59286
in-theory        59286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     21
proof            (modus-ponens tm-354 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59286.        ((A -> (B -> (C -> (B and C)))) and ((((D and E) and F) or (D and E)) -> E)), M:tm-354, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59287
in-theory        59287
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and (not (B -> (C -> (B and C))))) and D) or (A and (not (B -> (C -> (B and C)))))))
theorem-size     24
proof            (modus-ponens tm-350 tm-714 ((A (or (and (and Am (not (-> B (-> C (and B C))))) Cm) (and Am (not (-> B (-> C (and B C))))))) (Bm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-8 tm-3 tm-4)
proof-size       114
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59287.        (not (((A and (not (B -> (C -> (B and C))))) and D) or (A and (not (B -> (C -> (B and C))))))), M:tm-350, m:tm-714, u:((A (or (and (and Am (not (-> B (-> C (and B C))))) Cm) (and Am (not (-> B (-> C (and B C))))))) (Bm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-59288
in-theory        59288
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59288.        (((((A and B) and C) or (A and B)) -> B) and (D -> (E -> (D and E)))), M:tm-341, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59289
in-theory        59289
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C and D) and E) or (C and D)) -> D))
theorem-size     21
proof            (modus-ponens tm-338 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59289.        (((A -> B) -> (A -> (A and B))) and ((((C and D) and E) or (C and D)) -> D)), M:tm-338, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59290
in-theory        59290
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and ((((A and B) and C) or (A and B)) -> ((((A and B) and C) or (A and B)) and B)))
theorem-size     33
proof            (modus-ponens tm-328 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59290.        (((((A and B) and C) or (A and B)) -> B) and ((((A and B) and C) or (A and B)) -> ((((A and B) and C) or (A and B)) and B))), M:tm-328, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-59291
in-theory        59291
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and ((D -> (E -> (D and E))) and ((((A and B) and C) or (A and B)) -> B)))
theorem-size     31
proof            (modus-ponens tm-327 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59291.        (((((A and B) and C) or (A and B)) -> B) and ((D -> (E -> (D and E))) and ((((A and B) and C) or (A and B)) -> B))), M:tm-327, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59292
in-theory        59292
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and (((D and E) -> E) and ((((A and B) and C) or (A and B)) -> B)))
theorem-size     29
proof            (modus-ponens tm-326 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59292.        (((((A and B) and C) or (A and B)) -> B) and (((D and E) -> E) and ((((A and B) and C) or (A and B)) -> B))), M:tm-326, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59293
in-theory        59293
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and (((D and E) -> D) and ((((A and B) and C) or (A and B)) -> B)))
theorem-size     29
proof            (modus-ponens tm-325 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59293.        (((((A and B) and C) or (A and B)) -> B) and (((D and E) -> D) and ((((A and B) and C) or (A and B)) -> B))), M:tm-325, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59294
in-theory        59294
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A and B) and C) or (A and B)) -> B)))
theorem-size     37
proof            (modus-ponens tm-324 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59294.        (((((A and B) and C) or (A and B)) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A and B) and C) or (A and B)) -> B))), M:tm-324, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59295
in-theory        59295
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and ((D -> (E -> D)) and ((((A and B) and C) or (A and B)) -> B)))
theorem-size     29
proof            (modus-ponens tm-323 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59295.        (((((A and B) and C) or (A and B)) -> B) and ((D -> (E -> D)) and ((((A and B) and C) or (A and B)) -> B))), M:tm-323, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59296
in-theory        59296
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59296.        (((((A and B) and C) or (A and B)) -> B) and ((D and E) -> E)), M:tm-322, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59297
in-theory        59297
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59297.        (((((A and B) and C) or (A and B)) -> B) and ((D and E) -> D)), M:tm-320, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59298
in-theory        59298
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59298.        (((((A and B) and C) or (A and B)) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59299
in-theory        59299
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and ((((A and B) and C) or (A and B)) -> (((A and B) and C) or (A and B))))
theorem-size     31
proof            (modus-ponens tm-316 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59299.        (((((A and B) and C) or (A and B)) -> B) and ((((A and B) and C) or (A and B)) -> (((A and B) and C) or (A and B)))), M:tm-316, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-59300
in-theory        59300
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59300.        (((((A and B) and C) or (A and B)) -> B) and (D -> (E -> D))), M:tm-315, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59301
in-theory        59301
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and (((((A and B) and C) or (A and B)) -> (not B)) -> (not (((A and B) and C) or (A and B)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59301.        (((((A and B) and C) or (A and B)) -> B) and (((((A and B) and C) or (A and B)) -> (not B)) -> (not (((A and B) and C) or (A and B))))), M:tm-313, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-59302
in-theory        59302
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and ((B -> D) -> (((((A and B) and C) or (A and B)) or B) -> D)))
theorem-size     29
proof            (modus-ponens tm-312 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59302.        (((((A and B) and C) or (A and B)) -> B) and ((B -> D) -> (((((A and B) and C) or (A and B)) or B) -> D))), M:tm-312, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-59303
in-theory        59303
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and (D or ((((A and B) and C) or (A and B)) -> B)))
theorem-size     25
proof            (modus-ponens tm-311 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59303.        (((((A and B) and C) or (A and B)) -> B) and (D or ((((A and B) and C) or (A and B)) -> B))), M:tm-311, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59304
in-theory        59304
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and (((((A and B) and C) or (A and B)) -> B) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59304.        (((((A and B) and C) or (A and B)) -> B) and (((((A and B) and C) or (A and B)) -> B) or D)), M:tm-310, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59305
in-theory        59305
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and (D -> (((((A and B) and C) or (A and B)) -> B) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59305.        (((((A and B) and C) or (A and B)) -> B) and (D -> (((((A and B) and C) or (A and B)) -> B) and D))), M:tm-309, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59306
in-theory        59306
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) and D) or (A and (B -> C))) -> (B -> C)) and (((((A and (B -> C)) and D) or (A and (B -> C))) -> B) -> ((((A and (B -> C)) and D) or (A and (B -> C))) -> C)))
theorem-size     49
proof            (modus-ponens tm-306 tm-714 ((A (or (and (and Am (-> B C)) Cm) (and Am (-> B C)))) (Bm (-> B C))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59306.        (((((A and (B -> C)) and D) or (A and (B -> C))) -> (B -> C)) and (((((A and (B -> C)) and D) or (A and (B -> C))) -> B) -> ((((A and (B -> C)) and D) or (A and (B -> C))) -> C))), M:tm-306, m:tm-714, u:((A (or (and (and Am (-> B C)) Cm) (and Am (-> B C)))) (Bm (-> B C)))
================================================================
tm-name          tm-59307
in-theory        59307
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and (D -> ((((A and B) and C) or (A and B)) -> B)))
theorem-size     25
proof            (modus-ponens tm-305 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59307.        (((((A and B) and C) or (A and B)) -> B) and (D -> ((((A and B) and C) or (A and B)) -> B))), M:tm-305, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59308
in-theory        59308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     23
proof            (modus-ponens tm-303 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59308.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-303, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59309
in-theory        59309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     21
proof            (modus-ponens tm-270 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59309.        ((A -> (((B and C) -> C) and A)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-270, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59310
in-theory        59310
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     21
proof            (modus-ponens tm-239 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59310.        ((A -> (((B and C) -> B) and A)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-239, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59311
in-theory        59311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and F) and G) or (E and F)) -> F))
theorem-size     29
proof            (modus-ponens tm-210 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59311.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E and F) and G) or (E and F)) -> F)), M:tm-210, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59312
in-theory        59312
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     21
proof            (modus-ponens tm-183 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59312.        ((A -> ((B -> (C -> B)) and A)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-183, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59313
in-theory        59313
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) and D) or (A and (B and C))) -> C)
theorem-size     15
proof            (modus-ponens tm-158 tm-714 ((A (or (and (and Am (and B C)) Cm) (and Am (and B C)))) (Bm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59313.        ((((A and (B and C)) and D) or (A and (B and C))) -> C), M:tm-158, m:tm-714, u:((A (or (and (and Am (and B C)) Cm) (and Am (and B C)))) (Bm (and B C)))
================================================================
tm-name          tm-59314
in-theory        59314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-157 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59314.        ((A -> ((B and C) -> C)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-157, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59315
in-theory        59315
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and (not ((B and C) -> C))) and D) or (A and (not ((B and C) -> C)))))
theorem-size     20
proof            (modus-ponens tm-153 tm-714 ((A (or (and (and Am (not (-> (and B C) C))) Cm) (and Am (not (-> (and B C) C))))) (Bm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-8 tm-3)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59315.        (not (((A and (not ((B and C) -> C))) and D) or (A and (not ((B and C) -> C))))), M:tm-153, m:tm-714, u:((A (or (and (and Am (not (-> (and B C) C))) Cm) (and Am (not (-> (and B C) C))))) (Bm (not (-> (and B C) C))))
================================================================
tm-name          tm-59316
in-theory        59316
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     27
proof            (modus-ponens tm-147 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59316.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-147, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59317
in-theory        59317
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) and D) or (A and (B and C))) -> B)
theorem-size     15
proof            (modus-ponens tm-135 tm-714 ((A (or (and (and Am (and B C)) Cm) (and Am (and B C)))) (Bm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59317.        ((((A and (B and C)) and D) or (A and (B and C))) -> B), M:tm-135, m:tm-714, u:((A (or (and (and Am (and B C)) Cm) (and Am (and B C)))) (Bm (and B C)))
================================================================
tm-name          tm-59318
in-theory        59318
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-134 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59318.        ((A -> ((B and C) -> B)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-134, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59319
in-theory        59319
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and (not ((B and C) -> B))) and D) or (A and (not ((B and C) -> B)))))
theorem-size     20
proof            (modus-ponens tm-130 tm-714 ((A (or (and (and Am (not (-> (and B C) B))) Cm) (and Am (not (-> (and B C) B))))) (Bm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-8 tm-4)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59319.        (not (((A and (not ((B and C) -> B))) and D) or (A and (not ((B and C) -> B))))), M:tm-130, m:tm-714, u:((A (or (and (and Am (not (-> (and B C) B))) Cm) (and Am (not (-> (and B C) B))))) (Bm (not (-> (and B C) B))))
================================================================
tm-name          tm-59320
in-theory        59320
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     27
proof            (modus-ponens tm-125 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59320.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-125, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59321
in-theory        59321
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) and E) or (A and (B -> (C -> D)))) -> ((B -> C) -> (B -> D)))
theorem-size     25
proof            (modus-ponens tm-114 tm-714 ((A (or (and (and Am (-> B (-> C D))) Cm) (and Am (-> B (-> C D))))) (Bm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59321.        ((((A and (B -> (C -> D))) and E) or (A and (B -> (C -> D)))) -> ((B -> C) -> (B -> D))), M:tm-114, m:tm-714, u:((A (or (and (and Am (-> B (-> C D))) Cm) (and Am (-> B (-> C D))))) (Bm (-> B (-> C D))))
================================================================
tm-name          tm-59322
in-theory        59322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) and G) or (E and F)) -> F))
theorem-size     27
proof            (modus-ponens tm-113 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59322.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E and F) and G) or (E and F)) -> F)), M:tm-113, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59323
in-theory        59323
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and E) or (A and (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))
theorem-size     36
proof            (modus-ponens tm-109 tm-714 ((A (or (and (and Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Cm) (and Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-8 tm-3 tm-4)
proof-size       144
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59323.        (not (((A and (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and E) or (A and (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))), M:tm-109, m:tm-714, u:((A (or (and (and Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))) Cm) (and Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-59324
in-theory        59324
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     31
proof            (modus-ponens tm-105 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59324.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D and E) and F) or (D and E)) -> E)), M:tm-105, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59325
in-theory        59325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C and D) and E) or (C and D)) -> D))
theorem-size     19
proof            (modus-ponens tm-95 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59325.        (((A -> B) -> (A -> A)) and ((((C and D) and E) or (C and D)) -> D)), M:tm-95, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59326
in-theory        59326
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) and D) or (A and (B -> C))) -> (B -> C))
theorem-size     17
proof            (modus-ponens tm-87 tm-714 ((A (or (and (and Am (-> B C)) Cm) (and Am (-> B C)))) (Bm (-> B C))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59326.        ((((A and (B -> C)) and D) or (A and (B -> C))) -> (B -> C)), M:tm-87, m:tm-714, u:((A (or (and (and Am (-> B C)) Cm) (and Am (-> B C)))) (Bm (-> B C)))
================================================================
tm-name          tm-59327
in-theory        59327
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> (D -> B))
theorem-size     13
proof            (modus-ponens tm-84 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59327.        ((((A and B) and C) or (A and B)) -> (D -> B)), M:tm-84, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-59328
in-theory        59328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-83 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59328.        ((A -> (B -> (C -> B))) and ((((D and E) and F) or (D and E)) -> E)), M:tm-83, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59329
in-theory        59329
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and (not (B -> (C -> B)))) and D) or (A and (not (B -> (C -> B))))))
theorem-size     20
proof            (modus-ponens tm-79 tm-714 ((A (or (and (and Am (not (-> B (-> C B)))) Cm) (and Am (not (-> B (-> C B)))))) (Bm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-8 tm-3 tm-4)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59329.        (not (((A and (not (B -> (C -> B)))) and D) or (A and (not (B -> (C -> B)))))), M:tm-79, m:tm-714, u:((A (or (and (and Am (not (-> B (-> C B)))) Cm) (and Am (not (-> B (-> C B)))))) (Bm (not (-> B (-> C B)))))
================================================================
tm-name          tm-59330
in-theory        59330
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B and C) and D) or (B and C)) -> C))
theorem-size     17
proof            (modus-ponens tm-76 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59330.        (((not (not A)) -> A) and ((((B and C) and D) or (B and C)) -> C)), M:tm-76, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59331
in-theory        59331
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A and B) and C) or (A and B)))) or (((A and B) and C) or (A and B))) -> B)
theorem-size     23
proof            (modus-ponens tm-73 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-8 tm-10 tm-3 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59331.        (((not (not (((A and B) and C) or (A and B)))) or (((A and B) and C) or (A and B))) -> B), M:tm-73, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-59332
in-theory        59332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and D) and E) or (C and D)) -> D))
theorem-size     23
proof            (modus-ponens tm-69 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-4)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59332.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C and D) and E) or (C and D)) -> D)), M:tm-69, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59333
in-theory        59333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     25
proof            (modus-ponens tm-54 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59333.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D and E) and F) or (D and E)) -> E)), M:tm-54, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59334
in-theory        59334
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or (((A and B) and C) or (A and B))) -> B)
theorem-size     15
proof            (modus-ponens tm-50 tm-714 ((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Bm)))
axioms-used      (tm-8 tm-7 tm-3 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59334.        (((A and B) or (((A and B) and C) or (A and B))) -> B), M:tm-50, m:tm-714, u:((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Bm))
================================================================
tm-name          tm-59335
in-theory        59335
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (((A and B) and C) or (A and B))) -> B)
theorem-size     17
proof            (modus-ponens tm-49 tm-714 ((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Bm)))
axioms-used      (tm-8 tm-6 tm-3 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59335.        ((((A and B) and C) or (((A and B) and C) or (A and B))) -> B), M:tm-49, m:tm-714, u:((A (and (and Am Bm) Cm)) (B (and Am Bm)) (C Bm))
================================================================
tm-name          tm-59336
in-theory        59336
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) and D) or (B and C))) or (((B and C) and D) or (B and C))) -> C)
theorem-size     23
proof            (modus-ponens tm-47 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-8 tm-4 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59336.        (((A and (((B and C) and D) or (B and C))) or (((B and C) and D) or (B and C))) -> C), M:tm-47, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-59337
in-theory        59337
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) and C) or (A and B)) and D) or (((A and B) and C) or (A and B))) -> B)
theorem-size     23
proof            (modus-ponens tm-46 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-8 tm-3 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59337.        ((((((A and B) and C) or (A and B)) and D) or (((A and B) and C) or (A and B))) -> B), M:tm-46, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-59338
in-theory        59338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C and D) and E) or (C and D)) -> D))
theorem-size     17
proof            (modus-ponens tm-42 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59338.        ((A -> (B or A)) and ((((C and D) and E) or (C and D)) -> D)), M:tm-42, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59339
in-theory        59339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C and D) and E) or (C and D)) -> D))
theorem-size     17
proof            (modus-ponens tm-32 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59339.        ((A -> (A or B)) and ((((C and D) and E) or (C and D)) -> D)), M:tm-32, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59340
in-theory        59340
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) and C) or (A and B)) -> ((((A and B) and C) or (A and B)) and B))
theorem-size     21
proof            (modus-ponens tm-24 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59340.        ((((A and B) and C) or (A and B)) -> ((((A and B) and C) or (A and B)) and B)), M:tm-24, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-59341
in-theory        59341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C and D) and E) or (C and D)) -> D))
theorem-size     19
proof            (modus-ponens tm-23 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59341.        ((A -> (B -> (A and B))) and ((((C and D) and E) or (C and D)) -> D)), M:tm-23, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59342
in-theory        59342
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C and D) and E) or (C and D)) -> D))
theorem-size     17
proof            (modus-ponens tm-22 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59342.        (((A and B) -> B) and ((((C and D) and E) or (C and D)) -> D)), M:tm-22, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59343
in-theory        59343
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C and D) and E) or (C and D)) -> D))
theorem-size     17
proof            (modus-ponens tm-21 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59343.        (((A and B) -> A) and ((((C and D) and E) or (C and D)) -> D)), M:tm-21, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59344
in-theory        59344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     25
proof            (modus-ponens tm-20 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59344.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D and E) and F) or (D and E)) -> E)), M:tm-20, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59345
in-theory        59345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C and D) and E) or (C and D)) -> D))
theorem-size     17
proof            (modus-ponens tm-19 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59345.        ((A -> (B -> A)) and ((((C and D) and E) or (C and D)) -> D)), M:tm-19, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59346
in-theory        59346
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> (not B)) -> (not (((A and B) and C) or (A and B))))
theorem-size     23
proof            (modus-ponens tm-9 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-9 tm-8 tm-3 tm-4)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59346.        (((((A and B) and C) or (A and B)) -> (not B)) -> (not (((A and B) and C) or (A and B)))), M:tm-9, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-59347
in-theory        59347
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((((C and A) and D) or (C and A)) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-8 tm-3 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59347.        ((A -> B) -> (((((C and A) and D) or (C and A)) or A) -> B)), M:tm-8, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-59348
in-theory        59348
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B and C) and D) or (B and C)) -> C))
theorem-size     13
proof            (modus-ponens tm-7 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-7 tm-8 tm-3 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59348.        (A or ((((B and C) and D) or (B and C)) -> C)), M:tm-7, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59349
in-theory        59349
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-6 tm-8 tm-3 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59349.        (((((A and B) and C) or (A and B)) -> B) or D), M:tm-6, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59350
in-theory        59350
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B and C) and D) or (B and C)) -> C) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59350.        (A -> (((((B and C) and D) or (B and C)) -> C) and A)), M:tm-5, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59351
in-theory        59351
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) and D) or (A and (B -> C))) -> B) -> ((((A and (B -> C)) and D) or (A and (B -> C))) -> C))
theorem-size     31
proof            (modus-ponens tm-2 tm-714 ((A (or (and (and Am (-> B C)) Cm) (and Am (-> B C)))) (Bm (-> B C))))
axioms-used      (tm-2 tm-8 tm-3 tm-4)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59351.        (((((A and (B -> C)) and D) or (A and (B -> C))) -> B) -> ((((A and (B -> C)) and D) or (A and (B -> C))) -> C)), M:tm-2, m:tm-714, u:((A (or (and (and Am (-> B C)) Cm) (and Am (-> B C)))) (Bm (-> B C)))
================================================================
tm-name          tm-59352
in-theory        59352
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) and D) or (B and C)) -> C))
theorem-size     13
proof            (modus-ponens tm-1 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-1 tm-8 tm-3 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-59352.        (A -> ((((B and C) and D) or (B and C)) -> C)), M:tm-1, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-59353
in-theory        59353
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (G -> (E and G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59353.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (G -> (E and G)))), M:tm-708, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59354
in-theory        59354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59354.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-665, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59355
in-theory        59355
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (D -> (A and D))))
theorem-size     13
proof            (modus-ponens tm-623 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59355.        (((A and B) or A) -> (C or (D -> (A and D)))), M:tm-623, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59356
in-theory        59356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59356.        ((A -> (B -> (C or B))) and (((D and E) or D) -> (F -> (D and F)))), M:tm-622, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59357
in-theory        59357
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (C or ((A and B) or A))))
theorem-size     15
proof            (modus-ponens tm-617 tm-715 ((A (or (and Am Bm) Am)) (Cm (or B (or (and Am Bm) Am))) (C (and Am (or B (or (and Am Bm) Am))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-5)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59357.        (((A and B) or A) -> (A and (C or ((A and B) or A)))), M:tm-617, m:tm-715, u:((A (or (and Am Bm) Am)) (Cm (or B (or (and Am Bm) Am))) (C (and Am (or B (or (and Am Bm) Am)))))
================================================================
tm-name          tm-59358
in-theory        59358
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59358.        ((((A and B) or A) -> (C -> (A and C))) and (D -> (E or D))), M:tm-609, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59359
in-theory        59359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59359.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-605, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59360
in-theory        59360
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and ((D -> (E or D)) and (((A and B) or A) -> (C -> (A and C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59360.        ((((A and B) or A) -> (C -> (A and C))) and ((D -> (E or D)) and (((A and B) or A) -> (C -> (A and C))))), M:tm-595, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59361
in-theory        59361
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59361.        (((A -> (B or A)) or C) and (((D and E) or D) -> (F -> (D and F)))), M:tm-550, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59362
in-theory        59362
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59362.        ((A or (B -> (C or B))) and (((D and E) or D) -> (F -> (D and F)))), M:tm-540, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59363
in-theory        59363
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59363.        ((A or (B -> (B or C))) and (((D and E) or D) -> (F -> (D and F)))), M:tm-530, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59364
in-theory        59364
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59364.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (D and F)))), M:tm-520, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59365
in-theory        59365
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59365.        ((A or ((B and C) -> C)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-510, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59366
in-theory        59366
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59366.        ((A or ((B and C) -> B)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-500, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59367
in-theory        59367
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (E and G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59367.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (E and G)))), M:tm-490, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59368
in-theory        59368
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59368.        ((A or (B -> (C -> B))) and (((D and E) or D) -> (F -> (D and F)))), M:tm-480, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59369
in-theory        59369
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (A and C)) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59369.        (((A and B) or A) -> ((C -> (A and C)) or D)), M:tm-470, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59370
in-theory        59370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59370.        ((A -> (B -> (B or C))) and (((D and E) or D) -> (F -> (D and F)))), M:tm-469, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59371
in-theory        59371
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (((A and B) or A) or C)))
theorem-size     15
proof            (modus-ponens tm-464 tm-715 ((A (or (and Am Bm) Am)) (Cm (or (or (and Am Bm) Am) B)) (C (and Am (or (or (and Am Bm) Am) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-5)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59371.        (((A and B) or A) -> (A and (((A and B) or A) or C))), M:tm-464, m:tm-715, u:((A (or (and Am Bm) Am)) (Cm (or (or (and Am Bm) Am) B)) (C (and Am (or (or (and Am Bm) Am) B))))
================================================================
tm-name          tm-59372
in-theory        59372
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59372.        ((((A and B) or A) -> (C -> (A and C))) and (D -> (D or E))), M:tm-456, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59373
in-theory        59373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59373.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-453, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59374
in-theory        59374
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and ((D -> (D or E)) and (((A and B) or A) -> (C -> (A and C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59374.        ((((A and B) or A) -> (C -> (A and C))) and ((D -> (D or E)) and (((A and B) or A) -> (C -> (A and C))))), M:tm-443, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59375
in-theory        59375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59375.        (((A -> (A or B)) or C) and (((D and E) or D) -> (F -> (D and F)))), M:tm-409, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59376
in-theory        59376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59376.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (F -> (D and F)))), M:tm-400, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59377
in-theory        59377
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59377.        ((((A and B) -> B) or C) and (((D and E) or D) -> (F -> (D and F)))), M:tm-391, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59378
in-theory        59378
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59378.        ((((A and B) -> A) or C) and (((D and E) or D) -> (F -> (D and F)))), M:tm-382, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59379
in-theory        59379
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (G -> (E and G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59379.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (G -> (E and G)))), M:tm-373, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59380
in-theory        59380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59380.        (((A -> (B -> A)) or C) and (((D and E) or D) -> (F -> (D and F)))), M:tm-364, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59381
in-theory        59381
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D -> (A and D)) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59381.        (((A and B) or A) -> (C -> ((D -> (A and D)) and C))), M:tm-355, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59382
in-theory        59382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59382.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (D and F)))), M:tm-354, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59383
in-theory        59383
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (C -> (((A and B) or A) and C))))
theorem-size     17
proof            (modus-ponens tm-349 tm-715 ((A (or (and Am Bm) Am)) (Cm (-> B (and (or (and Am Bm) Am) B))) (C (and Am (-> B (and (or (and Am Bm) Am) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59383.        (((A and B) or A) -> (A and (C -> (((A and B) or A) and C)))), M:tm-349, m:tm-715, u:((A (or (and Am Bm) Am)) (Cm (-> B (and (or (and Am Bm) Am) B))) (C (and Am (-> B (and (or (and Am Bm) Am) B)))))
================================================================
tm-name          tm-59384
in-theory        59384
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59384.        ((((A and B) or A) -> (C -> (A and C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59385
in-theory        59385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (E -> (C and E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59385.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (E -> (C and E)))), M:tm-338, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59386
in-theory        59386
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (((A and B) or A) -> (((A and B) or A) and (C -> (A and C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59386.        ((((A and B) or A) -> (C -> (A and C))) and (((A and B) or A) -> (((A and B) or A) and (C -> (A and C))))), M:tm-328, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59387
in-theory        59387
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and ((D -> (E -> (D and E))) and (((A and B) or A) -> (C -> (A and C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59387.        ((((A and B) or A) -> (C -> (A and C))) and ((D -> (E -> (D and E))) and (((A and B) or A) -> (C -> (A and C))))), M:tm-327, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59388
in-theory        59388
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (((D and E) -> E) and (((A and B) or A) -> (C -> (A and C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59388.        ((((A and B) or A) -> (C -> (A and C))) and (((D and E) -> E) and (((A and B) or A) -> (C -> (A and C))))), M:tm-326, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59389
in-theory        59389
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (((D and E) -> D) and (((A and B) or A) -> (C -> (A and C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59389.        ((((A and B) or A) -> (C -> (A and C))) and (((D and E) -> D) and (((A and B) or A) -> (C -> (A and C))))), M:tm-325, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59390
in-theory        59390
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or A) -> (C -> (A and C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59390.        ((((A and B) or A) -> (C -> (A and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or A) -> (C -> (A and C))))), M:tm-324, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59391
in-theory        59391
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and ((D -> (E -> D)) and (((A and B) or A) -> (C -> (A and C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59391.        ((((A and B) or A) -> (C -> (A and C))) and ((D -> (E -> D)) and (((A and B) or A) -> (C -> (A and C))))), M:tm-323, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59392
in-theory        59392
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59392.        ((((A and B) or A) -> (C -> (A and C))) and ((D and E) -> E)), M:tm-322, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59393
in-theory        59393
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59393.        ((((A and B) or A) -> (C -> (A and C))) and ((D and E) -> D)), M:tm-320, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59394
in-theory        59394
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59394.        ((((A and B) or A) -> (C -> (A and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59395
in-theory        59395
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     23
proof            (modus-ponens tm-316 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59395.        ((((A and B) or A) -> (C -> (A and C))) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59396
in-theory        59396
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59396.        ((((A and B) or A) -> (C -> (A and C))) and (D -> (E -> D))), M:tm-315, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59397
in-theory        59397
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and ((((A and B) or A) -> (not (C -> (A and C)))) -> (not ((A and B) or A))))
theorem-size     31
proof            (modus-ponens tm-313 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59397.        ((((A and B) or A) -> (C -> (A and C))) and ((((A and B) or A) -> (not (C -> (A and C)))) -> (not ((A and B) or A)))), M:tm-313, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59398
in-theory        59398
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (((C -> (A and C)) -> D) -> ((((A and B) or A) or (C -> (A and C))) -> D)))
theorem-size     33
proof            (modus-ponens tm-312 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59398.        ((((A and B) or A) -> (C -> (A and C))) and (((C -> (A and C)) -> D) -> ((((A and B) or A) or (C -> (A and C))) -> D))), M:tm-312, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59399
in-theory        59399
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (D or (((A and B) or A) -> (C -> (A and C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59399.        ((((A and B) or A) -> (C -> (A and C))) and (D or (((A and B) or A) -> (C -> (A and C))))), M:tm-311, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59400
in-theory        59400
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and ((((A and B) or A) -> (C -> (A and C))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59400.        ((((A and B) or A) -> (C -> (A and C))) and ((((A and B) or A) -> (C -> (A and C))) or D)), M:tm-310, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59401
in-theory        59401
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (D -> ((((A and B) or A) -> (C -> (A and C))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59401.        ((((A and B) or A) -> (C -> (A and C))) and (D -> ((((A and B) or A) -> (C -> (A and C))) and D))), M:tm-309, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59402
in-theory        59402
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and ((((A and B) or A) -> C) -> (((A and B) or A) -> (A and C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-715 ((A (or (and Am Bm) Am)) (B Cm) (C (and Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59402.        ((((A and B) or A) -> (C -> (A and C))) and ((((A and B) or A) -> C) -> (((A and B) or A) -> (A and C)))), M:tm-306, m:tm-715, u:((A (or (and Am Bm) Am)) (B Cm) (C (and Am Cm)))
================================================================
tm-name          tm-59403
in-theory        59403
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (D -> (((A and B) or A) -> (C -> (A and C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59403.        ((((A and B) or A) -> (C -> (A and C))) and (D -> (((A and B) or A) -> (C -> (A and C))))), M:tm-305, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59404
in-theory        59404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59404.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-303, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59405
in-theory        59405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59405.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-270, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59406
in-theory        59406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59406.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-239, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59407
in-theory        59407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (G -> (E and G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59407.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (G -> (E and G)))), M:tm-210, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59408
in-theory        59408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59408.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-183, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59409
in-theory        59409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59409.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-157, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59410
in-theory        59410
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59410.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-147, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59411
in-theory        59411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59411.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-134, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59412
in-theory        59412
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59412.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-125, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59413
in-theory        59413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (E and G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59413.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (E and G)))), M:tm-113, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59414
in-theory        59414
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59414.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (F -> (D and F)))), M:tm-105, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59415
in-theory        59415
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and ((A and B) or A)))
theorem-size     13
proof            (modus-ponens tm-99 tm-715 ((Cm (or (and Am Bm) Am)) (A (or (and Am Bm) Am)) (B (and Am (or (and Am Bm) Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-5)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59415.        (((A and B) or A) -> (A and ((A and B) or A))), M:tm-99, m:tm-715, u:((Cm (or (and Am Bm) Am)) (A (or (and Am Bm) Am)) (B (and Am (or (and Am Bm) Am))))
================================================================
tm-name          tm-59416
in-theory        59416
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (A and (C -> ((A and B) or A))))
theorem-size     15
proof            (modus-ponens tm-98 tm-715 ((A (or (and Am Bm) Am)) (Cm (-> B (or (and Am Bm) Am))) (C (and Am (-> B (or (and Am Bm) Am))))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-5)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59416.        (((A and B) or A) -> (A and (C -> ((A and B) or A)))), M:tm-98, m:tm-715, u:((A (or (and Am Bm) Am)) (Cm (-> B (or (and Am Bm) Am))) (C (and Am (-> B (or (and Am Bm) Am)))))
================================================================
tm-name          tm-59417
in-theory        59417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> (E -> (C and E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59417.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> (E -> (C and E)))), M:tm-95, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59418
in-theory        59418
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (D -> (A and D))))
theorem-size     13
proof            (modus-ponens tm-84 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59418.        (((A and B) or A) -> (C -> (D -> (A and D)))), M:tm-84, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59419
in-theory        59419
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59419.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> (F -> (D and F)))), M:tm-83, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59420
in-theory        59420
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> (D -> (B and D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59420.        (((not (not A)) -> A) and (((B and C) or B) -> (D -> (B and D)))), M:tm-76, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59421
in-theory        59421
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> (C -> (A and C)))
theorem-size     19
proof            (modus-ponens tm-73 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-8 tm-10 tm-3 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59421.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> (C -> (A and C))), M:tm-73, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59422
in-theory        59422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (E -> (C and E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59422.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (E -> (C and E)))), M:tm-69, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59423
in-theory        59423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59423.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (F -> (D and F)))), M:tm-54, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59424
in-theory        59424
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> (C -> (A and C)))
theorem-size     13
proof            (modus-ponens tm-50 tm-715 ((A (and Am Bm)) (B Am) (C (-> Cm (and Am Cm)))))
axioms-used      (tm-8 tm-7 tm-3 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59424.        ((A or ((A and B) or A)) -> (C -> (A and C))), M:tm-50, m:tm-715, u:((A (and Am Bm)) (B Am) (C (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59425
in-theory        59425
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> (C -> (A and C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-715 ((A (and Am Bm)) (B Am) (C (-> Cm (and Am Cm)))))
axioms-used      (tm-8 tm-6 tm-3 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59425.        (((A and B) or ((A and B) or A)) -> (C -> (A and C))), M:tm-49, m:tm-715, u:((A (and Am Bm)) (B Am) (C (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59426
in-theory        59426
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> (D -> (B and D)))
theorem-size     19
proof            (modus-ponens tm-47 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-8 tm-4 tm-3 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59426.        (((A and ((B and C) or B)) or ((B and C) or B)) -> (D -> (B and D))), M:tm-47, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59427
in-theory        59427
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> (D -> (A and D)))
theorem-size     19
proof            (modus-ponens tm-46 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59427.        (((((A and B) or A) and C) or ((A and B) or A)) -> (D -> (A and D))), M:tm-46, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59428
in-theory        59428
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> (E -> (C and E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59428.        ((A -> (B or A)) and (((C and D) or C) -> (E -> (C and E)))), M:tm-42, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59429
in-theory        59429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> (E -> (C and E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59429.        ((A -> (A or B)) and (((C and D) or C) -> (E -> (C and E)))), M:tm-32, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59430
in-theory        59430
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and (C -> (A and C))))
theorem-size     17
proof            (modus-ponens tm-24 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59430.        (((A and B) or A) -> (((A and B) or A) and (C -> (A and C)))), M:tm-24, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59431
in-theory        59431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> (E -> (C and E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59431.        ((A -> (B -> (A and B))) and (((C and D) or C) -> (E -> (C and E)))), M:tm-23, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59432
in-theory        59432
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> (E -> (C and E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59432.        (((A and B) -> B) and (((C and D) or C) -> (E -> (C and E)))), M:tm-22, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59433
in-theory        59433
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> (E -> (C and E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59433.        (((A and B) -> A) and (((C and D) or C) -> (E -> (C and E)))), M:tm-21, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59434
in-theory        59434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59434.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (F -> (D and F)))), M:tm-20, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59435
in-theory        59435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> (E -> (C and E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59435.        ((A -> (B -> A)) and (((C and D) or C) -> (E -> (C and E)))), M:tm-19, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59436
in-theory        59436
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not (C -> (A and C)))) -> (not ((A and B) or A)))
theorem-size     19
proof            (modus-ponens tm-9 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-9 tm-8 tm-3 tm-5)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59436.        ((((A and B) or A) -> (not (C -> (A and C)))) -> (not ((A and B) or A))), M:tm-9, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59437
in-theory        59437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> ((((B and D) or B) or (A -> (B and A))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59437.        (((A -> (B and A)) -> C) -> ((((B and D) or B) or (A -> (B and A))) -> C)), M:tm-8, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-59438
in-theory        59438
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> (D -> (B and D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-7 tm-8 tm-3 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59438.        (A or (((B and C) or B) -> (D -> (B and D)))), M:tm-7, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59439
in-theory        59439
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-6 tm-8 tm-3 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59439.        ((((A and B) or A) -> (C -> (A and C))) or D), M:tm-6, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59440
in-theory        59440
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> (D -> (B and D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59440.        (A -> ((((B and C) or B) -> (D -> (B and D))) and A)), M:tm-5, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59441
in-theory        59441
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> C) -> (((A and B) or A) -> (A and C)))
theorem-size     17
proof            (modus-ponens tm-2 tm-715 ((A (or (and Am Bm) Am)) (B Cm) (C (and Am Cm))))
axioms-used      (tm-2 tm-8 tm-3 tm-5)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59441.        ((((A and B) or A) -> C) -> (((A and B) or A) -> (A and C))), M:tm-2, m:tm-715, u:((A (or (and Am Bm) Am)) (B Cm) (C (and Am Cm)))
================================================================
tm-name          tm-59442
in-theory        59442
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> (D -> (B and D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-1 tm-8 tm-3 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-59442.        (A -> (((B and C) or B) -> (D -> (B and D)))), M:tm-1, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-59443
in-theory        59443
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (E or G)))
theorem-size     35
proof            (modus-ponens tm-708 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-6)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59443.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (E or G))), M:tm-708, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59444
in-theory        59444
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (D or F)))
theorem-size     23
proof            (modus-ponens tm-665 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59444.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (D or F))), M:tm-665, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59445
in-theory        59445
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (A or D)))
theorem-size     11
proof            (modus-ponens tm-623 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59445.        (((A and B) or A) -> (C or (A or D))), M:tm-623, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-59446
in-theory        59446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-622 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59446.        ((A -> (B -> (C or B))) and (((D and E) or D) -> (D or F))), M:tm-622, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59447
in-theory        59447
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59447.        ((((A and B) or A) -> (A or C)) and (D -> (E or D))), M:tm-609, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59448
in-theory        59448
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (D or F)))
theorem-size     19
proof            (modus-ponens tm-605 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59448.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (D or F))), M:tm-605, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59449
in-theory        59449
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and ((D -> (E or D)) and (((A and B) or A) -> (A or C))))
theorem-size     25
proof            (modus-ponens tm-595 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59449.        ((((A and B) or A) -> (A or C)) and ((D -> (E or D)) and (((A and B) or A) -> (A or C)))), M:tm-595, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59450
in-theory        59450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-550 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59450.        (((A -> (B or A)) or C) and (((D and E) or D) -> (D or F))), M:tm-550, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59451
in-theory        59451
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-540 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59451.        ((A or (B -> (C or B))) and (((D and E) or D) -> (D or F))), M:tm-540, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59452
in-theory        59452
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-530 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59452.        ((A or (B -> (B or C))) and (((D and E) or D) -> (D or F))), M:tm-530, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59453
in-theory        59453
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (D or F)))
theorem-size     19
proof            (modus-ponens tm-520 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59453.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (D or F))), M:tm-520, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59454
in-theory        59454
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-510 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59454.        ((A or ((B and C) -> C)) and (((D and E) or D) -> (D or F))), M:tm-510, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59455
in-theory        59455
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-500 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59455.        ((A or ((B and C) -> B)) and (((D and E) or D) -> (D or F))), M:tm-500, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59456
in-theory        59456
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (E or G)))
theorem-size     25
proof            (modus-ponens tm-490 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59456.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (E or G))), M:tm-490, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59457
in-theory        59457
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-480 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59457.        ((A or (B -> (C -> B))) and (((D and E) or D) -> (D or F))), M:tm-480, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59458
in-theory        59458
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((A or C) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59458.        (((A and B) or A) -> ((A or C) or D)), M:tm-470, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-59459
in-theory        59459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-469 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59459.        ((A -> (B -> (B or C))) and (((D and E) or D) -> (D or F))), M:tm-469, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59460
in-theory        59460
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59460.        ((((A and B) or A) -> (A or C)) and (D -> (D or E))), M:tm-456, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59461
in-theory        59461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (D or F)))
theorem-size     19
proof            (modus-ponens tm-453 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59461.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (D or F))), M:tm-453, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59462
in-theory        59462
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and ((D -> (D or E)) and (((A and B) or A) -> (A or C))))
theorem-size     25
proof            (modus-ponens tm-443 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59462.        ((((A and B) or A) -> (A or C)) and ((D -> (D or E)) and (((A and B) or A) -> (A or C)))), M:tm-443, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59463
in-theory        59463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-409 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59463.        (((A -> (A or B)) or C) and (((D and E) or D) -> (D or F))), M:tm-409, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59464
in-theory        59464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (D or F)))
theorem-size     19
proof            (modus-ponens tm-400 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59464.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (D or F))), M:tm-400, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59465
in-theory        59465
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-391 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59465.        ((((A and B) -> B) or C) and (((D and E) or D) -> (D or F))), M:tm-391, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59466
in-theory        59466
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-382 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59466.        ((((A and B) -> A) or C) and (((D and E) or D) -> (D or F))), M:tm-382, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59467
in-theory        59467
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (E or G)))
theorem-size     25
proof            (modus-ponens tm-373 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59467.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (E or G))), M:tm-373, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59468
in-theory        59468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-364 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59468.        (((A -> (B -> A)) or C) and (((D and E) or D) -> (D or F))), M:tm-364, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59469
in-theory        59469
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((A or D) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59469.        (((A and B) or A) -> (C -> ((A or D) and C))), M:tm-355, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-59470
in-theory        59470
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (D or F)))
theorem-size     19
proof            (modus-ponens tm-354 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59470.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (D or F))), M:tm-354, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59471
in-theory        59471
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59471.        ((((A and B) or A) -> (A or C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59472
in-theory        59472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (C or E)))
theorem-size     19
proof            (modus-ponens tm-338 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59472.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (C or E))), M:tm-338, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59473
in-theory        59473
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (((A and B) or A) -> (((A and B) or A) and (A or C))))
theorem-size     25
proof            (modus-ponens tm-328 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59473.        ((((A and B) or A) -> (A or C)) and (((A and B) or A) -> (((A and B) or A) and (A or C)))), M:tm-328, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-59474
in-theory        59474
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and ((D -> (E -> (D and E))) and (((A and B) or A) -> (A or C))))
theorem-size     27
proof            (modus-ponens tm-327 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59474.        ((((A and B) or A) -> (A or C)) and ((D -> (E -> (D and E))) and (((A and B) or A) -> (A or C)))), M:tm-327, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59475
in-theory        59475
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (((D and E) -> E) and (((A and B) or A) -> (A or C))))
theorem-size     25
proof            (modus-ponens tm-326 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59475.        ((((A and B) or A) -> (A or C)) and (((D and E) -> E) and (((A and B) or A) -> (A or C)))), M:tm-326, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59476
in-theory        59476
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (((D and E) -> D) and (((A and B) or A) -> (A or C))))
theorem-size     25
proof            (modus-ponens tm-325 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59476.        ((((A and B) or A) -> (A or C)) and (((D and E) -> D) and (((A and B) or A) -> (A or C)))), M:tm-325, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59477
in-theory        59477
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or A) -> (A or C))))
theorem-size     33
proof            (modus-ponens tm-324 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59477.        ((((A and B) or A) -> (A or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or A) -> (A or C)))), M:tm-324, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59478
in-theory        59478
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and ((D -> (E -> D)) and (((A and B) or A) -> (A or C))))
theorem-size     25
proof            (modus-ponens tm-323 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59478.        ((((A and B) or A) -> (A or C)) and ((D -> (E -> D)) and (((A and B) or A) -> (A or C)))), M:tm-323, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59479
in-theory        59479
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59479.        ((((A and B) or A) -> (A or C)) and ((D and E) -> E)), M:tm-322, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59480
in-theory        59480
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59480.        ((((A and B) or A) -> (A or C)) and ((D and E) -> D)), M:tm-320, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59481
in-theory        59481
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59481.        ((((A and B) or A) -> (A or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59482
in-theory        59482
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     21
proof            (modus-ponens tm-316 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59482.        ((((A and B) or A) -> (A or C)) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-59483
in-theory        59483
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59483.        ((((A and B) or A) -> (A or C)) and (D -> (E -> D))), M:tm-315, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59484
in-theory        59484
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and ((((A and B) or A) -> (not (A or C))) -> (not ((A and B) or A))))
theorem-size     27
proof            (modus-ponens tm-313 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59484.        ((((A and B) or A) -> (A or C)) and ((((A and B) or A) -> (not (A or C))) -> (not ((A and B) or A)))), M:tm-313, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-59485
in-theory        59485
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (((A or C) -> D) -> ((((A and B) or A) or (A or C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-312 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59485.        ((((A and B) or A) -> (A or C)) and (((A or C) -> D) -> ((((A and B) or A) or (A or C)) -> D))), M:tm-312, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-59486
in-theory        59486
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (D or (((A and B) or A) -> (A or C))))
theorem-size     21
proof            (modus-ponens tm-311 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59486.        ((((A and B) or A) -> (A or C)) and (D or (((A and B) or A) -> (A or C)))), M:tm-311, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59487
in-theory        59487
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and ((((A and B) or A) -> (A or C)) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59487.        ((((A and B) or A) -> (A or C)) and ((((A and B) or A) -> (A or C)) or D)), M:tm-310, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59488
in-theory        59488
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (D -> ((((A and B) or A) -> (A or C)) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59488.        ((((A and B) or A) -> (A or C)) and (D -> ((((A and B) or A) -> (A or C)) and D))), M:tm-309, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59489
in-theory        59489
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (D -> (((A and B) or A) -> (A or C))))
theorem-size     21
proof            (modus-ponens tm-305 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59489.        ((((A and B) or A) -> (A or C)) and (D -> (((A and B) or A) -> (A or C)))), M:tm-305, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59490
in-theory        59490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (D or F)))
theorem-size     21
proof            (modus-ponens tm-303 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59490.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (D or F))), M:tm-303, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59491
in-theory        59491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (D or F)))
theorem-size     19
proof            (modus-ponens tm-270 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59491.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (D or F))), M:tm-270, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59492
in-theory        59492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (D or F)))
theorem-size     19
proof            (modus-ponens tm-239 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59492.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (D or F))), M:tm-239, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59493
in-theory        59493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (E or G)))
theorem-size     27
proof            (modus-ponens tm-210 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59493.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (E or G))), M:tm-210, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59494
in-theory        59494
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (D or F)))
theorem-size     19
proof            (modus-ponens tm-183 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59494.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (D or F))), M:tm-183, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59495
in-theory        59495
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-157 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59495.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> (D or F))), M:tm-157, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59496
in-theory        59496
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (D or F)))
theorem-size     25
proof            (modus-ponens tm-147 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59496.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (D or F))), M:tm-147, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59497
in-theory        59497
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-134 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59497.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> (D or F))), M:tm-134, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59498
in-theory        59498
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (D or F)))
theorem-size     25
proof            (modus-ponens tm-125 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59498.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (D or F))), M:tm-125, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59499
in-theory        59499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (E or G)))
theorem-size     25
proof            (modus-ponens tm-113 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59499.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (E or G))), M:tm-113, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59500
in-theory        59500
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (D or F)))
theorem-size     29
proof            (modus-ponens tm-105 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59500.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (D or F))), M:tm-105, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59501
in-theory        59501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> (C or E)))
theorem-size     17
proof            (modus-ponens tm-95 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59501.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> (C or E))), M:tm-95, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59502
in-theory        59502
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (A or D)))
theorem-size     11
proof            (modus-ponens tm-84 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59502.        (((A and B) or A) -> (C -> (A or D))), M:tm-84, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-59503
in-theory        59503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> (D or F)))
theorem-size     17
proof            (modus-ponens tm-83 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59503.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> (D or F))), M:tm-83, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59504
in-theory        59504
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> (B or D)))
theorem-size     15
proof            (modus-ponens tm-76 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59504.        (((not (not A)) -> A) and (((B and C) or B) -> (B or D))), M:tm-76, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59505
in-theory        59505
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> (A or C))
theorem-size     17
proof            (modus-ponens tm-73 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-8 tm-10 tm-3 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59505.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> (A or C)), M:tm-73, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-59506
in-theory        59506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (C or E)))
theorem-size     21
proof            (modus-ponens tm-69 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59506.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (C or E))), M:tm-69, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59507
in-theory        59507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (D or F)))
theorem-size     23
proof            (modus-ponens tm-54 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59507.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (D or F))), M:tm-54, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59508
in-theory        59508
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> (A or C))
theorem-size     11
proof            (modus-ponens tm-50 tm-716 ((A (and Am Bm)) (B Am) (C (or Am Cm))))
axioms-used      (tm-8 tm-7 tm-3 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59508.        ((A or ((A and B) or A)) -> (A or C)), M:tm-50, m:tm-716, u:((A (and Am Bm)) (B Am) (C (or Am Cm)))
================================================================
tm-name          tm-59509
in-theory        59509
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> (A or C))
theorem-size     13
proof            (modus-ponens tm-49 tm-716 ((A (and Am Bm)) (B Am) (C (or Am Cm))))
axioms-used      (tm-8 tm-6 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59509.        (((A and B) or ((A and B) or A)) -> (A or C)), M:tm-49, m:tm-716, u:((A (and Am Bm)) (B Am) (C (or Am Cm)))
================================================================
tm-name          tm-59510
in-theory        59510
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> (B or D))
theorem-size     17
proof            (modus-ponens tm-47 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-8 tm-4 tm-3 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59510.        (((A and ((B and C) or B)) or ((B and C) or B)) -> (B or D)), M:tm-47, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-59511
in-theory        59511
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> (A or D))
theorem-size     17
proof            (modus-ponens tm-46 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-8 tm-3 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59511.        (((((A and B) or A) and C) or ((A and B) or A)) -> (A or D)), M:tm-46, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-59512
in-theory        59512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> (C or E)))
theorem-size     15
proof            (modus-ponens tm-42 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59512.        ((A -> (B or A)) and (((C and D) or C) -> (C or E))), M:tm-42, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59513
in-theory        59513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> (C or E)))
theorem-size     15
proof            (modus-ponens tm-32 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59513.        ((A -> (A or B)) and (((C and D) or C) -> (C or E))), M:tm-32, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59514
in-theory        59514
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and (A or C)))
theorem-size     15
proof            (modus-ponens tm-24 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59514.        (((A and B) or A) -> (((A and B) or A) and (A or C))), M:tm-24, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-59515
in-theory        59515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> (C or E)))
theorem-size     17
proof            (modus-ponens tm-23 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59515.        ((A -> (B -> (A and B))) and (((C and D) or C) -> (C or E))), M:tm-23, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59516
in-theory        59516
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> (C or E)))
theorem-size     15
proof            (modus-ponens tm-22 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59516.        (((A and B) -> B) and (((C and D) or C) -> (C or E))), M:tm-22, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59517
in-theory        59517
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> (C or E)))
theorem-size     15
proof            (modus-ponens tm-21 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59517.        (((A and B) -> A) and (((C and D) or C) -> (C or E))), M:tm-21, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59518
in-theory        59518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (D or F)))
theorem-size     23
proof            (modus-ponens tm-20 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59518.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (D or F))), M:tm-20, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59519
in-theory        59519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> (C or E)))
theorem-size     15
proof            (modus-ponens tm-19 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59519.        ((A -> (B -> A)) and (((C and D) or C) -> (C or E))), M:tm-19, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59520
in-theory        59520
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not (A or C))) -> (not ((A and B) or A)))
theorem-size     17
proof            (modus-ponens tm-9 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-9 tm-8 tm-3 tm-6)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59520.        ((((A and B) or A) -> (not (A or C))) -> (not ((A and B) or A))), M:tm-9, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-59521
in-theory        59521
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> ((((A and D) or A) or (A or B)) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-8 tm-3 tm-6)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59521.        (((A or B) -> C) -> ((((A and D) or A) or (A or B)) -> C)), M:tm-8, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-59522
in-theory        59522
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> (B or D)))
theorem-size     11
proof            (modus-ponens tm-7 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-7 tm-8 tm-3 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59522.        (A or (((B and C) or B) -> (B or D))), M:tm-7, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59523
in-theory        59523
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-6 tm-8 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59523.        ((((A and B) or A) -> (A or C)) or D), M:tm-6, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59524
in-theory        59524
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> (B or D)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59524.        (A -> ((((B and C) or B) -> (B or D)) and A)), M:tm-5, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59525
in-theory        59525
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> (B or D)))
theorem-size     11
proof            (modus-ponens tm-1 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-1 tm-8 tm-3 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-59525.        (A -> (((B and C) or B) -> (B or D))), M:tm-1, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-59526
in-theory        59526
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (G or E)))
theorem-size     35
proof            (modus-ponens tm-708 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-7)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59526.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (G or E))), M:tm-708, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59527
in-theory        59527
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (F or D)))
theorem-size     23
proof            (modus-ponens tm-665 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59527.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (F or D))), M:tm-665, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59528
in-theory        59528
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (D or A)))
theorem-size     11
proof            (modus-ponens tm-623 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59528.        (((A and B) or A) -> (C or (D or A))), M:tm-623, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-59529
in-theory        59529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-622 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59529.        ((A -> (B -> (C or B))) and (((D and E) or D) -> (F or D))), M:tm-622, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59530
in-theory        59530
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59530.        ((((A and B) or A) -> (C or A)) and (D -> (E or D))), M:tm-609, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59531
in-theory        59531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (F or D)))
theorem-size     19
proof            (modus-ponens tm-605 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59531.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (F or D))), M:tm-605, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59532
in-theory        59532
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and ((D -> (E or D)) and (((A and B) or A) -> (C or A))))
theorem-size     25
proof            (modus-ponens tm-595 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59532.        ((((A and B) or A) -> (C or A)) and ((D -> (E or D)) and (((A and B) or A) -> (C or A)))), M:tm-595, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59533
in-theory        59533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-550 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59533.        (((A -> (B or A)) or C) and (((D and E) or D) -> (F or D))), M:tm-550, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59534
in-theory        59534
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-540 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59534.        ((A or (B -> (C or B))) and (((D and E) or D) -> (F or D))), M:tm-540, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59535
in-theory        59535
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-530 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59535.        ((A or (B -> (B or C))) and (((D and E) or D) -> (F or D))), M:tm-530, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59536
in-theory        59536
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (F or D)))
theorem-size     19
proof            (modus-ponens tm-520 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59536.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (F or D))), M:tm-520, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59537
in-theory        59537
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-510 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59537.        ((A or ((B and C) -> C)) and (((D and E) or D) -> (F or D))), M:tm-510, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59538
in-theory        59538
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-500 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59538.        ((A or ((B and C) -> B)) and (((D and E) or D) -> (F or D))), M:tm-500, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59539
in-theory        59539
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G or E)))
theorem-size     25
proof            (modus-ponens tm-490 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59539.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G or E))), M:tm-490, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59540
in-theory        59540
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-480 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59540.        ((A or (B -> (C -> B))) and (((D and E) or D) -> (F or D))), M:tm-480, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59541
in-theory        59541
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C or A) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59541.        (((A and B) or A) -> ((C or A) or D)), M:tm-470, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-59542
in-theory        59542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-469 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59542.        ((A -> (B -> (B or C))) and (((D and E) or D) -> (F or D))), M:tm-469, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59543
in-theory        59543
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59543.        ((((A and B) or A) -> (C or A)) and (D -> (D or E))), M:tm-456, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59544
in-theory        59544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (F or D)))
theorem-size     19
proof            (modus-ponens tm-453 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59544.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (F or D))), M:tm-453, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59545
in-theory        59545
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and ((D -> (D or E)) and (((A and B) or A) -> (C or A))))
theorem-size     25
proof            (modus-ponens tm-443 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59545.        ((((A and B) or A) -> (C or A)) and ((D -> (D or E)) and (((A and B) or A) -> (C or A)))), M:tm-443, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59546
in-theory        59546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-409 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59546.        (((A -> (A or B)) or C) and (((D and E) or D) -> (F or D))), M:tm-409, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59547
in-theory        59547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (F or D)))
theorem-size     19
proof            (modus-ponens tm-400 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59547.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (F or D))), M:tm-400, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59548
in-theory        59548
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-391 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59548.        ((((A and B) -> B) or C) and (((D and E) or D) -> (F or D))), M:tm-391, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59549
in-theory        59549
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-382 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59549.        ((((A and B) -> A) or C) and (((D and E) or D) -> (F or D))), M:tm-382, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59550
in-theory        59550
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (G or E)))
theorem-size     25
proof            (modus-ponens tm-373 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59550.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (G or E))), M:tm-373, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59551
in-theory        59551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-364 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59551.        (((A -> (B -> A)) or C) and (((D and E) or D) -> (F or D))), M:tm-364, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59552
in-theory        59552
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D or A) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59552.        (((A and B) or A) -> (C -> ((D or A) and C))), M:tm-355, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-59553
in-theory        59553
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (F or D)))
theorem-size     19
proof            (modus-ponens tm-354 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59553.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (F or D))), M:tm-354, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59554
in-theory        59554
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59554.        ((((A and B) or A) -> (C or A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59555
in-theory        59555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (E or C)))
theorem-size     19
proof            (modus-ponens tm-338 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59555.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (E or C))), M:tm-338, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59556
in-theory        59556
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (((A and B) or A) -> (((A and B) or A) and (C or A))))
theorem-size     25
proof            (modus-ponens tm-328 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59556.        ((((A and B) or A) -> (C or A)) and (((A and B) or A) -> (((A and B) or A) and (C or A)))), M:tm-328, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-59557
in-theory        59557
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and ((D -> (E -> (D and E))) and (((A and B) or A) -> (C or A))))
theorem-size     27
proof            (modus-ponens tm-327 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59557.        ((((A and B) or A) -> (C or A)) and ((D -> (E -> (D and E))) and (((A and B) or A) -> (C or A)))), M:tm-327, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59558
in-theory        59558
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (((D and E) -> E) and (((A and B) or A) -> (C or A))))
theorem-size     25
proof            (modus-ponens tm-326 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59558.        ((((A and B) or A) -> (C or A)) and (((D and E) -> E) and (((A and B) or A) -> (C or A)))), M:tm-326, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59559
in-theory        59559
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (((D and E) -> D) and (((A and B) or A) -> (C or A))))
theorem-size     25
proof            (modus-ponens tm-325 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59559.        ((((A and B) or A) -> (C or A)) and (((D and E) -> D) and (((A and B) or A) -> (C or A)))), M:tm-325, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59560
in-theory        59560
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or A) -> (C or A))))
theorem-size     33
proof            (modus-ponens tm-324 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59560.        ((((A and B) or A) -> (C or A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or A) -> (C or A)))), M:tm-324, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59561
in-theory        59561
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and ((D -> (E -> D)) and (((A and B) or A) -> (C or A))))
theorem-size     25
proof            (modus-ponens tm-323 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59561.        ((((A and B) or A) -> (C or A)) and ((D -> (E -> D)) and (((A and B) or A) -> (C or A)))), M:tm-323, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59562
in-theory        59562
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59562.        ((((A and B) or A) -> (C or A)) and ((D and E) -> E)), M:tm-322, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59563
in-theory        59563
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59563.        ((((A and B) or A) -> (C or A)) and ((D and E) -> D)), M:tm-320, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59564
in-theory        59564
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59564.        ((((A and B) or A) -> (C or A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59565
in-theory        59565
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     21
proof            (modus-ponens tm-316 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59565.        ((((A and B) or A) -> (C or A)) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-59566
in-theory        59566
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59566.        ((((A and B) or A) -> (C or A)) and (D -> (E -> D))), M:tm-315, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59567
in-theory        59567
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and ((((A and B) or A) -> (not (C or A))) -> (not ((A and B) or A))))
theorem-size     27
proof            (modus-ponens tm-313 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59567.        ((((A and B) or A) -> (C or A)) and ((((A and B) or A) -> (not (C or A))) -> (not ((A and B) or A)))), M:tm-313, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-59568
in-theory        59568
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (((C or A) -> D) -> ((((A and B) or A) or (C or A)) -> D)))
theorem-size     27
proof            (modus-ponens tm-312 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59568.        ((((A and B) or A) -> (C or A)) and (((C or A) -> D) -> ((((A and B) or A) or (C or A)) -> D))), M:tm-312, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-59569
in-theory        59569
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (D or (((A and B) or A) -> (C or A))))
theorem-size     21
proof            (modus-ponens tm-311 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59569.        ((((A and B) or A) -> (C or A)) and (D or (((A and B) or A) -> (C or A)))), M:tm-311, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59570
in-theory        59570
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and ((((A and B) or A) -> (C or A)) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59570.        ((((A and B) or A) -> (C or A)) and ((((A and B) or A) -> (C or A)) or D)), M:tm-310, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59571
in-theory        59571
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (D -> ((((A and B) or A) -> (C or A)) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59571.        ((((A and B) or A) -> (C or A)) and (D -> ((((A and B) or A) -> (C or A)) and D))), M:tm-309, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59572
in-theory        59572
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (D -> (((A and B) or A) -> (C or A))))
theorem-size     21
proof            (modus-ponens tm-305 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59572.        ((((A and B) or A) -> (C or A)) and (D -> (((A and B) or A) -> (C or A)))), M:tm-305, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59573
in-theory        59573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (F or D)))
theorem-size     21
proof            (modus-ponens tm-303 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59573.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (F or D))), M:tm-303, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59574
in-theory        59574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (F or D)))
theorem-size     19
proof            (modus-ponens tm-270 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59574.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (F or D))), M:tm-270, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59575
in-theory        59575
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (F or D)))
theorem-size     19
proof            (modus-ponens tm-239 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59575.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (F or D))), M:tm-239, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59576
in-theory        59576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (G or E)))
theorem-size     27
proof            (modus-ponens tm-210 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59576.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (G or E))), M:tm-210, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59577
in-theory        59577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (F or D)))
theorem-size     19
proof            (modus-ponens tm-183 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59577.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (F or D))), M:tm-183, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59578
in-theory        59578
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-157 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59578.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> (F or D))), M:tm-157, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59579
in-theory        59579
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (F or D)))
theorem-size     25
proof            (modus-ponens tm-147 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59579.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (F or D))), M:tm-147, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59580
in-theory        59580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-134 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59580.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> (F or D))), M:tm-134, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59581
in-theory        59581
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (F or D)))
theorem-size     25
proof            (modus-ponens tm-125 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59581.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (F or D))), M:tm-125, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59582
in-theory        59582
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G or E)))
theorem-size     25
proof            (modus-ponens tm-113 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59582.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G or E))), M:tm-113, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59583
in-theory        59583
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (F or D)))
theorem-size     29
proof            (modus-ponens tm-105 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59583.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (F or D))), M:tm-105, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59584
in-theory        59584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> (E or C)))
theorem-size     17
proof            (modus-ponens tm-95 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59584.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> (E or C))), M:tm-95, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59585
in-theory        59585
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (D or A)))
theorem-size     11
proof            (modus-ponens tm-84 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59585.        (((A and B) or A) -> (C -> (D or A))), M:tm-84, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-59586
in-theory        59586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> (F or D)))
theorem-size     17
proof            (modus-ponens tm-83 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59586.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> (F or D))), M:tm-83, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59587
in-theory        59587
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> (D or B)))
theorem-size     15
proof            (modus-ponens tm-76 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59587.        (((not (not A)) -> A) and (((B and C) or B) -> (D or B))), M:tm-76, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59588
in-theory        59588
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> (C or A))
theorem-size     17
proof            (modus-ponens tm-73 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-8 tm-10 tm-3 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59588.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> (C or A)), M:tm-73, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-59589
in-theory        59589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (E or C)))
theorem-size     21
proof            (modus-ponens tm-69 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59589.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (E or C))), M:tm-69, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59590
in-theory        59590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (F or D)))
theorem-size     23
proof            (modus-ponens tm-54 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59590.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (F or D))), M:tm-54, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59591
in-theory        59591
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> (C or A))
theorem-size     11
proof            (modus-ponens tm-50 tm-717 ((A (and Am Bm)) (B Am) (C (or Cm Am))))
axioms-used      (tm-8 tm-7 tm-3)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59591.        ((A or ((A and B) or A)) -> (C or A)), M:tm-50, m:tm-717, u:((A (and Am Bm)) (B Am) (C (or Cm Am)))
================================================================
tm-name          tm-59592
in-theory        59592
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> (C or A))
theorem-size     13
proof            (modus-ponens tm-49 tm-717 ((A (and Am Bm)) (B Am) (C (or Cm Am))))
axioms-used      (tm-8 tm-6 tm-3 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59592.        (((A and B) or ((A and B) or A)) -> (C or A)), M:tm-49, m:tm-717, u:((A (and Am Bm)) (B Am) (C (or Cm Am)))
================================================================
tm-name          tm-59593
in-theory        59593
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> (D or B))
theorem-size     17
proof            (modus-ponens tm-47 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-8 tm-4 tm-3 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59593.        (((A and ((B and C) or B)) or ((B and C) or B)) -> (D or B)), M:tm-47, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-59594
in-theory        59594
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> (D or A))
theorem-size     17
proof            (modus-ponens tm-46 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-8 tm-3 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59594.        (((((A and B) or A) and C) or ((A and B) or A)) -> (D or A)), M:tm-46, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-59595
in-theory        59595
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> (E or C)))
theorem-size     15
proof            (modus-ponens tm-42 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59595.        ((A -> (B or A)) and (((C and D) or C) -> (E or C))), M:tm-42, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59596
in-theory        59596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> (E or C)))
theorem-size     15
proof            (modus-ponens tm-32 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59596.        ((A -> (A or B)) and (((C and D) or C) -> (E or C))), M:tm-32, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59597
in-theory        59597
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and (C or A)))
theorem-size     15
proof            (modus-ponens tm-24 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59597.        (((A and B) or A) -> (((A and B) or A) and (C or A))), M:tm-24, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-59598
in-theory        59598
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> (E or C)))
theorem-size     17
proof            (modus-ponens tm-23 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59598.        ((A -> (B -> (A and B))) and (((C and D) or C) -> (E or C))), M:tm-23, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59599
in-theory        59599
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> (E or C)))
theorem-size     15
proof            (modus-ponens tm-22 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59599.        (((A and B) -> B) and (((C and D) or C) -> (E or C))), M:tm-22, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59600
in-theory        59600
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> (E or C)))
theorem-size     15
proof            (modus-ponens tm-21 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59600.        (((A and B) -> A) and (((C and D) or C) -> (E or C))), M:tm-21, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59601
in-theory        59601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (F or D)))
theorem-size     23
proof            (modus-ponens tm-20 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59601.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (F or D))), M:tm-20, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59602
in-theory        59602
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> (E or C)))
theorem-size     15
proof            (modus-ponens tm-19 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59602.        ((A -> (B -> A)) and (((C and D) or C) -> (E or C))), M:tm-19, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59603
in-theory        59603
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not (C or A))) -> (not ((A and B) or A)))
theorem-size     17
proof            (modus-ponens tm-9 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-9 tm-8 tm-3 tm-7)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59603.        ((((A and B) or A) -> (not (C or A))) -> (not ((A and B) or A))), M:tm-9, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-59604
in-theory        59604
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> ((((B and D) or B) or (A or B)) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-8 tm-3 tm-7)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59604.        (((A or B) -> C) -> ((((B and D) or B) or (A or B)) -> C)), M:tm-8, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-59605
in-theory        59605
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> (D or B)))
theorem-size     11
proof            (modus-ponens tm-7 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-7 tm-8 tm-3)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59605.        (A or (((B and C) or B) -> (D or B))), M:tm-7, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59606
in-theory        59606
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-6 tm-8 tm-3 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59606.        ((((A and B) or A) -> (C or A)) or D), M:tm-6, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59607
in-theory        59607
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> (D or B)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59607.        (A -> ((((B and C) or B) -> (D or B)) and A)), M:tm-5, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59608
in-theory        59608
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> (D or B)))
theorem-size     11
proof            (modus-ponens tm-1 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-1 tm-8 tm-3 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-59608.        (A -> (((B and C) or B) -> (D or B))), M:tm-1, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-59609
in-theory        59609
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H))))
theorem-size     45
proof            (modus-ponens tm-708 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59609.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H)))), M:tm-708, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59610
in-theory        59610
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     33
proof            (modus-ponens tm-665 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59610.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-665, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59611
in-theory        59611
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D or ((B -> E) -> ((A or B) -> E))))
theorem-size     21
proof            (modus-ponens tm-623 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59611.        ((((A -> B) and C) or (A -> B)) -> (D or ((B -> E) -> ((A or B) -> E)))), M:tm-623, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59612
in-theory        59612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-622 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59612.        ((A -> (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-622, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59613
in-theory        59613
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59613.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (E -> (F or E))), M:tm-609, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59614
in-theory        59614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     29
proof            (modus-ponens tm-605 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59614.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-605, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59615
in-theory        59615
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((E -> (F or E)) and ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59615.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((E -> (F or E)) and ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))))), M:tm-595, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59616
in-theory        59616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-550 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59616.        (((A -> (B or A)) or C) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-550, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59617
in-theory        59617
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-540 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59617.        ((A or (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-540, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59618
in-theory        59618
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-530 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59618.        ((A or (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-530, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59619
in-theory        59619
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     29
proof            (modus-ponens tm-520 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59619.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-520, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59620
in-theory        59620
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-510 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59620.        ((A or ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-510, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59621
in-theory        59621
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-500 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59621.        ((A or ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-500, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59622
in-theory        59622
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H))))
theorem-size     35
proof            (modus-ponens tm-490 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59622.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H)))), M:tm-490, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59623
in-theory        59623
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-480 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59623.        ((A or (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-480, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59624
in-theory        59624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (((B -> D) -> ((A or B) -> D)) or E))
theorem-size     21
proof            (modus-ponens tm-470 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59624.        ((((A -> B) and C) or (A -> B)) -> (((B -> D) -> ((A or B) -> D)) or E)), M:tm-470, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59625
in-theory        59625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-469 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59625.        ((A -> (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-469, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59626
in-theory        59626
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59626.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (E -> (E or F))), M:tm-456, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59627
in-theory        59627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     29
proof            (modus-ponens tm-453 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59627.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-453, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59628
in-theory        59628
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((E -> (E or F)) and ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59628.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((E -> (E or F)) and ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))))), M:tm-443, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59629
in-theory        59629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-409 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59629.        (((A -> (A or B)) or C) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-409, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59630
in-theory        59630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     29
proof            (modus-ponens tm-400 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59630.        (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-400, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59631
in-theory        59631
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-391 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59631.        ((((A and B) -> B) or C) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-391, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59632
in-theory        59632
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-382 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59632.        ((((A and B) -> A) or C) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-382, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59633
in-theory        59633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H))))
theorem-size     35
proof            (modus-ponens tm-373 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59633.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H)))), M:tm-373, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59634
in-theory        59634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-364 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59634.        (((A -> (B -> A)) or C) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-364, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59635
in-theory        59635
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D -> (((B -> E) -> ((A or B) -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-355 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59635.        ((((A -> B) and C) or (A -> B)) -> (D -> (((B -> E) -> ((A or B) -> E)) and D))), M:tm-355, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59636
in-theory        59636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     29
proof            (modus-ponens tm-354 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59636.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-354, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59637
in-theory        59637
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((A or B) -> ((((A -> B) and C) or (A -> B)) and B)))
theorem-size     25
proof            (modus-ponens tm-349 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B Bm) (Dm (and (or (and (-> Am Bm) Cm) (-> Am Bm)) Bm)) (C (-> (or Am Bm) (and (or (and (-> Am Bm) Cm) (-> Am Bm)) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59637.        ((((A -> B) and C) or (A -> B)) -> ((A or B) -> ((((A -> B) and C) or (A -> B)) and B))), M:tm-349, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B Bm) (Dm (and (or (and (-> Am Bm) Cm) (-> Am Bm)) Bm)) (C (-> (or Am Bm) (and (or (and (-> Am Bm) Cm) (-> Am Bm)) Bm))))
================================================================
tm-name          tm-59638
in-theory        59638
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59638.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59639
in-theory        59639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F))))
theorem-size     29
proof            (modus-ponens tm-338 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59639.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F)))), M:tm-338, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59640
in-theory        59640
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and ((B -> D) -> ((A or B) -> D)))))
theorem-size     49
proof            (modus-ponens tm-328 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59640.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and ((B -> D) -> ((A or B) -> D))))), M:tm-328, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59641
in-theory        59641
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((E -> (F -> (E and F))) and ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59641.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((E -> (F -> (E and F))) and ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))))), M:tm-327, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59642
in-theory        59642
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((E and F) -> F) and ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59642.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((E and F) -> F) and ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))))), M:tm-326, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59643
in-theory        59643
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((E and F) -> E) and ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59643.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((E and F) -> E) and ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))))), M:tm-325, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59644
in-theory        59644
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59644.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))))), M:tm-324, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59645
in-theory        59645
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((E -> (F -> E)) and ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59645.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((E -> (F -> E)) and ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))))), M:tm-323, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59646
in-theory        59646
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59646.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59647
in-theory        59647
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59647.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59648
in-theory        59648
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59648.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59649
in-theory        59649
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((((A -> B) and C) or (A -> B)) -> (((A -> B) and C) or (A -> B))))
theorem-size     39
proof            (modus-ponens tm-316 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59649.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((((A -> B) and C) or (A -> B)) -> (((A -> B) and C) or (A -> B)))), M:tm-316, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59650
in-theory        59650
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59650.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59651
in-theory        59651
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((((A -> B) and C) or (A -> B)) -> (not ((B -> D) -> ((A or B) -> D)))) -> (not (((A -> B) and C) or (A -> B)))))
theorem-size     51
proof            (modus-ponens tm-313 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59651.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((((A -> B) and C) or (A -> B)) -> (not ((B -> D) -> ((A or B) -> D)))) -> (not (((A -> B) and C) or (A -> B))))), M:tm-313, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59652
in-theory        59652
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((((B -> D) -> ((A or B) -> D)) -> E) -> (((((A -> B) and C) or (A -> B)) or ((B -> D) -> ((A or B) -> D))) -> E)))
theorem-size     53
proof            (modus-ponens tm-312 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59652.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((((B -> D) -> ((A or B) -> D)) -> E) -> (((((A -> B) and C) or (A -> B)) or ((B -> D) -> ((A or B) -> D))) -> E))), M:tm-312, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59653
in-theory        59653
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (E or ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59653.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (E or ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))))), M:tm-311, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59654
in-theory        59654
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59654.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) or E)), M:tm-310, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59655
in-theory        59655
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (E -> (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59655.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (E -> (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and E))), M:tm-309, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59656
in-theory        59656
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((((A -> B) and C) or (A -> B)) -> (B -> D)) -> ((((A -> B) and C) or (A -> B)) -> ((A or B) -> D))))
theorem-size     49
proof            (modus-ponens tm-306 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Bm Dm)) (C (-> (or Am Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59656.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (((((A -> B) and C) or (A -> B)) -> (B -> D)) -> ((((A -> B) and C) or (A -> B)) -> ((A or B) -> D)))), M:tm-306, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Bm Dm)) (C (-> (or Am Bm) Dm)))
================================================================
tm-name          tm-59657
in-theory        59657
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (E -> ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59657.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and (E -> ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))))), M:tm-305, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59658
in-theory        59658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     31
proof            (modus-ponens tm-303 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59658.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-303, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59659
in-theory        59659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     29
proof            (modus-ponens tm-270 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59659.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-270, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59660
in-theory        59660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     29
proof            (modus-ponens tm-239 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59660.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-239, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59661
in-theory        59661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H))))
theorem-size     37
proof            (modus-ponens tm-210 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59661.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H)))), M:tm-210, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59662
in-theory        59662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     29
proof            (modus-ponens tm-183 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59662.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-183, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59663
in-theory        59663
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-157 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59663.        ((A -> ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-157, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59664
in-theory        59664
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     35
proof            (modus-ponens tm-147 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59664.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-147, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59665
in-theory        59665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-134 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59665.        ((A -> ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-134, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59666
in-theory        59666
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     35
proof            (modus-ponens tm-125 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59666.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-125, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59667
in-theory        59667
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (((B -> D) -> (A or B)) -> ((B -> D) -> D)))
theorem-size     23
proof            (modus-ponens tm-114 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Bm Dm)) (C (or Am Bm)) (D Dm)))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59667.        ((((A -> B) and C) or (A -> B)) -> (((B -> D) -> (A or B)) -> ((B -> D) -> D))), M:tm-114, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Bm Dm)) (C (or Am Bm)) (D Dm))
================================================================
tm-name          tm-59668
in-theory        59668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H))))
theorem-size     35
proof            (modus-ponens tm-113 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59668.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> ((F -> H) -> ((E or F) -> H)))), M:tm-113, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59669
in-theory        59669
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     39
proof            (modus-ponens tm-105 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59669.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-105, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59670
in-theory        59670
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((A or B) -> (((A -> B) and C) or (A -> B))))
theorem-size     23
proof            (modus-ponens tm-98 tm-718 ((Dm (or (and (-> Am Bm) Cm) (-> Am Bm))) (B Bm) (A (or (and (-> Am Bm) Cm) (-> Am Bm))) (C (-> (or Am Bm) (or (and (-> Am Bm) Cm) (-> Am Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59670.        ((((A -> B) and C) or (A -> B)) -> ((A or B) -> (((A -> B) and C) or (A -> B)))), M:tm-98, m:tm-718, u:((Dm (or (and (-> Am Bm) Cm) (-> Am Bm))) (B Bm) (A (or (and (-> Am Bm) Cm) (-> Am Bm))) (C (-> (or Am Bm) (or (and (-> Am Bm) Cm) (-> Am Bm)))))
================================================================
tm-name          tm-59671
in-theory        59671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F))))
theorem-size     27
proof            (modus-ponens tm-95 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59671.        (((A -> B) -> (A -> A)) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F)))), M:tm-95, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59672
in-theory        59672
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D -> ((B -> E) -> ((A or B) -> E))))
theorem-size     21
proof            (modus-ponens tm-84 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59672.        ((((A -> B) and C) or (A -> B)) -> (D -> ((B -> E) -> ((A or B) -> E)))), M:tm-84, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59673
in-theory        59673
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     27
proof            (modus-ponens tm-83 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59673.        ((A -> (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-83, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59674
in-theory        59674
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) and D) or (B -> C)) -> ((C -> E) -> ((B or C) -> E))))
theorem-size     25
proof            (modus-ponens tm-76 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59674.        (((not (not A)) -> A) and ((((B -> C) and D) or (B -> C)) -> ((C -> E) -> ((B or C) -> E)))), M:tm-76, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59675
in-theory        59675
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) and C) or (A -> B)))) or (((A -> B) and C) or (A -> B))) -> ((B -> D) -> ((A or B) -> D)))
theorem-size     31
proof            (modus-ponens tm-73 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-8 tm-10 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59675.        (((not (not (((A -> B) and C) or (A -> B)))) or (((A -> B) and C) or (A -> B))) -> ((B -> D) -> ((A or B) -> D))), M:tm-73, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59676
in-theory        59676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F))))
theorem-size     31
proof            (modus-ponens tm-69 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59676.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F)))), M:tm-69, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59677
in-theory        59677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     33
proof            (modus-ponens tm-54 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59677.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-54, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59678
in-theory        59678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A -> B) and C) or (A -> B))) -> ((B -> D) -> ((A or B) -> D)))
theorem-size     23
proof            (modus-ponens tm-50 tm-718 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-8 tm-7 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59678.        (((A -> B) or (((A -> B) and C) or (A -> B))) -> ((B -> D) -> ((A or B) -> D))), M:tm-50, m:tm-718, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59679
in-theory        59679
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> ((B -> D) -> ((A or B) -> D)))
theorem-size     25
proof            (modus-ponens tm-49 tm-718 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-8 tm-6 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59679.        ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> ((B -> D) -> ((A or B) -> D))), M:tm-49, m:tm-718, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59680
in-theory        59680
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) or (B -> C))) or (((B -> C) and D) or (B -> C))) -> ((C -> E) -> ((B or C) -> E)))
theorem-size     31
proof            (modus-ponens tm-47 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-8 tm-4 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59680.        (((A and (((B -> C) and D) or (B -> C))) or (((B -> C) and D) or (B -> C))) -> ((C -> E) -> ((B or C) -> E))), M:tm-47, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59681
in-theory        59681
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> ((B -> E) -> ((A or B) -> E)))
theorem-size     31
proof            (modus-ponens tm-46 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-8 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59681.        ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> ((B -> E) -> ((A or B) -> E))), M:tm-46, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59682
in-theory        59682
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F))))
theorem-size     25
proof            (modus-ponens tm-42 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59682.        ((A -> (B or A)) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F)))), M:tm-42, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59683
in-theory        59683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F))))
theorem-size     25
proof            (modus-ponens tm-32 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59683.        ((A -> (A or B)) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F)))), M:tm-32, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59684
in-theory        59684
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and ((B -> D) -> ((A or B) -> D))))
theorem-size     29
proof            (modus-ponens tm-24 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59684.        ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and ((B -> D) -> ((A or B) -> D)))), M:tm-24, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59685
in-theory        59685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F))))
theorem-size     27
proof            (modus-ponens tm-23 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59685.        ((A -> (B -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F)))), M:tm-23, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59686
in-theory        59686
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F))))
theorem-size     25
proof            (modus-ponens tm-22 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59686.        (((A and B) -> B) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F)))), M:tm-22, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59687
in-theory        59687
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F))))
theorem-size     25
proof            (modus-ponens tm-21 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59687.        (((A and B) -> A) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F)))), M:tm-21, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59688
in-theory        59688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     33
proof            (modus-ponens tm-20 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59688.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-20, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59689
in-theory        59689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F))))
theorem-size     25
proof            (modus-ponens tm-19 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59689.        ((A -> (B -> A)) and ((((C -> D) and E) or (C -> D)) -> ((D -> F) -> ((C or D) -> F)))), M:tm-19, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59690
in-theory        59690
times-derived    6
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (((A -> B) and C) or (A -> B)))
theorem-size     19
proof            (modus-ponens tm-12 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59690.        ((((A -> B) and C) or (A -> B)) -> (((A -> B) and C) or (A -> B))), M:tm-12, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59691
in-theory        59691
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (not ((B -> D) -> ((A or B) -> D)))) -> (not (((A -> B) and C) or (A -> B))))
theorem-size     31
proof            (modus-ponens tm-9 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-9 tm-8 tm-3)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59691.        (((((A -> B) and C) or (A -> B)) -> (not ((B -> D) -> ((A or B) -> D)))) -> (not (((A -> B) and C) or (A -> B)))), M:tm-9, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59692
in-theory        59692
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> (((((C -> A) and E) or (C -> A)) or ((A -> B) -> ((C or A) -> B))) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-8 tm-3)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59692.        ((((A -> B) -> ((C or A) -> B)) -> D) -> (((((C -> A) and E) or (C -> A)) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-59693
in-theory        59693
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) and D) or (B -> C)) -> ((C -> E) -> ((B or C) -> E))))
theorem-size     21
proof            (modus-ponens tm-7 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-7 tm-8 tm-3)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59693.        (A or ((((B -> C) and D) or (B -> C)) -> ((C -> E) -> ((B or C) -> E)))), M:tm-7, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59694
in-theory        59694
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-6 tm-8 tm-3)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59694.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) or E), M:tm-6, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59695
in-theory        59695
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) and D) or (B -> C)) -> ((C -> E) -> ((B or C) -> E))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59695.        (A -> (((((B -> C) and D) or (B -> C)) -> ((C -> E) -> ((B or C) -> E))) and A)), M:tm-5, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59696
in-theory        59696
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (B -> D)) -> ((((A -> B) and C) or (A -> B)) -> ((A or B) -> D)))
theorem-size     29
proof            (modus-ponens tm-2 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Bm Dm)) (C (-> (or Am Bm) Dm))))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59696.        (((((A -> B) and C) or (A -> B)) -> (B -> D)) -> ((((A -> B) and C) or (A -> B)) -> ((A or B) -> D))), M:tm-2, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Bm Dm)) (C (-> (or Am Bm) Dm)))
================================================================
tm-name          tm-59697
in-theory        59697
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) and D) or (B -> C)) -> ((C -> E) -> ((B or C) -> E))))
theorem-size     21
proof            (modus-ponens tm-1 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-59697.        (A -> ((((B -> C) and D) or (B -> C)) -> ((C -> E) -> ((B or C) -> E)))), M:tm-1, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-59698
in-theory        59698
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     43
proof            (modus-ponens tm-708 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-9)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59698.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-708, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59699
in-theory        59699
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     31
proof            (modus-ponens tm-665 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-9)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59699.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-665, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59700
in-theory        59700
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D or ((A -> (not B)) -> (not A))))
theorem-size     19
proof            (modus-ponens tm-623 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59700.        ((((A -> B) and C) or (A -> B)) -> (D or ((A -> (not B)) -> (not A)))), M:tm-623, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59701
in-theory        59701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-622 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59701.        ((A -> (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-622, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59702
in-theory        59702
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-609 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59702.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (D -> (E or D))), M:tm-609, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59703
in-theory        59703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-605 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59703.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-605, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59704
in-theory        59704
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((D -> (E or D)) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59704.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((D -> (E or D)) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))))), M:tm-595, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59705
in-theory        59705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-550 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59705.        (((A -> (B or A)) or C) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-550, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59706
in-theory        59706
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-540 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59706.        ((A or (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-540, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59707
in-theory        59707
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-530 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59707.        ((A or (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-530, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59708
in-theory        59708
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-520 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59708.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-520, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59709
in-theory        59709
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-510 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59709.        ((A or ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-510, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59710
in-theory        59710
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-500 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59710.        ((A or ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-500, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59711
in-theory        59711
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     33
proof            (modus-ponens tm-490 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59711.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-490, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59712
in-theory        59712
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-480 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59712.        ((A or (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-480, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59713
in-theory        59713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (((A -> (not B)) -> (not A)) or D))
theorem-size     19
proof            (modus-ponens tm-470 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59713.        ((((A -> B) and C) or (A -> B)) -> (((A -> (not B)) -> (not A)) or D)), M:tm-470, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59714
in-theory        59714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-469 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59714.        ((A -> (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-469, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59715
in-theory        59715
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-456 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59715.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (D -> (D or E))), M:tm-456, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59716
in-theory        59716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-453 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59716.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-453, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59717
in-theory        59717
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((D -> (D or E)) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59717.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((D -> (D or E)) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))))), M:tm-443, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59718
in-theory        59718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-409 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59718.        (((A -> (A or B)) or C) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-409, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59719
in-theory        59719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-400 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59719.        (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-400, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59720
in-theory        59720
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-391 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59720.        ((((A and B) -> B) or C) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-391, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59721
in-theory        59721
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-382 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59721.        ((((A and B) -> A) or C) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-382, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59722
in-theory        59722
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     33
proof            (modus-ponens tm-373 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59722.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-373, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59723
in-theory        59723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-364 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59723.        (((A -> (B -> A)) or C) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-364, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59724
in-theory        59724
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D -> (((A -> (not B)) -> (not A)) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59724.        ((((A -> B) and C) or (A -> B)) -> (D -> (((A -> (not B)) -> (not A)) and D))), M:tm-355, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59725
in-theory        59725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-354 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59725.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-354, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59726
in-theory        59726
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-341 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-9)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59726.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59727
in-theory        59727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C))))
theorem-size     27
proof            (modus-ponens tm-338 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59727.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C)))), M:tm-338, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59728
in-theory        59728
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and ((A -> (not B)) -> (not A)))))
theorem-size     45
proof            (modus-ponens tm-328 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59728.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and ((A -> (not B)) -> (not A))))), M:tm-328, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59729
in-theory        59729
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((D -> (E -> (D and E))) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59729.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((D -> (E -> (D and E))) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))))), M:tm-327, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59730
in-theory        59730
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((D and E) -> E) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59730.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((D and E) -> E) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))))), M:tm-326, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59731
in-theory        59731
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((D and E) -> D) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59731.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((D and E) -> D) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))))), M:tm-325, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59732
in-theory        59732
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59732.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))))), M:tm-324, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59733
in-theory        59733
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((D -> (E -> D)) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59733.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((D -> (E -> D)) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))))), M:tm-323, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59734
in-theory        59734
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-322 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59734.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((D and E) -> E)), M:tm-322, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59735
in-theory        59735
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-320 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59735.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((D and E) -> D)), M:tm-320, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59736
in-theory        59736
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-318 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-9)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59736.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59737
in-theory        59737
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((((A -> B) and C) or (A -> B)) -> (((A -> B) and C) or (A -> B))))
theorem-size     37
proof            (modus-ponens tm-316 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59737.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((((A -> B) and C) or (A -> B)) -> (((A -> B) and C) or (A -> B)))), M:tm-316, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59738
in-theory        59738
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-315 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59738.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (D -> (E -> D))), M:tm-315, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59739
in-theory        59739
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((((A -> B) and C) or (A -> B)) -> (not ((A -> (not B)) -> (not A)))) -> (not (((A -> B) and C) or (A -> B)))))
theorem-size     47
proof            (modus-ponens tm-313 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59739.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((((A -> B) and C) or (A -> B)) -> (not ((A -> (not B)) -> (not A)))) -> (not (((A -> B) and C) or (A -> B))))), M:tm-313, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59740
in-theory        59740
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((((A -> (not B)) -> (not A)) -> D) -> (((((A -> B) and C) or (A -> B)) or ((A -> (not B)) -> (not A))) -> D)))
theorem-size     47
proof            (modus-ponens tm-312 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59740.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((((A -> (not B)) -> (not A)) -> D) -> (((((A -> B) and C) or (A -> B)) or ((A -> (not B)) -> (not A))) -> D))), M:tm-312, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59741
in-theory        59741
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (D or ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59741.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (D or ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))))), M:tm-311, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59742
in-theory        59742
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) or D))
theorem-size     37
proof            (modus-ponens tm-310 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59742.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) or D)), M:tm-310, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59743
in-theory        59743
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (D -> (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and D)))
theorem-size     39
proof            (modus-ponens tm-309 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59743.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (D -> (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and D))), M:tm-309, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59744
in-theory        59744
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((((A -> B) and C) or (A -> B)) -> (A -> (not B))) -> ((((A -> B) and C) or (A -> B)) -> (not A))))
theorem-size     45
proof            (modus-ponens tm-306 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (not Bm))) (C (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59744.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (((((A -> B) and C) or (A -> B)) -> (A -> (not B))) -> ((((A -> B) and C) or (A -> B)) -> (not A)))), M:tm-306, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (not Bm))) (C (not Am)))
================================================================
tm-name          tm-59745
in-theory        59745
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (D -> ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59745.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and (D -> ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))))), M:tm-305, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59746
in-theory        59746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     29
proof            (modus-ponens tm-303 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59746.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-303, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59747
in-theory        59747
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-270 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59747.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-270, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59748
in-theory        59748
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-239 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59748.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-239, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59749
in-theory        59749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     35
proof            (modus-ponens tm-210 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-9)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59749.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-210, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59750
in-theory        59750
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-183 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59750.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-183, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59751
in-theory        59751
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-157 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59751.        ((A -> ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-157, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59752
in-theory        59752
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     33
proof            (modus-ponens tm-147 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59752.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-147, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59753
in-theory        59753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-134 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59753.        ((A -> ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-134, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59754
in-theory        59754
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     33
proof            (modus-ponens tm-125 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59754.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-125, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59755
in-theory        59755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     33
proof            (modus-ponens tm-113 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59755.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-113, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59756
in-theory        59756
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     37
proof            (modus-ponens tm-105 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-9)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59756.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-105, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59757
in-theory        59757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C))))
theorem-size     25
proof            (modus-ponens tm-95 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59757.        (((A -> B) -> (A -> A)) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C)))), M:tm-95, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59758
in-theory        59758
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D -> ((A -> (not B)) -> (not A))))
theorem-size     19
proof            (modus-ponens tm-84 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59758.        ((((A -> B) and C) or (A -> B)) -> (D -> ((A -> (not B)) -> (not A)))), M:tm-84, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59759
in-theory        59759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-83 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59759.        ((A -> (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-83, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59760
in-theory        59760
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) and D) or (B -> C)) -> ((B -> (not C)) -> (not B))))
theorem-size     23
proof            (modus-ponens tm-76 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59760.        (((not (not A)) -> A) and ((((B -> C) and D) or (B -> C)) -> ((B -> (not C)) -> (not B)))), M:tm-76, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59761
in-theory        59761
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) and C) or (A -> B)))) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A)))
theorem-size     29
proof            (modus-ponens tm-73 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-8 tm-10 tm-3 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59761.        (((not (not (((A -> B) and C) or (A -> B)))) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A))), M:tm-73, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59762
in-theory        59762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C))))
theorem-size     29
proof            (modus-ponens tm-69 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59762.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C)))), M:tm-69, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59763
in-theory        59763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     31
proof            (modus-ponens tm-54 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59763.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-54, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59764
in-theory        59764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A)))
theorem-size     21
proof            (modus-ponens tm-50 tm-719 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-8 tm-7 tm-3 tm-9)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59764.        (((A -> B) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A))), M:tm-50, m:tm-719, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59765
in-theory        59765
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A)))
theorem-size     23
proof            (modus-ponens tm-49 tm-719 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-8 tm-6 tm-3 tm-9)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59765.        ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A))), M:tm-49, m:tm-719, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59766
in-theory        59766
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) or (B -> C))) or (((B -> C) and D) or (B -> C))) -> ((B -> (not C)) -> (not B)))
theorem-size     29
proof            (modus-ponens tm-47 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-8 tm-4 tm-3 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59766.        (((A and (((B -> C) and D) or (B -> C))) or (((B -> C) and D) or (B -> C))) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59767
in-theory        59767
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A)))
theorem-size     29
proof            (modus-ponens tm-46 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-8 tm-3 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59767.        ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59768
in-theory        59768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C))))
theorem-size     23
proof            (modus-ponens tm-42 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59768.        ((A -> (B or A)) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59769
in-theory        59769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C))))
theorem-size     23
proof            (modus-ponens tm-32 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59769.        ((A -> (A or B)) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59770
in-theory        59770
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and ((A -> (not B)) -> (not A))))
theorem-size     27
proof            (modus-ponens tm-24 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59770.        ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59771
in-theory        59771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C))))
theorem-size     25
proof            (modus-ponens tm-23 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59771.        ((A -> (B -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59772
in-theory        59772
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C))))
theorem-size     23
proof            (modus-ponens tm-22 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59772.        (((A and B) -> B) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59773
in-theory        59773
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C))))
theorem-size     23
proof            (modus-ponens tm-21 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-3 tm-8 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59773.        (((A and B) -> A) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59774
in-theory        59774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     31
proof            (modus-ponens tm-20 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59774.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59775
in-theory        59775
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C))))
theorem-size     23
proof            (modus-ponens tm-19 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59775.        ((A -> (B -> A)) and ((((C -> D) and E) or (C -> D)) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59776
in-theory        59776
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (not ((A -> (not B)) -> (not A)))) -> (not (((A -> B) and C) or (A -> B))))
theorem-size     29
proof            (modus-ponens tm-9 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-9 tm-8 tm-3)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59776.        (((((A -> B) and C) or (A -> B)) -> (not ((A -> (not B)) -> (not A)))) -> (not (((A -> B) and C) or (A -> B)))), M:tm-9, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59777
in-theory        59777
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> C) -> (((((A -> B) and D) or (A -> B)) or ((A -> (not B)) -> (not A))) -> C))
theorem-size     29
proof            (modus-ponens tm-8 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-8 tm-3 tm-9)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59777.        ((((A -> (not B)) -> (not A)) -> C) -> (((((A -> B) and D) or (A -> B)) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-59778
in-theory        59778
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) and D) or (B -> C)) -> ((B -> (not C)) -> (not B))))
theorem-size     19
proof            (modus-ponens tm-7 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-7 tm-8 tm-3 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59778.        (A or ((((B -> C) and D) or (B -> C)) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59779
in-theory        59779
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) or D)
theorem-size     19
proof            (modus-ponens tm-6 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-6 tm-8 tm-3 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59779.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) or D), M:tm-6, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59780
in-theory        59780
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) and D) or (B -> C)) -> ((B -> (not C)) -> (not B))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59780.        (A -> (((((B -> C) and D) or (B -> C)) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59781
in-theory        59781
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (not B))) -> ((((A -> B) and C) or (A -> B)) -> (not A)))
theorem-size     27
proof            (modus-ponens tm-2 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (not Bm))) (C (not Am))))
axioms-used      (tm-2 tm-8 tm-3 tm-9)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59781.        (((((A -> B) and C) or (A -> B)) -> (A -> (not B))) -> ((((A -> B) and C) or (A -> B)) -> (not A))), M:tm-2, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (not Bm))) (C (not Am)))
================================================================
tm-name          tm-59782
in-theory        59782
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) and D) or (B -> C)) -> ((B -> (not C)) -> (not B))))
theorem-size     19
proof            (modus-ponens tm-1 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-1 tm-8 tm-3 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-59782.        (A -> ((((B -> C) and D) or (B -> C)) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-59783
in-theory        59783
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((not (not E)) and F) or (not (not E))) -> E))
theorem-size     37
proof            (modus-ponens tm-708 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-10)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59783.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((not (not E)) and F) or (not (not E))) -> E)), M:tm-708, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59784
in-theory        59784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     25
proof            (modus-ponens tm-665 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-10)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59784.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-665, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59785
in-theory        59785
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) and B) or (not (not A))) -> (C or A))
theorem-size     13
proof            (modus-ponens tm-623 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59785.        ((((not (not A)) and B) or (not (not A))) -> (C or A)), M:tm-623, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59786
in-theory        59786
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-622 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59786.        ((A -> (B -> (C or B))) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-622, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59787
in-theory        59787
times-derived    1
----------------------------------------------------------------
theorem          (not (((not (not (not (A -> (B or A))))) and C) or (not (not (not (A -> (B or A)))))))
theorem-size     20
proof            (modus-ponens tm-618 tm-720 ((A (or (and (not (not (not (-> B (or C B))))) Bm) (not (not (not (-> B (or C B))))))) (Am (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-8 tm-3 tm-10)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59787.        (not (((not (not (not (A -> (B or A))))) and C) or (not (not (not (A -> (B or A))))))), M:tm-618, m:tm-720, u:((A (or (and (not (not (not (-> B (or C B))))) Bm) (not (not (not (-> B (or C B))))))) (Am (not (-> B (or C B)))))
================================================================
tm-name          tm-59788
in-theory        59788
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-609 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59788.        (((((not (not A)) and B) or (not (not A))) -> A) and (C -> (D or C))), M:tm-609, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59789
in-theory        59789
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     21
proof            (modus-ponens tm-605 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59789.        ((A -> ((B -> (C or B)) and A)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-605, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59790
in-theory        59790
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and ((C -> (D or C)) and ((((not (not A)) and B) or (not (not A))) -> A)))
theorem-size     29
proof            (modus-ponens tm-595 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59790.        (((((not (not A)) and B) or (not (not A))) -> A) and ((C -> (D or C)) and ((((not (not A)) and B) or (not (not A))) -> A))), M:tm-595, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59791
in-theory        59791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-550 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59791.        (((A -> (B or A)) or C) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-550, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59792
in-theory        59792
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-540 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59792.        ((A or (B -> (C or B))) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-540, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59793
in-theory        59793
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-530 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59793.        ((A or (B -> (B or C))) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-530, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59794
in-theory        59794
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     21
proof            (modus-ponens tm-520 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59794.        ((A or (B -> (C -> (B and C)))) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-520, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59795
in-theory        59795
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-510 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59795.        ((A or ((B and C) -> C)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-510, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59796
in-theory        59796
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-500 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59796.        ((A or ((B and C) -> B)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-500, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59797
in-theory        59797
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((not (not E)) and F) or (not (not E))) -> E))
theorem-size     27
proof            (modus-ponens tm-490 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59797.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((not (not E)) and F) or (not (not E))) -> E)), M:tm-490, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59798
in-theory        59798
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-480 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59798.        ((A or (B -> (C -> B))) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-480, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59799
in-theory        59799
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) and B) or (not (not A))) -> (A or C))
theorem-size     13
proof            (modus-ponens tm-470 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59799.        ((((not (not A)) and B) or (not (not A))) -> (A or C)), M:tm-470, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59800
in-theory        59800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-469 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59800.        ((A -> (B -> (B or C))) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-469, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59801
in-theory        59801
times-derived    1
----------------------------------------------------------------
theorem          (not (((not (not (not (A -> (A or B))))) and C) or (not (not (not (A -> (A or B)))))))
theorem-size     20
proof            (modus-ponens tm-465 tm-720 ((A (or (and (not (not (not (-> B (or B C))))) Bm) (not (not (not (-> B (or B C))))))) (Am (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-8 tm-3 tm-10)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59801.        (not (((not (not (not (A -> (A or B))))) and C) or (not (not (not (A -> (A or B))))))), M:tm-465, m:tm-720, u:((A (or (and (not (not (not (-> B (or B C))))) Bm) (not (not (not (-> B (or B C))))))) (Am (not (-> B (or B C)))))
================================================================
tm-name          tm-59802
in-theory        59802
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-456 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59802.        (((((not (not A)) and B) or (not (not A))) -> A) and (C -> (C or D))), M:tm-456, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59803
in-theory        59803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     21
proof            (modus-ponens tm-453 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59803.        ((A -> ((B -> (B or C)) and A)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-453, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59804
in-theory        59804
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and ((C -> (C or D)) and ((((not (not A)) and B) or (not (not A))) -> A)))
theorem-size     29
proof            (modus-ponens tm-443 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59804.        (((((not (not A)) and B) or (not (not A))) -> A) and ((C -> (C or D)) and ((((not (not A)) and B) or (not (not A))) -> A))), M:tm-443, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59805
in-theory        59805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-409 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59805.        (((A -> (A or B)) or C) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-409, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59806
in-theory        59806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     21
proof            (modus-ponens tm-400 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59806.        (((A -> (B -> (A and B))) or C) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-400, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59807
in-theory        59807
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-391 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59807.        ((((A and B) -> B) or C) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-391, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59808
in-theory        59808
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-382 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59808.        ((((A and B) -> A) or C) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-382, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59809
in-theory        59809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((not (not E)) and F) or (not (not E))) -> E))
theorem-size     27
proof            (modus-ponens tm-373 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59809.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((not (not E)) and F) or (not (not E))) -> E)), M:tm-373, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59810
in-theory        59810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-364 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59810.        (((A -> (B -> A)) or C) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-364, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59811
in-theory        59811
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) and B) or (not (not A))) -> (C -> (A and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3 tm-10)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59811.        ((((not (not A)) and B) or (not (not A))) -> (C -> (A and C))), M:tm-355, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59812
in-theory        59812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     21
proof            (modus-ponens tm-354 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59812.        ((A -> (B -> (C -> (B and C)))) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-354, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59813
in-theory        59813
times-derived    1
----------------------------------------------------------------
theorem          (not (((not (not (not (A -> (B -> (A and B)))))) and C) or (not (not (not (A -> (B -> (A and B))))))))
theorem-size     24
proof            (modus-ponens tm-350 tm-720 ((A (or (and (not (not (not (-> B (-> C (and B C)))))) Bm) (not (not (not (-> B (-> C (and B C)))))))) (Am (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-8 tm-3 tm-10)
proof-size       114
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59813.        (not (((not (not (not (A -> (B -> (A and B)))))) and C) or (not (not (not (A -> (B -> (A and B)))))))), M:tm-350, m:tm-720, u:((A (or (and (not (not (not (-> B (-> C (and B C)))))) Bm) (not (not (not (-> B (-> C (and B C)))))))) (Am (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-59814
in-theory        59814
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and (C -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-341 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-10)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59814.        (((((not (not A)) and B) or (not (not A))) -> A) and (C -> (D -> (C and D)))), M:tm-341, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59815
in-theory        59815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((not (not C)) and D) or (not (not C))) -> C))
theorem-size     21
proof            (modus-ponens tm-338 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-10)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59815.        (((A -> B) -> (A -> (A and B))) and ((((not (not C)) and D) or (not (not C))) -> C)), M:tm-338, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59816
in-theory        59816
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and ((((not (not A)) and B) or (not (not A))) -> ((((not (not A)) and B) or (not (not A))) and A)))
theorem-size     33
proof            (modus-ponens tm-328 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-10)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59816.        (((((not (not A)) and B) or (not (not A))) -> A) and ((((not (not A)) and B) or (not (not A))) -> ((((not (not A)) and B) or (not (not A))) and A))), M:tm-328, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59817
in-theory        59817
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and ((C -> (D -> (C and D))) and ((((not (not A)) and B) or (not (not A))) -> A)))
theorem-size     31
proof            (modus-ponens tm-327 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-10)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59817.        (((((not (not A)) and B) or (not (not A))) -> A) and ((C -> (D -> (C and D))) and ((((not (not A)) and B) or (not (not A))) -> A))), M:tm-327, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59818
in-theory        59818
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and (((C and D) -> D) and ((((not (not A)) and B) or (not (not A))) -> A)))
theorem-size     29
proof            (modus-ponens tm-326 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59818.        (((((not (not A)) and B) or (not (not A))) -> A) and (((C and D) -> D) and ((((not (not A)) and B) or (not (not A))) -> A))), M:tm-326, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59819
in-theory        59819
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and (((C and D) -> C) and ((((not (not A)) and B) or (not (not A))) -> A)))
theorem-size     29
proof            (modus-ponens tm-325 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59819.        (((((not (not A)) and B) or (not (not A))) -> A) and (((C and D) -> C) and ((((not (not A)) and B) or (not (not A))) -> A))), M:tm-325, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59820
in-theory        59820
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((not (not A)) and B) or (not (not A))) -> A)))
theorem-size     37
proof            (modus-ponens tm-324 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-10)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59820.        (((((not (not A)) and B) or (not (not A))) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((((not (not A)) and B) or (not (not A))) -> A))), M:tm-324, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59821
in-theory        59821
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and ((C -> (D -> C)) and ((((not (not A)) and B) or (not (not A))) -> A)))
theorem-size     29
proof            (modus-ponens tm-323 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59821.        (((((not (not A)) and B) or (not (not A))) -> A) and ((C -> (D -> C)) and ((((not (not A)) and B) or (not (not A))) -> A))), M:tm-323, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59822
in-theory        59822
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-322 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59822.        (((((not (not A)) and B) or (not (not A))) -> A) and ((C and D) -> D)), M:tm-322, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59823
in-theory        59823
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-320 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59823.        (((((not (not A)) and B) or (not (not A))) -> A) and ((C and D) -> C)), M:tm-320, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59824
in-theory        59824
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-318 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-10)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59824.        (((((not (not A)) and B) or (not (not A))) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59825
in-theory        59825
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and ((((not (not A)) and B) or (not (not A))) -> (((not (not A)) and B) or (not (not A)))))
theorem-size     31
proof            (modus-ponens tm-316 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-10)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59825.        (((((not (not A)) and B) or (not (not A))) -> A) and ((((not (not A)) and B) or (not (not A))) -> (((not (not A)) and B) or (not (not A))))), M:tm-316, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59826
in-theory        59826
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-315 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59826.        (((((not (not A)) and B) or (not (not A))) -> A) and (C -> (D -> C))), M:tm-315, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59827
in-theory        59827
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and (((((not (not A)) and B) or (not (not A))) -> (not A)) -> (not (((not (not A)) and B) or (not (not A))))))
theorem-size     35
proof            (modus-ponens tm-313 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-10)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59827.        (((((not (not A)) and B) or (not (not A))) -> A) and (((((not (not A)) and B) or (not (not A))) -> (not A)) -> (not (((not (not A)) and B) or (not (not A)))))), M:tm-313, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59828
in-theory        59828
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and ((A -> C) -> (((((not (not A)) and B) or (not (not A))) or A) -> C)))
theorem-size     29
proof            (modus-ponens tm-312 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-10)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59828.        (((((not (not A)) and B) or (not (not A))) -> A) and ((A -> C) -> (((((not (not A)) and B) or (not (not A))) or A) -> C))), M:tm-312, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59829
in-theory        59829
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and (C or ((((not (not A)) and B) or (not (not A))) -> A)))
theorem-size     25
proof            (modus-ponens tm-311 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59829.        (((((not (not A)) and B) or (not (not A))) -> A) and (C or ((((not (not A)) and B) or (not (not A))) -> A))), M:tm-311, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59830
in-theory        59830
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and (((((not (not A)) and B) or (not (not A))) -> A) or C))
theorem-size     25
proof            (modus-ponens tm-310 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59830.        (((((not (not A)) and B) or (not (not A))) -> A) and (((((not (not A)) and B) or (not (not A))) -> A) or C)), M:tm-310, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59831
in-theory        59831
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and (C -> (((((not (not A)) and B) or (not (not A))) -> A) and C)))
theorem-size     27
proof            (modus-ponens tm-309 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59831.        (((((not (not A)) and B) or (not (not A))) -> A) and (C -> (((((not (not A)) and B) or (not (not A))) -> A) and C))), M:tm-309, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59832
in-theory        59832
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not (A -> B))) and C) or (not (not (A -> B)))) -> (A -> B)) and (((((not (not (A -> B))) and C) or (not (not (A -> B)))) -> A) -> ((((not (not (A -> B))) and C) or (not (not (A -> B)))) -> B)))
theorem-size     49
proof            (modus-ponens tm-306 tm-720 ((A (or (and (not (not (-> B C))) Bm) (not (not (-> B C))))) (Am (-> B C))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-10)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59832.        (((((not (not (A -> B))) and C) or (not (not (A -> B)))) -> (A -> B)) and (((((not (not (A -> B))) and C) or (not (not (A -> B)))) -> A) -> ((((not (not (A -> B))) and C) or (not (not (A -> B)))) -> B))), M:tm-306, m:tm-720, u:((A (or (and (not (not (-> B C))) Bm) (not (not (-> B C))))) (Am (-> B C)))
================================================================
tm-name          tm-59833
in-theory        59833
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and (C -> ((((not (not A)) and B) or (not (not A))) -> A)))
theorem-size     25
proof            (modus-ponens tm-305 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59833.        (((((not (not A)) and B) or (not (not A))) -> A) and (C -> ((((not (not A)) and B) or (not (not A))) -> A))), M:tm-305, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59834
in-theory        59834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     23
proof            (modus-ponens tm-303 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-8 tm-3 tm-10)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59834.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-303, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59835
in-theory        59835
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     21
proof            (modus-ponens tm-270 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59835.        ((A -> (((B and C) -> C) and A)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-270, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59836
in-theory        59836
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     21
proof            (modus-ponens tm-239 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-3 tm-8 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59836.        ((A -> (((B and C) -> B) and A)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-239, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59837
in-theory        59837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((not (not E)) and F) or (not (not E))) -> E))
theorem-size     29
proof            (modus-ponens tm-210 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-10)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59837.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((not (not E)) and F) or (not (not E))) -> E)), M:tm-210, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59838
in-theory        59838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     21
proof            (modus-ponens tm-183 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59838.        ((A -> ((B -> (C -> B)) and A)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-183, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59839
in-theory        59839
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A and B))) and C) or (not (not (A and B)))) -> B)
theorem-size     15
proof            (modus-ponens tm-158 tm-720 ((A (or (and (not (not (and B C))) Bm) (not (not (and B C))))) (Am (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-8 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59839.        ((((not (not (A and B))) and C) or (not (not (A and B)))) -> B), M:tm-158, m:tm-720, u:((A (or (and (not (not (and B C))) Bm) (not (not (and B C))))) (Am (and B C)))
================================================================
tm-name          tm-59840
in-theory        59840
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-157 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59840.        ((A -> ((B and C) -> C)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-157, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59841
in-theory        59841
times-derived    1
----------------------------------------------------------------
theorem          (not (((not (not (not ((A and B) -> B)))) and C) or (not (not (not ((A and B) -> B))))))
theorem-size     20
proof            (modus-ponens tm-153 tm-720 ((A (or (and (not (not (not (-> (and B C) C)))) Bm) (not (not (not (-> (and B C) C)))))) (Am (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-8 tm-3 tm-10)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59841.        (not (((not (not (not ((A and B) -> B)))) and C) or (not (not (not ((A and B) -> B)))))), M:tm-153, m:tm-720, u:((A (or (and (not (not (not (-> (and B C) C)))) Bm) (not (not (not (-> (and B C) C)))))) (Am (not (-> (and B C) C))))
================================================================
tm-name          tm-59842
in-theory        59842
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     27
proof            (modus-ponens tm-147 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59842.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-147, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59843
in-theory        59843
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A and B))) and C) or (not (not (A and B)))) -> A)
theorem-size     15
proof            (modus-ponens tm-135 tm-720 ((A (or (and (not (not (and B C))) Bm) (not (not (and B C))))) (Am (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-8 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59843.        ((((not (not (A and B))) and C) or (not (not (A and B)))) -> A), M:tm-135, m:tm-720, u:((A (or (and (not (not (and B C))) Bm) (not (not (and B C))))) (Am (and B C)))
================================================================
tm-name          tm-59844
in-theory        59844
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-134 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59844.        ((A -> ((B and C) -> B)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-134, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59845
in-theory        59845
times-derived    1
----------------------------------------------------------------
theorem          (not (((not (not (not ((A and B) -> A)))) and C) or (not (not (not ((A and B) -> A))))))
theorem-size     20
proof            (modus-ponens tm-130 tm-720 ((A (or (and (not (not (not (-> (and B C) B)))) Bm) (not (not (not (-> (and B C) B)))))) (Am (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-8 tm-10)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59845.        (not (((not (not (not ((A and B) -> A)))) and C) or (not (not (not ((A and B) -> A)))))), M:tm-130, m:tm-720, u:((A (or (and (not (not (not (-> (and B C) B)))) Bm) (not (not (not (-> (and B C) B)))))) (Am (not (-> (and B C) B))))
================================================================
tm-name          tm-59846
in-theory        59846
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     27
proof            (modus-ponens tm-125 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59846.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-125, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59847
in-theory        59847
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> (B -> C)))) and D) or (not (not (A -> (B -> C))))) -> ((A -> B) -> (A -> C)))
theorem-size     25
proof            (modus-ponens tm-114 tm-720 ((A (or (and (not (not (-> B (-> C D)))) Bm) (not (not (-> B (-> C D)))))) (Am (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-10)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59847.        ((((not (not (A -> (B -> C)))) and D) or (not (not (A -> (B -> C))))) -> ((A -> B) -> (A -> C))), M:tm-114, m:tm-720, u:((A (or (and (not (not (-> B (-> C D)))) Bm) (not (not (-> B (-> C D)))))) (Am (-> B (-> C D))))
================================================================
tm-name          tm-59848
in-theory        59848
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((not (not E)) and F) or (not (not E))) -> E))
theorem-size     27
proof            (modus-ponens tm-113 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59848.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((not (not E)) and F) or (not (not E))) -> E)), M:tm-113, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59849
in-theory        59849
times-derived    1
----------------------------------------------------------------
theorem          (not (((not (not (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))) and D) or (not (not (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))))))
theorem-size     36
proof            (modus-ponens tm-109 tm-720 ((A (or (and (not (not (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))) Bm) (not (not (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))) (Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-8 tm-3 tm-10)
proof-size       144
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59849.        (not (((not (not (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))) and D) or (not (not (not ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))))))), M:tm-109, m:tm-720, u:((A (or (and (not (not (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))) Bm) (not (not (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))) (Am (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-59850
in-theory        59850
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     31
proof            (modus-ponens tm-105 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-10)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59850.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-105, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59851
in-theory        59851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((not (not C)) and D) or (not (not C))) -> C))
theorem-size     19
proof            (modus-ponens tm-95 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59851.        (((A -> B) -> (A -> A)) and ((((not (not C)) and D) or (not (not C))) -> C)), M:tm-95, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59852
in-theory        59852
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) and C) or (not (not (A -> B)))) -> (A -> B))
theorem-size     17
proof            (modus-ponens tm-87 tm-720 ((A (or (and (not (not (-> B C))) Bm) (not (not (-> B C))))) (Am (-> B C))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59852.        ((((not (not (A -> B))) and C) or (not (not (A -> B)))) -> (A -> B)), M:tm-87, m:tm-720, u:((A (or (and (not (not (-> B C))) Bm) (not (not (-> B C))))) (Am (-> B C)))
================================================================
tm-name          tm-59853
in-theory        59853
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) and B) or (not (not A))) -> (C -> A))
theorem-size     13
proof            (modus-ponens tm-84 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59853.        ((((not (not A)) and B) or (not (not A))) -> (C -> A)), M:tm-84, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59854
in-theory        59854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-83 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59854.        ((A -> (B -> (C -> B))) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-83, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59855
in-theory        59855
times-derived    1
----------------------------------------------------------------
theorem          (not (((not (not (not (A -> (B -> A))))) and C) or (not (not (not (A -> (B -> A)))))))
theorem-size     20
proof            (modus-ponens tm-79 tm-720 ((A (or (and (not (not (not (-> B (-> C B))))) Bm) (not (not (not (-> B (-> C B))))))) (Am (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-8 tm-3 tm-10)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59855.        (not (((not (not (not (A -> (B -> A))))) and C) or (not (not (not (A -> (B -> A))))))), M:tm-79, m:tm-720, u:((A (or (and (not (not (not (-> B (-> C B))))) Bm) (not (not (not (-> B (-> C B))))))) (Am (not (-> B (-> C B)))))
================================================================
tm-name          tm-59856
in-theory        59856
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((not (not B)) and C) or (not (not B))) -> B))
theorem-size     17
proof            (modus-ponens tm-76 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59856.        (((not (not A)) -> A) and ((((not (not B)) and C) or (not (not B))) -> B)), M:tm-76, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59857
in-theory        59857
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((not (not A)) and B) or (not (not A))))) or (((not (not A)) and B) or (not (not A)))) -> A)
theorem-size     23
proof            (modus-ponens tm-73 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-8 tm-10 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59857.        (((not (not (((not (not A)) and B) or (not (not A))))) or (((not (not A)) and B) or (not (not A)))) -> A), M:tm-73, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59858
in-theory        59858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((not (not C)) and D) or (not (not C))) -> C))
theorem-size     23
proof            (modus-ponens tm-69 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-10)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59858.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((not (not C)) and D) or (not (not C))) -> C)), M:tm-69, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59859
in-theory        59859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     25
proof            (modus-ponens tm-54 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-8 tm-3 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59859.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-54, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59860
in-theory        59860
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or (((not (not A)) and B) or (not (not A)))) -> A)
theorem-size     15
proof            (modus-ponens tm-50 tm-720 ((A (and (not (not Am)) Bm)) (B (not (not Am))) (C Am)))
axioms-used      (tm-8 tm-7 tm-3 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59860.        (((not (not A)) or (((not (not A)) and B) or (not (not A)))) -> A), M:tm-50, m:tm-720, u:((A (and (not (not Am)) Bm)) (B (not (not Am))) (C Am))
================================================================
tm-name          tm-59861
in-theory        59861
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) and B) or (((not (not A)) and B) or (not (not A)))) -> A)
theorem-size     17
proof            (modus-ponens tm-49 tm-720 ((A (and (not (not Am)) Bm)) (B (not (not Am))) (C Am)))
axioms-used      (tm-8 tm-6 tm-3 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59861.        ((((not (not A)) and B) or (((not (not A)) and B) or (not (not A)))) -> A), M:tm-49, m:tm-720, u:((A (and (not (not Am)) Bm)) (B (not (not Am))) (C Am))
================================================================
tm-name          tm-59862
in-theory        59862
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((not (not B)) and C) or (not (not B)))) or (((not (not B)) and C) or (not (not B)))) -> B)
theorem-size     23
proof            (modus-ponens tm-47 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-8 tm-4 tm-3 tm-10)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59862.        (((A and (((not (not B)) and C) or (not (not B)))) or (((not (not B)) and C) or (not (not B)))) -> B), M:tm-47, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59863
in-theory        59863
times-derived    1
----------------------------------------------------------------
theorem          ((((((not (not A)) and B) or (not (not A))) and C) or (((not (not A)) and B) or (not (not A)))) -> A)
theorem-size     23
proof            (modus-ponens tm-46 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-8 tm-3 tm-10)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59863.        ((((((not (not A)) and B) or (not (not A))) and C) or (((not (not A)) and B) or (not (not A)))) -> A), M:tm-46, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59864
in-theory        59864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((not (not C)) and D) or (not (not C))) -> C))
theorem-size     17
proof            (modus-ponens tm-42 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59864.        ((A -> (B or A)) and ((((not (not C)) and D) or (not (not C))) -> C)), M:tm-42, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59865
in-theory        59865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((not (not C)) and D) or (not (not C))) -> C))
theorem-size     17
proof            (modus-ponens tm-32 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59865.        ((A -> (A or B)) and ((((not (not C)) and D) or (not (not C))) -> C)), M:tm-32, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59866
in-theory        59866
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) and B) or (not (not A))) -> ((((not (not A)) and B) or (not (not A))) and A))
theorem-size     21
proof            (modus-ponens tm-24 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-10)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59866.        ((((not (not A)) and B) or (not (not A))) -> ((((not (not A)) and B) or (not (not A))) and A)), M:tm-24, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59867
in-theory        59867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((not (not C)) and D) or (not (not C))) -> C))
theorem-size     19
proof            (modus-ponens tm-23 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-8 tm-3 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59867.        ((A -> (B -> (A and B))) and ((((not (not C)) and D) or (not (not C))) -> C)), M:tm-23, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59868
in-theory        59868
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((not (not C)) and D) or (not (not C))) -> C))
theorem-size     17
proof            (modus-ponens tm-22 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59868.        (((A and B) -> B) and ((((not (not C)) and D) or (not (not C))) -> C)), M:tm-22, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59869
in-theory        59869
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((not (not C)) and D) or (not (not C))) -> C))
theorem-size     17
proof            (modus-ponens tm-21 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-3 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59869.        (((A and B) -> A) and ((((not (not C)) and D) or (not (not C))) -> C)), M:tm-21, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59870
in-theory        59870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     25
proof            (modus-ponens tm-20 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59870.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-20, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59871
in-theory        59871
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((not (not C)) and D) or (not (not C))) -> C))
theorem-size     17
proof            (modus-ponens tm-19 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59871.        ((A -> (B -> A)) and ((((not (not C)) and D) or (not (not C))) -> C)), M:tm-19, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59872
in-theory        59872
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) and B) or (not (not A))) -> (((not (not A)) and B) or (not (not A))))
theorem-size     19
proof            (modus-ponens tm-12 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59872.        ((((not (not A)) and B) or (not (not A))) -> (((not (not A)) and B) or (not (not A)))), M:tm-12, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59873
in-theory        59873
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> (not A)) -> (not (((not (not A)) and B) or (not (not A)))))
theorem-size     23
proof            (modus-ponens tm-9 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-9 tm-8 tm-3 tm-10)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59873.        (((((not (not A)) and B) or (not (not A))) -> (not A)) -> (not (((not (not A)) and B) or (not (not A))))), M:tm-9, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59874
in-theory        59874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((((not (not A)) and C) or (not (not A))) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-8 tm-3 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59874.        ((A -> B) -> (((((not (not A)) and C) or (not (not A))) or A) -> B)), M:tm-8, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-59875
in-theory        59875
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((not (not B)) and C) or (not (not B))) -> B))
theorem-size     13
proof            (modus-ponens tm-7 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-7 tm-8 tm-3 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59875.        (A or ((((not (not B)) and C) or (not (not B))) -> B)), M:tm-7, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59876
in-theory        59876
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) or C)
theorem-size     13
proof            (modus-ponens tm-6 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-6 tm-8 tm-3 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59876.        (((((not (not A)) and B) or (not (not A))) -> A) or C), M:tm-6, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59877
in-theory        59877
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((not (not B)) and C) or (not (not B))) -> B) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-8 tm-3 tm-10)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59877.        (A -> (((((not (not B)) and C) or (not (not B))) -> B) and A)), M:tm-5, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59878
in-theory        59878
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not (A -> B))) and C) or (not (not (A -> B)))) -> A) -> ((((not (not (A -> B))) and C) or (not (not (A -> B)))) -> B))
theorem-size     31
proof            (modus-ponens tm-2 tm-720 ((A (or (and (not (not (-> B C))) Bm) (not (not (-> B C))))) (Am (-> B C))))
axioms-used      (tm-2 tm-8 tm-3 tm-10)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59878.        (((((not (not (A -> B))) and C) or (not (not (A -> B)))) -> A) -> ((((not (not (A -> B))) and C) or (not (not (A -> B)))) -> B)), M:tm-2, m:tm-720, u:((A (or (and (not (not (-> B C))) Bm) (not (not (-> B C))))) (Am (-> B C)))
================================================================
tm-name          tm-59879
in-theory        59879
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((not (not B)) and C) or (not (not B))) -> B))
theorem-size     13
proof            (modus-ponens tm-1 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-1 tm-8 tm-3 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-59879.        (A -> ((((not (not B)) and C) or (not (not B))) -> B)), M:tm-1, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-59880
in-theory        59880
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (G -> (H -> G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59880.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (G -> (H -> G)))), M:tm-708, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59881
in-theory        59881
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59881.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-665, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59882
in-theory        59882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59882.        ((A -> (B -> (C or B))) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-622, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59883
in-theory        59883
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (D or ((A and B) or A))))
theorem-size     15
proof            (modus-ponens tm-617 tm-721 ((A (or (and Am Bm) Am)) (Cm (or B (or (and Am Bm) Am))) (C (-> Dm (or B (or (and Am Bm) Am))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59883.        (((A and B) or A) -> (C -> (D or ((A and B) or A)))), M:tm-617, m:tm-721, u:((A (or (and Am Bm) Am)) (Cm (or B (or (and Am Bm) Am))) (C (-> Dm (or B (or (and Am Bm) Am)))))
================================================================
tm-name          tm-59884
in-theory        59884
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59884.        ((((A and B) or A) -> (C -> (D -> C))) and (E -> (F or E))), M:tm-609, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59885
in-theory        59885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59885.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-605, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59886
in-theory        59886
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and ((E -> (F or E)) and (((A and B) or A) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59886.        ((((A and B) or A) -> (C -> (D -> C))) and ((E -> (F or E)) and (((A and B) or A) -> (C -> (D -> C))))), M:tm-595, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59887
in-theory        59887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59887.        (((A -> (B or A)) or C) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-550, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59888
in-theory        59888
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59888.        ((A or (B -> (C or B))) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-540, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59889
in-theory        59889
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59889.        ((A or (B -> (B or C))) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-530, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59890
in-theory        59890
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59890.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-520, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59891
in-theory        59891
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59891.        ((A or ((B and C) -> C)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-510, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59892
in-theory        59892
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59892.        ((A or ((B and C) -> B)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-500, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59893
in-theory        59893
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59893.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (H -> G)))), M:tm-490, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59894
in-theory        59894
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59894.        ((A or (B -> (C -> B))) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-480, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59895
in-theory        59895
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59895.        ((A -> (B -> (B or C))) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-469, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59896
in-theory        59896
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (((A and B) or A) or D)))
theorem-size     15
proof            (modus-ponens tm-464 tm-721 ((A (or (and Am Bm) Am)) (Cm (or (or (and Am Bm) Am) B)) (C (-> Dm (or (or (and Am Bm) Am) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59896.        (((A and B) or A) -> (C -> (((A and B) or A) or D))), M:tm-464, m:tm-721, u:((A (or (and Am Bm) Am)) (Cm (or (or (and Am Bm) Am) B)) (C (-> Dm (or (or (and Am Bm) Am) B))))
================================================================
tm-name          tm-59897
in-theory        59897
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59897.        ((((A and B) or A) -> (C -> (D -> C))) and (E -> (E or F))), M:tm-456, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59898
in-theory        59898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59898.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-453, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59899
in-theory        59899
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and ((E -> (E or F)) and (((A and B) or A) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59899.        ((((A and B) or A) -> (C -> (D -> C))) and ((E -> (E or F)) and (((A and B) or A) -> (C -> (D -> C))))), M:tm-443, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59900
in-theory        59900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59900.        (((A -> (A or B)) or C) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-409, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59901
in-theory        59901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59901.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-400, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59902
in-theory        59902
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59902.        ((((A and B) -> B) or C) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-391, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59903
in-theory        59903
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59903.        ((((A and B) -> A) or C) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-382, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59904
in-theory        59904
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59904.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (G -> (H -> G)))), M:tm-373, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59905
in-theory        59905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59905.        (((A -> (B -> A)) or C) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-364, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59906
in-theory        59906
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59906.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-354, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59907
in-theory        59907
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (D -> (((A and B) or A) and D))))
theorem-size     17
proof            (modus-ponens tm-349 tm-721 ((A (or (and Am Bm) Am)) (Cm (-> B (and (or (and Am Bm) Am) B))) (C (-> Dm (-> B (and (or (and Am Bm) Am) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59907.        (((A and B) or A) -> (C -> (D -> (((A and B) or A) and D)))), M:tm-349, m:tm-721, u:((A (or (and Am Bm) Am)) (Cm (-> B (and (or (and Am Bm) Am) B))) (C (-> Dm (-> B (and (or (and Am Bm) Am) B)))))
================================================================
tm-name          tm-59908
in-theory        59908
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59908.        ((((A and B) or A) -> (C -> (D -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59909
in-theory        59909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59909.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (E -> (F -> E)))), M:tm-338, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59910
in-theory        59910
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (((A and B) or A) -> (((A and B) or A) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-721 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59910.        ((((A and B) or A) -> (C -> (D -> C))) and (((A and B) or A) -> (((A and B) or A) and (C -> (D -> C))))), M:tm-328, m:tm-721, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-59911
in-theory        59911
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and ((E -> (F -> (E and F))) and (((A and B) or A) -> (C -> (D -> C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59911.        ((((A and B) or A) -> (C -> (D -> C))) and ((E -> (F -> (E and F))) and (((A and B) or A) -> (C -> (D -> C))))), M:tm-327, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59912
in-theory        59912
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (((E and F) -> F) and (((A and B) or A) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59912.        ((((A and B) or A) -> (C -> (D -> C))) and (((E and F) -> F) and (((A and B) or A) -> (C -> (D -> C))))), M:tm-326, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59913
in-theory        59913
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (((E and F) -> E) and (((A and B) or A) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59913.        ((((A and B) or A) -> (C -> (D -> C))) and (((E and F) -> E) and (((A and B) or A) -> (C -> (D -> C))))), M:tm-325, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59914
in-theory        59914
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> (C -> (D -> C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59914.        ((((A and B) or A) -> (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> (C -> (D -> C))))), M:tm-324, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59915
in-theory        59915
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and ((E -> (F -> E)) and (((A and B) or A) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59915.        ((((A and B) or A) -> (C -> (D -> C))) and ((E -> (F -> E)) and (((A and B) or A) -> (C -> (D -> C))))), M:tm-323, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59916
in-theory        59916
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59916.        ((((A and B) or A) -> (C -> (D -> C))) and ((E and F) -> F)), M:tm-322, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59917
in-theory        59917
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59917.        ((((A and B) or A) -> (C -> (D -> C))) and ((E and F) -> E)), M:tm-320, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59918
in-theory        59918
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59918.        ((((A and B) or A) -> (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59919
in-theory        59919
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     23
proof            (modus-ponens tm-316 tm-721 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59919.        ((((A and B) or A) -> (C -> (D -> C))) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-721, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-59920
in-theory        59920
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59920.        ((((A and B) or A) -> (C -> (D -> C))) and (E -> (F -> E))), M:tm-315, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59921
in-theory        59921
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and ((((A and B) or A) -> (not (C -> (D -> C)))) -> (not ((A and B) or A))))
theorem-size     31
proof            (modus-ponens tm-313 tm-721 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59921.        ((((A and B) or A) -> (C -> (D -> C))) and ((((A and B) or A) -> (not (C -> (D -> C)))) -> (not ((A and B) or A)))), M:tm-313, m:tm-721, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-59922
in-theory        59922
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (((C -> (D -> C)) -> E) -> ((((A and B) or A) or (C -> (D -> C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-721 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59922.        ((((A and B) or A) -> (C -> (D -> C))) and (((C -> (D -> C)) -> E) -> ((((A and B) or A) or (C -> (D -> C))) -> E))), M:tm-312, m:tm-721, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-59923
in-theory        59923
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (E or (((A and B) or A) -> (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59923.        ((((A and B) or A) -> (C -> (D -> C))) and (E or (((A and B) or A) -> (C -> (D -> C))))), M:tm-311, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59924
in-theory        59924
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and ((((A and B) or A) -> (C -> (D -> C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59924.        ((((A and B) or A) -> (C -> (D -> C))) and ((((A and B) or A) -> (C -> (D -> C))) or E)), M:tm-310, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59925
in-theory        59925
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (E -> ((((A and B) or A) -> (C -> (D -> C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59925.        ((((A and B) or A) -> (C -> (D -> C))) and (E -> ((((A and B) or A) -> (C -> (D -> C))) and E))), M:tm-309, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59926
in-theory        59926
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and ((((A and B) or A) -> C) -> (((A and B) or A) -> (D -> C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-721 ((A (or (and Am Bm) Am)) (B Cm) (C (-> Dm Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59926.        ((((A and B) or A) -> (C -> (D -> C))) and ((((A and B) or A) -> C) -> (((A and B) or A) -> (D -> C)))), M:tm-306, m:tm-721, u:((A (or (and Am Bm) Am)) (B Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-59927
in-theory        59927
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (E -> (((A and B) or A) -> (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59927.        ((((A and B) or A) -> (C -> (D -> C))) and (E -> (((A and B) or A) -> (C -> (D -> C))))), M:tm-305, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59928
in-theory        59928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59928.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-303, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59929
in-theory        59929
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59929.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-270, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59930
in-theory        59930
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59930.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-239, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59931
in-theory        59931
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59931.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (G -> (H -> G)))), M:tm-210, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59932
in-theory        59932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59932.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-183, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59933
in-theory        59933
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59933.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-157, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59934
in-theory        59934
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59934.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-147, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59935
in-theory        59935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59935.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-134, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59936
in-theory        59936
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59936.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-125, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59937
in-theory        59937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59937.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (H -> G)))), M:tm-113, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59938
in-theory        59938
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59938.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-105, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59939
in-theory        59939
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((A and B) or A)))
theorem-size     13
proof            (modus-ponens tm-99 tm-721 ((Cm (or (and Am Bm) Am)) (A (or (and Am Bm) Am)) (B (-> Dm (or (and Am Bm) Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59939.        (((A and B) or A) -> (C -> ((A and B) or A))), M:tm-99, m:tm-721, u:((Cm (or (and Am Bm) Am)) (A (or (and Am Bm) Am)) (B (-> Dm (or (and Am Bm) Am))))
================================================================
tm-name          tm-59940
in-theory        59940
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (D -> ((A and B) or A))))
theorem-size     15
proof            (modus-ponens tm-98 tm-721 ((A (or (and Am Bm) Am)) (Cm (-> B (or (and Am Bm) Am))) (C (-> Dm (-> B (or (and Am Bm) Am))))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59940.        (((A and B) or A) -> (C -> (D -> ((A and B) or A)))), M:tm-98, m:tm-721, u:((A (or (and Am Bm) Am)) (Cm (-> B (or (and Am Bm) Am))) (C (-> Dm (-> B (or (and Am Bm) Am)))))
================================================================
tm-name          tm-59941
in-theory        59941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59941.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> (E -> (F -> E)))), M:tm-95, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59942
in-theory        59942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59942.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-83, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59943
in-theory        59943
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> (D -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59943.        (((not (not A)) -> A) and (((B and C) or B) -> (D -> (E -> D)))), M:tm-76, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59944
in-theory        59944
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> (C -> (D -> C)))
theorem-size     19
proof            (modus-ponens tm-73 tm-721 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-10 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59944.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> (C -> (D -> C))), M:tm-73, m:tm-721, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-59945
in-theory        59945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59945.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (E -> (F -> E)))), M:tm-69, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59946
in-theory        59946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59946.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-54, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59947
in-theory        59947
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-50 tm-721 ((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-7 tm-3 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59947.        ((A or ((A and B) or A)) -> (C -> (D -> C))), M:tm-50, m:tm-721, u:((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-59948
in-theory        59948
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-721 ((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-6 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59948.        (((A and B) or ((A and B) or A)) -> (C -> (D -> C))), M:tm-49, m:tm-721, u:((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-59949
in-theory        59949
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-47 tm-721 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-4 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59949.        (((A and ((B and C) or B)) or ((B and C) or B)) -> (D -> (E -> D))), M:tm-47, m:tm-721, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-59950
in-theory        59950
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-46 tm-721 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59950.        (((((A and B) or A) and C) or ((A and B) or A)) -> (D -> (E -> D))), M:tm-46, m:tm-721, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-59951
in-theory        59951
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59951.        ((A -> (B or A)) and (((C and D) or C) -> (E -> (F -> E)))), M:tm-42, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59952
in-theory        59952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59952.        ((A -> (A or B)) and (((C and D) or C) -> (E -> (F -> E)))), M:tm-32, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59953
in-theory        59953
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and (C -> (D -> C))))
theorem-size     17
proof            (modus-ponens tm-24 tm-721 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59953.        (((A and B) or A) -> (((A and B) or A) and (C -> (D -> C)))), M:tm-24, m:tm-721, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-59954
in-theory        59954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59954.        ((A -> (B -> (A and B))) and (((C and D) or C) -> (E -> (F -> E)))), M:tm-23, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59955
in-theory        59955
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59955.        (((A and B) -> B) and (((C and D) or C) -> (E -> (F -> E)))), M:tm-22, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59956
in-theory        59956
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59956.        (((A and B) -> A) and (((C and D) or C) -> (E -> (F -> E)))), M:tm-21, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59957
in-theory        59957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59957.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-20, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59958
in-theory        59958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59958.        ((A -> (B -> A)) and (((C and D) or C) -> (E -> (F -> E)))), M:tm-19, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59959
in-theory        59959
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not (C -> (D -> C)))) -> (not ((A and B) or A)))
theorem-size     19
proof            (modus-ponens tm-9 tm-721 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-9 tm-8 tm-3 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59959.        ((((A and B) or A) -> (not (C -> (D -> C)))) -> (not ((A and B) or A))), M:tm-9, m:tm-721, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-59960
in-theory        59960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> ((((D and E) or D) or (A -> (B -> A))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-721 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59960.        (((A -> (B -> A)) -> C) -> ((((D and E) or D) or (A -> (B -> A))) -> C)), M:tm-8, m:tm-721, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-59961
in-theory        59961
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-7 tm-8 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59961.        (A or (((B and C) or B) -> (D -> (E -> D)))), M:tm-7, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59962
in-theory        59962
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-6 tm-8 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59962.        ((((A and B) or A) -> (C -> (D -> C))) or E), M:tm-6, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59963
in-theory        59963
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> (D -> (E -> D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59963.        (A -> ((((B and C) or B) -> (D -> (E -> D))) and A)), M:tm-5, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59964
in-theory        59964
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> C) -> (((A and B) or A) -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-2 tm-721 ((A (or (and Am Bm) Am)) (B Cm) (C (-> Dm Cm))))
axioms-used      (tm-2 tm-8 tm-3 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59964.        ((((A and B) or A) -> C) -> (((A and B) or A) -> (D -> C))), M:tm-2, m:tm-721, u:((A (or (and Am Bm) Am)) (B Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-59965
in-theory        59965
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-59965.        (A -> (((B and C) or B) -> (D -> (E -> D)))), M:tm-1, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-59966
in-theory        59966
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (E -> E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59966.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (E -> E))), M:tm-708, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59967
in-theory        59967
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59967.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-665, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59968
in-theory        59968
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D or (A -> A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59968.        ((((A -> B) and C) or (A -> B)) -> (D or (A -> A))), M:tm-623, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-59969
in-theory        59969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59969.        ((A -> (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-622, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59970
in-theory        59970
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59970.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (D -> (E or D))), M:tm-609, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59971
in-theory        59971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59971.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-605, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59972
in-theory        59972
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((D -> (E or D)) and ((((A -> B) and C) or (A -> B)) -> (A -> A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59972.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((D -> (E or D)) and ((((A -> B) and C) or (A -> B)) -> (A -> A)))), M:tm-595, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59973
in-theory        59973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59973.        (((A -> (B or A)) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-550, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59974
in-theory        59974
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59974.        ((A or (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-540, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59975
in-theory        59975
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59975.        ((A or (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-530, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59976
in-theory        59976
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59976.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-520, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59977
in-theory        59977
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59977.        ((A or ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-510, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59978
in-theory        59978
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59978.        ((A or ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-500, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59979
in-theory        59979
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (E -> E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59979.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (E -> E))), M:tm-490, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59980
in-theory        59980
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59980.        ((A or (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-480, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59981
in-theory        59981
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((A -> A) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59981.        ((((A -> B) and C) or (A -> B)) -> ((A -> A) or D)), M:tm-470, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-59982
in-theory        59982
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59982.        ((A -> (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-469, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59983
in-theory        59983
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59983.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (D -> (D or E))), M:tm-456, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59984
in-theory        59984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59984.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-453, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59985
in-theory        59985
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((D -> (D or E)) and ((((A -> B) and C) or (A -> B)) -> (A -> A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59985.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((D -> (D or E)) and ((((A -> B) and C) or (A -> B)) -> (A -> A)))), M:tm-443, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59986
in-theory        59986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59986.        (((A -> (A or B)) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-409, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59987
in-theory        59987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59987.        (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-400, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59988
in-theory        59988
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59988.        ((((A and B) -> B) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-391, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59989
in-theory        59989
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59989.        ((((A and B) -> A) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-382, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59990
in-theory        59990
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (E -> E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59990.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (E -> E))), M:tm-373, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59991
in-theory        59991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59991.        (((A -> (B -> A)) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-364, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59992
in-theory        59992
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D -> ((A -> A) and D)))
theorem-size     17
proof            (modus-ponens tm-355 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59992.        ((((A -> B) and C) or (A -> B)) -> (D -> ((A -> A) and D))), M:tm-355, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-59993
in-theory        59993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59993.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-354, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59994
in-theory        59994
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59994.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59995
in-theory        59995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (C -> C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59995.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (C -> C))), M:tm-338, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59996
in-theory        59996
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (A -> A))))
theorem-size     37
proof            (modus-ponens tm-328 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59996.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (A -> A)))), M:tm-328, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-59997
in-theory        59997
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((D -> (E -> (D and E))) and ((((A -> B) and C) or (A -> B)) -> (A -> A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59997.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((D -> (E -> (D and E))) and ((((A -> B) and C) or (A -> B)) -> (A -> A)))), M:tm-327, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59998
in-theory        59998
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((D and E) -> E) and ((((A -> B) and C) or (A -> B)) -> (A -> A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59998.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((D and E) -> E) and ((((A -> B) and C) or (A -> B)) -> (A -> A)))), M:tm-326, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-59999
in-theory        59999
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((D and E) -> D) and ((((A -> B) and C) or (A -> B)) -> (A -> A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-59999.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((D and E) -> D) and ((((A -> B) and C) or (A -> B)) -> (A -> A)))), M:tm-325, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60000
in-theory        60000
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) and C) or (A -> B)) -> (A -> A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60000.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) and C) or (A -> B)) -> (A -> A)))), M:tm-324, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60001
in-theory        60001
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((D -> (E -> D)) and ((((A -> B) and C) or (A -> B)) -> (A -> A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60001.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((D -> (E -> D)) and ((((A -> B) and C) or (A -> B)) -> (A -> A)))), M:tm-323, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60002
in-theory        60002
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60002.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((D and E) -> E)), M:tm-322, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60003
in-theory        60003
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60003.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((D and E) -> D)), M:tm-320, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60004
in-theory        60004
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60004.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60005
in-theory        60005
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((((A -> B) and C) or (A -> B)) -> (((A -> B) and C) or (A -> B))))
theorem-size     33
proof            (modus-ponens tm-316 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60005.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((((A -> B) and C) or (A -> B)) -> (((A -> B) and C) or (A -> B)))), M:tm-316, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-60006
in-theory        60006
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60006.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (D -> (E -> D))), M:tm-315, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60007
in-theory        60007
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((((A -> B) and C) or (A -> B)) -> (not (A -> A))) -> (not (((A -> B) and C) or (A -> B)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60007.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((((A -> B) and C) or (A -> B)) -> (not (A -> A))) -> (not (((A -> B) and C) or (A -> B))))), M:tm-313, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-60008
in-theory        60008
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((A -> A) -> D) -> (((((A -> B) and C) or (A -> B)) or (A -> A)) -> D)))
theorem-size     35
proof            (modus-ponens tm-312 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60008.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((A -> A) -> D) -> (((((A -> B) and C) or (A -> B)) or (A -> A)) -> D))), M:tm-312, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-60009
in-theory        60009
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (D or ((((A -> B) and C) or (A -> B)) -> (A -> A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60009.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (D or ((((A -> B) and C) or (A -> B)) -> (A -> A)))), M:tm-311, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60010
in-theory        60010
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((((A -> B) and C) or (A -> B)) -> (A -> A)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60010.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((((A -> B) and C) or (A -> B)) -> (A -> A)) or D)), M:tm-310, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60011
in-theory        60011
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (D -> (((((A -> B) and C) or (A -> B)) -> (A -> A)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60011.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (D -> (((((A -> B) and C) or (A -> B)) -> (A -> A)) and D))), M:tm-309, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60012
in-theory        60012
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((((A -> B) and C) or (A -> B)) -> A) -> ((((A -> B) and C) or (A -> B)) -> A)))
theorem-size     37
proof            (modus-ponens tm-306 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B Am) (C Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60012.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (((((A -> B) and C) or (A -> B)) -> A) -> ((((A -> B) and C) or (A -> B)) -> A))), M:tm-306, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B Am) (C Am))
================================================================
tm-name          tm-60013
in-theory        60013
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (D -> ((((A -> B) and C) or (A -> B)) -> (A -> A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60013.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and (D -> ((((A -> B) and C) or (A -> B)) -> (A -> A)))), M:tm-305, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60014
in-theory        60014
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60014.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-303, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60015
in-theory        60015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60015.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-270, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60016
in-theory        60016
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60016.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-239, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60017
in-theory        60017
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) or (E -> F)) -> (E -> E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60017.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) or (E -> F)) -> (E -> E))), M:tm-210, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60018
in-theory        60018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60018.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-183, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60019
in-theory        60019
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60019.        ((A -> ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-157, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60020
in-theory        60020
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60020.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-147, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60021
in-theory        60021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60021.        ((A -> ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-134, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60022
in-theory        60022
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60022.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-125, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60023
in-theory        60023
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (((A -> B) -> A) -> ((A -> B) -> B)))
theorem-size     25
proof            (modus-ponens tm-114 tm-722 ((A (or (and (-> (-> C D) Bm) Cm) (-> (-> C D) Bm))) (B (-> C D)) (Am (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60023.        (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (((A -> B) -> A) -> ((A -> B) -> B))), M:tm-114, m:tm-722, u:((A (or (and (-> (-> C D) Bm) Cm) (-> (-> C D) Bm))) (B (-> C D)) (Am (-> C D)))
================================================================
tm-name          tm-60024
in-theory        60024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (E -> E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60024.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (E -> E))), M:tm-113, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60025
in-theory        60025
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60025.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-105, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60026
in-theory        60026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) and E) or (C -> D)) -> (C -> C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60026.        (((A -> B) -> (A -> A)) and ((((C -> D) and E) or (C -> D)) -> (C -> C))), M:tm-95, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60027
in-theory        60027
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D -> (A -> A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60027.        ((((A -> B) and C) or (A -> B)) -> (D -> (A -> A))), M:tm-84, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-60028
in-theory        60028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60028.        ((A -> (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-83, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60029
in-theory        60029
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) and D) or (B -> C)) -> (B -> B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60029.        (((not (not A)) -> A) and ((((B -> C) and D) or (B -> C)) -> (B -> B))), M:tm-76, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60030
in-theory        60030
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) and C) or (A -> B)))) or (((A -> B) and C) or (A -> B))) -> (A -> A))
theorem-size     25
proof            (modus-ponens tm-73 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-8 tm-10 tm-3 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60030.        (((not (not (((A -> B) and C) or (A -> B)))) or (((A -> B) and C) or (A -> B))) -> (A -> A)), M:tm-73, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-60031
in-theory        60031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) or (C -> D)) -> (C -> C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-2 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60031.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) or (C -> D)) -> (C -> C))), M:tm-69, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60032
in-theory        60032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60032.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-54, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60033
in-theory        60033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A -> B) and C) or (A -> B))) -> (A -> A))
theorem-size     17
proof            (modus-ponens tm-50 tm-722 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am Am))))
axioms-used      (tm-8 tm-7 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60033.        (((A -> B) or (((A -> B) and C) or (A -> B))) -> (A -> A)), M:tm-50, m:tm-722, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am Am)))
================================================================
tm-name          tm-60034
in-theory        60034
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (A -> A))
theorem-size     19
proof            (modus-ponens tm-49 tm-722 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am Am))))
axioms-used      (tm-8 tm-6 tm-3 tm-2 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60034.        ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (A -> A)), M:tm-49, m:tm-722, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am Am)))
================================================================
tm-name          tm-60035
in-theory        60035
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) or (B -> C))) or (((B -> C) and D) or (B -> C))) -> (B -> B))
theorem-size     25
proof            (modus-ponens tm-47 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-8 tm-4 tm-3 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60035.        (((A and (((B -> C) and D) or (B -> C))) or (((B -> C) and D) or (B -> C))) -> (B -> B)), M:tm-47, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-60036
in-theory        60036
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> (A -> A))
theorem-size     25
proof            (modus-ponens tm-46 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60036.        ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> (A -> A)), M:tm-46, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-60037
in-theory        60037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) and E) or (C -> D)) -> (C -> C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60037.        ((A -> (B or A)) and ((((C -> D) and E) or (C -> D)) -> (C -> C))), M:tm-42, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60038
in-theory        60038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) and E) or (C -> D)) -> (C -> C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60038.        ((A -> (A or B)) and ((((C -> D) and E) or (C -> D)) -> (C -> C))), M:tm-32, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60039
in-theory        60039
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (A -> A)))
theorem-size     23
proof            (modus-ponens tm-24 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60039.        ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (A -> A))), M:tm-24, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-60040
in-theory        60040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (C -> C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60040.        ((A -> (B -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (C -> C))), M:tm-23, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60041
in-theory        60041
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) and E) or (C -> D)) -> (C -> C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60041.        (((A and B) -> B) and ((((C -> D) and E) or (C -> D)) -> (C -> C))), M:tm-22, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60042
in-theory        60042
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) and E) or (C -> D)) -> (C -> C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60042.        (((A and B) -> A) and ((((C -> D) and E) or (C -> D)) -> (C -> C))), M:tm-21, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60043
in-theory        60043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60043.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-20, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60044
in-theory        60044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) and E) or (C -> D)) -> (C -> C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60044.        ((A -> (B -> A)) and ((((C -> D) and E) or (C -> D)) -> (C -> C))), M:tm-19, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60045
in-theory        60045
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (not (A -> A))) -> (not (((A -> B) and C) or (A -> B))))
theorem-size     25
proof            (modus-ponens tm-9 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-9 tm-8 tm-3 tm-2 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60045.        (((((A -> B) and C) or (A -> B)) -> (not (A -> A))) -> (not (((A -> B) and C) or (A -> B)))), M:tm-9, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-60046
in-theory        60046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> B) -> (((((A -> C) and D) or (A -> C)) or (A -> A)) -> B))
theorem-size     21
proof            (modus-ponens tm-8 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60046.        (((A -> A) -> B) -> (((((A -> C) and D) or (A -> C)) or (A -> A)) -> B)), M:tm-8, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-60047
in-theory        60047
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) and D) or (B -> C)) -> (B -> B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-7 tm-8 tm-3 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60047.        (A or ((((B -> C) and D) or (B -> C)) -> (B -> B))), M:tm-7, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60048
in-theory        60048
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-6 tm-8 tm-3 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60048.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) or D), M:tm-6, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60049
in-theory        60049
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) and D) or (B -> C)) -> (B -> B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60049.        (A -> (((((B -> C) and D) or (B -> C)) -> (B -> B)) and A)), M:tm-5, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60050
in-theory        60050
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> A) -> ((((A -> B) and C) or (A -> B)) -> A))
theorem-size     23
proof            (modus-ponens tm-2 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B Am) (C Am)))
axioms-used      (tm-2 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60050.        (((((A -> B) and C) or (A -> B)) -> A) -> ((((A -> B) and C) or (A -> B)) -> A)), M:tm-2, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B Am) (C Am))
================================================================
tm-name          tm-60051
in-theory        60051
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) and D) or (B -> C)) -> (B -> B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-1 tm-8 tm-3 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-60051.        (A -> ((((B -> C) and D) or (B -> C)) -> (B -> B))), M:tm-1, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-60052
in-theory        60052
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> (F -> G)) -> (E -> F)) and H) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     57
proof            (modus-ponens tm-708 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60052.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> (F -> G)) -> (E -> F)) and H) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-708, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60053
in-theory        60053
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     45
proof            (modus-ponens tm-665 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60053.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-665, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60054
in-theory        60054
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (E or ((A -> (B -> C)) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-623 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60054.        (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (E or ((A -> (B -> C)) -> (A -> C)))), M:tm-623, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60055
in-theory        60055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-622 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60055.        ((A -> (B -> (C or B))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-622, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60056
in-theory        60056
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (E -> (F or E)))
theorem-size     37
proof            (modus-ponens tm-609 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60056.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (E -> (F or E))), M:tm-609, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60057
in-theory        60057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-605 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60057.        ((A -> ((B -> (C or B)) and A)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-605, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60058
in-theory        60058
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((E -> (F or E)) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-595 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60058.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((E -> (F or E)) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-595, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60059
in-theory        60059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-550 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60059.        (((A -> (B or A)) or C) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-550, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60060
in-theory        60060
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-540 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60060.        ((A or (B -> (C or B))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-540, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60061
in-theory        60061
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-530 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60061.        ((A or (B -> (B or C))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-530, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60062
in-theory        60062
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-520 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60062.        ((A or (B -> (C -> (B and C)))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-520, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60063
in-theory        60063
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-510 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60063.        ((A or ((B and C) -> C)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-510, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60064
in-theory        60064
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-500 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60064.        ((A or ((B and C) -> B)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-500, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60065
in-theory        60065
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) -> (E -> F)) and H) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     47
proof            (modus-ponens tm-490 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60065.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) -> (E -> F)) and H) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-490, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60066
in-theory        60066
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-480 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60066.        ((A or (B -> (C -> B))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-480, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60067
in-theory        60067
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> C)) or E))
theorem-size     33
proof            (modus-ponens tm-470 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60067.        (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> C)) or E)), M:tm-470, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60068
in-theory        60068
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-469 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60068.        ((A -> (B -> (B or C))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-469, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60069
in-theory        60069
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (E -> (E or F)))
theorem-size     37
proof            (modus-ponens tm-456 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60069.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (E -> (E or F))), M:tm-456, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60070
in-theory        60070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-453 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60070.        ((A -> ((B -> (B or C)) and A)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-453, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60071
in-theory        60071
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((E -> (E or F)) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-443 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60071.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((E -> (E or F)) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-443, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60072
in-theory        60072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-409 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60072.        (((A -> (A or B)) or C) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-409, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60073
in-theory        60073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-400 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60073.        (((A -> (B -> (A and B))) or C) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-400, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60074
in-theory        60074
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-391 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60074.        ((((A and B) -> B) or C) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-391, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60075
in-theory        60075
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-382 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60075.        ((((A and B) -> A) or C) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-382, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60076
in-theory        60076
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> (F -> G)) -> (E -> F)) and H) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     47
proof            (modus-ponens tm-373 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60076.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> (F -> G)) -> (E -> F)) and H) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-373, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60077
in-theory        60077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-364 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60077.        (((A -> (B -> A)) or C) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-364, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60078
in-theory        60078
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (E -> (((A -> (B -> C)) -> (A -> C)) and E)))
theorem-size     35
proof            (modus-ponens tm-355 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60078.        (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (E -> (((A -> (B -> C)) -> (A -> C)) and E))), M:tm-355, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60079
in-theory        60079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-354 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60079.        ((A -> (B -> (C -> (B and C)))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-354, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60080
in-theory        60080
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (E -> (F -> (E and F))))
theorem-size     39
proof            (modus-ponens tm-341 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60080.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60081
in-theory        60081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     41
proof            (modus-ponens tm-338 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60081.        (((A -> B) -> (A -> (A and B))) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-338, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60082
in-theory        60082
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     85
proof            (modus-ponens tm-328 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       261
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60082.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) and ((A -> (B -> C)) -> (A -> C))))), M:tm-328, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60083
in-theory        60083
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((E -> (F -> (E and F))) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     71
proof            (modus-ponens tm-327 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60083.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((E -> (F -> (E and F))) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-327, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60084
in-theory        60084
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((E and F) -> F) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-326 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60084.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((E and F) -> F) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-326, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60085
in-theory        60085
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((E and F) -> E) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-325 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60085.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((E and F) -> E) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-325, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60086
in-theory        60086
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     77
proof            (modus-ponens tm-324 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       267
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60086.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-324, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60087
in-theory        60087
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((E -> (F -> E)) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-323 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60087.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((E -> (F -> E)) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-323, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60088
in-theory        60088
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((E and F) -> F))
theorem-size     37
proof            (modus-ponens tm-322 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60088.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((E and F) -> F)), M:tm-322, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60089
in-theory        60089
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((E and F) -> E))
theorem-size     37
proof            (modus-ponens tm-320 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60089.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((E and F) -> E)), M:tm-320, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60090
in-theory        60090
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-318 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60090.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60091
in-theory        60091
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))))
theorem-size     75
proof            (modus-ponens tm-316 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       245
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60091.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))))), M:tm-316, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60092
in-theory        60092
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (E -> (F -> E)))
theorem-size     37
proof            (modus-ponens tm-315 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60092.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (E -> (F -> E))), M:tm-315, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60093
in-theory        60093
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))))))
theorem-size     87
proof            (modus-ponens tm-313 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60093.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))))), M:tm-313, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60094
in-theory        60094
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> C)) -> E) -> ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> C))) -> E)))
theorem-size     77
proof            (modus-ponens tm-312 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60094.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((A -> (B -> C)) -> (A -> C)) -> E) -> ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> C))) -> E))), M:tm-312, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60095
in-theory        60095
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (E or (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-311 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60095.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (E or (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-311, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60096
in-theory        60096
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) or E))
theorem-size     65
proof            (modus-ponens tm-310 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60096.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) or E)), M:tm-310, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60097
in-theory        60097
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (E -> ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and E)))
theorem-size     67
proof            (modus-ponens tm-309 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60097.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (E -> ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and E))), M:tm-309, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60098
in-theory        60098
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (A -> (B -> C))) -> (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (A -> C))))
theorem-size     85
proof            (modus-ponens tm-306 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       251
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60098.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (A -> (B -> C))) -> (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (A -> C)))), M:tm-306, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
================================================================
tm-name          tm-60099
in-theory        60099
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (E -> (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-305 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60099.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (E -> (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))), M:tm-305, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60100
in-theory        60100
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-303 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60100.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-303, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60101
in-theory        60101
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-270 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60101.        ((A -> (((B and C) -> C) and A)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-270, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60102
in-theory        60102
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-239 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60102.        ((A -> (((B and C) -> B) and A)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-239, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60103
in-theory        60103
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> (F -> G)) -> (E -> F)) and H) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     49
proof            (modus-ponens tm-210 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60103.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> (F -> G)) -> (E -> F)) and H) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-210, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60104
in-theory        60104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-183 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60104.        ((A -> ((B -> (C -> B)) and A)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-183, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60105
in-theory        60105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-157 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60105.        ((A -> ((B and C) -> C)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-157, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60106
in-theory        60106
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     47
proof            (modus-ponens tm-147 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60106.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-147, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60107
in-theory        60107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-134 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60107.        ((A -> ((B and C) -> B)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-134, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60108
in-theory        60108
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     47
proof            (modus-ponens tm-125 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60108.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-125, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60109
in-theory        60109
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> C)))
theorem-size     37
proof            (modus-ponens tm-114 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C Am) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60109.        (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> A) -> ((A -> (B -> C)) -> C))), M:tm-114, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C Am) (D Cm))
================================================================
tm-name          tm-60110
in-theory        60110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) -> (E -> F)) and H) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     47
proof            (modus-ponens tm-113 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60110.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> (F -> G)) -> (E -> F)) and H) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-113, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60111
in-theory        60111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     51
proof            (modus-ponens tm-105 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60111.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-105, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60112
in-theory        60112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     39
proof            (modus-ponens tm-95 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60112.        (((A -> B) -> (A -> A)) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-95, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60113
in-theory        60113
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (E -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-84 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60113.        (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (E -> ((A -> (B -> C)) -> (A -> C)))), M:tm-84, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60114
in-theory        60114
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-83 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60114.        ((A -> (B -> (C -> B))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-83, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60115
in-theory        60115
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> (C -> D)) -> (B -> C)) and E) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     37
proof            (modus-ponens tm-76 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60115.        (((not (not A)) -> A) and (((((B -> (C -> D)) -> (B -> C)) and E) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-76, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60116
in-theory        60116
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))))) or ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     55
proof            (modus-ponens tm-73 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-10 tm-3 tm-2)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60116.        (((not (not ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))))) or ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-73, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60117
in-theory        60117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     43
proof            (modus-ponens tm-69 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60117.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-69, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60118
in-theory        60118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     45
proof            (modus-ponens tm-54 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60118.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-54, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60119
in-theory        60119
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     41
proof            (modus-ponens tm-50 tm-723 ((A (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm)) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-7 tm-3 tm-2)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60119.        ((((A -> (B -> C)) -> (A -> B)) or ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-50, m:tm-723, u:((A (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm)) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60120
in-theory        60120
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) and D) or ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     43
proof            (modus-ponens tm-49 tm-723 ((A (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm)) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-6 tm-3 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60120.        (((((A -> (B -> C)) -> (A -> B)) and D) or ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-49, m:tm-723, u:((A (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm)) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60121
in-theory        60121
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B -> (C -> D)) -> (B -> C)) and E) or ((B -> (C -> D)) -> (B -> C)))) or ((((B -> (C -> D)) -> (B -> C)) and E) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D)))
theorem-size     55
proof            (modus-ponens tm-47 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-4 tm-3 tm-2)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60121.        (((A and ((((B -> (C -> D)) -> (B -> C)) and E) or ((B -> (C -> D)) -> (B -> C)))) or ((((B -> (C -> D)) -> (B -> C)) and E) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60122
in-theory        60122
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) and E) or ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     55
proof            (modus-ponens tm-46 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60122.        (((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) and E) or ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60123
in-theory        60123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     37
proof            (modus-ponens tm-42 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60123.        ((A -> (B or A)) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60124
in-theory        60124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     37
proof            (modus-ponens tm-32 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60124.        ((A -> (A or B)) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60125
in-theory        60125
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     53
proof            (modus-ponens tm-24 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60125.        (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60126
in-theory        60126
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     39
proof            (modus-ponens tm-23 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60126.        ((A -> (B -> (A and B))) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60127
in-theory        60127
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     37
proof            (modus-ponens tm-22 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60127.        (((A and B) -> B) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60128
in-theory        60128
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     37
proof            (modus-ponens tm-21 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60128.        (((A and B) -> A) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60129
in-theory        60129
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     45
proof            (modus-ponens tm-20 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60129.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60130
in-theory        60130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     37
proof            (modus-ponens tm-19 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60130.        ((A -> (B -> A)) and (((((C -> (D -> E)) -> (C -> D)) and F) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60131
in-theory        60131
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))))
theorem-size     43
proof            (modus-ponens tm-12 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60131.        (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))), M:tm-12, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60132
in-theory        60132
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))))
theorem-size     55
proof            (modus-ponens tm-9 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-9 tm-8 tm-3 tm-2)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60132.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))))), M:tm-9, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60133
in-theory        60133
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((((A -> (B -> C)) -> (A -> B)) and E) or ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> C))) -> D))
theorem-size     45
proof            (modus-ponens tm-8 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60133.        ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((((A -> (B -> C)) -> (A -> B)) and E) or ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-60134
in-theory        60134
times-derived    1
----------------------------------------------------------------
theorem          (A or (((((B -> (C -> D)) -> (B -> C)) and E) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     33
proof            (modus-ponens tm-7 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-7 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60134.        (A or (((((B -> (C -> D)) -> (B -> C)) and E) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60135
in-theory        60135
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) or E)
theorem-size     33
proof            (modus-ponens tm-6 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-6 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60135.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) or E), M:tm-6, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60136
in-theory        60136
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B -> (C -> D)) -> (B -> C)) and E) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60136.        (A -> ((((((B -> (C -> D)) -> (B -> C)) and E) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60137
in-theory        60137
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (A -> (B -> C))) -> (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (A -> C)))
theorem-size     53
proof            (modus-ponens tm-2 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60137.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (A -> (B -> C))) -> (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (A -> C))), M:tm-2, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
================================================================
tm-name          tm-60138
in-theory        60138
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> (C -> D)) -> (B -> C)) and E) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     33
proof            (modus-ponens tm-1 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-1 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-60138.        (A -> (((((B -> (C -> D)) -> (B -> C)) and E) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-60139
in-theory        60139
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60139.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-708, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60140
in-theory        60140
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60140.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-665, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60141
in-theory        60141
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60141.        ((A -> (B -> (C or B))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-622, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60142
in-theory        60142
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60142.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60143
in-theory        60143
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60143.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-605, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60144
in-theory        60144
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60144.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-595, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60145
in-theory        60145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60145.        (((A -> (B or A)) or C) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-550, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60146
in-theory        60146
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60146.        ((A or (B -> (C or B))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-540, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60147
in-theory        60147
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60147.        ((A or (B -> (B or C))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-530, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60148
in-theory        60148
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60148.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-520, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60149
in-theory        60149
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60149.        ((A or ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-510, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60150
in-theory        60150
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60150.        ((A or ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-500, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60151
in-theory        60151
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60151.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-490, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60152
in-theory        60152
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60152.        ((A or (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-480, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60153
in-theory        60153
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60153.        ((A -> (B -> (B or C))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-469, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60154
in-theory        60154
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60154.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60155
in-theory        60155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60155.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-453, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60156
in-theory        60156
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60156.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-443, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60157
in-theory        60157
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60157.        (((A -> (A or B)) or C) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-409, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60158
in-theory        60158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60158.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-400, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60159
in-theory        60159
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60159.        ((((A and B) -> B) or C) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-391, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60160
in-theory        60160
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60160.        ((((A and B) -> A) or C) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-382, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60161
in-theory        60161
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60161.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-373, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60162
in-theory        60162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60162.        (((A -> (B -> A)) or C) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-364, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60163
in-theory        60163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60163.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-354, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60164
in-theory        60164
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60164.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60165
in-theory        60165
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60165.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-338, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60166
in-theory        60166
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A and B) or A) -> (((A and B) or A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-328 tm-724 ((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60166.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A and B) or A) -> (((A and B) or A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-328, m:tm-724, u:((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-60167
in-theory        60167
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60167.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-327, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60168
in-theory        60168
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60168.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-326, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60169
in-theory        60169
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60169.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-325, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60170
in-theory        60170
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60170.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-324, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60171
in-theory        60171
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60171.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-323, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60172
in-theory        60172
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60172.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60173
in-theory        60173
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60173.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60174
in-theory        60174
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60174.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60175
in-theory        60175
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     31
proof            (modus-ponens tm-316 tm-724 ((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60175.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-724, u:((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-60176
in-theory        60176
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60176.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60177
in-theory        60177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) or A) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not ((A and B) or A))))
theorem-size     47
proof            (modus-ponens tm-313 tm-724 ((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60177.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) or A) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not ((A and B) or A)))), M:tm-313, m:tm-724, u:((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-60178
in-theory        60178
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((((A and B) or A) or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     57
proof            (modus-ponens tm-312 tm-724 ((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60178.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((((A and B) or A) or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-312, m:tm-724, u:((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-60179
in-theory        60179
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60179.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-311, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60180
in-theory        60180
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60180.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-310, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60181
in-theory        60181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60181.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F))), M:tm-309, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60182
in-theory        60182
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) or A) -> (C -> (D -> E))) -> (((A and B) or A) -> ((C -> D) -> (C -> E)))))
theorem-size     45
proof            (modus-ponens tm-306 tm-724 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60182.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) or A) -> (C -> (D -> E))) -> (((A and B) or A) -> ((C -> D) -> (C -> E))))), M:tm-306, m:tm-724, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-60183
in-theory        60183
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60183.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-305, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60184
in-theory        60184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60184.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-303, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60185
in-theory        60185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60185.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-270, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60186
in-theory        60186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60186.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-239, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60187
in-theory        60187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60187.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-210, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60188
in-theory        60188
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60188.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-183, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60189
in-theory        60189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60189.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-157, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60190
in-theory        60190
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60190.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-147, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60191
in-theory        60191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60191.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-134, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60192
in-theory        60192
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60192.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-125, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60193
in-theory        60193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60193.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-113, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60194
in-theory        60194
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60194.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-105, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60195
in-theory        60195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60195.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-95, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60196
in-theory        60196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60196.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-83, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60197
in-theory        60197
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-1 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60197.        (((not (not A)) -> A) and (((B and C) or B) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-76, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60198
in-theory        60198
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-73 tm-724 ((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-10 tm-3 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60198.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-73, m:tm-724, u:((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-60199
in-theory        60199
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-1 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60199.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-69, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60200
in-theory        60200
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60200.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-54, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60201
in-theory        60201
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-50 tm-724 ((A (and Am Bm)) (B Am) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-7 tm-3 tm-1 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60201.        ((A or ((A and B) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-50, m:tm-724, u:((A (and Am Bm)) (B Am) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-60202
in-theory        60202
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-49 tm-724 ((A (and Am Bm)) (B Am) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-6 tm-3 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60202.        (((A and B) or ((A and B) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-49, m:tm-724, u:((A (and Am Bm)) (B Am) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-60203
in-theory        60203
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-47 tm-724 ((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-4 tm-3 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60203.        (((A and ((B and C) or B)) or ((B and C) or B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-47, m:tm-724, u:((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-60204
in-theory        60204
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-46 tm-724 ((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60204.        (((((A and B) or A) and C) or ((A and B) or A)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-46, m:tm-724, u:((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-60205
in-theory        60205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60205.        ((A -> (B or A)) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-42, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60206
in-theory        60206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60206.        ((A -> (A or B)) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-32, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60207
in-theory        60207
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     25
proof            (modus-ponens tm-24 tm-724 ((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60207.        (((A and B) or A) -> (((A and B) or A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-24, m:tm-724, u:((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-60208
in-theory        60208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60208.        ((A -> (B -> (A and B))) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-23, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60209
in-theory        60209
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60209.        (((A and B) -> B) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-22, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60210
in-theory        60210
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60210.        (((A and B) -> A) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-21, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60211
in-theory        60211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60211.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-20, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60212
in-theory        60212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60212.        ((A -> (B -> A)) and (((C and D) or C) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-19, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60213
in-theory        60213
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not ((A and B) or A)))
theorem-size     27
proof            (modus-ponens tm-9 tm-724 ((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-9 tm-8 tm-3 tm-1 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60213.        ((((A and B) or A) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not ((A and B) or A))), M:tm-9, m:tm-724, u:((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-60214
in-theory        60214
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((((E and F) or E) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-724 ((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60214.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((((E and F) or E) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-724, u:((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-60215
in-theory        60215
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-7 tm-8 tm-3 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60215.        (A or (((B and C) or B) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-7, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60216
in-theory        60216
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-6 tm-8 tm-3 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60216.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F), M:tm-6, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60217
in-theory        60217
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60217.        (A -> ((((B and C) or B) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)), M:tm-5, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60218
in-theory        60218
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> E))) -> (((A and B) or A) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-2 tm-724 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-2 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60218.        ((((A and B) or A) -> (C -> (D -> E))) -> (((A and B) or A) -> ((C -> D) -> (C -> E)))), M:tm-2, m:tm-724, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-60219
in-theory        60219
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-1 tm-8 tm-3 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-60219.        (A -> (((B and C) or B) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-1, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-60220
in-theory        60220
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((((E -> F) and G) -> E) and H) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     51
proof            (modus-ponens tm-708 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60220.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((((E -> F) and G) -> E) and H) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-708, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60221
in-theory        60221
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     39
proof            (modus-ponens tm-665 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60221.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-665, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60222
in-theory        60222
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (E or (((A -> B) and C) -> B)))
theorem-size     27
proof            (modus-ponens tm-623 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60222.        ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (E or (((A -> B) and C) -> B))), M:tm-623, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60223
in-theory        60223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-622 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60223.        ((A -> (B -> (C or B))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-622, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60224
in-theory        60224
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (E -> (F or E)))
theorem-size     31
proof            (modus-ponens tm-609 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60224.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (E -> (F or E))), M:tm-609, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60225
in-theory        60225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-605 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60225.        ((A -> ((B -> (C or B)) and A)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-605, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60226
in-theory        60226
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((E -> (F or E)) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     57
proof            (modus-ponens tm-595 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60226.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((E -> (F or E)) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-595, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60227
in-theory        60227
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-550 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60227.        (((A -> (B or A)) or C) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-550, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60228
in-theory        60228
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-540 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60228.        ((A or (B -> (C or B))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-540, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60229
in-theory        60229
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-530 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60229.        ((A or (B -> (B or C))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-530, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60230
in-theory        60230
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-520 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60230.        ((A or (B -> (C -> (B and C)))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-520, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60231
in-theory        60231
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-510 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60231.        ((A or ((B and C) -> C)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-510, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60232
in-theory        60232
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-500 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60232.        ((A or ((B and C) -> B)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-500, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60233
in-theory        60233
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((((E -> F) and G) -> E) and H) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     41
proof            (modus-ponens tm-490 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60233.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((((E -> F) and G) -> E) and H) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-490, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60234
in-theory        60234
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-480 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60234.        ((A or (B -> (C -> B))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-480, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60235
in-theory        60235
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> B) or E))
theorem-size     27
proof            (modus-ponens tm-470 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60235.        ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> B) or E)), M:tm-470, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60236
in-theory        60236
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-469 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60236.        ((A -> (B -> (B or C))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-469, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60237
in-theory        60237
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (E -> (E or F)))
theorem-size     31
proof            (modus-ponens tm-456 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60237.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (E -> (E or F))), M:tm-456, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60238
in-theory        60238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-453 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60238.        ((A -> ((B -> (B or C)) and A)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-453, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60239
in-theory        60239
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((E -> (E or F)) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     57
proof            (modus-ponens tm-443 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60239.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((E -> (E or F)) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-443, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60240
in-theory        60240
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-409 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60240.        (((A -> (A or B)) or C) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-409, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60241
in-theory        60241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-400 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60241.        (((A -> (B -> (A and B))) or C) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-400, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60242
in-theory        60242
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-391 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60242.        ((((A and B) -> B) or C) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-391, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60243
in-theory        60243
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-382 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60243.        ((((A and B) -> A) or C) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-382, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60244
in-theory        60244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((((E -> F) and G) -> E) and H) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     41
proof            (modus-ponens tm-373 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60244.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((((E -> F) and G) -> E) and H) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-373, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60245
in-theory        60245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-364 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60245.        (((A -> (B -> A)) or C) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-364, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60246
in-theory        60246
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (E -> ((((A -> B) and C) -> B) and E)))
theorem-size     29
proof            (modus-ponens tm-355 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60246.        ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (E -> ((((A -> B) and C) -> B) and E))), M:tm-355, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60247
in-theory        60247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-354 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60247.        ((A -> (B -> (C -> (B and C)))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-354, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60248
in-theory        60248
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (E -> (F -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-341 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60248.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60249
in-theory        60249
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     35
proof            (modus-ponens tm-338 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60249.        (((A -> B) -> (A -> (A and B))) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-338, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60250
in-theory        60250
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) and (((A -> B) and C) -> B))))
theorem-size     69
proof            (modus-ponens tm-328 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60250.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) and (((A -> B) and C) -> B)))), M:tm-328, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60251
in-theory        60251
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((E -> (F -> (E and F))) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     59
proof            (modus-ponens tm-327 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60251.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((E -> (F -> (E and F))) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-327, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60252
in-theory        60252
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((E and F) -> F) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     57
proof            (modus-ponens tm-326 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60252.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((E and F) -> F) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-326, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60253
in-theory        60253
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((E and F) -> E) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     57
proof            (modus-ponens tm-325 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60253.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((E and F) -> E) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-325, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60254
in-theory        60254
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     65
proof            (modus-ponens tm-324 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       237
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60254.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-324, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60255
in-theory        60255
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((E -> (F -> E)) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     57
proof            (modus-ponens tm-323 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60255.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((E -> (F -> E)) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-323, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60256
in-theory        60256
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((E and F) -> F))
theorem-size     31
proof            (modus-ponens tm-322 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60256.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((E and F) -> F)), M:tm-322, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60257
in-theory        60257
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((E and F) -> E))
theorem-size     31
proof            (modus-ponens tm-320 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60257.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((E and F) -> E)), M:tm-320, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60258
in-theory        60258
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-318 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60258.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60259
in-theory        60259
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A))))
theorem-size     61
proof            (modus-ponens tm-316 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60259.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)))), M:tm-316, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60260
in-theory        60260
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (E -> (F -> E)))
theorem-size     31
proof            (modus-ponens tm-315 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60260.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (E -> (F -> E))), M:tm-315, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60261
in-theory        60261
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (not (((A -> B) and C) -> B))) -> (not (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)))))
theorem-size     71
proof            (modus-ponens tm-313 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60261.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (not (((A -> B) and C) -> B))) -> (not (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A))))), M:tm-313, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60262
in-theory        60262
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((((A -> B) and C) -> B) -> E) -> (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) or (((A -> B) and C) -> B)) -> E)))
theorem-size     63
proof            (modus-ponens tm-312 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60262.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((((A -> B) and C) -> B) -> E) -> (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) or (((A -> B) and C) -> B)) -> E))), M:tm-312, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60263
in-theory        60263
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (E or ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     53
proof            (modus-ponens tm-311 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60263.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (E or ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-311, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60264
in-theory        60264
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) or E))
theorem-size     53
proof            (modus-ponens tm-310 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60264.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) or E)), M:tm-310, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60265
in-theory        60265
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (E -> (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and E)))
theorem-size     55
proof            (modus-ponens tm-309 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60265.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (E -> (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and E))), M:tm-309, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60266
in-theory        60266
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> ((A -> B) and C)) -> ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> B)))
theorem-size     69
proof            (modus-ponens tm-306 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (and (-> Am Bm) Cm)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60266.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> ((A -> B) and C)) -> ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> B))), M:tm-306, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (and (-> Am Bm) Cm)) (C Bm))
================================================================
tm-name          tm-60267
in-theory        60267
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (E -> ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))))
theorem-size     53
proof            (modus-ponens tm-305 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60267.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and (E -> ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))), M:tm-305, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60268
in-theory        60268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     37
proof            (modus-ponens tm-303 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60268.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-303, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60269
in-theory        60269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-270 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60269.        ((A -> (((B and C) -> C) and A)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-270, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60270
in-theory        60270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-239 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60270.        ((A -> (((B and C) -> B) and A)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-239, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60271
in-theory        60271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((((E -> F) and G) -> E) and H) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     43
proof            (modus-ponens tm-210 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60271.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((((E -> F) and G) -> E) and H) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-210, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60272
in-theory        60272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-183 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60272.        ((A -> ((B -> (C -> B)) and A)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-183, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60273
in-theory        60273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-157 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60273.        ((A -> ((B and C) -> C)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-157, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60274
in-theory        60274
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     41
proof            (modus-ponens tm-147 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60274.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-147, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60275
in-theory        60275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-134 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60275.        ((A -> ((B and C) -> B)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-134, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60276
in-theory        60276
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     41
proof            (modus-ponens tm-125 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60276.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-125, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60277
in-theory        60277
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) and D) -> A) and E) or (((A -> (B -> C)) and D) -> A)) -> ((((A -> (B -> C)) and D) -> B) -> (((A -> (B -> C)) and D) -> C)))
theorem-size     41
proof            (modus-ponens tm-114 tm-725 ((A (or (and (-> (and (-> Am (-> C D)) Cm) Am) Dm) (-> (and (-> Am (-> C D)) Cm) Am))) (B (and (-> Am (-> C D)) Cm)) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60277.        ((((((A -> (B -> C)) and D) -> A) and E) or (((A -> (B -> C)) and D) -> A)) -> ((((A -> (B -> C)) and D) -> B) -> (((A -> (B -> C)) and D) -> C))), M:tm-114, m:tm-725, u:((A (or (and (-> (and (-> Am (-> C D)) Cm) Am) Dm) (-> (and (-> Am (-> C D)) Cm) Am))) (B (and (-> Am (-> C D)) Cm)) (Bm (-> C D)))
================================================================
tm-name          tm-60278
in-theory        60278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((((E -> F) and G) -> E) and H) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     41
proof            (modus-ponens tm-113 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60278.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((((E -> F) and G) -> E) and H) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-113, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60279
in-theory        60279
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     45
proof            (modus-ponens tm-105 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60279.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-105, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60280
in-theory        60280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     33
proof            (modus-ponens tm-95 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60280.        (((A -> B) -> (A -> A)) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-95, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60281
in-theory        60281
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (E -> (((A -> B) and C) -> B)))
theorem-size     27
proof            (modus-ponens tm-84 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60281.        ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (E -> (((A -> B) and C) -> B))), M:tm-84, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60282
in-theory        60282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-83 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60282.        ((A -> (B -> (C -> B))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-83, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60283
in-theory        60283
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((((B -> C) and D) -> B) and E) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-76 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60283.        (((not (not A)) -> A) and ((((((B -> C) and D) -> B) and E) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))), M:tm-76, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60284
in-theory        60284
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)))) or (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))
theorem-size     45
proof            (modus-ponens tm-73 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-10 tm-3 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60284.        (((not (not (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)))) or (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)), M:tm-73, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60285
in-theory        60285
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     37
proof            (modus-ponens tm-69 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60285.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-69, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60286
in-theory        60286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     39
proof            (modus-ponens tm-54 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60286.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-54, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60287
in-theory        60287
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))
theorem-size     33
proof            (modus-ponens tm-50 tm-725 ((A (and (-> (and (-> Am Bm) Cm) Am) Dm)) (B (-> (and (-> Am Bm) Cm) Am)) (C (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-7 tm-3 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60287.        (((((A -> B) and C) -> A) or (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)), M:tm-50, m:tm-725, u:((A (and (-> (and (-> Am Bm) Cm) Am) Dm)) (B (-> (and (-> Am Bm) Cm) Am)) (C (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60288
in-theory        60288
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) and D) or (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))
theorem-size     35
proof            (modus-ponens tm-49 tm-725 ((A (and (-> (and (-> Am Bm) Cm) Am) Dm)) (B (-> (and (-> Am Bm) Cm) Am)) (C (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-6 tm-3 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60288.        ((((((A -> B) and C) -> A) and D) or (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)), M:tm-49, m:tm-725, u:((A (and (-> (and (-> Am Bm) Cm) Am) Dm)) (B (-> (and (-> Am Bm) Cm) Am)) (C (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60289
in-theory        60289
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((((B -> C) and D) -> B) and E) or (((B -> C) and D) -> B))) or (((((B -> C) and D) -> B) and E) or (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C))
theorem-size     45
proof            (modus-ponens tm-47 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-4 tm-3 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60289.        (((A and (((((B -> C) and D) -> B) and E) or (((B -> C) and D) -> B))) or (((((B -> C) and D) -> B) and E) or (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60290
in-theory        60290
times-derived    1
----------------------------------------------------------------
theorem          ((((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) and E) or (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))
theorem-size     45
proof            (modus-ponens tm-46 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60290.        ((((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) and E) or (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60291
in-theory        60291
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     31
proof            (modus-ponens tm-42 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60291.        ((A -> (B or A)) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60292
in-theory        60292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     31
proof            (modus-ponens tm-32 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60292.        ((A -> (A or B)) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60293
in-theory        60293
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) and (((A -> B) and C) -> B)))
theorem-size     43
proof            (modus-ponens tm-24 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60293.        ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) and (((A -> B) and C) -> B))), M:tm-24, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60294
in-theory        60294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     33
proof            (modus-ponens tm-23 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60294.        ((A -> (B -> (A and B))) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60295
in-theory        60295
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     31
proof            (modus-ponens tm-22 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60295.        (((A and B) -> B) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60296
in-theory        60296
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     31
proof            (modus-ponens tm-21 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60296.        (((A and B) -> A) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60297
in-theory        60297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     39
proof            (modus-ponens tm-20 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60297.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60298
in-theory        60298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     31
proof            (modus-ponens tm-19 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60298.        ((A -> (B -> A)) and ((((((C -> D) and E) -> C) and F) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60299
in-theory        60299
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)))
theorem-size     35
proof            (modus-ponens tm-12 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60299.        ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A))), M:tm-12, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60300
in-theory        60300
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (not (((A -> B) and C) -> B))) -> (not (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A))))
theorem-size     45
proof            (modus-ponens tm-9 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-9 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60300.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (not (((A -> B) and C) -> B))) -> (not (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)))), M:tm-9, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60301
in-theory        60301
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> D) -> (((((((A -> B) and C) -> A) and E) or (((A -> B) and C) -> A)) or (((A -> B) and C) -> B)) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60301.        (((((A -> B) and C) -> B) -> D) -> (((((((A -> B) and C) -> A) and E) or (((A -> B) and C) -> A)) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-60302
in-theory        60302
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((((B -> C) and D) -> B) and E) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))
theorem-size     27
proof            (modus-ponens tm-7 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-7 tm-8 tm-3 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60302.        (A or ((((((B -> C) and D) -> B) and E) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60303
in-theory        60303
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) or E)
theorem-size     27
proof            (modus-ponens tm-6 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-6 tm-8 tm-3 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60303.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) or E), M:tm-6, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60304
in-theory        60304
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((((B -> C) and D) -> B) and E) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60304.        (A -> (((((((B -> C) and D) -> B) and E) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60305
in-theory        60305
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> ((A -> B) and C)) -> ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> B))
theorem-size     43
proof            (modus-ponens tm-2 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (and (-> Am Bm) Cm)) (C Bm)))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60305.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> ((A -> B) and C)) -> ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> B)), M:tm-2, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (and (-> Am Bm) Cm)) (C Bm))
================================================================
tm-name          tm-60306
in-theory        60306
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) and D) -> B) and E) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))
theorem-size     27
proof            (modus-ponens tm-1 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-1 tm-8 tm-3 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-60306.        (A -> ((((((B -> C) and D) -> B) and E) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-60307
in-theory        60307
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> ((G and H) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60307.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> ((G and H) -> G))), M:tm-708, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60308
in-theory        60308
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60308.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-665, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60309
in-theory        60309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60309.        ((A -> (B -> (C or B))) and (((D and E) or D) -> ((F and G) -> F))), M:tm-622, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60310
in-theory        60310
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60310.        ((((A and B) or A) -> ((C and D) -> C)) and (E -> (F or E))), M:tm-609, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60311
in-theory        60311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60311.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-605, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60312
in-theory        60312
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and ((E -> (F or E)) and (((A and B) or A) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60312.        ((((A and B) or A) -> ((C and D) -> C)) and ((E -> (F or E)) and (((A and B) or A) -> ((C and D) -> C)))), M:tm-595, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60313
in-theory        60313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60313.        (((A -> (B or A)) or C) and (((D and E) or D) -> ((F and G) -> F))), M:tm-550, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60314
in-theory        60314
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60314.        ((A or (B -> (C or B))) and (((D and E) or D) -> ((F and G) -> F))), M:tm-540, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60315
in-theory        60315
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60315.        ((A or (B -> (B or C))) and (((D and E) or D) -> ((F and G) -> F))), M:tm-530, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60316
in-theory        60316
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60316.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F and G) -> F))), M:tm-520, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60317
in-theory        60317
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60317.        ((A or ((B and C) -> C)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-510, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60318
in-theory        60318
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60318.        ((A or ((B and C) -> B)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-500, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60319
in-theory        60319
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60319.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G and H) -> G))), M:tm-490, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60320
in-theory        60320
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60320.        ((A or (B -> (C -> B))) and (((D and E) or D) -> ((F and G) -> F))), M:tm-480, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60321
in-theory        60321
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60321.        ((A -> (B -> (B or C))) and (((D and E) or D) -> ((F and G) -> F))), M:tm-469, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60322
in-theory        60322
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60322.        ((((A and B) or A) -> ((C and D) -> C)) and (E -> (E or F))), M:tm-456, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60323
in-theory        60323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60323.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-453, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60324
in-theory        60324
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and ((E -> (E or F)) and (((A and B) or A) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60324.        ((((A and B) or A) -> ((C and D) -> C)) and ((E -> (E or F)) and (((A and B) or A) -> ((C and D) -> C)))), M:tm-443, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60325
in-theory        60325
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60325.        (((A -> (A or B)) or C) and (((D and E) or D) -> ((F and G) -> F))), M:tm-409, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60326
in-theory        60326
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60326.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> ((F and G) -> F))), M:tm-400, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60327
in-theory        60327
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60327.        ((((A and B) -> B) or C) and (((D and E) or D) -> ((F and G) -> F))), M:tm-391, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60328
in-theory        60328
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60328.        ((((A and B) -> A) or C) and (((D and E) or D) -> ((F and G) -> F))), M:tm-382, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60329
in-theory        60329
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60329.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> ((G and H) -> G))), M:tm-373, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60330
in-theory        60330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60330.        (((A -> (B -> A)) or C) and (((D and E) or D) -> ((F and G) -> F))), M:tm-364, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60331
in-theory        60331
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60331.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F and G) -> F))), M:tm-354, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60332
in-theory        60332
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60332.        ((((A and B) or A) -> ((C and D) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60333
in-theory        60333
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60333.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> ((E and F) -> E))), M:tm-338, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60334
in-theory        60334
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (((A and B) or A) -> (((A and B) or A) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-328 tm-726 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60334.        ((((A and B) or A) -> ((C and D) -> C)) and (((A and B) or A) -> (((A and B) or A) and ((C and D) -> C)))), M:tm-328, m:tm-726, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-60335
in-theory        60335
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> ((C and D) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60335.        ((((A and B) or A) -> ((C and D) -> C)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> ((C and D) -> C)))), M:tm-327, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60336
in-theory        60336
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (((E and F) -> F) and (((A and B) or A) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60336.        ((((A and B) or A) -> ((C and D) -> C)) and (((E and F) -> F) and (((A and B) or A) -> ((C and D) -> C)))), M:tm-326, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60337
in-theory        60337
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (((E and F) -> E) and (((A and B) or A) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60337.        ((((A and B) or A) -> ((C and D) -> C)) and (((E and F) -> E) and (((A and B) or A) -> ((C and D) -> C)))), M:tm-325, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60338
in-theory        60338
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> ((C and D) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60338.        ((((A and B) or A) -> ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> ((C and D) -> C)))), M:tm-324, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60339
in-theory        60339
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and ((E -> (F -> E)) and (((A and B) or A) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60339.        ((((A and B) or A) -> ((C and D) -> C)) and ((E -> (F -> E)) and (((A and B) or A) -> ((C and D) -> C)))), M:tm-323, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60340
in-theory        60340
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60340.        ((((A and B) or A) -> ((C and D) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60341
in-theory        60341
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60341.        ((((A and B) or A) -> ((C and D) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60342
in-theory        60342
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60342.        ((((A and B) or A) -> ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60343
in-theory        60343
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     23
proof            (modus-ponens tm-316 tm-726 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60343.        ((((A and B) or A) -> ((C and D) -> C)) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-726, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-60344
in-theory        60344
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60344.        ((((A and B) or A) -> ((C and D) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60345
in-theory        60345
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and ((((A and B) or A) -> (not ((C and D) -> C))) -> (not ((A and B) or A))))
theorem-size     31
proof            (modus-ponens tm-313 tm-726 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60345.        ((((A and B) or A) -> ((C and D) -> C)) and ((((A and B) or A) -> (not ((C and D) -> C))) -> (not ((A and B) or A)))), M:tm-313, m:tm-726, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-60346
in-theory        60346
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and ((((C and D) -> C) -> E) -> ((((A and B) or A) or ((C and D) -> C)) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-726 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60346.        ((((A and B) or A) -> ((C and D) -> C)) and ((((C and D) -> C) -> E) -> ((((A and B) or A) or ((C and D) -> C)) -> E))), M:tm-312, m:tm-726, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-60347
in-theory        60347
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (E or (((A and B) or A) -> ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60347.        ((((A and B) or A) -> ((C and D) -> C)) and (E or (((A and B) or A) -> ((C and D) -> C)))), M:tm-311, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60348
in-theory        60348
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and ((((A and B) or A) -> ((C and D) -> C)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60348.        ((((A and B) or A) -> ((C and D) -> C)) and ((((A and B) or A) -> ((C and D) -> C)) or E)), M:tm-310, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60349
in-theory        60349
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (E -> ((((A and B) or A) -> ((C and D) -> C)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60349.        ((((A and B) or A) -> ((C and D) -> C)) and (E -> ((((A and B) or A) -> ((C and D) -> C)) and E))), M:tm-309, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60350
in-theory        60350
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and ((((A and B) or A) -> (C and D)) -> (((A and B) or A) -> C)))
theorem-size     29
proof            (modus-ponens tm-306 tm-726 ((A (or (and Am Bm) Am)) (B (and Cm Dm)) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60350.        ((((A and B) or A) -> ((C and D) -> C)) and ((((A and B) or A) -> (C and D)) -> (((A and B) or A) -> C))), M:tm-306, m:tm-726, u:((A (or (and Am Bm) Am)) (B (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-60351
in-theory        60351
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (E -> (((A and B) or A) -> ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60351.        ((((A and B) or A) -> ((C and D) -> C)) and (E -> (((A and B) or A) -> ((C and D) -> C)))), M:tm-305, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60352
in-theory        60352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60352.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-303, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60353
in-theory        60353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60353.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-270, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60354
in-theory        60354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60354.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-239, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60355
in-theory        60355
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60355.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> ((G and H) -> G))), M:tm-210, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60356
in-theory        60356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60356.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-183, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60357
in-theory        60357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60357.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-157, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60358
in-theory        60358
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60358.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-147, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60359
in-theory        60359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60359.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-134, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60360
in-theory        60360
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60360.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-125, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60361
in-theory        60361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60361.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G and H) -> G))), M:tm-113, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60362
in-theory        60362
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60362.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> ((F and G) -> F))), M:tm-105, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60363
in-theory        60363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60363.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> ((E and F) -> E))), M:tm-95, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60364
in-theory        60364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60364.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> ((F and G) -> F))), M:tm-83, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60365
in-theory        60365
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> ((D and E) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60365.        (((not (not A)) -> A) and (((B and C) or B) -> ((D and E) -> D))), M:tm-76, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60366
in-theory        60366
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> ((C and D) -> C))
theorem-size     19
proof            (modus-ponens tm-73 tm-726 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-10 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60366.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> ((C and D) -> C)), M:tm-73, m:tm-726, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-60367
in-theory        60367
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60367.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> ((E and F) -> E))), M:tm-69, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60368
in-theory        60368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60368.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> ((F and G) -> F))), M:tm-54, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60369
in-theory        60369
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-50 tm-726 ((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-7 tm-3 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60369.        ((A or ((A and B) or A)) -> ((C and D) -> C)), M:tm-50, m:tm-726, u:((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-60370
in-theory        60370
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-49 tm-726 ((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-6 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60370.        (((A and B) or ((A and B) or A)) -> ((C and D) -> C)), M:tm-49, m:tm-726, u:((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-60371
in-theory        60371
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-47 tm-726 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-4 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60371.        (((A and ((B and C) or B)) or ((B and C) or B)) -> ((D and E) -> D)), M:tm-47, m:tm-726, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-60372
in-theory        60372
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-46 tm-726 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60372.        (((((A and B) or A) and C) or ((A and B) or A)) -> ((D and E) -> D)), M:tm-46, m:tm-726, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-60373
in-theory        60373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60373.        ((A -> (B or A)) and (((C and D) or C) -> ((E and F) -> E))), M:tm-42, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60374
in-theory        60374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60374.        ((A -> (A or B)) and (((C and D) or C) -> ((E and F) -> E))), M:tm-32, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60375
in-theory        60375
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and ((C and D) -> C)))
theorem-size     17
proof            (modus-ponens tm-24 tm-726 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60375.        (((A and B) or A) -> (((A and B) or A) and ((C and D) -> C))), M:tm-24, m:tm-726, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-60376
in-theory        60376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60376.        ((A -> (B -> (A and B))) and (((C and D) or C) -> ((E and F) -> E))), M:tm-23, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60377
in-theory        60377
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60377.        (((A and B) -> B) and (((C and D) or C) -> ((E and F) -> E))), M:tm-22, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60378
in-theory        60378
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60378.        (((A and B) -> A) and (((C and D) or C) -> ((E and F) -> E))), M:tm-21, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60379
in-theory        60379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60379.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> ((F and G) -> F))), M:tm-20, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60380
in-theory        60380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60380.        ((A -> (B -> A)) and (((C and D) or C) -> ((E and F) -> E))), M:tm-19, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60381
in-theory        60381
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not ((C and D) -> C))) -> (not ((A and B) or A)))
theorem-size     19
proof            (modus-ponens tm-9 tm-726 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-9 tm-8 tm-3 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60381.        ((((A and B) or A) -> (not ((C and D) -> C))) -> (not ((A and B) or A))), M:tm-9, m:tm-726, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-60382
in-theory        60382
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> ((((D and E) or D) or ((A and B) -> A)) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-726 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60382.        ((((A and B) -> A) -> C) -> ((((D and E) or D) or ((A and B) -> A)) -> C)), M:tm-8, m:tm-726, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-60383
in-theory        60383
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-7 tm-8 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60383.        (A or (((B and C) or B) -> ((D and E) -> D))), M:tm-7, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60384
in-theory        60384
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-6 tm-8 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60384.        ((((A and B) or A) -> ((C and D) -> C)) or E), M:tm-6, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60385
in-theory        60385
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> ((D and E) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60385.        (A -> ((((B and C) or B) -> ((D and E) -> D)) and A)), M:tm-5, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60386
in-theory        60386
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C and D)) -> (((A and B) or A) -> C))
theorem-size     17
proof            (modus-ponens tm-2 tm-726 ((A (or (and Am Bm) Am)) (B (and Cm Dm)) (C Cm)))
axioms-used      (tm-2 tm-8 tm-3 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60386.        ((((A and B) or A) -> (C and D)) -> (((A and B) or A) -> C)), M:tm-2, m:tm-726, u:((A (or (and Am Bm) Am)) (B (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-60387
in-theory        60387
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-60387.        (A -> (((B and C) or B) -> ((D and E) -> D))), M:tm-1, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-60388
in-theory        60388
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E and (F -> G)) -> F) and H) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     51
proof            (modus-ponens tm-708 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-4)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60388.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E and (F -> G)) -> F) and H) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-708, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60389
in-theory        60389
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     39
proof            (modus-ponens tm-665 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60389.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-665, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60390
in-theory        60390
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (E or ((A and (B -> C)) -> C)))
theorem-size     27
proof            (modus-ponens tm-623 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60390.        (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (E or ((A and (B -> C)) -> C))), M:tm-623, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60391
in-theory        60391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-622 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60391.        ((A -> (B -> (C or B))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-622, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60392
in-theory        60392
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (E -> (F or E)))
theorem-size     31
proof            (modus-ponens tm-609 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60392.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (E -> (F or E))), M:tm-609, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60393
in-theory        60393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     35
proof            (modus-ponens tm-605 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60393.        ((A -> ((B -> (C or B)) and A)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-605, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60394
in-theory        60394
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((E -> (F or E)) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))))
theorem-size     57
proof            (modus-ponens tm-595 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60394.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((E -> (F or E)) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)))), M:tm-595, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60395
in-theory        60395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-550 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60395.        (((A -> (B or A)) or C) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-550, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60396
in-theory        60396
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-540 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60396.        ((A or (B -> (C or B))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-540, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60397
in-theory        60397
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-530 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60397.        ((A or (B -> (B or C))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-530, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60398
in-theory        60398
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     35
proof            (modus-ponens tm-520 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60398.        ((A or (B -> (C -> (B and C)))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-520, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60399
in-theory        60399
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-510 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60399.        ((A or ((B and C) -> C)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-510, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60400
in-theory        60400
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-500 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60400.        ((A or ((B and C) -> B)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-500, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60401
in-theory        60401
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and (F -> G)) -> F) and H) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     41
proof            (modus-ponens tm-490 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60401.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and (F -> G)) -> F) and H) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-490, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60402
in-theory        60402
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-480 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60402.        ((A or (B -> (C -> B))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-480, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60403
in-theory        60403
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (((A and (B -> C)) -> C) or E))
theorem-size     27
proof            (modus-ponens tm-470 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60403.        (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (((A and (B -> C)) -> C) or E)), M:tm-470, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60404
in-theory        60404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-469 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60404.        ((A -> (B -> (B or C))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-469, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60405
in-theory        60405
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (E -> (E or F)))
theorem-size     31
proof            (modus-ponens tm-456 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60405.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (E -> (E or F))), M:tm-456, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60406
in-theory        60406
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     35
proof            (modus-ponens tm-453 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60406.        ((A -> ((B -> (B or C)) and A)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-453, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60407
in-theory        60407
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((E -> (E or F)) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))))
theorem-size     57
proof            (modus-ponens tm-443 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60407.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((E -> (E or F)) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)))), M:tm-443, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60408
in-theory        60408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-409 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60408.        (((A -> (A or B)) or C) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-409, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60409
in-theory        60409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     35
proof            (modus-ponens tm-400 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60409.        (((A -> (B -> (A and B))) or C) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-400, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60410
in-theory        60410
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-391 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60410.        ((((A and B) -> B) or C) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-391, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60411
in-theory        60411
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-382 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60411.        ((((A and B) -> A) or C) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-382, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60412
in-theory        60412
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E and (F -> G)) -> F) and H) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     41
proof            (modus-ponens tm-373 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60412.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E and (F -> G)) -> F) and H) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-373, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60413
in-theory        60413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-364 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60413.        (((A -> (B -> A)) or C) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-364, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60414
in-theory        60414
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (E -> (((A and (B -> C)) -> C) and E)))
theorem-size     29
proof            (modus-ponens tm-355 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60414.        (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (E -> (((A and (B -> C)) -> C) and E))), M:tm-355, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60415
in-theory        60415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     35
proof            (modus-ponens tm-354 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60415.        ((A -> (B -> (C -> (B and C)))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-354, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60416
in-theory        60416
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (E -> (F -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-341 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60416.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60417
in-theory        60417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E)))
theorem-size     35
proof            (modus-ponens tm-338 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60417.        (((A -> B) -> (A -> (A and B))) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E))), M:tm-338, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60418
in-theory        60418
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) and ((A and (B -> C)) -> C))))
theorem-size     69
proof            (modus-ponens tm-328 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60418.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) and ((A and (B -> C)) -> C)))), M:tm-328, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60419
in-theory        60419
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((E -> (F -> (E and F))) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))))
theorem-size     59
proof            (modus-ponens tm-327 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60419.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((E -> (F -> (E and F))) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)))), M:tm-327, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60420
in-theory        60420
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (((E and F) -> F) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))))
theorem-size     57
proof            (modus-ponens tm-326 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60420.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (((E and F) -> F) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)))), M:tm-326, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60421
in-theory        60421
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (((E and F) -> E) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))))
theorem-size     57
proof            (modus-ponens tm-325 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60421.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (((E and F) -> E) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)))), M:tm-325, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60422
in-theory        60422
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))))
theorem-size     65
proof            (modus-ponens tm-324 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       237
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60422.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)))), M:tm-324, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60423
in-theory        60423
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((E -> (F -> E)) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))))
theorem-size     57
proof            (modus-ponens tm-323 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60423.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((E -> (F -> E)) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)))), M:tm-323, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60424
in-theory        60424
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((E and F) -> F))
theorem-size     31
proof            (modus-ponens tm-322 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60424.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60425
in-theory        60425
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((E and F) -> E))
theorem-size     31
proof            (modus-ponens tm-320 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60425.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60426
in-theory        60426
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-318 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60426.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60427
in-theory        60427
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B))))
theorem-size     61
proof            (modus-ponens tm-316 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60427.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)))), M:tm-316, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60428
in-theory        60428
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (E -> (F -> E)))
theorem-size     31
proof            (modus-ponens tm-315 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60428.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60429
in-theory        60429
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (not ((A and (B -> C)) -> C))) -> (not ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)))))
theorem-size     71
proof            (modus-ponens tm-313 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-4)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60429.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (not ((A and (B -> C)) -> C))) -> (not ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B))))), M:tm-313, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60430
in-theory        60430
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((((A and (B -> C)) -> C) -> E) -> ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> C)) -> E)))
theorem-size     63
proof            (modus-ponens tm-312 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60430.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((((A and (B -> C)) -> C) -> E) -> ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> C)) -> E))), M:tm-312, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60431
in-theory        60431
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (E or (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))))
theorem-size     53
proof            (modus-ponens tm-311 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60431.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (E or (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)))), M:tm-311, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60432
in-theory        60432
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) or E))
theorem-size     53
proof            (modus-ponens tm-310 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60432.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) or E)), M:tm-310, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60433
in-theory        60433
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (E -> ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and E)))
theorem-size     55
proof            (modus-ponens tm-309 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60433.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (E -> ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and E))), M:tm-309, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60434
in-theory        60434
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (A and (B -> C))) -> (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> C)))
theorem-size     69
proof            (modus-ponens tm-306 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (and Am (-> Bm Cm))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60434.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (A and (B -> C))) -> (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> C))), M:tm-306, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (and Am (-> Bm Cm))) (C Cm))
================================================================
tm-name          tm-60435
in-theory        60435
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (E -> (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))))
theorem-size     53
proof            (modus-ponens tm-305 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60435.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (E -> (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)))), M:tm-305, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60436
in-theory        60436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     37
proof            (modus-ponens tm-303 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60436.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-303, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60437
in-theory        60437
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     35
proof            (modus-ponens tm-270 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60437.        ((A -> (((B and C) -> C) and A)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-270, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60438
in-theory        60438
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     35
proof            (modus-ponens tm-239 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60438.        ((A -> (((B and C) -> B) and A)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-239, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60439
in-theory        60439
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E and (F -> G)) -> F) and H) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     43
proof            (modus-ponens tm-210 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60439.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E and (F -> G)) -> F) and H) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-210, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60440
in-theory        60440
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     35
proof            (modus-ponens tm-183 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60440.        ((A -> ((B -> (C -> B)) and A)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-183, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60441
in-theory        60441
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-157 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60441.        ((A -> ((B and C) -> C)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-157, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60442
in-theory        60442
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     41
proof            (modus-ponens tm-147 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60442.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-147, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60443
in-theory        60443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-134 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60443.        ((A -> ((B and C) -> B)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-134, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60444
in-theory        60444
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     41
proof            (modus-ponens tm-125 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60444.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-125, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60445
in-theory        60445
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> (C -> D))) -> B) and E) or ((A and (B -> (C -> D))) -> B)) -> (((A and (B -> (C -> D))) -> C) -> ((A and (B -> (C -> D))) -> D)))
theorem-size     41
proof            (modus-ponens tm-114 tm-727 ((A (or (and (-> (and Am (-> Bm (-> C D))) Bm) Dm) (-> (and Am (-> Bm (-> C D))) Bm))) (B (and Am (-> Bm (-> C D)))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60445.        (((((A and (B -> (C -> D))) -> B) and E) or ((A and (B -> (C -> D))) -> B)) -> (((A and (B -> (C -> D))) -> C) -> ((A and (B -> (C -> D))) -> D))), M:tm-114, m:tm-727, u:((A (or (and (-> (and Am (-> Bm (-> C D))) Bm) Dm) (-> (and Am (-> Bm (-> C D))) Bm))) (B (and Am (-> Bm (-> C D)))) (Cm (-> C D)))
================================================================
tm-name          tm-60446
in-theory        60446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and (F -> G)) -> F) and H) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     41
proof            (modus-ponens tm-113 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60446.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and (F -> G)) -> F) and H) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-113, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60447
in-theory        60447
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     45
proof            (modus-ponens tm-105 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60447.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-105, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60448
in-theory        60448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E)))
theorem-size     33
proof            (modus-ponens tm-95 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60448.        (((A -> B) -> (A -> A)) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E))), M:tm-95, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60449
in-theory        60449
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (E -> ((A and (B -> C)) -> C)))
theorem-size     27
proof            (modus-ponens tm-84 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60449.        (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (E -> ((A and (B -> C)) -> C))), M:tm-84, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60450
in-theory        60450
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-83 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60450.        ((A -> (B -> (C -> B))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-83, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60451
in-theory        60451
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B and (C -> D)) -> C) and E) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)))
theorem-size     31
proof            (modus-ponens tm-76 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60451.        (((not (not A)) -> A) and (((((B and (C -> D)) -> C) and E) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))), M:tm-76, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60452
in-theory        60452
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)))) or ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C))
theorem-size     45
proof            (modus-ponens tm-73 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-8 tm-10 tm-3 tm-2 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60452.        (((not (not ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)))) or ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C)), M:tm-73, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60453
in-theory        60453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E)))
theorem-size     37
proof            (modus-ponens tm-69 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-2 tm-4)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60453.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E))), M:tm-69, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60454
in-theory        60454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     39
proof            (modus-ponens tm-54 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60454.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-54, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60455
in-theory        60455
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C))
theorem-size     33
proof            (modus-ponens tm-50 tm-727 ((A (and (-> (and Am (-> Bm Cm)) Bm) Dm)) (B (-> (and Am (-> Bm Cm)) Bm)) (C (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-8 tm-7 tm-3 tm-2 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60455.        ((((A and (B -> C)) -> B) or ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C)), M:tm-50, m:tm-727, u:((A (and (-> (and Am (-> Bm Cm)) Bm) Dm)) (B (-> (and Am (-> Bm Cm)) Bm)) (C (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60456
in-theory        60456
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) and D) or ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C))
theorem-size     35
proof            (modus-ponens tm-49 tm-727 ((A (and (-> (and Am (-> Bm Cm)) Bm) Dm)) (B (-> (and Am (-> Bm Cm)) Bm)) (C (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-8 tm-6 tm-3 tm-2 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60456.        (((((A and (B -> C)) -> B) and D) or ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C)), M:tm-49, m:tm-727, u:((A (and (-> (and Am (-> Bm Cm)) Bm) Dm)) (B (-> (and Am (-> Bm Cm)) Bm)) (C (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60457
in-theory        60457
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B and (C -> D)) -> C) and E) or ((B and (C -> D)) -> C))) or ((((B and (C -> D)) -> C) and E) or ((B and (C -> D)) -> C))) -> ((B and (C -> D)) -> D))
theorem-size     45
proof            (modus-ponens tm-47 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-8 tm-4 tm-3 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60457.        (((A and ((((B and (C -> D)) -> C) and E) or ((B and (C -> D)) -> C))) or ((((B and (C -> D)) -> C) and E) or ((B and (C -> D)) -> C))) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60458
in-theory        60458
times-derived    1
----------------------------------------------------------------
theorem          (((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) and E) or ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C))
theorem-size     45
proof            (modus-ponens tm-46 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-4)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60458.        (((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) and E) or ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60459
in-theory        60459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E)))
theorem-size     31
proof            (modus-ponens tm-42 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60459.        ((A -> (B or A)) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60460
in-theory        60460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E)))
theorem-size     31
proof            (modus-ponens tm-32 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60460.        ((A -> (A or B)) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60461
in-theory        60461
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) and ((A and (B -> C)) -> C)))
theorem-size     43
proof            (modus-ponens tm-24 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60461.        (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60462
in-theory        60462
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E)))
theorem-size     33
proof            (modus-ponens tm-23 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60462.        ((A -> (B -> (A and B))) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60463
in-theory        60463
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E)))
theorem-size     31
proof            (modus-ponens tm-22 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60463.        (((A and B) -> B) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60464
in-theory        60464
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E)))
theorem-size     31
proof            (modus-ponens tm-21 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60464.        (((A and B) -> A) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60465
in-theory        60465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     39
proof            (modus-ponens tm-20 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60465.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60466
in-theory        60466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E)))
theorem-size     31
proof            (modus-ponens tm-19 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60466.        ((A -> (B -> A)) and (((((C and (D -> E)) -> D) and F) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60467
in-theory        60467
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)))
theorem-size     35
proof            (modus-ponens tm-12 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60467.        (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B))), M:tm-12, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60468
in-theory        60468
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (not ((A and (B -> C)) -> C))) -> (not ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B))))
theorem-size     45
proof            (modus-ponens tm-9 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-9 tm-8 tm-3 tm-2 tm-4)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60468.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (not ((A and (B -> C)) -> C))) -> (not ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)))), M:tm-9, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60469
in-theory        60469
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> D) -> ((((((A and (B -> C)) -> B) and E) or ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> C)) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-4)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60469.        ((((A and (B -> C)) -> C) -> D) -> ((((((A and (B -> C)) -> B) and E) or ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-60470
in-theory        60470
times-derived    1
----------------------------------------------------------------
theorem          (A or (((((B and (C -> D)) -> C) and E) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)))
theorem-size     27
proof            (modus-ponens tm-7 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-7 tm-8 tm-3 tm-2 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60470.        (A or (((((B and (C -> D)) -> C) and E) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60471
in-theory        60471
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) or E)
theorem-size     27
proof            (modus-ponens tm-6 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-6 tm-8 tm-3 tm-2 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60471.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) or E), M:tm-6, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60472
in-theory        60472
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B and (C -> D)) -> C) and E) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60472.        (A -> ((((((B and (C -> D)) -> C) and E) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60473
in-theory        60473
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (A and (B -> C))) -> (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> C))
theorem-size     43
proof            (modus-ponens tm-2 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (and Am (-> Bm Cm))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-3 tm-4)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60473.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (A and (B -> C))) -> (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> C)), M:tm-2, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (and Am (-> Bm Cm))) (C Cm))
================================================================
tm-name          tm-60474
in-theory        60474
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B and (C -> D)) -> C) and E) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)))
theorem-size     27
proof            (modus-ponens tm-1 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-1 tm-8 tm-3 tm-2 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-60474.        (A -> (((((B and (C -> D)) -> C) and E) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-60475
in-theory        60475
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> ((G and H) -> H)))
theorem-size     37
proof            (modus-ponens tm-708 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60475.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> ((G and H) -> H))), M:tm-708, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60476
in-theory        60476
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-665 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60476.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-665, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60477
in-theory        60477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-622 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60477.        ((A -> (B -> (C or B))) and (((D and E) or D) -> ((F and G) -> G))), M:tm-622, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60478
in-theory        60478
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3 tm-4)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60478.        ((((A and B) or A) -> ((C and D) -> D)) and (E -> (F or E))), M:tm-609, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60479
in-theory        60479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-605 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60479.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-605, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60480
in-theory        60480
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and ((E -> (F or E)) and (((A and B) or A) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-595 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1 tm-4)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60480.        ((((A and B) or A) -> ((C and D) -> D)) and ((E -> (F or E)) and (((A and B) or A) -> ((C and D) -> D)))), M:tm-595, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60481
in-theory        60481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-550 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-1 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60481.        (((A -> (B or A)) or C) and (((D and E) or D) -> ((F and G) -> G))), M:tm-550, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60482
in-theory        60482
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-540 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60482.        ((A or (B -> (C or B))) and (((D and E) or D) -> ((F and G) -> G))), M:tm-540, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60483
in-theory        60483
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-530 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-1 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60483.        ((A or (B -> (B or C))) and (((D and E) or D) -> ((F and G) -> G))), M:tm-530, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60484
in-theory        60484
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-520 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60484.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F and G) -> G))), M:tm-520, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60485
in-theory        60485
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-510 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60485.        ((A or ((B and C) -> C)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-510, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60486
in-theory        60486
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-500 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60486.        ((A or ((B and C) -> B)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-500, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60487
in-theory        60487
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-490 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-1 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60487.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G and H) -> H))), M:tm-490, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60488
in-theory        60488
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-480 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60488.        ((A or (B -> (C -> B))) and (((D and E) or D) -> ((F and G) -> G))), M:tm-480, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60489
in-theory        60489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-469 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60489.        ((A -> (B -> (B or C))) and (((D and E) or D) -> ((F and G) -> G))), M:tm-469, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60490
in-theory        60490
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3 tm-4)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60490.        ((((A and B) or A) -> ((C and D) -> D)) and (E -> (E or F))), M:tm-456, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60491
in-theory        60491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-453 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60491.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-453, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60492
in-theory        60492
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and ((E -> (E or F)) and (((A and B) or A) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-443 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1 tm-4)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60492.        ((((A and B) or A) -> ((C and D) -> D)) and ((E -> (E or F)) and (((A and B) or A) -> ((C and D) -> D)))), M:tm-443, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60493
in-theory        60493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-409 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60493.        (((A -> (A or B)) or C) and (((D and E) or D) -> ((F and G) -> G))), M:tm-409, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60494
in-theory        60494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-400 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60494.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> ((F and G) -> G))), M:tm-400, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60495
in-theory        60495
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-391 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60495.        ((((A and B) -> B) or C) and (((D and E) or D) -> ((F and G) -> G))), M:tm-391, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60496
in-theory        60496
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-382 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60496.        ((((A and B) -> A) or C) and (((D and E) or D) -> ((F and G) -> G))), M:tm-382, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60497
in-theory        60497
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-373 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-1 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60497.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> ((G and H) -> H))), M:tm-373, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60498
in-theory        60498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-364 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60498.        (((A -> (B -> A)) or C) and (((D and E) or D) -> ((F and G) -> G))), M:tm-364, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60499
in-theory        60499
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-354 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60499.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F and G) -> G))), M:tm-354, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60500
in-theory        60500
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60500.        ((((A and B) or A) -> ((C and D) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60501
in-theory        60501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-338 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60501.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> ((E and F) -> F))), M:tm-338, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60502
in-theory        60502
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (((A and B) or A) -> (((A and B) or A) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-328 tm-728 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60502.        ((((A and B) or A) -> ((C and D) -> D)) and (((A and B) or A) -> (((A and B) or A) and ((C and D) -> D)))), M:tm-328, m:tm-728, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-60503
in-theory        60503
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> ((C and D) -> D))))
theorem-size     31
proof            (modus-ponens tm-327 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60503.        ((((A and B) or A) -> ((C and D) -> D)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> ((C and D) -> D)))), M:tm-327, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60504
in-theory        60504
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (((E and F) -> F) and (((A and B) or A) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-326 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60504.        ((((A and B) or A) -> ((C and D) -> D)) and (((E and F) -> F) and (((A and B) or A) -> ((C and D) -> D)))), M:tm-326, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60505
in-theory        60505
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (((E and F) -> E) and (((A and B) or A) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-325 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-4)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60505.        ((((A and B) or A) -> ((C and D) -> D)) and (((E and F) -> E) and (((A and B) or A) -> ((C and D) -> D)))), M:tm-325, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60506
in-theory        60506
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> ((C and D) -> D))))
theorem-size     37
proof            (modus-ponens tm-324 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60506.        ((((A and B) or A) -> ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> ((C and D) -> D)))), M:tm-324, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60507
in-theory        60507
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and ((E -> (F -> E)) and (((A and B) or A) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-323 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60507.        ((((A and B) or A) -> ((C and D) -> D)) and ((E -> (F -> E)) and (((A and B) or A) -> ((C and D) -> D)))), M:tm-323, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60508
in-theory        60508
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60508.        ((((A and B) or A) -> ((C and D) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60509
in-theory        60509
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60509.        ((((A and B) or A) -> ((C and D) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60510
in-theory        60510
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60510.        ((((A and B) or A) -> ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60511
in-theory        60511
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     23
proof            (modus-ponens tm-316 tm-728 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60511.        ((((A and B) or A) -> ((C and D) -> D)) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-728, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-60512
in-theory        60512
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60512.        ((((A and B) or A) -> ((C and D) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60513
in-theory        60513
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and ((((A and B) or A) -> (not ((C and D) -> D))) -> (not ((A and B) or A))))
theorem-size     31
proof            (modus-ponens tm-313 tm-728 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-1 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60513.        ((((A and B) or A) -> ((C and D) -> D)) and ((((A and B) or A) -> (not ((C and D) -> D))) -> (not ((A and B) or A)))), M:tm-313, m:tm-728, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-60514
in-theory        60514
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and ((((C and D) -> D) -> E) -> ((((A and B) or A) or ((C and D) -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-728 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60514.        ((((A and B) or A) -> ((C and D) -> D)) and ((((C and D) -> D) -> E) -> ((((A and B) or A) or ((C and D) -> D)) -> E))), M:tm-312, m:tm-728, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-60515
in-theory        60515
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (E or (((A and B) or A) -> ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-311 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60515.        ((((A and B) or A) -> ((C and D) -> D)) and (E or (((A and B) or A) -> ((C and D) -> D)))), M:tm-311, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60516
in-theory        60516
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and ((((A and B) or A) -> ((C and D) -> D)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60516.        ((((A and B) or A) -> ((C and D) -> D)) and ((((A and B) or A) -> ((C and D) -> D)) or E)), M:tm-310, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60517
in-theory        60517
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (E -> ((((A and B) or A) -> ((C and D) -> D)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60517.        ((((A and B) or A) -> ((C and D) -> D)) and (E -> ((((A and B) or A) -> ((C and D) -> D)) and E))), M:tm-309, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60518
in-theory        60518
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and ((((A and B) or A) -> (C and D)) -> (((A and B) or A) -> D)))
theorem-size     29
proof            (modus-ponens tm-306 tm-728 ((A (or (and Am Bm) Am)) (B (and Cm Dm)) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60518.        ((((A and B) or A) -> ((C and D) -> D)) and ((((A and B) or A) -> (C and D)) -> (((A and B) or A) -> D))), M:tm-306, m:tm-728, u:((A (or (and Am Bm) Am)) (B (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-60519
in-theory        60519
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (E -> (((A and B) or A) -> ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-305 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60519.        ((((A and B) or A) -> ((C and D) -> D)) and (E -> (((A and B) or A) -> ((C and D) -> D)))), M:tm-305, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60520
in-theory        60520
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-303 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60520.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-303, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60521
in-theory        60521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-270 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60521.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-270, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60522
in-theory        60522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-239 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60522.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-239, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60523
in-theory        60523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-210 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60523.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> ((G and H) -> H))), M:tm-210, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60524
in-theory        60524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-183 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60524.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-183, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60525
in-theory        60525
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-157 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60525.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-157, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60526
in-theory        60526
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-147 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60526.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-147, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60527
in-theory        60527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-134 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60527.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-134, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60528
in-theory        60528
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-125 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60528.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-125, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60529
in-theory        60529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-113 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60529.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G and H) -> H))), M:tm-113, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60530
in-theory        60530
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-105 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60530.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> ((F and G) -> G))), M:tm-105, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60531
in-theory        60531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-95 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60531.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> ((E and F) -> F))), M:tm-95, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60532
in-theory        60532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-83 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60532.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> ((F and G) -> G))), M:tm-83, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60533
in-theory        60533
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> ((D and E) -> E)))
theorem-size     17
proof            (modus-ponens tm-76 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-1 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60533.        (((not (not A)) -> A) and (((B and C) or B) -> ((D and E) -> E))), M:tm-76, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60534
in-theory        60534
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> ((C and D) -> D))
theorem-size     19
proof            (modus-ponens tm-73 tm-728 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-10 tm-3 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60534.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> ((C and D) -> D)), M:tm-73, m:tm-728, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-60535
in-theory        60535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-69 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-1 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60535.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> ((E and F) -> F))), M:tm-69, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60536
in-theory        60536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-54 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60536.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> ((F and G) -> G))), M:tm-54, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60537
in-theory        60537
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-50 tm-728 ((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-7 tm-3 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60537.        ((A or ((A and B) or A)) -> ((C and D) -> D)), M:tm-50, m:tm-728, u:((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-60538
in-theory        60538
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-49 tm-728 ((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-6 tm-3 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60538.        (((A and B) or ((A and B) or A)) -> ((C and D) -> D)), M:tm-49, m:tm-728, u:((A (and Am Bm)) (B Am) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-60539
in-theory        60539
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-47 tm-728 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-4 tm-3 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60539.        (((A and ((B and C) or B)) or ((B and C) or B)) -> ((D and E) -> E)), M:tm-47, m:tm-728, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-60540
in-theory        60540
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-46 tm-728 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60540.        (((((A and B) or A) and C) or ((A and B) or A)) -> ((D and E) -> E)), M:tm-46, m:tm-728, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-60541
in-theory        60541
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-42 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60541.        ((A -> (B or A)) and (((C and D) or C) -> ((E and F) -> F))), M:tm-42, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60542
in-theory        60542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-32 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60542.        ((A -> (A or B)) and (((C and D) or C) -> ((E and F) -> F))), M:tm-32, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60543
in-theory        60543
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and ((C and D) -> D)))
theorem-size     17
proof            (modus-ponens tm-24 tm-728 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60543.        (((A and B) or A) -> (((A and B) or A) and ((C and D) -> D))), M:tm-24, m:tm-728, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-60544
in-theory        60544
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-23 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60544.        ((A -> (B -> (A and B))) and (((C and D) or C) -> ((E and F) -> F))), M:tm-23, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60545
in-theory        60545
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-22 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60545.        (((A and B) -> B) and (((C and D) or C) -> ((E and F) -> F))), M:tm-22, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60546
in-theory        60546
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-21 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60546.        (((A and B) -> A) and (((C and D) or C) -> ((E and F) -> F))), M:tm-21, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60547
in-theory        60547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-20 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60547.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> ((F and G) -> G))), M:tm-20, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60548
in-theory        60548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-19 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60548.        ((A -> (B -> A)) and (((C and D) or C) -> ((E and F) -> F))), M:tm-19, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60549
in-theory        60549
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not ((C and D) -> D))) -> (not ((A and B) or A)))
theorem-size     19
proof            (modus-ponens tm-9 tm-728 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-9 tm-8 tm-3 tm-1 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60549.        ((((A and B) or A) -> (not ((C and D) -> D))) -> (not ((A and B) or A))), M:tm-9, m:tm-728, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-60550
in-theory        60550
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> ((((D and E) or D) or ((A and B) -> B)) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-728 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60550.        ((((A and B) -> B) -> C) -> ((((D and E) or D) or ((A and B) -> B)) -> C)), M:tm-8, m:tm-728, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-60551
in-theory        60551
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-7 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-7 tm-8 tm-3 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60551.        (A or (((B and C) or B) -> ((D and E) -> E))), M:tm-7, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60552
in-theory        60552
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-6 tm-8 tm-3 tm-1 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60552.        ((((A and B) or A) -> ((C and D) -> D)) or E), M:tm-6, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60553
in-theory        60553
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> ((D and E) -> E)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60553.        (A -> ((((B and C) or B) -> ((D and E) -> E)) and A)), M:tm-5, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60554
in-theory        60554
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C and D)) -> (((A and B) or A) -> D))
theorem-size     17
proof            (modus-ponens tm-2 tm-728 ((A (or (and Am Bm) Am)) (B (and Cm Dm)) (C Dm)))
axioms-used      (tm-2 tm-8 tm-3 tm-1 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60554.        ((((A and B) or A) -> (C and D)) -> (((A and B) or A) -> D)), M:tm-2, m:tm-728, u:((A (or (and Am Bm) Am)) (B (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-60555
in-theory        60555
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-1 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-1 tm-8 tm-3 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-60555.        (A -> (((B and C) or B) -> ((D and E) -> E))), M:tm-1, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-60556
in-theory        60556
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> ((G -> (H -> G)) and E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60556.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> ((G -> (H -> G)) and E))), M:tm-708, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60557
in-theory        60557
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60557.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-665, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60558
in-theory        60558
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or ((D -> (E -> D)) and A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60558.        (((A and B) or A) -> (C or ((D -> (E -> D)) and A))), M:tm-623, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60559
in-theory        60559
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60559.        ((A -> (B -> (C or B))) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-622, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60560
in-theory        60560
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60560.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (E -> (F or E))), M:tm-609, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60561
in-theory        60561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60561.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-605, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60562
in-theory        60562
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((E -> (F or E)) and (((A and B) or A) -> ((C -> (D -> C)) and A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60562.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((E -> (F or E)) and (((A and B) or A) -> ((C -> (D -> C)) and A)))), M:tm-595, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60563
in-theory        60563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60563.        (((A -> (B or A)) or C) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-550, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60564
in-theory        60564
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60564.        ((A or (B -> (C or B))) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-540, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60565
in-theory        60565
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60565.        ((A or (B -> (B or C))) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-530, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60566
in-theory        60566
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60566.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-520, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60567
in-theory        60567
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60567.        ((A or ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-510, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60568
in-theory        60568
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60568.        ((A or ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-500, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60569
in-theory        60569
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H -> G)) and E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60569.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H -> G)) and E))), M:tm-490, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60570
in-theory        60570
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60570.        ((A or (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-480, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60571
in-theory        60571
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> (D -> C)) and A) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60571.        (((A and B) or A) -> (((C -> (D -> C)) and A) or E)), M:tm-470, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60572
in-theory        60572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60572.        ((A -> (B -> (B or C))) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-469, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60573
in-theory        60573
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60573.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (E -> (E or F))), M:tm-456, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60574
in-theory        60574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60574.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-453, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60575
in-theory        60575
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((E -> (E or F)) and (((A and B) or A) -> ((C -> (D -> C)) and A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60575.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((E -> (E or F)) and (((A and B) or A) -> ((C -> (D -> C)) and A)))), M:tm-443, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60576
in-theory        60576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60576.        (((A -> (A or B)) or C) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-409, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60577
in-theory        60577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60577.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-400, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60578
in-theory        60578
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60578.        ((((A and B) -> B) or C) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-391, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60579
in-theory        60579
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60579.        ((((A and B) -> A) or C) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-382, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60580
in-theory        60580
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> ((G -> (H -> G)) and E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60580.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> ((G -> (H -> G)) and E))), M:tm-373, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60581
in-theory        60581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60581.        (((A -> (B -> A)) or C) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-364, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60582
in-theory        60582
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (((D -> (E -> D)) and A) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60582.        (((A and B) or A) -> (C -> (((D -> (E -> D)) and A) and C))), M:tm-355, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60583
in-theory        60583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60583.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-354, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60584
in-theory        60584
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60584.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60585
in-theory        60585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> ((E -> (F -> E)) and C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60585.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> ((E -> (F -> E)) and C))), M:tm-338, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60586
in-theory        60586
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((A and B) or A) -> (((A and B) or A) and ((C -> (D -> C)) and A))))
theorem-size     33
proof            (modus-ponens tm-328 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60586.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((A and B) or A) -> (((A and B) or A) and ((C -> (D -> C)) and A)))), M:tm-328, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60587
in-theory        60587
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> ((C -> (D -> C)) and A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60587.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> ((C -> (D -> C)) and A)))), M:tm-327, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60588
in-theory        60588
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((E and F) -> F) and (((A and B) or A) -> ((C -> (D -> C)) and A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60588.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((E and F) -> F) and (((A and B) or A) -> ((C -> (D -> C)) and A)))), M:tm-326, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60589
in-theory        60589
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((E and F) -> E) and (((A and B) or A) -> ((C -> (D -> C)) and A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60589.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((E and F) -> E) and (((A and B) or A) -> ((C -> (D -> C)) and A)))), M:tm-325, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60590
in-theory        60590
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> ((C -> (D -> C)) and A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60590.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> ((C -> (D -> C)) and A)))), M:tm-324, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60591
in-theory        60591
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((E -> (F -> E)) and (((A and B) or A) -> ((C -> (D -> C)) and A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60591.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((E -> (F -> E)) and (((A and B) or A) -> ((C -> (D -> C)) and A)))), M:tm-323, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60592
in-theory        60592
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60592.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60593
in-theory        60593
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60593.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60594
in-theory        60594
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60594.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60595
in-theory        60595
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     25
proof            (modus-ponens tm-316 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60595.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60596
in-theory        60596
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60596.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60597
in-theory        60597
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((((A and B) or A) -> (not ((C -> (D -> C)) and A))) -> (not ((A and B) or A))))
theorem-size     35
proof            (modus-ponens tm-313 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60597.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((((A and B) or A) -> (not ((C -> (D -> C)) and A))) -> (not ((A and B) or A)))), M:tm-313, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60598
in-theory        60598
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((((C -> (D -> C)) and A) -> E) -> ((((A and B) or A) or ((C -> (D -> C)) and A)) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60598.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((((C -> (D -> C)) and A) -> E) -> ((((A and B) or A) or ((C -> (D -> C)) and A)) -> E))), M:tm-312, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60599
in-theory        60599
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (E or (((A and B) or A) -> ((C -> (D -> C)) and A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60599.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (E or (((A and B) or A) -> ((C -> (D -> C)) and A)))), M:tm-311, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60600
in-theory        60600
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((((A and B) or A) -> ((C -> (D -> C)) and A)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60600.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and ((((A and B) or A) -> ((C -> (D -> C)) and A)) or E)), M:tm-310, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60601
in-theory        60601
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (E -> ((((A and B) or A) -> ((C -> (D -> C)) and A)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60601.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (E -> ((((A and B) or A) -> ((C -> (D -> C)) and A)) and E))), M:tm-309, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60602
in-theory        60602
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (E -> (((A and B) or A) -> ((C -> (D -> C)) and A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60602.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (E -> (((A and B) or A) -> ((C -> (D -> C)) and A)))), M:tm-305, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60603
in-theory        60603
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60603.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-303, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60604
in-theory        60604
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60604.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-270, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60605
in-theory        60605
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60605.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-239, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60606
in-theory        60606
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> ((G -> (H -> G)) and E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60606.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> ((G -> (H -> G)) and E))), M:tm-210, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60607
in-theory        60607
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60607.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-183, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60608
in-theory        60608
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60608.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-157, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60609
in-theory        60609
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60609.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-147, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60610
in-theory        60610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60610.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-134, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60611
in-theory        60611
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60611.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-125, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60612
in-theory        60612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H -> G)) and E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60612.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H -> G)) and E))), M:tm-113, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60613
in-theory        60613
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60613.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-105, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60614
in-theory        60614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> ((E -> (F -> E)) and C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60614.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> ((E -> (F -> E)) and C))), M:tm-95, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60615
in-theory        60615
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D -> (E -> D)) and A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60615.        (((A and B) or A) -> (C -> ((D -> (E -> D)) and A))), M:tm-84, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60616
in-theory        60616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60616.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-83, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60617
in-theory        60617
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> ((D -> (E -> D)) and B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60617.        (((not (not A)) -> A) and (((B and C) or B) -> ((D -> (E -> D)) and B))), M:tm-76, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60618
in-theory        60618
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> ((C -> (D -> C)) and A))
theorem-size     21
proof            (modus-ponens tm-73 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-8 tm-10 tm-3 tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60618.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> ((C -> (D -> C)) and A)), M:tm-73, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60619
in-theory        60619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> ((E -> (F -> E)) and C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60619.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> ((E -> (F -> E)) and C))), M:tm-69, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60620
in-theory        60620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60620.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-54, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60621
in-theory        60621
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> ((C -> (D -> C)) and A))
theorem-size     15
proof            (modus-ponens tm-50 tm-729 ((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-8 tm-7 tm-3 tm-5 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60621.        ((A or ((A and B) or A)) -> ((C -> (D -> C)) and A)), M:tm-50, m:tm-729, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60622
in-theory        60622
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> ((C -> (D -> C)) and A))
theorem-size     17
proof            (modus-ponens tm-49 tm-729 ((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-8 tm-6 tm-3 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60622.        (((A and B) or ((A and B) or A)) -> ((C -> (D -> C)) and A)), M:tm-49, m:tm-729, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60623
in-theory        60623
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> ((D -> (E -> D)) and B))
theorem-size     21
proof            (modus-ponens tm-47 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-8 tm-4 tm-3 tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60623.        (((A and ((B and C) or B)) or ((B and C) or B)) -> ((D -> (E -> D)) and B)), M:tm-47, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60624
in-theory        60624
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> ((D -> (E -> D)) and A))
theorem-size     21
proof            (modus-ponens tm-46 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60624.        (((((A and B) or A) and C) or ((A and B) or A)) -> ((D -> (E -> D)) and A)), M:tm-46, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60625
in-theory        60625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> ((E -> (F -> E)) and C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60625.        ((A -> (B or A)) and (((C and D) or C) -> ((E -> (F -> E)) and C))), M:tm-42, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60626
in-theory        60626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> ((E -> (F -> E)) and C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60626.        ((A -> (A or B)) and (((C and D) or C) -> ((E -> (F -> E)) and C))), M:tm-32, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60627
in-theory        60627
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and ((C -> (D -> C)) and A)))
theorem-size     19
proof            (modus-ponens tm-24 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60627.        (((A and B) or A) -> (((A and B) or A) and ((C -> (D -> C)) and A))), M:tm-24, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60628
in-theory        60628
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> ((E -> (F -> E)) and C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60628.        ((A -> (B -> (A and B))) and (((C and D) or C) -> ((E -> (F -> E)) and C))), M:tm-23, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60629
in-theory        60629
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> ((E -> (F -> E)) and C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60629.        (((A and B) -> B) and (((C and D) or C) -> ((E -> (F -> E)) and C))), M:tm-22, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60630
in-theory        60630
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> ((E -> (F -> E)) and C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60630.        (((A and B) -> A) and (((C and D) or C) -> ((E -> (F -> E)) and C))), M:tm-21, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60631
in-theory        60631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60631.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-20, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60632
in-theory        60632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> ((E -> (F -> E)) and C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60632.        ((A -> (B -> A)) and (((C and D) or C) -> ((E -> (F -> E)) and C))), M:tm-19, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60633
in-theory        60633
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not ((C -> (D -> C)) and A))) -> (not ((A and B) or A)))
theorem-size     21
proof            (modus-ponens tm-9 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-9 tm-8 tm-3 tm-5 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60633.        ((((A and B) or A) -> (not ((C -> (D -> C)) and A))) -> (not ((A and B) or A))), M:tm-9, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60634
in-theory        60634
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and C) -> D) -> ((((C and E) or C) or ((A -> (B -> A)) and C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60634.        ((((A -> (B -> A)) and C) -> D) -> ((((C and E) or C) or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-60635
in-theory        60635
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> ((D -> (E -> D)) and B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-7 tm-8 tm-3 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60635.        (A or (((B and C) or B) -> ((D -> (E -> D)) and B))), M:tm-7, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60636
in-theory        60636
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-6 tm-8 tm-3 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60636.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) or E), M:tm-6, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60637
in-theory        60637
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> ((D -> (E -> D)) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60637.        (A -> ((((B and C) or B) -> ((D -> (E -> D)) and B)) and A)), M:tm-5, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60638
in-theory        60638
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> ((D -> (E -> D)) and B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-1 tm-8 tm-3 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-60638.        (A -> (((B and C) or B) -> ((D -> (E -> D)) and B))), M:tm-1, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-60639
in-theory        60639
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E)))
theorem-size     47
proof            (modus-ponens tm-708 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60639.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E))), M:tm-708, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60640
in-theory        60640
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     35
proof            (modus-ponens tm-665 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60640.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-665, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60641
in-theory        60641
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and A)))
theorem-size     23
proof            (modus-ponens tm-623 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-5)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60641.        (((A and B) or A) -> (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and A))), M:tm-623, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60642
in-theory        60642
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-622 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60642.        ((A -> (B -> (C or B))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-622, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60643
in-theory        60643
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60643.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (F -> (G or F))), M:tm-609, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60644
in-theory        60644
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     31
proof            (modus-ponens tm-605 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60644.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-605, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60645
in-theory        60645
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((F -> (G or F)) and (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))))
theorem-size     49
proof            (modus-ponens tm-595 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60645.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((F -> (G or F)) and (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))), M:tm-595, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60646
in-theory        60646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-550 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60646.        (((A -> (B or A)) or C) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-550, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60647
in-theory        60647
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-540 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60647.        ((A or (B -> (C or B))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-540, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60648
in-theory        60648
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-530 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60648.        ((A or (B -> (B or C))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-530, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60649
in-theory        60649
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     31
proof            (modus-ponens tm-520 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60649.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-520, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60650
in-theory        60650
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-510 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60650.        ((A or ((B and C) -> C)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-510, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60651
in-theory        60651
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-500 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60651.        ((A or ((B and C) -> B)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-500, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60652
in-theory        60652
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E)))
theorem-size     37
proof            (modus-ponens tm-490 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60652.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E))), M:tm-490, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60653
in-theory        60653
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-480 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60653.        ((A or (B -> (C -> B))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-480, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60654
in-theory        60654
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A) or F))
theorem-size     23
proof            (modus-ponens tm-470 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-5)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60654.        (((A and B) or A) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A) or F)), M:tm-470, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60655
in-theory        60655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-469 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60655.        ((A -> (B -> (B or C))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-469, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60656
in-theory        60656
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60656.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (F -> (F or G))), M:tm-456, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60657
in-theory        60657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     31
proof            (modus-ponens tm-453 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60657.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-453, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60658
in-theory        60658
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((F -> (F or G)) and (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))))
theorem-size     49
proof            (modus-ponens tm-443 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60658.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((F -> (F or G)) and (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))), M:tm-443, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60659
in-theory        60659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-409 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60659.        (((A -> (A or B)) or C) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-409, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60660
in-theory        60660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     31
proof            (modus-ponens tm-400 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60660.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-400, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60661
in-theory        60661
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-391 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60661.        ((((A and B) -> B) or C) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-391, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60662
in-theory        60662
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-382 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60662.        ((((A and B) -> A) or C) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-382, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60663
in-theory        60663
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E)))
theorem-size     37
proof            (modus-ponens tm-373 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60663.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E))), M:tm-373, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60664
in-theory        60664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-364 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60664.        (((A -> (B -> A)) or C) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-364, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60665
in-theory        60665
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and A) and C)))
theorem-size     25
proof            (modus-ponens tm-355 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60665.        (((A and B) or A) -> (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and A) and C))), M:tm-355, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60666
in-theory        60666
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     31
proof            (modus-ponens tm-354 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60666.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-354, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60667
in-theory        60667
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60667.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60668
in-theory        60668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C)))
theorem-size     31
proof            (modus-ponens tm-338 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60668.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C))), M:tm-338, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60669
in-theory        60669
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((A and B) or A) -> (((A and B) or A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))))
theorem-size     49
proof            (modus-ponens tm-328 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60669.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((A and B) or A) -> (((A and B) or A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))), M:tm-328, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60670
in-theory        60670
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((F -> (G -> (F and G))) and (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))))
theorem-size     51
proof            (modus-ponens tm-327 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60670.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((F -> (G -> (F and G))) and (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))), M:tm-327, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60671
in-theory        60671
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((F and G) -> G) and (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))))
theorem-size     49
proof            (modus-ponens tm-326 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60671.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((F and G) -> G) and (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))), M:tm-326, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60672
in-theory        60672
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((F and G) -> F) and (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))))
theorem-size     49
proof            (modus-ponens tm-325 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60672.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((F and G) -> F) and (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))), M:tm-325, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60673
in-theory        60673
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))))
theorem-size     57
proof            (modus-ponens tm-324 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60673.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))), M:tm-324, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60674
in-theory        60674
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((F -> (G -> F)) and (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))))
theorem-size     49
proof            (modus-ponens tm-323 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60674.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((F -> (G -> F)) and (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))), M:tm-323, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60675
in-theory        60675
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60675.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((F and G) -> G)), M:tm-322, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60676
in-theory        60676
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60676.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((F and G) -> F)), M:tm-320, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60677
in-theory        60677
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60677.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60678
in-theory        60678
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     33
proof            (modus-ponens tm-316 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60678.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60679
in-theory        60679
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60679.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (F -> (G -> F))), M:tm-315, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60680
in-theory        60680
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((((A and B) or A) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))) -> (not ((A and B) or A))))
theorem-size     51
proof            (modus-ponens tm-313 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60680.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((((A and B) or A) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))) -> (not ((A and B) or A)))), M:tm-313, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60681
in-theory        60681
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A) -> F) -> ((((A and B) or A) or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) -> F)))
theorem-size     63
proof            (modus-ponens tm-312 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60681.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A) -> F) -> ((((A and B) or A) or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) -> F))), M:tm-312, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60682
in-theory        60682
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (F or (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))))
theorem-size     45
proof            (modus-ponens tm-311 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60682.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (F or (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))), M:tm-311, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60683
in-theory        60683
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60683.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) or F)), M:tm-310, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60684
in-theory        60684
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (F -> ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60684.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (F -> ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and F))), M:tm-309, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60685
in-theory        60685
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (F -> (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))))
theorem-size     45
proof            (modus-ponens tm-305 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60685.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (F -> (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))), M:tm-305, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60686
in-theory        60686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     33
proof            (modus-ponens tm-303 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60686.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-303, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60687
in-theory        60687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     31
proof            (modus-ponens tm-270 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60687.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-270, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60688
in-theory        60688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     31
proof            (modus-ponens tm-239 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60688.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-239, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60689
in-theory        60689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E)))
theorem-size     39
proof            (modus-ponens tm-210 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60689.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E))), M:tm-210, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60690
in-theory        60690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     31
proof            (modus-ponens tm-183 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60690.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-183, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60691
in-theory        60691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-157 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60691.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-157, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60692
in-theory        60692
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     37
proof            (modus-ponens tm-147 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60692.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-147, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60693
in-theory        60693
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-134 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60693.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-134, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60694
in-theory        60694
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     37
proof            (modus-ponens tm-125 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60694.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-125, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60695
in-theory        60695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E)))
theorem-size     37
proof            (modus-ponens tm-113 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60695.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and E))), M:tm-113, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60696
in-theory        60696
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     41
proof            (modus-ponens tm-105 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60696.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-105, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60697
in-theory        60697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C)))
theorem-size     29
proof            (modus-ponens tm-95 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60697.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C))), M:tm-95, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60698
in-theory        60698
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and A)))
theorem-size     23
proof            (modus-ponens tm-84 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-5)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60698.        (((A and B) or A) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and A))), M:tm-84, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60699
in-theory        60699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     29
proof            (modus-ponens tm-83 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60699.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-83, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60700
in-theory        60700
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B)))
theorem-size     27
proof            (modus-ponens tm-76 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60700.        (((not (not A)) -> A) and (((B and C) or B) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B))), M:tm-76, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60701
in-theory        60701
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))
theorem-size     29
proof            (modus-ponens tm-73 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-8 tm-10 tm-3 tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60701.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-73, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60702
in-theory        60702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C)))
theorem-size     33
proof            (modus-ponens tm-69 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60702.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C))), M:tm-69, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60703
in-theory        60703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     35
proof            (modus-ponens tm-54 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60703.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-54, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60704
in-theory        60704
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))
theorem-size     23
proof            (modus-ponens tm-50 tm-730 ((A (and Am Bm)) (B Am) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-8 tm-7 tm-3 tm-5 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60704.        ((A or ((A and B) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-50, m:tm-730, u:((A (and Am Bm)) (B Am) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60705
in-theory        60705
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))
theorem-size     25
proof            (modus-ponens tm-49 tm-730 ((A (and Am Bm)) (B Am) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-8 tm-6 tm-3 tm-5 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60705.        (((A and B) or ((A and B) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-49, m:tm-730, u:((A (and Am Bm)) (B Am) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60706
in-theory        60706
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B))
theorem-size     29
proof            (modus-ponens tm-47 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-8 tm-4 tm-3 tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60706.        (((A and ((B and C) or B)) or ((B and C) or B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B)), M:tm-47, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60707
in-theory        60707
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and A))
theorem-size     29
proof            (modus-ponens tm-46 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60707.        (((((A and B) or A) and C) or ((A and B) or A)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and A)), M:tm-46, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60708
in-theory        60708
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C)))
theorem-size     27
proof            (modus-ponens tm-42 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60708.        ((A -> (B or A)) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C))), M:tm-42, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60709
in-theory        60709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C)))
theorem-size     27
proof            (modus-ponens tm-32 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60709.        ((A -> (A or B)) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C))), M:tm-32, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60710
in-theory        60710
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))
theorem-size     27
proof            (modus-ponens tm-24 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60710.        (((A and B) or A) -> (((A and B) or A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))), M:tm-24, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60711
in-theory        60711
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C)))
theorem-size     29
proof            (modus-ponens tm-23 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60711.        ((A -> (B -> (A and B))) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C))), M:tm-23, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60712
in-theory        60712
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C)))
theorem-size     27
proof            (modus-ponens tm-22 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60712.        (((A and B) -> B) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C))), M:tm-22, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60713
in-theory        60713
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C)))
theorem-size     27
proof            (modus-ponens tm-21 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60713.        (((A and B) -> A) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C))), M:tm-21, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60714
in-theory        60714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     35
proof            (modus-ponens tm-20 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60714.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-20, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60715
in-theory        60715
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C)))
theorem-size     27
proof            (modus-ponens tm-19 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60715.        ((A -> (B -> A)) and (((C and D) or C) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and C))), M:tm-19, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60716
in-theory        60716
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))) -> (not ((A and B) or A)))
theorem-size     29
proof            (modus-ponens tm-9 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-9 tm-8 tm-3 tm-5 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60716.        ((((A and B) or A) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))) -> (not ((A and B) or A))), M:tm-9, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60717
in-theory        60717
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((((D and F) or D) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))
theorem-size     41
proof            (modus-ponens tm-8 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60717.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((((D and F) or D) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-60718
in-theory        60718
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B)))
theorem-size     23
proof            (modus-ponens tm-7 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-7 tm-8 tm-3 tm-5 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60718.        (A or (((B and C) or B) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B))), M:tm-7, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60719
in-theory        60719
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-6 tm-8 tm-3 tm-5 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60719.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) or F), M:tm-6, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60720
in-theory        60720
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60720.        (A -> ((((B and C) or B) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B)) and A)), M:tm-5, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60721
in-theory        60721
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B)))
theorem-size     23
proof            (modus-ponens tm-1 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-1 tm-8 tm-3 tm-5 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-60721.        (A -> (((B and C) or B) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B))), M:tm-1, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-60722
in-theory        60722
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (((G and H) -> G) and E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60722.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (((G and H) -> G) and E))), M:tm-708, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60723
in-theory        60723
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60723.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-665, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60724
in-theory        60724
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (((D and E) -> D) and A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60724.        (((A and B) or A) -> (C or (((D and E) -> D) and A))), M:tm-623, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60725
in-theory        60725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60725.        ((A -> (B -> (C or B))) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-622, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60726
in-theory        60726
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60726.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (E -> (F or E))), M:tm-609, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60727
in-theory        60727
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60727.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-605, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60728
in-theory        60728
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and ((E -> (F or E)) and (((A and B) or A) -> (((C and D) -> C) and A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60728.        ((((A and B) or A) -> (((C and D) -> C) and A)) and ((E -> (F or E)) and (((A and B) or A) -> (((C and D) -> C) and A)))), M:tm-595, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60729
in-theory        60729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60729.        (((A -> (B or A)) or C) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-550, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60730
in-theory        60730
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60730.        ((A or (B -> (C or B))) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-540, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60731
in-theory        60731
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60731.        ((A or (B -> (B or C))) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-530, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60732
in-theory        60732
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60732.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-520, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60733
in-theory        60733
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60733.        ((A or ((B and C) -> C)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-510, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60734
in-theory        60734
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60734.        ((A or ((B and C) -> B)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-500, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60735
in-theory        60735
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (((G and H) -> G) and E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60735.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (((G and H) -> G) and E))), M:tm-490, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60736
in-theory        60736
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60736.        ((A or (B -> (C -> B))) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-480, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60737
in-theory        60737
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C and D) -> C) and A) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60737.        (((A and B) or A) -> ((((C and D) -> C) and A) or E)), M:tm-470, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60738
in-theory        60738
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60738.        ((A -> (B -> (B or C))) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-469, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60739
in-theory        60739
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60739.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (E -> (E or F))), M:tm-456, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60740
in-theory        60740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60740.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-453, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60741
in-theory        60741
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and ((E -> (E or F)) and (((A and B) or A) -> (((C and D) -> C) and A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60741.        ((((A and B) or A) -> (((C and D) -> C) and A)) and ((E -> (E or F)) and (((A and B) or A) -> (((C and D) -> C) and A)))), M:tm-443, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60742
in-theory        60742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60742.        (((A -> (A or B)) or C) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-409, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60743
in-theory        60743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60743.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-400, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60744
in-theory        60744
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60744.        ((((A and B) -> B) or C) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-391, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60745
in-theory        60745
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60745.        ((((A and B) -> A) or C) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-382, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60746
in-theory        60746
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (((G and H) -> G) and E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60746.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (((G and H) -> G) and E))), M:tm-373, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60747
in-theory        60747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60747.        (((A -> (B -> A)) or C) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-364, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60748
in-theory        60748
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((((D and E) -> D) and A) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60748.        (((A and B) or A) -> (C -> ((((D and E) -> D) and A) and C))), M:tm-355, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60749
in-theory        60749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60749.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-354, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60750
in-theory        60750
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60750.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60751
in-theory        60751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (((E and F) -> E) and C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60751.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (((E and F) -> E) and C))), M:tm-338, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60752
in-theory        60752
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (((A and B) or A) -> (((A and B) or A) and (((C and D) -> C) and A))))
theorem-size     33
proof            (modus-ponens tm-328 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60752.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (((A and B) or A) -> (((A and B) or A) and (((C and D) -> C) and A)))), M:tm-328, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60753
in-theory        60753
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> (((C and D) -> C) and A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60753.        ((((A and B) or A) -> (((C and D) -> C) and A)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> (((C and D) -> C) and A)))), M:tm-327, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60754
in-theory        60754
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (((E and F) -> F) and (((A and B) or A) -> (((C and D) -> C) and A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60754.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (((E and F) -> F) and (((A and B) or A) -> (((C and D) -> C) and A)))), M:tm-326, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60755
in-theory        60755
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (((E and F) -> E) and (((A and B) or A) -> (((C and D) -> C) and A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60755.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (((E and F) -> E) and (((A and B) or A) -> (((C and D) -> C) and A)))), M:tm-325, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60756
in-theory        60756
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> (((C and D) -> C) and A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60756.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> (((C and D) -> C) and A)))), M:tm-324, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60757
in-theory        60757
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and ((E -> (F -> E)) and (((A and B) or A) -> (((C and D) -> C) and A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60757.        ((((A and B) or A) -> (((C and D) -> C) and A)) and ((E -> (F -> E)) and (((A and B) or A) -> (((C and D) -> C) and A)))), M:tm-323, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60758
in-theory        60758
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60758.        ((((A and B) or A) -> (((C and D) -> C) and A)) and ((E and F) -> F)), M:tm-322, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60759
in-theory        60759
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60759.        ((((A and B) or A) -> (((C and D) -> C) and A)) and ((E and F) -> E)), M:tm-320, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60760
in-theory        60760
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60760.        ((((A and B) or A) -> (((C and D) -> C) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60761
in-theory        60761
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     25
proof            (modus-ponens tm-316 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60761.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60762
in-theory        60762
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60762.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (E -> (F -> E))), M:tm-315, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60763
in-theory        60763
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and ((((A and B) or A) -> (not (((C and D) -> C) and A))) -> (not ((A and B) or A))))
theorem-size     35
proof            (modus-ponens tm-313 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60763.        ((((A and B) or A) -> (((C and D) -> C) and A)) and ((((A and B) or A) -> (not (((C and D) -> C) and A))) -> (not ((A and B) or A)))), M:tm-313, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60764
in-theory        60764
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (((((C and D) -> C) and A) -> E) -> ((((A and B) or A) or (((C and D) -> C) and A)) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60764.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (((((C and D) -> C) and A) -> E) -> ((((A and B) or A) or (((C and D) -> C) and A)) -> E))), M:tm-312, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60765
in-theory        60765
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (E or (((A and B) or A) -> (((C and D) -> C) and A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60765.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (E or (((A and B) or A) -> (((C and D) -> C) and A)))), M:tm-311, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60766
in-theory        60766
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and ((((A and B) or A) -> (((C and D) -> C) and A)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60766.        ((((A and B) or A) -> (((C and D) -> C) and A)) and ((((A and B) or A) -> (((C and D) -> C) and A)) or E)), M:tm-310, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60767
in-theory        60767
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (E -> ((((A and B) or A) -> (((C and D) -> C) and A)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60767.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (E -> ((((A and B) or A) -> (((C and D) -> C) and A)) and E))), M:tm-309, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60768
in-theory        60768
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (E -> (((A and B) or A) -> (((C and D) -> C) and A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60768.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (E -> (((A and B) or A) -> (((C and D) -> C) and A)))), M:tm-305, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60769
in-theory        60769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60769.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-303, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60770
in-theory        60770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60770.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-270, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60771
in-theory        60771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60771.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-239, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60772
in-theory        60772
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (((G and H) -> G) and E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60772.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (((G and H) -> G) and E))), M:tm-210, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60773
in-theory        60773
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60773.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-183, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60774
in-theory        60774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60774.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-157, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60775
in-theory        60775
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60775.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-147, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60776
in-theory        60776
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60776.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-134, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60777
in-theory        60777
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60777.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-125, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60778
in-theory        60778
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (((G and H) -> G) and E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60778.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (((G and H) -> G) and E))), M:tm-113, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60779
in-theory        60779
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60779.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-105, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60780
in-theory        60780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> (((E and F) -> E) and C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60780.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> (((E and F) -> E) and C))), M:tm-95, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60781
in-theory        60781
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (((D and E) -> D) and A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60781.        (((A and B) or A) -> (C -> (((D and E) -> D) and A))), M:tm-84, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60782
in-theory        60782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60782.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-83, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60783
in-theory        60783
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> (((D and E) -> D) and B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60783.        (((not (not A)) -> A) and (((B and C) or B) -> (((D and E) -> D) and B))), M:tm-76, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60784
in-theory        60784
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> (((C and D) -> C) and A))
theorem-size     21
proof            (modus-ponens tm-73 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-8 tm-10 tm-3 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60784.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> (((C and D) -> C) and A)), M:tm-73, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60785
in-theory        60785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (((E and F) -> E) and C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60785.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (((E and F) -> E) and C))), M:tm-69, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60786
in-theory        60786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60786.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-54, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60787
in-theory        60787
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> (((C and D) -> C) and A))
theorem-size     15
proof            (modus-ponens tm-50 tm-731 ((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-8 tm-7 tm-3 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60787.        ((A or ((A and B) or A)) -> (((C and D) -> C) and A)), M:tm-50, m:tm-731, u:((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60788
in-theory        60788
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> (((C and D) -> C) and A))
theorem-size     17
proof            (modus-ponens tm-49 tm-731 ((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-8 tm-6 tm-3 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60788.        (((A and B) or ((A and B) or A)) -> (((C and D) -> C) and A)), M:tm-49, m:tm-731, u:((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60789
in-theory        60789
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> (((D and E) -> D) and B))
theorem-size     21
proof            (modus-ponens tm-47 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-8 tm-4 tm-3 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60789.        (((A and ((B and C) or B)) or ((B and C) or B)) -> (((D and E) -> D) and B)), M:tm-47, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60790
in-theory        60790
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> (((D and E) -> D) and A))
theorem-size     21
proof            (modus-ponens tm-46 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60790.        (((((A and B) or A) and C) or ((A and B) or A)) -> (((D and E) -> D) and A)), M:tm-46, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60791
in-theory        60791
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> (((E and F) -> E) and C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60791.        ((A -> (B or A)) and (((C and D) or C) -> (((E and F) -> E) and C))), M:tm-42, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60792
in-theory        60792
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> (((E and F) -> E) and C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60792.        ((A -> (A or B)) and (((C and D) or C) -> (((E and F) -> E) and C))), M:tm-32, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60793
in-theory        60793
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and (((C and D) -> C) and A)))
theorem-size     19
proof            (modus-ponens tm-24 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60793.        (((A and B) or A) -> (((A and B) or A) and (((C and D) -> C) and A))), M:tm-24, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60794
in-theory        60794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> (((E and F) -> E) and C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60794.        ((A -> (B -> (A and B))) and (((C and D) or C) -> (((E and F) -> E) and C))), M:tm-23, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60795
in-theory        60795
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> (((E and F) -> E) and C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60795.        (((A and B) -> B) and (((C and D) or C) -> (((E and F) -> E) and C))), M:tm-22, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60796
in-theory        60796
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> (((E and F) -> E) and C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60796.        (((A and B) -> A) and (((C and D) or C) -> (((E and F) -> E) and C))), M:tm-21, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60797
in-theory        60797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60797.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-20, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60798
in-theory        60798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> (((E and F) -> E) and C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60798.        ((A -> (B -> A)) and (((C and D) or C) -> (((E and F) -> E) and C))), M:tm-19, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60799
in-theory        60799
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not (((C and D) -> C) and A))) -> (not ((A and B) or A)))
theorem-size     21
proof            (modus-ponens tm-9 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-9 tm-8 tm-3 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60799.        ((((A and B) or A) -> (not (((C and D) -> C) and A))) -> (not ((A and B) or A))), M:tm-9, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60800
in-theory        60800
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and C) -> D) -> ((((C and E) or C) or (((A and B) -> A) and C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60800.        (((((A and B) -> A) and C) -> D) -> ((((C and E) or C) or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-60801
in-theory        60801
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> (((D and E) -> D) and B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-7 tm-8 tm-3 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60801.        (A or (((B and C) or B) -> (((D and E) -> D) and B))), M:tm-7, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60802
in-theory        60802
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-6 tm-8 tm-3 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60802.        ((((A and B) or A) -> (((C and D) -> C) and A)) or E), M:tm-6, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60803
in-theory        60803
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> (((D and E) -> D) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60803.        (A -> ((((B and C) or B) -> (((D and E) -> D) and B)) and A)), M:tm-5, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60804
in-theory        60804
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> (((D and E) -> D) and B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-1 tm-8 tm-3 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-60804.        (A -> (((B and C) or B) -> (((D and E) -> D) and B))), M:tm-1, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-60805
in-theory        60805
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (((G and H) -> H) and E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-4)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60805.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (((G and H) -> H) and E))), M:tm-708, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60806
in-theory        60806
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60806.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-665, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60807
in-theory        60807
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (((D and E) -> E) and A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-5 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60807.        (((A and B) or A) -> (C or (((D and E) -> E) and A))), M:tm-623, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60808
in-theory        60808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60808.        ((A -> (B -> (C or B))) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-622, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60809
in-theory        60809
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60809.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (E -> (F or E))), M:tm-609, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60810
in-theory        60810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60810.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-605, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60811
in-theory        60811
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and ((E -> (F or E)) and (((A and B) or A) -> (((C and D) -> D) and A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60811.        ((((A and B) or A) -> (((C and D) -> D) and A)) and ((E -> (F or E)) and (((A and B) or A) -> (((C and D) -> D) and A)))), M:tm-595, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60812
in-theory        60812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60812.        (((A -> (B or A)) or C) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-550, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60813
in-theory        60813
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60813.        ((A or (B -> (C or B))) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-540, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60814
in-theory        60814
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60814.        ((A or (B -> (B or C))) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-530, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60815
in-theory        60815
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60815.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-520, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60816
in-theory        60816
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60816.        ((A or ((B and C) -> C)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-510, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60817
in-theory        60817
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60817.        ((A or ((B and C) -> B)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-500, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60818
in-theory        60818
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (((G and H) -> H) and E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60818.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (((G and H) -> H) and E))), M:tm-490, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60819
in-theory        60819
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60819.        ((A or (B -> (C -> B))) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-480, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60820
in-theory        60820
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((C and D) -> D) and A) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-5 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60820.        (((A and B) or A) -> ((((C and D) -> D) and A) or E)), M:tm-470, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60821
in-theory        60821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60821.        ((A -> (B -> (B or C))) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-469, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60822
in-theory        60822
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60822.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (E -> (E or F))), M:tm-456, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60823
in-theory        60823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60823.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-453, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60824
in-theory        60824
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and ((E -> (E or F)) and (((A and B) or A) -> (((C and D) -> D) and A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60824.        ((((A and B) or A) -> (((C and D) -> D) and A)) and ((E -> (E or F)) and (((A and B) or A) -> (((C and D) -> D) and A)))), M:tm-443, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60825
in-theory        60825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60825.        (((A -> (A or B)) or C) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-409, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60826
in-theory        60826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60826.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-400, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60827
in-theory        60827
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60827.        ((((A and B) -> B) or C) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-391, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60828
in-theory        60828
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60828.        ((((A and B) -> A) or C) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-382, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60829
in-theory        60829
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (((G and H) -> H) and E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60829.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (((G and H) -> H) and E))), M:tm-373, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60830
in-theory        60830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60830.        (((A -> (B -> A)) or C) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-364, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60831
in-theory        60831
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((((D and E) -> E) and A) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60831.        (((A and B) or A) -> (C -> ((((D and E) -> E) and A) and C))), M:tm-355, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60832
in-theory        60832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60832.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-354, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60833
in-theory        60833
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60833.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60834
in-theory        60834
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (((E and F) -> F) and C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60834.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (((E and F) -> F) and C))), M:tm-338, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60835
in-theory        60835
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (((A and B) or A) -> (((A and B) or A) and (((C and D) -> D) and A))))
theorem-size     33
proof            (modus-ponens tm-328 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60835.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (((A and B) or A) -> (((A and B) or A) and (((C and D) -> D) and A)))), M:tm-328, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60836
in-theory        60836
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> (((C and D) -> D) and A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60836.        ((((A and B) or A) -> (((C and D) -> D) and A)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> (((C and D) -> D) and A)))), M:tm-327, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60837
in-theory        60837
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (((E and F) -> F) and (((A and B) or A) -> (((C and D) -> D) and A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60837.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (((E and F) -> F) and (((A and B) or A) -> (((C and D) -> D) and A)))), M:tm-326, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60838
in-theory        60838
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (((E and F) -> E) and (((A and B) or A) -> (((C and D) -> D) and A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60838.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (((E and F) -> E) and (((A and B) or A) -> (((C and D) -> D) and A)))), M:tm-325, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60839
in-theory        60839
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> (((C and D) -> D) and A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60839.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> (((C and D) -> D) and A)))), M:tm-324, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60840
in-theory        60840
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and ((E -> (F -> E)) and (((A and B) or A) -> (((C and D) -> D) and A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60840.        ((((A and B) or A) -> (((C and D) -> D) and A)) and ((E -> (F -> E)) and (((A and B) or A) -> (((C and D) -> D) and A)))), M:tm-323, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60841
in-theory        60841
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60841.        ((((A and B) or A) -> (((C and D) -> D) and A)) and ((E and F) -> F)), M:tm-322, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60842
in-theory        60842
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60842.        ((((A and B) or A) -> (((C and D) -> D) and A)) and ((E and F) -> E)), M:tm-320, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60843
in-theory        60843
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60843.        ((((A and B) or A) -> (((C and D) -> D) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60844
in-theory        60844
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     25
proof            (modus-ponens tm-316 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60844.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60845
in-theory        60845
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60845.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (E -> (F -> E))), M:tm-315, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60846
in-theory        60846
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and ((((A and B) or A) -> (not (((C and D) -> D) and A))) -> (not ((A and B) or A))))
theorem-size     35
proof            (modus-ponens tm-313 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60846.        ((((A and B) or A) -> (((C and D) -> D) and A)) and ((((A and B) or A) -> (not (((C and D) -> D) and A))) -> (not ((A and B) or A)))), M:tm-313, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60847
in-theory        60847
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (((((C and D) -> D) and A) -> E) -> ((((A and B) or A) or (((C and D) -> D) and A)) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60847.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (((((C and D) -> D) and A) -> E) -> ((((A and B) or A) or (((C and D) -> D) and A)) -> E))), M:tm-312, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60848
in-theory        60848
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (E or (((A and B) or A) -> (((C and D) -> D) and A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60848.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (E or (((A and B) or A) -> (((C and D) -> D) and A)))), M:tm-311, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60849
in-theory        60849
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and ((((A and B) or A) -> (((C and D) -> D) and A)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60849.        ((((A and B) or A) -> (((C and D) -> D) and A)) and ((((A and B) or A) -> (((C and D) -> D) and A)) or E)), M:tm-310, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60850
in-theory        60850
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (E -> ((((A and B) or A) -> (((C and D) -> D) and A)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60850.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (E -> ((((A and B) or A) -> (((C and D) -> D) and A)) and E))), M:tm-309, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60851
in-theory        60851
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (E -> (((A and B) or A) -> (((C and D) -> D) and A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60851.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (E -> (((A and B) or A) -> (((C and D) -> D) and A)))), M:tm-305, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60852
in-theory        60852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60852.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-303, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60853
in-theory        60853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60853.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-270, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60854
in-theory        60854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60854.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-239, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60855
in-theory        60855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (((G and H) -> H) and E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60855.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (((G and H) -> H) and E))), M:tm-210, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60856
in-theory        60856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60856.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-183, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60857
in-theory        60857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60857.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-157, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60858
in-theory        60858
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60858.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-147, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60859
in-theory        60859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60859.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-134, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60860
in-theory        60860
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60860.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-125, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60861
in-theory        60861
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (((G and H) -> H) and E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60861.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (((G and H) -> H) and E))), M:tm-113, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60862
in-theory        60862
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60862.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-105, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60863
in-theory        60863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> (((E and F) -> F) and C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60863.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> (((E and F) -> F) and C))), M:tm-95, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60864
in-theory        60864
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (((D and E) -> E) and A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-5 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60864.        (((A and B) or A) -> (C -> (((D and E) -> E) and A))), M:tm-84, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60865
in-theory        60865
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60865.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-83, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60866
in-theory        60866
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> (((D and E) -> E) and B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60866.        (((not (not A)) -> A) and (((B and C) or B) -> (((D and E) -> E) and B))), M:tm-76, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60867
in-theory        60867
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> (((C and D) -> D) and A))
theorem-size     21
proof            (modus-ponens tm-73 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-8 tm-10 tm-3 tm-5 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60867.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> (((C and D) -> D) and A)), M:tm-73, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60868
in-theory        60868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (((E and F) -> F) and C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60868.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (((E and F) -> F) and C))), M:tm-69, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60869
in-theory        60869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60869.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-54, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60870
in-theory        60870
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> (((C and D) -> D) and A))
theorem-size     15
proof            (modus-ponens tm-50 tm-732 ((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-8 tm-7 tm-3 tm-5 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60870.        ((A or ((A and B) or A)) -> (((C and D) -> D) and A)), M:tm-50, m:tm-732, u:((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60871
in-theory        60871
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> (((C and D) -> D) and A))
theorem-size     17
proof            (modus-ponens tm-49 tm-732 ((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-8 tm-6 tm-3 tm-5 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60871.        (((A and B) or ((A and B) or A)) -> (((C and D) -> D) and A)), M:tm-49, m:tm-732, u:((A (and Am Bm)) (B Am) (C (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60872
in-theory        60872
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> (((D and E) -> E) and B))
theorem-size     21
proof            (modus-ponens tm-47 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-8 tm-4 tm-3 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60872.        (((A and ((B and C) or B)) or ((B and C) or B)) -> (((D and E) -> E) and B)), M:tm-47, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60873
in-theory        60873
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> (((D and E) -> E) and A))
theorem-size     21
proof            (modus-ponens tm-46 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60873.        (((((A and B) or A) and C) or ((A and B) or A)) -> (((D and E) -> E) and A)), M:tm-46, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60874
in-theory        60874
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> (((E and F) -> F) and C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60874.        ((A -> (B or A)) and (((C and D) or C) -> (((E and F) -> F) and C))), M:tm-42, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60875
in-theory        60875
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> (((E and F) -> F) and C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60875.        ((A -> (A or B)) and (((C and D) or C) -> (((E and F) -> F) and C))), M:tm-32, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60876
in-theory        60876
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and (((C and D) -> D) and A)))
theorem-size     19
proof            (modus-ponens tm-24 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60876.        (((A and B) or A) -> (((A and B) or A) and (((C and D) -> D) and A))), M:tm-24, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60877
in-theory        60877
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> (((E and F) -> F) and C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60877.        ((A -> (B -> (A and B))) and (((C and D) or C) -> (((E and F) -> F) and C))), M:tm-23, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60878
in-theory        60878
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> (((E and F) -> F) and C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60878.        (((A and B) -> B) and (((C and D) or C) -> (((E and F) -> F) and C))), M:tm-22, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60879
in-theory        60879
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> (((E and F) -> F) and C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60879.        (((A and B) -> A) and (((C and D) or C) -> (((E and F) -> F) and C))), M:tm-21, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60880
in-theory        60880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60880.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-20, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60881
in-theory        60881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> (((E and F) -> F) and C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60881.        ((A -> (B -> A)) and (((C and D) or C) -> (((E and F) -> F) and C))), M:tm-19, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60882
in-theory        60882
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not (((C and D) -> D) and A))) -> (not ((A and B) or A)))
theorem-size     21
proof            (modus-ponens tm-9 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-9 tm-8 tm-3 tm-5 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60882.        ((((A and B) or A) -> (not (((C and D) -> D) and A))) -> (not ((A and B) or A))), M:tm-9, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60883
in-theory        60883
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and C) -> D) -> ((((C and E) or C) or (((A and B) -> B) and C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-4)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60883.        (((((A and B) -> B) and C) -> D) -> ((((C and E) or C) or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-60884
in-theory        60884
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> (((D and E) -> E) and B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-7 tm-8 tm-3 tm-5 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60884.        (A or (((B and C) or B) -> (((D and E) -> E) and B))), M:tm-7, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60885
in-theory        60885
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-6 tm-8 tm-3 tm-5 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60885.        ((((A and B) or A) -> (((C and D) -> D) and A)) or E), M:tm-6, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60886
in-theory        60886
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> (((D and E) -> E) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60886.        (A -> ((((B and C) or B) -> (((D and E) -> E) and B)) and A)), M:tm-5, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60887
in-theory        60887
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> (((D and E) -> E) and B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-1 tm-8 tm-3 tm-5 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-60887.        (A -> (((B and C) or B) -> (((D and E) -> E) and B))), M:tm-1, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-60888
in-theory        60888
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E)))
theorem-size     41
proof            (modus-ponens tm-708 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60888.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E))), M:tm-708, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60889
in-theory        60889
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     29
proof            (modus-ponens tm-665 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60889.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-665, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60890
in-theory        60890
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or ((D -> (E -> (D and E))) and A)))
theorem-size     17
proof            (modus-ponens tm-623 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60890.        (((A and B) or A) -> (C or ((D -> (E -> (D and E))) and A))), M:tm-623, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60891
in-theory        60891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-622 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60891.        ((A -> (B -> (C or B))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-622, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60892
in-theory        60892
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60892.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (E -> (F or E))), M:tm-609, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60893
in-theory        60893
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     25
proof            (modus-ponens tm-605 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60893.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-605, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60894
in-theory        60894
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((E -> (F or E)) and (((A and B) or A) -> ((C -> (D -> (C and D))) and A))))
theorem-size     37
proof            (modus-ponens tm-595 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60894.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((E -> (F or E)) and (((A and B) or A) -> ((C -> (D -> (C and D))) and A)))), M:tm-595, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60895
in-theory        60895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-550 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60895.        (((A -> (B or A)) or C) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-550, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60896
in-theory        60896
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-540 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60896.        ((A or (B -> (C or B))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-540, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60897
in-theory        60897
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-530 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60897.        ((A or (B -> (B or C))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-530, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60898
in-theory        60898
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     25
proof            (modus-ponens tm-520 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60898.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-520, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60899
in-theory        60899
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-510 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60899.        ((A or ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-510, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60900
in-theory        60900
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-500 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60900.        ((A or ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-500, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60901
in-theory        60901
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E)))
theorem-size     31
proof            (modus-ponens tm-490 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60901.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E))), M:tm-490, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60902
in-theory        60902
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-480 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60902.        ((A or (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-480, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60903
in-theory        60903
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> (D -> (C and D))) and A) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60903.        (((A and B) or A) -> (((C -> (D -> (C and D))) and A) or E)), M:tm-470, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60904
in-theory        60904
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-469 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60904.        ((A -> (B -> (B or C))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-469, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60905
in-theory        60905
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60905.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (E -> (E or F))), M:tm-456, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60906
in-theory        60906
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     25
proof            (modus-ponens tm-453 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60906.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-453, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60907
in-theory        60907
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((E -> (E or F)) and (((A and B) or A) -> ((C -> (D -> (C and D))) and A))))
theorem-size     37
proof            (modus-ponens tm-443 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60907.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((E -> (E or F)) and (((A and B) or A) -> ((C -> (D -> (C and D))) and A)))), M:tm-443, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60908
in-theory        60908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-409 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60908.        (((A -> (A or B)) or C) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-409, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60909
in-theory        60909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     25
proof            (modus-ponens tm-400 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60909.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-400, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60910
in-theory        60910
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-391 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60910.        ((((A and B) -> B) or C) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-391, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60911
in-theory        60911
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-382 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60911.        ((((A and B) -> A) or C) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-382, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60912
in-theory        60912
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E)))
theorem-size     31
proof            (modus-ponens tm-373 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60912.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E))), M:tm-373, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60913
in-theory        60913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-364 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60913.        (((A -> (B -> A)) or C) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-364, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60914
in-theory        60914
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (((D -> (E -> (D and E))) and A) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60914.        (((A and B) or A) -> (C -> (((D -> (E -> (D and E))) and A) and C))), M:tm-355, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60915
in-theory        60915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     25
proof            (modus-ponens tm-354 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60915.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-354, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60916
in-theory        60916
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60916.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60917
in-theory        60917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C)))
theorem-size     25
proof            (modus-ponens tm-338 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60917.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C))), M:tm-338, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60918
in-theory        60918
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((A and B) or A) -> (((A and B) or A) and ((C -> (D -> (C and D))) and A))))
theorem-size     37
proof            (modus-ponens tm-328 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60918.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((A and B) or A) -> (((A and B) or A) and ((C -> (D -> (C and D))) and A)))), M:tm-328, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60919
in-theory        60919
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> ((C -> (D -> (C and D))) and A))))
theorem-size     39
proof            (modus-ponens tm-327 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60919.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> ((C -> (D -> (C and D))) and A)))), M:tm-327, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60920
in-theory        60920
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((E and F) -> F) and (((A and B) or A) -> ((C -> (D -> (C and D))) and A))))
theorem-size     37
proof            (modus-ponens tm-326 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60920.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((E and F) -> F) and (((A and B) or A) -> ((C -> (D -> (C and D))) and A)))), M:tm-326, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60921
in-theory        60921
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((E and F) -> E) and (((A and B) or A) -> ((C -> (D -> (C and D))) and A))))
theorem-size     37
proof            (modus-ponens tm-325 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60921.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((E and F) -> E) and (((A and B) or A) -> ((C -> (D -> (C and D))) and A)))), M:tm-325, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60922
in-theory        60922
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> ((C -> (D -> (C and D))) and A))))
theorem-size     45
proof            (modus-ponens tm-324 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60922.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> ((C -> (D -> (C and D))) and A)))), M:tm-324, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60923
in-theory        60923
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((E -> (F -> E)) and (((A and B) or A) -> ((C -> (D -> (C and D))) and A))))
theorem-size     37
proof            (modus-ponens tm-323 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60923.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((E -> (F -> E)) and (((A and B) or A) -> ((C -> (D -> (C and D))) and A)))), M:tm-323, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60924
in-theory        60924
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60924.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((E and F) -> F)), M:tm-322, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60925
in-theory        60925
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60925.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((E and F) -> E)), M:tm-320, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60926
in-theory        60926
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60926.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60927
in-theory        60927
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     27
proof            (modus-ponens tm-316 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60927.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60928
in-theory        60928
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60928.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (E -> (F -> E))), M:tm-315, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60929
in-theory        60929
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((((A and B) or A) -> (not ((C -> (D -> (C and D))) and A))) -> (not ((A and B) or A))))
theorem-size     39
proof            (modus-ponens tm-313 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60929.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((((A and B) or A) -> (not ((C -> (D -> (C and D))) and A))) -> (not ((A and B) or A)))), M:tm-313, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60930
in-theory        60930
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((((C -> (D -> (C and D))) and A) -> E) -> ((((A and B) or A) or ((C -> (D -> (C and D))) and A)) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60930.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((((C -> (D -> (C and D))) and A) -> E) -> ((((A and B) or A) or ((C -> (D -> (C and D))) and A)) -> E))), M:tm-312, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60931
in-theory        60931
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (E or (((A and B) or A) -> ((C -> (D -> (C and D))) and A))))
theorem-size     33
proof            (modus-ponens tm-311 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60931.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (E or (((A and B) or A) -> ((C -> (D -> (C and D))) and A)))), M:tm-311, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60932
in-theory        60932
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60932.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) or E)), M:tm-310, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60933
in-theory        60933
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (E -> ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60933.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (E -> ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and E))), M:tm-309, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60934
in-theory        60934
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (E -> (((A and B) or A) -> ((C -> (D -> (C and D))) and A))))
theorem-size     33
proof            (modus-ponens tm-305 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60934.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (E -> (((A and B) or A) -> ((C -> (D -> (C and D))) and A)))), M:tm-305, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60935
in-theory        60935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     27
proof            (modus-ponens tm-303 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60935.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-303, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60936
in-theory        60936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     25
proof            (modus-ponens tm-270 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60936.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-270, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60937
in-theory        60937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     25
proof            (modus-ponens tm-239 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60937.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-239, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60938
in-theory        60938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E)))
theorem-size     33
proof            (modus-ponens tm-210 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60938.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E))), M:tm-210, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60939
in-theory        60939
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     25
proof            (modus-ponens tm-183 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60939.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-183, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60940
in-theory        60940
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-157 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60940.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-157, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60941
in-theory        60941
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     31
proof            (modus-ponens tm-147 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60941.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-147, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60942
in-theory        60942
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-134 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60942.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-134, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60943
in-theory        60943
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     31
proof            (modus-ponens tm-125 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60943.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-125, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60944
in-theory        60944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E)))
theorem-size     31
proof            (modus-ponens tm-113 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60944.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H -> (G and H))) and E))), M:tm-113, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60945
in-theory        60945
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     35
proof            (modus-ponens tm-105 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60945.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-105, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60946
in-theory        60946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C)))
theorem-size     23
proof            (modus-ponens tm-95 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60946.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C))), M:tm-95, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60947
in-theory        60947
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D -> (E -> (D and E))) and A)))
theorem-size     17
proof            (modus-ponens tm-84 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60947.        (((A and B) or A) -> (C -> ((D -> (E -> (D and E))) and A))), M:tm-84, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60948
in-theory        60948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     23
proof            (modus-ponens tm-83 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60948.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-83, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60949
in-theory        60949
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> ((D -> (E -> (D and E))) and B)))
theorem-size     21
proof            (modus-ponens tm-76 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60949.        (((not (not A)) -> A) and (((B and C) or B) -> ((D -> (E -> (D and E))) and B))), M:tm-76, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60950
in-theory        60950
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> ((C -> (D -> (C and D))) and A))
theorem-size     23
proof            (modus-ponens tm-73 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-8 tm-10 tm-3 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60950.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> ((C -> (D -> (C and D))) and A)), M:tm-73, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60951
in-theory        60951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C)))
theorem-size     27
proof            (modus-ponens tm-69 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60951.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C))), M:tm-69, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60952
in-theory        60952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     29
proof            (modus-ponens tm-54 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60952.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-54, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60953
in-theory        60953
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> ((C -> (D -> (C and D))) and A))
theorem-size     17
proof            (modus-ponens tm-50 tm-733 ((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-8 tm-7 tm-3 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60953.        ((A or ((A and B) or A)) -> ((C -> (D -> (C and D))) and A)), M:tm-50, m:tm-733, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60954
in-theory        60954
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> ((C -> (D -> (C and D))) and A))
theorem-size     19
proof            (modus-ponens tm-49 tm-733 ((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-8 tm-6 tm-3 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60954.        (((A and B) or ((A and B) or A)) -> ((C -> (D -> (C and D))) and A)), M:tm-49, m:tm-733, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60955
in-theory        60955
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> ((D -> (E -> (D and E))) and B))
theorem-size     23
proof            (modus-ponens tm-47 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-8 tm-4 tm-3 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60955.        (((A and ((B and C) or B)) or ((B and C) or B)) -> ((D -> (E -> (D and E))) and B)), M:tm-47, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60956
in-theory        60956
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> ((D -> (E -> (D and E))) and A))
theorem-size     23
proof            (modus-ponens tm-46 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60956.        (((((A and B) or A) and C) or ((A and B) or A)) -> ((D -> (E -> (D and E))) and A)), M:tm-46, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60957
in-theory        60957
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C)))
theorem-size     21
proof            (modus-ponens tm-42 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60957.        ((A -> (B or A)) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C))), M:tm-42, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60958
in-theory        60958
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C)))
theorem-size     21
proof            (modus-ponens tm-32 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60958.        ((A -> (A or B)) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C))), M:tm-32, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60959
in-theory        60959
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and ((C -> (D -> (C and D))) and A)))
theorem-size     21
proof            (modus-ponens tm-24 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60959.        (((A and B) or A) -> (((A and B) or A) and ((C -> (D -> (C and D))) and A))), M:tm-24, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60960
in-theory        60960
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C)))
theorem-size     23
proof            (modus-ponens tm-23 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60960.        ((A -> (B -> (A and B))) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C))), M:tm-23, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60961
in-theory        60961
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C)))
theorem-size     21
proof            (modus-ponens tm-22 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60961.        (((A and B) -> B) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C))), M:tm-22, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60962
in-theory        60962
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C)))
theorem-size     21
proof            (modus-ponens tm-21 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60962.        (((A and B) -> A) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C))), M:tm-21, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60963
in-theory        60963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     29
proof            (modus-ponens tm-20 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60963.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-20, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60964
in-theory        60964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C)))
theorem-size     21
proof            (modus-ponens tm-19 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60964.        ((A -> (B -> A)) and (((C and D) or C) -> ((E -> (F -> (E and F))) and C))), M:tm-19, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60965
in-theory        60965
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not ((C -> (D -> (C and D))) and A))) -> (not ((A and B) or A)))
theorem-size     23
proof            (modus-ponens tm-9 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-9 tm-8 tm-3 tm-5)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60965.        ((((A and B) or A) -> (not ((C -> (D -> (C and D))) and A))) -> (not ((A and B) or A))), M:tm-9, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60966
in-theory        60966
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and C) -> D) -> ((((C and E) or C) or ((A -> (B -> (A and B))) and C)) -> D))
theorem-size     29
proof            (modus-ponens tm-8 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60966.        ((((A -> (B -> (A and B))) and C) -> D) -> ((((C and E) or C) or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-60967
in-theory        60967
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> ((D -> (E -> (D and E))) and B)))
theorem-size     17
proof            (modus-ponens tm-7 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-7 tm-8 tm-3 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60967.        (A or (((B and C) or B) -> ((D -> (E -> (D and E))) and B))), M:tm-7, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60968
in-theory        60968
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-6 tm-8 tm-3 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60968.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) or E), M:tm-6, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60969
in-theory        60969
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> ((D -> (E -> (D and E))) and B)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60969.        (A -> ((((B and C) or B) -> ((D -> (E -> (D and E))) and B)) and A)), M:tm-5, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60970
in-theory        60970
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> ((D -> (E -> (D and E))) and B)))
theorem-size     17
proof            (modus-ponens tm-1 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-1 tm-8 tm-3 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-60970.        (A -> (((B and C) or B) -> ((D -> (E -> (D and E))) and B))), M:tm-1, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-60971
in-theory        60971
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F))))
theorem-size     41
proof            (modus-ponens tm-708 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60971.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F)))), M:tm-708, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60972
in-theory        60972
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-665 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60972.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-665, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60973
in-theory        60973
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D or (A -> (A and B))))
theorem-size     17
proof            (modus-ponens tm-623 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60973.        ((((A -> B) and C) or (A -> B)) -> (D or (A -> (A and B)))), M:tm-623, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-60974
in-theory        60974
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-622 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60974.        ((A -> (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-622, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60975
in-theory        60975
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60975.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (D -> (E or D))), M:tm-609, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60976
in-theory        60976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-605 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60976.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-605, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60977
in-theory        60977
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((D -> (E or D)) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60977.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((D -> (E or D)) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))))), M:tm-595, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60978
in-theory        60978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-550 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60978.        (((A -> (B or A)) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-550, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60979
in-theory        60979
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-540 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60979.        ((A or (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-540, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60980
in-theory        60980
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-530 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60980.        ((A or (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-530, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60981
in-theory        60981
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-520 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60981.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-520, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60982
in-theory        60982
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-510 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60982.        ((A or ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-510, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60983
in-theory        60983
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-500 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60983.        ((A or ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-500, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60984
in-theory        60984
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-490 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60984.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F)))), M:tm-490, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60985
in-theory        60985
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-480 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60985.        ((A or (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-480, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60986
in-theory        60986
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((A -> (A and B)) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60986.        ((((A -> B) and C) or (A -> B)) -> ((A -> (A and B)) or D)), M:tm-470, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-60987
in-theory        60987
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-469 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60987.        ((A -> (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-469, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60988
in-theory        60988
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60988.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (D -> (D or E))), M:tm-456, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60989
in-theory        60989
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-453 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60989.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-453, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60990
in-theory        60990
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((D -> (D or E)) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60990.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((D -> (D or E)) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))))), M:tm-443, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60991
in-theory        60991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-409 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60991.        (((A -> (A or B)) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-409, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60992
in-theory        60992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-400 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60992.        (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-400, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60993
in-theory        60993
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-391 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60993.        ((((A and B) -> B) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-391, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60994
in-theory        60994
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-382 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60994.        ((((A and B) -> A) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-382, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60995
in-theory        60995
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-373 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60995.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F)))), M:tm-373, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60996
in-theory        60996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-364 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60996.        (((A -> (B -> A)) or C) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-364, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60997
in-theory        60997
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D -> ((A -> (A and B)) and D)))
theorem-size     19
proof            (modus-ponens tm-355 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60997.        ((((A -> B) and C) or (A -> B)) -> (D -> ((A -> (A and B)) and D))), M:tm-355, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-60998
in-theory        60998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-354 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60998.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-354, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-60999
in-theory        60999
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-60999.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61000
in-theory        61000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D))))
theorem-size     25
proof            (modus-ponens tm-338 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61000.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D)))), M:tm-338, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61001
in-theory        61001
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (A -> (A and B)))))
theorem-size     41
proof            (modus-ponens tm-328 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61001.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (A -> (A and B))))), M:tm-328, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-61002
in-theory        61002
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((D -> (E -> (D and E))) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61002.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((D -> (E -> (D and E))) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))))), M:tm-327, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61003
in-theory        61003
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((D and E) -> E) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61003.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((D and E) -> E) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))))), M:tm-326, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61004
in-theory        61004
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((D and E) -> D) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61004.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((D and E) -> D) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))))), M:tm-325, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61005
in-theory        61005
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61005.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))))), M:tm-324, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61006
in-theory        61006
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((D -> (E -> D)) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61006.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((D -> (E -> D)) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))))), M:tm-323, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61007
in-theory        61007
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61007.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((D and E) -> E)), M:tm-322, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61008
in-theory        61008
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61008.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((D and E) -> D)), M:tm-320, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61009
in-theory        61009
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61009.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61010
in-theory        61010
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((((A -> B) and C) or (A -> B)) -> (((A -> B) and C) or (A -> B))))
theorem-size     35
proof            (modus-ponens tm-316 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61010.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((((A -> B) and C) or (A -> B)) -> (((A -> B) and C) or (A -> B)))), M:tm-316, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-61011
in-theory        61011
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61011.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (D -> (E -> D))), M:tm-315, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61012
in-theory        61012
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((((A -> B) and C) or (A -> B)) -> (not (A -> (A and B)))) -> (not (((A -> B) and C) or (A -> B)))))
theorem-size     43
proof            (modus-ponens tm-313 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61012.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((((A -> B) and C) or (A -> B)) -> (not (A -> (A and B)))) -> (not (((A -> B) and C) or (A -> B))))), M:tm-313, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-61013
in-theory        61013
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((A -> (A and B)) -> D) -> (((((A -> B) and C) or (A -> B)) or (A -> (A and B))) -> D)))
theorem-size     41
proof            (modus-ponens tm-312 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61013.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((A -> (A and B)) -> D) -> (((((A -> B) and C) or (A -> B)) or (A -> (A and B))) -> D))), M:tm-312, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-61014
in-theory        61014
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (D or ((((A -> B) and C) or (A -> B)) -> (A -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61014.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (D or ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))))), M:tm-311, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61015
in-theory        61015
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61015.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) or D)), M:tm-310, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61016
in-theory        61016
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (D -> (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61016.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (D -> (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and D))), M:tm-309, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61017
in-theory        61017
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((((A -> B) and C) or (A -> B)) -> A) -> ((((A -> B) and C) or (A -> B)) -> (A and B))))
theorem-size     41
proof            (modus-ponens tm-306 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B Am) (C (and Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61017.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (((((A -> B) and C) or (A -> B)) -> A) -> ((((A -> B) and C) or (A -> B)) -> (A and B)))), M:tm-306, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B Am) (C (and Am Bm)))
================================================================
tm-name          tm-61018
in-theory        61018
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (D -> ((((A -> B) and C) or (A -> B)) -> (A -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61018.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and (D -> ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))))), M:tm-305, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61019
in-theory        61019
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-303 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61019.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-303, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61020
in-theory        61020
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-270 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61020.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-270, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61021
in-theory        61021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-239 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61021.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-239, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61022
in-theory        61022
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-210 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61022.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F)))), M:tm-210, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61023
in-theory        61023
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-183 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61023.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-183, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61024
in-theory        61024
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-157 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61024.        ((A -> ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-157, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61025
in-theory        61025
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-147 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61025.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-147, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61026
in-theory        61026
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-134 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61026.        ((A -> ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-134, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61027
in-theory        61027
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     31
proof            (modus-ponens tm-125 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61027.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-125, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61028
in-theory        61028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-113 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61028.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (E -> (E and F)))), M:tm-113, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61029
in-theory        61029
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     35
proof            (modus-ponens tm-105 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61029.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-105, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61030
in-theory        61030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-95 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61030.        (((A -> B) -> (A -> A)) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D)))), M:tm-95, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61031
in-theory        61031
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D -> (A -> (A and B))))
theorem-size     17
proof            (modus-ponens tm-84 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61031.        ((((A -> B) and C) or (A -> B)) -> (D -> (A -> (A and B)))), M:tm-84, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-61032
in-theory        61032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-83 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61032.        ((A -> (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-83, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61033
in-theory        61033
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) and D) or (B -> C)) -> (B -> (B and C))))
theorem-size     21
proof            (modus-ponens tm-76 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61033.        (((not (not A)) -> A) and ((((B -> C) and D) or (B -> C)) -> (B -> (B and C)))), M:tm-76, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61034
in-theory        61034
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) and C) or (A -> B)))) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B)))
theorem-size     27
proof            (modus-ponens tm-73 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-8 tm-10 tm-3 tm-2 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61034.        (((not (not (((A -> B) and C) or (A -> B)))) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B))), M:tm-73, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-61035
in-theory        61035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D))))
theorem-size     27
proof            (modus-ponens tm-69 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61035.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D)))), M:tm-69, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61036
in-theory        61036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-54 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61036.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-54, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61037
in-theory        61037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-734 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am (and Am Bm)))))
axioms-used      (tm-8 tm-7 tm-3 tm-2 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61037.        (((A -> B) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B))), M:tm-50, m:tm-734, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am (and Am Bm))))
================================================================
tm-name          tm-61038
in-theory        61038
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B)))
theorem-size     21
proof            (modus-ponens tm-49 tm-734 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am (and Am Bm)))))
axioms-used      (tm-8 tm-6 tm-3 tm-2 tm-5)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61038.        ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B))), M:tm-49, m:tm-734, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> Am (and Am Bm))))
================================================================
tm-name          tm-61039
in-theory        61039
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) or (B -> C))) or (((B -> C) and D) or (B -> C))) -> (B -> (B and C)))
theorem-size     27
proof            (modus-ponens tm-47 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-8 tm-4 tm-3 tm-2 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61039.        (((A and (((B -> C) and D) or (B -> C))) or (((B -> C) and D) or (B -> C))) -> (B -> (B and C))), M:tm-47, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-61040
in-theory        61040
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B)))
theorem-size     27
proof            (modus-ponens tm-46 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61040.        ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B))), M:tm-46, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-61041
in-theory        61041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-42 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61041.        ((A -> (B or A)) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D)))), M:tm-42, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61042
in-theory        61042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-32 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61042.        ((A -> (A or B)) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D)))), M:tm-32, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61043
in-theory        61043
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (A -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-24 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61043.        ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (A -> (A and B)))), M:tm-24, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-61044
in-theory        61044
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D))))
theorem-size     23
proof            (modus-ponens tm-23 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61044.        ((A -> (B -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D)))), M:tm-23, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61045
in-theory        61045
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-22 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61045.        (((A and B) -> B) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D)))), M:tm-22, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61046
in-theory        61046
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-21 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61046.        (((A and B) -> A) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D)))), M:tm-21, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61047
in-theory        61047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     29
proof            (modus-ponens tm-20 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61047.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-20, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61048
in-theory        61048
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-19 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61048.        ((A -> (B -> A)) and ((((C -> D) and E) or (C -> D)) -> (C -> (C and D)))), M:tm-19, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61049
in-theory        61049
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (not (A -> (A and B)))) -> (not (((A -> B) and C) or (A -> B))))
theorem-size     27
proof            (modus-ponens tm-9 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-9 tm-8 tm-3 tm-2 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61049.        (((((A -> B) and C) or (A -> B)) -> (not (A -> (A and B)))) -> (not (((A -> B) and C) or (A -> B)))), M:tm-9, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-61050
in-theory        61050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A and B)) -> C) -> (((((A -> B) and D) or (A -> B)) or (A -> (A and B))) -> C))
theorem-size     25
proof            (modus-ponens tm-8 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61050.        (((A -> (A and B)) -> C) -> (((((A -> B) and D) or (A -> B)) or (A -> (A and B))) -> C)), M:tm-8, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-61051
in-theory        61051
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) and D) or (B -> C)) -> (B -> (B and C))))
theorem-size     17
proof            (modus-ponens tm-7 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-7 tm-8 tm-3 tm-2 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61051.        (A or ((((B -> C) and D) or (B -> C)) -> (B -> (B and C)))), M:tm-7, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61052
in-theory        61052
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-6 tm-8 tm-3 tm-2 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61052.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) or D), M:tm-6, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61053
in-theory        61053
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) and D) or (B -> C)) -> (B -> (B and C))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61053.        (A -> (((((B -> C) and D) or (B -> C)) -> (B -> (B and C))) and A)), M:tm-5, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61054
in-theory        61054
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> A) -> ((((A -> B) and C) or (A -> B)) -> (A and B)))
theorem-size     25
proof            (modus-ponens tm-2 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B Am) (C (and Am Bm))))
axioms-used      (tm-2 tm-8 tm-3 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61054.        (((((A -> B) and C) or (A -> B)) -> A) -> ((((A -> B) and C) or (A -> B)) -> (A and B))), M:tm-2, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B Am) (C (and Am Bm)))
================================================================
tm-name          tm-61055
in-theory        61055
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) and D) or (B -> C)) -> (B -> (B and C))))
theorem-size     17
proof            (modus-ponens tm-1 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-1 tm-8 tm-3 tm-2 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-61055.        (A -> ((((B -> C) and D) or (B -> C)) -> (B -> (B and C)))), M:tm-1, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-61056
in-theory        61056
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (G -> (H -> (G and H)))))
theorem-size     39
proof            (modus-ponens tm-708 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61056.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (G -> (H -> (G and H))))), M:tm-708, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61057
in-theory        61057
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-665 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61057.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-665, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61058
in-theory        61058
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-622 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61058.        ((A -> (B -> (C or B))) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-622, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61059
in-theory        61059
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D or ((A and B) or A)) and C)))
theorem-size     17
proof            (modus-ponens tm-617 tm-735 ((A (or (and Am Bm) Am)) (Cm (or B (or (and Am Bm) Am))) (C (-> Dm (and (or B (or (and Am Bm) Am)) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-5)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61059.        (((A and B) or A) -> (C -> ((D or ((A and B) or A)) and C))), M:tm-617, m:tm-735, u:((A (or (and Am Bm) Am)) (Cm (or B (or (and Am Bm) Am))) (C (-> Dm (and (or B (or (and Am Bm) Am)) Dm))))
================================================================
tm-name          tm-61060
in-theory        61060
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61060.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (E -> (F or E))), M:tm-609, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61061
in-theory        61061
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-605 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61061.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-605, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61062
in-theory        61062
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((E -> (F or E)) and (((A and B) or A) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-595 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61062.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((E -> (F or E)) and (((A and B) or A) -> (C -> (D -> (C and D)))))), M:tm-595, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61063
in-theory        61063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-550 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61063.        (((A -> (B or A)) or C) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-550, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61064
in-theory        61064
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-540 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61064.        ((A or (B -> (C or B))) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-540, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61065
in-theory        61065
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-530 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61065.        ((A or (B -> (B or C))) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-530, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61066
in-theory        61066
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-520 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61066.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-520, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61067
in-theory        61067
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-510 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61067.        ((A or ((B and C) -> C)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-510, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61068
in-theory        61068
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-500 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61068.        ((A or ((B and C) -> B)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-500, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61069
in-theory        61069
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-490 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61069.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (H -> (G and H))))), M:tm-490, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61070
in-theory        61070
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-480 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61070.        ((A or (B -> (C -> B))) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-480, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61071
in-theory        61071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-469 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61071.        ((A -> (B -> (B or C))) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-469, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61072
in-theory        61072
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((((A and B) or A) or D) and C)))
theorem-size     17
proof            (modus-ponens tm-464 tm-735 ((A (or (and Am Bm) Am)) (Cm (or (or (and Am Bm) Am) B)) (C (-> Dm (and (or (or (and Am Bm) Am) B) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-5)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61072.        (((A and B) or A) -> (C -> ((((A and B) or A) or D) and C))), M:tm-464, m:tm-735, u:((A (or (and Am Bm) Am)) (Cm (or (or (and Am Bm) Am) B)) (C (-> Dm (and (or (or (and Am Bm) Am) B) Dm))))
================================================================
tm-name          tm-61073
in-theory        61073
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61073.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (E -> (E or F))), M:tm-456, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61074
in-theory        61074
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-453 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61074.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-453, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61075
in-theory        61075
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((E -> (E or F)) and (((A and B) or A) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-443 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61075.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((E -> (E or F)) and (((A and B) or A) -> (C -> (D -> (C and D)))))), M:tm-443, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61076
in-theory        61076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-409 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61076.        (((A -> (A or B)) or C) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-409, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61077
in-theory        61077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-400 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61077.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-400, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61078
in-theory        61078
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-391 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61078.        ((((A and B) -> B) or C) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-391, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61079
in-theory        61079
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-382 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61079.        ((((A and B) -> A) or C) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-382, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61080
in-theory        61080
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-373 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61080.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (G -> (H -> (G and H))))), M:tm-373, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61081
in-theory        61081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-364 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61081.        (((A -> (B -> A)) or C) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-364, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61082
in-theory        61082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-354 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61082.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-354, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61083
in-theory        61083
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D -> (((A and B) or A) and D)) and C)))
theorem-size     19
proof            (modus-ponens tm-349 tm-735 ((A (or (and Am Bm) Am)) (Cm (-> B (and (or (and Am Bm) Am) B))) (C (-> Dm (and (-> B (and (or (and Am Bm) Am) B)) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61083.        (((A and B) or A) -> (C -> ((D -> (((A and B) or A) and D)) and C))), M:tm-349, m:tm-735, u:((A (or (and Am Bm) Am)) (Cm (-> B (and (or (and Am Bm) Am) B))) (C (-> Dm (and (-> B (and (or (and Am Bm) Am) B)) Dm))))
================================================================
tm-name          tm-61084
in-theory        61084
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61084.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61085
in-theory        61085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (E -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-338 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61085.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (E -> (F -> (E and F))))), M:tm-338, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61086
in-theory        61086
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((A and B) or A) -> (((A and B) or A) and (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-328 tm-735 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61086.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((A and B) or A) -> (((A and B) or A) and (C -> (D -> (C and D)))))), M:tm-328, m:tm-735, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-61087
in-theory        61087
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and (((A and B) or A) -> (C -> (D -> (C and D))))))
theorem-size     35
proof            (modus-ponens tm-327 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61087.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((E -> (F -> (E and F))) and (((A and B) or A) -> (C -> (D -> (C and D)))))), M:tm-327, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61088
in-theory        61088
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((E and F) -> F) and (((A and B) or A) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-326 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61088.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((E and F) -> F) and (((A and B) or A) -> (C -> (D -> (C and D)))))), M:tm-326, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61089
in-theory        61089
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((E and F) -> E) and (((A and B) or A) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-325 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61089.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((E and F) -> E) and (((A and B) or A) -> (C -> (D -> (C and D)))))), M:tm-325, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61090
in-theory        61090
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> (C -> (D -> (C and D))))))
theorem-size     41
proof            (modus-ponens tm-324 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61090.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> (C -> (D -> (C and D)))))), M:tm-324, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61091
in-theory        61091
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((E -> (F -> E)) and (((A and B) or A) -> (C -> (D -> (C and D))))))
theorem-size     33
proof            (modus-ponens tm-323 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61091.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((E -> (F -> E)) and (((A and B) or A) -> (C -> (D -> (C and D)))))), M:tm-323, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61092
in-theory        61092
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61092.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((E and F) -> F)), M:tm-322, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61093
in-theory        61093
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61093.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((E and F) -> E)), M:tm-320, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61094
in-theory        61094
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61094.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61095
in-theory        61095
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     25
proof            (modus-ponens tm-316 tm-735 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61095.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-735, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-61096
in-theory        61096
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61096.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (E -> (F -> E))), M:tm-315, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61097
in-theory        61097
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((((A and B) or A) -> (not (C -> (D -> (C and D))))) -> (not ((A and B) or A))))
theorem-size     35
proof            (modus-ponens tm-313 tm-735 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61097.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((((A and B) or A) -> (not (C -> (D -> (C and D))))) -> (not ((A and B) or A)))), M:tm-313, m:tm-735, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-61098
in-theory        61098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((C -> (D -> (C and D))) -> E) -> ((((A and B) or A) or (C -> (D -> (C and D)))) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-735 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61098.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((C -> (D -> (C and D))) -> E) -> ((((A and B) or A) or (C -> (D -> (C and D)))) -> E))), M:tm-312, m:tm-735, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-61099
in-theory        61099
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (E or (((A and B) or A) -> (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-311 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61099.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (E or (((A and B) or A) -> (C -> (D -> (C and D)))))), M:tm-311, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61100
in-theory        61100
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((((A and B) or A) -> (C -> (D -> (C and D)))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61100.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((((A and B) or A) -> (C -> (D -> (C and D)))) or E)), M:tm-310, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61101
in-theory        61101
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (E -> ((((A and B) or A) -> (C -> (D -> (C and D)))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61101.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (E -> ((((A and B) or A) -> (C -> (D -> (C and D)))) and E))), M:tm-309, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61102
in-theory        61102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((((A and B) or A) -> C) -> (((A and B) or A) -> (D -> (C and D)))))
theorem-size     33
proof            (modus-ponens tm-306 tm-735 ((A (or (and Am Bm) Am)) (B Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61102.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and ((((A and B) or A) -> C) -> (((A and B) or A) -> (D -> (C and D))))), M:tm-306, m:tm-735, u:((A (or (and Am Bm) Am)) (B Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-61103
in-theory        61103
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (E -> (((A and B) or A) -> (C -> (D -> (C and D))))))
theorem-size     29
proof            (modus-ponens tm-305 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61103.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (E -> (((A and B) or A) -> (C -> (D -> (C and D)))))), M:tm-305, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61104
in-theory        61104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-303 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61104.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-303, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61105
in-theory        61105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-270 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61105.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-270, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61106
in-theory        61106
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-239 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61106.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-239, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61107
in-theory        61107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (G -> (H -> (G and H)))))
theorem-size     31
proof            (modus-ponens tm-210 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61107.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (G -> (H -> (G and H))))), M:tm-210, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61108
in-theory        61108
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     23
proof            (modus-ponens tm-183 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61108.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-183, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61109
in-theory        61109
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-157 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61109.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-157, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61110
in-theory        61110
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-147 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61110.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-147, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61111
in-theory        61111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-134 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61111.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-134, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61112
in-theory        61112
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-125 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61112.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-125, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61113
in-theory        61113
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (H -> (G and H)))))
theorem-size     29
proof            (modus-ponens tm-113 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61113.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (H -> (G and H))))), M:tm-113, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61114
in-theory        61114
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     33
proof            (modus-ponens tm-105 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61114.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-105, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61115
in-theory        61115
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (((A and B) or A) and C)))
theorem-size     15
proof            (modus-ponens tm-99 tm-735 ((Cm (or (and Am Bm) Am)) (A (or (and Am Bm) Am)) (B (-> Dm (and (or (and Am Bm) Am) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-5)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61115.        (((A and B) or A) -> (C -> (((A and B) or A) and C))), M:tm-99, m:tm-735, u:((Cm (or (and Am Bm) Am)) (A (or (and Am Bm) Am)) (B (-> Dm (and (or (and Am Bm) Am) Dm))))
================================================================
tm-name          tm-61116
in-theory        61116
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D -> ((A and B) or A)) and C)))
theorem-size     17
proof            (modus-ponens tm-98 tm-735 ((A (or (and Am Bm) Am)) (Cm (-> B (or (and Am Bm) Am))) (C (-> Dm (and (-> B (or (and Am Bm) Am)) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-5)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61116.        (((A and B) or A) -> (C -> ((D -> ((A and B) or A)) and C))), M:tm-98, m:tm-735, u:((A (or (and Am Bm) Am)) (Cm (-> B (or (and Am Bm) Am))) (C (-> Dm (and (-> B (or (and Am Bm) Am)) Dm))))
================================================================
tm-name          tm-61117
in-theory        61117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-95 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61117.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> (E -> (F -> (E and F))))), M:tm-95, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61118
in-theory        61118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     21
proof            (modus-ponens tm-83 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61118.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-83, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61119
in-theory        61119
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> (D -> (E -> (D and E)))))
theorem-size     19
proof            (modus-ponens tm-76 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61119.        (((not (not A)) -> A) and (((B and C) or B) -> (D -> (E -> (D and E))))), M:tm-76, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61120
in-theory        61120
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> (C -> (D -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-73 tm-735 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-10 tm-3 tm-1 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61120.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> (C -> (D -> (C and D)))), M:tm-73, m:tm-735, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-61121
in-theory        61121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (E -> (F -> (E and F)))))
theorem-size     25
proof            (modus-ponens tm-69 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61121.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (E -> (F -> (E and F))))), M:tm-69, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61122
in-theory        61122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-54 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61122.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-54, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61123
in-theory        61123
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> (C -> (D -> (C and D))))
theorem-size     15
proof            (modus-ponens tm-50 tm-735 ((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-7 tm-3 tm-1 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61123.        ((A or ((A and B) or A)) -> (C -> (D -> (C and D)))), M:tm-50, m:tm-735, u:((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-61124
in-theory        61124
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> (C -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-49 tm-735 ((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-6 tm-3 tm-1 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61124.        (((A and B) or ((A and B) or A)) -> (C -> (D -> (C and D)))), M:tm-49, m:tm-735, u:((A (and Am Bm)) (B Am) (C (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-61125
in-theory        61125
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-47 tm-735 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-4 tm-3 tm-1 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61125.        (((A and ((B and C) or B)) or ((B and C) or B)) -> (D -> (E -> (D and E)))), M:tm-47, m:tm-735, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-61126
in-theory        61126
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-46 tm-735 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61126.        (((((A and B) or A) and C) or ((A and B) or A)) -> (D -> (E -> (D and E)))), M:tm-46, m:tm-735, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-61127
in-theory        61127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-42 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61127.        ((A -> (B or A)) and (((C and D) or C) -> (E -> (F -> (E and F))))), M:tm-42, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61128
in-theory        61128
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-32 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61128.        ((A -> (A or B)) and (((C and D) or C) -> (E -> (F -> (E and F))))), M:tm-32, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61129
in-theory        61129
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and (C -> (D -> (C and D)))))
theorem-size     19
proof            (modus-ponens tm-24 tm-735 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61129.        (((A and B) or A) -> (((A and B) or A) and (C -> (D -> (C and D))))), M:tm-24, m:tm-735, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-61130
in-theory        61130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-23 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61130.        ((A -> (B -> (A and B))) and (((C and D) or C) -> (E -> (F -> (E and F))))), M:tm-23, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61131
in-theory        61131
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-22 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61131.        (((A and B) -> B) and (((C and D) or C) -> (E -> (F -> (E and F))))), M:tm-22, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61132
in-theory        61132
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-21 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61132.        (((A and B) -> A) and (((C and D) or C) -> (E -> (F -> (E and F))))), M:tm-21, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61133
in-theory        61133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-20 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61133.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-20, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61134
in-theory        61134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> (E -> (F -> (E and F)))))
theorem-size     19
proof            (modus-ponens tm-19 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61134.        ((A -> (B -> A)) and (((C and D) or C) -> (E -> (F -> (E and F))))), M:tm-19, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61135
in-theory        61135
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not (C -> (D -> (C and D))))) -> (not ((A and B) or A)))
theorem-size     21
proof            (modus-ponens tm-9 tm-735 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-9 tm-8 tm-3 tm-1 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61135.        ((((A and B) or A) -> (not (C -> (D -> (C and D))))) -> (not ((A and B) or A))), M:tm-9, m:tm-735, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-61136
in-theory        61136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) -> C) -> ((((D and E) or D) or (A -> (B -> (A and B)))) -> C))
theorem-size     25
proof            (modus-ponens tm-8 tm-735 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61136.        (((A -> (B -> (A and B))) -> C) -> ((((D and E) or D) or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-735, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-61137
in-theory        61137
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-7 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-7 tm-8 tm-3 tm-1 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61137.        (A or (((B and C) or B) -> (D -> (E -> (D and E))))), M:tm-7, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61138
in-theory        61138
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-6 tm-8 tm-3 tm-1 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61138.        ((((A and B) or A) -> (C -> (D -> (C and D)))) or E), M:tm-6, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61139
in-theory        61139
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> (D -> (E -> (D and E)))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61139.        (A -> ((((B and C) or B) -> (D -> (E -> (D and E)))) and A)), M:tm-5, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61140
in-theory        61140
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> C) -> (((A and B) or A) -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-2 tm-735 ((A (or (and Am Bm) Am)) (B Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-2 tm-8 tm-3 tm-1 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61140.        ((((A and B) or A) -> C) -> (((A and B) or A) -> (D -> (C and D)))), M:tm-2, m:tm-735, u:((A (or (and Am Bm) Am)) (B Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-61141
in-theory        61141
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> (D -> (E -> (D and E)))))
theorem-size     15
proof            (modus-ponens tm-1 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-1 tm-8 tm-3 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-61141.        (A -> (((B and C) or B) -> (D -> (E -> (D and E))))), M:tm-1, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-61142
in-theory        61142
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> ((G -> (G or H)) and E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-6)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61142.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> ((G -> (G or H)) and E))), M:tm-708, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61143
in-theory        61143
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61143.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-665, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61144
in-theory        61144
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or ((D -> (D or E)) and A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-5 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61144.        (((A and B) or A) -> (C or ((D -> (D or E)) and A))), M:tm-623, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61145
in-theory        61145
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61145.        ((A -> (B -> (C or B))) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-622, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61146
in-theory        61146
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3 tm-6)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61146.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (E -> (F or E))), M:tm-609, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61147
in-theory        61147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61147.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-605, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61148
in-theory        61148
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((E -> (F or E)) and (((A and B) or A) -> ((C -> (C or D)) and A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61148.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((E -> (F or E)) and (((A and B) or A) -> ((C -> (C or D)) and A)))), M:tm-595, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61149
in-theory        61149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61149.        (((A -> (B or A)) or C) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-550, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61150
in-theory        61150
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61150.        ((A or (B -> (C or B))) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-540, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61151
in-theory        61151
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61151.        ((A or (B -> (B or C))) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-530, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61152
in-theory        61152
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61152.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-520, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61153
in-theory        61153
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61153.        ((A or ((B and C) -> C)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-510, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61154
in-theory        61154
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61154.        ((A or ((B and C) -> B)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-500, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61155
in-theory        61155
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (G or H)) and E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61155.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (G or H)) and E))), M:tm-490, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61156
in-theory        61156
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61156.        ((A or (B -> (C -> B))) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-480, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61157
in-theory        61157
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> (C or D)) and A) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61157.        (((A and B) or A) -> (((C -> (C or D)) and A) or E)), M:tm-470, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61158
in-theory        61158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61158.        ((A -> (B -> (B or C))) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-469, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61159
in-theory        61159
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61159.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (E -> (E or F))), M:tm-456, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61160
in-theory        61160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61160.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-453, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61161
in-theory        61161
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((E -> (E or F)) and (((A and B) or A) -> ((C -> (C or D)) and A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61161.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((E -> (E or F)) and (((A and B) or A) -> ((C -> (C or D)) and A)))), M:tm-443, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61162
in-theory        61162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61162.        (((A -> (A or B)) or C) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-409, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61163
in-theory        61163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61163.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-400, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61164
in-theory        61164
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61164.        ((((A and B) -> B) or C) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-391, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61165
in-theory        61165
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61165.        ((((A and B) -> A) or C) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-382, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61166
in-theory        61166
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> ((G -> (G or H)) and E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61166.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> ((G -> (G or H)) and E))), M:tm-373, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61167
in-theory        61167
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61167.        (((A -> (B -> A)) or C) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-364, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61168
in-theory        61168
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (((D -> (D or E)) and A) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3 tm-6)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61168.        (((A and B) or A) -> (C -> (((D -> (D or E)) and A) and C))), M:tm-355, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61169
in-theory        61169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61169.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-354, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61170
in-theory        61170
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61170.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61171
in-theory        61171
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> ((E -> (E or F)) and C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61171.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> ((E -> (E or F)) and C))), M:tm-338, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61172
in-theory        61172
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((A and B) or A) -> (((A and B) or A) and ((C -> (C or D)) and A))))
theorem-size     33
proof            (modus-ponens tm-328 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61172.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((A and B) or A) -> (((A and B) or A) and ((C -> (C or D)) and A)))), M:tm-328, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61173
in-theory        61173
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> ((C -> (C or D)) and A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61173.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> ((C -> (C or D)) and A)))), M:tm-327, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61174
in-theory        61174
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((E and F) -> F) and (((A and B) or A) -> ((C -> (C or D)) and A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61174.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((E and F) -> F) and (((A and B) or A) -> ((C -> (C or D)) and A)))), M:tm-326, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61175
in-theory        61175
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((E and F) -> E) and (((A and B) or A) -> ((C -> (C or D)) and A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61175.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((E and F) -> E) and (((A and B) or A) -> ((C -> (C or D)) and A)))), M:tm-325, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61176
in-theory        61176
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> ((C -> (C or D)) and A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61176.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> ((C -> (C or D)) and A)))), M:tm-324, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61177
in-theory        61177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((E -> (F -> E)) and (((A and B) or A) -> ((C -> (C or D)) and A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61177.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((E -> (F -> E)) and (((A and B) or A) -> ((C -> (C or D)) and A)))), M:tm-323, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61178
in-theory        61178
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3 tm-6)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61178.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61179
in-theory        61179
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61179.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61180
in-theory        61180
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61180.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61181
in-theory        61181
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     25
proof            (modus-ponens tm-316 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61181.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61182
in-theory        61182
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61182.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61183
in-theory        61183
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((((A and B) or A) -> (not ((C -> (C or D)) and A))) -> (not ((A and B) or A))))
theorem-size     35
proof            (modus-ponens tm-313 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61183.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((((A and B) or A) -> (not ((C -> (C or D)) and A))) -> (not ((A and B) or A)))), M:tm-313, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61184
in-theory        61184
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((((C -> (C or D)) and A) -> E) -> ((((A and B) or A) or ((C -> (C or D)) and A)) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61184.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((((C -> (C or D)) and A) -> E) -> ((((A and B) or A) or ((C -> (C or D)) and A)) -> E))), M:tm-312, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61185
in-theory        61185
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (E or (((A and B) or A) -> ((C -> (C or D)) and A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61185.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (E or (((A and B) or A) -> ((C -> (C or D)) and A)))), M:tm-311, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61186
in-theory        61186
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((((A and B) or A) -> ((C -> (C or D)) and A)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61186.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and ((((A and B) or A) -> ((C -> (C or D)) and A)) or E)), M:tm-310, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61187
in-theory        61187
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (E -> ((((A and B) or A) -> ((C -> (C or D)) and A)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61187.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (E -> ((((A and B) or A) -> ((C -> (C or D)) and A)) and E))), M:tm-309, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61188
in-theory        61188
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (E -> (((A and B) or A) -> ((C -> (C or D)) and A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61188.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (E -> (((A and B) or A) -> ((C -> (C or D)) and A)))), M:tm-305, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61189
in-theory        61189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61189.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-303, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61190
in-theory        61190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61190.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-270, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61191
in-theory        61191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61191.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-239, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61192
in-theory        61192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> ((G -> (G or H)) and E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61192.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> ((G -> (G or H)) and E))), M:tm-210, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61193
in-theory        61193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61193.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-183, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61194
in-theory        61194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61194.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-157, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61195
in-theory        61195
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61195.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-147, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61196
in-theory        61196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61196.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-134, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61197
in-theory        61197
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61197.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-125, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61198
in-theory        61198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (G or H)) and E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61198.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (G or H)) and E))), M:tm-113, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61199
in-theory        61199
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-6)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61199.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-105, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61200
in-theory        61200
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> ((E -> (E or F)) and C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61200.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> ((E -> (E or F)) and C))), M:tm-95, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61201
in-theory        61201
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D -> (D or E)) and A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-5 tm-6)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61201.        (((A and B) or A) -> (C -> ((D -> (D or E)) and A))), M:tm-84, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61202
in-theory        61202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61202.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-83, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61203
in-theory        61203
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> ((D -> (D or E)) and B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61203.        (((not (not A)) -> A) and (((B and C) or B) -> ((D -> (D or E)) and B))), M:tm-76, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61204
in-theory        61204
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> ((C -> (C or D)) and A))
theorem-size     21
proof            (modus-ponens tm-73 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-8 tm-10 tm-3 tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61204.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> ((C -> (C or D)) and A)), M:tm-73, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61205
in-theory        61205
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> ((E -> (E or F)) and C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61205.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> ((E -> (E or F)) and C))), M:tm-69, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61206
in-theory        61206
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61206.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-54, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61207
in-theory        61207
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> ((C -> (C or D)) and A))
theorem-size     15
proof            (modus-ponens tm-50 tm-736 ((A (and Am Bm)) (B Am) (C (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-8 tm-7 tm-3 tm-5 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61207.        ((A or ((A and B) or A)) -> ((C -> (C or D)) and A)), M:tm-50, m:tm-736, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61208
in-theory        61208
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> ((C -> (C or D)) and A))
theorem-size     17
proof            (modus-ponens tm-49 tm-736 ((A (and Am Bm)) (B Am) (C (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-8 tm-6 tm-3 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61208.        (((A and B) or ((A and B) or A)) -> ((C -> (C or D)) and A)), M:tm-49, m:tm-736, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61209
in-theory        61209
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> ((D -> (D or E)) and B))
theorem-size     21
proof            (modus-ponens tm-47 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-8 tm-4 tm-3 tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61209.        (((A and ((B and C) or B)) or ((B and C) or B)) -> ((D -> (D or E)) and B)), M:tm-47, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61210
in-theory        61210
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> ((D -> (D or E)) and A))
theorem-size     21
proof            (modus-ponens tm-46 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61210.        (((((A and B) or A) and C) or ((A and B) or A)) -> ((D -> (D or E)) and A)), M:tm-46, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61211
in-theory        61211
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> ((E -> (E or F)) and C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61211.        ((A -> (B or A)) and (((C and D) or C) -> ((E -> (E or F)) and C))), M:tm-42, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61212
in-theory        61212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> ((E -> (E or F)) and C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61212.        ((A -> (A or B)) and (((C and D) or C) -> ((E -> (E or F)) and C))), M:tm-32, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61213
in-theory        61213
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and ((C -> (C or D)) and A)))
theorem-size     19
proof            (modus-ponens tm-24 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61213.        (((A and B) or A) -> (((A and B) or A) and ((C -> (C or D)) and A))), M:tm-24, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61214
in-theory        61214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> ((E -> (E or F)) and C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61214.        ((A -> (B -> (A and B))) and (((C and D) or C) -> ((E -> (E or F)) and C))), M:tm-23, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61215
in-theory        61215
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> ((E -> (E or F)) and C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61215.        (((A and B) -> B) and (((C and D) or C) -> ((E -> (E or F)) and C))), M:tm-22, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61216
in-theory        61216
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> ((E -> (E or F)) and C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61216.        (((A and B) -> A) and (((C and D) or C) -> ((E -> (E or F)) and C))), M:tm-21, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61217
in-theory        61217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61217.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-20, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61218
in-theory        61218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> ((E -> (E or F)) and C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61218.        ((A -> (B -> A)) and (((C and D) or C) -> ((E -> (E or F)) and C))), M:tm-19, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61219
in-theory        61219
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not ((C -> (C or D)) and A))) -> (not ((A and B) or A)))
theorem-size     21
proof            (modus-ponens tm-9 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-9 tm-8 tm-3 tm-5 tm-6)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61219.        ((((A and B) or A) -> (not ((C -> (C or D)) and A))) -> (not ((A and B) or A))), M:tm-9, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61220
in-theory        61220
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) and C) -> D) -> ((((C and E) or C) or ((A -> (A or B)) and C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61220.        ((((A -> (A or B)) and C) -> D) -> ((((C and E) or C) or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-61221
in-theory        61221
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> ((D -> (D or E)) and B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-7 tm-8 tm-3 tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61221.        (A or (((B and C) or B) -> ((D -> (D or E)) and B))), M:tm-7, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61222
in-theory        61222
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-6 tm-8 tm-3 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61222.        ((((A and B) or A) -> ((C -> (C or D)) and A)) or E), M:tm-6, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61223
in-theory        61223
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> ((D -> (D or E)) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61223.        (A -> ((((B and C) or B) -> ((D -> (D or E)) and B)) and A)), M:tm-5, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61224
in-theory        61224
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> ((D -> (D or E)) and B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-1 tm-8 tm-3 tm-5 tm-6)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-61224.        (A -> (((B and C) or B) -> ((D -> (D or E)) and B))), M:tm-1, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-61225
in-theory        61225
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (G -> (G or H))))
theorem-size     37
proof            (modus-ponens tm-708 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61225.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (G -> (G or H)))), M:tm-708, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61226
in-theory        61226
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-665 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61226.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-665, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61227
in-theory        61227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-622 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61227.        ((A -> (B -> (C or B))) and (((D and E) or D) -> (F -> (F or G)))), M:tm-622, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61228
in-theory        61228
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C or ((A and B) or A)) or D))
theorem-size     15
proof            (modus-ponens tm-617 tm-737 ((A (or (and Am Bm) Am)) (Cm (or B (or (and Am Bm) Am))) (C (or (or B (or (and Am Bm) Am)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61228.        (((A and B) or A) -> ((C or ((A and B) or A)) or D)), M:tm-617, m:tm-737, u:((A (or (and Am Bm) Am)) (Cm (or B (or (and Am Bm) Am))) (C (or (or B (or (and Am Bm) Am)) Dm)))
================================================================
tm-name          tm-61229
in-theory        61229
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3 tm-6)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61229.        ((((A and B) or A) -> (C -> (C or D))) and (E -> (F or E))), M:tm-609, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61230
in-theory        61230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-605 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61230.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-605, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61231
in-theory        61231
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and ((E -> (F or E)) and (((A and B) or A) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1 tm-6)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61231.        ((((A and B) or A) -> (C -> (C or D))) and ((E -> (F or E)) and (((A and B) or A) -> (C -> (C or D))))), M:tm-595, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61232
in-theory        61232
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-550 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61232.        (((A -> (B or A)) or C) and (((D and E) or D) -> (F -> (F or G)))), M:tm-550, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61233
in-theory        61233
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-540 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1 tm-6)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61233.        ((A or (B -> (C or B))) and (((D and E) or D) -> (F -> (F or G)))), M:tm-540, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61234
in-theory        61234
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-530 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61234.        ((A or (B -> (B or C))) and (((D and E) or D) -> (F -> (F or G)))), M:tm-530, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61235
in-theory        61235
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-520 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61235.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (F or G)))), M:tm-520, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61236
in-theory        61236
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-510 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-1 tm-6)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61236.        ((A or ((B and C) -> C)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-510, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61237
in-theory        61237
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-500 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1 tm-6)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61237.        ((A or ((B and C) -> B)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-500, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61238
in-theory        61238
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-490 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-1 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61238.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (G or H)))), M:tm-490, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61239
in-theory        61239
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-480 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61239.        ((A or (B -> (C -> B))) and (((D and E) or D) -> (F -> (F or G)))), M:tm-480, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61240
in-theory        61240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-469 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61240.        ((A -> (B -> (B or C))) and (((D and E) or D) -> (F -> (F or G)))), M:tm-469, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61241
in-theory        61241
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((((A and B) or A) or C) or D))
theorem-size     15
proof            (modus-ponens tm-464 tm-737 ((A (or (and Am Bm) Am)) (Cm (or (or (and Am Bm) Am) B)) (C (or (or (or (and Am Bm) Am) B) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61241.        (((A and B) or A) -> ((((A and B) or A) or C) or D)), M:tm-464, m:tm-737, u:((A (or (and Am Bm) Am)) (Cm (or (or (and Am Bm) Am) B)) (C (or (or (or (and Am Bm) Am) B) Dm)))
================================================================
tm-name          tm-61242
in-theory        61242
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61242.        ((((A and B) or A) -> (C -> (C or D))) and (E -> (E or F))), M:tm-456, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61243
in-theory        61243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-453 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61243.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-453, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61244
in-theory        61244
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and ((E -> (E or F)) and (((A and B) or A) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61244.        ((((A and B) or A) -> (C -> (C or D))) and ((E -> (E or F)) and (((A and B) or A) -> (C -> (C or D))))), M:tm-443, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61245
in-theory        61245
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-409 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61245.        (((A -> (A or B)) or C) and (((D and E) or D) -> (F -> (F or G)))), M:tm-409, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61246
in-theory        61246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-400 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61246.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (F -> (F or G)))), M:tm-400, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61247
in-theory        61247
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-391 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61247.        ((((A and B) -> B) or C) and (((D and E) or D) -> (F -> (F or G)))), M:tm-391, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61248
in-theory        61248
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-382 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61248.        ((((A and B) -> A) or C) and (((D and E) or D) -> (F -> (F or G)))), M:tm-382, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61249
in-theory        61249
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-373 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61249.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (G -> (G or H)))), M:tm-373, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61250
in-theory        61250
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-364 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61250.        (((A -> (B -> A)) or C) and (((D and E) or D) -> (F -> (F or G)))), M:tm-364, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61251
in-theory        61251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-354 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61251.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (F or G)))), M:tm-354, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61252
in-theory        61252
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> (((A and B) or A) and C)) or D))
theorem-size     17
proof            (modus-ponens tm-349 tm-737 ((A (or (and Am Bm) Am)) (Cm (-> B (and (or (and Am Bm) Am) B))) (C (or (-> B (and (or (and Am Bm) Am) B)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3 tm-6)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61252.        (((A and B) or A) -> ((C -> (((A and B) or A) and C)) or D)), M:tm-349, m:tm-737, u:((A (or (and Am Bm) Am)) (Cm (-> B (and (or (and Am Bm) Am) B))) (C (or (-> B (and (or (and Am Bm) Am) B)) Dm)))
================================================================
tm-name          tm-61253
in-theory        61253
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61253.        ((((A and B) or A) -> (C -> (C or D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61254
in-theory        61254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (E -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-338 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61254.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (E -> (E or F)))), M:tm-338, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61255
in-theory        61255
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (((A and B) or A) -> (((A and B) or A) and (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-737 ((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61255.        ((((A and B) or A) -> (C -> (C or D))) and (((A and B) or A) -> (((A and B) or A) and (C -> (C or D))))), M:tm-328, m:tm-737, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-61256
in-theory        61256
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and ((E -> (F -> (E and F))) and (((A and B) or A) -> (C -> (C or D)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61256.        ((((A and B) or A) -> (C -> (C or D))) and ((E -> (F -> (E and F))) and (((A and B) or A) -> (C -> (C or D))))), M:tm-327, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61257
in-theory        61257
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (((E and F) -> F) and (((A and B) or A) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-1 tm-6)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61257.        ((((A and B) or A) -> (C -> (C or D))) and (((E and F) -> F) and (((A and B) or A) -> (C -> (C or D))))), M:tm-326, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61258
in-theory        61258
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (((E and F) -> E) and (((A and B) or A) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61258.        ((((A and B) or A) -> (C -> (C or D))) and (((E and F) -> E) and (((A and B) or A) -> (C -> (C or D))))), M:tm-325, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61259
in-theory        61259
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> (C -> (C or D)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61259.        ((((A and B) or A) -> (C -> (C or D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> (C -> (C or D))))), M:tm-324, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61260
in-theory        61260
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and ((E -> (F -> E)) and (((A and B) or A) -> (C -> (C or D)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61260.        ((((A and B) or A) -> (C -> (C or D))) and ((E -> (F -> E)) and (((A and B) or A) -> (C -> (C or D))))), M:tm-323, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61261
in-theory        61261
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3 tm-6)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61261.        ((((A and B) or A) -> (C -> (C or D))) and ((E and F) -> F)), M:tm-322, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61262
in-theory        61262
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61262.        ((((A and B) or A) -> (C -> (C or D))) and ((E and F) -> E)), M:tm-320, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61263
in-theory        61263
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61263.        ((((A and B) or A) -> (C -> (C or D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61264
in-theory        61264
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     23
proof            (modus-ponens tm-316 tm-737 ((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61264.        ((((A and B) or A) -> (C -> (C or D))) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-737, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-61265
in-theory        61265
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61265.        ((((A and B) or A) -> (C -> (C or D))) and (E -> (F -> E))), M:tm-315, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61266
in-theory        61266
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and ((((A and B) or A) -> (not (C -> (C or D)))) -> (not ((A and B) or A))))
theorem-size     31
proof            (modus-ponens tm-313 tm-737 ((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-1 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61266.        ((((A and B) or A) -> (C -> (C or D))) and ((((A and B) or A) -> (not (C -> (C or D)))) -> (not ((A and B) or A)))), M:tm-313, m:tm-737, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-61267
in-theory        61267
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (((C -> (C or D)) -> E) -> ((((A and B) or A) or (C -> (C or D))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-737 ((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61267.        ((((A and B) or A) -> (C -> (C or D))) and (((C -> (C or D)) -> E) -> ((((A and B) or A) or (C -> (C or D))) -> E))), M:tm-312, m:tm-737, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-61268
in-theory        61268
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (E or (((A and B) or A) -> (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61268.        ((((A and B) or A) -> (C -> (C or D))) and (E or (((A and B) or A) -> (C -> (C or D))))), M:tm-311, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61269
in-theory        61269
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and ((((A and B) or A) -> (C -> (C or D))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61269.        ((((A and B) or A) -> (C -> (C or D))) and ((((A and B) or A) -> (C -> (C or D))) or E)), M:tm-310, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61270
in-theory        61270
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (E -> ((((A and B) or A) -> (C -> (C or D))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61270.        ((((A and B) or A) -> (C -> (C or D))) and (E -> ((((A and B) or A) -> (C -> (C or D))) and E))), M:tm-309, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61271
in-theory        61271
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and ((((A and B) or A) -> C) -> (((A and B) or A) -> (C or D))))
theorem-size     29
proof            (modus-ponens tm-306 tm-737 ((A (or (and Am Bm) Am)) (B Cm) (C (or Cm Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61271.        ((((A and B) or A) -> (C -> (C or D))) and ((((A and B) or A) -> C) -> (((A and B) or A) -> (C or D)))), M:tm-306, m:tm-737, u:((A (or (and Am Bm) Am)) (B Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-61272
in-theory        61272
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (E -> (((A and B) or A) -> (C -> (C or D)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61272.        ((((A and B) or A) -> (C -> (C or D))) and (E -> (((A and B) or A) -> (C -> (C or D))))), M:tm-305, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61273
in-theory        61273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-303 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61273.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-303, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61274
in-theory        61274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-270 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61274.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-270, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61275
in-theory        61275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-239 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61275.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-239, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61276
in-theory        61276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (G -> (G or H))))
theorem-size     29
proof            (modus-ponens tm-210 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61276.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (G -> (G or H)))), M:tm-210, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61277
in-theory        61277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     21
proof            (modus-ponens tm-183 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61277.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-183, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61278
in-theory        61278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-157 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61278.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-157, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61279
in-theory        61279
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-147 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-1 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61279.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-147, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61280
in-theory        61280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-134 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-6)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61280.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-134, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61281
in-theory        61281
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     27
proof            (modus-ponens tm-125 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61281.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-125, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61282
in-theory        61282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (G or H))))
theorem-size     27
proof            (modus-ponens tm-113 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61282.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (G or H)))), M:tm-113, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61283
in-theory        61283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     31
proof            (modus-ponens tm-105 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1 tm-6)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61283.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (F -> (F or G)))), M:tm-105, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61284
in-theory        61284
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) or C))
theorem-size     13
proof            (modus-ponens tm-99 tm-737 ((Cm (or (and Am Bm) Am)) (A (or (and Am Bm) Am)) (B (or (or (and Am Bm) Am) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-6)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61284.        (((A and B) or A) -> (((A and B) or A) or C)), M:tm-99, m:tm-737, u:((Cm (or (and Am Bm) Am)) (A (or (and Am Bm) Am)) (B (or (or (and Am Bm) Am) Dm)))
================================================================
tm-name          tm-61285
in-theory        61285
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> ((A and B) or A)) or D))
theorem-size     15
proof            (modus-ponens tm-98 tm-737 ((A (or (and Am Bm) Am)) (Cm (-> B (or (and Am Bm) Am))) (C (or (-> B (or (and Am Bm) Am)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-6)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61285.        (((A and B) or A) -> ((C -> ((A and B) or A)) or D)), M:tm-98, m:tm-737, u:((A (or (and Am Bm) Am)) (Cm (-> B (or (and Am Bm) Am))) (C (or (-> B (or (and Am Bm) Am)) Dm)))
================================================================
tm-name          tm-61286
in-theory        61286
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-95 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 tm-6)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61286.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> (E -> (E or F)))), M:tm-95, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61287
in-theory        61287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     19
proof            (modus-ponens tm-83 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61287.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> (F -> (F or G)))), M:tm-83, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61288
in-theory        61288
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> (D -> (D or E))))
theorem-size     17
proof            (modus-ponens tm-76 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-1 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61288.        (((not (not A)) -> A) and (((B and C) or B) -> (D -> (D or E)))), M:tm-76, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61289
in-theory        61289
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> (C -> (C or D)))
theorem-size     19
proof            (modus-ponens tm-73 tm-737 ((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-10 tm-3 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61289.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> (C -> (C or D))), M:tm-73, m:tm-737, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-61290
in-theory        61290
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (E -> (E or F))))
theorem-size     23
proof            (modus-ponens tm-69 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61290.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (E -> (E or F)))), M:tm-69, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61291
in-theory        61291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-54 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61291.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (F -> (F or G)))), M:tm-54, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61292
in-theory        61292
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> (C -> (C or D)))
theorem-size     13
proof            (modus-ponens tm-50 tm-737 ((A (and Am Bm)) (B Am) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-7 tm-3 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61292.        ((A or ((A and B) or A)) -> (C -> (C or D))), M:tm-50, m:tm-737, u:((A (and Am Bm)) (B Am) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-61293
in-theory        61293
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> (C -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-49 tm-737 ((A (and Am Bm)) (B Am) (C (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-6 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61293.        (((A and B) or ((A and B) or A)) -> (C -> (C or D))), M:tm-49, m:tm-737, u:((A (and Am Bm)) (B Am) (C (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-61294
in-theory        61294
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-47 tm-737 ((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-4 tm-3 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61294.        (((A and ((B and C) or B)) or ((B and C) or B)) -> (D -> (D or E))), M:tm-47, m:tm-737, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-61295
in-theory        61295
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-46 tm-737 ((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61295.        (((((A and B) or A) and C) or ((A and B) or A)) -> (D -> (D or E))), M:tm-46, m:tm-737, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-61296
in-theory        61296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-42 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61296.        ((A -> (B or A)) and (((C and D) or C) -> (E -> (E or F)))), M:tm-42, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61297
in-theory        61297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-32 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61297.        ((A -> (A or B)) and (((C and D) or C) -> (E -> (E or F)))), M:tm-32, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61298
in-theory        61298
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and (C -> (C or D))))
theorem-size     17
proof            (modus-ponens tm-24 tm-737 ((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61298.        (((A and B) or A) -> (((A and B) or A) and (C -> (C or D)))), M:tm-24, m:tm-737, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-61299
in-theory        61299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-23 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61299.        ((A -> (B -> (A and B))) and (((C and D) or C) -> (E -> (E or F)))), M:tm-23, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61300
in-theory        61300
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-22 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61300.        (((A and B) -> B) and (((C and D) or C) -> (E -> (E or F)))), M:tm-22, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61301
in-theory        61301
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-21 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61301.        (((A and B) -> A) and (((C and D) or C) -> (E -> (E or F)))), M:tm-21, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61302
in-theory        61302
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-20 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61302.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (F -> (F or G)))), M:tm-20, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61303
in-theory        61303
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> (E -> (E or F))))
theorem-size     17
proof            (modus-ponens tm-19 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61303.        ((A -> (B -> A)) and (((C and D) or C) -> (E -> (E or F)))), M:tm-19, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61304
in-theory        61304
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not (C -> (C or D)))) -> (not ((A and B) or A)))
theorem-size     19
proof            (modus-ponens tm-9 tm-737 ((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-9 tm-8 tm-3 tm-1 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61304.        ((((A and B) or A) -> (not (C -> (C or D)))) -> (not ((A and B) or A))), M:tm-9, m:tm-737, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-61305
in-theory        61305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) -> C) -> ((((D and E) or D) or (A -> (A or B))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-737 ((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61305.        (((A -> (A or B)) -> C) -> ((((D and E) or D) or (A -> (A or B))) -> C)), M:tm-8, m:tm-737, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-61306
in-theory        61306
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-7 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-7 tm-8 tm-3 tm-1 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61306.        (A or (((B and C) or B) -> (D -> (D or E)))), M:tm-7, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61307
in-theory        61307
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-6 tm-8 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61307.        ((((A and B) or A) -> (C -> (C or D))) or E), M:tm-6, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61308
in-theory        61308
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> (D -> (D or E))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61308.        (A -> ((((B and C) or B) -> (D -> (D or E))) and A)), M:tm-5, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61309
in-theory        61309
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> C) -> (((A and B) or A) -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-2 tm-737 ((A (or (and Am Bm) Am)) (B Cm) (C (or Cm Dm))))
axioms-used      (tm-2 tm-8 tm-3 tm-1 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61309.        ((((A and B) or A) -> C) -> (((A and B) or A) -> (C or D))), M:tm-2, m:tm-737, u:((A (or (and Am Bm) Am)) (B Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-61310
in-theory        61310
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> (D -> (D or E))))
theorem-size     13
proof            (modus-ponens tm-1 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-1 tm-8 tm-3 tm-6)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-61310.        (A -> (((B and C) or B) -> (D -> (D or E)))), M:tm-1, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-61311
in-theory        61311
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> ((G -> (H or G)) and E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-7)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61311.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> ((G -> (H or G)) and E))), M:tm-708, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61312
in-theory        61312
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61312.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-665, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61313
in-theory        61313
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or ((D -> (E or D)) and A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61313.        (((A and B) or A) -> (C or ((D -> (E or D)) and A))), M:tm-623, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61314
in-theory        61314
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61314.        ((A -> (B -> (C or B))) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-622, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61315
in-theory        61315
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61315.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (E -> (F or E))), M:tm-609, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61316
in-theory        61316
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61316.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-605, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61317
in-theory        61317
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((E -> (F or E)) and (((A and B) or A) -> ((C -> (D or C)) and A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61317.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((E -> (F or E)) and (((A and B) or A) -> ((C -> (D or C)) and A)))), M:tm-595, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61318
in-theory        61318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61318.        (((A -> (B or A)) or C) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-550, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61319
in-theory        61319
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61319.        ((A or (B -> (C or B))) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-540, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61320
in-theory        61320
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61320.        ((A or (B -> (B or C))) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-530, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61321
in-theory        61321
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61321.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-520, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61322
in-theory        61322
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61322.        ((A or ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-510, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61323
in-theory        61323
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61323.        ((A or ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-500, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61324
in-theory        61324
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H or G)) and E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61324.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H or G)) and E))), M:tm-490, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61325
in-theory        61325
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61325.        ((A or (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-480, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61326
in-theory        61326
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> (D or C)) and A) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-5 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61326.        (((A and B) or A) -> (((C -> (D or C)) and A) or E)), M:tm-470, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61327
in-theory        61327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61327.        ((A -> (B -> (B or C))) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-469, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61328
in-theory        61328
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3 tm-7)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61328.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (E -> (E or F))), M:tm-456, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61329
in-theory        61329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61329.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-453, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61330
in-theory        61330
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((E -> (E or F)) and (((A and B) or A) -> ((C -> (D or C)) and A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61330.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((E -> (E or F)) and (((A and B) or A) -> ((C -> (D or C)) and A)))), M:tm-443, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61331
in-theory        61331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61331.        (((A -> (A or B)) or C) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-409, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61332
in-theory        61332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61332.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-400, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61333
in-theory        61333
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61333.        ((((A and B) -> B) or C) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-391, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61334
in-theory        61334
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61334.        ((((A and B) -> A) or C) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-382, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61335
in-theory        61335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> ((G -> (H or G)) and E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61335.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> ((G -> (H or G)) and E))), M:tm-373, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61336
in-theory        61336
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61336.        (((A -> (B -> A)) or C) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-364, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61337
in-theory        61337
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> (((D -> (E or D)) and A) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3 tm-7)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61337.        (((A and B) or A) -> (C -> (((D -> (E or D)) and A) and C))), M:tm-355, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61338
in-theory        61338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61338.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-354, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61339
in-theory        61339
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61339.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61340
in-theory        61340
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> ((E -> (F or E)) and C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61340.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> ((E -> (F or E)) and C))), M:tm-338, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61341
in-theory        61341
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((A and B) or A) -> (((A and B) or A) and ((C -> (D or C)) and A))))
theorem-size     33
proof            (modus-ponens tm-328 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61341.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((A and B) or A) -> (((A and B) or A) and ((C -> (D or C)) and A)))), M:tm-328, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61342
in-theory        61342
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> ((C -> (D or C)) and A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61342.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((E -> (F -> (E and F))) and (((A and B) or A) -> ((C -> (D or C)) and A)))), M:tm-327, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61343
in-theory        61343
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((E and F) -> F) and (((A and B) or A) -> ((C -> (D or C)) and A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61343.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((E and F) -> F) and (((A and B) or A) -> ((C -> (D or C)) and A)))), M:tm-326, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61344
in-theory        61344
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((E and F) -> E) and (((A and B) or A) -> ((C -> (D or C)) and A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61344.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((E and F) -> E) and (((A and B) or A) -> ((C -> (D or C)) and A)))), M:tm-325, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61345
in-theory        61345
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> ((C -> (D or C)) and A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61345.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> ((C -> (D or C)) and A)))), M:tm-324, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61346
in-theory        61346
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((E -> (F -> E)) and (((A and B) or A) -> ((C -> (D or C)) and A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61346.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((E -> (F -> E)) and (((A and B) or A) -> ((C -> (D or C)) and A)))), M:tm-323, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61347
in-theory        61347
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3 tm-7)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61347.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61348
in-theory        61348
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61348.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61349
in-theory        61349
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61349.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61350
in-theory        61350
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     25
proof            (modus-ponens tm-316 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61350.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61351
in-theory        61351
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61351.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61352
in-theory        61352
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((((A and B) or A) -> (not ((C -> (D or C)) and A))) -> (not ((A and B) or A))))
theorem-size     35
proof            (modus-ponens tm-313 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-7)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61352.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((((A and B) or A) -> (not ((C -> (D or C)) and A))) -> (not ((A and B) or A)))), M:tm-313, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61353
in-theory        61353
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((((C -> (D or C)) and A) -> E) -> ((((A and B) or A) or ((C -> (D or C)) and A)) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61353.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((((C -> (D or C)) and A) -> E) -> ((((A and B) or A) or ((C -> (D or C)) and A)) -> E))), M:tm-312, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61354
in-theory        61354
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (E or (((A and B) or A) -> ((C -> (D or C)) and A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61354.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (E or (((A and B) or A) -> ((C -> (D or C)) and A)))), M:tm-311, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61355
in-theory        61355
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((((A and B) or A) -> ((C -> (D or C)) and A)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61355.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and ((((A and B) or A) -> ((C -> (D or C)) and A)) or E)), M:tm-310, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61356
in-theory        61356
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (E -> ((((A and B) or A) -> ((C -> (D or C)) and A)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61356.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (E -> ((((A and B) or A) -> ((C -> (D or C)) and A)) and E))), M:tm-309, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61357
in-theory        61357
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (E -> (((A and B) or A) -> ((C -> (D or C)) and A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61357.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (E -> (((A and B) or A) -> ((C -> (D or C)) and A)))), M:tm-305, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61358
in-theory        61358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61358.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-303, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61359
in-theory        61359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61359.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-270, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61360
in-theory        61360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61360.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-239, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61361
in-theory        61361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> ((G -> (H or G)) and E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61361.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> ((G -> (H or G)) and E))), M:tm-210, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61362
in-theory        61362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61362.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-183, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61363
in-theory        61363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61363.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-157, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61364
in-theory        61364
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61364.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-147, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61365
in-theory        61365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61365.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-134, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61366
in-theory        61366
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61366.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-125, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61367
in-theory        61367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H or G)) and E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61367.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> ((G -> (H or G)) and E))), M:tm-113, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61368
in-theory        61368
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-7)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61368.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-105, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61369
in-theory        61369
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> ((E -> (F or E)) and C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61369.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> ((E -> (F or E)) and C))), M:tm-95, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61370
in-theory        61370
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C -> ((D -> (E or D)) and A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-5 tm-7)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61370.        (((A and B) or A) -> (C -> ((D -> (E or D)) and A))), M:tm-84, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61371
in-theory        61371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61371.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-83, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61372
in-theory        61372
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> ((D -> (E or D)) and B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61372.        (((not (not A)) -> A) and (((B and C) or B) -> ((D -> (E or D)) and B))), M:tm-76, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61373
in-theory        61373
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> ((C -> (D or C)) and A))
theorem-size     21
proof            (modus-ponens tm-73 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-8 tm-10 tm-3 tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61373.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> ((C -> (D or C)) and A)), M:tm-73, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61374
in-theory        61374
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> ((E -> (F or E)) and C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61374.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> ((E -> (F or E)) and C))), M:tm-69, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61375
in-theory        61375
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61375.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-54, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61376
in-theory        61376
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> ((C -> (D or C)) and A))
theorem-size     15
proof            (modus-ponens tm-50 tm-738 ((A (and Am Bm)) (B Am) (C (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-8 tm-7 tm-3 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61376.        ((A or ((A and B) or A)) -> ((C -> (D or C)) and A)), M:tm-50, m:tm-738, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61377
in-theory        61377
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> ((C -> (D or C)) and A))
theorem-size     17
proof            (modus-ponens tm-49 tm-738 ((A (and Am Bm)) (B Am) (C (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-8 tm-6 tm-3 tm-5 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61377.        (((A and B) or ((A and B) or A)) -> ((C -> (D or C)) and A)), M:tm-49, m:tm-738, u:((A (and Am Bm)) (B Am) (C (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61378
in-theory        61378
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> ((D -> (E or D)) and B))
theorem-size     21
proof            (modus-ponens tm-47 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-8 tm-4 tm-3 tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61378.        (((A and ((B and C) or B)) or ((B and C) or B)) -> ((D -> (E or D)) and B)), M:tm-47, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61379
in-theory        61379
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> ((D -> (E or D)) and A))
theorem-size     21
proof            (modus-ponens tm-46 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61379.        (((((A and B) or A) and C) or ((A and B) or A)) -> ((D -> (E or D)) and A)), M:tm-46, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61380
in-theory        61380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> ((E -> (F or E)) and C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61380.        ((A -> (B or A)) and (((C and D) or C) -> ((E -> (F or E)) and C))), M:tm-42, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61381
in-theory        61381
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> ((E -> (F or E)) and C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61381.        ((A -> (A or B)) and (((C and D) or C) -> ((E -> (F or E)) and C))), M:tm-32, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61382
in-theory        61382
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and ((C -> (D or C)) and A)))
theorem-size     19
proof            (modus-ponens tm-24 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61382.        (((A and B) or A) -> (((A and B) or A) and ((C -> (D or C)) and A))), M:tm-24, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61383
in-theory        61383
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> ((E -> (F or E)) and C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61383.        ((A -> (B -> (A and B))) and (((C and D) or C) -> ((E -> (F or E)) and C))), M:tm-23, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61384
in-theory        61384
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> ((E -> (F or E)) and C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61384.        (((A and B) -> B) and (((C and D) or C) -> ((E -> (F or E)) and C))), M:tm-22, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61385
in-theory        61385
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> ((E -> (F or E)) and C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61385.        (((A and B) -> A) and (((C and D) or C) -> ((E -> (F or E)) and C))), M:tm-21, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61386
in-theory        61386
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61386.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-20, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61387
in-theory        61387
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> ((E -> (F or E)) and C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61387.        ((A -> (B -> A)) and (((C and D) or C) -> ((E -> (F or E)) and C))), M:tm-19, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61388
in-theory        61388
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not ((C -> (D or C)) and A))) -> (not ((A and B) or A)))
theorem-size     21
proof            (modus-ponens tm-9 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-9 tm-8 tm-3 tm-5 tm-7)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61388.        ((((A and B) or A) -> (not ((C -> (D or C)) and A))) -> (not ((A and B) or A))), M:tm-9, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61389
in-theory        61389
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) and C) -> D) -> ((((C and E) or C) or ((A -> (B or A)) and C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61389.        ((((A -> (B or A)) and C) -> D) -> ((((C and E) or C) or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-61390
in-theory        61390
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> ((D -> (E or D)) and B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-7 tm-8 tm-3 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61390.        (A or (((B and C) or B) -> ((D -> (E or D)) and B))), M:tm-7, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61391
in-theory        61391
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-6 tm-8 tm-3 tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61391.        ((((A and B) or A) -> ((C -> (D or C)) and A)) or E), M:tm-6, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61392
in-theory        61392
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> ((D -> (E or D)) and B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61392.        (A -> ((((B and C) or B) -> ((D -> (E or D)) and B)) and A)), M:tm-5, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61393
in-theory        61393
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> ((D -> (E or D)) and B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-1 tm-8 tm-3 tm-5 tm-7)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-61393.        (A -> (((B and C) or B) -> ((D -> (E or D)) and B))), M:tm-1, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-61394
in-theory        61394
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (G -> (H or G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1 tm-7)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61394.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or E) -> (G -> (H or G)))), M:tm-708, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61395
in-theory        61395
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61395.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-665, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61396
in-theory        61396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61396.        ((A -> (B -> (C or B))) and (((D and E) or D) -> (F -> (G or F)))), M:tm-622, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61397
in-theory        61397
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (D or ((A and B) or A))))
theorem-size     15
proof            (modus-ponens tm-617 tm-739 ((A (or (and Am Bm) Am)) (Cm (or B (or (and Am Bm) Am))) (C (or Dm (or B (or (and Am Bm) Am))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61397.        (((A and B) or A) -> (C or (D or ((A and B) or A)))), M:tm-617, m:tm-739, u:((A (or (and Am Bm) Am)) (Cm (or B (or (and Am Bm) Am))) (C (or Dm (or B (or (and Am Bm) Am)))))
================================================================
tm-name          tm-61398
in-theory        61398
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61398.        ((((A and B) or A) -> (C -> (D or C))) and (E -> (F or E))), M:tm-609, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61399
in-theory        61399
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61399.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-605, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61400
in-theory        61400
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and ((E -> (F or E)) and (((A and B) or A) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61400.        ((((A and B) or A) -> (C -> (D or C))) and ((E -> (F or E)) and (((A and B) or A) -> (C -> (D or C))))), M:tm-595, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61401
in-theory        61401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61401.        (((A -> (B or A)) or C) and (((D and E) or D) -> (F -> (G or F)))), M:tm-550, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61402
in-theory        61402
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61402.        ((A or (B -> (C or B))) and (((D and E) or D) -> (F -> (G or F)))), M:tm-540, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61403
in-theory        61403
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61403.        ((A or (B -> (B or C))) and (((D and E) or D) -> (F -> (G or F)))), M:tm-530, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61404
in-theory        61404
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61404.        ((A or (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (G or F)))), M:tm-520, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61405
in-theory        61405
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61405.        ((A or ((B and C) -> C)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-510, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61406
in-theory        61406
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61406.        ((A or ((B and C) -> B)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-500, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61407
in-theory        61407
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61407.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (H or G)))), M:tm-490, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61408
in-theory        61408
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61408.        ((A or (B -> (C -> B))) and (((D and E) or D) -> (F -> (G or F)))), M:tm-480, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61409
in-theory        61409
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61409.        ((A -> (B -> (B or C))) and (((D and E) or D) -> (F -> (G or F)))), M:tm-469, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61410
in-theory        61410
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (((A and B) or A) or D)))
theorem-size     15
proof            (modus-ponens tm-464 tm-739 ((A (or (and Am Bm) Am)) (Cm (or (or (and Am Bm) Am) B)) (C (or Dm (or (or (and Am Bm) Am) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61410.        (((A and B) or A) -> (C or (((A and B) or A) or D))), M:tm-464, m:tm-739, u:((A (or (and Am Bm) Am)) (Cm (or (or (and Am Bm) Am) B)) (C (or Dm (or (or (and Am Bm) Am) B))))
================================================================
tm-name          tm-61411
in-theory        61411
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3 tm-7)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61411.        ((((A and B) or A) -> (C -> (D or C))) and (E -> (E or F))), M:tm-456, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61412
in-theory        61412
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61412.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-453, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61413
in-theory        61413
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and ((E -> (E or F)) and (((A and B) or A) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1 tm-7)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61413.        ((((A and B) or A) -> (C -> (D or C))) and ((E -> (E or F)) and (((A and B) or A) -> (C -> (D or C))))), M:tm-443, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61414
in-theory        61414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1 tm-7)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61414.        (((A -> (A or B)) or C) and (((D and E) or D) -> (F -> (G or F)))), M:tm-409, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61415
in-theory        61415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61415.        (((A -> (B -> (A and B))) or C) and (((D and E) or D) -> (F -> (G or F)))), M:tm-400, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61416
in-theory        61416
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-1 tm-7)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61416.        ((((A and B) -> B) or C) and (((D and E) or D) -> (F -> (G or F)))), M:tm-391, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61417
in-theory        61417
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1 tm-7)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61417.        ((((A and B) -> A) or C) and (((D and E) or D) -> (F -> (G or F)))), M:tm-382, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61418
in-theory        61418
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-1 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61418.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or E) -> (G -> (H or G)))), M:tm-373, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61419
in-theory        61419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61419.        (((A -> (B -> A)) or C) and (((D and E) or D) -> (F -> (G or F)))), M:tm-364, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61420
in-theory        61420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61420.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or D) -> (F -> (G or F)))), M:tm-354, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61421
in-theory        61421
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (D -> (((A and B) or A) and D))))
theorem-size     17
proof            (modus-ponens tm-349 tm-739 ((A (or (and Am Bm) Am)) (Cm (-> B (and (or (and Am Bm) Am) B))) (C (or Dm (-> B (and (or (and Am Bm) Am) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3 tm-7)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61421.        (((A and B) or A) -> (C or (D -> (((A and B) or A) and D)))), M:tm-349, m:tm-739, u:((A (or (and Am Bm) Am)) (Cm (-> B (and (or (and Am Bm) Am) B))) (C (or Dm (-> B (and (or (and Am Bm) Am) B)))))
================================================================
tm-name          tm-61422
in-theory        61422
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61422.        ((((A and B) or A) -> (C -> (D or C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61423
in-theory        61423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (E -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61423.        (((A -> B) -> (A -> (A and B))) and (((C and D) or C) -> (E -> (F or E)))), M:tm-338, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61424
in-theory        61424
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (((A and B) or A) -> (((A and B) or A) and (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-739 ((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61424.        ((((A and B) or A) -> (C -> (D or C))) and (((A and B) or A) -> (((A and B) or A) and (C -> (D or C))))), M:tm-328, m:tm-739, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-61425
in-theory        61425
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and ((E -> (F -> (E and F))) and (((A and B) or A) -> (C -> (D or C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61425.        ((((A and B) or A) -> (C -> (D or C))) and ((E -> (F -> (E and F))) and (((A and B) or A) -> (C -> (D or C))))), M:tm-327, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61426
in-theory        61426
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (((E and F) -> F) and (((A and B) or A) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-1 tm-7)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61426.        ((((A and B) or A) -> (C -> (D or C))) and (((E and F) -> F) and (((A and B) or A) -> (C -> (D or C))))), M:tm-326, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61427
in-theory        61427
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (((E and F) -> E) and (((A and B) or A) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61427.        ((((A and B) or A) -> (C -> (D or C))) and (((E and F) -> E) and (((A and B) or A) -> (C -> (D or C))))), M:tm-325, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61428
in-theory        61428
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> (C -> (D or C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61428.        ((((A and B) or A) -> (C -> (D or C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or A) -> (C -> (D or C))))), M:tm-324, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61429
in-theory        61429
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and ((E -> (F -> E)) and (((A and B) or A) -> (C -> (D or C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61429.        ((((A and B) or A) -> (C -> (D or C))) and ((E -> (F -> E)) and (((A and B) or A) -> (C -> (D or C))))), M:tm-323, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61430
in-theory        61430
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3 tm-7)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61430.        ((((A and B) or A) -> (C -> (D or C))) and ((E and F) -> F)), M:tm-322, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61431
in-theory        61431
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61431.        ((((A and B) or A) -> (C -> (D or C))) and ((E and F) -> E)), M:tm-320, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61432
in-theory        61432
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61432.        ((((A and B) or A) -> (C -> (D or C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61433
in-theory        61433
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (((A and B) or A) -> ((A and B) or A)))
theorem-size     23
proof            (modus-ponens tm-316 tm-739 ((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61433.        ((((A and B) or A) -> (C -> (D or C))) and (((A and B) or A) -> ((A and B) or A))), M:tm-316, m:tm-739, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-61434
in-theory        61434
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61434.        ((((A and B) or A) -> (C -> (D or C))) and (E -> (F -> E))), M:tm-315, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61435
in-theory        61435
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and ((((A and B) or A) -> (not (C -> (D or C)))) -> (not ((A and B) or A))))
theorem-size     31
proof            (modus-ponens tm-313 tm-739 ((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-1 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61435.        ((((A and B) or A) -> (C -> (D or C))) and ((((A and B) or A) -> (not (C -> (D or C)))) -> (not ((A and B) or A)))), M:tm-313, m:tm-739, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-61436
in-theory        61436
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (((C -> (D or C)) -> E) -> ((((A and B) or A) or (C -> (D or C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-739 ((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61436.        ((((A and B) or A) -> (C -> (D or C))) and (((C -> (D or C)) -> E) -> ((((A and B) or A) or (C -> (D or C))) -> E))), M:tm-312, m:tm-739, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-61437
in-theory        61437
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (E or (((A and B) or A) -> (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61437.        ((((A and B) or A) -> (C -> (D or C))) and (E or (((A and B) or A) -> (C -> (D or C))))), M:tm-311, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61438
in-theory        61438
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and ((((A and B) or A) -> (C -> (D or C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61438.        ((((A and B) or A) -> (C -> (D or C))) and ((((A and B) or A) -> (C -> (D or C))) or E)), M:tm-310, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61439
in-theory        61439
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (E -> ((((A and B) or A) -> (C -> (D or C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61439.        ((((A and B) or A) -> (C -> (D or C))) and (E -> ((((A and B) or A) -> (C -> (D or C))) and E))), M:tm-309, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61440
in-theory        61440
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and ((((A and B) or A) -> C) -> (((A and B) or A) -> (D or C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-739 ((A (or (and Am Bm) Am)) (B Cm) (C (or Dm Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61440.        ((((A and B) or A) -> (C -> (D or C))) and ((((A and B) or A) -> C) -> (((A and B) or A) -> (D or C)))), M:tm-306, m:tm-739, u:((A (or (and Am Bm) Am)) (B Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-61441
in-theory        61441
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (E -> (((A and B) or A) -> (C -> (D or C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61441.        ((((A and B) or A) -> (C -> (D or C))) and (E -> (((A and B) or A) -> (C -> (D or C))))), M:tm-305, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61442
in-theory        61442
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61442.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-303, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61443
in-theory        61443
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61443.        ((A -> (((B and C) -> C) and A)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-270, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61444
in-theory        61444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61444.        ((A -> (((B and C) -> B) and A)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-239, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61445
in-theory        61445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (G -> (H or G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61445.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or E) -> (G -> (H or G)))), M:tm-210, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61446
in-theory        61446
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61446.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-183, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61447
in-theory        61447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61447.        ((A -> ((B and C) -> C)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-157, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61448
in-theory        61448
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-1 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61448.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-147, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61449
in-theory        61449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-7)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61449.        ((A -> ((B and C) -> B)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-134, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61450
in-theory        61450
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61450.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-125, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61451
in-theory        61451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (H or G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61451.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or E) -> (G -> (H or G)))), M:tm-113, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61452
in-theory        61452
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1 tm-7)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61452.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or D) -> (F -> (G or F)))), M:tm-105, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61453
in-theory        61453
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or ((A and B) or A)))
theorem-size     13
proof            (modus-ponens tm-99 tm-739 ((Cm (or (and Am Bm) Am)) (A (or (and Am Bm) Am)) (B (or Dm (or (and Am Bm) Am)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-7)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61453.        (((A and B) or A) -> (C or ((A and B) or A))), M:tm-99, m:tm-739, u:((Cm (or (and Am Bm) Am)) (A (or (and Am Bm) Am)) (B (or Dm (or (and Am Bm) Am))))
================================================================
tm-name          tm-61454
in-theory        61454
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (C or (D -> ((A and B) or A))))
theorem-size     15
proof            (modus-ponens tm-98 tm-739 ((A (or (and Am Bm) Am)) (Cm (-> B (or (and Am Bm) Am))) (C (or Dm (-> B (or (and Am Bm) Am))))))
axioms-used      (tm-2 tm-1 tm-8 tm-3 tm-7)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61454.        (((A and B) or A) -> (C or (D -> ((A and B) or A)))), M:tm-98, m:tm-739, u:((A (or (and Am Bm) Am)) (Cm (-> B (or (and Am Bm) Am))) (C (or Dm (-> B (or (and Am Bm) Am)))))
================================================================
tm-name          tm-61455
in-theory        61455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or C) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3 tm-7)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61455.        (((A -> B) -> (A -> A)) and (((C and D) or C) -> (E -> (F or E)))), M:tm-95, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61456
in-theory        61456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61456.        ((A -> (B -> (C -> B))) and (((D and E) or D) -> (F -> (G or F)))), M:tm-83, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61457
in-theory        61457
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or B) -> (D -> (E or D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-1 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61457.        (((not (not A)) -> A) and (((B and C) or B) -> (D -> (E or D)))), M:tm-76, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61458
in-theory        61458
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or A))) or ((A and B) or A)) -> (C -> (D or C)))
theorem-size     19
proof            (modus-ponens tm-73 tm-739 ((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-10 tm-3 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61458.        (((not (not ((A and B) or A))) or ((A and B) or A)) -> (C -> (D or C))), M:tm-73, m:tm-739, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-61459
in-theory        61459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (E -> (F or E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61459.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or C) -> (E -> (F or E)))), M:tm-69, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61460
in-theory        61460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61460.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or D) -> (F -> (G or F)))), M:tm-54, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61461
in-theory        61461
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((A and B) or A)) -> (C -> (D or C)))
theorem-size     13
proof            (modus-ponens tm-50 tm-739 ((A (and Am Bm)) (B Am) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-7 tm-3 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61461.        ((A or ((A and B) or A)) -> (C -> (D or C))), M:tm-50, m:tm-739, u:((A (and Am Bm)) (B Am) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-61462
in-theory        61462
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or A)) -> (C -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-739 ((A (and Am Bm)) (B Am) (C (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-6 tm-3 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61462.        (((A and B) or ((A and B) or A)) -> (C -> (D or C))), M:tm-49, m:tm-739, u:((A (and Am Bm)) (B Am) (C (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-61463
in-theory        61463
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or B)) or ((B and C) or B)) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-47 tm-739 ((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-4 tm-3 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61463.        (((A and ((B and C) or B)) or ((B and C) or B)) -> (D -> (E or D))), M:tm-47, m:tm-739, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-61464
in-theory        61464
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) and C) or ((A and B) or A)) -> (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-46 tm-739 ((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61464.        (((((A and B) or A) and C) or ((A and B) or A)) -> (D -> (E or D))), M:tm-46, m:tm-739, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-61465
in-theory        61465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or C) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61465.        ((A -> (B or A)) and (((C and D) or C) -> (E -> (F or E)))), M:tm-42, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61466
in-theory        61466
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or C) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61466.        ((A -> (A or B)) and (((C and D) or C) -> (E -> (F or E)))), M:tm-32, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61467
in-theory        61467
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((A and B) or A) and (C -> (D or C))))
theorem-size     17
proof            (modus-ponens tm-24 tm-739 ((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61467.        (((A and B) or A) -> (((A and B) or A) and (C -> (D or C)))), M:tm-24, m:tm-739, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-61468
in-theory        61468
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or C) -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61468.        ((A -> (B -> (A and B))) and (((C and D) or C) -> (E -> (F or E)))), M:tm-23, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61469
in-theory        61469
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or C) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61469.        (((A and B) -> B) and (((C and D) or C) -> (E -> (F or E)))), M:tm-22, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61470
in-theory        61470
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or C) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-1 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61470.        (((A and B) -> A) and (((C and D) or C) -> (E -> (F or E)))), M:tm-21, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61471
in-theory        61471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61471.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or D) -> (F -> (G or F)))), M:tm-20, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61472
in-theory        61472
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or C) -> (E -> (F or E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61472.        ((A -> (B -> A)) and (((C and D) or C) -> (E -> (F or E)))), M:tm-19, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61473
in-theory        61473
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (not (C -> (D or C)))) -> (not ((A and B) or A)))
theorem-size     19
proof            (modus-ponens tm-9 tm-739 ((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-9 tm-8 tm-3 tm-1 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61473.        ((((A and B) or A) -> (not (C -> (D or C)))) -> (not ((A and B) or A))), M:tm-9, m:tm-739, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-61474
in-theory        61474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) -> C) -> ((((D and E) or D) or (A -> (B or A))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-739 ((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61474.        (((A -> (B or A)) -> C) -> ((((D and E) or D) or (A -> (B or A))) -> C)), M:tm-8, m:tm-739, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-61475
in-theory        61475
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or B) -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-7 tm-8 tm-3 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61475.        (A or (((B and C) or B) -> (D -> (E or D)))), M:tm-7, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61476
in-theory        61476
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-6 tm-8 tm-3 tm-1 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61476.        ((((A and B) or A) -> (C -> (D or C))) or E), M:tm-6, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61477
in-theory        61477
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or B) -> (D -> (E or D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61477.        (A -> ((((B and C) or B) -> (D -> (E or D))) and A)), M:tm-5, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61478
in-theory        61478
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> C) -> (((A and B) or A) -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-2 tm-739 ((A (or (and Am Bm) Am)) (B Cm) (C (or Dm Cm))))
axioms-used      (tm-2 tm-8 tm-3 tm-1 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61478.        ((((A and B) or A) -> C) -> (((A and B) or A) -> (D or C))), M:tm-2, m:tm-739, u:((A (or (and Am Bm) Am)) (B Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-61479
in-theory        61479
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> (D -> (E or D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-1 tm-8 tm-3 tm-7)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-61479.        (A -> (((B and C) or B) -> (D -> (E or D)))), M:tm-1, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-61480
in-theory        61480
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) -> G) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     47
proof            (modus-ponens tm-708 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3 tm-1)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61480.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E -> F) -> G) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-708, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61481
in-theory        61481
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-665 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61481.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-665, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61482
in-theory        61482
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (E or ((B or (A -> B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-623 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61482.        (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (E or ((B or (A -> B)) -> C))), M:tm-623, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61483
in-theory        61483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-622 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61483.        ((A -> (B -> (C or B))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-622, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61484
in-theory        61484
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61484.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (E -> (F or E))), M:tm-609, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61485
in-theory        61485
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-605 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61485.        ((A -> ((B -> (C or B)) and A)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-605, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61486
in-theory        61486
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((E -> (F or E)) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-595 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61486.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((E -> (F or E)) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)))), M:tm-595, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61487
in-theory        61487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-550 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61487.        (((A -> (B or A)) or C) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-550, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61488
in-theory        61488
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-540 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61488.        ((A or (B -> (C or B))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-540, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61489
in-theory        61489
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-530 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61489.        ((A or (B -> (B or C))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-530, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61490
in-theory        61490
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-520 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61490.        ((A or (B -> (C -> (B and C)))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-520, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61491
in-theory        61491
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-510 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61491.        ((A or ((B and C) -> C)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-510, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61492
in-theory        61492
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-500 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61492.        ((A or ((B and C) -> B)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-500, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61493
in-theory        61493
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> G) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-490 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61493.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> G) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-490, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61494
in-theory        61494
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-480 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61494.        ((A or (B -> (C -> B))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-480, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61495
in-theory        61495
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (((B or (A -> B)) -> C) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61495.        (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (((B or (A -> B)) -> C) or E)), M:tm-470, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61496
in-theory        61496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-469 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61496.        ((A -> (B -> (B or C))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-469, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61497
in-theory        61497
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61497.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (E -> (E or F))), M:tm-456, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61498
in-theory        61498
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-453 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61498.        ((A -> ((B -> (B or C)) and A)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-453, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61499
in-theory        61499
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((E -> (E or F)) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-443 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61499.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((E -> (E or F)) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)))), M:tm-443, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61500
in-theory        61500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-409 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61500.        (((A -> (A or B)) or C) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-409, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61501
in-theory        61501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-400 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61501.        (((A -> (B -> (A and B))) or C) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-400, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61502
in-theory        61502
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-391 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61502.        ((((A and B) -> B) or C) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-391, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61503
in-theory        61503
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-382 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61503.        ((((A and B) -> A) or C) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-382, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61504
in-theory        61504
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) -> G) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-373 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61504.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E -> F) -> G) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-373, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61505
in-theory        61505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-364 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61505.        (((A -> (B -> A)) or C) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-364, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61506
in-theory        61506
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (E -> (((B or (A -> B)) -> C) and E)))
theorem-size     25
proof            (modus-ponens tm-355 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61506.        (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (E -> (((B or (A -> B)) -> C) and E))), M:tm-355, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61507
in-theory        61507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-354 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61507.        ((A -> (B -> (C -> (B and C)))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-354, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61508
in-theory        61508
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61508.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61509
in-theory        61509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E)))
theorem-size     31
proof            (modus-ponens tm-338 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61509.        (((A -> B) -> (A -> (A and B))) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E))), M:tm-338, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61510
in-theory        61510
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (((((A -> B) -> C) and D) or ((A -> B) -> C)) and ((B or (A -> B)) -> C))))
theorem-size     57
proof            (modus-ponens tm-328 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61510.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (((((A -> B) -> C) and D) or ((A -> B) -> C)) and ((B or (A -> B)) -> C)))), M:tm-328, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61511
in-theory        61511
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((E -> (F -> (E and F))) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C))))
theorem-size     51
proof            (modus-ponens tm-327 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61511.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((E -> (F -> (E and F))) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)))), M:tm-327, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61512
in-theory        61512
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (((E and F) -> F) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-326 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61512.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (((E and F) -> F) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)))), M:tm-326, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61513
in-theory        61513
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (((E and F) -> E) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-325 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61513.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (((E and F) -> E) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)))), M:tm-325, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61514
in-theory        61514
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C))))
theorem-size     57
proof            (modus-ponens tm-324 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       223
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61514.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)))), M:tm-324, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61515
in-theory        61515
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((E -> (F -> E)) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C))))
theorem-size     49
proof            (modus-ponens tm-323 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61515.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((E -> (F -> E)) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)))), M:tm-323, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61516
in-theory        61516
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61516.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61517
in-theory        61517
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61517.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61518
in-theory        61518
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61518.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61519
in-theory        61519
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((((A -> B) -> C) and D) or ((A -> B) -> C))))
theorem-size     49
proof            (modus-ponens tm-316 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61519.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((((A -> B) -> C) and D) or ((A -> B) -> C)))), M:tm-316, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61520
in-theory        61520
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61520.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61521
in-theory        61521
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (not ((B or (A -> B)) -> C))) -> (not ((((A -> B) -> C) and D) or ((A -> B) -> C)))))
theorem-size     59
proof            (modus-ponens tm-313 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61521.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (not ((B or (A -> B)) -> C))) -> (not ((((A -> B) -> C) and D) or ((A -> B) -> C))))), M:tm-313, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61522
in-theory        61522
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((((B or (A -> B)) -> C) -> E) -> ((((((A -> B) -> C) and D) or ((A -> B) -> C)) or ((B or (A -> B)) -> C)) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61522.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((((B or (A -> B)) -> C) -> E) -> ((((((A -> B) -> C) and D) or ((A -> B) -> C)) or ((B or (A -> B)) -> C)) -> E))), M:tm-312, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61523
in-theory        61523
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (E or (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C))))
theorem-size     45
proof            (modus-ponens tm-311 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61523.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (E or (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)))), M:tm-311, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61524
in-theory        61524
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61524.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) or E)), M:tm-310, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61525
in-theory        61525
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (E -> ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61525.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (E -> ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and E))), M:tm-309, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61526
in-theory        61526
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (B or (A -> B))) -> (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> C)))
theorem-size     57
proof            (modus-ponens tm-306 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (or Bm (-> Am Bm))) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61526.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (B or (A -> B))) -> (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> C))), M:tm-306, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (or Bm (-> Am Bm))) (C Cm))
================================================================
tm-name          tm-61527
in-theory        61527
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (E -> (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C))))
theorem-size     45
proof            (modus-ponens tm-305 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61527.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (E -> (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)))), M:tm-305, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61528
in-theory        61528
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-303 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61528.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-303, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61529
in-theory        61529
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-270 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61529.        ((A -> (((B and C) -> C) and A)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-270, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61530
in-theory        61530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-239 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61530.        ((A -> (((B and C) -> B) and A)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-239, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61531
in-theory        61531
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) -> G) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-210 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61531.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E -> F) -> G) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-210, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61532
in-theory        61532
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-183 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61532.        ((A -> ((B -> (C -> B)) and A)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-183, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61533
in-theory        61533
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-157 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61533.        ((A -> ((B and C) -> C)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-157, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61534
in-theory        61534
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-147 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61534.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-147, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61535
in-theory        61535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-134 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61535.        ((A -> ((B and C) -> B)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-134, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61536
in-theory        61536
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     37
proof            (modus-ponens tm-125 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61536.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-125, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61537
in-theory        61537
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (C -> D)) and E) or ((A -> B) -> (C -> D))) -> (((B or (A -> B)) -> C) -> ((B or (A -> B)) -> D)))
theorem-size     33
proof            (modus-ponens tm-114 tm-740 ((A (or (and (-> (-> Am Bm) (-> C D)) Dm) (-> (-> Am Bm) (-> C D)))) (B (or Bm (-> Am Bm))) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61537.        (((((A -> B) -> (C -> D)) and E) or ((A -> B) -> (C -> D))) -> (((B or (A -> B)) -> C) -> ((B or (A -> B)) -> D))), M:tm-114, m:tm-740, u:((A (or (and (-> (-> Am Bm) (-> C D)) Dm) (-> (-> Am Bm) (-> C D)))) (B (or Bm (-> Am Bm))) (Cm (-> C D)))
================================================================
tm-name          tm-61538
in-theory        61538
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> G) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-113 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61538.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E -> F) -> G) and H) or ((E -> F) -> G)) -> ((F or (E -> F)) -> G))), M:tm-113, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61539
in-theory        61539
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     41
proof            (modus-ponens tm-105 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61539.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-105, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61540
in-theory        61540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-95 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61540.        (((A -> B) -> (A -> A)) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E))), M:tm-95, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61541
in-theory        61541
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (E -> ((B or (A -> B)) -> C)))
theorem-size     23
proof            (modus-ponens tm-84 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61541.        (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (E -> ((B or (A -> B)) -> C))), M:tm-84, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61542
in-theory        61542
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-83 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61542.        ((A -> (B -> (C -> B))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-83, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61543
in-theory        61543
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B -> C) -> D) and E) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-76 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61543.        (((not (not A)) -> A) and (((((B -> C) -> D) and E) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D))), M:tm-76, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61544
in-theory        61544
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A -> B) -> C) and D) or ((A -> B) -> C)))) or ((((A -> B) -> C) and D) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C))
theorem-size     37
proof            (modus-ponens tm-73 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-8 tm-10 tm-3 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61544.        (((not (not ((((A -> B) -> C) and D) or ((A -> B) -> C)))) or ((((A -> B) -> C) and D) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C)), M:tm-73, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61545
in-theory        61545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-69 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61545.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E))), M:tm-69, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61546
in-theory        61546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-54 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61546.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-54, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61547
in-theory        61547
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((((A -> B) -> C) and D) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C))
theorem-size     27
proof            (modus-ponens tm-50 tm-740 ((A (and (-> (-> Am Bm) Cm) Dm)) (B (-> (-> Am Bm) Cm)) (C (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-8 tm-7 tm-3 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61547.        ((((A -> B) -> C) or ((((A -> B) -> C) and D) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C)), M:tm-50, m:tm-740, u:((A (and (-> (-> Am Bm) Cm) Dm)) (B (-> (-> Am Bm) Cm)) (C (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61548
in-theory        61548
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) and D) or ((((A -> B) -> C) and D) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C))
theorem-size     29
proof            (modus-ponens tm-49 tm-740 ((A (and (-> (-> Am Bm) Cm) Dm)) (B (-> (-> Am Bm) Cm)) (C (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-8 tm-6 tm-3 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61548.        (((((A -> B) -> C) and D) or ((((A -> B) -> C) and D) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C)), M:tm-49, m:tm-740, u:((A (and (-> (-> Am Bm) Cm) Dm)) (B (-> (-> Am Bm) Cm)) (C (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61549
in-theory        61549
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((((B -> C) -> D) and E) or ((B -> C) -> D))) or ((((B -> C) -> D) and E) or ((B -> C) -> D))) -> ((C or (B -> C)) -> D))
theorem-size     37
proof            (modus-ponens tm-47 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-8 tm-4 tm-3 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61549.        (((A and ((((B -> C) -> D) and E) or ((B -> C) -> D))) or ((((B -> C) -> D) and E) or ((B -> C) -> D))) -> ((C or (B -> C)) -> D)), M:tm-47, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61550
in-theory        61550
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> C) and D) or ((A -> B) -> C)) and E) or ((((A -> B) -> C) and D) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C))
theorem-size     37
proof            (modus-ponens tm-46 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61550.        (((((((A -> B) -> C) and D) or ((A -> B) -> C)) and E) or ((((A -> B) -> C) and D) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61551
in-theory        61551
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-42 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61551.        ((A -> (B or A)) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61552
in-theory        61552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-32 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61552.        ((A -> (A or B)) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61553
in-theory        61553
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (((((A -> B) -> C) and D) or ((A -> B) -> C)) and ((B or (A -> B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-24 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61553.        (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (((((A -> B) -> C) and D) or ((A -> B) -> C)) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61554
in-theory        61554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-23 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61554.        ((A -> (B -> (A and B))) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61555
in-theory        61555
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-22 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61555.        (((A and B) -> B) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61556
in-theory        61556
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-21 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61556.        (((A and B) -> A) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61557
in-theory        61557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-20 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61557.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61558
in-theory        61558
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-19 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61558.        ((A -> (B -> A)) and (((((C -> D) -> E) and F) or ((C -> D) -> E)) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61559
in-theory        61559
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((((A -> B) -> C) and D) or ((A -> B) -> C)))
theorem-size     27
proof            (modus-ponens tm-12 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61559.        (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((((A -> B) -> C) and D) or ((A -> B) -> C))), M:tm-12, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61560
in-theory        61560
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (not ((B or (A -> B)) -> C))) -> (not ((((A -> B) -> C) and D) or ((A -> B) -> C))))
theorem-size     37
proof            (modus-ponens tm-9 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-9 tm-8 tm-3 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61560.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (not ((B or (A -> B)) -> C))) -> (not ((((A -> B) -> C) and D) or ((A -> B) -> C)))), M:tm-9, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61561
in-theory        61561
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) -> C) -> D) -> ((((((B -> A) -> C) and E) or ((B -> A) -> C)) or ((A or (B -> A)) -> C)) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61561.        ((((A or (B -> A)) -> C) -> D) -> ((((((B -> A) -> C) and E) or ((B -> A) -> C)) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-61562
in-theory        61562
times-derived    1
----------------------------------------------------------------
theorem          (A or (((((B -> C) -> D) and E) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-7 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-7 tm-8 tm-3 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61562.        (A or (((((B -> C) -> D) and E) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61563
in-theory        61563
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-6 tm-8 tm-3 tm-1)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61563.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) or E), M:tm-6, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61564
in-theory        61564
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) -> D) and E) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61564.        (A -> ((((((B -> C) -> D) and E) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61565
in-theory        61565
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (B or (A -> B))) -> (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> C))
theorem-size     35
proof            (modus-ponens tm-2 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (or Bm (-> Am Bm))) (C Cm)))
axioms-used      (tm-2 tm-8 tm-3 tm-1)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61565.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (B or (A -> B))) -> (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> C)), M:tm-2, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (or Bm (-> Am Bm))) (C Cm))
================================================================
tm-name          tm-61566
in-theory        61566
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) -> D) and E) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D)))
theorem-size     23
proof            (modus-ponens tm-1 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-61566.        (A -> (((((B -> C) -> D) and E) or ((B -> C) -> D)) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-61567
in-theory        61567
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((((E -> F) -> (E -> G)) -> H) and I) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     63
proof            (modus-ponens tm-708 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       267
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61567.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((((E -> F) -> (E -> G)) -> H) and I) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-708, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61568
in-theory        61568
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     51
proof            (modus-ponens tm-665 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3 tm-2)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61568.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-665, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61569
in-theory        61569
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     39
proof            (modus-ponens tm-623 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61569.        ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (F or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-623, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61570
in-theory        61570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-622 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61570.        ((A -> (B -> (C or B))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-622, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61571
in-theory        61571
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (F -> (G or F)))
theorem-size     43
proof            (modus-ponens tm-609 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61571.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (F -> (G or F))), M:tm-609, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61572
in-theory        61572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     47
proof            (modus-ponens tm-605 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61572.        ((A -> ((B -> (C or B)) and A)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-605, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61573
in-theory        61573
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((F -> (G or F)) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     81
proof            (modus-ponens tm-595 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       259
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61573.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((F -> (G or F)) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-595, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61574
in-theory        61574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-550 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61574.        (((A -> (B or A)) or C) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-550, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61575
in-theory        61575
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-540 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61575.        ((A or (B -> (C or B))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-540, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61576
in-theory        61576
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-530 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61576.        ((A or (B -> (B or C))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-530, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61577
in-theory        61577
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     47
proof            (modus-ponens tm-520 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61577.        ((A or (B -> (C -> (B and C)))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-520, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61578
in-theory        61578
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-510 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61578.        ((A or ((B and C) -> C)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-510, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61579
in-theory        61579
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-500 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61579.        ((A or ((B and C) -> B)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-500, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61580
in-theory        61580
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((((E -> F) -> (E -> G)) -> H) and I) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     53
proof            (modus-ponens tm-490 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61580.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((((E -> F) -> (E -> G)) -> H) and I) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-490, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61581
in-theory        61581
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-480 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61581.        ((A or (B -> (C -> B))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-480, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61582
in-theory        61582
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) or F))
theorem-size     39
proof            (modus-ponens tm-470 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61582.        ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) or F)), M:tm-470, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61583
in-theory        61583
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-469 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61583.        ((A -> (B -> (B or C))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-469, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61584
in-theory        61584
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (F -> (F or G)))
theorem-size     43
proof            (modus-ponens tm-456 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61584.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (F -> (F or G))), M:tm-456, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61585
in-theory        61585
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     47
proof            (modus-ponens tm-453 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61585.        ((A -> ((B -> (B or C)) and A)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-453, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61586
in-theory        61586
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((F -> (F or G)) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     81
proof            (modus-ponens tm-443 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       259
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61586.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((F -> (F or G)) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-443, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61587
in-theory        61587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-409 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61587.        (((A -> (A or B)) or C) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-409, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61588
in-theory        61588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     47
proof            (modus-ponens tm-400 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61588.        (((A -> (B -> (A and B))) or C) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-400, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61589
in-theory        61589
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-391 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61589.        ((((A and B) -> B) or C) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-391, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61590
in-theory        61590
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-382 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61590.        ((((A and B) -> A) or C) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-382, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61591
in-theory        61591
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((((E -> F) -> (E -> G)) -> H) and I) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     53
proof            (modus-ponens tm-373 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61591.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((((E -> F) -> (E -> G)) -> H) and I) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-373, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61592
in-theory        61592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-364 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61592.        (((A -> (B -> A)) or C) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-364, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61593
in-theory        61593
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and F)))
theorem-size     41
proof            (modus-ponens tm-355 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61593.        ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (F -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and F))), M:tm-355, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61594
in-theory        61594
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     47
proof            (modus-ponens tm-354 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61594.        ((A -> (B -> (C -> (B and C)))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-354, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61595
in-theory        61595
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (F -> (G -> (F and G))))
theorem-size     45
proof            (modus-ponens tm-341 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       223
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61595.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61596
in-theory        61596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     47
proof            (modus-ponens tm-338 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61596.        (((A -> B) -> (A -> (A and B))) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-338, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61597
in-theory        61597
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     97
proof            (modus-ponens tm-328 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       285
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61597.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-328, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61598
in-theory        61598
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((F -> (G -> (F and G))) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     83
proof            (modus-ponens tm-327 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       267
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61598.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((F -> (G -> (F and G))) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-327, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61599
in-theory        61599
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((F and G) -> G) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     81
proof            (modus-ponens tm-326 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       259
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61599.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((F and G) -> G) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-326, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61600
in-theory        61600
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((F and G) -> F) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     81
proof            (modus-ponens tm-325 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       259
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61600.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((F and G) -> F) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-325, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61601
in-theory        61601
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     89
proof            (modus-ponens tm-324 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       291
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61601.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-324, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61602
in-theory        61602
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((F -> (G -> F)) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     81
proof            (modus-ponens tm-323 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       259
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61602.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((F -> (G -> F)) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-323, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61603
in-theory        61603
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((F and G) -> G))
theorem-size     43
proof            (modus-ponens tm-322 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61603.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((F and G) -> G)), M:tm-322, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61604
in-theory        61604
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((F and G) -> F))
theorem-size     43
proof            (modus-ponens tm-320 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61604.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((F and G) -> F)), M:tm-320, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61605
in-theory        61605
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     51
proof            (modus-ponens tm-318 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       247
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61605.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61606
in-theory        61606
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D))))
theorem-size     81
proof            (modus-ponens tm-316 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       263
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61606.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)))), M:tm-316, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61607
in-theory        61607
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (F -> (G -> F)))
theorem-size     43
proof            (modus-ponens tm-315 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61607.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (F -> (G -> F))), M:tm-315, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61608
in-theory        61608
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)))))
theorem-size     99
proof            (modus-ponens tm-313 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       271
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61608.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D))))), M:tm-313, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61609
in-theory        61609
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> F) -> (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> F)))
theorem-size     95
proof            (modus-ponens tm-312 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       271
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61609.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> F) -> (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> F))), M:tm-312, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61610
in-theory        61610
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (F or ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     77
proof            (modus-ponens tm-311 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61610.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (F or ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-311, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61611
in-theory        61611
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or F))
theorem-size     77
proof            (modus-ponens tm-310 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61611.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or F)), M:tm-310, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61612
in-theory        61612
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (F -> (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and F)))
theorem-size     79
proof            (modus-ponens tm-309 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61612.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (F -> (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and F))), M:tm-309, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61613
in-theory        61613
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> D)))
theorem-size     97
proof            (modus-ponens tm-306 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       275
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61613.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> D))), M:tm-306, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
================================================================
tm-name          tm-61614
in-theory        61614
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (F -> ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     77
proof            (modus-ponens tm-305 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       235
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61614.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (F -> ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-305, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61615
in-theory        61615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     49
proof            (modus-ponens tm-303 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61615.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-303, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61616
in-theory        61616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     47
proof            (modus-ponens tm-270 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61616.        ((A -> (((B and C) -> C) and A)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-270, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61617
in-theory        61617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     47
proof            (modus-ponens tm-239 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61617.        ((A -> (((B and C) -> B) and A)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-239, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61618
in-theory        61618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((((E -> F) -> (E -> G)) -> H) and I) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     55
proof            (modus-ponens tm-210 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61618.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((((E -> F) -> (E -> G)) -> H) and I) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-210, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61619
in-theory        61619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     47
proof            (modus-ponens tm-183 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61619.        ((A -> ((B -> (C -> B)) and A)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-183, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61620
in-theory        61620
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-157 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61620.        ((A -> ((B and C) -> C)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-157, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61621
in-theory        61621
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     53
proof            (modus-ponens tm-147 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61621.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-147, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61622
in-theory        61622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-134 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61622.        ((A -> ((B and C) -> B)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-134, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61623
in-theory        61623
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     53
proof            (modus-ponens tm-125 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61623.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-125, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61624
in-theory        61624
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> (D -> E)) and F) or (((A -> B) -> (A -> C)) -> (D -> E))) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E)))
theorem-size     57
proof            (modus-ponens tm-114 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> C D)) Em) (-> (-> (-> Am Bm) (-> Am Cm)) (-> C D)))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61624.        ((((((A -> B) -> (A -> C)) -> (D -> E)) and F) or (((A -> B) -> (A -> C)) -> (D -> E))) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> E))), M:tm-114, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) (-> C D)) Em) (-> (-> (-> Am Bm) (-> Am Cm)) (-> C D)))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (Dm (-> C D)))
================================================================
tm-name          tm-61625
in-theory        61625
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((((E -> F) -> (E -> G)) -> H) and I) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))
theorem-size     53
proof            (modus-ponens tm-113 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61625.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((((E -> F) -> (E -> G)) -> H) and I) or (((E -> F) -> (E -> G)) -> H)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))), M:tm-113, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61626
in-theory        61626
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     57
proof            (modus-ponens tm-105 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61626.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-105, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61627
in-theory        61627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     45
proof            (modus-ponens tm-95 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61627.        (((A -> B) -> (A -> A)) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-95, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61628
in-theory        61628
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     39
proof            (modus-ponens tm-84 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61628.        ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (F -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-84, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61629
in-theory        61629
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-83 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61629.        ((A -> (B -> (C -> B))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-83, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61630
in-theory        61630
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((((B -> C) -> (B -> D)) -> E) and F) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     43
proof            (modus-ponens tm-76 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61630.        (((not (not A)) -> A) and ((((((B -> C) -> (B -> D)) -> E) and F) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-76, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61631
in-theory        61631
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)))) or (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     61
proof            (modus-ponens tm-73 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-10 tm-3 tm-2)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61631.        (((not (not (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)))) or (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-73, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61632
in-theory        61632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     49
proof            (modus-ponens tm-69 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3 tm-2)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61632.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-69, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61633
in-theory        61633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     51
proof            (modus-ponens tm-54 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61633.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-54, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61634
in-theory        61634
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     47
proof            (modus-ponens tm-50 tm-741 ((A (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-7 tm-3 tm-2)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61634.        (((((A -> B) -> (A -> C)) -> D) or (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-50, m:tm-741, u:((A (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61635
in-theory        61635
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) and E) or (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     49
proof            (modus-ponens tm-49 tm-741 ((A (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-6 tm-3 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61635.        ((((((A -> B) -> (A -> C)) -> D) and E) or (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-49, m:tm-741, u:((A (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61636
in-theory        61636
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((((B -> C) -> (B -> D)) -> E) and F) or (((B -> C) -> (B -> D)) -> E))) or (((((B -> C) -> (B -> D)) -> E) and F) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))
theorem-size     61
proof            (modus-ponens tm-47 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-4 tm-3 tm-2)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61636.        (((A and (((((B -> C) -> (B -> D)) -> E) and F) or (((B -> C) -> (B -> D)) -> E))) or (((((B -> C) -> (B -> D)) -> E) and F) or (((B -> C) -> (B -> D)) -> E))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)), M:tm-47, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61637
in-theory        61637
times-derived    1
----------------------------------------------------------------
theorem          ((((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) and F) or (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))
theorem-size     61
proof            (modus-ponens tm-46 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       207
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61637.        ((((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) and F) or (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61638
in-theory        61638
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     43
proof            (modus-ponens tm-42 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61638.        ((A -> (B or A)) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61639
in-theory        61639
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     43
proof            (modus-ponens tm-32 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61639.        ((A -> (A or B)) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61640
in-theory        61640
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     59
proof            (modus-ponens tm-24 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61640.        ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61641
in-theory        61641
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     45
proof            (modus-ponens tm-23 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61641.        ((A -> (B -> (A and B))) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61642
in-theory        61642
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     43
proof            (modus-ponens tm-22 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61642.        (((A and B) -> B) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61643
in-theory        61643
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     43
proof            (modus-ponens tm-21 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61643.        (((A and B) -> A) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61644
in-theory        61644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     51
proof            (modus-ponens tm-20 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       205
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61644.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61645
in-theory        61645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F)))
theorem-size     43
proof            (modus-ponens tm-19 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61645.        ((A -> (B -> A)) and ((((((C -> D) -> (C -> E)) -> F) and G) or (((C -> D) -> (C -> E)) -> F)) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61646
in-theory        61646
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)))
theorem-size     43
proof            (modus-ponens tm-12 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61646.        ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D))), M:tm-12, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61647
in-theory        61647
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D))))
theorem-size     61
proof            (modus-ponens tm-9 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-9 tm-8 tm-3 tm-2)
proof-size       189
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61647.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)))), M:tm-9, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61648
in-theory        61648
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((((A -> B) -> (A -> C)) -> D) and F) or (((A -> B) -> (A -> C)) -> D)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))
theorem-size     57
proof            (modus-ponens tm-8 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       187
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61648.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((((A -> B) -> (A -> C)) -> D) and F) or (((A -> B) -> (A -> C)) -> D)) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-61649
in-theory        61649
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((((B -> C) -> (B -> D)) -> E) and F) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     39
proof            (modus-ponens tm-7 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-7 tm-8 tm-3 tm-2)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61649.        (A or ((((((B -> C) -> (B -> D)) -> E) and F) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61650
in-theory        61650
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or F)
theorem-size     39
proof            (modus-ponens tm-6 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-6 tm-8 tm-3 tm-2)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61650.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or F), M:tm-6, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61651
in-theory        61651
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((((B -> C) -> (B -> D)) -> E) and F) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))
theorem-size     41
proof            (modus-ponens tm-5 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61651.        (A -> (((((((B -> C) -> (B -> D)) -> E) and F) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61652
in-theory        61652
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> D))
theorem-size     59
proof            (modus-ponens tm-2 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       189
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61652.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> D)), M:tm-2, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
================================================================
tm-name          tm-61653
in-theory        61653
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((((B -> C) -> (B -> D)) -> E) and F) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     39
proof            (modus-ponens tm-1 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-1 tm-8 tm-3 tm-2)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-61653.        (A -> ((((((B -> C) -> (B -> D)) -> E) and F) or (((B -> C) -> (B -> D)) -> E)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-61654
in-theory        61654
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F)))
theorem-size     43
proof            (modus-ponens tm-708 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61654.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F))), M:tm-708, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61655
in-theory        61655
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     31
proof            (modus-ponens tm-665 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61655.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-665, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61656
in-theory        61656
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D or (((A and E) or A) -> B)))
theorem-size     19
proof            (modus-ponens tm-623 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61656.        ((((A -> B) and C) or (A -> B)) -> (D or (((A and E) or A) -> B))), M:tm-623, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61657
in-theory        61657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-622 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61657.        ((A -> (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-622, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61658
in-theory        61658
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (E -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-609 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61658.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (E -> (F or E))), M:tm-609, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61659
in-theory        61659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-605 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61659.        ((A -> ((B -> (C or B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-605, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61660
in-theory        61660
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((E -> (F or E)) and ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B))))
theorem-size     41
proof            (modus-ponens tm-595 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61660.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((E -> (F or E)) and ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)))), M:tm-595, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61661
in-theory        61661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-550 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61661.        (((A -> (B or A)) or C) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-550, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61662
in-theory        61662
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-540 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61662.        ((A or (B -> (C or B))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-540, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61663
in-theory        61663
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-530 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61663.        ((A or (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-530, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61664
in-theory        61664
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-520 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61664.        ((A or (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-520, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61665
in-theory        61665
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-510 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61665.        ((A or ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-510, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61666
in-theory        61666
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-500 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61666.        ((A or ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-500, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61667
in-theory        61667
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F)))
theorem-size     33
proof            (modus-ponens tm-490 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61667.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F))), M:tm-490, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61668
in-theory        61668
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-480 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61668.        ((A or (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-480, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61669
in-theory        61669
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((((A and D) or A) -> B) or E))
theorem-size     19
proof            (modus-ponens tm-470 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61669.        ((((A -> B) and C) or (A -> B)) -> ((((A and D) or A) -> B) or E)), M:tm-470, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61670
in-theory        61670
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-469 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61670.        ((A -> (B -> (B or C))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-469, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61671
in-theory        61671
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (E -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-456 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61671.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (E -> (E or F))), M:tm-456, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61672
in-theory        61672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-453 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61672.        ((A -> ((B -> (B or C)) and A)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-453, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61673
in-theory        61673
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((E -> (E or F)) and ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B))))
theorem-size     41
proof            (modus-ponens tm-443 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61673.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((E -> (E or F)) and ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)))), M:tm-443, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61674
in-theory        61674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-409 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61674.        (((A -> (A or B)) or C) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-409, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61675
in-theory        61675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-400 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61675.        (((A -> (B -> (A and B))) or C) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-400, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61676
in-theory        61676
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-391 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61676.        ((((A and B) -> B) or C) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-391, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61677
in-theory        61677
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-382 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61677.        ((((A and B) -> A) or C) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-382, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61678
in-theory        61678
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F)))
theorem-size     33
proof            (modus-ponens tm-373 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61678.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F))), M:tm-373, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61679
in-theory        61679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-364 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61679.        (((A -> (B -> A)) or C) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-364, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61680
in-theory        61680
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D -> ((((A and E) or A) -> B) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61680.        ((((A -> B) and C) or (A -> B)) -> (D -> ((((A and E) or A) -> B) and D))), M:tm-355, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61681
in-theory        61681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-354 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61681.        ((A -> (B -> (C -> (B and C)))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-354, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61682
in-theory        61682
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (E -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-341 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61682.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61683
in-theory        61683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D)))
theorem-size     27
proof            (modus-ponens tm-338 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61683.        (((A -> B) -> (A -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D))), M:tm-338, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61684
in-theory        61684
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (((A and D) or A) -> B))))
theorem-size     45
proof            (modus-ponens tm-328 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61684.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (((A and D) or A) -> B)))), M:tm-328, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61685
in-theory        61685
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((E -> (F -> (E and F))) and ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B))))
theorem-size     43
proof            (modus-ponens tm-327 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61685.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((E -> (F -> (E and F))) and ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)))), M:tm-327, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61686
in-theory        61686
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((E and F) -> F) and ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B))))
theorem-size     41
proof            (modus-ponens tm-326 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61686.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((E and F) -> F) and ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)))), M:tm-326, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61687
in-theory        61687
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((E and F) -> E) and ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B))))
theorem-size     41
proof            (modus-ponens tm-325 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61687.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((E and F) -> E) and ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)))), M:tm-325, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61688
in-theory        61688
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B))))
theorem-size     49
proof            (modus-ponens tm-324 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61688.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)))), M:tm-324, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61689
in-theory        61689
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((E -> (F -> E)) and ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B))))
theorem-size     41
proof            (modus-ponens tm-323 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61689.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((E -> (F -> E)) and ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)))), M:tm-323, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61690
in-theory        61690
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((E and F) -> F))
theorem-size     23
proof            (modus-ponens tm-322 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61690.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((E and F) -> F)), M:tm-322, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61691
in-theory        61691
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((E and F) -> E))
theorem-size     23
proof            (modus-ponens tm-320 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61691.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((E and F) -> E)), M:tm-320, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61692
in-theory        61692
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-318 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61692.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61693
in-theory        61693
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((((A -> B) and C) or (A -> B)) -> (((A -> B) and C) or (A -> B))))
theorem-size     37
proof            (modus-ponens tm-316 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61693.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((((A -> B) and C) or (A -> B)) -> (((A -> B) and C) or (A -> B)))), M:tm-316, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61694
in-theory        61694
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (E -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-315 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61694.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (E -> (F -> E))), M:tm-315, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61695
in-theory        61695
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((((A -> B) and C) or (A -> B)) -> (not (((A and D) or A) -> B))) -> (not (((A -> B) and C) or (A -> B)))))
theorem-size     47
proof            (modus-ponens tm-313 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61695.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((((A -> B) and C) or (A -> B)) -> (not (((A and D) or A) -> B))) -> (not (((A -> B) and C) or (A -> B))))), M:tm-313, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61696
in-theory        61696
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((((A and D) or A) -> B) -> E) -> (((((A -> B) and C) or (A -> B)) or (((A and D) or A) -> B)) -> E)))
theorem-size     47
proof            (modus-ponens tm-312 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61696.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((((A and D) or A) -> B) -> E) -> (((((A -> B) and C) or (A -> B)) or (((A and D) or A) -> B)) -> E))), M:tm-312, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61697
in-theory        61697
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (E or ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B))))
theorem-size     37
proof            (modus-ponens tm-311 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61697.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (E or ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)))), M:tm-311, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61698
in-theory        61698
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) or E))
theorem-size     37
proof            (modus-ponens tm-310 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61698.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) or E)), M:tm-310, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61699
in-theory        61699
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (E -> (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and E)))
theorem-size     39
proof            (modus-ponens tm-309 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61699.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (E -> (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and E))), M:tm-309, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61700
in-theory        61700
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((((A -> B) and C) or (A -> B)) -> ((A and D) or A)) -> ((((A -> B) and C) or (A -> B)) -> B)))
theorem-size     45
proof            (modus-ponens tm-306 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (or (and Am Dm) Am)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61700.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (((((A -> B) and C) or (A -> B)) -> ((A and D) or A)) -> ((((A -> B) and C) or (A -> B)) -> B))), M:tm-306, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (or (and Am Dm) Am)) (C Bm))
================================================================
tm-name          tm-61701
in-theory        61701
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (E -> ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B))))
theorem-size     37
proof            (modus-ponens tm-305 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61701.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and (E -> ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)))), M:tm-305, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61702
in-theory        61702
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-303 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61702.        ((A -> ((B -> (C -> (B and C))) and A)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-303, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61703
in-theory        61703
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-270 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61703.        ((A -> (((B and C) -> C) and A)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-270, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61704
in-theory        61704
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-239 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61704.        ((A -> (((B and C) -> B) and A)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-239, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61705
in-theory        61705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F)))
theorem-size     35
proof            (modus-ponens tm-210 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61705.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F))), M:tm-210, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61706
in-theory        61706
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-183 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61706.        ((A -> ((B -> (C -> B)) and A)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-183, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61707
in-theory        61707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-157 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61707.        ((A -> ((B and C) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-157, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61708
in-theory        61708
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     33
proof            (modus-ponens tm-147 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61708.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-147, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61709
in-theory        61709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-134 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61709.        ((A -> ((B and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-134, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61710
in-theory        61710
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     33
proof            (modus-ponens tm-125 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61710.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-125, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61711
in-theory        61711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((((A and E) or A) -> B) -> (((A and E) or A) -> C)))
theorem-size     29
proof            (modus-ponens tm-114 tm-742 ((A (or (and (-> Am (-> C D)) Cm) (-> Am (-> C D)))) (B (or (and Am Dm) Am)) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61711.        ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((((A and E) or A) -> B) -> (((A and E) or A) -> C))), M:tm-114, m:tm-742, u:((A (or (and (-> Am (-> C D)) Cm) (-> Am (-> C D)))) (B (or (and Am Dm) Am)) (Bm (-> C D)))
================================================================
tm-name          tm-61712
in-theory        61712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F)))
theorem-size     33
proof            (modus-ponens tm-113 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61712.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((((E -> F) and G) or (E -> F)) -> (((E and H) or E) -> F))), M:tm-113, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61713
in-theory        61713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     37
proof            (modus-ponens tm-105 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61713.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-105, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61714
in-theory        61714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D)))
theorem-size     25
proof            (modus-ponens tm-95 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61714.        (((A -> B) -> (A -> A)) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D))), M:tm-95, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61715
in-theory        61715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (D -> (((A and E) or A) -> B)))
theorem-size     19
proof            (modus-ponens tm-84 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61715.        ((((A -> B) and C) or (A -> B)) -> (D -> (((A and E) or A) -> B))), M:tm-84, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61716
in-theory        61716
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-83 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61716.        ((A -> (B -> (C -> B))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-83, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61717
in-theory        61717
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((B -> C) and D) or (B -> C)) -> (((B and E) or B) -> C)))
theorem-size     23
proof            (modus-ponens tm-76 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61717.        (((not (not A)) -> A) and ((((B -> C) and D) or (B -> C)) -> (((B and E) or B) -> C))), M:tm-76, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61718
in-theory        61718
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (((A -> B) and C) or (A -> B)))) or (((A -> B) and C) or (A -> B))) -> (((A and D) or A) -> B))
theorem-size     29
proof            (modus-ponens tm-73 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-8 tm-10 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61718.        (((not (not (((A -> B) and C) or (A -> B)))) or (((A -> B) and C) or (A -> B))) -> (((A and D) or A) -> B)), M:tm-73, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61719
in-theory        61719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-69 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61719.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D))), M:tm-69, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61720
in-theory        61720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     31
proof            (modus-ponens tm-54 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61720.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-54, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61721
in-theory        61721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A -> B) and C) or (A -> B))) -> (((A and D) or A) -> B))
theorem-size     21
proof            (modus-ponens tm-50 tm-742 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-8 tm-7 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61721.        (((A -> B) or (((A -> B) and C) or (A -> B))) -> (((A and D) or A) -> B)), M:tm-50, m:tm-742, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61722
in-theory        61722
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (((A and D) or A) -> B))
theorem-size     23
proof            (modus-ponens tm-49 tm-742 ((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-8 tm-6 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61722.        ((((A -> B) and C) or (((A -> B) and C) or (A -> B))) -> (((A and D) or A) -> B)), M:tm-49, m:tm-742, u:((A (and (-> Am Bm) Cm)) (B (-> Am Bm)) (C (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61723
in-theory        61723
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) or (B -> C))) or (((B -> C) and D) or (B -> C))) -> (((B and E) or B) -> C))
theorem-size     29
proof            (modus-ponens tm-47 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-8 tm-4 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61723.        (((A and (((B -> C) and D) or (B -> C))) or (((B -> C) and D) or (B -> C))) -> (((B and E) or B) -> C)), M:tm-47, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61724
in-theory        61724
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> (((A and E) or A) -> B))
theorem-size     29
proof            (modus-ponens tm-46 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61724.        ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> (((A and E) or A) -> B)), M:tm-46, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61725
in-theory        61725
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-42 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61725.        ((A -> (B or A)) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D))), M:tm-42, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61726
in-theory        61726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-32 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61726.        ((A -> (A or B)) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D))), M:tm-32, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61727
in-theory        61727
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (((A and D) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-24 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61727.        ((((A -> B) and C) or (A -> B)) -> ((((A -> B) and C) or (A -> B)) and (((A and D) or A) -> B))), M:tm-24, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61728
in-theory        61728
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D)))
theorem-size     25
proof            (modus-ponens tm-23 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61728.        ((A -> (B -> (A and B))) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D))), M:tm-23, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61729
in-theory        61729
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-22 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61729.        (((A and B) -> B) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D))), M:tm-22, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61730
in-theory        61730
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-21 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61730.        (((A and B) -> A) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D))), M:tm-21, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61731
in-theory        61731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     31
proof            (modus-ponens tm-20 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61731.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-20, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61732
in-theory        61732
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-19 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61732.        ((A -> (B -> A)) and ((((C -> D) and E) or (C -> D)) -> (((C and F) or C) -> D))), M:tm-19, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61733
in-theory        61733
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (not (((A and D) or A) -> B))) -> (not (((A -> B) and C) or (A -> B))))
theorem-size     29
proof            (modus-ponens tm-9 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-9 tm-8 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61733.        (((((A -> B) and C) or (A -> B)) -> (not (((A and D) or A) -> B))) -> (not (((A -> B) and C) or (A -> B)))), M:tm-9, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61734
in-theory        61734
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> D) -> (((((A -> C) and E) or (A -> C)) or (((A and B) or A) -> C)) -> D))
theorem-size     29
proof            (modus-ponens tm-8 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-8 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61734.        (((((A and B) or A) -> C) -> D) -> (((((A -> C) and E) or (A -> C)) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-61735
in-theory        61735
times-derived    1
----------------------------------------------------------------
theorem          (A or ((((B -> C) and D) or (B -> C)) -> (((B and E) or B) -> C)))
theorem-size     19
proof            (modus-ponens tm-7 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-7 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61735.        (A or ((((B -> C) and D) or (B -> C)) -> (((B and E) or B) -> C))), M:tm-7, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61736
in-theory        61736
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) or E)
theorem-size     19
proof            (modus-ponens tm-6 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-6 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61736.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) or E), M:tm-6, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61737
in-theory        61737
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((((B -> C) and D) or (B -> C)) -> (((B and E) or B) -> C)) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61737.        (A -> (((((B -> C) and D) or (B -> C)) -> (((B and E) or B) -> C)) and A)), M:tm-5, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61738
in-theory        61738
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A and D) or A)) -> ((((A -> B) and C) or (A -> B)) -> B))
theorem-size     27
proof            (modus-ponens tm-2 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (or (and Am Dm) Am)) (C Bm)))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61738.        (((((A -> B) and C) or (A -> B)) -> ((A and D) or A)) -> ((((A -> B) and C) or (A -> B)) -> B)), M:tm-2, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (or (and Am Dm) Am)) (C Bm))
================================================================
tm-name          tm-61739
in-theory        61739
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) and D) or (B -> C)) -> (((B and E) or B) -> C)))
theorem-size     19
proof            (modus-ponens tm-1 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-61739.        (A -> ((((B -> C) and D) or (B -> C)) -> (((B and E) or B) -> C))), M:tm-1, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-61740
in-theory        61740
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (A -> (A -> B)))
theorem-size     15
proof            (modus-ponens tm-743 tm-34 ((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B))))
axioms-used      (tm-8 tm-2 tm-3 tm-7 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-61740.        ((((A -> B) and C) or (A -> B)) -> (A -> (A -> B))), M:tm-743, m:tm-34, u:((Am (-> Cm (-> B (-> Cm B)))) (Bm (-> Cm B)) (A Cm) (C (-> Cm B)))
================================================================
tm-name          tm-61741
in-theory        61741
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (A -> ((A -> B) and A)))
theorem-size     17
proof            (modus-ponens tm-743 tm-38 ((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm))))
axioms-used      (tm-8 tm-2 tm-3 tm-7 tm-5)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-61741.        ((((A -> B) and C) or (A -> B)) -> (A -> ((A -> B) and A))), M:tm-743, m:tm-38, u:((Am (-> Cm (-> B (and (-> Cm B) Cm)))) (Bm (-> Cm B)) (A Cm) (C (and (-> Cm B) Cm)))
================================================================
tm-name          tm-61742
in-theory        61742
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> A) and C) or ((A -> B) -> A)) -> ((A -> B) -> (((A -> B) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-743 tm-52 ((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm))))
axioms-used      (tm-8 tm-2 tm-3 tm-7)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-61742.        (((((A -> B) -> A) and C) or ((A -> B) -> A)) -> ((A -> B) -> (((A -> B) or A) -> B))), M:tm-743, m:tm-52, u:((Am (-> (-> Cm Dm) (-> Cm (-> (or (-> Cm Dm) Cm) Dm)))) (Bm (-> Cm Dm)) (B Cm) (A (-> Cm Dm)) (C (-> (or (-> Cm Dm) Cm) Dm)))
================================================================
tm-name          tm-61743
in-theory        61743
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (A -> (D -> A)))
theorem-size     15
proof            (modus-ponens tm-743 tm-81 ((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm))))
axioms-used      (tm-8 tm-2 tm-3 tm-7 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-61743.        ((((A -> B) and C) or (A -> B)) -> (A -> (D -> A))), M:tm-743, m:tm-81, u:((Am (-> Cm (-> B (-> Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-61744
in-theory        61744
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> D) and E) or ((A -> (B -> C)) -> D)) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     31
proof            (modus-ponens tm-743 tm-111 ((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-8 tm-2 tm-3 tm-7 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-61744.        (((((A -> (B -> C)) -> D) and E) or ((A -> (B -> C)) -> D)) -> ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-743, m:tm-111, u:((Am (-> (-> Cm (-> Dm Em)) (-> B (-> (-> Cm Dm) (-> Cm Em))))) (Bm (-> (-> Cm (-> Dm Em)) B)) (A (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-61745
in-theory        61745
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> C) and D) or ((A and B) -> C)) -> ((A and B) -> A))
theorem-size     19
proof            (modus-ponens tm-743 tm-132 ((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm)))
axioms-used      (tm-8 tm-2 tm-3 tm-7 tm-1)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-61745.        (((((A and B) -> C) and D) or ((A and B) -> C)) -> ((A and B) -> A)), M:tm-743, m:tm-132, u:((Am (-> (and Cm Dm) (-> B Cm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-61746
in-theory        61746
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> C) and D) or ((A and B) -> C)) -> ((A and B) -> B))
theorem-size     19
proof            (modus-ponens tm-743 tm-155 ((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm)))
axioms-used      (tm-8 tm-2 tm-3 tm-7 tm-1 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-61746.        (((((A and B) -> C) and D) or ((A and B) -> C)) -> ((A and B) -> B)), M:tm-743, m:tm-155, u:((Am (-> (and Cm Dm) (-> B Dm))) (Bm (-> (and Cm Dm) B)) (A (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-61747
in-theory        61747
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (A -> (D -> (A and D))))
theorem-size     17
proof            (modus-ponens tm-743 tm-352 ((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-7 tm-1 tm-5)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-61747.        ((((A -> B) and C) or (A -> B)) -> (A -> (D -> (A and D)))), M:tm-743, m:tm-352, u:((Am (-> Cm (-> B (-> Dm (and Cm Dm))))) (Bm (-> Cm B)) (A Cm) (C (-> Dm (and Cm Dm))))
================================================================
tm-name          tm-61748
in-theory        61748
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (A -> (A or D)))
theorem-size     15
proof            (modus-ponens tm-743 tm-467 ((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm))))
axioms-used      (tm-8 tm-2 tm-3 tm-7 tm-1 tm-6)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-61748.        ((((A -> B) and C) or (A -> B)) -> (A -> (A or D))), M:tm-743, m:tm-467, u:((Am (-> Cm (-> B (or Cm Dm)))) (Bm (-> Cm B)) (A Cm) (C (or Cm Dm)))
================================================================
tm-name          tm-61749
in-theory        61749
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> (A -> (D or A)))
theorem-size     15
proof            (modus-ponens tm-743 tm-620 ((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm))))
axioms-used      (tm-8 tm-2 tm-3 tm-7 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-61749.        ((((A -> B) and C) or (A -> B)) -> (A -> (D or A))), M:tm-743, m:tm-620, u:((Am (-> Cm (-> B (or Dm Cm)))) (Bm (-> Cm B)) (A Cm) (C (or Dm Cm)))
================================================================
tm-name          tm-61750
in-theory        61750
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((((E -> F) and H) or (E -> F)) -> (E -> G))))
theorem-size     53
proof            (modus-ponens tm-708 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61750.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((((E -> F) and H) or (E -> F)) -> (E -> G)))), M:tm-708, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61751
in-theory        61751
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-665 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61751.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-665, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61752
in-theory        61752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((((A -> B) and E) or (A -> B)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-623 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61752.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((((A -> B) and E) or (A -> B)) -> (A -> C)))), M:tm-623, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61753
in-theory        61753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-622 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61753.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-622, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61754
in-theory        61754
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (E -> (F or E)))
theorem-size     33
proof            (modus-ponens tm-609 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61754.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (E -> (F or E))), M:tm-609, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61755
in-theory        61755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-605 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61755.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-605, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61756
in-theory        61756
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-595 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61756.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((E -> (F or E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))))), M:tm-595, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61757
in-theory        61757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-550 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61757.        (((A -> (B or A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-550, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61758
in-theory        61758
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-540 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61758.        ((A or (B -> (C or B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-540, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61759
in-theory        61759
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-530 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61759.        ((A or (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-530, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61760
in-theory        61760
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-520 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61760.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-520, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61761
in-theory        61761
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-510 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61761.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-510, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61762
in-theory        61762
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-500 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61762.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-500, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61763
in-theory        61763
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((((E -> F) and H) or (E -> F)) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-490 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61763.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((((E -> F) and H) or (E -> F)) -> (E -> G)))), M:tm-490, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61764
in-theory        61764
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-480 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61764.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-480, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61765
in-theory        61765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((A -> B) and D) or (A -> B)) -> (A -> C)) or E))
theorem-size     29
proof            (modus-ponens tm-470 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61765.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((A -> B) and D) or (A -> B)) -> (A -> C)) or E)), M:tm-470, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61766
in-theory        61766
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-469 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61766.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-469, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61767
in-theory        61767
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (E -> (E or F)))
theorem-size     33
proof            (modus-ponens tm-456 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61767.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (E -> (E or F))), M:tm-456, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61768
in-theory        61768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-453 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61768.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-453, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61769
in-theory        61769
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-443 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61769.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((E -> (E or F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))))), M:tm-443, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61770
in-theory        61770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-409 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61770.        (((A -> (A or B)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-409, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61771
in-theory        61771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-400 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61771.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-400, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61772
in-theory        61772
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-391 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61772.        ((((A and B) -> B) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-391, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61773
in-theory        61773
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-382 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61773.        ((((A and B) -> A) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-382, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61774
in-theory        61774
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((((E -> F) and H) or (E -> F)) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-373 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61774.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((((E -> F) and H) or (E -> F)) -> (E -> G)))), M:tm-373, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61775
in-theory        61775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-364 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61775.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-364, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61776
in-theory        61776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((((A -> B) and E) or (A -> B)) -> (A -> C)) and D)))
theorem-size     31
proof            (modus-ponens tm-355 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61776.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((((A -> B) and E) or (A -> B)) -> (A -> C)) and D))), M:tm-355, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61777
in-theory        61777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-354 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61777.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-354, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61778
in-theory        61778
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (E -> (F -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-341 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61778.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61779
in-theory        61779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E))))
theorem-size     37
proof            (modus-ponens tm-338 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61779.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E)))), M:tm-338, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61780
in-theory        61780
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((((A -> B) and D) or (A -> B)) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-328 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       247
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61780.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((((A -> B) and D) or (A -> B)) -> (A -> C))))), M:tm-328, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61781
in-theory        61781
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))))
theorem-size     63
proof            (modus-ponens tm-327 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       237
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61781.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((E -> (F -> (E and F))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))))), M:tm-327, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61782
in-theory        61782
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-326 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61782.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((E and F) -> F) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))))), M:tm-326, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61783
in-theory        61783
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-325 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61783.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((E and F) -> E) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))))), M:tm-325, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61784
in-theory        61784
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))))
theorem-size     69
proof            (modus-ponens tm-324 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       261
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61784.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))))), M:tm-324, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61785
in-theory        61785
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-323 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61785.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((E -> (F -> E)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))))), M:tm-323, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61786
in-theory        61786
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((E and F) -> F))
theorem-size     33
proof            (modus-ponens tm-322 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61786.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((E and F) -> F)), M:tm-322, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61787
in-theory        61787
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((E and F) -> E))
theorem-size     33
proof            (modus-ponens tm-320 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61787.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((E and F) -> E)), M:tm-320, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61788
in-theory        61788
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-318 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61788.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61789
in-theory        61789
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     55
proof            (modus-ponens tm-316 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61789.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-316, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61790
in-theory        61790
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (E -> (F -> E)))
theorem-size     33
proof            (modus-ponens tm-315 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61790.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (E -> (F -> E))), M:tm-315, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61791
in-theory        61791
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((((A -> B) and D) or (A -> B)) -> (A -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))))
theorem-size     71
proof            (modus-ponens tm-313 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61791.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((((A -> B) and D) or (A -> B)) -> (A -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))), M:tm-313, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61792
in-theory        61792
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((((((A -> B) and D) or (A -> B)) -> (A -> C)) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((((A -> B) and D) or (A -> B)) -> (A -> C))) -> E)))
theorem-size     73
proof            (modus-ponens tm-312 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       239
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61792.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((((((A -> B) and D) or (A -> B)) -> (A -> C)) -> E) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) or ((((A -> B) and D) or (A -> B)) -> (A -> C))) -> E))), M:tm-312, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61793
in-theory        61793
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-311 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61793.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (E or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))))), M:tm-311, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61794
in-theory        61794
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) or E))
theorem-size     57
proof            (modus-ponens tm-310 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61794.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) or E)), M:tm-310, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61795
in-theory        61795
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and E)))
theorem-size     59
proof            (modus-ponens tm-309 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61795.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (E -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and E))), M:tm-309, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61796
in-theory        61796
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) and D) or (A -> B))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> C))))
theorem-size     69
proof            (modus-ponens tm-306 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (and (-> Am Bm) Dm) (-> Am Bm))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61796.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) and D) or (A -> B))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> C)))), M:tm-306, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (and (-> Am Bm) Dm) (-> Am Bm))) (C (-> Am Cm)))
================================================================
tm-name          tm-61797
in-theory        61797
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))))
theorem-size     57
proof            (modus-ponens tm-305 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61797.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (E -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))))), M:tm-305, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61798
in-theory        61798
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-303 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61798.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-303, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61799
in-theory        61799
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-270 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61799.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-270, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61800
in-theory        61800
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-239 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61800.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-239, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61801
in-theory        61801
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((((E -> F) and H) or (E -> F)) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-210 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61801.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((((E -> F) and H) or (E -> F)) -> (E -> G)))), M:tm-210, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61802
in-theory        61802
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-183 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61802.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-183, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61803
in-theory        61803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-157 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61803.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-157, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61804
in-theory        61804
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-147 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61804.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-147, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61805
in-theory        61805
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-134 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61805.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-134, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61806
in-theory        61806
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-125 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61806.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-125, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61807
in-theory        61807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((A -> B) and D) or (A -> B)) -> A) -> ((((A -> B) and D) or (A -> B)) -> C)))
theorem-size     37
proof            (modus-ponens tm-114 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (and (-> Am Bm) Dm) (-> Am Bm))) (C Am) (D Cm)))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61807.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((((A -> B) and D) or (A -> B)) -> A) -> ((((A -> B) and D) or (A -> B)) -> C))), M:tm-114, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (and (-> Am Bm) Dm) (-> Am Bm))) (C Am) (D Cm))
================================================================
tm-name          tm-61808
in-theory        61808
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((((E -> F) and H) or (E -> F)) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-113 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61808.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> ((((E -> F) and H) or (E -> F)) -> (E -> G)))), M:tm-113, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61809
in-theory        61809
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     47
proof            (modus-ponens tm-105 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61809.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-105, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61810
in-theory        61810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-95 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61810.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E)))), M:tm-95, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61811
in-theory        61811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((A -> B) and E) or (A -> B)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-84 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61811.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((((A -> B) and E) or (A -> B)) -> (A -> C)))), M:tm-84, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61812
in-theory        61812
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-83 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61812.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-83, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61813
in-theory        61813
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((((B -> C) and E) or (B -> C)) -> (B -> D))))
theorem-size     33
proof            (modus-ponens tm-76 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-2 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61813.        (((not (not A)) -> A) and (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((((B -> C) and E) or (B -> C)) -> (B -> D)))), M:tm-76, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61814
in-theory        61814
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))
theorem-size     43
proof            (modus-ponens tm-73 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-3)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61814.        (((not (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-73, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61815
in-theory        61815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E))))
theorem-size     39
proof            (modus-ponens tm-69 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-2 tm-3)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61815.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E)))), M:tm-69, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61816
in-theory        61816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-54 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61816.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-54, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61817
in-theory        61817
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))
theorem-size     35
proof            (modus-ponens tm-50 tm-743 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-7 tm-2 tm-3)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61817.        ((((A -> B) -> (A -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-50, m:tm-743, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61818
in-theory        61818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))
theorem-size     33
proof            (modus-ponens tm-49 tm-743 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-6 tm-2 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61818.        (((A -> (B -> C)) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-49, m:tm-743, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))) (C (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61819
in-theory        61819
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((((B -> C) and E) or (B -> C)) -> (B -> D)))
theorem-size     43
proof            (modus-ponens tm-47 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-3)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61819.        (((A and ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) or ((B -> (C -> D)) or ((B -> C) -> (B -> D)))) -> ((((B -> C) and E) or (B -> C)) -> (B -> D))), M:tm-47, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61820
in-theory        61820
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) and E) or (A -> B)) -> (A -> C)))
theorem-size     43
proof            (modus-ponens tm-46 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61820.        (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) and E) or (A -> B)) -> (A -> C))), M:tm-46, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61821
in-theory        61821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-42 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-2 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61821.        ((A -> (B or A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E)))), M:tm-42, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61822
in-theory        61822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-32 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-2 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61822.        ((A -> (A or B)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E)))), M:tm-32, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61823
in-theory        61823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((((A -> B) and D) or (A -> B)) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-24 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61823.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) and ((((A -> B) and D) or (A -> B)) -> (A -> C)))), M:tm-24, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61824
in-theory        61824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E))))
theorem-size     35
proof            (modus-ponens tm-23 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61824.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E)))), M:tm-23, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61825
in-theory        61825
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-22 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61825.        (((A and B) -> B) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E)))), M:tm-22, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61826
in-theory        61826
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-21 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61826.        (((A and B) -> A) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E)))), M:tm-21, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61827
in-theory        61827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-20 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61827.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-20, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61828
in-theory        61828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-19 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-2 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61828.        ((A -> (B -> A)) and (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> ((((C -> D) and F) or (C -> D)) -> (C -> E)))), M:tm-19, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61829
in-theory        61829
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((((A -> B) and D) or (A -> B)) -> (A -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C)))))
theorem-size     43
proof            (modus-ponens tm-9 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-9 tm-8 tm-2 tm-3)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61829.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (not ((((A -> B) and D) or (A -> B)) -> (A -> C)))) -> (not ((A -> (B -> C)) or ((A -> B) -> (A -> C))))), M:tm-9, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61830
in-theory        61830
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) or (A -> B)) -> (A -> D)) -> E) -> ((((A -> (B -> D)) or ((A -> B) -> (A -> D))) or ((((A -> B) and C) or (A -> B)) -> (A -> D))) -> E))
theorem-size     45
proof            (modus-ponens tm-8 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61830.        ((((((A -> B) and C) or (A -> B)) -> (A -> D)) -> E) -> ((((A -> (B -> D)) or ((A -> B) -> (A -> D))) or ((((A -> B) and C) or (A -> B)) -> (A -> D))) -> E)), M:tm-8, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-61831
in-theory        61831
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((((B -> C) and E) or (B -> C)) -> (B -> D))))
theorem-size     29
proof            (modus-ponens tm-7 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-7 tm-8 tm-2 tm-3)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61831.        (A or (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((((B -> C) and E) or (B -> C)) -> (B -> D)))), M:tm-7, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61832
in-theory        61832
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) or E)
theorem-size     29
proof            (modus-ponens tm-6 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-6 tm-8 tm-2 tm-3)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61832.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) or E), M:tm-6, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61833
in-theory        61833
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((((B -> C) and E) or (B -> C)) -> (B -> D))) and A))
theorem-size     31
proof            (modus-ponens tm-5 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       145
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61833.        (A -> ((((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((((B -> C) and E) or (B -> C)) -> (B -> D))) and A)), M:tm-5, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61834
in-theory        61834
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) and D) or (A -> B))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> C)))
theorem-size     41
proof            (modus-ponens tm-2 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (and (-> Am Bm) Dm) (-> Am Bm))) (C (-> Am Cm))))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61834.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) and D) or (A -> B))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (A -> C))), M:tm-2, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (and (-> Am Bm) Dm) (-> Am Bm))) (C (-> Am Cm)))
================================================================
tm-name          tm-61835
in-theory        61835
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((((B -> C) and E) or (B -> C)) -> (B -> D))))
theorem-size     29
proof            (modus-ponens tm-1 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-1 tm-8 tm-2 tm-3)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-61835.        (A -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> ((((B -> C) and E) or (B -> C)) -> (B -> D)))), M:tm-1, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-61836
in-theory        61836
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (((F and G) or F) -> E)))
theorem-size     39
proof            (modus-ponens tm-708 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61836.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E or (F -> E)) -> (((F and G) or F) -> E))), M:tm-708, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61837
in-theory        61837
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     27
proof            (modus-ponens tm-665 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61837.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-665, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61838
in-theory        61838
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C or (((B and D) or B) -> A)))
theorem-size     15
proof            (modus-ponens tm-623 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61838.        ((A or (B -> A)) -> (C or (((B and D) or B) -> A))), M:tm-623, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61839
in-theory        61839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-622 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61839.        ((A -> (B -> (C or B))) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-622, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61840
in-theory        61840
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61840.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (D -> (E or D))), M:tm-609, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61841
in-theory        61841
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-605 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61841.        ((A -> ((B -> (C or B)) and A)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-605, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61842
in-theory        61842
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((D -> (E or D)) and ((A or (B -> A)) -> (((B and C) or B) -> A))))
theorem-size     33
proof            (modus-ponens tm-595 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61842.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((D -> (E or D)) and ((A or (B -> A)) -> (((B and C) or B) -> A)))), M:tm-595, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61843
in-theory        61843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-550 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61843.        (((A -> (B or A)) or C) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-550, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61844
in-theory        61844
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-540 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61844.        ((A or (B -> (C or B))) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-540, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61845
in-theory        61845
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-530 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61845.        ((A or (B -> (B or C))) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-530, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61846
in-theory        61846
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-520 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61846.        ((A or (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-520, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61847
in-theory        61847
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-510 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61847.        ((A or ((B and C) -> C)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-510, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61848
in-theory        61848
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-500 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61848.        ((A or ((B and C) -> B)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-500, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61849
in-theory        61849
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((F and G) or F) -> E)))
theorem-size     29
proof            (modus-ponens tm-490 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61849.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((F and G) or F) -> E))), M:tm-490, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61850
in-theory        61850
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-480 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61850.        ((A or (B -> (C -> B))) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-480, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61851
in-theory        61851
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((((B and C) or B) -> A) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61851.        ((A or (B -> A)) -> ((((B and C) or B) -> A) or D)), M:tm-470, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61852
in-theory        61852
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-469 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61852.        ((A -> (B -> (B or C))) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-469, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61853
in-theory        61853
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61853.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (D -> (D or E))), M:tm-456, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61854
in-theory        61854
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-453 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61854.        ((A -> ((B -> (B or C)) and A)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-453, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61855
in-theory        61855
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((D -> (D or E)) and ((A or (B -> A)) -> (((B and C) or B) -> A))))
theorem-size     33
proof            (modus-ponens tm-443 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61855.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((D -> (D or E)) and ((A or (B -> A)) -> (((B and C) or B) -> A)))), M:tm-443, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61856
in-theory        61856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-409 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61856.        (((A -> (A or B)) or C) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-409, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61857
in-theory        61857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-400 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61857.        (((A -> (B -> (A and B))) or C) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-400, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61858
in-theory        61858
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-391 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61858.        ((((A and B) -> B) or C) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-391, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61859
in-theory        61859
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-382 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61859.        ((((A and B) -> A) or C) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-382, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61860
in-theory        61860
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (((F and G) or F) -> E)))
theorem-size     29
proof            (modus-ponens tm-373 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61860.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E or (F -> E)) -> (((F and G) or F) -> E))), M:tm-373, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61861
in-theory        61861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-364 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61861.        (((A -> (B -> A)) or C) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-364, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61862
in-theory        61862
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> ((((B and D) or B) -> A) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61862.        ((A or (B -> A)) -> (C -> ((((B and D) or B) -> A) and C))), M:tm-355, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61863
in-theory        61863
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-354 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61863.        ((A -> (B -> (C -> (B and C)))) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-354, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61864
in-theory        61864
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61864.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61865
in-theory        61865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (((D and E) or D) -> C)))
theorem-size     23
proof            (modus-ponens tm-338 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61865.        (((A -> B) -> (A -> (A and B))) and ((C or (D -> C)) -> (((D and E) or D) -> C))), M:tm-338, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61866
in-theory        61866
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((A or (B -> A)) -> ((A or (B -> A)) and (((B and C) or B) -> A))))
theorem-size     33
proof            (modus-ponens tm-328 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61866.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((A or (B -> A)) -> ((A or (B -> A)) and (((B and C) or B) -> A)))), M:tm-328, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61867
in-theory        61867
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((D -> (E -> (D and E))) and ((A or (B -> A)) -> (((B and C) or B) -> A))))
theorem-size     35
proof            (modus-ponens tm-327 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61867.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((D -> (E -> (D and E))) and ((A or (B -> A)) -> (((B and C) or B) -> A)))), M:tm-327, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61868
in-theory        61868
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((D and E) -> E) and ((A or (B -> A)) -> (((B and C) or B) -> A))))
theorem-size     33
proof            (modus-ponens tm-326 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61868.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((D and E) -> E) and ((A or (B -> A)) -> (((B and C) or B) -> A)))), M:tm-326, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61869
in-theory        61869
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((D and E) -> D) and ((A or (B -> A)) -> (((B and C) or B) -> A))))
theorem-size     33
proof            (modus-ponens tm-325 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-1)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61869.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((D and E) -> D) and ((A or (B -> A)) -> (((B and C) or B) -> A)))), M:tm-325, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61870
in-theory        61870
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> A)) -> (((B and C) or B) -> A))))
theorem-size     41
proof            (modus-ponens tm-324 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61870.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A or (B -> A)) -> (((B and C) or B) -> A)))), M:tm-324, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61871
in-theory        61871
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((D -> (E -> D)) and ((A or (B -> A)) -> (((B and C) or B) -> A))))
theorem-size     33
proof            (modus-ponens tm-323 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61871.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((D -> (E -> D)) and ((A or (B -> A)) -> (((B and C) or B) -> A)))), M:tm-323, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61872
in-theory        61872
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61872.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((D and E) -> E)), M:tm-322, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61873
in-theory        61873
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61873.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((D and E) -> D)), M:tm-320, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61874
in-theory        61874
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61874.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61875
in-theory        61875
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((A or (B -> A)) -> (A or (B -> A))))
theorem-size     25
proof            (modus-ponens tm-316 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61875.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((A or (B -> A)) -> (A or (B -> A)))), M:tm-316, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61876
in-theory        61876
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61876.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (D -> (E -> D))), M:tm-315, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61877
in-theory        61877
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((A or (B -> A)) -> (not (((B and C) or B) -> A))) -> (not (A or (B -> A)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-1 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61877.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((A or (B -> A)) -> (not (((B and C) or B) -> A))) -> (not (A or (B -> A))))), M:tm-313, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61878
in-theory        61878
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((((B and C) or B) -> A) -> D) -> (((A or (B -> A)) or (((B and C) or B) -> A)) -> D)))
theorem-size     39
proof            (modus-ponens tm-312 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61878.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((((B and C) or B) -> A) -> D) -> (((A or (B -> A)) or (((B and C) or B) -> A)) -> D))), M:tm-312, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61879
in-theory        61879
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (D or ((A or (B -> A)) -> (((B and C) or B) -> A))))
theorem-size     29
proof            (modus-ponens tm-311 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61879.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (D or ((A or (B -> A)) -> (((B and C) or B) -> A)))), M:tm-311, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61880
in-theory        61880
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((A or (B -> A)) -> (((B and C) or B) -> A)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61880.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((A or (B -> A)) -> (((B and C) or B) -> A)) or D)), M:tm-310, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61881
in-theory        61881
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (D -> (((A or (B -> A)) -> (((B and C) or B) -> A)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61881.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (D -> (((A or (B -> A)) -> (((B and C) or B) -> A)) and D))), M:tm-309, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61882
in-theory        61882
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((A or (B -> A)) -> ((B and C) or B)) -> ((A or (B -> A)) -> A)))
theorem-size     33
proof            (modus-ponens tm-306 tm-744 ((A (or Am (-> Bm Am))) (B (or (and Bm Cm) Bm)) (C Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61882.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (((A or (B -> A)) -> ((B and C) or B)) -> ((A or (B -> A)) -> A))), M:tm-306, m:tm-744, u:((A (or Am (-> Bm Am))) (B (or (and Bm Cm) Bm)) (C Am))
================================================================
tm-name          tm-61883
in-theory        61883
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and (D -> ((A or (B -> A)) -> (((B and C) or B) -> A))))
theorem-size     29
proof            (modus-ponens tm-305 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61883.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and (D -> ((A or (B -> A)) -> (((B and C) or B) -> A)))), M:tm-305, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61884
in-theory        61884
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     25
proof            (modus-ponens tm-303 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61884.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-303, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61885
in-theory        61885
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-270 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61885.        ((A -> (((B and C) -> C) and A)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-270, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61886
in-theory        61886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-239 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61886.        ((A -> (((B and C) -> B) and A)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-239, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61887
in-theory        61887
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (((F and G) or F) -> E)))
theorem-size     31
proof            (modus-ponens tm-210 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61887.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E or (F -> E)) -> (((F and G) or F) -> E))), M:tm-210, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61888
in-theory        61888
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     23
proof            (modus-ponens tm-183 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61888.        ((A -> ((B -> (C -> B)) and A)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-183, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61889
in-theory        61889
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-157 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61889.        ((A -> ((B and C) -> C)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-157, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61890
in-theory        61890
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     29
proof            (modus-ponens tm-147 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61890.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-147, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61891
in-theory        61891
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-134 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61891.        ((A -> ((B and C) -> B)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-134, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61892
in-theory        61892
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     29
proof            (modus-ponens tm-125 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61892.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-125, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61893
in-theory        61893
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (C -> (A -> B))) -> ((((C and D) or C) -> A) -> (((C and D) or C) -> B)))
theorem-size     25
proof            (modus-ponens tm-114 tm-744 ((A (or (-> C D) (-> Bm (-> C D)))) (B (or (and Bm Cm) Bm)) (Am (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61893.        (((A -> B) or (C -> (A -> B))) -> ((((C and D) or C) -> A) -> (((C and D) or C) -> B))), M:tm-114, m:tm-744, u:((A (or (-> C D) (-> Bm (-> C D)))) (B (or (and Bm Cm) Bm)) (Am (-> C D)))
================================================================
tm-name          tm-61894
in-theory        61894
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((F and G) or F) -> E)))
theorem-size     29
proof            (modus-ponens tm-113 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61894.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E or (F -> E)) -> (((F and G) or F) -> E))), M:tm-113, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61895
in-theory        61895
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     33
proof            (modus-ponens tm-105 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61895.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-105, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61896
in-theory        61896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (((D and E) or D) -> C)))
theorem-size     21
proof            (modus-ponens tm-95 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61896.        (((A -> B) -> (A -> A)) and ((C or (D -> C)) -> (((D and E) or D) -> C))), M:tm-95, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61897
in-theory        61897
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (C -> (((B and D) or B) -> A)))
theorem-size     15
proof            (modus-ponens tm-84 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61897.        ((A or (B -> A)) -> (C -> (((B and D) or B) -> A))), M:tm-84, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61898
in-theory        61898
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     21
proof            (modus-ponens tm-83 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61898.        ((A -> (B -> (C -> B))) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-83, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61899
in-theory        61899
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B or (C -> B)) -> (((C and D) or C) -> B)))
theorem-size     19
proof            (modus-ponens tm-76 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61899.        (((not (not A)) -> A) and ((B or (C -> B)) -> (((C and D) or C) -> B))), M:tm-76, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61900
in-theory        61900
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (((B and C) or B) -> A))
theorem-size     21
proof            (modus-ponens tm-73 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-8 tm-10 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61900.        (((not (not (A or (B -> A)))) or (A or (B -> A))) -> (((B and C) or B) -> A)), M:tm-73, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61901
in-theory        61901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (((D and E) or D) -> C)))
theorem-size     25
proof            (modus-ponens tm-69 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-1 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61901.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C or (D -> C)) -> (((D and E) or D) -> C))), M:tm-69, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61902
in-theory        61902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     27
proof            (modus-ponens tm-54 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61902.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-54, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61903
in-theory        61903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (B or (A -> B))) -> (((A and C) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-50 tm-744 ((A Am) (B (-> Bm Am)) (C (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-8 tm-7 tm-1 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61903.        (((A -> B) or (B or (A -> B))) -> (((A and C) or A) -> B)), M:tm-50, m:tm-744, u:((A Am) (B (-> Bm Am)) (C (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61904
in-theory        61904
times-derived    1
----------------------------------------------------------------
theorem          ((A or (A or (B -> A))) -> (((B and C) or B) -> A))
theorem-size     15
proof            (modus-ponens tm-49 tm-744 ((A Am) (B (-> Bm Am)) (C (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-8 tm-6 tm-1 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61904.        ((A or (A or (B -> A))) -> (((B and C) or B) -> A)), M:tm-49, m:tm-744, u:((A Am) (B (-> Bm Am)) (C (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61905
in-theory        61905
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B or (C -> B))) or (B or (C -> B))) -> (((C and D) or C) -> B))
theorem-size     21
proof            (modus-ponens tm-47 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-8 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61905.        (((A and (B or (C -> B))) or (B or (C -> B))) -> (((C and D) or C) -> B)), M:tm-47, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61906
in-theory        61906
times-derived    1
----------------------------------------------------------------
theorem          ((((A or (B -> A)) and C) or (A or (B -> A))) -> (((B and D) or B) -> A))
theorem-size     21
proof            (modus-ponens tm-46 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61906.        ((((A or (B -> A)) and C) or (A or (B -> A))) -> (((B and D) or B) -> A)), M:tm-46, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61907
in-theory        61907
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C or (D -> C)) -> (((D and E) or D) -> C)))
theorem-size     19
proof            (modus-ponens tm-42 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61907.        ((A -> (B or A)) and ((C or (D -> C)) -> (((D and E) or D) -> C))), M:tm-42, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61908
in-theory        61908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C or (D -> C)) -> (((D and E) or D) -> C)))
theorem-size     19
proof            (modus-ponens tm-32 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61908.        ((A -> (A or B)) and ((C or (D -> C)) -> (((D and E) or D) -> C))), M:tm-32, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61909
in-theory        61909
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((A or (B -> A)) and (((B and C) or B) -> A)))
theorem-size     19
proof            (modus-ponens tm-24 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61909.        ((A or (B -> A)) -> ((A or (B -> A)) and (((B and C) or B) -> A))), M:tm-24, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61910
in-theory        61910
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (((D and E) or D) -> C)))
theorem-size     21
proof            (modus-ponens tm-23 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61910.        ((A -> (B -> (A and B))) and ((C or (D -> C)) -> (((D and E) or D) -> C))), M:tm-23, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61911
in-theory        61911
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C or (D -> C)) -> (((D and E) or D) -> C)))
theorem-size     19
proof            (modus-ponens tm-22 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61911.        (((A and B) -> B) and ((C or (D -> C)) -> (((D and E) or D) -> C))), M:tm-22, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61912
in-theory        61912
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C or (D -> C)) -> (((D and E) or D) -> C)))
theorem-size     19
proof            (modus-ponens tm-21 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-3 tm-8 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61912.        (((A and B) -> A) and ((C or (D -> C)) -> (((D and E) or D) -> C))), M:tm-21, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61913
in-theory        61913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     27
proof            (modus-ponens tm-20 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-1 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61913.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-20, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61914
in-theory        61914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C or (D -> C)) -> (((D and E) or D) -> C)))
theorem-size     19
proof            (modus-ponens tm-19 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61914.        ((A -> (B -> A)) and ((C or (D -> C)) -> (((D and E) or D) -> C))), M:tm-19, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61915
in-theory        61915
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (not (((B and C) or B) -> A))) -> (not (A or (B -> A))))
theorem-size     21
proof            (modus-ponens tm-9 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-9 tm-8 tm-1 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61915.        (((A or (B -> A)) -> (not (((B and C) or B) -> A))) -> (not (A or (B -> A)))), M:tm-9, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61916
in-theory        61916
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> D) -> (((C or (A -> C)) or (((A and B) or A) -> C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61916.        (((((A and B) or A) -> C) -> D) -> (((C or (A -> C)) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-61917
in-theory        61917
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B or (C -> B)) -> (((C and D) or C) -> B)))
theorem-size     15
proof            (modus-ponens tm-7 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-7 tm-8 tm-1 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61917.        (A or ((B or (C -> B)) -> (((C and D) or C) -> B))), M:tm-7, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61918
in-theory        61918
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-6 tm-8 tm-1 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61918.        (((A or (B -> A)) -> (((B and C) or B) -> A)) or D), M:tm-6, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61919
in-theory        61919
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B or (C -> B)) -> (((C and D) or C) -> B)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61919.        (A -> (((B or (C -> B)) -> (((C and D) or C) -> B)) and A)), M:tm-5, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61920
in-theory        61920
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B and C) or B)) -> ((A or (B -> A)) -> A))
theorem-size     19
proof            (modus-ponens tm-2 tm-744 ((A (or Am (-> Bm Am))) (B (or (and Bm Cm) Bm)) (C Am)))
axioms-used      (tm-2 tm-8 tm-1 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61920.        (((A or (B -> A)) -> ((B and C) or B)) -> ((A or (B -> A)) -> A)), M:tm-2, m:tm-744, u:((A (or Am (-> Bm Am))) (B (or (and Bm Cm) Bm)) (C Am))
================================================================
tm-name          tm-61921
in-theory        61921
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B or (C -> B)) -> (((C and D) or C) -> B)))
theorem-size     15
proof            (modus-ponens tm-1 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-61921.        (A -> ((B or (C -> B)) -> (((C and D) or C) -> B))), M:tm-1, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-61922
in-theory        61922
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     43
proof            (modus-ponens tm-708 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61922.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-708, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61923
in-theory        61923
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-665 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61923.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-665, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61924
in-theory        61924
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-622 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61924.        ((A -> (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-622, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61925
in-theory        61925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61925.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G or F))), M:tm-609, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61926
in-theory        61926
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-605 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61926.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-605, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61927
in-theory        61927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61927.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G or F)) and ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-595, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61928
in-theory        61928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-550 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61928.        (((A -> (B or A)) or C) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-550, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61929
in-theory        61929
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-540 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61929.        ((A or (B -> (C or B))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-540, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61930
in-theory        61930
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-530 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61930.        ((A or (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-530, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61931
in-theory        61931
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-520 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61931.        ((A or (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-520, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61932
in-theory        61932
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-510 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61932.        ((A or ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-510, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61933
in-theory        61933
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-500 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61933.        ((A or ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-500, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61934
in-theory        61934
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-490 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61934.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-490, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61935
in-theory        61935
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-480 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61935.        ((A or (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-480, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61936
in-theory        61936
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-469 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61936.        ((A -> (B -> (B or C))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-469, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61937
in-theory        61937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61937.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (F or G))), M:tm-456, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61938
in-theory        61938
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-453 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61938.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-453, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61939
in-theory        61939
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61939.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (F or G)) and ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-443, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61940
in-theory        61940
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-409 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61940.        (((A -> (A or B)) or C) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-409, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61941
in-theory        61941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-400 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61941.        (((A -> (B -> (A and B))) or C) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-400, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61942
in-theory        61942
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-391 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61942.        ((((A and B) -> B) or C) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-391, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61943
in-theory        61943
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-382 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61943.        ((((A and B) -> A) or C) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-382, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61944
in-theory        61944
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-373 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61944.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-373, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61945
in-theory        61945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-364 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61945.        (((A -> (B -> A)) or C) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-364, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61946
in-theory        61946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-354 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61946.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-354, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61947
in-theory        61947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61947.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61948
in-theory        61948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-338 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61948.        (((A -> B) -> (A -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-338, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61949
in-theory        61949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61949.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-327, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61950
in-theory        61950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61950.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> G) and ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-326, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61951
in-theory        61951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-8)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61951.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> F) and ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-325, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61952
in-theory        61952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61952.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-324, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61953
in-theory        61953
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61953.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> F)) and ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-323, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61954
in-theory        61954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61954.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61955
in-theory        61955
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61955.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61956
in-theory        61956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61956.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61957
in-theory        61957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61957.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61958
in-theory        61958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F or ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61958.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F or ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-311, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61959
in-theory        61959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61959.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) or F)), M:tm-310, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61960
in-theory        61960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61960.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and F))), M:tm-309, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61961
in-theory        61961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-308 tm-745 ((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61961.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-308, m:tm-745, u:((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))
================================================================
tm-name          tm-61962
in-theory        61962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (A -> (B or A)))
theorem-size     23
proof            (modus-ponens tm-307 tm-745 ((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61962.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (A -> (B or A))), M:tm-307, m:tm-745, u:((A (-> Am (or Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))
================================================================
tm-name          tm-61963
in-theory        61963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61963.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-305, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61964
in-theory        61964
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-303 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61964.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-303, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61965
in-theory        61965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-270 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61965.        ((A -> (((B and C) -> C) and A)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-270, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61966
in-theory        61966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-239 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61966.        ((A -> (((B and C) -> B) and A)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-239, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61967
in-theory        61967
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-210 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61967.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-210, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61968
in-theory        61968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-183 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61968.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-183, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61969
in-theory        61969
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-157 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61969.        ((A -> ((B and C) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-157, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61970
in-theory        61970
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-147 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61970.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-147, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61971
in-theory        61971
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-134 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61971.        ((A -> ((B and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-134, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61972
in-theory        61972
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-125 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61972.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-125, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61973
in-theory        61973
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-113 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61973.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F or E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-113, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61974
in-theory        61974
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-105 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61974.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-105, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61975
in-theory        61975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-95 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61975.        (((A -> B) -> (A -> A)) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-95, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61976
in-theory        61976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-83 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61976.        ((A -> (B -> (C -> B))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-83, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61977
in-theory        61977
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-76 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61977.        (((not (not A)) -> A) and ((B -> (C or B)) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-76, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61978
in-theory        61978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-69 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61978.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-69, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61979
in-theory        61979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-54 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61979.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-54, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61980
in-theory        61980
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-42 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61980.        ((A -> (B or A)) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-42, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61981
in-theory        61981
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-32 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61981.        ((A -> (A or B)) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-32, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61982
in-theory        61982
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-23 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61982.        ((A -> (B -> (A and B))) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-23, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61983
in-theory        61983
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-22 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61983.        (((A and B) -> B) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-22, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61984
in-theory        61984
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-21 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61984.        (((A and B) -> A) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-21, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61985
in-theory        61985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-20 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61985.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-20, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61986
in-theory        61986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-19 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61986.        ((A -> (B -> A)) and ((C -> (D or C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-19, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61987
in-theory        61987
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C or B)) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-7 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61987.        (A or ((B -> (C or B)) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-7, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61988
in-theory        61988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-6 tm-5 tm-7 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61988.        (((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))) or F), M:tm-6, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61989
in-theory        61989
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C or B)) and ((D -> E) -> (((D and F) or D) -> E))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61989.        (A -> (((B -> (C or B)) and ((D -> E) -> (((D and F) or D) -> E))) and A)), M:tm-5, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61990
in-theory        61990
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C or B)) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-1 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-1 tm-5 tm-7 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61990.        (A -> ((B -> (C or B)) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-1, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61991
in-theory        61991
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     43
proof            (modus-ponens tm-708 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61991.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-708, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61992
in-theory        61992
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-665 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61992.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-665, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61993
in-theory        61993
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-622 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61993.        ((A -> (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-622, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61994
in-theory        61994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61994.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G or F))), M:tm-609, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61995
in-theory        61995
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-605 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61995.        ((A -> ((B -> (C or B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-605, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61996
in-theory        61996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61996.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G or F)) and ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-595, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61997
in-theory        61997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-550 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61997.        (((A -> (B or A)) or C) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-550, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61998
in-theory        61998
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-540 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61998.        ((A or (B -> (C or B))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-540, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-61999
in-theory        61999
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-530 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-61999.        ((A or (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-530, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62000
in-theory        62000
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-520 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62000.        ((A or (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-520, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62001
in-theory        62001
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-510 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62001.        ((A or ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-510, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62002
in-theory        62002
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-500 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62002.        ((A or ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-500, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62003
in-theory        62003
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-490 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62003.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-490, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62004
in-theory        62004
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-480 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62004.        ((A or (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-480, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62005
in-theory        62005
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-469 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62005.        ((A -> (B -> (B or C))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-469, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62006
in-theory        62006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62006.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (F or G))), M:tm-456, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62007
in-theory        62007
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-453 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62007.        ((A -> ((B -> (B or C)) and A)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-453, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62008
in-theory        62008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62008.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (F or G)) and ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-443, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62009
in-theory        62009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-409 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62009.        (((A -> (A or B)) or C) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-409, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62010
in-theory        62010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-400 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62010.        (((A -> (B -> (A and B))) or C) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-400, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62011
in-theory        62011
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-391 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62011.        ((((A and B) -> B) or C) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-391, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62012
in-theory        62012
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-382 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62012.        ((((A and B) -> A) or C) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-382, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62013
in-theory        62013
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-373 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62013.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-373, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62014
in-theory        62014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-364 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62014.        (((A -> (B -> A)) or C) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-364, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62015
in-theory        62015
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-354 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62015.        ((A -> (B -> (C -> (B and C)))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-354, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62016
in-theory        62016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62016.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62017
in-theory        62017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-338 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62017.        (((A -> B) -> (A -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-338, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62018
in-theory        62018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62018.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-327, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62019
in-theory        62019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62019.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> G) and ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-326, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62020
in-theory        62020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-8)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62020.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> F) and ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-325, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62021
in-theory        62021
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62021.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-324, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62022
in-theory        62022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62022.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> F)) and ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-323, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62023
in-theory        62023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62023.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62024
in-theory        62024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62024.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62025
in-theory        62025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62025.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62026
in-theory        62026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62026.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62027
in-theory        62027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (F or ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62027.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (F or ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-311, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62028
in-theory        62028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62028.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) or F)), M:tm-310, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62029
in-theory        62029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62029.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and F))), M:tm-309, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62030
in-theory        62030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-308 tm-746 ((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62030.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-308, m:tm-746, u:((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))
================================================================
tm-name          tm-62031
in-theory        62031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (A -> (A or B)))
theorem-size     23
proof            (modus-ponens tm-307 tm-746 ((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62031.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (A -> (A or B))), M:tm-307, m:tm-746, u:((A (-> Am (or Am Bm))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))
================================================================
tm-name          tm-62032
in-theory        62032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62032.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-305, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62033
in-theory        62033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-303 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62033.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-303, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62034
in-theory        62034
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-270 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62034.        ((A -> (((B and C) -> C) and A)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-270, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62035
in-theory        62035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-239 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62035.        ((A -> (((B and C) -> B) and A)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-239, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62036
in-theory        62036
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-210 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62036.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-210, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62037
in-theory        62037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-183 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62037.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-183, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62038
in-theory        62038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-157 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62038.        ((A -> ((B and C) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-157, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62039
in-theory        62039
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-147 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62039.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-147, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62040
in-theory        62040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-134 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62040.        ((A -> ((B and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-134, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62041
in-theory        62041
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-125 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62041.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-125, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62042
in-theory        62042
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-113 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62042.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (E or F)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-113, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62043
in-theory        62043
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-105 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62043.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-105, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62044
in-theory        62044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-95 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62044.        (((A -> B) -> (A -> A)) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-95, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62045
in-theory        62045
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-83 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62045.        ((A -> (B -> (C -> B))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-83, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62046
in-theory        62046
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-76 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-10 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62046.        (((not (not A)) -> A) and ((B -> (B or C)) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-76, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62047
in-theory        62047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-69 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-9 tm-6 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62047.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-69, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62048
in-theory        62048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-54 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-6 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62048.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-54, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62049
in-theory        62049
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-42 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62049.        ((A -> (B or A)) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-42, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62050
in-theory        62050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-32 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62050.        ((A -> (A or B)) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-32, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62051
in-theory        62051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-23 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62051.        ((A -> (B -> (A and B))) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-23, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62052
in-theory        62052
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-22 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62052.        (((A and B) -> B) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-22, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62053
in-theory        62053
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-21 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62053.        (((A and B) -> A) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-21, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62054
in-theory        62054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-20 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62054.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-20, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62055
in-theory        62055
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-19 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62055.        ((A -> (B -> A)) and ((C -> (C or D)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-19, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62056
in-theory        62056
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (B or C)) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-7 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-7 tm-5 tm-6 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62056.        (A or ((B -> (B or C)) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-7, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62057
in-theory        62057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62057.        (((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))) or F), M:tm-6, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62058
in-theory        62058
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (B or C)) and ((D -> E) -> (((D and F) or D) -> E))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62058.        (A -> (((B -> (B or C)) and ((D -> E) -> (((D and F) or D) -> E))) and A)), M:tm-5, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62059
in-theory        62059
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (B or C)) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-1 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-1 tm-5 tm-6 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62059.        (A -> ((B -> (B or C)) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-1, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62060
in-theory        62060
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((A and C) or A) -> (B -> A)))
theorem-size     15
proof            (modus-ponens tm-747 tm-1 ((A Am) (B (-> Bm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-62060.        ((A -> (B -> A)) and (((A and C) or A) -> (B -> A))), M:tm-747, m:tm-1, u:((A Am) (B (-> Bm Am)))
================================================================
tm-name          tm-62061
in-theory        62061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-747 tm-2 ((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62061.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))), M:tm-747, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-62062
in-theory        62062
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((((A and B) and C) or (A and B)) -> A))
theorem-size     17
proof            (modus-ponens tm-747 tm-3 ((A (and Am Bm)) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62062.        (((A and B) -> A) and ((((A and B) and C) or (A and B)) -> A)), M:tm-747, m:tm-3, u:((A (and Am Bm)) (B Am))
================================================================
tm-name          tm-62063
in-theory        62063
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((((A and B) and C) or (A and B)) -> B))
theorem-size     17
proof            (modus-ponens tm-747 tm-4 ((A (and Am Bm)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-62063.        (((A and B) -> B) and ((((A and B) and C) or (A and B)) -> B)), M:tm-747, m:tm-4, u:((A (and Am Bm)) (B Bm))
================================================================
tm-name          tm-62064
in-theory        62064
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((A and C) or A) -> (B -> (A and B))))
theorem-size     19
proof            (modus-ponens tm-747 tm-5 ((A Am) (B (-> Bm (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62064.        ((A -> (B -> (A and B))) and (((A and C) or A) -> (B -> (A and B)))), M:tm-747, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
================================================================
tm-name          tm-62065
in-theory        62065
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((A and C) or A) -> (A or B)))
theorem-size     15
proof            (modus-ponens tm-747 tm-6 ((A Am) (B (or Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-62065.        ((A -> (A or B)) and (((A and C) or A) -> (A or B))), M:tm-747, m:tm-6, u:((A Am) (B (or Am Bm)))
================================================================
tm-name          tm-62066
in-theory        62066
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((A and C) or A) -> (B or A)))
theorem-size     15
proof            (modus-ponens tm-747 tm-7 ((A Am) (B (or Bm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-62066.        ((A -> (B or A)) and (((A and C) or A) -> (B or A))), M:tm-747, m:tm-7, u:((A Am) (B (or Bm Am)))
================================================================
tm-name          tm-62067
in-theory        62067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((A -> B) and D) or (A -> B)) -> ((B -> C) -> ((A or B) -> C))))
theorem-size     33
proof            (modus-ponens tm-747 tm-8 ((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62067.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((((A -> B) and D) or (A -> B)) -> ((B -> C) -> ((A or B) -> C)))), M:tm-747, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-62068
in-theory        62068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))))
theorem-size     29
proof            (modus-ponens tm-747 tm-9 ((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62068.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A)))), M:tm-747, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-62069
in-theory        62069
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((((not (not A)) and B) or (not (not A))) -> A))
theorem-size     17
proof            (modus-ponens tm-747 tm-10 ((A (not (not Am))) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-10)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-62069.        (((not (not A)) -> A) and ((((not (not A)) and B) or (not (not A))) -> A)), M:tm-747, m:tm-10, u:((A (not (not Am))) (B Am))
================================================================
tm-name          tm-62070
in-theory        62070
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((A and D) or A) -> (B -> (C -> B))))
theorem-size     19
proof            (modus-ponens tm-747 tm-11 ((A Am) (B (-> Bm (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-62070.        ((A -> (B -> (C -> B))) and (((A and D) or A) -> (B -> (C -> B)))), M:tm-747, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-62071
in-theory        62071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((((A -> B) and C) or (A -> B)) -> (A -> A)))
theorem-size     21
proof            (modus-ponens tm-747 tm-12 ((A (-> Am Bm)) (B (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-62071.        (((A -> B) -> (A -> A)) and ((((A -> B) and C) or (A -> B)) -> (A -> A))), M:tm-747, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
================================================================
tm-name          tm-62072
in-theory        62072
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     51
proof            (modus-ponens tm-747 tm-13 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-62072.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-747, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-62073
in-theory        62073
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((A and E) or A) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     35
proof            (modus-ponens tm-747 tm-14 ((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-62073.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((A and E) or A) -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-747, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-62074
in-theory        62074
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)))
theorem-size     41
proof            (modus-ponens tm-747 tm-15 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-62074.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B))), M:tm-747, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-62075
in-theory        62075
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((A and D) or A) -> ((B and C) -> B)))
theorem-size     19
proof            (modus-ponens tm-747 tm-16 ((A Am) (B (-> (and Bm Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-62075.        ((A -> ((B and C) -> B)) and (((A and D) or A) -> ((B and C) -> B))), M:tm-747, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-62076
in-theory        62076
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)))
theorem-size     41
proof            (modus-ponens tm-747 tm-17 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-62076.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C))), M:tm-747, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-62077
in-theory        62077
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((A and D) or A) -> ((B and C) -> C)))
theorem-size     19
proof            (modus-ponens tm-747 tm-18 ((A Am) (B (-> (and Bm Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-62077.        ((A -> ((B and C) -> C)) and (((A and D) or A) -> ((B and C) -> C))), M:tm-747, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-62078
in-theory        62078
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((A and D) or A) -> ((B -> (C -> B)) and A)))
theorem-size     23
proof            (modus-ponens tm-747 tm-19 ((A Am) (B (and (-> Bm (-> Cm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-62078.        ((A -> ((B -> (C -> B)) and A)) and (((A and D) or A) -> ((B -> (C -> B)) and A))), M:tm-747, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
================================================================
tm-name          tm-62079
in-theory        62079
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((A and E) or A) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     39
proof            (modus-ponens tm-747 tm-20 ((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-62079.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((A and E) or A) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-747, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-62080
in-theory        62080
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((A and D) or A) -> (((B and C) -> B) and A)))
theorem-size     23
proof            (modus-ponens tm-747 tm-21 ((A Am) (B (and (-> (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-62080.        ((A -> (((B and C) -> B) and A)) and (((A and D) or A) -> (((B and C) -> B) and A))), M:tm-747, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-62081
in-theory        62081
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((A and D) or A) -> (((B and C) -> C) and A)))
theorem-size     23
proof            (modus-ponens tm-747 tm-22 ((A Am) (B (and (-> (and Bm Cm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-62081.        ((A -> (((B and C) -> C) and A)) and (((A and D) or A) -> (((B and C) -> C) and A))), M:tm-747, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
================================================================
tm-name          tm-62082
in-theory        62082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((A and D) or A) -> ((B -> (C -> (B and C))) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-23 ((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-62082.        ((A -> ((B -> (C -> (B and C))) and A)) and (((A and D) or A) -> ((B -> (C -> (B and C))) and A))), M:tm-747, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
================================================================
tm-name          tm-62083
in-theory        62083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-747 tm-24 ((A (-> Am Bm)) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62083.        (((A -> B) -> (A -> (A and B))) and ((((A -> B) and C) or (A -> B)) -> (A -> (A and B)))), M:tm-747, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-62084
in-theory        62084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((A and D) or A) -> (B -> (C -> (B and C)))))
theorem-size     23
proof            (modus-ponens tm-747 tm-25 ((A Am) (B (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-62084.        ((A -> (B -> (C -> (B and C)))) and (((A and D) or A) -> (B -> (C -> (B and C))))), M:tm-747, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-62085
in-theory        62085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((A and D) or A) -> ((B -> (B or C)) and A)))
theorem-size     23
proof            (modus-ponens tm-747 tm-32 ((A Am) (B (and (-> Bm (or Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-62085.        ((A -> ((B -> (B or C)) and A)) and (((A and D) or A) -> ((B -> (B or C)) and A))), M:tm-747, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
================================================================
tm-name          tm-62086
in-theory        62086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((A and D) or A) -> (B -> (B or C))))
theorem-size     19
proof            (modus-ponens tm-747 tm-33 ((A Am) (B (-> Bm (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-62086.        ((A -> (B -> (B or C))) and (((A and D) or A) -> (B -> (B or C)))), M:tm-747, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-62087
in-theory        62087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((A and D) or A) -> ((B -> (C or B)) and A)))
theorem-size     23
proof            (modus-ponens tm-747 tm-42 ((A Am) (B (and (-> Bm (or Cm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-62087.        ((A -> ((B -> (C or B)) and A)) and (((A and D) or A) -> ((B -> (C or B)) and A))), M:tm-747, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
================================================================
tm-name          tm-62088
in-theory        62088
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((A and D) or A) -> (B -> (C or B))))
theorem-size     19
proof            (modus-ponens tm-747 tm-43 ((A Am) (B (-> Bm (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-62088.        ((A -> (B -> (C or B))) and (((A and D) or A) -> (B -> (C or B)))), M:tm-747, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-62089
in-theory        62089
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-747 tm-44 ((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-62089.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C))), M:tm-747, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-62090
in-theory        62090
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     63
proof            (modus-ponens tm-747 tm-45 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-62090.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-747, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-62091
in-theory        62091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((A -> B) and D) or (A -> B)) -> (((A and C) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-747 tm-46 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62091.        (((A -> B) -> (((A and C) or A) -> B)) and ((((A -> B) and D) or (A -> B)) -> (((A and C) or A) -> B))), M:tm-747, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
================================================================
tm-name          tm-62092
in-theory        62092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C and A) or A) -> B)) and ((((A -> B) and D) or (A -> B)) -> (((C and A) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-747 tm-47 ((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-62092.        (((A -> B) -> (((C and A) or A) -> B)) and ((((A -> B) and D) or (A -> B)) -> (((C and A) or A) -> B))), M:tm-747, m:tm-47, u:((A (-> Am Bm)) (B (-> (or (and Cm Am) Am) Bm)))
================================================================
tm-name          tm-62093
in-theory        62093
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C)))
theorem-size     45
proof            (modus-ponens tm-747 tm-48 ((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-62093.        ((((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)) and (((((A -> (B and A)) -> C) and D) or ((A -> (B and A)) -> C)) -> ((B or (A -> (B and A))) -> C))), M:tm-747, m:tm-48, u:((A (-> (-> Am (and Bm Am)) Cm)) (B (-> (or Bm (-> Am (and Bm Am))) Cm)))
================================================================
tm-name          tm-62094
in-theory        62094
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-747 tm-49 ((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-62094.        ((((A or B) -> C) -> ((A or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((A or (A or B)) -> C))), M:tm-747, m:tm-49, u:((A (-> (or Am Bm) Cm)) (B (-> (or Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-62095
in-theory        62095
times-derived    1
----------------------------------------------------------------
theorem          ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C)))
theorem-size     35
proof            (modus-ponens tm-747 tm-50 ((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-62095.        ((((A or B) -> C) -> ((B or (A or B)) -> C)) and (((((A or B) -> C) and D) or ((A or B) -> C)) -> ((B or (A or B)) -> C))), M:tm-747, m:tm-50, u:((A (-> (or Am Bm) Cm)) (B (-> (or Bm (or Am Bm)) Cm)))
================================================================
tm-name          tm-62096
in-theory        62096
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)))
theorem-size     69
proof            (modus-ponens tm-747 tm-51 ((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       195
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-62096.        (((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)) and ((((((A -> B) -> ((C or A) -> B)) -> D) and E) or (((A -> B) -> ((C or A) -> B)) -> D)) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D))), M:tm-747, m:tm-51, u:((A (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm)) (B (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))
================================================================
tm-name          tm-62097
in-theory        62097
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (((A and E) or A) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)))
theorem-size     39
proof            (modus-ponens tm-747 tm-54 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-62097.        ((A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)) and (((A and E) or A) -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A))), M:tm-747, m:tm-54, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))
================================================================
tm-name          tm-62098
in-theory        62098
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((((A -> B) -> (B -> C)) and D) or ((A -> B) -> (B -> C))) -> ((A -> B) -> ((A or B) -> C))))
theorem-size     45
proof            (modus-ponens tm-747 tm-55 ((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-62098.        ((((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))) and (((((A -> B) -> (B -> C)) and D) or ((A -> B) -> (B -> C))) -> ((A -> B) -> ((A or B) -> C)))), M:tm-747, m:tm-55, u:((A (-> (-> Am Bm) (-> Bm Cm))) (B (-> (-> Am Bm) (-> (or Am Bm) Cm))))
================================================================
tm-name          tm-62099
in-theory        62099
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((A and E) or A) -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     35
proof            (modus-ponens tm-747 tm-56 ((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-62099.        ((A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))) and (((A and E) or A) -> ((B -> C) -> ((C -> D) -> ((B or C) -> D))))), M:tm-747, m:tm-56, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-62100
in-theory        62100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> A))) -> (not A)) and ((((A -> (not (B -> A))) and C) or (A -> (not (B -> A)))) -> (not A)))
theorem-size     28
proof            (modus-ponens tm-747 tm-57 ((A (-> Am (not (-> Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-1)
proof-size       126
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-62100.        (((A -> (not (B -> A))) -> (not A)) and ((((A -> (not (B -> A))) and C) or (A -> (not (B -> A)))) -> (not A))), M:tm-747, m:tm-57, u:((A (-> Am (not (-> Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-62101
in-theory        62101
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) and D) or ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C)))))
theorem-size     60
proof            (modus-ponens tm-747 tm-58 ((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       178
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-62101.        ((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))) and (((((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) and D) or ((A -> (B -> C)) -> (not ((A -> B) -> (A -> C))))) -> (not (A -> (B -> C))))), M:tm-747, m:tm-58, u:((A (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm))))) (B (not (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-62102
in-theory        62102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not A)) -> (not (A and B))) and (((((A and B) -> (not A)) and C) or ((A and B) -> (not A))) -> (not (A and B))))
theorem-size     32
proof            (modus-ponens tm-747 tm-59 ((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       132
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-62102.        ((((A and B) -> (not A)) -> (not (A and B))) and (((((A and B) -> (not A)) and C) or ((A and B) -> (not A))) -> (not (A and B)))), M:tm-747, m:tm-59, u:((A (-> (and Am Bm) (not Am))) (B (not (and Am Bm))))
================================================================
tm-name          tm-62103
in-theory        62103
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (not B)) -> (not (A and B))) and (((((A and B) -> (not B)) and C) or ((A and B) -> (not B))) -> (not (A and B))))
theorem-size     32
proof            (modus-ponens tm-747 tm-60 ((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-4)
proof-size       132
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-62103.        ((((A and B) -> (not B)) -> (not (A and B))) and (((((A and B) -> (not B)) and C) or ((A and B) -> (not B))) -> (not (A and B)))), M:tm-747, m:tm-60, u:((A (-> (and Am Bm) (not Bm))) (B (not (and Am Bm))))
================================================================
tm-name          tm-62104
in-theory        62104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (A and B)))) -> (not A)) and ((((A -> (not (B -> (A and B)))) and C) or (A -> (not (B -> (A and B))))) -> (not A)))
theorem-size     34
proof            (modus-ponens tm-747 tm-61 ((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       136
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-62104.        (((A -> (not (B -> (A and B)))) -> (not A)) and ((((A -> (not (B -> (A and B)))) and C) or (A -> (not (B -> (A and B))))) -> (not A))), M:tm-747, m:tm-61, u:((A (-> Am (not (-> Bm (and Am Bm))))) (B (not Am)))
================================================================
tm-name          tm-62105
in-theory        62105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (A or B))) -> (not A)) and ((((A -> (not (A or B))) and C) or (A -> (not (A or B)))) -> (not A)))
theorem-size     28
proof            (modus-ponens tm-747 tm-62 ((A (-> Am (not (or Am Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-6)
proof-size       126
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-62105.        (((A -> (not (A or B))) -> (not A)) and ((((A -> (not (A or B))) and C) or (A -> (not (A or B)))) -> (not A))), M:tm-747, m:tm-62, u:((A (-> Am (not (or Am Bm)))) (B (not Am)))
================================================================
tm-name          tm-62106
in-theory        62106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or A))) -> (not A)) and ((((A -> (not (B or A))) and C) or (A -> (not (B or A)))) -> (not A)))
theorem-size     28
proof            (modus-ponens tm-747 tm-63 ((A (-> Am (not (or Bm Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-7)
proof-size       126
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-62106.        (((A -> (not (B or A))) -> (not A)) and ((((A -> (not (B or A))) and C) or (A -> (not (B or A)))) -> (not A))), M:tm-747, m:tm-63, u:((A (-> Am (not (or Bm Am)))) (B (not Am)))
================================================================
tm-name          tm-62107
in-theory        62107
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) and D) or ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))) -> (not (A -> B))))
theorem-size     56
proof            (modus-ponens tm-747 tm-64 ((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       172
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-62107.        ((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))) and (((((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) and D) or ((A -> B) -> (not ((B -> C) -> ((A or B) -> C))))) -> (not (A -> B)))), M:tm-747, m:tm-64, u:((A (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62108
in-theory        62108
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((((A -> B) -> (not ((A -> (not B)) -> (not A)))) and C) or ((A -> B) -> (not ((A -> (not B)) -> (not A))))) -> (not (A -> B))))
theorem-size     50
proof            (modus-ponens tm-747 tm-65 ((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       162
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-62108.        ((((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))) and (((((A -> B) -> (not ((A -> (not B)) -> (not A)))) and C) or ((A -> B) -> (not ((A -> (not B)) -> (not A))))) -> (not (A -> B)))), M:tm-747, m:tm-65, u:((A (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62109
in-theory        62109
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((((((A -> (not B)) -> (not A)) -> C) and D) or (((A -> (not B)) -> (not A)) -> C)) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)))
theorem-size     59
proof            (modus-ponens tm-747 tm-66 ((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-62109.        (((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)) and ((((((A -> (not B)) -> (not A)) -> C) and D) or (((A -> (not B)) -> (not A)) -> C)) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C))), M:tm-747, m:tm-66, u:((A (-> (-> (-> Am (not Bm)) (not Am)) Cm)) (B (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-62110
in-theory        62110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (((A and D) or A) -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)))
theorem-size     35
proof            (modus-ponens tm-747 tm-69 ((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-62110.        ((A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)) and (((A and D) or A) -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A))), M:tm-747, m:tm-69, u:((A Am) (B (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))
================================================================
tm-name          tm-62111
in-theory        62111
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((((A -> B) -> (A -> (not B))) and C) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A))))
theorem-size     42
proof            (modus-ponens tm-747 tm-70 ((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-62111.        ((((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))) and (((((A -> B) -> (A -> (not B))) and C) or ((A -> B) -> (A -> (not B)))) -> ((A -> B) -> (not A)))), M:tm-747, m:tm-70, u:((A (-> (-> Am Bm) (-> Am (not Bm)))) (B (-> (-> Am Bm) (not Am))))
================================================================
tm-name          tm-62112
in-theory        62112
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((A and D) or A) -> ((B -> C) -> ((B -> (not C)) -> (not B)))))
theorem-size     31
proof            (modus-ponens tm-747 tm-71 ((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-62112.        ((A -> ((B -> C) -> ((B -> (not C)) -> (not B)))) and (((A and D) or A) -> ((B -> C) -> ((B -> (not C)) -> (not B))))), M:tm-747, m:tm-71, u:((A Am) (B (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-62113
in-theory        62113
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((((not (not A)) -> (not A)) and B) or ((not (not A)) -> (not A))) -> (not (not (not A)))))
theorem-size     32
proof            (modus-ponens tm-747 tm-72 ((A (-> (not (not Am)) (not Am))) (B (not (not (not Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-10)
proof-size       132
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-62113.        ((((not (not A)) -> (not A)) -> (not (not (not A)))) and (((((not (not A)) -> (not A)) and B) or ((not (not A)) -> (not A))) -> (not (not (not A))))), M:tm-747, m:tm-72, u:((A (-> (not (not Am)) (not Am))) (B (not (not (not Am)))))
================================================================
tm-name          tm-62114
in-theory        62114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((not (not A)) or A) -> B)) and ((((A -> B) and C) or (A -> B)) -> (((not (not A)) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-747 tm-73 ((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-62114.        (((A -> B) -> (((not (not A)) or A) -> B)) and ((((A -> B) and C) or (A -> B)) -> (((not (not A)) or A) -> B))), M:tm-747, m:tm-73, u:((A (-> Am Bm)) (B (-> (or (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-62115
in-theory        62115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((not (not B)) -> B) and A)) and (((A and C) or A) -> (((not (not B)) -> B) and A)))
theorem-size     23
proof            (modus-ponens tm-747 tm-76 ((A Am) (B (and (-> (not (not Bm)) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-62115.        ((A -> (((not (not B)) -> B) and A)) and (((A and C) or A) -> (((not (not B)) -> B) and A))), M:tm-747, m:tm-76, u:((A Am) (B (and (-> (not (not Bm)) Bm) Am)))
================================================================
tm-name          tm-62116
in-theory        62116
times-derived    1
----------------------------------------------------------------
theorem          ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (((((not (not (A -> B))) -> A) and C) or ((not (not (A -> B))) -> A)) -> ((not (not (A -> B))) -> B)))
theorem-size     41
proof            (modus-ponens tm-747 tm-77 ((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-10)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-62116.        ((((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)) and (((((not (not (A -> B))) -> A) and C) or ((not (not (A -> B))) -> A)) -> ((not (not (A -> B))) -> B))), M:tm-747, m:tm-77, u:((A (-> (not (not (-> Am Bm))) Am)) (B (-> (not (not (-> Am Bm))) Bm)))
================================================================
tm-name          tm-62117
in-theory        62117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((not (not B)) -> B)) and (((A and C) or A) -> ((not (not B)) -> B)))
theorem-size     19
proof            (modus-ponens tm-747 tm-78 ((A Am) (B (-> (not (not Bm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-10)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-62117.        ((A -> ((not (not B)) -> B)) and (((A and C) or A) -> ((not (not B)) -> B))), M:tm-747, m:tm-78, u:((A Am) (B (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-62118
in-theory        62118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) -> (not A)) and ((((A -> (not (B -> (C -> B)))) and D) or (A -> (not (B -> (C -> B))))) -> (not A)))
theorem-size     34
proof            (modus-ponens tm-747 tm-79 ((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-1)
proof-size       146
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-62118.        (((A -> (not (B -> (C -> B)))) -> (not A)) and ((((A -> (not (B -> (C -> B)))) and D) or (A -> (not (B -> (C -> B))))) -> (not A))), M:tm-747, m:tm-79, u:((A (-> Am (not (-> Bm (-> Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-62119
in-theory        62119
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (((((A -> (B -> A)) -> C) and E) or ((A -> (B -> A)) -> C)) -> ((D or (A -> (B -> A))) -> C)))
theorem-size     45
proof            (modus-ponens tm-747 tm-80 ((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-62119.        ((((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)) and (((((A -> (B -> A)) -> C) and E) or ((A -> (B -> A)) -> C)) -> ((D or (A -> (B -> A))) -> C))), M:tm-747, m:tm-80, u:((A (-> (-> Am (-> Bm Am)) Cm)) (B (-> (or Dm (-> Am (-> Bm Am))) Cm)))
================================================================
tm-name          tm-62120
in-theory        62120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> C))) and A)) and (((A and E) or A) -> ((B -> (C -> (D -> C))) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-83 ((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-62120.        ((A -> ((B -> (C -> (D -> C))) and A)) and (((A and E) or A) -> ((B -> (C -> (D -> C))) and A))), M:tm-747, m:tm-83, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-62121
in-theory        62121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> B))) and ((((A -> B) and D) or (A -> B)) -> (A -> (C -> B))))
theorem-size     25
proof            (modus-ponens tm-747 tm-84 ((A (-> Am Bm)) (B (-> Am (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-62121.        (((A -> B) -> (A -> (C -> B))) and ((((A -> B) and D) or (A -> B)) -> (A -> (C -> B)))), M:tm-747, m:tm-84, u:((A (-> Am Bm)) (B (-> Am (-> Cm Bm))))
================================================================
tm-name          tm-62122
in-theory        62122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> C)))) and (((A and E) or A) -> (B -> (C -> (D -> C)))))
theorem-size     23
proof            (modus-ponens tm-747 tm-85 ((A Am) (B (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-62122.        ((A -> (B -> (C -> (D -> C)))) and (((A and E) or A) -> (B -> (C -> (D -> C))))), M:tm-747, m:tm-85, u:((A Am) (B (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-62123
in-theory        62123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> A) and (((A and B) or A) -> A))
theorem-size     11
proof            (modus-ponens tm-747 tm-86 ((A Am) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-62123.        ((A -> A) and (((A and B) or A) -> A)), M:tm-747, m:tm-86, u:((A Am) (B Am))
================================================================
tm-name          tm-62124
in-theory        62124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> (A -> (B -> C))) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> (B -> C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-87 ((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-62124.        (((A -> (B -> C)) -> (A -> (B -> C))) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> (B -> C)))), M:tm-747, m:tm-87, u:((A (-> Am (-> Bm Cm))) (B (-> Am (-> Bm Cm))))
================================================================
tm-name          tm-62125
in-theory        62125
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> (A and B)) and ((((A and B) and C) or (A and B)) -> (A and B)))
theorem-size     21
proof            (modus-ponens tm-747 tm-88 ((A (and Am Bm)) (B (and Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-62125.        (((A and B) -> (A and B)) and ((((A and B) and C) or (A and B)) -> (A and B))), M:tm-747, m:tm-88, u:((A (and Am Bm)) (B (and Am Bm)))
================================================================
tm-name          tm-62126
in-theory        62126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> B)) and ((((A -> B) and C) or (A -> B)) -> (A -> B)))
theorem-size     21
proof            (modus-ponens tm-747 tm-89 ((A (-> Am Bm)) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-62126.        (((A -> B) -> (A -> B)) and ((((A -> B) and C) or (A -> B)) -> (A -> B))), M:tm-747, m:tm-89, u:((A (-> Am Bm)) (B (-> Am Bm)))
================================================================
tm-name          tm-62127
in-theory        62127
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> (not (not A))) and ((((not (not A)) and B) or (not (not A))) -> (not (not A))))
theorem-size     21
proof            (modus-ponens tm-747 tm-90 ((A (not (not Am))) (B (not (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-10)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-62127.        (((not (not A)) -> (not (not A))) and ((((not (not A)) and B) or (not (not A))) -> (not (not A)))), M:tm-747, m:tm-90, u:((A (not (not Am))) (B (not (not Am))))
================================================================
tm-name          tm-62128
in-theory        62128
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((((A -> B) -> (not (A -> A))) and C) or ((A -> B) -> (not (A -> A)))) -> (not (A -> B))))
theorem-size     38
proof            (modus-ponens tm-747 tm-91 ((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-1)
proof-size       160
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-62128.        ((((A -> B) -> (not (A -> A))) -> (not (A -> B))) and (((((A -> B) -> (not (A -> A))) and C) or ((A -> B) -> (not (A -> A)))) -> (not (A -> B)))), M:tm-747, m:tm-91, u:((A (-> (-> Am Bm) (not (-> Am Am)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62129
in-theory        62129
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((((A -> A) -> B) and D) or ((A -> A) -> B)) -> (((A -> C) or (A -> A)) -> B)))
theorem-size     39
proof            (modus-ponens tm-747 tm-92 ((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-62129.        ((((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)) and (((((A -> A) -> B) and D) or ((A -> A) -> B)) -> (((A -> C) or (A -> A)) -> B))), M:tm-747, m:tm-92, u:((A (-> (-> Am Am) Bm)) (B (-> (or (-> Am Cm) (-> Am Am)) Bm)))
================================================================
tm-name          tm-62130
in-theory        62130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> B)) and A)) and (((A and D) or A) -> (((B -> C) -> (B -> B)) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-95 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-62130.        ((A -> (((B -> C) -> (B -> B)) and A)) and (((A and D) or A) -> (((B -> C) -> (B -> B)) and A))), M:tm-747, m:tm-95, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))
================================================================
tm-name          tm-62131
in-theory        62131
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> A)) and (((((A -> B) -> A) and C) or ((A -> B) -> A)) -> ((A -> B) -> A)))
theorem-size     31
proof            (modus-ponens tm-747 tm-96 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-62131.        ((((A -> B) -> A) -> ((A -> B) -> A)) and (((((A -> B) -> A) and C) or ((A -> B) -> A)) -> ((A -> B) -> A))), M:tm-747, m:tm-96, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) Am)))
================================================================
tm-name          tm-62132
in-theory        62132
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> B))) and (((A and D) or A) -> ((B -> C) -> (B -> B))))
theorem-size     23
proof            (modus-ponens tm-747 tm-97 ((A Am) (B (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-62132.        ((A -> ((B -> C) -> (B -> B))) and (((A and D) or A) -> ((B -> C) -> (B -> B)))), M:tm-747, m:tm-97, u:((A Am) (B (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-62133
in-theory        62133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> A) -> C)) -> (A -> C)) and ((((A -> ((B -> A) -> C)) and D) or (A -> ((B -> A) -> C))) -> (A -> C)))
theorem-size     33
proof            (modus-ponens tm-747 tm-98 ((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-62133.        (((A -> ((B -> A) -> C)) -> (A -> C)) and ((((A -> ((B -> A) -> C)) and D) or (A -> ((B -> A) -> C))) -> (A -> C))), M:tm-747, m:tm-98, u:((A (-> Am (-> (-> Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-62134
in-theory        62134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A -> B)) -> (A -> B)) and ((((A -> (A -> B)) and C) or (A -> (A -> B))) -> (A -> B)))
theorem-size     27
proof            (modus-ponens tm-747 tm-99 ((A (-> Am (-> Am Bm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-62134.        (((A -> (A -> B)) -> (A -> B)) and ((((A -> (A -> B)) and C) or (A -> (A -> B))) -> (A -> B))), M:tm-747, m:tm-99, u:((A (-> Am (-> Am Bm))) (B (-> Am Bm)))
================================================================
tm-name          tm-62135
in-theory        62135
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B))))
theorem-size     51
proof            (modus-ponens tm-747 tm-100 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-62135.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> B)))), M:tm-747, m:tm-100, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-62136
in-theory        62136
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) and D) or (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C))))) -> (not ((A -> (B -> C)) -> (A -> B)))))
theorem-size     86
proof            (modus-ponens tm-747 tm-101 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       246
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-62136.        (((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))) and ((((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) and D) or (((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C))))) -> (not ((A -> (B -> C)) -> (A -> B))))), M:tm-747, m:tm-101, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm))))) (B (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-62137
in-theory        62137
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((((((A -> (B -> C)) -> (A -> C)) -> D) and E) or (((A -> (B -> C)) -> (A -> C)) -> D)) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)))
theorem-size     81
proof            (modus-ponens tm-747 tm-102 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       245
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-62137.        (((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)) and ((((((A -> (B -> C)) -> (A -> C)) -> D) and E) or (((A -> (B -> C)) -> (A -> C)) -> D)) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D))), M:tm-747, m:tm-102, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm)) (B (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-62138
in-theory        62138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (((A and E) or A) -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)))
theorem-size     51
proof            (modus-ponens tm-747 tm-105 ((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-62138.        ((A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)) and (((A and E) or A) -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A))), M:tm-747, m:tm-105, u:((A Am) (B (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-62139
in-theory        62139
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) and D) or (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))))
theorem-size     77
proof            (modus-ponens tm-747 tm-106 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-62139.        (((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))) and ((((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) and D) or (((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C)))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C)))), M:tm-747, m:tm-106, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm)))) (B (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-62140
in-theory        62140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((A and E) or A) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     47
proof            (modus-ponens tm-747 tm-107 ((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-62140.        ((A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))) and (((A and E) or A) -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))))), M:tm-747, m:tm-107, u:((A Am) (B (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-62141
in-theory        62141
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) and E) or ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))) -> ((A -> (B -> C)) -> D)))
theorem-size     65
proof            (modus-ponens tm-747 tm-108 ((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       239
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-62141.        ((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)) and (((((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) and E) or ((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D))) -> ((A -> (B -> C)) -> D))), M:tm-747, m:tm-108, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (-> Am (-> Bm Cm)) Dm)))
================================================================
tm-name          tm-62142
in-theory        62142
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and E) or (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not A)))
theorem-size     58
proof            (modus-ponens tm-747 tm-109 ((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-1)
proof-size       194
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-62142.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)) and ((((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and E) or (A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not A))), M:tm-747, m:tm-109, u:((A (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))) (B (not Am)))
================================================================
tm-name          tm-62143
in-theory        62143
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and F) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D)) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)))
theorem-size     85
proof            (modus-ponens tm-747 tm-110 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       237
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-62143.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)) and ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and F) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D)) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))), M:tm-747, m:tm-110, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) (B (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))
================================================================
tm-name          tm-62144
in-theory        62144
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((A and F) or A) -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))
theorem-size     43
proof            (modus-ponens tm-747 tm-113 ((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-62144.        ((A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((A and F) or A) -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))), M:tm-747, m:tm-113, u:((A Am) (B (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-62145
in-theory        62145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((((A -> (B -> (C -> D))) and E) or (A -> (B -> (C -> D)))) -> (A -> ((B -> C) -> (B -> D)))))
theorem-size     45
proof            (modus-ponens tm-747 tm-114 ((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-62145.        (((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))) and ((((A -> (B -> (C -> D))) and E) or (A -> (B -> (C -> D)))) -> (A -> ((B -> C) -> (B -> D))))), M:tm-747, m:tm-114, u:((A (-> Am (-> Bm (-> Cm Dm)))) (B (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-62146
in-theory        62146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((A and F) or A) -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     39
proof            (modus-ponens tm-747 tm-115 ((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-62146.        ((A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((A and F) or A) -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-747, m:tm-115, u:((A Am) (B (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-62147
in-theory        62147
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and A) -> B) and (((((A -> B) and A) and C) or ((A -> B) and A)) -> B))
theorem-size     23
proof            (modus-ponens tm-747 tm-116 ((A (and (-> Am Bm) Am)) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-62147.        ((((A -> B) and A) -> B) and (((((A -> B) and A) and C) or ((A -> B) and A)) -> B)), M:tm-747, m:tm-116, u:((A (and (-> Am Bm) Am)) (B Bm))
================================================================
tm-name          tm-62148
in-theory        62148
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) -> C) and D) -> C) and ((((((A -> (B -> A)) -> C) and D) and E) or (((A -> (B -> A)) -> C) and D)) -> C))
theorem-size     35
proof            (modus-ponens tm-747 tm-117 ((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-62148.        (((((A -> (B -> A)) -> C) and D) -> C) and ((((((A -> (B -> A)) -> C) and D) and E) or (((A -> (B -> A)) -> C) and D)) -> C)), M:tm-747, m:tm-117, u:((A (and (-> (-> Am (-> Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-62149
in-theory        62149
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) and F) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E)) -> D))
theorem-size     59
proof            (modus-ponens tm-747 tm-118 ((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-62149.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D) and (((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) and F) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E)) -> D)), M:tm-747, m:tm-118, u:((A (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B Dm))
================================================================
tm-name          tm-62150
in-theory        62150
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((((((A -> B) -> A) and C) -> (A -> B)) and D) or ((((A -> B) -> A) and C) -> (A -> B))) -> ((((A -> B) -> A) and C) -> B)))
theorem-size     57
proof            (modus-ponens tm-747 tm-119 ((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-62150.        ((((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)) and (((((((A -> B) -> A) and C) -> (A -> B)) and D) or ((((A -> B) -> A) and C) -> (A -> B))) -> ((((A -> B) -> A) and C) -> B))), M:tm-747, m:tm-119, u:((A (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm))) (B (-> (and (-> (-> Am Bm) Am) Cm) Bm)))
================================================================
tm-name          tm-62151
in-theory        62151
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> A)))
theorem-size     41
proof            (modus-ponens tm-747 tm-120 ((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-62151.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> A))), M:tm-747, m:tm-120, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Am)))
================================================================
tm-name          tm-62152
in-theory        62152
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) and D) or ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B)))) -> (not (((A -> B) and C) -> A))))
theorem-size     70
proof            (modus-ponens tm-747 tm-121 ((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       212
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-62152.        ((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))) and (((((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) and D) or ((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B)))) -> (not (((A -> B) and C) -> A)))), M:tm-747, m:tm-121, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm)))) (B (not (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-62153
in-theory        62153
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((((((A -> B) and C) -> B) -> D) and E) or ((((A -> B) and C) -> B) -> D)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)))
theorem-size     67
proof            (modus-ponens tm-747 tm-122 ((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-62153.        ((((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)) and (((((((A -> B) and C) -> B) -> D) and E) or ((((A -> B) and C) -> B) -> D)) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D))), M:tm-747, m:tm-122, u:((A (-> (-> (and (-> Am Bm) Cm) Bm) Dm)) (B (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-62154
in-theory        62154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (((A and E) or A) -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)))
theorem-size     43
proof            (modus-ponens tm-747 tm-125 ((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-62154.        ((A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)) and (((A and E) or A) -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A))), M:tm-747, m:tm-125, u:((A Am) (B (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))
================================================================
tm-name          tm-62155
in-theory        62155
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (((((((A -> B) and C) -> A) -> ((A -> B) and C)) and D) or ((((A -> B) and C) -> A) -> ((A -> B) and C))) -> ((((A -> B) and C) -> A) -> B)))
theorem-size     63
proof            (modus-ponens tm-747 tm-126 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-62155.        ((((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)) and (((((((A -> B) and C) -> A) -> ((A -> B) and C)) and D) or ((((A -> B) and C) -> A) -> ((A -> B) and C))) -> ((((A -> B) and C) -> A) -> B))), M:tm-747, m:tm-126, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm))) (B (-> (-> (and (-> Am Bm) Cm) Am) Bm)))
================================================================
tm-name          tm-62156
in-theory        62156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((A and E) or A) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))))
theorem-size     39
proof            (modus-ponens tm-747 tm-127 ((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-62156.        ((A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))) and (((A and E) or A) -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)))), M:tm-747, m:tm-127, u:((A Am) (B (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-62157
in-theory        62157
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) -> C) and D) -> C) and (((((((A and B) -> A) -> C) and D) and E) or ((((A and B) -> A) -> C) and D)) -> C))
theorem-size     35
proof            (modus-ponens tm-747 tm-128 ((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-62157.        ((((((A and B) -> A) -> C) and D) -> C) and (((((((A and B) -> A) -> C) and D) and E) or ((((A and B) -> A) -> C) and D)) -> C)), M:tm-747, m:tm-128, u:((A (and (-> (-> (and Am Bm) Am) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-62158
in-theory        62158
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((((A and B) -> (A -> C)) and D) or ((A and B) -> (A -> C))) -> ((A and B) -> C)))
theorem-size     37
proof            (modus-ponens tm-747 tm-129 ((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-62158.        ((((A and B) -> (A -> C)) -> ((A and B) -> C)) and (((((A and B) -> (A -> C)) and D) or ((A and B) -> (A -> C))) -> ((A and B) -> C))), M:tm-747, m:tm-129, u:((A (-> (and Am Bm) (-> Am Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-62159
in-theory        62159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) -> (not A)) and ((((A -> (not ((B and C) -> B))) and D) or (A -> (not ((B and C) -> B)))) -> (not A)))
theorem-size     34
proof            (modus-ponens tm-747 tm-130 ((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-1)
proof-size       146
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-62159.        (((A -> (not ((B and C) -> B))) -> (not A)) and ((((A -> (not ((B and C) -> B))) and D) or (A -> (not ((B and C) -> B)))) -> (not A))), M:tm-747, m:tm-130, u:((A (-> Am (not (-> (and Bm Cm) Bm)))) (B (not Am)))
================================================================
tm-name          tm-62160
in-theory        62160
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((((((A and B) -> A) -> C) and E) or (((A and B) -> A) -> C)) -> ((D or ((A and B) -> A)) -> C)))
theorem-size     45
proof            (modus-ponens tm-747 tm-131 ((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-62160.        (((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)) and ((((((A and B) -> A) -> C) and E) or (((A and B) -> A) -> C)) -> ((D or ((A and B) -> A)) -> C))), M:tm-747, m:tm-131, u:((A (-> (-> (and Am Bm) Am) Cm)) (B (-> (or Dm (-> (and Am Bm) Am)) Cm)))
================================================================
tm-name          tm-62161
in-theory        62161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> C)) and A)) and (((A and E) or A) -> ((B -> ((C and D) -> C)) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-134 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-62161.        ((A -> ((B -> ((C and D) -> C)) and A)) and (((A and E) or A) -> ((B -> ((C and D) -> C)) and A))), M:tm-747, m:tm-134, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-62162
in-theory        62162
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> B)) and ((((A -> (B and C)) and D) or (A -> (B and C))) -> (A -> B)))
theorem-size     27
proof            (modus-ponens tm-747 tm-135 ((A (-> Am (and Bm Cm))) (B (-> Am Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-62162.        (((A -> (B and C)) -> (A -> B)) and ((((A -> (B and C)) and D) or (A -> (B and C))) -> (A -> B))), M:tm-747, m:tm-135, u:((A (-> Am (and Bm Cm))) (B (-> Am Bm)))
================================================================
tm-name          tm-62163
in-theory        62163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> C))) and (((A and E) or A) -> (B -> ((C and D) -> C))))
theorem-size     23
proof            (modus-ponens tm-747 tm-136 ((A Am) (B (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-62163.        ((A -> (B -> ((C and D) -> C))) and (((A and E) or A) -> (B -> ((C and D) -> C)))), M:tm-747, m:tm-136, u:((A Am) (B (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-62164
in-theory        62164
times-derived    1
----------------------------------------------------------------
theorem          (((A and (A -> B)) -> B) and ((((A and (A -> B)) and C) or (A and (A -> B))) -> B))
theorem-size     23
proof            (modus-ponens tm-747 tm-137 ((A (and Am (-> Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-62164.        (((A and (A -> B)) -> B) and ((((A and (A -> B)) and C) or (A and (A -> B))) -> B)), M:tm-747, m:tm-137, u:((A (and Am (-> Am Bm))) (B Bm))
================================================================
tm-name          tm-62165
in-theory        62165
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> B)) -> D)) -> D) and ((((A and ((B -> (C -> B)) -> D)) and E) or (A and ((B -> (C -> B)) -> D))) -> D))
theorem-size     35
proof            (modus-ponens tm-747 tm-138 ((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-62165.        (((A and ((B -> (C -> B)) -> D)) -> D) and ((((A and ((B -> (C -> B)) -> D)) and E) or (A and ((B -> (C -> B)) -> D))) -> D)), M:tm-747, m:tm-138, u:((A (and Am (-> (-> Bm (-> Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-62166
in-theory        62166
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) and F) or (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E))) -> E))
theorem-size     59
proof            (modus-ponens tm-747 tm-139 ((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-62166.        (((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E) and ((((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) and F) or (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E))) -> E)), M:tm-747, m:tm-139, u:((A (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))) (B Em))
================================================================
tm-name          tm-62167
in-theory        62167
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> B) -> D)) -> D) and ((((A and (((B and C) -> B) -> D)) and E) or (A and (((B and C) -> B) -> D))) -> D))
theorem-size     35
proof            (modus-ponens tm-747 tm-140 ((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-62167.        (((A and (((B and C) -> B) -> D)) -> D) and ((((A and (((B and C) -> B) -> D)) and E) or (A and (((B and C) -> B) -> D))) -> D)), M:tm-747, m:tm-140, u:((A (and Am (-> (-> (and Bm Cm) Bm) Dm))) (B Dm))
================================================================
tm-name          tm-62168
in-theory        62168
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((((A and ((B -> C) -> B)) -> (B -> C)) and D) or ((A and ((B -> C) -> B)) -> (B -> C))) -> ((A and ((B -> C) -> B)) -> C)))
theorem-size     57
proof            (modus-ponens tm-747 tm-141 ((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-62168.        ((((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)) and (((((A and ((B -> C) -> B)) -> (B -> C)) and D) or ((A and ((B -> C) -> B)) -> (B -> C))) -> ((A and ((B -> C) -> B)) -> C))), M:tm-747, m:tm-141, u:((A (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm))) (B (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))
================================================================
tm-name          tm-62169
in-theory        62169
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> B)))
theorem-size     41
proof            (modus-ponens tm-747 tm-142 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-62169.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> B))), M:tm-747, m:tm-142, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Bm)))
================================================================
tm-name          tm-62170
in-theory        62170
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) and D) or (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C)))) -> (not ((A and (B -> C)) -> B))))
theorem-size     70
proof            (modus-ponens tm-747 tm-143 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-4)
proof-size       212
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-62170.        (((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))) and ((((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) and D) or (((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C)))) -> (not ((A and (B -> C)) -> B)))), M:tm-747, m:tm-143, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm)))) (B (not (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-62171
in-theory        62171
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((((((A and (B -> C)) -> C) -> D) and E) or (((A and (B -> C)) -> C) -> D)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)))
theorem-size     67
proof            (modus-ponens tm-747 tm-144 ((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-62171.        (((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)) and ((((((A and (B -> C)) -> C) -> D) and E) or (((A and (B -> C)) -> C) -> D)) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D))), M:tm-747, m:tm-144, u:((A (-> (-> (and Am (-> Bm Cm)) Cm) Dm)) (B (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-62172
in-theory        62172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (((A and E) or A) -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)))
theorem-size     43
proof            (modus-ponens tm-747 tm-147 ((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-62172.        ((A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)) and (((A and E) or A) -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A))), M:tm-747, m:tm-147, u:((A Am) (B (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))
================================================================
tm-name          tm-62173
in-theory        62173
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((((((A and (B -> C)) -> B) -> (A and (B -> C))) and D) or (((A and (B -> C)) -> B) -> (A and (B -> C)))) -> (((A and (B -> C)) -> B) -> C)))
theorem-size     63
proof            (modus-ponens tm-747 tm-148 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-62173.        (((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)) and ((((((A and (B -> C)) -> B) -> (A and (B -> C))) and D) or (((A and (B -> C)) -> B) -> (A and (B -> C)))) -> (((A and (B -> C)) -> B) -> C))), M:tm-747, m:tm-148, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm)))) (B (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))
================================================================
tm-name          tm-62174
in-theory        62174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((A and E) or A) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))))
theorem-size     39
proof            (modus-ponens tm-747 tm-149 ((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-62174.        ((A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))) and (((A and E) or A) -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)))), M:tm-747, m:tm-149, u:((A Am) (B (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-62175
in-theory        62175
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B and C) -> C) -> D)) -> D) and ((((A and (((B and C) -> C) -> D)) and E) or (A and (((B and C) -> C) -> D))) -> D))
theorem-size     35
proof            (modus-ponens tm-747 tm-150 ((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-62175.        (((A and (((B and C) -> C) -> D)) -> D) and ((((A and (((B and C) -> C) -> D)) and E) or (A and (((B and C) -> C) -> D))) -> D)), M:tm-747, m:tm-150, u:((A (and Am (-> (-> (and Bm Cm) Cm) Dm))) (B Dm))
================================================================
tm-name          tm-62176
in-theory        62176
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) -> C) and D) -> C) and (((((((A and B) -> B) -> C) and D) and E) or ((((A and B) -> B) -> C) and D)) -> C))
theorem-size     35
proof            (modus-ponens tm-747 tm-151 ((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-62176.        ((((((A and B) -> B) -> C) and D) -> C) and (((((((A and B) -> B) -> C) and D) and E) or ((((A and B) -> B) -> C) and D)) -> C)), M:tm-747, m:tm-151, u:((A (and (-> (-> (and Am Bm) Bm) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-62177
in-theory        62177
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((((A and B) -> (B -> C)) and D) or ((A and B) -> (B -> C))) -> ((A and B) -> C)))
theorem-size     37
proof            (modus-ponens tm-747 tm-152 ((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-62177.        ((((A and B) -> (B -> C)) -> ((A and B) -> C)) and (((((A and B) -> (B -> C)) and D) or ((A and B) -> (B -> C))) -> ((A and B) -> C))), M:tm-747, m:tm-152, u:((A (-> (and Am Bm) (-> Bm Cm))) (B (-> (and Am Bm) Cm)))
================================================================
tm-name          tm-62178
in-theory        62178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) -> (not A)) and ((((A -> (not ((B and C) -> C))) and D) or (A -> (not ((B and C) -> C)))) -> (not A)))
theorem-size     34
proof            (modus-ponens tm-747 tm-153 ((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-1 tm-4)
proof-size       146
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-62178.        (((A -> (not ((B and C) -> C))) -> (not A)) and ((((A -> (not ((B and C) -> C))) and D) or (A -> (not ((B and C) -> C)))) -> (not A))), M:tm-747, m:tm-153, u:((A (-> Am (not (-> (and Bm Cm) Cm)))) (B (not Am)))
================================================================
tm-name          tm-62179
in-theory        62179
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((((((A and B) -> B) -> C) and E) or (((A and B) -> B) -> C)) -> ((D or ((A and B) -> B)) -> C)))
theorem-size     45
proof            (modus-ponens tm-747 tm-154 ((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-62179.        (((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)) and ((((((A and B) -> B) -> C) and E) or (((A and B) -> B) -> C)) -> ((D or ((A and B) -> B)) -> C))), M:tm-747, m:tm-154, u:((A (-> (-> (and Am Bm) Bm) Cm)) (B (-> (or Dm (-> (and Am Bm) Bm)) Cm)))
================================================================
tm-name          tm-62180
in-theory        62180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C and D) -> D)) and A)) and (((A and E) or A) -> ((B -> ((C and D) -> D)) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-157 ((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-62180.        ((A -> ((B -> ((C and D) -> D)) and A)) and (((A and E) or A) -> ((B -> ((C and D) -> D)) and A))), M:tm-747, m:tm-157, u:((A Am) (B (and (-> Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-62181
in-theory        62181
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) -> (A -> C)) and ((((A -> (B and C)) and D) or (A -> (B and C))) -> (A -> C)))
theorem-size     27
proof            (modus-ponens tm-747 tm-158 ((A (-> Am (and Bm Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-62181.        (((A -> (B and C)) -> (A -> C)) and ((((A -> (B and C)) and D) or (A -> (B and C))) -> (A -> C))), M:tm-747, m:tm-158, u:((A (-> Am (and Bm Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-62182
in-theory        62182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C and D) -> D))) and (((A and E) or A) -> (B -> ((C and D) -> D))))
theorem-size     23
proof            (modus-ponens tm-747 tm-159 ((A Am) (B (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-62182.        ((A -> (B -> ((C and D) -> D))) and (((A and E) or A) -> (B -> ((C and D) -> D)))), M:tm-747, m:tm-159, u:((A Am) (B (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-62183
in-theory        62183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((((A -> (not ((B -> (C -> B)) and A))) and D) or (A -> (not ((B -> (C -> B)) and A)))) -> (not A)))
theorem-size     40
proof            (modus-ponens tm-747 tm-179 ((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-1)
proof-size       158
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-62183.        (((A -> (not ((B -> (C -> B)) and A))) -> (not A)) and ((((A -> (not ((B -> (C -> B)) and A))) and D) or (A -> (not ((B -> (C -> B)) and A)))) -> (not A))), M:tm-747, m:tm-179, u:((A (-> Am (not (and (-> Bm (-> Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-62184
in-theory        62184
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((((((A -> (B -> A)) and C) -> D) and E) or (((A -> (B -> A)) and C) -> D)) -> ((C or ((A -> (B -> A)) and C)) -> D)))
theorem-size     55
proof            (modus-ponens tm-747 tm-180 ((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-62184.        (((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)) and ((((((A -> (B -> A)) and C) -> D) and E) or (((A -> (B -> A)) and C) -> D)) -> ((C or ((A -> (B -> A)) and C)) -> D))), M:tm-747, m:tm-180, u:((A (-> (and (-> Am (-> Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-62185
in-theory        62185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (((A and E) or A) -> ((B -> ((C -> (D -> C)) and B)) and A)))
theorem-size     31
proof            (modus-ponens tm-747 tm-183 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-62185.        ((A -> ((B -> ((C -> (D -> C)) and B)) and A)) and (((A and E) or A) -> ((B -> ((C -> (D -> C)) and B)) and A))), M:tm-747, m:tm-183, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-62186
in-theory        62186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> C)) and B))) and (((A and E) or A) -> (B -> ((C -> (D -> C)) and B))))
theorem-size     27
proof            (modus-ponens tm-747 tm-184 ((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-62186.        ((A -> (B -> ((C -> (D -> C)) and B))) and (((A and E) or A) -> (B -> ((C -> (D -> C)) and B)))), M:tm-747, m:tm-184, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-62187
in-theory        62187
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and E) or (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))) -> (not A)))
theorem-size     64
proof            (modus-ponens tm-747 tm-206 ((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       206
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-62187.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)) and ((((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and E) or (A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))) -> (not A))), M:tm-747, m:tm-206, u:((A (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-62188
in-theory        62188
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) and F) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E)) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)))
theorem-size     95
proof            (modus-ponens tm-747 tm-207 ((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-62188.        ((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)) and (((((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) and F) or ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E)) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))), M:tm-747, m:tm-207, u:((A (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-62189
in-theory        62189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (((A and F) or A) -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)))
theorem-size     47
proof            (modus-ponens tm-747 tm-210 ((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-62189.        ((A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)) and (((A and F) or A) -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A))), M:tm-747, m:tm-210, u:((A Am) (B (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))
================================================================
tm-name          tm-62190
in-theory        62190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((A and F) or A) -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     43
proof            (modus-ponens tm-747 tm-211 ((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-62190.        ((A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) and (((A and F) or A) -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-747, m:tm-211, u:((A Am) (B (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-62191
in-theory        62191
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((((A -> (not (((B and C) -> B) and A))) and D) or (A -> (not (((B and C) -> B) and A)))) -> (not A)))
theorem-size     40
proof            (modus-ponens tm-747 tm-235 ((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       158
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-62191.        (((A -> (not (((B and C) -> B) and A))) -> (not A)) and ((((A -> (not (((B and C) -> B) and A))) and D) or (A -> (not (((B and C) -> B) and A)))) -> (not A))), M:tm-747, m:tm-235, u:((A (-> Am (not (and (-> (and Bm Cm) Bm) Am)))) (B (not Am)))
================================================================
tm-name          tm-62192
in-theory        62192
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (((((((A and B) -> A) and C) -> D) and E) or ((((A and B) -> A) and C) -> D)) -> ((C or (((A and B) -> A) and C)) -> D)))
theorem-size     55
proof            (modus-ponens tm-747 tm-236 ((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-62192.        ((((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)) and (((((((A and B) -> A) and C) -> D) and E) or ((((A and B) -> A) and C) -> D)) -> ((C or (((A and B) -> A) and C)) -> D))), M:tm-747, m:tm-236, u:((A (-> (and (-> (and Am Bm) Am) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-62193
in-theory        62193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (((A and E) or A) -> ((B -> (((C and D) -> C) and B)) and A)))
theorem-size     31
proof            (modus-ponens tm-747 tm-239 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-62193.        ((A -> ((B -> (((C and D) -> C) and B)) and A)) and (((A and E) or A) -> ((B -> (((C and D) -> C) and B)) and A))), M:tm-747, m:tm-239, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))
================================================================
tm-name          tm-62194
in-theory        62194
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> C) and B))) and (((A and E) or A) -> (B -> (((C and D) -> C) and B))))
theorem-size     27
proof            (modus-ponens tm-747 tm-240 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-62194.        ((A -> (B -> (((C and D) -> C) and B))) and (((A and E) or A) -> (B -> (((C and D) -> C) and B)))), M:tm-747, m:tm-240, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-62195
in-theory        62195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((((A -> (not (((B and C) -> C) and A))) and D) or (A -> (not (((B and C) -> C) and A)))) -> (not A)))
theorem-size     40
proof            (modus-ponens tm-747 tm-266 ((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-4)
proof-size       158
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-62195.        (((A -> (not (((B and C) -> C) and A))) -> (not A)) and ((((A -> (not (((B and C) -> C) and A))) and D) or (A -> (not (((B and C) -> C) and A)))) -> (not A))), M:tm-747, m:tm-266, u:((A (-> Am (not (and (-> (and Bm Cm) Cm) Am)))) (B (not Am)))
================================================================
tm-name          tm-62196
in-theory        62196
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (((((((A and B) -> B) and C) -> D) and E) or ((((A and B) -> B) and C) -> D)) -> ((C or (((A and B) -> B) and C)) -> D)))
theorem-size     55
proof            (modus-ponens tm-747 tm-267 ((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-62196.        ((((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)) and (((((((A and B) -> B) and C) -> D) and E) or ((((A and B) -> B) and C) -> D)) -> ((C or (((A and B) -> B) and C)) -> D))), M:tm-747, m:tm-267, u:((A (-> (and (-> (and Am Bm) Bm) Cm) Dm)) (B (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))
================================================================
tm-name          tm-62197
in-theory        62197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (((A and E) or A) -> ((B -> (((C and D) -> D) and B)) and A)))
theorem-size     31
proof            (modus-ponens tm-747 tm-270 ((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-62197.        ((A -> ((B -> (((C and D) -> D) and B)) and A)) and (((A and E) or A) -> ((B -> (((C and D) -> D) and B)) and A))), M:tm-747, m:tm-270, u:((A Am) (B (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))
================================================================
tm-name          tm-62198
in-theory        62198
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (((C and D) -> D) and B))) and (((A and E) or A) -> (B -> (((C and D) -> D) and B))))
theorem-size     27
proof            (modus-ponens tm-747 tm-271 ((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-62198.        ((A -> (B -> (((C and D) -> D) and B))) and (((A and E) or A) -> (B -> (((C and D) -> D) and B)))), M:tm-747, m:tm-271, u:((A Am) (B (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-62199
in-theory        62199
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((((A -> (not ((B -> (C -> (B and C))) and A))) and D) or (A -> (not ((B -> (C -> (B and C))) and A)))) -> (not A)))
theorem-size     46
proof            (modus-ponens tm-747 tm-299 ((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       170
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-62199.        (((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)) and ((((A -> (not ((B -> (C -> (B and C))) and A))) and D) or (A -> (not ((B -> (C -> (B and C))) and A)))) -> (not A))), M:tm-747, m:tm-299, u:((A (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am)))) (B (not Am)))
================================================================
tm-name          tm-62200
in-theory        62200
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((((((A -> (B -> (A and B))) and C) -> D) and E) or (((A -> (B -> (A and B))) and C) -> D)) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)))
theorem-size     65
proof            (modus-ponens tm-747 tm-300 ((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-62200.        (((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)) and ((((((A -> (B -> (A and B))) and C) -> D) and E) or (((A -> (B -> (A and B))) and C) -> D)) -> ((C or ((A -> (B -> (A and B))) and C)) -> D))), M:tm-747, m:tm-300, u:((A (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))
================================================================
tm-name          tm-62201
in-theory        62201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (((A and E) or A) -> ((B -> ((C -> (D -> (C and D))) and B)) and A)))
theorem-size     35
proof            (modus-ponens tm-747 tm-303 ((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-62201.        ((A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)) and (((A and E) or A) -> ((B -> ((C -> (D -> (C and D))) and B)) and A))), M:tm-747, m:tm-303, u:((A Am) (B (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))
================================================================
tm-name          tm-62202
in-theory        62202
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (((A and E) or A) -> (B -> ((C -> (D -> (C and D))) and B))))
theorem-size     31
proof            (modus-ponens tm-747 tm-304 ((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-62202.        ((A -> (B -> ((C -> (D -> (C and D))) and B))) and (((A and E) or A) -> (B -> ((C -> (D -> (C and D))) and B)))), M:tm-747, m:tm-304, u:((A Am) (B (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-62203
in-theory        62203
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> A))) and (((A and C) or A) -> (A and (B -> A))))
theorem-size     19
proof            (modus-ponens tm-747 tm-305 ((A Am) (B (and Am (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-62203.        ((A -> (A and (B -> A))) and (((A and C) or A) -> (A and (B -> A)))), M:tm-747, m:tm-305, u:((A Am) (B (and Am (-> Bm Am))))
================================================================
tm-name          tm-62204
in-theory        62204
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))))
theorem-size     47
proof            (modus-ponens tm-747 tm-306 ((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-62204.        (((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C))))), M:tm-747, m:tm-306, u:((A (-> Am (-> Bm Cm))) (B (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-62205
in-theory        62205
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and A)) and ((((A and B) and C) or (A and B)) -> ((A and B) and A)))
theorem-size     25
proof            (modus-ponens tm-747 tm-307 ((A (and Am Bm)) (B (and (and Am Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-62205.        (((A and B) -> ((A and B) and A)) and ((((A and B) and C) or (A and B)) -> ((A and B) and A))), M:tm-747, m:tm-307, u:((A (and Am Bm)) (B (and (and Am Bm) Am)))
================================================================
tm-name          tm-62206
in-theory        62206
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> ((A and B) and B)) and ((((A and B) and C) or (A and B)) -> ((A and B) and B)))
theorem-size     25
proof            (modus-ponens tm-747 tm-308 ((A (and Am Bm)) (B (and (and Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-62206.        (((A and B) -> ((A and B) and B)) and ((((A and B) and C) or (A and B)) -> ((A and B) and B))), M:tm-747, m:tm-308, u:((A (and Am Bm)) (B (and (and Am Bm) Bm)))
================================================================
tm-name          tm-62207
in-theory        62207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (A and B)))) and (((A and C) or A) -> (A and (B -> (A and B)))))
theorem-size     23
proof            (modus-ponens tm-747 tm-309 ((A Am) (B (and Am (-> Bm (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-62207.        ((A -> (A and (B -> (A and B)))) and (((A and C) or A) -> (A and (B -> (A and B))))), M:tm-747, m:tm-309, u:((A Am) (B (and Am (-> Bm (and Am Bm)))))
================================================================
tm-name          tm-62208
in-theory        62208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (A or B))) and (((A and C) or A) -> (A and (A or B))))
theorem-size     19
proof            (modus-ponens tm-747 tm-310 ((A Am) (B (and Am (or Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-62208.        ((A -> (A and (A or B))) and (((A and C) or A) -> (A and (A or B)))), M:tm-747, m:tm-310, u:((A Am) (B (and Am (or Am Bm))))
================================================================
tm-name          tm-62209
in-theory        62209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B or A))) and (((A and C) or A) -> (A and (B or A))))
theorem-size     19
proof            (modus-ponens tm-747 tm-311 ((A Am) (B (and Am (or Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-62209.        ((A -> (A and (B or A))) and (((A and C) or A) -> (A and (B or A)))), M:tm-747, m:tm-311, u:((A Am) (B (and Am (or Bm Am))))
================================================================
tm-name          tm-62210
in-theory        62210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) and D) or (A -> B)) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-747 tm-312 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-62210.        (((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))) and ((((A -> B) and D) or (A -> B)) -> ((A -> B) and ((B -> C) -> ((A or B) -> C))))), M:tm-747, m:tm-312, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-62211
in-theory        62211
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((((A -> B) and C) or (A -> B)) -> ((A -> B) and ((A -> (not B)) -> (not A)))))
theorem-size     37
proof            (modus-ponens tm-747 tm-313 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-62211.        (((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))) and ((((A -> B) and C) or (A -> B)) -> ((A -> B) and ((A -> (not B)) -> (not A))))), M:tm-747, m:tm-313, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-62212
in-theory        62212
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> ((not (not A)) and A)) and ((((not (not A)) and B) or (not (not A))) -> ((not (not A)) and A)))
theorem-size     25
proof            (modus-ponens tm-747 tm-314 ((A (not (not Am))) (B (and (not (not Am)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-10)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-62212.        (((not (not A)) -> ((not (not A)) and A)) and ((((not (not A)) and B) or (not (not A))) -> ((not (not A)) and A))), M:tm-747, m:tm-314, u:((A (not (not Am))) (B (and (not (not Am)) Am)))
================================================================
tm-name          tm-62213
in-theory        62213
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> B)))) and (((A and D) or A) -> (A and (B -> (C -> B)))))
theorem-size     23
proof            (modus-ponens tm-747 tm-315 ((A Am) (B (and Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-62213.        ((A -> (A and (B -> (C -> B)))) and (((A and D) or A) -> (A and (B -> (C -> B))))), M:tm-747, m:tm-315, u:((A Am) (B (and Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-62214
in-theory        62214
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> A))) and ((((A -> B) and C) or (A -> B)) -> ((A -> B) and (A -> A))))
theorem-size     29
proof            (modus-ponens tm-747 tm-316 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-62214.        (((A -> B) -> ((A -> B) and (A -> A))) and ((((A -> B) and C) or (A -> B)) -> ((A -> B) and (A -> A)))), M:tm-747, m:tm-316, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-62215
in-theory        62215
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))))
theorem-size     71
proof            (modus-ponens tm-747 tm-317 ((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       247
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-62215.        ((((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))) and (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C))))), M:tm-747, m:tm-317, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-62216
in-theory        62216
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (((A and E) or A) -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))
theorem-size     39
proof            (modus-ponens tm-747 tm-318 ((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-62216.        ((A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) and (((A and E) or A) -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))), M:tm-747, m:tm-318, u:((A Am) (B (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-62217
in-theory        62217
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))))
theorem-size     57
proof            (modus-ponens tm-747 tm-319 ((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-62217.        (((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))) and ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B)))), M:tm-747, m:tm-319, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-62218
in-theory        62218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> B))) and (((A and D) or A) -> (A and ((B and C) -> B))))
theorem-size     23
proof            (modus-ponens tm-747 tm-320 ((A Am) (B (and Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-62218.        ((A -> (A and ((B and C) -> B))) and (((A and D) or A) -> (A and ((B and C) -> B)))), M:tm-747, m:tm-320, u:((A Am) (B (and Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-62219
in-theory        62219
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))))
theorem-size     57
proof            (modus-ponens tm-747 tm-321 ((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-62219.        ((((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))) and (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C)))), M:tm-747, m:tm-321, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-62220
in-theory        62220
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B and C) -> C))) and (((A and D) or A) -> (A and ((B and C) -> C))))
theorem-size     23
proof            (modus-ponens tm-747 tm-322 ((A Am) (B (and Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-62220.        ((A -> (A and ((B and C) -> C))) and (((A and D) or A) -> (A and ((B and C) -> C)))), M:tm-747, m:tm-322, u:((A Am) (B (and Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-62221
in-theory        62221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> B)) and A))) and (((A and D) or A) -> (A and ((B -> (C -> B)) and A))))
theorem-size     27
proof            (modus-ponens tm-747 tm-323 ((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-62221.        ((A -> (A and ((B -> (C -> B)) and A))) and (((A and D) or A) -> (A and ((B -> (C -> B)) and A)))), M:tm-747, m:tm-323, u:((A Am) (B (and Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-62222
in-theory        62222
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (((A and E) or A) -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))))
theorem-size     43
proof            (modus-ponens tm-747 tm-324 ((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-62222.        ((A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) and (((A and E) or A) -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))), M:tm-747, m:tm-324, u:((A Am) (B (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-62223
in-theory        62223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> B) and A))) and (((A and D) or A) -> (A and (((B and C) -> B) and A))))
theorem-size     27
proof            (modus-ponens tm-747 tm-325 ((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-62223.        ((A -> (A and (((B and C) -> B) and A))) and (((A and D) or A) -> (A and (((B and C) -> B) and A)))), M:tm-747, m:tm-325, u:((A Am) (B (and Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-62224
in-theory        62224
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (((B and C) -> C) and A))) and (((A and D) or A) -> (A and (((B and C) -> C) and A))))
theorem-size     27
proof            (modus-ponens tm-747 tm-326 ((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-62224.        ((A -> (A and (((B and C) -> C) and A))) and (((A and D) or A) -> (A and (((B and C) -> C) and A)))), M:tm-747, m:tm-326, u:((A Am) (B (and Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-62225
in-theory        62225
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C -> (B and C))) and A))) and (((A and D) or A) -> (A and ((B -> (C -> (B and C))) and A))))
theorem-size     31
proof            (modus-ponens tm-747 tm-327 ((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-62225.        ((A -> (A and ((B -> (C -> (B and C))) and A))) and (((A and D) or A) -> (A and ((B -> (C -> (B and C))) and A)))), M:tm-747, m:tm-327, u:((A Am) (B (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-62226
in-theory        62226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((((A -> B) and C) or (A -> B)) -> ((A -> B) and (A -> (A and B)))))
theorem-size     33
proof            (modus-ponens tm-747 tm-328 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-62226.        (((A -> B) -> ((A -> B) and (A -> (A and B)))) and ((((A -> B) and C) or (A -> B)) -> ((A -> B) and (A -> (A and B))))), M:tm-747, m:tm-328, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-62227
in-theory        62227
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((((A -> B) -> (not (A -> (A and B)))) and C) or ((A -> B) -> (not (A -> (A and B))))) -> (not (A -> B))))
theorem-size     44
proof            (modus-ponens tm-747 tm-334 ((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       172
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-62227.        ((((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))) and (((((A -> B) -> (not (A -> (A and B)))) and C) or ((A -> B) -> (not (A -> (A and B))))) -> (not (A -> B)))), M:tm-747, m:tm-334, u:((A (-> (-> Am Bm) (not (-> Am (and Am Bm))))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62228
in-theory        62228
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((((A -> (A and B)) -> C) and D) or ((A -> (A and B)) -> C)) -> (((A -> B) or (A -> (A and B))) -> C)))
theorem-size     49
proof            (modus-ponens tm-747 tm-335 ((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-62228.        ((((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)) and (((((A -> (A and B)) -> C) and D) or ((A -> (A and B)) -> C)) -> (((A -> B) or (A -> (A and B))) -> C))), M:tm-747, m:tm-335, u:((A (-> (-> Am (and Am Bm)) Cm)) (B (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-62229
in-theory        62229
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (((A and D) or A) -> (((B -> C) -> (B -> (B and C))) and A)))
theorem-size     31
proof            (modus-ponens tm-747 tm-338 ((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-62229.        ((A -> (((B -> C) -> (B -> (B and C))) and A)) and (((A and D) or A) -> (((B -> C) -> (B -> (B and C))) and A))), M:tm-747, m:tm-338, u:((A Am) (B (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))
================================================================
tm-name          tm-62230
in-theory        62230
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (((((A -> B) -> A) and C) or ((A -> B) -> A)) -> ((A -> B) -> (A and B))))
theorem-size     35
proof            (modus-ponens tm-747 tm-339 ((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-62230.        ((((A -> B) -> A) -> ((A -> B) -> (A and B))) and (((((A -> B) -> A) and C) or ((A -> B) -> A)) -> ((A -> B) -> (A and B)))), M:tm-747, m:tm-339, u:((A (-> (-> Am Bm) Am)) (B (-> (-> Am Bm) (and Am Bm))))
================================================================
tm-name          tm-62231
in-theory        62231
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (B -> (B and C)))) and (((A and D) or A) -> ((B -> C) -> (B -> (B and C)))))
theorem-size     27
proof            (modus-ponens tm-747 tm-340 ((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-62231.        ((A -> ((B -> C) -> (B -> (B and C)))) and (((A and D) or A) -> ((B -> C) -> (B -> (B and C))))), M:tm-747, m:tm-340, u:((A Am) (B (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-62232
in-theory        62232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C -> (B and C))))) and (((A and D) or A) -> (A and (B -> (C -> (B and C))))))
theorem-size     27
proof            (modus-ponens tm-747 tm-341 ((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-62232.        ((A -> (A and (B -> (C -> (B and C))))) and (((A and D) or A) -> (A and (B -> (C -> (B and C)))))), M:tm-747, m:tm-341, u:((A Am) (B (and Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-62233
in-theory        62233
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((((A and ((B -> (C -> (B and C))) -> D)) and E) or (A and ((B -> (C -> (B and C))) -> D))) -> D))
theorem-size     41
proof            (modus-ponens tm-747 tm-347 ((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-62233.        (((A and ((B -> (C -> (B and C))) -> D)) -> D) and ((((A and ((B -> (C -> (B and C))) -> D)) and E) or (A and ((B -> (C -> (B and C))) -> D))) -> D)), M:tm-747, m:tm-347, u:((A (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm))) (B Dm))
================================================================
tm-name          tm-62234
in-theory        62234
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((((((A -> (B -> (A and B))) -> C) and D) and E) or (((A -> (B -> (A and B))) -> C) and D)) -> C))
theorem-size     41
proof            (modus-ponens tm-747 tm-348 ((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-62234.        (((((A -> (B -> (A and B))) -> C) and D) -> C) and ((((((A -> (B -> (A and B))) -> C) and D) and E) or (((A -> (B -> (A and B))) -> C) and D)) -> C)), M:tm-747, m:tm-348, u:((A (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-62235
in-theory        62235
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((((A -> ((B -> (A and B)) -> C)) and D) or (A -> ((B -> (A and B)) -> C))) -> (A -> C)))
theorem-size     39
proof            (modus-ponens tm-747 tm-349 ((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-62235.        (((A -> ((B -> (A and B)) -> C)) -> (A -> C)) and ((((A -> ((B -> (A and B)) -> C)) and D) or (A -> ((B -> (A and B)) -> C))) -> (A -> C))), M:tm-747, m:tm-349, u:((A (-> Am (-> (-> Bm (and Am Bm)) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-62236
in-theory        62236
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((((A -> (not (B -> (C -> (B and C))))) and D) or (A -> (not (B -> (C -> (B and C)))))) -> (not A)))
theorem-size     40
proof            (modus-ponens tm-747 tm-350 ((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-1)
proof-size       158
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-62236.        (((A -> (not (B -> (C -> (B and C))))) -> (not A)) and ((((A -> (not (B -> (C -> (B and C))))) and D) or (A -> (not (B -> (C -> (B and C)))))) -> (not A))), M:tm-747, m:tm-350, u:((A (-> Am (not (-> Bm (-> Cm (and Bm Cm)))))) (B (not Am)))
================================================================
tm-name          tm-62237
in-theory        62237
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (((((A -> (B -> (A and B))) -> C) and E) or ((A -> (B -> (A and B))) -> C)) -> ((D or (A -> (B -> (A and B)))) -> C)))
theorem-size     55
proof            (modus-ponens tm-747 tm-351 ((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-62237.        ((((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)) and (((((A -> (B -> (A and B))) -> C) and E) or ((A -> (B -> (A and B))) -> C)) -> ((D or (A -> (B -> (A and B)))) -> C))), M:tm-747, m:tm-351, u:((A (-> (-> Am (-> Bm (and Am Bm))) Cm)) (B (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))
================================================================
tm-name          tm-62238
in-theory        62238
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (((A and E) or A) -> ((B -> (C -> (D -> (C and D)))) and A)))
theorem-size     31
proof            (modus-ponens tm-747 tm-354 ((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-62238.        ((A -> ((B -> (C -> (D -> (C and D)))) and A)) and (((A and E) or A) -> ((B -> (C -> (D -> (C and D)))) and A))), M:tm-747, m:tm-354, u:((A Am) (B (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-62239
in-theory        62239
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C -> (B and C)))) and ((((A -> B) and D) or (A -> B)) -> (A -> (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-747 tm-355 ((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-62239.        (((A -> B) -> (A -> (C -> (B and C)))) and ((((A -> B) and D) or (A -> B)) -> (A -> (C -> (B and C))))), M:tm-747, m:tm-355, u:((A (-> Am Bm)) (B (-> Am (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-62240
in-theory        62240
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D -> (C and D))))) and (((A and E) or A) -> (B -> (C -> (D -> (C and D))))))
theorem-size     27
proof            (modus-ponens tm-747 tm-356 ((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-62240.        ((A -> (B -> (C -> (D -> (C and D))))) and (((A and E) or A) -> (B -> (C -> (D -> (C and D)))))), M:tm-747, m:tm-356, u:((A Am) (B (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-62241
in-theory        62241
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> B)) or D) and A)) and (((A and E) or A) -> (((B -> (C -> B)) or D) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-364 ((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-62241.        ((A -> (((B -> (C -> B)) or D) and A)) and (((A and E) or A) -> (((B -> (C -> B)) or D) and A))), M:tm-747, m:tm-364, u:((A Am) (B (and (or (-> Bm (-> Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-62242
in-theory        62242
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) or D)) and (((A and E) or A) -> ((B -> (C -> B)) or D)))
theorem-size     23
proof            (modus-ponens tm-747 tm-365 ((A Am) (B (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-62242.        ((A -> ((B -> (C -> B)) or D)) and (((A and E) or A) -> ((B -> (C -> B)) or D))), M:tm-747, m:tm-365, u:((A Am) (B (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-62243
in-theory        62243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (((A and F) or A) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)))
theorem-size     43
proof            (modus-ponens tm-747 tm-373 ((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-62243.        ((A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)) and (((A and F) or A) -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A))), M:tm-747, m:tm-373, u:((A Am) (B (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))
================================================================
tm-name          tm-62244
in-theory        62244
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((A and F) or A) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)))
theorem-size     39
proof            (modus-ponens tm-747 tm-374 ((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-62244.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)) and (((A and F) or A) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E))), M:tm-747, m:tm-374, u:((A Am) (B (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-62245
in-theory        62245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> B) or D) and A)) and (((A and E) or A) -> ((((B and C) -> B) or D) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-382 ((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-62245.        ((A -> ((((B and C) -> B) or D) and A)) and (((A and E) or A) -> ((((B and C) -> B) or D) and A))), M:tm-747, m:tm-382, u:((A Am) (B (and (or (-> (and Bm Cm) Bm) Dm) Am)))
================================================================
tm-name          tm-62246
in-theory        62246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) or D)) and (((A and E) or A) -> (((B and C) -> B) or D)))
theorem-size     23
proof            (modus-ponens tm-747 tm-383 ((A Am) (B (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-62246.        ((A -> (((B and C) -> B) or D)) and (((A and E) or A) -> (((B and C) -> B) or D))), M:tm-747, m:tm-383, u:((A Am) (B (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-62247
in-theory        62247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B and C) -> C) or D) and A)) and (((A and E) or A) -> ((((B and C) -> C) or D) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-391 ((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-62247.        ((A -> ((((B and C) -> C) or D) and A)) and (((A and E) or A) -> ((((B and C) -> C) or D) and A))), M:tm-747, m:tm-391, u:((A Am) (B (and (or (-> (and Bm Cm) Cm) Dm) Am)))
================================================================
tm-name          tm-62248
in-theory        62248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) or D)) and (((A and E) or A) -> (((B and C) -> C) or D)))
theorem-size     23
proof            (modus-ponens tm-747 tm-392 ((A Am) (B (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-62248.        ((A -> (((B and C) -> C) or D)) and (((A and E) or A) -> (((B and C) -> C) or D))), M:tm-747, m:tm-392, u:((A Am) (B (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-62249
in-theory        62249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> (B and C))) or D) and A)) and (((A and E) or A) -> (((B -> (C -> (B and C))) or D) and A)))
theorem-size     31
proof            (modus-ponens tm-747 tm-400 ((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-62249.        ((A -> (((B -> (C -> (B and C))) or D) and A)) and (((A and E) or A) -> (((B -> (C -> (B and C))) or D) and A))), M:tm-747, m:tm-400, u:((A Am) (B (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))
================================================================
tm-name          tm-62250
in-theory        62250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) or D)) and (((A and E) or A) -> ((B -> (C -> (B and C))) or D)))
theorem-size     27
proof            (modus-ponens tm-747 tm-401 ((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-62250.        ((A -> ((B -> (C -> (B and C))) or D)) and (((A and E) or A) -> ((B -> (C -> (B and C))) or D))), M:tm-747, m:tm-401, u:((A Am) (B (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-62251
in-theory        62251
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (B or C)) or D) and A)) and (((A and E) or A) -> (((B -> (B or C)) or D) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-409 ((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-62251.        ((A -> (((B -> (B or C)) or D) and A)) and (((A and E) or A) -> (((B -> (B or C)) or D) and A))), M:tm-747, m:tm-409, u:((A Am) (B (and (or (-> Bm (or Bm Cm)) Dm) Am)))
================================================================
tm-name          tm-62252
in-theory        62252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) or D)) and (((A and E) or A) -> ((B -> (B or C)) or D)))
theorem-size     23
proof            (modus-ponens tm-747 tm-410 ((A Am) (B (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-62252.        ((A -> ((B -> (B or C)) or D)) and (((A and E) or A) -> ((B -> (B or C)) or D))), M:tm-747, m:tm-410, u:((A Am) (B (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-62253
in-theory        62253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (B or C)) and A))) and (((A and D) or A) -> (A and ((B -> (B or C)) and A))))
theorem-size     27
proof            (modus-ponens tm-747 tm-443 ((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-62253.        ((A -> (A and ((B -> (B or C)) and A))) and (((A and D) or A) -> (A and ((B -> (B or C)) and A)))), M:tm-747, m:tm-443, u:((A Am) (B (and Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-62254
in-theory        62254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((((A -> (not ((B -> (B or C)) and A))) and D) or (A -> (not ((B -> (B or C)) and A)))) -> (not A)))
theorem-size     40
proof            (modus-ponens tm-747 tm-449 ((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-6)
proof-size       158
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-62254.        (((A -> (not ((B -> (B or C)) and A))) -> (not A)) and ((((A -> (not ((B -> (B or C)) and A))) and D) or (A -> (not ((B -> (B or C)) and A)))) -> (not A))), M:tm-747, m:tm-449, u:((A (-> Am (not (and (-> Bm (or Bm Cm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-62255
in-theory        62255
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((((((A -> (A or B)) and C) -> D) and E) or (((A -> (A or B)) and C) -> D)) -> ((C or ((A -> (A or B)) and C)) -> D)))
theorem-size     55
proof            (modus-ponens tm-747 tm-450 ((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-62255.        (((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)) and ((((((A -> (A or B)) and C) -> D) and E) or (((A -> (A or B)) and C) -> D)) -> ((C or ((A -> (A or B)) and C)) -> D))), M:tm-747, m:tm-450, u:((A (-> (and (-> Am (or Am Bm)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-62256
in-theory        62256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (((A and E) or A) -> ((B -> ((C -> (C or D)) and B)) and A)))
theorem-size     31
proof            (modus-ponens tm-747 tm-453 ((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-62256.        ((A -> ((B -> ((C -> (C or D)) and B)) and A)) and (((A and E) or A) -> ((B -> ((C -> (C or D)) and B)) and A))), M:tm-747, m:tm-453, u:((A Am) (B (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))
================================================================
tm-name          tm-62257
in-theory        62257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (C or D)) and B))) and (((A and E) or A) -> (B -> ((C -> (C or D)) and B))))
theorem-size     27
proof            (modus-ponens tm-747 tm-454 ((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-62257.        ((A -> (B -> ((C -> (C or D)) and B))) and (((A and E) or A) -> (B -> ((C -> (C or D)) and B)))), M:tm-747, m:tm-454, u:((A Am) (B (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-62258
in-theory        62258
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (B or C)))) and (((A and D) or A) -> (A and (B -> (B or C)))))
theorem-size     23
proof            (modus-ponens tm-747 tm-456 ((A Am) (B (and Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-62258.        ((A -> (A and (B -> (B or C)))) and (((A and D) or A) -> (A and (B -> (B or C))))), M:tm-747, m:tm-456, u:((A Am) (B (and Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-62259
in-theory        62259
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (B or C)) -> D)) -> D) and ((((A and ((B -> (B or C)) -> D)) and E) or (A and ((B -> (B or C)) -> D))) -> D))
theorem-size     35
proof            (modus-ponens tm-747 tm-462 ((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-1 tm-6)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-62259.        (((A and ((B -> (B or C)) -> D)) -> D) and ((((A and ((B -> (B or C)) -> D)) and E) or (A and ((B -> (B or C)) -> D))) -> D)), M:tm-747, m:tm-462, u:((A (and Am (-> (-> Bm (or Bm Cm)) Dm))) (B Dm))
================================================================
tm-name          tm-62260
in-theory        62260
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (A or B)) -> C) and D) -> C) and ((((((A -> (A or B)) -> C) and D) and E) or (((A -> (A or B)) -> C) and D)) -> C))
theorem-size     35
proof            (modus-ponens tm-747 tm-463 ((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-62260.        (((((A -> (A or B)) -> C) and D) -> C) and ((((((A -> (A or B)) -> C) and D) and E) or (((A -> (A or B)) -> C) and D)) -> C)), M:tm-747, m:tm-463, u:((A (and (-> (-> Am (or Am Bm)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-62261
in-theory        62261
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((A or B) -> C)) -> (A -> C)) and ((((A -> ((A or B) -> C)) and D) or (A -> ((A or B) -> C))) -> (A -> C)))
theorem-size     33
proof            (modus-ponens tm-747 tm-464 ((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-62261.        (((A -> ((A or B) -> C)) -> (A -> C)) and ((((A -> ((A or B) -> C)) and D) or (A -> ((A or B) -> C))) -> (A -> C))), M:tm-747, m:tm-464, u:((A (-> Am (-> (or Am Bm) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-62262
in-theory        62262
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) -> (not A)) and ((((A -> (not (B -> (B or C)))) and D) or (A -> (not (B -> (B or C))))) -> (not A)))
theorem-size     34
proof            (modus-ponens tm-747 tm-465 ((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-1 tm-6)
proof-size       146
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-62262.        (((A -> (not (B -> (B or C)))) -> (not A)) and ((((A -> (not (B -> (B or C)))) and D) or (A -> (not (B -> (B or C))))) -> (not A))), M:tm-747, m:tm-465, u:((A (-> Am (not (-> Bm (or Bm Cm))))) (B (not Am)))
================================================================
tm-name          tm-62263
in-theory        62263
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (((((A -> (A or B)) -> C) and E) or ((A -> (A or B)) -> C)) -> ((D or (A -> (A or B))) -> C)))
theorem-size     45
proof            (modus-ponens tm-747 tm-466 ((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-62263.        ((((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)) and (((((A -> (A or B)) -> C) and E) or ((A -> (A or B)) -> C)) -> ((D or (A -> (A or B))) -> C))), M:tm-747, m:tm-466, u:((A (-> (-> Am (or Am Bm)) Cm)) (B (-> (or Dm (-> Am (or Am Bm))) Cm)))
================================================================
tm-name          tm-62264
in-theory        62264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (C or D))) and A)) and (((A and E) or A) -> ((B -> (C -> (C or D))) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-469 ((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-62264.        ((A -> ((B -> (C -> (C or D))) and A)) and (((A and E) or A) -> ((B -> (C -> (C or D))) and A))), M:tm-747, m:tm-469, u:((A Am) (B (and (-> Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-62265
in-theory        62265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (B or C))) and ((((A -> B) and D) or (A -> B)) -> (A -> (B or C))))
theorem-size     25
proof            (modus-ponens tm-747 tm-470 ((A (-> Am Bm)) (B (-> Am (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-62265.        (((A -> B) -> (A -> (B or C))) and ((((A -> B) and D) or (A -> B)) -> (A -> (B or C)))), M:tm-747, m:tm-470, u:((A (-> Am Bm)) (B (-> Am (or Bm Cm))))
================================================================
tm-name          tm-62266
in-theory        62266
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (C or D)))) and (((A and E) or A) -> (B -> (C -> (C or D)))))
theorem-size     23
proof            (modus-ponens tm-747 tm-471 ((A Am) (B (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-62266.        ((A -> (B -> (C -> (C or D)))) and (((A and E) or A) -> (B -> (C -> (C or D))))), M:tm-747, m:tm-471, u:((A Am) (B (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-62267
in-theory        62267
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> C))) and A)) and (((A and E) or A) -> ((B or (C -> (D -> C))) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-480 ((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-62267.        ((A -> ((B or (C -> (D -> C))) and A)) and (((A and E) or A) -> ((B or (C -> (D -> C))) and A))), M:tm-747, m:tm-480, u:((A Am) (B (and (or Bm (-> Cm (-> Dm Cm))) Am)))
================================================================
tm-name          tm-62268
in-theory        62268
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> C)))) and (((A and E) or A) -> (B or (C -> (D -> C)))))
theorem-size     23
proof            (modus-ponens tm-747 tm-481 ((A Am) (B (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-62268.        ((A -> (B or (C -> (D -> C)))) and (((A and E) or A) -> (B or (C -> (D -> C))))), M:tm-747, m:tm-481, u:((A Am) (B (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-62269
in-theory        62269
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((A and F) or A) -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)))
theorem-size     43
proof            (modus-ponens tm-747 tm-490 ((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-62269.        ((A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)) and (((A and F) or A) -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A))), M:tm-747, m:tm-490, u:((A Am) (B (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))
================================================================
tm-name          tm-62270
in-theory        62270
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((A and F) or A) -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     39
proof            (modus-ponens tm-747 tm-491 ((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-62270.        ((A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) and (((A and F) or A) -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-747, m:tm-491, u:((A Am) (B (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-62271
in-theory        62271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> C)) and A)) and (((A and E) or A) -> ((B or ((C and D) -> C)) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-500 ((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-62271.        ((A -> ((B or ((C and D) -> C)) and A)) and (((A and E) or A) -> ((B or ((C and D) -> C)) and A))), M:tm-747, m:tm-500, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Cm)) Am)))
================================================================
tm-name          tm-62272
in-theory        62272
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> C))) and (((A and E) or A) -> (B or ((C and D) -> C))))
theorem-size     23
proof            (modus-ponens tm-747 tm-501 ((A Am) (B (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-62272.        ((A -> (B or ((C and D) -> C))) and (((A and E) or A) -> (B or ((C and D) -> C)))), M:tm-747, m:tm-501, u:((A Am) (B (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-62273
in-theory        62273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or ((C and D) -> D)) and A)) and (((A and E) or A) -> ((B or ((C and D) -> D)) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-510 ((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-62273.        ((A -> ((B or ((C and D) -> D)) and A)) and (((A and E) or A) -> ((B or ((C and D) -> D)) and A))), M:tm-747, m:tm-510, u:((A Am) (B (and (or Bm (-> (and Cm Dm) Dm)) Am)))
================================================================
tm-name          tm-62274
in-theory        62274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or ((C and D) -> D))) and (((A and E) or A) -> (B or ((C and D) -> D))))
theorem-size     23
proof            (modus-ponens tm-747 tm-511 ((A Am) (B (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-62274.        ((A -> (B or ((C and D) -> D))) and (((A and E) or A) -> (B or ((C and D) -> D)))), M:tm-747, m:tm-511, u:((A Am) (B (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-62275
in-theory        62275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (((A and E) or A) -> ((B or (C -> (D -> (C and D)))) and A)))
theorem-size     31
proof            (modus-ponens tm-747 tm-520 ((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-62275.        ((A -> ((B or (C -> (D -> (C and D)))) and A)) and (((A and E) or A) -> ((B or (C -> (D -> (C and D)))) and A))), M:tm-747, m:tm-520, u:((A Am) (B (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))
================================================================
tm-name          tm-62276
in-theory        62276
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D -> (C and D))))) and (((A and E) or A) -> (B or (C -> (D -> (C and D))))))
theorem-size     27
proof            (modus-ponens tm-747 tm-521 ((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-62276.        ((A -> (B or (C -> (D -> (C and D))))) and (((A and E) or A) -> (B or (C -> (D -> (C and D)))))), M:tm-747, m:tm-521, u:((A Am) (B (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-62277
in-theory        62277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (C or D))) and A)) and (((A and E) or A) -> ((B or (C -> (C or D))) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-530 ((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-62277.        ((A -> ((B or (C -> (C or D))) and A)) and (((A and E) or A) -> ((B or (C -> (C or D))) and A))), M:tm-747, m:tm-530, u:((A Am) (B (and (or Bm (-> Cm (or Cm Dm))) Am)))
================================================================
tm-name          tm-62278
in-theory        62278
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (C or D)))) and (((A and E) or A) -> (B or (C -> (C or D)))))
theorem-size     23
proof            (modus-ponens tm-747 tm-531 ((A Am) (B (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-62278.        ((A -> (B or (C -> (C or D)))) and (((A and E) or A) -> (B or (C -> (C or D))))), M:tm-747, m:tm-531, u:((A Am) (B (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-62279
in-theory        62279
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B or (C -> (D or C))) and A)) and (((A and E) or A) -> ((B or (C -> (D or C))) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-540 ((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-62279.        ((A -> ((B or (C -> (D or C))) and A)) and (((A and E) or A) -> ((B or (C -> (D or C))) and A))), M:tm-747, m:tm-540, u:((A Am) (B (and (or Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-62280
in-theory        62280
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or (C -> (D or C)))) and (((A and E) or A) -> (B or (C -> (D or C)))))
theorem-size     23
proof            (modus-ponens tm-747 tm-541 ((A Am) (B (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-62280.        ((A -> (B or (C -> (D or C)))) and (((A and E) or A) -> (B or (C -> (D or C))))), M:tm-747, m:tm-541, u:((A Am) (B (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-62281
in-theory        62281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C or B)) or D) and A)) and (((A and E) or A) -> (((B -> (C or B)) or D) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-550 ((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-62281.        ((A -> (((B -> (C or B)) or D) and A)) and (((A and E) or A) -> (((B -> (C or B)) or D) and A))), M:tm-747, m:tm-550, u:((A Am) (B (and (or (-> Bm (or Cm Bm)) Dm) Am)))
================================================================
tm-name          tm-62282
in-theory        62282
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) or D)) and (((A and E) or A) -> ((B -> (C or B)) or D)))
theorem-size     23
proof            (modus-ponens tm-747 tm-551 ((A Am) (B (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-62282.        ((A -> ((B -> (C or B)) or D)) and (((A and E) or A) -> ((B -> (C or B)) or D))), M:tm-747, m:tm-551, u:((A Am) (B (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-62283
in-theory        62283
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and ((B -> (C or B)) and A))) and (((A and D) or A) -> (A and ((B -> (C or B)) and A))))
theorem-size     27
proof            (modus-ponens tm-747 tm-595 ((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-62283.        ((A -> (A and ((B -> (C or B)) and A))) and (((A and D) or A) -> (A and ((B -> (C or B)) and A)))), M:tm-747, m:tm-595, u:((A Am) (B (and Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-62284
in-theory        62284
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((((A -> (not ((B -> (C or B)) and A))) and D) or (A -> (not ((B -> (C or B)) and A)))) -> (not A)))
theorem-size     40
proof            (modus-ponens tm-747 tm-601 ((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-7)
proof-size       158
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-62284.        (((A -> (not ((B -> (C or B)) and A))) -> (not A)) and ((((A -> (not ((B -> (C or B)) and A))) and D) or (A -> (not ((B -> (C or B)) and A)))) -> (not A))), M:tm-747, m:tm-601, u:((A (-> Am (not (and (-> Bm (or Cm Bm)) Am)))) (B (not Am)))
================================================================
tm-name          tm-62285
in-theory        62285
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((((((A -> (B or A)) and C) -> D) and E) or (((A -> (B or A)) and C) -> D)) -> ((C or ((A -> (B or A)) and C)) -> D)))
theorem-size     55
proof            (modus-ponens tm-747 tm-602 ((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-62285.        (((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)) and ((((((A -> (B or A)) and C) -> D) and E) or (((A -> (B or A)) and C) -> D)) -> ((C or ((A -> (B or A)) and C)) -> D))), M:tm-747, m:tm-602, u:((A (-> (and (-> Am (or Bm Am)) Cm) Dm)) (B (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-62286
in-theory        62286
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (((A and E) or A) -> ((B -> ((C -> (D or C)) and B)) and A)))
theorem-size     31
proof            (modus-ponens tm-747 tm-605 ((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-62286.        ((A -> ((B -> ((C -> (D or C)) and B)) and A)) and (((A and E) or A) -> ((B -> ((C -> (D or C)) and B)) and A))), M:tm-747, m:tm-605, u:((A Am) (B (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))
================================================================
tm-name          tm-62287
in-theory        62287
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> ((C -> (D or C)) and B))) and (((A and E) or A) -> (B -> ((C -> (D or C)) and B))))
theorem-size     27
proof            (modus-ponens tm-747 tm-606 ((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-62287.        ((A -> (B -> ((C -> (D or C)) and B))) and (((A and E) or A) -> (B -> ((C -> (D or C)) and B)))), M:tm-747, m:tm-606, u:((A Am) (B (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-62288
in-theory        62288
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A and (B -> (C or B)))) and (((A and D) or A) -> (A and (B -> (C or B)))))
theorem-size     23
proof            (modus-ponens tm-747 tm-609 ((A Am) (B (and Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       151
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-62288.        ((A -> (A and (B -> (C or B)))) and (((A and D) or A) -> (A and (B -> (C or B))))), M:tm-747, m:tm-609, u:((A Am) (B (and Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-62289
in-theory        62289
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C or B)) -> D)) -> D) and ((((A and ((B -> (C or B)) -> D)) and E) or (A and ((B -> (C or B)) -> D))) -> D))
theorem-size     35
proof            (modus-ponens tm-747 tm-615 ((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-1 tm-7)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-62289.        (((A and ((B -> (C or B)) -> D)) -> D) and ((((A and ((B -> (C or B)) -> D)) and E) or (A and ((B -> (C or B)) -> D))) -> D)), M:tm-747, m:tm-615, u:((A (and Am (-> (-> Bm (or Cm Bm)) Dm))) (B Dm))
================================================================
tm-name          tm-62290
in-theory        62290
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B or A)) -> C) and D) -> C) and ((((((A -> (B or A)) -> C) and D) and E) or (((A -> (B or A)) -> C) and D)) -> C))
theorem-size     35
proof            (modus-ponens tm-747 tm-616 ((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-62290.        (((((A -> (B or A)) -> C) and D) -> C) and ((((((A -> (B or A)) -> C) and D) and E) or (((A -> (B or A)) -> C) and D)) -> C)), M:tm-747, m:tm-616, u:((A (and (-> (-> Am (or Bm Am)) Cm) Dm)) (B Cm))
================================================================
tm-name          tm-62291
in-theory        62291
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or A) -> C)) -> (A -> C)) and ((((A -> ((B or A) -> C)) and D) or (A -> ((B or A) -> C))) -> (A -> C)))
theorem-size     33
proof            (modus-ponens tm-747 tm-617 ((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-62291.        (((A -> ((B or A) -> C)) -> (A -> C)) and ((((A -> ((B or A) -> C)) and D) or (A -> ((B or A) -> C))) -> (A -> C))), M:tm-747, m:tm-617, u:((A (-> Am (-> (or Bm Am) Cm))) (B (-> Am Cm)))
================================================================
tm-name          tm-62292
in-theory        62292
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) -> (not A)) and ((((A -> (not (B -> (C or B)))) and D) or (A -> (not (B -> (C or B))))) -> (not A)))
theorem-size     34
proof            (modus-ponens tm-747 tm-618 ((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-1 tm-7)
proof-size       146
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-62292.        (((A -> (not (B -> (C or B)))) -> (not A)) and ((((A -> (not (B -> (C or B)))) and D) or (A -> (not (B -> (C or B))))) -> (not A))), M:tm-747, m:tm-618, u:((A (-> Am (not (-> Bm (or Cm Bm))))) (B (not Am)))
================================================================
tm-name          tm-62293
in-theory        62293
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (((((A -> (B or A)) -> C) and E) or ((A -> (B or A)) -> C)) -> ((D or (A -> (B or A))) -> C)))
theorem-size     45
proof            (modus-ponens tm-747 tm-619 ((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-62293.        ((((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)) and (((((A -> (B or A)) -> C) and E) or ((A -> (B or A)) -> C)) -> ((D or (A -> (B or A))) -> C))), M:tm-747, m:tm-619, u:((A (-> (-> Am (or Bm Am)) Cm)) (B (-> (or Dm (-> Am (or Bm Am))) Cm)))
================================================================
tm-name          tm-62294
in-theory        62294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (D or C))) and A)) and (((A and E) or A) -> ((B -> (C -> (D or C))) and A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-622 ((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-62294.        ((A -> ((B -> (C -> (D or C))) and A)) and (((A and E) or A) -> ((B -> (C -> (D or C))) and A))), M:tm-747, m:tm-622, u:((A Am) (B (and (-> Bm (-> Cm (or Dm Cm))) Am)))
================================================================
tm-name          tm-62295
in-theory        62295
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (C or B))) and ((((A -> B) and D) or (A -> B)) -> (A -> (C or B))))
theorem-size     25
proof            (modus-ponens tm-747 tm-623 ((A (-> Am Bm)) (B (-> Am (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-62295.        (((A -> B) -> (A -> (C or B))) and ((((A -> B) and D) or (A -> B)) -> (A -> (C or B)))), M:tm-747, m:tm-623, u:((A (-> Am Bm)) (B (-> Am (or Cm Bm))))
================================================================
tm-name          tm-62296
in-theory        62296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (D or C)))) and (((A and E) or A) -> (B -> (C -> (D or C)))))
theorem-size     23
proof            (modus-ponens tm-747 tm-624 ((A Am) (B (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-62296.        ((A -> (B -> (C -> (D or C)))) and (((A and E) or A) -> (B -> (C -> (D or C))))), M:tm-747, m:tm-624, u:((A Am) (B (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-62297
in-theory        62297
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (B -> A))) and ((((A or (B -> A)) and D) or (A or (B -> A))) -> (C -> (B -> A))))
theorem-size     31
proof            (modus-ponens tm-747 tm-625 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-62297.        (((A or (B -> A)) -> (C -> (B -> A))) and ((((A or (B -> A)) and D) or (A or (B -> A))) -> (C -> (B -> A)))), M:tm-747, m:tm-625, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Bm Am))))
================================================================
tm-name          tm-62298
in-theory        62298
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((((A -> B) or (C -> (A -> B))) and D) or ((A -> B) or (C -> (A -> B)))) -> ((C -> A) -> (C -> B))))
theorem-size     47
proof            (modus-ponens tm-747 tm-626 ((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-62298.        ((((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))) and (((((A -> B) or (C -> (A -> B))) and D) or ((A -> B) or (C -> (A -> B)))) -> ((C -> A) -> (C -> B)))), M:tm-747, m:tm-626, u:((A (or (-> Am Bm) (-> Cm (-> Am Bm)))) (B (-> (-> Cm Am) (-> Cm Bm))))
================================================================
tm-name          tm-62299
in-theory        62299
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((((A or (B -> A)) and D) or (A or (B -> A))) -> (C -> ((B -> A) and C))))
theorem-size     35
proof            (modus-ponens tm-747 tm-627 ((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-62299.        (((A or (B -> A)) -> (C -> ((B -> A) and C))) and ((((A or (B -> A)) and D) or (A or (B -> A))) -> (C -> ((B -> A) and C)))), M:tm-747, m:tm-627, u:((A (or Am (-> Bm Am))) (B (-> Cm (and (-> Bm Am) Cm))))
================================================================
tm-name          tm-62300
in-theory        62300
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> A) or C)) and ((((A or (B -> A)) and D) or (A or (B -> A))) -> ((B -> A) or C)))
theorem-size     31
proof            (modus-ponens tm-747 tm-628 ((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-62300.        (((A or (B -> A)) -> ((B -> A) or C)) and ((((A or (B -> A)) and D) or (A or (B -> A))) -> ((B -> A) or C))), M:tm-747, m:tm-628, u:((A (or Am (-> Bm Am))) (B (or (-> Bm Am) Cm)))
================================================================
tm-name          tm-62301
in-theory        62301
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C or (B -> A))) and ((((A or (B -> A)) and D) or (A or (B -> A))) -> (C or (B -> A))))
theorem-size     31
proof            (modus-ponens tm-747 tm-629 ((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-62301.        (((A or (B -> A)) -> (C or (B -> A))) and ((((A or (B -> A)) and D) or (A or (B -> A))) -> (C or (B -> A)))), M:tm-747, m:tm-629, u:((A (or Am (-> Bm Am))) (B (or Cm (-> Bm Am))))
================================================================
tm-name          tm-62302
in-theory        62302
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((((A or (B -> A)) and D) or (A or (B -> A))) -> ((A -> C) -> ((B or A) -> C))))
theorem-size     39
proof            (modus-ponens tm-747 tm-630 ((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-62302.        (((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))) and ((((A or (B -> A)) and D) or (A or (B -> A))) -> ((A -> C) -> ((B or A) -> C)))), M:tm-747, m:tm-630, u:((A (or Am (-> Bm Am))) (B (-> (-> Am Cm) (-> (or Bm Am) Cm))))
================================================================
tm-name          tm-62303
in-theory        62303
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((B -> (not A)) -> (not B))))
theorem-size     35
proof            (modus-ponens tm-747 tm-631 ((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-9)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-62303.        (((A or (B -> A)) -> ((B -> (not A)) -> (not B))) and ((((A or (B -> A)) and C) or (A or (B -> A))) -> ((B -> (not A)) -> (not B)))), M:tm-747, m:tm-631, u:((A (or Am (-> Bm Am))) (B (-> (-> Bm (not Am)) (not Bm))))
================================================================
tm-name          tm-62304
in-theory        62304
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> C))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> (C -> (D -> C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-632 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-62304.        (((A or (B -> A)) -> (C -> (D -> C))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> (C -> (D -> C)))), M:tm-747, m:tm-632, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-62305
in-theory        62305
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> B)) and ((((A or (B -> A)) and C) or (A or (B -> A))) -> (B -> B)))
theorem-size     27
proof            (modus-ponens tm-747 tm-633 ((A (or Am (-> Bm Am))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-62305.        (((A or (B -> A)) -> (B -> B)) and ((((A or (B -> A)) and C) or (A or (B -> A))) -> (B -> B))), M:tm-747, m:tm-633, u:((A (or Am (-> Bm Am))) (B (-> Bm Bm)))
================================================================
tm-name          tm-62306
in-theory        62306
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((((A -> B) or ((A -> (B -> C)) -> (A -> B))) and D) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     63
proof            (modus-ponens tm-747 tm-634 ((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-62306.        ((((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((((A -> B) or ((A -> (B -> C)) -> (A -> B))) and D) or ((A -> B) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-747, m:tm-634, u:((A (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-62307
in-theory        62307
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A or (B -> A)) and F) or (A or (B -> A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     47
proof            (modus-ponens tm-747 tm-635 ((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-62307.        (((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A or (B -> A)) and F) or (A or (B -> A))) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-747, m:tm-635, u:((A (or Am (-> Bm Am))) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-62308
in-theory        62308
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((((A or (((A -> B) and C) -> A)) and D) or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)))
theorem-size     47
proof            (modus-ponens tm-747 tm-636 ((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-62308.        (((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((((A or (((A -> B) and C) -> A)) and D) or (A or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))), M:tm-747, m:tm-636, u:((A (or Am (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-62309
in-theory        62309
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> C)) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> ((C and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-747 tm-637 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-62309.        (((A or (B -> A)) -> ((C and D) -> C)) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> ((C and D) -> C))), M:tm-747, m:tm-637, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-62310
in-theory        62310
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((((A or ((B and (A -> C)) -> A)) and D) or (A or ((B and (A -> C)) -> A))) -> ((B and (A -> C)) -> C)))
theorem-size     47
proof            (modus-ponens tm-747 tm-638 ((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-62310.        (((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)) and ((((A or ((B and (A -> C)) -> A)) and D) or (A or ((B and (A -> C)) -> A))) -> ((B and (A -> C)) -> C))), M:tm-747, m:tm-638, u:((A (or Am (-> (and Bm (-> Am Cm)) Am))) (B (-> (and Bm (-> Am Cm)) Cm)))
================================================================
tm-name          tm-62311
in-theory        62311
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C and D) -> D)) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> ((C and D) -> D)))
theorem-size     31
proof            (modus-ponens tm-747 tm-639 ((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-62311.        (((A or (B -> A)) -> ((C and D) -> D)) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> ((C and D) -> D))), M:tm-747, m:tm-639, u:((A (or Am (-> Bm Am))) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-62312
in-theory        62312
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> ((C -> (D -> C)) and (B -> A))))
theorem-size     39
proof            (modus-ponens tm-747 tm-640 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-62312.        (((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> ((C -> (D -> C)) and (B -> A)))), M:tm-747, m:tm-640, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-62313
in-theory        62313
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((((A or (B -> A)) and F) or (A or (B -> A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))))
theorem-size     55
proof            (modus-ponens tm-747 tm-641 ((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-62313.        (((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))) and ((((A or (B -> A)) and F) or (A or (B -> A))) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A)))), M:tm-747, m:tm-641, u:((A (or Am (-> Bm Am))) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))
================================================================
tm-name          tm-62314
in-theory        62314
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> (((C and D) -> C) and (B -> A))))
theorem-size     39
proof            (modus-ponens tm-747 tm-642 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-62314.        (((A or (B -> A)) -> (((C and D) -> C) and (B -> A))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> (((C and D) -> C) and (B -> A)))), M:tm-747, m:tm-642, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Cm) (-> Bm Am))))
================================================================
tm-name          tm-62315
in-theory        62315
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> (((C and D) -> D) and (B -> A))))
theorem-size     39
proof            (modus-ponens tm-747 tm-643 ((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-62315.        (((A or (B -> A)) -> (((C and D) -> D) and (B -> A))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> (((C and D) -> D) and (B -> A)))), M:tm-747, m:tm-643, u:((A (or Am (-> Bm Am))) (B (and (-> (and Cm Dm) Dm) (-> Bm Am))))
================================================================
tm-name          tm-62316
in-theory        62316
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> ((C -> (D -> (C and D))) and (B -> A))))
theorem-size     43
proof            (modus-ponens tm-747 tm-644 ((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-62316.        (((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> ((C -> (D -> (C and D))) and (B -> A)))), M:tm-747, m:tm-644, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))
================================================================
tm-name          tm-62317
in-theory        62317
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (B -> (B and A))) and ((((A or (B -> A)) and C) or (A or (B -> A))) -> (B -> (B and A))))
theorem-size     31
proof            (modus-ponens tm-747 tm-645 ((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-62317.        (((A or (B -> A)) -> (B -> (B and A))) and ((((A or (B -> A)) and C) or (A or (B -> A))) -> (B -> (B and A)))), M:tm-747, m:tm-645, u:((A (or Am (-> Bm Am))) (B (-> Bm (and Bm Am))))
================================================================
tm-name          tm-62318
in-theory        62318
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> (C -> (D -> (C and D)))))
theorem-size     35
proof            (modus-ponens tm-747 tm-646 ((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-62318.        (((A or (B -> A)) -> (C -> (D -> (C and D)))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> (C -> (D -> (C and D))))), M:tm-747, m:tm-646, u:((A (or Am (-> Bm Am))) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-62319
in-theory        62319
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> ((C -> (C or D)) and (B -> A))))
theorem-size     39
proof            (modus-ponens tm-747 tm-647 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-62319.        (((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> ((C -> (C or D)) and (B -> A)))), M:tm-747, m:tm-647, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Cm Dm)) (-> Bm Am))))
================================================================
tm-name          tm-62320
in-theory        62320
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (C or D))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> (C -> (C or D))))
theorem-size     31
proof            (modus-ponens tm-747 tm-648 ((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-62320.        (((A or (B -> A)) -> (C -> (C or D))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> (C -> (C or D)))), M:tm-747, m:tm-648, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-62321
in-theory        62321
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> ((C -> (D or C)) and (B -> A))))
theorem-size     39
proof            (modus-ponens tm-747 tm-649 ((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-62321.        (((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> ((C -> (D or C)) and (B -> A)))), M:tm-747, m:tm-649, u:((A (or Am (-> Bm Am))) (B (and (-> Cm (or Dm Cm)) (-> Bm Am))))
================================================================
tm-name          tm-62322
in-theory        62322
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (C -> (D or C))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> (C -> (D or C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-650 ((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       163
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-62322.        (((A or (B -> A)) -> (C -> (D or C))) and ((((A or (B -> A)) and E) or (A or (B -> A))) -> (C -> (D or C)))), M:tm-747, m:tm-650, u:((A (or Am (-> Bm Am))) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-62323
in-theory        62323
times-derived    1
----------------------------------------------------------------
theorem          (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((((A or ((B -> C) -> A)) and D) or (A or ((B -> C) -> A))) -> ((C or (B -> C)) -> A)))
theorem-size     41
proof            (modus-ponens tm-747 tm-651 ((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       191
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-62323.        (((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)) and ((((A or ((B -> C) -> A)) and D) or (A or ((B -> C) -> A))) -> ((C or (B -> C)) -> A))), M:tm-747, m:tm-651, u:((A (or Am (-> (-> Bm Cm) Am))) (B (-> (or Cm (-> Bm Cm)) Am)))
================================================================
tm-name          tm-62324
in-theory        62324
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))))
theorem-size     47
proof            (modus-ponens tm-747 tm-654 ((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-62324.        ((((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> (((A -> B) -> C) and ((B or (A -> B)) -> C)))), M:tm-747, m:tm-654, u:((A (-> (-> Am Bm) Cm)) (B (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-62325
in-theory        62325
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((A -> B) -> C)) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((A -> B) -> C)))
theorem-size     31
proof            (modus-ponens tm-747 tm-660 ((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-62325.        ((((A -> B) -> C) -> ((A -> B) -> C)) and (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((A -> B) -> C))), M:tm-747, m:tm-660, u:((A (-> (-> Am Bm) Cm)) (B (-> (-> Am Bm) Cm)))
================================================================
tm-name          tm-62326
in-theory        62326
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) and D) or (((A -> B) -> C) -> (not ((B or (A -> B)) -> C)))) -> (not ((A -> B) -> C))))
theorem-size     60
proof            (modus-ponens tm-747 tm-661 ((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9 tm-1)
proof-size       196
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-62326.        (((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))) and ((((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) and D) or (((A -> B) -> C) -> (not ((B or (A -> B)) -> C)))) -> (not ((A -> B) -> C)))), M:tm-747, m:tm-661, u:((A (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm)))) (B (not (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-62327
in-theory        62327
times-derived    1
----------------------------------------------------------------
theorem          (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((((((A or (B -> A)) -> C) -> D) and E) or (((A or (B -> A)) -> C) -> D)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)))
theorem-size     63
proof            (modus-ponens tm-747 tm-662 ((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-62327.        (((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)) and ((((((A or (B -> A)) -> C) -> D) and E) or (((A or (B -> A)) -> C) -> D)) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D))), M:tm-747, m:tm-662, u:((A (-> (-> (or Am (-> Bm Am)) Cm) Dm)) (B (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))
================================================================
tm-name          tm-62328
in-theory        62328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (((A and E) or A) -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)))
theorem-size     39
proof            (modus-ponens tm-747 tm-665 ((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-62328.        ((A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)) and (((A and E) or A) -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A))), M:tm-747, m:tm-665, u:((A Am) (B (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))
================================================================
tm-name          tm-62329
in-theory        62329
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((((((A -> B) -> C) -> (B or (A -> B))) and D) or (((A -> B) -> C) -> (B or (A -> B)))) -> (((A -> B) -> C) -> C)))
theorem-size     53
proof            (modus-ponens tm-747 tm-666 ((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-62329.        (((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)) and ((((((A -> B) -> C) -> (B or (A -> B))) and D) or (((A -> B) -> C) -> (B or (A -> B)))) -> (((A -> B) -> C) -> C))), M:tm-747, m:tm-666, u:((A (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm)))) (B (-> (-> (-> Am Bm) Cm) Cm)))
================================================================
tm-name          tm-62330
in-theory        62330
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((A and E) or A) -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))))
theorem-size     35
proof            (modus-ponens tm-747 tm-667 ((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-62330.        ((A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))) and (((A and E) or A) -> (((B -> C) -> D) -> ((C or (B -> C)) -> D)))), M:tm-747, m:tm-667, u:((A Am) (B (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-62331
in-theory        62331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> ((A -> B) -> (A -> C)))))
theorem-size     63
proof            (modus-ponens tm-747 tm-668 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-62331.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> ((A -> B) -> (A -> C))))), M:tm-747, m:tm-668, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-62332
in-theory        62332
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> A) -> ((A -> B) -> C))))
theorem-size     67
proof            (modus-ponens tm-747 tm-669 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-62332.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> A) -> ((A -> B) -> C)))), M:tm-747, m:tm-669, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-62333
in-theory        62333
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (((A -> B) -> (A -> C)) and D))))
theorem-size     67
proof            (modus-ponens tm-747 tm-670 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-62333.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (((A -> B) -> (A -> C)) and D)))), M:tm-747, m:tm-670, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-62334
in-theory        62334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) or D)))
theorem-size     63
proof            (modus-ponens tm-747 tm-671 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-62334.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (A -> C)) or D))), M:tm-747, m:tm-671, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-62335
in-theory        62335
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D or ((A -> B) -> (A -> C)))))
theorem-size     63
proof            (modus-ponens tm-747 tm-672 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-62335.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D or ((A -> B) -> (A -> C))))), M:tm-747, m:tm-672, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (or Dm (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-62336
in-theory        62336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))))
theorem-size     75
proof            (modus-ponens tm-747 tm-673 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-62336.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D)))), M:tm-747, m:tm-673, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-62337
in-theory        62337
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))))
theorem-size     71
proof            (modus-ponens tm-747 tm-674 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       233
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-62337.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B))))), M:tm-747, m:tm-674, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62338
in-theory        62338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> D))))
theorem-size     55
proof            (modus-ponens tm-747 tm-675 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-62338.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> D)))), M:tm-747, m:tm-675, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em Dm))))
================================================================
tm-name          tm-62339
in-theory        62339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B))))
theorem-size     59
proof            (modus-ponens tm-747 tm-676 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-62339.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> (A -> B)))), M:tm-747, m:tm-676, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-62340
in-theory        62340
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) and D) or ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     75
proof            (modus-ponens tm-747 tm-677 ((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       271
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-62340.        ((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) and D) or ((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-747, m:tm-677, u:((A (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-62341
in-theory        62341
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and G) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     71
proof            (modus-ponens tm-747 tm-678 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       255
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-62341.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and G) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-747, m:tm-678, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))
================================================================
tm-name          tm-62342
in-theory        62342
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> D)))
theorem-size     55
proof            (modus-ponens tm-747 tm-679 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-62342.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> D))), M:tm-747, m:tm-679, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Dm)))
================================================================
tm-name          tm-62343
in-theory        62343
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> E)))
theorem-size     55
proof            (modus-ponens tm-747 tm-680 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-62343.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D and E) -> E))), M:tm-747, m:tm-680, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (and Dm Em) Em)))
================================================================
tm-name          tm-62344
in-theory        62344
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))))
theorem-size     71
proof            (modus-ponens tm-747 tm-681 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-62344.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C))))), M:tm-747, m:tm-681, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-62345
in-theory        62345
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and G) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))))
theorem-size     87
proof            (modus-ponens tm-747 tm-682 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       283
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-62345.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and G) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C))))), M:tm-747, m:tm-682, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-62346
in-theory        62346
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))))
theorem-size     71
proof            (modus-ponens tm-747 tm-683 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-62346.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> D) and ((A -> B) -> (A -> C))))), M:tm-747, m:tm-683, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-62347
in-theory        62347
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))))
theorem-size     71
proof            (modus-ponens tm-747 tm-684 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-62347.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (((D and E) -> E) and ((A -> B) -> (A -> C))))), M:tm-747, m:tm-684, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-62348
in-theory        62348
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))))
theorem-size     75
proof            (modus-ponens tm-747 tm-685 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       253
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-62348.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C))))), M:tm-747, m:tm-685, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-62349
in-theory        62349
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> ((A -> B) and (A -> C)))))
theorem-size     67
proof            (modus-ponens tm-747 tm-686 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       245
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-62349.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((A -> B) -> ((A -> B) and (A -> C))))), M:tm-747, m:tm-686, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-62350
in-theory        62350
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> (D and E)))))
theorem-size     59
proof            (modus-ponens tm-747 tm-687 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       225
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-62350.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E -> (D and E))))), M:tm-747, m:tm-687, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (-> Em (and Dm Em)))))
================================================================
tm-name          tm-62351
in-theory        62351
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))))
theorem-size     71
proof            (modus-ponens tm-747 tm-688 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-62351.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C))))), M:tm-747, m:tm-688, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-62352
in-theory        62352
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (D or E))))
theorem-size     55
proof            (modus-ponens tm-747 tm-689 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-62352.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (D or E)))), M:tm-747, m:tm-689, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Dm Em))))
================================================================
tm-name          tm-62353
in-theory        62353
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))))
theorem-size     71
proof            (modus-ponens tm-747 tm-690 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-62353.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C))))), M:tm-747, m:tm-690, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-62354
in-theory        62354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E or D))))
theorem-size     55
proof            (modus-ponens tm-747 tm-691 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       215
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-62354.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and F) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> (D -> (E or D)))), M:tm-747, m:tm-691, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> Dm (or Em Dm))))
================================================================
tm-name          tm-62355
in-theory        62355
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((B or (A -> B)) -> (A -> C))))
theorem-size     63
proof            (modus-ponens tm-747 tm-692 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-62355.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and D) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((B or (A -> B)) -> (A -> C)))), M:tm-747, m:tm-692, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or Bm (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-62356
in-theory        62356
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) and E) or (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))))
theorem-size     113
proof            (modus-ponens tm-747 tm-693 ((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       331
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-62356.        (((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))) and ((((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) and E) or (((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D)))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D)))), M:tm-747, m:tm-693, u:((A (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm)))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))
================================================================
tm-name          tm-62357
in-theory        62357
times-derived    1
----------------------------------------------------------------
theorem          (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((((A or (((B -> C) -> (B -> D)) -> A)) and E) or (A or (((B -> C) -> (B -> D)) -> A))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)))
theorem-size     69
proof            (modus-ponens tm-747 tm-694 ((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       251
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-62357.        (((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)) and ((((A or (((B -> C) -> (B -> D)) -> A)) and E) or (A or (((B -> C) -> (B -> D)) -> A))) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A))), M:tm-747, m:tm-694, u:((A (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am))) (B (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
================================================================
tm-name          tm-62358
in-theory        62358
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))))
theorem-size     83
proof            (modus-ponens tm-747 tm-697 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       271
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-62358.        (((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))), M:tm-747, m:tm-697, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-62359
in-theory        62359
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> B) -> (A -> C)) -> D)))
theorem-size     51
proof            (modus-ponens tm-747 tm-703 ((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-62359.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)) and ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> B) -> (A -> C)) -> D))), M:tm-747, m:tm-703, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))
================================================================
tm-name          tm-62360
in-theory        62360
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and E) or ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (not (((A -> B) -> (A -> C)) -> D))))
theorem-size     104
proof            (modus-ponens tm-747 tm-704 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       276
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-62360.        ((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))) and (((((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) and E) or ((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))) -> (not (((A -> B) -> (A -> C)) -> D)))), M:tm-747, m:tm-704, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))) (B (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-62361
in-theory        62361
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) and F) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)))
theorem-size     111
proof            (modus-ponens tm-747 tm-705 ((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       293
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-62361.        ((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)) and (((((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) and F) or ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E)) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E))), M:tm-747, m:tm-705, u:((A (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)) (B (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-62362
in-theory        62362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (((A and F) or A) -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)))
theorem-size     63
proof            (modus-ponens tm-747 tm-708 ((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       223
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-62362.        ((A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)) and (((A and F) or A) -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A))), M:tm-747, m:tm-708, u:((A Am) (B (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))
================================================================
tm-name          tm-62363
in-theory        62363
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) and E) or ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) -> ((((A -> B) -> (A -> C)) -> D) -> D)))
theorem-size     97
proof            (modus-ponens tm-747 tm-709 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       269
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-62363.        ((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)) and (((((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) and E) or ((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C))))) -> ((((A -> B) -> (A -> C)) -> D) -> D))), M:tm-747, m:tm-709, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))) (B (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))
================================================================
tm-name          tm-62364
in-theory        62364
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((A and F) or A) -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))))
theorem-size     59
proof            (modus-ponens tm-747 tm-710 ((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       215
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-62364.        ((A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))) and (((A and F) or A) -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)))), M:tm-747, m:tm-710, u:((A Am) (B (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-62365
in-theory        62365
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> A)) and (((((A and B) or A) and D) or ((A and B) or A)) -> (C -> A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-711 ((A (or (and Am Bm) Am)) (B (-> Cm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-62365.        ((((A and B) or A) -> (C -> A)) and (((((A and B) or A) and D) or ((A and B) or A)) -> (C -> A))), M:tm-747, m:tm-711, u:((A (or (and Am Bm) Am)) (B (-> Cm Am)))
================================================================
tm-name          tm-62366
in-theory        62366
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((((((A -> (B -> C)) and D) or (A -> (B -> C))) and E) or (((A -> (B -> C)) and D) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C))))
theorem-size     59
proof            (modus-ponens tm-747 tm-712 ((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-62366.        (((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))) and ((((((A -> (B -> C)) and D) or (A -> (B -> C))) and E) or (((A -> (B -> C)) and D) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C)))), M:tm-747, m:tm-712, u:((A (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm)))) (B (-> (-> Am Bm) (-> Am Cm))))
================================================================
tm-name          tm-62367
in-theory        62367
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> A) and ((((((A and B) and C) or (A and B)) and D) or (((A and B) and C) or (A and B))) -> A))
theorem-size     35
proof            (modus-ponens tm-747 tm-713 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-62367.        (((((A and B) and C) or (A and B)) -> A) and ((((((A and B) and C) or (A and B)) and D) or (((A and B) and C) or (A and B))) -> A)), M:tm-747, m:tm-713, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Am))
================================================================
tm-name          tm-62368
in-theory        62368
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) and C) or (A and B)) -> B) and ((((((A and B) and C) or (A and B)) and D) or (((A and B) and C) or (A and B))) -> B))
theorem-size     35
proof            (modus-ponens tm-747 tm-714 ((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-62368.        (((((A and B) and C) or (A and B)) -> B) and ((((((A and B) and C) or (A and B)) and D) or (((A and B) and C) or (A and B))) -> B)), M:tm-747, m:tm-714, u:((A (or (and (and Am Bm) Cm) (and Am Bm))) (B Bm))
================================================================
tm-name          tm-62369
in-theory        62369
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (A and C))) and (((((A and B) or A) and D) or ((A and B) or A)) -> (C -> (A and C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-715 ((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-62369.        ((((A and B) or A) -> (C -> (A and C))) and (((((A and B) or A) and D) or ((A and B) or A)) -> (C -> (A and C)))), M:tm-747, m:tm-715, u:((A (or (and Am Bm) Am)) (B (-> Cm (and Am Cm))))
================================================================
tm-name          tm-62370
in-theory        62370
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (A or C)) and (((((A and B) or A) and D) or ((A and B) or A)) -> (A or C)))
theorem-size     27
proof            (modus-ponens tm-747 tm-716 ((A (or (and Am Bm) Am)) (B (or Am Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-62370.        ((((A and B) or A) -> (A or C)) and (((((A and B) or A) and D) or ((A and B) or A)) -> (A or C))), M:tm-747, m:tm-716, u:((A (or (and Am Bm) Am)) (B (or Am Cm)))
================================================================
tm-name          tm-62371
in-theory        62371
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C or A)) and (((((A and B) or A) and D) or ((A and B) or A)) -> (C or A)))
theorem-size     27
proof            (modus-ponens tm-747 tm-717 ((A (or (and Am Bm) Am)) (B (or Cm Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-62371.        ((((A and B) or A) -> (C or A)) and (((((A and B) or A) and D) or ((A and B) or A)) -> (C or A))), M:tm-747, m:tm-717, u:((A (or (and Am Bm) Am)) (B (or Cm Am)))
================================================================
tm-name          tm-62372
in-theory        62372
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((((((A -> B) and C) or (A -> B)) and E) or (((A -> B) and C) or (A -> B))) -> ((B -> D) -> ((A or B) -> D))))
theorem-size     51
proof            (modus-ponens tm-747 tm-718 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-62372.        (((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))) and ((((((A -> B) and C) or (A -> B)) and E) or (((A -> B) and C) or (A -> B))) -> ((B -> D) -> ((A or B) -> D)))), M:tm-747, m:tm-718, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Bm Dm) (-> (or Am Bm) Dm))))
================================================================
tm-name          tm-62373
in-theory        62373
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A))))
theorem-size     47
proof            (modus-ponens tm-747 tm-719 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-62373.        (((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))) and ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> ((A -> (not B)) -> (not A)))), M:tm-747, m:tm-719, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (-> Am (not Bm)) (not Am))))
================================================================
tm-name          tm-62374
in-theory        62374
times-derived    1
----------------------------------------------------------------
theorem          (((((not (not A)) and B) or (not (not A))) -> A) and ((((((not (not A)) and B) or (not (not A))) and C) or (((not (not A)) and B) or (not (not A)))) -> A))
theorem-size     35
proof            (modus-ponens tm-747 tm-720 ((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-10)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-62374.        (((((not (not A)) and B) or (not (not A))) -> A) and ((((((not (not A)) and B) or (not (not A))) and C) or (((not (not A)) and B) or (not (not A)))) -> A)), M:tm-747, m:tm-720, u:((A (or (and (not (not Am)) Bm) (not (not Am)))) (B Am))
================================================================
tm-name          tm-62375
in-theory        62375
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> C))) and (((((A and B) or A) and E) or ((A and B) or A)) -> (C -> (D -> C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-721 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-62375.        ((((A and B) or A) -> (C -> (D -> C))) and (((((A and B) or A) and E) or ((A and B) or A)) -> (C -> (D -> C)))), M:tm-747, m:tm-721, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-62376
in-theory        62376
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> (A -> A)))
theorem-size     39
proof            (modus-ponens tm-747 tm-722 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-62376.        (((((A -> B) and C) or (A -> B)) -> (A -> A)) and ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> (A -> A))), M:tm-747, m:tm-722, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am Am)))
================================================================
tm-name          tm-62377
in-theory        62377
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) and E) or ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))))
theorem-size     87
proof            (modus-ponens tm-747 tm-723 ((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       265
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-62377.        ((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))) and (((((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) and E) or ((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))), M:tm-747, m:tm-723, u:((A (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-62378
in-theory        62378
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((((A and B) or A) and F) or ((A and B) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     47
proof            (modus-ponens tm-747 tm-724 ((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-62378.        ((((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((((A and B) or A) and F) or ((A and B) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-747, m:tm-724, u:((A (or (and Am Bm) Am)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-62379
in-theory        62379
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) and E) or (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)))
theorem-size     71
proof            (modus-ponens tm-747 tm-725 ((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-62379.        (((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)) and ((((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) and E) or (((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))), M:tm-747, m:tm-725, u:((A (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am))) (B (-> (and (-> Am Bm) Cm) Bm)))
================================================================
tm-name          tm-62380
in-theory        62380
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> C)) and (((((A and B) or A) and E) or ((A and B) or A)) -> ((C and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-747 tm-726 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-62380.        ((((A and B) or A) -> ((C and D) -> C)) and (((((A and B) or A) and E) or ((A and B) or A)) -> ((C and D) -> C))), M:tm-747, m:tm-726, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-62381
in-theory        62381
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) and E) or ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C)))
theorem-size     71
proof            (modus-ponens tm-747 tm-727 ((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-62381.        ((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)) and (((((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) and E) or ((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C))), M:tm-747, m:tm-727, u:((A (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm))) (B (-> (and Am (-> Bm Cm)) Cm)))
================================================================
tm-name          tm-62382
in-theory        62382
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C and D) -> D)) and (((((A and B) or A) and E) or ((A and B) or A)) -> ((C and D) -> D)))
theorem-size     31
proof            (modus-ponens tm-747 tm-728 ((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-62382.        ((((A and B) or A) -> ((C and D) -> D)) and (((((A and B) or A) and E) or ((A and B) or A)) -> ((C and D) -> D))), M:tm-747, m:tm-728, u:((A (or (and Am Bm) Am)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-62383
in-theory        62383
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((((A and B) or A) and E) or ((A and B) or A)) -> ((C -> (D -> C)) and A)))
theorem-size     35
proof            (modus-ponens tm-747 tm-729 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-62383.        ((((A and B) or A) -> ((C -> (D -> C)) and A)) and (((((A and B) or A) and E) or ((A and B) or A)) -> ((C -> (D -> C)) and A))), M:tm-747, m:tm-729, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm Cm)) Am)))
================================================================
tm-name          tm-62384
in-theory        62384
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((((A and B) or A) and F) or ((A and B) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)))
theorem-size     51
proof            (modus-ponens tm-747 tm-730 ((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-62384.        ((((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)) and (((((A and B) or A) and F) or ((A and B) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))), M:tm-747, m:tm-730, u:((A (or (and Am Bm) Am)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))
================================================================
tm-name          tm-62385
in-theory        62385
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> C) and A)) and (((((A and B) or A) and E) or ((A and B) or A)) -> (((C and D) -> C) and A)))
theorem-size     35
proof            (modus-ponens tm-747 tm-731 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-62385.        ((((A and B) or A) -> (((C and D) -> C) and A)) and (((((A and B) or A) and E) or ((A and B) or A)) -> (((C and D) -> C) and A))), M:tm-747, m:tm-731, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Cm) Am)))
================================================================
tm-name          tm-62386
in-theory        62386
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (((C and D) -> D) and A)) and (((((A and B) or A) and E) or ((A and B) or A)) -> (((C and D) -> D) and A)))
theorem-size     35
proof            (modus-ponens tm-747 tm-732 ((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-62386.        ((((A and B) or A) -> (((C and D) -> D) and A)) and (((((A and B) or A) and E) or ((A and B) or A)) -> (((C and D) -> D) and A))), M:tm-747, m:tm-732, u:((A (or (and Am Bm) Am)) (B (and (-> (and Cm Dm) Dm) Am)))
================================================================
tm-name          tm-62387
in-theory        62387
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((((A and B) or A) and E) or ((A and B) or A)) -> ((C -> (D -> (C and D))) and A)))
theorem-size     39
proof            (modus-ponens tm-747 tm-733 ((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-62387.        ((((A and B) or A) -> ((C -> (D -> (C and D))) and A)) and (((((A and B) or A) and E) or ((A and B) or A)) -> ((C -> (D -> (C and D))) and A))), M:tm-747, m:tm-733, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (-> Dm (and Cm Dm))) Am)))
================================================================
tm-name          tm-62388
in-theory        62388
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B))))
theorem-size     43
proof            (modus-ponens tm-747 tm-734 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-62388.        (((((A -> B) and C) or (A -> B)) -> (A -> (A and B))) and ((((((A -> B) and C) or (A -> B)) and D) or (((A -> B) and C) or (A -> B))) -> (A -> (A and B)))), M:tm-747, m:tm-734, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> Am (and Am Bm))))
================================================================
tm-name          tm-62389
in-theory        62389
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((((A and B) or A) and E) or ((A and B) or A)) -> (C -> (D -> (C and D)))))
theorem-size     35
proof            (modus-ponens tm-747 tm-735 ((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-62389.        ((((A and B) or A) -> (C -> (D -> (C and D)))) and (((((A and B) or A) and E) or ((A and B) or A)) -> (C -> (D -> (C and D))))), M:tm-747, m:tm-735, u:((A (or (and Am Bm) Am)) (B (-> Cm (-> Dm (and Cm Dm)))))
================================================================
tm-name          tm-62390
in-theory        62390
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((((A and B) or A) and E) or ((A and B) or A)) -> ((C -> (C or D)) and A)))
theorem-size     35
proof            (modus-ponens tm-747 tm-736 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-6)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-62390.        ((((A and B) or A) -> ((C -> (C or D)) and A)) and (((((A and B) or A) and E) or ((A and B) or A)) -> ((C -> (C or D)) and A))), M:tm-747, m:tm-736, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Cm Dm)) Am)))
================================================================
tm-name          tm-62391
in-theory        62391
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (C or D))) and (((((A and B) or A) and E) or ((A and B) or A)) -> (C -> (C or D))))
theorem-size     31
proof            (modus-ponens tm-747 tm-737 ((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-62391.        ((((A and B) or A) -> (C -> (C or D))) and (((((A and B) or A) and E) or ((A and B) or A)) -> (C -> (C or D)))), M:tm-747, m:tm-737, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Cm Dm))))
================================================================
tm-name          tm-62392
in-theory        62392
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((((A and B) or A) and E) or ((A and B) or A)) -> ((C -> (D or C)) and A)))
theorem-size     35
proof            (modus-ponens tm-747 tm-738 ((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-7)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-62392.        ((((A and B) or A) -> ((C -> (D or C)) and A)) and (((((A and B) or A) and E) or ((A and B) or A)) -> ((C -> (D or C)) and A))), M:tm-747, m:tm-738, u:((A (or (and Am Bm) Am)) (B (and (-> Cm (or Dm Cm)) Am)))
================================================================
tm-name          tm-62393
in-theory        62393
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or A) -> (C -> (D or C))) and (((((A and B) or A) and E) or ((A and B) or A)) -> (C -> (D or C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-739 ((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-62393.        ((((A and B) or A) -> (C -> (D or C))) and (((((A and B) or A) and E) or ((A and B) or A)) -> (C -> (D or C)))), M:tm-747, m:tm-739, u:((A (or (and Am Bm) Am)) (B (-> Cm (or Dm Cm))))
================================================================
tm-name          tm-62394
in-theory        62394
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (((((((A -> B) -> C) and D) or ((A -> B) -> C)) and E) or ((((A -> B) -> C) and D) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C)))
theorem-size     59
proof            (modus-ponens tm-747 tm-740 ((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-62394.        ((((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)) and (((((((A -> B) -> C) and D) or ((A -> B) -> C)) and E) or ((((A -> B) -> C) and D) or ((A -> B) -> C))) -> ((B or (A -> B)) -> C))), M:tm-747, m:tm-740, u:((A (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm))) (B (-> (or Bm (-> Am Bm)) Cm)))
================================================================
tm-name          tm-62395
in-theory        62395
times-derived    1
----------------------------------------------------------------
theorem          (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) and F) or (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     99
proof            (modus-ponens tm-747 tm-741 ((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       289
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-62395.        (((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) and F) or (((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-747, m:tm-741, u:((A (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-62396
in-theory        62396
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((((((A -> B) and C) or (A -> B)) and E) or (((A -> B) and C) or (A -> B))) -> (((A and D) or A) -> B)))
theorem-size     47
proof            (modus-ponens tm-747 tm-742 ((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62396.        (((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)) and ((((((A -> B) and C) or (A -> B)) and E) or (((A -> B) and C) or (A -> B))) -> (((A and D) or A) -> B))), M:tm-747, m:tm-742, u:((A (or (and (-> Am Bm) Cm) (-> Am Bm))) (B (-> (or (and Am Dm) Am) Bm)))
================================================================
tm-name          tm-62397
in-theory        62397
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))))
theorem-size     71
proof            (modus-ponens tm-747 tm-743 ((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       251
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-62397.        ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))), M:tm-747, m:tm-743, u:((A (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))
================================================================
tm-name          tm-62398
in-theory        62398
times-derived    1
----------------------------------------------------------------
theorem          (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((((A or (B -> A)) and D) or (A or (B -> A))) -> (((B and C) or B) -> A)))
theorem-size     35
proof            (modus-ponens tm-747 tm-744 ((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-62398.        (((A or (B -> A)) -> (((B and C) or B) -> A)) and ((((A or (B -> A)) and D) or (A or (B -> A))) -> (((B and C) or B) -> A))), M:tm-747, m:tm-744, u:((A (or Am (-> Bm Am))) (B (-> (or (and Bm Cm) Bm) Am)))
================================================================
tm-name          tm-62399
in-theory        62399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((((A -> B) and D) or (A -> B)) -> ((A -> B) and (((A and C) or A) -> B))))
theorem-size     37
proof            (modus-ponens tm-747 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       183
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62399.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((((A -> B) and D) or (A -> B)) -> ((A -> B) and (((A and C) or A) -> B)))), M:tm-747, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62400
in-theory        62400
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F))))
theorem-size     41
proof            (modus-ponens tm-708 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62400.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F)))), M:tm-708, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62401
in-theory        62401
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D)))
theorem-size     73
proof            (modus-ponens tm-705 tm-747 ((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (or (and (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       255
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62401.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) and (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) and E) or ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> D))), M:tm-705, m:tm-747, u:((Am (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D Bm) (E (and (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Bm) (-> (or (and (or (-> A (-> B C)) (-> (-> A B) (-> A C))) Cm) (or (-> A (-> B C)) (-> (-> A B) (-> A C)))) Bm))))
================================================================
tm-name          tm-62402
in-theory        62402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((((A -> B) and D) or (A -> B)) -> (A -> C))))
theorem-size     29
proof            (modus-ponens tm-703 tm-747 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62402.        (((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((((A -> B) and D) or (A -> B)) -> (A -> C)))), M:tm-703, m:tm-747, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (or (and (-> A B) Cm) (-> A B)) (-> A C)))))
================================================================
tm-name          tm-62403
in-theory        62403
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((((A -> B) and D) or (A -> B)) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((((A -> B) and D) or (A -> B)) -> (A -> C)))))
theorem-size     65
proof            (modus-ponens tm-697 tm-747 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       253
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62403.        ((((A -> B) -> (A -> C)) -> (((A -> B) -> (A -> C)) and ((((A -> B) and D) or (A -> B)) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((((A -> B) and D) or (A -> B)) -> (A -> C))))), M:tm-697, m:tm-747, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (or (and (-> A B) Cm) (-> A B)) (-> A C)))))
================================================================
tm-name          tm-62404
in-theory        62404
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-665 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62404.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-665, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62405
in-theory        62405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((((B or (A -> B)) and D) or (B or (A -> B))) -> C)))
theorem-size     37
proof            (modus-ponens tm-662 tm-747 ((Am (or A (-> B A))) (C Bm) (D (and (-> (or A (-> B A)) Bm) (-> (or (and (or A (-> B A)) Cm) (or A (-> B A))) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62405.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((B or (A -> B)) -> C) and ((((B or (A -> B)) and D) or (B or (A -> B))) -> C))), M:tm-662, m:tm-747, u:((Am (or A (-> B A))) (C Bm) (D (and (-> (or A (-> B A)) Bm) (-> (or (and (or A (-> B A)) Cm) (or A (-> B A))) Bm))))
================================================================
tm-name          tm-62406
in-theory        62406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((B or (A -> B)) -> ((A -> B) and (((A and C) or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-654 tm-747 ((A Am) (B Bm) (C (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62406.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((B or (A -> B)) -> ((A -> B) and (((A and C) or A) -> B)))), M:tm-654, m:tm-747, u:((A Am) (B Bm) (C (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62407
in-theory        62407
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C or ((A -> B) and (((A and D) or A) -> B))))
theorem-size     17
proof            (modus-ponens tm-623 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62407.        ((A -> B) -> (C or ((A -> B) and (((A and D) or A) -> B)))), M:tm-623, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62408
in-theory        62408
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-622 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62408.        ((A -> (B -> (C or B))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-622, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62409
in-theory        62409
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((B -> (C or B)) and (((B and D) or B) -> (C or B))))
theorem-size     23
proof            (modus-ponens tm-619 tm-747 ((A Am) (Bm (or B Am)) (C (and (-> Am (or B Am)) (-> (or (and Am Cm) Am) (or B Am))))))
axioms-used      (tm-8 tm-1 tm-7 tm-2 tm-5 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62409.        ((A or (B -> (C or B))) -> ((B -> (C or B)) and (((B and D) or B) -> (C or B)))), M:tm-619, m:tm-747, u:((A Am) (Bm (or B Am)) (C (and (-> Am (or B Am)) (-> (or (and Am Cm) Am) (or B Am)))))
================================================================
tm-name          tm-62410
in-theory        62410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62410.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (D -> (E or D))), M:tm-609, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62411
in-theory        62411
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-605 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62411.        ((A -> ((B -> (C or B)) and A)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-605, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62412
in-theory        62412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((D -> (E or D)) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62412.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((D -> (E or D)) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))))), M:tm-595, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62413
in-theory        62413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-550 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62413.        (((A -> (B or A)) or C) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-550, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62414
in-theory        62414
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-540 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62414.        ((A or (B -> (C or B))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-540, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62415
in-theory        62415
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-530 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62415.        ((A or (B -> (B or C))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-530, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62416
in-theory        62416
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-520 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62416.        ((A or (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-520, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62417
in-theory        62417
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-510 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62417.        ((A or ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-510, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62418
in-theory        62418
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-500 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62418.        ((A or ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-500, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62419
in-theory        62419
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-490 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62419.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F)))), M:tm-490, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62420
in-theory        62420
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-480 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62420.        ((A or (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-480, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62421
in-theory        62421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((A -> B) and (((A and C) or A) -> B)) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62421.        ((A -> B) -> (((A -> B) and (((A and C) or A) -> B)) or D)), M:tm-470, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62422
in-theory        62422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-469 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62422.        ((A -> (B -> (B or C))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-469, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62423
in-theory        62423
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((B -> (B or C)) and (((B and D) or B) -> (B or C))))
theorem-size     23
proof            (modus-ponens tm-466 tm-747 ((A Am) (Bm (or Am B)) (C (and (-> Am (or Am B)) (-> (or (and Am Cm) Am) (or Am B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-2 tm-5 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62423.        ((A or (B -> (B or C))) -> ((B -> (B or C)) and (((B and D) or B) -> (B or C)))), M:tm-466, m:tm-747, u:((A Am) (Bm (or Am B)) (C (and (-> Am (or Am B)) (-> (or (and Am Cm) Am) (or Am B)))))
================================================================
tm-name          tm-62424
in-theory        62424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62424.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (D -> (D or E))), M:tm-456, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62425
in-theory        62425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-453 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62425.        ((A -> ((B -> (B or C)) and A)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-453, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62426
in-theory        62426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((D -> (D or E)) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62426.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((D -> (D or E)) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))))), M:tm-443, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62427
in-theory        62427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-409 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62427.        (((A -> (A or B)) or C) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-409, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62428
in-theory        62428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-400 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62428.        (((A -> (B -> (A and B))) or C) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-400, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62429
in-theory        62429
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-391 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62429.        ((((A and B) -> B) or C) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-391, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62430
in-theory        62430
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-382 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62430.        ((((A and B) -> A) or C) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-382, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62431
in-theory        62431
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-373 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62431.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F)))), M:tm-373, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62432
in-theory        62432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-364 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62432.        (((A -> (B -> A)) or C) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-364, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62433
in-theory        62433
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> (((A -> B) and (((A and D) or A) -> B)) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62433.        ((A -> B) -> (C -> (((A -> B) and (((A and D) or A) -> B)) and C))), M:tm-355, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62434
in-theory        62434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-354 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62434.        ((A -> (B -> (C -> (B and C)))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-354, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62435
in-theory        62435
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (((B and D) or B) -> (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-351 tm-747 ((A Am) (Bm (-> B (and Am B))) (C (and (-> Am (-> B (and Am B))) (-> (or (and Am Cm) Am) (-> B (and Am B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62435.        ((A or (B -> (C -> (B and C)))) -> ((B -> (C -> (B and C))) and (((B and D) or B) -> (C -> (B and C))))), M:tm-351, m:tm-747, u:((A Am) (Bm (-> B (and Am B))) (C (and (-> Am (-> B (and Am B))) (-> (or (and Am Cm) Am) (-> B (and Am B))))))
================================================================
tm-name          tm-62436
in-theory        62436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62436.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62437
in-theory        62437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D))))
theorem-size     25
proof            (modus-ponens tm-338 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62437.        (((A -> B) -> (A -> (A and B))) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D)))), M:tm-338, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62438
in-theory        62438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (((A and C) or A) -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-335 tm-747 ((A Am) (Bm (and Am B)) (C (and (-> Am (and Am B)) (-> (or (and Am Cm) Am) (and Am B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62438.        (((A -> B) or (A -> (A and B))) -> ((A -> (A and B)) and (((A and C) or A) -> (A and B)))), M:tm-335, m:tm-747, u:((A Am) (Bm (and Am B)) (C (and (-> Am (and Am B)) (-> (or (and Am Cm) Am) (and Am B)))))
================================================================
tm-name          tm-62439
in-theory        62439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((A -> B) -> ((A -> B) and ((A -> B) and (((A and C) or A) -> B)))))
theorem-size     35
proof            (modus-ponens tm-328 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62439.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((A -> B) -> ((A -> B) and ((A -> B) and (((A and C) or A) -> B))))), M:tm-328, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62440
in-theory        62440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((D -> (E -> (D and E))) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62440.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((D -> (E -> (D and E))) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))))), M:tm-327, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62441
in-theory        62441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (((D and E) -> E) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62441.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (((D and E) -> E) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))))), M:tm-326, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62442
in-theory        62442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (((D and E) -> D) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62442.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (((D and E) -> D) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))))), M:tm-325, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62443
in-theory        62443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62443.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))))), M:tm-324, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62444
in-theory        62444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((D -> (E -> D)) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62444.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((D -> (E -> D)) and ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))))), M:tm-323, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62445
in-theory        62445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62445.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((D and E) -> E)), M:tm-322, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62446
in-theory        62446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62446.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((D and E) -> D)), M:tm-320, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62447
in-theory        62447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62447.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62448
in-theory        62448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((A -> B) -> (A -> B)))
theorem-size     23
proof            (modus-ponens tm-316 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62448.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((A -> B) -> (A -> B))), M:tm-316, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62449
in-theory        62449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62449.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (D -> (E -> D))), M:tm-315, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62450
in-theory        62450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (((A -> B) -> (not ((A -> B) and (((A and C) or A) -> B)))) -> (not (A -> B))))
theorem-size     37
proof            (modus-ponens tm-313 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62450.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (((A -> B) -> (not ((A -> B) and (((A and C) or A) -> B)))) -> (not (A -> B)))), M:tm-313, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62451
in-theory        62451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((((A -> B) and (((A and C) or A) -> B)) -> D) -> (((A -> B) or ((A -> B) and (((A and C) or A) -> B))) -> D)))
theorem-size     47
proof            (modus-ponens tm-312 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62451.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and ((((A -> B) and (((A and C) or A) -> B)) -> D) -> (((A -> B) or ((A -> B) and (((A and C) or A) -> B))) -> D))), M:tm-312, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62452
in-theory        62452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (D or ((A -> B) -> ((A -> B) and (((A and C) or A) -> B)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62452.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (D or ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))))), M:tm-311, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62453
in-theory        62453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62453.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) or D)), M:tm-310, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62454
in-theory        62454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (D -> (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62454.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (D -> (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and D))), M:tm-309, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62455
in-theory        62455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (D -> ((A -> B) -> ((A -> B) and (((A and C) or A) -> B)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62455.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) and (D -> ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))))), M:tm-305, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62456
in-theory        62456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-303 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62456.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-303, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62457
in-theory        62457
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-270 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62457.        ((A -> (((B and C) -> C) and A)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-270, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62458
in-theory        62458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-239 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62458.        ((A -> (((B and C) -> B) and A)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-239, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62459
in-theory        62459
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-210 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62459.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F)))), M:tm-210, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62460
in-theory        62460
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-183 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62460.        ((A -> ((B -> (C -> B)) and A)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-183, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62461
in-theory        62461
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-157 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62461.        ((A -> ((B and C) -> C)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-157, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62462
in-theory        62462
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((((B and C) and D) or (B and C)) -> C)))
theorem-size     25
proof            (modus-ponens tm-154 tm-747 ((Am (and A Bm)) (B Bm) (C (and (-> (and A Bm) Bm) (-> (or (and (and A Bm) Cm) (and A Bm)) Bm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-2 tm-5 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62462.        ((A or ((B and C) -> C)) -> (((B and C) -> C) and ((((B and C) and D) or (B and C)) -> C))), M:tm-154, m:tm-747, u:((Am (and A Bm)) (B Bm) (C (and (-> (and A Bm) Bm) (-> (or (and (and A Bm) Cm) (and A Bm)) Bm))))
================================================================
tm-name          tm-62463
in-theory        62463
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     31
proof            (modus-ponens tm-147 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62463.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-147, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62464
in-theory        62464
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((((A and (B -> C)) and D) or (A and (B -> C))) -> C)))
theorem-size     39
proof            (modus-ponens tm-144 tm-747 ((Am (and A (-> B Bm))) (C Bm) (D (and (-> (and A (-> B Bm)) Bm) (-> (or (and (and A (-> B Bm)) Cm) (and A (-> B Bm))) Bm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62464.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((A and (B -> C)) -> C) and ((((A and (B -> C)) and D) or (A and (B -> C))) -> C))), M:tm-144, m:tm-747, u:((Am (and A (-> B Bm))) (C Bm) (D (and (-> (and A (-> B Bm)) Bm) (-> (or (and (and A (-> B Bm)) Cm) (and A (-> B Bm))) Bm))))
================================================================
tm-name          tm-62465
in-theory        62465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-134 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62465.        ((A -> ((B and C) -> B)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-134, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62466
in-theory        62466
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((((B and C) and D) or (B and C)) -> B)))
theorem-size     25
proof            (modus-ponens tm-131 tm-747 ((Am (and Bm B)) (A Bm) (C (and (-> (and Bm B) Bm) (-> (or (and (and Bm B) Cm) (and Bm B)) Bm)))))
axioms-used      (tm-8 tm-1 tm-3 tm-2 tm-5)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62466.        ((A or ((B and C) -> B)) -> (((B and C) -> B) and ((((B and C) and D) or (B and C)) -> B))), M:tm-131, m:tm-747, u:((Am (and Bm B)) (A Bm) (C (and (-> (and Bm B) Bm) (-> (or (and (and Bm B) Cm) (and Bm B)) Bm))))
================================================================
tm-name          tm-62467
in-theory        62467
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     31
proof            (modus-ponens tm-125 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62467.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-125, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62468
in-theory        62468
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (((((A -> B) and C) and D) or ((A -> B) and C)) -> B)))
theorem-size     39
proof            (modus-ponens tm-122 tm-747 ((Am (and (-> A Bm) C)) (B Bm) (D (and (-> (and (-> A Bm) C) Bm) (-> (or (and (and (-> A Bm) C) Cm) (and (-> A Bm) C)) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62468.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((((A -> B) and C) -> B) and (((((A -> B) and C) and D) or ((A -> B) and C)) -> B))), M:tm-122, m:tm-747, u:((Am (and (-> A Bm) C)) (B Bm) (D (and (-> (and (-> A Bm) C) Bm) (-> (or (and (and (-> A Bm) C) Cm) (and (-> A Bm) C)) Bm))))
================================================================
tm-name          tm-62469
in-theory        62469
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-113 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62469.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> F) -> ((E -> F) and (((E and G) or E) -> F)))), M:tm-113, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62470
in-theory        62470
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((B -> (C -> D)) and E) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))))
theorem-size     51
proof            (modus-ponens tm-110 tm-747 ((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (or (and (-> A (-> B C)) Cm) (-> A (-> B C))) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62470.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((((B -> (C -> D)) and E) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-747, u:((Am (-> A (-> B C))) (Bm (-> (-> A B) (-> A C))) (D (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) (-> (or (and (-> A (-> B C)) Cm) (-> A (-> B C))) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-62471
in-theory        62471
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     35
proof            (modus-ponens tm-105 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62471.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-105, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62472
in-theory        62472
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> C))))
theorem-size     47
proof            (modus-ponens tm-102 tm-747 ((Am (-> A (-> B C))) (Bm (-> A C)) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (or (and (-> A (-> B C)) Cm) (-> A (-> B C))) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62472.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((A -> (B -> C)) -> (A -> C)) and ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> (A -> C)))), M:tm-102, m:tm-747, u:((Am (-> A (-> B C))) (Bm (-> A C)) (D (and (-> (-> A (-> B C)) (-> A C)) (-> (or (and (-> A (-> B C)) Cm) (-> A (-> B C))) (-> A C)))))
================================================================
tm-name          tm-62473
in-theory        62473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-95 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62473.        (((A -> B) -> (A -> A)) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D)))), M:tm-95, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62474
in-theory        62474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((A -> A) and (((A and C) or A) -> A)))
theorem-size     19
proof            (modus-ponens tm-92 tm-747 ((Bm Am) (A Am) (B (and (-> Am Am) (-> (or (and Am Cm) Am) Am)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62474.        (((A -> B) or (A -> A)) -> ((A -> A) and (((A and C) or A) -> A))), M:tm-92, m:tm-747, u:((Bm Am) (A Am) (B (and (-> Am Am) (-> (or (and Am Cm) Am) Am))))
================================================================
tm-name          tm-62475
in-theory        62475
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (C -> ((A -> B) and (((A and D) or A) -> B))))
theorem-size     17
proof            (modus-ponens tm-84 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62475.        ((A -> B) -> (C -> ((A -> B) and (((A and D) or A) -> B)))), M:tm-84, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62476
in-theory        62476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-83 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62476.        ((A -> (B -> (C -> B))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-83, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62477
in-theory        62477
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (((B and D) or B) -> (C -> B))))
theorem-size     23
proof            (modus-ponens tm-80 tm-747 ((A Am) (Bm (-> B Am)) (C (and (-> Am (-> B Am)) (-> (or (and Am Cm) Am) (-> B Am))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62477.        ((A or (B -> (C -> B))) -> ((B -> (C -> B)) and (((B and D) or B) -> (C -> B)))), M:tm-80, m:tm-747, u:((A Am) (Bm (-> B Am)) (C (and (-> Am (-> B Am)) (-> (or (and Am Cm) Am) (-> B Am)))))
================================================================
tm-name          tm-62478
in-theory        62478
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> C) -> ((B -> C) and (((B and D) or B) -> C))))
theorem-size     21
proof            (modus-ponens tm-76 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62478.        (((not (not A)) -> A) and ((B -> C) -> ((B -> C) and (((B and D) or B) -> C)))), M:tm-76, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62479
in-theory        62479
times-derived    1
----------------------------------------------------------------
theorem          (((not (not (A -> B))) or (A -> B)) -> ((A -> B) and (((A and C) or A) -> B)))
theorem-size     21
proof            (modus-ponens tm-73 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-8 tm-10 tm-2 tm-5 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62479.        (((not (not (A -> B))) or (A -> B)) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-73, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62480
in-theory        62480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D))))
theorem-size     27
proof            (modus-ponens tm-69 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62480.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D)))), M:tm-69, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62481
in-theory        62481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((((A -> (not B)) and C) or (A -> (not B))) -> (not A))))
theorem-size     34
proof            (modus-ponens tm-66 tm-747 ((Am (-> A (not B))) (Bm (not A)) (C (and (-> (-> A (not B)) (not A)) (-> (or (and (-> A (not B)) Cm) (-> A (not B))) (not A))))))
axioms-used      (tm-8 tm-9 tm-2 tm-5 tm-3)
proof-size       154
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62481.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((A -> (not B)) -> (not A)) and ((((A -> (not B)) and C) or (A -> (not B))) -> (not A)))), M:tm-66, m:tm-747, u:((Am (-> A (not B))) (Bm (not A)) (C (and (-> (-> A (not B)) (not A)) (-> (or (and (-> A (not B)) Cm) (-> A (not B))) (not A)))))
================================================================
tm-name          tm-62482
in-theory        62482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-54 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62482.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-54, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62483
in-theory        62483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C))))
theorem-size     39
proof            (modus-ponens tm-51 tm-747 ((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (or (and (-> A B) Cm) (-> A B)) (-> (or C A) B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62483.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((B -> C) -> ((A or B) -> C)) and ((((B -> C) and D) or (B -> C)) -> ((A or B) -> C)))), M:tm-51, m:tm-747, u:((Am (-> A B)) (Bm (-> (or C A) B)) (D (and (-> (-> A B) (-> (or C A) B)) (-> (or (and (-> A B) Cm) (-> A B)) (-> (or C A) B)))))
================================================================
tm-name          tm-62484
in-theory        62484
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((B -> (A and B)) and (((B and C) or B) -> (A and B))))
theorem-size     23
proof            (modus-ponens tm-48 tm-747 ((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> (or (and Am Cm) Am) (and B Am))))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62484.        ((A or (B -> (A and B))) -> ((B -> (A and B)) and (((B and C) or B) -> (A and B)))), M:tm-48, m:tm-747, u:((A Am) (Bm (and B Am)) (C (and (-> Am (and B Am)) (-> (or (and Am Cm) Am) (and B Am)))))
================================================================
tm-name          tm-62485
in-theory        62485
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((B -> C) and (((B and D) or B) -> C)))
theorem-size     21
proof            (modus-ponens tm-47 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62485.        (((A and (B -> C)) or (B -> C)) -> ((B -> C) and (((B and D) or B) -> C))), M:tm-47, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62486
in-theory        62486
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and C) or (A -> B)) -> ((A -> B) and (((A and D) or A) -> B)))
theorem-size     21
proof            (modus-ponens tm-46 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62486.        ((((A -> B) and C) or (A -> B)) -> ((A -> B) and (((A and D) or A) -> B))), M:tm-46, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62487
in-theory        62487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((((A -> B) and D) or (A -> B)) -> (A -> C))))
theorem-size     35
proof            (modus-ponens tm-45 tm-747 ((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62487.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) and ((((A -> B) and D) or (A -> B)) -> (A -> C)))), M:tm-45, m:tm-747, u:((Am (-> A B)) (Bm (-> A C)) (D (and (-> (-> A B) (-> A C)) (-> (or (and (-> A B) Cm) (-> A B)) (-> A C)))))
================================================================
tm-name          tm-62488
in-theory        62488
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((B -> A) and (((B and C) or B) -> A)))
theorem-size     17
proof            (modus-ponens tm-44 tm-747 ((A Am) (B Bm) (C (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62488.        ((A or (B -> A)) -> ((B -> A) and (((B and C) or B) -> A))), M:tm-44, m:tm-747, u:((A Am) (B Bm) (C (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62489
in-theory        62489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D))))
theorem-size     21
proof            (modus-ponens tm-42 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62489.        ((A -> (B or A)) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D)))), M:tm-42, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62490
in-theory        62490
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D))))
theorem-size     21
proof            (modus-ponens tm-32 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62490.        ((A -> (A or B)) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D)))), M:tm-32, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62491
in-theory        62491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((A -> B) and ((A -> B) and (((A and C) or A) -> B))))
theorem-size     19
proof            (modus-ponens tm-24 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62491.        ((A -> B) -> ((A -> B) and ((A -> B) and (((A and C) or A) -> B)))), M:tm-24, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62492
in-theory        62492
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D))))
theorem-size     23
proof            (modus-ponens tm-23 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62492.        ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D)))), M:tm-23, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62493
in-theory        62493
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D))))
theorem-size     21
proof            (modus-ponens tm-22 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62493.        (((A and B) -> B) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D)))), M:tm-22, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62494
in-theory        62494
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D))))
theorem-size     21
proof            (modus-ponens tm-21 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62494.        (((A and B) -> A) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D)))), M:tm-21, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62495
in-theory        62495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     29
proof            (modus-ponens tm-20 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62495.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-20, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62496
in-theory        62496
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D))))
theorem-size     21
proof            (modus-ponens tm-19 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62496.        ((A -> (B -> A)) and ((C -> D) -> ((C -> D) and (((C and E) or C) -> D)))), M:tm-19, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62497
in-theory        62497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not ((A -> B) and (((A and C) or A) -> B)))) -> (not (A -> B)))
theorem-size     21
proof            (modus-ponens tm-9 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-9 tm-2 tm-5 tm-8 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62497.        (((A -> B) -> (not ((A -> B) and (((A and C) or A) -> B)))) -> (not (A -> B))), M:tm-9, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62498
in-theory        62498
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) and (((A and C) or A) -> B)) -> D) -> (((A -> B) or ((A -> B) and (((A and C) or A) -> B))) -> D))
theorem-size     31
proof            (modus-ponens tm-8 tm-747 ((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62498.        ((((A -> B) and (((A and C) or A) -> B)) -> D) -> (((A -> B) or ((A -> B) and (((A and C) or A) -> B))) -> D)), M:tm-8, m:tm-747, u:((A (-> Am Bm)) (B (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-62499
in-theory        62499
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> C) -> ((B -> C) and (((B and D) or B) -> C))))
theorem-size     17
proof            (modus-ponens tm-7 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-7 tm-2 tm-5 tm-8 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62499.        (A or ((B -> C) -> ((B -> C) and (((B and D) or B) -> C)))), M:tm-7, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62500
in-theory        62500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) or D)
theorem-size     17
proof            (modus-ponens tm-6 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-6 tm-2 tm-5 tm-8 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62500.        (((A -> B) -> ((A -> B) and (((A and C) or A) -> B))) or D), M:tm-6, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62501
in-theory        62501
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((B -> C) and (((B and D) or B) -> C))) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62501.        (A -> (((B -> C) -> ((B -> C) and (((B and D) or B) -> C))) and A)), M:tm-5, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62502
in-theory        62502
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> C) -> ((B -> C) and (((B and D) or B) -> C))))
theorem-size     17
proof            (modus-ponens tm-1 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-1 tm-2 tm-5 tm-8 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62502.        (A -> ((B -> C) -> ((B -> C) and (((B and D) or B) -> C)))), M:tm-1, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-62503
in-theory        62503
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-708 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62503.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> (E and F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-708, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62504
in-theory        62504
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-665 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62504.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-665, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62505
in-theory        62505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-622 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62505.        ((A -> (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-622, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62506
in-theory        62506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62506.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G or F))), M:tm-609, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62507
in-theory        62507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-605 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62507.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-605, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62508
in-theory        62508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62508.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G or F)) and ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-595, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62509
in-theory        62509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-550 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62509.        (((A -> (B or A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-550, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62510
in-theory        62510
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-540 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62510.        ((A or (B -> (C or B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-540, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62511
in-theory        62511
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-530 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62511.        ((A or (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-530, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62512
in-theory        62512
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-520 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62512.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-520, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62513
in-theory        62513
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-510 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62513.        ((A or ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-510, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62514
in-theory        62514
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-500 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62514.        ((A or ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-500, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62515
in-theory        62515
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-490 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62515.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-490, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62516
in-theory        62516
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-480 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62516.        ((A or (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-480, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62517
in-theory        62517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-469 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62517.        ((A -> (B -> (B or C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-469, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62518
in-theory        62518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62518.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (F or G))), M:tm-456, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62519
in-theory        62519
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-453 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62519.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-453, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62520
in-theory        62520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62520.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (F or G)) and ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-443, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62521
in-theory        62521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-409 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62521.        (((A -> (A or B)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-409, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62522
in-theory        62522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-400 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62522.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-400, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62523
in-theory        62523
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-391 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62523.        ((((A and B) -> B) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-391, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62524
in-theory        62524
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-382 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62524.        ((((A and B) -> A) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-382, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62525
in-theory        62525
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-373 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62525.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> (E and F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-373, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62526
in-theory        62526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-364 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62526.        (((A -> (B -> A)) or C) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-364, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62527
in-theory        62527
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-354 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62527.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-354, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62528
in-theory        62528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62528.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62529
in-theory        62529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-338 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62529.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-338, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62530
in-theory        62530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62530.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-327, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62531
in-theory        62531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62531.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> G) and ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-326, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62532
in-theory        62532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62532.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> F) and ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-325, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62533
in-theory        62533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62533.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-324, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62534
in-theory        62534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62534.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> F)) and ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-323, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62535
in-theory        62535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62535.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62536
in-theory        62536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62536.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62537
in-theory        62537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62537.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62538
in-theory        62538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62538.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62539
in-theory        62539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (F or ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62539.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (F or ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-311, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62540
in-theory        62540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62540.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) or F)), M:tm-310, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62541
in-theory        62541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62541.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and F))), M:tm-309, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62542
in-theory        62542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     31
proof            (modus-ponens tm-308 tm-748 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62542.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-308, m:tm-748, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))
================================================================
tm-name          tm-62543
in-theory        62543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (A -> (B -> (A and B))))
theorem-size     27
proof            (modus-ponens tm-307 tm-748 ((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62543.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (A -> (B -> (A and B)))), M:tm-307, m:tm-748, u:((A (-> Am (-> Bm (and Am Bm)))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))
================================================================
tm-name          tm-62544
in-theory        62544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62544.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-305, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62545
in-theory        62545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-303 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62545.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-303, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62546
in-theory        62546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-270 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62546.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-270, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62547
in-theory        62547
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-239 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62547.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-239, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62548
in-theory        62548
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     37
proof            (modus-ponens tm-210 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62548.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> (E and F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-210, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62549
in-theory        62549
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-183 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62549.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-183, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62550
in-theory        62550
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-157 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62550.        ((A -> ((B and C) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-157, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62551
in-theory        62551
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-147 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62551.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-147, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62552
in-theory        62552
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-134 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62552.        ((A -> ((B and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-134, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62553
in-theory        62553
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-125 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62553.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-125, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62554
in-theory        62554
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-113 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62554.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> (E and F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-113, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62555
in-theory        62555
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     39
proof            (modus-ponens tm-105 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62555.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-105, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62556
in-theory        62556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-95 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62556.        (((A -> B) -> (A -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-95, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62557
in-theory        62557
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-83 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62557.        ((A -> (B -> (C -> B))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-83, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62558
in-theory        62558
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-76 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62558.        (((not (not A)) -> A) and ((B -> (C -> (B and C))) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-76, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62559
in-theory        62559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-69 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62559.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-69, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62560
in-theory        62560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-54 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62560.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-54, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62561
in-theory        62561
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-42 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62561.        ((A -> (B or A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-42, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62562
in-theory        62562
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-32 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62562.        ((A -> (A or B)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-32, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62563
in-theory        62563
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-23 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62563.        ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-23, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62564
in-theory        62564
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-22 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62564.        (((A and B) -> B) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-22, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62565
in-theory        62565
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-21 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62565.        (((A and B) -> A) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-21, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62566
in-theory        62566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-20 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62566.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-20, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62567
in-theory        62567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-19 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62567.        ((A -> (B -> A)) and ((C -> (D -> (C and D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-19, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62568
in-theory        62568
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> (B and C))) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-7 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-7 tm-5 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62568.        (A or ((B -> (C -> (B and C))) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-7, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62569
in-theory        62569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-6 tm-5 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62569.        (((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))) or F), M:tm-6, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62570
in-theory        62570
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> (B and C))) and ((D -> E) -> (((D and F) or D) -> E))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62570.        (A -> (((B -> (C -> (B and C))) and ((D -> E) -> (((D and F) or D) -> E))) and A)), M:tm-5, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62571
in-theory        62571
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> (B and C))) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-1 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62571.        (A -> ((B -> (C -> (B and C))) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-1, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62572
in-theory        62572
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     43
proof            (modus-ponens tm-708 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62572.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-708, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62573
in-theory        62573
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-665 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62573.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-665, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62574
in-theory        62574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-622 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62574.        ((A -> (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-622, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62575
in-theory        62575
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-4 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62575.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G or F))), M:tm-609, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62576
in-theory        62576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-605 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62576.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-605, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62577
in-theory        62577
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62577.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G or F)) and (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-595, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62578
in-theory        62578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-550 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62578.        (((A -> (B or A)) or C) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-550, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62579
in-theory        62579
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-540 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62579.        ((A or (B -> (C or B))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-540, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62580
in-theory        62580
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-530 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62580.        ((A or (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-530, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62581
in-theory        62581
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-520 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62581.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-520, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62582
in-theory        62582
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-510 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62582.        ((A or ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-510, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62583
in-theory        62583
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-500 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-4 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62583.        ((A or ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-500, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62584
in-theory        62584
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-490 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-4 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62584.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-490, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62585
in-theory        62585
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-480 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62585.        ((A or (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-480, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62586
in-theory        62586
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-469 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62586.        ((A -> (B -> (B or C))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-469, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62587
in-theory        62587
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-4 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62587.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (F or G))), M:tm-456, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62588
in-theory        62588
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-453 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62588.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-453, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62589
in-theory        62589
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62589.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (F or G)) and (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-443, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62590
in-theory        62590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-409 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62590.        (((A -> (A or B)) or C) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-409, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62591
in-theory        62591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-400 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62591.        (((A -> (B -> (A and B))) or C) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-400, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62592
in-theory        62592
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-391 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62592.        ((((A and B) -> B) or C) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-391, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62593
in-theory        62593
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-382 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-4 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62593.        ((((A and B) -> A) or C) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-382, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62594
in-theory        62594
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-373 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-4 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62594.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-373, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62595
in-theory        62595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-364 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62595.        (((A -> (B -> A)) or C) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-364, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62596
in-theory        62596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-354 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62596.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-354, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62597
in-theory        62597
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62597.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62598
in-theory        62598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-338 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62598.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-338, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62599
in-theory        62599
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62599.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-327, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62600
in-theory        62600
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> G) and (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62600.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> G) and (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-326, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62601
in-theory        62601
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> F) and (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-8)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62601.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> F) and (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-325, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62602
in-theory        62602
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62602.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-324, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62603
in-theory        62603
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62603.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> F)) and (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-323, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62604
in-theory        62604
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62604.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62605
in-theory        62605
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-4 tm-8)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62605.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62606
in-theory        62606
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62606.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62607
in-theory        62607
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62607.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62608
in-theory        62608
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (F or (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62608.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (F or (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-311, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62609
in-theory        62609
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62609.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) or F)), M:tm-310, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62610
in-theory        62610
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62610.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and F))), M:tm-309, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62611
in-theory        62611
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-308 tm-749 ((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62611.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-308, m:tm-749, u:((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))
================================================================
tm-name          tm-62612
in-theory        62612
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((A and B) -> B))
theorem-size     23
proof            (modus-ponens tm-307 tm-749 ((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-4 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62612.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and ((A and B) -> B)), M:tm-307, m:tm-749, u:((A (-> (and Am Bm) Bm)) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))
================================================================
tm-name          tm-62613
in-theory        62613
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62613.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-305, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62614
in-theory        62614
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-303 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62614.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-303, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62615
in-theory        62615
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-270 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62615.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-270, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62616
in-theory        62616
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-239 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62616.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-239, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62617
in-theory        62617
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-210 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62617.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-210, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62618
in-theory        62618
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-183 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62618.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-183, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62619
in-theory        62619
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-157 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62619.        ((A -> ((B and C) -> C)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-157, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62620
in-theory        62620
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-147 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62620.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-147, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62621
in-theory        62621
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-134 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-4 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62621.        ((A -> ((B and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-134, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62622
in-theory        62622
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-125 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-4 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62622.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-125, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62623
in-theory        62623
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-113 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-4 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62623.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> F) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-113, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62624
in-theory        62624
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-105 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62624.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-105, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62625
in-theory        62625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-95 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62625.        (((A -> B) -> (A -> A)) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-95, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62626
in-theory        62626
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-83 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62626.        ((A -> (B -> (C -> B))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-83, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62627
in-theory        62627
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> C) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-76 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-10 tm-4 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62627.        (((not (not A)) -> A) and (((B and C) -> C) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-76, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62628
in-theory        62628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-69 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-9 tm-4 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62628.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-69, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62629
in-theory        62629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-54 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62629.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-54, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62630
in-theory        62630
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-42 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62630.        ((A -> (B or A)) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-42, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62631
in-theory        62631
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-32 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62631.        ((A -> (A or B)) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-32, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62632
in-theory        62632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-23 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62632.        ((A -> (B -> (A and B))) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-23, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62633
in-theory        62633
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-22 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62633.        (((A and B) -> B) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-22, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62634
in-theory        62634
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-21 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-4 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62634.        (((A and B) -> A) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-21, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62635
in-theory        62635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-20 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62635.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-20, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62636
in-theory        62636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-19 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62636.        ((A -> (B -> A)) and (((C and D) -> D) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-19, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62637
in-theory        62637
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> C) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-7 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-7 tm-5 tm-4 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62637.        (A or (((B and C) -> C) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-7, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62638
in-theory        62638
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-6 tm-5 tm-4 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62638.        ((((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))) or F), M:tm-6, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62639
in-theory        62639
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> C) and ((D -> E) -> (((D and F) or D) -> E))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62639.        (A -> ((((B and C) -> C) and ((D -> E) -> (((D and F) or D) -> E))) and A)), M:tm-5, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62640
in-theory        62640
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> C) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-1 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-1 tm-5 tm-4 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62640.        (A -> (((B and C) -> C) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-1, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62641
in-theory        62641
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     43
proof            (modus-ponens tm-708 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62641.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-708, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62642
in-theory        62642
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-665 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62642.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-665, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62643
in-theory        62643
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-622 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62643.        ((A -> (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-622, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62644
in-theory        62644
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-3 tm-8)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62644.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G or F))), M:tm-609, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62645
in-theory        62645
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-605 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62645.        ((A -> ((B -> (C or B)) and A)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-605, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62646
in-theory        62646
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-8)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62646.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G or F)) and (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-595, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62647
in-theory        62647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-550 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62647.        (((A -> (B or A)) or C) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-550, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62648
in-theory        62648
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-540 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62648.        ((A or (B -> (C or B))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-540, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62649
in-theory        62649
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-530 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62649.        ((A or (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-530, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62650
in-theory        62650
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-520 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62650.        ((A or (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-520, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62651
in-theory        62651
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-510 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62651.        ((A or ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-510, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62652
in-theory        62652
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-500 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62652.        ((A or ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-500, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62653
in-theory        62653
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-490 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-3 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62653.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-490, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62654
in-theory        62654
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-480 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62654.        ((A or (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-480, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62655
in-theory        62655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-469 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62655.        ((A -> (B -> (B or C))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-469, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62656
in-theory        62656
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-3 tm-8)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62656.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (F or G))), M:tm-456, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62657
in-theory        62657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-453 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62657.        ((A -> ((B -> (B or C)) and A)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-453, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62658
in-theory        62658
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-8)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62658.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (F or G)) and (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-443, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62659
in-theory        62659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-409 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62659.        (((A -> (A or B)) or C) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-409, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62660
in-theory        62660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-400 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62660.        (((A -> (B -> (A and B))) or C) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-400, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62661
in-theory        62661
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-391 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62661.        ((((A and B) -> B) or C) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-391, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62662
in-theory        62662
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-382 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62662.        ((((A and B) -> A) or C) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-382, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62663
in-theory        62663
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-373 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-3 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62663.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-373, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62664
in-theory        62664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-364 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62664.        (((A -> (B -> A)) or C) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-364, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62665
in-theory        62665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-354 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62665.        ((A -> (B -> (C -> (B and C)))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-354, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62666
in-theory        62666
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62666.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62667
in-theory        62667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-338 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62667.        (((A -> B) -> (A -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-338, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62668
in-theory        62668
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62668.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> (F and G))) and (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-327, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62669
in-theory        62669
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> G) and (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-8)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62669.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> G) and (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-326, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62670
in-theory        62670
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> F) and (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62670.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> F) and (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-325, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62671
in-theory        62671
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62671.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-324, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62672
in-theory        62672
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62672.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> F)) and (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-323, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62673
in-theory        62673
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-3 tm-8)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62673.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62674
in-theory        62674
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62674.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62675
in-theory        62675
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62675.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62676
in-theory        62676
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62676.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62677
in-theory        62677
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (F or (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-3 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62677.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (F or (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-311, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62678
in-theory        62678
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-3 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62678.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) or F)), M:tm-310, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62679
in-theory        62679
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62679.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and F))), M:tm-309, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62680
in-theory        62680
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-308 tm-750 ((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-3 tm-8)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62680.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-308, m:tm-750, u:((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))
================================================================
tm-name          tm-62681
in-theory        62681
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((A and B) -> A))
theorem-size     23
proof            (modus-ponens tm-307 tm-750 ((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62681.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and ((A and B) -> A)), M:tm-307, m:tm-750, u:((A (-> (and Am Bm) Am)) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))
================================================================
tm-name          tm-62682
in-theory        62682
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62682.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-305, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62683
in-theory        62683
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-303 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62683.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-303, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62684
in-theory        62684
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-270 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62684.        ((A -> (((B and C) -> C) and A)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-270, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62685
in-theory        62685
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-239 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62685.        ((A -> (((B and C) -> B) and A)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-239, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62686
in-theory        62686
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-210 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62686.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-210, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62687
in-theory        62687
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-183 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62687.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-183, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62688
in-theory        62688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-157 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62688.        ((A -> ((B and C) -> C)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-157, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62689
in-theory        62689
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-147 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-3 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62689.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-147, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62690
in-theory        62690
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-134 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62690.        ((A -> ((B and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-134, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62691
in-theory        62691
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-125 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62691.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-125, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62692
in-theory        62692
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-113 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-3 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62692.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) -> E) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-113, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62693
in-theory        62693
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-105 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62693.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-105, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62694
in-theory        62694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-95 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62694.        (((A -> B) -> (A -> A)) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-95, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62695
in-theory        62695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-83 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62695.        ((A -> (B -> (C -> B))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-83, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62696
in-theory        62696
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) -> B) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-76 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-10 tm-3 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62696.        (((not (not A)) -> A) and (((B and C) -> B) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-76, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62697
in-theory        62697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-69 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-9 tm-3 tm-8)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62697.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-69, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62698
in-theory        62698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-54 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62698.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-54, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62699
in-theory        62699
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-42 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62699.        ((A -> (B or A)) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-42, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62700
in-theory        62700
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-32 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62700.        ((A -> (A or B)) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-32, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62701
in-theory        62701
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-23 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62701.        ((A -> (B -> (A and B))) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-23, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62702
in-theory        62702
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-22 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-3 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62702.        (((A and B) -> B) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-22, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62703
in-theory        62703
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-21 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62703.        (((A and B) -> A) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-21, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62704
in-theory        62704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-20 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62704.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-20, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62705
in-theory        62705
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-19 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62705.        ((A -> (B -> A)) and (((C and D) -> C) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-19, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62706
in-theory        62706
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) -> B) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-7 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-7 tm-5 tm-3 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62706.        (A or (((B and C) -> B) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-7, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62707
in-theory        62707
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-6 tm-5 tm-3 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62707.        ((((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))) or F), M:tm-6, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62708
in-theory        62708
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) -> B) and ((D -> E) -> (((D and F) or D) -> E))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62708.        (A -> ((((B and C) -> B) and ((D -> E) -> (((D and F) or D) -> E))) and A)), M:tm-5, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62709
in-theory        62709
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) -> B) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-1 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-1 tm-5 tm-3 tm-8)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62709.        (A -> (((B and C) -> B) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-1, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62710
in-theory        62710
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((H and J) or H) -> I))))
theorem-size     51
proof            (modus-ponens tm-708 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62710.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-708, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62711
in-theory        62711
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-665 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62711.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-665, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62712
in-theory        62712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-622 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62712.        ((A -> (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-622, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62713
in-theory        62713
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (H or G)))
theorem-size     31
proof            (modus-ponens tm-609 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62713.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (H or G))), M:tm-609, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62714
in-theory        62714
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-605 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62714.        ((A -> ((B -> (C or B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-605, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62715
in-theory        62715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-595 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62715.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H or G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-595, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62716
in-theory        62716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-550 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62716.        (((A -> (B or A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-550, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62717
in-theory        62717
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-540 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62717.        ((A or (B -> (C or B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-540, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62718
in-theory        62718
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-530 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62718.        ((A or (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-530, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62719
in-theory        62719
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-520 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62719.        ((A or (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-520, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62720
in-theory        62720
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-510 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62720.        ((A or ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-510, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62721
in-theory        62721
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-500 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62721.        ((A or ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-500, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62722
in-theory        62722
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((H and J) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-490 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62722.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-490, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62723
in-theory        62723
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-480 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62723.        ((A or (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-480, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62724
in-theory        62724
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-469 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62724.        ((A -> (B -> (B or C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-469, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62725
in-theory        62725
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (G or H)))
theorem-size     31
proof            (modus-ponens tm-456 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62725.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (G or H))), M:tm-456, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62726
in-theory        62726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-453 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62726.        ((A -> ((B -> (B or C)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-453, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62727
in-theory        62727
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-443 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62727.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (G or H)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-443, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62728
in-theory        62728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-409 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62728.        (((A -> (A or B)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-409, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62729
in-theory        62729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-400 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62729.        (((A -> (B -> (A and B))) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-400, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62730
in-theory        62730
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-391 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62730.        ((((A and B) -> B) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-391, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62731
in-theory        62731
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-382 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62731.        ((((A and B) -> A) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-382, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62732
in-theory        62732
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((H and J) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-373 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62732.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-373, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62733
in-theory        62733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-364 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62733.        (((A -> (B -> A)) or C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-364, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62734
in-theory        62734
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-354 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62734.        ((A -> (B -> (C -> (B and C)))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-354, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62735
in-theory        62735
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (H -> (G and H))))
theorem-size     33
proof            (modus-ponens tm-341 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62735.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (H -> (G and H)))), M:tm-341, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62736
in-theory        62736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-338 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62736.        (((A -> B) -> (A -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-338, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62737
in-theory        62737
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     59
proof            (modus-ponens tm-327 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       217
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62737.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H -> (G and H))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-327, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62738
in-theory        62738
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-326 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62738.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (((G and H) -> H) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-326, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62739
in-theory        62739
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-325 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62739.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (((G and H) -> G) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-325, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62740
in-theory        62740
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     65
proof            (modus-ponens tm-324 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       241
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62740.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-324, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62741
in-theory        62741
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     57
proof            (modus-ponens tm-323 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62741.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H -> G)) and (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-323, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62742
in-theory        62742
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G and H) -> H))
theorem-size     31
proof            (modus-ponens tm-322 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62742.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G and H) -> H)), M:tm-322, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62743
in-theory        62743
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G and H) -> G))
theorem-size     31
proof            (modus-ponens tm-320 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62743.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G and H) -> G)), M:tm-320, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62744
in-theory        62744
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))
theorem-size     39
proof            (modus-ponens tm-318 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       209
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62744.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))), M:tm-318, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62745
in-theory        62745
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (H -> G)))
theorem-size     31
proof            (modus-ponens tm-315 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62745.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (H -> G))), M:tm-315, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62746
in-theory        62746
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     53
proof            (modus-ponens tm-311 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62746.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-311, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62747
in-theory        62747
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) or G))
theorem-size     53
proof            (modus-ponens tm-310 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62747.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) or G)), M:tm-310, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62748
in-theory        62748
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and G)))
theorem-size     55
proof            (modus-ponens tm-309 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62748.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and G))), M:tm-309, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62749
in-theory        62749
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     37
proof            (modus-ponens tm-308 tm-751 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62749.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-308, m:tm-751, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))
================================================================
tm-name          tm-62750
in-theory        62750
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C))))
theorem-size     39
proof            (modus-ponens tm-307 tm-751 ((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62750.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))), M:tm-307, m:tm-751, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (B (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))
================================================================
tm-name          tm-62751
in-theory        62751
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E)))))
theorem-size     53
proof            (modus-ponens tm-305 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62751.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) and (G -> (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))))), M:tm-305, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62752
in-theory        62752
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     37
proof            (modus-ponens tm-303 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62752.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-303, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62753
in-theory        62753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-270 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62753.        ((A -> (((B and C) -> C) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-270, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62754
in-theory        62754
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-239 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62754.        ((A -> (((B and C) -> B) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-239, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62755
in-theory        62755
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((H and J) or H) -> I))))
theorem-size     43
proof            (modus-ponens tm-210 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62755.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-210, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62756
in-theory        62756
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-183 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62756.        ((A -> ((B -> (C -> B)) and A)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-183, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62757
in-theory        62757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-157 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62757.        ((A -> ((B and C) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-157, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62758
in-theory        62758
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     41
proof            (modus-ponens tm-147 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62758.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-147, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62759
in-theory        62759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-134 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62759.        ((A -> ((B and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-134, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62760
in-theory        62760
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     41
proof            (modus-ponens tm-125 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62760.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-125, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62761
in-theory        62761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((H and J) or H) -> I))))
theorem-size     41
proof            (modus-ponens tm-113 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62761.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and ((H -> I) -> (((H and J) or H) -> I)))), M:tm-113, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62762
in-theory        62762
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-105 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62762.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-105, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62763
in-theory        62763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-95 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62763.        (((A -> B) -> (A -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-95, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62764
in-theory        62764
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-83 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62764.        ((A -> (B -> (C -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-83, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62765
in-theory        62765
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-76 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62765.        (((not (not A)) -> A) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-76, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62766
in-theory        62766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-69 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62766.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-69, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62767
in-theory        62767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-54 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62767.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-54, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62768
in-theory        62768
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-42 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62768.        ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-42, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62769
in-theory        62769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-32 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62769.        ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-32, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62770
in-theory        62770
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-23 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62770.        ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-23, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62771
in-theory        62771
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-22 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62771.        (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-22, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62772
in-theory        62772
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-21 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62772.        (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-21, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62773
in-theory        62773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     39
proof            (modus-ponens tm-20 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62773.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-20, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62774
in-theory        62774
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-19 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62774.        ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-19, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62775
in-theory        62775
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-7 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-7 tm-5 tm-2 tm-8 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62775.        (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-7, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62776
in-theory        62776
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) or G)
theorem-size     27
proof            (modus-ponens tm-6 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-6 tm-5 tm-2 tm-8 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62776.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))) or G), M:tm-6, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62777
in-theory        62777
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (((E and G) or E) -> F))) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62777.        (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (((E and G) or E) -> F))) and A)), M:tm-5, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62778
in-theory        62778
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-1 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-1 tm-5 tm-2 tm-8 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62778.        (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-1, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-62779
in-theory        62779
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     43
proof            (modus-ponens tm-708 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62779.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-708, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62780
in-theory        62780
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-665 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62780.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-665, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62781
in-theory        62781
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-622 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62781.        ((A -> (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-622, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62782
in-theory        62782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G or F)))
theorem-size     23
proof            (modus-ponens tm-609 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62782.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G or F))), M:tm-609, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62783
in-theory        62783
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-605 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62783.        ((A -> ((B -> (C or B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-605, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62784
in-theory        62784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62784.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G or F)) and ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-595, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62785
in-theory        62785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-550 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62785.        (((A -> (B or A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-550, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62786
in-theory        62786
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-540 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62786.        ((A or (B -> (C or B))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-540, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62787
in-theory        62787
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-530 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62787.        ((A or (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-530, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62788
in-theory        62788
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-520 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62788.        ((A or (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-520, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62789
in-theory        62789
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-510 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62789.        ((A or ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-510, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62790
in-theory        62790
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-500 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62790.        ((A or ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-500, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62791
in-theory        62791
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-490 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62791.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-490, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62792
in-theory        62792
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-480 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62792.        ((A or (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-480, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62793
in-theory        62793
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-469 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62793.        ((A -> (B -> (B or C))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-469, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62794
in-theory        62794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (F or G)))
theorem-size     23
proof            (modus-ponens tm-456 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62794.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (F or G))), M:tm-456, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62795
in-theory        62795
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-453 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62795.        ((A -> ((B -> (B or C)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-453, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62796
in-theory        62796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62796.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (F or G)) and ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-443, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62797
in-theory        62797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-409 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62797.        (((A -> (A or B)) or C) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-409, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62798
in-theory        62798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-400 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62798.        (((A -> (B -> (A and B))) or C) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-400, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62799
in-theory        62799
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-391 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62799.        ((((A and B) -> B) or C) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-391, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62800
in-theory        62800
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-382 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62800.        ((((A and B) -> A) or C) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-382, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62801
in-theory        62801
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-373 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62801.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-373, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62802
in-theory        62802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-364 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62802.        (((A -> (B -> A)) or C) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-364, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62803
in-theory        62803
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-354 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62803.        ((A -> (B -> (C -> (B and C)))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-354, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62804
in-theory        62804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> (F and G))))
theorem-size     25
proof            (modus-ponens tm-341 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62804.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62805
in-theory        62805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-338 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62805.        (((A -> B) -> (A -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-338, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62806
in-theory        62806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62806.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> (F and G))) and ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-327, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62807
in-theory        62807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62807.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> G) and ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-326, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62808
in-theory        62808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62808.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F and G) -> F) and ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-325, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62809
in-theory        62809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62809.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-324, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62810
in-theory        62810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62810.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> F)) and ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-323, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62811
in-theory        62811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> G))
theorem-size     23
proof            (modus-ponens tm-322 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62811.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> G)), M:tm-322, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62812
in-theory        62812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> F))
theorem-size     23
proof            (modus-ponens tm-320 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62812.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F and G) -> F)), M:tm-320, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62813
in-theory        62813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     31
proof            (modus-ponens tm-318 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62813.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62814
in-theory        62814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> F)))
theorem-size     23
proof            (modus-ponens tm-315 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62814.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (G -> F))), M:tm-315, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62815
in-theory        62815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F or ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62815.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F or ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-311, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62816
in-theory        62816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) or F))
theorem-size     37
proof            (modus-ponens tm-310 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62816.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) or F)), M:tm-310, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62817
in-theory        62817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and F)))
theorem-size     39
proof            (modus-ponens tm-309 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62817.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and F))), M:tm-309, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62818
in-theory        62818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-308 tm-752 ((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62818.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-308, m:tm-752, u:((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))
================================================================
tm-name          tm-62819
in-theory        62819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (A -> (B -> A)))
theorem-size     23
proof            (modus-ponens tm-307 tm-752 ((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62819.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (A -> (B -> A))), M:tm-307, m:tm-752, u:((A (-> Am (-> Bm Am))) (B (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))
================================================================
tm-name          tm-62820
in-theory        62820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62820.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) and (F -> ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))))), M:tm-305, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62821
in-theory        62821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-303 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62821.        ((A -> ((B -> (C -> (B and C))) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-303, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62822
in-theory        62822
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-270 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62822.        ((A -> (((B and C) -> C) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-270, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62823
in-theory        62823
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-239 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62823.        ((A -> (((B and C) -> B) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-239, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62824
in-theory        62824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-210 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62824.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-210, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62825
in-theory        62825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-183 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62825.        ((A -> ((B -> (C -> B)) and A)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-183, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62826
in-theory        62826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-157 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62826.        ((A -> ((B and C) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-157, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62827
in-theory        62827
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-147 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62827.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-147, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62828
in-theory        62828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-134 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62828.        ((A -> ((B and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-134, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62829
in-theory        62829
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-125 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62829.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-125, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62830
in-theory        62830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     33
proof            (modus-ponens tm-113 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62830.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and ((E -> (F -> E)) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-113, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62831
in-theory        62831
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     37
proof            (modus-ponens tm-105 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62831.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-105, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62832
in-theory        62832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-95 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62832.        (((A -> B) -> (A -> A)) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-95, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62833
in-theory        62833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     25
proof            (modus-ponens tm-83 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62833.        ((A -> (B -> (C -> B))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-83, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62834
in-theory        62834
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-76 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62834.        (((not (not A)) -> A) and ((B -> (C -> B)) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-76, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62835
in-theory        62835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-69 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62835.        (((A -> B) -> ((A -> (not B)) -> (not A))) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-69, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62836
in-theory        62836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-54 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62836.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-54, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62837
in-theory        62837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-42 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62837.        ((A -> (B or A)) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-42, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62838
in-theory        62838
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-32 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62838.        ((A -> (A or B)) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-32, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62839
in-theory        62839
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-23 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62839.        ((A -> (B -> (A and B))) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-23, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62840
in-theory        62840
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-22 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62840.        (((A and B) -> B) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-22, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62841
in-theory        62841
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-21 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62841.        (((A and B) -> A) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-21, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62842
in-theory        62842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-20 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62842.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-20, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62843
in-theory        62843
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-19 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62843.        ((A -> (B -> A)) and ((C -> (D -> C)) and ((E -> F) -> (((E and G) or E) -> F)))), M:tm-19, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62844
in-theory        62844
times-derived    1
----------------------------------------------------------------
theorem          (A or ((B -> (C -> B)) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-7 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-7 tm-5 tm-1 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62844.        (A or ((B -> (C -> B)) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-7, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62845
in-theory        62845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) or F)
theorem-size     19
proof            (modus-ponens tm-6 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-6 tm-5 tm-1 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62845.        (((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))) or F), M:tm-6, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62846
in-theory        62846
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> (C -> B)) and ((D -> E) -> (((D and F) or D) -> E))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62846.        (A -> (((B -> (C -> B)) and ((D -> E) -> (((D and F) or D) -> E))) and A)), M:tm-5, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62847
in-theory        62847
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((B -> (C -> B)) and ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-1 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-1 tm-5 tm-8 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-62847.        (A -> ((B -> (C -> B)) and ((D -> E) -> (((D and F) or D) -> E)))), M:tm-1, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-62848
in-theory        62848
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((((A -> B) -> (not (((A and C) or A) -> B))) and D) or ((A -> B) -> (not (((A and C) or A) -> B)))) -> (not (A -> B))))
theorem-size     50
proof            (modus-ponens tm-747 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-9)
proof-size       180
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62848.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((((A -> B) -> (not (((A and C) or A) -> B))) and D) or ((A -> B) -> (not (((A and C) or A) -> B)))) -> (not (A -> B)))), M:tm-747, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62849
in-theory        62849
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F))))
theorem-size     43
proof            (modus-ponens tm-708 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-9 tm-3)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62849.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F)))), M:tm-708, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62850
in-theory        62850
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-665 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-9 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62850.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-665, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62851
in-theory        62851
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((not (((A and C) or A) -> B)) or ((A -> B) -> (not (((A and C) or A) -> B)))) -> (not (A -> B))))
theorem-size     44
proof            (modus-ponens tm-654 tm-753 ((A (-> Am Bm)) (B (not (-> (or (and Am Cm) Am) Bm))) (C (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-9 tm-3)
proof-size       180
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62851.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((not (((A and C) or A) -> B)) or ((A -> B) -> (not (((A and C) or A) -> B)))) -> (not (A -> B)))), M:tm-654, m:tm-753, u:((A (-> Am Bm)) (B (not (-> (or (and Am Cm) Am) Bm))) (C (not (-> Am Bm))))
================================================================
tm-name          tm-62852
in-theory        62852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((A and C) or A) -> B))) -> (D or (not (A -> B))))
theorem-size     19
proof            (modus-ponens tm-623 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-9 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62852.        (((A -> B) -> (not (((A and C) or A) -> B))) -> (D or (not (A -> B)))), M:tm-623, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62853
in-theory        62853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-622 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-9 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62853.        ((A -> (B -> (C or B))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-622, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62854
in-theory        62854
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B or A)) -> (not (((A and C) or A) -> (B or A)))))
theorem-size     17
proof            (modus-ponens tm-618 tm-753 ((A (-> (-> Am (or C Am)) (not (-> (or (and Am Cm) Am) (or C Am))))) (B Am) (Bm (or C Am))))
axioms-used      (tm-9 tm-1 tm-7 tm-8 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62854.        (not ((A -> (B or A)) -> (not (((A and C) or A) -> (B or A))))), M:tm-618, m:tm-753, u:((A (-> (-> Am (or C Am)) (not (-> (or (and Am Cm) Am) (or C Am))))) (B Am) (Bm (or C Am)))
================================================================
tm-name          tm-62855
in-theory        62855
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-609 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-9 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62855.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (D -> (E or D))), M:tm-609, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62856
in-theory        62856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-605 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62856.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-605, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62857
in-theory        62857
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((D -> (E or D)) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62857.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((D -> (E or D)) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))))), M:tm-595, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62858
in-theory        62858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-550 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-9 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62858.        (((A -> (B or A)) or C) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-550, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62859
in-theory        62859
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-540 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62859.        ((A or (B -> (C or B))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-540, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62860
in-theory        62860
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-530 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-9 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62860.        ((A or (B -> (B or C))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-530, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62861
in-theory        62861
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-520 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62861.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-520, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62862
in-theory        62862
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-510 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-9 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62862.        ((A or ((B and C) -> C)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-510, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62863
in-theory        62863
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-500 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-9 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62863.        ((A or ((B and C) -> B)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-500, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62864
in-theory        62864
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-490 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-9 tm-8 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62864.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F)))), M:tm-490, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62865
in-theory        62865
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-480 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-9 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62865.        ((A or (B -> (C -> B))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-480, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62866
in-theory        62866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((A and C) or A) -> B))) -> ((not (A -> B)) or D))
theorem-size     19
proof            (modus-ponens tm-470 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-9 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62866.        (((A -> B) -> (not (((A and C) or A) -> B))) -> ((not (A -> B)) or D)), M:tm-470, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62867
in-theory        62867
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-469 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-9 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62867.        ((A -> (B -> (B or C))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-469, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62868
in-theory        62868
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (A or B)) -> (not (((A and C) or A) -> (A or B)))))
theorem-size     17
proof            (modus-ponens tm-465 tm-753 ((A (-> (-> Am (or Am C)) (not (-> (or (and Am Cm) Am) (or Am C))))) (B Am) (Bm (or Am C))))
axioms-used      (tm-9 tm-1 tm-6 tm-8 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62868.        (not ((A -> (A or B)) -> (not (((A and C) or A) -> (A or B))))), M:tm-465, m:tm-753, u:((A (-> (-> Am (or Am C)) (not (-> (or (and Am Cm) Am) (or Am C))))) (B Am) (Bm (or Am C)))
================================================================
tm-name          tm-62869
in-theory        62869
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-456 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-9 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62869.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (D -> (D or E))), M:tm-456, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62870
in-theory        62870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-453 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62870.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-453, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62871
in-theory        62871
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((D -> (D or E)) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62871.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((D -> (D or E)) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))))), M:tm-443, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62872
in-theory        62872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-409 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62872.        (((A -> (A or B)) or C) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-409, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62873
in-theory        62873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-400 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62873.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-400, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62874
in-theory        62874
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-391 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-9 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62874.        ((((A and B) -> B) or C) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-391, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62875
in-theory        62875
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-382 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-9 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62875.        ((((A and B) -> A) or C) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-382, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62876
in-theory        62876
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-373 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-9 tm-8 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62876.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F)))), M:tm-373, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62877
in-theory        62877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-364 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-9 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62877.        (((A -> (B -> A)) or C) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-364, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62878
in-theory        62878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((A and C) or A) -> B))) -> (D -> ((not (A -> B)) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-9 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62878.        (((A -> B) -> (not (((A and C) or A) -> B))) -> (D -> ((not (A -> B)) and D))), M:tm-355, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62879
in-theory        62879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-354 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62879.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-354, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62880
in-theory        62880
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> (A and B))) -> (not (((A and C) or A) -> (B -> (A and B))))))
theorem-size     21
proof            (modus-ponens tm-350 tm-753 ((A (-> (-> Am (-> C (and Am C))) (not (-> (or (and Am Cm) Am) (-> C (and Am C)))))) (B Am) (Bm (-> C (and Am C)))))
axioms-used      (tm-9 tm-1 tm-5 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62880.        (not ((A -> (B -> (A and B))) -> (not (((A and C) or A) -> (B -> (A and B)))))), M:tm-350, m:tm-753, u:((A (-> (-> Am (-> C (and Am C))) (not (-> (or (and Am Cm) Am) (-> C (and Am C)))))) (B Am) (Bm (-> C (and Am C))))
================================================================
tm-name          tm-62881
in-theory        62881
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-341 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62881.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62882
in-theory        62882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D))))
theorem-size     27
proof            (modus-ponens tm-338 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62882.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D)))), M:tm-338, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62883
in-theory        62883
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (((A -> B) -> (not (((A and C) or A) -> B))) and (not (A -> B)))))
theorem-size     48
proof            (modus-ponens tm-328 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       176
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62883.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (((A -> B) -> (not (((A and C) or A) -> B))) and (not (A -> B))))), M:tm-328, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62884
in-theory        62884
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((D -> (E -> (D and E))) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62884.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((D -> (E -> (D and E))) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))))), M:tm-327, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62885
in-theory        62885
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((D and E) -> E) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-9 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62885.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((D and E) -> E) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))))), M:tm-326, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62886
in-theory        62886
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((D and E) -> D) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-9 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62886.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((D and E) -> D) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))))), M:tm-325, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62887
in-theory        62887
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62887.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))))), M:tm-324, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62888
in-theory        62888
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((D -> (E -> D)) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62888.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((D -> (E -> D)) and (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))))), M:tm-323, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62889
in-theory        62889
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-322 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-9 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62889.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((D and E) -> E)), M:tm-322, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62890
in-theory        62890
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-320 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-9 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62890.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((D and E) -> D)), M:tm-320, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62891
in-theory        62891
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-318 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62891.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62892
in-theory        62892
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((A -> B) -> (not (((A and C) or A) -> B))) -> ((A -> B) -> (not (((A and C) or A) -> B)))))
theorem-size     43
proof            (modus-ponens tm-316 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62892.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((A -> B) -> (not (((A and C) or A) -> B))) -> ((A -> B) -> (not (((A and C) or A) -> B))))), M:tm-316, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62893
in-theory        62893
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-315 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62893.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (D -> (E -> D))), M:tm-315, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62894
in-theory        62894
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (((A and C) or A) -> B))))))
theorem-size     50
proof            (modus-ponens tm-313 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       162
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62894.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (((A and C) or A) -> B)))))), M:tm-313, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62895
in-theory        62895
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((not (A -> B)) -> D) -> ((((A -> B) -> (not (((A and C) or A) -> B))) or (not (A -> B))) -> D)))
theorem-size     44
proof            (modus-ponens tm-312 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-9 tm-3)
proof-size       160
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62895.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (((not (A -> B)) -> D) -> ((((A -> B) -> (not (((A and C) or A) -> B))) or (not (A -> B))) -> D))), M:tm-312, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62896
in-theory        62896
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (D or (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-9 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62896.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (D or (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))))), M:tm-311, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62897
in-theory        62897
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) or D))
theorem-size     37
proof            (modus-ponens tm-310 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-9 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62897.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) or D)), M:tm-310, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62898
in-theory        62898
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (D -> ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and D)))
theorem-size     39
proof            (modus-ponens tm-309 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62898.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (D -> ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and D))), M:tm-309, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62899
in-theory        62899
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (D -> (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-9 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62899.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) and (D -> (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))))), M:tm-305, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62900
in-theory        62900
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-303 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62900.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-303, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62901
in-theory        62901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-270 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62901.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-270, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62902
in-theory        62902
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-239 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62902.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-239, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62903
in-theory        62903
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F))))
theorem-size     35
proof            (modus-ponens tm-210 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 tm-3)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62903.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F)))), M:tm-210, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62904
in-theory        62904
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-183 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62904.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-183, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62905
in-theory        62905
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-157 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-9 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62905.        ((A -> ((B and C) -> C)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-157, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62906
in-theory        62906
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> B) -> (not ((((A and B) and C) or (A and B)) -> B))))
theorem-size     19
proof            (modus-ponens tm-153 tm-753 ((A (-> (-> (and B Bm) Bm) (not (-> (or (and (and B Bm) Cm) (and B Bm)) Bm)))) (Am (and B Bm)) (C Bm)))
axioms-used      (tm-9 tm-1 tm-4 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62906.        (not (((A and B) -> B) -> (not ((((A and B) and C) or (A and B)) -> B)))), M:tm-153, m:tm-753, u:((A (-> (-> (and B Bm) Bm) (not (-> (or (and (and B Bm) Cm) (and B Bm)) Bm)))) (Am (and B Bm)) (C Bm))
================================================================
tm-name          tm-62907
in-theory        62907
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     33
proof            (modus-ponens tm-147 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-9 tm-8 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62907.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-147, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62908
in-theory        62908
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-134 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-9 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62908.        ((A -> ((B and C) -> B)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-134, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62909
in-theory        62909
times-derived    1
----------------------------------------------------------------
theorem          (not (((A and B) -> A) -> (not ((((A and B) and C) or (A and B)) -> A))))
theorem-size     19
proof            (modus-ponens tm-130 tm-753 ((A (-> (-> (and Bm C) Bm) (not (-> (or (and (and Bm C) Cm) (and Bm C)) Bm)))) (Am (and Bm C)) (B Bm)))
axioms-used      (tm-9 tm-1 tm-3 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62909.        (not (((A and B) -> A) -> (not ((((A and B) and C) or (A and B)) -> A)))), M:tm-130, m:tm-753, u:((A (-> (-> (and Bm C) Bm) (not (-> (or (and (and Bm C) Cm) (and Bm C)) Bm)))) (Am (and Bm C)) (B Bm))
================================================================
tm-name          tm-62910
in-theory        62910
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     33
proof            (modus-ponens tm-125 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-9 tm-8)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62910.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-125, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62911
in-theory        62911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F))))
theorem-size     33
proof            (modus-ponens tm-113 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-9 tm-8 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62911.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (not (((E and G) or E) -> F))) -> (not (E -> F)))), M:tm-113, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62912
in-theory        62912
times-derived    1
----------------------------------------------------------------
theorem          (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))))))
theorem-size     37
proof            (modus-ponens tm-109 tm-753 ((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (or (and (-> B (-> C D)) Cm) (-> B (-> C D))) (-> (-> B C) (-> B D)))))) (Am (-> B (-> C D))) (Bm (-> (-> B C) (-> B D)))))
axioms-used      (tm-9 tm-1 tm-2 tm-8 tm-3)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62912.        (not (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> (not ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C)))))), M:tm-109, m:tm-753, u:((A (-> (-> (-> B (-> C D)) (-> (-> B C) (-> B D))) (not (-> (or (and (-> B (-> C D)) Cm) (-> B (-> C D))) (-> (-> B C) (-> B D)))))) (Am (-> B (-> C D))) (Bm (-> (-> B C) (-> B D))))
================================================================
tm-name          tm-62913
in-theory        62913
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     37
proof            (modus-ponens tm-105 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62913.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-105, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62914
in-theory        62914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D))))
theorem-size     25
proof            (modus-ponens tm-95 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-9 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62914.        (((A -> B) -> (A -> A)) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D)))), M:tm-95, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62915
in-theory        62915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((A and C) or A) -> B))) -> (D -> (not (A -> B))))
theorem-size     19
proof            (modus-ponens tm-84 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62915.        (((A -> B) -> (not (((A and C) or A) -> B))) -> (D -> (not (A -> B)))), M:tm-84, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62916
in-theory        62916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-83 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62916.        ((A -> (B -> (C -> B))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-83, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62917
in-theory        62917
times-derived    1
----------------------------------------------------------------
theorem          (not ((A -> (B -> A)) -> (not (((A and C) or A) -> (B -> A)))))
theorem-size     17
proof            (modus-ponens tm-79 tm-753 ((A (-> (-> Am (-> C Am)) (not (-> (or (and Am Cm) Am) (-> C Am))))) (B Am) (Bm (-> C Am))))
axioms-used      (tm-9 tm-1 tm-8 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62917.        (not ((A -> (B -> A)) -> (not (((A and C) or A) -> (B -> A))))), M:tm-79, m:tm-753, u:((A (-> (-> Am (-> C Am)) (not (-> (or (and Am Cm) Am) (-> C Am))))) (B Am) (Bm (-> C Am)))
================================================================
tm-name          tm-62918
in-theory        62918
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> (not (((B and D) or B) -> C))) -> (not (B -> C))))
theorem-size     23
proof            (modus-ponens tm-76 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-10 tm-9 tm-8 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62918.        (((not (not A)) -> A) and (((B -> C) -> (not (((B and D) or B) -> C))) -> (not (B -> C)))), M:tm-76, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62919
in-theory        62919
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> (not (((A and C) or A) -> B))))) or ((A -> B) -> (not (((A and C) or A) -> B)))) -> (not (A -> B)))
theorem-size     32
proof            (modus-ponens tm-73 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-10 tm-9 tm-3)
proof-size       118
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62919.        (((not (not ((A -> B) -> (not (((A and C) or A) -> B))))) or ((A -> B) -> (not (((A and C) or A) -> B)))) -> (not (A -> B))), M:tm-73, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62920
in-theory        62920
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D))))
theorem-size     29
proof            (modus-ponens tm-69 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62920.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D)))), M:tm-69, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62921
in-theory        62921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-54 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-9 tm-3)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62921.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-54, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62922
in-theory        62922
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> (not (((B and D) or B) -> C)))) or ((B -> C) -> (not (((B and D) or B) -> C)))) -> (not (B -> C)))
theorem-size     32
proof            (modus-ponens tm-47 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-4 tm-9 tm-3)
proof-size       118
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62922.        (((A and ((B -> C) -> (not (((B and D) or B) -> C)))) or ((B -> C) -> (not (((B and D) or B) -> C)))) -> (not (B -> C))), M:tm-47, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62923
in-theory        62923
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (not (((A and C) or A) -> B))) and D) or ((A -> B) -> (not (((A and C) or A) -> B)))) -> (not (A -> B)))
theorem-size     32
proof            (modus-ponens tm-46 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-3 tm-9)
proof-size       118
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62923.        (((((A -> B) -> (not (((A and C) or A) -> B))) and D) or ((A -> B) -> (not (((A and C) or A) -> B)))) -> (not (A -> B))), M:tm-46, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62924
in-theory        62924
times-derived    1
----------------------------------------------------------------
theorem          (((not (((A and B) or A) -> C)) or ((A -> C) -> (not (((A and B) or A) -> C)))) -> (not (A -> C)))
theorem-size     26
proof            (modus-ponens tm-44 tm-753 ((A (-> Am Bm)) (B (not (-> (or (and Am Cm) Am) Bm))) (C (not (-> Am Bm)))))
axioms-used      (tm-8 tm-1 tm-9 tm-3)
proof-size       114
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62924.        (((not (((A and B) or A) -> C)) or ((A -> C) -> (not (((A and B) or A) -> C)))) -> (not (A -> C))), M:tm-44, m:tm-753, u:((A (-> Am Bm)) (B (not (-> (or (and Am Cm) Am) Bm))) (C (not (-> Am Bm))))
================================================================
tm-name          tm-62925
in-theory        62925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-42 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-7 tm-9 tm-8 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62925.        ((A -> (B or A)) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D)))), M:tm-42, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62926
in-theory        62926
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-32 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-6 tm-9 tm-8 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62926.        ((A -> (A or B)) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D)))), M:tm-32, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62927
in-theory        62927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((A and C) or A) -> B))) -> (((A -> B) -> (not (((A and C) or A) -> B))) and (not (A -> B))))
theorem-size     30
proof            (modus-ponens tm-24 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       116
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62927.        (((A -> B) -> (not (((A and C) or A) -> B))) -> (((A -> B) -> (not (((A and C) or A) -> B))) and (not (A -> B)))), M:tm-24, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62928
in-theory        62928
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D))))
theorem-size     25
proof            (modus-ponens tm-23 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62928.        ((A -> (B -> (A and B))) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D)))), M:tm-23, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62929
in-theory        62929
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-22 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-4 tm-9 tm-8 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62929.        (((A and B) -> B) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D)))), M:tm-22, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62930
in-theory        62930
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-21 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-3 tm-9 tm-8)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62930.        (((A and B) -> A) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D)))), M:tm-21, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62931
in-theory        62931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-20 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-2 tm-9 tm-8 tm-3)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62931.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-20, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62932
in-theory        62932
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D))))
theorem-size     23
proof            (modus-ponens tm-19 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-1 tm-9 tm-8 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62932.        ((A -> (B -> A)) and (((C -> D) -> (not (((C and E) or C) -> D))) -> (not (C -> D)))), M:tm-19, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62933
in-theory        62933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (not (((A and C) or A) -> B))) -> ((A -> B) -> (not (((A and C) or A) -> B))))
theorem-size     25
proof            (modus-ponens tm-12 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-2 tm-1 tm-9 tm-8 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62933.        (((A -> B) -> (not (((A and C) or A) -> B))) -> ((A -> B) -> (not (((A and C) or A) -> B)))), M:tm-12, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62934
in-theory        62934
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (((A and C) or A) -> B)))))
theorem-size     32
proof            (modus-ponens tm-9 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-9 tm-8 tm-3)
proof-size       100
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62934.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (not (A -> B)))) -> (not ((A -> B) -> (not (((A and C) or A) -> B))))), M:tm-9, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62935
in-theory        62935
times-derived    1
----------------------------------------------------------------
theorem          (((not (A -> B)) -> C) -> ((((A -> B) -> (not (((A and D) or A) -> B))) or (not (A -> B))) -> C))
theorem-size     26
proof            (modus-ponens tm-8 tm-753 ((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm)))))
axioms-used      (tm-8 tm-9 tm-3)
proof-size       96
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62935.        (((not (A -> B)) -> C) -> ((((A -> B) -> (not (((A and D) or A) -> B))) or (not (A -> B))) -> C)), M:tm-8, m:tm-753, u:((A (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm)))) (B (not (-> Am Bm))))
================================================================
tm-name          tm-62936
in-theory        62936
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B -> C) -> (not (((B and D) or B) -> C))) -> (not (B -> C))))
theorem-size     19
proof            (modus-ponens tm-7 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-7 tm-9 tm-8 tm-3)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62936.        (A or (((B -> C) -> (not (((B and D) or B) -> C))) -> (not (B -> C)))), M:tm-7, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62937
in-theory        62937
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) or D)
theorem-size     19
proof            (modus-ponens tm-6 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-6 tm-9 tm-8 tm-3)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62937.        ((((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))) or D), M:tm-6, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62938
in-theory        62938
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (not (((B and D) or B) -> C))) -> (not (B -> C))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62938.        (A -> ((((B -> C) -> (not (((B and D) or B) -> C))) -> (not (B -> C))) and A)), M:tm-5, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62939
in-theory        62939
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (not (((B and D) or B) -> C))) -> (not (B -> C))))
theorem-size     19
proof            (modus-ponens tm-1 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-1 tm-9 tm-8 tm-3)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62939.        (A -> (((B -> C) -> (not (((B and D) or B) -> C))) -> (not (B -> C)))), M:tm-1, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-62940
in-theory        62940
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> (((A and C) or A) -> B)))
theorem-size     21
proof            (modus-ponens tm-754 tm-1 ((Am (-> (or (and A B) A) C)) (D (-> Bm (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-62940.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> (((A and C) or A) -> B))), M:tm-754, m:tm-1, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62941
in-theory        62941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((A and D) or A) -> (B -> C))) -> ((((A and D) or A) -> B) -> (((A and D) or A) -> C)))
theorem-size     31
proof            (modus-ponens tm-754 tm-2 ((Am (or (and A B) A)) (C (-> Bm Cm)) (D (-> (-> (or (and A B) A) Bm) (-> (or (and A B) A) Cm)))))
axioms-used      (tm-8 tm-3 tm-2)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-62941.        (((A -> (B -> C)) or (((A and D) or A) -> (B -> C))) -> ((((A and D) or A) -> B) -> (((A and D) or A) -> C))), M:tm-754, m:tm-2, u:((Am (or (and A B) A)) (C (-> Bm Cm)) (D (-> (-> (or (and A B) A) Bm) (-> (or (and A B) A) Cm))))
================================================================
tm-name          tm-62942
in-theory        62942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((((A and C) or A) -> B) and D)))
theorem-size     23
proof            (modus-ponens tm-754 tm-5 ((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> (or (and A B) A) C) Bm)))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-62942.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((((A and C) or A) -> B) and D))), M:tm-754, m:tm-5, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> (or (and A B) A) C) Bm))))
================================================================
tm-name          tm-62943
in-theory        62943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) or D))
theorem-size     21
proof            (modus-ponens tm-754 tm-6 ((Am (-> (or (and A B) A) C)) (D (or (-> (or (and A B) A) C) Bm))))
axioms-used      (tm-8 tm-3 tm-6)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-62943.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) or D)), M:tm-754, m:tm-6, u:((Am (-> (or (and A B) A) C)) (D (or (-> (or (and A B) A) C) Bm)))
================================================================
tm-name          tm-62944
in-theory        62944
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D or (((A and C) or A) -> B)))
theorem-size     21
proof            (modus-ponens tm-754 tm-7 ((Am (-> (or (and A B) A) C)) (D (or Bm (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-7)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-62944.        (((A -> B) or (((A and C) or A) -> B)) -> (D or (((A and C) or A) -> B))), M:tm-754, m:tm-7, u:((Am (-> (or (and A B) A) C)) (D (or Bm (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62945
in-theory        62945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((B -> D) -> ((((A and C) or A) or B) -> D)))
theorem-size     25
proof            (modus-ponens tm-754 tm-8 ((Am (or (and A B) A)) (C Bm) (D (-> (-> Bm Cm) (-> (or (or (and A B) A) Bm) Cm)))))
axioms-used      (tm-8 tm-3)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62945.        (((A -> B) or (((A and C) or A) -> B)) -> ((B -> D) -> ((((A and C) or A) or B) -> D))), M:tm-754, m:tm-8, u:((Am (or (and A B) A)) (C Bm) (D (-> (-> Bm Cm) (-> (or (or (and A B) A) Bm) Cm))))
================================================================
tm-name          tm-62946
in-theory        62946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> (not B)) -> (not ((A and C) or A))))
theorem-size     27
proof            (modus-ponens tm-754 tm-9 ((Am (or (and A B) A)) (C Bm) (D (-> (-> (or (and A B) A) (not Bm)) (not (or (and A B) A))))))
axioms-used      (tm-8 tm-3 tm-9)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-62946.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> (not B)) -> (not ((A and C) or A)))), M:tm-754, m:tm-9, u:((Am (or (and A B) A)) (C Bm) (D (-> (-> (or (and A B) A) (not Bm)) (not (or (and A B) A)))))
================================================================
tm-name          tm-62947
in-theory        62947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-754 tm-11 ((Am (-> (or (and A B) A) C)) (D (-> Bm (-> Cm Bm)))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-62947.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> (E -> D))), M:tm-754, m:tm-11, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (-> Cm Bm))))
================================================================
tm-name          tm-62948
in-theory        62948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or A) -> ((A and C) or A)))
theorem-size     23
proof            (modus-ponens tm-754 tm-12 ((Am (or (and A B) A)) (C Bm) (D (-> (or (and A B) A) (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-62948.        (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or A) -> ((A and C) or A))), M:tm-754, m:tm-12, u:((Am (or (and A B) A)) (C Bm) (D (-> (or (and A B) A) (or (and A B) A))))
================================================================
tm-name          tm-62949
in-theory        62949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-754 tm-14 ((Am (-> (or (and A B) A) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-62949.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-754, m:tm-14, u:((Am (-> (or (and A B) A) C)) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-62950
in-theory        62950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-754 tm-16 ((Am (-> (or (and A B) A) C)) (D (-> (and Bm Cm) Bm))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-62950.        (((A -> B) or (((A and C) or A) -> B)) -> ((D and E) -> D)), M:tm-754, m:tm-16, u:((Am (-> (or (and A B) A) C)) (D (-> (and Bm Cm) Bm)))
================================================================
tm-name          tm-62951
in-theory        62951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-754 tm-18 ((Am (-> (or (and A B) A) C)) (D (-> (and Bm Cm) Cm))))
axioms-used      (tm-8 tm-3 tm-1 tm-4)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-62951.        (((A -> B) or (((A and C) or A) -> B)) -> ((D and E) -> E)), M:tm-754, m:tm-18, u:((Am (-> (or (and A B) A) C)) (D (-> (and Bm Cm) Cm)))
================================================================
tm-name          tm-62952
in-theory        62952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> D)) and (((A and C) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-754 tm-19 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> Cm Bm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-62952.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> D)) and (((A and C) or A) -> B))), M:tm-754, m:tm-19, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> Cm Bm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62953
in-theory        62953
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and C) or A) -> B)))
theorem-size     33
proof            (modus-ponens tm-754 tm-20 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-62953.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and C) or A) -> B))), M:tm-754, m:tm-20, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62954
in-theory        62954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D and E) -> D) and (((A and C) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-754 tm-21 ((Am (-> (or (and A B) A) C)) (D (and (-> (and Bm Cm) Bm) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-62954.        (((A -> B) or (((A and C) or A) -> B)) -> (((D and E) -> D) and (((A and C) or A) -> B))), M:tm-754, m:tm-21, u:((Am (-> (or (and A B) A) C)) (D (and (-> (and Bm Cm) Bm) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62955
in-theory        62955
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D and E) -> E) and (((A and C) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-754 tm-22 ((Am (-> (or (and A B) A) C)) (D (and (-> (and Bm Cm) Cm) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-62955.        (((A -> B) or (((A and C) or A) -> B)) -> (((D and E) -> E) and (((A and C) or A) -> B))), M:tm-754, m:tm-22, u:((Am (-> (or (and A B) A) C)) (D (and (-> (and Bm Cm) Cm) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62956
in-theory        62956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> (D and E))) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-23 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-62956.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> (D and E))) and (((A and C) or A) -> B))), M:tm-754, m:tm-23, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62957
in-theory        62957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or A) -> (((A and C) or A) and B)))
theorem-size     25
proof            (modus-ponens tm-754 tm-24 ((Am (or (and A B) A)) (C Bm) (D (-> (or (and A B) A) (and (or (and A B) A) Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-62957.        (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or A) -> (((A and C) or A) and B))), M:tm-754, m:tm-24, u:((Am (or (and A B) A)) (C Bm) (D (-> (or (and A B) A) (and (or (and A B) A) Bm))))
================================================================
tm-name          tm-62958
in-theory        62958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-754 tm-25 ((Am (-> (or (and A B) A) C)) (D (-> Bm (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-62958.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> (E -> (D and E)))), M:tm-754, m:tm-25, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-62959
in-theory        62959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (D or E)) and (((A and C) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-754 tm-32 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (or Bm Cm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-62959.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (D or E)) and (((A and C) or A) -> B))), M:tm-754, m:tm-32, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (or Bm Cm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62960
in-theory        62960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-754 tm-33 ((Am (-> (or (and A B) A) C)) (D (-> Bm (or Bm Cm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-62960.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> (D or E))), M:tm-754, m:tm-33, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (or Bm Cm))))
================================================================
tm-name          tm-62961
in-theory        62961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E or D)) and (((A and C) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-754 tm-42 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (or Cm Bm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-62961.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E or D)) and (((A and C) or A) -> B))), M:tm-754, m:tm-42, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (or Cm Bm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62962
in-theory        62962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-754 tm-43 ((Am (-> (or (and A B) A) C)) (D (-> Bm (or Cm Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-62962.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> (E or D))), M:tm-754, m:tm-43, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (or Cm Bm))))
================================================================
tm-name          tm-62963
in-theory        62963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((((A and C) or A) and D) or ((A and C) or A)) -> B))
theorem-size     27
proof            (modus-ponens tm-754 tm-46 ((Am (or (and A B) A)) (C Bm) (D (-> (or (and (or (and A B) A) Cm) (or (and A B) A)) Bm))))
axioms-used      (tm-8 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-62963.        (((A -> B) or (((A and C) or A) -> B)) -> (((((A and C) or A) and D) or ((A and C) or A)) -> B)), M:tm-754, m:tm-46, u:((Am (or (and A B) A)) (C Bm) (D (-> (or (and (or (and A B) A) Cm) (or (and A B) A)) Bm)))
================================================================
tm-name          tm-62964
in-theory        62964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D and ((A and C) or A)) or ((A and C) or A)) -> B))
theorem-size     27
proof            (modus-ponens tm-754 tm-47 ((Am (or (and A B) A)) (C Bm) (D (-> (or (and Cm (or (and A B) A)) (or (and A B) A)) Bm))))
axioms-used      (tm-8 tm-3 tm-4)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-62964.        (((A -> B) or (((A and C) or A) -> B)) -> (((D and ((A and C) or A)) or ((A and C) or A)) -> B)), M:tm-754, m:tm-47, u:((Am (or (and A B) A)) (C Bm) (D (-> (or (and Cm (or (and A B) A)) (or (and A B) A)) Bm)))
================================================================
tm-name          tm-62965
in-theory        62965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or ((A and C) or A)) -> B))
theorem-size     23
proof            (modus-ponens tm-754 tm-49 ((Am (and Bm B)) (A Bm) (C Cm) (D (-> (or (and Bm B) (or (and Bm B) Bm)) Cm))))
axioms-used      (tm-8 tm-3 tm-6)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-62965.        (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or ((A and C) or A)) -> B)), M:tm-754, m:tm-49, u:((Am (and Bm B)) (A Bm) (C Cm) (D (-> (or (and Bm B) (or (and Bm B) Bm)) Cm)))
================================================================
tm-name          tm-62966
in-theory        62966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((A or ((A and C) or A)) -> B))
theorem-size     21
proof            (modus-ponens tm-754 tm-50 ((Am (and Bm B)) (A Bm) (C Cm) (D (-> (or Bm (or (and Bm B) Bm)) Cm))))
axioms-used      (tm-8 tm-3 tm-7)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-62966.        (((A -> B) or (((A and C) or A) -> B)) -> ((A or ((A and C) or A)) -> B)), M:tm-754, m:tm-50, u:((Am (and Bm B)) (A Bm) (C Cm) (D (-> (or Bm (or (and Bm B) Bm)) Cm)))
================================================================
tm-name          tm-62967
in-theory        62967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((A and C) or A) -> B)))
theorem-size     33
proof            (modus-ponens tm-754 tm-54 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-62967.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> ((E -> F) -> ((D or E) -> F))) and (((A and C) or A) -> B))), M:tm-754, m:tm-54, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62968
in-theory        62968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-754 tm-56 ((Am (-> (or (and A B) A) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-62968.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-754, m:tm-56, u:((Am (-> (or (and A B) A) C)) (D (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-62969
in-theory        62969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> ((A and C) or A)))) or (((A and C) or A) -> (not (B -> ((A and C) or A))))) -> (not ((A and C) or A)))
theorem-size     32
proof            (modus-ponens tm-754 tm-57 ((Am (or (and A B) A)) (C (not (-> Bm (or (and A B) A)))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-1)
proof-size       122
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-62969.        (((A -> (not (B -> ((A and C) or A)))) or (((A and C) or A) -> (not (B -> ((A and C) or A))))) -> (not ((A and C) or A))), M:tm-754, m:tm-57, u:((Am (or (and A B) A)) (C (not (-> Bm (or (and A B) A)))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-62970
in-theory        62970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (((A and C) or A) and B)))) or (((A and C) or A) -> (not (B -> (((A and C) or A) and B))))) -> (not ((A and C) or A)))
theorem-size     36
proof            (modus-ponens tm-754 tm-61 ((Am (or (and A B) A)) (C (not (-> Bm (and (or (and A B) A) Bm)))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-5)
proof-size       130
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-62970.        (((A -> (not (B -> (((A and C) or A) and B)))) or (((A and C) or A) -> (not (B -> (((A and C) or A) and B))))) -> (not ((A and C) or A))), M:tm-754, m:tm-61, u:((Am (or (and A B) A)) (C (not (-> Bm (and (or (and A B) A) Bm)))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-62971
in-theory        62971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((A and B) or A) or C))) or (((A and B) or A) -> (not (((A and B) or A) or C)))) -> (not ((A and B) or A)))
theorem-size     32
proof            (modus-ponens tm-754 tm-62 ((Am (or (and A B) A)) (C (not (or (or (and A B) A) Bm))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-6)
proof-size       122
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-62971.        (((A -> (not (((A and B) or A) or C))) or (((A and B) or A) -> (not (((A and B) or A) or C)))) -> (not ((A and B) or A))), M:tm-754, m:tm-62, u:((Am (or (and A B) A)) (C (not (or (or (and A B) A) Bm))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-62972
in-theory        62972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B or ((A and C) or A)))) or (((A and C) or A) -> (not (B or ((A and C) or A))))) -> (not ((A and C) or A)))
theorem-size     32
proof            (modus-ponens tm-754 tm-63 ((Am (or (and A B) A)) (C (not (or Bm (or (and A B) A)))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-7)
proof-size       122
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-62972.        (((A -> (not (B or ((A and C) or A)))) or (((A and C) or A) -> (not (B or ((A and C) or A))))) -> (not ((A and C) or A))), M:tm-754, m:tm-63, u:((Am (or (and A B) A)) (C (not (or Bm (or (and A B) A)))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-62973
in-theory        62973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (((A and C) or A) -> B)))
theorem-size     31
proof            (modus-ponens tm-754 tm-69 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-9)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-62973.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> ((D -> (not E)) -> (not D))) and (((A and C) or A) -> B))), M:tm-754, m:tm-69, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62974
in-theory        62974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-754 tm-71 ((Am (-> (or (and A B) A) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-62974.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-754, m:tm-71, u:((Am (-> (or (and A B) A) C)) (D (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-62975
in-theory        62975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((not (not ((A and C) or A))) or ((A and C) or A)) -> B))
theorem-size     27
proof            (modus-ponens tm-754 tm-73 ((Am (or (and A B) A)) (C Bm) (D (-> (or (not (not (or (and A B) A))) (or (and A B) A)) Bm))))
axioms-used      (tm-8 tm-3 tm-10)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-62975.        (((A -> B) or (((A and C) or A) -> B)) -> (((not (not ((A and C) or A))) or ((A and C) or A)) -> B)), M:tm-754, m:tm-73, u:((Am (or (and A B) A)) (C Bm) (D (-> (or (not (not (or (and A B) A))) (or (and A B) A)) Bm)))
================================================================
tm-name          tm-62976
in-theory        62976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((not (not D)) -> D) and (((A and C) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-754 tm-76 ((Am (-> (or (and A B) A) C)) (D (and (-> (not (not Bm)) Bm) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-10)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-62976.        (((A -> B) or (((A and C) or A) -> B)) -> (((not (not D)) -> D) and (((A and C) or A) -> B))), M:tm-754, m:tm-76, u:((Am (-> (or (and A B) A) C)) (D (and (-> (not (not Bm)) Bm) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62977
in-theory        62977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((not (not D)) -> D))
theorem-size     17
proof            (modus-ponens tm-754 tm-78 ((Am (-> (or (and A B) A) C)) (D (-> (not (not Bm)) Bm))))
axioms-used      (tm-8 tm-3 tm-1 tm-10)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-62977.        (((A -> B) or (((A and C) or A) -> B)) -> ((not (not D)) -> D)), M:tm-754, m:tm-78, u:((Am (-> (or (and A B) A) C)) (D (-> (not (not Bm)) Bm)))
================================================================
tm-name          tm-62978
in-theory        62978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> B)))) or (((A and D) or A) -> (not (B -> (C -> B))))) -> (not ((A and D) or A)))
theorem-size     28
proof            (modus-ponens tm-754 tm-79 ((Am (or (and A B) A)) (C (not (-> Bm (-> Cm Bm)))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-1)
proof-size       132
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-62978.        (((A -> (not (B -> (C -> B)))) or (((A and D) or A) -> (not (B -> (C -> B))))) -> (not ((A and D) or A))), M:tm-754, m:tm-79, u:((Am (or (and A B) A)) (C (not (-> Bm (-> Cm Bm)))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-62979
in-theory        62979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> (F -> E))) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-83 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-62979.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> (F -> E))) and (((A and C) or A) -> B))), M:tm-754, m:tm-83, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> Cm (-> Dm Cm))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62980
in-theory        62980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or A) -> (D -> B)))
theorem-size     21
proof            (modus-ponens tm-754 tm-84 ((Am (or (and A B) A)) (C Bm) (D (-> (or (and A B) A) (-> Cm Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-62980.        (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or A) -> (D -> B))), M:tm-754, m:tm-84, u:((Am (or (and A B) A)) (C Bm) (D (-> (or (and A B) A) (-> Cm Bm))))
================================================================
tm-name          tm-62981
in-theory        62981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-754 tm-85 ((Am (-> (or (and A B) A) C)) (D (-> Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-62981.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> (E -> (F -> E)))), M:tm-754, m:tm-85, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-62982
in-theory        62982
times-derived    3
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or A) -> B))
theorem-size     19
proof            (modus-ponens tm-754 tm-86 ((Am (-> (or (and A B) A) C)) (D (-> (or (and A B) A) C))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-62982.        (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or A) -> B)), M:tm-754, m:tm-86, u:((Am (-> (or (and A B) A) C)) (D (-> (or (and A B) A) C)))
================================================================
tm-name          tm-62983
in-theory        62983
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((A and D) or A) -> (B -> C))) -> (((A and D) or A) -> (B -> C)))
theorem-size     25
proof            (modus-ponens tm-754 tm-87 ((Am (or (and A B) A)) (C (-> Bm Cm)) (D (-> (or (and A B) A) (-> Bm Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-62983.        (((A -> (B -> C)) or (((A and D) or A) -> (B -> C))) -> (((A and D) or A) -> (B -> C))), M:tm-754, m:tm-87, u:((Am (or (and A B) A)) (C (-> Bm Cm)) (D (-> (or (and A B) A) (-> Bm Cm))))
================================================================
tm-name          tm-62984
in-theory        62984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> (D -> D)) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-95 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-2 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-62984.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> (D -> D)) and (((A and C) or A) -> B))), M:tm-754, m:tm-95, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> Bm Bm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62985
in-theory        62985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> E) -> (D -> D)))
theorem-size     19
proof            (modus-ponens tm-754 tm-97 ((Am (-> (or (and A B) A) C)) (D (-> (-> Bm Cm) (-> Bm Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-62985.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> E) -> (D -> D))), M:tm-754, m:tm-97, u:((Am (-> (or (and A B) A) C)) (D (-> (-> Bm Cm) (-> Bm Bm))))
================================================================
tm-name          tm-62986
in-theory        62986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> ((A and C) or A)) -> D)) or (((A and C) or A) -> ((B -> ((A and C) or A)) -> D))) -> (((A and C) or A) -> D))
theorem-size     35
proof            (modus-ponens tm-754 tm-98 ((Am (or (and A B) A)) (C (-> (-> Bm (or (and A B) A)) Cm)) (D (-> (or (and A B) A) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-62986.        (((A -> ((B -> ((A and C) or A)) -> D)) or (((A and C) or A) -> ((B -> ((A and C) or A)) -> D))) -> (((A and C) or A) -> D)), M:tm-754, m:tm-98, u:((Am (or (and A B) A)) (C (-> (-> Bm (or (and A B) A)) Cm)) (D (-> (or (and A B) A) Cm)))
================================================================
tm-name          tm-62987
in-theory        62987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (((A and B) or A) -> C)) or (((A and B) or A) -> (((A and B) or A) -> C))) -> (((A and B) or A) -> C))
theorem-size     31
proof            (modus-ponens tm-754 tm-99 ((Am (or (and A B) A)) (C (-> (or (and A B) A) Bm)) (D (-> (or (and A B) A) Bm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-62987.        (((A -> (((A and B) or A) -> C)) or (((A and B) or A) -> (((A and B) or A) -> C))) -> (((A and B) or A) -> C)), M:tm-754, m:tm-99, u:((Am (or (and A B) A)) (C (-> (or (and A B) A) Bm)) (D (-> (or (and A B) A) Bm)))
================================================================
tm-name          tm-62988
in-theory        62988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (((A and C) or A) -> B)))
theorem-size     39
proof            (modus-ponens tm-754 tm-105 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-62988.        (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) and (((A and C) or A) -> B))), M:tm-754, m:tm-105, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62989
in-theory        62989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-754 tm-107 ((Am (-> (or (and A B) A) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-62989.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-754, m:tm-107, u:((Am (-> (or (and A B) A) C)) (D (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-62990
in-theory        62990
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) or (((A and E) or A) -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not ((A and E) or A)))
theorem-size     44
proof            (modus-ponens tm-754 tm-109 ((Am (or (and A B) A)) (C (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-1 tm-2)
proof-size       172
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-62990.        (((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) or (((A and E) or A) -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))) -> (not ((A and E) or A))), M:tm-754, m:tm-109, u:((Am (or (and A B) A)) (C (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-62991
in-theory        62991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((A and C) or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-754 tm-113 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-1 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-62991.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((A and C) or A) -> B))), M:tm-754, m:tm-113, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62992
in-theory        62992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (C -> D))) or (((A and E) or A) -> (B -> (C -> D)))) -> (((A and E) or A) -> ((B -> C) -> (B -> D))))
theorem-size     33
proof            (modus-ponens tm-754 tm-114 ((Am (or (and A B) A)) (C (-> Bm (-> Cm Dm))) (D (-> (or (and A B) A) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-62992.        (((A -> (B -> (C -> D))) or (((A and E) or A) -> (B -> (C -> D)))) -> (((A and E) or A) -> ((B -> C) -> (B -> D)))), M:tm-754, m:tm-114, u:((Am (or (and A B) A)) (C (-> Bm (-> Cm Dm))) (D (-> (or (and A B) A) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-62993
in-theory        62993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-754 tm-115 ((Am (-> (or (and A B) A) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-62993.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-754, m:tm-115, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-62994
in-theory        62994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (((A and C) or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-754 tm-125 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-62994.        (((A -> B) or (((A and C) or A) -> B)) -> (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) and (((A and C) or A) -> B))), M:tm-754, m:tm-125, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62995
in-theory        62995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-754 tm-127 ((Am (-> (or (and A B) A) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-62995.        (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-754, m:tm-127, u:((Am (-> (or (and A B) A) C)) (D (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-62996
in-theory        62996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> B))) or (((A and D) or A) -> (not ((B and C) -> B)))) -> (not ((A and D) or A)))
theorem-size     28
proof            (modus-ponens tm-754 tm-130 ((Am (or (and A B) A)) (C (not (-> (and Bm Cm) Bm))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-1)
proof-size       132
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-62996.        (((A -> (not ((B and C) -> B))) or (((A and D) or A) -> (not ((B and C) -> B)))) -> (not ((A and D) or A))), M:tm-754, m:tm-130, u:((Am (or (and A B) A)) (C (not (-> (and Bm Cm) Bm))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-62997
in-theory        62997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> ((E and F) -> E)) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-134 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-62997.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> ((E and F) -> E)) and (((A and C) or A) -> B))), M:tm-754, m:tm-134, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> (and Cm Dm) Cm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-62998
in-theory        62998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) or (((A and D) or A) -> (B and C))) -> (((A and D) or A) -> B))
theorem-size     23
proof            (modus-ponens tm-754 tm-135 ((Am (or (and A B) A)) (C (and Bm Cm)) (D (-> (or (and A B) A) Bm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-62998.        (((A -> (B and C)) or (((A and D) or A) -> (B and C))) -> (((A and D) or A) -> B)), M:tm-754, m:tm-135, u:((Am (or (and A B) A)) (C (and Bm Cm)) (D (-> (or (and A B) A) Bm)))
================================================================
tm-name          tm-62999
in-theory        62999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-754 tm-136 ((Am (-> (or (and A B) A) C)) (D (-> Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-62999.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((E and F) -> E))), M:tm-754, m:tm-136, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-63000
in-theory        63000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (((A and C) or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-754 tm-147 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-2 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-63000.        (((A -> B) or (((A and C) or A) -> B)) -> ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) and (((A and C) or A) -> B))), M:tm-754, m:tm-147, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63001
in-theory        63001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-754 tm-149 ((Am (-> (or (and A B) A) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-2 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-63001.        (((A -> B) or (((A and C) or A) -> B)) -> (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-754, m:tm-149, u:((Am (-> (or (and A B) A) C)) (D (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-63002
in-theory        63002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B and C) -> C))) or (((A and D) or A) -> (not ((B and C) -> C)))) -> (not ((A and D) or A)))
theorem-size     28
proof            (modus-ponens tm-754 tm-153 ((Am (or (and A B) A)) (C (not (-> (and Bm Cm) Cm))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-1 tm-4)
proof-size       132
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-63002.        (((A -> (not ((B and C) -> C))) or (((A and D) or A) -> (not ((B and C) -> C)))) -> (not ((A and D) or A))), M:tm-754, m:tm-153, u:((Am (or (and A B) A)) (C (not (-> (and Bm Cm) Cm))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-63003
in-theory        63003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> ((E and F) -> F)) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-157 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-1 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-63003.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> ((E and F) -> F)) and (((A and C) or A) -> B))), M:tm-754, m:tm-157, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> (and Cm Dm) Dm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63004
in-theory        63004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and C)) or (((A and D) or A) -> (B and C))) -> (((A and D) or A) -> C))
theorem-size     23
proof            (modus-ponens tm-754 tm-158 ((Am (or (and A B) A)) (C (and Bm Cm)) (D (-> (or (and A B) A) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-63004.        (((A -> (B and C)) or (((A and D) or A) -> (B and C))) -> (((A and D) or A) -> C)), M:tm-754, m:tm-158, u:((Am (or (and A B) A)) (C (and Bm Cm)) (D (-> (or (and A B) A) Cm)))
================================================================
tm-name          tm-63005
in-theory        63005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-754 tm-159 ((Am (-> (or (and A B) A) C)) (D (-> Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-63005.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((E and F) -> F))), M:tm-754, m:tm-159, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-63006
in-theory        63006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> B)) and ((A and D) or A)))) or (((A and D) or A) -> (not ((B -> (C -> B)) and ((A and D) or A))))) -> (not ((A and D) or A)))
theorem-size     40
proof            (modus-ponens tm-754 tm-179 ((Am (or (and A B) A)) (C (not (and (-> Bm (-> Cm Bm)) (or (and A B) A)))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-5 tm-1)
proof-size       150
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-63006.        (((A -> (not ((B -> (C -> B)) and ((A and D) or A)))) or (((A and D) or A) -> (not ((B -> (C -> B)) and ((A and D) or A))))) -> (not ((A and D) or A))), M:tm-754, m:tm-179, u:((Am (or (and A B) A)) (C (not (and (-> Bm (-> Cm Bm)) (or (and A B) A)))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-63007
in-theory        63007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> ((E -> (F -> E)) and D)) and (((A and C) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-754 tm-183 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-63007.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> ((E -> (F -> E)) and D)) and (((A and C) or A) -> B))), M:tm-754, m:tm-183, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63008
in-theory        63008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((E -> (F -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-754 tm-184 ((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-63008.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((E -> (F -> E)) and D))), M:tm-754, m:tm-184, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-63009
in-theory        63009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((A and E) or A)))) or (((A and E) or A) -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((A and E) or A))))) -> (not ((A and E) or A)))
theorem-size     56
proof            (modus-ponens tm-754 tm-206 ((Am (or (and A B) A)) (C (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or (and A B) A)))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-5 tm-2)
proof-size       190
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-63009.        (((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((A and E) or A)))) or (((A and E) or A) -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and ((A and E) or A))))) -> (not ((A and E) or A))), M:tm-754, m:tm-206, u:((Am (or (and A B) A)) (C (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (or (and A B) A)))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-63010
in-theory        63010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (((A and C) or A) -> B)))
theorem-size     37
proof            (modus-ponens tm-754 tm-210 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-63010.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) and (((A and C) or A) -> B))), M:tm-754, m:tm-210, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63011
in-theory        63011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     29
proof            (modus-ponens tm-754 tm-211 ((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-63011.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-754, m:tm-211, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-63012
in-theory        63012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> B) and ((A and D) or A)))) or (((A and D) or A) -> (not (((B and C) -> B) and ((A and D) or A))))) -> (not ((A and D) or A)))
theorem-size     40
proof            (modus-ponens tm-754 tm-235 ((Am (or (and A B) A)) (C (not (and (-> (and Bm Cm) Bm) (or (and A B) A)))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-5)
proof-size       150
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-63012.        (((A -> (not (((B and C) -> B) and ((A and D) or A)))) or (((A and D) or A) -> (not (((B and C) -> B) and ((A and D) or A))))) -> (not ((A and D) or A))), M:tm-754, m:tm-235, u:((Am (or (and A B) A)) (C (not (and (-> (and Bm Cm) Bm) (or (and A B) A)))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-63013
in-theory        63013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (((E and F) -> E) and D)) and (((A and C) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-754 tm-239 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-63013.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (((E and F) -> E) and D)) and (((A and C) or A) -> B))), M:tm-754, m:tm-239, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63014
in-theory        63014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> (((E and F) -> E) and D)))
theorem-size     21
proof            (modus-ponens tm-754 tm-240 ((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-63014.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> (((E and F) -> E) and D))), M:tm-754, m:tm-240, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-63015
in-theory        63015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (((B and C) -> C) and ((A and D) or A)))) or (((A and D) or A) -> (not (((B and C) -> C) and ((A and D) or A))))) -> (not ((A and D) or A)))
theorem-size     40
proof            (modus-ponens tm-754 tm-266 ((Am (or (and A B) A)) (C (not (and (-> (and Bm Cm) Cm) (or (and A B) A)))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-5 tm-4)
proof-size       150
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-63015.        (((A -> (not (((B and C) -> C) and ((A and D) or A)))) or (((A and D) or A) -> (not (((B and C) -> C) and ((A and D) or A))))) -> (not ((A and D) or A))), M:tm-754, m:tm-266, u:((Am (or (and A B) A)) (C (not (and (-> (and Bm Cm) Cm) (or (and A B) A)))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-63016
in-theory        63016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (((E and F) -> F) and D)) and (((A and C) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-754 tm-270 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-63016.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (((E and F) -> F) and D)) and (((A and C) or A) -> B))), M:tm-754, m:tm-270, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63017
in-theory        63017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> (((E and F) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-754 tm-271 ((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-63017.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> (((E and F) -> F) and D))), M:tm-754, m:tm-271, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-63018
in-theory        63018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C -> (B and C))) and ((A and D) or A)))) or (((A and D) or A) -> (not ((B -> (C -> (B and C))) and ((A and D) or A))))) -> (not ((A and D) or A)))
theorem-size     44
proof            (modus-ponens tm-754 tm-299 ((Am (or (and A B) A)) (C (not (and (-> Bm (-> Cm (and Bm Cm))) (or (and A B) A)))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-5)
proof-size       160
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-63018.        (((A -> (not ((B -> (C -> (B and C))) and ((A and D) or A)))) or (((A and D) or A) -> (not ((B -> (C -> (B and C))) and ((A and D) or A))))) -> (not ((A and D) or A))), M:tm-754, m:tm-299, u:((Am (or (and A B) A)) (C (not (and (-> Bm (-> Cm (and Bm Cm))) (or (and A B) A)))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-63019
in-theory        63019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> ((E -> (F -> (E and F))) and D)) and (((A and C) or A) -> B)))
theorem-size     31
proof            (modus-ponens tm-754 tm-303 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-63019.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> ((E -> (F -> (E and F))) and D)) and (((A and C) or A) -> B))), M:tm-754, m:tm-303, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63020
in-theory        63020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-754 tm-304 ((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-63020.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((E -> (F -> (E and F))) and D))), M:tm-754, m:tm-304, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-63021
in-theory        63021
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (D -> (((A and C) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-754 tm-305 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> Bm (-> (or (and A B) A) C))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-63021.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (D -> (((A and C) or A) -> B)))), M:tm-754, m:tm-305, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> Bm (-> (or (and A B) A) C)))))
================================================================
tm-name          tm-63022
in-theory        63022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or (((A and D) or A) -> (B -> C))) -> ((((A and D) or A) -> (B -> C)) and ((((A and D) or A) -> B) -> (((A and D) or A) -> C))))
theorem-size     41
proof            (modus-ponens tm-754 tm-306 ((Am (or (and A B) A)) (C (-> Bm Cm)) (D (and (-> (or (and A B) A) (-> Bm Cm)) (-> (-> (or (and A B) A) Bm) (-> (or (and A B) A) Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-63022.        (((A -> (B -> C)) or (((A and D) or A) -> (B -> C))) -> ((((A and D) or A) -> (B -> C)) and ((((A and D) or A) -> B) -> (((A and D) or A) -> C)))), M:tm-754, m:tm-306, u:((Am (or (and A B) A)) (C (-> Bm Cm)) (D (and (-> (or (and A B) A) (-> Bm Cm)) (-> (-> (or (and A B) A) Bm) (-> (or (and A B) A) Cm)))))
================================================================
tm-name          tm-63023
in-theory        63023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (D -> ((((A and C) or A) -> B) and D))))
theorem-size     31
proof            (modus-ponens tm-754 tm-309 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> Bm (and (-> (or (and A B) A) C) Bm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-63023.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (D -> ((((A and C) or A) -> B) and D)))), M:tm-754, m:tm-309, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> Bm (and (-> (or (and A B) A) C) Bm)))))
================================================================
tm-name          tm-63024
in-theory        63024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((((A and C) or A) -> B) or D)))
theorem-size     29
proof            (modus-ponens tm-754 tm-310 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (or (-> (or (and A B) A) C) Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-63024.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((((A and C) or A) -> B) or D))), M:tm-754, m:tm-310, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (or (-> (or (and A B) A) C) Bm))))
================================================================
tm-name          tm-63025
in-theory        63025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (D or (((A and C) or A) -> B))))
theorem-size     29
proof            (modus-ponens tm-754 tm-311 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (or Bm (-> (or (and A B) A) C))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-63025.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (D or (((A and C) or A) -> B)))), M:tm-754, m:tm-311, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (or Bm (-> (or (and A B) A) C)))))
================================================================
tm-name          tm-63026
in-theory        63026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((B -> D) -> ((((A and C) or A) or B) -> D))))
theorem-size     33
proof            (modus-ponens tm-754 tm-312 ((Am (or (and A B) A)) (C Bm) (D (and (-> (or (and A B) A) Bm) (-> (-> Bm Cm) (-> (or (or (and A B) A) Bm) Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-63026.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((B -> D) -> ((((A and C) or A) or B) -> D)))), M:tm-754, m:tm-312, u:((Am (or (and A B) A)) (C Bm) (D (and (-> (or (and A B) A) Bm) (-> (-> Bm Cm) (-> (or (or (and A B) A) Bm) Cm)))))
================================================================
tm-name          tm-63027
in-theory        63027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((((A and C) or A) -> (not B)) -> (not ((A and C) or A)))))
theorem-size     35
proof            (modus-ponens tm-754 tm-313 ((Am (or (and A B) A)) (C Bm) (D (and (-> (or (and A B) A) Bm) (-> (-> (or (and A B) A) (not Bm)) (not (or (and A B) A)))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-9)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-63027.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((((A and C) or A) -> (not B)) -> (not ((A and C) or A))))), M:tm-754, m:tm-313, u:((Am (or (and A B) A)) (C Bm) (D (and (-> (or (and A B) A) Bm) (-> (-> (or (and A B) A) (not Bm)) (not (or (and A B) A))))))
================================================================
tm-name          tm-63028
in-theory        63028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (D -> (E -> D))))
theorem-size     25
proof            (modus-ponens tm-754 tm-315 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> Bm (-> Cm Bm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-63028.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (D -> (E -> D)))), M:tm-754, m:tm-315, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-63029
in-theory        63029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((A and C) or A) -> ((A and C) or A))))
theorem-size     31
proof            (modus-ponens tm-754 tm-316 ((Am (or (and A B) A)) (C Bm) (D (and (-> (or (and A B) A) Bm) (-> (or (and A B) A) (or (and A B) A))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-63029.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((A and C) or A) -> ((A and C) or A)))), M:tm-754, m:tm-316, u:((Am (or (and A B) A)) (C Bm) (D (and (-> (or (and A B) A) Bm) (-> (or (and A B) A) (or (and A B) A)))))
================================================================
tm-name          tm-63030
in-theory        63030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     33
proof            (modus-ponens tm-754 tm-318 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-63030.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-754, m:tm-318, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-63031
in-theory        63031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((D and E) -> D)))
theorem-size     25
proof            (modus-ponens tm-754 tm-320 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> (and Bm Cm) Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-63031.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((D and E) -> D))), M:tm-754, m:tm-320, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-63032
in-theory        63032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((D and E) -> E)))
theorem-size     25
proof            (modus-ponens tm-754 tm-322 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> (and Bm Cm) Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-63032.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((D and E) -> E))), M:tm-754, m:tm-322, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-63033
in-theory        63033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((D -> (E -> D)) and (((A and C) or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-754 tm-323 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (and (-> Bm (-> Cm Bm)) (-> (or (and A B) A) C))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-63033.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((D -> (E -> D)) and (((A and C) or A) -> B)))), M:tm-754, m:tm-323, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (and (-> Bm (-> Cm Bm)) (-> (or (and A B) A) C)))))
================================================================
tm-name          tm-63034
in-theory        63034
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and C) or A) -> B))))
theorem-size     41
proof            (modus-ponens tm-754 tm-324 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (and A B) A) C))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-63034.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and C) or A) -> B)))), M:tm-754, m:tm-324, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (or (and A B) A) C)))))
================================================================
tm-name          tm-63035
in-theory        63035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((D and E) -> D) and (((A and C) or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-754 tm-325 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (and (-> (and Bm Cm) Bm) (-> (or (and A B) A) C))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-63035.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((D and E) -> D) and (((A and C) or A) -> B)))), M:tm-754, m:tm-325, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (and (-> (and Bm Cm) Bm) (-> (or (and A B) A) C)))))
================================================================
tm-name          tm-63036
in-theory        63036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((D and E) -> E) and (((A and C) or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-754 tm-326 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (and (-> (and Bm Cm) Cm) (-> (or (and A B) A) C))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-63036.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((D and E) -> E) and (((A and C) or A) -> B)))), M:tm-754, m:tm-326, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (and (-> (and Bm Cm) Cm) (-> (or (and A B) A) C)))))
================================================================
tm-name          tm-63037
in-theory        63037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((D -> (E -> (D and E))) and (((A and C) or A) -> B))))
theorem-size     35
proof            (modus-ponens tm-754 tm-327 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (and A B) A) C))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-63037.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((D -> (E -> (D and E))) and (((A and C) or A) -> B)))), M:tm-754, m:tm-327, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (and (-> Bm (-> Cm (and Bm Cm))) (-> (or (and A B) A) C)))))
================================================================
tm-name          tm-63038
in-theory        63038
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((A and C) or A) -> (((A and C) or A) and B))))
theorem-size     33
proof            (modus-ponens tm-754 tm-328 ((Am (or (and A B) A)) (C Bm) (D (and (-> (or (and A B) A) Bm) (-> (or (and A B) A) (and (or (and A B) A) Bm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-63038.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((A and C) or A) -> (((A and C) or A) and B)))), M:tm-754, m:tm-328, u:((Am (or (and A B) A)) (C Bm) (D (and (-> (or (and A B) A) Bm) (-> (or (and A B) A) (and (or (and A B) A) Bm)))))
================================================================
tm-name          tm-63039
in-theory        63039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> (D -> (D and E))) and (((A and C) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-754 tm-338 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-63039.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> (D -> (D and E))) and (((A and C) or A) -> B))), M:tm-754, m:tm-338, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63040
in-theory        63040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> E) -> (D -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-754 tm-340 ((Am (-> (or (and A B) A) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-2 tm-5)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-63040.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> E) -> (D -> (D and E)))), M:tm-754, m:tm-340, u:((Am (-> (or (and A B) A) C)) (D (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-63041
in-theory        63041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (D -> (E -> (D and E)))))
theorem-size     27
proof            (modus-ponens tm-754 tm-341 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-63041.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (D -> (E -> (D and E))))), M:tm-754, m:tm-341, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-63042
in-theory        63042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B -> (((A and C) or A) and B)) -> D)) or (((A and C) or A) -> ((B -> (((A and C) or A) and B)) -> D))) -> (((A and C) or A) -> D))
theorem-size     39
proof            (modus-ponens tm-754 tm-349 ((Am (or (and A B) A)) (C (-> (-> Bm (and (or (and A B) A) Bm)) Cm)) (D (-> (or (and A B) A) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-5)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-63042.        (((A -> ((B -> (((A and C) or A) and B)) -> D)) or (((A and C) or A) -> ((B -> (((A and C) or A) and B)) -> D))) -> (((A and C) or A) -> D)), M:tm-754, m:tm-349, u:((Am (or (and A B) A)) (C (-> (-> Bm (and (or (and A B) A) Bm)) Cm)) (D (-> (or (and A B) A) Cm)))
================================================================
tm-name          tm-63043
in-theory        63043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C -> (B and C))))) or (((A and D) or A) -> (not (B -> (C -> (B and C)))))) -> (not ((A and D) or A)))
theorem-size     32
proof            (modus-ponens tm-754 tm-350 ((Am (or (and A B) A)) (C (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-1 tm-5)
proof-size       142
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-63043.        (((A -> (not (B -> (C -> (B and C))))) or (((A and D) or A) -> (not (B -> (C -> (B and C)))))) -> (not ((A and D) or A))), M:tm-754, m:tm-350, u:((Am (or (and A B) A)) (C (not (-> Bm (-> Cm (and Bm Cm))))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-63044
in-theory        63044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> (F -> (E and F)))) and (((A and C) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-754 tm-354 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63044.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> (F -> (E and F)))) and (((A and C) or A) -> B))), M:tm-754, m:tm-354, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63045
in-theory        63045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or A) -> (D -> (B and D))))
theorem-size     23
proof            (modus-ponens tm-754 tm-355 ((Am (or (and A B) A)) (C Bm) (D (-> (or (and A B) A) (-> Cm (and Bm Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-5)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-63045.        (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or A) -> (D -> (B and D)))), M:tm-754, m:tm-355, u:((Am (or (and A B) A)) (C Bm) (D (-> (or (and A B) A) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-63046
in-theory        63046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-754 tm-356 ((Am (-> (or (and A B) A) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-3 tm-1 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63046.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> (E -> (F -> (E and F))))), M:tm-754, m:tm-356, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-63047
in-theory        63047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (E -> D)) or F) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-364 ((Am (-> (or (and A B) A) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-6 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-63047.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (E -> D)) or F) and (((A and C) or A) -> B))), M:tm-754, m:tm-364, u:((Am (-> (or (and A B) A) C)) (D (and (or (-> Bm (-> Cm Bm)) Dm) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63048
in-theory        63048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-754 tm-365 ((Am (-> (or (and A B) A) C)) (D (or (-> Bm (-> Cm Bm)) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-63048.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> D)) or F)), M:tm-754, m:tm-365, u:((Am (-> (or (and A B) A) C)) (D (or (-> Bm (-> Cm Bm)) Dm)))
================================================================
tm-name          tm-63049
in-theory        63049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (((A and C) or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-754 tm-373 ((Am (-> (or (and A B) A) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-6 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-63049.        (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) and (((A and C) or A) -> B))), M:tm-754, m:tm-373, u:((Am (-> (or (and A B) A) C)) (D (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63050
in-theory        63050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     27
proof            (modus-ponens tm-754 tm-374 ((Am (-> (or (and A B) A) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
axioms-used      (tm-8 tm-3 tm-1 tm-6 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-63050.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-754, m:tm-374, u:((Am (-> (or (and A B) A) C)) (D (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))
================================================================
tm-name          tm-63051
in-theory        63051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((D and E) -> D) or F) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-382 ((Am (-> (or (and A B) A) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-63051.        (((A -> B) or (((A and C) or A) -> B)) -> ((((D and E) -> D) or F) and (((A and C) or A) -> B))), M:tm-754, m:tm-382, u:((Am (-> (or (and A B) A) C)) (D (and (or (-> (and Bm Cm) Bm) Dm) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63052
in-theory        63052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D and E) -> D) or F))
theorem-size     19
proof            (modus-ponens tm-754 tm-383 ((Am (-> (or (and A B) A) C)) (D (or (-> (and Bm Cm) Bm) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-63052.        (((A -> B) or (((A and C) or A) -> B)) -> (((D and E) -> D) or F)), M:tm-754, m:tm-383, u:((Am (-> (or (and A B) A) C)) (D (or (-> (and Bm Cm) Bm) Dm)))
================================================================
tm-name          tm-63053
in-theory        63053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((D and E) -> E) or F) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-391 ((Am (-> (or (and A B) A) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-6 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-63053.        (((A -> B) or (((A and C) or A) -> B)) -> ((((D and E) -> E) or F) and (((A and C) or A) -> B))), M:tm-754, m:tm-391, u:((Am (-> (or (and A B) A) C)) (D (and (or (-> (and Bm Cm) Cm) Dm) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63054
in-theory        63054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D and E) -> E) or F))
theorem-size     19
proof            (modus-ponens tm-754 tm-392 ((Am (-> (or (and A B) A) C)) (D (or (-> (and Bm Cm) Cm) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-6 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-63054.        (((A -> B) or (((A and C) or A) -> B)) -> (((D and E) -> E) or F)), M:tm-754, m:tm-392, u:((Am (-> (or (and A B) A) C)) (D (or (-> (and Bm Cm) Cm) Dm)))
================================================================
tm-name          tm-63055
in-theory        63055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (E -> (D and E))) or F) and (((A and C) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-754 tm-400 ((Am (-> (or (and A B) A) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-63055.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (E -> (D and E))) or F) and (((A and C) or A) -> B))), M:tm-754, m:tm-400, u:((Am (-> (or (and A B) A) C)) (D (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63056
in-theory        63056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> (D and E))) or F))
theorem-size     21
proof            (modus-ponens tm-754 tm-401 ((Am (-> (or (and A B) A) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-6 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-63056.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> (D and E))) or F)), M:tm-754, m:tm-401, u:((Am (-> (or (and A B) A) C)) (D (or (-> Bm (-> Cm (and Bm Cm))) Dm)))
================================================================
tm-name          tm-63057
in-theory        63057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (D or E)) or F) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-409 ((Am (-> (or (and A B) A) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-63057.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (D or E)) or F) and (((A and C) or A) -> B))), M:tm-754, m:tm-409, u:((Am (-> (or (and A B) A) C)) (D (and (or (-> Bm (or Bm Cm)) Dm) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63058
in-theory        63058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (D or E)) or F))
theorem-size     19
proof            (modus-ponens tm-754 tm-410 ((Am (-> (or (and A B) A) C)) (D (or (-> Bm (or Bm Cm)) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-63058.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (D or E)) or F)), M:tm-754, m:tm-410, u:((Am (-> (or (and A B) A) C)) (D (or (-> Bm (or Bm Cm)) Dm)))
================================================================
tm-name          tm-63059
in-theory        63059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((D -> (D or E)) and (((A and C) or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-754 tm-443 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (and (-> Bm (or Bm Cm)) (-> (or (and A B) A) C))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-63059.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((D -> (D or E)) and (((A and C) or A) -> B)))), M:tm-754, m:tm-443, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (and (-> Bm (or Bm Cm)) (-> (or (and A B) A) C)))))
================================================================
tm-name          tm-63060
in-theory        63060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (B or C)) and ((A and D) or A)))) or (((A and D) or A) -> (not ((B -> (B or C)) and ((A and D) or A))))) -> (not ((A and D) or A)))
theorem-size     40
proof            (modus-ponens tm-754 tm-449 ((Am (or (and A B) A)) (C (not (and (-> Bm (or Bm Cm)) (or (and A B) A)))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-5 tm-6)
proof-size       150
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-63060.        (((A -> (not ((B -> (B or C)) and ((A and D) or A)))) or (((A and D) or A) -> (not ((B -> (B or C)) and ((A and D) or A))))) -> (not ((A and D) or A))), M:tm-754, m:tm-449, u:((Am (or (and A B) A)) (C (not (and (-> Bm (or Bm Cm)) (or (and A B) A)))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-63061
in-theory        63061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> ((E -> (E or F)) and D)) and (((A and C) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-754 tm-453 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-63061.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> ((E -> (E or F)) and D)) and (((A and C) or A) -> B))), M:tm-754, m:tm-453, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63062
in-theory        63062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((E -> (E or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-754 tm-454 ((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-63062.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((E -> (E or F)) and D))), M:tm-754, m:tm-454, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> Cm (or Cm Dm)) Bm))))
================================================================
tm-name          tm-63063
in-theory        63063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (D -> (D or E))))
theorem-size     25
proof            (modus-ponens tm-754 tm-456 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> Bm (or Bm Cm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-63063.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (D -> (D or E)))), M:tm-754, m:tm-456, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-63064
in-theory        63064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((((A and B) or A) or C) -> D)) or (((A and B) or A) -> ((((A and B) or A) or C) -> D))) -> (((A and B) or A) -> D))
theorem-size     35
proof            (modus-ponens tm-754 tm-464 ((Am (or (and A B) A)) (C (-> (or (or (and A B) A) Bm) Cm)) (D (-> (or (and A B) A) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-6)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-63064.        (((A -> ((((A and B) or A) or C) -> D)) or (((A and B) or A) -> ((((A and B) or A) or C) -> D))) -> (((A and B) or A) -> D)), M:tm-754, m:tm-464, u:((Am (or (and A B) A)) (C (-> (or (or (and A B) A) Bm) Cm)) (D (-> (or (and A B) A) Cm)))
================================================================
tm-name          tm-63065
in-theory        63065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (B or C)))) or (((A and D) or A) -> (not (B -> (B or C))))) -> (not ((A and D) or A)))
theorem-size     28
proof            (modus-ponens tm-754 tm-465 ((Am (or (and A B) A)) (C (not (-> Bm (or Bm Cm)))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-1 tm-6)
proof-size       132
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-63065.        (((A -> (not (B -> (B or C)))) or (((A and D) or A) -> (not (B -> (B or C))))) -> (not ((A and D) or A))), M:tm-754, m:tm-465, u:((Am (or (and A B) A)) (C (not (-> Bm (or Bm Cm)))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-63066
in-theory        63066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> (E or F))) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-469 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-63066.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> (E or F))) and (((A and C) or A) -> B))), M:tm-754, m:tm-469, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> Cm (or Cm Dm))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63067
in-theory        63067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or A) -> (B or D)))
theorem-size     21
proof            (modus-ponens tm-754 tm-470 ((Am (or (and A B) A)) (C Bm) (D (-> (or (and A B) A) (or Bm Cm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-63067.        (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or A) -> (B or D))), M:tm-754, m:tm-470, u:((Am (or (and A B) A)) (C Bm) (D (-> (or (and A B) A) (or Bm Cm))))
================================================================
tm-name          tm-63068
in-theory        63068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-754 tm-471 ((Am (-> (or (and A B) A) C)) (D (-> Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-63068.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> (E -> (E or F)))), M:tm-754, m:tm-471, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-63069
in-theory        63069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D or (E -> (F -> E))) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-480 ((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-7 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-63069.        (((A -> B) or (((A and C) or A) -> B)) -> ((D or (E -> (F -> E))) and (((A and C) or A) -> B))), M:tm-754, m:tm-480, u:((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> Cm (-> Dm Cm))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63070
in-theory        63070
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D or (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-754 tm-481 ((Am (-> (or (and A B) A) C)) (D (or Bm (-> Cm (-> Dm Cm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-63070.        (((A -> B) or (((A and C) or A) -> B)) -> (D or (E -> (F -> E)))), M:tm-754, m:tm-481, u:((Am (-> (or (and A B) A) C)) (D (or Bm (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-63071
in-theory        63071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((A and C) or A) -> B)))
theorem-size     35
proof            (modus-ponens tm-754 tm-490 ((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-7 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63071.        (((A -> B) or (((A and C) or A) -> B)) -> ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) and (((A and C) or A) -> B))), M:tm-754, m:tm-490, u:((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63072
in-theory        63072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-754 tm-491 ((Am (-> (or (and A B) A) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-8 tm-3 tm-1 tm-7 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63072.        (((A -> B) or (((A and C) or A) -> B)) -> (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-754, m:tm-491, u:((Am (-> (or (and A B) A) C)) (D (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-63073
in-theory        63073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D or ((E and F) -> E)) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-500 ((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-63073.        (((A -> B) or (((A and C) or A) -> B)) -> ((D or ((E and F) -> E)) and (((A and C) or A) -> B))), M:tm-754, m:tm-500, u:((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> (and Cm Dm) Cm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63074
in-theory        63074
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D or ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-754 tm-501 ((Am (-> (or (and A B) A) C)) (D (or Bm (-> (and Cm Dm) Cm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-63074.        (((A -> B) or (((A and C) or A) -> B)) -> (D or ((E and F) -> E))), M:tm-754, m:tm-501, u:((Am (-> (or (and A B) A) C)) (D (or Bm (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-63075
in-theory        63075
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D or ((E and F) -> F)) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-510 ((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-7 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-63075.        (((A -> B) or (((A and C) or A) -> B)) -> ((D or ((E and F) -> F)) and (((A and C) or A) -> B))), M:tm-754, m:tm-510, u:((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> (and Cm Dm) Dm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63076
in-theory        63076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D or ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-754 tm-511 ((Am (-> (or (and A B) A) C)) (D (or Bm (-> (and Cm Dm) Dm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-7 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-63076.        (((A -> B) or (((A and C) or A) -> B)) -> (D or ((E and F) -> F))), M:tm-754, m:tm-511, u:((Am (-> (or (and A B) A) C)) (D (or Bm (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-63077
in-theory        63077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D or (E -> (F -> (E and F)))) and (((A and C) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-754 tm-520 ((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63077.        (((A -> B) or (((A and C) or A) -> B)) -> ((D or (E -> (F -> (E and F)))) and (((A and C) or A) -> B))), M:tm-754, m:tm-520, u:((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63078
in-theory        63078
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D or (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-754 tm-521 ((Am (-> (or (and A B) A) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-8 tm-3 tm-1 tm-7 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63078.        (((A -> B) or (((A and C) or A) -> B)) -> (D or (E -> (F -> (E and F))))), M:tm-754, m:tm-521, u:((Am (-> (or (and A B) A) C)) (D (or Bm (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-63079
in-theory        63079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D or (E -> (E or F))) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-530 ((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-7 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-63079.        (((A -> B) or (((A and C) or A) -> B)) -> ((D or (E -> (E or F))) and (((A and C) or A) -> B))), M:tm-754, m:tm-530, u:((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> Cm (or Cm Dm))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63080
in-theory        63080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D or (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-754 tm-531 ((Am (-> (or (and A B) A) C)) (D (or Bm (-> Cm (or Cm Dm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-7 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-63080.        (((A -> B) or (((A and C) or A) -> B)) -> (D or (E -> (E or F)))), M:tm-754, m:tm-531, u:((Am (-> (or (and A B) A) C)) (D (or Bm (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-63081
in-theory        63081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D or (E -> (F or E))) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-540 ((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-63081.        (((A -> B) or (((A and C) or A) -> B)) -> ((D or (E -> (F or E))) and (((A and C) or A) -> B))), M:tm-754, m:tm-540, u:((Am (-> (or (and A B) A) C)) (D (and (or Bm (-> Cm (or Dm Cm))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63082
in-theory        63082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D or (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-754 tm-541 ((Am (-> (or (and A B) A) C)) (D (or Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-63082.        (((A -> B) or (((A and C) or A) -> B)) -> (D or (E -> (F or E)))), M:tm-754, m:tm-541, u:((Am (-> (or (and A B) A) C)) (D (or Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-63083
in-theory        63083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (E or D)) or F) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-550 ((Am (-> (or (and A B) A) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-6 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-63083.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> (E or D)) or F) and (((A and C) or A) -> B))), M:tm-754, m:tm-550, u:((Am (-> (or (and A B) A) C)) (D (and (or (-> Bm (or Cm Bm)) Dm) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63084
in-theory        63084
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E or D)) or F))
theorem-size     19
proof            (modus-ponens tm-754 tm-551 ((Am (-> (or (and A B) A) C)) (D (or (-> Bm (or Cm Bm)) Dm))))
axioms-used      (tm-8 tm-3 tm-1 tm-6 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-63084.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E or D)) or F)), M:tm-754, m:tm-551, u:((Am (-> (or (and A B) A) C)) (D (or (-> Bm (or Cm Bm)) Dm)))
================================================================
tm-name          tm-63085
in-theory        63085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((D -> (E or D)) and (((A and C) or A) -> B))))
theorem-size     33
proof            (modus-ponens tm-754 tm-595 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (and (-> Bm (or Cm Bm)) (-> (or (and A B) A) C))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-63085.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and ((D -> (E or D)) and (((A and C) or A) -> B)))), M:tm-754, m:tm-595, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (and (-> Bm (or Cm Bm)) (-> (or (and A B) A) C)))))
================================================================
tm-name          tm-63086
in-theory        63086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((B -> (C or B)) and ((A and D) or A)))) or (((A and D) or A) -> (not ((B -> (C or B)) and ((A and D) or A))))) -> (not ((A and D) or A)))
theorem-size     40
proof            (modus-ponens tm-754 tm-601 ((Am (or (and A B) A)) (C (not (and (-> Bm (or Cm Bm)) (or (and A B) A)))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-5 tm-7)
proof-size       150
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-63086.        (((A -> (not ((B -> (C or B)) and ((A and D) or A)))) or (((A and D) or A) -> (not ((B -> (C or B)) and ((A and D) or A))))) -> (not ((A and D) or A))), M:tm-754, m:tm-601, u:((Am (or (and A B) A)) (C (not (and (-> Bm (or Cm Bm)) (or (and A B) A)))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-63087
in-theory        63087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> ((E -> (F or E)) and D)) and (((A and C) or A) -> B)))
theorem-size     29
proof            (modus-ponens tm-754 tm-605 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-63087.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> ((E -> (F or E)) and D)) and (((A and C) or A) -> B))), M:tm-754, m:tm-605, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63088
in-theory        63088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((E -> (F or E)) and D)))
theorem-size     21
proof            (modus-ponens tm-754 tm-606 ((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
axioms-used      (tm-8 tm-3 tm-1 tm-5 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-63088.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> ((E -> (F or E)) and D))), M:tm-754, m:tm-606, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (and (-> Cm (or Dm Cm)) Bm))))
================================================================
tm-name          tm-63089
in-theory        63089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (D -> (E or D))))
theorem-size     25
proof            (modus-ponens tm-754 tm-609 ((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> Bm (or Cm Bm))))))
axioms-used      (tm-8 tm-3 tm-2 tm-5 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-63089.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (D -> (E or D)))), M:tm-754, m:tm-609, u:((Am (-> (or (and A B) A) C)) (D (and (-> (or (and A B) A) C) (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-63090
in-theory        63090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> ((B or ((A and C) or A)) -> D)) or (((A and C) or A) -> ((B or ((A and C) or A)) -> D))) -> (((A and C) or A) -> D))
theorem-size     35
proof            (modus-ponens tm-754 tm-617 ((Am (or (and A B) A)) (C (-> (or Bm (or (and A B) A)) Cm)) (D (-> (or (and A B) A) Cm))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-7)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-63090.        (((A -> ((B or ((A and C) or A)) -> D)) or (((A and C) or A) -> ((B or ((A and C) or A)) -> D))) -> (((A and C) or A) -> D)), M:tm-754, m:tm-617, u:((Am (or (and A B) A)) (C (-> (or Bm (or (and A B) A)) Cm)) (D (-> (or (and A B) A) Cm)))
================================================================
tm-name          tm-63091
in-theory        63091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not (B -> (C or B)))) or (((A and D) or A) -> (not (B -> (C or B))))) -> (not ((A and D) or A)))
theorem-size     28
proof            (modus-ponens tm-754 tm-618 ((Am (or (and A B) A)) (C (not (-> Bm (or Cm Bm)))) (D (not (or (and A B) A)))))
axioms-used      (tm-8 tm-3 tm-9 tm-1 tm-7)
proof-size       132
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-63091.        (((A -> (not (B -> (C or B)))) or (((A and D) or A) -> (not (B -> (C or B))))) -> (not ((A and D) or A))), M:tm-754, m:tm-618, u:((Am (or (and A B) A)) (C (not (-> Bm (or Cm Bm)))) (D (not (or (and A B) A))))
================================================================
tm-name          tm-63092
in-theory        63092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> (F or E))) and (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-754 tm-622 ((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-63092.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> (E -> (F or E))) and (((A and C) or A) -> B))), M:tm-754, m:tm-622, u:((Am (-> (or (and A B) A) C)) (D (and (-> Bm (-> Cm (or Dm Cm))) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63093
in-theory        63093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or A) -> (D or B)))
theorem-size     21
proof            (modus-ponens tm-754 tm-623 ((Am (or (and A B) A)) (C Bm) (D (-> (or (and A B) A) (or Cm Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-1 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-63093.        (((A -> B) or (((A and C) or A) -> B)) -> (((A and C) or A) -> (D or B))), M:tm-754, m:tm-623, u:((Am (or (and A B) A)) (C Bm) (D (-> (or (and A B) A) (or Cm Bm))))
================================================================
tm-name          tm-63094
in-theory        63094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (D -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-754 tm-624 ((Am (-> (or (and A B) A) C)) (D (-> Bm (-> Cm (or Dm Cm))))))
axioms-used      (tm-8 tm-3 tm-1 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-63094.        (((A -> B) or (((A and C) or A) -> B)) -> (D -> (E -> (F or E)))), M:tm-754, m:tm-624, u:((Am (-> (or (and A B) A) C)) (D (-> Bm (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-63095
in-theory        63095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (((A and C) or A) -> B)))
theorem-size     33
proof            (modus-ponens tm-754 tm-665 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-1)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-63095.        (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) and (((A and C) or A) -> B))), M:tm-754, m:tm-665, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63096
in-theory        63096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-754 tm-667 ((Am (-> (or (and A B) A) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-63096.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-754, m:tm-667, u:((Am (-> (or (and A B) A) C)) (D (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-63097
in-theory        63097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (((A and C) or A) -> B)))
theorem-size     45
proof            (modus-ponens tm-754 tm-708 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-63097.        (((A -> B) or (((A and C) or A) -> B)) -> (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) and (((A and C) or A) -> B))), M:tm-754, m:tm-708, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-63098
in-theory        63098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     37
proof            (modus-ponens tm-754 tm-710 ((Am (-> (or (and A B) A) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-8 tm-3 tm-1 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-63098.        (((A -> B) or (((A and C) or A) -> B)) -> ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-754, m:tm-710, u:((Am (-> (or (and A B) A) C)) (D (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-63099
in-theory        63099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((((A and C) or A) and D) or ((A and C) or A)) -> B)))
theorem-size     35
proof            (modus-ponens tm-754 tm-747 ((Am (or (and A B) A)) (C Bm) (D (and (-> (or (and A B) A) Bm) (-> (or (and (or (and A B) A) Cm) (or (and A B) A)) Bm)))))
axioms-used      (tm-8 tm-3 tm-2 tm-5)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63099.        (((A -> B) or (((A and C) or A) -> B)) -> ((((A and C) or A) -> B) and (((((A and C) or A) and D) or ((A and C) or A)) -> B))), M:tm-754, m:tm-747, u:((Am (or (and A B) A)) (C Bm) (D (and (-> (or (and A B) A) Bm) (-> (or (and (or (and A B) A) Cm) (or (and A B) A)) Bm))))
================================================================
tm-name          tm-63100
in-theory        63100
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((((((A and B) or A) -> C) -> D) and E) or ((((A and B) or A) -> C) -> D)) -> (((A -> C) or (((A and B) or A) -> C)) -> D)))
theorem-size     59
proof            (modus-ponens tm-747 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63100.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((((((A and B) or A) -> C) -> D) and E) or ((((A and B) or A) -> C) -> D)) -> (((A -> C) or (((A and B) or A) -> C)) -> D))), M:tm-747, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63101
in-theory        63101
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E and F) or E) -> G) -> H) -> (((E -> G) or (((E and F) or E) -> G)) -> H)))
theorem-size     49
proof            (modus-ponens tm-708 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       201
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63101.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((((E and F) or E) -> G) -> H) -> (((E -> G) or (((E and F) or E) -> G)) -> H))), M:tm-708, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63102
in-theory        63102
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> (((A and B) or A) -> D)) -> (((A -> C) or (((A and B) or A) -> C)) -> (((A and B) or A) -> D)))
theorem-size     35
proof            (modus-ponens tm-703 tm-754 ((A (or (and Am Bm) Am)) (B Cm) (Dm (-> (or (and Am Bm) Am) C)) (D (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (-> (or (and Am Bm) Am) C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63102.        (((((A and B) or A) -> C) -> (((A and B) or A) -> D)) -> (((A -> C) or (((A and B) or A) -> C)) -> (((A and B) or A) -> D))), M:tm-703, m:tm-754, u:((A (or (and Am Bm) Am)) (B Cm) (Dm (-> (or (and Am Bm) Am) C)) (D (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (-> (or (and Am Bm) Am) C))))
================================================================
tm-name          tm-63103
in-theory        63103
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> (((A and B) or A) -> D)) -> (((A -> C) or (((A and B) or A) -> C)) -> (((A and B) or A) -> D))) and (((((A and B) or A) -> (C -> D)) or ((((A and B) or A) -> C) -> (((A and B) or A) -> D))) -> (((A -> C) or (((A and B) or A) -> C)) -> (((A and B) or A) -> D))))
theorem-size     81
proof            (modus-ponens tm-697 tm-754 ((A (or (and Am Bm) Am)) (B Cm) (Dm (-> (or (and Am Bm) Am) C)) (D (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (-> (or (and Am Bm) Am) C)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       261
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63103.        ((((((A and B) or A) -> C) -> (((A and B) or A) -> D)) -> (((A -> C) or (((A and B) or A) -> C)) -> (((A and B) or A) -> D))) and (((((A and B) or A) -> (C -> D)) or ((((A and B) or A) -> C) -> (((A and B) or A) -> D))) -> (((A -> C) or (((A and B) or A) -> C)) -> (((A and B) or A) -> D)))), M:tm-697, m:tm-754, u:((A (or (and Am Bm) Am)) (B Cm) (Dm (-> (or (and Am Bm) Am) C)) (D (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (-> (or (and Am Bm) Am) C))))
================================================================
tm-name          tm-63104
in-theory        63104
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-665 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63104.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-665, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63105
in-theory        63105
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((D or ((((A and B) or A) -> C) -> D)) -> (((A -> C) or (((A and B) or A) -> C)) -> D)))
theorem-size     49
proof            (modus-ponens tm-654 tm-754 ((A (-> (or (and Am Bm) Am) Cm)) (B Dm) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63105.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((D or ((((A and B) or A) -> C) -> D)) -> (((A -> C) or (((A and B) or A) -> C)) -> D))), M:tm-654, m:tm-754, u:((A (-> (or (and Am Bm) Am) Cm)) (B Dm) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63106
in-theory        63106
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> D) -> (E or (((A -> C) or (((A and B) or A) -> C)) -> D)))
theorem-size     25
proof            (modus-ponens tm-623 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63106.        (((((A and B) or A) -> C) -> D) -> (E or (((A -> C) or (((A and B) or A) -> C)) -> D))), M:tm-623, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63107
in-theory        63107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-622 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63107.        ((A -> (B -> (C or B))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-622, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63108
in-theory        63108
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) or B) -> D) -> (E or (((B and C) or B) -> D)))) -> (((B -> D) or (((B and C) or B) -> D)) -> (E or (((B and C) or B) -> D))))
theorem-size     41
proof            (modus-ponens tm-619 tm-754 ((A (-> (or (and Am Bm) Am) Cm)) (Dm (or B (-> (or (and Am Bm) Am) Cm))) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (or B (-> (or (and Am Bm) Am) Cm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63108.        ((A or ((((B and C) or B) -> D) -> (E or (((B and C) or B) -> D)))) -> (((B -> D) or (((B and C) or B) -> D)) -> (E or (((B and C) or B) -> D)))), M:tm-619, m:tm-754, u:((A (-> (or (and Am Bm) Am) Cm)) (Dm (or B (-> (or (and Am Bm) Am) Cm))) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (or B (-> (or (and Am Bm) Am) Cm)))))
================================================================
tm-name          tm-63109
in-theory        63109
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (E -> (F or E)))
theorem-size     29
proof            (modus-ponens tm-609 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63109.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63110
in-theory        63110
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-605 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63110.        ((A -> ((B -> (C or B)) and A)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-605, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63111
in-theory        63111
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((E -> (F or E)) and (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-595 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63111.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((E -> (F or E)) and (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)))), M:tm-595, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63112
in-theory        63112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-550 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63112.        (((A -> (B or A)) or C) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-550, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63113
in-theory        63113
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-540 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63113.        ((A or (B -> (C or B))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-540, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63114
in-theory        63114
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-530 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63114.        ((A or (B -> (B or C))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-530, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63115
in-theory        63115
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-520 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63115.        ((A or (B -> (C -> (B and C)))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-520, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63116
in-theory        63116
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-510 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63116.        ((A or ((B and C) -> C)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-510, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63117
in-theory        63117
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-500 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63117.        ((A or ((B and C) -> B)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-500, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63118
in-theory        63118
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) or E) -> G) -> H) -> (((E -> G) or (((E and F) or E) -> G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-490 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63118.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) or E) -> G) -> H) -> (((E -> G) or (((E and F) or E) -> G)) -> H))), M:tm-490, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63119
in-theory        63119
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-480 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63119.        ((A or (B -> (C -> B))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-480, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63120
in-theory        63120
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> D) -> ((((A -> C) or (((A and B) or A) -> C)) -> D) or E))
theorem-size     25
proof            (modus-ponens tm-470 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63120.        (((((A and B) or A) -> C) -> D) -> ((((A -> C) or (((A and B) or A) -> C)) -> D) or E)), M:tm-470, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63121
in-theory        63121
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-469 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63121.        ((A -> (B -> (B or C))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-469, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63122
in-theory        63122
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) or B) -> D) -> ((((B and C) or B) -> D) or E))) -> (((B -> D) or (((B and C) or B) -> D)) -> ((((B and C) or B) -> D) or E)))
theorem-size     41
proof            (modus-ponens tm-466 tm-754 ((A (-> (or (and Am Bm) Am) Cm)) (Dm (or (-> (or (and Am Bm) Am) Cm) B)) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (or (-> (or (and Am Bm) Am) Cm) B)))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63122.        ((A or ((((B and C) or B) -> D) -> ((((B and C) or B) -> D) or E))) -> (((B -> D) or (((B and C) or B) -> D)) -> ((((B and C) or B) -> D) or E))), M:tm-466, m:tm-754, u:((A (-> (or (and Am Bm) Am) Cm)) (Dm (or (-> (or (and Am Bm) Am) Cm) B)) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (or (-> (or (and Am Bm) Am) Cm) B))))
================================================================
tm-name          tm-63123
in-theory        63123
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (E -> (E or F)))
theorem-size     29
proof            (modus-ponens tm-456 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63123.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63124
in-theory        63124
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-453 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63124.        ((A -> ((B -> (B or C)) and A)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-453, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63125
in-theory        63125
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((E -> (E or F)) and (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-443 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63125.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((E -> (E or F)) and (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)))), M:tm-443, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63126
in-theory        63126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-409 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63126.        (((A -> (A or B)) or C) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-409, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63127
in-theory        63127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-400 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63127.        (((A -> (B -> (A and B))) or C) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-400, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63128
in-theory        63128
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-391 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63128.        ((((A and B) -> B) or C) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-391, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63129
in-theory        63129
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-382 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63129.        ((((A and B) -> A) or C) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-382, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63130
in-theory        63130
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E and F) or E) -> G) -> H) -> (((E -> G) or (((E and F) or E) -> G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-373 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63130.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((((E and F) or E) -> G) -> H) -> (((E -> G) or (((E and F) or E) -> G)) -> H))), M:tm-373, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63131
in-theory        63131
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-364 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63131.        (((A -> (B -> A)) or C) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-364, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63132
in-theory        63132
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> D) -> (E -> ((((A -> C) or (((A and B) or A) -> C)) -> D) and E)))
theorem-size     27
proof            (modus-ponens tm-355 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63132.        (((((A and B) or A) -> C) -> D) -> (E -> ((((A -> C) or (((A and B) or A) -> C)) -> D) and E))), M:tm-355, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63133
in-theory        63133
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-354 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63133.        ((A -> (B -> (C -> (B and C)))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-354, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63134
in-theory        63134
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) or B) -> D) -> (E -> ((((B and C) or B) -> D) and E)))) -> (((B -> D) or (((B and C) or B) -> D)) -> (E -> ((((B and C) or B) -> D) and E))))
theorem-size     45
proof            (modus-ponens tm-351 tm-754 ((A (-> (or (and Am Bm) Am) Cm)) (Dm (-> B (and (-> (or (and Am Bm) Am) Cm) B))) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (-> B (and (-> (or (and Am Bm) Am) Cm) B))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63134.        ((A or ((((B and C) or B) -> D) -> (E -> ((((B and C) or B) -> D) and E)))) -> (((B -> D) or (((B and C) or B) -> D)) -> (E -> ((((B and C) or B) -> D) and E)))), M:tm-351, m:tm-754, u:((A (-> (or (and Am Bm) Am) Cm)) (Dm (-> B (and (-> (or (and Am Bm) Am) Cm) B))) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (-> B (and (-> (or (and Am Bm) Am) Cm) B)))))
================================================================
tm-name          tm-63135
in-theory        63135
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (E -> (F -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-341 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63135.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63136
in-theory        63136
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-338 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63136.        (((A -> B) -> (A -> (A and B))) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F))), M:tm-338, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63137
in-theory        63137
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) or ((((A and B) or A) -> C) -> ((((A and B) or A) -> C) and D))) -> (((A -> C) or (((A and B) or A) -> C)) -> ((((A and B) or A) -> C) and D)))
theorem-size     49
proof            (modus-ponens tm-335 tm-754 ((A (-> (or (and Am Bm) Am) Cm)) (Dm (and (-> (or (and Am Bm) Am) Cm) B)) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (and (-> (or (and Am Bm) Am) Cm) B)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63137.        ((((((A and B) or A) -> C) -> D) or ((((A and B) or A) -> C) -> ((((A and B) or A) -> C) and D))) -> (((A -> C) or (((A and B) or A) -> C)) -> ((((A and B) or A) -> C) and D))), M:tm-335, m:tm-754, u:((A (-> (or (and Am Bm) Am) Cm)) (Dm (and (-> (or (and Am Bm) Am) Cm) B)) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (and (-> (or (and Am Bm) Am) Cm) B))))
================================================================
tm-name          tm-63138
in-theory        63138
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((((A and B) or A) -> C) -> D) -> (((((A and B) or A) -> C) -> D) and (((A -> C) or (((A and B) or A) -> C)) -> D))))
theorem-size     57
proof            (modus-ponens tm-328 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63138.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((((A and B) or A) -> C) -> D) -> (((((A and B) or A) -> C) -> D) and (((A -> C) or (((A and B) or A) -> C)) -> D)))), M:tm-328, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63139
in-theory        63139
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((E -> (F -> (E and F))) and (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D))))
theorem-size     55
proof            (modus-ponens tm-327 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63139.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((E -> (F -> (E and F))) and (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)))), M:tm-327, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63140
in-theory        63140
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((E and F) -> F) and (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-326 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63140.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((E and F) -> F) and (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)))), M:tm-326, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63141
in-theory        63141
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((E and F) -> E) and (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-325 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63141.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((E and F) -> E) and (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)))), M:tm-325, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63142
in-theory        63142
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D))))
theorem-size     61
proof            (modus-ponens tm-324 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63142.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)))), M:tm-324, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63143
in-theory        63143
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((E -> (F -> E)) and (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D))))
theorem-size     53
proof            (modus-ponens tm-323 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63143.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((E -> (F -> E)) and (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)))), M:tm-323, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63144
in-theory        63144
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((E and F) -> F))
theorem-size     29
proof            (modus-ponens tm-322 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63144.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63145
in-theory        63145
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((E and F) -> E))
theorem-size     29
proof            (modus-ponens tm-320 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63145.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63146
in-theory        63146
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-318 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63146.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63147
in-theory        63147
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((((A and B) or A) -> C) -> D) -> ((((A and B) or A) -> C) -> D)))
theorem-size     43
proof            (modus-ponens tm-316 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63147.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((((A and B) or A) -> C) -> D) -> ((((A and B) or A) -> C) -> D))), M:tm-316, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63148
in-theory        63148
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (E -> (F -> E)))
theorem-size     29
proof            (modus-ponens tm-315 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63148.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63149
in-theory        63149
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((((((A and B) or A) -> C) -> D) -> (not (((A -> C) or (((A and B) or A) -> C)) -> D))) -> (not ((((A and B) or A) -> C) -> D))))
theorem-size     59
proof            (modus-ponens tm-313 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63149.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((((((A and B) or A) -> C) -> D) -> (not (((A -> C) or (((A and B) or A) -> C)) -> D))) -> (not ((((A and B) or A) -> C) -> D)))), M:tm-313, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63150
in-theory        63150
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((((A -> C) or (((A and B) or A) -> C)) -> D) -> E) -> ((((((A and B) or A) -> C) -> D) or (((A -> C) or (((A and B) or A) -> C)) -> D)) -> E)))
theorem-size     65
proof            (modus-ponens tm-312 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63150.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (((((A -> C) or (((A and B) or A) -> C)) -> D) -> E) -> ((((((A and B) or A) -> C) -> D) or (((A -> C) or (((A and B) or A) -> C)) -> D)) -> E))), M:tm-312, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63151
in-theory        63151
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (E or (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-311 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63151.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (E or (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)))), M:tm-311, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63152
in-theory        63152
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) or E))
theorem-size     49
proof            (modus-ponens tm-310 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63152.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) or E)), M:tm-310, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63153
in-theory        63153
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (E -> ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and E)))
theorem-size     51
proof            (modus-ponens tm-309 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63153.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (E -> ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and E))), M:tm-309, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63154
in-theory        63154
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((((((A and B) or A) -> C) -> D) -> ((A -> C) or (((A and B) or A) -> C))) -> (((((A and B) or A) -> C) -> D) -> D)))
theorem-size     57
proof            (modus-ponens tm-306 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63154.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and ((((((A and B) or A) -> C) -> D) -> ((A -> C) or (((A and B) or A) -> C))) -> (((((A and B) or A) -> C) -> D) -> D))), M:tm-306, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm))) (C Dm))
================================================================
tm-name          tm-63155
in-theory        63155
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (E -> (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D))))
theorem-size     49
proof            (modus-ponens tm-305 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63155.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) and (E -> (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)))), M:tm-305, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63156
in-theory        63156
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-303 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63156.        ((A -> ((B -> (C -> (B and C))) and A)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-303, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63157
in-theory        63157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-270 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63157.        ((A -> (((B and C) -> C) and A)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-270, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63158
in-theory        63158
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-239 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63158.        ((A -> (((B and C) -> B) and A)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-239, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63159
in-theory        63159
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E and F) or E) -> G) -> H) -> (((E -> G) or (((E and F) or E) -> G)) -> H)))
theorem-size     41
proof            (modus-ponens tm-210 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63159.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((((E and F) or E) -> G) -> H) -> (((E -> G) or (((E and F) or E) -> G)) -> H))), M:tm-210, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63160
in-theory        63160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-183 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63160.        ((A -> ((B -> (C -> B)) and A)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-183, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63161
in-theory        63161
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-157 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63161.        ((A -> ((B and C) -> C)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-157, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63162
in-theory        63162
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-147 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63162.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-147, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63163
in-theory        63163
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-134 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63163.        ((A -> ((B and C) -> B)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-134, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63164
in-theory        63164
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-125 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63164.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-125, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63165
in-theory        63165
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> (D -> E)) -> ((((A -> C) or (((A and B) or A) -> C)) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> E)))
theorem-size     39
proof            (modus-ponens tm-114 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) (-> C D))) (B (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63165.        (((((A and B) or A) -> C) -> (D -> E)) -> ((((A -> C) or (((A and B) or A) -> C)) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> E))), M:tm-114, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) (-> C D))) (B (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm))) (Dm (-> C D)))
================================================================
tm-name          tm-63166
in-theory        63166
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) or E) -> G) -> H) -> (((E -> G) or (((E and F) or E) -> G)) -> H)))
theorem-size     39
proof            (modus-ponens tm-113 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63166.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((((E and F) or E) -> G) -> H) -> (((E -> G) or (((E and F) or E) -> G)) -> H))), M:tm-113, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63167
in-theory        63167
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) or B) -> (D -> E)) -> ((((B and C) or B) -> D) -> (((B and C) or B) -> E)))) -> (((B -> (D -> E)) or (((B and C) or B) -> (D -> E))) -> ((((B and C) or B) -> D) -> (((B and C) or B) -> E))))
theorem-size     59
proof            (modus-ponens tm-110 tm-754 ((A (or (and Am Bm) Am)) (Cm (-> B C)) (Dm (-> (-> (or (and Am Bm) Am) B) (-> (or (and Am Bm) Am) C))) (D (-> (or (-> Am (-> B C)) (-> (or (and Am Bm) Am) (-> B C))) (-> (-> (or (and Am Bm) Am) B) (-> (or (and Am Bm) Am) C))))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       203
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63167.        ((A or ((((B and C) or B) -> (D -> E)) -> ((((B and C) or B) -> D) -> (((B and C) or B) -> E)))) -> (((B -> (D -> E)) or (((B and C) or B) -> (D -> E))) -> ((((B and C) or B) -> D) -> (((B and C) or B) -> E)))), M:tm-110, m:tm-754, u:((A (or (and Am Bm) Am)) (Cm (-> B C)) (Dm (-> (-> (or (and Am Bm) Am) B) (-> (or (and Am Bm) Am) C))) (D (-> (or (-> Am (-> B C)) (-> (or (and Am Bm) Am) (-> B C))) (-> (-> (or (and Am Bm) Am) B) (-> (or (and Am Bm) Am) C)))))
================================================================
tm-name          tm-63168
in-theory        63168
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     43
proof            (modus-ponens tm-105 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63168.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-105, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63169
in-theory        63169
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> (C -> D)) -> (((A and B) or A) -> C)) or ((((A and B) or A) -> (C -> D)) -> (((A and B) or A) -> D))) -> (((A -> (C -> D)) or (((A and B) or A) -> (C -> D))) -> (((A and B) or A) -> D)))
theorem-size     59
proof            (modus-ponens tm-102 tm-754 ((A (or (and Am Bm) Am)) (Cm (-> B C)) (Dm (-> (or (and Am Bm) Am) C)) (D (-> (or (-> Am (-> B C)) (-> (or (and Am Bm) Am) (-> B C))) (-> (or (and Am Bm) Am) C)))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       215
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63169.        ((((((A and B) or A) -> (C -> D)) -> (((A and B) or A) -> C)) or ((((A and B) or A) -> (C -> D)) -> (((A and B) or A) -> D))) -> (((A -> (C -> D)) or (((A and B) or A) -> (C -> D))) -> (((A and B) or A) -> D))), M:tm-102, m:tm-754, u:((A (or (and Am Bm) Am)) (Cm (-> B C)) (Dm (-> (or (and Am Bm) Am) C)) (D (-> (or (-> Am (-> B C)) (-> (or (and Am Bm) Am) (-> B C))) (-> (or (and Am Bm) Am) C))))
================================================================
tm-name          tm-63170
in-theory        63170
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-95 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63170.        (((A -> B) -> (A -> A)) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F))), M:tm-95, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63171
in-theory        63171
times-derived    1
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) or ((((A and B) or A) -> C) -> (((A and B) or A) -> C))) -> (((A -> C) or (((A and B) or A) -> C)) -> (((A and B) or A) -> C)))
theorem-size     45
proof            (modus-ponens tm-92 tm-754 ((Dm (-> (or (and Am Bm) Am) Cm)) (A (-> (or (and Am Bm) Am) Cm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (-> (or (and Am Bm) Am) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63171.        ((((((A and B) or A) -> C) -> D) or ((((A and B) or A) -> C) -> (((A and B) or A) -> C))) -> (((A -> C) or (((A and B) or A) -> C)) -> (((A and B) or A) -> C))), M:tm-92, m:tm-754, u:((Dm (-> (or (and Am Bm) Am) Cm)) (A (-> (or (and Am Bm) Am) Cm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (-> (or (and Am Bm) Am) Cm))))
================================================================
tm-name          tm-63172
in-theory        63172
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> D) -> (E -> (((A -> C) or (((A and B) or A) -> C)) -> D)))
theorem-size     25
proof            (modus-ponens tm-84 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63172.        (((((A and B) or A) -> C) -> D) -> (E -> (((A -> C) or (((A and B) or A) -> C)) -> D))), M:tm-84, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63173
in-theory        63173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-83 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63173.        ((A -> (B -> (C -> B))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-83, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63174
in-theory        63174
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((((B and C) or B) -> D) -> (E -> (((B and C) or B) -> D)))) -> (((B -> D) or (((B and C) or B) -> D)) -> (E -> (((B and C) or B) -> D))))
theorem-size     41
proof            (modus-ponens tm-80 tm-754 ((A (-> (or (and Am Bm) Am) Cm)) (Dm (-> B (-> (or (and Am Bm) Am) Cm))) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (-> B (-> (or (and Am Bm) Am) Cm))))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63174.        ((A or ((((B and C) or B) -> D) -> (E -> (((B and C) or B) -> D)))) -> (((B -> D) or (((B and C) or B) -> D)) -> (E -> (((B and C) or B) -> D)))), M:tm-80, m:tm-754, u:((A (-> (or (and Am Bm) Am) Cm)) (Dm (-> B (-> (or (and Am Bm) Am) Cm))) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (-> B (-> (or (and Am Bm) Am) Cm)))))
================================================================
tm-name          tm-63175
in-theory        63175
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((((B and C) or B) -> D) -> E) -> (((B -> D) or (((B and C) or B) -> D)) -> E)))
theorem-size     29
proof            (modus-ponens tm-76 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63175.        (((not (not A)) -> A) and (((((B and C) or B) -> D) -> E) -> (((B -> D) or (((B and C) or B) -> D)) -> E))), M:tm-76, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63176
in-theory        63176
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((((A and B) or A) -> C) -> D))) or ((((A and B) or A) -> C) -> D)) -> (((A -> C) or (((A and B) or A) -> C)) -> D))
theorem-size     35
proof            (modus-ponens tm-73 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-8 tm-10 tm-3)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63176.        (((not (not ((((A and B) or A) -> C) -> D))) or ((((A and B) or A) -> C) -> D)) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-73, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63177
in-theory        63177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F)))
theorem-size     35
proof            (modus-ponens tm-69 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63177.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F))), M:tm-69, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63178
in-theory        63178
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) or ((((A and B) or A) -> (not C)) -> (not ((A and B) or A)))) -> (((A -> (not C)) or (((A and B) or A) -> (not C))) -> (not ((A and B) or A))))
theorem-size     44
proof            (modus-ponens tm-66 tm-754 ((A (or (and Am Bm) Am)) (Cm (not B)) (Dm (not (or (and Am Bm) Am))) (C (-> (or (-> Am (not B)) (-> (or (and Am Bm) Am) (not B))) (not (or (and Am Bm) Am))))))
axioms-used      (tm-8 tm-9 tm-3)
proof-size       156
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63178.        (((((A and B) or A) -> C) or ((((A and B) or A) -> (not C)) -> (not ((A and B) or A)))) -> (((A -> (not C)) or (((A and B) or A) -> (not C))) -> (not ((A and B) or A)))), M:tm-66, m:tm-754, u:((A (or (and Am Bm) Am)) (Cm (not B)) (Dm (not (or (and Am Bm) Am))) (C (-> (or (-> Am (not B)) (-> (or (and Am Bm) Am) (not B))) (not (or (and Am Bm) Am)))))
================================================================
tm-name          tm-63179
in-theory        63179
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> ((A -> C) or (((A and B) or A) -> C))) -> (((((A and B) or A) -> C) or ((A -> C) or (((A and B) or A) -> C))) -> ((A -> C) or (((A and B) or A) -> C))))
theorem-size     51
proof            (modus-ponens tm-55 tm-754 ((A (-> (or (and Am Bm) Am) Cm)) (Dm (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm))) (B (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm))) (C (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)))))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       159
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63179.        (((((A and B) or A) -> C) -> ((A -> C) or (((A and B) or A) -> C))) -> (((((A and B) or A) -> C) or ((A -> C) or (((A and B) or A) -> C))) -> ((A -> C) or (((A and B) or A) -> C)))), M:tm-55, m:tm-754, u:((A (-> (or (and Am Bm) Am) Cm)) (Dm (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm))) (B (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm))) (C (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm))))
================================================================
tm-name          tm-63180
in-theory        63180
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-54 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63180.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-54, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63181
in-theory        63181
times-derived    2
----------------------------------------------------------------
theorem          (((A -> ((B and C) or B)) or ((((B and C) or B) -> D) -> ((A or ((B and C) or B)) -> D))) -> (((B -> D) or (((B and C) or B) -> D)) -> ((A or ((B and C) or B)) -> D)))
theorem-size     47
proof            (modus-ponens tm-51 tm-754 ((A (or (and Am Bm) Am)) (B Cm) (Dm (-> (or C (or (and Am Bm) Am)) Cm)) (D (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (-> (or C (or (and Am Bm) Am)) Cm)))))
axioms-used      (tm-8 tm-3)
proof-size       165
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63181.        (((A -> ((B and C) or B)) or ((((B and C) or B) -> D) -> ((A or ((B and C) or B)) -> D))) -> (((B -> D) or (((B and C) or B) -> D)) -> ((A or ((B and C) or B)) -> D))), M:tm-51, m:tm-754, u:((A (or (and Am Bm) Am)) (B Cm) (Dm (-> (or C (or (and Am Bm) Am)) Cm)) (D (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (-> (or C (or (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-63182
in-theory        63182
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B and C) or B) -> D) -> (A and (((B and C) or B) -> D)))) -> (((B -> D) or (((B and C) or B) -> D)) -> (A and (((B and C) or B) -> D))))
theorem-size     41
proof            (modus-ponens tm-48 tm-754 ((A (-> (or (and Am Bm) Am) Cm)) (Dm (and B (-> (or (and Am Bm) Am) Cm))) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (and B (-> (or (and Am Bm) Am) Cm))))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63182.        ((A or ((((B and C) or B) -> D) -> (A and (((B and C) or B) -> D)))) -> (((B -> D) or (((B and C) or B) -> D)) -> (A and (((B and C) or B) -> D)))), M:tm-48, m:tm-754, u:((A (-> (or (and Am Bm) Am) Cm)) (Dm (and B (-> (or (and Am Bm) Am) Cm))) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (and B (-> (or (and Am Bm) Am) Cm)))))
================================================================
tm-name          tm-63183
in-theory        63183
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((((B and C) or B) -> D) -> E)) or ((((B and C) or B) -> D) -> E)) -> (((B -> D) or (((B and C) or B) -> D)) -> E))
theorem-size     35
proof            (modus-ponens tm-47 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-8 tm-4 tm-3)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63183.        (((A and ((((B and C) or B) -> D) -> E)) or ((((B and C) or B) -> D) -> E)) -> (((B -> D) or (((B and C) or B) -> D)) -> E)), M:tm-47, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63184
in-theory        63184
times-derived    2
----------------------------------------------------------------
theorem          (((((((A and B) or A) -> C) -> D) and E) or ((((A and B) or A) -> C) -> D)) -> (((A -> C) or (((A and B) or A) -> C)) -> D))
theorem-size     35
proof            (modus-ponens tm-46 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-8 tm-3)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63184.        (((((((A and B) or A) -> C) -> D) and E) or ((((A and B) or A) -> C) -> D)) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-46, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63185
in-theory        63185
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) or A) -> (C -> D)) or ((((A and B) or A) -> C) -> (((A and B) or A) -> D))) -> (((A -> C) or (((A and B) or A) -> C)) -> (((A and B) or A) -> D)))
theorem-size     45
proof            (modus-ponens tm-45 tm-754 ((A (or (and Am Bm) Am)) (B Cm) (Dm (-> (or (and Am Bm) Am) C)) (D (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (-> (or (and Am Bm) Am) C)))))
axioms-used      (tm-8 tm-2 tm-3)
proof-size       161
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63185.        (((((A and B) or A) -> (C -> D)) or ((((A and B) or A) -> C) -> (((A and B) or A) -> D))) -> (((A -> C) or (((A and B) or A) -> C)) -> (((A and B) or A) -> D))), M:tm-45, m:tm-754, u:((A (or (and Am Bm) Am)) (B Cm) (Dm (-> (or (and Am Bm) Am) C)) (D (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) (-> (or (and Am Bm) Am) C))))
================================================================
tm-name          tm-63186
in-theory        63186
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((((B and C) or B) -> D) -> A)) -> (((B -> D) or (((B and C) or B) -> D)) -> A))
theorem-size     25
proof            (modus-ponens tm-44 tm-754 ((A (-> (or (and Am Bm) Am) Cm)) (B Dm) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63186.        ((A or ((((B and C) or B) -> D) -> A)) -> (((B -> D) or (((B and C) or B) -> D)) -> A)), M:tm-44, m:tm-754, u:((A (-> (or (and Am Bm) Am) Cm)) (B Dm) (C (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63187
in-theory        63187
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-42 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63187.        ((A -> (B or A)) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F))), M:tm-42, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63188
in-theory        63188
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-32 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63188.        ((A -> (A or B)) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F))), M:tm-32, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63189
in-theory        63189
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> D) -> (((((A and B) or A) -> C) -> D) and (((A -> C) or (((A and B) or A) -> C)) -> D)))
theorem-size     33
proof            (modus-ponens tm-24 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63189.        (((((A and B) or A) -> C) -> D) -> (((((A and B) or A) -> C) -> D) and (((A -> C) or (((A and B) or A) -> C)) -> D))), M:tm-24, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63190
in-theory        63190
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F)))
theorem-size     31
proof            (modus-ponens tm-23 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63190.        ((A -> (B -> (A and B))) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F))), M:tm-23, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63191
in-theory        63191
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-22 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63191.        (((A and B) -> B) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F))), M:tm-22, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63192
in-theory        63192
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-21 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63192.        (((A and B) -> A) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F))), M:tm-21, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63193
in-theory        63193
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-20 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63193.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-20, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63194
in-theory        63194
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-19 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63194.        ((A -> (B -> A)) and (((((C and D) or C) -> E) -> F) -> (((C -> E) or (((C and D) or C) -> E)) -> F))), M:tm-19, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63195
in-theory        63195
times-derived    2
----------------------------------------------------------------
theorem          (((((A and B) or A) -> C) -> D) -> ((((A and B) or A) -> C) -> D))
theorem-size     19
proof            (modus-ponens tm-12 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63195.        (((((A and B) or A) -> C) -> D) -> ((((A and B) or A) -> C) -> D)), M:tm-12, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63196
in-theory        63196
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (not (((A -> C) or (((A and B) or A) -> C)) -> D))) -> (not ((((A and B) or A) -> C) -> D)))
theorem-size     35
proof            (modus-ponens tm-9 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-9 tm-8 tm-3)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63196.        ((((((A and B) or A) -> C) -> D) -> (not (((A -> C) or (((A and B) or A) -> C)) -> D))) -> (not ((((A and B) or A) -> C) -> D))), M:tm-9, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63197
in-theory        63197
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) or (((A and C) or A) -> B)) -> D) -> E) -> ((((((A and C) or A) -> B) -> D) or (((A -> B) or (((A and C) or A) -> B)) -> D)) -> E))
theorem-size     41
proof            (modus-ponens tm-8 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
axioms-used      (tm-8 tm-3)
proof-size       119
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63197.        (((((A -> B) or (((A and C) or A) -> B)) -> D) -> E) -> ((((((A and C) or A) -> B) -> D) or (((A -> B) or (((A and C) or A) -> B)) -> D)) -> E)), M:tm-8, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))
================================================================
tm-name          tm-63198
in-theory        63198
times-derived    2
----------------------------------------------------------------
theorem          (A or (((((B and C) or B) -> D) -> E) -> (((B -> D) or (((B and C) or B) -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-7 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-3)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63198.        (A or (((((B and C) or B) -> D) -> E) -> (((B -> D) or (((B and C) or B) -> D)) -> E))), M:tm-7, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63199
in-theory        63199
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) or E)
theorem-size     25
proof            (modus-ponens tm-6 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-3)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63199.        ((((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)) or E), M:tm-6, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63200
in-theory        63200
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((((B and C) or B) -> D) -> E) -> (((B -> D) or (((B and C) or B) -> D)) -> E)) and A))
theorem-size     27
proof            (modus-ponens tm-5 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63200.        (A -> ((((((B and C) or B) -> D) -> E) -> (((B -> D) or (((B and C) or B) -> D)) -> E)) and A)), M:tm-5, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63201
in-theory        63201
times-derived    2
----------------------------------------------------------------
theorem          ((((((A and B) or A) -> C) -> D) -> ((A -> C) or (((A and B) or A) -> C))) -> (((((A and B) or A) -> C) -> D) -> D))
theorem-size     33
proof            (modus-ponens tm-2 tm-754 ((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-3)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63201.        ((((((A and B) or A) -> C) -> D) -> ((A -> C) or (((A and B) or A) -> C))) -> (((((A and B) or A) -> C) -> D) -> D)), M:tm-2, m:tm-754, u:((A (-> (-> (or (and Am Bm) Am) Cm) Dm)) (B (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm))) (C Dm))
================================================================
tm-name          tm-63202
in-theory        63202
times-derived    2
----------------------------------------------------------------
theorem          (A -> (((((B and C) or B) -> D) -> E) -> (((B -> D) or (((B and C) or B) -> D)) -> E)))
theorem-size     25
proof            (modus-ponens tm-1 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-3)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-63202.        (A -> (((((B and C) or B) -> D) -> E) -> (((B -> D) or (((B and C) or B) -> D)) -> E))), M:tm-1, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63203
in-theory        63203
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-7 tm-3)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63203.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E or ((F -> G) -> (((F and H) or F) -> G)))), M:tm-708, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63204
in-theory        63204
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-7 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63204.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-665, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63205
in-theory        63205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63205.        ((A -> (B -> (C or B))) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-622, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63206
in-theory        63206
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63206.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and (E -> (F or E))), M:tm-609, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63207
in-theory        63207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63207.        ((A -> ((B -> (C or B)) and A)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-605, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63208
in-theory        63208
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F or E)) and (A or ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63208.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F or E)) and (A or ((B -> C) -> (((B and D) or B) -> C))))), M:tm-595, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63209
in-theory        63209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63209.        (((A -> (B or A)) or C) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-550, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63210
in-theory        63210
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63210.        ((A or (B -> (C or B))) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-540, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63211
in-theory        63211
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63211.        ((A or (B -> (B or C))) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-530, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63212
in-theory        63212
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63212.        ((A or (B -> (C -> (B and C)))) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-520, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63213
in-theory        63213
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63213.        ((A or ((B and C) -> C)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-510, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63214
in-theory        63214
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63214.        ((A or ((B and C) -> B)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-500, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63215
in-theory        63215
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63215.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (((F and H) or F) -> G)))), M:tm-490, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63216
in-theory        63216
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63216.        ((A or (B -> (C -> B))) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-480, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63217
in-theory        63217
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63217.        ((A -> (B -> (B or C))) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-469, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63218
in-theory        63218
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-7 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63218.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and (E -> (E or F))), M:tm-456, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63219
in-theory        63219
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63219.        ((A -> ((B -> (B or C)) and A)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-453, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63220
in-theory        63220
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (E or F)) and (A or ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63220.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (E or F)) and (A or ((B -> C) -> (((B and D) or B) -> C))))), M:tm-443, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63221
in-theory        63221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63221.        (((A -> (A or B)) or C) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-409, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63222
in-theory        63222
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63222.        (((A -> (B -> (A and B))) or C) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-400, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63223
in-theory        63223
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63223.        ((((A and B) -> B) or C) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-391, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63224
in-theory        63224
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-7 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63224.        ((((A and B) -> A) or C) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-382, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63225
in-theory        63225
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63225.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E or ((F -> G) -> (((F and H) or F) -> G)))), M:tm-373, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63226
in-theory        63226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63226.        (((A -> (B -> A)) or C) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-364, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63227
in-theory        63227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63227.        ((A -> (B -> (C -> (B and C)))) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-354, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63228
in-theory        63228
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63228.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63229
in-theory        63229
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C or ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63229.        (((A -> B) -> (A -> (A and B))) and (C or ((D -> E) -> (((D and F) or D) -> E)))), M:tm-338, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63230
in-theory        63230
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F -> (E and F))) and (A or ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63230.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F -> (E and F))) and (A or ((B -> C) -> (((B and D) or B) -> C))))), M:tm-327, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63231
in-theory        63231
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and (((E and F) -> F) and (A or ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-7 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63231.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and (((E and F) -> F) and (A or ((B -> C) -> (((B and D) or B) -> C))))), M:tm-326, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63232
in-theory        63232
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and (((E and F) -> E) and (A or ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-7 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63232.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and (((E and F) -> E) and (A or ((B -> C) -> (((B and D) or B) -> C))))), M:tm-325, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63233
in-theory        63233
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63233.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A or ((B -> C) -> (((B and D) or B) -> C))))), M:tm-324, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63234
in-theory        63234
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F -> E)) and (A or ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63234.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F -> E)) and (A or ((B -> C) -> (((B and D) or B) -> C))))), M:tm-323, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63235
in-theory        63235
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-7 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63235.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((E and F) -> F)), M:tm-322, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63236
in-theory        63236
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63236.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((E and F) -> E)), M:tm-320, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63237
in-theory        63237
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63237.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63238
in-theory        63238
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63238.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and (E -> (F -> E))), M:tm-315, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63239
in-theory        63239
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and (E or (A or ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63239.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and (E or (A or ((B -> C) -> (((B and D) or B) -> C))))), M:tm-311, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63240
in-theory        63240
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((A or ((B -> C) -> (((B and D) or B) -> C))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63240.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and ((A or ((B -> C) -> (((B and D) or B) -> C))) or E)), M:tm-310, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63241
in-theory        63241
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and (E -> ((A or ((B -> C) -> (((B and D) or B) -> C))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63241.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and (E -> ((A or ((B -> C) -> (((B and D) or B) -> C))) and E))), M:tm-309, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63242
in-theory        63242
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) and (E -> (A or ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63242.        ((A or ((B -> C) -> (((B and D) or B) -> C))) and (E -> (A or ((B -> C) -> (((B and D) or B) -> C))))), M:tm-305, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63243
in-theory        63243
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63243.        ((A -> ((B -> (C -> (B and C))) and A)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-303, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63244
in-theory        63244
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63244.        ((A -> (((B and C) -> C) and A)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-270, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63245
in-theory        63245
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63245.        ((A -> (((B and C) -> B) and A)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-239, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63246
in-theory        63246
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63246.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E or ((F -> G) -> (((F and H) or F) -> G)))), M:tm-210, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63247
in-theory        63247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63247.        ((A -> ((B -> (C -> B)) and A)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-183, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63248
in-theory        63248
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63248.        ((A -> ((B and C) -> C)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-157, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63249
in-theory        63249
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63249.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-147, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63250
in-theory        63250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-7 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63250.        ((A -> ((B and C) -> B)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-134, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63251
in-theory        63251
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-7 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63251.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-125, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63252
in-theory        63252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-7 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63252.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E or ((F -> G) -> (((F and H) or F) -> G)))), M:tm-113, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63253
in-theory        63253
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63253.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-105, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63254
in-theory        63254
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C or ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63254.        (((A -> B) -> (A -> A)) and (C or ((D -> E) -> (((D and F) or D) -> E)))), M:tm-95, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63255
in-theory        63255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63255.        ((A -> (B -> (C -> B))) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-83, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63256
in-theory        63256
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B or ((C -> D) -> (((C and E) or C) -> D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-10 tm-7 tm-8 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63256.        (((not (not A)) -> A) and (B or ((C -> D) -> (((C and E) or C) -> D)))), M:tm-76, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63257
in-theory        63257
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-7 tm-8 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63257.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C or ((D -> E) -> (((D and F) or D) -> E)))), M:tm-69, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63258
in-theory        63258
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-7 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63258.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-54, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63259
in-theory        63259
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C or ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-42 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63259.        ((A -> (B or A)) and (C or ((D -> E) -> (((D and F) or D) -> E)))), M:tm-42, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63260
in-theory        63260
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C or ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-32 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63260.        ((A -> (A or B)) and (C or ((D -> E) -> (((D and F) or D) -> E)))), M:tm-32, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63261
in-theory        63261
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C or ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-23 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63261.        ((A -> (B -> (A and B))) and (C or ((D -> E) -> (((D and F) or D) -> E)))), M:tm-23, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63262
in-theory        63262
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C or ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-22 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-7 tm-8 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63262.        (((A and B) -> B) and (C or ((D -> E) -> (((D and F) or D) -> E)))), M:tm-22, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63263
in-theory        63263
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C or ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-21 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-7 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63263.        (((A and B) -> A) and (C or ((D -> E) -> (((D and F) or D) -> E)))), M:tm-21, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63264
in-theory        63264
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-20 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-7 tm-8 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63264.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-20, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63265
in-theory        63265
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C or ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-19 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63265.        ((A -> (B -> A)) and (C or ((D -> E) -> (((D and F) or D) -> E)))), M:tm-19, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63266
in-theory        63266
times-derived    2
----------------------------------------------------------------
theorem          (A or (B or ((C -> D) -> (((C and E) or C) -> D))))
theorem-size     15
proof            (modus-ponens tm-7 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-7 tm-8 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63266.        (A or (B or ((C -> D) -> (((C and E) or C) -> D)))), M:tm-7, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63267
in-theory        63267
times-derived    2
----------------------------------------------------------------
theorem          ((A or ((B -> C) -> (((B and D) or B) -> C))) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-6 tm-7 tm-8 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63267.        ((A or ((B -> C) -> (((B and D) or B) -> C))) or E), M:tm-6, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63268
in-theory        63268
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B or ((C -> D) -> (((C and E) or C) -> D))) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63268.        (A -> ((B or ((C -> D) -> (((C and E) or C) -> D))) and A)), M:tm-5, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63269
in-theory        63269
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B or ((C -> D) -> (((C and E) or C) -> D))))
theorem-size     15
proof            (modus-ponens tm-1 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-1 tm-7 tm-8 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63269.        (A -> (B or ((C -> D) -> (((C and E) or C) -> D)))), M:tm-1, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-63270
in-theory        63270
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-744 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-3 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63270.        (((A and B) or A) -> ((C -> D) -> (((C and E) or C) -> D))), M:tm-744, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63271
in-theory        63271
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> ((A and C) or A)) and D) or ((A -> B) -> ((A and C) or A))) -> ((A -> B) -> B))
theorem-size     27
proof            (modus-ponens tm-743 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-6)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-6.            (A -> (A or B)), axiom
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63271.        (((((A -> B) -> ((A and C) or A)) and D) or ((A -> B) -> ((A and C) or A))) -> ((A -> B) -> B)), M:tm-743, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63272
in-theory        63272
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (((E and G) or E) -> F)) or H))
theorem-size     39
proof            (modus-ponens tm-708 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-2 tm-6 tm-3)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63272.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> (((E and G) or E) -> F)) or H)), M:tm-708, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63273
in-theory        63273
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-694 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> (-> (-> B C) (-> B D)) (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63273.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-694, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> (-> (-> B C) (-> B D)) (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63274
in-theory        63274
times-derived    2
----------------------------------------------------------------
theorem          ((((A and B) or A) or ((A -> C) -> ((A and B) or A))) -> ((A -> C) -> C))
theorem-size     21
proof            (modus-ponens tm-692 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63274.        ((((A and B) or A) or ((A -> C) -> ((A and B) or A))) -> ((A -> C) -> C)), M:tm-692, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63275
in-theory        63275
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-690 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-7 tm-6 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63275.        ((A -> (B or A)) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D))), M:tm-690, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63276
in-theory        63276
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-688 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63276.        ((A -> (A or B)) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D))), M:tm-688, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63277
in-theory        63277
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((A and C) or A)) -> (((A -> B) -> ((A and C) or A)) and ((A -> B) -> B)))
theorem-size     25
proof            (modus-ponens tm-686 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63277.        (((A -> B) -> ((A and C) or A)) -> (((A -> B) -> ((A and C) or A)) and ((A -> B) -> B))), M:tm-686, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63278
in-theory        63278
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D)))
theorem-size     23
proof            (modus-ponens tm-685 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-3)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63278.        ((A -> (B -> (A and B))) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D))), M:tm-685, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63279
in-theory        63279
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-684 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-4 tm-6 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63279.        (((A and B) -> B) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D))), M:tm-684, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63280
in-theory        63280
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-683 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63280.        (((A and B) -> A) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D))), M:tm-683, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63281
in-theory        63281
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     29
proof            (modus-ponens tm-682 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-3)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63281.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-682, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63282
in-theory        63282
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D)))
theorem-size     21
proof            (modus-ponens tm-681 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-6 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63282.        ((A -> (B -> A)) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D))), M:tm-681, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63283
in-theory        63283
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> ((A and C) or A)))
theorem-size     19
proof            (modus-ponens tm-676 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63283.        (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> ((A and C) or A))), M:tm-676, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63284
in-theory        63284
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> (not ((A -> B) -> B))) -> (not ((A -> B) -> ((A and C) or A))))
theorem-size     27
proof            (modus-ponens tm-674 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-9 tm-6 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63284.        ((((A -> B) -> ((A and C) or A)) -> (not ((A -> B) -> B))) -> (not ((A -> B) -> ((A and C) or A)))), M:tm-674, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63285
in-theory        63285
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> B) -> C) -> ((((A -> B) -> ((A and D) or A)) or ((A -> B) -> B)) -> C))
theorem-size     25
proof            (modus-ponens tm-673 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-6 tm-3)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63285.        ((((A -> B) -> B) -> C) -> ((((A -> B) -> ((A and D) or A)) or ((A -> B) -> B)) -> C)), M:tm-673, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63286
in-theory        63286
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> C) -> ((B and D) or B)) -> ((B -> C) -> C)))
theorem-size     17
proof            (modus-ponens tm-672 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-7 tm-6 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63286.        (A or (((B -> C) -> ((B and D) or B)) -> ((B -> C) -> C))), M:tm-672, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63287
in-theory        63287
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) or D)
theorem-size     17
proof            (modus-ponens tm-671 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-6 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63287.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) or D), M:tm-671, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63288
in-theory        63288
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> ((B and D) or B)) -> ((B -> C) -> C)) and A))
theorem-size     19
proof            (modus-ponens tm-670 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-6 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63288.        (A -> ((((B -> C) -> ((B and D) or B)) -> ((B -> C) -> C)) and A)), M:tm-670, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63289
in-theory        63289
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> (A -> B)) -> (((A -> B) -> ((A and C) or A)) -> B))
theorem-size     25
proof            (modus-ponens tm-669 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-6 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63289.        ((((A -> B) -> ((A and C) or A)) -> (A -> B)) -> (((A -> B) -> ((A and C) or A)) -> B)), M:tm-669, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63290
in-theory        63290
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> ((B and D) or B)) -> ((B -> C) -> C)))
theorem-size     17
proof            (modus-ponens tm-668 tm-756 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-6 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63290.        (A -> (((B -> C) -> ((B and D) or B)) -> ((B -> C) -> C))), M:tm-668, m:tm-756, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm) (Dm (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-63291
in-theory        63291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-665 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-1 tm-6 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63291.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-665, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63292
in-theory        63292
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-651 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> (-> B C) (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63292.        ((A or (B -> A)) -> ((C -> D) -> (((C and E) or C) -> D))), M:tm-651, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> (-> B C) (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63293
in-theory        63293
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-649 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-7 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63293.        ((A -> (B or A)) and (C -> ((D -> E) -> (((D and F) or D) -> E)))), M:tm-649, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63294
in-theory        63294
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-647 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63294.        ((A -> (A or B)) and (C -> ((D -> E) -> (((D and F) or D) -> E)))), M:tm-647, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63295
in-theory        63295
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and ((B -> C) -> (((B and D) or B) -> C))))
theorem-size     15
proof            (modus-ponens tm-645 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63295.        (A -> (A and ((B -> C) -> (((B and D) or B) -> C)))), M:tm-645, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63296
in-theory        63296
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-644 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63296.        ((A -> (B -> (A and B))) and (C -> ((D -> E) -> (((D and F) or D) -> E)))), M:tm-644, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63297
in-theory        63297
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-643 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-4 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63297.        (((A and B) -> B) and (C -> ((D -> E) -> (((D and F) or D) -> E)))), M:tm-643, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63298
in-theory        63298
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-642 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63298.        (((A and B) -> A) and (C -> ((D -> E) -> (((D and F) or D) -> E)))), M:tm-642, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63299
in-theory        63299
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-641 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-2 tm-6 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63299.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-641, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63300
in-theory        63300
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     19
proof            (modus-ponens tm-640 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63300.        ((A -> (B -> A)) and (C -> ((D -> E) -> (((D and F) or D) -> E)))), M:tm-640, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63301
in-theory        63301
times-derived    2
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> (((B and D) or B) -> C)) -> E)) -> E)
theorem-size     17
proof            (modus-ponens tm-638 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> (and B (-> (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) C)) (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-4 tm-6 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63301.        ((A and (((B -> C) -> (((B and D) or B) -> C)) -> E)) -> E), M:tm-638, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> (and B (-> (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) C)) (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63302
in-theory        63302
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (((A and C) or A) -> B)) -> D) and E) -> D)
theorem-size     17
proof            (modus-ponens tm-636 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> (and (-> (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) B) C) (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-3 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63302.        (((((A -> B) -> (((A and C) or A) -> B)) -> D) and E) -> D), M:tm-636, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> (and (-> (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) B) C) (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63303
in-theory        63303
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((((A and C) or A) -> B) -> D)) -> ((A -> B) -> D))
theorem-size     19
proof            (modus-ponens tm-634 tm-756 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)) (Dm (-> (-> (-> Am Bm) (-> (-> (or (and Am Cm) Am) Bm) C)) (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63303.        (((A -> B) -> ((((A and C) or A) -> B) -> D)) -> ((A -> B) -> D)), M:tm-634, m:tm-756, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)) (Dm (-> (-> (-> Am Bm) (-> (-> (or (and Am Cm) Am) Bm) C)) (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63304
in-theory        63304
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not ((B -> C) -> (((B and D) or B) -> C)))) -> (not A))
theorem-size     17
proof            (modus-ponens tm-631 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-9 tm-6 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63304.        ((A -> (not ((B -> C) -> (((B and D) or B) -> C)))) -> (not A)), M:tm-631, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63305
in-theory        63305
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) -> D) -> ((E or ((A -> B) -> (((A and C) or A) -> B))) -> D))
theorem-size     29
proof            (modus-ponens tm-630 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63305.        ((((A -> B) -> (((A and C) or A) -> B)) -> D) -> ((E or ((A -> B) -> (((A and C) or A) -> B))) -> D)), M:tm-630, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63306
in-theory        63306
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> ((C -> D) -> (((C and E) or C) -> D))))
theorem-size     15
proof            (modus-ponens tm-629 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-7 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63306.        (A or (B -> ((C -> D) -> (((C and E) or C) -> D)))), M:tm-629, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63307
in-theory        63307
times-derived    2
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) or E)
theorem-size     15
proof            (modus-ponens tm-628 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63307.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) or E), M:tm-628, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63308
in-theory        63308
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> ((C -> D) -> (((C and E) or C) -> D))) and A))
theorem-size     17
proof            (modus-ponens tm-627 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-5 tm-6 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63308.        (A -> ((B -> ((C -> D) -> (((C and E) or C) -> D))) and A)), M:tm-627, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63309
in-theory        63309
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> (A -> (((B and D) or B) -> C)))
theorem-size     15
proof            (modus-ponens tm-626 tm-756 ((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)) (Dm (-> C (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-2 tm-6 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63309.        ((A -> (B -> C)) -> (A -> (((B and D) or B) -> C))), M:tm-626, m:tm-756, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)) (Dm (-> C (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63310
in-theory        63310
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> ((C -> D) -> (((C and E) or C) -> D))))
theorem-size     15
proof            (modus-ponens tm-625 tm-756 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63310.        (A -> (B -> ((C -> D) -> (((C and E) or C) -> D)))), M:tm-625, m:tm-756, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))) (Dm (-> B (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-63311
in-theory        63311
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-622 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-7 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63311.        ((A -> (B -> (C or B))) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-622, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63312
in-theory        63312
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-6 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63312.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and (E -> (F or E))), M:tm-609, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63313
in-theory        63313
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-605 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63313.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-605, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63314
in-theory        63314
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((E -> (F or E)) and (((A -> B) -> (((A and C) or A) -> B)) or D)))
theorem-size     33
proof            (modus-ponens tm-595 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63314.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((E -> (F or E)) and (((A -> B) -> (((A and C) or A) -> B)) or D))), M:tm-595, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63315
in-theory        63315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-550 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63315.        (((A -> (B or A)) or C) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-550, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63316
in-theory        63316
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-540 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63316.        ((A or (B -> (C or B))) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-540, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63317
in-theory        63317
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-530 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63317.        ((A or (B -> (B or C))) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-530, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63318
in-theory        63318
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-520 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63318.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-520, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63319
in-theory        63319
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-510 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-4 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63319.        ((A or ((B and C) -> C)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-510, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63320
in-theory        63320
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-500 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-3 tm-6 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63320.        ((A or ((B and C) -> B)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-500, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63321
in-theory        63321
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (((E and G) or E) -> F)) or H))
theorem-size     29
proof            (modus-ponens tm-490 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-2 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63321.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (((E and G) or E) -> F)) or H)), M:tm-490, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63322
in-theory        63322
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-480 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-1 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63322.        ((A or (B -> (C -> B))) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-480, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63323
in-theory        63323
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-469 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63323.        ((A -> (B -> (B or C))) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-469, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63324
in-theory        63324
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63324.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and (E -> (E or F))), M:tm-456, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63325
in-theory        63325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-453 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63325.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-453, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63326
in-theory        63326
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((E -> (E or F)) and (((A -> B) -> (((A and C) or A) -> B)) or D)))
theorem-size     33
proof            (modus-ponens tm-443 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63326.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((E -> (E or F)) and (((A -> B) -> (((A and C) or A) -> B)) or D))), M:tm-443, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63327
in-theory        63327
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-409 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63327.        (((A -> (A or B)) or C) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-409, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63328
in-theory        63328
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-400 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63328.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-400, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63329
in-theory        63329
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-391 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63329.        ((((A and B) -> B) or C) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-391, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63330
in-theory        63330
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-382 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63330.        ((((A and B) -> A) or C) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-382, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63331
in-theory        63331
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (((E and G) or E) -> F)) or H))
theorem-size     29
proof            (modus-ponens tm-373 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63331.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> (((E and G) or E) -> F)) or H)), M:tm-373, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63332
in-theory        63332
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-364 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63332.        (((A -> (B -> A)) or C) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-364, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63333
in-theory        63333
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-354 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63333.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-354, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63334
in-theory        63334
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63334.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and (E -> (F -> (E and F)))), M:tm-341, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63335
in-theory        63335
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (((C and E) or C) -> D)) or F))
theorem-size     23
proof            (modus-ponens tm-338 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63335.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> (((C and E) or C) -> D)) or F)), M:tm-338, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63336
in-theory        63336
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((E -> (F -> (E and F))) and (((A -> B) -> (((A and C) or A) -> B)) or D)))
theorem-size     35
proof            (modus-ponens tm-327 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63336.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((E -> (F -> (E and F))) and (((A -> B) -> (((A and C) or A) -> B)) or D))), M:tm-327, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63337
in-theory        63337
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and (((E and F) -> F) and (((A -> B) -> (((A and C) or A) -> B)) or D)))
theorem-size     33
proof            (modus-ponens tm-326 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-4 tm-6 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63337.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and (((E and F) -> F) and (((A -> B) -> (((A and C) or A) -> B)) or D))), M:tm-326, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63338
in-theory        63338
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and (((E and F) -> E) and (((A -> B) -> (((A and C) or A) -> B)) or D)))
theorem-size     33
proof            (modus-ponens tm-325 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-3 tm-6 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63338.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and (((E and F) -> E) and (((A -> B) -> (((A and C) or A) -> B)) or D))), M:tm-325, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63339
in-theory        63339
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) -> (((A and C) or A) -> B)) or D)))
theorem-size     41
proof            (modus-ponens tm-324 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63339.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A -> B) -> (((A and C) or A) -> B)) or D))), M:tm-324, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63340
in-theory        63340
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((E -> (F -> E)) and (((A -> B) -> (((A and C) or A) -> B)) or D)))
theorem-size     33
proof            (modus-ponens tm-323 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63340.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((E -> (F -> E)) and (((A -> B) -> (((A and C) or A) -> B)) or D))), M:tm-323, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63341
in-theory        63341
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-6 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63341.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((E and F) -> F)), M:tm-322, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63342
in-theory        63342
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63342.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((E and F) -> E)), M:tm-320, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63343
in-theory        63343
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63343.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63344
in-theory        63344
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63344.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and (E -> (F -> E))), M:tm-315, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63345
in-theory        63345
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and (E or (((A -> B) -> (((A and C) or A) -> B)) or D)))
theorem-size     29
proof            (modus-ponens tm-311 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63345.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and (E or (((A -> B) -> (((A and C) or A) -> B)) or D))), M:tm-311, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63346
in-theory        63346
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((((A -> B) -> (((A and C) or A) -> B)) or D) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63346.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and ((((A -> B) -> (((A and C) or A) -> B)) or D) or E)), M:tm-310, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63347
in-theory        63347
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and (E -> ((((A -> B) -> (((A and C) or A) -> B)) or D) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63347.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and (E -> ((((A -> B) -> (((A and C) or A) -> B)) or D) and E))), M:tm-309, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63348
in-theory        63348
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) and (E -> (((A -> B) -> (((A and C) or A) -> B)) or D)))
theorem-size     29
proof            (modus-ponens tm-305 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63348.        ((((A -> B) -> (((A and C) or A) -> B)) or D) and (E -> (((A -> B) -> (((A and C) or A) -> B)) or D))), M:tm-305, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63349
in-theory        63349
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-303 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63349.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-303, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63350
in-theory        63350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-270 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63350.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-270, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63351
in-theory        63351
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-239 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63351.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-239, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63352
in-theory        63352
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (((E and G) or E) -> F)) or H))
theorem-size     31
proof            (modus-ponens tm-210 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63352.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> (((E and G) or E) -> F)) or H)), M:tm-210, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63353
in-theory        63353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     23
proof            (modus-ponens tm-183 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63353.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-183, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63354
in-theory        63354
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-157 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-4 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63354.        ((A -> ((B and C) -> C)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-157, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63355
in-theory        63355
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     29
proof            (modus-ponens tm-147 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-4 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63355.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-147, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63356
in-theory        63356
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-134 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-3 tm-6 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63356.        ((A -> ((B and C) -> B)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-134, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63357
in-theory        63357
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     29
proof            (modus-ponens tm-125 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-3 tm-6 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63357.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-125, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63358
in-theory        63358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (((E and G) or E) -> F)) or H))
theorem-size     29
proof            (modus-ponens tm-113 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-2 tm-6 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63358.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> (((E and G) or E) -> F)) or H)), M:tm-113, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63359
in-theory        63359
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     33
proof            (modus-ponens tm-105 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63359.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-105, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63360
in-theory        63360
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> (((C and E) or C) -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-95 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63360.        (((A -> B) -> (A -> A)) and (((C -> D) -> (((C and E) or C) -> D)) or F)), M:tm-95, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63361
in-theory        63361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-83 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63361.        ((A -> (B -> (C -> B))) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-83, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63362
in-theory        63362
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> (((B and D) or B) -> C)) or E))
theorem-size     19
proof            (modus-ponens tm-76 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-10 tm-6 tm-8 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63362.        (((not (not A)) -> A) and (((B -> C) -> (((B and D) or B) -> C)) or E)), M:tm-76, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63363
in-theory        63363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (((C and E) or C) -> D)) or F))
theorem-size     25
proof            (modus-ponens tm-69 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-9 tm-6 tm-8 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63363.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> (((C and E) or C) -> D)) or F)), M:tm-69, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63364
in-theory        63364
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-54 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-6 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63364.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-54, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63365
in-theory        63365
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C -> D) -> (((C and E) or C) -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-42 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63365.        ((A -> (B or A)) and (((C -> D) -> (((C and E) or C) -> D)) or F)), M:tm-42, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63366
in-theory        63366
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C -> D) -> (((C and E) or C) -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-32 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63366.        ((A -> (A or B)) and (((C -> D) -> (((C and E) or C) -> D)) or F)), M:tm-32, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63367
in-theory        63367
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C -> D) -> (((C and E) or C) -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-23 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63367.        ((A -> (B -> (A and B))) and (((C -> D) -> (((C and E) or C) -> D)) or F)), M:tm-23, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63368
in-theory        63368
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C -> D) -> (((C and E) or C) -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-22 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-4 tm-6 tm-8 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63368.        (((A and B) -> B) and (((C -> D) -> (((C and E) or C) -> D)) or F)), M:tm-22, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63369
in-theory        63369
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C -> D) -> (((C and E) or C) -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-21 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-3 tm-6 tm-8)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63369.        (((A and B) -> A) and (((C -> D) -> (((C and E) or C) -> D)) or F)), M:tm-21, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63370
in-theory        63370
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     27
proof            (modus-ponens tm-20 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-2 tm-6 tm-8 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63370.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-20, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63371
in-theory        63371
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C -> D) -> (((C and E) or C) -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-19 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63371.        ((A -> (B -> A)) and (((C -> D) -> (((C and E) or C) -> D)) or F)), M:tm-19, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63372
in-theory        63372
times-derived    2
----------------------------------------------------------------
theorem          (A or (((B -> C) -> (((B and D) or B) -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-7 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-7 tm-6 tm-8 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63372.        (A or (((B -> C) -> (((B and D) or B) -> C)) or E)), M:tm-7, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63373
in-theory        63373
times-derived    2
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) or D) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-6 tm-8 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63373.        ((((A -> B) -> (((A and C) or A) -> B)) or D) or E), M:tm-6, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63374
in-theory        63374
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (((B and D) or B) -> C)) or E) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63374.        (A -> ((((B -> C) -> (((B and D) or B) -> C)) or E) and A)), M:tm-5, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63375
in-theory        63375
times-derived    3
----------------------------------------------------------------
theorem          (A -> (((B -> C) -> (((B and D) or B) -> C)) or E))
theorem-size     15
proof            (modus-ponens tm-1 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-1 tm-6 tm-8 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63375.        (A -> (((B -> C) -> (((B and D) or B) -> C)) or E)), M:tm-1, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-63376
in-theory        63376
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-8 ((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63376.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-757, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-63377
in-theory        63377
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-757 tm-9 ((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-63377.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-757, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-63378
in-theory        63378
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((not (not D)) -> D))
theorem-size     17
proof            (modus-ponens tm-757 tm-10 ((A (-> (not (not Am)) Am))))
axioms-used      (tm-5 tm-8 tm-3 tm-10)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-63378.        (((A -> B) -> (((A and C) or A) -> B)) and ((not (not D)) -> D)), M:tm-757, m:tm-10, u:((A (-> (not (not Am)) Am)))
================================================================
tm-name          tm-63379
in-theory        63379
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-757 tm-11 ((A (-> Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-63379.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (F -> E)))), M:tm-757, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-63380
in-theory        63380
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (D -> D)))
theorem-size     19
proof            (modus-ponens tm-757 tm-12 ((A (-> (-> Am Bm) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-63380.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (D -> D))), M:tm-757, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
================================================================
tm-name          tm-63381
in-theory        63381
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-757 tm-13 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-63381.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-757, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-63382
in-theory        63382
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-14 ((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-63382.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-757, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-63383
in-theory        63383
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)))
theorem-size     27
proof            (modus-ponens tm-757 tm-15 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-63383.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-757, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-63384
in-theory        63384
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-757 tm-16 ((A (-> Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-63384.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E and F) -> E))), M:tm-757, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-63385
in-theory        63385
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)))
theorem-size     27
proof            (modus-ponens tm-757 tm-17 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-63385.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-757, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-63386
in-theory        63386
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-757 tm-18 ((A (-> Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-63386.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E and F) -> F))), M:tm-757, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-63387
in-theory        63387
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-757 tm-19 ((A (-> Am (and (-> Bm (-> Cm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-63387.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> E)) and D))), M:tm-757, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
================================================================
tm-name          tm-63388
in-theory        63388
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     29
proof            (modus-ponens tm-757 tm-20 ((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-63388.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-757, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-63389
in-theory        63389
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E and F) -> E) and D)))
theorem-size     21
proof            (modus-ponens tm-757 tm-21 ((A (-> Am (and (-> (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-63389.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E and F) -> E) and D))), M:tm-757, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-63390
in-theory        63390
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E and F) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-757 tm-22 ((A (-> Am (and (-> (and Bm Cm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-63390.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E and F) -> F) and D))), M:tm-757, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
================================================================
tm-name          tm-63391
in-theory        63391
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-23 ((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-63391.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-757, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
================================================================
tm-name          tm-63392
in-theory        63392
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (D -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-757 tm-24 ((A (-> (-> Am Bm) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-63392.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (D -> (D and E)))), M:tm-757, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-63393
in-theory        63393
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-25 ((A (-> Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-63393.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (F -> (E and F))))), M:tm-757, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-63394
in-theory        63394
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) or F))
theorem-size     19
proof            (modus-ponens tm-757 tm-26 ((A (or (-> Am (-> Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-63394.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) or F)), M:tm-757, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
================================================================
tm-name          tm-63395
in-theory        63395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G))
theorem-size     27
proof            (modus-ponens tm-757 tm-27 ((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-63395.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-757, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-63396
in-theory        63396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) or F))
theorem-size     19
proof            (modus-ponens tm-757 tm-28 ((A (or (-> (and Am Bm) Am) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-63396.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) or F)), M:tm-757, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
================================================================
tm-name          tm-63397
in-theory        63397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) or F))
theorem-size     19
proof            (modus-ponens tm-757 tm-29 ((A (or (-> (and Am Bm) Bm) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-63397.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) or F)), M:tm-757, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
================================================================
tm-name          tm-63398
in-theory        63398
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) or F))
theorem-size     21
proof            (modus-ponens tm-757 tm-30 ((A (or (-> Am (-> Bm (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-63398.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) or F)), M:tm-757, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
================================================================
tm-name          tm-63399
in-theory        63399
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) or F))
theorem-size     19
proof            (modus-ponens tm-757 tm-31 ((A (or (-> Am (or Am Bm)) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-63399.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) or F)), M:tm-757, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
================================================================
tm-name          tm-63400
in-theory        63400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (E or F)) and D)))
theorem-size     21
proof            (modus-ponens tm-757 tm-32 ((A (-> Am (and (-> Bm (or Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-63400.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (E or F)) and D))), M:tm-757, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
================================================================
tm-name          tm-63401
in-theory        63401
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-757 tm-33 ((A (-> Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-63401.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (E or F)))), M:tm-757, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-63402
in-theory        63402
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-757 tm-34 ((A (or Am (-> Bm (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-63402.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (F -> E)))), M:tm-757, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
================================================================
tm-name          tm-63403
in-theory        63403
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-35 ((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-63403.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-757, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-63404
in-theory        63404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-757 tm-36 ((A (or Am (-> (and Bm Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-63404.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E and F) -> E))), M:tm-757, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
================================================================
tm-name          tm-63405
in-theory        63405
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-757 tm-37 ((A (or Am (-> (and Bm Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-63405.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E and F) -> F))), M:tm-757, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
================================================================
tm-name          tm-63406
in-theory        63406
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (F -> (E and F)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-38 ((A (or Am (-> Bm (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-63406.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (F -> (E and F))))), M:tm-757, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-63407
in-theory        63407
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (E or F))))
theorem-size     19
proof            (modus-ponens tm-757 tm-39 ((A (or Am (-> Bm (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-63407.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (E or F)))), M:tm-757, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
================================================================
tm-name          tm-63408
in-theory        63408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-757 tm-40 ((A (or Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-63408.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (F or E)))), M:tm-757, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-63409
in-theory        63409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) or F))
theorem-size     19
proof            (modus-ponens tm-757 tm-41 ((A (or (-> Am (or Bm Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-63409.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) or F)), M:tm-757, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
================================================================
tm-name          tm-63410
in-theory        63410
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F or E)) and D)))
theorem-size     21
proof            (modus-ponens tm-757 tm-42 ((A (-> Am (and (-> Bm (or Cm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-63410.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F or E)) and D))), M:tm-757, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
================================================================
tm-name          tm-63411
in-theory        63411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (F or E))))
theorem-size     19
proof            (modus-ponens tm-757 tm-43 ((A (-> Am (-> Bm (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-63411.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (F or E)))), M:tm-757, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
================================================================
tm-name          tm-63412
in-theory        63412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-757 tm-44 ((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-63412.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-757, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-63413
in-theory        63413
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     37
proof            (modus-ponens tm-757 tm-45 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-63413.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-757, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-63414
in-theory        63414
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-757 tm-46 ((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-63414.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-757, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
================================================================
tm-name          tm-63415
in-theory        63415
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (((F and D) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-757 tm-47 ((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-63415.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (((F and D) or D) -> E))), M:tm-757, m:tm-47, u:((A (-> (-> Am Bm) (-> (or (and Cm Am) Am) Bm))))
================================================================
tm-name          tm-63416
in-theory        63416
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F)))
theorem-size     29
proof            (modus-ponens tm-757 tm-48 ((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-63416.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E and D)) -> F) -> ((E or (D -> (E and D))) -> F))), M:tm-757, m:tm-48, u:((A (-> (-> (-> Am (and Bm Am)) Cm) (-> (or Bm (-> Am (and Bm Am))) Cm))))
================================================================
tm-name          tm-63417
in-theory        63417
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-757 tm-49 ((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-63417.        (((A -> B) -> (((A and C) or A) -> B)) and (((D or E) -> F) -> ((D or (D or E)) -> F))), M:tm-757, m:tm-49, u:((A (-> (-> (or Am Bm) Cm) (-> (or Am (or Am Bm)) Cm))))
================================================================
tm-name          tm-63418
in-theory        63418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F)))
theorem-size     25
proof            (modus-ponens tm-757 tm-50 ((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-63418.        (((A -> B) -> (((A and C) or A) -> B)) and (((D or E) -> F) -> ((E or (D or E)) -> F))), M:tm-757, m:tm-50, u:((A (-> (-> (or Am Bm) Cm) (-> (or Bm (or Am Bm)) Cm))))
================================================================
tm-name          tm-63419
in-theory        63419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G)))
theorem-size     39
proof            (modus-ponens tm-757 tm-51 ((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-63419.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> ((F or D) -> E)) -> G) -> (((F -> D) or ((D -> E) -> ((F or D) -> E))) -> G))), M:tm-757, m:tm-51, u:((A (-> (-> (-> (-> Am Bm) (-> (or Cm Am) Bm)) Dm) (-> (or (-> Cm Am) (-> (-> Am Bm) (-> (or Cm Am) Bm))) Dm))))
================================================================
tm-name          tm-63420
in-theory        63420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-52 ((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-52.           (A or ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-7, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-63420.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-757, m:tm-52, u:((A (or Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-63421
in-theory        63421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G))
theorem-size     27
proof            (modus-ponens tm-757 tm-53 ((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-53.           (((A -> B) -> ((B -> C) -> ((A or B) -> C))) or D), M:tm-6, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-63421.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((E -> F) -> ((D or E) -> F))) or G)), M:tm-757, m:tm-53, u:((A (or (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))) Dm)))
================================================================
tm-name          tm-63422
in-theory        63422
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D)))
theorem-size     29
proof            (modus-ponens tm-757 tm-54 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-63422.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> ((F -> G) -> ((E or F) -> G))) and D))), M:tm-757, m:tm-54, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))) Am))))
================================================================
tm-name          tm-63423
in-theory        63423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-757 tm-55 ((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-63423.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (E -> F)) -> ((D -> E) -> ((D or E) -> F)))), M:tm-757, m:tm-55, u:((A (-> (-> (-> Am Bm) (-> Bm Cm)) (-> (-> Am Bm) (-> (or Am Bm) Cm)))))
================================================================
tm-name          tm-63424
in-theory        63424
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-56 ((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-56.           (A -> ((B -> C) -> ((C -> D) -> ((B or C) -> D)))), M:tm-1, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-63424.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> F) -> ((F -> G) -> ((E or F) -> G))))), M:tm-757, m:tm-56, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
================================================================
tm-name          tm-63425
in-theory        63425
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (E -> D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-757 tm-57 ((A (-> (-> Am (not (-> Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-57.           ((A -> (not (B -> A))) -> (not A)), M:tm-9, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-63425.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (E -> D))) -> (not D))), M:tm-757, m:tm-57, u:((A (-> (-> Am (not (-> Bm Am))) (not Am))))
================================================================
tm-name          tm-63426
in-theory        63426
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-58 ((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-58.           (((A -> (B -> C)) -> (not ((A -> B) -> (A -> C)))) -> (not (A -> (B -> C)))), M:tm-9, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-63426.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> (not ((D -> E) -> (D -> F)))) -> (not (D -> (E -> F))))), M:tm-757, m:tm-58, u:((A (-> (-> (-> Am (-> Bm Cm)) (not (-> (-> Am Bm) (-> Am Cm)))) (not (-> Am (-> Bm Cm))))))
================================================================
tm-name          tm-63427
in-theory        63427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> (not D)) -> (not (D and E))))
theorem-size     23
proof            (modus-ponens tm-757 tm-59 ((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-59.           (((A and B) -> (not A)) -> (not (A and B))), M:tm-9, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-63427.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> (not D)) -> (not (D and E)))), M:tm-757, m:tm-59, u:((A (-> (-> (and Am Bm) (not Am)) (not (and Am Bm)))))
================================================================
tm-name          tm-63428
in-theory        63428
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> (not E)) -> (not (D and E))))
theorem-size     23
proof            (modus-ponens tm-757 tm-60 ((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-4)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-60.           (((A and B) -> (not B)) -> (not (A and B))), M:tm-9, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-63428.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> (not E)) -> (not (D and E)))), M:tm-757, m:tm-60, u:((A (-> (-> (and Am Bm) (not Bm)) (not (and Am Bm)))))
================================================================
tm-name          tm-63429
in-theory        63429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (E -> (D and E)))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-61 ((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-61.           ((A -> (not (B -> (A and B)))) -> (not A)), M:tm-9, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-63429.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (E -> (D and E)))) -> (not D))), M:tm-757, m:tm-61, u:((A (-> (-> Am (not (-> Bm (and Am Bm)))) (not Am))))
================================================================
tm-name          tm-63430
in-theory        63430
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (D or E))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-757 tm-62 ((A (-> (-> Am (not (or Am Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-62.           ((A -> (not (A or B))) -> (not A)), M:tm-9, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-63430.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (D or E))) -> (not D))), M:tm-757, m:tm-62, u:((A (-> (-> Am (not (or Am Bm))) (not Am))))
================================================================
tm-name          tm-63431
in-theory        63431
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (E or D))) -> (not D)))
theorem-size     21
proof            (modus-ponens tm-757 tm-63 ((A (-> (-> Am (not (or Bm Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-63.           ((A -> (not (B or A))) -> (not A)), M:tm-9, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-63431.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (E or D))) -> (not D))), M:tm-757, m:tm-63, u:((A (-> (-> Am (not (or Bm Am))) (not Am))))
================================================================
tm-name          tm-63432
in-theory        63432
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E))))
theorem-size     31
proof            (modus-ponens tm-757 tm-64 ((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-64.           (((A -> B) -> (not ((B -> C) -> ((A or B) -> C)))) -> (not (A -> B))), M:tm-9, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-63432.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (not ((E -> F) -> ((D or E) -> F)))) -> (not (D -> E)))), M:tm-757, m:tm-64, u:((A (-> (-> (-> Am Bm) (not (-> (-> Bm Cm) (-> (or Am Bm) Cm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-63433
in-theory        63433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-757 tm-65 ((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-65.           (((A -> B) -> (not ((A -> (not B)) -> (not A)))) -> (not (A -> B))), M:tm-9, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-63433.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (not ((D -> (not E)) -> (not D)))) -> (not (D -> E)))), M:tm-757, m:tm-65, u:((A (-> (-> (-> Am Bm) (not (-> (-> Am (not Bm)) (not Am)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-63434
in-theory        63434
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F)))
theorem-size     35
proof            (modus-ponens tm-757 tm-66 ((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       133
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-63434.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (not E)) -> (not D)) -> F) -> (((D -> E) or ((D -> (not E)) -> (not D))) -> F))), M:tm-757, m:tm-66, u:((A (-> (-> (-> (-> Am (not Bm)) (not Am)) Cm) (-> (or (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
================================================================
tm-name          tm-63435
in-theory        63435
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-67 ((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-67.           (A or ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-7, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-63435.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-757, m:tm-67, u:((A (or Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-63436
in-theory        63436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F))
theorem-size     25
proof            (modus-ponens tm-757 tm-68 ((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-68.           (((A -> B) -> ((A -> (not B)) -> (not A))) or C), M:tm-6, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-63436.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((D -> (not E)) -> (not D))) or F)), M:tm-757, m:tm-68, u:((A (or (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am))) Cm)))
================================================================
tm-name          tm-63437
in-theory        63437
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D)))
theorem-size     27
proof            (modus-ponens tm-757 tm-69 ((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-63437.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> ((E -> (not F)) -> (not E))) and D))), M:tm-757, m:tm-69, u:((A (-> Am (and (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))) Am))))
================================================================
tm-name          tm-63438
in-theory        63438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-757 tm-70 ((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-9)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-63438.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (D -> (not E))) -> ((D -> E) -> (not D)))), M:tm-757, m:tm-70, u:((A (-> (-> (-> Am Bm) (-> Am (not Bm))) (-> (-> Am Bm) (not Am)))))
================================================================
tm-name          tm-63439
in-theory        63439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-71 ((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-9)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-71.           (A -> ((B -> C) -> ((B -> (not C)) -> (not B)))), M:tm-1, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-63439.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> F) -> ((E -> (not F)) -> (not E))))), M:tm-757, m:tm-71, u:((A (-> Am (-> (-> Bm Cm) (-> (-> Bm (not Cm)) (not Bm))))))
================================================================
tm-name          tm-63440
in-theory        63440
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((not (not D)) -> (not D)) -> (not (not (not D)))))
theorem-size     23
proof            (modus-ponens tm-757 tm-72 ((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-10)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-72.           (((not (not A)) -> (not A)) -> (not (not (not A)))), M:tm-9, m:tm-10, u:((A (not (not Am))) (B Am))
tm-63440.        (((A -> B) -> (((A and C) or A) -> B)) and (((not (not D)) -> (not D)) -> (not (not (not D))))), M:tm-757, m:tm-72, u:((A (-> (-> (not (not Am)) (not Am)) (not (not (not Am))))))
================================================================
tm-name          tm-63441
in-theory        63441
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (((not (not D)) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-757 tm-73 ((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-10)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-63441.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (((not (not D)) or D) -> E))), M:tm-757, m:tm-73, u:((A (-> (-> Am Bm) (-> (or (not (not Am)) Am) Bm))))
================================================================
tm-name          tm-63442
in-theory        63442
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-757 tm-74 ((A (or Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-74.           (A or ((not (not B)) -> B)), M:tm-7, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-63442.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((not (not E)) -> E))), M:tm-757, m:tm-74, u:((A (or Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-63443
in-theory        63443
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((not (not D)) -> D) or E))
theorem-size     19
proof            (modus-ponens tm-757 tm-75 ((A (or (-> (not (not Am)) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-75.           (((not (not A)) -> A) or B), M:tm-6, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-63443.        (((A -> B) -> (((A and C) or A) -> B)) and (((not (not D)) -> D) or E)), M:tm-757, m:tm-75, u:((A (or (-> (not (not Am)) Am) Bm)))
================================================================
tm-name          tm-63444
in-theory        63444
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((not (not E)) -> E) and D)))
theorem-size     21
proof            (modus-ponens tm-757 tm-76 ((A (-> Am (and (-> (not (not Bm)) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-63444.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((not (not E)) -> E) and D))), M:tm-757, m:tm-76, u:((A (-> Am (and (-> (not (not Bm)) Bm) Am))))
================================================================
tm-name          tm-63445
in-theory        63445
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E)))
theorem-size     27
proof            (modus-ponens tm-757 tm-77 ((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-10)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-63445.        (((A -> B) -> (((A and C) or A) -> B)) and (((not (not (D -> E))) -> D) -> ((not (not (D -> E))) -> E))), M:tm-757, m:tm-77, u:((A (-> (-> (not (not (-> Am Bm))) Am) (-> (not (not (-> Am Bm))) Bm))))
================================================================
tm-name          tm-63446
in-theory        63446
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((not (not E)) -> E)))
theorem-size     19
proof            (modus-ponens tm-757 tm-78 ((A (-> Am (-> (not (not Bm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-10)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-78.           (A -> ((not (not B)) -> B)), M:tm-1, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-63446.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((not (not E)) -> E))), M:tm-757, m:tm-78, u:((A (-> Am (-> (not (not Bm)) Bm))))
================================================================
tm-name          tm-63447
in-theory        63447
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (E -> (F -> E)))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-79 ((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-63447.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (E -> (F -> E)))) -> (not D))), M:tm-757, m:tm-79, u:((A (-> (-> Am (not (-> Bm (-> Cm Bm)))) (not Am))))
================================================================
tm-name          tm-63448
in-theory        63448
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F)))
theorem-size     29
proof            (modus-ponens tm-757 tm-80 ((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-63448.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> D)) -> F) -> ((G or (D -> (E -> D))) -> F))), M:tm-757, m:tm-80, u:((A (-> (-> (-> Am (-> Bm Am)) Cm) (-> (or Dm (-> Am (-> Bm Am))) Cm))))
================================================================
tm-name          tm-63449
in-theory        63449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-81 ((A (or Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-81.           (A or (B -> (C -> (D -> C)))), M:tm-7, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-63449.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (F -> (G -> F))))), M:tm-757, m:tm-81, u:((A (or Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-63450
in-theory        63450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (F -> E))) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-82 ((A (or (-> Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-82.           ((A -> (B -> (C -> B))) or D), M:tm-6, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-63450.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (F -> E))) or G)), M:tm-757, m:tm-82, u:((A (or (-> Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-63451
in-theory        63451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> (G -> F))) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-83 ((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-63451.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> (G -> F))) and D))), M:tm-757, m:tm-83, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-63452
in-theory        63452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (D -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-757 tm-84 ((A (-> (-> Am Bm) (-> Am (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-63452.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (D -> (F -> E)))), M:tm-757, m:tm-84, u:((A (-> (-> Am Bm) (-> Am (-> Cm Bm)))))
================================================================
tm-name          tm-63453
in-theory        63453
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-85 ((A (-> Am (-> Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-85.           (A -> (B -> (C -> (D -> C)))), M:tm-1, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-63453.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (F -> (G -> F))))), M:tm-757, m:tm-85, u:((A (-> Am (-> Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-63454
in-theory        63454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> D))
theorem-size     15
proof            (modus-ponens tm-757 tm-86 ((A (-> Am Am))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-86.           (A -> A), M:tm-12, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-63454.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> D)), M:tm-757, m:tm-86, u:((A (-> Am Am)))
================================================================
tm-name          tm-63455
in-theory        63455
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> F)) -> (D -> (E -> F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-87 ((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-63455.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> F)) -> (D -> (E -> F)))), M:tm-757, m:tm-87, u:((A (-> (-> Am (-> Bm Cm)) (-> Am (-> Bm Cm)))))
================================================================
tm-name          tm-63456
in-theory        63456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D and E) -> (D and E)))
theorem-size     19
proof            (modus-ponens tm-757 tm-88 ((A (-> (and Am Bm) (and Am Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-88.           ((A and B) -> (A and B)), M:tm-12, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-63456.        (((A -> B) -> (((A and C) or A) -> B)) and ((D and E) -> (D and E))), M:tm-757, m:tm-88, u:((A (-> (and Am Bm) (and Am Bm))))
================================================================
tm-name          tm-63457
in-theory        63457
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (D -> E)))
theorem-size     19
proof            (modus-ponens tm-757 tm-89 ((A (-> (-> Am Bm) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-89.           ((A -> B) -> (A -> B)), M:tm-12, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-63457.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (D -> E))), M:tm-757, m:tm-89, u:((A (-> (-> Am Bm) (-> Am Bm))))
================================================================
tm-name          tm-63458
in-theory        63458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((not (not D)) -> (not (not D))))
theorem-size     19
proof            (modus-ponens tm-757 tm-90 ((A (-> (not (not Am)) (not (not Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-10.           ((not (not A)) -> A), axiom
tm-90.           ((not (not A)) -> (not (not A))), M:tm-12, m:tm-10, u:((A (not (not Am))) (B Am))
tm-63458.        (((A -> B) -> (((A and C) or A) -> B)) and ((not (not D)) -> (not (not D)))), M:tm-757, m:tm-90, u:((A (-> (not (not Am)) (not (not Am)))))
================================================================
tm-name          tm-63459
in-theory        63459
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E))))
theorem-size     25
proof            (modus-ponens tm-757 tm-91 ((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-2 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-91.           (((A -> B) -> (not (A -> A))) -> (not (A -> B))), M:tm-9, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-63459.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (not (D -> D))) -> (not (D -> E)))), M:tm-757, m:tm-91, u:((A (-> (-> (-> Am Bm) (not (-> Am Am))) (not (-> Am Bm)))))
================================================================
tm-name          tm-63460
in-theory        63460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E)))
theorem-size     27
proof            (modus-ponens tm-757 tm-92 ((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-63460.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> D) -> E) -> (((D -> F) or (D -> D)) -> E))), M:tm-757, m:tm-92, u:((A (-> (-> (-> Am Am) Bm) (-> (or (-> Am Cm) (-> Am Am)) Bm))))
================================================================
tm-name          tm-63461
in-theory        63461
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-757 tm-93 ((A (or Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-93.           (A or ((B -> C) -> (B -> B))), M:tm-7, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-63461.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> F) -> (E -> E)))), M:tm-757, m:tm-93, u:((A (or Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-63462
in-theory        63462
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (D -> D)) or F))
theorem-size     21
proof            (modus-ponens tm-757 tm-94 ((A (or (-> (-> Am Bm) (-> Am Am)) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-94.           (((A -> B) -> (A -> A)) or C), M:tm-6, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-63462.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (D -> D)) or F)), M:tm-757, m:tm-94, u:((A (or (-> (-> Am Bm) (-> Am Am)) Cm)))
================================================================
tm-name          tm-63463
in-theory        63463
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> (E -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-95 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-63463.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> (E -> E)) and D))), M:tm-757, m:tm-95, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm Bm)) Am))))
================================================================
tm-name          tm-63464
in-theory        63464
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> D) -> ((D -> E) -> D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-96 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-63464.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> D) -> ((D -> E) -> D))), M:tm-757, m:tm-96, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Am))))
================================================================
tm-name          tm-63465
in-theory        63465
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> F) -> (E -> E))))
theorem-size     21
proof            (modus-ponens tm-757 tm-97 ((A (-> Am (-> (-> Bm Cm) (-> Bm Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-97.           (A -> ((B -> C) -> (B -> B))), M:tm-1, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-63465.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> F) -> (E -> E)))), M:tm-757, m:tm-97, u:((A (-> Am (-> (-> Bm Cm) (-> Bm Bm)))))
================================================================
tm-name          tm-63466
in-theory        63466
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E -> D) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-98 ((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-63466.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E -> D) -> F)) -> (D -> F))), M:tm-757, m:tm-98, u:((A (-> (-> Am (-> (-> Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-63467
in-theory        63467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D -> E)) -> (D -> E)))
theorem-size     21
proof            (modus-ponens tm-757 tm-99 ((A (-> (-> Am (-> Am Bm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-63467.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D -> E)) -> (D -> E))), M:tm-757, m:tm-99, u:((A (-> (-> Am (-> Am Bm)) (-> Am Bm))))
================================================================
tm-name          tm-63468
in-theory        63468
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E))))
theorem-size     31
proof            (modus-ponens tm-757 tm-100 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-63468.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> E)))), M:tm-757, m:tm-100, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))
================================================================
tm-name          tm-63469
in-theory        63469
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E)))))
theorem-size     43
proof            (modus-ponens tm-757 tm-101 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-101.          ((((A -> (B -> C)) -> (A -> B)) -> (not ((A -> (B -> C)) -> (A -> C)))) -> (not ((A -> (B -> C)) -> (A -> B)))), M:tm-9, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-63469.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (not ((D -> (E -> F)) -> (D -> F)))) -> (not ((D -> (E -> F)) -> (D -> E))))), M:tm-757, m:tm-101, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (not (-> (-> Am (-> Bm Cm)) (-> Am Cm)))) (not (-> (-> Am (-> Bm Cm)) (-> Am Bm))))))
================================================================
tm-name          tm-63470
in-theory        63470
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G)))
theorem-size     45
proof            (modus-ponens tm-757 tm-102 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-63470.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> F)) -> (D -> F)) -> G) -> ((((D -> (E -> F)) -> (D -> E)) or ((D -> (E -> F)) -> (D -> F))) -> G))), M:tm-757, m:tm-102, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Cm)) Dm) (-> (or (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-63471
in-theory        63471
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-103 ((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-103.          (A or (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-7, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-63471.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-757, m:tm-103, u:((A (or Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-63472
in-theory        63472
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G))
theorem-size     33
proof            (modus-ponens tm-757 tm-104 ((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-104.          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) or D), M:tm-6, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-63472.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F))) or G)), M:tm-757, m:tm-104, u:((A (or (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))) Dm)))
================================================================
tm-name          tm-63473
in-theory        63473
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D)))
theorem-size     35
proof            (modus-ponens tm-757 tm-105 ((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-63473.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))) and D))), M:tm-757, m:tm-105, u:((A (-> Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-63474
in-theory        63474
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-757 tm-106 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-63474.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> F)) -> (D -> E)) -> (D -> (E -> F))) -> (((D -> (E -> F)) -> (D -> E)) -> (D -> F)))), M:tm-757, m:tm-106, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am (-> Bm Cm))) (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-63475
in-theory        63475
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-107 ((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-107.          (A -> (((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-1, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-63475.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (F -> G)) -> (E -> F)) -> ((E -> (F -> G)) -> (E -> G))))), M:tm-757, m:tm-107, u:((A (-> Am (-> (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
================================================================
tm-name          tm-63476
in-theory        63476
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-757 tm-108 ((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-63476.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> (((D -> E) -> (D -> F)) -> G)) -> ((D -> (E -> F)) -> G))), M:tm-757, m:tm-108, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (-> Am (-> Bm Cm)) Dm))))
================================================================
tm-name          tm-63477
in-theory        63477
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D)))
theorem-size     31
proof            (modus-ponens tm-757 tm-109 ((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-1 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-63477.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))) -> (not D))), M:tm-757, m:tm-109, u:((A (-> (-> Am (not (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))) (not Am))))
================================================================
tm-name          tm-63478
in-theory        63478
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G)))
theorem-size     45
proof            (modus-ponens tm-757 tm-110 ((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-63478.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) -> ((H or ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) -> G))), M:tm-757, m:tm-110, u:((A (-> (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) (-> (or Em (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) Dm))))
================================================================
tm-name          tm-63479
in-theory        63479
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-757 tm-111 ((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-111.          (A or (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63479.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-757, m:tm-111, u:((A (or Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-63480
in-theory        63480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     29
proof            (modus-ponens tm-757 tm-112 ((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-112.          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63480.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-757, m:tm-112, u:((A (or (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-63481
in-theory        63481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     31
proof            (modus-ponens tm-757 tm-113 ((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63481.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-757, m:tm-113, u:((A (-> Am (and (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-63482
in-theory        63482
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-757 tm-114 ((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-63482.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (F -> G))) -> (D -> ((E -> F) -> (E -> G))))), M:tm-757, m:tm-114, u:((A (-> (-> Am (-> Bm (-> Cm Dm))) (-> Am (-> (-> Bm Cm) (-> Bm Dm))))))
================================================================
tm-name          tm-63483
in-theory        63483
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-757 tm-115 ((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-115.          (A -> (B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63483.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-757, m:tm-115, u:((A (-> Am (-> Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-63484
in-theory        63484
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) and D) -> E))
theorem-size     19
proof            (modus-ponens tm-757 tm-116 ((A (-> (and (-> Am Bm) Am) Bm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-4.            ((A and B) -> B), axiom
tm-116.          (((A -> B) and A) -> B), M:tm-15, m:tm-4, u:((Am (-> Bm B)) (C Bm) (A Bm))
tm-63484.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) and D) -> E)), M:tm-757, m:tm-116, u:((A (-> (and (-> Am Bm) Am) Bm)))
================================================================
tm-name          tm-63485
in-theory        63485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> D)) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-757 tm-117 ((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-117.          ((((A -> (B -> A)) -> C) and D) -> C), M:tm-15, m:tm-11, u:((Am (and (-> (-> Bm (-> Cm Bm)) B) C)) (A (-> Bm (-> Cm Bm))))
tm-63485.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> D)) -> F) and G) -> F)), M:tm-757, m:tm-117, u:((A (-> (and (-> (-> Am (-> Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-63486
in-theory        63486
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G))
theorem-size     31
proof            (modus-ponens tm-757 tm-118 ((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-118.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) and E) -> D), M:tm-15, m:tm-14, u:((Am (and (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) B) C)) (A (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-63486.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) -> G) and H) -> G)), M:tm-757, m:tm-118, u:((A (-> (and (-> (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) Dm)))
================================================================
tm-name          tm-63487
in-theory        63487
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-757 tm-119 ((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-63487.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) -> D) and F) -> (D -> E)) -> ((((D -> E) -> D) and F) -> E))), M:tm-757, m:tm-119, u:((A (-> (-> (and (-> (-> Am Bm) Am) Cm) (-> Am Bm)) (-> (and (-> (-> Am Bm) Am) Cm) Bm))))
================================================================
tm-name          tm-63488
in-theory        63488
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D)))
theorem-size     27
proof            (modus-ponens tm-757 tm-120 ((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-63488.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> D))), M:tm-757, m:tm-120, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Am))))
================================================================
tm-name          tm-63489
in-theory        63489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D))))
theorem-size     37
proof            (modus-ponens tm-757 tm-121 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-121.          (((((A -> B) and C) -> A) -> (not (((A -> B) and C) -> B))) -> (not (((A -> B) and C) -> A))), M:tm-9, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-63489.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) and F) -> D) -> (not (((D -> E) and F) -> E))) -> (not (((D -> E) and F) -> D)))), M:tm-757, m:tm-121, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (not (-> (and (-> Am Bm) Cm) Bm))) (not (-> (and (-> Am Bm) Cm) Am)))))
================================================================
tm-name          tm-63490
in-theory        63490
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G)))
theorem-size     39
proof            (modus-ponens tm-757 tm-122 ((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-63490.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) and F) -> E) -> G) -> (((((D -> E) and F) -> D) or (((D -> E) and F) -> E)) -> G))), M:tm-757, m:tm-122, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Bm) Dm) (-> (or (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
================================================================
tm-name          tm-63491
in-theory        63491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-757 tm-123 ((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-123.          (A or ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-7, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-63491.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-757, m:tm-123, u:((A (or Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-63492
in-theory        63492
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G))
theorem-size     29
proof            (modus-ponens tm-757 tm-124 ((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-124.          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) or D), M:tm-6, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-63492.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) and F) -> D) -> (((D -> E) and F) -> E)) or G)), M:tm-757, m:tm-124, u:((A (or (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)) Dm)))
================================================================
tm-name          tm-63493
in-theory        63493
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D)))
theorem-size     31
proof            (modus-ponens tm-757 tm-125 ((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-63493.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)) and D))), M:tm-757, m:tm-125, u:((A (-> Am (and (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)) Am))))
================================================================
tm-name          tm-63494
in-theory        63494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E)))
theorem-size     35
proof            (modus-ponens tm-757 tm-126 ((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-126.          (((((A -> B) and C) -> A) -> ((A -> B) and C)) -> ((((A -> B) and C) -> A) -> B)), M:tm-2, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (and (-> Am Bm) Cm)) (C Bm))
tm-63494.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) and F) -> D) -> ((D -> E) and F)) -> ((((D -> E) and F) -> D) -> E))), M:tm-757, m:tm-126, u:((A (-> (-> (-> (and (-> Am Bm) Cm) Am) (and (-> Am Bm) Cm)) (-> (-> (and (-> Am Bm) Cm) Am) Bm))))
================================================================
tm-name          tm-63495
in-theory        63495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F))))
theorem-size     29
proof            (modus-ponens tm-757 tm-127 ((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-127.          (A -> ((((B -> C) and D) -> B) -> (((B -> C) and D) -> C))), M:tm-1, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-63495.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> F) and G) -> E) -> (((E -> F) and G) -> F)))), M:tm-757, m:tm-127, u:((A (-> Am (-> (-> (and (-> Bm Cm) Dm) Bm) (-> (and (-> Bm Cm) Dm) Cm)))))
================================================================
tm-name          tm-63496
in-theory        63496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D and E) -> D) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-757 tm-128 ((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-128.          (((((A and B) -> A) -> C) and D) -> C), M:tm-15, m:tm-16, u:((Am (and (-> (-> (and Bm Cm) Bm) B) C)) (A (-> (and Bm Cm) Bm)))
tm-63496.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D and E) -> D) -> F) and G) -> F)), M:tm-757, m:tm-128, u:((A (-> (and (-> (-> (and Am Bm) Am) Cm) Dm) Cm)))
================================================================
tm-name          tm-63497
in-theory        63497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> (D -> F)) -> ((D and E) -> F)))
theorem-size     25
proof            (modus-ponens tm-757 tm-129 ((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-63497.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> (D -> F)) -> ((D and E) -> F))), M:tm-757, m:tm-129, u:((A (-> (-> (and Am Bm) (-> Am Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-63498
in-theory        63498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not ((E and F) -> E))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-130 ((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-63498.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not ((E and F) -> E))) -> (not D))), M:tm-757, m:tm-130, u:((A (-> (-> Am (not (-> (and Bm Cm) Bm))) (not Am))))
================================================================
tm-name          tm-63499
in-theory        63499
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F)))
theorem-size     29
proof            (modus-ponens tm-757 tm-131 ((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-63499.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D and E) -> D) -> F) -> ((G or ((D and E) -> D)) -> F))), M:tm-757, m:tm-131, u:((A (-> (-> (-> (and Am Bm) Am) Cm) (-> (or Dm (-> (and Am Bm) Am)) Cm))))
================================================================
tm-name          tm-63500
in-theory        63500
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-757 tm-132 ((A (or Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-132.          (A or (B -> ((C and D) -> C))), M:tm-7, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-63500.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> ((F and G) -> F)))), M:tm-757, m:tm-132, u:((A (or Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-63501
in-theory        63501
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E and F) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-133 ((A (or (-> Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-133.          ((A -> ((B and C) -> B)) or D), M:tm-6, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-63501.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E and F) -> E)) or G)), M:tm-757, m:tm-133, u:((A (or (-> Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-63502
in-theory        63502
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> ((F and G) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-134 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-63502.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> ((F and G) -> F)) and D))), M:tm-757, m:tm-134, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-63503
in-theory        63503
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E and F)) -> (D -> E)))
theorem-size     21
proof            (modus-ponens tm-757 tm-135 ((A (-> (-> Am (and Bm Cm)) (-> Am Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-63503.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E and F)) -> (D -> E))), M:tm-757, m:tm-135, u:((A (-> (-> Am (and Bm Cm)) (-> Am Bm))))
================================================================
tm-name          tm-63504
in-theory        63504
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-757 tm-136 ((A (-> Am (-> Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-136.          (A -> (B -> ((C and D) -> C))), M:tm-1, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-63504.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> ((F and G) -> F)))), M:tm-757, m:tm-136, u:((A (-> Am (-> Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-63505
in-theory        63505
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D and (D -> E)) -> E))
theorem-size     19
proof            (modus-ponens tm-757 tm-137 ((A (-> (and Am (-> Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-137.          ((A and (A -> B)) -> B), M:tm-17, m:tm-3, u:((A Am) (Bm (-> Am C)) (B Am))
tm-63505.        (((A -> B) -> (((A and C) or A) -> B)) and ((D and (D -> E)) -> E)), M:tm-757, m:tm-137, u:((A (-> (and Am (-> Am Bm)) Bm)))
================================================================
tm-name          tm-63506
in-theory        63506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D and ((E -> (F -> E)) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-757 tm-138 ((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-138.          ((A and ((B -> (C -> B)) -> D)) -> D), M:tm-17, m:tm-11, u:((Am (and A (-> (-> Bm (-> Cm Bm)) C))) (B (-> Bm (-> Cm Bm))))
tm-63506.        (((A -> B) -> (((A and C) or A) -> B)) and ((D and ((E -> (F -> E)) -> G)) -> G)), M:tm-757, m:tm-138, u:((A (-> (and Am (-> (-> Bm (-> Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-63507
in-theory        63507
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H))
theorem-size     31
proof            (modus-ponens tm-757 tm-139 ((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-139.          ((A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) -> E)) -> E), M:tm-17, m:tm-14, u:((Am (and A (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) C))) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-63507.        (((A -> B) -> (((A and C) or A) -> B)) and ((D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) -> H)) -> H)), M:tm-757, m:tm-139, u:((A (-> (and Am (-> (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Em)))
================================================================
tm-name          tm-63508
in-theory        63508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D and (((E and F) -> E) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-757 tm-140 ((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-140.          ((A and (((B and C) -> B) -> D)) -> D), M:tm-17, m:tm-16, u:((Am (and A (-> (-> (and Bm Cm) Bm) C))) (B (-> (and Bm Cm) Bm)))
tm-63508.        (((A -> B) -> (((A and C) or A) -> B)) and ((D and (((E and F) -> E) -> G)) -> G)), M:tm-757, m:tm-140, u:((A (-> (and Am (-> (-> (and Bm Cm) Bm) Dm)) Dm)))
================================================================
tm-name          tm-63509
in-theory        63509
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-757 tm-141 ((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-63509.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and ((E -> F) -> E)) -> (E -> F)) -> ((D and ((E -> F) -> E)) -> F))), M:tm-757, m:tm-141, u:((A (-> (-> (and Am (-> (-> Bm Cm) Bm)) (-> Bm Cm)) (-> (and Am (-> (-> Bm Cm) Bm)) Cm))))
================================================================
tm-name          tm-63510
in-theory        63510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E)))
theorem-size     27
proof            (modus-ponens tm-757 tm-142 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-63510.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> E))), M:tm-757, m:tm-142, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Bm))))
================================================================
tm-name          tm-63511
in-theory        63511
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E))))
theorem-size     37
proof            (modus-ponens tm-757 tm-143 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-2 tm-4)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-143.          ((((A and (B -> C)) -> B) -> (not ((A and (B -> C)) -> C))) -> (not ((A and (B -> C)) -> B))), M:tm-9, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-63511.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D and (E -> F)) -> E) -> (not ((D and (E -> F)) -> F))) -> (not ((D and (E -> F)) -> E)))), M:tm-757, m:tm-143, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (not (-> (and Am (-> Bm Cm)) Cm))) (not (-> (and Am (-> Bm Cm)) Bm)))))
================================================================
tm-name          tm-63512
in-theory        63512
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G)))
theorem-size     39
proof            (modus-ponens tm-757 tm-144 ((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-63512.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D and (E -> F)) -> F) -> G) -> ((((D and (E -> F)) -> E) or ((D and (E -> F)) -> F)) -> G))), M:tm-757, m:tm-144, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Cm) Dm) (-> (or (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
================================================================
tm-name          tm-63513
in-theory        63513
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-757 tm-145 ((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-145.          (A or (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-7, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-63513.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-757, m:tm-145, u:((A (or Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-63514
in-theory        63514
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G))
theorem-size     29
proof            (modus-ponens tm-757 tm-146 ((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-146.          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) or D), M:tm-6, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-63514.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F)) or G)), M:tm-757, m:tm-146, u:((A (or (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)) Dm)))
================================================================
tm-name          tm-63515
in-theory        63515
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D)))
theorem-size     31
proof            (modus-ponens tm-757 tm-147 ((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-63515.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)) and D))), M:tm-757, m:tm-147, u:((A (-> Am (and (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)) Am))))
================================================================
tm-name          tm-63516
in-theory        63516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F)))
theorem-size     35
proof            (modus-ponens tm-757 tm-148 ((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-148.          ((((A and (B -> C)) -> B) -> (A and (B -> C))) -> (((A and (B -> C)) -> B) -> C)), M:tm-2, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (and Am (-> Bm Cm))) (C Cm))
tm-63516.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D and (E -> F)) -> E) -> (D and (E -> F))) -> (((D and (E -> F)) -> E) -> F))), M:tm-757, m:tm-148, u:((A (-> (-> (-> (and Am (-> Bm Cm)) Bm) (and Am (-> Bm Cm))) (-> (-> (and Am (-> Bm Cm)) Bm) Cm))))
================================================================
tm-name          tm-63517
in-theory        63517
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G))))
theorem-size     29
proof            (modus-ponens tm-757 tm-149 ((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-149.          (A -> (((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D))), M:tm-1, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-63517.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E and (F -> G)) -> F) -> ((E and (F -> G)) -> G)))), M:tm-757, m:tm-149, u:((A (-> Am (-> (-> (and Bm (-> Cm Dm)) Cm) (-> (and Bm (-> Cm Dm)) Dm)))))
================================================================
tm-name          tm-63518
in-theory        63518
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D and (((E and F) -> F) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-757 tm-150 ((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-150.          ((A and (((B and C) -> C) -> D)) -> D), M:tm-17, m:tm-18, u:((Am (and A (-> (-> (and Bm Cm) Cm) C))) (B (-> (and Bm Cm) Cm)))
tm-63518.        (((A -> B) -> (((A and C) or A) -> B)) and ((D and (((E and F) -> F) -> G)) -> G)), M:tm-757, m:tm-150, u:((A (-> (and Am (-> (-> (and Bm Cm) Cm) Dm)) Dm)))
================================================================
tm-name          tm-63519
in-theory        63519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D and E) -> E) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-757 tm-151 ((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-151.          (((((A and B) -> B) -> C) and D) -> C), M:tm-15, m:tm-18, u:((Am (and (-> (-> (and Bm Cm) Cm) B) C)) (A (-> (and Bm Cm) Cm)))
tm-63519.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D and E) -> E) -> F) and G) -> F)), M:tm-757, m:tm-151, u:((A (-> (and (-> (-> (and Am Bm) Bm) Cm) Dm) Cm)))
================================================================
tm-name          tm-63520
in-theory        63520
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> (E -> F)) -> ((D and E) -> F)))
theorem-size     25
proof            (modus-ponens tm-757 tm-152 ((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-63520.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> (E -> F)) -> ((D and E) -> F))), M:tm-757, m:tm-152, u:((A (-> (-> (and Am Bm) (-> Bm Cm)) (-> (and Am Bm) Cm))))
================================================================
tm-name          tm-63521
in-theory        63521
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not ((E and F) -> F))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-153 ((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-1 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-63521.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not ((E and F) -> F))) -> (not D))), M:tm-757, m:tm-153, u:((A (-> (-> Am (not (-> (and Bm Cm) Cm))) (not Am))))
================================================================
tm-name          tm-63522
in-theory        63522
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F)))
theorem-size     29
proof            (modus-ponens tm-757 tm-154 ((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-63522.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D and E) -> E) -> F) -> ((G or ((D and E) -> E)) -> F))), M:tm-757, m:tm-154, u:((A (-> (-> (-> (and Am Bm) Bm) Cm) (-> (or Dm (-> (and Am Bm) Bm)) Cm))))
================================================================
tm-name          tm-63523
in-theory        63523
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-757 tm-155 ((A (or Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-155.          (A or (B -> ((C and D) -> D))), M:tm-7, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-63523.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> ((F and G) -> G)))), M:tm-757, m:tm-155, u:((A (or Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-63524
in-theory        63524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E and F) -> F)) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-156 ((A (or (-> Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-156.          ((A -> ((B and C) -> C)) or D), M:tm-6, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-63524.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E and F) -> F)) or G)), M:tm-757, m:tm-156, u:((A (or (-> Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-63525
in-theory        63525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> ((F and G) -> G)) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-157 ((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-63525.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> ((F and G) -> G)) and D))), M:tm-757, m:tm-157, u:((A (-> Am (and (-> Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-63526
in-theory        63526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E and F)) -> (D -> F)))
theorem-size     21
proof            (modus-ponens tm-757 tm-158 ((A (-> (-> Am (and Bm Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-63526.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E and F)) -> (D -> F))), M:tm-757, m:tm-158, u:((A (-> (-> Am (and Bm Cm)) (-> Am Cm))))
================================================================
tm-name          tm-63527
in-theory        63527
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-757 tm-159 ((A (-> Am (-> Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-159.          (A -> (B -> ((C and D) -> D))), M:tm-1, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-63527.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> ((F and G) -> G)))), M:tm-757, m:tm-159, u:((A (-> Am (-> Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-63528
in-theory        63528
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-160 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-160.          ((A -> (B -> A)) and (C -> (D -> C))), M:tm-19, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-63528.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> F)))), M:tm-757, m:tm-160, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-63529
in-theory        63529
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-161 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-161.          ((A -> (B -> A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-19, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-63529.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-757, m:tm-161, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-63530
in-theory        63530
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-162 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-162.          ((A -> (B -> A)) and ((C and D) -> C)), M:tm-19, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-63530.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F and G) -> F))), M:tm-757, m:tm-162, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-63531
in-theory        63531
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-757 tm-163 ((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-163.          ((A -> (B -> A)) and ((C and D) -> D)), M:tm-19, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-63531.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F and G) -> G))), M:tm-757, m:tm-163, u:((A (and (-> Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-63532
in-theory        63532
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-164 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-164.          ((A -> (B -> A)) and (C -> (D -> (C and D)))), M:tm-19, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-63532.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (F and G))))), M:tm-757, m:tm-164, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-63533
in-theory        63533
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-757 tm-165 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-165.          ((A -> (B -> A)) and (C -> (C or D))), M:tm-19, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-63533.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (F or G)))), M:tm-757, m:tm-165, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-63534
in-theory        63534
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-166 ((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-166.          ((A -> (B -> A)) and (C -> (D or C))), M:tm-19, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-63534.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (G or F)))), M:tm-757, m:tm-166, u:((A (and (-> Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-63535
in-theory        63535
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-167 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-167.          ((A -> (B -> A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-19, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-63535.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-757, m:tm-167, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-63536
in-theory        63536
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-757 tm-168 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-168.          ((A -> (B -> A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-19, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-63536.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-757, m:tm-168, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-63537
in-theory        63537
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-169 ((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-169.          ((A -> (B -> A)) and ((not (not C)) -> C)), M:tm-19, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-63537.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((not (not F)) -> F))), M:tm-757, m:tm-169, u:((A (and (-> Am (-> Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-63538
in-theory        63538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-170 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-170.          ((A -> (B -> A)) and (C -> (D -> (E -> D)))), M:tm-19, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-63538.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> G))))), M:tm-757, m:tm-170, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-63539
in-theory        63539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-171 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-171.          ((A -> (B -> A)) and ((C -> D) -> (C -> C))), M:tm-19, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-63539.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> F)))), M:tm-757, m:tm-171, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-63540
in-theory        63540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-757 tm-172 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-172.          ((A -> (B -> A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-19, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-63540.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-757, m:tm-172, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-63541
in-theory        63541
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-173 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-173.          ((A -> (B -> A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63541.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-757, m:tm-173, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-63542
in-theory        63542
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-757 tm-174 ((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-174.          ((A -> (B -> A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-19, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-63542.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-757, m:tm-174, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-63543
in-theory        63543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-757 tm-175 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-175.          ((A -> (B -> A)) and (C -> ((D and E) -> D))), M:tm-19, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-63543.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> G)))), M:tm-757, m:tm-175, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-63544
in-theory        63544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-757 tm-176 ((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-176.          ((A -> (B -> A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-19, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-63544.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-757, m:tm-176, u:((A (and (-> Am (-> Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-63545
in-theory        63545
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-757 tm-177 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-177.          ((A -> (B -> A)) and (C -> ((D and E) -> E))), M:tm-19, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-63545.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G and H) -> H)))), M:tm-757, m:tm-177, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-63546
in-theory        63546
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-178 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-178.          ((A -> (B -> A)) and (C -> ((D -> (E -> D)) and C))), M:tm-19, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-63546.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-757, m:tm-178, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-63547
in-theory        63547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-179 ((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-179.          ((A -> (not ((B -> (C -> B)) and A))) -> (not A)), M:tm-9, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-63547.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not ((E -> (F -> E)) and D))) -> (not D))), M:tm-757, m:tm-179, u:((A (-> (-> Am (not (and (-> Bm (-> Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-63548
in-theory        63548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-757 tm-180 ((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-63548.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> D)) and F) -> G) -> ((F or ((D -> (E -> D)) and F)) -> G))), M:tm-757, m:tm-180, u:((A (-> (-> (and (-> Am (-> Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-63549
in-theory        63549
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-757 tm-181 ((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-181.          (A or (B -> ((C -> (D -> C)) and B))), M:tm-7, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-63549.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> ((F -> (G -> F)) and E)))), M:tm-757, m:tm-181, u:((A (or Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-63550
in-theory        63550
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E -> (F -> E)) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-757 tm-182 ((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-182.          ((A -> ((B -> (C -> B)) and A)) or D), M:tm-6, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-63550.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E -> (F -> E)) and D)) or G)), M:tm-757, m:tm-182, u:((A (or (-> Am (and (-> Bm (-> Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-63551
in-theory        63551
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-183 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-63551.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> ((F -> (G -> F)) and E)) and D))), M:tm-757, m:tm-183, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-63552
in-theory        63552
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> ((F -> (G -> F)) and E))))
theorem-size     23
proof            (modus-ponens tm-757 tm-184 ((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-184.          (A -> (B -> ((C -> (D -> C)) and B))), M:tm-1, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-63552.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> ((F -> (G -> F)) and E)))), M:tm-757, m:tm-184, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm Cm)) Bm)))))
================================================================
tm-name          tm-63553
in-theory        63553
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G))))
theorem-size     31
proof            (modus-ponens tm-757 tm-185 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-185.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> D))), M:tm-20, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-63553.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> G)))), M:tm-757, m:tm-185, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-63554
in-theory        63554
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-186 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-186.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-20, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-63554.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-757, m:tm-186, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-63555
in-theory        63555
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G)))
theorem-size     31
proof            (modus-ponens tm-757 tm-187 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-187.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> D)), M:tm-20, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-63555.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> G))), M:tm-757, m:tm-187, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-63556
in-theory        63556
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H)))
theorem-size     31
proof            (modus-ponens tm-757 tm-188 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-188.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D and E) -> E)), M:tm-20, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-63556.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G and H) -> H))), M:tm-757, m:tm-188, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-63557
in-theory        63557
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-189 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-189.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (D and E)))), M:tm-20, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-63557.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (G and H))))), M:tm-757, m:tm-189, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-63558
in-theory        63558
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-190 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-6)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-190.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (D or E))), M:tm-20, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-63558.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (G or H)))), M:tm-757, m:tm-190, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-63559
in-theory        63559
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G))))
theorem-size     31
proof            (modus-ponens tm-757 tm-191 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-7)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-191.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E or D))), M:tm-20, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-63559.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H or G)))), M:tm-757, m:tm-191, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-63560
in-theory        63560
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-192 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-192.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((E -> F) -> ((D or E) -> F)))), M:tm-20, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-63560.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((H -> I) -> ((G or H) -> I))))), M:tm-757, m:tm-192, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Em Fm) (-> (or Dm Em) Fm))))))
================================================================
tm-name          tm-63561
in-theory        63561
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G)))))
theorem-size     37
proof            (modus-ponens tm-757 tm-193 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-9)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-193.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> ((D -> (not E)) -> (not D)))), M:tm-20, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-63561.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> ((G -> (not H)) -> (not G))))), M:tm-757, m:tm-193, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (-> Dm (not Em)) (not Dm))))))
================================================================
tm-name          tm-63562
in-theory        63562
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G)))
theorem-size     31
proof            (modus-ponens tm-757 tm-194 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-10)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-194.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((not (not D)) -> D)), M:tm-20, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-63562.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((not (not G)) -> G))), M:tm-757, m:tm-194, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (not (not Dm)) Dm))))
================================================================
tm-name          tm-63563
in-theory        63563
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-195 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-195.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> E)))), M:tm-20, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-63563.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> H))))), M:tm-757, m:tm-195, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-63564
in-theory        63564
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G))))
theorem-size     33
proof            (modus-ponens tm-757 tm-196 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-196.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> D))), M:tm-20, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-63564.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> G)))), M:tm-757, m:tm-196, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm Dm)))))
================================================================
tm-name          tm-63565
in-theory        63565
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-757 tm-197 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-197.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> (D -> E)) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-20, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-63565.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> (G -> H)) -> ((G -> (H -> I)) -> (G -> I))))), M:tm-757, m:tm-197, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm (-> Em Fm)) (-> Dm Em)) (-> (-> Dm (-> Em Fm)) (-> Dm Fm))))))
================================================================
tm-name          tm-63566
in-theory        63566
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     41
proof            (modus-ponens tm-757 tm-198 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-198.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63566.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-757, m:tm-198, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-63567
in-theory        63567
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H))))
theorem-size     41
proof            (modus-ponens tm-757 tm-199 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-199.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) and F) -> D) -> (((D -> E) and F) -> E))), M:tm-20, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-63567.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) and I) -> G) -> (((G -> H) and I) -> H)))), M:tm-757, m:tm-199, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and (-> Dm Em) Fm) Dm) (-> (and (-> Dm Em) Fm) Em)))))
================================================================
tm-name          tm-63568
in-theory        63568
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H))))
theorem-size     33
proof            (modus-ponens tm-757 tm-200 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-200.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> E))), M:tm-20, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-63568.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> H)))), M:tm-757, m:tm-200, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-63569
in-theory        63569
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I))))
theorem-size     41
proof            (modus-ponens tm-757 tm-201 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-201.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) -> E) -> ((D and (E -> F)) -> F))), M:tm-20, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-63569.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and (H -> I)) -> H) -> ((G and (H -> I)) -> I)))), M:tm-757, m:tm-201, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (and Dm (-> Em Fm)) Em) (-> (and Dm (-> Em Fm)) Fm)))))
================================================================
tm-name          tm-63570
in-theory        63570
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I))))
theorem-size     33
proof            (modus-ponens tm-757 tm-202 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-202.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E and F) -> F))), M:tm-20, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-63570.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H and I) -> I)))), M:tm-757, m:tm-202, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-63571
in-theory        63571
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G))))
theorem-size     35
proof            (modus-ponens tm-757 tm-203 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-203.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> E)) and D))), M:tm-20, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-63571.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> H)) and G)))), M:tm-757, m:tm-203, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm Em)) Dm)))))
================================================================
tm-name          tm-63572
in-theory        63572
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G))))
theorem-size     43
proof            (modus-ponens tm-757 tm-204 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-204.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-20, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-63572.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H -> (I -> J)) -> ((H -> I) -> (H -> J))) and G)))), M:tm-757, m:tm-204, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))) Dm)))))
================================================================
tm-name          tm-63573
in-theory        63573
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-757 tm-205 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-205.          ((A -> (B -> A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-19, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-63573.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-757, m:tm-205, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-63574
in-theory        63574
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D)))
theorem-size     33
proof            (modus-ponens tm-757 tm-206 ((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-206.          ((A -> (not (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))) -> (not A)), M:tm-9, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-63574.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))) -> (not D))), M:tm-757, m:tm-206, u:((A (-> (-> Am (not (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))) (not Am))))
================================================================
tm-name          tm-63575
in-theory        63575
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H)))
theorem-size     49
proof            (modus-ponens tm-757 tm-207 ((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-63575.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G) -> H) -> ((G or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and G)) -> H))), M:tm-757, m:tm-207, u:((A (-> (-> (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or Dm (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-63576
in-theory        63576
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-757 tm-208 ((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-208.          (A or (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-7, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-63576.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-757, m:tm-208, u:((A (or Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-63577
in-theory        63577
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H))
theorem-size     31
proof            (modus-ponens tm-757 tm-209 ((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-209.          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) or E), M:tm-6, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-63577.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)) or H)), M:tm-757, m:tm-209, u:((A (or (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)) Em)))
================================================================
tm-name          tm-63578
in-theory        63578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D)))
theorem-size     33
proof            (modus-ponens tm-757 tm-210 ((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-63578.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)) and D))), M:tm-757, m:tm-210, u:((A (-> Am (and (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)) Am))))
================================================================
tm-name          tm-63579
in-theory        63579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))))
theorem-size     31
proof            (modus-ponens tm-757 tm-211 ((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-211.          (A -> (B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-1, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-63579.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))), M:tm-757, m:tm-211, u:((A (-> Am (-> Bm (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
================================================================
tm-name          tm-63580
in-theory        63580
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-212 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-212.          (((A and B) -> A) and (C -> (D -> C))), M:tm-21, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-63580.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (G -> F)))), M:tm-757, m:tm-212, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-63581
in-theory        63581
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-213 ((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-213.          (((A and B) -> A) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-21, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-63581.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-757, m:tm-213, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-63582
in-theory        63582
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-214 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-214.          (((A and B) -> A) and ((C and D) -> C)), M:tm-21, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-63582.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F and G) -> F))), M:tm-757, m:tm-214, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-63583
in-theory        63583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-757 tm-215 ((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-215.          (((A and B) -> A) and ((C and D) -> D)), M:tm-21, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-63583.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F and G) -> G))), M:tm-757, m:tm-215, u:((A (and (-> (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-63584
in-theory        63584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-216 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-216.          (((A and B) -> A) and (C -> (D -> (C and D)))), M:tm-21, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-63584.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (F and G))))), M:tm-757, m:tm-216, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-63585
in-theory        63585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-757 tm-217 ((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-217.          (((A and B) -> A) and (C -> (C or D))), M:tm-21, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-63585.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (F or G)))), M:tm-757, m:tm-217, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-63586
in-theory        63586
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-218 ((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-218.          (((A and B) -> A) and (C -> (D or C))), M:tm-21, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-63586.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (G or F)))), M:tm-757, m:tm-218, u:((A (and (-> (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-63587
in-theory        63587
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-219 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-219.          (((A and B) -> A) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-21, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-63587.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-757, m:tm-219, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-63588
in-theory        63588
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-757 tm-220 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-220.          (((A and B) -> A) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-21, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-63588.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-757, m:tm-220, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-63589
in-theory        63589
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-221 ((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-10.           ((not (not A)) -> A), axiom
tm-221.          (((A and B) -> A) and ((not (not C)) -> C)), M:tm-21, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-63589.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((not (not F)) -> F))), M:tm-757, m:tm-221, u:((A (and (-> (and Am Bm) Am) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-63590
in-theory        63590
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-222 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-222.          (((A and B) -> A) and (C -> (D -> (E -> D)))), M:tm-21, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-63590.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> G))))), M:tm-757, m:tm-222, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-63591
in-theory        63591
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-223 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-223.          (((A and B) -> A) and ((C -> D) -> (C -> C))), M:tm-21, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-63591.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> F)))), M:tm-757, m:tm-223, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-63592
in-theory        63592
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-757 tm-224 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-224.          (((A and B) -> A) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-21, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-63592.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-757, m:tm-224, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-63593
in-theory        63593
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-225 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-225.          (((A and B) -> A) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63593.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-757, m:tm-225, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-63594
in-theory        63594
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-757 tm-226 ((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-226.          (((A and B) -> A) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-21, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-63594.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-757, m:tm-226, u:((A (and (-> (and Am Bm) Am) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-63595
in-theory        63595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-757 tm-227 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-227.          (((A and B) -> A) and (C -> ((D and E) -> D))), M:tm-21, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-63595.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> G)))), M:tm-757, m:tm-227, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-63596
in-theory        63596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-757 tm-228 ((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-228.          (((A and B) -> A) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-21, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-63596.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-757, m:tm-228, u:((A (and (-> (and Am Bm) Am) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-63597
in-theory        63597
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-757 tm-229 ((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-229.          (((A and B) -> A) and (C -> ((D and E) -> E))), M:tm-21, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-63597.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> ((G and H) -> H)))), M:tm-757, m:tm-229, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-63598
in-theory        63598
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-230 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-230.          (((A and B) -> A) and (C -> ((D -> (E -> D)) and C))), M:tm-21, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-63598.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> G)) and F)))), M:tm-757, m:tm-230, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-63599
in-theory        63599
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-757 tm-231 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-231.          (((A and B) -> A) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-21, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-63599.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-757, m:tm-231, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-63600
in-theory        63600
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-232 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-232.          (((A and B) -> A) and (C -> (((D and E) -> D) and C))), M:tm-21, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-63600.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> G) and F)))), M:tm-757, m:tm-232, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-63601
in-theory        63601
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G))))
theorem-size     35
proof            (modus-ponens tm-757 tm-233 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-233.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> E) and D))), M:tm-20, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-63601.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> H) and G)))), M:tm-757, m:tm-233, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Em) Dm)))))
================================================================
tm-name          tm-63602
in-theory        63602
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-234 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-234.          ((A -> (B -> A)) and (C -> (((D and E) -> D) and C))), M:tm-19, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-63602.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> G) and F)))), M:tm-757, m:tm-234, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-63603
in-theory        63603
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (((E and F) -> E) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-235 ((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-235.          ((A -> (not (((B and C) -> B) and A))) -> (not A)), M:tm-9, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-63603.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (((E and F) -> E) and D))) -> (not D))), M:tm-757, m:tm-235, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Bm) Am))) (not Am))))
================================================================
tm-name          tm-63604
in-theory        63604
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-757 tm-236 ((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-63604.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D and E) -> D) and F) -> G) -> ((F or (((D and E) -> D) and F)) -> G))), M:tm-757, m:tm-236, u:((A (-> (-> (and (-> (and Am Bm) Am) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-63605
in-theory        63605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-757 tm-237 ((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-237.          (A or (B -> (((C and D) -> C) and B))), M:tm-7, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-63605.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (((F and G) -> F) and E)))), M:tm-757, m:tm-237, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-63606
in-theory        63606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (((E and F) -> E) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-757 tm-238 ((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-238.          ((A -> (((B and C) -> B) and A)) or D), M:tm-6, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-63606.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (((E and F) -> E) and D)) or G)), M:tm-757, m:tm-238, u:((A (or (-> Am (and (-> (and Bm Cm) Bm) Am)) Dm)))
================================================================
tm-name          tm-63607
in-theory        63607
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (((F and G) -> F) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-239 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-63607.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (((F and G) -> F) and E)) and D))), M:tm-757, m:tm-239, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Cm) Bm)) Am))))
================================================================
tm-name          tm-63608
in-theory        63608
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (((F and G) -> F) and E))))
theorem-size     23
proof            (modus-ponens tm-757 tm-240 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-240.          (A -> (B -> (((C and D) -> C) and B))), M:tm-1, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-63608.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (((F and G) -> F) and E)))), M:tm-757, m:tm-240, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Cm) Bm)))))
================================================================
tm-name          tm-63609
in-theory        63609
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-241 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-241.          (((A and B) -> B) and (C -> (D -> C))), M:tm-22, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-63609.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (G -> F)))), M:tm-757, m:tm-241, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-63610
in-theory        63610
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-242 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-242.          (((A and B) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-22, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-63610.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-757, m:tm-242, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-63611
in-theory        63611
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-243 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-243.          (((A and B) -> B) and ((C and D) -> C)), M:tm-22, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-63611.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F and G) -> F))), M:tm-757, m:tm-243, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-63612
in-theory        63612
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-757 tm-244 ((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-244.          (((A and B) -> B) and ((C and D) -> D)), M:tm-22, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-63612.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F and G) -> G))), M:tm-757, m:tm-244, u:((A (and (-> (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-63613
in-theory        63613
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-245 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-245.          (((A and B) -> B) and (C -> (D -> (C and D)))), M:tm-22, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-63613.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (F and G))))), M:tm-757, m:tm-245, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-63614
in-theory        63614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-757 tm-246 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-246.          (((A and B) -> B) and (C -> (C or D))), M:tm-22, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-63614.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (F or G)))), M:tm-757, m:tm-246, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-63615
in-theory        63615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-247 ((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-247.          (((A and B) -> B) and (C -> (D or C))), M:tm-22, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-63615.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (G or F)))), M:tm-757, m:tm-247, u:((A (and (-> (and Am Bm) Bm) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-63616
in-theory        63616
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-248 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-248.          (((A and B) -> B) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-22, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-63616.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-757, m:tm-248, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-63617
in-theory        63617
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-757 tm-249 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-249.          (((A and B) -> B) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-22, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-63617.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-757, m:tm-249, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-63618
in-theory        63618
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-250 ((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-250.          (((A and B) -> B) and ((not (not C)) -> C)), M:tm-22, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-63618.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((not (not F)) -> F))), M:tm-757, m:tm-250, u:((A (and (-> (and Am Bm) Bm) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-63619
in-theory        63619
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-251 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-251.          (((A and B) -> B) and (C -> (D -> (E -> D)))), M:tm-22, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-63619.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> G))))), M:tm-757, m:tm-251, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-63620
in-theory        63620
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-252 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-252.          (((A and B) -> B) and ((C -> D) -> (C -> C))), M:tm-22, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-63620.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> F)))), M:tm-757, m:tm-252, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-63621
in-theory        63621
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-757 tm-253 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-253.          (((A and B) -> B) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-22, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-63621.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-757, m:tm-253, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-63622
in-theory        63622
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-254 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-254.          (((A and B) -> B) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63622.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-757, m:tm-254, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-63623
in-theory        63623
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-757 tm-255 ((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-255.          (((A and B) -> B) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-22, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-63623.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-757, m:tm-255, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-63624
in-theory        63624
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-757 tm-256 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-256.          (((A and B) -> B) and (C -> ((D and E) -> D))), M:tm-22, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-63624.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> G)))), M:tm-757, m:tm-256, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-63625
in-theory        63625
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-757 tm-257 ((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-257.          (((A and B) -> B) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-22, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-63625.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-757, m:tm-257, u:((A (and (-> (and Am Bm) Bm) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-63626
in-theory        63626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-757 tm-258 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-258.          (((A and B) -> B) and (C -> ((D and E) -> E))), M:tm-22, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-63626.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> ((G and H) -> H)))), M:tm-757, m:tm-258, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-63627
in-theory        63627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-259 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-259.          (((A and B) -> B) and (C -> ((D -> (E -> D)) and C))), M:tm-22, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-63627.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> G)) and F)))), M:tm-757, m:tm-259, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-63628
in-theory        63628
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-757 tm-260 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-260.          (((A and B) -> B) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-22, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-63628.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-757, m:tm-260, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-63629
in-theory        63629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-261 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-261.          (((A and B) -> B) and (C -> (((D and E) -> D) and C))), M:tm-22, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-63629.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> G) and F)))), M:tm-757, m:tm-261, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-63630
in-theory        63630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-262 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-262.          (((A and B) -> B) and (C -> (((D and E) -> E) and C))), M:tm-22, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-63630.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (((G and H) -> H) and F)))), M:tm-757, m:tm-262, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-63631
in-theory        63631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-263 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-263.          (((A and B) -> A) and (C -> (((D and E) -> E) and C))), M:tm-21, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-63631.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (((G and H) -> H) and F)))), M:tm-757, m:tm-263, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-63632
in-theory        63632
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G))))
theorem-size     35
proof            (modus-ponens tm-757 tm-264 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-264.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E and F) -> F) and D))), M:tm-20, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-63632.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (((H and I) -> I) and G)))), M:tm-757, m:tm-264, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (and Em Fm) Fm) Dm)))))
================================================================
tm-name          tm-63633
in-theory        63633
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-265 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-265.          ((A -> (B -> A)) and (C -> (((D and E) -> E) and C))), M:tm-19, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-63633.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (((G and H) -> H) and F)))), M:tm-757, m:tm-265, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-63634
in-theory        63634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (((E and F) -> F) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-266 ((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-266.          ((A -> (not (((B and C) -> C) and A))) -> (not A)), M:tm-9, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-63634.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (((E and F) -> F) and D))) -> (not D))), M:tm-757, m:tm-266, u:((A (-> (-> Am (not (and (-> (and Bm Cm) Cm) Am))) (not Am))))
================================================================
tm-name          tm-63635
in-theory        63635
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-757 tm-267 ((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-63635.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D and E) -> E) and F) -> G) -> ((F or (((D and E) -> E) and F)) -> G))), M:tm-757, m:tm-267, u:((A (-> (-> (and (-> (and Am Bm) Bm) Cm) Dm) (-> (or Cm (and (-> (and Am Bm) Bm) Cm)) Dm))))
================================================================
tm-name          tm-63636
in-theory        63636
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-757 tm-268 ((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-268.          (A or (B -> (((C and D) -> D) and B))), M:tm-7, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-63636.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (((F and G) -> G) and E)))), M:tm-757, m:tm-268, u:((A (or Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-63637
in-theory        63637
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (((E and F) -> F) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-757 tm-269 ((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-269.          ((A -> (((B and C) -> C) and A)) or D), M:tm-6, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-63637.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (((E and F) -> F) and D)) or G)), M:tm-757, m:tm-269, u:((A (or (-> Am (and (-> (and Bm Cm) Cm) Am)) Dm)))
================================================================
tm-name          tm-63638
in-theory        63638
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (((F and G) -> G) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-270 ((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-63638.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (((F and G) -> G) and E)) and D))), M:tm-757, m:tm-270, u:((A (-> Am (and (-> Bm (and (-> (and Cm Dm) Dm) Bm)) Am))))
================================================================
tm-name          tm-63639
in-theory        63639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (((F and G) -> G) and E))))
theorem-size     23
proof            (modus-ponens tm-757 tm-271 ((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-271.          (A -> (B -> (((C and D) -> D) and B))), M:tm-1, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-63639.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (((F and G) -> G) and E)))), M:tm-757, m:tm-271, u:((A (-> Am (-> Bm (and (-> (and Cm Dm) Dm) Bm)))))
================================================================
tm-name          tm-63640
in-theory        63640
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-272 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-272.          ((A -> (B -> (A and B))) and (C -> (D -> C))), M:tm-23, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-63640.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> F)))), M:tm-757, m:tm-272, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-63641
in-theory        63641
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-273 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-273.          ((A -> (B -> (A and B))) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-23, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-63641.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-757, m:tm-273, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-63642
in-theory        63642
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-757 tm-274 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-274.          ((A -> (B -> (A and B))) and ((C and D) -> C)), M:tm-23, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-63642.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> F))), M:tm-757, m:tm-274, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-63643
in-theory        63643
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-757 tm-275 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-275.          ((A -> (B -> (A and B))) and ((C and D) -> D)), M:tm-23, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-63643.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F and G) -> G))), M:tm-757, m:tm-275, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-63644
in-theory        63644
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-276 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-276.          ((A -> (B -> (A and B))) and (C -> (D -> (C and D)))), M:tm-23, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-63644.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (F and G))))), M:tm-757, m:tm-276, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-63645
in-theory        63645
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (F or G))))
theorem-size     25
proof            (modus-ponens tm-757 tm-277 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-277.          ((A -> (B -> (A and B))) and (C -> (C or D))), M:tm-23, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-63645.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (F or G)))), M:tm-757, m:tm-277, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-63646
in-theory        63646
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G or F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-278 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-278.          ((A -> (B -> (A and B))) and (C -> (D or C))), M:tm-23, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-63646.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G or F)))), M:tm-757, m:tm-278, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-63647
in-theory        63647
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-279 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-279.          ((A -> (B -> (A and B))) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-23, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-63647.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-757, m:tm-279, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-63648
in-theory        63648
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-280 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-280.          ((A -> (B -> (A and B))) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-23, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-63648.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-757, m:tm-280, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-63649
in-theory        63649
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F)))
theorem-size     25
proof            (modus-ponens tm-757 tm-281 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-10.           ((not (not A)) -> A), axiom
tm-281.          ((A -> (B -> (A and B))) and ((not (not C)) -> C)), M:tm-23, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-63649.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((not (not F)) -> F))), M:tm-757, m:tm-281, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-63650
in-theory        63650
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-282 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-282.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> D)))), M:tm-23, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-63650.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> G))))), M:tm-757, m:tm-282, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-63651
in-theory        63651
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-283 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-283.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> C))), M:tm-23, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-63651.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> F)))), M:tm-757, m:tm-283, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-63652
in-theory        63652
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-284 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-284.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-23, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-63652.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-757, m:tm-284, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-63653
in-theory        63653
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-757 tm-285 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-285.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63653.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-757, m:tm-285, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-63654
in-theory        63654
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     35
proof            (modus-ponens tm-757 tm-286 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-286.          ((A -> (B -> (A and B))) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-23, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-63654.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-757, m:tm-286, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-63655
in-theory        63655
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-757 tm-287 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-287.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> D))), M:tm-23, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-63655.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> G)))), M:tm-757, m:tm-287, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-63656
in-theory        63656
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     35
proof            (modus-ponens tm-757 tm-288 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-288.          ((A -> (B -> (A and B))) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-23, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-63656.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-757, m:tm-288, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-63657
in-theory        63657
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-757 tm-289 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-289.          ((A -> (B -> (A and B))) and (C -> ((D and E) -> E))), M:tm-23, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-63657.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G and H) -> H)))), M:tm-757, m:tm-289, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-63658
in-theory        63658
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F))))
theorem-size     29
proof            (modus-ponens tm-757 tm-290 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-290.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> D)) and C))), M:tm-23, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-63658.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> G)) and F)))), M:tm-757, m:tm-290, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-63659
in-theory        63659
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     37
proof            (modus-ponens tm-757 tm-291 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-291.          ((A -> (B -> (A and B))) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-23, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-63659.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-757, m:tm-291, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-63660
in-theory        63660
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F))))
theorem-size     29
proof            (modus-ponens tm-757 tm-292 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-292.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> D) and C))), M:tm-23, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-63660.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> G) and F)))), M:tm-757, m:tm-292, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-63661
in-theory        63661
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F))))
theorem-size     29
proof            (modus-ponens tm-757 tm-293 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-293.          ((A -> (B -> (A and B))) and (C -> (((D and E) -> E) and C))), M:tm-23, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-63661.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (((G and H) -> H) and F)))), M:tm-757, m:tm-293, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-63662
in-theory        63662
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     31
proof            (modus-ponens tm-757 tm-294 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-294.          ((A -> (B -> (A and B))) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-23, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-63662.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-757, m:tm-294, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-63663
in-theory        63663
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-757 tm-295 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-295.          (((A and B) -> B) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-22, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-63663.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-757, m:tm-295, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-63664
in-theory        63664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-757 tm-296 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-296.          (((A and B) -> A) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-21, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-63664.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-757, m:tm-296, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-63665
in-theory        63665
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G))))
theorem-size     37
proof            (modus-ponens tm-757 tm-297 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-297.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F -> (E and F))) and D))), M:tm-20, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-63665.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I -> (H and I))) and G)))), M:tm-757, m:tm-297, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (-> Fm (and Em Fm))) Dm)))))
================================================================
tm-name          tm-63666
in-theory        63666
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-757 tm-298 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-298.          ((A -> (B -> A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-19, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-63666.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-757, m:tm-298, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-63667
in-theory        63667
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D)))
theorem-size     27
proof            (modus-ponens tm-757 tm-299 ((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-299.          ((A -> (not ((B -> (C -> (B and C))) and A))) -> (not A)), M:tm-9, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-63667.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not ((E -> (F -> (E and F))) and D))) -> (not D))), M:tm-757, m:tm-299, u:((A (-> (-> Am (not (and (-> Bm (-> Cm (and Bm Cm))) Am))) (not Am))))
================================================================
tm-name          tm-63668
in-theory        63668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-757 tm-300 ((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-63668.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> (D and E))) and F) -> G) -> ((F or ((D -> (E -> (D and E))) and F)) -> G))), M:tm-757, m:tm-300, u:((A (-> (-> (and (-> Am (-> Bm (and Am Bm))) Cm) Dm) (-> (or Cm (and (-> Am (-> Bm (and Am Bm))) Cm)) Dm))))
================================================================
tm-name          tm-63669
in-theory        63669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-757 tm-301 ((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-301.          (A or (B -> ((C -> (D -> (C and D))) and B))), M:tm-7, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-63669.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> ((F -> (G -> (F and G))) and E)))), M:tm-757, m:tm-301, u:((A (or Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-63670
in-theory        63670
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E -> (F -> (E and F))) and D)) or G))
theorem-size     25
proof            (modus-ponens tm-757 tm-302 ((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-302.          ((A -> ((B -> (C -> (B and C))) and A)) or D), M:tm-6, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-63670.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E -> (F -> (E and F))) and D)) or G)), M:tm-757, m:tm-302, u:((A (or (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am)) Dm)))
================================================================
tm-name          tm-63671
in-theory        63671
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D)))
theorem-size     27
proof            (modus-ponens tm-757 tm-303 ((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-63671.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> ((F -> (G -> (F and G))) and E)) and D))), M:tm-757, m:tm-303, u:((A (-> Am (and (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)) Am))))
================================================================
tm-name          tm-63672
in-theory        63672
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> ((F -> (G -> (F and G))) and E))))
theorem-size     25
proof            (modus-ponens tm-757 tm-304 ((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-304.          (A -> (B -> ((C -> (D -> (C and D))) and B))), M:tm-1, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-63672.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> ((F -> (G -> (F and G))) and E)))), M:tm-757, m:tm-304, u:((A (-> Am (-> Bm (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
================================================================
tm-name          tm-63673
in-theory        63673
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (E -> D))))
theorem-size     19
proof            (modus-ponens tm-757 tm-305 ((A (-> Am (and Am (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-63673.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (E -> D)))), M:tm-757, m:tm-305, u:((A (-> Am (and Am (-> Bm Am)))))
================================================================
tm-name          tm-63674
in-theory        63674
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-306 ((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-63674.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> F)) -> ((D -> (E -> F)) and ((D -> E) -> (D -> F))))), M:tm-757, m:tm-306, u:((A (-> (-> Am (-> Bm Cm)) (and (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-63675
in-theory        63675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D and E) -> ((D and E) and D)))
theorem-size     21
proof            (modus-ponens tm-757 tm-307 ((A (-> (and Am Bm) (and (and Am Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-307.          ((A and B) -> ((A and B) and A)), M:tm-24, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-63675.        (((A -> B) -> (((A and C) or A) -> B)) and ((D and E) -> ((D and E) and D))), M:tm-757, m:tm-307, u:((A (-> (and Am Bm) (and (and Am Bm) Am))))
================================================================
tm-name          tm-63676
in-theory        63676
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D and E) -> ((D and E) and E)))
theorem-size     21
proof            (modus-ponens tm-757 tm-308 ((A (-> (and Am Bm) (and (and Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-308.          ((A and B) -> ((A and B) and B)), M:tm-24, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-63676.        (((A -> B) -> (((A and C) or A) -> B)) and ((D and E) -> ((D and E) and E))), M:tm-757, m:tm-308, u:((A (-> (and Am Bm) (and (and Am Bm) Bm))))
================================================================
tm-name          tm-63677
in-theory        63677
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (E -> (D and E)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-309 ((A (-> Am (and Am (-> Bm (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-63677.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (E -> (D and E))))), M:tm-757, m:tm-309, u:((A (-> Am (and Am (-> Bm (and Am Bm))))))
================================================================
tm-name          tm-63678
in-theory        63678
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (D or E))))
theorem-size     19
proof            (modus-ponens tm-757 tm-310 ((A (-> Am (and Am (or Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-63678.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (D or E)))), M:tm-757, m:tm-310, u:((A (-> Am (and Am (or Am Bm)))))
================================================================
tm-name          tm-63679
in-theory        63679
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (E or D))))
theorem-size     19
proof            (modus-ponens tm-757 tm-311 ((A (-> Am (and Am (or Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-63679.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (E or D)))), M:tm-757, m:tm-311, u:((A (-> Am (and Am (or Bm Am)))))
================================================================
tm-name          tm-63680
in-theory        63680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F)))))
theorem-size     29
proof            (modus-ponens tm-757 tm-312 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-63680.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((D -> E) and ((E -> F) -> ((D or E) -> F))))), M:tm-757, m:tm-312, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm))))))
================================================================
tm-name          tm-63681
in-theory        63681
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-313 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-63681.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((D -> E) and ((D -> (not E)) -> (not D))))), M:tm-757, m:tm-313, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (-> Am (not Bm)) (not Am))))))
================================================================
tm-name          tm-63682
in-theory        63682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((not (not D)) -> ((not (not D)) and D)))
theorem-size     21
proof            (modus-ponens tm-757 tm-314 ((A (-> (not (not Am)) (and (not (not Am)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-10)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-10.           ((not (not A)) -> A), axiom
tm-314.          ((not (not A)) -> ((not (not A)) and A)), M:tm-24, m:tm-10, u:((A (not (not Am))) (B Am))
tm-63682.        (((A -> B) -> (((A and C) or A) -> B)) and ((not (not D)) -> ((not (not D)) and D))), M:tm-757, m:tm-314, u:((A (-> (not (not Am)) (and (not (not Am)) Am))))
================================================================
tm-name          tm-63683
in-theory        63683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (E -> (F -> E)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-315 ((A (-> Am (and Am (-> Bm (-> Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-63683.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (E -> (F -> E))))), M:tm-757, m:tm-315, u:((A (-> Am (and Am (-> Bm (-> Cm Bm))))))
================================================================
tm-name          tm-63684
in-theory        63684
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((D -> E) and (D -> D))))
theorem-size     23
proof            (modus-ponens tm-757 tm-316 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-63684.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((D -> E) and (D -> D)))), M:tm-757, m:tm-316, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am Am)))))
================================================================
tm-name          tm-63685
in-theory        63685
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-757 tm-317 ((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-63685.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> (D -> E)) -> (((D -> (E -> F)) -> (D -> E)) and ((D -> (E -> F)) -> (D -> F))))), M:tm-757, m:tm-317, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
================================================================
tm-name          tm-63686
in-theory        63686
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))))
theorem-size     29
proof            (modus-ponens tm-757 tm-318 ((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-63686.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))), M:tm-757, m:tm-318, u:((A (-> Am (and Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))))
================================================================
tm-name          tm-63687
in-theory        63687
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E))))
theorem-size     35
proof            (modus-ponens tm-757 tm-319 ((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-63687.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) -> D) -> ((((D -> E) and F) -> D) and (((D -> E) and F) -> E)))), M:tm-757, m:tm-319, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (and (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm)))))
================================================================
tm-name          tm-63688
in-theory        63688
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and ((E and F) -> E))))
theorem-size     21
proof            (modus-ponens tm-757 tm-320 ((A (-> Am (and Am (-> (and Bm Cm) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-63688.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and ((E and F) -> E)))), M:tm-757, m:tm-320, u:((A (-> Am (and Am (-> (and Bm Cm) Bm)))))
================================================================
tm-name          tm-63689
in-theory        63689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F))))
theorem-size     35
proof            (modus-ponens tm-757 tm-321 ((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-63689.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) -> E) -> (((D and (E -> F)) -> E) and ((D and (E -> F)) -> F)))), M:tm-757, m:tm-321, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (and (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm)))))
================================================================
tm-name          tm-63690
in-theory        63690
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and ((E and F) -> F))))
theorem-size     21
proof            (modus-ponens tm-757 tm-322 ((A (-> Am (and Am (-> (and Bm Cm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-63690.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and ((E and F) -> F)))), M:tm-757, m:tm-322, u:((A (-> Am (and Am (-> (and Bm Cm) Cm)))))
================================================================
tm-name          tm-63691
in-theory        63691
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and ((E -> (F -> E)) and D))))
theorem-size     23
proof            (modus-ponens tm-757 tm-323 ((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-63691.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and ((E -> (F -> E)) and D)))), M:tm-757, m:tm-323, u:((A (-> Am (and Am (and (-> Bm (-> Cm Bm)) Am)))))
================================================================
tm-name          tm-63692
in-theory        63692
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))))
theorem-size     31
proof            (modus-ponens tm-757 tm-324 ((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-63692.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))), M:tm-757, m:tm-324, u:((A (-> Am (and Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
================================================================
tm-name          tm-63693
in-theory        63693
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (((E and F) -> E) and D))))
theorem-size     23
proof            (modus-ponens tm-757 tm-325 ((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-63693.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (((E and F) -> E) and D)))), M:tm-757, m:tm-325, u:((A (-> Am (and Am (and (-> (and Bm Cm) Bm) Am)))))
================================================================
tm-name          tm-63694
in-theory        63694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (((E and F) -> F) and D))))
theorem-size     23
proof            (modus-ponens tm-757 tm-326 ((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-63694.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (((E and F) -> F) and D)))), M:tm-757, m:tm-326, u:((A (-> Am (and Am (and (-> (and Bm Cm) Cm) Am)))))
================================================================
tm-name          tm-63695
in-theory        63695
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and ((E -> (F -> (E and F))) and D))))
theorem-size     25
proof            (modus-ponens tm-757 tm-327 ((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-63695.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and ((E -> (F -> (E and F))) and D)))), M:tm-757, m:tm-327, u:((A (-> Am (and Am (and (-> Bm (-> Cm (and Bm Cm))) Am)))))
================================================================
tm-name          tm-63696
in-theory        63696
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((D -> E) and (D -> (D and E)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-328 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-63696.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((D -> E) and (D -> (D and E))))), M:tm-757, m:tm-328, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> Am (and Am Bm))))))
================================================================
tm-name          tm-63697
in-theory        63697
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G)))))
theorem-size     29
proof            (modus-ponens tm-757 tm-329 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-329.          ((A -> (B -> (A and B))) and ((C -> D) -> (C -> (C and D)))), M:tm-23, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-63697.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (F -> (F and G))))), M:tm-757, m:tm-329, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-63698
in-theory        63698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-330 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-330.          (((A and B) -> B) and ((C -> D) -> (C -> (C and D)))), M:tm-22, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-63698.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (F -> (F and G))))), M:tm-757, m:tm-330, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-63699
in-theory        63699
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-331 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-331.          (((A and B) -> A) and ((C -> D) -> (C -> (C and D)))), M:tm-21, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-63699.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (F -> (F and G))))), M:tm-757, m:tm-331, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-63700
in-theory        63700
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H)))))
theorem-size     35
proof            (modus-ponens tm-757 tm-332 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-332.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (D -> (D and E)))), M:tm-20, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-63700.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (G -> (G and H))))), M:tm-757, m:tm-332, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> Dm (and Dm Em))))))
================================================================
tm-name          tm-63701
in-theory        63701
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-333 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-333.          ((A -> (B -> A)) and ((C -> D) -> (C -> (C and D)))), M:tm-19, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-63701.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (F -> (F and G))))), M:tm-757, m:tm-333, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-63702
in-theory        63702
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E))))
theorem-size     27
proof            (modus-ponens tm-757 tm-334 ((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-334.          (((A -> B) -> (not (A -> (A and B)))) -> (not (A -> B))), M:tm-9, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-63702.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (not (D -> (D and E)))) -> (not (D -> E)))), M:tm-757, m:tm-334, u:((A (-> (-> (-> Am Bm) (not (-> Am (and Am Bm)))) (not (-> Am Bm)))))
================================================================
tm-name          tm-63703
in-theory        63703
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F)))
theorem-size     31
proof            (modus-ponens tm-757 tm-335 ((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-63703.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (D and E)) -> F) -> (((D -> E) or (D -> (D and E))) -> F))), M:tm-757, m:tm-335, u:((A (-> (-> (-> Am (and Am Bm)) Cm) (-> (or (-> Am Bm) (-> Am (and Am Bm))) Cm))))
================================================================
tm-name          tm-63704
in-theory        63704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-757 tm-336 ((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-336.          (A or ((B -> C) -> (B -> (B and C)))), M:tm-7, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-63704.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> F) -> (E -> (E and F))))), M:tm-757, m:tm-336, u:((A (or Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-63705
in-theory        63705
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (D -> (D and E))) or F))
theorem-size     23
proof            (modus-ponens tm-757 tm-337 ((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-337.          (((A -> B) -> (A -> (A and B))) or C), M:tm-6, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-63705.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (D -> (D and E))) or F)), M:tm-757, m:tm-337, u:((A (or (-> (-> Am Bm) (-> Am (and Am Bm))) Cm)))
================================================================
tm-name          tm-63706
in-theory        63706
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> (E -> (E and F))) and D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-338 ((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-63706.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> (E -> (E and F))) and D))), M:tm-757, m:tm-338, u:((A (-> Am (and (-> (-> Bm Cm) (-> Bm (and Bm Cm))) Am))))
================================================================
tm-name          tm-63707
in-theory        63707
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> D) -> ((D -> E) -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-757 tm-339 ((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-63707.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> D) -> ((D -> E) -> (D and E)))), M:tm-757, m:tm-339, u:((A (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) (and Am Bm)))))
================================================================
tm-name          tm-63708
in-theory        63708
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> F) -> (E -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-757 tm-340 ((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-340.          (A -> ((B -> C) -> (B -> (B and C)))), M:tm-1, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-63708.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> F) -> (E -> (E and F))))), M:tm-757, m:tm-340, u:((A (-> Am (-> (-> Bm Cm) (-> Bm (and Bm Cm))))))
================================================================
tm-name          tm-63709
in-theory        63709
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (E -> (F -> (E and F))))))
theorem-size     23
proof            (modus-ponens tm-757 tm-341 ((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-63709.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (E -> (F -> (E and F)))))), M:tm-757, m:tm-341, u:((A (-> Am (and Am (-> Bm (-> Cm (and Bm Cm)))))))
================================================================
tm-name          tm-63710
in-theory        63710
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-757 tm-342 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-342.          ((A -> (B -> (A and B))) and (C -> (D -> (E -> (D and E))))), M:tm-23, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63710.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H -> (G and H)))))), M:tm-757, m:tm-342, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-63711
in-theory        63711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-757 tm-343 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-343.          (((A and B) -> B) and (C -> (D -> (E -> (D and E))))), M:tm-22, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63711.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (H -> (G and H)))))), M:tm-757, m:tm-343, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-63712
in-theory        63712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-757 tm-344 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-344.          (((A and B) -> A) and (C -> (D -> (E -> (D and E))))), M:tm-21, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63712.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (H -> (G and H)))))), M:tm-757, m:tm-344, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-63713
in-theory        63713
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I))))))
theorem-size     35
proof            (modus-ponens tm-757 tm-345 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-345.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F -> (E and F))))), M:tm-20, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63713.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I -> (H and I)))))), M:tm-757, m:tm-345, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-63714
in-theory        63714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-757 tm-346 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-346.          ((A -> (B -> A)) and (C -> (D -> (E -> (D and E))))), M:tm-19, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63714.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H -> (G and H)))))), M:tm-757, m:tm-346, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-63715
in-theory        63715
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G))
theorem-size     25
proof            (modus-ponens tm-757 tm-347 ((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-347.          ((A and ((B -> (C -> (B and C))) -> D)) -> D), M:tm-17, m:tm-25, u:((Am (and A (-> (-> Bm (-> Cm (and Bm Cm))) C))) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-63715.        (((A -> B) -> (((A and C) or A) -> B)) and ((D and ((E -> (F -> (E and F))) -> G)) -> G)), M:tm-757, m:tm-347, u:((A (-> (and Am (-> (-> Bm (-> Cm (and Bm Cm))) Dm)) Dm)))
================================================================
tm-name          tm-63716
in-theory        63716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> (D and E))) -> F) and G) -> F))
theorem-size     25
proof            (modus-ponens tm-757 tm-348 ((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-348.          ((((A -> (B -> (A and B))) -> C) and D) -> C), M:tm-15, m:tm-25, u:((Am (and (-> (-> Bm (-> Cm (and Bm Cm))) B) C)) (A (-> Bm (-> Cm (and Bm Cm)))))
tm-63716.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> (D and E))) -> F) and G) -> F)), M:tm-757, m:tm-348, u:((A (-> (and (-> (-> Am (-> Bm (and Am Bm))) Cm) Dm) Cm)))
================================================================
tm-name          tm-63717
in-theory        63717
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F)))
theorem-size     25
proof            (modus-ponens tm-757 tm-349 ((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-63717.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E -> (D and E)) -> F)) -> (D -> F))), M:tm-757, m:tm-349, u:((A (-> (-> Am (-> (-> Bm (and Am Bm)) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-63718
in-theory        63718
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-350 ((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-63718.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (E -> (F -> (E and F))))) -> (not D))), M:tm-757, m:tm-350, u:((A (-> (-> Am (not (-> Bm (-> Cm (and Bm Cm))))) (not Am))))
================================================================
tm-name          tm-63719
in-theory        63719
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F)))
theorem-size     33
proof            (modus-ponens tm-757 tm-351 ((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-63719.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> (D and E))) -> F) -> ((G or (D -> (E -> (D and E)))) -> F))), M:tm-757, m:tm-351, u:((A (-> (-> (-> Am (-> Bm (and Am Bm))) Cm) (-> (or Dm (-> Am (-> Bm (and Am Bm)))) Cm))))
================================================================
tm-name          tm-63720
in-theory        63720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-757 tm-352 ((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-352.          (A or (B -> (C -> (D -> (C and D))))), M:tm-7, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63720.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (F -> (G -> (F and G)))))), M:tm-757, m:tm-352, u:((A (or Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-63721
in-theory        63721
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (F -> (E and F)))) or G))
theorem-size     23
proof            (modus-ponens tm-757 tm-353 ((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-353.          ((A -> (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63721.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (F -> (E and F)))) or G)), M:tm-757, m:tm-353, u:((A (or (-> Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-63722
in-theory        63722
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> (G -> (F and G)))) and D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-354 ((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63722.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> (G -> (F and G)))) and D))), M:tm-757, m:tm-354, u:((A (-> Am (and (-> Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-63723
in-theory        63723
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (D -> (F -> (E and F)))))
theorem-size     23
proof            (modus-ponens tm-757 tm-355 ((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-63723.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (D -> (F -> (E and F))))), M:tm-757, m:tm-355, u:((A (-> (-> Am Bm) (-> Am (-> Cm (and Bm Cm))))))
================================================================
tm-name          tm-63724
in-theory        63724
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-757 tm-356 ((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-356.          (A -> (B -> (C -> (D -> (C and D))))), M:tm-1, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63724.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (F -> (G -> (F and G)))))), M:tm-757, m:tm-356, u:((A (-> Am (-> Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-63725
in-theory        63725
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H)))
theorem-size     27
proof            (modus-ponens tm-757 tm-357 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-357.          ((A -> (B -> (A and B))) and ((C -> (D -> C)) or E)), M:tm-23, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-63725.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> F)) or H))), M:tm-757, m:tm-357, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-63726
in-theory        63726
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-358 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-358.          (((A and B) -> B) and ((C -> (D -> C)) or E)), M:tm-22, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-63726.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> (G -> F)) or H))), M:tm-757, m:tm-358, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-63727
in-theory        63727
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-359 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-359.          (((A and B) -> A) and ((C -> (D -> C)) or E)), M:tm-21, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-63727.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> (G -> F)) or H))), M:tm-757, m:tm-359, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-63728
in-theory        63728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-360 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-6 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-360.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> D)) or F)), M:tm-20, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-63728.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> G)) or I))), M:tm-757, m:tm-360, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em Dm)) Fm))))
================================================================
tm-name          tm-63729
in-theory        63729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-361 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-361.          ((A -> (B -> A)) and ((C -> (D -> C)) or E)), M:tm-19, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-63729.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G -> F)) or H))), M:tm-757, m:tm-361, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-63730
in-theory        63730
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-757 tm-362 ((A (or Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-362.          (A or ((B -> (C -> B)) or D)), M:tm-7, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-63730.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> (F -> E)) or G))), M:tm-757, m:tm-362, u:((A (or Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-63731
in-theory        63731
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> D)) or F) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-363 ((A (or (or (-> Am (-> Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-363.          (((A -> (B -> A)) or C) or D), M:tm-6, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-63731.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> D)) or F) or G)), M:tm-757, m:tm-363, u:((A (or (or (-> Am (-> Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-63732
in-theory        63732
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (F -> E)) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-364 ((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-63732.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (F -> E)) or G) and D))), M:tm-757, m:tm-364, u:((A (-> Am (and (or (-> Bm (-> Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-63733
in-theory        63733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> E)) or G)))
theorem-size     21
proof            (modus-ponens tm-757 tm-365 ((A (-> Am (or (-> Bm (-> Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-365.          (A -> ((B -> (C -> B)) or D)), M:tm-1, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-63733.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> E)) or G))), M:tm-757, m:tm-365, u:((A (-> Am (or (-> Bm (-> Cm Bm)) Dm))))
================================================================
tm-name          tm-63734
in-theory        63734
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     35
proof            (modus-ponens tm-757 tm-366 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-366.          ((A -> (B -> (A and B))) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-23, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-63734.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-757, m:tm-366, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-63735
in-theory        63735
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-367 ((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-367.          (((A and B) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-22, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-63735.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-757, m:tm-367, u:((A (and (-> (and Am Bm) Bm) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-63736
in-theory        63736
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-368 ((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-368.          (((A and B) -> A) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-21, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-63736.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-757, m:tm-368, u:((A (and (-> (and Am Bm) Am) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-63737
in-theory        63737
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J)))
theorem-size     41
proof            (modus-ponens tm-757 tm-369 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-6)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-369.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G)), M:tm-20, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-63737.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) or J))), M:tm-757, m:tm-369, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))
================================================================
tm-name          tm-63738
in-theory        63738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-370 ((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-370.          ((A -> (B -> A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-19, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-63738.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-757, m:tm-370, u:((A (and (-> Am (-> Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-63739
in-theory        63739
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-757 tm-371 ((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-371.          (A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-7, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-63739.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-757, m:tm-371, u:((A (or Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-63740
in-theory        63740
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H))
theorem-size     29
proof            (modus-ponens tm-757 tm-372 ((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-372.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) or E), M:tm-6, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-63740.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) or G) or H)), M:tm-757, m:tm-372, u:((A (or (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em)))
================================================================
tm-name          tm-63741
in-theory        63741
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D)))
theorem-size     31
proof            (modus-ponens tm-757 tm-373 ((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-63741.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H) and D))), M:tm-757, m:tm-373, u:((A (-> Am (and (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em) Am))))
================================================================
tm-name          tm-63742
in-theory        63742
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H)))
theorem-size     29
proof            (modus-ponens tm-757 tm-374 ((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-374.          (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E)), M:tm-1, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-63742.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) or H))), M:tm-757, m:tm-374, u:((A (-> Am (or (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))
================================================================
tm-name          tm-63743
in-theory        63743
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H)))
theorem-size     27
proof            (modus-ponens tm-757 tm-375 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-375.          ((A -> (B -> (A and B))) and (((C and D) -> C) or E)), M:tm-23, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-63743.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> F) or H))), M:tm-757, m:tm-375, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-63744
in-theory        63744
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-376 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-376.          (((A and B) -> B) and (((C and D) -> C) or E)), M:tm-22, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-63744.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F and G) -> F) or H))), M:tm-757, m:tm-376, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-63745
in-theory        63745
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-377 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-377.          (((A and B) -> A) and (((C and D) -> C) or E)), M:tm-21, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-63745.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F and G) -> F) or H))), M:tm-757, m:tm-377, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-63746
in-theory        63746
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-378 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-378.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> D) or F)), M:tm-20, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-63746.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> G) or I))), M:tm-757, m:tm-378, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Dm) Fm))))
================================================================
tm-name          tm-63747
in-theory        63747
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-379 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-379.          ((A -> (B -> A)) and (((C and D) -> C) or E)), M:tm-19, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-63747.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F and G) -> F) or H))), M:tm-757, m:tm-379, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-63748
in-theory        63748
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-757 tm-380 ((A (or Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-380.          (A or (((B and C) -> B) or D)), M:tm-7, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-63748.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E and F) -> E) or G))), M:tm-757, m:tm-380, u:((A (or Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-63749
in-theory        63749
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D and E) -> D) or F) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-381 ((A (or (or (-> (and Am Bm) Am) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-381.          ((((A and B) -> A) or C) or D), M:tm-6, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-63749.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D and E) -> D) or F) or G)), M:tm-757, m:tm-381, u:((A (or (or (-> (and Am Bm) Am) Cm) Dm)))
================================================================
tm-name          tm-63750
in-theory        63750
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E and F) -> E) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-382 ((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-63750.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E and F) -> E) or G) and D))), M:tm-757, m:tm-382, u:((A (-> Am (and (or (-> (and Bm Cm) Bm) Dm) Am))))
================================================================
tm-name          tm-63751
in-theory        63751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E and F) -> E) or G)))
theorem-size     21
proof            (modus-ponens tm-757 tm-383 ((A (-> Am (or (-> (and Bm Cm) Bm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-383.          (A -> (((B and C) -> B) or D)), M:tm-1, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-63751.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E and F) -> E) or G))), M:tm-757, m:tm-383, u:((A (-> Am (or (-> (and Bm Cm) Bm) Dm))))
================================================================
tm-name          tm-63752
in-theory        63752
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H)))
theorem-size     27
proof            (modus-ponens tm-757 tm-384 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-384.          ((A -> (B -> (A and B))) and (((C and D) -> D) or E)), M:tm-23, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-63752.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F and G) -> G) or H))), M:tm-757, m:tm-384, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-63753
in-theory        63753
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-385 ((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-385.          (((A and B) -> B) and (((C and D) -> D) or E)), M:tm-22, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-63753.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F and G) -> G) or H))), M:tm-757, m:tm-385, u:((A (and (-> (and Am Bm) Bm) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-63754
in-theory        63754
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-386 ((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-386.          (((A and B) -> A) and (((C and D) -> D) or E)), M:tm-21, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-63754.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F and G) -> G) or H))), M:tm-757, m:tm-386, u:((A (and (-> (and Am Bm) Am) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-63755
in-theory        63755
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-387 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-6 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-387.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) -> E) or F)), M:tm-20, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-63755.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G and H) -> H) or I))), M:tm-757, m:tm-387, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (and Dm Em) Em) Fm))))
================================================================
tm-name          tm-63756
in-theory        63756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-388 ((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-388.          ((A -> (B -> A)) and (((C and D) -> D) or E)), M:tm-19, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-63756.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F and G) -> G) or H))), M:tm-757, m:tm-388, u:((A (and (-> Am (-> Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-63757
in-theory        63757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-757 tm-389 ((A (or Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-389.          (A or (((B and C) -> C) or D)), M:tm-7, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-63757.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E and F) -> F) or G))), M:tm-757, m:tm-389, u:((A (or Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-63758
in-theory        63758
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D and E) -> E) or F) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-390 ((A (or (or (-> (and Am Bm) Bm) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-390.          ((((A and B) -> B) or C) or D), M:tm-6, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-63758.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D and E) -> E) or F) or G)), M:tm-757, m:tm-390, u:((A (or (or (-> (and Am Bm) Bm) Cm) Dm)))
================================================================
tm-name          tm-63759
in-theory        63759
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E and F) -> F) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-391 ((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-63759.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E and F) -> F) or G) and D))), M:tm-757, m:tm-391, u:((A (-> Am (and (or (-> (and Bm Cm) Cm) Dm) Am))))
================================================================
tm-name          tm-63760
in-theory        63760
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E and F) -> F) or G)))
theorem-size     21
proof            (modus-ponens tm-757 tm-392 ((A (-> Am (or (-> (and Bm Cm) Cm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-392.          (A -> (((B and C) -> C) or D)), M:tm-1, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-63760.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E and F) -> F) or G))), M:tm-757, m:tm-392, u:((A (-> Am (or (-> (and Bm Cm) Cm) Dm))))
================================================================
tm-name          tm-63761
in-theory        63761
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H)))
theorem-size     29
proof            (modus-ponens tm-757 tm-393 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-393.          ((A -> (B -> (A and B))) and ((C -> (D -> (C and D))) or E)), M:tm-23, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-63761.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G -> (F and G))) or H))), M:tm-757, m:tm-393, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-63762
in-theory        63762
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-757 tm-394 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-394.          (((A and B) -> B) and ((C -> (D -> (C and D))) or E)), M:tm-22, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-63762.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> (G -> (F and G))) or H))), M:tm-757, m:tm-394, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-63763
in-theory        63763
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-757 tm-395 ((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-395.          (((A and B) -> A) and ((C -> (D -> (C and D))) or E)), M:tm-21, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-63763.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> (G -> (F and G))) or H))), M:tm-757, m:tm-395, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-63764
in-theory        63764
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I)))
theorem-size     35
proof            (modus-ponens tm-757 tm-396 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-396.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E -> (D and E))) or F)), M:tm-20, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-63764.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H -> (G and H))) or I))), M:tm-757, m:tm-396, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (-> Em (and Dm Em))) Fm))))
================================================================
tm-name          tm-63765
in-theory        63765
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-757 tm-397 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-397.          ((A -> (B -> A)) and ((C -> (D -> (C and D))) or E)), M:tm-19, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-63765.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G -> (F and G))) or H))), M:tm-757, m:tm-397, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-63766
in-theory        63766
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-757 tm-398 ((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-398.          (A or ((B -> (C -> (B and C))) or D)), M:tm-7, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-63766.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> (F -> (E and F))) or G))), M:tm-757, m:tm-398, u:((A (or Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-63767
in-theory        63767
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> (D and E))) or F) or G))
theorem-size     23
proof            (modus-ponens tm-757 tm-399 ((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-399.          (((A -> (B -> (A and B))) or C) or D), M:tm-6, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-63767.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> (D and E))) or F) or G)), M:tm-757, m:tm-399, u:((A (or (or (-> Am (-> Bm (and Am Bm))) Cm) Dm)))
================================================================
tm-name          tm-63768
in-theory        63768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (F -> (E and F))) or G) and D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-400 ((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-63768.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (F -> (E and F))) or G) and D))), M:tm-757, m:tm-400, u:((A (-> Am (and (or (-> Bm (-> Cm (and Bm Cm))) Dm) Am))))
================================================================
tm-name          tm-63769
in-theory        63769
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> (E and F))) or G)))
theorem-size     23
proof            (modus-ponens tm-757 tm-401 ((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-401.          (A -> ((B -> (C -> (B and C))) or D)), M:tm-1, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-63769.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> (E and F))) or G))), M:tm-757, m:tm-401, u:((A (-> Am (or (-> Bm (-> Cm (and Bm Cm))) Dm))))
================================================================
tm-name          tm-63770
in-theory        63770
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H)))
theorem-size     27
proof            (modus-ponens tm-757 tm-402 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-402.          ((A -> (B -> (A and B))) and ((C -> (C or D)) or E)), M:tm-23, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-63770.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (F or G)) or H))), M:tm-757, m:tm-402, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-63771
in-theory        63771
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-403 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-403.          (((A and B) -> B) and ((C -> (C or D)) or E)), M:tm-22, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-63771.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> (F or G)) or H))), M:tm-757, m:tm-403, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-63772
in-theory        63772
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-404 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-404.          (((A and B) -> A) and ((C -> (C or D)) or E)), M:tm-21, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-63772.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> (F or G)) or H))), M:tm-757, m:tm-404, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-63773
in-theory        63773
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-405 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-405.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (D or E)) or F)), M:tm-20, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-63773.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (G or H)) or I))), M:tm-757, m:tm-405, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Dm Em)) Fm))))
================================================================
tm-name          tm-63774
in-theory        63774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-406 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-406.          ((A -> (B -> A)) and ((C -> (C or D)) or E)), M:tm-19, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-63774.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> (F or G)) or H))), M:tm-757, m:tm-406, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-63775
in-theory        63775
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-757 tm-407 ((A (or Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-407.          (A or ((B -> (B or C)) or D)), M:tm-7, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-63775.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> (E or F)) or G))), M:tm-757, m:tm-407, u:((A (or Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-63776
in-theory        63776
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (D or E)) or F) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-408 ((A (or (or (-> Am (or Am Bm)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-408.          (((A -> (A or B)) or C) or D), M:tm-6, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-63776.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (D or E)) or F) or G)), M:tm-757, m:tm-408, u:((A (or (or (-> Am (or Am Bm)) Cm) Dm)))
================================================================
tm-name          tm-63777
in-theory        63777
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (E or F)) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-409 ((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-63777.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (E or F)) or G) and D))), M:tm-757, m:tm-409, u:((A (-> Am (and (or (-> Bm (or Bm Cm)) Dm) Am))))
================================================================
tm-name          tm-63778
in-theory        63778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (E or F)) or G)))
theorem-size     21
proof            (modus-ponens tm-757 tm-410 ((A (-> Am (or (-> Bm (or Bm Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-410.          (A -> ((B -> (B or C)) or D)), M:tm-1, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-63778.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (E or F)) or G))), M:tm-757, m:tm-410, u:((A (-> Am (or (-> Bm (or Bm Cm)) Dm))))
================================================================
tm-name          tm-63779
in-theory        63779
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-411 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-411.          ((A -> (A or B)) and (C -> (D -> C))), M:tm-32, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-63779.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> F)))), M:tm-757, m:tm-411, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-63780
in-theory        63780
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-412 ((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-412.          ((A -> (A or B)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-32, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-63780.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-757, m:tm-412, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-63781
in-theory        63781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-413 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-413.          ((A -> (A or B)) and ((C and D) -> C)), M:tm-32, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-63781.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F and G) -> F))), M:tm-757, m:tm-413, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-63782
in-theory        63782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-757 tm-414 ((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-414.          ((A -> (A or B)) and ((C and D) -> D)), M:tm-32, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-63782.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F and G) -> G))), M:tm-757, m:tm-414, u:((A (and (-> Am (or Am Bm)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-63783
in-theory        63783
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-415 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-415.          ((A -> (A or B)) and (C -> (D -> (C and D)))), M:tm-32, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-63783.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (F and G))))), M:tm-757, m:tm-415, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-63784
in-theory        63784
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-757 tm-416 ((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-416.          ((A -> (A or B)) and (C -> (C or D))), M:tm-32, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-63784.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (F or G)))), M:tm-757, m:tm-416, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-63785
in-theory        63785
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-417 ((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-417.          ((A -> (A or B)) and (C -> (D or C))), M:tm-32, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-63785.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (G or F)))), M:tm-757, m:tm-417, u:((A (and (-> Am (or Am Bm)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-63786
in-theory        63786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-418 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-418.          ((A -> (A or B)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-32, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-63786.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-757, m:tm-418, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-63787
in-theory        63787
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-757 tm-419 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-419.          ((A -> (A or B)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-32, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-63787.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-757, m:tm-419, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-63788
in-theory        63788
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-420 ((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-420.          ((A -> (A or B)) and ((not (not C)) -> C)), M:tm-32, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-63788.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((not (not F)) -> F))), M:tm-757, m:tm-420, u:((A (and (-> Am (or Am Bm)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-63789
in-theory        63789
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-421 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-421.          ((A -> (A or B)) and (C -> (D -> (E -> D)))), M:tm-32, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-63789.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> G))))), M:tm-757, m:tm-421, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-63790
in-theory        63790
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-422 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-422.          ((A -> (A or B)) and ((C -> D) -> (C -> C))), M:tm-32, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-63790.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> F)))), M:tm-757, m:tm-422, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-63791
in-theory        63791
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-757 tm-423 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-423.          ((A -> (A or B)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-32, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-63791.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-757, m:tm-423, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-63792
in-theory        63792
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-424 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-424.          ((A -> (A or B)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63792.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-757, m:tm-424, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-63793
in-theory        63793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-757 tm-425 ((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-425.          ((A -> (A or B)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-32, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-63793.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-757, m:tm-425, u:((A (and (-> Am (or Am Bm)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-63794
in-theory        63794
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-757 tm-426 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-426.          ((A -> (A or B)) and (C -> ((D and E) -> D))), M:tm-32, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-63794.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> G)))), M:tm-757, m:tm-426, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-63795
in-theory        63795
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-757 tm-427 ((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-427.          ((A -> (A or B)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-32, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-63795.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-757, m:tm-427, u:((A (and (-> Am (or Am Bm)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-63796
in-theory        63796
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-757 tm-428 ((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-428.          ((A -> (A or B)) and (C -> ((D and E) -> E))), M:tm-32, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-63796.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> ((G and H) -> H)))), M:tm-757, m:tm-428, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-63797
in-theory        63797
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-429 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-429.          ((A -> (A or B)) and (C -> ((D -> (E -> D)) and C))), M:tm-32, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-63797.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> G)) and F)))), M:tm-757, m:tm-429, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-63798
in-theory        63798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-757 tm-430 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-430.          ((A -> (A or B)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-32, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-63798.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-757, m:tm-430, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-63799
in-theory        63799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-431 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-431.          ((A -> (A or B)) and (C -> (((D and E) -> D) and C))), M:tm-32, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-63799.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> G) and F)))), M:tm-757, m:tm-431, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-63800
in-theory        63800
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-432 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-432.          ((A -> (A or B)) and (C -> (((D and E) -> E) and C))), M:tm-32, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-63800.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (((G and H) -> H) and F)))), M:tm-757, m:tm-432, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-63801
in-theory        63801
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-757 tm-433 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-433.          ((A -> (A or B)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-32, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-63801.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-757, m:tm-433, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-63802
in-theory        63802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-434 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-434.          ((A -> (A or B)) and ((C -> D) -> (C -> (C and D)))), M:tm-32, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-63802.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (F -> (F and G))))), M:tm-757, m:tm-434, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-63803
in-theory        63803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-757 tm-435 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-435.          ((A -> (A or B)) and (C -> (D -> (E -> (D and E))))), M:tm-32, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63803.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (H -> (G and H)))))), M:tm-757, m:tm-435, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-63804
in-theory        63804
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-436 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-436.          ((A -> (A or B)) and ((C -> (D -> C)) or E)), M:tm-32, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-63804.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> (G -> F)) or H))), M:tm-757, m:tm-436, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-63805
in-theory        63805
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-437 ((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-437.          ((A -> (A or B)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-32, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-63805.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-757, m:tm-437, u:((A (and (-> Am (or Am Bm)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-63806
in-theory        63806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-438 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-438.          ((A -> (A or B)) and (((C and D) -> C) or E)), M:tm-32, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-63806.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F and G) -> F) or H))), M:tm-757, m:tm-438, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-63807
in-theory        63807
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-439 ((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-439.          ((A -> (A or B)) and (((C and D) -> D) or E)), M:tm-32, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-63807.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F and G) -> G) or H))), M:tm-757, m:tm-439, u:((A (and (-> Am (or Am Bm)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-63808
in-theory        63808
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-757 tm-440 ((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-440.          ((A -> (A or B)) and ((C -> (D -> (C and D))) or E)), M:tm-32, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-63808.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> (G -> (F and G))) or H))), M:tm-757, m:tm-440, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-63809
in-theory        63809
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-441 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-441.          ((A -> (A or B)) and ((C -> (C or D)) or E)), M:tm-32, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-63809.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> (F or G)) or H))), M:tm-757, m:tm-441, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-63810
in-theory        63810
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-442 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-442.          ((A -> (A or B)) and (C -> ((D -> (D or E)) and C))), M:tm-32, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-63810.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (G or H)) and F)))), M:tm-757, m:tm-442, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-63811
in-theory        63811
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and ((E -> (E or F)) and D))))
theorem-size     23
proof            (modus-ponens tm-757 tm-443 ((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-63811.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and ((E -> (E or F)) and D)))), M:tm-757, m:tm-443, u:((A (-> Am (and Am (and (-> Bm (or Bm Cm)) Am)))))
================================================================
tm-name          tm-63812
in-theory        63812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F))))
theorem-size     29
proof            (modus-ponens tm-757 tm-444 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-444.          ((A -> (B -> (A and B))) and (C -> ((D -> (D or E)) and C))), M:tm-23, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-63812.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (G or H)) and F)))), M:tm-757, m:tm-444, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-63813
in-theory        63813
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-445 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-445.          (((A and B) -> B) and (C -> ((D -> (D or E)) and C))), M:tm-22, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-63813.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (G or H)) and F)))), M:tm-757, m:tm-445, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-63814
in-theory        63814
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-446 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-446.          (((A and B) -> A) and (C -> ((D -> (D or E)) and C))), M:tm-21, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-63814.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (G or H)) and F)))), M:tm-757, m:tm-446, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-63815
in-theory        63815
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G))))
theorem-size     35
proof            (modus-ponens tm-757 tm-447 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-6)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-447.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (E or F)) and D))), M:tm-20, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-63815.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (H or I)) and G)))), M:tm-757, m:tm-447, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Em Fm)) Dm)))))
================================================================
tm-name          tm-63816
in-theory        63816
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-448 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-448.          ((A -> (B -> A)) and (C -> ((D -> (D or E)) and C))), M:tm-19, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-63816.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (G or H)) and F)))), M:tm-757, m:tm-448, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-63817
in-theory        63817
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-449 ((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-449.          ((A -> (not ((B -> (B or C)) and A))) -> (not A)), M:tm-9, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-63817.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not ((E -> (E or F)) and D))) -> (not D))), M:tm-757, m:tm-449, u:((A (-> (-> Am (not (and (-> Bm (or Bm Cm)) Am))) (not Am))))
================================================================
tm-name          tm-63818
in-theory        63818
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-757 tm-450 ((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-63818.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (D or E)) and F) -> G) -> ((F or ((D -> (D or E)) and F)) -> G))), M:tm-757, m:tm-450, u:((A (-> (-> (and (-> Am (or Am Bm)) Cm) Dm) (-> (or Cm (and (-> Am (or Am Bm)) Cm)) Dm))))
================================================================
tm-name          tm-63819
in-theory        63819
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-757 tm-451 ((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-451.          (A or (B -> ((C -> (C or D)) and B))), M:tm-7, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-63819.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> ((F -> (F or G)) and E)))), M:tm-757, m:tm-451, u:((A (or Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-63820
in-theory        63820
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E -> (E or F)) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-757 tm-452 ((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-452.          ((A -> ((B -> (B or C)) and A)) or D), M:tm-6, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-63820.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E -> (E or F)) and D)) or G)), M:tm-757, m:tm-452, u:((A (or (-> Am (and (-> Bm (or Bm Cm)) Am)) Dm)))
================================================================
tm-name          tm-63821
in-theory        63821
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> ((F -> (F or G)) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-453 ((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-63821.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> ((F -> (F or G)) and E)) and D))), M:tm-757, m:tm-453, u:((A (-> Am (and (-> Bm (and (-> Cm (or Cm Dm)) Bm)) Am))))
================================================================
tm-name          tm-63822
in-theory        63822
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> ((F -> (F or G)) and E))))
theorem-size     23
proof            (modus-ponens tm-757 tm-454 ((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-454.          (A -> (B -> ((C -> (C or D)) and B))), M:tm-1, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-63822.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> ((F -> (F or G)) and E)))), M:tm-757, m:tm-454, u:((A (-> Am (-> Bm (and (-> Cm (or Cm Dm)) Bm)))))
================================================================
tm-name          tm-63823
in-theory        63823
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-455 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-455.          ((A -> (A or B)) and (C -> (D -> (D or E)))), M:tm-32, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-63823.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (G or H))))), M:tm-757, m:tm-455, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-63824
in-theory        63824
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (E -> (E or F)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-456 ((A (-> Am (and Am (-> Bm (or Bm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-63824.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (E -> (E or F))))), M:tm-757, m:tm-456, u:((A (-> Am (and Am (-> Bm (or Bm Cm))))))
================================================================
tm-name          tm-63825
in-theory        63825
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-457 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-457.          ((A -> (B -> (A and B))) and (C -> (D -> (D or E)))), M:tm-23, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-63825.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (G or H))))), M:tm-757, m:tm-457, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-63826
in-theory        63826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-458 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-458.          (((A and B) -> B) and (C -> (D -> (D or E)))), M:tm-22, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-63826.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (G or H))))), M:tm-757, m:tm-458, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-63827
in-theory        63827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-459 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-459.          (((A and B) -> A) and (C -> (D -> (D or E)))), M:tm-21, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-63827.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (G or H))))), M:tm-757, m:tm-459, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-63828
in-theory        63828
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-460 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-460.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (E or F)))), M:tm-20, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-63828.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (H or I))))), M:tm-757, m:tm-460, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-63829
in-theory        63829
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-461 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-461.          ((A -> (B -> A)) and (C -> (D -> (D or E)))), M:tm-19, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-63829.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (G or H))))), M:tm-757, m:tm-461, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-63830
in-theory        63830
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D and ((E -> (E or F)) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-757 tm-462 ((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-462.          ((A and ((B -> (B or C)) -> D)) -> D), M:tm-17, m:tm-33, u:((Am (and A (-> (-> Bm (or Bm Cm)) C))) (B (-> Bm (or Bm Cm))))
tm-63830.        (((A -> B) -> (((A and C) or A) -> B)) and ((D and ((E -> (E or F)) -> G)) -> G)), M:tm-757, m:tm-462, u:((A (-> (and Am (-> (-> Bm (or Bm Cm)) Dm)) Dm)))
================================================================
tm-name          tm-63831
in-theory        63831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (D or E)) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-757 tm-463 ((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-463.          ((((A -> (A or B)) -> C) and D) -> C), M:tm-15, m:tm-33, u:((Am (and (-> (-> Bm (or Bm Cm)) B) C)) (A (-> Bm (or Bm Cm))))
tm-63831.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (D or E)) -> F) and G) -> F)), M:tm-757, m:tm-463, u:((A (-> (and (-> (-> Am (or Am Bm)) Cm) Dm) Cm)))
================================================================
tm-name          tm-63832
in-theory        63832
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((D or E) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-464 ((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-63832.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((D or E) -> F)) -> (D -> F))), M:tm-757, m:tm-464, u:((A (-> (-> Am (-> (or Am Bm) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-63833
in-theory        63833
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (E -> (E or F)))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-465 ((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-1 tm-6)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-63833.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (E -> (E or F)))) -> (not D))), M:tm-757, m:tm-465, u:((A (-> (-> Am (not (-> Bm (or Bm Cm)))) (not Am))))
================================================================
tm-name          tm-63834
in-theory        63834
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F)))
theorem-size     29
proof            (modus-ponens tm-757 tm-466 ((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-63834.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (D or E)) -> F) -> ((G or (D -> (D or E))) -> F))), M:tm-757, m:tm-466, u:((A (-> (-> (-> Am (or Am Bm)) Cm) (-> (or Dm (-> Am (or Am Bm))) Cm))))
================================================================
tm-name          tm-63835
in-theory        63835
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-467 ((A (or Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-467.          (A or (B -> (C -> (C or D)))), M:tm-7, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-63835.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (F -> (F or G))))), M:tm-757, m:tm-467, u:((A (or Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-63836
in-theory        63836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (E or F))) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-468 ((A (or (-> Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-468.          ((A -> (B -> (B or C))) or D), M:tm-6, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-63836.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (E or F))) or G)), M:tm-757, m:tm-468, u:((A (or (-> Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-63837
in-theory        63837
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> (F or G))) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-469 ((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-63837.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> (F or G))) and D))), M:tm-757, m:tm-469, u:((A (-> Am (and (-> Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-63838
in-theory        63838
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (D -> (E or F))))
theorem-size     21
proof            (modus-ponens tm-757 tm-470 ((A (-> (-> Am Bm) (-> Am (or Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-63838.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (D -> (E or F)))), M:tm-757, m:tm-470, u:((A (-> (-> Am Bm) (-> Am (or Bm Cm)))))
================================================================
tm-name          tm-63839
in-theory        63839
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-471 ((A (-> Am (-> Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-471.          (A -> (B -> (C -> (C or D)))), M:tm-1, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-63839.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (F -> (F or G))))), M:tm-757, m:tm-471, u:((A (-> Am (-> Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-63840
in-theory        63840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-472 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-472.          ((A -> (A or B)) and (C or (D -> (E -> D)))), M:tm-32, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-63840.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> G))))), M:tm-757, m:tm-472, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-63841
in-theory        63841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-473 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-473.          ((A -> (B -> (A and B))) and (C or (D -> (E -> D)))), M:tm-23, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-63841.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> G))))), M:tm-757, m:tm-473, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-63842
in-theory        63842
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-474 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-474.          (((A and B) -> B) and (C or (D -> (E -> D)))), M:tm-22, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-63842.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or (G -> (H -> G))))), M:tm-757, m:tm-474, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-63843
in-theory        63843
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-475 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-475.          (((A and B) -> A) and (C or (D -> (E -> D)))), M:tm-21, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-63843.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or (G -> (H -> G))))), M:tm-757, m:tm-475, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-63844
in-theory        63844
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-476 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-7 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-476.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> E)))), M:tm-20, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-63844.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> H))))), M:tm-757, m:tm-476, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm Em))))))
================================================================
tm-name          tm-63845
in-theory        63845
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-477 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-477.          ((A -> (B -> A)) and (C or (D -> (E -> D)))), M:tm-19, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-63845.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> G))))), M:tm-757, m:tm-477, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-63846
in-theory        63846
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-478 ((A (or Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-478.          (A or (B or (C -> (D -> C)))), M:tm-7, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-63846.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or (F -> (G -> F))))), M:tm-757, m:tm-478, u:((A (or Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-63847
in-theory        63847
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (F -> E))) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-479 ((A (or (or Am (-> Bm (-> Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-479.          ((A or (B -> (C -> B))) or D), M:tm-6, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-63847.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (F -> E))) or G)), M:tm-757, m:tm-479, u:((A (or (or Am (-> Bm (-> Cm Bm))) Dm)))
================================================================
tm-name          tm-63848
in-theory        63848
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or (F -> (G -> F))) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-480 ((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-63848.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or (F -> (G -> F))) and D))), M:tm-757, m:tm-480, u:((A (-> Am (and (or Bm (-> Cm (-> Dm Cm))) Am))))
================================================================
tm-name          tm-63849
in-theory        63849
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or (F -> (G -> F)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-481 ((A (-> Am (or Bm (-> Cm (-> Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-481.          (A -> (B or (C -> (D -> C)))), M:tm-1, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-63849.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or (F -> (G -> F))))), M:tm-757, m:tm-481, u:((A (-> Am (or Bm (-> Cm (-> Dm Cm))))))
================================================================
tm-name          tm-63850
in-theory        63850
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-482 ((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-482.          ((A -> (A or B)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-32, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63850.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-757, m:tm-482, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-63851
in-theory        63851
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     35
proof            (modus-ponens tm-757 tm-483 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-483.          ((A -> (B -> (A and B))) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-23, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63851.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-757, m:tm-483, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-63852
in-theory        63852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-484 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-484.          (((A and B) -> B) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-22, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63852.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-757, m:tm-484, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-63853
in-theory        63853
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-485 ((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-485.          (((A and B) -> A) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-21, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63853.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-757, m:tm-485, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-63854
in-theory        63854
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J))))))
theorem-size     41
proof            (modus-ponens tm-757 tm-486 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-7)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-486.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-20, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63854.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H -> (I -> J)) -> ((H -> I) -> (H -> J)))))), M:tm-757, m:tm-486, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Em (-> Fm Gm)) (-> (-> Em Fm) (-> Em Gm)))))))
================================================================
tm-name          tm-63855
in-theory        63855
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-487 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-487.          ((A -> (B -> A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-19, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63855.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-757, m:tm-487, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-63856
in-theory        63856
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-757 tm-488 ((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-488.          (A or (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-7, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63856.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-757, m:tm-488, u:((A (or Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-63857
in-theory        63857
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H))
theorem-size     29
proof            (modus-ponens tm-757 tm-489 ((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-489.          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) or E), M:tm-6, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63857.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))) or H)), M:tm-757, m:tm-489, u:((A (or (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))) Em)))
================================================================
tm-name          tm-63858
in-theory        63858
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D)))
theorem-size     31
proof            (modus-ponens tm-757 tm-490 ((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63858.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))) and D))), M:tm-757, m:tm-490, u:((A (-> Am (and (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))) Am))))
================================================================
tm-name          tm-63859
in-theory        63859
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))))
theorem-size     29
proof            (modus-ponens tm-757 tm-491 ((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-491.          (A -> (B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-1, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63859.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))), M:tm-757, m:tm-491, u:((A (-> Am (or Bm (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
================================================================
tm-name          tm-63860
in-theory        63860
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-757 tm-492 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-492.          ((A -> (A or B)) and (C or ((D and E) -> D))), M:tm-32, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-63860.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> G)))), M:tm-757, m:tm-492, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-63861
in-theory        63861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G))))
theorem-size     27
proof            (modus-ponens tm-757 tm-493 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-493.          ((A -> (B -> (A and B))) and (C or ((D and E) -> D))), M:tm-23, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-63861.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> G)))), M:tm-757, m:tm-493, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-63862
in-theory        63862
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-757 tm-494 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-494.          (((A and B) -> B) and (C or ((D and E) -> D))), M:tm-22, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-63862.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or ((G and H) -> G)))), M:tm-757, m:tm-494, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-63863
in-theory        63863
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-757 tm-495 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-495.          (((A and B) -> A) and (C or ((D and E) -> D))), M:tm-21, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-63863.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or ((G and H) -> G)))), M:tm-757, m:tm-495, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-63864
in-theory        63864
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H))))
theorem-size     33
proof            (modus-ponens tm-757 tm-496 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-496.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> E))), M:tm-20, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-63864.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> H)))), M:tm-757, m:tm-496, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Em)))))
================================================================
tm-name          tm-63865
in-theory        63865
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-757 tm-497 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-497.          ((A -> (B -> A)) and (C or ((D and E) -> D))), M:tm-19, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-63865.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> G)))), M:tm-757, m:tm-497, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-63866
in-theory        63866
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-757 tm-498 ((A (or Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-498.          (A or (B or ((C and D) -> C))), M:tm-7, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-63866.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or ((F and G) -> F)))), M:tm-757, m:tm-498, u:((A (or Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-63867
in-theory        63867
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E and F) -> E)) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-499 ((A (or (or Am (-> (and Bm Cm) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-499.          ((A or ((B and C) -> B)) or D), M:tm-6, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-63867.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E and F) -> E)) or G)), M:tm-757, m:tm-499, u:((A (or (or Am (-> (and Bm Cm) Bm)) Dm)))
================================================================
tm-name          tm-63868
in-theory        63868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or ((F and G) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-500 ((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-63868.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or ((F and G) -> F)) and D))), M:tm-757, m:tm-500, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Cm)) Am))))
================================================================
tm-name          tm-63869
in-theory        63869
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or ((F and G) -> F))))
theorem-size     21
proof            (modus-ponens tm-757 tm-501 ((A (-> Am (or Bm (-> (and Cm Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-501.          (A -> (B or ((C and D) -> C))), M:tm-1, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-63869.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or ((F and G) -> F)))), M:tm-757, m:tm-501, u:((A (-> Am (or Bm (-> (and Cm Dm) Cm)))))
================================================================
tm-name          tm-63870
in-theory        63870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-757 tm-502 ((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-502.          ((A -> (A or B)) and (C or ((D and E) -> E))), M:tm-32, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-63870.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or ((G and H) -> H)))), M:tm-757, m:tm-502, u:((A (and (-> Am (or Am Bm)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-63871
in-theory        63871
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H))))
theorem-size     27
proof            (modus-ponens tm-757 tm-503 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-503.          ((A -> (B -> (A and B))) and (C or ((D and E) -> E))), M:tm-23, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-63871.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or ((G and H) -> H)))), M:tm-757, m:tm-503, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-63872
in-theory        63872
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-757 tm-504 ((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-504.          (((A and B) -> B) and (C or ((D and E) -> E))), M:tm-22, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-63872.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or ((G and H) -> H)))), M:tm-757, m:tm-504, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-63873
in-theory        63873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-757 tm-505 ((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-505.          (((A and B) -> A) and (C or ((D and E) -> E))), M:tm-21, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-63873.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or ((G and H) -> H)))), M:tm-757, m:tm-505, u:((A (and (-> (and Am Bm) Am) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-63874
in-theory        63874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I))))
theorem-size     33
proof            (modus-ponens tm-757 tm-506 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-7 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-506.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or ((E and F) -> F))), M:tm-20, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-63874.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or ((H and I) -> I)))), M:tm-757, m:tm-506, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (and Em Fm) Fm)))))
================================================================
tm-name          tm-63875
in-theory        63875
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-757 tm-507 ((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-507.          ((A -> (B -> A)) and (C or ((D and E) -> E))), M:tm-19, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-63875.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or ((G and H) -> H)))), M:tm-757, m:tm-507, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-63876
in-theory        63876
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-757 tm-508 ((A (or Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-508.          (A or (B or ((C and D) -> D))), M:tm-7, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-63876.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or ((F and G) -> G)))), M:tm-757, m:tm-508, u:((A (or Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-63877
in-theory        63877
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E and F) -> F)) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-509 ((A (or (or Am (-> (and Bm Cm) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-509.          ((A or ((B and C) -> C)) or D), M:tm-6, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-63877.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E and F) -> F)) or G)), M:tm-757, m:tm-509, u:((A (or (or Am (-> (and Bm Cm) Cm)) Dm)))
================================================================
tm-name          tm-63878
in-theory        63878
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or ((F and G) -> G)) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-510 ((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-63878.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or ((F and G) -> G)) and D))), M:tm-757, m:tm-510, u:((A (-> Am (and (or Bm (-> (and Cm Dm) Dm)) Am))))
================================================================
tm-name          tm-63879
in-theory        63879
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or ((F and G) -> G))))
theorem-size     21
proof            (modus-ponens tm-757 tm-511 ((A (-> Am (or Bm (-> (and Cm Dm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-511.          (A -> (B or ((C and D) -> D))), M:tm-1, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-63879.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or ((F and G) -> G)))), M:tm-757, m:tm-511, u:((A (-> Am (or Bm (-> (and Cm Dm) Dm)))))
================================================================
tm-name          tm-63880
in-theory        63880
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-757 tm-512 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-512.          ((A -> (A or B)) and (C or (D -> (E -> (D and E))))), M:tm-32, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63880.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (H -> (G and H)))))), M:tm-757, m:tm-512, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-63881
in-theory        63881
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H))))))
theorem-size     29
proof            (modus-ponens tm-757 tm-513 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-513.          ((A -> (B -> (A and B))) and (C or (D -> (E -> (D and E))))), M:tm-23, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63881.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H -> (G and H)))))), M:tm-757, m:tm-513, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-63882
in-theory        63882
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-757 tm-514 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-514.          (((A and B) -> B) and (C or (D -> (E -> (D and E))))), M:tm-22, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63882.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or (G -> (H -> (G and H)))))), M:tm-757, m:tm-514, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-63883
in-theory        63883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-757 tm-515 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-515.          (((A and B) -> A) and (C or (D -> (E -> (D and E))))), M:tm-21, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63883.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or (G -> (H -> (G and H)))))), M:tm-757, m:tm-515, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-63884
in-theory        63884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I))))))
theorem-size     35
proof            (modus-ponens tm-757 tm-516 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-516.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F -> (E and F))))), M:tm-20, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63884.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I -> (H and I)))))), M:tm-757, m:tm-516, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (-> Fm (and Em Fm)))))))
================================================================
tm-name          tm-63885
in-theory        63885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-757 tm-517 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-517.          ((A -> (B -> A)) and (C or (D -> (E -> (D and E))))), M:tm-19, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63885.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (H -> (G and H)))))), M:tm-757, m:tm-517, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-63886
in-theory        63886
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-757 tm-518 ((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-518.          (A or (B or (C -> (D -> (C and D))))), M:tm-7, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63886.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or (F -> (G -> (F and G)))))), M:tm-757, m:tm-518, u:((A (or Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-63887
in-theory        63887
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (F -> (E and F)))) or G))
theorem-size     23
proof            (modus-ponens tm-757 tm-519 ((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-519.          ((A or (B -> (C -> (B and C)))) or D), M:tm-6, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63887.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (F -> (E and F)))) or G)), M:tm-757, m:tm-519, u:((A (or (or Am (-> Bm (-> Cm (and Bm Cm)))) Dm)))
================================================================
tm-name          tm-63888
in-theory        63888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or (F -> (G -> (F and G)))) and D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-520 ((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63888.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or (F -> (G -> (F and G)))) and D))), M:tm-757, m:tm-520, u:((A (-> Am (and (or Bm (-> Cm (-> Dm (and Cm Dm)))) Am))))
================================================================
tm-name          tm-63889
in-theory        63889
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or (F -> (G -> (F and G))))))
theorem-size     23
proof            (modus-ponens tm-757 tm-521 ((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-521.          (A -> (B or (C -> (D -> (C and D))))), M:tm-1, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63889.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or (F -> (G -> (F and G)))))), M:tm-757, m:tm-521, u:((A (-> Am (or Bm (-> Cm (-> Dm (and Cm Dm)))))))
================================================================
tm-name          tm-63890
in-theory        63890
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-522 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-522.          ((A -> (A or B)) and (C or (D -> (D or E)))), M:tm-32, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-63890.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (G or H))))), M:tm-757, m:tm-522, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-63891
in-theory        63891
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-523 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-523.          ((A -> (B -> (A and B))) and (C or (D -> (D or E)))), M:tm-23, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-63891.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (G or H))))), M:tm-757, m:tm-523, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-63892
in-theory        63892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-524 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-524.          (((A and B) -> B) and (C or (D -> (D or E)))), M:tm-22, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-63892.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or (G -> (G or H))))), M:tm-757, m:tm-524, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-63893
in-theory        63893
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-525 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-525.          (((A and B) -> A) and (C or (D -> (D or E)))), M:tm-21, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-63893.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or (G -> (G or H))))), M:tm-757, m:tm-525, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-63894
in-theory        63894
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-526 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-7 tm-6)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-526.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (E or F)))), M:tm-20, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-63894.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (H or I))))), M:tm-757, m:tm-526, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Em Fm))))))
================================================================
tm-name          tm-63895
in-theory        63895
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-527 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-527.          ((A -> (B -> A)) and (C or (D -> (D or E)))), M:tm-19, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-63895.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (G or H))))), M:tm-757, m:tm-527, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-63896
in-theory        63896
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-528 ((A (or Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-528.          (A or (B or (C -> (C or D)))), M:tm-7, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-63896.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or (F -> (F or G))))), M:tm-757, m:tm-528, u:((A (or Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-63897
in-theory        63897
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (E or F))) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-529 ((A (or (or Am (-> Bm (or Bm Cm))) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-529.          ((A or (B -> (B or C))) or D), M:tm-6, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-63897.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (E or F))) or G)), M:tm-757, m:tm-529, u:((A (or (or Am (-> Bm (or Bm Cm))) Dm)))
================================================================
tm-name          tm-63898
in-theory        63898
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or (F -> (F or G))) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-530 ((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-63898.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or (F -> (F or G))) and D))), M:tm-757, m:tm-530, u:((A (-> Am (and (or Bm (-> Cm (or Cm Dm))) Am))))
================================================================
tm-name          tm-63899
in-theory        63899
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or (F -> (F or G)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-531 ((A (-> Am (or Bm (-> Cm (or Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-531.          (A -> (B or (C -> (C or D)))), M:tm-1, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-63899.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or (F -> (F or G))))), M:tm-757, m:tm-531, u:((A (-> Am (or Bm (-> Cm (or Cm Dm))))))
================================================================
tm-name          tm-63900
in-theory        63900
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-532 ((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-532.          ((A -> (A or B)) and (C or (D -> (E or D)))), M:tm-32, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-63900.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F or (G -> (H or G))))), M:tm-757, m:tm-532, u:((A (and (-> Am (or Am Bm)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-63901
in-theory        63901
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-533 ((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-533.          ((A -> (B -> (A and B))) and (C or (D -> (E or D)))), M:tm-23, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-63901.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F or (G -> (H or G))))), M:tm-757, m:tm-533, u:((A (and (-> Am (-> Bm (and Am Bm))) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-63902
in-theory        63902
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-534 ((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-534.          (((A and B) -> B) and (C or (D -> (E or D)))), M:tm-22, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-63902.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F or (G -> (H or G))))), M:tm-757, m:tm-534, u:((A (and (-> (and Am Bm) Bm) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-63903
in-theory        63903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-535 ((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-535.          (((A and B) -> A) and (C or (D -> (E or D)))), M:tm-21, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-63903.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F or (G -> (H or G))))), M:tm-757, m:tm-535, u:((A (and (-> (and Am Bm) Am) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-63904
in-theory        63904
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-536 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-536.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D or (E -> (F or E)))), M:tm-20, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-63904.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G or (H -> (I or H))))), M:tm-757, m:tm-536, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-63905
in-theory        63905
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-537 ((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-537.          ((A -> (B -> A)) and (C or (D -> (E or D)))), M:tm-19, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-63905.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F or (G -> (H or G))))), M:tm-757, m:tm-537, u:((A (and (-> Am (-> Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-63906
in-theory        63906
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-538 ((A (or Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-538.          (A or (B or (C -> (D or C)))), M:tm-7, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-63906.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E or (F -> (G or F))))), M:tm-757, m:tm-538, u:((A (or Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-63907
in-theory        63907
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (F or E))) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-539 ((A (or (or Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-539.          ((A or (B -> (C or B))) or D), M:tm-6, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-63907.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> (F or E))) or G)), M:tm-757, m:tm-539, u:((A (or (or Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-63908
in-theory        63908
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or (F -> (G or F))) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-540 ((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-63908.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E or (F -> (G or F))) and D))), M:tm-757, m:tm-540, u:((A (-> Am (and (or Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-63909
in-theory        63909
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-541 ((A (-> Am (or Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-541.          (A -> (B or (C -> (D or C)))), M:tm-1, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-63909.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E or (F -> (G or F))))), M:tm-757, m:tm-541, u:((A (-> Am (or Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-63910
in-theory        63910
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-542 ((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-542.          ((A -> (A or B)) and ((C -> (D or C)) or E)), M:tm-32, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-63910.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> (G or F)) or H))), M:tm-757, m:tm-542, u:((A (and (-> Am (or Am Bm)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-63911
in-theory        63911
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H)))
theorem-size     27
proof            (modus-ponens tm-757 tm-543 ((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-543.          ((A -> (B -> (A and B))) and ((C -> (D or C)) or E)), M:tm-23, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-63911.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> (G or F)) or H))), M:tm-757, m:tm-543, u:((A (and (-> Am (-> Bm (and Am Bm))) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-63912
in-theory        63912
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-544 ((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-544.          (((A and B) -> B) and ((C -> (D or C)) or E)), M:tm-22, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-63912.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> (G or F)) or H))), M:tm-757, m:tm-544, u:((A (and (-> (and Am Bm) Bm) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-63913
in-theory        63913
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-545 ((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-545.          (((A and B) -> A) and ((C -> (D or C)) or E)), M:tm-21, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-63913.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> (G or F)) or H))), M:tm-757, m:tm-545, u:((A (and (-> (and Am Bm) Am) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-63914
in-theory        63914
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-546 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-6 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-546.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> (E or D)) or F)), M:tm-20, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-63914.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> (H or G)) or I))), M:tm-757, m:tm-546, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> Dm (or Em Dm)) Fm))))
================================================================
tm-name          tm-63915
in-theory        63915
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-547 ((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-547.          ((A -> (B -> A)) and ((C -> (D or C)) or E)), M:tm-19, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-63915.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> (G or F)) or H))), M:tm-757, m:tm-547, u:((A (and (-> Am (-> Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-63916
in-theory        63916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-757 tm-548 ((A (or Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-548.          (A or ((B -> (C or B)) or D)), M:tm-7, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-63916.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> (F or E)) or G))), M:tm-757, m:tm-548, u:((A (or Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-63917
in-theory        63917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E or D)) or F) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-549 ((A (or (or (-> Am (or Bm Am)) Cm) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-549.          (((A -> (B or A)) or C) or D), M:tm-6, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-63917.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E or D)) or F) or G)), M:tm-757, m:tm-549, u:((A (or (or (-> Am (or Bm Am)) Cm) Dm)))
================================================================
tm-name          tm-63918
in-theory        63918
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (F or E)) or G) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-550 ((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-63918.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> (F or E)) or G) and D))), M:tm-757, m:tm-550, u:((A (-> Am (and (or (-> Bm (or Cm Bm)) Dm) Am))))
================================================================
tm-name          tm-63919
in-theory        63919
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F or E)) or G)))
theorem-size     21
proof            (modus-ponens tm-757 tm-551 ((A (-> Am (or (-> Bm (or Cm Bm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-551.          (A -> ((B -> (C or B)) or D)), M:tm-1, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-63919.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F or E)) or G))), M:tm-757, m:tm-551, u:((A (-> Am (or (-> Bm (or Cm Bm)) Dm))))
================================================================
tm-name          tm-63920
in-theory        63920
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-552 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-552.          ((A -> (B or A)) and (C -> (D -> C))), M:tm-42, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-63920.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> F)))), M:tm-757, m:tm-552, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-63921
in-theory        63921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-553 ((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-553.          ((A -> (B or A)) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-42, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-63921.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-757, m:tm-553, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-63922
in-theory        63922
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-554 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-554.          ((A -> (B or A)) and ((C and D) -> C)), M:tm-42, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-63922.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F and G) -> F))), M:tm-757, m:tm-554, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-63923
in-theory        63923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-757 tm-555 ((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-555.          ((A -> (B or A)) and ((C and D) -> D)), M:tm-42, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-63923.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F and G) -> G))), M:tm-757, m:tm-555, u:((A (and (-> Am (or Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-63924
in-theory        63924
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-556 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-556.          ((A -> (B or A)) and (C -> (D -> (C and D)))), M:tm-42, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-63924.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (F and G))))), M:tm-757, m:tm-556, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-63925
in-theory        63925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-757 tm-557 ((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-557.          ((A -> (B or A)) and (C -> (C or D))), M:tm-42, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-63925.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (F or G)))), M:tm-757, m:tm-557, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-63926
in-theory        63926
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-558 ((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-558.          ((A -> (B or A)) and (C -> (D or C))), M:tm-42, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-63926.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (G or F)))), M:tm-757, m:tm-558, u:((A (and (-> Am (or Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-63927
in-theory        63927
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-559 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-559.          ((A -> (B or A)) and ((C -> D) -> ((D -> E) -> ((C or D) -> E)))), M:tm-42, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-63927.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((G -> H) -> ((F or G) -> H))))), M:tm-757, m:tm-559, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Dm Em) (-> (or Cm Dm) Em))))))
================================================================
tm-name          tm-63928
in-theory        63928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F)))))
theorem-size     29
proof            (modus-ponens tm-757 tm-560 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-9)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-560.          ((A -> (B or A)) and ((C -> D) -> ((C -> (not D)) -> (not C)))), M:tm-42, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-63928.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> ((F -> (not G)) -> (not F))))), M:tm-757, m:tm-560, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (-> Cm (not Dm)) (not Cm))))))
================================================================
tm-name          tm-63929
in-theory        63929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((not (not F)) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-561 ((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-10.           ((not (not A)) -> A), axiom
tm-561.          ((A -> (B or A)) and ((not (not C)) -> C)), M:tm-42, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-63929.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((not (not F)) -> F))), M:tm-757, m:tm-561, u:((A (and (-> Am (or Bm Am)) (-> (not (not Cm)) Cm))))
================================================================
tm-name          tm-63930
in-theory        63930
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-562 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-562.          ((A -> (B or A)) and (C -> (D -> (E -> D)))), M:tm-42, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-63930.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> G))))), M:tm-757, m:tm-562, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-63931
in-theory        63931
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-563 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-563.          ((A -> (B or A)) and ((C -> D) -> (C -> C))), M:tm-42, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-63931.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> F)))), M:tm-757, m:tm-563, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm Cm)))))
================================================================
tm-name          tm-63932
in-theory        63932
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H)))))
theorem-size     37
proof            (modus-ponens tm-757 tm-564 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-564.          ((A -> (B or A)) and (((C -> (D -> E)) -> (C -> D)) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-42, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-63932.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> (F -> G)) -> ((F -> (G -> H)) -> (F -> H))))), M:tm-757, m:tm-564, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm (-> Dm Em)) (-> Cm Dm)) (-> (-> Cm (-> Dm Em)) (-> Cm Em))))))
================================================================
tm-name          tm-63933
in-theory        63933
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-565 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-565.          ((A -> (B or A)) and (C -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63933.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-757, m:tm-565, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-63934
in-theory        63934
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G))))
theorem-size     33
proof            (modus-ponens tm-757 tm-566 ((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-566.          ((A -> (B or A)) and ((((C -> D) and E) -> C) -> (((C -> D) and E) -> D))), M:tm-42, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-63934.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((((F -> G) and H) -> F) -> (((F -> G) and H) -> G)))), M:tm-757, m:tm-566, u:((A (and (-> Am (or Bm Am)) (-> (-> (and (-> Cm Dm) Em) Cm) (-> (and (-> Cm Dm) Em) Dm)))))
================================================================
tm-name          tm-63935
in-theory        63935
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-757 tm-567 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-567.          ((A -> (B or A)) and (C -> ((D and E) -> D))), M:tm-42, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-63935.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> G)))), M:tm-757, m:tm-567, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-63936
in-theory        63936
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H))))
theorem-size     33
proof            (modus-ponens tm-757 tm-568 ((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-568.          ((A -> (B or A)) and (((C and (D -> E)) -> D) -> ((C and (D -> E)) -> E))), M:tm-42, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-63936.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F and (G -> H)) -> G) -> ((F and (G -> H)) -> H)))), M:tm-757, m:tm-568, u:((A (and (-> Am (or Bm Am)) (-> (-> (and Cm (-> Dm Em)) Dm) (-> (and Cm (-> Dm Em)) Em)))))
================================================================
tm-name          tm-63937
in-theory        63937
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-757 tm-569 ((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-569.          ((A -> (B or A)) and (C -> ((D and E) -> E))), M:tm-42, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-63937.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> ((G and H) -> H)))), M:tm-757, m:tm-569, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-63938
in-theory        63938
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-570 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-570.          ((A -> (B or A)) and (C -> ((D -> (E -> D)) and C))), M:tm-42, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-63938.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> G)) and F)))), M:tm-757, m:tm-570, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em Dm)) Cm)))))
================================================================
tm-name          tm-63939
in-theory        63939
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))))
theorem-size     35
proof            (modus-ponens tm-757 tm-571 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-571.          ((A -> (B or A)) and (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-42, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-63939.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))), M:tm-757, m:tm-571, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Cm)))))
================================================================
tm-name          tm-63940
in-theory        63940
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-572 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-572.          ((A -> (B or A)) and (C -> (((D and E) -> D) and C))), M:tm-42, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-63940.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> G) and F)))), M:tm-757, m:tm-572, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Dm) Cm)))))
================================================================
tm-name          tm-63941
in-theory        63941
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-573 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-573.          ((A -> (B or A)) and (C -> (((D and E) -> E) and C))), M:tm-42, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-63941.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (((G and H) -> H) and F)))), M:tm-757, m:tm-573, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> (and Dm Em) Em) Cm)))))
================================================================
tm-name          tm-63942
in-theory        63942
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F))))
theorem-size     29
proof            (modus-ponens tm-757 tm-574 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-574.          ((A -> (B or A)) and (C -> ((D -> (E -> (D and E))) and C))), M:tm-42, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-63942.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H -> (G and H))) and F)))), M:tm-757, m:tm-574, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (-> Em (and Dm Em))) Cm)))))
================================================================
tm-name          tm-63943
in-theory        63943
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-575 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-575.          ((A -> (B or A)) and ((C -> D) -> (C -> (C and D)))), M:tm-42, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-63943.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (F -> (F and G))))), M:tm-757, m:tm-575, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> Cm (and Cm Dm))))))
================================================================
tm-name          tm-63944
in-theory        63944
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-757 tm-576 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-576.          ((A -> (B or A)) and (C -> (D -> (E -> (D and E))))), M:tm-42, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63944.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (H -> (G and H)))))), M:tm-757, m:tm-576, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-63945
in-theory        63945
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> (G -> F)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-577 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-577.          ((A -> (B or A)) and ((C -> (D -> C)) or E)), M:tm-42, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-63945.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> (G -> F)) or H))), M:tm-757, m:tm-577, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm Cm)) Em))))
================================================================
tm-name          tm-63946
in-theory        63946
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I)))
theorem-size     33
proof            (modus-ponens tm-757 tm-578 ((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-578.          ((A -> (B or A)) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) or F)), M:tm-42, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-63946.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) or I))), M:tm-757, m:tm-578, u:((A (and (-> Am (or Bm Am)) (or (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))
================================================================
tm-name          tm-63947
in-theory        63947
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F and G) -> F) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-579 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-579.          ((A -> (B or A)) and (((C and D) -> C) or E)), M:tm-42, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-63947.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F and G) -> F) or H))), M:tm-757, m:tm-579, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Cm) Em))))
================================================================
tm-name          tm-63948
in-theory        63948
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F and G) -> G) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-580 ((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-580.          ((A -> (B or A)) and (((C and D) -> D) or E)), M:tm-42, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-63948.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F and G) -> G) or H))), M:tm-757, m:tm-580, u:((A (and (-> Am (or Bm Am)) (or (-> (and Cm Dm) Dm) Em))))
================================================================
tm-name          tm-63949
in-theory        63949
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H)))
theorem-size     27
proof            (modus-ponens tm-757 tm-581 ((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-581.          ((A -> (B or A)) and ((C -> (D -> (C and D))) or E)), M:tm-42, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-63949.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> (G -> (F and G))) or H))), M:tm-757, m:tm-581, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (-> Dm (and Cm Dm))) Em))))
================================================================
tm-name          tm-63950
in-theory        63950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> (F or G)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-582 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-582.          ((A -> (B or A)) and ((C -> (C or D)) or E)), M:tm-42, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-63950.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> (F or G)) or H))), M:tm-757, m:tm-582, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Cm Dm)) Em))))
================================================================
tm-name          tm-63951
in-theory        63951
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-583 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-583.          ((A -> (B or A)) and (C -> ((D -> (D or E)) and C))), M:tm-42, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-63951.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (G or H)) and F)))), M:tm-757, m:tm-583, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Dm Em)) Cm)))))
================================================================
tm-name          tm-63952
in-theory        63952
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-584 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-584.          ((A -> (B or A)) and (C -> (D -> (D or E)))), M:tm-42, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-63952.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (G or H))))), M:tm-757, m:tm-584, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-63953
in-theory        63953
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-585 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-585.          ((A -> (B or A)) and (C or (D -> (E -> D)))), M:tm-42, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-63953.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> G))))), M:tm-757, m:tm-585, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em Dm))))))
================================================================
tm-name          tm-63954
in-theory        63954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))))
theorem-size     33
proof            (modus-ponens tm-757 tm-586 ((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-586.          ((A -> (B or A)) and (C or ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-42, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-63954.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))), M:tm-757, m:tm-586, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
================================================================
tm-name          tm-63955
in-theory        63955
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> G))))
theorem-size     25
proof            (modus-ponens tm-757 tm-587 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-587.          ((A -> (B or A)) and (C or ((D and E) -> D))), M:tm-42, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-63955.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> G)))), M:tm-757, m:tm-587, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Dm)))))
================================================================
tm-name          tm-63956
in-theory        63956
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> H))))
theorem-size     25
proof            (modus-ponens tm-757 tm-588 ((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-588.          ((A -> (B or A)) and (C or ((D and E) -> E))), M:tm-42, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-63956.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or ((G and H) -> H)))), M:tm-757, m:tm-588, u:((A (and (-> Am (or Bm Am)) (or Cm (-> (and Dm Em) Em)))))
================================================================
tm-name          tm-63957
in-theory        63957
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H))))))
theorem-size     27
proof            (modus-ponens tm-757 tm-589 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em))))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-589.          ((A -> (B or A)) and (C or (D -> (E -> (D and E))))), M:tm-42, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-63957.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (H -> (G and H)))))), M:tm-757, m:tm-589, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (-> Em (and Dm Em)))))))
================================================================
tm-name          tm-63958
in-theory        63958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (G or H)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-590 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-590.          ((A -> (B or A)) and (C or (D -> (D or E)))), M:tm-42, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-63958.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (G or H))))), M:tm-757, m:tm-590, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Dm Em))))))
================================================================
tm-name          tm-63959
in-theory        63959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-591 ((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-591.          ((A -> (B or A)) and (C or (D -> (E or D)))), M:tm-42, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-63959.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F or (G -> (H or G))))), M:tm-757, m:tm-591, u:((A (and (-> Am (or Bm Am)) (or Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-63960
in-theory        63960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> (G or F)) or H)))
theorem-size     25
proof            (modus-ponens tm-757 tm-592 ((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-6)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-6.            (A -> (A or B)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-592.          ((A -> (B or A)) and ((C -> (D or C)) or E)), M:tm-42, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-63960.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> (G or F)) or H))), M:tm-757, m:tm-592, u:((A (and (-> Am (or Bm Am)) (or (-> Cm (or Dm Cm)) Em))))
================================================================
tm-name          tm-63961
in-theory        63961
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-593 ((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-593.          ((A -> (B or A)) and (C -> ((D -> (E or D)) and C))), M:tm-42, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-63961.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> ((G -> (H or G)) and F)))), M:tm-757, m:tm-593, u:((A (and (-> Am (or Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-63962
in-theory        63962
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-594 ((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-594.          ((A -> (A or B)) and (C -> ((D -> (E or D)) and C))), M:tm-32, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-63962.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> ((G -> (H or G)) and F)))), M:tm-757, m:tm-594, u:((A (and (-> Am (or Am Bm)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-63963
in-theory        63963
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and ((E -> (F or E)) and D))))
theorem-size     23
proof            (modus-ponens tm-757 tm-595 ((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-63963.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and ((E -> (F or E)) and D)))), M:tm-757, m:tm-595, u:((A (-> Am (and Am (and (-> Bm (or Cm Bm)) Am)))))
================================================================
tm-name          tm-63964
in-theory        63964
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F))))
theorem-size     29
proof            (modus-ponens tm-757 tm-596 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-596.          ((A -> (B -> (A and B))) and (C -> ((D -> (E or D)) and C))), M:tm-23, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-63964.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> ((G -> (H or G)) and F)))), M:tm-757, m:tm-596, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-63965
in-theory        63965
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-597 ((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-597.          (((A and B) -> B) and (C -> ((D -> (E or D)) and C))), M:tm-22, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-63965.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> ((G -> (H or G)) and F)))), M:tm-757, m:tm-597, u:((A (and (-> (and Am Bm) Bm) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-63966
in-theory        63966
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-598 ((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-598.          (((A and B) -> A) and (C -> ((D -> (E or D)) and C))), M:tm-21, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-63966.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> ((G -> (H or G)) and F)))), M:tm-757, m:tm-598, u:((A (and (-> (and Am Bm) Am) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-63967
in-theory        63967
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G))))
theorem-size     35
proof            (modus-ponens tm-757 tm-599 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-7)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-599.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> ((E -> (F or E)) and D))), M:tm-20, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-63967.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> ((H -> (I or H)) and G)))), M:tm-757, m:tm-599, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> Em (or Fm Em)) Dm)))))
================================================================
tm-name          tm-63968
in-theory        63968
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-600 ((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-600.          ((A -> (B -> A)) and (C -> ((D -> (E or D)) and C))), M:tm-19, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-63968.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> ((G -> (H or G)) and F)))), M:tm-757, m:tm-600, u:((A (and (-> Am (-> Bm Am)) (-> Cm (and (-> Dm (or Em Dm)) Cm)))))
================================================================
tm-name          tm-63969
in-theory        63969
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-601 ((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-601.          ((A -> (not ((B -> (C or B)) and A))) -> (not A)), M:tm-9, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-63969.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not ((E -> (F or E)) and D))) -> (not D))), M:tm-757, m:tm-601, u:((A (-> (-> Am (not (and (-> Bm (or Cm Bm)) Am))) (not Am))))
================================================================
tm-name          tm-63970
in-theory        63970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G)))
theorem-size     33
proof            (modus-ponens tm-757 tm-602 ((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-63970.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E or D)) and F) -> G) -> ((F or ((D -> (E or D)) and F)) -> G))), M:tm-757, m:tm-602, u:((A (-> (-> (and (-> Am (or Bm Am)) Cm) Dm) (-> (or Cm (and (-> Am (or Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-63971
in-theory        63971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-757 tm-603 ((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-603.          (A or (B -> ((C -> (D or C)) and B))), M:tm-7, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-63971.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> ((F -> (G or F)) and E)))), M:tm-757, m:tm-603, u:((A (or Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-63972
in-theory        63972
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E -> (F or E)) and D)) or G))
theorem-size     23
proof            (modus-ponens tm-757 tm-604 ((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-604.          ((A -> ((B -> (C or B)) and A)) or D), M:tm-6, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-63972.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E -> (F or E)) and D)) or G)), M:tm-757, m:tm-604, u:((A (or (-> Am (and (-> Bm (or Cm Bm)) Am)) Dm)))
================================================================
tm-name          tm-63973
in-theory        63973
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> ((F -> (G or F)) and E)) and D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-605 ((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-63973.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> ((F -> (G or F)) and E)) and D))), M:tm-757, m:tm-605, u:((A (-> Am (and (-> Bm (and (-> Cm (or Dm Cm)) Bm)) Am))))
================================================================
tm-name          tm-63974
in-theory        63974
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> ((F -> (G or F)) and E))))
theorem-size     23
proof            (modus-ponens tm-757 tm-606 ((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-606.          (A -> (B -> ((C -> (D or C)) and B))), M:tm-1, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-63974.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> ((F -> (G or F)) and E)))), M:tm-757, m:tm-606, u:((A (-> Am (-> Bm (and (-> Cm (or Dm Cm)) Bm)))))
================================================================
tm-name          tm-63975
in-theory        63975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-607 ((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-607.          ((A -> (B or A)) and (C -> (D -> (E or D)))), M:tm-42, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-63975.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (F -> (G -> (H or G))))), M:tm-757, m:tm-607, u:((A (and (-> Am (or Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-63976
in-theory        63976
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-608 ((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-608.          ((A -> (A or B)) and (C -> (D -> (E or D)))), M:tm-32, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-63976.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (F -> (G -> (H or G))))), M:tm-757, m:tm-608, u:((A (and (-> Am (or Am Bm)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-63977
in-theory        63977
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (E -> (F or E)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-609 ((A (-> Am (and Am (-> Bm (or Cm Bm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-63977.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (D and (E -> (F or E))))), M:tm-757, m:tm-609, u:((A (-> Am (and Am (-> Bm (or Cm Bm))))))
================================================================
tm-name          tm-63978
in-theory        63978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G)))))
theorem-size     27
proof            (modus-ponens tm-757 tm-610 ((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-610.          ((A -> (B -> (A and B))) and (C -> (D -> (E or D)))), M:tm-23, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-63978.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (F -> (G -> (H or G))))), M:tm-757, m:tm-610, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-63979
in-theory        63979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-611 ((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-611.          (((A and B) -> B) and (C -> (D -> (E or D)))), M:tm-22, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-63979.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (F -> (G -> (H or G))))), M:tm-757, m:tm-611, u:((A (and (-> (and Am Bm) Bm) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-63980
in-theory        63980
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-612 ((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-612.          (((A and B) -> A) and (C -> (D -> (E or D)))), M:tm-21, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-63980.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (F -> (G -> (H or G))))), M:tm-757, m:tm-612, u:((A (and (-> (and Am Bm) Am) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-63981
in-theory        63981
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-613 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-7)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-613.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (E -> (F or E)))), M:tm-20, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-63981.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (G -> (H -> (I or H))))), M:tm-757, m:tm-613, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (or Fm Em))))))
================================================================
tm-name          tm-63982
in-theory        63982
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H or G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-614 ((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-614.          ((A -> (B -> A)) and (C -> (D -> (E or D)))), M:tm-19, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-63982.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (F -> (G -> (H or G))))), M:tm-757, m:tm-614, u:((A (and (-> Am (-> Bm Am)) (-> Cm (-> Dm (or Em Dm))))))
================================================================
tm-name          tm-63983
in-theory        63983
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D and ((E -> (F or E)) -> G)) -> G))
theorem-size     23
proof            (modus-ponens tm-757 tm-615 ((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-615.          ((A and ((B -> (C or B)) -> D)) -> D), M:tm-17, m:tm-43, u:((Am (and A (-> (-> Bm (or Cm Bm)) C))) (B (-> Bm (or Cm Bm))))
tm-63983.        (((A -> B) -> (((A and C) or A) -> B)) and ((D and ((E -> (F or E)) -> G)) -> G)), M:tm-757, m:tm-615, u:((A (-> (and Am (-> (-> Bm (or Cm Bm)) Dm)) Dm)))
================================================================
tm-name          tm-63984
in-theory        63984
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E or D)) -> F) and G) -> F))
theorem-size     23
proof            (modus-ponens tm-757 tm-616 ((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-7)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-616.          ((((A -> (B or A)) -> C) and D) -> C), M:tm-15, m:tm-43, u:((Am (and (-> (-> Bm (or Cm Bm)) B) C)) (A (-> Bm (or Cm Bm))))
tm-63984.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E or D)) -> F) and G) -> F)), M:tm-757, m:tm-616, u:((A (-> (and (-> (-> Am (or Bm Am)) Cm) Dm) Cm)))
================================================================
tm-name          tm-63985
in-theory        63985
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E or D) -> F)) -> (D -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-617 ((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-63985.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> ((E or D) -> F)) -> (D -> F))), M:tm-757, m:tm-617, u:((A (-> (-> Am (-> (or Bm Am) Cm)) (-> Am Cm))))
================================================================
tm-name          tm-63986
in-theory        63986
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (E -> (F or E)))) -> (not D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-618 ((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-1 tm-7)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-63986.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (not (E -> (F or E)))) -> (not D))), M:tm-757, m:tm-618, u:((A (-> (-> Am (not (-> Bm (or Cm Bm)))) (not Am))))
================================================================
tm-name          tm-63987
in-theory        63987
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F)))
theorem-size     29
proof            (modus-ponens tm-757 tm-619 ((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-63987.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E or D)) -> F) -> ((G or (D -> (E or D))) -> F))), M:tm-757, m:tm-619, u:((A (-> (-> (-> Am (or Bm Am)) Cm) (-> (or Dm (-> Am (or Bm Am))) Cm))))
================================================================
tm-name          tm-63988
in-theory        63988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-620 ((A (or Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-620.          (A or (B -> (C -> (D or C)))), M:tm-7, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-63988.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (E -> (F -> (G or F))))), M:tm-757, m:tm-620, u:((A (or Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-63989
in-theory        63989
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (F or E))) or G))
theorem-size     21
proof            (modus-ponens tm-757 tm-621 ((A (or (-> Am (-> Bm (or Cm Bm))) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-621.          ((A -> (B -> (C or B))) or D), M:tm-6, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-63989.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (F or E))) or G)), M:tm-757, m:tm-621, u:((A (or (-> Am (-> Bm (or Cm Bm))) Dm)))
================================================================
tm-name          tm-63990
in-theory        63990
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> (G or F))) and D)))
theorem-size     23
proof            (modus-ponens tm-757 tm-622 ((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-63990.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> (F -> (G or F))) and D))), M:tm-757, m:tm-622, u:((A (-> Am (and (-> Bm (-> Cm (or Dm Cm))) Am))))
================================================================
tm-name          tm-63991
in-theory        63991
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (D -> (F or E))))
theorem-size     21
proof            (modus-ponens tm-757 tm-623 ((A (-> (-> Am Bm) (-> Am (or Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-63991.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> (D -> (F or E)))), M:tm-757, m:tm-623, u:((A (-> (-> Am Bm) (-> Am (or Cm Bm)))))
================================================================
tm-name          tm-63992
in-theory        63992
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (F -> (G or F)))))
theorem-size     21
proof            (modus-ponens tm-757 tm-624 ((A (-> Am (-> Bm (-> Cm (or Dm Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-624.          (A -> (B -> (C -> (D or C)))), M:tm-1, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-63992.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (E -> (F -> (G or F))))), M:tm-757, m:tm-624, u:((A (-> Am (-> Bm (-> Cm (or Dm Cm))))))
================================================================
tm-name          tm-63993
in-theory        63993
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (F -> (E -> D))))
theorem-size     23
proof            (modus-ponens tm-757 tm-625 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-625.          ((A or (B -> A)) -> (C -> (B -> A))), M:tm-44, m:tm-1, u:((Am (-> A B)) (C (-> Bm (-> A B))))
tm-63993.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (F -> (E -> D)))), M:tm-757, m:tm-625, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Bm Am)))))
================================================================
tm-name          tm-63994
in-theory        63994
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E))))
theorem-size     29
proof            (modus-ponens tm-757 tm-626 ((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-626.          (((A -> B) or (C -> (A -> B))) -> ((C -> A) -> (C -> B))), M:tm-44, m:tm-2, u:((A Am) (B (-> Bm Cm)) (C (-> (-> Am Bm) (-> Am Cm))))
tm-63994.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or (F -> (D -> E))) -> ((F -> D) -> (F -> E)))), M:tm-757, m:tm-626, u:((A (-> (or (-> Am Bm) (-> Cm (-> Am Bm))) (-> (-> Cm Am) (-> Cm Bm)))))
================================================================
tm-name          tm-63995
in-theory        63995
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (F -> ((E -> D) and F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-627 ((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-627.          ((A or (B -> A)) -> (C -> ((B -> A) and C))), M:tm-44, m:tm-5, u:((Am (-> A B)) (C (-> Bm (and (-> A B) Bm))))
tm-63995.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (F -> ((E -> D) and F)))), M:tm-757, m:tm-627, u:((A (-> (or Am (-> Bm Am)) (-> Cm (and (-> Bm Am) Cm)))))
================================================================
tm-name          tm-63996
in-theory        63996
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((E -> D) or F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-628 ((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-628.          ((A or (B -> A)) -> ((B -> A) or C)), M:tm-44, m:tm-6, u:((Am (-> A B)) (C (or (-> A B) Bm)))
tm-63996.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((E -> D) or F))), M:tm-757, m:tm-628, u:((A (-> (or Am (-> Bm Am)) (or (-> Bm Am) Cm))))
================================================================
tm-name          tm-63997
in-theory        63997
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (F or (E -> D))))
theorem-size     23
proof            (modus-ponens tm-757 tm-629 ((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-629.          ((A or (B -> A)) -> (C or (B -> A))), M:tm-44, m:tm-7, u:((Am (-> A B)) (C (or Bm (-> A B))))
tm-63997.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (F or (E -> D)))), M:tm-757, m:tm-629, u:((A (-> (or Am (-> Bm Am)) (or Cm (-> Bm Am)))))
================================================================
tm-name          tm-63998
in-theory        63998
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-630 ((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-630.          ((A or (B -> A)) -> ((A -> C) -> ((B or A) -> C))), M:tm-44, m:tm-8, u:((A Am) (B Bm) (C (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-63998.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((D -> F) -> ((E or D) -> F)))), M:tm-757, m:tm-630, u:((A (-> (or Am (-> Bm Am)) (-> (-> Am Cm) (-> (or Bm Am) Cm)))))
================================================================
tm-name          tm-63999
in-theory        63999
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-757 tm-631 ((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-9)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-631.          ((A or (B -> A)) -> ((B -> (not A)) -> (not B))), M:tm-44, m:tm-9, u:((A Am) (B Bm) (C (-> (-> Am (not Bm)) (not Am))))
tm-63999.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((E -> (not D)) -> (not E)))), M:tm-757, m:tm-631, u:((A (-> (or Am (-> Bm Am)) (-> (-> Bm (not Am)) (not Bm)))))
================================================================
tm-name          tm-64000
in-theory        64000
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-632 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-632.          ((A or (B -> A)) -> (C -> (D -> C))), M:tm-44, m:tm-11, u:((Am (-> A B)) (C (-> Bm (-> Cm Bm))))
tm-64000.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (F -> (G -> F)))), M:tm-757, m:tm-632, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-64001
in-theory        64001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-757 tm-633 ((A (-> (or Am (-> Bm Am)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-633.          ((A or (B -> A)) -> (B -> B)), M:tm-44, m:tm-12, u:((A Am) (B Bm) (C (-> Am Am)))
tm-64001.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (E -> E))), M:tm-757, m:tm-633, u:((A (-> (or Am (-> Bm Am)) (-> Bm Bm))))
================================================================
tm-name          tm-64002
in-theory        64002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-757 tm-634 ((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-634.          (((A -> B) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-44, m:tm-13, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-64002.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-757, m:tm-634, u:((A (-> (or (-> Am Bm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-64003
in-theory        64003
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-635 ((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-635.          ((A or (B -> A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-44, m:tm-14, u:((Am (-> A B)) (C (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-64003.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-757, m:tm-635, u:((A (-> (or Am (-> Bm Am)) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-64004
in-theory        64004
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     29
proof            (modus-ponens tm-757 tm-636 ((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-636.          ((A or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-44, m:tm-15, u:((A (and (-> Am Bm) Cm)) (B Am) (C (-> (and (-> Am Bm) Cm) Bm)))
tm-64004.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-757, m:tm-636, u:((A (-> (or Am (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-64005
in-theory        64005
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-637 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-637.          ((A or (B -> A)) -> ((C and D) -> C)), M:tm-44, m:tm-16, u:((Am (-> A B)) (C (-> (and Bm Cm) Bm)))
tm-64005.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((F and G) -> F))), M:tm-757, m:tm-637, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-64006
in-theory        64006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F)))
theorem-size     29
proof            (modus-ponens tm-757 tm-638 ((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-638.          ((A or ((B and (A -> C)) -> A)) -> ((B and (A -> C)) -> C)), M:tm-44, m:tm-17, u:((A (and Am (-> Bm Cm))) (B Bm) (C (-> (and Am (-> Bm Cm)) Cm)))
tm-64006.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E and (D -> F)) -> D)) -> ((E and (D -> F)) -> F))), M:tm-757, m:tm-638, u:((A (-> (or Am (-> (and Bm (-> Am Cm)) Am)) (-> (and Bm (-> Am Cm)) Cm))))
================================================================
tm-name          tm-64007
in-theory        64007
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-757 tm-639 ((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-639.          ((A or (B -> A)) -> ((C and D) -> D)), M:tm-44, m:tm-18, u:((Am (-> A B)) (C (-> (and Bm Cm) Cm)))
tm-64007.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((F and G) -> G))), M:tm-757, m:tm-639, u:((A (-> (or Am (-> Bm Am)) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-64008
in-theory        64008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-757 tm-640 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-640.          ((A or (B -> A)) -> ((C -> (D -> C)) and (B -> A))), M:tm-44, m:tm-19, u:((Am (-> A B)) (C (and (-> Bm (-> Cm Bm)) (-> A B))))
tm-64008.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G -> F)) and (E -> D)))), M:tm-757, m:tm-640, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-64009
in-theory        64009
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D))))
theorem-size     35
proof            (modus-ponens tm-757 tm-641 ((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-641.          ((A or (B -> A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (B -> A))), M:tm-44, m:tm-20, u:((Am (-> A B)) (C (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> A B))))
tm-64009.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (E -> D)))), M:tm-757, m:tm-641, u:((A (-> (or Am (-> Bm Am)) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) (-> Bm Am)))))
================================================================
tm-name          tm-64010
in-theory        64010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-757 tm-642 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-642.          ((A or (B -> A)) -> (((C and D) -> C) and (B -> A))), M:tm-44, m:tm-21, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Bm) (-> A B))))
tm-64010.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (((F and G) -> F) and (E -> D)))), M:tm-757, m:tm-642, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Cm) (-> Bm Am)))))
================================================================
tm-name          tm-64011
in-theory        64011
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-757 tm-643 ((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-643.          ((A or (B -> A)) -> (((C and D) -> D) and (B -> A))), M:tm-44, m:tm-22, u:((Am (-> A B)) (C (and (-> (and Bm Cm) Cm) (-> A B))))
tm-64011.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (((F and G) -> G) and (E -> D)))), M:tm-757, m:tm-643, u:((A (-> (or Am (-> Bm Am)) (and (-> (and Cm Dm) Dm) (-> Bm Am)))))
================================================================
tm-name          tm-64012
in-theory        64012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D))))
theorem-size     29
proof            (modus-ponens tm-757 tm-644 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-644.          ((A or (B -> A)) -> ((C -> (D -> (C and D))) and (B -> A))), M:tm-44, m:tm-23, u:((Am (-> A B)) (C (and (-> Bm (-> Cm (and Bm Cm))) (-> A B))))
tm-64012.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G -> (F and G))) and (E -> D)))), M:tm-757, m:tm-644, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (-> Dm (and Cm Dm))) (-> Bm Am)))))
================================================================
tm-name          tm-64013
in-theory        64013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (E -> (E and D))))
theorem-size     23
proof            (modus-ponens tm-757 tm-645 ((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-645.          ((A or (B -> A)) -> (B -> (B and A))), M:tm-44, m:tm-24, u:((A Am) (B Bm) (C (-> Am (and Am Bm))))
tm-64013.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (E -> (E and D)))), M:tm-757, m:tm-645, u:((A (-> (or Am (-> Bm Am)) (-> Bm (and Bm Am)))))
================================================================
tm-name          tm-64014
in-theory        64014
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-646 ((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-646.          ((A or (B -> A)) -> (C -> (D -> (C and D)))), M:tm-44, m:tm-25, u:((Am (-> A B)) (C (-> Bm (-> Cm (and Bm Cm)))))
tm-64014.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (F -> (G -> (F and G))))), M:tm-757, m:tm-646, u:((A (-> (or Am (-> Bm Am)) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-64015
in-theory        64015
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-757 tm-647 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-647.          ((A or (B -> A)) -> ((C -> (C or D)) and (B -> A))), M:tm-44, m:tm-32, u:((Am (-> A B)) (C (and (-> Bm (or Bm Cm)) (-> A B))))
tm-64015.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((F -> (F or G)) and (E -> D)))), M:tm-757, m:tm-647, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Cm Dm)) (-> Bm Am)))))
================================================================
tm-name          tm-64016
in-theory        64016
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-757 tm-648 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-648.          ((A or (B -> A)) -> (C -> (C or D))), M:tm-44, m:tm-33, u:((Am (-> A B)) (C (-> Bm (or Bm Cm))))
tm-64016.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (F -> (F or G)))), M:tm-757, m:tm-648, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-64017
in-theory        64017
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D))))
theorem-size     27
proof            (modus-ponens tm-757 tm-649 ((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-649.          ((A or (B -> A)) -> ((C -> (D or C)) and (B -> A))), M:tm-44, m:tm-42, u:((Am (-> A B)) (C (and (-> Bm (or Cm Bm)) (-> A B))))
tm-64017.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> ((F -> (G or F)) and (E -> D)))), M:tm-757, m:tm-649, u:((A (-> (or Am (-> Bm Am)) (and (-> Cm (or Dm Cm)) (-> Bm Am)))))
================================================================
tm-name          tm-64018
in-theory        64018
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-650 ((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-650.          ((A or (B -> A)) -> (C -> (D or C))), M:tm-44, m:tm-43, u:((Am (-> A B)) (C (-> Bm (or Cm Bm))))
tm-64018.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (F -> (G or F)))), M:tm-757, m:tm-650, u:((A (-> (or Am (-> Bm Am)) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-64019
in-theory        64019
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D)))
theorem-size     27
proof            (modus-ponens tm-757 tm-651 ((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-651.          ((A or ((B -> C) -> A)) -> ((C or (B -> C)) -> A)), M:tm-44, m:tm-44, u:((A (-> Am Bm)) (B Cm) (C (-> (or Bm (-> Am Bm)) Cm)))
tm-64019.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or ((E -> F) -> D)) -> ((F or (E -> F)) -> D))), M:tm-757, m:tm-651, u:((A (-> (or Am (-> (-> Bm Cm) Am)) (-> (or Cm (-> Bm Cm)) Am))))
================================================================
tm-name          tm-64020
in-theory        64020
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-652 ((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-652.          ((A -> (B or A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-42, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-64020.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-757, m:tm-652, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-64021
in-theory        64021
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-653 ((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-653.          ((A -> (A or B)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-32, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-64021.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-757, m:tm-653, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-64022
in-theory        64022
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F))))
theorem-size     31
proof            (modus-ponens tm-757 tm-654 ((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-64022.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> F) -> (((D -> E) -> F) and ((E or (D -> E)) -> F)))), M:tm-757, m:tm-654, u:((A (-> (-> (-> Am Bm) Cm) (and (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)))))
================================================================
tm-name          tm-64023
in-theory        64023
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     33
proof            (modus-ponens tm-757 tm-655 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-655.          ((A -> (B -> (A and B))) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-23, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-64023.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-757, m:tm-655, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-64024
in-theory        64024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-656 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-656.          (((A and B) -> B) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-22, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-64024.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-757, m:tm-656, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-64025
in-theory        64025
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-657 ((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-657.          (((A and B) -> A) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-21, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-64025.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-757, m:tm-657, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-64026
in-theory        64026
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I))))
theorem-size     39
proof            (modus-ponens tm-757 tm-658 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-658.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D -> E) -> F) -> ((E or (D -> E)) -> F))), M:tm-20, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-64026.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((G -> H) -> I) -> ((H or (G -> H)) -> I)))), M:tm-757, m:tm-658, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Dm Em) Fm) (-> (or Em (-> Dm Em)) Fm)))))
================================================================
tm-name          tm-64027
in-theory        64027
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-659 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-659.          ((A -> (B -> A)) and (((C -> D) -> E) -> ((D or (C -> D)) -> E))), M:tm-19, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-64027.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and (((F -> G) -> H) -> ((G or (F -> G)) -> H)))), M:tm-757, m:tm-659, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> Cm Dm) Em) (-> (or Dm (-> Cm Dm)) Em)))))
================================================================
tm-name          tm-64028
in-theory        64028
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> F) -> ((D -> E) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-660 ((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-64028.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> F) -> ((D -> E) -> F))), M:tm-757, m:tm-660, u:((A (-> (-> (-> Am Bm) Cm) (-> (-> Am Bm) Cm))))
================================================================
tm-name          tm-64029
in-theory        64029
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F))))
theorem-size     33
proof            (modus-ponens tm-757 tm-661 ((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-661.          ((((A -> B) -> C) -> (not ((B or (A -> B)) -> C))) -> (not ((A -> B) -> C))), M:tm-9, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-64029.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> F) -> (not ((E or (D -> E)) -> F))) -> (not ((D -> E) -> F)))), M:tm-757, m:tm-661, u:((A (-> (-> (-> (-> Am Bm) Cm) (not (-> (or Bm (-> Am Bm)) Cm))) (not (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-64030
in-theory        64030
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G)))
theorem-size     37
proof            (modus-ponens tm-757 tm-662 ((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-64030.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D or (E -> D)) -> F) -> G) -> ((((E -> D) -> F) or ((D or (E -> D)) -> F)) -> G))), M:tm-757, m:tm-662, u:((A (-> (-> (-> (or Am (-> Bm Am)) Cm) Dm) (-> (or (-> (-> Bm Am) Cm) (-> (or Am (-> Bm Am)) Cm)) Dm))))
================================================================
tm-name          tm-64031
in-theory        64031
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-757 tm-663 ((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-663.          (A or (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-7, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-64031.        (((A -> B) -> (((A and C) or A) -> B)) and (D or (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-757, m:tm-663, u:((A (or Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-64032
in-theory        64032
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G))
theorem-size     27
proof            (modus-ponens tm-757 tm-664 ((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-664.          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) or D), M:tm-6, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-64032.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> F) -> ((E or (D -> E)) -> F)) or G)), M:tm-757, m:tm-664, u:((A (or (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm)) Dm)))
================================================================
tm-name          tm-64033
in-theory        64033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D)))
theorem-size     29
proof            (modus-ponens tm-757 tm-665 ((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-64033.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> F) -> G) -> ((F or (E -> F)) -> G)) and D))), M:tm-757, m:tm-665, u:((A (-> Am (and (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)) Am))))
================================================================
tm-name          tm-64034
in-theory        64034
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-757 tm-666 ((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-666.          ((((A -> B) -> C) -> (B or (A -> B))) -> (((A -> B) -> C) -> C)), M:tm-2, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (or Bm (-> Am Bm))) (C Cm))
tm-64034.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> F) -> (E or (D -> E))) -> (((D -> E) -> F) -> F))), M:tm-757, m:tm-666, u:((A (-> (-> (-> (-> Am Bm) Cm) (or Bm (-> Am Bm))) (-> (-> (-> Am Bm) Cm) Cm))))
================================================================
tm-name          tm-64035
in-theory        64035
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G))))
theorem-size     27
proof            (modus-ponens tm-757 tm-667 ((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-667.          (A -> (((B -> C) -> D) -> ((C or (B -> C)) -> D))), M:tm-1, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-64035.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> G) -> ((F or (E -> F)) -> G)))), M:tm-757, m:tm-667, u:((A (-> Am (-> (-> (-> Bm Cm) Dm) (-> (or Cm (-> Bm Cm)) Dm)))))
================================================================
tm-name          tm-64036
in-theory        64036
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-757 tm-668 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-668.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> ((A -> B) -> (A -> C)))), M:tm-45, m:tm-1, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> (-> A B) (-> A C)))))
tm-64036.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> ((D -> E) -> (D -> F))))), M:tm-757, m:tm-668, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-64037
in-theory        64037
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F))))
theorem-size     37
proof            (modus-ponens tm-757 tm-669 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-669.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> A) -> ((A -> B) -> C))), M:tm-45, m:tm-2, u:((Am (-> Bm B)) (A Bm) (C Cm) (D (-> (-> (-> Bm B) Bm) (-> (-> Bm B) Cm))))
tm-64037.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> D) -> ((D -> E) -> F)))), M:tm-757, m:tm-669, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) Am) (-> (-> Am Bm) Cm)))))
================================================================
tm-name          tm-64038
in-theory        64038
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G))))
theorem-size     37
proof            (modus-ponens tm-757 tm-670 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-670.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (((A -> B) -> (A -> C)) and D))), M:tm-45, m:tm-5, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (and (-> (-> A B) (-> A C)) Bm))))
tm-64038.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (((D -> E) -> (D -> F)) and G)))), M:tm-757, m:tm-670, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (and (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-64039
in-theory        64039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G)))
theorem-size     35
proof            (modus-ponens tm-757 tm-671 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-6)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-671.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (A -> C)) or D)), M:tm-45, m:tm-6, u:((Am (-> (-> A B) (-> A C))) (D (or (-> (-> A B) (-> A C)) Bm)))
tm-64039.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (D -> F)) or G))), M:tm-757, m:tm-671, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-64040
in-theory        64040
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F)))))
theorem-size     35
proof            (modus-ponens tm-757 tm-672 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-7)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-672.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D or ((A -> B) -> (A -> C)))), M:tm-45, m:tm-7, u:((Am (-> (-> A B) (-> A C))) (D (or Bm (-> (-> A B) (-> A C)))))
tm-64040.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G or ((D -> E) -> (D -> F))))), M:tm-757, m:tm-672, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (or Dm (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-64041
in-theory        64041
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G))))
theorem-size     41
proof            (modus-ponens tm-757 tm-673 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-673.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> C) -> D) -> (((A -> B) or (A -> C)) -> D))), M:tm-45, m:tm-8, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A C) Cm) (-> (or (-> A B) (-> A C)) Cm))))
tm-64041.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> F) -> G) -> (((D -> E) or (D -> F)) -> G)))), M:tm-757, m:tm-673, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Cm) Dm) (-> (or (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-64042
in-theory        64042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-674 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-9)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-674.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((A -> B) -> (not (A -> C))) -> (not (A -> B)))), M:tm-45, m:tm-9, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> (-> A B) (not (-> A C))) (not (-> A B)))))
tm-64042.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((D -> E) -> (not (D -> F))) -> (not (D -> E))))), M:tm-757, m:tm-674, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> Am Bm) (not (-> Am Cm))) (not (-> Am Bm))))))
================================================================
tm-name          tm-64043
in-theory        64043
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G))))
theorem-size     31
proof            (modus-ponens tm-757 tm-675 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-675.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> D))), M:tm-45, m:tm-11, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm Bm))))
tm-64043.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> G)))), M:tm-757, m:tm-675, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em Dm)))))
================================================================
tm-name          tm-64044
in-theory        64044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E))))
theorem-size     33
proof            (modus-ponens tm-757 tm-676 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-676.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> (A -> B))), M:tm-45, m:tm-12, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (-> A B))))
tm-64044.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> (D -> E)))), M:tm-757, m:tm-676, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (-> Am Bm)))))
================================================================
tm-name          tm-64045
in-theory        64045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-757 tm-677 ((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-677.          (((A -> ((B -> C) -> B)) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-45, m:tm-13, u:((B (-> Bm Cm)) (A Am) (C Bm) (D (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-64045.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> ((E -> F) -> E)) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-757, m:tm-677, u:((A (-> (or (-> Am (-> (-> Bm Cm) Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-64046
in-theory        64046
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-678 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-678.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-45, m:tm-14, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-64046.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-757, m:tm-678, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))))))
================================================================
tm-name          tm-64047
in-theory        64047
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G)))
theorem-size     31
proof            (modus-ponens tm-757 tm-679 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-679.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> D)), M:tm-45, m:tm-16, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Bm)))
tm-64047.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> G))), M:tm-757, m:tm-679, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Dm))))
================================================================
tm-name          tm-64048
in-theory        64048
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H)))
theorem-size     31
proof            (modus-ponens tm-757 tm-680 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-680.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D and E) -> E)), M:tm-45, m:tm-18, u:((Am (-> (-> A B) (-> A C))) (D (-> (and Bm Cm) Cm)))
tm-64048.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G and H) -> H))), M:tm-757, m:tm-680, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (and Dm Em) Em))))
================================================================
tm-name          tm-64049
in-theory        64049
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-681 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-681.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-19, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm Bm)) (-> (-> A B) (-> A C)))))
tm-64049.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> G)) and ((D -> E) -> (D -> F))))), M:tm-757, m:tm-681, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-64050
in-theory        64050
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F)))))
theorem-size     47
proof            (modus-ponens tm-757 tm-682 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-682.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-20, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) (-> (-> A B) (-> A C)))))
tm-64050.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and ((D -> E) -> (D -> F))))), M:tm-757, m:tm-682, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-64051
in-theory        64051
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-683 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-683.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> D) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-21, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Bm) (-> (-> A B) (-> A C)))))
tm-64051.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> G) and ((D -> E) -> (D -> F))))), M:tm-757, m:tm-683, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Dm) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-64052
in-theory        64052
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-684 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-684.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D and E) -> E) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-22, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (and Bm Cm) Cm) (-> (-> A B) (-> A C)))))
tm-64052.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (((G and H) -> H) and ((D -> E) -> (D -> F))))), M:tm-757, m:tm-684, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> (and Dm Em) Em) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-64053
in-theory        64053
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F)))))
theorem-size     41
proof            (modus-ponens tm-757 tm-685 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-685.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E -> (D and E))) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-23, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (-> Cm (and Bm Cm))) (-> (-> A B) (-> A C)))))
tm-64053.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H -> (G and H))) and ((D -> E) -> (D -> F))))), M:tm-757, m:tm-685, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (-> Em (and Dm Em))) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-64054
in-theory        64054
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F)))))
theorem-size     37
proof            (modus-ponens tm-757 tm-686 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-686.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> ((A -> B) and (A -> C)))), M:tm-45, m:tm-24, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (-> A B) (and (-> A B) (-> A C)))))
tm-64054.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> ((D -> E) and (D -> F))))), M:tm-757, m:tm-686, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) (and (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-64055
in-theory        64055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H)))))
theorem-size     33
proof            (modus-ponens tm-757 tm-687 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-687.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E -> (D and E)))), M:tm-45, m:tm-25, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (-> Cm (and Bm Cm)))))
tm-64055.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H -> (G and H))))), M:tm-757, m:tm-687, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (-> Em (and Dm Em))))))
================================================================
tm-name          tm-64056
in-theory        64056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-688 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-6)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-688.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (D or E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-32, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Bm Cm)) (-> (-> A B) (-> A C)))))
tm-64056.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (G or H)) and ((D -> E) -> (D -> F))))), M:tm-757, m:tm-688, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Dm Em)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-64057
in-theory        64057
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H))))
theorem-size     31
proof            (modus-ponens tm-757 tm-689 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-6)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-689.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (D or E))), M:tm-45, m:tm-33, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Bm Cm))))
tm-64057.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (G or H)))), M:tm-757, m:tm-689, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Dm Em)))))
================================================================
tm-name          tm-64058
in-theory        64058
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F)))))
theorem-size     39
proof            (modus-ponens tm-757 tm-690 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-7)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-690.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> (E or D)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-42, u:((Am (-> (-> A B) (-> A C))) (D (and (-> Bm (or Cm Bm)) (-> (-> A B) (-> A C)))))
tm-64058.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((G -> (H or G)) and ((D -> E) -> (D -> F))))), M:tm-757, m:tm-690, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (and (-> Dm (or Em Dm)) (-> (-> Am Bm) (-> Am Cm))))))
================================================================
tm-name          tm-64059
in-theory        64059
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G))))
theorem-size     31
proof            (modus-ponens tm-757 tm-691 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1 tm-7)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-691.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (D -> (E or D))), M:tm-45, m:tm-43, u:((Am (-> (-> A B) (-> A C))) (D (-> Bm (or Cm Bm))))
tm-64059.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> (G -> (H or G)))), M:tm-757, m:tm-691, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> Dm (or Em Dm)))))
================================================================
tm-name          tm-64060
in-theory        64060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F))))
theorem-size     35
proof            (modus-ponens tm-757 tm-692 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-692.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((B or (A -> B)) -> (A -> C))), M:tm-45, m:tm-44, u:((A Am) (B Bm) (Cm (-> Am C)) (D (-> (or Bm (-> Am Bm)) (-> Am C))))
tm-64060.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((E or (D -> E)) -> (D -> F)))), M:tm-757, m:tm-692, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or Bm (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-64061
in-theory        64061
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G))))
theorem-size     55
proof            (modus-ponens tm-757 tm-693 ((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       251
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-693.          ((((A -> B) -> ((A -> C) -> D)) or (((A -> B) -> (A -> C)) -> ((A -> B) -> D))) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((A -> B) -> D))), M:tm-45, m:tm-45, u:((A (-> Am Bm)) (B (-> Am Cm)) (Dm (-> (-> Am Bm) C)) (D (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) C))))
tm-64061.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> ((D -> F) -> G)) or (((D -> E) -> (D -> F)) -> ((D -> E) -> G))) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((D -> E) -> G)))), M:tm-757, m:tm-693, u:((A (-> (or (-> (-> Am Bm) (-> (-> Am Cm) Dm)) (-> (-> (-> Am Bm) (-> Am Cm)) (-> (-> Am Bm) Dm))) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Am Bm) Dm)))))
================================================================
tm-name          tm-64062
in-theory        64062
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D)))
theorem-size     39
proof            (modus-ponens tm-757 tm-694 ((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-694.          ((A or (((B -> C) -> (B -> D)) -> A)) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> A)), M:tm-44, m:tm-45, u:((A (-> (-> Am Bm) (-> Am Cm))) (B Dm) (C (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-64062.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (((E -> F) -> (E -> G)) -> D)) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> D))), M:tm-757, m:tm-694, u:((A (-> (or Am (-> (-> (-> Bm Cm) (-> Bm Dm)) Am)) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
================================================================
tm-name          tm-64063
in-theory        64063
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-757 tm-695 ((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-695.          ((A -> (B or A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-42, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-64063.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-757, m:tm-695, u:((A (and (-> Am (or Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-64064
in-theory        64064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-757 tm-696 ((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-696.          ((A -> (A or B)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-32, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-64064.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-757, m:tm-696, u:((A (and (-> Am (or Am Bm)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-64065
in-theory        64065
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))))
theorem-size     47
proof            (modus-ponens tm-757 tm-697 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-64065.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> ((((D -> E) -> (D -> F)) -> G) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))), M:tm-757, m:tm-697, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
================================================================
tm-name          tm-64066
in-theory        64066
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     45
proof            (modus-ponens tm-757 tm-698 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-698.          ((A -> (B -> (A and B))) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-23, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-64066.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-757, m:tm-698, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-64067
in-theory        64067
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-757 tm-699 ((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-699.          (((A and B) -> B) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-22, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-64067.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-757, m:tm-699, u:((A (and (-> (and Am Bm) Bm) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-64068
in-theory        64068
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-757 tm-700 ((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-700.          (((A and B) -> A) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-21, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-64068.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-757, m:tm-700, u:((A (and (-> (and Am Bm) Am) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-64069
in-theory        64069
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J))))
theorem-size     51
proof            (modus-ponens tm-757 tm-701 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       229
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-701.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-20, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-64069.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((((G -> H) -> (G -> I)) -> J) -> (((G -> (H -> I)) or ((G -> H) -> (G -> I))) -> J)))), M:tm-757, m:tm-701, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> (-> (-> Dm Em) (-> Dm Fm)) Gm) (-> (or (-> Dm (-> Em Fm)) (-> (-> Dm Em) (-> Dm Fm))) Gm)))))
================================================================
tm-name          tm-64070
in-theory        64070
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I))))
theorem-size     43
proof            (modus-ponens tm-757 tm-702 ((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-702.          ((A -> (B -> A)) and ((((C -> D) -> (C -> E)) -> F) -> (((C -> (D -> E)) or ((C -> D) -> (C -> E))) -> F))), M:tm-19, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-64070.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((((F -> G) -> (F -> H)) -> I) -> (((F -> (G -> H)) or ((F -> G) -> (F -> H))) -> I)))), M:tm-757, m:tm-702, u:((A (and (-> Am (-> Bm Am)) (-> (-> (-> (-> Cm Dm) (-> Cm Em)) Fm) (-> (or (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Fm)))))
================================================================
tm-name          tm-64071
in-theory        64071
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G)))
theorem-size     31
proof            (modus-ponens tm-757 tm-703 ((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-64071.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) -> (D -> F)) -> G) -> (((D -> E) -> (D -> F)) -> G))), M:tm-757, m:tm-703, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))
================================================================
tm-name          tm-64072
in-theory        64072
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G))))
theorem-size     49
proof            (modus-ponens tm-757 tm-704 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9 tm-2)
proof-size       199
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-704.          (((((A -> B) -> (A -> C)) -> D) -> (not (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))) -> (not (((A -> B) -> (A -> C)) -> D))), M:tm-9, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-64072.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (not (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))) -> (not (((D -> E) -> (D -> F)) -> G)))), M:tm-757, m:tm-704, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (not (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))) (not (-> (-> (-> Am Bm) (-> Am Cm)) Dm)))))
================================================================
tm-name          tm-64073
in-theory        64073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H)))
theorem-size     57
proof            (modus-ponens tm-757 tm-705 ((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       217
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-64073.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G) -> H) -> (((((D -> E) -> (D -> F)) -> G) or (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) -> H))), M:tm-757, m:tm-705, u:((A (-> (-> (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm) Em) (-> (or (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
================================================================
tm-name          tm-64074
in-theory        64074
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-757 tm-706 ((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-706.          (A or ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-7, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-64074.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-757, m:tm-706, u:((A (or Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-64075
in-theory        64075
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H))
theorem-size     39
proof            (modus-ponens tm-757 tm-707 ((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em))))
axioms-used      (tm-5 tm-8 tm-3 tm-6 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-707.          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) or E), M:tm-6, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-64075.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)) or H)), M:tm-757, m:tm-707, u:((A (or (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)) Em)))
================================================================
tm-name          tm-64076
in-theory        64076
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D)))
theorem-size     41
proof            (modus-ponens tm-757 tm-708 ((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-64076.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)) and D))), M:tm-757, m:tm-708, u:((A (-> Am (and (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)) Am))))
================================================================
tm-name          tm-64077
in-theory        64077
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G)))
theorem-size     47
proof            (modus-ponens tm-757 tm-709 ((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-709.          (((((A -> B) -> (A -> C)) -> D) -> ((A -> (B -> C)) or ((A -> B) -> (A -> C)))) -> ((((A -> B) -> (A -> C)) -> D) -> D)), M:tm-2, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (C Dm))
tm-64077.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) -> (D -> F)) -> G) -> ((D -> (E -> F)) or ((D -> E) -> (D -> F)))) -> ((((D -> E) -> (D -> F)) -> G) -> G))), M:tm-757, m:tm-709, u:((A (-> (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))) (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Dm))))
================================================================
tm-name          tm-64078
in-theory        64078
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H))))
theorem-size     39
proof            (modus-ponens tm-757 tm-710 ((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-710.          (A -> ((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E))), M:tm-1, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-64078.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((((E -> F) -> (E -> G)) -> H) -> (((E -> (F -> G)) or ((E -> F) -> (E -> G))) -> H)))), M:tm-757, m:tm-710, u:((A (-> Am (-> (-> (-> (-> Bm Cm) (-> Bm Dm)) Em) (-> (or (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Em)))))
================================================================
tm-name          tm-64079
in-theory        64079
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (F -> D)))
theorem-size     21
proof            (modus-ponens tm-757 tm-711 ((A (-> (or (and Am Bm) Am) (-> Cm Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-711.          (((A and B) or A) -> (C -> A)), M:tm-46, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64079.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (F -> D))), M:tm-757, m:tm-711, u:((A (-> (or (and Am Bm) Am) (-> Cm Am))))
================================================================
tm-name          tm-64080
in-theory        64080
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-757 tm-712 ((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-712.          ((((A -> (B -> C)) and D) or (A -> (B -> C))) -> ((A -> B) -> (A -> C))), M:tm-46, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64080.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> (E -> F)) and G) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-757, m:tm-712, u:((A (-> (or (and (-> Am (-> Bm Cm)) Dm) (-> Am (-> Bm Cm))) (-> (-> Am Bm) (-> Am Cm)))))
================================================================
tm-name          tm-64081
in-theory        64081
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D and E) and F) or (D and E)) -> D))
theorem-size     23
proof            (modus-ponens tm-757 tm-713 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-713.          ((((A and B) and C) or (A and B)) -> A), M:tm-46, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64081.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D and E) and F) or (D and E)) -> D)), M:tm-757, m:tm-713, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Am)))
================================================================
tm-name          tm-64082
in-theory        64082
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D and E) and F) or (D and E)) -> E))
theorem-size     23
proof            (modus-ponens tm-757 tm-714 ((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-714.          ((((A and B) and C) or (A and B)) -> B), M:tm-46, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64082.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D and E) and F) or (D and E)) -> E)), M:tm-757, m:tm-714, u:((A (-> (or (and (and Am Bm) Cm) (and Am Bm)) Bm)))
================================================================
tm-name          tm-64083
in-theory        64083
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (F -> (D and F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-715 ((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-715.          (((A and B) or A) -> (C -> (A and C))), M:tm-46, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64083.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (F -> (D and F)))), M:tm-757, m:tm-715, u:((A (-> (or (and Am Bm) Am) (-> Cm (and Am Cm)))))
================================================================
tm-name          tm-64084
in-theory        64084
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (D or F)))
theorem-size     21
proof            (modus-ponens tm-757 tm-716 ((A (-> (or (and Am Bm) Am) (or Am Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-716.          (((A and B) or A) -> (A or C)), M:tm-46, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64084.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (D or F))), M:tm-757, m:tm-716, u:((A (-> (or (and Am Bm) Am) (or Am Cm))))
================================================================
tm-name          tm-64085
in-theory        64085
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (F or D)))
theorem-size     21
proof            (modus-ponens tm-757 tm-717 ((A (-> (or (and Am Bm) Am) (or Cm Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-717.          (((A and B) or A) -> (C or A)), M:tm-46, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64085.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (F or D))), M:tm-757, m:tm-717, u:((A (-> (or (and Am Bm) Am) (or Cm Am))))
================================================================
tm-name          tm-64086
in-theory        64086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G))))
theorem-size     31
proof            (modus-ponens tm-757 tm-718 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-718.          ((((A -> B) and C) or (A -> B)) -> ((B -> D) -> ((A or B) -> D))), M:tm-46, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-64086.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((E -> G) -> ((D or E) -> G)))), M:tm-757, m:tm-718, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Bm Dm) (-> (or Am Bm) Dm)))))
================================================================
tm-name          tm-64087
in-theory        64087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     29
proof            (modus-ponens tm-757 tm-719 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-719.          ((((A -> B) and C) or (A -> B)) -> ((A -> (not B)) -> (not A))), M:tm-46, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-64087.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-757, m:tm-719, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (-> Am (not Bm)) (not Am)))))
================================================================
tm-name          tm-64088
in-theory        64088
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((not (not D)) and E) or (not (not D))) -> D))
theorem-size     23
proof            (modus-ponens tm-757 tm-720 ((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am))))
axioms-used      (tm-5 tm-8 tm-3 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-10.           ((not (not A)) -> A), axiom
tm-720.          ((((not (not A)) and B) or (not (not A))) -> A), M:tm-46, m:tm-10, u:((A (not (not Am))) (B Am))
tm-64088.        (((A -> B) -> (((A and C) or A) -> B)) and ((((not (not D)) and E) or (not (not D))) -> D)), M:tm-757, m:tm-720, u:((A (-> (or (and (not (not Am)) Bm) (not (not Am))) Am)))
================================================================
tm-name          tm-64089
in-theory        64089
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-721 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-721.          (((A and B) or A) -> (C -> (D -> C))), M:tm-46, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-64089.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (F -> (G -> F)))), M:tm-757, m:tm-721, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-64090
in-theory        64090
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-722 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-722.          ((((A -> B) and C) or (A -> B)) -> (A -> A)), M:tm-46, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-64090.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> D))), M:tm-757, m:tm-722, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am Am))))
================================================================
tm-name          tm-64091
in-theory        64091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-757 tm-723 ((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-723.          (((((A -> (B -> C)) -> (A -> B)) and D) or ((A -> (B -> C)) -> (A -> B))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-46, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-64091.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> (E -> F)) -> (D -> E)) and G) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-757, m:tm-723, u:((A (-> (or (and (-> (-> Am (-> Bm Cm)) (-> Am Bm)) Dm) (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
================================================================
tm-name          tm-64092
in-theory        64092
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-724 ((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-724.          (((A and B) or A) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-46, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-64092.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-757, m:tm-724, u:((A (-> (or (and Am Bm) Am) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-64093
in-theory        64093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     37
proof            (modus-ponens tm-757 tm-725 ((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-725.          ((((((A -> B) and C) -> A) and D) or (((A -> B) and C) -> A)) -> (((A -> B) and C) -> B)), M:tm-46, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-64093.        (((A -> B) -> (((A and C) or A) -> B)) and ((((((D -> E) and F) -> D) and G) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-757, m:tm-725, u:((A (-> (or (and (-> (and (-> Am Bm) Cm) Am) Dm) (-> (and (-> Am Bm) Cm) Am)) (-> (and (-> Am Bm) Cm) Bm))))
================================================================
tm-name          tm-64094
in-theory        64094
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-726 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-726.          (((A and B) or A) -> ((C and D) -> C)), M:tm-46, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-64094.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> ((F and G) -> F))), M:tm-757, m:tm-726, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-64095
in-theory        64095
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     37
proof            (modus-ponens tm-757 tm-727 ((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-727.          (((((A and (B -> C)) -> B) and D) or ((A and (B -> C)) -> B)) -> ((A and (B -> C)) -> C)), M:tm-46, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-64095.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D and (E -> F)) -> E) and G) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-757, m:tm-727, u:((A (-> (or (and (-> (and Am (-> Bm Cm)) Bm) Dm) (-> (and Am (-> Bm Cm)) Bm)) (-> (and Am (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-64096
in-theory        64096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-757 tm-728 ((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-728.          (((A and B) or A) -> ((C and D) -> D)), M:tm-46, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-64096.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> ((F and G) -> G))), M:tm-757, m:tm-728, u:((A (-> (or (and Am Bm) Am) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-64097
in-theory        64097
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> ((F -> (G -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-729 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-729.          (((A and B) or A) -> ((C -> (D -> C)) and A)), M:tm-46, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-64097.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> ((F -> (G -> F)) and D))), M:tm-757, m:tm-729, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm Cm)) Am))))
================================================================
tm-name          tm-64098
in-theory        64098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D)))
theorem-size     33
proof            (modus-ponens tm-757 tm-730 ((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-730.          (((A and B) or A) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-46, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-64098.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and D))), M:tm-757, m:tm-730, u:((A (-> (or (and Am Bm) Am) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Am))))
================================================================
tm-name          tm-64099
in-theory        64099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (((F and G) -> F) and D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-731 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-731.          (((A and B) or A) -> (((C and D) -> C) and A)), M:tm-46, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-64099.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (((F and G) -> F) and D))), M:tm-757, m:tm-731, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Cm) Am))))
================================================================
tm-name          tm-64100
in-theory        64100
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (((F and G) -> G) and D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-732 ((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-732.          (((A and B) or A) -> (((C and D) -> D) and A)), M:tm-46, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-64100.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (((F and G) -> G) and D))), M:tm-757, m:tm-732, u:((A (-> (or (and Am Bm) Am) (and (-> (and Cm Dm) Dm) Am))))
================================================================
tm-name          tm-64101
in-theory        64101
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D)))
theorem-size     27
proof            (modus-ponens tm-757 tm-733 ((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-733.          (((A and B) or A) -> ((C -> (D -> (C and D))) and A)), M:tm-46, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-64101.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> ((F -> (G -> (F and G))) and D))), M:tm-757, m:tm-733, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (-> Dm (and Cm Dm))) Am))))
================================================================
tm-name          tm-64102
in-theory        64102
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-757 tm-734 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-734.          ((((A -> B) and C) or (A -> B)) -> (A -> (A and B))), M:tm-46, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-64102.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (D -> (D and E)))), M:tm-757, m:tm-734, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> Am (and Am Bm)))))
================================================================
tm-name          tm-64103
in-theory        64103
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (F -> (G -> (F and G)))))
theorem-size     25
proof            (modus-ponens tm-757 tm-735 ((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-735.          (((A and B) or A) -> (C -> (D -> (C and D)))), M:tm-46, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-64103.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (F -> (G -> (F and G))))), M:tm-757, m:tm-735, u:((A (-> (or (and Am Bm) Am) (-> Cm (-> Dm (and Cm Dm))))))
================================================================
tm-name          tm-64104
in-theory        64104
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> ((F -> (F or G)) and D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-736 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-736.          (((A and B) or A) -> ((C -> (C or D)) and A)), M:tm-46, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-64104.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> ((F -> (F or G)) and D))), M:tm-757, m:tm-736, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Cm Dm)) Am))))
================================================================
tm-name          tm-64105
in-theory        64105
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (F -> (F or G))))
theorem-size     23
proof            (modus-ponens tm-757 tm-737 ((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-6)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-737.          (((A and B) or A) -> (C -> (C or D))), M:tm-46, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-64105.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (F -> (F or G)))), M:tm-757, m:tm-737, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Cm Dm)))))
================================================================
tm-name          tm-64106
in-theory        64106
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> ((F -> (G or F)) and D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-738 ((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-738.          (((A and B) or A) -> ((C -> (D or C)) and A)), M:tm-46, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-64106.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> ((F -> (G or F)) and D))), M:tm-757, m:tm-738, u:((A (-> (or (and Am Bm) Am) (and (-> Cm (or Dm Cm)) Am))))
================================================================
tm-name          tm-64107
in-theory        64107
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (F -> (G or F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-739 ((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1 tm-7)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-739.          (((A and B) or A) -> (C -> (D or C))), M:tm-46, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-64107.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or D) -> (F -> (G or F)))), M:tm-757, m:tm-739, u:((A (-> (or (and Am Bm) Am) (-> Cm (or Dm Cm)))))
================================================================
tm-name          tm-64108
in-theory        64108
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F)))
theorem-size     33
proof            (modus-ponens tm-757 tm-740 ((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-740.          (((((A -> B) -> C) and D) or ((A -> B) -> C)) -> ((B or (A -> B)) -> C)), M:tm-46, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-64108.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D -> E) -> F) and G) or ((D -> E) -> F)) -> ((E or (D -> E)) -> F))), M:tm-757, m:tm-740, u:((A (-> (or (and (-> (-> Am Bm) Cm) Dm) (-> (-> Am Bm) Cm)) (-> (or Bm (-> Am Bm)) Cm))))
================================================================
tm-name          tm-64109
in-theory        64109
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G)))
theorem-size     49
proof            (modus-ponens tm-757 tm-741 ((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-741.          ((((((A -> B) -> (A -> C)) -> D) and E) or (((A -> B) -> (A -> C)) -> D)) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-46, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-64109.        (((A -> B) -> (((A and C) or A) -> B)) and ((((((D -> E) -> (D -> F)) -> G) and H) or (((D -> E) -> (D -> F)) -> G)) -> (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> G))), M:tm-757, m:tm-741, u:((A (-> (or (and (-> (-> (-> Am Bm) (-> Am Cm)) Dm) Em) (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
================================================================
tm-name          tm-64110
in-theory        64110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E)))
theorem-size     29
proof            (modus-ponens tm-757 tm-742 ((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-742.          ((((A -> B) and C) or (A -> B)) -> (((A and D) or A) -> B)), M:tm-46, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-64110.        (((A -> B) -> (((A and C) or A) -> B)) and ((((D -> E) and F) or (D -> E)) -> (((D and G) or D) -> E))), M:tm-757, m:tm-742, u:((A (-> (or (and (-> Am Bm) Cm) (-> Am Bm)) (-> (or (and Am Dm) Am) Bm))))
================================================================
tm-name          tm-64111
in-theory        64111
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-757 tm-743 ((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-743.          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-45, m:tm-46, u:((Am (-> A B)) (Bm (-> A C)) (D (-> (or (and (-> A B) Cm) (-> A B)) (-> A C))))
tm-64111.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) or ((D -> E) -> (D -> F))) -> ((((D -> E) and G) or (D -> E)) -> (D -> F)))), M:tm-757, m:tm-743, u:((A (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (or (and (-> Am Bm) Dm) (-> Am Bm)) (-> Am Cm)))))
================================================================
tm-name          tm-64112
in-theory        64112
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (((E and F) or E) -> D)))
theorem-size     25
proof            (modus-ponens tm-757 tm-744 ((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am)))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-744.          ((A or (B -> A)) -> (((B and C) or B) -> A)), M:tm-44, m:tm-46, u:((A Am) (B Bm) (C (-> (or (and Am Cm) Am) Bm)))
tm-64112.        (((A -> B) -> (((A and C) or A) -> B)) and ((D or (E -> D)) -> (((E and F) or E) -> D))), M:tm-757, m:tm-744, u:((A (-> (or Am (-> Bm Am)) (-> (or (and Bm Cm) Bm) Am))))
================================================================
tm-name          tm-64113
in-theory        64113
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-757 tm-745 ((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-745.          ((A -> (B or A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-42, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64113.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E or D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-757, m:tm-745, u:((A (and (-> Am (or Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-64114
in-theory        64114
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-757 tm-746 ((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-746.          ((A -> (A or B)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-32, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64114.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (D or E)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-757, m:tm-746, u:((A (and (-> Am (or Am Bm)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-64115
in-theory        64115
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E))))
theorem-size     27
proof            (modus-ponens tm-757 tm-747 ((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-64115.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> E) -> ((D -> E) and (((D and F) or D) -> E)))), M:tm-757, m:tm-747, u:((A (-> (-> Am Bm) (and (-> Am Bm) (-> (or (and Am Cm) Am) Bm)))))
================================================================
tm-name          tm-64116
in-theory        64116
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-757 tm-748 ((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-748.          ((A -> (B -> (A and B))) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-23, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64116.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> (D and E))) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-757, m:tm-748, u:((A (and (-> Am (-> Bm (and Am Bm))) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-64117
in-theory        64117
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-757 tm-749 ((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-749.          (((A and B) -> B) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-22, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64117.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> E) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-757, m:tm-749, u:((A (and (-> (and Am Bm) Bm) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-64118
in-theory        64118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-757 tm-750 ((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-750.          (((A and B) -> A) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-21, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64118.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) -> D) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-757, m:tm-750, u:((A (and (-> (and Am Bm) Am) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-64119
in-theory        64119
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H))))
theorem-size     37
proof            (modus-ponens tm-757 tm-751 ((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em))))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-751.          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and ((D -> E) -> (((D and F) or D) -> E))), M:tm-20, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64119.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and ((G -> H) -> (((G and I) or G) -> H)))), M:tm-757, m:tm-751, u:((A (and (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) (-> (-> Dm Em) (-> (or (and Dm Fm) Dm) Em)))))
================================================================
tm-name          tm-64120
in-theory        64120
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-757 tm-752 ((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-752.          ((A -> (B -> A)) and ((C -> D) -> (((C and E) or C) -> D))), M:tm-19, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64120.        (((A -> B) -> (((A and C) or A) -> B)) and ((D -> (E -> D)) and ((F -> G) -> (((F and H) or F) -> G)))), M:tm-757, m:tm-752, u:((A (and (-> Am (-> Bm Am)) (-> (-> Cm Dm) (-> (or (and Cm Em) Cm) Dm)))))
================================================================
tm-name          tm-64121
in-theory        64121
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E))))
theorem-size     29
proof            (modus-ponens tm-757 tm-753 ((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-753.          (((A -> B) -> (not (((A and C) or A) -> B))) -> (not (A -> B))), M:tm-9, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-64121.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (not (((D and F) or D) -> E))) -> (not (D -> E)))), M:tm-757, m:tm-753, u:((A (-> (-> (-> Am Bm) (not (-> (or (and Am Cm) Am) Bm))) (not (-> Am Bm)))))
================================================================
tm-name          tm-64122
in-theory        64122
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G)))
theorem-size     35
proof            (modus-ponens tm-757 tm-754 ((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-64122.        (((A -> B) -> (((A and C) or A) -> B)) and (((((D and E) or D) -> F) -> G) -> (((D -> F) or (((D and E) or D) -> F)) -> G))), M:tm-757, m:tm-754, u:((A (-> (-> (-> (or (and Am Bm) Am) Cm) Dm) (-> (or (-> Am Cm) (-> (or (and Am Bm) Am) Cm)) Dm))))
================================================================
tm-name          tm-64123
in-theory        64123
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-755 ((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-7)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-7.            (A -> (B or A)), axiom
tm-755.          (A or ((B -> C) -> (((B and D) or B) -> C))), M:tm-7, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64123.        (((A -> B) -> (((A and C) or A) -> B)) and (D or ((E -> F) -> (((E and G) or E) -> F)))), M:tm-757, m:tm-755, u:((A (or Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64124
in-theory        64124
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (((D and F) or D) -> E)) or G))
theorem-size     25
proof            (modus-ponens tm-757 tm-756 ((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm))))
axioms-used      (tm-5 tm-8 tm-3 tm-6)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-6.            (A -> (A or B)), axiom
tm-756.          (((A -> B) -> (((A and C) or A) -> B)) or D), M:tm-6, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64124.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> (((D and F) or D) -> E)) or G)), M:tm-757, m:tm-756, u:((A (or (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm)) Dm)))
================================================================
tm-name          tm-64125
in-theory        64125
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-757 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64125.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-757, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64126
in-theory        64126
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> (((D and F) or D) -> E)) and (((A and C) or A) -> B)))
theorem-size     31
proof            (modus-ponens tm-754 tm-757 ((Am (-> (or (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or (and A B) A) C)))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64126.        (((A -> B) or (((A and C) or A) -> B)) -> (((D -> E) -> (((D and F) or D) -> E)) and (((A and C) or A) -> B))), M:tm-754, m:tm-757, u:((Am (-> (or (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or (and A B) A) C))))
================================================================
tm-name          tm-64127
in-theory        64127
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (((A and E) or A) -> (((B -> C) -> (((B and D) or B) -> C)) and A)))
theorem-size     35
proof            (modus-ponens tm-747 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64127.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (((A and E) or A) -> (((B -> C) -> (((B and D) or B) -> C)) and A))), M:tm-747, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64128
in-theory        64128
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E)))
theorem-size     41
proof            (modus-ponens tm-708 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64128.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E))), M:tm-708, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64129
in-theory        64129
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> (((E and G) or E) -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)))
theorem-size     53
proof            (modus-ponens tm-705 tm-757 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       213
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64129.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> (((E -> F) -> (((E and G) or E) -> F)) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-705, m:tm-757, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-64130
in-theory        64130
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> B) -> (A -> C))))
theorem-size     27
proof            (modus-ponens tm-703 tm-757 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64130.        (((A -> B) -> (A -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> B) -> (A -> C)))), M:tm-703, m:tm-757, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-64131
in-theory        64131
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> B) -> (A -> C)))))
theorem-size     61
proof            (modus-ponens tm-697 tm-757 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       227
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64131.        ((((A -> B) -> (A -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> B) -> (A -> C)))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> B) -> (A -> C))))), M:tm-697, m:tm-757, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-64132
in-theory        64132
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-665 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64132.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-665, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64133
in-theory        64133
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B or (A -> B)) -> C)))
theorem-size     33
proof            (modus-ponens tm-662 tm-757 ((Am (-> (or A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or A (-> B A)) C)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64133.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B or (A -> B)) -> C))), M:tm-662, m:tm-757, u:((Am (-> (or A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (or A (-> B A)) C))))
================================================================
tm-name          tm-64134
in-theory        64134
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> B)))
theorem-size     19
proof            (modus-ponens tm-660 tm-757 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A B)))))
axioms-used      (tm-2 tm-1 tm-8 tm-5 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64134.        ((A -> B) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> B))), M:tm-660, m:tm-757, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A B))))
================================================================
tm-name          tm-64135
in-theory        64135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> B))) and ((B or (A -> B)) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> B))))
theorem-size     41
proof            (modus-ponens tm-654 tm-757 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A B)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64135.        (((A -> B) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> B))) and ((B or (A -> B)) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> B)))), M:tm-654, m:tm-757, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A B))))
================================================================
tm-name          tm-64136
in-theory        64136
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B or (((C -> D) -> (((C and E) or C) -> D)) and A)))
theorem-size     17
proof            (modus-ponens tm-623 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-7 tm-5 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64136.        (A -> (B or (((C -> D) -> (((C and E) or C) -> D)) and A))), M:tm-623, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64137
in-theory        64137
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-622 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64137.        ((A -> (B -> (C or B))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-622, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64138
in-theory        64138
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> (((D -> E) -> (((D and F) or D) -> E)) and (B -> (C or B))))
theorem-size     25
proof            (modus-ponens tm-619 tm-757 ((Am (-> A (or B A))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A (or B A))))))
axioms-used      (tm-8 tm-1 tm-7 tm-5 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64138.        ((A or (B -> (C or B))) -> (((D -> E) -> (((D and F) or D) -> E)) and (B -> (C or B)))), M:tm-619, m:tm-757, u:((Am (-> A (or B A))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A (or B A)))))
================================================================
tm-name          tm-64139
in-theory        64139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64139.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (E -> (F or E))), M:tm-609, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64140
in-theory        64140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-605 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64140.        ((A -> ((B -> (C or B)) and A)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-605, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64141
in-theory        64141
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B -> (C or B)) and A)))
theorem-size     29
proof            (modus-ponens tm-602 tm-757 ((Am (and (-> A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (and (-> A (or B A)) C)))))
axioms-used      (tm-8 tm-5 tm-7 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64141.        ((A or ((B -> (C or B)) and A)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B -> (C or B)) and A))), M:tm-602, m:tm-757, u:((Am (and (-> A (or B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (and (-> A (or B A)) C))))
================================================================
tm-name          tm-64142
in-theory        64142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((E -> (F or E)) and (A -> (((B -> C) -> (((B and D) or B) -> C)) and A))))
theorem-size     37
proof            (modus-ponens tm-595 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64142.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((E -> (F or E)) and (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)))), M:tm-595, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64143
in-theory        64143
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-550 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64143.        (((A -> (B or A)) or C) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-550, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64144
in-theory        64144
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-540 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64144.        ((A or (B -> (C or B))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-540, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64145
in-theory        64145
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-530 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64145.        ((A or (B -> (B or C))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-530, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64146
in-theory        64146
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-520 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64146.        ((A or (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-520, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64147
in-theory        64147
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-510 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64147.        ((A or ((B and C) -> C)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-510, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64148
in-theory        64148
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-500 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64148.        ((A or ((B and C) -> B)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-500, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64149
in-theory        64149
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E)))
theorem-size     31
proof            (modus-ponens tm-490 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64149.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E))), M:tm-490, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64150
in-theory        64150
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-480 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64150.        ((A or (B -> (C -> B))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-480, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64151
in-theory        64151
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B -> C) -> (((B and D) or B) -> C)) and A) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-6 tm-5 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64151.        (A -> ((((B -> C) -> (((B and D) or B) -> C)) and A) or E)), M:tm-470, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64152
in-theory        64152
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-469 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64152.        ((A -> (B -> (B or C))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-469, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64153
in-theory        64153
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> (((D -> E) -> (((D and F) or D) -> E)) and (B -> (B or C))))
theorem-size     25
proof            (modus-ponens tm-466 tm-757 ((Am (-> A (or A B))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A (or A B))))))
axioms-used      (tm-8 tm-1 tm-6 tm-5 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64153.        ((A or (B -> (B or C))) -> (((D -> E) -> (((D and F) or D) -> E)) and (B -> (B or C)))), M:tm-466, m:tm-757, u:((Am (-> A (or A B))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A (or A B)))))
================================================================
tm-name          tm-64154
in-theory        64154
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64154.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (E -> (E or F))), M:tm-456, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64155
in-theory        64155
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-453 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64155.        ((A -> ((B -> (B or C)) and A)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-453, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64156
in-theory        64156
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B -> (B or C)) and A)))
theorem-size     29
proof            (modus-ponens tm-450 tm-757 ((Am (and (-> A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (and (-> A (or A B)) C)))))
axioms-used      (tm-8 tm-5 tm-6 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64156.        ((A or ((B -> (B or C)) and A)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B -> (B or C)) and A))), M:tm-450, m:tm-757, u:((Am (and (-> A (or A B)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (and (-> A (or A B)) C))))
================================================================
tm-name          tm-64157
in-theory        64157
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((E -> (E or F)) and (A -> (((B -> C) -> (((B and D) or B) -> C)) and A))))
theorem-size     37
proof            (modus-ponens tm-443 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64157.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((E -> (E or F)) and (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)))), M:tm-443, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64158
in-theory        64158
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-409 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64158.        (((A -> (A or B)) or C) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-409, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64159
in-theory        64159
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-400 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64159.        (((A -> (B -> (A and B))) or C) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-400, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64160
in-theory        64160
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-391 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64160.        ((((A and B) -> B) or C) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-391, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64161
in-theory        64161
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-382 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64161.        ((((A and B) -> A) or C) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-382, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64162
in-theory        64162
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E)))
theorem-size     31
proof            (modus-ponens tm-373 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64162.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E))), M:tm-373, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64163
in-theory        64163
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-364 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64163.        (((A -> (B -> A)) or C) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-364, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64164
in-theory        64164
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> ((((C -> D) -> (((C and E) or C) -> D)) and A) and B)))
theorem-size     19
proof            (modus-ponens tm-355 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64164.        (A -> (B -> ((((C -> D) -> (((C and E) or C) -> D)) and A) and B))), M:tm-355, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64165
in-theory        64165
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-354 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64165.        ((A -> (B -> (C -> (B and C)))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-354, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64166
in-theory        64166
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> (((D and F) or D) -> E)) and (B -> (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-351 tm-757 ((Am (-> A (-> B (and A B)))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A (-> B (and A B)))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64166.        ((A or (B -> (C -> (B and C)))) -> (((D -> E) -> (((D and F) or D) -> E)) and (B -> (C -> (B and C))))), M:tm-351, m:tm-757, u:((Am (-> A (-> B (and A B)))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A (-> B (and A B))))))
================================================================
tm-name          tm-64167
in-theory        64167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64167.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64168
in-theory        64168
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C)))
theorem-size     25
proof            (modus-ponens tm-338 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64168.        (((A -> B) -> (A -> (A and B))) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C))), M:tm-338, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64169
in-theory        64169
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> (A and B))))
theorem-size     27
proof            (modus-ponens tm-335 tm-757 ((Am (-> A (and A B))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A (and A B))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64169.        (((A -> B) or (A -> (A and B))) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> (A and B)))), M:tm-335, m:tm-757, u:((Am (-> A (and A B))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A (and A B)))))
================================================================
tm-name          tm-64170
in-theory        64170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (A -> (A and (((B -> C) -> (((B and D) or B) -> C)) and A))))
theorem-size     33
proof            (modus-ponens tm-328 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64170.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (A -> (A and (((B -> C) -> (((B and D) or B) -> C)) and A)))), M:tm-328, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64171
in-theory        64171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> C) -> (((B and D) or B) -> C)) and A))))
theorem-size     39
proof            (modus-ponens tm-327 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64171.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((E -> (F -> (E and F))) and (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)))), M:tm-327, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64172
in-theory        64172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (((E and F) -> F) and (A -> (((B -> C) -> (((B and D) or B) -> C)) and A))))
theorem-size     37
proof            (modus-ponens tm-326 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64172.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (((E and F) -> F) and (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)))), M:tm-326, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64173
in-theory        64173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (((E and F) -> E) and (A -> (((B -> C) -> (((B and D) or B) -> C)) and A))))
theorem-size     37
proof            (modus-ponens tm-325 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64173.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (((E and F) -> E) and (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)))), M:tm-325, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64174
in-theory        64174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> C) -> (((B and D) or B) -> C)) and A))))
theorem-size     45
proof            (modus-ponens tm-324 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64174.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)))), M:tm-324, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64175
in-theory        64175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((E -> (F -> E)) and (A -> (((B -> C) -> (((B and D) or B) -> C)) and A))))
theorem-size     37
proof            (modus-ponens tm-323 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64175.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((E -> (F -> E)) and (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)))), M:tm-323, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64176
in-theory        64176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64176.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((E and F) -> F)), M:tm-322, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64177
in-theory        64177
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64177.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((E and F) -> E)), M:tm-320, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64178
in-theory        64178
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64178.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64179
in-theory        64179
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (A -> A))
theorem-size     19
proof            (modus-ponens tm-316 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64179.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (A -> A)), M:tm-316, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64180
in-theory        64180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64180.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (E -> (F -> E))), M:tm-315, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64181
in-theory        64181
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((A -> (not (((B -> C) -> (((B and D) or B) -> C)) and A))) -> (not A)))
theorem-size     35
proof            (modus-ponens tm-313 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64181.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((A -> (not (((B -> C) -> (((B and D) or B) -> C)) and A))) -> (not A))), M:tm-313, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64182
in-theory        64182
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (((((B -> C) -> (((B and D) or B) -> C)) and A) -> E) -> ((A or (((B -> C) -> (((B and D) or B) -> C)) and A)) -> E)))
theorem-size     49
proof            (modus-ponens tm-312 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64182.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (((((B -> C) -> (((B and D) or B) -> C)) and A) -> E) -> ((A or (((B -> C) -> (((B and D) or B) -> C)) and A)) -> E))), M:tm-312, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64183
in-theory        64183
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (E or (A -> (((B -> C) -> (((B and D) or B) -> C)) and A))))
theorem-size     33
proof            (modus-ponens tm-311 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64183.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (E or (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)))), M:tm-311, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64184
in-theory        64184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64184.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) or E)), M:tm-310, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64185
in-theory        64185
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (E -> ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64185.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (E -> ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and E))), M:tm-309, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64186
in-theory        64186
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (E -> (A -> (((B -> C) -> (((B and D) or B) -> C)) and A))))
theorem-size     33
proof            (modus-ponens tm-305 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64186.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) and (E -> (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)))), M:tm-305, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64187
in-theory        64187
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     27
proof            (modus-ponens tm-303 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64187.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-303, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64188
in-theory        64188
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B -> (C -> (B and C))) and A)))
theorem-size     33
proof            (modus-ponens tm-300 tm-757 ((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (and (-> A (-> B (and A B))) C)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64188.        ((A or ((B -> (C -> (B and C))) and A)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B -> (C -> (B and C))) and A))), M:tm-300, m:tm-757, u:((Am (and (-> A (-> B (and A B))) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (and (-> A (-> B (and A B))) C))))
================================================================
tm-name          tm-64189
in-theory        64189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-270 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64189.        ((A -> (((B and C) -> C) and A)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-270, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64190
in-theory        64190
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> (((D -> E) -> (((D and F) or D) -> E)) and (((B and C) -> C) and A)))
theorem-size     29
proof            (modus-ponens tm-267 tm-757 ((Am (and (-> (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (and (-> (and A B) B) C)))))
axioms-used      (tm-8 tm-5 tm-4 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64190.        ((A or (((B and C) -> C) and A)) -> (((D -> E) -> (((D and F) or D) -> E)) and (((B and C) -> C) and A))), M:tm-267, m:tm-757, u:((Am (and (-> (and A B) B) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (and (-> (and A B) B) C))))
================================================================
tm-name          tm-64191
in-theory        64191
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-239 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64191.        ((A -> (((B and C) -> B) and A)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-239, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64192
in-theory        64192
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> (((D -> E) -> (((D and F) or D) -> E)) and (((B and C) -> B) and A)))
theorem-size     29
proof            (modus-ponens tm-236 tm-757 ((Am (and (-> (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (and (-> (and A B) A) C)))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64192.        ((A or (((B and C) -> B) and A)) -> (((D -> E) -> (((D and F) or D) -> E)) and (((B and C) -> B) and A))), M:tm-236, m:tm-757, u:((Am (and (-> (and A B) A) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (and (-> (and A B) A) C))))
================================================================
tm-name          tm-64193
in-theory        64193
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E)))
theorem-size     33
proof            (modus-ponens tm-210 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64193.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E))), M:tm-210, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64194
in-theory        64194
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> (((E and G) or E) -> F)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)))
theorem-size     45
proof            (modus-ponens tm-207 tm-757 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)))))
axioms-used      (tm-8 tm-5 tm-2 tm-3)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64194.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> (((E -> F) -> (((E and G) or E) -> F)) and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-207, m:tm-757, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D))))
================================================================
tm-name          tm-64195
in-theory        64195
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     25
proof            (modus-ponens tm-183 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64195.        ((A -> ((B -> (C -> B)) and A)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-183, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64196
in-theory        64196
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B -> (C -> B)) and A)))
theorem-size     29
proof            (modus-ponens tm-180 tm-757 ((Am (and (-> A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (and (-> A (-> B A)) C)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64196.        ((A or ((B -> (C -> B)) and A)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B -> (C -> B)) and A))), M:tm-180, m:tm-757, u:((Am (and (-> A (-> B A)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (and (-> A (-> B A)) C))))
================================================================
tm-name          tm-64197
in-theory        64197
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-157 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64197.        ((A -> ((B and C) -> C)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-157, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64198
in-theory        64198
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B and C) -> C)))
theorem-size     25
proof            (modus-ponens tm-154 tm-757 ((Am (-> (and A B) B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (and A B) B)))))
axioms-used      (tm-8 tm-1 tm-4 tm-5 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64198.        ((A or ((B and C) -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B and C) -> C))), M:tm-154, m:tm-757, u:((Am (-> (and A B) B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (and A B) B))))
================================================================
tm-name          tm-64199
in-theory        64199
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     31
proof            (modus-ponens tm-147 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64199.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-147, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64200
in-theory        64200
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A and (B -> C)) -> C)))
theorem-size     35
proof            (modus-ponens tm-144 tm-757 ((Am (-> (and A (-> B C)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (and A (-> B C)) C)))))
axioms-used      (tm-8 tm-2 tm-4 tm-5 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64200.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A and (B -> C)) -> C))), M:tm-144, m:tm-757, u:((Am (-> (and A (-> B C)) C)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (and A (-> B C)) C))))
================================================================
tm-name          tm-64201
in-theory        64201
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-134 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64201.        ((A -> ((B and C) -> B)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-134, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64202
in-theory        64202
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B and C) -> B)))
theorem-size     25
proof            (modus-ponens tm-131 tm-757 ((Am (-> (and A B) A)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (and A B) A)))))
axioms-used      (tm-8 tm-1 tm-3 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64202.        ((A or ((B and C) -> B)) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B and C) -> B))), M:tm-131, m:tm-757, u:((Am (-> (and A B) A)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (and A B) A))))
================================================================
tm-name          tm-64203
in-theory        64203
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     31
proof            (modus-ponens tm-125 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64203.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-125, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64204
in-theory        64204
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> (((D and F) or D) -> E)) and (((A -> B) and C) -> B)))
theorem-size     35
proof            (modus-ponens tm-122 tm-757 ((Am (-> (and (-> A B) C) B)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (and (-> A B) C) B)))))
axioms-used      (tm-8 tm-2 tm-3 tm-5)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64204.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> (((D -> E) -> (((D and F) or D) -> E)) and (((A -> B) and C) -> B))), M:tm-122, m:tm-757, u:((Am (-> (and (-> A B) C) B)) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (and (-> A B) C) B))))
================================================================
tm-name          tm-64205
in-theory        64205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E)))
theorem-size     31
proof            (modus-ponens tm-113 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64205.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> (((F -> G) -> (((F and H) or F) -> G)) and E))), M:tm-113, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64206
in-theory        64206
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> (((E and G) or E) -> F)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))
theorem-size     41
proof            (modus-ponens tm-110 tm-757 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))))))
axioms-used      (tm-8 tm-1 tm-2 tm-5 tm-3)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64206.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> (((E -> F) -> (((E and G) or E) -> F)) and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-110, m:tm-757, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> A (-> B C)) (-> (-> A B) (-> A C))))))
================================================================
tm-name          tm-64207
in-theory        64207
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     35
proof            (modus-ponens tm-105 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64207.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-105, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64208
in-theory        64208
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> (B -> C)) -> (A -> C))))
theorem-size     41
proof            (modus-ponens tm-102 tm-757 ((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> A (-> B C)) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       183
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64208.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-102, m:tm-757, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> A (-> B C)) (-> A C)))))
================================================================
tm-name          tm-64209
in-theory        64209
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C)))
theorem-size     23
proof            (modus-ponens tm-95 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64209.        (((A -> B) -> (A -> A)) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C))), M:tm-95, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64210
in-theory        64210
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> A)))
theorem-size     23
proof            (modus-ponens tm-92 tm-757 ((Am (-> A A)) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A A)))))
axioms-used      (tm-8 tm-2 tm-1 tm-5 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64210.        (((A -> B) or (A -> A)) -> (((C -> D) -> (((C and E) or C) -> D)) and (A -> A))), M:tm-92, m:tm-757, u:((Am (-> A A)) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A A))))
================================================================
tm-name          tm-64211
in-theory        64211
times-derived    1
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> D) -> (((C and E) or C) -> D)) and A)))
theorem-size     17
proof            (modus-ponens tm-84 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64211.        (A -> (B -> (((C -> D) -> (((C and E) or C) -> D)) and A))), M:tm-84, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64212
in-theory        64212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     23
proof            (modus-ponens tm-83 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64212.        ((A -> (B -> (C -> B))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-83, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64213
in-theory        64213
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> (((D -> E) -> (((D and F) or D) -> E)) and (B -> (C -> B))))
theorem-size     25
proof            (modus-ponens tm-80 tm-757 ((Am (-> A (-> B A))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A (-> B A))))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64213.        ((A or (B -> (C -> B))) -> (((D -> E) -> (((D and F) or D) -> E)) and (B -> (C -> B)))), M:tm-80, m:tm-757, u:((Am (-> A (-> B A))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A (-> B A)))))
================================================================
tm-name          tm-64214
in-theory        64214
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> (((C -> D) -> (((C and E) or C) -> D)) and B)))
theorem-size     21
proof            (modus-ponens tm-76 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-10 tm-8 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64214.        (((not (not A)) -> A) and (B -> (((C -> D) -> (((C and E) or C) -> D)) and B))), M:tm-76, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64215
in-theory        64215
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> (((B -> C) -> (((B and D) or B) -> C)) and A))
theorem-size     19
proof            (modus-ponens tm-73 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-8 tm-10 tm-5 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64215.        (((not (not A)) or A) -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-73, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64216
in-theory        64216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C)))
theorem-size     27
proof            (modus-ponens tm-69 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-9 tm-8 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64216.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C))), M:tm-69, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64217
in-theory        64217
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> (((C and E) or C) -> D)) and ((A -> (not B)) -> (not A))))
theorem-size     31
proof            (modus-ponens tm-66 tm-757 ((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> A (not B)) (not A))))))
axioms-used      (tm-8 tm-9 tm-5 tm-3)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64217.        (((A -> B) or ((A -> (not B)) -> (not A))) -> (((C -> D) -> (((C and E) or C) -> D)) and ((A -> (not B)) -> (not A)))), M:tm-66, m:tm-757, u:((Am (-> (-> A (not B)) (not A))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> A (not B)) (not A)))))
================================================================
tm-name          tm-64218
in-theory        64218
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-54 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64218.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-54, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64219
in-theory        64219
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B -> C) -> ((A or B) -> C))))
theorem-size     35
proof            (modus-ponens tm-51 tm-757 ((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> A B) (-> (or C A) B))))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       139
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64219.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> (((D -> E) -> (((D and F) or D) -> E)) and ((B -> C) -> ((A or B) -> C)))), M:tm-51, m:tm-757, u:((Am (-> (-> A B) (-> (or C A) B))) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> A B) (-> (or C A) B)))))
================================================================
tm-name          tm-64220
in-theory        64220
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> (((C -> D) -> (((C and E) or C) -> D)) and (B or A)))
theorem-size     21
proof            (modus-ponens tm-50 tm-757 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (or A B)))))
axioms-used      (tm-8 tm-7 tm-5 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64220.        ((A or (B or A)) -> (((C -> D) -> (((C and E) or C) -> D)) and (B or A))), M:tm-50, m:tm-757, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (or A B))))
================================================================
tm-name          tm-64221
in-theory        64221
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> (((C -> D) -> (((C and E) or C) -> D)) and (A or B)))
theorem-size     21
proof            (modus-ponens tm-49 tm-757 ((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (or A B)))))
axioms-used      (tm-8 tm-6 tm-5 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64221.        ((A or (A or B)) -> (((C -> D) -> (((C and E) or C) -> D)) and (A or B))), M:tm-49, m:tm-757, u:((Am (or A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (or A B))))
================================================================
tm-name          tm-64222
in-theory        64222
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> (((C -> D) -> (((C and E) or C) -> D)) and (B -> (A and B))))
theorem-size     25
proof            (modus-ponens tm-48 tm-757 ((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A (and B A))))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64222.        ((A or (B -> (A and B))) -> (((C -> D) -> (((C and E) or C) -> D)) and (B -> (A and B)))), M:tm-48, m:tm-757, u:((Am (-> A (and B A))) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A (and B A)))))
================================================================
tm-name          tm-64223
in-theory        64223
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> D) -> (((C and E) or C) -> D)) and B))
theorem-size     19
proof            (modus-ponens tm-47 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-8 tm-4 tm-5 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64223.        (((A and B) or B) -> (((C -> D) -> (((C and E) or C) -> D)) and B)), M:tm-47, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64224
in-theory        64224
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or A) -> (((C -> D) -> (((C and E) or C) -> D)) and A))
theorem-size     19
proof            (modus-ponens tm-46 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-8 tm-3 tm-5)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-5.            (A -> (B -> (A and B))), axiom
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64224.        (((A and B) or A) -> (((C -> D) -> (((C and E) or C) -> D)) and A)), M:tm-46, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64225
in-theory        64225
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> B) -> (A -> C))))
theorem-size     33
proof            (modus-ponens tm-45 tm-757 ((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> A B) (-> A C))))))
axioms-used      (tm-8 tm-2 tm-5 tm-3)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64225.        (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> (((D -> E) -> (((D and F) or D) -> E)) and ((A -> B) -> (A -> C)))), M:tm-45, m:tm-757, u:((Am (-> (-> A B) (-> A C))) (D (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> A B) (-> A C)))))
================================================================
tm-name          tm-64226
in-theory        64226
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> A)) -> (((C -> D) -> (((C and E) or C) -> D)) and (B -> A)))
theorem-size     21
proof            (modus-ponens tm-44 tm-757 ((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A B)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64226.        ((A or (B -> A)) -> (((C -> D) -> (((C and E) or C) -> D)) and (B -> A))), M:tm-44, m:tm-757, u:((Am (-> A B)) (C (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> A B))))
================================================================
tm-name          tm-64227
in-theory        64227
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C)))
theorem-size     21
proof            (modus-ponens tm-42 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-7 tm-8 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64227.        ((A -> (B or A)) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C))), M:tm-42, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64228
in-theory        64228
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C)))
theorem-size     21
proof            (modus-ponens tm-32 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-6 tm-8 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64228.        ((A -> (A or B)) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C))), M:tm-32, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64229
in-theory        64229
times-derived    2
----------------------------------------------------------------
theorem          (A -> (A and (((B -> C) -> (((B and D) or B) -> C)) and A)))
theorem-size     17
proof            (modus-ponens tm-24 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64229.        (A -> (A and (((B -> C) -> (((B and D) or B) -> C)) and A))), M:tm-24, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64230
in-theory        64230
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C)))
theorem-size     23
proof            (modus-ponens tm-23 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64230.        ((A -> (B -> (A and B))) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C))), M:tm-23, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64231
in-theory        64231
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> B) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C)))
theorem-size     21
proof            (modus-ponens tm-22 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64231.        (((A and B) -> B) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C))), M:tm-22, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64232
in-theory        64232
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) -> A) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C)))
theorem-size     21
proof            (modus-ponens tm-21 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-3 tm-8)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64232.        (((A and B) -> A) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C))), M:tm-21, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64233
in-theory        64233
times-derived    2
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D)))
theorem-size     29
proof            (modus-ponens tm-20 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64233.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (D -> (((E -> F) -> (((E and G) or E) -> F)) and D))), M:tm-20, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64234
in-theory        64234
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C)))
theorem-size     21
proof            (modus-ponens tm-19 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64234.        ((A -> (B -> A)) and (C -> (((D -> E) -> (((D and F) or D) -> E)) and C))), M:tm-19, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64235
in-theory        64235
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (not (((B -> C) -> (((B and D) or B) -> C)) and A))) -> (not A))
theorem-size     19
proof            (modus-ponens tm-9 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-9 tm-5 tm-8 tm-3)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64235.        ((A -> (not (((B -> C) -> (((B and D) or B) -> C)) and A))) -> (not A)), M:tm-9, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64236
in-theory        64236
times-derived    2
----------------------------------------------------------------
theorem          (((((A -> B) -> (((A and C) or A) -> B)) and D) -> E) -> ((D or (((A -> B) -> (((A and C) or A) -> B)) and D)) -> E))
theorem-size     33
proof            (modus-ponens tm-8 tm-757 ((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
axioms-used      (tm-8 tm-5 tm-3)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64236.        (((((A -> B) -> (((A and C) or A) -> B)) and D) -> E) -> ((D or (((A -> B) -> (((A and C) or A) -> B)) and D)) -> E)), M:tm-8, m:tm-757, u:((A Am) (B (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))
================================================================
tm-name          tm-64237
in-theory        64237
times-derived    2
----------------------------------------------------------------
theorem          (A or (B -> (((C -> D) -> (((C and E) or C) -> D)) and B)))
theorem-size     17
proof            (modus-ponens tm-7 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-7 tm-5 tm-8 tm-3)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64237.        (A or (B -> (((C -> D) -> (((C and E) or C) -> D)) and B))), M:tm-7, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64238
in-theory        64238
times-derived    2
----------------------------------------------------------------
theorem          ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-6 tm-5 tm-8 tm-3)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64238.        ((A -> (((B -> C) -> (((B and D) or B) -> C)) and A)) or E), M:tm-6, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64239
in-theory        64239
times-derived    2
----------------------------------------------------------------
theorem          (A -> ((B -> (((C -> D) -> (((C and E) or C) -> D)) and B)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-5 tm-8 tm-3)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64239.        (A -> ((B -> (((C -> D) -> (((C and E) or C) -> D)) and B)) and A)), M:tm-5, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64240
in-theory        64240
times-derived    3
----------------------------------------------------------------
theorem          (A -> (B -> (((C -> D) -> (((C and E) or C) -> D)) and B)))
theorem-size     17
proof            (modus-ponens tm-1 tm-757 ((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am)))))
axioms-used      (tm-1 tm-5 tm-8 tm-3)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64240.        (A -> (B -> (((C -> D) -> (((C and E) or C) -> D)) and B))), M:tm-1, m:tm-757, u:((A (-> Am (and (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) Am))))
================================================================
tm-name          tm-64241
in-theory        64241
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     27
proof            (modus-ponens tm-757 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64241.        (((A -> B) -> (((A and C) or A) -> B)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-757, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64242
in-theory        64242
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (((((A -> B) -> ((A and C) or A)) and D) or ((A -> B) -> ((A and C) or A))) -> ((A -> B) -> B)))
theorem-size     43
proof            (modus-ponens tm-747 tm-758 ((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64242.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (((((A -> B) -> ((A and C) or A)) and D) or ((A -> B) -> ((A and C) or A))) -> ((A -> B) -> B))), M:tm-747, m:tm-758, u:((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-64243
in-theory        64243
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F)))
theorem-size     41
proof            (modus-ponens tm-708 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       185
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64243.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F))), M:tm-708, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64244
in-theory        64244
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     29
proof            (modus-ponens tm-665 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-2 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64244.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-665, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64245
in-theory        64245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((((A and C) or A) or ((A -> B) -> ((A and C) or A))) -> ((A -> B) -> B)))
theorem-size     37
proof            (modus-ponens tm-654 tm-758 ((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64245.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((((A and C) or A) or ((A -> B) -> ((A and C) or A))) -> ((A -> B) -> B))), M:tm-654, m:tm-758, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-64246
in-theory        64246
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A and C) or A)) -> (D or ((A -> B) -> B)))
theorem-size     17
proof            (modus-ponens tm-623 tm-758 ((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64246.        (((A -> B) -> ((A and C) or A)) -> (D or ((A -> B) -> B))), M:tm-623, m:tm-758, u:((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-64247
in-theory        64247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-622 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64247.        ((A -> (B -> (C or B))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-622, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64248
in-theory        64248
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64248.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (D -> (E or D))), M:tm-609, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64249
in-theory        64249
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-605 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64249.        ((A -> ((B -> (C or B)) and A)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-605, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64250
in-theory        64250
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((D -> (E or D)) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B))))
theorem-size     37
proof            (modus-ponens tm-595 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64250.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((D -> (E or D)) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)))), M:tm-595, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64251
in-theory        64251
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-550 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64251.        (((A -> (B or A)) or C) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-550, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64252
in-theory        64252
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-540 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64252.        ((A or (B -> (C or B))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-540, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64253
in-theory        64253
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-530 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64253.        ((A or (B -> (B or C))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-530, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64254
in-theory        64254
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-520 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64254.        ((A or (B -> (C -> (B and C)))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-520, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64255
in-theory        64255
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-510 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64255.        ((A or ((B and C) -> C)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-510, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64256
in-theory        64256
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-500 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-2 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64256.        ((A or ((B and C) -> B)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-500, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64257
in-theory        64257
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-490 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64257.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F))), M:tm-490, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64258
in-theory        64258
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-480 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64258.        ((A or (B -> (C -> B))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-480, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64259
in-theory        64259
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A and C) or A)) -> (((A -> B) -> B) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-758 ((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64259.        (((A -> B) -> ((A and C) or A)) -> (((A -> B) -> B) or D)), M:tm-470, m:tm-758, u:((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-64260
in-theory        64260
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-469 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64260.        ((A -> (B -> (B or C))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-469, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64261
in-theory        64261
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64261.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (D -> (D or E))), M:tm-456, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64262
in-theory        64262
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-453 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64262.        ((A -> ((B -> (B or C)) and A)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-453, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64263
in-theory        64263
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((D -> (D or E)) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B))))
theorem-size     37
proof            (modus-ponens tm-443 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64263.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((D -> (D or E)) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)))), M:tm-443, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64264
in-theory        64264
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-409 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64264.        (((A -> (A or B)) or C) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-409, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64265
in-theory        64265
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-400 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64265.        (((A -> (B -> (A and B))) or C) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-400, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64266
in-theory        64266
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-391 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64266.        ((((A and B) -> B) or C) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-391, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64267
in-theory        64267
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-382 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-2 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64267.        ((((A and B) -> A) or C) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-382, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64268
in-theory        64268
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-373 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64268.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F))), M:tm-373, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64269
in-theory        64269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-364 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64269.        (((A -> (B -> A)) or C) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-364, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64270
in-theory        64270
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A and C) or A)) -> (D -> (((A -> B) -> B) and D)))
theorem-size     19
proof            (modus-ponens tm-355 tm-758 ((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64270.        (((A -> B) -> ((A and C) or A)) -> (D -> (((A -> B) -> B) and D))), M:tm-355, m:tm-758, u:((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-64271
in-theory        64271
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-354 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64271.        ((A -> (B -> (C -> (B and C)))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-354, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64272
in-theory        64272
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64272.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64273
in-theory        64273
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D)))
theorem-size     25
proof            (modus-ponens tm-338 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64273.        (((A -> B) -> (A -> (A and B))) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D))), M:tm-338, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64274
in-theory        64274
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (((A -> B) -> ((A and C) or A)) -> (((A -> B) -> ((A and C) or A)) and ((A -> B) -> B))))
theorem-size     41
proof            (modus-ponens tm-328 tm-758 ((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64274.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (((A -> B) -> ((A and C) or A)) -> (((A -> B) -> ((A and C) or A)) and ((A -> B) -> B)))), M:tm-328, m:tm-758, u:((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-64275
in-theory        64275
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((D -> (E -> (D and E))) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B))))
theorem-size     39
proof            (modus-ponens tm-327 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64275.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((D -> (E -> (D and E))) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)))), M:tm-327, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64276
in-theory        64276
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (((D and E) -> E) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B))))
theorem-size     37
proof            (modus-ponens tm-326 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64276.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (((D and E) -> E) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)))), M:tm-326, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64277
in-theory        64277
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (((D and E) -> D) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B))))
theorem-size     37
proof            (modus-ponens tm-325 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64277.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (((D and E) -> D) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)))), M:tm-325, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64278
in-theory        64278
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B))))
theorem-size     45
proof            (modus-ponens tm-324 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64278.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)))), M:tm-324, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64279
in-theory        64279
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((D -> (E -> D)) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B))))
theorem-size     37
proof            (modus-ponens tm-323 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64279.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((D -> (E -> D)) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)))), M:tm-323, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64280
in-theory        64280
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64280.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((D and E) -> E)), M:tm-322, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64281
in-theory        64281
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64281.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((D and E) -> D)), M:tm-320, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64282
in-theory        64282
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64282.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64283
in-theory        64283
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> ((A and C) or A))))
theorem-size     35
proof            (modus-ponens tm-316 tm-758 ((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64283.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> ((A and C) or A)))), M:tm-316, m:tm-758, u:((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-64284
in-theory        64284
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64284.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (D -> (E -> D))), M:tm-315, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64285
in-theory        64285
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> ((A and C) or A)) -> (not ((A -> B) -> B))) -> (not ((A -> B) -> ((A and C) or A)))))
theorem-size     43
proof            (modus-ponens tm-313 tm-758 ((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64285.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> ((A and C) or A)) -> (not ((A -> B) -> B))) -> (not ((A -> B) -> ((A and C) or A))))), M:tm-313, m:tm-758, u:((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-64286
in-theory        64286
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> B) -> D) -> ((((A -> B) -> ((A and C) or A)) or ((A -> B) -> B)) -> D)))
theorem-size     41
proof            (modus-ponens tm-312 tm-758 ((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64286.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> B) -> D) -> ((((A -> B) -> ((A and C) or A)) or ((A -> B) -> B)) -> D))), M:tm-312, m:tm-758, u:((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-64287
in-theory        64287
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (D or (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B))))
theorem-size     33
proof            (modus-ponens tm-311 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64287.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (D or (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)))), M:tm-311, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64288
in-theory        64288
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64288.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) or D)), M:tm-310, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64289
in-theory        64289
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (D -> ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64289.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (D -> ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and D))), M:tm-309, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64290
in-theory        64290
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> ((A and C) or A)) -> (A -> B)) -> (((A -> B) -> ((A and C) or A)) -> B)))
theorem-size     41
proof            (modus-ponens tm-306 tm-758 ((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> Am Bm)) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64290.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and ((((A -> B) -> ((A and C) or A)) -> (A -> B)) -> (((A -> B) -> ((A and C) or A)) -> B))), M:tm-306, m:tm-758, u:((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> Am Bm)) (C Bm))
================================================================
tm-name          tm-64291
in-theory        64291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (D -> (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B))))
theorem-size     33
proof            (modus-ponens tm-305 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64291.        ((((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)) and (D -> (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)))), M:tm-305, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64292
in-theory        64292
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     27
proof            (modus-ponens tm-303 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64292.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-303, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64293
in-theory        64293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-270 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-4 tm-2 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64293.        ((A -> (((B and C) -> C) and A)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-270, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64294
in-theory        64294
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-239 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-3 tm-2 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64294.        ((A -> (((B and C) -> B) and A)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-239, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64295
in-theory        64295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F)))
theorem-size     33
proof            (modus-ponens tm-210 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64295.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F))), M:tm-210, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64296
in-theory        64296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     25
proof            (modus-ponens tm-183 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64296.        ((A -> ((B -> (C -> B)) and A)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-183, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64297
in-theory        64297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-157 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64297.        ((A -> ((B and C) -> C)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-157, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64298
in-theory        64298
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     31
proof            (modus-ponens tm-147 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64298.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-147, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64299
in-theory        64299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-134 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-2 tm-8)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64299.        ((A -> ((B and C) -> B)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-134, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64300
in-theory        64300
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     31
proof            (modus-ponens tm-125 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64300.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-125, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64301
in-theory        64301
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A and D) or A)) -> (((A -> (B -> C)) -> B) -> ((A -> (B -> C)) -> C)))
theorem-size     27
proof            (modus-ponens tm-114 tm-758 ((A (-> (-> Am (-> C D)) (or (and Am Cm) Am))) (B (-> Am (-> C D))) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64301.        (((A -> (B -> C)) -> ((A and D) or A)) -> (((A -> (B -> C)) -> B) -> ((A -> (B -> C)) -> C))), M:tm-114, m:tm-758, u:((A (-> (-> Am (-> C D)) (or (and Am Cm) Am))) (B (-> Am (-> C D))) (Bm (-> C D)))
================================================================
tm-name          tm-64302
in-theory        64302
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F)))
theorem-size     31
proof            (modus-ponens tm-113 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64302.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E -> F) -> ((E and G) or E)) -> ((E -> F) -> F))), M:tm-113, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64303
in-theory        64303
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     35
proof            (modus-ponens tm-105 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-3)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64303.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-105, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64304
in-theory        64304
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D)))
theorem-size     23
proof            (modus-ponens tm-95 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64304.        (((A -> B) -> (A -> A)) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D))), M:tm-95, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64305
in-theory        64305
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A and C) or A)) -> (D -> ((A -> B) -> B)))
theorem-size     17
proof            (modus-ponens tm-84 tm-758 ((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64305.        (((A -> B) -> ((A and C) or A)) -> (D -> ((A -> B) -> B))), M:tm-84, m:tm-758, u:((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-64306
in-theory        64306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     23
proof            (modus-ponens tm-83 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64306.        ((A -> (B -> (C -> B))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-83, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64307
in-theory        64307
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B -> C) -> ((B and D) or B)) -> ((B -> C) -> C)))
theorem-size     21
proof            (modus-ponens tm-76 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-10 tm-2 tm-8 tm-3)
proof-size       99
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64307.        (((not (not A)) -> A) and (((B -> C) -> ((B and D) or B)) -> ((B -> C) -> C))), M:tm-76, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64308
in-theory        64308
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A -> B) -> ((A and C) or A)))) or ((A -> B) -> ((A and C) or A))) -> ((A -> B) -> B))
theorem-size     27
proof            (modus-ponens tm-73 tm-758 ((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-8 tm-10 tm-2 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64308.        (((not (not ((A -> B) -> ((A and C) or A)))) or ((A -> B) -> ((A and C) or A))) -> ((A -> B) -> B)), M:tm-73, m:tm-758, u:((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-64309
in-theory        64309
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (not ((A and B) or A))) -> ((A and B) or A)) -> (not (A -> (not ((A and B) or A)))))
theorem-size     24
proof            (modus-ponens tm-70 tm-758 ((B (or (and Am Cm) Am)) (A (-> Am (not (or (and Am Cm) Am)))) (Bm (not (or (and Am Cm) Am)))))
axioms-used      (tm-2 tm-9 tm-8 tm-3)
proof-size       120
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-70.           (((A -> B) -> (A -> (not B))) -> ((A -> B) -> (not A))), M:tm-2, m:tm-9, u:((A (-> Am Bm)) (B (-> Am (not Bm))) (C (not Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64309.        (((A -> (not ((A and B) or A))) -> ((A and B) or A)) -> (not (A -> (not ((A and B) or A))))), M:tm-70, m:tm-758, u:((B (or (and Am Cm) Am)) (A (-> Am (not (or (and Am Cm) Am)))) (Bm (not (or (and Am Cm) Am))))
================================================================
tm-name          tm-64310
in-theory        64310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D)))
theorem-size     27
proof            (modus-ponens tm-69 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-9 tm-2 tm-8 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64310.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C -> D) -> ((C and E) or C)) -> ((C -> D) -> D))), M:tm-69, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64311
in-theory        64311
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E)))
theorem-size     29
proof            (modus-ponens tm-54 tm-758 ((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64311.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D -> E) -> ((D and F) or D)) -> ((D -> E) -> E))), M:tm-54, m:tm-758, u:((A (-> (-> (-> Am Bm) (or (and Am Cm) Am)) (-> (-> Am Bm) Bm))))
================================================================
tm-name          tm-64312
in-theory        64312
times-derived    2
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> ((B and D) or B))) or ((B -> C) -> ((B and D) or B))) -> ((B -> C) -> C))
theorem-size     27
proof            (modus-ponens tm-47 tm-758 ((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-3)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-758.          (((A -> B) -> ((A and C) or A)) -> ((A -> B) -> B)), M:tm-2, m:tm-46, u:((A (-> Am Bm)) (B (or (and Am Cm) Am)) (C Bm))
tm-64312.        (((A and ((B -> C) -> ((B and D) or B))) or ((B -> C) -> ((B and D) or B))) -> ((B -> C) -> C)), M:tm-47, m:tm-758, u:((A (-> (-> Am Bm) (or (and Am Cm) Am))) (B (-> (-> Am Bm) Bm)))
================================================================
tm-name          tm-64313
in-theory        64313
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-757 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64313.        (((A -> B) -> (((A and C) or A) -> B)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-757, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64314
in-theory        64314
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (((A and C) or A) -> B)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-754 tm-759 ((Am (-> (or (and A B) A) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-3 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-754.          (((((A and B) or A) -> C) -> D) -> (((A -> C) or (((A and B) or A) -> C)) -> D)), M:tm-8, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64314.        (((A -> B) or (((A and C) or A) -> B)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-754, m:tm-759, u:((Am (-> (or (and A B) A) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64315
in-theory        64315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (((A and E) or A) -> ((B -> C) -> (((B and D) or B) -> C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-759 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64315.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (((A and E) or A) -> ((B -> C) -> (((B and D) or B) -> C)))), M:tm-747, m:tm-759, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64316
in-theory        64316
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     39
proof            (modus-ponens tm-708 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-1 tm-3)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64316.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (E -> ((F -> G) -> (((F and H) or F) -> G)))), M:tm-708, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64317
in-theory        64317
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> F) -> (((E and G) or E) -> F)))
theorem-size     37
proof            (modus-ponens tm-705 tm-759 ((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-705.          (((((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D) -> E) -> (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> E)), M:tm-8, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64317.        (((((A -> B) -> (A -> C)) -> D) or (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) -> ((E -> F) -> (((E and G) or E) -> F))), M:tm-705, m:tm-759, u:((Am (-> (or (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64318
in-theory        64318
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> C)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-703 tm-759 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-703.          ((((A -> B) -> (A -> C)) -> D) -> (((A -> B) -> (A -> C)) -> D)), M:tm-12, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64318.        (((A -> B) -> (A -> C)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-703, m:tm-759, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64319
in-theory        64319
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> ((D -> E) -> (((D and F) or D) -> E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     45
proof            (modus-ponens tm-697 tm-759 ((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-697.          ((((A -> B) -> (A -> C)) -> D) -> ((((A -> B) -> (A -> C)) -> D) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D))), M:tm-24, m:tm-45, u:((A (-> (-> (-> Am Bm) (-> Am Cm)) Dm)) (B (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64319.        ((((A -> B) -> (A -> C)) -> ((D -> E) -> (((D and F) or D) -> E))) and (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> ((D -> E) -> (((D and F) or D) -> E)))), M:tm-697, m:tm-759, u:((Am (-> (-> A B) (-> A C))) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64320
in-theory        64320
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-665 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64320.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-665, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64321
in-theory        64321
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-662 tm-759 ((Am (-> (or A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-662.          ((((A or (B -> A)) -> C) -> D) -> ((((B -> A) -> C) or ((A or (B -> A)) -> C)) -> D)), M:tm-8, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64321.        ((((A -> B) -> C) or ((B or (A -> B)) -> C)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-662, m:tm-759, u:((Am (-> (or A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64322
in-theory        64322
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     15
proof            (modus-ponens tm-660 tm-759 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-660.          (((A -> B) -> C) -> ((A -> B) -> C)), M:tm-12, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64322.        ((A -> B) -> ((C -> D) -> (((C and E) or C) -> D))), M:tm-660, m:tm-759, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64323
in-theory        64323
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((C -> D) -> (((C and E) or C) -> D))) and ((B or (A -> B)) -> ((C -> D) -> (((C and E) or C) -> D))))
theorem-size     33
proof            (modus-ponens tm-654 tm-759 ((Am (-> A B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-654.          (((A -> B) -> C) -> (((A -> B) -> C) and ((B or (A -> B)) -> C))), M:tm-24, m:tm-44, u:((A (-> (-> Am Bm) Cm)) (B (-> (or Bm (-> Am Bm)) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64323.        (((A -> B) -> ((C -> D) -> (((C and E) or C) -> D))) and ((B or (A -> B)) -> ((C -> D) -> (((C and E) or C) -> D)))), M:tm-654, m:tm-759, u:((Am (-> A B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64324
in-theory        64324
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-622 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64324.        ((A -> (B -> (C or B))) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-622, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64325
in-theory        64325
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-619 tm-759 ((Am (-> A (or B A))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-7 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-619.          (((A -> (B or A)) -> C) -> ((D or (A -> (B or A))) -> C)), M:tm-8, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64325.        ((A or (B -> (C or B))) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-619, m:tm-759, u:((Am (-> A (or B A))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64326
in-theory        64326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64326.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (E -> (F or E))), M:tm-609, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64327
in-theory        64327
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-605 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64327.        ((A -> ((B -> (C or B)) and A)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-605, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64328
in-theory        64328
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C or B)) and A)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-602 tm-759 ((Am (and (-> A (or B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-5 tm-7 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-602.          ((((A -> (B or A)) and C) -> D) -> ((C or ((A -> (B or A)) and C)) -> D)), M:tm-8, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64328.        ((A or ((B -> (C or B)) and A)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-602, m:tm-759, u:((Am (and (-> A (or B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64329
in-theory        64329
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F or E)) and (A -> ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-595 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64329.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F or E)) and (A -> ((B -> C) -> (((B and D) or B) -> C))))), M:tm-595, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64330
in-theory        64330
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-550 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64330.        (((A -> (B or A)) or C) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-550, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64331
in-theory        64331
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-540 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64331.        ((A or (B -> (C or B))) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-540, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64332
in-theory        64332
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-530 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64332.        ((A or (B -> (B or C))) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-530, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64333
in-theory        64333
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-520 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64333.        ((A or (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-520, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64334
in-theory        64334
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-510 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64334.        ((A or ((B and C) -> C)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-510, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64335
in-theory        64335
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-500 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-1 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64335.        ((A or ((B and C) -> B)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-500, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64336
in-theory        64336
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-490 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64336.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (((F and H) or F) -> G)))), M:tm-490, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64337
in-theory        64337
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-480 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64337.        ((A or (B -> (C -> B))) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-480, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64338
in-theory        64338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-469 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64338.        ((A -> (B -> (B or C))) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-469, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64339
in-theory        64339
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-466 tm-759 ((Am (-> A (or A B))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-6 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-466.          (((A -> (A or B)) -> C) -> ((D or (A -> (A or B))) -> C)), M:tm-8, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64339.        ((A or (B -> (B or C))) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-466, m:tm-759, u:((Am (-> A (or A B))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64340
in-theory        64340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64340.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (E -> (E or F))), M:tm-456, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64341
in-theory        64341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-453 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64341.        ((A -> ((B -> (B or C)) and A)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-453, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64342
in-theory        64342
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (B or C)) and A)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-450 tm-759 ((Am (and (-> A (or A B)) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-5 tm-6 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-450.          ((((A -> (A or B)) and C) -> D) -> ((C or ((A -> (A or B)) and C)) -> D)), M:tm-8, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64342.        ((A or ((B -> (B or C)) and A)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-450, m:tm-759, u:((Am (and (-> A (or A B)) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64343
in-theory        64343
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (E or F)) and (A -> ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-443 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64343.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (E or F)) and (A -> ((B -> C) -> (((B and D) or B) -> C))))), M:tm-443, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64344
in-theory        64344
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-409 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64344.        (((A -> (A or B)) or C) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-409, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64345
in-theory        64345
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-400 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64345.        (((A -> (B -> (A and B))) or C) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-400, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64346
in-theory        64346
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-391 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64346.        ((((A and B) -> B) or C) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-391, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64347
in-theory        64347
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-382 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-1 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64347.        ((((A and B) -> A) or C) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-382, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64348
in-theory        64348
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-373 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64348.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (E -> ((F -> G) -> (((F and H) or F) -> G)))), M:tm-373, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64349
in-theory        64349
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-364 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64349.        (((A -> (B -> A)) or C) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-364, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64350
in-theory        64350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-354 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64350.        ((A -> (B -> (C -> (B and C)))) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-354, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64351
in-theory        64351
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-351 tm-759 ((Am (-> A (-> B (and A B)))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-5 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-351.          (((A -> (B -> (A and B))) -> C) -> ((D or (A -> (B -> (A and B)))) -> C)), M:tm-8, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64351.        ((A or (B -> (C -> (B and C)))) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-351, m:tm-759, u:((Am (-> A (-> B (and A B)))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64352
in-theory        64352
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> (A and B)))
theorem-size     11
proof            (modus-ponens tm-349 tm-759 ((A Am) (B Bm) (Cm (and Am Bm)) (C (-> (or (and Bm Dm) Bm) (and Am Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64352.        (A -> (((B and C) or B) -> (A and B))), M:tm-349, m:tm-759, u:((A Am) (B Bm) (Cm (and Am Bm)) (C (-> (or (and Bm Dm) Bm) (and Am Bm))))
================================================================
tm-name          tm-64353
in-theory        64353
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64353.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64354
in-theory        64354
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) -> D) -> (((A -> B) -> (((A and C) or A) -> B)) and D))
theorem-size     27
proof            (modus-ponens tm-339 tm-759 ((Am (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) B)) (A (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-339.          (((A -> B) -> A) -> ((A -> B) -> (A and B))), M:tm-2, m:tm-24, u:((A (-> Am Bm)) (B Am) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64354.        ((((A -> B) -> (((A and C) or A) -> B)) -> D) -> (((A -> B) -> (((A and C) or A) -> B)) and D)), M:tm-339, m:tm-759, u:((Am (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) B)) (A (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64355
in-theory        64355
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (C -> ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     23
proof            (modus-ponens tm-338 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64355.        (((A -> B) -> (A -> (A and B))) and (C -> ((D -> E) -> (((D and F) or D) -> E)))), M:tm-338, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64356
in-theory        64356
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> (A and B))) -> ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     21
proof            (modus-ponens tm-335 tm-759 ((Am (-> A (and A B))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-2 tm-5 tm-1 tm-3)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-335.          (((A -> (A and B)) -> C) -> (((A -> B) or (A -> (A and B))) -> C)), M:tm-8, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64356.        (((A -> B) or (A -> (A and B))) -> ((C -> D) -> (((C and E) or C) -> D))), M:tm-335, m:tm-759, u:((Am (-> A (and A B))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64357
in-theory        64357
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (A -> (A and ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-759 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64357.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (A -> (A and ((B -> C) -> (((B and D) or B) -> C))))), M:tm-328, m:tm-759, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64358
in-theory        64358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F -> (E and F))) and (A -> ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     35
proof            (modus-ponens tm-327 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64358.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F -> (E and F))) and (A -> ((B -> C) -> (((B and D) or B) -> C))))), M:tm-327, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64359
in-theory        64359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (((E and F) -> F) and (A -> ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-326 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64359.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (((E and F) -> F) and (A -> ((B -> C) -> (((B and D) or B) -> C))))), M:tm-326, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64360
in-theory        64360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (((E and F) -> E) and (A -> ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-325 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64360.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (((E and F) -> E) and (A -> ((B -> C) -> (((B and D) or B) -> C))))), M:tm-325, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64361
in-theory        64361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     41
proof            (modus-ponens tm-324 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64361.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (A -> ((B -> C) -> (((B and D) or B) -> C))))), M:tm-324, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64362
in-theory        64362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F -> E)) and (A -> ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     33
proof            (modus-ponens tm-323 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64362.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F -> E)) and (A -> ((B -> C) -> (((B and D) or B) -> C))))), M:tm-323, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64363
in-theory        64363
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64363.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((E and F) -> F)), M:tm-322, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64364
in-theory        64364
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) -> (((B and D) or B) -> C)) -> E)) -> ((B -> C) -> (((B and D) or B) -> C))) and ((A and (((B -> C) -> (((B and D) or B) -> C)) -> E)) -> E))
theorem-size     45
proof            (modus-ponens tm-321 tm-759 ((Am (and A (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) C))) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-1 tm-8 tm-3)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-321.          (((A and (B -> C)) -> B) -> (((A and (B -> C)) -> B) and ((A and (B -> C)) -> C))), M:tm-24, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64364.        (((A and (((B -> C) -> (((B and D) or B) -> C)) -> E)) -> ((B -> C) -> (((B and D) or B) -> C))) and ((A and (((B -> C) -> (((B and D) or B) -> C)) -> E)) -> E)), M:tm-321, m:tm-759, u:((Am (and A (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) C))) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64365
in-theory        64365
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64365.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((E and F) -> E)), M:tm-320, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64366
in-theory        64366
times-derived    1
----------------------------------------------------------------
theorem          ((((((A -> B) -> (((A and C) or A) -> B)) -> D) and E) -> ((A -> B) -> (((A and C) or A) -> B))) and (((((A -> B) -> (((A and C) or A) -> B)) -> D) and E) -> D))
theorem-size     45
proof            (modus-ponens tm-319 tm-759 ((Am (and (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) B) C)) (A (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-1 tm-8)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-319.          ((((A -> B) and C) -> A) -> ((((A -> B) and C) -> A) and (((A -> B) and C) -> B))), M:tm-24, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64366.        ((((((A -> B) -> (((A and C) or A) -> B)) -> D) and E) -> ((A -> B) -> (((A and C) or A) -> B))) and (((((A -> B) -> (((A and C) or A) -> B)) -> D) and E) -> D)), M:tm-319, m:tm-759, u:((Am (and (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) B) C)) (A (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64367
in-theory        64367
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64367.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64368
in-theory        64368
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((((A and C) or A) -> B) -> D)) -> ((A -> B) -> (((A and C) or A) -> B))) and (((A -> B) -> ((((A and C) or A) -> B) -> D)) -> ((A -> B) -> D)))
theorem-size     45
proof            (modus-ponens tm-317 tm-759 ((Am (-> (-> Bm Cm) (-> (-> (or (and Bm Dm) Bm) Cm) C))) (A (-> Bm Cm)) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-317.          (((A -> (B -> C)) -> (A -> B)) -> (((A -> (B -> C)) -> (A -> B)) and ((A -> (B -> C)) -> (A -> C)))), M:tm-24, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64368.        ((((A -> B) -> ((((A and C) or A) -> B) -> D)) -> ((A -> B) -> (((A and C) or A) -> B))) and (((A -> B) -> ((((A and C) or A) -> B) -> D)) -> ((A -> B) -> D))), M:tm-317, m:tm-759, u:((Am (-> (-> Bm Cm) (-> (-> (or (and Bm Dm) Bm) Cm) C))) (A (-> Bm Cm)) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-64369
in-theory        64369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (A -> A))
theorem-size     17
proof            (modus-ponens tm-316 tm-759 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64369.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (A -> A)), M:tm-316, m:tm-759, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64370
in-theory        64370
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64370.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (E -> (F -> E))), M:tm-315, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64371
in-theory        64371
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((A -> (not ((B -> C) -> (((B and D) or B) -> C)))) -> (not A)))
theorem-size     31
proof            (modus-ponens tm-313 tm-759 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-1 tm-8 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64371.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((A -> (not ((B -> C) -> (((B and D) or B) -> C)))) -> (not A))), M:tm-313, m:tm-759, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64372
in-theory        64372
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((((B -> C) -> (((B and D) or B) -> C)) -> E) -> ((A or ((B -> C) -> (((B and D) or B) -> C))) -> E)))
theorem-size     43
proof            (modus-ponens tm-312 tm-759 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-1 tm-3)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64372.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((((B -> C) -> (((B and D) or B) -> C)) -> E) -> ((A or ((B -> C) -> (((B and D) or B) -> C))) -> E))), M:tm-312, m:tm-759, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64373
in-theory        64373
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (E or (A -> ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-311 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-1 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64373.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (E or (A -> ((B -> C) -> (((B and D) or B) -> C))))), M:tm-311, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64374
in-theory        64374
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((A -> ((B -> C) -> (((B and D) or B) -> C))) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-1 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64374.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((A -> ((B -> C) -> (((B and D) or B) -> C))) or E)), M:tm-310, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64375
in-theory        64375
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (E -> ((A -> ((B -> C) -> (((B and D) or B) -> C))) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64375.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (E -> ((A -> ((B -> C) -> (((B and D) or B) -> C))) and E))), M:tm-309, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64376
in-theory        64376
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((A -> (B -> C)) -> (A -> (((B and D) or B) -> C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-759 ((A Am) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64376.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and ((A -> (B -> C)) -> (A -> (((B and D) or B) -> C)))), M:tm-306, m:tm-759, u:((A Am) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-64377
in-theory        64377
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (E -> (A -> ((B -> C) -> (((B and D) or B) -> C)))))
theorem-size     29
proof            (modus-ponens tm-305 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64377.        ((A -> ((B -> C) -> (((B and D) or B) -> C))) and (E -> (A -> ((B -> C) -> (((B and D) or B) -> C))))), M:tm-305, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64378
in-theory        64378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-303 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64378.        ((A -> ((B -> (C -> (B and C))) and A)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-303, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64379
in-theory        64379
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     23
proof            (modus-ponens tm-300 tm-759 ((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-300.          ((((A -> (B -> (A and B))) and C) -> D) -> ((C or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64379.        ((A or ((B -> (C -> (B and C))) and A)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-300, m:tm-759, u:((Am (and (-> A (-> B (and A B))) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64380
in-theory        64380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-270 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-4 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64380.        ((A -> (((B and C) -> C) and A)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-270, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64381
in-theory        64381
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> C) and A)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-267 tm-759 ((Am (and (-> (and A B) B) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-5 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-267.          (((((A and B) -> B) and C) -> D) -> ((C or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64381.        ((A or (((B and C) -> C) and A)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-267, m:tm-759, u:((Am (and (-> (and A B) B) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64382
in-theory        64382
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-239 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-3 tm-1 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64382.        ((A -> (((B and C) -> B) and A)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-239, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64383
in-theory        64383
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B and C) -> B) and A)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-236 tm-759 ((Am (and (-> (and A B) A) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-5 tm-3 tm-1)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-236.          (((((A and B) -> A) and C) -> D) -> ((C or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64383.        ((A or (((B and C) -> B) and A)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-236, m:tm-759, u:((Am (and (-> (and A B) A) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64384
in-theory        64384
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-210 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64384.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (E -> ((F -> G) -> (((F and H) or F) -> G)))), M:tm-210, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64385
in-theory        64385
times-derived    1
----------------------------------------------------------------
theorem          ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> F) -> (((E and G) or E) -> F)))
theorem-size     29
proof            (modus-ponens tm-207 tm-759 ((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-5 tm-2 tm-1 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-207.          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((D or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64385.        ((A or (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) -> ((E -> F) -> (((E and G) or E) -> F))), M:tm-207, m:tm-759, u:((Am (and (-> (-> A (-> B C)) (-> (-> A B) (-> A C))) D)) (E (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64386
in-theory        64386
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     23
proof            (modus-ponens tm-183 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64386.        ((A -> ((B -> (C -> B)) and A)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-183, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64387
in-theory        64387
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> B)) and A)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     21
proof            (modus-ponens tm-180 tm-759 ((Am (and (-> A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-180.          ((((A -> (B -> A)) and C) -> D) -> ((C or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64387.        ((A or ((B -> (C -> B)) and A)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-180, m:tm-759, u:((Am (and (-> A (-> B A)) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64388
in-theory        64388
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-157 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64388.        ((A -> ((B and C) -> C)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-157, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64389
in-theory        64389
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-154 tm-759 ((Am (-> (and A B) B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-4 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-154.          ((((A and B) -> B) -> C) -> ((D or ((A and B) -> B)) -> C)), M:tm-8, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64389.        ((A or ((B and C) -> C)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-154, m:tm-759, u:((Am (-> (and A B) B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64390
in-theory        64390
times-derived    1
----------------------------------------------------------------
theorem          ((A and (B -> C)) -> (((B and D) or B) -> C))
theorem-size     13
proof            (modus-ponens tm-152 tm-759 ((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-152.          (((A and B) -> (B -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-18, u:((Am (-> (and Bm Cm) (-> Cm C))) (A (and Bm Cm)) (B Cm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64390.        ((A and (B -> C)) -> (((B and D) or B) -> C)), M:tm-152, m:tm-759, u:((Am (and A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-64391
in-theory        64391
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-147 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-1 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64391.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-147, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64392
in-theory        64392
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-144 tm-759 ((Am (-> (and A (-> B C)) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-2 tm-4 tm-1 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-144.          ((((A and (B -> C)) -> C) -> D) -> ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64392.        ((((A and (B -> C)) -> B) or ((A and (B -> C)) -> C)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-144, m:tm-759, u:((Am (-> (and A (-> B C)) C)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64393
in-theory        64393
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> (((B and D) or B) -> C)) -> E)) -> ((B -> C) -> (((B and D) or B) -> C)))
theorem-size     27
proof            (modus-ponens tm-142 tm-759 ((Am (and A (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) C))) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-4 tm-8 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-142.          (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> B)), M:tm-12, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64393.        ((A and (((B -> C) -> (((B and D) or B) -> C)) -> E)) -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-142, m:tm-759, u:((Am (and A (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) C))) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64394
in-theory        64394
times-derived    1
----------------------------------------------------------------
theorem          ((A and (((B -> C) -> (((B and D) or B) -> C)) -> (B -> C))) -> (((B and D) or B) -> C))
theorem-size     25
proof            (modus-ponens tm-141 tm-759 ((Am (and A (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> Bm Cm)))) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-4 tm-1 tm-8 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-141.          (((A and ((B -> C) -> B)) -> (B -> C)) -> ((A and ((B -> C) -> B)) -> C)), M:tm-13, m:tm-17, u:((Bm (-> Cm C)) (A (and Am (-> (-> Cm C) Cm))) (B Cm))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64394.        ((A and (((B -> C) -> (((B and D) or B) -> C)) -> (B -> C))) -> (((B and D) or B) -> C)), M:tm-141, m:tm-759, u:((Am (and A (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> Bm Cm)))) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-64395
in-theory        64395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-134 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64395.        ((A -> ((B and C) -> B)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-134, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64396
in-theory        64396
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-131 tm-759 ((Am (-> (and A B) A)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-131.          ((((A and B) -> A) -> C) -> ((D or ((A and B) -> A)) -> C)), M:tm-8, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64396.        ((A or ((B and C) -> B)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-131, m:tm-759, u:((Am (-> (and A B) A)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64397
in-theory        64397
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) and C) -> (((A and D) or A) -> B))
theorem-size     13
proof            (modus-ponens tm-129 tm-759 ((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-3 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-129.          (((A and B) -> (A -> C)) -> ((A and B) -> C)), M:tm-13, m:tm-16, u:((Am (-> (and Bm Cm) (-> Bm C))) (A (and Bm Cm)) (B Bm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64397.        (((A -> B) and C) -> (((A and D) or A) -> B)), M:tm-129, m:tm-759, u:((Am (and (-> Bm Cm) B)) (A (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-64398
in-theory        64398
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-125 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-1 tm-8)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64398.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-125, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64399
in-theory        64399
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     27
proof            (modus-ponens tm-122 tm-759 ((Am (-> (and (-> A B) C) B)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-2 tm-3 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-122.          (((((A -> B) and C) -> B) -> D) -> (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64399.        (((((A -> B) and C) -> A) or (((A -> B) and C) -> B)) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-122, m:tm-759, u:((Am (-> (and (-> A B) C) B)) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64400
in-theory        64400
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (((A and C) or A) -> B)) -> D) and E) -> ((A -> B) -> (((A and C) or A) -> B)))
theorem-size     27
proof            (modus-ponens tm-120 tm-759 ((Am (and (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) B) C)) (A (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-3 tm-8)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-120.          ((((A -> B) and C) -> A) -> (((A -> B) and C) -> A)), M:tm-12, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64400.        (((((A -> B) -> (((A and C) or A) -> B)) -> D) and E) -> ((A -> B) -> (((A and C) or A) -> B))), M:tm-120, m:tm-759, u:((Am (and (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) B) C)) (A (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64401
in-theory        64401
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (((A and C) or A) -> B)) -> (A -> B)) and D) -> (((A and C) or A) -> B))
theorem-size     25
proof            (modus-ponens tm-119 tm-759 ((Am (and (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> Bm Cm)) C)) (A (-> Bm Cm)) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-3 tm-1 tm-8)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-119.          (((((A -> B) -> A) and C) -> (A -> B)) -> ((((A -> B) -> A) and C) -> B)), M:tm-13, m:tm-15, u:((Am (-> Bm C)) (A (and (-> (-> Bm C) Bm) Cm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64401.        (((((A -> B) -> (((A and C) or A) -> B)) -> (A -> B)) and D) -> (((A and C) or A) -> B)), M:tm-119, m:tm-759, u:((Am (and (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> Bm Cm)) C)) (A (-> Bm Cm)) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-64402
in-theory        64402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (((F and H) or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-113 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64402.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (E -> ((F -> G) -> (((F and H) or F) -> G)))), M:tm-113, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64403
in-theory        64403
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> F) -> (((E and G) or E) -> F)))
theorem-size     27
proof            (modus-ponens tm-110 tm-759 ((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-110.          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((E or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64403.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) -> ((E -> F) -> (((E and G) or E) -> F))), M:tm-110, m:tm-759, u:((Am (-> (-> A (-> B C)) (-> (-> A B) (-> A C)))) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64404
in-theory        64404
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((((A -> B) and D) or (A -> B)) -> (A -> C)))
theorem-size     19
proof            (modus-ponens tm-108 tm-759 ((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (-> (or (and (-> A B) Dm) (-> A B)) (-> A C)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-108.          (((A -> (B -> C)) -> (((A -> B) -> (A -> C)) -> D)) -> ((A -> (B -> C)) -> D)), M:tm-13, m:tm-14, u:((Am (-> (-> Bm (-> Cm Dm)) (-> (-> (-> Bm Cm) (-> Bm Dm)) C))) (A (-> Bm (-> Cm Dm))) (B (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64404.        ((A -> (B -> C)) -> ((((A -> B) and D) or (A -> B)) -> (A -> C))), M:tm-108, m:tm-759, u:((Am (-> A (-> B C))) (Bm (-> A B)) (Cm (-> A C)) (D (-> (or (and (-> A B) Dm) (-> A B)) (-> A C))))
================================================================
tm-name          tm-64405
in-theory        64405
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) -> ((A -> B) -> ((A and C) or A))) -> ((A -> B) -> B))
theorem-size     27
proof            (modus-ponens tm-106 tm-759 ((Am (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> Bm Cm) (or (and Bm Dm) Bm)))) (A (-> Bm Cm)) (B (or (and Bm Dm) Bm)) (C Cm)))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-106.          ((((A -> (B -> C)) -> (A -> B)) -> (A -> (B -> C))) -> (((A -> (B -> C)) -> (A -> B)) -> (A -> C))), M:tm-2, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> Am (-> Bm Cm))) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64405.        ((((A -> B) -> (((A and C) or A) -> B)) -> ((A -> B) -> ((A and C) or A))) -> ((A -> B) -> B)), M:tm-106, m:tm-759, u:((Am (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) (-> (-> Bm Cm) (or (and Bm Dm) Bm)))) (A (-> Bm Cm)) (B (or (and Bm Dm) Bm)) (C Cm))
================================================================
tm-name          tm-64406
in-theory        64406
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     33
proof            (modus-ponens tm-105 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64406.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-105, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64407
in-theory        64407
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     31
proof            (modus-ponens tm-102 tm-759 ((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-102.          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64407.        ((((A -> (B -> C)) -> (A -> B)) or ((A -> (B -> C)) -> (A -> C))) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-102, m:tm-759, u:((Am (-> (-> A (-> B C)) (-> A C))) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64408
in-theory        64408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((((A and C) or A) -> B) -> D)) -> ((A -> B) -> (((A and C) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-100 tm-759 ((Am (-> (-> Bm Cm) (-> (-> (or (and Bm Dm) Bm) Cm) C))) (A (-> Bm Cm)) (B (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-100.          (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> B))), M:tm-12, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64408.        (((A -> B) -> ((((A and C) or A) -> B) -> D)) -> ((A -> B) -> (((A and C) or A) -> B))), M:tm-100, m:tm-759, u:((Am (-> (-> Bm Cm) (-> (-> (or (and Bm Dm) Bm) Cm) C))) (A (-> Bm Cm)) (B (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-64409
in-theory        64409
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or B) -> A))
theorem-size     9
proof            (modus-ponens tm-98 tm-759 ((Cm Am) (B Bm) (A Am) (C (-> (or (and Bm Dm) Bm) Am))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64409.        (A -> (((B and C) or B) -> A)), M:tm-98, m:tm-759, u:((Cm Am) (B Bm) (A Am) (C (-> (or (and Bm Dm) Bm) Am)))
================================================================
tm-name          tm-64410
in-theory        64410
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (((A and C) or A) -> B)) -> D) -> ((A -> B) -> (((A and C) or A) -> B)))
theorem-size     25
proof            (modus-ponens tm-96 tm-759 ((Am (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) B)) (A (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-96.           (((A -> B) -> A) -> ((A -> B) -> A)), M:tm-2, m:tm-12, u:((A (-> Am Bm)) (B Am) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64410.        ((((A -> B) -> (((A and C) or A) -> B)) -> D) -> ((A -> B) -> (((A and C) or A) -> B))), M:tm-96, m:tm-759, u:((Am (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) B)) (A (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64411
in-theory        64411
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (C -> ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-95 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64411.        (((A -> B) -> (A -> A)) and (C -> ((D -> E) -> (((D and F) or D) -> E)))), M:tm-95, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64412
in-theory        64412
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or (A -> A)) -> ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-92 tm-759 ((Am (-> A A)) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-2 tm-1 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-92.           (((A -> A) -> B) -> (((A -> C) or (A -> A)) -> B)), M:tm-8, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64412.        (((A -> B) or (A -> A)) -> ((C -> D) -> (((C and E) or C) -> D))), M:tm-92, m:tm-759, u:((Am (-> A A)) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64413
in-theory        64413
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     21
proof            (modus-ponens tm-83 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64413.        ((A -> (B -> (C -> B))) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-83, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64414
in-theory        64414
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     19
proof            (modus-ponens tm-80 tm-759 ((Am (-> A (-> B A))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-80.           (((A -> (B -> A)) -> C) -> ((D or (A -> (B -> A))) -> C)), M:tm-8, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64414.        ((A or (B -> (C -> B))) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-80, m:tm-759, u:((Am (-> A (-> B A))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64415
in-theory        64415
times-derived    1
----------------------------------------------------------------
theorem          ((not (not (((A -> B) -> (((A and C) or A) -> B)) -> D))) -> D)
theorem-size     17
proof            (modus-ponens tm-77 tm-759 ((Am (not (not (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) B)))) (A (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-2 tm-10 tm-1 tm-8 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-77.           (((not (not (A -> B))) -> A) -> ((not (not (A -> B))) -> B)), M:tm-2, m:tm-10, u:((A (not (not (-> B C)))) (Am (-> B C)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64415.        ((not (not (((A -> B) -> (((A and C) or A) -> B)) -> D))) -> D), M:tm-77, m:tm-759, u:((Am (not (not (-> (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)) B)))) (A (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64416
in-theory        64416
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (B -> ((C -> D) -> (((C and E) or C) -> D))))
theorem-size     19
proof            (modus-ponens tm-76 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-10 tm-1 tm-8 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64416.        (((not (not A)) -> A) and (B -> ((C -> D) -> (((C and E) or C) -> D)))), M:tm-76, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64417
in-theory        64417
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or A) -> ((B -> C) -> (((B and D) or B) -> C)))
theorem-size     17
proof            (modus-ponens tm-73 tm-759 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-10 tm-1 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64417.        (((not (not A)) or A) -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-73, m:tm-759, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64418
in-theory        64418
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> E) -> (((D and F) or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-69 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-9 tm-1 tm-8 tm-3)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64418.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (C -> ((D -> E) -> (((D and F) or D) -> E)))), M:tm-69, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64419
in-theory        64419
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     23
proof            (modus-ponens tm-66 tm-759 ((Am (-> (-> A (not B)) (not A))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-9 tm-1 tm-3)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-66.           ((((A -> (not B)) -> (not A)) -> C) -> (((A -> B) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64419.        (((A -> B) or ((A -> (not B)) -> (not A))) -> ((C -> D) -> (((C and E) or C) -> D))), M:tm-66, m:tm-759, u:((Am (-> (-> A (not B)) (not A))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64420
in-theory        64420
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> C)) -> ((A or (B -> C)) -> (((B and D) or B) -> C)))
theorem-size     19
proof            (modus-ponens tm-55 tm-759 ((Am (-> A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm))))
axioms-used      (tm-2 tm-8 tm-1 tm-3)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-55.           (((A -> B) -> (B -> C)) -> ((A -> B) -> ((A or B) -> C))), M:tm-2, m:tm-8, u:((A (-> Am Bm)) (B (-> Bm Cm)) (C (-> (or Am Bm) Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64420.        ((A -> (B -> C)) -> ((A or (B -> C)) -> (((B and D) or B) -> C))), M:tm-55, m:tm-759, u:((Am (-> A (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (or (and Bm Dm) Bm) Cm)))
================================================================
tm-name          tm-64421
in-theory        64421
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> F) -> (((E and G) or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-54 tm-759 ((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-3)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64421.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (D -> ((E -> F) -> (((E and G) or E) -> F)))), M:tm-54, m:tm-759, u:((A (-> Am (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
================================================================
tm-name          tm-64422
in-theory        64422
times-derived    2
----------------------------------------------------------------
theorem          (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> (((D and F) or D) -> E)))
theorem-size     25
proof            (modus-ponens tm-51 tm-759 ((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-1 tm-3)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-51.           ((((A -> B) -> ((C or A) -> B)) -> D) -> (((C -> A) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64422.        (((A -> B) or ((B -> C) -> ((A or B) -> C))) -> ((D -> E) -> (((D and F) or D) -> E))), M:tm-51, m:tm-759, u:((Am (-> (-> A B) (-> (or C A) B))) (D (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64423
in-theory        64423
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B or A)) -> ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-50 tm-759 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-7 tm-1 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64423.        ((A or (B or A)) -> ((C -> D) -> (((C and E) or C) -> D))), M:tm-50, m:tm-759, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64424
in-theory        64424
times-derived    2
----------------------------------------------------------------
theorem          ((A or (A or B)) -> ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-49 tm-759 ((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-6 tm-1 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64424.        ((A or (A or B)) -> ((C -> D) -> (((C and E) or C) -> D))), M:tm-49, m:tm-759, u:((Am (or A B)) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64425
in-theory        64425
times-derived    2
----------------------------------------------------------------
theorem          ((A or (B -> (A and B))) -> ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     19
proof            (modus-ponens tm-48 tm-759 ((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-5 tm-1 tm-3)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-48.           (((A -> (B and A)) -> C) -> ((B or (A -> (B and A))) -> C)), M:tm-8, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64425.        ((A or (B -> (A and B))) -> ((C -> D) -> (((C and E) or C) -> D))), M:tm-48, m:tm-759, u:((Am (-> A (and B A))) (C (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64426
in-theory        64426
times-derived    2
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> D) -> (((C and E) or C) -> D)))
theorem-size     17
proof            (modus-ponens tm-47 tm-759 ((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm)))))
axioms-used      (tm-8 tm-4 tm-1 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-759.          (A -> ((B -> C) -> (((B and D) or B) -> C))), M:tm-1, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-64426.        (((A and B) or B) -> ((C -> D) -> (((C and E) or C) -> D))), M:tm-47, m:tm-759, u:((A Am) (B (-> (-> Bm Cm) (-> (or (and Bm Dm) Bm) Cm))))
================================================================
tm-name          tm-64427
in-theory        64427
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-757 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64427.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (F -> E))), M:tm-757, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64428
in-theory        64428
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (((((A and B) or B) and D) or ((A and B) or B)) -> (C -> B)))
theorem-size     27
proof            (modus-ponens tm-747 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64428.        ((((A and B) or B) -> (C -> B)) and (((((A and B) or B) and D) or ((A and B) or B)) -> (C -> B))), M:tm-747, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64429
in-theory        64429
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (G -> F)))
theorem-size     35
proof            (modus-ponens tm-708 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64429.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (G -> F))), M:tm-708, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64430
in-theory        64430
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-665 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64430.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (F -> E))), M:tm-665, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64431
in-theory        64431
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (D -> B)))
theorem-size     11
proof            (modus-ponens tm-623 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64431.        (((A and B) or B) -> (C or (D -> B))), M:tm-623, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64432
in-theory        64432
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-622 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64432.        ((A -> (B -> (C or B))) and (((D and E) or E) -> (F -> E))), M:tm-622, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64433
in-theory        64433
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64433.        ((((A and B) or B) -> (C -> B)) and (D -> (E or D))), M:tm-609, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64434
in-theory        64434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-605 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64434.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (F -> E))), M:tm-605, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64435
in-theory        64435
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and ((D -> (E or D)) and (((A and B) or B) -> (C -> B))))
theorem-size     25
proof            (modus-ponens tm-595 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64435.        ((((A and B) or B) -> (C -> B)) and ((D -> (E or D)) and (((A and B) or B) -> (C -> B)))), M:tm-595, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64436
in-theory        64436
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-550 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64436.        (((A -> (B or A)) or C) and (((D and E) or E) -> (F -> E))), M:tm-550, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64437
in-theory        64437
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-540 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64437.        ((A or (B -> (C or B))) and (((D and E) or E) -> (F -> E))), M:tm-540, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64438
in-theory        64438
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-530 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64438.        ((A or (B -> (B or C))) and (((D and E) or E) -> (F -> E))), M:tm-530, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64439
in-theory        64439
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-520 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64439.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> E))), M:tm-520, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64440
in-theory        64440
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-510 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64440.        ((A or ((B and C) -> C)) and (((D and E) or E) -> (F -> E))), M:tm-510, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64441
in-theory        64441
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-500 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64441.        ((A or ((B and C) -> B)) and (((D and E) or E) -> (F -> E))), M:tm-500, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64442
in-theory        64442
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-490 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64442.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> F))), M:tm-490, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64443
in-theory        64443
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-480 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64443.        ((A or (B -> (C -> B))) and (((D and E) or E) -> (F -> E))), M:tm-480, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64444
in-theory        64444
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> B) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64444.        (((A and B) or B) -> ((C -> B) or D)), M:tm-470, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64445
in-theory        64445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-469 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64445.        ((A -> (B -> (B or C))) and (((D and E) or E) -> (F -> E))), M:tm-469, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64446
in-theory        64446
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64446.        ((((A and B) or B) -> (C -> B)) and (D -> (D or E))), M:tm-456, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64447
in-theory        64447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-453 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64447.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (F -> E))), M:tm-453, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64448
in-theory        64448
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and ((D -> (D or E)) and (((A and B) or B) -> (C -> B))))
theorem-size     25
proof            (modus-ponens tm-443 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64448.        ((((A and B) or B) -> (C -> B)) and ((D -> (D or E)) and (((A and B) or B) -> (C -> B)))), M:tm-443, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64449
in-theory        64449
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-409 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64449.        (((A -> (A or B)) or C) and (((D and E) or E) -> (F -> E))), M:tm-409, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64450
in-theory        64450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-400 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64450.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (F -> E))), M:tm-400, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64451
in-theory        64451
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-391 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64451.        ((((A and B) -> B) or C) and (((D and E) or E) -> (F -> E))), M:tm-391, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64452
in-theory        64452
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-382 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64452.        ((((A and B) -> A) or C) and (((D and E) or E) -> (F -> E))), M:tm-382, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64453
in-theory        64453
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-373 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64453.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (G -> F))), M:tm-373, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64454
in-theory        64454
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-364 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64454.        (((A -> (B -> A)) or C) and (((D and E) or E) -> (F -> E))), M:tm-364, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64455
in-theory        64455
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D -> B) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64455.        (((A and B) or B) -> (C -> ((D -> B) and C))), M:tm-355, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64456
in-theory        64456
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-354 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64456.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> E))), M:tm-354, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64457
in-theory        64457
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64457.        ((((A and B) or B) -> (C -> B)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64458
in-theory        64458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-338 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64458.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (E -> D))), M:tm-338, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64459
in-theory        64459
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (((A and B) or B) -> (((A and B) or B) and (C -> B))))
theorem-size     25
proof            (modus-ponens tm-328 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64459.        ((((A and B) or B) -> (C -> B)) and (((A and B) or B) -> (((A and B) or B) and (C -> B)))), M:tm-328, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64460
in-theory        64460
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and ((D -> (E -> (D and E))) and (((A and B) or B) -> (C -> B))))
theorem-size     27
proof            (modus-ponens tm-327 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64460.        ((((A and B) or B) -> (C -> B)) and ((D -> (E -> (D and E))) and (((A and B) or B) -> (C -> B)))), M:tm-327, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64461
in-theory        64461
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (((D and E) -> E) and (((A and B) or B) -> (C -> B))))
theorem-size     25
proof            (modus-ponens tm-326 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64461.        ((((A and B) or B) -> (C -> B)) and (((D and E) -> E) and (((A and B) or B) -> (C -> B)))), M:tm-326, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64462
in-theory        64462
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (((D and E) -> D) and (((A and B) or B) -> (C -> B))))
theorem-size     25
proof            (modus-ponens tm-325 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64462.        ((((A and B) or B) -> (C -> B)) and (((D and E) -> D) and (((A and B) or B) -> (C -> B)))), M:tm-325, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64463
in-theory        64463
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or B) -> (C -> B))))
theorem-size     33
proof            (modus-ponens tm-324 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64463.        ((((A and B) or B) -> (C -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or B) -> (C -> B)))), M:tm-324, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64464
in-theory        64464
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and ((D -> (E -> D)) and (((A and B) or B) -> (C -> B))))
theorem-size     25
proof            (modus-ponens tm-323 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64464.        ((((A and B) or B) -> (C -> B)) and ((D -> (E -> D)) and (((A and B) or B) -> (C -> B)))), M:tm-323, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64465
in-theory        64465
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64465.        ((((A and B) or B) -> (C -> B)) and ((D and E) -> E)), M:tm-322, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64466
in-theory        64466
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64466.        ((((A and B) or B) -> (C -> B)) and ((D and E) -> D)), M:tm-320, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64467
in-theory        64467
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64467.        ((((A and B) or B) -> (C -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64468
in-theory        64468
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     21
proof            (modus-ponens tm-316 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64468.        ((((A and B) or B) -> (C -> B)) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64469
in-theory        64469
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64469.        ((((A and B) or B) -> (C -> B)) and (D -> (E -> D))), M:tm-315, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64470
in-theory        64470
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and ((((A and B) or B) -> (not (C -> B))) -> (not ((A and B) or B))))
theorem-size     27
proof            (modus-ponens tm-313 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64470.        ((((A and B) or B) -> (C -> B)) and ((((A and B) or B) -> (not (C -> B))) -> (not ((A and B) or B)))), M:tm-313, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64471
in-theory        64471
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (((C -> B) -> D) -> ((((A and B) or B) or (C -> B)) -> D)))
theorem-size     27
proof            (modus-ponens tm-312 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64471.        ((((A and B) or B) -> (C -> B)) and (((C -> B) -> D) -> ((((A and B) or B) or (C -> B)) -> D))), M:tm-312, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64472
in-theory        64472
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (D or (((A and B) or B) -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-311 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64472.        ((((A and B) or B) -> (C -> B)) and (D or (((A and B) or B) -> (C -> B)))), M:tm-311, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64473
in-theory        64473
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and ((((A and B) or B) -> (C -> B)) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64473.        ((((A and B) or B) -> (C -> B)) and ((((A and B) or B) -> (C -> B)) or D)), M:tm-310, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64474
in-theory        64474
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (D -> ((((A and B) or B) -> (C -> B)) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64474.        ((((A and B) or B) -> (C -> B)) and (D -> ((((A and B) or B) -> (C -> B)) and D))), M:tm-309, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64475
in-theory        64475
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and ((((A and B) or B) -> C) -> (((A and B) or B) -> B)))
theorem-size     25
proof            (modus-ponens tm-306 tm-760 ((A (or (and Am Bm) Bm)) (B Cm) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64475.        ((((A and B) or B) -> (C -> B)) and ((((A and B) or B) -> C) -> (((A and B) or B) -> B))), M:tm-306, m:tm-760, u:((A (or (and Am Bm) Bm)) (B Cm) (C Bm))
================================================================
tm-name          tm-64476
in-theory        64476
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) and (D -> (((A and B) or B) -> (C -> B))))
theorem-size     21
proof            (modus-ponens tm-305 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64476.        ((((A and B) or B) -> (C -> B)) and (D -> (((A and B) or B) -> (C -> B)))), M:tm-305, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64477
in-theory        64477
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-303 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64477.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (F -> E))), M:tm-303, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64478
in-theory        64478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-270 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64478.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (F -> E))), M:tm-270, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64479
in-theory        64479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-239 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64479.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (F -> E))), M:tm-239, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64480
in-theory        64480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-210 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64480.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (G -> F))), M:tm-210, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64481
in-theory        64481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-183 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64481.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (F -> E))), M:tm-183, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64482
in-theory        64482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-157 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64482.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> (F -> E))), M:tm-157, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64483
in-theory        64483
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-147 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64483.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (F -> E))), M:tm-147, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64484
in-theory        64484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-134 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64484.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> (F -> E))), M:tm-134, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64485
in-theory        64485
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-125 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64485.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (F -> E))), M:tm-125, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64486
in-theory        64486
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((D -> B) -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-114 tm-760 ((A (or (and Am (-> C D)) (-> C D))) (B Cm) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64486.        (((A and (B -> C)) or (B -> C)) -> ((D -> B) -> (D -> C))), M:tm-114, m:tm-760, u:((A (or (and Am (-> C D)) (-> C D))) (B Cm) (Bm (-> C D)))
================================================================
tm-name          tm-64487
in-theory        64487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-113 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64487.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> F))), M:tm-113, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64488
in-theory        64488
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (F -> E)))
theorem-size     29
proof            (modus-ponens tm-105 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64488.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (F -> E))), M:tm-105, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64489
in-theory        64489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-95 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64489.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> (E -> D))), M:tm-95, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64490
in-theory        64490
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (D -> B)))
theorem-size     11
proof            (modus-ponens tm-84 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64490.        (((A and B) or B) -> (C -> (D -> B))), M:tm-84, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64491
in-theory        64491
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-83 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64491.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> (F -> E))), M:tm-83, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64492
in-theory        64492
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-76 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64492.        (((not (not A)) -> A) and (((B and C) or C) -> (D -> C))), M:tm-76, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64493
in-theory        64493
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> (C -> B))
theorem-size     17
proof            (modus-ponens tm-73 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-8 tm-10 tm-4 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64493.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> (C -> B)), M:tm-73, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64494
in-theory        64494
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-69 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-1)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64494.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (E -> D))), M:tm-69, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64495
in-theory        64495
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-54 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64495.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (F -> E))), M:tm-54, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64496
in-theory        64496
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> (C -> A))
theorem-size     11
proof            (modus-ponens tm-50 tm-760 ((A (and Am Bm)) (B Bm) (C (-> Cm Bm))))
axioms-used      (tm-8 tm-7 tm-4 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64496.        ((A or ((B and A) or A)) -> (C -> A)), M:tm-50, m:tm-760, u:((A (and Am Bm)) (B Bm) (C (-> Cm Bm)))
================================================================
tm-name          tm-64497
in-theory        64497
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> (C -> B))
theorem-size     13
proof            (modus-ponens tm-49 tm-760 ((A (and Am Bm)) (B Bm) (C (-> Cm Bm))))
axioms-used      (tm-8 tm-6 tm-4 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64497.        (((A and B) or ((A and B) or B)) -> (C -> B)), M:tm-49, m:tm-760, u:((A (and Am Bm)) (B Bm) (C (-> Cm Bm)))
================================================================
tm-name          tm-64498
in-theory        64498
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> (D -> C))
theorem-size     17
proof            (modus-ponens tm-47 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64498.        (((A and ((B and C) or C)) or ((B and C) or C)) -> (D -> C)), M:tm-47, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64499
in-theory        64499
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> (D -> B))
theorem-size     17
proof            (modus-ponens tm-46 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-8 tm-3 tm-4 tm-1)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64499.        (((((A and B) or B) and C) or ((A and B) or B)) -> (D -> B)), M:tm-46, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64500
in-theory        64500
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-42 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64500.        ((A -> (B or A)) and (((C and D) or D) -> (E -> D))), M:tm-42, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64501
in-theory        64501
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-32 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64501.        ((A -> (A or B)) and (((C and D) or D) -> (E -> D))), M:tm-32, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64502
in-theory        64502
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and (C -> B)))
theorem-size     15
proof            (modus-ponens tm-24 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64502.        (((A and B) or B) -> (((A and B) or B) and (C -> B))), M:tm-24, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64503
in-theory        64503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-23 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64503.        ((A -> (B -> (A and B))) and (((C and D) or D) -> (E -> D))), M:tm-23, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64504
in-theory        64504
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-22 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64504.        (((A and B) -> B) and (((C and D) or D) -> (E -> D))), M:tm-22, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64505
in-theory        64505
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-21 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64505.        (((A and B) -> A) and (((C and D) or D) -> (E -> D))), M:tm-21, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64506
in-theory        64506
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (F -> E)))
theorem-size     23
proof            (modus-ponens tm-20 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64506.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (F -> E))), M:tm-20, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64507
in-theory        64507
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-19 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64507.        ((A -> (B -> A)) and (((C and D) or D) -> (E -> D))), M:tm-19, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64508
in-theory        64508
times-derived    18
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((A and B) or B))
theorem-size     11
proof            (modus-ponens tm-12 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64508.        (((A and B) or B) -> ((A and B) or B)), M:tm-12, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64509
in-theory        64509
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not (C -> B))) -> (not ((A and B) or B)))
theorem-size     17
proof            (modus-ponens tm-9 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-9 tm-8 tm-4 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64509.        ((((A and B) or B) -> (not (C -> B))) -> (not ((A and B) or B))), M:tm-9, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64510
in-theory        64510
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> C) -> ((((D and B) or B) or (A -> B)) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-760 ((A (or (and Am Bm) Bm)) (B (-> Cm Bm))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64510.        (((A -> B) -> C) -> ((((D and B) or B) or (A -> B)) -> C)), M:tm-8, m:tm-760, u:((A (or (and Am Bm) Bm)) (B (-> Cm Bm)))
================================================================
tm-name          tm-64511
in-theory        64511
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> (D -> C)))
theorem-size     11
proof            (modus-ponens tm-7 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-7 tm-8 tm-4 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64511.        (A or (((B and C) or C) -> (D -> C))), M:tm-7, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64512
in-theory        64512
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> B)) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-6 tm-8 tm-4 tm-1)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64512.        ((((A and B) or B) -> (C -> B)) or D), M:tm-6, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64513
in-theory        64513
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> (D -> C)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64513.        (A -> ((((B and C) or C) -> (D -> C)) and A)), M:tm-5, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64514
in-theory        64514
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> C) -> (((A and B) or B) -> B))
theorem-size     15
proof            (modus-ponens tm-2 tm-760 ((A (or (and Am Bm) Bm)) (B Cm) (C Bm)))
axioms-used      (tm-2 tm-8 tm-4 tm-1)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64514.        ((((A and B) or B) -> C) -> (((A and B) or B) -> B)), M:tm-2, m:tm-760, u:((A (or (and Am Bm) Bm)) (B Cm) (C Bm))
================================================================
tm-name          tm-64515
in-theory        64515
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> (D -> C)))
theorem-size     11
proof            (modus-ponens tm-1 tm-760 ((A (-> (or (and Am Bm) Bm) (-> Cm Bm)))))
axioms-used      (tm-1 tm-8 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-760.          (((A and B) or B) -> (C -> B)), M:tm-47, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-64515.        (A -> (((B and C) or C) -> (D -> C))), M:tm-1, m:tm-760, u:((A (-> (or (and Am Bm) Bm) (-> Cm Bm))))
================================================================
tm-name          tm-64516
in-theory        64516
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-757 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64516.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-757, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64517
in-theory        64517
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((((A and (B -> (C -> D))) or (B -> (C -> D))) and E) or ((A and (B -> (C -> D))) or (B -> (C -> D)))) -> ((B -> C) -> (B -> D))))
theorem-size     59
proof            (modus-ponens tm-747 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64517.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((((A and (B -> (C -> D))) or (B -> (C -> D))) and E) or ((A and (B -> (C -> D))) or (B -> (C -> D)))) -> ((B -> C) -> (B -> D)))), M:tm-747, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64518
in-theory        64518
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H))))
theorem-size     47
proof            (modus-ponens tm-708 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       197
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64518.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H)))), M:tm-708, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64519
in-theory        64519
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-665 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64519.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-665, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64520
in-theory        64520
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (E or ((B -> C) -> (B -> D))))
theorem-size     23
proof            (modus-ponens tm-623 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64520.        (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (E or ((B -> C) -> (B -> D)))), M:tm-623, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64521
in-theory        64521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-622 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64521.        ((A -> (B -> (C or B))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-622, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64522
in-theory        64522
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (E -> (F or E)))
theorem-size     27
proof            (modus-ponens tm-609 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64522.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (E -> (F or E))), M:tm-609, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64523
in-theory        64523
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-605 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64523.        ((A -> ((B -> (C or B)) and A)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-605, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64524
in-theory        64524
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((E -> (F or E)) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))))
theorem-size     49
proof            (modus-ponens tm-595 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64524.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((E -> (F or E)) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))), M:tm-595, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64525
in-theory        64525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-550 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64525.        (((A -> (B or A)) or C) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-550, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64526
in-theory        64526
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-540 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64526.        ((A or (B -> (C or B))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-540, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64527
in-theory        64527
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-530 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64527.        ((A or (B -> (B or C))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-530, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64528
in-theory        64528
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-520 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64528.        ((A or (B -> (C -> (B and C)))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-520, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64529
in-theory        64529
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-510 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64529.        ((A or ((B and C) -> C)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-510, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64530
in-theory        64530
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-500 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64530.        ((A or ((B and C) -> B)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-500, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64531
in-theory        64531
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-490 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64531.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H)))), M:tm-490, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64532
in-theory        64532
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-480 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64532.        ((A or (B -> (C -> B))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-480, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64533
in-theory        64533
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (((B -> C) -> (B -> D)) or E))
theorem-size     23
proof            (modus-ponens tm-470 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64533.        (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (((B -> C) -> (B -> D)) or E)), M:tm-470, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64534
in-theory        64534
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-469 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64534.        ((A -> (B -> (B or C))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-469, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64535
in-theory        64535
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (E -> (E or F)))
theorem-size     27
proof            (modus-ponens tm-456 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64535.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (E -> (E or F))), M:tm-456, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64536
in-theory        64536
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-453 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64536.        ((A -> ((B -> (B or C)) and A)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-453, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64537
in-theory        64537
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((E -> (E or F)) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))))
theorem-size     49
proof            (modus-ponens tm-443 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64537.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((E -> (E or F)) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))), M:tm-443, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64538
in-theory        64538
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-409 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64538.        (((A -> (A or B)) or C) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-409, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64539
in-theory        64539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-400 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64539.        (((A -> (B -> (A and B))) or C) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-400, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64540
in-theory        64540
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-391 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64540.        ((((A and B) -> B) or C) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-391, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64541
in-theory        64541
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-382 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64541.        ((((A and B) -> A) or C) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-382, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64542
in-theory        64542
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-373 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64542.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H)))), M:tm-373, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64543
in-theory        64543
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-364 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64543.        (((A -> (B -> A)) or C) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-364, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64544
in-theory        64544
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (E -> (((B -> C) -> (B -> D)) and E)))
theorem-size     25
proof            (modus-ponens tm-355 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64544.        (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (E -> (((B -> C) -> (B -> D)) and E))), M:tm-355, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64545
in-theory        64545
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-354 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64545.        ((A -> (B -> (C -> (B and C)))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-354, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64546
in-theory        64546
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (E -> (F -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-341 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64546.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64547
in-theory        64547
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-338 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64547.        (((A -> B) -> (A -> (A and B))) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-338, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64548
in-theory        64548
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (((A and (B -> (C -> D))) or (B -> (C -> D))) and ((B -> C) -> (B -> D)))))
theorem-size     57
proof            (modus-ponens tm-328 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64548.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (((A and (B -> (C -> D))) or (B -> (C -> D))) and ((B -> C) -> (B -> D))))), M:tm-328, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64549
in-theory        64549
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((E -> (F -> (E and F))) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))))
theorem-size     51
proof            (modus-ponens tm-327 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64549.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((E -> (F -> (E and F))) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))), M:tm-327, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64550
in-theory        64550
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((E and F) -> F) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))))
theorem-size     49
proof            (modus-ponens tm-326 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64550.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((E and F) -> F) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))), M:tm-326, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64551
in-theory        64551
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((E and F) -> E) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))))
theorem-size     49
proof            (modus-ponens tm-325 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64551.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((E and F) -> E) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))), M:tm-325, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64552
in-theory        64552
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))))
theorem-size     57
proof            (modus-ponens tm-324 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64552.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))), M:tm-324, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64553
in-theory        64553
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((E -> (F -> E)) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))))
theorem-size     49
proof            (modus-ponens tm-323 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64553.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((E -> (F -> E)) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))), M:tm-323, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64554
in-theory        64554
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((E and F) -> F))
theorem-size     27
proof            (modus-ponens tm-322 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64554.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((E and F) -> F)), M:tm-322, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64555
in-theory        64555
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((E and F) -> E))
theorem-size     27
proof            (modus-ponens tm-320 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64555.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((E and F) -> E)), M:tm-320, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64556
in-theory        64556
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-318 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64556.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64557
in-theory        64557
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((A and (B -> (C -> D))) or (B -> (C -> D)))))
theorem-size     49
proof            (modus-ponens tm-316 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64557.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((A and (B -> (C -> D))) or (B -> (C -> D))))), M:tm-316, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64558
in-theory        64558
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (E -> (F -> E)))
theorem-size     27
proof            (modus-ponens tm-315 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64558.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (E -> (F -> E))), M:tm-315, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64559
in-theory        64559
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> (not ((B -> C) -> (B -> D)))) -> (not ((A and (B -> (C -> D))) or (B -> (C -> D))))))
theorem-size     59
proof            (modus-ponens tm-313 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64559.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> (not ((B -> C) -> (B -> D)))) -> (not ((A and (B -> (C -> D))) or (B -> (C -> D)))))), M:tm-313, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64560
in-theory        64560
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((((B -> C) -> (B -> D)) -> E) -> ((((A and (B -> (C -> D))) or (B -> (C -> D))) or ((B -> C) -> (B -> D))) -> E)))
theorem-size     55
proof            (modus-ponens tm-312 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64560.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((((B -> C) -> (B -> D)) -> E) -> ((((A and (B -> (C -> D))) or (B -> (C -> D))) or ((B -> C) -> (B -> D))) -> E))), M:tm-312, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64561
in-theory        64561
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (E or (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))))
theorem-size     45
proof            (modus-ponens tm-311 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64561.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (E or (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))), M:tm-311, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64562
in-theory        64562
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) or E))
theorem-size     45
proof            (modus-ponens tm-310 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64562.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) or E)), M:tm-310, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64563
in-theory        64563
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (E -> ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and E)))
theorem-size     47
proof            (modus-ponens tm-309 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64563.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (E -> ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and E))), M:tm-309, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64564
in-theory        64564
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> (B -> C)) -> (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (B -> D))))
theorem-size     57
proof            (modus-ponens tm-306 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> Bm Cm)) (C (-> Bm Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64564.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> (B -> C)) -> (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (B -> D)))), M:tm-306, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> Bm Cm)) (C (-> Bm Dm)))
================================================================
tm-name          tm-64565
in-theory        64565
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (E -> (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D)))))
theorem-size     45
proof            (modus-ponens tm-305 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64565.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) and (E -> (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))))), M:tm-305, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64566
in-theory        64566
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-303 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64566.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-303, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64567
in-theory        64567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-270 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64567.        ((A -> (((B and C) -> C) and A)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-270, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64568
in-theory        64568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-239 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64568.        ((A -> (((B and C) -> B) and A)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-239, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64569
in-theory        64569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H))))
theorem-size     39
proof            (modus-ponens tm-210 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64569.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H)))), M:tm-210, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64570
in-theory        64570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     31
proof            (modus-ponens tm-183 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64570.        ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-183, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64571
in-theory        64571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-157 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64571.        ((A -> ((B and C) -> C)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-157, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64572
in-theory        64572
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-147 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64572.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-147, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64573
in-theory        64573
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-134 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64573.        ((A -> ((B and C) -> B)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-134, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64574
in-theory        64574
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     37
proof            (modus-ponens tm-125 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64574.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-125, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64575
in-theory        64575
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (((B -> C) -> B) -> ((B -> C) -> D)))
theorem-size     25
proof            (modus-ponens tm-114 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> Bm Cm)) (C Bm) (D Dm)))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64575.        (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (((B -> C) -> B) -> ((B -> C) -> D))), M:tm-114, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> Bm Cm)) (C Bm) (D Dm))
================================================================
tm-name          tm-64576
in-theory        64576
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H))))
theorem-size     37
proof            (modus-ponens tm-113 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64576.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> (G -> H))) or (F -> (G -> H))) -> ((F -> G) -> (F -> H)))), M:tm-113, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64577
in-theory        64577
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-105 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64577.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-105, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64578
in-theory        64578
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-95 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64578.        (((A -> B) -> (A -> A)) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-95, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64579
in-theory        64579
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (E -> ((B -> C) -> (B -> D))))
theorem-size     23
proof            (modus-ponens tm-84 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64579.        (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (E -> ((B -> C) -> (B -> D)))), M:tm-84, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64580
in-theory        64580
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-83 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64580.        ((A -> (B -> (C -> B))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-83, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64581
in-theory        64581
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (C -> (D -> E))) or (C -> (D -> E))) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-76 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64581.        (((not (not A)) -> A) and (((B and (C -> (D -> E))) or (C -> (D -> E))) -> ((C -> D) -> (C -> E)))), M:tm-76, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64582
in-theory        64582
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (B -> (C -> D))) or (B -> (C -> D))))) or ((A and (B -> (C -> D))) or (B -> (C -> D)))) -> ((B -> C) -> (B -> D)))
theorem-size     37
proof            (modus-ponens tm-73 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-8 tm-10 tm-4 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64582.        (((not (not ((A and (B -> (C -> D))) or (B -> (C -> D))))) or ((A and (B -> (C -> D))) or (B -> (C -> D)))) -> ((B -> C) -> (B -> D))), M:tm-73, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64583
in-theory        64583
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     33
proof            (modus-ponens tm-69 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64583.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-69, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64584
in-theory        64584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-54 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64584.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-54, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64585
in-theory        64585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) or ((D and (A -> (B -> C))) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C)))
theorem-size     27
proof            (modus-ponens tm-50 tm-761 ((A (and Am (-> Bm (-> Cm Dm)))) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-8 tm-7 tm-4 tm-2)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64585.        (((A -> (B -> C)) or ((D and (A -> (B -> C))) or (A -> (B -> C)))) -> ((A -> B) -> (A -> C))), M:tm-50, m:tm-761, u:((A (and Am (-> Bm (-> Cm Dm)))) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64586
in-theory        64586
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> D))) or ((A and (B -> (C -> D))) or (B -> (C -> D)))) -> ((B -> C) -> (B -> D)))
theorem-size     29
proof            (modus-ponens tm-49 tm-761 ((A (and Am (-> Bm (-> Cm Dm)))) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-8 tm-6 tm-4 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64586.        (((A and (B -> (C -> D))) or ((A and (B -> (C -> D))) or (B -> (C -> D)))) -> ((B -> C) -> (B -> D))), M:tm-49, m:tm-761, u:((A (and Am (-> Bm (-> Cm Dm)))) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64587
in-theory        64587
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> (D -> E))) or (C -> (D -> E)))) or ((B and (C -> (D -> E))) or (C -> (D -> E)))) -> ((C -> D) -> (C -> E)))
theorem-size     37
proof            (modus-ponens tm-47 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64587.        (((A and ((B and (C -> (D -> E))) or (C -> (D -> E)))) or ((B and (C -> (D -> E))) or (C -> (D -> E)))) -> ((C -> D) -> (C -> E))), M:tm-47, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64588
in-theory        64588
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> (C -> D))) or (B -> (C -> D))) and E) or ((A and (B -> (C -> D))) or (B -> (C -> D)))) -> ((B -> C) -> (B -> D)))
theorem-size     37
proof            (modus-ponens tm-46 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-8 tm-3 tm-4 tm-2)
proof-size       129
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64588.        (((((A and (B -> (C -> D))) or (B -> (C -> D))) and E) or ((A and (B -> (C -> D))) or (B -> (C -> D)))) -> ((B -> C) -> (B -> D))), M:tm-46, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64589
in-theory        64589
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-42 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64589.        ((A -> (B or A)) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-42, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64590
in-theory        64590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-32 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64590.        ((A -> (A or B)) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-32, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64591
in-theory        64591
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (((A and (B -> (C -> D))) or (B -> (C -> D))) and ((B -> C) -> (B -> D))))
theorem-size     35
proof            (modus-ponens tm-24 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64591.        (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (((A and (B -> (C -> D))) or (B -> (C -> D))) and ((B -> C) -> (B -> D)))), M:tm-24, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64592
in-theory        64592
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-23 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64592.        ((A -> (B -> (A and B))) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-23, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64593
in-theory        64593
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-22 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64593.        (((A and B) -> B) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-22, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64594
in-theory        64594
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-21 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64594.        (((A and B) -> A) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-21, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64595
in-theory        64595
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G))))
theorem-size     35
proof            (modus-ponens tm-20 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       135
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64595.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> (F -> G))) or (E -> (F -> G))) -> ((E -> F) -> (E -> G)))), M:tm-20, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64596
in-theory        64596
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-19 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64596.        ((A -> (B -> A)) and (((C and (D -> (E -> F))) or (D -> (E -> F))) -> ((D -> E) -> (D -> F)))), M:tm-19, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64597
in-theory        64597
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((A and (B -> (C -> D))) or (B -> (C -> D))))
theorem-size     27
proof            (modus-ponens tm-12 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64597.        (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((A and (B -> (C -> D))) or (B -> (C -> D)))), M:tm-12, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64598
in-theory        64598
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> (not ((B -> C) -> (B -> D)))) -> (not ((A and (B -> (C -> D))) or (B -> (C -> D)))))
theorem-size     37
proof            (modus-ponens tm-9 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-9 tm-8 tm-4 tm-2)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64598.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> (not ((B -> C) -> (B -> D)))) -> (not ((A and (B -> (C -> D))) or (B -> (C -> D))))), M:tm-9, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64599
in-theory        64599
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> (A -> C)) -> D) -> ((((E and (A -> (B -> C))) or (A -> (B -> C))) or ((A -> B) -> (A -> C))) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm)))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       109
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64599.        ((((A -> B) -> (A -> C)) -> D) -> ((((E and (A -> (B -> C))) or (A -> (B -> C))) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> (-> Bm Cm) (-> Bm Dm))))
================================================================
tm-name          tm-64600
in-theory        64600
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (C -> (D -> E))) or (C -> (D -> E))) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-7 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-7 tm-8 tm-4 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64600.        (A or (((B and (C -> (D -> E))) or (C -> (D -> E))) -> ((C -> D) -> (C -> E)))), M:tm-7, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64601
in-theory        64601
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) or E)
theorem-size     23
proof            (modus-ponens tm-6 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-6 tm-8 tm-4 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64601.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))) or E), M:tm-6, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64602
in-theory        64602
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (C -> (D -> E))) or (C -> (D -> E))) -> ((C -> D) -> (C -> E))) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       95
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64602.        (A -> ((((B and (C -> (D -> E))) or (C -> (D -> E))) -> ((C -> D) -> (C -> E))) and A)), M:tm-5, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64603
in-theory        64603
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> (B -> C)) -> (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (B -> D)))
theorem-size     35
proof            (modus-ponens tm-2 tm-761 ((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> Bm Cm)) (C (-> Bm Dm))))
axioms-used      (tm-2 tm-8 tm-4)
proof-size       111
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64603.        ((((A and (B -> (C -> D))) or (B -> (C -> D))) -> (B -> C)) -> (((A and (B -> (C -> D))) or (B -> (C -> D))) -> (B -> D))), M:tm-2, m:tm-761, u:((A (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm)))) (B (-> Bm Cm)) (C (-> Bm Dm)))
================================================================
tm-name          tm-64604
in-theory        64604
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (C -> (D -> E))) or (C -> (D -> E))) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-1 tm-761 ((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm))))))
axioms-used      (tm-1 tm-8 tm-4 tm-2)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-761.          (((A and (B -> (C -> D))) or (B -> (C -> D))) -> ((B -> C) -> (B -> D))), M:tm-47, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-64604.        (A -> (((B and (C -> (D -> E))) or (C -> (D -> E))) -> ((C -> D) -> (C -> E)))), M:tm-1, m:tm-761, u:((A (-> (or (and Am (-> Bm (-> Cm Dm))) (-> Bm (-> Cm Dm))) (-> (-> Bm Cm) (-> Bm Dm)))))
================================================================
tm-name          tm-64605
in-theory        64605
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     23
proof            (modus-ponens tm-757 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64605.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-757, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64606
in-theory        64606
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (((((A and (B and C)) or (B and C)) and D) or ((A and (B and C)) or (B and C))) -> B))
theorem-size     35
proof            (modus-ponens tm-747 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64606.        ((((A and (B and C)) or (B and C)) -> B) and (((((A and (B and C)) or (B and C)) and D) or ((A and (B and C)) or (B and C))) -> B)), M:tm-747, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64607
in-theory        64607
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F and G)) or (F and G)) -> F))
theorem-size     37
proof            (modus-ponens tm-708 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-3)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64607.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F and G)) or (F and G)) -> F)), M:tm-708, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64608
in-theory        64608
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     25
proof            (modus-ponens tm-665 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-3)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64608.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-665, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64609
in-theory        64609
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> (D or B))
theorem-size     13
proof            (modus-ponens tm-623 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64609.        (((A and (B and C)) or (B and C)) -> (D or B)), M:tm-623, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64610
in-theory        64610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-622 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64610.        ((A -> (B -> (C or B))) and (((D and (E and F)) or (E and F)) -> E)), M:tm-622, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64611
in-theory        64611
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and ((not (B -> (C or B))) and D)) or ((not (B -> (C or B))) and D)))
theorem-size     20
proof            (modus-ponens tm-618 tm-762 ((A (or (and Am (and (not (-> B (or C B))) Cm)) (and (not (-> B (or C B))) Cm))) (Bm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-8 tm-4 tm-3)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64611.        (not ((A and ((not (B -> (C or B))) and D)) or ((not (B -> (C or B))) and D))), M:tm-618, m:tm-762, u:((A (or (and Am (and (not (-> B (or C B))) Cm)) (and (not (-> B (or C B))) Cm))) (Bm (not (-> B (or C B)))))
================================================================
tm-name          tm-64612
in-theory        64612
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64612.        ((((A and (B and C)) or (B and C)) -> B) and (D -> (E or D))), M:tm-609, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64613
in-theory        64613
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     21
proof            (modus-ponens tm-605 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64613.        ((A -> ((B -> (C or B)) and A)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-605, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64614
in-theory        64614
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and ((D -> (E or D)) and (((A and (B and C)) or (B and C)) -> B)))
theorem-size     29
proof            (modus-ponens tm-595 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64614.        ((((A and (B and C)) or (B and C)) -> B) and ((D -> (E or D)) and (((A and (B and C)) or (B and C)) -> B))), M:tm-595, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64615
in-theory        64615
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-550 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64615.        (((A -> (B or A)) or C) and (((D and (E and F)) or (E and F)) -> E)), M:tm-550, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64616
in-theory        64616
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-540 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64616.        ((A or (B -> (C or B))) and (((D and (E and F)) or (E and F)) -> E)), M:tm-540, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64617
in-theory        64617
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-530 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64617.        ((A or (B -> (B or C))) and (((D and (E and F)) or (E and F)) -> E)), M:tm-530, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64618
in-theory        64618
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     21
proof            (modus-ponens tm-520 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64618.        ((A or (B -> (C -> (B and C)))) and (((D and (E and F)) or (E and F)) -> E)), M:tm-520, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64619
in-theory        64619
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-510 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64619.        ((A or ((B and C) -> C)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-510, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64620
in-theory        64620
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-500 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64620.        ((A or ((B and C) -> B)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-500, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64621
in-theory        64621
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F and G)) or (F and G)) -> F))
theorem-size     27
proof            (modus-ponens tm-490 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64621.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F and G)) or (F and G)) -> F)), M:tm-490, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64622
in-theory        64622
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-480 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64622.        ((A or (B -> (C -> B))) and (((D and (E and F)) or (E and F)) -> E)), M:tm-480, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64623
in-theory        64623
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> (B or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64623.        (((A and (B and C)) or (B and C)) -> (B or D)), M:tm-470, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64624
in-theory        64624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-469 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64624.        ((A -> (B -> (B or C))) and (((D and (E and F)) or (E and F)) -> E)), M:tm-469, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64625
in-theory        64625
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and ((not (B -> (B or C))) and D)) or ((not (B -> (B or C))) and D)))
theorem-size     20
proof            (modus-ponens tm-465 tm-762 ((A (or (and Am (and (not (-> B (or B C))) Cm)) (and (not (-> B (or B C))) Cm))) (Bm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-8 tm-4 tm-3)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64625.        (not ((A and ((not (B -> (B or C))) and D)) or ((not (B -> (B or C))) and D))), M:tm-465, m:tm-762, u:((A (or (and Am (and (not (-> B (or B C))) Cm)) (and (not (-> B (or B C))) Cm))) (Bm (not (-> B (or B C)))))
================================================================
tm-name          tm-64626
in-theory        64626
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64626.        ((((A and (B and C)) or (B and C)) -> B) and (D -> (D or E))), M:tm-456, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64627
in-theory        64627
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     21
proof            (modus-ponens tm-453 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64627.        ((A -> ((B -> (B or C)) and A)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-453, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64628
in-theory        64628
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and ((D -> (D or E)) and (((A and (B and C)) or (B and C)) -> B)))
theorem-size     29
proof            (modus-ponens tm-443 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64628.        ((((A and (B and C)) or (B and C)) -> B) and ((D -> (D or E)) and (((A and (B and C)) or (B and C)) -> B))), M:tm-443, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64629
in-theory        64629
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-409 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64629.        (((A -> (A or B)) or C) and (((D and (E and F)) or (E and F)) -> E)), M:tm-409, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64630
in-theory        64630
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     21
proof            (modus-ponens tm-400 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64630.        (((A -> (B -> (A and B))) or C) and (((D and (E and F)) or (E and F)) -> E)), M:tm-400, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64631
in-theory        64631
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-391 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64631.        ((((A and B) -> B) or C) and (((D and (E and F)) or (E and F)) -> E)), M:tm-391, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64632
in-theory        64632
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-382 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64632.        ((((A and B) -> A) or C) and (((D and (E and F)) or (E and F)) -> E)), M:tm-382, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64633
in-theory        64633
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F and G)) or (F and G)) -> F))
theorem-size     27
proof            (modus-ponens tm-373 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64633.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F and G)) or (F and G)) -> F)), M:tm-373, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64634
in-theory        64634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-364 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64634.        (((A -> (B -> A)) or C) and (((D and (E and F)) or (E and F)) -> E)), M:tm-364, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64635
in-theory        64635
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> (D -> (B and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64635.        (((A and (B and C)) or (B and C)) -> (D -> (B and D))), M:tm-355, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64636
in-theory        64636
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     21
proof            (modus-ponens tm-354 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64636.        ((A -> (B -> (C -> (B and C)))) and (((D and (E and F)) or (E and F)) -> E)), M:tm-354, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64637
in-theory        64637
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and ((not (B -> (C -> (B and C)))) and D)) or ((not (B -> (C -> (B and C)))) and D)))
theorem-size     24
proof            (modus-ponens tm-350 tm-762 ((A (or (and Am (and (not (-> B (-> C (and B C)))) Cm)) (and (not (-> B (-> C (and B C)))) Cm))) (Bm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-8 tm-4 tm-3)
proof-size       114
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64637.        (not ((A and ((not (B -> (C -> (B and C)))) and D)) or ((not (B -> (C -> (B and C)))) and D))), M:tm-350, m:tm-762, u:((A (or (and Am (and (not (-> B (-> C (and B C)))) Cm)) (and (not (-> B (-> C (and B C)))) Cm))) (Bm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-64638
in-theory        64638
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64638.        ((((A and (B and C)) or (B and C)) -> B) and (D -> (E -> (D and E)))), M:tm-341, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64639
in-theory        64639
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (D and E)) or (D and E)) -> D))
theorem-size     21
proof            (modus-ponens tm-338 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64639.        (((A -> B) -> (A -> (A and B))) and (((C and (D and E)) or (D and E)) -> D)), M:tm-338, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64640
in-theory        64640
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (((A and (B and C)) or (B and C)) -> (((A and (B and C)) or (B and C)) and B)))
theorem-size     33
proof            (modus-ponens tm-328 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64640.        ((((A and (B and C)) or (B and C)) -> B) and (((A and (B and C)) or (B and C)) -> (((A and (B and C)) or (B and C)) and B))), M:tm-328, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64641
in-theory        64641
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and ((D -> (E -> (D and E))) and (((A and (B and C)) or (B and C)) -> B)))
theorem-size     31
proof            (modus-ponens tm-327 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64641.        ((((A and (B and C)) or (B and C)) -> B) and ((D -> (E -> (D and E))) and (((A and (B and C)) or (B and C)) -> B))), M:tm-327, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64642
in-theory        64642
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (((D and E) -> E) and (((A and (B and C)) or (B and C)) -> B)))
theorem-size     29
proof            (modus-ponens tm-326 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64642.        ((((A and (B and C)) or (B and C)) -> B) and (((D and E) -> E) and (((A and (B and C)) or (B and C)) -> B))), M:tm-326, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64643
in-theory        64643
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (((D and E) -> D) and (((A and (B and C)) or (B and C)) -> B)))
theorem-size     29
proof            (modus-ponens tm-325 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64643.        ((((A and (B and C)) or (B and C)) -> B) and (((D and E) -> D) and (((A and (B and C)) or (B and C)) -> B))), M:tm-325, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64644
in-theory        64644
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B and C)) or (B and C)) -> B)))
theorem-size     37
proof            (modus-ponens tm-324 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64644.        ((((A and (B and C)) or (B and C)) -> B) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B and C)) or (B and C)) -> B))), M:tm-324, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64645
in-theory        64645
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and ((D -> (E -> D)) and (((A and (B and C)) or (B and C)) -> B)))
theorem-size     29
proof            (modus-ponens tm-323 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64645.        ((((A and (B and C)) or (B and C)) -> B) and ((D -> (E -> D)) and (((A and (B and C)) or (B and C)) -> B))), M:tm-323, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64646
in-theory        64646
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64646.        ((((A and (B and C)) or (B and C)) -> B) and ((D and E) -> E)), M:tm-322, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64647
in-theory        64647
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64647.        ((((A and (B and C)) or (B and C)) -> B) and ((D and E) -> D)), M:tm-320, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64648
in-theory        64648
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64648.        ((((A and (B and C)) or (B and C)) -> B) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64649
in-theory        64649
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (((A and (B and C)) or (B and C)) -> ((A and (B and C)) or (B and C))))
theorem-size     31
proof            (modus-ponens tm-316 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64649.        ((((A and (B and C)) or (B and C)) -> B) and (((A and (B and C)) or (B and C)) -> ((A and (B and C)) or (B and C)))), M:tm-316, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64650
in-theory        64650
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64650.        ((((A and (B and C)) or (B and C)) -> B) and (D -> (E -> D))), M:tm-315, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64651
in-theory        64651
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and ((((A and (B and C)) or (B and C)) -> (not B)) -> (not ((A and (B and C)) or (B and C)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 tm-3)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64651.        ((((A and (B and C)) or (B and C)) -> B) and ((((A and (B and C)) or (B and C)) -> (not B)) -> (not ((A and (B and C)) or (B and C))))), M:tm-313, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64652
in-theory        64652
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and ((B -> D) -> ((((A and (B and C)) or (B and C)) or B) -> D)))
theorem-size     29
proof            (modus-ponens tm-312 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64652.        ((((A and (B and C)) or (B and C)) -> B) and ((B -> D) -> ((((A and (B and C)) or (B and C)) or B) -> D))), M:tm-312, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64653
in-theory        64653
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (D or (((A and (B and C)) or (B and C)) -> B)))
theorem-size     25
proof            (modus-ponens tm-311 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64653.        ((((A and (B and C)) or (B and C)) -> B) and (D or (((A and (B and C)) or (B and C)) -> B))), M:tm-311, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64654
in-theory        64654
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and ((((A and (B and C)) or (B and C)) -> B) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64654.        ((((A and (B and C)) or (B and C)) -> B) and ((((A and (B and C)) or (B and C)) -> B) or D)), M:tm-310, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64655
in-theory        64655
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (D -> ((((A and (B and C)) or (B and C)) -> B) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64655.        ((((A and (B and C)) or (B and C)) -> B) and (D -> ((((A and (B and C)) or (B and C)) -> B) and D))), M:tm-309, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64656
in-theory        64656
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) and D)) or ((B -> C) and D)) -> (B -> C)) and ((((A and ((B -> C) and D)) or ((B -> C) and D)) -> B) -> (((A and ((B -> C) and D)) or ((B -> C) and D)) -> C)))
theorem-size     49
proof            (modus-ponens tm-306 tm-762 ((A (or (and Am (and (-> B C) Cm)) (and (-> B C) Cm))) (Bm (-> B C))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64656.        ((((A and ((B -> C) and D)) or ((B -> C) and D)) -> (B -> C)) and ((((A and ((B -> C) and D)) or ((B -> C) and D)) -> B) -> (((A and ((B -> C) and D)) or ((B -> C) and D)) -> C))), M:tm-306, m:tm-762, u:((A (or (and Am (and (-> B C) Cm)) (and (-> B C) Cm))) (Bm (-> B C)))
================================================================
tm-name          tm-64657
in-theory        64657
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) and (D -> (((A and (B and C)) or (B and C)) -> B)))
theorem-size     25
proof            (modus-ponens tm-305 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64657.        ((((A and (B and C)) or (B and C)) -> B) and (D -> (((A and (B and C)) or (B and C)) -> B))), M:tm-305, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64658
in-theory        64658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     23
proof            (modus-ponens tm-303 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-8 tm-4 tm-3)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64658.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-303, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64659
in-theory        64659
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     21
proof            (modus-ponens tm-270 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64659.        ((A -> (((B and C) -> C) and A)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-270, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64660
in-theory        64660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     21
proof            (modus-ponens tm-239 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64660.        ((A -> (((B and C) -> B) and A)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-239, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64661
in-theory        64661
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F and G)) or (F and G)) -> F))
theorem-size     29
proof            (modus-ponens tm-210 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64661.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F and G)) or (F and G)) -> F)), M:tm-210, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64662
in-theory        64662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     21
proof            (modus-ponens tm-183 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64662.        ((A -> ((B -> (C -> B)) and A)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-183, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64663
in-theory        64663
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) and D)) or ((B and C) and D)) -> C)
theorem-size     15
proof            (modus-ponens tm-158 tm-762 ((A (or (and Am (and (and B C) Cm)) (and (and B C) Cm))) (Bm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64663.        (((A and ((B and C) and D)) or ((B and C) and D)) -> C), M:tm-158, m:tm-762, u:((A (or (and Am (and (and B C) Cm)) (and (and B C) Cm))) (Bm (and B C)))
================================================================
tm-name          tm-64664
in-theory        64664
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-157 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64664.        ((A -> ((B and C) -> C)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-157, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64665
in-theory        64665
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and ((not ((B and C) -> C)) and D)) or ((not ((B and C) -> C)) and D)))
theorem-size     20
proof            (modus-ponens tm-153 tm-762 ((A (or (and Am (and (not (-> (and B C) C)) Cm)) (and (not (-> (and B C) C)) Cm))) (Bm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-8 tm-3)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64665.        (not ((A and ((not ((B and C) -> C)) and D)) or ((not ((B and C) -> C)) and D))), M:tm-153, m:tm-762, u:((A (or (and Am (and (not (-> (and B C) C)) Cm)) (and (not (-> (and B C) C)) Cm))) (Bm (not (-> (and B C) C))))
================================================================
tm-name          tm-64666
in-theory        64666
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     27
proof            (modus-ponens tm-147 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64666.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-147, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64667
in-theory        64667
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) and D)) or ((B and C) and D)) -> B)
theorem-size     15
proof            (modus-ponens tm-135 tm-762 ((A (or (and Am (and (and B C) Cm)) (and (and B C) Cm))) (Bm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64667.        (((A and ((B and C) and D)) or ((B and C) and D)) -> B), M:tm-135, m:tm-762, u:((A (or (and Am (and (and B C) Cm)) (and (and B C) Cm))) (Bm (and B C)))
================================================================
tm-name          tm-64668
in-theory        64668
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-134 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64668.        ((A -> ((B and C) -> B)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-134, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64669
in-theory        64669
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and ((not ((B and C) -> B)) and D)) or ((not ((B and C) -> B)) and D)))
theorem-size     20
proof            (modus-ponens tm-130 tm-762 ((A (or (and Am (and (not (-> (and B C) B)) Cm)) (and (not (-> (and B C) B)) Cm))) (Bm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-8 tm-4)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64669.        (not ((A and ((not ((B and C) -> B)) and D)) or ((not ((B and C) -> B)) and D))), M:tm-130, m:tm-762, u:((A (or (and Am (and (not (-> (and B C) B)) Cm)) (and (not (-> (and B C) B)) Cm))) (Bm (not (-> (and B C) B))))
================================================================
tm-name          tm-64670
in-theory        64670
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     27
proof            (modus-ponens tm-125 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64670.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E and F)) or (E and F)) -> E)), M:tm-125, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64671
in-theory        64671
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) and E)) or ((B -> (C -> D)) and E)) -> ((B -> C) -> (B -> D)))
theorem-size     25
proof            (modus-ponens tm-114 tm-762 ((A (or (and Am (and (-> B (-> C D)) Cm)) (and (-> B (-> C D)) Cm))) (Bm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-3)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64671.        (((A and ((B -> (C -> D)) and E)) or ((B -> (C -> D)) and E)) -> ((B -> C) -> (B -> D))), M:tm-114, m:tm-762, u:((A (or (and Am (and (-> B (-> C D)) Cm)) (and (-> B (-> C D)) Cm))) (Bm (-> B (-> C D))))
================================================================
tm-name          tm-64672
in-theory        64672
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F and G)) or (F and G)) -> F))
theorem-size     27
proof            (modus-ponens tm-113 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 tm-3)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64672.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F and G)) or (F and G)) -> F)), M:tm-113, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64673
in-theory        64673
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and ((not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E)) or ((not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E)))
theorem-size     36
proof            (modus-ponens tm-109 tm-762 ((A (or (and Am (and (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))) Cm)) (and (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))) Cm))) (Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-8 tm-4 tm-3)
proof-size       144
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64673.        (not ((A and ((not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E)) or ((not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and E))), M:tm-109, m:tm-762, u:((A (or (and Am (and (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))) Cm)) (and (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))) Cm))) (Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-64674
in-theory        64674
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     31
proof            (modus-ponens tm-105 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64674.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E and F)) or (E and F)) -> E)), M:tm-105, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64675
in-theory        64675
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (D and E)) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-95 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 tm-3)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64675.        (((A -> B) -> (A -> A)) and (((C and (D and E)) or (D and E)) -> D)), M:tm-95, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64676
in-theory        64676
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) and D)) or ((B -> C) and D)) -> (B -> C))
theorem-size     17
proof            (modus-ponens tm-87 tm-762 ((A (or (and Am (and (-> B C) Cm)) (and (-> B C) Cm))) (Bm (-> B C))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64676.        (((A and ((B -> C) and D)) or ((B -> C) and D)) -> (B -> C)), M:tm-87, m:tm-762, u:((A (or (and Am (and (-> B C) Cm)) (and (-> B C) Cm))) (Bm (-> B C)))
================================================================
tm-name          tm-64677
in-theory        64677
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> (D -> B))
theorem-size     13
proof            (modus-ponens tm-84 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-3)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64677.        (((A and (B and C)) or (B and C)) -> (D -> B)), M:tm-84, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64678
in-theory        64678
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     19
proof            (modus-ponens tm-83 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64678.        ((A -> (B -> (C -> B))) and (((D and (E and F)) or (E and F)) -> E)), M:tm-83, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64679
in-theory        64679
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and ((not (B -> (C -> B))) and D)) or ((not (B -> (C -> B))) and D)))
theorem-size     20
proof            (modus-ponens tm-79 tm-762 ((A (or (and Am (and (not (-> B (-> C B))) Cm)) (and (not (-> B (-> C B))) Cm))) (Bm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-8 tm-4 tm-3)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64679.        (not ((A and ((not (B -> (C -> B))) and D)) or ((not (B -> (C -> B))) and D))), M:tm-79, m:tm-762, u:((A (or (and Am (and (not (-> B (-> C B))) Cm)) (and (not (-> B (-> C B))) Cm))) (Bm (not (-> B (-> C B)))))
================================================================
tm-name          tm-64680
in-theory        64680
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (C and D)) or (C and D)) -> C))
theorem-size     17
proof            (modus-ponens tm-76 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64680.        (((not (not A)) -> A) and (((B and (C and D)) or (C and D)) -> C)), M:tm-76, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64681
in-theory        64681
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (B and C)) or (B and C)))) or ((A and (B and C)) or (B and C))) -> B)
theorem-size     23
proof            (modus-ponens tm-73 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-8 tm-10 tm-4 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64681.        (((not (not ((A and (B and C)) or (B and C)))) or ((A and (B and C)) or (B and C))) -> B), M:tm-73, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64682
in-theory        64682
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D and E)) or (D and E)) -> D))
theorem-size     23
proof            (modus-ponens tm-69 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64682.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D and E)) or (D and E)) -> D)), M:tm-69, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64683
in-theory        64683
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     25
proof            (modus-ponens tm-54 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-8 tm-4 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64683.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E and F)) or (E and F)) -> E)), M:tm-54, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64684
in-theory        64684
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((C and (A and B)) or (A and B))) -> A)
theorem-size     15
proof            (modus-ponens tm-50 tm-762 ((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Bm)))
axioms-used      (tm-8 tm-7 tm-4 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64684.        (((A and B) or ((C and (A and B)) or (A and B))) -> A), M:tm-50, m:tm-762, u:((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Bm))
================================================================
tm-name          tm-64685
in-theory        64685
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or ((A and (B and C)) or (B and C))) -> B)
theorem-size     17
proof            (modus-ponens tm-49 tm-762 ((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Bm)))
axioms-used      (tm-8 tm-6 tm-4 tm-3)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64685.        (((A and (B and C)) or ((A and (B and C)) or (B and C))) -> B), M:tm-49, m:tm-762, u:((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Bm))
================================================================
tm-name          tm-64686
in-theory        64686
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C and D)) or (C and D))) or ((B and (C and D)) or (C and D))) -> C)
theorem-size     23
proof            (modus-ponens tm-47 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-8 tm-4 tm-3)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64686.        (((A and ((B and (C and D)) or (C and D))) or ((B and (C and D)) or (C and D))) -> C), M:tm-47, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64687
in-theory        64687
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B and C)) or (B and C)) and D) or ((A and (B and C)) or (B and C))) -> B)
theorem-size     23
proof            (modus-ponens tm-46 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-8 tm-3 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64687.        (((((A and (B and C)) or (B and C)) and D) or ((A and (B and C)) or (B and C))) -> B), M:tm-46, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64688
in-theory        64688
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (D and E)) or (D and E)) -> D))
theorem-size     17
proof            (modus-ponens tm-42 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64688.        ((A -> (B or A)) and (((C and (D and E)) or (D and E)) -> D)), M:tm-42, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64689
in-theory        64689
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (D and E)) or (D and E)) -> D))
theorem-size     17
proof            (modus-ponens tm-32 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64689.        ((A -> (A or B)) and (((C and (D and E)) or (D and E)) -> D)), M:tm-32, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64690
in-theory        64690
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> (((A and (B and C)) or (B and C)) and B))
theorem-size     21
proof            (modus-ponens tm-24 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64690.        (((A and (B and C)) or (B and C)) -> (((A and (B and C)) or (B and C)) and B)), M:tm-24, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64691
in-theory        64691
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (D and E)) or (D and E)) -> D))
theorem-size     19
proof            (modus-ponens tm-23 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-8 tm-4 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64691.        ((A -> (B -> (A and B))) and (((C and (D and E)) or (D and E)) -> D)), M:tm-23, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64692
in-theory        64692
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (D and E)) or (D and E)) -> D))
theorem-size     17
proof            (modus-ponens tm-22 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64692.        (((A and B) -> B) and (((C and (D and E)) or (D and E)) -> D)), M:tm-22, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64693
in-theory        64693
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (D and E)) or (D and E)) -> D))
theorem-size     17
proof            (modus-ponens tm-21 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64693.        (((A and B) -> A) and (((C and (D and E)) or (D and E)) -> D)), M:tm-21, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64694
in-theory        64694
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E and F)) or (E and F)) -> E))
theorem-size     25
proof            (modus-ponens tm-20 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-3)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64694.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E and F)) or (E and F)) -> E)), M:tm-20, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64695
in-theory        64695
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (D and E)) or (D and E)) -> D))
theorem-size     17
proof            (modus-ponens tm-19 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64695.        ((A -> (B -> A)) and (((C and (D and E)) or (D and E)) -> D)), M:tm-19, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64696
in-theory        64696
times-derived    2
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> ((A and (B and C)) or (B and C)))
theorem-size     19
proof            (modus-ponens tm-12 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-3)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64696.        (((A and (B and C)) or (B and C)) -> ((A and (B and C)) or (B and C))), M:tm-12, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64697
in-theory        64697
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> (not B)) -> (not ((A and (B and C)) or (B and C))))
theorem-size     23
proof            (modus-ponens tm-9 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-9 tm-8 tm-4 tm-3)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64697.        ((((A and (B and C)) or (B and C)) -> (not B)) -> (not ((A and (B and C)) or (B and C)))), M:tm-9, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64698
in-theory        64698
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C and (A and D)) or (A and D)) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-762 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm)))
axioms-used      (tm-8 tm-4 tm-3)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64698.        ((A -> B) -> ((((C and (A and D)) or (A and D)) or A) -> B)), M:tm-8, m:tm-762, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Bm))
================================================================
tm-name          tm-64699
in-theory        64699
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (C and D)) or (C and D)) -> C))
theorem-size     13
proof            (modus-ponens tm-7 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-7 tm-8 tm-4 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64699.        (A or (((B and (C and D)) or (C and D)) -> C)), M:tm-7, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64700
in-theory        64700
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> B) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-6 tm-8 tm-4 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64700.        ((((A and (B and C)) or (B and C)) -> B) or D), M:tm-6, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64701
in-theory        64701
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (C and D)) or (C and D)) -> C) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-5 tm-8 tm-4 tm-3)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64701.        (A -> ((((B and (C and D)) or (C and D)) -> C) and A)), M:tm-5, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64702
in-theory        64702
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> C) and D)) or ((B -> C) and D)) -> B) -> (((A and ((B -> C) and D)) or ((B -> C) and D)) -> C))
theorem-size     31
proof            (modus-ponens tm-2 tm-762 ((A (or (and Am (and (-> B C) Cm)) (and (-> B C) Cm))) (Bm (-> B C))))
axioms-used      (tm-2 tm-8 tm-4 tm-3)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64702.        ((((A and ((B -> C) and D)) or ((B -> C) and D)) -> B) -> (((A and ((B -> C) and D)) or ((B -> C) and D)) -> C)), M:tm-2, m:tm-762, u:((A (or (and Am (and (-> B C) Cm)) (and (-> B C) Cm))) (Bm (-> B C)))
================================================================
tm-name          tm-64703
in-theory        64703
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (C and D)) or (C and D)) -> C))
theorem-size     13
proof            (modus-ponens tm-1 tm-762 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm))))
axioms-used      (tm-1 tm-8 tm-4 tm-3)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-762.          (((A and (B and C)) or (B and C)) -> B), M:tm-47, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-64703.        (A -> (((B and (C and D)) or (C and D)) -> C)), M:tm-1, m:tm-762, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Bm)))
================================================================
tm-name          tm-64704
in-theory        64704
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     23
proof            (modus-ponens tm-757 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64704.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-757, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64705
in-theory        64705
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (((((A and (B and C)) or (B and C)) and D) or ((A and (B and C)) or (B and C))) -> C))
theorem-size     35
proof            (modus-ponens tm-747 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64705.        ((((A and (B and C)) or (B and C)) -> C) and (((((A and (B and C)) or (B and C)) and D) or ((A and (B and C)) or (B and C))) -> C)), M:tm-747, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64706
in-theory        64706
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F and G)) or (F and G)) -> G))
theorem-size     37
proof            (modus-ponens tm-708 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64706.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F and G)) or (F and G)) -> G)), M:tm-708, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64707
in-theory        64707
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     25
proof            (modus-ponens tm-665 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64707.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-665, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64708
in-theory        64708
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> (D or C))
theorem-size     13
proof            (modus-ponens tm-623 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64708.        (((A and (B and C)) or (B and C)) -> (D or C)), M:tm-623, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64709
in-theory        64709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-622 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64709.        ((A -> (B -> (C or B))) and (((D and (E and F)) or (E and F)) -> F)), M:tm-622, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64710
in-theory        64710
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and (B and (not (C -> (D or C))))) or (B and (not (C -> (D or C))))))
theorem-size     20
proof            (modus-ponens tm-618 tm-763 ((A (or (and Am (and Bm (not (-> B (or C B))))) (and Bm (not (-> B (or C B)))))) (Cm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-8 tm-4)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64710.        (not ((A and (B and (not (C -> (D or C))))) or (B and (not (C -> (D or C)))))), M:tm-618, m:tm-763, u:((A (or (and Am (and Bm (not (-> B (or C B))))) (and Bm (not (-> B (or C B)))))) (Cm (not (-> B (or C B)))))
================================================================
tm-name          tm-64711
in-theory        64711
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64711.        ((((A and (B and C)) or (B and C)) -> C) and (D -> (E or D))), M:tm-609, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64712
in-theory        64712
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     21
proof            (modus-ponens tm-605 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64712.        ((A -> ((B -> (C or B)) and A)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-605, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64713
in-theory        64713
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and ((D -> (E or D)) and (((A and (B and C)) or (B and C)) -> C)))
theorem-size     29
proof            (modus-ponens tm-595 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64713.        ((((A and (B and C)) or (B and C)) -> C) and ((D -> (E or D)) and (((A and (B and C)) or (B and C)) -> C))), M:tm-595, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64714
in-theory        64714
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-550 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64714.        (((A -> (B or A)) or C) and (((D and (E and F)) or (E and F)) -> F)), M:tm-550, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64715
in-theory        64715
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-540 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64715.        ((A or (B -> (C or B))) and (((D and (E and F)) or (E and F)) -> F)), M:tm-540, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64716
in-theory        64716
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-530 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64716.        ((A or (B -> (B or C))) and (((D and (E and F)) or (E and F)) -> F)), M:tm-530, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64717
in-theory        64717
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     21
proof            (modus-ponens tm-520 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64717.        ((A or (B -> (C -> (B and C)))) and (((D and (E and F)) or (E and F)) -> F)), M:tm-520, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64718
in-theory        64718
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-510 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64718.        ((A or ((B and C) -> C)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-510, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64719
in-theory        64719
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-500 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64719.        ((A or ((B and C) -> B)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-500, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64720
in-theory        64720
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F and G)) or (F and G)) -> G))
theorem-size     27
proof            (modus-ponens tm-490 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64720.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F and G)) or (F and G)) -> G)), M:tm-490, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64721
in-theory        64721
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-480 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64721.        ((A or (B -> (C -> B))) and (((D and (E and F)) or (E and F)) -> F)), M:tm-480, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64722
in-theory        64722
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> (C or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64722.        (((A and (B and C)) or (B and C)) -> (C or D)), M:tm-470, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64723
in-theory        64723
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-469 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64723.        ((A -> (B -> (B or C))) and (((D and (E and F)) or (E and F)) -> F)), M:tm-469, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64724
in-theory        64724
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and (B and (not (C -> (C or D))))) or (B and (not (C -> (C or D))))))
theorem-size     20
proof            (modus-ponens tm-465 tm-763 ((A (or (and Am (and Bm (not (-> B (or B C))))) (and Bm (not (-> B (or B C)))))) (Cm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-8 tm-4)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64724.        (not ((A and (B and (not (C -> (C or D))))) or (B and (not (C -> (C or D)))))), M:tm-465, m:tm-763, u:((A (or (and Am (and Bm (not (-> B (or B C))))) (and Bm (not (-> B (or B C)))))) (Cm (not (-> B (or B C)))))
================================================================
tm-name          tm-64725
in-theory        64725
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64725.        ((((A and (B and C)) or (B and C)) -> C) and (D -> (D or E))), M:tm-456, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64726
in-theory        64726
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     21
proof            (modus-ponens tm-453 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64726.        ((A -> ((B -> (B or C)) and A)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-453, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64727
in-theory        64727
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and ((D -> (D or E)) and (((A and (B and C)) or (B and C)) -> C)))
theorem-size     29
proof            (modus-ponens tm-443 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64727.        ((((A and (B and C)) or (B and C)) -> C) and ((D -> (D or E)) and (((A and (B and C)) or (B and C)) -> C))), M:tm-443, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64728
in-theory        64728
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-409 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64728.        (((A -> (A or B)) or C) and (((D and (E and F)) or (E and F)) -> F)), M:tm-409, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64729
in-theory        64729
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     21
proof            (modus-ponens tm-400 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64729.        (((A -> (B -> (A and B))) or C) and (((D and (E and F)) or (E and F)) -> F)), M:tm-400, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64730
in-theory        64730
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-391 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64730.        ((((A and B) -> B) or C) and (((D and (E and F)) or (E and F)) -> F)), M:tm-391, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64731
in-theory        64731
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-382 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64731.        ((((A and B) -> A) or C) and (((D and (E and F)) or (E and F)) -> F)), M:tm-382, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64732
in-theory        64732
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F and G)) or (F and G)) -> G))
theorem-size     27
proof            (modus-ponens tm-373 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64732.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F and G)) or (F and G)) -> G)), M:tm-373, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64733
in-theory        64733
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-364 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64733.        (((A -> (B -> A)) or C) and (((D and (E and F)) or (E and F)) -> F)), M:tm-364, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64734
in-theory        64734
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> (D -> (C and D)))
theorem-size     15
proof            (modus-ponens tm-355 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64734.        (((A and (B and C)) or (B and C)) -> (D -> (C and D))), M:tm-355, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64735
in-theory        64735
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     21
proof            (modus-ponens tm-354 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64735.        ((A -> (B -> (C -> (B and C)))) and (((D and (E and F)) or (E and F)) -> F)), M:tm-354, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64736
in-theory        64736
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and (B and (not (C -> (D -> (C and D)))))) or (B and (not (C -> (D -> (C and D)))))))
theorem-size     24
proof            (modus-ponens tm-350 tm-763 ((A (or (and Am (and Bm (not (-> B (-> C (and B C)))))) (and Bm (not (-> B (-> C (and B C))))))) (Cm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-8 tm-4)
proof-size       114
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64736.        (not ((A and (B and (not (C -> (D -> (C and D)))))) or (B and (not (C -> (D -> (C and D))))))), M:tm-350, m:tm-763, u:((A (or (and Am (and Bm (not (-> B (-> C (and B C)))))) (and Bm (not (-> B (-> C (and B C))))))) (Cm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-64737
in-theory        64737
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64737.        ((((A and (B and C)) or (B and C)) -> C) and (D -> (E -> (D and E)))), M:tm-341, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64738
in-theory        64738
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (D and E)) or (D and E)) -> E))
theorem-size     21
proof            (modus-ponens tm-338 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64738.        (((A -> B) -> (A -> (A and B))) and (((C and (D and E)) or (D and E)) -> E)), M:tm-338, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64739
in-theory        64739
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (((A and (B and C)) or (B and C)) -> (((A and (B and C)) or (B and C)) and C)))
theorem-size     33
proof            (modus-ponens tm-328 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64739.        ((((A and (B and C)) or (B and C)) -> C) and (((A and (B and C)) or (B and C)) -> (((A and (B and C)) or (B and C)) and C))), M:tm-328, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64740
in-theory        64740
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and ((D -> (E -> (D and E))) and (((A and (B and C)) or (B and C)) -> C)))
theorem-size     31
proof            (modus-ponens tm-327 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64740.        ((((A and (B and C)) or (B and C)) -> C) and ((D -> (E -> (D and E))) and (((A and (B and C)) or (B and C)) -> C))), M:tm-327, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64741
in-theory        64741
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (((D and E) -> E) and (((A and (B and C)) or (B and C)) -> C)))
theorem-size     29
proof            (modus-ponens tm-326 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64741.        ((((A and (B and C)) or (B and C)) -> C) and (((D and E) -> E) and (((A and (B and C)) or (B and C)) -> C))), M:tm-326, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64742
in-theory        64742
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (((D and E) -> D) and (((A and (B and C)) or (B and C)) -> C)))
theorem-size     29
proof            (modus-ponens tm-325 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64742.        ((((A and (B and C)) or (B and C)) -> C) and (((D and E) -> D) and (((A and (B and C)) or (B and C)) -> C))), M:tm-325, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64743
in-theory        64743
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B and C)) or (B and C)) -> C)))
theorem-size     37
proof            (modus-ponens tm-324 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64743.        ((((A and (B and C)) or (B and C)) -> C) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B and C)) or (B and C)) -> C))), M:tm-324, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64744
in-theory        64744
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and ((D -> (E -> D)) and (((A and (B and C)) or (B and C)) -> C)))
theorem-size     29
proof            (modus-ponens tm-323 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64744.        ((((A and (B and C)) or (B and C)) -> C) and ((D -> (E -> D)) and (((A and (B and C)) or (B and C)) -> C))), M:tm-323, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64745
in-theory        64745
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64745.        ((((A and (B and C)) or (B and C)) -> C) and ((D and E) -> E)), M:tm-322, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64746
in-theory        64746
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64746.        ((((A and (B and C)) or (B and C)) -> C) and ((D and E) -> D)), M:tm-320, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64747
in-theory        64747
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64747.        ((((A and (B and C)) or (B and C)) -> C) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64748
in-theory        64748
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (((A and (B and C)) or (B and C)) -> ((A and (B and C)) or (B and C))))
theorem-size     31
proof            (modus-ponens tm-316 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64748.        ((((A and (B and C)) or (B and C)) -> C) and (((A and (B and C)) or (B and C)) -> ((A and (B and C)) or (B and C)))), M:tm-316, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64749
in-theory        64749
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64749.        ((((A and (B and C)) or (B and C)) -> C) and (D -> (E -> D))), M:tm-315, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64750
in-theory        64750
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and ((((A and (B and C)) or (B and C)) -> (not C)) -> (not ((A and (B and C)) or (B and C)))))
theorem-size     35
proof            (modus-ponens tm-313 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64750.        ((((A and (B and C)) or (B and C)) -> C) and ((((A and (B and C)) or (B and C)) -> (not C)) -> (not ((A and (B and C)) or (B and C))))), M:tm-313, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64751
in-theory        64751
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and ((C -> D) -> ((((A and (B and C)) or (B and C)) or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-312 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64751.        ((((A and (B and C)) or (B and C)) -> C) and ((C -> D) -> ((((A and (B and C)) or (B and C)) or C) -> D))), M:tm-312, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64752
in-theory        64752
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (D or (((A and (B and C)) or (B and C)) -> C)))
theorem-size     25
proof            (modus-ponens tm-311 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64752.        ((((A and (B and C)) or (B and C)) -> C) and (D or (((A and (B and C)) or (B and C)) -> C))), M:tm-311, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64753
in-theory        64753
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and ((((A and (B and C)) or (B and C)) -> C) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64753.        ((((A and (B and C)) or (B and C)) -> C) and ((((A and (B and C)) or (B and C)) -> C) or D)), M:tm-310, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64754
in-theory        64754
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (D -> ((((A and (B and C)) or (B and C)) -> C) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64754.        ((((A and (B and C)) or (B and C)) -> C) and (D -> ((((A and (B and C)) or (B and C)) -> C) and D))), M:tm-309, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64755
in-theory        64755
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and (C -> D))) or (B and (C -> D))) -> (C -> D)) and ((((A and (B and (C -> D))) or (B and (C -> D))) -> C) -> (((A and (B and (C -> D))) or (B and (C -> D))) -> D)))
theorem-size     49
proof            (modus-ponens tm-306 tm-763 ((A (or (and Am (and Bm (-> B C))) (and Bm (-> B C)))) (Cm (-> B C))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64755.        ((((A and (B and (C -> D))) or (B and (C -> D))) -> (C -> D)) and ((((A and (B and (C -> D))) or (B and (C -> D))) -> C) -> (((A and (B and (C -> D))) or (B and (C -> D))) -> D))), M:tm-306, m:tm-763, u:((A (or (and Am (and Bm (-> B C))) (and Bm (-> B C)))) (Cm (-> B C)))
================================================================
tm-name          tm-64756
in-theory        64756
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) and (D -> (((A and (B and C)) or (B and C)) -> C)))
theorem-size     25
proof            (modus-ponens tm-305 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64756.        ((((A and (B and C)) or (B and C)) -> C) and (D -> (((A and (B and C)) or (B and C)) -> C))), M:tm-305, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64757
in-theory        64757
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     23
proof            (modus-ponens tm-303 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64757.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-303, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64758
in-theory        64758
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     21
proof            (modus-ponens tm-270 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64758.        ((A -> (((B and C) -> C) and A)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-270, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64759
in-theory        64759
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     21
proof            (modus-ponens tm-239 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64759.        ((A -> (((B and C) -> B) and A)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-239, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64760
in-theory        64760
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F and G)) or (F and G)) -> G))
theorem-size     29
proof            (modus-ponens tm-210 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64760.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F and G)) or (F and G)) -> G)), M:tm-210, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64761
in-theory        64761
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     21
proof            (modus-ponens tm-183 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64761.        ((A -> ((B -> (C -> B)) and A)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-183, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64762
in-theory        64762
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and (C and D))) or (B and (C and D))) -> D)
theorem-size     15
proof            (modus-ponens tm-158 tm-763 ((A (or (and Am (and Bm (and B C))) (and Bm (and B C)))) (Cm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-8)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64762.        (((A and (B and (C and D))) or (B and (C and D))) -> D), M:tm-158, m:tm-763, u:((A (or (and Am (and Bm (and B C))) (and Bm (and B C)))) (Cm (and B C)))
================================================================
tm-name          tm-64763
in-theory        64763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-157 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64763.        ((A -> ((B and C) -> C)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-157, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64764
in-theory        64764
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and (B and (not ((C and D) -> D)))) or (B and (not ((C and D) -> D)))))
theorem-size     20
proof            (modus-ponens tm-153 tm-763 ((A (or (and Am (and Bm (not (-> (and B C) C)))) (and Bm (not (-> (and B C) C))))) (Cm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-8)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64764.        (not ((A and (B and (not ((C and D) -> D)))) or (B and (not ((C and D) -> D))))), M:tm-153, m:tm-763, u:((A (or (and Am (and Bm (not (-> (and B C) C)))) (and Bm (not (-> (and B C) C))))) (Cm (not (-> (and B C) C))))
================================================================
tm-name          tm-64765
in-theory        64765
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     27
proof            (modus-ponens tm-147 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64765.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-147, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64766
in-theory        64766
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and (C and D))) or (B and (C and D))) -> C)
theorem-size     15
proof            (modus-ponens tm-135 tm-763 ((A (or (and Am (and Bm (and B C))) (and Bm (and B C)))) (Cm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64766.        (((A and (B and (C and D))) or (B and (C and D))) -> C), M:tm-135, m:tm-763, u:((A (or (and Am (and Bm (and B C))) (and Bm (and B C)))) (Cm (and B C)))
================================================================
tm-name          tm-64767
in-theory        64767
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-134 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64767.        ((A -> ((B and C) -> B)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-134, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64768
in-theory        64768
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and (B and (not ((C and D) -> C)))) or (B and (not ((C and D) -> C)))))
theorem-size     20
proof            (modus-ponens tm-130 tm-763 ((A (or (and Am (and Bm (not (-> (and B C) B)))) (and Bm (not (-> (and B C) B))))) (Cm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-8 tm-4)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64768.        (not ((A and (B and (not ((C and D) -> C)))) or (B and (not ((C and D) -> C))))), M:tm-130, m:tm-763, u:((A (or (and Am (and Bm (not (-> (and B C) B)))) (and Bm (not (-> (and B C) B))))) (Cm (not (-> (and B C) B))))
================================================================
tm-name          tm-64769
in-theory        64769
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     27
proof            (modus-ponens tm-125 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64769.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E and F)) or (E and F)) -> F)), M:tm-125, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64770
in-theory        64770
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and (C -> (D -> E)))) or (B and (C -> (D -> E)))) -> ((C -> D) -> (C -> E)))
theorem-size     25
proof            (modus-ponens tm-114 tm-763 ((A (or (and Am (and Bm (-> B (-> C D)))) (and Bm (-> B (-> C D))))) (Cm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64770.        (((A and (B and (C -> (D -> E)))) or (B and (C -> (D -> E)))) -> ((C -> D) -> (C -> E))), M:tm-114, m:tm-763, u:((A (or (and Am (and Bm (-> B (-> C D)))) (and Bm (-> B (-> C D))))) (Cm (-> B (-> C D))))
================================================================
tm-name          tm-64771
in-theory        64771
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F and G)) or (F and G)) -> G))
theorem-size     27
proof            (modus-ponens tm-113 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64771.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F and G)) or (F and G)) -> G)), M:tm-113, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64772
in-theory        64772
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and (B and (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) or (B and (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))))
theorem-size     36
proof            (modus-ponens tm-109 tm-763 ((A (or (and Am (and Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))) (and Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Cm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-8 tm-4)
proof-size       144
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64772.        (not ((A and (B and (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))) or (B and (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))), M:tm-109, m:tm-763, u:((A (or (and Am (and Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))) (and Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (Cm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-64773
in-theory        64773
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     31
proof            (modus-ponens tm-105 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64773.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E and F)) or (E and F)) -> F)), M:tm-105, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64774
in-theory        64774
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (D and E)) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-95 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64774.        (((A -> B) -> (A -> A)) and (((C and (D and E)) or (D and E)) -> E)), M:tm-95, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64775
in-theory        64775
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and (C -> D))) or (B and (C -> D))) -> (C -> D))
theorem-size     17
proof            (modus-ponens tm-87 tm-763 ((A (or (and Am (and Bm (-> B C))) (and Bm (-> B C)))) (Cm (-> B C))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64775.        (((A and (B and (C -> D))) or (B and (C -> D))) -> (C -> D)), M:tm-87, m:tm-763, u:((A (or (and Am (and Bm (-> B C))) (and Bm (-> B C)))) (Cm (-> B C)))
================================================================
tm-name          tm-64776
in-theory        64776
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> (D -> C))
theorem-size     13
proof            (modus-ponens tm-84 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64776.        (((A and (B and C)) or (B and C)) -> (D -> C)), M:tm-84, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64777
in-theory        64777
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     19
proof            (modus-ponens tm-83 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64777.        ((A -> (B -> (C -> B))) and (((D and (E and F)) or (E and F)) -> F)), M:tm-83, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64778
in-theory        64778
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and (B and (not (C -> (D -> C))))) or (B and (not (C -> (D -> C))))))
theorem-size     20
proof            (modus-ponens tm-79 tm-763 ((A (or (and Am (and Bm (not (-> B (-> C B))))) (and Bm (not (-> B (-> C B)))))) (Cm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-8 tm-4)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64778.        (not ((A and (B and (not (C -> (D -> C))))) or (B and (not (C -> (D -> C)))))), M:tm-79, m:tm-763, u:((A (or (and Am (and Bm (not (-> B (-> C B))))) (and Bm (not (-> B (-> C B)))))) (Cm (not (-> B (-> C B)))))
================================================================
tm-name          tm-64779
in-theory        64779
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (C and D)) or (C and D)) -> D))
theorem-size     17
proof            (modus-ponens tm-76 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64779.        (((not (not A)) -> A) and (((B and (C and D)) or (C and D)) -> D)), M:tm-76, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64780
in-theory        64780
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (B and C)) or (B and C)))) or ((A and (B and C)) or (B and C))) -> C)
theorem-size     23
proof            (modus-ponens tm-73 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-8 tm-10 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64780.        (((not (not ((A and (B and C)) or (B and C)))) or ((A and (B and C)) or (B and C))) -> C), M:tm-73, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64781
in-theory        64781
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D and E)) or (D and E)) -> E))
theorem-size     23
proof            (modus-ponens tm-69 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64781.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D and E)) or (D and E)) -> E)), M:tm-69, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64782
in-theory        64782
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     25
proof            (modus-ponens tm-54 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64782.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E and F)) or (E and F)) -> F)), M:tm-54, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64783
in-theory        64783
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((C and (A and B)) or (A and B))) -> B)
theorem-size     15
proof            (modus-ponens tm-50 tm-763 ((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Cm)))
axioms-used      (tm-8 tm-7 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64783.        (((A and B) or ((C and (A and B)) or (A and B))) -> B), M:tm-50, m:tm-763, u:((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Cm))
================================================================
tm-name          tm-64784
in-theory        64784
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or ((A and (B and C)) or (B and C))) -> C)
theorem-size     17
proof            (modus-ponens tm-49 tm-763 ((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Cm)))
axioms-used      (tm-8 tm-6 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64784.        (((A and (B and C)) or ((A and (B and C)) or (B and C))) -> C), M:tm-49, m:tm-763, u:((A (and Am (and Bm Cm))) (B (and Bm Cm)) (C Cm))
================================================================
tm-name          tm-64785
in-theory        64785
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C and D)) or (C and D))) or ((B and (C and D)) or (C and D))) -> D)
theorem-size     23
proof            (modus-ponens tm-47 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-8 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64785.        (((A and ((B and (C and D)) or (C and D))) or ((B and (C and D)) or (C and D))) -> D), M:tm-47, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64786
in-theory        64786
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B and C)) or (B and C)) and D) or ((A and (B and C)) or (B and C))) -> C)
theorem-size     23
proof            (modus-ponens tm-46 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-8 tm-3 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64786.        (((((A and (B and C)) or (B and C)) and D) or ((A and (B and C)) or (B and C))) -> C), M:tm-46, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64787
in-theory        64787
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (D and E)) or (D and E)) -> E))
theorem-size     17
proof            (modus-ponens tm-42 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64787.        ((A -> (B or A)) and (((C and (D and E)) or (D and E)) -> E)), M:tm-42, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64788
in-theory        64788
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (D and E)) or (D and E)) -> E))
theorem-size     17
proof            (modus-ponens tm-32 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64788.        ((A -> (A or B)) and (((C and (D and E)) or (D and E)) -> E)), M:tm-32, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64789
in-theory        64789
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B and C)) or (B and C)) -> (((A and (B and C)) or (B and C)) and C))
theorem-size     21
proof            (modus-ponens tm-24 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64789.        (((A and (B and C)) or (B and C)) -> (((A and (B and C)) or (B and C)) and C)), M:tm-24, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64790
in-theory        64790
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (D and E)) or (D and E)) -> E))
theorem-size     19
proof            (modus-ponens tm-23 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64790.        ((A -> (B -> (A and B))) and (((C and (D and E)) or (D and E)) -> E)), M:tm-23, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64791
in-theory        64791
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (D and E)) or (D and E)) -> E))
theorem-size     17
proof            (modus-ponens tm-22 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64791.        (((A and B) -> B) and (((C and (D and E)) or (D and E)) -> E)), M:tm-22, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64792
in-theory        64792
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (D and E)) or (D and E)) -> E))
theorem-size     17
proof            (modus-ponens tm-21 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64792.        (((A and B) -> A) and (((C and (D and E)) or (D and E)) -> E)), M:tm-21, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64793
in-theory        64793
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E and F)) or (E and F)) -> F))
theorem-size     25
proof            (modus-ponens tm-20 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64793.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E and F)) or (E and F)) -> F)), M:tm-20, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64794
in-theory        64794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (D and E)) or (D and E)) -> E))
theorem-size     17
proof            (modus-ponens tm-19 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64794.        ((A -> (B -> A)) and (((C and (D and E)) or (D and E)) -> E)), M:tm-19, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64795
in-theory        64795
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> (not C)) -> (not ((A and (B and C)) or (B and C))))
theorem-size     23
proof            (modus-ponens tm-9 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-9 tm-8 tm-4)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64795.        ((((A and (B and C)) or (B and C)) -> (not C)) -> (not ((A and (B and C)) or (B and C)))), M:tm-9, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64796
in-theory        64796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C and (D and A)) or (D and A)) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-763 ((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm)))
axioms-used      (tm-8 tm-4)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64796.        ((A -> B) -> ((((C and (D and A)) or (D and A)) or A) -> B)), M:tm-8, m:tm-763, u:((A (or (and Am (and Bm Cm)) (and Bm Cm))) (B Cm))
================================================================
tm-name          tm-64797
in-theory        64797
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (C and D)) or (C and D)) -> D))
theorem-size     13
proof            (modus-ponens tm-7 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-7 tm-8 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64797.        (A or (((B and (C and D)) or (C and D)) -> D)), M:tm-7, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64798
in-theory        64798
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and C)) or (B and C)) -> C) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-6 tm-8 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64798.        ((((A and (B and C)) or (B and C)) -> C) or D), M:tm-6, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64799
in-theory        64799
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (C and D)) or (C and D)) -> D) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64799.        (A -> ((((B and (C and D)) or (C and D)) -> D) and A)), M:tm-5, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64800
in-theory        64800
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B and (C -> D))) or (B and (C -> D))) -> C) -> (((A and (B and (C -> D))) or (B and (C -> D))) -> D))
theorem-size     31
proof            (modus-ponens tm-2 tm-763 ((A (or (and Am (and Bm (-> B C))) (and Bm (-> B C)))) (Cm (-> B C))))
axioms-used      (tm-2 tm-8 tm-4)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64800.        ((((A and (B and (C -> D))) or (B and (C -> D))) -> C) -> (((A and (B and (C -> D))) or (B and (C -> D))) -> D)), M:tm-2, m:tm-763, u:((A (or (and Am (and Bm (-> B C))) (and Bm (-> B C)))) (Cm (-> B C)))
================================================================
tm-name          tm-64801
in-theory        64801
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (C and D)) or (C and D)) -> D))
theorem-size     13
proof            (modus-ponens tm-1 tm-763 ((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm))))
axioms-used      (tm-1 tm-8 tm-4)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-763.          (((A and (B and C)) or (B and C)) -> C), M:tm-47, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-64801.        (A -> (((B and (C and D)) or (C and D)) -> D)), M:tm-1, m:tm-763, u:((A (-> (or (and Am (and Bm Cm)) (and Bm Cm)) Cm)))
================================================================
tm-name          tm-64802
in-theory        64802
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64802.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-757, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64803
in-theory        64803
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (((((A and B) or B) and D) or ((A and B) or B)) -> (C -> (B and C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64803.        ((((A and B) or B) -> (C -> (B and C))) and (((((A and B) or B) and D) or ((A and B) or B)) -> (C -> (B and C)))), M:tm-747, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64804
in-theory        64804
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (G -> (F and G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64804.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (G -> (F and G)))), M:tm-708, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64805
in-theory        64805
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64805.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-665, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64806
in-theory        64806
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (D -> (B and D))))
theorem-size     13
proof            (modus-ponens tm-623 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64806.        (((A and B) or B) -> (C or (D -> (B and D)))), M:tm-623, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64807
in-theory        64807
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64807.        ((A -> (B -> (C or B))) and (((D and E) or E) -> (F -> (E and F)))), M:tm-622, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64808
in-theory        64808
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (C or ((A and B) or B))))
theorem-size     15
proof            (modus-ponens tm-617 tm-764 ((A (or (and Am Bm) Bm)) (Cm (or B (or (and Am Bm) Bm))) (C (and Bm (or B (or (and Am Bm) Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 tm-5)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64808.        (((A and B) or B) -> (B and (C or ((A and B) or B)))), M:tm-617, m:tm-764, u:((A (or (and Am Bm) Bm)) (Cm (or B (or (and Am Bm) Bm))) (C (and Bm (or B (or (and Am Bm) Bm)))))
================================================================
tm-name          tm-64809
in-theory        64809
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (D -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-609 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64809.        ((((A and B) or B) -> (C -> (B and C))) and (D -> (E or D))), M:tm-609, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64810
in-theory        64810
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64810.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-605, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64811
in-theory        64811
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and ((D -> (E or D)) and (((A and B) or B) -> (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64811.        ((((A and B) or B) -> (C -> (B and C))) and ((D -> (E or D)) and (((A and B) or B) -> (C -> (B and C))))), M:tm-595, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64812
in-theory        64812
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64812.        (((A -> (B or A)) or C) and (((D and E) or E) -> (F -> (E and F)))), M:tm-550, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64813
in-theory        64813
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64813.        ((A or (B -> (C or B))) and (((D and E) or E) -> (F -> (E and F)))), M:tm-540, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64814
in-theory        64814
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64814.        ((A or (B -> (B or C))) and (((D and E) or E) -> (F -> (E and F)))), M:tm-530, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64815
in-theory        64815
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64815.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (E and F)))), M:tm-520, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64816
in-theory        64816
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64816.        ((A or ((B and C) -> C)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-510, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64817
in-theory        64817
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64817.        ((A or ((B and C) -> B)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-500, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64818
in-theory        64818
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64818.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (F and G)))), M:tm-490, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64819
in-theory        64819
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64819.        ((A or (B -> (C -> B))) and (((D and E) or E) -> (F -> (E and F)))), M:tm-480, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64820
in-theory        64820
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C -> (B and C)) or D))
theorem-size     13
proof            (modus-ponens tm-470 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64820.        (((A and B) or B) -> ((C -> (B and C)) or D)), M:tm-470, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64821
in-theory        64821
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64821.        ((A -> (B -> (B or C))) and (((D and E) or E) -> (F -> (E and F)))), M:tm-469, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64822
in-theory        64822
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (((A and B) or B) or C)))
theorem-size     15
proof            (modus-ponens tm-464 tm-764 ((A (or (and Am Bm) Bm)) (Cm (or (or (and Am Bm) Bm) B)) (C (and Bm (or (or (and Am Bm) Bm) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 tm-5)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64822.        (((A and B) or B) -> (B and (((A and B) or B) or C))), M:tm-464, m:tm-764, u:((A (or (and Am Bm) Bm)) (Cm (or (or (and Am Bm) Bm) B)) (C (and Bm (or (or (and Am Bm) Bm) B))))
================================================================
tm-name          tm-64823
in-theory        64823
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (D -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-456 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64823.        ((((A and B) or B) -> (C -> (B and C))) and (D -> (D or E))), M:tm-456, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64824
in-theory        64824
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64824.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-453, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64825
in-theory        64825
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and ((D -> (D or E)) and (((A and B) or B) -> (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64825.        ((((A and B) or B) -> (C -> (B and C))) and ((D -> (D or E)) and (((A and B) or B) -> (C -> (B and C))))), M:tm-443, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64826
in-theory        64826
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64826.        (((A -> (A or B)) or C) and (((D and E) or E) -> (F -> (E and F)))), M:tm-409, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64827
in-theory        64827
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64827.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (F -> (E and F)))), M:tm-400, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64828
in-theory        64828
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64828.        ((((A and B) -> B) or C) and (((D and E) or E) -> (F -> (E and F)))), M:tm-391, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64829
in-theory        64829
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64829.        ((((A and B) -> A) or C) and (((D and E) or E) -> (F -> (E and F)))), M:tm-382, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64830
in-theory        64830
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64830.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (G -> (F and G)))), M:tm-373, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64831
in-theory        64831
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64831.        (((A -> (B -> A)) or C) and (((D and E) or E) -> (F -> (E and F)))), M:tm-364, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64832
in-theory        64832
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D -> (B and D)) and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64832.        (((A and B) or B) -> (C -> ((D -> (B and D)) and C))), M:tm-355, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64833
in-theory        64833
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64833.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (E and F)))), M:tm-354, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64834
in-theory        64834
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (C -> (((A and B) or B) and C))))
theorem-size     17
proof            (modus-ponens tm-349 tm-764 ((A (or (and Am Bm) Bm)) (Cm (-> B (and (or (and Am Bm) Bm) B))) (C (and Bm (-> B (and (or (and Am Bm) Bm) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64834.        (((A and B) or B) -> (B and (C -> (((A and B) or B) and C)))), M:tm-349, m:tm-764, u:((A (or (and Am Bm) Bm)) (Cm (-> B (and (or (and Am Bm) Bm) B))) (C (and Bm (-> B (and (or (and Am Bm) Bm) B)))))
================================================================
tm-name          tm-64835
in-theory        64835
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (D -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-341 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64835.        ((((A and B) or B) -> (C -> (B and C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64836
in-theory        64836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64836.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (E -> (D and E)))), M:tm-338, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64837
in-theory        64837
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (((A and B) or B) -> (((A and B) or B) and (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64837.        ((((A and B) or B) -> (C -> (B and C))) and (((A and B) or B) -> (((A and B) or B) and (C -> (B and C))))), M:tm-328, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64838
in-theory        64838
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and ((D -> (E -> (D and E))) and (((A and B) or B) -> (C -> (B and C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64838.        ((((A and B) or B) -> (C -> (B and C))) and ((D -> (E -> (D and E))) and (((A and B) or B) -> (C -> (B and C))))), M:tm-327, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64839
in-theory        64839
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (((D and E) -> E) and (((A and B) or B) -> (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64839.        ((((A and B) or B) -> (C -> (B and C))) and (((D and E) -> E) and (((A and B) or B) -> (C -> (B and C))))), M:tm-326, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64840
in-theory        64840
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (((D and E) -> D) and (((A and B) or B) -> (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64840.        ((((A and B) or B) -> (C -> (B and C))) and (((D and E) -> D) and (((A and B) or B) -> (C -> (B and C))))), M:tm-325, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64841
in-theory        64841
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or B) -> (C -> (B and C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64841.        ((((A and B) or B) -> (C -> (B and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or B) -> (C -> (B and C))))), M:tm-324, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64842
in-theory        64842
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and ((D -> (E -> D)) and (((A and B) or B) -> (C -> (B and C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64842.        ((((A and B) or B) -> (C -> (B and C))) and ((D -> (E -> D)) and (((A and B) or B) -> (C -> (B and C))))), M:tm-323, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64843
in-theory        64843
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and ((D and E) -> E))
theorem-size     17
proof            (modus-ponens tm-322 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64843.        ((((A and B) or B) -> (C -> (B and C))) and ((D and E) -> E)), M:tm-322, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64844
in-theory        64844
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and ((D and E) -> D))
theorem-size     17
proof            (modus-ponens tm-320 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64844.        ((((A and B) or B) -> (C -> (B and C))) and ((D and E) -> D)), M:tm-320, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64845
in-theory        64845
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     25
proof            (modus-ponens tm-318 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64845.        ((((A and B) or B) -> (C -> (B and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64846
in-theory        64846
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     23
proof            (modus-ponens tm-316 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64846.        ((((A and B) or B) -> (C -> (B and C))) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64847
in-theory        64847
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (D -> (E -> D)))
theorem-size     17
proof            (modus-ponens tm-315 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64847.        ((((A and B) or B) -> (C -> (B and C))) and (D -> (E -> D))), M:tm-315, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64848
in-theory        64848
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and ((((A and B) or B) -> (not (C -> (B and C)))) -> (not ((A and B) or B))))
theorem-size     31
proof            (modus-ponens tm-313 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64848.        ((((A and B) or B) -> (C -> (B and C))) and ((((A and B) or B) -> (not (C -> (B and C)))) -> (not ((A and B) or B)))), M:tm-313, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64849
in-theory        64849
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (((C -> (B and C)) -> D) -> ((((A and B) or B) or (C -> (B and C))) -> D)))
theorem-size     33
proof            (modus-ponens tm-312 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64849.        ((((A and B) or B) -> (C -> (B and C))) and (((C -> (B and C)) -> D) -> ((((A and B) or B) or (C -> (B and C))) -> D))), M:tm-312, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64850
in-theory        64850
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (D or (((A and B) or B) -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64850.        ((((A and B) or B) -> (C -> (B and C))) and (D or (((A and B) or B) -> (C -> (B and C))))), M:tm-311, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64851
in-theory        64851
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and ((((A and B) or B) -> (C -> (B and C))) or D))
theorem-size     25
proof            (modus-ponens tm-310 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64851.        ((((A and B) or B) -> (C -> (B and C))) and ((((A and B) or B) -> (C -> (B and C))) or D)), M:tm-310, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64852
in-theory        64852
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (D -> ((((A and B) or B) -> (C -> (B and C))) and D)))
theorem-size     27
proof            (modus-ponens tm-309 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64852.        ((((A and B) or B) -> (C -> (B and C))) and (D -> ((((A and B) or B) -> (C -> (B and C))) and D))), M:tm-309, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64853
in-theory        64853
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and ((((A and B) or B) -> C) -> (((A and B) or B) -> (B and C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-764 ((A (or (and Am Bm) Bm)) (B Cm) (C (and Bm Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64853.        ((((A and B) or B) -> (C -> (B and C))) and ((((A and B) or B) -> C) -> (((A and B) or B) -> (B and C)))), M:tm-306, m:tm-764, u:((A (or (and Am Bm) Bm)) (B Cm) (C (and Bm Cm)))
================================================================
tm-name          tm-64854
in-theory        64854
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) and (D -> (((A and B) or B) -> (C -> (B and C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64854.        ((((A and B) or B) -> (C -> (B and C))) and (D -> (((A and B) or B) -> (C -> (B and C))))), M:tm-305, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64855
in-theory        64855
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64855.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-303, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64856
in-theory        64856
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64856.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-270, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64857
in-theory        64857
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64857.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-239, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64858
in-theory        64858
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64858.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (G -> (F and G)))), M:tm-210, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64859
in-theory        64859
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64859.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-183, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64860
in-theory        64860
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64860.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-157, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64861
in-theory        64861
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64861.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-147, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64862
in-theory        64862
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64862.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-134, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64863
in-theory        64863
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64863.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (F -> (E and F)))), M:tm-125, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64864
in-theory        64864
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64864.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (F and G)))), M:tm-113, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64865
in-theory        64865
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64865.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (F -> (E and F)))), M:tm-105, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64866
in-theory        64866
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and ((A and B) or B)))
theorem-size     13
proof            (modus-ponens tm-99 tm-764 ((Cm (or (and Am Bm) Bm)) (A (or (and Am Bm) Bm)) (B (and Bm (or (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-5)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64866.        (((A and B) or B) -> (B and ((A and B) or B))), M:tm-99, m:tm-764, u:((Cm (or (and Am Bm) Bm)) (A (or (and Am Bm) Bm)) (B (and Bm (or (and Am Bm) Bm))))
================================================================
tm-name          tm-64867
in-theory        64867
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (B and (C -> ((A and B) or B))))
theorem-size     15
proof            (modus-ponens tm-98 tm-764 ((A (or (and Am Bm) Bm)) (Cm (-> B (or (and Am Bm) Bm))) (C (and Bm (-> B (or (and Am Bm) Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-5)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64867.        (((A and B) or B) -> (B and (C -> ((A and B) or B)))), M:tm-98, m:tm-764, u:((A (or (and Am Bm) Bm)) (Cm (-> B (or (and Am Bm) Bm))) (C (and Bm (-> B (or (and Am Bm) Bm)))))
================================================================
tm-name          tm-64868
in-theory        64868
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64868.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> (E -> (D and E)))), M:tm-95, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64869
in-theory        64869
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (D -> (B and D))))
theorem-size     13
proof            (modus-ponens tm-84 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-5)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64869.        (((A and B) or B) -> (C -> (D -> (B and D)))), M:tm-84, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64870
in-theory        64870
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64870.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> (F -> (E and F)))), M:tm-83, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64871
in-theory        64871
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> (D -> (C and D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64871.        (((not (not A)) -> A) and (((B and C) or C) -> (D -> (C and D)))), M:tm-76, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64872
in-theory        64872
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> (C -> (B and C)))
theorem-size     19
proof            (modus-ponens tm-73 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-8 tm-10 tm-4 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64872.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> (C -> (B and C))), M:tm-73, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64873
in-theory        64873
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64873.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (E -> (D and E)))), M:tm-69, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64874
in-theory        64874
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64874.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (F -> (E and F)))), M:tm-54, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64875
in-theory        64875
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> (C -> (A and C)))
theorem-size     13
proof            (modus-ponens tm-50 tm-764 ((A (and Am Bm)) (B Bm) (C (-> Cm (and Bm Cm)))))
axioms-used      (tm-8 tm-7 tm-4 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64875.        ((A or ((B and A) or A)) -> (C -> (A and C))), M:tm-50, m:tm-764, u:((A (and Am Bm)) (B Bm) (C (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64876
in-theory        64876
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> (C -> (B and C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-764 ((A (and Am Bm)) (B Bm) (C (-> Cm (and Bm Cm)))))
axioms-used      (tm-8 tm-6 tm-4 tm-5)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64876.        (((A and B) or ((A and B) or B)) -> (C -> (B and C))), M:tm-49, m:tm-764, u:((A (and Am Bm)) (B Bm) (C (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64877
in-theory        64877
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> (D -> (C and D)))
theorem-size     19
proof            (modus-ponens tm-47 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64877.        (((A and ((B and C) or C)) or ((B and C) or C)) -> (D -> (C and D))), M:tm-47, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64878
in-theory        64878
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> (D -> (B and D)))
theorem-size     19
proof            (modus-ponens tm-46 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-8 tm-3 tm-4 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64878.        (((((A and B) or B) and C) or ((A and B) or B)) -> (D -> (B and D))), M:tm-46, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64879
in-theory        64879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64879.        ((A -> (B or A)) and (((C and D) or D) -> (E -> (D and E)))), M:tm-42, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64880
in-theory        64880
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64880.        ((A -> (A or B)) and (((C and D) or D) -> (E -> (D and E)))), M:tm-32, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64881
in-theory        64881
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and (C -> (B and C))))
theorem-size     17
proof            (modus-ponens tm-24 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64881.        (((A and B) or B) -> (((A and B) or B) and (C -> (B and C)))), M:tm-24, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64882
in-theory        64882
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> (E -> (D and E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64882.        ((A -> (B -> (A and B))) and (((C and D) or D) -> (E -> (D and E)))), M:tm-23, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64883
in-theory        64883
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64883.        (((A and B) -> B) and (((C and D) or D) -> (E -> (D and E)))), M:tm-22, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64884
in-theory        64884
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64884.        (((A and B) -> A) and (((C and D) or D) -> (E -> (D and E)))), M:tm-21, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64885
in-theory        64885
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (F -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64885.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (F -> (E and F)))), M:tm-20, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64886
in-theory        64886
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64886.        ((A -> (B -> A)) and (((C and D) or D) -> (E -> (D and E)))), M:tm-19, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64887
in-theory        64887
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not (C -> (B and C)))) -> (not ((A and B) or B)))
theorem-size     19
proof            (modus-ponens tm-9 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-9 tm-8 tm-4 tm-5)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64887.        ((((A and B) or B) -> (not (C -> (B and C)))) -> (not ((A and B) or B))), M:tm-9, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64888
in-theory        64888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B and A)) -> C) -> ((((D and B) or B) or (A -> (B and A))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-764 ((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm)))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64888.        (((A -> (B and A)) -> C) -> ((((D and B) or B) or (A -> (B and A))) -> C)), M:tm-8, m:tm-764, u:((A (or (and Am Bm) Bm)) (B (-> Cm (and Bm Cm))))
================================================================
tm-name          tm-64889
in-theory        64889
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> (D -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-7 tm-8 tm-4 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64889.        (A or (((B and C) or C) -> (D -> (C and D)))), M:tm-7, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64890
in-theory        64890
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (B and C))) or D)
theorem-size     13
proof            (modus-ponens tm-6 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-6 tm-8 tm-4 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64890.        ((((A and B) or B) -> (C -> (B and C))) or D), M:tm-6, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64891
in-theory        64891
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> (D -> (C and D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       69
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64891.        (A -> ((((B and C) or C) -> (D -> (C and D))) and A)), M:tm-5, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64892
in-theory        64892
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> C) -> (((A and B) or B) -> (B and C)))
theorem-size     17
proof            (modus-ponens tm-2 tm-764 ((A (or (and Am Bm) Bm)) (B Cm) (C (and Bm Cm))))
axioms-used      (tm-2 tm-8 tm-4 tm-5)
proof-size       77
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64892.        ((((A and B) or B) -> C) -> (((A and B) or B) -> (B and C))), M:tm-2, m:tm-764, u:((A (or (and Am Bm) Bm)) (B Cm) (C (and Bm Cm)))
================================================================
tm-name          tm-64893
in-theory        64893
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> (D -> (C and D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-764 ((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm))))))
axioms-used      (tm-1 tm-8 tm-4 tm-5)
proof-size       65
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-764.          (((A and B) or B) -> (C -> (B and C))), M:tm-47, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-64893.        (A -> (((B and C) or C) -> (D -> (C and D)))), M:tm-1, m:tm-764, u:((A (-> (or (and Am Bm) Bm) (-> Cm (and Bm Cm)))))
================================================================
tm-name          tm-64894
in-theory        64894
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-757 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-6)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64894.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (E or F))), M:tm-757, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64895
in-theory        64895
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (((((A and B) or B) and D) or ((A and B) or B)) -> (B or C)))
theorem-size     27
proof            (modus-ponens tm-747 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-6)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64895.        ((((A and B) or B) -> (B or C)) and (((((A and B) or B) and D) or ((A and B) or B)) -> (B or C))), M:tm-747, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64896
in-theory        64896
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (F or G)))
theorem-size     35
proof            (modus-ponens tm-708 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-6)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64896.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (F or G))), M:tm-708, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64897
in-theory        64897
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-665 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-6)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64897.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (E or F))), M:tm-665, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64898
in-theory        64898
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (B or D)))
theorem-size     11
proof            (modus-ponens tm-623 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64898.        (((A and B) or B) -> (C or (B or D))), M:tm-623, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64899
in-theory        64899
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-622 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64899.        ((A -> (B -> (C or B))) and (((D and E) or E) -> (E or F))), M:tm-622, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64900
in-theory        64900
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64900.        ((((A and B) or B) -> (B or C)) and (D -> (E or D))), M:tm-609, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64901
in-theory        64901
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-605 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64901.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (E or F))), M:tm-605, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64902
in-theory        64902
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and ((D -> (E or D)) and (((A and B) or B) -> (B or C))))
theorem-size     25
proof            (modus-ponens tm-595 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64902.        ((((A and B) or B) -> (B or C)) and ((D -> (E or D)) and (((A and B) or B) -> (B or C)))), M:tm-595, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64903
in-theory        64903
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-550 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64903.        (((A -> (B or A)) or C) and (((D and E) or E) -> (E or F))), M:tm-550, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64904
in-theory        64904
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-540 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64904.        ((A or (B -> (C or B))) and (((D and E) or E) -> (E or F))), M:tm-540, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64905
in-theory        64905
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-530 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64905.        ((A or (B -> (B or C))) and (((D and E) or E) -> (E or F))), M:tm-530, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64906
in-theory        64906
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-520 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64906.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (E or F))), M:tm-520, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64907
in-theory        64907
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-510 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64907.        ((A or ((B and C) -> C)) and (((D and E) or E) -> (E or F))), M:tm-510, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64908
in-theory        64908
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-500 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64908.        ((A or ((B and C) -> B)) and (((D and E) or E) -> (E or F))), M:tm-500, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64909
in-theory        64909
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-490 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64909.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (F or G))), M:tm-490, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64910
in-theory        64910
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-480 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64910.        ((A or (B -> (C -> B))) and (((D and E) or E) -> (E or F))), M:tm-480, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64911
in-theory        64911
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((B or C) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64911.        (((A and B) or B) -> ((B or C) or D)), M:tm-470, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64912
in-theory        64912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-469 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64912.        ((A -> (B -> (B or C))) and (((D and E) or E) -> (E or F))), M:tm-469, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64913
in-theory        64913
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64913.        ((((A and B) or B) -> (B or C)) and (D -> (D or E))), M:tm-456, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64914
in-theory        64914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-453 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64914.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (E or F))), M:tm-453, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64915
in-theory        64915
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and ((D -> (D or E)) and (((A and B) or B) -> (B or C))))
theorem-size     25
proof            (modus-ponens tm-443 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64915.        ((((A and B) or B) -> (B or C)) and ((D -> (D or E)) and (((A and B) or B) -> (B or C)))), M:tm-443, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64916
in-theory        64916
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-409 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64916.        (((A -> (A or B)) or C) and (((D and E) or E) -> (E or F))), M:tm-409, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64917
in-theory        64917
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-400 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64917.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (E or F))), M:tm-400, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64918
in-theory        64918
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-391 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64918.        ((((A and B) -> B) or C) and (((D and E) or E) -> (E or F))), M:tm-391, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64919
in-theory        64919
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-382 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64919.        ((((A and B) -> A) or C) and (((D and E) or E) -> (E or F))), M:tm-382, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64920
in-theory        64920
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-373 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64920.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (F or G))), M:tm-373, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64921
in-theory        64921
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-364 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64921.        (((A -> (B -> A)) or C) and (((D and E) or E) -> (E or F))), M:tm-364, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64922
in-theory        64922
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((B or D) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4 tm-6)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64922.        (((A and B) or B) -> (C -> ((B or D) and C))), M:tm-355, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64923
in-theory        64923
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-354 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64923.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (E or F))), M:tm-354, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64924
in-theory        64924
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-6)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64924.        ((((A and B) or B) -> (B or C)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64925
in-theory        64925
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-338 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64925.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (D or E))), M:tm-338, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64926
in-theory        64926
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (((A and B) or B) -> (((A and B) or B) and (B or C))))
theorem-size     25
proof            (modus-ponens tm-328 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64926.        ((((A and B) or B) -> (B or C)) and (((A and B) or B) -> (((A and B) or B) and (B or C)))), M:tm-328, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64927
in-theory        64927
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and ((D -> (E -> (D and E))) and (((A and B) or B) -> (B or C))))
theorem-size     27
proof            (modus-ponens tm-327 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64927.        ((((A and B) or B) -> (B or C)) and ((D -> (E -> (D and E))) and (((A and B) or B) -> (B or C)))), M:tm-327, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64928
in-theory        64928
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (((D and E) -> E) and (((A and B) or B) -> (B or C))))
theorem-size     25
proof            (modus-ponens tm-326 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64928.        ((((A and B) or B) -> (B or C)) and (((D and E) -> E) and (((A and B) or B) -> (B or C)))), M:tm-326, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64929
in-theory        64929
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (((D and E) -> D) and (((A and B) or B) -> (B or C))))
theorem-size     25
proof            (modus-ponens tm-325 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64929.        ((((A and B) or B) -> (B or C)) and (((D and E) -> D) and (((A and B) or B) -> (B or C)))), M:tm-325, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64930
in-theory        64930
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or B) -> (B or C))))
theorem-size     33
proof            (modus-ponens tm-324 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64930.        ((((A and B) or B) -> (B or C)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or B) -> (B or C)))), M:tm-324, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64931
in-theory        64931
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and ((D -> (E -> D)) and (((A and B) or B) -> (B or C))))
theorem-size     25
proof            (modus-ponens tm-323 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64931.        ((((A and B) or B) -> (B or C)) and ((D -> (E -> D)) and (((A and B) or B) -> (B or C)))), M:tm-323, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64932
in-theory        64932
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64932.        ((((A and B) or B) -> (B or C)) and ((D and E) -> E)), M:tm-322, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64933
in-theory        64933
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64933.        ((((A and B) or B) -> (B or C)) and ((D and E) -> D)), M:tm-320, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64934
in-theory        64934
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-6)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64934.        ((((A and B) or B) -> (B or C)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64935
in-theory        64935
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     21
proof            (modus-ponens tm-316 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-6)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64935.        ((((A and B) or B) -> (B or C)) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64936
in-theory        64936
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-6)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64936.        ((((A and B) or B) -> (B or C)) and (D -> (E -> D))), M:tm-315, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64937
in-theory        64937
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and ((((A and B) or B) -> (not (B or C))) -> (not ((A and B) or B))))
theorem-size     27
proof            (modus-ponens tm-313 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 tm-6)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64937.        ((((A and B) or B) -> (B or C)) and ((((A and B) or B) -> (not (B or C))) -> (not ((A and B) or B)))), M:tm-313, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64938
in-theory        64938
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (((B or C) -> D) -> ((((A and B) or B) or (B or C)) -> D)))
theorem-size     27
proof            (modus-ponens tm-312 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64938.        ((((A and B) or B) -> (B or C)) and (((B or C) -> D) -> ((((A and B) or B) or (B or C)) -> D))), M:tm-312, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64939
in-theory        64939
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (D or (((A and B) or B) -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-311 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64939.        ((((A and B) or B) -> (B or C)) and (D or (((A and B) or B) -> (B or C)))), M:tm-311, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64940
in-theory        64940
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and ((((A and B) or B) -> (B or C)) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64940.        ((((A and B) or B) -> (B or C)) and ((((A and B) or B) -> (B or C)) or D)), M:tm-310, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64941
in-theory        64941
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (D -> ((((A and B) or B) -> (B or C)) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64941.        ((((A and B) or B) -> (B or C)) and (D -> ((((A and B) or B) -> (B or C)) and D))), M:tm-309, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64942
in-theory        64942
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) and (D -> (((A and B) or B) -> (B or C))))
theorem-size     21
proof            (modus-ponens tm-305 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-6)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64942.        ((((A and B) or B) -> (B or C)) and (D -> (((A and B) or B) -> (B or C)))), M:tm-305, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64943
in-theory        64943
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-303 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64943.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (E or F))), M:tm-303, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64944
in-theory        64944
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-270 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64944.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (E or F))), M:tm-270, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64945
in-theory        64945
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-239 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64945.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (E or F))), M:tm-239, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64946
in-theory        64946
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-210 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-6)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64946.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (F or G))), M:tm-210, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64947
in-theory        64947
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-183 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64947.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (E or F))), M:tm-183, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64948
in-theory        64948
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-157 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64948.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> (E or F))), M:tm-157, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64949
in-theory        64949
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-147 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64949.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (E or F))), M:tm-147, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64950
in-theory        64950
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-134 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64950.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> (E or F))), M:tm-134, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64951
in-theory        64951
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-125 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64951.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (E or F))), M:tm-125, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64952
in-theory        64952
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-113 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 tm-6)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64952.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (F or G))), M:tm-113, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64953
in-theory        64953
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (E or F)))
theorem-size     29
proof            (modus-ponens tm-105 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-6)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64953.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (E or F))), M:tm-105, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64954
in-theory        64954
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-95 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 tm-6)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64954.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> (D or E))), M:tm-95, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64955
in-theory        64955
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (B or D)))
theorem-size     11
proof            (modus-ponens tm-84 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-6)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64955.        (((A and B) or B) -> (C -> (B or D))), M:tm-84, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64956
in-theory        64956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-83 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-6)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64956.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> (E or F))), M:tm-83, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64957
in-theory        64957
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> (C or D)))
theorem-size     15
proof            (modus-ponens tm-76 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64957.        (((not (not A)) -> A) and (((B and C) or C) -> (C or D))), M:tm-76, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64958
in-theory        64958
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> (B or C))
theorem-size     17
proof            (modus-ponens tm-73 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-8 tm-10 tm-4 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64958.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> (B or C)), M:tm-73, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64959
in-theory        64959
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-69 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-6)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64959.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (D or E))), M:tm-69, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64960
in-theory        64960
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-54 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64960.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (E or F))), M:tm-54, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64961
in-theory        64961
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> (A or C))
theorem-size     11
proof            (modus-ponens tm-50 tm-765 ((A (and Am Bm)) (B Bm) (C (or Bm Cm))))
axioms-used      (tm-8 tm-7 tm-4 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64961.        ((A or ((B and A) or A)) -> (A or C)), M:tm-50, m:tm-765, u:((A (and Am Bm)) (B Bm) (C (or Bm Cm)))
================================================================
tm-name          tm-64962
in-theory        64962
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> (B or C))
theorem-size     13
proof            (modus-ponens tm-49 tm-765 ((A (and Am Bm)) (B Bm) (C (or Bm Cm))))
axioms-used      (tm-8 tm-6 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64962.        (((A and B) or ((A and B) or B)) -> (B or C)), M:tm-49, m:tm-765, u:((A (and Am Bm)) (B Bm) (C (or Bm Cm)))
================================================================
tm-name          tm-64963
in-theory        64963
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> (C or D))
theorem-size     17
proof            (modus-ponens tm-47 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-8 tm-4 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64963.        (((A and ((B and C) or C)) or ((B and C) or C)) -> (C or D)), M:tm-47, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64964
in-theory        64964
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> (B or D))
theorem-size     17
proof            (modus-ponens tm-46 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-8 tm-3 tm-4 tm-6)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64964.        (((((A and B) or B) and C) or ((A and B) or B)) -> (B or D)), M:tm-46, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64965
in-theory        64965
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-42 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64965.        ((A -> (B or A)) and (((C and D) or D) -> (D or E))), M:tm-42, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64966
in-theory        64966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-32 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64966.        ((A -> (A or B)) and (((C and D) or D) -> (D or E))), M:tm-32, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64967
in-theory        64967
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and (B or C)))
theorem-size     15
proof            (modus-ponens tm-24 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-6)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64967.        (((A and B) or B) -> (((A and B) or B) and (B or C))), M:tm-24, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64968
in-theory        64968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> (D or E)))
theorem-size     17
proof            (modus-ponens tm-23 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64968.        ((A -> (B -> (A and B))) and (((C and D) or D) -> (D or E))), M:tm-23, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64969
in-theory        64969
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-22 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64969.        (((A and B) -> B) and (((C and D) or D) -> (D or E))), M:tm-22, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64970
in-theory        64970
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-21 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64970.        (((A and B) -> A) and (((C and D) or D) -> (D or E))), M:tm-21, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64971
in-theory        64971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (E or F)))
theorem-size     23
proof            (modus-ponens tm-20 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-6)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64971.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (E or F))), M:tm-20, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64972
in-theory        64972
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-19 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-6)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64972.        ((A -> (B -> A)) and (((C and D) or D) -> (D or E))), M:tm-19, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64973
in-theory        64973
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not (B or C))) -> (not ((A and B) or B)))
theorem-size     17
proof            (modus-ponens tm-9 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-9 tm-8 tm-4 tm-6)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64973.        ((((A and B) or B) -> (not (B or C))) -> (not ((A and B) or B))), M:tm-9, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64974
in-theory        64974
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> ((((D and A) or A) or (A or B)) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-765 ((A (or (and Am Bm) Bm)) (B (or Bm Cm))))
axioms-used      (tm-8 tm-4 tm-6)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64974.        (((A or B) -> C) -> ((((D and A) or A) or (A or B)) -> C)), M:tm-8, m:tm-765, u:((A (or (and Am Bm) Bm)) (B (or Bm Cm)))
================================================================
tm-name          tm-64975
in-theory        64975
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> (C or D)))
theorem-size     11
proof            (modus-ponens tm-7 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-7 tm-8 tm-4 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64975.        (A or (((B and C) or C) -> (C or D))), M:tm-7, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64976
in-theory        64976
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (B or C)) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-6 tm-8 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64976.        ((((A and B) or B) -> (B or C)) or D), M:tm-6, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64977
in-theory        64977
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> (C or D)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-6)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64977.        (A -> ((((B and C) or C) -> (C or D)) and A)), M:tm-5, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64978
in-theory        64978
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> (C or D)))
theorem-size     11
proof            (modus-ponens tm-1 tm-765 ((A (-> (or (and Am Bm) Bm) (or Bm Cm)))))
axioms-used      (tm-1 tm-8 tm-4 tm-6)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-6.            (A -> (A or B)), axiom
tm-765.          (((A and B) or B) -> (B or C)), M:tm-47, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-64978.        (A -> (((B and C) or C) -> (C or D))), M:tm-1, m:tm-765, u:((A (-> (or (and Am Bm) Bm) (or Bm Cm))))
================================================================
tm-name          tm-64979
in-theory        64979
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-757 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-7)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64979.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (F or E))), M:tm-757, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64980
in-theory        64980
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (((((A and B) or B) and D) or ((A and B) or B)) -> (C or B)))
theorem-size     27
proof            (modus-ponens tm-747 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-7)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64980.        ((((A and B) or B) -> (C or B)) and (((((A and B) or B) and D) or ((A and B) or B)) -> (C or B))), M:tm-747, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-64981
in-theory        64981
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (G or F)))
theorem-size     35
proof            (modus-ponens tm-708 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-7)
proof-size       165
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64981.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (G or F))), M:tm-708, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64982
in-theory        64982
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-665 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-7)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64982.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (F or E))), M:tm-665, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64983
in-theory        64983
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (D or B)))
theorem-size     11
proof            (modus-ponens tm-623 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64983.        (((A and B) or B) -> (C or (D or B))), M:tm-623, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-64984
in-theory        64984
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-622 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64984.        ((A -> (B -> (C or B))) and (((D and E) or E) -> (F or E))), M:tm-622, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64985
in-theory        64985
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (D -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-609 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64985.        ((((A and B) or B) -> (C or B)) and (D -> (E or D))), M:tm-609, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64986
in-theory        64986
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-605 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64986.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (F or E))), M:tm-605, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64987
in-theory        64987
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and ((D -> (E or D)) and (((A and B) or B) -> (C or B))))
theorem-size     25
proof            (modus-ponens tm-595 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64987.        ((((A and B) or B) -> (C or B)) and ((D -> (E or D)) and (((A and B) or B) -> (C or B)))), M:tm-595, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64988
in-theory        64988
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-550 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64988.        (((A -> (B or A)) or C) and (((D and E) or E) -> (F or E))), M:tm-550, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64989
in-theory        64989
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-540 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64989.        ((A or (B -> (C or B))) and (((D and E) or E) -> (F or E))), M:tm-540, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64990
in-theory        64990
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-530 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64990.        ((A or (B -> (B or C))) and (((D and E) or E) -> (F or E))), M:tm-530, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64991
in-theory        64991
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-520 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64991.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (F or E))), M:tm-520, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64992
in-theory        64992
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-510 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64992.        ((A or ((B and C) -> C)) and (((D and E) or E) -> (F or E))), M:tm-510, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64993
in-theory        64993
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-500 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64993.        ((A or ((B and C) -> B)) and (((D and E) or E) -> (F or E))), M:tm-500, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64994
in-theory        64994
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-490 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64994.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G or F))), M:tm-490, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64995
in-theory        64995
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-480 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64995.        ((A or (B -> (C -> B))) and (((D and E) or E) -> (F or E))), M:tm-480, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64996
in-theory        64996
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((C or B) or D))
theorem-size     11
proof            (modus-ponens tm-470 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64996.        (((A and B) or B) -> ((C or B) or D)), M:tm-470, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-64997
in-theory        64997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-469 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64997.        ((A -> (B -> (B or C))) and (((D and E) or E) -> (F or E))), M:tm-469, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64998
in-theory        64998
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (D -> (D or E)))
theorem-size     15
proof            (modus-ponens tm-456 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64998.        ((((A and B) or B) -> (C or B)) and (D -> (D or E))), M:tm-456, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-64999
in-theory        64999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-453 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-64999.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (F or E))), M:tm-453, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65000
in-theory        65000
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and ((D -> (D or E)) and (((A and B) or B) -> (C or B))))
theorem-size     25
proof            (modus-ponens tm-443 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65000.        ((((A and B) or B) -> (C or B)) and ((D -> (D or E)) and (((A and B) or B) -> (C or B)))), M:tm-443, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65001
in-theory        65001
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-409 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65001.        (((A -> (A or B)) or C) and (((D and E) or E) -> (F or E))), M:tm-409, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65002
in-theory        65002
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-400 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65002.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (F or E))), M:tm-400, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65003
in-theory        65003
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-391 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65003.        ((((A and B) -> B) or C) and (((D and E) or E) -> (F or E))), M:tm-391, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65004
in-theory        65004
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-382 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65004.        ((((A and B) -> A) or C) and (((D and E) or E) -> (F or E))), M:tm-382, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65005
in-theory        65005
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-373 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65005.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (G or F))), M:tm-373, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65006
in-theory        65006
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-364 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65006.        (((A -> (B -> A)) or C) and (((D and E) or E) -> (F or E))), M:tm-364, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65007
in-theory        65007
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D or B) and C)))
theorem-size     13
proof            (modus-ponens tm-355 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4 tm-7)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65007.        (((A and B) or B) -> (C -> ((D or B) and C))), M:tm-355, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-65008
in-theory        65008
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-354 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65008.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (F or E))), M:tm-354, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65009
in-theory        65009
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (D -> (E -> (D and E))))
theorem-size     17
proof            (modus-ponens tm-341 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-7)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65009.        ((((A and B) or B) -> (C or B)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65010
in-theory        65010
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-338 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65010.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (E or D))), M:tm-338, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65011
in-theory        65011
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (((A and B) or B) -> (((A and B) or B) and (C or B))))
theorem-size     25
proof            (modus-ponens tm-328 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65011.        ((((A and B) or B) -> (C or B)) and (((A and B) or B) -> (((A and B) or B) and (C or B)))), M:tm-328, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-65012
in-theory        65012
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and ((D -> (E -> (D and E))) and (((A and B) or B) -> (C or B))))
theorem-size     27
proof            (modus-ponens tm-327 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65012.        ((((A and B) or B) -> (C or B)) and ((D -> (E -> (D and E))) and (((A and B) or B) -> (C or B)))), M:tm-327, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65013
in-theory        65013
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (((D and E) -> E) and (((A and B) or B) -> (C or B))))
theorem-size     25
proof            (modus-ponens tm-326 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65013.        ((((A and B) or B) -> (C or B)) and (((D and E) -> E) and (((A and B) or B) -> (C or B)))), M:tm-326, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65014
in-theory        65014
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (((D and E) -> D) and (((A and B) or B) -> (C or B))))
theorem-size     25
proof            (modus-ponens tm-325 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65014.        ((((A and B) or B) -> (C or B)) and (((D and E) -> D) and (((A and B) or B) -> (C or B)))), M:tm-325, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65015
in-theory        65015
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or B) -> (C or B))))
theorem-size     33
proof            (modus-ponens tm-324 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65015.        ((((A and B) or B) -> (C or B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and B) or B) -> (C or B)))), M:tm-324, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65016
in-theory        65016
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and ((D -> (E -> D)) and (((A and B) or B) -> (C or B))))
theorem-size     25
proof            (modus-ponens tm-323 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65016.        ((((A and B) or B) -> (C or B)) and ((D -> (E -> D)) and (((A and B) or B) -> (C or B)))), M:tm-323, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65017
in-theory        65017
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and ((D and E) -> E))
theorem-size     15
proof            (modus-ponens tm-322 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65017.        ((((A and B) or B) -> (C or B)) and ((D and E) -> E)), M:tm-322, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65018
in-theory        65018
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and ((D and E) -> D))
theorem-size     15
proof            (modus-ponens tm-320 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65018.        ((((A and B) or B) -> (C or B)) and ((D and E) -> D)), M:tm-320, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65019
in-theory        65019
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     23
proof            (modus-ponens tm-318 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-7)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65019.        ((((A and B) or B) -> (C or B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65020
in-theory        65020
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     21
proof            (modus-ponens tm-316 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-7)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65020.        ((((A and B) or B) -> (C or B)) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-65021
in-theory        65021
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (D -> (E -> D)))
theorem-size     15
proof            (modus-ponens tm-315 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-7)
proof-size       113
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65021.        ((((A and B) or B) -> (C or B)) and (D -> (E -> D))), M:tm-315, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65022
in-theory        65022
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and ((((A and B) or B) -> (not (C or B))) -> (not ((A and B) or B))))
theorem-size     27
proof            (modus-ponens tm-313 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 tm-7)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65022.        ((((A and B) or B) -> (C or B)) and ((((A and B) or B) -> (not (C or B))) -> (not ((A and B) or B)))), M:tm-313, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-65023
in-theory        65023
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (((C or B) -> D) -> ((((A and B) or B) or (C or B)) -> D)))
theorem-size     27
proof            (modus-ponens tm-312 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65023.        ((((A and B) or B) -> (C or B)) and (((C or B) -> D) -> ((((A and B) or B) or (C or B)) -> D))), M:tm-312, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-65024
in-theory        65024
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (D or (((A and B) or B) -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-311 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65024.        ((((A and B) or B) -> (C or B)) and (D or (((A and B) or B) -> (C or B)))), M:tm-311, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65025
in-theory        65025
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and ((((A and B) or B) -> (C or B)) or D))
theorem-size     21
proof            (modus-ponens tm-310 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65025.        ((((A and B) or B) -> (C or B)) and ((((A and B) or B) -> (C or B)) or D)), M:tm-310, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65026
in-theory        65026
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (D -> ((((A and B) or B) -> (C or B)) and D)))
theorem-size     23
proof            (modus-ponens tm-309 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65026.        ((((A and B) or B) -> (C or B)) and (D -> ((((A and B) or B) -> (C or B)) and D))), M:tm-309, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65027
in-theory        65027
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) and (D -> (((A and B) or B) -> (C or B))))
theorem-size     21
proof            (modus-ponens tm-305 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-7)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65027.        ((((A and B) or B) -> (C or B)) and (D -> (((A and B) or B) -> (C or B)))), M:tm-305, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65028
in-theory        65028
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-303 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65028.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (F or E))), M:tm-303, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65029
in-theory        65029
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-270 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65029.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (F or E))), M:tm-270, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65030
in-theory        65030
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-239 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65030.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (F or E))), M:tm-239, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65031
in-theory        65031
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-210 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-7)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65031.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (G or F))), M:tm-210, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65032
in-theory        65032
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-183 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65032.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (F or E))), M:tm-183, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65033
in-theory        65033
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-157 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65033.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> (F or E))), M:tm-157, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65034
in-theory        65034
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-147 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65034.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (F or E))), M:tm-147, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65035
in-theory        65035
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-134 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65035.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> (F or E))), M:tm-134, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65036
in-theory        65036
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-125 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65036.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (F or E))), M:tm-125, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65037
in-theory        65037
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-113 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 tm-7)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65037.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G or F))), M:tm-113, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65038
in-theory        65038
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (F or E)))
theorem-size     29
proof            (modus-ponens tm-105 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-7)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65038.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (F or E))), M:tm-105, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65039
in-theory        65039
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-95 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 tm-7)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65039.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> (E or D))), M:tm-95, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65040
in-theory        65040
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (D or B)))
theorem-size     11
proof            (modus-ponens tm-84 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-7)
proof-size       93
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65040.        (((A and B) or B) -> (C -> (D or B))), M:tm-84, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-65041
in-theory        65041
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-83 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-7)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65041.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> (F or E))), M:tm-83, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65042
in-theory        65042
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> (D or C)))
theorem-size     15
proof            (modus-ponens tm-76 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65042.        (((not (not A)) -> A) and (((B and C) or C) -> (D or C))), M:tm-76, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65043
in-theory        65043
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> (C or B))
theorem-size     17
proof            (modus-ponens tm-73 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-8 tm-10 tm-4 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65043.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> (C or B)), M:tm-73, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-65044
in-theory        65044
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-69 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-7)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65044.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (E or D))), M:tm-69, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65045
in-theory        65045
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-54 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65045.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (F or E))), M:tm-54, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65046
in-theory        65046
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> (C or A))
theorem-size     11
proof            (modus-ponens tm-50 tm-766 ((A (and Am Bm)) (B Bm) (C (or Cm Bm))))
axioms-used      (tm-8 tm-7 tm-4)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65046.        ((A or ((B and A) or A)) -> (C or A)), M:tm-50, m:tm-766, u:((A (and Am Bm)) (B Bm) (C (or Cm Bm)))
================================================================
tm-name          tm-65047
in-theory        65047
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> (C or B))
theorem-size     13
proof            (modus-ponens tm-49 tm-766 ((A (and Am Bm)) (B Bm) (C (or Cm Bm))))
axioms-used      (tm-8 tm-6 tm-4 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65047.        (((A and B) or ((A and B) or B)) -> (C or B)), M:tm-49, m:tm-766, u:((A (and Am Bm)) (B Bm) (C (or Cm Bm)))
================================================================
tm-name          tm-65048
in-theory        65048
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> (D or C))
theorem-size     17
proof            (modus-ponens tm-47 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-8 tm-4 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65048.        (((A and ((B and C) or C)) or ((B and C) or C)) -> (D or C)), M:tm-47, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-65049
in-theory        65049
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> (D or B))
theorem-size     17
proof            (modus-ponens tm-46 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-8 tm-3 tm-4 tm-7)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65049.        (((((A and B) or B) and C) or ((A and B) or B)) -> (D or B)), M:tm-46, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-65050
in-theory        65050
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-42 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65050.        ((A -> (B or A)) and (((C and D) or D) -> (E or D))), M:tm-42, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65051
in-theory        65051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-32 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65051.        ((A -> (A or B)) and (((C and D) or D) -> (E or D))), M:tm-32, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65052
in-theory        65052
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and (C or B)))
theorem-size     15
proof            (modus-ponens tm-24 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-7)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65052.        (((A and B) or B) -> (((A and B) or B) and (C or B))), M:tm-24, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-65053
in-theory        65053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> (E or D)))
theorem-size     17
proof            (modus-ponens tm-23 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
proof-size       85
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65053.        ((A -> (B -> (A and B))) and (((C and D) or D) -> (E or D))), M:tm-23, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65054
in-theory        65054
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-22 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65054.        (((A and B) -> B) and (((C and D) or D) -> (E or D))), M:tm-22, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65055
in-theory        65055
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-21 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65055.        (((A and B) -> A) and (((C and D) or D) -> (E or D))), M:tm-21, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65056
in-theory        65056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (F or E)))
theorem-size     23
proof            (modus-ponens tm-20 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-7)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65056.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (F or E))), M:tm-20, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65057
in-theory        65057
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> (E or D)))
theorem-size     15
proof            (modus-ponens tm-19 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-7)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65057.        ((A -> (B -> A)) and (((C and D) or D) -> (E or D))), M:tm-19, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65058
in-theory        65058
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not (C or B))) -> (not ((A and B) or B)))
theorem-size     17
proof            (modus-ponens tm-9 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-9 tm-8 tm-4 tm-7)
proof-size       71
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65058.        ((((A and B) or B) -> (not (C or B))) -> (not ((A and B) or B))), M:tm-9, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-65059
in-theory        65059
times-derived    1
----------------------------------------------------------------
theorem          (((A or B) -> C) -> ((((D and B) or B) or (A or B)) -> C))
theorem-size     17
proof            (modus-ponens tm-8 tm-766 ((A (or (and Am Bm) Bm)) (B (or Cm Bm))))
axioms-used      (tm-8 tm-4 tm-7)
proof-size       73
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65059.        (((A or B) -> C) -> ((((D and B) or B) or (A or B)) -> C)), M:tm-8, m:tm-766, u:((A (or (and Am Bm) Bm)) (B (or Cm Bm)))
================================================================
tm-name          tm-65060
in-theory        65060
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> (D or C)))
theorem-size     11
proof            (modus-ponens tm-7 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-7 tm-8 tm-4)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65060.        (A or (((B and C) or C) -> (D or C))), M:tm-7, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65061
in-theory        65061
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C or B)) or D)
theorem-size     11
proof            (modus-ponens tm-6 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-6 tm-8 tm-4 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65061.        ((((A and B) or B) -> (C or B)) or D), M:tm-6, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65062
in-theory        65062
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> (D or C)) and A))
theorem-size     13
proof            (modus-ponens tm-5 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-7)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65062.        (A -> ((((B and C) or C) -> (D or C)) and A)), M:tm-5, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65063
in-theory        65063
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> (D or C)))
theorem-size     11
proof            (modus-ponens tm-1 tm-766 ((A (-> (or (and Am Bm) Bm) (or Cm Bm)))))
axioms-used      (tm-1 tm-8 tm-4 tm-7)
proof-size       59
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-7.            (A -> (B or A)), axiom
tm-766.          (((A and B) or B) -> (C or B)), M:tm-47, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-65063.        (A -> (((B and C) or C) -> (D or C))), M:tm-1, m:tm-766, u:((A (-> (or (and Am Bm) Bm) (or Cm Bm))))
================================================================
tm-name          tm-65064
in-theory        65064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-757 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65064.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-757, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65065
in-theory        65065
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((((A and (B -> C)) or (B -> C)) and E) or ((A and (B -> C)) or (B -> C))) -> ((C -> D) -> ((B or C) -> D))))
theorem-size     51
proof            (modus-ponens tm-747 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65065.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((((A and (B -> C)) or (B -> C)) and E) or ((A and (B -> C)) or (B -> C))) -> ((C -> D) -> ((B or C) -> D)))), M:tm-747, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65066
in-theory        65066
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H))))
theorem-size     45
proof            (modus-ponens tm-708 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       193
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65066.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H)))), M:tm-708, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65067
in-theory        65067
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-665 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65067.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-665, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65068
in-theory        65068
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D or ((C -> E) -> ((B or C) -> E))))
theorem-size     21
proof            (modus-ponens tm-623 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65068.        (((A and (B -> C)) or (B -> C)) -> (D or ((C -> E) -> ((B or C) -> E)))), M:tm-623, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65069
in-theory        65069
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-622 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65069.        ((A -> (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-622, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65070
in-theory        65070
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F or E)))
theorem-size     25
proof            (modus-ponens tm-609 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65070.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F or E))), M:tm-609, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65071
in-theory        65071
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-605 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65071.        ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-605, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65072
in-theory        65072
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F or E)) and (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-595 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65072.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F or E)) and (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))))), M:tm-595, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65073
in-theory        65073
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-550 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65073.        (((A -> (B or A)) or C) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-550, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65074
in-theory        65074
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-540 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65074.        ((A or (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-540, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65075
in-theory        65075
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-530 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65075.        ((A or (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-530, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65076
in-theory        65076
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-520 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65076.        ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-520, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65077
in-theory        65077
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-510 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65077.        ((A or ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-510, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65078
in-theory        65078
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-500 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65078.        ((A or ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-500, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65079
in-theory        65079
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-490 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65079.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H)))), M:tm-490, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65080
in-theory        65080
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-480 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65080.        ((A or (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-480, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65081
in-theory        65081
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (((C -> D) -> ((B or C) -> D)) or E))
theorem-size     21
proof            (modus-ponens tm-470 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65081.        (((A and (B -> C)) or (B -> C)) -> (((C -> D) -> ((B or C) -> D)) or E)), M:tm-470, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65082
in-theory        65082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-469 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65082.        ((A -> (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-469, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65083
in-theory        65083
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (E -> (E or F)))
theorem-size     25
proof            (modus-ponens tm-456 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65083.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (E -> (E or F))), M:tm-456, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65084
in-theory        65084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-453 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65084.        ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-453, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65085
in-theory        65085
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (E or F)) and (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-443 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65085.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (E or F)) and (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))))), M:tm-443, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65086
in-theory        65086
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-409 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65086.        (((A -> (A or B)) or C) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-409, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65087
in-theory        65087
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-400 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65087.        (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-400, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65088
in-theory        65088
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-391 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65088.        ((((A and B) -> B) or C) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-391, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65089
in-theory        65089
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-382 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65089.        ((((A and B) -> A) or C) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-382, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65090
in-theory        65090
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-373 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65090.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H)))), M:tm-373, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65091
in-theory        65091
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-364 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65091.        (((A -> (B -> A)) or C) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-364, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65092
in-theory        65092
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D -> (((C -> E) -> ((B or C) -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-355 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65092.        (((A and (B -> C)) or (B -> C)) -> (D -> (((C -> E) -> ((B or C) -> E)) and D))), M:tm-355, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65093
in-theory        65093
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-354 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65093.        ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-354, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65094
in-theory        65094
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((B or C) -> (((A and (B -> C)) or (B -> C)) and C)))
theorem-size     25
proof            (modus-ponens tm-349 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B Cm) (Dm (and (or (and Am (-> Bm Cm)) (-> Bm Cm)) Cm)) (C (-> (or Bm Cm) (and (or (and Am (-> Bm Cm)) (-> Bm Cm)) Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65094.        (((A and (B -> C)) or (B -> C)) -> ((B or C) -> (((A and (B -> C)) or (B -> C)) and C))), M:tm-349, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B Cm) (Dm (and (or (and Am (-> Bm Cm)) (-> Bm Cm)) Cm)) (C (-> (or Bm Cm) (and (or (and Am (-> Bm Cm)) (-> Bm Cm)) Cm))))
================================================================
tm-name          tm-65095
in-theory        65095
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-341 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65095.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65096
in-theory        65096
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     29
proof            (modus-ponens tm-338 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65096.        (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F)))), M:tm-338, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65097
in-theory        65097
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and ((C -> D) -> ((B or C) -> D)))))
theorem-size     49
proof            (modus-ponens tm-328 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65097.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and ((C -> D) -> ((B or C) -> D))))), M:tm-328, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65098
in-theory        65098
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> (E and F))) and (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     47
proof            (modus-ponens tm-327 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65098.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> (E and F))) and (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))))), M:tm-327, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65099
in-theory        65099
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> F) and (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-326 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65099.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> F) and (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))))), M:tm-326, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65100
in-theory        65100
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> E) and (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-325 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65100.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((E and F) -> E) and (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))))), M:tm-325, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65101
in-theory        65101
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     53
proof            (modus-ponens tm-324 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65101.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))))), M:tm-324, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65102
in-theory        65102
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> E)) and (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     45
proof            (modus-ponens tm-323 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65102.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> E)) and (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))))), M:tm-323, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65103
in-theory        65103
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> F))
theorem-size     25
proof            (modus-ponens tm-322 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65103.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> F)), M:tm-322, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65104
in-theory        65104
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> E))
theorem-size     25
proof            (modus-ponens tm-320 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65104.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((E and F) -> E)), M:tm-320, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65105
in-theory        65105
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     33
proof            (modus-ponens tm-318 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65105.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65106
in-theory        65106
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((A and (B -> C)) or (B -> C)) -> ((A and (B -> C)) or (B -> C))))
theorem-size     39
proof            (modus-ponens tm-316 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65106.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (((A and (B -> C)) or (B -> C)) -> ((A and (B -> C)) or (B -> C)))), M:tm-316, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65107
in-theory        65107
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> E)))
theorem-size     25
proof            (modus-ponens tm-315 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65107.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (E -> (F -> E))), M:tm-315, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65108
in-theory        65108
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((((A and (B -> C)) or (B -> C)) -> (not ((C -> D) -> ((B or C) -> D)))) -> (not ((A and (B -> C)) or (B -> C)))))
theorem-size     51
proof            (modus-ponens tm-313 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       167
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65108.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((((A and (B -> C)) or (B -> C)) -> (not ((C -> D) -> ((B or C) -> D)))) -> (not ((A and (B -> C)) or (B -> C))))), M:tm-313, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65109
in-theory        65109
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((((C -> D) -> ((B or C) -> D)) -> E) -> ((((A and (B -> C)) or (B -> C)) or ((C -> D) -> ((B or C) -> D))) -> E)))
theorem-size     53
proof            (modus-ponens tm-312 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65109.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((((C -> D) -> ((B or C) -> D)) -> E) -> ((((A and (B -> C)) or (B -> C)) or ((C -> D) -> ((B or C) -> D))) -> E))), M:tm-312, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65110
in-theory        65110
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (E or (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-311 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65110.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (E or (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))))), M:tm-311, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65111
in-theory        65111
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) or E))
theorem-size     41
proof            (modus-ponens tm-310 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65111.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) or E)), M:tm-310, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65112
in-theory        65112
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and E)))
theorem-size     43
proof            (modus-ponens tm-309 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65112.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (E -> ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and E))), M:tm-309, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65113
in-theory        65113
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((((A and (B -> C)) or (B -> C)) -> (C -> D)) -> (((A and (B -> C)) or (B -> C)) -> ((B or C) -> D))))
theorem-size     49
proof            (modus-ponens tm-306 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Cm Dm)) (C (-> (or Bm Cm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       171
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65113.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and ((((A and (B -> C)) or (B -> C)) -> (C -> D)) -> (((A and (B -> C)) or (B -> C)) -> ((B or C) -> D)))), M:tm-306, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Cm Dm)) (C (-> (or Bm Cm) Dm)))
================================================================
tm-name          tm-65114
in-theory        65114
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D)))))
theorem-size     41
proof            (modus-ponens tm-305 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65114.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) and (E -> (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))))), M:tm-305, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65115
in-theory        65115
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     31
proof            (modus-ponens tm-303 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65115.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-303, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65116
in-theory        65116
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-270 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65116.        ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-270, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65117
in-theory        65117
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-239 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65117.        ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-239, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65118
in-theory        65118
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H))))
theorem-size     37
proof            (modus-ponens tm-210 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65118.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H)))), M:tm-210, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65119
in-theory        65119
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     29
proof            (modus-ponens tm-183 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65119.        ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-183, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65120
in-theory        65120
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-157 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65120.        ((A -> ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-157, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65121
in-theory        65121
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-147 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65121.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-147, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65122
in-theory        65122
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-134 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65122.        ((A -> ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-134, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65123
in-theory        65123
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     35
proof            (modus-ponens tm-125 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65123.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-125, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65124
in-theory        65124
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (((C -> D) -> (B or C)) -> ((C -> D) -> D)))
theorem-size     23
proof            (modus-ponens tm-114 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Cm Dm)) (C (or Bm Cm)) (D Dm)))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65124.        (((A and (B -> C)) or (B -> C)) -> (((C -> D) -> (B or C)) -> ((C -> D) -> D))), M:tm-114, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Cm Dm)) (C (or Bm Cm)) (D Dm))
================================================================
tm-name          tm-65125
in-theory        65125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H))))
theorem-size     35
proof            (modus-ponens tm-113 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65125.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> ((G -> H) -> ((F or G) -> H)))), M:tm-113, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65126
in-theory        65126
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     39
proof            (modus-ponens tm-105 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       175
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65126.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-105, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65127
in-theory        65127
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((B or C) -> ((A and (B -> C)) or (B -> C))))
theorem-size     23
proof            (modus-ponens tm-98 tm-767 ((Dm (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B Cm) (A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (C (-> (or Bm Cm) (or (and Am (-> Bm Cm)) (-> Bm Cm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65127.        (((A and (B -> C)) or (B -> C)) -> ((B or C) -> ((A and (B -> C)) or (B -> C)))), M:tm-98, m:tm-767, u:((Dm (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B Cm) (A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (C (-> (or Bm Cm) (or (and Am (-> Bm Cm)) (-> Bm Cm)))))
================================================================
tm-name          tm-65128
in-theory        65128
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-95 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65128.        (((A -> B) -> (A -> A)) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F)))), M:tm-95, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65129
in-theory        65129
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D -> ((C -> E) -> ((B or C) -> E))))
theorem-size     21
proof            (modus-ponens tm-84 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65129.        (((A and (B -> C)) or (B -> C)) -> (D -> ((C -> E) -> ((B or C) -> E)))), M:tm-84, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65130
in-theory        65130
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     27
proof            (modus-ponens tm-83 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65130.        ((A -> (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-83, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65131
in-theory        65131
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (C -> D)) or (C -> D)) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     25
proof            (modus-ponens tm-76 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65131.        (((not (not A)) -> A) and (((B and (C -> D)) or (C -> D)) -> ((D -> E) -> ((C or D) -> E)))), M:tm-76, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65132
in-theory        65132
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (B -> C)) or (B -> C)))) or ((A and (B -> C)) or (B -> C))) -> ((C -> D) -> ((B or C) -> D)))
theorem-size     31
proof            (modus-ponens tm-73 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-8 tm-10 tm-4)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65132.        (((not (not ((A and (B -> C)) or (B -> C)))) or ((A and (B -> C)) or (B -> C))) -> ((C -> D) -> ((B or C) -> D))), M:tm-73, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65133
in-theory        65133
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     31
proof            (modus-ponens tm-69 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65133.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F)))), M:tm-69, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65134
in-theory        65134
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-54 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65134.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-54, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65135
in-theory        65135
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((C and (A -> B)) or (A -> B))) -> ((B -> D) -> ((A or B) -> D)))
theorem-size     23
proof            (modus-ponens tm-50 tm-767 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-8 tm-7 tm-4)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65135.        (((A -> B) or ((C and (A -> B)) or (A -> B))) -> ((B -> D) -> ((A or B) -> D))), M:tm-50, m:tm-767, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65136
in-theory        65136
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> ((C -> D) -> ((B or C) -> D)))
theorem-size     25
proof            (modus-ponens tm-49 tm-767 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-8 tm-6 tm-4)
proof-size       117
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65136.        (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> ((C -> D) -> ((B or C) -> D))), M:tm-49, m:tm-767, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65137
in-theory        65137
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) or (C -> D))) or ((B and (C -> D)) or (C -> D))) -> ((D -> E) -> ((C or D) -> E)))
theorem-size     31
proof            (modus-ponens tm-47 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-8 tm-4)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65137.        (((A and ((B and (C -> D)) or (C -> D))) or ((B and (C -> D)) or (C -> D))) -> ((D -> E) -> ((C or D) -> E))), M:tm-47, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65138
in-theory        65138
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> ((C -> E) -> ((B or C) -> E)))
theorem-size     31
proof            (modus-ponens tm-46 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-8 tm-3 tm-4)
proof-size       121
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65138.        (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> ((C -> E) -> ((B or C) -> E))), M:tm-46, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65139
in-theory        65139
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-42 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65139.        ((A -> (B or A)) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F)))), M:tm-42, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65140
in-theory        65140
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-32 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65140.        ((A -> (A or B)) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F)))), M:tm-32, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65141
in-theory        65141
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and ((C -> D) -> ((B or C) -> D))))
theorem-size     29
proof            (modus-ponens tm-24 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65141.        (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and ((C -> D) -> ((B or C) -> D)))), M:tm-24, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65142
in-theory        65142
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     27
proof            (modus-ponens tm-23 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65142.        ((A -> (B -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F)))), M:tm-23, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65143
in-theory        65143
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-22 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65143.        (((A and B) -> B) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F)))), M:tm-22, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65144
in-theory        65144
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-21 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65144.        (((A and B) -> A) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F)))), M:tm-21, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65145
in-theory        65145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G))))
theorem-size     33
proof            (modus-ponens tm-20 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65145.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> ((F -> G) -> ((E or F) -> G)))), M:tm-20, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65146
in-theory        65146
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F))))
theorem-size     25
proof            (modus-ponens tm-19 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65146.        ((A -> (B -> A)) and (((C and (D -> E)) or (D -> E)) -> ((E -> F) -> ((D or E) -> F)))), M:tm-19, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65147
in-theory        65147
times-derived    6
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((A and (B -> C)) or (B -> C)))
theorem-size     19
proof            (modus-ponens tm-12 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       105
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65147.        (((A and (B -> C)) or (B -> C)) -> ((A and (B -> C)) or (B -> C))), M:tm-12, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65148
in-theory        65148
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (not ((C -> D) -> ((B or C) -> D)))) -> (not ((A and (B -> C)) or (B -> C))))
theorem-size     31
proof            (modus-ponens tm-9 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-9 tm-8 tm-4)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65148.        ((((A and (B -> C)) or (B -> C)) -> (not ((C -> D) -> ((B or C) -> D)))) -> (not ((A and (B -> C)) or (B -> C)))), M:tm-9, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65149
in-theory        65149
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((E and (C -> A)) or (C -> A)) or ((A -> B) -> ((C or A) -> B))) -> D))
theorem-size     33
proof            (modus-ponens tm-8 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
axioms-used      (tm-8 tm-4)
proof-size       107
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65149.        ((((A -> B) -> ((C or A) -> B)) -> D) -> ((((E and (C -> A)) or (C -> A)) or ((A -> B) -> ((C or A) -> B))) -> D)), M:tm-8, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))
================================================================
tm-name          tm-65150
in-theory        65150
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (C -> D)) or (C -> D)) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-7 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-7 tm-8 tm-4)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65150.        (A or (((B and (C -> D)) or (C -> D)) -> ((D -> E) -> ((C or D) -> E)))), M:tm-7, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65151
in-theory        65151
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) or E)
theorem-size     21
proof            (modus-ponens tm-6 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-6 tm-8 tm-4)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65151.        ((((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))) or E), M:tm-6, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65152
in-theory        65152
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (C -> D)) or (C -> D)) -> ((D -> E) -> ((C or D) -> E))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       91
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65152.        (A -> ((((B and (C -> D)) or (C -> D)) -> ((D -> E) -> ((C or D) -> E))) and A)), M:tm-5, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65153
in-theory        65153
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (C -> D)) -> (((A and (B -> C)) or (B -> C)) -> ((B or C) -> D)))
theorem-size     29
proof            (modus-ponens tm-2 tm-767 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Cm Dm)) (C (-> (or Bm Cm) Dm))))
axioms-used      (tm-2 tm-8 tm-4)
proof-size       103
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65153.        ((((A and (B -> C)) or (B -> C)) -> (C -> D)) -> (((A and (B -> C)) or (B -> C)) -> ((B or C) -> D))), M:tm-2, m:tm-767, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Cm Dm)) (C (-> (or Bm Cm) Dm)))
================================================================
tm-name          tm-65154
in-theory        65154
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (C -> D)) or (C -> D)) -> ((D -> E) -> ((C or D) -> E))))
theorem-size     21
proof            (modus-ponens tm-1 tm-767 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm))))))
axioms-used      (tm-1 tm-8 tm-4)
proof-size       87
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-767.          (((A and (B -> C)) or (B -> C)) -> ((C -> D) -> ((B or C) -> D))), M:tm-47, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-65154.        (A -> (((B and (C -> D)) or (C -> D)) -> ((D -> E) -> ((C or D) -> E)))), M:tm-1, m:tm-767, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Cm Dm) (-> (or Bm Cm) Dm)))))
================================================================
tm-name          tm-65155
in-theory        65155
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     29
proof            (modus-ponens tm-757 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-9)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65155.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-757, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65156
in-theory        65156
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> ((B -> (not C)) -> (not B))))
theorem-size     47
proof            (modus-ponens tm-747 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-9)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65156.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> ((B -> (not C)) -> (not B)))), M:tm-747, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65157
in-theory        65157
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F))))
theorem-size     43
proof            (modus-ponens tm-708 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-9)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65157.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F)))), M:tm-708, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65158
in-theory        65158
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-665 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-9)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65158.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-665, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65159
in-theory        65159
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D or ((B -> (not C)) -> (not B))))
theorem-size     19
proof            (modus-ponens tm-623 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65159.        (((A and (B -> C)) or (B -> C)) -> (D or ((B -> (not C)) -> (not B)))), M:tm-623, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65160
in-theory        65160
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-622 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65160.        ((A -> (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-622, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65161
in-theory        65161
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (D -> (E or D)))
theorem-size     23
proof            (modus-ponens tm-609 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65161.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (D -> (E or D))), M:tm-609, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65162
in-theory        65162
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-605 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65162.        ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-605, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65163
in-theory        65163
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((D -> (E or D)) and (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B)))))
theorem-size     41
proof            (modus-ponens tm-595 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65163.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((D -> (E or D)) and (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))))), M:tm-595, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65164
in-theory        65164
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-550 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65164.        (((A -> (B or A)) or C) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-550, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65165
in-theory        65165
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-540 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65165.        ((A or (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-540, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65166
in-theory        65166
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-530 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65166.        ((A or (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-530, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65167
in-theory        65167
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-520 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65167.        ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-520, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65168
in-theory        65168
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-510 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65168.        ((A or ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-510, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65169
in-theory        65169
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-500 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65169.        ((A or ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-500, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65170
in-theory        65170
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F))))
theorem-size     33
proof            (modus-ponens tm-490 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65170.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F)))), M:tm-490, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65171
in-theory        65171
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-480 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65171.        ((A or (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-480, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65172
in-theory        65172
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (((B -> (not C)) -> (not B)) or D))
theorem-size     19
proof            (modus-ponens tm-470 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65172.        (((A and (B -> C)) or (B -> C)) -> (((B -> (not C)) -> (not B)) or D)), M:tm-470, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65173
in-theory        65173
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-469 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65173.        ((A -> (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-469, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65174
in-theory        65174
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (D -> (D or E)))
theorem-size     23
proof            (modus-ponens tm-456 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65174.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (D -> (D or E))), M:tm-456, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65175
in-theory        65175
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-453 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65175.        ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-453, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65176
in-theory        65176
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((D -> (D or E)) and (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B)))))
theorem-size     41
proof            (modus-ponens tm-443 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65176.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((D -> (D or E)) and (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))))), M:tm-443, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65177
in-theory        65177
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-409 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65177.        (((A -> (A or B)) or C) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-409, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65178
in-theory        65178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-400 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65178.        (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-400, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65179
in-theory        65179
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-391 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65179.        ((((A and B) -> B) or C) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-391, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65180
in-theory        65180
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-382 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65180.        ((((A and B) -> A) or C) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-382, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65181
in-theory        65181
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F))))
theorem-size     33
proof            (modus-ponens tm-373 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65181.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F)))), M:tm-373, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65182
in-theory        65182
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-364 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65182.        (((A -> (B -> A)) or C) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-364, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65183
in-theory        65183
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D -> (((B -> (not C)) -> (not B)) and D)))
theorem-size     21
proof            (modus-ponens tm-355 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4 tm-9)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65183.        (((A and (B -> C)) or (B -> C)) -> (D -> (((B -> (not C)) -> (not B)) and D))), M:tm-355, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65184
in-theory        65184
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-354 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65184.        ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-354, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65185
in-theory        65185
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (D -> (E -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-341 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-9)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65185.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65186
in-theory        65186
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     27
proof            (modus-ponens tm-338 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65186.        (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-338, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65187
in-theory        65187
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and ((B -> (not C)) -> (not B)))))
theorem-size     45
proof            (modus-ponens tm-328 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-9)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65187.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and ((B -> (not C)) -> (not B))))), M:tm-328, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65188
in-theory        65188
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((D -> (E -> (D and E))) and (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B)))))
theorem-size     43
proof            (modus-ponens tm-327 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-9)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65188.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((D -> (E -> (D and E))) and (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))))), M:tm-327, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65189
in-theory        65189
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((D and E) -> E) and (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B)))))
theorem-size     41
proof            (modus-ponens tm-326 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65189.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((D and E) -> E) and (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))))), M:tm-326, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65190
in-theory        65190
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((D and E) -> D) and (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B)))))
theorem-size     41
proof            (modus-ponens tm-325 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65190.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((D and E) -> D) and (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))))), M:tm-325, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65191
in-theory        65191
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B)))))
theorem-size     49
proof            (modus-ponens tm-324 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-9)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65191.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))))), M:tm-324, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65192
in-theory        65192
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((D -> (E -> D)) and (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B)))))
theorem-size     41
proof            (modus-ponens tm-323 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65192.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((D -> (E -> D)) and (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))))), M:tm-323, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65193
in-theory        65193
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((D and E) -> E))
theorem-size     23
proof            (modus-ponens tm-322 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65193.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((D and E) -> E)), M:tm-322, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65194
in-theory        65194
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((D and E) -> D))
theorem-size     23
proof            (modus-ponens tm-320 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65194.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((D and E) -> D)), M:tm-320, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65195
in-theory        65195
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     31
proof            (modus-ponens tm-318 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-9)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65195.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65196
in-theory        65196
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((A and (B -> C)) or (B -> C)) -> ((A and (B -> C)) or (B -> C))))
theorem-size     37
proof            (modus-ponens tm-316 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-9)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65196.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (((A and (B -> C)) or (B -> C)) -> ((A and (B -> C)) or (B -> C)))), M:tm-316, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65197
in-theory        65197
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (D -> (E -> D)))
theorem-size     23
proof            (modus-ponens tm-315 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-9)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65197.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (D -> (E -> D))), M:tm-315, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65198
in-theory        65198
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((((A and (B -> C)) or (B -> C)) -> (not ((B -> (not C)) -> (not B)))) -> (not ((A and (B -> C)) or (B -> C)))))
theorem-size     47
proof            (modus-ponens tm-313 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65198.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((((A and (B -> C)) or (B -> C)) -> (not ((B -> (not C)) -> (not B)))) -> (not ((A and (B -> C)) or (B -> C))))), M:tm-313, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65199
in-theory        65199
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((((B -> (not C)) -> (not B)) -> D) -> ((((A and (B -> C)) or (B -> C)) or ((B -> (not C)) -> (not B))) -> D)))
theorem-size     47
proof            (modus-ponens tm-312 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-9)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65199.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((((B -> (not C)) -> (not B)) -> D) -> ((((A and (B -> C)) or (B -> C)) or ((B -> (not C)) -> (not B))) -> D))), M:tm-312, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65200
in-theory        65200
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (D or (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B)))))
theorem-size     37
proof            (modus-ponens tm-311 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65200.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (D or (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))))), M:tm-311, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65201
in-theory        65201
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) or D))
theorem-size     37
proof            (modus-ponens tm-310 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65201.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) or D)), M:tm-310, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65202
in-theory        65202
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (D -> ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and D)))
theorem-size     39
proof            (modus-ponens tm-309 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-9)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65202.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (D -> ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and D))), M:tm-309, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65203
in-theory        65203
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((((A and (B -> C)) or (B -> C)) -> (B -> (not C))) -> (((A and (B -> C)) or (B -> C)) -> (not B))))
theorem-size     45
proof            (modus-ponens tm-306 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (not Cm))) (C (not Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-9)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65203.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and ((((A and (B -> C)) or (B -> C)) -> (B -> (not C))) -> (((A and (B -> C)) or (B -> C)) -> (not B)))), M:tm-306, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (not Cm))) (C (not Bm)))
================================================================
tm-name          tm-65204
in-theory        65204
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (D -> (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B)))))
theorem-size     37
proof            (modus-ponens tm-305 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-9)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65204.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) and (D -> (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))))), M:tm-305, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65205
in-theory        65205
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     29
proof            (modus-ponens tm-303 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-9)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65205.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-303, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65206
in-theory        65206
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-270 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65206.        ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-270, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65207
in-theory        65207
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-239 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65207.        ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-239, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65208
in-theory        65208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F))))
theorem-size     35
proof            (modus-ponens tm-210 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-9)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65208.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F)))), M:tm-210, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65209
in-theory        65209
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     27
proof            (modus-ponens tm-183 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65209.        ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-183, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65210
in-theory        65210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-157 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65210.        ((A -> ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-157, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65211
in-theory        65211
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     33
proof            (modus-ponens tm-147 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65211.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-147, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65212
in-theory        65212
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-134 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65212.        ((A -> ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-134, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65213
in-theory        65213
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     33
proof            (modus-ponens tm-125 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65213.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-125, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65214
in-theory        65214
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F))))
theorem-size     33
proof            (modus-ponens tm-113 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 tm-9)
proof-size       149
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65214.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> ((F -> (not G)) -> (not F)))), M:tm-113, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65215
in-theory        65215
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     37
proof            (modus-ponens tm-105 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-9)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65215.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-105, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65216
in-theory        65216
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-95 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 tm-9)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65216.        (((A -> B) -> (A -> A)) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-95, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65217
in-theory        65217
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D -> ((B -> (not C)) -> (not B))))
theorem-size     19
proof            (modus-ponens tm-84 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-9)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65217.        (((A and (B -> C)) or (B -> C)) -> (D -> ((B -> (not C)) -> (not B)))), M:tm-84, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65218
in-theory        65218
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     25
proof            (modus-ponens tm-83 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-9)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65218.        ((A -> (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-83, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65219
in-theory        65219
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (C -> D)) or (C -> D)) -> ((C -> (not D)) -> (not C))))
theorem-size     23
proof            (modus-ponens tm-76 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65219.        (((not (not A)) -> A) and (((B and (C -> D)) or (C -> D)) -> ((C -> (not D)) -> (not C)))), M:tm-76, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65220
in-theory        65220
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (B -> C)) or (B -> C)))) or ((A and (B -> C)) or (B -> C))) -> ((B -> (not C)) -> (not B)))
theorem-size     29
proof            (modus-ponens tm-73 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-8 tm-10 tm-4 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65220.        (((not (not ((A and (B -> C)) or (B -> C)))) or ((A and (B -> C)) or (B -> C))) -> ((B -> (not C)) -> (not B))), M:tm-73, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65221
in-theory        65221
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     29
proof            (modus-ponens tm-69 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65221.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-69, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65222
in-theory        65222
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-54 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65222.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-54, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65223
in-theory        65223
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((C and (A -> B)) or (A -> B))) -> ((A -> (not B)) -> (not A)))
theorem-size     21
proof            (modus-ponens tm-50 tm-768 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-8 tm-7 tm-4 tm-9)
proof-size       109
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65223.        (((A -> B) or ((C and (A -> B)) or (A -> B))) -> ((A -> (not B)) -> (not A))), M:tm-50, m:tm-768, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65224
in-theory        65224
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> ((B -> (not C)) -> (not B)))
theorem-size     23
proof            (modus-ponens tm-49 tm-768 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-8 tm-6 tm-4 tm-9)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65224.        (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> ((B -> (not C)) -> (not B))), M:tm-49, m:tm-768, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65225
in-theory        65225
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) or (C -> D))) or ((B and (C -> D)) or (C -> D))) -> ((C -> (not D)) -> (not C)))
theorem-size     29
proof            (modus-ponens tm-47 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-8 tm-4 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65225.        (((A and ((B and (C -> D)) or (C -> D))) or ((B and (C -> D)) or (C -> D))) -> ((C -> (not D)) -> (not C))), M:tm-47, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65226
in-theory        65226
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> ((B -> (not C)) -> (not B)))
theorem-size     29
proof            (modus-ponens tm-46 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-8 tm-3 tm-4 tm-9)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65226.        (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> ((B -> (not C)) -> (not B))), M:tm-46, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65227
in-theory        65227
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-42 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65227.        ((A -> (B or A)) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-42, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65228
in-theory        65228
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-32 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65228.        ((A -> (A or B)) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-32, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65229
in-theory        65229
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and ((B -> (not C)) -> (not B))))
theorem-size     27
proof            (modus-ponens tm-24 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-9)
proof-size       113
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65229.        (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and ((B -> (not C)) -> (not B)))), M:tm-24, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65230
in-theory        65230
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     25
proof            (modus-ponens tm-23 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-9)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65230.        ((A -> (B -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-23, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65231
in-theory        65231
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-22 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65231.        (((A and B) -> B) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-22, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65232
in-theory        65232
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-21 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65232.        (((A and B) -> A) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-21, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65233
in-theory        65233
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E))))
theorem-size     31
proof            (modus-ponens tm-20 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-9)
proof-size       125
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65233.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> ((E -> (not F)) -> (not E)))), M:tm-20, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65234
in-theory        65234
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D))))
theorem-size     23
proof            (modus-ponens tm-19 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-9)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65234.        ((A -> (B -> A)) and (((C and (D -> E)) or (D -> E)) -> ((D -> (not E)) -> (not D)))), M:tm-19, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65235
in-theory        65235
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (not ((B -> (not C)) -> (not B)))) -> (not ((A and (B -> C)) or (B -> C))))
theorem-size     29
proof            (modus-ponens tm-9 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-9 tm-8 tm-4)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65235.        ((((A and (B -> C)) or (B -> C)) -> (not ((B -> (not C)) -> (not B)))) -> (not ((A and (B -> C)) or (B -> C)))), M:tm-9, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65236
in-theory        65236
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (not B)) -> (not A)) -> C) -> ((((D and (A -> B)) or (A -> B)) or ((A -> (not B)) -> (not A))) -> C))
theorem-size     29
proof            (modus-ponens tm-8 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm)))))
axioms-used      (tm-8 tm-4 tm-9)
proof-size       99
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65236.        ((((A -> (not B)) -> (not A)) -> C) -> ((((D and (A -> B)) or (A -> B)) or ((A -> (not B)) -> (not A))) -> C)), M:tm-8, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> (-> Bm (not Cm)) (not Bm))))
================================================================
tm-name          tm-65237
in-theory        65237
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (C -> D)) or (C -> D)) -> ((C -> (not D)) -> (not C))))
theorem-size     19
proof            (modus-ponens tm-7 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-7 tm-8 tm-4 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65237.        (A or (((B and (C -> D)) or (C -> D)) -> ((C -> (not D)) -> (not C)))), M:tm-7, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65238
in-theory        65238
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) or D)
theorem-size     19
proof            (modus-ponens tm-6 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-6 tm-8 tm-4 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65238.        ((((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))) or D), M:tm-6, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65239
in-theory        65239
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (C -> D)) or (C -> D)) -> ((C -> (not D)) -> (not C))) and A))
theorem-size     21
proof            (modus-ponens tm-5 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-9)
proof-size       85
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65239.        (A -> ((((B and (C -> D)) or (C -> D)) -> ((C -> (not D)) -> (not C))) and A)), M:tm-5, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65240
in-theory        65240
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (not C))) -> (((A and (B -> C)) or (B -> C)) -> (not B)))
theorem-size     27
proof            (modus-ponens tm-2 tm-768 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (not Cm))) (C (not Bm))))
axioms-used      (tm-2 tm-8 tm-4 tm-9)
proof-size       97
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65240.        ((((A and (B -> C)) or (B -> C)) -> (B -> (not C))) -> (((A and (B -> C)) or (B -> C)) -> (not B))), M:tm-2, m:tm-768, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (not Cm))) (C (not Bm)))
================================================================
tm-name          tm-65241
in-theory        65241
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (C -> D)) or (C -> D)) -> ((C -> (not D)) -> (not C))))
theorem-size     19
proof            (modus-ponens tm-1 tm-768 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm))))))
axioms-used      (tm-1 tm-8 tm-4 tm-9)
proof-size       81
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-768.          (((A and (B -> C)) or (B -> C)) -> ((B -> (not C)) -> (not B))), M:tm-47, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-65241.        (A -> (((B and (C -> D)) or (C -> D)) -> ((C -> (not D)) -> (not C)))), M:tm-1, m:tm-768, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> (-> Bm (not Cm)) (not Bm)))))
================================================================
tm-name          tm-65242
in-theory        65242
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     23
proof            (modus-ponens tm-757 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-10)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65242.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-757, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65243
in-theory        65243
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (((((A and (not (not B))) or (not (not B))) and C) or ((A and (not (not B))) or (not (not B)))) -> B))
theorem-size     35
proof            (modus-ponens tm-747 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-10)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65243.        ((((A and (not (not B))) or (not (not B))) -> B) and (((((A and (not (not B))) or (not (not B))) and C) or ((A and (not (not B))) or (not (not B)))) -> B)), M:tm-747, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65244
in-theory        65244
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (not (not F))) or (not (not F))) -> F))
theorem-size     37
proof            (modus-ponens tm-708 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-10)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65244.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (not (not F))) or (not (not F))) -> F)), M:tm-708, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65245
in-theory        65245
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     25
proof            (modus-ponens tm-665 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-10)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65245.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-665, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65246
in-theory        65246
times-derived    1
----------------------------------------------------------------
theorem          (((A and (not (not B))) or (not (not B))) -> (C or B))
theorem-size     13
proof            (modus-ponens tm-623 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65246.        (((A and (not (not B))) or (not (not B))) -> (C or B)), M:tm-623, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65247
in-theory        65247
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-622 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65247.        ((A -> (B -> (C or B))) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-622, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65248
in-theory        65248
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and (not (not (not (B -> (C or B)))))) or (not (not (not (B -> (C or B)))))))
theorem-size     20
proof            (modus-ponens tm-618 tm-769 ((A (or (and Am (not (not (not (-> B (or C B)))))) (not (not (not (-> B (or C B))))))) (Bm (not (-> B (or C B))))))
axioms-used      (tm-9 tm-1 tm-7 tm-8 tm-4 tm-10)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-618.          ((A -> (not (B -> (C or B)))) -> (not A)), M:tm-9, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65248.        (not ((A and (not (not (not (B -> (C or B)))))) or (not (not (not (B -> (C or B))))))), M:tm-618, m:tm-769, u:((A (or (and Am (not (not (not (-> B (or C B)))))) (not (not (not (-> B (or C B))))))) (Bm (not (-> B (or C B)))))
================================================================
tm-name          tm-65249
in-theory        65249
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (C -> (D or C)))
theorem-size     17
proof            (modus-ponens tm-609 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65249.        ((((A and (not (not B))) or (not (not B))) -> B) and (C -> (D or C))), M:tm-609, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65250
in-theory        65250
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     21
proof            (modus-ponens tm-605 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65250.        ((A -> ((B -> (C or B)) and A)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-605, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65251
in-theory        65251
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and ((C -> (D or C)) and (((A and (not (not B))) or (not (not B))) -> B)))
theorem-size     29
proof            (modus-ponens tm-595 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65251.        ((((A and (not (not B))) or (not (not B))) -> B) and ((C -> (D or C)) and (((A and (not (not B))) or (not (not B))) -> B))), M:tm-595, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65252
in-theory        65252
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-550 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65252.        (((A -> (B or A)) or C) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-550, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65253
in-theory        65253
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-540 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65253.        ((A or (B -> (C or B))) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-540, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65254
in-theory        65254
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-530 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65254.        ((A or (B -> (B or C))) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-530, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65255
in-theory        65255
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     21
proof            (modus-ponens tm-520 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65255.        ((A or (B -> (C -> (B and C)))) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-520, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65256
in-theory        65256
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-510 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65256.        ((A or ((B and C) -> C)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-510, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65257
in-theory        65257
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-500 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65257.        ((A or ((B and C) -> B)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-500, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65258
in-theory        65258
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (not (not F))) or (not (not F))) -> F))
theorem-size     27
proof            (modus-ponens tm-490 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65258.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (not (not F))) or (not (not F))) -> F)), M:tm-490, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65259
in-theory        65259
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-480 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65259.        ((A or (B -> (C -> B))) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-480, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65260
in-theory        65260
times-derived    1
----------------------------------------------------------------
theorem          (((A and (not (not B))) or (not (not B))) -> (B or C))
theorem-size     13
proof            (modus-ponens tm-470 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65260.        (((A and (not (not B))) or (not (not B))) -> (B or C)), M:tm-470, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65261
in-theory        65261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-469 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65261.        ((A -> (B -> (B or C))) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-469, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65262
in-theory        65262
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and (not (not (not (B -> (B or C)))))) or (not (not (not (B -> (B or C)))))))
theorem-size     20
proof            (modus-ponens tm-465 tm-769 ((A (or (and Am (not (not (not (-> B (or B C)))))) (not (not (not (-> B (or B C))))))) (Bm (not (-> B (or B C))))))
axioms-used      (tm-9 tm-1 tm-6 tm-8 tm-4 tm-10)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-465.          ((A -> (not (B -> (B or C)))) -> (not A)), M:tm-9, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65262.        (not ((A and (not (not (not (B -> (B or C)))))) or (not (not (not (B -> (B or C))))))), M:tm-465, m:tm-769, u:((A (or (and Am (not (not (not (-> B (or B C)))))) (not (not (not (-> B (or B C))))))) (Bm (not (-> B (or B C)))))
================================================================
tm-name          tm-65263
in-theory        65263
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (C -> (C or D)))
theorem-size     17
proof            (modus-ponens tm-456 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65263.        ((((A and (not (not B))) or (not (not B))) -> B) and (C -> (C or D))), M:tm-456, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65264
in-theory        65264
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     21
proof            (modus-ponens tm-453 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65264.        ((A -> ((B -> (B or C)) and A)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-453, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65265
in-theory        65265
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and ((C -> (C or D)) and (((A and (not (not B))) or (not (not B))) -> B)))
theorem-size     29
proof            (modus-ponens tm-443 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65265.        ((((A and (not (not B))) or (not (not B))) -> B) and ((C -> (C or D)) and (((A and (not (not B))) or (not (not B))) -> B))), M:tm-443, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65266
in-theory        65266
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-409 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65266.        (((A -> (A or B)) or C) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-409, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65267
in-theory        65267
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     21
proof            (modus-ponens tm-400 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65267.        (((A -> (B -> (A and B))) or C) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-400, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65268
in-theory        65268
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-391 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65268.        ((((A and B) -> B) or C) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-391, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65269
in-theory        65269
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-382 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65269.        ((((A and B) -> A) or C) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-382, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65270
in-theory        65270
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (not (not F))) or (not (not F))) -> F))
theorem-size     27
proof            (modus-ponens tm-373 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65270.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (not (not F))) or (not (not F))) -> F)), M:tm-373, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65271
in-theory        65271
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-364 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65271.        (((A -> (B -> A)) or C) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-364, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65272
in-theory        65272
times-derived    1
----------------------------------------------------------------
theorem          (((A and (not (not B))) or (not (not B))) -> (C -> (B and C)))
theorem-size     15
proof            (modus-ponens tm-355 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4 tm-10)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65272.        (((A and (not (not B))) or (not (not B))) -> (C -> (B and C))), M:tm-355, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65273
in-theory        65273
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     21
proof            (modus-ponens tm-354 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65273.        ((A -> (B -> (C -> (B and C)))) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-354, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65274
in-theory        65274
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and (not (not (not (B -> (C -> (B and C))))))) or (not (not (not (B -> (C -> (B and C))))))))
theorem-size     24
proof            (modus-ponens tm-350 tm-769 ((A (or (and Am (not (not (not (-> B (-> C (and B C))))))) (not (not (not (-> B (-> C (and B C)))))))) (Bm (not (-> B (-> C (and B C)))))))
axioms-used      (tm-9 tm-1 tm-5 tm-8 tm-4 tm-10)
proof-size       114
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-350.          ((A -> (not (B -> (C -> (B and C))))) -> (not A)), M:tm-9, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65274.        (not ((A and (not (not (not (B -> (C -> (B and C))))))) or (not (not (not (B -> (C -> (B and C)))))))), M:tm-350, m:tm-769, u:((A (or (and Am (not (not (not (-> B (-> C (and B C))))))) (not (not (not (-> B (-> C (and B C)))))))) (Bm (not (-> B (-> C (and B C))))))
================================================================
tm-name          tm-65275
in-theory        65275
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (C -> (D -> (C and D))))
theorem-size     19
proof            (modus-ponens tm-341 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-10)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65275.        ((((A and (not (not B))) or (not (not B))) -> B) and (C -> (D -> (C and D)))), M:tm-341, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65276
in-theory        65276
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (not (not D))) or (not (not D))) -> D))
theorem-size     21
proof            (modus-ponens tm-338 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-10)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65276.        (((A -> B) -> (A -> (A and B))) and (((C and (not (not D))) or (not (not D))) -> D)), M:tm-338, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65277
in-theory        65277
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (((A and (not (not B))) or (not (not B))) -> (((A and (not (not B))) or (not (not B))) and B)))
theorem-size     33
proof            (modus-ponens tm-328 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-10)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65277.        ((((A and (not (not B))) or (not (not B))) -> B) and (((A and (not (not B))) or (not (not B))) -> (((A and (not (not B))) or (not (not B))) and B))), M:tm-328, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65278
in-theory        65278
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and ((C -> (D -> (C and D))) and (((A and (not (not B))) or (not (not B))) -> B)))
theorem-size     31
proof            (modus-ponens tm-327 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-10)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65278.        ((((A and (not (not B))) or (not (not B))) -> B) and ((C -> (D -> (C and D))) and (((A and (not (not B))) or (not (not B))) -> B))), M:tm-327, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65279
in-theory        65279
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (((C and D) -> D) and (((A and (not (not B))) or (not (not B))) -> B)))
theorem-size     29
proof            (modus-ponens tm-326 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65279.        ((((A and (not (not B))) or (not (not B))) -> B) and (((C and D) -> D) and (((A and (not (not B))) or (not (not B))) -> B))), M:tm-326, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65280
in-theory        65280
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (((C and D) -> C) and (((A and (not (not B))) or (not (not B))) -> B)))
theorem-size     29
proof            (modus-ponens tm-325 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65280.        ((((A and (not (not B))) or (not (not B))) -> B) and (((C and D) -> C) and (((A and (not (not B))) or (not (not B))) -> B))), M:tm-325, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65281
in-theory        65281
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A and (not (not B))) or (not (not B))) -> B)))
theorem-size     37
proof            (modus-ponens tm-324 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-10)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65281.        ((((A and (not (not B))) or (not (not B))) -> B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and (((A and (not (not B))) or (not (not B))) -> B))), M:tm-324, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65282
in-theory        65282
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and ((C -> (D -> C)) and (((A and (not (not B))) or (not (not B))) -> B)))
theorem-size     29
proof            (modus-ponens tm-323 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-10)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65282.        ((((A and (not (not B))) or (not (not B))) -> B) and ((C -> (D -> C)) and (((A and (not (not B))) or (not (not B))) -> B))), M:tm-323, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65283
in-theory        65283
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and ((C and D) -> D))
theorem-size     17
proof            (modus-ponens tm-322 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65283.        ((((A and (not (not B))) or (not (not B))) -> B) and ((C and D) -> D)), M:tm-322, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65284
in-theory        65284
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and ((C and D) -> C))
theorem-size     17
proof            (modus-ponens tm-320 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65284.        ((((A and (not (not B))) or (not (not B))) -> B) and ((C and D) -> C)), M:tm-320, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65285
in-theory        65285
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-318 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-10)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65285.        ((((A and (not (not B))) or (not (not B))) -> B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-318, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65286
in-theory        65286
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (((A and (not (not B))) or (not (not B))) -> ((A and (not (not B))) or (not (not B)))))
theorem-size     31
proof            (modus-ponens tm-316 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-10)
proof-size       141
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65286.        ((((A and (not (not B))) or (not (not B))) -> B) and (((A and (not (not B))) or (not (not B))) -> ((A and (not (not B))) or (not (not B))))), M:tm-316, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65287
in-theory        65287
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (C -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-315 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-10)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65287.        ((((A and (not (not B))) or (not (not B))) -> B) and (C -> (D -> C))), M:tm-315, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65288
in-theory        65288
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and ((((A and (not (not B))) or (not (not B))) -> (not B)) -> (not ((A and (not (not B))) or (not (not B))))))
theorem-size     35
proof            (modus-ponens tm-313 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 tm-10)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65288.        ((((A and (not (not B))) or (not (not B))) -> B) and ((((A and (not (not B))) or (not (not B))) -> (not B)) -> (not ((A and (not (not B))) or (not (not B)))))), M:tm-313, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65289
in-theory        65289
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and ((B -> C) -> ((((A and (not (not B))) or (not (not B))) or B) -> C)))
theorem-size     29
proof            (modus-ponens tm-312 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-10)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65289.        ((((A and (not (not B))) or (not (not B))) -> B) and ((B -> C) -> ((((A and (not (not B))) or (not (not B))) or B) -> C))), M:tm-312, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65290
in-theory        65290
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (C or (((A and (not (not B))) or (not (not B))) -> B)))
theorem-size     25
proof            (modus-ponens tm-311 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65290.        ((((A and (not (not B))) or (not (not B))) -> B) and (C or (((A and (not (not B))) or (not (not B))) -> B))), M:tm-311, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65291
in-theory        65291
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and ((((A and (not (not B))) or (not (not B))) -> B) or C))
theorem-size     25
proof            (modus-ponens tm-310 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65291.        ((((A and (not (not B))) or (not (not B))) -> B) and ((((A and (not (not B))) or (not (not B))) -> B) or C)), M:tm-310, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65292
in-theory        65292
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (C -> ((((A and (not (not B))) or (not (not B))) -> B) and C)))
theorem-size     27
proof            (modus-ponens tm-309 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-10)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65292.        ((((A and (not (not B))) or (not (not B))) -> B) and (C -> ((((A and (not (not B))) or (not (not B))) -> B) and C))), M:tm-309, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65293
in-theory        65293
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not (B -> C)))) or (not (not (B -> C)))) -> (B -> C)) and ((((A and (not (not (B -> C)))) or (not (not (B -> C)))) -> B) -> (((A and (not (not (B -> C)))) or (not (not (B -> C)))) -> C)))
theorem-size     49
proof            (modus-ponens tm-306 tm-769 ((A (or (and Am (not (not (-> B C)))) (not (not (-> B C))))) (Bm (-> B C))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-10)
proof-size       155
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65293.        ((((A and (not (not (B -> C)))) or (not (not (B -> C)))) -> (B -> C)) and ((((A and (not (not (B -> C)))) or (not (not (B -> C)))) -> B) -> (((A and (not (not (B -> C)))) or (not (not (B -> C)))) -> C))), M:tm-306, m:tm-769, u:((A (or (and Am (not (not (-> B C)))) (not (not (-> B C))))) (Bm (-> B C)))
================================================================
tm-name          tm-65294
in-theory        65294
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) and (C -> (((A and (not (not B))) or (not (not B))) -> B)))
theorem-size     25
proof            (modus-ponens tm-305 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65294.        ((((A and (not (not B))) or (not (not B))) -> B) and (C -> (((A and (not (not B))) or (not (not B))) -> B))), M:tm-305, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65295
in-theory        65295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     23
proof            (modus-ponens tm-303 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-8 tm-4 tm-10)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65295.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-303, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65296
in-theory        65296
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     21
proof            (modus-ponens tm-270 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-4 tm-8 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65296.        ((A -> (((B and C) -> C) and A)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-270, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65297
in-theory        65297
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     21
proof            (modus-ponens tm-239 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65297.        ((A -> (((B and C) -> B) and A)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-239, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65298
in-theory        65298
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (not (not F))) or (not (not F))) -> F))
theorem-size     29
proof            (modus-ponens tm-210 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-10)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65298.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (not (not F))) or (not (not F))) -> F)), M:tm-210, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65299
in-theory        65299
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     21
proof            (modus-ponens tm-183 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65299.        ((A -> ((B -> (C -> B)) and A)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-183, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65300
in-theory        65300
times-derived    1
----------------------------------------------------------------
theorem          (((A and (not (not (B and C)))) or (not (not (B and C)))) -> C)
theorem-size     15
proof            (modus-ponens tm-158 tm-769 ((A (or (and Am (not (not (and B C)))) (not (not (and B C))))) (Bm (and B C))))
axioms-used      (tm-2 tm-1 tm-4 tm-8 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-158.          ((A -> (B and C)) -> (A -> C)), M:tm-2, m:tm-18, u:((A Am) (B (and Bm Cm)) (C Cm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65300.        (((A and (not (not (B and C)))) or (not (not (B and C)))) -> C), M:tm-158, m:tm-769, u:((A (or (and Am (not (not (and B C)))) (not (not (and B C))))) (Bm (and B C)))
================================================================
tm-name          tm-65301
in-theory        65301
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-157 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65301.        ((A -> ((B and C) -> C)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-157, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65302
in-theory        65302
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and (not (not (not ((B and C) -> C))))) or (not (not (not ((B and C) -> C))))))
theorem-size     20
proof            (modus-ponens tm-153 tm-769 ((A (or (and Am (not (not (not (-> (and B C) C))))) (not (not (not (-> (and B C) C)))))) (Bm (not (-> (and B C) C)))))
axioms-used      (tm-9 tm-1 tm-4 tm-8 tm-10)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-153.          ((A -> (not ((B and C) -> C))) -> (not A)), M:tm-9, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65302.        (not ((A and (not (not (not ((B and C) -> C))))) or (not (not (not ((B and C) -> C)))))), M:tm-153, m:tm-769, u:((A (or (and Am (not (not (not (-> (and B C) C))))) (not (not (not (-> (and B C) C)))))) (Bm (not (-> (and B C) C))))
================================================================
tm-name          tm-65303
in-theory        65303
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     27
proof            (modus-ponens tm-147 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65303.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-147, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65304
in-theory        65304
times-derived    1
----------------------------------------------------------------
theorem          (((A and (not (not (B and C)))) or (not (not (B and C)))) -> B)
theorem-size     15
proof            (modus-ponens tm-135 tm-769 ((A (or (and Am (not (not (and B C)))) (not (not (and B C))))) (Bm (and B C))))
axioms-used      (tm-2 tm-1 tm-3 tm-8 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-135.          ((A -> (B and C)) -> (A -> B)), M:tm-2, m:tm-16, u:((A Am) (B (and Bm Cm)) (C Bm))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65304.        (((A and (not (not (B and C)))) or (not (not (B and C)))) -> B), M:tm-135, m:tm-769, u:((A (or (and Am (not (not (and B C)))) (not (not (and B C))))) (Bm (and B C)))
================================================================
tm-name          tm-65305
in-theory        65305
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-134 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65305.        ((A -> ((B and C) -> B)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-134, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65306
in-theory        65306
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and (not (not (not ((B and C) -> B))))) or (not (not (not ((B and C) -> B))))))
theorem-size     20
proof            (modus-ponens tm-130 tm-769 ((A (or (and Am (not (not (not (-> (and B C) B))))) (not (not (not (-> (and B C) B)))))) (Bm (not (-> (and B C) B)))))
axioms-used      (tm-9 tm-1 tm-3 tm-8 tm-4 tm-10)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-130.          ((A -> (not ((B and C) -> B))) -> (not A)), M:tm-9, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65306.        (not ((A and (not (not (not ((B and C) -> B))))) or (not (not (not ((B and C) -> B)))))), M:tm-130, m:tm-769, u:((A (or (and Am (not (not (not (-> (and B C) B))))) (not (not (not (-> (and B C) B)))))) (Bm (not (-> (and B C) B))))
================================================================
tm-name          tm-65307
in-theory        65307
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     27
proof            (modus-ponens tm-125 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65307.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-125, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65308
in-theory        65308
times-derived    1
----------------------------------------------------------------
theorem          (((A and (not (not (B -> (C -> D))))) or (not (not (B -> (C -> D))))) -> ((B -> C) -> (B -> D)))
theorem-size     25
proof            (modus-ponens tm-114 tm-769 ((A (or (and Am (not (not (-> B (-> C D))))) (not (not (-> B (-> C D)))))) (Bm (-> B (-> C D)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-10)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65308.        (((A and (not (not (B -> (C -> D))))) or (not (not (B -> (C -> D))))) -> ((B -> C) -> (B -> D))), M:tm-114, m:tm-769, u:((A (or (and Am (not (not (-> B (-> C D))))) (not (not (-> B (-> C D)))))) (Bm (-> B (-> C D))))
================================================================
tm-name          tm-65309
in-theory        65309
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (not (not F))) or (not (not F))) -> F))
theorem-size     27
proof            (modus-ponens tm-113 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 tm-10)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65309.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (not (not F))) or (not (not F))) -> F)), M:tm-113, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65310
in-theory        65310
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and (not (not (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))) or (not (not (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))))
theorem-size     36
proof            (modus-ponens tm-109 tm-769 ((A (or (and Am (not (not (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (not (not (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))) (Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))
axioms-used      (tm-9 tm-1 tm-2 tm-8 tm-4 tm-10)
proof-size       144
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-109.          ((A -> (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))) -> (not A)), M:tm-9, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65310.        (not ((A and (not (not (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))))) or (not (not (not ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))))))), M:tm-109, m:tm-769, u:((A (or (and Am (not (not (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))) (not (not (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D)))))))) (Bm (not (-> (-> B (-> C D)) (-> (-> B C) (-> B D))))))
================================================================
tm-name          tm-65311
in-theory        65311
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     31
proof            (modus-ponens tm-105 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-10)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65311.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-105, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65312
in-theory        65312
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (not (not D))) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-95 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 tm-10)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65312.        (((A -> B) -> (A -> A)) and (((C and (not (not D))) or (not (not D))) -> D)), M:tm-95, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65313
in-theory        65313
times-derived    1
----------------------------------------------------------------
theorem          (((A and (not (not (B -> C)))) or (not (not (B -> C)))) -> (B -> C))
theorem-size     17
proof            (modus-ponens tm-87 tm-769 ((A (or (and Am (not (not (-> B C)))) (not (not (-> B C))))) (Bm (-> B C))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-10)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-87.           ((A -> (B -> C)) -> (A -> (B -> C))), M:tm-12, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65313.        (((A and (not (not (B -> C)))) or (not (not (B -> C)))) -> (B -> C)), M:tm-87, m:tm-769, u:((A (or (and Am (not (not (-> B C)))) (not (not (-> B C))))) (Bm (-> B C)))
================================================================
tm-name          tm-65314
in-theory        65314
times-derived    1
----------------------------------------------------------------
theorem          (((A and (not (not B))) or (not (not B))) -> (C -> B))
theorem-size     13
proof            (modus-ponens tm-84 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-10)
proof-size       97
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65314.        (((A and (not (not B))) or (not (not B))) -> (C -> B)), M:tm-84, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65315
in-theory        65315
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     19
proof            (modus-ponens tm-83 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-10)
proof-size       99
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65315.        ((A -> (B -> (C -> B))) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-83, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65316
in-theory        65316
times-derived    1
----------------------------------------------------------------
theorem          (not ((A and (not (not (not (B -> (C -> B)))))) or (not (not (not (B -> (C -> B)))))))
theorem-size     20
proof            (modus-ponens tm-79 tm-769 ((A (or (and Am (not (not (not (-> B (-> C B)))))) (not (not (not (-> B (-> C B))))))) (Bm (not (-> B (-> C B))))))
axioms-used      (tm-9 tm-1 tm-8 tm-4 tm-10)
proof-size       104
proof-steps      11
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-79.           ((A -> (not (B -> (C -> B)))) -> (not A)), M:tm-9, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65316.        (not ((A and (not (not (not (B -> (C -> B)))))) or (not (not (not (B -> (C -> B))))))), M:tm-79, m:tm-769, u:((A (or (and Am (not (not (not (-> B (-> C B)))))) (not (not (not (-> B (-> C B))))))) (Bm (not (-> B (-> C B)))))
================================================================
tm-name          tm-65317
in-theory        65317
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (not (not C))) or (not (not C))) -> C))
theorem-size     17
proof            (modus-ponens tm-76 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65317.        (((not (not A)) -> A) and (((B and (not (not C))) or (not (not C))) -> C)), M:tm-76, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65318
in-theory        65318
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (not (not B))) or (not (not B))))) or ((A and (not (not B))) or (not (not B)))) -> B)
theorem-size     23
proof            (modus-ponens tm-73 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-8 tm-10 tm-4)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65318.        (((not (not ((A and (not (not B))) or (not (not B))))) or ((A and (not (not B))) or (not (not B)))) -> B), M:tm-73, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65319
in-theory        65319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (not (not D))) or (not (not D))) -> D))
theorem-size     23
proof            (modus-ponens tm-69 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-10)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65319.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (not (not D))) or (not (not D))) -> D)), M:tm-69, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65320
in-theory        65320
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     25
proof            (modus-ponens tm-54 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-8 tm-4 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65320.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-54, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65321
in-theory        65321
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) or ((B and (not (not A))) or (not (not A)))) -> A)
theorem-size     15
proof            (modus-ponens tm-50 tm-769 ((A (and Am (not (not Bm)))) (B (not (not Bm))) (C Bm)))
axioms-used      (tm-8 tm-7 tm-4 tm-10)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65321.        (((not (not A)) or ((B and (not (not A))) or (not (not A)))) -> A), M:tm-50, m:tm-769, u:((A (and Am (not (not Bm)))) (B (not (not Bm))) (C Bm))
================================================================
tm-name          tm-65322
in-theory        65322
times-derived    1
----------------------------------------------------------------
theorem          (((A and (not (not B))) or ((A and (not (not B))) or (not (not B)))) -> B)
theorem-size     17
proof            (modus-ponens tm-49 tm-769 ((A (and Am (not (not Bm)))) (B (not (not Bm))) (C Bm)))
axioms-used      (tm-8 tm-6 tm-4 tm-10)
proof-size       93
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65322.        (((A and (not (not B))) or ((A and (not (not B))) or (not (not B)))) -> B), M:tm-49, m:tm-769, u:((A (and Am (not (not Bm)))) (B (not (not Bm))) (C Bm))
================================================================
tm-name          tm-65323
in-theory        65323
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (not (not C))) or (not (not C)))) or ((B and (not (not C))) or (not (not C)))) -> C)
theorem-size     23
proof            (modus-ponens tm-47 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-8 tm-4 tm-10)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65323.        (((A and ((B and (not (not C))) or (not (not C)))) or ((B and (not (not C))) or (not (not C)))) -> C), M:tm-47, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65324
in-theory        65324
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (not (not B))) or (not (not B))) and C) or ((A and (not (not B))) or (not (not B)))) -> B)
theorem-size     23
proof            (modus-ponens tm-46 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-8 tm-3 tm-4 tm-10)
proof-size       97
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65324.        (((((A and (not (not B))) or (not (not B))) and C) or ((A and (not (not B))) or (not (not B)))) -> B), M:tm-46, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65325
in-theory        65325
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (not (not D))) or (not (not D))) -> D))
theorem-size     17
proof            (modus-ponens tm-42 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65325.        ((A -> (B or A)) and (((C and (not (not D))) or (not (not D))) -> D)), M:tm-42, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65326
in-theory        65326
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (not (not D))) or (not (not D))) -> D))
theorem-size     17
proof            (modus-ponens tm-32 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65326.        ((A -> (A or B)) and (((C and (not (not D))) or (not (not D))) -> D)), M:tm-32, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65327
in-theory        65327
times-derived    1
----------------------------------------------------------------
theorem          (((A and (not (not B))) or (not (not B))) -> (((A and (not (not B))) or (not (not B))) and B))
theorem-size     21
proof            (modus-ponens tm-24 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-10)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65327.        (((A and (not (not B))) or (not (not B))) -> (((A and (not (not B))) or (not (not B))) and B)), M:tm-24, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65328
in-theory        65328
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (not (not D))) or (not (not D))) -> D))
theorem-size     19
proof            (modus-ponens tm-23 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-8 tm-4 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65328.        ((A -> (B -> (A and B))) and (((C and (not (not D))) or (not (not D))) -> D)), M:tm-23, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65329
in-theory        65329
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (not (not D))) or (not (not D))) -> D))
theorem-size     17
proof            (modus-ponens tm-22 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-4 tm-8 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65329.        (((A and B) -> B) and (((C and (not (not D))) or (not (not D))) -> D)), M:tm-22, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65330
in-theory        65330
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (not (not D))) or (not (not D))) -> D))
theorem-size     17
proof            (modus-ponens tm-21 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65330.        (((A and B) -> A) and (((C and (not (not D))) or (not (not D))) -> D)), M:tm-21, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65331
in-theory        65331
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (not (not E))) or (not (not E))) -> E))
theorem-size     25
proof            (modus-ponens tm-20 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-10)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65331.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (not (not E))) or (not (not E))) -> E)), M:tm-20, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65332
in-theory        65332
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (not (not D))) or (not (not D))) -> D))
theorem-size     17
proof            (modus-ponens tm-19 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-10)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65332.        ((A -> (B -> A)) and (((C and (not (not D))) or (not (not D))) -> D)), M:tm-19, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65333
in-theory        65333
times-derived    1
----------------------------------------------------------------
theorem          (((A and (not (not B))) or (not (not B))) -> ((A and (not (not B))) or (not (not B))))
theorem-size     19
proof            (modus-ponens tm-12 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-10)
proof-size       89
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65333.        (((A and (not (not B))) or (not (not B))) -> ((A and (not (not B))) or (not (not B)))), M:tm-12, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65334
in-theory        65334
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> (not B)) -> (not ((A and (not (not B))) or (not (not B)))))
theorem-size     23
proof            (modus-ponens tm-9 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-9 tm-8 tm-4 tm-10)
proof-size       79
proof-steps      7
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65334.        ((((A and (not (not B))) or (not (not B))) -> (not B)) -> (not ((A and (not (not B))) or (not (not B))))), M:tm-9, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65335
in-theory        65335
times-derived    1
----------------------------------------------------------------
theorem          ((A -> B) -> ((((C and (not (not A))) or (not (not A))) or A) -> B))
theorem-size     17
proof            (modus-ponens tm-8 tm-769 ((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm)))
axioms-used      (tm-8 tm-4 tm-10)
proof-size       75
proof-steps      7
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65335.        ((A -> B) -> ((((C and (not (not A))) or (not (not A))) or A) -> B)), M:tm-8, m:tm-769, u:((A (or (and Am (not (not Bm))) (not (not Bm)))) (B Bm))
================================================================
tm-name          tm-65336
in-theory        65336
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (not (not C))) or (not (not C))) -> C))
theorem-size     13
proof            (modus-ponens tm-7 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-7 tm-8 tm-4 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65336.        (A or (((B and (not (not C))) or (not (not C))) -> C)), M:tm-7, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65337
in-theory        65337
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not B))) or (not (not B))) -> B) or C)
theorem-size     13
proof            (modus-ponens tm-6 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-6 tm-8 tm-4 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65337.        ((((A and (not (not B))) or (not (not B))) -> B) or C), M:tm-6, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65338
in-theory        65338
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (not (not C))) or (not (not C))) -> C) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-5 tm-8 tm-4 tm-10)
proof-size       67
proof-steps      7
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65338.        (A -> ((((B and (not (not C))) or (not (not C))) -> C) and A)), M:tm-5, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65339
in-theory        65339
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (not (not (B -> C)))) or (not (not (B -> C)))) -> B) -> (((A and (not (not (B -> C)))) or (not (not (B -> C)))) -> C))
theorem-size     31
proof            (modus-ponens tm-2 tm-769 ((A (or (and Am (not (not (-> B C)))) (not (not (-> B C))))) (Bm (-> B C))))
axioms-used      (tm-2 tm-8 tm-4 tm-10)
proof-size       89
proof-steps      7
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65339.        ((((A and (not (not (B -> C)))) or (not (not (B -> C)))) -> B) -> (((A and (not (not (B -> C)))) or (not (not (B -> C)))) -> C)), M:tm-2, m:tm-769, u:((A (or (and Am (not (not (-> B C)))) (not (not (-> B C))))) (Bm (-> B C)))
================================================================
tm-name          tm-65340
in-theory        65340
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (not (not C))) or (not (not C))) -> C))
theorem-size     13
proof            (modus-ponens tm-1 tm-769 ((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm))))
axioms-used      (tm-1 tm-8 tm-4 tm-10)
proof-size       63
proof-steps      7
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-10.           ((not (not A)) -> A), axiom
tm-769.          (((A and (not (not B))) or (not (not B))) -> B), M:tm-47, m:tm-10, u:((A (not (not Am))) (B Am))
tm-65340.        (A -> (((B and (not (not C))) or (not (not C))) -> C)), M:tm-1, m:tm-769, u:((A (-> (or (and Am (not (not Bm))) (not (not Bm))) Bm)))
================================================================
tm-name          tm-65341
in-theory        65341
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-757 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65341.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-757, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65342
in-theory        65342
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (((((A and B) or B) and E) or ((A and B) or B)) -> (C -> (D -> C))))
theorem-size     31
proof            (modus-ponens tm-747 tm-770 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65342.        ((((A and B) or B) -> (C -> (D -> C))) and (((((A and B) or B) and E) or ((A and B) or B)) -> (C -> (D -> C)))), M:tm-747, m:tm-770, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-65343
in-theory        65343
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (G -> (H -> G))))
theorem-size     37
proof            (modus-ponens tm-708 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65343.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (G -> (H -> G)))), M:tm-708, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65344
in-theory        65344
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-665 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65344.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-665, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65345
in-theory        65345
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-622 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65345.        ((A -> (B -> (C or B))) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-622, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65346
in-theory        65346
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (D or ((A and B) or B))))
theorem-size     15
proof            (modus-ponens tm-617 tm-770 ((A (or (and Am Bm) Bm)) (Cm (or B (or (and Am Bm) Bm))) (C (-> Dm (or B (or (and Am Bm) Bm))))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-617.          ((A -> ((B or A) -> C)) -> (A -> C)), M:tm-13, m:tm-43, u:((Am (-> Bm (-> (or Cm Bm) C))) (A Bm) (B (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65346.        (((A and B) or B) -> (C -> (D or ((A and B) or B)))), M:tm-617, m:tm-770, u:((A (or (and Am Bm) Bm)) (Cm (or B (or (and Am Bm) Bm))) (C (-> Dm (or B (or (and Am Bm) Bm)))))
================================================================
tm-name          tm-65347
in-theory        65347
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65347.        ((((A and B) or B) -> (C -> (D -> C))) and (E -> (F or E))), M:tm-609, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65348
in-theory        65348
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-605 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65348.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-605, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65349
in-theory        65349
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and ((E -> (F or E)) and (((A and B) or B) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-595 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65349.        ((((A and B) or B) -> (C -> (D -> C))) and ((E -> (F or E)) and (((A and B) or B) -> (C -> (D -> C))))), M:tm-595, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65350
in-theory        65350
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-550 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65350.        (((A -> (B or A)) or C) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-550, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65351
in-theory        65351
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-540 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65351.        ((A or (B -> (C or B))) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-540, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65352
in-theory        65352
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-530 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65352.        ((A or (B -> (B or C))) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-530, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65353
in-theory        65353
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-520 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65353.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-520, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65354
in-theory        65354
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-510 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65354.        ((A or ((B and C) -> C)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-510, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65355
in-theory        65355
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-500 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65355.        ((A or ((B and C) -> B)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-500, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65356
in-theory        65356
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-490 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65356.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (H -> G)))), M:tm-490, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65357
in-theory        65357
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-480 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65357.        ((A or (B -> (C -> B))) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-480, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65358
in-theory        65358
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-469 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65358.        ((A -> (B -> (B or C))) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-469, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65359
in-theory        65359
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (((A and B) or B) or D)))
theorem-size     15
proof            (modus-ponens tm-464 tm-770 ((A (or (and Am Bm) Bm)) (Cm (or (or (and Am Bm) Bm) B)) (C (-> Dm (or (or (and Am Bm) Bm) B)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-464.          ((A -> ((A or B) -> C)) -> (A -> C)), M:tm-13, m:tm-33, u:((Am (-> Bm (-> (or Bm Cm) C))) (A Bm) (B (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65359.        (((A and B) or B) -> (C -> (((A and B) or B) or D))), M:tm-464, m:tm-770, u:((A (or (and Am Bm) Bm)) (Cm (or (or (and Am Bm) Bm) B)) (C (-> Dm (or (or (and Am Bm) Bm) B))))
================================================================
tm-name          tm-65360
in-theory        65360
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65360.        ((((A and B) or B) -> (C -> (D -> C))) and (E -> (E or F))), M:tm-456, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65361
in-theory        65361
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-453 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65361.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-453, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65362
in-theory        65362
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and ((E -> (E or F)) and (((A and B) or B) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-443 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65362.        ((((A and B) or B) -> (C -> (D -> C))) and ((E -> (E or F)) and (((A and B) or B) -> (C -> (D -> C))))), M:tm-443, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65363
in-theory        65363
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-409 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65363.        (((A -> (A or B)) or C) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-409, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65364
in-theory        65364
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-400 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65364.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-400, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65365
in-theory        65365
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-391 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65365.        ((((A and B) -> B) or C) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-391, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65366
in-theory        65366
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-382 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65366.        ((((A and B) -> A) or C) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-382, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65367
in-theory        65367
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-373 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65367.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (G -> (H -> G)))), M:tm-373, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65368
in-theory        65368
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-364 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65368.        (((A -> (B -> A)) or C) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-364, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65369
in-theory        65369
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-354 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65369.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-354, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65370
in-theory        65370
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (D -> (((A and B) or B) and D))))
theorem-size     17
proof            (modus-ponens tm-349 tm-770 ((A (or (and Am Bm) Bm)) (Cm (-> B (and (or (and Am Bm) Bm) B))) (C (-> Dm (-> B (and (or (and Am Bm) Bm) B))))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-349.          ((A -> ((B -> (A and B)) -> C)) -> (A -> C)), M:tm-13, m:tm-25, u:((Am (-> Bm (-> (-> Cm (and Bm Cm)) C))) (A Bm) (B (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65370.        (((A and B) or B) -> (C -> (D -> (((A and B) or B) and D)))), M:tm-349, m:tm-770, u:((A (or (and Am Bm) Bm)) (Cm (-> B (and (or (and Am Bm) Bm) B))) (C (-> Dm (-> B (and (or (and Am Bm) Bm) B)))))
================================================================
tm-name          tm-65371
in-theory        65371
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65371.        ((((A and B) or B) -> (C -> (D -> C))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65372
in-theory        65372
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (E -> (F -> E))))
theorem-size     21
proof            (modus-ponens tm-338 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65372.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (E -> (F -> E)))), M:tm-338, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65373
in-theory        65373
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (((A and B) or B) -> (((A and B) or B) and (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-328 tm-770 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65373.        ((((A and B) or B) -> (C -> (D -> C))) and (((A and B) or B) -> (((A and B) or B) and (C -> (D -> C))))), M:tm-328, m:tm-770, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-65374
in-theory        65374
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and ((E -> (F -> (E and F))) and (((A and B) or B) -> (C -> (D -> C)))))
theorem-size     31
proof            (modus-ponens tm-327 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65374.        ((((A and B) or B) -> (C -> (D -> C))) and ((E -> (F -> (E and F))) and (((A and B) or B) -> (C -> (D -> C))))), M:tm-327, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65375
in-theory        65375
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (((E and F) -> F) and (((A and B) or B) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-326 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65375.        ((((A and B) or B) -> (C -> (D -> C))) and (((E and F) -> F) and (((A and B) or B) -> (C -> (D -> C))))), M:tm-326, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65376
in-theory        65376
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (((E and F) -> E) and (((A and B) or B) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-325 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65376.        ((((A and B) or B) -> (C -> (D -> C))) and (((E and F) -> E) and (((A and B) or B) -> (C -> (D -> C))))), M:tm-325, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65377
in-theory        65377
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> (C -> (D -> C)))))
theorem-size     37
proof            (modus-ponens tm-324 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65377.        ((((A and B) or B) -> (C -> (D -> C))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> (C -> (D -> C))))), M:tm-324, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65378
in-theory        65378
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and ((E -> (F -> E)) and (((A and B) or B) -> (C -> (D -> C)))))
theorem-size     29
proof            (modus-ponens tm-323 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65378.        ((((A and B) or B) -> (C -> (D -> C))) and ((E -> (F -> E)) and (((A and B) or B) -> (C -> (D -> C))))), M:tm-323, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65379
in-theory        65379
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65379.        ((((A and B) or B) -> (C -> (D -> C))) and ((E and F) -> F)), M:tm-322, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65380
in-theory        65380
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65380.        ((((A and B) or B) -> (C -> (D -> C))) and ((E and F) -> E)), M:tm-320, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65381
in-theory        65381
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65381.        ((((A and B) or B) -> (C -> (D -> C))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65382
in-theory        65382
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     23
proof            (modus-ponens tm-316 tm-770 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65382.        ((((A and B) or B) -> (C -> (D -> C))) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-770, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-65383
in-theory        65383
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65383.        ((((A and B) or B) -> (C -> (D -> C))) and (E -> (F -> E))), M:tm-315, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65384
in-theory        65384
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and ((((A and B) or B) -> (not (C -> (D -> C)))) -> (not ((A and B) or B))))
theorem-size     31
proof            (modus-ponens tm-313 tm-770 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65384.        ((((A and B) or B) -> (C -> (D -> C))) and ((((A and B) or B) -> (not (C -> (D -> C)))) -> (not ((A and B) or B)))), M:tm-313, m:tm-770, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-65385
in-theory        65385
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (((C -> (D -> C)) -> E) -> ((((A and B) or B) or (C -> (D -> C))) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-770 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65385.        ((((A and B) or B) -> (C -> (D -> C))) and (((C -> (D -> C)) -> E) -> ((((A and B) or B) or (C -> (D -> C))) -> E))), M:tm-312, m:tm-770, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-65386
in-theory        65386
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (E or (((A and B) or B) -> (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-311 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65386.        ((((A and B) or B) -> (C -> (D -> C))) and (E or (((A and B) or B) -> (C -> (D -> C))))), M:tm-311, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65387
in-theory        65387
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and ((((A and B) or B) -> (C -> (D -> C))) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65387.        ((((A and B) or B) -> (C -> (D -> C))) and ((((A and B) or B) -> (C -> (D -> C))) or E)), M:tm-310, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65388
in-theory        65388
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (E -> ((((A and B) or B) -> (C -> (D -> C))) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65388.        ((((A and B) or B) -> (C -> (D -> C))) and (E -> ((((A and B) or B) -> (C -> (D -> C))) and E))), M:tm-309, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65389
in-theory        65389
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and ((((A and B) or B) -> C) -> (((A and B) or B) -> (D -> C))))
theorem-size     29
proof            (modus-ponens tm-306 tm-770 ((A (or (and Am Bm) Bm)) (B Cm) (C (-> Dm Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65389.        ((((A and B) or B) -> (C -> (D -> C))) and ((((A and B) or B) -> C) -> (((A and B) or B) -> (D -> C)))), M:tm-306, m:tm-770, u:((A (or (and Am Bm) Bm)) (B Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-65390
in-theory        65390
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) and (E -> (((A and B) or B) -> (C -> (D -> C)))))
theorem-size     25
proof            (modus-ponens tm-305 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65390.        ((((A and B) or B) -> (C -> (D -> C))) and (E -> (((A and B) or B) -> (C -> (D -> C))))), M:tm-305, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65391
in-theory        65391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     23
proof            (modus-ponens tm-303 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65391.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-303, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65392
in-theory        65392
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-270 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65392.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-270, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65393
in-theory        65393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-239 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65393.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-239, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65394
in-theory        65394
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (G -> (H -> G))))
theorem-size     29
proof            (modus-ponens tm-210 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65394.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (G -> (H -> G)))), M:tm-210, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65395
in-theory        65395
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     21
proof            (modus-ponens tm-183 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65395.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-183, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65396
in-theory        65396
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-157 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65396.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-157, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65397
in-theory        65397
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-147 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65397.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-147, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65398
in-theory        65398
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-134 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65398.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-134, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65399
in-theory        65399
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     27
proof            (modus-ponens tm-125 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65399.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-125, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65400
in-theory        65400
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (H -> G))))
theorem-size     27
proof            (modus-ponens tm-113 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65400.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (G -> (H -> G)))), M:tm-113, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65401
in-theory        65401
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     31
proof            (modus-ponens tm-105 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65401.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-105, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65402
in-theory        65402
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((A and B) or B)))
theorem-size     13
proof            (modus-ponens tm-99 tm-770 ((Cm (or (and Am Bm) Bm)) (A (or (and Am Bm) Bm)) (B (-> Dm (or (and Am Bm) Bm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-99.           ((A -> (A -> B)) -> (A -> B)), M:tm-13, m:tm-12, u:((Bm (-> Am C)) (A Am) (B Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65402.        (((A and B) or B) -> (C -> ((A and B) or B))), M:tm-99, m:tm-770, u:((Cm (or (and Am Bm) Bm)) (A (or (and Am Bm) Bm)) (B (-> Dm (or (and Am Bm) Bm))))
================================================================
tm-name          tm-65403
in-theory        65403
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (D -> ((A and B) or B))))
theorem-size     15
proof            (modus-ponens tm-98 tm-770 ((A (or (and Am Bm) Bm)) (Cm (-> B (or (and Am Bm) Bm))) (C (-> Dm (-> B (or (and Am Bm) Bm))))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-98.           ((A -> ((B -> A) -> C)) -> (A -> C)), M:tm-13, m:tm-11, u:((Am (-> Bm (-> (-> Cm Bm) C))) (A Bm) (B (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65403.        (((A and B) or B) -> (C -> (D -> ((A and B) or B)))), M:tm-98, m:tm-770, u:((A (or (and Am Bm) Bm)) (Cm (-> B (or (and Am Bm) Bm))) (C (-> Dm (-> B (or (and Am Bm) Bm)))))
================================================================
tm-name          tm-65404
in-theory        65404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-95 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65404.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> (E -> (F -> E)))), M:tm-95, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65405
in-theory        65405
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     19
proof            (modus-ponens tm-83 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65405.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-83, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65406
in-theory        65406
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> (D -> (E -> D))))
theorem-size     17
proof            (modus-ponens tm-76 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65406.        (((not (not A)) -> A) and (((B and C) or C) -> (D -> (E -> D)))), M:tm-76, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65407
in-theory        65407
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> (C -> (D -> C)))
theorem-size     19
proof            (modus-ponens tm-73 tm-770 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-10 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65407.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> (C -> (D -> C))), M:tm-73, m:tm-770, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-65408
in-theory        65408
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (E -> (F -> E))))
theorem-size     23
proof            (modus-ponens tm-69 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65408.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (E -> (F -> E)))), M:tm-69, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65409
in-theory        65409
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-54 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65409.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-54, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65410
in-theory        65410
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> (C -> (D -> C)))
theorem-size     13
proof            (modus-ponens tm-50 tm-770 ((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-7 tm-4 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65410.        ((A or ((B and A) or A)) -> (C -> (D -> C))), M:tm-50, m:tm-770, u:((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-65411
in-theory        65411
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> (C -> (D -> C)))
theorem-size     15
proof            (modus-ponens tm-49 tm-770 ((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-6 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65411.        (((A and B) or ((A and B) or B)) -> (C -> (D -> C))), M:tm-49, m:tm-770, u:((A (and Am Bm)) (B Bm) (C (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-65412
in-theory        65412
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-47 tm-770 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65412.        (((A and ((B and C) or C)) or ((B and C) or C)) -> (D -> (E -> D))), M:tm-47, m:tm-770, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-65413
in-theory        65413
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-46 tm-770 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-3 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65413.        (((((A and B) or B) and C) or ((A and B) or B)) -> (D -> (E -> D))), M:tm-46, m:tm-770, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-65414
in-theory        65414
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-42 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65414.        ((A -> (B or A)) and (((C and D) or D) -> (E -> (F -> E)))), M:tm-42, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65415
in-theory        65415
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-32 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65415.        ((A -> (A or B)) and (((C and D) or D) -> (E -> (F -> E)))), M:tm-32, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65416
in-theory        65416
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and (C -> (D -> C))))
theorem-size     17
proof            (modus-ponens tm-24 tm-770 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65416.        (((A and B) or B) -> (((A and B) or B) and (C -> (D -> C)))), M:tm-24, m:tm-770, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-65417
in-theory        65417
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> (E -> (F -> E))))
theorem-size     19
proof            (modus-ponens tm-23 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65417.        ((A -> (B -> (A and B))) and (((C and D) or D) -> (E -> (F -> E)))), M:tm-23, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65418
in-theory        65418
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-22 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65418.        (((A and B) -> B) and (((C and D) or D) -> (E -> (F -> E)))), M:tm-22, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65419
in-theory        65419
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-21 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65419.        (((A and B) -> A) and (((C and D) or D) -> (E -> (F -> E)))), M:tm-21, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65420
in-theory        65420
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (F -> (G -> F))))
theorem-size     25
proof            (modus-ponens tm-20 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65420.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (F -> (G -> F)))), M:tm-20, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65421
in-theory        65421
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> (E -> (F -> E))))
theorem-size     17
proof            (modus-ponens tm-19 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65421.        ((A -> (B -> A)) and (((C and D) or D) -> (E -> (F -> E)))), M:tm-19, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65422
in-theory        65422
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not (C -> (D -> C)))) -> (not ((A and B) or B)))
theorem-size     19
proof            (modus-ponens tm-9 tm-770 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-9 tm-8 tm-4 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65422.        ((((A and B) or B) -> (not (C -> (D -> C)))) -> (not ((A and B) or B))), M:tm-9, m:tm-770, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-65423
in-theory        65423
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) -> C) -> ((((D and E) or E) or (A -> (B -> A))) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-770 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm)))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65423.        (((A -> (B -> A)) -> C) -> ((((D and E) or E) or (A -> (B -> A))) -> C)), M:tm-8, m:tm-770, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Cm))))
================================================================
tm-name          tm-65424
in-theory        65424
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-7 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-7 tm-8 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65424.        (A or (((B and C) or C) -> (D -> (E -> D)))), M:tm-7, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65425
in-theory        65425
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> C))) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-6 tm-8 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65425.        ((((A and B) or B) -> (C -> (D -> C))) or E), M:tm-6, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65426
in-theory        65426
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> (D -> (E -> D))) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65426.        (A -> ((((B and C) or C) -> (D -> (E -> D))) and A)), M:tm-5, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65427
in-theory        65427
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> C) -> (((A and B) or B) -> (D -> C)))
theorem-size     17
proof            (modus-ponens tm-2 tm-770 ((A (or (and Am Bm) Bm)) (B Cm) (C (-> Dm Cm))))
axioms-used      (tm-2 tm-8 tm-4 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65427.        ((((A and B) or B) -> C) -> (((A and B) or B) -> (D -> C))), M:tm-2, m:tm-770, u:((A (or (and Am Bm) Bm)) (B Cm) (C (-> Dm Cm)))
================================================================
tm-name          tm-65428
in-theory        65428
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> (D -> (E -> D))))
theorem-size     13
proof            (modus-ponens tm-1 tm-770 ((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm))))))
axioms-used      (tm-1 tm-8 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-770.          (((A and B) or B) -> (C -> (D -> C))), M:tm-47, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-65428.        (A -> (((B and C) or C) -> (D -> (E -> D)))), M:tm-1, m:tm-770, u:((A (-> (or (and Am Bm) Bm) (-> Cm (-> Dm Cm)))))
================================================================
tm-name          tm-65429
in-theory        65429
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     25
proof            (modus-ponens tm-757 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65429.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-757, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65430
in-theory        65430
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> (B -> B)))
theorem-size     39
proof            (modus-ponens tm-747 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65430.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> (B -> B))), M:tm-747, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65431
in-theory        65431
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) or (F -> G)) -> (F -> F)))
theorem-size     39
proof            (modus-ponens tm-708 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65431.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) or (F -> G)) -> (F -> F))), M:tm-708, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65432
in-theory        65432
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     27
proof            (modus-ponens tm-665 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65432.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-665, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65433
in-theory        65433
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D or (B -> B)))
theorem-size     15
proof            (modus-ponens tm-623 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65433.        (((A and (B -> C)) or (B -> C)) -> (D or (B -> B))), M:tm-623, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65434
in-theory        65434
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-622 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65434.        ((A -> (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-622, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65435
in-theory        65435
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (D -> (E or D)))
theorem-size     19
proof            (modus-ponens tm-609 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65435.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (D -> (E or D))), M:tm-609, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65436
in-theory        65436
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-605 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65436.        ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-605, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65437
in-theory        65437
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((D -> (E or D)) and (((A and (B -> C)) or (B -> C)) -> (B -> B))))
theorem-size     33
proof            (modus-ponens tm-595 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65437.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((D -> (E or D)) and (((A and (B -> C)) or (B -> C)) -> (B -> B)))), M:tm-595, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65438
in-theory        65438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-550 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65438.        (((A -> (B or A)) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-550, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65439
in-theory        65439
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-540 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65439.        ((A or (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-540, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65440
in-theory        65440
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-530 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65440.        ((A or (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-530, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65441
in-theory        65441
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-520 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65441.        ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-520, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65442
in-theory        65442
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-510 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65442.        ((A or ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-510, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65443
in-theory        65443
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-500 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65443.        ((A or ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-500, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65444
in-theory        65444
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (F -> F)))
theorem-size     29
proof            (modus-ponens tm-490 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65444.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (F -> F))), M:tm-490, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65445
in-theory        65445
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-480 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65445.        ((A or (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-480, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65446
in-theory        65446
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((B -> B) or D))
theorem-size     15
proof            (modus-ponens tm-470 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65446.        (((A and (B -> C)) or (B -> C)) -> ((B -> B) or D)), M:tm-470, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65447
in-theory        65447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-469 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65447.        ((A -> (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-469, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65448
in-theory        65448
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (D -> (D or E)))
theorem-size     19
proof            (modus-ponens tm-456 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65448.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (D -> (D or E))), M:tm-456, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65449
in-theory        65449
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-453 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65449.        ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-453, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65450
in-theory        65450
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((D -> (D or E)) and (((A and (B -> C)) or (B -> C)) -> (B -> B))))
theorem-size     33
proof            (modus-ponens tm-443 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65450.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((D -> (D or E)) and (((A and (B -> C)) or (B -> C)) -> (B -> B)))), M:tm-443, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65451
in-theory        65451
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-409 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65451.        (((A -> (A or B)) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-409, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65452
in-theory        65452
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-400 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65452.        (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-400, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65453
in-theory        65453
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-391 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65453.        ((((A and B) -> B) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-391, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65454
in-theory        65454
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-382 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-2 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65454.        ((((A and B) -> A) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-382, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65455
in-theory        65455
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (F -> F)))
theorem-size     29
proof            (modus-ponens tm-373 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65455.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (F -> F))), M:tm-373, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65456
in-theory        65456
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-364 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65456.        (((A -> (B -> A)) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-364, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65457
in-theory        65457
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D -> ((B -> B) and D)))
theorem-size     17
proof            (modus-ponens tm-355 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65457.        (((A and (B -> C)) or (B -> C)) -> (D -> ((B -> B) and D))), M:tm-355, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65458
in-theory        65458
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-354 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65458.        ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-354, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65459
in-theory        65459
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (D -> (E -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-341 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65459.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (D -> (E -> (D and E)))), M:tm-341, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65460
in-theory        65460
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (D -> D)))
theorem-size     23
proof            (modus-ponens tm-338 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65460.        (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (D -> D))), M:tm-338, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65461
in-theory        65461
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (B -> B))))
theorem-size     37
proof            (modus-ponens tm-328 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65461.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (B -> B)))), M:tm-328, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65462
in-theory        65462
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((D -> (E -> (D and E))) and (((A and (B -> C)) or (B -> C)) -> (B -> B))))
theorem-size     35
proof            (modus-ponens tm-327 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65462.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((D -> (E -> (D and E))) and (((A and (B -> C)) or (B -> C)) -> (B -> B)))), M:tm-327, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65463
in-theory        65463
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((D and E) -> E) and (((A and (B -> C)) or (B -> C)) -> (B -> B))))
theorem-size     33
proof            (modus-ponens tm-326 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65463.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((D and E) -> E) and (((A and (B -> C)) or (B -> C)) -> (B -> B)))), M:tm-326, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65464
in-theory        65464
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((D and E) -> D) and (((A and (B -> C)) or (B -> C)) -> (B -> B))))
theorem-size     33
proof            (modus-ponens tm-325 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65464.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((D and E) -> D) and (((A and (B -> C)) or (B -> C)) -> (B -> B)))), M:tm-325, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65465
in-theory        65465
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B -> C)) or (B -> C)) -> (B -> B))))
theorem-size     41
proof            (modus-ponens tm-324 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65465.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B -> C)) or (B -> C)) -> (B -> B)))), M:tm-324, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65466
in-theory        65466
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((D -> (E -> D)) and (((A and (B -> C)) or (B -> C)) -> (B -> B))))
theorem-size     33
proof            (modus-ponens tm-323 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65466.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((D -> (E -> D)) and (((A and (B -> C)) or (B -> C)) -> (B -> B)))), M:tm-323, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65467
in-theory        65467
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-322 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65467.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((D and E) -> E)), M:tm-322, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65468
in-theory        65468
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-320 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65468.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((D and E) -> D)), M:tm-320, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65469
in-theory        65469
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-318 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65469.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65470
in-theory        65470
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((A and (B -> C)) or (B -> C)) -> ((A and (B -> C)) or (B -> C))))
theorem-size     33
proof            (modus-ponens tm-316 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65470.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((A and (B -> C)) or (B -> C)) -> ((A and (B -> C)) or (B -> C)))), M:tm-316, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65471
in-theory        65471
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (D -> (E -> D)))
theorem-size     19
proof            (modus-ponens tm-315 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       141
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65471.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (D -> (E -> D))), M:tm-315, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65472
in-theory        65472
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((((A and (B -> C)) or (B -> C)) -> (not (B -> B))) -> (not ((A and (B -> C)) or (B -> C)))))
theorem-size     39
proof            (modus-ponens tm-313 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65472.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((((A and (B -> C)) or (B -> C)) -> (not (B -> B))) -> (not ((A and (B -> C)) or (B -> C))))), M:tm-313, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65473
in-theory        65473
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((B -> B) -> D) -> ((((A and (B -> C)) or (B -> C)) or (B -> B)) -> D)))
theorem-size     35
proof            (modus-ponens tm-312 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65473.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (((B -> B) -> D) -> ((((A and (B -> C)) or (B -> C)) or (B -> B)) -> D))), M:tm-312, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65474
in-theory        65474
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (D or (((A and (B -> C)) or (B -> C)) -> (B -> B))))
theorem-size     29
proof            (modus-ponens tm-311 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65474.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (D or (((A and (B -> C)) or (B -> C)) -> (B -> B)))), M:tm-311, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65475
in-theory        65475
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((((A and (B -> C)) or (B -> C)) -> (B -> B)) or D))
theorem-size     29
proof            (modus-ponens tm-310 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65475.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((((A and (B -> C)) or (B -> C)) -> (B -> B)) or D)), M:tm-310, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65476
in-theory        65476
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (D -> ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and D)))
theorem-size     31
proof            (modus-ponens tm-309 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65476.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (D -> ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and D))), M:tm-309, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65477
in-theory        65477
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((((A and (B -> C)) or (B -> C)) -> B) -> (((A and (B -> C)) or (B -> C)) -> B)))
theorem-size     37
proof            (modus-ponens tm-306 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B Bm) (C Bm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       165
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65477.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and ((((A and (B -> C)) or (B -> C)) -> B) -> (((A and (B -> C)) or (B -> C)) -> B))), M:tm-306, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B Bm) (C Bm))
================================================================
tm-name          tm-65478
in-theory        65478
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (D -> (((A and (B -> C)) or (B -> C)) -> (B -> B))))
theorem-size     29
proof            (modus-ponens tm-305 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65478.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) and (D -> (((A and (B -> C)) or (B -> C)) -> (B -> B)))), M:tm-305, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65479
in-theory        65479
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     25
proof            (modus-ponens tm-303 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65479.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-303, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65480
in-theory        65480
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-270 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65480.        ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-270, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65481
in-theory        65481
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-239 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65481.        ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-239, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65482
in-theory        65482
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) or (F -> G)) -> (F -> F)))
theorem-size     31
proof            (modus-ponens tm-210 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65482.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) or (F -> G)) -> (F -> F))), M:tm-210, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65483
in-theory        65483
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     23
proof            (modus-ponens tm-183 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65483.        ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-183, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65484
in-theory        65484
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-157 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65484.        ((A -> ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-157, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65485
in-theory        65485
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     29
proof            (modus-ponens tm-147 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65485.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-147, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65486
in-theory        65486
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-134 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65486.        ((A -> ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-134, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65487
in-theory        65487
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     29
proof            (modus-ponens tm-125 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 tm-1)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65487.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-125, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65488
in-theory        65488
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (((B -> C) -> B) -> ((B -> C) -> C)))
theorem-size     25
proof            (modus-ponens tm-114 tm-771 ((A (or (and Am (-> (-> C D) Cm)) (-> (-> C D) Cm))) (B (-> C D)) (Bm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65488.        (((A and ((B -> C) -> D)) or ((B -> C) -> D)) -> (((B -> C) -> B) -> ((B -> C) -> C))), M:tm-114, m:tm-771, u:((A (or (and Am (-> (-> C D) Cm)) (-> (-> C D) Cm))) (B (-> C D)) (Bm (-> C D)))
================================================================
tm-name          tm-65489
in-theory        65489
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (F -> F)))
theorem-size     29
proof            (modus-ponens tm-113 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65489.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (F -> F))), M:tm-113, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65490
in-theory        65490
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     33
proof            (modus-ponens tm-105 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65490.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-105, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65491
in-theory        65491
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (D -> E)) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-95 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65491.        (((A -> B) -> (A -> A)) and (((C and (D -> E)) or (D -> E)) -> (D -> D))), M:tm-95, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65492
in-theory        65492
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D -> (B -> B)))
theorem-size     15
proof            (modus-ponens tm-84 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       121
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65492.        (((A and (B -> C)) or (B -> C)) -> (D -> (B -> B))), M:tm-84, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65493
in-theory        65493
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     21
proof            (modus-ponens tm-83 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65493.        ((A -> (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-83, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65494
in-theory        65494
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (C -> D)) or (C -> D)) -> (C -> C)))
theorem-size     19
proof            (modus-ponens tm-76 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65494.        (((not (not A)) -> A) and (((B and (C -> D)) or (C -> D)) -> (C -> C))), M:tm-76, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65495
in-theory        65495
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (B -> C)) or (B -> C)))) or ((A and (B -> C)) or (B -> C))) -> (B -> B))
theorem-size     25
proof            (modus-ponens tm-73 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-8 tm-10 tm-4 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65495.        (((not (not ((A and (B -> C)) or (B -> C)))) or ((A and (B -> C)) or (B -> C))) -> (B -> B)), M:tm-73, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65496
in-theory        65496
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) or (D -> E)) -> (D -> D)))
theorem-size     25
proof            (modus-ponens tm-69 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-2 tm-1)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65496.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) or (D -> E)) -> (D -> D))), M:tm-69, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65497
in-theory        65497
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     27
proof            (modus-ponens tm-54 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65497.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-54, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65498
in-theory        65498
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((C and (A -> B)) or (A -> B))) -> (A -> A))
theorem-size     17
proof            (modus-ponens tm-50 tm-771 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm Bm))))
axioms-used      (tm-8 tm-7 tm-4 tm-2 tm-1)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65498.        (((A -> B) or ((C and (A -> B)) or (A -> B))) -> (A -> A)), M:tm-50, m:tm-771, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm Bm)))
================================================================
tm-name          tm-65499
in-theory        65499
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (B -> B))
theorem-size     19
proof            (modus-ponens tm-49 tm-771 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm Bm))))
axioms-used      (tm-8 tm-6 tm-4 tm-2 tm-1)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65499.        (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (B -> B)), M:tm-49, m:tm-771, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm Bm)))
================================================================
tm-name          tm-65500
in-theory        65500
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) or (C -> D))) or ((B and (C -> D)) or (C -> D))) -> (C -> C))
theorem-size     25
proof            (modus-ponens tm-47 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65500.        (((A and ((B and (C -> D)) or (C -> D))) or ((B and (C -> D)) or (C -> D))) -> (C -> C)), M:tm-47, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65501
in-theory        65501
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> (B -> B))
theorem-size     25
proof            (modus-ponens tm-46 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-8 tm-3 tm-4 tm-2 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65501.        (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> (B -> B)), M:tm-46, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65502
in-theory        65502
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (D -> E)) or (D -> E)) -> (D -> D)))
theorem-size     19
proof            (modus-ponens tm-42 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65502.        ((A -> (B or A)) and (((C and (D -> E)) or (D -> E)) -> (D -> D))), M:tm-42, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65503
in-theory        65503
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (D -> E)) or (D -> E)) -> (D -> D)))
theorem-size     19
proof            (modus-ponens tm-32 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65503.        ((A -> (A or B)) and (((C and (D -> E)) or (D -> E)) -> (D -> D))), M:tm-32, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65504
in-theory        65504
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (B -> B)))
theorem-size     23
proof            (modus-ponens tm-24 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65504.        (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (B -> B))), M:tm-24, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65505
in-theory        65505
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (D -> D)))
theorem-size     21
proof            (modus-ponens tm-23 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65505.        ((A -> (B -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (D -> D))), M:tm-23, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65506
in-theory        65506
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (D -> E)) or (D -> E)) -> (D -> D)))
theorem-size     19
proof            (modus-ponens tm-22 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65506.        (((A and B) -> B) and (((C and (D -> E)) or (D -> E)) -> (D -> D))), M:tm-22, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65507
in-theory        65507
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (D -> E)) or (D -> E)) -> (D -> D)))
theorem-size     19
proof            (modus-ponens tm-21 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-2 tm-1)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65507.        (((A and B) -> A) and (((C and (D -> E)) or (D -> E)) -> (D -> D))), M:tm-21, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65508
in-theory        65508
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (E -> E)))
theorem-size     27
proof            (modus-ponens tm-20 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       131
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65508.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (E -> E))), M:tm-20, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65509
in-theory        65509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (D -> E)) or (D -> E)) -> (D -> D)))
theorem-size     19
proof            (modus-ponens tm-19 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       107
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65509.        ((A -> (B -> A)) and (((C and (D -> E)) or (D -> E)) -> (D -> D))), M:tm-19, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65510
in-theory        65510
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (not (B -> B))) -> (not ((A and (B -> C)) or (B -> C))))
theorem-size     25
proof            (modus-ponens tm-9 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-9 tm-8 tm-4 tm-2 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65510.        ((((A and (B -> C)) or (B -> C)) -> (not (B -> B))) -> (not ((A and (B -> C)) or (B -> C)))), M:tm-9, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65511
in-theory        65511
times-derived    1
----------------------------------------------------------------
theorem          (((A -> A) -> B) -> ((((C and (A -> D)) or (A -> D)) or (A -> A)) -> B))
theorem-size     21
proof            (modus-ponens tm-8 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm))))
axioms-used      (tm-8 tm-4 tm-2 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65511.        (((A -> A) -> B) -> ((((C and (A -> D)) or (A -> D)) or (A -> A)) -> B)), M:tm-8, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm Bm)))
================================================================
tm-name          tm-65512
in-theory        65512
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (C -> D)) or (C -> D)) -> (C -> C)))
theorem-size     15
proof            (modus-ponens tm-7 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-7 tm-8 tm-4 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65512.        (A or (((B and (C -> D)) or (C -> D)) -> (C -> C))), M:tm-7, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65513
in-theory        65513
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> B)) or D)
theorem-size     15
proof            (modus-ponens tm-6 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-6 tm-8 tm-4 tm-2 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65513.        ((((A and (B -> C)) or (B -> C)) -> (B -> B)) or D), M:tm-6, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65514
in-theory        65514
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (C -> D)) or (C -> D)) -> (C -> C)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65514.        (A -> ((((B and (C -> D)) or (C -> D)) -> (C -> C)) and A)), M:tm-5, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65515
in-theory        65515
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> B) -> (((A and (B -> C)) or (B -> C)) -> B))
theorem-size     23
proof            (modus-ponens tm-2 tm-771 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B Bm) (C Bm)))
axioms-used      (tm-2 tm-8 tm-4 tm-1)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65515.        ((((A and (B -> C)) or (B -> C)) -> B) -> (((A and (B -> C)) or (B -> C)) -> B)), M:tm-2, m:tm-771, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B Bm) (C Bm))
================================================================
tm-name          tm-65516
in-theory        65516
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (C -> D)) or (C -> D)) -> (C -> C)))
theorem-size     15
proof            (modus-ponens tm-1 tm-771 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm)))))
axioms-used      (tm-1 tm-8 tm-4 tm-2)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-771.          (((A and (B -> C)) or (B -> C)) -> (B -> B)), M:tm-47, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-65516.        (A -> (((B and (C -> D)) or (C -> D)) -> (C -> C))), M:tm-1, m:tm-771, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm Bm))))
================================================================
tm-name          tm-65517
in-theory        65517
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-757 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2)
proof-size       199
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65517.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-757, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65518
in-theory        65518
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) and E) or ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     87
proof            (modus-ponens tm-747 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       265
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65518.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) and E) or ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D)))), M:tm-747, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65519
in-theory        65519
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and ((F -> (G -> H)) -> (F -> G))) or ((F -> (G -> H)) -> (F -> G))) -> ((F -> (G -> H)) -> (F -> H))))
theorem-size     57
proof            (modus-ponens tm-708 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       249
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65519.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and ((F -> (G -> H)) -> (F -> G))) or ((F -> (G -> H)) -> (F -> G))) -> ((F -> (G -> H)) -> (F -> H)))), M:tm-708, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65520
in-theory        65520
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-665 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65520.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-665, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65521
in-theory        65521
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (E or ((B -> (C -> D)) -> (B -> D))))
theorem-size     33
proof            (modus-ponens tm-623 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65521.        (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (E or ((B -> (C -> D)) -> (B -> D)))), M:tm-623, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65522
in-theory        65522
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-622 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65522.        ((A -> (B -> (C or B))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-622, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65523
in-theory        65523
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (E -> (F or E)))
theorem-size     37
proof            (modus-ponens tm-609 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65523.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (E -> (F or E))), M:tm-609, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65524
in-theory        65524
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-605 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65524.        ((A -> ((B -> (C or B)) and A)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-605, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65525
in-theory        65525
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((E -> (F or E)) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     69
proof            (modus-ponens tm-595 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65525.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((E -> (F or E)) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))), M:tm-595, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65526
in-theory        65526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-550 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65526.        (((A -> (B or A)) or C) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-550, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65527
in-theory        65527
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-540 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65527.        ((A or (B -> (C or B))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-540, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65528
in-theory        65528
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-530 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65528.        ((A or (B -> (B or C))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-530, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65529
in-theory        65529
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-520 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65529.        ((A or (B -> (C -> (B and C)))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-520, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65530
in-theory        65530
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-510 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65530.        ((A or ((B and C) -> C)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-510, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65531
in-theory        65531
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-500 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65531.        ((A or ((B and C) -> B)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-500, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65532
in-theory        65532
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> (G -> H)) -> (F -> G))) or ((F -> (G -> H)) -> (F -> G))) -> ((F -> (G -> H)) -> (F -> H))))
theorem-size     47
proof            (modus-ponens tm-490 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65532.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> (G -> H)) -> (F -> G))) or ((F -> (G -> H)) -> (F -> G))) -> ((F -> (G -> H)) -> (F -> H)))), M:tm-490, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65533
in-theory        65533
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-480 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65533.        ((A or (B -> (C -> B))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-480, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65534
in-theory        65534
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (((B -> (C -> D)) -> (B -> D)) or E))
theorem-size     33
proof            (modus-ponens tm-470 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65534.        (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (((B -> (C -> D)) -> (B -> D)) or E)), M:tm-470, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65535
in-theory        65535
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-469 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65535.        ((A -> (B -> (B or C))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-469, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65536
in-theory        65536
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (E -> (E or F)))
theorem-size     37
proof            (modus-ponens tm-456 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65536.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (E -> (E or F))), M:tm-456, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65537
in-theory        65537
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-453 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65537.        ((A -> ((B -> (B or C)) and A)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-453, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65538
in-theory        65538
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((E -> (E or F)) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     69
proof            (modus-ponens tm-443 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65538.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((E -> (E or F)) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))), M:tm-443, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65539
in-theory        65539
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-409 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65539.        (((A -> (A or B)) or C) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-409, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65540
in-theory        65540
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-400 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65540.        (((A -> (B -> (A and B))) or C) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-400, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65541
in-theory        65541
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-391 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65541.        ((((A and B) -> B) or C) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-391, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65542
in-theory        65542
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-382 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65542.        ((((A and B) -> A) or C) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-382, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65543
in-theory        65543
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and ((F -> (G -> H)) -> (F -> G))) or ((F -> (G -> H)) -> (F -> G))) -> ((F -> (G -> H)) -> (F -> H))))
theorem-size     47
proof            (modus-ponens tm-373 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65543.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and ((F -> (G -> H)) -> (F -> G))) or ((F -> (G -> H)) -> (F -> G))) -> ((F -> (G -> H)) -> (F -> H)))), M:tm-373, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65544
in-theory        65544
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-364 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65544.        (((A -> (B -> A)) or C) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-364, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65545
in-theory        65545
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (E -> (((B -> (C -> D)) -> (B -> D)) and E)))
theorem-size     35
proof            (modus-ponens tm-355 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       185
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65545.        (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (E -> (((B -> (C -> D)) -> (B -> D)) and E))), M:tm-355, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65546
in-theory        65546
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-354 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65546.        ((A -> (B -> (C -> (B and C)))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-354, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65547
in-theory        65547
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (E -> (F -> (E and F))))
theorem-size     39
proof            (modus-ponens tm-341 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65547.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (E -> (F -> (E and F)))), M:tm-341, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65548
in-theory        65548
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     41
proof            (modus-ponens tm-338 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65548.        (((A -> B) -> (A -> (A and B))) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-338, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65549
in-theory        65549
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) and ((B -> (C -> D)) -> (B -> D)))))
theorem-size     85
proof            (modus-ponens tm-328 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       261
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65549.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) and ((B -> (C -> D)) -> (B -> D))))), M:tm-328, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65550
in-theory        65550
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((E -> (F -> (E and F))) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     71
proof            (modus-ponens tm-327 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       243
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65550.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((E -> (F -> (E and F))) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))), M:tm-327, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65551
in-theory        65551
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (((E and F) -> F) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     69
proof            (modus-ponens tm-326 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65551.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (((E and F) -> F) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))), M:tm-326, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65552
in-theory        65552
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (((E and F) -> E) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     69
proof            (modus-ponens tm-325 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65552.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (((E and F) -> E) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))), M:tm-325, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65553
in-theory        65553
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     77
proof            (modus-ponens tm-324 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       267
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65553.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))), M:tm-324, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65554
in-theory        65554
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((E -> (F -> E)) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     69
proof            (modus-ponens tm-323 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       235
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65554.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((E -> (F -> E)) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))), M:tm-323, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65555
in-theory        65555
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((E and F) -> F))
theorem-size     37
proof            (modus-ponens tm-322 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65555.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((E and F) -> F)), M:tm-322, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65556
in-theory        65556
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((E and F) -> E))
theorem-size     37
proof            (modus-ponens tm-320 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65556.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((E and F) -> E)), M:tm-320, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65557
in-theory        65557
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-318 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65557.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65558
in-theory        65558
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))))
theorem-size     75
proof            (modus-ponens tm-316 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       245
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65558.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))))), M:tm-316, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65559
in-theory        65559
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (E -> (F -> E)))
theorem-size     37
proof            (modus-ponens tm-315 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65559.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (E -> (F -> E))), M:tm-315, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65560
in-theory        65560
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (not ((B -> (C -> D)) -> (B -> D)))) -> (not ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))))))
theorem-size     87
proof            (modus-ponens tm-313 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       247
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65560.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (not ((B -> (C -> D)) -> (B -> D)))) -> (not ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))))), M:tm-313, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65561
in-theory        65561
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((((B -> (C -> D)) -> (B -> D)) -> E) -> ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> D))) -> E)))
theorem-size     77
proof            (modus-ponens tm-312 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       241
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65561.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((((B -> (C -> D)) -> (B -> D)) -> E) -> ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> D))) -> E))), M:tm-312, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65562
in-theory        65562
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (E or (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     65
proof            (modus-ponens tm-311 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65562.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (E or (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))), M:tm-311, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65563
in-theory        65563
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) or E))
theorem-size     65
proof            (modus-ponens tm-310 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65563.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) or E)), M:tm-310, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65564
in-theory        65564
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (E -> ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and E)))
theorem-size     67
proof            (modus-ponens tm-309 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65564.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (E -> ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and E))), M:tm-309, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65565
in-theory        65565
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (B -> (C -> D))) -> (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (B -> D))))
theorem-size     85
proof            (modus-ponens tm-306 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> Bm (-> Cm Dm))) (C (-> Bm Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       251
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65565.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (B -> (C -> D))) -> (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (B -> D)))), M:tm-306, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> Bm (-> Cm Dm))) (C (-> Bm Dm)))
================================================================
tm-name          tm-65566
in-theory        65566
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (E -> (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D)))))
theorem-size     65
proof            (modus-ponens tm-305 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65566.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) and (E -> (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))))), M:tm-305, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65567
in-theory        65567
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     43
proof            (modus-ponens tm-303 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65567.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-303, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65568
in-theory        65568
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-270 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65568.        ((A -> (((B and C) -> C) and A)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-270, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65569
in-theory        65569
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-239 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65569.        ((A -> (((B and C) -> B) and A)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-239, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65570
in-theory        65570
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and ((F -> (G -> H)) -> (F -> G))) or ((F -> (G -> H)) -> (F -> G))) -> ((F -> (G -> H)) -> (F -> H))))
theorem-size     49
proof            (modus-ponens tm-210 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       219
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65570.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and ((F -> (G -> H)) -> (F -> G))) or ((F -> (G -> H)) -> (F -> G))) -> ((F -> (G -> H)) -> (F -> H)))), M:tm-210, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65571
in-theory        65571
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     41
proof            (modus-ponens tm-183 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65571.        ((A -> ((B -> (C -> B)) and A)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-183, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65572
in-theory        65572
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-157 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65572.        ((A -> ((B and C) -> C)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-157, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65573
in-theory        65573
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     47
proof            (modus-ponens tm-147 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65573.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-147, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65574
in-theory        65574
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-134 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65574.        ((A -> ((B and C) -> B)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-134, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65575
in-theory        65575
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     47
proof            (modus-ponens tm-125 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65575.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-125, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65576
in-theory        65576
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (((B -> (C -> D)) -> B) -> ((B -> (C -> D)) -> D)))
theorem-size     37
proof            (modus-ponens tm-114 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> Bm (-> Cm Dm))) (C Bm) (D Dm)))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       205
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65576.        (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (((B -> (C -> D)) -> B) -> ((B -> (C -> D)) -> D))), M:tm-114, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> Bm (-> Cm Dm))) (C Bm) (D Dm))
================================================================
tm-name          tm-65577
in-theory        65577
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> (G -> H)) -> (F -> G))) or ((F -> (G -> H)) -> (F -> G))) -> ((F -> (G -> H)) -> (F -> H))))
theorem-size     47
proof            (modus-ponens tm-113 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       211
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65577.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F -> (G -> H)) -> (F -> G))) or ((F -> (G -> H)) -> (F -> G))) -> ((F -> (G -> H)) -> (F -> H)))), M:tm-113, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65578
in-theory        65578
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     51
proof            (modus-ponens tm-105 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       231
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65578.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-105, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65579
in-theory        65579
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-95 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65579.        (((A -> B) -> (A -> A)) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-95, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65580
in-theory        65580
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (E -> ((B -> (C -> D)) -> (B -> D))))
theorem-size     33
proof            (modus-ponens tm-84 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65580.        (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (E -> ((B -> (C -> D)) -> (B -> D)))), M:tm-84, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65581
in-theory        65581
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-83 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65581.        ((A -> (B -> (C -> B))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-83, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65582
in-theory        65582
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and ((C -> (D -> E)) -> (C -> D))) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     37
proof            (modus-ponens tm-76 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65582.        (((not (not A)) -> A) and (((B and ((C -> (D -> E)) -> (C -> D))) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-76, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65583
in-theory        65583
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))))) or ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D)))
theorem-size     55
proof            (modus-ponens tm-73 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-8 tm-10 tm-4 tm-2)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65583.        (((not (not ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))))) or ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-73, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65584
in-theory        65584
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     43
proof            (modus-ponens tm-69 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-2)
proof-size       181
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65584.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-69, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65585
in-theory        65585
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-54 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65585.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-54, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65586
in-theory        65586
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) or ((D and ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C)))
theorem-size     41
proof            (modus-ponens tm-50 tm-772 ((A (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-8 tm-7 tm-4 tm-2)
proof-size       177
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65586.        ((((A -> (B -> C)) -> (A -> B)) or ((D and ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> B)))) -> ((A -> (B -> C)) -> (A -> C))), M:tm-50, m:tm-772, u:((A (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65587
in-theory        65587
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> (B -> C))) or ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D)))
theorem-size     43
proof            (modus-ponens tm-49 tm-772 ((A (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-8 tm-6 tm-4 tm-2)
proof-size       179
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65587.        (((A and ((B -> (C -> D)) -> (B -> C))) or ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-49, m:tm-772, u:((A (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (C (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65588
in-theory        65588
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and ((C -> (D -> E)) -> (C -> D))) or ((C -> (D -> E)) -> (C -> D)))) or ((B and ((C -> (D -> E)) -> (C -> D))) or ((C -> (D -> E)) -> (C -> D)))) -> ((C -> (D -> E)) -> (C -> E)))
theorem-size     55
proof            (modus-ponens tm-47 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65588.        (((A and ((B and ((C -> (D -> E)) -> (C -> D))) or ((C -> (D -> E)) -> (C -> D)))) or ((B and ((C -> (D -> E)) -> (C -> D))) or ((C -> (D -> E)) -> (C -> D)))) -> ((C -> (D -> E)) -> (C -> E))), M:tm-47, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65589
in-theory        65589
times-derived    1
----------------------------------------------------------------
theorem          (((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) and E) or ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D)))
theorem-size     55
proof            (modus-ponens tm-46 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-8 tm-3 tm-4 tm-2)
proof-size       189
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65589.        (((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) and E) or ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-46, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65590
in-theory        65590
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-42 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65590.        ((A -> (B or A)) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-42, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65591
in-theory        65591
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-32 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65591.        ((A -> (A or B)) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-32, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65592
in-theory        65592
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) and ((B -> (C -> D)) -> (B -> D))))
theorem-size     53
proof            (modus-ponens tm-24 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65592.        (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) and ((B -> (C -> D)) -> (B -> D)))), M:tm-24, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65593
in-theory        65593
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     39
proof            (modus-ponens tm-23 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       169
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65593.        ((A -> (B -> (A and B))) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-23, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65594
in-theory        65594
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-22 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65594.        (((A and B) -> B) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-22, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65595
in-theory        65595
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-21 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65595.        (((A and B) -> A) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-21, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65596
in-theory        65596
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G))))
theorem-size     45
proof            (modus-ponens tm-20 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       187
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65596.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and ((E -> (F -> G)) -> (E -> F))) or ((E -> (F -> G)) -> (E -> F))) -> ((E -> (F -> G)) -> (E -> G)))), M:tm-20, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65597
in-theory        65597
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F))))
theorem-size     37
proof            (modus-ponens tm-19 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65597.        ((A -> (B -> A)) and (((C and ((D -> (E -> F)) -> (D -> E))) or ((D -> (E -> F)) -> (D -> E))) -> ((D -> (E -> F)) -> (D -> F)))), M:tm-19, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65598
in-theory        65598
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))))
theorem-size     43
proof            (modus-ponens tm-12 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       173
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65598.        (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))), M:tm-12, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65599
in-theory        65599
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (not ((B -> (C -> D)) -> (B -> D)))) -> (not ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C)))))
theorem-size     55
proof            (modus-ponens tm-9 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-9 tm-8 tm-4 tm-2)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65599.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (not ((B -> (C -> D)) -> (B -> D)))) -> (not ((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))))), M:tm-9, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65600
in-theory        65600
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((E and ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> C))) -> D))
theorem-size     45
proof            (modus-ponens tm-8 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       163
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65600.        ((((A -> (B -> C)) -> (A -> C)) -> D) -> ((((E and ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> B))) or ((A -> (B -> C)) -> (A -> C))) -> D)), M:tm-8, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))
================================================================
tm-name          tm-65601
in-theory        65601
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and ((C -> (D -> E)) -> (C -> D))) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-7 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-7 tm-8 tm-4 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65601.        (A or (((B and ((C -> (D -> E)) -> (C -> D))) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-7, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65602
in-theory        65602
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) or E)
theorem-size     33
proof            (modus-ponens tm-6 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-6 tm-8 tm-4 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65602.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))) or E), M:tm-6, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65603
in-theory        65603
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and ((C -> (D -> E)) -> (C -> D))) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))) and A))
theorem-size     35
proof            (modus-ponens tm-5 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       147
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65603.        (A -> ((((B and ((C -> (D -> E)) -> (C -> D))) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))) and A)), M:tm-5, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65604
in-theory        65604
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (B -> (C -> D))) -> (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (B -> D)))
theorem-size     53
proof            (modus-ponens tm-2 tm-772 ((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> Bm (-> Cm Dm))) (C (-> Bm Dm))))
axioms-used      (tm-2 tm-8 tm-4)
proof-size       171
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65604.        ((((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (B -> (C -> D))) -> (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> (B -> D))), M:tm-2, m:tm-772, u:((A (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm)))) (B (-> Bm (-> Cm Dm))) (C (-> Bm Dm)))
================================================================
tm-name          tm-65605
in-theory        65605
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and ((C -> (D -> E)) -> (C -> D))) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E))))
theorem-size     33
proof            (modus-ponens tm-1 tm-772 ((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm))))))
axioms-used      (tm-1 tm-8 tm-4 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-772.          (((A and ((B -> (C -> D)) -> (B -> C))) or ((B -> (C -> D)) -> (B -> C))) -> ((B -> (C -> D)) -> (B -> D))), M:tm-47, m:tm-13, u:((A (-> (-> Am (-> Bm Cm)) (-> Am Bm))) (B (-> (-> Am (-> Bm Cm)) (-> Am Cm))))
tm-65605.        (A -> (((B and ((C -> (D -> E)) -> (C -> D))) or ((C -> (D -> E)) -> (C -> D))) -> ((C -> (D -> E)) -> (C -> E)))), M:tm-1, m:tm-772, u:((A (-> (or (and Am (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Cm))) (-> (-> Bm (-> Cm Dm)) (-> Bm Dm)))))
================================================================
tm-name          tm-65606
in-theory        65606
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-757 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65606.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-757, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65607
in-theory        65607
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((((A and B) or B) and F) or ((A and B) or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     47
proof            (modus-ponens tm-747 tm-773 ((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65607.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((((A and B) or B) and F) or ((A and B) or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-747, m:tm-773, u:((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-65608
in-theory        65608
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     45
proof            (modus-ponens tm-708 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65608.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-708, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65609
in-theory        65609
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-665 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65609.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-665, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65610
in-theory        65610
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-622 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65610.        ((A -> (B -> (C or B))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-622, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65611
in-theory        65611
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F)))
theorem-size     25
proof            (modus-ponens tm-609 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65611.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G or F))), M:tm-609, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65612
in-theory        65612
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-605 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65612.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-605, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65613
in-theory        65613
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-595 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65613.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G or F)) and (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-595, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65614
in-theory        65614
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-550 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65614.        (((A -> (B or A)) or C) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-550, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65615
in-theory        65615
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-540 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65615.        ((A or (B -> (C or B))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-540, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65616
in-theory        65616
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-530 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65616.        ((A or (B -> (B or C))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-530, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65617
in-theory        65617
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-520 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65617.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-520, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65618
in-theory        65618
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-510 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65618.        ((A or ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-510, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65619
in-theory        65619
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-500 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65619.        ((A or ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-500, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65620
in-theory        65620
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-490 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65620.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-490, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65621
in-theory        65621
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-480 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65621.        ((A or (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-480, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65622
in-theory        65622
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-469 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65622.        ((A -> (B -> (B or C))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-469, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65623
in-theory        65623
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G)))
theorem-size     25
proof            (modus-ponens tm-456 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65623.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (F or G))), M:tm-456, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65624
in-theory        65624
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-453 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65624.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-453, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65625
in-theory        65625
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-443 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65625.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (F or G)) and (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-443, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65626
in-theory        65626
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-409 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65626.        (((A -> (A or B)) or C) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-409, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65627
in-theory        65627
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-400 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65627.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-400, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65628
in-theory        65628
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-391 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65628.        ((((A and B) -> B) or C) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-391, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65629
in-theory        65629
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-382 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-1 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65629.        ((((A and B) -> A) or C) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-382, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65630
in-theory        65630
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-373 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65630.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-373, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65631
in-theory        65631
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-364 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65631.        (((A -> (B -> A)) or C) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-364, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65632
in-theory        65632
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-354 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65632.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-354, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65633
in-theory        65633
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G))))
theorem-size     27
proof            (modus-ponens tm-341 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65633.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> (F and G)))), M:tm-341, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65634
in-theory        65634
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     29
proof            (modus-ponens tm-338 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65634.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-338, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65635
in-theory        65635
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A and B) or B) -> (((A and B) or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-328 tm-773 ((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65635.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A and B) or B) -> (((A and B) or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-328, m:tm-773, u:((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-65636
in-theory        65636
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     47
proof            (modus-ponens tm-327 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       195
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65636.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> (F and G))) and (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-327, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65637
in-theory        65637
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-326 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65637.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> G) and (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-326, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65638
in-theory        65638
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-325 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65638.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F and G) -> F) and (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-325, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65639
in-theory        65639
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     53
proof            (modus-ponens tm-324 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       219
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65639.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-324, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65640
in-theory        65640
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     45
proof            (modus-ponens tm-323 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       187
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65640.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> F)) and (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-323, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65641
in-theory        65641
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G))
theorem-size     25
proof            (modus-ponens tm-322 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65641.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> G)), M:tm-322, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65642
in-theory        65642
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F))
theorem-size     25
proof            (modus-ponens tm-320 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65642.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F and G) -> F)), M:tm-320, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65643
in-theory        65643
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     33
proof            (modus-ponens tm-318 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       193
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65643.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65644
in-theory        65644
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     31
proof            (modus-ponens tm-316 tm-773 ((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65644.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-773, u:((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-65645
in-theory        65645
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F)))
theorem-size     25
proof            (modus-ponens tm-315 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65645.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (G -> F))), M:tm-315, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65646
in-theory        65646
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) or B) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not ((A and B) or B))))
theorem-size     47
proof            (modus-ponens tm-313 tm-773 ((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65646.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) or B) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not ((A and B) or B)))), M:tm-313, m:tm-773, u:((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-65647
in-theory        65647
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((((A and B) or B) or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F)))
theorem-size     57
proof            (modus-ponens tm-312 tm-773 ((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65647.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) -> F) -> ((((A and B) or B) or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) -> F))), M:tm-312, m:tm-773, u:((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-65648
in-theory        65648
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-311 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65648.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F or (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-311, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65649
in-theory        65649
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F))
theorem-size     41
proof            (modus-ponens tm-310 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65649.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)), M:tm-310, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65650
in-theory        65650
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F)))
theorem-size     43
proof            (modus-ponens tm-309 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       169
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65650.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and F))), M:tm-309, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65651
in-theory        65651
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) or B) -> (C -> (D -> E))) -> (((A and B) or B) -> ((C -> D) -> (C -> E)))))
theorem-size     45
proof            (modus-ponens tm-306 tm-773 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65651.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and ((((A and B) or B) -> (C -> (D -> E))) -> (((A and B) or B) -> ((C -> D) -> (C -> E))))), M:tm-306, m:tm-773, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-65652
in-theory        65652
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))))
theorem-size     41
proof            (modus-ponens tm-305 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65652.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and (F -> (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))), M:tm-305, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65653
in-theory        65653
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     31
proof            (modus-ponens tm-303 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65653.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-303, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65654
in-theory        65654
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-270 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65654.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-270, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65655
in-theory        65655
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-239 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-1 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65655.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-239, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65656
in-theory        65656
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     37
proof            (modus-ponens tm-210 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65656.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-210, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65657
in-theory        65657
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     29
proof            (modus-ponens tm-183 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65657.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-183, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65658
in-theory        65658
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-157 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65658.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-157, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65659
in-theory        65659
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-147 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65659.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-147, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65660
in-theory        65660
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-134 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65660.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-134, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65661
in-theory        65661
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     35
proof            (modus-ponens tm-125 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 tm-1)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65661.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-125, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65662
in-theory        65662
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I)))))
theorem-size     35
proof            (modus-ponens tm-113 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65662.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H -> I)) -> ((G -> H) -> (G -> I))))), M:tm-113, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65663
in-theory        65663
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     39
proof            (modus-ponens tm-105 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65663.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-105, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65664
in-theory        65664
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-95 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65664.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-95, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65665
in-theory        65665
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     27
proof            (modus-ponens tm-83 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65665.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-83, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65666
in-theory        65666
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     25
proof            (modus-ponens tm-76 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-1 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65666.        (((not (not A)) -> A) and (((B and C) or C) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-76, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65667
in-theory        65667
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     27
proof            (modus-ponens tm-73 tm-773 ((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-10 tm-4 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65667.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-73, m:tm-773, u:((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-65668
in-theory        65668
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     31
proof            (modus-ponens tm-69 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-1 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65668.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-69, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65669
in-theory        65669
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-54 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65669.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-54, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65670
in-theory        65670
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     21
proof            (modus-ponens tm-50 tm-773 ((A (and Am Bm)) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-7 tm-4 tm-1 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65670.        ((A or ((B and A) or A)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-50, m:tm-773, u:((A (and Am Bm)) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-65671
in-theory        65671
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))
theorem-size     23
proof            (modus-ponens tm-49 tm-773 ((A (and Am Bm)) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-6 tm-4 tm-1 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65671.        (((A and B) or ((A and B) or B)) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-49, m:tm-773, u:((A (and Am Bm)) (B Bm) (C (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-65672
in-theory        65672
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-47 tm-773 ((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65672.        (((A and ((B and C) or C)) or ((B and C) or C)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-47, m:tm-773, u:((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-65673
in-theory        65673
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     27
proof            (modus-ponens tm-46 tm-773 ((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-3 tm-4 tm-1 tm-2)
proof-size       137
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65673.        (((((A and B) or B) and C) or ((A and B) or B)) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-46, m:tm-773, u:((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-65674
in-theory        65674
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-42 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65674.        ((A -> (B or A)) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-42, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65675
in-theory        65675
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-32 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65675.        ((A -> (A or B)) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-32, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65676
in-theory        65676
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))))
theorem-size     25
proof            (modus-ponens tm-24 tm-773 ((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65676.        (((A and B) or B) -> (((A and B) or B) and ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))), M:tm-24, m:tm-773, u:((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-65677
in-theory        65677
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     27
proof            (modus-ponens tm-23 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65677.        ((A -> (B -> (A and B))) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-23, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65678
in-theory        65678
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-22 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65678.        (((A and B) -> B) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-22, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65679
in-theory        65679
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-21 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-1 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65679.        (((A and B) -> A) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-21, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65680
in-theory        65680
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))))
theorem-size     33
proof            (modus-ponens tm-20 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65680.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))), M:tm-20, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65681
in-theory        65681
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))))
theorem-size     25
proof            (modus-ponens tm-19 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65681.        ((A -> (B -> A)) and (((C and D) or D) -> ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))), M:tm-19, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65682
in-theory        65682
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not ((A and B) or B)))
theorem-size     27
proof            (modus-ponens tm-9 tm-773 ((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-9 tm-8 tm-4 tm-1 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65682.        ((((A and B) or B) -> (not ((C -> (D -> E)) -> ((C -> D) -> (C -> E))))) -> (not ((A and B) or B))), M:tm-9, m:tm-773, u:((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-65683
in-theory        65683
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((((E and F) or F) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-773 ((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
axioms-used      (tm-8 tm-4 tm-1 tm-2)
proof-size       131
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65683.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) -> D) -> ((((E and F) or F) or ((A -> (B -> C)) -> ((A -> B) -> (A -> C)))) -> D)), M:tm-8, m:tm-773, u:((A (or (and Am Bm) Bm)) (B (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))
================================================================
tm-name          tm-65684
in-theory        65684
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-7 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-7 tm-8 tm-4 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65684.        (A or (((B and C) or C) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-7, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65685
in-theory        65685
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F)
theorem-size     21
proof            (modus-ponens tm-6 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-6 tm-8 tm-4 tm-1 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65685.        ((((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) or F), M:tm-6, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65686
in-theory        65686
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A))
theorem-size     23
proof            (modus-ponens tm-5 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-2)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65686.        (A -> ((((B and C) or C) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))) and A)), M:tm-5, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65687
in-theory        65687
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C -> (D -> E))) -> (((A and B) or B) -> ((C -> D) -> (C -> E))))
theorem-size     25
proof            (modus-ponens tm-2 tm-773 ((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em)))))
axioms-used      (tm-2 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65687.        ((((A and B) or B) -> (C -> (D -> E))) -> (((A and B) or B) -> ((C -> D) -> (C -> E)))), M:tm-2, m:tm-773, u:((A (or (and Am Bm) Bm)) (B (-> Cm (-> Dm Em))) (C (-> (-> Cm Dm) (-> Cm Em))))
================================================================
tm-name          tm-65688
in-theory        65688
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))))
theorem-size     21
proof            (modus-ponens tm-1 tm-773 ((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em)))))))
axioms-used      (tm-1 tm-8 tm-4 tm-2)
proof-size       107
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-773.          (((A and B) or B) -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))), M:tm-47, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-65688.        (A -> (((B and C) or C) -> ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))), M:tm-1, m:tm-773, u:((A (-> (or (and Am Bm) Bm) (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))))))
================================================================
tm-name          tm-65689
in-theory        65689
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     37
proof            (modus-ponens tm-757 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65689.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-757, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65690
in-theory        65690
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) and E) or ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C)))
theorem-size     71
proof            (modus-ponens tm-747 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65690.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) and E) or ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C))), M:tm-747, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65691
in-theory        65691
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (((F -> G) and H) -> F)) or (((F -> G) and H) -> F)) -> (((F -> G) and H) -> G)))
theorem-size     51
proof            (modus-ponens tm-708 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-3)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65691.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (((F -> G) and H) -> F)) or (((F -> G) and H) -> F)) -> (((F -> G) and H) -> G))), M:tm-708, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65692
in-theory        65692
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     39
proof            (modus-ponens tm-665 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65692.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-665, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65693
in-theory        65693
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (E or (((B -> C) and D) -> C)))
theorem-size     27
proof            (modus-ponens tm-623 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65693.        (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (E or (((B -> C) and D) -> C))), M:tm-623, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65694
in-theory        65694
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-622 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65694.        ((A -> (B -> (C or B))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-622, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65695
in-theory        65695
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (E -> (F or E)))
theorem-size     31
proof            (modus-ponens tm-609 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65695.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (E -> (F or E))), M:tm-609, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65696
in-theory        65696
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     35
proof            (modus-ponens tm-605 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65696.        ((A -> ((B -> (C or B)) and A)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-605, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65697
in-theory        65697
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((E -> (F or E)) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))))
theorem-size     57
proof            (modus-ponens tm-595 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65697.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((E -> (F or E)) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))), M:tm-595, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65698
in-theory        65698
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-550 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65698.        (((A -> (B or A)) or C) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-550, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65699
in-theory        65699
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-540 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65699.        ((A or (B -> (C or B))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-540, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65700
in-theory        65700
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-530 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65700.        ((A or (B -> (B or C))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-530, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65701
in-theory        65701
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     35
proof            (modus-ponens tm-520 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65701.        ((A or (B -> (C -> (B and C)))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-520, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65702
in-theory        65702
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-510 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65702.        ((A or ((B and C) -> C)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-510, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65703
in-theory        65703
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-500 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65703.        ((A or ((B and C) -> B)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-500, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65704
in-theory        65704
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (((F -> G) and H) -> F)) or (((F -> G) and H) -> F)) -> (((F -> G) and H) -> G)))
theorem-size     41
proof            (modus-ponens tm-490 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65704.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (((F -> G) and H) -> F)) or (((F -> G) and H) -> F)) -> (((F -> G) and H) -> G))), M:tm-490, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65705
in-theory        65705
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-480 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65705.        ((A or (B -> (C -> B))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-480, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65706
in-theory        65706
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> ((((B -> C) and D) -> C) or E))
theorem-size     27
proof            (modus-ponens tm-470 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65706.        (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> ((((B -> C) and D) -> C) or E)), M:tm-470, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65707
in-theory        65707
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-469 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65707.        ((A -> (B -> (B or C))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-469, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65708
in-theory        65708
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (E -> (E or F)))
theorem-size     31
proof            (modus-ponens tm-456 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65708.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (E -> (E or F))), M:tm-456, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65709
in-theory        65709
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     35
proof            (modus-ponens tm-453 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65709.        ((A -> ((B -> (B or C)) and A)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-453, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65710
in-theory        65710
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((E -> (E or F)) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))))
theorem-size     57
proof            (modus-ponens tm-443 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65710.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((E -> (E or F)) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))), M:tm-443, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65711
in-theory        65711
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-409 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65711.        (((A -> (A or B)) or C) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-409, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65712
in-theory        65712
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     35
proof            (modus-ponens tm-400 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65712.        (((A -> (B -> (A and B))) or C) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-400, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65713
in-theory        65713
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-391 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65713.        ((((A and B) -> B) or C) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-391, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65714
in-theory        65714
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-382 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65714.        ((((A and B) -> A) or C) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-382, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65715
in-theory        65715
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (((F -> G) and H) -> F)) or (((F -> G) and H) -> F)) -> (((F -> G) and H) -> G)))
theorem-size     41
proof            (modus-ponens tm-373 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65715.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (((F -> G) and H) -> F)) or (((F -> G) and H) -> F)) -> (((F -> G) and H) -> G))), M:tm-373, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65716
in-theory        65716
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-364 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65716.        (((A -> (B -> A)) or C) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-364, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65717
in-theory        65717
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (E -> ((((B -> C) and D) -> C) and E)))
theorem-size     29
proof            (modus-ponens tm-355 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65717.        (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (E -> ((((B -> C) and D) -> C) and E))), M:tm-355, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65718
in-theory        65718
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     35
proof            (modus-ponens tm-354 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65718.        ((A -> (B -> (C -> (B and C)))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-354, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65719
in-theory        65719
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (E -> (F -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-341 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65719.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65720
in-theory        65720
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     35
proof            (modus-ponens tm-338 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65720.        (((A -> B) -> (A -> (A and B))) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-338, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65721
in-theory        65721
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) and (((B -> C) and D) -> C))))
theorem-size     69
proof            (modus-ponens tm-328 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65721.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) and (((B -> C) and D) -> C)))), M:tm-328, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65722
in-theory        65722
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((E -> (F -> (E and F))) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))))
theorem-size     59
proof            (modus-ponens tm-327 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65722.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((E -> (F -> (E and F))) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))), M:tm-327, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65723
in-theory        65723
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((E and F) -> F) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))))
theorem-size     57
proof            (modus-ponens tm-326 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65723.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((E and F) -> F) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))), M:tm-326, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65724
in-theory        65724
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((E and F) -> E) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))))
theorem-size     57
proof            (modus-ponens tm-325 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65724.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((E and F) -> E) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))), M:tm-325, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65725
in-theory        65725
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))))
theorem-size     65
proof            (modus-ponens tm-324 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       237
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65725.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))), M:tm-324, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65726
in-theory        65726
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((E -> (F -> E)) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))))
theorem-size     57
proof            (modus-ponens tm-323 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65726.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((E -> (F -> E)) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))), M:tm-323, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65727
in-theory        65727
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((E and F) -> F))
theorem-size     31
proof            (modus-ponens tm-322 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65727.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65728
in-theory        65728
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((E and F) -> E))
theorem-size     31
proof            (modus-ponens tm-320 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65728.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65729
in-theory        65729
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-318 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65729.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65730
in-theory        65730
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B))))
theorem-size     61
proof            (modus-ponens tm-316 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65730.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)))), M:tm-316, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65731
in-theory        65731
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (E -> (F -> E)))
theorem-size     31
proof            (modus-ponens tm-315 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65731.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65732
in-theory        65732
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (not (((B -> C) and D) -> C))) -> (not ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)))))
theorem-size     71
proof            (modus-ponens tm-313 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 tm-3)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65732.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (not (((B -> C) and D) -> C))) -> (not ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B))))), M:tm-313, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65733
in-theory        65733
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((((B -> C) and D) -> C) -> E) -> ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) or (((B -> C) and D) -> C)) -> E)))
theorem-size     63
proof            (modus-ponens tm-312 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65733.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (((((B -> C) and D) -> C) -> E) -> ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) or (((B -> C) and D) -> C)) -> E))), M:tm-312, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65734
in-theory        65734
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (E or (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))))
theorem-size     53
proof            (modus-ponens tm-311 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65734.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (E or (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))), M:tm-311, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65735
in-theory        65735
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) or E))
theorem-size     53
proof            (modus-ponens tm-310 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65735.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) or E)), M:tm-310, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65736
in-theory        65736
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (E -> ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and E)))
theorem-size     55
proof            (modus-ponens tm-309 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65736.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (E -> ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and E))), M:tm-309, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65737
in-theory        65737
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> ((B -> C) and D)) -> (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> C)))
theorem-size     69
proof            (modus-ponens tm-306 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (and (-> Bm Cm) Dm)) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65737.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> ((B -> C) and D)) -> (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> C))), M:tm-306, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (and (-> Bm Cm) Dm)) (C Cm))
================================================================
tm-name          tm-65738
in-theory        65738
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (E -> (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C))))
theorem-size     53
proof            (modus-ponens tm-305 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65738.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) and (E -> (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)))), M:tm-305, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65739
in-theory        65739
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     37
proof            (modus-ponens tm-303 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65739.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-303, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65740
in-theory        65740
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     35
proof            (modus-ponens tm-270 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65740.        ((A -> (((B and C) -> C) and A)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-270, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65741
in-theory        65741
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     35
proof            (modus-ponens tm-239 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65741.        ((A -> (((B and C) -> B) and A)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-239, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65742
in-theory        65742
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (((F -> G) and H) -> F)) or (((F -> G) and H) -> F)) -> (((F -> G) and H) -> G)))
theorem-size     43
proof            (modus-ponens tm-210 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-3)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65742.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (((F -> G) and H) -> F)) or (((F -> G) and H) -> F)) -> (((F -> G) and H) -> G))), M:tm-210, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65743
in-theory        65743
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     35
proof            (modus-ponens tm-183 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65743.        ((A -> ((B -> (C -> B)) and A)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-183, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65744
in-theory        65744
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-157 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65744.        ((A -> ((B and C) -> C)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-157, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65745
in-theory        65745
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     41
proof            (modus-ponens tm-147 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65745.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-147, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65746
in-theory        65746
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-134 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65746.        ((A -> ((B and C) -> B)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-134, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65747
in-theory        65747
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     41
proof            (modus-ponens tm-125 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65747.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-125, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65748
in-theory        65748
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> (C -> D)) and E) -> B)) or (((B -> (C -> D)) and E) -> B)) -> ((((B -> (C -> D)) and E) -> C) -> (((B -> (C -> D)) and E) -> D)))
theorem-size     41
proof            (modus-ponens tm-114 tm-774 ((A (or (and Am (-> (and (-> Bm (-> C D)) Dm) Bm)) (-> (and (-> Bm (-> C D)) Dm) Bm))) (B (and (-> Bm (-> C D)) Dm)) (Cm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-3)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65748.        (((A and (((B -> (C -> D)) and E) -> B)) or (((B -> (C -> D)) and E) -> B)) -> ((((B -> (C -> D)) and E) -> C) -> (((B -> (C -> D)) and E) -> D))), M:tm-114, m:tm-774, u:((A (or (and Am (-> (and (-> Bm (-> C D)) Dm) Bm)) (-> (and (-> Bm (-> C D)) Dm) Bm))) (B (and (-> Bm (-> C D)) Dm)) (Cm (-> C D)))
================================================================
tm-name          tm-65749
in-theory        65749
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (((F -> G) and H) -> F)) or (((F -> G) and H) -> F)) -> (((F -> G) and H) -> G)))
theorem-size     41
proof            (modus-ponens tm-113 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 tm-3)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65749.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (((F -> G) and H) -> F)) or (((F -> G) and H) -> F)) -> (((F -> G) and H) -> G))), M:tm-113, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65750
in-theory        65750
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     45
proof            (modus-ponens tm-105 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-3)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65750.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-105, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65751
in-theory        65751
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-95 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65751.        (((A -> B) -> (A -> A)) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-95, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65752
in-theory        65752
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (E -> (((B -> C) and D) -> C)))
theorem-size     27
proof            (modus-ponens tm-84 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65752.        (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (E -> (((B -> C) and D) -> C))), M:tm-84, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65753
in-theory        65753
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     33
proof            (modus-ponens tm-83 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2 tm-3)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65753.        ((A -> (B -> (C -> B))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-83, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65754
in-theory        65754
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (((C -> D) and E) -> C)) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     31
proof            (modus-ponens tm-76 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65754.        (((not (not A)) -> A) and (((B and (((C -> D) and E) -> C)) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-76, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65755
in-theory        65755
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)))) or ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C))
theorem-size     45
proof            (modus-ponens tm-73 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-8 tm-10 tm-4 tm-2 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65755.        (((not (not ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)))) or ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C)), M:tm-73, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65756
in-theory        65756
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     37
proof            (modus-ponens tm-69 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-2 tm-3)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65756.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-69, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65757
in-theory        65757
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     39
proof            (modus-ponens tm-54 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65757.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-54, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65758
in-theory        65758
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) or ((D and (((A -> B) and C) -> A)) or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B))
theorem-size     33
proof            (modus-ponens tm-50 tm-774 ((A (and Am (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-8 tm-7 tm-4 tm-2 tm-3)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65758.        (((((A -> B) and C) -> A) or ((D and (((A -> B) and C) -> A)) or (((A -> B) and C) -> A))) -> (((A -> B) and C) -> B)), M:tm-50, m:tm-774, u:((A (and Am (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65759
in-theory        65759
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) -> B)) or ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C))
theorem-size     35
proof            (modus-ponens tm-49 tm-774 ((A (and Am (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-8 tm-6 tm-4 tm-2 tm-3)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65759.        (((A and (((B -> C) and D) -> B)) or ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C)), M:tm-49, m:tm-774, u:((A (and Am (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Bm)) (C (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65760
in-theory        65760
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (((C -> D) and E) -> C)) or (((C -> D) and E) -> C))) or ((B and (((C -> D) and E) -> C)) or (((C -> D) and E) -> C))) -> (((C -> D) and E) -> D))
theorem-size     45
proof            (modus-ponens tm-47 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-3)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65760.        (((A and ((B and (((C -> D) and E) -> C)) or (((C -> D) and E) -> C))) or ((B and (((C -> D) and E) -> C)) or (((C -> D) and E) -> C))) -> (((C -> D) and E) -> D)), M:tm-47, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65761
in-theory        65761
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) and E) or ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C))
theorem-size     45
proof            (modus-ponens tm-46 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-8 tm-3 tm-4 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65761.        (((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) and E) or ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B))) -> (((B -> C) and D) -> C)), M:tm-46, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65762
in-theory        65762
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-42 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65762.        ((A -> (B or A)) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-42, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65763
in-theory        65763
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-32 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65763.        ((A -> (A or B)) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-32, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65764
in-theory        65764
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) and (((B -> C) and D) -> C)))
theorem-size     43
proof            (modus-ponens tm-24 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65764.        (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) and (((B -> C) and D) -> C))), M:tm-24, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65765
in-theory        65765
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     33
proof            (modus-ponens tm-23 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-3)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65765.        ((A -> (B -> (A and B))) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-23, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65766
in-theory        65766
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-22 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65766.        (((A and B) -> B) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-22, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65767
in-theory        65767
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-21 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65767.        (((A and B) -> A) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-21, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65768
in-theory        65768
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F)))
theorem-size     39
proof            (modus-ponens tm-20 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-3)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65768.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and (((E -> F) and G) -> E)) or (((E -> F) and G) -> E)) -> (((E -> F) and G) -> F))), M:tm-20, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65769
in-theory        65769
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E)))
theorem-size     31
proof            (modus-ponens tm-19 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2 tm-3)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65769.        ((A -> (B -> A)) and (((C and (((D -> E) and F) -> D)) or (((D -> E) and F) -> D)) -> (((D -> E) and F) -> E))), M:tm-19, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65770
in-theory        65770
times-derived    1
----------------------------------------------------------------
theorem          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)))
theorem-size     35
proof            (modus-ponens tm-12 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-3)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65770.        (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B))), M:tm-12, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65771
in-theory        65771
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (not (((B -> C) and D) -> C))) -> (not ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B))))
theorem-size     45
proof            (modus-ponens tm-9 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-9 tm-8 tm-4 tm-2 tm-3)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65771.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (not (((B -> C) and D) -> C))) -> (not ((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)))), M:tm-9, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65772
in-theory        65772
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> B) -> D) -> ((((E and (((A -> B) and C) -> A)) or (((A -> B) and C) -> A)) or (((A -> B) and C) -> B)) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm))))
axioms-used      (tm-8 tm-4 tm-2 tm-3)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65772.        (((((A -> B) and C) -> B) -> D) -> ((((E and (((A -> B) and C) -> A)) or (((A -> B) and C) -> A)) or (((A -> B) and C) -> B)) -> D)), M:tm-8, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (-> (and (-> Bm Cm) Dm) Cm)))
================================================================
tm-name          tm-65773
in-theory        65773
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and (((C -> D) and E) -> C)) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-7 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-7 tm-8 tm-4 tm-2 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65773.        (A or (((B and (((C -> D) and E) -> C)) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-7, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65774
in-theory        65774
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) or E)
theorem-size     27
proof            (modus-ponens tm-6 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-6 tm-8 tm-4 tm-2 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65774.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)) or E), M:tm-6, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65775
in-theory        65775
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and (((C -> D) and E) -> C)) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2 tm-3)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65775.        (A -> ((((B and (((C -> D) and E) -> C)) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)) and A)), M:tm-5, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65776
in-theory        65776
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> ((B -> C) and D)) -> (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> C))
theorem-size     43
proof            (modus-ponens tm-2 tm-774 ((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (and (-> Bm Cm) Dm)) (C Cm)))
axioms-used      (tm-2 tm-8 tm-4 tm-3)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65776.        ((((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> ((B -> C) and D)) -> (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> C)), M:tm-2, m:tm-774, u:((A (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm))) (B (and (-> Bm Cm) Dm)) (C Cm))
================================================================
tm-name          tm-65777
in-theory        65777
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and (((C -> D) and E) -> C)) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D)))
theorem-size     27
proof            (modus-ponens tm-1 tm-774 ((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm)))))
axioms-used      (tm-1 tm-8 tm-4 tm-2 tm-3)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-774.          (((A and (((B -> C) and D) -> B)) or (((B -> C) and D) -> B)) -> (((B -> C) and D) -> C)), M:tm-47, m:tm-15, u:((A (-> (and (-> Am Bm) Cm) Am)) (B (-> (and (-> Am Bm) Cm) Bm)))
tm-65777.        (A -> (((B and (((C -> D) and E) -> C)) or (((C -> D) and E) -> C)) -> (((C -> D) and E) -> D))), M:tm-1, m:tm-774, u:((A (-> (or (and Am (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Bm)) (-> (and (-> Bm Cm) Dm) Cm))))
================================================================
tm-name          tm-65778
in-theory        65778
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-757 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65778.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-757, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65779
in-theory        65779
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (((((A and B) or B) and E) or ((A and B) or B)) -> ((C and D) -> C)))
theorem-size     31
proof            (modus-ponens tm-747 tm-775 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65779.        ((((A and B) or B) -> ((C and D) -> C)) and (((((A and B) or B) and E) or ((A and B) or B)) -> ((C and D) -> C))), M:tm-747, m:tm-775, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-65780
in-theory        65780
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> ((G and H) -> G)))
theorem-size     37
proof            (modus-ponens tm-708 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1 tm-3)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65780.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> ((G and H) -> G))), M:tm-708, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65781
in-theory        65781
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-665 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-3)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65781.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-665, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65782
in-theory        65782
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-622 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65782.        ((A -> (B -> (C or B))) and (((D and E) or E) -> ((F and G) -> F))), M:tm-622, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65783
in-theory        65783
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65783.        ((((A and B) or B) -> ((C and D) -> C)) and (E -> (F or E))), M:tm-609, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65784
in-theory        65784
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-605 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65784.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-605, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65785
in-theory        65785
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and ((E -> (F or E)) and (((A and B) or B) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-595 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-1 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65785.        ((((A and B) or B) -> ((C and D) -> C)) and ((E -> (F or E)) and (((A and B) or B) -> ((C and D) -> C)))), M:tm-595, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65786
in-theory        65786
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-550 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-1 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65786.        (((A -> (B or A)) or C) and (((D and E) or E) -> ((F and G) -> F))), M:tm-550, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65787
in-theory        65787
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-540 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65787.        ((A or (B -> (C or B))) and (((D and E) or E) -> ((F and G) -> F))), M:tm-540, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65788
in-theory        65788
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-530 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-1 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65788.        ((A or (B -> (B or C))) and (((D and E) or E) -> ((F and G) -> F))), M:tm-530, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65789
in-theory        65789
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-520 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65789.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F and G) -> F))), M:tm-520, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65790
in-theory        65790
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-510 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65790.        ((A or ((B and C) -> C)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-510, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65791
in-theory        65791
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-500 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65791.        ((A or ((B and C) -> B)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-500, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65792
in-theory        65792
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-490 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 tm-1 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65792.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G and H) -> G))), M:tm-490, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65793
in-theory        65793
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-480 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65793.        ((A or (B -> (C -> B))) and (((D and E) or E) -> ((F and G) -> F))), M:tm-480, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65794
in-theory        65794
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-469 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65794.        ((A -> (B -> (B or C))) and (((D and E) or E) -> ((F and G) -> F))), M:tm-469, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65795
in-theory        65795
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65795.        ((((A and B) or B) -> ((C and D) -> C)) and (E -> (E or F))), M:tm-456, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65796
in-theory        65796
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-453 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65796.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-453, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65797
in-theory        65797
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and ((E -> (E or F)) and (((A and B) or B) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-443 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-1 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65797.        ((((A and B) or B) -> ((C and D) -> C)) and ((E -> (E or F)) and (((A and B) or B) -> ((C and D) -> C)))), M:tm-443, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65798
in-theory        65798
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-409 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65798.        (((A -> (A or B)) or C) and (((D and E) or E) -> ((F and G) -> F))), M:tm-409, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65799
in-theory        65799
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-400 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65799.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> ((F and G) -> F))), M:tm-400, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65800
in-theory        65800
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-391 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65800.        ((((A and B) -> B) or C) and (((D and E) or E) -> ((F and G) -> F))), M:tm-391, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65801
in-theory        65801
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-382 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65801.        ((((A and B) -> A) or C) and (((D and E) or E) -> ((F and G) -> F))), M:tm-382, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65802
in-theory        65802
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-373 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 tm-1 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65802.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> ((G and H) -> G))), M:tm-373, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65803
in-theory        65803
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-364 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65803.        (((A -> (B -> A)) or C) and (((D and E) or E) -> ((F and G) -> F))), M:tm-364, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65804
in-theory        65804
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-354 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65804.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F and G) -> F))), M:tm-354, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65805
in-theory        65805
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65805.        ((((A and B) or B) -> ((C and D) -> C)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65806
in-theory        65806
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> ((E and F) -> E)))
theorem-size     21
proof            (modus-ponens tm-338 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65806.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> ((E and F) -> E))), M:tm-338, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65807
in-theory        65807
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (((A and B) or B) -> (((A and B) or B) and ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-328 tm-775 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65807.        ((((A and B) or B) -> ((C and D) -> C)) and (((A and B) or B) -> (((A and B) or B) and ((C and D) -> C)))), M:tm-328, m:tm-775, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-65808
in-theory        65808
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> ((C and D) -> C))))
theorem-size     31
proof            (modus-ponens tm-327 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1 tm-3)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65808.        ((((A and B) or B) -> ((C and D) -> C)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> ((C and D) -> C)))), M:tm-327, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65809
in-theory        65809
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (((E and F) -> F) and (((A and B) or B) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-326 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65809.        ((((A and B) or B) -> ((C and D) -> C)) and (((E and F) -> F) and (((A and B) or B) -> ((C and D) -> C)))), M:tm-326, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65810
in-theory        65810
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (((E and F) -> E) and (((A and B) or B) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-325 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65810.        ((((A and B) or B) -> ((C and D) -> C)) and (((E and F) -> E) and (((A and B) or B) -> ((C and D) -> C)))), M:tm-325, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65811
in-theory        65811
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> ((C and D) -> C))))
theorem-size     37
proof            (modus-ponens tm-324 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1 tm-3)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65811.        ((((A and B) or B) -> ((C and D) -> C)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> ((C and D) -> C)))), M:tm-324, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65812
in-theory        65812
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and ((E -> (F -> E)) and (((A and B) or B) -> ((C and D) -> C))))
theorem-size     29
proof            (modus-ponens tm-323 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65812.        ((((A and B) or B) -> ((C and D) -> C)) and ((E -> (F -> E)) and (((A and B) or B) -> ((C and D) -> C)))), M:tm-323, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65813
in-theory        65813
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65813.        ((((A and B) or B) -> ((C and D) -> C)) and ((E and F) -> F)), M:tm-322, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65814
in-theory        65814
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65814.        ((((A and B) or B) -> ((C and D) -> C)) and ((E and F) -> E)), M:tm-320, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65815
in-theory        65815
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65815.        ((((A and B) or B) -> ((C and D) -> C)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65816
in-theory        65816
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     23
proof            (modus-ponens tm-316 tm-775 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65816.        ((((A and B) or B) -> ((C and D) -> C)) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-775, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-65817
in-theory        65817
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65817.        ((((A and B) or B) -> ((C and D) -> C)) and (E -> (F -> E))), M:tm-315, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65818
in-theory        65818
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and ((((A and B) or B) -> (not ((C and D) -> C))) -> (not ((A and B) or B))))
theorem-size     31
proof            (modus-ponens tm-313 tm-775 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 tm-1 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65818.        ((((A and B) or B) -> ((C and D) -> C)) and ((((A and B) or B) -> (not ((C and D) -> C))) -> (not ((A and B) or B)))), M:tm-313, m:tm-775, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-65819
in-theory        65819
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and ((((C and D) -> C) -> E) -> ((((A and B) or B) or ((C and D) -> C)) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-775 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1 tm-3)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65819.        ((((A and B) or B) -> ((C and D) -> C)) and ((((C and D) -> C) -> E) -> ((((A and B) or B) or ((C and D) -> C)) -> E))), M:tm-312, m:tm-775, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-65820
in-theory        65820
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (E or (((A and B) or B) -> ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-311 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65820.        ((((A and B) or B) -> ((C and D) -> C)) and (E or (((A and B) or B) -> ((C and D) -> C)))), M:tm-311, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65821
in-theory        65821
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and ((((A and B) or B) -> ((C and D) -> C)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-1 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65821.        ((((A and B) or B) -> ((C and D) -> C)) and ((((A and B) or B) -> ((C and D) -> C)) or E)), M:tm-310, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65822
in-theory        65822
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (E -> ((((A and B) or B) -> ((C and D) -> C)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1 tm-3)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65822.        ((((A and B) or B) -> ((C and D) -> C)) and (E -> ((((A and B) or B) -> ((C and D) -> C)) and E))), M:tm-309, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65823
in-theory        65823
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and ((((A and B) or B) -> (C and D)) -> (((A and B) or B) -> C)))
theorem-size     29
proof            (modus-ponens tm-306 tm-775 ((A (or (and Am Bm) Bm)) (B (and Cm Dm)) (C Cm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1 tm-3)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65823.        ((((A and B) or B) -> ((C and D) -> C)) and ((((A and B) or B) -> (C and D)) -> (((A and B) or B) -> C))), M:tm-306, m:tm-775, u:((A (or (and Am Bm) Bm)) (B (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-65824
in-theory        65824
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) and (E -> (((A and B) or B) -> ((C and D) -> C))))
theorem-size     25
proof            (modus-ponens tm-305 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65824.        ((((A and B) or B) -> ((C and D) -> C)) and (E -> (((A and B) or B) -> ((C and D) -> C)))), M:tm-305, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65825
in-theory        65825
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     23
proof            (modus-ponens tm-303 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65825.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-303, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65826
in-theory        65826
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-270 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65826.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-270, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65827
in-theory        65827
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-239 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65827.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-239, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65828
in-theory        65828
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> ((G and H) -> G)))
theorem-size     29
proof            (modus-ponens tm-210 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65828.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> ((G and H) -> G))), M:tm-210, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65829
in-theory        65829
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     21
proof            (modus-ponens tm-183 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65829.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-183, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65830
in-theory        65830
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-157 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65830.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-157, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65831
in-theory        65831
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-147 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65831.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-147, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65832
in-theory        65832
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-134 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65832.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-134, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65833
in-theory        65833
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     27
proof            (modus-ponens tm-125 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65833.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> ((F and G) -> F))), M:tm-125, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65834
in-theory        65834
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G and H) -> G)))
theorem-size     27
proof            (modus-ponens tm-113 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 tm-3)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65834.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G and H) -> G))), M:tm-113, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65835
in-theory        65835
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     31
proof            (modus-ponens tm-105 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1 tm-3)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65835.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> ((F and G) -> F))), M:tm-105, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65836
in-theory        65836
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-95 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65836.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> ((E and F) -> E))), M:tm-95, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65837
in-theory        65837
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     19
proof            (modus-ponens tm-83 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65837.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> ((F and G) -> F))), M:tm-83, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65838
in-theory        65838
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> ((D and E) -> D)))
theorem-size     17
proof            (modus-ponens tm-76 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-1 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65838.        (((not (not A)) -> A) and (((B and C) or C) -> ((D and E) -> D))), M:tm-76, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65839
in-theory        65839
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> ((C and D) -> C))
theorem-size     19
proof            (modus-ponens tm-73 tm-775 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-10 tm-4 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65839.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> ((C and D) -> C)), M:tm-73, m:tm-775, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-65840
in-theory        65840
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> ((E and F) -> E)))
theorem-size     23
proof            (modus-ponens tm-69 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-1 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65840.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> ((E and F) -> E))), M:tm-69, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65841
in-theory        65841
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-54 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65841.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> ((F and G) -> F))), M:tm-54, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65842
in-theory        65842
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> ((C and D) -> C))
theorem-size     13
proof            (modus-ponens tm-50 tm-775 ((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-7 tm-4 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65842.        ((A or ((B and A) or A)) -> ((C and D) -> C)), M:tm-50, m:tm-775, u:((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-65843
in-theory        65843
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> ((C and D) -> C))
theorem-size     15
proof            (modus-ponens tm-49 tm-775 ((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-6 tm-4 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65843.        (((A and B) or ((A and B) or B)) -> ((C and D) -> C)), M:tm-49, m:tm-775, u:((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-65844
in-theory        65844
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-47 tm-775 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-4 tm-1 tm-3)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65844.        (((A and ((B and C) or C)) or ((B and C) or C)) -> ((D and E) -> D)), M:tm-47, m:tm-775, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-65845
in-theory        65845
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> ((D and E) -> D))
theorem-size     19
proof            (modus-ponens tm-46 tm-775 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-3 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65845.        (((((A and B) or B) and C) or ((A and B) or B)) -> ((D and E) -> D)), M:tm-46, m:tm-775, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-65846
in-theory        65846
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-42 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65846.        ((A -> (B or A)) and (((C and D) or D) -> ((E and F) -> E))), M:tm-42, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65847
in-theory        65847
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-32 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65847.        ((A -> (A or B)) and (((C and D) or D) -> ((E and F) -> E))), M:tm-32, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65848
in-theory        65848
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and ((C and D) -> C)))
theorem-size     17
proof            (modus-ponens tm-24 tm-775 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65848.        (((A and B) or B) -> (((A and B) or B) and ((C and D) -> C))), M:tm-24, m:tm-775, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-65849
in-theory        65849
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> ((E and F) -> E)))
theorem-size     19
proof            (modus-ponens tm-23 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-3)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65849.        ((A -> (B -> (A and B))) and (((C and D) or D) -> ((E and F) -> E))), M:tm-23, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65850
in-theory        65850
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-22 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65850.        (((A and B) -> B) and (((C and D) or D) -> ((E and F) -> E))), M:tm-22, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65851
in-theory        65851
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-21 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65851.        (((A and B) -> A) and (((C and D) or D) -> ((E and F) -> E))), M:tm-21, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65852
in-theory        65852
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> ((F and G) -> F)))
theorem-size     25
proof            (modus-ponens tm-20 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1 tm-3)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65852.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> ((F and G) -> F))), M:tm-20, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65853
in-theory        65853
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> ((E and F) -> E)))
theorem-size     17
proof            (modus-ponens tm-19 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65853.        ((A -> (B -> A)) and (((C and D) or D) -> ((E and F) -> E))), M:tm-19, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65854
in-theory        65854
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not ((C and D) -> C))) -> (not ((A and B) or B)))
theorem-size     19
proof            (modus-ponens tm-9 tm-775 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-9 tm-8 tm-4 tm-1 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65854.        ((((A and B) or B) -> (not ((C and D) -> C))) -> (not ((A and B) or B))), M:tm-9, m:tm-775, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-65855
in-theory        65855
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) -> C) -> ((((D and E) or E) or ((A and B) -> A)) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-775 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm))))
axioms-used      (tm-8 tm-4 tm-1 tm-3)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65855.        ((((A and B) -> A) -> C) -> ((((D and E) or E) or ((A and B) -> A)) -> C)), M:tm-8, m:tm-775, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Cm)))
================================================================
tm-name          tm-65856
in-theory        65856
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-7 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-7 tm-8 tm-4 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65856.        (A or (((B and C) or C) -> ((D and E) -> D))), M:tm-7, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65857
in-theory        65857
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> C)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-6 tm-8 tm-4 tm-1 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65857.        ((((A and B) or B) -> ((C and D) -> C)) or E), M:tm-6, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65858
in-theory        65858
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> ((D and E) -> D)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1 tm-3)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65858.        (A -> ((((B and C) or C) -> ((D and E) -> D)) and A)), M:tm-5, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65859
in-theory        65859
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C and D)) -> (((A and B) or B) -> C))
theorem-size     17
proof            (modus-ponens tm-2 tm-775 ((A (or (and Am Bm) Bm)) (B (and Cm Dm)) (C Cm)))
axioms-used      (tm-2 tm-8 tm-4 tm-1 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65859.        ((((A and B) or B) -> (C and D)) -> (((A and B) or B) -> C)), M:tm-2, m:tm-775, u:((A (or (and Am Bm) Bm)) (B (and Cm Dm)) (C Cm))
================================================================
tm-name          tm-65860
in-theory        65860
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> ((D and E) -> D)))
theorem-size     13
proof            (modus-ponens tm-1 tm-775 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm)))))
axioms-used      (tm-1 tm-8 tm-4 tm-3)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-775.          (((A and B) or B) -> ((C and D) -> C)), M:tm-47, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-65860.        (A -> (((B and C) or C) -> ((D and E) -> D))), M:tm-1, m:tm-775, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Cm))))
================================================================
tm-name          tm-65861
in-theory        65861
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     37
proof            (modus-ponens tm-757 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65861.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-757, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65862
in-theory        65862
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) and E) or ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C))) -> ((B and (C -> D)) -> D)))
theorem-size     71
proof            (modus-ponens tm-747 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       231
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65862.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) and E) or ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C))) -> ((B and (C -> D)) -> D))), M:tm-747, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65863
in-theory        65863
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and ((F and (G -> H)) -> G)) or ((F and (G -> H)) -> G)) -> ((F and (G -> H)) -> H)))
theorem-size     51
proof            (modus-ponens tm-708 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       225
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65863.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and ((F and (G -> H)) -> G)) or ((F and (G -> H)) -> G)) -> ((F and (G -> H)) -> H))), M:tm-708, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65864
in-theory        65864
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     39
proof            (modus-ponens tm-665 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65864.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-665, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65865
in-theory        65865
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (E or ((B and (C -> D)) -> D)))
theorem-size     27
proof            (modus-ponens tm-623 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65865.        (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (E or ((B and (C -> D)) -> D))), M:tm-623, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65866
in-theory        65866
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-622 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65866.        ((A -> (B -> (C or B))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-622, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65867
in-theory        65867
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (E -> (F or E)))
theorem-size     31
proof            (modus-ponens tm-609 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65867.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (E -> (F or E))), M:tm-609, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65868
in-theory        65868
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     35
proof            (modus-ponens tm-605 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65868.        ((A -> ((B -> (C or B)) and A)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-605, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65869
in-theory        65869
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((E -> (F or E)) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))))
theorem-size     57
proof            (modus-ponens tm-595 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65869.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((E -> (F or E)) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)))), M:tm-595, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65870
in-theory        65870
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-550 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65870.        (((A -> (B or A)) or C) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-550, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65871
in-theory        65871
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-540 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65871.        ((A or (B -> (C or B))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-540, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65872
in-theory        65872
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-530 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65872.        ((A or (B -> (B or C))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-530, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65873
in-theory        65873
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     35
proof            (modus-ponens tm-520 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65873.        ((A or (B -> (C -> (B and C)))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-520, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65874
in-theory        65874
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-510 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65874.        ((A or ((B and C) -> C)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-510, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65875
in-theory        65875
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-500 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65875.        ((A or ((B and C) -> B)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-500, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65876
in-theory        65876
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F and (G -> H)) -> G)) or ((F and (G -> H)) -> G)) -> ((F and (G -> H)) -> H)))
theorem-size     41
proof            (modus-ponens tm-490 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65876.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F and (G -> H)) -> G)) or ((F and (G -> H)) -> G)) -> ((F and (G -> H)) -> H))), M:tm-490, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65877
in-theory        65877
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-480 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65877.        ((A or (B -> (C -> B))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-480, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65878
in-theory        65878
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (((B and (C -> D)) -> D) or E))
theorem-size     27
proof            (modus-ponens tm-470 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65878.        (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (((B and (C -> D)) -> D) or E)), M:tm-470, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65879
in-theory        65879
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-469 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65879.        ((A -> (B -> (B or C))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-469, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65880
in-theory        65880
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (E -> (E or F)))
theorem-size     31
proof            (modus-ponens tm-456 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65880.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (E -> (E or F))), M:tm-456, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65881
in-theory        65881
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     35
proof            (modus-ponens tm-453 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65881.        ((A -> ((B -> (B or C)) and A)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-453, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65882
in-theory        65882
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((E -> (E or F)) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))))
theorem-size     57
proof            (modus-ponens tm-443 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65882.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((E -> (E or F)) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)))), M:tm-443, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65883
in-theory        65883
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-409 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65883.        (((A -> (A or B)) or C) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-409, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65884
in-theory        65884
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     35
proof            (modus-ponens tm-400 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65884.        (((A -> (B -> (A and B))) or C) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-400, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65885
in-theory        65885
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-391 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65885.        ((((A and B) -> B) or C) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-391, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65886
in-theory        65886
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-382 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65886.        ((((A and B) -> A) or C) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-382, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65887
in-theory        65887
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and ((F and (G -> H)) -> G)) or ((F and (G -> H)) -> G)) -> ((F and (G -> H)) -> H)))
theorem-size     41
proof            (modus-ponens tm-373 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65887.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and ((F and (G -> H)) -> G)) or ((F and (G -> H)) -> G)) -> ((F and (G -> H)) -> H))), M:tm-373, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65888
in-theory        65888
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-364 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65888.        (((A -> (B -> A)) or C) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-364, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65889
in-theory        65889
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (E -> (((B and (C -> D)) -> D) and E)))
theorem-size     29
proof            (modus-ponens tm-355 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65889.        (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (E -> (((B and (C -> D)) -> D) and E))), M:tm-355, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65890
in-theory        65890
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     35
proof            (modus-ponens tm-354 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65890.        ((A -> (B -> (C -> (B and C)))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-354, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65891
in-theory        65891
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (E -> (F -> (E and F))))
theorem-size     33
proof            (modus-ponens tm-341 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65891.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65892
in-theory        65892
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     35
proof            (modus-ponens tm-338 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65892.        (((A -> B) -> (A -> (A and B))) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-338, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65893
in-theory        65893
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) and ((B and (C -> D)) -> D))))
theorem-size     69
proof            (modus-ponens tm-328 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       227
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65893.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) and ((B and (C -> D)) -> D)))), M:tm-328, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65894
in-theory        65894
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((E -> (F -> (E and F))) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))))
theorem-size     59
proof            (modus-ponens tm-327 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65894.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((E -> (F -> (E and F))) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)))), M:tm-327, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65895
in-theory        65895
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (((E and F) -> F) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))))
theorem-size     57
proof            (modus-ponens tm-326 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65895.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (((E and F) -> F) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)))), M:tm-326, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65896
in-theory        65896
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (((E and F) -> E) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))))
theorem-size     57
proof            (modus-ponens tm-325 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65896.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (((E and F) -> E) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)))), M:tm-325, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65897
in-theory        65897
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))))
theorem-size     65
proof            (modus-ponens tm-324 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       237
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65897.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)))), M:tm-324, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65898
in-theory        65898
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((E -> (F -> E)) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))))
theorem-size     57
proof            (modus-ponens tm-323 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65898.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((E -> (F -> E)) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)))), M:tm-323, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65899
in-theory        65899
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((E and F) -> F))
theorem-size     31
proof            (modus-ponens tm-322 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65899.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65900
in-theory        65900
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((E and F) -> E))
theorem-size     31
proof            (modus-ponens tm-320 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65900.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65901
in-theory        65901
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     39
proof            (modus-ponens tm-318 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65901.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65902
in-theory        65902
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C))))
theorem-size     61
proof            (modus-ponens tm-316 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       213
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65902.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)))), M:tm-316, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65903
in-theory        65903
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (E -> (F -> E)))
theorem-size     31
proof            (modus-ponens tm-315 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65903.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65904
in-theory        65904
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (not ((B and (C -> D)) -> D))) -> (not ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)))))
theorem-size     71
proof            (modus-ponens tm-313 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       213
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65904.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (not ((B and (C -> D)) -> D))) -> (not ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C))))), M:tm-313, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65905
in-theory        65905
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((((B and (C -> D)) -> D) -> E) -> ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> D)) -> E)))
theorem-size     63
proof            (modus-ponens tm-312 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65905.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((((B and (C -> D)) -> D) -> E) -> ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> D)) -> E))), M:tm-312, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65906
in-theory        65906
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (E or (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))))
theorem-size     53
proof            (modus-ponens tm-311 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65906.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (E or (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)))), M:tm-311, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65907
in-theory        65907
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) or E))
theorem-size     53
proof            (modus-ponens tm-310 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65907.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) or E)), M:tm-310, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65908
in-theory        65908
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (E -> ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and E)))
theorem-size     55
proof            (modus-ponens tm-309 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65908.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (E -> ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and E))), M:tm-309, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65909
in-theory        65909
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (B and (C -> D))) -> (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> D)))
theorem-size     69
proof            (modus-ponens tm-306 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (and Bm (-> Cm Dm))) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       217
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65909.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (B and (C -> D))) -> (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> D))), M:tm-306, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (and Bm (-> Cm Dm))) (C Dm))
================================================================
tm-name          tm-65910
in-theory        65910
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (E -> (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D))))
theorem-size     53
proof            (modus-ponens tm-305 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65910.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) and (E -> (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)))), M:tm-305, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65911
in-theory        65911
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     37
proof            (modus-ponens tm-303 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65911.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-303, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65912
in-theory        65912
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     35
proof            (modus-ponens tm-270 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65912.        ((A -> (((B and C) -> C) and A)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-270, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65913
in-theory        65913
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     35
proof            (modus-ponens tm-239 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65913.        ((A -> (((B and C) -> B) and A)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-239, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65914
in-theory        65914
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and ((F and (G -> H)) -> G)) or ((F and (G -> H)) -> G)) -> ((F and (G -> H)) -> H)))
theorem-size     43
proof            (modus-ponens tm-210 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       195
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65914.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and ((F and (G -> H)) -> G)) or ((F and (G -> H)) -> G)) -> ((F and (G -> H)) -> H))), M:tm-210, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65915
in-theory        65915
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     35
proof            (modus-ponens tm-183 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65915.        ((A -> ((B -> (C -> B)) and A)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-183, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65916
in-theory        65916
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-157 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65916.        ((A -> ((B and C) -> C)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-157, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65917
in-theory        65917
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     41
proof            (modus-ponens tm-147 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65917.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-147, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65918
in-theory        65918
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-134 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65918.        ((A -> ((B and C) -> B)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-134, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65919
in-theory        65919
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     41
proof            (modus-ponens tm-125 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65919.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-125, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65920
in-theory        65920
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> (D -> E))) -> C)) or ((B and (C -> (D -> E))) -> C)) -> (((B and (C -> (D -> E))) -> D) -> ((B and (C -> (D -> E))) -> E)))
theorem-size     41
proof            (modus-ponens tm-114 tm-776 ((A (or (and Am (-> (and Bm (-> Cm (-> C D))) Cm)) (-> (and Bm (-> Cm (-> C D))) Cm))) (B (and Bm (-> Cm (-> C D)))) (Dm (-> C D))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-114.          ((A -> (B -> (C -> D))) -> (A -> ((B -> C) -> (B -> D)))), M:tm-2, m:tm-14, u:((A Am) (B (-> Bm (-> Cm Dm))) (C (-> (-> Bm Cm) (-> Bm Dm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65920.        (((A and ((B and (C -> (D -> E))) -> C)) or ((B and (C -> (D -> E))) -> C)) -> (((B and (C -> (D -> E))) -> D) -> ((B and (C -> (D -> E))) -> E))), M:tm-114, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm (-> C D))) Cm)) (-> (and Bm (-> Cm (-> C D))) Cm))) (B (and Bm (-> Cm (-> C D)))) (Dm (-> C D)))
================================================================
tm-name          tm-65921
in-theory        65921
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F and (G -> H)) -> G)) or ((F and (G -> H)) -> G)) -> ((F and (G -> H)) -> H)))
theorem-size     41
proof            (modus-ponens tm-113 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       187
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65921.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and ((F and (G -> H)) -> G)) or ((F and (G -> H)) -> G)) -> ((F and (G -> H)) -> H))), M:tm-113, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65922
in-theory        65922
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     45
proof            (modus-ponens tm-105 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       207
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65922.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-105, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65923
in-theory        65923
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-95 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65923.        (((A -> B) -> (A -> A)) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-95, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65924
in-theory        65924
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (E -> ((B and (C -> D)) -> D)))
theorem-size     27
proof            (modus-ponens tm-84 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65924.        (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (E -> ((B and (C -> D)) -> D))), M:tm-84, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65925
in-theory        65925
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     33
proof            (modus-ponens tm-83 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       155
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65925.        ((A -> (B -> (C -> B))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-83, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65926
in-theory        65926
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and ((C and (D -> E)) -> D)) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E)))
theorem-size     31
proof            (modus-ponens tm-76 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65926.        (((not (not A)) -> A) and (((B and ((C and (D -> E)) -> D)) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E))), M:tm-76, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65927
in-theory        65927
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)))) or ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C))) -> ((B and (C -> D)) -> D))
theorem-size     45
proof            (modus-ponens tm-73 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-8 tm-10 tm-4 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65927.        (((not (not ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)))) or ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C))) -> ((B and (C -> D)) -> D)), M:tm-73, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65928
in-theory        65928
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     37
proof            (modus-ponens tm-69 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-2)
proof-size       157
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65928.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-69, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65929
in-theory        65929
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     39
proof            (modus-ponens tm-54 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65929.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-54, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65930
in-theory        65930
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) or ((D and ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C))
theorem-size     33
proof            (modus-ponens tm-50 tm-776 ((A (and Am (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-8 tm-7 tm-4 tm-2)
proof-size       151
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65930.        ((((A and (B -> C)) -> B) or ((D and ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> B))) -> ((A and (B -> C)) -> C)), M:tm-50, m:tm-776, u:((A (and Am (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65931
in-theory        65931
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) -> C)) or ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C))) -> ((B and (C -> D)) -> D))
theorem-size     35
proof            (modus-ponens tm-49 tm-776 ((A (and Am (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-8 tm-6 tm-4 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65931.        (((A and ((B and (C -> D)) -> C)) or ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C))) -> ((B and (C -> D)) -> D)), M:tm-49, m:tm-776, u:((A (and Am (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Cm)) (C (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65932
in-theory        65932
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and ((C and (D -> E)) -> D)) or ((C and (D -> E)) -> D))) or ((B and ((C and (D -> E)) -> D)) or ((C and (D -> E)) -> D))) -> ((C and (D -> E)) -> E))
theorem-size     45
proof            (modus-ponens tm-47 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65932.        (((A and ((B and ((C and (D -> E)) -> D)) or ((C and (D -> E)) -> D))) or ((B and ((C and (D -> E)) -> D)) or ((C and (D -> E)) -> D))) -> ((C and (D -> E)) -> E)), M:tm-47, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65933
in-theory        65933
times-derived    1
----------------------------------------------------------------
theorem          (((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) and E) or ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C))) -> ((B and (C -> D)) -> D))
theorem-size     45
proof            (modus-ponens tm-46 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-8 tm-3 tm-4 tm-2)
proof-size       161
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65933.        (((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) and E) or ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C))) -> ((B and (C -> D)) -> D)), M:tm-46, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65934
in-theory        65934
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-42 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65934.        ((A -> (B or A)) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-42, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65935
in-theory        65935
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-32 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65935.        ((A -> (A or B)) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-32, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65936
in-theory        65936
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) and ((B and (C -> D)) -> D)))
theorem-size     43
proof            (modus-ponens tm-24 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65936.        (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) and ((B and (C -> D)) -> D))), M:tm-24, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65937
in-theory        65937
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     33
proof            (modus-ponens tm-23 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65937.        ((A -> (B -> (A and B))) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-23, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65938
in-theory        65938
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-22 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65938.        (((A and B) -> B) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-22, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65939
in-theory        65939
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-21 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65939.        (((A and B) -> A) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-21, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65940
in-theory        65940
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G)))
theorem-size     39
proof            (modus-ponens tm-20 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       163
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65940.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and ((E and (F -> G)) -> F)) or ((E and (F -> G)) -> F)) -> ((E and (F -> G)) -> G))), M:tm-20, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65941
in-theory        65941
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F)))
theorem-size     31
proof            (modus-ponens tm-19 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65941.        ((A -> (B -> A)) and (((C and ((D and (E -> F)) -> E)) or ((D and (E -> F)) -> E)) -> ((D and (E -> F)) -> F))), M:tm-19, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65942
in-theory        65942
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)))
theorem-size     35
proof            (modus-ponens tm-12 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4)
proof-size       147
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65942.        (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C))), M:tm-12, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65943
in-theory        65943
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (not ((B and (C -> D)) -> D))) -> (not ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C))))
theorem-size     45
proof            (modus-ponens tm-9 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-9 tm-8 tm-4 tm-2)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65943.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (not ((B and (C -> D)) -> D))) -> (not ((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)))), M:tm-9, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65944
in-theory        65944
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> C) -> D) -> ((((E and ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> C)) -> D))
theorem-size     37
proof            (modus-ponens tm-8 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm))))
axioms-used      (tm-8 tm-4 tm-2)
proof-size       137
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65944.        ((((A and (B -> C)) -> C) -> D) -> ((((E and ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> B)) or ((A and (B -> C)) -> C)) -> D)), M:tm-8, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (-> (and Bm (-> Cm Dm)) Dm)))
================================================================
tm-name          tm-65945
in-theory        65945
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and ((C and (D -> E)) -> D)) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E)))
theorem-size     27
proof            (modus-ponens tm-7 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-7 tm-8 tm-4 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65945.        (A or (((B and ((C and (D -> E)) -> D)) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E))), M:tm-7, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65946
in-theory        65946
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) or E)
theorem-size     27
proof            (modus-ponens tm-6 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-6 tm-8 tm-4 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65946.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)) or E), M:tm-6, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65947
in-theory        65947
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and ((C and (D -> E)) -> D)) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E)) and A))
theorem-size     29
proof            (modus-ponens tm-5 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       123
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65947.        (A -> ((((B and ((C and (D -> E)) -> D)) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E)) and A)), M:tm-5, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65948
in-theory        65948
times-derived    1
----------------------------------------------------------------
theorem          ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (B and (C -> D))) -> (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> D))
theorem-size     43
proof            (modus-ponens tm-2 tm-776 ((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (and Bm (-> Cm Dm))) (C Dm)))
axioms-used      (tm-2 tm-8 tm-4)
proof-size       143
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65948.        ((((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> (B and (C -> D))) -> (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> D)), M:tm-2, m:tm-776, u:((A (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm))) (B (and Bm (-> Cm Dm))) (C Dm))
================================================================
tm-name          tm-65949
in-theory        65949
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and ((C and (D -> E)) -> D)) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E)))
theorem-size     27
proof            (modus-ponens tm-1 tm-776 ((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm)))))
axioms-used      (tm-1 tm-8 tm-4 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-776.          (((A and ((B and (C -> D)) -> C)) or ((B and (C -> D)) -> C)) -> ((B and (C -> D)) -> D)), M:tm-47, m:tm-17, u:((A (-> (and Am (-> Bm Cm)) Bm)) (B (-> (and Am (-> Bm Cm)) Cm)))
tm-65949.        (A -> (((B and ((C and (D -> E)) -> D)) or ((C and (D -> E)) -> D)) -> ((C and (D -> E)) -> E))), M:tm-1, m:tm-776, u:((A (-> (or (and Am (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Cm)) (-> (and Bm (-> Cm Dm)) Dm))))
================================================================
tm-name          tm-65950
in-theory        65950
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-757 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65950.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-757, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65951
in-theory        65951
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (((((A and B) or B) and E) or ((A and B) or B)) -> ((C and D) -> D)))
theorem-size     31
proof            (modus-ponens tm-747 tm-777 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65951.        ((((A and B) or B) -> ((C and D) -> D)) and (((((A and B) or B) and E) or ((A and B) or B)) -> ((C and D) -> D))), M:tm-747, m:tm-777, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-65952
in-theory        65952
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> ((G and H) -> H)))
theorem-size     37
proof            (modus-ponens tm-708 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       181
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65952.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> ((G and H) -> H))), M:tm-708, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65953
in-theory        65953
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-665 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65953.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-665, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65954
in-theory        65954
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-622 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65954.        ((A -> (B -> (C or B))) and (((D and E) or E) -> ((F and G) -> G))), M:tm-622, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65955
in-theory        65955
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (E -> (F or E)))
theorem-size     17
proof            (modus-ponens tm-609 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65955.        ((((A and B) or B) -> ((C and D) -> D)) and (E -> (F or E))), M:tm-609, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65956
in-theory        65956
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-605 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65956.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-605, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65957
in-theory        65957
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and ((E -> (F or E)) and (((A and B) or B) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-595 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65957.        ((((A and B) or B) -> ((C and D) -> D)) and ((E -> (F or E)) and (((A and B) or B) -> ((C and D) -> D)))), M:tm-595, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65958
in-theory        65958
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-550 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65958.        (((A -> (B or A)) or C) and (((D and E) or E) -> ((F and G) -> G))), M:tm-550, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65959
in-theory        65959
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-540 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65959.        ((A or (B -> (C or B))) and (((D and E) or E) -> ((F and G) -> G))), M:tm-540, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65960
in-theory        65960
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-530 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65960.        ((A or (B -> (B or C))) and (((D and E) or E) -> ((F and G) -> G))), M:tm-530, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65961
in-theory        65961
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-520 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65961.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F and G) -> G))), M:tm-520, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65962
in-theory        65962
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-510 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65962.        ((A or ((B and C) -> C)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-510, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65963
in-theory        65963
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-500 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65963.        ((A or ((B and C) -> B)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-500, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65964
in-theory        65964
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-490 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65964.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G and H) -> H))), M:tm-490, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65965
in-theory        65965
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-480 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65965.        ((A or (B -> (C -> B))) and (((D and E) or E) -> ((F and G) -> G))), M:tm-480, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65966
in-theory        65966
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-469 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65966.        ((A -> (B -> (B or C))) and (((D and E) or E) -> ((F and G) -> G))), M:tm-469, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65967
in-theory        65967
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (E -> (E or F)))
theorem-size     17
proof            (modus-ponens tm-456 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65967.        ((((A and B) or B) -> ((C and D) -> D)) and (E -> (E or F))), M:tm-456, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65968
in-theory        65968
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-453 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65968.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-453, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65969
in-theory        65969
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and ((E -> (E or F)) and (((A and B) or B) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-443 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65969.        ((((A and B) or B) -> ((C and D) -> D)) and ((E -> (E or F)) and (((A and B) or B) -> ((C and D) -> D)))), M:tm-443, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65970
in-theory        65970
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-409 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65970.        (((A -> (A or B)) or C) and (((D and E) or E) -> ((F and G) -> G))), M:tm-409, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65971
in-theory        65971
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-400 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65971.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> ((F and G) -> G))), M:tm-400, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65972
in-theory        65972
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-391 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65972.        ((((A and B) -> B) or C) and (((D and E) or E) -> ((F and G) -> G))), M:tm-391, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65973
in-theory        65973
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-382 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65973.        ((((A and B) -> A) or C) and (((D and E) or E) -> ((F and G) -> G))), M:tm-382, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65974
in-theory        65974
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-373 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65974.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> ((G and H) -> H))), M:tm-373, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65975
in-theory        65975
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-364 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65975.        (((A -> (B -> A)) or C) and (((D and E) or E) -> ((F and G) -> G))), M:tm-364, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65976
in-theory        65976
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-354 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65976.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F and G) -> G))), M:tm-354, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65977
in-theory        65977
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (E -> (F -> (E and F))))
theorem-size     19
proof            (modus-ponens tm-341 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65977.        ((((A and B) or B) -> ((C and D) -> D)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65978
in-theory        65978
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> ((E and F) -> F)))
theorem-size     21
proof            (modus-ponens tm-338 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65978.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> ((E and F) -> F))), M:tm-338, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65979
in-theory        65979
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (((A and B) or B) -> (((A and B) or B) and ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-328 tm-777 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65979.        ((((A and B) or B) -> ((C and D) -> D)) and (((A and B) or B) -> (((A and B) or B) and ((C and D) -> D)))), M:tm-328, m:tm-777, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-65980
in-theory        65980
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> ((C and D) -> D))))
theorem-size     31
proof            (modus-ponens tm-327 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       155
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65980.        ((((A and B) or B) -> ((C and D) -> D)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> ((C and D) -> D)))), M:tm-327, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65981
in-theory        65981
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (((E and F) -> F) and (((A and B) or B) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-326 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65981.        ((((A and B) or B) -> ((C and D) -> D)) and (((E and F) -> F) and (((A and B) or B) -> ((C and D) -> D)))), M:tm-326, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65982
in-theory        65982
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (((E and F) -> E) and (((A and B) or B) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-325 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65982.        ((((A and B) or B) -> ((C and D) -> D)) and (((E and F) -> E) and (((A and B) or B) -> ((C and D) -> D)))), M:tm-325, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65983
in-theory        65983
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> ((C and D) -> D))))
theorem-size     37
proof            (modus-ponens tm-324 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65983.        ((((A and B) or B) -> ((C and D) -> D)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> ((C and D) -> D)))), M:tm-324, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65984
in-theory        65984
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and ((E -> (F -> E)) and (((A and B) or B) -> ((C and D) -> D))))
theorem-size     29
proof            (modus-ponens tm-323 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       147
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65984.        ((((A and B) or B) -> ((C and D) -> D)) and ((E -> (F -> E)) and (((A and B) or B) -> ((C and D) -> D)))), M:tm-323, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65985
in-theory        65985
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and ((E and F) -> F))
theorem-size     17
proof            (modus-ponens tm-322 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65985.        ((((A and B) or B) -> ((C and D) -> D)) and ((E and F) -> F)), M:tm-322, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65986
in-theory        65986
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and ((E and F) -> E))
theorem-size     17
proof            (modus-ponens tm-320 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65986.        ((((A and B) or B) -> ((C and D) -> D)) and ((E and F) -> E)), M:tm-320, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65987
in-theory        65987
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     25
proof            (modus-ponens tm-318 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65987.        ((((A and B) or B) -> ((C and D) -> D)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65988
in-theory        65988
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     23
proof            (modus-ponens tm-316 tm-777 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65988.        ((((A and B) or B) -> ((C and D) -> D)) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-777, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-65989
in-theory        65989
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (E -> (F -> E)))
theorem-size     17
proof            (modus-ponens tm-315 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       129
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65989.        ((((A and B) or B) -> ((C and D) -> D)) and (E -> (F -> E))), M:tm-315, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65990
in-theory        65990
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and ((((A and B) or B) -> (not ((C and D) -> D))) -> (not ((A and B) or B))))
theorem-size     31
proof            (modus-ponens tm-313 tm-777 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65990.        ((((A and B) or B) -> ((C and D) -> D)) and ((((A and B) or B) -> (not ((C and D) -> D))) -> (not ((A and B) or B)))), M:tm-313, m:tm-777, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-65991
in-theory        65991
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and ((((C and D) -> D) -> E) -> ((((A and B) or B) or ((C and D) -> D)) -> E)))
theorem-size     33
proof            (modus-ponens tm-312 tm-777 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65991.        ((((A and B) or B) -> ((C and D) -> D)) and ((((C and D) -> D) -> E) -> ((((A and B) or B) or ((C and D) -> D)) -> E))), M:tm-312, m:tm-777, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-65992
in-theory        65992
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (E or (((A and B) or B) -> ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-311 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65992.        ((((A and B) or B) -> ((C and D) -> D)) and (E or (((A and B) or B) -> ((C and D) -> D)))), M:tm-311, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65993
in-theory        65993
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and ((((A and B) or B) -> ((C and D) -> D)) or E))
theorem-size     25
proof            (modus-ponens tm-310 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65993.        ((((A and B) or B) -> ((C and D) -> D)) and ((((A and B) or B) -> ((C and D) -> D)) or E)), M:tm-310, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65994
in-theory        65994
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (E -> ((((A and B) or B) -> ((C and D) -> D)) and E)))
theorem-size     27
proof            (modus-ponens tm-309 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65994.        ((((A and B) or B) -> ((C and D) -> D)) and (E -> ((((A and B) or B) -> ((C and D) -> D)) and E))), M:tm-309, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65995
in-theory        65995
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and ((((A and B) or B) -> (C and D)) -> (((A and B) or B) -> D)))
theorem-size     29
proof            (modus-ponens tm-306 tm-777 ((A (or (and Am Bm) Bm)) (B (and Cm Dm)) (C Dm)))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65995.        ((((A and B) or B) -> ((C and D) -> D)) and ((((A and B) or B) -> (C and D)) -> (((A and B) or B) -> D))), M:tm-306, m:tm-777, u:((A (or (and Am Bm) Bm)) (B (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-65996
in-theory        65996
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) and (E -> (((A and B) or B) -> ((C and D) -> D))))
theorem-size     25
proof            (modus-ponens tm-305 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       123
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65996.        ((((A and B) or B) -> ((C and D) -> D)) and (E -> (((A and B) or B) -> ((C and D) -> D)))), M:tm-305, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65997
in-theory        65997
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     23
proof            (modus-ponens tm-303 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65997.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-303, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65998
in-theory        65998
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-270 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65998.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-270, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-65999
in-theory        65999
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-239 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-65999.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-239, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66000
in-theory        66000
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> ((G and H) -> H)))
theorem-size     29
proof            (modus-ponens tm-210 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66000.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> ((G and H) -> H))), M:tm-210, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66001
in-theory        66001
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     21
proof            (modus-ponens tm-183 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66001.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-183, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66002
in-theory        66002
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-157 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66002.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-157, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66003
in-theory        66003
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-147 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66003.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-147, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66004
in-theory        66004
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-134 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66004.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-134, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66005
in-theory        66005
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     27
proof            (modus-ponens tm-125 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 tm-1)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66005.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> ((F and G) -> G))), M:tm-125, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66006
in-theory        66006
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G and H) -> H)))
theorem-size     27
proof            (modus-ponens tm-113 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66006.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G and H) -> H))), M:tm-113, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66007
in-theory        66007
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     31
proof            (modus-ponens tm-105 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66007.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> ((F and G) -> G))), M:tm-105, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66008
in-theory        66008
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-95 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66008.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> ((E and F) -> F))), M:tm-95, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66009
in-theory        66009
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     19
proof            (modus-ponens tm-83 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       111
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66009.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> ((F and G) -> G))), M:tm-83, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66010
in-theory        66010
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> ((D and E) -> E)))
theorem-size     17
proof            (modus-ponens tm-76 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66010.        (((not (not A)) -> A) and (((B and C) or C) -> ((D and E) -> E))), M:tm-76, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66011
in-theory        66011
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> ((C and D) -> D))
theorem-size     19
proof            (modus-ponens tm-73 tm-777 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-10 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66011.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> ((C and D) -> D)), M:tm-73, m:tm-777, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-66012
in-theory        66012
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> ((E and F) -> F)))
theorem-size     23
proof            (modus-ponens tm-69 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66012.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> ((E and F) -> F))), M:tm-69, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66013
in-theory        66013
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-54 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66013.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> ((F and G) -> G))), M:tm-54, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66014
in-theory        66014
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> ((C and D) -> D))
theorem-size     13
proof            (modus-ponens tm-50 tm-777 ((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-7 tm-4 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66014.        ((A or ((B and A) or A)) -> ((C and D) -> D)), M:tm-50, m:tm-777, u:((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-66015
in-theory        66015
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> ((C and D) -> D))
theorem-size     15
proof            (modus-ponens tm-49 tm-777 ((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-6 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66015.        (((A and B) or ((A and B) or B)) -> ((C and D) -> D)), M:tm-49, m:tm-777, u:((A (and Am Bm)) (B Bm) (C (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-66016
in-theory        66016
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-47 tm-777 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66016.        (((A and ((B and C) or C)) or ((B and C) or C)) -> ((D and E) -> E)), M:tm-47, m:tm-777, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-66017
in-theory        66017
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> ((D and E) -> E))
theorem-size     19
proof            (modus-ponens tm-46 tm-777 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-3 tm-4 tm-1)
proof-size       105
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66017.        (((((A and B) or B) and C) or ((A and B) or B)) -> ((D and E) -> E)), M:tm-46, m:tm-777, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-66018
in-theory        66018
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-42 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66018.        ((A -> (B or A)) and (((C and D) or D) -> ((E and F) -> F))), M:tm-42, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66019
in-theory        66019
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-32 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66019.        ((A -> (A or B)) and (((C and D) or D) -> ((E and F) -> F))), M:tm-32, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66020
in-theory        66020
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and ((C and D) -> D)))
theorem-size     17
proof            (modus-ponens tm-24 tm-777 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66020.        (((A and B) or B) -> (((A and B) or B) and ((C and D) -> D))), M:tm-24, m:tm-777, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-66021
in-theory        66021
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> ((E and F) -> F)))
theorem-size     19
proof            (modus-ponens tm-23 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       101
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66021.        ((A -> (B -> (A and B))) and (((C and D) or D) -> ((E and F) -> F))), M:tm-23, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66022
in-theory        66022
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-22 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66022.        (((A and B) -> B) and (((C and D) or D) -> ((E and F) -> F))), M:tm-22, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66023
in-theory        66023
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-21 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66023.        (((A and B) -> A) and (((C and D) or D) -> ((E and F) -> F))), M:tm-21, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66024
in-theory        66024
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> ((F and G) -> G)))
theorem-size     25
proof            (modus-ponens tm-20 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66024.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> ((F and G) -> G))), M:tm-20, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66025
in-theory        66025
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> ((E and F) -> F)))
theorem-size     17
proof            (modus-ponens tm-19 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       95
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66025.        ((A -> (B -> A)) and (((C and D) or D) -> ((E and F) -> F))), M:tm-19, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66026
in-theory        66026
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not ((C and D) -> D))) -> (not ((A and B) or B)))
theorem-size     19
proof            (modus-ponens tm-9 tm-777 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-9 tm-8 tm-4 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66026.        ((((A and B) or B) -> (not ((C and D) -> D))) -> (not ((A and B) or B))), M:tm-9, m:tm-777, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-66027
in-theory        66027
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) -> C) -> ((((D and E) or E) or ((A and B) -> B)) -> C))
theorem-size     21
proof            (modus-ponens tm-8 tm-777 ((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm))))
axioms-used      (tm-8 tm-4 tm-1)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66027.        ((((A and B) -> B) -> C) -> ((((D and E) or E) or ((A and B) -> B)) -> C)), M:tm-8, m:tm-777, u:((A (or (and Am Bm) Bm)) (B (-> (and Cm Dm) Dm)))
================================================================
tm-name          tm-66028
in-theory        66028
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-7 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-7 tm-8 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66028.        (A or (((B and C) or C) -> ((D and E) -> E))), M:tm-7, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66029
in-theory        66029
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C and D) -> D)) or E)
theorem-size     13
proof            (modus-ponens tm-6 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-6 tm-8 tm-4 tm-1)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66029.        ((((A and B) or B) -> ((C and D) -> D)) or E), M:tm-6, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66030
in-theory        66030
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> ((D and E) -> E)) and A))
theorem-size     15
proof            (modus-ponens tm-5 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       79
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66030.        (A -> ((((B and C) or C) -> ((D and E) -> E)) and A)), M:tm-5, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66031
in-theory        66031
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (C and D)) -> (((A and B) or B) -> D))
theorem-size     17
proof            (modus-ponens tm-2 tm-777 ((A (or (and Am Bm) Bm)) (B (and Cm Dm)) (C Dm)))
axioms-used      (tm-2 tm-8 tm-4 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66031.        ((((A and B) or B) -> (C and D)) -> (((A and B) or B) -> D)), M:tm-2, m:tm-777, u:((A (or (and Am Bm) Bm)) (B (and Cm Dm)) (C Dm))
================================================================
tm-name          tm-66032
in-theory        66032
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> ((D and E) -> E)))
theorem-size     13
proof            (modus-ponens tm-1 tm-777 ((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm)))))
axioms-used      (tm-1 tm-8 tm-4)
proof-size       75
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-777.          (((A and B) or B) -> ((C and D) -> D)), M:tm-47, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-66032.        (A -> (((B and C) or C) -> ((D and E) -> E))), M:tm-1, m:tm-777, u:((A (-> (or (and Am Bm) Bm) (-> (and Cm Dm) Dm))))
================================================================
tm-name          tm-66033
in-theory        66033
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     25
proof            (modus-ponens tm-757 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66033.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-757, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66034
in-theory        66034
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((((A and B) or B) and E) or ((A and B) or B)) -> ((C -> (D -> C)) and B)))
theorem-size     35
proof            (modus-ponens tm-747 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4 tm-1)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66034.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((((A and B) or B) and E) or ((A and B) or B)) -> ((C -> (D -> C)) and B))), M:tm-747, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66035
in-theory        66035
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> ((G -> (H -> G)) and F)))
theorem-size     39
proof            (modus-ponens tm-708 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-1)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66035.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> ((G -> (H -> G)) and F))), M:tm-708, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66036
in-theory        66036
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     27
proof            (modus-ponens tm-665 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66036.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-665, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66037
in-theory        66037
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or ((D -> (E -> D)) and B)))
theorem-size     15
proof            (modus-ponens tm-623 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66037.        (((A and B) or B) -> (C or ((D -> (E -> D)) and B))), M:tm-623, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66038
in-theory        66038
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-622 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66038.        ((A -> (B -> (C or B))) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-622, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66039
in-theory        66039
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66039.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (E -> (F or E))), M:tm-609, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66040
in-theory        66040
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     23
proof            (modus-ponens tm-605 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66040.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-605, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66041
in-theory        66041
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((E -> (F or E)) and (((A and B) or B) -> ((C -> (D -> C)) and B))))
theorem-size     33
proof            (modus-ponens tm-595 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66041.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((E -> (F or E)) and (((A and B) or B) -> ((C -> (D -> C)) and B)))), M:tm-595, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66042
in-theory        66042
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-550 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66042.        (((A -> (B or A)) or C) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-550, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66043
in-theory        66043
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-540 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66043.        ((A or (B -> (C or B))) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-540, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66044
in-theory        66044
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-530 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66044.        ((A or (B -> (B or C))) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-530, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66045
in-theory        66045
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     23
proof            (modus-ponens tm-520 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66045.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-520, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66046
in-theory        66046
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-510 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66046.        ((A or ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-510, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66047
in-theory        66047
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-500 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66047.        ((A or ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-500, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66048
in-theory        66048
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H -> G)) and F)))
theorem-size     29
proof            (modus-ponens tm-490 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66048.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H -> G)) and F))), M:tm-490, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66049
in-theory        66049
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-480 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66049.        ((A or (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-480, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66050
in-theory        66050
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> (D -> C)) and B) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66050.        (((A and B) or B) -> (((C -> (D -> C)) and B) or E)), M:tm-470, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66051
in-theory        66051
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-469 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66051.        ((A -> (B -> (B or C))) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-469, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66052
in-theory        66052
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66052.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (E -> (E or F))), M:tm-456, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66053
in-theory        66053
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     23
proof            (modus-ponens tm-453 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66053.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-453, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66054
in-theory        66054
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((E -> (E or F)) and (((A and B) or B) -> ((C -> (D -> C)) and B))))
theorem-size     33
proof            (modus-ponens tm-443 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66054.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((E -> (E or F)) and (((A and B) or B) -> ((C -> (D -> C)) and B)))), M:tm-443, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66055
in-theory        66055
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-409 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66055.        (((A -> (A or B)) or C) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-409, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66056
in-theory        66056
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     23
proof            (modus-ponens tm-400 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66056.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-400, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66057
in-theory        66057
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-391 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66057.        ((((A and B) -> B) or C) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-391, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66058
in-theory        66058
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-382 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-1)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66058.        ((((A and B) -> A) or C) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-382, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66059
in-theory        66059
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> ((G -> (H -> G)) and F)))
theorem-size     29
proof            (modus-ponens tm-373 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66059.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> ((G -> (H -> G)) and F))), M:tm-373, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66060
in-theory        66060
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-364 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66060.        (((A -> (B -> A)) or C) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-364, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66061
in-theory        66061
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (((D -> (E -> D)) and B) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66061.        (((A and B) or B) -> (C -> (((D -> (E -> D)) and B) and C))), M:tm-355, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66062
in-theory        66062
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     23
proof            (modus-ponens tm-354 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66062.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-354, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66063
in-theory        66063
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66063.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66064
in-theory        66064
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> ((E -> (F -> E)) and D)))
theorem-size     23
proof            (modus-ponens tm-338 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66064.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> ((E -> (F -> E)) and D))), M:tm-338, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66065
in-theory        66065
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((A and B) or B) -> (((A and B) or B) and ((C -> (D -> C)) and B))))
theorem-size     33
proof            (modus-ponens tm-328 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66065.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((A and B) or B) -> (((A and B) or B) and ((C -> (D -> C)) and B)))), M:tm-328, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66066
in-theory        66066
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> ((C -> (D -> C)) and B))))
theorem-size     35
proof            (modus-ponens tm-327 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66066.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> ((C -> (D -> C)) and B)))), M:tm-327, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66067
in-theory        66067
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((E and F) -> F) and (((A and B) or B) -> ((C -> (D -> C)) and B))))
theorem-size     33
proof            (modus-ponens tm-326 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66067.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((E and F) -> F) and (((A and B) or B) -> ((C -> (D -> C)) and B)))), M:tm-326, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66068
in-theory        66068
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((E and F) -> E) and (((A and B) or B) -> ((C -> (D -> C)) and B))))
theorem-size     33
proof            (modus-ponens tm-325 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66068.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((E and F) -> E) and (((A and B) or B) -> ((C -> (D -> C)) and B)))), M:tm-325, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66069
in-theory        66069
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> ((C -> (D -> C)) and B))))
theorem-size     41
proof            (modus-ponens tm-324 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66069.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> ((C -> (D -> C)) and B)))), M:tm-324, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66070
in-theory        66070
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((E -> (F -> E)) and (((A and B) or B) -> ((C -> (D -> C)) and B))))
theorem-size     33
proof            (modus-ponens tm-323 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66070.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((E -> (F -> E)) and (((A and B) or B) -> ((C -> (D -> C)) and B)))), M:tm-323, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66071
in-theory        66071
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66071.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((E and F) -> F)), M:tm-322, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66072
in-theory        66072
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66072.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((E and F) -> E)), M:tm-320, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66073
in-theory        66073
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66073.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66074
in-theory        66074
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     25
proof            (modus-ponens tm-316 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66074.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66075
in-theory        66075
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66075.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (E -> (F -> E))), M:tm-315, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66076
in-theory        66076
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((((A and B) or B) -> (not ((C -> (D -> C)) and B))) -> (not ((A and B) or B))))
theorem-size     35
proof            (modus-ponens tm-313 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 tm-1)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66076.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((((A and B) or B) -> (not ((C -> (D -> C)) and B))) -> (not ((A and B) or B)))), M:tm-313, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66077
in-theory        66077
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((((C -> (D -> C)) and B) -> E) -> ((((A and B) or B) or ((C -> (D -> C)) and B)) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66077.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((((C -> (D -> C)) and B) -> E) -> ((((A and B) or B) or ((C -> (D -> C)) and B)) -> E))), M:tm-312, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66078
in-theory        66078
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (E or (((A and B) or B) -> ((C -> (D -> C)) and B))))
theorem-size     29
proof            (modus-ponens tm-311 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66078.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (E or (((A and B) or B) -> ((C -> (D -> C)) and B)))), M:tm-311, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66079
in-theory        66079
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((((A and B) or B) -> ((C -> (D -> C)) and B)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66079.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and ((((A and B) or B) -> ((C -> (D -> C)) and B)) or E)), M:tm-310, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66080
in-theory        66080
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (E -> ((((A and B) or B) -> ((C -> (D -> C)) and B)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66080.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (E -> ((((A and B) or B) -> ((C -> (D -> C)) and B)) and E))), M:tm-309, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66081
in-theory        66081
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (E -> (((A and B) or B) -> ((C -> (D -> C)) and B))))
theorem-size     29
proof            (modus-ponens tm-305 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66081.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) and (E -> (((A and B) or B) -> ((C -> (D -> C)) and B)))), M:tm-305, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66082
in-theory        66082
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     25
proof            (modus-ponens tm-303 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66082.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-303, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66083
in-theory        66083
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     23
proof            (modus-ponens tm-270 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66083.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-270, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66084
in-theory        66084
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     23
proof            (modus-ponens tm-239 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66084.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-239, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66085
in-theory        66085
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> ((G -> (H -> G)) and F)))
theorem-size     31
proof            (modus-ponens tm-210 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66085.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> ((G -> (H -> G)) and F))), M:tm-210, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66086
in-theory        66086
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     23
proof            (modus-ponens tm-183 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66086.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-183, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66087
in-theory        66087
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-157 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66087.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-157, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66088
in-theory        66088
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     29
proof            (modus-ponens tm-147 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66088.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-147, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66089
in-theory        66089
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-134 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66089.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-134, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66090
in-theory        66090
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     29
proof            (modus-ponens tm-125 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4 tm-1)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66090.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-125, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66091
in-theory        66091
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H -> G)) and F)))
theorem-size     29
proof            (modus-ponens tm-113 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66091.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H -> G)) and F))), M:tm-113, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66092
in-theory        66092
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     33
proof            (modus-ponens tm-105 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66092.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-105, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66093
in-theory        66093
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> ((E -> (F -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-95 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66093.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> ((E -> (F -> E)) and D))), M:tm-95, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66094
in-theory        66094
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D -> (E -> D)) and B)))
theorem-size     15
proof            (modus-ponens tm-84 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66094.        (((A and B) or B) -> (C -> ((D -> (E -> D)) and B))), M:tm-84, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66095
in-theory        66095
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     21
proof            (modus-ponens tm-83 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66095.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-83, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66096
in-theory        66096
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> ((D -> (E -> D)) and C)))
theorem-size     19
proof            (modus-ponens tm-76 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66096.        (((not (not A)) -> A) and (((B and C) or C) -> ((D -> (E -> D)) and C))), M:tm-76, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66097
in-theory        66097
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> ((C -> (D -> C)) and B))
theorem-size     21
proof            (modus-ponens tm-73 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-8 tm-10 tm-4 tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66097.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> ((C -> (D -> C)) and B)), M:tm-73, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66098
in-theory        66098
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> ((E -> (F -> E)) and D)))
theorem-size     25
proof            (modus-ponens tm-69 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-1)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66098.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> ((E -> (F -> E)) and D))), M:tm-69, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66099
in-theory        66099
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     27
proof            (modus-ponens tm-54 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66099.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-54, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66100
in-theory        66100
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> ((C -> (D -> C)) and A))
theorem-size     15
proof            (modus-ponens tm-50 tm-778 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-8 tm-7 tm-4 tm-5 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66100.        ((A or ((B and A) or A)) -> ((C -> (D -> C)) and A)), M:tm-50, m:tm-778, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66101
in-theory        66101
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> ((C -> (D -> C)) and B))
theorem-size     17
proof            (modus-ponens tm-49 tm-778 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-8 tm-6 tm-4 tm-5 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66101.        (((A and B) or ((A and B) or B)) -> ((C -> (D -> C)) and B)), M:tm-49, m:tm-778, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66102
in-theory        66102
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> ((D -> (E -> D)) and C))
theorem-size     21
proof            (modus-ponens tm-47 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-8 tm-4 tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66102.        (((A and ((B and C) or C)) or ((B and C) or C)) -> ((D -> (E -> D)) and C)), M:tm-47, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66103
in-theory        66103
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> ((D -> (E -> D)) and B))
theorem-size     21
proof            (modus-ponens tm-46 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-8 tm-3 tm-4 tm-5 tm-1)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66103.        (((((A and B) or B) and C) or ((A and B) or B)) -> ((D -> (E -> D)) and B)), M:tm-46, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66104
in-theory        66104
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-42 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66104.        ((A -> (B or A)) and (((C and D) or D) -> ((E -> (F -> E)) and D))), M:tm-42, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66105
in-theory        66105
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-32 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66105.        ((A -> (A or B)) and (((C and D) or D) -> ((E -> (F -> E)) and D))), M:tm-32, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66106
in-theory        66106
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and ((C -> (D -> C)) and B)))
theorem-size     19
proof            (modus-ponens tm-24 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-1)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66106.        (((A and B) or B) -> (((A and B) or B) and ((C -> (D -> C)) and B))), M:tm-24, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66107
in-theory        66107
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> ((E -> (F -> E)) and D)))
theorem-size     21
proof            (modus-ponens tm-23 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66107.        ((A -> (B -> (A and B))) and (((C and D) or D) -> ((E -> (F -> E)) and D))), M:tm-23, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66108
in-theory        66108
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-22 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66108.        (((A and B) -> B) and (((C and D) or D) -> ((E -> (F -> E)) and D))), M:tm-22, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66109
in-theory        66109
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-21 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-1)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66109.        (((A and B) -> A) and (((C and D) or D) -> ((E -> (F -> E)) and D))), M:tm-21, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66110
in-theory        66110
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> ((F -> (G -> F)) and E)))
theorem-size     27
proof            (modus-ponens tm-20 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-1)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66110.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> ((F -> (G -> F)) and E))), M:tm-20, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66111
in-theory        66111
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> ((E -> (F -> E)) and D)))
theorem-size     19
proof            (modus-ponens tm-19 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66111.        ((A -> (B -> A)) and (((C and D) or D) -> ((E -> (F -> E)) and D))), M:tm-19, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66112
in-theory        66112
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not ((C -> (D -> C)) and B))) -> (not ((A and B) or B)))
theorem-size     21
proof            (modus-ponens tm-9 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-9 tm-8 tm-4 tm-5 tm-1)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66112.        ((((A and B) or B) -> (not ((C -> (D -> C)) and B))) -> (not ((A and B) or B))), M:tm-9, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66113
in-theory        66113
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> A)) and C) -> D) -> ((((E and C) or C) or ((A -> (B -> A)) and C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-778 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm))))
axioms-used      (tm-8 tm-4 tm-5 tm-1)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66113.        ((((A -> (B -> A)) and C) -> D) -> ((((E and C) or C) or ((A -> (B -> A)) and C)) -> D)), M:tm-8, m:tm-778, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm Cm)) Bm)))
================================================================
tm-name          tm-66114
in-theory        66114
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> ((D -> (E -> D)) and C)))
theorem-size     15
proof            (modus-ponens tm-7 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-7 tm-8 tm-4 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66114.        (A or (((B and C) or C) -> ((D -> (E -> D)) and C))), M:tm-7, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66115
in-theory        66115
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> C)) and B)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-6 tm-8 tm-4 tm-5 tm-1)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66115.        ((((A and B) or B) -> ((C -> (D -> C)) and B)) or E), M:tm-6, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66116
in-theory        66116
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> ((D -> (E -> D)) and C)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-1)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66116.        (A -> ((((B and C) or C) -> ((D -> (E -> D)) and C)) and A)), M:tm-5, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66117
in-theory        66117
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> ((D -> (E -> D)) and C)))
theorem-size     15
proof            (modus-ponens tm-1 tm-778 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm)))))
axioms-used      (tm-1 tm-8 tm-4 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-778.          (((A and B) or B) -> ((C -> (D -> C)) and B)), M:tm-47, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-66117.        (A -> (((B and C) or C) -> ((D -> (E -> D)) and C))), M:tm-1, m:tm-778, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm Cm)) Bm))))
================================================================
tm-name          tm-66118
in-theory        66118
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     33
proof            (modus-ponens tm-757 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66118.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-757, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66119
in-theory        66119
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((((A and B) or B) and F) or ((A and B) or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))
theorem-size     51
proof            (modus-ponens tm-747 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       211
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66119.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((((A and B) or B) and F) or ((A and B) or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-747, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66120
in-theory        66120
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))
theorem-size     47
proof            (modus-ponens tm-708 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       221
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66120.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))), M:tm-708, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66121
in-theory        66121
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     35
proof            (modus-ponens tm-665 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       177
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66121.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-665, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66122
in-theory        66122
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B)))
theorem-size     23
proof            (modus-ponens tm-623 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 tm-5)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66122.        (((A and B) or B) -> (C or (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B))), M:tm-623, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66123
in-theory        66123
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-622 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66123.        ((A -> (B -> (C or B))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-622, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66124
in-theory        66124
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (F -> (G or F)))
theorem-size     27
proof            (modus-ponens tm-609 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66124.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (F -> (G or F))), M:tm-609, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66125
in-theory        66125
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     31
proof            (modus-ponens tm-605 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66125.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-605, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66126
in-theory        66126
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((F -> (G or F)) and (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     49
proof            (modus-ponens tm-595 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66126.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((F -> (G or F)) and (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-595, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66127
in-theory        66127
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-550 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66127.        (((A -> (B or A)) or C) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-550, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66128
in-theory        66128
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-540 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66128.        ((A or (B -> (C or B))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-540, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66129
in-theory        66129
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-530 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66129.        ((A or (B -> (B or C))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-530, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66130
in-theory        66130
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     31
proof            (modus-ponens tm-520 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66130.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-520, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66131
in-theory        66131
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-510 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66131.        ((A or ((B and C) -> C)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-510, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66132
in-theory        66132
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-500 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66132.        ((A or ((B and C) -> B)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-500, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66133
in-theory        66133
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))
theorem-size     37
proof            (modus-ponens tm-490 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66133.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))), M:tm-490, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66134
in-theory        66134
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-480 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66134.        ((A or (B -> (C -> B))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-480, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66135
in-theory        66135
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B) or F))
theorem-size     23
proof            (modus-ponens tm-470 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 tm-5)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66135.        (((A and B) or B) -> ((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B) or F)), M:tm-470, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66136
in-theory        66136
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-469 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66136.        ((A -> (B -> (B or C))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-469, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66137
in-theory        66137
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (F -> (F or G)))
theorem-size     27
proof            (modus-ponens tm-456 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66137.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (F -> (F or G))), M:tm-456, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66138
in-theory        66138
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     31
proof            (modus-ponens tm-453 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66138.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-453, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66139
in-theory        66139
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((F -> (F or G)) and (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     49
proof            (modus-ponens tm-443 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66139.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((F -> (F or G)) and (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-443, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66140
in-theory        66140
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-409 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66140.        (((A -> (A or B)) or C) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-409, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66141
in-theory        66141
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     31
proof            (modus-ponens tm-400 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66141.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-400, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66142
in-theory        66142
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-391 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66142.        ((((A and B) -> B) or C) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-391, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66143
in-theory        66143
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-382 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66143.        ((((A and B) -> A) or C) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-382, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66144
in-theory        66144
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))
theorem-size     37
proof            (modus-ponens tm-373 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66144.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))), M:tm-373, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66145
in-theory        66145
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-364 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66145.        (((A -> (B -> A)) or C) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-364, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66146
in-theory        66146
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B) and C)))
theorem-size     25
proof            (modus-ponens tm-355 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66146.        (((A and B) or B) -> (C -> ((((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B) and C))), M:tm-355, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66147
in-theory        66147
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     31
proof            (modus-ponens tm-354 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66147.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-354, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66148
in-theory        66148
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (F -> (G -> (F and G))))
theorem-size     29
proof            (modus-ponens tm-341 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66148.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (F -> (G -> (F and G)))), M:tm-341, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66149
in-theory        66149
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     31
proof            (modus-ponens tm-338 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66149.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-338, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66150
in-theory        66150
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((A and B) or B) -> (((A and B) or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     49
proof            (modus-ponens tm-328 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       207
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66150.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((A and B) or B) -> (((A and B) or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-328, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66151
in-theory        66151
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((F -> (G -> (F and G))) and (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     51
proof            (modus-ponens tm-327 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       205
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66151.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((F -> (G -> (F and G))) and (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-327, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66152
in-theory        66152
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((F and G) -> G) and (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     49
proof            (modus-ponens tm-326 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66152.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((F and G) -> G) and (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-326, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66153
in-theory        66153
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((F and G) -> F) and (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     49
proof            (modus-ponens tm-325 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66153.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((F and G) -> F) and (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-325, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66154
in-theory        66154
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     57
proof            (modus-ponens tm-324 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       229
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66154.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-324, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66155
in-theory        66155
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((F -> (G -> F)) and (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     49
proof            (modus-ponens tm-323 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       197
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66155.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((F -> (G -> F)) and (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-323, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66156
in-theory        66156
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((F and G) -> G))
theorem-size     27
proof            (modus-ponens tm-322 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66156.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((F and G) -> G)), M:tm-322, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66157
in-theory        66157
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((F and G) -> F))
theorem-size     27
proof            (modus-ponens tm-320 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66157.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((F and G) -> F)), M:tm-320, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66158
in-theory        66158
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H))))
theorem-size     35
proof            (modus-ponens tm-318 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       201
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66158.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((F -> (G -> H)) -> ((F -> G) -> (F -> H)))), M:tm-318, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66159
in-theory        66159
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     33
proof            (modus-ponens tm-316 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66159.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66160
in-theory        66160
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (F -> (G -> F)))
theorem-size     27
proof            (modus-ponens tm-315 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66160.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (F -> (G -> F))), M:tm-315, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66161
in-theory        66161
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((((A and B) or B) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) -> (not ((A and B) or B))))
theorem-size     51
proof            (modus-ponens tm-313 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       193
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66161.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((((A and B) or B) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) -> (not ((A and B) or B)))), M:tm-313, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66162
in-theory        66162
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B) -> F) -> ((((A and B) or B) or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) -> F)))
theorem-size     63
proof            (modus-ponens tm-312 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       209
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66162.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (((((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B) -> F) -> ((((A and B) or B) or (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) -> F))), M:tm-312, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66163
in-theory        66163
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (F or (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     45
proof            (modus-ponens tm-311 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66163.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (F or (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-311, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66164
in-theory        66164
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) or F))
theorem-size     45
proof            (modus-ponens tm-310 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66164.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) or F)), M:tm-310, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66165
in-theory        66165
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (F -> ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and F)))
theorem-size     47
proof            (modus-ponens tm-309 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66165.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (F -> ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and F))), M:tm-309, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66166
in-theory        66166
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (F -> (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))))
theorem-size     45
proof            (modus-ponens tm-305 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66166.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and (F -> (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))), M:tm-305, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66167
in-theory        66167
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     33
proof            (modus-ponens tm-303 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66167.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-303, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66168
in-theory        66168
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     31
proof            (modus-ponens tm-270 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66168.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-270, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66169
in-theory        66169
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     31
proof            (modus-ponens tm-239 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66169.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-239, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66170
in-theory        66170
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))
theorem-size     39
proof            (modus-ponens tm-210 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       191
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66170.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))), M:tm-210, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66171
in-theory        66171
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     31
proof            (modus-ponens tm-183 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66171.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-183, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66172
in-theory        66172
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-157 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66172.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-157, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66173
in-theory        66173
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     37
proof            (modus-ponens tm-147 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66173.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-147, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66174
in-theory        66174
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-134 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66174.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-134, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66175
in-theory        66175
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     37
proof            (modus-ponens tm-125 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66175.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-125, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66176
in-theory        66176
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F)))
theorem-size     37
proof            (modus-ponens tm-113 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66176.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (((G -> (H -> I)) -> ((G -> H) -> (G -> I))) and F))), M:tm-113, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66177
in-theory        66177
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     41
proof            (modus-ponens tm-105 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       203
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66177.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-105, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66178
in-theory        66178
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     29
proof            (modus-ponens tm-95 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66178.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-95, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66179
in-theory        66179
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B)))
theorem-size     23
proof            (modus-ponens tm-84 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-5)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66179.        (((A and B) or B) -> (C -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B))), M:tm-84, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66180
in-theory        66180
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     29
proof            (modus-ponens tm-83 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66180.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-83, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66181
in-theory        66181
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     27
proof            (modus-ponens tm-76 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66181.        (((not (not A)) -> A) and (((B and C) or C) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-76, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66182
in-theory        66182
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))
theorem-size     29
proof            (modus-ponens tm-73 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-8 tm-10 tm-4 tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66182.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-73, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66183
in-theory        66183
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     33
proof            (modus-ponens tm-69 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-2)
proof-size       153
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66183.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-69, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66184
in-theory        66184
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     35
proof            (modus-ponens tm-54 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66184.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-54, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66185
in-theory        66185
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A))
theorem-size     23
proof            (modus-ponens tm-50 tm-779 ((A (and Am Bm)) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-8 tm-7 tm-4 tm-5 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66185.        ((A or ((B and A) or A)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and A)), M:tm-50, m:tm-779, u:((A (and Am Bm)) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66186
in-theory        66186
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))
theorem-size     25
proof            (modus-ponens tm-49 tm-779 ((A (and Am Bm)) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-8 tm-6 tm-4 tm-5 tm-2)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66186.        (((A and B) or ((A and B) or B)) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-49, m:tm-779, u:((A (and Am Bm)) (B Bm) (C (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66187
in-theory        66187
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))
theorem-size     29
proof            (modus-ponens tm-47 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66187.        (((A and ((B and C) or C)) or ((B and C) or C)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)), M:tm-47, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66188
in-theory        66188
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B))
theorem-size     29
proof            (modus-ponens tm-46 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-8 tm-3 tm-4 tm-5 tm-2)
proof-size       145
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66188.        (((((A and B) or B) and C) or ((A and B) or B)) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and B)), M:tm-46, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66189
in-theory        66189
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-42 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66189.        ((A -> (B or A)) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-42, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66190
in-theory        66190
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-32 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66190.        ((A -> (A or B)) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-32, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66191
in-theory        66191
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)))
theorem-size     27
proof            (modus-ponens tm-24 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       143
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66191.        (((A and B) or B) -> (((A and B) or B) and (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))), M:tm-24, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66192
in-theory        66192
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     29
proof            (modus-ponens tm-23 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       141
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66192.        ((A -> (B -> (A and B))) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-23, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66193
in-theory        66193
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-22 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66193.        (((A and B) -> B) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-22, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66194
in-theory        66194
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-21 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66194.        (((A and B) -> A) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-21, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66195
in-theory        66195
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E)))
theorem-size     35
proof            (modus-ponens tm-20 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       159
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66195.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (((F -> (G -> H)) -> ((F -> G) -> (F -> H))) and E))), M:tm-20, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66196
in-theory        66196
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D)))
theorem-size     27
proof            (modus-ponens tm-19 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66196.        ((A -> (B -> A)) and (((C and D) or D) -> (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and D))), M:tm-19, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66197
in-theory        66197
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) -> (not ((A and B) or B)))
theorem-size     29
proof            (modus-ponens tm-9 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-9 tm-8 tm-4 tm-5 tm-2)
proof-size       127
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66197.        ((((A and B) or B) -> (not (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B))) -> (not ((A and B) or B))), M:tm-9, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66198
in-theory        66198
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((((F and D) or D) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E))
theorem-size     41
proof            (modus-ponens tm-8 tm-779 ((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
axioms-used      (tm-8 tm-4 tm-5 tm-2)
proof-size       141
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66198.        (((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D) -> E) -> ((((F and D) or D) or (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and D)) -> E)), M:tm-8, m:tm-779, u:((A (or (and Am Bm) Bm)) (B (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))
================================================================
tm-name          tm-66199
in-theory        66199
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-7 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-7 tm-8 tm-4 tm-5 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66199.        (A or (((B and C) or C) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-7, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66200
in-theory        66200
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) or F)
theorem-size     23
proof            (modus-ponens tm-6 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-6 tm-8 tm-4 tm-5 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66200.        ((((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) or F), M:tm-6, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66201
in-theory        66201
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and A))
theorem-size     25
proof            (modus-ponens tm-5 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       119
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66201.        (A -> ((((B and C) or C) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)) and A)), M:tm-5, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66202
in-theory        66202
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C)))
theorem-size     23
proof            (modus-ponens tm-1 tm-779 ((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm)))))
axioms-used      (tm-1 tm-8 tm-4 tm-5 tm-2)
proof-size       115
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-779.          (((A and B) or B) -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)), M:tm-47, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-66202.        (A -> (((B and C) or C) -> (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and C))), M:tm-1, m:tm-779, u:((A (-> (or (and Am Bm) Bm) (and (-> (-> Cm (-> Dm Em)) (-> (-> Cm Dm) (-> Cm Em))) Bm))))
================================================================
tm-name          tm-66203
in-theory        66203
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     25
proof            (modus-ponens tm-757 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66203.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-757, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66204
in-theory        66204
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (((((A and B) or B) and E) or ((A and B) or B)) -> (((C and D) -> C) and B)))
theorem-size     35
proof            (modus-ponens tm-747 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66204.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (((((A and B) or B) and E) or ((A and B) or B)) -> (((C and D) -> C) and B))), M:tm-747, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66205
in-theory        66205
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (((G and H) -> G) and F)))
theorem-size     39
proof            (modus-ponens tm-708 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4 tm-3)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66205.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (((G and H) -> G) and F))), M:tm-708, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66206
in-theory        66206
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     27
proof            (modus-ponens tm-665 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-3)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66206.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-665, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66207
in-theory        66207
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (((D and E) -> D) and B)))
theorem-size     15
proof            (modus-ponens tm-623 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 tm-5 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66207.        (((A and B) or B) -> (C or (((D and E) -> D) and B))), M:tm-623, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66208
in-theory        66208
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-622 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66208.        ((A -> (B -> (C or B))) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-622, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66209
in-theory        66209
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66209.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (E -> (F or E))), M:tm-609, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66210
in-theory        66210
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     23
proof            (modus-ponens tm-605 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66210.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-605, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66211
in-theory        66211
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and ((E -> (F or E)) and (((A and B) or B) -> (((C and D) -> C) and B))))
theorem-size     33
proof            (modus-ponens tm-595 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66211.        ((((A and B) or B) -> (((C and D) -> C) and B)) and ((E -> (F or E)) and (((A and B) or B) -> (((C and D) -> C) and B)))), M:tm-595, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66212
in-theory        66212
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-550 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66212.        (((A -> (B or A)) or C) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-550, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66213
in-theory        66213
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-540 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66213.        ((A or (B -> (C or B))) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-540, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66214
in-theory        66214
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-530 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66214.        ((A or (B -> (B or C))) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-530, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66215
in-theory        66215
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     23
proof            (modus-ponens tm-520 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66215.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-520, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66216
in-theory        66216
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-510 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66216.        ((A or ((B and C) -> C)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-510, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66217
in-theory        66217
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-500 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66217.        ((A or ((B and C) -> B)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-500, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66218
in-theory        66218
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (((G and H) -> G) and F)))
theorem-size     29
proof            (modus-ponens tm-490 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66218.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (((G and H) -> G) and F))), M:tm-490, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66219
in-theory        66219
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-480 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66219.        ((A or (B -> (C -> B))) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-480, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66220
in-theory        66220
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C and D) -> C) and B) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 tm-5 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66220.        (((A and B) or B) -> ((((C and D) -> C) and B) or E)), M:tm-470, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66221
in-theory        66221
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-469 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66221.        ((A -> (B -> (B or C))) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-469, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66222
in-theory        66222
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66222.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (E -> (E or F))), M:tm-456, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66223
in-theory        66223
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     23
proof            (modus-ponens tm-453 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66223.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-453, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66224
in-theory        66224
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and ((E -> (E or F)) and (((A and B) or B) -> (((C and D) -> C) and B))))
theorem-size     33
proof            (modus-ponens tm-443 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66224.        ((((A and B) or B) -> (((C and D) -> C) and B)) and ((E -> (E or F)) and (((A and B) or B) -> (((C and D) -> C) and B)))), M:tm-443, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66225
in-theory        66225
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-409 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66225.        (((A -> (A or B)) or C) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-409, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66226
in-theory        66226
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     23
proof            (modus-ponens tm-400 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66226.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-400, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66227
in-theory        66227
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-391 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66227.        ((((A and B) -> B) or C) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-391, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66228
in-theory        66228
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-382 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66228.        ((((A and B) -> A) or C) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-382, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66229
in-theory        66229
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (((G and H) -> G) and F)))
theorem-size     29
proof            (modus-ponens tm-373 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66229.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (((G and H) -> G) and F))), M:tm-373, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66230
in-theory        66230
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-364 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66230.        (((A -> (B -> A)) or C) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-364, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66231
in-theory        66231
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((((D and E) -> D) and B) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4 tm-3)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66231.        (((A and B) or B) -> (C -> ((((D and E) -> D) and B) and C))), M:tm-355, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66232
in-theory        66232
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     23
proof            (modus-ponens tm-354 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66232.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-354, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66233
in-theory        66233
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66233.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66234
in-theory        66234
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (((E and F) -> E) and D)))
theorem-size     23
proof            (modus-ponens tm-338 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66234.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (((E and F) -> E) and D))), M:tm-338, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66235
in-theory        66235
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (((A and B) or B) -> (((A and B) or B) and (((C and D) -> C) and B))))
theorem-size     33
proof            (modus-ponens tm-328 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66235.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (((A and B) or B) -> (((A and B) or B) and (((C and D) -> C) and B)))), M:tm-328, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66236
in-theory        66236
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> (((C and D) -> C) and B))))
theorem-size     35
proof            (modus-ponens tm-327 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66236.        ((((A and B) or B) -> (((C and D) -> C) and B)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> (((C and D) -> C) and B)))), M:tm-327, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66237
in-theory        66237
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (((E and F) -> F) and (((A and B) or B) -> (((C and D) -> C) and B))))
theorem-size     33
proof            (modus-ponens tm-326 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66237.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (((E and F) -> F) and (((A and B) or B) -> (((C and D) -> C) and B)))), M:tm-326, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66238
in-theory        66238
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (((E and F) -> E) and (((A and B) or B) -> (((C and D) -> C) and B))))
theorem-size     33
proof            (modus-ponens tm-325 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66238.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (((E and F) -> E) and (((A and B) or B) -> (((C and D) -> C) and B)))), M:tm-325, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66239
in-theory        66239
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> (((C and D) -> C) and B))))
theorem-size     41
proof            (modus-ponens tm-324 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66239.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> (((C and D) -> C) and B)))), M:tm-324, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66240
in-theory        66240
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and ((E -> (F -> E)) and (((A and B) or B) -> (((C and D) -> C) and B))))
theorem-size     33
proof            (modus-ponens tm-323 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66240.        ((((A and B) or B) -> (((C and D) -> C) and B)) and ((E -> (F -> E)) and (((A and B) or B) -> (((C and D) -> C) and B)))), M:tm-323, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66241
in-theory        66241
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66241.        ((((A and B) or B) -> (((C and D) -> C) and B)) and ((E and F) -> F)), M:tm-322, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66242
in-theory        66242
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66242.        ((((A and B) or B) -> (((C and D) -> C) and B)) and ((E and F) -> E)), M:tm-320, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66243
in-theory        66243
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66243.        ((((A and B) or B) -> (((C and D) -> C) and B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66244
in-theory        66244
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     25
proof            (modus-ponens tm-316 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66244.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66245
in-theory        66245
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66245.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (E -> (F -> E))), M:tm-315, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66246
in-theory        66246
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and ((((A and B) or B) -> (not (((C and D) -> C) and B))) -> (not ((A and B) or B))))
theorem-size     35
proof            (modus-ponens tm-313 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4 tm-3)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66246.        ((((A and B) or B) -> (((C and D) -> C) and B)) and ((((A and B) or B) -> (not (((C and D) -> C) and B))) -> (not ((A and B) or B)))), M:tm-313, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66247
in-theory        66247
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (((((C and D) -> C) and B) -> E) -> ((((A and B) or B) or (((C and D) -> C) and B)) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66247.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (((((C and D) -> C) and B) -> E) -> ((((A and B) or B) or (((C and D) -> C) and B)) -> E))), M:tm-312, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66248
in-theory        66248
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (E or (((A and B) or B) -> (((C and D) -> C) and B))))
theorem-size     29
proof            (modus-ponens tm-311 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66248.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (E or (((A and B) or B) -> (((C and D) -> C) and B)))), M:tm-311, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66249
in-theory        66249
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and ((((A and B) or B) -> (((C and D) -> C) and B)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66249.        ((((A and B) or B) -> (((C and D) -> C) and B)) and ((((A and B) or B) -> (((C and D) -> C) and B)) or E)), M:tm-310, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66250
in-theory        66250
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (E -> ((((A and B) or B) -> (((C and D) -> C) and B)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66250.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (E -> ((((A and B) or B) -> (((C and D) -> C) and B)) and E))), M:tm-309, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66251
in-theory        66251
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) and (E -> (((A and B) or B) -> (((C and D) -> C) and B))))
theorem-size     29
proof            (modus-ponens tm-305 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66251.        ((((A and B) or B) -> (((C and D) -> C) and B)) and (E -> (((A and B) or B) -> (((C and D) -> C) and B)))), M:tm-305, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66252
in-theory        66252
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     25
proof            (modus-ponens tm-303 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-3)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66252.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-303, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66253
in-theory        66253
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     23
proof            (modus-ponens tm-270 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66253.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-270, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66254
in-theory        66254
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     23
proof            (modus-ponens tm-239 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66254.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-239, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66255
in-theory        66255
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (((G and H) -> G) and F)))
theorem-size     31
proof            (modus-ponens tm-210 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-3)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66255.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (((G and H) -> G) and F))), M:tm-210, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66256
in-theory        66256
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     23
proof            (modus-ponens tm-183 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66256.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-183, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66257
in-theory        66257
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-157 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66257.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-157, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66258
in-theory        66258
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     29
proof            (modus-ponens tm-147 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66258.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-147, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66259
in-theory        66259
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-134 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66259.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-134, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66260
in-theory        66260
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     29
proof            (modus-ponens tm-125 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66260.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-125, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66261
in-theory        66261
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (((G and H) -> G) and F)))
theorem-size     29
proof            (modus-ponens tm-113 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4 tm-3)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66261.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (((G and H) -> G) and F))), M:tm-113, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66262
in-theory        66262
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     33
proof            (modus-ponens tm-105 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-3)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66262.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-105, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66263
in-theory        66263
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> (((E and F) -> E) and D)))
theorem-size     21
proof            (modus-ponens tm-95 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4 tm-3)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66263.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> (((E and F) -> E) and D))), M:tm-95, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66264
in-theory        66264
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (((D and E) -> D) and B)))
theorem-size     15
proof            (modus-ponens tm-84 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-5 tm-3)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66264.        (((A and B) or B) -> (C -> (((D and E) -> D) and B))), M:tm-84, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66265
in-theory        66265
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     21
proof            (modus-ponens tm-83 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66265.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-83, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66266
in-theory        66266
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> (((D and E) -> D) and C)))
theorem-size     19
proof            (modus-ponens tm-76 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66266.        (((not (not A)) -> A) and (((B and C) or C) -> (((D and E) -> D) and C))), M:tm-76, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66267
in-theory        66267
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> (((C and D) -> C) and B))
theorem-size     21
proof            (modus-ponens tm-73 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-8 tm-10 tm-4 tm-5 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66267.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> (((C and D) -> C) and B)), M:tm-73, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66268
in-theory        66268
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (((E and F) -> E) and D)))
theorem-size     25
proof            (modus-ponens tm-69 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-3)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66268.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (((E and F) -> E) and D))), M:tm-69, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66269
in-theory        66269
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     27
proof            (modus-ponens tm-54 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66269.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-54, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66270
in-theory        66270
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> (((C and D) -> C) and A))
theorem-size     15
proof            (modus-ponens tm-50 tm-780 ((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-8 tm-7 tm-4 tm-5 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66270.        ((A or ((B and A) or A)) -> (((C and D) -> C) and A)), M:tm-50, m:tm-780, u:((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66271
in-theory        66271
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> (((C and D) -> C) and B))
theorem-size     17
proof            (modus-ponens tm-49 tm-780 ((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-8 tm-6 tm-4 tm-5 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66271.        (((A and B) or ((A and B) or B)) -> (((C and D) -> C) and B)), M:tm-49, m:tm-780, u:((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66272
in-theory        66272
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> (((D and E) -> D) and C))
theorem-size     21
proof            (modus-ponens tm-47 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-8 tm-4 tm-5 tm-3)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66272.        (((A and ((B and C) or C)) or ((B and C) or C)) -> (((D and E) -> D) and C)), M:tm-47, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66273
in-theory        66273
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> (((D and E) -> D) and B))
theorem-size     21
proof            (modus-ponens tm-46 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-8 tm-3 tm-4 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66273.        (((((A and B) or B) and C) or ((A and B) or B)) -> (((D and E) -> D) and B)), M:tm-46, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66274
in-theory        66274
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-42 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66274.        ((A -> (B or A)) and (((C and D) or D) -> (((E and F) -> E) and D))), M:tm-42, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66275
in-theory        66275
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-32 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66275.        ((A -> (A or B)) and (((C and D) or D) -> (((E and F) -> E) and D))), M:tm-32, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66276
in-theory        66276
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and (((C and D) -> C) and B)))
theorem-size     19
proof            (modus-ponens tm-24 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4 tm-3)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66276.        (((A and B) or B) -> (((A and B) or B) and (((C and D) -> C) and B))), M:tm-24, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66277
in-theory        66277
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> (((E and F) -> E) and D)))
theorem-size     21
proof            (modus-ponens tm-23 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-3)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66277.        ((A -> (B -> (A and B))) and (((C and D) or D) -> (((E and F) -> E) and D))), M:tm-23, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66278
in-theory        66278
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-22 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-4 tm-8 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66278.        (((A and B) -> B) and (((C and D) or D) -> (((E and F) -> E) and D))), M:tm-22, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66279
in-theory        66279
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-21 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66279.        (((A and B) -> A) and (((C and D) or D) -> (((E and F) -> E) and D))), M:tm-21, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66280
in-theory        66280
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (((F and G) -> F) and E)))
theorem-size     27
proof            (modus-ponens tm-20 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4 tm-3)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66280.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (((F and G) -> F) and E))), M:tm-20, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66281
in-theory        66281
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> (((E and F) -> E) and D)))
theorem-size     19
proof            (modus-ponens tm-19 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-3)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66281.        ((A -> (B -> A)) and (((C and D) or D) -> (((E and F) -> E) and D))), M:tm-19, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66282
in-theory        66282
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not (((C and D) -> C) and B))) -> (not ((A and B) or B)))
theorem-size     21
proof            (modus-ponens tm-9 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-9 tm-8 tm-4 tm-5 tm-3)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66282.        ((((A and B) or B) -> (not (((C and D) -> C) and B))) -> (not ((A and B) or B))), M:tm-9, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66283
in-theory        66283
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> A) and C) -> D) -> ((((E and C) or C) or (((A and B) -> A) and C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-780 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm))))
axioms-used      (tm-8 tm-4 tm-5 tm-3)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66283.        (((((A and B) -> A) and C) -> D) -> ((((E and C) or C) or (((A and B) -> A) and C)) -> D)), M:tm-8, m:tm-780, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Cm) Bm)))
================================================================
tm-name          tm-66284
in-theory        66284
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> (((D and E) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-7 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-7 tm-8 tm-4 tm-5 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66284.        (A or (((B and C) or C) -> (((D and E) -> D) and C))), M:tm-7, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66285
in-theory        66285
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> C) and B)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-6 tm-8 tm-4 tm-5 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66285.        ((((A and B) or B) -> (((C and D) -> C) and B)) or E), M:tm-6, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66286
in-theory        66286
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> (((D and E) -> D) and C)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4 tm-3)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66286.        (A -> ((((B and C) or C) -> (((D and E) -> D) and C)) and A)), M:tm-5, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66287
in-theory        66287
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> (((D and E) -> D) and C)))
theorem-size     15
proof            (modus-ponens tm-1 tm-780 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm)))))
axioms-used      (tm-1 tm-8 tm-4 tm-5 tm-3)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-780.          (((A and B) or B) -> (((C and D) -> C) and B)), M:tm-47, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-66287.        (A -> (((B and C) or C) -> (((D and E) -> D) and C))), M:tm-1, m:tm-780, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Cm) Bm))))
================================================================
tm-name          tm-66288
in-theory        66288
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     25
proof            (modus-ponens tm-757 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66288.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-757, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66289
in-theory        66289
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (((((A and B) or B) and E) or ((A and B) or B)) -> (((C and D) -> D) and B)))
theorem-size     35
proof            (modus-ponens tm-747 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66289.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (((((A and B) or B) and E) or ((A and B) or B)) -> (((C and D) -> D) and B))), M:tm-747, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66290
in-theory        66290
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (((G and H) -> H) and F)))
theorem-size     39
proof            (modus-ponens tm-708 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       189
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66290.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> (((G and H) -> H) and F))), M:tm-708, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66291
in-theory        66291
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     27
proof            (modus-ponens tm-665 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       145
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66291.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-665, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66292
in-theory        66292
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or (((D and E) -> E) and B)))
theorem-size     15
proof            (modus-ponens tm-623 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66292.        (((A and B) or B) -> (C or (((D and E) -> E) and B))), M:tm-623, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66293
in-theory        66293
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-622 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66293.        ((A -> (B -> (C or B))) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-622, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66294
in-theory        66294
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (E -> (F or E)))
theorem-size     19
proof            (modus-ponens tm-609 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66294.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (E -> (F or E))), M:tm-609, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66295
in-theory        66295
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     23
proof            (modus-ponens tm-605 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66295.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-605, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66296
in-theory        66296
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and ((E -> (F or E)) and (((A and B) or B) -> (((C and D) -> D) and B))))
theorem-size     33
proof            (modus-ponens tm-595 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66296.        ((((A and B) or B) -> (((C and D) -> D) and B)) and ((E -> (F or E)) and (((A and B) or B) -> (((C and D) -> D) and B)))), M:tm-595, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66297
in-theory        66297
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-550 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66297.        (((A -> (B or A)) or C) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-550, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66298
in-theory        66298
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-540 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66298.        ((A or (B -> (C or B))) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-540, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66299
in-theory        66299
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-530 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66299.        ((A or (B -> (B or C))) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-530, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66300
in-theory        66300
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     23
proof            (modus-ponens tm-520 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66300.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-520, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66301
in-theory        66301
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-510 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66301.        ((A or ((B and C) -> C)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-510, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66302
in-theory        66302
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-500 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66302.        ((A or ((B and C) -> B)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-500, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66303
in-theory        66303
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (((G and H) -> H) and F)))
theorem-size     29
proof            (modus-ponens tm-490 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66303.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (((G and H) -> H) and F))), M:tm-490, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66304
in-theory        66304
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-480 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66304.        ((A or (B -> (C -> B))) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-480, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66305
in-theory        66305
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> ((((C and D) -> D) and B) or E))
theorem-size     15
proof            (modus-ponens tm-470 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66305.        (((A and B) or B) -> ((((C and D) -> D) and B) or E)), M:tm-470, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66306
in-theory        66306
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-469 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66306.        ((A -> (B -> (B or C))) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-469, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66307
in-theory        66307
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (E -> (E or F)))
theorem-size     19
proof            (modus-ponens tm-456 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66307.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (E -> (E or F))), M:tm-456, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66308
in-theory        66308
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     23
proof            (modus-ponens tm-453 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66308.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-453, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66309
in-theory        66309
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and ((E -> (E or F)) and (((A and B) or B) -> (((C and D) -> D) and B))))
theorem-size     33
proof            (modus-ponens tm-443 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66309.        ((((A and B) or B) -> (((C and D) -> D) and B)) and ((E -> (E or F)) and (((A and B) or B) -> (((C and D) -> D) and B)))), M:tm-443, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66310
in-theory        66310
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-409 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66310.        (((A -> (A or B)) or C) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-409, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66311
in-theory        66311
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     23
proof            (modus-ponens tm-400 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66311.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-400, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66312
in-theory        66312
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-391 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66312.        ((((A and B) -> B) or C) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-391, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66313
in-theory        66313
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-382 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66313.        ((((A and B) -> A) or C) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-382, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66314
in-theory        66314
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (((G and H) -> H) and F)))
theorem-size     29
proof            (modus-ponens tm-373 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66314.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> (((G and H) -> H) and F))), M:tm-373, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66315
in-theory        66315
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-364 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66315.        (((A -> (B -> A)) or C) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-364, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66316
in-theory        66316
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((((D and E) -> E) and B) and C)))
theorem-size     17
proof            (modus-ponens tm-355 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66316.        (((A and B) or B) -> (C -> ((((D and E) -> E) and B) and C))), M:tm-355, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66317
in-theory        66317
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     23
proof            (modus-ponens tm-354 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66317.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-354, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66318
in-theory        66318
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (E -> (F -> (E and F))))
theorem-size     21
proof            (modus-ponens tm-341 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66318.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66319
in-theory        66319
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (((E and F) -> F) and D)))
theorem-size     23
proof            (modus-ponens tm-338 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66319.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> (((E and F) -> F) and D))), M:tm-338, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66320
in-theory        66320
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (((A and B) or B) -> (((A and B) or B) and (((C and D) -> D) and B))))
theorem-size     33
proof            (modus-ponens tm-328 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66320.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (((A and B) or B) -> (((A and B) or B) and (((C and D) -> D) and B)))), M:tm-328, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66321
in-theory        66321
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> (((C and D) -> D) and B))))
theorem-size     35
proof            (modus-ponens tm-327 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       165
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66321.        ((((A and B) or B) -> (((C and D) -> D) and B)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> (((C and D) -> D) and B)))), M:tm-327, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66322
in-theory        66322
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (((E and F) -> F) and (((A and B) or B) -> (((C and D) -> D) and B))))
theorem-size     33
proof            (modus-ponens tm-326 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66322.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (((E and F) -> F) and (((A and B) or B) -> (((C and D) -> D) and B)))), M:tm-326, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66323
in-theory        66323
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (((E and F) -> E) and (((A and B) or B) -> (((C and D) -> D) and B))))
theorem-size     33
proof            (modus-ponens tm-325 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66323.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (((E and F) -> E) and (((A and B) or B) -> (((C and D) -> D) and B)))), M:tm-325, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66324
in-theory        66324
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> (((C and D) -> D) and B))))
theorem-size     41
proof            (modus-ponens tm-324 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66324.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> (((C and D) -> D) and B)))), M:tm-324, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66325
in-theory        66325
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and ((E -> (F -> E)) and (((A and B) or B) -> (((C and D) -> D) and B))))
theorem-size     33
proof            (modus-ponens tm-323 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66325.        ((((A and B) or B) -> (((C and D) -> D) and B)) and ((E -> (F -> E)) and (((A and B) or B) -> (((C and D) -> D) and B)))), M:tm-323, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66326
in-theory        66326
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and ((E and F) -> F))
theorem-size     19
proof            (modus-ponens tm-322 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66326.        ((((A and B) or B) -> (((C and D) -> D) and B)) and ((E and F) -> F)), M:tm-322, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66327
in-theory        66327
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and ((E and F) -> E))
theorem-size     19
proof            (modus-ponens tm-320 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66327.        ((((A and B) or B) -> (((C and D) -> D) and B)) and ((E and F) -> E)), M:tm-320, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66328
in-theory        66328
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     27
proof            (modus-ponens tm-318 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       169
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66328.        ((((A and B) or B) -> (((C and D) -> D) and B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66329
in-theory        66329
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     25
proof            (modus-ponens tm-316 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66329.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66330
in-theory        66330
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (E -> (F -> E)))
theorem-size     19
proof            (modus-ponens tm-315 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       137
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66330.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (E -> (F -> E))), M:tm-315, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66331
in-theory        66331
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and ((((A and B) or B) -> (not (((C and D) -> D) and B))) -> (not ((A and B) or B))))
theorem-size     35
proof            (modus-ponens tm-313 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66331.        ((((A and B) or B) -> (((C and D) -> D) and B)) and ((((A and B) or B) -> (not (((C and D) -> D) and B))) -> (not ((A and B) or B)))), M:tm-313, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66332
in-theory        66332
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (((((C and D) -> D) and B) -> E) -> ((((A and B) or B) or (((C and D) -> D) and B)) -> E)))
theorem-size     39
proof            (modus-ponens tm-312 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       161
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66332.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (((((C and D) -> D) and B) -> E) -> ((((A and B) or B) or (((C and D) -> D) and B)) -> E))), M:tm-312, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66333
in-theory        66333
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (E or (((A and B) or B) -> (((C and D) -> D) and B))))
theorem-size     29
proof            (modus-ponens tm-311 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66333.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (E or (((A and B) or B) -> (((C and D) -> D) and B)))), M:tm-311, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66334
in-theory        66334
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and ((((A and B) or B) -> (((C and D) -> D) and B)) or E))
theorem-size     29
proof            (modus-ponens tm-310 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66334.        ((((A and B) or B) -> (((C and D) -> D) and B)) and ((((A and B) or B) -> (((C and D) -> D) and B)) or E)), M:tm-310, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66335
in-theory        66335
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (E -> ((((A and B) or B) -> (((C and D) -> D) and B)) and E)))
theorem-size     31
proof            (modus-ponens tm-309 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66335.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (E -> ((((A and B) or B) -> (((C and D) -> D) and B)) and E))), M:tm-309, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66336
in-theory        66336
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) and (E -> (((A and B) or B) -> (((C and D) -> D) and B))))
theorem-size     29
proof            (modus-ponens tm-305 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66336.        ((((A and B) or B) -> (((C and D) -> D) and B)) and (E -> (((A and B) or B) -> (((C and D) -> D) and B)))), M:tm-305, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66337
in-theory        66337
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     25
proof            (modus-ponens tm-303 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66337.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-303, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66338
in-theory        66338
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     23
proof            (modus-ponens tm-270 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66338.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-270, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66339
in-theory        66339
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     23
proof            (modus-ponens tm-239 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66339.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-239, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66340
in-theory        66340
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (((G and H) -> H) and F)))
theorem-size     31
proof            (modus-ponens tm-210 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66340.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> (((G and H) -> H) and F))), M:tm-210, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66341
in-theory        66341
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     23
proof            (modus-ponens tm-183 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66341.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-183, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66342
in-theory        66342
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-157 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66342.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-157, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66343
in-theory        66343
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     29
proof            (modus-ponens tm-147 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66343.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-147, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66344
in-theory        66344
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-134 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66344.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-134, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66345
in-theory        66345
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     29
proof            (modus-ponens tm-125 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66345.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-125, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66346
in-theory        66346
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (((G and H) -> H) and F)))
theorem-size     29
proof            (modus-ponens tm-113 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66346.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> (((G and H) -> H) and F))), M:tm-113, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66347
in-theory        66347
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     33
proof            (modus-ponens tm-105 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66347.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-105, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66348
in-theory        66348
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> (((E and F) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-95 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66348.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> (((E and F) -> F) and D))), M:tm-95, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66349
in-theory        66349
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (((D and E) -> E) and B)))
theorem-size     15
proof            (modus-ponens tm-84 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-5)
proof-size       117
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66349.        (((A and B) or B) -> (C -> (((D and E) -> E) and B))), M:tm-84, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66350
in-theory        66350
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     21
proof            (modus-ponens tm-83 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       119
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66350.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-83, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66351
in-theory        66351
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> (((D and E) -> E) and C)))
theorem-size     19
proof            (modus-ponens tm-76 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66351.        (((not (not A)) -> A) and (((B and C) or C) -> (((D and E) -> E) and C))), M:tm-76, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66352
in-theory        66352
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> (((C and D) -> D) and B))
theorem-size     21
proof            (modus-ponens tm-73 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-8 tm-10 tm-4 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66352.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> (((C and D) -> D) and B)), M:tm-73, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66353
in-theory        66353
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (((E and F) -> F) and D)))
theorem-size     25
proof            (modus-ponens tm-69 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66353.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> (((E and F) -> F) and D))), M:tm-69, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66354
in-theory        66354
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     27
proof            (modus-ponens tm-54 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66354.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-54, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66355
in-theory        66355
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> (((C and D) -> D) and A))
theorem-size     15
proof            (modus-ponens tm-50 tm-781 ((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-8 tm-7 tm-4 tm-5)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66355.        ((A or ((B and A) or A)) -> (((C and D) -> D) and A)), M:tm-50, m:tm-781, u:((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66356
in-theory        66356
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> (((C and D) -> D) and B))
theorem-size     17
proof            (modus-ponens tm-49 tm-781 ((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-8 tm-6 tm-4 tm-5)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66356.        (((A and B) or ((A and B) or B)) -> (((C and D) -> D) and B)), M:tm-49, m:tm-781, u:((A (and Am Bm)) (B Bm) (C (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66357
in-theory        66357
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> (((D and E) -> E) and C))
theorem-size     21
proof            (modus-ponens tm-47 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66357.        (((A and ((B and C) or C)) or ((B and C) or C)) -> (((D and E) -> E) and C)), M:tm-47, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66358
in-theory        66358
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> (((D and E) -> E) and B))
theorem-size     21
proof            (modus-ponens tm-46 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-8 tm-3 tm-4 tm-5)
proof-size       113
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66358.        (((((A and B) or B) and C) or ((A and B) or B)) -> (((D and E) -> E) and B)), M:tm-46, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66359
in-theory        66359
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-42 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66359.        ((A -> (B or A)) and (((C and D) or D) -> (((E and F) -> F) and D))), M:tm-42, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66360
in-theory        66360
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-32 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66360.        ((A -> (A or B)) and (((C and D) or D) -> (((E and F) -> F) and D))), M:tm-32, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66361
in-theory        66361
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and (((C and D) -> D) and B)))
theorem-size     19
proof            (modus-ponens tm-24 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66361.        (((A and B) or B) -> (((A and B) or B) and (((C and D) -> D) and B))), M:tm-24, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66362
in-theory        66362
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> (((E and F) -> F) and D)))
theorem-size     21
proof            (modus-ponens tm-23 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       109
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66362.        ((A -> (B -> (A and B))) and (((C and D) or D) -> (((E and F) -> F) and D))), M:tm-23, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66363
in-theory        66363
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-22 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66363.        (((A and B) -> B) and (((C and D) or D) -> (((E and F) -> F) and D))), M:tm-22, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66364
in-theory        66364
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-21 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66364.        (((A and B) -> A) and (((C and D) or D) -> (((E and F) -> F) and D))), M:tm-21, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66365
in-theory        66365
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (((F and G) -> G) and E)))
theorem-size     27
proof            (modus-ponens tm-20 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       127
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66365.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> (((F and G) -> G) and E))), M:tm-20, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66366
in-theory        66366
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> (((E and F) -> F) and D)))
theorem-size     19
proof            (modus-ponens tm-19 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       103
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66366.        ((A -> (B -> A)) and (((C and D) or D) -> (((E and F) -> F) and D))), M:tm-19, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66367
in-theory        66367
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not (((C and D) -> D) and B))) -> (not ((A and B) or B)))
theorem-size     21
proof            (modus-ponens tm-9 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-9 tm-8 tm-4 tm-5)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66367.        ((((A and B) or B) -> (not (((C and D) -> D) and B))) -> (not ((A and B) or B))), M:tm-9, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66368
in-theory        66368
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) -> B) and C) -> D) -> ((((E and C) or C) or (((A and B) -> B) and C)) -> D))
theorem-size     25
proof            (modus-ponens tm-8 tm-781 ((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       101
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66368.        (((((A and B) -> B) and C) -> D) -> ((((E and C) or C) or (((A and B) -> B) and C)) -> D)), M:tm-8, m:tm-781, u:((A (or (and Am Bm) Bm)) (B (and (-> (and Cm Dm) Dm) Bm)))
================================================================
tm-name          tm-66369
in-theory        66369
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> (((D and E) -> E) and C)))
theorem-size     15
proof            (modus-ponens tm-7 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-7 tm-8 tm-4 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66369.        (A or (((B and C) or C) -> (((D and E) -> E) and C))), M:tm-7, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66370
in-theory        66370
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (((C and D) -> D) and B)) or E)
theorem-size     15
proof            (modus-ponens tm-6 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-6 tm-8 tm-4 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66370.        ((((A and B) or B) -> (((C and D) -> D) and B)) or E), M:tm-6, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66371
in-theory        66371
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> (((D and E) -> E) and C)) and A))
theorem-size     17
proof            (modus-ponens tm-5 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       87
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66371.        (A -> ((((B and C) or C) -> (((D and E) -> E) and C)) and A)), M:tm-5, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66372
in-theory        66372
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> (((D and E) -> E) and C)))
theorem-size     15
proof            (modus-ponens tm-1 tm-781 ((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm)))))
axioms-used      (tm-1 tm-8 tm-4 tm-5)
proof-size       83
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-781.          (((A and B) or B) -> (((C and D) -> D) and B)), M:tm-47, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-66372.        (A -> (((B and C) or C) -> (((D and E) -> E) and C))), M:tm-1, m:tm-781, u:((A (-> (or (and Am Bm) Bm) (and (-> (and Cm Dm) Dm) Bm))))
================================================================
tm-name          tm-66373
in-theory        66373
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     27
proof            (modus-ponens tm-757 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-3 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66373.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-757, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66374
in-theory        66374
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((((A and B) or B) and E) or ((A and B) or B)) -> ((C -> (D -> (C and D))) and B)))
theorem-size     39
proof            (modus-ponens tm-747 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66374.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((((A and B) or B) and E) or ((A and B) or B)) -> ((C -> (D -> (C and D))) and B))), M:tm-747, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66375
in-theory        66375
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F)))
theorem-size     41
proof            (modus-ponens tm-708 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       197
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66375.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F))), M:tm-708, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66376
in-theory        66376
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     29
proof            (modus-ponens tm-665 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-1 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66376.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-665, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66377
in-theory        66377
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C or ((D -> (E -> (D and E))) and B)))
theorem-size     17
proof            (modus-ponens tm-623 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66377.        (((A and B) or B) -> (C or ((D -> (E -> (D and E))) and B))), M:tm-623, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66378
in-theory        66378
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-622 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66378.        ((A -> (B -> (C or B))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-622, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66379
in-theory        66379
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (E -> (F or E)))
theorem-size     21
proof            (modus-ponens tm-609 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66379.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (E -> (F or E))), M:tm-609, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66380
in-theory        66380
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     25
proof            (modus-ponens tm-605 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66380.        ((A -> ((B -> (C or B)) and A)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-605, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66381
in-theory        66381
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((E -> (F or E)) and (((A and B) or B) -> ((C -> (D -> (C and D))) and B))))
theorem-size     37
proof            (modus-ponens tm-595 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66381.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((E -> (F or E)) and (((A and B) or B) -> ((C -> (D -> (C and D))) and B)))), M:tm-595, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66382
in-theory        66382
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-550 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66382.        (((A -> (B or A)) or C) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-550, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66383
in-theory        66383
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-540 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66383.        ((A or (B -> (C or B))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-540, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66384
in-theory        66384
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-530 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66384.        ((A or (B -> (B or C))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-530, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66385
in-theory        66385
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     25
proof            (modus-ponens tm-520 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66385.        ((A or (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-520, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66386
in-theory        66386
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-510 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-4 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66386.        ((A or ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-510, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66387
in-theory        66387
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-500 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66387.        ((A or ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-500, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66388
in-theory        66388
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F)))
theorem-size     31
proof            (modus-ponens tm-490 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66388.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F))), M:tm-490, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66389
in-theory        66389
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-480 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66389.        ((A or (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-480, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66390
in-theory        66390
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((C -> (D -> (C and D))) and B) or E))
theorem-size     17
proof            (modus-ponens tm-470 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66390.        (((A and B) or B) -> (((C -> (D -> (C and D))) and B) or E)), M:tm-470, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66391
in-theory        66391
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-469 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66391.        ((A -> (B -> (B or C))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-469, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66392
in-theory        66392
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (E -> (E or F)))
theorem-size     21
proof            (modus-ponens tm-456 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66392.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (E -> (E or F))), M:tm-456, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66393
in-theory        66393
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     25
proof            (modus-ponens tm-453 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66393.        ((A -> ((B -> (B or C)) and A)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-453, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66394
in-theory        66394
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((E -> (E or F)) and (((A and B) or B) -> ((C -> (D -> (C and D))) and B))))
theorem-size     37
proof            (modus-ponens tm-443 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66394.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((E -> (E or F)) and (((A and B) or B) -> ((C -> (D -> (C and D))) and B)))), M:tm-443, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66395
in-theory        66395
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-409 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66395.        (((A -> (A or B)) or C) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-409, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66396
in-theory        66396
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     25
proof            (modus-ponens tm-400 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66396.        (((A -> (B -> (A and B))) or C) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-400, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66397
in-theory        66397
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-391 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-4 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66397.        ((((A and B) -> B) or C) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-391, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66398
in-theory        66398
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-382 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66398.        ((((A and B) -> A) or C) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-382, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66399
in-theory        66399
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F)))
theorem-size     31
proof            (modus-ponens tm-373 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66399.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F))), M:tm-373, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66400
in-theory        66400
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-364 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66400.        (((A -> (B -> A)) or C) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-364, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66401
in-theory        66401
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> (((D -> (E -> (D and E))) and B) and C)))
theorem-size     19
proof            (modus-ponens tm-355 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       133
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66401.        (((A and B) or B) -> (C -> (((D -> (E -> (D and E))) and B) and C))), M:tm-355, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66402
in-theory        66402
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     25
proof            (modus-ponens tm-354 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66402.        ((A -> (B -> (C -> (B and C)))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-354, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66403
in-theory        66403
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (E -> (F -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-341 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       153
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66403.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (E -> (F -> (E and F)))), M:tm-341, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66404
in-theory        66404
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D)))
theorem-size     25
proof            (modus-ponens tm-338 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66404.        (((A -> B) -> (A -> (A and B))) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D))), M:tm-338, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66405
in-theory        66405
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((A and B) or B) -> (((A and B) or B) and ((C -> (D -> (C and D))) and B))))
theorem-size     37
proof            (modus-ponens tm-328 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66405.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((A and B) or B) -> (((A and B) or B) and ((C -> (D -> (C and D))) and B)))), M:tm-328, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66406
in-theory        66406
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> ((C -> (D -> (C and D))) and B))))
theorem-size     39
proof            (modus-ponens tm-327 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       175
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66406.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((E -> (F -> (E and F))) and (((A and B) or B) -> ((C -> (D -> (C and D))) and B)))), M:tm-327, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66407
in-theory        66407
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((E and F) -> F) and (((A and B) or B) -> ((C -> (D -> (C and D))) and B))))
theorem-size     37
proof            (modus-ponens tm-326 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66407.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((E and F) -> F) and (((A and B) or B) -> ((C -> (D -> (C and D))) and B)))), M:tm-326, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66408
in-theory        66408
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((E and F) -> E) and (((A and B) or B) -> ((C -> (D -> (C and D))) and B))))
theorem-size     37
proof            (modus-ponens tm-325 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66408.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((E and F) -> E) and (((A and B) or B) -> ((C -> (D -> (C and D))) and B)))), M:tm-325, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66409
in-theory        66409
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> ((C -> (D -> (C and D))) and B))))
theorem-size     45
proof            (modus-ponens tm-324 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       199
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66409.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((E -> (F -> G)) -> ((E -> F) -> (E -> G))) and (((A and B) or B) -> ((C -> (D -> (C and D))) and B)))), M:tm-324, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66410
in-theory        66410
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((E -> (F -> E)) and (((A and B) or B) -> ((C -> (D -> (C and D))) and B))))
theorem-size     37
proof            (modus-ponens tm-323 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       167
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66410.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((E -> (F -> E)) and (((A and B) or B) -> ((C -> (D -> (C and D))) and B)))), M:tm-323, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66411
in-theory        66411
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((E and F) -> F))
theorem-size     21
proof            (modus-ponens tm-322 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66411.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((E and F) -> F)), M:tm-322, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66412
in-theory        66412
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((E and F) -> E))
theorem-size     21
proof            (modus-ponens tm-320 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66412.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((E and F) -> E)), M:tm-320, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66413
in-theory        66413
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G))))
theorem-size     29
proof            (modus-ponens tm-318 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       177
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66413.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((E -> (F -> G)) -> ((E -> F) -> (E -> G)))), M:tm-318, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66414
in-theory        66414
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((A and B) or B) -> ((A and B) or B)))
theorem-size     27
proof            (modus-ponens tm-316 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       161
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66414.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (((A and B) or B) -> ((A and B) or B))), M:tm-316, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66415
in-theory        66415
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (E -> (F -> E)))
theorem-size     21
proof            (modus-ponens tm-315 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       145
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66415.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (E -> (F -> E))), M:tm-315, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66416
in-theory        66416
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((((A and B) or B) -> (not ((C -> (D -> (C and D))) and B))) -> (not ((A and B) or B))))
theorem-size     39
proof            (modus-ponens tm-313 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66416.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((((A and B) or B) -> (not ((C -> (D -> (C and D))) and B))) -> (not ((A and B) or B)))), M:tm-313, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66417
in-theory        66417
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((((C -> (D -> (C and D))) and B) -> E) -> ((((A and B) or B) or ((C -> (D -> (C and D))) and B)) -> E)))
theorem-size     45
proof            (modus-ponens tm-312 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66417.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((((C -> (D -> (C and D))) and B) -> E) -> ((((A and B) or B) or ((C -> (D -> (C and D))) and B)) -> E))), M:tm-312, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66418
in-theory        66418
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (E or (((A and B) or B) -> ((C -> (D -> (C and D))) and B))))
theorem-size     33
proof            (modus-ponens tm-311 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66418.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (E or (((A and B) or B) -> ((C -> (D -> (C and D))) and B)))), M:tm-311, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66419
in-theory        66419
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) or E))
theorem-size     33
proof            (modus-ponens tm-310 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66419.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) or E)), M:tm-310, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66420
in-theory        66420
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (E -> ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and E)))
theorem-size     35
proof            (modus-ponens tm-309 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       149
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66420.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (E -> ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and E))), M:tm-309, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66421
in-theory        66421
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (E -> (((A and B) or B) -> ((C -> (D -> (C and D))) and B))))
theorem-size     33
proof            (modus-ponens tm-305 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66421.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) and (E -> (((A and B) or B) -> ((C -> (D -> (C and D))) and B)))), M:tm-305, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66422
in-theory        66422
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     27
proof            (modus-ponens tm-303 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       143
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66422.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-303, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66423
in-theory        66423
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     25
proof            (modus-ponens tm-270 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66423.        ((A -> (((B and C) -> C) and A)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-270, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66424
in-theory        66424
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     25
proof            (modus-ponens tm-239 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66424.        ((A -> (((B and C) -> B) and A)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-239, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66425
in-theory        66425
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F)))
theorem-size     33
proof            (modus-ponens tm-210 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       167
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66425.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F))), M:tm-210, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66426
in-theory        66426
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     25
proof            (modus-ponens tm-183 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66426.        ((A -> ((B -> (C -> B)) and A)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-183, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66427
in-theory        66427
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-157 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-4 tm-8)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66427.        ((A -> ((B and C) -> C)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-157, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66428
in-theory        66428
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     31
proof            (modus-ponens tm-147 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66428.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-147, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66429
in-theory        66429
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-134 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66429.        ((A -> ((B and C) -> B)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-134, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66430
in-theory        66430
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     31
proof            (modus-ponens tm-125 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66430.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-125, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66431
in-theory        66431
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F)))
theorem-size     31
proof            (modus-ponens tm-113 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       159
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66431.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and F) or F) -> ((G -> (H -> (G and H))) and F))), M:tm-113, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66432
in-theory        66432
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     35
proof            (modus-ponens tm-105 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       179
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66432.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-105, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66433
in-theory        66433
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-95 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       135
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66433.        (((A -> B) -> (A -> A)) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D))), M:tm-95, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66434
in-theory        66434
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (C -> ((D -> (E -> (D and E))) and B)))
theorem-size     17
proof            (modus-ponens tm-84 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-5)
proof-size       125
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66434.        (((A and B) or B) -> (C -> ((D -> (E -> (D and E))) and B))), M:tm-84, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66435
in-theory        66435
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     23
proof            (modus-ponens tm-83 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       127
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66435.        ((A -> (B -> (C -> B))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-83, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66436
in-theory        66436
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and C) or C) -> ((D -> (E -> (D and E))) and C)))
theorem-size     21
proof            (modus-ponens tm-76 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-10 tm-8 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66436.        (((not (not A)) -> A) and (((B and C) or C) -> ((D -> (E -> (D and E))) and C))), M:tm-76, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66437
in-theory        66437
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and B) or B))) or ((A and B) or B)) -> ((C -> (D -> (C and D))) and B))
theorem-size     23
proof            (modus-ponens tm-73 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-8 tm-10 tm-4 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66437.        (((not (not ((A and B) or B))) or ((A and B) or B)) -> ((C -> (D -> (C and D))) and B)), M:tm-73, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66438
in-theory        66438
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D)))
theorem-size     27
proof            (modus-ponens tm-69 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-9 tm-8 tm-4)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66438.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D))), M:tm-69, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66439
in-theory        66439
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     29
proof            (modus-ponens tm-54 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66439.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-54, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66440
in-theory        66440
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and A) or A)) -> ((C -> (D -> (C and D))) and A))
theorem-size     17
proof            (modus-ponens tm-50 tm-782 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-8 tm-7 tm-4 tm-5)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66440.        ((A or ((B and A) or A)) -> ((C -> (D -> (C and D))) and A)), M:tm-50, m:tm-782, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66441
in-theory        66441
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or ((A and B) or B)) -> ((C -> (D -> (C and D))) and B))
theorem-size     19
proof            (modus-ponens tm-49 tm-782 ((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-8 tm-6 tm-4 tm-5)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66441.        (((A and B) or ((A and B) or B)) -> ((C -> (D -> (C and D))) and B)), M:tm-49, m:tm-782, u:((A (and Am Bm)) (B Bm) (C (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66442
in-theory        66442
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and C) or C)) or ((B and C) or C)) -> ((D -> (E -> (D and E))) and C))
theorem-size     23
proof            (modus-ponens tm-47 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66442.        (((A and ((B and C) or C)) or ((B and C) or C)) -> ((D -> (E -> (D and E))) and C)), M:tm-47, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66443
in-theory        66443
times-derived    1
----------------------------------------------------------------
theorem          (((((A and B) or B) and C) or ((A and B) or B)) -> ((D -> (E -> (D and E))) and B))
theorem-size     23
proof            (modus-ponens tm-46 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-8 tm-3 tm-4 tm-5)
proof-size       121
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66443.        (((((A and B) or B) and C) or ((A and B) or B)) -> ((D -> (E -> (D and E))) and B)), M:tm-46, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66444
in-theory        66444
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-42 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-7 tm-8 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66444.        ((A -> (B or A)) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D))), M:tm-42, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66445
in-theory        66445
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (A or B)) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-32 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-6 tm-8 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66445.        ((A -> (A or B)) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D))), M:tm-32, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66446
in-theory        66446
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) or B) -> (((A and B) or B) and ((C -> (D -> (C and D))) and B)))
theorem-size     21
proof            (modus-ponens tm-24 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       119
proof-steps      11
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66446.        (((A and B) or B) -> (((A and B) or B) and ((C -> (D -> (C and D))) and B))), M:tm-24, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66447
in-theory        66447
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (A and B))) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D)))
theorem-size     23
proof            (modus-ponens tm-23 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       117
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66447.        ((A -> (B -> (A and B))) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D))), M:tm-23, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66448
in-theory        66448
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> B) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-22 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-4 tm-8)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66448.        (((A and B) -> B) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D))), M:tm-22, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66449
in-theory        66449
times-derived    1
----------------------------------------------------------------
theorem          (((A and B) -> A) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-21 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-3 tm-8 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66449.        (((A and B) -> A) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D))), M:tm-21, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66450
in-theory        66450
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E)))
theorem-size     29
proof            (modus-ponens tm-20 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       135
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66450.        (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) and (((D and E) or E) -> ((F -> (G -> (F and G))) and E))), M:tm-20, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66451
in-theory        66451
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> A)) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D)))
theorem-size     21
proof            (modus-ponens tm-19 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-1 tm-8 tm-4)
proof-size       111
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66451.        ((A -> (B -> A)) and (((C and D) or D) -> ((E -> (F -> (E and F))) and D))), M:tm-19, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66452
in-theory        66452
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> (not ((C -> (D -> (C and D))) and B))) -> (not ((A and B) or B)))
theorem-size     23
proof            (modus-ponens tm-9 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-9 tm-8 tm-4 tm-5)
proof-size       103
proof-steps      9
----------------------------------------------------------------
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66452.        ((((A and B) or B) -> (not ((C -> (D -> (C and D))) and B))) -> (not ((A and B) or B))), M:tm-9, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66453
in-theory        66453
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> (A and B))) and C) -> D) -> ((((E and C) or C) or ((A -> (B -> (A and B))) and C)) -> D))
theorem-size     29
proof            (modus-ponens tm-8 tm-782 ((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
axioms-used      (tm-8 tm-4 tm-5)
proof-size       111
proof-steps      9
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66453.        ((((A -> (B -> (A and B))) and C) -> D) -> ((((E and C) or C) or ((A -> (B -> (A and B))) and C)) -> D)), M:tm-8, m:tm-782, u:((A (or (and Am Bm) Bm)) (B (and (-> Cm (-> Dm (and Cm Dm))) Bm)))
================================================================
tm-name          tm-66454
in-theory        66454
times-derived    1
----------------------------------------------------------------
theorem          (A or (((B and C) or C) -> ((D -> (E -> (D and E))) and C)))
theorem-size     17
proof            (modus-ponens tm-7 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-7 tm-8 tm-4 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-7.            (A -> (B or A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66454.        (A or (((B and C) or C) -> ((D -> (E -> (D and E))) and C))), M:tm-7, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66455
in-theory        66455
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) or E)
theorem-size     17
proof            (modus-ponens tm-6 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-6 tm-8 tm-4 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-6.            (A -> (A or B)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66455.        ((((A and B) or B) -> ((C -> (D -> (C and D))) and B)) or E), M:tm-6, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66456
in-theory        66456
times-derived    1
----------------------------------------------------------------
theorem          (A -> ((((B and C) or C) -> ((D -> (E -> (D and E))) and C)) and A))
theorem-size     19
proof            (modus-ponens tm-5 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-5 tm-8 tm-4)
proof-size       95
proof-steps      9
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66456.        (A -> ((((B and C) or C) -> ((D -> (E -> (D and E))) and C)) and A)), M:tm-5, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66457
in-theory        66457
times-derived    1
----------------------------------------------------------------
theorem          (A -> (((B and C) or C) -> ((D -> (E -> (D and E))) and C)))
theorem-size     17
proof            (modus-ponens tm-1 tm-782 ((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm)))))
axioms-used      (tm-1 tm-8 tm-4 tm-5)
proof-size       91
proof-steps      9
----------------------------------------------------------------
tm-1.            (A -> (B -> A)), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-782.          (((A and B) or B) -> ((C -> (D -> (C and D))) and B)), M:tm-47, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-66457.        (A -> (((B and C) or C) -> ((D -> (E -> (D and E))) and C))), M:tm-1, m:tm-782, u:((A (-> (or (and Am Bm) Bm) (and (-> Cm (-> Dm (and Cm Dm))) Bm))))
================================================================
tm-name          tm-66458
in-theory        66458
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-757 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-3 tm-4 tm-2)
proof-size       151
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-757.          (A -> (((B -> C) -> (((B and D) or B) -> C)) and A)), M:tm-5, m:tm-46, u:((A (-> (-> Am Bm) (-> (or (and Am Cm) Am) Bm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66458.        (((A -> B) -> (((A and C) or A) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-757, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66459
in-theory        66459
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> (B -> (B and C))))
theorem-size     43
proof            (modus-ponens tm-747 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-3 tm-4)
proof-size       189
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-747.          ((A -> B) -> ((A -> B) and (((A and C) or A) -> B))), M:tm-24, m:tm-46, u:((A (-> Am Bm)) (B (-> (or (and Am Cm) Am) Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66459.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> (B -> (B and C)))), M:tm-747, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66460
in-theory        66460
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G))))
theorem-size     41
proof            (modus-ponens tm-708 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-2 tm-4)
proof-size       201
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-45.           ((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)), M:tm-8, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-708.          (A -> (((((B -> C) -> (B -> D)) -> E) -> (((B -> (C -> D)) or ((B -> C) -> (B -> D))) -> E)) and A)), M:tm-5, m:tm-45, u:((A (-> (-> (-> (-> Am Bm) (-> Am Cm)) Dm) (-> (or (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66460.        (((((A -> B) -> (A -> C)) -> D) -> (((A -> (B -> C)) or ((A -> B) -> (A -> C))) -> D)) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G)))), M:tm-708, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66461
in-theory        66461
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-665 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-1 tm-4 tm-2)
proof-size       157
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-44.           (((A -> B) -> C) -> ((B or (A -> B)) -> C)), M:tm-8, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-665.          (A -> ((((B -> C) -> D) -> ((C or (B -> C)) -> D)) and A)), M:tm-5, m:tm-44, u:((A (-> (-> (-> Am Bm) Cm) (-> (or Bm (-> Am Bm)) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66461.        ((((A -> B) -> C) -> ((B or (A -> B)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-665, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66462
in-theory        66462
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D or (B -> (B and C))))
theorem-size     17
proof            (modus-ponens tm-623 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-7 tm-8 tm-4 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-623.          ((A -> B) -> (A -> (C or B))), M:tm-2, m:tm-43, u:((A Am) (B Bm) (C (or Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66462.        (((A and (B -> C)) or (B -> C)) -> (D or (B -> (B and C)))), M:tm-623, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66463
in-theory        66463
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-622 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-7 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-622.          (A -> ((B -> (C -> (D or C))) and A)), M:tm-5, m:tm-43, u:((A (-> Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66463.        ((A -> (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-622, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66464
in-theory        66464
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (D -> (E or D)))
theorem-size     21
proof            (modus-ponens tm-609 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-7 tm-8 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-7.            (A -> (B or A)), axiom
tm-43.           (A -> (B -> (C or B))), M:tm-1, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-609.          (A -> (A and (B -> (C or B)))), M:tm-24, m:tm-43, u:((A Am) (B (-> Bm (or Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66464.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (D -> (E or D))), M:tm-609, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66465
in-theory        66465
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-605 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-605.          (A -> ((B -> ((C -> (D or C)) and B)) and A)), M:tm-5, m:tm-42, u:((A (-> Am (and (-> Bm (or Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66465.        ((A -> ((B -> (C or B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-605, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66466
in-theory        66466
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((D -> (E or D)) and (((A and (B -> C)) or (B -> C)) -> (B -> (B and C)))))
theorem-size     37
proof            (modus-ponens tm-595 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-595.          (A -> (A and ((B -> (C or B)) and A))), M:tm-24, m:tm-42, u:((A Am) (B (and (-> Bm (or Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66466.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((D -> (E or D)) and (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))))), M:tm-595, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66467
in-theory        66467
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B or A)) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-550 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-7 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-7.            (A -> (B or A)), axiom
tm-41.           ((A -> (B or A)) or C), M:tm-6, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-550.          (A -> (((B -> (C or B)) or D) and A)), M:tm-5, m:tm-41, u:((A (or (-> Am (or Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66467.        (((A -> (B or A)) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-550, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66468
in-theory        66468
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-540 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-40.           (A or (B -> (C or B))), M:tm-7, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-540.          (A -> ((B or (C -> (D or C))) and A)), M:tm-5, m:tm-40, u:((A (or Am (-> Bm (or Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66468.        ((A or (B -> (C or B))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-540, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66469
in-theory        66469
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-530 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-6 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-39.           (A or (B -> (B or C))), M:tm-7, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-530.          (A -> ((B or (C -> (C or D))) and A)), M:tm-5, m:tm-39, u:((A (or Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66469.        ((A or (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-530, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66470
in-theory        66470
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-520 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-38.           (A or (B -> (C -> (B and C)))), M:tm-7, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-520.          (A -> ((B or (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-38, u:((A (or Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66470.        ((A or (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-520, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66471
in-theory        66471
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-510 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-4 tm-8 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-37.           (A or ((B and C) -> C)), M:tm-7, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-510.          (A -> ((B or ((C and D) -> D)) and A)), M:tm-5, m:tm-37, u:((A (or Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66471.        ((A or ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-510, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66472
in-theory        66472
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-500 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-3 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-36.           (A or ((B and C) -> B)), M:tm-7, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-500.          (A -> ((B or ((C and D) -> C)) and A)), M:tm-5, m:tm-36, u:((A (or Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66472.        ((A or ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-500, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66473
in-theory        66473
times-derived    1
----------------------------------------------------------------
theorem          ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-490 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-2 tm-8 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-35.           (A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-7, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-490.          (A -> ((B or ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-35, u:((A (or Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66473.        ((A or ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G)))), M:tm-490, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66474
in-theory        66474
times-derived    1
----------------------------------------------------------------
theorem          ((A or (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-480 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-1 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-34.           (A or (B -> (C -> B))), M:tm-7, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-480.          (A -> ((B or (C -> (D -> C))) and A)), M:tm-5, m:tm-34, u:((A (or Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66474.        ((A or (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-480, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66475
in-theory        66475
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> ((B -> (B and C)) or D))
theorem-size     17
proof            (modus-ponens tm-470 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-6 tm-8 tm-4 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-470.          ((A -> B) -> (A -> (B or C))), M:tm-2, m:tm-33, u:((A Am) (B Bm) (C (or Bm Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66475.        (((A and (B -> C)) or (B -> C)) -> ((B -> (B and C)) or D)), M:tm-470, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66476
in-theory        66476
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-469 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-6 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-469.          (A -> ((B -> (C -> (C or D))) and A)), M:tm-5, m:tm-33, u:((A (-> Am (-> Bm (or Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66476.        ((A -> (B -> (B or C))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-469, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66477
in-theory        66477
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (D -> (D or E)))
theorem-size     21
proof            (modus-ponens tm-456 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-6 tm-8 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-6.            (A -> (A or B)), axiom
tm-33.           (A -> (B -> (B or C))), M:tm-1, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-456.          (A -> (A and (B -> (B or C)))), M:tm-24, m:tm-33, u:((A Am) (B (-> Bm (or Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66477.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (D -> (D or E))), M:tm-456, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66478
in-theory        66478
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-453 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-453.          (A -> ((B -> ((C -> (C or D)) and B)) and A)), M:tm-5, m:tm-32, u:((A (-> Am (and (-> Bm (or Bm Cm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66478.        ((A -> ((B -> (B or C)) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-453, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66479
in-theory        66479
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((D -> (D or E)) and (((A and (B -> C)) or (B -> C)) -> (B -> (B and C)))))
theorem-size     37
proof            (modus-ponens tm-443 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-32.           (A -> ((B -> (B or C)) and A)), M:tm-5, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-443.          (A -> (A and ((B -> (B or C)) and A))), M:tm-24, m:tm-32, u:((A Am) (B (and (-> Bm (or Bm Cm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66479.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((D -> (D or E)) and (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))))), M:tm-443, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66480
in-theory        66480
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (A or B)) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-409 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-31.           ((A -> (A or B)) or C), M:tm-6, m:tm-6, u:((A (-> Am (or Am Bm))))
tm-409.          (A -> (((B -> (B or C)) or D) and A)), M:tm-5, m:tm-31, u:((A (or (-> Am (or Am Bm)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66480.        (((A -> (A or B)) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-409, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66481
in-theory        66481
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-400 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-8 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-30.           ((A -> (B -> (A and B))) or C), M:tm-6, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-400.          (A -> (((B -> (C -> (B and C))) or D) and A)), M:tm-5, m:tm-30, u:((A (or (-> Am (-> Bm (and Am Bm))) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66481.        (((A -> (B -> (A and B))) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-400, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66482
in-theory        66482
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> B) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-391 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-4 tm-8 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-4.            ((A and B) -> B), axiom
tm-29.           (((A and B) -> B) or C), M:tm-6, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-391.          (A -> ((((B and C) -> C) or D) and A)), M:tm-5, m:tm-29, u:((A (or (-> (and Am Bm) Bm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66482.        ((((A and B) -> B) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-391, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66483
in-theory        66483
times-derived    1
----------------------------------------------------------------
theorem          ((((A and B) -> A) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-382 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-3 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-3.            ((A and B) -> A), axiom
tm-28.           (((A and B) -> A) or C), M:tm-6, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-382.          (A -> ((((B and C) -> B) or D) and A)), M:tm-5, m:tm-28, u:((A (or (-> (and Am Bm) Am) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66483.        ((((A and B) -> A) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-382, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66484
in-theory        66484
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-373 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-2 tm-8 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-27.           (((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D), M:tm-6, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-373.          (A -> ((((B -> (C -> D)) -> ((B -> C) -> (B -> D))) or E) and A)), M:tm-5, m:tm-27, u:((A (or (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm))) Dm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66484.        ((((A -> (B -> C)) -> ((A -> B) -> (A -> C))) or D) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G)))), M:tm-373, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66485
in-theory        66485
times-derived    1
----------------------------------------------------------------
theorem          (((A -> (B -> A)) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-364 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-6 tm-1 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-6.            (A -> (A or B)), axiom
tm-1.            (A -> (B -> A)), axiom
tm-26.           ((A -> (B -> A)) or C), M:tm-6, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-364.          (A -> (((B -> (C -> B)) or D) and A)), M:tm-5, m:tm-26, u:((A (or (-> Am (-> Bm Am)) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66485.        (((A -> (B -> A)) or C) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-364, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66486
in-theory        66486
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D -> ((B -> (B and C)) and D)))
theorem-size     19
proof            (modus-ponens tm-355 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-5 tm-8 tm-4)
proof-size       137
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-355.          ((A -> B) -> (A -> (C -> (B and C)))), M:tm-2, m:tm-25, u:((A Am) (B Bm) (C (-> Cm (and Bm Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66486.        (((A and (B -> C)) or (B -> C)) -> (D -> ((B -> (B and C)) and D))), M:tm-355, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66487
in-theory        66487
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-354 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-354.          (A -> ((B -> (C -> (D -> (C and D)))) and A)), M:tm-5, m:tm-25, u:((A (-> Am (-> Bm (-> Cm (and Bm Cm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66487.        ((A -> (B -> (C -> (B and C)))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-354, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66488
in-theory        66488
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (D -> (E -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-341 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       157
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-25.           (A -> (B -> (C -> (B and C)))), M:tm-1, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-341.          (A -> (A and (B -> (C -> (B and C))))), M:tm-24, m:tm-25, u:((A Am) (B (-> Bm (-> Cm (and Bm Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66488.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (D -> (E -> (D and E)))), M:tm-341, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66489
in-theory        66489
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E))))
theorem-size     25
proof            (modus-ponens tm-338 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-338.          (A -> (((B -> C) -> (B -> (B and C))) and A)), M:tm-5, m:tm-24, u:((A (-> (-> Am Bm) (-> Am (and Am Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66489.        (((A -> B) -> (A -> (A and B))) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E)))), M:tm-338, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66490
in-theory        66490
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (B -> (B and C)))))
theorem-size     41
proof            (modus-ponens tm-328 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       185
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-328.          ((A -> B) -> ((A -> B) and (A -> (A and B)))), M:tm-24, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66490.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((A and (B -> C)) or (B -> C)) -> (((A and (B -> C)) or (B -> C)) and (B -> (B and C))))), M:tm-328, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66491
in-theory        66491
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((D -> (E -> (D and E))) and (((A and (B -> C)) or (B -> C)) -> (B -> (B and C)))))
theorem-size     39
proof            (modus-ponens tm-327 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       179
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-327.          (A -> (A and ((B -> (C -> (B and C))) and A))), M:tm-24, m:tm-23, u:((A Am) (B (and (-> Bm (-> Cm (and Bm Cm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66491.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((D -> (E -> (D and E))) and (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))))), M:tm-327, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66492
in-theory        66492
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((D and E) -> E) and (((A and (B -> C)) or (B -> C)) -> (B -> (B and C)))))
theorem-size     37
proof            (modus-ponens tm-326 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-4 tm-8)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-326.          (A -> (A and (((B and C) -> C) and A))), M:tm-24, m:tm-22, u:((A Am) (B (and (-> (and Bm Cm) Cm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66492.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((D and E) -> E) and (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))))), M:tm-326, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66493
in-theory        66493
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((D and E) -> D) and (((A and (B -> C)) or (B -> C)) -> (B -> (B and C)))))
theorem-size     37
proof            (modus-ponens tm-325 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-3 tm-8 tm-4)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-325.          (A -> (A and (((B and C) -> B) and A))), M:tm-24, m:tm-21, u:((A Am) (B (and (-> (and Bm Cm) Bm) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66493.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((D and E) -> D) and (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))))), M:tm-325, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66494
in-theory        66494
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B -> C)) or (B -> C)) -> (B -> (B and C)))))
theorem-size     45
proof            (modus-ponens tm-324 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       203
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-324.          (A -> (A and (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A))), M:tm-24, m:tm-20, u:((A Am) (B (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66494.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((D -> (E -> F)) -> ((D -> E) -> (D -> F))) and (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))))), M:tm-324, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66495
in-theory        66495
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((D -> (E -> D)) and (((A and (B -> C)) or (B -> C)) -> (B -> (B and C)))))
theorem-size     37
proof            (modus-ponens tm-323 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       171
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-323.          (A -> (A and ((B -> (C -> B)) and A))), M:tm-24, m:tm-19, u:((A Am) (B (and (-> Bm (-> Cm Bm)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66495.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((D -> (E -> D)) and (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))))), M:tm-323, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66496
in-theory        66496
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((D and E) -> E))
theorem-size     21
proof            (modus-ponens tm-322 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-4 tm-8)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-322.          (A -> (A and ((B and C) -> C))), M:tm-24, m:tm-18, u:((A Am) (B (-> (and Bm Cm) Cm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66496.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((D and E) -> E)), M:tm-322, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66497
in-theory        66497
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((D and E) -> D))
theorem-size     21
proof            (modus-ponens tm-320 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-3 tm-8 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-320.          (A -> (A and ((B and C) -> B))), M:tm-24, m:tm-16, u:((A Am) (B (-> (and Bm Cm) Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66497.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((D and E) -> D)), M:tm-320, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66498
in-theory        66498
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F))))
theorem-size     29
proof            (modus-ponens tm-318 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       181
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-318.          (A -> (A and ((B -> (C -> D)) -> ((B -> C) -> (B -> D))))), M:tm-24, m:tm-14, u:((A Am) (B (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66498.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((D -> (E -> F)) -> ((D -> E) -> (D -> F)))), M:tm-318, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66499
in-theory        66499
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((A and (B -> C)) or (B -> C)) -> ((A and (B -> C)) or (B -> C))))
theorem-size     35
proof            (modus-ponens tm-316 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       173
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-316.          ((A -> B) -> ((A -> B) and (A -> A))), M:tm-24, m:tm-12, u:((A (-> Am Bm)) (B (-> Am Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66499.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((A and (B -> C)) or (B -> C)) -> ((A and (B -> C)) or (B -> C)))), M:tm-316, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66500
in-theory        66500
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (D -> (E -> D)))
theorem-size     21
proof            (modus-ponens tm-315 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       149
proof-steps      15
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-315.          (A -> (A and (B -> (C -> B)))), M:tm-24, m:tm-11, u:((A Am) (B (-> Bm (-> Cm Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66500.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (D -> (E -> D))), M:tm-315, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66501
in-theory        66501
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((((A and (B -> C)) or (B -> C)) -> (not (B -> (B and C)))) -> (not ((A and (B -> C)) or (B -> C)))))
theorem-size     43
proof            (modus-ponens tm-313 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-9 tm-8 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-313.          ((A -> B) -> ((A -> B) and ((A -> (not B)) -> (not A)))), M:tm-24, m:tm-9, u:((A (-> Am Bm)) (B (-> (-> Am (not Bm)) (not Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66501.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((((A and (B -> C)) or (B -> C)) -> (not (B -> (B and C)))) -> (not ((A and (B -> C)) or (B -> C))))), M:tm-313, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66502
in-theory        66502
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((B -> (B and C)) -> D) -> ((((A and (B -> C)) or (B -> C)) or (B -> (B and C))) -> D)))
theorem-size     41
proof            (modus-ponens tm-312 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       173
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-312.          ((A -> B) -> ((A -> B) and ((B -> C) -> ((A or B) -> C)))), M:tm-24, m:tm-8, u:((A (-> Am Bm)) (B (-> (-> Bm Cm) (-> (or Am Bm) Cm))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66502.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (((B -> (B and C)) -> D) -> ((((A and (B -> C)) or (B -> C)) or (B -> (B and C))) -> D))), M:tm-312, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66503
in-theory        66503
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (D or (((A and (B -> C)) or (B -> C)) -> (B -> (B and C)))))
theorem-size     33
proof            (modus-ponens tm-311 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-7 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-7.            (A -> (B or A)), axiom
tm-311.          (A -> (A and (B or A))), M:tm-24, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66503.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (D or (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))))), M:tm-311, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66504
in-theory        66504
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) or D))
theorem-size     33
proof            (modus-ponens tm-310 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-6 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-6.            (A -> (A or B)), axiom
tm-310.          (A -> (A and (A or B))), M:tm-24, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66504.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) or D)), M:tm-310, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66505
in-theory        66505
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (D -> ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and D)))
theorem-size     35
proof            (modus-ponens tm-309 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       153
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-309.          (A -> (A and (B -> (A and B)))), M:tm-24, m:tm-5, u:((A Am) (B (-> Bm (and Am Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66505.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (D -> ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and D))), M:tm-309, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66506
in-theory        66506
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((((A and (B -> C)) or (B -> C)) -> B) -> (((A and (B -> C)) or (B -> C)) -> (B and C))))
theorem-size     41
proof            (modus-ponens tm-306 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B Bm) (C (and Bm Cm))))
axioms-used      (tm-2 tm-5 tm-8 tm-4)
proof-size       175
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-306.          ((A -> (B -> C)) -> ((A -> (B -> C)) and ((A -> B) -> (A -> C)))), M:tm-24, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> (-> Am Bm) (-> Am Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66506.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and ((((A and (B -> C)) or (B -> C)) -> B) -> (((A and (B -> C)) or (B -> C)) -> (B and C)))), M:tm-306, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B Bm) (C (and Bm Cm)))
================================================================
tm-name          tm-66507
in-theory        66507
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (D -> (((A and (B -> C)) or (B -> C)) -> (B -> (B and C)))))
theorem-size     33
proof            (modus-ponens tm-305 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-2 tm-5 tm-1 tm-8 tm-4)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-1.            (A -> (B -> A)), axiom
tm-305.          (A -> (A and (B -> A))), M:tm-24, m:tm-1, u:((A Am) (B (-> Bm Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66507.        ((((A and (B -> C)) or (B -> C)) -> (B -> (B and C))) and (D -> (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))))), M:tm-305, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66508
in-theory        66508
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     27
proof            (modus-ponens tm-303 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       147
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-23.           (A -> ((B -> (C -> (B and C))) and A)), M:tm-5, m:tm-5, u:((A (-> Am (-> Bm (and Am Bm)))))
tm-303.          (A -> ((B -> ((C -> (D -> (C and D))) and B)) and A)), M:tm-5, m:tm-23, u:((A (-> Am (and (-> Bm (-> Cm (and Bm Cm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66508.        ((A -> ((B -> (C -> (B and C))) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-303, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66509
in-theory        66509
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-270 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-4 tm-8 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-4.            ((A and B) -> B), axiom
tm-22.           (A -> (((B and C) -> C) and A)), M:tm-5, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-270.          (A -> ((B -> (((C and D) -> D) and B)) and A)), M:tm-5, m:tm-22, u:((A (-> Am (and (-> (and Bm Cm) Cm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66509.        ((A -> (((B and C) -> C) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-270, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66510
in-theory        66510
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-239 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-3 tm-8 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-3.            ((A and B) -> A), axiom
tm-21.           (A -> (((B and C) -> B) and A)), M:tm-5, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-239.          (A -> ((B -> (((C and D) -> C) and B)) and A)), M:tm-5, m:tm-21, u:((A (-> Am (and (-> (and Bm Cm) Bm) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66510.        ((A -> (((B and C) -> B) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-239, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66511
in-theory        66511
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G))))
theorem-size     33
proof            (modus-ponens tm-210 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       171
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-20.           (A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)), M:tm-5, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-210.          (A -> ((B -> (((C -> (D -> E)) -> ((C -> D) -> (C -> E))) and B)) and A)), M:tm-5, m:tm-20, u:((A (-> Am (and (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66511.        ((A -> (((B -> (C -> D)) -> ((B -> C) -> (B -> D))) and A)) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G)))), M:tm-210, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66512
in-theory        66512
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     25
proof            (modus-ponens tm-183 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-19.           (A -> ((B -> (C -> B)) and A)), M:tm-5, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-183.          (A -> ((B -> ((C -> (D -> C)) and B)) and A)), M:tm-5, m:tm-19, u:((A (-> Am (and (-> Bm (-> Cm Bm)) Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66512.        ((A -> ((B -> (C -> B)) and A)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-183, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66513
in-theory        66513
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-157 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-4 tm-8 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-4.            ((A and B) -> B), axiom
tm-18.           (A -> ((B and C) -> C)), M:tm-1, m:tm-4, u:((A (-> (and Am Bm) Bm)))
tm-157.          (A -> ((B -> ((C and D) -> D)) and A)), M:tm-5, m:tm-18, u:((A (-> Am (-> (and Bm Cm) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66513.        ((A -> ((B and C) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-157, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66514
in-theory        66514
times-derived    1
----------------------------------------------------------------
theorem          ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-147 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-4 tm-8)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-17.           (((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)), M:tm-2, m:tm-4, u:((A (and Am (-> B C))) (Bm (-> B C)))
tm-147.          (A -> ((((B and (C -> D)) -> C) -> ((B and (C -> D)) -> D)) and A)), M:tm-5, m:tm-17, u:((A (-> (-> (and Am (-> Bm Cm)) Bm) (-> (and Am (-> Bm Cm)) Cm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66514.        ((((A and (B -> C)) -> B) -> ((A and (B -> C)) -> C)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-147, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66515
in-theory        66515
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-134 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-3 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-3.            ((A and B) -> A), axiom
tm-16.           (A -> ((B and C) -> B)), M:tm-1, m:tm-3, u:((A (-> (and Am Bm) Am)))
tm-134.          (A -> ((B -> ((C and D) -> C)) and A)), M:tm-5, m:tm-16, u:((A (-> Am (-> (and Bm Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66515.        ((A -> ((B and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-134, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66516
in-theory        66516
times-derived    1
----------------------------------------------------------------
theorem          (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     31
proof            (modus-ponens tm-125 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-3 tm-8 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-15.           ((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)), M:tm-2, m:tm-3, u:((A (and (-> B C) Bm)) (Am (-> B C)))
tm-125.          (A -> (((((B -> C) and D) -> B) -> (((B -> C) and D) -> C)) and A)), M:tm-5, m:tm-15, u:((A (-> (-> (and (-> Am Bm) Cm) Am) (-> (and (-> Am Bm) Cm) Bm))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66516.        (((((A -> B) and C) -> A) -> (((A -> B) and C) -> B)) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-125, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66517
in-theory        66517
times-derived    1
----------------------------------------------------------------
theorem          ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G))))
theorem-size     31
proof            (modus-ponens tm-113 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-2 tm-8 tm-4)
proof-size       163
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-14.           (A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))), M:tm-1, m:tm-2, u:((A (-> (-> Am (-> Bm Cm)) (-> (-> Am Bm) (-> Am Cm)))))
tm-113.          (A -> ((B -> ((C -> (D -> E)) -> ((C -> D) -> (C -> E)))) and A)), M:tm-5, m:tm-14, u:((A (-> Am (-> (-> Bm (-> Cm Dm)) (-> (-> Bm Cm) (-> Bm Dm))))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66517.        ((A -> ((B -> (C -> D)) -> ((B -> C) -> (B -> D)))) and (((E and (F -> G)) or (F -> G)) -> (F -> (F and G)))), M:tm-113, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66518
in-theory        66518
times-derived    1
----------------------------------------------------------------
theorem          ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     35
proof            (modus-ponens tm-105 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-8 tm-4)
proof-size       183
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-13.           (((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))), M:tm-2, m:tm-2, u:((A (-> Am (-> Bm Cm))) (B (-> Am Bm)) (C (-> Am Cm)))
tm-105.          (A -> ((((B -> (C -> D)) -> (B -> C)) -> ((B -> (C -> D)) -> (B -> D))) and A)), M:tm-5, m:tm-13, u:((A (-> (-> (-> Am (-> Bm Cm)) (-> Am Bm)) (-> (-> Am (-> Bm Cm)) (-> Am Cm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66518.        ((((A -> (B -> C)) -> (A -> B)) -> ((A -> (B -> C)) -> (A -> C))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-105, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66519
in-theory        66519
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> (A -> A)) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E))))
theorem-size     23
proof            (modus-ponens tm-95 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-2 tm-1 tm-8 tm-4)
proof-size       139
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-12.           ((A -> B) -> (A -> A)), M:tm-2, m:tm-1, u:((A Am) (B Bm) (C Am))
tm-95.           (A -> (((B -> C) -> (B -> B)) and A)), M:tm-5, m:tm-12, u:((A (-> (-> Am Bm) (-> Am Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66519.        (((A -> B) -> (A -> A)) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E)))), M:tm-95, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66520
in-theory        66520
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or (B -> C)) -> (D -> (B -> (B and C))))
theorem-size     17
proof            (modus-ponens tm-84 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-2 tm-1 tm-8 tm-4 tm-5)
proof-size       129
proof-steps      13
----------------------------------------------------------------
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-84.           ((A -> B) -> (A -> (C -> B))), M:tm-2, m:tm-11, u:((A Am) (B Bm) (C (-> Cm Bm)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66520.        (((A and (B -> C)) or (B -> C)) -> (D -> (B -> (B and C)))), M:tm-84, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66521
in-theory        66521
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     23
proof            (modus-ponens tm-83 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-1 tm-8 tm-4 tm-2)
proof-size       131
proof-steps      13
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-1.            (A -> (B -> A)), axiom
tm-11.           (A -> (B -> (C -> B))), M:tm-1, m:tm-1, u:((A (-> Am (-> Bm Am))))
tm-83.           (A -> ((B -> (C -> (D -> C))) and A)), M:tm-5, m:tm-11, u:((A (-> Am (-> Bm (-> Cm Bm)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66521.        ((A -> (B -> (C -> B))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-83, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66522
in-theory        66522
times-derived    1
----------------------------------------------------------------
theorem          (((not (not A)) -> A) and (((B and (C -> D)) or (C -> D)) -> (C -> (C and D))))
theorem-size     21
proof            (modus-ponens tm-76 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-10 tm-8 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-76.           (A -> (((not (not B)) -> B) and A)), M:tm-5, m:tm-10, u:((A (-> (not (not Am)) Am)))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66522.        (((not (not A)) -> A) and (((B and (C -> D)) or (C -> D)) -> (C -> (C and D)))), M:tm-76, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66523
in-theory        66523
times-derived    1
----------------------------------------------------------------
theorem          (((not (not ((A and (B -> C)) or (B -> C)))) or ((A and (B -> C)) or (B -> C))) -> (B -> (B and C)))
theorem-size     27
proof            (modus-ponens tm-73 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-8 tm-10 tm-4 tm-2 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-10.           ((not (not A)) -> A), axiom
tm-73.           ((A -> B) -> (((not (not A)) or A) -> B)), M:tm-8, m:tm-10, u:((A (not (not Am))) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66523.        (((not (not ((A and (B -> C)) or (B -> C)))) or ((A and (B -> C)) or (B -> C))) -> (B -> (B and C))), M:tm-73, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66524
in-theory        66524
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E))))
theorem-size     27
proof            (modus-ponens tm-69 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-9 tm-8 tm-4 tm-2)
proof-size       133
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-9.            ((A -> B) -> ((A -> (not B)) -> (not A))), axiom
tm-69.           (A -> (((B -> C) -> ((B -> (not C)) -> (not B))) and A)), M:tm-5, m:tm-9, u:((A (-> (-> Am Bm) (-> (-> Am (not Bm)) (not Am)))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66524.        (((A -> B) -> ((A -> (not B)) -> (not A))) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E)))), M:tm-69, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66525
in-theory        66525
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F))))
theorem-size     29
proof            (modus-ponens tm-54 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-8 tm-4 tm-2)
proof-size       139
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-54.           (A -> (((B -> C) -> ((C -> D) -> ((B or C) -> D))) and A)), M:tm-5, m:tm-8, u:((A (-> (-> Am Bm) (-> (-> Bm Cm) (-> (or Am Bm) Cm)))))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66525.        (((A -> B) -> ((B -> C) -> ((A or B) -> C))) and (((D and (E -> F)) or (E -> F)) -> (E -> (E and F)))), M:tm-54, m:tm-783, u:((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm)))))
================================================================
tm-name          tm-66526
in-theory        66526
times-derived    1
----------------------------------------------------------------
theorem          (((A -> B) or ((C and (A -> B)) or (A -> B))) -> (A -> (A and B)))
theorem-size     19
proof            (modus-ponens tm-50 tm-783 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm)))))
axioms-used      (tm-8 tm-7 tm-4 tm-2 tm-5)
proof-size       123
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-7.            (A -> (B or A)), axiom
tm-50.           (((A or B) -> C) -> ((B or (A or B)) -> C)), M:tm-8, m:tm-7, u:((A Am) (B (or Bm Am)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66526.        (((A -> B) or ((C and (A -> B)) or (A -> B))) -> (A -> (A and B))), M:tm-50, m:tm-783, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66527
in-theory        66527
times-derived    1
----------------------------------------------------------------
theorem          (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (B -> (B and C)))
theorem-size     21
proof            (modus-ponens tm-49 tm-783 ((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm)))))
axioms-used      (tm-8 tm-6 tm-4 tm-2 tm-5)
proof-size       125
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-6.            (A -> (A or B)), axiom
tm-49.           (((A or B) -> C) -> ((A or (A or B)) -> C)), M:tm-8, m:tm-6, u:((A Am) (B (or Am Bm)))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66527.        (((A and (B -> C)) or ((A and (B -> C)) or (B -> C))) -> (B -> (B and C))), M:tm-49, m:tm-783, u:((A (and Am (-> Bm Cm))) (B (-> Bm Cm)) (C (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66528
in-theory        66528
times-derived    1
----------------------------------------------------------------
theorem          (((A and ((B and (C -> D)) or (C -> D))) or ((B and (C -> D)) or (C -> D))) -> (C -> (C and D)))
theorem-size     27
proof            (modus-ponens tm-47 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-8 tm-4 tm-2 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66528.        (((A and ((B and (C -> D)) or (C -> D))) or ((B and (C -> D)) or (C -> D))) -> (C -> (C and D))), M:tm-47, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66529
in-theory        66529
times-derived    1
----------------------------------------------------------------
theorem          (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> (B -> (B and C)))
theorem-size     27
proof            (modus-ponens tm-46 tm-783 ((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm)))))
axioms-used      (tm-8 tm-3 tm-4 tm-2 tm-5)
proof-size       129
proof-steps      11
----------------------------------------------------------------
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-3.            ((A and B) -> A), axiom
tm-46.           ((A -> B) -> (((A and C) or A) -> B)), M:tm-8, m:tm-3, u:((A (and Am Bm)) (B Am))
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)) -> ((A -> B) -> (A -> C))), axiom
tm-5.            (A -> (B -> (A and B))), axiom
tm-24.           ((A -> B) -> (A -> (A and B))), M:tm-2, m:tm-5, u:((A Am) (B Bm) (C (and Am Bm)))
tm-783.          (((A and (B -> C)) or (B -> C)) -> (B -> (B and C))), M:tm-47, m:tm-24, u:((A (-> Am Bm)) (B (-> Am (and Am Bm))))
tm-66529.        (((((A and (B -> C)) or (B -> C)) and D) or ((A and (B -> C)) or (B -> C))) -> (B -> (B and C))), M:tm-46, m:tm-783, u:((A (or (and Am (-> Bm Cm)) (-> Bm Cm))) (B (-> Bm (and Bm Cm))))
================================================================
tm-name          tm-66530
in-theory        66530
times-derived    1
----------------------------------------------------------------
theorem          ((A -> (B or A)) and (((C and (D -> E)) or (D -> E)) -> (D -> (D and E))))
theorem-size     21
proof            (modus-ponens tm-42 tm-783 ((A (-> (or (and Am (-> Bm Cm)) (-> Bm Cm)) (-> Bm (and Bm Cm))))))
axioms-used      (tm-5 tm-7 tm-8 tm-4 tm-2)
proof-size       115
proof-steps      11
----------------------------------------------------------------
tm-5.            (A -> (B -> (A and B))), axiom
tm-7.            (A -> (B or A)), axiom
tm-42.           (A -> ((B -> (C or B)) and A)), M:tm-5, m:tm-7, u:((A (-> Am (or Bm Am))))
tm-8.            ((A -> B) -> ((B -> C) -> ((A or B) -> C))), axiom
tm-4.            ((A and B) -> B), axiom
tm-47.           ((A -> B) -> (((C and A) or A) -> B)), M:tm-8, m:tm-4, u:((A (and Am Bm)) (B Bm))
tm-2.            ((A -> (B -> C)